23
aaaaababbabbababaabababaaabababbbabaaaabaaabbabbaabbbabaaaabaaabbabaaababbbabbaaaaabaabaaaababbabbabaabaaaabaaaaabaabbbabbabbaabbaabbbbbbaabbbaaaaaaaabbbbbaabaaabababbaaabaabaabbaaabaabbbbbbabbbbaaabbababaabbbaababbaaabaaaabbabbbbbaabbabbbbbabaabaaabbbbbaaabaababbbaaabbbbbabbaabaabbbaaabbababbabaabbaababababaabbbbbaabbabaaabbbbbbaabaaaabbaaabbbbbbabbaabbababbabbaaabbababbbbabbaababbabbabbbbaaabaabbbbabbabbbbbababbbbbbaaabaaabaaabaaaaabbabbabbbbabaabaaabaaababbabbbabaabbababbaaaababbbbbaabaaabaaaaabbbbbababbababbbaababbbabbbbaaababaabaaabaaaababbaabbbabaaaabbabaabbbaaababaabbbabaabaabaaaaababababbaabbaaaabbababaaabaabaaaaaaababaaabbaabbabaabbababbaabbaabbbbabbbaabbaaaaabaabbbabbaaaababbbabbbbabaabababaaabbaabaababaabbaabbababbaabaabbbbbabaababababbabbaaabaaaaaaaabaaabbabaaaabbbaababbabbaaaababaaabaaaabaaababbaaabbabbaabbabbabaabbbbbaabbabbbabbabbababaaaababbaaaaaaabaababbbbabbbaaaaaabbbabbaabaabbaabaaabaabaaababaabababaabbaaaabbaabbbbbaaaabbaabaababaabbabbabbabbabaabbaabbbaaabbabbbaaabbbaabaabbbbbabaaaabaabaaaabaabbaabbbbbaaababaabbbabaaaaababababaababaababbababbaabbabbabbaabbaaabaababbaabaaabbabbabaaaaabbbbbbaaababbabaaabbaaabaaabbaaaabbabbaabbaabbbabbabababbbbbbaaabbbababbaaabbbbabaabaabbbabbaaaaabbabbbabbbbaaababaabaabaababbbababaaaaaabaaaaabaaabbabbabbbbababbabbaabbbbaaababbabaaabaaababbaaaaabbbaaaabaabbababbbbaababaabbbabbbbabbabbbbaabbbbabaaaaaaabaaabbbbabbabaababbabaabaabbbaaabaabbbbbbaabbabaaaabaabaaaaabbbabaaababaababbaabaabbaabbbaaabbbbabbabbabbbabbababbbaaabaababbaabaababaabaabaabaaabaabbbababbaaaabbaaabbbaabaabbaaaaabbbbaabaaaabbbabaabaabbaabaabaabaaaabbaabaababbbabababbbbbabbabbbbaabbababbaaaabbabbbbbabababbbbbbbbaaababbbabbbbbbaaabbbaabaaabbbabaababbabbbbabbbbaababaaaabaabbbaaaaaaabaaabbabbbaaabbbbaabbbabababaaababaabbbbbaaaaabbbaabbbababbbbbabbaaabbbbbbabbaaaaabbbbaaabbbbaaaabbbabbabbbaabaaababbabbabaabbabbabaabbbabaaabbbabbabbababbbbabbbbababbbaabbbbaaaaaaabbaaabaabbbababaabaabbbabbaaaaaabbababaaababbbabaabbbbaabbabbbbbbbabbbabbaabbabbaaabababaabbbababbabaaaababbbabbabbaaaaabbbabbbabbabbbabaaabbaababaaabaabbabaabbbbbabbabbaabbaababbabaaaabaaabbaaaaaaabbaaabaaaaaabbaaabaaaabaabbbaabbaabbaaaababbaaaabbbbaaabaabbababbaaabaaabaaaaaabbbaabbabaaababbbbbbaabbaabbbabababbbbaaaaaabaababaaaabaabbabbbbaaabaaaababaaabbabaababbabbbbaabbaabbaaaaaababababbbabbaabaaababaabaaaabaabbabbaaababbbabaabababbaabbabaaaaaaaabaabbbbbbababbbbbabaaababbbbabbbaaaababaaababbbaaaaaabaabbbbbabaabaaaaabaaabbbaaaabbbbabaabbaaabbbabbbbbabaaaaabbaaaaabbbbabaaaabbbbabbaaabbabbabaabaabbbababbabbaababbbaababbababbbbbabbaabbbaaabbbbbbbaaaabababaaaaaaabbaaaaaabaaaaaababaababbbaaaabbabbaabbbaabbaabaaababaabaaaabababababbbbaabbababbbaaabaabbaaabaabbbbabbbbabbbaaaaaaaaaabbaabaababaaabaababaaabaaabbaabbabbbbbabaabbabaaaaabbaaabbabbaababaababaabbaabaabaabbaababaababaaaabbaaaabbaabbbabababbaaaaababbbabbabaabaaaaabbabaabbbbbabbababaaaaaabababaaabaabbbbbbbbbbabaabaabbbbaabaaaaabbbaabaabaabaabbaaaabbbbabbbbababbbabbbbbabababbaababbaabababaabaaabbaaababbbbbbbbbbabbabbaaaabbbbababaaaaabbaaaaaaababbbaabaaabbaaababbbaabaaaaaaaabbababbbbbbabbababbabbbaababaaabaabbbbbababbbaaabbbbbbaababaabaabaabababbbaabaababbbaabbbbababbaaabbabaaaabbabbbaaaaabbbababaabbbbabbbababaabbabbbaaabababbbbaaabaabbaabaabaabaabbabaabbabbbbbaaaababbaaabaabaabbbaabbbbaaabaabbbbbbaababababbababbbabbaaabbbaababaabaaababbabaabbbabaabbaabbabaabaaabbbaababbbaabbbaaabbaababbabbaaaaaaaaaababbaaabaaaaabaaabbaaaabbbbbaabbbbaaabaabbabbaaabbbabbabbbbbababbbbbaabbbaaaabaaababaabaaaaaabaabbabbbabbabbbbbbbababbabbbaaaabbabaabaaaaabbaaabababbabababbbabbbabbbbbbaababbbaabbbbbaaababaabbbaabbabbbabaaaabbaabaabaaaabbabababaabbabababaabaaabbabaabaabbbaaaaaaabaababbabbaabaaabbbbbaabaabbaabbbbbabbabaabbaabbbaababbabaabbbbbaaaaaaaaabbbbbbbbabaaababbabaabaabbabaabbbabaabaaabbbbabaabaabbbaabbbbbbbbaaabbaabbbababbbbabbbbabbbabbbbbabaababaabababaabaabaabbbabaaabaabbbaababaababbaabaaaababaabbabbabababbbbabbaaaaaaaababbbabbabaabaabbbbaaaaabbabbaaaaabaababaaaaaabbaaabbbbbabbbbbaaaaabaaababaabbaabbbabaabbaaaabaabaababbbababaaaaabaabababbbbaabbabbaabaabababbbaababbbaababbaaaabaaababaabababbabbbabbabaababababaaabaabbbabbbbbbbbbabbaaaabaabbaababbbaabbaabbbabaaaababbbbabbababaaabbbbaabbabaaaabbababbababaabbaababbaaaaabbabbbbaabaaaababbaaaaababaaaabaabbabbabbbabbbaabbabaabbabbbbbbabbbabaaababbbabbaaababbabaabbabbaabaabaaaabbaaabbababbabbaababbabaabbababbbaabbabbbbaaabbabaabbaabaabbabbbaabbaaaaaabbbaabbbaabaaabbabaabbbbaaabbbbaabbabbaaaabaaaabbbaaaaabaababaabbbaaabaabababababbaababbabbbabaaaabbaaabaaaabbbbabbaaaaaabbbaaabbababaababbbbbabbbbbbaaababbbaabbaababaabbabaabbabababbbabaabbabababbbbbbbababbbaaabaaaabbbbbbaababbaaabbaaaaababbaabbbabaaaaabbbaabbaabbabbabaabbaaaabbabababbaabbbbaabaabbabaaabaaaaaabababbaaaabaaaabababbbbbaaaabbbbbabaaaaabaabababbbaaababbbbbbabbbaabaabbabbbababaaabaaabaabaaababbabbabbaabababbbababaabbbbbaabaabbabbbbbbbaabaabbabbaaaabbaabbbaababaababaabbabababaabbaabbbaaaababbabaabaaabbaabbabbaababaaababbaabaaaabaaabbabbbaaabababbbbaaaaaaabbbbaaaababbbbbabbbbbbabaaabbbabbbbbabbbaaaaabbbabbabababbaabaaaaaaabbaaabbabbaaabbbbbaaaabbababaaaabbbbbbaabaababbbbbaaaaaabaabaaaaababaaabbbabaaaabaababbbaababaaababbabaabaabbbabbabbaabbbaaabbabbabbbaaaababaabaabbbababaabbbbbabbbabbbbbbbaaabaaaaaaaaaabaaaabbabbabaaaaabbaaaaaabbaabbabbaababaaababbbbabbbaabbbbbaabbabbaabbaabbbbbaaaaaabbbaaabbbbabbaaababbbabaabbaabbbbaaabaabbbabbaaabbaabaaababbabbaabaabaaaabbbaaabbabaababaaabbbbbbbababaabaabbabaabaaaaaabbbbbaaaaaabbaaaabbaabbbbbbaabaaaaaababaaabaababbbbbbaababbbaabbabbbaaaabbbaababaabbaabaaabbbbaabaabaabbababbbbbaaaaaabaaaababaababbbaaababbaabaabbabbbbaabbbbbabbbbbababbaabaabbbaaaabbaaaababbbababbbabbbbbaaaaabababbbaaaaaabbbabbbbbaababaabbbbbbaaabbbaababbbbbabbbbbabaabbbbbababaaabbababbbabbaabbabbbbaaaaabaaaaabbaabaabbaabbaaaaabaababbbbabaaaaaabaaaaabbaabbbababababaabaaaaaaabbaaabbbaabaabaaabaabbaabbbbababbabbababaabbaaaaabbabbbabbbababbaabbabaabbabbabbabbbbbbbbabbabaababbbbaaabababaababbbaabbaabbaababaabbaabbbbabaabbbabaabaabbbbbaaaaabaaababbbabaaabaaababaaabbbbbbaaabbbaaabbaaabbbbaaaaaaaaabbbbbabbbaababbbbabbabbbaaaaabbbaabbabbbbabbbabbbbbabbbbabaabbaabbabababaaababaabbaaaaaaabaabbaaabbbababbabaabbbbbbbbababaabbabbbaaabbabbbaabbbbaabbbaaaaabbbababbabbabbaaaaabbaabababbababaaaabababbbaaabaabbabbabababbaabbbbabbbbabaaababaabababaabaaaababbaaababaaaaabbaabaabbaababbabbabababaabaaaabaaabbabbaabababaababbabaabbbaabbaababbaabbaaaabbaaababaabababaabbbbbaaabbbbaaabaaaabaabbabbaababbbaaaabbababbaabbbbababababbaaabbababbaaabaabbbbaaababbbabaababbaaaabbbabababbbaaaabaabbabbabbbaabbaaaaaaaaaaaaabbbbbaabbbbababbaabaaabbbaababbaabbbabbababbaaabbabaaababaabbababaabbaaaaaaabbbbabbbbabaaabbabbaabbbbbabaaababbbaabbaabbaaabbabbaababababbabbbbabaaabbabaaaababaabbbabbabbabbbbbbaabbbabbbbabbbaababbaaaaababaabbbabbabbbbaaaaabbbaabbbbaabbabbbbabaaaababababbbbaababababbbaababaabbaaabbabbaaaabbaababbaabaaaabbaaabbababbbababbbabbaababbbbaaaabababbaabbbbaababbaaabbbabbbbbabbbaabbabbbbabababbababbaaabaababbbaababbbbabaaabaabbbabbaababbbbbbababbbbbabbaababbaaabaaababbbbababbaabbabaaabbbabbaababbabbabaababbabaaababbbbaabbbbaaaaababbaaabaaaaabbaaaaaaaaaabbbabababaabbabaabbbbbbbaabaabbbaaabababbbbbaabbabbaabbabbaababababbaaabbaaaababbababbbbbbaabbbaabbbaaaababbabaaaabaabaabbaabaaaaabaaabaabbabbbabbbaababaaaaaaaababaaabbabbbababaaababbbbaabbbbbbaaabbabaabbabbabbbaabaabaaaaaaaabbabaabaaabbaaabababbabaaabbabbabbababababaabababaaaaaabababbaaabbbaabbabaabbbbbbababaabaaabababbaaabbbbbbbaabababbabaaaabaaabaaaabaaaaaaaaababaabbaaaaabbbababbaabbababbabbabaabaababbbbababbbabaabbabaabbbababaaabbbbbbaaaaaababaabaaabbaabbaabbbbbbabbbaaaabbabaabbbaabaababaaabbaabaaaabbaabbabbbabbabbbaaaaaababbabbbbbbaaaabaaaaabbabbaababaaaabbabbbababbbbabaababbbaaababbabbbabbababbabababaaabaabbbbbbbaaaabbbbaaababaabbaababbabbabaababaaaaabaabbaaaaabaabbababaabaabbbbbababaaabababbbbaababbabbababaabaaababbababaaabaaabbabaabaababbaabbaabaabbbabaabbaaaabaaaababbaaaababbabbbbbbbbababbbbbbbbbaaaabbaabaaabaababbbaababaaabbaaababbaaabbaabbbbaaaabbbbaaababaabaaaaabaaabbabaabbaaaaabbabbbbabaabbabbaaaabaabaaabaabbabababbbbbabaaaaaabaabbaaabbababbabaaaaaaaabbaaaababbabaaaaaaaabaabaaaabbababaabbabaabbaaaabbbaaaababbabaaababbaaaaaababbbbaabaababbbbaababaabbbbaaaabaaaaabbbbbbaabaabaabbababaabaaabaabbabaabbbabbaaaabbbbbbbbbabbbbabbaababbbaaabbbbbbababbaabbbaababababbaabbbabaaabbbbbbabbbbbaabaaaabaabaaabbbaabbbbbbababbaabaabbbaaaabaaabbabaaaaaaaababbbbabaabbbbaabaaabababaaabbbbbbaaaaaaabbaaaabbbaaabbbbbbaababbbbaababbbbabbbbbbabbbababaabaabbbbababaaabaaabbbbabababbbaabbbabbbaaababaaaaaabbaaabbaabbaaaabbaaaabbabbbaabaaabbbbbbabaabbabbaabbbaabbbbbbbaabaaaaabbabbaabaabbaabbbbaabbbbabaabaabaababbabbabababbbabbaaaabaabaabbaaaaabaaabbbaaaababbaaaaaabbaabbbabababbbbabbbaababaaabbaabbbbabbbabababbababaabaabbababaabbbababbaaabaabaaabbbabaababbbbbbbbabbbaaabbabbbabbbaaabbbaaabbabbaababbaabbabbbbaaaaabaaabbbbbbbbababaabbbaaabbaabaaaaaaaabababbababbbabbbbaaaabbabbabbbbbababbbaabbbabbaaabbbbabababbaababbbbbbabbbbbaabbaabbaabbaabababbabbbbabaabbabbbbabbaabbbabbbbaaabaabbbaabbaaaaababbaabbbaabbbabbbababbbbbbbaabbbbbabbbbbababaaaaabbbbbbabaabbabbbbbabbababaabbabababbaaaaaababbbbaabaaaabaabaabbabaaaaabbbbaaaaaababababaabaaabbbabbbbabbabbbaababaabaababbbbababababababbbabbaaababbbabbbababaaaababababaaaabaababbaaababaaabbabbaaababbabbbababbbabaababbaabbbbabaaabbbbabbbabbabbbaaaaaaabaaababaabababbabbbaabbaabbbbabbbabaabbabaabaababbaabababaabaaabababaabaaaaaaabaabbbbaabababbbbbbbbbbabaababbabaaabbabaaabaaaabbbbaaaaaaabbabaababaabbbbbbbbaabbbbaaaabbabbabbaaababaaababbbbbaaabaaabaabaababbbaaaaababaabaabbaaabbababaabababbababbabaabbaabbbaababbabababbbbbaabababbaaaabaabbbaaabaabbabbbaaaabbbabaabbbababaabababbabababbaabaababaabaaaabbaabaabbaaaaaabbabbaabaaabaabbabaaababbabababbaabbaaaaaabaabababbbbbbbababbbaababaaaababbaabaaaabaabbbbabbbabaaababbabaaaaababaabbbaaaaabababaaabbabbaaaabaabaaabababbbabababbbbbbaaabbbabbabbabbbbabbbbabbbbbbaaababbaaabababaaabbabaabaabbbbbbbabaaabbabaabaaabaabaabbabaabbbbabbababaaabbbabbaababbaaaaabbbabaabaabaaaabaababbabaabbbabbbaabbabababaabbbbabbbaabaabaabbababbaaababbaabbbbaaababbbbbbaabaaaaaaabaaaaaaabaabbabbbaabbaabbbbaaaabbabaaaabaabaaabaabbabaabaabbbaaababbbababbababaaaaabbbabbbababbbabaaaaaaaaabaaaabbbbbabaabbbabaaaabababbbbabbaaaaaaabaabaaabaaaaaaaaabababaaaaabaabbbbabbbbbabbaabbaababbaabaaababbbabaaabbaababbabbaabbbbbbbbaaaabbbbababaaabbaabaabbababaabbbbbabbaababbaaabbaabbaaaaabaaaaaaaaaaaaabbbabbbbbaabbabbababaaaababaaaababaababbbaabaaabbbbbbaaaaababababaababbbababbbbbabaabaaabbaabbaabababbbabbabbbbabbbbbababbaaababaaaaaaabbbaaaaaabbaaababbaaabbbbbbabaaabbabbbababbbbabbaaababaaaaabaaabbbabbaaabaabbabbaaaabbabbabaaaaaabbaaabbbbbbbbbaaabaabbabbbabaaaabbaabbaabbabbbaaabbbaaabbabbaaaaabaabbaabbbaaaabbbbbbaaaaaaaabababbbabbbbbababbbabababaabbabbaabaabaabaaaabaabaabaaaabbabaaaabaaabbababaaabaababbbaabbaabbaabaabaaaabbababbabbabbbaabaaabbabababaabbaaabbaaaabaabbbaabaabaaaaaaaaaaaaabaabbbaabbbbbbbaabbbaabbabbabbaaabaabbabbaababaaaabbabbaaaaabbbbbbaaaaaababbbabbabaaaabbabaabababbbbaaaabbbabbaaababbaabaaabbabababbbbbaaaabbaabbaabbababababaaaabababaaababaabaaabbbaabbbaabbbabbabaaaaabbbaabbbbabbaaabbabaabbbaabbabbabbbaaaaababbaaaabbbbbbabaabaaabbabbbabbbbbbbbaaabbbaabbabbbbbbbaaaabbbaabbababbaabaababbbaabbbbabbbaabbaabaaabbbaaabaaaaaaaabaaabababbaaaaabaabaabababaabaababbababbbbaaababbbabbbaaaaabbaaababbbaaaaaaabbaaaabbbbaaabbaababbbbbabaabbbabaababaaabbbbabbabaabbbbaaabaabababbaababaabbaabbaababbaaababaabbbbbaabbbbaaabaabbabbbbbaabbbaabbbbababbbaabbbababaabbbbabaaaabbbbaababaabbbaababbaaaaabaaaababbbbaabaaabbababbaaabaabbbbbbbabbabababaaababbbbaabbbababaabaaaabbbbaabbabbbababbabbbbbabbaaaabababaaaabbbbbaaaaabaaabbbababaabaabaabaabaabababababbaaaabaababbaababaaaaaaabbaaaabaabbbaabbaaabbbaaababbaabbbbabbaaaabbabaaabbabbabaabaabaababaabaaaaabbabbabbababababbbbbabbbbbbbbabbabbbbaabbaaabaabbbaabaababaabbaaaaaabababbaabbbaabbaaaaabbbababaaabaabababbababbbbbabbbbabaaaaababaababbabaabaaabbaaabbabaaababbaaaabbaabbbbbaabaaabbbaaababbbbbbaaabaabaaabababaaaaabbbaabaabbbaababababbbababbbabaabaaabbbbbabaabbaaaabaabaaabbaaabbbaaababbababbababababbabaababbbbababaaababbbbabaababaaaababaaabbbaaaaabbbaaabbbbaaaaaaabaaabbaababbabaabaabbbaaabbaabbbaababbbbbaabaabaabbabaaaaababbbbaabbaaababaaabbabbbaaababbabbabbbaabbbaabbaaababaaaaabbbabbabbaaaaaaabbaaaaabaaaaababbabababbbbaaaababbaabbbbbbababaabaaaaaabaababbabbbabababbbaabaaabbaabbbbabbabaabaabbabbbababbababbaaababaaabaaaabaabbabbbbbbbaaabbbbaabaabbbbabaabaababbbbbabbabbabbabbbaaabaababbbbaaaabbbbaababaababbaaaaaabaabbaababbbbbbaababbaaaabababbbbaabbaababaabaaaabaabbbabbbababaaaabbaaaabbabbbaabaabaaaabaaaaaabbbbaabaababaaaaabaabbababaabbabaabbabbbbbaaabbabaabaaabbbbaaaaaaaaabbabaabaaabbaaabbbabaabbbbbaabaabbaabaabbbbaaabbababbaabbbbababaabaabbbbabbababbabbbbaabaababaaabbbbbbbbbabbaabbaabbbbbbbbbbaaaabaabbbaaaaaabababbbbbbababaabbaaaabbbabaaaababaababbabbaabbbbaabbabbaababbaabbabbabbaababbababbabbabaabaabbaabaababaaabbbbbbbbaababaaaabbbbabababbbabbaababbbaaaabaababbaababbbaaababbbabababaabbababaabbbbabbbaabaabaaabababbbaaaaaabaaabaababababaababaababababbabbabbabaabbaaabbbaaababaaaabbaaaabbabbabaaaaababbbbbbbaaabbabbabaabbbbbaaabbbaaabbbaaabbabaaababbabababbababaabaabbabaaaaaaaabaabbbabbbaaaaababbaaaaabbabaaabaaabbbbabaaabaabaabbbaabbaabaabbaabbbabbbababbbaaaaababbbbaaabbababaabaababbbaabbbbbaaabbababbbaababaaabaabaaaabbbbaaaaabbbaababbbbabbbbaabaaababbbabbbbbbaaaabaaabbababaabbbaaabababbbababbabbabaababaaaababababbaabaababababaaabaaaabbabaaaabbbbbaaaabaabaaaaabaaaaaabbbbbabbbbabbbbbabbbbbaaaaaabbbababbbaabaaabbbaabbaaabbaabaababbaabbbbbbaaaabaaabbbababbbababaababbaabbabaabbbbbbbbbabbbabaaaaabababbbabbbbbabbababbababbbbbbbbbbaaabbbbaabababbbababbbbabaabababaaaaabbbbaaaaaabbbaaabaaaaaabbbbaaabaaaabbbbbbabbbbbbbbbbbabaabaaabbabbabbbbbbbaaabbaaababbbbbbbaabaaabbbbbaaabbabaaaabbbbaaabababbbaaabbbbaabbbbbbabbbababaabaababbaabbabbbbbbabaabbbabaababbaabbbbabaaabbbabbabbbbaabaabbbaaabbbbbbaaaabbbbabaabbbbaaaaabaababbabbbbbaabbbaabbabaaaababaaaababaaabbaaabbbabaaaaaaaababaabbbabbaaabaabbbbaaaaabababbbbbbabbbabbaabaababaabaaabaaaaaaaabbaabaabbababaababaabaabbaababaabaaabbababbababbbbaaaaaaabbbaaababaabababaaaababaaaabbbabaababaabbbbbbaaaaabbbaabaaabaabbbaabaaaaaabbaaaabbbabbbbbabbbaaaaaababbaabaabaaabbbababababbabaaabbabbaaaabaaaabbbbaaaaabbabbbaabbaaabaaaaaababababbbbbbbabaaababbbbbabbabababaabbabbababbbbabababbbbbbbaaabaaababaaaaaaaaaaabbbbbaaabbababaabbbaaababababaaaabbbbbaabbaaaababaaabbbabaaabaabababbbaaababbbbbaaaabbbbbaabaabbabababbbaabbaaabbbabababbabaaaababaababbbbaabaaabbbabaaaaabaaaaabaaaabbbbabbaababbbbbababbaaabbbbbbabbaabaababaaabbaababbaabbaaaabbbbbaabaaaababbbabbaabbabbaaabbbbabbbabbbabaaabbbaaaabbaababababaababaabbaaaabababaaabbbaabaabbbaabaaababaaabaaabbbabaaababbababbaaaaabbabaabaabbbabaaaaabaaabbbbbaaabbabaaaabbabbaaabaaabaaabbabbbaabbbaaababbabbbbbbabaaabaabaabbbbaabbabbbbababbbbbbbabbabababababaabbabaabaaabaabbbbaaababbaaabbbbbbabbabaababbabbaaaaaaaabbbbaabaabaababbaaabbaabbbbaabababababbaaaabababbaaabbabaabaabababaaabbaaaaababaabaababbabbaabbaaababbbaaaababbbbaaaabbaabbbaaababbaabbbbaaabaaababaaabaabbbbaaaaabbaaabbbbaaaaaabaaababbbaababaabbbabaaaaaabbaabbaabaaaabaaaabbbbaaaaaabbbbaababaaabbabbbaaaabaaaaaaaaaaaababbabbaaaaabaabbababbaaaabaabaaaabbbabaabaabaabababbaabaabbabbababbbbbbbaaaaaabaaabbaaabaabbbaabbaaabbbaaabbababbbbaabaabaaababbbaababaaaaaaaaaaaaaaaaabaaaabbaaaabaaabbbbaaabbaaabbaaaaaaaaabaaaabbbababababababaaabaaaabbababaabbaabbbbbbbabababaaaabaabbbbababababaabababbbabbaabbaaabaaaaabbbabbbbbbabaabbabaaaabababbabbabbbabbaabbababbbaaabaababbbabaaabbbbbabbaabaaaabbbaaabbbbbaabbaababbbbaaaababbabbaaabaababaabbabbabbbaaabaaaabbaaabababaaabaabbbaabababaababbaaabaabbbbababbbbabbaaabbbaaabaabbaabbabaaaaababbaaaabbbaabbabbabaabababababbbabaaaaabaaabaaaaaabaabbabaaaaaabaaabbabbabbaaabbabbbaabbbaabbaabbaaaaabbbaabbababbbaabaabbaaaabbaaaaaabbaaaaaaaaabbbabbbabbbabbababbbaabbbabbbbbbbabaaabbbbbbbbbabaaabbabbbbabaababaabbbbbaabaaaaabaabbaabbbaabaaaabbabaaababbaabaabaaaaababbaabbabbbabbbbabbaaaaabbbbbaaaaabbabaaaabbaabbaaaabbabbbbabbbbaababaaaaabaabbaaaaaabbbbababababbbbbabaaaaabaabaababbabbabaaabaaabbaabaaaaabbbbbaaaaabbaaababbababbbabaabbabaabaaababbababababababbbabbbbabbaaaaabbabaaabbababbbbbabaabbaaaaaaabbaabaabbabaabbaaaaaabbaaabbaaabbbaabababaabaaaabbbaabaaaabbbaabbbbaababbbbbbaababbaaaaaaababbbbbbbbabbbabbaabbabbabbababbabbabbabababaabbaaaaabbabbbbbabbaabbabbbabbbbbaabababbabbaabaaabaaabbaaaababbbbbababbabaababaaabbbaaabaabbbabbbaaaaabababbbbbaaababbbbbbbbbaaabbaaaabaaaabbbbababbbbaaaaabbababbaabababbbabbbaaabbaaaaabaabaabbbaaabababababbbbbababaaaaabaabbbbabababbababaabababbabaabbaaaaaabbaaabbbbbabbabbbbaababaaaaabaabbabaaabbabbbbbabbababaaabbbbbbabbbbaababbaababaababaaaababbbaababababbbaaaabaabaaabbabbabbababbabbbaaababbaabaababaabbbbababbbabaaabaababbaaabbabbaabababbbbaabbbbbabbaabbaabbbabbbbaaabbabbaabbabbbbaabbbbbbbbbaabbababaaabbababbabaaabbaababbaaababababbbababaaabbbbaaabaabaaabbbbabbababaabbbaaabbbbabaaaabbbbaabbbaabaaaaabaabbabababaababbaaabaaabaabaaabaaaababbbbabaaabbbaaabbbaababaabbaaababaaabbaabababababbabbbbbabbbbaaabaabaaabbabbaaaaabbbabbbbbbbbaabbaaabbabbaabbbbbbbbaaaabbababbababaabbbbabbbaaaaabababbbababbbabaaaaaaababbabaababaabbaaabababaababbbbaaaabaabaabaaababaabaaabbbbabaababbaaabbbbabbbbbaaaabbbbaaabababababbbaabbbbabbaaaaaabaaabbaabaababaabaabbbaaabaabaaaabbabbabbabaaaaaaaabaabaaabbbaabababbaababbabbbbabaabbabababbbbbababababbabbabaaaabbbbbabaabaabbbbbabaabbbbaaaaabaabababbbabaaaaabaaabbabaaababaabbbbbaabbbabbbbbbabaaabbbbbbabbaaabbaaabaabaabaabaaabbbabababbaabaaabbaaaaabaaabbabbbaabbaaaaaabababbbbabbaabbaababbaabaaababaaababbaaababbbbabbbbaaababbbaaabbbaabaaabbabbbaabbaaabaabbabbbababbaabbbaaaaabbbabaaaababaabbabaaababaababbabbabbbabaababbababaaabbbbabbbbababaabbabbaabbaabababbbaaabaabbbbbaaabababbbabbababbbbaabbaaaabbabaaababaabaababbaaabbbaaaabbaaaaabaabaaaaabaabbbbbabbbaabaaaabaabaabaaaababbbababbabbbbbbaaababbbbaabbbbbbaaabababbbaababbbbbbabbabbbaaaaabaaabbbbababbabababaabbabaaaababbabaaababbbbabaaaaababbabbbbbaaabbabbbaabbbabbabaaababaabbbabaaaabbbbbbababbaaabbaaaaaaaaaabaababaaabaabbbabaaabbbaaaabababaaaabbaababbaabbbbaababbbbabaabaabbabbaababbababbbbbbbbbabbabaaaabbaaaabbbabaabbaaabbbaaaaaabababaaabaabbbbbaabbbabaaabababaaabaabbbaabaaababbbbaaabababbbabbbabaabaababbabbabbbbbbaaaabbbbbbbbaabaabaaabbaabbabbbabbaabbabbaabaaabaabbaabbbaaaabbbbbaabbababaabaaababbbaaaabbabaabbbaaababbaabaabbaaaabbaaaabbaabaaababbababaaaaaaaababaabaaaaaaabbbbbbbbabbbaaaaaaaaaaaaabaaaaabaaaabbabaaabaaabbbababbbbbbaababbabbbbabbaabaaabbbbabbaabaaabaabaabaaaaabbabaababbabbbabababaaabbaaaaabbabaaabaababbabbbabbaaabbbabbabbbbbbbbabbaaaaaaaabababbababbabaababbbaabbbbabbababbaababaaaaabbababbbbbabababbbbabaaabbbaaaaabbbbbbbbbbaabbbabbbbaaaaabababbbbbaaaaabbbbbbabbbabbababababaabbabbbbabaabbabbabbabaaaaabaabbbaaaabaababbaabbaabbbbaaaabbbabababababbbbaabbaaaaaabaaaabaaabbbababaaabaabbbaabbaabbabbbabaaaabbbbbbaababbaabbbbaabaabaabbababaababbbaaabbabbbaaaaabbbaaaaaaaaabbbabbbbaabbabaaaababaabbbabbbababbabaaabaaabaababaaaabbaaabbaaabaaaabaaaaaabbbbbabbbbbaabbaaababaababbbbabbbaaaaabbaabbbbaabbaaaabbabbbaabababaabbabaaabbaaabbaaaaabbbbbbbbbabaaabbabababaabbabababbabaaabbabbaaabbbbbbbbbaaabbaababababbabbabbababaababaababbaababbabbbababbaaaaaabaaaaaaaaaabbaabbbbbbbbaaaabbbabaabbbbabbbbabbaaabbaaaabaabaaabbbbbaabaaabbbabbaaaabaabbabaaabaaaabbaabababbaabaaaabbaabababaaaaaabaaabbabbaabbaaabbbababaabaaabaabaabbbaaabbaaaabbbaababbaaaabbbabaaaaabaaabbaaabaaaaaaaabbaabbabbbbaaaababbaaaaabbababbabaabbbbbbbaaaabbababababaaababbbababaaabaabbbaabaabaaaababaababbbabaabbabaaabaabbaaababbbbaaaabbabbabbaabaaabbbaabbaabbaaaabbaaabbbbbaabaaaaaaabbaaaaaaabababababbababaabbaabaabbbbbaaaababbabaaaaabbbbbababbababbaaabbabbbabaaaaaaababaaaaabbabbbbbbabbabaaabbbabbbbbbaaabaabaabbbbbbbabaaabaabbaabbabbbbaaaabaaababaabbbaabababbbabbabbbabbaabbaabaabaabbbbabbbaabaababbababbbaaaabababaaabbaabaabbaababaaaaaabbaabaababbababbabaabbbbaabbaaaabbbaabaabaabbbababbabbaababbabbaaaaaaaaaabaaaaabbabbabbabaabaaaaabbbbaaaabbaabbbaaabaabababbbaaabbbaabaaaababbbabbababbabbababaabbabaabbbaabaaabaaaababaaaabbbaabbabababababbabbbbabbbabbbaaabbbaababbaabaabbbbbaaababbbabaaabaaaabababababbbaabbaabababaaabbbbaaaabababbbbbaababaabaabaabaabaababaabbbbaabbbabbbbabbaabaaaabbaaaabaaaabbabaabbbbababbaabbbabbbaaabababaaaabababbabbabbabbabaaababababaabaaababaaabbbaababbbaabaaabbaaaaabbababaababbbaaabbbaaaababbaaabbbaabbbbbaaababaababbaabaaaabbaabbabbbabbaaaabbbbaaabaaaababbbbbbabbbbabbbaabbbaaaababababaaabaabbabbbbbaaaabababaabababaaaabaaaabaaaabababbbaabbbaaabbbbbaaabbbaabbbbbaababbbbbaababbbabaabaaabaababbbaaaabbbabbbaaaabbbabaaaaaabbaababbabbaabbbaaabababaabaabbbabbbbabbaabaabbabbbbaaaaaabbbbaabaabbababbaaaaaaabbababaaababaaaaaabbabbaabbababbaaababbbabbaaaaaaabbbbaaaaaaaabaabaaababaabbbaabbaababbabaaabababbaaaabaabbbaaabbaaaaabaabbbbbbabbabaaabbbbaaaababbaaabaaababaaaaaaabbaaabbabaabbaabbbababbaabababababbaabbaabbaaabbabbbbbababbbabaababbbabaababaaaaabaaaabaababbabbaabbbaaabbaaabbabbbbbbaaabbbbaaaabbaabbbbabbaabbaaabaaaabbbbaabaaababaaaabbbbabaabbabbbbabababbaaaabaaaaaaababababbbbbbbabbaaaaaabbabbabbaaaaaaaabbbbaabaabbabaabbaaaaaababbbbbbabababbaaaaababaaabaabbbbaabbabbbabbaaaabaabaabbababbabaaabaaabbaabbbabbbbbbabaaabbabbabbbabbabaabaaaaabaababaaabbabaaaabaaabbbababbabbbaaaabbbabaabbaaaaaaabaaababaaaaabbababbbbabbabbababbbbbabaabaabbbbbbbabaaabbbaabaaaaabbabbaaaaabbabbabbbabbabbabaaaaabbabaabaaaabbbaaabaabbbbabbbbabbbaabbaabbbaabbabbabbababaaabbbabbbabbabaababbbaabaaaaababbabbabbbbababbbbababaaababaaaaaababbbabbabbaaaaaaabbabbbaaaaabbabbaaaaabbaabaabababbaaabaaaaabaaabbaabbabbabaaabbabaabbaaabababbaaabbbabaaaaabababbbbaabaaaabaababbaabbbbaaaaabbbbbababbaaaabbbbaababaabbbbbabbabaabbbbabaaabababbbaabbabbbaaabaabaaaaabbbbaaabbbaabbaaababaabaabaaaaaaabababbaaabababbbabbbabbaaaaabbababbbbbbbbbbabaaabbbaaaabbbaabaabaabbaaaaabbbaabbbaaabbabaabaababbbaabaaaabaaababbbabbaaaaabbbbabbbbabbabbbbbbbbaabaaabbaaabbbaabbabaaaaabaabbaabbbaabbbbaaabaaabbbabababbbababbababbaaabbaababbbaaabbaababbbbababaabbbaaaabbabbaaabaaaaabbaabaaaaabbababbbabbabbaaabbbaaabbbabbbabbbaabaaaabbbbbaabababbaabaabbabaabaabaabbbaabbbabbabaaabbaaaababaaababaaabbaaaabbbbbaaabbbbbababaababbbaaaabbbbbabbbbaabbaababbbbbaaabaaaaaabbbbababbbbaabbababaabbabbabaaaaaaabbbaaabbbbabaabaabbaaabbabaababaabbbaaabaaabbbaaabbaaabbbbaaabbaabaaaaaaabaababbabbbababbbbbbbbbabaaaabaababbaabbbaaabaaaaaabbbabbbaaaaaabbaaabbbbbbbbabaababababbaaabababbbabaabaabbabababaaabbbaaabbbaaaaaabaaaabbbababaabbbaaabbbaabaabaaabaaababbbaabbaabbaababababaabbbbaabaaaaabbaaaabbaaabaaaabaaaaabababaaaaabbbabaaabbbbbbbbbbbbaaaaaaabbbbaabbbbaaabaaabbabaaabaabbbbbbaaaaaabaabababbbabbbbabaabaababbababbbbbabbbbababababbbaabbaabbaaabaabbabbbbbbabaaabaaaaabbabbbbbaaaabbbbbaabbabbabaaaabbabababababbbbaaabbaababaaaaaababbbaaabbbbaaaabbaababaabbabbbbbbbbaaaaaaaababbabbbaabaababbbbaaababbabbbbabababaabbabaabaaaaaabbbabbbbbbbaabaabaaabaabaababbabbaaaaaaaabbabaabbbbbaabaaababbaaaaaaaabaaaababbbbababaababbbaabaabbbbbabbbaabaaabbaaabaabbbbbabaaabbabbbbbbabaaabbabaabbaabbaaabbbabbbaabbaaaabababbbbbababaaabbbbabbaaabaaabaaababaabbaaaabbaabbababaaaabbaaabbbaababababaabbaabbbaabbbaaabbbbaaaabbbabbaaabbbbbbbbbbabaabaaaabbbbbbbabbaaaaababbbabaaaabaabbbbabbaababbbbaababaabaaabbbababbaabaaaaababbbaabbbbbababaaaababbabaabbabaaaaabbbbbaabbbbbabbbbbaabbbbbabbaabaabbbbbbaababbaabbabbbbabbaabbaaaaabbabababbbbbababaabbabaabbabbbababbabaababaabbaaabbaaabbbbababbbabaabbabaaaaabaaabaabbbababbaabbababbaaaaabbababbbaaaababaaabbaababbbabaabaabaabbbaaaababbbbbabaaaaabaabbaababbbbabaaaaaababbabaaabbabbabababbbbaabaabbbaaabbbabbbaabaabbaabbbaaabaaaaabbabaabababbaabbababbababaabaaaaaaabbabbaabbaaababbbbaabaaaaabbbaababbbababaabaabbbaabbaaaaabbaaabbabaaabbbbaababbbbabbaaabbbabbbbabbabababbaaabbbbabbbababbbbbbbababbbabbbbbabbbaabbaabbbbbabbabbabaaaabbababbbabaaaaaabaaabbaaabaabaaabaaaabbabbaabaaabbbabbaaaaabbabababbabbabaabaabbbbbbaaabbabaaabbbaaabababaaaaaabbbaaabaaababaabbababbaabbaaaaaabbbbabbbbbbaaaabaabbbbbbaaaabaabaabbaabbabbbbaaababaabbabbbbbaabbaabaabbabbbbbaaaaababbaaabbabaabaabbababbaababbabaabaaaaaabaaabaaababbabbbbabbaaaabbbbbabaaaaaaaabbbbbaaabbabbabbbabbbbabbabbbabaaabbbbababaababaaabbabababbbbabaababbbbaabbbabbbaaabbbababababbabbbabbbabababbbbbaababbbbbaaaaababbbbabbbbbbbbabbbbabbbbaaabbaaabaabaaababbbbbbabbaababbbbaabbbaaaaaaaabababaaaabbbaabbaababaabaaaababaabaaaaaaaaaaababaabbaaaabbababbbaabbbabaabaaaaaaabbbababaabbbabaaababaabbababbbabbbabaaabbbaaabababbaabbabbabbbbbbbbbabbbabaaababababbaaaaaaaaabaaabbbbaaabaaabaaababbbabaaaaababbababbabbbabababaaabbaabbabbbabbabbaabbbbabababbaaaaabbbaabbbabaaaaabbbbabaaabbabbbbaabbaaabbaabbbbabababababbaaaaabbabababbbabbaabbabbaaaaaaaaaababaaaaaabaabbbaabaabbababbbabbaabbaabbababaababababbabbbabaaaabaaabaabbabaaabbbbbaabbaaaabbaaaabbaabbbaaabbbabbaabbbbbabbbabababaabaabaaaaaabaaababbbbbbbbbbabbbabbbaabbabbabaabbaaabbaababbbaababbbaababbbbbbaaaabaaabbbbaabaaaababaaabababaabbaabaaabbbaabbbbabaaaabaaaaababbbabbbbaaabbabaababbbbbaaabbbabbbaaaabaabaabbaabbbabababbbbbababbabbaaabaabbabbaaababbaaaabbabaaabaababbaaababbabaabbbbababbabbbbbaabbbbbbaaabaabbababaaabaabbaaaabbabaaabbabbaaabbbaaaabbbbaaaabaababaaaabbaabaabbbaabaaaabbabbaaabbaaabbbabbbbabbabababbaababbbaaaabbbbbbbaabbbbbbaabbbbbbbbbbabbaaabbababaababbbaaaabbaaababbaaababbbababbaababaaabbabbaabaabbbbabaaababbabaaababbabaabbbabbabaabbabababbabaabaabababbabbbbbaaaaabaabbaabbaababaaabbabbaaaaababbaaabbbbabbaababbbabbbbaabababaaaaabababbabbbaabaababbbbbbaaaababbbabbaaaaabbbabbbabbabaaabbabbaaabbabbabbbaabaaabbaababababbababbaabaabbaabaababababbbabbabbbbabbbabaabbbbabbbaaaaabbabbbabaaaaabaababbaaababbaaabaabbababbabbaaaaabbabbbababaabaabbbbaaabbbababbababaaaabaaabaabbbabbabaaaaabbababbbabaaaaaabababbbababbaaabaaaabaabbbbabababbbbbbbababababbababbabbbbbaaabbaabbbbaaaaababaaabbaaaabaabaaabaabbbaaabbabbaababbaabaabbbaaabbbbbbaaaaababaabbbaabbabbaabaaaaababaaabaaabaaaabbbabbbbabaaabbaabbbababbabbbbabaabbbbbbabbaaaabbbabbaabbaaabbbaaabbaaaaabbaaabbbbbaaabbbbbaababababaabbaabaaabbabbaaabbaabbbabbabaabaaaabbabaabaabbbababbbabaabbababbbaaabbbbaaabaaababbaababbaababbabbbbbbababaababbbbaaaaaaaaaabaabbbaaabaabbbbababababbaabbbaababbbbbbaaabaaabaaabababbabaaabbabbbbaaabbababbaabbabaabaabbabbaaabbaaababbababbabbaabbabbabbabaaaabbbbbababaaaababbbbababaaabbaaababbabaaaabbaaababbbaababbbbbbbabbbaababbabbabaaaabaaaaaaabbbbbaaabbbaabbaaaabababaaabbbbaaaabbbbbbbbabbabbbaaaaababbabbbbbbbbababaabbbbaabaaaaaabbabbabbabaabababbbbbabbbbbbbbaababbabaaabbabbbabbbabbaaabbbaabbabbbbaabababbabababaabbbbaababaaaaaabbbbbabbababbaaababaabbbbbabaabaabbbaababbbbbaaabbbbababbbabbaaaaaaaaaababaababbaabbbbaabaaaabbabaaaabbbaabaabbbbaababaaabbbbbbbbbabbbbbaaabbbbabaabbbbabaababaaabaaabbaabababababbabaababaabbabbabbaaabbbabbbababbbaabbaaabababbababbbabbbababaaabababbaaaaaabbaaaaaaaabbbaabaabaabbbabababaabbbbbbbabaabbbbbaabaaaaaabbbaababbbbabaabaabbbbbbaaaabbabbbbaaabbbbbabbbbbaabbabbaabbaabaaabbbbbaabbaaabbbbbaabbbabbaaabbabbbbabbaaaabbaaabbbabbbbabababbbbbaabbabbabbbaabaaaaabbabbabaababaaabbbbaaabbabbabaabbbabbbbbabaabbabbaabbaaababbbbbbaaabbaabaaaaabbabbbabaabbbbbbaabbabbaaabaaabbaabbbbababbbbababaabbaabababbabbbaaabbaaaaaaababbababaabbaaabbbaaaaabaababababbabbaaaaabaaaabbaaabababbabbbababbbaabababaabaaabbabbabaababbbaabbbbaabbbbaabbbaabbbabbaaababbbaababbbababbaaaabaababaabaaabbbbabbbbbbabbbbabbabaabaababaabbabbaabbaaaaaaabbaabbaababaabbabaabbbaabbaaaaaaabbbaaababbabbbaaabababbaabbabbababaaabbabbbbabbbabbaabbabbaaabbbaabaaabaabaaaaabbabaabaabaabbbaaababbabbaaababababbaaaaabbbbaabababaababbaabbbaabaaaaaabbabbbaaaaabaabababaaaababbaabbbbbbbaabbbbbabababbaaaababbababbabbaabbbaaabbaabbabaabbabaabbaaabaaaabbabaaabaaabbaaabbaabbabbbaabbabababbaaaabaaaabaabbaabbbbbabbbbabbaabbbababbbabaababababaabbbbaababbbabaaabbbabbbaababbabbabbaababbbbaaaaaabaabbbbabbbbbbbaababbabaabbbbbbbabaababaaabaaabababaaabaabaaabbaaaababbbbabaaabaaabbbbbbbbaabaaabbaabbbbbaabbbaababbaaaababbbbbabbbbabbbbaabbaaaabaababbbbbbbbaabbbbaaabbbbbbbbbbbbbaaaabbbbabaabbbbbbaabababbaaaaaabbbbbbbbabaaaaabbbbaabaaabaaababaababaaaaaabbabaaabbaaabbbbbbabbabbbaabbabaaabbaaaabbaabaabbbbbbbbbababbaaababbbbabababbbaabbbbbabbabababbbbabbbaabababbbaabbbbbaabbabbbababbbababbbbaabaabaababababbabbaabbaabbbbaabbabbbabaaaaaabaabbabbbbbbabababbaaaabbaabbbababbaababbababaabbabbbaaaaaabbbaaabbbbabbbbbaabaabbabaaaabbbbbbaabbaaabaababababbbabbbabbbabaabaaababbabaaaaabaaaaaabaaabbababbbabababaabbbbbbbaabaabbababababababbababbbabbbbaabbbaabbaaabaaaaaaababbbbbbabababbbbbbabbbbbaababbabaaaaabbaaababbbabbaaaaaabbaaaababbbbbbbbbabaaabaabaabaabaaaaaaaabbbbbaabbaaababaaabbbababbaaaabbabaababbaaabababaaaabbaabaaabbabababaaabaaabbaababbaaaaabbaabbababaabaaaabaabbababbaaabbababaaabbbbbabbbabbaabbababababbbbabbbabbabaababbababaabbaaabbabaabbbababaabbbababbababbabbaabaababbbbbbbabbabaabaabbbbbbaaaaabbababbabbbbbbbbbbabaabbaaabbbaaabbbbbabaabbabbbbabbabbaaabaaababbabbbbababaabbaababbbabbaaabbabbbbababbbabbaabbbababbbbaaabaaaababbbbbbaaaabababbaaabbbabababbbabbbabbaabaababababaaabbbbbbbabbaaaaaaababaaaaaababbbaabbbaaabaabbababbaabbbaabbabbabbabaabbaababbabbbbbabaabbbabbabaaaaaaaaababbbabababbbbbabbbbbbabbabaabbaaaaaaaaaaaaaaaaabbaabaabbbbbbbabbabbabaaababaabbaabbaaaaababaabaababbbbbbbaaaaaaabbbbaaaaaaabbaaaaaabaaaabbababbabbbababaabababbaabbabbbbaabababbbbbaaaaabbaaaaaabaabbaaabaabaaaabbbbbabbabaaababaabbaabaababbbabaaaaabbabaabaabbabbbaaabbbbaaabbababbbaaababbbbbaaaaabaabaaabbaabbababbbaababbbabaabaaaaaaabbabbbabbaabbabbaaaaaabaaaabbbabbabaabaaabbbbabababbababbabbbbbbaaabaaabbbabaabaaababaaabaabbabbbbaababbbbbabaabbaabbbabaabaabbabababaaaaabaaabaaabaaaaababbaaaabaaaaabbbbbbaaaabaaabbbbbabbbabbbababbababbbbaaabaabbbbbbbaabaabababbabbbbaaaabbaaaabbbaabbbbbbaaaaaabbbaabbbaabbaabbbbaabbabbaaaababbbbabbaaaaabbabbabaaaaaaabbabbabaaabbaabaababaaaabbabaaabbaabbbbaabaaaaababaaababaaabbabbabaaaaababbbbbbaabbabaaabaaabaababbaabbaababbbbbaaaabbbbbabababbabbabababaabababababaabbbbabbbbbaababaaabbbbbabbbbbababbabbabbbabbbaaabaaaabbbbaaaaabababaabbaabbbbaababbbabababbabbaaaaaabbbaabbbabbbbababbbbababaabababbabbabaabbbbaabbbbbababbaaaaabbbbaabbbbaababababbbbaaabaababaaaabaabaababbaaabaaaabbaabbbbabbaaaabbbabababbabbababbaaaaaaaaaabbaabbbbbbbbaabaaaaaaabbabbbbbbbabbbaaababaaababbbabababbaabaabababbbbbaabbabbbbbaaabababbaabaaaaabaaaaabbaaabababbaaaaabbabbbbaaaaababbbabababaababbbbabbbbaaaaaaabbaabaaabbabbbabaabababbbaaaabbabbbaabaaabaaababbaaaaaababbbbbabbbbabbaabbbaabbaaabbbabaabaabaabbabaaababaaaabbbaaabbabbbabbbaaabbbbbaabbbaababaabababaabbbbaaababbbaabbbbbbbabbaabbbabbbbabaabbabaababababaababbbbbbbaaababaaaabaaabbababbaabbbbabbbabababaaaaabaaaabaaaabbbaabbababbaabaabbbaaabaabbbabbabbaabbaaabbababbbabababaaabaaaaaaaaaaabbbabaabababbabaaaaabbbbaaaaaaaababbbbbaabaabaaabaabbaaaabaaabaaabbababbaaaaabbbaaabbbbabbbabbbaabbbaaaaaabbababbbaabbababaabbbbbaabbbbaabaabbbbabbbabbbbabaaaabbababaaabbbaaaabbaaaaabbabbaabbbbbbbbaababbabbbbbbbbbaababababbaaaaabbbbbabbababaaabaabaaabbbbbabaabbabbbabaaabbbabbbbbaaabaaaaababbbaababbaaabbbababaabaaaabaabaabbbbbbabababaabaababbabaabbbbbbaaabbbbaaaaaabbaaabaaaaabaaaaaabbaaabbaabbbbabbbbabaabbbbbaabbbaaaaabbaaaaabbbbbbaaabbabbbaabbaaabbbbaaabaabaaaaaabbbbbaababbbabbabbabbbabbbbbbbbbaabbbbabbbbbbbbbabbaabaaababaabaaaaabababaaaaabbbbaaabbbaabaabbbbaaabbababababbabbbaaaabbaaaababbaaaabbabbbabbbbaabaaaaaaabbbbbbbbbbaaabaaabaaabbbabbbbbbaaababbabaaaabbbaabbbbaaaabababaaaaaaababaaabaabaaaaaaaababbbabbabbaabbbaabbbaaaaabbabbbaaaabbabaaabbbbabbbbbbbaaabbbbabaaabababbababbabaabbbababaababbababaabababbaaaabbabbabbbabababbbabbbabbbbabaaabbbabbbbbbbabbaabbbaaaaabaabbaaabbabbaabbbbaaabbababaaaaabbababbbababbbaaaabaaabbbbaababbbabababaaaaaabababaababaababbbbbaaabaaaabaababbabbbbabaaabbbbbbbbababaaaaaaaaabbabbbabbbaabbbabaabbbbbabbaabaaaaaababaabaabaaaaabbbaabbbababbbbbbabbbabaabaabbabaaabbbabbaabbabaaabbaabbabbbaabbbbabbabbbbabbaabaabbabbababababaabababaabbbbabaaabaaaaaaababaabbababaaaabaabaaaabababaabaabaaaabababbabaaabbbbbbbaabbabaaababaaabbbabbbabbbabbbaabaabbbbabbababaaabbbbbabaabababaabbaababbbabbabbaaaabbaabaababbbaabababbaababbaabbaaaabbaabbabbbabaabbabaabbbababbbbaabbbaaaaababaaabbbbbbbbaabbbbbbbbbbaababaababbbabbabaabababbbbabbabbaabaaaaabbbbaaaababbaaaababbabbaaaaabbaaabaabbbbababababaabbabbaaabbbaaabaabbabbbbaaabbaabbabababbabaabbabbbabbbbbbbbaaabbbabaaaabbaaabbaabaaaabaababababbabbaaabababaaabbababbbbbbabbaabbabbabbbbbbbbbbbbaaabaaabababbbabbbaabbababbbbabaabaaabaaaaaabaabababbabbbabbbaabaabaaabbabbbbabbbbaabbaaabbbbbabaaaaababbbaaababbbbbaaaabaaaababbaaaaabaabbababbaaaabbbbbbaaaaabbaaabbaaabbbbbbbabaaaaaabbbaaaabaaababaaabbaabaaabbbbaabbbaaabaaabaaababaabbbabbbabbababaaabaabaaababbbaaabaaabbbbbababbbbbbaabbaabbbbaababaaaaaaabaaaabbaaaaaaaabbbbbbabbbbaaaabbbbbabaababbababaaabbbaaaaabbbaaababbabbbbbbbbabaaabbbbabaaaaabaabaaabbaababbbaaaaaaaabaaabaabbaaabaaaaaaaabbbaabbabbbbaaabaabbababbbaaabaabaaaaaabbbbbabbababbbbbbaaaababbbbabbbabbbbbbbabaaaabbbaabaabaaababbababaaabaabbabbaaaaaaaaaababbbabbbbbbabbbbaabaabaaaaababbabbbbaabbbaaaabbaaababbababababaaababbbabaaabbbabaabbbbbbaabbbbaaaaaaabaaabbaaabbaaabbbabbbababbbbbaaaaabbaaababaaaaaaabaaaaabbbbbaabaaabababbabbbbaaaaaaabaababbababbbbabaabbaaaaabaaaaaaabbababaaababbbabbabaabbaaabaaabbbabbaababbbaaaababababaabaaabababbbbbbbabbbbababbbbbbabbbbbbaababbbaabaabaabaabbaabbbbaabbbbbaaabbbbbbaaabbaaabaaabbbaabaababaabababbabababbaaabbbaaabbabbabaabaaabaaabbbbabaabaaaabbaaabbaaabbaabbbbaabbaaaaabbaaaaaababaaabaaaabbaabbababababbabaabbaaaaabbbabbbababbbbabbbbbbbabaaaabbbbbbaababbbbaababbbaabaaaaaaabababbaabbbaabababaaaabaaaababbbaabbababbbbabaababaaaaaababbbbbbbaaaaaabbbaababbbbbbbabbaababbaaaababbaaabbaabbbbaaaaaabababaabbabbabaaabbaabaaabbaabbbabaaabbbabbaabaabbabaaabaaaaaababaaabbababaaabbaaabbabbbabaaaaaabababaabbbbbbabaabaaaaabababbbbaabbaaaaaababaaaabbbabbbbbbbabbbbbbabaabbbaabbbbaaabbbbaabaabbababbabaababbaabbbbbabbaabbaabbbabbaaaaabbabaaaaaabaaababbabbbbababaabbbbaaabbababababaaabaaabbabaabbbbaababbbabbabbbbbaabbbbbbbabaaaaaaabbabbaaabbbbaaaaaababbabbababbbbbaabaaaabbbbaabababbaaababaabbbabbbbaaabbabbaabbbbbbabbababaabbaaaaabbbabaababababbababaabbbabababaaabbaabbaaabaaabbbbabababbababbaaabbaaaabaaababbbabbbabbbbaaabaaabbbabaaaabbabbbbaabbabbaaabababaababaabaabbaaabbaabbaabbaabbababbbbababbbababbbbbabbabbbaabbaabaabbbababbbbbbbbabaaababaababbbaabbbbbaaababababaabababbababbabaababbaababbababbabaaaabbaabaaaaabbabaabbbababaaabbaabaaaabbabaabababbabababababababaaaaaabbaaaaaabbbbaaabbbabaaababaabbaabbaabaabaaabbbaaabaaaaabaaabaaabbbbaaaabbaaabababaaaabbbbababaabaabaaaaaabbabbbbabbbaababbbabbbbabbbaababbbaaabababbbbbbaabbbbbaaabaabaaaaabbbaababaaaaababbabbbaaaaaabaabbbbaabbabbbbbabaaababababaaaaabaabbaabaabaabbaaaabbaaabbaabaaabbbbabbabbbaaabbbbaaabbabbaaabbaaaabbabbbbababaaaabbbbababaabaaaaabababababaaaaaaaabbbbbbababababbbbaabaaaabbaaaabbababbabaaaaaaaabaaaabaabbababbbbabbaabbbbbbbaaababababbaababaaabbabaababaaabbbbbaabbabaabbaababaaaabbbbabbabbabbbabbbabaababbabababbaaaaaaaaaababababbbbbaabababbaaaaabbabaaabaaaaaabababaaaabaaaabbbaabbbbbaaabaabaaababbbbbbabbabaaabaaabaaabababaabaababaaaaabaaaaaabaaabaabbbbabbaaabbbababaaabaabababaaaaaabbbbbaabbabaaaababaabaabbbaaaabbabbbaabbabbbbbbbbabbabbaaaabbabbbbabaaabbaaaabaaaabbababbbababaaabbabbbabbbabbbbbbaaabaabbbaababbaaaaabbabbbbaaaababababaababbbababababbbbbaaaabbbbaabbabbaaaabbbaaabbabbababaabaaaabaaaaaababababbbbaabaabbbaabaabaaaaaababababbaaaabbabbbbabbbaaaabbbbaaabbbabaababbaabaaaabbaaaaaabaaaaaabbbbbbabaaaabbabaaaababaabaaabaabaaaaabbbbbabaaabababbabbaaaaabbbbabaabbababbaaabbaabaabbbabbaabbbbbaaaabaabaabaaabbabbaaaabbbbbbabbabbabaabbbbbababbbbbaabaabaaaaabbaaabbababaabbbabaaaabbbbbabababbbababababbaaabbaabbaaababaabbbbbabbbabbbabaaaaaaababbaaaaaaaaaaabbbaabbbbbbabbabbaaaaabaababbbaaaabaabbabaaaababbbabbbbaabbbabababbbbbabbaabbaabaaaababbbbaaababaabaabaabbaababbabababbaabbaaababbabbabababaabaabbbbaaaaaabbaaabbaaabaaabbbaababaabaaaaabbaaaabbabaaababaababbababbababbaaababaaaabaaababbabaaaaabaabbbabbbbbaaaaaabbabbaaabbaabaaababaabbabaaaaaabbabbaaabbbbabbbabaabbaabaabaabbaabaababbbbbaabababbaaabbbababbaabaababaaababaabaaabaabababaabbaababbbbbbbbabaabbbbaaaabbaaaaaaaaababbabbbbbabbabbaabbaabbaaaabbbbabbabaaaabababbaabaaababababbbbaaababbbaabbbbbaabbaabbababaaabbabaaaaababbbbabbbabaabaababaaabbbbaabbaaababaabbbbabbbaaaabaaaabaabbaababbababbabbbaabaababbbabaabababbbbbbaabbbaaabaababaabaabbabbbabbbbaababbabbaabaaaababaaaabaabbabbabbabbaaabbbaabbabaaaaaabaabaabaabaaabbbaabbbabaababbaaababbababababaaababaaaababbaabababbabababbabaaaabbbaaaababbbbbabbbbabbbbbabaabbabaaababbbabbabababbbbbbbbaaabbabaaaabaabbbbaaabbaaaabbbabbababbabbbbbbbaababaababbabaaaaababaabbbaaaabbaabbbbbabbabbabaaabbbbaabbaabbabaaaaababbbaaaabbabaaaaabababbabaaaaaabbbbaaabaabbbabaabbabaabbbababaaababbbabbbbabbabaabbaaabbbbbaabbababbabbaabbbbabaaabaaaabaababbaabbbbbbababaaabbaabbbaabababbbbbbabbabbaaabbbababaaaabbbabaabbbaaabbaababbbbbaabaaabaaaaaababbaaaabbaabbbabbabbababbabbababababaaabbbbaaaaaabbabaaaaababbbbbbbabbbbbbabbbbbbabaababaabbbbababababaaaaababbbaabbaaaabbabaabbbbbbbbabaababbabbbabbababbabbaababaaaabbababaaabbbbbbbaaaabbbbaabaaababababaaabbaabaaaababaababbbaabbaabbabbbabaabbaabababbabbbbabbaaabbbabbaabababbbababaababbabaaabbabbaaaaabaaabbbbbbbbaaabbaabbbbaababababbbaabaaabbbabbbababbbabaaaaababaaabaabaabbbbbbababaababaaabbaabbababababbaabaababbababababaaabaaaaaaaaabaaababbbbbbaaabaaaababbbabbabaabbbbbbbbaaaaabababababaaaababbaaaabababbabbabbbbbbbaaabababbababaabbababbabaaabbbbaabbabaabaaaaaaabbaabaaaabbbababbababbabbaaaaababababbbbaabbaabbbabaaabbbabbbbbaaaababababbaabbaaabababaaaabaabbbabababbbaaaaabbaababbababbbbabaabbbaabaabbaabbbbbabbaabbbbaabbaabaaababaaabbbbbbbabaaabaabababaaaaaaaaabbbaaaabaaabbbbaaaababbbabbbbaababaabaababbbabaabaaabaabbbabbbbbbbabbbbabaaabaabbabbbaaabababbaaaaabbbabaaaabaabaabbbbbbbbbabbaabbabaabbbabbbbbabaabbababbabbabbbbbbaabbbabbaaabbbabbaaabbabbbbabababbbbbbbabaabbabbbbbaaaababbababaabaababbbaaabaabbbbbabbbbabaaaaaabababbbabbbaabbabbababbbaaabbbbababaaaaabaababbabababbbbabbbbaaabaaabbbbbbbaaaaaaabaaaabbbbaabbbaaabaababbbbbbbaaabbbaabbbababbbbbbbabbbbbaabaaabbabbbabaabababaaabaaaababbabbbabbbbbaaaaaabaaaaabababbbaabaabbababbabaabbbbbbbbabaabaabbbabbbbaaaababbaaaabbaaabbaabbaaabbaaabbababbaabaaabbbbabaaaabbabbbbbbaabbaabaaaaababaaababaabbabaabaabbaabbbbbbaaabbabbbaaabbbbbaabbabbbaabaaabbababbabaabbbabaabaaabbababbbabbaabaabbbbabbaabaabbaabbbbaabbbaababababbabaaaabbbbbbbbabbbbbbaabbbaaababbaabaaaabbbbabaaaaaaaaabbbbababbbbaaaaababababbabbabbbbaabbbbbaabaabbbbbbbbabbabbbabbbaabbabbabaaabababbbbaabbbbababbaaaabbabbbbabbbbbbabbaababbaaabbaabbabaaaabaababbbbbbaaaaaaaaaabbaaaababbaaabbbbbbaaaaaaababaabbaabbbbaabaabbaaaaabbbbbabbbbaaabaaabbaababaaababbabaabaaabbbaabbabaabaabaabbbbabbaaababbaaaaabbbabbabaabbaabbbababbaaaabaaaaabbaaaabbbaababbbabbabbaabbaabbbbaabbaaabbbbaabbbbababaabbbbaabbbbbbbbbbaaaaaaaaaaabbbabaaaaabbaaaaabaabaabbbabaababababbaaabbaaaaabbbbbaaabbbabbbbbabaabbaaabbaabaabbaabababbbbbababaaabbaaabaabbabbaabbaaaabbaabbbbaabaababbbbbabaababbaabaaaababbbabababbabbbbbbbbababbbaaaaabaaaabababbabbbbbbabbbbbbbbbbababaaaabaaababbaabbbabaababababaaaababbbbbbabbbabbbaaaaaaaabaababbababaaaabaaaaaabbaabbabbbbbaabbbabbaaabbabaaababbbaaabbabbbaaaaaaaaabababaaabbabbaaaabbbbaaabbabaabbabbabbbaabaababbbbbbaaababbababbbabbbaabbbbabbabababbbabaabaabaabaaaabbababaaababbabbbaaabbaabbaabbaabbbbbbababbababbabaababbaabbbaaabbabbabaabaaaabbbaaaaabaaaabababaaaaaaaababaaaababbbabaaaabbbbbaaabbabaabbabaaabbaaaaaabababbababaabbbbaabaabbbbaaaabaaabbababbaaabbbaabaababbaababababbbaaaabaababbaababbabbababaaabbaaababaaabbaabaaabbbbabbbaaaabbbbbbabaababaabbaabbbaababbbbbaabaaabbabbbaaabbaabaaaaabbbbabaaababbaaaababbbbaaaabbbbbaaaabbbaaabaaabaaabbaaaaabbbaababbaaaabbaaaababaaabbaaaaaaababbaaaaabbabababababbbbaaabaaabbbbabbbbaaaababbaabbbabaababbbbababaaababbaababbbaababaabbbbbbaababbabbbabbbaababbbbbabbbbababababbbbbaaaabaaaabbaaabaababbbbabaaaaaaabbbaaaabbabababaabbabaabbbaaaaaaabbaaabbabbabababababbbbbabbabaaabbaaaaababbbaabaabaaababbbbbbbbbaabbbaaabaabbbbbbbbabbaaaaaaaaababaabbabbbababbbbabaababbbbbaaaabaaaabbabbbbababaabbabaababbbbabaaabbbabbabaaababaaabbbabbaabbbbbaabaabbbbaabbaabbabbababaaabbbbaabababaabbbaabaabbbaaaabbaababaabbbbbaaabbbbabbabaabbaaaaabbbbbbababbabbbabbaaaaababbabaabaabaabaaababaabaaaaaaababaaaabbbbabaabaabbbabaabaabbbbabbbbabbabbbbaabaaabaabbaaabbaaaababbbabaabbababaabbbbabbaaaaaabbbbbbbaaabbbabbbbabbbbaaaaababbbbabbbbabbabbbbaaaabbabaaaaabaabbaababaabaabaaabbbabaaaaabbabbabbbabbbabaabbbabbbabbbabbbbaaabaaabbaabaababbbaaabbbbabaabbbaaaaaaabbbaabaaaaaaabbbaaabaabaaabababbbbaabbaaaaaabbaabaababbbbbbbbbabaaabbbababbaabbababaababbbabaaabaabaabbaaaabbababbbbbaabaaabaabbaaabbbaabbbaaabababaababbaabaabbbabaababababaaaaaabaabaaabbaaaabaabaaabbabbbabbaaaababbabaabbaababbabbaaabaaabaabbaaaababaabaabbbbaabbaaaaaabaabbaabbababbbbbaabaaabbaaaabaabababbabaabbaabbaaabbbaabbbbaabbaabaabbaabaaabbaaabbabbaababbabbabbaaabbabbabaababaabbababaabbbababbbabbaababababaaabbbabaaaaabbbabaabaabbabbaabbbaaabbbaaaabbabbbbbabbaabbbbbaabbababbbbabaabbabababbbbbababaaabbabbbbbbaaaabaabbabbbaabaaaababbababbaaabaabaabbbbaaabbababaaaaaabaabaabbbaaabbbabbabaabbaababbababbaababbaabbbbbbaaababaaaaabaaababaaabaaabbabababaabbabbababbabbaaababbbaabbbbbbbbaaabbbbbbaabaaaabaaabbabaaaabbaaaaaaabbabbaabaababaaabaabbaaabaabbabbaaabababaaababababaabababbaaababaabaaaabaaabbabaabbabaabaabbbbabbabababbbbaaaabaaaaaaabbababbbaababbbabbaababbababababbbbaaaababbaabbaaaaabbabbaaabbabbbababbbabbaaabaabbbaaabaaabaabbbbabbbbaaababbbaabbbbbaabbbaabbaabaaabaababbbbbaabaabbbbaaaaababbaabbbbbbbbbaabaabbabaaabbabaaaabaaaaaaaaaaabbabaaabaaabababababbaaaaaaabaaaaaaaaaabbabbabbbaabaabbaabbbabbabbaaabbbbbbabbbbbbabbaaaabbaaaabbbabbbaabbbbaabbaaaaabbababbbbabbabbbababababbbbbbaabbbbaaababaaaaaababbaabbbbbaabbabababbbaabbaabaaabbaabaaaabbabbabbbaaabbabaaaaaaabbabaabbbabbbaababbbabbabaabbaabbbbbbbabbabbaaababbaaabaaabbabaaababaaabbabbabbabaaabbbabababbbaabbaabbbbbaabbbbbaaaabbaabbbabaabbbbbbababbbaaabbaabbbababaabbaaaabbbababababbaabbabbbbaaabaabaaabbabbbbaaaaaababaabaabaaaaabbabaababbaaabaabaabaaabaaabbbaabbbaaaaabaabababaabaababbaabababaabbabbbaaabbbabaaabbaabbbaabbaabbaababbabbaabaabbababbbbabaabababaaaaabaaabaabaabbbaaaabababaabbbaababaababbbbaabaaaabbbaaabbbabababbababbbabaabaaabaababbbbbaaabbbabababbbabbbababaaaabbaaabaabaaababbababaaababbbaaaaaaabbabbaaaaaaaaaababbbbabaababababbaabbbbbbabaabbbbababbaaabbbbbaaaaaaabbaabaabbbabbabbbaaaaabbababbbbaabbbabbbabaabbaaaabbabbaaaaaabaabbbbbaababbabbbababbbbaabbbbbbbaabaaaabbbaaaabbbbababbaaaababaaabaababbbbaabaaaaaaabbbaaabaababbbbaabbaaabaababbbbaabbbabbabaabbbabbbaabaabaabaabaaabbbbbbbbaaaaaaabaabbbbaabbaababbaabbaaabaaaabbbaabaabbabbaabbbbabbabbabbbaaaaabbaabbbbabaabaaabaaaaaabbaabbbbbaaaaabaabaaabaaabbbbaaaaaabaaaaabababbbabbaabbabbabbbabbbaababbaaaaabaababaaaaaabbaabaaaaabababaababbaabbbababababbbaaabababbbababaabbaabababaaabbbbaaabaabaabaababaabababaaaabbaabbbbbaabbabaaaabbababaaaaaabbbbbbbaabbaabbaaabbaaabababbababbabbaaaabbbbbabbaaaaabbbbaaaaaaaaabaaaaababababbaabbbbabaaaaaaabbbbaaaabababbbabbaabbabbbbbbabaabbabbbaabaabbbababbbabbbaabbbbaaababbabbbabaaaabaabaabbbbbaabaaaaaabbbaaaabbbababaabaaabbababbbbbabbaabaababbbaaabbaabbababaaaaaaaabaababaaabaaaaabbaaaabbabaaababbbaababbbaaaaabbabaabbaaaababaaaaaabaabaabbbbbbabbabbbaababaababbaaaabbabbbbaabbbbbbbaabbbabaabbabaaaabaababbabaabaabaaababaabbaabbabbbbbbaaababbabaaaaababababbababbbbbbbbbbabbbbabbbabbaaabbbabaaabbabaaabbabbbabaaabbbbbabaaaaabaaababbbbbbbbbaaaaabbabbbabaaaaabbbaabababbaaabbbaaababbbababaaabaaabaabababaabbabababaaaaabaaabababbbbabbababbababbbaababbbaaaabababaaaabbbbbaabbababbaaaaaabbbbababbbaabaabbbbaaaaaabbbbbbbbbaaabbaaaabaababaaabbbabaabbaabbabbabaaababbbababaabbbaabbbabaababbbaabbabbbabbaabbbbbbbaaababbbababbaabaaaaaabbabaaabaababbbbaaaabaaaabababbbbaabaaabaaabbbbbbbaababbaaababaaaaabbbbabbaaababbaaaaaabbabababaaabaaabaabbbabaaabbaabbaababbaababbbbaabababbaaaaabaabbbbabaababaabaabaaaabaaabbbaabaaaaabbabbbaaabbbbaaaabbaaaaaababaabbbaabaaababbaaabbaaabbbbabbbaaabbababaabbaaaabbaabaabbaabbbabbbaabbbbabaaabaaabbbaabaaabababbbbababbbbaaabaabbaabbbaabababaaababaaaabaaabaaaabbbaaabbbabaabaabbbbbaaaababaababaaaaabbaabbbbaaababbbabaaaabaabbaabbabaababbbbaababaabbbbbabaaabbbbbbabbaabbaaabaaabaaaabbaaaaaabaaaabbbabbabbbaaaabbabbbbaaaabbabbaabbabbaaababbabbbbbababababbabaabaababbbbbaaababbbabbaaabbaabbabaaaaababbbbaaabbbbbbababaababbbbbabaaaaababaababbabbabaabaaabababbabaaabbbbbaabbbbbbabaaaaabbaabbabbaabaaababbbabbaababaababaaabaabbababbababbbbabaaaababbaabbbbbababbbbbabbababbaaabbaaaaaaaaabbbbabbbaabbaaabaabaabababababaaabbaaaabaabbaabbaabaabaabaababaaaabababaabaaabbababaabababaabbbbaaabababbbbbbabbbbabababbaababaaabaaabbaaabaaabbbaaaaaabbbaababaababaabbaaaabbaababbbbbbbabaababaaabbabbbaabaababbaabbaaababbaabbababababbaaaabaabbbaaabbaabbaaaabbaababaaababbabaabababbabaabbaabbbaabbabababbbaaabaabbbbbaabbababbaaabaaabaaaaabbbbbbbabaaabbbbabbabbaabaaabbbaaabbabaaabbbbababbaabababbbbbbbaaabaababaaababaaababaabababababbbabbbabbaabbaabbabbabbbbbaababaabbbabbaabbbbbbaabababbabababbabbaaabaaabaabbbbabaababbaabaaaaabbaaaaaaabaabbabbbabaabaaaabababaabaabbbbbbabbbaabbabaabbbbabbaababaabaabbbbbaaabaabbbababaaaaabbabbabbbbababbbbaabaaaaaaabbabaabbbaabaabbaabaababbbbabbbaababbbababaaabbbbbaaababbaabbaaaabbabbbabbabababababaaabbaabaaababaaaaaaabababbaaaababbbaabaabbbaabaaaabababbbabaaabbbababbabbbaaaabaaabaaabbbaaababaaababaaabbbabbbbabbabbababbbaabaabababbaabaaabbaabbbbbabbbbbabababbbbbaaaaaabbbabaabbaabababbabbaababbbbaaaaaabbabaabbaabaababbbbaaabbaaaaabbbababbabaabaaaaaaaaabaaaaabaababbbbababaabbbbaabbaabaaabaaabbbaababbababaaabbbaaaabbbbbbaaabaabbabbaaaabbbbabaabbbbabbbabbbbaabababbaabbaabababaababbaaabbbabbabaabbaaaabbaabababbabaababaaaabbbbaabbbbaaaababbababaabaabbbaabbbaaaababbbbbaaabbbaaabbbbbabbbaaababaaababbbbaaabbabaaabbababaaabbbaaabaabaabaaababbbaaaaaaabbaabbabababbabbbaababbaabbbbbababbbaaaababbaabaabbbbbbabbabbaabbabbabaabbabbbbbbbababbaabbaaabababbbabbaaaaabbabbbaabbbabbbbbabababababaabbaabbabaabbbbbbbabaababbbbbabbaabbbababababbbabaabaaaabaabababbabbabaabbbaabbababbbbbaababaabaabababbaaabbabbbbabaabbaaaabaabbbbbbbbbbaabbbbaaabbbbbabaaabababbabbbbbaaabbbabbbabaaababbbabaabbbabbababbaaabaaaaaabbbaaaaaaaabbbbaaaaaabaaaabbbaabbbbbbbaaaababaabbaaababaaaabaababbaaababbbababbabbbaaaabbabbabbaabbaaababaabbaabbababaabaaaababbabbaabbbbababaababbabbababbaaabaabbaaababbbabbbbabbabaaaaaaabaabaababaaabbbbbbaabaababbaaababbbaaabbabbabbababababbaabbbaaabbbabbbaaabbbabbaaabaabbbbababbabbbbababbaabaabbabaababbbaaaaaababaaababababbabaaabbbbabbabbabbaaababbaaababbbaaaababaabbbbbbabbbbaabbbbbababbbabbbabbbabaaababbabbbabbbbbabbabbaababaaababbaababbbbaaaaaabaabbbaaaabaaaababbbbbbaabbbbbbabbbbbbbababaaaabbbababababaaaaaaababaabaaaaabababbbaabaabbabbbaabababaabbbaaaababaaaaabaabaababbaaababbbbaaaaaabbbbaaaaaaaaaaaaaabbaaabaababbbbaababababaaababbbabaaababaabbaaaaabbaababbbbabbbaabaabbbababbababbaaaaabbbababbbbabbbaabbaaababbbabbabbbbbabbabbbbbbbbbbbaabbbbbbbbbbbbaabbabbabbbbbaaabbabababbabbbbabaabbaaabaababbaabbabbaaabaababbabbaaabaabaaababaaabaabbaabaaaaaaaaaaabaababbbbbabaabaaaaabaaaabbbbaabaaaabaababbaabbaabbbbbaabbbbaabbabbaaabbaababbbbbbbabbaaaaabaabaaabaaababbbbaabbbaabbbaabaaaaaaaaaaaaababaabaaabbbaaaaabbbabbabaaaaabaabbbabbbbbbabbbaabaabbbbbaabbbbaaaaabaaaaabaabaababbbaabbaaabaabaabbabbabbbaaabbbbbaaaababbbaabaaababbbbbabbaabaabbbabbabbbbbabaaaaaaaabaabbbabbbbaabbbbbaabbaaabaababbaaaabbbabbabaabaaabbbbabaabaaaaabbbaaababaabaaaaabaabbabbbbbbbababaabbbbaababbaaabbbabbbababbaabbaaaabaaabbabbbbbabbaaabaaaaabaaabaaaabbababaaaabbbbbabaabbbbabaabbbbbabbbababbabaaabbbabaaabaabbbaaaabbbaaaabbabbbaaaabaaabbabbbbbabaaabaabbbaabaaaabbaaabbbbbbbababbbbbbabaaaaaabababbaabbaababaaababaabaabaababaaabaaabbaababbbaaaaabbbabbaaaaabaabaabbaabbbbabbbbbbabbabbbaababbabbabaaabaaaabbaaabbbabbbbbaaaaabaababbbbabaaaaaaabbbbaaabbaaabbbaabbbbaababbabaaabababbbbaabababababababbaaaabbbaabbaaabbbaaaaaaabbbbbbabaababbbbabaaabbabbaaabbbaaaaaaaabbaaabbaabbbbbbbabaaabaaababbbbaabaabbaaaabbaaabaaaabaaabbbababbbbabbaabaabaabbaabaaaabbaaabaaaabbbabbaababbbaaaaaaaabbbaabbbbbbaabbbabbabbabbbabbbaababababbbbabaaabaabbaaaaabbaaaaaababbbbaabaababbbbbbabbbabbbbabbbbbbbababbaabbbaabbbabbbbbababbbbabaabaabbbbbabbbaabbaabbaabaabaaabbbaababaababbabbbababaaaabaaabbabbbbbbbaabbbaaaabbbabbbbbbaabbabababaabbbaabbbbabbbabbbbabaabaaabbaabababbbbbbbbaabaaabbabaaabbbbabbabbaabbabbabbabaabababbbbbabbaaaaaabaaaaabaabaaabaabaabaabbababababaaabbbbabbaabbbbbaababaaaabbbbbbbababbaabbabbbabbbbbabaabbaabbababbabababaaaabaaaaaaaabaaaaaaaaaababbbaabaaaabaaaaaabaaabbaaaaabaababaabbbabbaaaababbabaaababaaaabbababaabaaabbaaaabbbbaabbabbabbbbabaabbaaaabbbabaabaabaaabaabaaabbababbabbaaabbbbaaabaaaabbabbbaabbbaabbaabaabbbabbaababbaabbabaaaabbbbbaababbabbbaabaaaababbbbbbabbaabbaababbbbaabbbababbbaabaabbbbbabbaaabbbbbababbbbbbabbbbbabaaaaabaabbbbbbbaaaaaaabbababbbbbaabbaaaabaababbaaababbbbabbbbaaabaabaaaaabaaaaaabbaabaabaabaabaabbbabbbbabaabbaaabbabbabbbaababbaabbbaabbaabbabababbbbaaaabbbbbabaabbabababbaabbabaabbbaaaaabbabbabaaabbabaababbbbbbabbababbabbaabaabbbbbbabaaababbaaabbaaaabbbaaabbabababaababababbabbaabbababbaaabbaabaabaabbaabbbbaabaabbababbaabbbbaabaabaabaababbbabbbbbbabaaaaaabbaaaaabbbbaabbabbabaababaabaabbbbbbbbaabbabaaaabbaabbabaabbabaabbbababbaabbbabaabababbbbabbabaabaaababbbbaaababbbaabaabbbaabbaabbbabaabaaababaabbabaabbbaaabbaaaaabbbaaababbabaabaaabababbbbbaaaabaababbabaaabbbbabbbbbbababbaababbbaaababaabbaaabbbbaabbaabbabaabbabbaaabaaaaabbbbabababaababbaababbbabbaabbaabbababaaaabbabbaabaaabbababbabaabaabbaaaabbbbaababaaaaaaaaaaaabaaaababaabababbbaaabbbbbaabbaabbabaaabbabbaabbbbbbabbbaabbbabaaaaaababaaaaabaaababbaaababbbbabaaaabaaaabaaabbabbbbaabbaaababbbbbbbaabbbababbaabababbbbbabbabaabbbbaaaabaabbaababbaabbababbaabaaaaabbabaaabbbbbaabbbbbaabbbbbaabaabbabbaababbaaabaabababbbbabbaabbabbbbaaaabbbbabbbbbbabbabababbbaabbababbbabaabbababbababbbabbbaababaabbbbaababbaaaababaaaaaaabbabaabbbabababbbbaaaabaaababbaaabbbbabaabbbaaaaaabbbabaaabbbaabbaaaababbbaabaaabaaabababaaaaaaabbabaaabbbbaaaababbbaaaaaabaaababbaaaaababaaaaabaababaaabbabaabaabbbbababbbbabaaababbabbababbbbbaabababaaaaaabbbaabaaaabbaababaabbaaaaaaababaaababbaabaaaabaabababbaaaaabbabababaabbabbabbaabbaaaabbbbabaaabbbbbbbabbaabaabaaabaabbbbabbaabaaaaaabaaaaaabbabaabaaaabbababbbbbbbaaababbbaaabbbbabaababbbbabaababbaaaaaaababaaabbbaababaaaabaaabbbbbbbabbbabbabababbaaabaababaabbaaaabbabaabbbbbbbbbbbababbbbaababbbbbaaabbbababbababbbabbabaaaabbaababaaaaabbaabbaaaababbbbaaaaabaabbabbbaaabbbababaababaabababaaababbbabaabaababaaabaaaabbaabbbabaaaabaaaabaabbabbbbabaaaaaababbaaabbbbbaaabababaaaaaaaabaababbbbabaaabbbaabbbbabaabaaaabbbaababbbbbbbaabbaaabbaaaaababbbbbaabababbbbaaaabbababbabababbabbbababbbaabbbaabaaaaabbabaabaaaaabaaaababbbbbbabaababbbbbbbaabbaabbbaaaaaaaabbbaabbbaabbbaaaaabaaabaababbbaaaaababbbaaabaaabaaababaabbbaaabaabbabaabaabbabaabbbbaaabaabaababaaaaabaaaabbaababbaaabbabbaaabaaaabaaabbaaabbabbbbaaabbababababaabababbaaaabaaababbabaabbabbbbbababbabaabababaaabbabababbbabaaababbbbbaabbaabaabbbababaabababaaaababbaabbaabbabaaaababbbaabbabaaabbbaaabaaabbbbabbbabbaaaaabaabbbbabbbbabbababbbbabababbaaabbababaaabaaabaaaaaabababbbbbbbabaaabaababbbababbbabaaabbbbbbabbbbaabaabaaabbababaababaabbbababbabbabaabaaaaabbababaabbaaaababbabbbbabbaaabbbababbabbaababbbbabbbabaabababbaaabaaabbaaaaabaaababaaabababaaabbabbaaaabaaabbbabbaabbbaabaaaaaaaabababaababaaaabbbabbbaaabbaababaabbabbaabaaaaabaababbaaabaabbabbaababaabbabbaaabbbbbaabbbbbabbaabbbbaaaaaabbababbbababbabaaababbbbbbaabaabaabbbbabaabababaabbbbabaaababaabaabbbabbabababbaaabbababbbaaabbaabbaabbabaabbabbbbaaababaaaabbbbbbabbabaabababbabbbbabbbaabaaabbbaabaabaabaaababbbbaaaaaaaabaabbabbabbbbaaabaabbabbbabaabaaababaaabbaabbaabbaabbbabbaababbaabbabbaabbbaaabbabababbabbaaaaaababababaaabbaaabaaabbbbaaaababbbaaabbbbabbbbbbabbbbaabbbbbbbbbabbaaaaaaaaaaaaaabaaaaaababaaaaaabbabaaababbaabbaaaaaaabbbaaaaaabbbbaaaabbbaaaaaabbaaaaabbaaaabaaabbbabaabbbbbbaabbabbbbabaabbbabbaabbbbbbbbabaaabbbbabbbabbaaabbbabbbabbaaabaabaaababbaaabbbbabbbbaabbbbbbbbbaaabbbbbababaabaabbaababaaabbbbbbbababbbbaabbbabbaaabababaababababbaaabaaabaaaaaaaabaaabbbababbbbaabaababaabbbbaabbbbaabbaaabbababbaababbabbabababaaaabbaaabbabbbbabaaabaabaababababaabbabaaaabbabbabbaaaaaaababaaabbbababbaababaabbaaabbaababbbabbbbabaaaababbaabababbbabbabbbaaabababbaabaababaababbaabbbbaaababaabbaaaababaabbaababaababbaabbababababbaababbbaabbaabaabbbbaabaaaabbbbabbbbbabbbbaabbbaaabaaabababaabaabaaaaababbaaababababaaabbabbaababbaaaabbbbaaabbaaabbbaabbababbbbbbbbabaaaabaabaaabbbabbbabaabbaaaabaaabbbbaaabbabbbbbaaabbbabbabbbababbabbbaababaaabbbabaabbbabbaaaaababaaaabbbbbabaaabbabbaaabaaaaababaaaabbbababbbbbbaababaaaaabaaabbbaaabaabaaabbabbaaaabaaabaabbaababbbababbbabbbbbbbaabbabbbbaaaabbaaaabbaaabbaabaabbbaabaabbbbbbaabaabaaaaaabbaabaabbabaabaaabbbbaababaabbbbbbbaaaaaaaabbbbababbabaabbbababbaaaaabbaaaabbbaabbbabaabbabbbabbbbaaaabbbabaaabbaaaababaababababaabaabbbaababbabbbbbbbabbbbbabaaababbbaaaabbbbaaaaaaababbaabbabbbbbaabbbabbbaabbababaaaaaabbabaaaaaabaaabaaaabbaabbbabbbabbaaabbaaabbbbbbbabaaaabbabaabababbbbbbbababaababaaababaabaabbababbaabbbabbaabbaaaabbaaabaababababbbabbaabaabbabbababbbaabbaaaaaabaaabaaababbabbbbbbaabaaaaaabbbaabaababaaaaaaaaaaaabaaabaabbbabbabbbbbaabbbbbbababababbababbabbbababbabbaababbbaaaaaaabababbababaaabbaaaaabaababbbbababaababaaaabaaababbaaabbbaabbaaaaaaababbabbbbabbabaaaabaaababbbbbbabbabaabbabaaabaaaabaabbbbababbbbabbbaaabababbabaabbbababbabbabbbaabaaaabbaaaaaaabbbbbaabaabaabbabbabaaaaabababbbbabaababbbbaaaabaaababbbabbbabbaaababbaabbabbbaabbbbaaaabbbababbabbbabbaababaabbababaaaabbababbbbabbababababbabbbbbababbbaaabbaabbbaaababaabbaabbaaaaababaaabaaabbabbbbbabaabbbabbbaaabbabbbabababbabbabbaabaabbaaabaabaabaabaaaabbaaababbbaababbaabbbbaaaaaaaababbaaaabbaabbbabaababbaabaaabaabaaabaabbabbabbaabbbabbbaabbbabbbaabbbaabaaabaaabbbbbbababaabbababbbbbbaaababbbbaabbbaababbabbbabaaabbbabbbbababbbaabbababbbbabbbabaababbaabaaabbbbbbabbaaaabaabbaabababbbabbaaababbbaaaaaabbaaababaaabbaaababbabbbababbabbabbbabbbbaaabbabaabbabbbbbbbbaababbbaabbabababbbbabbabbaabaabaaaabbababaaababbabbabaabbabababaaabbaababbbbaaaabaabbbbbaaabbbabbbaabaaaabbabbabaabaaabbbabbaabababbbaabbbaaaaaabababbaaaaabbababbbababbabbaaabaaaaabbbaaabbaababababbbaaaaabaabbabaaababbbaaaaaababbbbaababaababbaaaaabbaabababbbbaabaabbbaababbbbbaabbabbbbabaaabababbaabbbaaabaabaaaabbbbaaababaababbbbabaabbabbaabbaababaaabbabaaaababaaaaaaabababbabbaabababbbbbaaabaabaabbbabaabbbbbabaabaaabaaababbbbaaabaaabaaaaaababbaaabaabbbbabbaaabaaaaabaabaabbbabbaaabaaabaaaabbbaaababaabbbaabbaabbabbbbbbbbabbbbabbbbbababbaabbbbbaabaaaabaabbbbabaaaaaabbabbaabaababaabaabbbaabbaaaaabaaabaaabbbabbbbabbbaabaabababbababbaabbabaaaaabbbbaabbababbbabaabbbaabbabbbaaaabbbaabbbbbaabbbbaaabbabbaabbbbabbaababbbaaaabbbabbbbbabababbbaababbaabaaaabbaaababababbaaabbaaabbbababaabbbaaaaaaabaabbababbabaaabaaabaaabbbababaaaabaaaabaabbbbbbbaaabbbaabbaabbbbbbaabbaabbbbbabaabaabbabbbbbbabaabaaaabbababbbbaababbaaabaaaababbbbabbbbabbbbabaabbababbabaababbaaaabbabbaabbaabbaaabbaabbaaaaaabaaaababbabbaaabbaababbaaaabbbbababaaaababaaabababbbbbbbbababbaaaabaaabababbbbabbabbbabababbbbababbaaaaaabbbabaabaabbbaaababbbbbbbbaababaabaabaaaabaabaaabaaaabbaaaaaaaaabaabbaabaaabbbbaabbbabbbbabbbababbbbbbbabbabbbabaaaaabbbbaabaaababbbbaaabaaabbabbbbaaabbbbbabbbaaabbbbbaabaaaabbbbabbbaaaaabbbabaaaabbbbbabbaabbabbabbabbabaaabbabbabbaaaaabbbabaabbbababbabbbbaabaabaababbaababbabbaaaabaabaaaabbbbabababbabaaaaaaaabaabaaabaabbbbaaaaabaabbbabbbbaaaabbaaabbbbababbbabbababbbbbbaabbabbbaabbabaaabababbbaababbbaaababaabbbabbabbabaababbbbbbababaaabbbababababbababaaabaaabbaabbbbbbabaabbbbbbabaababaababbbbabbabbbabaaaabaaabbaabaababbaabaabbabababaabbaabbbbababbbbbabbbbbbbaaabbaababbabbabaabaabbbaabaababbbabbbbabaabababaaaabbaaabaabbbaaaaaaaaabababbabbabaabaabbaaabbbbabbbbaaaaaaaaabbabaabbabaaaaabbabbbbabaabababbaabaabbabaaabbbabbabbbaabaabbabbabbbababababbabaabbababaabaabababbabbbbbabababaababaabababaababaabbbababbabaaababbbbababaabaaaabaaaabaabbaaaabaaabbabbbbbabbbaabaaaaabaabaaabbbabaabbaaaabbbaabbbbaaaabaabbaabbaabbbabaaabaaabaaaababaabbbbbaabaabbaabaabbababbbbaabaaabbbaabababaababaaababbbbabbbbbbbbabbbbaabbbaaabbbbbbaababbbbbababbbaababbbaaaabbababaaabababaabbbbaabbaaaabababbbbbabbbbbbbbbbabaaababbaaaabbaabababbbaabbabbabbabbbbbaababbbbaabbbbbbbbabbababbabaabaaababbababbbabaabbaaabaaabbaabbbbbabaaabbbabbaabaaaabaaaababbaabbaababbbaaabaabababbbbbabbbaabbbbababaabbabaaaabbbaaabbbaaaabaaabbabaaabbaaaaabbaabbabbbbababbbbbabbaabbbaabbaabbbbbbbbbbababbabaaabbaabbaaabbaaaaaaabbaaabbbbbbbaabbaaaaabababaabbbbbaaaaaabbaaaaaabaabbbabaabbabbaaabbbaabbbbaabbbabbbabbaabbabaabbbaaabbabaaaabababbbaaaabbbbaaabbbaaabbbbaababbbabaaaaaaaabbaaaaabaababbbbbbbaaabbaaabbaabbbaaabbbababaabbaabaabaabbabbabaaaabbababbbbbbabbbaaaaabbbbabbbbbbaababbbbabbabaaaabbbbbaaaabababaaabbbabbbbabbbaaabbabbbbbaabaabbaababababababaabbbbbbaabaaabbbaabaabbaabbaaabbaabbbaabbaabbabaababbaaaaaaaaaaaabaabbaaabaaaaabbaaaaabbbbaaaaaaaabbabbabbbbbabaabaabbabbabbaaabaaaaabbaaabaaaaaaaaaaaaaababaaaabbabbbaaaaabbbbaababbbbaaabababababbabbbaababaabaabaabbbbaaabbbbbaabbabbbaaaabbbbbbbbaaababbaaababaabbbbbbbbbabaaaababbaaabbaaabaabbbababbbbbbbaabbaabababbbaabaaaaaaaabbabbbbbabbababbbbbabbaaaaaababbabbaababbabbababbaabbbbbabbaabaabababbbaabaabbaaabaabababbabbabbbbbbbaaaaaabbabbbabbbaababbbbbaabbbaaaabaaabababbabababbaaaabbababaabbaabababaaaaabbaabbababbabaabbbbbbaaaaabbabbbbbababaababbbabbbbbabbabaaaaaabbabaaaaaaaaaaaaaabbbabaaabbabbbaabaabbbbaaaaababbbabbbbabbabbabaaabbbbaaaabaabbbabbbaaabbbaaababaabbaaabbbabbaabbaabbabbbaabbabaaababbbbaaaaaaaaaaaaabbaaaaabbbabbabbabaaaaaaabbaaaabbbaabaaaaaaaabbabaabbbabbbabbaaaabbbabbbabbbabababbbabaabbbbbbbbbaabaabbabaabbbbaaabbaabababbabaaaabbbaabbababababbabbaaaabbbbabbbabaaaaabaabaabaaababaaaababbbbbaaababbaabababababbababaaabbabaabbbbabbabababaaabaaaabaaaaabbaaabbbabbabbaabbbbbbaabaaababbbbbabbbabbaaabbaaabbbbbbaababbbaaaabababaaaababbaabbbbabaaababbaaaaababaaabaababaaabbbababaaabaabbababbaabbabaaaabaababbbaabbbaaababbbabaaaaabaabbabaababbbababaaabaaabbbbaaaababbbaababaaabbbbabbbaabaabbbabbaaabbbaabaababbbabbabbbabaaabbbaabaababbbbabaabbbabaabbbaaababbaabaaabaabaabbbbabbaabaabbbbbbababbbababbbabbbbbbbaaaaababababbbbaaabbabbaaabbaaabbbbbbbbbababababbbaabbabbabbbbababbaaabbabbbabaababbabababaaabaabaaababaabbbabaaaababbabbbaaabbababbbabbbbabbaabbbbababbbbbaaaabaababbbbabbaababbabbbbaabaaaabbbaaaaaabbaabbbbbbabaaabbabaabaabbaaaaaabbabaaaababaabaababbbababbbaaaaabbabbabbabbaabbabbbbbaaabbbbabaabaabaaaaaabbbabbbbbaabbaabaabbabaaaabbbaabbbbbaababbabbbbbaaaaababaabbbbbaaaabaabbabbbababbaaaaabbabbbababbbabaaabaabaabaaababbabbbbbbaabbabbbbaabbaaababbababbaaabbbbaaabbabbbababbabbaabaaaabbbbaaaaaabaaabbbbabaababbaababbabbbabaabbabbbaabaaabbaabababbaaabbabbbabbbbaaabbabbbbaabaabaabaabababaabaaabbbbbbbaababaaabaaaababaabaaabbbbabbbaaaaaaaababbbbabbaabbaaaaababababaabbaaaaaaaabaaaabbbbbbabababbbabaabaaaababaabaaabbaaabbabbaaaabbbbabbbabaabbaaaababbbbaabbaabbbaaaabababbbaabbbbbbbabaabbbaaaaababaabbaabaababbabbabaaaabababbbbabaaaabaaabaabbbbaaaabbababbbbaabbaaabbbabbbbbabbaaaababaaabaaaabaaababbabaabbbbbbabbbbaaabababbbbaaaaaabbbababaaabbbbabaabbbbbabaababbabbabaaabbbbaaaabbabbabaabbbbbbbabbaaaabaabaaabaabbababbbbbaaaabaaaabbbbaabaaabbaabbaaabaabbabababaaabbbbaabaababbbbbbaabbabbbbabaabaaaaababaaabaaabbbabbabbaabbaaaaabbabbbabaabaaabbbabbbaabbbabbbbbaabbbaababbaaaabbbbbbbbbbaabbbabbabaababaaabaaabaabbaaababaaaaababbbabbabaababaaaaabbaaababaaabaaabbbaabbbababbabbbbbbabbbaabaaaaaaaabbaabbbaaabbbbaababaababaabaabbaabbbbaaababbabaabaaaabbaabababbbabaaaaabbabbbabbabbbabbbababbabbbaabaaababbbabbabbbbabbbaaaabbababbaaabbaabbbababbbbbabbbbabaaaabbabababbbaaaabaababbabbbaaaaabbabbaaabaabaabbabbabaabbbaaabaaabbbaaaaabbaaaababababbbabbabbbaababbbbbbaaaabbbbbaaaaaabaaaabbbbbababaaaaabbbaaaabbabbbabbabbaabaaabbabbbbbabbabaaaabaaabbbbabaabaababbaabaababbbbaaaabababbbbaababbbabbbbbaabaabbbbabbbabbaaaaaabbbaabaababaaaabbaababaabaabaaabbaaababaabaaaababaabababbabbabaababbbaaabbabaaababaaaaaabbabbabbbbbbabababbabaaaabbaababbbbaaabbabbbaabaababbaaabbaaaabaabbbbbabaabbbbabbaabbbbaaaaababababaabaabbababaaaabbabaababbbbbabbbaaaaaabbaabababbaaababbabbbabbbabbbbabababaababbaababbbabbababbabbbbbbbbabbaaabbbabbbaaabbbabbaabbbaabaabababbaaababbaabbbaabbbaaaabaabbbbbbbbabbbbbbaababbaaabbbbbbbbaababbbabbbbbabbbaabbbbbaabbbbbbabbaababbaabaaaabbabaababbaaaaaabbaaabbbbabbbaabbbbbbbbbbbabbaaaaaaababaaabbbaabaabaabbbbababbbbaaabaaabbbbbbabaabaaaaaaaaabababbaabbababbbbabababaabaabbbabbbbabaaabaaaaaabbaaabaaaaaababbbaaaaaaaaaabbababababbaababbbbaabbbbbaabaaababbaabaababbbbbabbbbaabababbababbbababababbabaaaaabbbbbbbbbbabbbbaababababbababbabbbaabaaaaaaaaabababbabaaabbbaabababbbaaabbbaaaabbaaaaabbbaabbbbababaaaabaaaaaaabaabbbabbabbbbabbaabbbbaaaabbbbabaabbaaabaaaabbaabbbabbaabbabaabaaababaababbbaaaabbbababaabaabbaaabaabbaabbbbaaabaaabaabbbabbbabbbaabaabbbabababbaabaabababbaaaaaabbbbbbbbaaababbbbbbabaaabbbaaababbabbabbabaabbbabbbbabaaababbbaababbaaaaaaababbaaaaabaaabbbabbabababababbaaaaaaabaaabaaababbbabaabbbaaabababbbaaaaababaaaaaabbababbbabbbbbabababbaaabbbbbbaabbbaabbbaababaabaabbbbaaabaaababbabbbabbbbabbabaaaababbabbbbbbababbbaaabaaabbaaabbbaabbabaabbbaaabababbbaabbbbbbababbbbaaabbabbaabbbaaababbabbaabbbaaaabbabbbbbabbaabaaaaaabbbabbbaaaaabbaabbbabaaaabaaabbabbbabababbabaaaaaaaababbbabbbabbbaabaaaaaabbaaabbababbaabaabbbabaaaaaabbbaaaabbbababaababbbbbbabbbbaaababbbbaaababbbabbbbabbabbbbbababababbaabbbbbaabbbaababaaaaaabbbaabbaaabaaababbbbbaabababaaaabababbaaabbabbabbabbbababbbbabbaaaabababababbbabbabbbaaaaaaabbaabbbbaabababbbaabbbbaaaaaabaabaabaabaabbaabbbbaaabababbabbbaabbbbbbbaabababababbabaaabaaaaabbaaabbbbabbabbbbbbbbbaaaabaabbabaaababbbbaaabbbabbaaabababbabababaabbbaabbabaabbbaaaaabbaabbbabaabbbaaaaabbbabbabbbababbababbababbaaabbaaaaabaaabbbbabbbababaaababbbabbbabaabbabaaaaababbaaaaababaaabbaabababbaaaaaabbbaaaabaaaaababaababbbbbabbaabbbbbbabbbabbabbaabababaaabbabbabbaabaabaababbbabaaababaaababaabbbbbaaabaabbababbbbaaabbbbaabbbabaababbababaaabbbbbbbbbbbaaaabaabbbbbbbaabaababaaaaabaabbaaabbbabbbbbbabbbaabbaabbaaaaaaabbbaaabbbababbbaaaaabababbbbaaababbbabbbaaaaaabababbabababbbbbbabaaababababbabaababbbbaabaabbaabaaaaaaabbaaababbabbabbaababaabbbbaaabbbbbbabbabbbaaaabbbaabbbbabaabbaaababbaabaaaabbbababaaaaaaababbabaaaaabbaabbaaaaabaabaaabbbbabaaaabbababbbababbbabaabbbaabaabaaabaaaababaaaabaabaabbaabababababbbbbbbbabaababaabaaabababaaabbababababbababaaaabbbbbaaaabbbbaabbbaabbbbbbbabababbbabbbbbbabababaabbabbbbbbbaabbbabbabbbabaaaababababaababbabbbaabbabaabaaaababbabbbbaaabaabbaaababbaaabbbababbaababaaabbaabbaabaaabbabbbbbbbbbbababbbbabbaabaaaaabbbabbbbbbbbabbabbaaabababbbbababbbaabbbbaabbabbbbabaababbbaaaababaaabbbbaaaabababababbbabbbbababbbbababababaabbaabbaaababaaabbaaaabbaabaabbaabbaaaaaaaaaaaaaaaaaaabbbaaaaabbabbaabbbaaaaaaabababbbababaabaaabbbaabaaabbaaabbbabababbaaabaaaabbababbbbbbbaabbbababaaabbabbbbbbbbaaabbabbaabababbabbaabbbabaabaabaaaabbbaaaaabbbabaababababaaabaaabbaabaabababbaabbabaabbbababbbbababbbbbaabbbaaaabbbbabaaaababaaabbbabaababaaaabbbabaababbbabbbbbabaaabbbaaaaabbabbbababbaaaaaaabbbbababbaaabbaaaabaaaabababaabbabbbaabbababbabbbaaaaabaabbaababbaaabbbababbabbbaabbaabababaabbbaaabbbabbabaaaababababaaaaababbbbabababbaaababbabaaaabbabbabbbbabaaaaababababbaabababbbbbbabaabbbaabbbbbbbbabababaaabbbababbaaabbaabbaaaaaaaabbbaaaabbbaaabbaaabaabbbababbbabbabbabaabbbaabaaaababbabaaabbabbaabababbbbbaabbabbaababbbabbbaabababbababbbabbaaaaabbabbabbaaaabaababbbabaaabaaabababbbbbbaaaabaaababbabbbbaabbbbbaaabbbbabbbaabaaaaabababbbbbabaaaababbabbbbbbaabbaabaabaaaabbabaaaabbabbabaaabbabbaaabaababbabbbbbbbabbaabbaababaabbbabaaababaabbbbbbabaaaaabbaabbaabbaaabaabaabaaaaaaaaaabaababbbaaababbbbbaabaaaababbabbbbbabbbbbabbbbbabaabaaabbaaaabaaabbabbbaabbaaaaabbaabbbbabaaabaaabababbbbbbabaabbbababbabbabbabbbabbabaaabbabbbbbbbabbbbbabbabbbbaababbbabbbbbbbbabbbaaabababbaaabaabbaabaabaaaabaaababbbbbaaababbaaababaabaaabaaababbabbaaababbabbaababaaaababbababbaabbbabbabaabaaaabbbabaaaababbabbaaabaaabbbbbababbabababaabaaaaaaabababbbaabaabaaaaaaaaaaabbbabbbbbbabbbbbbaabababaaaabbbababaababbbbbaababbabbbbbaabababbababbbbbbabababbaaababaaaabaabaaabbbaaabbbbbabaababbbbbabbaaaaaabaaabbbabbbbaaababbaabbabbbabbabbaaaaabbaabaaaaabaabaaaaabbabbaabaabaaaaaaabaaabbabbabaaabaabaaaaaabaaabaaabaaaaababaaaaaaaabaabaabbbaaababbbaabaababbabbabbabaabbabbbbbbbabaabaabaabababaabaabbaabbaabaababbabbbbbbbabaaabaababbabbaabaaaaabbbbbbaabbaabababababaababbbbaabaaabbbaaabaaabaaaabbbaabbbaaaaabbbabbababbbabbbaaaababbaabbaaabaaaaabaaaaaaaabbbbbbbbaabbbbbbaabaabaaaabbaaaaaaababbabbabbaabbabababbbabbbbbbbbaababbbabaaabbbaababaabbbbbbbaabbaababbabaaaaabaaaaaaaaabbaaababaaabbabbbbababbabbbaabbbbbbabbbbaabbabbabbaabbbaaabbbbabbbaabbbbbbbbbbabbbababbbbbbaabbbbbababbabbaaaababbbaababababaaabaaaabaaaaababaaabbbbabbabbabbaaabaaabbaaababbbbabaabbaaabbabbabbbaabbaabbbbabbbaaabababbbbabaabbaaaaabaabaaaabaaaaabbabbbbbaababbbabbbabbaaabababbbaaaaabbaabbbbaabaaaaaaaabbaabbbbaaababaaabbbaaabbbbabbbbabbababbbaaaaabbaabaababbaaaaababbaabaabaabbabaabbbbbbabaaabbbabaabaabaababaabbbababbbaabbabbabaaaaaaababbbaabbbaabaaabaababababbabbbbaaaaaabbabaabaabbbabaababbbaabababbbaaababbbabbbbbabababaaaabbbbbbaabbabaaabaabaaabbbbaabbbbaabbbbaabaabaaabbbaaaaabbbabbbabbababbbbaaaaabbbbbaabbbbbbbbbaabbaaababbbaaaababababaabbaababbbbaaabababaaababaabaaabbaabaaabbbbaaababababbbbaaabbbaababbbabaabaaabaababbbbbbbaabbababaabbabbbabbbaaaabbbaaaabbabbaabaaaabbaabbabbbabababbbbbababababaaabababbaabaabaababbabbbbbabbababaababbabbbabababbbabbbbbbbaabaaaaabaababaaaabababbaabbaabaabababaabaabbabababbaaabbababbabbaaaabababaaabbbaaaabbbbbbabaababbbbbababaabaaababbbbbbaabababababbbbaaababaabaaaabbbaaabbbbbababbabaaaaabaabbbbbaabababbabbabbbaaabaaabaaabbababababaaabaaabbbaaaabbaabbabaabaaaaabaabbabaabbbbaabbbbaababbaaaaabaaabaaabbaabbbaabbbaaaabbbbbbbbbbbbbbbbbbaabaaabbaaababaaabbababaaababaabbbbbbabbbaabbbbaababababbbbabaabbababbaababbbaaababbaaabbbaaaabbbabaabbbbaaaababaaababaabbabbabbbbabbbabbbbbbbbbaaaabbbabaabaabbabaabaaabbbbababababbabaabbbbabaaaabbbaaaabababbaaaabbbbbbbbaabbaaaabbabbaaabbbbbababbabbbbbaaaababaabbabbababbabbabbbabbaaabbbabababbaabbbbbaabbbaaaaababbbabaabaabbbabbbaaabbaaaabbababaaaaababbbabaaabaaaaabbbaabbabaabaaaaabbbabbababaabbaaabbbabababaabaababaabbaaaaabbaabbbabbbaaaabbaabbbabbbbbabaaaababbabbbaaaabbaaabbbbaaabbbbbbabbaaaaaaaaabaababbbbabbaaaaabbbaabbaaabaaabaababbbbabbbabaaabababbabaabbaabbabaabaabbbbaabaabaaaabaaabaaababbbabbabbaabbaaabababababababbbaabbbaaabbababaaababbbabbbabbabbabbaaaaabbbbbbbbabbbbabbababbabbbaabababbabaaabababbbabbbaaaaabababbaaaabaabbaaabaabbababbbbbabbbbbaabbaaabaabababaaaabbbbbabbbbbbbabbbbabbaaaaaaabaaabbbaabbababaaabbabbbaababbaababaaaaaaabaabbabbabbbbbabbbabbbbbbababaabaaaaaababbbbbaaababbabbababaaabbbabbababbababbbaababbbabaaabababbaabaaabababababbabbaaaabbabbbaabaabbbbaaababbaabaabbbabbabbabababbbbaaabbabbbababbbaababaaabbaabbaabbbbababbbbaabbaabaaabbaababbbabbabaabbbbbbbaaaaababbabbaaaabbbababbaaaaabaababbabababbabbabbbaabbaaaaaaabbbabbbaaaaabaabbbbaabababaaaabbbabaabbaabbaaaabbbabbbaabaaaababbaaababbbabbabbbbbabbbbbababaaaaababbabbbbaabbbbaaaabaaabababaabaaabbabbbaabbaaabbbaaaabbabbabaababbbababbaaaaaabaaabbaaaabbaabaabbaaaabbaabbbabbbbaaaabbbabbbbbabababbababaabaabaaaabaabbbbbabbbaabbbbabababaabaababbaaabbabaabaaaabaaaababbbabbbaababababaabaaaabbbaabbbbbbbbabbbabaabbaaabaabbabbabbaabaabbbbaababbbbbbaaaaaaaabababbabbaaababaaaaaababbbbbbababaaaaaaababbabbbaaaabaabbbabbababaaabbbbababaabbaabbbaaaabbbaababbaabbabbaabaaababbbbbbabbbaabbbaaaaaabaaabbbbbbaaabbabababbabaababbabbbaabaaaabaabbbbaabbbabaaabbbabbbaabbbaaaababbbbbaaaaaaabbabbabbaaabbabbaabbbababaabbbabbbaabaabbabbaabbbbbbababaabaababbbbbababbbaabbbaababbbbbaaaabbababaabbbabbabbabbaaabbaabbaaaaabbabaabbaaaabbabbabbbbbabbbabbabbaaaaabbaaabbaababbaabaabbbbabaaabbababaaabbaaaabaaabbabaabaabbbaabbabbbaaabbbabbaaaababaabaaabbbaabbaaaaaaaabaabbaabbbbabbabbaaabbbabaaaaabbabbbabbabaaaabbaabbaabaaaabababbbaaababababaaaaaabababaababbaabaaababbbabaabbbabbbaabbaaaabaabaaaaabaaabaaaabaaaaaaabbbaabaaabbbaababaabbabaababbbababaaabaabbbbbbbabbabaabaababaaaaaababbbbbbabaababbbbabababbbbbbbbaababbabbbbbababbbabbbbbbabbbaabbabbaaaaaabaabbababaabbbababbaabaabaaabbaaabbababababbaabaaababbbbbbbbabbaabbbabaabaabbbaabaaabaabaaabaabbabbabaabbaaabbbabbababaababbabbbaaabbababaaaabbbbaaaababbbaabaabaaabababbaaaaababbbababababaaaaaaaaabaaaabbbaaaaabbbabbbabbbabbaaabaaabbbbbabababaaabababaabbaaabbabbabbbabaaabbbaaaabaaabbaabbaababbaaaaabbbbbbaaabaabbabaababaaaaabbbaabbaaabbababababbbababbabbabbbbbabaabbbbbbbaaaaabbabbbaabbbabbbaaabbbabaaabbbbabbbabaabbbbbbbbbababbbaaabaababbbbababbabbbbbbbabbaaababbabbaabbbbabbabaabbbabbbbabbaabbbaabbabababababaaaabbbbabbbaaabbaabbbbbaabaaaaabaabbbbbbaababbababbaaabaabbbaabbaabbbabaabaaaabaabbaabaabbbabbbbababaaabbbaababababbabbbbbabbabbbabbbbaabbabababaabbbaaaabbbbabababbbabaabbaabaabaababaabbaabababaabaaababbbbaababababaaaababbbaabbbbbaabbbabaaaaabaaabbaabbbaaabbbaabbbbbbbbbbbaaababababbaabbbbaaababbbbaabbabbbababababbabbabaaababaaaaabaabaaabbababbabbbbbaaabababaaaaabbbabbaaaababbbaababbababaaabbbababababbaabaababaaaabaaaaaababbbbbaabbbbbaaabbaabbabaaaabbaabababbbbbbbabbabaaaaaababbabbaaaaaaaaaaaaababababaaabbbabbbbbbbbabbababbaabaaaabbabbbaabbbbbaaabaaaabbbabbbaaababbaabbbbbbaaaaaaabaababaaaaababbbbbbbbaaababaaaaabbbbbbbaabaabbaaaaabbbbaaaabbaabbbabaabbaabbaabaaaababbbbaabbbbababbbbaabababbaaaabbabaabbbbbabbbabababbaaaaaaaaabbaaaabaabbaaabbaababbbbbaabbbaabbbabababbabbbabbabaabaabbaabbaabbabbaaaabaaaabbabbaaaaaaabbaaabbaaaaaabbabaaabaaababbaabaaaabbababaaabaaaababbaabbaaabbabbbabababaabababaaaaababbbabbbbbaabbababbabaabbaaaabbabaaaabaabbbaabaaaabbabbabaabbabababbbabbbbbaaabbbababaaaabbbabaaabbbaaabbaaaababbbaabbaaabbbbbbabbabbbbbbbbbbbaaaabaabbaaaabbbaaaabbbabbbaabaaabbbbbaabbaabaabbaaabaaaaabaababbababbbbabaaaabbaaaababbaaaabbbabbabbbbaaabbabbbbbabaabbababbaaaaabaaaababbbbbabaaaaaabaaaaabaabaaabbabaaabbbaabbaaaaaabaaaaabaabababbbababbabaaabbbbbabbbaaaabbbaaaaabaaaaaaabbaabbbbbababababaabaaabbabbabaabababbbbbbababbabaaaabbaaabbbbbaabaaabbabbbababbbbaaaaaaaababbbbabbaababbabaaaaaabaaabbaababababbbaaabaaaabbababbaaaabbabbbaaabbbabaaabaaaaaaabbbbbaabaaabaabababbbbbbabbbabbbbaaaaaabbbbabaaaaabaaaabaaabaaababbbaaaaaaaabaaabbabaaababbaaabaaaabbbbababbbabaabbaaababababababbaabaabbababababaabbbbbbaabaabbaabaaabbbabbaaaaabbbaabbaabababbababbaaabaabbabbbaaabbaaabaabbbbbbbbbbbabaaaaaabbabbbbabaababaabbaabbaaaabaabbaabababaaababaaabbaaaaabbabbaaaaaabbbabbbaaaabaaaaaabbbabaabaaabbabaaaabaaababaaabbaabaabaaaabbaaababbbabaabbaabbbbabaabbbbaaabbbbbababbbbaabbbabbaaaaaabbaabbabbaabbbbbaaababbaabbbaaaaabbabbbabbabaaaabaabaabbbbbbaaabaabbbbbabbaaabbabbaabaabababaaaabaabbbbabaaabaabaabbbbaabababaababaaaabbaaaaaaaaaaababbbbababbbabbbbbabaaaaaaabbbaabaababbbabbbaaaaabbbaaaabaaababbbabaababaaabbaaabbbbaaaaabbabbababbbbabaaaaaabbbaabaaabaaabaaabababaababbbaaabaaabaabbbbaabbaaaabbababaaaaaabbaaaaaaaaaaabaaaabaabbabaababababaabaaaaaabbbaababbbbbbbaabbaabbbbaaabaabaabaaabaaaabaaaabaaabbaabaabbabbabaaabbaaaabbbababaabbbaaaaaaaaaaaaaabbbabbaaabbbababbaababbbbbaaababbbbbabbabababaaabababbabbbbaaaaaabababbbaabaaaabbbbbbbbbabbaababbababababaabbbababbaabbbbabaaaabbaabaabaaabbababaabbabbaabbabbaaaaaabaabaabaabbaababbbaaabbaaabababbaaaabaaabbbbabaabaaabbbbaabababaaaabaaaaabaaabbaabaabaaaaaaabaabbababaabbbaaabbaaabaabaaaabbaaabbaaaaabbababbbaaaabaaaababbabbababbbabababbaabababbabbababbabbaababbabbabbbabbaaabbabaaabaaaaaaaabbbbbbbababbbabaaaaaabaabbaaaaabaababbbbaaabbbababaabbaaaabaaaaabbbbabbaabbbbababbaababaaaabbabaaaabaabbaaabbbaabbabaaababbabbaabbaaababbbbbabbabbaabaaabbbbbbbaaabbbbaaaaaabbbbbbaaaaabbaaabababbbaabaabbbaaabbaaababbaabaaaababbabbbbbbababaababaaabbbaabbabaaaabaabaabaababbabbabbababbaabbbaaaaababbaabaabbababaaabbaababaababaabbbbbaabbbbaababbbaaaabbabbaaabaaaaaaaabbbabababaaabbbaababaaabaaaaabbbbaaaabbbabbbabbbaabbabbbbbbbabaabaaabbaaabbbbbaababaaabababbaaaaaaabbabaabbabaabaaabbaabbaaababbaaaaaaaabbabbbababaababaaabababbabaabbbaabbbabaabaabaaaababbaaabaaabbababbabaaabbbbbaaaaabbaaaabbabbabbaabbaabaaababbbbbaabbbaaaababaababaabaabbbaaababaaabaaabaaabbbbababbbabbaabaabaaabbbaabbaabbbaababbababbaaabaabababbaabbbabbbaaababbbaabbbbbbbabbbaabaabbbbabaabaabababbbaaabbbabbababbbaabbbababbaababbaaababbbbaabbaabbabbbabbaabaaabbbbbaaaabaaaababaabbabbbaabbbaaaabbbaababaabaababbabbaaaabbbbabbaababbaabaabbbabaaaababbabaaabbbbabbbababbbbbaaababbbbbbbabaaabbabaabaabbbbaabbabbbbbbababbbbbbabbaaaabaaaabbaabbbababbaababaababaabbabbaabbbbaaabaaaaabbabbabbbabbbbaaababaaabbaaaaabbbaaababaaabababaaabaabbbbbbbaababbbaabaaaaabbbabababbbbaabbbbbbbbbaabababbabbaaabbababbaababbabbbaaabbbbabbabbaaaaababaaabbbababbbabbbbaaabbaabbbbaabbabbbaaaaabaaaaababbbaaaaabaabbaaabaaabaaababbbabbabaaaabaaabaaaaabbbababbaaabaaaaaaaabaaabbaaabbababbabaaaabbaabbbbbbbaaaababbbbbbbaabababbabaaaaabbabaabbaabbababbababbbbaaaaababaabbbbbabbbabbabbbbababbabaabbbbbabbbbabbbabbabaabaaabaabbabbabbbabbbbbaababaabaababbabbbbaabaabbabbabababaaabababbbbbbbbbbaaaaabbbaabaabababbbaabbbababbbbbbaabbabaaaababaaabbbaaabbbababbabaaaabbabbaaabbbabbbbbabbaabbbabbaababbbbaabbaaaaaaabbabbaaababbbaabababababbaaaabbbabbaaabaaababbaaabbaaabbaabbbbbabbaabbbaabaaaaabababbababaabbbbbbbaababbabaababbbbabaabbbaaababaababbaaaaabaabbbbbbaabbbbbbbabaaababbbaaaabbbbaabbabbababababbababbabbbbaaaababababaababbabbabaaaabbbaabbbaabbbabbaababbabaaabbaabbaabbbbababbbabbabaaaabbaabaabaabaabababaabaaabaabbbabaabaababbabaaaaabbababaababaaaaabbabbbbaaabaaaabbaaabaaaaaaabababbaaabbbababaaababbaabaaabbbabbaabbbaaabbaaababbbbbbaabaabbbbaabbabbbabaabbababaababbbbbaaababbbaabbbbbaaabbbabaababababbbbbbaaabbbaaaaaabbababaababaaaaabbabbbbabbaababaabbabbaaabaaabababaaabaaababbaabaaababbbbaaababbbbbbbabbababaaabbbbaaaababababaabaaaaaaaabaabbbbaabbaababbabbaabbababbbabaabaabaaabaabbaaaabbaaaabbbbbbaabbababaabbbbbaaabaababaabbbaaaabababbbabaaaabbababbbbaabaaabbaaababbaaaaaabaaabaaaaaabaababbaabbbaaaabaaaabbaaaaaaabaabbbabbbbabaaaabaabbaabaaaababbbbaaabbaaabbababaabaaaaaabaabaababbabbaabababaabbaababbabaaaabbbbabaaabbbaababbababaaaabbbbaabababaabbbbaabaaaabaabbaabababbbbbbbbbaababbbaababababaabbbbabbbabbbbbabbbbbababaabbbaaabaabaabbbbbaabbabbaabbabababaaababbaabbbbbaabaabaabbbbaaabbababaaabbbbbbabbbaaaabaabbaabaabaaaaaaaababbbaabbaabbabbaaabbabbababaabbbabaaaabaaabbbbabbbbababbbbbababbabbbaaabbabaababbabaabbaaabbbabbaabbabbbbabbabaababaaaabbabaababbbabaaaabbbbbabbbbababbbababaabbabbababbbaaaababbabbaaaaaaabbabbbababbaabbbbbbaaabbbabaaaaaabaaabbbabaaabbabbabbababbbabbbaaabaaaabaababaaabaaabaaaaaaabbbaaaaabbbbababaaaaababbbbbbababaababbbaaabaabbabbbabbbabaabbabaabbaabbababbabbbaabbbbabaabbbaabbaabbbbababbaaaaabbaabbbabaabababbbbaabbbbbbbbabbaabaababbaabbaaabaaaababaaabbbabbaabaabaabbabbbbbaaaaaaaaaabbabbabbaabaaabbbababaabababbbbbaaabaaaaababaabaabbabbaaaaaababbababbaaabbbabbabbbabbbbaabbabbaaaabababbaaaaaabbaaabaabbabbbabaabaaaaabbbbbbbaaabbaaabbbbababbbbaaabbaaabbbabbaaaaabababaaabbaabaaabbabbabbbababaaabbabaaaaaaaaababbaabbbbaababbbbababbabbaabababbbabaaaabbaaaaabbababaabaaabaababbbbbbbabaaabaabaaaaabbabaaaaababaaabbababbbbbababbbbbbbbbaaababbabbabbbabaabbaababababbaabbabbabbababbbbbbabbaabaabbaabbabaababbbaababbabbbbabbbaabbbbaabbbbabbbbabaaaabaaaabbbabbabbaabaaabaaaaabbbaabaaaabbabbaabbabbbabbabababbbaaabababaaabaabbaaaabaabaabababababbabbbbbabaabbbababaababbbaabababababbbbabbbbbbbababbbababaabaaabbabababbbaaaababbababbbbabbabbaabbbabaabababababbbaabaababbabaabaabababbbbbabbaabaababaabbbabbaabababbbbbbbabbbaaababbbaabababbbabbbaabaaaababaabbbabaaabbbbabaababaabaaabbbaabaabababbbbbabababbbababbabaabbabaaabaababbabaaaaabbabbababbabbabbaabbbaabbaaabababbaabbbabbbbaaabbabbabababaaaabbaabaaaabbaabbbbbaaabbababaabaaabbbbbbbabababbabbbbbbbabaaaababaabbaababbbabbaabaaaabababbbbbbbbbaaaaabbabbaabbaababbaabaabbaabbaabbbabbaabbbbaababbabbaabaabbbabbbaaaaaabbbbababaaaaaaaaaabbbabbbaabababaabbaaaaaabbaabaaabaaaabbbaabaabbaabaabbaaabaababbaaabaaababbbabbbbbabbbbaaabbbbabbbabbbbbaaabaaabbabaaaabaabaaabbbbabbbbaaabbababbaaabbaaaabbaaabaababababbbaaabaabaababbbbbbbabbbaabbbbbaaabaaaababbbbabbaaabbbbabbaaaaaaaaaabbaaaabaaaaaabbabababbaaaabbbaaaabababbaabbabbaaabbbaabbbbaaabaabaababbbaaabaabaaabaaababbbabbaaababaabaaaabaabbabaaaaabbbbbbabbbbbaababbabaabbabbbaaaaaabaaabbababababaabaabbaaaababbbbaabbbabaabaabaabaabaaaabbbaabbbababbbbbaabaabbbabababaabbbbabababbaaaaababbbabbaabbbabababbbabaabaaabbaababbabbaabbbaabaaabbbabbaabaaaaaabaaababaabbbbababbaabaababbbbababbbbbaabaaabbaaabbaababababaaabababbabbabaaaaaababababbabaaaaaabbbbabbbabababaabbbaabbabbbaaabbbabaaaabaababaabaabbabaababaabbbbbaaaabbbaabbbabaabbbbbbababababbbbababbbaabbaaaaabbbabbaabbbaaababbbbbbbbbaaabaabbbaaaabbbaaaaabbbbbbabaaaabbaabbbaabbaaaaaabababbababbabbbbabbabaabaaaababaabaababbabaaabbbaaaabbbbbbbbbabbbbbaaaabbabababababbabababbbbbabaaabbaabbaaaababaabbbbbabaaaabbaabbaabbabbaaabaabbababaabbbbbbbbabaabaabaabaabbaaabbbaaaabaaabbabaaababbbbabbbbaabababbabbbbbbbbaabababbabbaaaabbbaaabaabbaabaabaababbbaaababbaaabaabaabbbaaaababaaaaaaaabababaababbababaabbbbbbabaaabaaaaaababaaaaaaabbabbbbaababaaabbbbaabaabbbbbaaabbbbbbabbbabbbaabbaabaaabbbababbbbabbaaaabbbbabbababbbababaabbaabbbabbabaaabaaabaaaaaababbbaaabaaaabbbabaabaaaaabbabaababbabaaaabbbbbbaabbbbbabbbbbbaabaabbbbaaaababaaaabababaabaabababaabbbabaaaababbababbbabbbbabbababababaabaaabbabaabaaabbaabaabbbabbaabbaaabbaaaabaaaababbbbbbbbaabaabaababaaabbabbabbaabbbababbabaabbbbaabbbbbbabaaabbbbaaababbbababbabbbaabbbbaaaabaaaaabbababaaabbabaaaabbbaaabbbabbaabaabbbaabbaaaabbbbaaababbbabbaabbbbbbabbabbabaabbababbbbbaaabbbababbaabbbbbbbabbabaabbababaaaaaaabbbbbbbbaabbabbbaababbbabaabbbbbaaaabababaaabbabbaaaaaabbbbbabbabbbababaaaaabbbbbbaaaaabbbabaaabbabbabbaabbaaaaaaaaaaaaaaaabbbbbabaabaaaabbaababbababaabaaaabbaabbbabbbabbbabaababbaabbbbbabbaabababbabbabaababaabababaabbabbbbaaabaaaaabaabbabbbbbbababbaabbbbaabababbabbbbbabaababaabbaaaabbaabbbbaaababbbabbabababaabbabbabaabbbabbaaaababbaababaababbabbbaaabaabbbabaaaabbaaaabbbababbbbbbbaabbbbbbaaaabbbaababbabbababaaaaaaaaaaaabaabaabaabbaaaaabbbabbababaaababaaaaaabaaabbbabaabbaaabaabbaaabbaababaabbaaabababbabbaabaababaaabbbabaabbaabbaaabbaaabaababbbabababaaaabaabbaabbabaababaababbbbaabaabbbaaababbaaaababaababbbaabbabbabbabbaaaabbbabbbbbbaaabaaaaaabaaaabbaabaabaaabbaabaababbbabbabbbbaaabbaaaaabbbbbbabaababbbbabbbaabaaaaaaaabaaabbbaaaabaababaababaabbaaaabbabbbbaaabbbaaaababbbbaabbbbbaaabaaaabbbbbaabbabbbbababbbbbaaabbbaababbbaabbbaabbababbaaababbabaababaabaabaaabbabbaabbbababaaaabbaaaaabababbbbbbababaababbaababbbbbaaaaaaababaaabaaabbabbababaabbbbaabbbaababaabaaaabbaaabaabababaabaaaabaabbbbbabaababaaabbbbbabbbaababbbaabbaabaababaababbbbababaaaaaabbabaababababaaaabbaabaaababbbabbaaaabbabbbbaaaaaabbaabbaabaaabbaabbaabbabaabaaababaaabbbaaababbbbbabbbbaaababbbabbababbbaababaabbbabbaabaabababaababbaababbbbabbbbbbabbbababbbbabbabaabaabbbababbbaabbbbababaabaaabababaaabaabbaababbabbbaaabbbbbbbbabbbabaabababbabbabbbbbbaaaabbbabbbbbbaaabaaaaaabaaaabbaaabaababababaabaaaabbbbbbaabbbaaaaabbbbabbbabaabbbbaaaaababaaaababbabaaaabbaaaaaabbaaababbbababaababbababbabaaababbbaaabbabaabbabaaaabbaaaaaabbbaabababaabbabaabaabbbbbaabbaaaaabbaababbaaabbaaabbabbaaaaaaabbabbabbbbbaabaaabbaaaaabaabaaabaaabbaababaabbabaaaabbbbbaaaababbabbbaabaaabaababbaabbaaabbaababbaaaaaabbbbababbbaabbbbbaabbbabbabaabbbbaabbbabbababaabbbaaabbaabbbbaaabaaaaaabababbbbbbababababbbbaaababaabbbbabaabbabbabbbaaaaababbaababaabbaababbbababbaabbbbabaaaaabbbabaabbbbabbaababbaaaaaaaabbbbaabbbaababbbbbaabababbbaababbbbababaabaaabbaabbababbbbabbbbbaabaaabbababababaaaaaababbabbbabbbaabbbaaaabbbaaaabbbaaaabaaaaabbababaaaaaaaabbaabaaababbbaababababbbbbababaaaaababbbabbbaabbabbabaababaabbaabbabbbaaaaaababaaabbabababbababaaaaababaabaababbbbbaaaaabbbbabbabaaaabbaaaabaababbbababbaaaaaaabbbaaaabaaaaaabbbaabaaaabbbbbbbaabbaaabaaaababaabaabbbaaabaabbbaabbababbaaabaaaabbaabbaaabaabaabbaaaabaaaaabbbabababababbbbabaabaabbaaababbbbbaabbbbaaabbbaabaababbabbaaabbabaababbbabaababaabbabbbaabbbabaabbabababaaaaabbaabbbaaaaababaaababbaabbaababababbbabaabbbabaababababababbabbbbbabaababbbbabaabaaababaabbaaabaabaaabaababbababaaaaabaaaaabbaaabaabaaaaaaaaabaaaababbbaabbbbbaaabbbaabbbaabbbbbbbaabbaababbaabaaabbbbbbbbbaababbaaaabbaaaabbbbaabaababbaaabababaaaababbababbbaabbabbbbabbbbbabaabaabaabbabbbaabbbabbbbbbaaaabbabababbaabaabbbabbbabababbaabbabbaaabaaabbaaaababbbbbaaabaababaabbaaabbabaaabbabaaaabbaabbbbbbaababaaababaaabbbbbababaaaaaababbbbbaaaabaabbabbbaababbbbbaaaababbbbbbabaababbbaaababbbabbbbbaabbaaaaabbbbabaaababbaabababbbababbbaaaabaababaaabaaabaaaabaabbbaabbabababaabaabbbbaabaaaabbaabbabababbbaababaabbbababaabbabababbababbabbabbabbbaaaabaabbaabaaabaabbaaabbbbbbaaabbbabaaaabababbaaabbbbababbabaabbabaaaabaaabbbbabaabaaaababaaabbbbbabbaabbbaaabbbabbababbababbaabbbbbbbbabaaaaaaabababbbbabbbabbbbababbbbaabbbbaabbabbbbabbaabaabbabbaabbabbabaaaaaababbaabaaabaaabaaabbabbababaabaabbabbbbabbbbbbabbbabaabbbabaaabbababbabbbbbbbbaabbabbbbbbbaaaabbababaaabababbbbababaabbbbaaaabbaaabaaaabaaabbaabaababbbbabbaaaaaababbababaabbaabbbaaaaabbaaaabbbbabbababababbaaaabbbabbababbabababbbabbaaabababbbbbbbaaabbaabababbbbabaababbaaaabababbababbbbbaaaabbabbbaabbaaaabaababbaaabababaabaababbbabbbaaabbabbabaabaaaaaaabababababaaabbbbababbbbbbbaaaababbbbbaaabbbbaaaaaaaaabaaabaaaaaaababaabbbabaabbaaabaaaaabbaababbabbabaababbabaabababaabbbbabababaababbaabaabbbbaaabbaaabaabaaabaabbaabbabbaaababbbbaabbaabaababbabaaabbaaaaababbaabaabbabbaabbbbabaaaaababbbbbabbbbbaaabbabbabbaaaababaaaabbababbaababbabbbaababaabbaabababbbaabbaabbbaaabbabbbbaaaababbbaababbbbababbaabbaaaaaabaaababbbabbbbbaaaababababbbaaabbabbaaabaabaaabaaaababbababbbabaaabbabbabababaabbabaaabbbaaaaabbbaababaaaabaabbaabaaabababababababbbbbaaabaabaabbbabbaaaabbabbaaabbbaaaaaaaaabbabbbaabbbbbabbbaaaabbabbaababbaabbbbbaaabaabbababbabbbbbababaabaaabaabbbababaaaabaabaabbabaaaabbabaaabbababaabbbbaaabbbbaabbaaaababaabbababaaabbbabaababababbbabbaaababaabaaabbbbababaaaaaabbababaaaaaabbaaaaaaaaaaaababbbaababbaabaabbaabbbaabbabbbbbaaaabbbbbbbaaaabbabbbbabababbaabaababbbababbabbbbabbaabaababbbabaabaabaaabbbabbaaabbabbabbaabababbabaabbbbbbaaabbbbaabaaabbabbbabbabaaaabababbbbbbbbbbaabaaabbbaaaaababababbbaabbaabbbbaabaabaabbbbabbbbabaabbbaaaabbaaabbaababaaabaaabbababaababbbbaaaaaabbababaaabbbbbabbbbbbbababbbaaaababbbbbaaaaaaaaababaabbabaabbbbabaaabbaaabaaaabbaabbbaababaabaaaaabaaaaaababbabbaabbabaabbbababaaaaaabaaaabbbaababbaababaaaabbbbabbbabbbbabaabbaabbbaabbbaabaaabbbbbaaaaababaaaaaaabaaabbbabbbaaaaaababbabbbbbaaabaabbaabaaabbababbbbabbbaabaaaababababbbbabaaaaabbbaababbbbaabbabbaabbbbbabbaaaabbbabbbbaabbbabaabbaaabbaaababaaabaabbaaaaababbaabaabababbbbabaabbaabbaaababbaabababbaabbaaabbabbbbbbbaaaabaabababaaaababaabaabaabababbbaababababbabbbbabbaaaabbaabbaaabaaaaaababaabaaaaabaabbbaaabbaabababaaaaaabaaabbbbbaaabbbaaaaabbabbbbabaabbbbaaabaaabaabbabbaaaaaabbabbabaaaaabaaaaaaaabbaaaaabbaaabbbbaabaabababbbababaaabbbaaabbaabbbaabbaaabbabbaaabbbbbaababababbaaabaaaabbbbaaabbabbabbbbabbaaaaabbaabbabbbabaaabababaaaabbaabaabbbaaababbbbabaabbbbababbbbabbabbabbaababbbaaabbaaaaaabbaaabbaababaaaababababaaabaaaaaabbaaabaaaabbaaaaaaabbbaaabbababbababbbbbbbababaabbbabaabbbbaaabbaaababbaabbabbbababaaaaaaababbbababbbabbaaaaaaababaabaababbaabaaaaababaaaaabbaaaaabbababaaaaaabbabaabbabbbbbbaaaabbaabaaaaababaabaaaabbbaabbbaaabbbababbbbabbbbbabbbaabbababbababbbabbbbaabbbbaaaabaababbaabbaababaabbabbbbaabaaabbabbbaabbbbbabbabbabaaabbbbaabbaaaabbaabbbabaaababababaaabbabaaaabbbababbbbbaabbbbaaabaabaabbaaaaabbaaababaaaaababbaaabbbbbbabbaaabaababaaabbaaaaaabbababbbbaaabaaababbaaabaaabbabbaaaabbabbaaaaabaaabbbabbabbabbaaabababbbaaaabbbbbbaaaaabababaabaabbabbabaaabbbbbbbbbababaabaabbabbaabbabbababbabbbabbbaaaabbbabaaaabbabaaabaabbbaaabaaabaaabbaabbbabbabaaabbbbabaabbabbaaabbbbbaabbbbbabaabbabaaabbaaababbbbbbbaababaabbbbaabbabbbbbabbaaababbbbbbabaaaabbbbbabaaaaababbbaabbaabbbbaaaaaaaaaabaaaaabbbabbaaaababbaaaabbabbbbaabaaabaaababbbbaaaabbaaaaabbaabbbaaaaaabbbababbbbbaababbbbbbbabbaabaaabaaabbabbbabaaaabbabbbbabbaababbbbaaabbabaabbabbbababbbbaaabababaaaaaaababbbaaabbaaaaaaaabbbbbabbaaabaababaaabbaaaabaaabbbbbbaaabaaabbbaabaaaaaaababababaabaababbaababbabbaabbbaaabbabbbbaaabbbbbaaabbbaaabaaababbabbababbbbaabaaabaabbaaaaaaabaababaabababbbbaaaaabaabaabaabaabbabbbaaaaabababbbbaababbbabaabaaaababbaaaaabbabaaabbbabbaababaaaaaabbaaababababaaabaaaaaabbbbbbbabbaaaaabbaabaabbabaaaaaaaabababbaabbbabbbabaabbbbaabaabababbbbaabbbabbaabbbabbabbbbbbaabbbbbaabbabbababaaaabbabaabbbaababbbabbaaaababbbaaaaaabbbaabaabaabaaababaaababaaaababaaaabaaaaabbabaaaaaabaabbaababababaabbaabbbbaabaaabaaaabbbbababbbabbaabbbbbbabaaabbbbbbbaabaaaaaaaabbbabbbabbabbaaabaabbbabbabbbabbbbbaabbababababbbbaaabbbaaabbababbaababbbbbbaaabbabaaaabaaaabbbbaaabbbabbbbbbababaaaababbbaabbabbbaabaabbabaaabbbaabaababbbbbbbbaabaabababbababbbaaaabbabaabaabbaaaabaaaabbabbbabbaaaabbbabbbbaaababbbaababaaaabababbbbaabbaaaaaababbabbaaaabaababbaaabaabbbaabbabaababaabbaabbabbaabbababbbbbbbaabbaababbabbaababbbaaaabbaabbaababaabbbabaabbbaabaaaaaabababbbaaaabababaaaaabaabbabbbababbaabbbabbbaaabbbbbabaabababbbbbaaabbbbababbaaabbaabbbaababbbbbabbaaabbaabbbbabbabaaabbaabaaaababaababbbbbbabaababaaabaabaabaabbbaaabbaabbaabaaaaaabaabababaaaaabaaabaabaabbbbbaaaaababbabbbbabaabaaaabbbaabababaaabbaabaaabbbabbbbaabababbbaaaabaaaababaaaaaababaabbaabaababbabbbbabbababbbbbbbbbaaababababbbababaaaababbbbbaabaabbbaabbbbabbbabaabbaabbbabaaaabbbbbaabbaaaaaaaababaabaababaabaaababbaaabbbaaababaaababbabbbbbabaabaabbabababbabbbabaabaaababbaababbaabaabbaaaaaaaaaaabaababbaaababbabaaaaabbbbbbbbbaaabaaaaaabaabbbaaaabbaaababbbabbbbbabababababbbaabbbaaabbbabbaabbaaabbbbbaaabbaababbaabaaaaaabbbababbbabbaabbabbaabbabbbaabbaabaaabbabbaaabbbbbbbaaababbaaaababbbbaabbbbababbbbaababaabaaabbabbababaabbaabbabbbbbabbababbabaaabaaaabbabaababbaaabaaaabbbababbaabbabbbabaaabaaabbabbabbababbabbaaabaabbbbabababaaaababbaabbbabaabbabababbbaabababaabaaabaaababbaaabbbabbabbbbaabbbaaaaaababaabaabbaaabbbbbbbbababaabaaababbaababbaaabbabaabbbbbbaaabababababbabbabaaabbbabbbabaabbaaaaabbaabbabbaabbbababbbbababaaaaabaabaaaaaaaabbaabaabbaaaaaabbabbbbaaabbbababbababbabaaababaabbbaaaabbaaaaaaaaabaabbaaaaaaababaaabbabbaaaabaaaabbaababaaababbaaaababbababbabbaabbabaabbbabbabbabababbbababaaaabbaabbabbaaabaaabbaaabbaaaabbbbbbbbbabbaabbbababbbababaabbbbbbbbbaaabbaaabbabbbbbbbabaabbaabaaabaababbbaabbbbbabbbababbaaabababaaabaabbaabaaababbbaaaabbbaabbababbbbbbbaababbbaaababaabaaaaabbaaabbabbbbbaabbaababbabbaabaabbbaabbbabababaaaabbbbbbaababababbabbaaababaaabbabbababbbaababaabbbbbabbababbaabababbababaaababbbaababaaabbaaaaabbbabaababaabbabaaabaaaaabbababbababaabaabbaaaaaabbbbabbbaaabbbabbbababababbabbbaabbbabbbaabaabaabaababaaaaabbbabaaabbaabaababbaabaaaaabbabaababaabbabaaaabbbabbbbbbbabbbbbaabbaaabbabababaababaabbbabbbbababaabbabbbbbaabbbbababbbbbbbabbbbaaabbabbabbabbababbaaabbbabbaababbaaaaababbbbabababbbbbabbabbbabbbaaababaabaabbbabbbbbaabbabbbbabaaaaabbaabaabbbaaaaabaaabbaaabbabbabababbaaaaaabbaabbabbabbbabaabbaabaaaababbaaaababbaabbbababaaabaabababbaaaaaabbababaaababababaaaaabbabababbbababaabbbbbbbaaabbaaabbbbbbbbaabaababbaaaabbabaababbaaababbaaabaabbbabbbababbaabaabbbaababbabaaaaaaaaaaaabbabaabbbaaabbbabbbaaabbbbabbbaaabababbaaababbbabaabbbbaabaabababaaabaabaaabbbbbbababbaaaaabbbabababababaababbabbbbaaabaabbbbbbaabaaabababbabbaababababbbbabbbbbbbbbabaabaaabbbbaaaaabaababaabbababababbbabbbaaabbbbababbbbaabbababbbabbaababbaaaababababaabbbabaaabbababaabbbaaabababbaabbbbbbaaababaaabbabbaabbbbbaababaabbbababbbbabbaabaabaaaabbbababbbbaaabbbaaaabbaababbbbbbabaaabbbbbbbaabbabaabaababbaababaaabaababbaaababbaaabbbabaabbbbbaabbbbabbababbababbbbaabbbabaabbabbbabbaababbababaaaabbbbbabaabbbbbaaabaababbabaababbbaaabbbbbabbabbabaabaabbaaaaabbbaabbbabaabaabbabaaaabbabaaaaaabbaababbbabbababbbbbabababbababbbaaabbaaaabaabbabaaabbbbbbbabbbabbbbabaabbbaabaaabaabaabaaaabaabbaaaaababaaaabaaabaaaaabaaabbaaabbaaaabbbabbbbbbabbabbbaaaabbaaaabbaaabbaabbbbaaaabbbabbbaabbababaaabbbaabbbbabbaabbabbabaabbbabbaaaabaaabbaaaaabbaaabababababbababaaaabbabbbbaabbaababaaabbababbbababaabbabaabbbbbbbbabbabbbbbbbabaaabbbaaaabababaabaaaaabbaabaaabbaaabababbaabbabaaabbbabababbabbaaabbbaaabbbaaabbaabaabbbbbaaaaaaaabbbaababbbbabbbbbaabbbbbabbbaaaabbaabbbbaaabababbbbbbababaabababaabaabaababbbaabababaabaaaabbababbaababbaaaaaabaaabaabbbabbaaaabbaabaaabbabbbbbabaabbababbbbbbbbabbbbaababbaaabaabbabbbabaabbaaabaaaaaabbbaabaaabbbbabbabbbbabbabaabaababbbbbbaaaabbbaaaaaabbabababbbbabaaaaabbababaaabbabbbbbaabaababbaabaabaaaaabababbabbaabbababbabbbabaaaababaaaaabaabbabaabbabbbaaaaaaababbabaaaababaabbaaaaabbaabbbaabbaaabbbaaabaaaabbbbabbbabaabbbabbabbababaaaaaabbabaaaabbbbabbaabbbbbbabbaaaabbbaaaaabababbaaabababbbabbaaaaababbaaaababbbbbbbbbaaaabbbaabbbbbbbabaaaaaaaaaaaaaaabbaabbbababbbaaabababaaaabbabbabbbbaaaababbabaaaaaaabbbbaabaaaaababbabababbbaabaabbbbbbaaaabbaabbababbaabbababababbaabbbbbaaaabaababbbababbaaabaaababbbabaabbbbaabbababbbbabababababaabbabbbabaabbbaabbbbaaabbbaaaabbbaaabbababbbbbaaabbabaabbabbaabaaabbababaabbbbabbaaaabbaababbbbbbaaaaababaababbaaabbabbabbbbabbbbabababbbabbbbbbbbbaabaaabaaaabbababbabaaabbabbbaaabbbaaabbababaaaabbbaaabaabbabbbabbaabbabbbbbaaaabbabbbabbaabbabbbbaaaaabaabbbbabbabbabbbaabbaaaaababbbbaabaabbbabababbaababaaababbaaaaaabaaaaaaaabaaaaababbaabbabbababaaababaabbababbabbabbbaabbbbaaabbbbaaababbbabbababbaaabbbaabbaabaabbaabbbbababbabbaaaaabaaaababbaaabbabbbbabaaabaabbbabbababbaabbbababbabaaabbbbbbbbabbabababbbabbbabbaabbbabaaabbaabbbaabaabbbaabbabaaaaaabbabbaaabbabbaabaaaabbaabbbaabbaabaaabbabbbaaaababbaaabbbaabbaaaaabbabbbbaaaababbbbbbbbbaababaaabbababaabbaaabababbbbbabaaabbaababbabaabbaaabaabbabbaaaabaabbbababbbaabbaabaabbbabbabaaababbabababbabbabbbbbbbaaaabbbbaabbababbbaabaabbbabbbabaaaaabaabbbbaababaaaaaababbbabbaabaabbbbbabaaaaaababbaabbbababaaaaaabaabaaaabbbbabababbaaaababbabbaaaabaabbabbbbbaaaabaaaabbbaaaabaababbabaaabbbbbabbbabbbbbaaaaaababbaabbababaabbabababaababbababbabaabbbbbbabbabbaabaaabbbbabbbbbbabbbababbbbbbaabbaabaababaabaabaababbbbbabaababaabbbbbbbaabbabbbbbabbbaabaabbaababbabbbaabbaaaaaaababaaaababbbaaabbabaababbbbabbaaabbabbabbabbababaaabaabbababbabbbbbbbabababbbababbabbbbaaaaabbabbabbabbaabaabbbabaaabaaaaabbaababbaaabbaaaaaabbaabaaaaaabbabbaaababbaabaaaababaababaabaababbababbabbaaaaababbbbbaaabaaabababbbaabbbbbaaaabbbbaabbbbbbbbabaabbabbaaabababaaaaaabbbbaabbabbbabbababaabaaabababababaabbbbaabbbaaabaabbbbbaabbbbabbbbbbaababbbabaabbbabbbaabbbbaaabbabaaaaabaaaababbaaaaaaabbbbbabbbabaabbbababaaaaabaabbbbababbaaaabbbaabbbaaabbaababbbabaaaababbababbabbbbbaabbbaabbbbbbbbabaabababaabbbaabaaabababbabaabaabbabaabbaabbaabaabbbbaaaabbbbababbbbbabbbaaaabababababbaaabbbabababaabaaaabababaaaaaabbbbaaaaaabaaaaabbbbbbbabaababaabaabaaaaaabbabbbbabbbabaaaaababbbbabbbbbbabaaabbbbbaaabababbbbaabbabbaaababbabbbabbaaaaaabbbbbbabbabbbbabbabbaaabbbbbabbabbabbaaababaaaabbbbabbaaaabaabbabbabbabaaaaabbabaaabbbabbaabbbaaabbaaabbaababbabbaababbbabbabbaaabbaabaaabbabbbbbbbbabbbaaaabaaaaaabaabbbabbabbbbbabbbbaaabbbaaabaaaabababbbbbabbabbabbabbbbbbaabbaaaaabbabbbbbabaaaababbaabaabbababbaabbbbabaaaababaaaaabaabbaaaaaaaaabbbbbbaababaaabbaababababbabababbbbbbbaabaaabbabaaaaababbabbaababbaaabbaabbbbaababbbaaabbabbbbaabaabaaabaaabbbaaabbbabbabbbabbaaaaabaaababbbabbbbbababaabbbbbaaabbbabbabbaaaaaaababbbaaaaaabbbbbabbaabbbbbaaaaaabbaabaabbbbaabbbbabaabbbabbabaabbbaaabaaabababaababbabbbbbaabbababbbbabbbbbbbbbaaababbbbbbbbaabaabbbbaababaabbaaaaabbabbababbaabbababbaaabaabbaabbbbabbbbaababababaabbbabbbaaababaaaabaaabbbabbabbbbbbabbaabbbabbaabaaabaabbabaabbbbbabbababababbabbbaababbbbbaaabbabaabbaaaaaaaaababaabaaaabbbabbabaaaaabbbbbbabaababaaaaaaabbabbbabbbaababbabbabbbaabbbbbaaaaababaabbbbaaaabbbaaabbaaabbaaaaabbbbabbbbaabaaaabaabbaabbaabbbabbbbaabbbaabbbaaaaaababaabbbbabababababbbaaabbbabaabbaababbbaababbabbaaabbbabbbabaabbbaabababaaabaababaabaaaabbbaaaaabbaaaabbbbbbabaaaabaabaaabbbbababaabbaaaabaaabbbababababaaabaabbbaaabbaabaaaababbaaabbbbabaaabaabaabbbababaaabbbbaaaabbbababbaaabbbabbbbabbbabbabaaaaababbbbabbabaabaababbabbbbabbbaabaaaabbaabbbbbaaabaaabaaababaabbabbaaabbabababbabaaaabaabaabbbaabbbababaabababaabaabbbabbaabaaabaabbaabbbaaabaaaababbaabaababaabbbbaaabbbbbaababbbbaabbbbbababbbbaabbabaaababaaaaabbabbbabaaaaaaaaaabaababbabbaabaaabbbbbaabbaabaaababbbbaaaabaaabaababbbabaaabbaaababaaaabbbaabaabbaabbabbaaaaaabaaaaaababbbbbbbabbabaabaabbaaaababbaaabbaabaabaabaababaaababaaaaabbbabaabababaaaabbabbbbbaababbaaaabbbbababbaaaababaaaabaaaaaaabbabaabaabbbababbabaaaaabababaabababbaaaabbbaaabaabaabaaabbaababbaabbaabbababababaaaabbaaaaaaaabaaaaabbabbabaaaaaababbbaabaaaaaaabbbaababbabbbaaababbabbabaaaaabbbaaababbaaaabaaaaaabbabaabbaababaaabaabbaaaabaabbbababbaababbbbabbabababbbababbbababaaaaaabbbbaababbaaaabbaaaaaaaabbbbbaaaabbaaababbbbbbbaabbaabbabbbabbbbabaabbbbabbaaaabbababaaabaaaaaaaaaaaabbababaaabbbbabbaaabaabaababaaabaaaabbbabbbaabababbabbbbaabbbabbabbaabbabbbbabaaabbaabaaabaabaabaaabbaaaaaaababbbbbbbabbabbbbbaaabbaababaabababaaaababbbaabbbababbaabaaabaabaabaaabaaabaaabbaabbbbbaabbababbbbaaaaabbaaaabbaabbbaaabbbbaababbbabaaabaabbaaababbabbaaaabbabaabaaabbbaaabbbabbaaabaabbaaaabbbabbabbaaaabbababbbbbabababaaaabaabaaabaaabbbbbaaaabbbbaabbbbbbaabbbbbababbbabbaabaababbbbabaaabbbababbaabaaabbbaabbaaabbbaabbabbbababaabaabbbababaaaabbaabbbabbbabbbaabbbaabbbbbbbaabaabbaaaaaabaababaaaababaabbbbabbbbaaabbbabbbbbbbaabaaaabbaabbabbbaabababababbabbbbababbbbbbbbaabaaabababbababbbaababbaaaabaaaaabbaabababbbbbbaabbbabbabbbabbbbabaaabbbbababbbaabaaaaabbbbabbbabaabbabbbababbbbbbababbabbababbbababbabbababababaabbabbaabbabaabbbbaaaabbbaaababbbaaaabbabaaababbbbaabbbbbababbbbbaabbabbbababbbabbbbaababbbbaaaabbbabbaabbaabbabbbabbbaaababaababaabbbbaabbaababaaaaaabaabbabbaababababbaaabbbbbabbabaabbbabbbbbbbabbbaaababbaaaababbabbaababaaabbbabaaabbbaaaababaaaabbabbbbaaaababbaabaabbaaaabaaaababaabbababbababbaaaaabbbbbaabbaaaababbabbababbaabaaaaaaabbabbbabbbbbbaaabbababaabbabaababababababaabbaababaaaaaaaabaabaabaaaaaabbaaaabaaababbabbababbbbbaababaaababbaabbaabbbaabbbbbababbaaabababbbbaabaabbaaabaaabbabbbaaaaaaabbbaabaaaaabbaaabbaaabaaabbbabbababaaaabbbbaaaaaaaabaabaaababbaabaabbaaaaabaaabaaabbbabbbabbaaaaabaabbaababbbbabaaaabbbaabbabbbbbababbabaaabaabbaababbaabbabaababbaaaaaaabaabaabaabbbbbaabaaabbbaabbbbabbabbaabbbaaaaaaaaaabaabbbbaaaabbbabbabbbbbabbbbbbaaaababbababbaaaababbaabbbbbaababbbaaabbbababbabbaaabaaabbabaabaababbaabbabaaaaaababaaaabaaabbaabbbaabbbaaabaabaaabbaabbababbabaababbbababbbbabbabbbbbabbbaaaabbabbababbababbbaabbbbaaaaaaaaaaabbaaabbbbbbabbbaaabbabbaabababbbaaabaaabaabbbbbabaaaabbbababbbaaababbbbabbbaaaaaabbabababaaabbabaabbbabbbbbabbbabbaababaabbbbaabbbbbbabbbbaaaaaaaaaaabbabbabaabaabbaababbabbaaabaaabbbbabbbaaaabbbbbaabbabbaaaabbabbaabbbababbbababaabaaabaaaaaaaaaababbabbabbaabbabaaaabababbaaabbabbabbbbbbaababbbbbbbbbbbaaabbaaaabbbbabaaaaaaaaaabbababbbbbbaaabbaaabaaabbbabbaabbaaaaaabbaabbaaabaaaabaabaaabbaababbaabbbbaaaabbbaabbbbaabaaabababbbbbbabbbabaaaaaabbabaabbbbbbababbbbaaabaabbaaaabababaaababbaaaabbaabbabbaabaabaabbabbbbbbbbabbbbaababbabbabbabaaababbbbaababbbbabbababbbabbaaababbbabbbaabbaaabaaabbaabbbaabbababbaabbbbaaaabbbbbbbbabaabababbaababbbbabaaababbaaababaaaaababaaaaabbabbbbbbbaaabaababaabbaaabaaababababbabaaaabbbbbbaaaabababbabbbaababaabbbabbabbbabbabbaabaaabaabaababbbbbbbbbabaaabbbbbabaabaaaabbbbaaabaabbbabbaaabbbaabbbbbaabaabbbabaaabbabbabbabaaaaabbaaabaabaabbabbbbabaabbbabbabaabbaabababaabaabbbababbbabbabbabbabbaababbaabaaaabaaaaaaababaaaabaaaaaaaabbaabbabbababbabbbbababaabbbbbbbbaaaabbbababaaaabaabbbbbbabbbbaaaaababbbbabbbbaabaabbaaaaabaaaabbbaabbbaaabbbabababbaabaabaaabbbbabbbaaaabbabbbbbbaaaabbabbaaabbbbabbbaabbaaababbbbbabbbbbabbabaabaabaabbbbbbbbbabababbabbbbbababaaababbbbbaabaabaaaabaabbbabaaabbbbbabaaaabbaaabbbaaabbbaabaabaabbabbbbabababbabaabaabaaababaabbbabbbbaaaabbabbbbbaaabbaaaaaabababbbbabbbaaababbbbbaaabbabbaabbbbbbbbabaaabbabaabbabababbbbabaabaaaabbabaaabbbbabbabbbbaaaaaaabbababbabbabbababaaaabbbabbaabaaabbaabaaaabbaaaabaaabaaabbbbaaabbbaaabbbbaaaaabaabbbabbbabaababbbabaabbbaabbaabaabbababaabaaaababaabbabbbabaabbabababbbbbbaaabbbbabaaabbaaabaababaaabaabbabaaabababbbbbaaabbbaaabaaabaaaabbabaababbabbababababbabbbbabbaabaabaabaabaaabbababbbaabbbbaabbabbbbababbbabbbaaaaaababbaaabbbaaaabbbaaaaabbaaaabbaaabbbbbbbabbbaaaaaababbbbbaabbaabbabbbaaaaabbbaabbbaabbaaabaababbabbaababbbabbbabaabaaabaaababbaababbaaaaaaaabbbbbaabbaaabaaabbbabbaabbbbaaabaabbabbaaaabbabababbaaaaababbbbaaabbbbbbabbababaabbbababbbababaaabbabababbbbbbababaaabbbabbbbbbbabaababbabbbbaaababbabbaabbbbababbaaaabaaababaaabaabbaaaaaaabababbbaaabbbabbbaabaabbbabbababaabbbaabaabababbaaababbbabbabbbaaabababbababbbbbbbababbaaaaaaaaaaaaaabbabbababaabbaaaaabbbaaaabaabbaabbabbaabbabbbabbbbbaaabbaabbbaaaabbaabaabbbbaaaabaabbbbbbabbabbbbbaaabbaaaabaaabbaabbbaababbbaabbbbabaabaabaabbbaaaaaabaaabbabbabbbbabbbbabbbbbaaababbaababbbbabaabbaaabaabbaabbaabbabaabbabbaabaabbabaaaabbaaaaaaaabbabbaaaaaaabbaaabbabbbaaababbbabaaaabbbbaabaaaaaaababaabababbbaabbabbbaabaaaabaaaaababbabbabbaaaaaabbabaabbabbbbabbbaababababaabbabbbaabaaaaaaabbbbabbbbbabaaaabaabbaabbabbababbaabaaababbbbabbbabbbababaaaabbababbbbbbaabbaaaaaababaaabbbbaaaaabbbbbbabaaaaaabbababaabaaaaaababbaaaabbbabbaabbbaabbabaaaabababaabaaabaaaabbbbbbbbbaabbabbaaaaabaabbabbabbbbbaaabbbababbbaababbabaabbabbbbbbbabaaababbabbaabaabaaaaaaaaaabbbaabbabaababbabbbababaabbbbabbaaabaabbbababbabbaabbbaabbbaaababbbbabbaabbaaaaabaaabbababaaabbbaabbbaaabaaaabbbaaaababbaababaaabbbaabbbbabbabababaabbbbbbaabababbaaababbbaaaabbaaabbabbabbbaababbbbabbabaababbbbabbbababaaabababbabbaaaabaababaabaaababaabaaabbaaabbbaababaaabbbbaaaaaababaabaaaaaabbaababaaaaaaaabbabbaaaabbbbbabbbabaaaaaababaababbaaaabaaaabaabaababbbbbbababbbaaaaaabbabababbaaabaabaabbbbaababaabaabaababaabbbaaabababbabaaabaababbbabbababbaabbabbaaabaababbbabaaaabaaaabbbaabaababbaaabbbababaaababaababbabbaaabbbbbaaabbaaabbbaaaaabaabaaabbbbbbabbabbbababbbaabbbabbbaaababababaaaaaababbabbaababbabbaabbabbaabbbbbaaaabbabbabaabbaaabbabbbbaaaabaabbababbbaabbabbaabbaabaaaaaabbbbbbabababbbbaabaaaaabbbbaaaaabbaaaaaaaaaaaabbbbaaaabaaabbaaabbabbaaaababaabbaaababbabbabaaabbabababbbbabaaabababbbbaaabbbaaababbbbbbababbbabaabbbbbaaabbbaaaaabbabbaaaabbaaabbbbbbaaaaabaaaabbaabbbbaabababbaaabbbbbaaabbabaabbababbaabaaabbaabbababbbbaaaabbbbbaabababbaabaababbaaaababaabbbbabaabaababbbbbabbaabaaabbaaaaababaabbabbbbabbbabababbabbabbaaababaabbbaaabababbabbbaabbabbaaabbababababbbbbbabbbaabbbaabbaabbaabbbbbbbbabbaaababababaabaabaaababbaababababaabbaababbbabaabbaababbbbbabbaaabbbbabbaaaabaaaabaaababbbaabbbabababbabaaaabbbabbabaabaabbaaaaaababbabaabbababbaabbaaaabababababaababbaaaaaaabbaaabbbbabaabababbaaaababaaaaaabababaaabbbabbbaaaaababbabaaaabbabaabaabbbaabaabbbbbbbbaabaaaaaabbbabbabaaaabbbaabaababbabbbaabbbaaabbabaabaabbaabbabbabbbbabbbbbbabbbaabaabbbbbabbabbabbaabbbaaaaabaaaabaababaababbbababbbbbbbabbbababaabaabbbaababbabbbabbbbababbbaaababbbaababbbbbbabaabaabaaaaaabaaabbbabaaabaabbaaaaabaaaabaaababbbbaaaabbabaaaabaabaaabbaaaaaabbabaabbaaaaaabbbbbbbbbbbaabbaababababbabbabaaaaababaabbbbbbabbabbbababbaabbbbabbabbbbaaaaaaabbaaaabababaaaaaaaaaaabbbbbababaababbababbabababaaabbabbabaaabbbaaabbbabbbabbbbbaabbbabaabbbbbabbaabababbaabaaabaabbbabaababbbabbbaaabaaabbaaaaaaaabaaaababbaaaabbbaaabbbbbbabbabaaabaaabababaabbbaabbbbaabbbbbbaaaabbbbabbabbabaaabaabababbbbbbabaaababbbbabaabbabbaaabbbbaabbbaabbbbbbbaaaababaaaaabbbabaabbaaabbbbbbbabbbabaaaaaababbaaabbbabbaaaabaabaaaaaabbaaaaaaabababbabbbbaabbaaaaaabaabbaabbabbbaaaabbaabaaaabaabaababaabbbabababbabbbaaabbaaaaabbabaaaababbaabbaaabbbbbaaabbbabbbaababababbbababababaaaaaababbaabbbaabaaabbbbababaaabaaaabbabbbbbbbabbaaabbaabbabbababaaabaabbaababaababbbaabbaabbaaaabbbbaabbbaaaaabbbbbabbbaaaabbbaabaababbaabbabbabbaabbaaaabaabbbbabbbabbabbbbabaaabaaabaabbbbbbbabbaabbbabbbabababaaabbbaabbabbbabbababaaababbaaaaaababbabaabbbabbbbabbaaaaaababbaabababababbaabbabaabbbbaabbbabbaaabbaaaaabbaabbabbabbbabbabbbabbbbabaababaaaababaaabaaabaaabbbbaabbaabaabbaaaabaabbabbababaabaaaabaaaabbaabbbbabbaaabaaaaaaaabbabbbabbbaabbababbbbbbaababbbabaaabbbabbabbbabbaaabbbbbbbbaaaaabaaaabbbaabbaababbaaaaabbaabbababaaaabaabaaabaabbaaabaaabbababbabbaabaaabaaabbaaaababbaabbbababaaabababbbbaaababaabbbbaaaaaabbaaababaaaabbaaabababbbbabaabbaabbaabbbbbbbaaaabaaaaababababbbaabbbababbabbaaaaaababaabababaaaaaaabaababbabaabbbbbabababaaabbababbaab
aaababbaaaabbaabaababbababbabbabababbbbaaaaaaaabbbababbaabaabaaabbabbaabbaaabbaabbbbaabaaabbbababbabbaababbbbbbbbbbaaababbababaaaababbbaaaababbbabbaabbbaaabbabaabaabbbaaaabaaaababbabababaabbbabaabbbbbbbabaababaaaaaaabababababbbabbaabbbaababbababbbabaaaabaabbabbababababbbaababaaabaabaaaaaaabaabaaabaabaaabbaabababbbabaabbbbbaaabbbaaaaabaababbaaabbaababbaabaababaabbbbbaabbbabaaabbbabababbbbbbbbbbaabaaababbabbaaabababbabbbbaabaababbabaaaabbbbaaaabababbababbbababbabaaabbaaaabbbaaababbbbabaabbaabbbbbaaabbbaabbbabaaaaaabbbbabbaabbbbababaabbaabbaaaababbabbabbabaaababbaaabaabbbabbbbababbabaabababaaabbaababbbbbaabbabbbbbbabbaaaaababaababaaabbababbbaabaabbabaabbbbbbbababbbaaabababbbbbbbabbabbbaaabaaabbaaabaaaabaaabbaaaabaabaabbbabaabbbbbbaaaaabbbababbaababaabaababbbbaaabbabaabaaaabbbabbabbbabbaabababbaabaabababababbbaabbbbaaaaabbabaaaaabbbabbabaabbbbbabbabbaaaabbabbabbbbbbabbabbbbaaaabbbbaabbaabbabbbbaabbaaabbababaababbabbaaaaabbbbabaaaaababaabbaabbabaababababbabaababbbaabbaaaabaababbaabbabbbbabaabbbaaabbbbaabaabbabbbbbbaaaaaabbbabababaaaabbbbbbaabbabbbbaaaabbabababbbbbbaaabaaaabaaaaababbbaaaaabbababaaabababbbbababbababbbababbbabaaaabaabbaaaababababaaabaababaaabbbbbbabbbbaabbbbabaaabababaaaabbabbbabbaabbaaabaabbabbbbbaabbbababbaababaaaabaabbaabbbbabaaabbababbbbbbbbaabbaaaaaabaababbbbabaaabbaabbabbaaaabbbaaabbbaaabbbbbbaabaaaababbbaaaabaaaaabbabbbbbabbaabababbaabbbabaaabbaabaabaaabaaabaaaaaabbbaaaaaabaabbbabbbaababaabaaabbabaabaaaabaababbbaaaabbbaababbaabaabbaaaaababaabbbbaabbbbabababbbbbbbaaaabbbbabaabbbaababbaaaaaaabbbbaaabbabbaabbbabbbaabbbbbbbbabaaababbbbbbbaabbaaaabbbabbbaabaabbaaaababbababbbabaabbababbabbbabbaabbabbaabbaabaababbabbaaabaaabbababaababbabbbaabbbbabbabaaabbaaababaabbbbaabbababbbabababaabaaabaabaaaaaaabaaabaaaababbaabbbabbabbabaaabbbaabbabaaabbbaaabbaaabbbabaabbbaaababaabbaabaaaaababaabbbbaababaababbbbaabbbbabbbbabbaaabaabaaabababbaabaaaaaabaabaaaaaabbbaaabbaaaabaaaaaababbbabaabbababbbbbbaaabbabaabababbbababaabbabaabbbbbbbbbaaabbaaabaabababbbbabbbabaaabbbababbbaaabbbaaaaabbaaaabaabbbbabaaababaabbabaabbbaaaaaababbbbbabaabbababaaabaabbbaaaaabbbaaababaaaabbbaaaaabbaaabbaaabababbbbababbaababbbbabaaabbbaaaaaabbaaabbbbaaababbabbbababaaabbaaaabbbababaabaaaaabbaaaaabbbabbbbbaabbbbabaaababaabbabaababaaaaaaabbabaababbbaabababbabbababaaaababbbbabaabbaabbaaabbaaaaaabaaaababbaabbbaaaaaabababaaabbaaaaabbbbbaaabbabbbbbbaaaababbbabbbbbbbaaaaaaaababaababaabababababaaaaaaaaabbbbabaaaabbbbababaabbabaabaabbbbbaabbbbbbaababbbbabbbbbbbaabbaabaaaaabaababababaababbabbbbbaabababaaaaabaaaababbababbbbbaaabbaaabbaaababbababbababbbabbaabbaaaababbbababbbababbaabaaababaababbbabbaabaaaabbaabaaabaabbaabababaababaaaaababbbbbaabbbbaabaaabbabbabaaabbabbaaababbbaababbbaaaabbabbabbaaaaabaaabaabbbababaabbbbbbaaabbaaaaaaaabaaaababbaabbbbbaaabaabbbbaaabaaaaaabaaaaababbbbababaabbbabababbabbbaabbabbaaabbbbaaabababaaaabaaaabbbabbbbabbabaaaaaaaaabbbaaabbbbaabbaabbbaaabbbaababaabbabababbbbbaababbbbaaaaaaaabbabbaaaaaababaabbaaaaaabbabaaaabbaaaaabbbabbbabbaaabbbaabbaabbabbbbabbabbbabaaabbaabbabbbaabbaabaabaabbbbababbbbbbabbabaaabaabaababaaabbaababaaaabaabbbabbbaaaabbaabbababaaabaabbbbaaaabbaabbbaabbababaabaaababaaabbaaaaaaaaabababbbaaababaaaaaabbbaababaabaaabababbaabbaabbababbbabbbaabbaabbabaaababaabbaaaabbbbbaaabaabbabbababaababaabbbabaaaaaabbaabaaaaabbbbbaabbababbbaaabababbaabbaaaabbabbbbabaaaaabbaabaaabbabbabaababaabaaaaabaabbabbbbaaabaabaaabbbbbbbbabaababaabbbbbbbaaaabaaabbbbbbbabbbaabbbababbbbbaaaabababbbbbbbabbbbaabbaabbaaabaaaaababaabbabbabbaaabbabbbbbabbbaaaaabaabbaaabbbabaabbbababaaaaabbbabbabbaaabbbbbaaaabbbabaabbaabbbbaababbbbabbbbbaaaabbabaabbabbabbaabbaabbbbbababbbabbaabaabaababaaaabbaaaabbaaabbaaaabbbbbaababaabaaabbbaabbababaaabbaabababaabbaaaabbbaabbbaabaaabbbbabbabaabbbabababbaabbabaabbbabbababaabababbabbaaabbabbbaabababaaaaabababaabaabbbbaaabbbaaababbbbaababbbbbaabbababababbababbbbababaabaaaaabaabbaabbaaaabaabaaabbbbaabaabaaabbbbbbbababaabbaaaabbabbbababbbaaaaabaabbbbabaabbbabbbababaaaaabbbaabaababbbbabbaabbbababaababbaaabbabbaaaabaaabbbbaabaaabbbbbabbabbbbaaabababaaaabaabaaaaababbbaababbababaaabbbaaaaabbbaabbaaaabbbaaabbaaaaabbaaabbbbbbbbbaabbaaaababababaabaabbaabababaabbaaabbbbaaaabbbabaabbbbababaaaababbbbbbabbabbbaababaabaabaabbbbbbabaababbaabbbbabaaabbaaababbaabbabaaaaaababbabaabaabbbbbbaabaabbbaaabaababbbbababbbaaaabababbaababbabbabaaaaaabbaabbbababaaabbabbaaaaabababaabaaaaabababbbabbabaaaaaababbaabbbbaaaaaaabbaabaaabaabbbbabbaaaabbbbabaabababbbbbbbbbbbabaabbabbaabaaabaaabaabaaaaaaabbbbbbbaabaabbaabbbbbbabbaaabaaaaaababababaaaaababbbabbbbabbbbbaaabbbabbbbbbbababaaabbabbabbbbbbbabbaaabaaababbbaaaaaabbabaababbbaababbbbabbbbbbbaabababbbaabbabababaabaabaaabababbbaaaaaabbabbbbbbaaababbbbbbbbbaababaabaabbbbabaabbabbaabbbbabaabaabaaabbababbbbbaaaababaabbabaababbaaaabaaabbaaaaababaaaabbabaaabababbbbaaabbbaabbaaaaabaaabbbbabbabbaaabbaabaaabaaaababbbbaaabbbbaababaabbaabbbabaaaaaaaaaabbbaaaaaabaababbbbbaabaababbabbbbabaaaabbbabbabbaaaabababbbabaaabbbbaabbbbababbbaabaabbabababaaaabbbabbaabaaaaabbaababbabbbbbbbbabbaaaaabbabbaaaaababababababaabaaabbbbaabbaabaabaaababababaaaabbabbaabbaaabababaababbbbaaaabbbbaaaabbaababbbbabbababbaaababbbaaabaababbaaababaababbaaaababaaabbbbaabbbbaaaabbabbbaabbbbaabaabbbbbbbbabbabaaaaabaaaaabbabaabaababaaaaaaabbaaabbbbbababbaaabbabababababbaaaabaaabbbbababaabbbbbababababbbbbbabbbabbabbbbabbaababbabaabbbbbbbbabaaabbbabbabbabbaabbbabbbabbaaabaabbabaabbbabaaabaaababababababbbaabbaabbbbbabaabbbbbaabaaaabbaaabbbbbbabbaaaababbbabaabbabbbbbaabbaaabababbbbaaaaaaaabbbaaaabbaaabbbbbabaaabbbbaabaaababbaaaaaaabbabaabbaaabbbbaabaabababaaaabbbbababbaaaabbaabaaaabaabbbaaaaabbabbaababaabbabaabbbbbbbabaabbabbbbaaabaaabbaababbababaaaabbaaaaaaabbbbaabababbaabbbbbbaaabaabaaabababbaabaaabbabbbbabbaabbbaaabbaaababaabbabaabbbbbabaabaaaababbabbababbababaaaaabaaaaaaabbbabaabbbbbaabbaaaaaaaaabaabababaabbbaabbbaabaaabbbbabbbbbbbaabaaaaaaabaaabbbbbbbabbaabaabbaabbbbabaabaabbbaabbaaabaabbbaabaabbababbaabaaabbbabbbaabbaabbbbbababbaabababaababbbbabaabbabbabbabaabaaababababbaaaaaabaaabababbbababbaabbaabbaababbbbbaaabaabbbbabaaaabaaaabbabbbbaaaaabaaaaabaabaaaababbbabbaaaaaaabaaabaaaaaababaabbaabbaabbbbbbaaabbbbbaabbbaaaabbabbababbbbaaaabbbbaaaaabaaaababbbaaabaabbaaabaabbaaabbbbaaaaaaaaabababbbbaabaabaaabaabababbbbababbbbbaaabbaabbbaababbaaaabbbbbaaabababaaaabaaaabbabaabaabaababbbbbbbaabababaabaaababababbaaaabbbbbbaaababbbabbbbbbabaaaabbbabaaaabbbaaabbaaabbbaabbbaabaaabaababaaaaaaaabbbaabbbaabaabbbbaababbbbababbababaaaabbabaabbbbabbabbbaabbbbabbbbbabbaaaaaaababbaabbaaaaabababbbbababbbbabbbabaaabaaabababaabbbbabbbbbabababbbbabbbaaaaaaabababbabbaabbabbaaaaabbabbbabbaabbbaabbabababbbbaaaabaaabaababaaabbaababaabaababbababaababbbbbbbabaabbbbaababaabbbbbabbaabbaaaaabaabbbbabbbaaabbaaaababbbbaaaaaaaaabbbabbaaaabaababbababbabbbababbbabbabbbaaababaabaabbbabbbbbbbbaaaaaaaababbabbabaabbabbbaababbababbaabbabababbabbbaaaaaaaabbbbaabaababaaabababbabbabbbbbbbaabaabaaaabbbaaabaababbabbaababaabaaabbbabaabaabbbbaabbbabaabaaababaaababbbabbaabbaaaaaabaababaaaababbaabbbabbabbbabaabbaabaababbaabbbababbababbabaabbbbbaabbaababbbbaababaabaaaabbaaababbaaabaabbaabaababaaabbabbbababaaaaabbabbabaaabbbabbbbbbaabbbabbbaaaabbbbababaaababbbbaaabbaaabbabababaabaabbbbbbbbbbababbbbbaabaaaaaabbaaababaaaabaaabbbbaabaababbababbaaabbabaabbbbbabbbbaabbabaabbabbbababaabaabaababbaabbbaaabaabaaaabaabaaaaaabaabaabbbabaababaaabaabababaababaabbaaaabbbaababbabaabbaaabbbabaabbbbbbaaabbbabbaaaabbabaabbabbababbbaabaabaaaabbaabbaabaababbaababababbbababbaabbabababbbbbaaabbaababbabbababaaabbaabaabaaaabababbbbbaabbababaaabbbaabbabbbbabbbbbaabaaabababbbabbabbaaabaaabbbaaaaaabbbbababaabaaabbabababaaaaaabbbaabbabaabaabaaabbaaaabbababbbbbaabbabbaabbbbaaabaabbaabbbbaaaaabbabaaabbbababbbbbbbbababbbbbbababbbbbbabaaaababbbabbabbaabababbabbbbbaababbbbbabaaabaabbbaabbaabbaababbabbaabbabbbbbabaaaaabbbabaaaabbbaabaaababbbbbbbbbbbabbabaaaaaaabaababaabbbbaaabaaababaaabbaaaabababaabaababbbbbbaaabaaaabaabbbbbabbbaabbbaaababbaabbabbbabbaaabbabbbbaabbbaaaaabaabaabaaabbaabbabbaababbbbaaabbbabaabbabbabbbaababaabbaabaaaabaaabaababaabbaababbaaaaaabbbabbbbbaababababbabbbbbbaaaabbabbabbabbaababbbbbbaabaabbbbbaababaaabaabbaabbaabbbaaaabaaabbabbaababaababbbabbaaaabbaaabbbababbaaaaabaabbbbbaabaaaabaabbbaabbbbbbbabaababbbbbbabbababbbbabbaaababbababbbbaaaaaaababaabbabaaabaababbababbbaaaaaaabbaaabbaababbbabaabbbbbabaabaaaaaaaaabbaabbbbbbaaaabaabbaabbabbbabbbbbbbbaaabbbbbabbbbbbbbabbaabbbbaaabbbaaaabaaaaaababbabaabbbabaaaaabbabaabbabbabbbbbaababbababaaababbaaabbbababbababbbbbbaababbbaabaaabaabbaabaabbbbabaaaaabbaaabbabaaaaaaababaabbaaaaaabbaaaaabaaababaaaaaabbbbbbbaababaabaabbaaabaaabaaaabaabaaaaabbbabbbaaababbbbaaaabaaaabbabbbaababbbabbbbabbbbaabbbbbbbaabbaaaababbbaabbaabbbbaaabbabaaabababbaababbbbbbbbabbabbabbbaaaaaaaaabbbbbbabbaaaaaaaaaabbaaabaaabbbbaaaababaaaabbbbbbabbbbaaabbaabaaaaaabbbabaaabaaaaabbbabaaaaaabbbbbaababbbbbaababbaabbaaaaaabbabbbabaaaabbbbbaabbaaaabaaabbbaaababaabaabbabbaabbbbabaaaabaaaabbaaabaaaaabaaabaabbbbaabbababaabbabaabaaabbababaabaaaaabababaabbbabaaaababbabbaaaaaaaabaaaaabbabaabbbbabbbbbaabbaabbbbbbbabbbbabbbbababbbbaaaabbbabbaababbaaababbababbbaabababbbbaaabbbbbababbaabaaabbabbaaaaaaaaaabbabababbbababaabbbbaaabbababbaaabbbabbaaaabbbbaaaabaababbaaaaaaaaaababbbaaaabbbababbbabbbbbbbaaaabaaaabbabbbbaabaaabbaabbabaaaabaabaababbbabaabababbbbbbbbbaabbbabaaabbbabbbabbaaabbbbbabaaaabaabbbbbbaaaabbaaaabbaaaabaababababaabbaaabbaababaaaabaabbabbabaaabbbbabaaaabbabaababbaabbabaaabaaabbabbbabbaabbbbaabbabababaaaaaabbaaabbbabbbabbbbbbabaababbbabaabbbbbbbbabbaaaabaaaaaabbbaabaaabbabaaabbbbbbbbbababaaabaabbbabaaabaaababbbabbaaabaaaaaabaabbabbbbbbbbabbbaabbbbbbaaababababababbabbbabbbaaabbbbbabbbabbaababbaaabbbbabbbaabababbabaaaabaaaababbaaabababbbabbaabbbbaabbbbabbaabbababbaaaabbabbabbbaabababbbbaaaabaabbabbbbbbabbaabaabbbaabbbababbabaaaabaababaabaababaaabbbbbbababbabaaabaabaaabbbaabbbaabaabaaababaaabbbbaababbaababbbbbbabbaaabababaaabbabaabbbbbaababbbbaabbabbabbaabaaaaaababaabaababbababaababbbbbabbabaabaababbbbabbaabbabbabbabbbabaaababbababbbabbbaabbaaabbababbaaababbaaaabaabbbbabbbababbabaaababbaabbbbbbbabaabbbaabaabbbbabaabaaabbaaaaabbaabababaaaaaaaaababaabaaabbbaaabbbbabbbbbbaaabbaabbbbbabaababbbabaaabbbabbbbabaabbbababbbbbabaaabaaabbabbabbbbbaabbbbaaabbaabaababaabbaabaabbbabbbabaabaaabaaabaaaaabaabaaaaabbbbbaabbbaabaaaabaabaaababbbbaaabbabbbabababbababbabbaaaaaaaabaaaaabbabaababbbbbababbbbabbbbbaababbabbaaaabbbabbabbaaaaaabababaababbbaaaabbabaabababbaababababbbaabbabababbababababbabbbabaaabbaaabbbaabbaaabababbbabbbaabbabababbaaabaabaabbaabbbbabbbbabaaaabbbbbbbaabbbaabababaabbaabbaaabbaaaaabbbbbaaaaabababbabbaaaaababbaabbbbbbaaaabababbaabbabaaabaaaabaabaabbbabbbbaabaaaaaaaaaaaabbbabbbbaaabbaaaaabaaabbaabbabaabbbbabbabbaaababbbaaaaabbabaababababaababaabbbaababaabbbabaababaaaabbaaabbbabaabaabbaaabaaababbaabaaaabbaaaaabababaabbbaaaaaaabbbbbbbbbabbabbaababaaabbbaababaaaabababababbaaabaaabaababaabbabbabaaaababaaabaabbbbababbabaabbbaabbbbabbabababbbaaaaaaaaababaaabbaabababbaababbaabbaabaaaaaaababbbbbbabbbababababbbbabbaabbbbabbbaababaababbbbbbaababbbabaaabbbbabbbabbabbbaaaabbaababaabaabbbbaaaaabababaababaababbbabbabbbbbaaababaaaaaababbababaababbbbbbaaaababbabbaabbbbbbbbbbabbbbababaabaabaababbbaabbababbbaabaabbbaabbbbbabbbbaaabaababbaaaaabaaabaaaaabbabaaabaabbbbabababbbababaabbbabbbaaaaababbbaaabbbbabababbbababbbaaaaabbbbbbabaaaababaaaaabbbaabbbabaabbbbbaabbaaaabaabbbaaaaabbaababbababbbbbabbbabababababbabaaababbbbbbaabbbaaaabbabababaabbababbaaabaabbaabbbbbbbaaabababaabaababbaaabaabababababaabaabaababbbabbabbbbaababbaabababaabbbaaaabaababbabaabaabbbbaabaaaabaaaabbbbbbabbabbaaababbababbbabbaabaaabbabbbaaaaababbabaabaabaabbbabbabbabbbaaaaabbbbabababbaaaabbababbbbbaaaaabbaababaabbaaaababbbabbbbbabbbabbaabababbbbabbbbaaabbbbaabbbaababbbbbabbababababbaabbbbabbaaababbbbbabbaabaabbabaabbbbbbaabbaaabbaabbbaaabbbabaabbbabaaababbabaabaabbabbaaaabbbaabbaaaabbaabbbbaabababbbaababaaabbabbabababbbabbbaabaaaabaabbbabbbbbabbaabbbbbaabbaaabbbbaabaaaabbbbabaabbabaabaaababbbbbababbabaabbabbbaaaaaaaaabaaaaaabbaaaababbaabaaaaaabbaaabaabbbaabbaabaabbbbbbbaaababbaaababbababbbaaababaaaabbaaaabababaabbabbbbababbaaababaabbabbbabaaabbaabaabbbaababaabbbabbbbaaababbaaaabbabbaaababbbbabbbababbbbabaaaaabbbababbabbbbbbbaaaababbabbabbbaababbbbbbaaaaaaaabbababbbabababbbabbbabaaabaabbabbbabbbaaabbbbabbbbaaabbabbbabababbaababaabaabbababbaaabbabbaabaabaababbbaaabbabbbbaabbbaaaaababbaaaabaaababbbbaaaaaaaaababbbbbaabaaabbabaaaabbbaabbabbabbbbbbbabbbbabbaabaaaaabbbabbaaaaaabaabbbaaaabbbbabbbbbaaabbaabbbaababaaaaabbabaaaaaaabaaabaaaabababbabbbabbabaabbbbbaababbbaabbaabbbabaabaaabbaaaaaaaaabbbababbbaaabbaabbbaaabbbabaabbbaabbbabbbbaaaababaaabbbabbaabbbaabbabbaabaabaabbaabbaaabbbaaaabbbbbbbabbababbbabaaaaababbababaabababababbaaaabbbaaaababbabbabbbaaaababbbbaabbabbbaaaabbbaaabbaabbbaaaaaabaaabbabaabbbbbaaaaabbbaaabbabaabbabaaaabbbababababababaaabbbaabaaaaabbaaaababaaabbaababbbbabaabaaababbbaabaaabbbbababbabaabaaaabbbaabbbbaabbbbbbabaabaabbbaaabaabbabbabbbbbbbaabababaaabbbbabbabbbbaababbbabaabaabbaaabbababbaababaabaaaaaaababbabaabbaaaabaaabbabaaaabaabbbabbabbbbbbbbbbabbbaabbabbababbabbbabbabbaaababbbbaabaababbabbbabaabbbbaabbbbabababbababaaaaabaabbabbbabaaabbaaabaaabaabaaaabbabaaabaabaaaaaabbabaabbaabbbaaaaaabbbbbabbbaaabbaaababaaabbbabbabbbbababbabbbaaaabbababababbabbbabaaaaabbabababbabaaaabbbabbaaaabbbaaaabbabaaaaaababbbaababbbbabbbabbabaaabbaaabbaabaaaaababaaabaaabbbaabaaaabaababababaabbaaabbababaabaababbabbbabbbaabbbabbbababbbbbabaaabbbbbbbbbbbabbbbbbabbaababaaababbabaaabbabaabaaabaabbaabbbaabaabaaababaaabababbbbaabbbaaabaaababaaabbbaaabababbabbaabaabaaabbabbababbbabbbbabbbbbababaabbbabbabaaaaabaaabbabbbbbbbbbbabaaabbbaabbababbbaaaabaaabbabaababbaaaabbaabbbabaaabaabbbababbabbbaababaabaaabbbaaabbbabaaaabaaaaabababaabaabbaabbbababababaaabaabaabbabbbaaaaaabbaaabbbaabbbaaabbbbbbaabbabbabaabbbabbbbbababbaaababbaabbbaaaaabaaaabababbaabbbbbbbaaabbaaabbbbbbbababababaabbaaababbaabbbaaabbbabaaabbbabbabaaaabaababaaaaaaaabbabaaabbbbabbbbbbbabaabaaabbbabaaabbbabbbabaabaaaaababaaaabaabaaabbbabbababbabbbbbbababaaabbbbaaaaabbaaaababbababaabbaababbbbaaababbbabbababbaaaaababbabababbbabbaabaabbbbbabbbbbababaaaabaabaaaaabbbbbbbaaababaaabaababbbaabbabbabbabaabaaababaaabbbbbaaaabbaabbbaabbbbbbbbabbbbbbababbabbbaabbaababbabbabaabbbabbabaabbabaaabbbbbbbaaaabaabaaaaaaabababbbbaaaaaaaabbbaababaababbbaabaaabbaaababbabbbbbaabbbabaaaaaabaabbaaabbbababaaabbbbbbabaabaaabbabbababaaabbbbaaabbabbabbabaabaababbaabbbbaaabbaabbabaaaabbababaaabbaabababbabbabbbbaaabbbabbabaaababaaaabbaabababbababbbbababbaababbabababbbabbbaaaababbbaabaabbaaaaababbabbaaaabbbbbaabbbbabbabbaabaaabbaababababaabbaabaaaaabaaaabbbbbbbabbaaabaaaaaabaabbbabababbaabbabaaabbbbbbaabaaaabaabbbbabbaaaaaaababaabaaabbaabbabaaaaaabbbaabbabbabaaababbbaaaaabaaaabbaaababbbbaabbbbbabbbabbbbabaaababaaabbaabababbaabaaabababaabbababbbabbaaababbbbaabbabaaaaaabbbbababbaababbabaabbbaaaaaabbbbabbbbbbaaabbbbbaaaaaababbabaabbbbaababababababbabbbbaabbbaaabaabaaabbaabbaaaaababbababaaaaaabbaaabbaaaaaaaaabbabaaabbbbaababbabababbabbbbbabbbaabbabbbababaabbbaaaaabbbbababbbbaabaaaabaabbbbbbaaabaabaaababaabbbabbbbbabbbbbbaabbaabaaabbababaabbabababbababaaabbabbabaabbabbbbbaabbbbbbbaaaabaabaaaaaaaaaabbaaaabbabbbabaababbbabbaabbabbabababaabbbbbabbbababbbbbbabbbbbbbaabbabbbaabbabbbbbaaababaaaabababbbababababbbaabababbabbaabbbbaabbaaababaaabbaaaaabaabbbaaaababaaabbbabbabaabaaabbbabbabbabbabababababaaaabbaaaaaaabbbaababaabbabbaababbbaaaabbbbbbaabbbbabaabbbabaaaaaaabbaabbbbbabbabaaababaababbbaaabbabbabbabbbaabbbbbaabbbbaaabaaabbbbbababaaabbbbabbbaabbbbaaaabaaabaabbbbbabaaabbbaaabbababaaaaaabaaaaaabaabbabbbaaaababaababbbbbabababbaabbbabbbbbbbbbbabaaabbbbbaabbbbabbaabbababaabaaaababbaabaabbaaababbaaababbabbbbabbbbbababbabaaabbababaaabbbaaabbbababbbabbabbbbaabbbbaaabbbbbabbbababbababaabbabbaaabbaaaaababaaabbbaabbaaaaabababbbbbbababbbbababbbaaaabbbaaaabaababbababaabbababbaaaaaaaaabbaabbabaaabaabbababaabaabbbbbababbbabbabbaabaabbbbbabbbaabbaababbbaabbbababbbaabbbababaaaababbbbbbbabaabbbabbbbbabaabbaababababbabaaabababbaaabbaabaaaaaaabbaababbbbbaaababbabbababbbaaabaabaaabbaabaaabaabaababbbbbaaaabaabbababbbbabbbbbbbbaaabbabaaaabaaaaaaabaaaaabaabbbaaababbbbaaabbbabaaabaaabbaaabbaaababbabbabaaabbbaaabaabbbbbaaabaabbaababaababababababbbabbbbaaabbaaabbbbaaabaabaabbababbbbaababbaaabbaabbbaaabbaababbababbbabbbbbaabbbaabbabbaabbabaaaabaabaaaabaababbbbababbbabbbbbaaababbababbbbaabbaabaaabbbabbbbbbaabbbabaaabbbbbaabbbbbababaabaababbbaaabaababababbaaaaabbaaabaabaabaaaaabbbbbabaaabaaaabaabbbbaaaaaaaaabaababaabaabaabbbbbababbbbbbaabbbbabbbaababaaababbbaaaabababbbaaaaabaabbbbbbbbabbbaabbabbaabaaaabababaaaabbabaabababbbaabbbabbaaaababababbbbaababaabbaaabababbbaabaaabbabbabbaababaabaaaaaaaaaaaaabaabbbbbaaabbabaaaabbbaaaabaaabaaaabbaaababbbaabbbaaaaaaaabbbabbababaaabbbaabbababaabababaababaababababbababaaaabaaaaabbbbbbaabbbbbbbbababbaabaaabbaaababbabaaaabbaaabbabaabbabbabbabbaabbabbbabbababbabaaaaaabbababbbababbaababbbbbaaababaabbbaabbabbaababbabbbbbaabbbabababaabababbabbabbbaabbaaaabbabaaabbaababaabbababbababbbababbbababbbaabbabaaaabaabbaabbabbaabaabbaaabbaabbabbbabaaababbaabaabaaabbbaabbbabbbaaabbabbbabbbbababbaaabbababababbaaabbbbbabbbbbbbbbbaaaaabaabaabbbbbbabbababbbbaabbbaabbaabaaaaaabaabbababbbbabbaabbbabbaabbaaabbaabbababbabbbaaaaaabbbaabaaabbbababababbbabbbabbabaaabbbbabaabbbbbbbbababbaabbbbbbbbbbbbaababaaabaabbbbaaaabbbbbabbbbabbabaaabaaaaabbbaaaabbbbbaabaaaaababaaaaaababbabbbbaabbbbbaaabbabababaabbabbaaaabaaabbababbaabbaaaaabbbababababababbabbabbaaabbbabbaababbaabaababaababbaaaabaaabaaaabbbbbbbbbbababbaaababbabaaaabbaababaaaabaaaaaabbabaaabbbbabaaaaabaababbbaabababaaaaaaabbbbabbbaabbbabaabbabbbaaabaabaaabaaabaabaaabaaaaaaabbbbbbaabbaaaabbbbbaabbbbaabbaabbabaabbbbaabaaaabbbabaaaababbaaaaabbbaaabbabbbaabbbbbabaabaaaabbaaaabababbbbaaabaabbabaababbaaabbababbbaabaabaaabababbbbaabaaaaaabbabbaabbabbabbbaabbaababbbaababaaabaaabbbbbaabaabaaaaabbbbbbaabbaaaabaababbabbaabbabbbababaaaabaabaababbbaaabaaabaabbaaabbbaaaabbbabbabbaababbbabbaaabaabbbbbbabbabaaaaaaabaaabbabbbbbbbaababaaaaabbaabbabaaabbaaaababbbabbaaaabbbaababababbabaaababbbabbababaabbaaababaaabababaabbabbabababbbaabbbaaaabbababaababbaaaaabaabbbabbaabababaaaabaaabbababbababbaabbabaaaababaabbabababababbbaaabbbbbbabbbbbbbaaaaababaaabaaababbabbbbaaaaababbababbbbbbabbbaaaabbaabbbaaaaaabaaaabbbaaaaabbabbbbababbabbabbabbabbaabbbaababbababbaaababaaababbaaaaaabaaaaaaaababbaababbabbabbabbbaaababababbbabbbaaaababbabbabaabbbbaaabaaaabababaaabababaabaaabbbbbabbabbbbaabaabbbaabbbbaabaaaabababaaabbaaababbbaabbbabbbabbbaaabbbbbbaaaabbabbbaaaaabbbabababbabbbbbbabbbaaabbbabaaaaabbbbbbbbbbbabbaababbabbabbaaabbabbaabbaabbbbbbbbaaaabaabbbbaabbbbbabbabbabbaaababbabaabbbbbbaabaababbbbababbaaaaabaaabbabaabbababbbbbabaabaaabbbbbbabbbaaaaabbabbbabbaaabaaabaaababbabbbaabaabbbbbababaaabaabbbbaabbbbababaaaabbbbbaabbabbbbbababaaaabaabbabbbaaaabababaababbbbbaaaaaaaababbbbbaababbbaabbbbbababbababbabbbbaabbbaaaaaabbaaabaabbabbaaabbabbaabbbbbabaabbbababaaabbaaaababbbbbbabbabbbaaabbbbbbbbbbbabbbabbabbabbaababaababaabbaabbaababaaabbbbabbabbaabaabaabaabbabaaaaabaabbaabaaaaaaaababbbbaabbabbaabaabbbbabaaaabbbababaabaababaaaabaaabababaabbaabbaabababbaaaabaabbbbbabbaaaabaaabbbabaaaaabaaabbbbbbbabbbbaabbabbabbbbabbaaaabbbbababaabaabbaaabbabbbbabbbabaaabbabaaaababbaabbbbbbabaaaababaabababbabbaabbaaabbbbbaaaabbbbbbbaabbaabbaababbabbbbbaaaaaaaabbbaabaaaaabbabaabaaabbaaabaababbbabbbbaabbababbaabaaabaababbabaabbbaababbbabaaaaabbbababaabbbabaaaabaaabaabaaaabaaabbbbabaabaaababaabbabbbaaaaabbabbbabbaababbbbbababbbaabbaaababaabaabbabbabbbaaabbbaabaaaaaabbabaababaaaabbbbaabbabbbabaabaaabaabababaaaabaabbaaabbbbabaaaaaabbbabbabaabbbabaabaabbbbbbabaabbbbbabbbabaaabbbabbabaaabaabbbaabaaababaabbbababbbaaaababbaabbababbbaabaaaabbabbaaaabaabaabaabaabbbbaabaaabbbabbbbbaababaaaabbaabbbaabbaaaabababababbaaabbaaaaabbabbbabbabaaaabbbbababaaaaababaaaabbbaaaababbbababaaababbaababaababababbbbbaabaabbaababbababaabaaabbaabbbbaabbabbbbaabaabaaaabbbaaabbbababbabaababbabaaaaabaabbabababbaababbaaababbaaabbababaaabbababaabaabbbbabbbaaabaaabbaaababbaabaabbaaabbaaabbbbbbbaaaabbbabbbbabbbabaaabaaababbaaabbbbbbabbaaaabaabbbaabaabaabbaabababbbbabbbbbbaabbaabbabaababaaaabaaabbbbababbaaabaaaaaabaababaabbbaaababbaabaaaaaabbbbabaabbbaabbbabaabaaaababbaabbbbaaaabaaababbbabaaaaaaaabaaabaabaabbabbaaaaabbababbbbaabaababbabaabaaabbbabbababaabbaaaaaaaabaaababbbaaaabbbbbaabbbbbbbabbbbabbaaababbbbababbabababbabbaaaaabaaaaaabbababbabbbabaabaaaaababbabaabbaaaababaaaabbababbbabbbbbaababaaaabbbabaaabbbbaaaaabaaabbbbbbaaababbbaaabbbabbabbaabaaabaababbbaaaaabaabbaababbbabbbbabbbbbbaaaabbaabaabaaaababbabaabbbbabbbabbaabbbbaabababbbbaabbbaaabaaabaaaaaabbbbbbbbbabbbbbabbabaaaaabbaaabbaababbaaabaaabaabbbabbbababbaaaabababbbbaabbbabbbbbbabbbbbbbaababaaabaaaabbababbabbbabaabbbbbbaaabbbbbabbaaaabbabbaabaaaabbabaabaaaaaaabbbabaaabbbaabbbaabbbbbbbbabaaabababbbbbabaaabbbbaaabaababababaabababbaaaabbbabbbbbbbaaabbbabbabbabaabbbbababbabbbaabaaaabaabaaabbbaabaaaabbaabbbbbabbaaaabbbabaaabbaaaaaabaabababbaaaabaabbbabababbabaababbbbabbababaabbaabaaaaaabbabababababaaaabaabbbbbaabaabbbbbbbbbabaaabbababaaababbaabbbaaabaaabbabaaabbbbabbaabbaabaaaaaabbbbabaabbbabaaabaabbbbbaaabbabaabbabbbbaabaaaaabbbaabaaaabaabbabbabababaabbbaabaabababaaabbbbabbaabbbbbaabababbbbabaaaaababaaabbbaaabbbababbaabbaaabbbaabbbaabbabbabbaabbbbbbaabaabbaabbaaababbabbbababababbabaababbbaaabbbbbbababaabbbbaaaaaaababbbabaababaaababbbaaaaaabbaabbbbaabbababaabbbaabbbbbbbbabaaabbababbbbbaabaabbabbbbbaaabbbbbbabbaabbbaabaaabbababbaaabaaabbbbababbabaaabbbbbaaababbbaaababaaabbbabaabbababaaaaaabbbbaaaaaabbbbaaababbbbabaaaaabbaabaaaababbabaabaabbaabaabbbabaaaaababbbbaabbababbbbaabaabaaabaabaabaabbbaabbbbbaaaabaabbbabaabbaabbabbbaabaaabaababababaabbabaaaaaabbbbbbbaabbbbbabaaaabbabbaabababbabbaaaaabbbabbbabaabaabbabbbaababababbaaaaaaabbaabbabbbbbaababaabbababaaabbbaababaabbbabbbbaabbabbaababbbbaabbabaababbbaabbbbbbbabbaaaabbabbaaaaabbbbbababaaaabbabbbabbbababbaaababababbbbaabbbaabbaabbbabaaaaabababbabbabbabababbbbabbababbaaaabaaababaaabbbaabbbbabaaabbabaaaabbaaabababbabbbababbaabbbbabbbabbbbaaaaabbaaabababababaababbbbbbbbaabaabbabaaaaabaabbbaabaababaaaaaabaababbbbababaaaaaaababbbabbabbabaabababaabaaabbbbaaabababaababababaababaaaaaaaaabbabbbbaaabbbaabaaaabbbbbabaabaaaaaaabababbbaabbbbbaababababbabaaaabbbaaabbbbaaaababaaabbbbaaabababaabababbabaaabaabaaabbbbbabbaaabbaaabbaaababbaaabbabbaaababaabaaaababaaaabababbbabbbbbbbbbabbaabbbaabbbabbaaabbbabaababbbabbaabbbabbabbabaabbbababbababbabbaababbaabbabbbbbbbaabbaabbaaaabbbabbaabbbababaabbbaabbababababaabaaabaababaabbbaaabaaaabaabbaaabaabbabaaaaabaaaababbbbabbaaabbabbabaaabbaaaabaaabaaabaaabbbbbbabbaaababbaabababbbaaaaaabaabbbabbaaabbaabbaaaababbababbaabbbaaaababbbabababaaabbabbbbaabaaabbbbababaabbbbaaabababbabbbaabaabaababaabbbabaababaabbabbaaabbababbbbaabaabbbaabaaabaaabbaababbbaabbabbaaaabbaabbaaaabbaaababbbaaababbbbaaabbaaaabaabbbbaabbaaabbbbaaaaababaabaaaababbabbbbaabaaababaababbaabaaabbabbabbaabababbabbabaabbaabbbaabaaaaabaaabaaaababaababaaabaabbbaababbaabbabbbaababaabbaabbaabaaaababaaabaaaaabbabaabbabababbbaaaabbbbbbbababbabbbababaaabbbbbaabaabaaabbbbbabbbbaababaabbabbaabbaaaaaaaabbbaabbbbbbabbbbaaabbbabbbbbaabbabbabaaaaaaabbaaababbababababbbabbabaabbbabbbaaababbbaabbabbabababababaaaabaaaabbaaabbababbbabaaaaaabbbaaabbaaaaababaabbbbaaabbaabaaaabaaaabbaabaaaaaaaaabbaabbbabbaabbbabbbaababbabbabbaabbbbbaabaabbbabbbbbababaaababbabbbbbaabbabaabbabaabbbababaabaabbaaaabbbaaabbaaabaaaaaaaabbbaababbababbabbabbbaaaaabababbabbbbbbabbbbbbbbababaabaaaaaabbbababbbaaaabbbbbbaaabbbaababbbbbbaaaaaabbaaaabbbabaabababaaabbabbaabaaabaabbaaabbaabbbabaabbbabbabaaabbbbbabbababbabbbbaabaabbaabbaaabbabbbbbbbaaabbabbabaaaaaaabbbbbabbabababbbbaaabbbbabbbbaabbabbbaaababbbaababbabbabaabbbabbaaabbbabbabaabaabaaabbababbabababaaaabbababaaaababbaaaabbbaaaababbbbbbabbabbbabbbaaaaaababbbaababbbbbaabababbbbabbbabbbabaaaabbbbababababaababbbabaababbbbbbabbbbbaaabaabaaababbbbaababbbaaabbbbabbbabbbaaaabbaaaaabbaabbaabaaabaabbbbabbabbbaaabaaababbaabaaaababbbbbbbababaaabbaababbbbabbbbbbbaabababbaabbababaababbbabaabbabbabaaaabaababbbbbaabaaabbbabaababaabbabababbabbabbbaabbaaabbbababbbbbaabaabbababaabaabaaabbaabbabbbbabaaabbababbbbbabbababbbaabaabbbbabbbbaabaabaababaabaaaaababbbaaaaabaabbaaaaaabbababaabababbabbbaaaaabbbbbabaabbaaabbbabaababbabbabbaabaababbaabaaabbaaaabaabbbbabbaaaabaaaaaababbaabaabbbaaaaaabaabbababbabababbbababbbabbaababbbbababababababbbaaaabbababbbaabaabaaabbbabbbaabbbabaabaabaaababbbbabbbaaaaabbaabbbabbabaabbaaaabaabbbaabbbbaabaabbaaababbababaabbbbbababaabbabaabbbabaabbabababaabaabbbbaababbbaababaabbaaabbbabbaabaaaaabbbaabbbabababababaabbabaaabbabbbababbbabbbbabbbbbbbbbaabbabaabbaabbbababbaabbaaabaabbbaaaaabbabbbaaaabbbabbabbbbabbbababbababaabaabaabbbaabbaababbbabbbbbbabaaababaabbbbbbbbbbbbbabbaabbabbabbbabaaaabbbbbabbabbaaaabbbaaaaaabaabaaabaaabbabbbaaaaaaaabaabbbabaabbbaaabbbbaaaaabaabbbababbaaababbabaabbababaababbbaabaabaaabbababaaababaabaaaabbbaaabaaabbabbabbaaaababaabbaabaabaaabaabbabbaabbaaabbbabbabaaabaaaabbbababbaabbbbaabbababaababbaabbbabbbbabbbbbaababbbaaabbabbbbbbbbbbbbababaabbbaabbabbbabbbaababaaaabaaabababbbbbbababbaaaabbbabbababbbabbababaabaabaaaabbbabbbbabababbabaaaaabaaaaabbaabbabaabbabbbabbababaaabbaabaabbabbababbabbbbaaaabbbbbbbbbababbaabaabbbbaaaabababaaabbabbaaaabbbbbbabbbabaaabbbaababaabaabaaabbabbbababbbabbabbbbaaabbbbbbabbaaaaaaaaaaaaaabbbbbaaabaaaaaaaaaabbbbbaabbbbbabaabbbbaaaaaaaababbbababbabbbabbbbbabbabababbbbabababbaabbaaabbabbbbabaaabaaaaaabaaaababaaabaabaaabbaabbabbaaabbaaaababbbbbababbbabbbabbbbbbbabbbabaababbabbaabaaaaaaaaaababaaaababbbababaaabaaaabbbabbbabbbbaabbbbbaaaabbbaaaaaaaabbbaabbabaaababbabababbaaababbbaabaabbbabbbbaababaaabbbbabaabbbaabbababaaababaaaaaabbaaabaababbbbabaabbbbbabbaaaabbaabbbaaabaaabbbbabababbbbbaaabbabbababaababbabbabbaabbaaaabababaaabaabaabbbbaaabbabaaaababbbbaababbbabbaaabbbabbababababbaabaabbbbbaaabbbababbabaabbbaabaaabaaaababbbabaababbababbbbaababbabbbabbbaaabaaabbabbaabbabbaaabbbbabaabbaaabaaaaaabbbbbbbbaaaaaabaaaaabbbbaaaabbabbaaabaababbabaaaababbbaaabababbabaaaababbbbbaaababbbbaaaaabbaaabbaabbbbbbbbbbababbabaaaabbbbabbbbbabbaabbabbbbaabbbbaaabaababbaaabbbabaaaaaababbbaaabbbbabaabbabaabaabbabbbbaabaabbabbbabbababaaabbbaaabbbbaaaaababaabbbaabbbbbbbaabbbaaaaabaaaabbaababaabaabbbbbababbbaaaabababbbaaabbbbabbaabbbbaababaabbbbbbbbababbbaaaaaaaaabababbbbabaabaababaababbabbbbbababababaabaaaaabaabbbbabbababbbabbbbbbbabbabbabbbbbaaabbabbbabbbbbabaaabbabbbbaabaabbbbaaabbaaaaabababaaabbaabbabababbabbabbabbabbbabaabbbabbbbabaabababaaaaabaabababaaaaaaabaabbbaababbaaaabababbababbaaabbabbabbaaaabbaaaaababbbabbbaabbbababbaababbbbbbabbbbbabababbaaabaababaaabaaaaaaaaaaaabaabbbbbbabbbaaababaabbbabaabbabbabbabbabaababbaabaaabbbbaabbbaaabbababbbbbaaaaaaaaaabaabbaaabbaaaaababaaabbaabababbaabaabbbbababbbbaaabbaabaabbbbbbabbabbbabababababbbbaabbbbbbbababbbbabaaaabbabbabbbaaabaabaaaabbbbbababaaaabaabaaaababababbabbaababbbbbaabbabbaaabbaababaaababbbbbababbbbababbaaaaabababbbababaaababaababbaabaabbbbbaaabbabbbaaabbbabbabaaaaabaabbbbabbaababbabababbabbbabbbabbbbbaababbbabaababaaaabbaabaabbbabbbabbabbaaaaaabaaaaaaaaaabaabaaabbaaaabbaabbbbbabababbbbbaabbbaabbbbbabbbabaababaaaabbbaabaaabbababbaababbbaaaaaababbaaabababaaabbaaaabbabbaaabaabbabbaabaabbbaabaaaaababbbbbababbbaaabbbababbabaabababbbbabbbabbabbabaaabbbbabbbbbaabababbaabababbabbaabbabbbaaababaabaaabaabbaaabaabaabaabbaaaabaabaabbabaabbaaabaabbbbbbbabaababbaaabaabaaabbabbbabbbbaaabaaaaabaaabbbabbbaabbaabbbbbaaabbaaaaaabbbabbabaabaabbbababbaaabbababbbbbabbbabababbaaabaabbabbbbabbaaaababbbaabaaaababbaaababbbaabbbabbabaababaaabbbababaababaaabbaaaabaaabaaabaaaabbbaaaabaababbbaababbbbbabaaaaaaaabaaaababaabbbabbbabbbaaaabbbaaabbbbaabaaaabaabaaaaababbbabbabaabbbabaabbabbbabaaabbbbbaabababababbabbaababaaabaabbaababaaabbabaabbbbbbabaabaabbabbaaaabbbabbaaaaaabaabbbbaaabbababbbbaaabaabababaaaaababaabaaaaaaabbbbaabaababaaaabaaaabbbabbbbabababaaaabbbabbabbbbbbabaaaabaabbaabbbbbbaaaaabbbbbabbababaabbbbabbabbbbbabbbbbbbababaabaaaabbbabbbaaaabbbbaaabbaabaabbbbabaaababaabaaaabbbbbbabaabbbbbbbaaabbbababbbaaaaabbbbbbaaaaabaabbabbababbaaabbbabbabbbabaaabaaababbbbbaabbabbbbbbaabbaaabbbbbbaaaaabbbababaaaabbbabaabaaabbaabaabbbbaababbaabbaabaababaabbaabaabbabbabbbbbaabbbabaabbbabaababbbbbbbbbbbbabbabaaababbbbbbbaaaabbabbabaababbababaabbaaabaaabababbbbaababaaaaaaabbabbbbbababbbbaabaabbabaabbabbbbabbabaabbbbabbbaababaaabbbbbabaaabbaaaaaaabbbbbaabaabbbbaaaababbbaaabbbbbbbabbabaabbabbababbabababababaababbaaaabbaaaabbbbaaabaabbbbaababbbaabababbaabbbaabbaaaaabbbababababababbbbababaababaaaabbbaabbaababaaaabbbaababbbaabbbabaaaabbbaaabbaaaaaabaabbaababaabaabbababaaabbaaabbbbbbbabbaabbaabbbaabbbaaaaaaaaaababaabbabbbbbbaaababaababbbaabbbaabbbbbbbaaabaaaabaaabbaabaaabaaaaaabbabaaabbabbababbbbaababaabbbabbbabababbaabaaabbbbbabababaabbbababbbbbabbaabbbaaaabbaabaaabaaabababaaabaabaaaaababaaaaaababbaaaaaaabaaaabbabbaaaaaaaaabbbbbbabaaaabbaaaaabbaabbbaaaabaabaaabbbbababaabbbbaabababaaaaaabbabbbabaaabaaaaabbabababaaaabbababbaaabbbabbaaabbbabaababbbabaaaaabbbabbbbabaabaabaaaabbaababbbbbbaabbabbbbbbbbbbaaaaaaaaabbbaaaaaaaaabababbaabaabbaabababaababaaaaabaabababaabbabbbabbaaabbbaabbabaabbababbbbbbabaaaababaaabbbbabbbbbababaaaaaabbbbbabaaaababbbbbabbaaaaaaabbbbaaaababbaababababababbbabaaaaabbaabbaababbbaabaaaababbbbaabbbabababbbababbabbabbbaababbaaababbbbbaaabbbaaababbabbaabbaabbbbbbbbaababbabbaabbabaabbaaaaababbaaabbbaabbaababbabbaaaababbbbbaabaabbbaababaabbbabaaabbbbbbbbbaaabaabbbbbabbbbaabbabbbbbbaaaababaaabaabbabababaabbbabbbabaaabbabbbbbababbbaabbbaabbaababbabaaabaabbbbbbbabaabbbbababbbaaaabbbabbbbaababbbaaabbabababbbbbbbaaaaabbaabaaaabbaaaaabaababbbaaabbbbbbbabbabbabbabbbaababaabbbabbbabbaabbbbaaababbaabbabaabababbbaababaabaaababbbbaababbbbbaabbbaaaabbbbabbbaabbaabbbbababaababbbbabaaaabbbbaaabbaaabaaabaababbaabbaababaababbbbaaaaababbbbbbaaabbbbbaaaabbbbaabbbabababaaaabbbbabaabbbbabaabbbabababaabbbbaaababbaababaaaaaaabbbbabbbbabbbaabbaaaaabbbbbaabbababbbbbbaabbabababbbabbabbabbbbbaaaaaabbaaababaabbbbabababbbabbabbababbaaaaababaaabbaaabbbaaaaaaabaabbababaabbbaaabbbabaaaaabbaaabbbbbbbbbabbababbbaaabaaabbbaabbbbbbbabaababbbbababaaabbbbaabaababaabbbbabababaaabbaabbabbaabababbbbbbbaaabbabbbbbbbbabbababbabbbabaabaaaabbababaabbabbbaabbabaaabbbbaabaaabbaabbabbbabbbbabbbbabbbababbbabaabbabaabaabbaaabbbbbaaabbbbbbbbbbaabbaababbbababbbabbababbaaabaaabbaaaaaabaabaaabbaaabbabbabaaabbababbaabababaabaaaaaababaaaababaabbaaaabaaaaabbaaaaababaaaabaaaabbbbbbbbabbbaaaaabababaabbbabaabababaabbabaabbaaaaaaaabbaaabbaaaabbbbabaaabaaaaaabaabbabbbbbabaababaabbabbababbabbaababaaaabbaabababbbaaababbbababbbbabaabbbbabbbaabaabaaabaaaaabbaabbabbbabaabaabaaaabbbbbaaabaabbaaabbabbbbaabbaaabaaaaabbaaaaaabaaaababbabaaaaaaaabbbbabaabaaaabbbbaabaaabbaabaaabaaaabaabaaabbbabaaaabaabbbbaabbabbabbaaababbabbbbbbabbbabaababbbbbbabbaaaababbabbabaaaababbabaabaabbabbbaabbaaaaaaaaabbaababaaaabaabaaaabaabaaabaababbaababbabbbaaabbbbaabbaaababbbbabaabbabababbabbbabbaababaaababbbaabbbbaaaabbaaaababaababbbbaaabbabbaaabaabaabbabababbaabbbaaababbaaababaabaaabbbbaaabbabaaabaabaabaaaaabbabbabaabbabbbbbbbbababbabaaabaaabaaaabbabbbaababbabababbabbbbbaabbaabbbbbbaaabbbbbbbaaaabaabbbabbaaababaabbbaaaaaabaababbabbbabbaababbbbbabbaaabbbbabababbabbbbabbbbbbbababaaaaabbbbabbaabbabaaabaaabbaaabbbaabababaaabaaaabbaaaabbbbbaaaaaabaabbbaaaabbbabbaabaabaabbaaaaabaabbbaabbbbabbbabbbbbababbbabaababbbbabbabbbabaabaaabaababaabbababbaabababaaaaabbabaabaaabaabaaabaabaababababaabaabbbbaaabbaaababaaaaaabbbbbbabaaaaabbaaabbbaababbaaabaaaabababbababababbaabbbbbbaabaaabbbbbbbbbbbbababbbababbaabbababbaaaaaabbaabaabbaabbabbbbbaaaaabbbaabbaaaababbbbbabbbabbbaabbaabbaaabaaabbbabaaabbbaaabababaabbaaaaaaabbbaabbbbabbbbbaabbabbbbbabbbbabaabbabbbaababaabbbabbbbbabaabbabaabbbaabbabbaaabbaabababbabaababbbababaaaabbbbaabbaabbaaabbbaaaaabbbaaaabaaaabbabaaabbbbaabaabbabababaababbaabaaaabaaaaaababbaabbbaabbbbabbabbababbbbbbbabbabbabbbbaaabbaaabaabaaabaabaaaaaabbbbbbbbbbbbbaaaaabbaabbbaabaababbaabbaaabaaabbbbabbaababbabaaabababaaaababbaaaaabbababbabaabbabbbabbababbbaababaaabbaaabaaaaaababbbaaabbbbbabaaaaabaaababbaaaabbbbabbbbbaaabbaaaaababaababbbbaabaaaaaabbaaabaaaabbbbbbabbaabbabaabbaaababbbbbabaaaaaaabbaabbbbaaababbbabbbbabbbaaababaaabbabbbbbbbaabbbaaabbbbaaabbbbabbbababbbbabbaaabbaaaaaababbaaaabbabababababbababbabbabaaabbabbbabbbbbbbaabaaabaabababbaaaabbbbaaaabbbabbaaaabbaabbaabaaabbbbaaabbaaaabaaaabbaababaabaabababbbaaabbbabababbaaabbabaabaaaaababaabbabbababbaaababaabbbbbaaaaabbababaaaaabababaabbbabaaabbbaababbaaabbbbbbbabbabaabbaaaaaababaabbbaabababababaaaabbbbbbabaaaaaaabaababbbbbbabaabaababbabbbbbbbbaabbbabbaabaaababaabbabbbbabbbaabaaaababaabbbbabaabbababbababbbbaabababbaabaaabbaabbbabbaabbaaaaabbabbbbbbabaabaaaaaabbaaabbbabbabbbababaabbbaaabbbabababbaaabaabbabaabababababbbbababbaaaaaaaaaaabaababaabaaaababaabbababbbbbabbbababaabbbbababbbbbbababbaabaaaaababaababbaaabaaaaababaaaabbaaaabaaaaaaabaaabbabbabaababbbababaabbbbabbbbabaaabaaaababbbbbaaaaabbbaabbbbaabaabaaaabbaaabaaabaabaababaababbababbaabbbabbaaabbabbbababbbbaabbabaabbbaaaabaabaaabbaaaabbabababbbaaabbabbbbaaabbaababaabaaabbbbabbaababababbabbbabbabbaabaabbbbaabbabbbaabababbabbbaaabababaababaabbaabbabbaaaabbbaabbbbbaabababbaaabaabababbbabbbaababbabaababbababbbbabbbbabbbaaabbbbabaabaabbbaabbaabbaaaabbbaabbbabbbbabbbbbaaabbabaaabbbabbaaaabbbbabbaaaaaaabaabbbbbbaaabaaabababbaabbbbaabbbaaabaaaabaaaaababbbaabbabbabaaabaaaabbbabbaabbaababbbaaaababbaabbbaabaaababbbbabbaabbbbbbaaababbaabaaaaaaaaababbababbababbbaabbbababbbbaaababbbbbbaaabaaaaabaababbbbababbabbabaabaabababbbabbababbaabbabaaabbaaaaabbbaabbaabababbbbaaabbbaaaaabaabbabaaaaababbabbabbbaaabbbbabbaaaababbabaaaaaabbbaabbaaaababaaaaaabaaabbabbabbbbbaabbbbbabbbbabbabaabbbbabbbaabbaaaaabbbbbbaaaabbaaabbbbbaaabbabbbbbabbbabaabbbbabaabbbaaaaabbabaaaabbaaabbbaaaabbaabaaabaabbaaaabbbbbbbaabaaabbabaaaabbbabababbbaabaaaaaaaabbabbaaaabbbababaabbaabaababbbbaabbaabbbbbbaaaaabbbbabbbbaabaaaabaaabbbabaaabaababababaabbabaabaababaabaaabbaaabaabbababaababaaaabaabbaababbbabbbbabbaabaaaaababababbbababaaaaaabbabaabbbaaabababaabbbbaababbaaaabbbbbbabbaabbbbaabaaabbabaabbbaaabababbbabbaaababbaabbaaababaaabbbaababbbbaaaabaaabbabaabaabaabaabaabbbaabaaabaabaabbaababbbaabbabbbbbabbbbababbbababbbababaabbaabbabbbaaaaaaaabaababbababbabababbabbaabaaaaabaabaabbabaababaabbabaaaaabbbbaaaaaabbbaabbabbbbbaaabaabbbababbbbabbbaaaabbaabaaaaaabaaaabbbbbaababbbabbaabaaababaabbbbaaaaaaaaababaaaabbaaaaabbababbbbaaabaaabbbaaababaabbabaabbbbbabababaaaabbbbaabbbaabbaabbbbaaabababbaabaaaabbaaaabaabaaaabbbababbbbaaaabbbbabaaabbabbabbaaabaaaaaaabbabbaaabbbbbbbaabaaabbbaabaababbabbabbbbbaabaaabbbbbbabbaaabaababaaabbbbaabbaabaabbbbbaaaababbababaaabbabbbaaabaaaabbbabababaaaababaabaaaaaaabbaaaaaabbaabbaaaabaabbbbaaabbbbababaaabbbbabbbabbababbbaabbaabbaaaaaabbabbbbabbbababaaabaabababbaaaaaaababbabbbabaaaaabbbabaabbbbabbbbabbabbbaaabbaabaaababaaaaaaabbbbbabbbabbbaabbaaaabaaaabbaabbbbbbbbbaaaaabaaaaabbbbbaabbbabbbabaabbabbaaaabbbaaaaaaabbababbabbbbabbabbbbababaaaabbabaaaaaabaaaaabababaaabbaabbabbabbbbbaaaaaabbabbaaabbbaabbbbabbabbaaaabbbbbbababbbbbbbabbababababbbabbbbbbabaabaaabaaabaababaaabbaabaaaabbbaabbbababaabbabbbaababababaaabaaabbaabaabbbababaabababbaabaabaaabbabbbbabaaaabbbabbaababababbbbbabbbbbaabaabbababbbbaabaabaabaababbabbaaaaabbbbbababbaaabaaabaabbabbbbabbbbbaabbabaabbaaababbabaaaabbbaababaabaababbbbababaaabaaabbbbbbababababaaabbbaabaababbabbbabaabbabbbbbaababbabbbabaaaaaabbbbababaabbbbbaabbbbababaaabbbaabbaabbbbbbaaabbabaaabaabbaaabbababbbaabbabbbbabbbabbbabbbbabbabaababbbbaabbbbbababbaabbaabaabaaabbababbbaaaaaaabbbababbbabaabbaabbabbaaababababbaabaabaaababbabaabbbabaabaaaabbbabbaaaabbbaaaabbbbbababababbaabbbbabbababaaabbaaabbaaabababbabaaaabbbaabaababbabaabbbabbaaabaaabaaabaaababbaaabaaaaaabababbbaaababaaaabbaabbaaabaabbaaaaababbaaaaabaaabbbaaaabbaabbbababbaaaaabbbbbaaaabbaaabbababbaaabbbbbbaabbabbaaaabbaaababababbababbabbaaaaaabbbabbaaabbbaaaaaabaabbababbaababbaabbabbababbbaababbaabbaabbabaaabaaaabbbababaaabbbaabbbbaaaaabaabbbaabbbbabbbaababaabababbbbaabbbbbabbaabbaaabbaabaababbaaabbabaaaaaaaabbbbbbaaaaaabbbaaaaaababbaaabbaaaaabbbaaabbabbbabbaabbaababbababaaaaaaabbabbaaabaaaabbbaaabaaaaaabbbbaabababababbaabbaaabaaabbbabbaabbbbbabbbbaabbaabaaaabbbabbaabababbabbbbbabaababbabaabbbaaaaaababbbabaabaaaabbabbaaaaabaaaabbbbbabaaaabbbbbaabbbababbabaaaaaabaaaabababbababbbbaaabaaabbbbabbbbbaaabbbbbaabbabababababaabbaaababbabbababbbabaaabbabaaaaaaaabaabbabbbabaabbaabaaaaaaababaaaaabbaabbabbbbabbabaababbbbbabbbaabbbabbbabaabbbabaaaabaabbbaabaabbabaabababababbabbbbaaaaabbbaababaabbbabbbabababbbbbaababaabbbabbaababbbbaaabbaaaaabaabbbababbabbbaababaabbabaaaaababbbaabbabababaaaabaabbbbaabbaaabbbaaaabaabaabaaaabaabbbbababbbbbbbabababababbababbaabbababaaabbbaabaababbbabababbbbabbabababbababaababaaabbaaaaabaaaaabaababbaababbababaaaabbbabbabbaaaabbbbabbbaaaabbaabbabbbbaabbbaaabbaabaababbbaabbbaabbabaabaabbabaaaaaaaaaababbaaabbbaaaabaabbbaababaababbbabbaaababababbaabababaabbbabaaaabaaababbabbbabaabaababababbabaaaaaaabaabbbbbababbbbaaaabbaabbabaabbabaabaaababbaabbbaababaaababaaaaabbabbabbbabbabbbaaaabbbabbaabaaaababaaaabbbbabbbbbababbaabaaabbaaababbbaabbbbbaabbababaaaaabbbbabbbbbbabbbaababbababaaabbbbabaabbabaabaaabbabbbbbbbabaaabbababaaaaaaabaaaaababbaabaaaabbabbabbaababababbababbaaabaaabbbabbabbaababaaaabaababababbabbaaabbaaaaaabbaababbbabaaabaaaaaabbbbabbaaababbabaaabaabbbabbaaabaabaaaabbbbaaaabbbbaabbbbabaaaabbbaabaababaaaababbaaaabbbbabbaababaaaaaaabbbbaaaaabbabbbaabbabbabaaabaababbbbabaabbababbaabaaaabababbaaaaababaababbbbbabaabaabaaaaabaabaaabaaabbabbbbbabababbbabbaababbabbabaaabbaababbbabbababbbaaaaaabaababaabbaaaabaaabbbabaaabbbbbbaabbaaabbabbbabbbababaaabbbabbabbabbaabaabaaabbbbbbaababaabbaaaababababbabaabababbbaaaabaaabababbbaaaaaaaabababaaabababbababbaaaabaaaabbaabaababaaaaabbbababbabaaaabbabbaaaaabbbbabbaabaaabbabaaabaabbabaabaaabbabaabaaaaabbbbaaabaabbbabbabbabbbbbbbbbbabaaaaabbbaaaabbbbbabaabbabbabaaabbababbbabbbbabaaaabbaaabaababbaaabababbbaabababbabbbbbaaababaabbabaabaabbaaababbbbaaaaaaaabaabbaabaaababbaababbaababaaabaaaabbbaaabaababbbabaaababaabaaabaaaaabbaaaabbaabababaaaaaaabbaaaabbbbbaabbaaaaabbbbbababababaabaaaaaabbaabbbbaaaaaaabaaaaabbabababbbaaaaaaabaabbaaabbabbabbbaabaabaaaabbbbbabbbbabaaababaaabbbaababaaabaababbbbbaababbabaabaababaabbababbaaaabbaaabbabbbbbbaabbbbbbbbbbaabaabaaaabbabbbbabaababaabbbabbabababbbababbaaabaaaabbaabaabaabbabaabbabaababaababbabbbababaababbbaaabaaaaaabaaabbbbbbbbaabbbbbabaaabaabbaababbaabbaaabbbabbaaaaaabbaaabbaabbababbaababaababbbbbbbbaaaaababbbbbbbaabbbabaabaababbbbaaababaaabababbabaabaaababbbabbbaaabbbbbbbbbaaababaaaaabbbbbbbbbababbaabaaaabbaabbbbabaabbabbaaaabbaabaaabbbbabaaaabaaaabaaaaabbbaababbbaabaabbabaabbbbabababbaaaabbbbaababaabaaabbaaababbbbaaaaababbaaababbbaaaaabbaaaababbaaababbaababbbbaabbbbaababbaabbaaababbbaaaaabbbbababbaababbbbabababbbbbbababbaaaabbbbabbabbabbabbabbababbbbbbaabaababbabaaaaaabaaabbbbaaabaabaabbbaaaaabaabaabbaaabababbabbbbbbbababbaabababbaabbbbabaabbaaababbababbbbbababaaababbabbabaabaaabbaaaabbbaaabbbbbaabbaabbaabbaabbabbaabbaaaabbbbbaabbbaaabbbbbabababbaaaaaaaaabbbabaabbabbaaaaabaaababaaababaaaabaabbbbaabababbabaabbababaabbaaabbabababbababbbbaaababababbabbbbbbbbbabbbabbabaabaabaabbbababaababbbbbbbbbabbababaabaaabbabbbbaaaabababaaaaaaaaabbbaabbbbabaaaabbaabaabbabbaabbaabbbaaaaabaabaaaaaabbaaababbabaabbabbabaaabbabbbbbabbabbbaabbbabbabbaaabaaaaaaaaabbabbabbbaaaabbbbaabaaabbbbbaabaababaaabaabaabaabbbaaabbabbbaabbaaaaaabaaabbbaabbaababbabaabbabbbaaabbbabbbbbabbbbababaabaaabbaababbababaaabbaabbbbbbaaababaaaabababaaaaaaaaaaaabbbaabaaaabaabbbaaabbbaabbabaaaaababaaabbaabbaaabbaaaabbbaabaabaabababaabbababbabaaababaaabbaababbbaabaababababbabaababaaabbbbbaabbbbbaabbbababbaaaaaababbbbbbabbaabbabaabbbaabababbbbaabbaaabbabbbabaababbbabaabaaabaababababbbbabababaaabbaaaaaabbbababbaabaaabaaabaaabbaaababbababbbaabababaabbaabaababaababaabaaabaababbbaabbaabbbabbabbaaabaababbababaabbbabaaaaaaaaaaaaabbbaaaaabbbababbabaaaabbabaabbabbaaaabbbbbababbbaabaabbbabbbabbabbaabbabaabbbbababaaabbabbbabbabaaabbabaaabaaaaaaaaaabaabaabbbbbabbbabbabbabbabbbabaaabbbbabaabaaabaaaaabaaabbaaaaaaabaaabbbbbaabaabababbbbbbabbabbaabaababbaaabbbbbaaabbbaaabaabbbbbaaaaabbabbbbaaabaaaaabaaaababbbaabaaaababaabaaabbabbbaaaabbaaaaabaabaaabbabaaaaaaaabababaaabbabbabbbbbaababbaabbbabaabbaaaaaabbabbabababbabbabbbbabbababbabbbaaabbaabaaaabaabbaabaaabababbabbaaaaabbbbbbbabababaaababbbbabbaababbaabbabbbabaaaabbbaabbbaaaaabbbbbaaabbbbabbbbbbaaaaabbbaabbbbaababaaaabaaaaaaaaaabbaabaaaaaabababaaabbaabaabababbabaaababbbbbabbabbaaaabbbbabaaaaabbababbbbaabaaabbabbbbaabbabaabaaabbbabaabbbbbbbabbababaabbaaabababaaaaabbbaabaaaabbaabbaaabbabbaababbbababaaabaaabbabbaaaabababaabaaabbaaaaababbabbababaaaabbaabaabaaabaaabbbbaaababbaabbaaaaabaabbbbbabababbaabbaabbabbbbbabaabbbbaabaaaabbbababaaaabbaaabaaabbbbababaabbbababbbbaabaabaaabbabbaababbaabbabaaaabaabaababbbbabbaabbbaabbbbbaabaaabaaaabaababbbababbbabbabbaabbabaabbbabbababbbbbbaaaaabaabbaabaaabbbaabbbbbbababbabbbabaaaaabbbabbbbbababaabbaabbbbaabaabaabaaaaabbaaabaabbbbaaababaabbbbaabbabaaaaaaaabbabababaababbabaabbaaaabbabaaabbabbabbabbabbbabbabbaaabaaabbabababbabbbabbaabababbaaaabaaabbababbbbbaababbaabbaaababbabbaaaabababaaabbbbbabbabaaabbabaabbbabaabbbabbbbaabbaabbaaabbabbabaaaaaaaabababaabaaababaaaaabaaabbbaaabaaabbaabababaabbaabbaabababababbaaabbaaaababbbbabbbaaaababbaababbaaaabbbbaaababababbaaabaaaaabaababbaabbbababaabbbabbaaaaabaaaaaabbbbbbaaabbababaaaababaaababbbabaabaaaabaabbbbaaababbbbbaaabaaaaaabbabbabaabbabababbbaabbbabbaaabaaaabaaaaaaaaababaabaabaaaabababbbabbbabaabbbaababaaabbaababaaababbababbababbabbbaaaabbbbaababaabaaababbbaabaabababbbabaababbbabaaabbaabbbaabbbbbabaabaaaaaaabbbbababbbbabbaabaababaaaaabbabbaaaabbaabbbabbabbbbaaabbbabaaabbabbbbaabbabbabbbbabaaabaaabbbbbbababbababbaabaabababaababaababaabbabababaaabbabaababbbababbbbbbaabbbbbbabbabaabbbaabbababaaaaaaaaaaaababbbbabbbbbbaaabaabbabbaababbbbabbababbaababaaabbabbbabbbababbbaabbbbbaabaabaabbabbbabbaaaabbbaabaaaabaaaaaabbabbaaabaababbbaaaaabbbbbabaabbbbaabbaabbbbaabaaaaabbbabbaabaaaaaaabbaabbbabaaabaabaaabababababaaaaaaabbbabbbaaabababbbbbbbaabaaaabbbbbbabbbbabaababbbbbababaabbbaabbbabbaaabbaabbaababbabaabbbbbaaaaaaaabbaaaaabbaaabababaaaabbbbabababbbababbabbaabbaaaabababaaaaaabaabaaaaabbabaabaababbaaaaaababbbbbababbabbbaabbbbbbabababaaaaabaaababaaaaabbbbabbaaaabbbabababaaaabaabaaaabababbabbabbaaabaaabbaaababbabbaababbbaaababababbbabbbababbaabbabbbbabbaaababaabbaababaaababbbaabbbaabbbabaaabbbbbbbbaaaabaaabbbbbbbabbabaabbaaabaabaabbaabababbaaabbbbbabbbbbaaabbaabbbaaaaaabbbabbbbbaaabaabbaabbabaabbbbbbaabaabaabababbabaaababbabaabbbabbbbbabbabbaababbabbbabbbbaabaababbbababbbaaaaabbaaaababbbabaaabaaabaababbaabbbabbbbbbbabbbbabbbabbbbabbbbababaaaabbbaababbaaabbaabbbaabbbaaabaababababbaabbabababbaabbababaaabaabaabbbabababaaabaaaaabbbbbaaaaaabbbababbaabaaaaabbaaaaaabaabbabaaabbbaabbbaaaabbbbabbbaabaaabbaaaaabaabaabbabababbbbabbbbabaabababbbabbbbabbabbaaabbaabaabbbabaabbbaaaaababbaababaaaaaaabbbabbabaaabaaabbabbaaabaaabbbbaaaaababbbababbaaabbabbabaabababaabbbbaaaaaaabaabababbbbbaabbbbbbabaababbbbabaabbbaaaaaabbababbbababaaaabbaaaaabaabbbabaaaaababbabaabaababababaaabaabaabbbbaababaaaababababbaababbabbababaabbbaabbbabaabaaabaaaabbbbaabbabbbbaabaabbaaaababbbaaaababbbbbabbbbbaaaabaabbbaabaaabaabaaabbabaaabaaabbabbbaaaaaabaabbaaabbbabaaaabbbabbababbaaabbbbbbbabaabaabababbaaaaaaaabbbbbabbbbbbbbaabbbababababbaabbabaabbbbbbbaabababbbaaababbaabababbaaaabbaabaabbbbbaabbaabaabbaaabbbbbbbaaabbbabbbbbbbaabbbaababbababbababbbbabbaaabbbaababaabababaaabbabaababaaabbbbaaaaaabbaababaaabbbbbbbabbbbbabbababbababbaaaaaabaabbabbabbbabaaabaaaaaabaababbbabababaaabbbbabbaabbbabababaabbabbbabbbbabaabbbababaaaabbabbbabaaaabaabaaababbabaaaabbaabbbababbbbbaaabbaabbaaaababababaababaaaabbaaaababbaaaababbabbbbbaababbbabbbaaababbbabbbabababbbbbbbaaababbaabbaaaabababbbbabbbabbaaabbaaaabaabbaabaaabbbbabaaaabbbaabaabababaaabbabbbbbbaabaabbabaaabbabbabbbbaababbaaaaaabbbabaabbabbaaabbbbabababbbaabbbaaaaaaabbababaabbbabaababbbabbbbbabaaaabbbbbbbbbbbbbaabaaabbabaaabbaaababaaaaabbabaabbbbbaabbaaaababbababbbbaaaaaababababaabababbaabbaaababbbababbbbbabbbbaabbbaababbbbaaabbabababaabaaaabaabbbaaaaababbbbbabaaabbabaaaabaabbaabbaaaabbbabaaaaabbabaaabaaabbbabaabaabbbbaaaaaabaaaaabaaaabbbaabbbbbbabbabababbbbababbaabbabbbbaaabbabbaababaaaababababbbbaaabbabbbabbbbabaaaabbbaaaabbbbaabbabbbbaaaabababaabbbbbaabbabbabbbbaabaababbbababaababaaababbbbabbbbbaaaabaabbbabbaaabbababbabbaaaaabbabaaabaabbbaaabaaaabaaaaaaaaaabbabbbabbabaaabaabaabaabbabaaaaabaabababbabaabababbbaaababbababbababbbbabaabbababbabbbbaaaaaabababbaaaaabaabababbaaaaaababbbabbbaababbabaaaabbbaaabbaaabbbbbbbbbbbaaabbbbababaabbabbaabbaaabaaabbbaabaaaaabbbababaaaabbabbaabaaabbaabbbbbbbbbbabaaaabbbaababbabaaaabbabababbaaabaaabaabbbabaababbbbbbabbbbabbbbaaabbbabbbbbbbbbaaaabbbaabaabaaaababbababaaabbbabbbaaababbbbabaababbbabbaababbaaaababbbbbbabaaaababbaabaaaabbabbabbaabbabbaaaabbaaabaabbaabbbbaaaaababbaabbbaabbbabaabaababaabbbabaaabbabbabbaababaaabaabaabaabaabbbbaabaabbbbaaaaaabaaaabbabbabbbbaaaaaabbbbbababbbbabbbbabbbaabaaaaaabababaaaaaabbaabbbabaababbbaabbbabaabababaaaabbbbabbaaaabaabbaabbbabbbbbabbaaababaaaababbaaabaabbbbbabaabbabbbbabbbbababbbbaaabaabbbbbababbbbbbaabaaaaabaabbababbabbaabaabaaaaaaaabababbabbababbaaabbababbababaaaabaaaaabaabaaababbaabbbaaaaaababbaabbbbbaaabbaabbaaabababaaaabaaabbaaabababbabababbbabaaaabbabbbabbabbbabbaaabbaabbbaaaaabbaaaaaaabbabbababaabbbabbbbababaaabbaababbabaabbbaaabaabbaabaaabaaaaababaabaaababaaabbabbbaabbaabaabbaabaabaabbbbabbaabbaaaababbbaaaaaababbabbbabbbbbbbabaaabababbaabaaababbbbbbabaaabbbbbbabbabaaaaaaaabaaaabbbbbababaabaabaababaabbaabbbbaaaababbabbaabbaaaaaabaabbbbabbbbabaaaaabaaaaababaabbaababbabbbbbbbbabbbaaaabbbbbaaabbbbbaababbaaabbbaabbbaaaabbaabbbbbaaababaabababbabababbbbbaabbbabbabbaaaabaaababaabaaaaabbabaabaabaaaabbaaaabbbabbbbaabaaaabababbaaababbbbaabaabbaaaabbbabbbbbbbabbaaaabaabaaaabbabbaabbaaaaaaaaabbababbbabbbbabaabbbbbbababaaaabaababbabbbabbbbababaaaabbbaabaaabbabbaababbbbbaabababababaaaabbbabaaababababbbabbabaaabababbbabbbaaaabbbbbabaabaabaababaabaaaabbbaabbabbbbbaabbbaaaaabbbaaaababbbbaaabbbababaababbabbabbaaabbaabaaaabababbaaabbaaaabbbbaabbabaabbbbabbaaabaabbaaabbabbabaaabababbaababaaabbbbaaabaaabaaaaabaabbaababababbbabbabbbaaaabbbaabbaaabaaaaaabaabbaaabbbaabbaaabaaaaabbaaabaaabbaabbbaabbaaaabbaabaaabbabaabbbbbbabaaaaaabbbbaabaababbbabbaaaabababaaaabbbabababababaaabaaabbbbabbbbabbabbbaabbabbaaabaabaabbabbbbbbabbbaaababbabbaaabaaaabaabaabaaaabbabbbaaaaaaaaaaababbbbbbbbbaaabaabbbbaaabbaaaabbbabbbbaaabbbaaaaababbaaaababbabbbaaabaabaabbbaaabbabaabbabaaaaabbaaabaaaaabaaaaaabaaabbbababaabbbabbababbaaabbbbbbababbbbabbabbabbbaaabaabababbaaaaaaaaaabaaaabbababbbbaabbabbbbbbaabbbaababbbbaaaaaaaaaaabbbbbbaaaaababbabaababaaaababbbaaaaababababababbbbaabaabaaaabababaaabababababaaabaaaaaabbaababaabbabbabaabababbbbababbaaababaababbaaababaabaaabbbbbbabbbabaaaaaabbaabaaaabaabaaaaaabaaaaaabababbaabaaabbbabaaaabababbbababbbaababaabbaababbbabbbabaabaabaabababababaaababaababaaabbaabaaaaaaaaaaabbbbabbaaaaaabbaabbbbbbbabbaababbbababbaaaabaabbaaabbbbaaaabaabababbbbabbaabbbbbaaaababbabbababababaaaabaababbaabbbaababbbbaabbaabbbbbaabababbbbaabababbbabbababababbaabaabbaabbabbbaabaabbababbbbbbabbabbaabbabaaaaaabbabbbbbbaabbaaabbbaababaaabbababaaababbbaaaabbaabbbababababababbabaaababaaababaaababbabbaaaaababbbaaaaaaaaabababbaaaabbbababaaaabbbbababbabbbbbbabbbbabaaaaaabbbbabaaaababbabaaaabbbbbaababbabbaababbbaaaabbbabbbababbaabaabbbbaaabaabbaaaabbaaabbbabbaaabbbabbbbabababaabbbbbabbbbaaabaaaaabbbbbbabaaaabaabbbbabbbbbbbabaaabbaaaababbaababbbbbabaabababbabbabaaabbbaaaaabababbbbbbbaabaabbbbbaabbbabaaaabbaababaabaaaababababaabaaaaababbbaaaaaabaabbbbabaaabbaababbaababbaabbaaaabbbabbbbbabbbbbbaaaaaabaaaaababbabaaaabbbbabbbbabbbbaabbaaaabbbbbababbbabbabababbaabaaaaaaababaababbbbbbababbabaabbbababaabbbaabaaababaababaababbababaaaabbaabbbbbbbbabbaaaaaaabababaabbabaababbababbbabbbbabbbbaabaaaaaaaabbbabbbbaaaaaaaabbbaaaabbabbaabaaababbbbbaaaabbabbbbbababbbabababbbbaaaabbbaabbbbaaaabaababbbbbaabbaabbbbbaaaaaabbbabbbaabaabbbbbbabbbabbbabbabbabaababbaababbabaabbabaaabababababbbbababaaabbbbabaaaaabbabbaabbbababbabaabbaaaaabbbbbaababbbbabababababbbbbababbbabbaaabaabbabbbbbaabbbbbababbbbbbaabbbaabbbababababaabaabbabbbbabbbbbabbbabbbbbbbaaaaaabbbaabbbbbaaabbabbaabbaaaabbbabaabaabbbbbbababaaaaabaabaabbbbbaabbbaabbabbbbaabaabbbbbbbabbbbbbbaaabbaabaababbbbabaaabaabaabaaaababbabbbaababbbaabaabbbaabaababaabbbbbbababaabbbaaabaaabaaabbabaaabaaabbabaabbbabbbabbbaaabbbbbaaaabababaabaabaaaaabababbbababababaaababbabbaabaaabbaaabbaabababaaaaabaabaabbaaabbaabbaaaabbbaaaaaabaaabbbaababaabbbbabbabbbaaabbabbbbabbbbabababbbbbbbbbbaaabbaaaaabbbbbbbbbabababababbbbbababbababbbbaaaaaaaabbbbbbaabaababbbabbbbaaababbbaabaabbbbabbaabaaaababbabbbbbaaababbabbaabbabbaabbbaaabbabbbaabaabaaaaaabbabbaabbaabbabbbaaaaabbbababaaaaabbbaabbbbaaaaaabbbbababaaaaaaaaababbbaabbabbbbbaabbababbaaaaaaabbbaaabbbbaaaabaabbabbbbabbbbabbbabbbabbabbabbbbabaaaaaabbabaabbbbaaabbbbbbbaaabaaabababbaabbaabbbbaababbbababbaabaaabaabbbbbbabbbabaabaaaabbbbababbbaabbabaabbbbbaaabaaaaabbbaaabbabaaaaabbbbbabbaaaabaabababbbbbaabbbababbaabbbabaabaaaabaaabaaababbabaabaaaaaabbaabbbbbaaaabaababbaaaabbababaaaaabbaabbbbaabbaabbaaaaaabaabababbbbbbbaabbaaabaabbbabbbbababaabaababbbabaaabbbababbbbaabbbaaababbaabbabbbbbbbabbbababaaaaaabaaaaaabbbbbbaaabbbbbbabbbbbabbaabaaabaaaabbaaabbbbaaabbaaaaaabababbabaababbbababbaaaabbbabbabababbbababbbbbabbababaaabaaaabaaaababbabbababaaabbabbabbbbbababbbbbabbbbabbabbaaabaababbabaaabbaabbbbabbabbababaaababbbbbaaaababbababaabababbabaaaaaaabaaaabaaababbabaabaabaababaabaabbbbaaaabbaabbabbbbbabbbbbbbbabbbbaabaabababbbbaabbbabbabbbababababaabbbaaababbbaabaababbbbabaabaabbbbbaaaababbabbbbbaababaabbbbababbaaabbabaaaaababbbaaaabbbaabaaaaaabbbabababaababbbbaababababbaabbaababbbabbababaababbbaabbbbaabaabbbbabbbaaaabaabbaaaaaabaabbbabbabbbabbbabbababbaaaaabbbababbaaabaaaabaabbabababaaaababbbaabbbbabaaababbabbbbaabababbabaaabbbbaabbbaabaaabbbaabaababaababababbbbbaabbaabaabbbaaabaababbababaabaabaabaabbaabaaaaaabaaabbbaabbbaaabaabbabaababababbaaabaababbabbababbbaaaaaabaabbbaaaababaaabbabbbbbbaaaaaabababaaabaaabaaabbabbbabaaababbbaaabaababaabaababbbaabaaabbabaabbbaaaaabbabbbbabaaaabababbbabbaaababbbbbaabababbbaaabbbbbabbabbbbabbbbbbaaababbbaabaaabaaaabbabbbaabababaaababbbabbaabbaaabaababbababbbabbabbababbaaabbbaaaabaaaaaabaaaaabaabaaaaaaabababababbbabaabbaaaaabbaabbbabababbbabbbaababaababbaaaaaaabbaaabbaaaaabbaabbbbbaaaaabbbbaabaaaaabbbbbbabaababbbbabaabaabaaaaaaaaabababbabbaabbbbaababbbbbaaabababbbbbbabbabbbbbbabbaaaaaaabbaaaaaabbababbbbabaaabbabbaaaabbbbabbbbbabaabbbababbbbbababbaabbaaabaaaaaabbbbbbaaabbabaaaababbbaabbaabaaababbbbbabbababaaabababaaaaaabbbbaabbbaabbabbababbaabaaaabbbabababbbbababaaaabbbbbaaabbbabaaaaabbababbababaaaaaaabbbaaabaabaaaabaabbbababaaaabbaabbaabbbaaabababbbbaaabbbbbbabaabbabababbabaaabbbaaaabbbbbbbaaabaababaabaaaaabbbbbabbaabbabbababaaabbabbaaabababbabbaabbbbabaabaabaabbabbabaaabababababbaaaabaaababaabababaabbaaaabbbbabababbbbbaaabbaabbbaaaababababbbbabaaaaaababbbaabbaababaaaaabbababbbaababbbaaabbbaababbbbbaabbaaababbaabbbbbababaaabbbbabbaabbbaabbbbbbbbabaaaabbbbaabababaababbbabaabbaabaabbaaabaabaabbbababbaaaabaaabbbbbbbabbbabbaabbaaaabaabaabbbbabbaaababbbabbabababaabbbbbaaabbbaabbbaaaaabaaabaabababaabaaaabbaaabbababbabbabaaabaaabbbabbabaaaaaaaaaabaaababbabaaaaaabaaabbbbaabbaabbbaababbaaabbabaaaaabbaaaaaabaabbbabaabbbbaaaabbabbbbbabababaabbbaabbaabbbabaaabbaaaaabbbabaabbabaabaaabbbbaabbbbabbaaaaabbabbabbbaabbbbbbbbbabbaabbaaaabbbbbabaaabaaaabaabbbbbabaabbbaaababaabbaaabbababaabaabbabbaaaaaaabbbaaaabbbbbbabaabbaabbbaaabbabbbaaaababaaaabababbbaaaaaaabbaabaabbbaabaababbbbbbaabbbaaabbabbabbabbababbbbabaabbaaabbbbbbaabaaaababbbbaababbbabbbaabbabaabbaabababaaaaaabbabaaabababbabbbaababbabbbaabbaaabbabbbbaabaabbbabbabbbbababbbbbabaaabbbabbbaaabaaaabbabaabbbbbbaabaaaabbabbbbaababaababbaaaaabbababbbbabbabbbabababbbababaabbbbbbbaababbabbaababbabbabaabbabbbabbababbbbbbaaabaaaabbbaabababbbbabbaaaabbaababbbbbbaabababbbbbbaaabbbaabbabbaabaaaaabbaaabbabbbbaaaaabbaababbbbaaabbababbababbaababaabbbabbbbbbbabbaabbbaababbbbabaaaabbabbbbbaaaaaaabbbbaabaaaaaaaaabaaababbbbbabbbbbbababababbbaaabababababbbbabbbbbaabaaababaabaaaaaabbbbaabbabaaaaabbbabaabaabbaaabaaababbabbabbbbbaaaaababbbbaaabbaaaaaabbaabbbaaaaaaababbaaaabbbbbaaabbabbbaababbbbaabbbbabbaaababbabbababbbaaaaaababaaababaabaaaaabbbabaaabbabbbaabbbababbbbbaabaababbaabaaaaabbbabbaaaaaabbbaaabbbbbbbaaabbbabaaabbababbbbaaabbabbbaabaaababbabbbbbbabaaaabaaabaaabababbbaaabababbbabbbbbabbbaaabbaaababbbaaaabababbbbbabbabbbaabababaabababbbabaaaabbbabbbbaabaababaabbaabbabababaaaababbbaabaabbaaabbbbbabaaabbabaabbabaaabbabbbaaaabbabababaabaaababbabbbabbaaaabaaaabababaabbababbabababbbbaabaaaababaabbbabaaaaaababbaaaabbaaabbaabababaaabbabaabaabbabbabbabbabbbaaaaaaaabaaabaaabaabababbabaabbabababaabaaaabbabaaabaaabbbbabaabaaabaaaaaaaaaaabbbaaaaabbbbbbaaababaaaaabbabbabbbbababbbbabbbbabbaabbabaaaabaabaababaabbbaabaaababaaaabbabaabaabbbbbbbaaabbaababbbbbbbababbaaaabbabbbabababbbbbaabaabababbabababbbaaaabbbabaaabababbbbbaaaaaaaaaabaabbbabaaabbbbbbababbbbbbabbaaabaaabaababbbaabaaaabbbabbabaabbaaabbaaabbababaabbababbbabaaaaabbaaababbbabaaabbabbbabaaaabababbaababaabaaaabbaabaaabbaaaaaaaababbabbbbabbbbababbaabbababbbbbbbbaababaabbaabbbaababbaaaabbbabababbbaabbaabbaabbbaaabaabaabbabbbababbbabbabbbbbbaaaabbbaabbabbaaabaababaabbbbabababaaaaabaaaabbababbbbbbababaabababaabbaaabaababaaabbbbaaabaaaabaaabbabababbaabbbbbabbababbababaabbbbbababbbbabbabbbbbaabbbaabbabababbaaabaaababbaaababbababaabbbbabaaababbbbbbaaabbbaabababbbbbaaaababbabbabbbaababaaabaaaaabaabababbaaaabbabaaabaaaabaabbbaaabaabaabbbbbaabbaabaabbbabaabbababbababbbbbaaaaabbaabbabbaaaaaabbabaaaaaabaaaaaaababbababaaababaaabbbbabbbbabbaababbaaaababaaabbbbaabbaaababaabaaaaaaabababbaaabababbbababbbbbaababaabbbabaabbaabaaabbaaabaabbbbaabaaabbabaaabbaabaabaababbbbababaabbabababbaabbaabaababaababbbababaabbaabaaaaabaabaabababbbaababbbaababaaabbbabaaaabbaabaaaabbbaaabbaababbababaaaabbbbaabbaabbbbabbbaababaabbbaaababbababbaabbaaababbbbbabbabababbbbabbbbbbbbaabaaaababbbabaaaaabbbbbaaaabaaabbabaaabbbbabbbaabaaabbaabaabbbbbbbaaaababbababababbaaaabbbaaababababaabaaababbaabbbbabbbabaaaaabbbbbbaabbbaabbaaabbbaabbbabbbbaabababaabaaaaabbbabbbabaababababbabbbbbbbaabbaabbbaabbbaabbabbabbbbabbababbbabbaabbaabaaaabbabaaabbabaabbbbabbaababbaaababaaaaaabbbbbbaaabaabbaabbabaaabbababababbabaaababbabbbaabbaaaabaaaabbbabbaabbbbaabbbaaabbabababaabbbabbbbbbbbbbaabbabbabbbaaabbabbaaaabababaaabbabaababaabbbbaabaaaaabaaabbabbbaabbaabbaaaababbbabbbabaaaaaabbabbbbabbabbbaaabbbbbabababaaaabbabaaabaaaaabaabbbaaabaaabbabbbabbbaabbbaaaaaaaababaaabbbbbbbbabbabbbbaabaaabbbbbbbbbaaababbbbbbbabbbaaababbbbbbbbabbbabbbbabbbaaaabbbababbaababbabbbbabbaababbaaaaaabaabbbaaabababbbbaaabbabaaaabbaabbbbaabbbbbabababaabaabbbbabaabbaaaababbaababbabbbbaaaabbbaaaabbaabbababbaaaabbabbaaaaaaaabbabaabbabbbaabbbabbabababbababababbbbbbabababbbabbbbbabaababaaabbbaaaababaabbaaaababaabaabaaaabbabbaabbaabbbbaaaaaaabbbbbbaababbbabaabbabaabbbaababbbabbbbabaaabbaaaabaaabaababbabbbabababbabbbaaababaaabbbaabaababbabbababaaaaabaaabaaaabababbaabaaabbbbabbaaababbabbbbbaabaaabaaabaabaabababbaaaaaabababaabbabbbaabaabbbbbbbaaabbbaaaabbbabbbaabbabaaaabbbabbbbababaabbabaababababbaabaabbabbaaabaaaaabaababbbbaabbbaaabaaabbaaabaaaabbabbabbabbaaabababbaabaaabababbabbbbabbabaababaaaabbabbaabbbbbaaabaaabaaaaaabababbaabbabbbaabaababbbababaabbbbbabbaabbaababbabaabaababbaaaababbbbbbaabbbaaaabbabbbbbbaaabbbaabbbbbaaaaababababbbaaabaabbbaababbaaaaaabbaababaabaababbaaaabbbababbabbbabaaaaabbaababaabaaababaabbbbbbbaabaababbabaaabbbaabbbbbaabbabbbabaabbbbbaabbaaaabaaabbaabbbbabbababaaabbabbbaabbabbabaabbbbabaaaaaaaabababbaabaabaaaababbaaabbbbbbaababaaabbbbabbaabaababaaabaabaabbaaabababbaaabaabbababbbabbababbabbbaababaaaaaabaabbbabaaabbbbbbbaabbaabbaaababbabbbbaaaaababbaaababbabbaabaaaaaaaababbaababbaabbbbabababbbbbbbaabababbbabbaaabbabaabbaaabaaaaabaabababbbababbbaababbaababaabbabaababbbbbbaaaabbbbbaabbbaaaaabbbbbbbabbaaaaabaaaaaaaaababbabbabbaaabaababbbaaaabaabbaabbbbaabbbabaababaabaaabbaabbabbbbaababaaaaaabbabbaabaabaaaaabbbbbabbababbbbbaababbbabbbaabbaabbbbbaaaabaabaaaabababbabbabababbbbaaaabaaaabbbbabbbaaababbaababaabbaaabbaaaaabbbaaabbabbaaababaaaabbbabbabbbbbbbbbaabbbbaabbabbbbaaabbabbabbbabaaaaabbbabbbaaaabbabaaaaababababbabaaababaabbbaabbaabbabbababbbbabaaaabbbbaabbabababaaaababbbaaaaabaaaababbaabaababbbabbaaaaaabbaaabbbbaabababbbabbababbbbbabbaaabbbbbbbbbbbbbbaaabbbabbbbbaabbbababbabbbbbaabaabaaaababbababaabbbbbaababababbbaaaaababbbaababbaaaabbbabbabaabbabaaaabababbabaabababaabaaaaaabaabaabbaababbaaabaaabbbbbbbbabbbabaaaabaaaabbbabababaababbabaaaabaaabbababbbbaabbbabaaabbaabbbbababbaababbbbaabbbbabbbbbabbaaababbbaaaaaabbbabbaaababaabbaababbaaabaababaaababbabbaabaabababaaabaabbaaabbbbbbbbaaabbaababbbbbbaabbabbbababbaabbaabbaaababbabaabaababababbababababbbbbbaabaababbbaaaabbaaabababaabaabaabaabbaabbbbbaaaaabbbaaaaaaabbbbabaaabbbbabaabaabbbbaaababbbbbbbabbbababbbbabaabbbabbaaaaabbaabaababbbabbababbbbabbabbbabaaabaabaabbaabbabbbababaabbbbaabbbbbbbbabbabbabbabbabbaaaabbaaabbbabbabbababbbaaaababbbaaababbabbbabaabaaabbbbbaabbbabbbbaaababbbaaabbbabaabababbbabaabaabbabbabbabaabbbbababaabaabbbaabbbbbaabbbbaabbababaabaaaaaaaaabaaabbbababbaaaabbbbbbbbababaabbbbbaabababaaabbbbbaaababbabaabbaaabbbbbbaabaabbaabaababbaabaabbaabbbaaabbaababaabaaaaabbbabababbbbbbbbbaaaababaaaaabababbaaaabbbbbabbabbbbababbaabbbaaaaabbbbbababbbbbababbbbbaabababbbbabbbbabbaabbbbababababbbaaababaabaaababababbaaaabbababbabbbabbaaababbbbbabbaaaababaabbbbbaaaaaaabbaaababbbabbabbaabbaaabbbaaaabbabaabbababababaaabbbbabbabbaabbbbababbabaaaaabbabbbbaabbaabbababbaabbbbaaaabbaabbbababaaaaaabbaaabbaabaabbaabbbbabbaaabbbabbbaaaabbaaabaabbaabaaababaabbabbbabbabbaabbaabbbbaaabbaaabbbabbabbbaaaaabaaaabbbaaaaabbbbabbbababbaaabbabbabbbbabaaababbbabaaaaabbbaabaabbbaabbbabbbbbbbaababbbabbbaaabbbbaabbbabbbaaababbabaababbbabbabbbbababbabbabaabbaabbababababbbabaaabbbbabbbbaabbabababaaabbaabaaaaabbaabaabbaaaabbbbbaabbaaabaababbbbaabbabbbbabbaaaaaaaababbaabbbaabbbbbbbbaabbbbaabbbbaaaaabbabbaababbaaaabaabbabaaabaaaabbbaabbaabbbbaabaababbaabaaabbbbabbbaabbabbaababbabaababbaabbaaabababaababababaaaabbaaaaabbaabbabaababbbabbaaabababbaabbabbaabbbaabbaaaaaaabbabbbbbbabaabbbaabbababaaabbabbabbaabbbbababbbaaaaaabaaababbbbaababbbabbbbabbbaabaababbbbababbaabbaaabbababaaaaaaaabaaabababbaaaababbabbbbbbbbbbbbbaabbabbabbbaabaabbbbabaababbaaaababbabbbababaabbbbaabbbbabbabaabbbaaababbaaabababbabbbabaababaaaabbbababaaababbaabbbababbabbbababaaaababbbababbbbabbbaababaaabbabbaaaaaaaabaaaaabaababaababbbaaabaabababaababbbaaaababaabbaabbbaabbbbaaabaaabbaaabbbbbbabbbbbabaabababbaaaaababbaabbbbaabbaaaaababaaabbbbabbbabbabaabbbaaabababbabbabbaaaaabaaabbabbbaabaabaababbaaabbbbbababaaabababbbaaaaaaabababbbbabaabbbabbbabbbbbbabbbbabbbaaabbaabbbabaababbbbbaaaababaaaabbabaabbbaabbbbabbbabaaabbbababbaaabbaaabababbabbababaaaabbbbbbabbbabaaabaabbabaaababaabbbbbaaaaababbaaababbabbabbaabbbaababaaaabbbbbbbabaaaababbaabaaaababaaaabbbbbbbaaabbaababaaaaaaabaaaabaabbbbbabbaababaaaabbbbbabbabbaaababbbabbbaabababbaaaababbaabbaaaaabbabaabaabbaaaabaaaaabbababaaaabaaabbbababbaaabaabbbaaabbbabbabbaabbbbabbbbaaabbabbaabbbbbbbaabaaaaaaabbaabbbbbabbbbbbbababaabaabbabbaababbbbbababaaaaabaaababbaaabaaaaaababaaababaabaaaaabaabaabaabbbbaaababbabbbbbaabaabaabbbaabbaabaaabbbababbbaaaaabbbaaabbbbbbabbbbbbaaabbabbbbaabbbbbbbbaaaaaaaabbbabbbbbbabababbaaabbbbaabbbbaabbabbabbaaabbbbbaabbbabbaabaabaababaabbbaaaaaaaababbbabbbaaaaaabaaabaababbababbaabababbbaaaaaabaaabababbabbaaabbbaaaabbabbbbbaababbbababaaaaaabaabbabbababbabbbabbaabaabbabbaabbaaaabbabbbbbaaaabaaaaabbababaaabaabbabaaabbaaaabbbabbaaabbabbbbaabaaabbbaaabaaaabbaabbabaaabaaaabaaababbbabaaaaaabbabaaabbababaabaababaaaaabbbaaaabababbaaabbbbbaaabababbbbbbbaababaababaababbbabaababaabbabbaaabbbbabaabbabbaaabbaaabbabababaabaabbabbaaabbaabbabbbaaabbabbbabbaaabbabaaabbbbbabbababaaaababbbababbaaaaaaaababbaaabbaaaaaaaaabbabbababaaaaabaaaaaaaabbaabbbbbaabbaaaaaaaabaabbbabbabaaabaabbaaaaaababaabaaabababaaabbbaaaabaaababbbbabbabbbaabababbaabbbabbbbaabaabbaaabbbbabaaabbbaaaababbabaabbababbabaaaabaabaaaaaabbabbbbabbabaaaaaaabbaabbbaabbaaabbbbaababbbbbaabbbbababbbbabbabaaababbbaabbaabbbbbaabababaaaaaababbbaababaaaaabbbaabbababbbbabbbbaaaaabaaabbaaabbbbbbaabbbaaaaababbabbabbaabababaabababaaaaababbbabbbaaaabbbabbbababaaabbaababaaaabbbbbabbabaaabaabaaaaaaabaabaaabbbaabaaabaaabaabbaaababbbbbbbbbbbaaaaaabbbbbabbbbbbbbaabaaabbabbbaaabaababbbabaaaabbabbaaabaaabbabbabaaabaaaaabbbabaaababbbbabbababaabbabbbbaabaabbaabaabbbaaaabbbbabababbaabbaabababbbabbabaabbbbbbaabbbbaabbaabbaabaabaaaaabbabbbabbaaabbababbbaabbbabaaaabbbbaabbbabaabaabaaaaaabaabbaabaaaabbaaaababaaaaaaaabbaabaaaaaaabbababbbababbbaaaaaaabaabbbbbabbabbbabbbbbbbaabaaaabaaaabaaaaabaabbabbaabababbbaababbaaaabbbaabbaaaaaabbbbbbabbbbaabaaaaababbabbbabaabbabbaabaababbaaabbaabaaabbbaaaababaaababbbaaabaabababbabbbbabbbabbaaaaabaaaaababbaababbbbababbabbbaaaababbabaaabbaaabababaaaabbabbbaabaabbbbabaabbaaaabbabaaaaabbaabbaababaabbaabaababaabbaababbbaaaabaaaaaaabaaabaababbbbabbaaaaabbabaabaabbbbbaaaaaabbbbaaabbbaabbbbbbabaababaaabaabbbbbaabbabbbaabbabbbabbbbababababbbabaabbaababaabaaaabababaabbabbbaaaabababaaabbaaabbbaabbbbabaabbaaaaaaaabaabbabbaaabbbbabbababbabaababbaabaabaaaabbbbbabbbabbbbabbaababbaababbababababaaabaabbaaaaababbabbbababbbabbaabaababbaabbaabbbbaaaaaabbbbbbabbaabbbababaababbabbabbbbbbbababaaaaaabbaababbabbbabbbbaabaabbaaabaaaaabaabaabbbbbabbbaabaabbabaaaaabbbbababaaababbbabaabbbaabaabaaabaabbbbbabababbbbaaaababaabbbbaaabbababbbabaabbbbaaabbabaababbbaaababaaaabaaabbbbaabaabaabbaabbbbabaaabaabbbaaababaaababbbabbbabbaababbbaabbbababbabbbbababbaabaaabababaaaabbbbbabaaabbaaabbbbbaabaaabbababaababbbabbaaabababbbabbabbabbabbbabbbbaabbabbbababbaabbbabaaaabaaabbabbbabbbaaaaabaaaaabbabbaaaababaaaaabbbaaaabbabbabaabbbabbbaaaaaaababbabbabbbbababbbabbaaabbabbabbaabbbbbbbaaabbabbababaababbaaabbbabbaababbbaabbbaaabaabbaabbabaabababbbbaaabaaaabbbbaabaababbaababaabbbabbabbbaaabaaaababaaabaabbabbaaaaaaaabbaaaaabaaaaaaaabaabbaabaaaabaaabaabbbbabbbabaabaabbabbbbaaababbbbaabbabbbbbaaabbabbabbbaabaabbaaaabbbbbaaabbabaabaabbaaababbbabaabababaababbabaabaabbbaabbababbaabbbbbbabbaaaabaaabababaabbbbbbbaaaababaaaabababaabbbbbabababbabbababaaaaababbaaababbabbaaabaababaaaaaaaaabbbbbbbababababaabbbbabbbabbababbbbabaababbbbbbbbaabbbaaaaaabaaababbabaaabbaaabbbaabbaaabababaaabbbbbbabaabbabaaabaaababbaabaababbbaaababbbababbbbabbbabaabbababbaaaabbbbaaabbabbbbababbbbbabaababaabbbaabbabaaaaabbabbbababbaababaaaabbbaaabaabbbbaabbaabaaaaabaabbbaaaaaaaaaababaababbaaaaababbbbabbababbbabaaaaaaaaababbbaabbbbbabbabbbaabaaaababaaaabbbaabaaaaabbabbabbbbbaabababaaababaaababbaabbaababbbaababbaaaababbbabbaaababbababbabbabaaabbbaaabbaababababbabaabbbbababbbbabbbabaaaabbbababaabbbaaaaaababaaabaaaaabbbaabbbbbabbaaaaaaabaaaabaaabaaaaabbabaaabaaabbbbbbbbbbaaabbbbbbbabbbaabaaaabaaabbbaaaaabaababaaababbbaaaababaabaababbbbbbaaaaababaaaabaaabababaaaabaababbbbbbbbbbbbaabbbbbbbabbabbaabbaabbbbbbabbabbaabababbabbabbaababbabbaabaaaabbaaaaaaabbbabaaabaaabbaaabbbbaaabbbaaabbaaaabababababbabbaababaaabbbbbbababbaaabaaabaabaabbbababbbbabaaabaabbabbababbaabaaabaaabaaabbbaaaabbabbaaababaabbaabbaabaabbaabbbbaabaaaabbaabbabbabbbaabbbbaaabaabaabbaaaabbbabbaabbbaababbbbabbaaabaaaaaabababbabbbaaabbbbaabaabbabaaaaaababbbababbababbaaaaaabbaabababbababaabbbbaaaaabaaabbaabbbbbbaabababbbbbbabaabbabbabbaaabbaabaabbabbbbbaaaaabbbbabaababbaabababbababbbbbbbbbbbabaaaaabaaabaababbbbbaabaabaaaaababbabbbbbaabbbbaaaaabbbbbbaababbbbbbaaaaabaabaaabaaaabaababbbbaabaaaabbbbbaaaaaabaabbaababbaaaabababbbbababaaaabbabbababbbaaaabaababbaaaaaabbbaabababababaabbbbaaaabbaabababbbaaaaaaabbbabaabaaabbbbbaaababbbabbaabbbababababbbabbabbbababbaabaaabaaabbbaaaabaabbaabbbaababbbbbabababbabababbbaabbbaaabbaababbabaaabaabbbbaaaaabbaabbbababbbbbabaabbabbabbabbababaabaaaaaaabbbaaabaaaababbaaabaababaabbbbbbabbbabbbbbaababaaaaaaaaabbbbbaaaaaabbaabaaabbaabbaaababaaaaabaababbbbaaaaaaabbabbabbbbbabbbbabbabbbaabaababaabaaabbbabbaaaabbbbaaaabaabaaaabaabbaaabababaababbabbabaaaabaababbababbabaabbabaabbaabaabbbbbbbbaabbabbaaababbbaaaaaabaabaaabababababaabbabbaaaababbaabbbbabbaabbaaabaaabbbaaabbaabbbabaabbbbabaaaabbbbaaabaaaaaabbaabaabaaaaabbbaaabbbaaaabaaabbbbbaaaabababbbabbbbabaaaababaaabababbbbaabababbaabbbaabbaabaabbabbaaabbbbaabbaabbbbabbaaaaaaabbbbabaabbaabbabaaababbbbbaabbbabbbbabaaaaaabbbabbaababbbaaaaaaabbbbaaaaabaaaabababbbababababbaabbbbabaaabaabaabbaaabbabbbbaaababbababbabbbbbababbbabbabaaababaabaaabababbbbaaaaabaaaaabaabbbabbabbaaababbabbbabaaaabaaabbbaaabbaabbbabbbabaaaaabbbbaabaabbaababaaaaabbbaaabbbbbbbbabaababbbababaabababbaabbbaabbbbaabbbbbabaababbaaabaaababbaabaaabaababaababaaabbaaaaaababbbabaabaababaababbbaababbaaabaabbabbbbbbaabbabaaabaaaabbaaabbbaababaabaababbabababbbbbbaaabbbbbababbbaabbaaabbaaaaaabaaaabbbbaaaaaabababababaaabbbbaaaabbabaaaaabababaaaabbabbbbbbbbbaaabbabbaaaabbabababaaaaaababbabbbabababababaaaaabbabaabbbaaabbbbabbabbbbbabbbbbbbbaaaaabaaaaabaabaabbbbbabbbabbbbabaaabbbaaabbbbbbbbbabaabbbbaaaaaaabbabbbaabbbbbbaabbabbbbbbaaababbaaaaaaabbbbbbababbbbbabbabbbaaaaababaaaaaabbbbabbbaaaababaababababbaaabaaaabaaabbaabaaaaaaabaabbabbaabbbbaababaaaababbbabaaabaaabbabbbbabbaaabaabbababbbaaaababbabbbbaaaabbbaabbabbbbbaaabaaabbbbbaabaabababaabbbbbbaabbbbbbabbbbbabbaaaabaabbabbabbababaabaabbbbabbaaababaabaaaababaaabbabbbaaabbbbabbbababbbababbaabbbbabbababbbbbababbbbbbabaaaaababbaabbbabbabaabbababbabaababaabbaaabbbbaaaaaaaaaaaabaaabaabaabbabbabbaabbabbbababbbabbbabaaababaababbaabbaababbbabbbbbbaabbabaabbabbbbbabbaabaabbabbaaabababaaaabbbaabbbbabababbaaabaaaabbaaaabbaaabbbabbbbbbabaababbabbbbabbaaabbbbaaaabbbbbbaabaababaabaaaababbbaababbaababbabaabababbababaabbbbaaaaabababbbbaaababbaaaabbababbbbabbaabaabaabbbbbbbabaaaaabbbbaabbbabaaaaabbabbbbbbaababbbbbaabbaabaaabbabbabaaaaabbabababbbabbbbabbbbbabbabaababaaaababbabaabbaaabbaaaabaaaababababbabbbabbbbabaaabaaabbbbaabbbabababababaaaabababbabbbbababbbbbabaaababaabaaabaabaabaabaaaabababbaabbaaabbbbaaaabbababbabbabbaabbbbabbaababbaabaabbbaaaaabbabaabbbabaaaabbbaaaaaaaabbabaaabbaaababbaabbabbaaabababaabababaaababbaaabbabbabaabbbabaabaaabaabbaabbabbbaaaabaabbbbbaabaababaabaabbababbbbaabaabababaababbabbabbaaababaabbabaaabaaaaabbaabaaaabbabaabbbbabbbabbbbbbbbbabbabbbababaabbabbbabbababbaaabbababbbabababbabaaaaaabababbaaaaaaabbbabaabbabaaabbbaababaabaabbaabaaaabbbbbabaaabaabbaaaaabaaababababbabaaabbbbbbaaabaabbaababbabbabbaaabaaabbabaabbaabaabbbabaaabaabaaaaabaaaabaabbbbbabbbabaabbbaaabbbaaabbbbbbbaababaabbbbbbbaaaaabbbbababbbaabbabbaabbbababbbabaabbaaabaabaabaaaaababbaabbbbabababaaaaabaababbbababbbaaababaabbbbabbaabbabbbbabaabaaabbbaabababbbabaaabaaabaaaaabbbabaaaaaababaaaaababaaabbbbababaaaababbabaabbbaababbabbbbababbbaabaabbabaabaabaababbbbbbbaaabbbbbbaabbbabbbabbbabbbbbbaabbbbbbbbbaabbaaaabbaaaaababbabbabbaaabbaaabbbaaabbbabbbbbabbabbabaabaaabbbaaabbabbbabbbabaaabbababbabbbababbbaaabbbbbbbabaaababbbababbabbababaabbabaaabbbabbbbaaabbababbaabbbbbbaabbaabaabbabbbbababbbbbaabbabaaabababbbabaaaabbaaababaaababbaabbbaaabaababbaaabbabaabbbababbbbbbabababbbbababbabababbabaababbabbaabbbbababaaabbaaaabaaaaabbabbababbaaabbbaabaababbbbaaabbabbbababaaabbaabbbabbaaabbaabbbbababbbbaaabbaaabaabbbbbbaababaaababbabaabbabaaababaaaabaababbaaaabbaabbabaababbabaaaabbaaabbbbbbaaabbbaaababbbaabbaababaabababaaaaaaabbbabbbabbbababaabbbbbaaaaaabbbbbabaaababbabababbabbaabababbaabaabaaabbbabbababbaabaabbaaabbaaaabbbaaaaabbabbbabbbabababbbbaaaaabbbbbaabbbbbabbababbaabbbaaabbbbbbabaaababababaabbabbabaabbababbbabaabbaabbaaaaabaababaabaabbaaaabbbbbababaaababaabbababaabbbbabaabbaabbbbaababbababbbbbbbbbabaaaaabaaabbbbaabbbaababaabbbbbaaaaabbaaababbabbaaaabaaabbbbbbbbbaaabbabbababbbababbbababbbbbaaaabbbaaaabbaaaabbabbbaabaabaabaabbabbaabbbabaabbabbbbbbaaabbbaaabaababaaabbbabaaaaabaaabbbbbaabaaabaababbaabaaaaaaababbbbbaaaabbbbbabbabaababbbbbbaabaaaabbaabaaababbaaaababaaaaababaaabaabbbbabbbbbbbbaaabaababbbbabbababaaababbbbaaabaababbbbbbbbbabbaaabaabbbaabbababbbbaabaaababbbabbbababaabaaababbabbbababbbabbbababbaaababbaabaaaaabbabababbaaaaaababbbbbbabaaabababbaabaaabababbaabbbbbbbababbbababaaabbbabbbabbabaaaaaaaaaaaababababaababaaabbbabaaaababbbbbaaababbaabbabbabaaabaababbabaaaaaaaaaababbaabbaaabbbaaabaabaabbbababbbaabbaaaabbabbabbaababababbabbabbbbbaabaabaabbbaabbbabbbaabaabbaaabbaaabaababbaabbabaaaabbbaabbbabbaaabaabbbbbabbbabaabaaabbbbbaabaaabbbabbbaababaabababbbaaababbaaabbbbabbaaababbbaaaabbabaaabaaabaaababbbababbababbbaababababaabbbbababbbbaaabbabababaabbaabbbbbbbbbbaabbbbbaaaaabbbbbaaaaaabbbbaaaabaabbabbbabbaaaaabababbaaaaabbbbabbaababaaaabbbaabaaabaaaaababaabbbabbbbbabaabbbaaaababbaabbbaabbbbbaababababbabbaaaabbbabbaaabbbbbabaaaaaababaabaaaabbababaaabbbabaabbabbbaabbaaaabaababbabbabbaaaaaabbbbaababaaaaabbaaaaaaaabaabbaaabbbbbaaabaababaaabbbbaabaabaabaaabbabaababaaabbbabaaababbabaaaaabbaabaaaaaaaabbbbaababbbbaaaaaaaaaaabbaabbaabbaabbabaaaabbbbbababbabbbbabaaaababbabaaabbaababbbbabaabbaaaaabaaababaaaaaabaaaaabbbabaaababbabbbabbaaabbabbbbababaabbbbbaaabbaabaabbbaababbabbbbaababbabbabbabbbaabbabbababababbbbbbbaaaaabaabaabbaaabaabbabbaababbabbbaaaabbaaaabbabbbabaababbbaabbabbaaaaaabbaaaabbbbaaaabbbabbbbaaaaabaaaabbabababbbbaaaaababbbabaabbbaababababbbabbaaaaaabbbabababaababbababababababaaabababbbababbaaaaaaaabababbabbbababbbaabbabaaaaabbbabaabaaaaababbbababaaaaaabaabaaaababbaabbbabababbaaaabbbbabbbbbaaaabababbabaaaaababbabbabaabaaabbaaaaababbaaabbabbabbbbababbaaabbbabbababbabbaaaabbaaaaabbbbbbabbabaaaabaaaaabbaaaabaababbbaabbbbaaabbaabaaabaabaababbbaabbaaaabaabbbaaabbabbabaaaabbaabaababaabaaaaaaabbaabaabababaabbbbababbbaaaabaaabbaabbabbbbabaabbabbbbbbabaaabaaabaaababbaaababaaabbabbbbababaabbaaaaabbbbbabbbbbabbaaabbbbaabaaaababbaaabaaaaababaabaabbbbbbabaabbbbbbbababbabaabababbbaaabbbbbbbbbbabbbabbabbabbbbbbaabbaaabaabbbbabbbaabbbbaabaaaaaabbabbababaaaaabbbbbaaabaaaaabbbabaabbbbbbaaabbaabbbbbaaabbaaaaaabbabaabbaaaabbabbabaabbbabbaababbbabbbbaaabbaaaaababaabaabbbaabbabbbbaaaaabbaabbbaaaaaaabbaabbabbbbbbbbababbababbbabaaabbbbabababbaaaaaaabbbbbabaaabbbaaabbbababaabbbabbabbabbaabbbabaabbbabaababbbabbbababaabbaabaaabaabbabbababbaaaabaaabaaaabaabaababaabaaaabbabbabbbabaaaaabbabbbaaaababbaaaabbbabbbabbababaaaabbabbabbaaaabababbabbabbaaaaabbaabaaabaaaabaaabbbabaaaababaaaaababaabaababbaababbbabaaabbaabababbbaaaaabaabaaabbaaaabbbbbbabaaabbbbabbabbbbbbbababababbbbbbababbbabbabbbbbbaaabbbabbababaabbaabbbabbbbbbbabbabaaabbbbaababaabababaabababbbaabbaabbababbaababbbbbbaabbaaabbabbaabbaabbabbbbabbbbaabaaaabbbabbbabbbbbbbbaaaabbbbbababaaabaabaaaabaaaaaabbaababbbbaaaabbabbaabbbbbaabbbabbbabbbababbbaababbbababbbbbababbababaabaabbaabaaaabbbbbbbbbabbbbabbbaaabbaababbbabbbbbaaababaabbaabaabbaaababbbaabbbbbbbbababbbbaabaaabbbabaaabababbbaaaaaababaabbaabbbbaaabaaaabbabbbabbababaaaabaabababbabaabaaabbbbbaabbabbbbaaabababbbabbaaaabaabbbbbbabbbababbabbaaaaabababbabbbaaaabbabbababbabbabaaabaabaababbbaaabbabaabaaabbaabaaaababbaababababbabbabbaababbbbbbaabbaababbabbabaaaabbbbbababababbbbaababaabaaabaaababababaabaaaabbbbaababbbbbaabababaabbaabbbbbaaabbbbabaabaaaaaabbaaabbbbabbbaabbaabbabbaabbbabaaabbbaabaabababbbbaaababbbaabababbaabababbaaabaabbbababbabababbbbabbaaaaabbbaaaaaaabaabaabaabbaaabbaababbabbabababaabbaabbbababbaaababbaaaaababbaaaaabaaabbbbabbaabbaaababbbbbaabababababababbbbabaabaabbaabaababbbbbbabaaabbbaabbbbbbbabbabaababbbaabbaaabaabbbbaababbbbbaabaaaabaaabbababbaabaaaaabbababbabbababababaaabababbbbaaaababbbbabababbabbabbbbbbbbaaababaabbbbbabaaabaabbbaaaaaabbabbbabaabbaaaabbaaabbababaabbabbbbbbaababbbbbbbaabaaaabbaaabbaabbaaabbbaaabbbabbabaaababbaabbabaaabbaababbaabbbbaaaabababbbbabaaababaabbbababbbabaaaaaaabababaabbbababbaaaaaaabaaaababbbaabbaaababaabababbaabaaabbbbbbbbaabaabbabbaaabbbbaabaababbabaabaaaaaaabababbaaaaaaabaaaaaabbbaaaabbabababbabbaaaabaaaabbbbbbbbababbbabaababbabbbaabbaaaaabbaaaababababaaababaaababbbabaaabaaaaabbbaabbaababbbabbaaabbabbabbbaabaabaabbaabbbbabbaababbbbaaababbbbabaaabbabbbbaababbaabaababaabaababbbbaababaaaababaabbaaabbbbbaabbbabbbbbbaabbbbbabaaababaabaabaaabaaaabaaababbbbabbaabbbaaaabbaabbabbabaabbbabbababaaaaabaaabbabaaaaaababaabbaaabbabbaaabaabaaababbbbbaaabaaabababaaaabbbbabbaabaaabaaaabbbbbabbabbaaaabbbbbbbbaabaababbbababbbabbbbabbbaabbbababbaaaaaabbabaaaabbabaaaaaaaaaaaaabaabababbaaababbaaaaaaabaaaaaaababaabaabbbbaaabbbbabbbbaabbaabbbbababbbbbbabaabbbababbababaabbaaabababbaabababbbbbaaaababaaababaabbabaabbbbaababaabaabbbababbaabaabababbbaaaabbaabbbbaabaabbbbbbbabbbbbbaabbaaaabbbbbbababaabbbbbaaaabbabbaaaabaabbababbbaababbaababbabbbbbabaaabababaabbbbbbaabaaabbaaababbabbbbbababbbabbabbbbaaabaaabaaaaabaaaaabaabaaabbababaaaabbabaabbaaaabbbaabaaabbbaaababaabaaabbbbbaabbbaaabbbbabbababaabaabaabaababaabaababbaababbabbbababbaabbaababbbbaabbaaaababaaaaababbbbbabbaabbaaabbbababaaaaabbbbaaaaabbbaabbbbabaaabbbbabbbbbaaabaabbbaaabbabaaababbbbbaaaaaabbbbabbbabbbbaabbbaababbbaaaabababbbaabbbaaaaabaabaaaabaabbbabaabbbbbbbbabaabbababbbaabbabbbaabbabbbaaabababababbaabbaabaaaaabbbbbababbababaaabbaababaaabbabababbababbbbaabbaababbbbabbabbbaaabbabbbaaabbabbaababaaaabbabababaaaaababbbabaababbbaabbaababbbaabbabaabaabbabbbababaabaaababbbbabbababbbbaabbbaaaababbabaabbbbbbaabbaabbbbababababbaabaabbbaabbbaaaaabbabababbbbbaaaaaaaabaabbaaaababbbbabbabbaaabbabbbbbabaabaaabbababaaaaabbbababbbbbaabbaaabbbaabbbbabbaababbabaaaaababaaabbabbbbabaabaabaababbbbabbbabababbaaaababbabbabaaabbbbabababbbaaaabbbaabbaababbbbbabbbabababaaaaaabbbaabaababbaabbbbabababababbbaabaabbaaaaaabaaaaaabaabaaabbbbaabaabababbbaabababbbaaabababaaabbabbabbababaaabbaabaababbaabbabbbabbbabbbbbaaabaaabaaaabaabbabbaabaaabbbbaaaababbabbbabbbbaababbbababbbaaabbaaaabaaabaaabbaabbbbaababbabbbabaabaabaabaabaaababbaabbaabbbabaaaaaabbbbbaaaaabbaabbbbbaabbbababbbbbaabbabbabbbabbabaabaabbbbaaaaababbabaababaabbaaaaaaabaabbabaaaaababbbabaaabbbaabbaaabbbbaaaabaabbabbbbabbaaaaabbabbabbbabbbbbabaabaabaabaabbabaaabaabbabaaabaaabbabbaaaaabbaabaabaabbbaaaaaabbaababbbaabaaabbaababaaababaabbabbabaaaabababbabbbababbaabbbbbbabbaababbabaabbabbbbbabbbbbabbbbababaaaabbbbaaaaaabbaabaabbbaaabaabababaabbbaababbbbabbabaabaaaaababbbbaaaabbbaabbbbbbaabbbbbbbbbaaaaaaabaabbaabbbbbababaaabbaabbbabbbabbbababbbbabaabaaabbababbabaabbbaabaabbaaabaabbbabaaaabbaabababbabaabababaabaabaabbaaaaabbaaaabbbaabbbbabaabbaabbabbbbbaaababaaabbbabaaaabbaaabbbababbbaaaabababbabbabbaaabaababaababaaaabbaabaaaaaababbabbabbbbbabbaabbabbabababbbbbbabaabbaaabaaabaaabbaababbbaabbbaababbbaaaaabbaabbaabbabbaaabaaabbabbbbbbabbbaaabbbababbaaaabbaaabaaaababbbabababbbbaabbaaaaaabbbbbbabbbbbabaabababbaabbaabababaaabbbaaaabbaabbbbbbbbbbaabaabaababababbbbaabbbabaaaaaabbaaabbbbaaaabbababbbabbabbbbbabaaabbbbbbbababbbbbbbaaaabbbaabbbbbaaabaabbaabaaabaaaabbbbbaaabbbababbabaaabbaabbabaabaabbaabbbbaaabaaaabbabaabbbababaabbbabaaabbabaaabaabaaabaaabbaaaabbbababbbabbababbababaabbbabbaaaaabaaabbbaababaaabbabbabbbbbaaaabaaabaabaabbbabbaaaaaabaaababababaababbabababbbbaaaabaaaaabaaaabaaaaaaabbabbbababababababaaababaabbaabbabbbabababbabbabbabaababaaabaabbabaabaababbbabbbaaaabbabaaaaababababaaaaabbbababbbbaaaaabababbababaabababbbbbabbbaabbababbbababbaababbbaaabababbaaabaabbbbaaaaabbaaaabbabaaaabaabababbaaaaaababbaababaaaabaaaaabbbbbaaabbbaaababbbbbbaaabbbaabababbaaabaaaaaaababbaaaaababbbaaabbabaaabbaaabbabbabaabaabaabbaaabbbaabbbaaaababbbbaababbaabbaaaaaabbbbbabbbabbbabbbbaaabbaaabbbbaababbaabbaaaabbaabbbbaabbababababbabbbaaaaabbaaababbabbaaaaaabbabbbbabbabaaabaabaababbbaaabbababbabbabbababaabaaaabaaabaababababbaabaaabababbbaaaabaababbabaabaaaabaaabbbabbbbbabbbababbbbabbbaaaababbaaabaaabbaaabbaabbabbbbbaaaababbbaabbbabaabbbabbaabbbaaaabbaaabaababaaaaaabaaabbbababaababbbbbbaaaaabbbaabaaabbabbaabbaaabbbbaaaaabbabaabbaaababbaabbaaabbbbbaaaaabbabbabbbaabababbabbaabbbbabbabbaabbbbbbbbaababbaabbaabbaaaaaaababbbbaaaabbabaabbbaabbaabaaabbabbbbabaaaabbaababbaabbaababbababbabbbbbbabbbaabaababbbaabaabbaaabaabbabbbabbbabababbbbaabaabbbaaaaaabbabaaaababaaababbabbaabaaababbabbbaabbabbabaabaabaababbaabbbabbbbbbaaabbabaaabaababbbaaababbbaaaaaaaabbabaaabaabaabbabaabababaabaaabababbbbbababbbabbbbaabababbbbabbaaaabaabaaabbbbbbbabaaaaababaabbbabbabaabbababbbaabaabaaabbaabaaaaaabbaababbaaaaabababaaaabbbbbbbbbbbabbbbabbaaaaaaababbbbaaaaaaabbaabaabaaabbabbbbaabbbaabbaaabbabbabbabbbaabaabbabaaaabaabbbaababbbbaaaaaabbbbbbbbbbbbaabaabaaaaababaaaaaababbababbbbaababbaabaaabbababbbabbbbaabaaabbabbabaaaababababababaaaaaaaaabbbaaababbbaaaaaabbbabbbbbbbbbabbbbbabbabbbbaaabbbbaabbbabbbbabbabbaaaaabababbbababbbaaaabaabbaabbbbbbaaaabbabbaaababbbbaaabbbbaabaaaaababaaaaaaababaaaabbabaaabaaababaabaabbaaabbbbabbbabbbababaaaabbaaaabbaabbbaaaaabbaaababbbaababbbbbbbabbababbababbbbabaababbbaababaabaabaabbbaaaabbbbaabaabbbbbabaabbaaaabaaabaaabaabaababbbabaaababaaabaabaaaaabbabaababababaababaababbabbbababbaaaabaabbbaababbbaaababbbabbaabaabaabbabbbabbaabbaaababbababbabbbbbbaababbabaababababaabbaabbbbaaaaaabbbaabbbaabbbbaaababbbbaaabaabbbbbbaaabbabbbbbaaabbbabbbbbaabbbaaabaaaabbaabbbaabaabbabaabaaaaaaabaaabaabbabbbbbabbbabbbaaaaaaaaabbbbbbbbbabbbaaaabbbaaabaaaaabaaabaaaaaabbbbbaaaabbbabbbabbbbbbaabaaaaaaaabbabbabbbaaabbaaaabbbbaabbaabaababaaababaaaaabbaaaabbaaababbaaabbbabbabbabbabbabaaaabaaaabbaabbbbababbbababaabbbabbabaaaaaabaaaaaabaaabaaabbbababbbaabbbbbbababbaaababbbbaabaaaabaaaabbaabbaabbbaababbaaababbbababbbbaabbbabababbbbbaabaaaaababbaabbbbbbbbbbbabbaababaabbaabababaabbbbabbbbaaaaabbbbbaaaabbbbababaaabaababbbaabababaababbbaaabbbbaabbaabbbbbababababaabababbbbbbaabbbabbbbbbababaabababbababbababaabaababbabbabbabbbbbbabaabbbbbbabaabbbababaaabaaabbaababbbaaaaaaabbbbabbbabbababbbababbababaabaabbbabaabbbaaaaaabbababbaababbbbaaabaaabbbbabbbbaabaababbabbbaabbbaabbababbbbabbaabbbbaababbbbbbbaaabbaabaabaaaabaaabaaaaabbaaaaabbaaabbbbbabbbaabbababababbbbbbbaababbbbabbabaababaabaaaababaabbbabbabbabbabbbabbbaababbababbabaaabaabaaaabbbbbabababbbabbabaabaaaaaabbbbbabaabbbabbbabbaabbabababababbabaabbbbbbaabbbabababbababbaaabaaabaabaabbabbbabbbaaaaabaaabaabbbaababbbbabbaabbabbabbaaabbbababbbaababbaaabbabaaaaabbbbbbaaabbababaaaaabbbabaaaaaaabbbabaaaababbaabbaabbbaababaaabbbbaaaabbbaaabbaaaaaabababbbaaabbaabbbbaaababbaababbbbbabbbbbaabbabaabbaaababbbbbbaaabbabbbbaabbbabbaaabbbaaaababaababbbbaaabaaaaaababbbabaabbbabbbabbaaabbbaaababababbbabaaaabbbbabbabbaabbbbbbbaaabbababbabaaaabbbbababbbaaabababbbabbaabbbabbaababaababaabaabbbbbabbaabababbbaabababaabbbbaababbabbaaaaaaaaabaaaaabbaaabaabaaababaababbababababbbabaabbbabbabbaabbaaabbbbabbabbaabbaabbbbbbbababaabaaababbaaababbaabbbaaabaabaaaababbaabbbbabbbbabbbaaaaababbbabbababbbbbabbabababbbaabaabbabaabbaaaaaaaaaabaabaaabbbbbbbabaabaaababbbbabbaaaaaababbbbabaabbbaabaabaaaaabbaababaaabaabaaabaababbbbbbbaaabbabaabbaaaabbabbabaaabaababbababababaaaabbbbaaabbaaabaaaabbbaaabbaaaabaabbabbaaababaaababababbaabbabbaaaabaabaabbbaabbbabbaabbbbbabaabbabababbaaaaaaabababbbbaabbbabbbbabababababbbbaabbaabbbbbaaaabbbbbaabaabbaaababaabbbababbaabbbbababbbaabbababbabbbbbaaaabaabbabbbababaaaaaabababbaaabaaabbbaaaaabbbbbbbbaaababaababbaaabaababbbbababbaaabaabbaababaabaabbbbaaabbbbbbbbbbbbbbbaabbbbbbabaaabbaabbaabaaaaaababbbabbbbaaabbbaaabbbabbabaabbbbabbaaaaaaaaabaabbabaaaaaaaababbaabbaaabbbabbaaabbbabbbbbbbbbbaabbaabbaaaaabbaabaabbbbabbbbaabaaaabababbaabbbaaaaababaaababbaaabbabbaaabaabababbbbabaaaabbaabbbbabaabbbaabbbaabbbaaababaaaaababbabaabbabaabbaaaababbbaabababbabbababbbaaabababaabbbabbaababaaabaabbbbaabbaababbbaababbbbaabbbbabbbbabaaaaabbbaabaaabbaaaabbababaaabbbbaabaababaabbaaababbbbbabababbaaaaaaabaabbaaabbaabaababbabbabaabbbaaaaaaaaaaaaaabbbaaabbbaabbbaaabaaaaaabaabbbbbbaaabbabbbbbbababbbbbabaaabbaaabaaaababbbabbababbbaabaaaabbaaababbabaaabbaabababbabbbaaabababaabbaabaabbaabbabbbbaabababbaabaaababaabababbaaabaababbbabaabaabbbababbabbaabaababaaabbaaabaaaabbbbaaababbabaaabbbbabbaababbbbbabaaaaaabbabbaabbbbbbaababbaabaababaaaaaabababbbbbaabbbaaaababbbaababbaabbabaabbbbbabbaababbaaaaaaaaabaaaabaababaaabbabbaaaabbbababbbaababbaaabaaaabbabbaaaabbbbbbaaaaaabbaaabbbabbbbaaaabbaabaabababaabaabaababbabaaaaaaaabbaabbbbbbbaababaaaabaabbbaaabbbaaaabaababbbbabbbabbababababaaaaabbaabababbaaabbaabbaaaabbababaaaabbbaaabbabbabaaaaaabaabbbababaabbababababaaabbbabbbababbababbabaaaababbbabaaaaaabbaaabaaaabbbaaabbbbabaaababbbabaabbaaabbaaabababbaaaaaabbbbbaaabaabaaabbbbabbbbbbaaaabbbbaaabaababbabbaabaabbbababbaaabbbbabaababbabababbbbaaabaaabababbbabbbbbbbbbbbbaabaaabbaababbbaaaabbaaaabbaaaaabaabbbbbbbbaabaaabbaaabaabbbabaaabbaaabaaabbbabbbbbbbabbaaabbbaabababbbbabaabbbaabaaaabaababbbabaaaaabaaabaaabbabababbbbaaaababbbabbababbbaaabababababaaabaababaaaabbbbbaabaaabbaabaababaaabbbbbbbbbbabaabbbbabbaabaaaabbbaaaabaaabbbaababbaaaabaaaabababbaabbbabbbaabbabbabbbbbabaabaaababbababbbaabbaababbabaababaaaaabbaaaabbabbbbbbabaababaaaaaaabaabbbbbbabbaaabbaaaaaaaabbaabaabaaababbaaaabaabbbbbaabaaaaabbbbbbaabbabaabbababbbbaabaaaabbabbaaaaaaaaaabbaaaabbabaabaaaabbabababbaaabaaaabbaaabaaabbaaaabaaaabaaabbbbbbabababbabaabbaabbabbbaaabaababaabbbbbaaaaabaabababbabaaaaababbabaaabbbbabaabbbbaaabaabbbabbaababababaabaaababbbaaaaabaaaaabbaaababbaaaabaababbabaabbabaabbababbabbaabaabaabaabbbbababaababbbbababbabaaaaaaaabbabaabbabbbaaabaabaabbaaababbbbaaaaaaaababbaabbbaaababbbaabbabaababbabababbabababbbabbaabbabaababaabbbaaabbbababbaaaaaababbbbbbbaababbaaaaaababaabbabbbababaabaabaababbbabbabaabbaababaaaabbbbbbbaaaababaabaabaababaabbababbaaabababaaaabbbabbabbaababaabbbaaaaabbaabbaabaababbababbabaabbaabababaaaaabbbbbaabbabbaabaaabbaaaaaabbbabbbbaabbaabbabbbbabbabaababaabababaababbbababbbbabbbbbbbbabaaabababaabbaabaabaaabbaaabbaaabaaaabbabbbaaaaabbabbababbbabbaaabaabbabaaabbbbabaaabbbbbbabaabababaaaaaabbbaaaaabbabababbbbbaabbaabbabbbbbabaaaabbaaaabaabbababbaaaaaaababbaabaaaaaabbabaaabbbaaaabbaabbbaabaaabababbbbbabbabbaaaabaaaababbabaabaabbbababbabbabbabbaaaaaababaaaaaaaaabaabaabaabaaaaaabbbbabaababbaababaabaaaaabaababbaaaabaabaabaabbbabbbaabbbbbbbbaaaaaabbabaabbbbbaaaabbabbababaabbbbaaaabbababbbabababbaababbabbaabaabaabbbbababbbbbbbabaabbaaaababbbbaaabaaababbbbbbbabaaaabbbabbbbabbabaabaaaaabaabbbaaaaaabaaabaabaaaabbbaaaaaabbbbaaaabbababaabbbaaabaabbbbbbbababbaaaaaaabbaabbabbbbababaabababbbabbaabbbbabbbabaaababbaaaabbabbabaaaabaabbaaaabaaabaabbbbaaaaaabaaabbaabbbabababaabbbababbbabbbbaabbaabbaabababababbaaabaababbabaaaaabababbbababbabbabababbaabbbaabbbaaaabbabbbaabbaaabbbaaabaaabbaaaababbabaaabbbaababbaababaaaabaabbabbbbaaaabbaaababaabbbabaababbaaaabaaaabbbaaababbbbabbbaaaaabbbbabaabbbaaaaaaaaaaababaaaabbaabbbaaabbbabbbababbbaabbbabaaaaaabbbbabaaabbaaaaaabababaaabbaaaababbbbabbbbbababbbaabaabbbabbabbbabbababbabaaaaabababaaaababbaaaabaabbababbbababbaabbbbbabbaabbbabbabbaabbbbbabababaaabbaaaaabbbbaabbaabaaabbbbaaabbbabaaababaaaabbbbbaaaabbaaabbbbbabbabaaaabaabaaaaaaaaababaabbabaabbbabbabbbabbaabaaabbaaababbabbbbbaaabaababbaababbbbaaaaaabaaaabbaaabbaaaaabbbaaaaababbabbbbaaaabababbaababbbabbbaaabbbaabaaabbabbbabbaaabbbbabaabbbbaaaaabbaaabbabaaaababaabaaabaabbbababaabaaaababbbaabaabababaabbbabababaababaaababaaaaabababaaabbbbababbbbbaababbaabaabbbababaaaababaaaabbabbbbbbbbbabaaaababaabababaaaabbbaaabbbbaabababbabbaababbbbaaabaaabbabaabaaaabaabaaaaabbbabaabbaaabaaabbaaabaaaabaaaaaabbbbbabbaaabbaabbaababbbaaaabbbaaaabbaabbabababbaaaabbababbabaabaabbbababbaaaabaaaaaaaabaabbaaaaabbbabbbbaaabbaaabaaabbbabbbbbabbbabaabbabbbbaaaaabbaabbababbaabbabbbbbabbabaaaaabaaabbbbabababaaaaabbbaabbabbbbaaaaabbabaabbababaaaabbbabbaaabbbbbabaaaabbaabaaaaabbabbaabbbababbabaabbbbaaaabbababbabaaabaabbbbabbabbaabababbabbbbbaaaabbbabbbabbbbabbbaabababbbbbabbbababbbabbbbbbabaabbabababbababbaabbaaabaaabbbbababababababbbbbabaaabbbaaaabbabbabbbbbaabbbbabbaabbaababbbbabbabbabababbabbabaaaaabababaaababbaaaaaabbababbbabababbabbaaabbbababbbabaabaababababaaabaabaabbbabaaaaaabbbabababaabbbbabaaaaaabbbaabaaaabaabababbaaabbaaaababbabbbbbabaabaaabaaaaabababaaaaabababaabbababababbababbaaabaabbbabaabbbbbbaaabaabbaaababbbbbbabaaaababbbaaabbbbbbbbabbbabaababaaababbbaaaaaaabababbabababbaabaabababbabbaabbabbbababaaaabbabbabbabaabbbabaabbbbabaaababaaabbbababababbaabaabbaaaabaabbbaaaaaaabaaaabbaaaaabbbbbbbbbbbabaaaabbbbaabaaaaaaabbbbbbababaaababbabbbabaaaabaaaabbabababaabbaabbbbaabaababaaababaababbbaaabaabaabbaaabaaaaabaabbabbabbbbbabaaaaababaaaaababbabababbbabbbbaabbababbaababaabbbaababaabaababbbabbaaababbbabaabaaabaaaaaaaabbaababaabababaaaabbaabaabaaaababbaabababaabbbababaabbabbbbbaabbbaabaaaaabaaaaaabbbababaaaabbbbaaaabababbaaabababbaabbaaababbbabbbbbaabaabbaabababaabbbbbbbbbaaabbaaabababbababbaababaababbbabbbaabbbababbbbaaaaabbabbaabaababbaabababaabaaaabaaaabbbbaabaaaabbaaaaababababaabbbbbaabbaaabaaaaabbabbbababaaabbaababaababbabbabaaababbabaababbaabbaabbabbaabaabaabbbbababaaaaabaabbabbababbaababbbbaabaaaaaaaababbaaabaabababaaababbbaababbabababbabaaabbaaaabaabaabbbbbaaababaababaaaaabbaaababaaaaaababbabbaaabbabaababbabbabbbaabaabaaabbbaaabaaaabbbbaaaaabbababbabbaaababaababbabaaabababaabbbbbbabbabaaaababbaaababbbbbbabbababbbbbbabbababbabbbbabbbbbabbaaaaabaaabbabbaaaaabbbbababaaaaabaabbbbbbbabaaabbbaabaaaaababbababaabababbabbbabaaaaabbbaabbaabbbabaababbbaababaaabaabababbaabaaaabbaabbababaababbabbababbbaabbaabaabbabbbbbaababbbaabbbaaabaabababbbaaabaaababbbabaabbbababbbaaaaabbbabaabbbbaaabbbbaabbaababbaaabbbbaabaaababbbbabaabbabbababaabbbbaabaabbbbaaaaabbabbaabbabaaaaababbabbaabbbaaaabaabaaababbaababaabbabaababbbbaaabbbbbababaaabbaababbbbbbbbaababbbbaaaaaaaabaabbbaabbaabaababbbabbbaaaabbbaaaaabbaaabababbbaaabaabaaaaaababbbbbabbaaaaababbaaabbaaabbabbbbbaabbbbbababbaaabbbaabbabaababbbabbbbbabbbabababbaabaabbbabbabbababbabbbbabbbabbbbbbabaabbabbbaaabaaaaaaabbabbaaababaabbaabababbbbbbbbabaabbaaaabbbbbabaaabbaaaaabbaababbbaabbbbaaaaaaaabaaabaabbbaabbabaaaaababbaaabbabaabbabbabbabaabaababbabbbaaaaaaaabbbaabbbaaaaabbaabbbabaaaabbbaaabaaabbbababbabbabaababaabbabaaabbaaabaaabbabbbbaaaaaabbbbbbbbaabbbbabbbaabbbabbabbbaabaaaaabaaababbaaaabbaaababaabaabbabaaababbbbbaabbbbbabbaaaabbbababaabbbaaaababbaabbaabbbabbbbaaaabbaabbbbabaaaaaaabbbaabaabbbbababababbaaaaaababbabbaaabbbabbbbbbbbabaaabaaabbabbabaababbaaababbabbbbbbbaaaabababbaaaababbbbbaabababbabbbbababbabaabbbaaaabbbaaaabababaabbbaabbabaabbabaabaaaaaabbaaababbaabaaabaabbababbaabbbbbababbababaaaabbaaaaaaabbabbabbbababbaaabbbababaabbbabbabaabababbbbbaabababaababbbaaaababbbbaababbbbbabbbabababbaabababbaaaabbabbbababbbbabbbbbbabbabbaababbababbaabaaaaaaaaaabaaaabbababbaabbaabbbbaababababaabbababbbbbaaaabbbabbbaabbaaabaabbbaaabbababbbbbaababaaabaabaaabbbabaababaababbbabaabbbbbaaaabababbabaaababababaaabbbbbbabababbbaabaababbbabbababbbbabbbbbaabaaaabaabaaaaaabbaaabbabbaabaabbbaababbbbbababbabaabbbaabbababbbababbaabbbaaaababbabbabababaaaaaaabaaabbabbabbabaabbbababaabbbababbbabbbabbaaabababbbaaaaaaababbbbaaabbababbabbabbababaaabaaabaabaabaaaaaaaaaabaabbaaaabbababbbabaaabbabbbaaaabbbbbbaaaaaababbababbabaaabbaaabbbbababbaabbbabbabbbabaaaabaababbbbaabbbbabaaaabaaaababbbaaabbbbbaaabbbabaaaaababbaaaaababbabbabaaaabbbbbbaabaabbbaaabbabbabbbbaababbaaaaabaaaaababaababaaabaabaabaabbbaabaaabbbabbbabaabbaabbabababaaaabbabbbabaababbaaababaaaaaaaababbbbbaababbbbababaaabbababaabbaabaabaaabaaaaababbabaabaabbbbaabbaabbbbbbbbaaaaaababbabababaaaaabaabbababababaaababbaababaaabaabbbaaaabaaababbabbbababbbbbaaaabaaaaaaabbbababaaaaaaaabbbbbabbbbbbbaabaaaabaaaabbaabaababaabbaaaabababaaaabaaaabbbbaabaaabbaababbaaabaaababbaaaabbbaabaabaaababababaaabaababbaabbabbbaaaabbbabaaaaaabbbbabbbbbbabaabbaaaabbaaabbabbabbbbabaabbabbbbbababbbabbbaaaaabbabababababaaaabbaaabbaaaaaaaaaaabababbbbabbbbbbbaabaaaaaabbabbbababaabababbbabbababbbbbabaaabababbabaaaabababaaaababbbbabaaaaababaaabaababbbbababbaababaabbbbabaaaaaaabbababbaabbbaaaabaaabbabbaaabaabbbaababbbbaabaababbaaaaabaababbabaaaabaaabbaaaaabbaaaaabbabbbbbaabaaaaaabaaaaabababbababaaabaaaabaaaabaaaaaabbbabbbbababababbabbbaabbabbabbbbbabbabaababaaabbbaabbaaababbbabaabbbaaabbbabaaababaabbaaabaabaaaaabbabbbaabaaaaaabbbbbbabaabababbaababbaaaaabbbabbbabbbaabaaabbaababbaaaaaababaaaaabaabababbbbbbaabbabbabbbbbbbabbababbbaaababaaaaabaaabbaaaaabbbbabbaabbbbabbbabababbaabababaaaaaabaaabbbbaabaabbbbbbababbbbaaaaabaabbbaabababaabbbabbbabbbaaababababbbbaabbbabaabbaaaababbbaabababaabababaabaaaabaabbabbbbabababbbaabaaabbbbbabbbaaaaaaaaabaabaaabaabbaababbbbaabbbabaabaabbbbabaaababbaaaaabbababbabbaaaababbaaaababbabbaaaaaaabbbbbbaababaaaabaabaabbabbaabbaaaaababaabbbbabbabaababaaaababbbaaaaabababbbbaababbbbabbbabaabbbaababbbabaaabaaaaabbababbaaaabbaaabbbbabaabaabbbbabbabbbaabababbbbbaaababaabbaababbbaababaabaabaababbaabbaabbaabbabbababbbbaaaabaaabbababaaabbbaaababbbabbabbbabbabbaabaaababaaaabbabbabbbbbbabbbaabaababbabaaabaaaaaabaaaaabbbbababbaaaaabbabaaabaaabaaaaaabbbbaaababbabbbbabbbabaabbbababbbaaaaaababbaababbbbabbbbababaaaaaabbaabbabbabbbbaaaaaabaaabaabbaaabaaaabaabbababbbaaaaaaabbbabbaabbaaaabbbbaababbabbbbbaabbbbbbbbbbaaabbaaabaaaababbbabbbbaabaaaabaaaabaabbabaaabbaabababaabbbbaaaabbbabaabbabbaabaabaabaabaaabbbbaaabbababaabbbbbaaabaabbaaaabbbaaabbaabaabaabaababbabbaaaaaababbaaaaaaabaaabaaaaabbbaababababbbabbbabababbaabbaabaaaaaaabbbbaababbbaabbaaabbbbbbbaababbaabbbaabbbabbbaaaaabababbabbbbabbaaababaaaaabbbbaaaabbbbbbbbbaaabbbabbbabbbbbbbabbaabaabbabbaabbbabbbabbabaabbabbabbaaaabbbbabaaaaaababbbbbbaabbbbabbbbabbaaaabbaaaabbabbbaaababbbbabbbbaabbaabbaababbbbbbababbabaaaaabbaaababbbbbbabaabbabaabaababbaaabababbbabbabbababbaabbabbaabbbabbaaaaaabababbabbbabbbbbaaabbaaababbaaaababababbababaabababaabaaabbaabbbbaabbabababbbabbabaabaabaaabaababaaaaaabbabbabbababbabbaaabaaababbaaababaaabbaabbababaababbbaabbababbaabaaaaabbaaabbababbbabaabbaaabbbaaaaabbbabbbaaaabbbbbaaaaabbbbbababaabaabbaaaabaaaababbbabbbaabbaababbaaabbabbbbbbaaaabbaabbaabaaaabaabbabaababbbaababaabaaaaaabbbbbbbbababaaabbabbaaaabbbbabbbbbbbbaaaabbbbbabbabaabbaaaaababbaababaaabbabaaababbbbaaaabababbbbaaabaabbaaababbabbaabbbabbaabababbbbbaabbabaabbbbbabaaabbbbbbbabbababaabbbaaaabbbaabaaababbaabaaaaabaabaabbbbaabbabbaaaabbaaabaaaaaabbbabbbabaabbbbaabbabbabaabbbbbbbbbbababababbaabbabbaaaabaabababbaabbabbaabbbbbbbbbbaabaababaabaaababbbbbaaabbbaaaaababaaabababbaaaaaaaaaabbbbabbbaabbbabaaabaaababaaabbaaabbbabaaabbbabababbbbabababaaabbababaaaaaabbbabaababbbaabaaabbaaababbababbbbbaabbaaabbbbbbbaaaabbaabbbbbbababbbaaababbbababababaaaababbbabbaabaabaaababbbbbbaababaaaaaabbaaabababbaabbbbababbbaabbabaabbaaaaaaababbaaaabaaabaaaaaabbaabbbabaaaabaaabbbbabaaabbabaabaabbabbabababbabbbaabaabbababaabbbbbaababbaaababbaabbabbbaabbbaabbabbabaaabbbabbabbabababbbabbabbbabbaaaababaabbabaabbababbababaaabaabaabbabbaaababbbbbbabaaaaaaaaaaaaaabababaabaabbbabbbbbbaaaaabaaaaaabababaaaaaaababababbbbbbaaaaabaabbaaaabababaababaabababaabbbabbbbaabbbbbbababbbbaabbbababababbabbaababbabaaaabbababababbabbaabbbbaababaabbbabbbbaababbbbaaaaabbbbbababbbbbabbaaabaabbbaabbbabbbababbaababbbababbbbaabbababbaabbbaaabaabaaaabbaabbabbbbababbabaabbaaabaaabbbaaabbaabaaabaaaaaababaaabaaababaababbabaaaaabbaaaabbbbbbbaaabaabbaabaaaaaabaabaaaaaaababaabbabbbabbbbaaaabbbaabababbbbaabaaaaaaabbbababababbbbbaabbbbbaaaaaaaaaaaabbababbabaaabaaaabbbbbabbbbaabbbbbbabaaaaaaaaaababababbaaaaaabbabababbaabbaaaabbaaabbbaaabbabbabbbaaabbababbaaaaaabababbabbbbbaaabbaabababbabbabbbbabaabbaabaababbaaaabbbabaabbbaaaababbbbaaaababaabbbaaabaabaaabbabbbbaaabaaabbbbbbbaaababababbaaabbbbabababababaabaababbaabbaabaaababbabbaabbbababbbabbabbbbbbbabbaabaabbbbaababbbbaaabbbbabbaabbbaabaaaababbabbbbabaaaaaabaabbbbababbabbaabbbbbababaaababababbaabaabaaabababbbaaaaaabbabbabbbababaaabbaaaababbbabbaaabaaaabababbbabaabbbaababbbbabaaaaabbaaaaaaaababbabbbbbbaaabbaabbbaaaabbaaabbaaaaaaababaaababaaaababbbabababbbabaaabaaaabbbbbababbaabaaaaaababbababbaaabbbabaabaabbaaaaabbaabbaaababbbaaabbaaabbaabbbaabbabaababbbbbbbababbbbaabbabbaabbbabbbbabbbaabaaaabaaabaabbbabbbbaaaaabbababbbbbaababaaaaaaabaaaaabababaaababbbabbabaaaababbbbbabaaabbabaabaaaabbbabaabaaabaaaabbbbaaabbababaaaabaaaabbaaaabaaabaaaabbabaabbabbaaaabaababaababbbbbbaabbbbabbaabbaaabaababbaabababbaaababbbbabbbaaaababbabaabbbaabaabbabaaabbbbabbbbaaabaaababaaabaaabbababbbababaaabbbaabbbbbbbababaabaabbabbbbabbbabbaaaabbabbbaaabababaabababbbabbabbbbbbbbbaaaabbbbbaaaaabababbbbaababbaabbaabbbbaabbabbbabaababababbabbbbabaabababababbaaabababbaabaabbbaaabaababbbbaabaaaaaaaabbaaabbabbaaaaaaabbababaabaaabaabbabaaaababbabababbabbabbababbaaaaabbaaaaababbbaabbabbbaababbababbbabbababaaabbbabbbaaaabaabbbabbaaabbababbabaaabbbabaababbbbaababaababbaaabbbbabbbbbbbbbbababbbbabbbaaaaabbbababbbbbbbabaabbabaaaababbbabaaaaabbababbbaaabbaaaababbbbbbbaaaaabababbaabaabbbabbbbbabbaaabbbbabbbaabbaaabbabbaababaabbbaaababababbbbabaaaaabbbababbabbbabbabbaabbbbbbbbbababababbbbabbbbbbaabababbabbabaaaabbbbaabaabbbbbaabbbabbaaaaabbbbabaaaaabaaaaaabbbaaabbaaababbbaaaaaaabbabaaaaaabaababaabbbbbbbbaabaabaababaabaabbbbabaaaabbabbbbbabbaaabaabaaabbbbbabbaaabbbabbbabaabbaaaaabaaabbabbaaaaaaabaabbbbbbabbabaababaabbabbabbbbbabbbbbbabbabbaaaabbaaabbbbaaabaabaaabbaabaababbaabbbaabbaabbaaababbbaababaabbbbbbaabaaababbaaabbbabaabaaabbaababbbbbbbabbbbbabbbaabbabbabbaabaaabaaabaababaaaabbaaabbaaaaaabbbbbbaaabbbaabbabbaabaaabbababbbaabbbabaabbbaababbabbaaababbbbaaabbabbbaaaaaaaabaabaabbbbbbbbabbaaababbaaabaabbaabbbbabababaaabaaaaaaababbbbbabbbbbbbaaabbbbbbaaabbbaabbbbbabababaaaabaabaaaaabbaaababababbbbabaababbbabbbabaaabbaabbbaabababaaaabbaaababababbbbbaabbaababbbaaaaababbbaabbbbaaabbabbbaaaabbaaababbbaabbaabbaaaabbbbaaabbabbbbaaaaaaaababbaabaaaabbbababbbbbbbabbaaaaabaabaaaaaaabbaabaaaaaaabaaaaaababbbbbaababbbaabaabaaaabbbaaabaababbbbabbababbababbabbbaababbbabaabbbbaababbbaaaabbabaabbbbbabaaaabaaaaabaaaaababbbababbbbabbaabaaabbaababbbbbababaaaababbbbbababbbaababababaabbbbbaababaaaabbabbababaabaabaababbbbababbbabababbabaaaabaababbbbbbbaaaababbaabbaabbabaabaabaaaaabbaabbabaaabbabbbabbaababaaaaababbbbbbabbaaaababbbbbbbbbababaabbbabaaabbbabaaaaaaababaabbaababbaaaaaabbbababbaabaaaabbaabbaaaaaaaabaababbaaaabbabbbabaaabaabaaabbabbbabababbbbababbaaaababaababaabababbabbababaaabbaaaababababaabaabbbaabaabbbaaabababbabbaabbaabaaabbbbaaabbbaaaabaabbaabbbbbaabbaaababbaababaabbaaaaabaaabbaabbbababbababababbbaabbbababbaabaabbaabababbabbbaabbbbaabaabbbbaabaaabaaaabaabbabbbaaabaabaabbaabbbbbababaababbbabbaabaabaaabaabbabbbbbaaabaabbaabbbababbbbbbaabbaaabbabaabbbbbaabaabaababbbbaabaaabbabbbbbabbbbbbbabaabbbbbabaabaaabbbaaaaaaaabaabaaabbbaaabaaaaabaaaababbbbbaaaaaaaaabababaabbaabaabbbabaabababbabbbbbbaabababaaaaababaaaaabbaaaabbaaabbbbbabbbbabbaabaaabbabaaabaabbbbaaabbaaabbaaaabaababbaaabbbbabbbabaababababbbababbbabbabbbaabaababbabaabbaabaabbbababaabaababaabbaaabbaaabbaaabbaabbaaabaaaabbabbbbbbbbababbabaabaabbabbbaaabbbaaabbbabbbaabbbabbbbababbbaabbbbbaaabbbbbbaaabbbabbbbaaabbbabbabbaabaabbbaabaabbbbaaaabbababbabaabbaababbbabaabaabaabaabababaaaabbabaaaabbbabaaabbbaaabbbbabbabbaabbbbaaabaabababababababaaabbbbababaaabababaaababbbbbaabbbbbabbaabaaaaaabbbabbaaaabbaaabaabbaaaaababaaaaabbabbbabbbaabaaabbbaaabbbaabbabbbbaaabbbbababbbbbbbababbaabaaaabbabaabaaabaabbaaabaaaabbbbaababaaabbaaabbaaaabbabaaaaaabbbbbbabaabbbbbababbabbabababaabbbbabbaaabaaaabaabbaaababbaaaababaababbabaababaabaabbabbbaabaaabaabbbbbbbaabbaabbaaaababaabbbabbabbbaaababaabbbbaabbabaababbbbaabbaaaaabababaaaabbabababbaabbbaaaabbbbbabbabbabbaabbbbbababbaaaaaaababaabbabbabbaabbaabbbaabaaababbbaaabaabaaabababaabbaabbabbbabbbbbbabbaabbbbbbababaababbbaaababbbaabaabbbaabaaaaababaabaababaababbbabbabbbbabbaaabaabbababbbbbbaaaabbaaabaabbaaababbabbbbbabbaababaabbabbbaabaaabaabaabbbbbbaabbbaaaababbbaaabbbaaaaabbaababbbababaaabaaaaabaaabbabbabbababaabababbababbbbababbbbaaabaababbbbabaabaababababbbaabbbbbaaabbbbababababbabbbbaabaababaabbbbaabbabbaabbbbbaaababbbaababbbbbbbbbaabaabbaaabaaaabaabababbbabaabaabbababbaaabbbbabaabbbbbbaabbaaabababbbbabbaababbbabaabbbabbabbbbbbbbaabbababbbaaaaaaaabbbaabaabbabaabaabababbbbaaabaabbabbaaaaababbaaaabbabbaabbaabbaaaababbabbbaaabbbbabbababbabaabaaaaabaabbabbbaabaaababbaaaaabbbbaabaaaaaabaabbbbaabaaabbbaabbaaabaabbaaaaaaabbbaaaababaabbaabaaabababaabbbbbabbbbbababbbbbaababbbbbaabaaabbaababbbbaabbbbbabbaaaabbabababbbabaaabbbabaaababbaaaaabbabababaaabbaaaaabbabaabaabaaabbabbaabbbaaabbbaaababbbaaaabbbaababaabbababbabbabaabbbabbabbaababbabbabaaaababbabaabababaaaabaaabbbaaaababaaababbabaabaaaaabaababbabbaababbabbbabaaaabbbaabaabbbabbaababbaaabbbbabbbbaabbabaababbbbbaaabaababbababbababbabbbbababbaaabaaaaaabbbaabbaabbaabbababaabbbabbaaabbbabaaaaababbbbaababbbbaaaaabbabaabaaabbabbaaabbabababaaaaabbbaaababbaaabbbabbbbbabaaaaababbaababbabbbbabbbbababaabababbbbaaaaabbaababbbaaaabbbbababaaaababbabbabaaabbaabbababbbbaaaaababaabbaaababbbaabaaaababaaaaaaababbbbaaaaaabbbaababbabaabababbabababbabbaabababbaaabaabbbbbbbbababaaaaabbbaaabbaabbbbbaabaababababbbaaaaababbbbaabbabababbababaababbbbbabbbbbbbabbbbaabbbbabbabbbaaaabbabbabbaabbabababbbaaabbbbbbabaabbbbabbbbbbaaabaaaabaaabaabaaabaaaababbbbbbbbabaabaabaababbbbbaaabbbbaabaaabaabbaabaaaaabaaaaabaaabbbbbbaaaaabaaabaaaabaaabbbbbaaaaabaabaabbabaabababbabaabaabbaabbabbaababbababbaabaaabaaaaaabaaabbbaaaabbbaabbbaaaabaabaaaaabbaaaaaaababbbbaababbaaabaaabaabbbababbbbaababbababbbbbbbabaabbaaaaaabaaaabaaabbbbaababbbbbbbbbababbaabaaabbababaabaaabaaaabbabbaaabbbaaaabbbbaabbaaababbabbaababbaaaabbbababbbbbabaaabbaaabbbbbbabbaabbabbbbaaabbabaabbabaaabbbabbbaaabaabababbabbababaaabaabaabaababbaaaabbaaabbbbaabaaabbbabaaaaaaaabbabaabbbabbbaaabababbbabbbabaabbaaabbbbbabbaabbaabbaaabbbbbbabbbbabaabbabaaabbabbabbbaababbabbaaaabbbbaaabaabaabbababaabaabbaaabaabaaaabaaabbababbbbaaabaababbaabbababbabbbbaabaabbbabbaaaaabbbaaabaabababaaaaaaaaaabbababbaaababbbaaaaabababbbbababbbbabaaaabbabbabbbbaaaaabbaaaababbbbaaabbbabababbbaaabbabbbbaaaaaababababbaababbabbaababaabbbbabababbbbbabaabbbaaaabbaaabbbababbaaaababbaabaabababbbbabbbbbaabaaaababaaabbbaaaabbabaaabbaabbaabaaabaaaabbbababbbaaababbbabaababaaabbaaabaabbbaaabbabbaabbbbbbaaaaaaaaababbbabaaaabbabbaaaabbaaabaabbbbaaabaaaabaaaaabaabaaabbbababaaabababaabaaabbabbabaabbaabbbaabaabbabbabbaaabaaabbaabaabbabbbabaabbbbbaaabababbbabbbabbababaabaabbaaaabababbabbabbbbbbbbbbaababaaaabababaabbbabbbbbbaaabaaaaabbabababaabaaababaabbbabaabbaabbaaabbbbaaabaabbabababbaaabbbaabbaabbababaabababbababaabaaaaabbbbbaaaaaababbabababbbbabaaabababaabbaabaaabaabbabbaaabbbbbababbbbbabbaabbbbaabaaabbbbbaababbbbaaabaaabababbbbbaabaaaabbaabbbabaaaaaababbbbbabababaaabbabbababbbbaaabababbbbababbabbbbbbaabbaabbaaabbbabaabbabaaaaabaaabbaaaaabaabbababbbbaabbbabbabaabaaaaabaaaabbababbaaaababbbaaaaabbababaabbaaabbabbaababaaaaaaaaaaaabbabaaaaabbbaaababababbbababbababbaabbbbababbbabaaababbbbbaababbbbababababbbbababaaaabbbabbaaababbabaabbbaabaaabbaabbbbbbbabababbaaabbabbabababbbbaaabababbbababbbbabaabbaaabaabaabbabaabbaabbbaabbababbabbababbaabaabaababbaabbbbbaabbbababbbbbbaaaababbaaaaabbbabaabbababbaabaababbbbaabbaabbaaabababbbabbbbbaabaabaaabbaabbabaabaaaabbabaaaabbabbbbaaaaaabaaaabbabbbabbaabbababababbabbabaaaaaaaabaaaaaaabbabaabaabbababbaaaaaaabaabbbbbaababaaababbabbabbbabababababbbaaabbbaabaaaabbbbbaaabbaabaabbbababbababaaabbaaaababaaabababbabbbbbaaababababbaabbbaaababbbbbabaabaaaababbabbababababbbbababababbbbbaaaaaaababaabbbaaabaabababbaaaaabbaabbbaabaaaabaaaabbaababaabbabaababbbbbabaaabbbaaaaabbaababaaabaabbbbbbbabaabbbbbbbbaabaabbbaababbaabbbbbbbabbaaabaabaababaababaabaaaaabbabaaabbbbbbababaaababaabbbabaabbbaaaabbbaaabbabaaaaaababbbbaaabbbabaaaabbababbbbaabaabbbbbabaaabbbaaabaababaaabaaabbbbaabaabbabaabbbbbbabbaaababaaabababaabbabaaabbbbbbabbbaabbbabbaabbababaaabbbaabbabaabaaabbaaabbababbaaaaaaaababbbaabaabbaabbbaabbbbabbaabbababbaabaabbbaaaaaababbbbbabbabbbbbabbababaabbbabbaaabbbaabbbbbabaabbaababbbaaabababaaabaabababbbbbbbbabbbbbbabaabaaaaababbabbaaaaabbbaaaaabaabaabbbaabbbabbabbaabaababbbaaaaaababaaaabaaabbababbaabbababaaabbababbabaabbbabbabaababbaabbaabababaaabbaabababbaaaababbbabbbbabbbbbbbbbbbbaababbaaabaabaaabaabbbbbababbbbababbabbbaabbaababbaaabaaaaaaaaaabbabaabaaabaaabbbababbaaaababbbaaaaaabaaabaaaaaabababbbbbbbababbbbbabbbabbbabababbabbbaabaabaabbabaaaaabaaabaababbaababaaabaaababbabaaaabbabaaaabbbbbbbbbaaababbbbbabbaabbaaaababbbbbbaaabaabbbabaabaabaabbbabbbababaababbbabbabaabbabaaabbaabaabbabaaaababbabaabbbabbbbbbabaabbbababbaaabbabbaaababbaaabaaaaaabaabbababbbbabaaaaabaabaababbabbabaabaaabbbbbbbbbbbaabbaabbbabaaaaabbababbbabbabaabbbaaaababbaaababbabbababaaabbabaabbabbaaabbabbbbbbababbbbbbbaababaabaaaaaabbaaaabbbbaaaaaabbbbabaaabbbbbbaabbbabababaaabababbbbaabbbbbababbabaaabaabbbababbabbbaabbbaaaaaaabaaababbbbabbbababbabbababaabbaaabbababbbaabbabaabababbbabbbbabbabbababaabaabaabbbaabbbababbaaabbbababbbbbbbbaabaaaabaaabbbabbbbaaababababaaaababaaabbbabbaaababababaaabbbababbbababbaabababbbbabbbaaaaaaaabbbbbaaababbbbabababababaaaaabaaabaaaaaaabababbaaabababbaaaaabbabbababbbaababaaabbababbaabaabababbabbaaaabbbbaabbbbbaabbabbabaaaababaaaaabbaababbbaaababbbbbabbbaaabaabaaabbabbabbababbaaaaaaabbbaaabbbaaabbbaaabbabbbbbbbbabbbabbbaaabaabbaabaababbaaabbaabababbbbbbbbaaababbabbbbbbaaaaaaaabbaabbababbaabbaaaabaaaaabbaaaaababbbbabbbaaaaaabbaababaabaabababaabbbbaabbbaaaabaaaababbbbababbabbaababaabaabbbabbbaabababaabbaaaaaaaaabbababababaabababababbbaaabbaaabbaaabbbbaaaabababbababbbabbabbbaabbabbabbbaabbaaabbabbbaabaababbaabaaabaaababbabaabaabbabbabbaabbaabbbbbbabbbbabaaabaababaaababbaaaabbbbbbbbabbabaabaaabbbbaaabaabaabbabababbaabababbababbabaababbbbaaaaaaaaababbabbabbbabaababbbabbbbaababaaaababbaabbbababb
ababaabbbbaabbbabbaabbbbabaaababbbbababbbbabbbbabaabbabbbababaabbbbaabbbbbbbabbbbbaababbabbbabaaababbbaaaaabababaaabbbbabaabbababbabbaabaabaabababbbaaababbababaaaababaaaaabbaabbabbaabaabaaaaabaabbaaababbabaaaabaaababaababbbaaabbabbbaababaaaabbaaabbabbbaaabbbababbabababbaabbabbbbababbabbabbbbaabbaaababbabaabaababbabbbbbbbaababaaaaaaaaaaaaabaaaabbaaabbaabbaaabbabaaaaaababbbbabbbabbbbbaabbaabbbbabababaaabbaaabababbbbbbbaaaaababaabbbaaaaaaabbbbbabaaababbbabbbbbbaaaababbaabaabbabababbaaaaaabaabaaabbbabbaabababbbababbaababbbabbbaabbaabbaababaababbaaaaabaabbababbbaabbaaabbaabbbabbaaabbbaaabaaaabaabbbbabbbabbabababbbaabbbbbbbbbaaaaababbabaababbaabababbbbabbabaaababaabbaaabaabbaaabbbaaababbbbaaabababbaaabbaabbabbbaaabaaabaaaababaabaababbbbbbabaabbaaabbbbbbabbaaabaabbbbaaabbbababbbabababbabaabbabbabaababbabaabbabbbaaababababaaaaaababbbabbbbaabbababbabbbbaabaababbaabbaabaaabaabababaaabbabaabbbbabbbbaaaabbaaabbabbabababbabbbbbbaabbabaabaababaaabbbbbbabbbbabbbaaabbaaaabaabbbbabbabaaaaaabbaabababbaaabbaaaaabbaaaaaababbbaabbabbabbaaabababaaaaabbaaaababaaaaaabbbabaabbabaaabaabbababbaaaaabaabbbbbbbbabbbbbabbbabbabbaaabbbaababbbbbaaaabbaabaabbaaabbaababbbaabbbbbbaabbbaaabaaaababbbbbaababbbaaabaababaabbbaaabbbabbabbaabbaaaaaabbaaaaaabbbaaabbbabbabaabaaabababaaabaabbbbbaaaaaababbbabaabbabaaaabaabbaaabbbabbaaaababaabbabbbabaaaaaaaaaaaaabaaabaabaabbbaabbababaaaaaaaababaababbbbabaaabaaaaaababbbbbabaababbbabaabbbaabbbaabaababbaaaabaabbaaabbbaaaababaaaaabbbaabbbbaabbbbbabbaaabaababababbaabababbbaaaabaabbbaaabaababbaaabaabbbbabaababbbabaabbabaaaabaaabaabaabbaabaabbaaabaabbbbababbababbbabbabbabaaaabbbaaaaaabaaababbbaabbbbaaaabaaaababbbaaabbbabbaababababbbbaaaabaaabbabaabbbbababababaaaabaabbbbbaaaabbbbaaaabbababaabababbbaababaabababaaaaaaaabaabbbabbaabbbbbaaaabbbbaabababaaaabaababababbababaabaababaaaaaaaabbabbbbbaaababbbbaababbaaababaabbaabaaaaabaabbaabbbbabbabbbbaababbaaaababbbbbabaaaababaaaabbbabaabaaababbbabbbbaaabbbbbbbabbbbaabbbbbaaabbabaababaabaaabbababbbababbbbabababbababaabbabaabbabababbababaabbaaabbabbabbaabbbaaabaaaaabbbaaaaabaaababbabaaaaabaabaaabbaaabaababaabaaaaabbbbbbaabbaaaaabaababaaabbbaaaaaaababbbbbbabbbbababaaabbbaaaaaaaaababbbbababbbaabbbabbbbaaabaababaaabaaaabababaaabaaabbbbaaabababbbbaabbbaabaaababbbabbabaabaaaaaaababbaabaaaabaaaaaaabaabaaabaabbabaabbbabbaaababbababaabaabbabbbabbaaaaabbbaabbababbabbaabababababbbbaabbababbabbbabbaaabaabbbbabbbbbbaaabaaaabbaabbbbaabbabaabaabaabbaabbbaaaabbbaabbabbbbbbbbaaaabaaababbbabbbbabbbbbbaabbaaaaababaababaaababaaaaabaabbaaaaaabaaaabbaababbaababbaabbababbbbabbbbaaaaaaababbbabbbbaaaababbabbbaabbbababaabbbbbaabbabaaabbabaababaababaaaabbbbbbbbaaaaabaabaaabbbbaabaaaabaabbbbbbababbaaabbaabaaaabbaaabaaabababaaaaabbababaaabaabaaaaabbaaaaaaabbabbbbbaabbaabbabababaaaaaabaabaabbaababbababbbbabbbbbaaaaabbbaaababbabababababbbaabbbbaaaaabababbabbaabaabbaabbaaaaaaabbbaabaaabaabbabababaaabbbbbaabbaabaabbbabbbaabababbaabababbbbbabbbbbaabbabaaabbbbbabababbaaaababaaabbbbaaabbaabbbbabababbabbaabbaaababbabbaaababbabbabaabbabaaabaabbabababababaababbbbbabbaaaaabbababaaaaababaaaaaaaaaaaabaabaaababbabbabbaabaaaaaabbbaabababaabaababbbbbabbbbababbabaabbabbabbabbaabbbabababaabbaaaabbabaaabaabbbbbaabaaaaabbabbabbbabaabababbababbabbababaaaaaaaabaabbbbabababbbbabbaaabbbbabaaaabbabbbababbabaabaaababaababaabaaaababaaaaababbbbababababbaaababbbbabaabbbaaaaaabbbababbaaaaabbabaaabaaababbaabbaabbaaaaabbabbaaabaaaaabaabbbaabaaaaaabababbbaaabbbaaabaabbababbaabaaabaabbaaaabaaaaababbabbbbabbaaabbbbabaaabababbbbababbbaabaaaaabbbabababababaaabaabbababababbbaaabbaaabaaabbaaabbaaabaababaaaaabaaaaaaabaaaababababbabaaabaaaabaaaabbbbaaaababbbabaaaaabbbaabbbaaaababbaaaabaaabaaabbbbaabaaabbbaababababbababaababbbaaabbbabbaabbbababbababbbbabaabbabbabbaaabaaaaaaaabbbbbaabbbbbbbaaababaaaabbaaabaaaaaabbaabbabbbbabababbaabbbbabbbaaaabbabbbaabbabbaaaababbabbabbabaaabaabbaaaaaaabbaaabbbbbaabaaaabababaaaabbbabaabaabaaaaaaaabbabababbbaaabaaaaabbabbbbaaabaabbbabbaabbbaaabbaaababbaabbabbbbaaabaaabaabbbbabbaaaabbaabaabaabbbbabababbaabaaaaababbbabbaabbababbaabaaabbababbbabbbbbbbbbaababbbbbabaaababbbbbaaaabbbabaaabaabaaaaababaaabbababbbaabbaaaaaabbabaabbbabbaaaaababaaaabaababaaabbabbabbabbaabaababbaaababbaababbabaaaabbbabaaaaababbbabbaabaabbabbbabbaabbaabbabbaaaaabbaaaabaaaabbaababaababbbabbaaabbbbabaabbbbbbbbbbbabbaabaabbbaaabaaababbbabbbbbaabbbbaabaabaababaaabbbbbabaababbbaaabbbaababaaaaababbbbababaabbbbbabbabbbaabbbbabbbbbabbaabaaabaababaaaaabaaababaabbbabaaaaaabbaababaabababbaabbaaaaaabbbbbaabaabbabbaaaabaabaaababaaabaabbbaabaaaabaaabbaaababbababbabaabaaaaaabbabababaabbabaabaabbbbbabbbaaababaaabbbaaabbbaabbabaabbbbbbabbbbabaababaabbaabbaabababbbbaabaaababaababaabbbbabbbbaaababbababbaabbbbbabababaababbabaabbaabbaaababaabbabbaabbbbbbabbaaabaababbbbabaaababbaaaabbababbaaaaabbaaaabbaaaabaabbabbbaaabaabbbbbbbaaaabaabbaabbabababbababaabbbaaaaaaaaaaaaabaaabababbbbbababbbbaabaaaababbabaabbabbbbabbabaabbbaabbbbabaaabaaaabaaaaabaaabbbabaaaabbaaaabbbbabbbaababbabbaababababbabbbbbababbbaabaaabbbaababbaaabbabbbababababbbabaaaaabaabaabababaaaaabbabbbaaabbbabbbaaaababbbaabbaaaabaaaaaaaaaababbbbbbbbabaabbbaababaabbabbbababaaaabbbabababaaabbbbabaaaaabababbaaabaaaabababaaabbbbbababbabbbbbbbababaabbaababaabbbbabbbbbbabbaaaaaabaababaababbaabaaabbbabbaabbaabababaaabaaaabbbbbabbbbaaabbbabbbbbabaabaabbbbbaaababbaabbaaabbabbabbbbababbbbaababaabaabbaababaabaaaaaabaababbaaabaabababbaabbbbaaaaababbaabbbabbbabaabaabaababaabaabbababaaabbbabbabaabbaabbbbabaabbaabbbbbaaabbbaabbabaaabbbbaabaababbabbabaaabbaaaabbbababaabbbababbabaaaaabbbaaabaabababaababababaababbbbbababaaababaabbbbabababbbbaabbaaaaabaaababbbaabbbaababaaabbbaabbabbabbaaaabbaaaaaaaabbabbabaaaabbabbaabaabaaaaaaaaabbbbaaabbbaaaaaaabbbaaabaabbbbbbbaababbabaaababaaaabbaabbaababbaabaaaaaabaabbababaaaaabababaaabaaabaaaaababbbbbbbabbbbabababbabaabaaaaaabbbaaabbaabbaaabbaaaaabaaabbabbbaabbbbaabbabaaababaababbbbaaabaaabababaabaabbababaababababababbabbbbbaabaababbbbbababbbabbabaabbbbbbbaaaaaaaaaabaaaaaabaabbabbabbbbabaababbbabaaaabbbaaabaaabbaaaaabaabaabbbbbabaaaaaabababaaaabaaaaababaaaabbbbabaaaabbabbaaabaabbabaabbbbabbaaabbbabbbbaaabbaaaabbabaababbaabbbaaabbaaabababaaaabbbaababbaaaaaaaababbbbbbbbabaaabaabbabaabbaabbabbbbaaaaabaabbaabbababbaabaabbbbaabbbbabbbbbbbababababaaaaaabaaaaaaaabbbbbabbaaaababbbaaaaabbabbaaababbabbbaababbbabbbababababaabaababbaaabbaabaabaaaabbbabbaabbaaababababbbbbabaaaaabaababbabbaababbaababbbabaaabbaabbbaaababaabaabababaaaaaabbbbbabbabbbaaaabbabbaaababbbbbabbabbabbababbaaababababbbbaabbaaabbaabaabbaaaabbbaaaabbbbaaaaabbbbbbbaabababbbbaaabbbabbaaabaabbabbbabababbbbababbababbbabbbbabaabbabababaabaabaabbaababaabaabbababbababbbbbbbababbbbababababbbbbaaaabbbbbbaabaabbaaaabaaaaabababaaaaabbbaaaaababbbabbaababbabbbaabbabbbaaabaabbbabbaabababbabbaaabbaabababaaabaabbbabbbaaaababbbbaabbbaaaabaabbabbbbabbabbbbabbbbabaababbbaaaaabbbabbbababaaaaaaabaaaaaaababbbaaaaababbbabbabaababbabbaaabababbaaabbabaabbabaaaaabaaaabaabbbbbaababbbababbabbbabaaababaaabbbbbaaaabbbbbbbbabbaaaaaaaababaabbbabbabbbbaabbbaabbbabbbbaabbaaaabaabbbaaaabbbabbbabbbbbababaabababbabababbabaabaabbbbbbaabbabbaaabbaabbbbabbaabbabbbaaababbaaabbbaabbaabaabababbabbbaabbbaabbaaaabababbaababaaaaabbababbbaaaaaaababaaabababaabaaaababbaababaabbaaabbabaabaabaabbaaabaaabbaababababbbabbaabbabbabaabababbbbbbabbbaaabaaabaabbbaaabbbbabbaaaaababaaaabaaaaaaaabbbbbbbaabbaaaaabbababababaabaabbabbaabaaabaaaabaababaaaaaaabbababbaaaaaaabbbabbbaabbabbbaaaaaaabaabbabbabbbbbabbabaaabbbaaabababbbaaabbaaabbbbbbaababaabbabaaabaababbabbbaaaababaaabbbbbbababaabbabbbbbabbabbbababbaaabbaabaabbbabaabbbbaaabbbbabababaabbabaaabbbabaaaaababbbbbbabbbbababbbababababababbabbabbaaaabaaabaababbbbbabbbaabaaababaabbababbabbbabaaaabbabbbaaaaaabbbaaaaabbabbaabbbbababaabbbbabababbbabbabbbbbbabababaaaaabaaabbbbabbabbabaaabaaaabbbbabbaaaaabaaabbbbabaabaaaabaaabbbababbbaaaaabaabbbbabbabababbaabaabbabababbbaaaabababbbabababaaaaaabbbbbbbbaababaaaaabbbaaaabaaaaaaabbbbaabbbbaaaaabbbaabbaaabbaabbbabbbaaababbaaabbabbbaabbbbaabbaaabaaaabaaaaaababaaabbbbbbaaabbbbbbbaaaaaaabbbaababababaaaaabbbaaaabbabaabbbaaaabaabbabbbbababbbaabbabbaababbaababbaabbbaabbbbabbabbababababbababbaaababbbbaabaabbbabbbabbaaabbaaabababbbbababbaabbbbabaabbbbbabbbbaaaabbaabbababaaaaaabaabaabababaaabbbaaaabaaabbabaaaababbbabbbaabaabbbaababaabaabbababbabbabbbbabaaabbabbbbbaaabaaaaaabaabbaababbbbaabaaaababbaabbabbabbabaabaaaabbbbbabbaaabbaabbaabbabaabaaaabaaabbaaaabbbbbaaabaabbaabbbbaabbbaaaaaaaabababbbbaaaaaababbbaaaaaababbaabaababbabbaabbaaabaabbbaaaaaaabbabaaabaabababbaaaabbaabbabbbbbabbaaababbbbabbbbbbababaaaaaabaabaabaabaababbbabaaabaabaaaaaaababababbbaababaabbaabbbabbbaaaababaaaababaaabbbbbabbbabaaabbbabbababbaabaabaababbaaaabaabbabaabbbbaabbaaabababbabbaabbabbabbbbbabbaababbaaabbbababababbaabbabaaabbbabaabbaabbbbabbbbbabbbbbabbbaabababaabbaabbbbabbbababbbbabbabaaabaaaabaaaaaaaabbbaaaabbabbaabbaabaabbaababbababbbaaabaaaabaaababaaabbbababbbaabbabbaabababbaaaaaaaaababbbbbabbbbaaaababaaabbbababababbbabaababbbbababbbbbbbbbbababababaabbabaabbaabbbaaaabaaabbabbaaaaabababbabababbbabbabbbaaaaaabaaaabbababbabaaababbbabbbbababaaaabbbabbbaaabbbbbabaabaaaaabaaabaabbbbbabbaaababbbaabbaaaaaabaabbbbaabaaababbabaabababbababbabbabbabbbbbbbbaaaaabaaabbbbaababbbabbbbbbabbbabababbaaabbabbbabbbbbabbaaaabbabbbaaaaabababbbaaaabbabaaaaabbabaabaabbaaabbababbaababaabbbaaabaaaabbbabbabbbaabababbaaaabbbbbbbaaaababbbaaaabababababaaabaaaaaaaabaaabaaabbbbbabbbbbabbbbabbbaabbaabbbbabaabbaaaabbbababbabbabbbabbabbbabbaaabbaabbaabbbbaaabaaaaaabbaababbbababbbbaaabbbbbbabbbbbabbaababaabbbabaaaaaabbbbbbaabababaabaaabaaabaabbaababbaabaaaabaaaaaaaaabbbbbaaababbabbbaaaaaabbbbabaabbabbabaaaabaaaabbabbbbbabbabbbbababbbaabbbabbaaabaabbbabaaabbbaabbbbaaabbbbbaabaabbbbbbbbbaabaaaaaabaabbabbabaaaabbaabbabaaababaaabbabbbbabbbaaabbababbaaaabbbabbabababaabbbabbbbabbbbaabbbabababbbaaaaaabbbaabaaaabbabaaababaabbaaabbaabaabababababbabbbbbbabaaabbbbbaabaaabaaabaaaabababbaababbabaaaaabbaaaabaabaaaaabaaabaabbbaaaaabaaaaaaaaabbbaababbbaaabbbbbabaaaaabaaababaabaababaababaabbbbabbbbabbaabaababaabbabaabbaabbabbbbaaabbbbbaaabbabaabbaabbaabbbababbbbbaabbbaaaabaababababbbaabbabaaaabbabaabbbbaaaaabaaabaaaaabaabbabbaabaaabbbbaaababbaabbaaaaabbbbbababbabbabaaabaaaaabbabababbaabbaaababaaabaaaabbabbbababbbaaababbaaabbaaabbbbaaaabaaaabbababbaabbabaaabaabbababbbbbabaaabbaaabaaabaabaabaabaabababbbbbbabaaaaaabaabaaabaabbbaaababbbbaaabaaabbbbabaabaaaabbbaaababbbaaaabbaaabbaaaabbbbabbaaabbaaaaababbbaabaaaabbbaaaabaabbabaabbbbbabbabaaabbaabbbaabbaaaaaaaaaaabaaaabbaabbbbaabbbaaaaaaabababbbababaaabababaaabbaabaabbaabaabaabbaaaabaabbaaaaababaaaababaababbaabbaababaabababaaaaabbababbbbaaabbbaabaaaaaabbaababaaababaabbbaaaaabbbabaabababbabbbaaaaaabbaaabaaaaaaababaaaabaaabbaabbbabaaabaabbaaabaabbabaaababaabbbabbbbaaaaabbababaaabaabbabbbaaababbbabbbbbbabaabaabaaabaaaaabbabbbbbbaaabaabbbaabaabbbaaabaabababbaaababbababbbaabaabbaababbaabbaababbaabbbababbbbbaaaaaabbbbbaaababbaabaabbabaaabbabbbbbaabbaababababbabbabaabbbaaababaaaaabaabaaababbbaabbaabaababbabbabbbbbbaaabababbbabababbaabbabbaabbbbabbbababbabbabbabababbabbaaabbaabbaaaabbabaaaaaaaaaaabbbaabaaabbaaabaabaabbbaaaabaaabbabaaabbbababbaaaabbbaabbbabbaaaababaaaaabbbabaababbbaaabaaaaabaabbbaabaaabababbabbbbbabbabbbbaaababbbbbbbbbbbaaaabaabbababbabbbabbbaababbbbbbbaababaaaaaabbaabbbbbabaaaabaabbabaabbbaaabbbabaaaaaaababbaabbabaababaabaabbbbaabbbabbbbbbbbaabbababbaaaabbababbaaaabaaaaabbaaababbbababbabbbababbbbbbbababbbbbabbbaaabbbabbaaaabbbbabababaabaaabbabbbbaaabbaaaabbbaaaaabaaabaaabaabaaaaabbabbbaabaaaabaababbaaaaababbbababaabbabababaababbabbabbaaabbbbbbbaabbbaaababbabbbbbababaaabbbaabbbbabababbabbaabbabbbbbbababbbbbaabbabababaabbabbaaabbbbaaaaabbaabbaaabbababbbaabbbaabaabbbaabbbbbabbaaabaabbabbbbababbaabbabbaaaaaabaabaaabbbaabaabaababbaabbababaabbbababbaabaabaababaabbbbaaabbaabbbbbabbbaabbabaaabababbabbaabbabaababbaabbbaabbbaabaabbbbbbabbaabbbaababaaaabbbbbaaaabbabaaabbaabbbbbbaababbbbbbbabbabbabbaabbbaabaababbaaababbabbbbbaaaaaabbabbabbbbababbabbababaaabbaaaaabaabbbbaabbbabababbaaaabbaabbaabbababbbbbbbbbbaaabbbabbaabbabaaaababaaabbaaaabbababbaaaabaaaaabbaabbbaaababaabbbbabbbabbbabaababbbabbbbaabaaaabaabbabaabaabbbaababbbbaaabaaabbbababbaabaababaababaabaaabbabbbabababaabaaaaabbbbbbaabbaabbbbabbbbbbaaaaabbbbaaaabaaaababaaabbabaaaaabbaabaaaababbbbbabbaaaaababbbabababbbbbaaabaabbaaaaaabbabbaaaabbabaaabaaaaabababababbababababaaabababbbbbaabaabbaabaabbaaaaaabbaababbbaabbbaaabaaabbabbbabaabaaababbbabbbbbabaabbababaaabbabbbbbababbaaaaabbabbbabaabbabbbbbaabaabbaabbababbbbbaabababbaabababbbabaabbbbbbbbbbaaabbbaabbaabbbbaabbbbbaaaababbbabaaaabaabbabbbaabbbbabbabbababbbaaabaabbabbbababbbbabababababbaabbbbbbbbbbaababbbbaababbbabbabbbbaababaaabbbabaabbbaaaabaabbaababababababbbaaabbbaabaababaabbababababbbabbaaabbabababbbabaabaabaabbababaaabbbbababbaaabbbaabaababbbabaababbbaaaababbaabbbaabbaabbaababbabbabaabababbaaabaaaababaaababababbbbbbababbbbbbbabbbbaaaabaabbbaaaaaaaababbaaaaabbbbaabbbbbbbbbbaaaabbabbbaabbabababbaaabbaaababbabbaabbabbbabbbaaaaaaabbbbbabaabababbabbbaaabababaabbbabbbabaaabaabbbabbabbbbaaaababbbbbabaaaaabaaabaabaabbbbaaabaaababbbaaaababbbbbbbaaaabaababababaaabbbbbabbaabaaabaababbbabbaabbaabaabbaabbbaabbbaabbbabbaabbbbbaabbaaaabaabbabbaaaabbbbababbbabbaaabbbabbaaaaabbbabbbabaabbaabaaabaaaaaababbbbbbbbaabaabbbabbbbaabbbaaaaababbbaaabbbbbababbabbaaaaabbaababaaaabaaababbaabaabbbaaaababaababbbbbaaaaaaaababaabbbbbaabbabbbaaabbabbaababbaabababbaabbbbabbbbabbabbababbabaababaababbbbbbbabaaababbaaaaabaabbaaabbaabbbabbabbbabaabbabaaabbbbaabbababbbbaababaaaabbabbbaaabaaaaabbbaabbabaaabaaaabaaabababbbabbbabbaaabbbabaaaaaabaaaaaabbabbbabababaababbabbbbbbaaabbaaaabbbaaaaabbbaabbbabababaaaaaabbaabbabaaaabaabbaababbbabbaabbaaabaabaaabbaaabbabbaababbaabbbbabbabababbbaabbaaaaaaaaaaaabbbaababaaababbaaaaaaaaabbababaaabbbbabaabbaaabbabbbbabaaabbaaabbaaaaabaabbbbbaababaaaabaaaabbaaaaaababbbbabbbbaabbaaababbbbbaabaaabaaaabaabbaababaaaabbaaababaaaaabbbbaababbbbbbbbaaabaaaaabbbababbbbababbbbaaababbbabababaaaaabbbaabbaababbaabbbbaaabbbbaababbbbbaaabaaaaaababbbbbabaaaaabaabbababaaabbabbbaaaaabbbbbbabbababaabbabbaababbbabbabaaaaaaaabaabbbbaaaaaabbbbbbabbababaaababaaabbaaaaaaabaabbaababbaaaabbaabbbbabbaaaabababaabaaaabbbbbbabaabbabaaaababaabbbbabbaaaabbaaabbababbaaababaabbbbababbaabbbbabaabaaaaabbbbaabaaabbabbbaaabbbaaaabbbbabbabababaaaabaabbaabbbbababababbaaaaaabaabbababbbbbbbaaaaaabaaaaabbabaaabbbabbaaaabbbbbaaaabbabbbaaaabaabaabbaaaaaabbbbbaabbabaababaabaabbaabaaaaaaaaabbbbbbabbabababbabbbabaaabbabababbaaabaaaababaaaabaabababaaabbbabbbbabbaabaababbbbaababbabbaabaaaaabbbbbaaabbabaabaabaaaaabaaaaabaaaabaaabaaaabbabbbaabaaaabaaababbaaababaabaabababaaabaaaababaaaaabbbaaaabbaaabbbbabbbabbaaabbaaabaabbbabbbababaaaaaabbabbabbbabaaaaaabbbbbabbabbaaaaaaaabbbbaabaabbbaabbbbbbabaabababbabbbaabaaabaaaabbabbaabbaabbbbbaaabbbbbaaaaabaaababababababbaaabbaabbbababbbbbbbababbaabbaabaaabbbbaababbabbbaaabaabaaabbbbabaaabaaabbaabbabbabbaabbaaaaaaaabaaabaababbbabbaababbbababbaabaaababbababaabbabbaaabbbbababbabaaaabaabbbaabaabbbabaaaaabaaaababaabaabbbbbaabbbbbaaaabbbbbbbaabaabaaaaababbaaaaabbabababaababbbbbbababaabbbaabaaabbababaaabbbbaaaaaababaaaaababbabababbbbbbabbabaabbbbbaabaaaabbbaabaaabbbbaabbaaabbbbabbaabaaababaabaabbbbababaaaaabaaabaaababbaaaababbbbaabbabaaababbababbabbababbbbbaabbbbaabababaaaabbbbaabaaabababababbaaababbabbbbbbaaabbaabaabaababbababaaaabaababaabbaabbbabbabbbbbbaaaaaabaababbbbbbaabbbbabbabaaabaababbabbaaabababaaaabbbabbbabaaabbbbababaabbaabbaabbabbabbbbaabaaaabbaababbababbaabbbbbbabaaaaabbbbbbbbbbbbbaabbabbbbbbbaaaabbbbbbaaabaababaaaaaaaaaababbababbbaabbbaabbbbbaabbaaaabbaabbabaabbbabbaabbbbbaabbbbbababbbaabbabbbbbbabaaaabbbaabaabaabbababbbbbbabbababbabbbaabbbbbbbbbaaabbabaabaababbbaaaaababaababbababbbaaabaabaabaaabbbbbbaabbaabaaaabbabaabbbbaabbababababaaabaaababbabaaababbabbbababbaaabaaabbababbbaabaabaaaababbaaaaaaaabbabbababaababbaaaabaaabaaabbbabbbbbabbababbabbbababbabbbaaabbbbbaabaaaabbbabbbaabbaabbaaabaabbabaabaabaabaaabbbbbaabaaaaabababaaaaababaabbaababbbbababaababbbaaabbbaaabbbaaabbbbbaaaaabaababaabbaabbbaabaaababbbbababbbbaaabbaababbbababbbbbbabababbabaabbabaabbbbbaaaaaabaaaabbabaaaababbabaaabaaaabbaababababbabbababababbaaabaaaaabbbbbaabbbaabbabaabbaabaaaaabbbababaabaaabbaabbaaaababbaaaaabbbaaababbbbaabbbabbabbaaabbbbabaaaaaaaabababbabbbbaabbabaaaaaaaaaaabaabbbabbabbaababbaaababbababbbbaabbbbbaaabbbbbaaaaaaaaabaaabbabaaabbbbbbbbbbbaababbaaaaababaabbbaababbbaaaaaabbbabaaababaaaaababbbbabbababababbaababbabbbbbabbaaaabbabbababababbbaaaabbbabaaabaaaaaabbaaaabbaabbbaaabababbbbbbaaabbababbaaaabbaaabbbbaaaaaaaabbbbbaaabbababbababaaabbbbbbbbaababbbbbaabaaabbbbaabbababbbabbbbbbaaaabbbbaaaaaaaaabbabbabaaaaabbaabbababaabbbabbbbbbbaaaabaaaabbbabbbbbbaaaaaaaababbbaaaaaaabaaabbaaaaaaabbababbbababbabaaabbbabbabaabbbbbabababbbaaabbabaabbabbbbbbaabbaaabababbbaababbaabababaabbabaaaabbabbbbbbbbbabbbabbbaabbaabaabbbbabbbbbbabaaabbabbbbbaaaabaaaaabaabbbbbbbbabbbaaabababbbabaaabaababbbbaaaabbbbabbaabaabababbabaabbaaabbaababaaabaaabbabbbbbbababaaababababbbababaabbbabbbbbaaabaaabaabaababaaabaaaabaabababbaabaabbbbabaaaabbabbbaabbbbaaabbaabababaaabaaaaabaaaabbbbabaaaabbbbbbaabbbaaabababbbabbabaabababaaaaabbabababaabbbbabbabbbabbbaababbbabbabbaabbbaababbaabbbbabaaabbabaaabbbaaabaabaaabbabababaaaabbaababababababaabbbbbbaaabababbabaaabaaaaabbabbbaabbabbabbabababbabbaaababbabbabbbabbaabbabbabbabbabbbbaabababaaaaaaaabababbbabbababaabbabbaaababaaaaaabbaabaaabaababaaaaaaaabbbbbabaaaabaaabaababbabbabbbbbbaaabaaababbaababbbabbbabbbaabbaabaabbababbbaaaababababaaaabbabbbabbaabaababbbbbaaaabbabaabbbababaababaabbbbabbbbaabaaabbbababaabbbbbbbbaabbabbabbabbbbbaaaaabbaaaaababbbbbaaaababaababbbbbabbaababbaaabaabbbabbabaabaaabbbbbbbababaababbbbbaaaaabababbbaaabaabbabbbaabababaababbbababaabbbabbbbbabaababbabababbaabaabbaaaababbaaabbbaabaaaaabbababaaabbababbbbabbbaababbbaabaabbaaaababbbbbbabbbaabbbabbabbabbaabaabbbaaaaaababababaabaaabbbabababbbaabbabaababbabbbbabababbaabaaaababbaabaaaabbaaaaaaaabaabababbbabaabbbbbaaaaaaabbbaaaaaaaabbaabbbbbbbabaaabbaaaabaaaaababaabbabaababbabaababbaababbabaaaaababaabaabbabbbbbaaaabbabbabaabbaaaaaabaaabaababbaabaababbbbbaabbabbabbbbbaaaabbabbbbabbabaaabbbbbabbbbabbbbababaabbabaabbbbaaaabaabbbabaababbaabaaaabaabaaaabbbbababaaaaababbbbaabbbaaaabbaabbbabaaabbabbaababbbbbbaabababaaaabbababbabbabbbaaaabaaaaaababababbabbbabbbaababbabaaaaabbbaaabbbababababbaaababaaaabbaaaaabaabbbbbabbbaabbbbbbaabbaabbaabaabbaaababbbbabbaabaabaabbbabbbababbabbbbaaaabbbaaaaaaabaaaaabaaaaaaaaaabbababbbaabaababbbaaabbabaababbbaabaaaabaababbbbbbabbaabaababaababaabbababababbaaababbbbbabbbaaaaababbaaabababaababbabbabbbbbbababaabbbabbaabaaaaabbabaaaababaaaabaaaaaabbbaabbaabbbbabaaaaaaaababaaaabaaaaabbaaababaaababaabaaabbbabababbbaabbabaabaaaaabaaabaabbbbbabaaababaaaabaaaaabbaaababbabbbbabbaaabbaababbabaababbabbabaababbaaaabaaababaabaaababbbaabbbaababaaabbbaabaaaabbaaaabbabbaaaabaaabbabaaaaaabbbaaababbababbabbaaaaaaaaabbbbbbaabbbabbabbbbbbabbbbaababbbbbbbbaaabaababbaabaabaaabbbbaaabaaaaababbbbbbbbaabbbaabbbbbbabababaabaabbababaaabbaabaaabababaabbbaaabbabbbbaabaaaaaaabaabbbabaaaaabbbababaabbabbbbbbabbbabbabaaababbaaabaabaaabbababbaaaabaabbababaabaabbbaababababbabbabbbaabbbbbaaaababaaabaaaababbbbababbbbbbbababbbaabbabbbbaaababbbbbbbbabbbbaaabaabaaaaaabbbbbbabaaaaabbbbabbaabaaababbbbbabaaaabbaabaababaabbaaaabbabaabbaabababbbaabbbaaaabaaabaabaabbaababbabbaaababaaababbaaabaababbaaabababaabaaaaaabbababaaabaababbaabaaaaaaaaabaabbbbbbbbaababbabbbaabbaaaaabbabaabbaaaabbbbbbaaabbbababbabbaaaababbaabbabbaaabaabbbbbaabaabbbabaabbbabaababbabbbbbaabaabaabaaabbababaaaabbaabbbabaabbababbaaaabaabaabbababaabaaaaababaabaaabbaabbbabbbbbabaabbababbbababbbbbaabbabaabbaaaababbaabaaabbbbaaabaaaaabababbbaaabaabaabababbbabbaaabbbbbbabbbabaaaabbabababbababbbbaabbbbbbaaababbbbabbaabbbbabaaaabbabbaababbabababbaaababbbbababbabaaabbabbaabbaabbbbaaabbaabbabbaabaaabbabbbaabbbaaaaabbaabbbaaababbaaabaabbbbaaaababaaababbabaaabbaaababaabbbabaabbaaaaaaaaaaabbabbbbbaabaaabbabbbaababaaabaabbababbbabbaaaaabbaaabbabaababbbbaabbaaabbbbabbbaabbaabbbabaabaabaabababbbaaaaabbaabaababbbbaabaabababbaaabaabbabbbaaaaabaaaaabaabbaabbabbabbbababaaaaaabaaaabbbbaaababbababaaababbbaaaabaaabaaabaaababbaaabaabbbabaaabaaaabbbaabbababaabbbabababbbbabbbbaabaaabbaaababbbbbbababbaabaabaaabbabaabaaabaaaabbbbbaaaabbbabbaabaaabaaababaabbaabababbaaaabbbbabbbbaaababbabbbababbaaaabaabababbbbabaaaabbaaabbbaaabbaabbbababababaabbaaabbaaaaabbbaababbaaaaabaaaaababbbbaabbbbbbbbbaabbaaabbabaaaaababbabbabaababababbbababaabaaaabbbbbbaabaaaabbbaabaababbbbabbbaabbbbbabbbbbababbaaaaabbaabaabbbbbaaabbaaababbabbbaababbaabbaabbababbbbbaaaaaaaabababbaaababbaaaaaaaaabbbabbabbbbbabbbabbbbbbbaaabaababbababbabbbbbaabaabaabbaaaabbbaaaabbababbaababaaabbbabbbbabaaabbaababaaabaaaaabbbabbbaaabaabaaaabaabbabbbaaaabbbbaababababbabbbaabbaabbabbabbaaabbbbbaabbbbbbbbbababbabaabaaaaabaaaaabababbabbabbbabaabaaababbababbaaabbaaaaaaaabbaaabbababbbabaabbbbbaaaababbbbbaaabbbaabbbbaabababaabaabbbbaaaaabbabbbabaaabbbaaaaaaabbaababbbaaaaabababbbbaabaababbbbbabbabaaabaaabbabbaabababababbaabaababbbbababaaabaabbbaaababbbbbabaaabbaabaabababbbabababababbaabbabababababbbbbaababbbaaababaaaaaaabaaabbaaaaabaaabbabaababbbabababbbbaababbbabbbaabbaaaabbbbaaabaabbaabbbbbbaaaabbaaaaababbaaaaaaabbaabbbabbbaabababaaaaabbabbaabbababbaaabaabaababbababbbaaabbbbbabbaaabaabaaaabbabaaaaaaabaaabaaaaabbaaabaabaabbbbbabbbaaabbaaaabbabbabbbaaabbaababaabaabaaaaabbabbbabbabaaabbabaaabababbbbbbaabbaabaabaaaabaababaabbbbaababaabbbaabbbbabbaaabbaaabaabaaabbaaabbaaabbabbabababbaabbaababbaabaabaabbbabbabbaababaaaabaabbbaabaaabbaaabababbaaabaaaaabbbabaaabaaaaaabbabbbbababaaababbbabbbabbaaaabbbbbabbbbaabbaabaaababaaabaabbaabbbbbaaaaaabbaaababbabbbaabbaabaabbbaabbaaabbbbaababaaaaabbabaabaaabbababbaaaaabbabaaaaabbaaaabaababbababbabbababaaaabbababbaabababbbbaaabbbaaabbbabaababaababbbbbbbbaaaaabbbaaabaaaaabbbbbaabbaababaabaabbbaaaabaaabaaaabbbababbabbabababbaabaaaaabaabaababaaabbaababbaaaaaaabbaabababbaaabaaabbabaaaabbaabbbbbaaaaababbbbbbbbbabababababbbbabbbabaababbbabbaaabbaabbaabababbbaababbaabbbaaaaabbabbaabaabbababbabbaabbbabbbbabbbbabbbbaaabbbbaaaaaabaabbbabaaaaabbabbaaaabaaabbbabbaabbbaabaaababbabbaaaaaaabbaabbabbaaaabbabbaababbababbbabaaabbabbaaababaaabbababaabbbbaabbbbaabbaaaabaaaaababaabaaabbabbbbaaaabaaaaabbababbaaaaaabaaaabbabaaaabaabbaaabaaababbaabaaabbbbaabbabbaababbbaaaaaaabbbbabaabbaaaabaabbabbbaabbbbababbbbaabababaabaababababbbbbaabbababbbabbabbbbababababbbababbbbbbaabaababbbbabaababaaaaaababaaaaaaaaaabababbbabaaabbaabbabbbbababbbbabbbbabbbbbbbbbaabbabaababaabbbbbbbabbbbbababaaababbbaabaabbaaabbbababababaaaabbbbbaabaaaaaabbbbbbbbbaabaaaaaabaabbababaabbaababbaaaabbabaabbbabbbbabbbaaabababbbbbabbbbbaaabaabbaabbaabbbbaabbbabaabbbaababbaaabaabaabbaabbbbabbbbbbaaababaaabbabbbbbababbbbbbbaabaabbbaabbbbbaabbbababababaabbaabbaaaaabbbaabbabbbabbabbabbbbaabaabaaababbbaaabbabbaabbbaaababbbaabaaaaaaaababaababababbbabababbababbaaabbaaabbabababaabbbaaaabaabaaaabbbbabbabbababbabbbaabaabbaabbbabbabaabbbabaababababaabbbbabbaabbaababbababaabbabbaaababaaabbbaabbbbabbaabbaabababbbbaabbbbbbaaabaaaababbbbabbbbbababbaababbbbabaabababababbbbabaabaaababbabbbbbbaabaaaabbbbabaaaabbaababbaaabbbabbbabaaabaaaaabababbaaabbaaabbabaabbabbaaabbbbbaabaaaabbaaababbbaabbaaaaabbaaaaabbaabbbbaabababaabaababbbabaaaaababbabaaaaaabababbaaaaabaabbbbbbababbbbbbaabbbabbbabbaabaababaaabbaabaaaabbaabaaabbaabbaabbbbbabbaabbbaaaabaaaabbbbbbaaabbbbbbabbaababbbbbababbbbaababbbaaaaaabbaaabbbaabaababababbabaabbabbaababbaaabbbaabaabbaaabbabbbbbabaabbabbbaabaaabbabababbaabaaaaababbbababbaababababbabbbabbbaaabbbabbbaaabbaababaabbabbababaabbabbbaabaabbbaabbbbbaabbbbaaaaaaababaaabababbbbbababbaaaabaababbbbabaabaaababababaaabaaabbaabbaaabbbbababbabbaaababbbbbabbabbbababbbbbbabaabbbbabbaababbbbabbbaaabbaaabbabbaaabbaabaaaabaabaababbaababbbaabaaaaabaaabbbabbbbbbaabbbbaaaaaabbbbaaaabaabbbbbaaabbaaaaaabbbabaaaaabbbaaaabbabbabbbbaabaaababababababbababbabaabaaabbbaaaabaabbaabbaabaababaabaabaabbaaaaaabaabaaababbabbabbbaaababababaabbabaabababbabbbbbabbababbabbbaaabbabaaabbbabaaaaaabaaaaabababbaaaaaabbaaabaababaababbaaaaabbaaaaaaaabaabaaabbabababbbaabbabbbababbaaabaabbbaaabbaabbabaaaabababaaabbbababaabbbaabbbbbbabbbaababbaaaaabbbbbbbbbabbaaabaaabababaaaabbbbbabaabbaaaabbabbaabbabbaaaababbbaabbbabaabbaaaaaababbbbbbabbbababbbbaaabbbaabbaababaabbabbabaabaababababbabaabaaaabbbaabbbbbabbbbbaaaaaababbabbabbaaaababbbbbaabbbaaabaaaababbbbbbabbaaaaaaabbabaabaabbaabbaabbbaaaabbabaaaabbbbbaabbabbabbabaaaaaaaabbbbaaaababbbbbaabbbbababbbabbbaababbabaabbaaabaaaabaaaabaaaaaabbbabbabbabbbaaabbbbbbbbbbaaaaaababaaabbabbbaababbbabaaaabbaaabbbbbaabbbababaabbabbbabbbbaaaaabbabbabbabababbaaabbbbaababbabababaababbaaaaabababbabaaababbbaabaabbaabaaaaaaabbbbbbabbaabababaaaaabaabbaaabaabbaaabaaaabbbbaabaabaaaabaaabbbbaababbbbbbabbbaabbaaabaabababbaabababaababbbbaabababbababaaaababbababbbabbbabaaaabbaaabbbababbbaaaababbbbbaaaaaababbaabaabababbabbbbbababbaabaababababababbabbbaabbabaabaababababaabaabbbbaababbbaabbabaababaabbaaaaaabbabaabbabbbaababbabbabaaababbbbbabbaaaaababababbbaaaababbaababbababbaaaaababbbabbaaabaababbaabbbbabbbbabababbbbbabbbbaababaabbabaaababbaaaabbbbaaaabbabaaababbabbbabbabbabbabbaaabaabbaaaaaababaaabaaabbaaabbbbbabaabaaabbababaabbabbababbabaaabbbababbbbbaabaabbabaaabbbbbabbbaaaaaababbbabababaabaabbbbaabbababaaaabbbaabababbbaabbbabababbaaabaabbbaaaaaabbabbbbaababaaababbabbbaaaaaaaabaabbaaaaabbbbabbbbbbaaababbabababbbbababbaababbabbaaabbbabbaaaabbbaabbabaaaaababaaabbaaaabbabaabaabbabbaababaaaabbaaaabbabaaaabbbaabbbbbabbbbabbbaaabaabbabaababbbbbbbbbabbaaababbabababababbbaaabaaabbaabbaaaaaabbaaabbabbbbbaabaaabaaabbbabbbbabbaaabababbabbbbabbbababaaaaababaabaaabaaaaaabbbaabbaababbbabaabaaabbababaabbbbaaabaabaabbaabaaaaaaaaaababbbbabbaabaaababbaaababaaaaaaaaabbbbabaabaabbbaaaaaabbbbbbbabbaaabbbabaaaabbbbaaaaabbaaababaabbbbaabbaabbabaababbaaaaaabaabaaaabaaaaabbaaaaabbbaaabbabbaaaabbbaaaabbabbbaaaaaaababbbbaabbbbabbabbabbbaabaabbaaabbabaabbaabaaaaaaaabbababbbaaaabababaabbabbabbabaabaaabbbabbbabaaabbababbaaabbababbaabbbaaabbbabbaabbaaaaabbbbaaabaaaababaabbbbaabbaabbbabaaababbbbbaabaaabbbbbbbbbaabbabbbaaababababbbbbabbaabaaaabbbbabbbaabbbbababaabbabbabaabbbababbbaabbaaaaaaabaabaaaaaababababaaaabababbbabbababbbbbaabbbaabbbbabbaaabbabaabbbaabbbabaaaabbabbbabaaabaaaaaabbaababbabbbabbaabaaababbbaabababaaaaaaabbbbbaaaabbabaaabababaaaaaaaaabaabbbbbaabbbabbabaaaaababbbbbbabbabaabbabbbaaaabbaaababbabaaaabbababaaabbbaaababbababaabbabbbbbbbbabbbabbaabbabbabbbabaabbbabbababaaaaaabbbabaaababababbbbbbababbaaaababaabaabbbaabaabaabbbababbbaaaaababbaaabaaababbabbababbbabbbbaababbaababbabbaaaabbbaabbaabbaaaababbbbbbabbbbabbabbababbbaaaaaabbababbaabbabbbbababbababaabaabaaaababaaaabbbabaaababaaaaabaaaabbbabaaaaaabaabbbbaaaaaabaababbbabbabbbbbababbbaabbbbaababaaababbabbbbbbabbabbaaaababbabababbabaabaaabaaababbabaabbaabaaababababaabbababbbbbaaaabbbbbabaaababaaaaaaaaaaaababbbbaabbabbabaaaabaaabaaaababaabbaabababbbaaaababaabababbabbbaabbbaababbaaaabbbbaaabaabaaabbbbbababbbaabaabbaabbabababbabbaabaaaaabbbbabbbbababbabaabbaababbbaaabaaaabaabbbbbabbbabababbaaaaababbbbbbbaabababaabaaabbabaababbaabbbabaabaaababababbbabaaababaabababaabbbababbbabbbaaaababbabababaaababbbabaaaaabbbaabbbaababbabbabaabaabbbbbabbbaabbaabaaabbbbaabaaaabbbababbbabaaabaabbbbaabbbababaabbabaababbbbabbaaaaabbbbbbbbbaaababbababaabbaaabbbababbbbbabbaaaabababbbbaaabaababaaaaaabaaaaababbbbaaabaabbbaaabbabbabbbabababaabbbbbbaaabababbbaaaabaaabbababaabbbbabaababababbabaaaaababaaaaaaabaaababbbbbbaaabbbbbbabbaaaaababbabbababaababbbabababaaaabaaabaabaabbababbababaabaabababbbbbbbbbabababababbabbabbbbbbbbbabbbbbaabbbaabbaabbabaabbbaaaaababaabbabbbaabababbababbbababbbbbaababaabbbbababbbababbbabaabbbbbbaaaaabbabbbbbaaabbabbbbbbbbababababbbaaabababbbbbbbaabbababbbbbabbbaabbaaabbbbaabaaaaaabbaabbbbbabbabbaaaaabbbaaabaaabababbabbbaaaabbbabbbbbbabbbabbbaabbaaababbababaaabbaabbabbbaababaabbbbbbbbaaabbaabababbbbbabbbababbabaabbbabbbabbaaababbbbaaabbabbabaabbabbbabbaabaabbbbaabaabbabaabababbabbbbaababbabaabaaaaabbaaabbababbababbbbaaaaaaaaaaababbbbaabbaaabbabbbaababbbabaababbbbabbbaabbabbabaaaaaaaaabbabbbbbbabaababaaababbaabababaaabaabbbbaaaabbbbabaabbaabbbbbaabaaabbbaabbbabbaaaabaaabaabababbaaaabbabbbababaabbaabaaabababbabababaaabbbbaaaababaababbabaaabababbbaabbbaababbbaabaaaabaaaaaaaabaababbabbbbaabbbaaabaababbabbbbabbaaaaaababaababbaaabbababbbbabaaaabbbbbbababababababaaabbbabbaaaabbbaabaaabaaababbaabbbbabaabbbbbaabbababbbabaaababbbaabbaaaabbbbababaaaabbabbbbaabbaabbabbaaaaaabaabbabbabbabbbababaaaaabbabbbbaaaababbbaaabbbbaabbaababbaaaaaaabbbabbbbbbbbaaaaaabbabaabbaababbbaaabbabaaabbbabaaabababaaaaababbbabbbbbaabaabbbbababaabaababbbaaaababbbbbbbaabbbbababbabbaaabbabaabbbbabbababbbbabaababaaabababbabbabbabaaabbbbbababbbaaaababbbaaabababaababaaaabbbabaaaababbabbbabaaabbabaabbbbbaabaabaabbbbabaaabaababbaabaaabbbbbbabababaaaabbbababbbbbbbaabaabbbabaaaaaabbbaaababaaababbbabbbbaabbabbbaaaababaabbaabbbaaabbbabbababbabaaabaaabaababbbbbbbababaaababbbaaabaabbabbbbbaaababbabaabbbbbaaabbbbbbbaabaababbbaabbababaababaaababbabaaabbbabbbbbbbaaaabbabaababbbbabbabbaaaaabbbbaaaaabbaaabbababbbabaabaaaabbbaabbabbaaaabbbabbaaabbabbababaaaabbaabbaaaaaabbabaababbbbbbbbaaaaabaabaabbaaaabbbbbbbabbbabaaababaaabbbbabababbabbbabbaabaababbbbbbbaabaaababbaaaabbaaabbbaabaabbbaabaabbbbbaababbaabbbbaabbabaababaaaabaabbabaaababababbbaaababbbaaababbabaaaababbbbabbaaaaabaabbaabaaabaaabbbaaaababaababbbaababaaaaaababaabbbbaaabbaabbbbbbbabaaabaaaabbbbbabbabbabababbbbbabbbaababbbabaabaaabaaabbbbbbabbabaaaaabbbaababaabbaaaababaababbbbbbabbbbaababbbabaaaabbaaaaaaabaabbaaaaababaaaabbabbbbababaaaabbaaaabbabbbaaabbabbbaaaababbbaaababbaaaababaabbaaaaaaaabbababbaaaaaabaaaaabaabaabbaababbbbbaaaaabaaabbababbbaaabbbaabaaababababbbbbbbabbbaababaaababbbbabbaabbaaaaabbbbaabaabbaabaababbaaaabbaabaaabbaaabbbababbaaaaabababaabbbaaaaabbbaaabaaabbabbbbaaabbaabaaabaabbbbaabbbbabaaabbabaabaaaabbaaaaabaabaabbaabbaaababbabbababbaabaabaabbaababbabbbaaaabbbaabbbbbababbabaaaaaabaabaabbaaaaabaabbababaababbaabababbaabaabababbbababbaaaabbaabaabaabababbabbabbabbbabaabbaabbabbbbabbaaabaaabbbbabaaaabbabaabaabbaabaaabbbbbbabbbbaabbaabbabababaaababbbaaaaaaaabbabbaabbbbbaaaabaababaaabbabbbaabababbaababababaaaaaaabbaaabbaaabbabbabaabbbaababababaaabbabaaabbababbabbbabbbbbabbbbbaabbbbbbbbbabaaaabababbbaabaaaaabbaabaaabbbbabbababbbbaabbbbaaaabbaabaabbbabaabaabbbbbbbabbbbbabbabaababbbbabbaabaabbaaabbaaaaaaaaaaabbbbbaabbbbaabbbbbbaabaabbabbaaaabaababbbaaaaabbbbbbbabaaabbbabaabbaaabaabababbbaabaaaabbbbabababaaaaabaabbbbbbbaabbabbaabbbabbbbabaaabaabbaaaaaaaabbaabbbabbaabbabbbaaabbaaaaaabaabbabaaaababbababbbbbbaabbaabbbbabbaaabaabaaabaaabbabaaabaaabaaaabaaaababaaabbbbaabbaaabbabbabababaabbbbabbbbbabbabbababbabaaaabababbbbbbbbaababababbbababaabbabaabaabbbaaaaaaabbabaababaabbaaaabbbabbaabbbbbbaababbbbbaaaabbaabbabbababbbbaababbaabbbabaababaabbbabbabbbaaaababbbbbabbaaaabbbaaaabbbbaabbbbabbbbaabaaabbbabaabbabbbbaaabbbbaaaabaabbaababaabbaaabbbabbabaaabababbabbbbabbbbabbbabaabbaaaaaaaabaababababbbabbbaabbbbaabbbababbaabaabbababbababbbabbbbbaaababbbaaaaaabbabaaaababbbababbababbaabbbbababaaabbbaaabbbaabaaabbababbbabbbaaaababababababbabaabaaababaaaabaabbbaaabbaaabbbaaabababaaaabbaaaabaaaaaabbbbbabbaaabbaabaabbbbaabbabbbaaabbabbbbbbaaaaaaabbbaabbbbbbbabaaaaabbbaababbbababaabaabbbabbbabaabbbabbaaabbbabbbaabaaaaaabaabaabaaaabbbbbabbbbbaaaabababbbabaaabbabaabababbbabaabbbababaaaaababbaabbbbbaaabbabbabbbbabaabbbaaaaabbbaababbbbbaaabbaaaababbabaaaaababbbabbbabbbbbbaaababbaaabaaabbaaabaabaabaabbbaaababbbbbbbbababaaaabaabaaabbbabbbaababbabbbbaaababbaaabbaabbbaaaabaaaaabaabbabaaaaabaababbaabbaaabbbaabbababaaababbbbbbbbabbababbbaabaaabaaaaaaaaabbbaabbbbbbbaaaabbbaabbaabbaababbaababaabaabbabbbaaabbabaaaaabaabbaabbaabaabaababaaababaaabaaaaabaaaaaabbbbabbaaaaabaaabaaabaaabababbaaabbbabbbbaabbbaaaabababbbaaabaabaabaabbbababaaaabababaabababababababbaabbbbabbaaaaaaaabbbbaabbbabbaaaaabbaabbabaabbbbaabbaababaabbaabaaabbbaaaaabbaabbbaaaaaabbbbabbbaaaababaabbabaabbaaabbbaaaaababaaaabaaaababaaabaaabababbbbaaabbbbaaababbbaababbaaaababbabbaabaaabaabbbbbabbabaaabaabaabaaabbaabaaabababbabbbbababaabbbbabbbbababbbbbaabababaaaabaabaabbbaabbbbabbaabbbababaabaaaaabbbbabbabbbabbbbabbbabbbabbbaaaababbbbabaabaaaababbabaaaabababbabbaabbababababbaaabbbbbbabababbaaababaaabbabababaabaababaabaaabbaabaaabbbababaabababaabbbaaaababaabbbbbaaaaaaaabbbabbbabbbbaaaaaaaabaaabbbaabbbbbbbaaabbbabababbbaabbababbabaaaabaabbbbaabbabbabbaabbabbbabbabbbaabaababbbbaabbaaabbaabbbabababbbabababaabbbaaabbbbaabbbaaabbabbaaaaababbbbababbbbbaababbababbaabbbbaabaaabaabaaaaaabaabbaaaabbabbbbbabaababaabbaaaaaaaababbbabbbbbabababbaaabbbbabbabbbbbabbbbabaabaaabaaababaabbaaabbabbbbbbbabaabaaaababbbbaaaaabbaabaaabaabababaaabbaaaaaaabbaaaabbbaaababbbaabbbaababbbaabaababaabaaabbaaabababaaaaabbbbabbaabbbbbabaaaaabaabbbbbbabaabaabbbbbababaababababaabababbbaaaabaabbababbbbbaababaaabaaabbbbbbbbaaababbaaabbbbaaabbaababbbabaabaaaabbbababbbbbbaaaababababbbbbaaabbaaaababbbbaabbababaababbaaaaaabbbababbbbaabaaabaabbbabbbaabaabaaabbaaaababbaabbbbaaabbababbaaaaababbabbbbabbaaaababbaaaaabaabbaaaabaaabbaabaaaabaaabbbbbaaaaaabaabaaabaaabbbbaabababaabbabbabaabaabaababbaabaabbabaabbbbabbbaabbbaaaabbbabaabbbabbbaababaabbaabbabbaaabbbbaaaaaaaababaabaaabaabbbbabbaabaaabbbbabbbbabbbbabaababaaababbbaaabaabbabbbabaabbababaaaabbaaaaaabbbaaabbbbababaaaaabbbbbbabaabaabaababbbbabaabaabaaaabaabaabbababaabbbaaabbbabbabababbbbabaabbabbbaabbaababbbbbaaabbbabbaaaaaabaaaababbbaaaaabaaabaabaababbabbbbbaabbbbaaabbabaababbbabbabaaabababbaabbaaaabbbabbaaaaabbababbbabababaabbbaabbaababbbbbababbabbbbabbabbbbbaaabbababaabaabbbabbbbbaaabbaaaabbabbaabbbbaaabaaabbbbbbababbaabababbbabbaababbbabbbbbaaaabbbaaabbaabbaabbbbbbabbababbababaabbaaaaabbabbbaababababababbbaaaaabbaaaabaaaaaaababaababaaababbabaaababababababaabbabbaaababbaabbaaaaaaaaaaababaabababaababbabbbbabaabbbababbbbbababbabaabbaababbbbaaababababbbabbbbabbabaaabbaabbaababaababbbaabbbbbabbbbababbbabaaaaabbabbababababbaaaaaabaabaaaaabbaabbaaaabbabbabaaaabbbbabbbaaaaaaababaaaabaaabbabbbbbbbbbaaabaabaaabbbbbbbbabbaababaabbaaabbababaabbabababbaabababbaaabbaaaaabbabababbbbbbbbbbaabbbbbabaabbbbabbabbaabbabaababbabababaaababbabaabbabbbabaabbbbaabbabbabbaaabbbbabaaabaaabbabbaaaababbbbbbbbbaaabbabbabbaaababaaabbaabbababbabbbbbbbaabbbbbbbababaabbaababbbbabbbbbbaabababbaabbaabbbbbbbaaabbbbababbababbbabaaaaaaabbaaaaaaababbbaaabbbabbbbbbbbaababbaabbbbbbbabbaaabaaabbababbbbababaaaabababaabaaaaaabaaaabbbabaaabbabbaababbbabbbaaaababaabbbaaaaabaaabbbbbbaaaabaaabbabaabbbaaababaabaaababbababaaabbaababbaaaaaabbbbbaabbaabbbbaaababbabaabbababababbbbbbbbbbbabaaaabbbbabaabbaababbabaaabbaabbbbbaabaabbaaaabbbbabbbaabbaaaabbbabaaabbabbaabbabbabaabababababbaaabaabbabaabbabaaabbabbaabbbabbbbabbbabbbbbabbaabbabbababbbabbbbbabbbbbbaabaabaaaaaabaaaabbaababbbababbabbbaabbaabbaaababbbbbabaaabbabbabbaaabaaabbabababbbaabbbbbbabababbabbbbabbabaaaaabbaababbaaaababbaaaaabaaabbbaababbbbabbbbbabbabbabaaaaababbabaaabbbabbbabaaabbaababbaababbbbabbbaaaaaaabbbababbbabaaabbbaabbbbaabbabbbbbabaaaabaaababbbbbaaababaaaabaabbbbbaabbbbbabbaaaaaaaababaaabaaabbbbbabaabaaaaaababbbabababbaaaaaabaabbbababbabaaaababbbaaababaabbbabbaaabaaaabaabaabbabaaaaabaabbabbaabaabbbababbabaaaababbaaaaabbbaabbbbbaaaabbbbbbbabaabaabbbbaabbaaaabbbababaaabbbaabbbbbbbbaabbaabbaabaaaababbbabaababbaabbbaabbaaaabbbaabbbbbaabbbbaabbbaaababbabbababaaaaaaababaabbbabbababbaabbaabbbbbabbbbabbabbbbababbababbbaaabbbbabbbbaaaaaabbbbbbbabbaaabbaaabbbaabaabbaabbbbbabaaababaabbbbbbbaaabbabbbbabaabbaaaaabbbbbbbabaabababbaaabbbaaaabbbaaabbbabababababbbaaaaaabbbaaaabbaababaaabababababbabbbbabbabbaabbaaaabbbbbaabaaababbaaaabbabbabaabbaaabaabaaaabaabaabbbabaababbabaaaabaaaaababaaaaaabaaabbaababbbbbbbbaabbbbabbbaaababbabaabbababbbaabbbbbbbababaaababbbbabaabbbbabaaaaaaaababababbaaaaaabbbbbabbababaabaabaabbbabbbbaabaabbaabababaabbaaabbaabbaabaabbbaaabaabababaababbbaaabbbaabbaabbaaabbabababaaabaabbabbbbaabbabaabbbbbabaaabbbabbaabaabaabababaabaaaabbbbbabbbababaabbbabbbababaababbbaaaabbbaabbaaabaaabbbbbaabbaaaaaabbabbbabaabaaaabbbabbaabbbabababbbaaababaaaabaaabaaaaababaaaabaaaababbbabbbabbabbbbaabbbaababaababaababbbababbbbbaaababaabbabbbaaaabbaaababbaaababbbaabbabaaabbaaaaaaaabbaaaaabaaabbbabaabbaabbbaabbabbaabaabbbabbbabbaababbbabababbbabbabaabbabaaabbbaabbbabaababababaaabaaaabaabaabababaababaaabbababbabbababbbbaabbbbaabbabbaabaabbaabaaabaaaaaaabbbbbabaabbbbababbabbababbabbababbabaaababbababaababbabaaaabababaaababababaabbbbaaaabababbabbbbbbaaabbabbaababbbaabbabaaabbbaabaaaaaabbaaaaaabaaabaaabaabaabababbbbbbbaabbbbbaabbaabbbbabbabbbababbbbbbbbabbbababbabababbbaaabbbabaabbaabbbbabaaaabbabbbaaabbaabbaabbabbbaaaabbaabbbababababbabbaabbabbbbbbbaaabbbabaabaabbbaabbabbaaaaaaababaababbbaaaabbabaaaaabaabaaaaaaaababbabbaaaaaaaaaabaaababbaaabbabababbaabbbababbaaaaaababbbbbbabbaabbbbbaaababbabbaaaabbaabaaababbabaabbbbaaabaababbbaaabaabbaaabaaaaaaabbbbaabababbaabaabbabaabbbaaabaaababbaaaaabbbababbaabbabababaabaabbabababbabbabbbabbabbabaabbaaabbbaababbaaabababaabbbabbbbabbbbaabbbbaaabbbbbaaaaaaabbabbbbaabbbbaabaaaaabaababbbbabbaaabbbbababaabbaaababbbabbbbaaaabbababbbbbaabbbabbaabbbbabbbaababababbbababbabbaabaaabbabaabbbbbaaaaaabbbbbabbbbaaaaabbbbbaaaabaaaaabbabbabbabaababaabbabbbbbbbbbaaabababbbbbabbaabbabbabbaaababaabaaababbabbbabbababbaabbaaabaabbbbabbabbaaabbaabababaababbbbbbbbbaaabbababbbabaaaaaaaaabaaabbababbbbbabbbbaaaaaaabbabbabbbbababbaaabbaabbbaabbaabbaaaabbaaababababaababbabaabaabababbabaabaabaabbbbabaaababbaaabbabbaaababaaaabbabbbaaababbbbbaabbbaabaaabbbabbabbaabaaabaaabbabaaabbbababaababaaababbbbbbbabbbbababbaaaabbaabaaabbaaabbbababbabbababaababbaabbbabbbababaabbababbbbaaabbbaabbbbbaabbbbaaaabaaaaaaaaababbaaabaababbbbaabababaabaababababbabbaaabbaabaaaaaaabaaababaaabbbabaaababaaabaaabbbaaaaaababaabbbbabaababaabaaaababbbaabbaabbaaaabbbabbbbbbabbbbababbabbbbbbaaaaabbbaabbaaaabbbbaaaaaaababaaaababaaabbbabbabaabbabaaaaaaaaaabaaaaaaaababbbababbbbbaaabbabbbabbbabbaabbabbaabbabaaabaabbabaababbbbaaabbaaaabaabbbbbbbaabbbbbaabaaabbaaaabaabaababababbababbaaabbaabaababbbbbbabbabaaabbaaaabaaabababbaabababaaabbaabaababababbaabaaaabbbaabbabbabbaaaabaaaaababbbabbbbaaabbbabbbbbbabbaaabbbbabaaabbbabbbabbbbbbabbbbbabbaabababaabaabbaaabbbbbbaaabbabaababaabbbbabbbaaabbabaaaababbbababbbababbbababababbaaaababaabaaabbbbbabbabaaaaababbbbabaabbbabaabaabbababbbaabbabaaabaabbbaaabbaaababaabbaababababbbbaaaaabbbbbaaaaaababaababaabaabbaabbbabbbbaaaaaaaaaaabbbabbbbaaabbbbbabbabaaabbbabababbbaabbaaabbabbaaabaababbaabbbbbbbbaabbaaaaaabaabbabbbbbbbaaaaabbbabaabababbaabbaaaabbbbaabaaabbbabbaaabbbabbbaabaabababaaaabbbbaaabababbaaaaabaabbbababbbbbaaababbbababbbabaaaabaabbabbbaaaaaaaababbaabababbabababbbabbaaaabbbbabbbbabbbbabbaabbbbbaaabbbaaabbbaaabaabbbbaaaaabbbbbabaaababaaababbbabababbbbbbabbbbbababaaabbbbbaabaaaabaaabbbbababaabaabaabbbaaabababbbbbabbbabbbabaabaaababbbabbababaaaabbbaababbaababbbbbbbbbbbaaaabaabaabbaaabbbbababababaaabababaaaaabaabbaababbbaabaaabbabbaaabbbababbabbababaababaaaaabbabaabbbbbbbbbababababbaabbbaabbaaaaababbbabbbbbbbaabaaaaabaaaabaabbbbbababaaabbbaaaabbbaaabbaabbbbbaabaaaabaaaaabbaaaabaabaaabbbaaabaababaababaaaabaabbbbaababaabbaabbbabbbbaabbaabbaababbbaabaabaabaaaaabbabbabaaaaababbaaabbaababbabababbaaabaaabbaaaaaabbbaaaabbbbababababbabaaaaabaababaaabaabbaabbabbbaababbbbabaabaaaabbababbbbaabaaabbaaabbbbbbbbabbabaaaabbbbabababbabababbbbaaaabaaababbaabbaabababaaaaabbaabbbbababababaaababbbbaaabaaaaabbaabbbaabbbbbabababaaaabaaabbbbbbbaaabbabbbabbbbbababaabbbaaaabaabbabbbbababababababaabaabbbabbbaabbbbabbbbbbbbbbbbbabbaaaaabbbbbabbbabaabbbbbaabbbbabaaabbbaaaabaabaaaabaaabbbaabbaaabbbaababbabababbbabaaababbaaabbabbabbaaabbbabbababbbbbbbbaaaaabababaaaabbaaababbaaabbaabaaaaaabaababaabaabbbabaaaaaaaababaabbbbaabbbbabbbbabaaababbabaabaaaaabbbabbababbababbbbbbbabbbbbbaabbbbbaabbbabaabbaaaababbbbabaaaabaabaababbbabbabbabbbbaabaabbabababaaabaaababbabababaababaabababababaabbababbabaaabbbababaaabbabbabbaabaaabbaaabbabababbaababbbaaaabaaabbbbaaababbaabbaabbbbbabbbbbbbaaabaabaaabbbbaabbaaaaabbbabaaaaabababbabbbbabbabbbbbaabbabbbbbbababbabaaaaabbabbbbbbbabbbbabbbbbbbbbbababababaabaabaaaaaabbaabaaaaaabbaaaabaabaaababababababbbbbabaababbaaaabaababababbabbbbaabbaabbaababbbbabbaabbabaabbabababbbbbbabbbaababbabbaabbbbbbbaababaaaaaabaabaabaabaabaabaaaaaabaabbaababbaabbaabbaabbbaababbbbbaabbabbaababaabaaabbaababbbbabaabaaaababbbbbababababaaabbaaabbaaabaaabbbaabaabbbabaabbabaabbbabbbbaaabbbaaabbbbbaaaaaabbaababbbbbabbaaaabbabbbabbaababbabaabbbaaaaaabbbabaaaaabbababaaabaabbbaaabbbbaabaabbabbbaaabaaaabaabaaabbbabaaaaabaabaabbbbaaabbbabbaabababbbbbbaabbabbbabbbabbbaaabbabbabaababbaababbabbbaabaabbabaaaabbaaabaaabbaaaabbaaaabaabaaaaabaaaabababbbbbbabbabbbbabbbaabbabbbabbabababbababbaaabbbbbabaaaaaababbbaaaaaababbbbaabbbbababababbbbaabaaabbabaabaabaababaaabaaabbbabaaaabbbbbaaabbaaabababbaaaabaabbbaabbbbabaaaaaabbbabbbbabbababaabaaaaabaaabbbbbababbbbbababaaababaabbaabbaaaabaaabbbbbbbababbaabaabbbbabaaababbabaaabababbbaabbbaaabaabaababbabababaabbbabbaabbbbbbbbbaaaababaaaabbaaabaababaabbabaababbaabaababbabbbabababbbbbabaaabbabbbbbabbabbbbaabbbabbabbaabbaaabbbabbaabaabbbaababaabbaaaabaaaabaabbaaabbaaabbaaaaabaabababaaabbaabaaaaabaababbabbbbbabbaaabbbaabaaababbabbaababbaabbbbababaaaabaabaabbbbabbbbbabaaaaabaabbaabbaabbbaababababaaabbabbbababababababaabbbabbaabbbaaaaabababbbaabbaabaababbabaabbbbbbabaaaaaababbbbaaababaaabaaabaabbbaaaaaabbbbbabaabaaabbbaabaabaabbbabbabbbaababbbababababbabaaaaaaaabaabbabababbaaabbaabbbbbaabbbbaabaabbbbaaabbabbbbbbaaababaaabbbbabaaaabaabaabaaababbbababbbbaababaabaabaabbaaaababababbabbabaabbabbabbbabaaaaaabbbbbaaaaaabbbbbabaabbabaaaaaaabaabbaaaaaabbbbabaababbbaaabbbaababbbaabbbbabaabbbbbbaaababbaaaaaaaaababbbbaaababaabbbbaaababaaaaaabaaaaaaabaaabbbbbabbbaababbbaaabaabbbbbbbbabbaabbabbabaabaabbbabbbbbabbbbbbabaababaabbaaaaaabbbabbabbabbbbbabaababbaaaabbbbabaaaabbbaaabaabbabbaabbbaaababbbababbababbbababbbbbaabaabaaaababaabaaaabaaaabbbaaabbbaaaaaaabbabababbaaababababbbbbabaabbbabaabababababbbaabbbaababbaabbbabaaabbbbbabbaaabaaaabbbabbaaabbabababbabbbabababaaabababaaabaaababbbababaaabbbbbabbaabbaaabaababaabaaaabbbabbabababbababbbaabbbbaaabbbbbabbaaabbaaabbababbabaaaabaabaaaabababbaabaaabaaaaabbaabbbbababbaaaaaaababaaabaababbababbabbabbaabaaabaabbaabaaabaaababbbbbbbbbbabaaaabbbabbbbbbabaaabbbbaabbbaaaabaaabaaababbaabbbbbbbbbaabbbbaabbbbbabbbaaaaabaabbbbbbbbaabaabbaaaaabababaaaaabaabbbbbbbbaaaaaaaababbabbbbaaaabaabababbbaaabbbbaaaaaaabbabbabbaabbbaaaabbbabaabbaaabbbababaababababbbbabaaaabbaababbbbabbabbabaabbbbaaaaabbabbabbaaaaababaabbabbaaabaabbaabaabbbbbabbabaabbabbaababaabbaaabbaaaaabaababababbbbbaabbbbaaabaaabaababbbbbabbaaaababbbaababbbbbaaaabaabaaabaabbabbababbababaabbabababbaaaaaaababaaaaaabbaaabababaaaababbabbbbbaabbababaaabbbaabbaaaabbbabbabababaaabbbaabaaabaaabbabaabababaaaabababbbaaabbbaaaaaaaababbbbbaabbaaabababbaabbababaaabaabababbbaaabaabbbbaaabbbbabbaaababaaabbabbbaababbababababbaaaabbbababaababbaaabababaaabbaabaabbabbaabaaaabbaaaabbbbabababaabbbaababbaabbbabbaabbaaabbbaaabbababbbbbbbbaabaababaaabbabbaaaaaaabbbababaabbabbaabbabaabbabbbababaababbbbaababaaaaaaaaabaaabaabaabbbbaabaabaabbbabaaababbaaababbbbbbbbbbabaabbabbaababbaabbaabaabbabaaabbaabbaabbbbbaababbabbbbbbababaabababbabaababbabbbbbabaabbabaabbaabbaaaaabaaaababbabbbaaaabaaaababbbbbababbaabbbabaabbaaabaabbbababbbabbaaaababaaababaabbaaaaaaaabaabbbbbbabbabababbabbbbabbbbbbaababbabbbbbbabaaaababaaaaaabbbaaaaaabbbaaaaabbabbabbbbbbaababaaaaabbbbbbaabbbaaabbaabbaabbbbbabbbaabababaaaababaabbbaabbaababbbabbbbbabababbababaabbaaaaabbabaaaababaabbbabbbbbbbbaaabbbbabaaaaabaaabbababaaaabbaabbbaabaaaaabbabaabbaabbbbabbabbabaaabbabbabbabbabababaaaaaabaaaabbabbabbaaabbbabbbbaaabbbabbbabbabbbbabaaaabbabababbbbabbbbabbababbbaabbabbbbbabbbaababbbbbbbbbaabababbbaaabaaaabbabbabbbaaabaaaabababbbababaabbbababbaaabaababbbabbbaabababbabbbaaabababaaaaabaabaabababaaabbbabbaaabbaabbabaaabbaabaaaabbaabbbabbabaabbabbabbbaabbaabaaabaabbaaaaababbaaabbbbaabbbbbbbbaabbabbaaababaabbbabaaaaaababababaaaabaaababaaaabbaabbbaaabaabbbababaababaabaabbbbbabaaabaabbbabbabababaaaabaaabaabbabbaaabbaaaaaaabbbbbbaabbabbabaaaabaaababbbbbabbbabbaabbbbbbaaababaabbbbbaabbaabbbabbaaaaabaabbbbabbbaaabababbabbbaabbaaabababaaabaaabbaaaababbaababababbabbabbaaaabbbbbbabbbbbabaabbaababbabaaabaabbabbaaaaabbbbaaaabbbabababbabaaabbaabaabaabaabababababbbaaaabbabbaabaaaaabaababbababbabbabbbbaababaaabbbababbbabaabbabababbbbbabbbabaaaaabbabbbbaaabbababbbababaaabaaaababaaaabbabbaaaabaabbabababababaaaabababbabbaabbbaaaabbabaabbbbaaaababbaabaaaaaaaabbaabaaaabbaaabbabbaababaaabaaabaaabbabbbababbbababaabbabbbaaaaaabaaabbbabbbbaabaaababaaabbaaabaaaaababbbabaababaaabaaababbbbbbbbababbbbbbbbbbaabaabbbabbbaaabaaaabbaaabababbabbbaabbbbbabbababbababbababababbabbababbbabbaabbaabbaaaababababababbbbbbbabaaaaabaabbbbaaabaababbababbababbbbaabbaabbabaaaabaabababababbbababbbbbaaabbabbaabbbabbbbabbaabbbaaabbaaabbababaaaaaaabbababbbaaaaaabaaabbbbbbaabababbabaaaabbababbbbabbbbbbababaaabbbabbbbabbababbbaababababbbaaabaaabbabaaabbbaabbbabbbabbbabbbbabbbaabaabbbabbaabaabbabbbbbababaababaaaabbbabbbabbbbbbababbbbbbbaabbbbbbbbabbabbbabbabbbbabaabbabbbbbbaaabbaababbababbbbaaabbbabababaabaababbabaababbbbbbbbaaaabbababbabbbaaaaababaabaaaabbbaabbaaabbbbabbbbbbbbababababbaabababbbbbbbbabbabababaabaababbabbabaabbbaaaababaabbabbbabaaababaabbaaabbabaaababbaabbabaaaaabbaaaabbbabababbbaaaaaaaabbabbabbbbaaabbbaaaaabaaaaabaaaabaabbbbaabbbababbbaaaaabbabababaaaaabababbabbaaaabbaabbbbbbaaabbaaabbabbbbbbaaabbbbbabaaaaabaaabaabaabbbbabaaaaaabbbbbbbaababbbabaaabbbabbababaaaabaabaaababbaabaaaabbbaaabbaaabbbaaaaababbbbabbabbaabbbabbbabaaaaabbaabababaaababbbaabaabbbaaaaabaaaaababbaaabababaababababbbbaababaabaababaabaaaabbbbaaaaabbbbbbbabbabbabaaabbbbabbabbabbabababbbaaabbaaaaaabaabbbababbbaabaaaabbbabbabaabaaaabbbbaabaabbabaaabbbaabbaababaabbaabbbbbabbbabbbbbaabbabbbaabbbaabaaabbaaabaaabaaabbbaaaaabbabbaabaabaabaabaaaaaaaaabbabbaababbbaabaabababababaaaabbabbaababababbabaaabbbbabbbbaaaabababbbaaaabbbbbabbaaabaaaabaaabbbbbbbbaabaababaababbbabbbaaaabbbaabaabbaabaabbaabbaaaaabbabbbaaaaabbbbbbbbbaaaaabaaaaababbabaabbababbbbbababbaabaabbbbbabbabbaababbbaabbbbaababaababbabbaababbabbbabababababbbaababbbabbaababaaaabbbabbbaabbaabbbabaabbbabbaabbbababaabaabbaabbabaabababbabbbbabbbaaaaaabbbaaababaabbbaababaaabbabbaabbbaaabaabaabbbbaaabbbbaabababbabbaaaaaababababbaabbabaaababbababbbbaaabbbabbaaabaababbbaabaaabbbabbbabbabaaaabbbbbbaaaabbbbbaaababaabbabaababbaaabaabbaabaabbabbbabbbaabbbbaaaaaaaabbaabaabbbbbbbabbbbaabaaaabababaaaabbbabbbabbabbbbabaaabaabababbbbbaabbabbbbaaaabbabbbbbbbabaaababbbbabbbaaaaabababbbbaabaabbbabaabababbababbbbbbaababbaabaabaabbaaabbbbbbbbbaabbaaaababbbbbbbaabaabbabaabbabbbbbbabbbbbabbabaabbabaaaaaabbbabbbbaabaabbabaaabaaabbaaaabbabbbbaaabaaabbaaabbbbbababbbababaabaaabbbabaababaabbbbbbabababbbaabababaabaaabaaaaabaaaabaaaaabbbabbabbaabbbbababbababbbabaaababaaabbbabaabaaaabaabbaabbbbababbbbabbaaaabbbbbababbbbaaabbababbabbababbaaabaaabbbbbbbbaabbabbabaabbbaaabaabbabbaaabaabaabbaababaaaabbbaaaaaaaabbbabaaaaabbbaaabbbbabaaabbabaaaaababbbabbbabaabbbaababbaabababbbbabaaaaaabbaabbbbbababbaabaaaaabbbbabbaaabbabaaabbaaabaaababaaaaabaaaaaaabaaabbabbababbabbaaababbbababaaaabaabbbabaaabbababaabbbbaaabaabababbaaabaabaaababbbbaaabaaabbababbbabbbaaababaabbaababaaabbbaaaaaaaaaabbbaabaababaaabababaabaababbaaaababbbbababbabaababbbbaabaabbbbaaaaaababbabbbbabaaaaaaaabbaaaaaaaabaaabbabaabbbabaaaabbabaabaaabaaabbaabbbabbabbbabbbbabaaabbbabbabbabbabbabbaabaabaaaabaaabbbaaabaaabbabbaababaaaaabaabbaabbaaabaaababbbaaabaaaabaabbabaaabbaaaaaabbaaaaaabbaabaabbbbbabbaaababbabaaabbabaababaabbabaaaabaaabbabbbaaaabababaaabbaababaababbaabbbbbbabbabbbbbabbabbbabbaabbbbabaaabbbababaabaabbbababababbbababbbabbbaaaabbaaabababbbbaaaaabbbaaabbaabbbaabbaababbbbaabbabbbaabaaabbabaabbabbabaabbbabbababbbbbabbbbbbaabbbabababbbbbabaaaabbabababbaaabaabbbbababbaababbbaaaabbabbabbbaaaababaababababbbbbbbabbbbbbbaababaabaabbaaabbaaaabaabaaaabaaabbbabbbababbaaaaabbbbbabbabaabbbbaababaaabbbaaaaabbaabbabaababababaaaabbbabababbabbaabaaabaabaaaababbababbbbabaabbbaabaaaababababbabbabbaaaabbbabbabababbbbbbbaabaaaabbbbabaababbbaaaabbbbbbaabbaaaaabbbbaabaabbbaabababbbaabaabababbababababbaaaaababaabbbaabaabbbaaaabbabbbababababbbababaabbaaaaabbbababbabaaaabaaabbbabaaabbbbababaabbaaabbabbaaabbaaabababbabaaaaaaaabbbaabbabaabbbababaaaaabbbaaaaaababbaabbabbababbbaaabbbbbbaabaababbabaaaabababbbaaaaababaaaaababababbbaabbaabbbabbaabaaabaaabbbbabbababaaababbaaabbababababbbbababaaaaabaaabbaabbbbaabaabbabaaaaaabaaababababaababbaaababbbbabbbbbbababaaaaaabababbbbaabbabbbbaababbababbbbbabbbbaabbabbabaaaaaaaabaabaabbabbbbbababbbbaabbbaabbaaabbaababababbaaaabbbbbabaaaaaabababbaabbabbababaaaaaabaaaaaabbbbaaaaaababbababaaaaaabbababbabaaaabbaababaababababbbaaaababaaaaabbabaabbaaabbbaaaababbabbabbabaabbababbaabaaababababbbabbaabbaaaabaaabbbbbaaaababbbaaaaabaabaabbaaabbaabbbbababaaaabbbababbaaabbaabaaabbbbaaaabaaaabbabbbbbbaabbaababbbaaaabbaaaabaabbaaababbabbaababbbbbababaabaabaaabaabbbaaabaababaababbabaaabaaabbaabababaabbabaabbababaaabbbaabbababbbaaaababaaaabaaabbabbbabbaaaababbbbabbbaababaaabbaaabbababaaababbaabbaababaaaabbbbaabbbaababbbbbaabbabababbabababaabaabbaaabaaabbaababbaabbbabaababbbabaabbbaaabbbaabababbababababbbababbaabababaababbaaabaabbbbabbbbaabbaaaabbaabbabaaaabaabbbbabbbaabbbbababbbbaabbabaaaaabbaabbbbbbbaaabaabababbaaaabbbbabbbbbbababaabbbabbbbbaabbbbbaabbbbabbabbababbbababbbbabaaaaaababbaabaababbbababbaabaaaaabababaabaababbbaaabababaabbbaabbbaaabbbaaaabbbaabbbbbaabbbbbbaababbbbbaaababaaaabababbaaaaababbabbababbbababaaabbaabaabbbaaaaaabaabbbaaabbaabababbbbbabbaabbabbbabaaabbbabbaaaabaabbbaaabbbaaaaababababbabbbbaaaabbabaababaaabaaabbabaaaabababbbabbabaabbbbaaabbabbbaabaaababbabbbbaaaabaababbbabbaaabaabababbbabbababbabaabbbababbaaaabbabbbbbbbbbbabbbaaabbbbabbaabbbbabaabbabbbbaaaabbbaababaaaaabbbbbaaaaaaabbbbaababaaaabaaaabaabababaabbaabbbaabbababaabaabaaaabbababbaabaaabaabbaaabbababbabaabbbababaabaaabaaaabbbaabaaababababbbababbaaabaabbabbbbbbaaabbbababaabaabbaaaaabbaabbbbabbaabbaabaaaaaabaaabbabbbbabbbabbbaabbbaabbbaaaabbaaaabbaabbaabaabbbababbbabaaaaabbbaabbaabababaababbabbaaababbabbbaaabaaaabbaababaababaabbabababaaaabbbbaaaaabaabaaaabbabaabbbbaaaabbbaabbabbbaaababbbbaabbbbbaabaaaaaabaaabaaaaabababbbbabaaaaabbbbbbaabbabaaaaabbbbbbbbbbbbabbbbbbaaabbbbaabbbbbaababaabbaababbbbaaabbaaaabbabbaabbbbbbbabaaababbbbaaaaababbaabababbabbabbaaabababbababbbaabbbbbbaabababbababbbbabbabababbaaaaabaaabaaababbabaaabaaabaaabbbaaaabbbaaaabbaabaabbbbabbbbabbbaabaababbababaaaabbbaaaaaaaaaababaaabbbbaabbaababaaaaabaaabbaabbbbababbaaaaabbbbabbababbaabaaabbaabbbaaabbbbbbabababbaabbbabbbbbaaabaaaaaaababbaaaabababbbaaababbbbbbaaababbbbaabbbabaababbaaabbbbbbaaaabbababaaababbaaabaaabbaaababaaabbbbabbabbabbabbbaaabbbbbbababaaaaabbabbbabaababbbabababbabbbbaabbbbbbbbbbaaabbbabbabbabbabbababaaabbaabbabbbbbaaaabbbaabaaabbbaaaaabababbbaaaabbbabaabaabaabbbbaaaaaaaabbaabbabababaabbabbbbbaaaabaababbbabbababaaabbbabbaabbaaaaaaabaaabaaabbbabaaababbabaababbabbabaabaabaaabaaabbabbaaababbbbabbbabbbbbbbbbbaaaabbaaaabbaaaabbabbabaaabbbbaabbbbaabbaaaaaabbaaabababaabbabbaaabbbababbbabbbbabbbaabaaabbaaaaaaabbbabbabaabbaaabbaabbaaaaabbababaabababaabbbaaabbbaaaabbbabaabaaaababaaaaabbabaaabbabbbbbaabbaaabbbbabaaababaabaaaaababbbbbbaabababbbaabaaaababbbaabbbbabbbabbaababbbabbabbaabbbbabbbbaababbabbaabbaaabbabbaaababbaaaaaaaaababbaaabbbbaaabbabbaababaabbbaababbabaabbabbaabbbbbaabbabbbbbbbbabbaaaaaaababbbabbbbabaabaaaabababbbbbbbbbbbbbbababababaaaababaabbbbaaabbaabbaabbbbbababbabbababbaabbaaaaabaabbaaabbbbbbbaaabbbbbababaaaabbbaaaaabaababbaaaabaabbbbaabbbbabbbbaabbbbabaababbbbbaaabaaaaaaabaabababbbaababbabaaababaaababbaabbabbbbaaaabaaaabbaaabaabaabbbaabbabbaaaabbbaaaaabbaabbaabbaaaababaabbbabbbaaababbaabbabbbbaaaaabbbbababaaaaaabbbbabaabaabaababaabbabbabaaaaabbaabaabbaabbbbbbbbbbabaababaabbaaabbabbbbbbbaabababaababbbabaaabaaabbbabbabbbabaabbbababbaabbbaaabaaaaababababbaaaabbabaaaaabbaaababbabbaaaabaabbabaababbaababbbbbabaaaaaaaaaabaaaabbabbbaabbaaabbbabbaabbbbbbabaabaaabbaaabbabbabbbaaabbaabaaabaabbbbbbbbaaababbbbaabbbaaaababbaabbabbbaaaaaabbbabbbabbabbaaabaababbbbbababaabbbaaaabbbaaaabbabbbabababbabaabbabaaaabbbbbaaaabbabbaaaaabbabbbbbabbaaabbabbaabaabaaaabaabbababbbbabababbbbbabaaabaaaabbabbbbbbbaabababbababaababbbbabbbbbbabbbaaabbbaabbbababbbbabaaaaaaababababababbaabababbabbbbbababbaabbbbaaabbbabbabbaababababbaaaaaabbbabbbaabbababbababababbabbababababbaabbaaaababbabaaabbbaaaaaaababbabbbaabbbaaaababbbabbbbabababbabaabbabababababaabaabbbaabaaabaabbaabbbaaababbbaabbbbaaababbbbbabbabaaaaabbabbbbbaaaaabbbbbabbaababbabbbaaaababbaaabbbababaaabbbabaaaabaabbbaabaabbbaaabbbbabbbbaababababbababaabbaaaaabbaabaabbaabbabbbabbbaabbbaababaabbaaaabbaabbaaabbabbabaaabbbbbbbbbbaabbabaababaaababaaaaabbbababbbbabaabaabbbbbbababbbabbbabbbbabbbaaabbabbabbbbbbaaaabbbbbababaaabbababbbaaaaaaabaaabbababbabbaaaaaaaababbabababbbbbbabbabbbbbbbaababaaabbabaabbbbaaabaabbaabbabbaaaaaaababbbbbbaaabaababbbbaaabbabaabbaaababaabbbbbabaabbababbbabaaababbababbaaaaaabbbbabbbabbabaabaabbabaaaabbbbbbaaaaabababaabaaabbaaababaaabbabbbababbaaaababbaaabaabbabaabbbaaababababbabbbaabbaabbbbbbbbabbbabbaaaaaaabbbaaaabbbaaababbbbaabbbbbbaabbabbabaaabbbabbbaaabaabbaababbbbababbaabaaaabbbaaaaaabbabaaaaabbaaaaaaabbbbaabbbabbaaabababbbbbaabbabbbaaababaabaabbaaabbaaaaabbbabbbaabbabbaababaabababbbbaaaabaababbabbbaaababbbabbbbaaabbbbaaaaaaaaaabbbbbababbaaaabbbaaabbbbbabbaaaaabababbabaabbabaababbbbbbbbbbaabaaabaaabbababbbbababbbababaabaaaabbbabbababbabbabbababbbaaabbbababbababababaabbbaaaababbaabbbabbaabbbabbaaabbaabaaabaabbabbbaaabababbbabbbbaaabaaaabbbbbaaabaabbbaababbaabaaabbbbabbbabaaaaabbabbabbabbabbbbaababaabaaababbabaaabababbaaababaaaaabaabbbbabbbbbbbaaaababbbbabababaaaaabbbbbbbabaaababbaaaabaaaaaababaaaaababababbaaababbabbaaabaabbbbbbaaabbaabababbbaaabbabbbbabbabbabaabbaababababbbbabaaaabbaaabaabbaaaaabbaabaabbaabaababbbbbbbbaabaaabbaaaabaabbbbabbabbbaabbabbaaaababbbabaababbbbbbbbaaababbaabbbbbababaaabbbabbabaaabbaaaabbababbbaaabaabbaaaabaaaaaabbbbabbbabbbaaaaaabaaabababbaaaaabbbabababaaaaabbbabbabbbaaaabbabaaaababbaabaaabaababaabbbabbbbaabbabaaaaababbbaaabbbababbbbabaaaaaababbbabababaaabababbaaababaabbbbaaaaabaaaabbbaaabaaabbaaaaaaaabaababbbaababbaaababbabaabbaabababaaaabaaaabaabaababbaaaaaaaaabababbbbababbbabaaaaaabbaaabbbbbabbbbaabbaaabbbababbaaaabaabaaaabbabbaaaabbaaabaaaabababbaaabaabaaababbbbaaabaababaabbaaaaabaabaaabaaabbaaabaabaaabbbabababbaabaaabaabbaaabbaaabbbaabbaaaababbabbbbababbbbabaabababbabbbababababbabbbbbbaabbbaababbbaaaaaaaaaabbbaaaaaabbabbabbbabababaababaabbaaaaabbaaabbbbaabbbaabaabbaabbabbababababaaaabbbbabaaabaabaaaaabbbbaaaaaabbbabbaaaaaabbaabbaaaabbaabaabaaabaaabaaabbbbababbbbabbbbaabbbaaabbaaaaaabaabbbaabbbbabbababbaabbabaabbaabbabaabaabbabaababbbbabbababaabbabbaabbbbbbaabbbaaababbbaabbbaaaaabbaaababbbabbaabbabaaabaabaabbaabbbaaabaabbabababbabaababaaababbbbabbabaaaaababaaabbbbababaabbbbbbabaaabbaaaabbbbabbabbbbbabababbaabbabaababbbbbbbaabbaababbababbabbbbabbaaabaaaaabbabbbaabbbbaababbbabbbbbaaaabaabaabbbbabababbbabbbaabbbabbababbaabaaaaababaababaaaabbbbbbbabbbbaabbaaabaaabbaababbbabbabbbaabbaaaabaaabababbbbabbaabbabaabaababbaabaabbabbbaaabbaaabaaaabbaabababbbaaaaabaaabbbabbbaababbaabbbbaabaabaaaaabaabbbbabaababbbbaabababaaabaabaabbababaaaabbaabbbababbababaabbbbbbabaaabbaaaaaabaabbaaaabbbabaabbbbbabababbbabbbabbabbabababaaabbbbaabbaabbaabababababbbbaaabbabababaaaaabbbbaaabbabaaabbaababbabbbaaaaaaaabbbbbbababbabbaabbbaababaaaabaabaabbabbabbbbbababbbbbabbaabaabaaaabbaaaabbabababbaabbbbbabbaaaabababababbaaabbaababaaaabbababbbbaaaabbabbbbababbabaababaaaaaaabababaaaababbbbbbbbabbaabaabbbbbbbbbabababaabbbabbbaaabaaababaaabbaababbaaabbbabbaaaabaaaaaaaabaaabbbbbaabbaaababbbababbaabbaaaaaaabbbbbbababbbbbabbbbbbabaaaababbbbabbbabbabaabaabbaabababbbbaaaaabbbbabaaaaaaaaaaabaaababbbaabaabbabbbbbbbbbaaabbbbabaaaabbbbbaabaabbabbbbbbabbbbbaabaaaaabbabbaabbbaaabbaabaabaaaaaabbbabaaaabaaaabaabababaaabaaaaabaaababbabaaaabbaabbabaaaaaabbaaababaaaaabbbbbbabbaabbaaaaababaabbbabbaabaabbbbbbbbbababbababbbaabbababbababababbaababbbaaabbbaaabbaaababbabaaaababaaabbbaaabbbbabbabababbbbbaabbabbaabaabaabbbbaaabbbaaaaabbbaaaabbbbabbabaabaabbbbbbbabaaababbaabbababbabaaabaabaaaabbaabaabbabbbaaabaaaabbabbaabbbabbabbabaabaabbbbabbabaaabbabbbbbbaababbababaababbabaaabbbaabaaabaaababbabbbbabbaaabababaaabbbaaaabaabaabaaaabbababbbbabaabaaabaaabbbbaabbbabbbabbbabaabbbbbbabaabaaababababbbbabbbaaababababbbbbabaaabbbaaabababbaaabbbaaabaabbabaaaabbbaaabaabbbaababaababbabaabbabaabaaaabaabaabaabaababbbbbbababababbbbabbbabbbabaaaaaababababaaaaaaaabbaaababababbbaaaabbabbabbbbbbbbabbbbbbbabaabbabbbbaabaabbaabaaabaababbbaabbbabbbbababaabaabbaaabbbaaaaababbbbbaaabbbabababbbabaaaababababbbbaabbabaaabbaabaaaababaaaaaabbaababbabbbbabbbaabbbbabaaabaaaababababbbbababababbabaabbaaaabbbaabbbabbbbbbbababbbaaabbbbabbaaaababbaabbbaaababbaababababaabbaaaaababaaabbbbbabaaaaabbbabbababaabababbaaabbaaaaaababaabaabaaaabbbbaaaabaaaaaaaaababbaabaaabbaaabbbaababaabaaabbbbaaaaabaaaaaabaabbbbaaaaaaaaaabbabaaaababbbaaaabbabaababaaaabbaaabaabbbbbaabaaabbbbaaaaaaaaaababbbabbbaaabbbaaababbabbababaaabaaabaaabbaaaabaaabbbbbababaaabbbbbababbaabbabababaabbabbababaabababbabaaababbabbbaaabaababaaaaabbabbababababaabbbbaaaaabbbbabbbbabbaaaaaabbabbabbabaababaabbbbbaababaabaaaabbababaababbaabbabbabaabbaaabaabbabbbbaaababbbaaaabaabbbaabbaaaaaabbbbaabaaaaaaabbbbaabbbabbabaababbaaabbaaaabbbbbaabaabbbabbaabaaabbbabbbabbbbabababbbbbbbbaabbbbabbababaaaaabbababbaaaabbaabbabbbaaaabbbbbaaaabababaaaaababaabaaabbaababbbabbbabaaaabbaabaabaabaaaabbabbbbaaabaaaabababbbbaaabaaabbbbbbaaabbababbbabaabbbaabababaaabaaaababaabbbaabaaababbabbaaaabbbabbabbabaababaababbaabbbaaabbbaababababbababaabaaabbaaabbabaaaaaaabaababbababbabbbbaaaaaabaabbbbbaaaaaaabababaabaababaaaaabbabbababbaaaaaabbbaaaaaababbabaaabbaaaaaaaabbaababbaaabbaaaaaaababababbaabbbaaaabbabbaaaaaabaabbababbbabbbaabbaabaaaababbbaabababaaaaaabbbbbababaaaaababbbaaaaaabbaaaaabaaaaaabbbabababbaabaabbbbbaabbbaaaaabaababaabbabaabbbbababbababbaaabbbbbaabababbbaaabaaaabbbaaaaabbbbbbbaabbaaaaaabbaaababaaabbbbaabaaaaaaababbbbbaaabaaaaabaaaaabbabbbaaaabaabbbaaaaabbbaabaabaababaaaaaababbbbbaabbabbbaabbabbaaabbbbbbababababbaabbbbbbbbaabbabbaaabaaabbbabbaaabababaabbaabbabbbaaaaaabaabaabababaaabbbabaabbbbbbaaaabaabbbababaaabbaabaaababababaababababbabaaaaabaaabaababbabbaaabbaabbababbbabbbbabaabbabababbaaaababababbaaabbababaabbbaaababbbbaabababaaabbbbbbbababbbabbaaaaaaaabbaaaaababbaabbbbabbbaabababaaaaaaaaaabbbaaabaaabbababbbaaababbababbbaabbaaaaababaabaaaaababaabaaaababaabbababbabbabbbabaabbbbaababaabbbaabaaabbabababbbaaaabaabaababbbbbabababbaaabaabbbaaaababbabbbabbaabbbaabbbaabbabaababaaabaabaababbaababbbbaaabaabbabbaabaaaaababbabbabbbabaaabaababbaabbbabbabbbbababaabbaabbabbabbbbabbbaabaabbbabaaaaaabbbbbababaababbaabbbaabaabbbabbabbaababaaabbbbbbbabaabbabbabbaababbabbaaaababaababbbbaabaaaaaabbaababbbbbbaaabbaabbbaabbaabbabbaababaaaaabaaaabaabaabbaabbbabbbbbaaaaaabbababbaabaaaaabbabbbabaaaabbabababbbabaabababbabbabbbabaaabaaabbaaabababbbabbbabbbbbbaababaabbaababbbbbbbabaaababbabbbabbbbbabbaabbbaabbaaabababbbaabbbaabbbaababbbbbabbbaabbbaaabaaabbbabbaabababbbbbabaaaabaabbabbabaabbaababbaabbabbbabbaaabbbababbbbbabbbababbabaababbbaabaaaabaaabbabbbbbaaabaaabaabbaaabababbbbbbbbababaabaaabbaaababbababbbaabbbabaabaaabbbabaabbbaaaabbababbaaaababaabbabaaaaabbabbababbbaababaabbbbabbabbaaaabbbaabbaabbbbababbbabbaabbaaababbbabbaaabbaaaaabaaaababbbaabaaabbabbaabaababbbbaababaaabbabaaabbaabababbaabaaababbbabbabaaaaaabbbabaaabaaaaaabbbaababaabbababbbbbbbbaabbaabababbaaaaabaaaabababaabbabbbabbbaabbaabbbbaaaaabbbbabbbbababaaabbbbaabbaabbbbabbbbbbbaababbbaaababbbbbabaabbbbbaabaabbbbaaabaababbabbbbbaababababbababaabbababbababaaababbbababbbbbbbbaaaabaaababbbbbabaaaabbbabbbbaaabababbbbbbaabbaabaababbaababaaaaaaaaababaaaabbbaabaaabbaaababbbabababbabbbbbbbaaaaaaabbabbababaabaababbaabbbaabbaababbabbbbaaaaababbaaabbbbbbabbabaaabaaababaaababbbbaaabbbabbbaabaabaaaababbbbabbbbbaabbabaaabbbabbbabaabbaabaaaababababbabaaaaaaaababbaabbabbaaaababbbbbabaaaabbaaaaabbbbbaababbbabaaaaabbabbabaabbbaabbaabaabbabbaabbabababbabbbbabbbbabbbababbbbabbbbbaaaaaabbaabbbaaaabaaababbbbbaaaabbaabbaaaabaabbaabbbbbbbaabbbbbbbbababbbbbaaaabbbbbababaaaababaababbabbbbbaabbbbbbabaabaabbbbbaaabaababaabbbbabbabbbabaaaaababbbbabaaaaabaabaababaaabaababababbbbbaaabaabbbbabbbbababababbbbbabaabbbabbbbbbbaabbabbabbbabbbabaaabaaaaaaababbabbbbbbaabbababbabbaabaababbbbaabaababaabbbbaaaaaabaababaaaaabbbaabbaababbaaababababbbbbbabaaaabababbabaababaaaaaabababaaaaaabbabbababbbbababababbbaabababbbaaaabbaabbababaabbbabbbbabbbbbbbaabbabababbababaaabaaabbbabbbbbaaaaabaabaaabbbbbabbababbbaaababbbababbabbbabaababaaabbbaaababbbaaaaaaaababbababbabbbbaababbabbababaabbbbbbaabaabbbbbaababbabbbaabbbbbbbbbababaababbbabbbbbbbbbbabbbbbabbbabaaaabaaaaababaaababbaaaababaabbaaababaaaabababababbbabbbaaaabbbabbbabbaabbaabbbaabaaaaaabbababbabaabaababbbbbbaababbbbaaabaababaabbaabbbabbabaaaabaababbbabbbabbbbaaaaabababbaaaaaabaaaabaababbbbbbbbaabbbbbbbaabbbaabbabbabaabaaabbbabaaaabbaaabaabaaaabbaababbbbaaababbbbababbaaabbbbaababbabaaaaabaaaaaabababbaabbaabbabaaabbabbabbabbbaabbababbbbaababbaaabaababaabbaaabbaaabbbaabaabbbbbaaabbbabbababbbbbbbbaaaaaababbbababababaabaaaabaababbbabaababbbaaabaabbbaabababbbbaaabbbbaabaaabbbbbbaabbabababbbbaaabaabbaaaaabbaababaaababbbbaabababaaaaabbbaaaabbbabbababaaaaaabbbababbbbbbaaaaaabbbbababbbaaababbbabbabbaaababbabbabaabbbbbbbaababbbababaaaaaaabbaabaabababbbbababababbaabbabababbbaaaaabaaaabaabbaaabbbaaabaabbbaaaabababaaabbaaaabbabaaaabaababbbbabbaababbababababbbbabaabbbaaaababaaaababbbaabbaaaababbbbbaabbababbaabbaaaaaabbabbabaaabaabbbbbaababaabbaaaaaaaabbaababbbbbabbaabaaabbaabbaabaaaaaababbbbaaaabbbababbaabbaabaabbbbbbbaabaabaabbbbaabbababaabaabbbabaaaabaaaabbbbbbbaaabaabbbababbaababaabbbaaaababbbbbaaabbabaabaabbbbaaaababbbbbababbbbabbaabbbabaababaabaabaabbbaabbababbaaabaaababaabbbbaabbbbabaabbbbbbbbaababbbabababaababbbbbabbababaabaabbabaaababbaabbababbbbbbbbbaaaaabbaabaabbaabbbaaaaababbabbabbaaaabbabaababbaaabababbaabbbaaabbbbbbbaabaaabbabaaaaaabbabbabaaaaaabbbaabbbbbababbaaaabbabaabbbabaaabaabaabbbaaabbbaaabababbaaabaaaaababaabbbbbaababbabbbaaabbabbbbaaaabbaabaabbbbbbaaabbbbbaabababbbaabbababbbbaabaabbbaabbaaaaababbbbbbabaabaaabaaaabaaabaaababbaaabbabbbbbabaabbbbaaaaaaabaabaaaaaabaabaaaaabbbaabababbbbabbaababaaaaaaabbaabbbbaabbaaaaaaaaaabaababbbaaabbabbbbbaabbaaaabbabbbbababababbbababaabbaaaabbaababbaaaaabbbbabaabaabbbabaababbbabbaaabbababbabbaaababaaaaabbaaabbbbbaabbbbbbbbbbaaababababaababbbbbabbbababaaabbbabaaaababbabbaabbbbbbabaabbbbabaaaababaaabbaaabbaaabbbabbbaaababbaaaaabababbbaaabaabbabaabbaaababbaabbbbbabbabbaabaabaababbabaaaaaababaabbabbbabaaababbbabbbabbbaabababbbabaabaabababaaabbbababaaabbaabbababaabbaababbabaabbaabbababbbabababaaabaaababaaaababaabaabaaaabababaaabbbbaabbabaabaaaaaaababababbbababbbaaaaaaaaabbbbabbaaabaabaababbaabbbbbababaaabbabbbbaaabbbababbaaaabbabbabbaabbaabaaabbaaaaabbbbbbababbabbabbbbaabbbaaabbaaababaabbabababbbabbbbbabaaabbbaaabbbbaabbbbbaabbbaaaababababababbababbbaaabbabbaaabaabaaabbabbbbbaaaababbbaabbaaaaabbaaabbaabbbbaabbaabbbbabaabbbbabaaaabaaabababababaaaababaabbaabbbaabaababbaaabbaaaaaababbbbababbabbabaabbaabbbaaaabaaaaabaaaaaababaabababbbabbbbbbbabbaababaaabbaaaababbbbbaaaaaabbbaababbbbaaaabbabbbbaabababbbbaaabbbaaababaaabbbbabababbabbbbbabababaababbbbbaababababaababaabbbaabbbaababbabbaaaabbbaabbbaabbbbbbaabbabaabbbababaaababbbbbbabaaaaabbabbbabaaabbaaabbababbaaaabaabaabaaabbbabaabbbbabaabbaabbbbabbaabbbbbaaabababbabaabbbbbabbbbabaaababbbabaaabbabbabbbababaaabaabbaabbbabaaabbaababababbababbabaabaaaababaaabaaabbaaaaaaabbbbabbabaabaaaaaabaaaabbabbabaabbbbaaaabbabaababbabbbbabbaabbabaaaaaabbbaaaaaaabaababbaabbaaabbaaabaaabaababbabbbbbaababbaabaabbbabbbbabbabbabbaaabaaaaababbaababaaabaaabbbaaababbaaaababbbaaabababbbbaabaabbbbaabababaabbbbbabbbabaaaaaaaaaaaabbbbbabaaabbaabbbbbbababaabbbabbbaababbbbabaaaaaaababababbbaababbbbabaaaaaaaaaabbbbabbbbabbbaabaababaaabbbababababbbbbbbabaabaaaaaaabbbaabbabaaaaaabbaaaaabababbaaabbbbaaaabbaaaaababaaababaabaaaabbababaaabababababbbaaaabbbbbaaabbbabbaabaaabbabbbbabaababbbbbbaaaabbaaabababbaaabbbaaaabbabbabaaaaabaabbbaabbbabbabbbbaaababbabaabbababaaabaaabababbaabbbbabbbbaaaabbababbaabbbabbaabaaabaabaabbaabbbbbbaabbbaaaabbbaaaaabaaabababbabbbabaaaaaaaaaaabaabbbabaaaabbaabaababbbbabbabbabbabbbbbaabbaababbabbbbaaabbaaabaaaabbaaabbaabbabbabbaaabbabaabbbbaaaaaabaabaaaabbaabaabbababbbaabbababbbaaaaaabbabbbbabaabbaaababababbababaabbbaabbbbbbaababbbaabaabbbaaabaabbbaaabababbbbabbabbbbbaababbbbaabaabbbabaaabbaababbabbabaaaaabaabbaaabaaabaabbbbbaabaaaaaabbabbbaaaabababaababbaaabbbabababbaabaaababbabbbaababbaaaabbbaaabbbabbabbbabbbbbaababaababbbbbbaabbbbbbaaaaabbbaaabbbabbabbabbbabbbbaabbabbbbabbbabbbaabaababaabbbababaabaaaabaaaababbaaabbaaaabaabaaabbaabaaabbbaaaababaaaaaaaaaabbbaaabbaabaaaabbbbabbbabbaabbbabaaaabbbbaaabbaaaabbabaaabbbbbabaaabbbbbbababbaaabababbbbaaaabaababaaaababaabbaaabbabbababbabbbbbbbabbbbbbabaabbaabaabbbabbaaabbbbbbaabbbabbbabaabbbaabbaabaaaaababbaababaababaabaabaaaabbababbbbabbbabbbbbabaabaabbbabbbaabaaaababababbaabbbaabaaaabababbababbabaabbabbbaaabaabababaaabbabaaaaabaababbbbababbaaababbbabbbbbbbaaabbbaababbaabaaabaabbbbbbbbbbaaaaabaaaaaaabababbbbbaabbbbbbaabbbbbaaaabbbbabbababbaaaabaaaabbbbbabaaabbabbbbbbbbaabbaabbabababbaaaabaabbbbababbaaaaaaabbabbababaaaabaabbaababbbaaabbaababbaabaabbaaabababaaabababbbbbbbaaaaaaabaabaababbbaaaabbbabaabbbaabbaaabababbaaabbbaaababbbbaabbbbaababbbaababababbbabbaabaabababababbabbbbabbbaaaabababbaabbabbbbbbaaaabaaabbabaababbbababaabaaaababbbbaabbabbbbaaaaaabbaaaaabbababbbbaaaaaaabababbaaababbbaaaabbbbbaaaababaabbbbbbbbbaabbbabbaababababbaaabbbabaaabbbbbbbbbabbbabbabbbabaaaaabbaabaaabbaabbbbaaababbbabbbbabaabbaaaabbabbbbaaabbbbaabbbbbaabbbbbaababbaaabbbbabbaaaabbaaaaaaabbaaaaabbabbbaaaababaaabaaaaaaabaabaababaaaaaabaaaaabbaabaaaaabbbabbababbbbbbbabaaababbaaababaaaababaaabbaaabaabbbaaaaaaababababbbabbbaaaabbaabaababababbbbbbaababaaaaaabbaababababbbaaabaaaababaababbabababbaabbbbbbbabababaaabbababbbaaaabbaaabaaabbabaabababaaaaaaaabbbabaababaabaaabaaabbbaaababaababbbbababbbaabbbbabaababbbbbababbbbaaabbabbababaaabaaababbbbbaaababbbabaaaaaaababaabaaabbbbbbbaabaaaaabaabaabbaaabbaaabababaaabbbbabbaaaabbbabaaaabaabbabbabbbbbbbaaaaaaabaaabaaaaaaaaabaabbaaabbbabababbaaaabbbaaabaabbabbaabbbbbaaabababbbaaaabbabbaababbabbaaaabaaabaabaabbababbbbbbabababbaaaaabaabbabaaabbbbbbabaabbbbaabbaabbbaabaaababaaabbabaabababababbbaabababababbbbbbbabbabaabababbaabbbabbbbaababbbabbaaaabbaaaaababbbaaaaababaaaababbaabbbbbbababababbbbabbabaaaababaaababbbabaabbbbbbbaaabbaabbaabbbbbbabbbbbaaaaaababaabbbbbbbbbbabbababbaabbbaababbbbaabaababaabbbbabababbaaabbaabbbbbbaabaaabababbbbaabbbabbababbbbbbbaabbbbababaaaabbaabbbbaaabbaaabaaabaaaabbaabbbabaababbababbaabaabbbbabaababaaabaabbaabbaabbaaabbbbabbabaaaaababaabbabbabbabbbbabbabaabbababaaaaaabbbbbabbbababaabaabbaaababbaaabaaabbbbaaaaaabbabbbbabbbbabbaaabbabaaaaabbbbbbbaaaababaababbabaabababbaaabbababbaaaaaaabaaaaaaaabbaaaabaabbabbbbabbbabaaaaabbbabbbabaaaabaabbbaaaaaababbbabaabbbbbaabbbaababbbbabbbabbabbabbbbbbbaaaaabbabbababbabbabbababbabbbaaabbbbbbabbbbaaabbbbbaaaababbabaabbaabaaabbabbbaaaaabbaaabbaaaabbabbabbaabaaaabbbababababbaaaaaaabbbabbbbbaaabbbbaaabbbabbabbaabbababbbbaaabaaaaaabaabbababaabaaaaaaaaaaabbbabbbabbbaaaabaaaabbabbbbabbbaabbabababbbbabababbaabababbaabbbbbaaaabaaaaabaaaaaabaabababbababbaabbbabbabaabaabaaaaababbabbbaaabababaababaabaaaabbabbbbbabaabababbaaabababaabababaabaaaaabbaababbbabbbbbabbabbbababbbaaaabbabbbbbabababababbbaaabbababaabaabaabaabbaaaabbabbaaabbaaaabbaaaaabbbabaabaabbababbbbaabbbabaabbabaabbabbbbbaabbbaaaaabababbabaabababaabbaabababbabbabaaaaabaabbbabaabbbaabaabbbbaabaaaabaabababaaabaaaabaabbabbabbababbbbbabbabbaaaababbbabaaaabaaabaaaaabbabaaaaaaabbaaaabaaababaaaababbaabbbbaabaaaabbabbbaaabaabbbaaaaabbbbabaabbaaabbbabbbbbbbbbabaaaaaaaabbabbabaaabaabbbaabbabbbabbbbbaabaaabaaabaaabbabbabbaababaaababababbbbbaaabbbabbaababaababbabbbaaaabababaabaaaababbbbaabaaababbbbbbbbababaabbabaabbbbbabbaabaaabbbbabbabbbaabaabaaabbbababaabbbbabaaaabbabbbbbbababaaaababbabaaaababbaabaaabaaababababaabbbbaaabbaaabbabababbabbbbabbabbaabbaaabababbbabaabbbabaaabbaababaabbabaaaaaaabaaaabaabbbbabbaaaaabababbbabbaabaabbbabbabbbbbbbbabbbbbaababbaababaaabbababbabbbbabbaabbabbbabbabababbbabaabbaaaabaaababbbbababaaabbaaaaaaababbbbbaababbbbabaabaabbabbbbaaababbabababbababbbaaaaabbbbaaaabaaaaababbaaaabaaababaaaaabaabababbbabbaabbaaaaaabbbbaababaabbaababbbababbbababaababaabbbbaabaaabbaabaaaabbbaabaabbbaaababaaababbabbbbabbbaababbbbbaabbbbaaaaaabaaaaaabaabababbababbabaaababbbaababbabbaaaaabbbaababbbaaabababaaabbaaaaaaaaaaabbaaaaabaabbbbababaababbbbaababababbaaababaaaabaababaabaababbaabaaabbbabbabbaababbaabbaaabaaaabbbaaababbaaaaaaabbaabaaaabbbabbbababbbbababbbbbababbaaabaabaaabaaabbbaaabaaabaaabbbaaaababbabaaaaaabbabaabbaabbabaabbbbabbbbaabbaaabaaabbbabaaaabbaaabbabbabbabbaababaabbabbaababbbbbabbabababbbbaabbbbaaaaaabbaabbaabbbbaaabbbbbabbbbaabbabbbabbbababbababbbbbbbabbaaabbabbbbbbaaaaaabbbbbabbaaabbabbaabaababbbaababbaabaaaaabbaabbbabbababaababbaabbbbaaaabaabbbabababbabbbbaabaaabbaaabbbabaaabbbaabbbbaaababbaaabaaaaaaaabbaabbbbbabbaababbbaabbbbabbaaaabbababbbabbabbbaababbaabbbbbbbbbbaabbbbababbabbbaaabaabbaabbbabbbbaaaaaababbbaaabbbabbaaabbabbbaaabbaabbbbbabaabaaaaabbbaaaaabaabaaaaaaabababbbababaababbbababababbbbbbabaabbabaaababbaabaabaabaababaaaabaaabbaaabaababbabababbbbaabaabaabbaabbbabbaaaaaabaaaabaabaaabbaababababbbbaaabaaaababbbababababaabbbbbababbbabaaabbbbbbabbbabaaaabbababbaaabaabbaaabbabbbabbbbbaaabbbabbababaabaaaabbbababbbabbabaabbbabbbabaaababbaaabbbaaababbbabbaaabaaabaaabbbbbaaaabaabaabbabbaaaababaabaaabbaababaaabbbbbbbaaabaaaaaabbabbababbbbbaabaabaaaaaaaaabbbaabaabbaaaaabbabbbabbbaaabbbabbabaabbabbbaabbaaabababbaabaaaabbabbbabbbaabbbaabbbabbbbbabbaaaabbbbbaabaabaabbaaaaababbabbbaaabbbaabbaaabbababbbbabbbaabaaaaaabbabaaaabbaabababbaabaabbbabaabababbabbabbbaababbababaabababbbaaaaaababaaabbaaaabaaaaaaabbbbababbbbbaabaaabbaaaabaabbaabbbbbabbaabaaaabaaababbabbabaaaabbbababbbbabbbbabaaaabbbabbbaabbabaabbbbbbbbbaaabbaabaabbbaaaaabababbabababbabaabaaababbabbaaaabbbbabbbbbbbbbbbaaabababababbbaaaabbbaababbababbabbaaabbbabaabbaaaabaaababbbaaababbababbbbbbabbabbbbbbaabbbbbaabbaaabbbbbbbbbabbaaabababaabbaaabaabbbbabbaaabaaabbbbaabbabbbbaabaaababababaabaaaaababbaabaaaababbbaaabbabbbaaaaababbaaaabbaababbabbbbbabaabbaaabbaabbaaabbbbbbbabbaaabbabbaabbaaababaaaabbbabaabbbaababbaabbabbbbabbabbabababbabaabaaababbaaabababbbbbbaabbbaabbbababbbaabaaabbbabbaaaabbbbaabaabaabbaaaabbaabaabbbbabbaabbaabaababbaabaabaaaabbbbbbbabbbaabaabaabbbbbbbbbabaaababaabaaabbabbbabaaababbbbababbaaaaabbbaababaabbaaabbaababaabbabababbaababaaaabaaaabbaababbbbaaabaababbbbaaaaabaaaababaaaaaaaabbaaaaabbbababaaabaabbbaaaaaabbabaabbababaaaabbbaabbbbabbbababbaabaababbbaaaaabbaaaaaaabaaaabbabbbabababababbbaaabbabbbaaaababbbbaababbaaaaabbabaaabbaaaaabbbbaabbbaabbababaaabbabbababaabaaabbababaabaaabaababaabaabbababbaaabbbbabaaababbaababaaabababaaababbbaabaabaabbbbbbabbbaabaabbababbbbbaaabbbbaaabbabbbbabbbabaabaababaaababababbabbabbabaaaabaabbabbabbabbabaaaaabababbbbbbabaabbbbbabbbbaaaaaaabbbaabaaababbbbaabbaaaaaabaabbbaabbbbabbbbbbbaaaaabbbbabaabbbbbbaabaaabbababaabaabbabbaaaaabbabbbabbbaaabbaaaaaabaaabaaabbbbaabaaabbbaaabbaabbaaabaaabbaabbabbababbababbbbaabaaaaaaaaaaabbaaabbbbaaaababbbbbaabaaababbbbaabbbabaabaaababbbaaaabbbaabbaaaaaaabaaaababbababbbabbbbababbaabbbbabbaaaababbaaababbaaaabaabaaabbabbaaaabbabaaaaabbbbaababbbaaabbaabaabaabbabbababbaaabbabaababbbaaaabaaaabbaaaababbaaaaaabaababaaaaabbabaaabaababababbabbbaaaaabbaabbaaaaabbabbaaabbaabbabaabbaaababbbbaabbbaaabbabbabaaababbabaaabbbbaaaaabbbababaababaabbaabaaabbbaabbbababaababaaababbaaabaabaababbbbbababbaaabaaabbaaabbaabbbbbbabbbababbbababbbbbbaaaaabaabaabaaaabaabbababababbaabbabaabbbaabbaaaaababbbaaaabbbbbbbaabaaabbabababbbabbbbabaaaabaaaaaabaaaaaababbaabbabbaaaabbbaaaabaaabbbabbabbbabbbbaabbabbabbbaababababaababbabaaaabaaababbabbaabaabbaabbaabbbabaabaabbababbababaaaaaaabaaaabbbbbbbabbaaaaaaaabbbbaabbbbabaababbbbaabaabbbbbbbbabbabaaaabaaaaaaaabbbabbbabbababbaaabbababaaabbbaabbaaababaabbababbbabbabbabababbababababbbbabbabaabbaaaaabaaabbaaabbabbaababbbbbbbbbabbaabbbbbbbbbbbbbaabbbbabaabaaababbbaaabbbbbbabbbbbaaaaaabbbbbbbbbabbababbbababbabbbabbababbaaabbaaaababbbbaabbbaaaabbaababbbbaabbaaaaaaaaabbabbbbbabbbabaabaaaabbaabaabbbabbaaaabababaaabbaaabbabbabbbbbabbabaaaababbaabbabbbaababbabbbabaaabaaabbbbbaaaaaabaaaaaabbbbabaaabbaabbabaaaaaaabbbaabbaabbabaaaaabbabaaaabaababbbbaababaabbbbbababbbbaaaabbbaaaaaabbaaaaababaababbabbaababbabbbbabaaabbabbbababbbbaaababaaaaabbbabbbbbbbaabbaaaaaabbbabaaabbabbabbbbbbbabaababbabaabaaaabbbbbbabbaaaabbabbaababbaabaabaaababbaabaababbbbbbaabbabbabababbbbaaaabbbaabbbaabbaabbbabaaaaababaababaabababbababbabababbabaaaabbbbbbababaaabaaabaaaabbabbaababaaaaabaaaaabaaaabaaaaabbabbaaabaaabbbbaaabbbaabbabababaabbbbabaabababbaaababbbbbaaaabbabbbaaababbaaaabaaaaaaaaaaababbaabbbaaabbabbaaabaaabbaaaaaabababababbabaabbabbbbabbbbbbbabaabbabaabaaaaabbbbaaaaaaabaaabbabbaaabbabababaaabbaaaabbabbabbaaaaabbabbbabbabaaabaabaaaaabbaaabbabaababbababaabbbbbaaabaaababbabbaabbbbabaaababbaaababbbbbbbabbbaabaaabaabaabbbabbbaabaaaaaaaaabbbabbbbaababbbabbabbbaaabbabbabbbbaaaabbaabbabbbbbabaaabaabbaaabaabbaabbbbbaaaababbaaaabbbaabaaabaaaaaaaaaaabbbaabbbaabbbbababbbaababbabaaaabbbbaabaaabbaabaabbbbabbbbbaababbabababbaabbbaaababaabaabbbaabbaaaaabbabbbbabbabbabbbaaabaaabbbababaaabbabababaaaaaaaaaabbababaabaabbabbabbbaaaaabaabbaabbbaaaaaabbbabaaaaababaabaabbaabbbbaababbbabaababbabbbaaababaaaabbabbbbabaaabbaabababbbababaabbabbaaaabbaaaaababbbaaaaaaababbbabbbbabbbbabbbbaabaabbbabaabbbababbbbbbaabaaababaaabababbabaabbbaaabbabaababaabbbbabbbabbabaaabbaaabbaaaabaabbbbabbababaabaaaaaaababbbbbbbbabbbbababbbbbbabaaaaabbbababbaaabaabbbaabbaababbababbbabababaabababbbbbbbaabbbbbbbbbaabababbabaabbaabbabaababbbaababbababbbbbbbabbbabbbbaabaabbbbbbabababbbaabbaabaabaaabbabaabbbaaaaaaabaaabbabaabbbabbbbbbabababbbbabaaaaaaabaabaaaabbaabaaabbbbbbbaabaabaababaabaaabababbabbabaabbbbaaabbaabaababbaabbababbaabbabbbaabbbaaababbaabbaabababbbaaabaaabbabbabbbababbaaabbaaaabbbbbaababbabbaaabaaaabaabbbabbabbabbbabbbbaabaaaaabbaaaabbbaaababbaabbbbbbbbaabaabbbbabbbbbbbbaabbbabbbbbabaabbbbaaaabbababbbbaaababbabbbabaaabbaabbbaabbbbbaabbbababaaababbaaabbabaaaabaabaabaaabbabbbbbbaabbaabbbaabaabaabbbababaaaaabababbabbbabbabbbbababbabbaabaabbbabbaabbabbbabbabbbaaaababbbbaaaabbabbbaabaabbabbbbbbbaaaabababaaaabbbabaabbabbbababbbbabbbbbaaabbaaaaaaabbaaabaaabbbaabbabbbbbbabbaaabbbbbaaabbababbaaaabbaaabbbabaabbaabbabaababbabbabaabaaaabbbaabaaababbbaababbbbbaabbbabaaabbbabbabababbbabbabaababbabbbabaabbbabbaaabbababbbaaabbaabbaaabaabaabbbaaabaaaaababababbbaaabbbbababaabaaabaababbbbaabaaabababbbbaababaabbaaaabaabbbbabbaabbabbabaabaabaabaaaaaabbbbbabbbbbabbbabaaabbaababbbbbbbbaabbbaabababbbaaabaaababaabaabbaabaaabbbbbabbbabababbaabaababaaaaaabbbbbbbaaabbbaabbbaaabbbbaaaababbbbbbbbaabbababbabbabbbbababbbbababbbbababbaaaabababbababababbbababababbbbaaabbbbbaababbabbaabaaaabbbbababaabbbbabbbabbbababbbbbaabaabbaaaabbabbaabbaabaaaabbbabbbbaaaaaabaabbaabbbaaaaabbbaaaabbababbbbabaababbaaabbbaaababaababaabbbababbbabbbaabbbaabaabbbaaabbbabbaaabbbabbbabbabbbbbaabbbaabbbabbaabbbaaaaaabbbaabbabbbbabababbaabbbbaababbaaaabbbbbaabbaabbbabbbababaabbbbaabbaaabaababbabbaabbbaaaababbabbbbbbbbbabbabbbbaabaabaabbbaaabbbbbaabbbbabbaaabbbbbaaaabbaaaaaabaaaaababbbababbbaaaaaabbababbabbaaabbbbaabaaaaababbbabbabbabaaaabbbabbaabbaaaaabaababbaaaabaaaaaabbaaabbababaaabbbababbbbbbabbaabbababbbaabbabababaaabaababbaaaabbabbababaaabaaaaabbbabaabbaabbaabbabbababbabaabbaabbabbbbaaabbaabaabbaaaabaaabbbabbbbbababbbaaaaaaaaaaaabbbbaababaababbababababbbbaabbbbaaaabbaababbaaaabbbbaabbbbaabaababbbbabaabbbbaaaabbabbbbbbaababbbaaabbbaaaaabbabbaabbbaaaaababbbaaaabaabaaabaaabaabababbbbbabbabaababbaabbbbbaabbbbabbbabbbbabbbabbbaabbbababaabaaabaaababaabababaaabbbbbbabaaabbabbbbaabaababbababbbababbbaabaaabbabbbbaaaababaaaabbbbaaaaabbbaabaaaababbaababbbabbbbbaaaaabbbbaabbabbababbbbbabbbabaaaabbaaabbaaabbaababaabababbabbbabaaaababbabaaaaaabbbbabbaababbabbbbbabbabbaaaaaaaabbbbaaaaabbbabbbabaaaaabbaababaabababbbbabbabbbaababbbaaaabbbbaabbabababbabaaaabbabbbbbbaabababbaaabbabbbbaabbaaabbababaaaabbabababbaababaabababaabaaaabbbaaaababaaaaabbbbabbbabbababaabbabaaabbaabbbbbaabaaabbbaaabaabaaabaabbaaabbabbaababbbababbbbaabbabbabbbbbbababbbabbbabbbabbabababbabbaabbababaaababbaaaabaabaabbbbbbbbabbabbbaabbaabbaaaaaaaaabaabbbbabbbabbbbbbbbaabbbbbabbbbbbbbbbbbbabbbabaabaabbbbabbaabbaabbaabaabaabbaabbbbaaaababbbaabababbababbabbabbaababbabaabbaaaaaaabbababbaababbaabbbabbaabbbbaaabbaabbabaaababbaababbaabbabbbaabbaabbbbbaaaaabbababbaaaaabaaabbabaaaabaaaaababaabaaabbbbabbaabbbabbaababbbbabbbabaabaaaababbbaaaaabbaabbaabbaaaaaaabbbabaabbbbbaaaabbbabaabbbbabbaaababbababbaaabaaaaabbbbbaaabbaaababbabbbaabaaaaabbbaaababbababbabaababbabbbbbaaaaaaaababbababbbabbaaaaabbaaaababbbbbaaaabbababaabbabaabbabbbbabaabbbbbbababbaaaaaabbaaabbbaabaaaabbbaaaabbbbabaabbabababaabbaaababaaaababaababaaabbaababaaababbaaabaaaaabaaabbbbbbaaaabaaaabbabaabbabababaaababbbbbaabbabbbbaababbababaaabbabbbbbbbbbbbbbbbabbbabbaabaabaaabaaabbaaabaabaaabaabaabbbabbaabaaaaaabbbbbabaabbaaaababaabaabbbabaababababaaabababaaaaababbaaaaaabbabaaabaabbabaaaaabaaaaaaaaaabbaababbabbbbbbbbbabaabaaababbbaaabbbabaababbaaaaababaaaaaaabbbbaaaabbabbbabaabbbbabbbbababbbaaaaababbabbbbbaaaaabaaabbabbaaaababbbaaabbbaabbabbaababbbbbbabbbaabbaabaabbbabbabaaabbabaaabaabbaaababbababaaaaabaabbabbbbbbababbbababaabbbbbabbabbbababbabbabbaabbaabaaaaabaaaaaababbbbaaabaaabaabbabaabaaabbaaaababbbabaabaaabaaaaababaabbbaaaabbbaabbaabbaaababbbbababbbbabababaaaaaabbaababbbbaabaaabaabbbabbbaabababaabbbaababbabaaaabbaabbbbabbbbbabaababbbaaaabaabbbaabbaaabaabaabbbbabbabbbabbaabaababbbabaaaaababbbbbbbbbbabaaaabbbabaabbababbababbababaabaaabaababbbabababaabbabaaababaababaabbaaaabbaaabaabbbbaaabbabbbaababbababbababbabaabbbaabbaaaaaaabaaabbaabaabaababbbbbbaaaaaaaaaaaabaababaababbaaababbbaaabbbabaabbbbbbbaaaabaaabaabbabbabaabbaaabaabaaabababbababaaaababbababbababbabbaaaabbbaaabbabaaabbbbabbbbabbbbabbaaaabbbaaababbbaabbbbabbbbbaaabaababbabbaabbaaabaabbabbbabbbbababaababbbbbbabaabbbabbabaaababaababbaababbbabaaabbbbbaabaababbaabbabbaabbaaabbbababaabaabbbbbaaabbbbbabaaaaaaaabbaaabaabaabbbaababbabbbbbababbabbabbbaabbbbaababbabaabbabbaabaabaaaabaaaaabbbaaaabaabaababbbbaababbaaaababaababaaabbbaaabbaaabbababbaabbbaabbabbbabaabaaabbaabbbaabaaababbaabaaabbababaaabbbbaaabbbbaabbabbbaaabbaabaaabaaaaaaaabbababbbbaaabbbaaaaaababbbbaababbbbbaaaababbbaabbbbbbbaabbaabbaabbbaaaaabbbbbabbaabbbbbaaabbbbabaaababaabbbbbbaabbbabbababbbabaabbbbaababbbabbabbbbbaababbababbbaabbbaababbbbbbabbbbbababbbbabbababbaaaabaaaababaababbbabbabbabaaaababaabbaaaabbabbaabbbababababaaaabbabaababbabbaabaababbbabbbaabaaababaaabaaabbbbbbabbabbaabbabaaababbaaabaabbbbabbbaababbbaaaaabaabbbbbbbbbaabbbbbbbabaaabbaababbaaabaabbabaabaaabaaaaaabaaaabaabbbababaaaaabbaaabbaaabbbbabbbaabaababaaabaababaaaabaaabbaabbababaaaababbaabaaaabbababbabaabbbbaabaaababaaaaababaaaaaaaaabbaabbbababababababbbbaabbbaaabbaaaaaaababbbbbbbbabaaabbbaaaaaabaaaabababbbbaaabbbababaaaabaabaabaababbbbbabbbaabbbaabaaababaaaababbabbaabaaabbaabbbbabbbabaaabaabbbbbaabbbbbaabaabbabaaabaaabbbbaabbbbbabbaababbbaaaaaabaaabaaababaabbbbaabbaaaaaabaaaaaaabbabbbbbbbaaaabbbbaabaabbbbaabbbbabbbbaaaaababbaababababbbbbabbaababbabbbababaabbbbbabaababbbbbbaaaaaaaaabababbabbaababbbbabbbaabaabbabbaaaaababbabbaaaababaaabaabbbabbaaaabaaaabbbbbbaaaaababaaaabaabbbaabababbbbbabaaabbabbbabbbabaabbbbabbabbbaaabaabbbaabbbaaababaabababbbaaabababaababbbaaaabbbabbbabbbabbbabaabaaaaaabaababbaaabababbababbbbbaababaaaabbbbbbaabbaaaaabbbaabbbbbbbaabbaababaabaaabbbabbabbaaaabbbaabaaaaabaabaababbbababbabaabbbbbbbabaaaaababbaaabbbabababbabaabbabababbbbababababbbabbaabbbbabaaaaabbbbaabbababaabbbaaabbbbbabaabababbababbbaababaaababbbbaaababbbaaaababbbbaaabaaabbbbababbbabaaabbbaaabbbbabaaabbbbaabaaaaaaaaabbabaabbabbbbbabbaabaaaabaabaababbabbbbbbabaaaabbabbbabaaabbbbaaaabaababbbbbbaaababbbbbbbbbbababbbbbabaaaabbaaabbaaaaaaaababaaabaaaaaabbbabbbbbaababbbbbbabbbabaabaaabbaabaabbbbbabaaabbbaabbbabbbbaaabaaabbbaaaaabaabaabbababbbbbaaabbbbaababbbbabbbaabbbaaaabbbbbaabbaabbbbbaabaabababaabaabaaaaaababbaaabaaaaaaabbbaaaaabbbbaabbbababbabbbbbbabbbbaabaaaaaaaabbabbbaabbaabbbabaaababbbbbbaabbabaaabbabaaabaabbbbbabbaaabbbabbbbabbbbabababaabbbbaabbaaaaabbabaabbaaaababaaabbabbbbabbaaaabaaabaaaaabbaaabbbbbaaabaaaabbabaabbbabbababababbbbababaabbbabbbaaaababbbbaabbabbabaaabaaaabaaabbaaaabbabbababaabbbbbbabababbbaabaabaaabaaaababababaaababaabbbaaaaabaaabbbbabbbaaabaabaaabbbbbabababbaaaaabbabaabaabbaabbaabaaabbbbbbabbabbbbbaaaaaabbaabaaaaababbbabbbababbabbbaaaaaaabbaaababbbbababbbaaabaaabbabbbaaabaaaabbabaababaaababbaaaaabaabaaaabbaabbbbbbbbaaaababbbabbbbbababbaabbbaabbbabbbabbabababbaabbbabbaabbabbbbbbbbaaabbaababaabaaaaabbbbaaabaaabaababaabbaababbbaaaaabababbbaabaabbbbaaababaaaabaabbbbbbbbbaabbbabaaaababbaaabbbabababbabaaabaaabbababbaaababbabbabaaaaabbbbaababbbbaabaaaababbbbbabaaabbabbbbaabaaaaaabbbbabbaabbbbbbaabbaaaaaaaabababaaabbabaaaaabaabbbaaabbbbbaabaaabbabbaabbaabaaabbaaaabbabbabbbbaabaaababbaaababbbbbbabbbaaaabbaabbbaaababaabbbbbabaaabaabaaabababaabbbbaabababbbaaaabababbbabaababaaabaaaaabaaaababbbaaabbaabbaabbaabababaaaabbaabbbbabbaaaabbbababbaabbbbbbaaaababbbabaaaabaabababbaabaababababbbbabaabbbabbabbaaaabbabbababaaabababaaababaabbbbabbabbbbbaaaabbbbbbaaabbbabbbbaaaaaababaaabbabbbbbaaaabaaaabbbabbaaaaababbbabbbabbbabbbabbaabbbbbbaababbbbbbababbababbbbbaabbaabaaaaabbbaaababababaaababbbbababaaaabaabbaaabbbbabbaaaabababaaababbaabbbbbbbabbaababbbaabbabababbaaabababbaaaaabbaaabababaabbaabbaaaaaababbbaabbaabaabbaababaabababbbbabbaaaabaabaaaabababbaaaabaabaaabbbaababababbbbabbabbbaaabbaababbbbabaababbbaaaabbabababababbabbbabaaaaaabaabbabbbabaabaabbabaaaaabbbbababaaabaaaaabbaabaaabaaabbabaaaaaabbbbbaaaaaaabbababbaabaabaaaaaaabbbbbabbbbabbabaaababaaaaaabbbaaabaaaaabbbababbbababaabaababaababbbbbabbaaaaaabbabbabbbbbababbababbbbbaaaabaababaaaababbbabaabbabbbaaabbbaabbabbaabbabbaabaabaaabbabbabababbababbbbababbbabbaabababbbbbbbaababbbabaabbbbbbabbabaababbbbbbaaaabbbbabababbbbaaababbabbbababaababaabbbbbaaaabbbaabbbaaaaabbbaaaaaabbababaaaabaabbbabbbaababbbaaababaabaabbbbbababbabbbbaaababababaaaabbbbabababbabaaabaaaabbbbabbabbaaabbbbabbabbabbbabaabababbbabbbabbababbbaaaaaaabaaaaaabbaaaabaababbbaabbaaabaaabbbabbbabbbbabbbbabbbaaabbbaaabbbaababbbbbbabbbababaaabbbbaabbabbabbababbaabbbababaaaaaaabaabaabbbaabaabbabaaaaaabbaabaaabaabbbbaabbbaaaabbaaaaaaaaabbaaaaaababaaaaaaabbbbabaaaaaabbabaaabaabbbbbabaaabbababbbbabaabbabbabbaaabababbbabaababbabaababbbbabbababababababbaaabbaabbaaaaaaabbaaabbbbbaabbaabaaaaabbbabbaababbabbbbbabbbaaabbaaabaaaaaabababbbabaababbbaaaababbbabaababababababaababbaaabbaababbbabbbabbaababaabaababaabbbbbaaaaaabaaabaaaaabaabbaaaaaaabbbbbabbabbababaabaabbaabbbbbabbaabbabbbbbbbbaabbaaabbbabbabaabbaabaabbabbbaabaaaaabbbabababbbbbbbaaaabaaaaaababbbbbbbaabbbbabbabbbababaabbaaaabaabaaaaaaabbaabbabaaabaabbbabbbaabbbaaabbbaabaaabbbabaababbbaaaaabbbbbbbbaaaaaaababbbbaabaabababaabbaaabbabbbabbabbbbaababbbbbaababbbbbaaaabbaaabaabbabbbbabbbbbabbabbabababbaaaaaaabbabbbabbbaaaaaaabaaabbbbabbbbbaabbaabaababababbbabaababbabbabbbbaaabbabaaabaaabaaabbbbabbabaababaabababbbabaabbbabaaaabbbaaabbaabbbbbbabbaabbbbbbbabbbbaaababaabaaabbbbbbbaabbababbaaabbaabaaaabbaabaababbbababbaaaaaaaaabbbaabaaaaabbbabbababbaabaabaababbbbaaabbbaaababbabaababaaabaaaababbabaabbabbbbaaaabaaaabaaaaabbbaabbaaabbaaabbaaabbbbbaaababbbaaaabbaaaabbaaaaaaabbaabbaabaaabbabbbbbbaabbbaababaaaaabbababbbbbbbaaaabaaabbaaaaaababaabaabbabbaaabbbababbbbbbabbbabaaaabbabbabbabbbbaabbabbbababaababbbbababbaababbbaabaababbbbbbbabaabbbbaabaabbbbbabaabbbbbbaabaabbbbabbbabaababaaabbaabbbabbaabbbbaabbaababbbabbbabababaaaabaaaabbaabbbbaaaababbaaaabbabbabbabbabbbbaaababbababaaababaaabbababaaabbbabbaabaaaaaaabbaabbabaaaaabbabbbbbbabaababbbaaaabbbabbabbbabababbaabbaabbaaaababbaaabbaabbbbabbbbbbbabbbbabaaabbabbbbbaaaabbaaaabaaabaabaabaabaaaabbaabbbbbbabbbabbabababaabaabbaaabbbbababababababababbbaababbabbaaaabaaabbabababbbabbaaaabaabbabaaaabaabbbaaabbbbaabbaaaaaaaababaabbabbaabababbaaaabaababbbbababbbaabaabababbaaaabbabaaaaaaababbabbaaabaaabbbabbabbabbbbbabaaaabbbbbbbbaabaabbbbabbaaabaabaaaaabaaabbbabaaaaaabaabbaababbbabbaabbaaabbbbbbaaabaababbbaabbbaabbaaaabaabaababbbbbbbbabbbabbaabbbbbababbaaaabbbbbaabbaaabaaaabbbbbbbbbaaaabaaaaaaaabaababaabbaaabbabbbaabbbaaabbababbbbbaabbbbabbabbbababbababbbbbaaaaaabbaabbabbbababbabaaaaaaaabbbababbaabaaabbbaaabaaaabbaaaabbbaabaaababaabbbaababbababaaaaaaabbbbbbbabbbbabbabaabbbbbabaaabbbbabbabbbababaaaabbbabaabaaaabbbabbaabbabbabbbaaabaabaabababaabbbaababbbabbababbbaaababbaabbbaabbbaaabbbabababbbbaabbabbbbbbbbaabbbaaaabaabbaaaababaabbaababbababbbabbaaabaaaabbaabbbbbbbbaaaabbabbbbaabaaabbbabaaabaaabaaababaaaabaabbaabbbabbabbbbbbabaaabaaabbaaaabbbbbaabaaaabbbbabbbabababbaaabbbbbbbbbaaabaabbabbaababaaabbaabbaaaaaabbbbaaababbabbbbabbbaabbbabababaaabaababbbabbabaabaaabaaabaababaababbaabbbbaabbabbbaaabaababbabbbaabbbbbaabbbaaababaaabbbbaaabbbababbbbaaaababaaaababbabbbbbabbbbbabaaabaaababbbababbbabaabbababababaabbbabbaaaaaaaaaabbaaaaaaabaabaabbbaababbaabbababbababbbabbbababbbbbbabbabbbabbbbabaababbabaabaababbbbaabababbbbabbabaabbaabaaabbabaabbabbbabbaaaaabbbbbbaabaaabbbbababaabababbbaababbbbabbabbaaaaaabaaabbbbaababaaababaaabbabbbbbbaaabaaabbbbbbbbabaabaaaaaabbbbaaabbbbbabaabababbaaaabbbbabbabaababbbbbbbabaaaaaaaababbbbabbbabaabaaabbaabbbbbbabaaaaababbaabbbaabababaaabababaaaabbaababbababaaaaabbbaaabaababaabbaabbbaabbabbaabbabbabbabbabbbbbbababbabaabbabbabaaababaabbbaaaaaababaabaaabbababaabbbbabbaaabaaaaaaabbbaabbbababaaababbaabbbababaaabbabbbbaabbbaabbaaabbbaabaaaaababbaaababaaaabbbabbabaababbbaaaabababaaaaababbbaaabbbaaabbaaabbbbaabbabaaabaaabbbabbbbabaaabbbababbababaaaaaababbaabbababbabbabaabbaaabaababababaaabaabbbbabaabbabbaabbaabbbaaabababaabababbabbbaabaabababbbbabbaaaaabbbaaaabbababbabaaaabbabbbaabbaabbbbbaaaabbaaababbabbbababaaaaaaaabbbabaabbbbbbababbbbabaaabbaababbbaaaaaaababbaabaaabbbabbaabaababaabababbbabbaabbaaabaaabaaabbbbbabbbbaaabaaaaaaaaaabaaaaaabbababbaababaabaaabbababbbabbaabbababababbbabaabbbbabbabbaaaabbbaaabababbbbbabaabaabbaaaabbbbabababbbbabbaabbbabbbbaaaaaabaabbbbaababbaababbaaaaaaabbbabababbaaaabaaaabbabaaaabaabbababaaabbababbbaaaabaabbabbbbaabbabbabbababbbaaaabaabbbbaabbaaaabababbabbaabbbbaaaabbbaababbababbbaabaabbbabaababaabbabbbbaabbbbababaabbabaabbaabbbaabababbaabbaaaaababbabbaaabbaaababbbbababaabaaaabbaaabbabbabaabababaaaabbbaaaaaaabbbababbbbabbabbaaabbbabaabbababaaabaaababbbbabbbbbabbaabaaababbbaaababbbbabbabbaaaaabbbabbbbaaabbbbaaaabbbbaaabbaaaaabaaababbaaabbabbabbbabbbaabbaabbbabaaababbaaabaabbabaabaaaaaabbaaabababaabaababaaaabbabbabbbaababbbbabaaaaaaabaaaabbbaabbbbaaabbaababaababbababbabbabbaabbababaaaabbabaaabaaaabababbbaabbababaabbbbabbbabbabbabbaaaababaabbbbabbabbbabaabbabbaabbaabbbaaaaababbbbabaabbbabbbabaabaabababababaaaaabbbbaabbaababbbaabbbaabababbaabbbbabaaababaabaababababbabbbbbabbaaabaaaabbbbaaaabbabbbbababbabbabaabaababaabbbbabbababbabbbbaabaaabbabababbaaababbbbbbbbaabaabababbabababaaaabbabbbaababbbbbabbbbbaabbbababaabbbbaababbbbbaaabbaabaabaabbbaaabaabaaaaabbaabbbbaaababbaabbbbaababaaabaabaaabbabbbbbbbaaababababbabaaaaabbbbbabbbababaabbbaaaabaabaaabaaaabaaabababbbbabbbaabbaaaabbbbabaaaaabbabbaabbaababbaababbabbbbabbbbaaabbbaababaababaaabaaaaaaaaabbaaaabbaabaaabbaabaaaaaabbbbbaabbaabaaababbbabbbaabababbaaaababaabaabbbabbbaababaababaabaabbabbabbbababbabbaaaaababbaabbbabababaaabbbabaabbbbbbbbbabaabbaaabaababbbaaaabbbaaababbaababbbbbaabbabaaabbbbaaaabbaaabbaabababaaaabbabbbbbaaababbbbabababbabaabbabbaaabbaaabbbbababaaabbaabbaaaabaaabbaaaabaabbababbbaaaabbbabbabaabbbabbbbbbbaabbababbbbbbbbbaaaaababaabaaabaabaabbabbababbaaaaaabaabbbaaaabaaaaaaaabbaabababababbbaabababbaabbaabbbbbaabbbaabababbbbbbaaaaabbbbbababaaaabaabbabababbbaaabbbaababbbaaaaaaaaabaabaabbaaababbbbbaabaaaaaabbbaabbabbbabaabbaababbaaabbaabbababbbbbbbaabbbaabaabaaabaaaababababbaaaabbaaabaaaaabbbbbaaabaaabaaaaababbbaababbaaabbabbabbaaaabaaaaababbaaabbabbaaababaaabbbbbabbaabbbabbbabbbbabaaaaaabbabaaaaaaaaabaaaaababbbbbbbbaababababbabbabbababbbaabbabaababbabbbbabaabaabbabbabababbbbbbbabbabbbbbbabababbbaabbbaaabbabbabbaabaabaaababbbbabababbaaababbbbbbaabaabbbbbbbaaaabbaababbabbbabbaaaabbabbbaaaaaaabababaabaabbaabbbbabbababaaaaaaabbabbbabaaaaaaabbababaaabaabbbaaaababbaabaaaaaababbababababbbbbaaabbbbabbaaaabaaaaaaaaabbbabbaaababbbabbaaaaaabbbbbaaaaabbbbaabbaabbaaabaabababaabaaaababbabbabbbaaabbaabbabaaabbbbabbaaaaababbaaabbaaabaabbabbaaaabaabbbabbbbaaabbaaabbaaaaabbbabbaaabbaaaabbaaaababbbabaaaaababababaabaaaabbabaaaaaaaabbbaaababaababaababaaaaababbbababbabbabbabbbbababbbbbabbbbbbaababbaaabbbbbaaaaabbbababaaaabbabbabababaabaabaabbbaabbbaababababbaabaabbaabbabbaabababaaaaabbbabaaaabababbbabbaabbbbabbabababbbaabaaabaaaaaabbbabaaababbabbabbababaabbaabababbbaaabbbbabbabababababbbbabbaaaaaabbbaabaababbaabaaabbaababaaaaaabaaaabaabbbbabbabbbaabbabbbabaaabbbaaaabbaaaababaababaaabbbbabbabaababaabbaaaaaabababbaaaabbabaabaaaaabbaaabaaaaabaabaaaaaabbbaaaaababaabaaaabbababaaaababbababbbbbaabaaaaababaabbababbbaabaaaaaabbbababbaaaaabaababbbbaabbabbabbbaaaababaaababaaabbababaaaaabbaaaabbbaabbabbbbababbabaabaaaaaabbaabaaaaaabbbbbaaabaabaaabbbbaaabaabbbbabbaababbaabbabaaaabbababbabaaabbabbaabbaaabaaaababaaaababbabaabbaaaaaababbbbbabababbaababbbbbbaaaabababbaaabbbaaaabbbaaabaabbbabbaaaaabbabbabbbbaabaabaabbbbabbbabbabbaabababaaaabbbbbbbaababbabaabbabababbaababbbbbaababbbababaaaaabbbaabbbabbbabaaaabababaababbbabaabbbbbaabbaababbbabbababbabbabaaabbbababaaabbbaabaaabbbbaaababaaabaaabaabbabbaaaaaabaababaaabaaabbbbbaabaaabbbabaabaaaaababbbbbbabbbabaabaaabbaabababaaababbaaaaabbbbaabbaaabababbaaaabbaaaabbbaabbaababbabbababaababbaaaaabbbabaabbabbaaaaababbabbbbabbabbbabaaaaabababbbababaabbbaaaaabbbbbbbaaabaaabbabbbbbbaaaaaaabaaabbaaaaabbbbaabbbaaababbabaabababbabbabbabaaababbabbbaabbaaaabbaaaaabbbabbaabbbabaabababbbbabbbbbaabaaababaaabbbbbababababbbbbababbaaabbbbbbbbababbabbbbabbabaaaababbbbbbbabaaaabbababaabbababbabaaaaabbaaaaabbaaaabbaabaabaaabbbaaabbbaaaaabaaaababbbbbabbabbabaaaababbaabaabbabaaabaabbabbaaaaaabaaabaabbabaaababbbabbbaaabaaabaabbbaaaabababaaabaaababaababaabbabababababbbaabbabbaaaabbaababaabaabbbbbaabaababaaabbbaaabbbabaaababbabaaabbabaaabaabbabbbbabbbbaaabbabbababbabbabbbbbbabbbbbabbbababbbaaabaaaabbbabaabbaaabbbbabbabaabbbbaaabbaabaaabaaababaabaabbabaaaabbabbabbabababbbaabbbbbbabbbbaabbabababbbbabbaabaabaaaabababaaaaaaababaabbbaabaababbbabbaaabababbabaababbbaabbaaaaaabaabaababbbabaababbaaabbaaabbabbbbabaabaabbbabbabbbaaababababaaaababbbaaaabababaaaabbbabbabbaaababbbaabbbabaaababbbbabaabbabbbbbbababbaaababaaaaaaabaabaaaaababbaabbababaaaababbaaaaaabbababaaaaabaaababbbbbaaaabbbabaaaaabbbbaaababaaaabaaaabbbaaaabaabaabaaaababababaaabaabbbaaaabaabbabbbbbbbbabababaaababbaabbbbabbabaabbaabbaabaaabbbabbbababababaabaababaaabbbbbababbaaabbbabababaabbbaaabbbaababaabbbaabbababbabababbbaabbbabbbbaaaabbbbababbbbbabbbbbbaababbbaaaababaaaababbaaababababbbababbbaaaabaaaabbbbabbaabaabbabbabaabbbaabbbababaaababbaaaabbaaaababbabaabaaaaabababaaaaababbbbbaaaaaaaaaabbbbbbababbabbbabaabbbbababbaabaaababaaababbabbbabbaababbabababaabbbaaaabaaabbbbaaabbbabbbaabbbbbaaaaabbbaaabbbaababbbbbbabbbabbbaaabbaaababbbaabbbbbbabbaaabbbaabaabbaabbbbabababbaaaaaabbbaababbbaaabbbaabbaaabbabbbaaaaabbaaaabbabaabbabbaaaaaaaaabbaabbaaaaababbaabbbbaaaaabaaaaabbbbabaaabaaaaabaabbababababbbbaaabbaabbbabbbbabbbbbbbbbbaaabaaabbbbbbaabbabbaabbaabbabbabbabaabbaaaaaaaaabbabbbabbaaaaaaaabbaaaabbabbbbaababbbbbbbabbaaaabaabbababaaaaaaabbabbaabbbbbbbaabaabaaabbbbbababbaaabbaabbbbbbabbaaaaaabababbaabbababbbbbbabbababaabaabbbabbabababbbbaaaaaabbbababbabbabaaabaaaaabbbaaababbabbabbbbaabaaaaabbbabbaababaabaaaabbaabaaaaababbabbabbabbaaababababaaaabababbaabbbaabbbbbbbaaaababaabaaabbbabbbabaaaaabaaabbaababaabbbaabaaaaaabababbaaabaababbbabaaabababbbaaabbbbbbaaabbbaaabaaaaababbabbabaabaabbabbabbaabaabbbaaababbaabbabbbbbabababbbbabbbaabbabaabaaabbbbbaabaaaababbbabaaaaabbabbabaabaaaaaaabaababaabbabbaaabbbbaabaaababababbbababaaaaabaababaabbabaaaaabaabaabaaabbbbaabbaabababbababbaaaaabbbbbbabbbabbbabaabaabbbaaaaaaaaaabbbabbaaababaabbbabbbababbaaabbbaabababaababaabaabbbaabbabbbbbababbaababbabaaaabbababbaaaaabaaababbbabaabbabbbbbbbbaababbababbaaabbbaabbbabbbbaaabbbaaabababbbaaaaaaabbbbaabaaaaabbbaaabbbababbbaabababaaaabaabaaabbbbaaaaaaabbbbbaaaaaaaababbaaaabbabaaabaabbaabaabababbaabaabbbaaabaaaabbabbababbbabbbaabbabbaaabaababbbabbbbabaaabbabbbabaababbabbababbabbabbbaaababbbababababababaaaaabbbabbbababbbabbbbbabaabbaaabaaababababbbbbaaaabbaabbaaabbabbabaababbabbbabababbbababbbbabaabbabbabaaabaabbbbaabbaaababbabbabbaaabbbabaabaaaabbbbbbbababababbaaaabbbbbbbaaaabbbaaabbaabaaaabbababaaababaabbbaaaabaabbbabaaaaaababbbaaababbaaababbbaabbbaaaaaaaaabbaaababbbbabbabababbbbaaaabbaaabbbababbaabaabababaabaabbaaaaabbabababaababaabaababaaaabaabaabbbaaaabbabbbbababbaaabbbbababababaabaaabaaabaaaababbabaabbbbaabbbbbaabbababbabbbaababaababbabaaabaaababbbbaabbaabababbbbbaaaabbbbbbaabbbbbbaabbaaabaababbbababbabbbbaaaabababbbbabbbabbbbbababbaaababbababaabbbbbabbbbabaabbaabababbaaaaaabaaaababaabababaabbaaabbbababababaabbaabaaaaabaabbaabbaaababaababaaabaaabbaaabbbbaaabaaaaaaabbabaabbaabbbbaababbabbbaabbabbbbbababbaaaaabbbaababbbbabababbbbbbbbaaaaaabababbbaabbaababaabbaaaaabaaaabbbabaaaaaabbaabaabbabbbbbbaaabbaabbaabaabaabbabbbbaaababbbabbbabbbbabbbbaabaaabbaabaababbbababaaaaaaabbbaabbbabbababbabbabbbaabaaaaaaaabaaabbbaabbaabaabbaaabaaaabbabababbabbababbaabbaaaabbababbaababaaaaaabbaababaabbabbaabbbbaababbabbbbaabbbaaaabbabaabaabbabbbbbaababbabbababbaaababaaabababbbaabbbababaabaabbbababbbabaababbbaabbaaababbaababaabbbabbbabbaabbaababbbaabaaaaabaabbbabaaabbbbaabbaababbaabbaaaaaabbaababaaababaabaaaaaaabbaaaababbabaaaaaaaaabbaaaabbabbbababbbbbabbbbaabababbbabaaabbaaaaababbbaabbaabbabaabbbbbaaabaabbabbaaabbabbbaabbbabaababbabaabbbabbbabbabbaabaaabbbbbbababbabaaaabbbbaababaabaabbaaaabbbaabbbaaaaabaaabaabbabaaaaabbbbaaaaaabbbbaaaabbababaabaaabbbaabbbababbbbaababbbbbbabababbaabbabbbbbbaabbaaabaabbbbbaaaaabaabababbababbbabababaababaabbabaabbbabbbaabbabbaabbaaaabababbabababbbaaabaababaabbbbbbbababbabbaababaaabababbabbaabbbbbabbbbabaaaabbaaabaaabbabbaabaaabbbbaabaabbbbbbbbaababaabaaaaaaaaaabaabababaaaaaaabaaabbaabbaaabbbbbaabbaabaaaaabaaabbbaaabbabaabbbaabbbbbbbbaabaaaaaabaaabbabbbbabaaaabbaabbbbbbbaaaaaabbaaaabaaabaaaaaaaaaababababaababaabaaaabbbaaaabbabababbabbabbaaababbbabaaaababaabaabbaaaaabbabaaababbaaababbabbaababbbbaaabbbabbbabbabbababaaabaabbabbaabbbbaaaaaabbbbbbbaaabaaaaabbbbbaaabbbbbabbbabaababbbbaabaaababbaaabbbbbbaabbabbaaabaabbbaabbbbbababababababbbaaabbabaabbbabbaabbaababbbbbbbbbbabaabbaabaabbbbbbaaaababbaabaabababbabbbbabbaabaabbababababaaaaaaaabbabababaaabaababaabbabaaaabbaababaabbabaaaaabababbaababbbabbabbaabaabaaaaaaaabaabaaabaababababbaaabbbaaababbabbaaabbbaaaaaabaabbabbbabbaaabaaaaabbaabaaaaabaabbabaababaaaaabbbabbbbbaaaabbabbabbbbbbabbbbabbbbaabababaaababbbbaabbbbaaabaaaaabaababbbaabababbbbbbaabbbbabbbbabaaaabbbababababaabbbbbabbbaaaaaababbaaaaaaaabbbbbbabbbabbbbaabaaabbbbaaaababbaabbabaaaababbababbabbabaabbabbaabbabaabbaabbbaabbbbabbbabbbbbbaabaaaabbaabaaaababaabbbbabbbbaaababaabaabbaabaaabbaaaaababbbaaabbbbbabbbbbaabababbaabbaaaaabaaaababbabbbbaabbbabbabbbaaaabaabaabababaaababaabbbbababaababbaabbaaaabaaaabbbbbbaaaaaabaabbaaabbbbbababbaababbaabaabbbabbabbabaaaaabbabbbaabbbbababaabbaaabaaaaaaaaabaaaaabaabbabaabababbabbbbbaaaaabaabbaabbbababaabbabaaaabbaaabaaaabbabbaabbbaaabbbababbaaababaaabbbbbaaaababbaaabbaaabaabbbbbabbaaabaabaababbbabbaaaaabababaabbabbabbaaababaaaabaabbabbbbbaabaaaaaabbabbbabaabaaabbaabaaabaaaaabaaaabbbbbbaabbbabbaabbbaabbaaaababbbbabababbaabaaaabbbbabbabaaaabbbaabbabaaaaaabaaabbabbbbbbaaabbaabbbabaaababbbaabaaaaaababbaaabaaaabababbabababbababbabababbbbabababaabababaaaababaaaabaabbaaaaabbbbabbbaabbbbaabbbbbaaabababbaaabbbabababaaaaabbaabababbbaabbbbaabbababaabaaabaaabbaaabbaababaaaaaaaabbaabaababbabababaaaabbbbaabbbbbaabbabbbababaaabaaaabbbaaaabbabbbbbabbabaaabaabaabbabbaaaabbbabaabbbababbbbababbabaabaababaabaabbbbbbbbabaabbbbbabbbaaaaabbbabbbbababaabbaaabaabaabababbbabababbabaaaababababbaabbaaaabbbbababbaaabaababbabaabbaabbabaabaabaaabababbbababbbbaaabaabbbabbababaabbaababaaabbabababbabaabaaaaaaababbbbbaaababaaabaaabaababaaababaaaabaaaaabababbbaaaaaaaaabbbbaabbbabaaaabbaaababbabbababaabaaababbaaababababababbabaabbaabaaaabaaaaabbbbababbbbbaaabbabbbbabababaabbbabaabaaabbbbbbaaaaaaaaababaaaabbbbbbaaabbbbabaabaabbbbabaabaabaaabbaabaabaaaababaaaabbabbabaabbbabaabbaabbbaabbbababbbbbbaababbaabbabbaaaaaaaaabbbaaabaabbbaaabbaaabaabaabaaaabbbbbbaaaaaaaaabbbaaabababbbbbbbaaaabaabbaaaaabababaababbaabbaaaabbabbbbaabababbbaaaabababbaaabbabbabbbabaaaaababaaaaababbbbbbbbbbbbbaaababbabaaaababbaaaabababbaabababbabababababaaaaabbbbbaabaabbababaabbabbaaaaababbbaabbbbaabbbbbabbaabbbaabaaabbbaaaabbbabbbbababaabbbaabbbbaabbbbabbbaabbaababbabbbabaabbbbababaaabbbababbabbbaaabaabbabbaabbbabababaaaaabaaabaababaaaababbabaaaabbbbababaabbbaabbbaabbaababbababbbbbababaababbaababbbaabaabbbbbbaaabbbbbababbaaabaaabababaaaaaaabbaaabaaabbaaaaaaabbaaabbbaababbbbabbaabbbaabbaaabaaabbbababaaaaaaabbbabbabbbbbbabbbbaaaabaaabbbabaabbbbaaabbababbbbabbaabbbbbaaababbbabbbababbbabaaaabbabbaaabaabaaabaaabaabaaaaabaaabbaaaabbabaabbbaaaabaaaabaabaabbbaabbaabaabbbaabbbabaabbbbbbabababaaaabaabababbabbbabbaabbbbababababbabbbababaabaaababaaabbbbabbabbbaabbabbaaabbaaaaababaaabaabaabbabbbbaaaaabbbbabbbbaaabbaabbaaaababaabaabbbaabaaaabaabababaaabbbbbabbbbaabaaaaababbaabbababbbabbbababbbbbbabbaaabbabaaababbbaaabaabbbbabbbaabbbbbabbabaababaaaaaabbbbaaabbbbabbabaaaabaaaaaaababaaaaaabbbaababbbabbaaaababababbbabbbbaaaaaaabaaabaaabbabbaaababaabaaabaaaaabaabbaaabaabbababbababbababbbbbbaaabababaabaabbbababababaabaaaababaabbabbaabbbabaaaaabaababbaaabbbabbbbaaaaabbaaaabbaaaaaaababaababbaabbabbbbabbabbaaabbaaabbbbbbbbbaabbbbbabaaabbbaaaaababaababaaabababbbbaababbbbbbabbbabbaaabbababbabaabaabbaaababababbbbbabbaabbaaaaabbbbabaaabababbaaabbbaababaabbbabaaaaababbaababaaabaabaaaabaaabaabbaaaaabbbbababbaaabbaabbbaaabbabaabbbbaabbbaaabaabaaaabaaabbbbaabaabbababbbbabaaabbaabbabababbbbbabbbabbabbabbbaabaabaabababbaabababbbababbbbaabbbabaaabababbababbabbbbbbbabbbaaabaaabbbbbbbbbbabbaaaaaaababaaabaaaabbbaaaabaaabbbababababbaababbaaaabbbaaabbbaaaaabbbbabaaabaaababbabaabbabaabbaaabbaabaabbbabbababbaaaabbbbabaaaabbbabbaabbbbbbabaaabbbabbaabbbbbbaaabbaaaaabaabbabbababaababbbaaaabbbaaababbbbbbaababbaaaaababbababbababbbbababbbaabaababbaabbbabababbbbbbbbababbabababaabbbbaaababbaaaabbabbaaabbbabababbabaababaabaabbbbbbaababababbabababbababaaaabbabbbabbbbaaaaaaaaaaaabbbaabbabaaabbbaaaabbbbbbaabaaaababbbbababbaaaaabbbbbbbbaaabaabbaabbaabaaaaabbbbbbbaabbaaaabbbaabbabaaabbaabbaaabbbbbaabbaabaababaaaaaabababbbaabaababaabbbbaabbbaaaaabaaabaaababbaaabbbbbaaaabbababaabbbabbaabaabbbabaabababaabaaaaababaabaabbbbabbababbaaaaabababababaaaabbbbbabbbbbababbbbaabbbbaabbbababbbbabbbbbabbaaaaaababbbbaaababbbbbbbbbaaaaaabbaabbbababbaabaabbaababaaabbabaababbaaababaababbbabbabbbabbbbbbbbaaabaabbaababbaababaaabbabbababbbabbbbaaababaababbbaaaaaaabbbabbbbabaaababbbbaabaaaaaaaaabbbbabaaabababbbbaabbbaabbabababbabaabbabbbbaaaabbaaababaaababbaaaabbaaaabbbbaaaaaaaababaabbbbabaaabbaababaaabaaaaabaaaabaabaaaabaabababaabbaabbbaaaabbabbbbababababbabbbbaabbbbbbabababaaaaabbabbbbbaabbabbabaabbbaabaababbbababbabbabaaabaabbbabbababbaaaaaaabbbbaababbbabbbaabbbaabaabbbaaababbbaabbabbaabaaaabbaaaabababbbbbbbaaabbababbabbbbbabbaaaabaaaaabbbbababbbaabaababababbbababbababaaabbbbbbbabbbbaabaabbaaaabbbbabababbbbaabbbaabbbbbabbbabbbbababaabbbbabbbababaabbabbbaaaabbaabaaaabbbaaaaaaaababaabaaaabbbbbababbbbbbaabbaababbabaaaabbabbabbabbbaabbababbbababbbbbaabbbbbababaaabbbbabaaabaaabbbabaababbaaabbbabbbbbabababbbaaaaabbbabbaabbabbbbabbbbbabbabbabababbabbbbbbbbaabbbabbabbbabbbbabbbaaaababaaaabaaabaaaaaaaaaaabaabaabaabaabbbbbabbbaabaaabbabbbaabababaaabbbabbbaaabbbbaababbbbababaabaaabaabaabbbabaabaabaabbababbbaaabaabababbbbbaababbababababbabbababaaababbaabaabbbbabbbbbaabbabababbabababbaabbaabbabbabbabbabbaababaaaaabaabaaaababbabbaaabaabbbbaababbabbaaabbbbaabbabbbbabbbaabbbaaabaaabababaabbbbbaabbabaaabaaaaababbababbaaabbbaaabbbbaababbbaabababbaabbbbaabbbabbbabbbabbbabbbabbbaaaaaaaaaaaabaabaaabaabaaaabbabbabbabababababbaabbaabbbbabaababbbbbbaaabbaababababbbbabbaaaaaaaaaabbaabbabbbbabbabbaaaabbaabbabbabbaaabababbbaababaaabbbaaaaaababbaabbbabbbaaabbaabbbbaaaaaaaaaaabaabbabbbaaaaaaabaaabbbaaabaaaaababbababbabbbababbabbabababbaaaaabbaaaabbaaabaabaabbbabbabbbbbbaabbababbbaaabbbabaaaaaaaaaabbaaabbbaaaaaaaaaaaababbbbabaaaaaabaabbaabbaababaabbaaabaaabbbbababbbabbaaaabbbbbbaaabbbabaaababaaaabaaababbaabbababbabaabbaababbbabaaabbabbbbaabaaaaabbababbaabaababaabbabaabaabbbbaabbababbabbbbaabbbaaaaaaabaabbabbbbbabbabbbbbbaabab
aabbbbabaaaaaababbbaababaababababbbaabababbabbbabbbbabbaaabbbbaabaaaabbaabbabbaaababababbbaabbbbbaabaaabbbbabbabbbaabbaabbbaabbaabbbbababbbaababaabbbbbabbabbbaaaaaabaabbbbabaaabbabaabbbaabaaaabababbaaaabaaaababaaabbaaabbbbbabbbbababbbabbbbabbaaabbbbaabbaabbabababbabbbaaababbabbbbabababbaabbbbbbbabbababbbaabbbbbaabaaaaaabbabaaaabbbbbbbaabaabbabbaabbbababbabbbabaaaaaabbaaaabbabababbbbabaabbbababbbbbbbaaaaabbbaababaabbaabaaaababaabaaabababaaaababbaaaaaaaaaabaabbbbabaabaaabaaaabaabaabaabbabaaabbbbbbabbbbbabaaaaaabaaaaaaabbbbbaaaaabbaaaaabbabbbbbbbaababaaabbbbabbbabbaaabaaabbabbbabbbbbbbaabbaabbbbbababaaaabababbbabbaaaababaaaaabbabbbbbbaabbbbaaabbaabbabbabbaabbbbbabbbbbabbbbbabaaaaaabaabaaababaabbbbaabbaabbabbaaababababbbabaaaabbbababbaaaabbabbaabbaaaaaabbabaabbaabababaaabbaabaabbababbabbbbaabbaababbaaababababbbaabaaaaaaababaabbaabbababbaabaaabbbabaabaabbbaaabbaabbbbbaaaabbaabaaababaabbbbbabaaaaaaabbababaabbbbbbbbaaaaaaaaaabababbabbbabbababababbaaaabbaabaaaabaaabaabbbaabaaabbbaaaaabbabbbbbbabbabaaaaaabaabbababbaabbaababaaabbbabababababaabbaabbbbaaababbaaabbabaabbabaabbababbaaabbabbababaabaabaaaabbbbaababaabababbabababbbbbbaaabbaabbabababbabbbbababbbabbbabababaaabbbbababbababaabaaaaabbbabbbaababbbbaabbaaabbbaabababababbabbabbaabababaabbabaabbbbabaaabbaabbbbbaaaaaaabbbbababaaaabbaababbbaabaaabbbabbbbbaabbbabbbaabbaaabababbbabaaabbbaabababaababbbbbbbbbabaabaabaaaabbbabbaaaaaaababababaabbaaababbabbbbbbbbabbabbabaabbbabbbbbababaababbaaaabbbbababaaaabaaaabaaaabbbaabbbbababbbaaababbaaaaabaaabbbabbbaabbbababbbaababbbaabbabbabbbbaabaabbaaaabaaabaaabaabbabbbabababaaabbbabbbbbbabbaababbaaaaaabbaabaabaabbbbbaaabaaabaabaabbbbbaabbbbbbabbbbbaaaabbbabaaabbbbabbbbbabaabbababaaaababbabababababbbbbaabababababbbbbbbaabbbbaaaaaabbabaaabaabaaaabaaabaaaabbbabbbabaaaaaaaababaabaabaababbaaaaaababbaabbabbaabbaabaabbabbaaaaaabaaaaaababaabbaabaababbbaaabaabbbbbaaaaaababbaaaaabbbaaaabbbabbababbaaaabaaaabbaaabaabaabbbaabbbabababaabbababbaaabbababbaaabababababaabaabababbbbaaabbbaabaabababbaabbbaabababbabbbaabbbbabababaaabaabbbababbbabbabbababbbbabbbbbbabbabbaaaababbbabbbaabbababbaabbabbabaabbabbabababaabaaaaaaaabbbbabaaabbbabaabbaabbaababbabbaaabaaabbabbbabbbbbabbbbabbaabbbbaaaababbabaaaabaabbbbbbbaaaaabaaabbabbababababbaaaabaabbbaaaaabbaaaababbaabababaabaaabababbaababaaabbababaabaaabbababababbbbbababaabbabbaababbbaaaaaaabaaaababbbabaaaabaaabaaaababbbbabbaabaabbbabbaababbabbaaaaaabbbbabaabaaabbaabbaabaaaabbabbbbbbababbabababaabbaababbbaaaabababaababbababaaaababbaabbabbabbaaaabaababaaaabbbbabababbaaabbbbabaabbbbabaababbabbbabbbbbaabaabbaabbabbbbbbabbbaaabbbbaabbaababbbaabbabaababbbbbabababaabbbaabbaaaaababbaaabbbaaabbaabaaaaababbaabaababaaaaaaabbbaaabbaaabbabbbbbababbaabbabaabbaaaaaaaaaababbbababbbaaabaabbaaabaabbabbaababbbabbbabaabababbaababbaabbabbbbaaaabbbaaabaabbababbbbabbaabbaabbabbbaabbbbbbbaaabaaaababaabbababbaabbaabaaaaabbaabbabbbabaabaaabbabbbaabbbaaababbbbbbaaabbbaabbbabaaaaaabbbababbbabbbabbabbaaaaabaababbbaababaaaaababaaabbbbaabbaababaaaabaababbbabbaaababbaaabbabaababaabbabaabbbbaaaaabababaabbbabbaaabbababaabbabbbababbbbbbbbbabbababaaaaabaabaaaabaaabbababbbbaabaabbbbaaaaaaabbbbbbbaabaababbbbaaaaaabaabbaaabbaabbbbabbbbabbaaabbabababaaaaababaaabbbaabbbbbbabbbbbbbbabbbbbababbbaaaaaaabbbababbabaaabbbbabbabaabbabbabaababbabaababbaaaaabbabbababbabaaaaabbbbbbabaabbaaaaabbababaabaaabbbaaabaaaabbbaaabaabbabbabbbaababbabababbaaaaababaaaaabababbbaaababbabbaaabbbbaaaaabbabbabbaabbbbaabaaabbaabaabbbbbaabaabababaabaaaaaabaabbabbbbaaabaababbabbbaaabbbbbbbbaabbbbaaaabbbbabaabaabbbbbbaabababaabaaaaabbbbbbbabbabaaaaaaabbbbabbbbaaabbbbabbaaaaabbbbbbabbaaabababaaaaaabbbbbbbaaaaaabbbbbbabaabbabbabababbbabbaaabbbbbaabaababbbbbabbbbbbbbabbbabababababbaabaababbbbbbaaaaaabbabbbabbbbaababaabbbbabbaababbbbaabbbbbaaaaaaaaaaabaabbaabbbbbbaababbbbbababbbabaabaaaabbaabbbaaabbbabbaaabbaabbabbabbbbbbbbaaaaaaabbbbaababababbababbbbaaabbbbbbbbbaaabbaabaabbaabaababbbaabaaabababaababaaaaababbbbabbabaabbbabbbabababaabbbbbbabbabbaabababbbbaabaabbaaaaabbbbbbabbbbaaaabbabbbabbaababaabbabbbbbabbaaababbbaaababbaabbbbabbabbaabaabaaababbaabbaabbbbaababbababaabbbbaaaabbbabbabbbbbbabbabaaaaababbbbbabbabbbabbaaaabbbbbaabbaaabbaaaabbbaaaababbbaabbabbaabbabbbabababbaaabbabbbaaababaabababaabbabaabaabbbbbababaabbaaaaababaabbbbabbaabbbaaabaabbbbaaaabbbabaaaaaaabbbaaaabbbbaabaabbbbaaaaaaaaaaabbbbaaaabbbaababaaaababababbaaaabbabaaaaaaabaaabbaaabbababbbaabaababaaaabaaabababbaabababbabaabbbbbbbabababbabbaabaaaaabbbbababaabaababaaaaabababbbbabbbbbabbaaabbabbaabaaabaababbbbbbaaaaaaaabaabaabbbbabbabababababbaaabababbaaababaabaaaabaabbaabbabaabaaaabbabababaaaaaabbbbabababbbabaabbbabbbabbbabbabababaabbaaababababbbaababaabaabbaaaabbbabbaabababaaaaababbaaaabaababbaabbbaaababbaabaaabaababababbaababaaababbabaaaabbaabbbabaabbbaabbabbbabbbabbbbaabbaabaabbbabbabbbbbbababaabaabababbbbaaababbbaaaabbbabababaabbbbbaabbbaababbbabbbbbbbaababaabbaabbbbabbbaaabbaabababbaaabbbbabaaabaaabbababaabaabaaabbbbbaababbabbaabbaaaaabbbbbabbbbababbabaabaaabaaaabbbbbbaabaaabbbbababbabbaaabbaabbabaababbababaababbbbbbbababaaabbbaaaabababaaaaabbabaabaaabbaaaabbbbbabbbbaaababbabbaaabaababbbbaababaaababaababbabbababbbbbbabbaaaaaababbabababbaabbbbabaabbaaabaababbaabbaaabbbbabbaabbababbbbaaababbbaaabbbbbbbaaaaabbbabbabbabbabbababbbbaababbaaaaaaaaabababbbbaaaabbbabbabaaababaaaaaaabbbabbbababbabbbabbaabbabbbabbbbaaaabbaaabbaaabababbbbaabaaaabbaabbaabaabbaaabbbabaaaaaabbbaaaaabbabaaaabaaaabbbaaaabaaababaaabaaababbaabaaabbaabaaababaababbabbaaaaabaababbbbaabaaaabbaabbababaabbaabaaabababbbaabbbaaabbbbaabaaaaaaababbbabaabbbbabaaaabaabbbbbbbbaabbbababaabbaaabaababababbabababbbbbababbbbabbaabbabaaabbbbabbbbaabbbabbaabaababbbaaaaabbaaaaabbabbbaababbaabbabbbbabaaaabbabaaababbaabaaaabababababbbbbababbbbbabbbababbbaaabaaaaabbbabaababbbaaaababbbaabaabbbabbbbabbbabbbaaaaabbababababaaaaabababbbabaaaaabbbababbaabaaabaababbbbabbbbabbaabaaababbbbabbbababbbabbaabaaaabaaaaaabbaabaaaabbbbbbbbbabbbabaababbaaabbbbbbbababaababaabbababbbaaabbabbaabaaaabbaabbbbababbabbaababbbabbaabbbbabbbaabbabbbaaaabbaaabaaaabaabbbababaaabbbaabbaabbbbababaabbbbaaabbaabbbbbaabbaabbbababaabbaaaaabaaabaabbbbbababbababbababbababbababaababaaababbaaaaaabbbbbbabbbbaabbaaabbbaaaabababbaaaaabbaaaabbaaabbaabbbaabbbbbabbbbabbababbaabbabaabbaabaaabbaabaaaaabbbabbaaababbbbabbaabbaaabbbbbbbabaaabaabaabbbaaabbbaaabaaababaabbbabbbabbbbabbbbabaaabaabababbabbbababbaababbabbbbbbbbbbbabbbabbaabbaabbbbababbbbabaaaaaabbabbaabbabbbaaabaaaababbbabbbbbbabaaaababaabbbbbabaaabbaaabbbaabaaaaabababbabbabbabaababaabbbbababbbbaaaaabbabaababbbbabaaabaaabaabaaabbbbbbbbbabababbbbbaabaaabaabbabbabaaabbabaaababbbabaaaabbaaabbabbaababbabababaabbbaaabbbaaabbbababababaabbabaaabaabbabbaaababaabaaaabaaababbbabbbbaaaabbaaaaaabbaabbabbbababbbbbbabababaabbbbbaabaabbbabbaabaaabbabbaabaabbbbaaaababbabaabbbababbbabbbbbabbbbaaaaababbbbbbbbbaabbbabbbbababbaabaaaaaabbbabbbbbbaabbaabbabababbaabbbabbabaabbbaaababbaabbaabaaabaabbbaaaabbaaaabbabbaabaabaaaabababbbbbaababbbbbabbaababbbaaaaaababbbbbabaababbbbabbbaababbabaabbbbbbbaaaaabbbaabbaaaaaabaabaabaabbaabababbbabbabbbabbaabaaabbbbbaabbbbabbaabbabaaabaaabbaaaabbbabbbbbaaabaabaabaaaabbbaabbbababbbbbaaabbbaaaaabbaabbababbabbbbaabaabbaaabbaaaaaaaaababbbaabbabaaaaabbaabaabbaabaababaabbabaababbaabbbabbabbbbbbbbaaabaabbabbabaaabaaabbbbbbabbaabaaaabbaabaaabbbbbbaabbbaabbbbabaaababababbbbabbabababaababbabaaaabaababaababbababaaaabaaaaabbabbaaaabbabbbabaabbabbabbabaaabbbaabbaaabbbbaaabbbbabbbbbaaabababbbaabbbbabaababbaabbabababbabbaabbbaaaaabbbbbabaababbbababaababababbbabaaabbabbbaaaabbabaababbbaaaaaababbabaababbbbbabaabaabbbbbbbbabbabbbbbabbbabbabbbaabbaababaababbbbaabbbbaabbbabaaaababaaabaabbbbbaaaabbbaaabbababbaaabababbbabbaaaabbabbaababaaabbabaaaabbaaabaaaabbbaaabbabaaaaabaaabaaabaaaabaaabbbbababababbbaababbbbaabbabbbaaabbbabbbbababaabbabbaababaaaabaabbbbbbabbbbbbaaaaababbbbabababaabaababababaabababababbaaaaaaabbbbabaaaabaaabbbabaaaabaaaabaabababaabaabaaaabbabbbabbaabaaabbbbbaababaaaababaabaaaababbbbabbaabbaabbabbaabbbaabaabbbbababbababbbaaaaaaababaabababaaabbaabbbbaaaabbabbaababbababaaaaabbabbaaabbaaaabbbbbaaabbabbbaaabbaabbaaaabaabaaaabbbbaababbabbbabbabbbbbaabaaabbbbabaabaaaabbbabbaaaabababbbabbbbbaaabbaaabaaaabbaababbaababbbaaaaabbabbabbbbbbabbbaabbaabbbaaababaabbaabaaaababbabbabaaabbbabbaaabaabbbaabaababbaabbbaabbbaabaabaabaabbaabbbbabbabaaaaaababbabbbbaaabbaaaaaaaabbabaabaabbbbbaaabaaaaaaabababbbbbabbbabbaaaaaabbbbbbbbbaaaaabaaabbbababbbabbbabaabababaaaaabaababaabbabaabababaababaabbbabbaabaaabbabbaaabbaaabbbbbaaababaaaaabbbbbabbabbbbbaaababbaaaaabbabaabbabbaabaaababbbbbbbbaaabbabbaaabaaaababbbbaaabbabaabababbbabbaaaaaaababaaaabbaaabbabababbaababbaaababaaabbabbbabbbbaabababbbbabababbabbbaababaaaaababbabaaabaabaaabaaaabaaaabababbababbbaaababbaabaabbabaaabbababaababaaabbababaabbbbaabaabbbaaaabaaabbaaababaabbbbbaaabbabbbabbbabaabbbabbbaabbbbbabbbbaababbaabaabbbbabaabbbbbbbbaabbbbaabaaaaaabaabaabbaabbbaababaabbbbaaaaabbbabbaaabbabababaabbabbbababbbaaabbabababbbbbbaaaababaababaabaababbababaabaababaaaabaabbbabaabbaababbabaababaabbbbbabbbabbbababababbaaabbabbabbabbbaabaababbaabbbbbbaabbbbabbaabaababbbababbaabaaabbabaababaaababbabaaaabaaabbbababbbaabbababbaabbbaabbaaaabbaaababbbbaabaabbabbbbabbabaabbbabaabbbbbabaababbabaababbbaaaaabbaaaabbbabbbbbbaababaababababaaaabbbabbabbbaaabaabbabbabaaaaababbaaaababbbbaaaababbbaabbaabbbbbaaabbbbaaabababababbaabbaaaaaaaabbabbbabababababaababbbbaaababbbabaaaabaabbabbaababaaaaababbbababababbbbababababaaabbaabaababbbbbbbababbbbababaaaaabbabbaaabbbaabaaaaaaaabaaaaaabaabbbbbaaaaaaababaabaaabaabababaabaaaabbababbaaabbbabbabbabbbbababbaaabbbaabababbabbbbaaabaabaaabbaabbaabaabbabbbaaababbbaaabaababbbaabbaaabbababbbabbabbbaaabbabaaaabbaaaabaabbaabbaaabbababbbbabbababbabbaabbbaababbabaababaababbbbbbbabaabbbbabbbbbbbababbbbbabaababbbaaaabbabbbbbababbbabbabbabbababbbaaabaabaabbabaaababaabbbbaaaaabbbabbaabbaaababbaaaaababaaababbabbaababbaaabaabbabbbaabaaaaaaabbbbbbbbbababbbabaaabbabababbbaaaaaababaaabbabbaaaabbaaababbabbbabaababbbaabbabbaaabbababaabbbabbababbaabbbbbbaababbbbbbbbaabbbbbbaaaababaabaabbaabbbabbabbbaaaaabbbabbabbbbabbababaabaaaabbababbaaababbbbbabbaaabaabaabbbababbbbaaaaabbbbaaaabbaaaabbbaabaabbaababbabbbbaaabbbbaaaaaabbabbbbaaabaaabbbaaabaabaaaaabaabbbbaaabbbaaaaaabbbbbbabbabbbbaabbbaaaaabababababbbaaaabababbaabbbbbaaaabaaabbaaabbabbbbbaaababbababbaabbabaaabbaabaababaabbbaabbaabbaabaabbabbbaaaaaaaabaaabbbaaaabaaaaaabbaaaaaaaabaaaaababbababbabbbbbbabbaaaabbbbbbabbbbaaabbabbbbbabbbabbabbabbbabbbbabbababaaaabbabaabaabababababbbabaaabaabbbabbabababababbbaabbbbaaaaaabaababbbbababaababbbaabbbaaabaaaaabbbbbaabaaabaababbaababbbbbbbabaaaaababbabbaaabbabbabbbbbaaaabaabababaababbaaaaabbbbabbbababaabbbbababaabbabbbaaababababbbaaabbaabbaaaaaaaabbababaaabaababbabbabaaaabababbbbbaabbabbbaababaabbabbbbabbbbbbbbababaaaabbbabbaabbabbabaaabbbbbbabbaabaabbbbbbbaabaabbabbbaaabaabbaabaabbaaaaabbabbbaaaabbaaaabaaaababbaabaabaaabababbaabaaaabaaabaaababbbbbabababbabbbabaaaaabaabbababaabbbabababbabaabbaaaaaabbababbbbaabaabbbabaababaabaaaababbbabbbbabaaabaabaaaabbaaaaabaaaababbaabaababababaabbbaaaababbaaababbbabbbbabaababababaaaabaaabbbbbbaaaaaaaaababaabaaabaabbaaaabaabaaabbbbabaabbbbbbbababbabbabbbabbbbaababababababbababbbabaaaabaabbbabbaababaaaabaaaababababaabbbbbbbaaabbbbaabaaaababaabbbbbbbabaabaaababaabaaaabbbbabbbbababbbaababababaabaaabaabbaaababababaababbbabaaababaaabaaabbababbabbababbbbaaaaababbbabbbbbabaabbabbbbabbbbabaababaaabbaaaaaabaaaababaaaaabaabaaaabbbaabaabbbbbbbbaaabbabaaababaaaaabbabaabbaabbabbbabbaabaaaabaababbaaabaabbbaabbaaaabaaabbabbbbbbbabaabbbaaaaabbaaaabaabababbababbbaabaababaaabbaabbabaababaaabbbbbbbbabbbbbabbaaabbabbbbabaabbabaaaabaabbaabaaabaaaaabbabaaabbabaaababaababbabaaaabaaaaabaabaaaababaabaabbaabaaababbaabbabbabaaaaaabbabbbbbbbbbbbaabaaaaaababbbaabaabbbbaaaababaaaaaaaabbabbbabbbbaababbabababaaabababbbaaaabbabaaabaaaaabbaaaaaaaaaaaaabbbbaaaabaabbbaababbaaabaabbbabaabbaaabbabbbabaaabbaabbbbbaaabaabbbbabbabaabbbbbabbaababbabaaababbabbabbaabbaabaabbabaaaabbbaabbabbaaababaaabbbbaabaaaabaababbbbbaabababbabbabaaabbbbabbaaaaabbaaaaaaaababbabbaabaaabaaaaabbbbbbaaabababababbbabbaababaaaabaaaabbbbbaaabbabaabaababbaabbaabbbbaabababaababbbabbabbabbbbbbbbbbbaaaabbbaaaaabbaabbaabaaaaaaaaabbbbabbaaaababbababbababbbaaaabbbabaaabbabbbbaaaabbbaaaaabbaabaababbabbabbbababbabaabbabababaaaaaaaabbabbbaababbbaaaaababaaabbaaabaaaaaaabaabbbbbaabbababaababbaaabbaaaaaabbbabbaaaaabbabbbabbbbbbbabababaaaabaaabaabaabbaaabbbbababaabbbabbbabaaaabaaaaababaaabbbabaaabaaaaaabbaaabbabbaabbbaaaabbabaaabbaaabaabbaabbbbbbbabbbababbaababbbababaabaaabbabbbbbbababbbbbabbabbbababbbbaaabaaabaababaaaabaabbbaabaabbaababababaaababaaaabbaabbaabbabaabbbbabbbbaaabaaabaaabbabaabaabaabbbbaabababaaaaabaabaabaabbbbaabaabbbabbabbaaaaabbbabbaabbbbaababbaaaabbbabbaabababbaababbaabbaabbaaabaaabaaabbbababaabbaababbbbbbabbbbbabaaabbabbabaabaaaabababbabababbabbabbabaaabbbabbbaaaabbabababababaabaaabababaaabaabbbaabbababbbbbbbbbababbbabaaabbbbbaaaaababbaabbabbbbaabbbabbaababbabbabbaaaaaababbbaaabbaaaaababbaabaabbbababaaabbbbabbbbbaabaaababaaaabaabbababaababbbbbbbabaaaabbaabaabbbaababbaabababaaabaabbabaabababbbbababbaabbbbbabbbaaaabbabbabaaababaaaabaabababbbbbaabbabbbaabababbabbaabbabbabaaaaaabbaabaaaaabaabbaaaabbabaabababaaaaabbbabbabbbbbbabbbbaabbabbabbabaaaaababbbaabbbbababbbbabbaaababbaaaabaaaaaababbabaaabbbbabaaabbaabbbbaaabbabbabbaaabbabbaaaaababaabaabbabbabbbbbababababaaaaabbbbbbbaaababaaababbaaaababbabbbababaabbaabaaabbaababbaabbbaaaabbbabbbabaabbabababbbbbaababbbbbbbbabbabbbababbaaababbbbabababaaaabbbabaabbbabbbbbbaaaaabaabbaabbbaaaaabaabaaababbbabaaabaababbbaaabababbbaabaaaabbaabbaabaababbbbbbbbbabbabaaabababbaababbaabaababaabbaabbbabbabaababaababaaabbaabbaaababbaabbbabbabaabbbabbbbbbaabbabbabbaaabbabbaaaaaaabbabaabbabbabaababbbaaaaaaaaababbbababbbaaaabaaabaabbbabbbabaabbababaaabaaaaababababbaabaabbbaaabbbbbbbaaaababaabbbbaabbaabababaababbabbabbabbbbaaaababaaaabbbbbbaaabbababaabbabbbabbaaaababaabababbbbaabbbaaaabbbbababbbbbaaababaabbbabbbbbbbabaaaaabbbbaaabbbabbbbbbaaababbabbbbaaaaaabbbbaaababbaaaabbbbaaabbabbaabbabaabbaaababbbaaaabaabbabaabbbabaaaabaabbbbabababbaabaaabaaabbababababaaabababbabbbabaaabaaabaabaabbabaabbabababbaabbbabaabbabaabbabaaabababbbaabaaaaaaaabbbaaaaabbabbaabbbbababaaaabbaaaababbaaaabaaabbababaaaabbbbbbbababaaaaaaabbaaababaabaabbabbbaabbbbbabbbbaaaababbbaabbbabbbbbbbbaaaabaaabaabaabbbaabbbbaaaabbababaabaabbabbbaaaaaabaaabaababbaaaabaaaaabbbabababaababbabaabbaabbaaabaaabbabbaabbbabbbbbbbababaaaababbbaabaabbaababbbbaababbaaaabaabaaabbaabbbaaaabbaaabbbababbaababbabaaaaaaabaabbbbbaabbbaababbbabbbababaaaaaabbbaababbaabbbabaabbaabbbbbbbbabaabaababbbbaababababaaaabbaabbabbbaabaababbbbbbabbababababababaababaabbbaaabbbaaaaababaaabbbaabbbabbbbbabbaaabbabbbababbabaaaaabaabaabbbbabbbaabbaabababababaabbbababaaaaaaaaaabbaabbaabababaabbaabbaabbabbbbaaaaaabbababbabababbbabbbbabbbaaaabaaaabbaaabbbaabbabbabaaaaabbbbbbaaabbabbbbbaaaabbbbabbaaaababbbbaababaabbbbaabaaabaaaaabaabababaaabbaabbaaabbaaaabbbabbbbaabbababaabbaaaaabaaabaabbabababaaabaabbaaabbbbabaabbbbbbabbbbbbaaaaabaabaaababbbabbaabbbbabaaababaababbbbaaabaababbaababbbbbababbbbabaabbaabaabaaaabbaaaaaaabbabbabbaaaabaabbabaaabaabbabbbbababbbababbbbbbbbbabbabbbbabbbbbbaababaaabbaaabaaaaaababbaaaaababbaabbbababbbbaabbaabbbbaaaabbbbbaabbbabababbabbabbaabbaabaaabaabbabaaabababbabbbbaaaabbbbbbabbabaabbaaaabbabbabababbabaabaabbabbabbbabbabbbabaabaaababbbbbabaabaaabbaabbbbaaababbbbaabaaaaabaababbbbaabaabaababaabbbabbbbabbbbabaaabbbbaabaaabababbbbbbbabaaabbbababbaaaaaaabaaababbbabbbaabababababaaabbabbaabbbbabbbbbabbabbaaabbbbbbabababbbabbbabbababbababaababaabababbbababaababababaaabbbaabaababaabbbaababaabababbabbbaabaaabbbbbbababbbabbbbabbbaaaaaabaaabababaabbbbaaaabbbbbbaaaaabbbabaabaababbaaabbabababbbabbbbbabbaabbbbaaabbbbaaababbaabbabababbaababbaaabbabbbabbbbbabababbabbbababbbbbbababaababaaaaaabbabbaaababababababbaabaaaaaaabbbbbaaabbbabbbababbabaaabbababbaabbaabbbabbbbbbababaaaababbaaaabbaaabaaabbaabbbbbaaaaaaaaabbbbaabbaaaaaabbbbabbbbaabbbaaabababbbabbbbbbabbababbabbbabbaaaabbababaaabbbabbbbbaaababbbbbbaababbbabbbabbaaabbabbbbabbabbababbaabaabbaabaabaaaaaaabbbaababbbaaabbbaaabbbbaaaaabbbabbaabbabaaabbaabbaabbaababaabbabaababaababaabbbaaabbabaababbbaaaababaabbbbaaabbabbaabbbbaabaabbababaabbbbbabaabbbaaaabaabaaaaaabbaaababbaabbaabbbaabaabaaaabbbaaabbbbabbaabababbabbbabbabbbbbbabbbaaaaabbbababaabbbabaaaaaaaaaababababaaaabaaaaabbaaababbbbbaaaababaabbbbbbaaabaaabaabaabbbabbbbaababaabbababbbbbbbabbabaabaabbabbaabaaabbbababbbaababbbbbaaaaababaabbbaaaaaaaaaababbbabbbabbabbabbababaaaabbbbaabaabaaaabababbbabbaaaaabaaaaaabaabbbaaabbbbbbbbbaaabaaabbbbbbabbaaaaabbbaaaaabbbbabbbbbababbabbbbabbbbabbbbabbbabbbaabaabbabaabbbabaaaabbbaabbbaabaaaabbbababbaababbbbaaaaaaaaabaaaabbbbaabaaaaabbbabbaabaabaaabbbabbbbbabbbaabbbaaababbabbbbaabbbbbbbabbaabaabbbbbabbababbabaababaaababaaabbbabababbabbaabababbabbaabbabbaaaaaabaaabaaaabbbbbbbaaabaabaaaababaaabbbaabbbabbabbaaaabaabbbbaaababbabbbababaabaabaaabbaaabaaaaabbbaaabbbabaaaabbaabababbbbbaabaabbbababbaabbbbbbbaabbbababaaabbbaabbbabaababaaaaababaababababbbbabbbabababbababababababaababbbabbaababbbbbbaabbbaaaaabbbbbbaaaaaabbaabaaaabbaabbaabbabaabababbbaaaaabbabababbbbaaabababaaabbbabbabbbaababaaabaabbababaabaaababbaaaaaabbaabaabaaaabaabbabbbababbaaabbbbaabaabaaababaaaaabbaaaaaabbabbbaabaaabbabbabaaabbbabbbbbaaaaabbbbabbaaaabbbaabbbbabaaabbabbaabbaababbbaabbbbbbaaaabaabababbbabbabbaababaaaaabbbaabbbbabbbabbbaabbbbaaababbababbbaabbabbbababababbbbbbbbbaaabbabbaabbabbaabaababaaabbbbbbabaaaababbbababaaababbaaababbbbbaabaababbbabbababbaaababbabbaabbabbbaaabbbabababbabababbaababbbbabbabbabaababbbbbabbbabaaaabbababbababbaabababbbaabaaaaaabbaaabbabbabbaaaaaaabbabaaaababaababbbbabbbaabbbaabbaabbbbbabbabbbbababbbabbaaaabbbbabbabaabababaabbabbbaabbabaababaaabababababaaabbabbaaabbabababbbabbbaaaabaabbbbbaaaabbbabababaabbbabbabaaaababbbbbbabbabbaaabbaaaababaaabaabaabbaabbbbabbaabbbabaaaabbaaabbbabbbabaaaaabbbaaabbaabaabaabbbbaabaaabaaaaaababbabbbabaabbbbbaaabbbaababaaabbbabbbbaaaaabababbabbabaaaaabbaabbbbabaabaabbabbababaaabababaabbaaabaaabaaabababaabaaaaabbaabbbaababbaaabbabaabbabaaabbabaaabaabaaabbaaaaabaaaaabababbbaaabbabbbbaaaabbbbbaabbaabaabbabababbbabbabbabaaababbbabbbaaabaaababbaabaabbababbbabaababaabaabbbaababababbbbbaababaababbbbababbbbabbaaaabbaaaabaabaaaaabbaaababababbbaabbaaabababbbbaabaaabaabbbabbbbbbbbbabbbabaabbbaabbbabaaaabbabbbabbabbbaabbaaabaabaaabbbbaabbaaabbbbbbbbbabbbbabaaababbbbaaaabababaaaababbbaabbbaabaabaaabaabbabbabbaababaabaabbaabbabbbbbbabbbbbabbbabbabbaabbabbabaababaabababaaabbbaaabbbbaaabbaaaabaabbbabaabaabababbaaabbabbabaaabbbabbbbbababaaabbbaaaabababaaabaababbbabbaabaaabbbabaaaabaaabbbaabaabaaaaaabbabababbaaabaababbabbbabbbabaabbbbbbabbbaabbaaaabbabbbbbbabbababbbbaaabbbaaabaabbbabbbabbaababbbabbabbbbaaaaaababbbaaabbaaaaaabbaabaabaaabaabaaaaaabbbbbabbbbbaabbbaabbabaaaabbaaaaaabaaaabababaababbaabbabaabaaabbaaaaabaaabbabaabbaabaaaabaaaabbbbbbaaabbabbbabaabaababbbaaabaaaaababbabaaaaabbbabaabbbaaaababbaabbaabbababbaabaabbbbbaaaabbbaabbabbbbabbabbaabaaabbabaaabaabbbbbaababaabbaaabbabbbaabbabbbaabbbabbababbaabaaaaaabbaabbabbabbbaabbbaabaababbbababaaababbababaaabbaabababaaabbbabbaabaabbbaaaabbabbaaaaaabaababaabaaabbaabbbbbaaabbaabaaaabbabbbaaabbbabbaabbbaabaaaaaaaaababbaaaaabbaabbaababbababbaabbabaaabbbaabbbabbbbbababaababbabbbaabaabbabaabbabbbbabbbbbbaabaabbababbaababaaabbbabbbabaaaababbaaababbbbbbaaabbbaaaaabbbaabbabbabbaaaabaabaabbaaabababbbabababababbabbabaabaaaabaababaaaababbbbabbbaababababaabbabbabaabbbbabaabbbbaaababaabaabbaaaababaaabbbbabaabaababbabaabbbababaababaababbabaabaaabbabbabbaabababbaaabbabbbabbabaaaabaababaabbabaabbabbaabaaaaaaaabaaaaababbbabbbabbbaabaaabbaaaaabbaaaaababaabbabaabaabbbbababbbaabbbababaabaabbabbabbababbababbbababbaabaaaaabbaaaaaaababaabaaaaabbbbbbabaababaabbabbbaaaaaabaaabbabaabaababaabbaabbbabbbbbabababbababbbbbbbbbabaaaababbbabbaababbbbabababbabbabbababaaabbbbabaaabbbabbaababaaaabbaabbbabaababbbbabbbaaaaabaaabaaababbbaaabbaabbabbaaaababbaabaaababbbabbabaaabaababaaaabaaababbbbaaaababbbbaaabbbabaababaababaaaabbabababaabaabaaababbaaaababaaabbaaaababaaabbaaabbabaaabbbbbaabbaabbaababbbbabbabaaaaaaababbbbbabbbbbbaaabaabbabaababaabbbbbabbbbbaaaababbabbababbbbababbaaabbbbbaabbaaabaabbabaabbabababbaabbbbbbabaaaaaabababbabbababbbaaaaaaabbabaababbabaabbabbaabaaaaabbabaabababbabaabbbabbaabbbbbbbbbbbaabbbbbbbbbabbaaaabbababaabbaabaaaabaaabbaaababababbbaabababbabbabbbbababbaaababbbbbaabababbaabbbbbbbbaababbababbaabbabababaaabbaaababaaaabbbbbaaabaababaaabbaaaaabbabbbbbababababbbbbbbaaaabbbaababbbbaabbabbbaaabbaaabbaabbbbbaaaaabbbbbabbaaabbbaaabbbaaababbaaabbabaaaaaaaabbabbabbbaaabababaaaaaababbbbbbaabaaaabaaabbaaabbabbbaaabababaaabbbaabbbbbabbbbbbaabbbbabbbaabababbabbabababbababaabbbaaaabaaaabbabaaabbabbbbabbbaaaaabbaaababaabbbbabaaabbababaababbbaababababaaabbababbabbabaaaaaaabbbbaaabaabababbbbbababbabaabbaabbbaaaaabaababaabbabbaabaabbbbaababaaaaabbbaaaaaabbababababbbbbaabbaabbaababbababbbbaaaabbaaaababaabaaababbbababbaabbabbaaaaabbbbbabababbaaabaabbaaaaabbaababbababaabaaababbbababbabbbbbaaaabbaaaaabbabbbabbbabbabbaabbabbabbaabbbabbabbabaaababaaaaabbbbbababbababbbaabbaaabbaabbabbabbbaaaaaaaabbaabbaabbaaabbaabaaaabbaabaaababbaaababaaabbbbabbababaaaabbbabbbabaaaabbabababbabaabbbabbaabbaaaababbabaaababbaaabaababbbabbaaabbbabaaaabbbabbbbabaaabbbaaabbbababaabbaaaabbbbbaabaaabbbbaabbbbbaababaaaaaaabaabaaaabbbbaaabababbababbbaababbbbbaaabbbbbaabaabbbaabaababbabbbababaaababaabbbbababaabbaaaabaaabbbaaaaaaababababbaabaaaabaaaaaaabbaaabbbaabbaaabaaababbbbbbabbbabbbaaaabababaabbbbabbbbaaaaaaababaaabbaabbaaabbbbaababbaaababaababaabbaaaababbabbaababaaabbaaabbabababababaaabbaabaaaaabbbbaaabbabababbbaaabbabababaaabbaaaabbabaaababbabbbbbabbbaababaabaaabaabbbaaaabbabbabbbabbaabbbbabbbbabbababaabbbababaabaaaaabaaabbbbbaabaaaabbbbaabbabaaaabbabbbbabbabbbaabaabaaabbaabbabbbbaaaabbaaabbaaabbbbaababbaaaaaababbaabababbbbbbaabbabaaabbabababaaabbababbbbabaaaabaaaabaaaaaaabbaaabaabbabaabaababbabbbbbaaaabbaabbaaaababbbbbbbaaabaabbbbaabaaabbabbabababaaabababbbbbabaaaaaabaababbaabaaabbbaabababbabbaababbbabababbababaaababbababbababbbbabaaaabbabbbbaababaababaabbbaaaaabbaaaabbaababbbaaaaaabababbbbbababbababaaaaabbbbabbabaaaaaaaabbaababaababbabbbbbbabbbbbbbbaabaabbbbbabbaababaabbbabbbbbababbabbaababbaabaaabbbaaaaabababbbabaaaaaababababbbbbaabbbbabaaaaaaabababaababaaaababaabaaababababbaaabbbbabaaabbaabababbbabababaababaababaabbaabaaabaaabaaaaabbbaaaabbaababaabaaaaaabbabbaabbbbbaabbaaaaababbaaabbaaabbbbbbbababaabaaaaabbabbaabbbbabababbaabaaaabbbaabbbbbaababbbbabbaaaabbaabbabababbbababaabbabaaabbaaaaaabababaaaaababababbaaaabbbaababaaabbbbbbbaaababaaababbabbbaabbabbaabbbbbbbabaabbbababbababababbabaaaabbabaaabbaababaaaabbbaaaaabaaaabaababbbabbbaabbababbbbbababbabbabaabbaabababbabbbbaababbaaaaaaabbbbbabbbaabaaabbababbabbaabbbbbbbbbbbbbabbbabbabbabababbbaabbaaababaabaabababaabaabaababbbbbbbbaaabbabbaabbaababaabbaaaabbaaabaabaaababaaabbbbaaabababbbaaaaaaaabaaabaababbbbabaabaaabbbabbaababbbabbbbbaaaaaaabaabaaabaaabaaaabbaaabbababaaaaaabbaababbaaaababbbabaaabaabbaababababbabaabbbbabababaabbbaababbaabaaaaaaabbaabaaabbbbbabbabbaaabbabbabbbaaabbbbaabababaaaaabbaaabbbbbaabbbbababaaabababaabababbbaababbbbaaababbbabbbaabbaaabababbaaaaabaaabababaababbabbbbbbaabaaaabbbbbbabbbbbaaaabaabaabbabbabaabbbbbaababbabbabaaababbbbabababbbbbaaabbbbabaabbbaaabbabaabbbbaabbbabaaabbbbbbaabbaabababaabaaabbbbabbaabbbbaaabaabaabaaaaababaaaaabbbbbaabbbbabbbbaababaabbbaaaaababaabbbabbabababbbbbabaaabbaaabbaabbbabbabbabbbbbbaaabaabbaaababbbabbbbaababbaabbababbababbbbabaaaaaaabababbaaabbaaabbabaaaabaababbbabbbbbabababbbaabbaaaaaabbaaaababbaaababababbbbbbabbbabbbaaabaaaabaaabbababaaabaabbaaabbbaabbbbaabaaabbbbbabbbaaaabababababaabbbbbababaaababbababaaabaaaaaaaaabbbbababaaabbabbbbaabaababaababaaabaaababaaababaababbbbbaabaaabbbaababbaaaabbaabbbaaabaaabaaaabaabbbaabbaabbbaabbaaaaaababbaabbbbbaababbaabbabaaabaabbbbaaaabbbbbbabaaabaaababaaaaaabbbaabbbbbbbaabaabbbbaabbabbbabbbbabababbbabbaaababbbabbbbaabbaabaababbbabaaabbabbbabbbbaababbabaabbbbaaabaaaaaaabaaaabbbbbbbbbbaaaabbaababbbbbabbbbbbabbabbaaaababaababbaaaaaaaaababaaaabababbaaabbabbbbbaababbabaaaaabbbbbbbababbaaabababbbaaaabbbabbbbbabaaaaaabaabbbbbbbaaaaabbbbbbabaabababbbaabaabaabaabaababaabababaaabbbbaaaaaabaaabaaabbbbbbbaaabbabbbbaabaabaaaabaaabaabbabaaabaabbaaaaaaaabbabbababbabbbabbabbbaaaaaaaaaaababbabaababbbaabbbabbaaabbbaabaaabbaaabababbabaaabaaaaaababbabaaabbbbaababaaaabbabaaabbaaababbbababaabbbbaaaabbabbaaaabbbbbbbabbbabbabbbbbaaaaaabbababbbbaaabaaabbaaabbbbabaaaaaaaaaabbaabaabbbaaaaaaabbbbbaabbabaabbaaababbaabbbabaaabbbbbaabaabbbabaabbbbaabbaabbaabbaaabbabaaaabbabbbaabaabbbbababbbbbbbabbababbaabbbbaabaaabababbbabbbabbabababaaaabbbbaaabbaabbbaaababbabaababaaabaaababaabbabbbbbbbabaabababbaabaabaaabaaaaababbabbaaabaaabbbabaaaaababaabbbabbbbbbabaabbaaababaaabaabaaaaabbaaaabababaabaaaaaabaababaaabaaababaababbbabaaaabaababaabbaabababbaabbbbbbaababbbaabbbbabaaabbbbaaabaaababbbbbbaabaaabbababbabaabaabbbaabaabaaabbababaaabbbababbbbbaababbababaababaaaabbbbababbabaabbbabaabababbabaabbbabbbaaabaaaabbbabaaabaabbbabaaaaaabababbaabbabbabbbaaabaababaabaaaaababbbbaaaaaaabbbaabaababbbbbbaabaaabbbababaabbabaaaabaababaabaabbbbbbabaaabababbabababbbabbbbbbbbababaababbaabaaaaaabbbbabbbbbabaabbaabababababbbababababbbbaaabbaabbbbaaababbaaaaaaaaaabaababbbabaabaaaaabaaaaaabbbaabbbababbbaaaabaabbbaaabababbabaaabbbbbbbbbbabbababaabaaaaaaababbbbabbabbabbbbabbbbbaaaaababaaabbbbaabbbabbbababaabbbbaabaaaabbabbaabbbaaaabaaaabbabbbaaabbabbabbaababbbbaaaaaabaabaababbbbaabbaaababaabbabbaabaaabbabbbbbababbabbbababbbbaaabbbabbbaabaaabaaaababbbaaababbaabaababaaaaaabaabaabaababbabaabbaabbabbaaababbbbababaaaabbbbbbababbbaaaaaaabbbaabbababbbbababaaaaababbabbbbbababbbaaaaaaabbbababbaababbaabababaaabbbbbbabbababbbaaababaabaaabbaaaaaabbbbabbababaabababaabbabbaabbbabbbbbbbbbbaaaabbabaaabaaaabaaabababbaabbaaabaabaabbabbbabbaaabbbababaabaaabbabbbabbaabaaabbaabaabbbaaaabbababaabaababbababbbabababababaaabaabaabbaaaaabaababaababaabbbababbbbaaaabbbbaabbabbbabababbbbababababaaaaabbabbbabbbaaabaabbababaaaaaabababbaaabaaabbaabbaaababbabaaaabababbaabaababbaaaaabbbbaaaabbabbbaaaababbbaabbbabaaaabbbbbbabbbabaababbabbaabaabbabbaaabbbaababaaabbbaaaaaabbaabbbbabaabbbbbbbaaaaaaababbabaaaaabbaaabaabbbaaabaaaaaaabbbabbaaaaaaabbbabbbababaaaaabbbbaababbbbaaaabaaabaabbaababbaabbabaabbbaabaabbabbaabaabbaaabbaabbaabaaaaabbaabbbaabbabbbbabbabbaaaabaaaaaababbaabababbabaabbbbaaaaabbbbaabaababaaabbbaabbbbabaaabbaaababaabbaaabaabaaabbabaaabaabbbababbbababbbbabbbaabaabbabaabbbbbabbbababaaaabaaaabbabaaababaaaaabbbbababaaababbbababaabaaabaaaaabbbbababaabaaaaabbaabbbabaabbaaaabaaaaabbaabaaaabbaabbbabbababbaaababaaaabbababbbababbbabbbbbabbbaaabaaababbbababbabaaaaaabbabbbaaaabbbababbaaaaabbabbabaabbabbabbaaaaabababababbaabaaabaaaaabababaababaabaabaaabaaaaabaaaaabbbbbabaabaaaaaaaaabababbaabaaabbabbbabaaabaabaaaaabaaaaaaabaabbbaabbbabaabababbbbabbababaaabbaabbbbbababbbbaabbbbabbaabbaaabaaaaababaaabaabbbaaababaabababbbbabbabaaaabababaaaaabaaababbabbabbaabaabaaababaaabbaaabbaaaabaaaaaaabaababbaababbabaabbabaababbbbabbaababbbbaaabaaabbaaaaabaababbababaaaaaaabbababbaaaaaabaabbbbbbbabbbababaaaabababbbbbabaaaaaabbabbaaaabaabaabaabbaabbbaababbbaababbaabbbaababbbabaabbaaaababbababababaaaaaabbaaaababaaabaaabbbbbaaaaaaabaaabaaababaabbabbbaaabbbaaabaaabbbabaaaaaaaabbbaaaaaabbabaabbbbabbaabaababbaabbaabbaaabbbbbbabbbaaabbbbbababbaaaababbaaababbbaaaaabaaababaababaabbababbbabaabbaaabababaaabaabaabaabbabbbaaaaaababbaaabaaaaaabbabaaabbbbbbbbbaababaabbbaabbbaababbabbaaababbabaabaaababaaabbbaaaaaabbbabaabaabababbabbababbabaaaaabaabbabaababaababbbabbbbaabaaabbaababbaaababababaaabaababbbbbbbabbbaabbabbbbaaabbbbbaabbabbaaaabbbbaabbbbabbbababababbbbbabbabaabbaabbbbaabaaabbabbbaaaaabbaabbaababbbbabbbabaabbaaabababbbaaaaaaaabbaaabbbbaabaabbbaaabbbabaaabbaaaabbbbabbbaabbbbbbbabbbabababaaabbabbbbaaaabaabaaaabaabbaaabbbbabaabaabbbbabbaaabbabbaaaaabbbabbabaabbbbabbbbbabaaababbaabaabababbbbaabbbaabbbbaaababbbaaaaabbbbabbbbaaaabaabbaaabaabaabaaaaabaaababbbbaabbaababaababbbbbaababbaabbbaaaaaaabaabbbbbabaaabaababababbbbbbabaabaabaabbabbabbbbbaaaababaaabbaaababababbabaaaabaaaaaabbaaaaabbabbabaabbbabaaabbaabaabbaaabaaababaaabaaababababbbaaabaabbaaababaaababbaabbbbbbabbbabbabbbaaabaaabbabaabbaaabbaabababbaabbbbbaabaaaabaaaaabaabbabbabbabbababaaabbbbaabbaaaaaaabbbbbababbbbaaaaabbabbbababbbbababbbbbbababbabbaaaabababbbbababaabbbbbabbaaaabaaabaaaababbababaabbaabbaaabbbabbbaaabaaabaabaaaabababbaaababbaabbaabbbababbaabbaaaaaaabbaabbaaabbaabbbabbbbaaaaaaabaaaabaaaaababbbbabbabaabbaaaaaaaaababbaaabbbaabaaabbaaaabbaababbbabbbbaabbbbbbbabbbbaaabaabaabaaaaaabbbabbbbbbbbaabaabbabaaaabaabbabababaabbbbaababaabaababaaaabaaaabbbbabbabaaabbaaabababbbababbabbbbbaabbababaaaaaabbbaaaabbabbbbbbaaabaabbabaaaabbbbabaabaababbbaabbabbbabbbbbaabbbbbbbabbbbaaabbaabbabaaabaaabaaaaaaabbaaaabbbbbaabababbaababbabbbabbbabbbbbbbbbabbbbabaababbbbbaabaaababbabbbaabbabbabbbbabaababbaabbabababbaabbabaabababbbbbbbabbaabbbabaababababaabaaaaabbbbaabbaaaaaabbbbbbaaabbbbbbabbabbbbbabbbbaaaaaaabaaabbbaabbaaaaabbbbbbbaabbbabbaabbababbbbababbbbaabbaaaaababababababbabbabaaaabaaaabaabaabaababbaaaaabbbabbbbbaaaabaaaaababbabbbbababaaaaaaabbaaaabababaaababbabbbababaabbaaababaaababbabbabbbbaababbabbbbbabbbabbbbbbbabbbaaaaabaabababbababaababbaabbabaaabbaaaabaaaabaabaaabbbaabbaaabbaaaaababbabbabbaabaaaaaababbabbaaaabaaaabbaaaaaaaaababbaaaaaabbbbababbbababbbbaabbbaaabaababbbabaababbaabbababababaabaabaaaababbbaaabbbaaababbabaabbbaaaababaaaabaaaaaabaabbaaaaabaaaababababbabaaaaaabbbabaabbaabbbbbaaabaaaababbabbababaaababbabbabbbbbbabbbbbaababaaabaabbbabbaababbbbbbabbabbaabaaabaaabaabaaaabbbbbabaaabaaabaabaaabaaaaabbaaaabaabaabbbabaabbbbabababbbbbaaaababaaabbbabbabbbaaaaaaaabaabbbababbbbbbbbbaaabbbbbbabaaaabaaaaababbbaaaaaaaaaaaaababbaabbabbbbabbbaaabaabbaaabbaaaaabbbaaabaaaabaaaaaaabbaabbbaaababbbaaaabaaabbbaabaaaabbaabbabaabbbbbbaaababbbbbbabbbbbbbbaabaabbbaaaaabbaabbaabaaaabbbaaababaabbaabbbaaaaaaaababaabbbbaaabaababbbbbbbaabbbbbaaaaabaaabbbaabaabaabbaaabbbbabababbbabababbabaaaaabababbbbababbaabaaababaaabbbababbbaabbabaabbaabbbbaaabbabbabbababbbbbbabaabbbaaaabbbbabbbaabbabbbbbbbbbbaabbbaaaaabaabbaaaaaabaaabbbabababbbbbbbababababaababaaaaabaaaaaaabaabaabbaaaabaaabbbbaaaaaabbababbbbbaabbaababbbbbababbbabbbaaaabbbabbbbabbbabaabbaaabaaababbabbababbaabbaaaaaabbbbababababbbbbbbbbbababababaababbbbabbaaabbbababbbbbbaabbabaaababaabbabaabbbabbbabbbbbababbbaaaabbbaaababaaabbbabaaabbaabaaaaaaababbabbaababbabaaaabaabbbbbaaabbbbaaaabbbaabbabbbbabaabaabbaababbabbabbbabaabaabaababbbabbaaaaaaababaaabbbbababbbbaaabbabbabbbbaabbababbaabbaaababbabbabababaababbbbaaababbabbbbaaabababaababbababbabbaabaaabaabbaaaabaabbaaaaabaabbaababbaaaaabaaabbaaaababaabaabbaabaabbbababbaaabaababbbbaaabababababaaababbaabaababbabaabbbbbaabaabbabababaaaaabbbaabbabaababaaaabaababaabbaaaaaaaaabaaaaaaaabbbbaaabaaabbbaabbbbaaaaaaaabbabababbbbaaababbbbabaaaabaabbbbababbababbabbaababbbbabaabbbabbababababbbaaaaababbaaabaabbaaaabbaaaaabababaabababaaaaaaaabbaabbbabbbbaaabaabaabababaaabbabaaabbaaabaababbbaababababbabaaababbbbaabbabbbbbbaabaaaaabbaabbabaaabbbbbbaaabaabbbbbbbabaaaaabaabaabababbabbaabaabaababbababbaabbbbbabbabaaaabaaaaaaabbbaaabaabaaaabbaabaaaaababbabbbbbabbbaabbaabaabbbbbbaaabbbabbabaabbababbaabbbbbbbbabbbbbbabbbaabaaababbbbaabababaaababbaabaababbbbbaabbabaabbaabaababbbbabbbbaababababaaabaaababababaaababaababaaaaabbbbbbbbbabbbbbababbaababaabbbabbbaaabbbbbaaabbbaabbbbabaabaabbaaabbaabaaabaaaabbabaabbbabbbbbbabbababaaabbbbbbaaabbbbaabbbabaabbabbababaaababababaabaaaaaaabbbaabaaabaaabababaaabbbbaaaaaaaaababbaabaababbababbabbabbbaababbaabbaabababaabaaaabbbbaaaaaaabbaaababbbbabbbbbaabaabbaaabbaaabbaababbbbbbaabababaababaabaaabaaabbbbaabaaabaaaabaababbabaabababbabbbaabaaaaaaababbaaababbbabbbababbabbbabbbbabbabbaaaabbaaabaaabaaabbbaaababaaaaabaaaaabbbabbabbabbaaabaabbababaaaaabbbbabbbaaaaaaaaaaabbbababbaabaaaabaabbbbbbbbaabaabbabbbabbaabbbbaabbaabaaababbbaabbbaabbbbbababaabaaaaaaaaababababbbaaabbbbaabbbaababbbbabbbbbbabaabbbaaaababaabbababbabbbbabbbbbaaaaababababaabbbabaababbabbaaabaaaababaaababbbbbbbbbbaaaaaabaababbaabaabbabbaababababaaaaababbaabbbbaaabaaabbbabaabbaaabbbaabbbabbabaabababbbaabababaaaaabbbbbbaabbbabaababababbabbabaabbaaaaaaaabbbaabbbababbbaabbbabaaaaaaabbbbaabaaabababbabbaaababaaaaaabbbabaabbaabaababbababbaabaaaabaabbbbaabbabbabbaaaababaaabababaabbaaaaaaaababaabbbaabaaaaabbabbbbbaaaabbbabbabbabaabbabbbaaabbababbaaababbaabaaaababbaababbaabbaabbbbbbaaababbbbaaabbaabbbaabbaabbaaaabbbbababbabaaaabbababaaabbabbbbbbabbaaabababbbbbbaabbbabbabababaaabbbaabaabaaaaaaabaabbabababaabbbbabaaabbaabbaaababbbbbaaaabbaaababaaabbaabaababaaaaabababbaaabbbabbbbabbaabbaaabbbaababaabbabaaaaaaababbabbbbaabbabbaabbbaaaabbabbaaaaaabaaabbbaaabbbbbaabababbaaaaabbbbabaaaaaaabbaabbbbabbbbaabaabbbbaaaabaaabbaaaaabbaababaabbbababaababaabaaababaaaaaaababbbabaababbbbbabbaaaabbbaaabaabaabaabbaabbbababbababbbbbbbbbbbabaaaaaaaabbaaaabbaaabbbaaaababbabbbbbaaaababbabaaaaaabbabbaaaabaaabaabaaaabbababbaabbbaaaabbabaababbbaababbbbaaaaaabaabbbaabbabbabaababaabbbababaabaabaabbaaabbabbabaaabbbbbabbbaabbbaabbbbaabbbbbbbbbaababbbbaaaabbbababaabbaabaabbabababbbbbaaababaaaabbababbaaaabbbabbbaababaaabaaaabbababaaabaababbbabbbaaaaaaabaabbbbababbaaababaabaababbababbbbaaabbbbbaababbbaabbaaaaaaaaaabbbabaababaaabaaabbbbbaababbabababaaabbaaaababaababaababaaaababbabaaabaababbbaabbbbaababbabbbaabbabbbbaababaaaabbabbaabbabaaabbbabbaababbaabbbabbaaabaabbabababbabababbaaaabaabbaababbbabbbbbabbbabbbbbaababaabbabaaaabbaaababaabaaabaaaabaaaaaabbaabbbaaaabaaabbbabaabbbbbaaababaaabbaabbabbbaaabbabbbbbbabababaaaaabababaaaababbaaababbbbabaaaaaaaabaaaabababbabbabaabababaabbbbaabbaababaaabbbabbbbbaabaaaabbbbabbbbbbaabbbaababbabbbaaabbaabbababaaaaabaababaaaaabaaaaaabbaabbbaabababbbabbabaabaaabbbabbbbbbbabbbbbabbbbbabaabababababbabbaaaabaaabababaababbbababaabaaabbbbababaaababbbaaaababbabbaabababbbbabaaabbbabbaabaaabbababaabbbaaaaaaabbbaabbbaaaaaabaabaaabababaabbababbbbbbaabbbbaabaabbabbbaaaabaaaaababbbabbaabaaaabbaaaabababbbbaaaababaababbaabaabaabbaaabbaaabaabaabbbbabbaababbbbaaababbaabbaaaaabbaabaababaabbaaabbaabbabbaabbabbaaaabaaabbaaabbaaaaaaaabbababaaabbbbababbaaaabaaaabbbbbababbaaabbaabaaaabbbabbabaaababbabbbaabbbaabababbbaaaabbabaabbaaaaaabbbbabbbabaabbaabaaabbaababaabaaaaabbbabbaaabababaabaaabaaabbaabbaaabbababbbbabbbbbabababbbaaaaaababbbbaabbabaabbbbaaaaabbaabbbbbaaababababbabbabbaaabaabbbbaaabaaabbbabbabbbabbbbabbbabaabbaabaaaabbaababababbbbbbabbbbabbbbbabbaabbbbabbaabbabbbbbbaaabaabaaaaaabaaabbbaaaaababbbabbabbaabbababbabbbabbabbbabaabaabbbabaaababbababbabbbbbbbaabbaaabbabbababaaabbabbbababbaabbabbbaaababaaababbababaabaaabbaaaababbaababababbababaabaaababaababbababaaaabbbbbabbabbaabbaaaabababbbaabbababababaabbaaabbaaababaabbaababbbbbbbaaabababbabbbaaaaabbbabbaaaabababaaabbbaaaabbbaababaaaabbabbbaaaababaabbbababababbaabbbabbbababbabaabaabbbabbaabbabbabaaaabbbbabbaaabbbbaaaabaaaabbababababbabbbbbaabbbbaaaabbabbbabbaabaaababaabbbbabbbbbaabbbbbaaabbababbbaaabbbabbaaabbaabababbbaaabbbbbaabbabaaababaabbaaabaaaaaabababbababaabaabaaababbbbbbaaaababbbabbbbbabaaababaaaabaaabbbbbabaabababaaaabaaababbabbaabbbbbbbbaabaaababaaabaaabbabaabaabbabaabbabaaabbaabaaaaababbbabaabbbbbabaabbabbababbbaabbabbabaaaaaababaaaabbbbaaabaabaabaabbbabbbbbaabaaababbaaaaabbbabaabaabbbababbaaabaabaaaabababaaabaabaaaabbaababbaaaaaabbabbaabaaabbaabbaaaaabbaaaaabaabbabbbaababababbaaaabbbbbaabbaabbbbbbbbabaaaabababaababaaabaabbbbbbaabbabaabbaaabbababbaaabbaababbaaabaaabbbbabaaaaaaabaabaabaabbaabaabbbaababbbaabbababababbbbbbbabbaaabaaaabaabbaabbbabababbbbaababaaababbbbabbababbabbaaaababbbbbbaabbaabaaabaaaaababbaabaabbaabbabbabaaababbabaaabaaaabbaababaaaabaaabaabaaaabababaaaabbbbbabbababbaaababbbaababbabababbbaabbbbbaababbaabaaabbabaaabaabbbbabaaabbbaaabaabababaababaabbbaaabaaaababaaaabbbbaabbbbabbbbbbababbbababbbabbbaaabbabbaabbbbbaaabbaababbbbaabbabbaababbaaabbbbaaaabbabaabbbabbbabbbbbbbbbabbaaaaabbbabaaabbbaabbbaabbaaaabbbaabbaaabaaabbbabbaabbbbaababbababaaaabbbabaaaabaabaabbbbbbbaabbabbbaaaaabbababbbabaabbaababbabbbaaaabbbbbbbababbbbbabbaaaabababaabaababbbbbbbbbaabababababbababbabbbaabbbabbbbbbaabbbbbbabbabaabaabbbaabaabbababaaabbaabbbaabbbaabbaabbbabaaaabbbabbabababababbbaaaabaabaaabbabbaabbbabbaababaaaabaaababaabbabbaaabaaaabbbaabbaaabbabaaababababaabbbbbbbaabbaaabaaaababbabaabbabbaaaaaababbaaaababaababaabababaabbbbaabaaabbabbbbaabbbabbabaabbbababaabbbbbaaabbbbababbaaaaaabaaabbbbbaaabaabaabbaaabaaabaaababbbbaaabaaaabbbabbbabbbbbabbbbbbbaaabaababaabbbbabbbbbabbaaababbbabaabaabbbbabaaabababbbbaabbbabbbaaabbbababbbbbbbbaaaaaabbbbababaaaabbabaaabaaabaababbbbaabbbabbabbbbaabbbabaababababbbbabaabbababbbbabbbaaabababbbababaaaabababababbbabaaabbabaababbabbbbabaababbaaaaaaabaaabbbabbbbbaaabaabbbaaaababaaabaabaabbbaaabbaababbabbbabbbbababbbbabbabbaaaaaaabbbbaaaabbbaaaabbbabbbaabaaaababababbabaaaaaabbbaaaabbbabbaababababbabbbbbabbabaabbabaaaabaaaababaabbbaaabababaabaaaababaababbaaabbbbbbbaaaaababaaabbbaabbbabbaaaaabaaabaababbbbbbaaabababbaabbbabbbabbaaabbbbbabababbaaaabaaaaaababbbbababbaaabababbbaababbaabbbbaababaabaaaabbbaabbbbabaabaaaaababababbbaabaabbbbabbbbbbabaaaaababbbabbaabababaababbbabbbaaaaabbaaaababbaabbbbbbbbaaabbbaaaababbbaababbaaabaababbbbbbabbbaababaabaaaaabbabbababbbababbabbabaabaabaaabbababbbabbbaaabbbbbabbabbabababbabbabbbbaabbaabbbbbbaabbaaaabbaababbbbababbbaabbaaabbaababbbbbabaabaaaabbaaaabbbbaabbaababbbbbababbbaaabbbbaaaaaaaaabbaaabbaaaaaabaabbaababbabbbbaababbbbbbbbaaaabaababbabbaabaabbaaaaaabaabbaabbbbabbbabbabbbababbaaaaabbababbaaabaaabbbabbaabbabbbaaaababbbaaabbbbaababababbaaabaaabbbbbbabaaabbbabbbbaaaababaaaaaaaaabbaaaabbaabbbbabababbbaabbabbaabaabbbbabbabaaaaabaaabbababaabbababbaababbbbaaabaabbbaabbbbababaaabbbabbbabaabbaaabbaabbbbaaaaaababaabbbbabbabbabbababbbabbaaaababaaaaabbbaaabbbbbaaaabaababaaabbbbbaaaabaaabaabbbaabbbbababaaaabbabbbbabbaaabbababbbbbbbbaaaaaabbaaaaabbabaabaaaabbabaabbbaabababbbbaabbbaaabbbbabbbbbaaaaabaaaabaababbbaababbaabbabbabbbaababbaabaaabbaabaaaabaaaabbaaaabbbaaaabbbbabbbbabbabbbabbbabbabbaabbbbababbabaaabbaaabbabaabababbabbabbaabaaaaabbbaabbbbaababbbbaaabaaabaababaabbaabbababbbbaabbaabbaaaaababbaabbaabbabaabbbabaabbbbbbaaabbbbaabbaaaabbaabaaababbabababaaabbabbaaaabbaaabaabbbbbabaaaabaabaabaabbbaababbbbbaaabbbabaaaaabbbbababaabaabbabbbbbaabbaaabbbbaaabbaaaababbbbbaabaaababbaabbaabbbbbababbababbbbbbabbbbaabbaaabbbabaabaabbbabbabaababbbbaaabbbabbbaabbaabbabababbbbabbbaaabababaabaababaaabbaababaabbbbababaababababaaabbbbabbababbbaabaaabbabbbbabbbaabaaaaabbbaaaaabaaabaabbbabbaababaaaababaaaabaaababaabbaabbaaaabaaaabbbbbbabaabbbaabababbabbababaaaaabbbababbbabbaaaaaabbbabbbabababbbbaaaaabbabbabababbababaabaabbaaaabababbabbaabbaaabbabaababababbabbaaaaabbabbbaabbaaaaaabbbaaaaaaabbbababbbbabbbbabbbabbbbaabaabaaabaabaaaabbbbbaaaabbabbabbababbaaaaabbabaababbababbaabaaabaaaaabbbbbbbaaaaaababbaababaababaaaabaabaaaaaabaaabaabaabbbaaaaaabaaabaaaaabbbbaaabababbabababbbabbbaababaabaabaabaabbaababaabababaabaabbbabbabbbabbaabbabbbaabaaaababaabaabbbbaabababbbbabbabbbbaababbbaababaabbabbaababbabababaaababbaaaaaaaababaaabaabbbbbabaabaaaaabbabaabaaabbaaabbabaaaaababaaaabbaabbabaabaabbbbbaabaaababbbbaaabaaaabbbabaaabaabaababbbbbbbaaaababbbbababababbbbabbabbbaaaaabbababbbababbaabbababaababbaaaaabaaaababaaaaaabbaaabababbabbbbbbbbbbbaabaabbababbbbbaaaaaaabbbbbbbbaababbaababbaaaabbbaabbbabbbbbaabaaaabaababbabbbaaaaaabbbbabaaabbbbaabaabbbbbaaaaabbbabaaaabbbabababaababaabbaabaababbbbaabbaaaaaabbaabaaabbbabbaaaaabbbabbbabbabbbabbbabaabbabbabbbabbabaabbaaababbbaabbaaaaabaaaaababaababaaaaaaaabbbbababaaaabbababbbababbbbabbabbbbabbbabaabaaaabaabbabaaaabaaaabbbbbabbbaabaababbaaaabababaababbabbbaaaabbbbbbbababbbbbbaaaabaaaabaabaaabbbbbabbabababaabaaaababbabbbbbbabaabbabaaaabbabbbaaabbbbbbbbaaabbabbaaabababbabaabbabbbaaabbabababababababbaaaaaababbbbbbabaaabaabbbbababbaaababbbbabbaaaaaabaabbbaaaababbbabaabbabbaaabaabbaaaaabbbaaabbbbaaaaaaabbbbaabbbabbababaaaaababbbabbbaaabbbaabbbaabbbbabaaaaaaaababbaabbabaabbbbbbabbaaababaabaaaabbaabbbaabbaaabaabbbabababbaaabbbabbabaabaabababbaabbbbaaaaabbaabaabbababbabbbaaaabababbbbbaaabbbbbbabaabaaaababbbaaabababababaaaabaababaabbabbabbbbbaababbababbaaababbbbabbbbbaabbbabaabaabbaaaabbbababaaaababbabbbaaaabbbaabbbaaaaaaaabbbbbaaabaaaaaaabaaaaabababbabbbbbbabbaabaabbababbababbbbbaabababbbabaabbaabbabbbbbaaababababbbabbbaaaabbbabaaaababbaaababaabbabaabbaabaabaaababbabaabaabaaaabbbaaaabababaaabababaabababbbaabaaabaabbababbbbbbbaabaabbabbbabbbbbabbbbababbaabbbbabaaabbbbabaabbaababbbababbbaaabbabbabbbbbbbabaaababaabaabbabbabbbbaaaabbabbabbabaaaabaaaaabbbaaabbbababbababaaabbabaaabbbbaaaabaaaaababbabbabbabbabaaaaabaabbababaabbbabbaaabaaababaaabababaaaaaaabaabbbaabbbabaabbaabbbabaaaabaaaaabbaababbbabababaabbabbaababbbaabbbabaaaabaabaabbbbbaaaaababaabbababbaaaaabababaaaabbbababbabbaaaaaaaabaabbbbbababbaabaaaabbabbabbabbabbaabaabbaababaabbbbaaaabbabbbabaabbbbbbbbaabbabaababbababaabbaababaabbbbaabbbaabbabbabaaabaaaabbbbabaabaaaaaaabbaaabbabaaaababbaaababaaabbbaabaabbabaabbbbbaaaaabbaabaabbaaabaabbababbbababbbaabaababbbaabbaabbbbbbaaabaabaabbaabababbabaababbbbabbaababbabbbbbbaaabaaaabbbabbbaabbaabaababababbaabbbabbaabbabaabaabbbbbbbbabbaaabbababbbaababbababbabbbbbbabbabaabbaabaabababaabababbaaaaababbaababaabababbabbabbbabaaaaaaabababbbaabbabaaaaabaaabbbabaaaabaaaaababbbbaabbaabababbbababaabaaabbbabababbbaabbbbbbabbbbbbbaabaaaaabbbaaaabbbaabbababababbbbbaaabbabbabbbbaaaaabaaaabbbabbaabaaaaaaaababababaaaabbbabaaaaabbbbaaaaabbbbaaaabbbaaabbbbabbbbbaaaaaabbabbababbbaabbbbaabbaabbaabbbbbbbabaababbbaaabbbbbabaaaaabaaaababaaabbbaababbbbabaababbaaaaabbbbbabaabababbbaaabbbabbabaaabbbabaaabababbbabbbbbbbaaaabaaabababbbbbbbbbabaaaaaabbabbaaaabbbabbabbbbbbabbbbabaaabbaaaababababbbabbabbaaabababbbabbaabbbbababbaabbbabbbbaababaabaaaaabaaaabbbbabbbaababbababaabbaabbaabaabbbabbbaabaaaaababbaaabaababbaabbbababbababaabbabbaaababbbaabaaabbbabaaabbbbababbabbbbabaaababaaaaaabaababbbaababbbabaaabbbabbaabbbbbaabababbbaabbbbbaabaaaaabababaabbaababbaabbaabaababbaaabaabbbbbabbbabbaaaabbbaaabbaaabbbabbbabbaabbabaabaaaaaababbabbbbaababbbabbbabbaababbababbbababbaabbbbabbabbbaaabbaabaaaaaabbaabaabbabaaaaaababbbbbbaabbabababbaababaababbbbbbbbababbbbbabaabbaaabbaaabbbbbbababbbaaaaaaaaabbbaaabbaaaaabbaaaaabbabababbabbabaabbaaaaabbabbaaaabbaaababbababbbabaabbaaabbbaaababbbbabbbbaabaaabbbabbbabbaaaababababaabaabbbaaaaaaabaaabbbabbababbabbbababbbabbbabbbaabbaaabbababbbaabbbbaaaabbaaabbabbabbaaaaabaaaaabababbbbaabbabbbbaaababbbbbaabbaaabaabbbabababbaaaaaabbabababaabababbbabbbbbbbabbaaabbbabaaabaababaabaababaaaaaabbaabaaaaaabbbaaabaaaaababbbbbbbbbaaabbabbabaababbbabbbaabaabaaaababbaaaabbbbbababbaaaaabababaabbbbbaababaabbbbbabaaabbbabbbbabaabbaabaaaaabbabaaabaababbabbabbbbaabaabbaaabbbbaabaaabaaabaabbbaabbabaabaaababaaaabbaabbbbaaababbbbaaaabbababababaaaabbaaabaaabbabbbbbbbbbabbaaabbbbbbbabbbaababbbaabababbababbbaababbaabbbabaaaaaabbbabaabaababbbaaaababaabbbbbbbaababaaabaababbabbbbbbbaabbaaabaaaaabaaabbbbabbbbabbbabaaabaaabbabababbbaaaababababbabbababbababbabaaababbbaaaabaabbabababbaaaababaaabbabbaabbbabbabbbabbbaaaaaabaaaaabaabbbbaababaabbabbbbabababbabbabbbaabaabbaaaabbabaabaaabababaabaabbabaaabbabbbabbaabababababbababbbbababbbbabaababbbaabbbababababababbbbabaaabbabaabaaabababbbabaababbbaababaaaababaaabbaaabbbaabbaaaaabbaaabaaabaababbaaababaabbbbaaabbabbbababaaaabababbbaaababaabbbabbbbaaaababbaaabbababbaaabaaaabbbaabaabaaabbbaabaababbabbaaaabbaaaaaaabaabababbaabbbbaababaaaaabbaabaabbaaabaababaaabbbaaaabbabbbaaabbbababaaaabaabbaaaaaaabbbbabbabaaaabaaabbbabbaabbaabaabaabababbaaabbaaabababbaaababaababbaabaabaaaaabbaaaababbabbabbbabbabbbbabbaaabaabbbbaaabbbaabbaaabbbbbabaabaabbbaaabaabbaababbbabbbbbbbabbabbaaaaaaabbaaabbabaabababaaaaaabaababbbaabababbaaabbbbaababbbaabbbaabbaababaabbbabaaababbbaaabbbbabbabbababaabbbbbbabbababbabbbabbabaabaabaabbbbaabbaaaaaabbabbbbabaabbaababbabaaaabbbabaaaaabbbbbbbabbbaabbbbbababbaaabbaaaababbbbabbbaabaaaaabaaabbbbbaababaaaabaaabaaabbbaabbbababbabbbbbbbaaabaabaaabbbaababbabbaaaabaaababbbbbaababbbbbababbbbaaaaaabaaaababbbabaaabbaaabababbbbbabaaaabbbbaababbbbbaaaaabbabaaabbbaaaaabaababbabaabbbbaabaabbbbbabbababbaaabbbababbabaabbabaaaaaaabbbbababaaabbabbaabaabbababbabbababbabaabababbaabbaabbbbabaaababbbbaabaaaaaaabaabaabbbbaaaaababbbbbaaabbabaabaabbaaabbaabbbababaaabaababbbabbbbbbaabbbabbababbbaaabbbbbbabbbbbbbbabbbbaababbaaabbaaaaaabbababbbbbbaaaaaabbbaaabbbbabbababaaaabaaaaaababbbbbaaaaaabbabbabaaabaaabaaabaaaababababbbbababbbbbbababbbaabbabababbbbbababaaaaaabaabbbbbbabaaabbbbbababbbabbaaaabaaaababbabbabaaaabbbaaaababaaaaaabbbaababaaaababbbaabababbbaababbababbabaabaaabbaabaaaabaabbbbbababbabbbaabaaaaababababbbababaaaabaaabbbaaaabaaabaaaaabaabbbbaabababaabaaaabbaabbaaaaaaaaababbabaabbaaaaaabbaaaabbabbababbababbbaabbaaaaaabaabbaabaabbaabbabbaababbbabbabaabaaabbbbaaaaabaabaabbbbaababaabbbbbabbaabbbbaabbbbbaabbbaabbababbbabbaabbbaaabbaaaaaabaaaaababbbababbaaabbbbabbaabbbbbaabaaababaaabaaaaabbbabbabaaaabbbabbaaaaaaabbbbaaaabbbaaaaaabbbabbbabababbaaabbbbaaabbbbbbbaaaabbabbbabbbaaababaaaabbbbabaabaabbbbbaabbbabbabababbbabbaababaaaabbbbbbabaaaabaaabaaaabbabaaaabaabbbbaabbbabbaaababbaabbbaaaaaabbbabbbbbabaaabbabaabbabababbbaabbbaaabbaaaaaaabbbabbaabbbaaaabbaababbbbbaaaaaabaaabbbbbbaaaaabaabbbbbbbaababbaaaaababaababbbaaabaaabbbabbbaaaaabbbbaabbbbabbbababaaaaaababbbababaababbabaabaababababaababbaaabbaabbbababbaabbbbaabbaaaabaaaababbbabbbaaaabababbababbabaaababaaabbaaaabbaaabaabaabaaaabbbbaaaaaaaaaababbbabbbbabbbabbaaabaababbbabbaaaabaabbbbaaaaabbababaabbbbbbbbaabbbbbbabbaababbababaabbabbaaaaaabaabbbabaaaababbaaaaaaabaaabbbbbbabbbbbabbbaaaabbabaabbbaabaabbbbbaabaaaaabaaaabbbbababaaaabbbabbabaabaaababbaaaabbbababaabaaaaabbbbbbaabbaaabbbaaabaabbaabbbbabaaaabbbabbaabaaabbbbabbbbbbbaabababbbbbbaaaaaababbbbabbbbbbabaabababbababbabababbbaabababbaaababbaaaabaaaabbbbbabaabaababbbbbaaababbaababbabbabbaabbbbbbbaaabbababbbbbabbabbbbabbbaaaabaabaabbaaabaaaaababbbbabbbababbbaababaabbbaaaababbabaaaabbbbabbaabbaaaaabbbbaaabaabbbbaabbaaabaaaabaaabbabbbbabaabaaabbbabababbabaaabbabaabbbbabababbabbaaabbaaababbbbbbbaabaaabaababaaaaaabbaaaabbaabbbbbbaabbaabbbabbbaababaaaaabbaaabbbbabaaaabbabaabbabbbbababaaabbaabbbbabaaababababababbbbbababaaaababbaaabaaabbaabaabbbbaabaaaabbabbbababaabaaababbabbabbabbbbbaabbabbbaabaaaaababaaabababaababaaaabbaaabbbabbbabbababbbbbabaaaaaabaaaabababbabbbabaaabababaaaabbaaabbabbaabbaaabaabbbbaaaaaaaaababbbababbbaababaabbbabbabaabaabbaabaaababbbbbbbbbbabaabbabbbabbabaaaabaabaaabbbaababbaababaababbaabbabaaaaabbbbbbaababbabaabaaaabaaabbabbabbbabaabaaaabbaaabbbbbaaaaaaabbabbabbbbaabbbbbbbbbbbaabbabaaababaaaaaabbabbaabbabaaaabaaabbbbbaaaaaaababaabbbabbbabbababababbabaaaaabbabbabbbabbaaaabaabbabababaaababbabbaaabbbbbabaabbabbbbaababaabbbbbbbabaabbbaaabaaaabaabbaaaaaaababbabaaaaabbbbbbbbabbbbbabbabbbababbbbbabbababbbbaabbbaaaaaaaaaabaabaabbabbbaaabbabbbaaaabbbaabbbaabbbabaaaaaabaababaabaabbaabaaaabaababaaaabbbabbaaabbaaabbaaaaaaaaabababbbababaaaaaabbababbbaaaabbabbbbaabaabaaaaaaabbbbbbbabbbaaabbbbbaabbbbaaaaaabbbbbbaaabbaaabbbaaabaabbaaaababaaabbabaaabaababbababaabbaabbaabbbbbaaabaabbbbbbbbbbabbaabbbbbbbbbaaabbaabbabbaabbabaaaaabaaabbabbbbaaaabbababbbbbbbabbaaaabaabbbbaaaababaaabbababbbbaabaabaababbaababbbababbababaaaaaaaabababaaabaaabaaabaabbbabaaaaaabaaabbaabaaabaabaaabaababaaaaabaabbbbbbbbbbbaaaabaaaabbabaababbaaababbbaaabbabbaabbbababbaabbabbabbbbaaaaabbbabbbabababaaaabaabbbbaabbaabbaaabaaaaabbbaaaaaaabbbaababababbabbbbababababbaaaaabaabbbbbabaabaabaaabbabbbababbaabaaababaabbbbbabbaababaaababbbaabbbbbabbaabbaabbbbbaaababbabbbaabbbbbabbababbabaaabbaaaaaabbababaabbbaabaabbabbabbbbbbbbbbbbbabbabaaaaabbbabbbbbbaabaabbbbabbbbabbaabbbbaaaabbaaaaaaabaaaabbababbbbaabababbaaaaabbaababbabbaaaabbaababbbaaaabaabababaaabbaababbbabbaaabaabbbbbbbaabbbbbbaaaaabaabbbbbbbbabababbabbaababaababaaaaaababbbbaabaaabbabbaaaababbaaaaabaaababbaababbabbbbbbaabbaababbbaaababaaaaabbbbbabbbbabbabaaaababbaaababaabbbababbabbbaaabbbbbaabbbbbbaaaababbabbbbabbbabbaaabbabaabbbbabbababaabaaaaaaaabaabaabbabaaabaaaabbaaaaabbabaabbababaaabbbbbbabbbaabbaabbbaabbbbbbbbbabbaabbabbbaababbababbbbaaaaabaabbbabbbaaaaababbbbababaaabaababbbbabbabaababbbabbbbaababaabaaaaabababaaababbbbbabababaabbabaaabbbabbbaabbaaabababbaabaaaabbbbababbbbaabbbbbabaabbaaaaaabbababbabbbbbaaababaabbaabaaaabbbaaababbaabababaababbbabbbbbaabbbaaaababbabaabbabbbbababaabbabaababbaaaabbbaababbbbbbbaaaabbbaaaabbbaaaabbabbabbbabaabbbbabbbbbabbabaabaababbbbaaaabbbbabbabbbabbabbabaabaaaaababaaaaababaabbababbaabaabbaaaaabbababbaabbababaaabaaabaabbbabbaaaabbaabaaaabababbaabaaaabbbbbbaaababaabbbbbabbbbbbabbbabaaaaabbbaaabbabaaabbbaabbaabbabaabbbaaaababaaaaaabaaaaaabaabaabbbababaaaaabbbbabbbbbbababbaabbbaaabbaababbbbababbaaaabaabbbaaabaababaaaaabbaababaabbbaabbbbabbabaaaababababbaaaabaaabbbaaabbaabbaabbbbaababbabbbabaabbaaaabbaabbaabbabbabbbbaaaaabbbabbabbbbbaaaababababbaaaababbbabaaababaaababbaabbbabbaabbaaaabbaaabbbaabaaaabaabbbaaaaabbbbbaaaababbabaaababbbabaaabbaaaaaaabbabbabbabbbaaabbbababaabbaababbababbbaaabbaaabaaabaaaabbaabaabbbaabbabababababbabababbaaaababaaaabbbabaaabbbaabbbbaaaaaaaabbbbbbbaaabbbbabbabbababbbbabbaabbabbababbbbbbaaaaabaabbabbaaaabbaabbbbaaababbaabbabbbbbbaabbbbabbbbbbaabaaababbabaaaabaabbaabaababaaababbaabbaaabbbabbaabaaaabbabaaabbbaabaaaabaabbababbabbabbaaabbaaabaabbabaaabaaaaabbaaabbbabbbbababaabbbaababbbbaabbbbbbbaabaababbabbbaaababaabbbaababbabbabababbabbbabaaaabbaaaabaabababbbbbbaabbabbaababababbaaabaaabbbbbbbbababbbabaaabaaaaabbabaaaaaaaaababbbbaaaaaabbabbabbabbaaababaabbabbbbbbababbbbbabbabbbbaaaabbbaaabbbabaaabbbabaabaabbbaaaababaabbabbbabbababababbbababbaaaaabaabaababaabbbaabbbbbbabbaaabbbbbbaabaabaaaabbabababbbbbabbbabbaaabaabbabaaaabbaaaaaaaaabaabaaaaabbababaabbaabaabababbbbbabbbbbabbbaaaaaabbbbaaaabaaaabaaaabbbabaaaabbbabaabaaabbbabbaabbabbabbaaabababababbbaababbbabbaaaabbabababaaaaababbbbbbaabbaaaaaaabbbaaabbbbaababbabbaababbbbabaaaaaaaabbabaabababaaababaaaababaabbabbaabbabbaabababaabaaabbabababbaababbbaabbbaaaaababbbabbaabaabbbbaabaabbabbbaaabaaabaaababbaaaaaaabbaabbabbbbbbaaabbaabaabbabbababbbaaaaaabaaabbbabbaaaaaabaabaaabbabbbabbaaaaaababbbbbbabababbabbabbbbbaaaabbabbbbbbbabbbbbbbbbbabaabaaaabbabaabbabbbaabbbbaaabbbaababaaaaaaaabbabbaaaabaabbbabbbabbabbbaaaababbbabbababbababbaaabababaaabaaabaaababbbbbbbaababbaabbaabaabaaabababaabaaaaababaabaabbbbaabaaaaaaabaabbabbabbababbbbbbbbababbabbabaaababbaaabaaababbabbbbabbbababababaabbbbbbbbbabaaabaabbababaabaaabaaabbbbaabaabbaababbaabbaabaabbbababbabbbabbbabaaaaaaababbbbaaabaabbbbabbbaaabbbaabaabbbbaaaaabbaaaabbbbaaabbabababbabbbabaababaabbaaabaaaaabbbbbaaababaaaababbbabaaaaaabaaaabbabbbbbaaabaabbbabbaaaaaaabbaaabbaabababbaaaaaabbaabaaabbbbbbaabababaababbbaabbbbabbaabbaaaabaaaaabaabaaabaabbbbbabaabaabbabbbbababbbbbbabbbabbbaabbababbabbbbabbababbabababaababbbaabaaabaaaabbbbabaabbaabbabaabaabbbbababaaabbbbbabbbbabaababababbbabababbabbabbbabbaaaababaabbbbabbbaaaaaaaaaabbbababaaababbbaababaabaabbbaababbaaaaababbabaaaabababbbaaabbaaabaaabbbbaaaaaaaabaaaabaaaaaabbbbbbbabaaaaaababbbabbbbaaabaabbaaabaabaabbbbbbbbabbaababbaabbaabbaaaababaabbabbaaaabaabbbbabababbbbbbaaabababbbbbbaabbbabaabbbbaabbbabbbbaabaabaaabbaabbbbabbbbaaaaabbabbabbbababbbabbbbabbbabababbabbbbaabbbaaabbaabbabbabbababbbbbbabbbabbababaaabaaaaaabaabaaaaabbaaaabbabababaaababbbaababbaaababbbbbababbaabbaabbabaaaaababaabaaabbbbbbbaabaaabbbaaabbbaabaabbabbaabbbabbbabaaaabaababbabbbaabbbbaabbaabbabaaaaabbbbbaaabaaabaabbbabaaabbbaaaaabaababaabbbbbbbaaabbaabbaababbababbbbaaabbbabbbbbababaaaaaaababbbabaaabaaabababbababababbaaababbaabbaabaaaabbabbabbabbaaaaabaabababaabaaaaabbabbbaabaabbbababaaaaaabbbbabbbabaaababbbbbaaabaaabaaabbbbaababbaaabbbbbbbabbaaabaababaaabbbbbaabababaaaabababaaaababaababbaaabbabaabbaabaabbbabbbabaaaabbbbbbbbbabaaabbaabbbbabbaababbaaaaaaabbabbaababbbbbababbabaabbbabaabaabbabaaaababababaababaaababababbbababbaabbaabaaabbaaabbaaabbbababbabbabbbaaababbbbaaabbbaaaabbaaabbbaaabbabaababbbaaaabbabbbababbbbbaaaababaabbaaaaabbaabbaaabbbbababbbaaabbbabaaababbbaaabaabaaabbbaaaabaaabbaabbaabaaabbabbababbbaaabbaaaababbaabbababaababbabaaaabaaaabbbbaabbabbbabaaaaabbabbaabaaaaabababaaaaaabbabbbaaaaaababaaaaaaabaaaabbbbbaabbaabbbaabbbbbabbabbaaabbbbaabaabababaabbabbbaabaaabaabbabbaababaaabbabaaaabaabababababbbbbbbbbabbababbbbabaabaaaaaaabaaaabaaaababbbaabaaabaabaabbabaaaabbbbabbabaabababbaababbabaaaababbbbbaaababababbbbababbabbaaababbababbbabaaabbbaaababaabbabaababaabbabaabbbaaabbbabbbaaaaabaaabababbbabbbababbbaaaaabbbbaabaaaaabaaabaabaabbbbbaaaabbabaaabbbaabaabbbbaaaaaaaaaabbbbabbabbababaabaabababbaaaaaaabbaabbbbbaabbbaabbabababbbabaabbabaababbabababbababbbabbbaaabbabbaaabaabbabbaaabbababbabbabbbbaabababaaaabbabbbbabababbabbbbbbaaabbaabaaababbbaaaabaabbaabaaaabaabbbbbabaaaabbbbaabaaabbabbaabbbbbaabbababaaaabababababbabababbbabbabbaaaababbbbbaaaabbbbbaabaaaaabababbbbbbbbbbabbabaaabbaabbbbabbbbbbabaaabaaaaaababbbbbaabbabbabbaaaaababbaaaabbaabaababbababbabbabababbbbaaaaaaaabbbababbaabaabaaabbabbaabbaaabbaabbbbaabaaabbbababbabbaababbbbbbbbbbaaababbababaaaababbbaaaababbbabbaabbbaaabbabaabaabbbaaaabaaaababbabababaabbbabaabbbbbbbabaababaaaaaaabababababbbabbaabbbaababbababbbabaaaabaabbabbababababbbaababaaabaabaaaaaaabaabaaabaabaaabbaabababbbabaabbbbbaaabbbaaaaabaababbaaabbaababbaabaababaabbbbbaabbbabaaabbbabababbbbbbbbbbaabaaababbabbaaabababbabbbbaabaababbabaaaabbbbaaaabababbababbbababbabaaabbaaaabbbaaababbbbabaabbaabbbbbaaabbbaabbbabaaaaaabbbbabbaabbbbababaabbaabbaaaababbabbabbabaaababbaaabaabbbabbbbababbabaabababaaabbaababbbbbaabbabbbbbbabbaaaaababaababaaabbababbbaabaabbabaabbbbbbbababbbaaabababbbbbbbabbabbbaaabaaabbaaabaaaabaaabbaaaabaabaabbbabaabbbbbbaaaaabbbababbaababaabaababbbbaaabbabaabaaaabbbabbabbbabbaabababbaabaabababababbbaabbbbaaaaabbabaaaaabbbabbabaabbbbbabbabbaaaabbabbabbbbbbabbabbbbaaaabbbbaabbaabbabbbbaabbaaabbababaababbabbaaaaabbbbabaaaaababaabbaabbabaababababbabaababbbaabbaaaabaababbaabbabbbbabaabbbaaabbbbaabaabbabbbbbbaaaaaabbbabababaaaabbbbbbaabbabbbbaaaabbabababbbbbbaaabaaaabaaaaababbbaaaaabbababaaabababbbbababbababbbababbbabaaaabaabbaaaababababaaabaababaaabbbbbbabbbbaabbbbabaaabababaaaabbabbbabbaabbaaabaabbabbbbbaabbbababbaababaaaabaabbaabbbbabaaabbababbbbbbbbaabbaaaaaabaababbbbabaaabbaabbabbaaaabbbaaabbbaaabbbbbbaabaaaababbbaaaabaaaaabbabbbbbabbaabababbaabbbabaaabbaabaabaaabaaabaaaaaabbbaaaaaabaabbbabbbaababaabaaabbabaabaaaabaababbbaaaabbbaababbaabaabbaaaaababaabbbbaabbbbabababbbbbbbaaaabbbbabaabbbaababbaaaaaaabbbbaaabbabbaabbbabbbaabbbbbbbbabaaababbbbbbbaabbaaaabbbabbbaabaabbaaaababbababbbabaabbababbabbbabbaabbabbaabbaabaababbabbaaabaaabbababaababbabbbaabbbbabbabaaabbaaababaabbbbaabbababbbabababaabaaabaabaaaaaaabaaabaaaababbaabbbabbabbabaaabbbaabbabaaabbbaaabbaaabbbabaabbbaaababaabbaabaaaaababaabbbbaababaababbbbaabbbbabbbbabbaaabaabaaabababbaabaaaaaabaabaaaaaabbbaaabbaaaabaaaaaababbbabaabbababbbbbbaaabbabaabababbbababaabbabaabbbbbbbbbaaabbaaabaabababbbbabbbabaaabbbababbbaaabbbaaaaabbaaaabaabbbbabaaababaabbabaabbbaaaaaababbbbbabaabbababaaabaabbbaaaaabbbaaababaaaabbbaaaaabbaaabbaaabababbbbababbaababbbbabaaabbbaaaaaabbaaabbbbaaababbabbbababaaabbaaaabbbababaabaaaaabbaaaaabbbabbbbbaabbbbabaaababaabbabaababaaaaaaabbabaababbbaabababbabbababaaaababbbbabaabbaabbaaabbaaaaaabaaaababbaabbbaaaaaabababaaabbaaaaabbbbbaaabbabbbbbbaaaababbbabbbbbbbaaaaaaaababaababaabababababaaaaaaaaabbbbabaaaabbbbababaabbabaabaabbbbbaabbbbbbaababbbbabbbbbbbaabbaabaaaaabaababababaababbabbbbbaabababaaaaabaaaababbababbbbbaaabbaaabbaaababbababbababbbabbaabbaaaababbbababbbababbaabaaababaababbbabbaabaaaabbaabaaabaabbaabababaababaaaaababbbbbaabbbbaabaaabbabbabaaabbabbaaababbbaababbbaaaabbabbabbaaaaabaaabaabbbababaabbbbbbaaabbaaaaaaaabaaaababbaabbbbbaaabaabbbbaaabaaaaaabaaaaababbbbababaabbbabababbabbbaabbabbaaabbbbaaabababaaaabaaaabbbabbbbabbabaaaaaaaaabbbaaabbbbaabbaabbbaaabbbaababaabbabababbbbbaababbbbaaaaaaaabbabbaaaaaababaabbaaaaaabbabaaaabbaaaaabbbabbbabbaaabbbaabbaabbabbbbabbabbbabaaabbaabbabbbaabbaabaabaabbbbababbbbbbabbabaaabaabaababaaabbaababaaaabaabbbabbbaaaabbaabbababaaabaabbbbaaaabbaabbbaabbababaabaaababaaabbaaaaaaaaabababbbaaababaaaaaabbbaababaabaaabababbaabbaabbababbbabbbaabbaabbabaaababaabbaaaabbbbbaaabaabbabbababaababaabbbabaaaaaabbaabaaaaabbbbbaabbababbbaaabababbaabbaaaabbabbbbabaaaaabbaabaaabbabbabaababaabaaaaabaabbabbbbaaabaabaaabbbbbbbbabaababaabbbbbbbaaaabaaabbbbbbbabbbaabbbababbbbbaaaabababbbbbbbabbbbaabbaabbaaabaaaaababaabbabbabbaaabbabbbbbabbbaaaaabaabbaaabbbabaabbbababaaaaabbbabbabbaaabbbbbaaaabbbabaabbaabbbbaababbbbabbbbbaaaabbabaabbabbabbaabbaabbbbbababbbabbaabaabaababaaaabbaaaabbaaabbaaaabbbbbaababaabaaabbbaabbababaaabbaabababaabbaaaabbbaabbbaabaaabbbbabbabaabbbabababbaabbabaabbbabbababaabababbabbaaabbabbbaabababaaaaabababaabaabbbbaaabbbaaababbbbaababbbbbaabbababababbababbbbababaabaaaaabaabbaabbaaaabaabaaabbbbaabaabaaabbbbbbbababaabbaaaabbabbbababbbaaaaabaabbbbabaabbbabbbababaaaaabbbaabaababbbbabbaabbbababaababbaaabbabbaaaabaaabbbbaabaaabbbbbabbabbbbaaabababaaaabaabaaaaababbbaababbababaaabbbaaaaabbbaabbaaaabbbaaabbaaaaabbaaabbbbbbbbbaabbaaaababababaabaabbaabababaabbaaabbbbaaaabbbabaabbbbababaaaababbbbbbabbabbbaababaabaabaabbbbbbabaababbaabbbbabaaabbaaababbaabbabaaaaaababbabaabaabbbbbbaabaabbbaaabaababbbbababbbaaaabababbaababbabbabaaaaaabbaabbbababaaabbabbaaaaabababaabaaaaabababbbabbabaaaaaababbaabbbbaaaaaaabbaabaaabaabbbbabbaaaabbbbabaabababbbbbbbbbbbabaabbabbaabaaabaaabaabaaaaaaabbbbbbbaabaabbaabbbbbbabbaaabaaaaaababababaaaaababbbabbbbabbbbbaaabbbabbbbbbbababaaabbabbabbbbbbbabbaaabaaababbbaaaaaabbabaababbbaababbbbabbbbbbbaabababbbaabbabababaabaabaaabababbbaaaaaabbabbbbbbaaababbbbbbbbbaababaabaabbbbabaabbabbaabbbbabaabaabaaabbababbbbbaaaababaabbabaababbaaaabaaabbaaaaababaaaabbabaaabababbbbaaabbbaabbaaaaabaaabbbbabbabbaaabbaabaaabaaaababbbbaaabbbbaababaabbaabbbabaaaaaaaaaabbbaaaaaabaababbbbbaabaababbabbbbabaaaabbbabbabbaaaabababbbabaaabbbbaabbbbababbbaabaabbabababaaaabbbabbaabaaaaabbaababbabbbbbbbbabbaaaaabbabbaaaaababababababaabaaabbbbaabbaabaabaaababababaaaabbabbaabbaaabababaababbbbaaaabbbbaaaabbaababbbbabbababbaaababbbaaabaababbaaababaababbaaaababaaabbbbaabbbbaaaabbabbbaabbbbaabaabbbbbbbbabbabaaaaabaaaaabbabaabaababaaaaaaabbaaabbbbbababbaaabbabababababbaaaabaaabbbbababaabbbbbababababbbbbbabbbabbabbbbabbaababbabaabbbbbbbbabaaabbbabbabbabbaabbbabbbabbaaabaabbabaabbbabaaabaaababababababbbaabbaabbbbbabaabbbbbaabaaaabbaaabbbbbbabbaaaababbbabaabbabbbbbaabbaaabababbbbaaaaaaaabbbaaaabbaaabbbbbabaaabbbbaabaaababbaaaaaaabbabaabbaaabbbbaabaabababaaaabbbbababbaaaabbaabaaaabaabbbaaaaabbabbaababaabbabaabbbbbbbabaabbabbbbaaabaaabbaababbababaaaabbaaaaaaabbbbaabababbaabbbbbbaaabaabaaabababbaabaaabbabbbbabbaabbbaaabbaaababaabbabaabbbbbabaabaaaababbabbababbababaaaaabaaaaaaabbbabaabbbbbaabbaaaaaaaaabaabababaabbbaabbbaabaaabbbbabbbbbbbaabaaaaaaabaaabbbbbbbabbaabaabbaabbbbabaabaabbbaabbaaabaabbbaabaabbababbaabaaabbbabbbaabbaabbbbbababbaabababaababbbbabaabbabbabbabaabaaababababbaaaaaabaaabababbbababbaabbaabbaababbbbbaaabaabbbbabaaaabaaaabbabbbbaaaaabaaaaabaabaaaababbbabbaaaaaaabaaabaaaaaababaabbaabbaabbbbbbaaabbbbbaabbbaaaabbabbababbbbaaaabbbbaaaaabaaaababbbaaabaabbaaabaabbaaabbbbaaaaaaaaabababbbbaabaabaaabaabababbbbababbbbbaaabbaabbbaababbaaaabbbbbaaabababaaaabaaaabbabaabaabaababbbbbbbaabababaabaaababababbaaaabbbbbbaaababbbabbbbbbabaaaabbbabaaaabbbaaabbaaabbbaabbbaabaaabaababaaaaaaaabbbaabbbaabaabbbbaababbbbababbababaaaabbabaabbbbabbabbbaabbbbabbbbbabbaaaaaaababbaabbaaaaabababbbbababbbbabbbabaaabaaabababaabbbbabbbbbabababbbbabbbaaaaaaabababbabbaabbabbaaaaabbabbbabbaabbbaabbabababbbbaaaabaaabaababaaabbaababaabaababbababaababbbbbbbabaabbbbaababaabbbbbabbaabbaaaaabaabbbbabbbaaabbaaaababbbbaaaaaaaaabbbabbaaaabaababbababbabbbababbbabbabbbaaababaabaabbbabbbbbbbbaaaaaaaababbabbabaabbabbbaababbababbaabbabababbabbbaaaaaaaabbbbaabaababaaabababbabbabbbbbbbaabaabaaaabbbaaabaababbabbaababaabaaabbbabaabaabbbbaabbbabaabaaababaaababbbabbaabbaaaaaabaababaaaababbaabbbabbabbbabaabbaabaababbaabbbababbababbabaabbbbbaabbaababbbbaababaabaaaabbaaababbaaabaabbaabaababaaabbabbbababaaaaabbabbabaaabbbabbbbbbaabbbabbbaaaabbbbababaaababbbbaaabbaaabbabababaabaabbbbbbbbbbababbbbbaabaaaaaabbaaababaaaabaaabbbbaabaababbababbaaabbabaabbbbbabbbbaabbabaabbabbbababaabaabaababbaabbbaaabaabaaaabaabaaaaaabaabaabbbabaababaaabaabababaababaabbaaaabbbaababbabaabbaaabbbabaabbbbbbaaabbbabbaaaabbabaabbabbababbbaabaabaaaabbaabbaabaababbaababababbbababbaabbabababbbbbaaabbaababbabbababaaabbaabaabaaaabababbbbbaabbababaaabbbaabbabbbbabbbbbaabaaabababbbabbabbaaabaaabbbaaaaaabbbbababaabaaabbabababaaaaaabbbaabbabaabaabaaabbaaaabbababbbbbaabbabbaabbbbaaabaabbaabbbbaaaaabbabaaabbbababbbbbbbbababbbbbbababbbbbbabaaaababbbabbabbaabababbabbbbbaababbbbbabaaabaabbbaabbaabbaababbabbaabbabbbbbabaaaaabbbabaaaabbbaabaaababbbbbbbbbbbabbabaaaaaaabaababaabbbbaaabaaababaaabbaaaabababaabaababbbbbbaaabaaaabaabbbbbabbbaabbbaaababbaabbabbbabbaaabbabbbbaabbbaaaaabaabaabaaabbaabbabbaababbbbaaabbbabaabbabbabbbaababaabbaabaaaabaaabaababaabbaababbaaaaaabbbabbbbbaababababbabbbbbbaaaabbabbabbabbaababbbbbbaabaabbbbbaababaaabaabbaabbaabbbaaaabaaabbabbaababaababbbabbaaaabbaaabbbababbaaaaabaabbbbbaabaaaabaabbbaabbbbbbbabaababbbbbbabbababbbbabbaaababbababbbbaaaaaaababaabbabaaabaababbababbbaaaaaaabbaaabbaababbbabaabbbbbabaabaaaaaaaaabbaabbbbbbaaaabaabbaabbabbbabbbbbbbbaaabbbbbabbbbbbbbabbaabbbbaaabbbaaaabaaaaaababbabaabbbabaaaaabbabaabbabbabbbbbaababbababaaababbaaabbbababbababbbbbbaababbbaabaaabaabbaabaabbbbabaaaaabbaaabbabaaaaaaababaabbaaaaaabbaaaaabaaababaaaaaabbbbbbbaababaabaabbaaabaaabaaaabaabaaaaabbbabbbaaababbbbaaaabaaaabbabbbaababbbabbbbabbbbaabbbbbbbaabbaaaababbbaabbaabbbbaaabbabaaabababbaababbbbbbbbabbabbabbbaaaaaaaaabbbbbbabbaaaaaaaaaabbaaabaaabbbbaaaababaaaabbbbbbabbbbaaabbaabaaaaaabbbabaaabaaaaabbbabaaaaaabbbbbaababbbbbaababbaabbaaaaaabbabbbabaaaabbbbbaabbaaaabaaabbbaaababaabaabbabbaabbbbabaaaabaaaabbaaabaaaaabaaabaabbbbaabbababaabbabaabaaabbababaabaaaaabababaabbbabaaaababbabbaaaaaaaabaaaaabbabaabbbbabbbbbaabbaabbbbbbbabbbbabbbbababbbbaaaabbbabbaababbaaababbababbbaabababbbbaaabbbbbababbaabaaabbabbaaaaaaaaaabbabababbbababaabbbbaaabbababbaaabbbabbaaaabbbbaaaabaababbaaaaaaaaaababbbaaaabbbababbbabbbbbbbaaaabaaaabbabbbbaabaaabbaabbabaaaabaabaababbbabaabababbbbbbbbbaabbbabaaabbbabbbabbaaabbbbbabaaaabaabbbbbbaaaabbaaaabbaaaabaababababaabbaaabbaababaaaabaabbabbabaaabbbbabaaaabbabaababbaabbabaaabaaabbabbbabbaabbbbaabbabababaaaaaabbaaabbbabbbabbbbbbabaababbbabaabbbbbbbbabbaaaabaaaaaabbbaabaaabbabaaabbbbbbbbbababaaabaabbbabaaabaaababbbabbaaabaaaaaabaabbabbbbbbbbabbbaabbbbbbaaababababababbabbbabbbaaabbbbbabbbabbaababbaaabbbbabbbaabababbabaaaabaaaababbaaabababbbabbaabbbbaabbbbabbaabbababbaaaabbabbabbbaabababbbbaaaabaabbabbbbbbabbaabaabbbaabbbababbabaaaabaababaabaababaaabbbbbbababbabaaabaabaaabbbaabbbaabaabaaababaaabbbbaababbaababbbbbbabbaaabababaaabbabaabbbbbaababbbbaabbabbabbaabaaaaaababaabaababbababaababbbbbabbabaabaababbbbabbaabbabbabbabbbabaaababbababbbabbbaabbaaabbababbaaababbaaaabaabbbbabbbababbabaaababbaabbbbbbbabaabbbaabaabbbbabaabaaabbaaaaabbaabababaaaaaaaaababaabaaabbbaaabbbbabbbbbbaaabbaabbbbbabaababbbabaaabbbabbbbabaabbbababbbbbabaaabaaabbabbabbbbbaabbbbaaabbaabaababaabbaabaabbbabbbabaabaaabaaabaaaaabaabaaaaabbbbbaabbbaabaaaabaabaaababbbbaaabbabbbabababbababbabbaaaaaaaabaaaaabbabaababbbbbababbbbabbbbbaababbabbaaaabbbabbabbaaaaaabababaababbbaaaabbabaabababbaababababbbaabbabababbababababbabbbabaaabbaaabbbaabbaaabababbbabbbaabbabababbaaabaabaabbaabbbbabbbbabaaaabbbbbbbaabbbaabababaabbaabbaaabbaaaaabbbbbaaaaabababbabbaaaaababbaabbbbbbaaaabababbaabbabaaabaaaabaabaabbbabbbbaabaaaaaaaaaaaabbbabbbbaaabbaaaaabaaabbaabbabaabbbbabbabbaaababbbaaaaabbabaababababaababaabbbaababaabbbabaababaaaabbaaabbbabaabaabbaaabaaababbaabaaaabbaaaaabababaabbbaaaaaaabbbbbbbbbabbabbaababaaabbbaababaaaabababababbaaabaaabaababaabbabbabaaaababaaabaabbbbababbabaabbbaabbbbabbabababbbaaaaaaaaababaaabbaabababbaababbaabbaabaaaaaaababbbbbbabbbababababbbbabbaabbbbabbbaababaababbbbbbaababbbabaaabbbbabbbabbabbbaaaabbaababaabaabbbbaaaaabababaababaababbbabbabbbbbaaababaaaaaababbababaababbbbbbaaaababbabbaabbbbbbbbbbabbbbababaabaabaababbbaabbababbbaabaabbbaabbbbbabbbbaaabaababbaaaaabaaabaaaaabbabaaabaabbbbabababbbababaabbbabbbaaaaababbbaaabbbbabababbbababbbaaaaabbbbbbabaaaababaaaaabbbaabbbabaabbbbbaabbaaaabaabbbaaaaabbaababbababbbbbabbbabababababbabaaababbbbbbaabbbaaaabbabababaabbababbaaabaabbaabbbbbbbaaabababaabaababbaaabaabababababaabaabaababbbabbabbbbaababbaabababaabbbaaaabaababbabaabaabbbbaabaaaabaaaabbbbbbabbabbaaababbababbbabbaabaaabbabbbaaaaababbabaabaabaabbbabbabbabbbaaaaabbbbabababbaaaabbababbbbbaaaaabbaababaabbaaaababbbabbbbbabbbabbaabababbbbabbbbaaabbbbaabbbaababbbbbabbababababbaabbbbabbaaababbbbbabbaabaabbabaabbbbbbaabbaaabbaabbbaaabbbabaabbbabaaababbabaabaabbabbaaaabbbaabbaaaabbaabbbbaabababbbaababaaabbabbabababbbabbbaabaaaabaabbbabbbbbabbaabbbbbaabbaaabbbbaabaaaabbbbabaabbabaabaaababbbbbababbabaabbabbbaaaaaaaaabaaaaaabbaaaababbaabaaaaaabbaaabaabbbaabbaabaabbbbbbbaaababbaaababbababbbaaababaaaabbaaaabababaabbabbbbababbaaababaabbabbbabaaabbaabaabbbaababaabbbabbbbaaababbaaaabbabbaaababbbbabbbababbbbabaaaaabbbababbabbbbbbbaaaababbabbabbbaababbbbbbaaaaaaaabbababbbabababbbabbbabaaabaabbabbbabbbaaabbbbabbbbaaabbabbbabababbaababaabaabbababbaaabbabbaabaabaababbbaaabbabbbbaabbbaaaaababbaaaabaaababbbbaaaaaaaaababbbbbaabaaabbabaaaabbbaabbabbabbbbbbbabbbbabbaabaaaaabbbabbaaaaaabaabbbaaaabbbbabbbbbaaabbaabbbaababaaaaabbabaaaaaaabaaabaaaabababbabbbabbabaabbbbbaababbbaabbaabbbabaabaaabbaaaaaaaaabbbababbbaaabbaabbbaaabbbabaabbbaabbbabbbbaaaababaaabbbabbaabbbaabbabbaabaabaabbaabbaaabbbaaaabbbbbbbabbababbbabaaaaababbababaabababababbaaaabbbaaaababbabbabbbaaaababbbbaabbabbbaaaabbbaaabbaabbbaaaaaabaaabbabaabbbbbaaaaabbbaaabbabaabbabaaaabbbababababababaaabbbaabaaaaabbaaaababaaabbaababbbbabaabaaababbbaabaaabbbbababbabaabaaaabbbaabbbbaabbbbbbabaabaabbbaaabaabbabbabbbbbbbaabababaaabbbbabbabbbbaababbbabaabaabbaaabbababbaababaabaaaaaaababbabaabbaaaabaaabbabaaaabaabbbabbabbbbbbbbbbabbbaabbabbababbabbbabbabbaaababbbbaabaababbabbbabaabbbbaabbbbabababbababaaaaabaabbabbbabaaabbaaabaaabaabaaaabbabaaabaabaaaaaabbabaabbaabbbaaaaaabbbbbabbbaaabbaaababaaabbbabbabbbbababbabbbaaaabbababababbabbbabaaaaabbabababbabaaaabbbabbaaaabbbaaaabbabaaaaaababbbaababbbbabbbabbabaaabbaaabbaabaaaaababaaabaaabbbaabaaaabaababababaabbaaabbababaabaababbabbbabbbaabbbabbbababbbbbabaaabbbbbbbbbbbabbbbbbabbaababaaababbabaaabbabaabaaabaabbaabbbaabaabaaababaaabababbbbaabbbaaabaaababaaabbbaaabababbabbaabaabaaabbabbababbbabbbbabbbbbababaabbbabbabaaaaabaaabbabbbbbbbbbbabaaabbbaabbababbbaaaabaaabbabaababbaaaabbaabbbabaaabaabbbababbabbbaababaabaaabbbaaabbbabaaaabaaaaabababaabaabbaabbbababababaaabaabaabbabbbaaaaaabbaaabbbaabbbaaabbbbbbaabbabbabaabbbabbbbbababbaaababbaabbbaaaaabaaaabababbaabbbbbbbaaabbaaabbbbbbbababababaabbaaababbaabbbaaabbbabaaabbbabbabaaaabaababaaaaaaaabbabaaabbbbabbbbbbbabaabaaabbbabaaabbbabbbabaabaaaaababaaaabaabaaabbbabbababbabbbbbbababaaabbbbaaaaabbaaaababbababaabbaababbbbaaababbbabbababbaaaaababbabababbbabbaabaabbbbbabbbbbababaaaabaabaaaaabbbbbbbaaababaaabaababbbaabbabbabbabaabaaababaaabbbbbaaaabbaabbbaabbbbbbbbabbbbbbababbabbbaabbaababbabbabaabbbabbabaabbabaaabbbbbbbaaaabaabaaaaaaabababbbbaaaaaaaabbbaababaababbbaabaaabbaaababbabbbbbaabbbabaaaaaabaabbaaabbbababaaabbbbbbabaabaaabbabbababaaabbbbaaabbabbabbabaabaababbaabbbbaaabbaabbabaaaabbababaaabbaabababbabbabbbbaaabbbabbabaaababaaaabbaabababbababbbbababbaababbabababbbabbbaaaababbbaabaabbaaaaababbabbaaaabbbbbaabbbbabbabbaabaaabbaababababaabbaabaaaaabaaaabbbbbbbabbaaabaaaaaabaabbbabababbaabbabaaabbbbbbaabaaaabaabbbbabbaaaaaaababaabaaabbaabbabaaaaaabbbaabbabbabaaababbbaaaaabaaaabbaaababbbbaabbbbbabbbabbbbabaaababaaabbaabababbaabaaabababaabbababbbabbaaababbbbaabbabaaaaaabbbbababbaababbabaabbbaaaaaabbbbabbbbbbaaabbbbbaaaaaababbabaabbbbaababababababbabbbbaabbbaaabaabaaabbaabbaaaaababbababaaaaaabbaaabbaaaaaaaaabbabaaabbbbaababbabababbabbbbbabbbaabbabbbababaabbbaaaaabbbbababbbbaabaaaabaabbbbbbaaabaabaaababaabbbabbbbbabbbbbbaabbaabaaabbababaabbabababbababaaabbabbabaabbabbbbbaabbbbbbbaaaabaabaaaaaaaaaabbaaaabbabbbabaababbbabbaabbabbabababaabbbbbabbbababbbbbbabbbbbbbaabbabbbaabbabbbbbaaababaaaabababbbababababbbaabababbabbaabbbbaabbaaababaaabbaaaaabaabbbaaaababaaabbbabbabaabaaabbbabbabbabbabababababaaaabbaaaaaaabbbaababaabbabbaababbbaaaabbbbbbaabbbbabaabbbabaaaaaaabbaabbbbbabbabaaababaababbbaaabbabbabbabbbaabbbbbaabbbbaaabaaabbbbbababaaabbbbabbbaabbbbaaaabaaabaabbbbbabaaabbbaaabbababaaaaaabaaaaaabaabbabbbaaaababaababbbbbabababbaabbbabbbbbbbbbbabaaabbbbbaabbbbabbaabbababaabaaaababbaabaabbaaababbaaababbabbbbabbbbbababbabaaabbababaaabbbaaabbbababbbabbabbbbaabbbbaaabbbbbabbbababbababaabbabbaaabbaaaaababaaabbbaabbaaaaabababbbbbbababbbbababbbaaaabbbaaaabaababbababaabbababbaaaaaaaaabbaabbabaaabaabbababaabaabbbbbababbbabbabbaabaabbbbbabbbaabbaababbbaabbbababbbaabbbababaaaababbbbbbbabaabbbabbbbbabaabbaababababbabaaabababbaaabbaabaaaaaaabbaababbbbbaaababbabbababbbaaabaabaaabbaabaaabaabaababbbbbaaaabaabbababbbbabbbbbbbbaaabbabaaaabaaaaaaabaaaaabaabbbaaababbbbaaabbbabaaabaaabbaaabbaaababbabbabaaabbbaaabaabbbbbaaabaabbaababaababababababbbabbbbaaabbaaabbbbaaabaabaabbababbbbaababbaaabbaabbbaaabbaababbababbbabbbbbaabbbaabbabbaabbabaaaabaabaaaabaababbbbababbbabbbbbaaababbababbbbaabbaabaaabbbabbbbbbaabbbabaaabbbbbaabbbbbababaabaababbbaaabaababababbaaaaabbaaabaabaabaaaaabbbbbabaaabaaaabaabbbbaaaaaaaaabaababaabaabaabbbbbababbbbbbaabbbbabbbaababaaababbbaaaabababbbaaaaabaabbbbbbbbabbbaabbabbaabaaaabababaaaabbabaabababbbaabbbabbaaaababababbbbaababaabbaaabababbbaabaaabbabbabbaababaabaaaaaaaaaaaaabaabbbbbaaabbabaaaabbbaaaabaaabaaaabbaaababbbaabbbaaaaaaaabbbabbababaaabbbaabbababaabababaababaababababbababaaaabaaaaabbbbbbaabbbbbbbbababbaabaaabbaaababbabaaaabbaaabbabaabbabbabbabbaabbabbbabbababbabaaaaaabbababbbababbaababbbbbaaababaabbbaabbabbaababbabbbbbaabbbabababaabababbabbabbbaabbaaaabbabaaabbaababaabbababbababbbababbbababbbaabbabaaaabaabbaabbabbaabaabbaaabbaabbabbbabaaababbaabaabaaabbbaabbbabbbaaabbabbbabbbbababbaaabbababababbaaabbbbbabbbbbbbbbbaaaaabaabaabbbbbbabbababbbbaabbbaabbaabaaaaaabaabbababbbbabbaabbbabbaabbaaabbaabbababbabbbaaaaaabbbaabaaabbbababababbbabbbabbabaaabbbbabaabbbbbbbbababbaabbbbbbbbbbbbaababaaabaabbbbaaaabbbbbabbbbabbabaaabaaaaabbbaaaabbbbbaabaaaaababaaaaaababbabbbbaabbbbbaaabbabababaabbabbaaaabaaabbababbaabbaaaaabbbababababababbabbabbaaabbbabbaababbaabaababaababbaaaabaaabaaaabbbbbbbbbbababbaaababbabaaaabbaababaaaabaaaaaabbabaaabbbbabaaaaabaababbbaabababaaaaaaabbbbabbbaabbbabaabbabbbaaabaabaaabaaabaabaaabaaaaaaabbbbbbaabbaaaabbbbbaabbbbaabbaabbabaabbbbaabaaaabbbabaaaababbaaaaabbbaaabbabbbaabbbbbabaabaaaabbaaaabababbbbaaabaabbabaababbaaabbababbbaabaabaaabababbbbaabaaaaaabbabbaabbabbabbbaabbaababbbaababaaabaaabbbbbaabaabaaaaabbbbbbaabbaaaabaababbabbaabbabbbababaaaabaabaababbbaaabaaabaabbaaabbbaaaabbbabbabbaababbbabbaaabaabbbbbbabbabaaaaaaabaaabbabbbbbbbaababaaaaabbaabbabaaabbaaaababbbabbaaaabbbaababababbabaaababbbabbababaabbaaababaaabababaabbabbabababbbaabbbaaaabbababaababbaaaaabaabbbabbaabababaaaabaaabbababbababbaabbabaaaababaabbabababababbbaaabbbbbbabbbbbbbaaaaababaaabaaababbabbbbaaaaababbababbbbbbabbbaaaabbaabbbaaaaaabaaaabbbaaaaabbabbbbababbabbabbabbabbaabbbaababbababbaaababaaababbaaaaaabaaaaaaaababbaababbabbabbabbbaaababababbbabbbaaaababbabbabaabbbbaaabaaaabababaaabababaabaaabbbbbabbabbbbaabaabbbaabbbbaabaaaabababaaabbaaababbbaabbbabbbabbbaaabbbbbbaaaabbabbbaaaaabbbabababbabbbbbbabbbaaabbbabaaaaabbbbbbbbbbbabbaababbabbabbaaabbabbaabbaabbbbbbbbaaaabaabbbbaabbbbbabbabbabbaaababbabaabbbbbbaabaababbbbababbaaaaabaaabbabaabbababbbbbabaabaaabbbbbbabbbaaaaabbabbbabbaaabaaabaaababbabbbaabaabbbbbababaaabaabbbbaabbbbababaaaabbbbbaabbabbbbbababaaaabaabbabbbaaaabababaababbbbbaaaaaaaababbbbbaababbbaabbbbbababbababbabbbbaabbbaaaaaabbaaabaabbabbaaabbabbaabbbbbabaabbbababaaabbaaaababbbbbbabbabbbaaabbbbbbbbbbbabbbabbabbabbaababaababaabbaabbaababaaabbbbabbabbaabaabaabaabbabaaaaabaabbaabaaaaaaaababbbbaabbabbaabaabbbbabaaaabbbababaabaababaaaabaaabababaabbaabbaabababbaaaabaabbbbbabbaaaabaaabbbabaaaaabaaabbbbbbbabbbbaabbabbabbbbabbaaaabbbbababaabaabbaaabbabbbbabbbabaaabbabaaaababbaabbbbbbabaaaababaabababbabbaabbaaabbbbbaaaabbbbbbbaabbaabbaababbabbbbbaaaaaaaabbbaabaaaaabbabaabaaabbaaabaababbbabbbbaabbababbaabaaabaababbabaabbbaababbbabaaaaabbbababaabbbabaaaabaaabaabaaaabaaabbbbabaabaaababaabbabbbaaaaabbabbbabbaababbbbbababbbaabbaaababaabaabbabbabbbaaabbbaabaaaaaabbabaababaaaabbbbaabbabbbabaabaaabaabababaaaabaabbaaabbbbabaaaaaabbbabbabaabbbabaabaabbbbbbabaabbbbbabbbabaaabbbabbabaaabaabbbaabaaababaabbbababbbaaaababbaabbababbbaabaaaabbabbaaaabaabaabaabaabbbbaabaaabbbabbbbbaababaaaabbaabbbaabbaaaabababababbaaabbaaaaabbabbbabbabaaaabbbbababaaaaababaaaabbbaaaababbbababaaababbaababaababababbbbbaabaabbaababbababaabaaabbaabbbbaabbabbbbaabaabaaaabbbaaabbbababbabaababbabaaaaabaabbabababbaababbaaababbaaabbababaaabbababaabaabbbbabbbaaabaaabbaaababbaabaabbaaabbaaabbbbbbbaaaabbbabbbbabbbabaaabaaababbaaabbbbbbabbaaaabaabbbaabaabaabbaabababbbbabbbbbbaabbaabbabaababaaaabaaabbbbababbaaabaaaaaabaababaabbbaaababbaabaaaaaabbbbabaabbbaabbbabaabaaaababbaabbbbaaaabaaababbbabaaaaaaaabaaabaabaabbabbaaaaabbababbbbaabaababbabaabaaabbbabbababaabbaaaaaaaabaaababbbaaaabbbbbaabbbbbbbabbbbabbaaababbbbababbabababbabbaaaaabaaaaaabbababbabbbabaabaaaaababbabaabbaaaababaaaabbababbbabbbbbaababaaaabbbabaaabbbbaaaaabaaabbbbbbaaababbbaaabbbabbabbaabaaabaababbbaaaaabaabbaababbbabbbbabbbbbbaaaabbaabaabaaaababbabaabbbbabbbabbaabbbbaabababbbbaabbbaaabaaabaaaaaabbbbbbbbbabbbbbabbabaaaaabbaaabbaababbaaabaaabaabbbabbbababbaaaabababbbbaabbbabbbbbbabbbbbbbaababaaabaaaabbababbabbbabaabbbbbbaaabbbbbabbaaaabbabbaabaaaabbabaabaaaaaaabbbabaaabbbaabbbaabbbbbbbbabaaabababbbbbabaaabbbbaaabaababababaabababbaaaabbbabbbbbbbaaabbbabbabbabaabbbbababbabbbaabaaaabaabaaabbbaabaaaabbaabbbbbabbaaaabbbabaaabbaaaaaabaabababbaaaabaabbbabababbabaababbbbabbababaabbaabaaaaaabbabababababaaaabaabbbbbaabaabbbbbbbbbabaaabbababaaababbaabbbaaabaaabbabaaabbbbabbaabbaabaaaaaabbbbabaabbbabaaabaabbbbbaaabbabaabbabbbbaabaaaaabbbaabaaaabaabbabbabababaabbbaabaabababaaabbbbabbaabbbbbaabababbbbabaaaaababaaabbbaaabbbababbaabbaaabbbaabbbaabbabbabbaabbbbbbaabaabbaabbaaababbabbbababababbabaababbbaaabbbbbbababaabbbbaaaaaaababbbabaababaaababbbaaaaaabbaabbbbaabbababaabbbaabbbbbbbbabaaabbababbbbbaabaabbabbbbbaaabbbbbbabbaabbbaabaaabbababbaaabaaabbbbababbabaaabbbbbaaababbbaaababaaabbbabaabbababaaaaaabbbbaaaaaabbbbaaababbbbabaaaaabbaabaaaababbabaabaabbaabaabbbabaaaaababbbbaabbababbbbaabaabaaabaabaabaabbbaabbbbbaaaabaabbbabaabbaabbabbbaabaaabaababababaabbabaaaaaabbbbbbbaabbbbbabaaaabbabbaabababbabbaaaaabbbabbbabaabaabbabbbaababababbaaaaaaabbaabbabbbbbaababaabbababaaabbbaababaabbbabbbbaabbabbaababbbbaabbabaababbbaabbbbbbbabbaaaabbabbaaaaabbbbbababaaaabbabbbabbbababbaaababababbbbaabbbaabbaabbbabaaaaabababbabbabbabababbbbabbababbaaaabaaababaaabbbaabbbbabaaabbabaaaabbaaabababbabbbababbaabbbbabbbabbbbaaaaabbaaabababababaababbbbbbbbaabaabbabaaaaabaabbbaabaababaaaaaabaababbbbababaaaaaaababbbabbabbabaabababaabaaabbbbaaabababaababababaababaaaaaaaaabbabbbbaaabbbaabaaaabbbbbabaabaaaaaaabababbbaabbbbbaababababbabaaaabbbaaabbbbaaaababaaabbbbaaabababaabababbabaaabaabaaabbbbbabbaaabbaaabbaaababbaaabbabbaaababaabaaaababaaaabababbbabbbbbbbbbabbaabbbaabbbabbaaabbbabaababbbabbaabbbabbabbabaabbbababbababbabbaababbaabbabbbbbbbaabbaabbaaaabbbabbaabbbababaabbbaabbababababaabaaabaababaabbbaaabaaaabaabbaaabaabbabaaaaabaaaababbbbabbaaabbabbabaaabbaaaabaaabaaabaaabbbbbbabbaaababbaabababbbaaaaaabaabbbabbaaabbaabbaaaababbababbaabbbaaaababbbabababaaabbabbbbaabaaabbbbababaabbbbaaabababbabbbaabaabaababaabbbabaababaabbabbaaabbababbbbaabaabbbaabaaabaaabbaababbbaabbabbaaaabbaabbaaaabbaaababbbaaababbbbaaabbaaaabaabbbbaabbaaabbbbaaaaababaabaaaababbabbbbaabaaababaababbaabaaabbabbabbaabababbabbabaabbaabbbaabaaaaabaaabaaaababaababaaabaabbbaababbaabbabbbaababaabbaabbaabaaaababaaabaaaaabbabaabbabababbbaaaabbbbbbbababbabbbababaaabbbbbaabaabaaabbbbbabbbbaababaabbabbaabbaaaaaaaabbbaabbbbbbabbbbaaabbbabbbbbaabbabbabaaaaaaabbaaababbababababbbabbabaabbbabbbaaababbbaabbabbabababababaaaabaaaabbaaabbababbbabaaaaaabbbaaabbaaaaababaabbbbaaabbaabaaaabaaaabbaabaaaaaaaaabbaabbbabbaabbbabbbaababbabbabbaabbbbbaabaabbbabbbbbababaaababbabbbbbaabbabaabbabaabbbababaabaabbaaaabbbaaabbaaabaaaaaaaabbbaababbababbabbabbbaaaaabababbabbbbbbabbbbbbbbababaabaaaaaabbbababbbaaaabbbbbbaaabbbaababbbbbbaaaaaabbaaaabbbabaabababaaabbabbaabaaabaabbaaabbaabbbabaabbbabbabaaabbbbbabbababbabbbbaabaabbaabbaaabbabbbbbbbaaabbabbabaaaaaaabbbbbabbabababbbbaaabbbbabbbbaabbabbbaaababbbaababbabbabaabbbabbaaabbbabbabaabaabaaabbababbabababaaaabbababaaaababbaaaabbbaaaababbbbbbabbabbbabbbaaaaaababbbaababbbbbaabababbbbabbbabbbabaaaabbbbababababaababbbabaababbbbbbabbbbbaaabaabaaababbbbaababbbaaabbbbabbbabbbaaaabbaaaaabbaabbaabaaabaabbbbabbabbbaaabaaababbaabaaaababbbbbbbababaaabbaababbbbabbbbbbbaabababbaabbababaababbbabaabbabbabaaaabaababbbbbaabaaabbbabaababaabbabababbabbabbbaabbaaabbbababbbbbaabaabbababaabaabaaabbaabbabbbbabaaabbababbbbbabbababbbaabaabbbbabbbbaabaabaababaabaaaaababbbaaaaabaabbaaaaaabbababaabababbabbbaaaaabbbbbabaabbaaabbbabaababbabbabbaabaababbaabaaabbaaaabaabbbbabbaaaabaaaaaababbaabaabbbaaaaaabaabbababbabababbbababbbabbaababbbbababababababbbaaaabbababbbaabaabaaabbbabbbaabbbabaabaabaaababbbbabbbaaaaabbaabbbabbabaabbaaaabaabbbaabbbbaabaabbaaababbababaabbbbbababaabbabaabbbabaabbabababaabaabbbbaababbbaababaabbaaabbbabbaabaaaaabbbaabbbabababababaabbabaaabbabbbababbbabbbbabbbbbbbbbaabbabaabbaabbbababbaabbaaabaabbbaaaaabbabbbaaaabbbabbabbbbabbbababbababaabaabaabbbaabbaababbbabbbbbbabaaababaabbbbbbbbbbbbbabbaabbabbabbbabaaaabbbbbabbabbaaaabbbaaaaaabaabaaabaaabbabbbaaaaaaaabaabbbabaabbbaaabbbbaaaaabaabbbababbaaababbabaabbababaababbbaabaabaaabbababaaababaabaaaabbbaaabaaabbabbabbaaaababaabbaabaabaaabaabbabbaabbaaabbbabbabaaabaaaabbbababbaabbbbaabbababaababbaabbbabbbbabbbbbaababbbaaabbabbbbbbbbbbbbababaabbbaabbabbbabbbaababaaaabaaabababbbbbbababbaaaabbbabbababbbabbababaabaabaaaabbbabbbbabababbabaaaaabaaaaabbaabbabaabbabbbabbababaaabbaabaabbabbababbabbbbaaaabbbbbbbbbababbaabaabbbbaaaabababaaabbabbaaaabbbbbbabbbabaaabbbaababaabaabaaabbabbbababbbabbabbbbaaabbbbbbabbaaaaaaaaaaaaaabbbbbaaabaaaaaaaaaabbbbbaabbbbbabaabbbbaaaaaaaababbbababbabbbabbbbbabbabababbbbabababbaabbaaabbabbbbabaaabaaaaaabaaaababaaabaabaaabbaabbabbaaabbaaaababbbbbababbbabbbabbbbbbbabbbabaababbabbaabaaaaaaaaaababaaaababbbababaaabaaaabbbabbbabbbbaabbbbbaaaabbbaaaaaaaabbbaabbabaaababbabababbaaababbbaabaabbbabbbbaababaaabbbbabaabbbaabbababaaababaaaaaabbaaabaababbbbabaabbbbbabbaaaabbaabbbaaabaaabbbbabababbbbbaaabbabbababaababbabbabbaabbaaaabababaaabaabaabbbbaaabbabaaaababbbbaababbbabbaaabbbabbababababbaabaabbbbbaaabbbababbabaabbbaabaaabaaaababbbabaababbababbbbaababbabbbabbbaaabaaabbabbaabbabbaaabbbbabaabbaaabaaaaaabbbbbbbbaaaaaabaaaaabbbbaaaabbabbaaabaababbabaaaababbbaaabababbabaaaababbbbbaaababbbbaaaaabbaaabbaabbbbbbbbbbababbabaaaabbbbabbbbbabbaabbabbbbaabbbbaaabaababbaaabbbabaaaaaababbbaaabbbbabaabbabaabaabbabbbbaabaabbabbbabbababaaabbbaaabbbbaaaaababaabbbaabbbbbbbaabbbaaaaabaaaabbaababaabaabbbbbababbbaaaabababbbaaabbbbabbaabbbbaababaabbbbbbbbababbbaaaaaaaaabababbbbabaabaababaababbabbbbbababababaabaaaaabaabbbbabbababbbabbbbbbbabbabbabbbbbaaabbabbbabbbbbabaaabbabbbbaabaabbbbaaabbaaaaabababaaabbaabbabababbabbabbabbabbbabaabbbabbbbabaabababaaaaabaabababaaaaaaabaabbbaababbaaaabababbababbaaabbabbabbaaaabbaaaaababbbabbbaabbbababbaababbbbbbabbbbbabababbaaabaababaaabaaaaaaaaaaaabaabbbbbbabbbaaababaabbbabaabbabbabbabbabaababbaabaaabbbbaabbbaaabbababbbbbaaaaaaaaaabaabbaaabbaaaaababaaabbaabababbaabaabbbbababbbbaaabbaabaabbbbbbabbabbbabababababbbbaabbbbbbbababbbbabaaaabbabbabbbaaabaabaaaabbbbbababaaaabaabaaaababababbabbaababbbbbaabbabbaaabbaababaaababbbbbababbbbababbaaaaabababbbababaaababaababbaabaabbbbbaaabbabbbaaabbbabbabaaaaabaabbbbabbaababbabababbabbbabbbabbbbbaababbbabaababaaaabbaabaabbbabbbabbabbaaaaaabaaaaaaaaaabaabaaabbaaaabbaabbbbbabababbbbbaabbbaabbbbbabbbabaababaaaabbbaabaaabbababbaababbbaaaaaababbaaabababaaabbaaaabbabbaaabaabbabbaabaabbbaabaaaaababbbbbababbbaaabbbababbabaabababbbbabbbabbabbabaaabbbbabbbbbaabababbaabababbabbaabbabbbaaababaabaaabaabbaaabaabaabaabbaaaabaabaabbabaabbaaabaabbbbbbbabaababbaaabaabaaabbabbbabbbbaaabaaaaabaaabbbabbbaabbaabbbbbaaabbaaaaaabbbabbabaabaabbbababbaaabbababbbbbabbbabababbaaabaabbabbbbabbaaaababbbaabaaaababbaaababbbaabbbabbabaababaaabbbababaababaaabbaaaabaaabaaabaaaabbbaaaabaababbbaababbbbbabaaaaaaaabaaaababaabbbabbbabbbaaaabbbaaabbbbaabaaaabaabaaaaababbbabbabaabbbabaabbabbbabaaabbbbbaabababababbabbaababaaabaabbaababaaabbabaabbbbbbabaabaabbabbaaaabbbabbaaaaaabaabbbbaaabbababbbbaaabaabababaaaaababaabaaaaaaabbbbaabaababaaaabaaaabbbabbbbabababaaaabbbabbabbbbbbabaaaabaabbaabbbbbbaaaaabbbbbabbababaabbbbabbabbbbbabbbbbbbababaabaaaabbbabbbaaaabbbbaaabbaabaabbbbabaaababaabaaaabbbbbbabaabbbbbbbaaabbbababbbaaaaabbbbbbaaaaabaabbabbababbaaabbbabbabbbabaaabaaababbbbbaabbabbbbbbaabbaaabbbbbbaaaaabbbababaaaabbbabaabaaabbaabaabbbbaababbaabbaabaababaabbaabaabbabbabbbbbaabbbabaabbbabaababbbbbbbbbbbbabbabaaababbbbbbbaaaabbabbabaababbababaabbaaabaaabababbbbaababaaaaaaabbabbbbbababbbbaabaabbabaabbabbbbabbabaabbbbabbbaababaaabbbbbabaaabbaaaaaaabbbbbaabaabbbbaaaababbbaaabbbbbbbabbabaabbabbababbabababababaababbaaaabbaaaabbbbaaabaabbbbaababbbaabababbaabbbaabbaaaaabbbababababababbbbababaababaaaabbbaabbaababaaaabbbaababbbaabbbabaaaabbbaaabbaaaaaabaabbaababaabaabbababaaabbaaabbbbbbbabbaabbaabbbaabbbaaaaaaaaaababaabbabbbbbbaaababaababbbaabbbaabbbbbbbaaabaaaabaaabbaabaaabaaaaaabbabaaabbabbababbbbaababaabbbabbbabababbaabaaabbbbbabababaabbbababbbbbabbaabbbaaaabbaabaaabaaabababaaabaabaaaaababaaaaaababbaaaaaaabaaaabbabbaaaaaaaaabbbbbbabaaaabbaaaaabbaabbbaaaabaabaaabbbbababaabbbbaabababaaaaaabbabbbabaaabaaaaabbabababaaaabbababbaaabbbabbaaabbbabaababbbabaaaaabbbabbbbabaabaabaaaabbaababbbbbbaabbabbbbbbbbbbaaaaaaaaabbbaaaaaaaaabababbaabaabbaabababaababaaaaabaabababaabbabbbabbaaabbbaabbabaabbababbbbbbabaaaababaaabbbbabbbbbababaaaaaabbbbbabaaaababbbbbabbaaaaaaabbbbaaaababbaababababababbbabaaaaabbaabbaababbbaabaaaababbbbaabbbabababbbababbabbabbbaababbaaababbbbbaaabbbaaababbabbaabbaabbbbbbbbaababbabbaabbabaabbaaaaababbaaabbbaabbaababbabbaaaababbbbbaabaabbbaababaabbbabaaabbbbbbbbbaaabaabbbbbabbbbaabbabbbbbbaaaababaaabaabbabababaabbbabbbabaaabbabbbbbababbbaabbbaabbaababbabaaabaabbbbbbbabaabbbbababbbaaaabbbabbbbaababbbaaabbabababbbbbbbaaaaabbaabaaaabbaaaaabaababbbaaabbbbbbbabbabbabbabbbaababaabbbabbbabbaabbbbaaababbaabbabaabababbbaababaabaaababbbbaababbbbbaabbbaaaabbbbabbbaabbaabbbbababaababbbbabaaaabbbbaaabbaaabaaabaababbaabbaababaababbbbaaaaababbbbbbaaabbbbbaaaabbbbaabbbabababaaaabbbbabaabbbbabaabbbabababaabbbbaaababbaababaaaaaaabbbbabbbbabbbaabbaaaaabbbbbaabbababbbbbbaabbabababbbabbabbabbbbbaaaaaabbaaababaabbbbabababbbabbabbababbaaaaababaaabbaaabbbaaaaaaabaabbababaabbbaaabbbabaaaaabbaaabbbbbbbbbabbababbbaaabaaabbbaabbbbbbbabaababbbbababaaabbbbaabaababaabbbbabababaaabbaabbabbaabababbbbbbbaaabbabbbbbbbbabbababbabbbabaabaaaabbababaabbabbbaabbabaaabbbbaabaaabbaabbabbbabbbbabbbbabbbababbbabaabbabaabaabbaaabbbbbaaabbbbbbbbbbaabbaababbbababbbabbababbaaabaaabbaaaaaabaabaaabbaaabbabbabaaabbababbaabababaabaaaaaababaaaababaabbaaaabaaaaabbaaaaababaaaabaaaabbbbbbbbabbbaaaaabababaabbbabaabababaabbabaabbaaaaaaaabbaaabbaaaabbbbabaaabaaaaaabaabbabbbbbabaababaabbabbababbabbaababaaaabbaabababbbaaababbbababbbbabaabbbbabbbaabaabaaabaaaaabbaabbabbbabaabaabaaaabbbbbaaabaabbaaabbabbbbaabbaaabaaaaabbaaaaaabaaaababbabaaaaaaaabbbbabaabaaaabbbbaabaaabbaabaaabaaaabaabaaabbbabaaaabaabbbbaabbabbabbaaababbabbbbbbabbbabaababbbbbbabbaaaababbabbabaaaababbabaabaabbabbbaabbaaaaaaaaabbaababaaaabaabaaaabaabaaabaababbaababbabbbaaabbbbaabbaaababbbbabaabbabababbabbbabbaababaaababbbaabbbbaaaabbaaaababaababbbbaaabbabbaaabaabaabbabababbaabbbaaababbaaababaabaaabbbbaaabbabaaabaabaabaaaaabbabbabaabbabbbbbbbbababbabaaabaaabaaaabbabbbaababbabababbabbbbbaabbaabbbbbbaaabbbbbbbaaaabaabbbabbaaababaabbbaaaaaabaababbabbbabbaababbbbbabbaaabbbbabababbabbbbabbbbbbbababaaaaabbbbabbaabbabaaabaaabbaaabbbaabababaaabaaaabbaaaabbbbbaaaaaabaabbbaaaabbbabbaabaabaabbaaaaabaabbbaabbbbabbbabbbbbababbbabaababbbbabbabbbabaabaaabaababaabbababbaabababaaaaabbabaabaaabaabaaabaabaababababaabaabbbbaaabbaaababaaaaaabbbbbbabaaaaabbaaabbbaababbaaabaaaabababbababababbaabbbbbbaabaaabbbbbbbbbbbbababbbababbaabbababbaaaaaabbaabaabbaabbabbbbbaaaaabbbaabbaaaababbbbbabbbabbbaabbaabbaaabaaabbbabaaabbbaaabababaabbaaaaaaabbbaabbbbabbbbbaabbabbbbbabbbbabaabbabbbaababaabbbabbbbbabaabbabaabbbaabbabbaaabbaabababbabaababbbababaaaabbbbaabbaabbaaabbbaaaaabbbaaaabaaaabbabaaabbbbaabaabbabababaababbaabaaaabaaaaaababbaabbbaabbbbabbabbababbbbbbbabbabbabbbbaaabbaaabaabaaabaabaaaaaabbbbbbbbbbbbbaaaaabbaabbbaabaababbaabbaaabaaabbbbabbaababbabaaabababaaaababbaaaaabbababbabaabbabbbabbababbbaababaaabbaaabaaaaaababbbaaabbbbbabaaaaabaaababbaaaabbbbabbbbbaaabbaaaaababaababbbbaabaaaaaabbaaabaaaabbbbbbabbaabbabaabbaaababbbbbabaaaaaaabbaabbbbaaababbbabbbbabbbaaababaaabbabbbbbbbaabbbaaabbbbaaabbbbabbbababbbbabbaaabbaaaaaababbaaaabbabababababbababbabbabaaabbabbbabbbbbbbaabaaabaabababbaaaabbbbaaaabbbabbaaaabbaabbaabaaabbbbaaabbaaaabaaaabbaababaabaabababbbaaabbbabababbaaabbabaabaaaaababaabbabbababbaaababaabbbbbaaaaabbababaaaaabababaabbbabaaabbbaababbaaabbbbbbbabbabaabbaaaaaababaabbbaabababababaaaabbbbbbabaaaaaaabaababbbbbbabaabaababbabbbbbbbbaabbbabbaabaaababaabbabbbbabbbaabaaaababaabbbbabaabbababbababbbbaabababbaabaaabbaabbbabbaabbaaaaabbabbbbbbabaabaaaaaabbaaabbbabbabbbababaabbbaaabbbabababbaaabaabbabaabababababbbbababbaaaaaaaaaaabaababaabaaaababaabbababbbbbabbbababaabbbbababbbbbbababbaabaaaaababaababbaaabaaaaababaaaabbaaaabaaaaaaabaaabbabbabaababbbababaabbbbabbbbabaaabaaaababbbbbaaaaabbbaabbbbaabaabaaaabbaaabaaabaabaababaababbababbaabbbabbaaabbabbbababbbbaabbabaabbbaaaabaabaaabbaaaabbabababbbaaabbabbbbaaabbaababaabaaabbbbabbaababababbabbbabbabbaabaabbbbaabbabbbaabababbabbbaaabababaababaabbaabbabbaaaabbbaabbbbbaabababbaaabaabababbbabbbaababbabaababbababbbbabbbbabbbaaabbbbabaabaabbbaabbaabbaaaabbbaabbbabbbbabbbbbaaabbabaaabbbabbaaaabbbbabbaaaaaaabaabbbbbbaaabaaabababbaabbbbaabbbaaabaaaabaaaaababbbaabbabbabaaabaaaabbbabbaabbaababbbaaaababbaabbbaabaaababbbbabbaabbbbbbaaababbaabaaaaaaaaababbababbababbbaabbbababbbbaaababbbbbbaaabaaaaabaababbbbababbabbabaabaabababbbabbababbaabbabaaabbaaaaabbbaabbaabababbbbaaabbbaaaaabaabbabaaaaababbabbabbbaaabbbbabbaaaababbabaaaaaabbbaabbaaaababaaaaaabaaabbabbabbbbbaabbbbbabbbbabbabaabbbbabbbaabbaaaaabbbbbbaaaabbaaabbbbbaaabbabbbbbabbbabaabbbbabaabbbaaaaabbabaaaabbaaabbbaaaabbaabaaabaabbaaaabbbbbbbaabaaabbabaaaabbbabababbbaabaaaaaaaabbabbaaaabbbababaabbaabaababbbbaabbaabbbbbbaaaaabbbbabbbbaabaaaabaaabbbabaaabaababababaabbabaabaababaabaaabbaaabaabbababaababaaaabaabbaababbbabbbbabbaabaaaaababababbbababaaaaaabbabaabbbaaabababaabbbbaababbaaaabbbbbbabbaabbbbaabaaabbabaabbbaaabababbbabbaaababbaabbaaababaaabbbaababbbbaaaabaaabbabaabaabaabaabaabbbaabaaabaabaabbaababbbaabbabbbbbabbbbababbbababbbababaabbaabbabbbaaaaaaaabaababbababbabababbabbaabaaaaabaabaabbabaababaabbabaaaaabbbbaaaaaabbbaabbabbbbbaaabaabbbababbbbabbbaaaabbaabaaaaaabaaaabbbbbaababbbabbaabaaababaabbbbaaaaaaaaababaaaabbaaaaabbababbbbaaabaaabbbaaababaabbabaabbbbbabababaaaabbbbaabbbaabbaabbbbaaabababbaabaaaabbaaaabaabaaaabbbababbbbaaaabbbbabaaabbabbabbaaabaaaaaaabbabbaaabbbbbbbaabaaabbbaabaababbabbabbbbbaabaaabbbbbbabbaaabaababaaabbbbaabbaabaabbbbbaaaababbababaaabbabbbaaabaaaabbbabababaaaababaabaaaaaaabbaaaaaabbaabbaaaabaabbbbaaabbbbababaaabbbbabbbabbababbbaabbaabbaaaaaabbabbbbabbbababaaabaabababbaaaaaaababbabbbabaaaaabbbabaabbbbabbbbabbabbbaaabbaabaaababaaaaaaabbbbbabbbabbbaabbaaaabaaaabbaabbbbbbbbbaaaaabaaaaabbbbbaabbbabbbabaabbabbaaaabbbaaaaaaabbababbabbbbabbabbbbababaaaabbabaaaaaabaaaaabababaaabbaabbabbabbbbbaaaaaabbabbaaabbbaabbbbabbabbaaaabbbbbbababbbbbbbabbababababbbabbbbbbabaabaaabaaabaababaaabbaabaaaabbbaabbbababaabbabbbaababababaaabaaabbaabaabbbababaabababbaabaabaaabbabbbbabaaaabbbabbaababababbbbbabbbbbaabaabbababbbbaabaabaabaababbabbaaaaabbbbbababbaaabaaabaabbabbbbabbbbbaabbabaabbaaababbabaaaabbbaababaabaababbbbababaaabaaabbbbbbababababaaabbbaabaababbabbbabaabbabbbbbaababbabbbabaaaaaabbbbababaabbbbbaabbbbababaaabbbaabbaabbbbbbaaabbabaaabaabbaaabbababbbaabbabbbbabbbabbbabbbbabbabaababbbbaabbbbbababbaabbaabaabaaabbababbbaaaaaaabbbababbbabaabbaabbabbaaababababbaabaabaaababbabaabbbabaabaaaabbbabbaaaabbbaaaabbbbbababababbaabbbbabbababaaabbaaabbaaabababbabaaaabbbaabaababbabaabbbabbaaabaaabaaabaaababbaaabaaaaaabababbbaaababaaaabbaabbaaabaabbaaaaababbaaaaabaaabbbaaaabbaabbbababbaaaaabbbbbaaaabbaaabbababbaaabbbbbbaabbabbaaaabbaaababababbababbabbaaaaaabbbabbaaabbbaaaaaabaabbababbaababbaabbabbababbbaababbaabbaabbabaaabaaaabbbababaaabbbaabbbbaaaaabaabbbaabbbbabbbaababaabababbbbaabbbbbabbaabbaaabbaabaababbaaabbabaaaaaaaabbbbbbaaaaaabbbaaaaaababbaaabbaaaaabbbaaabbabbbabbaabbaababbababaaaaaaabbabbaaabaaaabbbaaabaaaaaabbbbaabababababbaabbaaabaaabbbabbaabbbbbabbbbaabbaabaaaabbbabbaabababbabbbbbabaababbabaabbbaaaaaababbbabaabaaaabbabbaaaaabaaaabbbbbabaaaabbbbbaabbbababbabaaaaaabaaaabababbababbbbaaabaaabbbbabbbbbaaabbbbbaabbabababababaabbaaababbabbababbbabaaabbabaaaaaaaabaabbabbbabaabbaabaaaaaaababaaaaabbaabbabbbbabbabaababbbbbabbbaabbbabbbabaabbbabaaaabaabbbaabaabbabaabababababbabbbbaaaaabbbaababaabbbabbbabababbbbbaababaabbbabbaababbbbaaabbaaaaabaabbbababbabbbaababaabbabaaaaababbbaabbabababaaaabaabbbbaabbaaabbbaaaabaabaabaaaabaabbbbababbbbbbbabababababbababbaabbababaaabbbaabaababbbabababbbbabbabababbababaababaaabbaaaaabaaaaabaababbaababbababaaaabbbabbabbaaaabbbbabbbaaaabbaabbabbbbaabbbaaabbaabaababbbaabbbaabbabaabaabbabaaaaaaaaaababbaaabbbaaaabaabbbaababaababbbabbaaababababbaabababaabbbabaaaabaaababbabbbabaabaababababbabaaaaaaabaabbbbbababbbbaaaabbaabbabaabbabaabaaababbaabbbaababaaababaaaaabbabbabbbabbabbbaaaabbbabbaabaaaababaaaabbbbabbbbbababbaabaaabbaaababbbaabbbbbaabbababaaaaabbbbabbbbbbabbbaababbababaaabbbbabaabbabaabaaabbabbbbbbbabaaabbababaaaaaaabaaaaababbaabaaaabbabbabbaababababbababbaaabaaabbbabbabbaababaaaabaababababbabbaaabbaaaaaabbaababbbabaaabaaaaaabbbbabbaaababbabaaabaabbbabbaaabaabaaaabbbbaaaabbbbaabbbbabaaaabbbaabaababaaaababbaaaabbbbabbaababaaaaaaabbbbaaaaabbabbbaabbabbabaaabaababbbbabaabbababbaabaaaabababbaaaaababaababbbbbabaabaabaaaaabaabaaabaaabbabbbbbabababbbabbaababbabbabaaabbaababbbabbababbbaaaaaabaababaabbaaaabaaabbbabaaabbbbbbaabbaaabbabbbabbbababaaabbbabbabbabbaabaabaaabbbbbbaababaabbaaaababababbabaabababbbaaaabaaabababbbaaaaaaaabababaaabababbababbaaaabaaaabbaabaababaaaaabbbababbabaaaabbabbaaaaabbbbabbaabaaabbabaaabaabbabaabaaabbabaabaaaaabbbbaaabaabbbabbabbabbbbbbbbbbabaaaaabbbaaaabbbbbabaabbabbabaaabbababbbabbbbabaaaabbaaabaababbaaabababbbaabababbabbbbbaaababaabbabaabaabbaaababbbbaaaaaaaabaabbaabaaababbaababbaababaaabaaaabbbaaabaababbbabaaababaabaaabaaaaabbaaaabbaabababaaaaaaabbaaaabbbbbaabbaaaaabbbbbababababaabaaaaaabbaabbbbaaaaaaabaaaaabbabababbbaaaaaaabaabbaaabbabbabbbaabaabaaaabbbbbabbbbabaaababaaabbbaababaaabaababbbbbaababbabaabaababaabbababbaaaabbaaabbabbbbbbaabbbbbbbbbbaabaabaaaabbabbbbabaababaabbbabbabababbbababbaaabaaaabbaabaabaabbabaabbabaababaababbabbbababaababbbaaabaaaaaabaaabbbbbbbbaabbbbbabaaabaabbaababbaabbaaabbbabbaaaaaabbaaabbaabbababbaababaababbbbbbbbaaaaababbbbbbbaabbbabaabaababbbbaaababaaabababbabaabaaababbbabbbaaabbbbbbbbbaaababaaaaabbbbbbbbbababbaabaaaabbaabbbbabaabbabbaaaabbaabaaabbbbabaaaabaaaabaaaaabbbaababbbaabaabbabaabbbbabababbaaaabbbbaababaabaaabbaaababbbbaaaaababbaaababbbaaaaabbaaaababbaaababbaababbbbaabbbbaababbaabbaaababbbaaaaabbbbababbaababbbbabababbbbbbababbaaaabbbbabbabbabbabbabbababbbbbbaabaababbabaaaaaabaaabbbbaaabaabaabbbaaaaabaabaabbaaabababbabbbbbbbababbaabababbaabbbbabaabbaaababbababbbbbababaaababbabbabaabaaabbaaaabbbaaabbbbbaabbaabbaabbaabbabbaabbaaaabbbbbaabbbaaabbbbbabababbaaaaaaaaabbbabaabbabbaaaaabaaababaaababaaaabaabbbbaabababbabaabbababaabbaaabbabababbababbbbaaababababbabbbbbbbbbabbbabbabaabaabaabbbababaababbbbbbbbbabbababaabaaabbabbbbaaaabababaaaaaaaaabbbaabbbbabaaaabbaabaabbabbaabbaabbbaaaaabaabaaaaaabbaaababbabaabbabbabaaabbabbbbbabbabbbaabbbabbabbaaabaaaaaaaaabbabbabbbaaaabbbbaabaaabbbbbaabaababaaabaabaabaabbbaaabbabbbaabbaaaaaabaaabbbaabbaababbabaabbabbbaaabbbabbbbbabbbbababaabaaabbaababbababaaabbaabbbbbbaaababaaaabababaaaaaaaaaaaabbbaabaaaabaabbbaaabbbaabbabaaaaababaaabbaabbaaabbaaaabbbaabaabaabababaabbababbabaaababaaabbaababbbaabaababababbabaababaaabbbbbaabbbbbaabbbababbaaaaaababbbbbbabbaabbabaabbbaabababbbbaabbaaabbabbbabaababbbabaabaaabaababababbbbabababaaabbaaaaaabbbababbaabaaabaaabaaabbaaababbababbbaabababaabbaabaababaababaabaaabaababbbaabbaabbbabbabbaaabaababbababaabbbabaaaaaaaaaaaaabbbaaaaabbbababbabaaaabbabaabbabbaaaabbbbbababbbaabaabbbabbbabbabbaabbabaabbbbababaaabbabbbabbabaaabbabaaabaaaaaaaaaabaabaabbbbbabbbabbabbabbabbbabaaabbbbabaabaaabaaaaabaaabbaaaaaaabaaabbbbbaabaabababbbbbbabbabbaabaababbaaabbbbbaaabbbaaabaabbbbbaaaaabbabbbbaaabaaaaabaaaababbbaabaaaababaabaaabbabbbaaaabbaaaaabaabaaabbabaaaaaaaabababaaabbabbabbbbbaababbaabbbabaabbaaaaaabbabbabababbabbabbbbabbababbabbbaaabbaabaaaabaabbaabaaabababbabbaaaaabbbbbbbabababaaababbbbabbaababbaabbabbbabaaaabbbaabbbaaaaabbbbbaaabbbbabbbbbbaaaaabbbaabbbbaababaaaabaaaaaaaaaabbaabaaaaaabababaaabbaabaabababbabaaababbbbbabbabbaaaabbbbabaaaaabbababbbbaabaaabbabbbbaabbabaabaaabbbabaabbbbbbbabbababaabbaaabababaaaaabbbaabaaaabbaabbaaabbabbaababbbababaaabaaabbabbaaaabababaabaaabbaaaaababbabbababaaaabbaabaabaaabaaabbbbaaababbaabbaaaaabaabbbbbabababbaabbaabbabbbbbabaabbbbaabaaaabbbababaaaabbaaabaaabbbbababaabbbababbbbaabaabaaabbabbaababbaabbabaaaabaabaababbbbabbaabbbaabbbbbaabaaabaaaabaababbbababbbabbabbaabbabaabbbabbababbbbbbaaaaabaabbaabaaabbbaabbbbbbababbabbbabaaaaabbbabbbbbababaabbaabbbbaabaabaabaaaaabbaaabaabbbbaaababaabbbbaabbabaaaaaaaabbabababaababbabaabbaaaabbabaaabbabbabbabbabbbabbabbaaabaaabbabababbabbbabbaabababbaaaabaaabbababbbbbaababbaabbaaababbabbaaaabababaaabbbbbabbabaaabbabaabbbabaabbbabbbbaabbaabbaaabbabbabaaaaaaaabababaabaaababaaaaabaaabbbaaabaaabbaabababaabbaabbaabababababbaaabbaaaababbbbabbbaaaababbaababbaaaabbbbaaababababbaaabaaaaabaababbaabbbababaabbbabbaaaaabaaaaaabbbbbbaaabbababaaaababaaababbbabaabaaaabaabbbbaaababbbbbaaabaaaaaabbabbabaabbabababbbaabbbabbaaabaaaabaaaaaaaaababaabaabaaaabababbbabbbabaabbbaababaaabbaababaaababbababbababbabbbaaaabbbbaababaabaaababbbaabaabababbbabaababbbabaaabbaabbbaabbbbbabaabaaaaaaabbbbababbbbabbaabaababaaaaabbabbaaaabbaabbbabbabbbbaaabbbabaaabbabbbbaabbabbabbbbabaaabaaabbbbbbababbababbaabaabababaababaababaabbabababaaabbabaababbbababbbbbbaabbbbbbabbabaabbbaabbababaaaaaaaaaaaababbbbabbbbbbaaabaabbabbaababbbbabbababbaababaaabbabbbabbbababbbaabbbbbaabaabaabbabbbabbaaaabbbaabaaaabaaaaaabbabbaaabaababbbaaaaabbbbbabaabbbbaabbaabbbbaabaaaaabbbabbaabaaaaaaabbaabbbabaaabaabaaabababababaaaaaaabbbabbbaaabababbbbbbbaabaaaabbbbbbabbbbabaababbbbbababaabbbaabbbabbaaabbaabbaababbabaabbbbbaaaaaaaabbaaaaabbaaabababaaaabbbbabababbbababbabbaabbaaaabababaaaaaabaabaaaaabbabaabaababbaaaaaababbbbbababbabbbaabbbbbbabababaaaaabaaababaaaaabbbbabbaaaabbbabababaaaabaabaaaabababbabbabbaaabaaabbaaababbabbaababbbaaababababbbabbbababbaabbabbbbabbaaababaabbaababaaababbbaabbbaabbbabaaabbbbbbbbaaaabaaabbbbbbbabbabaabbaaabaabaabbaabababbaaabbbbbabbbbbaaabbaabbbaaaaaabbbabbbbbaaabaabbaabbabaabbbbbbaabaabaabababbabaaababbabaabbbabbbbbabbabbaababbabbbabbbbaabaababbbababbbaaaaabbaaaababbbabaaabaaabaababbaabbbabbbbbbbabbbbabbbabbbbabbbbababaaaabbbaababbaaabbaabbbaabbbaaabaababababbaabbabababbaabbababaaabaabaabbbabababaaabaaaaabbbbbaaaaaabbbababbaabaaaaabbaaaaaabaabbabaaabbbaabbbaaaabbbbabbbaabaaabbaaaaabaabaabbabababbbbabbbbabaabababbbabbbbabbabbaaabbaabaabbbabaabbbaaaaababbaababaaaaaaabbbabbabaaabaaabbabbaaabaaabbbbaaaaababbbababbaaabbabbabaabababaabbbbaaaaaaabaabababbbbbaabbbbbbabaababbbbabaabbbaaaaaabbababbbababaaaabbaaaaabaabbbabaaaaababbabaabaababababaaabaabaabbbbaababaaaababababbaababbabbababaabbbaabbbabaabaaabaaaabbbbaabbabbbbaabaabbaaaababbbaaaababbbbbabbbbbaaaabaabbbaabaaabaabaaabbabaaabaaabbabbbaaaaaabaabbaaabbbabaaaabbbabbababbaaabbbbbbbabaabaabababbaaaaaaaabbbbbabbbbbbbbaabbbababababbaabbabaabbbbbbbaabababbbaaababbaabababbaaaabbaabaabbbbbaabbaabaabbaaabbbbbbbaaabbbabbbbbbbaabbbaababbababbababbbbabbaaabbbaababaabababaaabbabaababaaabbbbaaaaaabbaababaaabbbbbbbabbbbbabbababbababbaaaaaabaabbabbabbbabaaabaaaaaabaababbbabababaaabbbbabbaabbbabababaabbabbbabbbbabaabbbababaaaabbabbbabaaaabaabaaababbabaaaabbaabbbababbbbbaaabbaabbaaaababababaababaaaabbaaaababbaaaababbabbbbbaababbbabbbaaababbbabbbabababbbbbbbaaababbaabbaaaabababbbbabbbabbaaabbaaaabaabbaabaaabbbbabaaaabbbaabaabababaaabbabbbbbbaabaabbabaaabbabbabbbbaababbaaaaaabbbabaabbabbaaabbbbabababbbaabbbaaaaaaabbababaabbbabaababbbabbbbbabaaaabbbbbbbbbbbbbaabaaabbabaaabbaaababaaaaabbabaabbbbbaabbaaaababbababbbbaaaaaababababaabababbaabbaaababbbababbbbbabbbbaabbbaababbbbaaabbabababaabaaaabaabbbaaaaababbbbbabaaabbabaaaabaabbaabbaaaabbbabaaaaabbabaaabaaabbbabaabaabbbbaaaaaabaaaaabaaaabbbaabbbbbbabbabababbbbababbaabbabbbbaaabbabbaababaaaababababbbbaaabbabbbabbbbabaaaabbbaaaabbbbaabbabbbbaaaabababaabbbbbaabbabbabbbbaabaababbbababaababaaababbbbabbbbbaaaabaabbbabbaaabbababbabbaaaaabbabaaabaabbbaaabaaaabaaaaaaaaaabbabbbabbabaaabaabaabaabbabaaaaabaabababbabaabababbbaaababbababbababbbbabaabbababbabbbbaaaaaabababbaaaaabaabababbaaaaaababbbabbbaababbabaaaabbbaaabbaaabbbbbbbbbbbaaabbbbababaabbabbaabbaaabaaabbbaabaaaaabbbababaaaabbabbaabaaabbaabbbbbbbbbbabaaaabbbaababbabaaaabbabababbaaabaaabaabbbabaababbbbbbabbbbabbbbaaabbbabbbbbbbbbaaaabbbaabaabaaaababbababaaabbbabbbaaababbbbabaababbbabbaababbaaaababbbbbbabaaaababbaabaaaabbabbabbaabbabbaaaabbaaabaabbaabbbbaaaaababbaabbbaabbbabaabaababaabbbabaaabbabbabbaababaaabaabaabaabaabbbbaabaabbbbaaaaaabaaaabbabbabbbbaaaaaabbbbbababbbbabbbbabbbaabaaaaaabababaaaaaabbaabbbabaababbbaabbbabaabababaaaabbbbabbaaaabaabbaabbbabbbbbabbaaababaaaababbaaabaabbbbbabaabbabbbbabbbbababbbbaaabaabbbbbababbbbbbaabaaaaabaabbababbabbaabaabaaaaaaaabababbabbababbaaabbababbababaaaabaaaaabaabaaababbaabbbaaaaaababbaabbbbbaaabbaabbaaabababaaaabaaabbaaabababbabababbbabaaaabbabbbabbabbbabbaaabbaabbbaaaaabbaaaaaaabbabbababaabbbabbbbababaaabbaababbabaabbbaaabaabbaabaaabaaaaababaabaaababaaabbabbbaabbaabaabbaabaabaabbbbabbaabbaaaababbbaaaaaababbabbbabbbbbbbabaaabababbaabaaababbbbbbabaaabbbbbbabbabaaaaaaaabaaaabbbbbababaabaabaababaabbaabbbbaaaababbabbaabbaaaaaabaabbbbabbbbabaaaaabaaaaababaabbaababbabbbbbbbbabbbaaaabbbbbaaabbbbbaababbaaabbbaabbbaaaabbaabbbbbaaababaabababbabababbbbbaabbbabbabbaaaabaaababaabaaaaabbabaabaabaaaabbaaaabbbabbbbaabaaaabababbaaababbbbaabaabbaaaabbbabbbbbbbabbaaaabaabaaaabbabbaabbaaaaaaaaabbababbbabbbbabaabbbbbbababaaaabaababbabbbabbbbababaaaabbbaabaaabbabbaababbbbbaabababababaaaabbbabaaababababbbabbabaaabababbbabbbaaaabbbbbabaabaabaababaabaaaabbbaabbabbbbbaabbbaaaaabbbaaaababbbbaaabbbababaababbabbabbaaabbaabaaaabababbaaabbaaaabbbbaabbabaabbbbabbaaabaabbaaabbabbabaaabababbaababaaabbbbaaabaaabaaaaabaabbaababababbbabbabbbaaaabbbaabbaaabaaaaaabaabbaaabbbaabbaaabaaaaabbaaabaaabbaabbbaabbaaaabbaabaaabbabaabbbbbbabaaaaaabbbbaabaababbbabbaaaabababaaaabbbabababababaaabaaabbbbabbbbabbabbbaabbabbaaabaabaabbabbbbbbabbbaaababbabbaaabaaaabaabaabaaaabbabbbaaaaaaaaaaababbbbbbbbbaaabaabbbbaaabbaaaabbbabbbbaaabbbaaaaababbaaaababbabbbaaabaabaabbbaaabbabaabbabaaaaabbaaabaaaaabaaaaaabaaabbbababaabbbabbababbaaabbbbbbababbbbabbabbabbbaaabaabababbaaaaaaaaaabaaaabbababbbbaabbabbbbbbaabbbaababbbbaaaaaaaaaaabbbbbbaaaaababbabaababaaaababbbaaaaababababababbbbaabaabaaaabababaaabababababaaabaaaaaabbaababaabbabbabaabababbbbababbaaababaababbaaababaabaaabbbbbbabbbabaaaaaabbaabaaaabaabaaaaaabaaaaaabababbaabaaabbbabaaaabababbbababbbaababaabbaababbbabbbabaabaabaabababababaaababaababaaabbaabaaaaaaaaaaabbbbabbaaaaaabbaabbbbbbbabbaababbbababbaaaabaabbaaabbbbaaaabaabababbbbabbaabbbbbaaaababbabbababababaaaabaababbaabbbaababbbbaabbaabbbbbaabababbbbaabababbbabbababababbaabaabbaabbabbbaabaabbababbbbbbabbabbaabbabaaaaaabbabbbbbbaabbaaabbbaababaaabbababaaababbbaaaabbaabbbababababababbabaaababaaababaaababbabbaaaaababbbaaaaaaaaabababbaaaabbbababaaaabbbbababbabbbbbbabbbbabaaaaaabbbbabaaaababbabaaaabbbbbaababbabbaababbbaaaabbbabbbababbaabaabbbbaaabaabbaaaabbaaabbbabbaaabbbabbbbabababaabbbbbabbbbaaabaaaaabbbbbbabaaaabaabbbbabbbbbbbabaaabbaaaababbaababbbbbabaabababbabbabaaabbbaaaaabababbbbbbbaabaabbbbbaabbbabaaaabbaababaabaaaababababaabaaaaababbbaaaaaabaabbbbabaaabbaababbaababbaabbaaaabbbabbbbbabbbbbbaaaaaabaaaaababbabaaaabbbbabbbbabbbbaabbaaaabbbbbababbbabbabababbaabaaaaaaababaababbbbbbababbabaabbbababaabbbaabaaababaaba
baabbaabbbbabaaaabaaaaaababaababbabababbbbbabbaababbabbabbbaabbbaaaaababbaaaabbaabababaaabababaabbbabbabbbabababbbbbbaaaabbabbbbaabbabbbabbbbabaaaabaabaabbbaabaaaaaababbbaaaaabbbabababababaaaababababbaaabbabbaabbbbabaabbbbbabbabaaaabbaababbabaaaaabbaabbbabbbaaaaabbbaaaabaababbabbababaaaababaabaaaabababbaababaabbbbabaaabbbabaaaababbbbabaaabaabbbaaabbaaabbbbbbaababaabbaaaaaaaaabaaababbabbaababaaaababbaababaaabbbababaaabbabaabaaaabbbabbbaaabaaaaababaaaaabbbbbaaaaabbaabbbbaaaababbabaaaabbaabababbababbbaaabbaabbbaaaaaaababbbbabaabbbabbbabaaabaabbaaaaabaaaabbbbabbbabaabaaabaaababaabbbbbabbbbabaabbabbaabbbbabbbaabbaaabbbbaaaabbabbbabababaabbabababbababbabbbbbbbbabbaaabaaaababbababbbbbaaaabaabbabbbbabaaaababbaaabaabbbbaabbaaababbbaaaaaaabbaaabbbabbabababbabbaaaabbabababbbbbbabbbaaabbaaababbbaabababbababbbbabbababbbbabbbaaabbaaabababbbbbbbaabaabbbbabbababbaabaaaaabbaaaabbaabbaaabaabbbabbabbbbabababaababaabbbaabbaabbaababbaaaaaababbaabbbabaaaaaaaaaabaaaaabbabaabbababaaaabbababbaaabbaabaabbaabaaaaaabbbbbabababaabbbaaabbabaaababbaaaaaabbbbbaaababbbaabbababbbaabaabbababbbbbabaabaaababaabbaaabbaaaaabbaababaabaababababaaaaaaabababbbbaaaabbbbbaabbbaaaaabbabaaabbaababbbaabaaaabaabaaaabbaabbaabababbabbbaaababaabaaaaaaaaaaaaaababbaababbaabababababbaaabbbbbbbbbbbbbbaabbaabbaaaaabaaaabaabbbabaaaababbbabbaabbbbbabbabaabbbbbabbaabababaaababbabbbbbbaaababbbabaabaaababababbaabbaaaabbaababbbaaaaaaabbbbbbaabbaababbabbaaabbaabbbbabbaaabaabbbbbaaaaaaaabaaaabbaaabbbbabbaaaaaabbabbaabbaaabaabbbabaabbabbbabbbbabbbaabbbaaaaabbaaabbbabababaabbbaabbbbaaaabaaabaaabbbaaabbbaabaabbaabbababaabbaababababbaabbabababaabaaaaabbabbbbabbbaaaabbbbaabbbbbaaabaababaabbbbabaabaabbababaabbaabbaababbabbbababbababaaabbbaababbbabbabbababbaabababbaaaaaabbaabbabaababbbbbbbbbaabbbaaabbbbbbabbabbbbabaabbbaababbbbaabaabaaabbbaababbbbaaabababbaabbaaaaaaaabaabbaabbaababaaaabbbbbaaaaabbabaaabababbabbbabbbabbbaabbbaaababaabaabbbabbbbaaaaabababaaaaaaaabaaaaabbabababbbababababbbaabbbbabbababbaaaabbaabbababbaaaaaababaabaaabaaaaaaabbbbbbbbbbaaabaaabaabbabbabbbbbabaaaababbabbaabaabaaaabaabababbabaaaabbbaabbaabaabbbbaabbababaababaabbaabbbaaaabbbaaabababbabababaabaaababaababaabbabbabbbbbaabbbabaababbaaabbbabaaaababbaaaabaabbaabbbababaaaababbbbbbaabbabbaaaabbbaababaabaababbbababababbaaaaabbbaaaabaabbbabbbaaaabbabbaabbbbbaaaabaaaabbabbaaaaaababaabaaaaaaabbbaaaababbbaaaaaabaaaabbabbabbbbaaaaabaaabaabaabbbabaaaabbbbaaaabbabaababaaabababbbbabbbbbbabaaabbaaabbaabbbabbaaabbbbabbbaaaaaabababbbbaaaaabbbaabbaaabbaaaabaaababbababaabaabaaaaabbbaababaaabababbabbbbbbabaabaaaabaabaaaabbbababbabbaabaabbbaabbabbbbbabaababaaababbbbaababababbbbaabbbababaabaabbabaaaaaaaaaabbbaabbabbaabbaaaaabbbaaabbababaaaaabbabbbaaaabbaaabaababbabababaabbaaabbbbabbabbabaaaaaabaabaabbbbababbaabababbbbaaaaabbaaaaabaaabbbabbababbaaabbabbaaabbbaaabbbabaabbaaabbbabbabbbbbbaababbaabbbaabbabbbbaaababbaabaabaabbaabaabaabbabaaabbaabbbbbbbabbababbbaabbbbbbbaabbbaabbbbbbbaaaaabaaaaaaabbaaaabbaabaaabbbaabaaabbbbaabaabbaabbabbabbbbbbababbaaaaaaabbaaabaabbbaabaaaabbaababaaabaababaaabbaaabbbaabababaababaaabaabbbabaaaabbabaabababaabbaabbbaaaaabbbbbababbbabbaabbaabaabbbbaaabbaabaabbabaabbaaabbabaababbabbababbaaabbababbbaaabbabbbaababbaabbabaabbabaabbbaabbababbaaaaaaaabbababaabaaabbbabbbbbbaaaaabbabaabaabbbabbbaaabaaaabbabbaaabbbbbababababbaaaaabbbaabbaabaabababbbaaaaaababababaaaaabbbbabababbbabaabaabbabbabbbbbababbbbbbbabaabbbabaaabbaabbbbabbabaaababababbbbaaaabaababbaabbabbabbabbbbaaababbaaaabbbbbabbabbabaaabaabbabaababbabaababbaabbbababaaababbbbbbaaaabaaabbaabbabbaaaabaabbabaaaaababbbbbbbbbbbaaabababbabbabbbbabbaaababaabbbabaabbbbaaababaabbaabaabaabaabbabaaaaabaabbaaabbaaaaabbbabbbabaabbababaaaabbabbbbaaaabbbbbbabbabababbabaaabbbabbaaaaabbbaaabbabbbbabaabababaaaabbbbabbbbbbabaaabaaaaabaabaaabbaabbbaabaababbbaabbbbbbabbababaaaabaaabbaaabbbbbbabbaaaababaaababaabbbabbbaababaababbbaabbababaabbaabbabbaababbaabaaaaabababbabbbbbababbbbabbabababbbbbababaababaaababaaabaaaaaaababababbbbbbabbbaaabbaabbbaaaabbabababbababbbabbaaabaababaaaaabbbbababaaabbbabbaaababbbbbbababbabaaaabaaaabbabbabbbabbbabbbbbbbbbbbabaababbaaabaababaabbbbbbbbaababaabaaabaabbbbaaaabbbabaabbababaaaaaabaaabbbaaabaaabbabbbbbabbbbaaabaababaaaabbbbbbbaaababbaabbaabbbbbabbababbabaabbaaabaaaaaabaababaaaabbaaaaababaabaabbbbaaabbbbbababaabbaaaaaaaabaaababbaaaaaabbaaaabbabbbabaabbbaaaaaabbaaabaaaaaababbaaabbbababababaababbabbbbaaaaaabbbbaabbbabaaaabbbabbaabababbabbaabbbabbbaaaaababaaabbaabbaaabbbbaaabbabaaaababbbaabbbaabbaabbbabaaaababbbbbabbababbaaabbabbbaabbbabbbbaabbbbbbbabaaababbbbaaababbbbabaaaababbaaabbbbaabaaabaabbbaaaababaabaabbabbbbbabaaabbbbbbababbbbbabaaaaaababbbaababbaabbbaaaabbaaaabbabbbaabbababbabbaaabaaabbbaaaabaabaabbaabbaaaabbabbaaabbbaaaaaaababaabbaababaaaababaabaaabbabaabbaabbaabbaababbaaaabbabaabbaabbbaaaaabaaaababaaabbaababbabaabbbbbbbabbbbbbbbabaaaabbaabbbbbbabaaaabaaabbbaabaababbabaaabbabbabbbbbaaabaaabaaabbaabaababaabbaaababaabbbabaaabaababbbbaababbababababababaaaabaaabaabbaaaabaaabaaaaabababaabaaaabbbbababaaaaaabaaaabababababaaaaabbbbbbaaaabbabaabaaabaabbbabaabbabbbaaabaaaaaaabaabaabaabbabaabbabbababbbaabbbaabaaababaabaaaabbbbaabaabaaaaaabbababbabbabbaaabbbbaabbbbabbaabaaaaababbaaabaaabaaaaaabaabaaabbbabaaaabbbabbbaabbbabbabaaaabbbaabbbabbabbaaababbaabaaababbbaaaaabbbaaaabbaaaabbaababbabbbabbabbbbbbbbaaaaababaabaaaabbaaababbaabbbbbbabbaabaaabaaaaaabaabbaaabaababaabbbaaabaaabaabbbbbbbabbabaabbabaabaaabaaabbabbaabaabababbabbaabbabbbaababbbabaabaabbbaababbaaaaababbabaaabbaaaabababbbaaaabbaabaabbbaabbbbabaabbabaaabbbabaaaaaabaabaaabbaabababaabbbabaabbaababbbbaaaaabbaaabaababbaaabaabbbbaaaabaabbbabbaabbaabababbabbbbbbaaabbbabbbbabaabbaaaaababbabababbabbabbbaaabbabbaabbababaabababbaaaabbbabbbabbbbaabbaabbababaabaaaababbbbbbaaaabbabbbbbbbbbbbaabbbabbbbaaaaabaabbababbabbabaaabaaabbbbbbbaaaabaabbbbbbabaaababbabaabbbabbbbbbaaabaaabbbbbabbaababbaabababaaababaaaaabaabbaabaaabababbbbbaaabbaaabababaabbabababbaababaaaabbabbababbabaabaabbbbbaabaabbbbabababbabbbababbabbaabaaaababbbababaabbbaaabaaaaaabaabaaabbbbbbbaabbbabbbbabbabaababaabbbabaabbbaaabbaabaabababbabababbbabaaaababaaababbabbaaabaaabbaaabaabaabbaaababaaabbabaabbabbbabbaabbaaabbabbbbbaabbaabababaaabaabaabbbbabbaabbbbaabaabbbaaababaaaaaabbaabaaaabbabbaabababbbbbaaabbbbbbbbbabbabaabbbbabbbbbbaaabbabaabaaababbaababbabbbabababababbbaabbababbbbaabbaaabbaaabbbbbaaabaabababbbbabaabaabbbaabaaaabababbaaaabaaababbabaababababbabababaabbabbbababbabbaabbaaababaaaaaabbbbabbabbbaabaaababbaaabbbbaaabbabaabaabbabbbaaaabababbaaabbbbbbbabaaababbbabbaabbabbbaababbaabbbbbabababbabbabbbaaaaabbbbababbbaaaaabaaaaababbbabaabaabaabaaaababbaabbbaabbbabaaabbaaaaabbabaaaaaaaabbbbbaabbaabababbabbbbaaabbbabaaabaabbabbbbbaabbabaaabaabaaababbabababbbbbbbbbabaabbbabaaaaabbaabbbbbbbababaaaabbbbaaaabbbbbabbaaaabbbabbabbababbbaaabbaaababaaaaaaaababbbbabbbbbaaabaababbabbbbbababababbbabbbabbbbbbbabbaaaabbaaabababaabbbababaaaaababababbbbbbaaabbaababbabbaabaaaabaabbaabbbbabbbaaaaaaababbaababbaaaabbabaabbaaaabbbaaaaabbbaaaabbabaaababaaababbbbbbbbbaaaaaaaabbabbbbbbabbaabbaabbbbbbabbbaabbabbbaabbbabaabbaabbaaabbbababbbaabbaabbbbabbbabbbbbbaabbabbaaaabbbabaabbabbabbbbbbbaababbbabbabaaaaabbabbabbbaabbaaabbaabbbbbababbabababaabbaababaabbaabaaabbaaababbbaabbabaababababbbbbabbbbaaaababbabbbbbaabaaaabbbabbaaabbaaababbbaabaaabbbbbabbbbabbabbbabbbbbabbbbbbaabbbabaabaababaaabaabababaaaaababaababababaabbbababbaabaaabababbaababababaabbbbbbabbabbbaaabbbabaabbbabaabbabaaabbbbaabbbbbaaaababaaabbaabaaabaaabaaaaaaabaaaabbabbaabaabababbaaaababbbbbbaababbaaaabbbbaaaaaababaaaabbbaabbbbbbaababbbbbbbbbabaaaababbbaaaaabbbaabbaabbbbababbbaaaaabaaabbababbaabbbbabbbbbbbabaabaabaaaaaababaaabbaabaababaabbaabaabbabbabbbabbbabbabaababaaaaaabbbbabbbabaababbababbaabbabbbababbabbaabbbaababbaababababbaaabbbabbabbabbaabbababbbbbbababaaaaabaabbbabaabbabaabaabbbbaaaababbbbbaabbaaabaaaabbaaabbabbabababbbbaabbaaabaababaabbabaabababbbaabaaaababbbbababaaaabbabbaabaaabbababbbbbaabaabaaababbbaabaabbbabaabbaabbaabbbbbaabbaabbabbabbbbbbabaabaaabbbbbababbbaabbbbbbabababaabbbabbbaaabaabbbbaabaabbaabaabbbabaabbbbbaabbaabbaaabbbbbaaaaaabaaaaaaababbaaabbaaabbababaabbabaabbbbaababbbabbaaaabbabbaaabaaabaaabbaaabaaaaaaabbaaaaaabbbbbaabbabababbaabaabbaaaabaabbabbaaaaaabbaabaaaababbbbaaabbabbbabaababaababbabaaabbbbaabaaabbbabbaaaaababaaabbbabbbbaaabbbabbabaaabbbbbaabababbbbaabbbbbbaaaababaaaabbabaaaaaaaaaaabbaaabababbbabbbbaaaaabaaaabbababababbaaabaaaababbabbbbbabbbbaaababbabaaababbbbabababaaabbbbbababaabaababbbbbbababbbbaaabaaaaaabbbbabbbabbaababababaaaabaaabbabbababbaababbbbbabaaabbbbbbababaabbbaaaabaababbabbaabbbbabbbbbbbbabbbbabaaaabaaaabbaaabbaaababbababaababaaaaaaabbbababbaababaababbbaaabbbbbbbbbbbbabaaabaaabbaaababbbaaabbaaaaababbbaaaabbaababbbbabaaaabbbbabbbababbbaaababbbbabbbabababbaababaababbbabbbababbababbbbabbbbbababaabbbbaaabaaaabbbbbbbbaaaabaababbbabababbbbbbabbaaabbaaabaabbbbbaabbbaaaabaabaabbbbbabbaabbbbaabaaaabbbabbbbbbaaaaaaababbbbaaababbaaaaaaaabbabaaaabbaaabaaaabaababbabbabaaabbbaabaabababaabaaaabbabbaaabaaaababbbabbabaabbabaaabbabbbbbbaaaaaaabbabbbbbabababbbbaabaabaabaabaabaabbabaaaaaabbababaaaabaaabbbbaababaaaabbbbabaaaabbaaabaaaabbababaabaaaaabbbbaaabbaaabbaabbbbabbaaaaabbabaabaaaaaabbbbbbaaaabbabbabaaabbabbbbabbabaabaaabbbbbaaabaabaabbaaaabbababaabaabbaabaaabaabaabbaabaabbabaaaaaabbaabbbbaaaabaaabaabbbbaaabbbaaaaaabbbbbbbaaaabbbabaaabbbaabbabaaaabbabababbbabaaaababbabaaababbabbaabaaaabaaabaababaabbaababbaababababababbabbabbaaabbbabaabbbbbaababbabbbaabbabbaaaabbabbbaaaaabbbbaabbbbbbbbbabbbbaabaabbbaabbbabbababaabaaababbbbababbbabbbbbabbabaababbaabbbaaaaaabaaabbaabaabaaaabbbbbbbabaabaabbabbaaaaaabbbbbbababbbbaabbabbabbbaabbbbaaaabbbaababababbbbbbabbbaaaabaaabbbbbaabbbaaabbabaaaaabbabbbbbbbbaabbbaaabbaabbbbbababaaaaabbaabbbbaaaaabbbbaabaabbaababbabbbaabbaabababababbbaabbbaaaabaabbbbabbbbbbaaabbbaaaababaababaaabbabbbaaabbbbaaaaabababbabaaaaababbbabbbbbababbbbbaaabbaabbbbaaababbabababbbaabaabbabbabbabababbaaabababaaaaabbabbbabaababbbaaaabbbaababbbabbabbbbaaabbaaaaabaaababbaabbabbabababaabaaababbabbaababbbaaaababbabaaaaaaabbbababaabbbbababbaabaabbaaabbabbababaaaabbbbababbbbabaabbbbabbababaaabaaababaaaaabaaaababaaaabbbaabbabbbbbaaababaabbbaaaaaabbaaabbbbbababbbaaabaaabbaaaabbaaaaaaababaabaaabaaabaaabaabaaabaabaabbaaaaabaababbbabbbbaaaabaaaabaaaabaaabababbbabbbababaabbbaabbaaaaabababbbaabbbbabbbaaabbbaaabbbababbaaababaabbbbaaaabbbaaaabbababbbbaabaababababaababbabbaaabbbababababbbbababbbbabbbaaaabbbbbbaaabababbababaabbbbbababaaaabaaaaaaabaabbbbbbaaaaaaaabababbbababbaaabbabaabbababaababaaabbababbabbaabaaabbababbbabbbbababbabaababbbaaaaabbbababbabbbaabaabaaaaaabbbabbabbbbbbbaaaaaabaabaabbaababbbbabbbbbababaabbbbabbababaaabaaababaaabbaaaaaaaaaabbababaabababbbaababbbbbaaaaaaabbbabbbaaabaaaaaaaaabaabbbbbbbbbbabbaaaabababbbabbbabbbaabbbabbbbbbaabbabbbbaaabaaaabbbabaaaabaabbbabaabbbaaaabaaabbabaaabbaaabbbaabbaaaaaabaabbaaabbbbbbbbabbbbabaaabbabaabbbaababaaababbbaabbabaaaaaaaabaabbaababbbabaabaabbaabbabaaabaaaaabbbabaaabaaaabbabbbbbbaabaaaaabbabaabbababbaaabbbabababababaaaabaaabbbaabbbbababbbbbbaabbaaaababbbabaaabbbbbabaabababbababbabbaabbabbbaababaaabaaababbabaaaabaaababaabaabbabbbababbbabbbababaabbbababbbbbbbabbabbaaaaabbaaabbaaaaaabbbababaaaaababbaaaaababbabaababbabbbaaabbabaaababaabbbbbbbbabababbbaaaaababbaaababbaaabaaabbaababbbbabbbaabbbbabaaababaaabbabbaabaababbbbaabababbbaaaaaabaaaabbbbbabaaaaabbbbbbababaaabbabbabbababbbbaaaaabbaabbabbbaaabbbbbbbbaaaaabaabaaabbbaaaaaabbbbbabaaaababbbbabaaaababaabaabaabbbbbbbbbaabbbaaabbaabbabbbbaaaababbababbbababaaaabbbbbaaaaabbbabaababbaaaabbaaaabbaaaabbbbabbabaaaabaaaabbabbbbabaaaabbbabbbaaaaaabbababbbaababbabaaabbabbbbbababbaaaababaaaaaaaaabbbaaaaabbabbbabbabbaaaabababbaababbababaababbabaaabbaabaabababbbbaababababaabbbaababbbbbbaaabbbabbabbbabbbaaaababbabaabbaabababababaabaabbabababbaaabbbbabbbbbbbabababaaabaabbaaabbaababbbaababaaaaaaaababaaaaabbbbbaaaaaaabbbabbabbaabaabbaabbbabbbababbaaaabaaaabbaaababaaabbbbaaaabbbbabaaababaaaabaaaaaababaabaabbaabbaaabaaaaaabaabbbabbbbaabbabbbabaabbbabaabaabbaaaaaaaababbaaaaaabbabbbbaabbbabaabaaabaaaaaaaabbbbabaabbabbbabbbabaabaabbbaaaabaabaaababbbbabbaabbaabbaaaaabbabbbbbabaaaaaaaaababbbabbabaabbaababbbaaabbbbbbbaaaaaaabbabababaaabaabbbbbabbbbaabaabababaabaabaabaaabababbbbbababbbbabaaaabbbbbbbbbbaabbababaaaababaabbbaabaabbbaaaaaaabaaabbaaaabaabbbababbabbbabbbbabbbaaabbabbbbbaabbbbabaaaababbaabbaaaabbaabaabaabbbbabaababbbbbaababbabbaaaaaaabbbaaabaabababaabaabbaababbbbabbbaaabbabbaababbbbabaaabbabbbaaabbbbaaaaaababababaababaabaaabbbaababbbbaabaabaaaaabbbaaabaabbaabbbaaaabaaabbaababbbaababaaaababbbaaababbaabbabbabbbabaaaabbbabbabbbbabaabbabbaaababbbaaaaabbbbbbbaaaaaaabbabbaaaaaabbbaababbbbbabbaaaabbbabbbabbaababaabbbbbbbabaabaabbbbbbababaaababbbbbbabababbbabbabaaabbaaaaaababbaaabbabbbaabaaabbabbbabbbbaaaaabaaabbabbbbbbaaaabababbbabbbaaaaaababbabbbbbbaaabbbabaaaaaaaabaababbaabbabbbaabbbbbaaaaaabbbabbabaabaabaaaababaaaaabbaaaaaaaabbaaaaaaaabbababbbbabababaaaaababaabbbaababbabbaabaabaaabbaaababaaabbbbbbabaaabaaaababbabbaabaabbaaabbabbbaaaabbbbbbbababaaaababbabbbbaaabbaabbbababbbabbbaaabbabbababaabaabbabaaaababaaabbaabbaaabbbaabbaaaaaabbabbbaaaaaabbbbbaaaaaaaaabbbbbbbaaaaababaaabbbaaaaabababbabbbabaaabbaaabbaaababbababbaaaabaababbbabbaaabbaababbbbbbbaaaaaaabbaababbbababbbaaaabbaaababbbbbbababbbbaabbabbbbabbababbbbbbbbbbaabaabbbbaabbabababbabbbabbaaaababbbbbaaaaaaaababaabbababbbaaabbaaaabbbaaaababbbaaaaaabbbaaababababababaaabbbabaaaabbbababaaabbbbbabbabbabbabbbbabaabbabbaaabbaaaaaaaababaabbaaabbaababaaabbabbaabaabbbababababaaabbbbaaababaaabbabbabbbaabaaababaabaaabaabbaaaabaaabbaabaabbabbbaaababaabbbbaaaababbbababbbabbbabaaabaabbbbbbabbababaabbabaaaaaaaaaaaaaaaabbaaaaabbbabbbaaabbbbaabbbbbaabaabbbbbbbabaabbbabbbabbbbaabbbbaabaaabbabaabbbabbabaabbabbaaabbbbaaaaaaababbaaabbbbaaaaabbbbaaaaaaabaaaaaababbbabbaabaaaabbbaaabbabababaabbabaabbaabaaaababbbbaaababbbabbababaaaabbbbbababaabaaaabbababababaaababbbbbabbabababababbaabbbabbbaaabaababaaaabbbaaabbbaaaabbabbaaaababbaabaaaaaabbaaaabbbbbbbbaaabbabaabbabbabaabbaaabbbaababbbabbbaabbbabababbaaaabbabbababaaaabbbaaaabaaaaaaaababaababbabababaaabbaabbabbabaaabbaabbabababbbbbaababaaabbbbbbaaaabaaabbbababbabbbabbaaaababbaabaaababbbbabaabaaaabbaaabbabbaabababbbbbabbbabaaabaabbaaaaababbaaaabbaabbbaabaabbabbabbaaabbbaaabbaababbbbbbaabaaaabbaaaaaaababaabbbbaabbbabbaabbbbabaaababbbbababbbbabbbbabaabbabbbababaabbbbaabbbbbbbabbbbbaababbabbbabaaababbbaaaaabababaaabbbbabaabbababbabbaabaabaabababbbaaababbababaaaababaaaaabbaabbabbaabaabaaaaabaabbaaababbabaaaabaaababaababbbaaabbabbbaababaaaabbaaabbabbbaaabbbababbabababbaabbabbbbababbabbabbbbaabbaaababbabaabaababbabbbbbbbaababaaaaaaaaaaaaabaaaabbaaabbaabbaaabbabaaaaaababbbbabbbabbbbbaabbaabbbbabababaaabbaaabababbbbbbbaaaaababaabbbaaaaaaabbbbbabaaababbbabbbbbbaaaababbaabaabbabababbaaaaaabaabaaabbbabbaabababbbababbaababbbabbbaabbaabbaababaababbaaaaabaabbababbbaabbaaabbaabbbabbaaabbbaaabaaaabaabbbbabbbabbabababbbaabbbbbbbbbaaaaababbabaababbaabababbbbabbabaaababaabbaaabaabbaaabbbaaababbbbaaabababbaaabbaabbabbbaaabaaabaaaababaabaababbbbbbabaabbaaabbbbbbabbaaabaabbbbaaabbbababbbabababbabaabbabbabaababbabaabbabbbaaababababaaaaaababbbabbbbaabbababbabbbbaabaababbaabbaabaaabaabababaaabbabaabbbbabbbbaaaabbaaabbabbabababbabbbbbbaabbabaabaababaaabbbbbbabbbbabbbaaabbaaaabaabbbbabbabaaaaaabbaabababbaaabbaaaaabbaaaaaababbbaabbabbabbaaabababaaaaabbaaaababaaaaaabbbabaabbabaaabaabbababbaaaaabaabbbbbbbbabbbbbabbbabbabbaaabbbaababbbbbaaaabbaabaabbaaabbaababbbaabbbbbbaabbbaaabaaaababbbbbaababbbaaabaababaabbbaaabbbabbabbaabbaaaaaabbaaaaaabbbaaabbbabbabaabaaabababaaabaabbbbbaaaaaababbbabaabbabaaaabaabbaaabbbabbaaaababaabbabbbabaaaaaaaaaaaaabaaabaabaabbbaabbababaaaaaaaababaababbbbabaaabaaaaaababbbbbabaababbbabaabbbaabbbaabaababbaaaabaabbaaabbbaaaababaaaaabbbaabbbbaabbbbbabbaaabaababababbaabababbbaaaabaabbbaaabaababbaaabaabbbbabaababbbabaabbabaaaabaaabaabaabbaabaabbaaabaabbbbababbababbbabbabbabaaaabbbaaaaaabaaababbbaabbbbaaaabaaaababbbaaabbbabbaababababbbbaaaabaaabbabaabbbbababababaaaabaabbbbbaaaabbbbaaaabbababaabababbbaababaabababaaaaaaaabaabbbabbaabbbbbaaaabbbbaabababaaaabaababababbababaabaababaaaaaaaabbabbbbbaaababbbbaababbaaababaabbaabaaaaabaabbaabbbbabbabbbbaababbaaaababbbbbabaaaababaaaabbbabaabaaababbbabbbbaaabbbbbbbabbbbaabbbbbaaabbabaababaabaaabbababbbababbbbabababbababaabbabaabbabababbababaabbaaabbabbabbaabbbaaabaaaaabbbaaaaabaaababbabaaaaabaabaaabbaaabaababaabaaaaabbbbbbaabbaaaaabaababaaabbbaaaaaaababbbbbbabbbbababaaabbbaaaaaaaaababbbbababbbaabbbabbbbaaabaababaaabaaaabababaaabaaabbbbaaabababbbbaabbbaabaaababbbabbabaabaaaaaaababbaabaaaabaaaaaaabaabaaabaabbabaabbbabbaaababbababaabaabbabbbabbaaaaabbbaabbababbabbaabababababbbbaabbababbabbbabbaaabaabbbbabbbbbbaaabaaaabbaabbbbaabbabaabaabaabbaabbbaaaabbbaabbabbbbbbbbaaaabaaababbbabbbbabbbbbbaabbaaaaababaababaaababaaaaabaabbaaaaaabaaaabbaababbaababbaabbababbbbabbbbaaaaaaababbbabbbbaaaababbabbbaabbbababaabbbbbaabbabaaabbabaababaababaaaabbbbbbbbaaaaabaabaaabbbbaabaaaabaabbbbbbababbaaabbaabaaaabbaaabaaabababaaaaabbababaaabaabaaaaabbaaaaaaabbabbbbbaabbaabbabababaaaaaabaabaabbaababbababbbbabbbbbaaaaabbbaaababbabababababbbaabbbbaaaaabababbabbaabaabbaabbaaaaaaabbbaabaaabaabbabababaaabbbbbaabbaabaabbbabbbaabababbaabababbbbbabbbbbaabbabaaabbbbbabababbaaaababaaabbbbaaabbaabbbbabababbabbaabbaaababbabbaaababbabbabaabbabaaabaabbabababababaababbbbbabbaaaaabbababaaaaababaaaaaaaaaaaabaabaaababbabbabbaabaaaaaabbbaabababaabaababbbbbabbbbababbabaabbabbabbabbaabbbabababaabbaaaabbabaaabaabbbbbaabaaaaabbabbabbbabaabababbababbabbababaaaaaaaabaabbbbabababbbbabbaaabbbbabaaaabbabbbababbabaabaaababaababaabaaaababaaaaababbbbababababbaaababbbbabaabbbaaaaaabbbababbaaaaabbabaaabaaababbaabbaabbaaaaabbabbaaabaaaaabaabbbaabaaaaaabababbbaaabbbaaabaabbababbaabaaabaabbaaaabaaaaababbabbbbabbaaabbbbabaaabababbbbababbbaabaaaaabbbabababababaaabaabbababababbbaaabbaaabaaabbaaabbaaabaababaaaaabaaaaaaabaaaababababbabaaabaaaabaaaabbbbaaaababbbabaaaaabbbaabbbaaaababbaaaabaaabaaabbbbaabaaabbbaababababbababaababbbaaabbbabbaabbbababbababbbbabaabbabbabbaaabaaaaaaaabbbbbaabbbbbbbaaababaaaabbaaabaaaaaabbaabbabbbbabababbaabbbbabbbaaaabbabbbaabbabbaaaababbabbabbabaaabaabbaaaaaaabbaaabbbbbaabaaaabababaaaabbbabaabaabaaaaaaaabbabababbbaaabaaaaabbabbbbaaabaabbbabbaabbbaaabbaaababbaabbabbbbaaabaaabaabbbbabbaaaabbaabaabaabbbbabababbaabaaaaababbbabbaabbababbaabaaabbababbbabbbbbbbbbaababbbbbabaaababbbbbaaaabbbabaaabaabaaaaababaaabbababbbaabbaaaaaabbabaabbbabbaaaaababaaaabaababaaabbabbabbabbaabaababbaaababbaababbabaaaabbbabaaaaababbbabbaabaabbabbbabbaabbaabbabbaaaaabbaaaabaaaabbaababaababbbabbaaabbbbabaabbbbbbbbbbbabbaabaabbbaaabaaababbbabbbbbaabbbbaabaabaababaaabbbbbabaababbbaaabbbaababaaaaababbbbababaabbbbbabbabbbaabbbbabbbbbabbaabaaabaababaaaaabaaababaabbbabaaaaaabbaababaabababbaabbaaaaaabbbbbaabaabbabbaaaabaabaaababaaabaabbbaabaaaabaaabbaaababbababbabaabaaaaaabbabababaabbabaabaabbbbbabbbaaababaaabbbaaabbbaabbabaabbbbbbabbbbabaababaabbaabbaabababbbbaabaaababaababaabbbbabbbbaaababbababbaabbbbbabababaababbabaabbaabbaaababaabbabbaabbbbbbabbaaabaababbbbabaaababbaaaabbababbaaaaabbaaaabbaaaabaabbabbbaaabaabbbbbbbaaaabaabbaabbabababbababaabbbaaaaaaaaaaaaabaaabababbbbbababbbbaabaaaababbabaabbabbbbabbabaabbbaabbbbabaaabaaaabaaaaabaaabbbabaaaabbaaaabbbbabbbaababbabbaababababbabbbbbababbbaabaaabbbaababbaaabbabbbababababbbabaaaaabaabaabababaaaaabbabbbaaabbbabbbaaaababbbaabbaaaabaaaaaaaaaababbbbbbbbabaabbbaababaabbabbbababaaaabbbabababaaabbbbabaaaaabababbaaabaaaabababaaabbbbbababbabbbbbbbababaabbaababaabbbbabbbbbbabbaaaaaabaababaababbaabaaabbbabbaabbaabababaaabaaaabbbbbabbbbaaabbbabbbbbabaabaabbbbbaaababbaabbaaabbabbabbbbababbbbaababaabaabbaababaabaaaaaabaababbaaabaabababbaabbbbaaaaababbaabbbabbbabaabaabaababaabaabbababaaabbbabbabaabbaabbbbabaabbaabbbbbaaabbbaabbabaaabbbbaabaababbabbabaaabbaaaabbbababaabbbababbabaaaaabbbaaabaabababaababababaababbbbbababaaababaabbbbabababbbbaabbaaaaabaaababbbaabbbaababaaabbbaabbabbabbaaaabbaaaaaaaabbabbabaaaabbabbaabaabaaaaaaaaabbbbaaabbbaaaaaaabbbaaabaabbbbbbbaababbabaaababaaaabbaabbaababbaabaaaaaabaabbababaaaaabababaaabaaabaaaaababbbbbbbabbbbabababbabaabaaaaaabbbaaabbaabbaaabbaaaaabaaabbabbbaabbbbaabbabaaababaababbbbaaabaaabababaabaabbababaababababababbabbbbbaabaababbbbbababbbabbabaabbbbbbbaaaaaaaaaabaaaaaabaabbabbabbbbabaababbbabaaaabbbaaabaaabbaaaaabaabaabbbbbabaaaaaabababaaaabaaaaababaaaabbbbabaaaabbabbaaabaabbabaabbbbabbaaabbbabbbbaaabbaaaabbabaababbaabbbaaabbaaabababaaaabbbaababbaaaaaaaababbbbbbbbabaaabaabbabaabbaabbabbbbaaaaabaabbaabbababbaabaabbbbaabbbbabbbbbbbababababaaaaaabaaaaaaaabbbbbabbaaaababbbaaaaabbabbaaababbabbbaababbbabbbababababaabaababbaaabbaabaabaaaabbbabbaabbaaababababbbbbabaaaaabaababbabbaababbaababbbabaaabbaabbbaaababaabaabababaaaaaabbbbbabbabbbaaaabbabbaaababbbbbabbabbabbababbaaababababbbbaabbaaabbaabaabbaaaabbbaaaabbbbaaaaabbbbbbbaabababbbbaaabbbabbaaabaabbabbbabababbbbababbababbbabbbbabaabbabababaabaabaabbaababaabaabbababbababbbbbbbababbbbababababbbbbaaaabbbbbbaabaabbaaaabaaaaabababaaaaabbbaaaaababbbabbaababbabbbaabbabbbaaabaabbbabbaabababbabbaaabbaabababaaabaabbbabbbaaaababbbbaabbbaaaabaabbabbbbabbabbbbabbbbabaababbbaaaaabbbabbbababaaaaaaabaaaaaaababbbaaaaababbbabbabaababbabbaaabababbaaabbabaabbabaaaaabaaaabaabbbbbaababbbababbabbbabaaababaaabbbbbaaaabbbbbbbbabbaaaaaaaababaabbbabbabbbbaabbbaabbbabbbbaabbaaaabaabbbaaaabbbabbbabbbbbababaabababbabababbabaabaabbbbbbaabbabbaaabbaabbbbabbaabbabbbaaababbaaabbbaabbaabaabababbabbbaabbbaabbaaaabababbaababaaaaabbababbbaaaaaaababaaabababaabaaaababbaababaabbaaabbabaabaabaabbaaabaaabbaababababbbabbaabbabbabaabababbbbbbabbbaaabaaabaabbbaaabbbbabbaaaaababaaaabaaaaaaaabbbbbbbaabbaaaaabbababababaabaabbabbaabaaabaaaabaababaaaaaaabbababbaaaaaaabbbabbbaabbabbbaaaaaaabaabbabbabbbbbabbabaaabbbaaabababbbaaabbaaabbbbbbaababaabbabaaabaababbabbbaaaababaaabbbbbbababaabbabbbbbabbabbbababbaaabbaabaabbbabaabbbbaaabbbbabababaabbabaaabbbabaaaaababbbbbbabbbbababbbababababababbabbabbaaaabaaabaababbbbbabbbaabaaababaabbababbabbbabaaaabbabbbaaaaaabbbaaaaabbabbaabbbbababaabbbbabababbbabbabbbbbbabababaaaaabaaabbbbabbabbabaaabaaaabbbbabbaaaaabaaabbbbabaabaaaabaaabbbababbbaaaaabaabbbbabbabababbaabaabbabababbbaaaabababbbabababaaaaaabbbbbbbbaababaaaaabbbaaaabaaaaaaabbbbaabbbbaaaaabbbaabbaaabbaabbbabbbaaababbaaabbabbbaabbbbaabbaaabaaaabaaaaaababaaabbbbbbaaabbbbbbbaaaaaaabbbaababababaaaaabbbaaaabbabaabbbaaaabaabbabbbbababbbaabbabbaababbaababbaabbbaabbbbabbabbababababbababbaaababbbbaabaabbbabbbabbaaabbaaabababbbbababbaabbbbabaabbbbbabbbbaaaabbaabbababaaaaaabaabaabababaaabbbaaaabaaabbabaaaababbbabbbaabaabbbaababaabaabbababbabbabbbbabaaabbabbbbbaaabaaaaaabaabbaababbbbaabaaaababbaabbabbabbabaabaaaabbbbbabbaaabbaabbaabbabaabaaaabaaabbaaaabbbbbaaabaabbaabbbbaabbbaaaaaaaabababbbbaaaaaababbbaaaaaababbaabaababbabbaabbaaabaabbbaaaaaaabbabaaabaabababbaaaabbaabbabbbbbabbaaababbbbabbbbbbababaaaaaabaabaabaabaababbbabaaabaabaaaaaaababababbbaababaabbaabbbabbbaaaababaaaababaaabbbbbabbbabaaabbbabbababbaabaabaababbaaaabaabbabaabbbbaabbaaabababbabbaabbabbabbbbbabbaababbaaabbbababababbaabbabaaabbbabaabbaabbbbabbbbbabbbbbabbbaabababaabbaabbbbabbbababbbbabbabaaabaaaabaaaaaaaabbbaaaabbabbaabbaabaabbaababbababbbaaabaaaabaaababaaabbbababbbaabbabbaabababbaaaaaaaaababbbbbabbbbaaaababaaabbbababababbbabaababbbbababbbbbbbbbbababababaabbabaabbaabbbaaaabaaabbabbaaaaabababbabababbbabbabbbaaaaaabaaaabbababbabaaababbbabbbbababaaaabbbabbbaaabbbbbabaabaaaaabaaabaabbbbbabbaaababbbaabbaaaaaabaabbbbaabaaababbabaabababbababbabbabbabbbbbbbbaaaaabaaabbbbaababbbabbbbbbabbbabababbaaabbabbbabbbbbabbaaaabbabbbaaaaabababbbaaaabbabaaaaabbabaabaabbaaabbababbaababaabbbaaabaaaabbbabbabbbaabababbaaaabbbbbbbaaaababbbaaaabababababaaabaaaaaaaabaaabaaabbbbbabbbbbabbbbabbbaabbaabbbbabaabbaaaabbbababbabbabbbabbabbbabbaaabbaabbaabbbbaaabaaaaaabbaababbbababbbbaaabbbbbbabbbbbabbaababaabbbabaaaaaabbbbbbaabababaabaaabaaabaabbaababbaabaaaabaaaaaaaaabbbbbaaababbabbbaaaaaabbbbabaabbabbabaaaabaaaabbabbbbbabbabbbbababbbaabbbabbaaabaabbbabaaabbbaabbbbaaabbbbbaabaabbbbbbbbbaabaaaaaabaabbabbabaaaabbaabbabaaababaaabbabbbbabbbaaabbababbaaaabbbabbabababaabbbabbbbabbbbaabbbabababbbaaaaaabbbaabaaaabbabaaababaabbaaabbaabaabababababbabbbbbbabaaabbbbbaabaaabaaabaaaabababbaababbabaaaaabbaaaabaabaaaaabaaabaabbbaaaaabaaaaaaaaabbbaababbbaaabbbbbabaaaaabaaababaabaababaababaabbbbabbbbabbaabaababaabbabaabbaabbabbbbaaabbbbbaaabbabaabbaabbaabbbababbbbbaabbbaaaabaababababbbaabbabaaaabbabaabbbbaaaaabaaabaaaaabaabbabbaabaaabbbbaaababbaabbaaaaabbbbbababbabbabaaabaaaaabbabababbaabbaaababaaabaaaabbabbbababbbaaababbaaabbaaabbbbaaaabaaaabbababbaabbabaaabaabbababbbbbabaaabbaaabaaabaabaabaabaabababbbbbbabaaaaaabaabaaabaabbbaaababbbbaaabaaabbbbabaabaaaabbbaaababbbaaaabbaaabbaaaabbbbabbaaabbaaaaababbbaabaaaabbbaaaabaabbabaabbbbbabbabaaabbaabbbaabbaaaaaaaaaaabaaaabbaabbbbaabbbaaaaaaabababbbababaaabababaaabbaabaabbaabaabaabbaaaabaabbaaaaababaaaababaababbaabbaababaabababaaaaabbababbbbaaabbbaabaaaaaabbaababaaababaabbbaaaaabbbabaabababbabbbaaaaaabbaaabaaaaaaababaaaabaaabbaabbbabaaabaabbaaabaabbabaaababaabbbabbbbaaaaabbababaaabaabbabbbaaababbbabbbbbbabaabaabaaabaaaaabbabbbbbbaaabaabbbaabaabbbaaabaabababbaaababbababbbaabaabbaababbaabbaababbaabbbababbbbbaaaaaabbbbbaaababbaabaabbabaaabbabbbbbaabbaababababbabbabaabbbaaababaaaaabaabaaababbbaabbaabaababbabbabbbbbbaaabababbbabababbaabbabbaabbbbabbbababbabbabbabababbabbaaabbaabbaaaabbabaaaaaaaaaaabbbaabaaabbaaabaabaabbbaaaabaaabbabaaabbbababbaaaabbbaabbbabbaaaababaaaaabbbabaababbbaaabaaaaabaabbbaabaaabababbabbbbbabbabbbbaaababbbbbbbbbbbaaaabaabbababbabbbabbbaababbbbbbbaababaaaaaabbaabbbbbabaaaabaabbabaabbbaaabbbabaaaaaaababbaabbabaababaabaabbbbaabbbabbbbbbbbaabbababbaaaabbababbaaaabaaaaabbaaababbbababbabbbababbbbbbbababbbbbabbbaaabbbabbaaaabbbbabababaabaaabbabbbbaaabbaaaabbbaaaaabaaabaaabaabaaaaabbabbbaabaaaabaababbaaaaababbbababaabbabababaababbabbabbaaabbbbbbbaabbbaaababbabbbbbababaaabbbaabbbbabababbabbaabbabbbbbbababbbbbaabbabababaabbabbaaabbbbaaaaabbaabbaaabbababbbaabbbaabaabbbaabbbbbabbaaabaabbabbbbababbaabbabbaaaaaabaabaaabbbaabaabaababbaabbababaabbbababbaabaabaababaabbbbaaabbaabbbbbabbbaabbabaaabababbabbaabbabaababbaabbbaabbbaabaabbbbbbabbaabbbaababaaaabbbbbaaaabbabaaabbaabbbbbbaababbbbbbbabbabbabbaabbbaabaababbaaababbabbbbbaaaaaabbabbabbbbababbabbababaaabbaaaaabaabbbbaabbbabababbaaaabbaabbaabbababbbbbbbbbbaaabbbabbaabbabaaaababaaabbaaaabbababbaaaabaaaaabbaabbbaaababaabbbbabbbabbbabaababbbabbbbaabaaaabaabbabaabaabbbaababbbbaaabaaabbbababbaabaababaababaabaaabbabbbabababaabaaaaabbbbbbaabbaabbbbabbbbbbaaaaabbbbaaaabaaaababaaabbabaaaaabbaabaaaababbbbbabbaaaaababbbabababbbbbaaabaabbaaaaaabbabbaaaabbabaaabaaaaabababababbababababaaabababbbbbaabaabbaabaabbaaaaaabbaababbbaabbbaaabaaabbabbbabaabaaababbbabbbbbabaabbababaaabbabbbbbababbaaaaabbabbbabaabbabbbbbaabaabbaabbababbbbbaabababbaabababbbabaabbbbbbbbbbaaabbbaabbaabbbbaabbbbbaaaababbbabaaaabaabbabbbaabbbbabbabbababbbaaabaabbabbbababbbbabababababbaabbbbbbbbbbaababbbbaababbbabbabbbbaababaaabbbabaabbbaaaabaabbaababababababbbaaabbbaabaababaabbababababbbabbaaabbabababbbabaabaabaabbababaaabbbbababbaaabbbaabaababbbabaababbbaaaababbaabbbaabbaabbaababbabbabaabababbaaabaaaababaaababababbbbbbababbbbbbbabbbbaaaabaabbbaaaaaaaababbaaaaabbbbaabbbbbbbbbbaaaabbabbbaabbabababbaaabbaaababbabbaabbabbbabbbaaaaaaabbbbbabaabababbabbbaaabababaabbbabbbabaaabaabbbabbabbbbaaaababbbbbabaaaaabaaabaabaabbbbaaabaaababbbaaaababbbbbbbaaaabaababababaaabbbbbabbaabaaabaababbbabbaabbaabaabbaabbbaabbbaabbbabbaabbbbbaabbaaaabaabbabbaaaabbbbababbbabbaaabbbabbaaaaabbbabbbabaabbaabaaabaaaaaababbbbbbbbaabaabbbabbbbaabbbaaaaababbbaaabbbbbababbabbaaaaabbaababaaaabaaababbaabaabbbaaaababaababbbbbaaaaaaaababaabbbbbaabbabbbaaabbabbaababbaabababbaabbbbabbbbabbabbababbabaababaababbbbbbbabaaababbaaaaabaabbaaabbaabbbabbabbbabaabbabaaabbbbaabbababbbbaababaaaabbabbbaaabaaaaabbbaabbabaaabaaaabaaabababbbabbbabbaaabbbabaaaaaabaaaaaabbabbbabababaababbabbbbbbaaabbaaaabbbaaaaabbbaabbbabababaaaaaabbaabbabaaaabaabbaababbbabbaabbaaabaabaaabbaaabbabbaababbaabbbbabbabababbbaabbaaaaaaaaaaaabbbaababaaababbaaaaaaaaabbababaaabbbbabaabbaaabbabbbbabaaabbaaabbaaaaabaabbbbbaababaaaabaaaabbaaaaaababbbbabbbbaabbaaababbbbbaabaaabaaaabaabbaababaaaabbaaababaaaaabbbbaababbbbbbbbaaabaaaaabbbababbbbababbbbaaababbbabababaaaaabbbaabbaababbaabbbbaaabbbbaababbbbbaaabaaaaaababbbbbabaaaaabaabbababaaabbabbbaaaaabbbbbbabbababaabbabbaababbbabbabaaaaaaaabaabbbbaaaaaabbbbbbabbababaaababaaabbaaaaaaabaabbaababbaaaabbaabbbbabbaaaabababaabaaaabbbbbbabaabbabaaaababaabbbbabbaaaabbaaabbababbaaababaabbbbababbaabbbbabaabaaaaabbbbaabaaabbabbbaaabbbaaaabbbbabbabababaaaabaabbaabbbbababababbaaaaaabaabbababbbbbbbaaaaaabaaaaabbabaaabbbabbaaaabbbbbaaaabbabbbaaaabaabaabbaaaaaabbbbbaabbabaababaabaabbaabaaaaaaaaabbbbbbabbabababbabbbabaaabbabababbaaabaaaababaaaabaabababaaabbbabbbbabbaabaababbbbaababbabbaabaaaaabbbbbaaabbabaabaabaaaaabaaaaabaaaabaaabaaaabbabbbaabaaaabaaababbaaababaabaabababaaabaaaababaaaaabbbaaaabbaaabbbbabbbabbaaabbaaabaabbbabbbababaaaaaabbabbabbbabaaaaaabbbbbabbabbaaaaaaaabbbbaabaabbbaabbbbbbabaabababbabbbaabaaabaaaabbabbaabbaabbbbbaaabbbbbaaaaabaaababababababbaaabbaabbbababbbbbbbababbaabbaabaaabbbbaababbabbbaaabaabaaabbbbabaaabaaabbaabbabbabbaabbaaaaaaaabaaabaababbbabbaababbbababbaabaaababbababaabbabbaaabbbbababbabaaaabaabbbaabaabbbabaaaaabaaaababaabaabbbbbaabbbbbaaaabbbbbbbaabaabaaaaababbaaaaabbabababaababbbbbbababaabbbaabaaabbababaaabbbbaaaaaababaaaaababbabababbbbbbabbabaabbbbbaabaaaabbbaabaaabbbbaabbaaabbbbabbaabaaababaabaabbbbababaaaaabaaabaaababbaaaababbbbaabbabaaababbababbabbababbbbbaabbbbaabababaaaabbbbaabaaabababababbaaababbabbbbbbaaabbaabaabaababbababaaaabaababaabbaabbbabbabbbbbbaaaaaabaababbbbbbaabbbbabbabaaabaababbabbaaabababaaaabbbabbbabaaabbbbababaabbaabbaabbabbabbbbaabaaaabbaababbababbaabbbbbbabaaaaabbbbbbbbbbbbbaabbabbbbbbbaaaabbbbbbaaabaababaaaaaaaaaababbababbbaabbbaabbbbbaabbaaaabbaabbabaabbbabbaabbbbbaabbbbbababbbaabbabbbbbbabaaaabbbaabaabaabbababbbbbbabbababbabbbaabbbbbbbbbaaabbabaabaababbbaaaaababaababbababbbaaabaabaabaaabbbbbbaabbaabaaaabbabaabbbbaabbababababaaabaaababbabaaababbabbbababbaaabaaabbababbbaabaabaaaababbaaaaaaaabbabbababaababbaaaabaaabaaabbbabbbbbabbababbabbbababbabbbaaabbbbbaabaaaabbbabbbaabbaabbaaabaabbabaabaabaabaaabbbbbaabaaaaabababaaaaababaabbaababbbbababaababbbaaabbbaaabbbaaabbbbbaaaaabaababaabbaabbbaabaaababbbbababbbbaaabbaababbbababbbbbbabababbabaabbabaabbbbbaaaaaabaaaabbabaaaababbabaaabaaaabbaababababbabbababababbaaabaaaaabbbbbaabbbaabbabaabbaabaaaaabbbababaabaaabbaabbaaaababbaaaaabbbaaababbbbaabbbabbabbaaabbbbabaaaaaaaabababbabbbbaabbabaaaaaaaaaaabaabbbabbabbaababbaaababbababbbbaabbbbbaaabbbbbaaaaaaaaabaaabbabaaabbbbbbbbbbbaababbaaaaababaabbbaababbbaaaaaabbbabaaababaaaaababbbbabbababababbaababbabbbbbabbaaaabbabbababababbbaaaabbbabaaabaaaaaabbaaaabbaabbbaaabababbbbbbaaabbababbaaaabbaaabbbbaaaaaaaabbbbbaaabbababbababaaabbbbbbbbaababbbbbaabaaabbbbaabbababbbabbbbbbaaaabbbbaaaaaaaaabbabbabaaaaabbaabbababaabbbabbbbbbbaaaabaaaabbbabbbbbbaaaaaaaababbbaaaaaaabaaabbaaaaaaabbababbbababbabaaabbbabbabaabbbbbabababbbaaabbabaabbabbbbbbaabbaaabababbbaababbaabababaabbabaaaabbabbbbbbbbbabbbabbbaabbaabaabbbbabbbbbbabaaabbabbbbbaaaabaaaaabaabbbbbbbbabbbaaabababbbabaaabaababbbbaaaabbbbabbaabaabababbabaabbaaabbaababaaabaaabbabbbbbbababaaababababbbababaabbbabbbbbaaabaaabaabaababaaabaaaabaabababbaabaabbbbabaaaabbabbbaabbbbaaabbaabababaaabaaaaabaaaabbbbabaaaabbbbbbaabbbaaabababbbabbabaabababaaaaabbabababaabbbbabbabbbabbbaababbbabbabbaabbbaababbaabbbbabaaabbabaaabbbaaabaabaaabbabababaaaabbaababababababaabbbbbbaaabababbabaaabaaaaabbabbbaabbabbabbabababbabbaaababbabbabbbabbaabbabbabbabbabbbbaabababaaaaaaaabababbbabbababaabbabbaaababaaaaaabbaabaaabaababaaaaaaaabbbbbabaaaabaaabaababbabbabbbbbbaaabaaababbaababbbabbbabbbaabbaabaabbababbbaaaababababaaaabbabbbabbaabaababbbbbaaaabbabaabbbababaababaabbbbabbbbaabaaabbbababaabbbbbbbbaabbabbabbabbbbbaaaaabbaaaaababbbbbaaaababaababbbbbabbaababbaaabaabbbabbabaabaaabbbbbbbababaababbbbbaaaaabababbbaaabaabbabbbaabababaababbbababaabbbabbbbbabaababbabababbaabaabbaaaababbaaabbbaabaaaaabbababaaabbababbbbabbbaababbbaabaabbaaaababbbbbbabbbaabbbabbabbabbaabaabbbaaaaaababababaabaaabbbabababbbaabbabaababbabbbbabababbaabaaaababbaabaaaabbaaaaaaaabaabababbbabaabbbbbaaaaaaabbbaaaaaaaabbaabbbbbbbabaaabbaaaabaaaaababaabbabaababbabaababbaababbabaaaaababaabaabbabbbbbaaaabbabbabaabbaaaaaabaaabaababbaabaababbbbbaabbabbabbbbbaaaabbabbbbabbabaaabbbbbabbbbabbbbababaabbabaabbbbaaaabaabbbabaababbaabaaaabaabaaaabbbbababaaaaababbbbaabbbaaaabbaabbbabaaabbabbaababbbbbbaabababaaaabbababbabbabbbaaaabaaaaaababababbabbbabbbaababbabaaaaabbbaaabbbababababbaaababaaaabbaaaaabaabbbbbabbbaabbbbbbaabbaabbaabaabbaaababbbbabbaabaabaabbbabbbababbabbbbaaaabbbaaaaaaabaaaaabaaaaaaaaaabbababbbaabaababbbaaabbabaababbbaabaaaabaababbbbbbabbaabaababaababaabbababababbaaababbbbbabbbaaaaababbaaabababaababbabbabbbbbbababaabbbabbaabaaaaabbabaaaababaaaabaaaaaabbbaabbaabbbbabaaaaaaaababaaaabaaaaabbaaababaaababaabaaabbbabababbbaabbabaabaaaaabaaabaabbbbbabaaababaaaabaaaaabbaaababbabbbbabbaaabbaababbabaababbabbabaababbaaaabaaababaabaaababbbaabbbaababaaabbbaabaaaabbaaaabbabbaaaabaaabbabaaaaaabbbaaababbababbabbaaaaaaaaabbbbbbaabbbabbabbbbbbabbbbaababbbbbbbbaaabaababbaabaabaaabbbbaaabaaaaababbbbbbbbaabbbaabbbbbbabababaabaabbababaaabbaabaaabababaabbbaaabbabbbbaabaaaaaaabaabbbabaaaaabbbababaabbabbbbbbabbbabbabaaababbaaabaabaaabbababbaaaabaabbababaabaabbbaababababbabbabbbaabbbbbaaaababaaabaaaababbbbababbbbbbbababbbaabbabbbbaaababbbbbbbbabbbbaaabaabaaaaaabbbbbbabaaaaabbbbabbaabaaababbbbbabaaaabbaabaababaabbaaaabbabaabbaabababbbaabbbaaaabaaabaabaabbaababbabbaaababaaababbaaabaababbaaabababaabaaaaaabbababaaabaababbaabaaaaaaaaabaabbbbbbbbaababbabbbaabbaaaaabbabaabbaaaabbbbbbaaabbbababbabbaaaababbaabbabbaaabaabbbbbaabaabbbabaabbbabaababbabbbbbaabaabaabaaabbababaaaabbaabbbabaabbababbaaaabaabaabbababaabaaaaababaabaaabbaabbbabbbbbabaabbababbbababbbbbaabbabaabbaaaababbaabaaabbbbaaabaaaaabababbbaaabaabaabababbbabbaaabbbbbbabbbabaaaabbabababbababbbbaabbbbbbaaababbbbabbaabbbbabaaaabbabbaababbabababbaaababbbbababbabaaabbabbaabbaabbbbaaabbaabbabbaabaaabbabbbaabbbaaaaabbaabbbaaababbaaabaabbbbaaaababaaababbabaaabbaaababaabbbabaabbaaaaaaaaaaabbabbbbbaabaaabbabbbaababaaabaabbababbbabbaaaaabbaaabbabaababbbbaabbaaabbbbabbbaabbaabbbabaabaabaabababbbaaaaabbaabaababbbbaabaabababbaaabaabbabbbaaaaabaaaaabaabbaabbabbabbbababaaaaaabaaaabbbbaaababbababaaababbbaaaabaaabaaabaaababbaaabaabbbabaaabaaaabbbaabbababaabbbabababbbbabbbbaabaaabbaaababbbbbbababbaabaabaaabbabaabaaabaaaabbbbbaaaabbbabbaabaaabaaababaabbaabababbaaaabbbbabbbbaaababbabbbababbaaaabaabababbbbabaaaabbaaabbbaaabbaabbbababababaabbaaabbaaaaabbbaababbaaaaabaaaaababbbbaabbbbbbbbbaabbaaabbabaaaaababbabbabaababababbbababaabaaaabbbbbbaabaaaabbbaabaababbbbabbbaabbbbbabbbbbababbaaaaabbaabaabbbbbaaabbaaababbabbbaababbaabbaabbababbbbbaaaaaaaabababbaaababbaaaaaaaaabbbabbabbbbbabbbabbbbbbbaaabaababbababbabbbbbaabaabaabbaaaabbbaaaabbababbaababaaabbbabbbbabaaabbaababaaabaaaaabbbabbbaaabaabaaaabaabbabbbaaaabbbbaababababbabbbaabbaabbabbabbaaabbbbbaabbbbbbbbbababbabaabaaaaabaaaaabababbabbabbbabaabaaababbababbaaabbaaaaaaaabbaaabbababbbabaabbbbbaaaababbbbbaaabbbaabbbbaabababaabaabbbbaaaaabbabbbabaaabbbaaaaaaabbaababbbaaaaabababbbbaabaababbbbbabbabaaabaaabbabbaabababababbaabaababbbbababaaabaabbbaaababbbbbabaaabbaabaabababbbabababababbaabbabababababbbbbaababbbaaababaaaaaaabaaabbaaaaabaaabbabaababbbabababbbbaababbbabbbaabbaaaabbbbaaabaabbaabbbbbbaaaabbaaaaababbaaaaaaabbaabbbabbbaabababaaaaabbabbaabbababbaaabaabaababbababbbaaabbbbbabbaaabaabaaaabbabaaaaaaabaaabaaaaabbaaabaabaabbbbbabbbaaabbaaaabbabbabbbaaabbaababaabaabaaaaabbabbbabbabaaabbabaaabababbbbbbaabbaabaabaaaabaababaabbbbaababaabbbaabbbbabbaaabbaaabaabaaabbaaabbaaabbabbabababbaabbaababbaabaabaabbbabbabbaababaaaabaabbbaabaaabbaaabababbaaabaaaaabbbabaaabaaaaaabbabbbbababaaababbbabbbabbaaaabbbbbabbbbaabbaabaaababaaabaabbaabbbbbaaaaaabbaaababbabbbaabbaabaabbbaabbaaabbbbaababaaaaabbabaabaaabbababbaaaaabbabaaaaabbaaaabaababbababbabbababaaaabbababbaabababbbbaaabbbaaabbbabaababaababbbbbbbbaaaaabbbaaabaaaaabbbbbaabbaababaabaabbbaaaabaaabaaaabbbababbabbabababbaabaaaaabaabaababaaabbaababbaaaaaaabbaabababbaaabaaabbabaaaabbaabbbbbaaaaababbbbbbbbbabababababbbbabbbabaababbbabbaaabbaabbaabababbbaababbaabbbaaaaabbabbaabaabbababbabbaabbbabbbbabbbbabbbbaaabbbbaaaaaabaabbbabaaaaabbabbaaaabaaabbbabbaabbbaabaaababbabbaaaaaaabbaabbabbaaaabbabbaababbababbbabaaabbabbaaababaaabbababaabbbbaabbbbaabbaaaabaaaaababaabaaabbabbbbaaaabaaaaabbababbaaaaaabaaaabbabaaaabaabbaaabaaababbaabaaabbbbaabbabbaababbbaaaaaaabbbbabaabbaaaabaabbabbbaabbbbababbbbaabababaabaababababbbbbaabbababbbabbabbbbababababbbababbbbbbaabaababbbbabaababaaaaaababaaaaaaaaaabababbbabaaabbaabbabbbbababbbbabbbbabbbbbbbbbaabbabaababaabbbbbbbabbbbbababaaababbbaabaabbaaabbbababababaaaabbbbbaabaaaaaabbbbbbbbbaabaaaaaabaabbababaabbaababbaaaabbabaabbbabbbbabbbaaabababbbbbabbbbbaaabaabbaabbaabbbbaabbbabaabbbaababbaaabaabaabbaabbbbabbbbbbaaababaaabbabbbbbababbbbbbbaabaabbbaabbbbbaabbbababababaabbaabbaaaaabbbaabbabbbabbabbabbbbaabaabaaababbbaaabbabbaabbbaaababbbaabaaaaaaaababaababababbbabababbababbaaabbaaabbabababaabbbaaaabaabaaaabbbbabbabbababbabbbaabaabbaabbbabbabaabbbabaababababaabbbbabbaabbaababbababaabbabbaaababaaabbbaabbbbabbaabbaabababbbbaabbbbbbaaabaaaababbbbabbbbbababbaababbbbabaabababababbbbabaabaaababbabbbbbbaabaaaabbbbabaaaabbaababbaaabbbabbbabaaabaaaaabababbaaabbaaabbabaabbabbaaabbbbbaabaaaabbaaababbbaabbaaaaabbaaaaabbaabbbbaabababaabaababbbabaaaaababbabaaaaaabababbaaaaabaabbbbbbababbbbbbaabbbabbbabbaabaababaaabbaabaaaabbaabaaabbaabbaabbbbbabbaabbbaaaabaaaabbbbbbaaabbbbbbabbaababbbbbababbbbaababbbaaaaaabbaaabbbaabaababababbabaabbabbaababbaaabbbaabaabbaaabbabbbbbabaabbabbbaabaaabbabababbaabaaaaababbbababbaababababbabbbabbbaaabbbabbbaaabbaababaabbabbababaabbabbbaabaabbbaabbbbbaabbbbaaaaaaababaaabababbbbbababbaaaabaababbbbabaabaaababababaaabaaabbaabbaaabbbbababbabbaaababbbbbabbabbbababbbbbbabaabbbbabbaababbbbabbbaaabbaaabbabbaaabbaabaaaabaabaababbaababbbaabaaaaabaaabbbabbbbbbaabbbbaaaaaabbbbaaaabaabbbbbaaabbaaaaaabbbabaaaaabbbaaaabbabbabbbbaabaaababababababbababbabaabaaabbbaaaabaabbaabbaabaababaabaabaabbaaaaaabaabaaababbabbabbbaaababababaabbabaabababbabbbbbabbababbabbbaaabbabaaabbbabaaaaaabaaaaabababbaaaaaabbaaabaababaababbaaaaabbaaaaaaaabaabaaabbabababbbaabbabbbababbaaabaabbbaaabbaabbabaaaabababaaabbbababaabbbaabbbbbbabbbaababbaaaaabbbbbbbbbabbaaabaaabababaaaabbbbbabaabbaaaabbabbaabbabbaaaababbbaabbbabaabbaaaaaababbbbbbabbbababbbbaaabbbaabbaababaabbabbabaabaababababbabaabaaaabbbaabbbbbabbbbbaaaaaababbabbabbaaaababbbbbaabbbaaabaaaababbbbbbabbaaaaaaabbabaabaabbaabbaabbbaaaabbabaaaabbbbbaabbabbabbabaaaaaaaabbbbaaaababbbbbaabbbbababbbabbbaababbabaabbaaabaaaabaaaabaaaaaabbbabbabbabbbaaabbbbbbbbbbaaaaaababaaabbabbbaababbbabaaaabbaaabbbbbaabbbababaabbabbbabbbbaaaaabbabbabbabababbaaabbbbaababbabababaababbaaaaabababbabaaababbbaabaabbaabaaaaaaabbbbbbabbaabababaaaaabaabbaaabaabbaaabaaaabbbbaabaabaaaabaaabbbbaababbbbbbabbbaabbaaabaabababbaabababaababbbbaabababbababaaaababbababbbabbbabaaaabbaaabbbababbbaaaababbbbbaaaaaababbaabaabababbabbbbbababbaabaababababababbabbbaabbabaabaababababaabaabbbbaababbbaabbabaababaabbaaaaaabbabaabbabbbaababbabbabaaababbbbbabbaaaaababababbbaaaababbaababbababbaaaaababbbabbaaabaababbaabbbbabbbbabababbbbbabbbbaababaabbabaaababbaaaabbbbaaaabbabaaababbabbbabbabbabbabbaaabaabbaaaaaababaaabaaabbaaabbbbbabaabaaabbababaabbabbababbabaaabbbababbbbbaabaabbabaaabbbbbabbbaaaaaababbbabababaabaabbbbaabbababaaaabbbaabababbbaabbbabababbaaabaabbbaaaaaabbabbbbaababaaababbabbbaaaaaaaabaabbaaaaabbbbabbbbbbaaababbabababbbbababbaababbabbaaabbbabbaaaabbbaabbabaaaaababaaabbaaaabbabaabaabbabbaababaaaabbaaaabbabaaaabbbaabbbbbabbbbabbbaaabaabbabaababbbbbbbbbabbaaababbabababababbbaaabaaabbaabbaaaaaabbaaabbabbbbbaabaaabaaabbbabbbbabbaaabababbabbbbabbbababaaaaababaabaaabaaaaaabbbaabbaababbbabaabaaabbababaabbbbaaabaabaabbaabaaaaaaaaaababbbbabbaabaaababbaaababaaaaaaaaabbbbabaabaabbbaaaaaabbbbbbbabbaaabbbabaaaabbbbaaaaabbaaababaabbbbaabbaabbabaababbaaaaaabaabaaaabaaaaabbaaaaabbbaaabbabbaaaabbbaaaabbabbbaaaaaaababbbbaabbbbabbabbabbbaabaabbaaabbabaabbaabaaaaaaaabbababbbaaaabababaabbabbabbabaabaaabbbabbbabaaabbababbaaabbababbaabbbaaabbbabbaabbaaaaabbbbaaabaaaababaabbbbaabbaabbbabaaababbbbbaabaaabbbbbbbbbaabbabbbaaababababbbbbabbaabaaaabbbbabbbaabbbbababaabbabbabaabbbababbbaabbaaaaaaabaabaaaaaababababaaaabababbbabbababbbbbaabbbaabbbbabbaaabbabaabbbaabbbabaaaabbabbbabaaabaaaaaabbaababbabbbabbaabaaababbbaabababaaaaaaabbbbbaaaabbabaaabababaaaaaaaaabaabbbbbaabbbabbabaaaaababbbbbbabbabaabbabbbaaaabbaaababbabaaaabbababaaabbbaaababbababaabbabbbbbbbbabbbabbaabbabbabbbabaabbbabbababaaaaaabbbabaaababababbbbbbababbaaaababaabaabbbaabaabaabbbababbbaaaaababbaaabaaababbabbababbbabbbbaababbaababbabbaaaabbbaabbaabbaaaababbbbbbabbbbabbabbababbbaaaaaabbababbaabbabbbbababbababaabaabaaaababaaaabbbabaaababaaaaabaaaabbbabaaaaaabaabbbbaaaaaabaababbbabbabbbbbababbbaabbbbaababaaababbabbbbbbabbabbaaaababbabababbabaabaaabaaababbabaabbaabaaababababaabbababbbbbaaaabbbbbabaaababaaaaaaaaaaaababbbbaabbabbabaaaabaaabaaaababaabbaabababbbaaaababaabababbabbbaabbbaababbaaaabbbbaaabaabaaabbbbbababbbaabaabbaabbabababbabbaabaaaaabbbbabbbbababbabaabbaababbbaaabaaaabaabbbbbabbbabababbaaaaababbbbbbbaabababaabaaabbabaababbaabbbabaabaaababababbbabaaababaabababaabbbababbbabbbaaaababbabababaaababbbabaaaaabbbaabbbaababbabbabaabaabbbbbabbbaabbaabaaabbbbaabaaaabbbababbbabaaabaabbbbaabbbababaabbabaababbbbabbaaaaabbbbbbbbbaaababbababaabbaaabbbababbbbbabbaaaabababbbbaaabaababaaaaaabaaaaababbbbaaabaabbbaaabbabbabbbabababaabbbbbbaaabababbbaaaabaaabbababaabbbbabaababababbabaaaaababaaaaaaabaaababbbbbbaaabbbbbbabbaaaaababbabbababaababbbabababaaaabaaabaabaabbababbababaabaabababbbbbbbbbabababababbabbabbbbbbbbbabbbbbaabbbaabbaabbabaabbbaaaaababaabbabbbaabababbababbbababbbbbaababaabbbbababbbababbbabaabbbbbbaaaaabbabbbbbaaabbabbbbbbbbababababbbaaabababbbbbbbaabbababbbbbabbbaabbaaabbbbaabaaaaaabbaabbbbbabbabbaaaaabbbaaabaaabababbabbbaaaabbbabbbbbbabbbabbbaabbaaababbababaaabbaabbabbbaababaabbbbbbbbaaabbaabababbbbbabbbababbabaabbbabbbabbaaababbbbaaabbabbabaabbabbbabbaabaabbbbaabaabbabaabababbabbbbaababbabaabaaaaabbaaabbababbababbbbaaaaaaaaaaababbbbaabbaaabbabbbaababbbabaababbbbabbbaabbabbabaaaaaaaaabbabbbbbbabaababaaababbaabababaaabaabbbbaaaabbbbabaabbaabbbbbaabaaabbbaabbbabbaaaabaaabaabababbaaaabbabbbababaabbaabaaabababbabababaaabbbbaaaababaababbabaaabababbbaabbbaababbbaabaaaabaaaaaaaabaababbabbbbaabbbaaabaababbabbbbabbaaaaaababaababbaaabbababbbbabaaaabbbbbbababababababaaabbbabbaaaabbbaabaaabaaababbaabbbbabaabbbbbaabbababbbabaaababbbaabbaaaabbbbababaaaabbabbbbaabbaabbabbaaaaaabaabbabbabbabbbababaaaaabbabbbbaaaababbbaaabbbbaabbaababbaaaaaaabbbabbbbbbbbaaaaaabbabaabbaababbbaaabbabaaabbbabaaabababaaaaababbbabbbbbaabaabbbbababaabaababbbaaaababbbbbbbaabbbbababbabbaaabbabaabbbbabbababbbbabaababaaabababbabbabbabaaabbbbbababbbaaaababbbaaabababaababaaaabbbabaaaababbabbbabaaabbabaabbbbbaabaabaabbbbabaaabaababbaabaaabbbbbbabababaaaabbbababbbbbbbaabaabbbabaaaaaabbbaaababaaababbbabbbbaabbabbbaaaababaabbaabbbaaabbbabbababbabaaabaaabaababbbbbbbababaaababbbaaabaabbabbbbbaaababbabaabbbbbaaabbbbbbbaabaababbbaabbababaababaaababbabaaabbbabbbbbbbaaaabbabaababbbbabbabbaaaaabbbbaaaaabbaaabbababbbabaabaaaabbbaabbabbaaaabbbabbaaabbabbababaaaabbaabbaaaaaabbabaababbbbbbbbaaaaabaabaabbaaaabbbbbbbabbbabaaababaaabbbbabababbabbbabbaabaababbbbbbbaabaaababbaaaabbaaabbbaabaabbbaabaabbbbbaababbaabbbbaabbabaababaaaabaabbabaaababababbbaaababbbaaababbabaaaababbbbabbaaaaabaabbaabaaabaaabbbaaaababaababbbaababaaaaaababaabbbbaaabbaabbbbbbbabaaabaaaabbbbbabbabbabababbbbbabbbaababbbabaabaaabaaabbbbbbabbabaaaaabbbaababaabbaaaababaababbbbbbabbbbaababbbabaaaabbaaaaaaabaabbaaaaababaaaabbabbbbababaaaabbaaaabbabbbaaabbabbbaaaababbbaaababbaaaababaabbaaaaaaaabbababbaaaaaabaaaaabaabaabbaababbbbbaaaaabaaabbababbbaaabbbaabaaababababbbbbbbabbbaababaaababbbbabbaabbaaaaabbbbaabaabbaabaababbaaaabbaabaaabbaaabbbababbaaaaabababaabbbaaaaabbbaaabaaabbabbbbaaabbaabaaabaabbbbaabbbbabaaabbabaabaaaabbaaaaabaabaabbaabbaaababbabbababbaabaabaabbaababbabbbaaaabbbaabbbbbababbabaaaaaabaabaabbaaaaabaabbababaababbaabababbaabaabababbbababbaaaabbaabaabaabababbabbabbabbbabaabbaabbabbbbabbaaabaaabbbbabaaaabbabaabaabbaabaaabbbbbbabbbbaabbaabbabababaaababbbaaaaaaaabbabbaabbbbbaaaabaababaaabbabbbaabababbaababababaaaaaaabbaaabbaaabbabbabaabbbaababababaaabbabaaabbababbabbbabbbbbabbbbbaabbbbbbbbbabaaaabababbbaabaaaaabbaabaaabbbbabbababbbbaabbbbaaaabbaabaabbbabaabaabbbbbbbabbbbbabbabaababbbbabbaabaabbaaabbaaaaaaaaaaabbbbbaabbbbaabbbbbbaabaabbabbaaaabaababbbaaaaabbbbbbbabaaabbbabaabbaaabaabababbbaabaaaabbbbabababaaaaabaabbbbbbbaabbabbaabbbabbbbabaaabaabbaaaaaaaabbaabbbabbaabbabbbaaabbaaaaaabaabbabaaaababbababbbbbbaabbaabbbbabbaaabaabaaabaaabbabaaabaaabaaaabaaaababaaabbbbaabbaaabbabbabababaabbbbabbbbbabbabbababbabaaaabababbbbbbbbaababababbbababaabbabaabaabbbaaaaaaabbabaababaabbaaaabbbabbaabbbbbbaababbbbbaaaabbaabbabbababbbbaababbaabbbabaababaabbbabbabbbaaaababbbbbabbaaaabbbaaaabbbbaabbbbabbbbaabaaabbbabaabbabbbbaaabbbbaaaabaabbaababaabbaaabbbabbabaaabababbabbbbabbbbabbbabaabbaaaaaaaabaababababbbabbbaabbbbaabbbababbaabaabbababbababbbabbbbbaaababbbaaaaaabbabaaaababbbababbababbaabbbbababaaabbbaaabbbaabaaabbababbbabbbaaaababababababbabaabaaababaaaabaabbbaaabbaaabbbaaabababaaaabbaaaabaaaaaabbbbbabbaaabbaabaabbbbaabbabbbaaabbabbbbbbaaaaaaabbbaabbbbbbbabaaaaabbbaababbbababaabaabbbabbbabaabbbabbaaabbbabbbaabaaaaaabaabaabaaaabbbbbabbbbbaaaabababbbabaaabbabaabababbbabaabbbababaaaaababbaabbbbbaaabbabbabbbbabaabbbaaaaabbbaababbbbbaaabbaaaababbabaaaaababbbabbbabbbbbbaaababbaaabaaabbaaabaabaabaabbbaaababbbbbbbbababaaaabaabaaabbbabbbaababbabbbbaaababbaaabbaabbbaaaabaaaaabaabbabaaaaabaababbaabbaaabbbaabbababaaababbbbbbbbabbababbbaabaaabaaaaaaaaabbbaabbbbbbbaaaabbbaabbaabbaababbaababaabaabbabbbaaabbabaaaaabaabbaabbaabaabaababaaababaaabaaaaabaaaaaabbbbabbaaaaabaaabaaabaaabababbaaabbbabbbbaabbbaaaabababbbaaabaabaabaabbbababaaaabababaabababababababbaabbbbabbaaaaaaaabbbbaabbbabbaaaaabbaabbabaabbbbaabbaababaabbaabaaabbbaaaaabbaabbbaaaaaabbbbabbbaaaababaabbabaabbaaabbbaaaaababaaaabaaaababaaabaaabababbbbaaabbbbaaababbbaababbaaaababbabbaabaaabaabbbbbabbabaaabaabaabaaabbaabaaabababbabbbbababaabbbbabbbbababbbbbaabababaaaabaabaabbbaabbbbabbaabbbababaabaaaaabbbbabbabbbabbbbabbbabbbabbbaaaababbbbabaabaaaababbabaaaabababbabbaabbababababbaaabbbbbbabababbaaababaaabbabababaabaababaabaaabbaabaaabbbababaabababaabbbaaaababaabbbbbaaaaaaaabbbabbbabbbbaaaaaaaabaaabbbaabbbbbbbaaabbbabababbbaabbababbabaaaabaabbbbaabbabbabbaabbabbbabbabbbaabaababbbbaabbaaabbaabbbabababbbabababaabbbaaabbbbaabbbaaabbabbaaaaababbbbababbbbbaababbababbaabbbbaabaaabaabaaaaaabaabbaaaabbabbbbbabaababaabbaaaaaaaababbbabbbbbabababbaaabbbbabbabbbbbabbbbabaabaaabaaababaabbaaabbabbbbbbbabaabaaaababbbbaaaaabbaabaaabaabababaaabbaaaaaaabbaaaabbbaaababbbaabbbaababbbaabaababaabaaabbaaabababaaaaabbbbabbaabbbbbabaaaaabaabbbbbbabaabaabbbbbababaababababaabababbbaaaabaabbababbbbbaababaaabaaabbbbbbbbaaababbaaabbbbaaabbaababbbabaabaaaabbbababbbbbbaaaababababbbbbaaabbaaaababbbbaabbababaababbaaaaaabbbababbbbaabaaabaabbbabbbaabaabaaabbaaaababbaabbbbaaabbababbaaaaababbabbbbabbaaaababbaaaaabaabbaaaabaaabbaabaaaabaaabbbbbaaaaaabaabaaabaaabbbbaabababaabbabbabaabaabaababbaabaabbabaabbbbabbbaabbbaaaabbbabaabbbabbbaababaabbaabbabbaaabbbbaaaaaaaababaabaaabaabbbbabbaabaaabbbbabbbbabbbbabaababaaababbbaaabaabbabbbabaabbababaaaabbaaaaaabbbaaabbbbababaaaaabbbbbbabaabaabaababbbbabaabaabaaaabaabaabbababaabbbaaabbbabbabababbbbabaabbabbbaabbaababbbbbaaabbbabbaaaaaabaaaababbbaaaaabaaabaabaababbabbbbbaabbbbaaabbabaababbbabbabaaabababbaabbaaaabbbabbaaaaabbababbbabababaabbbaabbaababbbbbababbabbbbabbabbbbbaaabbababaabaabbbabbbbbaaabbaaaabbabbaabbbbaaabaaabbbbbbababbaabababbbabbaababbbabbbbbaaaabbbaaabbaabbaabbbbbbabbababbababaabbaaaaabbabbbaababababababbbaaaaabbaaaabaaaaaaababaababaaababbabaaababababababaabbabbaaababbaabbaaaaaaaaaaababaabababaababbabbbbabaabbbababbbbbababbabaabbaababbbbaaababababbbabbbbabbabaaabbaabbaababaababbbaabbbbbabbbbababbbabaaaaabbabbababababbaaaaaabaabaaaaabbaabbaaaabbabbabaaaabbbbabbbaaaaaaababaaaabaaabbabbbbbbbbbaaabaabaaabbbbbbbbabbaababaabbaaabbababaabbabababbaabababbaaabbaaaaabbabababbbbbbbbbbaabbbbbabaabbbbabbabbaabbabaababbabababaaababbabaabbabbbabaabbbbaabbabbabbaaabbbbabaaabaaabbabbaaaababbbbbbbbbaaabbabbabbaaababaaabbaabbababbabbbbbbbaabbbbbbbababaabbaababbbbabbbbbbaabababbaabbaabbbbbbbaaabbbbababbababbbabaaaaaaabbaaaaaaababbbaaabbbabbbbbbbbaababbaabbbbbbbabbaaabaaabbababbbbababaaaabababaabaaaaaabaaaabbbabaaabbabbaababbbabbbaaaababaabbbaaaaabaaabbbbbbaaaabaaabbabaabbbaaababaabaaababbababaaabbaababbaaaaaabbbbbaabbaabbbbaaababbabaabbababababbbbbbbbbbbabaaaabbbbabaabbaababbabaaabbaabbbbbaabaabbaaaabbbbabbbaabbaaaabbbabaaabbabbaabbabbabaabababababbaaabaabbabaabbabaaabbabbaabbbabbbbabbbabbbbbabbaabbabbababbbabbbbbabbbbbbaabaabaaaaaabaaaabbaababbbababbabbbaabbaabbaaababbbbbabaaabbabbabbaaabaaabbabababbbaabbbbbbabababbabbbbabbabaaaaabbaababbaaaababbaaaaabaaabbbaababbbbabbbbbabbabbabaaaaababbabaaabbbabbbabaaabbaababbaababbbbabbbaaaaaaabbbababbbabaaabbbaabbbbaabbabbbbbabaaaabaaababbbbbaaababaaaabaabbbbbaabbbbbabbaaaaaaaababaaabaaabbbbbabaabaaaaaababbbabababbaaaaaabaabbbababbabaaaababbbaaababaabbbabbaaabaaaabaabaabbabaaaaabaabbabbaabaabbbababbabaaaababbaaaaabbbaabbbbbaaaabbbbbbbabaabaabbbbaabbaaaabbbababaaabbbaabbbbbbbbaabbaabbaabaaaababbbabaababbaabbbaabbaaaabbbaabbbbbaabbbbaabbbaaababbabbababaaaaaaababaabbbabbababbaabbaabbbbbabbbbabbabbbbababbababbbaaabbbbabbbbaaaaaabbbbbbbabbaaabbaaabbbaabaabbaabbbbbabaaababaabbbbbbbaaabbabbbbabaabbaaaaabbbbbbbabaabababbaaabbbaaaabbbaaabbbabababababbbaaaaaabbbaaaabbaababaaabababababbabbbbabbabbaabbaaaabbbbbaabaaababbaaaabbabbabaabbaaabaabaaaabaabaabbbabaababbabaaaabaaaaababaaaaaabaaabbaababbbbbbbbaabbbbabbbaaababbabaabbababbbaabbbbbbbababaaababbbbabaabbbbabaaaaaaaababababbaaaaaabbbbbabbababaabaabaabbbabbbbaabaabbaabababaabbaaabbaabbaabaabbbaaabaabababaababbbaaabbbaabbaabbaaabbabababaaabaabbabbbbaabbabaabbbbbabaaabbbabbaabaabaabababaabaaaabbbbbabbbababaabbbabbbababaababbbaaaabbbaabbaaabaaabbbbbaabbaaaaaabbabbbabaabaaaabbbabbaabbbabababbbaaababaaaabaaabaaaaababaaaabaaaababbbabbbabbabbbbaabbbaababaababaababbbababbbbbaaababaabbabbbaaaabbaaababbaaababbbaabbabaaabbaaaaaaaabbaaaaabaaabbbabaabbaabbbaabbabbaabaabbbabbbabbaababbbabababbbabbabaabbabaaabbbaabbbabaababababaaabaaaabaabaabababaababaaabbababbabbababbbbaabbbbaabbabbaabaabbaabaaabaaaaaaabbbbbabaabbbbababbabbababbabbababbabaaababbababaababbabaaaabababaaababababaabbbbaaaabababbabbbbbbaaabbabbaababbbaabbabaaabbbaabaaaaaabbaaaaaabaaabaaabaabaabababbbbbbbaabbbbbaabbaabbbbabbabbbababbbbbbbbabbbababbabababbbaaabbbabaabbaabbbbabaaaabbabbbaaabbaabbaabbabbbaaaabbaabbbababababbabbaabbabbbbbbbaaabbbabaabaabbbaabbabbaaaaaaababaababbbaaaabbabaaaaabaabaaaaaaaababbabbaaaaaaaaaabaaababbaaabbabababbaabbbababbaaaaaababbbbbbabbaabbbbbaaababbabbaaaabbaabaaababbabaabbbbaaabaababbbaaabaabbaaabaaaaaaabbbbaabababbaabaabbabaabbbaaabaaababbaaaaabbbababbaabbabababaabaabbabababbabbabbbabbabbabaabbaaabbbaababbaaabababaabbbabbbbabbbbaabbbbaaabbbbbaaaaaaabbabbbbaabbbbaabaaaaabaababbbbabbaaabbbbababaabbaaababbbabbbbaaaabbababbbbbaabbbabbaabbbbabbbaababababbbababbabbaabaaabbabaabbbbbaaaaaabbbbbabbbbaaaaabbbbbaaaabaaaaabbabbabbabaababaabbabbbbbbbbbaaabababbbbbabbaabbabbabbaaababaabaaababbabbbabbababbaabbaaabaabbbbabbabbaaabbaabababaababbbbbbbbbaaabbababbbabaaaaaaaaabaaabbababbbbbabbbbaaaaaaabbabbabbbbababbaaabbaabbbaabbaabbaaaabbaaababababaababbabaabaabababbabaabaabaabbbbabaaababbaaabbabbaaababaaaabbabbbaaababbbbbaabbbaabaaabbbabbabbaabaaabaaabbabaaabbbababaababaaababbbbbbbabbbbababbaaaabbaabaaabbaaabbbababbabbababaababbaabbbabbbababaabbababbbbaaabbbaabbbbbaabbbbaaaabaaaaaaaaababbaaabaababbbbaabababaabaababababbabbaaabbaabaaaaaaabaaababaaabbbabaaababaaabaaabbbaaaaaababaabbbbabaababaabaaaababbbaabbaabbaaaabbbabbbbbbabbbbababbabbbbbbaaaaabbbaabbaaaabbbbaaaaaaababaaaababaaabbbabbabaabbabaaaaaaaaaabaaaaaaaababbbababbbbbaaabbabbbabbbabbaabbabbaabbabaaabaabbabaababbbbaaabbaaaabaabbbbbbbaabbbbbaabaaabbaaaabaabaababababbababbaaabbaabaababbbbbbabbabaaabbaaaabaaabababbaabababaaabbaabaababababbaabaaaabbbaabbabbabbaaaabaaaaababbbabbbbaaabbbabbbbbbabbaaabbbbabaaabbbabbbabbbbbbabbbbbabbaabababaabaabbaaabbbbbbaaabbabaababaabbbbabbbaaabbabaaaababbbababbbababbbababababbaaaababaabaaabbbbbabbabaaaaababbbbabaabbbabaabaabbababbbaabbabaaabaabbbaaabbaaababaabbaababababbbbaaaaabbbbbaaaaaababaababaabaabbaabbbabbbbaaaaaaaaaaabbbabbbbaaabbbbbabbabaaabbbabababbbaabbaaabbabbaaabaababbaabbbbbbbbaabbaaaaaabaabbabbbbbbbaaaaabbbabaabababbaabbaaaabbbbaabaaabbbabbaaabbbabbbaabaabababaaaabbbbaaabababbaaaaabaabbbababbbbbaaababbbababbbabaaaabaabbabbbaaaaaaaababbaabababbabababbbabbaaaabbbbabbbbabbbbabbaabbbbbaaabbbaaabbbaaabaabbbbaaaaabbbbbabaaababaaababbbabababbbbbbabbbbbababaaabbbbbaabaaaabaaabbbbababaabaabaabbbaaabababbbbbabbbabbbabaabaaababbbabbababaaaabbbaababbaababbbbbbbbbbbaaaabaabaabbaaabbbbababababaaabababaaaaabaabbaababbbaabaaabbabbaaabbbababbabbababaababaaaaabbabaabbbbbbbbbababababbaabbbaabbaaaaababbbabbbbbbbaabaaaaabaaaabaabbbbbababaaabbbaaaabbbaaabbaabbbbbaabaaaabaaaaabbaaaabaabaaabbbaaabaababaababaaaabaabbbbaababaabbaabbbabbbbaabbaabbaababbbaabaabaabaaaaabbabbabaaaaababbaaabbaababbabababbaaabaaabbaaaaaabbbaaaabbbbababababbabaaaaabaababaaabaabbaabbabbbaababbbbabaabaaaabbababbbbaabaaabbaaabbbbbbbbabbabaaaabbbbabababbabababbbbaaaabaaababbaabbaabababaaaaabbaabbbbababababaaababbbbaaabaaaaabbaabbbaabbbbbabababaaaabaaabbbbbbbaaabbabbbabbbbbababaabbbaaaabaabbabbbbababababababaabaabbbabbbaabbbbabbbbbbbbbbbbbabbaaaaabbbbbabbbabaabbbbbaabbbbabaaabbbaaaabaabaaaabaaabbbaabbaaabbbaababbabababbbabaaababbaaabbabbabbaaabbbabbababbbbbbbbaaaaabababaaaabbaaababbaaabbaabaaaaaabaababaabaabbbabaaaaaaaababaabbbbaabbbbabbbbabaaababbabaabaaaaabbbabbababbababbbbbbbabbbbbbaabbbbbaabbbabaabbaaaababbbbabaaaabaabaababbbabbabbabbbbaabaabbabababaaabaaababbabababaababaabababababaabbababbabaaabbbababaaabbabbabbaabaaabbaaabbabababbaababbbaaaabaaabbbbaaababbaabbaabbbbbabbbbbbbaaabaabaaabbbbaabbaaaaabbbabaaaaabababbabbbbabbabbbbbaabbabbbbbbababbabaaaaabbabbbbbbbabbbbabbbbbbbbbbababababaabaabaaaaaabbaabaaaaaabbaaaabaabaaababababababbbbbabaababbaaaabaababababbabbbbaabbaabbaababbbbabbaabbabaabbabababbbbbbabbbaababbabbaabbbbbbbaababaaaaaabaabaabaabaabaabaaaaaabaabbaababbaabbaabbaabbbaababbbbbaabbabbaababaabaaabbaababbbbabaabaaaababbbbbababababaaabbaaabbaaabaaabbbaabaabbbabaabbabaabbbabbbbaaabbbaaabbbbbaaaaaabbaababbbbbabbaaaabbabbbabbaababbabaabbbaaaaaabbbabaaaaabbababaaabaabbbaaabbbbaabaabbabbbaaabaaaabaabaaabbbabaaaaabaabaabbbbaaabbbabbaabababbbbbbaabbabbbabbbabbbaaabbabbabaababbaababbabbbaabaabbabaaaabbaaabaaabbaaaabbaaaabaabaaaaabaaaabababbbbbbabbabbbbabbbaabbabbbabbabababbababbaaabbbbbabaaaaaababbbaaaaaababbbbaabbbbababababbbbaabaaabbabaabaabaababaaabaaabbbabaaaabbbbbaaabbaaabababbaaaabaabbbaabbbbabaaaaaabbbabbbbabbababaabaaaaabaaabbbbbababbbbbababaaababaabbaabbaaaabaaabbbbbbbababbaabaabbbbabaaababbabaaabababbbaabbbaaabaabaababbabababaabbbabbaabbbbbbbbbaaaababaaaabbaaabaababaabbabaababbaabaababbabbbabababbbbbabaaabbabbbbbabbabbbbaabbbabbabbaabbaaabbbabbaabaabbbaababaabbaaaabaaaabaabbaaabbaaabbaaaaabaabababaaabbaabaaaaabaababbabbbbbabbaaabbbaabaaababbabbaababbaabbbbababaaaabaabaabbbbabbbbbabaaaaabaabbaabbaabbbaababababaaabbabbbababababababaabbbabbaabbbaaaaabababbbaabbaabaababbabaabbbbbbabaaaaaababbbbaaababaaabaaabaabbbaaaaaabbbbbabaabaaabbbaabaabaabbbabbabbbaababbbababababbabaaaaaaaabaabbabababbaaabbaabbbbbaabbbbaabaabbbbaaabbabbbbbbaaababaaabbbbabaaaabaabaabaaababbbababbbbaababaabaabaabbaaaababababbabbabaabbabbabbbabaaaaaabbbbbaaaaaabbbbbabaabbabaaaaaaabaabbaaaaaabbbbabaababbbaaabbbaababbbaabbbbabaabbbbbbaaababbaaaaaaaaababbbbaaababaabbbbaaababaaaaaabaaaaaaabaaabbbbbabbbaababbbaaabaabbbbbbbbabbaabbabbabaabaabbbabbbbbabbbbbbabaababaabbaaaaaabbbabbabbabbbbbabaababbaaaabbbbabaaaabbbaaabaabbabbaabbbaaababbbababbababbbababbbbbaabaabaaaababaabaaaabaaaabbbaaabbbaaaaaaabbabababbaaababababbbbbabaabbbabaabababababbbaabbbaababbaabbbabaaabbbbbabbaaabaaaabbbabbaaabbabababbabbbabababaaabababaaabaaababbbababaaabbbbbabbaabbaaabaababaabaaaabbbabbabababbababbbaabbbbaaabbbbbabbaaabbaaabbababbabaaaabaabaaaabababbaabaaabaaaaabbaabbbbababbaaaaaaababaaabaababbababbabbabbaabaaabaabbaabaaabaaababbbbbbbbbbabaaaabbbabbbbbbabaaabbbbaabbbaaaabaaabaaababbaabbbbbbbbbaabbbbaabbbbbabbbaaaaabaabbbbbbbbaabaabbaaaaabababaaaaabaabbbbbbbbaaaaaaaababbabbbbaaaabaabababbbaaabbbbaaaaaaabbabbabbaabbbaaaabbbabaabbaaabbbababaababababbbbabaaaabbaababbbbabbabbabaabbbbaaaaabbabbabbaaaaababaabbabbaaabaabbaabaabbbbbabbabaabbabbaababaabbaaabbaaaaabaababababbbbbaabbbbaaabaaabaababbbbbabbaaaababbbaababbbbbaaaabaabaaabaabbabbababbababaabbabababbaaaaaaababaaaaaabbaaabababaaaababbabbbbbaabbababaaabbbaabbaaaabbbabbabababaaabbbaabaaabaaabbabaabababaaaabababbbaaabbbaaaaaaaababbbbbaabbaaabababbaabbababaaabaabababbbaaabaabbbbaaabbbbabbaaababaaabbabbbaababbababababbaaaabbbababaababbaaabababaaabbaabaabbabbaabaaaabbaaaabbbbabababaabbbaababbaabbbabbaabbaaabbbaaabbababbbbbbbbaabaababaaabbabbaaaaaaabbbababaabbabbaabbabaabbabbbababaababbbbaababaaaaaaaaabaaabaabaabbbbaabaabaabbbabaaababbaaababbbbbbbbbbabaabbabbaababbaabbaabaabbabaaabbaabbaabbbbbaababbabbbbbbababaabababbabaababbabbbbbabaabbabaabbaabbaaaaabaaaababbabbbaaaabaaaababbbbbababbaabbbabaabbaaabaabbbababbbabbaaaababaaababaabbaaaaaaaabaabbbbbbabbabababbabbbbabbbbbbaababbabbbbbbabaaaababaaaaaabbbaaaaaabbbaaaaabbabbabbbbbbaababaaaaabbbbbbaabbbaaabbaabbaabbbbbabbbaabababaaaababaabbbaabbaababbbabbbbbabababbababaabbaaaaabbabaaaababaabbbabbbbbbbbaaabbbbabaaaaabaaabbababaaaabbaabbbaabaaaaabbabaabbaabbbbabbabbabaaabbabbabbabbabababaaaaaabaaaabbabbabbaaabbbabbbbaaabbbabbbabbabbbbabaaaabbabababbbbabbbbabbababbbaabbabbbbbabbbaababbbbbbbbbaabababbbaaabaaaabbabbabbbaaabaaaabababbbababaabbbababbaaabaababbbabbbaabababbabbbaaabababaaaaabaabaabababaaabbbabbaaabbaabbabaaabbaabaaaabbaabbbabbabaabbabbabbbaabbaabaaabaabbaaaaababbaaabbbbaabbbbbbbbaabbabbaaababaabbbabaaaaaababababaaaabaaababaaaabbaabbbaaabaabbbababaababaabaabbbbbabaaabaabbbabbabababaaaabaaabaabbabbaaabbaaaaaaabbbbbbaabbabbabaaaabaaababbbbbabbbabbaabbbbbbaaababaabbbbbaabbaabbbabbaaaaabaabbbbabbbaaabababbabbbaabbaaabababaaabaaabbaaaababbaababababbabbabbaaaabbbbbbabbbbbabaabbaababbabaaabaabbabbaaaaabbbbaaaabbbabababbabaaabbaabaabaabaabababababbbaaaabbabbaabaaaaabaababbababbabbabbbbaababaaabbbababbbabaabbabababbbbbabbbabaaaaabbabbbbaaabbababbbababaaabaaaababaaaabbabbaaaabaabbabababababaaaabababbabbaabbbaaaabbabaabbbbaaaababbaabaaaaaaaabbaabaaaabbaaabbabbaababaaabaaabaaabbabbbababbbababaabbabbbaaaaaabaaabbbabbbbaabaaababaaabbaaabaaaaababbbabaababaaabaaababbbbbbbbababbbbbbbbbbaabaabbbabbbaaabaaaabbaaabababbabbbaabbbbbabbababbababbababababbabbababbbabbaabbaabbaaaababababababbbbbbbabaaaaabaabbbbaaabaababbababbababbbbaabbaabbabaaaabaabababababbbababbbbbaaabbabbaabbbabbbbabbaabbbaaabbaaabbababaaaaaaabbababbbaaaaaabaaabbbbbbaabababbabaaaabbababbbbabbbbbbababaaabbbabbbbabbababbbaababababbbaaabaaabbabaaabbbaabbbabbbabbbabbbbabbbaabaabbbabbaabaabbabbbbbababaababaaaabbbabbbabbbbbbababbbbbbbaabbbbbbbbabbabbbabbabbbbabaabbabbbbbbaaabbaababbababbbbaaabbbabababaabaababbabaababbbbbbbbaaaabbababbabbbaaaaababaabaaaabbbaabbaaabbbbabbbbbbbbababababbaabababbbbbbbbabbabababaabaababbabbabaabbbaaaababaabbabbbabaaababaabbaaabbabaaababbaabbabaaaaabbaaaabbbabababbbaaaaaaaabbabbabbbbaaabbbaaaaabaaaaabaaaabaabbbbaabbbababbbaaaaabbabababaaaaabababbabbaaaabbaabbbbbbaaabbaaabbabbbbbbaaabbbbbabaaaaabaaabaabaabbbbabaaaaaabbbbbbbaababbbabaaabbbabbababaaaabaabaaababbaabaaaabbbaaabbaaabbbaaaaababbbbabbabbaabbbabbbabaaaaabbaabababaaababbbaabaabbbaaaaabaaaaababbaaabababaababababbbbaababaabaababaabaaaabbbbaaaaabbbbbbbabbabbabaaabbbbabbabbabbabababbbaaabbaaaaaabaabbbababbbaabaaaabbbabbabaabaaaabbbbaabaabbabaaabbbaabbaababaabbaabbbbbabbbabbbbbaabbabbbaabbbaabaaabbaaabaaabaaabbbaaaaabbabbaabaabaabaabaaaaaaaaabbabbaababbbaabaabababababaaaabbabbaababababbabaaabbbbabbbbaaaabababbbaaaabbbbbabbaaabaaaabaaabbbbbbbbaabaababaababbbabbbaaaabbbaabaabbaabaabbaabbaaaaabbabbbaaaaabbbbbbbbbaaaaabaaaaababbabaabbababbbbbababbaabaabbbbbabbabbaababbbaabbbbaababaababbabbaababbabbbabababababbbaababbbabbaababaaaabbbabbbaabbaabbbabaabbbabbaabbbababaabaabbaabbabaabababbabbbbabbbaaaaaabbbaaababaabbbaababaaabbabbaabbbaaabaabaabbbbaaabbbbaabababbabbaaaaaababababbaabbabaaababbababbbbaaabbbabbaaabaababbbaabaaabbbabbbabbabaaaabbbbbbaaaabbbbbaaababaabbabaababbaaabaabbaabaabbabbbabbbaabbbbaaaaaaaabbaabaabbbbbbbabbbbaabaaaabababaaaabbbabbbabbabbbbabaaabaabababbbbbaabbabbbbaaaabbabbbbbbbabaaababbbbabbbaaaaabababbbbaabaabbbabaabababbababbbbbbaababbaabaabaabbaaabbbbbbbbbaabbaaaababbbbbbbaabaabbabaabbabbbbbbabbbbbabbabaabbabaaaaaabbbabbbbaabaabbabaaabaaabbaaaabbabbbbaaabaaabbaaabbbbbababbbababaabaaabbbabaababaabbbbbbabababbbaabababaabaaabaaaaabaaaabaaaaabbbabbabbaabbbbababbababbbabaaababaaabbbabaabaaaabaabbaabbbbababbbbabbaaaabbbbbababbbbaaabbababbabbababbaaabaaabbbbbbbbaabbabbabaabbbaaabaabbabbaaabaabaabbaababaaaabbbaaaaaaaabbbabaaaaabbbaaabbbbabaaabbabaaaaababbbabbbabaabbbaababbaabababbbbabaaaaaabbaabbbbbababbaabaaaaabbbbabbaaabbabaaabbaaabaaababaaaaabaaaaaaabaaabbabbababbabbaaababbbababaaaabaabbbabaaabbababaabbbbaaabaabababbaaabaabaaababbbbaaabaaabbababbbabbbaaababaabbaababaaabbbaaaaaaaaaabbbaabaababaaabababaabaababbaaaababbbbababbabaababbbbaabaabbbbaaaaaababbabbbbabaaaaaaaabbaaaaaaaabaaabbabaabbbabaaaabbabaabaaabaaabbaabbbabbabbbabbbbabaaabbbabbabbabbabbabbaabaabaaaabaaabbbaaabaaabbabbaababaaaaabaabbaabbaaabaaababbbaaabaaaabaabbabaaabbaaaaaabbaaaaaabbaabaabbbbbabbaaababbabaaabbabaababaabbabaaaabaaabbabbbaaaabababaaabbaababaababbaabbbbbbabbabbbbbabbabbbabbaabbbbabaaabbbababaabaabbbababababbbababbbabbbaaaabbaaabababbbbaaaaabbbaaabbaabbbaabbaababbbbaabbabbbaabaaabbabaabbabbabaabbbabbababbbbbabbbbbbaabbbabababbbbbabaaaabbabababbaaabaabbbbababbaababbbaaaabbabbabbbaaaababaababababbbbbbbabbbbbbbaababaabaabbaaabbaaaabaabaaaabaaabbbabbbababbaaaaabbbbbabbabaabbbbaababaaabbbaaaaabbaabbabaababababaaaabbbabababbabbaabaaabaabaaaababbababbbbabaabbbaabaaaababababbabbabbaaaabbbabbabababbbbbbbaabaaaabbbbabaababbbaaaabbbbbbaabbaaaaabbbbaabaabbbaabababbbaabaabababbababababbaaaaababaabbbaabaabbbaaaabbabbbababababbbababaabbaaaaabbbababbabaaaabaaabbbabaaabbbbababaabbaaabbabbaaabbaaabababbabaaaaaaaabbbaabbabaabbbababaaaaabbbaaaaaababbaabbabbababbbaaabbbbbbaabaababbabaaaabababbbaaaaababaaaaababababbbaabbaabbbabbaabaaabaaabbbbabbababaaababbaaabbababababbbbababaaaaabaaabbaabbbbaabaabbabaaaaaabaaababababaababbaaababbbbabbbbbbababaaaaaabababbbbaabbabbbbaababbababbbbbabbbbaabbabbabaaaaaaaabaabaabbabbbbbababbbbaabbbaabbaaabbaababababbaaaabbbbbabaaaaaabababbaabbabbababaaaaaabaaaaaabbbbaaaaaababbababaaaaaabbababbabaaaabbaababaababababbbaaaababaaaaabbabaabbaaabbbaaaababbabbabbabaabbababbaabaaababababbbabbaabbaaaabaaabbbbbaaaababbbaaaaabaabaabbaaabbaabbbbababaaaabbbababbaaabbaabaaabbbbaaaabaaaabbabbbbbbaabbaababbbaaaabbaaaabaabbaaababbabbaababbbbbababaabaabaaabaabbbaaabaababaababbabaaabaaabbaabababaabbabaabbababaaabbbaabbababbbaaaababaaaabaaabbabbbabbaaaababbbbabbbaababaaabbaaabbababaaababbaabbaababaaaabbbbaabbbaababbbbbaabbabababbabababaabaabbaaabaaabbaababbaabbbabaababbbabaabbbaaabbbaabababbababababbbababbaabababaababbaaabaabbbbabbbbaabbaaaabbaabbabaaaabaabbbbabbbaabbbbababbbbaabbabaaaaabbaabbbbbbbaaabaabababbaaaabbbbabbbbbbababaabbbabbbbbaabbbbbaabbbbabbabbababbbababbbbabaaaaaababbaabaababbbababbaabaaaaabababaabaababbbaaabababaabbbaabbbaaabbbaaaabbbaabbbbbaabbbbbbaababbbbbaaababaaaabababbaaaaababbabbababbbababaaabbaabaabbbaaaaaabaabbbaaabbaabababbbbbabbaabbabbbabaaabbbabbaaaabaabbbaaabbbaaaaababababbabbbbaaaabbabaababaaabaaabbabaaaabababbbabbabaabbbbaaabbabbbaabaaababbabbbbaaaabaababbbabbaaabaabababbbabbababbabaabbbababbaaaabbabbbbbbbbbbabbbaaabbbbabbaabbbbabaabbabbbbaaaabbbaababaaaaabbbbbaaaaaaabbbbaababaaaabaaaabaabababaabbaabbbaabbababaabaabaaaabbababbaabaaabaabbaaabbababbabaabbbababaabaaabaaaabbbaabaaababababbbababbaaabaabbabbbbbbaaabbbababaabaabbaaaaabbaabbbbabbaabbaabaaaaaabaaabbabbbbabbbabbbaabbbaabbbaaaabbaaaabbaabbaabaabbbababbbabaaaaabbbaabbaabababaababbabbaaababbabbbaaabaaaabbaababaababaabbabababaaaabbbbaaaaabaabaaaabbabaabbbbaaaabbbaabbabbbaaababbbbaabbbbbaabaaaaaabaaabaaaaabababbbbabaaaaabbbbbbaabbabaaaaabbbbbbbbbbbbabbbbbbaaabbbbaabbbbbaababaabbaababbbbaaabbaaaabbabbaabbbbbbbabaaababbbbaaaaababbaabababbabbabbaaabababbababbbaabbbbbbaabababbababbbbabbabababbaaaaabaaabaaababbabaaabaaabaaabbbaaaabbbaaaabbaabaabbbbabbbbabbbaabaababbababaaaabbbaaaaaaaaaababaaabbbbaabbaababaaaaabaaabbaabbbbababbaaaaabbbbabbababbaabaaabbaabbbaaabbbbbbabababbaabbbabbbbbaaabaaaaaaababbaaaabababbbaaababbbbbbaaababbbbaabbbabaababbaaabbbbbbaaaabbababaaababbaaabaaabbaaababaaabbbbabbabbabbabbbaaabbbbbbababaaaaabbabbbabaababbbabababbabbbbaabbbbbbbbbbaaabbbabbabbabbabbababaaabbaabbabbbbbaaaabbbaabaaabbbaaaaabababbbaaaabbbabaabaabaabbbbaaaaaaaabbaabbabababaabbabbbbbaaaabaababbbabbababaaabbbabbaabbaaaaaaabaaabaaabbbabaaababbabaababbabbabaabaabaaabaaabbabbaaababbbbabbbabbbbbbbbbbaaaabbaaaabbaaaabbabbabaaabbbbaabbbbaabbaaaaaabbaaabababaabbabbaaabbbababbbabbbbabbbaabaaabbaaaaaaabbbabbabaabbaaabbaabbaaaaabbababaabababaabbbaaabbbaaaabbbabaabaaaababaaaaabbabaaabbabbbbbaabbaaabbbbabaaababaabaaaaababbbbbbaabababbbaabaaaababbbaabbbbabbbabbaababbbabbabbaabbbbabbbbaababbabbaabbaaabbabbaaababbaaaaaaaaababbaaabbbbaaabbabbaababaabbbaababbabaabbabbaabbbbbaabbabbbbbbbbabbaaaaaaababbbabbbbabaabaaaabababbbbbbbbbbbbbbababababaaaababaabbbbaaabbaabbaabbbbbababbabbababbaabbaaaaabaabbaaabbbbbbbaaabbbbbababaaaabbbaaaaabaababbaaaabaabbbbaabbbbabbbbaabbbbabaababbbbbaaabaaaaaaabaabababbbaababbabaaababaaababbaabbabbbbaaaabaaaabbaaabaabaabbbaabbabbaaaabbbaaaaabbaabbaabbaaaababaabbbabbbaaababbaabbabbbbaaaaabbbbababaaaaaabbbbabaabaabaababaabbabbabaaaaabbaabaabbaabbbbbbbbbbabaababaabbaaabbabbbbbbbaabababaababbbabaaabaaabbbabbabbbabaabbbababbaabbbaaabaaaaababababbaaaabbabaaaaabbaaababbabbaaaabaabbabaababbaababbbbbabaaaaaaaaaabaaaabbabbbaabbaaabbbabbaabbbbbbabaabaaabbaaabbabbabbbaaabbaabaaabaabbbbbbbbaaababbbbaabbbaaaababbaabbabbbaaaaaabbbabbbabbabbaaabaababbbbbababaabbbaaaabbbaaaabbabbbabababbabaabbabaaaabbbbbaaaabbabbaaaaabbabbbbbabbaaabbabbaabaabaaaabaabbababbbbabababbbbbabaaabaaaabbabbbbbbbaabababbababaababbbbabbbbbbabbbaaabbbaabbbababbbbabaaaaaaababababababbaabababbabbbbbababbaabbbbaaabbbabbabbaababababbaaaaaabbbabbbaabbababbababababbabbababababbaabbaaaababbabaaabbbaaaaaaababbabbbaabbbaaaababbbabbbbabababbabaabbabababababaabaabbbaabaaabaabbaabbbaaababbbaabbbbaaababbbbbabbabaaaaabbabbbbbaaaaabbbbbabbaababbabbbaaaababbaaabbbababaaabbbabaaaabaabbbaabaabbbaaabbbbabbbbaababababbababaabbaaaaabbaabaabbaabbabbbabbbaabbbaababaabbaaaabbaabbaaabbabbabaaabbbbbbbbbbaabbabaababaaababaaaaabbbababbbbabaabaabbbbbbababbbabbbabbbbabbbaaabbabbabbbbbbaaaabbbbbababaaabbababbbaaaaaaabaaabbababbabbaaaaaaaababbabababbbbbbabbabbbbbbbaababaaabbabaabbbbaaabaabbaabbabbaaaaaaababbbbbbaaabaababbbbaaabbabaabbaaababaabbbbbabaabbababbbabaaababbababbaaaaaabbbbabbbabbabaabaabbabaaaabbbbbbaaaaabababaabaaabbaaababaaabbabbbababbaaaababbaaabaabbabaabbbaaababababbabbbaabbaabbbbbbbbabbbabbaaaaaaabbbaaaabbbaaababbbbaabbbbbbaabbabbabaaabbbabbbaaabaabbaababbbbababbaabaaaabbbaaaaaabbabaaaaabbaaaaaaabbbbaabbbabbaaabababbbbbaabbabbbaaababaabaabbaaabbaaaaabbbabbbaabbabbaababaabababbbbaaaabaababbabbbaaababbbabbbbaaabbbbaaaaaaaaaabbbbbababbaaaabbbaaabbbbbabbaaaaabababbabaabbabaababbbbbbbbbbaabaaabaaabbababbbbababbbababaabaaaabbbabbababbabbabbababbbaaabbbababbababababaabbbaaaababbaabbbabbaabbbabbaaabbaabaaabaabbabbbaaabababbbabbbbaaabaaaabbbbbaaabaabbbaababbaabaaabbbbabbbabaaaaabbabbabbabbabbbbaababaabaaababbabaaabababbaaababaaaaabaabbbbabbbbbbbaaaababbbbabababaaaaabbbbbbbabaaababbaaaabaaaaaababaaaaababababbaaababbabbaaabaabbbbbbaaabbaabababbbaaabbabbbbabbabbabaabbaababababbbbabaaaabbaaabaabbaaaaabbaabaabbaabaababbbbbbbbaabaaabbaaaabaabbbbabbabbbaabbabbaaaababbbabaababbbbbbbbaaababbaabbbbbababaaabbbabbabaaabbaaaabbababbbaaabaabbaaaabaaaaaabbbbabbbabbbaaaaaabaaabababbaaaaabbbabababaaaaabbbabbabbbaaaabbabaaaababbaabaaabaababaabbbabbbbaabbabaaaaababbbaaabbbababbbbabaaaaaababbbabababaaabababbaaababaabbbbaaaaabaaaabbbaaabaaabbaaaaaaaabaababbbaababbaaababbabaabbaabababaaaabaaaabaabaababbaaaaaaaaabababbbbababbbabaaaaaabbaaabbbbbabbbbaabbaaabbbababbaaaabaabaaaabbabbaaaabbaaabaaaabababbaaabaabaaababbbbaaabaababaabbaaaaabaabaaabaaabbaaabaabaaabbbabababbaabaaabaabbaaabbaaabbbaabbaaaababbabbbbababbbbabaabababbabbbababababbabbbbbbaabbbaababbbaaaaaaaaaabbbaaaaaabbabbabbbabababaababaabbaaaaabbaaabbbbaabbbaabaabbaabbabbababababaaaabbbbabaaabaabaaaaabbbbaaaaaabbbabbaaaaaabbaabbaaaabbaabaabaaabaaabaaabbbbababbbbabbbbaabbbaaabbaaaaaabaabbbaabbbbabbababbaabbabaabbaabbabaabaabbabaababbbbabbababaabbabbaabbbbbbaabbbaaababbbaabbbaaaaabbaaababbbabbaabbabaaabaabaabbaabbbaaabaabbabababbabaababaaababbbbabbabaaaaababaaabbbbababaabbbbbbabaaabbaaaabbbbabbabbbbbabababbaabbabaababbbbbbbaabbaababbababbabbbbabbaaabaaaaabbabbbaabbbbaababbbabbbbbaaaabaabaabbbbabababbbabbbaabbbabbababbaabaaaaababaababaaaabbbbbbbabbbbaabbaaabaaabbaababbbabbabbbaabbaaaabaaabababbbbabbaabbabaabaababbaabaabbabbbaaabbaaabaaaabbaabababbbaaaaabaaabbbabbbaababbaabbbbaabaabaaaaabaabbbbabaababbbbaabababaaabaabaabbababaaaabbaabbbababbababaabbbbbbabaaabbaaaaaabaabbaaaabbbabaabbbbbabababbbabbbabbabbabababaaabbbbaabbaabbaabababababbbbaaabbabababaaaaabbbbaaabbabaaabbaababbabbbaaaaaaaabbbbbbababbabbaabbbaababaaaabaabaabbabbabbbbbababbbbbabbaabaabaaaabbaaaabbabababbaabbbbbabbaaaabababababbaaabbaababaaaabbababbbbaaaabbabbbbababbabaababaaaaaaabababaaaababbbbbbbbabbaabaabbbbbbbbbabababaabbbabbbaaabaaababaaabbaababbaaabbbabbaaaabaaaaaaaabaaabbbbbaabbaaababbbababbaabbaaaaaaabbbbbbababbbbbabbbbbbabaaaababbbbabbbabbabaabaabbaabababbbbaaaaabbbbabaaaaaaaaaaabaaababbbaabaabbabbbbbbbbbaaabbbbabaaaabbbbbaabaabbabbbbbbabbbbbaabaaaaabbabbaabbbaaabbaabaabaaaaaabbbabaaaabaaaabaabababaaabaaaaabaaababbabaaaabbaabbabaaaaaabbaaababaaaaabbbbbbabbaabbaaaaababaabbbabbaabaabbbbbbbbbababbababbbaabbababbababababbaababbbaaabbbaaabbaaababbabaaaababaaabbbaaabbbbabbabababbbbbaabbabbaabaabaabbbbaaabbbaaaaabbbaaaabbbbabbabaabaabbbbbbbabaaababbaabbababbabaaabaabaaaabbaabaabbabbbaaabaaaabbabbaabbbabbabbabaabaabbbbabbabaaabbabbbbbbaababbababaababbabaaabbbaabaaabaaababbabbbbabbaaabababaaabbbaaaabaabaabaaaabbababbbbabaabaaabaaabbbbaabbbabbbabbbabaabbbbbbabaabaaababababbbbabbbaaababababbbbbabaaabbbaaabababbaaabbbaaabaabbabaaaabbbaaabaabbbaababaababbabaabbabaabaaaabaabaabaabaababbbbbbababababbbbabbbabbbabaaaaaababababaaaaaaaabbaaababababbbaaaabbabbabbbbbbbbabbbbbbbabaabbabbbbaabaabbaabaaabaababbbaabbbabbbbababaabaabbaaabbbaaaaababbbbbaaabbbabababbbabaaaababababbbbaabbabaaabbaabaaaababaaaaaabbaababbabbbbabbbaabbbbabaaabaaaababababbbbababababbabaabbaaaabbbaabbbabbbbbbbababbbaaabbbbabbaaaababbaabbbaaababbaababababaabbaaaaababaaabbbbbabaaaaabbbabbababaabababbaaabbaaaaaababaabaabaaaabbbbaaaabaaaaaaaaababbaabaaabbaaabbbaababaabaaabbbbaaaaabaaaaaabaabbbbaaaaaaaaaabbabaaaababbbaaaabbabaababaaaabbaaabaabbbbbaabaaabbbbaaaaaaaaaababbbabbbaaabbbaaababbabbababaaabaaabaaabbaaaabaaabbbbbababaaabbbbbababbaabbabababaabbabbababaabababbabaaababbabbbaaabaababaaaaabbabbababababaabbbbaaaaabbbbabbbbabbaaaaaabbabbabbabaababaabbbbbaababaabaaaabbababaababbaabbabbabaabbaaabaabbabbbbaaababbbaaaabaabbbaabbaaaaaabbbbaabaaaaaaabbbbaabbbabbabaababbaaabbaaaabbbbbaabaabbbabbaabaaabbbabbbabbbbabababbbbbbbbaabbbbabbababaaaaabbababbaaaabbaabbabbbaaaabbbbbaaaabababaaaaababaabaaabbaababbbabbbabaaaabbaabaabaabaaaabbabbbbaaabaaaabababbbbaaabaaabbbbbbaaabbababbbabaabbbaabababaaabaaaababaabbbaabaaababbabbaaaabbbabbabbabaababaababbaabbbaaabbbaababababbababaabaaabbaaabbabaaaaaaabaababbababbabbbbaaaaaabaabbbbbaaaaaaabababaabaababaaaaabbabbababbaaaaaabbbaaaaaababbabaaabbaaaaaaaabbaababbaaabbaaaaaaababababbaabbbaaaabbabbaaaaaabaabbababbbabbbaabbaabaaaababbbaabababaaaaaabbbbbababaaaaababbbaaaaaabbaaaaabaaaaaabbbabababbaabaabbbbbaabbbaaaaabaababaabbabaabbbbababbababbaaabbbbbaabababbbaaabaaaabbbaaaaabbbbbbbaabbaaaaaabbaaababaaabbbbaabaaaaaaababbbbbaaabaaaaabaaaaabbabbbaaaabaabbbaaaaabbbaabaabaababaaaaaababbbbbaabbabbbaabbabbaaabbbbbbababababbaabbbbbbbbaabbabbaaabaaabbbabbaaabababaabbaabbabbbaaaaaabaabaabababaaabbbabaabbbbbbaaaabaabbbababaaabbaabaaababababaababababbabaaaaabaaabaababbabbaaabbaabbababbbabbbbabaabbabababbaaaababababbaaabbababaabbbaaababbbbaabababaaabbbbbbbababbbabbaaaaaaaabbaaaaababbaabbbbabbbaabababaaaaaaaaaabbbaaabaaabbababbbaaababbababbbaabbaaaaababaabaaaaababaabaaaababaabbababbabbabbbabaabbbbaababaabbbaabaaabbabababbbaaaabaabaababbbbbabababbaaabaabbbaaaababbabbbabbaabbbaabbbaabbabaababaaabaabaababbaababbbbaaabaabbabbaabaaaaababbabbabbbabaaabaababbaabbbabbabbbbababaabbaabbabbabbbbabbbaabaabbbabaaaaaabbbbbababaababbaabbbaabaabbbabbabbaababaaabbbbbbbabaabbabbabbaababbabbaaaababaababbbbaabaaaaaabbaababbbbbbaaabbaabbbaabbaabbabbaababaaaaabaaaabaabaabbaabbbabbbbbaaaaaabbababbaabaaaaabbabbbabaaaabbabababbbabaabababbabbabbbabaaabaaabbaaabababbbabbbabbbbbbaababaabbaababbbbbbbabaaababbabbbabbbbbabbaabbbaabbaaabababbbaabbbaabbbaababbbbbabbbaabbbaaabaaabbbabbaabababbbbbabaaaabaabbabbabaabbaababbaabbabbbabbaaabbbababbbbbabbbababbabaababbbaabaaaabaaabbabbbbbaaabaaabaabbaaabababbbbbbbbababaabaaabbaaababbababbbaabbbabaabaaabbbabaabbbaaaabbababbaaaababaabbabaaaaabbabbababbbaababaabbbbabbabbaaaabbbaabbaabbbbababbbabbaabbaaababbbabbaaabbaaaaabaaaababbbaabaaabbabbaabaababbbbaababaaabbabaaabbaabababbaabaaababbbabbabaaaaaabbbabaaabaaaaaabbbaababaabbababbbbbbbbaabbaabababbaaaaabaaaabababaabbabbbabbbaabbaabbbbaaaaabbbbabbbbababaaabbbbaabbaabbbbabbbbbbbaababbbaaababbbbbabaabbbbbaabaabbbbaaabaababbabbbbbaababababbababaabbababbababaaababbbababbbbbbbbaaaabaaababbbbbabaaaabbbabbbbaaabababbbbbbaabbaabaababbaababaaaaaaaaababaaaabbbaabaaabbaaababbbabababbabbbbbbbaaaaaaabbabbababaabaababbaabbbaabbaababbabbbbaaaaababbaaabbbbbbabbabaaabaaababaaababbbbaaabbbabbbaabaabaaaababbbbabbbbbaabbabaaabbbabbbabaabbaabaaaababababbabaaaaaaaababbaabbabbaaaababbbbbabaaaabbaaaaabbbbbaababbbabaaaaabbabbabaabbbaabbaabaabbabbaabbabababbabbbbabbbbabbbababbbbabbbbbaaaaaabbaabbbaaaabaaababbbbbaaaabbaabbaaaabaabbaabbbbbbbaabbbbbbbbababbbbbaaaabbbbbababaaaababaababbabbbbbaabbbbbbabaabaabbbbbaaabaababaabbbbabbabbbabaaaaababbbbabaaaaabaabaababaaabaababababbbbbaaabaabbbbabbbbababababbbbbabaabbbabbbbbbbaabbabbabbbabbbabaaabaaaaaaababbabbbbbbaabbababbabbaabaababbbbaabaababaabbbbaaaaaabaababaaaaabbbaabbaababbaaababababbbbbbabaaaabababbabaababaaaaaabababaaaaaabbabbababbbbababababbbaabababbbaaaabbaabbababaabbbabbbbabbbbbbbaabbabababbababaaabaaabbbabbbbbaaaaabaabaaabbbbbabbababbbaaababbbababbabbbabaababaaabbbaaababbbaaaaaaaababbababbabbbbaababbabbababaabbbbbbaabaabbbbbaababbabbbaabbbbbbbbbababaababbbabbbbbbbbbbabbbbbabbbabaaaabaaaaababaaababbaaaababaabbaaababaaaabababababbbabbbaaaabbbabbbabbaabbaabbbaabaaaaaabbababbabaabaababbbbbbaababbbbaaabaababaabbaabbbabbabaaaabaababbbabbbabbbbaaaaabababbaaaaaabaaaabaababbbbbbbbaabbbbbbbaabbbaabbabbabaabaaabbbabaaaabbaaabaabaaaabbaababbbbaaababbbbababbaaabbbbaababbabaaaaabaaaaaabababbaabbaabbabaaabbabbabbabbbaabbababbbbaababbaaabaababaabbaaabbaaabbbaabaabbbbbaaabbbabbababbbbbbbbaaaaaababbbababababaabaaaabaababbbabaababbbaaabaabbbaabababbbbaaabbbbaabaaabbbbbbaabbabababbbbaaabaabbaaaaabbaababaaababbbbaabababaaaaabbbaaaabbbabbababaaaaaabbbababbbbbbaaaaaabbbbababbbaaababbbabbabbaaababbabbabaabbbbbbbaababbbababaaaaaaabbaabaabababbbbababababbaabbabababbbaaaaabaaaabaabbaaabbbaaabaabbbaaaabababaaabbaaaabbabaaaabaababbbbabbaababbababababbbbabaabbbaaaababaaaababbbaabbaaaababbbbbaabbababbaabbaaaaaabbabbabaaabaabbbbbaababaabbaaaaaaaabbaababbbbbabbaabaaabbaabbaabaaaaaababbbbaaaabbbababbaabbaabaabbbbbbbaabaabaabbbbaabbababaabaabbbabaaaabaaaabbbbbbbaaabaabbbababbaababaabbbaaaababbbbbaaabbabaabaabbbbaaaababbbbbababbbbabbaabbbabaababaabaabaabbbaabbababbaaabaaababaabbbbaabbbbabaabbbbbbbbaababbbabababaababbbbbabbababaabaabbabaaababbaabbababbbbbbbbbaaaaabbaabaabbaabbbaaaaababbabbabbaaaabbabaababbaaabababbaabbbaaabbbbbbbaabaaabbabaaaaaabbabbabaaaaaabbbaabbbbbababbaaaabbabaabbbabaaabaabaabbbaaabbbaaabababbaaabaaaaababaabbbbbaababbabbbaaabbabbbbaaaabbaabaabbbbbbaaabbbbbaabababbbaabbababbbbaabaabbbaabbaaaaababbbbbbabaabaaabaaaabaaabaaababbaaabbabbbbbabaabbbbaaaaaaabaabaaaaaabaabaaaaabbbaabababbbbabbaababaaaaaaabbaabbbbaabbaaaaaaaaaabaababbbaaabbabbbbbaabbaaaabbabbbbababababbbababaabbaaaabbaababbaaaaabbbbabaabaabbbabaababbbabbaaabbababbabbaaababaaaaabbaaabbbbbaabbbbbbbbbbaaababababaababbbbbabbbababaaabbbabaaaababbabbaabbbbbbabaabbbbabaaaababaaabbaaabbaaabbbabbbaaababbaaaaabababbbaaabaabbabaabbaaababbaabbbbbabbabbaabaabaababbabaaaaaababaabbabbbabaaababbbabbbabbbaabababbbabaabaabababaaabbbababaaabbaabbababaabbaababbabaabbaabbababbbabababaaabaaababaaaababaabaabaaaabababaaabbbbaabbabaabaaaaaaababababbbababbbaaaaaaaaabbbbabbaaabaabaababbaabbbbbababaaabbabbbbaaabbbababbaaaabbabbabbaabbaabaaabbaaaaabbbbbbababbabbabbbbaabbbaaabbaaababaabbabababbbabbbbbabaaabbbaaabbbbaabbbbbaabbbaaaababababababbababbbaaabbabbaaabaabaaabbabbbbbaaaababbbaabbaaaaabbaaabbaabbbbaabbaabbbbabaabbbbabaaaabaaabababababaaaababaabbaabbbaabaababbaaabbaaaaaababbbbababbabbabaabbaabbbaaaabaaaaabaaaaaababaabababbbabbbbbbbabbaababaaabbaaaababbbbbaaaaaabbbaababbbbaaaabbabbbbaabababbbbaaabbbaaababaaabbbbabababbabbbbbabababaababbbbbaababababaababaabbbaabbbaababbabbaaaabbbaabbbaabbbbbbaabbabaabbbababaaababbbbbbabaaaaabbabbbabaaabbaaabbababbaaaabaabaabaaabbbabaabbbbabaabbaabbbbabbaabbbbbaaabababbabaabbbbbabbbbabaaababbbabaaabbabbabbbababaaabaabbaabbbabaaabbaababababbababbabaabaaaababaaabaaabbaaaaaaabbbbabbabaabaaaaaabaaaabbabbabaabbbbaaaabbabaababbabbbbabbaabbabaaaaaabbbaaaaaaabaababbaabbaaabbaaabaaabaababbabbbbbaababbaabaabbbabbbbabbabbabbaaabaaaaababbaababaaabaaabbbaaababbaaaababbbaaabababbbbaabaabbbbaabababaabbbbbabbbabaaaaaaaaaaaabbbbbabaaabbaabbbbbbababaabbbabbbaababbbbabaaaaaaababababbbaababbbbabaaaaaaaaaabbbbabbbbabbbaabaababaaabbbababababbbbbbbabaabaaaaaaabbbaabbabaaaaaabbaaaaabababbaaabbbbaaaabbaaaaababaaababaabaaaabbababaaabababababbbaaaabbbbbaaabbbabbaabaaabbabbbbabaababbbbbbaaaabbaaabababbaaabbbaaaabbabbabaaaaabaabbbaabbbabbabbbbaaababbabaabbababaaabaaabababbaabbbbabbbbaaaabbababbaabbbabbaabaaabaabaabbaabbbbbbaabbbaaaabbbaaaaabaaabababbabbbabaaaaaaaaaaabaabbbabaaaabbaabaababbbbabbabbabbabbbbbaabbaababbabbbbaaabbaaabaaaabbaaabbaabbabbabbaaabbabaabbbbaaaaaabaabaaaabbaabaabbababbbaabbababbbaaaaaabbabbbbabaabbaaababababbababaabbbaabbbbbbaababbbaabaabbbaaabaabbbaaabababbbbabbabbbbbaababbbbaabaabbbabaaabbaababbabbabaaaaabaabbaaabaaabaabbbbbaabaaaaaabbabbbaaaabababaababbaaabbbabababbaabaaababbabbbaababbaaaabbbaaabbbabbabbbabbbbbaababaababbbbbbaabbbbbbaaaaabbbaaabbbabbabbabbbabbbbaabbabbbbabbbabbbaabaababaabbbababaabaaaabaaaababbaaabbaaaabaabaaabbaabaaabbbaaaababaaaaaaaaaabbbaaabbaabaaaabbbbabbbabbaabbbabaaaabbbbaaabbaaaabbabaaabbbbbabaaabbbbbbababbaaabababbbbaaaabaababaaaababaabbaaabbabbababbabbbbbbbabbbbbbabaabbaabaabbbabbaaabbbbbbaabbbabbbabaabbbaabbaabaaaaababbaababaababaabaabaaaabbababbbbabbbabbbbbabaabaabbbabbbaabaaaababababbaabbbaabaaaabababbababbabaabbabbbaaabaabababaaabbabaaaaabaababbbbababbaaababbbabbbbbbbaaabbbaababbaabaaabaabbbbbbbbbbaaaaabaaaaaaabababbbbbaabbbbbbaabbbbbaaaabbbbabbababbaaaabaaaabbbbbabaaabbabbbbbbbbaabbaabbabababbaaaabaabbbbababbaaaaaaabbabbababaaaabaabbaababbbaaabbaababbaabaabbaaabababaaabababbbbbbbaaaaaaabaabaababbbaaaabbbabaabbbaabbaaabababbaaabbbaaababbbbaabbbbaababbbaababababbbabbaabaabababababbabbbbabbbaaaabababbaabbabbbbbbaaaabaaabbabaababbbababaabaaaababbbbaabbabbbbaaaaaabbaaaaabbababbbbaaaaaaabababbaaababbbaaaabbbbbaaaababaabbbbbbbbbaabbbabbaababababbaaabbbabaaabbbbbbbbbabbbabbabbbabaaaaabbaabaaabbaabbbbaaababbbabbbbabaabbaaaabbabbbbaaabbbbaabbbbbaabbbbbaababbaaabbbbabbaaaabbaaaaaaabbaaaaabbabbbaaaababaaabaaaaaaabaabaababaaaaaabaaaaabbaabaaaaabbbabbababbbbbbbabaaababbaaababaaaababaaabbaaabaabbbaaaaaaababababbbabbbaaaabbaabaababababbbbbbaababaaaaaabbaababababbbaaabaaaababaababbabababbaabbbbbbbabababaaabbababbbaaaabbaaabaaabbabaabababaaaaaaaabbbabaababaabaaabaaabbbaaababaababbbbababbbaabbbbabaababbbbbababbbbaaabbabbababaaabaaababbbbbaaababbbabaaaaaaababaabaaabbbbbbbaabaaaaabaabaabbaaabbaaabababaaabbbbabbaaaabbbabaaaabaabbabbabbbbbbbaaaaaaabaaabaaaaaaaaabaabbaaabbbabababbaaaabbbaaabaabbabbaabbbbbaaabababbbaaaabbabbaababbabbaaaabaaabaabaabbababbbbbbabababbaaaaabaabbabaaabbbbbbabaabbbbaabbaabbbaabaaababaaabbabaabababababbbaabababababbbbbbbabbabaabababbaabbbabbbbaababbbabbaaaabbaaaaababbbaaaaababaaaababbaabbbbbbababababbbbabbabaaaababaaababbbabaabbbbbbbaaabbaabbaabbbbbbabbbbbaaaaaababaabbbbbbbbbbabbababbaabbbaababbbbaabaababaabbbbabababbaaabbaabbbbbbaabaaabababbbbaabbbabbababbbbbbbaabbbbababaaaabbaabbbbaaabbaaabaaabaaaabbaabbbabaababbababbaabaabbbbabaababaaabaabbaabbaabbaaabbbbabbabaaaaababaabbabbabbabbbbabbabaabbababaaaaaabbbbbabbbababaabaabbaaababbaaabaaabbbbaaaaaabbabbbbabbbbabbaaabbabaaaaabbbbbbbaaaababaababbabaabababbaaabbababbaaaaaaabaaaaaaaabbaaaabaabbabbbbabbbabaaaaabbbabbbabaaaabaabbbaaaaaababbbabaabbbbbaabbbaababbbbabbbabbabbabbbbbbbaaaaabbabbababbabbabbababbabbbaaabbbbbbabbbbaaabbbbbaaaababbabaabbaabaaabbabbbaaaaabbaaabbaaaabbabbabbaabaaaabbbababababbaaaaaaabbbabbbbbaaabbbbaaabbbabbabbaabbababbbbaaabaaaaaabaabbababaabaaaaaaaaaaabbbabbbabbbaaaabaaaabbabbbbabbbaabbabababbbbabababbaabababbaabbbbbaaaabaaaaabaaaaaabaabababbababbaabbbabbabaabaabaaaaababbabbbaaabababaababaabaaaabbabbbbbabaabababbaaabababaabababaabaaaaabbaababbbabbbbbabbabbbababbbaaaabbabbbbbabababababbbaaabbababaabaabaabaabbaaaabbabbaaabbaaaabbaaaaabbbabaabaabbababbbbaabbbabaabbabaabbabbbbbaabbbaaaaabababbabaabababaabbaabababbabbabaaaaabaabbbabaabbbaabaabbbbaabaaaabaabababaaabaaaabaabbabbabbababbbbbabbabbaaaababbbabaaaabaaabaaaaabbabaaaaaaabbaaaabaaababaaaababbaabbbbaabaaaabbabbbaaabaabbbaaaaabbbbabaabbaaabbbabbbbbbbbbabaaaaaaaabbabbabaaabaabbbaabbabbbabbbbbaabaaabaaabaaabbabbabbaababaaababababbbbbaaabbbabbaababaababbabbbaaaabababaabaaaababbbbaabaaababbbbbbbbababaabbabaabbbbbabbaabaaabbbbabbabbbaabaabaaabbbababaabbbbabaaaabbabbbbbbababaaaababbabaaaababbaabaaabaaababababaabbbbaaabbaaabbabababbabbbbabbabbaabbaaabababbbabaabbbabaaabbaababaabbabaaaaaaabaaaabaabbbbabbaaaaabababbbabbaabaabbbabbabbbbbbbbabbbbbaababbaababaaabbababbabbbbabbaabbabbbabbabababbbabaabbaaaabaaababbbbababaaabbaaaaaaababbbbbaababbbbabaabaabbabbbbaaababbabababbababbbaaaaabbbbaaaabaaaaababbaaaabaaababaaaaabaabababbbabbaabbaaaaaabbbbaababaabbaababbbababbbababaababaabbbbaabaaabbaabaaaabbbaabaabbbaaababaaababbabbbbabbbaababbbbbaabbbbaaaaaabaaaaaabaabababbababbabaaababbbaababbabbaaaaabbbaababbbaaabababaaabbaaaaaaaaaaabbaaaaabaabbbbababaababbbbaababababbaaababaaaabaababaabaababbaabaaabbbabbabbaababbaabbaaabaaaabbbaaababbaaaaaaabbaabaaaabbbabbbababbbbababbbbbababbaaabaabaaabaaabbbaaabaaabaaabbbaaaababbabaaaaaabbabaabbaabbabaabbbbabbbbaabbaaabaaabbbabaaaabbaaabbabbabbabbaababaabbabbaababbbbbabbabababbbbaabbbbaaaaaabbaabbaabbbbaaabbbbbabbbbaabbabbbabbbababbababbbbbbbabbaaabbabbbbbbaaaaaabbbbbabbaaabbabbaabaababbbaababbaabaaaaabbaabbbabbababaababbaabbbbaaaabaabbbabababbabbbbaabaaabbaaabbbabaaabbbaabbbbaaababbaaabaaaaaaaabbaabbbbbabbaababbbaabbbbabbaaaabbababbbabbabbbaababbaabbbbbbbbbbaabbbbababbabbbaaabaabbaabbbabbbbaaaaaababbbaaabbbabbaaabbabbbaaabbaabbbbbabaabaaaaabbbaaaaabaabaaaaaaabababbbababaababbbababababbbbbbabaabbabaaababbaabaabaabaababaaaabaaabbaaabaababbabababbbbaabaabaabbaabbbabbaaaaaabaaaabaabaaabbaababababbbbaaabaaaababbbababababaabbbbbababbbabaaabbbbbbabbbabaaaabbababbaaabaabbaaabbabbbabbbbbaaabbbabbababaabaaaabbbababbbabbabaabbbabbbabaaababbaaabbbaaababbbabbaaabaaabaaabbbbbaaaabaabaabbabbaaaababaabaaabbaababaaabbbbbbbaaabaaaaaabbabbababbbbbaabaabaaaaaaaaabbbaabaabbaaaaabbabbbabbbaaabbbabbabaabbabbbaabbaaabababbaabaaaabbabbbabbbaabbbaabbbabbbbbabbaaaabbbbbaabaabaabbaaaaababbabbbaaabbbaabbaaabbababbbbabbbaabaaaaaabbabaaaabbaabababbaabaabbbabaabababbabbabbbaababbababaabababbbaaaaaababaaabbaaaabaaaaaaabbbbababbbbbaabaaabbaaaabaabbaabbbbbabbaabaaaabaaababbabbabaaaabbbababbbbabbbbabaaaabbbabbbaabbabaabbbbbbbbbaaabbaabaabbbaaaaabababbabababbabaabaaababbabbaaaabbbbabbbbbbbbbbbaaabababababbbaaaabbbaababbababbabbaaabbbabaabbaaaabaaababbbaaababbababbbbbbabbabbbbbbaabbbbbaabbaaabbbbbbbbbabbaaabababaabbaaabaabbbbabbaaabaaabbbbaabbabbbbaabaaababababaabaaaaababbaabaaaababbbaaabbabbbaaaaababbaaaabbaababbabbbbbabaabbaaabbaabbaaabbbbbbbabbaaabbabbaabbaaababaaaabbbabaabbbaababbaabbabbbbabbabbabababbabaabaaababbaaabababbbbbbaabbbaabbbababbbaabaaabbbabbaaaabbbbaabaabaabbaaaabbaabaabbbbabbaabbaabaababbaabaabaaaabbbbbbbabbbaabaabaabbbbbbbbbabaaababaabaaabbabbbabaaababbbbababbaaaaabbbaababaabbaaabbaababaabbabababbaababaaaabaaaabbaababbbbaaabaababbbbaaaaabaaaababaaaaaaaabbaaaaabbbababaaabaabbbaaaaaabbabaabbababaaaabbbaabbbbabbbababbaabaababbbaaaaabbaaaaaaabaaaabbabbbabababababbbaaabbabbbaaaababbbbaababbaaaaabbabaaabbaaaaabbbbaabbbaabbababaaabbabbababaabaaabbababaabaaabaababaabaabbababbaaabbbbabaaababbaababaaabababaaababbbaabaabaabbbbbbabbbaabaabbababbbbbaaabbbbaaabbabbbbabbbabaabaababaaababababbabbabbabaaaabaabbabbabbabbabaaaaabababbbbbbabaabbbbbabbbbaaaaaaabbbaabaaababbbbaabbaaaaaabaabbbaabbbbabbbbbbbaaaaabbbbabaabbbbbbaabaaabbababaabaabbabbaaaaabbabbbabbbaaabbaaaaaabaaabaaabbbbaabaaabbbaaabbaabbaaabaaabbaabbabbababbababbbbaabaaaaaaaaaaabbaaabbbbaaaababbbbbaabaaababbbbaabbbabaabaaababbbaaaabbbaabbaaaaaaabaaaababbababbbabbbbababbaabbbbabbaaaababbaaababbaaaabaabaaabbabbaaaabbabaaaaabbbbaababbbaaabbaabaabaabbabbababbaaabbabaababbbaaaabaaaabbaaaababbaaaaaabaababaaaaabbabaaabaababababbabbbaaaaabbaabbaaaaabbabbaaabbaabbabaabbaaababbbbaabbbaaabbabbabaaababbabaaabbbbaaaaabbbababaababaabbaabaaabbbaabbbababaababaaababbaaabaabaababbbbbababbaaabaaabbaaabbaabbbbbbabbbababbbababbbbbbaaaaabaabaabaaaabaabbababababbaabbabaabbbaabbaaaaababbbaaaabbbbbbbaabaaabbabababbbabbbbabaaaabaaaaaabaaaaaababbaabbabbaaaabbbaaaabaaabbbabbabbbabbbbaabbabbabbbaababababaababbabaaaabaaababbabbaabaabbaabbaabbbabaabaabbababbababaaaaaaabaaaabbbbbbbabbaaaaaaaabbbbaabbbbabaababbbbaabaabbbbbbbbabbabaaaabaaaaaaaabbbabbbabbababbaaabbababaaabbbaabbaaababaabbababbbabbabbabababbababababbbbabbabaabbaaaaabaaabbaaabbabbaababbbbbbbbbabbaabbbbbbbbbbbbbaabbbbabaabaaababbbaaabbbbbbabbbbbaaaaaabbbbbbbbbabbababbbababbabbbabbababbaaabbaaaababbbbaabbbaaaabbaababbbbaabbaaaaaaaaabbabbbbbabbbabaabaaaabbaabaabbbabbaaaabababaaabbaaabbabbabbbbbabbabaaaababbaabbabbbaababbabbbabaaabaaabbbbbaaaaaabaaaaaabbbbabaaabbaabbabaaaaaaabbbaabbaabbabaaaaabbabaaaabaababbbbaababaabbbbbababbbbaaaabbbaaaaaabbaaaaababaababbabbaababbabbbbabaaabbabbbababbbbaaababaaaaabbbabbbbbbbaabbaaaaaabbbabaaabbabbabbbbbbbabaababbabaabaaaabbbbbbabbaaaabbabbaababbaabaabaaababbaabaababbbbbbaabbabbabababbbbaaaabbbaabbbaabbaabbbabaaaaababaababaabababbababbabababbabaaaabbbbbbababaaabaaabaaaabbabbaababaaaaabaaaaabaaaabaaaaabbabbaaabaaabbbbaaabbbaabbabababaabbbbabaabababbaaababbbbbaaaabbabbbaaababbaaaabaaaaaaaaaaababbaabbbaaabbabbaaabaaabbaaaaaabababababbabaabbabbbbabbbbbbbabaabbabaabaaaaabbbbaaaaaaabaaabbabbaaabbabababaaabbaaaabbabbabbaaaaabbabbbabbabaaabaabaaaaabbaaabbabaababbababaabbbbbaaabaaababbabbaabbbbabaaababbaaababbbbbbbabbbaabaaabaabaabbbabbbaabaaaaaaaaabbbabbbbaababbbabbabbbaaabbabbabbbbaaaabbaabbabbbbbabaaabaabbaaabaabbaabbbbbaaaababbaaaabbbaabaaabaaaaaaaaaaabbbaabbbaabbbbababbbaababbabaaaabbbbaabaaabbaabaabbbbabbbbbaababbabababbaabbbaaababaabaabbbaabbaaaaabbabbbbabbabbabbbaaabaaabbbababaaabbabababaaaaaaaaaabbababaabaabbabbabbbaaaaabaabbaabbbaaaaaabbbabaaaaababaabaabbaabbbbaababbbabaababbabbbaaababaaaabbabbbbabaaabbaabababbbababaabbabbaaaabbaaaaababbbaaaaaaababbbabbbbabbbbabbbbaabaabbbabaabbbababbbbbbaabaaababaaabababbabaabbbaaabbabaababaabbbbabbbabbabaaabbaaabbaaaabaabbbbabbababaabaaaaaaababbbbbbbbabbbbababbbbbbabaaaaabbbababbaaabaabbbaabbaababbababbbabababaabababbbbbbbaabbbbbbbbbaabababbabaabbaabbabaababbbaababbababbbbbbbabbbabbbbaabaabbbbbbabababbbaabbaabaabaaabbabaabbbaaaaaaabaaabbabaabbbabbbbbbabababbbbabaaaaaaabaabaaaabbaabaaabbbbbbbaabaabaababaabaaabababbabbabaabbbbaaabbaabaababbaabbababbaabbabbbaabbbaaababbaabbaabababbbaaabaaabbabbabbbababbaaabbaaaabbbbbaababbabbaaabaaaabaabbbabbabbabbbabbbbaabaaaaabbaaaabbbaaababbaabbbbbbbbaabaabbbbabbbbbbbbaabbbabbbbbabaabbbbaaaabbababbbbaaababbabbbabaaabbaabbbaabbbbbaabbbababaaababbaaabbabaaaabaabaabaaabbabbbbbbaabbaabbbaabaabaabbbababaaaaabababbabbbabbabbbbababbabbaabaabbbabbaabbabbbabbabbbaaaababbbbaaaabbabbbaabaabbabbbbbbbaaaabababaaaabbbabaabbabbbababbbbabbbbbaaabbaaaaaaabbaaabaaabbbaabbabbbbbbabbaaabbbbbaaabbababbaaaabbaaabbbabaabbaabbabaababbabbabaabaaaabbbaabaaababbbaababbbbbaabbbabaaabbbabbabababbbabbabaababbabbbabaabbbabbaaabbababbbaaabbaabbaaabaabaabbbaaabaaaaababababbbaaabbbbababaabaaabaababbbbaabaaabababbbbaababaabbaaaabaabbbbabbaabbabbabaabaabaabaaaaaabbbbbabbbbbabbbabaaabbaababbbbbbbbaabbbaabababbbaaabaaababaabaabbaabaaabbbbbabbbabababbaabaababaaaaaabbbbbbbaaabbbaabbbaaabbbbaaaababbbbbbbbaabbababbabbabbbbababbbbababbbbababbaaaabababbababababbbababababbbbaaabbbbbaababbabbaabaaaabbbbababaabbbbabbbabbbababbbbbaabaabbaaaabbabbaabbaabaaaabbbabbbbaaaaaabaabbaabbbaaaaabbbaaaabbababbbbabaababbaaabbbaaababaababaabbbababbbabbbaabbbaabaabbbaaabbbabbaaabbbabbbabbabbbbbaabbbaabbbabbaabbbaaaaaabbbaabbabbbbabababbaabbbbaababbaaaabbbbbaabbaabbbabbbababaabbbbaabbaaabaababbabbaabbbaaaababbabbbbbbbbbabbabbbbaabaabaabbbaaabbbbbaabbbbabbaaabbbbbaaaabbaaaaaabaaaaababbbababbbaaaaaabbababbabbaaabbbbaabaaaaababbbabbabbabaaaabbbabbaabbaaaaabaababbaaaabaaaaaabbaaabbababaaabbbababbbbbbabbaabbababbbaabbabababaaabaababbaaaabbabbababaaabaaaaabbbabaabbaabbaabbabbababbabaabbaabbabbbbaaabbaabaabbaaaabaaabbbabbbbbababbbaaaaaaaaaaaabbbbaababaababbababababbbbaabbbbaaaabbaababbaaaabbbbaabbbbaabaababbbbabaabbbbaaaabbabbbbbbaababbbaaabbbaaaaabbabbaabbbaaaaababbbaaaabaabaaabaaabaabababbbbbabbabaababbaabbbbbaabbbbabbbabbbbabbbabbbaabbbababaabaaabaaababaabababaaabbbbbbabaaabbabbbbaabaababbababbbababbbaabaaabbabbbbaaaababaaaabbbbaaaaabbbaabaaaababbaababbbabbbbbaaaaabbbbaabbabbababbbbbabbbabaaaabbaaabbaaabbaababaabababbabbbabaaaababbabaaaaaabbbbabbaababbabbbbbabbabbaaaaaaaabbbbaaaaabbbabbbabaaaaabbaababaabababbbbabbabbbaababbbaaaabbbbaabbabababbabaaaabbabbbbbbaabababbaaabbabbbbaabbaaabbababaaaabbabababbaababaabababaabaaaabbbaaaababaaaaabbbbabbbabbababaabbabaaabbaabbbbbaabaaabbbaaabaabaaabaabbaaabbabbaababbbababbbbaabbabbabbbbbbababbbabbbabbbabbabababbabbaabbababaaababbaaaabaabaabbbbbbbbabbabbbaabbaabbaaaaaaaaabaabbbbabbbabbbbbbbbaabbbbbabbbbbbbbbbbbbabbbabaabaabbbbabbaabbaabbaabaabaabbaabbbbaaaababbbaabababbababbabbabbaababbabaabbaaaaaaabbababbaababbaabbbabbaabbbbaaabbaabbabaaababbaababbaabbabbbaabbaabbbbbaaaaabbababbaaaaabaaabbabaaaabaaaaababaabaaabbbbabbaabbbabbaababbbbabbbabaabaaaababbbaaaaabbaabbaabbaaaaaaabbbabaabbbbbaaaabbbabaabbbbabbaaababbababbaaabaaaaabbbbbaaabbaaababbabbbaabaaaaabbbaaababbababbabaababbabbbbbaaaaaaaababbababbbabbaaaaabbaaaababbbbbaaaabbababaabbabaabbabbbbabaabbbbbbababbaaaaaabbaaabbbaabaaaabbbaaaabbbbabaabbabababaabbaaababaaaababaababaaabbaababaaababbaaabaaaaabaaabbbbbbaaaabaaaabbabaabbabababaaababbbbbaabbabbbbaababbababaaabbabbbbbbbbbbbbbbbabbbabbaabaabaaabaaabbaaabaabaaabaabaabbbabbaabaaaaaabbbbbabaabbaaaababaabaabbbabaababababaaabababaaaaababbaaaaaabbabaaabaabbabaaaaabaaaaaaaaaabbaababbabbbbbbbbbabaabaaababbbaaabbbabaababbaaaaababaaaaaaabbbbaaaabbabbbabaabbbbabbbbababbbaaaaababbabbbbbaaaaabaaabbabbaaaababbbaaabbbaabbabbaababbbbbbabbbaabbaabaabbbabbabaaabbabaaabaabbaaababbababaaaaabaabbabbbbbbababbbababaabbbbbabbabbbababbabbabbaabbaabaaaaabaaaaaababbbbaaabaaabaabbabaabaaabbaaaababbbabaabaaabaaaaababaabbbaaaabbbaabbaabbaaababbbbababbbbabababaaaaaabbaababbbbaabaaabaabbbabbbaabababaabbbaababbabaaaabbaabbbbabbbbbabaababbbaaaabaabbbaabbaaabaabaabbbbabbabbbabbaabaababbbabaaaaababbbbbbbbbbabaaaabbbabaabbababbababbababaabaaabaababbbabababaabbabaaababaababaabbaaaabbaaabaabbbbaaabbabbbaababbababbababbabaabbbaabbaaaaaaabaaabbaabaabaababbbbbbaaaaaaaaaaaabaababaababbaaababbbaaabbbabaabbbbbbbaaaabaaabaabbabbabaabbaaabaabaaabababbababaaaababbababbababbabbaaaabbbaaabbabaaabbbbabbbbabbbbabbaaaabbbaaababbbaabbbbabbbbbaaabaababbabbaabbaaabaabbabbbabbbbababaababbbbbbabaabbbabbabaaababaababbaababbbabaaabbbbbaabaababbaabbabbaabbaaabbbababaabaabbbbbaaabbbbbabaaaaaaaabbaaabaabaabbbaababbabbbbbababbabbabbbaabbbbaababbabaabbabbaabaabaaaabaaaaabbbaaaabaabaababbbbaababbaaaababaababaaabbbaaabbaaabbababbaabbbaabbabbbabaabaaabbaabbbaabaaababbaabaaabbababaaabbbbaaabbbbaabbabbbaaabbaabaaabaaaaaaaabbababbbbaaabbbaaaaaababbbbaababbbbbaaaababbbaabbbbbbbaabbaabbaabbbaaaaabbbbbabbaabbbbbaaabbbbabaaababaabbbbbbaabbbabbababbbabaabbbbaababbbabbabbbbbaababbababbbaabbbaababbbbbbabbbbbababbbbabbababbaaaabaaaababaababbbabbabbabaaaababaabbaaaabbabbaabbbababababaaaabbabaababbabbaabaababbbabbbaabaaababaaabaaabbbbbbabbabbaabbabaaababbaaabaabbbbabbbaababbbaaaaabaabbbbbbbbbaabbbbbbbabaaabbaababbaaabaabbabaabaaabaaaaaabaaaabaabbbababaaaaabbaaabbaaabbbbabbbaabaababaaabaababaaaabaaabbaabbababaaaababbaabaaaabbababbabaabbbbaabaaababaaaaababaaaaaaaaabbaabbbababababababbbbaabbbaaabbaaaaaaababbbbbbbbabaaabbbaaaaaabaaaabababbbbaaabbbababaaaabaabaabaababbbbbabbbaabbbaabaaababaaaababbabbaabaaabbaabbbbabbbabaaabaabbbbbaabbbbbaabaabbabaaabaaabbbbaabbbbbabbaababbbaaaaaabaaabaaababaabbbbaabbaaaaaabaaaaaaabbabbbbbbbaaaabbbbaabaabbbbaabbbbabbbbaaaaababbaababababbbbbabbaababbabbbababaabbbbbabaababbbbbbaaaaaaaaabababbabbaababbbbabbbaabaabbabbaaaaababbabbaaaababaaabaabbbabbaaaabaaaabbbbbbaaaaababaaaabaabbbaabababbbbbabaaabbabbbabbbabaabbbbabbabbbaaabaabbbaabbbaaababaabababbbaaabababaababbbaaaabbbabbbabbbabbbabaabaaaaaabaababbaaabababbababbbbbaababaaaabbbbbbaabbaaaaabbbaabbbbbbbaabbaababaabaaabbbabbabbaaaabbbaabaaaaabaabaababbbababbabaabbbbbbbabaaaaababbaaabbbabababbabaabbabababbbbababababbbabbaabbbbabaaaaabbbbaabbababaabbbaaabbbbbabaabababbababbbaababaaababbbbaaababbbaaaababbbbaaabaaabbbbababbbabaaabbbaaabbbbabaaabbbbaabaaaaaaaaabbabaabbabbbbbabbaabaaaabaabaababbabbbbbbabaaaabbabbbabaaabbbbaaaabaababbbbbbaaababbbbbbbbbbababbbbbabaaaabbaaabbaaaaaaaababaaabaaaaaabbbabbbbbaababbbbbbabbbabaabaaabbaabaabbbbbabaaabbbaabbbabbbbaaabaaabbbaaaaabaabaabbababbbbbaaabbbbaababbbbabbbaabbbaaaabbbbbaabbaabbbbbaabaabababaabaabaaaaaababbaaabaaaaaaabbbaaaaabbbbaabbbababbabbbbbbabbbbaabaaaaaaaabbabbbaabbaabbbabaaababbbbbbaabbabaaabbabaaabaabbbbbabbaaabbbabbbbabbbbabababaabbbbaabbaaaaabbabaabbaaaababaaabbabbbbabbaaaabaaabaaaaabbaaabbbbbaaabaaaabbabaabbbabbababababbbbababaabbbabbbaaaababbbbaabbabbabaaabaaaabaaabbaaaabbabbababaabbbbbbabababbbaabaabaaabaaaababababaaababaabbbaaaaabaaabbbbabbbaaabaabaaabbbbbabababbaaaaabbabaabaabbaabbaabaaabbbbbbabbabbbbbaaaaaabbaabaaaaababbbabbbababbabbbaaaaaaabbaaababbbbababbbaaabaaabbabbbaaabaaaabbabaababaaababbaaaaabaabaaaabbaabbbbbbbbaaaababbbabbbbbababbaabbbaabbbabbbabbabababbaabbbabbaabbabbbbbbbbaaabbaababaabaaaaabbbbaaabaaabaababaabbaababbbaaaaabababbbaabaabbbbaaababaaaabaabbbbbbbbbaabbbabaaaababbaaabbbabababbabaaabaaabbababbaaababbabbabaaaaabbbbaababbbbaabaaaababbbbbabaaabbabbbbaabaaaaaabbbbabbaabbbbbbaabbaaaaaaaabababaaabbabaaaaabaabbbaaabbbbbaabaaabbabbaabbaabaaabbaaaabbabbabbbbaabaaababbaaababbbbbbabbbaaaabbaabbbaaababaabbbbbabaaabaabaaabababaabbbbaabababbbaaaabababbbabaababaaabaaaaabaaaababbbaaabbaabbaabbaabababaaaabbaabbbbabbaaaabbbababbaabbbbbbaaaababbbabaaaabaabababbaabaababababbbbabaabbbabbabbaaaabbabbababaaabababaaababaabbbbabbabbbbbaaaabbbbbbaaabbbabbbbaaaaaababaaabbabbbbbaaaabaaaabbbabbaaaaababbbabbbabbbabbbabbaabbbbbbaababbbbbbababbababbbbbaabbaabaaaaabbbaaababababaaababbbbababaaaabaabbaaabbbbabbaaaabababaaababbaabbbbbbbabbaababbbaabbabababbaaabababbaaaaabbaaabababaabbaabbaaaaaababbbaabbaabaabbaababaabababbbbabbaaaabaabaaaabababbaaaabaabaaabbbaababababbbbabbabbbaaabbaababbbbabaababbbaaaabbabababababbabbbabaaaaaabaabbabbbabaabaabbabaaaaabbbbababaaabaaaaabbaabaaabaaabbabaaaaaabbbbbaaaaaaabbababbaabaabaaaaaaabbbbbabbbbabbabaaababaaaaaabbbaaabaaaaabbbababbbababaabaababaababbbbbabbaaaaaabbabbabbbbbababbababbbbbaaaabaababaaaababbbabaabbabbbaaabbbaabbabbaabbabbaabaabaaabbabbabababbababbbbababbbabbaabababbbbbbbaababbbabaabbbbbbabbabaababbbbbbaaaabbbbabababbbbaaababbabbbababaababaabbbbbaaaabbbaabbbaaaaabbbaaaaaabbababaaaabaabbbabbbaababbbaaababaabaabbbbbababbabbbbaaababababaaaabbbbabababbabaaabaaaabbbbabbabbaaabbbbabbabbabbbabaabababbbabbbabbababbbaaaaaaabaaaaaabbaaaabaababbbaabbaaabaaabbbabbbabbbbabbbbabbbaaabbbaaabbbaababbbbbbabbbababaaabbbbaabbabbabbababbaabbbababaaaaaaabaabaabbbaabaabbabaaaaaabbaabaaabaabbbbaabbbaaaabbaaaaaaaaabbaaaaaababaaaaaaabbbbabaaaaaabbabaaabaabbbbbabaaabbababbbbabaabbabbabbaaabababbbabaababbabaababbbbabbababababababbaaabbaabbaaaaaaabbaaabbbbbaabbaabaaaaabbbabbaababbabbbbbabbbaaabbaaabaaaaaabababbbabaababbbaaaababbbabaababababababaababbaaabbaababbbabbbabbaababaabaababaabbbbbaaaaaabaaabaaaaabaabbaaaaaaabbbbbabbabbababaabaabbaabbbbbabbaabbabbbbbbbbaabbaaabbbabbabaabbaabaabbabbbaabaaaaabbbabababbbbbbbaaaabaaaaaababbbbbbbaabbbbabbabbbababaabbaaaabaabaaaaaaabbaabbabaaabaabbbabbbaabbbaaabbbaabaaabbbabaababbbaaaaabbbbbbbbaaaaaaababbbbaabaabababaabbaaabbabbbabbabbbbaababbbbbaababbbbbaaaabbaaabaabbabbbbabbbbbabbabbabababbaaaaaaabbabbbabbbaaaaaaabaaabbbbabbbbbaabbaabaababababbbabaababbabbabbbbaaabbabaaabaaabaaabbbbabbabaababaabababbbabaabbbabaaaabbbaaabbaabbbbbbabbaabbbbbbbabbbbaaababaabaaabbbbbbbaabbababbaaabbaabaaaabbaabaababbbababbaaaaaaaaabbbaabaaaaabbbabbababbaabaabaababbbbaaabbbaaababbabaababaaabaaaababbabaabbabbbbaaaabaaaabaaaaabbbaabbaaabbaaabbaaabbbbbaaababbbaaaabbaaaabbaaaaaaabbaabbaabaaabbabbbbbbaabbbaababaaaaabbababbbbbbbaaaabaaabbaaaaaababaabaabbabbaaabbbababbbbbbabbbabaaaabbabbabbabbbbaabbabbbababaababbbbababbaababbbaabaababbbbbbbabaabbbbaabaabbbbbabaabbbbbbaabaabbbbabbbabaababaaabbaabbbabbaabbbbaabbaababbbabbbabababaaaabaaaabbaabbbbaaaababbaaaabbabbabbabbabbbbaaababbababaaababaaabbababaaabbbabbaabaaaaaaabbaabbabaaaaabbabbbbbbabaababbbaaaabbbabbabbbabababbaabbaabbaaaababbaaabbaabbbbabbbbbbbabbbbabaaabbabbbbbaaaabbaaaabaaabaabaabaabaaaabbaabbbbbbabbbabbabababaabaabbaaabbbbababababababababbbaababbabbaaaabaaabbabababbbabbaaaabaabbabaaaabaabbbaaabbbbaabbaaaaaaaababaabbabbaabababbaaaabaababbbbababbbaabaabababbaaaabbabaaaaaaababbabbaaabaaabbbabbabbabbbbbabaaaabbbbbbbbaabaabbbbabbaaabaabaaaaabaaabbbabaaaaaabaabbaababbbabbaabbaaabbbbbbaaabaababbbaabbbaabbaaaabaabaababbbbbbbbabbbabbaabbbbbababbaaaabbbbbaabbaaabaaaabbbbbbbbbaaaabaaaaaaaabaababaabbaaabbabbbaabbbaaabbababbbbbaabbbbabbabbbababbababbbbbaaaaaabbaabbabbbababbabaaaaaaaabbbababbaabaaabbbaaabaaaabbaaaabbbaabaaababaabbbaababbababaaaaaaabbbbbbbabbbbabbabaabbbbbabaaabbbbabbabbbababaaaabbbabaabaaaabbbabbaabbabbabbbaaabaabaabababaabbbaababbbabbababbbaaababbaabbbaabbbaaabbbabababbbbaabbabbbbbbbbaabbbaaaabaabbaaaababaabbaababbababbbabbaaabaaaabbaabbbbbbbbaaaabbabbbbaabaaabbbabaaabaaabaaababaaaabaabbaabbbabbabbbbbbabaaabaaabbaaaabbbbbaabaaaabbbbabbbabababbaaabbbbbbbbbaaabaabbabbaababaaabbaabbaaaaaabbbbaaababbabbbbabbbaabbbabababaaabaababbbabbabaabaaabaaabaababaababbaabbbbaabbabbbaaabaababbabbbaabbbbbaabbbaaababaaabbbbaaabbbababbbbaaaababaaaababbabbbbbabbbbbabaaabaaababbbababbbabaabbababababaabbbabbaaaaaaaaaabbaaaaaaabaabaabbbaababbaabbababbababbbabbbababbbbbbabbabbbabbbbabaababbabaabaababbbbaabababbbbabbabaabbaabaaabbabaabbabbbabbaaaaabbbbbbaabaaabbbbababaabababbbaababbbbabbabbaaaaaabaaabbbbaababaaababaaabbabbbbbbaaabaaabbbbbbbbabaabaaaaaabbbbaaabbbbbabaabababbaaaabbbbabbabaababbbbbbbabaaaaaaaababbbbabbbabaabaaabbaabbbbbbabaaaaababbaabbbaabababaaabababaaaabbaababbababaaaaabbbaaabaababaabbaabbbaabbabbaabbabbabbabbabbbbbbababbabaabbabbabaaababaabbbaaaaaababaabaaabbababaabbbbabbaaabaaaaaaabbbaabbbababaaababbaabbbababaaabbabbbbaabbbaabbaaabbbaabaaaaababbaaababaaaabbbabbabaababbbaaaabababaaaaababbbaaabbbaaabbaaabbbbaabbabaaabaaabbbabbbbabaaabbbababbababaaaaaababbaabbababbabbabaabbaaabaababababaaabaabbbbabaabbabbaabbaabbbaaabababaabababbabbbaabaabababbbbabbaaaaabbbaaaabbababbabaaaabbabbbaabbaabbbbbaaaabbaaababbabbbababaaaaaaaabbbabaabbbbbbababbbbabaaabbaababbbaaaaaaababbaabaaabbbabbaabaababaabababbbabbaabbaaabaaabaaabbbbbabbbbaaabaaaaaaaaaabaaaaaabbababbaababaabaaabbababbbabbaabbababababbbabaabbbbabbabbaaaabbbaaabababbbbbabaabaabbaaaabbbbabababbbbabbaabbbabbbbaaaaaabaabbbbaababbaababbaaaaaaabbbabababbaaaabaaaabbabaaaabaabbababaaabbababbbaaaabaabbabbbbaabbabbabbababbbaaaabaabbbbaabbaaaabababbabbaabbbbaaaabbbaababbababbbaabaabbbabaababaabbabbbbaabbbbababaabbabaabbaabbbaabababbaabbaaaaababbabbaaabbaaababbbbababaabaaaabbaaabbabbabaabababaaaabbbaaaaaaabbbababbbbabbabbaaabbbabaabbababaaabaa
bbabaaababaaaabaabbabbbaaaaaabaabbaabbababaabaabbabbabaabbaabbbaaabababbbaabaabaaaabaabbabbbbbaabbbaabbbaaaabaaaaaababbbaabbbbaaaaababaabaaaaaababaaabbbaaaabaabaabbbbbababababbabbaabbbaaabbbbabbbbabaabaaabbabbabaabbaaaaaabbbabbaabaaabbaaabbaabaaababbbbbabbbabaabaaaabbbbbbababababababaaaabaabbaaaabbabbbbaaabababbbbbbbaabaaaaababbabaabbabaabaaabababbaaaabaabbabaabbbbbaababbbaaaabaaaababbbaaaabbbaabaabbabbaabaabbbbabaabbaabbaaaabaaababbbbbaaabbaabbababaabbbbbbbbbbbaabaaababbabaaaabaabaaaabbabbaabbbbbbababbababaababbabbaabbbbaaababbaaaaaaaaabbababbaabbabbbbababbabbaaaabbbbbbbaabbabbaaabaaababbbabbbaabaababbbaaaababababbbaabbbbbbaaababbbababbaaaaabbbbaababbbbabbbbbabaaaaaabbaabbbbabaaaabbbabaaabbbbbbaabaabbbbabaabbaabbbabaaabbabaaaaaabbbbaaaababaaaaaaababababbabbabbbaaabaaabaaaabaabaabbabbabaaaabbaabbabbaabbababaabaabbaabbaabbbaabbabaaababaabbbbbbbbbaababbbbabbabbaabbaabbbbaaabababbaaabbaabaabbaabbabbaabbabaaabbbabbaababbabbbaabababbbbaababbababbbbababaabbaaabbaabaaabaaabaabaaaaaababaaaaabbabbaababbabbbbababaabbbbaaabbbabaaaabaabababbbbbbababbbbabbaabbbabaababaaaaababbbaababbaaabbbbbabaaaabbaaabaababbababbaaaaaabbbabaaaabaabababbbbaaaaaabbbabbabbaabbbaaaaabaaaabbabbbabbabbaaabbbbaabbaabbabbabbabbbabbbbbbbabbaaaaaaaaabbaaaaabbababaaaaaabaabbbbbbabbbabaababbbaaabbababaabababbbbaabbbaabbbaaaaabbaabbabbabbbbbbabaabbbbaaaabaabbbbbbbabbbbbbbbaaaaababaabbbaaaaaabbabbbaabbababbaababbaaababbaaaaaababbaaaaaaabbbbabaaaababbabbaaaababbaabbbbbbaabaabbbbabaabaabbaaaaabbabaaaababbbbbabbaabaaababaaaaabbbababaabbaaabbbaabaaabbabbbbaaaabababaaaabbaabababbaaaaabbabaaaabababaabbbaaababababbbbaaaababaabbbbaaaabbbabbaaababbabaabbababbaaaabbbbbbbbbababbabababbababaaaabbabbaabbbabbbababaaaaababbaabbaaaabaaaabaabbaabaaabbbaaabaaabbbbaaabaabbababbbaabababbaaababbbabbbaaabaababbbbabbbaaabaaabaaababaababababbaabababaaabaaabaaabbaaabaaababbabababbabaaaaaaaabaaabaaababbabbaaaabbaababbaaaaaabaaaaabbaabaaaabbaaaabaaaababaaababbbbbbbaaabababaababbbbbbbabaaabaabaaaaababbbbabbaabaabbabbbabbabbababaaaaabaabaaabbabbabaaaaaaababaabbbbbababbaababbaaabbaabaabbaabbaaaababababbaaabbbaaabaaaaabbaabaabbaabbbabbabbbbbbaaaababababaaaaabbbababaabbaabbbaabbbaabbababbaabaabbaabbbbaababaaaaaabbbabaaabbbbababbaabbabbaaabbbbbabababbaabbabbbabbbabaabaabbabbbbbbaaabaaaabaabbaaabbaaaabaabbbbbaabbbabbaaabbaaaabaaaaaabbbbabbbbabbbabbbabbbbbbbabababbabaaabbababbbbaaaabbbaaaabaaaaaabbbbbbbabbababaababbabaabbbaababbbaabbbbaabbbaaababbabaababbbbabbbaaabbbbabaaabbbaabababbbabaaabaabababbbaabaaabaabababbababbbbbbaaabbabbabaaababbbababbaabbabaababaabbbbbbbaaababababababbbaaaabaabbaaaaabaaabaabaaaabaabbbbbababbbbaaaaaabbbaaababbbabaaaababbabbbaabbbaaabbbabbbababaaaaaaabbbbbaaabbbbaaabbbababaabaaaabbaabaaaabaabaaabbabaabbbbbabaababaaaaaaaabbaaabbbabaababbabaaabbbbaabaabababbbbaababbababaabbaabbabaaabaabbaabaaabbaabbabbaabaaabbaabbaaaabbbbbbababaabababbbbbabbbbbaababaabababababbbbababbaabbabbbbbbaabbbbaabbbbababbabaababbababbaabaabaaaabaaababbaabaaaaaababbbabbabbabbbabbaababaababbbbbababaabbbabbabababbaaabbaaaaabaaabbbaaabaabaaabbbbaaabaabaaaaabbbbbaaabbbabaaaaaaababaaabbabbaaaaaababbaaaababbbbabbbbabbbbbbaaaabbbbbababbabbbbbbabbaaabaaabbbbaabaaabaaaabaabbabaabbbaabaaaaabbbbbabbbbaabababaabbbaaaabaaaaabaaabababbbabbbbbbababbaababbaaaabaababbbaababbbbbbbaabbbabbbaabbababaaabaababbbaaaababbbbabababababbaaaabbbabbabaabbaaaaaabbbbbbababbbaabaabababaaabbbababaababaaabbaaabbbaaaabaabaaaaababaaaaababbbabababbbaabaaabbaabbaaabababbbbaababbabbaabaaaaabbbbaaabababaaabababbbabbbababbababaabaabbababaaabbbabaaaabbbaaaaabbbaabbbbaabbbabababbaaaaaaaabaabbaabaabbaabbbabababbaabaababaabbbbbaaabbbbbbabababbabababbabbbaababbaabbaaabaababbbabbaababbabbaaaaabbbbabbbaaabbbabaabbaaaaabbbbbabababbaaaaaaabaabbaabababababaaaababbaababbaababaabbbbaabbabbbaaaababbabbbabaaaaaaaaabbbaaababaabaabbbaaaababbbbabbbbbaaabbabbbabbaabbbbabababaabaaaabaaababaaaaabababaaabbabaaabbbaaaababbbbbbaabbbabbbaaababbbababababbabbbbbbbabaabababaaabaabbbbbbabbbbaababbabaaaaaaababbabaabbaabaabbaaaaabbbaaabaabaababbabbaaaababbaabbaaabbaaababaaabbaaabbababbbabbbbbbabbaabbbabbbababaaaabbbbbaabaabbbabbabbbaababbbabbaabbbbaaaabbaaaaaabbbaabababaabbabaaaaabaaaaabbbbaabbbaaaabbabbabaaabbabbabbabbbaababbaabbaabababababaaabaaaaabaabbbabbaabbbbabbbaabababaaaababbbaabbabaabbbabbaabbabbbbaaaaaaabbaabbabaabbaabbabaababbbaabbaabbbbaababaabbaaaabaabaaaaabbbaabbbbbbbaabaababaaabbaaaaabaaaabaabbabbabbbabaaaaababbbbabbaaabbaabaabbbbaabbbbabbbbabaabbabbbbaabbaabbaaababaaaaabbaabbbababbbabbabaababbabaababbabababaaaaabababaabaababbbabababbaaabbbbaabbbbbbabbbbbbbababbbbaaabbbaabbaaaabaababaabababababbaabbbabbbabbaaaaabbbaaaababaaabbabbbaababaaaaaabbaaabbabbbabbaababbbbbbbbababbbbbbababababaaababaaababbabbbaaabbbbabbabababaabbabaaabbaaabbabbbbbababaaabaababbaabaaababbbbbbbbaaaabbabaaaabbbbaaabbbabaabababbabbbaaaaabbbbaaaaabbbbbbaabbbbaaaabbbbbbbaaaabbbaaaaabbabbabaabbbbbbbbbbbbaaabaabababbbbbaaaaaaabaaaaabbababababaabbbbbabbabbabababababbaabaaaabbbabaababbbbaababbbbbababbbbbabaaabbbababbbabaabbaababaaababbaabababbbaabaabaaaababbaabbbabaababababbbababaaaabbabaaabaaaaabbbbabaabababbabbbbbbaabaaababbabbaaabbbbaabbbbaaabababbababaabbbbabaababbaabbaaaabbabbabbbbaabaabaaaaabbaababbbbaabaabaabbabaaabbabababaabaabaabaabbaaaabaabbbbbbbaaaaaaaaaaabaaaababbbababbbbbbbbaaaabbbaaabaabbaaabaabaabbabbaaabbaaaabbaabaabbbaaaaaabbabaaabbbabaabbaabbabbbbbbbbbaaabbaabaaaababbbbabbaabaaaaaababababaaabbbababbbbabbaaaababbbaabbbbbbaabbbbbabbbbabaaaaaaabababaaababaaabbaabbbaabbaaaaabaaaabaababaaabbaabbbbbaababbbbbababbbbbaabbbbbabbaabbabbabbbaababbabbaababbabaaaaabaabababbaaaaabaaaaabaaababbbabaabbababbabaaaaaaabababbaaabbaabbabababababababbbaabaaaabaaaaaabbaabaaaabababbbbababbaabaabbabbbbbabbaaababaaabbabbbaaaaabbbaababbbaabbabaaaababaabbbbbababaaaababbabababbaaaabbbaabbbbbbaababaaabbbbbababbababbabbabbbbbbbabaaaabbbbabaaaabbaaabbbbbaaabbaabbbaabbbaabaaaababbbbbbbabaabbaababaababaababbaaaaababaabaaabbbaabaabaaababaaabaabbbabbabaaabbababababbabbbbbaaabaabbbabbbbababbbabaaaababbbbbaababbababbbaaababbbababababbbbaaaabbbbbbbababbbaaababbaabbbbbbabbbbbbaaaabbbabaabababaabaaababbaaaaaaaaaaaabbbbaabababaabaabbbbababaaabbbababbbbbaaababababaaabaabbbaaaaabbaabbbbbabbabbabaaaababbabbbaaaabbaabbbbbabbabbbaabaaabbbaaabbaabaabbbbbaababbbbbbbaabbbabaaababbbbaaabbabbbbbbbaaababaababaaaaaaaaaabbbbbbaababbaababbabaaababaaaaabbaaaabbabababbaabbabbbaabbaaabbbaaaabbaaabbbbaaabbababbbaaabbbaaababaaabbbababbababaaabbaabbabbbbbaaabababbbbbabaabaabaaabababbbaaaaababaabbbabababbaabbbaababbbabaabbbabbabababbaaaabaaabbbabaaaabbababbaababbaababaabbbbbaaaaaaabaaabaababaababbbaabaabaabbbaaaababbbbaaaaaaabbbbabaabbbbabbaaababbbabbaabbabbbabaaaabbabbabaabbababaabbbababbbababbababbbabababbababbbaaabababbaababbaabbabbbbaabababaaabaabaaabaabbbaabbaaabaaabbaaaabaabbaababbbaaaaabbabaaabbbbabaabbaabbabbababbaabaababaaaaabbbaaaabbaabbabaabababaabaaabbaabababbbabaaaabbababaaaaaaaabaaaaabaababbaababaaababaaaabbbababaaabbaabbaaaababaabaaabbabaabaabaabbababbabababababbbaabbaaababbaaabbaabbbaabaaaaababbbaababbbbaabaaaabaabaaabbaaaabbababbbaaaaaaaabbbababaabaaabaaababbbbbaaabbabbaaaaabbaababaabbabbbaababbabbbaaaabababbbbbbaabaabbbbbbbabaaaabbababaaaabaaababaabbbbbabaaabbaabaababbababaabbbbaaabababbbababababbaaaaaabbaaaabbabaabbabaabaabbabbbbaababaababbbaaaabbaaaaabbabbaabbbabbbaaababbaaaaabbaabaaabaaaababaabbaabbabaababbbbbabaabaababaaaaaaabbbbaaabbbbabbaabbaabbaabababaaabbbaabaaabbbbaabbabbbabbababbaabbbabababbaabbbbabaabababbaaabbbabbbabbababbbbabbaabbaaaabbabbabbbabbbaaabbbbbababbaababbaaabbabbbabbbabbabbbabbabbbabababbabababbbbaaabbbbbabbababbbbbaaaabaaabaaabbaabaabaabbabbbaabaabbabbaaabbbbabaaabbbaabbabababbbbbbbbbabbaabaaabbbbabababaaabbbbabbbabbbbabaabaaaaaabaabbbabbaaabababaaaabbbbbbbbbabbabbbabbbabbaaaaaabaabaaaabbaaabaaabbabbaabaaaaaaabaababbaabaabbbbabbabbaaaababbbababbaaabaaaaaababbaabbabaaabbabaaabbaababababbbbabbbabbbbaaabbbbbabbaaabbbaaaababababbbbababababbbbbabaaabababbbaaaaaababbaaaabbaaaabbaababbbbbababbbbabbabbaaaabbaabaabbbbbbbbabaabaaaaaabaababaabaaaaaababaaaaabbbababbbabababbabbbbbbbabbabbbbabbbbabbbbbabaaaaaabbaabbbbaabaabbbaabaabaabbbbbababbabaaabbbaabbbbbaaaababbbaabbaabbababbbaaaabbbabbabaaabbbaaabbbabbabbababaabbabababbaaaabbbaabbabaabaaabaaaabbbabaaaabbaabbbabbbbaababbbbaabaaaabbbababbaabbbbabaaaabaaaabaaaabababbbbaabaaabaaabbabbbabbbbaabababaababbaabbbabbabbabbbbaababbabaaabbabbbbaaaababbaaabaaababbaaababaabaabaababbaabbaaabaaaabbabaababaaabaabbbaabbababaaaaabaabbbbabbbaaabbaabbabaabaabaaabbaabbabbbabbbbbbbababbaababbabbaabaaaaaaabbaaabaabbabbabaababbabbbbbbababaabbaabbbabaabbbbaabaabbbaaaaabaabbaabaaaaaaaaabaaabbabaabaaabbabaabaababaabbbaaababbbabaaaaaaaababaaabbbabaaabababbbbaaaaababaaabbaababbabbabbaaaabbbaaabababababbbaababaaabbaaaabaabbbbaababaaaaabbabbababbabaabbbabaaaaabbbbbabababbaabbabaaabaaaabbaaabaababbaaaaabababaaaaaaaaaababbbaaabaaabbbbaaaaaabbaabbbbbbbbababaaabaabbbabaaabbbaaabbbbabbaabaaaababaaaabaaaaababbaabbababbabaabbbabbabbbaaabbaabbaabbabbabbbaaabbbbaaabaabbaaaaabbbbbbbaabbabbbaabbabbbabbbbbbabbaabababababababbabaabababbaabababbbbbabaaaabaabaaaaaaaabaaaaaaaababaaaaabbbbaabababbbaaaaaaabbababaaaaaabbabbbaabbbbababbbaabbaaababbbbaaabaabbabaabaaababbbbabababaaabbabbaaaabaaaaaaabaaaabaaabbbbaaabababbbaabbbbbabababbabbaaabbaaabaaabaaabaabbaaababbaaaabaaabaabaabbbaabbabbabbaaaaaabbbbaaabaaabbbabbabbaaabaaaabaabbaaabbbabaaaabbababbbaaababbabbababbabbbbababaabaabbbaaaabbbbbbbabaabaaaaabaabbabbaaabbaaabababbaabbbbbaaababbaabaabbabbabbbbbbababbbbbaabbbababaabbbbbbbaaabaaabbbaababbaaabbaabbbbaaababaabbaabaaababbabbabbabbabaabbbbbaaaabbabaaabbabbbbbababaaaaabaababbabbabbbabbabaaababbbabbbabaaaabbbbaaabbbbbbaabaaabbabababaaabbababbaabaaaabbaaabbbbbbababbaabbababbbabaabbbaabababbbaaababababaaabaaaaaababaabaaabbaabaaaabaaaababaabbbaaaaaaaaabaabbababbabababbbaaaaababbabbaaaaaabbaaabbbabbaaaababbbaababbaaababbaaababbbbbbabaaaaaabbbaabbbbabaaababbababaababbbaaaaabababababbaabbbbbbbabbbaaabaaabbbabbbabbaaabbabbbbaaabbaaaaaababbbbababaaaabbababaaaabbbbaabbabbbabbbbbaaabbbaaaabbaaaaaaaabbbabbbababbbabbaaaaaabababbbbbabaabaabaaaaaababbabaaaabbabaabbbbbbbbbabbaaababbbabaaabaababbbabbbbaababbabaaabbaabbabaabbaaababaaabbaaaababaaaababbaaaaaaaaabaabbbbbabaaaaaabbbaaaaabaabaaabbbbbbaaaaaaaababaaabbaabbabbbbbaaabbabaababbbaabbaaaabbaaaaaaabbaababaabaababaaabbaaaaabaaaabaabbbaaababbbbbabbabbababbaabbbaabbaaabbababbabbabaaabbbbbbaabbbababbaabbabaaabbabbbbaaabaaaababaabaabbbaaaaaabbababbaaabbaaaaabbaabbbaaaaabbbbbbbabbaabbbbbabbababbaabaaaabaabaabaaabbaaabaaababbababbbabbbbbbaaaabbaabaaaaabbbabbbabababaaaababbbabbaaaababbbbbaaaaababaaabbbabbaaabaaabbabbbaabbaaaabbaaaaabaababaaaaaaabbbabababbbaababbababbbababaaababaabbababbaabbaabbaabbaababbaaabaaabaaabbabbababbababaabbbbaabbabbbaabaabbbbbabaabbaabaaabaaaaabbbaabaaabbabaaabaaaaabbabbaabbaaaababbbbbbbaabbbabbbaabbaaaaaabbaabbabbabbbbaaababaabbabbbaaaabbbbbaababaababbbabbbabbbababaaaaabbabbbbbabbabbabbbaabbbbaaabbbabaaabaaabbbbbbabaaaabbabaabbabbaaaabaaabbbbabbaabaaabbbbbbbbabbbaababbbbbaabbbaabbbbbaabaaaaaaaabaabbbbbbbbbbaaaabaaabbbbabaaababaaababbbaabaaaabbaabaababbbbbbaaaaabaabbbbbaaaababbbaabaababbabababbabababaaaaabbaaaabbaabaaaaaababaaabaabbaababaaaaabbabbabaaaabbbbaabaabaaabaabbabaababaabbabbaabaabbbbbbaabaaabbaabbabbbaaababababaabaabbbabbbababbbbbaababbbabbbbbababbaababaaababbbaaabbabbbbbbbabbbbbbbabaabaaaaababbaababaaaaaabaabaaaababbababbababbbbabbabaaaabbabaabbaaaaabbaaaabaaaaaaaaabbaabaabbbbbabbbaabbbbaaababaaaaabaaaaabaaababaabbbabbbababababbabaaabbabbabbababbbbaabbbabaaabaabbabbbabaaaabaabbbbaabbaaabaaabbbbaababbbaabbbababbbbbbabbaaaaaaaababaabbbbabbbbaaaaaaaaabaababbaabbaabbabbbaabbbbbbbaabbaaabababbbbbabababbbaaaabbbaaaabbbabbaaabbbababaabaabaabbabbbbaaabaababbababbbaaabbaaaaabaaabbababaaabbbabbababbaabbbaababaabbabababbabbbaaaaaaaababaaabbabbbaabbaabbbbaabbaaababaababaaaabaaababbbbaababaaabbaababbbbbabbbaabbbbababbbaababaabbbabaaaaabaabbbbababaababbbbbaaababbaaabbabbaabaababbbbbbabaaabababbbbbbaabbaaaabbabbaabaababbabbbaaaabbbbababababbbabbabbbaabbbbaabbbaababaabbbbaaabbbabbaabaaaabaaabbaabbbbbbaabbabbabbaaabbbbbbaaabbaabbbaabaababbbbaabbabbabaaaababaaaaabaabaaaabbbbababbbbbbabbabbbbabbbbabbbababbaaaaabaabbabbbbbaaaabbabbbaaabababbaaabbbabbbaaaaaabbabbaaabbbaabaaaaabbaabbabbababbaaaaabaabbbbbbbbabbbabbaaaabbbaaaabbaabbbbabbbaabaabbaaaababababbbbaabaaaaabbbbabbbaababaaaaaabbbabaabaaaabaaabaabbaaaaabbabbbbbabbaabababaababaabbbbbbbbbaabbaaaabbbbaabaaabbbbbbaaabaabaabbbbaaaabbbbabaabbbbbaaabbaaaaaabbaababbabbabbabaabbbbabbbaaabaaababbabbbbabbaaabbabaabbbbaababbabbbbbabbbabbbbbbbaaaabaabaaabbbbaaabbbabbabaaaaabaaaabbaabaaababaaabaaaababbbabbbabbaaaaabaabbabbabaabaaabaabbbaababaabaabaabbababababbaaaabbbaabbabbababaaabbbabbabaaabbbbaabbbabbbbbbbabbbbbbaabababaaababbaaababbabaaababaabbbbaabbbbbbbaaaababbbbbabbbbaabababaabbabbabaaaaabbbaaababbbabaaaaaabbabbbbaaabaabaabbbabbaaababbaaaaaabbbaaaaaaabaaaaaabababaabbbabaabaabbaabbbbaabbabababbaaabbaaaaaaaaabbaabbbaabbabbabbaaaaaaabbbbbaabababbaaababaaaaababaaabaaabbbbbababaaabbabbbabbababaaababababbababaababbabbabaabaababaaaaaabbbabbaaabaaaababaabaaabababbaabbabaaababbaaabaabaabbaaabaaaabbbaaabaabaabaabaababbbbaababbaabbbaaaabababbababbaabaaabbaabaabbbbbbaaaabbabbaabbbbaabaababbbbbababaabbbbbbabbbabbbbbaaabbaabbbaaabaababbbaabbabbbbbabbbaabbbbabbbbabaaaaabbbbabbaaaabaabbbbabbabaaababaaaaaabaabababababaaaaaababaabaabbbabbbababaabaaaaaabbaaaaaaabbaaababaaaaaabbbaababaabaaaababbaaabbaaaaabbbaaababbbabaabaaaabaaaaaaaaabaabaabbbaaabaabaabbbbaababaaabbbbaaabbbbbbabbbbbabbabaabbabbbaaabaabbaabaaaabababaaabababaababaaababbabaaaababbbbbbbbbababaababbbababaababbbabbbbabbaaabaababbaabbbbbbbbababaabbbbbabbbaabbbbabaabbbbbababbbabbaabbbaaaabaaaaaaaaaaaaaabaabbbaabbbaabaaabbbbaaaaaaababaababaabbababbbaaabbaaabaaaaabbaabbbbaaabaabaabbaabbabbaaaaaaaaabbbbaaabaababababaabaaabaaababaabbbaabaaababaaabbbbabaaabbaaaabababaaaabbbabbaabbaabbbbbaababaaaababbaaaabbaaababbabbbabaaababbbbaaaababababaabbbabaaaaaaaabbbbabbbabbabbbbabaaaabbabbbbbbbbaababaaabbbbbaaaabbaaaabbbbabaabbaabbababababaabbabbbbbbbaaaaaaaaabaabaaabbabbabbbbaaabbabaaaababbbbbaaababaabbababaaabaaaabbabbbabaabbaabbbbbaaaabbbbaabbbbbbbbbabbaabbbabbaabaabbbaabbbabababbabababaaabaababaaabaaabaaabaaaabbbababaabbabbbabbababbbaaaabaabbabaabaaaabababbaabbbabaabaabbabaaabababbaaabbbbbbaabbbbbbbaabbabbbbabaabbabaabbbbabbbbabbaaababbabbbaaaaaaaaabaabaabababaabbbabbaabbbaabbbbaaaaaaaaababbbbabbbaabbbbaabaaabbbbabbbbbbbabaaababbabaaaaabababbababaabaaaaabaaaaaaabaaabaababbbbbbbaaabaabaaabbbaaabaabaaaabaabbbaaaaaabbabbbabaaabbbbabbbbbbaababaabaaaaaaaabaabbbaaabbaabbbabbaaaababaaaabbbbbbaaaaaabaabbbaabaabaaabababaabaabaabbbbababababaaabaabbababbbaabbbbbabbbaabbaaababbbabbbabbabbabaaaaaabbbaabbaaababbbabaaabbbaabbaabbaaaaabaaabaaaaabbbbbaaabaabbbbabaaaaaaabaaabaabababababbaaabbbabbbbbbaaaabaaaabbbaaaabbbbabbbabaabaaababaabbaaaaaabaaaabaaabaaababbbabaaaabbaaabbaababaaaaabaaaaaaaabbbbababbbbaaaaaaabaaaaabababbaabaaabbbaaaaabbbbbbaababbaaabababbabaababbbababbbbabbbbaaaaabaabababbaabbabbabbabaabbababaabbababbaaabbaaabbbaabaaaaabaababababbabbbbbbbbaababaabbaaaaabbbbbaaababbabaabbbbabbabbbaaaabaaabbaabababaabaabaabababbaaaabababaaababbbaabbabaabbbbaaababbaaabababbbabbabababbabaabbabaabbbabbbbbabaaaababbabbbbbbabbaaaaababbbbaababbabbabbbbbababaaabbbbaababbbbbaabbbabbbabbaaababbaabbabaaabaababababbaaabbababaaabbbaababbabbbbbabbababbabbbbabbaaabbbbbbbabbababaabaaababaababbaabbaaabbaaaaaabbbbbbbbbbabbbabaabbabbabbbaaaabbaaaababbabbaababababaaaaaabaaaaaaaaaaaaaaaaaaababaababaabbabbbabababbbbbbbbbbbbbaabababbaaabbbabbaaabbbbbbbbbabbbaabbabbbaaabaaaabaaabbaabbbbbbbaaaaaaabababbbbabbbbbaaaaaaabbaabbaabbaabbbabbbbbabbbabaabababaabaaaaabbbaabaababbbbbabaabbbababbbabbabbaababbbbbaabbabbabbababaaaaaababaabbbabababaabbaabbaaaaabbaaaabbbabbbabaaaaabaabbbaaabbbbaabbbaabbaaabbaabaabbabbaaaaabaaabbaabbabbbabaaabaabaaaabaabbabbabbbbaabbbaaababbbaaabaabbbbabaaaaabbbaaabaabbbaaaabbaabbbabaaaaababaabbbabaabbbaaaaaaaaaabbaaaabaaabaabbabbababbbbbabbbaabbaaabbabaaabaababbaabbbbabaabbbbbabaaabaabbaaaabbbabaaaababbabbaaaababbabaaaaabbaaababbbbbababbbabbbaababbbbaababaaaababbabbbbabbabaabbbaababbbabaaaaabbabbbbbabbbabbbabbabbbbbbbbabaaabbbabbaaabaabbababbaaaaaaabaaabaaabbbbaaaabababbbbabaabbaababbaaabbbbbaaaabbabaabaaaababaaaababbaabababbabbbabbbabbaabaaaabbbaaabbbabbbaaabaaaaabbabbababbbbaabbabbabbabbbaaabbbaaabbbaaaababbabbabaaaaababaabbbbbbaababbbabbabbbbaabaaabbbababbbbabaabababaabaaabbabaabbaaaabaababbbaaaaababaaaaaaabbabaabbaaababababaaaababbaabbbaabaaaabbbaaabaaabbaabababaabaabaabbababbbaababbbbbbababbabbaabaaabbabbbbbabaaaabaabbbbaaaaabaabbbabbaabaabbbababbaaaababaabaaabbababbaaaabbbaabbbbbaaaabbbaaabababbbbbabbbabbbabbaaabbbbaaababbaabaaaabbbaabaabbbbabbbbbaabaabaababababbababaaababbaaabbbaabbaababbbaaababbaabaaaaabbaabbbbbbaaaaaabaabababaabbbbababbaaabababaabbabbbaabbaaababaaaabababbaababaabbbaabbbaaaabaaaaaaabbbaaabbbaaaabbbaaabbaaabaaaaaabbbbaabbaaabaabbbbaaaabbaabbbababababbbaaaabbaaabbbbbbababbabbbaaaabbaababbbaabbabaaaaaabbabbbbbbbbbbaabaaaaababaaaaaaaaaaaaaabaabaaabaaaababbaaaababababbbbaaabbbabaababbbaaaaaabbbbaaabbbbbbabaabaababbababaabaababaaabbaaaaaaabaabbaaaaaaabbbaaabbbbbbaaabbbbaaabaaabababaaaaaababbbaaaabbaaaabababbaababaaababbabaabbbbbabaabbaabbabbababbaabaaaaaabbbbbbaabababaabbbaaabbbababbabbababaabbbbbaaaaabababaababbbaaaaaaabbbbbbbaaabaabaaaabbabbbaaabaabbbbbaababababbbbaabaaabbabbbbabaababbbbabbabbbabbbabaaabaabbbaaabaabbaaabbaaabbabaaaaaaaaabababbaaabaaaaaaaabaabaaabaaabbbbaaabaabbabbabbaabbaabaabbbabaaabaabbabbbbbaabbabbbbbababbbbaaabbbbabaabaaaaaaabaabaabbaabaabaaababaabaabbbabababbbbaaabbabbbbbbbbababaaabaabbbaabbabbabbbaaaaabbabaabbaaabbbabbaabbaaaabbbbaabaabaaabbaaabbabaaaaabaabaabbbaaaabbabbaabbbabbbbbababbaabaaabaaabbabaaababbaabbbabaabbaabbbbbabaabaaababbabababbaaababbbbbaababababaabaaabaaaabaaaaabbbabaaabaabbaaaababababaaabaabbaabbbababbaaaaaabbaabababbbbbbaabaabaabaaaababbbaabbbabbabaabbbaaabbbbabaaaababbaabbbabbababbbaaaaabaabbaabbbaaabbbbaaaabababbbbbabbbbbbbaaaabbabaaaabbabbbbbababaabbbabbaabbbbabaaabbabbbbbaabbabbbaabaabaaabaababababbbbaaababbbbbbabaaababaaabbababaaabaababaaaaabbbabaaabbaaaaaaabbaabbabaaabbabaaaabaabaaaaaaabbbabababaabbbababaabbbbbbbbbbaabbaabaaabbbbbabababaaaaabbbbabababaaaabbaaaaababaabaabaabababbbbbbababababbabbaabbaabaabaabbabababaabaaaaabbaaaaabaaaaababbbaababaaaaaabbaabbaaaabbaabaabaabbabbabbaaaabaababbbbbabbabbbabbaabbabbabbabaabbaaaabbababaaaaaababbaaaaabbbbbaaababbbbabbbabaaababbaaaabbbabaaaaabaaaaabbbbbbbabababbbbbaaaaaaabbbaabbbbbaabbbbbaaaabaaaaabbbbbbbbbaaaabbbabbabbbaabbbabbbbbbababaababbbaaababaaaaabbbbbbbbbbbababbbbbabaaabbbbaaaaaaabbabbaaabaabbbbbabaaaababababbaaabbaaaaabbabaaaaabbabbaaaabababbaabbabaabbbbaababababaaaaabbabababbababaaaabababababaabbabbabaaaaabaabbbabbaaaababaababbabaaaaaaaaaaabbaabbabbbbaababbbabbabaabbaabaabbabbaababaaabbbbbaabbabbabaabaabababaaaaabbababbabababbaabbabaabbbaaaaababbaabbabbbbabbaaabbabbabbabbaaabbbaaaabaaabbaababaabbbbaabaabbabbaaabaabababbabbbbbbbbabbabaaabaaaaaabaabaaaabbbbbbaaababbbbaababbbabbbabaabaaababbbaaabbbaabaaaabbabbbbbbbbbbbbabbabaaaaaabbbaabbabbbbababbbababaababbbbaabaabbbbaaabbbaaaaaaabbaaaaaabbbbababaababaabaaaaabababaaaaaaaabababbaabbbaaabbabaaabaaabaaaabbabbbaaaabbbabbabbbabbbbabbababaaaabbabbbaabaaaaaaabaabbaaaaabbbbbbbabaaabbababababaabbabbaaabababaaaabaabaabbbabaaababbbbabaaaabababbbbaaaaabaabaababbabbbbbbbaaabbaabbbbbbaaaabbaabaabaabaababbabbbaabababaabbbaaababbbabbbbbbababaaabaaaabaabbbaabbbaaaaabbbbbaaabaababbabbaaaaabbaaaaaaaaabbabaaaaababbabbbabaababaaaabaababbaabbbaaabaabbbbbaaaaabaaaaabbbababaababbbbbbabaabaaabaababbaaabbbaabaabbbaaabaaabaababababbbabbabaabaaabaabbbabbbabaabbaaaaaabaabbbbbaababababaaaaaababbaaabbabbaabbbbbbbbabaaababbaaaabbabbaababbbabbbaaabababbbaababbbaabbabbaabababaaaabbababaabbbbbaabbaaabaaababbabbbbbbaababbabbaabbabbbaabaaabbaaababaababbabaaaabbaababbaaaaababbaaaabbaaaabaabbbbaaaaaaababbaababaabababaabbbabaaabbbabaaaabaaaaaabbbabbaababbaabaabbbabbbbaaabbaabbabaabbabaaabaabbbbbababbaaaaaabaabbababbbbbaaaabaaabababbabbaaabbaabaabbbababbaaaababbbbbabbbbbbababbbbbbbabbbbbbaabbbabbbababbbbababaabaabbabaaabbababbaabbbbaaabbbbbabbaabaabbbabbbabbaaababaabaabbbbbabbabababbabaaaabbbaaaabbabababbabbbbaabababaaaabbaababbbabbbbaabaabababbabaaabababbbaabbbaaabbbabaaaabaabaabbabbaaaaaaabbbaabbaabbabbbaabaabbbabbbbbaaaabbbbbabbbaabbbaabbbbbbaaabbabbbbaababbbabbbbaaabbbbaaaaaabaaabbbbbbababbaaababaabaaaaababaaaaaaaaaabbaababababbaaabbabbabbbababaababaababbbabaaabbbababbbabbbababaabbbaaaabaabaabbbaaabbbaababbbaaabbaaabaaaabaabbbbbbabaaabbbabababbbbababaabbaabbbababaabbbbbaaaaabaabbaabaaababbabbbbaaabaaabbaabbbbbaabaaaababbbbbaaabbbabbbbbbaabaabbaaaababababbaabbbbabaaaabaaabaababaaaabbaaabaaaababbbbababaababababababbbabaaaababbaabbbbbbabbbabaaaaabbaabaabaaaabbbbbbababbaabaababaaaaaabaabbbabbbbaaaabbbabbbbbbbabbbaabbbbbabbabbaabbbbabbaabbbbabbaababaaabaabbaaaaaabbababaaabbbbaabbabbbbaaabaaaaabbababaaabbbbbbbaabaaabbaabbaabbbabbabaababbaaaabbbbbabbbbbaabbbaaaaabaaabbbababbababbaaabbbaabaaababababaabaabbaaababbabaaabbbbbbaaabbabbbbaabaaaaaababbbaabbabbbaaaabaaaabbaabbbbababbbaaabbbbaabbbbbbabbbabbaabbaabbabbbbabaabaaabaabbbbbbbbabbbbbbaabbaaaaabaaaabbbbaaabbabbbaabbabbabbabababbabaabababbbabababbababbaabbabbbbbbabaaaabaaaaaabababbbabbbabaabbaabbabaabaaaabbaaabaabbbbaaabbaabbbaabbabbbbbababaaabbaaabaabbbaabaababbbbabababbaaaababbabbbaaababababaabbaaabaabbabbaaabbaaabbabbaabaaabbabbabbaabaaabbbbbabbabbaaaabaabaababbbaaababbbbbbbabbaaaaaaaabbaababaababbababbabbabbbbaaaabbbaabbbbabbaaabbbbaabbaaabaaabbbbbbaaabbaaaaaaaabaabbbbaaaaaabaaabaabaaabbabbaaaaabbbaaaaaababbabbbbaaabaabbbabaabababbbbbbbbbaabbbbbabaaaaaabbaabaaaaaabbaaabaaabaabbbabaabbbaaabbaaababaababbaaababaabbbabaabbabbaabbbbbbbbbbabbbabbbbaababaabaaaabababbbababbbababbabbaaabbaaaaaaabaaababbaaabbaabaabaaaabbababbbabaaabbbbaabbaabbabbabbabbbbabbbbbbaabababbbbabbbaaaaaaabaaaabbbbaaaabbbbbbabbabbbbbbbbbaaaababbbaaaababbaaabbbaabbbaaabababbbbabbbbbaababababbabaaaabababbbbbaababbabbaaaaaaaaabbbaaaababbbbababababbaaaabbaababaabbbbabaaaaabbabbbabbbaabbaaabababaabbbbbababbbbbaabbbbabababababaabaaababbabaaaabbbabbabbbababaaaaabbabaaaabbbbbbaaaabaabbbbbabaaabbabbbabbabbabaabbabbbbbbabbbaaaaaaababbabbaabbababaaaaabbabbaabababbbaabaabbabbbaabababababbbbbbaaaabbbaabbbabaabbbaababbbabaabababaaabbabababbaabbbbaaaaababaabbabaaabbabbbbababbbababbbbabbbaabbbbbaaaababbbabaaababbaabbaaabbaabbbaabaaaaabbbbabababaababbbabbbabbbbbbabaaaabababababbabbbbbaaabaaaaaaaaaaaabaaabababbbabaabbabaaaabbbaaabbababababaabaabaabbaabaaabbabbbbbbbbbaabbbababbaaaabbbaababbbaababbababbbbaaababbbabbaaaaaabaabbbaabbbabbbabbaaaaaaaabbaababbbaaabaabbabbaaaaaabbabbaabbbbbbababababaaabaaabaabbababbbaaabaaabaabbbbaaababbaaaabababaabbbaabbabbbbbbbabaabbabbabaaababbaaaabbabababbbabaabaabbaaababbaabbbaaabaabaabbaaaabaabaabbbbbabaababbaaababababbbaaaaabbaabbbaaabaabbababbbbbabbbabaababbabbbbbaabaababbababaaaaaaabbbbaabaaabababbbaaabbaaabbbbaaabbabbaaabbabaaabbaabbbbabaaabbbaabaabaaabbaaabaaaabaabbabbaaabbbabbaabbababbabbaaabbbabaabbbbbbaabaaaaaabbaabbbaaaaabaabbaabaaaababbabaabbbbbabbabaababbbaaabbabbababbaaabaabaaaabababbabbabbbbabaabbbabbbabbbababaaabbaaaaaaaabbaaaabbaabbabbaabbabababbaababbbbababaaaabbaaabbabbbbaabbabbbaabaaaaaaabbbbaababbabaabababaaaaabbbabbaaababaabbbbbbbaabbaaabbaaabbaabbabbaaabbbaaabaaabababaabaabbbbaaabaaabbbbaabbabbbaaaabbaaaaabaabababbababbbbbabbbbbababbbabbbbbababbbabbbbaaabaabbabbbabbaaabbbaababaaaababbbbbaabababaaabaababababaabababaaabaaaabbaabbabbabaaabaaaababaaaabbabaabaabbaabababaaaabaabbaaabbbabbbbaaaabbabaababbaaaababaaaabbabbaabaaaaababaaaabaaabbaabbbbaababaabbaabaababbabbbbbabbbabbabbbbaabbaaabbbbbbbabbabbbaaabababbaaaabbbbbbabbaaaaaaaaaabbabaaaabbabbbaaababbbaaaaabbbbbabaaaababbabbbbbaaabbbababbaabbaabbbabaabbabababbbaaaaabbbbbaaabababbabaaaabaabaabbaabbaaababaaabbaaaaabbbabbaabaabbbbbbabbababababbabababaabbabaabbaaabaaabaabbbabbbbbbbaabaabbbabaaaabbbaabbabababbaabbaababaaabaabbabbbbaaabaababbbbaababababbbabbbbbaabaabbbababbbaaaabbbaabaabaaaabbbbaaaaabaabbbabbababbbbabbaabbbbbbabbbaaaaabbbabbbababbbbaaaabbbbaababbbbaabbaaabbbabaaaabbbaaaaabaaaabbbabababaaababaabbbbabaabbbbbbbabbaaaaabaaabaaaaaaaabababababbababbbbbabbaaabbaababbababababbababaabaabbbaaababaabbbbbbaaaaabbaaabbbaababaaaababbbbbbaabbbaababaaababbbababbbabbbabbbababbbbbbbbabbbbaabbbbbbaaabbabbabbabbbbbbaabbabaababababaaaaabbaababaaabbbabaaaabaaababbbbbaaaaaaabbabbbbbbabaabababbabbbbbaabaabbabaabbbaabbbabaabaababababbababbaabababaabbbbababaaaababbbabbbbbbabaaababaaaabaaabababaaabaabbbbaaaabaaababbbaaabbbabbbabaaaabbbbbbbaabaabbaaabaabbaaaabbabbbaabaababbaababbbaabbabbabaaaaabbbaababbababbbaabaabaaabbbbbaaababababbaaaaaaababababbbbabababbbbbbabbabbaababbbaaaaaabaaabbabbaaaaabbabbbabaaaabbbbaaaaababbbbaababbabbbaaabbbbaabaaabbabbaaaaaaabbaabaababaababbaaaabaababbaabbabbbbabaabbbbbababbbabbababbbaaaaabbbbbabaaabbbababababaabbaababbbbbbababababbabaaaaaabbbaabbbabbbaabbbbabaabbbbbaaaabbaabbaabbbaabbaabaaaabaaabbababaabaaaaaaabaabbaabbbabaaabbaabaabaaabaababaaabbbababbbbbbaabbaabbbbbaabbbbbbbaaabababaaaaaabbababbaaaaababbbababaaabbbbaaaaababbbbbabaaaabaabababaabbbbabbaababbabbbbbabaaaabbbbabbbbaaaaaaaababbbbabaabbabbbababbbbaaaaabbbabaabaaabbabbabaabaabbababbbbbaaaaabbbbabbbabaaaaabbaaaaabbbbabbbaabaaaabaabaaabbababbbbbbabababbbabbaababbbbbaabbbaaabaabbbaaaabaaabbabaabbabbbababbbaabaaabbaabbbbababaaabaabaababaaababbbabaabbbabababaaaabbbbabbaabbababbbaaaaaababbababaaababaabaababbaaabbabaabaaaaabbaababbabaaabaababababbaababaabaabbabbbbbaaaabbabbaabababaaaabbbabbaaabaababaaaaabbabbaababbaabbaaabbababbbbbaaaaabbbbbaabbbbababaaaabbbbabbaaabbbbbaaabaabbbbababbbbaaaaaabbabbbbbbabbaabbabbaaabababaabbbbaaabaabbabbabbaaaaabbabbaabbbabbbbabbbabbbbabbaaabaabbaabbbaaabbabbbbaaaabbbaabbabbbbbbbabbbabbaabbbbbbaababbbabbbaaaabbbbbaabaaabbaaabababbbbabbababbbbbbabaaaabaabbabaabbaabbababbabbaababbbabbbaabbabaaaaaaaaaaaabbbbbbababbbbaabbbbbbbbbabbbabbaaabbaaaabbababababbaaabbababaaabbbbbbbaaaabababbbababbaaaaaaaaaaabaabbaaabaabaaabaabaaabaaaaaaabaabaabaaaababaaabaaaaabaababaabbababaaaabaabbbaabaabababaababaaaaabbaababbbababbbbbaaaaababaabababaababbbabaababbabbbabbabaaabbabbabbbaababbababaaabbaaaababababaaaaabbaabaabbabbabaaaababbabaaababbababbbbaaabbaaabbaaabababbbbbabbabbbaaabbbababbabbabbabaabbbaabbaaabbbaabbaabbbaaabaaaaabaabbbabbabaabaaababbbababaaabbbbbbabbaababaabaaababbababbaabaaabababbbbbbbbababbbabbbabaaaaaabbaaaaabaaaaabbaaabbbbababaababaaabbabbabbabbaabbbaaababbaaaaaaabbbababbbabbaaabbaabbbabbaaababbbabbbaababbbbbbbaabaaaabbaabbbabaaabbbbababbbaaaaababbaaabbbbbbaaabaaaaabbbbbbbaabbbabaaabaaabababaabbabbbabbbaabaaaaababbbbbabbbbbaabaabbbaaaaaabaabaabbabbaababaaabbabaababbaaaabaabaabbbaaaababbbababaaaabababababaaaaaababbbbaaabbabaaabababbaabbbbabbabbbbaaaaabaabbbabaaabbbbbaaaabbbaabbaaababbabaabbabaaabaaabababaabababaaabaaaaabaababbaaaabbaabaabbbbaabaaaaabaabbabaabbbaaabbbabbbaaabbabbabbbbbabbbbbaababababaaaabbbaabbababaaaabbabaabbaababbbbaaaaabaaabbbbbabaaabbbaaabbaabaaaaabbabaabaaaababbabbaababbaaabbaaaaabbbaabbaaaaabaaaabbbaaabbabbabaaabaaaaabbabbaaaababbbbbbabaaaaaaaabbbbabbbbaaabbaababbbababbbbbbbbbaababaabaababbabbabbbbaabaabaabaaaabbabbabbbbaabbbaabbbbbbbaaababbaaababbbaabbababbaaabaaaaaaaaaabbbbaabaaaaaababaabababbabbaababbabbbaaabbbbaaabbababbbababbaaabbbabaabbabaaabbbaabaaaaababaaaaaaabaaaaaaaabababababaabbbbbbabababbbbaaabababaabbaabbaababbabbbbabaaaaabbbbabaababaaaaaabaabbbbbaabbbaaabbaabbbbbbbbaabbaabbbbabaaaaaabababbaababbbbaaaabbabbbababbaababbbabaabbabbaaaabbabbbabbababbbbabbbabaababbbababbbabbaabbaaababbbbabaabbbaabaaaaaabaabbbabbbabbaabbaabaababaaabaabbbbaababaaababababababbaaabbbabbabbbbbbbbaabbbababbabbaabbaaaababbaabaaabbbababbababaaabbbbaaabaabababbbbbbaaaabbbaaabbbbaabaaaabaaaaaabbabaabaababbbaababaaabaaaabbbabbbbbaabaabaaaabbbabbbaaaaaabbabababbbbabbaaaabaababbabbbbbbbbbaaaabbbaaaabaaaaaaaabbbabbababbbbaabbbbaaaabababaaaaabaababbbaababaabaaaababaabaaabaababbbaaabbbbababbabababaaaaaabbbbbbbabbbaabbbababaaaabbbbaaaaabbbbbbbaabbaabaaabbaabbbbbabbbbbbaabaabaaabbabbaaaabbaaaaaabaabaabbbaabbbbabababbbbabbbbbbbabbbaaabbbbabababaaabbaaaababbbaaaabbbbbaabaaabaabaaabbbaaabbaabbabbbbbaabbabababbabaaabbbaabaaabbaaabaaabbabbaaabbbabbbbbbabbbbbabaaaabbaabaabaaaaababaababaaabababbbbabababababaaabaabbbbababaabbbbbbaaaabbbaabababaaabbabbabaabababaabababaaaaabaaaaabaabbbaaaabababbabaabbbbaabababbbbaabbaaabaaaaabbaabbbbabaaabbbaababababababaaabbbbbbababbbababaabbbaabbaaabaabaaabaabababaaaabbbababbaaaabbaabbbaaaaabababaaabababbabababbbaabbbbbaaabaaaaabaababaaaababbbbababbaabaababbaaabbaaaaaabbaaaabbabbbbabbaabbaaaabbabbbbbbaaabbababbbbbbbbbbbabbbbababaaaabbbbbbabbbbabbababbbbabbbababbbabaaaabaabbbbababbaaabbaabbbabaaaabaabbaaaabbaabbababaabaabababbaaabbbbaaabbaaabbbbabaaaaabaabbababaabbbbabaabbaaabaabaabbbaaaaabbbbabaaabaaaaaaaabaaaababbabbbaababbaaabbabbbbbabbaabbbbabaaaabbabaaabbbbabbaabaabbbbbabbbbbbbabbbaabbbbabaababbbbaaaaabbbabbbabaabaaabaaabbbbbbaaaabbaabbaaabaabbaaabaabbabbbbbaaaaaaaaaaabaabaabbbbabaabababbabbbbbaaaabbaababbaaabababbabbaabaabaaabaaaaabbbaaabbaaaaabaaaaabbbbbbbababbaaaaabaabbbaaabbabbabaabbabbbbabbbaaaabbabaaabbbbabaaaaabbaaabbbaaabbaabbaabbaaabbabbababbaaaaaaabbaaababaaabbbaababbbbabbbbaabbababaaabbbaabbabbbabbabbbbbbabbabbabbaaaabbaaabbbaaaabbbbabaaabbbabbbabbbbbaabbabaabbababaabaaababbbbabbaabbaaababbabbababaaabbabbbabaabaabaabbbbbaaabbbbbbaababbabababaaabaaaabaaaabbbaaaaaabbabaaaaaaabbbaabaababbabbababbabaaabaaaaaabbbaabbbbbbbaaaaabbababbabbbaabaabbaabbbaaabaababbbaaabbabaabbbbaaaaaabbbbbbbabbaaaababbabbaaabbabbbabbbaababbbaaababaaaaabababbbabaabbaaaabbaaaaaaabaaaaabbbaaaabaababababaabaabbaabaaaabbbbaabbababbbbaabbbbbaabaababaabbabbababbabbbababbabbababbbbbabbaaaabbabbaaaabbabbbbabbbaaabbbabaababaabaabbaaaababbabababbbaabaabaaababaaaabbaababbbbababaabbabaaababaabaaababababaaabbaabbbabbbbbbbbaabbabbababbbbabbbaabaaabbaaabababaababbaaaaaabaabaaaabababaabbbababbbbbabaaabababababbbbbabababbaabbbabbbabbababbaaaabababaaabbaaabaabbabbabbabbbbbabaabaabbbabbabaababaaabbbabbbaabbbaaaabababbbabbababbaabbabaabbaaabaababaaabbabbbbbbbababbbabaaaabbbbabbbaababbababbbbbaaabbbababaaababaababbbbaabbaababbbabbbbaabbabbbbbaababbbaabbbaabbbbaaababababaaaaababaaaaabbbbbabababbbbbaabbbabbbbbbaabaaaaaabaabbaaabaababaababaaaaabbbabbbabababaabbbaabbbaaabbbbbbbaaabbbababbaaabaaaaaaaaaaaabbaaaaaaaabaabbabbbbbabbababbabaaabbbbbbabbabbbbbababbababbabaabbabaaabbbbbabbbaabaabbaaabbbbabbbbbabaaabaabbbaababbaabaabbbbbbbabbaabbbabaaaababaaaababaaabaababaabbbabbbbaaaaabaabbbabaabbbaaaaabbaabbaaabbaaaabbbbbabbababababbbaabaabbbbabbbbbaaabbaaaabbaaabaabaabbaababbbbaabbaaaaabbaaaaababaabaabaaabbaaabbbaaabaabaabbabbaababbaaabaaaaaabbbbbbabbaabbaaaaababbababaaabaaaaababaabbabaaababaaababbaaabbbbbbbbaabababbbbaaabbbbbbaaabbabbaaabbabbbbababbbbabbbbabbbaaaaaaabaaabbaabbaaabababaabbaabbbbbbaabbbbbbabbaaaabababbabababbaaabbaabbbaabbbaaabbaaabbbbaabbabbaaaababaaabbabbbbbaababaabbbabbabaabbabbbaabababbbbbbaabbaabbabbaabbaaabaaaabaabbbabbababababababbaaaabbababaabbabbababbbaaaaaabbbbaaabbababaaabbbabbaaabaaaababaabaaaabbaaaababaaaaabbbabaababbaabaabaabbbbbbbaababaababaabaabbbababaabbbabaabbbabbabaabaabaababaaababbabbaabababbbabaaaaaabbabbbbabbaaababbbbabaabbabababbaaabaabaababbbbbbbabaabaaababbbababbbbabaabbbabbbbbaaaaabbababbaaaaaaabbbabbabaaaabbbbbbaababbbaaabaabaaaaaaabbaaabbbbaabbababbaaabbabbabababababbbbabbaaaaaabbbabaaaababaaaaaaabaaaaaaababbbbaaabbbbbbbbaaaabbabbaaabaababaabaabababbabaaaabaabaaaabbabbbabaaaababaaaabbaabbbaaabaabaaabaaabbbaabbaaabaabaababaaaababbbbbabbaaaaaabaabbabaaabaaaabbbbbbbabbaabbbabbabababbbaaaababaabaaaaabbabababbbaaabaababaabbbabaaababbabbaabaaaababaabbaaaabaaaabbababbbbbbaabaababbabbabbbaaaaababaabaabbbbbbabbbbaabbaabbbbaaaaabbabbbabbaababababbabbbbaababbbaaabbababbaabbaaabbbababbaabbaabbbbababbaabaaabababbabbbbbbaaaaabbbbaaaaaaabbbbbabaaaabbbbabaabbbbaabbaaababbababaababbaaabbaaabbabbaaabbabbbabbaabbbbaabbbabaaaaaabaaaaaabbbababaabbabbbaabaabbaaabaaaaaabbbbbbaababbabaabbaabaaababababaabaabbaaabbabbbababaaaaaababbbbabaabaabbbbbababababbbaaabbaaabbbbabbaababbbabaaaabbaabbababababaaaabbbbaaabbbabaabbaabaabbabbaaaaaabababaabbbbbabbabaaaabbbbaabbaaabbbabaabbaabaaaabbaabaaaaaaabaaaaaabbbabbabbbbaabbbabbaaaabaabbababaaaababaaabbababbbabbabbbbabbbababbbbaaaabbabaaaaababaaaaabbbbabbbababbaabaaaaaaaaaabbaaababaaabbabbbbbaababaabbbbbabbabaaaaabbabaabababbaaaabbaabaaabaabaabbbabaaabbbbabaaabababababaabbaabbbaabababbaabbaaaaabbabbbbbbabbaaaababaaabaabaaaabbabbbbaaaaaaabbababbabaabbaaaababababaaabbababababbaabbbbbaaabbbbaabbabbbaabbabaabaabbaababaaaaabbabaabbabbbabaaabbabbbbbaabaaabbaabbbaababbbbbaabbaaabaaaaabbbabababbabbbabbbbaaaababbbbabaabbbaabaaaaabbaabbbbbabbabbaaaabbbaabbbababbbaabbbabbaababbaaaaabbabaaaaaabbaaaabaaababababbaaabbbbaabbabaabaaaaaababbbaaabaabbbbbaabaaaaaabababababaaabaababbbaabbbababbababaabbababbaabbabbaabbbabbabbabaabbbbaaabaabbbabaabaababababbabaaaaababbbabbbbbbaabababababbbabababaaabbabbbabaaaaaabaabbababaababbabbbbbbabababbabbbbaabaaabbaaaaaaabbaaaabbaababaaaaabbaaaaaaabbbababbababbabbbabbbabaaaaaaabababaabbbabbbbbbaaabbbbbbaabaaaaabbaaababaaaaabbbbbbabaabbabbababaaaababbbaabbaabaabababbabbbbababbbaaabbbaaabaabbaabbbaaaaabbaaabaababaabababbbbbbbaaabbabababbbbbaabbbaababbabbbbaaabbabbbaabaaabababaabbaaabbabbababbbbabbabaabbbababbbabaabaaabaabaaababbbabbbbaaabbbabaabbabbbbbaaaabbaabaabaabbaabaabbbbabbabaabbabbbaaabaaabababbaaaabbbabbbbabbabababaaabbbabaabbabbbaabbbaaababbbbbaabbbabaaaababaaababbabaaabbbbbbaabaabaabbbbbabbbbbbbbaabbbabbbbaaaabaababaababaababbbabaababaaababaabbbaabaababaabbaaaaabababbbbabaaabaaaabbaaabbbababaabbbbabababababaaababbaaabbabbaababababbabbaabbabaabbaaaabaabbbbaabaabbaaabaaaaababbaabbbabbbbbabbabbabbabaaabbaaabaaaaaaabbbaaabbabbabaaaabababbbaabbbaaabbbbbbabaabababbbbabbabbababbbaaaaaaabbbbabbbaabaaaaaaabbbaaabaaabbbbbaabbabbabbaaaabaabbbaabbbaaabbbabababaaaaabbabaabbbaabbabbbaabaaaabbaabbabbbabbbbaaaabbbbbbaabaababbabaababababaaaabaaaaaabaaabbababaabbababaabbaaaabbbbbbababbaababaaaaaaabbaabaaabaaaaaaaababaababbbabaaababaaaaabaaaaabaaaabbbbbaabaabaabababbaaaaaabbabaaababbbbbaababaabbabbbbbbabbabaaaabababaabbababbbaabaabaabbbbbabaaabaababaababbabbbbaabbbbbaababbbaabaaabaababaaaaabaaabbabbaaabbbbbabbbaaaabbbababaaaaababbbaaababbbaaaababababbabaaabbbbaabaaabbaaabbabbbbbbaabbbbbaabaababbbbbabbbaabaabaababbaaaaaaabbabababaabbbabbbbabaababaaaaaabbaaaaabaaabbbbbbbbbabbaabaababaabbbabbbbbabbaababbbbaabbaaabaababaabbbbbbbababaaaaabbaabbbbabbbaababbabbbbbaaaaabaaabaabaabbbabbaabababaabbabababbbaaaabababababaaaababbaabbabbbabababababaaabaabbabaabaababbaaabaaabaaaaaaabaabababbaabbabaaaaababbababbabbbabbbbababbbbaaaabbbbbaaabaabbaababbaabbaababbbbbbabbabbbbaabbababbbbbaaababaaabbbbbbaaabbbaaabbaaaababaaabaabbaaabaaaabaabbbabababaabbbbbabbbaabaababbaabbaaaaabababbaababaabaaaaaaaaaaabbabaabbabababbabbbbbaaaabaabbbbaaababbbbbaaaaabaabaabaaaaabbaaaabbbababbbaabaabbbbbaabbaababaaaaaabaabaababaaabbabaababbabaabbbbbbbbbbbabaabaabababbbabbaaaaabbbbabbbababbabbbaaabbababaaabbabaabbabbbabaaaaabbabbabbbaaabaaababbaaaabbbabbbbbbbaababbbbaaabbbbaabbbaaabaabbababbaabbababbabaabbbbbaabbbbaaaaabaabaabbabaabbbabbabbbbababbbabbbbabbbbbbbabbabbaabbabbbaaabaaaababaaabbaaaababbababaaababbbbbababbbbbbaabaabbabbaabbbabbbabababaababbbaaaaabbabababaabbbbaabaaabaabaabababbbaaaabbaababbabababbaaaaaabbaabaaaaabbbabbbaaaaaaaaababbaabbaabbbbbabbaabaaaaabbaaabbaababbbbaabababbbababaaaaabababbbaaaabbbaababaababbbaaabbbaaaaabbaaaaabbaaabbaabbabbaababbabaaaabbabababaaaaaabbaabaaaaabbaaaababbbaabaabbbbabbbabbbabaabbbbbabbbbabaabbaabbabaabaabbababaaaabaaabaaabbabbaabbaaaaabaaaaabbbaaabaababbbbaaaaaabbababaaaabbabbaaaaabaabaabaaaaaaaabbbbaaaaaaaabbbbaabbaaabbaaabbbababaaaabaabbbbabaabababbbaabaabbaaabbaabbabbaaaaaabbaaabababaabababbbbaabbaaaaaabaaaaaaaabbaabaabbbaaababbbaaabbabaabaabaaaaaaabaababbbabababbbaabbbbbbabbbbabaaaabbbbbabbbabbaaabbabbbaaaabbaababbbbabaaaabababbabaaabaaaaaabaabaabaabababbbaaabbbabbbaabaabbaabbbaaabaabaabbbbabbaaaabaabbbaaabaabababbbbabbaabbbbaaaabbbbbaaabaaabababababbbbbbbabaaaabbbbaaaabbbabababababaaabbaabbbbabbbaaabbbabbabbbaaaabababbaabaaabbbbbabbaabababbbabaababbabbbababaabbbaabbbbbaaaabbaaabaabbbbaaabaaaaaaaabbbabbbbabaaabbaabbaaaaaaabbabbbbbabaababaaababbbabbbabbbaaabbaababababbabbabbababbabbaabbbaabbbabbbabbbbbbbabababbabbababaabbbbaaabbbbbaaababbbbbaabbbbaabaaaaaaabbbababbbaaaaaaabbbbaabababbaaabbbbaabaababbbbbbbabbbaabbaaaabbbabaabbbbaaaaaaabaabbaaaaaaabaaabbbbabaaabbbabaaaababbabbabbaabbbbaaabbbbaaaaaaaabbbbabbaabbababbbaaaaaaaabaabaaaabbbbaabaabbaabaabbaabbbaaaababaaaaaaaabbaabbbaaabababaaababbbbbabbbbbbabababbaaaaabbbaababbabbaaabbbbaabaabaaaababbababababbbaabbabbbbbaababaaaaabaaaaabbbaabbbbabaabbaaababbabbbaabaabbabbaabaabbababbbbbabaaabbbbaabbbbababbabbabaababbbbaaabbaabbaabbbbaaabaabaaaabbbaaababbaabbaaaababababbbababbbbbbabbaaaabbababaabbabbabababaaababbaaaababbbbbbaaababbbabababbaaabaaabbbbbaababbbabbaabbbaaabaaaaababbaabbbaababaabbbbbbbbbaaabbaabbaaaabaabbabbabbbbaabababaabbabaaaaaaaabaaaaabbbbbbaababaaaabbbabbbaaaaaabaabbaaaabababbaabbbbabbbbaababbabbbbabaaaababaababaababbbabababbbabaaabbabbbbbabaaabbbaabbaaabbabaaabbbbbaabaababbbbaaaabaabbbaaaabbbbbaabbbbaababaabbbbbaababbabaaaaaabbaabbaaabaaabbbabbbbbabbaaaabbbbbbaabaabbaaabaabbbbbaaabbbbaaaaaaaaaabaaabbaaaabbbaabbbabababbaaaaaabbbbaabababaabbbbaababaabbaabbabbbabaabbbbbaabbbaabbbaabbaaaaababaabaabaabbaababaaababaaaaababaabbbbaabbbbbaababbaaaaaaabbbbababbababbbbabaaaabbbaabbbabbabbaaaabbbbaaaaabbaabaabbabbbbbaabaabaaabaabbabbaaaaababbaaaababbabaabbbabbbbaaabbabaabbababaabbaabbabbbbababbbbaaaaabbabbaaababbbbbabbbabaaababaaabbbabbabaababbbbaaaabbaaabbbbbbbbbaaabbbbbbabbbbabbaaaabbbabbbababbaababbbaabbababbbabbbbbbbabbabaaaabaababaabbabababbababbbaabbaaabbabbbbbabaaababaabbaaababaabbbbaabbaaababababbaaaababbabaaabaababaaabaabaabbaabababbaabaaaababbaabbbbabaaaabbaaaaaaaaaaaaabbabbbabaaababaabaabbaabbbbbbaabbaabaabbaaaaabababaabbaaabbaabbbababbbabbbaaabaaaababaababbaaaaabababbabbaabbababbabaaabaaaaaaabababaaabababbaaaaabbbbbbbaaabbbaabbbabaababbaabbaabbabaaaaabaaaaabbbbbbababbabbbaaababbabaabbbbbbabaaaababbbaabaaabbababbbbbbbabaabbbabababaaaabababbaaababbabbbbaabbaaaaaabaabbbabbaaaaaaaabababbbbaaabbabbbbbbbabbabbaaabbababbbabbbbbbbabaaabaaaaaabbaabbbbabaabbbbabbbababaaabbaabbaaaaabbbbabbabbbaabbbaabaaabaaabbbaaaabbabaabbabbabbbbbabbaabaaabbababbbaaaaaaaaaabbabbaabbaabbbbbbabaaabbbabbaabbaabaabababbbbabababbbbaaaabbbbaaabaabbbabbaabbaaaabbabaababaababaabbabbaabbbbbbbababbabaaabaaaaaaaaababbbabbaabbabbbabababaabaaaabbaabbaabbbbbaababbabbbaaaaababbaabaaaaaaabbaabbaaaabbababaaaabbababaabbabaaabaababbababbbbaababbaabaabbabaaabbababaababaaabbbaabbababbbbababbbbaaabbbaabbabbabbabaaabababaabbabbababababbaaabbbbbbaaabaaabbaabbaaaaaaabaabbabbabaaaabaabaabaabbaaabbbbbbababaaaabbbabbbbaaababbbababaabbabbbbbbbbbbbaaababaababbabaaaabbaaaaabbbbbbbabaababaaabaababbbaabbbbabaabaabbabbaabbabbbaabbababaabbabbbababbbbabbaaaaaabaaabbbabbbababbbbabbbbbbaabaabaabbbbabbbaaaaaaababaaaaaaaaaaababbbaaaabababbaaabbbbbbaababbbabbabaaaaabbaababbbababbbaaabaabaaabbbbabaabbbbabbbbbaaabbaabbabbaaabbaabbbbbbaabaaaaabbabaaabbabbabaaabbbbbbbbabaababaaaaabbbababaabaababbbbbbaabbaaaaabbabaaabbabaaabbabaabaabaaaaababaaabbbbaabbbaabbbababababaaabaaabbababbbbabaaabbbaabbaabaaaaabaaabaabbbbbabbbbabbbbbababbaabaaaaaabaabaaaaaaabbbaabaaaaaababababbabbbaabaabbaaaaaabbaaabbbabaababbbabbaabbaababbabaaabbabbaabbbbaabababababbbaabababaabbbbaaaaaabbbaaabbbabbabbbbbbabbaaabaaabbbbbaaababbbbababbbbabaaababbaababbbbbababbaaaabbbabbbbabbbbabaaaaabbaabbabbabaaabaabaabbbbababababbabbabaaaaabaaaaabbabaaabaabbaababbabbaababbbbbbbabbabbabaaabbbbabbaabababbababaabbbbabbabaaabaaaabbaabbbabbbaabbaabbaaaababbbbbabbaabbaaaabaaabababaaabaaaabbbaaabaabaabaabbbaaabababaaababaabaaababbabaaaaaaaaabbababaaababbbababbbbabababbbabbaaaabbbbbababbabbaababbbbaabaabbaaabaaabaababaaaaabbbbabbbabaabbaaaaabbaaababbababbbabbabbabababbbabbaabbbaabbbbabaaabababbbbbbabaabaaaaabbaaaabbabbbbbbbaaabaabbbbbaababbaaabaababbaaaabbaababaaabbaaaabababaaabbabaaabaaaaaaabaaaababbabbabbaaababaaabbaaaaaaabbbaabaaabababbbabaaabbbbabaaabbabbbabbabbbaababbabaaababababaabbaaabbbaaabaaabbababbaaaaaabbbbababbaabbbaababbabbbbabaabaaaaabbbabbbabababbaaabaabababababbabbaabbbabaabbbbbbaaabbabbaaaabaaaaabbbbbbabaaaaabbbbaaaabbbbabbbbabbabaababbabaabaaaabababaabaaaabbbbababababbbabbbabaaabbaabbbbabaaabbabbabaabaababaabaaababaaabaabaababbbababbaaaabbabaabbaabbbbbbabbbbabaabbbaababbbabbbabababaaabbabbabbaabbbbbabbabbbababbabaababbbabbbbbaabbbabaaaaabbbbbababaabbabbbabbabbaaabaaaabbaaabaabaaabababaaabbabababbabbaabaabbbaababbabbababaababbbaabbaaabbbbbababaabbbbbaabbbbabbbbaabaabaabbaababbabbaabababbbbaaaaabbabaaaabaabaaabababaabbaabbabbbbbbabababbabbabababaabbabaaabababbbabaaaaaaabbaaabbabbababaaabbbaaaaaaaababbabbbbbbbbbbbbaababaabbbaaaabbbbaabaaabbbbaabbbaaaabaabbbbabaaaaabbbabbbbaabbaabbaaabbbaabbabbababbbbababbbabbbbbbababbbbbaabbababbbaababaabbabbbababaababbbbaaabbaaaabaabbabbbaaaababbbbbabababbbbbbaaabaabbbabbabbaabaaabbbbbabaaabbbbabaaaabbbbbbabbababbaaabbaaaabbabaababbbbaaaabbbabaabaabbaaaaaaaaaaaaabbbabbbaabababaabbaaabbabababbbbaaababbaaabbbabaabbababbabababaabbaaaaaababbababbbaabaabbabbaabbbababbbbbababbbaaaabbbbbabbabababbbbbaaaabaaaabbbbababbaaabaabbaabbbabaaabbabaabbbbbababbbaaabaaabababbaaabaaaaababaabbbbaabbabaaaaabbaaaabaabbabaabbbbbbbaaabbabababbbbbabababaaababaaababbbabbbbabaabaaabbabbabaabaaaabbabbaabbbbbaabaaaaabbabbabbbaaabbabababbaabaaabbbaaabbababbbbbbaaaabaabbabababbbabababbbbbbababaaaaaaaabaaaaabaabbbaaabaabbaababbabbabbbaaaaaabaaabbabbaabbaaababbaabaabaabbaabaabbabaaaababbabbabbaabbbabaaaabbbbaaaabbbbabaabbbbbabbbaaababbbaabaaaabaabaabbbbbaababababaaaabaaabaabbaaabbbbaabbaaabaabbbbbbbabbabaaaaaaabbbabababaaababaabbbaaaaabbabbbbbbabaabaaaabbabaabaaaaaaabaabaaaabaaabbaaaabaaaabaaaaaaabaabaabaabbbbaabaaaaaaaabbabbbbbbbbbaaaabaabbbbaabbbbabaaaabbaaababababbaabbbabaaabbababaaababbabaababbbbbbabbbbbbbabbaaaaaabbbbbabaabbbaababbabaabaabababbbabbaaabbbbabbaabbbabaaababbbaaabaaababaabbbbababbbaabaabaaabbbbbabbaaaabbbaaaabbaaaababaaaabbbbbaababbabaaaabbbaaabaabbbbabbaaabbaaabaaabaabbbbabbabaabaaaaaabbbababaabbbbbabbaabaaabaabbababaabaabbabbaaabaabbaababaaaabaaabbabbabbaaabbbaabababbbbabbbbbbbabbabbaabbbabbaabbababaaaaaaaabababaababaababaabababababbaaabababaababbbbbbaabbabbaaabbbbaaabbbabbaaaaabaabbbaaabbbaabbabaabbbabbbbbaaaaaabaaaaaaaababaaabbaabbaaaaabbbabbabbaaabaababbabbabbbabbbbbaaaabbbaabbaaaabbbaaabaababbbbaaaaaaaabbaabaaabaaaaaabbaaaabbbabaaababaabbabbabaaaababbababbaababbaaaaabbbbbaaaabababababbabbabaaaaabbbaabbbaaaaababbbbabbaaaaaabbbaabbabababbbbbbbabaaabbabaaaaaaaababbbbaaaababaabbaaaabaaaababaaabbaaaaabbaaaaaababbbaaababbaabbbbaabaabbabbaaabbbbabaabaababababbabbababababbbbaaababbbbaaaaaababbbaaaaaaababbaabbbabaaabababbbbaabbbbbabbabbabababbaabaabbbaaababbababbbbbabbbbbbaabaaababbaaaaaabaababbabaabaaaaaaaabbaaaaabbabbaabaaabaaaabaabbbbabbababaabaaaabbabbbabbabbaaaabbbababaaaabbaaaabbaaaaaababababbbaabaababababbaaaaaaaaabbbbbaabaaaabbbaaabbbaababaaaabbabbaaababbabaaaabbbbbaaaaabbaabaabaaaabbbaaabaabbbaabbbaaababbaabbabbaabbabbbabbbaaabbabbbbbabbbbabbabaaababbabbbabaaababbaabababababababaababaabbaabbabaababbaabbbabbaabababababaaaaaabbbabbbbabbabbaababbaaabaabaaabaabbaaaababbaaabaaaabbabaabbbaaaaabaabbaaabbabbbbabbaaabaabaaaabaababababaabbabbabbbabbaaaabbbaaaaaabbaaaaababbaabbbababbbaababaaababbbabaaabbbbabbaaabbbaaaabbbabbbabababbaabbbabaababaabbabbbabaabababaaaababbbaabbaababaaaabababaabbbbaabbaaaaaaaaabaaaaaaaaaabbbbbaaabababbbbbbaabbbaaaabbaaaabbababaaaabbbbbaabaabaaabbbbbbbbaabbabaabbbabbaaaaabbbbaaabaaaaaaabaaabaabaabababbababaabaaaabaabbbbaaabbbbababbabbaabbaaababaabbabaaaabbbababbbaaabbabaababbbbbbbbabbbaaabbabbbabbaaaabababaabbbbabababaaaaaaaaaabaabaaaababaaaabbbbabbbaababbbababbaabbbabaaabbbbbbabbbaaaaaaabababaabaabbbbbbaabbabaababbbaabbabaabaabbbbaaabbbaababbbbbaaaabbbababbabbabbbbaaababbbabbbaabbaaaabbbaabbabbbabbbabbababababbababbabbabaaaabbaabbbaaaaabbbbbaabaaabbaabbbbabbaaabbabaaabbbabbbabbbbaaaababbbaaaaaabbbbbbababbbaabaabababbaaaabbaabbbbbbaaabbbaabbabbabbaababbbbabbabbbaaababbabbbabaaabaabbaabbbbabaaaaaababbbaababaababababbbaabababbabbbabbbbabbaaabbbbaabaaaabbaabbabbaaababababbbaabbbbbaabaaabbbbabbabbbaabbaabbbaabbaabbbbababbbaababaabbbbbabbabbbaaaaaabaabbbbabaaabbabaabbbaabaaaabababbaaaabaaaababaaabbaaabbbbbabbbbababbbabbbbabbaaabbbbaabbaabbabababbabbbaaababbabbbbabababbaabbbbbbbabbababbbaabbbbbaabaaaaaabbabaaaabbbbbbbaabaabbabbaabbbababbabbbabaaaaaabbaaaabbabababbbbabaabbbababbbbbbbaaaaabbbaababaabbaabaaaababaabaaabababaaaababbaaaaaaaaaabaabbbbabaabaaabaaaabaabaabaabbabaaabbbbbbabbbbbabaaaaaabaaaaaaabbbbbaaaaabbaaaaabbabbbbbbbaababaaabbbbabbbabbaaabaaabbabbbabbbbbbbaabbaabbbbbababaaaabababbbabbaaaababaaaaabbabbbbbbaabbbbaaabbaabbabbabbaabbbbbabbbbbabbbbbabaaaaaabaabaaababaabbbbaabbaabbabbaaababababbbabaaaabbbababbaaaabbabbaabbaaaaaabbabaabbaabababaaabbaabaabbababbabbbbaabbaababbaaababababbbaabaaaaaaababaabbaabbababbaabaaabbbabaabaabbbaaabbaabbbbbaaaabbaabaaababaabbbbbabaaaaaaabbababaabbbbbbbbaaaaaaaaaabababbabbbabbababababbaaaabbaabaaaabaaabaabbbaabaaabbbaaaaabbabbbbbbabbabaaaaaabaabbababbaabbaababaaabbbabababababaabbaabbbbaaababbaaabbabaabbabaabbababbaaabbabbababaabaabaaaabbbbaababaabababbabababbbbbbaaabbaabbabababbabbbbababbbabbbabababaaabbbbababbababaabaaaaabbbabbbaababbbbaabbaaabbbaabababababbabbabbaabababaabbabaabbbbabaaabbaabbbbbaaaaaaabbbbababaaaabbaababbbaabaaabbbabbbbbaabbbabbbaabbaaabababbbabaaabbbaabababaababbbbbbbbbabaabaabaaaabbbabbaaaaaaababababaabbaaababbabbbbbbbbabbabbabaabbbabbbbbababaababbaaaabbbbababaaaabaaaabaaaabbbaabbbbababbbaaababbaaaaabaaabbbabbbaabbbababbbaababbbaabbabbabbbbaabaabbaaaabaaabaaabaabbabbbabababaaabbbabbbbbbabbaababbaaaaaabbaabaabaabbbbbaaabaaabaabaabbbbbaabbbbbbabbbbbaaaabbbabaaabbbbabbbbbabaabbababaaaababbabababababbbbbaabababababbbbbbbaabbbbaaaaaabbabaaabaabaaaabaaabaaaabbbabbbabaaaaaaaababaabaabaababbaaaaaababbaabbabbaabbaabaabbabbaaaaaabaaaaaababaabbaabaababbbaaabaabbbbbaaaaaababbaaaaabbbaaaabbbabbababbaaaabaaaabbaaabaabaabbbaabbbabababaabbababbaaabbababbaaabababababaabaabababbbbaaabbbaabaabababbaabbbaabababbabbbaabbbbabababaaabaabbbababbbabbabbababbbbabbbbbbabbabbaaaababbbabbbaabbababbaabbabbabaabbabbabababaabaaaaaaaabbbbabaaabbbabaabbaabbaababbabbaaabaaabbabbbabbbbbabbbbabbaabbbbaaaababbabaaaabaabbbbbbbaaaaabaaabbabbababababbaaaabaabbbaaaaabbaaaababbaabababaabaaabababbaababaaabbababaabaaabbababababbbbbababaabbabbaababbbaaaaaaabaaaababbbabaaaabaaabaaaababbbbabbaabaabbbabbaababbabbaaaaaabbbbabaabaaabbaabbaabaaaabbabbbbbbababbabababaabbaababbbaaaabababaababbababaaaababbaabbabbabbaaaabaababaaaabbbbabababbaaabbbbabaabbbbabaababbabbbabbbbbaabaabbaabbabbbbbbabbbaaabbbbaabbaababbbaabbabaababbbbbabababaabbbaabbaaaaababbaaabbbaaabbaabaaaaababbaabaababaaaaaaabbbaaabbaaabbabbbbbababbaabbabaabbaaaaaaaaaababbbababbbaaabaabbaaabaabbabbaababbbabbbabaabababbaababbaabbabbbbaaaabbbaaabaabbababbbbabbaabbaabbabbbaabbbbbbbaaabaaaababaabbababbaabbaabaaaaabbaabbabbbabaabaaabbabbbaabbbaaababbbbbbaaabbbaabbbabaaaaaabbbababbbabbbabbabbaaaaabaababbbaababaaaaababaaabbbbaabbaababaaaabaababbbabbaaababbaaabbabaababaabbabaabbbbaaaaabababaabbbabbaaabbababaabbabbbababbbbbbbbbabbababaaaaabaabaaaabaaabbababbbbaabaabbbbaaaaaaabbbbbbbaabaababbbbaaaaaabaabbaaabbaabbbbabbbbabbaaabbabababaaaaababaaabbbaabbbbbbabbbbbbbbabbbbbababbbaaaaaaabbbababbabaaabbbbabbabaabbabbabaababbabaababbaaaaabbabbababbabaaaaabbbbbbabaabbaaaaabbababaabaaabbbaaabaaaabbbaaabaabbabbabbbaababbabababbaaaaababaaaaabababbbaaababbabbaaabbbbaaaaabbabbabbaabbbbaabaaabbaabaabbbbbaabaabababaabaaaaaabaabbabbbbaaabaababbabbbaaabbbbbbbbaabbbbaaaabbbbabaabaabbbbbbaabababaabaaaaabbbbbbbabbabaaaaaaabbbbabbbbaaabbbbabbaaaaabbbbbbabbaaabababaaaaaabbbbbbbaaaaaabbbbbbabaabbabbabababbbabbaaabbbbbaabaababbbbbabbbbbbbbabbbabababababbaabaababbbbbbaaaaaabbabbbabbbbaababaabbbbabbaababbbbaabbbbbaaaaaaaaaaabaabbaabbbbbbaababbbbbababbbabaabaaaabbaabbbaaabbbabbaaabbaabbabbabbbbbbbbaaaaaaabbbbaababababbababbbbaaabbbbbbbbbaaabbaabaabbaabaababbbaabaaabababaababaaaaababbbbabbabaabbbabbbabababaabbbbbbabbabbaabababbbbaabaabbaaaaabbbbbbabbbbaaaabbabbbabbaababaabbabbbbbabbaaababbbaaababbaabbbbabbabbaabaabaaababbaabbaabbbbaababbababaabbbbaaaabbbabbabbbbbbabbabaaaaababbbbbabbabbbabbaaaabbbbbaabbaaabbaaaabbbaaaababbbaabbabbaabbabbbabababbaaabbabbbaaababaabababaabbabaabaabbbbbababaabbaaaaababaabbbbabbaabbbaaabaabbbbaaaabbbabaaaaaaabbbaaaabbbbaabaabbbbaaaaaaaaaaabbbbaaaabbbaababaaaababababbaaaabbabaaaaaaabaaabbaaabbababbbaabaababaaaabaaabababbaabababbabaabbbbbbbabababbabbaabaaaaabbbbababaabaababaaaaabababbbbabbbbbabbaaabbabbaabaaabaababbbbbbaaaaaaaabaabaabbbbabbabababababbaaabababbaaababaabaaaabaabbaabbabaabaaaabbabababaaaaaabbbbabababbbabaabbbabbbabbbabbabababaabbaaababababbbaababaabaabbaaaabbbabbaabababaaaaababbaaaabaababbaabbbaaababbaabaaabaababababbaababaaababbabaaaabbaabbbabaabbbaabbabbbabbbabbbbaabbaabaabbbabbabbbbbbababaabaabababbbbaaababbbaaaabbbabababaabbbbbaabbbaababbbabbbbbbbaababaabbaabbbbabbbaaabbaabababbaaabbbbabaaabaaabbababaabaabaaabbbbbaababbabbaabbaaaaabbbbbabbbbababbabaabaaabaaaabbbbbbaabaaabbbbababbabbaaabbaabbabaababbababaababbbbbbbababaaabbbaaaabababaaaaabbabaabaaabbaaaabbbbbabbbbaaababbabbaaabaababbbbaababaaababaababbabbababbbbbbabbaaaaaababbabababbaabbbbabaabbaaabaababbaabbaaabbbbabbaabbababbbbaaababbbaaabbbbbbbaaaaabbbabbabbabbabbababbbbaababbaaaaaaaaabababbbbaaaabbbabbabaaababaaaaaaabbbabbbababbabbbabbaabbabbbabbbbaaaabbaaabbaaabababbbbaabaaaabbaabbaabaabbaaabbbabaaaaaabbbaaaaabbabaaaabaaaabbbaaaabaaababaaabaaababbaabaaabbaabaaababaababbabbaaaaabaababbbbaabaaaabbaabbababaabbaabaaabababbbaabbbaaabbbbaabaaaaaaababbbabaabbbbabaaaabaabbbbbbbbaabbbababaabbaaabaababababbabababbbbbababbbbabbaabbabaaabbbbabbbbaabbbabbaabaababbbaaaaabbaaaaabbabbbaababbaabbabbbbabaaaabbabaaababbaabaaaabababababbbbbababbbbbabbbababbbaaabaaaaabbbabaababbbaaaababbbaabaabbbabbbbabbbabbbaaaaabbababababaaaaabababbbabaaaaabbbababbaabaaabaababbbbabbbbabbaabaaababbbbabbbababbbabbaabaaaabaaaaaabbaabaaaabbbbbbbbbabbbabaababbaaabbbbbbbababaababaabbababbbaaabbabbaabaaaabbaabbbbababbabbaababbbabbaabbbbabbbaabbabbbaaaabbaaabaaaabaabbbababaaabbbaabbaabbbbababaabbbbaaabbaabbbbbaabbaabbbababaabbaaaaabaaabaabbbbbababbababbababbababbababaababaaababbaaaaaabbbbbbabbbbaabbaaabbbaaaabababbaaaaabbaaaabbaaabbaabbbaabbbbbabbbbabbababbaabbabaabbaabaaabbaabaaaaabbbabbaaababbbbabbaabbaaabbbbbbbabaaabaabaabbbaaabbbaaabaaababaabbbabbbabbbbabbbbabaaabaabababbabbbababbaababbabbbbbbbbbbbabbbabbaabbaabbbbababbbbabaaaaaabbabbaabbabbbaaabaaaababbbabbbbbbabaaaababaabbbbbabaaabbaaabbbaabaaaaabababbabbabbabaababaabbbbababbbbaaaaabbabaababbbbabaaabaaabaabaaabbbbbbbbbabababbbbbaabaaabaabbabbabaaabbabaaababbbabaaaabbaaabbabbaababbabababaabbbaaabbbaaabbbababababaabbabaaabaabbabbaaababaabaaaabaaababbbabbbbaaaabbaaaaaabbaabbabbbababbbbbbabababaabbbbbaabaabbbabbaabaaabbabbaabaabbbbaaaababbabaabbbababbbabbbbbabbbbaaaaababbbbbbbbbaabbbabbbbababbaabaaaaaabbbabbbbbbaabbaabbabababbaabbbabbabaabbbaaababbaabbaabaaabaabbbaaaabbaaaabbabbaabaabaaaabababbbbbaababbbbbabbaababbbaaaaaababbbbbabaababbbbabbbaababbabaabbbbbbbaaaaabbbaabbaaaaaabaabaabaabbaabababbbabbabbbabbaabaaabbbbbaabbbbabbaabbabaaabaaabbaaaabbbabbbbbaaabaabaabaaaabbbaabbbababbbbbaaabbbaaaaabbaabbababbabbbbaabaabbaaabbaaaaaaaaababbbaabbabaaaaabbaabaabbaabaababaabbabaababbaabbbabbabbbbbbbbaaabaabbabbabaaabaaabbbbbbabbaabaaaabbaabaaabbbbbbaabbbaabbbbabaaababababbbbabbabababaababbabaaaabaababaababbababaaaabaaaaabbabbaaaabbabbbabaabbabbabbabaaabbbaabbaaabbbbaaabbbbabbbbbaaabababbbaabbbbabaababbaabbabababbabbaabbbaaaaabbbbbabaababbbababaababababbbabaaabbabbbaaaabbabaababbbaaaaaababbabaababbbbbabaabaabbbbbbbbabbabbbbbabbbabbabbbaabbaababaababbbbaabbbbaabbbabaaaababaaabaabbbbbaaaabbbaaabbababbaaabababbbabbaaaabbabbaababaaabbabaaaabbaaabaaaabbbaaabbabaaaaabaaabaaabaaaabaaabbbbababababbbaababbbbaabbabbbaaabbbabbbbababaabbabbaababaaaabaabbbbbbabbbbbbaaaaababbbbabababaabaababababaabababababbaaaaaaabbbbabaaaabaaabbbabaaaabaaaabaabababaabaabaaaabbabbbabbaabaaabbbbbaababaaaababaabaaaababbbbabbaabbaabbabbaabbbaabaabbbbababbababbbaaaaaaababaabababaaabbaabbbbaaaabbabbaababbababaaaaabbabbaaabbaaaabbbbbaaabbabbbaaabbaabbaaaabaabaaaabbbbaababbabbbabbabbbbbaabaaabbbbabaabaaaabbbabbaaaabababbbabbbbbaaabbaaabaaaabbaababbaababbbaaaaabbabbabbbbbbabbbaabbaabbbaaababaabbaabaaaababbabbabaaabbbabbaaabaabbbaabaababbaabbbaabbbaabaabaabaabbaabbbbabbabaaaaaababbabbbbaaabbaaaaaaaabbabaabaabbbbbaaabaaaaaaabababbbbbabbbabbaaaaaabbbbbbbbbaaaaabaaabbbababbbabbbabaabababaaaaabaababaabbabaabababaababaabbbabbaabaaabbabbaaabbaaabbbbbaaababaaaaabbbbbabbabbbbbaaababbaaaaabbabaabbabbaabaaababbbbbbbbaaabbabbaaabaaaababbbbaaabbabaabababbbabbaaaaaaababaaaabbaaabbabababbaababbaaababaaabbabbbabbbbaabababbbbabababbabbbaababaaaaababbabaaabaabaaabaaaabaaaabababbababbbaaababbaabaabbabaaabbababaababaaabbababaabbbbaabaabbbaaaabaaabbaaababaabbbbbaaabbabbbabbbabaabbbabbbaabbbbbabbbbaababbaabaabbbbabaabbbbbbbbaabbbbaabaaaaaabaabaabbaabbbaababaabbbbaaaaabbbabbaaabbabababaabbabbbababbbaaabbabababbbbbbaaaababaababaabaababbababaabaababaaaabaabbbabaabbaababbabaababaabbbbbabbbabbbababababbaaabbabbabbabbbaabaababbaabbbbbbaabbbbabbaabaababbbababbaabaaabbabaababaaababbabaaaabaaabbbababbbaabbababbaabbbaabbaaaabbaaababbbbaabaabbabbbbabbabaabbbabaabbbbbabaababbabaababbbaaaaabbaaaabbbabbbbbbaababaababababaaaabbbabbabbbaaabaabbabbabaaaaababbaaaababbbbaaaababbbaabbaabbbbbaaabbbbaaabababababbaabbaaaaaaaabbabbbabababababaababbbbaaababbbabaaaabaabbabbaababaaaaababbbababababbbbababababaaabbaabaababbbbbbbababbbbababaaaaabbabbaaabbbaabaaaaaaaabaaaaaabaabbbbbaaaaaaababaabaaabaabababaabaaaabbababbaaabbbabbabbabbbbababbaaabbbaabababbabbbbaaabaabaaabbaabbaabaabbabbbaaababbbaaabaababbbaabbaaabbababbbabbabbbaaabbabaaaabbaaaabaabbaabbaaabbababbbbabbababbabbaabbbaababbabaababaababbbbbbbabaabbbbabbbbbbbababbbbbabaababbbaaaabbabbbbbababbbabbabbabbababbbaaabaabaabbabaaababaabbbbaaaaabbbabbaabbaaababbaaaaababaaababbabbaababbaaabaabbabbbaabaaaaaaabbbbbbbbbababbbabaaabbabababbbaaaaaababaaabbabbaaaabbaaababbabbbabaababbbaabbabbaaabbababaabbbabbababbaabbbbbbaababbbbbbbbaabbbbbbaaaababaabaabbaabbbabbabbbaaaaabbbabbabbbbabbababaabaaaabbababbaaababbbbbabbaaabaabaabbbababbbbaaaaabbbbaaaabbaaaabbbaabaabbaababbabbbbaaabbbbaaaaaabbabbbbaaabaaabbbaaabaabaaaaabaabbbbaaabbbaaaaaabbbbbbabbabbbbaabbbaaaaabababababbbaaaabababbaabbbbbaaaabaaabbaaabbabbbbbaaababbababbaabbabaaabbaabaababaabbbaabbaabbaabaabbabbbaaaaaaaabaaabbbaaaabaaaaaabbaaaaaaaabaaaaababbababbabbbbbbabbaaaabbbbbbabbbbaaabbabbbbbabbbabbabbabbbabbbbabbababaaaabbabaabaabababababbbabaaabaabbbabbabababababbbaabbbbaaaaaabaababbbbababaababbbaabbbaaabaaaaabbbbbaabaaabaababbaababbbbbbbabaaaaababbabbaaabbabbabbbbbaaaabaabababaababbaaaaabbbbabbbababaabbbbababaabbabbbaaababababbbaaabbaabbaaaaaaaabbababaaabaababbabbabaaaabababbbbbaabbabbbaababaabbabbbbabbbbbbbbababaaaabbbabbaabbabbabaaabbbbbbabbaabaabbbbbbbaabaabbabbbaaabaabbaabaabbaaaaabbabbbaaaabbaaaabaaaababbaabaabaaabababbaabaaaabaaabaaababbbbbabababbabbbabaaaaabaabbababaabbbabababbabaabbaaaaaabbababbbbaabaabbbabaababaabaaaababbbabbbbabaaabaabaaaabbaaaaabaaaababbaabaababababaabbbaaaababbaaababbbabbbbabaababababaaaabaaabbbbbbaaaaaaaaababaabaaabaabbaaaabaabaaabbbbabaabbbbbbbababbabbabbbabbbbaababababababbababbbabaaaabaabbbabbaababaaaabaaaababababaabbbbbbbaaabbbbaabaaaababaabbbbbbbabaabaaababaabaaaabbbbabbbbababbbaababababaabaaabaabbaaababababaababbbabaaababaaabaaabbababbabbababbbbaaaaababbbabbbbbabaabbabbbbabbbbabaababaaabbaaaaaabaaaababaaaaabaabaaaabbbaabaabbbbbbbbaaabbabaaababaaaaabbabaabbaabbabbbabbaabaaaabaababbaaabaabbbaabbaaaabaaabbabbbbbbbabaabbbaaaaabbaaaabaabababbababbbaabaababaaabbaabbabaababaaabbbbbbbbabbbbbabbaaabbabbbbabaabbabaaaabaabbaabaaabaaaaabbabaaabbabaaababaababbabaaaabaaaaabaabaaaababaabaabbaabaaababbaabbabbabaaaaaabbabbbbbbbbbbbaabaaaaaababbbaabaabbbbaaaababaaaaaaaabbabbbabbbbaababbabababaaabababbbaaaabbabaaabaaaaabbaaaaaaaaaaaaabbbbaaaabaabbbaababbaaabaabbbabaabbaaabbabbbabaaabbaabbbbbaaabaabbbbabbabaabbbbbabbaababbabaaababbabbabbaabbaabaabbabaaaabbbaabbabbaaababaaabbbbaabaaaabaababbbbbaabababbabbabaaabbbbabbaaaaabbaaaaaaaababbabbaabaaabaaaaabbbbbbaaabababababbbabbaababaaaabaaaabbbbbaaabbabaabaababbaabbaabbbbaabababaababbbabbabbabbbbbbbbbbbaaaabbbaaaaabbaabbaabaaaaaaaaabbbbabbaaaababbababbababbbaaaabbbabaaabbabbbbaaaabbbaaaaabbaabaababbabbabbbababbabaabbabababaaaaaaaabbabbbaababbbaaaaababaaabbaaabaaaaaaabaabbbbbaabbababaababbaaabbaaaaaabbbabbaaaaabbabbbabbbbbbbabababaaaabaaabaabaabbaaabbbbababaabbbabbbabaaaabaaaaababaaabbbabaaabaaaaaabbaaabbabbaabbbaaaabbabaaabbaaabaabbaabbbbbbbabbbababbaababbbababaabaaabbabbbbbbababbbbbabbabbbababbbbaaabaaabaababaaaabaabbbaabaabbaababababaaababaaaabbaabbaabbabaabbbbabbbbaaabaaabaaabbabaabaabaabbbbaabababaaaaabaabaabaabbbbaabaabbbabbabbaaaaabbbabbaabbbbaababbaaaabbbabbaabababbaababbaabbaabbaaabaaabaaabbbababaabbaababbbbbbabbbbbabaaabbabbabaabaaaabababbabababbabbabbabaaabbbabbbaaaabbabababababaabaaabababaaabaabbbaabbababbbbbbbbbababbbabaaabbbbbaaaaababbaabbabbbbaabbbabbaababbabbabbaaaaaababbbaaabbaaaaababbaabaabbbababaaabbbbabbbbbaabaaababaaaabaabbababaababbbbbbbabaaaabbaabaabbbaababbaabababaaabaabbabaabababbbbababbaabbbbbabbbaaaabbabbabaaababaaaabaabababbbbbaabbabbbaabababbabbaabbabbabaaaaaabbaabaaaaabaabbaaaabbabaabababaaaaabbbabbabbbbbbabbbbaabbabbabbabaaaaababbbaabbbbababbbbabbaaababbaaaabaaaaaababbabaaabbbbabaaabbaabbbbaaabbabbabbaaabbabbaaaaababaabaabbabbabbbbbababababaaaaabbbbbbbaaababaaababbaaaababbabbbababaabbaabaaabbaababbaabbbaaaabbbabbbabaabbabababbbbbaababbbbbbbbabbabbbababbaaababbbbabababaaaabbbabaabbbabbbbbbaaaaabaabbaabbbaaaaabaabaaababbbabaaabaababbbaaabababbbaabaaaabbaabbaabaababbbbbbbbbabbabaaabababbaababbaabaababaabbaabbbabbabaababaababaaabbaabbaaababbaabbbabbabaabbbabbbbbbaabbabbabbaaabbabbaaaaaaabbabaabbabbabaababbbaaaaaaaaababbbababbbaaaabaaabaabbbabbbabaabbababaaabaaaaababababbaabaabbbaaabbbbbbbaaaababaabbbbaabbaabababaababbabbabbabbbbaaaababaaaabbbbbbaaabbababaabbabbbabbaaaababaabababbbbaabbbaaaabbbbababbbbbaaababaabbbabbbbbbbabaaaaabbbbaaabbbabbbbbbaaababbabbbbaaaaaabbbbaaababbaaaabbbbaaabbabbaabbabaabbaaababbbaaaabaabbabaabbbabaaaabaabbbbabababbaabaaabaaabbababababaaabababbabbbabaaabaaabaabaabbabaabbabababbaabbbabaabbabaabbabaaabababbbaabaaaaaaaabbbaaaaabbabbaabbbbababaaaabbaaaababbaaaabaaabbababaaaabbbbbbbababaaaaaaabbaaababaabaabbabbbaabbbbbabbbbaaaababbbaabbbabbbbbbbbaaaabaaabaabaabbbaabbbbaaaabbababaabaabbabbbaaaaaabaaabaababbaaaabaaaaabbbabababaababbabaabbaabbaaabaaabbabbaabbbabbbbbbbababaaaababbbaabaabbaababbbbaababbaaaabaabaaabbaabbbaaaabbaaabbbababbaababbabaaaaaaabaabbbbbaabbbaababbbabbbababaaaaaabbbaababbaabbbabaabbaabbbbbbbbabaabaababbbbaababababaaaabbaabbabbbaabaababbbbbbabbababababababaababaabbbaaabbbaaaaababaaabbbaabbbabbbbbabbaaabbabbbababbabaaaaabaabaabbbbabbbaabbaabababababaabbbababaaaaaaaaaabbaabbaabababaabbaabbaabbabbbbaaaaaabbababbabababbbabbbbabbbaaaabaaaabbaaabbbaabbabbabaaaaabbbbbbaaabbabbbbbaaaabbbbabbaaaababbbbaababaabbbbaabaaabaaaaabaabababaaabbaabbaaabbaaaabbbabbbbaabbababaabbaaaaabaaabaabbabababaaabaabbaaabbbbabaabbbbbbabbbbbbaaaaabaabaaababbbabbaabbbbabaaababaababbbbaaabaababbaababbbbbababbbbabaabbaabaabaaaabbaaaaaaabbabbabbaaaabaabbabaaabaabbabbbbababbbababbbbbbbbbabbabbbbabbbbbbaababaaabbaaabaaaaaababbaaaaababbaabbbababbbbaabbaabbbbaaaabbbbbaabbbabababbabbabbaabbaabaaabaabbabaaabababbabbbbaaaabbbbbbabbabaabbaaaabbabbabababbabaabaabbabbabbbabbabbbabaabaaababbbbbabaabaaabbaabbbbaaababbbbaabaaaaabaababbbbaabaabaababaabbbabbbbabbbbabaaabbbbaabaaabababbbbbbbabaaabbbababbaaaaaaabaaababbbabbbaabababababaaabbabbaabbbbabbbbbabbabbaaabbbbbbabababbbabbbabbababbababaababaabababbbababaababababaaabbbaabaababaabbbaababaabababbabbbaabaaabbbbbbababbbabbbbabbbaaaaaabaaabababaabbbbaaaabbbbbbaaaaabbbabaabaababbaaabbabababbbabbbbbabbaabbbbaaabbbbaaababbaabbabababbaababbaaabbabbbabbbbbabababbabbbababbbbbbababaababaaaaaabbabbaaababababababbaabaaaaaaabbbbbaaabbbabbbababbabaaabbababbaabbaabbbabbbbbbababaaaababbaaaabbaaabaaabbaabbbbbaaaaaaaaabbbbaabbaaaaaabbbbabbbbaabbbaaabababbbabbbbbbabbababbabbbabbaaaabbababaaabbbabbbbbaaababbbbbbaababbbabbbabbaaabbabbbbabbabbababbaabaabbaabaabaaaaaaabbbaababbbaaabbbaaabbbbaaaaabbbabbaabbabaaabbaabbaabbaababaabbabaababaababaabbbaaabbabaababbbaaaababaabbbbaaabbabbaabbbbaabaabbababaabbbbbabaabbbaaaabaabaaaaaabbaaababbaabbaabbbaabaabaaaabbbaaabbbbabbaabababbabbbabbabbbbbbabbbaaaaabbbababaabbbabaaaaaaaaaababababaaaabaaaaabbaaababbbbbaaaababaabbbbbbaaabaaabaabaabbbabbbbaababaabbababbbbbbbabbabaabaabbabbaabaaabbbababbbaababbbbbaaaaababaabbbaaaaaaaaaababbbabbbabbabbabbababaaaabbbbaabaabaaaabababbbabbaaaaabaaaaaabaabbbaaabbbbbbbbbaaabaaabbbbbbabbaaaaabbbaaaaabbbbabbbbbababbabbbbabbbbabbbbabbbabbbaabaabbabaabbbabaaaabbbaabbbaabaaaabbbababbaababbbbaaaaaaaaabaaaabbbbaabaaaaabbbabbaabaabaaabbbabbbbbabbbaabbbaaababbabbbbaabbbbbbbabbaabaabbbbbabbababbabaababaaababaaabbbabababbabbaabababbabbaabbabbaaaaaabaaabaaaabbbbbbbaaabaabaaaababaaabbbaabbbabbabbaaaabaabbbbaaababbabbbababaabaabaaabbaaabaaaaabbbaaabbbabaaaabbaabababbbbbaabaabbbababbaabbbbbbbaabbbababaaabbbaabbbabaababaaaaababaababababbbbabbbabababbababababababaababbbabbaababbbbbbaabbbaaaaabbbbbbaaaaaabbaabaaaabbaabbaabbabaabababbbaaaaabbabababbbbaaabababaaabbbabbabbbaababaaabaabbababaabaaababbaaaaaabbaabaabaaaabaabbabbbababbaaabbbbaabaabaaababaaaaabbaaaaaabbabbbaabaaabbabbabaaabbbabbbbbaaaaabbbbabbaaaabbbaabbbbabaaabbabbaabbaababbbaabbbbbbaaaabaabababbbabbabbaababaaaaabbbaabbbbabbbabbbaabbbbaaababbababbbaabbabbbababababbbbbbbbbaaabbabbaabbabbaabaababaaabbbbbbabaaaababbbababaaababbaaababbbbbaabaababbbabbababbaaababbabbaabbabbbaaabbbabababbabababbaababbbbabbabbabaababbbbbabbbabaaaabbababbababbaabababbbaabaaaaaabbaaabbabbabbaaaaaaabbabaaaababaababbbbabbbaabbbaabbaabbbbbabbabbbbababbbabbaaaabbbbabbabaabababaabbabbbaabbabaababaaabababababaaabbabbaaabbabababbbabbbaaaabaabbbbbaaaabbbabababaabbbabbabaaaababbbbbbabbabbaaabbaaaababaaabaabaabbaabbbbabbaabbbabaaaabbaaabbbabbbabaaaaabbbaaabbaabaabaabbbbaabaaabaaaaaababbabbbabaabbbbbaaabbbaababaaabbbabbbbaaaaabababbabbabaaaaabbaabbbbabaabaabbabbababaaabababaabbaaabaaabaaabababaabaaaaabbaabbbaababbaaabbabaabbabaaabbabaaabaabaaabbaaaaabaaaaabababbbaaabbabbbbaaaabbbbbaabbaabaabbabababbbabbabbabaaababbbabbbaaabaaababbaabaabbababbbabaababaabaabbbaababababbbbbaababaababbbbababbbbabbaaaabbaaaabaabaaaaabbaaababababbbaabbaaabababbbbaabaaabaabbbabbbbbbbbbabbbabaabbbaabbbabaaaabbabbbabbabbbaabbaaabaabaaabbbbaabbaaabbbbbbbbbabbbbabaaababbbbaaaabababaaaababbbaabbbaabaabaaabaabbabbabbaababaabaabbaabbabbbbbbabbbbbabbbabbabbaabbabbabaababaabababaaabbbaaabbbbaaabbaaaabaabbbabaabaabababbaaabbabbabaaabbbabbbbbababaaabbbaaaabababaaabaababbbabbaabaaabbbabaaaabaaabbbaabaabaaaaaabbabababbaaabaababbabbbabbbabaabbbbbbabbbaabbaaaabbabbbbbbabbababbbbaaabbbaaabaabbbabbbabbaababbbabbabbbbaaaaaababbbaaabbaaaaaabbaabaabaaabaabaaaaaabbbbbabbbbbaabbbaabbabaaaabbaaaaaabaaaabababaababbaabbabaabaaabbaaaaabaaabbabaabbaabaaaabaaaabbbbbbaaabbabbbabaabaababbbaaabaaaaababbabaaaaabbbabaabbbaaaababbaabbaabbababbaabaabbbbbaaaabbbaabbabbbbabbabbaabaaabbabaaabaabbbbbaababaabbaaabbabbbaabbabbbaabbbabbababbaabaaaaaabbaabbabbabbbaabbbaabaababbbababaaababbababaaabbaabababaaabbbabbaabaabbbaaaabbabbaaaaaabaababaabaaabbaabbbbbaaabbaabaaaabbabbbaaabbbabbaabbbaabaaaaaaaaababbaaaaabbaabbaababbababbaabbabaaabbbaabbbabbbbbababaababbabbbaabaabbabaabbabbbbabbbbbbaabaabbababbaababaaabbbabbbabaaaababbaaababbbbbbaaabbbaaaaabbbaabbabbabbaaaabaabaabbaaabababbbabababababbabbabaabaaaabaababaaaababbbbabbbaababababaabbabbabaabbbbabaabbbbaaababaabaabbaaaababaaabbbbabaabaababbabaabbbababaababaababbabaabaaabbabbabbaabababbaaabbabbbabbabaaaabaababaabbabaabbabbaabaaaaaaaabaaaaababbbabbbabbbaabaaabbaaaaabbaaaaababaabbabaabaabbbbababbbaabbbababaabaabbabbabbababbababbbababbaabaaaaabbaaaaaaababaabaaaaabbbbbbabaababaabbabbbaaaaaabaaabbabaabaababaabbaabbbabbbbbabababbababbbbbbbbbabaaaababbbabbaababbbbabababbabbabbababaaabbbbabaaabbbabbaababaaaabbaabbbabaababbbbabbbaaaaabaaabaaababbbaaabbaabbabbaaaababbaabaaababbbabbabaaabaababaaaabaaababbbbaaaababbbbaaabbbabaababaababaaaabbabababaabaabaaababbaaaababaaabbaaaababaaabbaaabbabaaabbbbbaabbaabbaababbbbabbabaaaaaaababbbbbabbbbbbaaabaabbabaababaabbbbbabbbbbaaaababbabbababbbbababbaaabbbbbaabbaaabaabbabaabbabababbaabbbbbbabaaaaaabababbabbababbbaaaaaaabbabaababbabaabbabbaabaaaaabbabaabababbabaabbbabbaabbbbbbbbbbbaabbbbbbbbbabbaaaabbababaabbaabaaaabaaabbaaababababbbaabababbabbabbbbababbaaababbbbbaabababbaabbbbbbbbaababbababbaabbabababaaabbaaababaaaabbbbbaaabaababaaabbaaaaabbabbbbbababababbbbbbbaaaabbbaababbbbaabbabbbaaabbaaabbaabbbbbaaaaabbbbbabbaaabbbaaabbbaaababbaaabbabaaaaaaaabbabbabbbaaabababaaaaaababbbbbbaabaaaabaaabbaaabbabbbaaabababaaabbbaabbbbbabbbbbbaabbbbabbbaabababbabbabababbababaabbbaaaabaaaabbabaaabbabbbbabbbaaaaabbaaababaabbbbabaaabbababaababbbaababababaaabbababbabbabaaaaaaabbbbaaabaabababbbbbababbabaabbaabbbaaaaabaababaabbabbaabaabbbbaababaaaaabbbaaaaaabbababababbbbbaabbaabbaababbababbbbaaaabbaaaababaabaaababbbababbaabbabbaaaaabbbbbabababbaaabaabbaaaaabbaababbababaabaaababbbababbabbbbbaaaabbaaaaabbabbbabbbabbabbaabbabbabbaabbbabbabbabaaababaaaaabbbbbababbababbbaabbaaabbaabbabbabbbaaaaaaaabbaabbaabbaaabbaabaaaabbaabaaababbaaababaaabbbbabbababaaaabbbabbbabaaaabbabababbabaabbbabbaabbaaaababbabaaababbaaabaababbbabbaaabbbabaaaabbbabbbbabaaabbbaaabbbababaabbaaaabbbbbaabaaabbbbaabbbbbaababaaaaaaabaabaaaabbbbaaabababbababbbaababbbbbaaabbbbbaabaabbbaabaababbabbbababaaababaabbbbababaabbaaaabaaabbbaaaaaaababababbaabaaaabaaaaaaabbaaabbbaabbaaabaaababbbbbbabbbabbbaaaabababaabbbbabbbbaaaaaaababaaabbaabbaaabbbbaababbaaababaababaabbaaaababbabbaababaaabbaaabbabababababaaabbaabaaaaabbbbaaabbabababbbaaabbabababaaabbaaaabbabaaababbabbbbbabbbaababaabaaabaabbbaaaabbabbabbbabbaabbbbabbbbabbababaabbbababaabaaaaabaaabbbbbaabaaaabbbbaabbabaaaabbabbbbabbabbbaabaabaaabbaabbabbbbaaaabbaaabbaaabbbbaababbaaaaaababbaabababbbbbbaabbabaaabbabababaaabbababbbbabaaaabaaaabaaaaaaabbaaabaabbabaabaababbabbbbbaaaabbaabbaaaababbbbbbbaaabaabbbbaabaaabbabbabababaaabababbbbbabaaaaaabaababbaabaaabbbaabababbabbaababbbabababbababaaababbababbababbbbabaaaabbabbbbaababaababaabbbaaaaabbaaaabbaababbbaaaaaabababbbbbababbababaaaaabbbbabbabaaaaaaaabbaababaababbabbbbbbabbbbbbbbaabaabbbbbabbaababaabbbabbbbbababbabbaababbaabaaabbbaaaaabababbbabaaaaaababababbbbbaabbbbabaaaaaaabababaababaaaababaabaaababababbaaabbbbabaaabbaabababbbabababaababaababaabbaabaaabaaabaaaaabbbaaaabbaababaabaaaaaabbabbaabbbbbaabbaaaaababbaaabbaaabbbbbbbababaabaaaaabbabbaabbbbabababbaabaaaabbbaabbbbbaababbbbabbaaaabbaabbabababbbababaabbabaaabbaaaaaabababaaaaababababbaaaabbbaababaaabbbbbbbaaababaaababbabbbaabbabbaabbbbbbbabaabbbababbababababbabaaaabbabaaabbaababaaaabbbaaaaabaaaabaababbbabbbaabbababbbbbababbabbabaabbaabababbabbbbaababbaaaaaaabbbbbabbbaabaaabbababbabbaabbbbbbbbbbbbbabbbabbabbabababbbaabbaaababaabaabababaabaabaababbbbbbbbaaabbabbaabbaababaabbaaaabbaaabaabaaababaaabbbbaaabababbbaaaaaaaabaaabaababbbbabaabaaabbbabbaababbbabbbbbaaaaaaabaabaaabaaabaaaabbaaabbababaaaaaabbaababbaaaababbbabaaabaabbaababababbabaabbbbabababaabbbaababbaabaaaaaaabbaabaaabbbbbabbabbaaabbabbabbbaaabbbbaabababaaaaabbaaabbbbbaabbbbababaaabababaabababbbaababbbbaaababbbabbbaabbaaabababbaaaaabaaabababaababbabbbbbbaabaaaabbbbbbabbbbbaaaabaabaabbabbabaabbbbbaababbabbabaaababbbbabababbbbbaaabbbbabaabbbaaabbabaabbbbaabbbabaaabbbbbbaabbaabababaabaaabbbbabbaabbbbaaabaabaabaaaaababaaaaabbbbbaabbbbabbbbaababaabbbaaaaababaabbbabbabababbbbbabaaabbaaabbaabbbabbabbabbbbbbaaabaabbaaababbbabbbbaababbaabbababbababbbbabaaaaaaabababbaaabbaaabbabaaaabaababbbabbbbbabababbbaabbaaaaaabbaaaababbaaababababbbbbbabbbabbbaaabaaaabaaabbababaaabaabbaaabbbaabbbbaabaaabbbbbabbbaaaabababababaabbbbbababaaababbababaaabaaaaaaaaabbbbababaaabbabbbbaabaababaababaaabaaababaaababaababbbbbaabaaabbbaababbaaaabbaabbbaaabaaabaaaabaabbbaabbaabbbaabbaaaaaababbaabbbbbaababbaabbabaaabaabbbbaaaabbbbbbabaaabaaababaaaaaabbbaabbbbbbbaabaabbbbaabbabbbabbbbabababbbabbaaababbbabbbbaabbaabaababbbabaaabbabbbabbbbaababbabaabbbbaaabaaaaaaabaaaabbbbbbbbbbaaaabbaababbbbbabbbbbbabbabbaaaababaababbaaaaaaaaababaaaabababbaaabbabbbbbaababbabaaaaabbbbbbbababbaaabababbbaaaabbbabbbbbabaaaaaabaabbbbbbbaaaaabbbbbbabaabababbbaabaabaabaabaababaabababaaabbbbaaaaaabaaabaaabbbbbbbaaabbabbbbaabaabaaaabaaabaabbabaaabaabbaaaaaaaabbabbababbabbbabbabbbaaaaaaaaaaababbabaababbbaabbbabbaaabbbaabaaabbaaabababbabaaabaaaaaababbabaaabbbbaababaaaabbabaaabbaaababbbababaabbbbaaaabbabbaaaabbbbbbbabbbabbabbbbbaaaaaabbababbbbaaabaaabbaaabbbbabaaaaaaaaaabbaabaabbbaaaaaaabbbbbaabbabaabbaaababbaabbbabaaabbbbbaabaabbbabaabbbbaabbaabbaabbaaabbabaaaabbabbbaabaabbbbababbbbbbbabbababbaabbbbaabaaabababbbabbbabbabababaaaabbbbaaabbaabbbaaababbabaababaaabaaababaabbabbbbbbbabaabababbaabaabaaabaaaaababbabbaaabaaabbbabaaaaababaabbbabbbbbbabaabbaaababaaabaabaaaaabbaaaabababaabaaaaaabaababaaabaaababaababbbabaaaabaababaabbaabababbaabbbbbbaababbbaabbbbabaaabbbbaaabaaababbbbbbaabaaabbababbabaabaabbbaabaabaaabbababaaabbbababbbbbaababbababaababaaaabbbbababbabaabbbabaabababbabaabbbabbbaaabaaaabbbabaaabaabbbabaaaaaabababbaabbabbabbbaaabaababaabaaaaababbbbaaaaaaabbbaabaababbbbbbaabaaabbbababaabbabaaaabaababaabaabbbbbbabaaabababbabababbbabbbbbbbbababaababbaabaaaaaabbbbabbbbbabaabbaabababababbbababababbbbaaabbaabbbbaaababbaaaaaaaaaabaababbbabaabaaaaabaaaaaabbbaabbbababbbaaaabaabbbaaabababbabaaabbbbbbbbbbabbababaabaaaaaaababbbbabbabbabbbbabbbbbaaaaababaaabbbbaabbbabbbababaabbbbaabaaaabbabbaabbbaaaabaaaabbabbbaaabbabbabbaababbbbaaaaaabaabaababbbbaabbaaababaabbabbaabaaabbabbbbbababbabbbababbbbaaabbbabbbaabaaabaaaababbbaaababbaabaababaaaaaabaabaabaababbabaabbaabbabbaaababbbbababaaaabbbbbbababbbaaaaaaabbbaabbababbbbababaaaaababbabbbbbababbbaaaaaaabbbababbaababbaabababaaabbbbbbabbababbbaaababaabaaabbaaaaaabbbbabbababaabababaabbabbaabbbabbbbbbbbbbaaaabbabaaabaaaabaaabababbaabbaaabaabaabbabbbabbaaabbbababaabaaabbabbbabbaabaaabbaabaabbbaaaabbababaabaababbababbbabababababaaabaabaabbaaaaabaababaababaabbbababbbbaaaabbbbaabbabbbabababbbbababababaaaaabbabbbabbbaaabaabbababaaaaaabababbaaabaaabbaabbaaababbabaaaabababbaabaababbaaaaabbbbaaaabbabbbaaaababbbaabbbabaaaabbbbbbabbbabaababbabbaabaabbabbaaabbbaababaaabbbaaaaaabbaabbbbabaabbbbbbbaaaaaaababbabaaaaabbaaabaabbbaaabaaaaaaabbbabbaaaaaaabbbabbbababaaaaabbbbaababbbbaaaabaaabaabbaababbaabbabaabbbaabaabbabbaabaabbaaabbaabbaabaaaaabbaabbbaabbabbbbabbabbaaaabaaaaaababbaabababbabaabbbbaaaaabbbbaabaababaaabbbaabbbbabaaabbaaababaabbaaabaabaaabbabaaabaabbbababbbababbbbabbbaabaabbabaabbbbbabbbababaaaabaaaabbabaaababaaaaabbbbababaaababbbababaabaaabaaaaabbbbababaabaaaaabbaabbbabaabbaaaabaaaaabbaabaaaabbaabbbabbababbaaababaaaabbababbbababbbabbbbbabbbaaabaaababbbababbabaaaaaabbabbbaaaabbbababbaaaaabbabbabaabbabbabbaaaaabababababbaabaaabaaaaabababaababaabaabaaabaaaaabaaaaabbbbbabaabaaaaaaaaabababbaabaaabbabbbabaaabaabaaaaabaaaaaaabaabbbaabbbabaabababbbbabbababaaabbaabbbbbababbbbaabbbbabbaabbaaabaaaaababaaabaabbbaaababaabababbbbabbabaaaabababaaaaabaaababbabbabbaabaabaaababaaabbaaabbaaaabaaaaaaabaababbaababbabaabbabaababbbbabbaababbbbaaabaaabbaaaaabaababbababaaaaaaabbababbaaaaaabaabbbbbbbabbbababaaaabababbbbbabaaaaaabbabbaaaabaabaabaabbaabbbaababbbaababbaabbbaababbbabaabbaaaababbababababaaaaaabbaaaababaaabaaabbbbbaaaaaaabaaabaaababaabbabbbaaabbbaaabaaabbbabaaaaaaaabbbaaaaaabbabaabbbbabbaabaababbaabbaabbaaabbbbbbabbbaaabbbbbababbaaaababbaaababbbaaaaabaaababaababaabbababbbabaabbaaabababaaabaabaabaabbabbbaaaaaababbaaabaaaaaabbabaaabbbbbbbbbaababaabbbaabbbaababbabbaaababbabaabaaababaaabbbaaaaaabbbabaabaabababbabbababbabaaaaabaabbabaababaababbbabbbbaabaaabbaababbaaababababaaabaababbbbbbbabbbaabbabbbbaaabbbbbaabbabbaaaabbbbaabbbbabbbababababbbbbabbabaabbaabbbbaabaaabbabbbaaaaabbaabbaababbbbabbbabaabbaaabababbbaaaaaaaabbaaabbbbaabaabbbaaabbbabaaabbaaaabbbbabbbaabbbbbbbabbbabababaaabbabbbbaaaabaabaaaabaabbaaabbbbabaabaabbbbabbaaabbabbaaaaabbbabbabaabbbbabbbbbabaaababbaabaabababbbbaabbbaabbbbaaababbbaaaaabbbbabbbbaaaabaabbaaabaabaabaaaaabaaababbbbaabbaababaababbbbbaababbaabbbaaaaaaabaabbbbbabaaabaababababbbbbbabaabaabaabbabbabbbbbaaaababaaabbaaababababbabaaaabaaaaaabbaaaaabbabbabaabbbabaaabbaabaabbaaabaaababaaabaaababababbbaaabaabbaaababaaababbaabbbbbbabbbabbabbbaaabaaabbabaabbaaabbaabababbaabbbbbaabaaaabaaaaabaabbabbabbabbababaaabbbbaabbaaaaaaabbbbbababbbbaaaaabbabbbababbbbababbbbbbababbabbaaaabababbbbababaabbbbbabbaaaabaaabaaaababbababaabbaabbaaabbbabbbaaabaaabaabaaaabababbaaababbaabbaabbbababbaabbaaaaaaabbaabbaaabbaabbbabbbbaaaaaaabaaaabaaaaababbbbabbabaabbaaaaaaaaababbaaabbbaabaaabbaaaabbaababbbabbbbaabbbbbbbabbbbaaabaabaabaaaaaabbbabbbbbbbbaabaabbabaaaabaabbabababaabbbbaababaabaababaaaabaaaabbbbabbabaaabbaaabababbbababbabbbbbaabbababaaaaaabbbaaaabbabbbbbbaaabaabbabaaaabbbbabaabaababbbaabbabbbabbbbbaabbbbbbbabbbbaaabbaabbabaaabaaabaaaaaaabbaaaabbbbbaabababbaababbabbbabbbabbbbbbbbbabbbbabaababbbbbaabaaababbabbbaabbabbabbbbabaababbaabbabababbaabbabaabababbbbbbbabbaabbbabaababababaabaaaaabbbbaabbaaaaaabbbbbbaaabbbbbbabbabbbbbabbbbaaaaaaabaaabbbaabbaaaaabbbbbbbaabbbabbaabbababbbbababbbbaabbaaaaababababababbabbabaaaabaaaabaabaabaababbaaaaabbbabbbbbaaaabaaaaababbabbbbababaaaaaaabbaaaabababaaababbabbbababaabbaaababaaababbabbabbbbaababbabbbbbabbbabbbbbbbabbbaaaaabaabababbababaababbaabbabaaabbaaaabaaaabaabaaabbbaabbaaabbaaaaababbabbabbaabaaaaaababbabbaaaabaaaabbaaaaaaaaababbaaaaaabbbbababbbababbbbaabbbaaabaababbbabaababbaabbababababaabaabaaaababbbaaabbbaaababbabaabbbaaaababaaaabaaaaaabaabbaaaaabaaaababababbabaaaaaabbbabaabbaabbbbbaaabaaaababbabbababaaababbabbabbbbbbabbbbbaababaaabaabbbabbaababbbbbbabbabbaabaaabaaabaabaaaabbbbbabaaabaaabaabaaabaaaaabbaaaabaabaabbbabaabbbbabababbbbbaaaababaaabbbabbabbbaaaaaaaabaabbbababbbbbbbbbaaabbbbbbabaaaabaaaaababbbaaaaaaaaaaaaababbaabbabbbbabbbaaabaabbaaabbaaaaabbbaaabaaaabaaaaaaabbaabbbaaababbbaaaabaaabbbaabaaaabbaabbabaabbbbbbaaababbbbbbabbbbbbbbaabaabbbaaaaabbaabbaabaaaabbbaaababaabbaabbbaaaaaaaababaabbbbaaabaababbbbbbbaabbbbbaaaaabaaabbbaabaabaabbaaabbbbabababbbabababbabaaaaabababbbbababbaabaaababaaabbbababbbaabbabaabbaabbbbaaabbabbabbababbbbbbabaabbbaaaabbbbabbbaabbabbbbbbbbbbaabbbaaaaabaabbaaaaaabaaabbbabababbbbbbbababababaababaaaaabaaaaaaabaabaabbaaaabaaabbbbaaaaaabbababbbbbaabbaababbbbbababbbabbbaaaabbbabbbbabbbabaabbaaabaaababbabbababbaabbaaaaaabbbbababababbbbbbbbbbababababaababbbbabbaaabbbababbbbbbaabbabaaababaabbabaabbbabbbabbbbbababbbaaaabbbaaababaaabbbabaaabbaabaaaaaaababbabbaababbabaaaabaabbbbbaaabbbbaaaabbbaabbabbbbabaabaabbaababbabbabbbabaabaabaababbbabbaaaaaaababaaabbbbababbbbaaabbabbabbbbaabbababbaabbaaababbabbabababaababbbbaaababbabbbbaaabababaababbababbabbaabaaabaabbaaaabaabbaaaaabaabbaababbaaaaabaaabbaaaababaabaabbaabaabbbababbaaabaababbbbaaabababababaaababbaabaababbabaabbbbbaabaabbabababaaaaabbbaabbabaababaaaabaababaabbaaaaaaaaabaaaaaaaabbbbaaabaaabbbaabbbbaaaaaaaabbabababbbbaaababbbbabaaaabaabbbbababbababbabbaababbbbabaabbbabbababababbbaaaaababbaaabaabbaaaabbaaaaabababaabababaaaaaaaabbaabbbabbbbaaabaabaabababaaabbabaaabbaaabaababbbaababababbabaaababbbbaabbabbbbbbaabaaaaabbaabbabaaabbbbbbaaabaabbbbbbbabaaaaabaabaabababbabbaabaabaababbababbaabbbbbabbabaaaabaaaaaaabbbaaabaabaaaabbaabaaaaababbabbbbbabbbaabbaabaabbbbbbaaabbbabbabaabbababbaabbbbbbbbabbbbbbabbbaabaaababbbbaabababaaababbaabaababbbbbaabbabaabbaabaababbbbabbbbaababababaaabaaababababaaababaababaaaaabbbbbbbbbabbbbbababbaababaabbbabbbaaabbbbbaaabbbaabbbbabaabaabbaaabbaabaaabaaaabbabaabbbabbbbbbabbababaaabbbbbbaaabbbbaabbbabaabbabbababaaababababaabaaaaaaabbbaabaaabaaabababaaabbbbaaaaaaaaababbaabaababbababbabbabbbaababbaabbaabababaabaaaabbbbaaaaaaabbaaababbbbabbbbbaabaabbaaabbaaabbaababbbbbbaabababaababaabaaabaaabbbbaabaaabaaaabaababbabaabababbabbbaabaaaaaaababbaaababbbabbbababbabbbabbbbabbabbaaaabbaaabaaabaaabbbaaababaaaaabaaaaabbbabbabbabbaaabaabbababaaaaabbbbabbbaaaaaaaaaaabbbababbaabaaaabaabbbbbbbbaabaabbabbbabbaabbbbaabbaabaaababbbaabbbaabbbbbababaabaaaaaaaaababababbbaaabbbbaabbbaababbbbabbbbbbabaabbbaaaababaabbababbabbbbabbbbbaaaaababababaabbbabaababbabbaaabaaaababaaababbbbbbbbbbaaaaaabaababbaabaabbabbaababababaaaaababbaabbbbaaabaaabbbabaabbaaabbbaabbbabbabaabababbbaabababaaaaabbbbbbaabbbabaababababbabbabaabbaaaaaaaabbbaabbbababbbaabbbabaaaaaaabbbbaabaaabababbabbaaababaaaaaabbbabaabbaabaababbababbaabaaaabaabbbbaabbabbabbaaaababaaabababaabbaaaaaaaababaabbbaabaaaaabbabbbbbaaaabbbabbabbabaabbabbbaaabbababbaaababbaabaaaababbaababbaabbaabbbbbbaaababbbbaaabbaabbbaabbaabbaaaabbbbababbabaaaabbababaaabbabbbbbbabbaaabababbbbbbaabbbabbabababaaabbbaabaabaaaaaaabaabbabababaabbbbabaaabbaabbaaababbbbbaaaabbaaababaaabbaabaababaaaaabababbaaabbbabbbbabbaabbaaabbbaababaabbabaaaaaaababbabbbbaabbabbaabbbaaaabbabbaaaaaabaaabbbaaabbbbbaabababbaaaaabbbbabaaaaaaabbaabbbbabbbbaabaabbbbaaaabaaabbaaaaabbaababaabbbababaababaabaaababaaaaaaababbbabaababbbbbabbaaaabbbaaabaabaabaabbaabbbababbababbbbbbbbbbbabaaaaaaaabbaaaabbaaabbbaaaababbabbbbbaaaababbabaaaaaabbabbaaaabaaabaabaaaabbababbaabbbaaaabbabaababbbaababbbbaaaaaabaabbbaabbabbabaababaabbbababaabaabaabbaaabbabbabaaabbbbbabbbaabbbaabbbbaabbbbbbbbbaababbbbaaaabbbababaabbaabaabbabababbbbbaaababaaaabbababbaaaabbbabbbaababaaabaaaabbababaaabaababbbabbbaaaaaaabaabbbbababbaaababaabaababbababbbbaaabbbbbaababbbaabbaaaaaaaaaabbbabaababaaabaaabbbbbaababbabababaaabbaaaababaababaababaaaababbabaaabaababbbaabbbbaababbabbbaabbabbbbaababaaaabbabbaabbabaaabbbabbaababbaabbbabbaaabaabbabababbabababbaaaabaabbaababbbabbbbbabbbabbbbbaababaabbabaaaabbaaababaabaaabaaaabaaaaaabbaabbbaaaabaaabbbabaabbbbbaaababaaabbaabbabbbaaabbabbbbbbabababaaaaabababaaaababbaaababbbbabaaaaaaaabaaaabababbabbabaabababaabbbbaabbaababaaabbbabbbbbaabaaaabbbbabbbbbbaabbbaababbabbbaaabbaabbababaaaaabaababaaaaabaaaaaabbaabbbaabababbbabbabaabaaabbbabbbbbbbabbbbbabbbbbabaabababababbabbaaaabaaabababaababbbababaabaaabbbbababaaababbbaaaababbabbaabababbbbabaaabbbabbaabaaabbababaabbbaaaaaaabbbaabbbaaaaaabaabaaabababaabbababbbbbbaabbbbaabaabbabbbaaaabaaaaababbbabbaabaaaabbaaaabababbbbaaaababaababbaabaabaabbaaabbaaabaabaabbbbabbaababbbbaaababbaabbaaaaabbaabaababaabbaaabbaabbabbaabbabbaaaabaaabbaaabbaaaaaaaabbababaaabbbbababbaaaabaaaabbbbbababbaaabbaabaaaabbbabbabaaababbabbbaabbbaabababbbaaaabbabaabbaaaaaabbbbabbbabaabbaabaaabbaababaabaaaaabbbabbaaabababaabaaabaaabbaabbaaabbababbbbabbbbbabababbbaaaaaababbbbaabbabaabbbbaaaaabbaabbbbbaaababababbabbabbaaabaabbbbaaabaaabbbabbabbbabbbbabbbabaabbaabaaaabbaababababbbbbbabbbbabbbbbabbaabbbbabbaabbabbbbbbaaabaabaaaaaabaaabbbaaaaababbbabbabbaabbababbabbbabbabbbabaabaabbbabaaababbababbabbbbbbbaabbaaabbabbababaaabbabbbababbaabbabbbaaababaaababbababaabaaabbaaaababbaababababbababaabaaababaababbababaaaabbbbbabbabbaabbaaaabababbbaabbababababaabbaaabbaaababaabbaababbbbbbbaaabababbabbbaaaaabbbabbaaaabababaaabbbaaaabbbaababaaaabbabbbaaaababaabbbababababbaabbbabbbababbabaabaabbbabbaabbabbabaaaabbbbabbaaabbbbaaaabaaaabbababababbabbbbbaabbbbaaaabbabbbabbaabaaababaabbbbabbbbbaabbbbbaaabbababbbaaabbbabbaaabbaabababbbaaabbbbbaabbabaaababaabbaaabaaaaaabababbababaabaabaaababbbbbbaaaababbbabbbbbabaaababaaaabaaabbbbbabaabababaaaabaaababbabbaabbbbbbbbaabaaababaaabaaabbabaabaabbabaabbabaaabbaabaaaaababbbabaabbbbbabaabbabbababbbaabbabbabaaaaaababaaaabbbbaaabaabaabaabbbabbbbbaabaaababbaaaaabbbabaabaabbbababbaaabaabaaaabababaaabaabaaaabbaababbaaaaaabbabbaabaaabbaabbaaaaabbaaaaabaabbabbbaababababbaaaabbbbbaabbaabbbbbbbbabaaaabababaababaaabaabbbbbbaabbabaabbaaabbababbaaabbaababbaaabaaabbbbabaaaaaaabaabaabaabbaabaabbbaababbbaabbababababbbbbbbabbaaabaaaabaabbaabbbabababbbbaababaaababbbbabbababbabbaaaababbbbbbaabbaabaaabaaaaababbaabaabbaabbabbabaaababbabaaabaaaabbaababaaaabaaabaabaaaabababaaaabbbbbabbababbaaababbbaababbabababbbaabbbbbaababbaabaaabbabaaabaabbbbabaaabbbaaabaabababaababaabbbaaabaaaababaaaabbbbaabbbbabbbbbbababbbababbbabbbaaabbabbaabbbbbaaabbaababbbbaabbabbaababbaaabbbbaaaabbabaabbbabbbabbbbbbbbbabbaaaaabbbabaaabbbaabbbaabbaaaabbbaabbaaabaaabbbabbaabbbbaababbababaaaabbbabaaaabaabaabbbbbbbaabbabbbaaaaabbababbbabaabbaababbabbbaaaabbbbbbbababbbbbabbaaaabababaabaababbbbbbbbbaabababababbababbabbbaabbbabbbbbbaabbbbbbabbabaabaabbbaabaabbababaaabbaabbbaabbbaabbaabbbabaaaabbbabbabababababbbaaaabaabaaabbabbaabbbabbaababaaaabaaababaabbabbaaabaaaabbbaabbaaabbabaaababababaabbbbbbbaabbaaabaaaababbabaabbabbaaaaaababbaaaababaababaabababaabbbbaabaaabbabbbbaabbbabbabaabbbababaabbbbbaaabbbbababbaaaaaabaaabbbbbaaabaabaabbaaabaaabaaababbbbaaabaaaabbbabbbabbbbbabbbbbbbaaabaababaabbbbabbbbbabbaaababbbabaabaabbbbabaaabababbbbaabbbabbbaaabbbababbbbbbbbaaaaaabbbbababaaaabbabaaabaaabaababbbbaabbbabbabbbbaabbbabaababababbbbabaabbababbbbabbbaaabababbbababaaaabababababbbabaaabbabaababbabbbbabaababbaaaaaaabaaabbbabbbbbaaabaabbbaaaababaaabaabaabbbaaabbaababbabbbabbbbababbbbabbabbaaaaaaabbbbaaaabbbaaaabbbabbbaabaaaababababbabaaaaaabbbaaaabbbabbaababababbabbbbbabbabaabbabaaaabaaaababaabbbaaabababaabaaaababaababbaaabbbbbbbaaaaababaaabbbaabbbabbaaaaabaaabaababbbbbbaaabababbaabbbabbbabbaaabbbbbabababbaaaabaaaaaababbbbababbaaabababbbaababbaabbbbaababaabaaaabbbaabbbbabaabaaaaababababbbaabaabbbbabbbbbbabaaaaababbbabbaabababaababbbabbbaaaaabbaaaababbaabbbbbbbbaaabbbaaaababbbaababbaaabaababbbbbbabbbaababaabaaaaabbabbababbbababbabbabaabaabaaabbababbbabbbaaabbbbbabbabbabababbabbabbbbaabbaabbbbbbaabbaaaabbaababbbbababbbaabbaaabbaababbbbbabaabaaaabbaaaabbbbaabbaababbbbbababbbaaabbbbaaaaaaaaabbaaabbaaaaaabaabbaababbabbbbaababbbbbbbbaaaabaababbabbaabaabbaaaaaabaabbaabbbbabbbabbabbbababbaaaaabbababbaaabaaabbbabbaabbabbbaaaababbbaaabbbbaababababbaaabaaabbbbbbabaaabbbabbbbaaaababaaaaaaaaabbaaaabbaabbbbabababbbaabbabbaabaabbbbabbabaaaaabaaabbababaabbababbaababbbbaaabaabbbaabbbbababaaabbbabbbabaabbaaabbaabbbbaaaaaababaabbbbabbabbabbababbbabbaaaababaaaaabbbaaabbbbbaaaabaababaaabbbbbaaaabaaabaabbbaabbbbababaaaabbabbbbabbaaabbababbbbbbbbaaaaaabbaaaaabbabaabaaaabbabaabbbaabababbbbaabbbaaabbbbabbbbbaaaaabaaaabaababbbaababbaabbabbabbbaababbaabaaabbaabaaaabaaaabbaaaabbbaaaabbbbabbbbabbabbbabbbabbabbaabbbbababbabaaabbaaabbabaabababbabbabbaabaaaaabbbaabbbbaababbbbaaabaaabaababaabbaabbababbbbaabbaabbaaaaababbaabbaabbabaabbbabaabbbbbbaaabbbbaabbaaaabbaabaaababbabababaaabbabbaaaabbaaabaabbbbbabaaaabaabaabaabbbaababbbbbaaabbbabaaaaabbbbababaabaabbabbbbbaabbaaabbbbaaabbaaaababbbbbaabaaababbaabbaabbbbbababbababbbbbbabbbbaabbaaabbbabaabaabbbabbabaababbbbaaabbbabbbaabbaabbabababbbbabbbaaabababaabaababaaabbaababaabbbbababaababababaaabbbbabbababbbaabaaabbabbbbabbbaabaaaaabbbaaaaabaaabaabbbabbaababaaaababaaaabaaababaabbaabbaaaabaaaabbbbbbabaabbbaabababbabbababaaaaabbbababbbabbaaaaaabbbabbbabababbbbaaaaabbabbabababbababaabaabbaaaabababbabbaabbaaabbabaababababbabbaaaaabbabbbaabbaaaaaabbbaaaaaaabbbababbbbabbbbabbbabbbbaabaabaaabaabaaaabbbbbaaaabbabbabbababbaaaaabbabaababbababbaabaaabaaaaabbbbbbbaaaaaababbaababaababaaaabaabaaaaaabaaabaabaabbbaaaaaabaaabaaaaabbbbaaabababbabababbbabbbaababaabaabaabaabbaababaabababaabaabbbabbabbbabbaabbabbbaabaaaababaabaabbbbaabababbbbabbabbbbaababbbaababaabbabbaababbabababaaababbaaaaaaaababaaabaabbbbbabaabaaaaabbabaabaaabbaaabbabaaaaababaaaabbaabbabaabaabbbbbaabaaababbbbaaabaaaabbbabaaabaabaababbbbbbbaaaababbbbababababbbbabbabbbaaaaabbababbbababbaabbababaababbaaaaabaaaababaaaaaabbaaabababbabbbbbbbbbbbaabaabbababbbbbaaaaaaabbbbbbbbaababbaababbaaaabbbaabbbabbbbbaabaaaabaababbabbbaaaaaabbbbabaaabbbbaabaabbbbbaaaaabbbabaaaabbbabababaababaabbaabaababbbbaabbaaaaaabbaabaaabbbabbaaaaabbbabbbabbabbbabbbabaabbabbabbbabbabaabbaaababbbaabbaaaaabaaaaababaababaaaaaaaabbbbababaaaabbababbbababbbbabbabbbbabbbabaabaaaabaabbabaaaabaaaabbbbbabbbaabaababbaaaabababaababbabbbaaaabbbbbbbababbbbbbaaaabaaaabaabaaabbbbbabbabababaabaaaababbabbbbbbabaabbabaaaabbabbbaaabbbbbbbbaaabbabbaaabababbabaabbabbbaaabbabababababababbaaaaaababbbbbbabaaabaabbbbababbaaababbbbabbaaaaaabaabbbaaaababbbabaabbabbaaabaabbaaaaabbbaaabbbbaaaaaaabbbbaabbbabbababaaaaababbbabbbaaabbbaabbbaabbbbabaaaaaaaababbaabbabaabbbbbbabbaaababaabaaaabbaabbbaabbaaabaabbbabababbaaabbbabbabaabaabababbaabbbbaaaaabbaabaabbababbabbbaaaabababbbbbaaabbbbbbabaabaaaababbbaaabababababaaaabaababaabbabbabbbbbaababbababbaaababbbbabbbbbaabbbabaabaabbaaaabbbababaaaababbabbbaaaabbbaabbbaaaaaaaabbbbbaaabaaaaaaabaaaaabababbabbbbbbabbaabaabbababbababbbbbaabababbbabaabbaabbabbbbbaaababababbbabbbaaaabbbabaaaababbaaababaabbabaabbaabaabaaababbabaabaabaaaabbbaaaabababaaabababaabababbbaabaaabaabbababbbbbbbaabaabbabbbabbbbbabbbbababbaabbbbabaaabbbbabaabbaababbbababbbaaabbabbabbbbbbbabaaababaabaabbabbabbbbaaaabbabbabbabaaaabaaaaabbbaaabbbababbababaaabbabaaabbbbaaaabaaaaababbabbabbabbabaaaaabaabbababaabbbabbaaabaaababaaabababaaaaaaabaabbbaabbbabaabbaabbbabaaaabaaaaabbaababbbabababaabbabbaababbbaabbbabaaaabaabaabbbbbaaaaababaabbababbaaaaabababaaaabbbababbabbaaaaaaaabaabbbbbababbaabaaaabbabbabbabbabbaabaabbaababaabbbbaaaabbabbbabaabbbbbbbbaabbabaababbababaabbaababaabbbbaabbbaabbabbabaaabaaaabbbbabaabaaaaaaabbaaabbabaaaababbaaababaaabbbaabaabbabaabbbbbaaaaabbaabaabbaaabaabbababbbababbbaabaababbbaabbaabbbbbbaaabaabaabbaabababbabaababbbbabbaababbabbbbbbaaabaaaabbbabbbaabbaabaababababbaabbbabbaabbabaabaabbbbbbbbabbaaabbababbbaababbababbabbbbbbabbabaabbaabaabababaabababbaaaaababbaababaabababbabbabbbabaaaaaaabababbbaabbabaaaaabaaabbbabaaaabaaaaababbbbaabbaabababbbababaabaaabbbabababbbaabbbbbbabbbbbbbaabaaaaabbbaaaabbbaabbababababbbbbaaabbabbabbbbaaaaabaaaabbbabbaabaaaaaaaababababaaaabbbabaaaaabbbbaaaaabbbbaaaabbbaaabbbbabbbbbaaaaaabbabbababbbaabbbbaabbaabbaabbbbbbbabaababbbaaabbbbbabaaaaabaaaababaaabbbaababbbbabaababbaaaaabbbbbabaabababbbaaabbbabbabaaabbbabaaabababbbabbbbbbbaaaabaaabababbbbbbbbbabaaaaaabbabbaaaabbbabbabbbbbbabbbbabaaabbaaaababababbbabbabbaaabababbbabbaabbbbababbaabbbabbbbaababaabaaaaabaaaabbbbabbbaababbababaabbaabbaabaabbbabbbaabaaaaababbaaabaababbaabbbababbababaabbabbaaababbbaabaaabbbabaaabbbbababbabbbbabaaababaaaaaabaababbbaababbbabaaabbbabbaabbbbbaabababbbaabbbbbaabaaaaabababaabbaababbaabbaabaababbaaabaabbbbbabbbabbaaaabbbaaabbaaabbbabbbabbaabbabaabaaaaaababbabbbbaababbbabbbabbaababbababbbababbaabbbbabbabbbaaabbaabaaaaaabbaabaabbabaaaaaababbbbbbaabbabababbaababaababbbbbbbbababbbbbabaabbaaabbaaabbbbbbababbbaaaaaaaaabbbaaabbaaaaabbaaaaabbabababbabbabaabbaaaaabbabbaaaabbaaababbababbbabaabbaaabbbaaababbbbabbbbaabaaabbbabbbabbaaaababababaabaabbbaaaaaaabaaabbbabbababbabbbababbbabbbabbbaabbaaabbababbbaabbbbaaaabbaaabbabbabbaaaaabaaaaabababbbbaabbabbbbaaababbbbbaabbaaabaabbbabababbaaaaaabbabababaabababbbabbbbbbbabbaaabbbabaaabaababaabaababaaaaaabbaabaaaaaabbbaaabaaaaababbbbbbbbbaaabbabbabaababbbabbbaabaabaaaababbaaaabbbbbababbaaaaabababaabbbbbaababaabbbbbabaaabbbabbbbabaabbaabaaaaabbabaaabaababbabbabbbbaabaabbaaabbbbaabaaabaaabaabbbaabbabaabaaababaaaabbaabbbbaaababbbbaaaabbababababaaaabbaaabaaabbabbbbbbbbbabbaaabbbbbbbabbbaababbbaabababbababbbaababbaabbbabaaaaaabbbabaabaababbbaaaababaabbbbbbbaababaaabaababbabbbbbbbaabbaaabaaaaabaaabbbbabbbbabbbabaaabaaabbabababbbaaaababababbabbababbababbabaaababbbaaaabaabbabababbaaaababaaabbabbaabbbabbabbbabbbaaaaaabaaaaabaabbbbaababaabbabbbbabababbabbabbbaabaabbaaaabbabaabaaabababaabaabbabaaabbabbbabbaabababababbababbbbababbbbabaababbbaabbbababababababbbbabaaabbabaabaaabababbbabaababbbaababaaaababaaabbaaabbbaabbaaaaabbaaabaaabaababbaaababaabbbbaaabbabbbababaaaabababbbaaababaabbbabbbbaaaababbaaabbababbaaabaaaabbbaabaabaaabbbaabaababbabbaaaabbaaaaaaabaabababbaabbbbaababaaaaabbaabaabbaaabaababaaabbbaaaabbabbbaaabbbababaaaabaabbaaaaaaabbbbabbabaaaabaaabbbabbaabbaabaabaabababbaaabbaaabababbaaababaababbaabaabaaaaabbaaaababbabbabbbabbabbbbabbaaabaabbbbaaabbbaabbaaabbbbbabaabaabbbaaabaabbaababbbabbbbbbbabbabbaaaaaaabbaaabbabaabababaaaaaabaababbbaabababbaaabbbbaababbbaabbbaabbaababaabbbabaaababbbaaabbbbabbabbababaabbbbbbabbababbabbbabbabaabaabaabbbbaabbaaaaaabbabbbbabaabbaababbabaaaabbbabaaaaabbbbbbbabbbaabbbbbababbaaabbaaaababbbbabbbaabaaaaabaaabbbbbaababaaaabaaabaaabbbaabbbababbabbbbbbbaaabaabaaabbbaababbabbaaaabaaababbbbbaababbbbbababbbbaaaaaabaaaababbbabaaabbaaabababbbbbabaaaabbbbaababbbbbaaaaabbabaaabbbaaaaabaababbabaabbbbaabaabbbbbabbababbaaabbbababbabaabbabaaaaaaabbbbababaaabbabbaabaabbababbabbababbabaabababbaabbaabbbbabaaababbbbaabaaaaaaabaabaabbbbaaaaababbbbbaaabbabaabaabbaaabbaabbbababaaabaababbbabbbbbbaabbbabbababbbaaabbbbbbabbbbbbbbabbbbaababbaaabbaaaaaabbababbbbbbaaaaaabbbaaabbbbabbababaaaabaaaaaababbbbbaaaaaabbabbabaaabaaabaaabaaaababababbbbababbbbbbababbbaabbabababbbbbababaaaaaabaabbbbbbabaaabbbbbababbbabbaaaabaaaababbabbabaaaabbbaaaababaaaaaabbbaababaaaababbbaabababbbaababbababbabaabaaabbaabaaaabaabbbbbababbabbbaabaaaaababababbbababaaaabaaabbbaaaabaaabaaaaabaabbbbaabababaabaaaabbaabbaaaaaaaaababbabaabbaaaaaabbaaaabbabbababbababbbaabbaaaaaabaabbaabaabbaabbabbaababbbabbabaabaaabbbbaaaaabaabaabbbbaababaabbbbbabbaabbbbaabbbbbaabbbaabbababbbabbaabbbaaabbaaaaaabaaaaababbbababbaaabbbbabbaabbbbbaabaaababaaabaaaaabbbabbabaaaabbbabbaaaaaaabbbbaaaabbbaaaaaabbbabbbabababbaaabbbbaaabbbbbbbaaaabbabbbabbbaaababaaaabbbbabaabaabbbbbaabbbabbabababbbabbaababaaaabbbbbbabaaaabaaabaaaabbabaaaabaabbbbaabbbabbaaababbaabbbaaaaaabbbabbbbbabaaabbabaabbabababbbaabbbaaabbaaaaaaabbbabbaabbbaaaabbaababbbbbaaaaaabaaabbbbbbaaaaabaabbbbbbbaababbaaaaababaababbbaaabaaabbbabbbaaaaabbbbaabbbbabbbababaaaaaababbbababaababbabaabaababababaababbaaabbaabbbababbaabbbbaabbaaaabaaaababbbabbbaaaabababbababbabaaababaaabbaaaabbaaabaabaabaaaabbbbaaaaaaaaaababbbabbbbabbbabbaaabaababbbabbaaaabaabbbbaaaaabbababaabbbbbbbbaabbbbbbabbaababbababaabbabbaaaaaabaabbbabaaaababbaaaaaaabaaabbbbbbabbbbbabbbaaaabbabaabbbaabaabbbbbaabaaaaabaaaabbbbababaaaabbbabbabaabaaababbaaaabbbababaabaaaaabbbbbbaabbaaabbbaaabaabbaabbbbabaaaabbbabbaabaaabbbbabbbbbbbaabababbbbbbaaaaaababbbbabbbbbbabaabababbababbabababbbaabababbaaababbaaaabaaaabbbbbabaabaababbbbbaaababbaababbabbabbaabbbbbbbaaabbababbbbbabbabbbbabbbaaaabaabaabbaaabaaaaababbbbabbbababbbaababaabbbaaaababbabaaaabbbbabbaabbaaaaabbbbaaabaabbbbaabbaaabaaaabaaabbabbbbabaabaaabbbabababbabaaabbabaabbbbabababbabbaaabbaaababbbbbbbaabaaabaababaaaaaabbaaaabbaabbbbbbaabbaabbbabbbaababaaaaabbaaabbbbabaaaabbabaabbabbbbababaaabbaabbbbabaaababababababbbbbababaaaababbaaabaaabbaabaabbbbaabaaaabbabbbababaabaaababbabbabbabbbbbaabbabbbaabaaaaababaaabababaababaaaabbaaabbbabbbabbababbbbbabaaaaaabaaaabababbabbbabaaabababaaaabbaaabbabbaabbaaabaabbbbaaaaaaaaababbbababbbaababaabbbabbabaabaabbaabaaababbbbbbbbbbabaabbabbbabbabaaaabaabaaabbbaababbaababaababbaabbabaaaaabbbbbbaababbabaabaaaabaaabbabbabbbabaabaaaabbaaabbbbbaaaaaaabbabbabbbbaabbbbbbbbbbbaabbabaaababaaaaaabbabbaabbabaaaabaaabbbbbaaaaaaababaabbbabbbabbababababbabaaaaabbabbabbbabbaaaabaabbabababaaababbabbaaabbbbbabaabbabbbbaababaabbbbbbbabaabbbaaabaaaabaabbaaaaaaababbabaaaaabbbbbbbbabbbbbabbabbbababbbbbabbababbbbaabbbaaaaaaaaaabaabaabbabbbaaabbabbbaaaabbbaabbbaabbbabaaaaaabaababaabaabbaabaaaabaababaaaabbbabbaaabbaaabbaaaaaaaaabababbbababaaaaaabbababbbaaaabbabbbbaabaabaaaaaaabbbbbbbabbbaaabbbbbaabbbbaaaaaabbbbbbaaabbaaabbbaaabaabbaaaababaaabbabaaabaababbababaabbaabbaabbbbbaaabaabbbbbbbbbbabbaabbbbbbbbbaaabbaabbabbaabbabaaaaabaaabbabbbbaaaabbababbbbbbbabbaaaabaabbbbaaaababaaabbababbbbaabaabaababbaababbbababbababaaaaaaaabababaaabaaabaaabaabbbabaaaaaabaaabbaabaaabaabaaabaababaaaaabaabbbbbbbbbbbaaaabaaaabbabaababbaaababbbaaabbabbaabbbababbaabbabbabbbbaaaaabbbabbbabababaaaabaabbbbaabbaabbaaabaaaaabbbaaaaaaabbbaababababbabbbbababababbaaaaabaabbbbbabaabaabaaabbabbbababbaabaaababaabbbbbabbaababaaababbbaabbbbbabbaabbaabbbbbaaababbabbbaabbbbbabbababbabaaabbaaaaaabbababaabbbaabaabbabbabbbbbbbbbbbbbabbabaaaaabbbabbbbbbaabaabbbbabbbbabbaabbbbaaaabbaaaaaaabaaaabbababbbbaabababbaaaaabbaababbabbaaaabbaababbbaaaabaabababaaabbaababbbabbaaabaabbbbbbbaabbbbbbaaaaabaabbbbbbbbabababbabbaababaababaaaaaababbbbaabaaabbabbaaaababbaaaaabaaababbaababbabbbbbbaabbaababbbaaababaaaaabbbbbabbbbabbabaaaababbaaababaabbbababbabbbaaabbbbbaabbbbbbaaaababbabbbbabbbabbaaabbabaabbbbabbababaabaaaaaaaabaabaabbabaaabaaaabbaaaaabbabaabbababaaabbbbbbabbbaabbaabbbaabbbbbbbbbabbaabbabbbaababbababbbbaaaaabaabbbabbbaaaaababbbbababaaabaababbbbabbabaababbbabbbbaababaabaaaaabababaaababbbbbabababaabbabaaabbbabbbaabbaaabababbaabaaaabbbbababbbbaabbbbbabaabbaaaaaabbababbabbbbbaaababaabbaabaaaabbbaaababbaabababaababbbabbbbbaabbbaaaababbabaabbabbbbababaabbabaababbaaaabbbaababbbbbbbaaaabbbaaaabbbaaaabbabbabbbabaabbbbabbbbbabbabaabaababbbbaaaabbbbabbabbbabbabbabaabaaaaababaaaaababaabbababbaabaabbaaaaabbababbaabbababaaabaaabaabbbabbaaaabbaabaaaabababbaabaaaabbbbbbaaababaabbbbbabbbbbbabbbabaaaaabbbaaabbabaaabbbaabbaabbabaabbbaaaababaaaaaabaaaaaabaabaabbbababaaaaabbbbabbbbbbababbaabbbaaabbaababbbbababbaaaabaabbbaaabaababaaaaabbaababaabbbaabbbbabbabaaaababababbaaaabaaabbbaaabbaabbaabbbbaababbabbbabaabbaaaabbaabbaabbabbabbbbaaaaabbbabbabbbbbaaaababababbaaaababbbabaaababaaababbaabbbabbaabbaaaabbaaabbbaabaaaabaabbbaaaaabbbbbaaaababbabaaababbbabaaabbaaaaaaabbabbabbabbbaaabbbababaabbaababbababbbaaabbaaabaaabaaaabbaabaabbbaabbabababababbabababbaaaababaaaabbbabaaabbbaabbbbaaaaaaaabbbbbbbaaabbbbabbabbababbbbabbaabbabbababbbbbbaaaaabaabbabbaaaabbaabbbbaaababbaabbabbbbbbaabbbbabbbbbbaabaaababbabaaaabaabbaabaababaaababbaabbaaabbbabbaabaaaabbabaaabbbaabaaaabaabbababbabbabbaaabbaaabaabbabaaabaaaaabbaaabbbabbbbababaabbbaababbbbaabbbbbbbaabaababbabbbaaababaabbbaababbabbabababbabbbabaaaabbaaaabaabababbbbbbaabbabbaababababbaaabaaabbbbbbbbababbbabaaabaaaaabbabaaaaaaaaababbbbaaaaaabbabbabbabbaaababaabbabbbbbbababbbbbabbabbbbaaaabbbaaabbbabaaabbbabaabaabbbaaaababaabbabbbabbababababbbababbaaaaabaabaababaabbbaabbbbbbabbaaabbbbbbaabaabaaaabbabababbbbbabbbabbaaabaabbabaaaabbaaaaaaaaabaabaaaaabbababaabbaabaabababbbbbabbbbbabbbaaaaaabbbbaaaabaaaabaaaabbbabaaaabbbabaabaaabbbabbaabbabbabbaaabababababbbaababbbabbaaaabbabababaaaaababbbbbbaabbaaaaaaabbbaaabbbbaababbabbaababbbbabaaaaaaaabbabaabababaaababaaaababaabbabbaabbabbaabababaabaaabbabababbaababbbaabbbaaaaababbbabbaabaabbbbaabaabbabbbaaabaaabaaababbaaaaaaabbaabbabbbbbbaaabbaabaabbabbababbbaaaaaabaaabbbabbaaaaaabaabaaabbabbbabbaaaaaababbbbbbabababbabbabbbbbaaaabbabbbbbbbabbbbbbbbbbabaabaaaabbabaabbabbbaabbbbaaabbbaababaaaaaaaabbabbaaaabaabbbabbbabbabbbaaaababbbabbababbababbaaabababaaabaaabaaababbbbbbbaababbaabbaabaabaaabababaabaaaaababaabaabbbbaabaaaaaaabaabbabbabbababbbbbbbbababbabbabaaababbaaabaaababbabbbbabbbababababaabbbbbbbbbabaaabaabbababaabaaabaaabbbbaabaabbaababbaabbaabaabbbababbabbbabbbabaaaaaaababbbbaaabaabbbbabbbaaabbbaabaabbbbaaaaabbaaaabbbbaaabbabababbabbbabaababaabbaaabaaaaabbbbbaaababaaaababbbabaaaaaabaaaabbabbbbbaaabaabbbabbaaaaaaabbaaabbaabababbaaaaaabbaabaaabbbbbbaabababaababbbaabbbbabbaabbaaaabaaaaabaabaaabaabbbbbabaabaabbabbbbababbbbbbabbbabbbaabbababbabbbbabbababbabababaababbbaabaaabaaaabbbbabaabbaabbabaabaabbbbababaaabbbbbabbbbabaababababbbabababbabbabbbabbaaaababaabbbbabbbaaaaaaaaaabbbababaaababbbaababaabaabbbaababbaaaaababbabaaaabababbbaaabbaaabaaabbbbaaaaaaaabaaaabaaaaaabbbbbbbabaaaaaababbbabbbbaaabaabbaaabaabaabbbbbbbbabbaababbaabbaabbaaaababaabbabbaaaabaabbbbabababbbbbbaaabababbbbbbaabbbabaabbbbaabbbabbbbaabaabaaabbaabbbbabbbbaaaaabbabbabbbababbbabbbbabbbabababbabbbbaabbbaaabbaabbabbabbababbbbbbabbbabbababaaabaaaaaabaabaaaaabbaaaabbabababaaababbbaababbaaababbbbbababbaabbaabbabaaaaababaabaaabbbbbbbaabaaabbbaaabbbaabaabbabbaabbbabbbabaaaabaababbabbbaabbbbaabbaabbabaaaaabbbbbaaabaaabaabbbabaaabbbaaaaabaababaabbbbbbbaaabbaabbaababbababbbbaaabbbabbbbbababaaaaaaababbbabaaabaaabababbababababbaaababbaabbaabaaaabbabbabbabbaaaaabaabababaabaaaaabbabbbaabaabbbababaaaaaabbbbabbbabaaababbbbbaaabaaabaaabbbbaababbaaabbbbbbbabbaaabaababaaabbbbbaabababaaaabababaaaababaababbaaabbabaabbaabaabbbabbbabaaaabbbbbbbbbabaaabbaabbbbabbaababbaaaaaaabbabbaababbbbbababbabaabbbabaabaabbabaaaababababaababaaababababbbababbaabbaabaaabbaaabbaaabbbababbabbabbbaaababbbbaaabbbaaaabbaaabbbaaabbabaababbbaaaabbabbbababbbbbaaaababaabbaaaaabbaabbaaabbbbababbbaaabbbabaaababbbaaabaabaaabbbaaaabaaabbaabbaabaaabbabbababbbaaabbaaaababbaabbababaababbabaaaabaaaabbbbaabbabbbabaaaaabbabbaabaaaaabababaaaaaabbabbbaaaaaababaaaaaaabaaaabbbbbaabbaabbbaabbbbbabbabbaaabbbbaabaabababaabbabbbaabaaabaabbabbaababaaabbabaaaabaabababababbbbbbbbbabbababbbbabaabaaaaaaabaaaabaaaababbbaabaaabaabaabbabaaaabbbbabbabaabababbaababbabaaaababbbbbaaababababbbbababbabbaaababbababbbabaaabbbaaababaabbabaababaabbabaabbbaaabbbabbbaaaaabaaabababbbabbbababbbaaaaabbbbaabaaaaabaaabaabaabbbbbaaaabbabaaabbbaabaabbbbaaaaaaaaaabbbbabbabbababaabaabababbaaaaaaabbaabbbbbaabbbaabbabababbbabaabbabaababbabababbababbbabbbaaabbabbaaabaabbabbaaabbababbabbabbbbaabababaaaabbabbbbabababbabbbbbbaaabbaabaaababbbaaaabaabbaabaaaabaabbbbbabaaaabbbbaabaaabbabbaabbbbbaabbababaaaabababababbabababbbabbabbaaaababbbbbaaaabbbbbaabaaaaabababbbbbbbbbbabbabaaabbaabbbbabbbbbbabaaabaaaaaababbbbbaabbabbabbaaaaababbaaaabbaabaababbababbabbabababbbbaaaaaaaabbbababbaabaabaaabbabbaabbaaabbaabbbbaabaaabbbababbabbaababbbbbbbbbbaaababbababaaaababbbaaaababbbabbaabbbaaabbabaabaabbbaaaabaaaababbabababaabbbabaabbbbbbbabaababaaaaaaabababababbbabbaabbbaababbababbbabaaaabaabbabbababababbbaababaaabaabaaaaaaabaabaaabaabaaabbaabababbbabaabbbbbaaabbbaaaaabaababbaaabbaababbaabaababaabbbbbaabbbabaaabbbabababbbbbbbbbbaabaaababbabbaaabababbabbbbaabaababbabaaaabbbbaaaabababbababbbababbabaaabbaaaabbbaaababbbbabaabbaabbbbbaaabbbaabbbabaaaaaabbbbabbaabbbbababaabbaabbaaaababbabbabbabaaababbaaabaabbbabbbbababbabaabababaaabbaababbbbbaabbabbbbbbabbaaaaababaababaaabbababbbaabaabbabaabbbbbbbababbbaaabababbbbbbbabbabbbaaabaaabbaaabaaaabaaabbaaaabaabaabbbabaabbbbbbaaaaabbbababbaababaabaababbbbaaabbabaabaaaabbbabbabbbabbaabababbaabaabababababbbaabbbbaaaaabbabaaaaabbbabbabaabbbbbabbabbaaaabbabbabbbbbbabbabbbbaaaabbbbaabbaabbabbbbaabbaaabbababaababbabbaaaaabbbbabaaaaababaabbaabbabaababababbabaababbbaabbaaaabaababbaabbabbbbabaabbbaaabbbbaabaabbabbbbbbaaaaaabbbabababaaaabbbbbbaabbabbbbaaaabbabababbbbbbaaabaaaabaaaaababbbaaaaabbababaaabababbbbababbababbbababbbabaaaabaabbaaaababababaaabaababaaabbbbbbabbbbaabbbbabaaabababaaaabbabbbabbaabbaaabaabbabbbbbaabbbababbaababaaaabaabbaabbbbabaaabbababbbbbbbbaabbaaaaaabaababbbbabaaabbaabbabbaaaabbbaaabbbaaabbbbbbaabaaaababbbaaaabaaaaabbabbbbbabbaabababbaabbbabaaabbaabaabaaabaaabaaaaaabbbaaaaaabaabbbabbbaababaabaaabbabaabaaaabaababbbaaaabbbaababbaabaabbaaaaababaabbbbaabbbbabababbbbbbbaaaabbbbabaabbbaababbaaaaaaabbbbaaabbabbaabbbabbbaabbbbbbbbabaaababbbbbbbaabbaaaabbbabbbaabaabbaaaababbababbbabaabbababbabbbabbaabbabbaabbaabaababbabbaaabaaabbababaababbabbbaabbbbabbabaaabbaaababaabbbbaabbababbbabababaabaaabaabaaaaaaabaaabaaaababbaabbbabbabbabaaabbbaabbabaaabbbaaabbaaabbbabaabbbaaababaabbaabaaaaababaabbbbaababaababbbbaabbbbabbbbabbaaabaabaaabababbaabaaaaaabaabaaaaaabbbaaabbaaaabaaaaaababbbabaabbababbbbbbaaabbabaabababbbababaabbabaabbbbbbbbbaaabbaaabaabababbbbabbbabaaabbbababbbaaabbbaaaaabbaaaabaabbbbabaaababaabbabaabbbaaaaaababbbbbabaabbababaaabaabbbaaaaabbbaaababaaaabbbaaaaabbaaabbaaabababbbbababbaababbbbabaaabbbaaaaaabbaaabbbbaaababbabbbababaaabbaaaabbbababaabaaaaabbaaaaabbbabbbbbaabbbbabaaababaabbabaababaaaaaaabbabaababbbaabababbabbababaaaababbbbabaabbaabbaaabbaaaaaabaaaababbaabbbaaaaaabababaaabbaaaaabbbbbaaabbabbbbbbaaaababbbabbbbbbbaaaaaaaababaababaabababababaaaaaaaaabbbbabaaaabbbbababaabbabaabaabbbbbaabbbbbbaababbbbabbbbbbbaabbaabaaaaabaababababaababbabbbbbaabababaaaaabaaaababbababbbbbaaabbaaabbaaababbababbababbbabbaabbaaaababbbababbbababbaabaaababaababbbabbaabaaaabbaabaaabaabbaabababaababaaaaababbbbbaabbbbaabaaabbabbabaaabbabbaaababbbaababbbaaaabbabbabbaaaaabaaabaabbbababaabbbbbbaaabbaaaaaaaabaaaababbaabbbbbaaabaabbbbaaabaaaaaabaaaaababbbbababaabbbabababbabbbaabbabbaaabbbbaaabababaaaabaaaabbbabbbbabbabaaaaaaaaabbbaaabbbbaabbaabbbaaabbbaababaabbabababbbbbaababbbbaaaaaaaabbabbaaaaaababaabbaaaaaabbabaaaabbaaaaabbbabbbabbaaabbbaabbaabbabbbbabbabbbabaaabbaabbabbbaabbaabaabaabbbbababbbbbbabbabaaabaabaababaaabbaababaaaabaabbbabbbaaaabbaabbababaaabaabbbbaaaabbaabbbaabbababaabaaababaaabbaaaaaaaaabababbbaaababaaaaaabbbaababaabaaabababbaabbaabbababbbabbbaabbaabbabaaababaabbaaaabbbbbaaabaabbabbababaababaabbbabaaaaaabbaabaaaaabbbbbaabbababbbaaabababbaabbaaaabbabbbbabaaaaabbaabaaabbabbabaababaabaaaaabaabbabbbbaaabaabaaabbbbbbbbabaababaabbbbbbbaaaabaaabbbbbbbabbbaabbbababbbbbaaaabababbbbbbbabbbbaabbaabbaaabaaaaababaabbabbabbaaabbabbbbbabbbaaaaabaabbaaabbbabaabbba
bbabaabbbababaaaabbbbbaabbaabbbbbaaaabbabaabababaabbbbabbaaaababbaabbbbabbababbabaaaaaabbaababbaababbabbbbbabbbbaababbbbbaaaaaaaabbbabbaabaabaaaabbaabbaabaaaaabbbaaaaabbbbaaabaabaaaabbbbbbbababababaabbbaabaaabbbaaaaaabbabaababaabbbabbabbbabbaabbbabbaabababbbaaabbaababbbbbaabaaaabaababbbbabaabbbababbbaaaaababaaabbbaabbbbbaabbbbabbabbabababbababababbbbabbbbbababaabbbaabababaaaaabbbaaaabaaabbabbaaabaabbbabaabbbbbabbbbbabaabaabbbababbbaabaabbabbbbabbaaaaaaaaabbabaaaaababbbaabbbaaabbababaaaabbbabaabbbbababaaabbbbbaaabbabaaaabbbbbbaaaababbbabbbbbbababbabbaaaababaaababbabbabaabbabaababbabaabbbababbbbbbabbaabbababababbbbabbabbbaaaababbbbbaabbbababaaababaabbaaaaabbababbbbbabbaaaabbababbbababbabbabbbbabbaaabbaaaababaaaaaababbababbbabaaaaababaabaaabababbaabbbaaababaaababababbaabaaabaaaabbaaaabaabaababbaabbabaababbbaabbbbbbbbaaabbabbbabababbbbabbaabaabbbabbbabbbaabaabaabaabbaabbabbababbbaaaabbababbaababaaaabbbbaabbbbaababbbabbbbbaabbabbbbabbbbbbabbbbaaaaabaabbbbbabbbbbbbbbaababbabaabbbaaabbbbabaabbbabbaaababbbaabbaabbbbabaaaababbbaaabaaaaabaabaaabbbaaabbabbaababbaaabaaaabbabbaababbabbabbaaaabbbabbabbaabbabbbbbabbbaaabbbaabbaabababaabbbbabbbaababaaaabbabaaabaabaabbaaabaaaabbaabbaaaabbaababaabbbaaabbaabbbbabbaaabaabaaababaabbbababbababaaaaabbbbaaabbaabaaabaaaaabaabbabbaaaaaaabaaaaaababbbabaaabbaabbabaabababbabaaabbabbaabbababaaabaabaabbbaaabaaabaabbbaaaaabbaabbabbbababbaaaababaababaabbbababbbbbaabbabbbbbbaabbababbbababbabaaabbbbbaababbbabbaaabababababbabaaabaabaaaaaaabaabaabaabaaaabbabaaababababaabbaaaaababbbabbaaabbababbaabaabbbabbbbbbaaabbababbaabbbababaaabaabaabbaaabbababaabbabbbbbbbabbabbbbbababbbbbaababaaaaabaaaababbbbbbbaababbbbababbbbababaaabbabaababbaabbabbbbaababaabaaaaaaababaababbaababbaabaabbbbbbbaababbbabbbbbbaaaabaaaabbabbbbbbaabbaaaababbbbbaaaaabbbbbaabbababababbaabbbabaabaaabaaaabaabbbbbababbaabaabbaaabbbababaaaabaaabababbbaabbabaabbaabbabaaaaababbabbaaaaabbbbbaabaaaabaababbbbaabbababbbabbabaaaabbbabbbbbbaabaabaaaaaabaabaaaabaabaabaabbbbbabbbaaaaabaabbbaaaaaabaabbbaabbaaaabababaaaaaaaaaabbaaabbbbbbababaabbababbabbbababaaaabaaabaaaababbbaaabaabaababbbababbbbbababbabbbaaaabbaabaabaababbaaaababbaabababaaaababbabaabbbaaaabaaabaababbbababababbbbbbbbbbabaaabbabbbabbbbbabbbababaaaabbbabbabbbbabbaaaabbbbbbbbabaaabaaabbbbabaabbbbabababbaabaaabbababbbababbaabbaabababababaabbbaabbbabaababbababaabaaaaabbaababbbbaabbabbaaaabbbaaaabbbbabbaabbabbababbababbbbbaaaaabaaabaababbaaaaababbaaaabbbbaaabbbaabaaaaabbbbbabbabaaaaababbaabbbabbbabbbababbbaaaababbbbabbabbabaaabaaaaabaababbaaabababbbabbaababbbabbabbbbbbaaaaaaababaaaabbababbaabbbbbbbabbbbbababbaaaaabaabbabaabbbbbaaaabbaabababaaaabbbbabbbbbbabaabbaaaaaabaabbababbbabbabababbabaabaabbabbbaaabaaabbaabbbbbaaabbaaaabbbababbbabbaaabbabbbaabbbababbabbbaabbaabbaaaaabababaaabababbababbabbaababaabbbabbbbababaabaaaabbaaabbbbbababbbbbbaabbbbbbaabbaabbbabababbbbbbbbbaaaaabbbabababbaaabababaaaabbbbbabbababbaaaabbabbaaaabaabbababaababbbbbabaabbbbababaaaabaabbbaabaabbabbbaaaaaabababaaaaaaaabaaaabbbabaaaabbaabbabaaababbbbbabbbbabbaaaaaababaaabbbababbbbabababbaaabbaaaabaaaaabbababbabbaabbabababaaaababbabbaabbababaaabaabbbbbbbbbbbbabaaaaabbbbbabbbaabaabbaaabbababaabbbabaaaababbaabaabbbabaabaabbbabbbbbaaaabbababbbbbbaaaaaabaabababbbbbbaaaababaaabaabaababbbbbaababbbabbbbbaaabbaabababbaaabaabbaaaaabbaaababaabaaaaaaaaababaaaabbbbbbbbaabbbabbaaabababaabbaabbabbbababaabaaabbaaabaabbbaaabbbbbaabaaaabaabbababbaaabbabbabbaaababaabbbbababababbaaabbbbbbbabbbaabaaaababbbbaaabaaababaaaabaabbaabbbabababaababbbbbabbbaaabaabbaaaaabaaaabaaabbbaabbabbbaabbaabbaabbaabaabbbbaabaabbbbababbbbabaaabbaabababbababaabaabbaabababbabbaabababbbaababbaabaababababbbbabaabbaabbbaaababbbbbbaaabaabbbbabaaababaaaaabbaabbbbbabbababaabbbaaabbaaabbabbbbaaabaababbabaaababbabaabaababbbbabbbabaabbaababbbabbbaababaabbaabaabaaababaababbaabbbaabbaabaabbaaaaaaaaabbbaabbbabababbbbabaaaaabbbaababaaaabababaababbaaabbbaaabbbabbabbbabbaaaaababbbbbaabbbbbaabbaabbbabaabaaabaaaabaaababbbaaaaaaaabbaaaaabaabbababaaaaaaaaaabaababbababbaabaaabbbaabbbbaabbaabbaabbbbaabaaaaabbbbbbaaabbabbbbabbabaabbbaababbaabbaaaabbababbabbbaabaaabaaabaaabababbbbbabaaabbabaabaabaaababaababbabbabbbabbbabaaabababbabbabaaababbbbabbbbbababbbabbbbbbabaaabbaabaabbabbbaabbabbaaabbbbaabbaabbbbabaabbaabaaaaaaaaaaaaaaabaaaaabbabbaabbbbabbbbbaabbbbabbababbbbbbabbaabbbbbabbbaabbababbbbaabbababbabbbbaabbbbbbbbbaabbbabaaaaaababaaabbbbababaaababbbababaababaaabaaabbaabbbbbbabaaaabbabaaaaabaaabbaaaaababaaaaaaaabbbbbaaabaabbababbbabbbaaabaabaaabaabbabaaabaabaababbabbbbbbbaababbbabaababbbbbbbaabbbbbbbaabbabbbaabbabbabbabaaaabaabaaabbbabbaababbbbabababaabaaabaaabaabaababababbbbbabaaaabbabbabaabaaabbbbaabaabbbaabbbbaabbbbabababbababaabbbbbababababbbabbbbabbabbabbabaabbaababbabbbaabbabbabbbbabaaababababbbabbabbbabbbbbabbbabbabaaaaabbabaabaaaabbbaabbabbaabbbaabababbbababaabbbababbbaaabbbbbaabababaaabbbaaababababbaabbabbbbbbbbaabbaaabaababbaaabaaaaaaaaaaaabbbaabbababbaabbaaabbaaababababaaaabbaaaaaaabaaabaabbabbabaabbbbaaaaabbaababbaaabbbbaaaabbabaabbabbbbbbbbababbbabaaaabbbbaabbaabaaaabbbabababbbbaabababababaaabaabbabbaabbbababaaabbaaababbbbaabbabbbbbabbaaabbabbbbababaabbaababbbaabbabbbaabbbabbababbbbabaaabaabaababaaaababbbbbbaaaaabaabbabbabbbabaabbaabbabbabbbaaabbbaaaaabbbabababbaaabbaabbaaaaaabababaaabbbababbababbaabbbbababbbbaabbaaaaabbabaaaaaabbbbbaaabababaaabbabbbbbaaaaaaabaabaababababaaababbbbaabbbabaaabbbbaabaaabbabbbbaabbbbabaabaaababaabababababbbbbaabbbbbbaabaaababaabbababbbbaabaaaabbbabbabbabbababbaababbbbaaaaaaabaabbbbbbaababaabbabaaabbbbbabbabaabbbbbbaaaaabbaababbbbabbbaaaabbabaaaababbabaabbababbaabbbabbbbaaabbbbbaaabaaaabbbaabbbaaaabaaabaabaababbbbbbbbbbbbabbbababbbaaababbabaabaabbaabbaabaaaabababbbaabaaabbaabbaabbabaabbaaabbababbaaabaaaaabbaaabababaababaabbabbaaaaabbbbabaabbaabbbababbbbabbaabbbabaabbbabbbabbababbbbbaababbababbbbbaaaabaabbaababbababababaabbbabbbaaababbaaabaabbaabbaaababbaabbaaababbaabababbabbbaabbbaabaabaaababbaabaabbbbabbaabbabbbbbbaababbbbaaabaabbaaaabbbbbaaaabbbabbbababababaaaabbbbaaaaabaaaabaabababaabbaabbaabbaabaabaaababbabbbabbabaaaababaabaaaaaaaaaaabbbbabbbbbaabaabbbabbbababbababbabaaabbaabaaaaababbbabbaaaabaabaabaaabbbaabbabbaabababbaabbaaabaaaabaaabaabaababbaababaaabababbaabbbaabbabbabaaababaaababbbabbaaabbbbabbabbbbbbababbaaaaaaaaaababbabbaaaaabbabbabbbbbbbaaabbbbaabaabaaabbbabbaaabbbbababbbbaaaaabbbaaabbaaabababbaaaaabbababaaaababababbaaabaaaaabaaababaaababbabaaabaabbaaaaabbbbbbaabaababbabbbaaabaaabaabbbabbbaaabbbabbabbbabaabaabbabbbbbaaaaaabbababbabbaabbbaabaaaaaabaabaaaaaababaaabaaabaabaabbaabbaabbbbbaaababbabbabbabbbbababbaabbbaabbabbbaaabababbbbabbbaabbabaaabbaabbbbbbababababaababbbaaabbaabaabaababaabbaaabbabbaaaabbbaababbaaabbabababbabbababbbaabbbabbaababbaaaabbabbbbbabababbabbbabaaaaaaabbabbabaaaabaabbbbbababbbbbbababaabbbbabbaabbaaaabbbbbbbbbbaabbabbbaaaaaaabbbababbabababbbbbbbabaabbabbbaaaaabbbabababbaababababaaabbbababababaaababbbbbbbaaaabbabaabbabbbaabaabbabbaaaaabbabbbaaabbbabbbaabaabbbbbbaaabbaaabaabbababbbbaabaaaababbbaabbaaaaaaaabbaabbabbbbabbaaabaabaababbabbababaaaabaaaababbaabbaabbbbaaabbbabababbabbaaabaabbaaaaabaabaabababbbaaabbabaabababbbbbbbbbabaabaaabbbaaaaababbbbaaabaaaabbbbbbabbbbababbbababbbaaaaaababbaabbabaaaaabbaaaaaabaaabaaabbbbabaaabbbbaaaabbbbababbbbbbbaabaaaaabbababbbaaaabbbbbbbababaaaabaaabbaabbaaabbbaaaaaabaaaabbbbaaabbabababbbbaaaabbbbbbbbabaabbaababbaaaaabbaababbbaaabbbaaaabababbabbbababbababbbbbaaaababbaabaaababbabbaaabaababbbaabbababbbaabbaababaaaabbababaababbababababbaabbbbaaabaabaabbbbbbbaabbbbbbaaabbbbbbabbaabaaabaaaababaabaabbbaaabbabaaaaaaaaaaaabbbbaaababbbabaaaabbbaaaabaaabaabbbbabababbaaaaabbaabbbbaaaaaaaaababbbbbbbbbbbababaabbbbbbbaabaababbabbababbaabbbabaabaabbaaaabbbbabbaaababbbaabbaabbbbbaaabbbbbaababaabaaabaaaaabaaabaabbbbaabbbabaaabaabbabbbabbabbabbbbabbaaabbbbaaaabbbabbabbbbbabbbaaaaababbabbabbabbbbbbbbbaabaabbaabaabbbabaababaabbbaaaabaabaaaababbbaababbbbbbabaababaabbabaabbaabbabbaababbbaaabaaababbaaabbaaabbbaabbaaaabaabbabababaabaabbabbaabbabbbabbababaabbbabbbbaaababbaaabaaabaaaaaaababbabbbaaababaabababbbaaaaaaaabaaabaaabbbbbbabbaaaabababbaabbabaaabbbabbaaabaaabbabaababaaaabaaaaaabbaaabaababaaaabbbaaabbbbaabababbbbbabbabbbaabbababaabbbabaabbbabaabbbaababbbababaaaaabaaaaaaaabbbabbaaabbbbaaaabbbbbaabaabaabbbbaaabbbaabbbbbbaabababbaaaaabbaaaaabaaababbaaabaaabbabbabbbbbbabaabbaaabbaabbaabbaabaaaaaaabbaababbabbaababaababbbbbaaabaabbbabbbbbbbbabbababaaabbabaaabbaaaabbbababbaaababaaabaaaababbaabbbabbabbbbabaabbabbaabaabaabbbbbbbabaabaababaaaabaabaabbbababaabbbaaaabbabaaabbbbbbbabaabbbabaababbbababbaaaababbaaababaaaaaaaaabbbababbabbaaabbababbabbbabbaababbabaaababaabbaaabaabaaaaabaabbaababbabbabbabababaaaabbbabbaabbbaaabababbaabbbabbbbbbbbbbbabaabbabbabbaaababbbbbbaabbbbbbbbbaaaabbbbaaaabbbbababbabbabababaabaaaababaaaaabaabbbbbbbababaaabbbbbabbbbbbbaaaaaaabbbbbaabbabbbabaaaaabbaababaaaaaaabbabaababaabaabbaabbaabbbbaaaabbbabaaaaaaabbbabaababaabbababbabaabbbabbabbaaaaaabaaababbbbaabbbbbbababaabababbbbabbaabbaaaabbbaaababbbaabbbaabaaabaabaabaaaabaabaabbabaaababbabbbabbbabababbaaabbbbbbaaababbbaabaabaababbaaababaabbaabbabbabbabbaaaaaababbaaababbbabaabbaabbbabbbababababbababaaaaaabbabababbbbbababbaaaabbaabbababaaabbabababbbbbaabbbabbbbbababbbbbbbaaaaababbbababaaaabbabababababbaaabbabaababbbaaaaabababbbaabbbababbabbbbbbaabbbbbabbbbbaababbabaaabbaabaabaaabbabaaababbabbbbbaababaaabaababaaabaabbabbaaaaabbaabbabbbabaababbbaabaabbbabbababbbbabbbbbaabbbbabbaaababaababaaabbbbbbaabbbbaaabbbaaaabaabbaaaaaabbbaababaabaabbbabbbbbaaabbbbbababababbabababbaaaabaabaaabbaaaaaababbabaabbababbbbbababbaaabbabbbbaabbbbbabbaaababaabbaabbbababaabbbabbabaababaaabaaaaaaaabaaaaaabbbabababbaabaabbbbbbbabbbaaaabbbbaaaaaaabaababbababbaabaabbbbbbbbbabaabbbbaabbbbababaaaaaabaaabaabababbbbbabbbbbaababbaabbaababbaaaabaabbbbabbbbbabaaababaababbaababababbaabbaabababaaaaaabaabaabaaaabbbbabaaabbbbabbabbaabbabaabaaaaaaaaaabababbabbabaabaaababaaaabaabbababbabbaabbabbbbabbbaabaaaabbbaaaabbbbbababbabbbbbbbaaabbbbbaaabbbabbabbbbbbabbbbaaaabbbababbbbbbbaaabaaabbaaaababaaaaaaaaaaaabbaabbbbbbaaabababbbaaaaaabbbbaababbabbbaaaabaabbaabbabaababbaababaabbaabbbabaaaaabaababbababbbabaaababaaaabbababbaabbbaaabaabbaabbbabaaabbbaabbabbabbaabbaabaabbbbababbaababbaaaaaaaaaaabbabbaabbabaabaaaababaabaaaababbabaabbaaabaaaaaaabbaabbabaababbbbbabababababaaabbbabaabbaabbabbaaaaaabbbbbbaabaabaaabaabaabaaabaaabbaabbabbabaaabaabbabababaabaaaaaaabbbabbaabaaabbbbbbabbbbbbbaaaabaaaaabaaabababbabbbabbababababaabaabababbbababababbaabbababababbbaaaabbbabaaaabaabbaabbabbbbaabbbaababbbabaabbababaabbbaabbbbbabbbaabbabaababaaababbaaababbaabbaaaababbaabbababaaaaaabaaaabbababbbbbbbbaaabaababaabaabbababbbbbabbbaababaabbbbabaaabaabaaababbaaabaaaabaaaaabbaabaabaabbbabababbbbbbabbbbbbaaaaabababbaababbaaabbbbaabbababbbabbbaaaababaaaabaaabbbbaabaabaaaabbababababaababaabaabbabbbbaaaaabbbbaabbaabaabbbaaaaaaababaababbbababbabbababaabbbaabbbbabaababaabbaabbaaabbbaabbabbbbabbbbbaaaaaabbaabababbbbbbababaaaabbaaabbbabaabbaaaaababbaababbbaaaaabbbbabbbaaaaaaabbaabbaabbabaaaabaaabbbaaabbbaababbabaabbbababaabbababbabbaaabbbbbbbbaabbbbaaaaabaabaaababbaaababbabbaaabbbbbbabbbbbbbbabbbaaaaaabaababababaabaababbabaaabaabbabbabaaaaaaabbbbbaaabbabababbaaabbabaabaaabbbabbbaaabbbbbaaabbaababbbaaabbaaababbaaaabbaaaabbbbaababaaaaabbabbabbaabbabaaaaabaabaaaabbbaabaaabaaabbaababbabbbbbabaaabaabbbaabbbaaababbbbaaaabababbabaabbababbabbababaaabbabbbbabbaaabbabbbaaababbababbbababaaaaaaabbbbaabbbaaaabbbbbbabbabaabbbaaaaaaaaabbaabbabbbbbabaabaaabbbabaaaabbbbaaaabbbaaaaaabbaabbbbabaaaababababaabbbaabbabbbbaaabbbbbaaabaababaabbabbaaaabbaaababbbbbaabaabaaaabbbbaaabbbbbaabaabaaabaaaaababbbbbabbbabbaaaabbabaaabaaaaababbaababbbabbbaabbbaabaabbbababaabaaabbbababaabaaaaabaabbbbbaababaabaabbabaaabaabbaabbaaaaababbabaababababbbabaababbababbbbaabbbabaababaababbbbabbaabbbbbabbaaaabbabbaababbbbaababaaaabaaaababaaabbaabaaaabbbbbbaabbaabbbbbbbababbbaaaaabbababbabbbaabbaaabababaabbbababbabbbbbbbbbababbbabbbbbbaaaaaaababaaabbbbabaaabbaababaaaaaaabaaababbabbaaabababbbaaabbaaaaabbababbbbbbbbbabaaaabababaaaabaaaabbbababaaaabaabaaababbababaaabbbbbbbabbaaaaabbbaaababbabbbbbabaababaabbaabaabaabbaaabbaaabbbbbbaaabbbabbbabababbbabbaabaaaaabbaaabaabbabbaaaabababbabababbabbbbabababaaabbbbbaaababbaabaaabbaaaabaaaababbbbbbaabaabaabbabbbbbaabababbbbbbbabababababbbbabbaabbaaaabbbabbaaaabbbbabbbbbbaabbbaaabbbbaaabaabbbbabbbabbbbbaaaabaaababaabaabababbbbabaaaabbbbbbabbabbbbbabbbaaabaaaabbbabaababbbbbabaababaaaaaaaabaabaabbabbaabbbbaaaabbbaabbababaaaaabbabbbbbbbbaababaaabbaaabbbbbaaaabbbbaabbbaaaaaaaabbaaaaabbaabaaaaaabbbabbaababaabaaaaaaabaaabbabbaababbbaaaaabaaaaaaabaabbbaaabbbbaababbaabaabbababababbbbbbabbbbabbbbaabbabaababbbbabbbabbabaaabbbbbbabaabbbabbbbabbaabaabbbababaaabbaaabababbabaaabababbabbbbbabbbaabbbbaaababbaaaaabbabaababbbaaaaaabbabbbbababbaababaabbababbaabbbaabbbaaabababbabaababaababababaabbaaabbbaaaabbbabbabaabaaaaabbaabbabbbaabbabaabababbbababbbabaabaaaaabbbbaabababbbbabbababaaaaaabaabaaabbaabababaababbbaabbbbabaaaaaaabbbababbbbabaabaabbbaaabaaaaaababbaabaaaaaabbbbbabbbabbbbbbbaaabbbbbbaabaabbabbbbaabbaababbaababaaaababaaaababaaabababbabaababbbaabaaaaabaababaabababbababbbbabababaaaabbbbaaaabbbbbaabaaaaaabbabbababaabbaaababbabbbabaabbbbbabababababbbbbaaaabaababbabaaaabbbaababbaabbbabbaababaaaababaaaaabaabbabbabbaaababbbbbbbbbbaabaaaaaaabbabbbbbababaababbaabaabbaaaaaaaabbababbbaaabaabbbabbbaaaaabbbabaaaabaabbbaaaaaaabaabababbabaabababbabbbbabbbbbabbaaaabbbababbbbaabbaaaaabbbaabbaabaaaaabbbbaabbaaaabaababbababaabababaaabaaaabbbaaaaaabbaaaabbbbababbbbbaabbaabbabbaabababbbaaababbbaabbbbbaabaaabbaabbbaaabbbaaaaabaaabbabbbabaaaabaaababaababbaababbaababaabaaabbbbbbbabaabbbababbbaababbabbbabbaaaabbbbbbbabbababbbabbbbbabababbbbaaaabaabaabbbbbababaabbbbbbaaabbaaababbabababbabbaabbaaabaababbbbbbbabbabbbbbbaaababbbbbabbbbbbbababaaaabbaabbbbabababaaabaaaaabaabaabbaaaaaaababbaaabbababbbbbbbaaaaababaabbabaaabaaabaabbbaabbaaabaababbbbababbabaaabbaaaabaaababbbaaabbbbbbaaabbaabbaaabbaaaaaaabbababaaaaabbabaaabbbababaaaaaabbababbbabaaaabaababbbbbabbababaaaaaaabbaabbababbaabbabbbaaababbabaabaaabaaaababbabbbbbaaabbababbaabaabbabbbaabbaaabaabbbabbabbaabaababbbaabbbaaababbaabbbbabbbbbbbbbaaabbbbabbbbabababaabbbbababbaababaaabbabbaaababaaaaaabaaababbaabbbbabbaabbbabaabbbbaaaaabbabababaaaababbabaabbaaaaaabbabababababbaababaabababbaabaabbabaabaaaaaaababbbbabababbbbaaabbbabaabaaabbaaabbbaabbbbbaaabababbbaabaabaabaababaabaaaabababbbaabaabaabbbabaaaaabbaaaaaabbabaabbbbbabaabaababbaaabbabbbbbaaababaaababaabbabaaaababbaabaaaaaaababaabaabaabaaaaabbbaaabbababbbaabbababbbaaaaaabbbabbbabbbabaaaababbabbbbabbbbabbaabaabaaabbbaaabaaaaaaabbbabbbaababbababababbaaabbbbabbbaaaabbabaabbaabbabaaaabbbbbabbabaabbabababaaabababaabbbabbbbaaaabbbababbbbbbbabbbbaabaabbbababbbaabbbaababbbabaaaaaaaabababbaaabaaabbbbbbbbbbaabbaaaaabbbbbbaaaaababbabaaabbabaabbbbbababbabbbbaaaabbaabbbaababbababbbbabaababaababbbaababbbaabaabaaaaaaabbababbabbaaabbbbababaaababaabaabababbabbabababbbbabaaabaaaaaaaababababbbbaabbbbbaaaabaaabaaabbbaababaabbaabbababbaabbaabbbabbababaabbbabbabbabaaabaababbabbaabbabbbbbbabaaaabbabababaababbaaaababbabaaaaabbbabbbbaababbababaababababbbabbbabbababbbbbbbbbbaaaaaaabbbaaabbaabbabbabababbaabbbbabbbbaabbababababaabbbaaaaaababaaabbbabababaabbbbbaabaabbbbbaababbaabbbbbbaabaabbbabbbaababaababbbbabaababbababbaaabbbbbababbbaabbbbabaaaaabaabbabbaaaaabaabaabaabaaababbabbaaaaabaaaabbaabaaabbabbbbabbbabbbbaaaaaaaaaababbbaaaaaaaababbbbaabbaaaabbbabbaaaaabbbabbbbaaababbaaababaaaabaabbbaaaaaaabbaabbbabbbbaabbabbbbaaabaababaabbbaaaababbbaabababbababbabbaaababbbaabababaaabababababbaaabbbaaabbabaabaabaaaaabbbbbabbaaaabaabaaaabbaaabaabaabaaababaabbbbbbbbbbbbaaaaabbbbbbbbbaabbaabbbbbbbabbbaaabbababbbababaaabbaaabaaabababaabaababbbbbbaabbbaaabaaaaaabaaaaababbaababaabbbabbababbaabaaabaaabbababbabbaababbaababbabbaaabbaabbabaabababaaaaaabaabbaabbabaababbbbaaabaabbbbbbabbbabbaaaabbabbabbabbbaabaaabbbaabaabbbabbaaabbbaabaabaaaaaaaaaabaababababbaaabbbbaabbaabaaaabbababbabaababbaabbaaabbaababbbabaaabbbaabbabaabbabaaaabaaabbaabbaabaabbbbabbbabbbaaaabbaabbaabababbaabbbabbaaabababbaabababaabbabaaababaabbabbbbaabbaabbabbbabaababbabbababaaabaaaabbbbbaabaabbbaababbbabaaaabaaababababababaabbabaaabababababbbabbababbbaabbbabbbaababbbbbbabbbbaabbaababbabaaabbbabaabbbbbabaabbabbbaaabaababbababaaaababbbbbababbbaabaabbbbbaabbaababbababaabbbbbbbbbaaabbbbaabbbbaaabbbbbbbaaaaaaabbaabababbbabaaaaaababbbaabababaabbabaaabbabaaaaaaaaaaabbbbbaabbabbaaaababbbbaababbbaabbbbabbbbbabababbabaaaaabbaaabaabbabbbbaaabababbbaabbaaabaabaabbbabaabbaabbbabaaaaaaaabbabaabbbabbbbbabaaabaabaaabaaaaaaabbaabaabbbaabaabaaabbbbababbbbbbbbbbaabbbbaababbaaababbbbbaaaabbbaababbbbbbabbabbaaaabaaabaabbaaaabaaabaaabaaabbabababbaabaaabababbabbbaabbbabaaabbaaabbaabaabbababbbaaababbbbbabbaabbababbbbbaabbbbbbbaabaaabaabbaabbbbaaababbbbaaabaabbbbaabaaaababaababbbbababbbbaaabbaababbbbabbbabbbbbababbbbaaaabbababaababaabaabbbabbaaaabbaababbabaabbaaababbabbabaaaabaaabbbaabaaaabaabbaabbabbbaabbbbbbabbabababbbaabaaabaabbaaaaababaaaababababbbaaabaabbaababaaaabaabbabbabbbbbaaaababbbbbbabbabbbbbaababaabaaaababbbaabaabbbbbabaaabbabbbbabbaabbbaababbbaaaabaaaaababaabbbaabaabaabaabaaaaabbaaabbaabbbabbababaabababbababababaabbaabaaaabbabaaabbbbabbabbbabbaaabababbabaabbabbabaaaabbabbaaaaaaaababaababaaabbabaaaabaaabaaabaabaaabaababbbbaabbbbbbabbbbaaababaabbbabbbabbababbbbbbbabbbabaaaaabbababaabbaabbaaabaabaabaaaabbbbbabbaabbbaababbbbbbaabaabbabababaababbbbaabaabbbaaabbbabaababbbabbbabaababbabbbbbaaaabaabbabaabbababaababaabbbbbbababaababbabbaaaababababaaabbaabbabaabbaaabbababbabababbbababababbaaaabaaabaabaaabaaabbbaaaaaaabbbabbbaaaaaabababbbbabbaabaabaabbbbbaabababbbababbbbaababaabbabbbaabbbbbbbabaaaaababbbabaabbbbabbbaaabaaaabaaaabbabababaaaaaaaaaababbbbbbbaabaabbaaabbaaaababbbaabbbaaababbaaaaaabbababbaabbabbbbaaabbababbabaaabaababababababaabaabaaaabaabaabaababaabbabbabababbbaababaaaaaaaababbbbabbbabbbbbaabbbbaaaaabaababababbbbabbabbabaaaaaababbaabbbababbbabababbaaaabaaaababbbbbbbabbbbabaabbaaaabaabbbabababbabbaabbbaabbaaababbaababaaabbabbbaaaabbbababaaabaababbaabbaabaabbbaabaabbabbbbbbaaaaaabbbbaaabaabbbbababbabaaabaababababaaaabbabbaaabbaabbababbbbbabbbaabbabaabaababbbabbaabbaaaababbbaababaaaabaabaaaabbbbaabaabbbbbababbaabaabaaabaaabbaababababababaabbaabbbaaababbaaabbbaaabbabbabbbaabbbbaaaababbbbabbbaaaaabbbaababbaabbbaabbabbbaabaaaababbabbbbaabaabbbaaababbbbababbabbbbbaabaaaabaaaaabaabababbbbaaabbbbbaaababbaaabbbbbbbbbbbaaaabaababababbbbbbbaaaaababaabbbaaabbababaaabbbaaaabbabbabbbbbaaabaaaaabaaabaaababaaabaaabbbaabbbaababbaaabbbbababaabbbbbbbababbaaaaaabbbbbabbabbaaaaaaabababbbbababbaabbbbbbbbababbaaaabaaaabaaaaabaabbbbabaababbababaabbababaaaabbbbabbbbabbaabbaaabbbbbaaababbbbbbababaaaabababbbabbbbabbaabbbbbbbaabbaaabbabbbbabbbbbbbbaaaabbabaaaaabbaabbaaabbabbbbabbbabaabaabababbaabaabababaabababbbaaabaaaabbabaaababbbaaabaaabbbbbbaabbbbaabbbbabaaabaabaabaabbaaabaababbbaabbbbbabaabbabbbaabbbbbbaabbbbbaabbaaaabababaaaaaabaabbaaaabaaababbbabbababbabaabaabaaabbaaababbaababaaabaaabbbbaabaabbaaaababbabbaaaabbbaaaababbaabaabaababbbaaabbbbbbabbbaabaaabbbbbababaabbaabaababbbaabbbbaaaabbbbaababbaabbabbbbabaabaabaabbabaabaababbbbbbabbbabbaaabbabaabbbaaabaabbbbbbbabaaababbabbbbbbbabbbabaaaabaabbabbbaabaabbaabbbaaaaabbbababababaaaabbbabaaaaaaaababaaabababbbbaabbaabaababbbabababababaababbbbbbbaababbbbababbbaabbaabaaaabbabbbaaababaaaababbaaababbbabbbababbbbaababbbaabbbaababbaabbabbaaabbabbbbbababbaabaaaaababaaaabbaaabaabbabbaaabbbbbbbbaabbbabbabaabbaaaabaaabbbaaabbaabbabbababbaabaaaaabaaababbaabbbbababbabbababbbaaaabbbaaabbababbabbababbabbaaaaabbabbaaabbbbbababbaaaaaaaaaaabbaaaaababaababbbabbababababaababbbababbbaabbaaaaaabbbbabababaaabbaabbaaabbabbaaaaabbabaaaaaaabababbababbbbbaababbaababbaabaababaabaabbaababaaabbababaaababbaaaababaabbaaabbbbabbaabaabbbaaaaaabbbabaababbabbabaabbbbabababbbbaaabaabababbbababbbbababbabaabbabbabbaabbbaaaaabbbbaaaabaabaaabababbbbaaaaababbbababaaaababbbbbabaaaabbbbabbababbaababbbabaaaabbbaabbababbaabbbabaabbabbbabaabbbbbaababbbbabbbbababbbabbbabaaaaaabbbaabababbbaabbabbaaaaaaabbbbbabbbbbaaabaaaababaaaabbaaababbabbababababaabbbababbbaaaaaaabaaababbbabbaaaaababbbabaabaababbbabaaabbabbbbaabbbbbbabbaababbbabaabaaaaabaabbaaaaabbbaaaabbaaababbabaababaabbabbbbbbbabbaabbbaabbabbbabbabbaaaabbbaaabaaaabaabababbbbbbbaaaaaabaabbaababbbababbaabababbaabaaababbababbbbbaabbbbbbbaaababbbababbbaaaaababbbababaaaaabbabababbabbbaabbbaaabaabbbaabbabbabaabaabbbabaaaaaabbabbabbbaaababbababbbbbabaababbababbbbabbababaaaaaababaabbbbbbaababaaababbaaaabbaaaabbabaabbbbaaababaaaaaaabaaabaaaaabaabbaaaaababaaabbaabbabbbaaabbabbabaaaaaabaababaaaaaabababbbbaaaabababbabbbbbbbbaabbbbbbaaaabaaaaababbabababaaaabbbabbaabbbabbbbbbbbbbabbaabbbbaaaabaabbabbaabbbbabbaaaabbabbaabbabaabbaabbbbbbabbbbbbaabbaaababbbaaabbabaaaaababbbbbababababbbbbaabaababababbaaabaaabaabbbababaaaaaabbabbaaabbbbbbbaababaabaabbaaabaaaaaaaaaaabbbbaabbaabbaabaabaaaababbbababbabababbbbaabaaabbaababbabaabbbaaaaaaaabbaabbabbbabaabaaaabbbbabbbbbbbbabbbaaabaaababbaaaaabbaaaaaaababbaabbbbaaabbbbbaabbbbababbababaaababaaaabbbababbbabbbaabbabbaabbbaaabaabbaabababbbbbbabaaaababaaabbabababaaabaabaaaabaaaababbbbaabbaaaabaaaaaaabbaaaabbabbbaababaabbbaabaabbaabbbabbbaaaaaabaaaaabbaabaabbaabbabbbbbbbbbabaaabbbbaababaabababbaaaabababbbabbabbabbbbbabaaababbabaaaaaabaababababbababbbabbbbbbaabbbaabbbbbbbabababbbabbaaaabbababaabaaaabbababaabaaaaaaaaaabbabaababbbaaabbbbaabbabaabababaaaabaaaabbabaabababbbababbaaabbbbbabbbbbbababaabbbaabaabaaabaabababaaaabbabaabbaabaabbabbaaaabbabbbbbbbbbaabaabaabbabbbbaabbababbabababaabaabbababbbbabbaaaabbbbaabbabbabbbbaaabbbabbaababbbbbbbabbbbbaabaaabbaabbabbaaaaabababababaabbabbaababaaabbbabaaaabaabbabbbbababaaababbabbbabababaababaaabaabbbaaababaaabaabbaabbbbbbbbabbbbababababbabbabaabaaaaabbaabbbababbabaaaababbabaaaabbaaaabbabababaaaaabbbbbabbababbaabbabbbaabbbaababbbbbaababbaaabbbbabbbaababaababbaaaabbaaaabbabaabababbabbbaabbbabbbaabbaabbbbaababababaabaaaababbbaaabaabbaabbbbbbbbaabaabababababababbbbaabbaaaaabbbabaabbaabbbbbaaabbbbaaabaaaabaabbaabababbabaabaaaaaabababababbbbbbababbbabaabbaabaababbbaabaaaabaabbabbbaaababaababbaaabaaaabbabababbbbbbbababbbbbbbabababaabbaaaababbabbbbaabaabaabaaabbabbbbabaabbbabaabbabababbbbbabbbbbbababaaaaabbbbbabbaaabbabaaaabbbbabaabbaabbaaabbaaabbbbbabbbbaaabbaaabbaabbbbbaaabbabaaaaaabbaaabbbbaaaaaabbabbbbbaabaaaaabaaaaaaaababbbaabaaaaaaabaabaabbaaabbaabbabbabaaabaabbabaaabbabbbbbbbaaaababbbbaaabababbaabaaaabbbaabbababaabbbbbaaababababbabbabaabaababaabaababbbaaaaabaabaaabbabbaababbaaabababaaaaabbbaaababbababbababbabbbababbbabbbaaaabaabbbaaaaabbabbbbbabbaaabbbbbbbaabbbababbabaaaaabaabaabaaaaabbaaabaababbabbbbbabbabbababaaabbabaaaaaabaaaaabaaabbaaabaaaaabbbbabaababaaabaababbababbbbbbabaaabaabaaabaababbbaabababbbabaabbaaabababaabbababaabbababbaababaaaababbbaaabaaaababbaabaabaabbbaabbaabaaabaabaaababababbaaaaaabbbaabbbbababbabaaabbabbabbbbbbbabbbababababbabaabbaaaabbbaaabaaaababaaabaaababaababbabaaaaaabaabaabbabbaaaaabaaabaabaabbbbaaabbbbbbbabaaabbaabaabbabaaaaabbbbbababbbabbababababbbaababbbaaabbabaabbabaabbbbbabbaabaabbabaaabbbaabbbaabaabbabaaaaabaabbaababababaabbbabbbabbbbaaaababbaaabaaaabbabaaabbbaabaaabababbbabbaabbabbaababbaabbbabaabbbbabbabbbbbbbbbbabbbbaaabababbababbbbaabbaaaabaaaabaabaaabaaaaabbbbbaabbbbabaabaaaabababbababbbbaababaaaababbabababbabbbaabaaabbabaababbbaaaabbababbabbaaabbaabababaabaaababaaabaabababbbabbbaaabbbbaaaaabaaabaaabbbababbbbbaababbbbabbabbaabaaaababbabbbaaababbabaaabbbaaaababababaaabbbbaaabababaaaabbaababbbbabbaaaabaabaabbbabbaaabbaabbabbbbaaababbabbaababaaabaabbabaaababaaaaabbababaabbaabbbabababbabbababaababbabbababbbabbbbabbabbabbabaaaababbaabaabbbbabaaaaababaababaabbababaababaababababbbbbbbbbbaaaaabaaaaaabbbbbabbbbabaaababababbbaabbabbbbaabababbaabaaaaaaabaaabbaaaaabaabbaaaabaabaaaabbabbaabaabaaaaabaaaaabbaaaabbaaababaaababaababaaabaabaabbbabbbaababaaabaabbabaabaaababababaabbbababbbbabbbbbabbaabbaaabaabababaaabbabbaaaaabbababbbabbbbaabaaabaaaabbbbbababbabbbbbabbbbaabbbbbaaabbabaabaababaaabbaabaabbbbbbabbbaaaababaaaaababaabbaabbabbbbaaaaaaababaaaaaaaaaaaababaaaabbbabbaabaaaabaaaaabbabbbbababaabbaaabaaabbaabbabababbbaabbabbbaabaabbaaaaababbbbabbaabbabaabaaaaabaabababaaaaabaaaabbbbbbabbaaaabbabbabaaabbababbbaaaabbbabbabaabaabbbbabaaabaaaaaaabbabaabaabbbaaabbaabbaababaaaabbbbbbbbaabbaabbbbabbbbbbabbaaaaabbbabbbbabbabaaabaaabababaabbbbaaabbaaaabbbbaaaaabaabbabbbbaaaaabbbbabbbabaaaaaaabbbbababababbbbbbababababaaababbababbabababbabbabbaabaababbabbaabababbabaaaaabbbbbabbbbaaaabaaaaaaaaaaaaabbbaabbaaaaabbaababaabbbabbbaaabbabaababbaabbbabbbababbbbaaababbaababbabaaaaaabaaaaaabaaabaaababaabbbbababbbbbbaaaabbbbaababbbabababbbabbbbaabaababbbaabbbaabaabbbbbaabbbabaabbaaabaaaabababbabaaaabbaaaabbbababbbbbbaabbaaaaabaabbbabaabaaababbbbbbbbabbbbbbbababbbaaababbbabbbaabaaaaaaaabbabaaaabbbbbbabbbaaaaabbababaaabaabaaabbaaababaabaabaabbbaabbbabaabaaabbaababbabaaababbbbaaaaaaaabaababaabaababbaabbabaabbabbaaaaabaabaaaaabbbbbaaaabbaabaabbaaaaaabababaaaaabaababbbbbabbbaaababbbaaababbbaaaaababbaaaaaaaaaaababbbabbabbbababbbbbbbbbaaaaaaaaaabbabbbabbbbabbababaabaabbbbbbaaabbbbababbbbaabaaaababababbaaaababbabbbabababaaababbaaabbaaabbaaaaaaabbaabbbbbabbbbabababbabaaabababbaabaaabbbabaaabaabbbaaaabaaaaabbbabababbbaabaaabaaabbbaaaabaaababbbbaabbabbabbaaabaaabbaaabaabbbaabbbbabaabaaaabbababbbabbababbaabbaaabaaabbbaabaabbbbaaaaabbbabaaababbaababbabbaaabbabbaabbabbaabbbaabbabbbbbbabbaababaabbaabbaaaabbabaabaabaabaaaaaaababaaaaabaaaabbabaaaaaaabbabbaaaabaaabababbababaabaabbbbaabbbabaaabbbbaaaabaaaaaaabbaabbabaabababbbabbbbbbaaaabaaabbababbabbbaababaaabaabbaabaaababaababaababbaaabaaabaabbbbabaabbababaabbbbbbbaabbabababababaababbbbaababaababbbbbbbbbbaababaababbabbbbaabbaaabbababbabaababbabaabbabaaaababbabbbaaabbbabaabbaabbaababaaabababaaabbbbabbbabbabbbaabbbabaabaabbabaabbaaabbbabaabababaabbbaaaaaaabaabbbbbbbaaaaaabbaababaaaaaaabbbaababababbaaababbabbbbbaaaaababaaaabaaabbabaaababbbbababbbababbaababaaaabbbbbbaaaababbbabbbbabaaabbbababbabbbabaaabbabbbbbbaabbaabaaaaabbbbbbabbaabbbbbaabababbbbbbabbabaabbbaababbabbabaabbbabaaaaaabbabbbaaaaabaaaabaabaabbbbbbbbabbabbbbbbaabaabaaaababbbabbbabbabaabbabaaaaaabaabaaaabaabbaabaaabababbabaabbabbbbbbbbababbbbababbbbaaaabaaabaababbabbaabbbababbbaabbbaabbabbaabaaaaaaaabaabbabbbbbaababbbbbaabaabbaaaabbbaaaabbbabaabbbbbabbaaaabbbabbbaaabbbaabbababbbbbbbabbaabaaabbabbaaababbaabbbbaaabbaaabbbbbbabaaababbabbbababbabbabbbbaababbababbaaaabaaaababbbaabaabbbabbbbbabbbbbbabbaabbbbaabbabbbbaaaaaababbabbaaaaaabbaabbabbbbabbbbbaabbbbbbabaabaababaababbbbabaaaaaabbabaabaabbaaabaababaaaabababaaabbbbabababbbabbbabbbaabaaaaaabbbbbbabbbaabbbaabbbbbaabbaaaaabbbaaabaaaaabbaabbbaabbbbaababbabababbbbaabaabaaabbaaabbababbbbbbaaababbababbaabaaaaababbbabaaaaababbbbbbbabbaaabbbbbabbaababbaabbabbbabbaaabaaabbabbabbabbababababbbaaaaabaabababbbaabbababbabbbabbbabbabbbaababaaabaaababbaabbabbaaabaabaaaabbbabaabaaaabbbbbaababbbabababaabbbbaaaaaabaabaabaabababbbaaabbbaaaabbbbbbaaaababaabaabaaabbbaabababaabaaabbbbaaaaaaabaababaaababbbbabaaabbabbabaabbabaaaaaabaaaabbbbababbbbbbaaaaaababbaabbaaaababbaababbbabbabaababababaabaaaaabbaabaabababbababbaababbbaabbbbbaabbbababaaaababbbaabbabbaababaaaababaabababbaaaaaabaababbbbbaaabbbaaaabaabbaaaabaaabaabbaaaabbbbbabbbabbaababbbabaababbbabbababaaaaabbabbbbababbabbaabbbaabbbaababbabaaabaabbaabbbaaaabaababbabaaaaaaaababbbaaaababbabbbababaabbbaaaaabbabbbbababaabbbbabababbaaaaaaaabaababbaaabbabbaaabaaabbbabbabbbabbbabababaabbaaaaaabbabbaaaaaabbbbbaaababbbbbababbbbbabaabbababaaabaababbbbaaabaabbaaabbaabaabbbbabbaabbababaaabaaabbabaaabbbbbabbaababbbbabbaaaababbaaabbabbabbabbbbaaaabaabbbaaaaabaaabbaabbaaabbabbaaaaaaaaabbabbaabaaabbaaaaaaababbbbbababaaaaaaabaabbaaabbabbbaabaaababaabbbbbabbbaaaaaabbbbbaabbaabbaaabbbbbbbbaaabbbbbabaabbabbabbbbabbbaabbabbaabbbbbbaabbabbbabbbaabaaabbbabbabbaababbaabaababaabbabbbaaaababaababababbaabbbaabbbabaaabababbbabbabababbbaaabbaabbbabbbbbabbaabaaaabbaaabaaabbaaabbaaababbaabbaabbaabbababbbbabbbbababbabbbbabbaabbabbabababaabbaaabbbabababaaabaaaabbababababbbbbaaabbbbbaabbabbaabbbababbbbababaabbbaabbbaabbbbbbaaaabbbabbbaaaabbbabbaaabbaabbbbaabababaabbbababbbbbbbababbaabbbbbabbaababbbaaabbbaaaababbbababaabaabbbbbbbbaaaabbbaabbbaaaababaabaabbaaabbabbbbabbbaabbbaababbabaabbaaabababbbbaabaaabaabbbbaaaaababaabbaababbabaaabbabbbaabbbbbabbabbaaaabaabbabababbbabbabbbbabbbbbbaabaabbbabbaaaaaaaabbababbbabaabaabbababbaaaababbaababbbaabaababbabbabbaababaaabbabbbbbaabbaababaabbababaaabaaabaabbaaaabbaaabbbaabaaaaaababaaaaabababaabbbbaabaaaababababbabbaabbbbabbbbbbbaabaaabbbabbaaaabbbaabababbabbbbbabbababaaabbbaabaabaabbbbaabbbabbbbbbbaabaaabbbaaaabaaaabaabbabaabbbbabbbbabbabbbbbabbababaaababaaaabbbbbaabbaabababbabbbabbabbbbababbaabbbbbababbbbbbabbbaaaaabbaaabaaaabbaabbbabbaaabbabaaaaaaabbaaaaabbababbbabbaabbbbabbabbbabababbbaaaaaabbabbaaababbbbbabaaaabaaabbabaabaaabaaabbbabababaaabbaaaaabaababbabaababbbbbbaaabaaabbabbbabaabbaabaaaaaabbbbbbabbbbbbabbbbbabbaaaababbaaaababbaabaabaabababbaabababbababbabbaaabababaababaaaabababbaaaaabbbababbbbaabababbbbabbbbabaabbbbbaabaabbaabbbababaababbabbabaaabababbbbabbaaaabbabaabbbbababbbbabbabbabbabbabbabaaaaaabbbbaabbbbbabaaababaaaaababbabbababbbbabababababbabbabaabaaabbabbaaabbaababaabbaaaabbaaaabbbababaabaaabaabaabbaaabaabababbbbaababbaabbbaaaaaaabaabbbabbbabbabbabbabbababbaabbbbabbaababbbbaababbabbbbbabbaababaabbaaaaaabbbbbbabbabbabbbbaaabbbabaabbbabaabbabbaaaaabbbbbaaaaabbaabaabbaababbbbabbababaaaaababbabbbbaabbbbababaaaaaababbaaaaaaabaabbbabbabaaaabaababbababbabbabaabbabaaaabaaaababaabaaaaaaabbbaabaababababbaabbaabaaabbbaababbaabaaabaaaaaabbabbbabbbaaabababbbbbaaabbabababbaaaabbababbbbaabaaabbaabbaaaabbabababbbababaababbabaabbbbbbbbbbbbaaabaaaababaabbabaabbbabbbbbaabbbabaaabbababababaabaabbbaaababbbaaababaaaababbabbbaaabbbaabaaabaabababaabbabbbbbaaababbabaaaaaabbaababbbabbabbbabbaaababbaaababbbbabababbbabbaabbabbbbaaaaaaaabbabbbbaabbbabababbabbaaabaabbaaaabbbbabbabaabbbaabbbbabbbaaabaababbbbaabbabaaaaababbbbbbbbabbabbabaababbbaababbbbababaababbbaaabbaaabbabaaaaaaababbabbabbbbaabbabbaaaaababaaabbabbabbaabbbbbbbbabaaaabbbbbaabbbabaaaabbaabbabbaababbabaababbababbbbababaababbababbbabbaaaabbbabbbaabaaabaabbbbabbbbaaaaabbbbbaabbaabbbaabbbbabaaaaaaababbbbaabbaabbabbbabaaabaabaaabbbabbbbbbabbbbbbbbbaabaaabbbbbbbaaabbaabbbbaaabaaabbbabaabbbababbbaaabaaabbabaabbbbbababbaabbbabbababbbbaaaaaaaabaabaabaaabaaaababaaabbbaaaaabbabababaaaabaabbaaabbabbbbbabbabaaaabaabbbbbbbbbaabbbaaababaaaabaaaaabaaaaaabbaaaabaaabbbabaaababbbabbaabbaabbbaabaaaabaaaaaaaaababaababaabbaababaabaabbbbababababbbababaabbabaabaaaaaabbbbbaabbbaaababababaaaaababaaabbbbbbaabbbbbbaabbbaabbbabaabbbabbaaaabaababaabaabbbbbbabbaaabbbbbbbbabbbababbbabbaaabaaaaaaaaaaabaabbaaabbabaaaababbbaaaabbaababababbbabbbbbabaaabbaaaabbbbabbbabaababbaabbababaaaabbababaabaabaaaaabbaaababaababbbaabaababaabbbaaaaabaaabbbbbbbbbaaabaaaaabbbababbaaaaabbbababaabbbababbbabaabaaabaabbbaabbbbababaaabaaaaaabbaaaaaaaaaaaabbbabbabbbabababbbababababbaaaaabaabbaaaabbbabbbbaabbaaabaabaabababaaababbabbaaaaaabbabaaababababaabbbbaabbbbbabbabbababaaaaabbbbbbabaaaabbababbabbabaaabbbbbbbaabaabbbbabaaabbaababaaabaabbbabbbbbaabaababbabaabaabbababbbabbbaabababaaababbababaabbaabbababbabbbaabbbbabbabbaabbaabbbbbbababbaabaababbaaaabbbaabaaabaaaaaaabbabaaabaabbbaaaaaabbbaaaaaabbbaaababbaabaababaaaaaaaabbbbbaabbaaababbbbabbababbbbababbaaaaaabbbaaaaabaabbaabbabbabaaaaaabbabaabbababbbaaabaababaaaaabbabaaaabbbbbaabbabaabaabaaaabbaabbbbbabbaaaabaaaaaaabbaabbbaabaababbabbbaabbbbbbababbbabbabbbbbbbbbbabbbaabbaaaabbbbabaababababaabbbbbabbbaaabbabbbababbbaaaaaabababbaaabaaabaaaaaaaaaababbbbbbbaaaabbbabbbbaabaabaaababbbabbbbababababbbbaabaabbbabbabaaabaaabbbbababbbbbbabbaabaaabaabaaaaabbbbabbbbaaabbaaabbabababbbabaababbbabbbaaaabaaabbababbbbbabbbabaaaabababbbabaabbbaabaaabaabaaabaabbabababaabaaaabaabaabbaaaabaaaabaabaababaabbaaaabbbabaaaaabaabaabbbbbbbabaabaabbabaaababaababaabbbabaababbaababbaabbaaabbbbaabbaabaabaabbbabbaabbbaaaababababaaaaabaabbbaabbbababaaaaababbbaaababaaababbbaaabaababbabaaabaaababbababaaaabbababbbbaabbbababbbbbaabbbbbbaababaabaabbabaababbbbabbbabbabaaaababbbababbaabbaaaaabaaaabbaabbbababbbbaaabbabbabbbbabbabaaaaaaabbbabbbbabbbbabbaabbababbaaaaabbbbabbbbbbbaabbbaabbbabbaabbabbbaaaaaabbabaaababbaabbbbbbaababbbaaabbabbbbbbbbabaaaaabbabaaaabbabbababaabbaabbaaabbabbbbbababbaaabbbabbbaabaabbbaaaaaaabbbaaababbbabaaababaababababbbabaaaaababbbabbaaaababbbabbaaaabbaabbbbbabaaabbaabaaaabbbabbbabbbabababbbbbaabaaabaaabbaabbbbbbaababbbbabaababbbabbbbaabbabbbbaaababaabbaaababaabbbaaabbbbbabaabbabbbbabbaaaabbbaabbaaabbababbaabbabaaababbaabaaaabababbabbbaaabaababbbaabbbaaaaaabbabbbabbbbbabaabbaaabbbabbbaabaabaababaabbbbaabbbbbbababbbbabbaababaaaabbababbabbaaabbaabbabbbabbbbbbbbabbaaaabbbbabbbbabababbaabaaaaabbabbbbbbaaababbabababbbbaabaaaabaabbabbbaababbabaaabbaaabbaabbaaaababbabbaabbaababaaaabababbabbaaaaaaabbabbbbaabaaabbbbbabbbbaababbababbabbbbbbbbaabbbbabaabaaabaaaaabaaabbaaabbbabbabbaaaababbabaababbbaaaaaaabaabbbbbaaaabbbababbababaabaababbabaabaabbbaaababababbbaaabbaabbbabaaabbbbbaabbbbbabaabbabbbabbaaaaaabbabbbabbaaabbbbaaabaaabbaabaaaababaaabababaabbbaaaabaabbaababaaaaabaabaababbaaabababaaaabaaaaabbbabbbaababbaababbbabbaaababbbbabaaabbbaabaababbaaabbaabbaaaaaababbbaabaaaaababaabababbbbbbababaaabababbbbbbababbaabbbbabbaabbbabaabaaaaaababbbaababbaabbbbbaabbaaabaaabaabbabbbbabaaaabbbbaaabaabaaaaabbbbababbaaabbabaabababaababaabbbbabbbabbbbbbaaababbabaabaaababbbbabaaabbbbbaaabaabbbbaababbbabbbaaabbbabbbbbbbabbbaaaabaabaabbbaabbbaabbaaabbbaabbbbaaabbabaabbbbbbbbbbabbaabaabbabaabaababaabaaabbbbbbaaababbabbaabaaabaaaabbbbbaaaabaabbababaaabbbabaaaaababaaabbbbbaaabbbbaaabaabbbbaaabbbababbbbbabbababaaaabbbaaaaababaabbbaaaababbaaaaabbaaabbabbaabaaabaabaaabbbbaababaabbabbaaabbbabbaaaaaababababababbaabbbbbabbbbababaabababbbabaabbaabbabaaaabbaaabbaaaaaaaaabbbaababbaababbbbaabbaabbbbbbabbaaaabaabbabaaaaababbabaaabaaaaabbaabaabbbbaabbaabbaababbbababaaabbaabaaaaaaaabaaaabbbaabbbbbbabbbabbbabbabababbababbbbbabbbaabaabbbababbabaaabbaabababbaabaaabbababababbabbababaabbbbabbaabaabaaabbabbbaaabaaaabaabaaabbbaaababbabbbaaaaabbaabbbbabaaabbbbabaaabbbbbbbaabbabbabaaabaabbbbbaaaaababaaaaabbbbbabbbaababbaaaaaabbabaabaabbabaaaaababaabababbbababbaabbaaabbaabbbaabaaaabbbabbababababbbbbabbbbabbabaabaaabbaabbabababbbaaaaabbaaabbabaaaaaaaabbbabbababbbbbbbbaababbbaaababbbbababbbbabbabaabbaaaabbbaaabbbbbababaaaababbbbababababbbabbbbbbbabaabbbbabaababbababbabaaaababbaaaabaabbaaabaaababaabbaaabbaaaaabaaaaabaaaababaababaabbbaaabbaaaabbbbbaabaaabaabaabbaababbaabaabbababbbaababababbbbbbbbaabbbababbbbbbaabbbaabaaabbaabbaaaababbbbababbbabbbaababbaaabababaabbababaabbbbbbbaabbabbbbaaabbbaaaaaabaaabbbabaaaabbbaaaabbbababaaabbabaabbbbaaaaaabbbbababaabbbaaabbbbbaabbaabbbababbabbbaabbbbaaaababbbbabbbababbabbbaabaaaaabaababbbabaaabbbbababaababbbaabbbaabbababbbaabababbabaababbbaababbbbaabaaabbbaaaaabbbbabbaabbabaaabbbaaabbbbbaaabbbbaabaabbaaaabbbbaaaabbaabbababbaaabbabbbbaaaabbbaaabaabaaabbbaabababbbabbbabbbababaaaababbbabbabbabbbaabaaababbabbabbbaaaaaabababaabbabaaaaaabaaaaabaaaaaabbbaaabbbbbbbbbbbbbbbbaaaaaababbbbbabbabaabbababaabaabaabbbbaaaaabbabbbabaaaaabbbbabbbaabbabbaaabbbbbababbbaaaababbbbaaaabbaabaabbbaabaabbbbabbbbbaaaaababaaaabbabababababbabaababaaabbbaabbbbbbbbbbabbaaabbbababbababbbbbbaaababababbbaababbaabaabaababbbaabaaabaabbaaababbbaabbbbbbababbbbbaababbbabaababbababbbbabbbbaaabbababbbaabbbbbaabbabbbaabaabaaaabbaaabaaaaabbaabaaaabbaabbaaabbaabbababbabababbbbbabbabaabbabaaaaaabaabbbbbbbbbaabbaaaaabbbaaabbbaabaabbbababababbaaaaaabaabaabababbaaababbabbaaaababbabbbabbbbaaaabbaabbbabbababbbbaabaaaaabbbbaababbbabbaabbabbbbbbabababbbaabaabbaabbbbbaaaabaaabbaababbaabbabababbaaababaaababbbbaabbabbbababbbababbbabbbabbaaaaaaaabbabbbbbaaabaaabbbbbaabbbaabbaabaabbbbbbbbaaababaaaaabaabbbabababbabababbababaabbbbaababaaabbbbbbabababbbabbaaaaaabbbaabaabaababbbbbaaabbbbbabababbabaabbbbbababbbbabaaabbabaababbaabaaabbaaabbaaaaaabaaabbbbaabaababbbbabbbbbababbabbbbaaabaabbbaababaabbaaabbabaaaaaabaabbabbabaaabbbbbbabaabaaaaabaababbbabaabbaaabaabbbbbaabbabbaabbabbabbbbabaaaaaabaaaaababbbaaaabaaaaabbabbbabbabbaaabbbababbbbbaababaabbbbaabbbbaaaabbababbaababbbbbabbbbbabaaaabaaababaaabbbbaabaaaaabbabababbbbbaaabbabbbaaabaaaabbabaaaaabababaaabaabaabbbbaabbbabababbbaababbaababbaaabbbbabaaababaabbabbbaaabbbaaabbbbbababbbabbbabbaabaabbaabbbaabaaaaaabbaabaabbababbabaababbaaaababaababbbbabbbbaabbababaaabaaabbbbbaababbaaabababbbaaabbbbabbaabbbabbbbbabbbabbababbbbaababbbabaaabaaaaaaaaaaabbbbabaabaabbbbbbababaaaaabaaaaaabbabaababbbbabbabbaababbaabaabbbaaaabbbbabaaaababbbaabaabbabbaaaababbaaabaabaabbaaabbbbabaabababbabaababaababaaaaaaaabbabaaabbbaabbbbaababbaababbabaabaaaababaaabababbababaabbaaabbabaaabaabbbbbabaaabababbbaaababbbabbbaababaabbbaabbaabbbaabaababaabbbbabaabbbbabbbbbabbbaababbabaabbaaabbaababbbbaaababababaabbbaaabbaaaaaaababbbbbbbbbaaaaabaabbbbababbbabaabaababbababaabbaabbaabaaaaaaaaaabbbbbbbbabbabbaabbbaabbaaaaabaabababbabbbbaaabbbbbbabaaabbbaabbbbabababababaabbaababbbbbbabbaaaaaaaaababbbaabbbaaaababbaaabbabbaaaabbaaabaaaababbbbababbaaabababbbbabbaaababaaaaaabbaabbbbabbabbbbbaaaaabbabbbabbabaaababaabababaabbbbbabbababbaaaaababbaaaabaaaaaaabbbaabababbaaabbaaaabbbbbaabbbaaaabbababaaabaabbbbaaaaabbbaabbaaababbbabbabaaabaabbaabbabbbbaabbaaaabbbbabbbabbaabaaaabaaaaabbabababbbbbabbbbbabbbababbaabaabbbaabaabbbabbbababababbbbabbababaababbbabbabbbababababaaaabaababbabbbbababbbababaaaababbbabaabbbaaaaabaaaaaaaaaaabbaaabbabbaabaababaabbaaaaaaaabbabbabbbbaabbbaabbbaaaaabaaabbaaababaaabaaaaaaabaababaaaaaaaabbbbbbbbabbabbabbbbaabbaaaaaaabbabbaabaaaabbbbbbaababbbabbbabaaaaaaabaaabbbbbabbaabaababbaaaababaababbababaabbabbbbaabbbbbbbaaababbbaabbbaaabbabaaabaaaaabaabbbbababaababaaababaaaaabaababbbaaaababbaaabaabbbbbbaababaaaabbabbababbbaaababbbaabbbaabbabbababaababbabbbabbaaabaaababaaabbbbababbbabaababbbbbabaaabaaababaabbbababbaababababbabbbbabbaaabbbaaaaaabaababbabaaababbbaabbbbbabbbbbabababbabaaabbbaabbaaabbaabaababbbaabbbaaaabababbababbaababbabababbaababbbaabaabbabbababbbbababbabbbaabbbabaaaabababbabbaabaaabbbbabbabaabbaaabababbaaaaabaaaabaaaabaabbbbbabbbaababbabaaabababaabbbabbbbaabbbaaababaababbaabbaaaaaabbabbbbababbaaaabbbbbbaaaaabbbbaabbaaaaabababbbababbbaabaaababaabbbaaabbabaaaabbbaaabbaabbbbbaabaaabbabaababbaabbabaababbbabbaaaaaabaabbbbaaaabbaababaabbbabbbbbbbaabbbaaabbbababaaaabbaaaabaabbbabaabbaaabbbabaabaaabbbababaabbbabaabbaabbaabbbabaaaabbbbbbaabababaabababbbbaabbbabababbbbaabbbabbaabaaababbaabaabaabbbbbaabbbbbbaaababaabaaaabbbaaaaaabbaabaaaabbbaaaababbbaaaababbbabbbbbbbbaaabbabababbaababbaaabaaaabaabaaaabbbbabaababbaaaabbababbbbbbbaaaaaaabbbbaabaaabbaababbaabbababbbbaabababaabbbababaaaaaaaabbbbbabbaabaaaaabababbaaabaababbbabaabbabaaaaabbbbaaabbbababaaabaaaabaaaaabbbbbbbabbaaabbbaababbabbaaaaababbabaaabbbbaabbaabbbabaabbaababaabaababbabbbabbababbaabbaabbbbbababbbbababbbaaaabbabaaabbbbaabbabaabaabbbabaaaabbabbaababbabbbbbabaaaababababbbbaaababbbbabababbabbbbaaaababaabaabbababaaabaabaaabbabbbbbbbbbbbbabaabbbaabbbbbbabaababbaabbaabbbbbaaabbbbaababbbbbbbbabbbabbabbaabbbbbbabaaaabbbbaaaabbabbaababbababbbbaababbbbbaaaaabaaababababababbaabaababbbaaabaabaaabbbbabaababababaaabaabbaabbbbaaaababbaaaababbabbbabbabbbbaababbabbbaabababbaabbabbbaaaabbabbbaabbaabbbaaaaaaaaaaabbababbbbabaaabbaaaaabaabbbbaabbabbbbababaabbbbbabaabbbababaaaababaaabbbbbbabbabaaabaabbbbbbabaaaaaaaaaababaaabababbbbbaaabaaaaaababaabbbbbabababbbbabbbbabbbbbaaabbbbbababbbaabaabaaababbbabaabaabaaabaaaabababababababbbbbbaaabbbbbabaabaababbbababbbbbbbbbabbabaaabbbababbababbbaaabbaabbabbabbbbbbabbbbbaaabaabaaabababbaababaabaababaaaaababbbbabbaaabbbbbabbbbbbbaababaabbbbabbabababbabaabbbaaabaaababbbababbaababbbabaabaaababababbaaababbbaabbbbbaaaabbbaaabbabbabaaabbabaabbabaabbabaaaaabbbababbaaabaaaaabbbabbabaabbaabbbbbbbbbaabbaababababbaabababbbabababbabaabaaabbbaabbbaaaaaababbababababaaababbbbaaabbbaabbababaababaababbbaabbbbabbbbababababbabbbbababbabbbbaaabbaaabaabaababbbbbabbaaaaabababbaababbbababaaaabbbababaaaaabbbabbbabbababbbbbbbbabbabaabbaabaababaaabbbabbaaabaaaabbbbbabbbabbabbabaaaabbababaaabbbbbabbbaaaabbbbabbbbaabbababaabbbbbbbbbbaaabbbaabbabbaabaaaaabbabbbaabbbaaababbbaabbbbabbabaababbbaabaaabaaabababbbaabbbabaabbabbbabababbababbaabaaababaabaababbabaabbbabbaabaaaabbbabaaabaabbbabababbbaaabbbbababaababbabaabaababbaaaaaaaaababaaaaabbbbbaababbbbbababbababaabaabbbbabbbaaababaaabbababbbbbbabbaaabbbbbbbbababaabbbaaabbaaabbbabaabbbabaabaaabbabbababbbbbbbbabbbabbbbbbbbbabbaaaaaaabbaabbaababaabbababbabbababbbaabaaaaabaabbaabaabaabaaaaabbaababaabbaaaaaabaabaabaabbbabbababbbabaaaaabbbaababbaabaaabaabaabaabbabaabbbbabababaaabbbabbbbbbabbbbbababbabaabbaaaaaaabababaabababababbbaaababbaabaabaabbaabbabbaaabbaabaababbabbaaaabaababbababababababbbaaabaabaaaabbaaabaaaaaabbabaaaababababbbabbbaabaabbabaaaabaaaaabbabbbbaabaaaaaabbbbabbbbaaaaabaababbbbabaaabaaaabababaaabbaabbbababaabbaaababaaabaabaabaaabababaaaabaabbabbabbaaaaababbbabaaabbaaaababababbaababbababbbbaabbabbbbabbaaaaabbababbbbbaaaabbbbaaabaaabaababaaaabbaaaaabbabbbbbabbaaabaababaabababbabaaabbbbabbaaaababbabbbabbabaabbbabaabbbababbababbaababababbbbbabababbbbbbbaabbaaabaaabbbbbaabbbbbabbabbbbaaabbbbbaaaaabbbababbabbbabbaaaabaababbabaabaabaaaabbbaaaaaabbbbaaabbabaaabbbbabaaaabbaaabababaaaabbbbabbabbbaaaaaabbaaababbbaabbbbbabaaaabbabbaaaabbbbaaaabababbabbabbbabbaaaabbbababbaababababaaabbbabbbbaabbbaaabababaaabbbababaaaaaabaaabaaabaabbbaaaababbabaabbbabbbbabbbbbbbababbabbbbbbbbbaabaaaaaabbbabaaababaaaaaaaabbabbbabaababbaaabbbbbaabaaaaaabbbabbababbbbbabaabaabaaaaabbbbbbabbabaaabbaaaaabbbababbababbaaaaaaababbaababbabaaaaababbaababbaaabaabaabaaaaabbbaabbbababababbabbaabbaaaaabaaabbbbababbabbbbabbabaabbaabbabaabbbaabaaabbbaaababbbbaabbbababbaaaabaaaaaabaabababbbabaabbabaabbbbaaabbbaababbbbababaabbaabbbbabaabbababbaaaabbaaababbbaaaaaaababbaabbaaabbababbaabaaabbaaabbabababbaaaabbabbababbaabbbbabbbaababbbbaabbabaaaabbbaaaabbabbbabaababaababbababbabbbabbbbababbaaabbbbbbbbbbabbbabbbbaaaabbabbababbaabbabbaabababaabaabbaaaababbbabaaaabbaaababbbbbabaaaababbabaaaabaabababababaabaabbabbbbaaaabbaaaaaaaaaaabbbaaaaaaaaaaababbbaabbbaaaabaaaabaabaabbabbbabbabbbababbaaaabbabababaabbbbaaaababbabbabaaababbbabbbaabbababbbbaaabaaaabaabaabbabbaabbaaaababbaababbaaaabababbabababbbbbbaaaabababbabaaaaababaaabbbbababaabababbbbbabbabbaabbababaaabaaaababaaabaaabbaaaabbaaabbaaaaabababaababbbaabaabbbaaaaaabbbbabbbabababbbabbbaabbabababbbbbaaabaabaabaabbaababaaabbbababbbbababbbbbabbabbaabaaabbababaaabaaabaabaabababaaabbbaaabbbbbbbbabbbbaabababababaabaabbabababaababbababaaabbbaaaaaaaaabbbaabbaababbbbbabaabbbaabbaabaabaabbbbabbbabaabaaabbbbbbabaaabbbaabaabababaaabbaababbbababaabbaabbbbaabaaaabbaabbbbbabbabbbbbbabbbaaaaabaabbabaaaabaaaabbbabbabbbababbaababaabbaababaabbaababaaaaaaabbbabbbabbaabbbababbaaaaabaabaabaabbbabbaaabbbbbaaabbabbbaaaabbbaaaaabbaabbabbabababbbabbaabbaaabbaaaaababbbbaababbabaabbaababbbbabbaaabbabbaaabaaaaaaabaabbbbabbabaaababaabababbbbbabaabaabaabbbabbbbbbabaaaaaabbbabaabbaaababaabababbaaaaaabbbbbbaaabababababbbbbbaaaaaaababbbabaaababababbbbabbaabbabaaabbaaaaaaabbabababbaaabbaaabababaaabbbabbbabaaaababbbbbbbbbbaaaaaabaababbabbabbabbaabbaabaaaaaaaaabaaaaabbaabbabbabbabbbbbaabbbbbabbbbbabbbbabbbabaaaaaabbaaaabbaababbaabababbaaabbbaababaaabbabaaabbabababaaabbabbaababababbaababbbbaaabbbbabbbbaabaabaabaaaaaaabababababbbbbabaababbbbaabaaaabaaaaaabbbbabaaababbaaabbbabbababbbaabababaababbbbbabbbaaaaabbbaaabbaaabababbabbabbabbaaaabaaabababaaabababbaaabbbabbabbbbbabababbbabbababbbaabaabbabaaabbbaabbaaaaaababbbbabbababaabbababbbbbabbaababbbbabaaabbbababbbabbbbaaaaabaabaaaabaaaaaaaabbbbbaaabbbbabbbaaabaababbbababbbbaaaabaabaaaaabbababbabbaabbbbbbbaaabaaaabbabaabbbbaaaabababbbbbbaaabaaabababaaaaabaabbabaaaaababaabbabbabbabbabaabaaabbabaabaabababbaaabababbbaaaaabbbababaabbaabaaaaaaaabbaaaaabaaabbababaaaaaaababbbaabbbbbabaaabbaababaaaaabaaabbbabaababbbaaaaaaaabbaababbabbbbabbabbbbabbbababbabbabaababbbaaaabbbbbabaaaabbaababbabbbbaaaabbabbaabaabbbbbbbaaaabbbabbbaaabaaaaaabbbaaaaaabbabaabbaaabbbabbbbababbaaaaabbabbbbaaabbabbaabbabaaababbbbabbbababbabbababaabaababaababbaabbbbaaaabbbbbaaaaaaabbbbbbaaaaababbabaabbbabbaabbaabaaaabbaaabaababbabaaaaaabbbbaaabaabbbbbbaaaabaabbbbbaabaaabbbbabbbaabbbabbbabaababaaaabaaaabbbabbabaababaabbbabbaaaaabaaabaaababbabaababbaabbbaaaaababaaabbababbababaabbbbbbbabbaababababaabababababbaaaabbbbbabbbabbaaabbbbaaabbaaaaabaabbababbabaababbbaaaababababbbbbbbbaababbbabbaabaaabbbbbaaaabbbabaabaabaaabababbbaaaabbabaabbaaaababaabaabababaaaabbbaaababbabbbbaabbaaaaaaababbbaaaaaaaaaaaabaaaaabbbbbbaaaabbbbaaabbbbbbbaabbbbaabbababbbbbaaaabbbbaaaabbabaaabbababbabaabbbbbbbabbabbabaaaaaabaaabbaabbbababbaabaabbaaababbbabababbbaababbbbabaabbbabaabaabaabbaaaaabaabaaabbabbabaaaabaaaaababbaabbaaaaaabbbabbbabbbbbbbbbabbbbaabbaaabaabaaabbaabababaabbabbababbaaabbabbabaabbabbabbaabaaababbbbbbababbbaabbbbababbaaaabbbaaababbabbabaaaaabbabaaaaabbbbbbababaaaababaabaababaabaaaaabbaaaaaabbbabaababbaaaaabbabbbaabbbaabaabbbbaababbaaabbaabaaaabbbababababbabababbbbbbaaaaabbabbbababaaaaaabbabbaababbbaaababbbbaaabababaabbabbbabbabbabaabaaabaaabbbbaaaaaabbbbababbababbaaababababbbbbaababbababbbbaabbaabbaababbabbaaababaaabaaaabaaabaabaabbbaaababbbababbababbaabaabaaabbaabbbbaabbaababababbbbbabbaabaabbabababbaaababaabbbabaabaaabaaaaabbbbabbabbbbbbaaaaabaabbbbbbabbaaaabaaababbabbabbaabbaaabbbabaaaaabbaaabbbabbbaabbbbbaabbbabbabbabaabbabbaaaaabbababbabbbabbbabbabbabbaabbaababababaaabbabbbaaabaaabbbaababbabbbbabbaabaabbaaaaababbbbababbaabaaabbbabbbabbababaaaaabaabaaaaababbaaaabaabaabababaaabbbabbbabaaaaaabaaaaababbaabbabbaabbaaabbabbbbbbabbbbaaabbbabaabaababaabbbbbbabbbaaaaaabaaaaabbaaabaaaaabbbbabbabaabaababbbabababbbbbbbbaabaaaaaaaabababbaaabbbbabababbbbabaabbbbbaabbabaaabababbaaaaaaaababbaaaaaaaabbbbbbbaabbbbbbaabababbbababbabbbabbaabbbabbabbabaaaabbbbaaabbbbbbaaaabaabababbabbbabbbbaababbbabbbbabbbabababbbababbbaaabaababbbbbaaabbaaaabaabaaabbbaaababaababaaaabbbbbbbbbabbaaaabaababbbaabaaabaabaabbbbaaaabaaabbabaaaabaaabbaaabbaaaaabbbaabaaabbabaabaabbbababaaabaaabbaaaabaababbbbbbbabaababaaabbabbbbaabababbaaaaabbbbbaababbbbaabaababbaaababaaaababbbabbbaabbabbaabbbbaababbbbababababbbbbabaaaaabbbabaaaabbababababbaabaaabbbbbbbbaababaabbaaabbaaababaabbaaabbbabbbababbabbbabbbbbbbbabbbabaabaababbbaaabababbbbbbaaabbabaaaababbbabbbbabbbabbbaaabaaaabbaaaabbaaababababbbabbababbbbbabaaabbababaaaaabaaaaabbbbabbbaaaabbbbbbbbaaaababbbaabbabbbbbababbaaaabbbbbabbabaabbaaabababaabbaaabbbabbababaabababaaaababbabaaabbbbbbabbbaabbabaaababaaaaaaababaaaabbaaabbbbaababbaabbababbbbaabbaabbbbbabaabaabbbbbababaaaababbabaaabbababbbaabbaababbababbaaaabababbababbababbbbababbbabbaababbababbbabbbbbbbababbaaaaaaabababbbbabbaabbaaababbaaaaabaaababbbbababbababbbaaaaaababbbbbbbbabbaabbaabbaababaabbababbababbaababbbbabbbbbaaabbaaaabbaaaaabbaaaaaaaaabababaaaaababaabbaabaabbbbbaabbbbaaabbbaabbbababababbabaaaabbbaabaabababbaaaaababaaaaaaaabbbbbabaabbbaaaaaaaabaabbbbabbbbbbbaabaaabbaaaabaababbabbaababaabbbababbbaabaaabbbbbbaabbbaabababbbabbabaabbbabbaaaabaabbbabbabaababaaabaabababbbaaaaabaabbbbbaabbbbaabaaabbbbbbaabbbabaabaabababbaaabbbabbabaabababbbbabababbbababaabaabbbbabbbabbabaaaabbbabaaabaabababbaabbbabbbbbbbabbbaababbbabababbaaaaabbaabbaabbaaaaabaaabaaabaaaababaabaaabaaaaaabbaabbbaababbaaabababbbabaabbaaabbaaabbaabbbbabbaabaabbabaabaaababbababbbbbbaababbbbabbabaaabbaabaabbababbbaabaaabbabbabbaaabaaabbbbbbbbbababbaaabababaaabaababbbaababbbbbbbbbbbaaaababbbbabbabbaabaaabbbaabbbbbababbbabbbaabbaaaaababbbbbababababbabbababbaabbbababbabaabaabbaabbbabbbbabbabbabaaabababaabbaaababbbbbbbabbaaaaaaabaabaabbababbaababbabaabbbbbbabbabaabaabbaaabbaaabbbbbbaabbbabbbabaaabaabbaabbabbbabbaabbababaaabbabbbababbaaaaabbabbbabaaaabababbbabbaababaaabbaaababbaaaababaaabaabbbabababababbbbabababbabbbabbbbbbabbbababbbaabaabbaabaabaaaabaabaabbbbbbabbabbaaababbbbbaabababaabbaabababbaabaaababababbbbaababbabbbaabaabaaaabbabbbbabaabaaababaaaaaabbababaaababbbaababababaababbababbabaabbbbabbabaabbaaabababababbabbbbabbabbbaabbbaabbabaabbbabaabbbbbabaaababbbbabbbbaabaaababbbababaabbaaabbbaaabbababbababababbabbabbbbbaabbbbbaaaaaabaaababaaaabbabbabbaaabbabbabbaabbbabaaaaabbaababaaaabbaaaabbababababbbbbabbaabbabaaabbbbbbbbbababaabaabaaabaaaaabbababbbabbbaaaaabbaaaaaabbabbaabaaababaaaaabbaaabbaabaabaaaaaabaaabbabbababbabbaababaaabbbbbbaabaaaabaaaabbaabbbabbabbbababbbbabbbbbbaaaabbabaababbbbabaabbbbabbabbbabbbaababaabaabaaabaababababababaababaabaabbaaaaaaaabbbaaaaabbbabbabbbaaabbabbaababaabbbbaabaaaabababbbbbabaaabbabababbababbbbaaabbbabaaabaaabaaabbbbabbabaabbabbbbababbabbabbbbbbbababaabbbabbabaaaabbabbaabaaabbabbaaaabaabbaabbbbbbaaababbbbaabbaabbaabaaaaabbbbbbabbbabaabbaabaaababbabbbaaabbaabaabababaaaabbabaabababbaababaababbabaaaabbbaabbabaabbbaaaabbaabbbaabaabaaaabaaaaababbbbababababbbabbaaaabbbbaabbbaababaaababbaaabbbbbbbbababaaabaaaabbbaaabaaaaabababbbabaabababaaaabaababbbbbbabbbabaabaabbbaaabaabaaabaaaaabaabbbbaabbbababbaaabbabbaabbbbaabababaaaaabbaaaaabaaaabaabbbbabaaaaaaabaaabaaabaaabbbababbbaabababaabbbabbbababaabaabababababbbaaababbbbbbaaabaaabbbaaaaaaabaabaabbaaabbbbaaabbbaabaaababbbabababbabbbabbabbaababbbaaabbabaaabbabaabbaabaaaaaaabbbabbaaabbaabbababbbabbbbbbabbbbbbbaaabbaababbabaabbaaabaababaaabbaabbbbaabbbbabbaaaaaaabaaaabaabbabaabbbabbaaababaabaabaabbbbababbbabbabbbbbabbaabbbbbbbbabbbabbbabbbabbbaaaaaabaaabbabaababbabbbaabaabbaaababbbababaaabaaaabaaaabaaaabaaabbbababaabbaabaababbaabbaaaaabbaabaababbaaababbbaabbaaabaababbabbaaaabaaabbababaaabbbbababbabbaabababbababaaaababbaabababbbabbaaaaaabaababaabbabbbbbaabaabababaaabaaaabbaaabbaababababbbabbaaabbaaaabbabbaabbbaaaabbaabbbbaabaaaabaaabaaabaabbbbaaabaaabbaaababaabbbbbaaaaaaabbabbabbbbaaabbaaabaaaabbabaabbabaaabaabaaaaaaaabaaabbbaaaaababaababbbabbababbaabbababababaaabbbabbbbbbabbabbbbbabbbabbbbbbbbbabaaababaaaababbbbaababbabaabbbaabababbbabbaabbaabaaabababbbaabababaaabaaabbbbbbbaaabbbbabbbbabbabbbaaaaababbbbabaabbbabbbabbbbabaabbbbabbbabbbabbabbababbbbaabaabbaaabaaababaabbbaaababaaabbabbbabbbbbbbaaaabaabbabbaaaaabbbbaabaaabaabbbbbabaaabaaaabbbbbbbaababbabaababbbaaabbbbbbabbbaabbbaaaaaabbabbabaaabababbbbbbbbaaaabbaabaabbaaababaaaaababaaabaaabbbbaaabbaabbbabababbbbbaabaaaaaabaabbbbbbabaababbbbbabaabbbaaaaabbbaabaabaabbbbbbbbbabbababbabaaaabbbbababbaababbaabaaaabbbbaaaaabbbabbbaaaababbaaabbaababbaabababbaaababaaaababaabbbbabababbbbabbaabbbaababbbababbababaaaabaabaabbbaaabbaabbbbaabbbabaaabbbbbaabaaaaaaaabababbbabbababbbbbbbbbbbaaabbbbababbaababbaabbaaaaabbbaababbbbbabbabaabbababaaaababaabaaaababbabbbaabababaaaabbaaaaabbbaababaaaabaabaaaaababaaabaaabababaaaaaabbabaabbbbbbaaaabaababaaaaaabbababaababbbaabaabaaaaaabbaabbaaaaabbbaabaaabaaaabaabaaabbabbaaaaabbbababaaabbabbbbbaaabbabbbaaabbaabbabbbbababaabbbaababaabaaaaaaabbaabaabbaabbbbabaaaabbabaababbbaaaabaabaaabaaabbbaaaabbaabaababaaabbbaabbbbbabbbbaabbbbbabbbbaabbbbabaaabaabaababbbaaaabbabbabbaaabaaaaaabaaaaaabbbbbbaaaabbbbbabbbbbaaabababbbbbabbbbbbabaaabbbabbbbaaabbaaaabaababbbaabaaaabaaaaaabbabaaababbbaababaaabababbaaabbbbaabaababbababbabbbbabbbaababbaaabbabaaaaaaaaabbabbaaaaabaabbbaaaabbaaaaabbbbaababbbbbaabaabaabbbbbabaabaabbaabbbbabaaabaabbaaaababbbbaaabaabbbababbaabaaabaabbaabbbaabbbbbbbabbbbaaaabaabaabbbbbabbbbbbaaabbaabbaabbaaabbbabbbbbabaabbbaaabbbbbbabbabbbaabbaabbbabbbbaabbabababbbabaaaabbbaaabbabbbbbbabbabbaaaaaababbaabbbabaababbbbbabaabaabaaabbbaabbbaaabbbbbaaabbbabaaabbaabbbbabbaabababbaabaabbabbbaaabbbbbbbbbbbabbabbaaaabaaaaaabaaaabbbbbabaaabbbabaaababbbababaaaabababbbababaabbaaabaabaaabababaaaabbaababaaaaabababbbbabbbababababaaaababbbbbaabababababababbbababbaaaabaabbbbbaaababbaababbbbaaaabaababaaaabbabaabaaabbbbbabbbabbbbaabbbababaabbbaababbbaaaabbaabbbbaabbaabbbabbbabaabaaaaabbbbbaaabbabbbbabaaaababbbabaaaaababbbaaaabbbbbbabaababbbbbbaaaaaaabaaaaaabbabababbbabababbababaaaabaababababaabbbbbaabbabaaaabbabbbbaaabbbbaababbbbabbbbabaabaabbbbbbaabbbbaaabaabaababaababbababaaaabaabaaaabbbabbabbbaabaaabbbbababbabababbabbbaaabbaaabababaabbbbbbbaababbbaabaaaabbbbbababaabaabaaabbaaaabbaabbaaaabbbaabbbbbaabbabbbabbaaabbbbaaaababbaaabaabbaaabaaaabbabbbaaaabbaaaabaaaaaaaabbababaaabaababbaaaaaaaabbaaabbaabaababbabaaabbbbbbabaabaababaaaaaaabaababbabbaaaaabbababbaaaaaabbbabbbbabbbbaaabababbaabbbaaaabaaaabbbaaabbabaaaabbaaabbbabbaaabaaabbabbbbaabbbbbabababbbababbbababbababaaaababbbbaabbbbbbaabababbbbbbaabbbbabbabbabaaaabbbabbabababaabaaaaabbaaabababaababbbabbbabaaababbbaaabbbabbbaaaabbabaabaabbabbaabbaabaaabbbbabaaaabbbbabaabbaaabbbbbaaabaaabbbbaaababaabaaaaaaabbbababbbabaaaaababbbababbabaaabaaabbbbaaaaababbaabaababbbabbbabbabbabababbabbbaaaabaabbbbabbbbabababbbbaabbaabaabbabbaaabaaababbabbbbabaabbbbaaaaabbabbaabbababbaababbabbaaababbaabbbabababaaaababbbabbbabaabbababbababbabbaaabaabaaaaabaababaababbabbabaababbbbbbbbbbbbbababbbabaabbbbbabbaabababbbabaaaaabbaabbabaaaaaabaababbabbbbbaabbaabbababaaaaabaaaaaabbababaaaaaaaaabbabbabaaaabbbaabbaaabaaaaaabbbaabbaaabbbaabaaabaabbaaababbaaaabbbaababaabbbbbaabbbbaabbabbababaaababaaabbbbaaaabbabaaaaabababaabbbaabaaabbbbaabbbaaabaababbabaabaabbbaabbbbbbaaaabbbbabaaabbbabbbbbababbaabababbabbbbbbbbaaabaaaabaaabbbbbbabbaabbbbbabbbaabbaababaabaabababbaaaabbbbbbbaaaaaabaabaabaabaabbabbbbbabbbaaaaaaabbaabababaabbabaabababababbabbbbabaaaabbabaabbbaaaabbbbabaabbabbbbaabbbbaabbaaaaabaabaaabbabbbabbbbaaaabbaaabbbaababbabababbbbbababbbbababaaaababaababaababbbaaabababbabbaaabbbabbbababbaaabbabaabaaabbbbbbaabaaabaabbaabababbaabbbbaaaaaaaaaaabbbaabaaaabbabbbababbbbbaaaaaaabbaaaaaaaababaaaabbabababababaabbaaaaabbbbbbbabbbbaaaaabbaaaaabaaababbbbaaabaaababbabbbaaabbabaabbabbaaaabbbabaababbaabbbbbbabbbbbabbbababaaaaaaaababbabaabaaaaababaaaaaaaaaabbabbabbaaaababaaabbaabbbbaabbbaaaababababaaaaababbabbabbbbbbabbbabbaabbababbaabbbaaaaabaaababbbabaaababababaaaababbbbabababbbbbbaabaaaaababbabaababbbabbbbbaabaabbbabbabbaaabbaabbaabaabaabaabbaaabbbbabbbbaaabaaabaaaabaaabaaaaabaabbaaababaabbbabbbbabaabbabbaaaabbbbbbbabbabbabbbaabbbababbababaaaaaabababbbbaaabbaabaaaabaaaaabbbaaaabbbaababbabbababbbabaaabababbbababababbaaaabababaabbbbabbaabbaabbbabbbbbbabaababaaaabbbbbbaabbabbabaaabbbbbaaababbbababbbabbaaabbbbababaaaaabaabaabbbbabaabbaaaaaabaabbaabbbabababbbabaabaababbbbbababbaaabbbaababaabbaaaaabbaabbabbbababbbbabaabbbaabaababbaaaaabbababbbbabaabababbabbaaaabaabbbabbbbbabaaaaabbaabbaaaabbaababaaabbbbaabbbbbbbaaabbaaaaabbbbbbbbaabbaabaaabaaaaaabbaaaaaaabbbbaabbabaaabbbbaabbabbbbabbaaabbaaabababbbbabbababbbaabbabbaaabbaabaabaabaabaaababbaabaaaaabaabbbabaaababbbbabbabbbabbaaaabbbababbabababaabbabaababbabbaaaaaaabbaababbabbbaabaaaabaaaabbabaaaabbabbbbbaabbaabaababbaabbbbababbaabbbababaabbbbbbaaabbaaaabababbabaabbbabbbabbbabaaabbabbbbbaaaaaabbbabbbbbbabbbabaababbbabbbbbbabbaabaababbaababababbabbbaaaabbbaabbaababbbbbbaababababaaabbabbabbbbbbabbbbabaabbbbbabbababaaaaabbaababbbaabbaaababbbaababaabbaabbbbbababbabbbbbbabaaaabaabbaabbbbabbababababaaabababbaabababbaabbbbbbbabaaabaabaaaaaaabaaaaaaaaabbbabbabbaabbaabbabbbbbabbbaaaabaabaabaabaabaaabaabbabaaaaaaabaaaaaabaaababaaabbaaaababbaabababbabbbabaaaabababaaaabaabaabbbabababbabbbabaaabaababaabaaaaaaabaabaaabaabbbabbaabbabbbaabaabbbbabaabbaabbbbbbababbbaabbaababbbbbaaaababbbbbaabbbbbaaaaababaaabbbabbbbbaaaabbababaaaabbabbabbbbaabaabbbbbbabaaaaaaabaabaaabbbbbbbbabbaabbaaababaaaabaabaaababaaaaabbbbbbaaaababbbbabbbbaaaabbaabbabbabbaaabbababbaabbbabbaabbbbabababaabbabbaaaabbbaababbbaaababbaabbaabaabaabbbbababaababbbbbabbababbaabaabbbabbabbababbaababbbaaabbababbabbbaababababaaaababbababbbaaabaaabbaaaabbabbaababbbbaaaaababbbababbaabbaabbbaababaaabababababbbbaaaababbbbabbbbbbaabbbabaaababababbbaabbaabaaabbaaababbbbbbbaabbbbaabbaaababbaaabbabbbbabbbbaaabbabbaabbaaaaabbbababbabaaaabaaaaababbbaaaaabaabbbabbbabbaaabaaababbbbbabbbbbbabaabbbbaababbaaaaabbaabbaabbabbbbaabbabbaaaaabbababbababbbbabbabbaaaababbaabbbaabaababbabaaaaabaabaabbbaabaaaaabaaabaabbbababaabbaaaabaaababbabbabaaababbbababbabaaaaaaabbabbbaaabbbbabaabbaabbbbbabbbbbbabbbabababbbbaabaabbbbabbaabaababbbababbbaaababbbbaabbabbbbbbbbababbbbbaaabbbaaabbbbbabaaabababbbababababbbaababbbbbbababaaabbbabaabbabbbbaabbbbbbaabaaabaaaababaaaaaabbabaaabbbabbbaaababbbbabaaabababbbbbbbaabbababbaabaabbbbabaaabbaaaabbabbabbbbabbbabbabbbbaababbbbbaabaaaaabbabaababbbbabababbbabbbabaabaaaabbbabbbbabbababbbbabaaaaabbababbbaababbabbbbababbabbbbabaaaaabbbbabababaaaabaaabbabaababbaababababbbaabababaaaabbabbabaaabaabaabbababbabbbbbbaabbbbbbabaaaaababababbbbbbabbaabaaaababbaaabbbababaaabbbbbaababaabbaabaabbbabbbaababaabbbaaaaaabbbababaabababbaaabbbababaabaaabbbbbabbaaaaaaaabbabaabbaaababababaababaabaaabaabbaabbaabbabbaababbaabaaaabbaaabbaaaabbaaaabababbaaababaaaaababaaabaabbbaaaaabaaabbaabbbbaaababbaababaaabbaaaabaabababbbbbbbbbabaaaaaaababaabbbbabaaaababbaabbbbaaabaaabbaaabbbbbaaaabbaabbbababaaaaabbbaabaababbbbaaaabbbbabbaaababbabaabaaabbbbaaaabaabbbaaaaabbaabbaabbbaababbbbbaabbbbbbabaaabbbabababbaaaabbabbaaaaabbaaabaaabbabaabbbbabbbaabbaabbaabababbababbabbaaabbaabababbabbbabaababaababbbabbababaabbabbbbaabbbbabbaaaabaabbbabaaabbbabaaaabbbabbbabbbaaabbababaababbbabbbbbbabbbababaabaabaaabbabbabbbbbbabbabaabbbbaabbabbbbbbbbabbbaabbabbbbbabababbaaabaababaaabbbbbbbbaabaababbbabbaabbabbabababbaaabbabbaabbaabbbbbbbaabaaaaabbababbbaaabaabbbbaaaabbaabbaaaabbabbbbaabbababbababaabbbabbbbbbabbaabababbabbbababbabbabbabbbabbababbabbbbaabbaabababaaaabbabbabaaaabbbabababbabbabbabbaabaaababbabbbbaabbbbbaabbabbbaaaabaababbbabababbaaaabaabaabbbabaabbabbbbbbabbabaaaaabbaaababbbaaaaaaaaaaaabbaabbabaaabbaabbbaaaabbabababaaababbaaaaaaababbaaabaaaabaabbbbbaabaabbabbababbbbbaaabbaabababbbaababbbaababaaaababaabaaabaaabbbaaabaaababbaabaabaabbaabaabaaaaaaaaabbbbaaaaabaabaabbbaabaabababbaabbabbabbbaaabbbbbaabaabaaababbbabababaaaabbaabbbbaabbbaabbbbabbabaabbaaaaaaababaaaabbbbbbbababaaabaaabbaaaaaabbaaabababbabbababaaaaabbabbaabababbabaabbaaaabbabababaaabaabbbaaaabbbbbaaaabbbaaaaaaabaababbbbbbaaabbaabbbbbbabbaabbbaabbabbbbbabababaabbbaababaabbabbaaaaabbbbaabbbbabbaaaaabbaaabaaaaabbbbbbaabbababaabaabbaaaabaaabaabaabbabbabbbbabaabbaaaababbbabaaababababbbaabbbaaabbaabbaaaaabbbbbbbbabbbbabaaaabbaaababbbbbabbbabaaaaabaabaababbbbbbbbaaaababaaababbaabaabbbababbababaaaaabababaababbaabaabaabbabbbbababababbbabababaabbbaabaabbabbabbbbbababbaabbaaabbbaabaaaaaaabaaabababbbaabaaaaabbbaaabaaabbabbbbaaababbbbbabbaaababbaaabbbaaababaaaababbbbaaaaaabbaaabbbaaabbababbababaabaabbbbaaabbbaaabbabbaaaabbabbbaaabaaabbbbababaaaabaabaaabbbaabbbbbbabbbbabaababbbbbbabbaaaaaabbaabbababbaabbaabbaabbaaabaaabbbbabaababaababaaaaaaaabaabababbaaababbbbbbbbbaaabbabbabbaabbbababaabbbbaababaaaaaabbbbaabababaaababbabbbababaabbababbbbbaaaaaababaaabbabababbabbbababbbaaaabbbbbaaaaabbbabaaaabbbbaabaaaaabbbababbaabbbaaabbabbbaaabaaaaaaaaaaabbaabbbabbbaaaabaaaabbbaababaaababbaababbbaabbbabbbabaabbaaabababaaabaabbaaaabbbabbaaaabbbbbabbaabbbaaababbabbbbaaaaaabbaaaaababaababbbbbbbbbbbbbaabaabbababbabaaabaababbbaabbbbbaababaabababbbbbbbbabbaababaaaabbbabaaabbbbbaababaaaaabbbaabbabaabbaababaababbabaabbbbbbbbbaaaaaabbbbbbbabbbaaabbaaaabaaaaabbbbbaabbaaaaaaababaabbabaaabbaabaabaaaabbabaabbabbabbbbbabbaaabbbbabababbaabbaabaaaaaababaaabaababaaabbbbabaaabababaabbbbbbbabaaabbaabbbabababbbaababbbaabbbaaabbabaababbabaaabaabaababaaaaababbbbbaaabbaabaababbaaabaaaaabbbbbaababbabbbbbaaaaabbaaaabbabbabababaaababbaabbabbbabbaabbbbabbaabbabbabababbaaabbababbbaabaaaaaaaaabaabaaabbbaaaaaaaaaaabbbabbaaaaabbaaabbaabbabbaabbabaababaababbaababbbaaabababbbaabababaaababbaaabaaaaabaababbbbbbbaabbbbbbaaabbbabbbabbbabaaabbabbabbbbbaababbaabaabbbbbbbaaaaaaabaaababababbbbaabbaaaabbababaabbabbabbaabbbbaaabbbaabbaaaaabbbaabbaaaabaaaaabbbbababbbababbabbabbbabababbabaaaaababbabbbbabbabaabaabbbbbaabbaaaaaaaabaaaabaababaabbaabbaaaaaaabbbbababbaaaaaaaaabbabbaaaaaabbabbbbababaaabaababaabbbbbababbbabbaaabbbaaaabbbaaabbbbabababbaaababaaabbbbbaaaaaaabbbbaabbababbbbaaaabbaabaaabaabbabaaabbabaaaabaaabaaabaabbaabbaabbbaaababbbbabbbbaaaabaaabaaaabbabaababaaabaaaabaabbaabbababaabbbbaabababababaababaaabaabbbaabbaabbabbabbbbbbabbbaaaabbbbabbababaababbababbbaaaabbabaabbbbbaaaaaaabaaaabbaaabbbababbaababaaaabaaabbabababbbabbaabbbbaaabbbbbbbbbbaaabaababababaabababbbbbaaabbbabbbaababbbbbbababbaababbaabbaabaabababbbaabbbaabbabbabaaaaaaabaabaabaaaaaaabaaaabbaaaaabaaaaabbbaaaabbbbbbabaaabbbabababbaabbabaababbaabaaaabbbbbbbabbaababaabbbbbbbbbaabbaaabbabbabbabbabbbbabaababbbababbbabaaabbabaabbbaabbaaaaabaabbaababbaabbbbabbaabbaaabbaaababbbabbbbbabaabababbbbaabbabbabaaaabaaaaabbabbabbbaababaabaaaabaabbababbaaabaababaabaaaabbbbaaaaaababbbaaaabbabbaaabbabbaaabaabaabbabbaababbaababaabbaabaaaabbbbabababbbbabbbbbbaaaababbbaababbabbababaaaabbbabbaabbaaababaabaababbabaaabaababbabaabababbabbbbbaaababbaaaaabaababbabaabbabbaabbabaaaaabbaabbbbaababbbbabaaaababbaaababbbbbbabbbababaaabbbbabaabbaabbabaaaabababaaabbbaabbabaabaaaabaaababbbabbbabbabbaabaaaaaabbbbbababbaaabbaababaaabbaabbabbbbbaaababababbaaabbbabbabaabbabbbaabbbbabbbbaabaababababbaabaabbbaaaaaabbababbaaaaaababbababbbaabaaaaaaaaaabbbaaabaabbaababbbaaabbbaaababbbbbabaaaabbbabbbbbabbabaaaabbaaaaabababbaabbaaaaaaaabbaaaabbaabaababbbbbababbbaaabbaababaababaaaaaaabbbbabbbaabbabbabbaabbbbaabaababbbbbabababbbbbaabaabbbaabaaabbbabbbbbbaaabbaaababbaaababbbbababbbaaabbababaaaaaabaabaabaaaabaaaaabbabbabbaababbbabbaabbabbbbabaaaabaabbbbaaabbabbaababbbbbbabaaababbbaaaabbbabbbabbbabbabbbbaaaaabbabbbaabbabaaaabababaaababaaabbababaabbbbababbabaababbbaaabbabbabbabaabbababbbbbbaaababbaabbbbababbaabbbbbaaaaaaaaaabaabbaaabbabbaabaaabbaaaaabababaaaabbbabbaabbbbbabbbaaaaaaabaabbaabbbbaaaaaaabbbaaaaabaababaababbabbaabaaaaabbabbbabbbaaabbbbbabaabababbbabbbbbaaaabaaababbabbbbbaababbaaabbbbababaaabababbbbaaaabbbbbbaaabbbbbaabaaababababaabaababbaabbbbababbabbbbbbaaabaabaabbbaababaabaabaabaabaabaaaaaabbbababbababbbabbababbbbbbabbaababaabbbabbbbaaabbabaaaabbbabababaaaabbaaaaabbababaabbbbabaaaaabbbbbbaabbbbababaaaaaabbabbaababbbbbbbaabbbabbabbbbbaaaaaaaabaaabbbbaabaaabaaaaaaaabbbaabaabbbabbabbbbabaaaaaabbbaabababbabaabaabaaabbabbaaaabaabababbababaaabbbbbbbbbbabbbabbbaaaaababababbbaaaabaaababababaaababaabaaabbaabbbaaaabaaaaaaababbaabbaaaaaabbabaabbabbaaaaabaabaabaababbbbabbaaabbaabaabbaabaabbaabababbabbbbabbaabababbbbbbbababaaababbabbaaaababbaaabbbbaaabbbaaabaababbababbaabbbaabaabbaabaaaabbabababaaaaabbaaabbabbaabbaaaaaabaabaabbbbaabbbaaaaaaabababbbbbbaaabaababbbaaabbbabbabaabaaabbaaabbabbbbabaaaaabaaaababbbbababbbbaaaaaabaaaaaabbbaaaababbbbbbbbbbbbbabbaabaaabaababaabaaabbbaaaaabbaaaaaaabbabbbaaaabababaabbaabbaabbabbbabbaabaabbababbbaabababaaaababbbabaababaabaaababaaaabbabbabbaabaabbaabbbabaabbabaababbbaabbabbbaabbaaabbabbabbababaaabbbbaaabbbabaabbaaaabaabbbbaabaaaaaabaaaabbbbabababbabbababbbaabaaabaaababbbbbbbbbabbababbbbbbabaaabbbbababbabaaababbbbbbbbbbababaabaaababbabbabababbabbbaabaaaabbbbaabaabbbabbbabbbbabbabaababbaabbbbbaabbaaabaabbbbaabbbabbbaaaaabaabaabbaabbaabbabbbaabbababbabbaababaabbaaabbaaababbbaababbaaaabaaaaaabbabbbbaaaabababababbbbabaabbbaaabbabaababaaaaaaaabbabaabaabbbbaabbabbabaabaaaabaababbabaaababbabbbabaabaaaaaaaababaababaabbbabbaababbbbbbbabaaabaabbabaaabbbbbabbbbaaaaabbbabbbaaabaababbbbbbbaabbbbabbaabbbbaabaaabaaabbaabaababbabababbbabbabbaabbbbbabaababbbaaabbaaaaabbaabaaaabbbabaaabbaabaaabbaabbbabaaabaaabaaabbababaababbaaaabbbbbaabaaabaaabbbaaabbbbabbbbaabbbbbbabbbaaabaabbbaaaabbabaaaabaaaabaabbababbbbabbaababbbaababbbbbbabaabaabaabbbaaabaabbbbaabbbababbabbbbbbbbbaaabaaabaababbaabababbaaabbbabbaabaababbbababbababaabaababbaabbbbaaaabababbbbababaabaabbabbbaababaabbbbbbaabaaabbbabbbbbbbbbbaabbbbabbbbaabababaaaabbabbaabbbbbaaababababaabbabbabaababbbabaaaabaabbbbaabbbbbbbbbbaaababbaababbbaaabbabaababbaaaaaabaaabaaaaababbbabaabbabababbbbbaabaaaabbbbaaaaaabbaaabaabbababababbabbbbbaabaaababbababbbbaabaaabababbbaabbbbbbbaaaababaababbaabaabbbaabbabbabbbaaaaabbaababbbaabbbabbabaaaabaabbaabbbaabaaababbaabaabaabaaaaabbbabbbbabbaaaaabbbbabaaabaaabaabaaabbaabbabbaaabbaaaabbbababaaabaabbaabbababbbbbbbaabaabbbaaaabababbabbbbaaaababaaaaaaaaaaabbbbabbaabaaabaaaaaaaaaababbaaaabbabaaababbaaaabaababbbbbababaaaaaaaabaaaaababaabbbbbbabbbaababbabbbabaabaabaabbaaaaaaaaabaaaabbaaabaaaabaabbbaababaaaaaaaabaaaaabaabbbbbbabbbbaaaaababbbaaabbbbbaaabaabbaabababbaabbaaabaabbbabaabbaaaaabbaaaaabbbbaaaaabababaababbbaababbaaaabababbabbbabaaabbbbaabbbbabbabbabaaabbbbabaababbbbbaaababaababaabbbbaaabbbbbaabaaaabaaabbabbbbbbbaababaabbabababaabbbabaaaabbbabaaaaaababbaabaabbabbbaaabbbbaabbabbabaabbaabbabbaaaabbbaaaaaaabbbaabbabbabaaaaabbaaabbabaabbbabbbbabbbaabbaabaabbabbaabbaabaabbbaababaabbaabbbbbabbbbaabbaaabbbbbabbbbaaabaaaababbbababaabaaaababaaaaaaabbbaaaabaabaaaababbaabaaaabaaaabbaabbbabbaaabaabbbbbbbbabababbbabbaaaaabaaaabbbbaabaaabbabababbaaaabbabaaabbbababbabbbabababbbbbabaaabbbaababaabbabaaaababbbabbaabbbabbbbaaabaaaabbbbaabbbababaaaabbbbabaabbaabababbbabbbbaabaabbbaaaabbbaababababbbaabbabaaaabbbaaabaaaaabbbbaaaabbabbaaaabaaabbaabbabbbababaabbbbbbbaabaabbbabababbabbbbababbbabbbabababbbbaabababbbbaabaabbbabbbabbaaababbbbbabaaaaaabbaabaaaaababbababbbbababaabbababbbabaaababaabbaaaaabbaaababbbaaabbbbabbaaabbbabbabbbbbbbabbbaabaabbbaaababababaabbbaabbbabababbbbbbbbabbbabaababaabaaababababbbbabaaabaababbbabbabbbbbababaabbbbbaaabbbaabbbababaaaabbabbbaabaabbababaaaababaababaaababaaaaaabaaabbaababaababbbaaabbbbabbaabbbaabbaabaaababbbabbababaabbabbabbaabbaaabbabaaaaabaaababaaaaaabbaababbabbabbbabaabaabaaaabbbabbababababbbbaaaabbbaaaabaaabaaaabaaaaaaaaabbabbababbbbbaaababaaababbbbabbabaaaabbababbbbabbababbaabaabbbaaabbbbaaabaaabbbaaaaaaaabbbbabbaaaaababaaababbbabaaaabaaabbbababbbbabababbbabbbbabbabababaabbbabaababbbbabaabbbbbbbbabaabbbbbaaabaabbbaabaaabbbbbaaaaaaaaaabaaaabbbaabbbabbababbaaababbbabbbabbbbbababaaababaabbbbbabbaababbababbbbbabbbabbabbbaaabbbababaabaababbaaabbbaabababbaaabbaaaaaaabaaaaabbaabaabbaababbbbabbbabaabaaabaabaabbbbababbbababaaaabaabbabaabbbbaabbbaabaabbaaaaaaabbaaaaabaaaaabbbbbbbaababbbaaaaaabbbbabbabbbbabaaaabaabbaababbabaaababbaaaaababaaaababbbaaabbaaabbbbbaaaaabababbaabaabbbaababbbbbbbabbaabaabaaabbbbaaabbbaaabbaaabbbaaaaaaabaabbabaababbbbbbbbabbbabaaabaaaabbbaabbaabaabbbabaaaabaabababaabbaaabbbabbaabbabbbaabbbbaaaabbbaabbbbaabbabbaabbbaabbabbaaaaabbaaaabaabaaaaaaabaabaaaabaabaabbbabbaabaaabbababbaaaabbaabbaaaaabbbbabaabbababbabbaaabbbaababaaaaababbbabbaabbbabbaababbbbbababaabbaaaaabbabbabaabbbbbbbababbbabbbbbbbbabbbbbbbabbaababaabaaaababaaabaaabaababaababababbababaabaaababaabaaababbbaababaababbbaaaaababbbbaabbaaabbbababababaabbbabbaabbababbbabbabbabbbbabbababbbabaabbbababbabbbabbbabbbbbbaabbbbaaababbababbbbbaaaaabbbabbbbabababbbbaaaabbbbaabbbaaabbbaabaaabaababbaaaabbaabaaabbbababbabaabbaaababaaabbbbaabaabbaababbbaababbbbabababaabbaabbbbbbbbaaaaabababbaabaaabaaaabbbabbaabaaabbbaaaaaaabbbbbaaaababaabaabbbbaaabaaaabaaababaabbaaaaabaabbaabbaabbbbabaabbaaabababbbbbbababbbaaabbbbbbbbbaaababbbaaabaaabaaabbbabbbbbbabaaaaababbbbaaaabbaaabaabbabbbbbabbaaaaabbbaaaaaaaabbaaabaaaabbbaabababbbbaabbbbaaabababaababaabbaaabbbbaaaaababaaabababbabaabbaaabaaaaabababbbbbbaabbbbaababbabababbbbbbbbbbababaaabaabbbbabbbbbbabbabaabababbbbabbbbbbbaababaaaabababbababbabbbbaaabbbabaabbabaaaaaabbbabaaabbabbaaaababbbbabbaaabaababbaababbabaabbbabaaaabbbbbababbaabbbaabaabbaababbbbbaaabbbbaaabaaabbabaaaaabaaabaaababbbabaabbabababbbabbaaaaaaaabaaabbabbaabbabbbabbaabaabbaabbbbaaaaabaabaabaaabbabaaabbbabbabbbabaaabababbababbbbabababbabbbaabbabbaabaaaaababaaaababbbbaaaabaababaabbbbbbaabaabaaabbbbaabbbaaaabbbabaaababbbbaaabbaabaaaaabbbbabababbbbbbbaaabaaaaababbabaaaaababababaaaababbababbbaaabbbabbaaabbaabbbbbababbbabbbaaaabbbbbabbaabbaaabababbbbbbababbbabbbbbaabaabbbbaaabaaabaababbbabaabbbbabababbabbbbabbabbbaaabbabaaabbbabaaabbababaaababaaabbabbbabaaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaabbaaaaaabbbababaaaaaababbaabaaababbbbbaaabbbbbbaaaaaaaabaaaaaabbbaaaababaabbbbabbabaabbbaababbbabbaaaaaababbbaaabbaabbaaaaaaaabbbaabbbabbbababbbababbabaababbbbbaaabbbbaaaabaabaababababbbbabbabbaaaabaabbaaaaaabbbabbbabaabbabbaaaabbaaabbaababbbaabaaabbaababaaaaabaaabaabbbbabaaaaababaabaaaaabaaabbaaaaababbbaaabaaabbbaaaabbbaabbbabbbaabaababbaabbbbababbaabbbaabbaaaaabaabbbbbabbaababaaaabbbabbbbbbbbaaaabbbbabababbbbbbabbbabbbabbbababbabbabbbbaaabbbbbaabbabbbabababbaabababbbbbaabaabbbbabbbabaaaaaaabbbaabaabbababbaaabaaaabaababbbabbaaabbabaaababbabaabbbaabbaabbbabaaaaababaabaaababbbabaabbbbbbbabbbbabbaaabaabbbbaaaabbbaabbaaaababaabaabbababaaaabbaababababaaaabbbbbbbabaaabaaaabbbaaaaaaaaabababaababbbabaaababbbaababbbaabbaaaabaababbababaaaabbbaaaaaaabbbabababababaababbaaabbabaaaabbaabbaabaabaabaaaabbbabbbababaaabbabababaabbbaaababbaabaabbbbaaabbbbbababbababaabbbabbbbabbbabababbbbbbbbaabaabbabaabbbbbaabbbbbabababaabbaababbbbbbabaabbaaababbaababbaaabbbaaabaabbbabaaabaabbbaaaabaaaabbbbbbaaaabaaaababbaaabbaababbabbaababbaabbbababbaabababbabababbbbaaaaabbabaababaababbbabbbbbaaabaaaabbbbbbbabbabbaaaabbbbabbababbbbaabababaababababaabaabbaabaabbbbababbaaaaaaaabbababbbbaaaababbbabaabbbabbbaaabbbaabaaabbaaabbbabbababbbbbbbbababbaabbabbabaabbaaabaabababbbabbaabaabbbbabaaaabbbabbabbabbbbaabbababababababbbaabababbbabbabbaaabaaaaaaabbbaaabbbabaabababababbbbabbabbbbaabbababbabaabaaabababbbaaabbababbbababbbaaaabbbabaaabaabaaabbabbababaabbbaabbaabbbbaaabbabbbbbabbbbabababbabaaabbabbabbaaaabaabaaabbabaabaabbbaaaaabaaabbbaabababababbbabbaabbbaaabbbababbbbaabaabaabaabaaaaaabbbbbababbbbbbbabaabbabababbaaabaaaabbaaaabaabbabbbbbababaaaaabbababbabaaabaababaaaabaaaabbabbbbabaabbbbbbaabbbabbbbababbaababbaaabaaabbabaaababaabbabbaabaabaaabaabbbbabbabbaabbbaabaaaaaabaababbaaabbaabaabaabaabbabbaabbbaaabbabbbabbabbaabaaaaaabaababbaaaabbbbbabbbbababaaaabbbbaabbbbbaaabaabbabbabbababbbabaabbbbbbbbaaaababbbbabbababbaaaabaaaaaaabaabaababbaaabbaababbbaaababaaabaaabbbbbaaabaaaabbaaababaabaabaaaabbbaababbaaaabaaabbaaaaabaaababbbabaaaabbaabaabbbababaabbbababbababbaababaaabababbbbabababaabababbabbbabaaaababaabaaaaabbaabbbabbbaabababbabbbbabbaaaabbaaaabbabbbbabbabbabbbbbaaaabbabaaabbaaaabbabbbaabbabbbaabbabaabbbbaabbabaabbaabaabbbbabbbbbaaaabbaabbabaaabbbabbaaaaaabbbaabbababaaabbaabaabbbbbaabaaabbabaaabbbaabbbabaabababaabaaababbbabaaabbbaaabbbbaabbbbbbbbbbabbbaaaaaabbbabababbaaabbbbbbbaaaabaabbababaabbaaabbbbbbbabbbbaabaabbbbbbaaabbbabbabbaaaaaaaabbaaabbaaaabbaaaaabbabaaabbabbbbbaabaaaabaabbaaabaababbbababaaabbbbbaaaabbbaababbaaabbbabbbabbabaabbbaaaaaabbbaaaaaabbababbbbaaaaaababababbbbbabaaabaaababbbabbbaabbbbaabbbbabaabababaabbabbbaaabaaabbabababababbabbbbbaabbbababbaaabaabbaaaaaaaabaabbabbbbabbaabaabbbbababbabababababbababbbaaabaaabaaaaabbaabbbabaabbbabbbbaaabaabbbbabbaabbabbbababaabababbbbbaabbbaaaaabbbababbbaabaaaaaabaabbbaaaabaaabababaabbbbaabbababbabbaaaaaaabbaaaaabbbbbbaabbbaabaaaabbbaababaaaababaaabbabbabbbaabbbaabaaabbabaaaaaabaabbaaababbbabbaabbbaabbbababaaababbaaaababaabaaabbbbabaababbabbbababbabbbbababaaaabbbaaaaaaabaaaaaaababbbbababaaaaaabbbaabbbaabbbbbbabaabbbabbaaabbaaaaabaabbaaabbabbabbabbbbabaabbabbbbaabaaabbaababbaababababbbbabaaaaabbbbaaababbaaaabaaaababbaabbbbaaababbabbabaabaaabbbaaaaaabaaabbbabababaababbbabbbababbababaabbabbbabbabbbabaabbaaabaaaabaabbbbbbaabbbbaabaaaaabaaaaababbbbbabbbaaaaaababababbaaaabaaabbbaababbaababaabbaababbbabaaaaababbaaaabbabaaaabbbbababbabbaabbababbbbbbabaaabaaabbbbbaabaaabbaaaaaaaabbabbbaababbbbaabbaabaabaaaaabbaababaaabaaababaaaaabababaaaaaabbbabbbbaabaaaabaaabaabaaaababababbaabbaaababbbbabbabaaabbbbbaaaabbabaababbaabbbbbbbbbaaaaabbbbbabbaaaaaaabababaabbabaabababbbaabbabbababbbbbbabbabaabbbbababbabbbababaaaababbbaabbbbaaaabbabbbbabbaababbabaaaabbbabbbaaaababaaaabbbabaabaaaaaaabbaabbbaaaaabbbabbbaabaaabbababababaaabbaababbbabbaaababaabaabaaabbbbbaaabaabbababbabbbaaaaaaababaaabaabbbbababaabaaabbbbaabbbbbbbbaaabbbbbabbaaaabababbbbbbbbbababbbaabaaaaaaababbaababbbabababaaaaaabbaabaaaaaabababbbbabbbbbaaabababbbabbbbbaabaaaaaababbbabbaaaabbbbabbabbbaaaaababbabbabaabaabaaabaabbbabbbabbbabbaaaaabaabbaaaabbaabaaaabbaabaaaabaabaabaaabbbaabaabbababaabbaaabaaabaabaabaaaaaaaabbababbabbbabbbaabbbabbabbbaaababbbbaabababbabaaabbabaabbbabaabbbbbabbaaabbbbbbaabaabaaabbbbaaaaaaaaababbbbbaabbbaabbabaabababbaaabaabaabbbbbaabaabaabaabaaaaaabaaaaaaaababbababaabbaabbbbbbbabaaabbbbabbbbabbbbaaabaabbaabababbaaaaaabbaaaaaabbaabaabaaaaaaabbaaabaaaaaabaabbabaabaaaaaabbbabbaabababbaabaaabbabaabaabbbaababbaabaaaaabbbbbbaababbaaabbaabababbababbbaaabaabaaabbbaababbababbbbabbabaabbbbabababbbabababbaabbbbaaabbabbbbaaaabbabbabbaabbbbabbbabbbabababababaabbbbbabaaababaaaabbabaababbbbbabaabbabbabbbbbbbaabaaabbbbbaabbbbbbababbbbbaabbbaababaaaabababaabbaaaaaaaaabbbbbaaaaaaaaaaabbaaaaaabbbbaabaabaabaaaabbbaaabbbbbbbaaabbabaaabbaabbabbabbaaaabbbabbabbabbbabaabbaabaabaababbbbaabbaabbbaaaaaabaaaabbbaaaaabbaabababbaaabaabababbbbaaabbaabbbbaaabababaabaabbaaaabbabbbbbbbbaaaabbaaaabbabbbabbbabbaaabbaabaaabbbbababbabbaabbbabaaaabababbbaaaabbbbabaabbaaaabbaabababbbaaaabaaaaaaaabbaaabaaaabaaababaaaaaabbbabaaaabbabababaaabbbbabbaabbbbabbababbbbaabbbbbabbbbabaaabaabbabaaabaabaabbbabbabaabbabbbbbbaabaaabbaaaaaaaaababbaabaaabababbabaaabaabababbbbaaaaaaaaaaaaaabaabbabaabbabaaabbababbbabbabaabaababbbbbaaaabbabaabababbbbbaabaaaaabbbaabbababababbabaaabbbbabababaababbbbbaabababbabaabbaabababbbaabbbbbbaababbbbbaabababaabbbabbbbbbabaabababaabbbbabababbaabbbabbbbaaabababbbbaaabbabbabbbbbbbbabbbabbbbbbbababaabbabbbaaabaaabbaaaaabbbbbaaaababbaabaabaaababaaabbabaaabaabaaaaababbaaababaaabaababbabbbabbaabaabbbbbabbbbaaaabaaaaabbaabbbbaaabbbbbababababbaabbabbabaaaababababaabbaabaaaaaabbbbbaabaababaaabbabbaababaabbbbaaaaaaaaababbaaaaabaabaaaaaaaabbabaabaaaaabaabbabaaaababbaaabbaabbabbaabaaabbbbbaaaaababbababbaabbaaababbbbbbaababbbaaaababbbabbbbababbababbbabbababaaabaabaabababaaabaabbababbbbbabbabbabbabaaababaabbbbaaabaaaaaabbaaaabbbabaaaaabbbabbbaababbabbbabaaaababababababaaaababaaaaababbbbbabaaaabababbabaaaabaaabbbaaaaabbbbabbbbaabababbbbbaaaabbbaaaabaaaaaabbbaababbbbaaabaababaaabbbababababaabaaabaabbaaaabbbbbbaaabaaaabbabbbabaabbbbabbaaaaaabbaabbbabababbabaababaabaabaaaabbbbbbaaabbbaaababaabbabaabaaabbabaaababbaaabbbbbabbbbbaaababbbbbabbaababbbaabaaababbabababbaabaabbaaabaaabbabaaabbaabaabaaabbbbbbabbabbabababbbbbabababbababbbaabaaabaaaaabbaabbbababbbbababbabbbbbaababbbabaabaaaabbbbbbaaabbbabbbabbaaababbaaaabaabbabbbbabbbabaaabbabbabaabbbbbabbaabbbaababaabbbbababaabababbbbbbabbbbabababbbbabbbbbbbaaaabababaaabaaaabbabbbaababbbbabaaaaabbbabaaaabbbabbabaababaaaaaabbabbbbabbbbababaaaabbbaaabababaabaaababbaaaaababbababbbabaabaababbbabaaabaabaaabbabbabaaabbaaaaabbabbbaabbbaabbaabaababbabbbaaaababbbabbbbababbabbbbbbbbababbabbabaabbaabaabababbabbabbababaaaaaabbaabaabbbbbaaababbbaabbbabaaaabbabbaabbbbabbbaabbaabaabbbaabbaaababababaaaaaababbababaabaaabaababaabababbbabbabbbababbbbbaabababbabbabbbbbaabbbbababbabbbaabbbbababbabbbabaaaabaaaaaabbaababbbbbaababbabaababbbbbaabbbbbaaabbabbbbbbbaaabaabaaaabaaaaaaababbbbbbabaaababbabaabbbaaabaaaaababaabaabbbabbbababbbabbbabbaabaaaaaaaaaabbbbaababbbaaabbbbaaabaaaaabbbbabababaaaababbabbaababababbaaabbbbabbbbabaabababaabbbbabaaaabbabababbbbbabbbabbabbbabaabaabaaabbaabbbbabbbbbbbabbbaababbaaabbbbaaabbaabaababbabbabaaaaabaaabababbbbaabbbababbabbbabbabbbabbabbbbaaaaaaaabbbaaabbbabbabbbbababaabaaabbaaaaabaababbabbaabaaababbaaaababaababbbabbbbbabbaaaaabbbabbaaabaaaabbbbaababbabbbbababbbbbbaabbababbabaaabaaabaabbbbababbabbbabbbaaaaaabbbaabbbabbbaaabaabbabaababbbbabaaaababaaabaaaaabbaaaababbbbbabbabbbaabaaabbbbaaaaaabbaababbbaaabbbaabbababaaaababbbabbaababbabaabaaaaaababbabbbabbbaabbababbabbbaabbabbabaababbbbaabbbbbbbbabbaabbabbbbbbbaaabbbbbabaabbbbbbbaaababbaabaabbaaaabaabaabbbbbababbbbbaababbabaaabbbbaabababababbbaabbaabbbbaaaaabababbbbabbbbaaaabaabbbbbbbbababaaabaabaabaabbaaaaaabbbaaaaabaaabbababbabaaaaababaababbbbbabbbaaabaaaaaaaabbaabaabaaabaaabaaaaaababaaababbaabbabaababbaabbbabbabbaabaaaaaabbbababaabbbabaaaaabaabbbababaaabbbbabaabaaaaaabbaabababababaaaaabaabaaabbbabbbbbaabaaaabbaabbbabbbbabaababaaaabaaabaaabbaaabaaabbbbabbbaaaaabbbabbbbababbbaaababbababaaabbabbabbbabbaababbabbbbbaababbbaababbbbabbababbbbaabbabbbbaaaaabbbbabbbaaabababbaabaabbbaaabbbabbbbbabbbabbabbaaaababbbaabaababaaabababbabbbbbbbbbbababbabbaabbaaabaaabbabbbbababababbabaabbaaaabaabaabbbbabbbabaaabaabaaaababaaabaabaabbbbbabaaaabbbbbabbbbaababaaabababaaaaabbbabbabbbaaabaaabbbaaabbaabaaabbaabaaaabbabaabbbaabbbbbabaaababaaabbaaaabaaaabaabbabababbbbbbaaaabbbabbaaaabbabbaaaabaaaaababbabbbabbaabaabbbabbabbbaaabbbbbbaaaaaaabaaababbbbaaaabaabaabbabbbbbbabaabaaabababbababaabaaabbbababbbabaabaabaabbabbbaabbaaaabaaaabbababbabaaabbbbbbababbbbbbababaaabbaaaababbbbaaaabababbbaabbbbabababbbbabbbaaaaaaabbabbbbbaabbbbaaabaabbbbbbbaaaaaaaaaaaabaaabababbaabbabbbbabbabbbbbaabbbabbbaababbaabbbabbbbbbbbbbbababbaaabbababaaabaabbbabbbaabbbaababbbaaabbbaaaaaaaaaaabaaabababaaaabaabbbababbaaabaabbbbbabbababaaaabaabbababaaaabbbaabbbaaabbbbaabbabbababbabaabbbbababaababaabababaaaaabbaabbbbbabbabbbabaabbabbaababbabbaaabaababbaabbbaabbabbbabaaabbabaabaabaaaaaaabaaabaaaaaaabbbbabbabbbbbabaaaabbababaababbabaabaabaabbbbbbabbbaaabaaababaaaabaaabbbabaabbababbabaababbbbbbbbaabbbbabbabbbbbbbababbbaaaaaababaabaaaaabbaabaaabaabbbaabbaababbbbaaabaabaababaaaaaabbbabaabbabbaaaaabbbaabaabaabbababaabbbbbaaabbbaaabaaabababbbbbaaabbbbbaaabaaababaaaaaaabaabbbbabaabbaaababaabbabbbbbbaaababaabaabaabbaabaababaabaaaaabbaabababbaaabbabbaaabbbbaabaabbaaaaabbbbabbaaabbbaaabbababaaabaabbaaabbaabababbaabbbbbaaabaabbbabaabaaabaabababbbbabbbbbbbaabbbabbaabbaabbabbbabbaababbaaabaabbbbbbaabbaabbbabbabaaababbaabbaabbabbabbabbabbbaababaaabaaabaababbababaababaabbbababaaaaaaababbbaaabbbbabbbaabaaabbbbabbabbbbbbaabaaababbabbbbabbbbabbbbbbabaaabbabbabababbbaaabbaabaaabbbbbaabbababbbaabbabaaabaababbababbaabbabbaabbbabaaabaabbbbaabaaaaaaaaaabbbaaabababbabbabaabbbbababaabaaabbaaabbbbaabbbbabaaabaaaaaaaaaabbabababababaabaabbaaaabbbaaaabaabababaabbababaababbbbbabaaabaababbbbbbabbabbbababababbbabaaabaaaaabbbaabbbbabaabbbbbabbaaabbabbaabaabbaabaabbaaabbbbabbabbbbbabaaaabaaaaaabaababaaabbaaabbaaabbbabbbaabaaaabaabbbaaaaaababababababbaabbabbbaabaababbbaaababaaaaaababbababaaaaababbbbbbabaababaabbbaabaaaabbbaabababaaabaabababbbaaabbabaaabaaaaabaabaaaaabbabbbabbaabbaabbabbabbbbbaaaabbabbbbaabaaaabbaabaaaaabaabbababbaaaabababababaaabaaabbaababaabababababaaabaaabbaaaabbbaabaaaaaababababaabbaaaaaabaaabbbbbaaabbababbbabbbbaababbabaababbbababbabbbaabaabaabbaaabababaaabaabbaaabaaaabbbbabbabbabaabaaababbabaaaababbabbaaabababaabbbaabbbaabaabbabaabbabaaababbaaaabbaaabbaaaaabbaaabbbbbaaabbababaaaaaaabaaabababbaabbaabbabaababababbaaabbabaabaabbbabaaabbbaaabbbbbaaabaabaaaababbaaabbaabbabbbaababababaabbaabbabbabbbbbaaaabbbaaaabbabbbbbaaabbbabbbbbbbbababbaaabbbbaaabbbabaababbaabbbbaaaaabaabababbabaaaaaaaaabaababbabaabbbaabbaabbbaaababaabbaabbbbbabaaaabbbaabababbbaaabaabaabaaabbbaabbbbbbbaaaabbbabaababbabbaaaabaaababaaaabaaababbaaababaababbbabbabaaaaaabababbaaabaaaababbaaaaababbbabaaaabbaaabbbbbbaaabbabbbaaaabbbbbbaaaabbaabaaabbbaabbbbbabbbbbabbabbbbaaaaaaabbbaababbababbabbabbbabbbbaaabaaabbbaaaaaaaabababaaabaaabbbbbaabbbaaabbbaaaabaaabaabaabbbbaaababbbbbaaabbbbabbaaaabbbbbabbbaaabbbbbabbbbbaabababbbababbaaaabaaaaababaabaaaabbbbbababbbaaabababaaaabababaaaaaabbbabbbbabaaaaaabaabbaaaaabbabbbbbbaabbbbabbbaaaabbabbaababaabaaaaaabaabbbabaabbaababbabaabaabbbababababbaababaabbbbaaabbabbaabaaaabaaaaaaababaabaabaaaabbaaabbaaabbbbbaababbabbaaabbbabbbbbabbbbbabbbaabaaaaabbbaaaaaaabbbabbabbaabaaaaababbbaaaabaabbbbbbbaababaabbabbbaaababbaaaaaabbabaabbaaabaabababbaabbaababbaababaaabbababbbaababaabbababaaaabaabbababbbaabaaaabbababbabaaababaabbabbaaaaababaabbbbbaaabbbbababababbbbbaabaaabababaababbaaaabaaabbaaaabbbbaabaabaaaabbbaaaabaaaaaabaababbbaabbbbbabaabababbbbbaaabababbbbbaaabbaaaaabbbabbbabbaaaaabaababbaabbaabbbbbbabaabababaaababbabaaabbbbbbbbbabbabbababaaabbaaaabbaaababbababbbaabbaabaaaaabbbaaaabababbaaababbaaababbaaababbbbaaaababbbabbabaabaabaaabaaabababaaabbbaabbbaaabababaabaababbabaabbbababbbbbaabaaaaabbaabababbbabaabbabaaaaaabbaabbabaabbaaaaaabbaaaaabbabbbbbbbbabbabaabaaabbbbabaabababaaabbbbaababbbaaaabaaabbbbaaaaaabbabbbbbbbbbbabbaabbbbabbbbaabaaabbbbaabbabaaabaaabbbbabbbabbaaabbbbbabbbaaabbbbbbbabbbbaaaaabbaaabaaabaabaabbbbbaabbbaaaababbbbbabaabaaabbbbbaaababbaaaabaaabababaabbbaabbaaaabaaabbbaaaabbbbaabbabaabbaabaababbabbbbababbbaaabbababaaabaaaaaabbaaabbaaababbbbbaabaaabaabaabaababaabaaaaabbbbbbabbaababbabaaabbbabbaaaaaabaaabaaabbbaaabaaababbbbbbbaabaaababbaaaaaaababbaaabaaabbabbbbbabbaaaababaaaabaabbabaabbabbabbaababbbabbabbaaaaabbabbaabaaaababaaabbaaabaaabababbbbabbababbbabbbbabbbaaaababbbaabaabaaabbbbabbabaaaaaaaaaaaabaaaaabbbbbbaaaaabaabbabababbbbababaabaabaaababbbbbabbbaaaaabbbbbbbbbbababaaaababaabbbabbbbababaabbbbbbaabbabaabbabbaabababbbabaaaabbbabbbabaababaaabbaabbbbabaabaabbbaaabbbabaaabaaabaaabbaabbbabbabbabbbaaaabbabbababbaaaabbabbbbbbaaabaaaabbabbaaaaaaaababababbbaaabbababbbabababbbabababbaaabaaaabbaabababbabbababbbbbabbbabaabbbbabbbbbbabbabbabaabbaaaaaaabbbbabbaabbaabbabbbbbbabbbbbbbbaaaaaabbabbbabbbbbaababbaabbaabbbbabbbaabbbabaabbbaabaaaabaaabbabababaabbaaaaaababbbaabbbaaabaaaabbbbbabbabababaababbaabababaaabaaaabbbaababbaabaabbaabbbabbabbaaabaabbbabbbbbaabaaabbbbbbbbaaabaabaabaaabaabaabababbbbababaaabaabbbaabaaaaabaaabbaababaaababbabbabababbbababababbababbbbabaababbabbaaabbbbbaabaabababbbbaaabaaaaabaabbbabbbbabbaabbbaaabaaababbbbababbbaaabbaaabbbbabbbabbaaaababbabbabaabaabbbbababbabaaababbaaabaaaabbabbbababbbaaaaaaababbbaaaabaabaabbbaabaababbaaababaaaaabaaabbabbaaabbbabaaabbbaaaaabbbaaababbaaababbabbbbaaabbbbbaabbaaaaaabaabaaaabbabbababbabbabbbaabaaaabaabbaabaabbaaaabaabbbaaabbbbabaabbababbaabababaaabbbbababababbbbbabababbbbbbabbbaaabaaaaabbbaabababaabababbbabbbbaaabbaaabbbaaabbaaaabaaaabbbaaaaabbaabaaaaababbabbbbabbaababaaabaaababaababbbbbbbbaaaabbabbaaabaabbbbbaabbbaabbaaabbbabbaaabaabbbaaabaaaaaabaaaabababaaabbabaaabbaabbaabaaabbaaaaabababababbbbbaaaaaabaaabbaaaabbbbbabaaabaaaaabaabaaaabbbbbbabababaaaababbbbbbabaaabbbabbaaabbbbaaaabbbaababbabbaaabbaabbaaababababaabbabbabbabbaabaaabbabaabaaaabbbbabbaaaaaaabbbabbbaabaaaabbbabbbbbbabbbbabababbbbabbbabbabbbaababbababaabbbababbabbabaaababaabbbaabbabababbaabbaaaaaaaababbaaabbabbbbabbababbbbaababbbbbaababbbaaabababbbbbbbbabaaaaaabababbaaaabaaababbabbabbbababaaaaabaabbbababbabbbbbaabbaabbaaabbaabbababbaaabbbabbbabaabbbbaaababbbabbbbaaabbbbbabbabaaaaabaababbbbbabbababababbbbabaaaaaabbababaabbbbbababbaabaaaabaabbaaaabaabbbbbabbbaaaabbaababbbabaabaababbbabbbbabbbbabaabbabbbbbaaaabaaababaabbaaaaaaaaabbaabbabaaabbbbaababbabaaaaaaaaababbbaabbababbabbbbabbabbabbabaabaaabaaaabbbbabbbbabbabaaabbabbaaaaabaaabaabbabaaabbbabbaaabbaabbbababbabaabbaabababbbababbbbababaaabbaababaabaabaabababababbabaabbaaaaaaabbaabbabbbbbaaaababbaababaabbbababbbabbaaabaababbaaabbbbabbbabaabbbbabaaababbaabbbabbaabbbababbababbbaabaabbabbbabaaaaabaaabbaaabababaaaababbaabbbaaabaaaababbbaaabbbbabaabbabbabaaabaabaaabaabbbbabbbbbaababbaaaabbabbabbbbbbaabbbabbabaaaaababbbbbbbaaaaabbbaaaabaabbbaaabbbaaaaaaabbbbbabbaaaaaaabaaaabaaabbaaaabbabbbbaaabbbbbbabaaaababbbbbbababbaaabbababaabbbaaaaababbbbabbbabaaabaaaabaaaaabaaaabbaaababaabbbbaabbbabababbabbbabbababbaabbbabbbbbbbbbbaabababbbabbbabbaabababbabbabbaabaaabaaabaabbabbbaababbbabbabbabaaabbbaababaaaabaaaabbbabbbbaabbbbbbaabbbbbababbabbbbaabbabbaababaaaaaaaaabbbabaababaabbaabbbabaababaaaaaabbbbaababaaaabbaaabaabbbbaabbaaaabbbabbabbabbabaaaaaababbaaaababbbbbbbbaaabbabbaaabaaabaaabbabbbabaabbbababbabababbaaaabbbbaaaabbabbbbbbbabababbbbbbbaaabbabbbbabbbaaaaaaabaaabaababbaabbaabbbbabbbbaabbaababaaaaabaababaaabbbbababaaabbabaabbaabaaaabaaaaabbababaaaaabbbabaaabaabaaaaabababaaabbbbbaabaaabaaaabbaababbaaaabbaabababbbbbababbababaaabbbbbaabbaaaaabbbabbabbbbabaaabaaababbabbabbbabaabababaababbabbbabaaaabaaabbabbbbbaaaababbabbaabbbbbbbababbbbaabbbbbaaaaabbbbabaaabaabbaaabababaababaabbabbaaaaaaaabaabaabbaababbabaabbbbbabaabbbaaaabbabbabaaabaabbbbbaabbbbbbbbbabbbbbbbabaaaaabbabbaaaaabbabbbbbaaabbabaaaabbabbbbaaabaaaaabbbbbbbbbbbabbaabbbbaaabbbbbababababbbababaaaaaaaabbaabbaaabbbabaabbbaabbabbbaababaababbbbbbbababbaaaaababaabbaabbbbaabbbbbaaabbbbaababbababaaabbbbababbaaaabbabbbaaabbabaaabababbaaaabbbaababaaaaaaabaaabbbaaabbabbbbabbaabbbaaababbbaabaabaabaaaaaababaaaababbbbaabbabbbbbabbabbaaabaaaaababbbaaabaaabbaabaababbabaaabbabbbbaabababbabaabaaababbbaabbaabaabbabbababbabababaabbaababbbababbaaaaaabbbbaaaaaabaaabaabbababbbaaaaaaaaaaaaabaaaaaaabaabababbbabbbbbaababbbabaabbbababbaaabaaabbabababbabbbababaaabbabbbbabaabababbaabbabaabbbaaabaaaabbaaabaaaabbabbabababbabbbbabbaabbabbbabbbabbaaaaaaabbabbabaabbaabbaaabbbbbbbbaababaabbbaaababbbbbbaaaaaaaababaabbbabbbaabbabbbabbbbbabbaabbaaaababbaabbbbbbabaaababaaaababababbbbaaabaaabaaaabbbabaaaaabababbaabbbbbbbababbaabbbbbbbaabaaabababaabbababaaabbaabaaaabaaabbbbaaaaabbabaabbaabaaababbbabbbaababbbbbbabaaabaaaaaababaaabaaaaaabbaabababbbaaabaabaabbaabaababbbabaababbaaabbbaababaababbbbaaabbbbaababbbbbabaaababbaababbbaababbbabbbbaabbbbabbbbabbabaaaabbbbbabbabbabbaababbabababaaaaaaabbabbababaabaaabbbabbbabbbaabbbbbbaabbaabbbbbbbaaababbbbbabbbababbbabbbbaabbbaabaababababbbaaababaaaabbaaabbbbaababbbababaabbaababbaabbaababbbabbabbabababbbabababbaaaababbabaabbbaabaaabbbaaaaaaaaaaababaabaaaaaabbabaaaaabaabaaabaaabbaaabaababbbbaababaaaabababbbbbabaaabbabbbbbbabaababbababbbbabbbbbbbbabaabbbbababababaabbaabaaaabbbabababaabaabaaabbaaabbababbabbabbabbaabbbbabbbbbbaabbbbbbbbaaabbbbbaabbbbabbbbbaabbbbabbaaabababaabaaaaaaabbbbaaababababbbabbababaaaaabbabbbaaabaabbbbabbbbabbaaab
abaababbbbabaabbbabababaabbbabaabbbbbbbbabaababababbbabbaaabbaaabaaaaaaaababbababbbbbbbbbbabbbbabbababbbaabbabaababbbabaaababbabaaabbababaaaababaababbbaabaaababbabbababababababbbabbaaaabbbbababbbaaaabbaababaabbbbbaabaaaabaaababaaabaaabaabaabaaaabbaabaabbaaababaabaabbabbaababaabaabbbaaaababaababbaaaaaaaaabababbbaaaaaabaaaabbaabbbabbabbbaabaabbbbabaaababbabbabbabbaababbbbbbbbbbaabbabaabbbaabbbbaaaabaaabaabaaababaababaaaaabbaaaaaabbbbbababbaaabaaaababababbbaababababbbabbabbbaaaabaabaaaabbbbaabbbbababbbaababaaabbaabbaaabaababaabbbabababbabbababbbbaaabbbababbbabbabaaaababbbbabbaababbaabaabbaabbbaaaaabaabaababaaaaababaaaaabaaaaababbbaabbabbabbabbbabbbbbaaabaaabbabaabbbabaababbbababbaabaaaaaaaabbabbbbaaabbaabbbbaaabbbbabaaaabbbabbaabbaabbaabaababbaaabaaaaaababbbbbabbabaaabbbaabbaaaaaabbbbbabbbbbaababbabbbbabbabbbbaaaababaababbbabbbababababaabbabaaaaabbabaabbabaaabaabaabaaaaabaaaabaaaaabbbbbbaabbabbbabbabaabbaaababbbbaaaababbababbabaaabbabbbbbabbaaabbababaaaabbbababbbbbbabaabbbaaababbbaababababaabbabaaaabaaaaabbabaabbbbababbbbbabaabaabbabbaaabbabbbaaababababaabbaabbbabbbbabbbabbaabbbbbbabbbbbaaaabbaaabaababbbaabaaabbbaabbaababababbabababbbaaabbabbababaababbabaabbabababababbbbbaaabbbbabbbabaabaaabbbaabaabbbabbaababaabbaabaabbabaabbbaaabbbbaababaaabbbababbbaaabaabababaaabbaaaabbaaabababbaaaababbbababaaaaaabbbababbbbabbbbabbbaaaabbabbaaabbaabbaaabbabbaabbabaababaabbabbababaaaabbabbaabbaabaabbabbaaaabaabaaaaaaaabababaaaababbbabbbaaaaaababbababababbababaaaaaaaabaababbbaaabbbaabbbbabaaaabaaababaababbbababbbabbbabbbbbbbabbaabbabbbabbaabbabaaababaaabaaaabaaaaabbbbbaabababbbbabaabaaababbabaaaabaaaaabaabababaabbbababbbaaabbbbbababbbaabbaaabbabababbbbaabbbabbbbaabbaaaabbabbbaaaaabaabbaaababbbaaaaabaabaaabbaaababbbabbbaabaaaabbbaaabbbbaaabbbbbbaaabbaabaaaaabbbbbaaaabbaababaaabbabaaabbbabbbbabaaabbaaabbabbbbbabbbaabbbabababbbabbaaababbabbaabbbbbbbaabaababbbbaabbabbabaaaabbbababbbbaaababababaaaaaaaaaaaaabbbbabbbaaababbbbabbabbbbbabbabbaaaaabbaabababaaabaaabbbbbabaabbaabababbabaabaaaaababbaabbaaabbabaaabbaabbaaabaaaababbbaaabbbabbbbaabbaabaaaababbbbbababbbbbabaaaabaaaabbbaaaabbaabaababababaaaababaabbbbbababaaabaaaaabbaabaaaaaabbbaaabbaaabbbabbbbbaabbbbaaaabbbbbbbabaaababbabaaaaabbbaaaabbaaabbbabababbabbbaabbbbaabaabbbabbabbbbabaaabbaaabbaaaababbaaaaabbbaabaabbaaaaaaaabbbbaaabbbaaaababbbabbaabaabaabbaabbbaaaaabaabbbaabbabbaaabbaabbbaabaaabaaaababbbaaabbaabaababbbabbbbaaababaaaaabaabbbbbbababbaaabbabaaaabbabbaaaabaabbbbaabaabaaabbabbbabababbaaaaaabaaaabbaabbababbababababbabbbaababababbabbabbabababaabaaababbbbababbaabbaaabbbbbbabbaabaabaaaaababbabaabbaaaaaaaaaaababaaabbaabbbabbbaaaaabbbababbbbaababaabaabbbabbaabababbabaabbbbbabaaabbabaaabbbabbaaabaaaabbabababaabbabaabbbababbbbabaabbaaabbaaaaabbbaabababaabaaabbaaaabaaabaabaabbbababababaaaabbbbaaabbbababaaababbbaaababaabaabaaabbbbabaabbbbbbaaaababbbbabaabaaaababbbbabaaababbaaaababbaaaaaababbabbababaabaababbaaabbbaabbbabbbaabbbbaaaaaababbbabbabaabbbbaaabaaaaababaaaabbbaabbbbabbabaabbabbbaababbaababbbbabbaaabaababbaabaabbabbaabbaaaabaabbabababaabbaabaabbbabbbbabbbaabaababababaabbbbbaaabaabaaabaaaaaabaaabbbabaaabbbaabbabaaaaabbbabbaabababbaaaabaabbaabaaabbbaabbbbaabaabbbbbaababbabbbbbabbbbaaabbbbaabbaaaabbbbbabbbabbbbaababbabbbabbabbabbbabbbababbbbbabbbaababbabbbbabbbaababbabbbabaabaabbbabaaaababaaabaaabaabbbbaaaaababaabababababbabaabbaababaabbbaabaabaaabbbababbbabbababbbbbbabbaabbabbbbaaaaaabaabaabbaaabbabaabbbaabbbbaabaaabaaabaabbaabaababbbaabaabaaabbaaaaabaababbabaababababbaaabbbaabbaabbababbaaaaabaaabbaaaabbabaaabbababaabbbabababbbaabbaabbaaabbbabbbbaaaaaabaababbbbbaabbaabbabbabaabaaabaaaaabaabbaaabababbabbbbbaabbabbbababbaababaaaaabbaabbabbbaaababaabbaabbabababbabbbbabababbbaaaaaaabbaaabbaaabbbabbaaaabbbababbababbaabbbaaabbbaabaaaabbaaaaabaaababbaabababbbabbabbaaabbabbbaabaaabaaaaaaababbbbbbbaabaabaaabbbbbbbbaabbabbbababbbaababbbbabbabaabbbababbbbbabababbbababbbababbababbbbbbaaaaaaababbbbabbababbaabbbbababbaaaabbaaaabbbbbaabaabbaaabaababaaabaabbaababbababbbbabaabbabbbaabababbabaabbbaaaaabbabbbbaaaababaabaabaaaaaaababaaabbbbbababbaaababaabaabaabbaabaaaaabaaabbbabaabbabbaababbabaaabaababbbbaababbaabbbabaaaaaaaaaaabbaaabbabbabbbbaaabaaaaaaaabaababaaabaabbabababbaabaaabbaabbbaababbaaaaaababbbaaabaabaaabaaabaabbbaaaababbbbbbaaabbaabbabaaabbabbaabbbabaaaabbbaabbbbabbaabaababbbbaaaaaabbababaaabbabaaaaabbababaabbaabababbabababbababaaabbbaaabbabbbbbbbbbbbaabbbbbabbaabababaaaabbaabbaababbbbaaaaaabbbababbaabbbaaabbabbbbbbbabbbaabaaabbaababababbbbbbababbabbaabbaaaaababbbaababbaaaabbbbbbaabaabbabbaabbaababbbbaaabababaabbbbabaababaaaababaaabbabaaaaaabaaabaaabaababaabbaababbaabbaaabbabbbbaababaabaaaaabbabaaaabbababbaaabbababaabaaaabaaaaababaabaaabaaababaaaababaabbbbabbbababbbbabbaaaabaaaaaaaababbbbbbabbaaaababbabbbbaabbaaaabbabbbaabababbaaaaababaaaaaaaaabaababbaabbaaabbbbbbbaaabaabbbbaaabbaaababaabbbabababbaababaaaabaababbbbabbbabbbbbaabbbabababbbbbaaabbabbabbbaaabbabbbaaababbbaabbaaabaababbbbabbaabbaaaaabbaabbbbabbbaaaabbaaaaaabbababababbaaaabaababbaaabaaaabaaaabaaaaaaabbbbbbbbaabaaaaabbbababaababaaaabbabaaaababaabaabaaaaababaabaabbabbaabbbabbaaabbabbbbbbbabaabababbabbaabbbbabbabbbaaaabbbabaaabbaabbbaabbaabbabbabbbbbabaaababbbbabbaaaabaaaababaaabbababbbaaaabbbbbbabbaabbaabaaaabbbabbbababbabaababbbbbbabbbaabbbaaabaababbabbbaaaaabaaabaababaabbbbabbabaaabaaabaaababbabaaabbabbaaaabbbbbbbaabaaababbaabbbbbbbbbbbaababbbbbbbaaababaaabaabbbbababaabaaabbbbbaabbaabaaababbbaaaabbaabbbbaabbaabbabababbaaaabaabbbbbaaaaaabbababbaaaabbbbbbaaaabaabbaabbaaabaabbaaabaaabababaabbbbbbaaabbbabaabbabababaabbbbaaaabbbaabbabbbaabbbbbbababaabbabaabbaabababbababbbbaabbabaaabbbaaabbbaabaaaaaabaabbaabaaaabaabaabaaabbbaababbbbabaabbbaabaabaaaababaaabaaaabbbbbaaaabbabaaaaabbabbabbbabababaababbaabbaabaaaababababbbabbaaabaaabbbabbbbaabbbababbbaabbbbbbabbbbbbbbbbaaabbbbaababaabaaabababaaabababbbbaaabaaabbbaabaaabbbbabbbbaaabbaaaababbaababaaaababbaababbbaaaabababbaabababaaaaabbabaaabbbbbbbaabaabbabbbbbababbbaaabbbababbbabababababbbabbbbbbbbaabbaabaabbabaabaaabbabababbaabbaaabbaaaaabbaaaaaaaaabababbaabaaaaaaaaabbbabbbaaabbabaaababbbaabaabaababaabaaabaabbabaabbabaabbbaabbabbbbbbabbbbababbaaaaabbbbabaababaaaaabbaabbbaabaabbbbbababaaaaaaabaababbabababababbbaabbaababbaabaaaabbbabbabbaabbbbababbbbbbbaaabbbbaaaababaabaaabaabaabbabbabaabbaabaababbbbbbabbbbabaaaaaaaaaabaaaababaaabbaaaabaaaaabaababaababbbbabbababbbbaaabbbbbabababbababababbbbabbbbaabaabaabbbbbabaaabaaaaaaabbbabaabbaaabbababbabbabaaaabbbabbbbbabaabbaabaabbaaaababbbbabbbbbbbbabbaabaaabbbababbbaabbbbbbbbaabaaaabbaabbbababaabbbbbabbabbabbbbbabbabbaaaabbaababaabaaabbaaaabaabaabbaabababaabbbbabbabaaabbbbababbbaaaaaaabaaaabbbbbbabbaabbbabaabbababbabaabaabbaabaaaabababbabbbababbaaaaaaabbaabbbbbbaabaabaabbabbbbbbaaaabbbbaaaababbbbbaaabbaabaaaaaababbabbaaaabbaaaaabbaabaababaabbbbbbbbaaabbaababbabaabaabbbbbbbaabbbabaaababbaabbbababaaabbabbbaaaabababbaabbabbbabbabbbaaabbbbaaababbabaaabbbababbabbababbbabaabbbaaabbbababbaaabbbabaabbbaaaaababbbabbbabbbabbabbbaaaaaabbaabbbabbbabbaaabaaaaababbbabaabbbbbbbbaaababbabaabbbbabaabbbababbabbbaababaaaabaababbbbabbabbaaabbbbabbbaabababababbaaaabaabbbaabbaabaaaababbbbbbaabbbbaaabbabbabbaaabbbaaaabaaabbabbbbabababaababbaabaaabbababbbabbaaabaabbaaaaabbbaababbaaababababaabbaababaababbbbababbaabababaaabaabbbbbaabaaaaaabbbaaabaaabbbaaaabbaaaababbbabaabaabaaabbbabbbbbabbabababaabbbbbabbbbbabbabaabababbbbaabbaababbbbbaabaaaaabbbbbbbbbbabbbbbbababaabaaaababbbaaaabbabbabbbbaaaabaabbbabaaabbbbabbabbabbbbababbbababbbbaaaaaababbaabbbaabbbaaabbbaabaabbbbababababaaaabbbabbbbaabaabaaaaabaabbbababbaaabbabbbbaabbabbbbbabbabbabbbbbbaaaaabbaaabbbababbbbabaaaaaaaababaababbaabbabbbbbaaabababbbabaaabaababbababbbbabbaaaabaaabaaababbabaababaaaaaaaaabaaaaaabaabbbaabaaabababbbbbabbaababababbabaabbababbbbabaaabbabbbbbbbbaabbabaaabbbbabaabaabaaabaabbbbbaabbababbbbbaaababbabbabbbbaabaababbbabaabbaaabababbbaabbbaabaaabbbaaabbbaabaaabaabbbbbbbbabaaabababaaaaaaababababbababbbaaaaabaabaabbaabbbababbbbbaababbaababaabaaaabbaaaabaaababbbabaabbbbbbbbabbbbbaaaabaaabbabaaabaabbaababbbbabaaaaaabaaaaaaaaaababaabbbbbaaaabbaaabaaaabbababababaababbabaaababbbbbabaaababaaabbbbabaabaaabbbbaaaababbbababaaabbaabbaabababbaaaaaaabbabbbbbaaabbbbbabbababaabbbbabbbaaabaaabbbbbabbabbbabaabaabbbbbbbbbbbabbbabbaaabababbbbabaaabbababaabbbbaaaaaaabbbbaababbaabbaaaaaabaabbaaaaabaaaaabaabaababbbaaababbbbaaabaabbabbaabaaabbaababbbbbaababbbbbbbbabbabbabaabaaabaabaabbbbbaaaabbbbbbaaaaaabaabaaaaabbabaaaabbbbaabbabbaabaaabbaaaabaaabbbbababbbbaaabbbbbabaabbababaabaabbbababbbabbbbbbaaabbaababbabbabaaababaabbbbbabbaaaababaabaaaaabbaabbaaabbabbbaaabbabbaabbabaaabbbaabbabbbbabbbabbababbaabbaabbaaabaabbabbbbaaaaaabaabbababbbbaaaabbbbaabaaababbaaaabababaabbaabbbbbaaabaababbabaaaababbabbaaabbaabbabaabaabbabaabbabaaaaabbaaaabaabbabbbabbaabaabbbabbabaaabaaabaaabaaabbbaabbababbbaabbabaabbbaaababbbaaabbababbbbabbbabaabaaaababbababbbabbbbbababbbbabaaabaaaabbabbaaabaaabbaabbbbaaaaabbbaaaabbabaaababbaabaabaaabbbaabababbabaabaaaabbbaaaabababaaaabababbaaabbaababaabaaaaabbaaababaababaabaaaabbbbaabbaabaababaaaabaaaabbbaaaabbbbaaaababaaaaaaabaaaabbbaaaabbbabbbaaaaaaaabbbaaaabbabbbababaaaaaabbbaabbbaabaaabaabbaaababbbbaabbbbaabbabaababbababaabbaaabbbbbaabaabaabaabbbaaaaabaaaabababababbabaabbbbabbbabaaaabbababbabbabababbbaababbbbabaabbabaababbaababbaaaabaaaaaaabbaaabbaaaabaabbaaabbabbaaabbababaabbbbbabbbabbaaabaabbaababbabaaaaababbbaabaaaabbaabbababbababbbbbabbbbaabbbbabbbaabaabbbbaababaabbbababbabaababbaaabbabaaabbaaabababaaaaababbabbbbbaababbabbbbbaabbababbbbbbaabaabaababbbbbbbbaabbaaaabaabaabbbabbbbbbbabbaaabababbbbaaaababaabbbaabababbabbababaaaabbbabbaababbbbaaaaabbbbbbaaaaaaaaabbbbaababbaabaababbaabaaababbabbbbababbbaababaabbbabbabbbabbbabbabbbbaaabababbaaabbababbbbabbbaaababbbbaabbaaabaaabaabaabbaabaaaababbaaaababbbbbabababaabbaaabbaaabbbababababababbbbbbbabaaabbbaabaabaaabbbbabbaababaaabaaaabbaababaababbabbaababbbaaaaaabbbbbabbbbbbbaababbaabbbabababbabbbbbabbbabababbaabbbabbbaaaaaabbabbbbaabbbbbbaabbaaaaaabbbabbabaaaababababbaababbaaaabbababbaabaababbaabbaababbbabbbbbabababaaabbababbabaabaaabbbbaaaabbbabbbaabababbaaabbbaabbbbbaabababbbbbabababbbaaabbaabbabababbbabaaaaabbbbaababbbbabbbbaabbbbaaaaababbbabaaabaababbbbbababaaabaaababababbbbbbbbbbabaabababbbaabaaababbbabbbabaabaabbababbaabaabbabbbabbbbabaaaabbababaaabbaabababbbbabaabbaabaaaabbabaaabaaaaabbbbbaababaaabbaababbbababaababaaabbbaabbbaababbbaababbabaaabbbaaabaabbabaaabbbabababaaababbabbabbaaabbabbaaabaabbabbaaabaabbbbaaaaababbbababbaabbabaabaabbabbabbbbbaababababbabababbaabbbabaabbababbaaaaababbababbaaabbaababaaaaaaaabababbabbaababababbbbaaabaabbbbabbbabaaabbabbbbbabbababbababaabbbbbabbabbbaaaaabbaabbabaabbbaaabbabbbbabbababbababaaabbabbaabaaababbbababaababbbbaaaabbabaabaabababbabbaababbbbaaaabbababaaaaabbbbbbbababbabbaaaabbbaabbbaabaabbaababbbaaabbaaaaaaabbbbbbabababbaababbabaaabbababaababaabbabbbbabaabbabbbabbaaaaabaaabababbabaababbaaaaaabbbbabaabababbbbaaaaabbaaabaabaabaababbbaabaaaabbaabbaaaabaaabbbababaaaabbbaaababbaabbabababaabaaaaababbbaabbbababbaabbbbaabbbabbaaaababaaaaaaabaaabbabbbbabaabaabababaabbbbbbabbbaabaabaaaaababaabaaabbabbbabababbbbaaabbabaabbbbaabaaaaaabaaaaaaaaababaabbbbaaabbbaabaaabbbbbbabababbaaaaaaabaabbabaaaababaabaaaaaaabbaabaaabbbaabbbbbabababbaababaaaabbabbbaababbbabbabaaaabbbabaaaabaabbbbbaabbaaabaaabbbabbbbbabbbbabbabaaaaaaaaaaaaabbabbaabbbbabbabbabaabbbaaabbbbbabbabaaaaaabababbabababbbabbabbbabbbaabaaaaaabbabaaaabaababbbbbbbbabaabbaabbabbaabaababbaaabaabbbabaaaaabbbaaabaaabaabaabbbabbaabaabbaaabbbbbbbababbbaaaabababbbabbbaabaaaaabaabbabbabbbaaaababababbbabbabbbbbbaaabbbaaabbbabbbaabbbaabaaabbaaaabaabaaabaabbbabbabbbaaabbabbbabbabbaabaaababaabbabbaabbaaaababaabbaabbbabaaabaaabbaaaaaababbbbaabababaabbbababbaaaaabbaabaaababaabaaabbabbbabbbbabaababbbbbaabababbaababbbbaabbababbbaaaaaabbaabaaababbbaaabaabbbbaaababaabaaaaaababbaaaaaabaabbaababbaabaabbbbaabbbbbababaaaabbababaaabaaabaabbbbbabababaabbbbbbbbbbbaaabbabaaaababbbaabaaabaaaabbababababbaabababbabbaababababbabbbaabbbbbabbaabbbbabaaaabbbbaabaaabbabbaaaaaabbbbaabaaaaabbaabaabbabaabbaababbabbbbbbabbaabbbbabbabaaaabaaaaababaaabaaaaababbaabbabaaabbbbbababbabaaabbaaabbbbaababbaabaabbaaabaaabbabaabababbaabaababbbbabbbbabaabaaabbabaabaaabbbbbababbabbbbaaaaaabaababbbababaaaabbabbbbbbabbbababbaabbabbaabbabaaabababaaabbbaaabaabaaaabaaaabbabbbbbbaabaaabbaaaaabababaabaabbaababaababaabababbabbbbaabbbbbbbbaabbbabbaaabbbaaaaabbabbbbbbaabaababbbbbabbbbbaaaaaaabbaabbbaababaaaababaaaaabaaaabbababaababbbbbbaaababaaabbbabaabbabaaaaabaabbabbbbbabbababaaabaabaabaaaabbaabaaababbaabbbabbababbaaaaabababaabbabbabaabbbbbaabbababaaabbaaaaababbbbaaabbaabaababaaaaaaabababaababbaabaabaaaaabbabbbabaaaabaaaabaaabbbababbabbbaaabaaabbabbabaabbaaaaabbbbaaaababbbbabbbbaabaabaabaababbabababbbabbabbbabaaabbaabaabbbaabaabbbbbbbbaabbbbbbabbabababbaaabbbaabbababbbabbbaaabaaabbabbabaaaaaaabbabbbaabbbbbbbbbabbbbaabbbbabbbababbbababaaaabbbabaabababbbbaabbaaaabaababababbbaaaababbbabbabbaaaaabaaabbaabbabbbbbaaaabbabbababbabaaabaaaabbbaabaaabaaabababaabaabbbaaabbabababababaabaabbabbabbaaaabbbabaaaababaaaabaababbabbabbbbbaaaaaaaaabbbbaaaabbabbbbababababbaaaabbbbbbbabaababbabbaaaabaaaabbbabbbabbbaaaaaaabaabbbbababbbbaaabbbaaabbaabbaabaabaabaabbabbabbabbbabbaabababbbbbbbbbbaaabbbbbbbbabbbaaaaaaababaababbaabaaaabbaaaaabbbabbbaababbbabaababbababababbbbabbaabbaabbaabaaababbbaabbaabbabbabbabaababbabbabbbabbaabbbbababaaaabaabbaababaabbabbaabbababbabaaabaabaaaaaabbbaaababbbbaaabaaabbababaaaabbbbbabaabababbbaaababbaababbbaabbbabbababbbbbbbbaaabbbabbababaabaaaaaaabbbababbbbbabbbbbababbabababbaabbaaaaabbbbaabbbbbbbaababbaabbbabbabbaabaaaaabaabbbaabbaabbbbaaabaaabababaaabababbbaabaaaaaaaababbaaaaabaabababbbaabbbbaababbbaaababaabababbaabbaabaaaabbbabbabbbababbabbbbababbbbaabababbabbaaaaaababbaaabaababaabbaababbaaabbbaaaaaaabbabbabbaabbaabaaabbabaabbbabbbabaabbaaaaaaaaabbaaabbbbabaababbbbbabaaaaaaabababbababaaaabbbabbbbbbbaaaaabaabbbaabbaabbaabbbbaabbabaaaaabbbabbaabbaababababbabbbababbbbbbabbbabbbbababaababbaabbbabbaaaaaaababababaaabbabbbaabaabbaaabaabbbabaabaabbabaabaaabaaaabaaaaabaabbaaabaabbbabbbbabbbaabbaabbbbabbbbbaabaabbbbabbababaaaabbbbabababaabaabababaaabbbbbbbabbaabbbabbabaaaaaababbbaabbabbaaaabaaaaaaaabaabbabbbbbaaabbabbbbbbaabbabaabbbbaabbaaabbaaababbaaababaabaabbbbaaababababbbbabababaababbaababababbbabbbabaaaabbbababaaabbbbabbaabbbabababbbaabaabbbabaabbbbaaaaabaaaabaaaaaaabbaaaaabbaaabbbabbabababbbbbbbabaaabbbbbabaababbbbaabbbbbabbbbabababbabbabbbabababbbaabbaabaaaabbaabbbaababbbbbbaaaabbbbaabbbaaaaabbbbababbbbbaabbabbaaaaaabbbaaabbbabbbbbbaaaaababbbaabaaaaabbaaaabaaaabaaabbabaabaaaaabbabbabbbaababbaabaaabbabbbbbbabaaabbbaababaabbbbbabbaabbabbababbbabbbabaaababbaaabbbbabbababbbbbbabbbbbaabbbaabbaabbabbaaabbaabaabbabbaababaabbbaababaaabbaabbaabbaaabaabaaabbabbabaaababaaabaaaaabbbbbbbaabbaabbbaababbaababbbabbaaabaaaaaabbabaabbbbaabaaaaabbaaabaabaaabbabbbabaaabbabbaabbbabaabbbbbbabaaaaabbababaaabaaabbbbaababaabbbaaabbbbbbabbbaabbabbaaaaaaaabbababaaaabbbabbbbbbbbbababbaaaaaabbbbabaaaaabaabababbabbabbabaabbbabbabbbbababaaaababbbabbbbbabaabbbabbbbbabaaabbbababaaabbaaaababaababaabaabbbabbbabaabbbaaabbbbbbabaaaabbbbabbaaabbbaabbbbbaaaabbabbbbabaabbaababaababbaabaabaaaabaaaabaaaabaaaabbabbababbbabbbbaababbbbaabbabbbbbabbbaaaabaabbabbbaabbaaaabababbbbaabababbbbaababbabbaabbbabbabbabaabbaabbbaaababbaabbbabbabaaaababbbbbbbbbbabaababbaaaaaaaaaaabaaaabbabbbabbbabaababbaabbbaabaaaaaabbaaaababbbabbaaabbbaaabbabaabaaaababbbbbbbaaaaaababbaaaaabaaaaababbabaabbbbabababaaabbbbabbbbabbaabaababbbbbaabbabaabbbbbbaababaaaaaaaabbbbbbbaaabaabaabbbaaaabbabbbbbbbaaaabbabbabbbabbbbaaaaaaaababaabaaaabaaaaabbabababaabbbabaababaaaabaabaabaabbaaaaaaaaaaaabaaabbbbbbabaabaabbbbbbababbaaaababbbabbbaaaabbabbbbaabbbbbbbaabaabbabababbbbbbbbaabaabaabbbababbbabaababbabaaabbaaabaaaabaabaabbabababbbbababaaabbbaabbbaaababbbbbabababbbbabaabaaabaaababbabbbbabbababaaababaaabaabbbaabaabbbbabbabaabaababbaaabbbbaaabaaababaabbbaabbbbbbbbabbabbaaabaaabbaaabbbbaabababababbbbbabbabbabaababbbabbaabaabaaaaaaabbabbabbbabbaaaabbabababaababbaaababaaababababbbbababbababbabaaababbbaabaaaababaabaaababbbbbabaabbbaababaabbbbbbababaaaabbbaabbaababbabaaabababbbaabaaabbababbabbaaababbabaabbbaaabaaabaaaaababaabababbaaababababaaaaababababbaaabaabaabaabbaabaabbbbaaaaaabbababbbbaabaaaabaaabbbbbabbaaabaaaaabbaabaaaabbbbbababbaaabbabaaaaababaabaabaaabbbbbbababbbabababaaabaabaaababbaaaaabaabbaabaabbabbaabaaaabaabbbaabbbbbaaaabbaaaababbbbbbbaabbaabbbbbbaababbbbbabaabbaaababbaaabbbaabbabbbbbaaaabaaaaaabababbbababbabaabbbabaababaababaaabbaabbbbbabaabbbbabbbabbbababbbbaaaabaabaaaaababaaaabaabbbbbaababbbbaaaababbaaaabbbbabbbabbbbabbbabaaabaaabbabaaabbbabaabbbaabbbababaaabbbabbaabbaabbaabbbbbbbbbabaabababbbbabbabaabaabbbaabbaabbabaaaabbbabbbbbbbbabbbababaaaabaaaabababbbbaaabbabaabbaababbbaaaaaabbbabababbabaabaaaaaaaaaaaabbabbaabaaaabbaaabbaabbabbbaaaababbabbaaabbababaabaaabbbbbbabbaaaaabbabaaaababaaabbabbabaaaaaababbabaaaababbbbabbbbaaaaabaaababababbaababaaabbaaabbbaaabbbaabbabbbbbbbbbaaaababaaabaaaaaabbaababbbbaaaaababbababbabababaaabbababbabbababaabaabbabbbabababbaaaaaabbaabaabbaababbbbabbbbaaaaababababababbabbbabaaabaaaaababbbaaaaaababbabaabbaabababbbbaabaaababbaabababbbaaabaaaaabababbbabbabbabaaabaababbbaaaabbbaaabaaaabaabbabbbaaabaababbbaaaaabbababaabaabbbbbababbbbabbbaaaaabaaaabbaabbbbbaaabaaaaaaababaabbaababbbbabaabaaaaaabaaababaaaabbbbabaabbbabaabbabaaabbabbbaaaabbbbabbbaaabbbaaaaaababababababbbabbaaababbbaabaaaababaababbbbbbbaabbabbaababbbbbaaaabaababbbabbbaababaabbbbbaaabbabbbbaababbbabaabababbabbaabbaaabaabbbbabbabbabaaabbbaaaabaabaaaababaabbabbbabbbbbaababbaaaabbbabbbbaaabaabababbaabbaaaabaabbbaabbaaabbbbaaabaaaaabbabaabbbbaaabbaabbbbbbaabbaaabaabaabbaababaaabbbaabbabbbbabbaaababbbbbaaaaaaaaabbaabaaaabaabbbbbabbabbbbabbababbaabbaaababbbabaabbabbaabaaabababbbbbbaaabbaaabbbbbabbaabaaaabaabbbaaaaababbbabbbbaababbbaaaaababbaaabaababababbababaabaaaabaaabababaababbaabbaaaabbababbbaababaaaababbabaaaaaaaababaaabaaabaababbabaaabbbaabaaaabbaababaaabababbbbaaabbbbbbaababbbaabbbbbababbabaabbbbbbabbaaaabaaababbbababbbabaabaaabaabbabaabababaabbabbbababbbaaababbabbbbababbbaabaabaaabbababababbabaaabababaaaabaaaaaaababbbababaababaabababbbbabaaabbaabbabaabaababaaabbbaaaababbbabbbbbbbabaaaabbaaaaabaaaabaabbaaabbabbbaabbbabbaaababaaaabaaabbbababaabbaaaaaabaaabbababbaaabaabbabababbbababaaabbbbbaaaabbbbabbbbbbbbbbbbaabbbbbaabaabbababbaaabbbaaaabaaaaaaaaabbaabababaaaabbbabaaabbabbbbabbbbbabaabbaababbbaabaaabaabababbabbbababaaabaababbbaaaaaaababaaabbaababbaaabaaaabbbabbabbbabbbbabbabbbabbbbaaaaaaaabbaaaabbbabababbababbbbbbabbabbbbabbababbaabbbbabaabbbaaabaabbbabaabaabbbbabaaaabbaababaababbbbbbabbbbaaabbaaababbaabbbababaababababaaabbbababaaababbaaabababbabaaaaabbbbaaaaaaabbababbbbaababaabaaaaaaabaababaababababbbaaaababaabaaaabbaaabbbabababbbbaaabbbabbaabbbabababbabaabbbbaababbbabaababaaabbabaabaaababbbbbbbbbbaabaaabbaabababbbbabaabbbabaaabbbabbabbabaabbbabbbabbbaaabbabbaabbbaabbababaaabbaaaaaabaabaabaaaabababbbbabbabbaababababbbaaaaabbabbaabaabbaabbbbaaaaaaababbbbbbabbabbbabababbababbbabbbbaabbbbbbbabbbbaabbabbaabaababaabbabaaabbaabbaaaaababbbaaabbbaabbababbbaaababbaaaaaaaaaaabaaabbbbabababaabbbbaababaaaaaaababbabaabbbababababaabbabbbaabbababbbaabaaaabaaaabbbabbaabababbbbbbabaaaaaaabaabbaabaaabbbabbaaabbabbabaabaaabbbabaabbabbababbbbbaaabbbbabababbbaaababbaabbaabbababbbaabbababbaabbaaaababbaaabbbaaaaabbbbbbbbaaaabbaabaaaaabbaabbbbbbabaabbbabbaababaabaaaaabaaaaabbbabaabbbabbabaaaaabaabaababbbabababbbaaaaaaaaaaaabaaaabbabbaababbaabbaabbbbbbaabbbbbbaaababbabbaaababbbbbbabbbbbabbbbbabbabbabaaaabbabaaabaaaababbbbbabaaabbbaabaaabaababbaaaaabbbabbbaabbbbabbabbaabababbbaababababbababbbbbbaaaaabbaaabababbbaaaababbbabbaabaabaaababbaaaaabbabbbbabbaaabbbbabababaabbbbaabababbbbaababbabbaaaabababbbbaaaababababbababbababaaaabbbbabaabaababaaabaabbbaabababbabbbabbaabbabbbbbabbabbbbabbaabbabbabbababbbaaababaaaaabbbaababaabbababbaabbbaabaaabbaaaabbbabbabbbababaaaaabbbbbbbbbbabaaaaababaabaaaaaabbbabbbbbbbaaabababbaaabbbbaaaaababababaabbbbaaababaabbbabaabbbbbababbababaaabbbbbbabbabababbbaabaabbabaaaaabbaabaaabbabbaaabbbbaaabbabbbbabbaabbaaaabbbaababbabbaababbaabbaabbabbabbbabaabbabababbbbbaababaaababaababbbaaababbbabbbaabbbaaaaaaabbabaabbbabaaaaabaaabababbaabbbbbbaabbabbabbbbabbbbbbbbababbbabbbaaaaaaaaaaababbaaabaaabaababaaaabbbabbababbabbaaababaababbaaabaabbabbabbaaaaaaaababaaababaaaaaababbbbaabbbabbbaababababababaaaaabaaabbbbabaababbbaaaabbabbaaaaabaaaaaababbbbbbaabbaababaaaabaabbaaaabbbbbbbaababbbbbbbbaabbbaabaabbbaababbabbbbbbaaaaababbbbababbbabbbaabaabbaabbbaabbaabbaabaabababaaabbbaaababbabbbaaabbabbaaabbabbaaaabbbbaabbabbaaaababababababbbbaaababbababaaabaaaababbbababbbaababababbbbaabbaaabaababbbbbababaaabbaaabaaabbabababbbbbabbaaabaaabbbbaabaaabaaaabbabaaaaabaabbbaaaaaaaabaaaaaaaaabbbbaabbbabbbabbbabbbaaaabbbabbbbaaabaabbaababbbaaaaaabaababbabbaaaababbbabbbaaabbaababbbbaabaaabbabbabbbbbbaaaabaaabbbaaabaabaabaaaabbabbabbbabbbabbbaabaaabaabbbaaaababbaaaaaabaabbbaabababbaaababaaababbbabbaabbabbabbbbaabbaaabbabbabaaaaabaaaabaaaaaabaaabaaabaabbbaababbbbabbbbaaabbbabaaaabbaababbbabababaaabbbabbbbaabaaabbababbbbabbbaabaaabbababbbaaaaabbaabbabbbaababbaabbaababababbbbbabbabaaabaabbbabbabaabbbabbaaaaababaabbabaabaaaabbaaaaaabbbbaababbaababaababaabbbbabaaabaababbbababbbbabbaaaabbbaaabaabbbabbabbaabbababababaababaabaaabbabbaabaababbabaabaaababbbbbbbaaabbbaaabbbaabbabbbbbaabababababbaaabbbaaabbaaabbbaababbaaabbabbbbbbaaabbbababaabbbbbbbbaabababbaaabbbbaabbabababbbaababbabaababbabbabbbabbbababaaabbbbbbbbaaaaaaabbbabababaaabaabbabbbabbbabaabaabaabaabbbbaabababbabbaababaaaababababbabbbabbaaababbbbabbbaaabbbabbbbbaabbaaabbabbbaaaaaaababaababbaabbabbaaaaabbbaababbbbabababbbbaabbbbaabbaaaaabaababbbaabbabbaabbbbbbbaabbabaaaaaaababbbbbabbabababbabbbabaaaabbbabbabbbbbbbaaaabbbaaabababbbbbaaabaaababababaabbbabababababbbaabbaababababaababaaabbaababaaaabaaaabbbbaaabbaabbababaabbaaaababbabaabbaabbbaabababbaaaaaabbbabbbabbaaaababbbbbbbaaabaababababaaabababababbbbaaaabbaaaabbaaabbabbababaabbaabbbabaabbaabaaaaabbaaaabbaabaabbabbbbbababbaaaaaaaabbbbbabbbbbaabaaabbbabbbbbbbbbabbbbbabbbabbaabbababbbaaaaabbbabaaabaaabbbababaaababbbabaababbabbbaaabbbaabbbbabbbaabbbbabbaaabbaababbbbaaabaabaabaaaaabbbabbbbbabbaaaaaaabababbabbbaaaaaaabbaabbbbbbbbbbaabbaabbababbabaababbbbbabbbbabaababbababbbbabbaaababbbaabbaabbabbbbbbaababaaaaaaababbbbaaaababaabbbbbabbababababbbbabbbbabbaaabbaabaabbbaaababbbbaaaababbbababaabbabbbaaababbaaabbbbaaabbaababaabbabbbbbbabaabaabaaaaabaaaabbabbbbaabbabbaaabbbbbaabababbbbaaabaaaabbababbaabbbbbbbbbbbaaaabbabaaabbbbabaaaabaabbaaababbaabaabbabbbaaabbbbabbbbaaabbbbbbaaabbbbaababaababaaaabbabaabbbababbaaaaabaabbaabaabaabbbbbabbbaaabbbabbbbbbbbaabbbbbbbabbbaababaaaababababbbabbaaabbbabbbabbbbabbbbbbaababbbbaaabbabbbaabaabaaaabaabaaabbbabbabbbaaaaaabaaabbabbaaabbbbbababbbaaabbbbbbbabaaaababaaaaabbaabbaaaabbbbaaaabbbaaabaaabbaabababaaabbaaaaaaaabbababaababaabaaabbbbbbaaabbaabbabbabbabbbababbaaabbaabbbaabbbbbaabbbababbaabbaabaaababaaabaaabaabbbbaaaababaaaaaaaaabbbaaaaabababaabbbbbaaabaaaaababbaabbaaabaaabaabaabbababbaaabbbbaaabbbaabaabaabbaaaaababbaabaabbbbbbbabbbabaabbaabbbabaabbabbabbbabbbbabbabbaaaaaabbbbabaabababaaabbaaaabaabababbabbabbababbabbaabbbabbbaaaabbbababaaaabbaaaabbbbaabaabbabbbabbabbababbaabbabbbabbaabbaaabbabbbbbaabababbbabbbbbabababbbababaabbaaabbbbaaababbbbbbaabbbabbababbbbbbbbaaaaaaaaaababbbabaabbbbabaabababbaaabbbbaababbaabbaabaabaaabbbbbaabaabaababbbbaaaababbaaaabbaabbaabaaaaaaaaabaaaabababababbabbaaabbabbbaababababaaabbabbabbbaabbaabbbbbbabaabbabaaaaabaababbaabaabaaaaaaabbbabbaaabbbbbabaaabbbbaaaaabbbbaabbbaababbbaabbabbabaabaaabaaaaaababaaaaaaabbaabbbaabbbbbaabbababbbaabbabaabbaaaabababbaabbbbaabbbbbaababbbbbabbbabbaabbbbbabbbbbbbaabaaabbaaabaabbbabaaabaaabbababaaabbabaaaaababbbbbaabbaaaabbbbababbbbbbbbbbbabababaabaabbbaaabbbaaabaabbbbbbbababbaabbbaaaaaabbabababbbbbbbbbabaaabbbaabaabaaabababbbbbbaabbaabababbbbbaabbabaabbaaaabbabaabbbbbabbaaaaabbaaaabbabaaabbaaaabaabbbaabbbbbabbaaaaabaaabaabbbbbbabaabbabbbaabbbbababbbbbaaabbaaaaaabbaaababbabbbbbbabababbbabbabbbababbabaabbbbabaaabaaaabbaababbbaabababbbbaabbaaabbbbabbbbaaabbbaabaabbaaaaaabaabbaaababababbaabbbbbbbbaaabbbaaaaaabaabaaabaabbbbbabbabbabbabbaaaaabbbbbabaabbbbababbbbabababbabbbbabababbaaabbbabbbbabbaabbabaabaabbabbaabbbbbbababbaabbabbbbbbbaaabbaabbbbbbaaabbabaabbbbaabababbabbabbaabbabaaabbabaababbbbbaaabbbaaababaaabaaaabaaaababbaaabaabbabbabaaaaabbaaabbabbabbbbaaaaabbbbaaabbaaaaabbbbbbbaaabaabbaabaaabbbbabbaabaababbbaaabbbababaaaabaabaaaabbabbbbaaaababbaaaabaabbbaabbaabbaaaabbbaaababbaabbbaababbbababbaaaaaaabaaaaabbaaaabaabbbaababababaababbbaaaaabbbbaabababbbabaaababbaaaaaaabbabbbabaabbbabbbabbbbabaabbabababbbaabaaababbbbbbbbaaaaaabbabbbaaaaaaabbaaabbaaaabbaabbaaabbbaaabaabababbbaabbabbabbaaaaabbbabbabbbabaaabbbaaaaaababbbbbbbabababbababaaaabbbabbaabababbbaabababaaabbabbabbbaaaaaababaaaabaaababaaababbbbababbbbababbbbaaabaaabbbbaabbaabbbaababaabbbbabbbbaaababbabbbbaaaaaaabaaaaabaaabbabbbbbaaabbabababaaabbbbbbabababaabababbabbbababbabbaabbabbaabaabbbababbbbabaabbabbaabaabbaababaabaabbbbaaaabaababbbbaaaabbaabaabbbababbbbabbbaabbbbbabaaababbbabbaaaaaaaaaaabababaabbaaaabaabaabbabaaabaabababbbbaaaabaaaabbababbbbbaababbbababbabababaabaababababbaaaaaababbbbbbabbaababbaabaaaabbabaababbabbababbbbbaaaaaabbbbbabbbbbabbbaabbbbaababaaaaaaaaababbbabbbbaabbabaaababbabaabbabaabbabaabbabaaaaaaaaaabaababaaaaabbabababaabaabbbaaaababbbabbbbbaaabaabaabbbaabbbbbbbbbbbababbbabbabaababbbbaaaabaababbaaaaababaababbaaaabbbabbabaabaaaaabaaaaaabaaaabaaaababaabaaabababbabaabbbbbaaabaaabbbbbbabaababbbaabbabbbabbbabbbbbabaabaabbaabaabbbaabbbbbbbaababaaaabaabbbbbbbbabaaaabaababbaabbabbaabbbabbabbaabbaababbaabbbaaaabbabbbbaaabbababababaaaaabbbbbabaabaaabbaabaabaabbbababbaabbbbaaabaababaaaaaaabababbbbbbbbbaaabbababaaaaaaabbabaabbbbaaaaababaabbabbbababababbabaabbbbaabaabbbaaaababababbbabaaabbbabababbbabbbbaabaabbabaabababbbbaabababaababbabbbbabbaaabbaabaabbaabababababaabbbbbaabaaabaabbbabbbaaabbababbabbaaaabbbbbbbbbbbaabaaaaaabaabaaababbbababaaabaaaabbabaaaaaababbbbaaabbbbbbbbbabaaaaaabbaabbaaabaaabbabababaabbaaabbaabaabbbabaabbbbbbabaabbbbbbbababbaaabaaaabaaaabbaaaaabbabbbbaabbbaaaabbbaaabaabaaaaabbaabbababaaabaaabbbbbabaababbbaaabbbabbbababababbabaabaaababbaabbababbbababaabbbaabaaabbbbabaaabaaabbbaabbbbabbabababbbabaabbbaaabaabbabbbbabbbaababbabaabbbaabbbaaaaabaababbaaaaabbbbbbbaababbbababbabaabaaabaaaaabababaababababaababaaabababbaababbbaaabaabbbaabbababaaabbabaaaaabbabaaaabaaabbaabbaaaabbaababbbbabbababbbbabbbbaabaabbbaaabbabaababaaababbaababaabbbabaaaaaaabababbaabbbbabbbaaaabbbabbabbbaaaaaaabbaaabbbbaaaaaaaabbababaaaaabaaaaaabbbaabbbaabbaaaaaabbbbabababaaabbbbbabbaababbbbababbabaabaabbaaaaabaaaababbbbbabbaabbabbbababbabaababaaaaaabbbaabaabaabbaaaaaaaaabbabbabbbaabbababbbabbabbbbababbaabaabaabbbabaabbbaabbabaabbaabaaabaaabbbabbbaababaaaaabaaabbbaaaaaaabbbabbaababababbabbbaaabaaabaababbaabbaaababaaaaaaababbabaabbaabbbbbabbabbbbaaabababbaaaababbbbabbbaababbbaabababaaaaaababaaababaaabbbbbbabbbbbbaaabbbaaaabbaabababbaabaabaaaaaabababbbaabababaabaabbbbaababaabaaaabbaaabbababbbaabbabaaaaaabbabbabbbabbaaaaaabaaabaaaabbbbbbabbbbbbabbabaaaaababbaaaababbbabaabbbaaabbabbaaaabaabbabaaabbaabbabbaabaabaabababbbaaaaaaabaaaabbaaaaaabbaabbbbaaabaabbabaaaaabbbaababbaabbbbbbbbbbbaabaaabaaaaaaaaabaababaaabbbbbababaabbaaabaaaabbaaabaabababbaaaaaabaabbbbabbababbaababaabaaabbabbbbbbbbbabbaabaaaaaababbbbaabaaaababbbaaabbaababbbabbaaabbbbabaaaaaaaaabbaaabaabbbabaaabbbbaabbbbbbbabaabaabbababaaaababbaaaaabbabbbbbbaabbaabaaabbbbabbbabaaabbbabbaabaabbabbaaaaaaaaaabaaabbabaabbbbbbabaabbbaaabbbabbbbbaaabaabababaabaabbbbaaababaababbabbbbbabaabaaaabbaaabbbababbbaaaaaaababbabbabbbabbbbaabbababbbbaabababaabaaaabbabaabbababaabababbbbbbabababaaabbabbaabbaaabaaabaabaabaabbbaababbaabaaaabbaaaaabbabbabbbabbaabaaabbbaaaaabbbbaabbaaabaabaababbbbabbbbabbaaabbbaabaaaabbbbbaaaababbbababaaababbbbbaabaaaaaabbabbabbaabaaabaaaabaabaabaabbababaababaabbbaaabaaababbbaaaaababbabbabbabaaaaaabbbbbbaaabbbabaaabbbbaaaabbaaabbbbbbbabbaabbbabbbabaababbbaaaabbaabbabbabbbbaabbababbaabbabaabaaaaaabbabababbbbbabaabbbbbaaaaabbbaabbabbabbbbbbbabbababbababbbabbbaabbbaabbaaabaabaabababbaaabaaabbbababbabbbabbbbbabaaabbaabbaaabbbabaaaabaaaaabaabbaaaabbabbbabbbbaababbbbababaaaaaabaaabaaaaaabbbbbbbbbabbbbaaaabaaaababaaaaabbbbabbbbabbbbbababaabababaabbabaaabaaaaaaaaabbabbabbbbbbaababbaababbbbaabbbbabbabbaabbaaabaabbaaaaabbbaaaaaabbabaabbabbbbababababaaabbbaabbaabbaaaaaabbaabbbabaabbaaababaababaaabbaaaabbaabbaababababaaaaabaaabbaaaabbabbbaabaababaabaabaababababbbbbbabbbaaaabbbbabaabaaaabbaabbabbabaabbaabbabaabbabbbaaabaababbbaababbbaaababbbbbabbbbbbbbabbbbbaabbbabbbbbabaaabaabbbaaaabbaaabbbbbbbbbbbbaababaabbaabbbbabbabbabbaaaababbababaaaabbbaaabaabaababbabbaaaabbaabbbabaabaabaaabbabbbbabababbabbaaabbbaaaaabbaaaabaabbbbbabbbbaabbbbaabababbaababbbbbbaabaabaaabbbaabababbbabaabaaabbbbabbbbaaaabaaaabbbaabbbbababaaaabbabbabaaaaaabbaabbaabaabbaaabbabababaaaabbaaabaaaaababaaaabababababababbbaababaaababbbbbaabbabbbabbaabaaaabbbababbababaaaaaababaaaababaaabaabbababbbaaabbbbbbbaaabbabbbbbbabbaaabbabbbabababaaaabbaaabbaaaabbbbaababaabbabaaaaaaaaaaabbaabbbaabbbabbaabaababbabbaabbbbbbbbbabbababbbbabaaabbabaaaaabbbbababbabababbabbaabbaaabbbaaababbabaaabaaabaaabaaaabababbbaaabaaaaabbbbaabaaaaabaabbbababbbaabaabaaababaabbabbbbbbbbabaabbbbbabaaaaaabbabaabaabaabbbbabaaabbbabaabbbabbaabbbabbaababaabbbbbbaaaaaaababbaaaaabbaaaaaaabbaaababaaababaabababbbbbbabbabbbababaababbaabbabaabbbbabaaababbaababaaaabbaabbbaaaaabaabbbbbbabbbbaabbabbbbaabaaabbbbababaababababbbaabbbbabbaaababaaaaaababbaababbbaaaaaaaaaaabbbabababaaabbbaabbbaabababbbabbbbabbbbababbaaaaaabbabaaabaabbbbababbaaababbbbababbababaabaaaaabaaababbaababbbbbabaabbabbbaabbaaababaababbaaaaaababbbbbaaabbaabaaabbbbaaababbbabbaaaababbabbabaabbbbbbaababaaaaaababababaaaabaaaabbbbbabbaaabbbaaabababaabaabbbababbbaabbbaaaaabbabababbabaaaaaaabbbaababbaabbabaabbbaababaabbbaaaabaabaabbababbababaabaaabbaabaaabaabaaaaabbaaaaababbaaaaaabbaaaaabaabaababaabbaabbbbaababbaabbaaabbabbabaabbabbbaabaabaaaababbbbabbbbababbbbaaaabaaaaabaaabbabababbbbbabababaabababaabaabaaaabbbbbbbbabbbabababbaaabbabbaaaaaabbbaaaaabbababaaaaababbabaaabaaababbbaaaabaaaaaaabababbbaabbbbbaabbaaabbaaaabaabaabaabaabbabbabbabbbaababaabbaaaabaaaaabbbabaabbbbaabbababaabbbbbbbbabbbaabbbabaabababaabbbaababbaaabbbbaabaaaaaaabbabbaaabbbbaabbbbabbbabbbabbaabaaababaababbbbbbbaaaaaabbbbbbabaaabbbabbaaaaabaaaaabbbbaababbbbabbbbbaaabaabbabbaaababaabaaabbbababaababbbaabaaaababbabababaabbaababbaaabaabababbbaabbababaaaababaaabaaaaabbbaababbaabbbabbbbbbbbabbbabbababbabbabbbbabaabbbabbbbaabbaaaabbababbbabbbaabbababbaaabaabaaabbbbbbaabababbbbabbbabbbbbbaaabbbbbbabbbbababbbaabaabbbabbbbbbababababbbbaaababbbabbababbbaaabaabbbbbbaabbaaaaababbaabababbbbabbbaaabbaaaabbbbbbabbaaaabbaaaaabbababbabaabaababaaaaaababbbbbbbabbababbbbaabbbbbbbbaaababbaaabbaababbaabbbaaabbbabbbbbabbbbaabababbaabaaaabbaabaaaabaaaaabbbaaaaaaabbabbabbabbabbaabbaaaabbaaababaabbaaaaabaaaababaaabbabbabbaaaabbababbaaaaabbabaaabaabbbbaaabbbabbbabababbbbbaaaabbabbbbbbaababbbbaaaabbbaaabbbababbbaabbbabbaaaabaabbababaaaabbabbbaaaaabbabbaaaabbabbbbaababbbaaaaaabbbaabbbbbbbbbabaaaabbbbababbaabbaabbabbbabaabaabbaababbbbaaaabaabaabbaabababbbabbbbbbbbbbabaaabbbbbbbabaaabaaababbababbbbaaaaaabbbaaabbaabaabaaabababbaaababbaababbbabbbbabababbbbbaabaabbabbbabaabaabbaabaabaabbaabbbbbaabaaaababbababbaabbbaabbaaaaaabaaabaabaaaabababbbbbbbaabaaabbaabaaaaababbbbbababaababbaabbbabaaabbbabaaaaaaaaabbaaabaaaabababaaaabaabbabaabaabbabbbababbababbabbbabaababbbbaaaaaabbaabbabaabbaaabaaabbabbabaaaabbbaabbbbbbababbbbaabbbababaababababaabababbbaaababaaaaaababbabaabbabaaabaaaabbabbaaaabbbbaaababbbbbaaaaabaabaaaaaababbaabbbbbbbabbbbbbabbaaaabaaabbabaaabbbababaabbaaaababaabababaaaaabbbbaababaabbbbabababbbabbbaaaaaaaabbaabbbbaaaaaaababaabaabaaababbabbababababaabbbbaaababaabaabaababbaabbbaabaaababbbabaaabaaaabbbbbbbabaababaabaaaababbbbabbabbababbbaababbaaaaaabababbbabbaabababbbbaaaabaabababbbbbbabababbaaaaaababaabbabaaaaaababbabbabaaabbaabbabaaaababaaaabababbbbbbbaabbbbbbbbbbabbabbbbaabbaababbbababbababbaabababbababaaaaababbbabbbbbbababaaaaabbabaabaaaabaabbabbabbbbaaabaaaabbbbbbabaabbbabbbbbbabaaaabaaababbbaabbaaabbbaaaabababbbbbbbabbbbababaaaababaabbaabaaabbabbbbaaabaabbaaababaabaabbbbabbbbaaabbabaaaababbbababaaababaaaaaaabbbbabbaaabbabbabaaaababaabababbaaaaaabaababbabbbbbababbaabbabaaaabaabbaaabababbaaaabbabbababbaabbbbaabababaaaababababbabaabaaaabbaababbbbbabaaaabaaaabaaaabbbaaaabbbbabbaaabaabbbbbbaaababbbbbaabaaaaabbaabaaababaaaabaabbaababbaaababbbaaaababbabaaaabaabbbbbbaaababaaaabbabbaaabbabaababbaaaabaaaaaaaaabbbabababbbaaaabaaabaaabbbbaabaaababbbabaaabaababaabbbabbabbabaabaabbabbabbabbaababbbbbabbbabbabaababababaabbbaaaabaaaabababaabbaaaabbbabbaabaaabaaaabbabbaabbababaabbbabaaabbbabbbbbaaaababaabaaaabaabbaabbbaaabaaaaaabbbaabbbbbabaabbbabbbaaaaaaaaaaabbaababaabbababbabbaaaaaaaaaabbaaaaaaaabbaaababaaabbbaabababaaabababbabbabaaabbabbbbaabbbabaaabbaabbabaabbabbbaabaabbabbbaaaababaabbaaabbabababaaaabababaabbbbbabbaabbbbbbbaabaaabbabaabbaabbabbabaabbbaabababbaabbababbaabbbbbbbbaababbbabaabbbbbaaaabbbabaaababababbaaabaababbbabaabbababaabbabbaaabbabbbbabbabbabaaaaabbbabaabbbabbaaababbbababbaaabbababbaabbabbaabbabbaabbbbabbbaabbbabbbaabbabbbababbabaababbbbabaabbbaaaaabbbaaabbbaabaaabaaabaabaaaaababbbaaababbbbbbbababbabaaaababbbbaabbbbaaabbaababbbbababaabbababbbbbbbabaaaaabbabaabbbaaaabbbbbbbbabbababbbbaaababbaabaaaabbaabbbbabaabbabaabbababababaabbbbaabaaabaabbbbaaaabbaaabbbbbbbaaabababaaababbaabbaaaababbaaaaaaabaabbbbababbaaababbbbbaabbabbaaabbaabbbabaababaabbabbbbbbbaaababbabaababbabbaababaaaaaaaabaabbbabababbabaaaaaabbbbbbababaaababaabbababbaababbbabaaaabbbbbababaabbaabbbbbbaababbaababbaabbbbaabbbabbbaaabbbbbbbbbbbbabaabbbbaaabbbaabbbbabababbabaabaabbaaabbbabaaaababbabababbabbbaaababaaababbbbaaaabbaababbbabaabaabaaabbbbbbaaaaabababbbbabbbbbbbaabbaaaabbababbaaabbbbaaabbaaabbaabaabaabaabbabaaaabbabaabbbaabaaabbabbabbbbabbbaaabbbaabbababaabbaaaabbaaaabbaabbbaaaaaaabbbaaaaaaabbbaabaabbbababbbbabbbaabaaaabbaaaaaaabbabaabbbabbbabbbbbbbaababbabaabaabbabaabaabaababbbbbaaababbbabaaabbbabaaabaaaaaabbabaabbababbbbabbbbbaabababbbaababbbbabbaaabaabbaababbaabaababbabbaaaabbaabaabbbbbbbbbabaaaaabbbaaaaaabbbaaaabaaabbbbbabaaabababbaaabaabbabababbaabaabbbbababaaaabbaabbaaabbabbbbababbabbbbaabbaabababbaaabababaabbaababbbbbaaaaabbabaaaaababbabbaabbaaaaaaaabbabbabaabbabbaababaaababbbabbabbaabababaaaaaababbbbbbaabaaaaaabaabaabababaaaababaabbaabbababaaabaaababababababbbaaabaababbbbbaaaaaaabbaaaabbabbbaabaabababbabbbbbabbabaaaaabababaaabaaabaaabaaaaababaaabbabbaaababaabbabbbbbaaaaaabbbaaabbababbabaabbaabbaabbbbaabababbabababaabbaaaabbababbaaababbababaabaaabbbbbbbbaaababaaabbaabbaabbaaababbabbbaabbaaaabaabaaabaabbbbbabaababaaabaabbaaabaaabbaaabbabbbbbaaaaababaabbabaababbbbbaabbabbbbaabbbaabbaabaaababababbbaabbabbaabbaaaababaaaabbaaabbbbbbbaababbbbababbbbabababababaaabaabbbbbaabbabbabbbaababbabbababbabaaabbbbbbbabbbabaabbbbabbbbbbaabbbaababaababbabbaaaababbbbbaaabbbabaaabaaaababaabbbaaabaabaabaababbbaaaaaaaabababbbbaabaabaaabaabaaaabbbaabbbbababaaaaababbaaaababaabbabbbbaaababbbbabbbabaabbbaaaaabbaababbbbaaaaababaaabbbbbaabaaaababbabaaabbaaaaabbabaababaababbabbababbaabbbbbbbabbaaaaaabbabbbbaabbabbbbbbbbbbbaabbbababaaabbbabbbbbbbaaababbaababaabbabbbbbabbbabaaabbbabbbababbabbbaababbbbbbbbabbbbbaabbbabaabbabbaabaaaaaabaaaabaaaabaabbbbaaabbbaababaababbababbbbbaabbbbabaaabbbaaaabaaaababbaababaaaabaabaaaaaabbababbababaaabbbaaabbbabaaabbabbaaababbabbbbbbabaaaabaabbabaababbbabbabababbabbaabbabbaaabaabbbaaaababaaaabaaaabbabaaaabaaababbbbaaabaaaabaaabaabbabbababababbbaaaaababaabbbabbabbabaabbbabbbbababbbbaaaaaaaabbababaaaaaaababbbbabbbabaabbbbabbababaabaababbbabbabbabbaaaaaaaabbaaabaaabaababbababaaabaaabbababaaaabaaabbaabbabbbbaaaabbbaaabbabababbaaababaabaaabaabbbabaaaaababaaabababbaabaabaaaabaababbbaaabbbbbbbaaaaabbbabbbbbaaaabbaaababbaabbabababbbbabbaaababaaaaaababaaabbbabbbbbababababbabbbbbbbbaaabbbaaabaabaabaabaaabaaabbbabbabaaabbaababaaabbbababababaabababbbababbbaaababbabbbaababbabbaabbbaaaaaabbaaabbabababbbbbbbabbbbabbbbabbbbbbbabbaabbaaabbbabbbbbabbabbbbbabbbabababbbababbbbabbbbabbababaabbbabaaaabbabbababbbaaababbbaaabbbbbbbaabaabbbbbababbbaababbaaabaababbbaabbbabbabbbabaabaababaaaaabbbbbbababaaaaaaaabaababbababababbababbbbbaababbaabbbbbbbbbbababbbabaaababaabaababaabbaaababbbababbabaabbbabbaaabaababaabbbababaabaabbbabbbbbbbaaabaababaabbabaaabbbbbaabbbbabbababababbbbbbbbbbabaaabaaaababaabaaaabbabbaabbaabaaaaabbbaabbbbbbbbabbabaaababbaaaaaabbabaabbbaabbaabbbabbaaaaaaabbbaabaabbaaabbbbbaaabbababaabbaabbbaabaaaaababbbbaabaabbaabbabbbbababbbbbbaabaaaabaabbbaaaaabbaabbbbabbbbabbabaabaaabababbaabbbbbbabbababaabaabaaaaaaaaabbabbababaababbabaaabaaababbabbbaaababbabaabaabbbbbabababbbaabbbaaaabaaaabaaabbabababbbaaaabbbbabbaaaaabbbbbbbbabbbaaaababaaabbbaaabaaabababaaabaaaaaaabbabbabbabbbbbbabbbaaababbabbbaaabaababbbaaaaabaabbbbaaabaabbbaababbbbaaabbaaabaabbbbbababbaaaaabaaabbababaaaabbaabaabaaaababbbbabbbabbbabaababaabaabaaaaabbbbaababbababbabbbabbbabaaabaaabbbbabbaabababbabbabbbbbbabaaaaaabaaabbbaaaaabaaababaaabaabbbabababaabbbaabbaaabbbaabaabbabbaaabbaabbbbbaaabbabbbbaaabbbbababaaaabaababbbbabbbabbbaaabbbaaababbaaaaaaabaaababbaabaaaababbbababbaabbababaaabababbbaaabbababbbbbbababababaaaaabbaaaaaaaaaabbaabaaaaaabbaabaaabbabbababaaabbaabaaaababbaabababbaaaaaaaaabaabbbbabaababbabaabaaababbaabaabaabababbbbabaaaabaabbbaaaabbbbbbbaabaaaaabbabbaababaaaabbaabbaaaaaaababaabaaaabaabaabbbabaabbbbbbabbaabbababaaaabbaabbbbbababbabaababbbaaabaaabaaabbbbabbbaaababababbbbaabbaababbaaaaaaaaaaaabbbbbaababbbababbbbbbaabbabbaaababbabbabaabbbaabaaabaabbabaaabbbbbabaaaaaabbaabababbbaabbaabbaaaabbaabbabbbabaabbbbbabbbbbabaababbaabaabbbaabaabaaababababababaabbabbababbbbbbbabbbbbbbbaababbabbabababbbaababbbabbaaababaaabbbbbbaaaaaabbbbabbbaaabbbabaabbbabbababbbbabbaabaaaaaaaabbbbbbbabababbaababbaabaaaaababababbbbbbaaaaababbabaaabbaabbbbaaabababbbbbabaaaaabbaaaabbbbbabbbbaaabaaabbbaaaaaabaabbbbbaabbaababaabaabbbbababaaaabbaabbaaabaabbabaababbbaaaabbabbbbabababaaabbabaabbaaabbbbbbabbabaaabbabbabababaabbbbabaabababababbaaabbaabaaababbbabbabbaaabbabbabbabaabbaaabbabaaababbaaaaaabbbabbbbbabbbabaaabbaababbbbaaaabbbbbaabababbaaaababaaabbabababbaabaabaabbbbaaababababbbbbababbaaababaaaaabaaababaaaabaaabbaaababbbababbabbabbbbbaaabbbbaabaaaababbbbababaabbabbababaaaabababaabababbabbaaabbabbaabbbbbbbbbbaaaaabababbaabbbaaabbbabbaabbbbbaaabbababbaabbbbaaaabbbbaaabbbabbabbaaabaaabaaabbbaababbbaabaabbbaaaabbbbbbaaaabbbabbbbbbabbbaabaaaaaabbbbbaaabababababaaabbaaabaaabbbaabbaaaaaabbabababaaaaabbbbaabbbbbbabbaabbaaabaabbaaabaaabbaaaabaabbbabaabbabaaaabbbaabbabbaaaaaaaaaaaababaaaaabaabbabbbbababbbbbababbbabbababbabbaababbaababbabaabbabbaabababbabbbbababbaabbabaabaaaaaabbabbaaabababbabbabaaaaaabbabbaabbaaabbababaababbbababaaaaaaaabaabaabbaaabaabaabbabbaaabbbbaabbabaabbabbaabbbabaaaaabaaaababbabbaaabbbbaabbbababbabaaaaaaaaaababbbabaababbaababaaabaabbabbbbaaaaaabbaaaabababaaabbbabbaaaabbaaaababbabababbababbbaaaaabaaabbaabbbbbbbabbabbaaaabbabaabaaabbbbbbbbabbabbabbaaabbaaaaabaaaaaaababaabaaabbabababababaaababbaababaaababaababbaabaaabbbbaaabababaabababaaaabaabbaabaaabbbababbaaaabbaabbbabaaaababbabaaaaaababbabbabbababbbbbaabaaabaaabaaaababaababbbabbbbbbbaabaaaaaababbaababaabbaaabbaabbabbaaaaabbabaaabaaabbbabbbbbaaabaaabbbbabbabbaaaaabaabbababbaaaaaababbbbbbbbabaaaaaabbabababbaababbababaabaababbbaaabbabaaabababbbbbbbbabbbbbbaababbbbabbabbbbbabbbbaabaababbbbaabbaabbbaabbabbbababbaaabbaabaabbbbababbababbbbababaaaababbbaaaababbabbbbabbaaaabaababbabbbbaabbbaaaababaaaaabbbabaababbabbaabbababaaababaababbabaabbbababaabbbbababbaaaaaaabbaaaaaaababaaaaaabbaabaabbaaabbaaabbbababbbbaababaaabbaabbabbbbbbbaabbbbaabbabaaaabbaaaabbbaaabbabaaababababababbbbaaabbabbabbaaaabaabaababaabbbbbabaabaaaaabbbbbabbaabbaaabaaaabbbababbabaaaaaabaababbabbaaaabbaaabbbaabaaabaabbabbbbbaabababaaabaaabbbabaaabaaabababababbbbbaaaabaaaaaabaabaabbababbababaabaaaaababbbaaaaaabaaabbaabbabbabbbabbaaabaaabbababbbabbbababbbbbbbbbabbbababbbaaabbbbbaaaaabbbbaaaaaaabbabbabbaababbabaaabaababaaabaabbaababaaaaabaabababaabbbabababbabbbbbaaabbbbabababababaaaaaabbbbbabaabaaaaabababbbbababaabaabaabbbabaaabbabbbaabbbbabaaabbaaaaabbabbbbbbbabaabaaabaabbbabbaabbbbabbbaabbabbabbbabaabbbbabbbabbbbabaababbbabbbaaabbaaabaabbbbabbbabbbbababbbbaaaaababaabaabbaaabaaababbbbaabaabbababbabbababbaaababbaababbbbaababbabaaaabaabbaaaaabababaabababbbabbaabaaaaababbaaababbbaabbbaaabaaaaabbabaabaaabbaabaaabbaaaaababbaaabbbaaaabbbbaabbaaaaaaabaaabbbaaaabababaababbbbbbaabbabbbbbbbaababbbbbabaababaaaaabbbbbabaabbbaabbaaabaabbbabaabaabbaaaaaababbababaabbababbabbbbbbbbababbaabaaabbababbabbaaabbbbbabbaabbaaabababbbaabbbbaabbababaaaaaaaaaabbbabbabbaaabbaababaabbbaaababbbaabbbbbabaabaababaababbbabababbabbbabaaabaaabbbbbaaababbbbabbaaaaaaabbbaabbabababababbabbaaabaabbbaabaabbabaabbaaaaaababbbaaaabababbabbababbbbbaaabbaabbbbbbbbbabbbbbbbbabbaabbbbbaaaaaabaaaaaabbbbabaaabaabaabaabbbaabaaababaaabbabbbbbabbaaaabbabababababbaabbbbabbababbababbabaabaabbbbbbbbbaaabaaaabbbababababbaaaaabbaaabbbbbaabbbabbaabaaaaaabbabaaaabaaababaabbbbbabbbbbbabbbbbaaabaaabbbabababababbbaaabbbabbbbbbbababbbbbaaaaabbbaabaaaaaaaaababbbabbbbbbbbabbababbbbabaaaaabbbababaababbbaabbbbaaabbabbbbaabbbaabbabbbbbabbbaaabbbbbbbaababbbbabbbbabababbabbbbabaabaaabbbbaaaaaaabbababababaabaabaaabbbaaabbbbbaaabaabbbabbaaaaaaabbbbbabaabaaaabbabaaabbbbabbaabbaabbbbbabbbbabaaaabbbbaabbbbbbbbabbbabbbabababaabbababbabbaaabbbbbabbbaaaaaababbaaaabbbabaaabbbababbabbaabababbbbaaabbbaabababbaabbbbbbabaaababbabbbaabbabaabbabbbbbbbbaabbabaaabababbbaabbababbbaaaaabbaabbababbbabbbbbabbaabbbaaabaaaaababbabbbbbabbbbababbabaabbabbbabababaaaabbbbabbaaabbabaabaabaaabababaaabbbbaaababaaabbbbaabbbbaabbabaabbabbbbabbaaaaaaaabbbbbabbababaaabbaabbbabbbababbababbaababbababbababaabbababbbbaaaaabbbbabbbababbabaabaabaaababaababbbaabaaabaabaaabbabaaababbbabaabaaabbababaabbabbbbbbbbababaabaababaaabaaaaaabbaaaabbabbaabaababbaabbabaaabbbbaababbaaaabbbbaabbabbaabbbbbababaabbabbaaabbaabaababbbbbbabbaaaababaabaabaaabbbabbabaaaabababbbabbaabbbabbbbabaabababbabaaaaaaaababbaaaaaabaababaabbabaaababaaabaabbbbbbbbbabbbaaaaaabbbaabbabbabbbbbaaabbabbbaabababaaabaaaabaaababaaababbaaababbabababbbabbaaaaabaabaaabbabbbbbbbbbaaabababbbabaabbbaababbaabaabbaabbababbaabbabaababaaabbaaabbabbbbbaabbbbaabbbbbbbbabbbbaabbaaaaaabaabbbbbbabbabbbbaababbabababbbaabaababbbbaabaaabbbbbbbbaaabaaaaabbbbbaaabaabbbabbababbabaaabbaababbabbbabaaababaaabababbbabaabaaaababbbaabaabbbbbbaaaaabbbbababbabbbbbbbbaaabbaabbaabbaababbbaaaabababaaabbabaabababbaabaaabbbbaaaababbbabababbbbabbbaaaaaabaababaaabbbabbabaabababbbbbbbbbbbaabbabaababababbbbababababaaaabaaaabbaabbaaabbbaaaaaaaababbaabaabaaaaabbaaaabbabbababbbbbaababababababbbaaaabbbbbbbbaaabbbbaaaaabbabbaabaaabbbababbabbbabaaababbabaaababaaaabbbababbbbabaabbbaaababbbbababbbaaaabaabbbbabbaabaaabaabbbbbbabbaaababbaaabaababbabbaaabaaaabababababbbabababbbbabbbabaabbbbbbaababbaababaaaabababaaaaaaabbaaaabbbbabaaababbaabbabbbaaabaaabbbaaaabbaabbabbbbabbaabaabaaaaabbbbbbaaaababbaababbabbbbababbbaaabaabaaaababbbbbbaabbbabbbaabbaaabaababaabbaaabaabababbbbaaaabbbabaaaabaabbabbaaababbabaaaabaaaaaaaaaabbabbabbbaaabaaabaaaababaabaaabaaabbabababbabaabaaaabbabbababbbabbaaabbbbbbabbbababbabbbabbabababbbbbabbababbabaabbaabbaaabbbbabbabbabbabababaaabaabbbbbabbbbbbabbabbaaaaaaaaaaaabababbababbbbaabbababbabaaaaaababaaabbabbbbabaaabaaabbabaaabaabbbaabbbababbaaababbaabababbabbaaaabaaaabbbaabbbaaaabbbbbaabbaaabbaabbababbbabaababbabbaaaaaabaabbabababaabbaababbaabbaabbabbbababbbaabbabababbbabbaaababaabbababbbbaababbbbaababaaaabbbaaaabbbbbaaababaabaabaaabaaabaaaaabaaaabaabaabaaabaabbbbabbbaababaaababbbbbbaaaaaaabbaababaaaabbbbababaaaabaabbbaaabbabbaaabbbaaaaabbbaabbaabbaabaababbbababaaabbbabbabbbbbbabbababbaaaababaaabbaaabbbbaaaabbbbbbbaababbaababbbbbbbbbababbbabbaabbabbabbbabbaaabbbbbaabaabbabbbabaabaaaaaaabbbbabaaaabbbabaaaaababbaabbbbababaabaaababaaabbbabbabbabababbbbaaaaabbbaaaaaabbbabaababbbbbbaabababaaabbabbbaababbaaaaababbabbbbbabaabaaabbbbabbbbaabaababbbbabbbaaaaabaabbbbaaabaabbbbbbabbabababaabbbaabaaaaaabbbbababaaabbbaabaaaababbababbbabaaaabaaabbabaabaaabbbbaaabaababababbaababaabaaaabaaabababaaababbbbababbbabaaabbbabaabbaabaabbbaaabaabbabaaababababaabaaaaaabbbaabaaaabbabbaaaaaabaabbaabbbbbbaaabbaabbbbabbbabbbaaabbbaaabbabaaaabababbaabbabaabbbabbabaabababbabbabbaaabbbaaabbbbbbbabbabbbababbbaaaaaabbbaaaabaabaababbaabbaabbbabaaaaabaabbabbabbabababaabbaaabbbabbbbabaabaaabbbbababbbaaabababbbaaaaaabaabaabaabbaabaabbabbabababbbaababbaaaaabbbbabbbabbbabbbbaabbaabbbbbaaaabbaabababaaabbabababbaaababaabbabbbabbabababbbaabbbbbabbbbabbabababababababbabbbbbbbabbababbaaaaabaababbbbbabbbbbaabbbbbbbbbabaabbbaaaababbbbaaababbaaabbbbbbababbbbbbbbabbbaaaabaaababbbbbababaaabbbbaaababaabaabbabaabbabbabbbaaaabbbababbbababbababbbbabaaaaaababaaaaaabaabaabbabababbabaaaaaaaabaabbbbaaaaaaaabbababaabbbbababaabbbbbabaababbbbbababbaababaaaabababbababbbaaaaabbaaaaabbbabbbbbabbabaabaaabaabaaaabbbaaababbaaaabaabbbaabaaaaabbbabbabbbaaabaaaaabbbbababbbbababaabbbabaabbbbabaaaaababababbaababbabababbbabbabbabbaaababbaaaaabaaabbabbbabaababbabbabbabaaaabbbabbbaaababababbabbbabbbababaaaabbaabababababbbbaababbbbababababaabbbbbaaaaaaaabbabaabaabbabbbbaaaaabbbbbaababaaaaababbbbabaaaaaaababbabbaabaababaabbaabbabaaaabbbaaabaabbaabaaabaabaaaaababbbabababbabbababaaaaaabaaaaabaabaabbabbaabbabbbbaabbaabbbbabbaabaabbbbaabbbbbbaabbbabaabbababbaaabaabbabbbaaabbbbababbabbabbbaaaaaaaaaaaabbabbbbbaaaabbaabaabbbbabbabbaabaaaabababaababbabbaaababbabbbabaabbbbbbbabaaabbbaababbbbbaaabaabbaabbbbaaaaaaaabbababbaabaaaababbaaaaabbabbabaaaabbbbababbbabaabbaaaabbaabbababbabbaabaabbaaabbbabbaabbbbabbabaaaabbabbbbbbbbbabbabbaabaababbbabaababbabbbbbbabbbbabaaaaaabbaabbaabbaaaabbbaabbbbabbbabaaababbaabbabaaabbababbbbbababbbbbbbaaaababaabbbbaaababaabbbabbbbbaabbaaaaaabbbbaaabbaaababbbabbbaaabbbababaabaaaabbaaaabbababaaabaaabbbababaabbabbbbbbabbabbbbaabaabbabbbababababbabaababbabbabbbaaabbabbabbbabaaaaabbaaabbbbbaabbbbabbbaaababaaabaabaababbaaabbbaaaaaaababbabbaabaabababbabbaabbbababbaabbababbababbabbaabbbbaabaaabaaaaababbbabbbabbaabbabaababbbaaabbaaabbaaabaaaabababaababbbaabbabbbaabababbaaababbabaaabaaaaabbbaababbaabbabbabbababaaaaababaabbbaaababaabaaaabbaaaaaabaababaabbbaaabbabbabbaababbbbbabbbbaabbaaabababbbabbabbbabaabbabbbaababbbbbabbbabaababbbbabaabbbbbbaabbbbbaabbbaabbabbaaaababbbaaabaaabaabaaaabbbaabaabbabaaaaaaabbababbbbbabbabaabaababbbaabbbbbbbbbbbbaabbaaabbbaaabaabbbbbbbabaabaabbbabaabbbbbbabaaaabaabbbbbabababbbbababbbbbabaabbbaaaababaaaababbbbaaaaaaaababbbaabbaabbbbabaaaabaaaaaababaababbabababbbbbabbaababbabbabbbaabbbaaaaababbaaaabbaabababaaabababaabbbabbabbbabababbbbbbaaaabbabbbbaabbabbbabbbbabaaaabaabaabbbaabaaaaaababbbaaaaabbbabababababaaaababababbaaabbabbaabbbbabaabbbbbabbabaaaabbaababbabaaaaabbaabbbabbbaaaaabbbaaaabaababbabbababaaaababaabaaaabababbaababaabbbbabaaabbbabaaaababbbbabaaabaabbbaaabbaaabbbbbbaababaabbaaaaaaaaabaaababbabbaababaaaababbaababaaabbbababaaabbabaabaaaabbbabbbaaabaaaaababaaaaabbbbbaaaaabbaabbbbaaaababbabaaaabbaabababbababbbaaabbaabbbaaaaaaababbbbabaabbbabbbabaaabaabbaaaaabaaaabbbbabbbabaabaaabaaababaabbbbbabbbbabaabbabbaabbbbabbbaabbaaabbbbaaaabbabbbabababaabbabababbababbabbbbbbbbabbaaabaaaababbababbbbbaaaabaabbabbbbabaaaababbaaabaabbbbaabbaaababbbaaaaaaabbaaabbbabbabababbabbaaaabbabababbbbbbabbbaaabbaaababbbaabababbababbbbabbababbbbabbbaaabbaaabababbbbbbbaabaabbbbabbababbaabaaaaabbaaaabbaabbaaabaabbbabbabbbbabababaababaabbbaabbaabbaababbaaaaaababbaabbbabaaaaaaaaaabaaaaabbabaabbababaaaabbababbaaabbaabaabbaabaaaaaabbbbbabababaabbbaaabbabaaababbaaaaaabbbbbaaababbbaabbababbbaabaabbababbbbbabaabaaababaabbaaabbaaaaabbaababaabaababababaaaaaaabababbbbaaaabbbbbaabbbaaaaabbabaaabbaababbbaabaaaabaabaaaabbaabbaabababbabbbaaababaabaaaaaaaaaaaaaababbaababbaabababababbaaabbbbbbbbbbbbbbaabbaabbaaaaabaaaabaabbbabaaaababbbabbaabbbbbabbabaabbbbbabbaabababaaababbabbbbbbaaababbbabaabaaababababbaabbaaaabbaababbbaaaaaaabbbbbbaabbaababbabbaaabbaabbbbabbaaabaabbbbbaaaaaaaabaaaabbaaabbbbabbaaaaaabbabbaabbaaabaabbbabaabbabbbabbbbabbbaabbbaaaaabbaaabbbabababaabbbaabbbbaaaabaaabaaabbbaaabbbaabaabbaabbababaabbaababababbaabbabababaabaaaaabbabbbbabbbaaaabbbbaabbbbbaaabaababaabbbbabaabaabbababaabbaabbaababbabbbababbababaaabbbaababbbabbabbababbaabababbaaaaaabbaabbabaababbbbbbbbbaabbbaaabbbbbbabbabbbbabaabbbaababbbbaabaabaaabbbaababbbbaaabababbaabbaaaaaaaabaabbaabbaababaaaabbbbbaaaaabbabaaabababbabbbabbbabbbaabbbaaababaabaabbbabbbbaaaaabababaaaaaaaabaaaaabbabababbbababababbbaabbbbabbababbaaaabbaabbababbaaaaaababaabaaabaaaaaaabbbbbbbbbbaaabaaabaabbabbabbbbbabaaaababbabbaabaabaaaabaabababbabaaaabbbaabbaabaabbbbaabbababaababaabbaabbbaaaabbbaaabababbabababaabaaababaababaabbabbabbbbbaabbbabaababbaaabbbabaaaababbaaaabaabbaabbbababaaaababbbbbbaabbabbaaaabbbaababaabaababbbababababbaaaaabbbaaaabaabbbabbbaaaabbabbaabbbbbaaaabaaaabbabbaaaaaababaabaaaaaaabbbaaaababbbaaaaaabaaaabbabbabbbbaaaaabaaabaabaabbbabaaaabbbbaaaabbabaababaaabababbbbabbbbbbabaaabbaaabbaabbbabbaaabbbbabbbaaaaaabababbbbaaaaabbbaabbaaabbaaaabaaababbababaabaabaaaaabbbaababaaabababbabbbbbbabaabaaaabaabaaaabbbababbabbaabaabbbaabbabbbbbabaababaaababbbbaababababbbbaabbbababaabaabbabaaaaaaaaaabbbaabbabbaabbaaaaabbbaaabbababaaaaabbabbbaaaabbaaabaababbabababaabbaaabbbbabbabbabaaaaaabaabaabbbbababbaabababbbbaaaaabbaaaaabaaabbbabbababbaaabbabbaaabbbaaabbbabaabbaaabbbabbabbbbbbaababbaabbbaabbabbbbaaababbaabaabaabbaabaabaabbabaaabbaabbbbbbbabbababbbaabbbbbbbaabbbaabbbbbbbaaaaabaaaaaaabbaaaabbaabaaabbbaabaaabbbbaabaabbaabbabbabbbbbbababbaaaaaaabbaaabaabbbaabaaaabbaababaaabaababaaabbaaabbbaabababaababaaabaabbbabaaaabbabaabababaabbaabbbaaaaabbbbbababbbabbaabbaabaabbbbaaabbaabaabbabaabbaaabbabaababbabbababbaaabbababbbaaabbabbbaababbaabbabaabbabaabbbaabbababbaaaaaaaabbababaabaaabbbabbbbbbaaaaabbabaabaabbbabbbaaabaaaabbabbaaabbbbbababababbaaaaabbbaabbaabaabababbbaaaaaababababaaaaabbbbabababbbabaabaabbabbabbbbbababbbbbbbabaabbbabaaabbaabbbbabbabaaababababbbbaaaabaababbaabbabbabbabbbbaaababbaaaabbbbbabbabbabaaabaabbabaababbabaababbaabbbababaaababbbbbbaaaabaaabbaabbabbaaaabaabbabaaaaababbbbbbbbbbbaaabababbabbabbbbabbaaababaabbbabaabbbbaaababaabbaabaabaabaabbabaaaaabaabbaaabbaaaaabbbabbbabaabbababaaaabbabbbbaaaabbbbbbabbabababbabaaabbbabbaaaaabbbaaabbabbbbabaabababaaaabbbbabbbbbbabaaabaaaaabaabaaabbaabbbaabaababbbaabbbbbbabbababaaaabaaabbaaabbbbbbabbaaaababaaababaabbbabbbaababaababbbaabbababaabbaabbabbaababbaabaaaaabababbabbbbbababbbbabbabababbbbbababaababaaababaaabaaaaaaababababbbbbbabbbaaabbaabbbaaaabbabababbababbbabbaaabaababaaaaabbbbababaaabbbabbaaababbbbbbababbabaaaabaaaabbabbabbbabbbabbbbbbbbbbbabaababbaaabaababaabbbbbbbbaababaabaaabaabbbbaaaabbbabaabbababaaaaaabaaabbbaaabaaabbabbbbbabbbbaaabaababaaaabbbbbbbaaababbaabbaabbbbbabbababbabaabbaaabaaaaaabaababaaaabbaaaaababaabaabbbbaaabbbbbababaabbaaaaaaaabaaababbaaaaaabbaaaabbabbbabaabbbaaaaaabbaaabaaaaaababbaaabbbababababaababbabbbbaaaaaabbbbaabbbabaaaabbbabbaabababbabbaabbbabbbaaaaababaaabbaabbaaabbbbaaabbabaaaababbbaabbbaabbaabbbabaaaababbbbbabbababbaaabbabbbaabbbabbbbaabbbbbbbabaaababbbbaaababbbbabaaaababbaaabbbbaabaaabaabbbaaaababaabaabbabbbbbabaaabbbbbbababbbbbabaaaaaababbbaababbaabbbaaaabbaaaabbabbbaabbababbabbaaabaaabbbaaaabaabaabbaabbaaaabbabbaaabbbaaaaaaababaabbaababaaaababaabaaabbabaabbaabbaabbaababbaaaabbabaabbaabbbaaaaabaaaababaaabbaababbabaabbbbbbbabbbbbbbbabaaaabbaabbbbbbabaaaabaaabbbaabaababbabaaabbabbabbbbbaaabaaabaaabbaabaababaabbaaababaabbbabaaabaababbbbaababbababababababaaaabaaabaabbaaaabaaabaaaaabababaabaaaabbbbababaaaaaabaaaabababababaaaaabbbbbbaaaabbabaabaaabaabbbabaabbabbbaaabaaaaaaabaabaabaabbabaabbabbababbbaabbbaabaaababaabaaaabbbbaabaabaaaaaabbababbabbabbaaabbbbaabbbbabbaabaaaaababbaaabaaabaaaaaabaabaaabbbabaaaabbbabbbaabbbabbabaaaabbbaabbbabbabbaaababbaabaaababbbaaaaabbbaaaabbaaaabbaababbabbbabbabbbbbbbbaaaaababaabaaaabbaaababbaabbbbbbabbaabaaabaaaaaabaabbaaabaababaabbbaaabaaabaabbbbbbbabbabaabbabaabaaabaaabbabbaabaabababbabbaabbabbbaababbbabaabaabbbaababbaaaaababbabaaabbaaaabababbbaaaabbaabaabbbaabbbbabaabbabaaabbbabaaaaaabaabaaabbaabababaabbbabaabbaababbbbaaaaabbaaabaababbaaabaabbbbaaaabaabbbabbaabbaabababbabbbbbbaaabbbabbbbabaabbaaaaababbabababbabbabbbaaabbabbaabbababaabababbaaaabbbabbbabbbbaabbaabbababaabaaaababbbbbbaaaabbabbbbbbbbbbbaabbbabbbbaaaaabaabbababbabbabaaabaaabbbbbbbaaaabaabbbbbbabaaababbabaabbbabbbbbbaaabaaabbbbbabbaababbaabababaaababaaaaabaabbaabaaabababbbbbaaabbaaabababaabbabababbaababaaaabbabbababbabaabaabbbbbaabaabbbbabababbabbbababbabbaabaaaababbbababaabbbaaabaaaaaabaabaaabbbbbbbaabbbabbbbabbabaababaabbbabaabbbaaabbaabaabababbabababbbabaaaababaaababbabbaaabaaabbaaabaabaabbaaababaaabbabaabbabbbabbaabbaaabbabbbbbaabbaabababaaabaabaabbbbabbaabbbbaabaabbbaaababaaaaaabbaabaaaabbabbaabababbbbbaaabbbbbbbbbabbabaabbbbabbbbbbaaabbabaabaaababbaababbabbbabababababbbaabbababbbbaabbaaabbaaabbbbbaaabaabababbbbabaabaabbbaabaaaabababbaaaabaaababbabaababababbabababaabbabbbababbabbaabbaaababaaaaaabbbbabbabbbaabaaababbaaabbbbaaabbabaabaabbabbbaaaabababbaaabbbbbbbabaaababbbabbaabbabbbaababbaabbbbbabababbabbabbbaaaaabbbbababbbaaaaabaaaaababbbabaabaabaabaaaababbaabbbaabbbabaaabbaaaaabbabaaaaaaaabbbbbaabbaabababbabbbbaaabbbabaaabaabbabbbbbaabbabaaabaabaaababbabababbbbbbbbbabaabbbabaaaaabbaabbbbbbbababaaaabbbbaaaabbbbbabbaaaabbbabbabbababbbaaabbaaababaaaaaaaababbbbabbbbbaaabaababbabbbbbababababbbabbbabbbbbbbabbaaaabbaaabababaabbbababaaaaababababbbbbbaaabbaababbabbaabaaaabaabbaabbbbabbbaaaaaaababbaababbaaaabbabaabbaaaabbbaaaaabbbaaaabbabaaababaaababbbbbbbbbaaaaaaaabbabbbbbbabbaabbaabbbbbbabbbaabbabbbaabbbabaabbaabbaaabbbababbbaabbaabbbbabbbabbbbbbaabbabbaaaabbbabaabbabbabbbbbbbaababbbabbabaaaaabbabbabbbaabbaaabbaabbbbbababbabababaabbaababaabbaabaaabbaaababbbaabbabaababababbbbbabbbbaaaababbabbbbbaabaaaabbbabbaaabbaaababbbaabaaabbbbbabbbbabbabbbabbbbbabbbbbbaabbbabaabaababaaabaabababaaaaababaababababaabbbababbaabaaabababbaababababaabbbbbbabbabbbaaabbbabaabbbabaabbabaaabbbbaabbbbbaaaababaaabbaabaaabaaabaaaaaaabaaaabbabbaabaabababbaaaababbbbbbaababbaaaabbbbaaaaaababaaaabbbaabbbbbbaababbbbbbbbbabaaaababbbaaaaabbbaabbaabbbbababbbaaaaabaaabbababbaabbbbabbbbbbbabaabaabaaaaaababaaabbaabaababaabbaabaabbabbabbbabbbabbabaababaaaaaabbbbabbbabaababbababbaabbabbbababbabbaabbbaababbaababababbaaabbbabbabbabbaabbababbbbbbababaaaaabaabbbabaabbabaabaabbbbaaaababbbbbaabbaaabaaaabbaaabbabbabababbbbaabbaaabaababaabbabaabababbbaabaaaababbbbababaaaabbabbaabaaabbababbbbbaabaabaaababbbaabaabbbabaabbaabbaabbbbbaabbaabbabbabbbbbbabaabaaabbbbbababbbaabbbbbbabababaabbbabbbaaabaabbbbaabaabbaabaabbbabaabbbbbaabbaabbaaabbbbbaaaaaabaaaaaaababbaaabbaaabbababaabbabaabbbbaababbbabbaaaabbabbaaabaaabaaabbaaabaaaaaaabbaaaaaabbbbbaabbabababbaabaabbaaaabaabbabbaaaaaabbaabaaaababbbbaaabbabbbabaababaababbabaaabbbbaabaaabbbabbaaaaababaaabbbabbbbaaabbbabbabaaabbbbbaabababbbbaabbbbbbaaaababaaaabbabaaaaaaaaaaabbaaabababbbabbbbaaaaabaaaabbababababbaaabaaaababbabbbbbabbbbaaababbabaaababbbbabababaaabbbbbababaabaababbbbbbababbbbaaabaaaaaabbbbabbbabbaababababaaaabaaabbabbababbaababbbbbabaaabbbbbbababaabbbaaaabaababbabbaabbbbabbbbbbbbabbbbabaaaabaaaabbaaabbaaababbababaababaaaaaaabbbababbaababaababbbaaabbbbbbbbbbbbabaaabaaabbaaababbbaaabbaaaaababbbaaaabbaababbbbabaaaabbbbabbbababbbaaababbbbabbbabababbaababaababbbabbbababbababbbbabbbbbababaabbbbaaabaaaabbbbbbbbaaaabaababbbabababbbbbbabbaaabbaaabaabbbbbaabbbaaaabaabaabbbbbabbaabbbbaabaaaabbbabbbbbbaaaaaaababbbbaaababbaaaaaaaabbabaaaabbaaabaaaabaababbabbabaaabbbaabaabababaabaaaabbabbaaabaaaababbbabbabaabbabaaabbabbbbbbaaaaaaabbabbbbbabababbbbaabaabaabaabaabaabbabaaaaaabbababaaaabaaabbbbaababaaaabbbbabaaaabbaaabaaaabbababaabaaaaabbbbaaabbaaabbaabbbbabbaaaaabbabaabaaaaaabbbbbbaaaabbabbabaaabbabbbbabbabaabaaabbbbbaaabaabaabbaaaabbababaabaabbaabaaabaabaabbaabaabbabaaaaaabbaabbbbaaaabaaabaabbbbaaabbbaaaaaabbbbbbbaaaabbbabaaabbbaabbabaaaabbabababbbabaaaababbabaaababbabbaabaaaabaaabaababaabbaababbaababababababbabbabbaaabbbabaabbbbbaababbabbbaabbabbaaaabbabbbaaaaabbbbaabbbbbbbbbabbbbaabaabbbaabbbabbababaabaaababbbbababbbabbbbbabbabaababbaabbbaaaaaabaaabbaabaabaaaabbbbbbbabaabaabbabbaaaaaabbbbbbababbbbaabbabbabbbaabbbbaaaabbbaababababbbbbbabbbaaaabaaabbbbbaabbbaaabbabaaaaabbabbbbbbbbaabbbaaabbaabbbbbababaaaaabbaabbbbaaaaabbbbaabaabbaababbabbbaabbaabababababbbaabbbaaaabaabbbbabbbbbbaaabbbaaaababaababaaabbabbbaaabbbbaaaaabababbabaaaaababbbabbbbbababbbbbaaabbaabbbbaaababbabababbbaabaabbabbabbabababbaaabababaaaaabbabbbabaababbbaaaabbbaababbbabbabbbbaaabbaaaaabaaababbaabbabbabababaabaaababbabbaababbbaaaababbabaaaaaaabbbababaabbbbababbaabaabbaaabbabbababaaaabbbbababbbbabaabbbbabbababaaabaaababaaaaabaaaababaaaabbbaabbabbbbbaaababaabbbaaaaaabbaaabbbbbababbbaaabaaabbaaaabbaaaaaaababaabaaabaaabaaabaabaaabaabaabbaaaaabaababbbabbbbaaaabaaaabaaaabaaabababbbabbbababaabbbaabbaaaaabababbbaabbbbabbbaaabbbaaabbbababbaaababaabbbbaaaabbbaaaabbababbbbaabaababababaababbabbaaabbbababababbbbababbbbabbbaaaabbbbbbaaabababbababaabbbbbababaaaabaaaaaaabaabbbbbbaaaaaaaabababbbababbaaabbabaabbababaababaaabbababbabbaabaaabbababbbabbbbababbabaababbbaaaaabbbababbabbbaabaabaaaaaabbbabbabbbbbbbaaaaaabaabaabbaababbbbabbbbbababaabbbbabbababaaabaaababaaabbaaaaaaaaaabbababaabababbbaababbbbbaaaaaaabbbabbbaaabaaaaaaaaabaabbbbbbbbbbabbaaaabababbbabbbabbbaabbbabbbbbbaabbabbbbaaabaaaabbbabaaaabaabbbabaabbbaaaabaaabbabaaabbaaabbbaabbaaaaaabaabbaaabbbbbbbbabbbbabaaabbabaabbbaababaaababbbaabbabaaaaaaaabaabbaababbbabaabaabbaabbabaaabaaaaabbbabaaabaaaabbabbbbbbaabaaaaabbabaabbababbaaabbbabababababaaaabaaabbbaabbbbababbbbbbaabbaaaababbbabaaabbbbbabaabababbababbabbaabbabbbaababaaabaaababbabaaaabaaababaabaabbabbbababbbabbbababaabbbababbbbbbbabbabbaaaaabbaaabbaaaaaabbbababaaaaababbaaaaababbabaababbabbbaaabbabaaababaabbbbbbbbabababbbaaaaababbaaababbaaabaaabbaababbbbabbbaabbbbabaaababaaabbabbaabaababbbbaabababbbaaaaaabaaaabbbbbabaaaaabbbbbbababaaabbabbabbababbbbaaaaabbaabbabbbaaabbbbbbbbaaaaabaabaaabbbaaaaaabbbbbabaaaababbbbabaaaababaabaabaabbbbbbbbbaabbbaaabbaabbabbbbaaaababbababbbababaaaabbbbbaaaaabbbabaababbaaaabbaaaabbaaaabbbbabbabaaaabaaaabbabbbbabaaaabbbabbbaaaaaabbababbbaababbabaaabbabbbbbababbaaaababaaaaaaaaabbbaaaaabbabbbabbabbaaaabababbaababbababaababbabaaabbaabaabababbbbaababababaabbbaababbbbbbaaabbbabbabbbabbbaaaababbabaabbaabababababaabaabbabababbaaabbbbabbbbbbbabababaaabaabbaaabbaababbbaababaaaaaaaababaaaaabbbbbaaaaaaabbbabbabbaabaabbaabbbabbbababbaaaabaaaabbaaababaaabbbbaaaabbbbabaaababaaaabaaaaaababaabaabbaabbaaabaaaaaabaabbbabbbbaabbabbbabaabbbabaabaabbaaaaaaaababbaaaaaabbabbbbaabbbabaabaaabaaaaaaaabbbbabaabbabbbabbbabaabaabbbaaaabaabaaababbbbabbaabbaabbaaaaabbabbbbbabaaaaaaaaababbbabbabaabbaababbbaaabbbbbbbaaaaaaabbabababaaabaabbbbbabbbbaabaabababaabaabaabaaabababbbbbababbbbabaaaabbbbbbbbbbaabbababaaaababaabbbaabaabbbaaaaaaabaaabbaaaabaabbbababbabbbabbbbabbbaaabbabbbbbaabbbbabaaaababbaabbaaaabbaabaabaabbbbabaababbbbbaababbabbaaaaaaabbbaaabaabababaabaabbaababbbbabbbaaabbabbaababbbbabaaabbabbbaaabbbbaaaaaababababaababaabaaabbbaababbbbaabaabaaaaabbbaaabaabbaabbbaaaabaaabbaababbbaababaaaababbbaaababbaabbabbabbbabaaaabbbabbabbbbabaabbabbaaababbbaaaaabbbbbbbaaaaaaabbabbaaaaaabbbaababbbbbabbaaaabbbabbbabbaababaabbbbbbbabaabaabbbbbbababaaababbbbbbabababbbabbabaaabbaaaaaababbaaabbabbbaabaaabbabbbabbbbaaaaabaaabbabbbbbbaaaabababbbabbbaaaaaababbabbbbbbaaabbbabaaaaaaaabaababbaabbabbbaabbbbbaaaaaabbbabbabaabaabaaaababaaaaabbaaaaaaaabbaaaaaaaabbababbbbabababaaaaababaabbbaababbabbaabaabaaabbaaababaaabbbbbbabaaabaaaababbabbaabaabbaaabbabbbaaaabbbbbbbababaaaababbabbbbaaabbaabbbababbbabbbaaabbabbababaabaabbabaaaababaaabbaabbaaabbbaabbaaaaaabbabbbaaaaaabbbbbaaaaaaaaabbbbbbbaaaaababaaabbbaaaaabababbabbbabaaabbaaabbaaababbababbaaaabaababbbabbaaabbaababbbbbbbaaaaaaabbaababbbababbbaaaabbaaababbbbbbababbbbaabbabbbbabbababbbbbbbbbbaabaabbbbaabbabababbabbbabbaaaababbbbbaaaaaaaababaabbababbbaaabbaaaabbbaaaababbbaaaaaabbbaaababababababaaabbbabaaaabbbababaaabbbbbabbabbabbabbbbabaabbabbaaabbaaaaaaaababaabbaaabbaababaaabbabbaabaabbbababababaaabbbbaaababaaabbabbabbbaabaaababaabaaabaabbaaaabaaabbaabaabbabbbaaababaabbbbaaaababbbababbbabbbabaaabaabbbbbbabbababaabbabaaaaaaaaaaaaaaaabbaaaaabbbabbbaaabbbbaabbbbbaabaabbbbbbbabaabbbabbbabbbbaabbbbaabaaabbabaabbbabbabaabbabbaaabbbbaaaaaaababbaaabbbbaaaaabbbbaaaaaaabaaaaaababbbabbaabaaaabbbaaabbabababaabbabaabbaabaaaababbbbaaababbbabbababaaaabbbbbababaabaaaabbababababaaababbbbbabbabababababbaabbbabbbaaabaababaaaabbbaaabbbaaaabbabbaaaababbaabaaaaaabbaaaabbbbbbbbaaabbabaabbabbabaabbaaabbbaababbbabbbaabbbabababbaaaabbabbababaaaabbbaaaabaaaaaaaababaababbabababaaabbaabbabbabaaabbaabbabababbbbbaababaaabbbbbbaaaabaaabbbababbabbbabbaaaababbaabaaababbbbabaabaaaabbaaabbabbaabababbbbbabbbabaaabaabbaaaaababbaaaabbaabbbaabaabbabbabbaaabbbaaabbaababbbbbbaabaaaabbaaaaaaababaabbbbaabbbabbaabbbbabaaababbbbababbbbabbbbabaabbabbbababaabbbbaabbbbbbbabbbbbaababbabbbabaaababbbaaaaabababaaabbbbabaabbababbabbaabaabaabababbbaaababbababaaaababaaaaabbaabbabbaabaabaaaaabaabbaaababbabaaaabaaababaababbbaaabbabbbaababaaaabbaaabbabbbaaabbbababbabababbaabbabbbbababbabbabbbbaabbaaababbabaabaababbabbbbbbbaababaaaaaaaaaaaaabaaaabbaaabbaabbaaabbabaaaaaababbbbabbbabbbbbaabbaabbbbabababaaabbaaabababbbbbbbaaaaababaabbbaaaaaaabbbbbabaaababbbabbbbbbaaaababbaabaabbabababbaaaaaabaabaaabbbabbaabababbbababbaababbbabbbaabbaabbaababaababbaaaaabaabbababbbaabbaaabbaabbbabbaaabbbaaabaaaabaabbbbabbbabbabababbbaabbbbbbbbbaaaaababbabaababbaabababbbbabbabaaababaabbaaabaabbaaabbbaaababbbbaaabababbaaabbaabbabbbaaabaaabaaaababaabaababbbbbbabaabbaaabbbbbbabbaaabaabbbbaaabbbababbbabababbabaabbabbabaababbabaabbabbbaaababababaaaaaababbbabbbbaabbababbabbbbaabaababbaabbaabaaabaabababaaabbabaabbbbabbbbaaaabbaaabbabbabababbabbbbbbaabbabaabaababaaabbbbbbabbbbabbbaaabbaaaabaabbbbabbabaaaaaabbaabababbaaabbaaaaabbaaaaaababbbaabbabbabbaaabababaaaaabbaaaababaaaaaabbbabaabbabaaabaabbababbaaaaabaabbbbbbbbabbbbbabbbabbabbaaabbbaababbbbbaaaabbaabaabbaaabbaababbbaabbbbbbaabbbaaabaaaababbbbbaababbbaaabaababaabbbaaabbbabbabbaabbaaaaaabbaaaaaabbbaaabbbabbabaabaaabababaaabaabbbbbaaaaaababbbabaabbabaaaabaabbaaabbbabbaaaababaabbabbbabaaaaaaaaaaaaabaaabaabaabbbaabbababaaaaaaaababaababbbbabaaabaaaaaababbbbbabaababbbabaabbbaabbbaabaababbaaaabaabbaaabbbaaaababaaaaabbbaabbbbaabbbbbabbaaabaababababbaabababbbaaaabaabbbaaabaababbaaabaabbbbabaababbbabaabbabaaaabaaabaabaabbaabaabbaaabaabbbbababbababbbabbabbabaaaabbbaaaaaabaaababbbaabbbbaaaabaaaababbbaaabbbabbaababababbbbaaaabaaabbabaabbbbababababaaaabaabbbbbaaaabbbbaaaabbababaabababbbaababaabababaaaaaaaabaabbbabbaabbbbbaaaabbbbaabababaaaabaababababbababaabaababaaaaaaaabbabbbbbaaababbbbaababbaaababaabbaabaaaaabaabbaabbbbabbabbbbaababbaaaababbbbbabaaaababaaaabbbabaabaaababbbabbbbaaabbbbbbbabbbbaabbbbbaaabbabaababaabaaabbababbbababbbbabababbababaabbabaabbabababbababaabbaaabbabbabbaabbbaaabaaaaabbbaaaaabaaababbabaaaaabaabaaabbaaabaababaabaaaaabbbbbbaabbaaaaabaababaaabbbaaaaaaababbbbbbabbbbababaaabbbaaaaaaaaababbbbababbbaabbbabbbbaaabaababaaabaaaabababaaabaaabbbbaaabababbbbaabbbaabaaababbbabbabaabaaaaaaababbaabaaaabaaaaaaabaabaaabaabbabaabbbabbaaababbababaabaabbabbbabbaaaaabbbaabbababbabbaabababababbbbaabbababbabbbabbaaabaabbbbabbbbbbaaabaaaabbaabbbbaabbabaabaabaabbaabbbaaaabbbaabbabbbbbbbbaaaabaaababbbabbbbabbbbbbaabbaaaaababaababaaababaaaaabaabbaaaaaabaaaabbaababbaababbaabbababbbbabbbbaaaaaaababbbabbbbaaaababbabbbaabbbababaabbbbbaabbabaaabbabaababaababaaaabbbbbbbbaaaaabaabaaabbbbaabaaaabaabbbbbbababbaaabbaabaaaabbaaabaaabababaaaaabbababaaabaabaaaaabbaaaaaaabbabbbbbaabbaabbabababaaaaaabaabaabbaababbababbbbabbbbbaaaaabbbaaababbabababababbbaabbbbaaaaabababbabbaabaabbaabbaaaaaaabbbaabaaabaabbabababaaabbbbbaabbaabaabbbabbbaabababbaabababbbbbabbbbbaabbabaaabbbbbabababbaaaababaaabbbbaaabbaabbbbabababbabbaabbaaababbabbaaababbabbabaabbabaaabaabbabababababaababbbbbabbaaaaabbababaaaaababaaaaaaaaaaaabaabaaababbabbabbaabaaaaaabbbaabababaabaababbbbbabbbbababbabaabbabbabbabbaabbbabababaabbaaaabbabaaabaabbbbbaabaaaaabbabbabbbabaabababbababbabbababaaaaaaaabaabbbbabababbbbabbaaabbbbabaaaabbabbbababbabaabaaababaababaabaaaababaaaaababbbbababababbaaababbbbabaabbbaaaaaabbbababbaaaaabbabaaabaaababbaabbaabbaaaaabbabbaaabaaaaabaabbbaabaaaaaabababbbaaabbbaaabaabbababbaabaaabaabbaaaabaaaaababbabbbbabbaaabbbbabaaabababbbbababbbaabaaaaabbbabababababaaabaabbababababbbaaabbaaabaaabbaaabbaaabaababaaaaabaaaaaaabaaaababababbabaaabaaaabaaaabbbbaaaababbbabaaaaabbbaabbbaaaababbaaaabaaabaaabbbbaabaaabbbaababababbababaababbbaaabbbabbaabbbababbababbbbabaabbabbabbaaabaaaaaaaabbbbbaabbbbbbbaaababaaaabbaaabaaaaaabbaabbabbbbabababbaabbbbabbbaaaabbabbbaabbabbaaaababbabbabbabaaabaabbaaaaaaabbaaabbbbbaabaaaabababaaaabbbabaabaabaaaaaaaabbabababbbaaabaaaaabbabbbbaaabaabbbabbaabbbaaabbaaababbaabbabbbbaaabaaabaabbbbabbaaaabbaabaabaabbbbabababbaabaaaaababbbabbaabbababbaabaaabbababbbabbbbbbbbbaababbbbbabaaababbbbbaaaabbbabaaabaabaaaaababaaabbababbbaabbaaaaaabbabaabbbabbaaaaababaaaabaababaaabbabbabbabbaabaababbaaababbaababbabaaaabbbabaaaaababbbabbaabaabbabbbabbaabbaabbabbaaaaabbaaaabaaaabbaababaababbbabbaaabbbbabaabbbbbbbbbbbabbaabaabbbaaabaaababbbabbbbbaabbbbaabaabaababaaabbbbbabaababbbaaabbbaababaaaaababbbbababaabbbbbabbabbbaabbbbabbbbbabbaabaaabaababaaaaabaaababaabbbabaaaaaabbaababaabababbaabbaaaaaabbbbbaabaabbabbaaaabaabaaababaaabaabbbaabaaaabaaabbaaababbababbabaabaaaaaabbabababaabbabaabaabbbbbabbbaaababaaabbbaaabbbaabbabaabbbbbbabbbbabaababaabbaabbaabababbbbaabaaababaababaabbbbabbbbaaababbababbaabbbbbabababaababbabaabbaabbaaababaabbabbaabbbbbbabbaaabaababbbbabaaababbaaaabbababbaaaaabbaaaabbaaaabaabbabbbaaabaabbbbbbbaaaabaabbaabbabababbababaabbbaaaaaaaaaaaaabaaabababbbbbababbbbaabaaaababbabaabbabbbbabbabaabbbaabbbbabaaabaaaabaaaaabaaabbbabaaaabbaaaabbbbabbbaababbabbaababababbabbbbbababbbaabaaabbbaababbaaabbabbbababababbbabaaaaabaabaabababaaaaabbabbbaaabbbabbbaaaababbbaabbaaaabaaaaaaaaaababbbbbbbbabaabbbaababaabbabbbababaaaabbbabababaaabbbbabaaaaabababbaaabaaaabababaaabbbbbababbabbbbbbbababaabbaababaabbbbabbbbbbabbaaaaaabaababaababbaabaaabbbabbaabbaabababaaabaaaabbbbbabbbbaaabbbabbbbbabaabaabbbbbaaababbaabbaaabbabbabbbbababbbbaababaabaabbaababaabaaaaaabaababbaaabaabababbaabbbbaaaaababbaabbbabbbabaabaabaababaabaabbababaaabbbabbabaabbaabbbbabaabbaabbbbbaaabbbaabbabaaabbbbaabaababbabbabaaabbaaaabbbababaabbbababbabaaaaabbbaaabaabababaababababaababbbbbababaaababaabbbbabababbbbaabbaaaaabaaababbbaabbbaababaaabbbaabbabbabbaaaabbaaaaaaaabbabbabaaaabbabbaabaabaaaaaaaaabbbbaaabbbaaaaaaabbbaaabaabbbbbbbaababbabaaababaaaabbaabbaababbaabaaaaaabaabbababaaaaabababaaabaaabaaaaababbbbbbbabbbbabababbabaabaaaaaabbbaaabbaabbaaabbaaaaabaaabbabbbaabbbbaabbabaaababaababbbbaaabaaabababaabaabbababaababababababbabbbbbaabaababbbbbababbbabbabaabbbbbbbaaaaaaaaaabaaaaaabaabbabbabbbbabaababbbabaaaabbbaaabaaabbaaaaabaabaabbbbbabaaaaaabababaaaabaaaaababaaaabbbbabaaaabbabbaaabaabbabaabbbbabbaaabbbabbbbaaabbaaaabbabaababbaabbbaaabbaaabababaaaabbbaababbaaaaaaaababbbbbbbbabaaabaabbabaabbaabbabbbbaaaaabaabbaabbababbaabaabbbbaabbbbabbbbbbbababababaaaaaabaaaaaaaabbbbbabbaaaababbbaaaaabbabbaaababbabbbaababbbabbbababababaabaababbaaabbaabaabaaaabbbabbaabbaaababababbbbbabaaaaabaababbabbaababbaababbbabaaabbaabbbaaababaabaabababaaaaaabbbbbabbabbbaaaabbabbaaababbbbbabbabbabbababbaaababababbbbaabbaaabbaabaabbaaaabbbaaaabbbbaaaaabbbbbbbaabababbbbaaabbbabbaaabaabbabbbabababbbbababbababbbabbbbabaabbabababaabaabaabbaababaabaabbababbababbbbbbbababbbbababababbbbbaaaabbbbbbaabaabbaaaabaaaaabababaaaaabbbaaaaababbbabbaababbabbbaabbabbbaaabaabbbabbaabababbabbaaabbaabababaaabaabbbabbbaaaababbbbaabbbaaaabaabbabbbbabbabbbbabbbbabaababbbaaaaabbbabbbababaaaaaaabaaaaaaababbbaaaaababbbabbabaababbabbaaabababbaaabbabaabbabaaaaabaaaabaabbbbbaababbbababbabbbabaaababaaabbbbbaaaabbbbbbbbabbaaaaaaaababaabbbabbabbbbaabbbaabbbabbbbaabbaaaabaabbbaaaabbbabbbabbbbbababaabababbabababbabaabaabbbbbbaabbabbaaabbaabbbbabbaabbabbbaaababbaaabbbaabbaabaabababbabbbaabbbaabbaaaabababbaababaaaaabbababbbaaaaaaababaaabababaabaaaababbaababaabbaaabbabaabaabaabbaaabaaabbaababababbbabbaabbabbabaabababbbbbbabbbaaabaaabaabbbaaabbbbabbaaaaababaaaabaaaaaaaabbbbbbbaabbaaaaabbababababaabaabbabbaabaaabaaaabaababaaaaaaabbababbaaaaaaabbbabbbaabbabbbaaaaaaabaabbabbabbbbbabbabaaabbbaaabababbbaaabbaaabbbbbbaababaabbabaaabaababbabbbaaaababaaabbbbbbababaabbabbbbbabbabbbababbaaabbaabaabbbabaabbbbaaabbbbabababaabbabaaabbbabaaaaababbbbbbabbbbababbbababababababbabbabbaaaabaaabaababbbbbabbbaabaaababaabbababbabbbabaaaabbabbbaaaaaabbbaaaaabbabbaabbbbababaabbbbabababbbabbabbbbbbabababaaaaabaaabbbbabbabbabaaabaaaabbbbabbaaaaabaaabbbbabaabaaaabaaabbbababbbaaaaabaabbbbabbabababbaabaabbabababbbaaaabababbbabababaaaaaabbbbbbbbaababaaaaabbbaaaabaaaaaaabbbbaabbbbaaaaabbbaabbaaabbaabbbabbbaaababbaaabbabbbaabbbbaabbaaabaaaabaaaaaababaaabbbbbbaaabbbbbbbaaaaaaabbbaababababaaaaabbbaaaabbabaabbbaaaabaabbabbbbababbbaabbabbaababbaababbaabbbaabbbbabbabbababababbababbaaababbbbaabaabbbabbbabbaaabbaaabababbbbababbaabbbbabaabbbbbabbbbaaaabbaabbababaaaaaabaabaabababaaabbbaaaabaaabbabaaaababbbabbbaabaabbbaababaabaabbababbabbabbbbabaaabbabbbbbaaabaaaaaabaabbaababbbbaabaaaababbaabbabbabbabaabaaaabbbbbabbaaabbaabbaabbabaabaaaabaaabbaaaabbbbbaaabaabbaabbbbaabbbaaaaaaaabababbbbaaaaaababbbaaaaaababbaabaababbabbaabbaaabaabbbaaaaaaabbabaaabaabababbaaaabbaabbabbbbbabbaaababbbbabbbbbbababaaaaaabaabaabaabaababbbabaaabaabaaaaaaababababbbaababaabbaabbbabbbaaaababaaaababaaabbbbbabbbabaaabbbabbababbaabaabaababbaaaabaabbabaabbbbaabbaaabababbabbaabbabbabbbbbabbaababbaaabbbababababbaabbabaaabbbabaabbaabbbbabbbbbabbbbbabbbaabababaabbaabbbbabbbababbbbabbabaaabaaaabaaaaaaaabbbaaaabbabbaabbaabaabbaababbababbbaaabaaaabaaababaaabbbababbbaabbabbaabababbaaaaaaaaababbbbbabbbbaaaababaaabbbababababbbabaababbbbababbbbbbbbbbababababaabbabaabbaabbbaaaabaaabbabbaaaaabababbabababbbabbabbbaaaaaabaaaabbababbabaaababbbabbbbababaaaabbbabbbaaabbbbbabaabaaaaabaaabaabbbbbabbaaababbbaabbaaaaaabaabbbbaabaaababbabaabababbababbabbabbabbbbbbbbaaaaabaaabbbbaababbbabbbbbbabbbabababbaaabbabbbabbbbbabbaaaabbabbbaaaaabababbbaaaabbabaaaaabbabaabaabbaaabbababbaababaabbbaaabaaaabbbabbabbbaabababbaaaabbbbbbbaaaababbbaaaabababababaaabaaaaaaaabaaabaaabbbbbabbbbbabbbbabbbaabbaabbbbabaabbaaaabbbababbabbabbbabbabbbabbaaabbaabbaabbbbaaabaaaaaabbaababbbababbbbaaabbbbbbabbbbbabbaababaabbbabaaaaaabbbbbbaabababaabaaabaaabaabbaababbaabaaaabaaaaaaaaabbbbbaaababbabbbaaaaaabbbbabaabbabbabaaaabaaaabbabbbbbabbabbbbababbbaabbbabbaaabaabbbabaaabbbaabbbbaaabbbbbaabaabbbbbbbbbaabaaaaaabaabbabbabaaaabbaabbabaaababaaabbabbbbabbbaaabbababbaaaabbbabbabababaabbbabbbbabbbbaabbbabababbbaaaaaabbbaabaaaabbabaaababaabbaaabbaabaabababababbabbbbbbabaaabbbbbaabaaabaaabaaaabababbaababbabaaaaabbaaaabaabaaaaabaaabaabbbaaaaabaaaaaaaaabbbaababbbaaabbbbbabaaaaabaaababaabaababaababaabbbbabbbbabbaabaababaabbabaabbaabbabbbbaaabbbbbaaabbabaabbaabbaabbbababbbbbaabbbaaaabaababababbbaabbabaaaabbabaabbbbaaaaabaaabaaaaabaabbabbaabaaabbbbaaababbaabbaaaaabbbbbababbabbabaaabaaaaabbabababbaabbaaababaaabaaaabbabbbababbbaaababbaaabbaaabbbbaaaabaaaabbababbaabbabaaabaabbababbbbbabaaabbaaabaaabaabaabaabaabababbbbbbabaaaaaabaabaaabaabbbaaababbbbaaabaaabbbbabaabaaaabbbaaababbbaaaabbaaabbaaaabbbbabbaaabbaaaaababbbaabaaaabbbaaaabaabbabaabbbbbabbabaaabbaabbbaabbaaaaaaaaaaabaaaabbaabbbbaabbbaaaaaaabababbbababaaabababaaabbaabaabbaabaabaabbaaaabaabbaaaaababaaaababaababbaabbaababaabababaaaaabbababbbbaaabbbaabaaaaaabbaababaaababaabbbaaaaabbbabaabababbabbbaaaaaabbaaabaaaaaaababaaaabaaabbaabbbabaaabaabbaaabaabbabaaababaabbbabbbbaaaaabbababaaabaabbabbbaaababbbabbbbbbabaabaabaaabaaaaabbabbbbbbaaabaabbbaabaabbbaaabaabababbaaababbababbbaabaabbaababbaabbaababbaabbbababbbbbaaaaaabbbbbaaababbaabaabbabaaabbabbbbbaabbaababababbabbabaabbbaaababaaaaabaabaaababbbaabbaabaababbabbabbbbbbaaabababbbabababbaabbabbaabbbbabbbababbabbabbabababbabbaaabbaabbaaaabbabaaaaaaaaaaabbbaabaaabbaaabaabaabbbaaaabaaabbabaaabbbababbaaaabbbaabbbabbaaaababaaaaabbbabaababbbaaabaaaaabaabbbaabaaabababbabbbbbabbabbbbaaababbbbbbbbbbbaaaabaabbababbabbbabbbaababbbbbbbaababaaaaaabbaabbbbbabaaaabaabbabaabbbaaabbbabaaaaaaababbaabbabaababaabaabbbbaabbbabbbbbbbbaabbababbaaaabbababbaaaabaaaaabbaaababbbababbabbbababbbbbbbababbbbbabbbaaabbbabbaaaabbbbabababaabaaabbabbbbaaabbaaaabbbaaaaabaaabaaabaabaaaaabbabbbaabaaaabaababbaaaaababbbababaabbabababaababbabbabbaaabbbbbbbaabbbaaababbabbbbbababaaabbbaabbbbabababbabbaabbabbbbbbababbbbbaabbabababaabbabbaaabbbbaaaaabbaabbaaabbababbbaabbbaabaabbbaabbbbbabbaaabaabbabbbbababbaabbabbaaaaaabaabaaabbbaabaabaababbaabbababaabbbababbaabaabaababaabbbbaaabbaabbbbbabbbaabbabaaabababbabbaabbabaababbaabbbaabbbaabaabbbbbbabbaabbbaababaaaabbbbbaaaabbabaaabbaabbbbbbaababbbbbbbabbabbabbaabbbaabaababbaaababbabbbbbaaaaaabbabbabbbbababbabbababaaabbaaaaabaabbbbaabbbabababbaaaabbaabbaabbababbbbbbbbbbaaabbbabbaabbabaaaababaaabbaaaabbababbaaaabaaaaabbaabbbaaababaabbbbabbbabbbabaababbbabbbbaabaaaabaabbabaabaabbbaababbbbaaabaaabbbababbaabaababaababaabaaabbabbbabababaabaaaaabbbbbbaabbaabbbbabbbbbbaaaaabbbbaaaabaaaababaaabbabaaaaabbaabaaaababbbbbabbaaaaababbbabababbbbbaaabaabbaaaaaabbabbaaaabbabaaabaaaaabababababbababababaaabababbbbbaabaabbaabaabbaaaaaabbaababbbaabbbaaabaaabbabbbabaabaaababbbabbbbbabaabbababaaabbabbbbbababbaaaaabbabbbabaabbabbbbbaabaabbaabbababbbbbaabababbaabababbbabaabbbbbbbbbbaaabbbaabbaabbbbaabbbbbaaaababbbabaaaabaabbabbbaabbbbabbabbababbbaaabaabbabbbababbbbabababababbaabbbbbbbbbbaababbbbaababbbabbabbbbaababaaabbbabaabbbaaaabaabbaababababababbbaaabbbaabaababaabbababababbbabbaaabbabababbbabaabaabaabbababaaabbbbababbaaabbbaabaababbbabaababbbaaaababbaabbbaabbaabbaababbabbabaabababbaaabaaaababaaababababbbbbbababbbbbbbabbbbaaaabaabbbaaaaaaaababbaaaaabbbbaabbbbbbbbbbaaaabbabbbaabbabababbaaabbaaababbabbaabbabbbabbbaaaaaaabbbbbabaabababbabbbaaabababaabbbabbbabaaabaabbbabbabbbbaaaababbbbbabaaaaabaaabaabaabbbbaaabaaababbbaaaababbbbbbbaaaabaababababaaabbbbbabbaabaaabaababbbabbaabbaabaabbaabbbaabbbaabbbabbaabbbbbaabbaaaabaabbabbaaaabbbbababbbabbaaabbbabbaaaaabbbabbbabaabbaabaaabaaaaaababbbbbbbbaabaabbbabbbbaabbbaaaaababbbaaabbbbbababbabbaaaaabbaababaaaabaaababbaabaabbbaaaababaababbbbbaaaaaaaababaabbbbbaabbabbbaaabbabbaababbaabababbaabbbbabbbbabbabbababbabaababaababbbbbbbabaaababbaaaaabaabbaaabbaabbbabbabbbabaabbabaaabbbbaabbababbbbaababaaaabbabbbaaabaaaaabbbaabbabaaabaaaabaaabababbbabbbabbaaabbbabaaaaaabaaaaaabbabbbabababaababbabbbbbbaaabbaaaabbbaaaaabbbaabbbabababaaaaaabbaabbabaaaabaabbaababbbabbaabbaaabaabaaabbaaabbabbaababbaabbbbabbabababbbaabbaaaaaaaaaaaabbbaababaaababbaaaaaaaaabbababaaabbbbabaabbaaabbabbbbabaaabbaaabbaaaaabaabbbbbaababaaaabaaaabbaaaaaababbbbabbbbaabbaaababbbbbaabaaabaaaabaabbaababaaaabbaaababaaaaabbbbaababbbbbbbbaaabaaaaabbbababbbbababbbbaaababbbabababaaaaabbbaabbaababbaabbbbaaabbbbaababbbbbaaabaaaaaababbbbbabaaaaabaabbababaaabbabbbaaaaabbbbbbabbababaabbabbaababbbabbabaaaaaaaabaabbbbaaaaaabbbbbbabbababaaababaaabbaaaaaaabaabbaababbaaaabbaabbbbabbaaaabababaabaaaabbbbbbabaabbabaaaababaabbbbabbaaaabbaaabbababbaaababaabbbbababbaabbbbabaabaaaaabbbbaabaaabbabbbaaabbbaaaabbbbabbabababaaaabaabbaabbbbababababbaaaaaabaabbababbbbbbbaaaaaabaaaaabbabaaabbbabbaaaabbbbbaaaabbabbbaaaabaabaabbaaaaaabbbbbaabbabaababaabaabbaabaaaaaaaaabbbbbbabbabababbabbbabaaabbabababbaaabaaaababaaaabaabababaaabbbabbbbabbaabaababbbbaababbabbaabaaaaabbbbbaaabbabaabaabaaaaabaaaaabaaaabaaabaaaabbabbbaabaaaabaaababbaaababaabaabababaaabaaaababaaaaabbbaaaabbaaabbbbabbbabbaaabbaaabaabbbabbbababaaaaaabbabbabbbabaaaaaabbbbbabbabbaaaaaaaabbbbaabaabbbaabbbbbbabaabababbabbbaabaaabaaaabbabbaabbaabbbbbaaabbbbbaaaaabaaababababababbaaabbaabbbababbbbbbbababbaabbaabaaabbbbaababbabbbaaabaabaaabbbbabaaabaaabbaabbabbabbaabbaaaaaaaabaaabaababbbabbaababbbababbaabaaababbababaabbabbaaabbbbababbabaaaabaabbbaabaabbbabaaaaabaaaababaabaabbbbbaabbbbbaaaabbbbbbbaabaabaaaaababbaaaaabbabababaababbbbbbababaabbbaabaaabbababaaabbbbaaaaaababaaaaababbabababbbbbbabbabaabbbbbaabaaaabbbaabaaabbbbaabbaaabbbbabbaabaaababaabaabbbbababaaaaabaaabaaababbaaaababbbbaabbabaaababbababbabbababbbbbaabbbbaabababaaaabbbbaabaaabababababbaaababbabbbbbbaaabbaabaabaababbababaaaabaababaabbaabbbabbabbbbbbaaaaaabaababbbbbbaabbbbabbabaaabaababbabbaaabababaaaabbbabbbabaaabbbbababaabbaabbaabbabbabbbbaabaaaabbaababbababbaabbbbbbabaaaaabbbbbbbbbbbbbaabbabbbbbbbaaaabbbbbbaaabaababaaaaaaaaaababbababbbaabbbaabbbbbaabbaaaabbaabbabaabbbabbaabbbbbaabbbbbababbbaabbabbbbbbabaaaabbbaabaabaabbababbbbbbabbababbabbbaabbbbbbbbbaaabbabaabaababbbaaaaababaababbababbbaaabaabaabaaabbbbbbaabbaabaaaabbabaabbbbaabbababababaaabaaababbabaaababbabbbababbaaabaaabbababbbaabaabaaaababbaaaaaaaabbabbababaababbaaaabaaabaaabbbabbbbbabbababbabbbababbabbbaaabbbbbaabaaaabbbabbbaabbaabbaaabaabbabaabaabaabaaabbbbbaabaaaaabababaaaaababaabbaababbbbababaababbbaaabbbaaabbbaaabbbbbaaaaabaababaabbaabbbaabaaababbbbababbbbaaabbaababbbababbbbbbabababbabaabbabaabbbbbaaaaaabaaaabbabaaaababbabaaabaaaabbaababababbabbababababbaaabaaaaabbbbbaabbbaabbabaabbaabaaaaabbbababaabaaabbaabbaaaababbaaaaabbbaaababbbbaabbbabbabbaaabbbbabaaaaaaaabababbabbbbaabbabaaaaaaaaaaabaabbbabbabbaababbaaababbababbbbaabbbbbaaabbbbbaaaaaaaaabaaabbabaaabbbbbbbbbbbaababbaaaaababaabbbaababbbaaaaaabbbabaaababaaaaababbbbabbababababbaababbabbbbbabbaaaabbabbababababbbaaaabbbabaaabaaaaaabbaaaabbaabbbaaabababbbbbbaaabbababbaaaabbaaabbbbaaaaaaaabbbbbaaabbababbababaaabbbbbbbbaababbbbbaabaaabbbbaabbababbbabbbbbbaaaabbbbaaaaaaaaabbabbabaaaaabbaabbababaabbbabbbbbbbaaaabaaaabbbabbbbbbaaaaaaaababbbaaaaaaabaaabbaaaaaaabbababbbababbabaaabbbabbabaabbbbbabababbbaaabbabaabbabbbbbbaabbaaabababbbaababbaabababaabbabaaaabbabbbbbbbbbabbbabbbaabbaabaabbbbabbbbbbabaaabbabbbbbaaaabaaaaabaabbbbbbbbabbbaaabababbbabaaabaababbbbaaaabbbbabbaabaabababbabaabbaaabbaababaaabaaabbabbbbbbababaaababababbbababaabbbabbbbbaaabaaabaabaababaaabaaaabaabababbaabaabbbbabaaaabbabbbaabbbbaaabbaabababaaabaaaaabaaaabbbbabaaaabbbbbbaabbbaaabababbbabbabaabababaaaaabbabababaabbbbabbabbbabbbaababbbabbabbaabbbaababbaabbbbabaaabbabaaabbbaaabaabaaabbabababaaaabbaababababababaabbbbbbaaabababbabaaabaaaaabbabbbaabbabbabbabababbabbaaababbabbabbbabbaabbabbabbabbabbbbaabababaaaaaaaabababbbabbababaabbabbaaababaaaaaabbaabaaabaababaaaaaaaabbbbbabaaaabaaabaababbabbabbbbbbaaabaaababbaababbbabbbabbbaabbaabaabbababbbaaaababababaaaabbabbbabbaabaababbbbbaaaabbabaabbbababaababaabbbbabbbbaabaaabbbababaabbbbbbbbaabbabbabbabbbbbaaaaabbaaaaababbbbbaaaababaababbbbbabbaababbaaabaabbbabbabaabaaabbbbbbbababaababbbbbaaaaabababbbaaabaabbabbbaabababaababbbababaabbbabbbbbabaababbabababbaabaabbaaaababbaaabbbaabaaaaabbababaaabbababbbbabbbaababbbaabaabbaaaababbbbbbabbbaabbbabbabbabbaabaabbbaaaaaababababaabaaabbbabababbbaabbabaababbabbbbabababbaabaaaababbaabaaaabbaaaaaaaabaabababbbabaabbbbbaaaaaaabbbaaaaaaaabbaabbbbbbbabaaabbaaaabaaaaababaabbabaababbabaababbaababbabaaaaababaabaabbabbbbbaaaabbabbabaabbaaaaaabaaabaababbaabaababbbbbaabbabbabbbbbaaaabbabbbbabbabaaabbbbbabbbbabbbbababaabbabaabbbbaaaabaabbbabaababbaabaaaabaabaaaabbbbababaaaaababbbbaabbbaaaabbaabbbabaaabbabbaababbbbbbaabababaaaabbababbabbabbbaaaabaaaaaababababbabbbabbbaababbabaaaaabbbaaabbbababababbaaababaaaabbaaaaabaabbbbbabbbaabbbbbbaabbaabbaabaabbaaababbbbabbaabaabaabbbabbbababbabbbbaaaabbbaaaaaaabaaaaabaaaaaaaaaabbababbbaabaababbbaaabbabaababbbaabaaaabaababbbbbbabbaabaababaababaabbababababbaaababbbbbabbbaaaaababbaaabababaababbabbabbbbbbababaabbbabbaabaaaaabbabaaaababaaaabaaaaaabbbaabbaabbbbabaaaaaaaababaaaabaaaaabbaaababaaababaabaaabbbabababbbaabbabaabaaaaabaaabaabbbbbabaaababaaaabaaaaabbaaababbabbbbabbaaabbaababbabaababbabbabaababbaaaabaaababaabaaababbbaabbbaababaaabbbaabaaaabbaaaabbabbaaaabaaabbabaaaaaabbbaaababbababbabbaaaaaaaaabbbbbbaabbbabbabbbbbbabbbbaababbbbbbbbaaabaababbaabaabaaabbbbaaabaaaaababbbbbbbbaabbbaabbbbbbabababaabaabbababaaabbaabaaabababaabbbaaabbabbbbaabaaaaaaabaabbbabaaaaabbbababaabbabbbbbbabbbabbabaaababbaaabaabaaabbababbaaaabaabbababaabaabbbaababababbabbabbbaabbbbbaaaababaaabaaaababbbbababbbbbbbababbbaabbabbbbaaababbbbbbbbabbbbaaabaabaaaaaabbbbbbabaaaaabbbbabbaabaaababbbbbabaaaabbaabaababaabbaaaabbabaabbaabababbbaabbbaaaabaaabaabaabbaababbabbaaababaaababbaaabaababbaaabababaabaaaaaabbababaaabaababbaabaaaaaaaaabaabbbbbbbbaababbabbbaabbaaaaabbabaabbaaaabbbbbbaaabbbababbabbaaaababbaabbabbaaabaabbbbbaabaabbbabaabbbabaababbabbbbbaabaabaabaaabbababaaaabbaabbbabaabbababbaaaabaabaabbababaabaaaaababaabaaabbaabbbabbbbbabaabbababbbababbbbbaabbabaabbaaaababbaabaaabbbbaaabaaaaabababbbaaabaabaabababbbabbaaabbbbbbabbbabaaaabbabababbababbbbaabbbbbbaaababbbbabbaabbbbabaaaabbabbaababbabababbaaababbbbababbabaaabbabbaabbaabbbbaaabbaabbabbaabaaabbabbbaabbbaaaaabbaabbbaaababbaaabaabbbbaaaababaaababbabaaabbaaababaabbbabaabbaaaaaaaaaaabbabbbbbaabaaabbabbbaababaaabaabbababbbabbaaaaabbaaabbabaababbbbaabbaaabbbbabbbaabbaabbbabaabaabaabababbbaaaaabbaabaababbbbaabaabababbaaabaabbabbbaaaaabaaaaabaabbaabbabbabbbababaaaaaabaaaabbbbaaababbababaaababbbaaaabaaabaaabaaababbaaabaabbbabaaabaaaabbbaabbababaabbbabababbbbabbbbaabaaabbaaababbbbbbababbaabaabaaabbabaabaaabaaaabbbbbaaaabbbabbaabaaabaaababaabbaabababbaaaabbbbabbbbaaababbabbbababbaaaabaabababbbbabaaaabbaaabbbaaabbaabbbababababaabbaaabbaaaaabbbaababbaaaaabaaaaababbbbaabbbbbbbbbaabbaaabbabaaaaababbabbabaababababbbababaabaaaabbbbbbaabaaaabbbaabaababbbbabbbaabbbbbabbbbbababbaaaaabbaabaabbbbbaaabbaaababbabbbaababbaabbaabbababbbbbaaaaaaaabababbaaababbaaaaaaaaabbbabbabbbbbabbbabbbbbbbaaabaababbababbabbbbbaabaabaabbaaaabbbaaaabbababbaababaaabbbabbbbabaaabbaababaaabaaaaabbbabbbaaabaabaaaabaabbabbbaaaabbbbaababababbabbbaabbaabbabbabbaaabbbbbaabbbbbbbbbababbabaabaaaaabaaaaabababbabbabbbabaabaaababbababbaaabbaaaaaaaabbaaabbababbbabaabbbbbaaaababbbbbaaabbbaabbbbaabababaabaabbbbaaaaabbabbbabaaabbbaaaaaaabbaababbbaaaaabababbbbaabaababbbbbabbabaaabaaabbabbaabababababbaabaababbbbababaaabaabbbaaababbbbbabaaabbaabaabababbbabababababbaabbabababababbbbbaababbbaaababaaaaaaabaaabbaaaaabaaabbabaababbbabababbbbaababbbabbbaabbaaaabbbbaaabaabbaabbbbbbaaaabbaaaaababbaaaaaaabbaabbbabbbaabababaaaaabbabbaabbababbaaabaabaababbababbbaaabbbbbabbaaabaabaaaabbabaaaaaaabaaabaaaaabbaaabaabaabbbbbabbbaaabbaaaabbabbabbbaaabbaababaabaabaaaaabbabbbabbabaaabbabaaabababbbbbbaabbaabaabaaaabaababaabbbbaababaabbbaabbbbabbaaabbaaabaabaaabbaaabbaaabbabbabababbaabbaababbaabaabaabbbabbabbaababaaaabaabbbaabaaabbaaabababbaaabaaaaabbbabaaabaaaaaabbabbbbababaaababbbabbbabbaaaabbbbbabbbbaabbaabaaababaaabaabbaabbbbbaaaaaabbaaababbabbbaabbaabaabbbaabbaaabbbbaababaaaaabbabaabaaabbababbaaaaabbabaaaaabbaaaabaababbababbabbababaaaabbababbaabababbbbaaabbbaaabbbabaababaababbbbbbbbaaaaabbbaaabaaaaabbbbbaabbaababaabaabbbaaaabaaabaaaabbbababbabbabababbaabaaaaabaabaababaaabbaababbaaaaaaabbaabababbaaabaaabbabaaaabbaabbbbbaaaaababbbbbbbbbabababababbbbabbbabaababbbabbaaabbaabbaabababbbaababbaabbbaaaaabbabbaabaabbababbabbaabbbabbbbabbbbabbbbaaabbbbaaaaaabaabbbabaaaaabbabbaaaabaaabbbabbaabbbaabaaababbabbaaaaaaabbaabbabbaaaabbabbaababbababbbabaaabbabbaaababaaabbababaabbbbaabbbbaabbaaaabaaaaababaabaaabbabbbbaaaabaaaaabbababbaaaaaabaaaabbabaaaabaabbaaabaaababbaabaaabbbbaabbabbaababbbaaaaaaabbbbabaabbaaaabaabbabbbaabbbbababbbbaabababaabaababababbbbbaabbababbbabbabbbbababababbbababbbbbbaabaababbbbabaababaaaaaababaaaaaaaaaabababbbabaaabbaabbabbbbababbbbabbbbabbbbbbbbbaabbabaababaabbbbbbbabbbbbababaaababbbaabaabbaaabbbababababaaaabbbbbaabaaaaaabbbbbbbbbaabaaaaaabaabbababaabbaababbaaaabbabaabbbabbbbabbbaaabababbbbbabbbbbaaabaabbaabbaabbbbaabbbabaabbbaababbaaabaabaabbaabbbbabbbbbbaaababaaabbabbbbbababbbbbbbaabaabbbaabbbbbaabbbababababaabbaabbaaaaabbbaabbabbbabbabbabbbbaabaabaaababbbaaabbabbaabbbaaababbbaabaaaaaaaababaababababbbabababbababbaaabbaaabbabababaabbbaaaabaabaaaabbbbabbabbababbabbbaabaabbaabbbabbabaabbbabaababababaabbbbabbaabbaababbababaabbabbaaababaaabbbaabbbbabbaabbaabababbbbaabbbbbbaaabaaaababbbbabbbbbababbaababbbbabaabababababbbbabaabaaababbabbbbbbaabaaaabbbbabaaaabbaababbaaabbbabbbabaaabaaaaabababbaaabbaaabbabaabbabbaaabbbbbaabaaaabbaaababbbaabbaaaaabbaaaaabbaabbbbaabababaabaababbbabaaaaababbabaaaaaabababbaaaaabaabbbbbbababbbbbbaabbbabbbabbaabaababaaabbaabaaaabbaabaaabbaabbaabbbbbabbaabbbaaaabaaaabbbbbbaaabbbbbbabbaababbbbbababbbbaababbbaaaaaabbaaabbbaabaababababbabaabbabbaababbaaabbbaabaabbaaabbabbbbbabaabbabbbaabaaabbabababbaabaaaaababbbababbaababababbabbbabbbaaabbbabbbaaabbaababaabbabbababaabbabbbaabaabbbaabbbbbaabbbbaaaaaaababaaabababbbbbababbaaaabaababbbbabaabaaababababaaabaaabbaabbaaabbbbababbabbaaababbbbbabbabbbababbbbbbabaabbbbabbaababbbbabbbaaabbaaabbabbaaabbaabaaaabaabaababbaababbbaabaaaaabaaabbbabbbbbbaabbbbaaaaaabbbbaaaabaabbbbbaaabbaaaaaabbbabaaaaabbbaaaabbabbabbbbaabaaababababababbababbabaabaaabbbaaaabaabbaabbaabaababaabaabaabbaaaaaabaabaaababbabbabbbaaababababaabbabaabababbabbbbbabbababbabbbaaabbabaaabbbabaaaaaabaaaaabababbaaaaaabbaaabaababaababbaaaaabbaaaaaaaabaabaaabbabababbbaabbabbbababbaaabaabbbaaabbaabbabaaaabababaaabbbababaabbbaabbbbbbabbbaababbaaaaabbbbbbbbbabbaaabaaabababaaaabbbbbabaabbaaaabbabbaabbabbaaaababbbaabbbabaabbaaaaaababbbbbbabbbababbbbaaabbbaabbaababaabbabbabaabaababababbabaabaaaabbbaabbbbbabbbbbaaaaaababbabbabbaaaababbbbbaabbbaaabaaaababbbbbbabbaaaaaaabbabaabaabbaabbaabbbaaaabbabaaaabbbbbaabbabbabbabaaaaaaaabbbbaaaababbbbbaabbbbababbbabbbaababbabaabbaaabaaaabaaaabaaaaaabbbabbabbabbbaaabbbbbbbbbbaaaaaababaaabbabbbaababbbabaaaabbaaabbbbbaabbbababaabbabbbabbbbaaaaabbabbabbabababbaaabbbbaababbabababaababbaaaaabababbabaaababbbaabaabbaabaaaaaaabbbbbbabbaabababaaaaabaabbaaabaabbaaabaaaabbbbaabaabaaaabaaabbbbaababbbbbbabbbaabbaaabaabababbaabababaababbbbaabababbababaaaababbababbbabbbabaaaabbaaabbbababbbaaaababbbbbaaaaaababbaabaabababbabbbbbababbaabaababababababbabbbaabbabaabaababababaabaabbbbaababbbaabbabaababaabbaaaaaabbabaabbabbbaababbabbabaaababbbbbabbaaaaababababbbaaaababbaababbababbaaaaababbbabbaaabaababbaabbbbabbbbabababbbbbabbbbaababaabbabaaababbaaaabbbbaaaabbabaaababbabbbabbabbabbabbaaabaabbaaaaaababaaabaaabbaaabbbbbabaabaaabbababaabbabbababbabaaabbbababbbbbaabaabbabaaabbbbbabbbaaaaaababbbabababaabaabbbbaabbababaaaabbbaabababbbaabbbabababbaaabaabbbaaaaaabbabbbbaababaaababbabbbaaaaaaaabaabbaaaaabbbbabbbbbbaaababbabababbbbababbaababbabbaaabbbabbaaaabbbaabbabaaaaababaaabbaaaabbabaabaabbabbaababaaaabbaaaabbabaaaabbbaabbbbbabbbbabbbaaabaabbabaababbbbbbbbbabbaaababbabababababbbaaabaaabbaabbaaaaaabbaaabbabbbbbaabaaabaaabbbabbbbabbaaabababbabbbbabbbababaaaaababaabaaabaaaaaabbbaabbaababbbabaabaaabbababaabbbbaaabaabaabbaabaaaaaaaaaababbbbabbaabaaababbaaababaaaaaaaaabbbbabaabaabbbaaaaaabbbbbbbabbaaabbbabaaaabbbbaaaaabbaaababaabbbbaabbaabbabaababbaaaaaabaabaaaabaaaaabbaaaaabbbaaabbabbaaaabbbaaaabbabbbaaaaaaababbbbaabbbbabbabbabbbaabaabbaaabbabaabbaabaaaaaaaabbababbbaaaabababaabbabbabbabaabaaabbbabbbabaaabbababbaaabbababbaabbbaaabbbabbaabbaaaaabbbbaaabaaaababaabbbbaabbaabbbabaaababbbbbaabaaabbbbbbbbbaabbabbbaaababababbbbbabbaabaaaabbbbabbbaabbbbababaabbabbabaabbbababbbaabbaaaaaaabaabaaaaaababababaaaabababbbabbababbbbbaabbbaabbbbabbaaabbabaabbbaabbbabaaaabbabbbabaaabaaaaaabbaababbabbbabbaabaaababbbaabababaaaaaaabbbbbaaaabbabaaabababaaaaaaaaabaabbbbbaabbbabbabaaaaababbbbbbabbabaabbabbbaaaabbaaababbabaaaabbababaaabbbaaababbababaabbabbbbbbbbabbbabbaabbabbabbbabaabbbabbababaaaaaabbbabaaababababbbbbbababbaaaababaabaabbbaabaabaabbbababbbaaaaababbaaabaaababbabbababbbabbbbaababbaababbabbaaaabbbaabbaabbaaaababbbbbbabbbbabbabbababbbaaaaaabbababbaabbabbbbababbababaabaabaaaababaaaabbbabaaababaaaaabaaaabbbabaaaaaabaabbbbaaaaaabaababbbabbabbbbbababbbaabbbbaababaaababbabbbbbbabbabbaaaababbabababbabaabaaabaaababbabaabbaabaaababababaabbababbbbbaaaabbbbbabaaababaaaaaaaaaaaababbbbaabbabbabaaaabaaabaaaababaabbaabababbbaaaababaabababbabbbaabbbaababbaaaabbbbaaabaabaaabbbbbababbbaabaabbaabbabababbabbaabaaaaabbbbabbbbababbabaabbaababbbaaabaaaabaabbbbbabbbabababbaaaaababbbbbbbaabababaabaaabbabaababbaabbbabaabaaababababbbabaaababaabababaabbbababbbabbbaaaababbabababaaababbbabaaaaabbbaabbbaababbabbabaabaabbbbbabbbaabbaabaaabbbbaabaaaabbbababbbabaaabaabbbbaabbbababaabbabaababbbbabbaaaaabbbbbbbbbaaababbababaabbaaabbbababbbbbabbaaaabababbbbaaabaababaaaaaabaaaaababbbbaaabaabbbaaabbabbabbbabababaabbbbbbaaabababbbaaaabaaabbababaabbbbabaababababbabaaaaababaaaaaaabaaababbbbbbaaabbbbbbabbaaaaababbabbababaababbbabababaaaabaaabaabaabbababbababaabaabababbbbbbbbbabababababbabbabbbbbbbbbabbbbbaabbbaabbaabbabaabbbaaaaababaabbabbbaabababbababbbababbbbbaababaabbbbababbbababbbabaabbbbbbaaaaabbabbbbbaaabbabbbbbbbbababababbbaaabababbbbbbbaabbababbbbbabbbaabbaaabbbbaabaaaaaabbaabbbbbabbabbaaaaabbbaaabaaabababbabbbaaaabbbabbbbbbabbbabbbaabbaaababbababaaabbaabbabbbaababaabbbbbbbbaaabbaabababbbbbabbbababbabaabbbabbbabbaaababbbbaaabbabbabaabbabbbabbaabaabbbbaabaabbabaabababbabbbbaababbabaabaaaaabbaaabbababbababbbbaaaaaaaaaaababbbbaabbaaabbabbbaababbbabaababbbbabbbaabbabbabaaaaaaaaabbabbbbbbabaababaaababbaabababaaabaabbbbaaaabbbbabaabbaabbbbbaabaaabbbaabbbabbaaaabaaabaabababbaaaabbabbbababaabbaabaaabababbabababaaabbbbaaaababaababbabaaabababbbaabbbaababbbaabaaaabaaaaaaaabaababbabbbbaabbbaaabaababbabbbbabbaaaaaababaababbaaabbababbbbabaaaabbbbbbababababababaaabbbabbaaaabbbaabaaabaaababbaabbbbabaabbbbbaabbababbbabaaababbbaabbaaaabbbbababaaaabbabbbbaabbaabbabbaaaaaabaabbabbabbabbbababaaaaabbabbbbaaaababbbaaabbbbaabbaababbaaaaaaabbbabbbbbbbbaaaaaabbabaabbaababbbaaabbabaaabbbabaaabababaaaaababbbabbbbbaabaabbbbababaabaababbbaaaababbbbbbbaabbbbababbabbaaabbabaabbbbabbababbbbabaababaaabababbabbabbabaaabbbbbababbbaaaababbbaaabababaababaaaabbbabaaaababbabbbabaaabbabaabbbbbaabaabaabbbbabaaabaababbaabaaabbbbbbabababaaaabbbababbbbbbbaabaabbbabaaaaaabbbaaababaaababbbabbbbaabbabbbaaaababaabbaabbbaaabbbabbababbabaaabaaabaababbbbbbbababaaababbbaaabaabbabbbbbaaababbabaabbbbbaaabbbbbbbaabaababbbaabbababaababaaababbabaaabbbabbbbbbbaaaabbabaababbbbabbabbaaaaabbbbaaaaabbaaabbababbbabaabaaaabbbaabbabbaaaabbbabbaaabbabbababaaaabbaabbaaaaaabbabaababbbbbbbbaaaaabaabaabbaaaabbbbbbbabbbabaaababaaabbbbabababbabbbabbaabaababbbbbbbaabaaababbaaaabbaaabbbaabaabbbaabaabbbbbaababbaabbbbaabbabaababaaaabaabbabaaababababbbaaababbbaaababbabaaaababbbbabbaaaaabaabbaabaaabaaabbbaaaababaababbbaababaaaaaababaabbbbaaabbaabbbbbbbabaaabaaaabbbbbabbabbabababbbbbabbbaababbbabaabaaabaaabbbbbbabbabaaaaabbbaababaabbaaaababaababbbbbbabbbbaababbbabaaaabbaaaaaaabaabbaaaaababaaaabbabbbbababaaaabbaaaabbabbbaaabbabbbaaaababbbaaababbaaaababaabbaaaaaaaabbababbaaaaaabaaaaabaabaabbaababbbbbaaaaabaaabbababbbaaabbbaabaaababababbbbbbbabbbaababaaababbbbabbaabbaaaaabbbbaabaabbaabaababbaaaabbaabaaabbaaabbbababbaaaaabababaabbbaaaaabbbaaabaaabbabbbbaaabbaabaaabaabbbbaabbbbabaaabbabaabaaaabbaaaaabaabaabbaabbaaababbabbababbaabaabaabbaababbabbbaaaabbbaabbbbbababbabaaaaaabaabaabbaaaaabaabbababaababbaabababbaabaabababbbababbaaaabbaabaabaabababbabbabbabbbabaabbaabbabbbbabbaaabaaabbbbabaaaabbabaabaabbaabaaabbbbbbabbbbaabbaabbabababaaababbbaaaaaaaabbabbaabbbbbaaaabaababaaabbabbbaabababbaababababaaaaaaabbaaabbaaabbabbabaabbbaababababaaabbabaaabbababbabbbabbbbbabbbbbaabbbbbbbbbabaaaabababbbaabaaaaabbaabaaabbbbabbababbbbaabbbbaaaabbaabaabbbabaabaabbbbbbbabbbbbabbabaababbbbabbaabaabbaaabbaaaaaaaaaaabbbbbaabbbbaabbbbbbaabaabbabbaaaabaababbbaaaaabbbbbbbabaaabbbabaabbaaabaabababbbaabaaaabbbbabababaaaaabaabbbbbbbaabbabbaabbbabbbbabaaabaabbaaaaaaaabbaabbbabbaabbabbbaaabbaaaaaabaabbabaaaababbababbbbbbaabbaabbbbabbaaabaabaaabaaabbabaaabaaabaaaabaaaababaaabbbbaabbaaabbabbabababaabbbbabbbbbabbabbababbabaaaabababbbbbbbbaababababbbababaabbabaabaabbbaaaaaaabbabaababaabbaaaabbbabbaabbbbbbaababbbbbaaaabbaabbabbababbbbaababbaabbbabaababaabbbabbabbbaaaababbbbbabbaaaabbbaaaabbbbaabbbbabbbbaabaaabbbabaabbabbbbaaabbbbaaaabaabbaababaabbaaabbbabbabaaabababbabbbbabbbbabbbabaabbaaaaaaaabaababababbbabbbaabbbbaabbbababbaabaabbababbababbbabbbbbaaababbbaaaaaabbabaaaababbbababbababbaabbbbababaaabbbaaabbbaabaaabbababbbabbbaaaababababababbabaabaaababaaaabaabbbaaabbaaabbbaaabababaaaabbaaaabaaaaaabbbbbabbaaabbaabaabbbbaabbabbbaaabbabbbbbbaaaaaaabbbaabbbbbbbabaaaaabbbaababbbababaabaabbbabbbabaabbbabbaaabbbabbbaabaaaaaabaabaabaaaabbbbbabbbbbaaaabababbbabaaabbabaabababbbabaabbbababaaaaababbaabbbbbaaabbabbabbbbabaabbbaaaaabbbaababbbbbaaabbaaaababbabaaaaababbbabbbabbbbbbaaababbaaabaaabbaaabaabaabaabbbaaababbbbbbbbababaaaabaabaaabbbabbbaababbabbbbaaababbaaabbaabbbaaaabaaaaabaabbabaaaaabaababbaabbaaabbbaabbababaaababbbbbbbbabbababbbaabaaabaaaaaaaaabbbaabbbbbbbaaaabbbaabbaabbaababbaababaabaabbabbbaaabbabaaaaabaabbaabbaabaabaababaaababaaabaaaaabaaaaaabbbbabbaaaaabaaabaaabaaabababbaaabbbabbbbaabbbaaaabababbbaaabaabaabaabbbababaaaabababaabababababababbaabbbbabbaaaaaaaabbbbaabbbabbaaaaabbaabbabaabbbbaabbaababaabbaabaaabbbaaaaabbaabbbaaaaaabbbbabbbaaaababaabbabaabbaaabbbaaaaababaaaabaaaababaaabaaabababbbbaaabbbbaaababbbaababbaaaababbabbaabaaabaabbbbbabbabaaabaabaabaaabbaabaaabababbabbbbababaabbbbabbbbababbbbbaabababaaaabaabaabbbaabbbbabbaabbbababaabaaaaabbbbabbabbbabbbbabbbabbbabbbaaaababbbbabaabaaaababbabaaaabababbabbaabbababababbaaabbbbbbabababbaaababaaabbabababaabaababaabaaabbaabaaabbbababaabababaabbbaaaababaabbbbbaaaaaaaabbbabbbabbbbaaaaaaaabaaabbbaabbbbbbbaaabbbabababbbaabbababbabaaaabaabbbbaabbabbabbaabbabbbabbabbbaabaababbbbaabbaaabbaabbbabababbbabababaabbbaaabbbbaabbbaaabbabbaaaaababbbbababbbbbaababbababbaabbbbaabaaabaabaaaaaabaabbaaaabbabbbbbabaababaabbaaaaaaaababbbabbbbbabababbaaabbbbabbabbbbbabbbbabaabaaabaaababaabbaaabbabbbbbbbabaabaaaababbbbaaaaabbaabaaabaabababaaabbaaaaaaabbaaaabbbaaababbbaabbbaababbbaabaababaabaaabbaaabababaaaaabbbbabbaabbbbbabaaaaabaabbbbbbabaabaabbbbbababaababababaabababbbaaaabaabbababbbbbaababaaabaaabbbbbbbbaaababbaaabbbbaaabbaababbbabaabaaaabbbababbbbbbaaaababababbbbbaaabbaaaababbbbaabbababaababbaaaaaabbbababbbbaabaaabaabbbabbbaabaabaaabbaaaababbaabbbbaaabbababbaaaaababbabbbbabbaaaababbaaaaabaabbaaaabaaabbaabaaaabaaabbbbbaaaaaabaabaaabaaabbbbaabababaabbabbabaabaabaababbaabaabbabaabbbbabbbaabbbaaaabbbabaabbbabbbaababaabbaabbabbaaabbbbaaaaaaaababaabaaabaabbbbabbaabaaabbbbabbbbabbbbabaababaaababbbaaabaabbabbbabaabbababaaaabbaaaaaabbbaaabbbbababaaaaabbbbbbabaabaabaababbbbabaabaabaaaabaabaabbababaabbbaaabbbabbabababbbbabaabbabbbaabbaababbbbbaaabbbabbaaaaaabaaaababbbaaaaabaaabaabaababbabbbbbaabbbbaaabbabaababbbabbabaaabababbaabbaaaabbbabbaaaaabbababbbabababaabbbaabbaababbbbbababbabbbbabbabbbbbaaabbababaabaabbbabbbbbaaabbaaaabbabbaabbbbaaabaaabbbbbbababbaabababbbabbaababbbabbbbbaaaabbbaaabbaabbaabbbbbbabbababbababaabbaaaaabbabbbaababababababbbaaaaabbaaaabaaaaaaababaababaaababbabaaababababababaabbabbaaababbaabbaaaaaaaaaaababaabababaababbabbbbabaabbbababbbbbababbabaabbaababbbbaaababababbbabbbbabbabaaabbaabbaababaababbbaabbbbbabbbbababbbabaaaaabbabbababababbaaaaaabaabaaaaabbaabbaaaabbabbabaaaabbbbabbbaaaaaaababaaaabaaabbabbbbbbbbbaaabaabaaabbbbbbbbabbaababaabbaaabbababaabbabababbaabababbaaabbaaaaabbabababbbbbbbbbbaabbbbbabaabbbbabbabbaabbabaababbabababaaababbabaabbabbbabaabbbbaabbabbabbaaabbbbabaaabaaabbabbaaaababbbbbbbbbaaabbabbabbaaababaaabbaabbababbabbbbbbbaabbbbbbbababaabbaababbbbabbbbbbaabababbaabbaabbbbbbbaaabbbbababbababbbabaaaaaaabbaaaaaaababbbaaabbbabbbbbbbbaababbaabbbbbbbabbaaabaaabbababbbbababaaaabababaabaaaaaabaaaabbbabaaabbabbaababbbabbbaaaababaabbbaaaaabaaabbbbbbaaaabaaabbabaabbbaaababaabaaababbababaaabbaababbaaaaaabbbbbaabbaabbbbaaababbabaabbababababbbbbbbbbbbabaaaabbbbabaabbaababbabaaabbaabbbbbaabaabbaaaabbbbabbbaabbaaaabbbabaaabbabbaabbabbabaabababababbaaabaabbabaabbabaaabbabbaabbbabbbbabbbabbbbbabbaabbabbababbbabbbbbabbbbbbaabaabaaaaaabaaaabbaababbbababbabbbaabbaabbaaababbbbbabaaabbabbabbaaabaaabbabababbbaabbbbbbabababbabbbbabbabaaaaabbaababbaaaababbaaaaabaaabbbaababbbbabbbbbabbabbabaaaaababbabaaabbbabbbabaaabbaababbaababbbbabbbaaaaaaabbbababbbabaaabbbaabbbbaabbabbbbbabaaaabaaababbbbbaaababaaaabaabbbbbaabbbbbabbaaaaaaaababaaabaaabbbbbabaabaaaaaababbbabababbaaaaaabaabbbababbabaaaababbbaaababaabbbabbaaabaaaabaabaabbabaaaaabaabbabbaabaabbbababbabaaaababbaaaaabbbaabbbbbaaaabbbbbbbabaabaabbbbaabbaaaabbbababaaabbbaabbbbbbbbaabbaabbaabaaaababbbabaababbaabbbaabbaaaabbbaabbbbbaabbbbaabbbaaababbabbababaaaaaaababaabbbabbababbaabbaabbbbbabbbbabbabbbbababbababbbaaabbbbabbbbaaaaaabbbbbbbabbaaabbaaabbbaabaabbaabbbbbabaaababaabbbbbbbaaabbabbbbabaabbaaaaabbbbbbbabaabababbaaabbbaaaabbbaaabbbabababababbbaaaaaabbbaaaabbaababaaabababababbabbbbabbabbaabbaaaabbbbbaabaaababbaaaabbabbabaabbaaabaabaaaabaabaabbbabaababbabaaaabaaaaababaaaaaabaaabbaababbbbbbbbaabbbbabbbaaababbabaabbababbbaabbbbbbbababaaababbbbabaabbbbabaaaaaaaababababbaaaaaabbbbbabbababaabaabaabbbabbbbaabaabbaabababaabbaaabbaabbaabaabbbaaabaabababaababbbaaabbbaabbaabbaaabbabababaaabaabbabbbbaabbabaabbbbbabaaabbbabbaabaabaabababaabaaaabbbbbabbbababaabbbabbbababaababbbaaaabbbaabbaaabaaabbbbbaabbaaaaaabbabbbabaabaaaabbbabbaabbbabababbbaaababaaaabaaabaaaaababaaaabaaaababbbabbbabbabbbbaabbbaababaababaababbbababbbbbaaababaabbabbbaaaabbaaababbaaababbbaabbabaaabbaaaaaaaabbaaaaabaaabbbabaabbaabbbaabbabbaabaabbbabbbabbaababbbabababbbabbabaabbabaaabbbaabbbabaababababaaabaaaabaabaabababaababaaabbababbabbababbbbaabbbbaabbabbaabaabbaabaaabaaaaaaabbbbbabaabbbbababbabbababbabbababbabaaababbababaababbabaaaabababaaababababaabbbbaaaabababbabbbbbbaaabbabbaababbbaabbabaaabbbaabaaaaaabbaaaaaabaaabaaabaabaabababbbbbbbaabbbbbaabbaabbbbabbabbbababbbbbbbbabbbababbabababbbaaabbbabaabbaabbbbabaaaabbabbbaaabbaabbaabbabbbaaaabbaabbbababababbabbaabbabbbbbbbaaabbbabaabaabbbaabbabbaaaaaaababaababbbaaaabbabaaaaabaabaaaaaaaababbabbaaaaaaaaaabaaababbaaabbabababbaabbbababbaaaaaababbbbbbabbaabbbbbaaababbabbaaaabbaabaaababbabaabbbbaaabaababbbaaabaabbaaabaaaaaaabbbbaabababbaabaabbabaabbbaaabaaababbaaaaabbbababbaabbabababaabaabbabababbabbabbbabbabbabaabbaaabbbaababbaaabababaabbbabbbbabbbbaabbbbaaabbbbbaaaaaaabbabbbbaabbbbaabaaaaabaababbbbabbaaabbbbababaabbaaababbbabbbbaaaabbababbbbbaabbbabbaabbbbabbbaababababbbababbabbaabaaabbabaabbbbbaaaaaabbbbbabbbbaaaaabbbbbaaaabaaaaabbabbabbabaababaabbabbbbbbbbbaaabababbbbbabbaabbabbabbaaababaabaaababbabbbabbababbaabbaaabaabbbbabbabbaaabbaabababaababbbbbbbbbaaabbababbbabaaaaaaaaabaaabbababbbbbabbbbaaaaaaabbabbabbbbababbaaabbaabbbaabbaabbaaaabbaaababababaababbabaabaabababbabaabaabaabbbbabaaababbaaabbabbaaababaaaabbabbbaaababbbbbaabbbaabaaabbbabbabbaabaaabaaabbabaaabbbababaababaaababbbbbbbabbbbababbaaaabbaabaaabbaaabbbababbabbababaababbaabbbabbbababaabbababbbbaaabbbaabbbbbaabbbbaaaabaaaaaaaaababbaaabaababbbbaabababaabaababababbabbaaabbaabaaaaaaabaaababaaabbbabaaababaaabaaabbbaaaaaababaabbbbabaababaabaaaababbbaabbaabbaaaabbbabbbbbbabbbbababbabbbbbbaaaaabbbaabbaaaabbbbaaaaaaababaaaababaaabbbabbabaabbabaaaaaaaaaabaaaaaaaababbbababbbbbaaabbabbbabbbabbaabbabbaabbabaaabaabbabaababbbbaaabbaaaabaabbbbbbbaabbbbbaabaaabbaaaabaabaababababbababbaaabbaabaababbbbbbabbabaaabbaaaabaaabababbaabababaaabbaabaababababbaabaaaabbbaabbabbabbaaaabaaaaababbbabbbbaaabbbabbbbbbabbaaabbbbabaaabbbabbbabbbbbbabbbbbabbaabababaabaabbaaabbbbbbaaabbabaababaabbbbabbbaaabbabaaaababbbababbbababbbababababbaaaababaabaaabbbbbabbabaaaaababbbbabaabbbabaabaabbababbbaabbabaaabaabbbaaabbaaababaabbaababababbbbaaaaabbbbbaaaaaababaababaabaabbaabbbabbbbaaaaaaaaaaabbbabbbbaaabbbbbabbabaaabbbabababbbaabbaaabbabbaaabaababbaabbbbbbbbaabbaaaaaabaabbabbbbbbbaaaaabbbabaabababbaabbaaaabbbbaabaaabbbabbaaabbbabbbaabaabababaaaabbbbaaabababbaaaaabaabbbababbbbbaaababbbababbbabaaaabaabbabbbaaaaaaaababbaabababbabababbbabbaaaabbbbabbbbabbbbabbaabbbbbaaabbbaaabbbaaabaabbbbaaaaabbbbbabaaababaaababbbabababbbbbbabbbbbababaaabbbbbaabaaaabaaabbbbababaabaabaabbbaaabababbbbbabbbabbbabaabaaababbbabbababaaaabbbaababbaababbbbbbbbbbbaaaabaabaabbaaabbbbababababaaabababaaaaabaabbaababbbaabaaabbabbaaabbbababbabbababaababaaaaabbabaabbbbbbbbbababababbaabbbaabbaaaaababbbabbbbbbbaabaaaaabaaaabaabbbbbababaaabbbaaaabbbaaabbaabbbbbaabaaaabaaaaabbaaaabaabaaabbbaaabaababaababaaaabaabbbbaababaabbaabbbabbbbaabbaabbaababbbaabaabaabaaaaabbabbabaaaaababbaaabbaababbabababbaaabaaabbaaaaaabbbaaaabbbbababababbabaaaaabaababaaabaabbaabbabbbaababbbbabaabaaaabbababbbbaabaaabbaaabbbbbbbbabbabaaaabbbbabababbabababbbbaaaabaaababbaabbaabababaaaaabbaabbbbababababaaababbbbaaabaaaaabbaabbbaabbbbbabababaaaabaaabbbbbbbaaabbabbbabbbbbababaabbbaaaabaabbabbbbababababababaabaabbbabbbaabbbbabbbbbbbbbbbbbabbaaaaabbbbbabbbabaabbbbbaabbbbabaaabbbaaaabaabaaaabaaabbbaabbaaabbbaababbabababbbabaaababbaaabbabbabbaaabbbabbababbbbbbbbaaaaabababaaaabbaaababbaaabbaabaaaaaabaababaabaabbbabaaaaaaaababaabbbbaabbbbabbbbabaaababbabaabaaaaabbbabbababbababbbbbbbabbbbbbaabbbbbaabbbabaabbaaaababbbbabaaaabaabaababbbabbabbabbbbaabaabbabababaaabaaababbabababaababaabababababaabbababbabaaabbbababaaabbabbabbaabaaabbaaabbabababbaababbbaaaabaaabbbbaaababbaabbaabbbbbabbbbbbbaaabaabaaabbbbaabbaaaaabbbabaaaaabababbabbbbabbabbbbbaabbabbbbbbababbabaaaaabbabbbbbbbabbbbabbbbbbbbbbababababaabaabaaaaaabbaabaaaaaabbaaaabaabaaababababababbbbbabaababbaaaabaababababbabbbbaabbaabbaababbbbab
baaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaabbaaaaaabbbababaaaaaababbaabaaababbbbbaaabbbbbbaaaaaaaabaaaaaabbbaaaababaabbbbabbabaabbbaababbbabbaaaaaababbbaaabbaabbaaaaaaaabbbaabbbabbbababbbababbabaababbbbbaaabbbbaaaabaabaababababbbbabbabbaaaabaabbaaaaaabbbabbbabaabbabbaaaabbaaabbaababbbaabaaabbaababaaaaabaaabaabbbbabaaaaababaabaaaaabaaabbaaaaababbbaaabaaabbbaaaabbbaabbbabbbaabaababbaabbbbababbaabbbaabbaaaaabaabbbbbabbaababaaaabbbabbbbbbbbaaaabbbbabababbbbbbabbbabbbabbbababbabbabbbbaaabbbbbaabbabbbabababbaabababbbbbaabaabbbbabbbabaaaaaaabbbaabaabbababbaaabaaaabaababbbabbaaabbabaaababbabaabbbaabbaabbbabaaaaababaabaaababbbabaabbbbbbbabbbbabbaaabaabbbbaaaabbbaabbaaaababaabaabbababaaaabbaababababaaaabbbbbbbabaaabaaaabbbaaaaaaaaabababaababbbabaaababbbaababbbaabbaaaabaababbababaaaabbbaaaaaaabbbabababababaababbaaabbabaaaabbaabbaabaabaabaaaabbbabbbababaaabbabababaabbbaaababbaabaabbbbaaabbbbbababbababaabbbabbbbabbbabababbbbbbbbaabaabbabaabbbbbaabbbbbabababaabbaababbbbbbabaabbaaababbaababbaaabbbaaabaabbbabaaabaabbbaaaabaaaabbbbbbaaaabaaaababbaaabbaababbabbaababbaabbbababbaabababbabababbbbaaaaabbabaababaababbbabbbbbaaabaaaabbbbbbbabbabbaaaabbbbabbababbbbaabababaababababaabaabbaabaabbbbababbaaaaaaaabbababbbbaaaababbbabaabbbabbbaaabbbaabaaabbaaabbbabbababbbbbbbbababbaabbabbabaabbaaabaabababbbabbaabaabbbbabaaaabbbabbabbabbbbaabbababababababbbaabababbbabbabbaaabaaaaaaabbbaaabbbabaabababababbbbabbabbbbaabbababbabaabaaabababbbaaabbababbbababbbaaaabbbabaaabaabaaabbabbababaabbbaabbaabbbbaaabbabbbbbabbbbabababbabaaabbabbabbaaaabaabaaabbabaabaabbbaaaaabaaabbbaabababababbbabbaabbbaaabbbababbbbaabaabaabaabaaaaaabbbbbababbbbbbbabaabbabababbaaabaaaabbaaaabaabbabbbbbababaaaaabbababbabaaabaababaaaabaaaabbabbbbabaabbbbbbaabbbabbbbababbaababbaaabaaabbabaaababaabbabbaabaabaaabaabbbbabbabbaabbbaabaaaaaabaababbaaabbaabaabaabaabbabbaabbbaaabbabbbabbabbaabaaaaaabaababbaaaabbbbbabbbbababaaaabbbbaabbbbbaaabaabbabbabbababbbabaabbbbbbbbaaaababbbbabbababbaaaabaaaaaaabaabaababbaaabbaababbbaaababaaabaaabbbbbaaabaaaabbaaababaabaabaaaabbbaababbaaaabaaabbaaaaabaaababbbabaaaabbaabaabbbababaabbbababbababbaababaaabababbbbabababaabababbabbbabaaaababaabaaaaabbaabbbabbbaabababbabbbbabbaaaabbaaaabbabbbbabbabbabbbbbaaaabbabaaabbaaaabbabbbaabbabbbaabbabaabbbbaabbabaabbaabaabbbbabbbbbaaaabbaabbabaaabbbabbaaaaaabbbaabbababaaabbaabaabbbbbaabaaabbabaaabbbaabbbabaabababaabaaababbbabaaabbbaaabbbbaabbbbbbbbbbabbbaaaaaabbbabababbaaabbbbbbbaaaabaabbababaabbaaabbbbbbbabbbbaabaabbbbbbaaabbbabbabbaaaaaaaabbaaabbaaaabbaaaaabbabaaabbabbbbbaabaaaabaabbaaabaababbbababaaabbbbbaaaabbbaababbaaabbbabbbabbabaabbbaaaaaabbbaaaaaabbababbbbaaaaaababababbbbbabaaabaaababbbabbbaabbbbaabbbbabaabababaabbabbbaaabaaabbabababababbabbbbbaabbbababbaaabaabbaaaaaaaabaabbabbbbabbaabaabbbbababbabababababbababbbaaabaaabaaaaabbaabbbabaabbbabbbbaaabaabbbbabbaabbabbbababaabababbbbbaabbbaaaaabbbababbbaabaaaaaabaabbbaaaabaaabababaabbbbaabbababbabbaaaaaaabbaaaaabbbbbbaabbbaabaaaabbbaababaaaababaaabbabbabbbaabbbaabaaabbabaaaaaabaabbaaababbbabbaabbbaabbbababaaababbaaaababaabaaabbbbabaababbabbbababbabbbbababaaaabbbaaaaaaabaaaaaaababbbbababaaaaaabbbaabbbaabbbbbbabaabbbabbaaabbaaaaabaabbaaabbabbabbabbbbabaabbabbbbaabaaabbaababbaababababbbbabaaaaabbbbaaababbaaaabaaaababbaabbbbaaababbabbabaabaaabbbaaaaaabaaabbbabababaababbbabbbababbababaabbabbbabbabbbabaabbaaabaaaabaabbbbbbaabbbbaabaaaaabaaaaababbbbbabbbaaaaaababababbaaaabaaabbbaababbaababaabbaababbbabaaaaababbaaaabbabaaaabbbbababbabbaabbababbbbbbabaaabaaabbbbbaabaaabbaaaaaaaabbabbbaababbbbaabbaabaabaaaaabbaababaaabaaababaaaaabababaaaaaabbbabbbbaabaaaabaaabaabaaaababababbaabbaaababbbbabbabaaabbbbbaaaabbabaababbaabbbbbbbbbaaaaabbbbbabbaaaaaaabababaabbabaabababbbaabbabbababbbbbbabbabaabbbbababbabbbababaaaababbbaabbbbaaaabbabbbbabbaababbabaaaabbbabbbaaaababaaaabbbabaabaaaaaaabbaabbbaaaaabbbabbbaabaaabbababababaaabbaababbbabbaaababaabaabaaabbbbbaaabaabbababbabbbaaaaaaababaaabaabbbbababaabaaabbbbaabbbbbbbbaaabbbbbabbaaaabababbbbbbbbbababbbaabaaaaaaababbaababbbabababaaaaaabbaabaaaaaabababbbbabbbbbaaabababbbabbbbbaabaaaaaababbbabbaaaabbbbabbabbbaaaaababbabbabaabaabaaabaabbbabbbabbbabbaaaaabaabbaaaabbaabaaaabbaabaaaabaabaabaaabbbaabaabbababaabbaaabaaabaabaabaaaaaaaabbababbabbbabbbaabbbabbabbbaaababbbbaabababbabaaabbabaabbbabaabbbbbabbaaabbbbbbaabaabaaabbbbaaaaaaaaababbbbbaabbbaabbabaabababbaaabaabaabbbbbaabaabaabaabaaaaaabaaaaaaaababbababaabbaabbbbbbbabaaabbbbabbbbabbbbaaabaabbaabababbaaaaaabbaaaaaabbaabaabaaaaaaabbaaabaaaaaabaabbabaabaaaaaabbbabbaabababbaabaaabbabaabaabbbaababbaabaaaaabbbbbbaababbaaabbaabababbababbbaaabaabaaabbbaababbababbbbabbabaabbbbabababbbabababbaabbbbaaabbabbbbaaaabbabbabbaabbbbabbbabbbabababababaabbbbbabaaababaaaabbabaababbbbbabaabbabbabbbbbbbaabaaabbbbbaabbbbbbababbbbbaabbbaababaaaabababaabbaaaaaaaaabbbbbaaaaaaaaaaabbaaaaaabbbbaabaabaabaaaabbbaaabbbbbbbaaabbabaaabbaabbabbabbaaaabbbabbabbabbbabaabbaabaabaababbbbaabbaabbbaaaaaabaaaabbbaaaaabbaabababbaaabaabababbbbaaabbaabbbbaaabababaabaabbaaaabbabbbbbbbbaaaabbaaaabbabbbabbbabbaaabbaabaaabbbbababbabbaabbbabaaaabababbbaaaabbbbabaabbaaaabbaabababbbaaaabaaaaaaaabbaaabaaaabaaababaaaaaabbbabaaaabbabababaaabbbbabbaabbbbabbababbbbaabbbbbabbbbabaaabaabbabaaabaabaabbbabbabaabbabbbbbbaabaaabbaaaaaaaaababbaabaaabababbabaaabaabababbbbaaaaaaaaaaaaaabaabbabaabbabaaabbababbbabbabaabaababbbbbaaaabbabaabababbbbbaabaaaaabbbaabbababababbabaaabbbbabababaababbbbbaabababbabaabbaabababbbaabbbbbbaababbbbbaabababaabbbabbbbbbabaabababaabbbbabababbaabbbabbbbaaabababbbbaaabbabbabbbbbbbbabbbabbbbbbbababaabbabbbaaabaaabbaaaaabbbbbaaaababbaabaabaaababaaabbabaaabaabaaaaababbaaababaaabaababbabbbabbaabaabbbbbabbbbaaaabaaaaabbaabbbbaaabbbbbababababbaabbabbabaaaababababaabbaabaaaaaabbbbbaabaababaaabbabbaababaabbbbaaaaaaaaababbaaaaabaabaaaaaaaabbabaabaaaaabaabbabaaaababbaaabbaabbabbaabaaabbbbbaaaaababbababbaabbaaababbbbbbaababbbaaaababbbabbbbababbababbbabbababaaabaabaabababaaabaabbababbbbbabbabbabbabaaababaabbbbaaabaaaaaabbaaaabbbabaaaaabbbabbbaababbabbbabaaaababababababaaaababaaaaababbbbbabaaaabababbabaaaabaaabbbaaaaabbbbabbbbaabababbbbbaaaabbbaaaabaaaaaabbbaababbbbaaabaababaaabbbababababaabaaabaabbaaaabbbbbbaaabaaaabbabbbabaabbbbabbaaaaaabbaabbbabababbabaababaabaabaaaabbbbbbaaabbbaaababaabbabaabaaabbabaaababbaaabbbbbabbbbbaaababbbbbabbaababbbaabaaababbabababbaabaabbaaabaaabbabaaabbaabaabaaabbbbbbabbabbabababbbbbabababbababbbaabaaabaaaaabbaabbbababbbbababbabbbbbaababbbabaabaaaabbbbbbaaabbbabbbabbaaababbaaaabaabbabbbbabbbabaaabbabbabaabbbbbabbaabbbaababaabbbbababaabababbbbbbabbbbabababbbbabbbbbbbaaaabababaaabaaaabbabbbaababbbbabaaaaabbbabaaaabbbabbabaababaaaaaabbabbbbabbbbababaaaabbbaaabababaabaaababbaaaaababbababbbabaabaababbbabaaabaabaaabbabbabaaabbaaaaabbabbbaabbbaabbaabaababbabbbaaaababbbabbbbababbabbbbbbbbababbabbabaabbaabaabababbabbabbababaaaaaabbaabaabbbbbaaababbbaabbbabaaaabbabbaabbbbabbbaabbaabaabbbaabbaaababababaaaaaababbababaabaaabaababaabababbbabbabbbababbbbbaabababbabbabbbbbaabbbbababbabbbaabbbbababbabbbabaaaabaaaaaabbaababbbbbaababbabaababbbbbaabbbbbaaabbabbbbbbbaaabaabaaaabaaaaaaababbbbbbabaaababbabaabbbaaabaaaaababaabaabbbabbbababbbabbbabbaabaaaaaaaaaabbbbaababbbaaabbbbaaabaaaaabbbbabababaaaababbabbaababababbaaabbbbabbbbabaabababaabbbbabaaaabbabababbbbbabbbabbabbbabaabaabaaabbaabbbbabbbbbbbabbbaababbaaabbbbaaabbaabaababbabbabaaaaabaaabababbbbaabbbababbabbbabbabbbabbabbbbaaaaaaaabbbaaabbbabbabbbbababaabaaabbaaaaabaababbabbaabaaababbaaaababaababbbabbbbbabbaaaaabbbabbaaabaaaabbbbaababbabbbbababbbbbbaabbababbabaaabaaabaabbbbababbabbbabbbaaaaaabbbaabbbabbbaaabaabbabaababbbbabaaaababaaabaaaaabbaaaababbbbbabbabbbaabaaabbbbaaaaaabbaababbbaaabbbaabbababaaaababbbabbaababbabaabaaaaaababbabbbabbbaabbababbabbbaabbabbabaababbbbaabbbbbbbbabbaabbabbbbbbbaaabbbbbabaabbbbbbbaaababbaabaabbaaaabaabaabbbbbababbbbbaababbabaaabbbbaabababababbbaabbaabbbbaaaaabababbbbabbbbaaaabaabbbbbbbbababaaabaabaabaabbaaaaaabbbaaaaabaaabbababbabaaaaababaababbbbbabbbaaabaaaaaaaabbaabaabaaabaaabaaaaaababaaababbaabbabaababbaabbbabbabbaabaaaaaabbbababaabbbabaaaaabaabbbababaaabbbbabaabaaaaaabbaabababababaaaaabaabaaabbbabbbbbaabaaaabbaabbbabbbbabaababaaaabaaabaaabbaaabaaabbbbabbbaaaaabbbabbbbababbbaaababbababaaabbabbabbbabbaababbabbbbbaababbbaababbbbabbababbbbaabbabbbbaaaaabbbbabbbaaabababbaabaabbbaaabbbabbbbbabbbabbabbaaaababbbaabaababaaabababbabbbbbbbbbbababbabbaabbaaabaaabbabbbbababababbabaabbaaaabaabaabbbbabbbabaaabaabaaaababaaabaabaabbbbbabaaaabbbbbabbbbaababaaabababaaaaabbbabbabbbaaabaaabbbaaabbaabaaabbaabaaaabbabaabbbaabbbbbabaaababaaabbaaaabaaaabaabbabababbbbbbaaaabbbabbaaaabbabbaaaabaaaaababbabbbabbaabaabbbabbabbbaaabbbbbbaaaaaaabaaababbbbaaaabaabaabbabbbbbbabaabaaabababbababaabaaabbbababbbabaabaabaabbabbbaabbaaaabaaaabbababbabaaabbbbbbababbbbbbababaaabbaaaababbbbaaaabababbbaabbbbabababbbbabbbaaaaaaabbabbbbbaabbbbaaabaabbbbbbbaaaaaaaaaaaabaaabababbaabbabbbbabbabbbbbaabbbabbbaababbaabbbabbbbbbbbbbbababbaaabbababaaabaabbbabbbaabbbaababbbaaabbbaaaaaaaaaaabaaabababaaaabaabbbababbaaabaabbbbbabbababaaaabaabbababaaaabbbaabbbaaabbbbaabbabbababbabaabbbbababaababaabababaaaaabbaabbbbbabbabbbabaabbabbaababbabbaaabaababbaabbbaabbabbbabaaabbabaabaabaaaaaaabaaabaaaaaaabbbbabbabbbbbabaaaabbababaababbabaabaabaabbbbbbabbbaaabaaababaaaabaaabbbabaabbababbabaababbbbbbbbaabbbbabbabbbbbbbababbbaaaaaababaabaaaaabbaabaaabaabbbaabbaababbbbaaabaabaababaaaaaabbbabaabbabbaaaaabbbaabaabaabbababaabbbbbaaabbbaaabaaabababbbbbaaabbbbbaaabaaababaaaaaaabaabbbbabaabbaaababaabbabbbbbbaaababaabaabaabbaabaababaabaaaaabbaabababbaaabbabbaaabbbbaabaabbaaaaabbbbabbaaabbbaaabbababaaabaabbaaabbaabababbaabbbbbaaabaabbbabaabaaabaabababbbbabbbbbbbaabbbabbaabbaabbabbbabbaababbaaabaabbbbbbaabbaabbbabbabaaababbaabbaabbabbabbabbabbbaababaaabaaabaababbababaababaabbbababaaaaaaababbbaaabbbbabbbaabaaabbbbabbabbbbbbaabaaababbabbbbabbbbabbbbbbabaaabbabbabababbbaaabbaabaaabbbbbaabbababbbaabbabaaabaababbababbaabbabbaabbbabaaabaabbbbaabaaaaaaaaaabbbaaabababbabbabaabbbbababaabaaabbaaabbbbaabbbbabaaabaaaaaaaaaabbabababababaabaabbaaaabbbaaaabaabababaabbababaababbbbbabaaabaababbbbbbabbabbbababababbbabaaabaaaaabbbaabbbbabaabbbbbabbaaabbabbaabaabbaabaabbaaabbbbabbabbbbbabaaaabaaaaaabaababaaabbaaabbaaabbbabbbaabaaaabaabbbaaaaaababababababbaabbabbbaabaababbbaaababaaaaaababbababaaaaababbbbbbabaababaabbbaabaaaabbbaabababaaabaabababbbaaabbabaaabaaaaabaabaaaaabbabbbabbaabbaabbabbabbbbbaaaabbabbbbaabaaaabbaabaaaaabaabbababbaaaabababababaaabaaabbaababaabababababaaabaaabbaaaabbbaabaaaaaababababaabbaaaaaabaaabbbbbaaabbababbbabbbbaababbabaababbbababbabbbaabaabaabbaaabababaaabaabbaaabaaaabbbbabbabbabaabaaababbabaaaababbabbaaabababaabbbaabbbaabaabbabaabbabaaababbaaaabbaaabbaaaaabbaaabbbbbaaabbababaaaaaaabaaabababbaabbaabbabaababababbaaabbabaabaabbbabaaabbbaaabbbbbaaabaabaaaababbaaabbaabbabbbaababababaabbaabbabbabbbbbaaaabbbaaaabbabbbbbaaabbbabbbbbbbbababbaaabbbbaaabbbabaababbaabbbbaaaaabaabababbabaaaaaaaaabaababbabaabbbaabbaabbbaaababaabbaabbbbbabaaaabbbaabababbbaaabaabaabaaabbbaabbbbbbbaaaabbbabaababbabbaaaabaaababaaaabaaababbaaababaababbbabbabaaaaaabababbaaabaaaababbaaaaababbbabaaaabbaaabbbbbbaaabbabbbaaaabbbbbbaaaabbaabaaabbbaabbbbbabbbbbabbabbbbaaaaaaabbbaababbababbabbabbbabbbbaaabaaabbbaaaaaaaabababaaabaaabbbbbaabbbaaabbbaaaabaaabaabaabbbbaaababbbbbaaabbbbabbaaaabbbbbabbbaaabbbbbabbbbbaabababbbababbaaaabaaaaababaabaaaabbbbbababbbaaabababaaaabababaaaaaabbbabbbbabaaaaaabaabbaaaaabbabbbbbbaabbbbabbbaaaabbabbaababaabaaaaaabaabbbabaabbaababbabaabaabbbababababbaababaabbbbaaabbabbaabaaaabaaaaaaababaabaabaaaabbaaabbaaabbbbbaababbabbaaabbbabbbbbabbbbbabbbaabaaaaabbbaaaaaaabbbabbabbaabaaaaababbbaaaabaabbbbbbbaababaabbabbbaaababbaaaaaabbabaabbaaabaabababbaabbaababbaababaaabbababbbaababaabbababaaaabaabbababbbaabaaaabbababbabaaababaabbabbaaaaababaabbbbbaaabbbbababababbbbbaabaaabababaababbaaaabaaabbaaaabbbbaabaabaaaabbbaaaabaaaaaabaababbbaabbbbbabaabababbbbbaaabababbbbbaaabbaaaaabbbabbbabbaaaaabaababbaabbaabbbbbbabaabababaaababbabaaabbbbbbbbbabbabbababaaabbaaaabbaaababbababbbaabbaabaaaaabbbaaaabababbaaababbaaababbaaababbbbaaaababbbabbabaabaabaaabaaabababaaabbbaabbbaaabababaabaababbabaabbbababbbbbaabaaaaabbaabababbbabaabbabaaaaaabbaabbabaabbaaaaaabbaaaaabbabbbbbbbbabbabaabaaabbbbabaabababaaabbbbaababbbaaaabaaabbbbaaaaaabbabbbbbbbbbbabbaabbbbabbbbaabaaabbbbaabbabaaabaaabbbbabbbabbaaabbbbbabbbaaabbbbbbbabbbbaaaaabbaaabaaabaabaabbbbbaabbbaaaababbbbbabaabaaabbbbbaaababbaaaabaaabababaabbbaabbaaaabaaabbbaaaabbbbaabbabaabbaabaababbabbbbababbbaaabbababaaabaaaaaabbaaabbaaababbbbbaabaaabaabaabaababaabaaaaabbbbbbabbaababbabaaabbbabbaaaaaabaaabaaabbbaaabaaababbbbbbbaabaaababbaaaaaaababbaaabaaabbabbbbbabbaaaababaaaabaabbabaabbabbabbaababbbabbabbaaaaabbabbaabaaaababaaabbaaabaaabababbbbabbababbbabbbbabbbaaaababbbaabaabaaabbbbabbabaaaaaaaaaaaabaaaaabbbbbbaaaaabaabbabababbbbababaabaabaaababbbbbabbbaaaaabbbbbbbbbbababaaaababaabbbabbbbababaabbbbbbaabbabaabbabbaabababbbabaaaabbbabbbabaababaaabbaabbbbabaabaabbbaaabbbabaaabaaabaaabbaabbbabbabbabbbaaaabbabbababbaaaabbabbbbbbaaabaaaabbabbaaaaaaaababababbbaaabbababbbabababbbabababbaaabaaaabbaabababbabbababbbbbabbbabaabbbbabbbbbbabbabbabaabbaaaaaaabbbbabbaabbaabbabbbbbbabbbbbbbbaaaaaabbabbbabbbbbaababbaabbaabbbbabbbaabbbabaabbbaabaaaabaaabbabababaabbaaaaaababbbaabbbaaabaaaabbbbbabbabababaababbaabababaaabaaaabbbaababbaabaabbaabbbabbabbaaabaabbbabbbbbaabaaabbbbbbbbaaabaabaabaaabaabaabababbbbababaaabaabbbaabaaaaabaaabbaababaaababbabbabababbbababababbababbbbabaababbabbaaabbbbbaabaabababbbbaaabaaaaabaabbbabbbbabbaabbbaaabaaababbbbababbbaaabbaaabbbbabbbabbaaaababbabbabaabaabbbbababbabaaababbaaabaaaabbabbbababbbaaaaaaababbbaaaabaabaabbbaabaababbaaababaaaaabaaabbabbaaabbbabaaabbbaaaaabbbaaababbaaababbabbbbaaabbbbbaabbaaaaaabaabaaaabbabbababbabbabbbaabaaaabaabbaabaabbaaaabaabbbaaabbbbabaabbababbaabababaaabbbbababababbbbbabababbbbbbabbbaaabaaaaabbbaabababaabababbbabbbbaaabbaaabbbaaabbaaaabaaaabbbaaaaabbaabaaaaababbabbbbabbaababaaabaaababaababbbbbbbbaaaabbabbaaabaabbbbbaabbbaabbaaabbbabbaaabaabbbaaabaaaaaabaaaabababaaabbabaaabbaabbaabaaabbaaaaabababababbbbbaaaaaabaaabbaaaabbbbbabaaabaaaaabaabaaaabbbbbbabababaaaababbbbbbabaaabbbabbaaabbbbaaaabbbaababbabbaaabbaabbaaababababaabbabbabbabbaabaaabbabaabaaaabbbbabbaaaaaaabbbabbbaabaaaabbbabbbbbbabbbbabababbbbabbbabbabbbaababbababaabbbababbabbabaaababaabbbaabbabababbaabbaaaaaaaababbaaabbabbbbabbababbbbaababbbbbaababbbaaabababbbbbbbbabaaaaaabababbaaaabaaababbabbabbbababaaaaabaabbbababbabbbbbaabbaabbaaabbaabbababbaaabbbabbbabaabbbbaaababbbabbbbaaabbbbbabbabaaaaabaababbbbbabbababababbbbabaaaaaabbababaabbbbbababbaabaaaabaabbaaaabaabbbbbabbbaaaabbaababbbabaabaababbbabbbbabbbbabaabbabbbbbaaaabaaababaabbaaaaaaaaabbaabbabaaabbbbaababbabaaaaaaaaababbbaabbababbabbbbabbabbabbabaabaaabaaaabbbbabbbbabbabaaabbabbaaaaabaaabaabbabaaabbbabbaaabbaabbbababbabaabbaabababbbababbbbababaaabbaababaabaabaabababababbabaabbaaaaaaabbaabbabbbbbaaaababbaababaabbbababbbabbaaabaababbaaabbbbabbbabaabbbbabaaababbaabbbabbaabbbababbababbbaabaabbabbbabaaaaabaaabbaaabababaaaababbaabbbaaabaaaababbbaaabbbbabaabbabbabaaabaabaaabaabbbbabbbbbaababbaaaabbabbabbbbbbaabbbabbabaaaaababbbbbbbaaaaabbbaaaabaabbbaaabbbaaaaaaabbbbbabbaaaaaaabaaaabaaabbaaaabbabbbbaaabbbbbbabaaaababbbbbbababbaaabbababaabbbaaaaababbbbabbbabaaabaaaabaaaaabaaaabbaaababaabbbbaabbbabababbabbbabbababbaabbbabbbbbbbbbbaabababbbabbbabbaabababbabbabbaabaaabaaabaabbabbbaababbbabbabbabaaabbbaababaaaabaaaabbbabbbbaabbbbbbaabbbbbababbabbbbaabbabbaababaaaaaaaaabbbabaababaabbaabbbabaababaaaaaabbbbaababaaaabbaaabaabbbbaabbaaaabbbabbabbabbabaaaaaababbaaaababbbbbbbbaaabbabbaaabaaabaaabbabbbabaabbbababbabababbaaaabbbbaaaabbabbbbbbbabababbbbbbbaaabbabbbbabbbaaaaaaabaaabaababbaabbaabbbbabbbbaabbaababaaaaabaababaaabbbbababaaabbabaabbaabaaaabaaaaabbababaaaaabbbabaaabaabaaaaabababaaabbbbbaabaaabaaaabbaababbaaaabbaabababbbbbababbababaaabbbbbaabbaaaaabbbabbabbbbabaaabaaababbabbabbbabaabababaababbabbbabaaaabaaabbabbbbbaaaababbabbaabbbbbbbababbbbaabbbbbaaaaabbbbabaaabaabbaaabababaababaabbabbaaaaaaaabaabaabbaababbabaabbbbbabaabbbaaaabbabbabaaabaabbbbbaabbbbbbbbbabbbbbbbabaaaaabbabbaaaaabbabbbbbaaabbabaaaabbabbbbaaabaaaaabbbbbbbbbbbabbaabbbbaaabbbbbababababbbababaaaaaaaabbaabbaaabbbabaabbbaabbabbbaababaababbbbbbbababbaaaaababaabbaabbbbaabbbbbaaabbbbaababbababaaabbbbababbaaaabbabbbaaabbabaaabababbaaaabbbaababaaaaaaabaaabbbaaabbabbbbabbaabbbaaababbbaabaabaabaaaaaababaaaababbbbaabbabbbbbabbabbaaabaaaaababbbaaabaaabbaabaababbabaaabbabbbbaabababbabaabaaababbbaabbaabaabbabbababbabababaabbaababbbababbaaaaaabbbbaaaaaabaaabaabbababbbaaaaaaaaaaaaabaaaaaaabaabababbbabbbbbaababbbabaabbbababbaaabaaabbabababbabbbababaaabbabbbbabaabababbaabbabaabbbaaabaaaabbaaabaaaabbabbabababbabbbbabbaabbabbbabbbabbaaaaaaabbabbabaabbaabbaaabbbbbbbbaababaabbbaaababbbbbbaaaaaaaababaabbbabbbaabbabbbabbbbbabbaabbaaaababbaabbbbbbabaaababaaaababababbbbaaabaaabaaaabbbabaaaaabababbaabbbbbbbababbaabbbbbbbaabaaabababaabbababaaabbaabaaaabaaabbbbaaaaabbabaabbaabaaababbbabbbaababbbbbbabaaabaaaaaababaaabaaaaaabbaabababbbaaabaabaabbaabaababbbabaababbaaabbbaababaababbbbaaabbbbaababbbbbabaaababbaababbbaababbbabbbbaabbbbabbbbabbabaaaabbbbbabbabbabbaababbabababaaaaaaabbabbababaabaaabbbabbbabbbaabbbbbbaabbaabbbbbbbaaababbbbbabbbababbbabbbbaabbbaabaababababbbaaababaaaabbaaabbbbaababbbababaabbaababbaabbaababbbabbabbabababbbabababbaaaababbabaabbbaabaaabbbaaaaaaaaaaababaabaaaaaabbabaaaaabaabaaabaaabbaaabaababbbbaababaaaabababbbbbabaaabbabbbbbbabaababbababbbbabbbbbbbbabaabbbbababababaabbaabaaaabbbabababaabaabaaabbaaabbababbabbabbabbaabbbbabbbbbbaabbbbbbbbaaabbbbbaabbbbabbbbbaabbbbabbaaabababaabaaaaaaabbbbaaababababbbabbababaaaaabbabbbaaabaabbbbabbbbabbaaabbbaaaabbbbaabbbabbabababbbaaaabaabaaabbbaaabbaabbaaaaabbaababaababbababbabbbababbbbbbbababaabaabbbbaaaaaabbbaababaaaaaabbbbabbaaaababbaabaabbbaaababaaabbaabaaabbaaaababaabaaababbaaabbabbabaaabbaabbbaaaabbbaaaaaabbaabbbababbabbbaabbbbbbbaabbababaaababaabaaabbbaabaaaabbabbaabbaaaaabababaabaaabaabbaaabbababbbbbaababbbaaabbbbbabababbabbbaaabababaaabbaabababaababbabbbbaabaaababababbaaabbbbabaaabaabbbbbbbabbbabbbaababbaaababbbababaabaaabbbabababbbbbaabbabbaabbbaaaaaaabbabbabaaaaabababbbabbbbbaaabbbabaabbaababbbbababbababbaabaabbaabbbaababbbbbaaaaaaabbbabbbababbaababbbabbbbbbabbbbbabbabaaabbbabaabbbbbbabbaaaabbaaabbbabaaaabbbaaabaabaabaabaababaabbbabaaabaaaaabaabaabbbbbbaaabaaababbabbaaaabbabaabaaaabbababbbbbbbaaababbbbbbabaaabbabaabbaabaaaabaabbbbaabbaabbababaabbbbaaabbabaaabbbaaabbbababbbaababbbbbbaaaaaaabbbaaaaaababbbabaababbabbaabababaabbbbbabaaabbaaaabbaabbbbbaabbbabaaabbababaaabbabbaaaaabbaabaababaaaaabbbabababbabbbaaaabaabbbbabaaabaaabbababbaaaaabbaaabbbbbabaaaabaaabaababaabbababbaaababbbbabaabbabaabaaaaabbbbbabbabababbabbbabbbbaabbaabaaabbbbaabbbaabaaabbbabbabbbbbbabbbbbaaaabaabababaaababaabaabaabbabbabbabaaaabaabbbbabbaaaaaabaaabababbbbabbbaaaaabaaabbbbbabbbabaaaaaaabaaabbabbbabbabbaaaaabbababbbbbbabbbabaaaaababbbaaabaabbbbbbbbabbabbbbbbababbbababababbbababbabababbbbabbababbbbaabababbabbbaaabbbbbaabababbabaaaaabbbbaaaabaabaaaaababbbabbaabaababbbbbaaabaaabbbbaaaaabbaaaabbbbababaaaaababbababbabbababaababbbaababbaaabbbabaabbbbbbbababababbbbabaabbbabbaabababbbababbababaaabaaaaababaabbbbabaabaababbabaaaaabbabaabbbabbababbaabbaaabaabbbabbaaaabbaaaabaabababbaaabbbabbbbbbababbaaaaabbbaaababbbbaaaaabbbaaaabbbaaaabbaabaaaaaaaaaabbaaabbbaabababaaaaaaaabaaabbaababbaabaabaaaabbaabbaaaaabbabbaaabbaabababbbaabaaaababaabaabbababaababababababbaababbaabaabaaabaaabbabbaaaabbbbaababaaaabaabbbbbababbbbabbabaabbbaaaaabaabaabbababababababbbaababaaabbaaabaaabbabaaaaaaaaaaabbabbabbbbaaaabbbbabaaabbbbbbaaaababbbbaaababaaabbbbbaaaaaaaabbabbaababbaaaabbabaabbbaabbabbbbabaabababaaababbabbbbbaaaabbabababbbbaabaaaaaaabababaabbaaaaabababaaabaabbaaabaaababaaaaaaaabbbbababbabaabaaabaaaaabbaaaaabbabbbaaabababbbbbbabaaaaabaababbaaaaaaaabaabbbbabbbaabaaaaaababbbbaaaaabbbbabababbabaababaaaabbaaababbaabbaaaabbbabbbaabbbbbabbaabaabbbabaabaaabaaabbaababbabbabbaaaaaaababaaabbaabbbaaabbaababbbbbbaababbbaabaaaabbbaaabbbabbbbbbaaabaabaaabaaaaaabbaaabaabababbababbababbbbbaabbabaababaaabbbabaaabbbbbabbbaababbaaaaabbbbbaaaaababbabaaaaaaaaaabbabbbaabaaabbbbbbbbbbabababaaaaaaabbabbbaaaaabbbbbbbaaabaaabaabbbaaabaaaabbabaabbaabbaabababbbbaabababaabaaaabbbaabbabbbbbbaabbbbaabaabaaaaabbaabababaabbbbbabbabbbbaaabbbabababbbabbbabbababbaaaaabbbbbbbbaabbababbbabaabbaaaabbbabababbbbaaaaaababbaabbabaaaabaababbbaabbbbbbaaabababaabbbabbabbabaaaaaaabbabbabbaabbaaabaabbbbaaaaabbbbabbaababbabbaabbabbaababababbaaababbaaabbbaabaaabbaaaabbababbbababbbabbabbbaaaaababbaabababbabaababaabbaabbbaaaaabaabbbbabbbbbabaabaaaaaaaabaaabbabbbabbabaaababbbabbbbbaabbabababbaabaabbbbaaabbbbbaaabbababbbabaaabbbabaabbabbababaabbbabaaabaaabaaaaabbaabbbbbaaababbaabbbaabbbababbbbbbababbabaaababbaaaaabbababaaabbaaabbababbaaaaabbabbaaaabbbbbbaabbbabbaaababbabababababababababaaabaabababaaabbaabbbababbbaabaaabbbaaabbbbabbbbaaaababbbabaaaababbaaababababaaaaaaaaaababbbbabbbbbaabaabbbbbbaabbbabbbbabbabaaaaabbaabaaababbbaaaabbabaaaabaabbaaaabbbbbaaaababbbbbbababaababbbabaababababbaabbbbbbbaaaababbabbababbbabbaaabbbaaaabbbaabaaabaabbbbabababaabbbaabaabbbbababbababbabaabbaababbbaaaaababaababbabbabbabbaabbbbabbaabbbaabbbbabaababaabaaabaabbbbaabbbbabbbaabbabbbabbaaaaaaaababaabaabbbabbabababbbaaaaabaababbbbabaaababaaaabbbbbaaaabbabaaabbaabbaabaaaababbbbaabababbabbabaaabaabaabbaaaaaaaabababaababbbbbaaaaaababbaabaabbaabaaaaaaabbbabababbbaaabbababaabaabaabaabbbabaaaabbabbbababaabbaaaaaaaabaabaabbbaaabbbaaababaabaabbababbbbaabbbbbbaaaabbaabbaaabbbabaaaaabababbabbbbbabbabbaabbabbabbbabaaababbababbbabbbbabababbaaaaaabbaabaaaabbbbaaaabaabbbbabaaaaaaaabbbabbaaabbbbababbbbaabbbbbaaaaabbaabaabababaaaababbaabaabbbabaaabababbbaabaaabbaaabbbaaaabaaabaaabbbbbaaaaaabaabaabaabababaaaabaabbbbaaabbaaaabbbbaaaabbbaaabbababaaabaaaabbaaaabaaababbabbaaabaabbbaaabbaabbbbabaababbababbbbababaaaaababbaaabbbbbbbbabaaaabaaabbabbbaababababbaaaabbbaabababaaabbbbbaaababbababbabaaaaababaababbbbbaaaaaaaaaaaabbbbbbaabbbbbbabbbbabbbbaabaaabaaaaabbabbaabbbbabbbaababbbabababbaaaaaaaaabaabbbabbbbbababbabbbbbbaaaabbbbbabbbbaaabaaabbaabaabbbbaabbbbaababbaabaababaaabbaaabbbbbababaaaaaabababbbaaaababbbbbbbbbbbbabbaaaaabaabbababbbbbbbaaabaaaabbaabbbabaaaabaaabababbbaabbababbbaaabaabbbaaaaababbbbaaabbabaabbaaaaaabbbabbbabbbbbaabbabbaaaabbbabbbaabbbabaaaaabbaabaaabaabbabbabbaaababaaaaabbbbabbbaaabbbbaabbababbbabbaaabbbabbaaaaabaaaabbabaaaabbbbaaabbbbbbaaababbbaabaabababbababaabbbaaaaaabaababbbabbabbbababaabbbbaabababaaababbbaaaabbbbababbaaaabaaaabbaabbabbabbabaaababbbabaabbbababbbaabababaabbaabbabaabbabaaaabbaaababaaabbaabbababaabbbbbbbaaaabaabbaaababbbabaabbaababbabbbbbabaababababababbbabbabbbaaabbababbbabbabbbaabababaabbbbabbaabaaababaababaaabbbbbbababaabbaababaaabbbbbbbababbbababbbababbbabbbbbbaaaabbaababaaabbabbbaabbabbbbbabbbabaaababbbbbbbaabbaabaabbabaabbabbbbbbabbabaabbabaabbbbbbaaaaaabbababbaabbababbababbbaababaabbabbabaabbbaaabbbbbbbaaaaaabbabbaaaababbbbabbbaaaaaabaaabaaaabbbaaaaababbbabbabababaabbbaaababbbbababbababaaaaababbaaaaabaabaaabaabbbabbbaabbbbbabbabbaaaabbaabbbaaabbaaabaaaabbaabbaaaabaabbbabbbababbababaaaaaabaababababbbaabaaaabaaabaaaaabbbaabababbbaabaabaaaabbbbabbbbaabbbbbaaaaaaaaaabbabaaaabbbaaabbbaabbbbbabbbbbbaaababaabbaabbaabaaabbabbbabbabaabbbbaabaaaabbaaabbbabababaabababaaaababaaabaabababaaabbbabbbbaaababbbbbbbaababaaaaabaabaaabaabbbaaaabaabbaaabbababbabaaabaaabbabaabaabbbbabbbbaabbbaabbabaaababbbbbbbababaabaabbbbbaabbbbbbbbababaaaababbbababababbbbbaabbbaaababaabbabaababaaaaaabbabbbabbaabababaaaaaaaabaabbaabbbbbababaabbbaaaaabbbabbbaababbbbbabbbabbabbabbbbbbabbabababaabaabaabaabbbaabbaabbabababaaabaabbabaaaaaabbaabaabaaaaabaabbabbbbabbbaababbaabaaababbababaaabaaaaabbbabbbbababaababababbaaaabaaaaaabbbbabbabbbbababbbbbbbaabbabbababababaababaabaaaabababababababbabaaaabaaabaaabaabbababbaaaabababbbbabababbbbbbbbaababaababbaaabbabbaabaaababaaaabbaabbaabbbbaabbbaaabbaababaaabbababbabbaaabaaabaaabbbbababbabbbbabaabbbabbaaaaababababaabbbaaababaabaabbbbabbbabababaababbbabaaabbbaaaaaabaaaaaaaaabbabbbabaaabbabaaabaaabaaabbaaabaabbbbaaabbbbabaabbbababaaaaabaaaabbaaaaabbbbabbaaaaaaababababaaaaabbabbbbbbabbaaabbabbbbababababbbaabbbbaababaaaaaababbbaaaabbbbbabbabbabababbabaabbabbbbbaaaababbbbbbbabbbaabaabbabbbabaaaabbabaabbbaaabbbbabbabbbabbbbababbbabbaaaababbbaaabbaababaabbabaaaaababbaabbaabbbbabbbaaaabbaabbaaabbabbaaaabaababbbaabbabbbabbbbbbbaabbaabaabbbaaaaaabbbbbbabaaabbabaabbaabbbababbaabbbbbbbaaabbbbabaabbbbabaaabbaaaababbbbbabbabbaaabbbbbbaaabbbbabbbaaaaaaabaabbaabbaaaaaabbaaabaabbbbababbbbaabbabbabbbbaaabbbbabbbabaaabbbaaaabbababbaabaabababaaaabababaabbbaabaaababbbbbaabbbaaaaabbabbaaabbbabbbaabbbbbaababbbababaaaabbbbabaaaabaaabbbabaaabababaabbbbbaaabbaababaaababbbaabbababbabbbaababaaaaaaabaaabaabbaabbababbbababbaaababaababaaabaaaabbbabbbbbbaaaabaaaabababababbabbaaabaaaaaabbbbbaabaaabbabbabbbaababaabbababaaaababbaaaaaaaabbabaabbaabaabaabaaaabaabbababbbbabbbaabbbbabaaaaabaaaaaaaabbaabbbbbabaababaaaabaabbabbaabbbabbababaabbbbbaaaaabbabaabababbaaababbbababbbabbaabaabbabbbbababaabbbaabbbabbabbaabbbaaabbababaabbbbbbbbabbbaaaabaabbbbbaaabaaaabbabaaabaabbaabbbbbbbbbbabbabaabbabaabbbaaaabaabababaabaabaaabbbbbaabbbaaaabbaababbaaaaaaaaabbbaababbbaaababaaabababababbaabaabbaaababbbbabbbaabaabaabaababbbbbbbbaabaaabaabaabbbbabaaabaaabbaabbbbbbbbbaabbaabbbabbbbbabbbbabbabbaaaaabaabaaaabbbbbabbbbabaabaaabbbbabaabbabababaabaaaabbaaabbaaabaabbaabaabbaabbaaaabbbabbbaabbbabaaabaaabbbbbbbbbababbabbaaabbaabbbbbaaaabbbababbaaaaabbbabababbababaabaaabbbabbbabbaabaaaabbbbabbabaabbabbaaaabbbbbbabbbaaaababaaabaaaaabbababababababbaabbbaaabbabbbaabbbabbbbababbbbababbbaaabbaaabbbaabbbbbabbabbbabbaaaababbaabbbbababbaaaaaabbbaabbbabaaaabaabbaaababaabbaabbbbabbabbaabbbabbababaabaabaaaabbbabbbababbaaabababbaaaaababbbaababababbaabaaaabaabbbaaaababbabbbbabaabaaabbbbabaabaabaabbaaaabbbbabaaaaaabbbaabbbbbbbbbabbaaaababbbbbababbbabbbbababaabaabbabbbbabbbbbaabbaabbabaabbbbaabaaabbababbaaaaaabaaabbababbbabbbaabbabbbaabbbbbbabaaaabbbaaabababbbaaabaabbbaababbbaabaaabababaaabbabaaaaababbbbbbabaababbbbbbbabbbbbabbbbabababaaababbbaaaaabababbaaaaabbbabbbaabbaaabbbbaabbaaaaabaaabbabbbababbaaaabbbaabbbaaabbabbabbbabbbaaaabaaabbbaabaabbaabaaaaaabbbbbabbbbbabbbbabbbbbaaaabbaabbbbaaaabbbbbabbbabbbaababababaaaaaabbaaababbabbbbaaababbbbabbbaabbaaababbbaaabbbababbabaaababaaaaabbbaaababbabaabbaaaababbbaabbabbaaaaabbbababaabbbbbbaabbbabbaababbabbbaabbabbabbbbababaaabababbaabbbbbaaabbbaaababbaabaaabaaaabbbbaaaaabbabbbaaaababaababbaabbaabababbaabaabbaaaababbbbbaaaabaabaaaabbabbabbbbabbbaabbbbbaabaabaabbaabbababbaaabbbaaaabbaababababaabababaabaaaaabaaaaababbbbbbbbabababbbabaabbabaaaaaaababbabababbbbabbbbaabbabababbabbaabbbbbbaabbabbbababaabbaababbaaaabaabbbaabbaaaabbbaaabbbababbbaaabbbbbaaabbabbbbaabbaabbabbababbaabbababaabbababbaaaaababbbbbbbbabbbaaaaababaaabbaaaaabaaaaaabaaabbbabbaaaaaaaaaabbaaabbbbbaaabaabbbbbbbaaaababbabbabaabbabbababababbabaabbbaabbabbbbaaabbbbaaabbbbbaababababbbbaaabaabbaaaabbbaabbaabbbaabbaaaabbababaaaaabababaaaaaaaaabbbaaaabaaabbaabbaabbbababaaabbabbaaaabaabbaabbbababbbbaaaabbabbbbbbaabbbbabbaaaaabbaabababaaabababbaabbbbbabaabaabbbbbbaabbababbbbbbaabbaaabbaabbaaababaabababaabbaaaaaaaaabaabbbaaaaabbabbabbabaabababbbbaaabbbabaaaabbbbbabababbbaabbbbbbaabbabbbbbababbbababbbbbabbababbbbbabbbbaabbaaaaaababbabbabbbabbbbbbabababbaabbabbbbbbaaaaabaaaaaaabbbabbaabaababbaaaabbaabbbabbaaabaaaaaaabbbaaaabaababbbaaaaaaabaaaabaababbaaabbbbbbbbabbababaabbbbaaaaaabaabaababbbbababbbbabbbaababaabaaabbbabaaaabbbabaabaaaaaaabbabbaabbabaabaaabbbaabbababbbbababaabaaaabbbaaabbbabbbabbaaaabaabaaaaaaaaababbabbbaabaababbabaababbbbaabababbaabbabaaabbbbbbaaaabbaaaabbabaabbaaabaabbababbbbaabbabbabbaaaabaaaabbaababbbbaabaabaaaaaabaaaabbbaababababbbbbbbbabbbabbabbabbbbabbbaabbaaabbbaabaabbbbaaabaababaabbaaaaabaaaabababbbbaaaaabbaaaaabaaaaaabbabaaaaabbaaaaabbabbbaabaaabbaabbbabbababbabaaaaaabbaababababbabbaaaaaabaaaaabbbabaaaababbabbaabaabbabababbaabbabbaaaaababaabbbaaaabbabaabaaaaabaabbabaaabaaabaaabbbababbaaabaaaabababbbaabbaabbbbaaaabbabaabbaabbbbababbabababbbaaabbbabaaabaababbaabbaaaaabbaaabbbabbbbaaaabaaabbbaaaabbbbabbabbbbabbbaabaaaabaaabbababbaaaaabaaaababbabbbaabbbaababbaaababbaabbbabbbabbbaabbabbaababbaabaaabbaaaabaaaaaabbbbaaaababbbaabaaabbababaabaaaabbabbaaaaabbbabbbbaaaabbaabbbbbabbababbabbabaababbaabbaabbabaaabaabbaaabaaababaaabaaababaaaaaaaababbabbabaaaaabababaaabaaabbaaaabbbbbabaaaabbbaabaabaaaaabbabbbbbbbaabababbbabbaabaaabbabbbbbbabbbbabbababbababbaaabaabaababaabaabaaaabaaaababaaaaaabbbbabbbbbbabaabbbaabbaabaaabaabbbaababbbabbaabbabaaaaaababbbbbabbbaabbabbbbabaaaaabaaabaabaabbbbababababababbabbaaabaaaababbaabbaaaabaababaaabbbbbbaaaabbbbabbbabbabaaaabababaabbaaabaababbabbbabaabaabbaabaaaabbbabbababbbbabbbabbbbaaabaabababaabbaaaaabbabbaababbaabbaababbbbbbbaaabbbabbbbbbbbaaabbabbbbabbbababaabbabaaabbbaaaabbababaabbbbbabaaaaaaaaabaaababaaaababbabbabbababbababbaaababaaabbbbaabbbbbbbababbaabbbababaababbaabbbaabbbbaaaababbabbaabbbbbaaabaaabbabaabababaaababbabaaabaabaabbbbabbaabababaabbbbaabbababbbabaaaababbabaaabababbbbaaabaababaaabbaabbabaabaaababbaaaabbabbbabaabaaaaabbaaabbabaabbaaabaabbbaaaaaaabbbbbaaabbbabaaabaaaabbbbbaaaababbbbbbbabbaabababbabbbbbbbbbbabbbabbbbababaabaaaabbabbbabaabbbbaabbabaaaabbbababbbbaaababaaaaaaabbbabbbababaaabaababbaaabababbbbaaabaabbaabbbabbaabaaababaabbbaabaaaabbabaaaaababbbababbbbabaababbbbbbbbbabbbaabbbbbabaaabaaaabaaaaaaabbbabbaaabbaabababbbbbabaabbbaaaaaaabbabbbbbabbaabbababaababaaabbabaabbbaabababbbaaaaaaabaaabbbbbbabbaaabbabbababbbaabbababaababbbbaababbababaabbabbbbbabbbabaaaaaababaaaaaabaabaaabbbbbbababbaabbaabbbabbbbaabbbbbababbbbaaaaaaabababbbabaababaabbbabbabaaababbaaaaaaaaabbaaaaabbaabbaaababaabbababbaaaaababbabababbaaabbaaabaabaaaababaababbbbaaaabbbbababaababaaaabbaabaaabbaabbabababbababaaaaaabababbabbaabaababaabbbaabbaababbbabbbbbbbbaaabbababbaaabaaaabbabaabbaaaaaabbbabaabaaaaabaababbaabaabaaaaaaaaaababbabaabbaaababaababaabaabaababaabbbbbbbabaaaaabbaaaabbaababbbaaaaaaaaabaaaababababbaabbaabbabbbbaaabaaabababaabbbabbbbababbbabbaabbaabbbabbbbabbaaaaabbabaaabbbbbbaabaaaabbaabababababaabaaabbabbbaabaabbabbabaabbaaaabbababaaaaaabbabbbbbaababbabbbaaabababbaabaaaaaababbabbababaabbbbabbaabbaabaabbbababbbabbbabbbabaabbaabbaaaabbbbabbaaaaababababbaaabababaaaabaaaaababaabaabaabababbabaaabbbaabaabaabbbaabbbabbaaabbbaaaabbaaaabbabbaaabaabababbabbabaaabbbabaabbbbbbaaabbbabbaabaababababbbbabaaaaaababbbbaabbabaabaabbbbaaabbaaaaabbaaabbaabaaabaabababbaabbabaaabaaaabbbaaaaaabbbbbabbbbbbbbabbaaaaaabaaaaaabbabaaababbaaabbbbaaabbbabababbbbaabbbaaabbbaabbbbbbaababbbbbabbababaaabbabbaabaabbabbaabbababaaaabbbaaaaaabaaabbabaaabaababbbaaaabbaabbbbbbabaabbabbbbbbaabbbaaaaabbabbbaabbbababababaaabaabaabbbbaabbabbabaababbabbababbabbaaabbbbababbaababbaaabbaabababbaaaaaabaabbbbbabbabbbbbbaaabaaabaabbababaabaabbbbbaabaaabbababaababbbaaabbaabababaababbbabbababbaabaaaababaaaaabababaabbabbaaababbaabaababaaaaaabbabbbbbbbbababbbabbaabaaaabbbabababababaababbbabaaaaabbaabbbabaabbbbbbbaabbbbbbabbbaaabaabbbaaababbabaaaaaaabbbbbabaababbababaaababbaabbbbbaaababaabbbaaabaabbbabbaaabbabaaaaaaaaabaabbaaaabaabbaabaabaababaababbbaaabbabbaaabaabbbbbabbbbbaaabbbbbbbbbbbbababababbaaabaaababaaaaabbbaabbbbbabababbbaabaaaabbabbabababbbabbaaaaabababaabbaaaaaaabbabbaaaababbabbababbbbaabbabababaaaaaaaabaaabbabbaaaaaaabbbaabaaabababababbbabbbaaaabaaabbbbaaabaaababbaabbaaabbaaabaababaaababbbaabbaabbbaaabaaaabaababbbabbbabaaababbabaaabbabbbabaaaababbbbbaaabaabbbbaaabbaaaabbaaaaabbabbbbabaaaabbaababbababbabababbbabaabaaabaabaaaaabbbbbaaaabbbbbbaaabaaabaabababbabbbabababbabbbbbbabaaaaabbaababaaaabaabbababaaaabbabbaaabbbaaaaabbbabbaababbabaabaabbbababbabbabbabaaaabbabaaaaabbabababbbaaaabbaaaaaaaaabbaabaabbbbbabbababbbbaabbaabaaaaaababaaabbbabbbabababaaabbbbbbaabbaaababbabbbaaaababbbbbabbabaaaaabbabbaaaaabbbabaabbaabaaabbbababbababbabbbaabaaaabbbbbabaaaabbbaaabbbabbbbababbabaaabaabbbbaabbaaaabbbbbbabbbaaabaaaaabbbbbbbbbbabababaababbbbababbabbbbaabaaaababbabababbaaaabbbbaaaabaaaabababaabaababaababbabbbabbbbaababbbbaaaababaaaabaaaababaabaabbaaaaaabbbaaaaabaaaaabbabbbabaaaababbbaaaaaaabbaaaaaabaaabaababbabaabaaabbbaabbaabbaaaaababababaaaaaabaaababbbabbababababbbbbbabbabbbbbababbbbabbababbbabbabbabbbaaabbaabaababbbabbaababbabbaabbbbbbbbabbaabaaaaabaaabaaaabbabbbbbbaaaabaababaabbabbbabaaaabababaabbbaababaaaaaababbabbaababbaababaabbabababaaabbabbaabbbababbbbbabbaababbbabaabbababbaaaabbbbabaabbbbbbbaaabbbaaababaaaabbaabaabbbbaabbabaaabbbbabababbbabaababbbbabaabaaaabbbbabaabbaabbbaabaabaaaabbaaaaaababaabbbabbbaaabaaaabbbbaaaabbbaabaabaababbbabbbabbbaabbbbabbbbbaabbaabbbbbbaaabbbaabbbbbabbbbabbbbaabbaaaaaaabbaaaaaababaaabaabaaabbbaaabbbbababbabbbabbbbaabbabaabaaaaaaabbabbbbbbbaabaabbabbaabaababbbaabaaabbabbbababaaaaabaaabaaaaabbbbbabbbaabbbaababaaaabaaabbbbbababababbabababbabbababbabaaabbabbabbaaabaaaabaababbbaabbbabaababaaabbabbababbaabaabbbbbababaabbbaabbaabaababababbbbaabbabbbbbbabbabaabbbaaaababbaaaabbabbaabbbabaabaaaaabaababbaabababbbaaababbabbabbbabbabbabbbbaababbbaaabbbabbabbbabaaaaabaabbbbabaabbbabbabaaaabbabababbbbabababbbbabbaaabbbbaabbabbbaabbababbbaabbbbabbbaabababaabaababaabbaaaabbabaaaaaabbaabbbabbaabaaababbbbaaabbbabbbabababababbbabaaabbbaaaaaabababaaaaabbababbbaabaaabbaabbbababbabababababaabbbaaaabbabaaabbaaabbababbbbaabbbbaaabababaabbbabbaabbbabbababbbabaabaabaabbbaababaabbaabaabbbaabbbbaababbbabbaabbbbbabbaaabaaabbbbbbababaaabbbabbabbbbaabaaabaabbbbbabbbbbabababbbbbbabbbbbbaaabbabaaabababaabbaaabbbababaaaabbaaabbabbbaabbababaaabbbbaabababaabaaaabaaabaabaaabbabbabbbaabaabbabaabaababbabbbbaababbaabaaaababaabbabababbbaabaabbbbbabbabaabbbbbbbbbbabbababababbbbabbaabbbaaabbbbaababbababbbbbabababbbbabbaaaabbababbbaaabababaaabaababbbaabbbbbbbaabbbbbabbbbbaabbaaaababbbaaaaabbbabaabaabbbbbbbbaaaaaababaaabaabbbbaabaaabbbabbbbbabbaaabaaaaaaaababbaaabbaaaabbabaaaaabbbbbaabbbaabbaabbabbbbabbbaababaabbabaabababbbbbababbbbbaabbbbbbbbbbaaaabbabbaaabbaabaaabbbbaabbaabaaaabbabaaabbbbaabbabaaaabbabbaabaabaabbbabaabaaabaabaabaaabaaababaababbaaaaababbbabbbabbbbbabbaabbaabbbbabababbababaabbabbbababbbbbbababaabbbbbbaabbabbaabaababababbabbaabbaaababaaabbbbbbaabaabbaaababaaababababaabbbbaaaabbabbabaabaababbbbaabaabaabbababaaaaaaabaababbbbabbababbbabababaaabbbabbaaabbabbbbbababaabbaaaabbabbbbbabaabbabaabbbaabbbbbbaaabbbaaaabaaababaabbabbaaababbababbbbbabaabbaaabbaabbaaabbababbbbbaababbababaabbababbbabababbabbbabaaababaababbabaabbbbbbbaabbabbbabbbabababbabababbbbbabbababbaaaaabaabaaabbbabbbaaaabbaabbabbbbaabababbbabbbbabaaaaababaaaaaabbaaaabababaabbabbbbaaaaaaababababbbaaaaaaaaababbababbbaabaabaaabbbbabbbababbbbaabbbbbbbaababbabbababbbabbabbbaaaaababbbbaaabbaaababbabbbbaabbabbabaababbaaabbaaaababbbbaababaabbaaaabbabababbabaaabaababaabbbbbabbaaaaabbbbabbbbbaabbbaabbbabbabbbbbbaaaabbbabbbbbabbaababbaabbabaabababbaabbbabbaabbbbbbbbaaabaaabaaaabbaaabaaaabbababaababaabbbaababbbabbaaaabbbbabbbaabbaaaabbabbbabaabbaaaaaabaaaababbbabbbaaabbbbabaaaabaabbaabaaabbbaaabaababaaaaaaaaaaabbbaabbabbaabaaaaaabaabaaaabbabaaababaabbbaaaaababbababaaabbbbbaaaaaaabbababaabbbabbbbbbabbbbbabaababbbaaabbbbababbaaabbaabbbbbbbbabbbabbaababbbaabbbabbabaabaabbaabbbabbababaaaabbaaabbabaabbababbbaabbabbaaabbbbaabaabaaaaabbbbaaaabaabaabbbbbaabaaaaaaabbaaabbbabaabbbbabaaabbbbaabbbbaababbbaabbaabbaaabaaabbbbaabbaaaabbbaabaababbbabaaababaaaabbbaabbaaababbaabbaabbbaaaabbbaaaaabbbabaabababaababaaaaaababaaababbaaaababbaabbaabbbbaabbbabbbabaabaaaaabaabbababbbabaabbaaabbaabaabbbbabbaaabbabaabaabbaababbbaaabbabaaabaaababbbaabaabbaaabbabbbabbbaabababaaaaabaaaabbaaabbabaababaababbbbbabbbbabbbabbbbbbbabbabaababbaaaaabaaabbbabbaabbbaaabbabbaaaaaaaaabbbbababaaabaabbbababbbabbbbbbbbbbbaaaabbaabbbbbabbbaabbbabbbbaabaaaaabbbbabaaabbbbabbbbbaaaabbababbbabaaaabaabbbbaaababbaababaaabbbaabbaaabbbbabbabbaaababaabaaaabbaabbbabbbbbbbaaabbabbaababbbbaaabbbbbbaababbbbbabbbbbbbabbaaabbbbbbabbbbaabbaabbaaabbbbbaabbaabbabbbaaabaabbbbbbbabaababababbbabbbbabaaabbaabaaaaabbbbaabaabbabbaaabbbaaaabbaababaabaababbbbaabbabbabaaaaaaabababaaaabbbaaaaaababbbaabbabbabbbababbbbbabbabbabbabaabbaabbbabbbbbabbbbabbabbbaabbaabbabaabbbbabbaababaaaabbaaabbababbbbaaaabbbababbaaaabbbbaabaaabbaaaaaababbaaabbababbbaabaababbaabababbabbababababbbbbbabbbabaabbbbaaaabbaabaabaaaabbabbabbaabaaababbbaaabbabaabababaabaabaabababbabaaaaaaaaabaabaabababbaabbaaaaabbbbabbbabbaaaabbbaaaabbbababaaabbaaaaabbbabbabbbbbbbbababbbababbababaabbbbabababbbbabbbabaababababbbaaaabbbabbbbbaababbaaaabbaababbabbaabbaababaaaabbababbaabbabababaababbaaabbabaaabbbaababbbbabbbaabaaabbababbbbabaabbaaabbbbaabbbbaabababaabbabababbbaabbbbaaabbbabaaaabaaabbaaabbababbaabbbbaaabaabaababbbababbbabbaaabaaaababaabbbaabbbbbbaaabbaaabbaabbaaabaababbbbabbabaabbabaaaaabbbbaababbbbabaababbbbaabbaabaaaaaabbaabbaaabbbbaaaabaaabbabababbbbbbbbbababaabbbbbbaaabbbabaaaaabbbbabbbbaabbbabaaaaaabbbbabbbaabbbbbbbbaabbabaaaabbaabbbabbaaaaabbaabaababbbbbbaababbabababaabbbababbaaabbaabbbbbbbbababaaaaaabbbbaaaabaabaabaabbabbbbbabaabbbbaabbaabbbbaaabaabaaabbabbbbbbabababaaaaabababbbbaabababbbaabbbbabaabbabbabaabaaaabbabaaaabbbaababaabaaaaabababaabaaabaaabbaabbbbbabbbaabbabababbaaabbbbbbbbbaabaabbabababaaaaaabbbaabbabbbbaaaaabbbabbbabbaabbaaaaaababbbbaaaabbaaaabaaaaabbbbaaaaaaaabbaabbbbbbbbabbaaabbabbbaabaabbbabbbabbabbbabbbbaabbaaaaabaaabababaabbabababaaaaaaabaabaabbaabaabbabbbbaababaabbbabaaabaabaaaaaabaabbaabbaabbbbaabbbbbbbaaabbbbbbbbaababbbbabaaababaababababbabbbababbabbbbaabbaaabbaaababababbbbabaabaaaaababbbabaabbabbbaabaababbabbabaaaabbbabaaaaabbaaaaaaaababbabbabbabbbaaaaababbabbabbabbaabbaaabbbbaaabbababaabbbaabaabaaaabbabababbbababbabbabaaaaabbbbbbaabaaabbbaaabbabbbbbabbaaababaaaaaaaabaabbabaabbaaaaabbabbbbabaababaababbaababaaaaaababaaaabbabbbbbababbaabaaaabbbabaaabaabbaaabbbbaaababbbbaaabbabbbabbaabaabbabaabbaaaaabbabbabaabaaaaabababbabaabbbaabaaababbabbaabbaabbaabababbbaaaaabbaaaaabbbbaaaabaabbabbabaaaaabbbbbabaaaabbbbaaaabbbbaaaabbbaababbbababbbabababaaababaaaaaabaabbbaabaaabbababaaaabaabbaabaababbababaabbaabaabbaaaaabaaaaaabbbaabbabbabbbaabbabaaaabaaaabbbaabbabbabaaaaabaabbabaabaababaaaabababbbbbabbaaaabbbababbbbbbbabaabaababbababbbabbabbbbbabbababbbbabbabaabbaaabbbabaaaabbaabbbbaabaaabaaabbabaaaabaaaabaaaabaaabaabaaabaaaabbbbababbaaababbbbbabbbaabababbababaababaaabaabbabbbaabbabaababaaaaaaabbbbbbbabbbbbbabaaaaaaababbbabbabaabbbbabbbbbaabbbbabbbababbbababbaababaabaabbabaaabbbaaaabbbaabbbaabaaabaaaabbbaabbbbaaabaabbbabaaabbbabbaaababbaabbababbbbbbbbababaaabaababbabbbbbaababbbbaaaaabbababbaabbbababbabbbbabbbabbbbbbababaaaaabababaabababbbabbababaabbbabbbbabbbabbaaaaaaaaaaaaabababbbaabaaaaaabaaaabbabbaabbababbabaababbbaaaabaababbaabbabbbabbaabaabaaabbaaaaaaabbaabbbabbabaabaaaabbaabbaaabababbbbaaabbbbbaaaabaaabbbbbaabbbaabaaabbaaabbababbabaaaaababbababbbbaaabbaabbbaabaaabaaababbbbbabbbaabaaabbaaaaaabaabbbaabaaabbaaababbabbababbaabaaaabaaaaaabbabbaaaabbbabbaaaaaabaaabbaaaabaaaabaaaaaabbaaaaababbabbabaababaabaaaaabaaaaaaabbaabbbbabbaaaababaaababbbbbaabbbbbabbaabbaaabaaabaababbbaaaababbbaababbbbbaaaaaaaabbbaaaabbaabbabaaabababbbaaabaabaaaaabaabbbaaababbbaababbaaabbaabbbbaabaaaaabbbaabaaabaabaaabaabaabaabbaaabaababbbabbaaaaaaaaababaababbbbbbbbbbbaabbbbabbaaabbbbababbababaabbbaababbbbbbabbaabaaaaaabbaaabbaaaabaabaaabbaaaaabbbaabaaaaaabbabbbabaaaabaabbabaabbbbbabbbbabbbbaabaababbbbbbabbabbbababababbbbbbbbaabaabbaabbaaaaaababbabbabaababaabbbabbabaabaabababaabbbaababaababbbabaaaababbbbaaababbaabaaabbbaabbbbaaaaababbaaaaabababbbababbaaabaabbbbbaabaabaabbabaaaaaabaabbbaaaaababaaababbababaaababaabbbbaaaabaaaabaaaaabbabbaabababababaaaabaabbabaababbbaaaaaababbbbbaababaabaabbbabaaabbabbbbaaaabaabbbbbbbbbbbbaabababbabbabaaabbabbbbbbaabaabbaaabaaaabaaabbbaaaabaaaaaaaabbbababaaabbaabaabbaaaababaaaababbababaaaaabaababaaabbbabbbaabaabbbaaabaabbbbaaabababbabbbbabbabaaabaabaaaaaababaaabbabbbbbababbabbbaaaabbababaabbabbbbabbbaabbabbbaaabaaaaaaabbbbbbababbbabbaaabaabbaaabbbabaaabbbabaaaaaabababbbaabbbaabbbabaababababbbabababbbbaaabbbbbaabababaaabaaabaaabbbbbbaaaabaabbaaaaabbabbbabaaaaababbbabbabaabbabaababbabbaabaabbbbbbbaababaabbabaaababbaabbabaababbbaabbbbbbbabbabbaabbabbbbbbbbbbbaaaaabbbbaaaaabaababaabaaababbababbaabbbbabbbabbabbbbabaaabbaabaaabbabaababaaababaaabaaabbbbaabababaabbbbabababaabaababbbaababbbbabbabbbbabaaaabaaaaaaaabbaaabbbbbbaaaabbbababaaabbbbbbbbbabbabbaabbaaaabbaababbaabaaabbbabbbbabbabbbaabbbbabbbaabaabbaabaaaaaabbaababaaabbaabaabbaababbabaaaabaabbaabbbabababbbababaabababbabaabbabbababbaaaaabbababaaabababaaabaabbaaaabbbabababbabaabbabbaababaaaaaababaabaabbbbbaabbbababbbabbbbbbaaabbabbaaaabbbabbbbaabaabaabaabbaaabbaaaaabbbaabaaabbaabaaababaaaabbbabbabbbbabbabbababbaaabbaaaabbbbbbbaabababaaabbaabaaabaaaaabbaaaaaabbbabbbbbaaabbbaabbaaabababababbbbabbabbaaaabbabbaabaabaaaaabaabaabaaaaabbbbbabbbbaaaabbaaaababbbbbaaabbbaaababbbabbbabaaaaaabbbbbabaabbaabbaabbbababaabababbbbbbabbbaabbbaabbbaabaababaabbabbbbbbbaabababbbbaaabbabaabaaabbaabbbabbaabbaaabbbababaabbabbbaabbabaabababbbaaabbaaabbabaaaaaabbbaaaaababaaaaaabbabbaabbabbbaaaabababababbbaaaaabbbabaaaaaabaaaaaabbbbaaababababaaaaabbbaabaabaabbabababbbbbbbbabaababbbbabaabbaabbaababbbabbbaaabbaabbbababbbbabbaabbbaabbaabaaabaabbaaabbbbbbaaababbaaabaaaababbbbaabaaabbaaabbaaaabaaaaabbabbbaaabaabbbbbbaaabbaaababababababbbbbbbaabbabbbaababbababababbabbaaaaabbbbbabaaabaaaabbbbbaaaaababababaaababbbaaabaaabbaababbbbbbabaaaabaaaaaabbabaabababbaababbababababaabbbbbbaaabaabbabbbbbbbaabbaaaaabbabbbabbbbbbabaabbabbbbbabaabaaabbabbabbaaaaaababaabbaaaabbabbbbbbbbabbbabaabbaaabbbbaaaabbabaabbabaabbaababaabbabbaababbbbaaaabbababaabaaabbbbbbabbbbbabbaabbbabbbaaaabbbbababbbaaababababaaaababbababaaaabaaaabbbbaaaabbaabbabbaaaaabaaaababaaaababaababbababaaaabbaaabbbabaabaabbbbbbbbbabbbabbababbaaabababbabbababbaabaaaaababbaaaaaababbbbbbbbabaaaaabbaaaabbbaaaaabbbbabbbaababaabababbbbabbbbbaabbaababbbaaabaabaaaabbaaabababaaabababaaaaaababbbaabaabbaabbbbaabaabbaaabbbbaabbabbaabaabbbbabbbaabbaabbabaababbbbaabaaabbbaaabbababbbaaaabbbbbaabbabaabbabaaabbbaababaabbbbaaaaaaabababaababbabaaaaaabbaababbabaaaabbaaabbbbaabbabaaaaaaaabbabbbbbbabbaabbbabbbaaaababbbabbbabbbaaaabbababaaabbbaabbbaaaaaaaaabbbbabbbbbababbbabababbbabaaababbaaabbababbaababababbbbababbabaabaabbabaaabababbbbbaaaabaaababbabbaaabbbaaaaababbabbbababbaaaaaababbaaaabbabaababbabbbbabaabbbbaaabbbabaaaaaababaaabbbaaabaaabababbbabaaabaaaaaabbbabbbbbabbababbbbbbbabbbabababbbbaaabbabbaaabaabbbbabbaabbbabaaaabaabbbababbbaaaaabaabbbbbaabbaaaaabaaaabbbaaabaababaabbbaabbbabaaaaaabbbaaabaababbbaabaaaaabaaababbaabaaaaabbaabaaabbbabaababbaaabbababbbabbbabbbbbbbbaabaabbaaabaabababbaaaaaaabbabbbbbbbaaaabaabbaaabbaaabbaaabbabbaaabaabbaaababbabbabaaaababbaabbbaabbabbbabaababaaaabbbbaaaaabaabbbbaaaaabbaaabbbaaaabaaaabaabbababaaabaaaabbaaabbbaaaabababaaaababaabaabbabbabaaabbbbbbaababbaaabaabbbbabababbaabababbbbbabaababbabbbaabababbabaabaabababaabbbabababbbbbabaabbbbaaaabbabababbabbabbbabaabababbbaabaaaabbbbabaabaabaaaaababababbbbbbabbbbabbbabaabbbabababaaaababaaaabaabaaaabbababbbbbaabaaaabaabbbbbaaaabbbabababbbbbabbaaabaaaabbbbaabababbbaaaababbabbbaabaabbaaaaaaaaabbbaabbabbbbabbaabbabbbaaabaababbabaaabaabbabbbbbabbbaabaaabaaaaaababaaabbaaaabbabbbbbababbbbbaabaaaabaabbaaabaabbaabbbbababbaaabbabaabbbaaabbbbbaabbbbabaabbbbbbaaaabaaababbaaabaaabbbabbaabbababaaabaabaaaaabbabbbabababbabaabbbaaabaabbabaabaabbbbabbbbabbbbbbbbabaabababbabbbbbbabbbabaaaaababaaabbabababaaaabbabaabaabbbababbababbbaabbaaabbbbababababaabbaaaabbabbbaaaababaaababaaabaabaaaabaabbbaabbaabbabaabbaabbabbbaaaabbabbbbbaababbabbabbbbaaababbbbbababaaaaaabbbbbbaaabaabaaaabbbaaaaaaaabaabbbababaaaabbaabbabaababaaabbabaaabbaaaaababababbbaaabbabbbbbbaaaaabaababababbbbaabaabbbbaabbbabbbabbbababaabbababbabbbbbbbbababbbbabababbbabaabaabaaabbabbababaabaaaabbbbbabaaabbbbabababbababbabbbaaabbbbbaaabaaaabbaaaabbababababbbaabbababaabbaaaaabbbaabbababbaabbaaababbaabaabababbbaaaabbbaaaaaabbabbbbaabbabaaabaaababaabbbbabbabbbbabbbbaaabbbabbbbaaaaaaaababbaababaabbabaabbabbaabbbaabbbabaababbaaabaaaaabbbabbbababbbabbbbbbbaaababbaababaaababaababaabbbbaabbbabbbbaabaaabbbaaaaabaaababaaaaabaabaababababaaaaabbbababbbbabaabbababaaababaababbabbbaababbaabbbbbabaabbabaaaabaabbabbaaabbbbbabbbbbaaaaaaaaabbbbaababbabbbbabaabbabababbabababbabbaaababbaababaaabbbaaaaabaababbaababaaaabbaaabbabaabaababbaaababaaaabbabbaabaabbabbaabbabababbaaaaababbaabaabbabbbbbaaaaaabbaaaaaaaabaabbabaabaaaabbaabbababaaabababbbaaabaababbabbbbaaabbbabbbbbbbabbaaaabbabaaaabaaababbaabaaaabbbbbbbbbbbbbababbaabaabbbabbbaabaabbbbbbbbbbbbaaabbabbbaaaabbaaabaababbbbbaaabababaaababbbbaabbbabababbaaabaaabaabbbbabbbbaaabbaaaaaabbabaabbbbbabbbaabaabababaaabababaabbaaaaaabaaabbababbabbbaabbaabbaababaaabbbbbbbbaaababbaaabbababbaabbbbabaaaabbbbbbaaabbabaababbbbbaabaaaabbabbbabbabbbbabbaabababbaaaaaabbbaaaaaaaabbabbbabababaaabaabaaabbabababababbbabaabbabbbbbbbbbabbbbabbabababbaababbababbbaaababbbabbbbaaaaababbbaaabaabaababaabbabbabbbbbbbbababbbabaabaaaaababbbbbbaabaaababbbbbbaaaababbabaabbbabbaaaabababbbbaabaaaaababbaabbbbbabbabaabaababbbbaaabbabbbbbbaaaabbbbaabaabbbabaababbbabaaababbabbbbaaababaaabbabaaaaaabbbbaabbabbabaaaabbbaabbaaaabaabbbbaabbbbabababbaaaababbbbbbbabbbbbbaabbaaabbaaababbaabababaaaaaaaabaabaabbbabaabbababaabaaabbabbbaaaaabaabbaaabaaabbaabaabaabbabbaaaaabbaaabbbbbaaabbbbbabbabaaabbaabbbbaabbbbbabbabababbaabbababbaabbaaabaaaabbbbaabaabbabbbbaaabbaaabbbbabbbabbbbabaabbaaabaaaababbbababbabbbbbaabaabbbababbaabaaabbbbababbbaaaaaabbbbbbabaaabbbabbbababaabbbababbbabaaabbbbababababbabaaaaabaaaabbaaababbbaaabbbbabbbbaabaabbabbbaaababbbabbaaaaabaaaaabbbaababaaaabbbbbbabaabaaabababbbaaaaaababbbbbaababaaababbabbbbbaaaaaabaabaaababbbaababbbbaababaabbabbaaababbabbababbbaabaabbaababbbbbaaaaaabaabbbabbaabbbbabbbabbabbabbbbbaabbaabaabbababaaaabaabaabaababbbabbaaabaaabaabbbaaabaabaaaaaaabaaaaaaaaababaabbaaaabbababaaabaaabbbaababaabbabbabbaabbabaaaaabbabbaabbabbbbabaabaabbbbbbbbbaabbabbbaababbabaaabbaababbaaabbbaaaabaabbbabbabababbbbbbaaaabbabbababababaabbbbbbbbbbbabaaaabaaababbbbbbaabbbaaababbababbbabbaaababbbbaaaabbbbababaaabbbbbbbbaaabbbbabaaababbbabbaabaaaabbabaabbbaabbbbbbaabbbbabbaabbaababbbaabbbabbbaaaabbaaaabaaabaaaaaabaababbbbabbaabbaabaabbbbaaaabababaaabbaaaaaaababbbbaaabaaababaabaabaaaaaaaababaaabbbaabbbaabbaaabbbbbaabbaabaababbbbbaaabaaaabaaabbbaaaabbbbabaaabababaababbbbabbabaaababaabbabaabbabbbbaaaaabababbaaaaabbbbaaabaabbbbbbaabbbabaabbbabbabaaaaaaabababbaabbbbaabbaaaabaabaabaabaaabbbaabaaaabbabbbbabbbbaaabbabbaaaabbabaababbbbbabaabbaabababbabaaaaaaaaaababaabbbaaabaaaaaababbbabbaaababbbbaaabaaaaaaabbbababaabaaabaababbbaababaaaababaabaabaaaaaaaabbbaabaabbbbbbabaaabaaaaabbaabbaababbbbabbabbabababbababbaaaaaabbaababaaaabaaabbbbbbaababbaaaababaabaaaabbbabbaaaabbbabaababbbbbaaabaaabbababbbbbaabaaabbbaababababbabbbaabbababbbbaaabbabbababbbbbbababaaabbbbabaaaaaabaaaaabaaabababaabbaabbabbbbabbaabaaabababbbbbbaaaababbbbbabbbbbabbbabaabaabababbabaabababaaababaaaaaaabbabababbbabbabbaaaaabbbbaaaabaabbbbabbaabbaabbabbbbababbabaabbbaabbbbaabaaabaabbababbaabbbaabbbbbaabaaaabbabaaabaaaaabbbbabaabbaaaaaaabbbbaaaaaaaaaabbbabbabbaaaaaaabaaaaababababaaabbabaabaaababbaaabbbbbbaabaaaaaaaaabaaababaaabbbabbaabbbaaaaaabbbaaaaabaabbabbbbabbaabbbbaaabbbabaaabbabababbbaababbababbabaabbbabbbaaaaaaabbababbbabaababbaaaabaaaabbabbabbabaaaaabbbabbbababababaaabaaaaaabbbabbaaabaaabbbbbabbbbbabbbaabbbbbbaabbabababbababaabbaaabaabaabaaabababbaababbababbaaaaaabbbbbaabbbabbbbababababaabbababbabbbbaaabaaaaabaaaabaababbaaababbaabbbabbaababaabbababbbbaabbbabbbbbbaabaaaaabbaaababaaaababbabaabbbbabbbbaabbbababbbbaaaaabaaabaabaababaaabaababaaaaabbabaabaababbbbbbabaaababbbabbaaababaaaabaaabbaaabaabbbbbbbbbabbaaababbaaababbaabaabaabbabbabbaabaaaabbabaabbbbbbbbabbababbbbbbbababaaabaabbabbabbaaaabbaabbabaabbabbaababababbabaaabaaabaababbbabbbabbbabbaabbbabaaabbababaabaabaabaaababaaaabaaaaaaaaababbaabaaaaaaabbbaaabbbbbaabbbabbbbbaaaaababbbbaabaabaaaabbababbbaabaaabaaababbbabaaaaaabaababbababbbbaaaabbaabbababbaaabbabbbabbbbbbabbbababbaaaabaabbbbabbbbabbbbaabaababbbbababbaaabbbbbbbbbaabbbaaabaaabbabababbbbabaababbbbbbbbbbaababbbbabbaaabbbabbbabbbbbbaabababbbaaaabaababaabbabbabababbabbaabbabbabaababbbaababbaaaaaabaaabbabbaabbabbbbbbaaabaabababbbabbbbbaabbbbbbaabaaabababbbabbbabbbabbbbbaaaabaaabababbbaababaabbaababbbabbbbaaabbbabbbbaaaaabbbabaabaabaabaababbbbbabababaaabbbbbbbbbabbbbbbababbaabbbaababaaabbbbabaaaabaaaabaabbbbbabbbaaaabbabbbaaabbaaabaaaabbbbaaaaaaaaaabbbaabbbbbbaabaaaaababaaaabbbaabbaaaabaaabbbbbaabaaabbbaabaaabaabbaaaabbababaaaaaabbbaababbaaabaaabbbbaaababbaabbbaabbbabbbbbbbaaababbabbbbbabaaaaaabaabbbaabaaaaabbbbbbabaaaabbbbbaaaaaababbabaaabbbaaaaaabbbbaaabaabaabaaaabaaaaaabaaabbaaaaaabbbabaabbbbbbabbaabababbbaaabbaabbbaabbbaaababaaababbbaabaababbbaabbbabaaaabaababaabbbabbbbbaabbbbabbabababbabbabaaaaaabbbabbbaabbaaaaabbbbbbbaaabbaabaaaaaabaabbbbaaaabbbababbbaaaaabbabaaabbaaabbbaaaaabaabbabbabbbaaaaaaabbbbbaabaaabaabbaabababbabababaabaabaabaaabaaababaabaababbbbbbabababaababbabbaabaabaabaabbabaabbbbaabaababaabbabaabbaaaaabbabaaabaabaabaabbbaaababaaaababaababaaaaaaabbabbbabbabbbbbabbaabaabbabbbaabbabaaaabbbbaabaaababbbbbaabaaaaaaaaaabaabbbbbbaababbabbaaaaaabbbbbbbabaabbaaababbabbaabbaabbaabaaababaabbaaaabbbbbaababbabbbaaabbbbabbbabaaaaabbabababaabbbababbbaabbbbababbbabaabbabaaaabbbbabaababbbaabbbbbabbbabbaaaababbabbaaaaababbababbabbbbbababaaababaaabbbbbbbaabaabbabbabbbbbbbbabaaaaaaabbabbaaabbaabaabaababbbbbbaabbabbbaabaaababbbbbaabbbabbabaabbbbbaaababbaabaababaaaaabbaaababbbaaababbaaabababbaabaabaaababbbabbbabbaabbabbbaaabaaaaaaaaaaabaabbabbbbabbababbbbaaaabaabaaababbaaaaabbbbbabbaabaaaaabbbabbbaaabbbabbabbaabaabaabbaabbabbbaabbabbaababaabbaabbbbaabbbaababbabaaaabaaaabbaabaabbabaabaabbbbbaabbbabaaaaababbbaabaababbabbbabbbbbbbbbbabaaabbbbbaaaaabbbbaabaaaabbbbbbabbbababaaaabbbaaaaabbaaaaababaaabbababaabbbbbabbaabbbabbbbbbaaaaabaabababaaababbbabbbabbaabbaabbbababaabbaaabababaabbbbbbbbbaabaaabbaaabbbbaaaaaabaababababaabbbaabbbabbbbbabbaabbbaabbabbabaaaaabbababbabaabaabaaabaabbaabaababaababbbaabbbaabaabbaaabaabbbabbbaababbaabbaababbababbbbbbbaabaaabbaabababbabbababbbbaabbaabbabbaababbaabbbabbaabbabbbbabaabbbbabbbbabbbbabaabbbabaaabbaababaabaabababbaabaabbbbaaaabbbabbbaabbabbaaaababbbbababababbbbbaabbabaaaabbaaabbaabababbbbbbabaabbbaaabbbabbbaabaabaabababbaabababbbaaabaababbbabbabaaaaaaaabbaabababbabbaabbababbbbabbbbaaaaaabababbabaabbaaaaabbaaaaaabbbbabbbbbaabbbbabaabababbabbbbbbbbbabbbaabaababaaaaababababaaababbabaabaaaababaabbaaaaaabaabababaabaaaababaabbbbababbbaabbbbbabaabaaabaaaabaabaaaaaabaabaababbabbabbbbabaaabbabbaaaaaaabaabbbbabbbbbaabaabababbbbabaaaaaaabbaabbabaaaaababababbaaabaaaabababbabaaaaaabbbaabaaaabababbbaabbabbaaabbaababbbababbbbaabaaababbbbaaabababaaababbbbababbababbaabbaabbabbbabbbabbaaaaaaaaababbabbabaababbbaaabbbbaabbabaaabbabbbabbbabaabbbaabbaabbaabbaaabbaabbbaabbaaabaaabbbabbbbbbbabaaabababbbbbbabbabaabaabbbbaabbabaaabbabbbaabaabbbbaababababbbaabbbabbbbaaaaaaaaaabbababbaababbbbbbbbabbbaababbabbbaabbaaabbaabbbaaaabbbbbbaaaabbaaababaaaaaaaababbababbbaaababbabbaabaabbaabaabaabbaabbabbbaabaabbababaabbaaabbaabbbbaaaaabaabbbabbabbbbaaaabbbaaaabbabbabbbbbabbbbabababaabbbaaaababbbbbaabaabbbaaababaabbabbbbbbaaabaabbbaaaaaabbababbaaabaababababbbbababaaabbabaabaabbabbbabbababbbbaaaaaabbbaababaaabbbabbaabbbbaabaabaaaabaaaabaaaababbaababaaaaaabaaabbbaaabaaaababbbbaabababbbbaabbababaabababaaaabbabbbbabbbbaaaaaaabbaaaabbbaaaaabbbaabbbbbaabbaaaabababbbbaaabbabbbbbbabbbbbaaaaabbabbbbaaaaabbabbbbbbabbaaabbbbabababbabaabaaabababaaabbabbabbaaaabaaabbbaaabbbabbaaabaabbbababbaaaaabbababbaababaaabbbbabbaabbbbbbaabbbabbbbbbababbbaabbbabbababbaabbaaabababbbaaabbbaabbbababaaaabbbbabbbbbbaabaaaabbaababbabaaabaabbbaabbaabbbabaabbaaabaababbbaaabbbabababbbaabaaabbbaaababbbabbaaaaabaaaababbabbaaaabaaabbbbaababbbaabbbbbbbbaabababababbaababbabbbbbaaabaaaababbbaaabbaabbaaaaabaabaaabbaaaaabababbbbabbbabbaabbbbbbbabbbabbbabbaabbbaababbbbabaaabbabbbaaabbbabbababbabbaaababaabbbbbbaababbbaabbababababbaaaaaababbbbaaaabbababbbababbaaaabbbaabaaaabbaaabababbaaaabbbbaabaaababbbbabaabbaabaaabbbbaabaaabbabaaabaabbbaaaabbbababbaaabbbabbabbaabbabbabaabbbabaaabbababbbababaabbbbbbabababbabbaababaaabbbbbaabbbbbababaaaabbbbababbbabbaabaabaaaabbaaabbbbbbbbaaabbbbaaabbabbbabbbaaabaabbbabbbabbbbaaabbaabababaaaabbbbaabbaaaaaabababbaababaaaaabbbbbbabbabbbaabaaaaabaabbabbbbabbbbbbbabaaababbaabbabbabbbbaabbababaabbaaaabaabbaabbbbbbbaaaaabaaaabbabbaabaaabbabababbbabbbabbaaaaababbaaababaaaabbabbbbbababababbaabbbbabaaaababbbaabbaaaabbabaabbbbabbaaaabbaaaabababbbbabbbbabaabaababbaabbbaabbbbbaaabaabaaabbbabbabbaaaabbaabababbbbabbaabbbaaaaaabaabbbaabbaabaabababbabbbaabbbaaaaabbbbbabaaaaabbaaaabbbabababbbbabaaabbaaaaabbabaaabbabbbabbbbbbaaaabbaababbbbbbbabbabbbababababbabbabbabaabbbabbaaabaaaabbaabababaabaabbabbbbbaababaaabbbabbaaaaaaabbababaaaaabaababbabbbaaaabaababaabbaabbababbbabaaabaabbbababbaaabaaabaaabbbbbaaaaababaaabbabaabbaaaabbababababbbabbabbababbbbbbbbbabbabbbbbbababaaaaaaabaaaaabaabbbabaaababaabbbbbbabbaaababbaaabaaabbbbbaaabaabababbabaaaabbaababbbaaabbbbaaabaaaaabaabaaabbaaabbabaaaaaaabbaaabaaaabaaabaaabaaabbaababaaaababababababaababbbabaabbbababababaabbbabaabbbbbbabbababaaabbabaabaaabaabbbbbabaabbbbbabaaaaaabaaababaaaaabaaababaabbbaaabbbbabbbbbabaabbababbaabbaaaaaabaaaaaaabbaaabbbbaabbaabbaabaabaaaaaaabbbbababbbbabbbabaababbbbbaaabbabbabaabbaaaaabbaaaabbaababaabbbbababbabbaabaaabbbabaaabbaababbbbbaabaabaabaaabbababbabbaaaaababaababbbaabbabaabbbbaaabbababbbbaababbabbaabbbababbaaaaababbbbbabababaaaaaabbaabbaaaabaaaabaaabababbabababaabababbababbabbababbbaaabbabbbaaababaabbbbababbbabaabababbbabbbabbbbbbbabbabbbbababbaaababbaababbaabaaabbbbabbabaabbaaababbaabbabbabbaaabbabaaaabbbabbaabbbbaabbabababbaabbabaabaabbabbababbbaababaabaaaabbaabbbababababbaaabababbbabbabbaabbbbaaabaaababbbaaababbabbaabbbaaaabaabababaabaababbbbbabbbaabaabaaaababaaaaaabbbbbabaaaaaabaabababbbabbaabababababaaabbbaaabbaabaaababbbaaababaabbbabaaabbbabaababbababbbababaababbabababbbabbabaabaababbbbbbaababaabbbaabbbbaabbbbabbaaabaabbbaaaabbbbbbabaabbbbbbbbaabbbaabaabababbbbbaaaababbaaabbabaaabbaaaaaabbbabaaababaaaabbbbbaabbbbbaabbaabbbabaaaabbaabaababbaababaababaabbbaabaaaaababbaaababbaabbbabbaabbaabbbaabaaababbbbaababbbababaababbaaaaaaaaaaaaabbbababbbbbbaaabbaabbbabbabaabaaaaabababbbaaabaabbabbaabbabaaabbbababbaabbbaabbabaababbbbaaaaaabbbbaaaabbabbaabbabaabaaababbbaabaaabaaabbbbbbabbbaaabbbbababaaabbbbbbbabbbaabbbbbaabbaababababbaabbbabaababaaaabaabbabbaababababababaababaabbbbbabaaaaaabbbbaabbbbababbaaaabbabaababbbbabababababbbababbabbbabbbaababaabaaaaaabaabbbaaabbaabbabababaaaaabbaababaabbaaaaababababbaabbaabbbabbbbababbbbabaaabbbbaaabbbabbbaababbbbabbbbaaaabaabbbbbabbbbababbbbbaaabbbabbbbaaabbaaaaabbababaaaaabbabaabaababaaabbbbabbaaaabaaabbaabaaabababaababbaabbbababaabbbaabbaabbababaaaabbababaaaaaabaabababababaabbabaabaaababaaabbbbbbaaaabaaaabaabbbabaabaabbaabbbaabababbabaaaabbbbababaabbabbaaababbbabaabaabbabbabaabbaabbbbabaaaabbabbbaabaaaaaabbaaabaaabbbbababaabbbbababbbbaaabbaaabbaaababbaaaaabaaaaabaaababbaaaaaabaabbabbaaabaabaabbabbbaabaabaabbbababbbbaaaaababbabaabbaabbbabbbabbaabaabbaabaabbbaababbbaaabaaaabaabbabaaabbbbbaababbabbaabaaaabbabaaabbabbbaaaabbbbbbabaaaaabbbbabaabbbaababababbaaababaaabbababbaabbababbbbabbbaaabbaabbbaaabaabbbaaaaabbababbababbbababababbbaaaaabbaaaaababaabbbabbbbbabababbabbaaabaaabbaabaaababbabbabbbababbbabbaabbbaaabbbabbababbbaabbaabbbaabaabaaabbabbabbabbbbaabaabbaaabaaaaaabbbbbbaabbbbaababbbaaaaabbaabbaaabababaaaabbaaabbaabbbabbbabbabbbababaaaabaaaaabbaabbababaabbbabbabaaaaaabbbbbbababbabbabbbaaaaaabbabbbbaaaabbbbaabbbabbabbaabababaaaaaaaaaaaabbabaabbbbbbaabbabbbaabaabaabbbbbbbbbbabbbaaaabaaabaaabbbbabaabbaabababaababbbbaabbaababaaaabababbaaabaaabaabbabaababbaaaabbaaabbaaaabbbababbaabaabaabbabbbbbbbbbbaabaabbaaabababbbaabaabaaaaabbbaaabbaaabbbbaaababbaabababaabababbaaaaaaababbbbbabbbbbabaabbaabbaaaaaaababaaababaabababaaabaaaaaabababbbbbbbabaaaaabaababaabaaaaaabbaaabaaababaaaaaaaaaabbabaababbaabbbaabaabababaaabbbbbaabaabbaabbbabbaabaaabbbbabbbbaabaabbbbaabababaabaaaaabaabbabbabaabbbbababbbaaabbbaababbbbbaabababbaaaaabaaaabbbbaaababbbaaaababbbbbabababaabbaabbbbbaaaaaabbbabbabbbababbbabaabbbaaabbaabbbabbbabbabababababaaaabbaababbbaaaaaaaaaabaabbbbbbbbbaaabaaabaaaabaaabaabbaaabbaaabaaaabaababbaababbbbbabbaabbbbbbabbabbaabbbbbaabbbbaabaabaaaabababaabbbbababababaababaaaaaabaabbbbbaabbbbaaaaaaaabbbbaabbbaabaaabbababbbbaaabbbbbaaabbaaaabbbababaaababbaaababaababbbabbbaabbbaabbabaabaababbbbbaaaaabbabbbbbaabbbbbaabbaababbbbaabbaaabbbaaaababbbbbbaaaabbabababaababaaaaaaabbaabaabbbababaaababbbaaabbbbaabbbbbaababaaabbababbaabaaabbbaabaabbbabbbbaaaaaabbababbabbababbabaaabaabbababbbbbaaababbbbbaaaababbaaaababaabababaabbaabababbbabbbabbbbabbaabaabbaabbbbbbaabbbabaabababbbabbabaababaabbaaaabaabaabaaaaabbbbbbabbbabbabbaabaabababaabbbabbabbabaabbabaabbbbbaaaaaabaababbbbababaabaabbbaabbbbbaaabaababbbbabbbbabbabbbaababaaaaaaabbaaabaabbbaaabbbbaababbbaaababbbabaaaabbbabbbabaaabaabbbbbbabbaaabbabbbbaaababbabbaaabababaaaabaaaaaabbbbbbbabaaabbbababbbbababbbaaabbababababbabbabbaabaabbababababbbabbbbbbbaababaaaabaabbbbaabbabaaababababaaaaaaaabaabbbabbbabaabbaabbbbbababbaaaaabaabbabbbabbbbabaabbbaaaaaabaababbaaabababbbbaaaabaabaaabaabbababbbbabbbaabbbbabbbaaabaabbbabbbaabbababbbbaaaaaabbbabaaabbaabbabbabbbbbbabaabaabbbbbaabbbbbbbbbaabaaaaaababbbbbbaabbbaababaaabbbbabbaaaabbbbabaababaaaabbabbbaabbbabbaabaabbaaabaabbbaabbbabbaaaaababaaaaabbabaabaaaabaaabbbabbabaabbbbbaaaaabaabababababaabbbbbabaabababbabbbbbbaaabbabbaabbabbabbbaabababaabbabbbbaababbaaaabbbbaaaaaaababbbbaabaabaaaababaabababaabbbaaababbababbbbabbaaaabbabaababbabaabaaabaaaaaabbabaabbabaaaabbaaabbabbbbaaababbabaaaaabaabbaaaaaababbbbbaaabaaaaabbaaabbaabbabbaaaaaababbaabbaaabbbabababaabababbaaaaaaabaaabaabbabbaaaabbbbabaabbabbbbbbbabbbbaaabbabbabbaabbbaabaabaaabaabbbabbaabbaababaabbaaaaaaaaabbbaabaabbbbaabbabbbaabbabaabbbbbabababaabbabababaaaabbbaaaaabbabaaabaaabaabaabaabbbaabbaaababaabbabbbaaababbbbbbaaaaaabbbaaaaabbaaabaababaaaabababaabbbbbababbabbabbbbbbaaabbabbabbabbbabbaaaaabbbbaaabbabbaabbabbbaaabaabaaaaaaabbbbbbaababbaabaabaaaaaaaabaabbbbaabbbbbabaabbbaabbabaabbaaaaaaaabaaaabaaabbbabbbaaaabbbbaaabbabbabbbbbaabbbbbbbababaabbbaaaaabaaabaabaabbbbaaaaabababbaaabababbabaabaabaabbaaaabbbabaabbbabbbbaababbabbbbbbabbaaabaaaaaabbabbaaabbbaabbabbabbaaababaabaabbabbaabaababbaabbabbabaaabbabababbbbaabaabababbaaaaaaabaabababaaababaabaaabaabbabaabbaaaaabaaabababaaaaaaaabbbbbbaaaababbbbbaabababbbbabbabaabbabbaaaaabbaabaaaaaaaaabbbbabbaabbaabbaabaaaaaaaaaabbbbbabbbaaaaababaabbabbaabaaabbbabbbabbababbabaababbbbaababbbbaabbbabbbbabaaabbbbaaabbbbbabbaaabaabbaababbababbaaabbbbbabbbabbaaaabbbbababaaababbbaababbbaabbbaabbaabbaabbbbbbbbabbbaabaaaaababaababaaaaabaaaaaaaabbbbabbbbbabaabbaaabaaaaabbaaaaaabababbbaaabbbbbbaabbaaabaabaaaababbabbbabbababbabbaabaabbbaabbabaaababbaabaabbbbbaaabbababbaaabbaaaaaabaaaaaaaaaaababaabbbbbbabaaaabbaabaabbbaabbbbaabbbaaababbbababaabaabbbbaabababbbaabbaaaababbbaaabaabbaaababaababbabbabaabaaabaaabbaaaabaaaabaababbabbbaaabaaaabbbbbbbaababbbbaaaaaaabbabaaaaabbbababbaaababbaaababbbababbabbbbbabbbaaabaabbbaaaabbbbaaaaabaabaabbbaabaaaaabbbaaabbaababbbbbbbabbbbabaaabbbbbbbbabbabbbbaaaabbaaabbabbbabababaabbbabaabaaababbbaabababaabbabaaaaabbaabbbabbaabaaabaabaaaabbababbbabaaaababaabbabbbbaabaaabababaabbbbbabbababaaaabbbabaababbbababaaabbbbbbbabbabbbbaabababaabaabbaaababaaabbaabbaaabaaaababbabababbaabaaaabbabaaaaaabbbaabbbaaababaababbabbbbabbbababaaaabbbbaabbbbaababbabababbbbbbbabbaabbbaaabbaabbbbabbaabbbabbaababbbabbaabbbabaababbabbababbbbabbbbbaaabababbaaaaaababababbababaabababbbbabbababbaaabbabbbabbabbaabbabbbbaaabbbaabaabaaabbbaabababbabaaaaababbabaaaaaabbabaaabaabababbbbabbbbaaaabaaabababbabbaabaaaaaaabbaabababaaaabbbbbbbabaabbaababaaaabbababbbabaaaabbbaabaabbbaabaaabbabaaabbbbabbabbbaabbbbaabbbbbbbbaaabbaabaaababaaababaabbaabbababaaaaabaaaaababaabbaaaabbbaababaaabbbbaabaabbbabbabbbbaaabaaaabbaaababbababbababbbbbbaabaabaaaababbbabbabaaabbbababbbbbaaababaaaaabbabaabaabababbabaaabbbabbbabbbbaaabbbbbbaaaaabaaaababbaabbbaaaaaabbababbbbbbbabbabbbbbabaabbabaababbabbaaaaaabaaaabaabbbaaabbbbaaaabbaaabaaaabbaabaaabbbabaababaabbbaaababaabaabbababaaabbbaabbbabbbaaabaabbbbbaabbbabaabaababbabbbaaaaaabaaaaaabbaabaabbbabbbbaaabbababbabaababbaaabaababaabaabbaaaababbbbbbbabbaababbbbbabbaabaaabbbabbbaaaaabbbababbaabbbabbbbaabbbbbbbababbbababbbbbaaabbbbabbaabbabaaababaaaabbbaababbabbabbbbaabaabaababaaababbababaababaaaabbbabbababbababbbbabbbabaabbaaaabbbbbbabbbaabbbbbbbbbbbaabbbabbbabbbbababbababbbbbaabbababaababbabaabaaababbababbaabaaaaaabaaabaabbbabbababbbabaaabbbabaababbbaabaaabbbaabbbbbbbbabbbabababababbbbbbaaabaaaabbaaababbbaabaaaabaababbbabbabaabababaaabaaabababababaaabbaaaaaababbaaaaababbbbaaaaabbbbabaaabaaaabbabaaabaabaabbbbbabbabaabbbbabaabbbababbbbababbaaabbabbaaaaabbbabaaabbbbbbabbabbbabbbaababbbabbabaaabbabbabbbaaaaaaabaabbbaaaababbbabbaabaababbabaaaaaaababbbbbbbbabbbaaaabbaaabaaabababababbaabbabbaaabbabaabbbaababbbbabaabaabbaabbbaabbbbbbaabbabababbbbbaabaaaabbbbaabbbbaabaaaabbaaabbbbaaababbbaabbbbabaabbbbaabbaabaabbbbbbbbbbbaabbbaabbaaaabbbbabbabaabaabbabababbabaabaaabbbbababbbbbbbabbaaaabababaaabbaabbababbbabbabaabaababbbbaabbbbbbaaaaababbbaaaaabbabbabbbabbbbaabbaababbbbaaaababbabaaabaabbaaaaaaaabbababaaaabbababbbbabaabbbbababbaaabaabaabbbbaaaaaabbbbaaaabbabbabaaabaabaabbbababaaababaaabbaaababaaababaabaaabbbaabaaaabbabaaaababaabbaabbaabbaababababbbaabaabbababababbbababbbaabbbbbababababababbaaaaabaaabbaabbabbabbbaaaabaaabaabaaaaaaabbbbabbababbbbbabbbbaaabbaabbbaabbbabbabbabbbabaabbababbaabbabbaaaabbabbaaaababaabababaabaabababbbbaabaabaabbbbababaabbbaaaaaabababbbbabbababbbbababaababaaaaabbaaaabaaaababbababbaaabbbabbaababababbbbbbbaabaabbbbaaaabbaabaaaaababaabbaabaaaaaaaaabbbabbbaaaaabababaaababbababbaabbbabbaaababbaabbabababaaabaaaaaaaaaaabbbaaabaaaaabbbaabaaabbababbbbbbabbabbaabbaabbaaaaaabaaaaaababbabbbaabbabbaabababaaabbaaabaabaababbbabbbabbbabbababbbbbbbbaabbbaaababbaabaabbbaabbababaabbbabbbaababababaabbbbbbabbbaaabaababbaabbaabbbbbbaaaaaabbabbaabababbaababaabaaabbbbabbaabbbaabbaaabbababbbbbbaababaababbbbbababaababaabababbaaabbabbbbaabbbaabbbbbbaabaabababaaababbbbbaaabaaaaabbabbbbaaaaaabababbbbbbbaabbbbbabbabbaaaaaaaaaaaaabbbaabbabbaabababbaaaaabbaaababaabbaabbaaaaaaabbaaabaaabbbbbaaabbababababaabaabbababbabbbbbabbabbabbbabbbbabbaaabbaaabbbaabababaaaaaabbbbbbabaaaaabbbbabbabbababbaabababaaabbabbabbbabbbbbbbabbbbbaaaaababababbabaaabaaaabbbababbaabbbaababaabbababbbbabbabbbbaaaaaaabbaabababbabbaabbabaabaaaaabbbaabaaabbbbbaababbbabbababbbabaaabbbbbaaabaabaabbaabaaaabbbababababbabaabbbbababbbbbaaaababbabbbbabaabbabbaabababaaabaabbababbaabbabbbaaaabbaaaabbbbbaabbbbbbabaaabbbaaaaaabbabaaaabbbbaaaaabaabbabbbbbabbbababbaabbabaabbaabaabaaabababaaaaabbbabbabaaaaabaabbaabbaaabbbabaaaabbbbbbaabbbbabbbbbbaaaabababaabbbbbbbabaaabbbababbbbaaabbbabbabaabbbababaaabaabaaaaabaaaabbbaabababaaabababbbbbbbbbabaabbbbabbaaabaaabaababaaaaabababbaaaabbaaabaaabbbbbabaaabbbbbaabbbbabbbbbabaabaababbaaaabbbabaaabbaabbabbbaaaabbbbababaabababaaabbabbaababbbababaaaaaabbbbbbaaabbabbabababbbbbbaaaabbaabbababaabababaaabaabaaaaababaaabababbaaabbbbbabbaaabbbbaaababaaabbbaabbbaaabbbaabbaabaabbabaaaaabbbaaaabaababaabaabbbabaaabbbaaabbbabbaabababbbbbbbbabbbbbabbbababaaaabbaabaaabbaabaabbaababbaaabaabbbaaaabbbaaaaaabbaabbabaabaabaaabbbbbabbaabbaaaaababaaaaabaaaababaabaaabbaabbaabbabaabababbbbbaaaabbbbbbaabbbaabbbabaabaaabbabbaaaabbbbbbbabbaaabbabaaababbaabbbbaabbababbaabbbbbbbabbbabbbbbaabbbaaabbbabbabababbabbbbbaaabaabbabaabbbaababababababbbbabbbabbabbababbabbaabbaababbbabaabbabaabaababaabbbaabbaabaababbbaabbabaabbaabbbabbabbaaaabaaabaabaaabbbbabbbaaaaababbabaabbabbabaabbbaaabababbabaaaabaabbaaaaababbaabbbaaabbaababbbabbaaababbbaaaabaaababaabaabbbabbaaaaabaaababbbbbbbababbabbababbbbbbaaaaaabbabbaaabbaabbaaabbbbababbabababaaabaaaababaabbbbaaabbbbaaaaabbabbbbabbabababbabbbbbaabbbbbbbababaababbabaabbabbbbbabaababaabaaaababbbbabaabbbabbaaabaabaabaaaabbabbabbabbabaabababbabbaabbaaabbbaaabaabbaaaaabbaabbaaabbbaaabbbaabaabababaaababbabbbaaabaaaabbbaaabaabaaabbbbaaaaaaababbabbbabbbbabbbabbababbbaaababbbabbbaabbabbbbbaaabbbbbabbabbabaababbbbabbbbbabbaaabaaaaaaaabababbbaaaaaabaababaaaabbabbbaaaaabbaababbaabbbbaaaabaababababbbabbbbababbbbbbabbaabbbababbbbababaababaaababaaaabaabbbbbbabababbbababbabbbababbaabbbbbaaaabaabbbaabbabbababaabbbaabababaabbabbaaabbabbaaaabaabbaababaaabbbaaabaabbbbabbaababbbaaaaabaaabbbbabaaabbaaaabbbabbbaababbbaabbbabbbabbbababbaaabbabbbabbbaaabbaaaaababbbbbaabaaabbaaaaabbaaaabaabbbaaabbababababaaabbababababbaaaabbaaabbbbaabbbabbaaaababbbaaaababaaaabbaaabaababbaabbaaaabbbaabbbabbaaabaabbbabbbbaababbbabaaababbbabaababbbabbbbabbbaabbabababaaaabbbbabbbbbbbaababaababbaabbaaabaaabbbababbbaabbaaaaabbaaabbaaaaaaabaabaabaababbbbbbaababaaaababbbbbaaaabbbbbbbbabbbaabbbbbabbbabaaabbbbbbababaabbaabbbabbaaaabaabbaabbbaababbbbbababbababbaaabbaaaabbbbbbbabaababaaaabbbbbaaabbbbbaabbaabbababaaaaabbbbbbbaaabbaabaabbaabbabbbaabaabaabbaabbabaabbaabaaabbbbabaaaaaabbabaaaaababbbbababaabbbbabbabbbabbbabaabbbabbabaaaabbbbbababaabbbababbbbaaabbaabbaaabbbbabbaabaaabbabbbaaaaabaaaaabbbbabbbaabbbababbbbbabbbaaaabbbaaaabbaabaaabaaabaabbabaabbbaabbbaabaaabbbbaabbaabbbbbbabababbabbaaabbbbaabbbabbaababbbabbaabbaaaababbbababaabbbbbbabbbababaabbbbbabaabaaabbaaaabbbaabaabbbababbbaaaaabbbaabbabababbaababaaaababbbbababaabaaaabbbbbaaaaababaabaababbabbbababaabbaaabbbbaababbababaabbaaabbaabbbaaabaabbaaaabbbaaabbabaaabbbababaaaaabaaaabaaabbbaaaaabaabbaaaabbaaaaaaabbbaaabbaabaaaaababbbabbbbbbaaaababbbbabbaaabaabbaabbaababababaaaabbabbbaaaaaabaabaaababbbbababaaabababbaaabbbbabababbaaabaabbabbaabbaabbaabaabbaabaaabbaabbbaaabbbbbabbaabaaaabbaababbbbbbaaababababbaabbbabbbaabaaaaabbaababbbaaaabaaabbbabaaababaabbbbaaaaababababbaaababbabbbbabaaabbbaaaababaaabbaabbbabaaabaaabaabaabaaaaaabaaabbaaabaabaababbbabbabaaaaabababaaaaaaaaaababbbbbaaaaabbbaabbbbaaaaabbaabaaaabaaaababababbabababababbbabbbabbbaabbabbbaabbabbaababbbbbbbbbbbbaabbabaabbbbaabbabbabaaababbbaababbabbbbbaabaaabababaabaaaaabaabbaababbaabaababababbaaabbabbbaabbbaaabbbabbababaaabaaaaabaabbbbabbbaabaaabbbbaaaabbaaabaabaaaaaabaaababbaabbabbabbababbaaabbbbbbbbbabaaaabbabbbbaabbabbababababbaaaaaaabbaaabaaabbbabaaabaabbaaabbbaaabbabbbaababaabbbaaaaaababbaabaaaaaabaabbbaaababbabbaabbbbabbaabbbbabaaabaaabaaaaababaababbbbabaababbabaaababbbbaaabbbabbabbababaaabbabaabbbaabbbabaabaaaabbbabaaabbbabbbbaaaaabbbbbabaaaaaabbabbaaaaaabababbabbbbaabbaaabbbaaabbbbbbabababbbbaabababaaabaabaabaaabbbabaaabbabbbaaaaabababbbabaaaaaaaaaaaaaaababbbbbaabbbaabbabbbbabaabaaabbbaaaabbbbbabbaaaababaabaabbabbaabbabbbababaababaaaabaaabbbbbbabbabaaababaabbabbbbabaabbaabbaaabbaabaaabaabbbbaabaaaabbbbbbaabbbbaaababaaabbbbaaabaaaaabaabbbaabbaaababbabbabaabbbabaabbabbababbabababaabbaaaaaaabababaaaabbbabaaaaaaabbbababaaaaabaaaaabababbabbabbbabaaaabbbbabababbbbaaaabbbaaaababaaabbabbbabbabbbababbbaabababaababbbabbbbababbbaabbaaaaaabbaaaabaaaabbababaabaabaabbabbbaaaabbbbbbbbaabbabaaabaabaaaaabbabaaaabaababaabababaaaabbbabaabaaabaaaaabbaaabababababbaabaabbbbbabaaababbbaaaaabbaaaabbbabbbbbaabbbbaaabaababaababbbbabbbbbaabababaabbaabbbbbbabaaaaaaababbbbbabaaababbaababaaaaaabaaaaaabaababbbbbaaababaabbababaaababababbbaaaaaaabaabaababbbbabbbbabaababbabbbabaaabbabbbababaaaaaabbbbaabbbbbababababbaabababbabbababbabababbabaaaaaabaaaaaabaaabbbabbbabbaaabbbaaaababbabbaaabbaabaababbabaaaabbbaaabbaaaaabbbaaaabbabbaabaabababbbbbabbaaababaabaabbbabbbaaaaabababbaaaaaababaabababbaabbbabababbbaabbabbbbbbbabbabababbbbbbaaaababbbabaaabbbaaabaaabaaababbaaaababbbbaabbbababbbbabaabbbabbabbaabbbaaabababaaababababaabaaababbababaaaaabbabbbaabaabbbbbabaaaabbaaaaaabaaabbabaaabbbbaabbbaabaababbabbbabaababbbbabaabbbbbbabaababbbbbaaaabaaababaaaaabaabbbaaaababaaabaaabbbbbabbbaabbaaabbbbbaaaabbaabbbbbaabbaababbbbaaababaaabbbbaaaabbbaabababbbbaabbabaababbbaaababaabbaaababbbbabbaabbabbbaaaabaaabbabbababaabaaabbbbbbaabbaaababbbaaabaabbbabbbbabbabaabbbbabaababbbaaaababaaaaabbbbbabaaaababaabbbaababaaabbaaaaababbbbabbaabababbbbbbaaaaababbbbababaabbbabbabbbabaababbbaaababbbabababaabbababbabbbaaabbbbbaaabbabbbaaaabaaababbbaababaabbbabaabaaabaabbbbbabbbbbbabbababbbbbaababaaabbaabbabbbabbaabaabbabaaabaabaaababbbaaabbbabaaabbbbababbabbbbbababbaaabbababaaabaaabaabbabbabbbabaabbbaaabbaabbaaababaaabaaaabbaabbaaaabbaaabaabbbbabbabbbabaaabaaaabaaaaabaabbaabaabababbbaabbbabbaabaaaaabbaaaababaababbabaabbabbabbaaabbaaabbbabaabaaaabbbbbaabbbababaabaabbbbaabababbbbbababbaabaabbbabbababaaaaabaabaabbaabbaabbaabaabaaabbabababbaabbabbbbabbaaababaaabaabbaabababaaabababbaaaababbaaaabababababbbabbaaababaaabbabbaaaaabbaaabbbabaaaabaaabbabbbaaaabaaaaaaabbbbbababaaaaaababbbbababbababbbabababbbbbbabaaaabababbababbaababaaabbaabaaaabbbbbbabaababaababbabababbaaabbbabaabaaabaabaaabaabababaaaabbbababbababbaaaaaababbaaaaaabbabbbbbabbabaaaabababbaaaaaabbbaabbaabbbbbaabbbaaabbbbaaabbbbabbaabaaaaaabbbabbabaaaabbbbbbababbaaabbabbaabaaaabaaaaaababbababbaabbbbaaaaaabaaaaabbbbbbabaaabbaabbabababbbaaaaabaaaabbbaabbbbaaaabbabaabbababbabbaababaaabbaaababbbabbbbabbabaabaabababbbbbabaaabaabaababbbbabbbaaabaabbbbbaabbbabbbbbabbaaabababbaabaaaaaabbaabababbbbaaaabaaababaaabaaababbbababbaaabbabaaaababaaabbabaaababbbbaaaaabbaabaabbbbaabaaabbaabbababbbbbaaabbaaaabababbaabbbaababbbbaabbababaababbababbbaaaaaabaaaabaaaabaaabbaababbbabbbababbaaaababbabbbabaabbbabbbaaabbaaabaaaabbaabbbabaaaababaababbabbabbbbaaaabababaaababbbabaaabaabbbbbabbbaabaabababaaababababbbbaabbabbbabaabbbbabababbabbabaabbabaabbabababbaaabaabaababbbbaaaabbabbbaaabbbbbbabbaaabaabaabbbbbaaaabbbbabaabbaabbaaabbaaaababbabaabaabbbaabababbbabbaaaaabbaababbbbbabaabaabaaaabbbaaaababbbbabbaaabbbaabbaaaaabbbaaababbaaaabbbababaaabbaaabababbabaaaaabaabbabababababaaabbbbaaaabbaabaabbabbbbbabbabbbbbbbaaaaabbbbbabaaabbbabbbbbababaaaabbabbbbbbaabbbababbbbbbabbbbbbaabbbaaabbbabaaaaaaaaabbabaaaaabbbababbabaaaabbababbbaaabababababaabbbaaaaaaabaabaaabababbabbabbbabbbbaabbbaabbbaaaababbbbbabbaaaaaaabbabbabbbbabbaabbaabaaaaaababababbaababaabbabbababaaaabbbaaabbabaaaaabababaababbbbabbbabaaababababaabaabbbbaaaaabbaabaababbabbabbabaabbbaabaabbabbaaaabbaabbbaaababaabaabaaaaabbabaabbaababbbaabbabbaabbaaaabaaaabababaaaababaabbbbbabbaaabbaaaaababbaabaababaaabbbbaabaaaababbbabbababababaaabaababababaabaababbabbbabbaaabbbbbaabbaabbbabaababbaabbaabaaababbbaaabaaabbaaaaababbbbabbabbaabaabaaaaaaaababbaabbaabbbbaabbabbaababaababbbabaaabbbaaabaaaaabbbbbabbbabaaababaaaabbaaaabbaabaaababaaabbabbabbbbaabbbabbbabaabbbabbaaaaaabbabaabaabbbababbaabbabbaaaaabababababaaaabbababaabbabbabbbaababababbabbababaabababbaabbababaababbbbabbbabbbabbbbbbbbaabbaaabaaaaaabaababaaabbbaabbbbbbbbaababbbbaaabbaababaaaaabbaabaaabbabbabaaabbaabbabbabbbbababbbabbbbbbbaaababaaabbabbabbaababbaabaaabbbbbbbbbaaababbbbbbbaabaabbbbbbabbbbbbbaaaaabbbaaababababaaaaaaabbabbbabbaaaababbabbbbbaaababbbbabbbabaabbaaabaababbababbbbbabbbabbbaaaaaabaaabbabbaabbbbbaabaaaaaaaabbaaaaaabbbaaaabbbbaabbaaaaaaaaabbbaaaabbbbaaabbbaaaaabbabbbababbbabbbabbaaabbbbbbaaaabbabbbaaabbaababbbaabbbbbaabbabbababbababbaababaaababbbbaabbabbbbaabaaaababbbaaabbbabaaababababbbabaaaaaababbababbbbababababababaaabaaaaaababbbbabababababbbaaaabaabbaaaabbbabbbaabbababbaabbaabbbaabbbabbbbbaabbbbabaabaaaabbbbbbaabbbabbabbbababbbabbabbabaabaaaaaaaabbbaabbabaaaabbbbbbababbaabbabbababababbbaaaabbbaaaabaabbbaababaaabbbbaaabbbababbababbbbaaabbababbababaabbaaabbababbababbbabbbbbbbabaababbbaaababaaabbbabbabaaabaabbabaabbbaaabbaaabaababbabbbaaabbbaababaabbbbbaababaabaabaaababaabbbabbbbabbbaabbaaabbaaabbaaabababaababbaaaaaabaabbababbabaaaabaabaaaaabbbbbaababbaaabbbabaabbabababaaaaabbbaaabbbabbabbaaaabbabbababaabbbbbbbbababbbaababbaabbbabbabbbabbaabaaababbaabbbbaaabbbbbabbbaaabaababbaaabbbaabaaaabaabbabbababbbbbbbabbbbabbbbaababaabaaaaaaababbbaabaaaaabababaababaabbaaabbbabbbabababaaaabbabaabaaabaabaababbaababbbaaaaaabaabaababaaabaaabbbabbbabababaaabbaaabaaabbaaabbaabababbbabaababbbaaaabbabbbbaabaabaabbaaaaaabaaabbbbaabaaababaaaaaabbbababbbaaaaabaaababbbabbbabbaabaabaaaaabaabbbaaaaaaabababaaabababbabbbbabaabababbbbbbbabababbabbabbababaabbabbabbaababaaaaabbbbbbbbaaaabaabababbaabbbbbaaaabaababbaabbabbaababbbbbaaabaaaaaaaabbaabbbbbabbabbbaaababbbabaaabbaaaabaaaaabbabaaaaaabbbbaabaaababbabbaaaabbbbbbaaabbbbabababbbaabbbabaaabbaababbbbababaabbbabbaaaabbabbabbaaabbbaaaabaabbbbababbbababaabbabbaaaaabbaabaababbabaababbaaaabbbbbbbbaabaababbbbaabbbbaaabaaabbbaabbbaaababababbabaabababaaaabbbabbabaaabaabbbbaaabbbaabbaabaabbbaabaabababbabbabbaaabbaaabaaaababaaaaababaaabbbbaabbaabaabaaabbbbbbaabbbabbbaabbbbbabbbbbabbaabaaabbaabbbbbabaababbababbabbbbbbbaabababbaaabbbbaaaabaabbaababbaaaabbbabbabbabbaaaababbabababaabbbbbbabbbbabaabbaaaabbaaaabbbbbbbabaababbabbbbbaabbbaabaabaabbabaaabbbabaababbabbbbabbaabbbaaababbabbaaaabbbbabaababaaabbabbbabaabbaaabaaababaabbbbbababbbaaaaaabbbaababaabaabbbababaaaabbbbbbabbbaaaabbbbbaabbabbbaaaabaababababbabaaaabbbababaaaababbababbbabaaabaaababababababbbaabbbaabaaaabaabaabaaabbbaababaaaabbbaabbbbaaabbaaaabbabaaabbabbbabbaaabaaababbaaaabbbbbababaababaabbabbbbabaababaabbbababbabababbbbbbabbabbababbbaabbbababbaaabbaabaabbaaaaaabbbaaababaaabaaaababaabbaabbaaabbaabbaaaabaabaaaaaababbbbbbaaabaaaaabaabbbaababbbababbabbbbbabbbbaaaabbbbaabbbbaabbbaabbabbabbbbbbaabaababaabbbbabbaaaabaababaaabbaaaabbbabbbbaaaabbbaababaaaabbabaabaaaaaaabbababbababbaabbbbbababbaabaabaabbbbbbaaabbbabaaabaabababbaaaaabaabbabbbbabbbbabbababaaabbababbabbaabbaabbabbabbbaaabbbabbbbbabbabbbbbbaaabbbabaabaaababbbbbbabbabbbbabaabbaabaabbababaaaaaaaabbaaabaaababaabbaabaabbbbabbbababbaaabaaabbaabbababbbaaabababbbbbbbaaaababbabaaabaaaaababaaabbababaaaaaaabaababbaabbabaabbabbaabaaabbaaabaabbabbbabaababaaaaaaabbbaaabbbbbbbbbbaabbaababaaaabaaaabababbbbbaaababbbbbbabaabbabaaabaababbbabbbabaaaabbbbaaabbabbaaababaabaabaaaaabaabbbbbbbbabbaabbabaabaabaababbabaababbaaabbbaabaaaaabbaabbaabbababbabaababaababaaaababaabbababbbbbaaababbaababbabbababbaababbbababaaaabababaaaabababaaaabbaabbababbabbaabaabbbabbabbaaaabbaaaaabaababaaabbaababaabbbabbbbabaaabbbbabaaaaabbaabbaaabbabaaabbaaabbbbabbabaabbabababbbbbaaaabbbaaaabbaabbababbaabababbbbabbabbabbaabaaaabaabaaabaabbbbababbbbbaabababbbabaaabbabbbababbaaababbaaabbaabaabbbbbbaaaaaaaaaabaaaaababaaabbbabaaabaababaabaabababbbbabbababaaaaabaaabbbbbbabbbaaabbabaaababbbabaabbabbbaabbabbabbababbbbaababbabbbabbaabbbabbaaaabbaaaababbabbabbbaabababbbbabbbbbbabaaabaaabbbaababbbbbaaaabaabbbbaaabaaaababbabbabbbbababbaabbbabbbaaaabaaabaaaaaaabbaabbabbbbaabaabbabababbbabbbabaaaabbabababababbbaaabbbababbbbbbbabababababbaaabaababbaabaabbababbbababbbabbaababaabbbbabaaababbaaabbaabababbbbbabababaabbabaabaabbaabbbaabaaabbbabaaaabbabbbaaaaabbabaabbaaabbaaaabaabababbbaaababaaabbabbaaabaaababaaabbbabbaaaaaabaabaaabbababbbaababbaabbbabbaabbbabaabbaabbbbbbabbbababaaabbbaaabaababbbbbaabaaabaaaabbbbaabbbbabababbbbabababababbaabbabbbbababbbbabbababaaabababbbbbaaaaaababbaaaababaabaabababbbaaabbaaabbaaaabbaababbaabbaabbbaaababaabbbaabaaabbabbababaaababaababbababbaabbbbabbbbbaababaabaaaaaaaaaaababbbbbbbaabbaabaabbaabbaabbaaabbababbabbabbaaaabbbbbbbababaabbbabaababbbbbaaaabababbbbbbbabaaabbababaaaabaaaaabaababaaaabbbbabbbbaaabababbbbabaaabaabbbabaababbbabaabbababbabababbbaaaabaababaaaaababaaabbbbbbaabbbaaaaabaaaabababaabaabaaaaaababbbbbaabbaabbbaabbbaaaabbbaabbbbababbaaaaaaaababbababaaaabbaaabbabababbbbabbbababbaabaabbbabbbabbbaaabbaaaabaabaaaabbbbbbabbaabbbabababaaaaaabbbbbaaaababbbbaaaabbaaabbbbaaabaaaababbbbabaaaaababaaabaabbabaaabaaabaabbabbbbbaabbababaaaababbbbbaabbabaabbababaaabbbabababbbaaabbabaababbaabaababaaabbababaaaaababaaabbabaabbaaaaaababbbababaaababaaaabbbbbbbbbbbbaabbbbbaabbabbabaaabababaaaaabaaaabbbababaaaabbbbbaabbbbbabbbbbbbabbaababaabbaabbbaabbabaaabbbabbbaabbaaabbbbbabbbabbbabbbbaabbabbaaabbbabbaaabbbaabbbababbbbbaaababaaabbbaababbabbaabaabaababbaaabbbbbbabbbaabaababbbbbaabaaaaaaabbabaabbbaaaababbaabbaaabababbaaaaaaababaaababaaabaaabbbaabbabbaabbaabaaaabbbaabbaabbbabababbaabbbaaabbbaabaaaabbbaaaaaabaabaaaabaabaabbbbaabbbaaaaaabaabbabaaaabaaababababaaaaabababbabbbaaaaaaaaababbbaaaabbaaabaabaaabbbaababbbabbabaabbaaaaabbabbbbbabbbabaabbbbabbbbabababbbabaabbabbbabababbbbbaabbbbabbbabababbaabbaaabababbaabaaabbaabbaaabbbababbbaabbbabbabbbbbbaaaabbbbababbbabaaababbbbbbaababaaaabbaabbaaaabbabbbabbabbbbbaabaabababaabbaaaabbbbaabababbbbbaabbbaaaaaabbabbbaabbabababbbbbbbbbaabaabababbaabaabaabaaabbbbabbbaabaabaabbababbaabbbaabbbaaaaaaaabaabbabaabbaabbabbbaabbbbbbbbaabbbbbbabbaabbabbabbbbaabaababaaaabbaaaababbaabaabbbaabababbaaababbbbabbbbbaababaaaabaaabbbbbbbbabaabbabaabaabbabbbaaabaabaaaabaabaabaaabbbabaaabbbabbbbbbaaaabaababbabaaaabbaabbabbbabbababaababbbabbaaaaaaaabbaabbbaabbbbabbbbabbbbbabaabbbbabaaababbabbbaaaabaabababbabbbaabbbaabaaabaabbabbabaaaababaaabaabbbaabbbabbaababbaababaaabaaaabaabaabaababaabaaaaababaaabbbbaaaabbbbabaaabbbaaaabbaabbbbbbababaabaabbbbbbbbabaaaabbbbaaaaabbbabaababbabbbbaaaabaabaaaababababaaaaaabbbbaaabbaaabbbbabbaaabbabababbbbababbbaabbbbbbbaaababbaaababbabaaaaabbabbbaaaabbabbbbabbbabbbbabbbabbbabaababbaababababbbaaaaaaabbbbbbbabaaaabaabbabaabaabababaabaabaaabbbabaaaaaabaaabaabbabaaababaababbbabaaaaabaaabbaabababbaaaaabbababaabbaabbabaabbaaabbaabbaabbbbbbbbaaababaaaaaabbaabababbaababbaabaaababaaaaababaaababbbabbbaaaaaababbbbabaababbbaabbbbbbabbbbbaabbabbaaaabababbbbbbbaaabbbaaaaabaaaababbbabaabaabbbabaabbbaabbbbbbaabbaababbaabaaaaaababaabbbabaaabbbbbbabbbabbabbbbbbbaaabbababaaabbbbbabaabbababaaaaaaabbbaababbaaabaaabaabbbaaaaaabbababbbbbaabbaabaabbbaabababbbbbbbabaabbbbabbbbbabbbbabaabbababbbbbabbaababbbabbbbbabbbaababbbabbaaabbbbaaabbabbbbaabbbbbbababaaaaaabbabbbaaabbaaababaaaaaaaaaaabbbababbaaabbbababaaaabbabbabbaabbabbbbbbbbaaababbabbbbabaabbaabababbbbbbaabaabbbababaabbbbbabbabbabbaaaabbabbabaabbbbbbbbaabbaabbbbbaabababbbbabbaaaaabababbbaaaaaaaaabaaabaabaaabaabaababaaaabaabbabbaaabbbaababbbaaaaababbababbaaabbaaababababbabaababaaaaabbbaabbabaaabababbbaabbbbaaabababbaabaaaaabbbababaababaaaaabbaabbbaabbababbaabaababaaabbaabaabaabbaabaabaaaabbbbabbbaabaabbbabbabbbbaabbbbbbaaaababaababaabbbbbbbaaabbabbaabbbbababbaaababbbbabbbbaabbaabbbbaaabbaabbabbabaabaabaababbabbbaaababbbabaabbaababababaaabbbaabbbababbaaaabababbbabbaabbaabaabbbaaaaabbaaababbabbbbaaabbababbbbaabbaaabbaaaaabbaaabbaaaabbbbbbabaaaabbbbbaaabaabbabaabaaabababababaaaaaabbbabbbbbbbaaabaabbababbbbaaabbbbbababbbabaaaaabbabbaaabbabaaababbbaaabbaaaaabbbaaaaaabbaaaabaabaaabbbbbaaaabbbaaaababbbbabbbbaabbabaabaababaabbbabbaaaabbbbbbbaaabbaababbbababaaaaabaababbbbaabbababaababbbbbabbaaabaabaabbbaaabababbabbabbbbabababbbabbabbabbababbbbaaaabbaaabaaabbbbbabbbaaaabbababaabbaabaaaabbabbaaabababaabbbaaabbaaababbabaabbababaaabaaaaaabbbaaaabbaabbbbbabaaaaaaaabbbbbbbaababbbbaabbabbababbabbbaaabababaababaabaaaabbbaabaaabababbbaaaabbabaababbabaabbbababbbaabaabbbbababbbbbabaaaabababbbbaaaaabbbaabaabababbabbbaaababbabbbbbbabbbaaababaabbbabbbabbaaaababaabbbababbbbaabbbaaaaabaaaaababaaabaabbbbbbbbabbabbbbbbbbbabababbbaaabbbbabbbaabbbbbbababbbbbaabbbbbbbaaabaaababbbabbbabbaaabbaaaaaababaaaabbabbabbabbbabbaaababbaaababaaabbbaaaaabbbbbbabbaaabbbbbbababbbbbaaaaabbbabaaabbaaaabbaaaaababaaaaabbbabbabbaaaabaabbaabbaabbbbabbbaaabaaaabaabbababbbbaabbababbbaaabaabaaaaaaaaababbaabbbaaababbaabbbabaaaaaaabbaaabbaabaabbabababaaaabaaaaaaabbaaababbbbababaaaabaababbaaabaaabababbbbbbbbbbaaabbabbababbbabbbaabbabababaaabbaabbabaabbbbbabaabbababbababbbabbabaaaaababbaabbabbbaabbbababbaaabaabbbbbbbbbbaaaaababbabbbabbbababbabbbbaaaaaaabbbbbbabbbbbbbbbaababaaaabbbaababaabbbbbbbbbbbbbbabbabaaabbbbaabbbababbaabbabbbaaababbabaabbaababbbbabbaabababbaababbaabbbbabbaaaabbbbbbbbaabbbbaabbbabbabaaaabbabbbbbaabaabaabbbabaababbabaabaaaabbbabaaabbabaababbbbaaaabaabbbaaaabbaabbababbbabbabaababbbababbbaababbabababbabaaaabbabbbaabaabbbbaabbabbababaaabbbbbaaaababaabbbbabbbbababaaabbaaaaabaaabbaaabaabaaaaaaaabaaaabababbaabbbbbbbbbabaabaaaabababaaaaaaaaababbabbbabbaabbaabbbabbbabaababbbabbbaaaabbbaaababaaaabababaaabbabaababaaababbbbbaabbbaaabbaaaabbbaababbaaabbabbbababbbabbabaabbbaabaaaaabbbaaabbbbbbbaabbbbababbaaabbababababbbbaaabaaabbbbabbabbababababaabaaaaabbaaaabbbbbbbaabbaaaaaaaabaababbabbbaaaababbbbbbbabaaabbbbbaabaaaabbababbabbbabbaababababaaabbaaabbbbbababbbbabbababbabbabbaaababbaaaaaaaaaaaaabbabbabbabbbabbbbbababbaaaabbaabbbaaaabaaabbbbbbbbababaabbbbabaabbaaabbababaabaaabbbabbbbbbbbbbaaababaaaabbabaaaaaababbbbbabbabaabbbbaaabbaabbabbaabaabaaabbababbaaaaaaaabababbaaabaaabbbbbbbbbababaaabbaabaaaaabbabbbbabbabaabbbbabbbabbaabbaaabaabaaabbbbbabbaaababbbbaaabaaaabbbaaaaabbabbbabaaaabaabbbbabaaababaaababbaaaaabbbbbabaaabbbbbabbbbaaabbbabababaaaaaabababbaaabbabaabbbaaabaabaabbababaaabaabaaaaabbabaababaaaabbbbbabbabaababababaaababbabbabaabbaababbbaabaababaaaababbaabbabbabbbaabbabaaaaaaabbaabbbbabbbabaaabbabbbbbaaabaaaababbbabbaaaababaaaaaabaaabbbabbbbbabbbabbaaaababbbaabbabbbbababbbbbabbbbbbaaaaaabaaababaabbabbbbabaaababaabababbbabaababbaabbababbaabbbbababbaabbaaababbabaababbabaaababaabbbbbbbabaabababbbaababbbbababbbabbabaaaabbabaaaabbbaabaaabbbbabbaaabbaabbbbbbbaaabbaaaaabbbabbbbbaaabbaaabbabbababbaabbabaaabbbbbbbbbabaabbaababbbbbababaababbabbababaaaaaababbbbbaaabaaabbaababaaabaabbaababbbbaabaaabbaabbbaabbbbabababaaaabbbaaaabaabbbababaaabbbbbbbbaaabbababaaabbaaaabbabbbabaabaabbbbabbabbbaaabbababbabbabaaaabbbaaabaaaababbbbaabaabbabababbbbabbabbaaababbbababbaabbabbabbbaaababbaabbbbbababaaaababbababaabaabbbbabaabbbbbbaaaabbbbbabaaaabbabaabbbbabbbbbaabaabbaaaaaaaabbaaababababbabaabaaabbabbababaabbbbbbbbbabbbabbabbaabbbabbaabbbaaabaabaabbbbaabababbbaabbbaabbaabbaaabaaabbbbbabbbbaabaababaaaaaaabababaabaabbbbaaababbbabaaaaaababaaabbaabaaaaaabbbbbaabbbaaaaaabbbbabababbbabbbabaabbbaabbbbbbbbaaabbbbbaaabbabbbbbbbababbbabbbbbabbaaababbabbaabaaaaabbbbbbbbbbabbbbbaaaaaabbbbbabbaaaababbbaababaaabaabaaaaaaaabaaabaabbbaabbbbbbbaaabbbbaaaaabaaabbabaababababaaaaaaabbbbababaaaabaababaaabaaaabababaabbaaabaabbaabaabababaaabaaabbabbbbabbaaaabbbbbbaabbaabbbbbaaababaabaabbbabaabbaaaaaaababbabaabbbaaaaababababbbbbbbbbaababaabaaabbaabababaabbaaababbabbbaababbbbbbaaaabaaaaaaabbabbaabbbaabbbabbbbabbaabbbbabaabaaaaabababbbabbbabababaaabbaaaaabaaaaaabbbbaaaaaabbbbabbbabbbaababbaabbbbabaabbaaabaabbbaaabbbbbaababaabbabababbbabbabbbbbbabbaaaababaaabaaababbbbbbabbabbbbabbbaaabbbbbababaaabaababaaaabaabababaababbbbabbaabaabbaababbaaabbaababbaabbbbaabbbbabbaaaabababbbaabaabaaabbaaabaabbbabaaaabbaabaababaabbbababababbbbbbaaabaabbbaabbabbaabaaabbbabbbabbbabbbaabbaaabaaaababbaaabbbbaabbaaababbaababababbbbbbbbbaabaabbaaaaabbbbbabbbabaaaaaabbabbaaaaabbbaaabbaabbbbbbbbabbaabbabbaaababbbbbbaaaaabababababbbbbbabbaaaaaaaabaaaabaaabaaabaabbabbbabbbbbbababaababbbabababbbbababababbaaabbaababbabbaabaababaabbaaaabaaaaabbabbbaababaaabbbaabbabaaaaaabababaaabbbabbaabbababbbabaaabaaaaaabbaabaaabbabbbbbbbababbbbbbbbbaaabbbaaabbbbababababbbbbaaabababaaaaabbaaaabaabbaaaaaaababbbbabbababbabbabababaaabbababaababbababbbbabbaabaaaaaabbbabababbabaaabbaaaaabbabbabbbabbababababababbaaababbbbabaaaabbbbabbbabbaaaaabbabaabaaabbbaaaaaaababaaabbabbaaababaabaabbabbbabbbaaaaaaaaaabbbbbbaabaaaabaaabaaababbaaaaabaabbaaabaaabaaaaabaabbabaabbbabaaababbbaabbbbbaababbbabaabbbbabababbaababbbbababbbbbaababbbbababaaaaaaababaabaabaaabbaabbaabaaabbbababbbbbbbbaaabbbabbabaabababbabbaaabbabbbbaababbabababbbaaaabaabbababaababaaabbaaabbbbbabbbabaaaaababbbbabaabbbabbabbaaabbaaabaabaababaabbbbaaabaababbbbbbabbbaaabababbababbbaabaaababaababaabbaabbbbaabbbaabaababbaabbbaaaaabbbabbbaabbbbaaabbbaabbbaaaabbbbbababaababaaabbbbbbaaabbaabaababaabbaabbbaaaabbbbbabaaabbaabbabbbababbaaaaabaaababaabbbbaaaabbbabbbbbbbabaaaabaaabbbbaabbaaaababbaabbbabbabbbabbabbaaaababbaabbbbbaabaabababaabbabaaaaabbbababbbaaaabbaaaaabbbababbaabaababaaaaaabbbbaaaabaaaaaaaaaabbaabaaabbabbbabbaaabbabbaabbbbabbbaaabbabbaaaaaabbbabbabbbbabbaabbbbabaabbaaabbbbbababaaaabaabbaababbbaaabbaaaabbabaaababbabbbbbbaabababbaabbbbabbaaabaaababaabbabbaabaabbbabaaaaaababbababbabaaaaaaabbabbbbabababababbbbaabbaaababbaaaababbababaaabbababbbaabbaaaaaaabbbbaabbabbbbaabaaabbbaabbbbaaaabaabaaaababbaaabaabaaabaaaababbabbbbabaabbaaaaaabaabbabbabbababbbababbabaaaaabbaabbababbabaaabaababaaaaaabaabaabaabbababaaababaabbabbabbbbaaaababbbaaabbbababbabbbbabaabababaaabbbbbaabbabbabaaabaaaabbbbbbababaabbbbbaabaaaabbabaabaabbaabbbbbbaaaabbabaabbababbbbbaabbabbabbbabbbaaabbaabababaaaaabaaaaaabbbaaaabbbabbabbabbabbbbabbaaabaabbbaaabbbbaaabbbaababaababbaaaabbabaabaababaabbabaaaaaabbaaaaaaaaabbabaaaabbbbbababaabbaabbbbabaababbaabbbabbaabbabbbbbaabbbaabbabbbbbbabbbbababbbbbbbbaabbbabaaaaaaababaaabbaabbbbbaababbababbabaabbbbabbbbbbbbbbbbbaababbaaaabbbabbbbabbbbbbbaabaabbabaabbbaabbbaaaabbbbbabaaabababaaaabaaaaaabbaaaabbaaaaaabbabbaabaabaabbbbabbabbbabaaabbabbabbababbbabbbaabababbbbaabbaabbaaaaabbaaaaabaababbaaaaabbbbabaababbbbbbaabbabbbaaaabbbbbabbaaabaaaaaabbbbabaabaaaababbaababbabbbbbbbbbbabbbaabaaababbbbabaababbaabbbbaabaaabbaaabababbbabaaababaaaaabaaaaaabbbbbbbabbbbaaaabbbbaaababbabbbbaabaabaaaabaababbaaaaababbbabaaabbbabbbabaabbbabbabbabaabaaabaabbaaabbabbaabaaaaabbbbaabaaaaabaabaababababbabbabaaaabaababbbbbaaaabbaaaabbabbbbbabaaaaaabaababbababbbbbabaabaaababbabababaabababaaaaba
abbbbbabbaababbabbbabbbabaaabbbabaabbbbbbabaaaaaabbbbbbbbabbbabbbbaabababbaaaaaaaabaaababaaaaabaaaababbbbbbbbbbbabaabbabbbbbabaaaabbaaaaabbbbaaabaaabbabbbbbbabbabbbaaabbaabbbababaaaaaaaaaaaaaabababbbabaaaaabbabbaaaabbbbaabababbabaabbbbbaabbbbbaaabbbbbbbaababaabbbabaaabaababbbababbaaaabbbbabbabaabaabbaaabbababababbbabbaaaaaabbbbabbbaabbabbbabbbbbbbabbbaaaaabbaaaabbbbabbbbabbbabaaabaabbbaababbaabbaaaaaaababbbaaabbabbaaaaaaaaaabbbabbaaaaaababbabaabaaaaabbbbbbbababaaabbbbbbbbbbaaabbabbbbbbaaaaaabaaabbaaaabbabbbaabaabbaabbaaaabbbbaabbbaabbaaaabbababbaabaaaaabaabaaaaaaaaaaabbabaaaaabbbabbbbababababbababaaaaaaabaabbabbbbababaaaaaaaaabbbbbbbaaaabbbaaabbabaaaabbbbbbabaaabbaabbaaaabaababbbbbbbaabaaabbbbaaabbbaabababbbaababbbabaabaaaabaaabbaaabbbbbaaabbbbabaaabbabababababbababbabaabbaaaabaaaaaabbbaababaaaaaabbaabababbbbabbbbbbbbaaaabbbaaabaaabbaaabbaabaaaabbbbabaababbbbabababbbbaaaaabbabaabaaaabaababaaabbabbabbbbaabababaabababbbbbbaabaabbababbabaaabbaaabaabababababaabaaaabababbbbbbbbabbaaaaabbbabaabbbbbaaabababbaabababbaaaaabbaaaaaaaabaaaabbbaabbbabaaaaababbabaaabbabbbbabababbbbababbabbabaaabbbaabaaababaabbbbbbbbabbabaabaaaabaabaaabbaabbabaaaabbbababaabaaabbbbabbbabbbaabbaabaababaabaabaaaabbbaabbbaaaaaabbabbbbbbbbbbabaababbbabababbbbabbbbbabbabbabbbbabaababababbbbbabaabbabbababbaabbbbaaaaabbbabbbbabbbabaabaaaababbbabaaaaabbbabbbbbabababbabaaabbaaabaabbaaaababaabbaaaaaabbbaaabbbbaaabbaaaababaaaaababbbabbaabbbabbaaaabbaabbbbbbbabbababbabaaababaababbabaabbababbaabbabbbbaaababbbbaabaabbbabbababaababaababbaaaabaabaabbbabbbabbababaaabbbabbbabaabbaaabbaabbababaaabaabaaabbababbbababbbababbaabbbbaaabbbaaaababbaaabbababaaaaabbbabaabaaabaaaabbaaababbbbababbbbaaabbbabbaaaabababaabaaaaaabaabbaaababaaabbababaaaaababbaaabaabbbbbbbaaaabbaabbbbbbbbbbaaabaaaaaabbabbaaabaabbaaaaaaabaaaabaaabbabababbaabaaaabaabbbabbbaaabaababbbabaabbbabbbabbaabbbabaaabbabaaabbbaababbabaabbaaaaaababbaaabbbbbababaaaababbbbbaababaaabbbbbbbaaaaabbabbbabaabbbaaababbabbbbbbbaaaabbabbaabaaaabbabbaabbbbbabbabaabaabaaabbaaaaabbabbaaabbaaaabbabababaabbbbababbabababaaabaabbaabaaaabababbbbaaababbbbabbbbabbbbabaaaabababbbbbaabbbaaaabaaabbbbaabaababaaaaabaaaabbbaabaabbbabbbbbaaaaabaabbbabaaaaaabaabababbbabbaaaaaaaaababbaabaaaababaaabaaaaabbbaaaababbbbaaaaabababbbbbabbababaaabbaaaabbababaaaabbaababaaaabaababaababaaababbabaababbaababaaaabaaabaaaaabbabbabbbbaaaabbaababbbbaabbabaaaaaaababbbabbaaaabbaaaaabaabbababbabaaaaabaabbbabaaabbababaabbabbaabaaaaaabbaaababbaabababaaaaaabaaaaaaabbabbabbbabaabaaaabbbbaabbabbaabbaaabbbbbbbbabaabbababbabbaababaaaaabbaaabaabaabaaaabbaabbbbbbabaabbabbbbbabbaabbbbbbabbbbbaaabbabaabbbbaababbbbaabbbaaabababbbaaaabaaabbbbabbbbbabbaabbaabbabbbbbaabbaabbabbbaaabbabbaabbbbbbbababbbbaabaaaaaabbbbbaaaabaabaabbbabaabaababaababaaabaabbabbbbaaabbabbabbbaababbbbbbbbbaabbbabbbaaabbbbaabbabbbbabbbbabbbabbabaaabbbaaaabbabbaabbabababbaaabbbaabaabbbabaaabaabbbbbbabaabbbbbabaaabbbbababbbbababbbbbbbbaabbaabbbbaababaabbaaababaababaaaaaabbbabbbbbababbbaabbbaaabbbbbababbbabaabaabbaaaaaababbaabbaaaaaaaabbabababaabaaabbbabbaabababaaabaaaabaabbaabababbaabbabaaaaaabaaabaaaaabbaabaaaaaaababbabbabbaababaabbbaaabbbabbbbbbabaaabbbaaaabbaabaabaabbaaabababbbaaaabbbaaaabbbaaabaaabaaabababbaababbbabaaaaabbaabbaaabaaaaaababbaababababbaaaababaaaabababaababaabbaaaaaaaabbbabbbbbbbbbabaaaabbaabbaabaaababbbbabbabbbababbabaaabbaabbabaaababbbbaaabbbaabbaabbaababbbbabbabaaabababbabbbbbbbaabaabbbaaaaabaaaabbbbbaaabbbbbaaababbbbbababbbabaababaaaabbabbabbbabbaabbabbbbabaaaaabbbbbabbbabbbbabbabbbaaabbaaabbaabbbabaaaababaabaabbbaabbaaabbbbabababbaabaaabaabababbbababababbbaaababbbbbbaabaaabbaabbbbaababaaababaaabbbbbaaabababbaaaabababbbbabbbbababbaaabbbbbbbbbbbabbabbabaabaabbbbababbbbbabbbbaaaababaabbabbababbaaaaaabbbaabaabbabbaabaaabbbbbbaaaaaaabbababbaaabbababbbbababbbbbbbbbabaabaababbbaabbaaaaabaabbaabbbabaabbbbbbababbbbbabaabaabaaabbbabbaaaabaababbbbaaaabaabbaababbabbbbbabaaababaaaaaabaaaaaababbbabbbabaabbbbbabbbbbbbbaaaaaabbabbbbbaaabaabababababbbbbaaaababbbaaababaaaaaababaabbbbabababbababaabaaababababbbbaaaabbaaaaabaababaaabaabbaaababbbaababbbbbaaabbaabaaaaaabbabaaabbbaabbbaabaaaaabaabbaabbabaaabbbbbbbbbbaaaaabaaabaabbaabbbbbaababbabbbaaabbbaaabaababbbabbbababbbababbbaabbbababbaabbbbabbbbbaabbaabababbbbbbabaabbabbaabaabababbaababbabbabbbaaababbbabbabaaaabbababaabbbbbabaaabbbaaaabaaabbabbabbbabbabbbababbbaaabbbbabbabaaaabbabbaabbaaaabaabbbaaaaabaaababbabbbbabbbaaabababaabbbbabbbaabaaaaaaaaabbaabaababbabaaabaaabbbaabababbababbbbababbbaabaaabbbaaabbbaabaababbbbaaabbabaaabaaababbbabaabbabaabaabaaaaaabbababbbaabbbbaababbbbbabbbababababbbbabbbabbabaaaabbaababbaababbaabbbabbababbaaabaaaabbaaaaabbbbbbbbbaaababbbbbbaaababababbaaababbbaaaaabbbbbbbabbbaabbbaabbabbbbbbbbaaaaabaabaaabbbabababaaababbbbaaabaabbabaaabaabbbaaabbaabaaaaabbaaabbabbababaabbbaaabaabbbaabbbaaabaababaaaaabbbbbbbabbabaaababbaabbaaaaabaaaabaaabbbbabbbabaaabbbbabbabbabaaabbbabaababbbabbaabbababaabaaaabbaabbabaabaabbaaabaaaaabbbbabaaaababbbbbabbbbbbaaaaabbaababaaabbbabbababababbbabbababbaabaabaaababaaaaababbbabaabaaabaabbbbabaabbbbbbabbbbabbaaabbbabaabababaabaabbaabbbabbaaabaababbbaabbbabbbbabbbbaaababbaabbbbbbabbbbbaabbabbabaabbbbabbbabbaaabaabbbaaaaaaaabbbbbbbaaaaaaaaabbbbbbaabbaabbabaaaabbbbabbabbaaaaaaabbbbaaaaaaaaaaaaabaaabbbaabbbaabaabaabbaaaababbbaaaabaabbbabaabababbbaabbbbabbbaabbaabbabbbabaaaabaababbbaabaaababababbbabbbbbaaabaabaaaabbbbbbaabbaaababaaaaaabbabaaababaabbaababaabbbaaabaabbbabaaabbbbbbabaabaabbababaaabbbbababaaabbbbabbabaabababbbabbbaaabababbbaaabbaaabbabbbbaabbbbaabaaaaaabaabaabaabbabaabbbbabbbababbbbbbbabaaabaaabbbaabbabaaaabbaabaaaaabaabbbababbbabbbabaaabbabaabaababbbbbaaabbbabbabbaaabbbabaabbbabababbaaabaaaababaaababbbaabbaabbabbabaabbbabbbbabbbbbaaabaaabbaabbaaaaabbaaabaabbaaabaabaaaabbbbbbaabbaaaaabbbbaaaababbabababbaaabaaaabbaababaabaababbbaababbbbaabaaaabababaaaaaabbabbaabbabaaababbaaabababaabaabbabaabaaaabbabaabbabbbbbbbabababbbbabbbbbbaababbabbabbabbbbbaabbabababaaabbbaabbbaabbaabbabbbbabaabbbbbababbbababaabbbaabbaaabaaababbaaabaaabaabaaaabaaaabbbbabbaaaaaabbbabbbaabbabbabaaabaabaabbbbbaabbbbabbaaabbabbaababababbaabbabaabaabaabaaabbbabababbbaababbaabbbbbbaabbbbabababaabaaaabaaabbaabbabbaabbaaaabbaabaaababaabaaabaabbbabababbbbaababaabbabbbabaabaaaabababbabaabaabaabaaaaabaababbaaaaaaabbbbbbbbaabbababaabbaabbabbabaabbbabbbbbaabaaabbabaabababaabababbbabababbbaaabaabaaaabbabaababaaabbabbabbbbaabaabbbbabbaabaaabbaabaaaabaaababaaabbaabbbabbbbbabaaababbbbbaaabababbaaaaabbaabbbaababaaabbbbbaabbbaabaabababaaabababaaabbaaabbbbbbbaababaaaaaaababbaaabbaaaaababbbaaaaababbbbabaabbbbaaaabbbbbbbbbababbaaaabaaabaabbbbbaaaababababbbbaaaabaabaaaabbbabbbbabbaabbbbabbbaaabaabbaaaababbbabbbbbaaaaabbabababaabaabababbbabbbbbbabaaaabaabbbaabbabaabbbbbbababaaabbbbbabbbbaabaaababbabaaabbabbababbbbbababbbabbaaaaaaababbabaabbbabbbababbaaabbbbabaaabaaaaabbbaabaabbbbaaaaaabaaabbbbbbababbaabbbaaabbabaaabababbbbbbbbabaaaaaaabaabbabaaaaabbbabbbbbabbbbbabaabaababbaabaaabaabaabbbbabbbbaaabbababaabababbaaababaabbbbbbbabaabaaabaaaabbaaababaababbbaabaaabaaaabbbaaaababbabbaaaaabaabaabaaaaabbaaabbbbaabbbabaaaaabbbabaaaabbabaababbaaaaaabaaaaabbbbaababaabbbabbaaabaaaaaabaaaaaabbaabaabbaabaaababaababababbbbbaabbbaabaabaaaabbabbbaaabbabbabbbabbbbbaabaaaaaabaabbaabbbbabbabababbaabbbabbabaaaababbbbababbbbabbbbaabbbbbabbabbaababaabbbabbabbaabbbaaabbbaaabaababbbabaababbbbaabbaaabbaaaabaabbaaabababbbbaaaabbbababaaaaababbaaaabbaaabaabaabbaaaaaabbbabbaabbbbaabbabbbbbbbbaaabababbbbaabaabababbabaaaabaabababbbaabbbabbbababbaabbababaabbaaabbbaabbabbaabaabbbbabbaaabaabaaabaaababbabaababaabbaaabbabbaaabaaabbabbaaabbbabbaababbaabababaabaabbaabbbabaaaabbaabbbabaababaaabaabaaabbabbabaaababaaababbbaaabaaabbabbbabaabbabaabaaabbaaababbaabbbabbbbbababbaabbababbbabbbbababbbbbabbaababaaababbaaaababbbababaabbabaaaabbabbabababbbaaabaaababaaabbababbbbaabaabaaabbaaaabbabbbbbabababababbaabbaabaaaababaabaabaaaabaaabaaabbabbbbabaabaabbabaabbbabbbaabbbaaaaabbabbbbabbbaababaaaaababbaaabaabaababaaaabbbbbbaaabbbbaaabaababaabbaababbbbabbbbbabaaabbbbbabbbaabababbaabaabaaaababbaabbaabbbbbababbbbabaaabababbaaaaabbbaaabbaabbbbabaaabaabbbbababbabaabaaaabbbaaaaababaaabbabbaabbbaabaabbabbababaabaaabbbbbaabaabbbaabbabbababaabbbbbbbaababbabaaaababbaabbaabbabbaaabbaaaabbaabaabaabbaabbbaabbabbabbbaaaababbababbaaabbbbaaaabbabababaabababbaababaaaabbabbaabababbaabbaabaabbbaaabaabaababababbaaaaababaabaaaaaababbaaabbbabbabbaababaaaaaaaaaaaaaaabaaabaabbbbaabbbbaabaaababaabbbbaaababbbabaaaaabbbaaababaabbbbaaaabaabaababbaaababaabababababbaaababbaaabbbbababaaabbbaabaababbbbbbbabaaabaababaabababaababbbaaaabbaabaabaabaabbabaabbbabbbbaabbaababbaabaabbbaabbbbabbbabaabbbbaabbaaababbbaabaabbababbabbbbbabaabbbababbbabbababaaababbaabaabababbbbbabbbbabbabaabaaabababaabbaababababbbbaaabababaaaabbabbbabaaabaabbbbbaaaabaabaabaaaaaaaabaabbbaabaabaaaaababbabbababaabbbabaaabaabbaaabbaaabbbbbbaabaabbababbbbaabbbaaabbbbaaabbaabaaababbbaaabaabaababaaabbabbbbbaaabaabaabbbbabbbabbabbaabbbaabaabaaaababbbaabbbaaaababbbbbbaaabaababbabbabbbabaaabbabaabbaaababbaabaabbbabbaabaaaaabaababbbbaababaabaaaabbaaaaabababbbbbbbbabaaaaababaaaaabbabbaaaabaaaaaaabbbbbbababaaaaababbabbbaabbabaabbbababbabbbbababbbabaababbaabaabaabbbaabaaabaaaaabbaababaababbabbbbaabaabbababbbbabbbaabbbbaaabaaabaabbaaaabbbbabaabaaaaabbbbaaaabababbbaabaaaabbaabbabbabbbabaaaabbaababbaabaabbababbaabbbabaaaabbbbbaaaabbbbaababaabbabbbbabaabbaaaabaaabaabaabaabbabbbabbababbbbbaaaaabaaaabaaabbbababbaabababaababaaabbaaaabbaababaabaabababaaabaabbabbababaaababaabaaaaabbaaaaabbaababbabbabbabbababaaababaabbababbbbbabaababbabababaaabbbabaaabaabbababbaabbabbabbaaaabbbbabbaabbbbabaaabbabbbaabaaaabbbabaaaabbabababaabaabbbbaaaabbbbbbaaaaaaabbbaababaaaaababbbbbabbbababaaabbaaabbabaabbbaaabaababbaaabbbabaaaabbabaabbaaaaaaabbababbaababbabbaabbbbbbaabaababbbbaaaabababbbaaabbbaabaaabbbbaaaabbbbabbabbaaaabaababaabbaaaabaabaabababbaabbbbaaaabbaabaabaabbabaabbbabbaabbbababaabaaabbbbabaabbababaaaabbabaababbbaaaaabbababbbaaaaaaaabbabbaaabaaabbaabbabbbabaabbaababaabaabaabbbbbbabaaabbbbaaabbabbaabaaaabaaaaababbaaabaababbaabbbbabbbaabbabbbbbaaaaabbaababaaababaabaabbaabbbbbabaaabaabbbababbabaaabbbbbababbbbaababbabbaaaaaaababbaababbbaaabbaaababbbbbbbababbaaababbbabbbabbabaabbbbaabbabbababbbbbabbbbaababbbbbbabbaabaaabaaababbabaabbabbbaaaabbbbbbbabbabbbbbbbababbbbbbabbbbbbabbaabaaabbaaabaabbbbaabbbabbbaababaaaabbabaabbbabbaabbaaabaababbbbbaaaaaabaababaaaabaabbbbbababbabbabbababababbbbaabaabbbaabbabbbbaabaaababbbaaaabbbbbbabbbbaabbbbabaaaabbaabbababaaaaaababbaababaabbaaaabbbbabbbbbbbbbabbbaabaabbaaabbabbbbbabbbaaaabbababbbbbaabbbbbaaabbbbaababbbaabbbabbbabbbbaabaabbbabbbbaaabaaaaabaabbbaaababaaaaabbbabaaababaabbbbabaabaaabbbaabaababbaaaabbaaabbbbbbbabbbbabbabbabbabbbbbbaabbabaabababbabaabbbabaaaabaaaaaababbbaabbbaababbbaaaaabbbbbbabababababbbababaababaababaaaaabaaaabaaabbababaababaaaaaabaabbaabbabbababbaaaabbbaaabaaaaabbabaaabaabaaababaaabaaaaaabaaabbbababaababbbaaaababaabbbbabaaaabbbbbabbbbbbbbaaaaaaabbabbababbaabaaabaabbbbbbbbaababaaaababbbbbbbabababbbabbbabbabbbabbaaabbbabaaaaaaaabaaaabaaababbbbabbaaabbabaabbaabababaabbbbbabaaabaabbaaaabbbaaababbbaabbbbbaaaabaabbbaabbabaabaaaabaabbbabbbbaabbabbbaabaaabaababaaabbbbaabbababbbbabbaabbbabbbbbaaabbbbaaabaabbbbabbbbababbbaaabaaabaaabaababbabbbabaabbbabaabaabbbaaaaabbaaababaabbabaaabaababababbbabbaaaaaaaabbbbabaabbaabbbbbbabbaaaabbbaaababaabaaaaaaaabbbaaaabbaaaaabaabaabbabbabaabbaaabbabaaabbbabbababbaaaaabbaaabaaababbbababbaaaaababaaaaaabababbaabaaabbbaaabbbbbbababaabbababbaaaaaaaaaaabbbabaaaaabaabaabbbbbabaaabbbababbbbababbbbbabaaababbaabbbaaaabbabbbbbaaaaababaaabbaababbabbaaaababbabaabbbbbabbbabaababbaababbaabaabbbaaabababbbbaabbbbbaababbaaaaaabaaabaabaaaaaaabbbaaababbbbbababababaabbabaaaaaabbbaaaabbbbaaaabaabbabbabbbaaababbbbbbbbababbbabbababaaabbaabaabbbabbaaabaaaabbaabbbaabbaababaaabbbabaabaabaabaabbaabaabbbbabbaaababbabaaaaaababbabbbbabababaabababbbabbbbaabababababaabbababaabbababbabbbababaaabaaabaabbaabbabbbbbaaabaabaaaababbbbbaabababbabbbabbbabaaabbbaababaaabbabbaababaaabaaaaaaaabbabbbababbbabbabaabaaabbaababababbbbaabaaabbbaabbbaabbbbbbbababaababbbabaaaabababaabbbababbaababbbbbbabaababababbbbaabbbbabbbbabaababbbbbaabbbaabaababbababbbbbaabbababaaabaababbaaaabaaabaababbaabaabbbbbaabbbaaaabbbababbabbababaaababababbaabababbabbbabbbaabbbbaaabbabaabaaaabbbabbabbaaaababbbabaaaaabbaabbbbbabaabbbbaabbaaaaabbbabbaabbbaababbbaaaaaababbaaaabaabbabbabbabaababbbbaaaaabbabaaabbaabbbbabbbabbabbaaaabbbbaaababaababbbbaaabababababababaabbbaabbbabbbbbabbabaabbaaaababababaabbabbaaabaabbbabaababbabbababaaaaabaabbbababababbaabbabababaabaabbabaabaaaaabaabbbaabbbabaaaaaaabababaabbbaaaaaaabbaaaabbbbaaabbbbbaabbaaabaaaabaaababbabbaaaabbaabaabbaaabaabbbbaaabbabbbbabaabaabbaabbababababaabaabbbabababbbaaababbbbbabaabbabbbaabbababbaabaaabbabaaaababbbabaabbbaaabbbbbaaababbbbaaabbbbbbbabaaabbababbaabbbbbbaabbbbbbbaabbaababbbabaabaaaaaaaabaabbabbbbaabaabbabababababababbbaaabaabaababbbababbaaaaababbbbbbaabbbbbbbaabbabbbbbabbaabbaabaabaabbaabbabbbababbbbbabbbbaaaaabbbababaaaababaaaabbabbabaaaababbabbbbabbabbaabbbbbbbabbabbabbabaaaaababaabaaabaaababaaaabbbbabbbabaaaababbbaabbaababababaaabaabbaabaababbaaabaabbbbababbbaaaaaababababbbaaabaabbabaaaabbaabbbbaabaababaabaaaabbbbaabaaabbabbabaaabaabaababbbbbabaaababbbbbaabbabbbababbabbbabbaabababaababbababbaaabbaaabbbbbaaababbbbbbbbbbbaababababbbabbbbbaaaaaaabababbbbabbbbaaaaaaaaabbaaaaaabaaabbbbbbbabaabababaabbabbbbabbabbabbbabbbbabaabbaaaaabbaabbbaaaabbbbabaaaaabbbbabaabbbbaaababbbbaababaaaaabbaabababbaababbbbaaababbababbbbaabaaaabbbbabbbbbbbbbbbbabbbabaabbbbbbabbaaababaabbbaababbabbabbbababbbbbabbbaaaaabbbaaaaaaabbbbbbbbababaaaabaabbabbaabbbbbabaababababbbaababbbbbabbbabababaaaaaaaabbbababbaabbabbbabbbaaabababbbbabbbbaaaaaaabbbbabbabbaabbabbabbabbbabbbaaaababbabaaaababbbabaababaaaaaaabaaabbabaababbaaaaaabaabaabbbabbbbbabbabaababbbbbaaaabbaaabbaabbaaabbaabbabaaaaabbbbbbbabbbabbababaaaaababababababababababababbbabbabaaaaabbbaaaaabaaaaaabaaaababbaaabbaaabbabababbbaaaaaaaaaaabbaabaabbbababbabbaababbbbbbabaaaaabbabbaaabbabbbbbbaabaaaaaaabaaababbaabaababbaabbabababaabbabbaaabbabaaabbabaabbababaaababbaabaaabaaaaaaabbbabbaaaaabbaabbabbbaaaaabbbbbaabbbbaabbbaabbabaabbaababbbaabaabbbababaaababbaabaaaabbabbbbababbbabbbaabbaabaabbaabbbbbbbaaabbbbaabbaaaaaaabaabbbbbbabaabbbbaabaaaabaaaababaababbbbabaaabbaabbbaabbaabaabbaabbaaabbbbaaababaabababbbbbababaababbaaaabbabbabababbbbbaabbaababbbbbabbababbababaaabaaaaaabbbbbababaabbaabbabbabaabaabaabbaaabaababbaababbbbbaaaabbabbabbbabbabbbbbabbbabaabbbaaabbabaaaaaababaababaaaaaaaaaaababbbbbaaabababbbbaaababbabbaaabbabbaababaaabaaabaaabbaabbaaabaabbbaaaabaaaabbaaababaabaabbabbabbababbabbbababbaaaabaababbaaaabbbabbababababaaaaabbaabaaabaaaaabaabaaaabbbbaaaaaabbaaabaabbbababbbaaababbbbaababaabaaabbbbaababbbbababbbbabaaabbaaaaaabbbbbaabbbababbbaabababbbabaabaabbaabbaabaaaabbaabbbababbabaabbabababbbaaaaabaabbbbaabababbaabbbaabababababababbaabaabbabbaaaaabbbabaaabaaabababaaababaaaaabaabaabbbbbbbbbbbbaaabaaababbabbbbaabbaababbabbbaaaabbaabbababbbbaabaababaabaaaaaabaaaababaabbababbbbbbbaaabababaaababaabbbbabbbbabaaaabbabaababbbbbbbababbbaabaabaaaabbbbbabbbabbabbaaabbbbbbaabbbbababaabbbbbababbaaaaaababababbabaabbbabaaaabbababaabbbababbbbbaaababaaaaabaababbbabaabaabbbbaabbbaabaabbabbaaaabbaaaabaaaaabaabaaaabaababbabaaabbaaababaaaababaabaabbbaaaabaaaababaababaababbabaabaaababbbaaaabaaabbaabaaaabbabaaaaaabbbbbabbbbabababaaaabbbaaaababbbbbaaaaaabbbbbbababaaaaaaababbaabbaababaabbbaabaaaaabbababbbbbbbbaaabbaabaaabbababbbababbbbbbaabbaaabbabbababbbbbbabbabaabbbabbabaaaabbabbaabaababbbaabbbabbbbaaaababaaababbbbaababababaababbabbabbbaaaaabbbaaababbaaaaaabbbbabbbbaaabbabbaaabaaaabbabbabbbbbabbabbababaaaaabaaaabbabaabbaabbababbbaabaabbaaabbbaababbbbbabbbabbbaaaaabbbbaabbbabbbabaabaabbaaabbbbaabababaaabaaabababaababaabababbbaaabbbbbbaaabaaaababbaababbbbbabbaabbbbaaababaaaaabaaabbababbaabbaaabaaaabbaababbabbbbbbbbabaaaababbaaaaabaaaabbbbbabaaaaaaaababaaabbaabaaabaabbabbbabaabaabaaaaabababaaabaabbbbababbbabbabbbaaabaaaaabbabbababbababaaaaaababaaaabbbaabbabaaababaaabaaabababbaaaaaabbabbababaabbaaababbbbababbaabbbbbbababaabbaaabbbaaabbbbbbabbbbabaaabbaaaaabbabbbabbabbabbbbbaaaaaabbaaaaababbbbbabaabbaabbaabbababbbbaabaaabbaababbbaabbbabaaabbbabaabaaaabaabbabbaababbaababbbaababbaaabaaaaababaaabaabbbbbbaabbababbbaaabbaaabbbaaabaaaabaabaaabbabbaabaaabaabaaabbaababbbababbabbbbbbbbbbbbbbaabaababbbbbbabaaababbaabbbabaabaaabaaaaababbbbaabaaaabbaababbbbbaababbbbbaabbbbbbbaaabaaaabaaababbaabbabbabbbababaaabaabaabbabaababbaabbababaaababbbbaaabbbbaabababbbbababababbbbabbbbbbaaaabbbababaaaabaaabbbabbbabababbbabaabaabaabaabbbbbbaabaababbaababbbabaabbabaabbbaaaabbaabaababbbaaaaaabbabbababbaaabbaabbabaababbaabbbaababaabbbbbabbbbbbaabbabbbbbbababbaaabbbaabbababbbbbababaaaabbbbbabbbabbabaaaabbaaababbbabaabbbbaaabaababbbbbabababbaaabaabaabaaaaabaaabababaabbbaaabaaabaabaabbbaaaaaaabbaaaaabbaaaaaabaaabaaaaabababbbaabbabbbbaaaabababaabbabbabaaabbbbaabbbbbabaababbaaabaaaabbbabbaababbaaababaaabbaabaaaaaaaaabbbbbaabaaabababaabaabbbaaabbabaaabbbbaaabaaabbbabaabaababaababaaaaababbabaaabbabbaabbababbbabbbababbabbaabbabbbababbbabbaaaababbbbbabbbabaabbbabaababbabbbabbaababbbabbababbabbbbbbaababaabbabababbbbabbbbbabbaababbabbbbbabbbaaabbbaaabbbaabbbababbaabaabababbaaabbaababbaabbbbaabbbbbaabbbabbbabbaaababbbabbaabababbbbaabbbbbbababbabbaababaabbbaaababaaabbbbaaaaaabaabbbabaabbaabbaaabbbababaabaaaababbabbbabbaaabbbbabaaaababbaabbbbabbaaabababbbbbbaaaababbababaabaabaaaaaababaaaabaaabbbbbabaaabaaabbbbbbbbbbababbbbabaaaaabaaabababbbbbabbbabababaababbaaaabbabbbaaabababbbbbbaabbaabababbbbbababbbabbaabbbbaabbbababbbabbbabaabbbaaabbbbabbbaaaaabbbbbbbabbbbbbbaabbaababbbabbaababbbaaabababaabbaaabaababbaaaabbaababbbaabbbbabbbbbbbaabbbabaaabbbabbbaaabaaabbaabababbbabbbbbbabbabbbabbbbbbabbabaabaaababbaabaaaaababaabbaabbaaaaaabababbbbabaaaabbbbabbabbbabaaaaaaaababaabbbabaaaaabaaabbabbbbbbbabbababbbbabaaababbabaaaabbaaaabbbaaaaabababbababaaababbbbabbbbaabbbbbbababbaabbaabaabababbabaaabaaaabbbaabbbaabbaaaaaaababbaaaabbbbbbbbbabababbaaabbbabaabbbaaabbbbbbbbbbabaaaabababbbbbbbaababaababaaabbaabbaaaabababbabaaabaaaaaaabbabbbaaaababaaabaaabbbaaaabbbababbaaabbaabbbaabbabbbbbbbbaabbaababbababaaaabbaaabababbabbbabaaaabbaabbaaaabaaaabbbabababbababababbabaabbabbaaabbaaaababbbbbabababaababbbaaaaaabaabbbabbabaabaabbabaababaabbaababbaaaaaabbbabbbbbbaaaababbbabbaaaabababbbbaabbbbabbbbaaaaaaabaababaaabababaabbaaaaabbaaaabaabbbbababababbaaababbababaabbababbabbbbaaaaabaabbaabababbabbbbbababaabbbbababaaaabbababaaaabaabbbbaabbbabbaaababbbbbaabaaaabaabbbbbabbbbbbaaaaabaaaababbbbbabbabbbaaabbbbabaaababaaaaabbbabbaaaaaaabbbbabaabaaaabbbbbaaabbaabaaabbbaabaaabbabbaabbaaababbabbbabbbbbbbbabaabbbaabbaabaaaaaaababaaaaaaabbbaaabababbaabbabbbabbbabbabbabaaaaabbaabaababaaaababbbaaaaabbabbababbaaaaabbaabbbabbbbabaabbbaaaabaaabaaaaaaaababbbbababbbbbababbbabbaaaaaaabababaabaaaabbabbbbabbbbababbaaaabbbaaaabaaaaaaabbaaababbbbbbaaabaabbababababaababbabaaaabababbabaaaabbaaabaaaabbbbbbbbaabbabaaaabbbababbbabbaaaabaaabbbaaaabbbbbbbabaaababbaabbaabbaaaababaabbbabbbbabaababbbbaaabbaabaabbbaabbbbbababbabbabaabbabaababbbaaaabababbaaababbaabaabbabababbbabbbbabbaaabbbbaabbbbaabbaabaaabbababbbbabbabbbbabaabbaaaaabbbaaabbbbbababaababbbaaabbaaabaabbbbbbaaababaaabaaaababaaaaaaaabaaabbaaababaaaabababaababbaabbbbbaaababababbaaaabaaabbbbbaaabbbabbaaaababaaabbaabababbabbabbbaaabaaabaabaababbabbbaaabaaaabababaabbaaabbbababaabbababbabbbbbbbbabaaaabbaaaabbabbbbabaaabababaabaaababaabbbbbaaabbaaaababbbbabbabbbabaabbbbbabaabbbbbabababbbaaabaaabbbabababbabbababababbbbabbbaabbaaaaabbbbababbabababbababbbaabaaababbbbaaabbbbbabaaabbaabaaababaababbbbbabaabbbbabaabbbbaabaaabaaaaabaabaabababaabbbabbbaaabbbabbbabaaaabbaabbbaabbbaabbaaaabaabbbaabaaabbababbbaaabbbabbbaabbabbbaaaaaaaababaabbbbbabababbbaaabbbaababaabbbbaabbaaaababaaabaabababbaaaabbabbaabaabaaabababbabbbabbaaabbbbabbaabbbaaabbbabaabaabbbabaabbbbbbbababaabbbaabbabbbbababbaaabbaababbabaaaabbabaaaaaabbbabbababaabaababbaaabbbbabbbbaabbbbabbababaabaaaabbaabaabaabaaabaabababaaabaabbaaaabbaaabaaabaaaaabbbbababaaabbbbbbbbaabbaaaababbaababbbaabaaaaababbbabbbbbaaabaaabaabbbaaaaaaababbabaaaabbabbabbaaaababababbababbbbababbaaaabbaababbbbbabbaabaaaabaaababbbbaabababbbaabbaabaaababbbbabbbbbabababaabababaababababbbbaabaaaababaabbbaaabbbbbabababbbabbbbaaaaababbbbbabbbaaabbbbaaaabbbaaabababbbbababbababbbaaabaaaabbbaaabaaaaaabbaabbbaabababaaaaaabbbabbabbbababaaaababbaabbbaabababaaaaaabbbaaabbabbaaabaababbbaababaaababbbbaaabaaaabbbabbbbaaabbbaababbbbababbaaabaabbaaaabaaaabbabbaabbbbaabbbaaaaabbababbbbaaababaaabbbaaabaaabaabaaaabbaababbaaabbabbaababaabbbbaababbabaaaababababbbabaaaaaaababbabbbbbbbbaaaaaaababaaabbbbababbbaaabaaabbbbbabaabababaabaaaabababaaabaabbaaabbaababbbaaaabaabbbbbbbaabbbbababbaaabbabbbbbaaaabbbbbabaaabbbabbabaababaaabaaabababbababbabbbbaaaabaabbaabaaaababbabaabaaaaabbabbaaaaabaaaababababbbbaaababbabaaabbababbbaaabbaabaaabaaaaababbbbaaabbbaaaabaaabbabbaabaaaaaaabbbbabaabbabbaabbbbbbbbabbbababaaabaabaabaabbaabaaabaabaaaababbababbbbababbabbbbababbabbbbabaabbbbaaabaabaaabbabaaabbaaabaabbaabbaaabbabaaaabaabbabbaabbbabababaabbbabaaaaabbabaabaaabababbababbbaababaaababbabababbbaabbbaaabababbabbbbbbbbaaababaaabbaaabbaaababbbbaaabaabaaaabbbaaabbbaabbbaabbbababababbabbbbaabbaabbabaaaabaaaabbbabababbabbababbaaaababaabbbbaaaabaabbaabaabbbababaabbbbbbbabbabbbaaaaabaabaaababaabaaabbbbbbbbabbabaabaabbbaaabbbbbbabbbbababababaaabbbbaaababaaaaabbbbbaaaaababaaabbabbbabaababbbababbaabbbaaabababaaaabaaabbabaabaaaabbababbbaababbabbbbbbbabbbbbbaabaababbbaaaabaaaaabbababbbaabbaaaabbaabbbbaaaabbbbaaabbaabaaaabbabbabaabaaaaabaaabbbbaaababaabaaabbabaabbaaababaaaabababbbaabbbaababbababbbbaababbaabbabbbaaababbabbabbbaabaaaaaabaaaaaabbbbbbbabbabbbabbbbabbbbbbbaaabaababbaaaaabbbaaabababaababaaaabbbbaabbbaaaaaabaabaababaababaababababbbbaabaaababbaaabbbbbabababaaaabaabbbbaaaaabaaabaababaababbbabbabbabbabaabbaaaabbbbbbaabbbbabbaabaaabbabaaaababaaaaaaababaaaabbaababbabababbbaaaabbbbabaabbabaaababbbbbbbbaaabbababaababbbbbaabaaababaaabbabbbbbbbbabbaaabababbbaabbbbbbaababaababbaaabbababbbabbbbaaababaabbbabbaabbaaabaaabbabaababaabbabaaaaabaaaaaaaaaaaabbbabbaababbbaaabaabbbabaabaabababbbabbabbbbaababaabbbaaabbabbbbbabbababaabbbbbaaaaabaaaababaaabbbabbbbbbaababaabbbabaabaabaababaaabbaabbaaaabaabbbbbaabbabbabaabbbaabbbbbaaaabbababbbbbbbbbabbaaabbbbbbbbaaaaabaabbbbbbabbaaaaabbaaaabaabaababbbaaababababbbaaaaaabbbaababbaabbbababbbbbbbbababbababbaabbabababaababababaaaaabababbbaababaaabbabaaabbbbaaabaabbaabaabbabaaaaaababbaaabaababaabbbbbaaabbbabbaabaaaabbbbabaaababaabaabbbabaaabaaaabbaaababbbbaabaabababbbabaaabbbbbbbbabbabaaaabababababbbabaabaaaabbbbbaaaabaabbbababbbbaaaaabbbbbaabbababaabaaabaababaabbbaaaaaababbaaaaaabababbbaababbbabbbbbaababbaaaabbababbbabbbbbbabbbbbaabaaaaaababbbaabbaababbbaabbbaabaababbaabbabbabbbbabbabbbaaaaaabbbbaabbbbbbbbaabaaabbaaabbbbaaaabaabbbaabbabaaaabbbaabbaaaabaaabbbababaabaaaabaaaabbbbbbbbabaabbbabbbaabaababbababaaaabbbaaabbaabaabbabbabaababbbbababbaabbaabbababaabbaabbbaabbaaabbbaababbbbaaaabaabaabaabbbaaabbbbbbbbbabbbaabbbbbababaaaaabbbabbaabbabaaaabbbbbbbbbbbabaabbbabbbbbbbabbaaabaabbabbbbbbababbaabababbbababbabababaaabaabbbbaaabaaaaabbaaababbbbbbabbbbababbbbabbbabbabaababaaabbbbbabbabbaabbbbbbaabbaabababbbbaababbaaaaabbaababbbaabbbaababbbbbababaaabbaababbbaaabaaabbbabbbababaaabbbabbbbbaabbbbbaaabbaaaaaaaabaaababbaaabbaabbbbabbbbbbbbbabbbbabbbabbabbbbbbbababababbbabbabbbbaabbbbbbbbbbaaabbbaabaabaabbbbabaaaabaabbababbbbbbabaabbaaaababbabaaaababbbaaaaaabbbababaabbbababbaaaababaaabbbbaaabbabbabbbabaaaababbaabaabbbbbaaaabbbabbabaaaabbabbbabaabbaaabbabababbbaaabbbbababababbaaabbbaaabababbbbbbaaaaaabbbbababbaaaabaabbbaabbabbbaabaabbbaaaaaabbababababbbbaabaaabbbbbabaaaababbbbbababbaaabbbbabbaabbaabbbaabbaaabbabbbaaabaabaabaaabbabbbbabaabaabaaabbbabbbaabaabbaaaabbabaabbbbbbabbbabbbbbbabbabbabbbbbaaaaaabbbaaaaabbabbbbbabbbabbabbaabaaaaaaaabbabaabbbbbaabbbabbbbaaabaabaaabbababbaaaaaaaaaabaaaabbaabbabababaaabbabababbbababbbabababbbaabbaaaabbbbbbbabbaababbbbaaabbababbaabbbbaabbaabaaabbababbabaaaaabaaabaaabaaaabbbbaabbbabbaababbbbaaabbaabbbaaaaaaaaaababababaaaaabbbbbbaabaabbabaaaaabaaababaaabababbabbaaabaaabababababbbabbbabababaabaababbbbaaababbaabbbbbbbabbbaaabbabaabbbababaabbaaaaababaaabbbababaaabbbaaabaabbbabaabaabbaababbaabaabaababaaabbbaaabbbbbbabbabbabbbbbabbaaabaaabababaabbaabbbbaabaaabbbbaabababaaababbbabbabbbaaababbbaabbbbbabaabaaaababbaaabbaaaabbaaabbbbaaaababbaabababaaabaabbbbabababbbaababaabbaabaabbaabbaaaaabbabaabbbabbbbaababaaaababbabbababababbbaaababaabbbababbaabbabaababbbababbbabbaababbbaaababaaaabbaaabaabababbbabababaaabababababaabaaabaabbbabaaabbbbabbbabaababaaabaabaaaaabbbbbabaabababaabaabbabbbbbaaabababbaabababababaaabbbabbbababbbbababababaaababababbababbbabbabaaabaabaabaaaaaabaaabaaabbbbbbbbbababbbabbabbaaabaabaaaabbaababbbabbaaabaaabbbbbabaaaaabababaababaaaaabaababababaabbbabaaabbbabaaabaabababbaabbaaababbbbbabababaaabaaabbbaaabaaaaaabbabbbaabbababaabbbabbababbbabbaabbbababaaaabaaababbabbabaabbbaaabaaabbaaaabaaaabaabababaabaaabbbbabaaabaababbbaaababbbabaaabbbaabbbaaaabaabbababaaababbbbbaaabababaabababbababbbbbbbaabbabbbaaaaaaaaabbbbaababbababbaaababaabbaabaaaabbabaaabbbbbbabbaaaaabababaababaaaababbbbbabbabbaaaabaababbbabbaaaabaaabaaaababbaaaabaaaababaaaaaabababaabbbabbabbabbbbbaabbabbbbaaabbaaaabaaabaabbaaaaaabbbbbbbabbaaabaaaaabaaaababbbbaaaaaaabbbaabaaaaabaabbabbbbbaabbbbbbbbbabaabbaabaaaabbababbaaabbbbababbaabaaabbbbababaabaaabbaaabaaaaaabbbabaabbbababbbbaabbabaaaabbabbabaabbbbbaabbbaabbbaabaabbbaaaababaaaababbaaababaabbbbbabbaababaababaabbaaabbbabaabbbabbbbabaabbbbabbbaabbbbbaababbbbabaaaabbaaabababbbbabaabbabaabbabbbaaaababaabbabaaabaabbabbaabbaaaaabbaababbabbbabababbbbabbbbbababaaababbbabbababaaaaaabbaaababaabaabbbbababbaaabbaaabbbbbbabaabaababbaaaabaaabbabbabbaabbbbabababbabbababbaabbbaabbaaaabaaaabbbaabbbbabbaaabbbbabaabaababaaabbbbbabaabababbbbbaabaabaaababbbbaabaabaaaaabbbaaaababaabbaabbabaabaaaabbbaaabbabbbababbbaabbaabbabbbaababbabbabaaababbbabbabbabbabaaaabbbbbbaaabababaabbbbababbaababbbbabbbbbbbaaabbabaabbbbbaaabbbbbabbaaabbbbaaaabaabaaaaaabbabbbbbbbbaaabbbbaaaaaaabaabbbbbaababaaaabaaaaabaaabbaabaaababbabbaababbaabbabbbbbbabaabbbbbabbabaabaaaaabbbaabaabababbabaaabbbbbbababaabbbbaaaaaabbaabababaabbabbaabbaaabbbaaabaaaaabbabaababbbabaaaababbbbaaabaababbbabbabababbbaabbaabbaaaaaaababbbababbabaabbabaaabbbabbbbbbbaaababaaabbbbbaaabbbbabaabaabababbbaababaaaaabaaababaaabaaabaabaabbbaaaabbabbaaabbbabbbaabaababbbaaababbbbbabbabbbbbabbabbbbabbbaaaabbaabaaabbabbabbaaabaabbbbaaaaabbabbbbabaaaaabaaababaabaaabbbababbaaabbbabbababaaabaabbaabbbaabbaaabbbbababbaaaabbbabbaaababaababaaababaaabbaabbabababaaabaaaaabbbaabaaababaabbababbaaabbababaaaabaaababababbaaababaabaaabaabaaaaabbaabbabbbbbbbaaaaaaaabbaaabbabbbabaabaaababbbabbabaaaaaaabababaabbbabaababbbbaaabbbbabaaabaaaaaaaaabababbaaaabbbbbbbabbbabbababbbabbbbbbababbbbaabaabbbabababaabbbaabbbbbabbbababaabaabbaaabbabbbaababbbbaaabbaaaaabbbaaaaabababbbabbabbbabbaababbbbababbbabbbaabbabbabaabaabbababbbbabbaaababbaabbbbababababaabbbbaabababababbaabbbabbbaabbabababaabababbbabbbbabbbbabbbaabbbabbababbabababbabbbabbbbaabaaabbbbbaaaaabbaabababbababbaababbaaabbabbaabaaaaabbaaababaaabbababaaaaaabaabaaabaabbbbaabbbbabbabbbbbaaaabbbbbbaaaaaaabababbbbbabbbabbbabbbbabbbbbbaabaabbaababbbbaabaabababbaabaaabbbaabaaabbbaaabbaababbaaabbabaabababbaaaaabbbbbbabbaabaabbbbabbabbaabbababaabababbaabbaaabaabbbaaaaababbbbaabbbbbbaabababbbaababbbabbbbbbbbbbbbbaaabaabbaaaabbbbaabbbabbaaaabbabaabbbbaabbaabaabbbbbaaabbabababbbbbbaaaaabaabbbbaabbbaaabaababbbaaaabbbbaabaaabbaabbaabbaaaaaabbbaababbabbbbbababbababaaaaababbaabbaaaaaaaaabbbaabaabbabbbbbbababaaabbbbabbabbabbabaaaaaaabbabbaabbaaabaaabaaaabababbbaabbabbabaaababbbbaabaaabbaaabbbaababbabaabbbbbaabbbbbabbbaaababaaababaaababbabaaabbbaaabbaaababbbababbaaabababbaaaaaaabbaaaabbaaababaabbababbaababbbaabaabbbabbabbbbbabbbabbbaaabaaaaabbbababababbbbbabaaabaababaababaaaaabbabbbbaabbaabbaaaabbaaaabaaabbaaaabbbaaaabbababaabbbbbbbbbbabbabbbababaaabaaaabbaaaabbbaabbbbabbbbabbbaababbbaaababaabaaaaaabaabbbaabbabaababbbbbabaaabbbaaaaabaaaabaaaaaaaaaaabbaabaabaaabababbbbaaaaaaaabbbaaabbababbaabababaabababaaaabababbabbbaaaaaaabbaabbabaabbbbbaababaaaabbaabbbabbbaaababbabbabbaaaaaaabaabaaabbbbbaaababbbaaabbbabaabbbabaaabbbaaabbbabbbaabbaaaaaabaaabbaababbababaabbaaabaababbabbabbaabaaaabbaaaaaaabaabbbababbbbbbaabbbabaaabbbabbbabababbbbbaaabbbbbabbaabaaabbbbabbbababbbbabbbaaabbbaaaaabaabbbaaabbaaabbbabbbaabbabaaabbabbabaaabbbaabaababbbbbbbabbbbbaabbaabaaabbaabaaabababbbbaabbbbabaabaaaaabbbbbaababbbbabbaabaabbabbbbabbabbbabababaaaaaababababbbbabbabbbababbbbaaabbaababaababbbaaaabaabbaabbbbaaabbaaabaabbabbbaababbbabbaabbabbbbabaaaabbaababbbbbababbabbaabbaabaaaaaaaababbbabaaaabaaaabaabaabbabababbbbbbaaabbabbbbbaaaabaaaaaaabababbabbbaaaabbbaabbbbbababbbaaaaabbaababaabaaaaaaaababbbbbaabaabaabbabbabaabbaaaabaaabbbaaababaabbaaabbaabbaaaaababbaababababaababaaababbaaaaaaaaababbbbbbaabaabaabbaabaababbbbabbaabaaaaaaaabaabaabbababaaabaaaaabaaabbbbababababaabbbbbbaabbbaaaaaabababbbaabbbaabaabaabababbababaaabbabaaabaaabbaababbabbbbbbabbababaabbbabababbaaabbababbaabbbbababbbbaaababaabaaaabbbbbababbaaabababbbbbbbabbbbbbabaabaaaababbbaaabaaaabaabbaabaaaabaaabababaaabbaaaabbbabaaaaababbabbabbaababaabbbbaababaaaaaaaabaaaabbbbbbbabbbbabbbbabaaaaababababaabbbababbbbaaaabbbaabbaaabbabbaababbbbbabaabbbbbaabbbbbbaaabaabbabbaabaaabaababaaabbbbbabbaaabbbbbabaaaabbbbababaaaaabaabaaabbabaaabaaababbbbbabaabbbabaaababbaaaaabbbabaaaababbbababaaabbbbabaabbabaabaaabbaabaabbbabbbababbbabbbbabbbbbaaaabbbbbabbaaaaabbaaababaaabbbababbbaababababababaaababaaababaaaabaaaaaababbbabbabaabbbbababbbbbabaababaabbbabbabaaababbbaabbbbaaabbbaabaaaaaabaababbabaababaabaaabbaaababaaabababaaababbbbabaaabbbabaabababbbbbaabbbaaabaaabbbabbbbbbbbbabbababababbabbbabbabaabbbbabababbbbbabbbaaabaabbbbbaaabbabaaaaabbbbaaababaaabbaaaaaaabbbaaaaaabaaababababbbaaababbabbaabbaaaabaabaabaabbbbababaaaaabbaabbaaabbbaaaaababaabbaaababbabbbbbaabbbbaaabbbbbaaaabaabaaaabbabbaaaaaababbbaabbbbbaaaabbabbabbaababbbababaaaabaaabaaaaaaababababaaaaababbabbaaaabbbbaaabababaaaababbabbabbaababababbbabbbababaabababbbbabaababbbbaabababbabbabbbbababbabbbaaaaaaaaaaaabaabaabbbbababbbbbaabbabbabaaabababaaaabaaabbbbabbabbbbabbabaababbaaaaabbabbbbbbbbaaabaabaabaabbaababbaabaaabbaabbaaaabaaaabbbaabbbabbaabbbbbabbabbababaaaabbabaabbbabaaabbababbbaababaaaabbaabaaababbbabbabaabbbbaaaabaabababaababbbbbaabaabababbbaabbaaabaabbbaaaabbaaaaaababbbbbbbaaabbabbbaaabbbaaababaaaaaaaabbababbabababababbbbaabbbabaabbaaaababbbabbaabaabaaabbbbbababbbbaaaabbbbbbbababbbababbabababaaababaaabbbbbabbbabaaababaaaaabbbaaabbbabbbabbbbbabbbbbbbaabbaabaaababaabbbbbababababbbaabaaabbabbbbabaaabbbbaabaaaaaaabbbaababaababbbbbbbbbbbbbaaaaabaaaaaabbbbbaaabbababbbbaabaaabaabbbbbbbaaaaaabbbbabbabaabbaababaababbbbbababaaababaabbbbabaabbbaabaabbabababaaabbbaabbabaaaaabaabbbaabbbaaababababbabababbaaabbabaaaaababbaabbaaababbbaaaabbaabaabbbbbabbbaaabbbababbabaabababbaaabaabbbbbbabaabbaabbbbbbaaaababbaaaaabababbbbbaaabbbaabbaababbabaaaaaabbbbabbaaabbaababaabaaabbbbbaabbbababbbbaabbabbbaaabbababbbaabbaaaaabbaaabbbabbbbbbbaabbbbbaaaababbabbaaaaaabaabababbbabaaabbaaabaaababbaaaababaaaaaabbabbababbaaaababababbabbbbabaabaaabbaabaabaaaabaaaaababbbbbbaabbaababaaabababbbbbaababbbabbaaaababbababababbbaabbbbbabbabaaaaababaabbabababbbbbaabbabaababbababaaabaabbababbbaaababbbaabbabaaabaabbabbbaaaabaabbaabbbabababbabaabaabbbbaababaaaabbaababaaabbababbbaaaabababbababbabbaababbababaabaaaabbbaabaaababbbbabbbbbabbaaaaaabababbabbbaabbbaaaaababbaaababbaaababbbabbaabbbaabaabbbabbbbbaabbabbbaabababababbbababbbbababbaabbbbbbbbbabbbbabaaabbbbbbababbbabbbbbabbaaabbaaaabbaaabbaabbbbaaabbbaabbbaaaaaabababbbbabbababbbaaaaaabbaabaabaabaaabbabbbbbbbaabbbbbbbaaababbbabaaaabbabbbaabbbaababaabaabbbaababaababbbaaaabbaaaabbabbbabbbbbabaabbbbbbababbaabbaaaabaabbbbbbaabbbaababbabbaaabaabbaaabbaaaaabaaabbaaaabbbbbabbababbabbbbababababbaabaaabaaabbabbbbabaabbabbababbabababaabbbaabbabbbaaabaaabbbaaaaababababbabaabaabbbbabaabbaabbbaabaaaaaaababaabaaabaabbabaaabbabbbaabaaaabbaabbaabbbbaaabbaababbbbababaabbbbbbbaaababbababbbbbbaaabaabbbabbbabaaaaaaaaaaaabbabaaababaaaaabbaabaabbbaabbabbbaabbaabaaaaabbaaaabbbbbabbaababbbbbaaabbaaababababbbababbbbabaaaabbbabbababbabbabaabaaaaabbbababbabbbabbbbabbbaaabababbabbaababaaabbbaaabbaabbbbabaabbaaabbbabaabbbabbbbabaaabbababaababbaaabaaaabaababbbabbaaabbbabbbababaaabaaabababbbbaaaabbabbbbaababbbbaaaababaabaaabaaaaabbaaabbbaaaaabbbbaaabaaabbabaababaaaaabaaabbbabbababbaabbababbbbbababaababbaaaababbbbbabaababbbabbaabbbbaaabbabababaaaaaabbaababbbbbbaabbbaababbaaabbbabbbbabaaaabbabbbbbaaababaababababbbabbbbbbabbaabbbbaabaabbbbaaababbaabaaabbbbaaaaabbaabbabbbbaabbaaaaaaaabbabbabaaaabbbabbabaabaaabbbbbaabbabbbbbaabaaababbbabbbabbabbbbbaabbabaaabbababaaaaaabaabaaaaabaababaabbabaabbbbaaaaaaaabbbaababaaaabbbaaaaabaaaaaaabaaaaababaaabababaaabbaaaaabbaababbbbbabbabaaaabbbbabaaabaabbaabaaabbbbbbbbbbaaababbbaaaaabbaaabbabbbaabaabbbbbaaababbbaaabbbabaababaabbbabbaabbaabbbabbaababaaabbbabbabbbabbbaaababbaaabbbbaaaaabaaaabbbbbbaaaabbabaaababbbaabbbabbbbabbbaaaabaaaabaabaaabbbbabbbababaaababbbbaababbbbbaabbaaabbabbbaababaaabbabaaaabbbbaaaaaabbabbbabbbbababbababaabbbabababaabbbbbabbbbbbbbbbaaaabaabaaaaabaabbababaabbbbaaaaabaabaaaaaaaabbaabbbaaaababaabaaaabbbbbbaaaabaaabbaaaabbbbbabbbbbaabaabbababbaaabaaaaabbbbaababaaabbababbaaaabaabbaaaaaaabbbababaababababaaaabaaabaaaaabaaabbabbbabbbbbbababbbbbaabbaaabaaaababaaabbbbbaababbbbbaaaabbaaaabbabbbbbaabababaabaababbbaaaabbabbaabbbaababbaabbbbaababbaaaabbaaaaaaaabbaabbbbbabbbababbaabaaabbaaababbaaabbbbbbaabaaaaabbbbaabbbababaababbabababbaabbabaababaabaabbbbbbaaabbbabaaaabababaabababbbbbabbaaaabbabbbbbbbaabbbbbbababbbbaababbbaaabababaabbbbbbabbaaabbbbaababaaababaabaabbababaababbbbbbbaaabaaabaababbabbaaaaaabaaaaaaababbaabababaaabbbabbbabaabbaabbaaaaabbabbaababbaaaaabbaababaaabbbbabbbbababbaabbbbbbbabaabbbaabaaaaabaaaabaabbbbaaabbbaabbbbaabbabbaaaabbbaaabbaabababbbabbbbaabbbbabbaaabbbaabbbbbbbabbbaaaaabaaaabbabbbbbabaaabbbaabbbababbbaabaababbabbabaabbabababbbbaabbbaaabbaaabababbaabbbbaaababbaaabbbaabaabbbbbabbaabaaababbbaabaaabbbbabaaabbbbbbbbbbaabababbaabbbaaabababbbbaababaababaabbaaabababbbaabbbabbbbabbbbabaaaaaaabaaabaaabaabbaabaaabbaabbbbbbabaabbbbbbaaabbbaaaabaabababbbabaababbbabaabaaaabbbbbbbbbbbbabbbbaabbabbaabbabbaaaaababaaabbbbaabbaababbbaababbabbbabbababbbaabaaabaabaaabaaababbbbbaabbbaaabaabbabbbaabaaaaabaabbabaabbaaabbaabbabbababaabbbbabababaaaabbbabbabaaaabbbabbabbaabaaabababbaaaaaaabbaabbbbabababaabbaababaaaaabbabbbaaabbbababababbbabbbababbbabbaaaabbbbaaabaaaabaabaaabaabbabaabbbabbbbabbabbabbaaabbbaabbbbababaaabbbbaabbaaabaaababbbaabaaaabbababbbbbbbbaabaaaabababbbbabbabbbbabaabaababbbaabbbbaaaabaabbaaabbabaabbaaaaaabbaaabababaabababbbbaaaaabbbaaaabaababbbaababbabaaaabaaaaaaaaababbaaaabbbbabbabaaaaaaaabbababbabbababbbaaaaaaaaaabbaababbbbbabbaabaaabaabbaababaaaabbabbbaabaabbaaabababbbbaababaabbbbbbaabbbbababaaabbbbbbbbaabbaabbbabbbaabbabbbaabbbbbaabbbbaababbbbbaaaaaaabbabbbbbabaaabaaababaababbaabaabbabaabbbabbabbaabaaabbabaaaaaabbbbbbaaabbbbbabbbbaaabaababaabbbbaaaabaaaabbaaabbbaabbabaaaaabaaabbbababbbaaabbbabababaababaaaaaabbbaabaabaaaaaabbbababbbaaaabababbbaababaaabbaabbabbbbbbbbabaababbbbbbbbaaababaaaabababbbbbbbababbbbababbbaabbbbabaaabbababbaabbbaabbbbbabaabbabbbaaabaabbbbaabbabababaababbbbabbbabbabbbababaaabbbaaaabbaaaaabaaaababbaaabaaababababaaaaaaabbbababaabbbababaababbbbbbabaabaabaaaabbbaaaaabbababaabbbaabbaaabbbbaaaaabbaaaabaabaaabababbbbabaaaabaabbabaabbabbaabbbabbbaaabbabaaabaaababaaaabaaaaaabaabbaabbaababbaaabababbaaabbabaaabbbaabaaabbbbaabbbaabbbababbbbbabaabbbbbbaabababbbbaababbbbaaaabaababbbaabbbbbaaaaabaabaaaabbbaabbbbabbabbbbaaaabbbababbabaaabbaabaaabbbbbbbaababbbbaaabbaaabaaabaabbaaaaabababaabbbbaaabaabababbaabbabbbbabbbbaabbabbababaaabaaabbaababaaaaaabbaabbabbbbbbabaabababbaaaabbababbbaaabbbbabaaaaabaaaaabaabbbaaaaaaabbabbaaababbbabaaabbbabbabbbabaaabbabbbaaaababaaaaabbbbbbabababababbababaaaaaababbaabaaaaabababbaaabbaabaaabbbaaaabbbabbbaabaaaaabbabbbaaaaabbabbabbbbbbaaaaababababbaaabbabbababaabbbaababbaaababaaaaaabbabbaabaabbbbbabbbbaaababbababbbbbaabbabbabaaababbbbaabaaabaaabbaaabbabbabbbbbaabababbbbbaaaaaaaabbabbbbabbaaababbbaabbaabbbbabaababbabbbbaaaaabbabbbaaabbbbbaabaaabbbaaaabbbbababbbaaabaaaaababbbaaaaaabbbaababababbabbbbbabbbaabbbbabbbbbabbabbabaaababaaabbabababbbababababbbaaaaabbbaabaabbbbbbaaaababababbbaabbababbabaaababaaaabaabbaaabababbbaabbbaabbbbabaababaababaabbbabbabbababbababbbbaaaaabbaaaababbbbabbabaababbaaababaaaaaaaabbbaaaaaaaaaabbbaaabbbbababbaaababbbabbbbbbbababbbbbbbbabaabbbaaaababbbbbabbbbababaabababababababaaaaaabaaabaaabbabbbaaabbbbabaaababbbaaaaabaabbaababbaababbbaabaabbbbababaababbaaaabbbababaabbaaaaaaabaaaababaaabbababaaabaabaaaabaabbbabaababbbabbabaabaaababaaabaabbbbaabaabaabbaaaabbbbabbbaaaaaaabbaabaabaaaabbbbaaabbbabaabbaaaaabbabbbabaaabbabbaabbbbaaaaababbaaabaaabaaaaabbabaababaaaaaaabbbaababbbbbaababbabaaaaabaaabbbaabbbaababbaabbbaaaababbbaabbabbaabbbbbbbabaaaabbaababbbaaaaabaabbbaabbbabaabbbaaabbaabaababbbabbaaabbaaaaaababaabaabbbabaaabbaabaabaabaaaabbabbabbbabbaabaaaababbbbbbaaababbbbbabaaabbabaaabababbbbabbbbbabbababbbbabbbabbbaabbabbbbbabbbbbaaaaabbbbababbaaabaaababbabaabbaababaabbbbbaababaabbbabbabaabbaaabbbbabbbaaaabaabaabaaaabbabbaababaaabbbbaabbbbbbbbaaaababbababbabaabbaaaaaabbaabbbbaabbaaaababbbaaababbbaabaabababaabaabbbaababbbbbababbaaaabababaaaaaaaabbbbaaabbbababaaabaabababaababaababbbbaabbbbbbbbbbabbabbaabababababbbaabbbaaabbaaaaabbbabaababababbbaabbbaaabbabbababbbabaaabaaaaaababbbbbababbaabbabaaaabbbaaabbbaabbabaaaabbaaabbbbbbabbaaabbaaaababbaaaaaababaaaabbbaabbbabaabbbbaabbbbbbaaabbbababaabbbabbbbabbaaaaabaaabbaabbaaabbbbbabbabbaabbbbbbbbaabaabbbaaabbabaaabbbabaaabbabbababbbabababaabbbbbbababaaabaaabbababaaaaabbbbbbbaabaaaabaabaaaaabbabbabbbaabbbbaaaabbbaaabbbaabaaaaabaaaabbaabbbabbbbbbbbbabbababbbabaaaabaaabbabbbaabababbababbbabaaababbbbaaaaaaaababbababbbabaabbbbbbbbaabbaaababaabaaababaabbbabbbbbababbaababaaabbabababbbbabababbabaababbaababababaabbbababaaabbaaaaabaabbabbababaaaababbbababbabaababaabaaabbbbbbaaaaaaabbaabbbaaaaabbbaaabaababababaaaabbababbaaaaabaababbbaaabbbaabaaaabbbbababaaaabbbabbabbaabababaaaabaabbbaababbbaaabbabbaabbbaababbaabbbaabbababaaaaaababbbbaababbaaababbaaabbbbbaabbbabbabaaababbabaaabaabaabbababbbbbbbabbbabaaabaabbbbaaaabaabbbabababaabaaabaabbbabbabaaaaababbababbabbababaaaabbbbabbaababaaaababaaaaababbbabbbbabaabbbaaabaabbbabbbbbbababbabababbaaabbaabbaaaabaaabbabbabababaabaaaabaababaaababaaaaaabbababbbbaababbbbababaabaabbbaabbbbbbbbabbbabbbbabbaaababaaaabaabababaaabaabbbaaaabbbbbabaaaabaaaabbaabbbaaababbaaabbabaaaabbabaabbabbaaabbaabbabbaaabbabbbbabbbbaaaabbbabbaabbabaaabaabbbababbbbabbabaaabbabbabababbbabababaabaaabaaabbbbbabbbbbbbbaaaababaaaabbbbbaabaabbbbbabbaaababaababaabbbbbbbbabababbbabbbaababbbbababaaaaabbabaabaaaaabbaababbbbbaaabbabaabaaaaaabbbaababaabbabaaaabaabaababaaaaabbbabbabaabbababbabbbabaabbaaabbaaaababbbbaaabbbabbbaaabababbbababbbbabbbbaaababbabbbbaaabaabbaaaaabbbbbabababaabbbbbbbbabababaaaaaababbbabaaabbbaabbbbabaaabbbabbbbabbbbababbbbaabbbbbbbbaaaabaababaabbbabbabbabbaababaaabaaabbababaaaaaaabbbbbbbababaaaabaababbabaababbbaabbbabbbbbabbabaaababbbbabaabbaaabbbabbbabbbbbbabbabbaabbbaabbbaabbaaaaaabbabbabbbbbababbababbabaaaabbbbbbabbbabbaababbaabababaaabaabaababbbbaaabbabbaabbaabaabbbbababbaaabbabbabbaabbbaaabbaaabaaaaabbbaababaabbaabbbabbaaabbaabbaaabbbabbaaabbababaabbbbabababaaaaabbabbbbbaabbaabaaaaabaabaabbabaababaabaabbbaaaabaaaaabbaaabbabaaaababaababababababbabbabaaabaaabbabbbbbaaaaabbbbbababbbabbbbbbaabbabbaabbbaaaabbabbbbbbbbaabbbbaabbbaabaaabbbaabbbbaabababbaabababbababbbbbbbbaabaabaaababaaaabbbbbaabbbbaabaabaaabbbbbaabbabbbabbabaababbbbabbaaaaaaabaabaababaabababaababababbbbaabaaaaaaabbbabbaababaaaaababbabababbabbaabababbaabaabaabaababababaaaaaaabaabbbabbabbaaabaaabaabbbababbbabbababbaabbababababbbababbaabaaabbaaabbbbbababbabbbaaaabbbbabbababaaabbabbbabbbaaaaabbbbbbbbbaabaaababbabaabbabbbababbbbababbbbbbababbbabaaaabbaaaaabababaababbaaaaababbbabbbaaabaaaaaabaaaabaaabbbbabbbabaababbbabaaaababababaaabbaaabbababababaabaabbbbbbbaabbbbbaabaaaaaaaabbbbabaabbbaabbabaabaaabbbaababbabbaababaabbabaabaaaabbbbaaababbababbabbabaaaabbaabbaabaaabbbabbbbaababaaaabaaaabbabbaaaaabaabbaabaaababaaabaabaaababbaaababbbbabbabbbabbaabbaaaababbbaaaababaababbbaaabaabbaaabbabaabaaabbabbabaabaaaababaababaaabbbbaabbababaabbaaabbbbabbabaabbbababbbbabbbbbaaabaabababbbabbabbbbabbbabbabbbababbbabbaabbaaaabaaaaaababbabababbabaabbbababbabbbbabbbabbabbaaaabbbaabbabaabbbabbbbbaaababbbabbbaababbabbbabbaabbbababbbbbaaababaabaaaababababbbbaabaababababbbbbabbabbbabbababbbabbabbaaaaabbbaaababbaaabbbabaabababbaabaabbabaabbabbaabbaaaabbaaabbbbbabaababbaabaabbaabaabaaaaabbabbbabaabaabbbbaabbbbabaaaaababbbababababbbababbbbaabbbabababbbabbbaabaaaabbabaaaabaaaaaabbbaabaaaaaabaabaaaaaabaaabaaababaaabbaaaaaaabbaaaabbababbbbababbaabbbbaaaababbabbaabbbaabbabbbbbbbbabbbbbaaabaaabbbbabbbbabbabbaaaaaaabbabbbababababbaaabbbabbaabbabbbaaaabbbbaaaabbbbbabaaabbbbbabbabbabaabaaababaaaabbabbabaaabbaaababbabaabbbbbbbbabbabaaababaaaaaabaaaaaaabbbababbaaababbbbabbbaaaabaaabbbaabbbbbaabbaababaaabbbabaaaaaabababbabbbbaabbbabbbbbbaabbbaabbaabaabbabbbabaabbaaababbbabbbbabbaababaaaabaaabbaabaabaaabaabbabbabbbbbabbbabbbaaaaaaaabbbbbaaaabbbbbbbabababbaababababbbbababbaabbababbaaabaabaabbaaabaaaaaababbababbbbbbbbbabaababaaabbababbbbabbbabbbababbbbabbaabbbbaabababaaaaabbbbaaaababbaaabbbbababaabbaaaabaabaabbaabbababbaaaababbbabaaabbaaaabbbbaabbbabbbbbbbbaaaababbabaaabbabbabaabababbbabbabbbbbababbbbbaabbabababbbbabbbabbaaabbbbaabaabaabbbbbaabbbaaabaabbbbbbbabbbaaabbbabbaaaababaaaabbaaabbbabbbaabbbbabbaabbabbaabababababaabbaababaabbbabbbbbaaabaabbaababbaabaababababbbaabbaabababbbbbbbbbbaaabbaaaaaababbbaabaabbbbbaabbbaaabababbbbbbbababbaababaaaaabaaabbbbbaaabbbbaababbababababaabaaaaababbbabbabaaaababbabbbaaaaabaabbbbbaaabaababababbabaaaabababaaabbaaaabbbabbaabbbbaaaaabaababbaababbbbbaabbabbbbbbbbbbbbbbaabbabbbaaaaabbaabbaaabaabababababaabbbababbabababaaaaaaabbbbbbabaabaabbbaababbabbbbbaabbababaaaaaaaaaaaabaabbbbaaabbbbababbaaaaaabbaaabbabbabbabbabbbabbbabbbbaabaabbbabaaabaaabbbaabaabbbabaaabbbbabbaabbabaabbabbabbaaaabbbbababababaaaaabbababbababaabbbaaaabaabaaaababababbaaabbaaaaabaaabbaabbaabbaaaaaabaaaaabbaabbabaabbaaaaaabbbbabaabbabbbbababaabaabaabbababababbbbabbbaaabbbbbbbaaaaaaaabbaabbbabbaaaabbbbbbababbabaaabbaaaaabaabaabababbbababbabbaaaaabbaabbbabbaaaaaabaababbbaabbabbbbabbbabaaaabaabaaabbbabaaaaaabbaaaabaabbbbabbabaaaababbababaababbaaaaabbbababaaabaaaaababaaaabaabaabbaababbbababababbbbabaabaaaaabababababbabbababaaabbbaabbaaaababbbbabbbaabbbaababbababbababbaabaaababaaababaaababbbbbbbbbbbbbaababbabbbabbaababababbbbaaaaaabbaaaabbbbbaaaabbbaababaaababbabbaaaabbaaaaaaaaaabaaabbbabbaaaababaaabbbbbababbbbbbbabaabaabbaaabbabbbabbbabababaabbbbaaaaaabbabaabbbbbabbbbaaaaaaaaaabbabbabaaabbaabbaaaababbbbabababbbbbaaaabbababbbbbaaaabbaaaaaaaaaaabaaababaabbaabbbaaabbbbbabbbbabbaaaabaaaabbaaaabababbabaababaaaaaaabaaaabbbbaaababbbabbaabaaababaaabbaaabbabbbaaabbbbaabbbaaabbbabbbbaaabbaabbaaaabbbbaaaaabbbbaaaabbbabbbabbaabbaababaabaabbabaaaabbbbaaabbbbabbabbbaababaaababaabaaaaaababbbbbabbaaabbaaabbabaabbbabbaaaabaabbabbabbabaabbbaaaaaaabbaaababbabaabaaaababbababbbaabbbabaabbbbaaaaaabbaabababaaaaabbbaabbaaabaababbabababbbbabbbabaabbbbaabbabbbbbabbabbabbbbaabbaabbaabbaababbaabaaabbbbabaabababbaabbabbaaaabaabaaabaaaabaaabbbaabbabaabbaaabbbbaaabaaaaaaabbbbbbbbabbbbbbabaaaaababbabbbaabbbabbbabaabaaabbaababaabbaabaaababbbbabaabaaabbaabbaaabbbaababbabaaabbaaabbbaabaabbabaaaaaabbaaaaaabbabaaaabbabbababbabbbbbaaababbbaababbaaaabaababbbbaaabbabbbaaaaaaabaaaaaabababaabbaabbaaaaaababbababaaaabbaaaabbbbaaaabaaabaaabbbaaaaaaaabbbbaabbbababbabaaaabaaaaaaabbbbabbabbabaaaababbaabbbbaabaaaaabbbabbbaabbbbaaaaaaaabbbaaaaabbbbbbaaabbaabbaabaabababaaabbaaabaabbaabbbaabbaabaaabaabbaabbababaaaabbbaaabbbabbabbabaababbaaabbabbabaabababbabaaaababbbbabbaaababaaabbbbababbbbbababbbbababababbaabbbbbbababbbbaabaaaabaaabaabbbbababbbaababbbbabaababbabbaaaaaaababaaabaabbabbabbabbababbaabaabaaaabaaaabbaabbababaaaabbababbbbbbbaabbbaaabbaaaaaaaaaaaabbabaababbbbabaaabbaabbababaabbbbbaabbbbbbabbaabbabbaaabbbbaaababbbabaaaabbabaababaabaaabbaaabaabbaabbabbaaaabbaabaaaaabbaabbabbbbabbbabbbaababbaaaababbbbbabaababbaaaaaababaabababaabbbbaabaabaabbbbbabbbabaaaabbababbabbbbaabbbabbaaaabaaaaaaaabababababbaabbaaabbaaababbaaaabbaaaaabbbbbaaabbaaababaaaabaaaaabbaabababbabbabababaabaababababaaabbbbbbbaababaabaaaaaaaaaaabbabaaaabaababaaabababbbbabbaaabbbaaaabbbbabbaaaabaabaaaabbabbababaabbbbbaabbabbbabaaaabaaabaabaaababaababbbbbbabbbaabbababababbbabbaaaaaabbaababbbbbbabaaabaaaababbbbbaabbabbabbbabbbabbabbababababaabaabbabbaaabbabbaababbabbaabbaaabaabababaaaaabaabaaabaabbabaabbbaaabaabbabbaaabbababaaabbaabbbabbaaaabbaaaabbaababbbbbbababaabbbbbbbbbabaaabbaaabbaaaaabbbabbbaabbbabbababaaabbaaaabbbabaabbbabaaabbabaababaabbabbaababbaaaabbbabaaaabaaaaaaabbabababaabbbbbbabbbbabbbbaababbbbaabbbbbbaababaaabbbbaaaababbababbbbbbbbaaaaabbbbbabbbbbabababbbababbbbbbababaaaaababbaabbbbaaabbbaababbabbabbaababaaaaaabababbaaaababbbabbbbbaabbbbbabbabbbaaabaaabbabaaababbababaaaabaaabbbaaaaaaaabbaaaababbbbbaabbbabbbaaaaaaaaaaababbbabaabbababaaabababbabaaaabbaabbbaaabbaababbbbaabbbbbaabbabbbbbbabbabbabbabbbaaaababaabbabaabaaabaaaaabaabbaaaabbabbabbaabbbbabbaaabbabaabaabbbabbbbabbbabbbbabbbbbbaabbbaaaabababbbbbaabaabbbbbaabbabbaaabaaaabbaaaaababababbbabaaaababbbbabbbbabaabbbabaabbbaaaaabaabbababbbbaaaabbabbbabbaaababbabababbaabaaabbaabbaaababbaaabaabbabbbaaabbaabbabbbaababbbbaabbbbaabaaabaabbbabaababaabaabbaaabbaaaaaababbaaababbaaabbbaabaaabbbaaabbaabaaabbabaabaaabbaaabbbbbabaabbabbbaaabaaabaabbbaabababbbaabababbbaaaabbbbbaababaaabaabbbababbbbabbaaaaabaabbbaaaaabaaabbabbbbabaabaabbaabaaabababababbabbaabaabbbaabaaaabaaaaaaaababaabababbbaaababbababaaabbbbababbbaabaaababbbababbbbaaababbabaabbabaabbbbbaabbabbbaaababbbabaaabababbbabababbaaaaaabaaaaaaaabaabbabababaaabbaaabbaaabbbbaaabbbbbaaabbaaabbababaabbaabbbbbbbbababbaaababaabbabbbbbbabaabbbbbaaababbaabababaaaabbabaabaabbababaabaabaaaaabbbbababbaabbaaaaaabababbaaabbababbbbbbbbabbaaababbababbbbaaabbaaabbbabaaabaabaabaaaabbbbbbabaaaabaaabaaaabbbaaaaabbbabababababababbbbaaababbaaaaabbbbabbbababaaabbabbbbaaaaaaababbaabbabbaababaabbbaaaaaaaaabbbaaabababbabaabbabaabbbbaabbbbbaaababbabbabbaabbaabbbaaabbbaabbabbbabbabaaabaaaaababbabbbaaabbaaabbaaababaaabbbabbbaaaabbbbbabbaaabababbaabbabbbabbabbbbaaaaaaabbbbabbaabbaaabbbbbabbaababbbaababaababaaaabbbbbaaabbbaaabbaaaaabaabbababbbbbbbbbabaabaaaaaaaaabababaaabaabbabababbbbababbabbaabaabbbabbaabababbbbbbbabbbaabaaababbbababababbbbaababbbabaabbaaabaababbababbaababbbbbbabbabbbbbbbbbbbabbbabaaabbaaabbbaaaaaabaabbaaabbaaaabaaabbababaababbbbbabbaaaaabaabbaaaabbabbbbaababbbabbbaabaaaababbaabbaabaaaabbbaaaabbaaaaabaaababbbaaabbbabbbbabbbbbbbaabbbaaabaabaaababaabaaabbaabaababaabaabaabbbabbbabaaaabbbababbaaababaaaababbbaaabbbbaababaabaaaabbbaababaabbbaabbabbaababbababaababbbaaaabbaaabaabababaabbabaabaabbaabbbaaabbbbbbbaabababaabbbababaabaabaaabbbbbbbababaababbaabaabbaaababbaabaabbaaabbabaaabbbaaabbaababaababbbabaaaabababbaaaabbaaabbbbabbbbbbaababaabbbbaaababababbbbaabababaaaababababbbbbbababbbaababbbbbbbaabbaaabbbaaaabbbbababbaabaaaabaabaababbabbabaabbaaaabbbaabbabaaababbbaabaabaababbbabbbbbbaaabbabbabababbbaabbbbaaaababaabbbbbabbbaabbabaababbbbbabaaabbbbabaababbabbbbbbabbababbaaabbbbbbbaaaaaaaaaaaaaabbbbaaaaabbabaaabbbaabbbabbbbabbbbaaaabbababaaaaaabbabbaaabbbbbaababababbabaabbbbbaababaababbbaabaabaaaabaaabbbbbaabbabaabbaabbbabbaabbaabaababbbbabbbabaaabbaaabbbaabaabababbabbbbbbbbbbbabaabaabababbbbbbaaaabaabbbabaaaaabaabbbbaabaaabaaabbbaaaaaaabaabbabbabababbabaabaabaaaaaaabbabbbbabbbaabbbaaabababbbbbbabbbbaaabbbbbbbbaababbbbaaabbaabbbbaaaaaabbbbbaabbbababaaaabbaabbbbbaaaaababbaabbbabbbabaaaaaabbaabbbabbabaabbbbbbbaababbbbabaabaaabababbabbbbaababbaababbaaabbaaabbabbaaabbbbaabaabbabaaabaababbbababbaaabaaaabaaaaaaaabbabbaabbabaabbababbaabababaabbbaaabbaaaabaaabaaabaaaaabbbbaaabbaabaaaaaaaabababbabbbbbabbbaababbbaabaaababbbabbababbaaabbbabbbaabbabbaababbabaaaabbabbbbabaabbbaaaabbbababbbbbabbaabbababbababbabbbbbbbbbaababbabbbaaaabbabbbaaabbaaaaaaabaabaababababbabbbbaaabbabbbabbababbbbbaaabaaabbbaabbaabbbabbbaaababaaaaaaabaabaaabaabbaabaabababbabaaababbbabbbabaababaaaaaabbbababbbaabaabbaaababbbaaabaaabaaabbaaaaaabbbbaaaaabbbabbabaaaabbaaaaaabaaababbbbaaababbaabaabbabaaaaaabbabaaaabbbbbbabbbbbaabaabababbaabbaababaaabaaaabbaabababababbaaaaaaaabbbbbababbababbbababbbbaabbaabbbbabbbbaababbbbbbabbbaaaaabbabbbbaabbbbabaabbbaaabbbbaaaabbbbbabbbaabaaaaabbbbbbbbbbbababbaaabbbbbbaaaababababbaaabbbabbbaabbabbaabaabbaaaababaaaaaaaabbbaabbaaaabbabbaaabaaaaabbaaaabbbaaaaabbbbaaabbabbabaaaaaabbbabbaaaabbbbabbabbbbbbaabababbbaabbaababbbabaababbababbbbbabaabbabbbbaaabbbbabbbababaabaaaaaabbbabbbabbbbabaaaabbaaabbaabaaabaabbababbabaaabbbabbababaaaabbbbbbbababbaaaaaababaabaaabbaaabaaaaaabaabaabbababaaaababaabaaaaabbbaabaaaabbbbabbabaaabbabbbbbbbabbbabbbabababaaaabaababbabbaabaaaabbaabaaaabaabbaaaaaabaaaaabababaaabababababbbaaabaaaaaabbaabbabaaaaaabaaababbbbabbbbbbbbbaaabbaabbbaaababbbbabaaababbbabbaaabababbabbaabaababaaabbbabaaaabaabbbabaaababbbbaabaaababbbabaabbaaabbbabbbaaabababbbbbbbbbaabbbaaababaabbabaabaaabaababaabbbaaababbaaabbbbababbbabaaaababbbaaaaaababbbbbaabbaaabaabbaabaaaaababbbabaabaabaaaabbaaababbaaabbbabbababbaabbbbbababbaabaabbbbbbaabbaaaaaaaaaaaaaaaaabbabbbbaabbabbabababbbbbbabaaabaababbbabaababbbbaababbababababbbabbaaabbaaababbaaaaabbbbaaaabbbbaaabbbaabbbbbbbbaaababbabbbbabbbabbbbbabbbaabbabbbabaaaababbbbabaabbbbbabababbabaabaabbaabbbbbaaaabbaababaaabababbaaabbbabbbabbababbabbababababababaaaaababbaababbabbbabbabaabbabaaabaaaaaabaaaaaaaaabbabbabaabaaaabaabbaabbbaaabaaaaaaaabbaabaaabaaabbbabaabaababaabbbabbbbbabbabbabbabaaaaabbaababbbbbaaabbbabbbabbaabbbabbbbbababaabbaabbaaabbbaabbbbbabbabbababbaabbbaaaaaababbabaaaabbbbbaaaaababaaabbbbbaaabaaaaaabbbbaabbbbbabbbabbbbbababaaababbbbbbbbbbabaabbababaaaaababaabbbaabbabbbaabababbbaabaababaaaaabbbbababababbbbabbaaaaabbabbabbbaaaaaababbbabbabbaabaabbaaabbabbabbbabbaababbabaabaaaaabbabaaabbaababbaabaaababaabaaaaaaaaaaabaabbabaaababbababbbbbaaaabbbbabbaababbabbaaaaabbaabbbbbbbaabbbaabbbbaaabbbbbbaaaaaaabaaabaaabbabbaaaabaabaabaaabbaababaabbaababaaaababbbbaabaaaabbaabbabaababbbbabbbaabaaabaababbbbaabbbaaaabaabbaaabbabbbbbabaaabbaabbbaaaabbbaabaaaababbaabbaaaaaaabbaaaaaaaabbbbababababbbbbbbbbbabbaabaaabababbbbbbbabbbbaaabbabaabaababbaabaaaaabaabbabaabbbbabbabbbaaabbbbbbbbbabbababaabbbbbbaababbaabbabaaaabaabaabbbbaabaaababbbbbbaaaabbabaaabbaabaabbbaababbaaaaaaabbaabaababbabaabbbaaaabbaabbbbbaababaaabaaaabaaabababbbaaabbbbbabbbabbbbaaababababaaaababaababababbbbbbabbaabbaababbbaaaaabbbbbbbaaabaaaaabbbbabaaaabbbbbbabaaaababaaaababbbbabbbabaaaabaabbbbaabaaaababbaabbaaababaaaabbaababbbabbbabbbaaabbbbbaabbaaaabaaaabbbbababbababbbbbbbbabbbbbabbabababbbbabaaabbaaaababbbabbbbbabbbbbabbaabaababbaaababaaabbbabbbababbaaabbabbaababbaaabbbabaabaaaaaaaaabbbabbabaaaabaaaababbbabbababbbbbaaabbaabababaaabbbaaaabaabaabbabbbaaaabbbabbaabaaaabbbaabbbbaabbbabbaababbbaababaabbbababbaaababbbaababaabaaabaaaabaaababaabaabbaaabbabbbabaaaaaabbabbbbabaaaabbabbaaabbbaabababaabbabbbbbabaaaababaaabaababaaabaaaaabbaabababbbbbbaaabbabbabaaaababbbbbabbbbaabbbabbababbbaaabbaaaaabbbbabaabbababbaaaaababaaabbbaabbbbbbbabaaaaabbbaabaaabbaaabbbbaabaaaaabaaaaaabbbaabbbbbbbbbaaabbbbababbabaaaaaabbaabaabbaaabaabbbababbbababbabbabbaaabbbbabbabbbababbaabbbbabbaabaababaaabababbbbbaaabbbabaaababaaaabababbbbaabbabbbabbaaababababaaabbabaaabaabbbbaabaababaaaabaabbbbbbaabbbabaaaabaaabaabbababbabbbaaaaabaaabaaaaaabaababbbaabbbbabbbaaabaaabababbbaaaabaabbaaababbaaabbabababbbabbbbbabbbbbbababaaabbababbaabbababaaabbbbaaababbbbaaabbaabbabbbaabbababababaaaaaaaabaaabbaabaabbaaabaabababababaaabaababababaabbaaabbabaaaabbaaabbbaabababbaabaaaababbababbaabababbabbbababbabbbbbbbbabbaaaaabbbabbaabaaaaabbbbabbbaabaabaaabaabbbabbbbbaabbaabbaaabbabbbaaaaaabbbbabbbabaababababaaaaaababaaaabbbababaaabbaaaaabaabababbbaaababbbbaabaaaaaaaaaaabbaabaaabababbabbbbbabbbaabaaabbbaabaaababbbbbbbbaababbabbabaaaabbaabaabaabbaabbabababaaababaaabaababbbbbbaababaabbbabbbbbbaaabababaabaabaababbbbaaaabbabbbaaabaababbbaaabaabbabbbabaabaabbaababbababbbabbaaababbbaababbababaabbaabbaabbbbbbaabbabaaaaaabbababaabaabbaabbbaaaaaaabbaaabbbbaaaaababbababbaaabaabbaabbbaabababbbbbbabbbbababbababbaaabbbbaaaaabbabbabbabaabbaababbababaabbbbaabbabaabbaaaaaaabbbbbbabbaabaaaaaaaababbabbabbbababaabbbaabbbbaabbaaaaaaabababaabbaabaabaabbbabaaabbabbaabbaabaaabbbbbbbaabbbbaaabbaaabababbbbbbbbabbabaaababaabaaaaabbbbbbaabaabbbababababbbaaaabaaaaabaabaaaababbbbaabbaaabbabbaabababbabbaaaaababbbaaaaabbbaaaaababbbababbaabaabbaabaabbbbabaabaabbbaaaaaabbbaababbaabaabbababaaabbaaabbaaabbabbbbbabaabaaabaababbbaabbbbbabbbbaaaaaaaaaababababbbbbbbbaaaabbbaaaababbbabbabbaabbbaabbbababbbabbbaaaabbbabbaaaabaaababaaabbbbbbaabbbbaaabbbabbabaaabbaabbaaaababaababaaababbaabbbabbaaaabaaaabababbaabbbbbbbabbaaaabbaabbabbabbbbaabaabaabbbbbbababbaaabbbabaaaabbaaababbaaabbbabbaabbaabaaaaababbbbbbabbbaaabbaaaaaabbbabbbbbaaaaabbaabbababbbaababbbbbbbbaababbbaaaaababbbaaaabaabbabbaaaabaabbabbbbbbaabbaabbbbaaabbbbaaababaaaaaabaabaaaaaaaaabaabbbababaaaabbbbbaaaabbaabbabababbabbabaaaaaaabbaaaaababaaabaaabaaabbaaabbbbbbbaababaabaabbababbaabaabaaababaababbbabaabbbbabbaaaabaabaaabaababaabbabaaaababaabbbbbbaaabababbababaabbaabbababbbaababbbabbbbbbbababaababbbaaababbaaabababbbbbabbababaaaababaaabbbabbbbbbabaabbbabbbabaabbababbbbbbabbababaaabbababbbabaaabaaaababababababaaababaaabbabbabbaabbbabababaaabababbabaaaabbbaabbaaaaaaabbbbabbaaabbbbaabbababababbbbabababbbbbbaaabbabbaaaababaabbbabbabaabaaaabaaabbaabbababbbabbbaaabaaaaabbbabbabbaabababbabbbababbbbbbaaaabaaababbabbaaababbbbbabbaabbaababbbabaaaaababbbbbbabbbabbaabaaaabbabaabaaaababaabbbbbabbaabbbbabbbbbbbabbbbabaaaabaabbbbbaaabbaaaaaaaabbbbbbbaaabaabababbbbbaaaababbaabaabbbbbabaabaaabbabaababababababbabbbabbbbbbabbbababbaabbabaaaaabababaabababbbabbbbbababbbbbbbbbbbbbbaaabaabbaababbbbabbaaabaabaabaaaabbbbaaaabbabbbaabbbaabbababbbbaaabaabbabbaaabaababababbbbaaaaaababbbaaabbaaabbbabbbbaaababbbaaabaaabaababbaaabbbaabbbabbabbbabbbbabbbaabababababaabbbaabbbababaaaabbabbbbabbabbbaaabbbbaababbaaaaabbabbaabbaabbbbbbbaaabbaababbbaaabbbbabbbabbaabbaaababbbbaaabababaaaaabaabaaaaabaabbbaabbbbbaaabababbbabbaaaaaaabbbabbbbaabaabbbbbbbaaababbbbababaabbaabbaabbbaaabbaababbabababbaaaabaaaababaabbaaabbababbbaaaaaabbaababbbababbbbbabbababaababbababbbaabbaaabbbabbbbbaabbabaaabaaabababbaaabaaabbabababaaaababbaabbaaababbbabbbabaabaabaaaaabbbaaababbbbabbabaabbabbbabbabaaabbaabbbaaabaabaabaababbaabbbbbabbbabbabbabaaaaaabaabbbababbbaaabbbababbbbbbbbbaaabbaaaaaaabbbabaabbbbbbbaaabbaababababababbbaaaaababaabbaababbababaaaabaaabbaabaaaaaabaabbabbbaabaabbbaaaaabbbbbbbbbbbaaaaaabbabbababbabbbbbaabbababbabbbbaababaabaabbabbbabababbaaaaababbbaababaaaabbbbaabaababaabbabbabaaaaabaabbbbabaabbabbbbbaaabbaabbaaaababbbbbbbaababbabaaaabbababaabbababaabbbbbabbaaabaababbabaabbaababababaabbbbbaaaabbbabbaaaaaaaaababbbababbbbbbabbaabbbaabaabbbabbbbbabbbbaabbbbbbbbabaaabbaaabaaaaaaaaaabbaaaabbbaaaabbaaabaaabababbabbbbbbbbbbbbababaababbabbbaaabbababaaaabababbaabbbbbbbbbabaabaabaaaaaabaabaabbababbabaaaabbbbaaaababbaaabaabaabbbaababaaaabaaaababbbbabbbababbabaaaaababbbaabbbaaabbbbbaaaaaabbaabababbbbbaaabbbbabbababbbbaaabbbbbbbbaaaabaabbaaaabbaaabaaabbaaabbababaaaababbbbbbabaabababaaababababaaabbaaabbababaaaabbabbbaaabaaabbaaabaaaaaaaaabbbaaaaabaaabbabbbbbbbbabbbabbbbbaaaaababbbabaabaababbbbabbbabbbbaaaaabbaaabbbabbbaabbbabbbabbabbaababaaaabbaaaabbaababaabbaabbabbbbaabaaababbaaaabababbbaaabbbbbbbbbabbbbbaababbabababaabbbabaababaaababbabbababbbbbaababbbbabbbaabaababbababbaabbbbbaaabbbbabbaabbbbbbaaabbbaabaabbaaabbabbaaaabababaababbbbaabbbaabbbaababaaabbababbbbaabbabbbababababababaaabbabaabbaaaaababbbbabbabaabbaaaaabaabbbbaabbbaaaaabaaaababbbbabbbbbbbaaabaabbbbbabbbbbaabbabaaaaabaaaabababababbbabbabbabbaabbbabababaaaabbbaaababababbaabbabbbaaaaaaababbbababbaabbabaabaaaaabababbbbaaaaaaaaabbbbbbaabaabbbaaabaaabbaaabaabababaababaaaaaaabbbbabbaabaababbaababababaababbaababbbababaaaabaaaabbbaabbaaabbaabbbbbabbbbaaabaaaababaabbaabbaaabaabbabaaaabbbbaaabbababbababbababaabbaaaabbaaaaaaabbbaaaaabababbaabbbbaaaaabaabaaaabbaaaaaabbbbaaaabbabaaabbaababbaaaabbabaaabbaabaaabbbabaaabbaabaabababbaaaabaabbababaabbababbabbabbbabbaaabbbaabbbabaababbaabbabaaabaaabbbaabaabaaaabbaabbaaabbbbaaabbabaaabbabaabaabbbbaaababbababbbabbabbaabaaabbbabaaabababbaaaabbaaabbabaabababbbaabbbababbabbaabbaabbaaaaababbbbaabbbaaaaaaabaaabbbaabbbabbaababbabaaaaaaababbbababbbbbabbbababaaabbabaaabaabaababbbaaabaaaaababbabbbbbaababababbbababababaaabababaabaababbabbbaabaaababababbababbbbbbbaaaabbbbbaababbabaabaaaaabbbbaabbbabbbabaabbbbabaabbabbabbabbaabaabbbbabbbbbabbbaabbbbbbaabbabaaaabbbbbaaabaababababababaababaaabbbbbabbbabbaabaabababaaabbabbbaaabaaabbaabbaababbbbbbaabbabbabbbaaabbabbbbabaaaabbbabaaababbaabaaaaaababbaabababaaaabbbbaaaaabaaabbbaaabaaaaaaabbbbbaaabababaaabbbabbbbababaabbaaaabbabbbabbbaababbbabababbbbbbbbabbabaabbaaabbbbabbaaabababaaaabbbbaaababaaaabaabaabaabaaaaabbbbaaaabaababbbbabbbbbbbbbaababbbababbabaabaaababaaababbaabbbbaaababaaabaaabbaaaababbabaaaaaabbbaaaabaabababaaaaabbaabaabbabbaabbbaaaabababaabbbabbbbbabbbabaabbbbbbbabbbababbbbaabaabbabbaababbaabbbaaaabaaabbaaababbbabaaabbbbaaaabbbaaaaaaaaaabbabbababbbaabbaaaaaabbabbbbabbbbaaaaabbabaaaaabaaaaaaaaaaabaabaabbbbbbbbabaabbabbabbbaabbaaabaabababaaaabbbabbbbabababaaaabbbaabbbbbbbbbbbabbababaaababbabbabbabbbbbbaabbbbaaabaabaaabbbabbbaabbbababaabaaaabaababaabaaabaababbbbaaabbaaaaabaaabaabbababbaaaaabbbaaabaaabbbbbbaaaababbbabaabbbaaabbbbbbbababbbbabaababbabbabbbabbaaaaabaaabbbaaaababaaaabbabbabaabbbbaaaaaaababbbbaaabaababbbbabbbbbaaabaaababaabbbaabbbbbbbbbbbabababaabbbabbaababaabbbaabaababbbabbbabbbbbbabbabaabaaabbaaabbaababbbabbbaaabbababbaababababababaaabaaabbbbaaabbbbaabbbaaaaaabaaabbbaaabbbaabaababaababbbabaabbabbabaaaaabbaaabaabbabbabaabababbbaaaabaaaaabbaaaabbaaaababababbabbaaabbbaaaabaabaaaaabbaabaabababaabbbbbaaababaabbabbbaabbbabbbaaaaabbaababbbaababbbabbbbbbbbaabbbabaababbaabbbbabbabbababbaabbabbaaabbababbabbbbabaabbaabaaabbbaaaaaaabbaaaaaaaabbbbbbabaabbbaaaaaabaaabaaabaabbaabaabaabbbabbaabaaaabbababbabbabaaabbbabababbbbaababaababbbaababbaaababbabaaabbbbaabaabbaaaaaabaabaaabbbbabaaababbbbabbbbabbaababbaabbbbabbbbabababbabbbabbbbbabbabaabbaaabbbaabaaaabbbabaabaaaaabbabbbbbaabbaabbbbbbbbbaaaabbbbabbaaaabbaaaabaabababbaaabaabbabbaaabbbbababbababaabaaabaaaaabaaabbbaaabbbbaababbaaaabaaaaaaabbaaabaaabbbbbbbbbaabaaabbabaaabaabaaabaababaabaaababababbbabbabbaabaaaaaabaabbaababbbbbbbbbbbabbbaaaaaabbbbaababbaaaabbabaaababbbbbbabaabbabaabaabbabaaabaabbaaabbaaaabbbbbabbbabaaabababaababaaabbabbbbaaaabaabbbabbbaababbbbbbaaaaaabbbabbbaabbbabaababbbaabbababbaabbaaaabaaaaabbabbbbababbaabbbbbbbbbbbabbaaabaabaaaababbaabbbaabaaabbabaaabbbbabbababaabbaaaabbbabaabaabbbabbabbabbabbbaabbbbabbbaaaabaaabaababbbbabbbbabbbbbaabbbababaaaaabaaaabbbbbbabbbabbbabbbabbbbbbbaaaaabababaabbbabaabaaaabaaaaabbbbbbaababaaabbaababbababaaaaaabbabaababbbaabababbbabbbbaababbbaabbbabaabaaababababbbabaabbaabbbaabbabbabbbbabababbaaaabbaabaaaabbbabaabbabbaaaaaaaabababbbbbaabaaaaaaaaabaaabbaabaababaaaaaaaabbbbaababbabbbabbabaabababaabbabaaabbaaaaabbbbbbbbaaababbbbabbabaaabbbabaaaaabbbbbaabbbaaaababbbbbababababaabbbabbababbbbbababaaaabaabbababbbbbbabbabbbaabbbbababbbbbbbaababbaaababbaabbabaaabaabbbaaaaabbabaaaaabbbaaaaaaaaaabbbabababaabbbaabaaabaabaababaaaaaaabababbbabbbaabbaabbaabababaabbaaabbbbaabbabbbbbababbbbbbabbabbbabbbbbabbaabbaaaabbaaaaaababbbbbbbaaabbbaaaaaabbaaabbabababbaabbaaaaaabababbbbbbabababbbabaabbabbbbbbbbbbaabbbaababaababbbbbaababbbabbabbbababbbbabbbabaaaaaabbbaabbbabababbbbbbabbbabaabaaababbaababaaaabaabababbbabbbaabbbabaabbbbbabaabbbababbbbbaabaaababaabbaaaabbbbbaabbabbbabbabaabbaababbbbabbbbbaabbabababbaaaabbaabbbaabbabaaaabbabaaababaaabbabbaaaabbbabaabaaaaaaababbaabbbbaaabaaaaaaaabbbaabbbbaaabbbaaabaaabbabbbababaababababbbabaaaabaaababbbbbbabbabbaaababaaaaaaaaaaabbaabbaaaaaabbbaabaaabbabbabbabababbabaabbababbbbabaaaaabbbaaabaaababaaaaabbaaaaababbabbbbbbabaaaabbabbbaabaabaababaabaabbbbababbaaaaabbbbbbaababbbaabbaababaabbababbabbabababbbaaabbbaaabbbbbbbabbbaaabaaaaaaabaaabaababbaaababbbaabbbaaabbaaabaabaaabaabababbabaaabbbbabaaaaaabbabaabbbabaaaaabbbabaaabbababbababaabbbaaabaabbbaaaabbbababbbaaabbabbabaabbaabababbbbbaabbbbabaabaabbbbbaaaaabbbabbbbbbaaabaabbaabbaabaabbaaabbbabababaabbabaaabaaabbabbababbbbbabbbaababaaaababbbbbaaabbbabbbaaabbbabaababbaababbaaaaaabbabbabaabbaaaaabbabbaabaaaaaaaaaaabbbabbbbaaaabbbbbbbbbbbaaaaaaabaaaababaaaabbbaabbaaabaabaaabbbaaaaaabbbbaaaaabbbaabaabbbbbabaabbaaabbabaababababbbbababbbabaaaabbbbbabbbabbaaaabbababaababbababbaabaaabbbbaaabaabbbaaaababbabbababbabaabaabaabaaaabaaabbaabbbbaababaabbabbaaabbbbbaaaaabaabbabaabbbbabbbbbbabababbbaaabaaaabbaaaaabbbaaaabababaaaaaabaabaaaabababbaabbbabaaabaaabbaabbbbaabbababbaabbaaaabbbabbbaaabababaababbabbbbbaabaabbabbbaabbababaababababaaaaabaaabababaaababaabbbabaaabababbbabbaaabbaabbaabbbbaababbabaaaaaaaaaaaaabbbaabaaabaaaaabaaaaabbaababbabaababbbaaabaaabbaaabaabbbbabbababaaabaaabbabbbaaabaabababbaaababaaaaaaabbbbbbabbaabababababbaaaaabaabaabaaabaabbbbabbbbbaaabbabbbaaaaababbaabbbaabaababaaaaabbaaabaaaabbaaabaabbabbbbbbabababbaababbbbbbabaabbabbbbaabaabbaababaaaabbbaaaabbababbbabbbbaabbaabbabbababbbabbaabbabbbbbababbaaabaabbbaaaaabbbbaabbbbbaaabbbababbbaaababbbababbbaabababbabbbabbabbaababaabaabbbaabbbaaababababababaabbbbabbababbaabaaaababbabaabbaaabaaaaaaaaabaabababababbbaaabbabbaaaabbbbaaaaabaabbabaababaaaabbbaababababbbaababbbabaaaaaababbaaaababababbaaabbaaaaabaaabbbababababaaabbaaabbabaababbabbabaabbbbbaaabbaabaaaaababbbbbaabbaaaaaaaaabbbabaabbbaabaababbbbbbabababbbabaaaaabbbababbababbbaaaaaabbaaabaabbbbbababbbabbaaaabaabaababbbbabaabaaaababbbbbbaaabaaaaaabbaabbabaabaaababbabbbaaaaaaabbbbbbbabbbbbbaabbaaababbbbaabbbbabbaaaaabababbaabbbabbaaaabbababbabbaaaaaabbababbaaaabbabbbababbbbabbbbabbaaaaabaaaabbaabaabaaaababaabbaaaaaababaabbbbabbababbbbabbbaabbabaaaababbbbaaaabbbbaabbbbbaabaabaaaabbbabaaababaaabaabbbaababbbbaaababbababbbbbbbabaaaabbbbbaabbaaababbabbaaabbbbaaaabbabbbaabbbaaabbabbaaaaabaaaaababbaabbabbaabaaaaababaababaaabbbabababaabbaaabaabaaabbbbababbaababbbbbaabbaabaaaaaabaabababbabbbaabbbbbaabbbabaaababaaaaabbbabaaabbaaaababaabaabbabbbaaaabbbbaabbaabbbaaaaaaaababbaababbaabbababbabbabaaabbbbabaaabbabbbababababbaaaabbabaaaabbbabaaaabbbabbaaaabbaaabbabaabbbaaaaababbbababbabbbbaabbbabbbabbbbaabaabaaabbabbaaaabbbaabababaabaabbaabaaaabaabbabbbaababbabbabbbabbbaaabaaaaababbbbbaaaaaababbaababaabbaaaabbbbbbabbbbababaabbaabbaaabbbaababaabbaaaabbbaaababbabaaabbaababaaabaabbbbabbbabbaababaabababaaababbabbbbbabbbbaabaaabbbaaaaaabbaaaabbbabbabbabbbbbabbaabaababaababaabbbbbbabbbbaabbaabbabaabbaabbabbbbbabbbaaaabbaabbbaaabbbbbabbaabaaabaaabababbaaaabaababaaabbbbaaaaaaabbaaaababbbababaabaababaaabbbaabaaababbbabbabbbaabbbbbbbaaaabbabbabbbaababbababaabbbbabbbbaaaaaabbaaabbaaaabaabbbbaababaaaaaaaababbababbabaaabbabbbabbbaabbaabbaaaaabbbabaabbbbbabbbbaababbbbbbababbabaaaabbbbaabbbbbbbbabbbbbaaababbabbabbabababaabbabababbbaaaabbabbaabaaaabbbbbababbbbbaabbbbbaabbbbbababbbabbababbaaabbbbaaaabbaababbbbbabbababbabaabbabbabbaabababaabaabbbbaababbaabaaaaabbabaaaabbabbbaabbbaabbbbbbbbbaabababbaaaaabbabbabbaaaaabbaababbbbaabbaaaaaaaababaaabababaabbaababbbabaabbbbabaaaabaabbaaaabbbaaaaaabaabaabaaabababaabbbaababaabbaaaabaaabaaababaabbabababbaababbbbaababbbbabaabbbbbabbabaaaaabbabbaabababbabbbabbabbbbababbbaaababaaabaabbbaabbbbaaababbbbabababbaabaaaaabbbabbbbaababbabbbbbbbbbaabbaaabbabaaaaabababaaabbbbbaabaabbbabaaaabbbbababababaabbbabbbaabaabbaababbbabbaaaabbaaaabbbbaabaaabbabababbaaaaabaaabaaabbaabaaababaabbbbbaaaaabbaaaaaababbbbbbbaabbaaababaabbbabbbbabbbaabbbbabbaabababaaabaabbbabaaaaaababbbaabaabbaabaababbbaaababbbabbbbaabbbbbaabbbababababaaababbabaababbaaabbbaaabaabbbabaabababbaaababbabbaaabaaabbabbbbbababbbababbababaababbaabbabbbbbaabaababaabaaabbaabbbbabaababbabbabbabaaaaababbabbbaaabaababbabaabaabbbabaabbbbabbaababaaabbbaaabbabbbaaaababbaabaababababbbbaababbbbbbbbabbaabbbbaaaabbabbababbbaabbabbabbbababaaaababaababaababbbbbabbabaabaabbbaaaabaabababbbabbabaaaabbaaabababaabbbabbbabbabbbbbbaabaabbbabbbaabaaaaabbabbbaaabbaabbbaabbbbbbbbbbbaababbabaababbabbbabbbabaabbbbbabbabbaabbbbaaaaaaaabbbbabaaababbbaaabaabbabbaaaabababaabbaabbaabbabbababbbbaaaababbbbaabbaabbabbbbaaabbabbaabaabbbbbabbbabbbbaaaaababbbabbbabbaaaaabbaaabaaaaabababaabaaabaababaaaababbbaabbaabbaabbabbabababbaabbbbbbaabbbaaaaaabaababaaabababbbaaabaabbabbaabbaaaaaabbababbbbaababbbaaaabbaaaabbbaabbababaabababbbabbabaaaabbbaaaabaaaaaaabaabbaaababaaaabbabaaabbbabaaaabbbbababbbbabaaaabbaaabaabaababababaabbbbbaaabaaabaabaaaaabaaaaaaaaaaaabbabababbbbaaabbbaaababbababaaaaabaaabaabaaaabababbbbbaabaaabbbabbbabaaababbbbaaabbaaaabbbbaaabababaaabaabaabbabbababbbabbababaabbbaaabbbabbbbbbbaaabbaabaaabbbbabbabaaabbbabbaaababaabbaaabaaaabbbaabbaabbaaabaabbbbabababbbbbaabbbbabbbbbabbbabbabbaabaabaaaababaabaababababaabababbbbbabbbaaaaaabbaabaabbbbbbababbbaaabaabbbabaaaababbaaabbbbbbaaabbbbbaaaaabbabbabbbbabbaaabaabbbbaababbbbaaaabaaabbbbbbabababaabaaabaabbbbabababbbababaabaababbbaaaabbaaaabbaabbbaaabbbbbbbbbbbaabbaaaaaababaababaaaaaaaabbbbbbbbbbbabbbbaabbabbbbabbbaabaababbbaaabbaababbabbabbabaabbababbbbbbbaababbbaabaabaabbbababbbaaabbbbbabbababbababaaaaababbabbaababbbbabbabbabbabbabaabbbababbaabbbbbbaababbbaaababbaabaabbaaababbabbbaaabbabbbaaaabbabababbabbbabbbbbaaabababbabbaabbabaabbbbabaaababaaababbbaaababaabbbbaabaaabaaaababbababaabbababaababbbbbabbbaababaabbbaaaabbabbbabaaaabaabaaaaababaabbbbbbaaababbbaabababbbabbaabbbabaabaaabbbbaaabaabbbbabaaabaaaabbbaaabaaaaabbbaabbabbbaaaababbababaabbbaabbaaaabbbbabaabaabbababaabbbaabbbbababbaaabababaabbbabaabbbbaaaaababbbabbaaabaaaabbaabbaabaaaabbaaababbbabaabababbbabbabaabbaabbbbaabaaababbabaaaaabbabaaaaabaabbbbaaabbbaabbaababbbbabbbabbbabbbbabbababbbbbbbbbaabbbbaabbbbbabbaaabaababaabababababbbaabbababbababbbababbaababbabaaababaaabaaababaabbabbbabaabbabbababaabbbaaabbbbababbbbbabaaaabaabbbabaabbaabbbbaabbbbabbabbbbbbabaaaabbaaaababaababbabbabbaabbabaaababaabbababbbabbbabbbabababaabbbbbbbbbbabbbababbbbabbbbabbbbbaababaaaabaabaabbbbabbabaaaaaabbabbbaaaaababbabbaabaababbaabbbaabaababbabbabbbbababaabaababbbaabaaaabaababbababbabbaabbabbbaabaaabaaababaabbbbbbbaabaabaababbbbaababaaaabbabbaaabbbbbaabbababaababbabbbaabbbbabbbbaabaaaabbbaaababbababbbabababbbabbbaabbbbabaabbbbaabbbbabbaaaaabbbbaaabaaaaabbabbaabaaaabaababbbbaabbbbbaababaaaaaabbbbabbaaabbbbaaabbbbabbababbbbbaabbabababbaabaaaabaaaabaaaaaabaaaaaabbbaaabbabbbabbbabbbaabaababaaababaabbabbaababaaabaaababababaabbbaabaaaaaabbababbbbaabaababbbabababbabbaaabbaaaabbaabaaababbaabbaabaaabbabbbaaabaabababaaaaaaabbbaaaaabaabbbaaaabbbbabbbabbbbaabaabbbabbabaaabababaabbbbbbbaaabbaaaabbabbaabababbbabaaababbaabaabbbaabbabaabaabaaabaaabababaabaaabbaabbabbbbbaabababaaababaabbbaabababbbababababbbbababbaaabaaaabaaababbaabbbbabbaabaabbbbbbbaaaabaaaaaaababbaaaaaabaabbabaaabbaabbababaaabababbbaababbababaabbbababbaaaaabbaabaabaabbaababbbaabababbaabbababaabaababaababbbaaabaabbbbaaabbbaaaabaaabaaaabaaaabbabbabbbbaaaabaabaaabbbbabbbaababbabbbaaabbbbababbabbaaabaabaabbaaaabbabbaababababbbbaabaabaaabbaabaabaabababbbbaababaababaabbababaabbbabbaababbbbbbaabaabbbbbbaabbbbabbbaaabbaaaabaaababaababbbbabbbaaabaabbabaabaaaaabbabbaaabbbabaabbbaabbbabababbaaababaababbabbbbbabaaaababaabaababbaabbabbbabbbbaabbbaaabbabaabbbabababbbbaaabbbaabbaababababababaaaaaaaaaabaabbababbaaaabaaaaaaaababaabaabbaaaaababbbababbaaaaaabaaabbbabbbabbbbbbaabababbabbbbabaaaabaabbbbababbabaabbaaaabaabbbaabaaabbbbbabbabbbababbbaaabaaabaaababbabbbabbaabbbaaaaabbabbbaaabbababbbaabaabaaabbbabbabbabababaabbaaabaaababbbabbbbabbaabbaaabbabbabbbaaaaaaaaaabaaaaabaabbaaaabbbababbbbabbaaaabbbbbabbabbaabbbababaaababbbbbbabbbbbababbbbbababbbabbbbbaaabbabaaabbaababbaaaabbbbaaabbaabbabbaaabbbbbabbabbbbabbbaaabbbbbbbbabbbbbbbaabbaababbaabbbabaaaabbabbbabbabbbbaabbbbabbabaaababbabaaaaaaabbbbbbbabaaaabbbbbbabaaaaabbaaaabaaaaaaaaabbabbbbaabbaaabbbaaaaaabbbbbabbaababbbbaabbbabaabbbaaaabaabaaaababababaaabaababbbbbbaabaabbaabaaaabbbaabaabbabbbabbbababbababbbbbaaaaaaabbbabaabaababaabababbaabaabbbbbbbaabbbbbabababbbaabbbaaaabbababababbbabbabbbbaaabbaaaabbabbaababaaabaaababbabbaaaabbbabbbbbbababaabbbabbaabbbbbbbabbbaaaabaabaababaaaabbabbabbbaaaabbaabaabaaaabbbabbbbabbaabbbaabababbababbaabaabbaaaaaabaabaaaaaabaaabababbbbbaabbbaababbbabbaabaabbaababbbabbbabbaaaaaaaabababbaababaaaaabaababbaabbaaaabaabbaababbaabbabaaaabbabbaaaabaababababababbbbabbbababbaaaaaabbabaabaaabbaabbabbbababaaaaaabbbbbaaaaaabaabbbabbbbababbbabaaaaaaababbabaabbbaaabbbbabbaabbbbbabbbaaabaabbbabbbbabbbaabaabaabbaabbbabbabaababbaaabbababbabaaababbbbbbaabaabbaaabababbababbbbabaaabbabbaabbabbbaabaabbabaabaaabbbbabbbaabbaaaaaabbaabaabbbaaaaabaabbababababaaabbbbaaabbababaabababbbabbaaaabbabbbbabbbaaaabbbbaaaabbaabaabbbaaaabbbbbbbbbabbababbabaababbabbbbabaabbbabbbbbabbabbaaaabaaabaaaaaabbbbabbbaaaabaaaaabaaaabaabaaaaaaababaababbbbbabbbaaababbaaaaaabbabbaaaaaaaabbbbbababababaaabbabaabbbbbbbabbbabbabbbbababbabaabbbbbababaaaababbbaabbbaabaabbaaaaababbbaaabaaabaabbaaaaabaababbaababaabaaabbbaaababaababbbbabaabbbaabbbbbbbaabbbabbabbababbaaaaaabbaaaababbbbaaaaaaaaabaaaaabbaaaabbbaababaaaabaabbaaaaababbbbabbaaaabbbabaaaaabaaabaabbbbbbbababaaaaababbababaabbbbbaabaaabbaaaabbbababbabbbbbaabaabaabbabbabaaaabbbaabbbbbaabababbaabbababaabbbaabbbaaababaabbbbabbabbbbaaaababbbaaabbbbbbaaabbbbbababbbaabbbbabaabaaabbbababbbbbbbbabaaaaaaabbbbaaaaaaabbabbaabbaabaaababbbaabaaabbbbbabaaabbababbabaaabaabaaababaaababaabbababaaaabababbaaababbabbabaaaabbbbababbabababbaababbbabaabbbaabbaabababbbabbbabababaabbaaabbbbaaabbaaaabaaaaaaaaabaaaabbbaababbaaabaaaaababbbabbababbabbabaaaabbbbbabbabbaaabbbaaaaabbaababaaaaabbbbbbbbbababaaabbbbbbababbabababbbbaabbabaaaaaaababbaabbbbbaabbbbaaabaaabbabbbaabaabaabaababababbbbbbbabaaabbabbbbaabaaaababbaabbababbbaababaaabbbaaabbaabbababbbbbbbaaabbbbbabbbbabaaabaababbaaabbaabbaaabbabbabaaaaabbbabaaabbaabbbbbababbbaaababbaababbaabaabaabbbabaaaaabbbbabaabbbbbbbbabbaabaaabababbabababbabbaaabbbbbabbbabbaaaaabbbbbaaabababaaaababaabbabbababaabaabbbbbabbbbabbaaabbabbaabaaaaabbaabaaabbaaababbabaabbbbaababaababaababaaabbbaabbaaaaaaabbbbbabaabbaaabbabbaabbbbbbbaaabaaababbbbabaababaaabaaaaababbbababbaabbbaabababaabaabbbbbbabbbabbababbbabaabaabbaabababaaabaababbababaabbbaaabbbbabbaabaabbbbabaabbbaaabbbbbaabbbaabaaaabbaaaaabaaaabbbbabbabbbaaaababaabbabaaaabbaaabaabbbbabaaabbaabbbbbbbabaababaabaabbbaaababbbabbaababbabbaabbbabbbaabaaaabbaaaaaabbbaaababbaaaababababababbaaaabaabbabababbabbaabbbabbaaaaabbaaabbaababaaaaabbbabbabababbbaabbbabbbabbaaaabaababbbbaaaabaaabbbbaababbbabbabaaaaabaabbbababbbabbbabaabbababbaaaabababbaaaabaababbbaaababbabbbaaabbabaabbaabbbababbaabaaabaabaaabaabbaabababababaababbbbbabbbbbbbbabbaababbaaababbaaaaabaabbbabbbaaaabbaaaaabbbaabaaabaaabaabbabbbaaaabbabbbbaaabaababbababbbabbbbabbaaababaaaabbbbbaaabbbababaabbbbbaaaaabbbabbbaaaabaaabbbaaababbbbbabbabbbbbaaaabaaaabbbaabaabbbbabbaabbbaababbaababababaaaaabababaabbaabbabbabbabbaabaaabbaabbbabaaabaabaabaabaaabaaaaaaabbbbaabaababaabbbbaababbaabbaaaaabbbabbaaababbabbbaaabbbaaaaabaabaabbbaabaabbabaaabaaabbbabbaababbbabbbbabbabbbbbabbabbaababbbaaaabbabaaaabbaaaaaabaabbbbaababbbbaaaaaabaabbbbbbabbbaaaababbbbbbaaabbabbbabbababbbbbbbababababbbababbbbbbabbbbabaababbbbbbaabbabbaaaaaaaaaabbbabbbbaabbabbaabbaaaaaababbababaabbabbabbaababbababaabbaabbaabaabbaaaabbbaababbbabbbabaaabbbabaaaabaaaababbaababaaaabbaaabbbbababbaabbbababaaabaabaabbabaababbaababbbaaaababbabababaabbbaaaaaaabbbabaaabaaabaaaabbabbbaabaabbabbabaaabbaababababbaaaaaaabaabbaaaaababbaabaaaaababaaaabbbbbbbbbbaabaaabbbababaabababaabbbababbabbabbbaaaabbaabaaababbbabababbaaaabbababbaaabbbbaaabaaaaaaababbbabaabbbbbaaabbabaabbbaabaabaabbabaababaaaaaaaaaabbbaaaababbbaababbabbababbaaababbaaabaaabaaaabbaabbbabaaababaaaaabbbabbbabaaabaaaaaaaababaaabaaabaaabaaaabbabbaaabaaaabbbbaaabbbaabbbabbbbabbbabbbbaababbbbaabbabbbbbabababbabbbababbbbaaabbaabbaaaabababababaaaabaababbaaaabaabaabbbabaababaaabaabababaaaaabbababaababaabababaaaaabbbaaabbbabaabaaabaaabbbbbababbaabbabaababaabbbabaabaababaabbabaaaaabbaababbaaabababbabbbbbbabbaaaabbabbaababaaabaaababaaabaaaabbbabababaabbbaaabbbababbabbaabbaaabaabbaaaabababaabaaaaaaaabaabaaababaaababbaababaabbbbaaaabbaaaaababbaaaaababbababaabaabababbbbbabbbbbaaabababbaabbabababbabaaaaabaaaabbbbaaabababbbaaaaaaaaabbbaaaabaabbbaabbabaaaabbbaaaaaabaaabaabbabbabaaaaabaaabbbbbbbababbbbbabaabbbbbbbbaaaabbbaaaaaababaaaaaabbaabbbbabbbbaabbbbabbaabbababbaaaaaaaaabbbabbabbbbabbbbbabaabbaabaababbaaabbaaabbaabbaaabbbabbbbaaababbaaabbabaaaaabbababaabababababaabaabbbbbbababbaabbbbaaaaaabbaabbbbabaaaabbbabbbababaabaabaaabaaababbaaabbabbababbabbbaabaaaaaaabaaabbbbbbbbaaabbbbabbaababbbabbbaaababaaaababaaabbbbaababaaabbabbbaabaabaabbabbaaaabaabbaaaaaaabbabbabbbabbbbbaabbababbabbbaabbbbbaaabbbabaabaaababaaaabbbabababbabbbaababaaabaababaabaaabbbbbbaababbbaaabaabbaaabbabaaabbababbababbbbaaabbaaaaabbaaaaaabbbbabbabbabbaaaaaaabaaaaabbbaababbbabbabbabbaaabaaaababababbababaabaaaabbbaababaaaabbbaabbaabbbabbabaaabaaababbbbabaaaaabbbbaabbabaabbbbbaaabbabbbabbbabbabbbbaababababbbaaabaabbbbaaabbaabababaaababbababbbaaabbaabababaaaaabababababaabaabbbbaabbababbaaababbbbbbaaabaaabababaababbaaabaaaaaaababbabaabbbbbaaaaaabbbbabaaabaaaababbabbaaaabbbaaaabbbaabaaababbbabaaababaababababbbabbaaaababbabbaababaaabbbaaabaaaaaaabaaabababaabbbaababbaaabbbabaaabababbbabbababbbaaaabaaababbabaabbbbaabbaaababaababbabbaaaaaababaababababbbbaaabbbababbabaaaaaabbbbbbbababaaaaaabaabbbaaababbbabbbbaababaabaabaabaabaaabababbabbbbbabbabbabaababbbbaaaabbaabbbabbbababbaaabbaabbbbaaaaaababbabbabbababbaaababbbaabaababbabbaabbabbbabbbaabbbbbabbabbaaaabbaabbbbbabbababaaaaabbabababaaabbbabaaaabababaaababbbbbbabbbbbabaabbabbbabbaabababbaabbabbabbbabaaaaabaabbbaaaabbbababbabababaabaaaabbaababbabbabbaaabbaaaabbbbabaaabbbbbbbbbabbbbbabaaaaaaabbababbbbaabbababbbbaaaabbaabbaaaaabbbbbababbaaaababaaaabbabaabbaaaaaaabaaabbbababbabbaabaabbbbaababbabaaaabbaabaabaababababbaabbbbabaaaaaaabbaaaaababaabbbabbabbbbbbabbaaabbabbabbaababbbbbabaababbabaabababbabaaaababbaaababbbbabbbbababaabbbabbaaabbbbaaaaaababbbaabbbbaaaabaaababbbbbbbbaababaababbaababaabbabbaabbbababbbbbabaabbbbbbabaaabababbabbabaabaabbbaabbbaabaabaababaaaaaabbabaababbaabbaaabaabbbabbabbbaabaababbbbaababbbababaaabbbababababbaaaaabaabbbabaabaabbabbbbabbaabaaaaaabaaaabaabbaaabbaababbabbaabaaabbbbababbaabaabbababbabaaabaaabaabbabaabbaabbaaabbabbababbabaaabbbbababaaabbabbababbbaaaabababaabbbbababaaabbbbbabbaababbaaababbbaabbbaaaaaabbbbaaaabaaaabaaababaaabbbaababbabbbbbbbbbbbbbabbbabaabbbbbbaaababaaababaaaaabbbbbaabaaabbbabbabaaabaaabbabaaabbbbbbaabbbbbbbaaaababaaaabaabbabbbbbbaabaaaaababaaabbabbbbbaababbababbbaabaaaabbaaaababbaabababababbabababaabbabaaaaabbaababbaaabbabbababbabaababaababbaaabaabaabbbbaaabababbbaabaaabbbabbbaaabbababaabbabaabaaababbbbaaabbaabbbbabbbabaabbaaaababbaaabbabbaaaaaaaaaaabbbbbbbaaaaaabbbbbaababaaaaababbabaabbaaabaabababbbabaabbabbbbbbababbbabaabaababbaabbbbabbabaabaabaababbbbbaabaabbbaaaabaabaabbbbbbbaabaababaaaaaaaabbaabbbaabbaaaaaabbbbbbbabaaaaabbabbbaabbbbaabbbbbaababbaabbbaabababbbaababaaabaaaaabbbbabbabbaabbaaabbabbaaabbaabaaababbbbaabaaaabaabbbbaaaabbbbbaaabaabbbbabbbaabbababbababbaaaaaaaaabbbbabbabbabaabbbaaaaaababbbbababbbbabaaababaaaababbbbabbbabbbbababbbabbabaabaabbaabaaababbbaabbbaaabbbbbaaabaaaabababaababbababababaabbababababaababbabaaabbbabaabbaaaaabbaaaaaaaabaaabbbbbbabaabbbbabbaaaabbbaabbbababbababbaabaaabbabbbbbbaaaabbabbabbabbabbbbaabbaaabaabbaaabbbababaababbaabbbaaababbbbbabbaabbaababbbaabbabaaababbaaabbabaabaabbbbbbbbabbbaaababbbaaabbbabbbbaaabbbaabbbbabaabaaabbabbabbaaababbabababaabbabaaaaababababaaaaaabaaababbbababaabbaababaaabbabbabbabbbaabbbababbabbabbbbbaaabbbabbaaaabaaabaabbabaabaaaabababaabbabbaaaaababaabbbbbbaabaaabbabbaaaaababbababbbaaabbabaaababbabbaaabaaabaababbabaaaaaaababbaaaaababababbabaaaabbbababbaaabaabbbaaabbaabbaaaaaaabbbbaabaaaaabbbaaaababaaabaababaabbaabbaaababbabbbabbabbbabbabababbaaaaaabbbbaabbbbbaaabbbabaabbbbbbaabaababbaaababbbabbbbbbbabbbaababbbabaaaaababbabbbbbabbabaababaaaaabababbababbabbbbbaaabaababaaabaaaabaaaaaaababbaababbbbbabababbbbbabbabbbabbbbbababbaaabbaabbabbbababbbbbaaaaaabbaaabbaaabbbabbaabbabbbbbaabbbaababbaaabaaabbbbabbabaaaabbbbababbaaabbaabbaabaababbbaabbabbabbaaabbabaaaabaabbaaabbaabbaaabbbababbabaaabbbabbbbabbbbbbabbabbbbbababbbabbababaabbbbbbbabbbaaaaaabaabbabbaababbaabaabababbbaabbabababbaabbabbaabaaabbabbbbbbaaaabaababbaaabbaabababbbabbbabbbaababbaaaaabaaaaabbbbbbbababaaababaababbbbbbbbbabaababbaabaaaabbbbaababaaaabababbbbbbbbabbaabaabaaaababaaaaababbbabaaaaabaaaabbaabbbaabaaabaabbaababbabababbbbbbbabbabaaababaaaaabbbababbabbbaabaabaaaaaaaababababaabbabbbbbabbbbaabababbbaaababaaaaabaaabbbbaaabaabbababbaabaabaaaaabbabbaaababaaaaaaabaaabababaaabbabbbbaabbababbbaabbaabababababbbbbbabbaabbaabaabbbbaaaaaababbbbbaabbbbbbbbbaaabbbbbabaababaabbbbbaabaabaaaaaaabaaabbaaabbbbaabaabbababbaabaaaaaaabaabaabbaabaaaabbaababbbabbbbabbaaababaaaabbbaabbbbbbaaaaaabbbaaaaabbbbaaaabaabbbaaabbabbaaababbbbbbbbaabbbaaaabbbbbbbbbaaaaaaabbaaabbbbbaaabbaabbbaababaaaababbaaaaaababbbbabbbbbaaabaaabbaabbaaababbaabaaabbababbbbaaababbbaaabaaaabbaabbaabaabbabaabbabaaabbaabbabbababbaabbabaaaaaabaaababaabbaabbaabbaaaababbaabbbaabbabbbabbbbbaabaabababaaabbaaabaabbbabaabaababaabbbaabbababaaaaabbbbabbbbaaaabbbabababaaabbaaaaaaaababbbababaaabbabbbbaabaababbabaaaababaaaaababbaaaabbaabaababbbaaabbbbabbbbbbbaaaaaaaaabababbbbaaabaabbbabbaaaabaaabaababababaabbbbbbbbaabaaabbbbaabbbbaabbbaabbabbbbaabababbbbabbbbaaaaabbaaabbababbabbbaababbabbbabbbababbaabbbbbaabaabaaabbbaabbaaaaabababbabbaaaabbabbabbabababaabaaaabaabababbaabaaaaabaabbbbbaabaabbbbbaababbbbbbababbbaabbbbaabaabaabaaababbaaababbababbabababbababaaaaababbaaaaabbabbbabaaaaaabbbbaaabbbbaabaabaaabbababbabbbbbababbbbaaaabbabbabaabaaaaabbbbabaabbabaaabbbaabaaaababbbabababbabababaaaabbaaaabbabbaabbbbaaabaabbaaabbbbabaababbaabbbbbbbabbbaababbabbbbbabbaabbbbabaaababaabbbbaaabaaabaabbabbbabaabbbaabaabbaaabaaaaabaabaabbbbbbaaabaaaabaaabbabbbbabbbabbababbbababaabbaababaaaababbaababbbabbabbabbbbbaabbabaaaaabaabbabbaaabaabbbbabaaaabbabbabaaababbaabbbaaabaaabbaaabbbaabbabbabaabbbabbbbababbbbabaabbabababaaabaabbabbabbaabbaaababbbbbabaaaaaabaabaaababaabbbbbabbbaaaaaabbbaabaaabaabbbaaababbbbbaaabbbaabbaabbbbabaaaabbbaabbbabbaabaaaabbaababbbbaababbbbbbaabbbbbbaaabbbbbbbbaaaabbaabbaabbabbabababbaaababaabbbbbbbbaabbaabbaabaabaababbbbbabaaaaaabbbbbbbaabbabaaaabbaaabbbaabaababbabaaaababababbbababbbabaabaabbaabbabbaaaabbaaaaaaabababbbbabbababaaaaaaabbabbabaaaabbbbbaabaaabbbaaabbbbbbbaabababbbbbaaaaabababababbaaaabaaabaabbabbaababaaababbbbabbbaaababaaabbaabbaaabbaabbabbbababbbabbabaababaabbbaaabbaabbabbbaabaaababbabaaabaabbaaababaaababababbbabbabaaabaababaaaaabbaabaabbababbabaaaabbbabbbbabaaababaaaabababaabbabbaabbaaabbbbaaabababaabbbbbbabababbbbbbbabbababbbaabbababbabbabbbabbbbaababababbbbaaababbbaaaaabbababbaabbbbaabbaaabbbbaabaabaaaaaabaabaabbbbbbababaababbaaabbaabbaabbababaaabaabbabaabaaababbabbbbaaababababaaabaaaabbbbbabaaabbabaabaabbbaaaababbbbabaabaabbbaababbaaabbbbaababbbabbbabbbabbbbabaabbaabbabaaabbbaabbbbabbaababaaaababbbaabbbbaabaaaaaabbabbabbbaaaaaabbabbabbaaaabaabaabbaabaabaaaabaaaaabbbaaababbabbbabaabaabbabbbbbbabbbbbbbaabaaabaaabababbaababbabbabababbaabbababbbbbabaababbabbbaabaaabbabbababaaaababbbaabababbabbbabaabaabbaabbbaababbbabbabbbaabaabbaababbabbbaaaabaaabbaaaaaaabbaaabababbbababaabbbaaabbabaaaabaaaabaaabbababbbaaabbaabaabaaaaabaabaabbababaaaabbabbaaababaabaabbabbbabaaabaaabababbaabbbabbabaababbaaaaabbbbaaaabbbaaaabbbbbabababaabbabbaabaabbabbbaaabbbbbaaaabbbbaaabbabbabbaaabababaababaababababaabbbbaababbababbbbbbbbaabaaabbbaabbabbbaaaabbbbaaaabbaaaabaabbabbbaabaabaababbbbbbbbabbbbaaaaaaaabbbbbbaabaaabbabbbbbbbababbbbaaabbabaaaabbaaabbaabababbbbbabbabbababaaaabaabbabaabbbababababbbabababbabbbbaabbbbabbbababbaabaababbbaababbbaaabaaaaabbabbabbabbbbabbbabbbabaaaabbabbbababbbabbababbabaaaaaaababbabbaaabaababaababbbbbbbaaaababbabbbbbaaabababaababbbbbbabbbbbbbabaaaabaaabbaababbbabbaaabbabbaaaaaaabbbbbbbbababbabbbbbbbbaaabbaaabbababbaababaaabaabbbbbbbbbbabbababbbbbbabbababaabbaaaabbbabaababbabaabbababbabaaaaababaabaaababbaabaaabbbbabbaaaabaaaaaabaabbabbbabaabaabaaaaabbaaababaaaaabbbabbbbbbaaaaaababaabbababbaabbaababbbabaaabbbbbaabaaabbbaaabbbaabbaabaaaaaabaaabbaabbbaababbaaabbabaaabbbbaabaabbbbabbbaaabbbbbbbabaaabbbbabababbabbaabaaaabbaaaaabbaaabbabbbbbbaaabbbaaaaaabaaaabbbababbbbabbaabbaabaabbbaabbbbaabbaabbabbbaaabaababbabaaabaababaaabababbbbbbbbabbaaabaaaaaaaaaabababbbabaabbaaabaaabaababbaaaaabbaabaaabbaaaaabbaabaaabbababbaaabbbbbbaabbababbbbbabaaaabaaabbbbbbbababbbaaabbabbbaabaaaababbabbabbbbaabaabbbaaaaababaaaaaaabbbbbbbabbabaaaaababbabbabbbbaaaaaabaaaabaaaaabbaaaabaabbbababaaabbbbbbaaabaaababbbaaaaabbabbababbaaabaaaabaababbbbabbaaaabbbbbabbbaaabbbaabbbbaaabaabaabaaaabababababaaabbbbbaaabbabbbaaabaabbbabbbbabaabbbababbaabbbaabbabaaaababaabbababbabbabbababbabaabbbbbabbababbbabaaaaaabbbaaaabbbaabbaababbbababaaaaaaaababbabaaabababbbbaaabaababaaabaabaaabbbbbabbaaaabaabaabbaababbbaabababbabaabbbabbbabaababababbabbaaabbababaaaabbbababbaabaababaabbaaabbbabbaabbaaabababbaabababbbabbbbbbabbababaaaaabbbabbaaaaaaabbbabbbaabaaabababbbaabbaabaaabaaaabbbbaabaaaabbbabbbabbbaabbaabbbbaaaaabaabbbaaabbabbbbbaababaababbabbaabbbbbbabababbbaaaabbbaaabbaaabbbabaaaabbaabbbbabaaabbbaabaabbaaabaaaabbbbbbbabbaababaabaabbaababaaaaaababbbabbabbaaabbbbabaabaabbbabababbbaaaabababaababaaaabaabbaabbaababbbaabbbbbaaabaaababbbabbbbbaaaabbabaaaabababbbbbabbaabbaaaaaaababaaabbabbbbbaaabaabbbaabaaaaaabbbbababbbbbbbbaabbaaabaaabababaabababaaaaaaaababbaaaabaaababbaaaabbaaabbaaabbbaabbabbabbaaaaaaaabbbbbaabaababaabbbabaabbabaabbbbbabbaabbaaababbaabaaabbabbabababbaabbbbbabbaabbbbabbbbaabbbabbbabbbbbbbbbaabbaaaabbabaaabbaabbbbbbbaabababbbaaabbbabbbbbbbbbabbbabbaabbabaaabaabbbbabbbbbaabbbaabbbbaaababaaaabbbababaaabbbbabbababbababababababaabbbabbaaabbaaaaaaabbbababbbababbabbaababbaaabbbbbaabaabbabbaabbbabaababbabbaaaabaaaaaaaaabbbbbbaabbaaabaababbbabbbaabbbbbabbabbaaaaabababaabababbbbabbbababbababaabaaabaabaabbbbbbbababaaabbabaaabaaababbbaabbbbbaababaabababaaaababbbabaabbaaabaaabbaabaabbabbabbabaaaaabbbabababaaabaaaaabbbbababbaabbbbaabbaabbbaaababbabbabbbbaaaabaababaaaabaabbbbbabaaaabbbabababbaaaabbabbbbabbbababbaabaaababababaaaaaabbabaabaaaaababbaaaaaaabaaabaaabaabbaaaaababaabaaabbaaaabbaaaaabbaabbababaabaaaabbababbbaabaaababbbaaababaabbbaaababbbbababbabbbaabaabbaababbabaaabbaaaaabaabaabaaaaaaabbaabbbbaaabaabaaaabbbabbaaabaabbbabbbbaabbaaabbababaaabbababbbbbbbababbbbababbabbabbbaabaabaaaabaaaabababababbaabbbabbbbbbaaabbabbbbbabaaaaaaabaababaaabbbaaaaaabaaabbbabbbbabbbaabbbaababbbaaaabbaabbaabaaabbbabbaabbabaababbbbbbabababbbbababbabbabbbbaaabaaaabaaaaabaaaaaabbabbbabbbaabbaabbbabaaabbbaaabbbabbaaababbbabaaabbaaaaaabbbaaaabbaaababbaaaabaaaaaaabbaaaaaaabababaaaaababbabbbabaaaababbbaabaababbababaaabaabaaaaaaaaabababababbbbaaabbbaababbaabbbabababaaaababaabbbaaaababbbabbaaabababaabaaaaabbaabbbbbaaaabaabababbabaaabbbbbbabbbbabbbaabaabbabbbabbbaaabbbabbaabbaabbaaababbbababaaabbabaaabaaabbababaabbbbbababaababaaababbabaaaaaaaabbbbbbaaabaabbbbbaaabbbabbabbabbbbbaaabaabababbaaaabbaababbaaabbbbabaaaaabbaabaabbabababaabababaabababbbbbaaabbbbbbaababaaabaaaaaabbbbabaaaabbaaabaabaaabbbbbbbbaaabbbbaabbabbaaaaabaabaabaaaaaababbaabbababaaaabbbbbbabbbbaababaaabbaaababbabbbabbaabbbababbaabaaaaaaaaabbbbabbaaabbabbabababaaaabaabbababbbabbbaaabababbbbbbabaaabaaabbbbbbabaabbabaaabbabbabaabbabbaabbbabbababaaaabbbaaabbbbaababbbbaaaabbbbbbbbbbabababbbaabbbbbbabaaabbbaabaaaaaabababbbaabbaabbbbaaababababaaaaabaabaababaaaaabbbabbabbbbbabbbbbaaabaabbaaababaaaababbabbbbbabbbbbaaabbbbabbbaababaaaabbabaabbbbbbabaababababbbbaabbaaaaaaaababbaabbaaabaaaaaaabbbbbaaaabbaabbbbbbabbbaabbabababaaabbaaabaaaaabaaabbabbabaabbbaababbabbaaaaaaabbbaaababbabaabbbbaabaabaababbbbbbababbaaaabbabaabaabbaabbababbabaaababbbaabbaabbaaabaabbababbbbababbaabbbaaabaaaabaabbbabababbababbabbaaabbabbbbbbaaaaaaaaabaaaaaabbabaaaaaaaaabaabbabaabbbaabaababaabaaabaabbaababababbbabbaaaabbaabbabbbaaaabbaababaabaabababaaaaaaabaaaaabbbabaaababbaaaabaaababbbabababbabbbbbaababbbaabababaabaabbabbabaaabbabbbaaaaaaaabababbabbabaababbbbaaabbaaabaabaabaabaaabbbabbbbabbbbbbbaaabbabbaabaabbbabbbabbbababbaaabbabbbbbbbaaabbbabaaaabaaaaabbbbbbbbbbbbabbbbabbbbabbbbbbbaaababbaaaabbbabbabbbaabbaabbaaaababaaaabaaabbbaaababaabbabbabaabbbaabbbabbaabaaabaabbbaaabbabaababbababaabaabaabababbbabaaabaabbabbababbaaabaaababbbbbbbbaabaabbaabbbbabaaabbabaaaababbaaaaaabaabbbbabaaaabbaabbbaaaaabbaaaabbaabaaaababaaabaaaaaababbbbaaababaaaaaaaaaabbbbaaabbbbbbabaaabbabaaaabaababbaababbbaabbbaaabbaabbabbaaabbaaaabbabababbaaababbaabbbaaabbabbbabbaaaaabaaababbbaabaabaabaabaabababaabbbbbbaababbabbabbbbbabbababbaaaaababbaabbbbabbaabbabaaababbbaabbabbabaabaaabbbaaabaaaabbaaabbbbaaaaaabbbbabbbbbbaaaabbaaabbabbaaaabaaababbaabbbabaaabbbbbbabababaabbbbbbbbbbaabbababaaabbbabbaaaaaaaabbbaabababbbbbabbaabbbbabbaabaabaababababbbbababaabbbabaabbababbbabaaaaaabaaaaaabbbababaaaabaaabbbbbbbbbabbbbabababbbababbaabababbabbbababbbbabaababbbababaaabbabbbbbaaaaaabbbbbbabaaabbabbbaaaabababbaababababaaaaabaababbbbbbbbabbbaabaaaabbaabbbabaaaabbabbbbbabbbabbabaaabaaabbbaabbabbabbaababaabbbabbabaaabbbabaaabaabbbbaabbbbabaaaaaababaabaaabbbabbbbabbbbbbaaaabaaababbaaabbababbaababbbbbaabbbaabaabaababbbaabababbabbbabbbabbbabaabaabaabbbaaaaaabbaaaaababababbababbbaaabababbabbaaabaaabaabbbababaababaaabbabbbbabbaaaabababaaaaabbbbbbabaabbbaababababbbbbabbbaaaaabaabbbaabbaaababaaabaaabbaaaababbaaababbbaabaabbbbaabbbabbaabbababaababbabaaaaaabaaababbbabbaababaaabaababbbbababbababaaaabbaaababbbbbbabababaabbaaababaababaabbaabbaaababbbbbbabaabbaababbabbbabaabaaabbabbaaaabaaabaabbaabbbaaababbabbbaabbaababababaababbaababababaabbbbbbabaaabaababaababbaaabbaabababababbbababbabbabaaabbaabaababbbababbbababbabababbabaaaaabbbbaabbaabaaaaaaabbaaaabababbbaabaabaaaaababaababbaabaabbaaababbbbaababbababaabbbbbaabaaaabbaabbbbbbbbbabbaaabbaaaababaabbbabbbaabaaaaaababababaaaabaaaaabaaabaaabababaabababbbbbbbbbbabbbaabbbababbbbbabaaabbaabaabbaaaababbabababbabbabbabababbbbabbabbaabaaaaaabbbaaababbababbabbaaabbabaababbbbaabbbaaabbabbabaabaabbabbaabaaabaabababbbabababaaabbabbabaaabababbabaaaaaabbbbbbaaabbbaaaabaabbabbbabbabaababbaababaaabaabbaaaaababbbbbaabaabbbbbbabaaabbbbbaaabaaaababbabaabbaaabababaababbbababbaabbaaababbaababbababababbaaaabaaaaaaabaababbabbbaaababaaaaaaabaaaaabaabbbabaabaabaabbabaaabbaaababbbbabaaaabbabbbbbabbaaaabbbbbabaaaaaaaaababababbabaaaabaaaabbaaaabaaababbbbbbbaaaabaabbbbbbaababaaaaababbaaabbabaaaabaababbababaabbaaaababbaabaabbbbbbaaabbabbaabbababbaabbaabbaababbbbabaaababaabababbaabbaaaaabbaaaabbbbaaaaaaaaaaaaaabbbaaaabbababbbbabbaaaabbbbbbabbaaabaabaababbaaaaaaabbbababaaababbbbabbabaabaaaabaaabbbaaaababaaabaaabababababbbabbabababbabababbbbbabaaaaabaaababbbbbbaaabbabaabbababbbaaabaaaababbbbbbbbabbaabababbbaababbaabaabbababaaaaabbabbaaababbbbbabaabaaababbabaabaaaababbbaaabbbaaaaaaabbbaabbbbbabaaaababbaaaabaabaaaaabbaaabbbbbabbabaabbbabbaaabababbaabbabaabbbbbabbbaaaaabbbbabbbaabaabbabbbbbbbbabaabbbbaabaabaaababaabaaababaaaaabbaabaabbaaaabbbaaaabbbaababaabbababbabaaabaaabbbbbaaabbabaaabbbabbbbabbbaaabbaabbbabaababaabbabbbbaaabbbabababbbbbabaaaabaabbabbbaabbababbbababbbabaababbbbbbbabbabbbbaabbabaaaabbaaaabaaaabaabbbbbaabbababbaaabbabbbaabbbabbaaaabaaabaaaabaabbbaaaababaabaabbaaaaaabaabbbbbbaaaabaabbababbaaaaabbbbbabbbbabaaaabbbaabbbaabbababaaababababbaaaaaabaabbbbbbabbabaabbbababbababbabbabbaaabaaabbabbabbbaaaaabbbbabbbbaaabababbaaaaabbbbbbbababaaaabaaabababbaabaabbbabbaaababbbbababbbbbbaabbabaabbaabbbabbbaabababbbbbaaabbbbbabababbbabbabaabbabbbbbbbaabbaabaabbbbbbabbbaaaabbbbbbbbbbbabbaabaaabbbbbabbbabbaaababaaabbbbbaabbbabbabbabbabaababaaaaababbabbbbaabbaabbbabbabbbaabbaaabbbababaabababbaaaaabaabbabaababbbbaabbaabbbabbbaababbabaabbbababbbbbaabbababaaabbbababaabaabbbababaabbabaaabaaabaabaaabbbabbabbabaabbbabbbabaabbbbbbbbaaabbbbbbbbaabaaaababababaababbaababaababbbbbaabaaaaaabaaaaababbbbabbabbabbaaabbbbbababbabbbbabaababbbabaabaabababbaabaabbaaabbbabbaaababaaabbabbabbabababaabbbbbbabbaaabbababbbbabababbbaaabbbbbaabbabababaabababbabaabbabbaabbbbaabbababaababaababbabbabaaaaaaabbababbbbababaababbbabaaaabaaabaaaaaababbabbabbbaaababbbbbbbaaaabaaababaaaabaaabbaaaaaaababbbbaabaaababbabbbababbabbaabbabbabbbaabaaaaabbaaaabaabbababaaaabaabbaaababaabaabbaaaabaaaaabaaaaabababbbbabaaaaaaababbaabababbbaaababababbbbababaabaababaaababababbabaababbaabaaaabaaaabbbaabbabaabbbbabaabbbabbababbbabbbbbaabbaaabaaaabaabbbabaaaaaabaabbbabaababaabbbbbaaabbbabbabbbaabbbabbbaaabaaabbaaaaababababbbabaabaabbbbbbabaaabaaabbabbbabbbaababbaaaabbaaaabbaabaaabbbaaaaabbbaaaaaaaaababbbababaaabaaaabaabbbaabbbbabbaaaaaaaaabbaaaabbbbabababaaabbababaaabbabbbbaabbabaabbbabbabaabbbbbbababaaabababbaabbbaabababbbbabaaaabbbbaaaababbbaaaabaababbbbbbbbbababbbbabbabbbbababbbbabbabaaabaabbaaabbabbbabbabaaabaaabaaaabbaaaabbababaabaaabaababbaaabbbbaabaaabababbbabbbaaaabababbabbaaabbbaaabaaababbbbabbaaaaaabbabbbaaaaaabbabababaaaaabbbababaababbabababbbbbbabbabbabbaabaabbabaaababababbaabababbabbaaaababbabaaabababbbbbaaababbabbabaabbababbbbaabaabbbbbaaaaaaaaaabbabbbababbabbbbabbbbbabaabbbabbabbababbababbbbbabbaaabaaabbaaaabaabaaaababababbbaababbbbabaabbbbabbbbabaabbabbabbbabbabaababbaaabbbaaabbbaaabbababbbbababbaaaaabbbabbbbaaabababaaaabaababbaabaaaaaaaabbaaaaaabbabaabaabababbaaabbaaababaabaaaaabbaaaaabbabbbabaabbbaababbbbbaaaaaabababaaaaaaabbbabbbbbbbbbabaaabbbbaaaabbbbaaabbababaaaabbabbbaaabbaaabaabbbaabaaabbabbabbababbbababbbabbaabbbbaababbbbbaaaabaaaaaabaaabbbaababbabbbaababaaaaababbabbababbbabbbbbababbabbabaaaabbbbbbaababbaabbbaaaaabbbaababababbbababbbbaabbbbbaabbaaaaaaabaababbbabbbbbbbbabaaabaaabbaabbbbaaabbbbbaabbbaabbbaaabbaaaabaaaabbaabaaaabaaabbaababbbaaabbbbabbabbbbaababbbbaabaabbabbbbaaaabbbbbababaabbbabbaaabbbbaaabaaabbabbbbaaaabbbbbabbaababbabaabbaabbbabaabbbabbaabbbbabaabababbbbbabbbababaaaabbbbbbbbabaabbbbbaaaababaabababbbaaabbaaaabbaababaabaaababaaababbbbababbabaaaaabbaabbaabababbaaaaabbbbbbabbbbababaabababbabaaabbbaaababbbbabbbaaaabbbbbbbbaaaabaaabbaabaabaaaaaabbbaaabbaabababbaabaaaaabbaaababbaabbbbbabaaaaabaaabbaaaabbbbbbababbaabbaabaabaaaabbbbbaabaabababaababbabbbbaaabaabaaaabbabbabaaabaaaaabbabbbaaaabbbbbaaaaaaabbaaaababbaaaaaabaaaaababababbabbababaaababbaaaaabaabbbaaaababaaaabaaaabbbbaaabaabaababbbbaaaabaaabaabbaabbbbabaabaaabababaaaabbbabbbaabbaababbabaaaaabbaaaaaabbbaabaabbabbbbaabaabbbaabaaaabbaabababbbaabbbbaaaaaabaabababaabaaaabababababbabaabbabbabbabaaabbbbabbbbbbaabbabbaabbabbbbaaabaabbabbbbaabaabaaaabbbbabaabaaabbaababbbbabaaaaaaabbbbbbaabbbabbbbabbabbbbaaaaaabaabaabbbabbbbaabaabbbababaabbabbababbbbbbbabababbbbababbaabbabbaaabbbbbababbaaabbbbaaaaaabbbaababaabbabababbbbabbababbbbbbaabaaababbbbabbbbabaabbbabababaaaaabbabbaabbbabbbababbaaababbbaabaaaaabaaabbaabbbabaabaabbaaababbbbabbaabaabaabbbbabbbbbaabbbbaaababaabaabbbababaabbbaabaaabaaaaaabaabaaabbbabaaabaaabaaaaabbbaaaaaabbbabaaabbbabbabaaaabbabaaaababbbbaabbbabbaaabaabbaaaabbaabaababbabaabbbaabbbbabaaaaaaaaabbaaabaaaaaaaabbbbaabbbaaabbaaaabaaabbbbabbabaaabbababbbbbaabbaaabbbabaabbababbbbbbababaababbaaababbbbaabbaaabbaababaabaababbaababababbbaaabaabbaaaaaaabbaaaaaabbbaabaaababaabbaaabaabbaabbbbababaaaaaabbaabaabbabaabbaaaaabbabaabbbaabbbbbbbbabbbabbaaaababaaaaaaaaaaabbbbabaabaaabaabbaababbabbaababaaaabbbababaabbaaaaaabbbbabbbbaaaabaabbbbaaabababbbabbabbbbbaaaaabaabaabbbbabaababababbbabbababbbababbaaababaabbaabbabababaababbabbbaabbbbbabbababbabaababbbabbbbbababbbbabbbbaabbbaaabaababbbabbabbbaabbbaabbaaababaababaababbbbbbaaaababababbabbbbabaaabbabbbabbbbabbabaabaababbbaabbbbabbbbbbbabbaabaaabaaabaabbbbaabbbaabbbbabaaabbababbbbabababaabbbabbabbabbabbabaabaaaabbbbbaaaabbabbabbaabbbbaabbbbbabbbabbabaabbabababbbbbbbbbbaaaabaababaabbababbbbaababbbbbbababaaaababaaaababaabbbabbbaabababaabbabbbbbbabababbbbabbaabbabbaabbaaaabaababbbbbabbabbbaabaabbbbabbaabbbaaaaabbbbbbbbbbbbbabbaabaaababbbbabbbbbbbbbbaaaaaababbbaaababaabbaaabbbbabbaabababbbbbbabaababbbbbbbabbbbaabbaabababaaaaaaaabbaabbbbababaaaaaaabbbbbababbbaaaabbbabaabbabaaaabaaabababbabbbbbbaaabbbbaaaabaaabbbabbbabbbbbaaabaaaabaaaaabbaaababaaabbbbababaaabbaababaababbbaaaaaaabaabbaabbbbaaabbbababaabbbbbabbabaabababbabbbbaaabbbabaababbababbbbaaabaaaaabbababbbaaaaaabababbaababababbbbbaaabaaaabbabababaabaababaababaaabbbbaaababbbbaaabbbaaaaaaaabababaabaaabaabaabbaabbaabaababababbaabbaaabbbbbabbbaaaaabbababbbbaabbabbabaaabaabaaaaaaababaabaaaaabbaabbaabbaaabaababbbabbabbabababaaababbaabbaabbbaaaabaaaaabbabbaabbaabaabaaaaaabbbabbabbaaababaaaabbaaaabbabbbaaabbbabaababaabbabbaaaaaabbbbaababaabbababaabababababbaaabbababbbbbbbabbbbabbbbaababbabbaaaaaaababbabbbbaabbbbbbaabaabbabaaabababababababbaabaaaaaabbababbaaaabaaabbbabbbaabaabababbbaabbaabbbabbabaaaabababbabaabaabaababababbaababbabbaaaabbbbaabbbbaaabaabbbbababbbbbaababbaababaababbbabbabaababaaaabbbaaaababababbbabbabbaaaaabbabbaaabbbbbbbbaabaabbbbbbbaaabaaabbababaaababbaaaabbaaaabbaaaabaabbbabbabbabbababbbabbbbaababbbbbbabaaaabbbbaabababbababababbbbbabbbaaaaaababaaababaabbbaaabaaabbaabaabbababbaaaabaaaabaaababbbaaabaaababbbabbbabaaaabbbbbababbabbbbbbaaabaaabaabbbaaaababaaaabbbbbbababbabaaabbababbabaaaabbbbabbbabababbabaabbbabbbaababbabaaabbaabbabbbabababbaababbaabbaaabbaabbaaaababbabbaabbababaabbabbbaaaaabbbabaabbabbabbbabaabaabaaabbabaabaaaaaabbbbaabbbabbabbbabaabaabaaabababaabbbaabbaaabbbbabaaaabbabbaabaaaabaaabbaaaabaababbbbbbbbbbaabaaabbabbbbaabbabbaaabaabaababaaabaabbbbabbbaaaabbbbabbabbbaabbaabbaabbbaabaaabababbbbbabbbababbabbbaabbbaababbababaaabbaabbaabbaaaabbabaababbaaababbbaabaababbabbabaaaababababbbaabaabbabbbaaaaaaabbbaabbbababbaaabaababaabbaabababaaaabbabbbababbaaababaabaaababbababbbbaaaaabaaabaaaaababbababababababababbbaaabbababaaaabbbabbbbbbaabbababbbbbbabbbaababaaaabbbaabbbbbbabababbbbaaaaababaaaaabbabbabaaabbbaaabbabaabbbaabbaaaaabbabbaabaaaaaaabbbbbabbaababaabbabbbbababbababbaaabbbbbabbaaabbabbababbaababbabaabbbbbabbbbabbbbbbbbaaaaabbabbaababbaaaabbabbbbbaababbbbbaababbbaabaaabababbaaaaababbabaabbaababababbaaaabbbabababbbaaaabababaaabbbaabbababaaabbbbaabaaabbabbababbaabbaabbaaababbbabaaabbbabaaababababaaababbabaabaaaaabaabaaaaabbabaaababbaababaabbbaaababaaabbababababbbbabbbaaaabaabbbabbbabbbaaaabaabbbbbabbaaabaababbbbbbabbbaaabbaababbbbbbbbabaaaaabaaabbaabbaabbbbbaababaaaababbabaaabbabaaaababaaabbbabbbbbabaabbaaaabbbbbaabbbbbaaabbbaabbabbbbabbbaabbaabbbabbababbabbbaababaabbbaabaaaaabaabbaabbbabaabbaabbaabaabaaaababbaabaababbaabaabaaaaaaaabbbaabbbbaaabaaabaabbbaaabbaabbbaaaaaaaabbaaaaabbbaaaabbaabaabbabaabaaabaaabbbabbaabaaabbaabaaabbbbabbaababbabaaabbbbbbabbaabababaababbbaababababbabbbbbaabaabaaabbbaabaabbbabbbababababbababaaaababbaabbaaaabbbbabbababbaababbabbabbababababaaabbabbbbbaababbbabaaaaabbaabaabaaababaabababbbbabaababbababaababaaabbabbbabaaababbbbabbbbbbabbbaaaabbaaababbbbaababbabaabaabbbaaaabaaaaabbbaabbabaabbaaaababaaaabbbaaaabaababbabaababbbbbbaaabbbaaabbbaabbbbaaababbaabbabaaaaabaaabbbaabaaaababaabbbbbabbbbaabbbbbabbabaaaabababaabbaabbbaabbaabbbaaabbbabbaabbbaabbbabbaaabbbaaabaaabbbbaababaaabbaaabbaaaabbabaabaaabaaaaaabababababbaabbbababaabbbbbbbaabbbababababaaababaabaabaaabbbbaabbbbbbabaabaaaaabaabaababbaabaabaaababbaaabaabbbbaaababaaabbaaaaaabbaaaabaabbaaaabababbaaabbabbbaaaaaaabbbabaaaabbababbbabaaaabababbaabbbbaaaaabbabbbabbaabbbbbbbbabbbaaaaabbbbaaabbabaababaaaababbaaabbbaabbbaabbaaabaabbbabaabababbabbaaaaaababbbabbbaaabbababbbabbbbbbbabbbbbbaaabaaaaaabbaaabababbabbbbaaabaabaaabbbbbbaabaabbbaababaabbbbbbabbbabaaababbaabbaabbabbababbbaaaabbabbabbbbbbbbabaaaabbababaaaaababbaabbaababababaababababbababbbabbabaabbbbbaabbaaababaaabaabaaaababaaabababbbaaaaabbbbbbabbaabaabbabbaabbbaaabbbaaabbbaaaaabbbaaabbbbaaaabbaaabaaabaabbbbaaaaaabaaaaabbaababaababaabbbbabaaaaabbbbbbbababbbbbababbbaabaaaaabababaaababababababbbabaaaababababababbaaaabaaabbaaabaabbbbbabaaabbbbabbbbbbabababbbbaabaaabaaabaaababaabaabbaaabbaaabbaabbabababbaaaabbbbaabaaabaaabbabababaabbbaaaabbbabbabbabaabbbaaaabababaabbabbabbaababbbbabbaaaaaaaabbbbabbbbbbabbabbabaaaababaaaabababbbbbbaaaabababaabaaabbbaaabaabaaabababbaaaaabbaaababbaababaaaabaababbbaaabaabaaabababbababaaaaaaaabbaabababbbbbbaababaabbbabbaabbaaaaaaabbabbababababbbbbababbabbbabbaabaababaaabbabbaaaabaaaaabbabbbbbabbbbbaabbbbaaabbabbaabbaaaaabbbbaabbaaaabbbbbbbaaabbbbaaaababbbbaabbbaaaabbbaabaabbabaaabaabbbbaaaabbabbaaaabababaaaaaaaabbaabbbaaabbbbaabbabbbabbbbabbbbaaabaaabbbbbababaaaaabbaaababbababbabbbaaaaaababababbbbbbbbbabbabaaaaabbbababbbabbaabaaababaaabbbbabbbbabbbbbabbabbabbabbbababbbbaaabbaaabaaaabbbbbbbabbaaababababaabbaaabbababbaababbabbaabbaaaabbbaababbbabbabbbabbaaabaaaababbabbbaaaaababbbbbaabbbabbbaaaababbaababbaaaaaabbbbabaababbbbbabbbbbaaabbbbaaabaaabaaabbaaabbbbabaaabbababaabbabbbbaabaaaaaabbbbaaabaaababbaabbaaabaabaabbababbbabaabbabbbabbaaabbbaababbaabababbaabbbbbabaaabababbabbbababbaaabbaaabaaabbabbbbbbaabbbabaabaabbaaabaabbaaaaabababaabaabbbabbbaaabababaaabbabbbbaababaabbbbbbbabbaabbbbbbbabaababaabbbbabaaabbaabaaabbaaabbbababbbaaaabbabbaabbabaababbabbbbbbababaabbaabbbabababbabbbabaaababbabaababbaabaaaabbaabababaabbbbbaababaaaabbaaaaaabbabbaaabbababaababbabbbaabbbabababaababbbaaabbbaaabaababbaaaabbaabaaaaabbbaabbbbabbaaababaaabbababbbababbaaabbabbabbabbaaabaaabbaaabababaababbbbbaabaababababaabaabaabbbabaabaaaababbaaaaabbbaaabaaabababbaabababbbbbbbbaaaaababaababaaabbbaabbabaabaaaaabaabaabaaabaabaaaababaabbbbbbabbbbaabbabbbabbbbbaaabaabaaaabaaabababaabbabaaabaaabbbbbbabbabaaabbbbababbbabaaabbbbaabbaaabbbbbbbabbbaabaaabaaaaaaabbaababaaaaabaaaaaaabbbababbbbbbbababbaaabaabbabbbbbaabbaabaabaaaaaababbbabaabbbbaaabaabbaaabbbbabbaaabbbbbbabbabaabbbbbbbabbbaaabbbbababaaaaabababaabaaabbaabbaaaabaababbaaabbbabbbaaabaabaaabbbbbabababbbbbbaaaaababbbbbaababbbbabbabaababbbbbaaaaabaaabbaababaaabbabbbabbaaabbbbbbaaaaabababbbbbabababbabbbaabbbbabaabababbbbbaaabbbaaabaaababbbababbbbbaabbbbaaabbbbabbaaabababbbaaababaaabbaabbbaabaaabbaaaabbbbbbabaaaaabbbabbabbbbbaaabbbbababaaaaabbabbaaaababbabaababbaaaabaaababbbbaabbbabaababbbbbaabbabaaabbbbabababaaabbabbabaabbbbaaabaabbabaabababbabbbaaabaabbbbaaaaaabbbbabbaabbbbababaabababbaaaabaabaaaabaaabbababababbbaaababaaabbaaaaabbbbbabbbaabaababaabababbabaabbaaababbabbabbaabbabbbbbaabaaabbbbbbbaabaaaaabbaabbabbaabbaabbabbbbbbbabaabaaabaaababbbaababbabbababababaaababbaabaabbbabbbaaabaaaaabaabaabababbbbaaabbaaabbbabababbbbabbaabaababaabbbbaaabaabaabbabbbbbaaabbbabaabbaaaababbbbabababbbaaaabbaaaabbaabbaaaabbabbbbbabbabbabaabbbaabaaabaaaabbbaaabaaabbbaabbbabbaabbaabaabbbabaaaaababbbabbbababaabaabbbaabbbbabbbabaaabaaaabaabbbabababbaaabbbaabababbaaaaaabbbbbbbbbabbbbbabbbbbabaabbbabbaabbbabaaaabbbbbbaaabaabbbbaabbbbbbabababaaabaaabbbaabbbaabbabbabaaabababbabaabbaaaaaabbaaaaabaabbaababaabaabbbabbaabbabbabbabaabaabbabbbabaabbaabaabbabbabbbbbbbaabbbbabaaabbabbaaaaaaaaabaaababbabaaababaaabaabbbbaaabbaaaabaaaaabbaabbabaababbbaababbbabaabaaaabaaabbaabaabaababbabababababbbbaaabbabbaababaababbabbbabbbbabababbbababaaaabbbbbaabbbabaabaaaababbbaababbbbaaaaaaaabbbaaaaabaaabaaababaabbbabbaabbbbabbbbbbabaaaabaaaaaaaabbaaabbbaaaaabbbbaabbaaaaabaababaaaabbaabbbbabaaaaaaabababbbaaabbbbbbbbabbabaabbaababbabbbbbbaaabaabaabaaaaabbbaabbbbbaaabaabbbabbabbabbabbbabaaabbabbbabbbbabbabaabbbbbbbaabbbaaababaabbabbbbaaaababaabbbaabbbabbabbaabaaabbbbbabaabbbaaabababbaaaaabaababbaabbbabaababaaaaabbbaaaababbaabbaaaababaababaabbbbbbbaabbaababbaababbbabaabababbababbbaabbbbaabbbaabbbabbbabbabbbababbaabbabbbbaaabbaaababaaaaabbabaaababbbbabaaabaaabbbbabbbaaababaaabbababbbababaaaabaabbabbbbbbaabaabaababbaabbbabbabbaaaabbaaabbbbbbbababbabbbabbabbaaaaaaabbaaabaabbbaaabaaaabababbbbababaabbbbbababbbbaaabaaaabababababbaaaaaabaababbabaaaababbabbaabbbbbbbaabbabbaaabaabbbaabababaabbbbaabbaaaababbaaabbabbbababbabbbabaaaaabbaabaaaaabaaaaaaaabbbaaaabaabababbbbbaababbaaabaaaaaabbbababbabbaaaaababaaabbbbbaabababbbabababaabaaaabaababaaabbbbabaabbbbbaaaaababbabbbbabbbababbaabaaaaabbbbbbbbaabbbbbbbaaabaabaabbabbbabbaabaaababbabbabbabbabaababbbababaabaabaaaabaababaabbbabbaabbaaaaabaaaababaaaaaabaaababbabbbbabaaaabbaaababbabbaabaabbbabbaababaaababbabaaaaabbbabbbbaabbabbababbbbbbbabbaabbbabbbbbaababababbbaaaabbbbbabbbbbabababbaaabbbabaaaaabbbbabbabbaabaaababaabbabbaabaaaabaaabbabababbbabababaaabaabbbaaaabbbaaaabbbabbabbababbaaaabbbabaaaabbabaaabaabbabbabababababaaabaaaabbaaaaaababbaaaabbabababbabaaaaabbbaabbaaaabbaaabbaababbbaabbaabababbaabbabaabaabaabbabbbaaabbbabbabbaabaababbaaabbabbabababaabbaaaaaaaaabaaaababbbababaabaabbbbbbbaabaabbababbaaabbabbabababaabbbbbbbbababbbbbaaabaaaaaaaabbaaaaabbbabaaaabaaaabbabbbababaaaababbabbbbbaabbaaabbbabaabaaaaabbbbabbabbababbbbbbabaaabbaababbaababaaaaaaabbbbbbbababbbababaaabbaaabbbbaabaaabbbaabbbaabbabbabbbbababaaababaaaaaababaaababbbbabbbbbbaabbbbbabaabaababaaababbbbabaaaabbabbabaaabbbbbaaababbababbbbaaaaabaabbbabababababaabaabbaaabaaabbbbaababbbaabaabbbbabaaaaabbbabbbbabaaabbaaabababbbaabaaa
abbbabbbaaaabbbabaaaabbabaaabaabbbaaabaaabaaabbaabbbabbabaaabbbbabaabbabbaaabbbbbaabbbbbabaabbabaaabbaaababbbbbbbaababaabbbbaabbabbbbbabbaaababbbbbbabaaaabbbbbabaaaaababbbaabbaabbbbaaaaaaaaaabaaaaabbbabbaaaababbaaaabbabbbbaabaaabaaababbbbaaaabbaaaaabbaabbbaaaaaabbbababbbbbaababbbbbbbabbaabaaabaaabbabbbabaaaabbabbbbabbaababbbbaaabbabaabbabbbababbbbaaabababaaaaaaababbbaaabbaaaaaaaabbbbbabbaaabaababaaabbaaaabaaabbbbbbaaabaaabbbaabaaaaaaababababaabaababbaababbabbaabbbaaabbabbbbaaabbbbbaaabbbaaabaaababbabbababbbbaabaaabaabbaaaaaaabaababaabababbbbaaaaabaabaabaabaabbabbbaaaaabababbbbaababbbabaabaaaababbaaaaabbabaaabbbabbaababaaaaaabbaaababababaaabaaaaaabbbbbbbabbaaaaabbaabaabbabaaaaaaaabababbaabbbabbbabaabbbbaabaabababbbbaabbbabbaabbbabbabbbbbbaabbbbbaabbabbababaaaabbabaabbbaababbbabbaaaababbbaaaaaabbbaabaabaabaaababaaababaaaababaaaabaaaaabbabaaaaaabaabbaababababaabbaabbbbaabaaabaaaabbbbababbbabbaabbbbbbabaaabbbbbbbaabaaaaaaaabbbabbbabbabbaaabaabbbabbabbbabbbbbaabbababababbbbaaabbbaaabbababbaababbbbbbaaabbabaaaabaaaabbbbaaabbbabbbbbbababaaaababbbaabbabbbaabaabbabaaabbbaabaababbbbbbbbaabaabababbababbbaaaabbabaabaabbaaaabaaaabbabbbabbaaaabbbabbbbaaababbbaababaaaabababbbbaabbaaaaaababbabbaaaabaababbaaabaabbbaabbabaababaabbaabbabbaabbababbbbbbbaabbaababbabbaababbbaaaabbaabbaababaabbbabaabbbaabaaaaaabababbbaaaabababaaaaabaabbabbbababbaabbbabbbaaabbbbbabaabababbbbbaaabbbbababbaaabbaabbbaababbbbbabbaaabbaabbbbabbabaaabbaabaaaababaababbbbbbabaababaaabaabaabaabbbaaabbaabbaabaaaaaabaabababaaaaabaaabaabaabbbbbaaaaababbabbbbabaabaaaabbbaabababaaabbaabaaabbbabbbbaabababbbaaaabaaaababaaaaaababaabbaabaababbabbbbabbababbbbbbbbbaaababababbbababaaaababbbbbaabaabbbaabbbbabbbabaabbaabbbabaaaabbbbbaabbaaaaaaaababaabaababaabaaababbaaabbbaaababaaababbabbbbbabaabaabbabababbabbbabaabaaababbaababbaabaabbaaaaaaaaaaabaababbaaababbabaaaaabbbbbbbbbaaabaaaaaabaabbbaaaabbaaababbbabbbbbabababababbbaabbbaaabbbabbaabbaaabbbbbaaabbaababbaabaaaaaabbbababbbabbaabbabbaabbabbbaabbaabaaabbabbaaabbbbbbbaaababbaaaababbbbaabbbbababbbbaababaabaaabbabbababaabbaabbabbbbbabbababbabaaabaaaabbabaababbaaabaaaabbbababbaabbabbbabaaabaaabbabbabbababbabbaaabaabbbbabababaaaababbaabbbabaabbabababbbaabababaabaaabaaababbaaabbbabbabbbbaabbbaaaaaababaabaabbaaabbbbbbbbababaabaaababbaababbaaabbabaabbbbbbaaabababababbabbabaaabbbabbbabaabbaaaaabbaabbabbaabbbababbbbababaaaaabaabaaaaaaaabbaabaabbaaaaaabbabbbbaaabbbababbababbabaaababaabbbaaaabbaaaaaaaaabaabbaaaaaaababaaabbabbaaaabaaaabbaababaaababbaaaababbababbabbaabbabaabbbabbabbabababbbababaaaabbaabbabbaaabaaabbaaabbaaaabbbbbbbbbabbaabbbababbbababaabbbbbbbbbaaabbaaabbabbbbbbbabaabbaabaaabaababbbaabbbbbabbbababbaaabababaaabaabbaabaaababbbaaaabbbaabbababbbbbbbaababbbaaababaabaaaaabbaaabbabbbbbaabbaababbabbaabaabbbaabbbabababaaaabbbbbbaababababbabbaaababaaabbabbababbbaababaabbbbbabbababbaabababbababaaababbbaababaaabbaaaaabbbabaababaabbabaaabaaaaabbababbababaabaabbaaaaaabbbbabbbaaabbbabbbababababbabbbaabbbabbbaabaabaabaababaaaaabbbabaaabbaabaababbaabaaaaabbabaababaabbabaaaabbbabbbbbbbabbbbbaabbaaabbabababaababaabbbabbbbababaabbabbbbbaabbbbababbbbbbbabbbbaaabbabbabbabbababbaaabbbabbaababbaaaaababbbbabababbbbbabbabbbabbbaaababaabaabbbabbbbbaabbabbbbabaaaaabbaabaabbbaaaaabaaabbaaabbabbabababbaaaaaabbaabbabbabbbabaabbaabaaaababbaaaababbaabbbababaaabaabababbaaaaaabbababaaababababaaaaabbabababbbababaabbbbbbbaaabbaaabbbbbbbbaabaababbaaaabbabaababbaaababbaaabaabbbabbbababbaabaabbbaababbabaaaaaaaaaaaabbabaabbbaaabbbabbbaaabbbbabbbaaabababbaaababbbabaabbbbaabaabababaaabaabaaabbbbbbababbaaaaabbbabababababaababbabbbbaaabaabbbbbbaabaaabababbabbaababababbbbabbbbbbbbbabaabaaabbbbaaaaabaababaabbababababbbabbbaaabbbbababbbbaabbababbbabbaababbaaaababababaabbbabaaabbababaabbbaaabababbaabbbbbbaaababaaabbabbaabbbbbaababaabbbababbbbabbaabaabaaaabbbababbbbaaabbbaaaabbaababbbbbbabaaabbbbbbbaabbabaabaababbaababaaabaababbaaababbaaabbbabaabbbbbaabbbbabbababbababbbbaabbbabaabbabbbabbaababbababaaaabbbbbabaabbbbbaaabaababbabaababbbaaabbbbbabbabbabaabaabbaaaaabbbaabbbabaabaabbabaaaabbabaaaaaabbaababbbabbababbbbbabababbababbbaaabbaaaabaabbabaaabbbbbbbabbbabbbbabaabbbaabaaabaabaabaaaabaabbaaaaababaaaabaaabaaaaabaaabbaaabbaaaabbbabbbbbbabbabbbaaaabbaaaabbaaabbaabbbbaaaabbbabbbaabbababaaabbbaabbbbabbaabbabbabaabbbabbaaaabaaabbaaaaabbaaabababababbababaaaabbabbbbaabbaababaaabbababbbababaabbabaabbbbbbbbabbabbbbbbbabaaabbbaaaabababaabaaaaabbaabaaabbaaabababbaabbabaaabbbabababbabbaaabbbaaabbbaaabbaabaabbbbbaaaaaaaabbbaababbbbabbbbbaabbbbbabbbaaaabbaabbbbaaabababbbbbbababaabababaabaabaababbbaabababaabaaaabbababbaababbaaaaaabaaabaabbbabbaaaabbaabaaabbabbbbbabaabbababbbbbbbbabbbbaababbaaabaabbabbbabaabbaaabaaaaaabbbaabaaabbbbabbabbbbabbabaabaababbbbbbaaaabbbaaaaaabbabababbbbabaaaaabbababaaabbabbbbbaabaababbaabaabaaaaabababbabbaabbababbabbbabaaaababaaaaabaabbabaabbabbbaaaaaaababbabaaaababaabbaaaaabbaabbbaabbaaabbbaaabaaaabbbbabbbabaabbbabbabbababaaaaaabbabaaaabbbbabbaabbbbbbabbaaaabbbaaaaabababbaaabababbbabbaaaaababbaaaababbbbbbbbbaaaabbbaabbbbbbbabaaaaaaaaaaaaaaabbaabbbababbbaaabababaaaabbabbabbbbaaaababbabaaaaaaabbbbaabaaaaababbabababbbaabaabbbbbbaaaabbaabbababbaabbababababbaabbbbbaaaabaababbbababbaaabaaababbbabaabbbbaabbababbbbabababababaabbabbbabaabbbaabbbbaaabbbaaaabbbaaabbababbbbbaaabbabaabbabbaabaaabbababaabbbbabbaaaabbaababbbbbbaaaaababaababbaaabbabbabbbbabbbbabababbbabbbbbbbbbaabaaabaaaabbababbabaaabbabbbaaabbbaaabbababaaaabbbaaabaabbabbbabbaabbabbbbbaaaabbabbbabbaabbabbbbaaaaabaabbbbabbabbabbbaabbaaaaababbbbaabaabbbabababbaababaaababbaaaaaabaaaaaaaabaaaaababbaabbabbababaaababaabbababbabbabbbaabbbbaaabbbbaaababbbabbababbaaabbbaabbaabaabbaabbbbababbabbaaaaabaaaababbaaabbabbbbabaaabaabbbabbababbaabbbababbabaaabbbbbbbbabbabababbbabbbabbaabbbabaaabbaabbbaabaabbbaabbabaaaaaabbabbaaabbabbaabaaaabbaabbbaabbaabaaabbabbbaaaababbaaabbbaabbaaaaabbabbbbaaaababbbbbbbbbaababaaabbababaabbaaabababbbbbabaaabbaababbabaabbaaabaabbabbaaaabaabbbababbbaabbaabaabbbabbabaaababbabababbabbabbbbbbbaaaabbbbaabbababbbaabaabbbabbbabaaaaabaabbbbaababaaaaaababbbabbaabaabbbbbabaaaaaababbaabbbababaaaaaabaabaaaabbbbabababbaaaababbabbaaaabaabbabbbbbaaaabaaaabbbaaaabaababbabaaabbbbbabbbabbbbbaaaaaababbaabbababaabbabababaababbababbabaabbbbbbabbabbaabaaabbbbabbbbbbabbbababbbbbbaabbaabaababaabaabaababbbbbabaababaabbbbbbbaabbabbbbbabbbaabaabbaababbabbbaabbaaaaaaababaaaababbbaaabbabaababbbbabbaaabbabbabbabbababaaabaabbababbabbbbbbbabababbbababbabbbbaaaaabbabbabbabbaabaabbbabaaabaaaaabbaababbaaabbaaaaaabbaabaaaaaabbabbaaababbaabaaaababaababaabaababbababbabbaaaaababbbbbaaabaaabababbbaabbbbbaaaabbbbaabbbbbbbbabaabbabbaaabababaaaaaabbbbaabbabbbabbababaabaaabababababaabbbbaabbbaaabaabbbbbaabbbbabbbbbbaababbbabaabbbabbbaabbbbaaabbabaaaaabaaaababbaaaaaaabbbbbabbbabaabbbababaaaaabaabbbbababbaaaabbbaabbbaaabbaababbbabaaaababbababbabbbbbaabbbaabbbbbbbbabaabababaabbbaabaaabababbabaabaabbabaabbaabbaabaabbbbaaaabbbbababbbbbabbbaaaabababababbaaabbbabababaabaaaabababaaaaaabbbbaaaaaabaaaaabbbbbbbabaababaabaabaaaaaabbabbbbabbbabaaaaababbbbabbbbbbabaaabbbbbaaabababbbbaabbabbaaababbabbbabbaaaaaabbbbbbabbabbbbabbabbaaabbbbbabbabbabbaaababaaaabbbbabbaaaabaabbabbabbabaaaaabbabaaabbbabbaabbbaaabbaaabbaababbabbaababbbabbabbaaabbaabaaabbabbbbbbbbabbbaaaabaaaaaabaabbbabbabbbbbabbbbaaabbbaaabaaaabababbbbbabbabbabbabbbbbbaabbaaaaabbabbbbbabaaaababbaabaabbababbaabbbbabaaaababaaaaabaabbaaaaaaaaabbbbbbaababaaabbaababababbabababbbbbbbaabaaabbabaaaaababbabbaababbaaabbaabbbbaababbbaaabbabbbbaabaabaaabaaabbbaaabbbabbabbbabbaaaaabaaababbbabbbbbababaabbbbbaaabbbabbabbaaaaaaababbbaaaaaabbbbbabbaabbbbbaaaaaabbaabaabbbbaabbbbabaabbbabbabaabbbaaabaaabababaababbabbbbbaabbababbbbabbbbbbbbbaaababbbbbbbbaabaabbbbaababaabbaaaaabbabbababbaabbababbaaabaabbaabbbbabbbbaababababaabbbabbbaaababaaaabaaabbbabbabbbbbbabbaabbbabbaabaaabaabbabaabbbbbabbababababbabbbaababbbbbaaabbabaabbaaaaaaaaababaabaaaabbbabbabaaaaabbbbbbabaababaaaaaaabbabbbabbbaababbabbabbbaabbbbbaaaaababaabbbbaaaabbbaaabbaaabbaaaaabbbbabbbbaabaaaabaabbaabbaabbbabbbbaabbbaabbbaaaaaababaabbbbabababababbbaaabbbabaabbaababbbaababbabbaaabbbabbbabaabbbaabababaaabaababaabaaaabbbaaaaabbaaaabbbbbbabaaaabaabaaabbbbababaabbaaaabaaabbbababababaaabaabbbaaabbaabaaaababbaaabbbbabaaabaabaabbbababaaabbbbaaaabbbababbaaabbbabbbbabbbabbabaaaaababbbbabbabaabaababbabbbbabbbaabaaaabbaabbbbbaaabaaabaaababaabbabbaaabbabababbabaaaabaabaabbbaabbbababaabababaabaabbbabbaabaaabaabbaabbbaaabaaaababbaabaababaabbbbaaabbbbbaababbbbaabbbbbababbbbaabbabaaababaaaaabbabbbabaaaaaaaaaabaababbabbaabaaabbbbbaabbaabaaababbbbaaaabaaabaababbbabaaabbaaababaaaabbbaabaabbaabbabbaaaaaabaaaaaababbbbbbbabbabaabaabbaaaababbaaabbaabaabaabaababaaababaaaaabbbabaabababaaaabbabbbbbaababbaaaabbbbababbaaaababaaaabaaaaaaabbabaabaabbbababbabaaaaabababaabababbaaaabbbaaabaabaabaaabbaababbaabbaabbababababaaaabbaaaaaaaabaaaaabbabbabaaaaaababbbaabaaaaaaabbbaababbabbbaaababbabbabaaaaabbbaaababbaaaabaaaaaabbabaabbaababaaabaabbaaaabaabbbababbaababbbbabbabababbbababbbababaaaaaabbbbaababbaaaabbaaaaaaaabbbbbaaaabbaaababbbbbbbaabbaabbabbbabbbbabaabbbbabbaaaabbababaaabaaaaaaaaaaaabbababaaabbbbabbaaabaabaababaaabaaaabbbabbbaabababbabbbbaabbbabbabbaabbabbbbabaaabbaabaaabaabaabaaabbaaaaaaababbbbbbbabbabbbbbaaabbaababaabababaaaababbbaabbbababbaabaaabaabaabaaabaaabaaabbaabbbbbaabbababbbbaaaaabbaaaabbaabbbaaabbbbaababbbabaaabaabbaaababbabbaaaabbabaabaaabbbaaabbbabbaaabaabbaaaabbbabbabbaaaabbababbbbbabababaaaabaabaaabaaabbbbbaaaabbbbaabbbbbbaabbbbbababbbabbaabaababbbbabaaabbbababbaabaaabbbaabbaaabbbaabbabbbababaabaabbbababaaaabbaabbbabbbabbbaabbbaabbbbbbbaabaabbaaaaaabaababaaaababaabbbbabbbbaaabbbabbbbbbbaabaaaabbaabbabbbaabababababbabbbbababbbbbbbbaabaaabababbababbbaababbaaaabaaaaabbaabababbbbbbaabbbabbabbbabbbbabaaabbbbababbbaabaaaaabbbbabbbabaabbabbbababbbbbbababbabbababbbababbabbababababaabbabbaabbabaabbbbaaaabbbaaababbbaaaabbabaaababbbbaabbbbbababbbbbaabbabbbababbbabbbbaababbbbaaaabbbabbaabbaabbabbbabbbaaababaababaabbbbaabbaababaaaaaabaabbabbaababababbaaabbbbbabbabaabbbabbbbbbbabbbaaababbaaaababbabbaababaaabbbabaaabbbaaaababaaaabbabbbbaaaababbaabaabbaaaabaaaababaabbababbababbaaaaabbbbbaabbaaaababbabbababbaabaaaaaaabbabbbabbbbbbaaabbababaabbabaababababababaabbaababaaaaaaaabaabaabaaaaaabbaaaabaaababbabbababbbbbaababaaababbaabbaabbbaabbbbbababbaaabababbbbaabaabbaaabaaabbabbbaaaaaaabbbaabaaaaabbaaabbaaabaaabbbabbababaaaabbbbaaaaaaaabaabaaababbaabaabbaaaaabaaabaaabbbabbbabbaaaaabaabbaababbbbabaaaabbbaabbabbbbbababbabaaabaabbaababbaabbabaababbaaaaaaabaabaabaabbbbbaabaaabbbaabbbbabbabbaabbbaaaaaaaaaabaabbbbaaaabbbabbabbbbbabbbbbbaaaababbababbaaaababbaabbbbbaababbbaaabbbababbabbaaabaaabbabaabaababbaabbabaaaaaababaaaabaaabbaabbbaabbbaaabaabaaabbaabbababbabaababbbababbbbabbabbbbbabbbaaaabbabbababbababbbaabbbbaaaaaaaaaaabbaaabbbbbbabbbaaabbabbaabababbbaaabaaabaabbbbbabaaaabbbababbbaaababbbbabbbaaaaaabbabababaaabbabaabbbabbbbbabbbabbaababaabbbbaabbbbbbabbbbaaaaaaaaaaabbabbabaabaabbaababbabbaaabaaabbbbabbbaaaabbbbbaabbabbaaaabbabbaabbbababbbababaabaaabaaaaaaaaaababbabbabbaabbabaaaabababbaaabbabbabbbbbbaababbbbbbbbbbbaaabbaaaabbbbabaaaaaaaaaabbababbbbbbaaabbaaabaaabbbabbaabbaaaaaabbaabbaaabaaaabaabaaabbaababbaabbbbaaaabbbaabbbbaabaaabababbbbbbabbbabaaaaaabbabaabbbbbbababbbbaaabaabbaaaabababaaababbaaaabbaabbabbaabaabaabbabbbbbbbbabbbbaababbabbabbabaaababbbbaababbbbabbababbbabbaaababbbabbbaabbaaabaaabbaabbbaabbababbaabbbbaaaabbbbbbbbabaabababbaababbbbabaaababbaaababaaaaababaaaaabbabbbbbbbaaabaababaabbaaabaaababababbabaaaabbbbbbaaaabababbabbbaababaabbbabbabbbabbabbaabaaabaabaababbbbbbbbbabaaabbbbbabaabaaaabbbbaaabaabbbabbaaabbbaabbbbbaabaabbbabaaabbabbabbabaaaaabbaaabaabaabbabbbbabaabbbabbabaabbaabababaabaabbbababbbabbabbabbabbaababbaabaaaabaaaaaaababaaaabaaaaaaaabbaabbabbababbabbbbababaabbbbbbbbaaaabbbababaaaabaabbbbbbabbbbaaaaababbbbabbbbaabaabbaaaaabaaaabbbaabbbaaabbbabababbaabaabaaabbbbabbbaaaabbabbbbbbaaaabbabbaaabbbbabbbaabbaaababbbbbabbbbbabbabaabaabaabbbbbbbbbabababbabbbbbababaaababbbbbaabaabaaaabaabbbabaaabbbbbabaaaabbaaabbbaaabbbaabaabaabbabbbbabababbabaabaabaaababaabbbabbbbaaaabbabbbbbaaabbaaaaaabababbbbabbbaaababbbbbaaabbabbaabbbbbbbbabaaabbabaabbabababbbbabaabaaaabbabaaabbbbabbabbbbaaaaaaabbababbabbabbababaaaabbbabbaabaaabbaabaaaabbaaaabaaabaaabbbbaaabbbaaabbbbaaaaabaabbbabbbabaababbbabaabbbaabbaabaabbababaabaaaababaabbabbbabaabbabababbbbbbaaabbbbabaaabbaaabaababaaabaabbabaaabababbbbbaaabbbaaabaaabaaaabbabaababbabbababababbabbbbabbaabaabaabaabaaabbababbbaabbbbaabbabbbbababbbabbbaaaaaababbaaabbbaaaabbbaaaaabbaaaabbaaabbbbbbbabbbaaaaaababbbbbaabbaabbabbbaaaaabbbaabbbaabbaaabaababbabbaababbbabbbabaabaaabaaababbaababbaaaaaaaabbbbbaabbaaabaaabbbabbaabbbbaaabaabbabbaaaabbabababbaaaaababbbbaaabbbbbbabbababaabbbababbbababaaabbabababbbbbbababaaabbbabbbbbbbabaababbabbbbaaababbabbaabbbbababbaaaabaaababaaabaabbaaaaaaabababbbaaabbbabbbaabaabbbabbababaabbbaabaabababbaaababbbabbabbbaaabababbababbbbbbbababbaaaaaaaaaaaaaabbabbababaabbaaaaabbbaaaabaabbaabbabbaabbabbbabbbbbaaabbaabbbaaaabbaabaabbbbaaaabaabbbbbbabbabbbbbaaabbaaaabaaabbaabbbaababbbaabbbbabaabaabaabbbaaaaaabaaabbabbabbbbabbbbabbbbbaaababbaababbbbabaabbaaabaabbaabbaabbabaabbabbaabaabbabaaaabbaaaaaaaabbabbaaaaaaabbaaabbabbbaaababbbabaaaabbbbaabaaaaaaababaabababbbaabbabbbaabaaaabaaaaababbabbabbaaaaaabbabaabbabbbbabbbaababababaabbabbbaabaaaaaaabbbbabbbbbabaaaabaabbaabbabbababbaabaaababbbbabbbabbbababaaaabbababbbbbbaabbaaaaaababaaabbbbaaaaabbbbbbabaaaaaabbababaabaaaaaababbaaaabbbabbaabbbaabbabaaaabababaabaaabaaaabbbbbbbbbaabbabbaaaaabaabbabbabbbbbaaabbbababbbaababbabaabbabbbbbbbabaaababbabbaabaabaaaaaaaaaabbbaabbabaababbabbbababaabbbbabbaaabaabbbababbabbaabbbaabbbaaababbbbabbaabbaaaaabaaabbababaaabbbaabbbaaabaaaabbbaaaababbaababaaabbbaabbbbabbabababaabbbbbbaabababbaaababbbaaaabbaaabbabbabbbaababbbbabbabaababbbbabbbababaaabababbabbaaaabaababaabaaababaabaaabbaaabbbaababaaabbbbaaaaaababaabaaaaaabbaababaaaaaaaabbabbaaaabbbbbabbbabaaaaaababaababbaaaabaaaabaabaababbbbbbababbbaaaaaabbabababbaaabaabaabbbbaababaabaabaababaabbbaaabababbabaaabaababbbabbababbaabbabbaaabaababbbabaaaabaaaabbbaabaababbaaabbbababaaababaababbabbaaabbbbbaaabbaaabbbaaaaabaabaaabbbbbbabbabbbababbbaabbbabbbaaababababaaaaaababbabbaababbabbaabbabbaabbbbbaaaabbabbabaabbaaabbabbbbaaaabaabbababbbaabbabbaabbaabaaaaaabbbbbbabababbbbaabaaaaabbbbaaaaabbaaaaaaaaaaaabbbbaaaabaaabbaaabbabbaaaababaabbaaababbabbabaaabbabababbbbabaaabababbbbaaabbbaaababbbbbbababbbabaabbbbbaaabbbaaaaabbabbaaaabbaaabbbbbbaaaaabaaaabbaabbbbaabababbaaabbbbbaaabbabaabbababbaabaaabbaabbababbbbaaaabbbbbaabababbaabaababbaaaababaabbbbabaabaababbbbbabbaabaaabbaaaaababaabbabbbbabbbabababbabbabbaaababaabbbaaabababbabbbaabbabbaaabbababababbbbbbabbbaabbbaabbaabbaabbbbbbbbabbaaababababaabaabaaababbaababababaabbaababbbabaabbaababbbbbabbaaabbbbabbaaaabaaaabaaababbbaabbbabababbabaaaabbbabbabaabaabbaaaaaababbabaabbababbaabbaaaabababababaababbaaaaaaabbaaabbbbabaabababbaaaababaaaaaabababaaabbbabbbaaaaababbabaaaabbabaabaabbbaabaabbbbbbbbaabaaaaaabbbabbabaaaabbbaabaababbabbbaabbbaaabbabaabaabbaabbabbabbbbabbbbbbabbbaabaabbbbbabbabbabbaabbbaaaaabaaaabaababaababbbababbbbbbbabbbababaabaabbbaababbabbbabbbbababbbaaababbbaababbbbbbabaabaabaaaaaabaaabbbabaaabaabbaaaaabaaaabaaababbbbaaaabbabaaaabaabaaabbaaaaaabbabaabbaaaaaabbbbbbbbbbbaabbaababababbabbabaaaaababaabbbbbbabbabbbababbaabbbbabbabbbbaaaaaaabbaaaabababaaaaaaaaaaabbbbbababaababbababbabababaaabbabbabaaabbbaaabbbabbbabbbbbaabbbabaabbbbbabbaabababbaabaaabaabbbabaababbbabbbaaabaaabbaaaaaaaabaaaababbaaaabbbaaabbbbbbabbabaaabaaabababaabbbaabbbbaabbbbbbaaaabbbbabbabbabaaabaabababbbbbbabaaababbbbabaabbabbaaabbbbaabbbaabbbbbbbaaaababaaaaabbbabaabbaaabbbbbbbabbbabaaaaaababbaaabbbabbaaaabaabaaaaaabbaaaaaaabababbabbbbaabbaaaaaabaabbaabbabbbaaaabbaabaaaabaabaababaabbbabababbabbbaaabbaaaaabbabaaaababbaabbaaabbbbbaaabbbabbbaababababbbababababaaaaaababbaabbbaabaaabbbbababaaabaaaabbabbbbbbbabbaaabbaabbabbababaaabaabbaababaababbbaabbaabbaaaabbbbaabbbaaaaabbbbbabbbaaaabbbaabaababbaabbabbabbaabbaaaabaabbbbabbbabbabbbbabaaabaaabaabbbbbbbabbaabbbabbbabababaaabbbaabbabbbabbababaaababbaaaaaababbabaabbbabbbbabbaaaaaababbaabababababbaabbabaabbbbaabbbabbaaabbaaaaabbaabbabbabbbabbabbbabbbbabaababaaaababaaabaaabaaabbbbaabbaabaabbaaaabaabbabbababaabaaaabaaaabbaabbbbabbaaabaaaaaaaabbabbbabbbaabbababbbbbbaababbbabaaabbbabbabbbabbaaabbbbbbbbaaaaabaaaabbbaabbaababbaaaaabbaabbababaaaabaabaaabaabbaaabaaabbababbabbaabaaabaaabbaaaababbaabbbababaaabababbbbaaababaabbbbaaaaaabbaaababaaaabbaaabababbbbabaabbaabbaabbbbbbbaaaabaaaaababababbbaabbbababbabbaaaaaababaabababaaaaaaabaababbabaabbbbbabababaaabbababbaabaaaaabaaaaaaabbbaaabbabababbbbabbbbaaaaabbbbaababaaabbbabbaabbbbabaabbaaaabbaaaaaabbaababbbabbaabababaaaaaabbbbbabbbabaaabbbbbbaabbbbbbabbabbabbbabbbbbbbbababbbbbbabbbabbbbbaabaaaaabbaaaaababababaaaabbbbbaabbabaababbbbaaabaaabaabbabaababaabbbaabbbbaabbaaabbbbbbabbbababaaaaabbbbaabbababbbbaabbbabbababbabbbaabababababbbbaababaababbabbaaabbbabbbaabbaabaabababaabbaaabbbbabbbbbbaaababbaaababbbbabababbabbabaabbabbababbabbaaaaabbbbabaaaabbbbaabaabaaaaabaaabaaaaabbbaaabbaabbababbbbbaaaabbabbabaaabbbabaabaabaaababbaabbaaabbaababbaababaabbbbbbbbabbbbbaabababbbbbabbbbbaaaaabaabbbababbbaabaaaaabbabbbabbbbbbbaabaaabaabaaaabaaaabaabaaabbaaaabbbbaaaaaabbbabaabaaababbbabbbaaaabbaabbbabaabbaabbabaaabbbbbaababbababbbaabaaaaaabbaababbbaaabbaaabaabaaababbbaabaaababbbabbaababababbaaabaaaabbbbabbabaabaaaababbbabbaababaabbaaabaababbbabbabababbbbbabaabbbbbbbbaabaabbaababbababbaabaaaabbabaaaabbbabbbaaaababbbbbbabbbbbbababbbababaabbbbbabababbbbbbbbaaaaabbabbbabbabbbabaaaabbababaaabaaaaabaaabaaabbabbabaabbaaaaababbbbabbaaabbabbaabbbababaababbbbabbbbbbbbabaaaababaaabbbbabaaaaabbabaabaababbbbbaabbaabbbaaabbbbaabbaaaabbbbbabbaaababaababbbaabaabbaabbabbaabbbaabbbbaaabaaaabababbaabbbbaabaabaababbababbaabaaababbbbaaabaababababaaabbbaababbabbaaaabbaabaaabbabbabbababbabaabbabbbaababbabaaaaaaabaaababaabababaabaaaabaaaaaaabbbbabbbaabbaaaabbbbaabaabaababababaaabbaabaababbbbaaaaaabbbbaabaaaabbaaababaaabaaaaaaaaaababababaaaabbbbaabbbabbabaabaabbbbbaabbbbaaabbbaaabbbabaabaaaabbbbbbbbabbbabbaabbbabbbabbaabbaabbbbabaaaaabaabaabaaaabaabaaabbaaababaaabababaaaababbaaabbbabbaaabaaaaaabaabaaababbaaabaaaabbabbaaabaabaabbababaaaaabaabbababbbabbabbababbbababababababbbbaaabbabababbbbbababaabbabbaaaabbabbaababaabbbaabababbabbabaababbbbaabbbaaabbbababbaaabbbabaaabaaaabbabaabbbabbbbbabbbaaabaaababaaaabbbabababaabaaaababbabbaababababbbaaabaaabaabbbbaaaaaabbbbbabbababbbbabaaabaabbbbbababbbbbabaababaabababbbabaabaaaaabbabbabbabbabbbabaababaababaaaaabababbaaaabaabbbbaaaabaabbabbbababbbbbbabbbababababababbaaaabbabbababbaaaaabbaaabbabaaabbabbbababbbbbbaaaabbbaaabbbaaabbbabbbbaaaaaabbaaaaaabbabaaaaaabbbaababbbbabbbaaaabbabbaabbbbaabababbbabbaababbbbabbbabaabbabaaaabbbbbbbbbabaabaabbbabbbbbbbbabaaabbbbababaabaababbabbabbababaabbabbabbabbbabbbabaaaaaaababaaabaabaaaaaabaaaabaaabaaaaaaaaaaaabbaaaabababababbbbbaaabbbabaaababbabaabbbbababaaaaaaabbbababbabaaaaabaaaabbbbabbabbababaaabbabaabbaabbbaabbaaabaaaaaababaaaaabbabbbbbbbbbaaabaabbbabbbbbbabaaaaaaaaaabbaaabbbaabbaaaaababbaaaaaababbaaaabbaabaaaaaaaaabaaabbaabaabbaaabaaabaaaaabaaabaaaaaabaaabbaabaababbababbabaabbaabbbabaabaabbbbabaabaaababbbabbabaaababbaabbabaabaaaabbabaaababbabbababbbabaaabbabbbaabaabaabbbbaabaabbaaabaaaaababaaaabbbbabbbbababaabbbbaababaabaabbabbaaabbbabbbbbbbbababbaaaabbaabbabaaaaaaaaabaaaabbabbbbaabbabbbaaaaabbabaabaabaaabbababbabbaaabaabbbbabaabaababaaabbaababbabaabaabbbbbabbabbaaaababbbaaabbaabaabaababbaabbaaaabaabaaaabbabbaabaabbaabbbbabaaababbaaabbabbbababaabaaaaabaaabbbaaaaaaaabbaaabbabaabbabbbbbbbbabababbaaaababaabbabbbababbbaabbabaabbaabaabbabaaaaaaaaaaaaaababbaabbbbababbabaaaaaaaaabbababaaaaabbbbbaaabaaabbaabaabbbaababbaabaaabbababaabbaaaabbabaaaaabaaaaabaabbabbbaababbaabababbabaaaaaaabbbaabbabbabaaabbaaababaaababaaaaaaaabbbaaabaabbbbbbbaababaabbabaaabbabbbaaabbaaaaababbbaaabbaaabbbbababaabbabaababbabbbbbaaabbbababbbbbbabaaaaababbbababaaaabbbbabbaabbabbbabaaabbaabaaaaabaaaabaabbabbbaaabbbaaababbbaaaaaaaaabaaabbbabbaaaaababbbabababbbabbababbbbbbbbabaababbaabbabbaababbaaabbbababbaabbbababbbabbaaaaaabbabaaaabaaabbabbaababaabbabbbbbbbbabbaaabbbbbbabbaabbaaabbabbbaabaaaabbbbaababbbabaabbbbbbaaaaaaaabbbabaabaaaaabaaabbbaababbbbabababaaababbabaabbbbaaaababbabaabbaabbbbabbabaabbbaaabbbababbaaaababbabbaabbaaabbbbbbaaabbbaaaaaabaaababbbabbbabbbbbaaabaaababbabababbbbaabbaaabbbbabbabababbbbbbababbababbaabababaabbbbaababbabbbabbbbaaabaaabbabababaabbbbaaaaababbbaaabbbaaaaabbbbbabbbbabaabbbaababbbbbbaaababbbbaaaaabbbbaabbbbaaaabababababbbabaaabaabbabbaaaaabbbbaabbaababaaaaaaaaabbaaaaaaaaaaabbaaaabbbabbbabaaaaaabbbabaaaabbabbbabaaabaababbbbbababaaabbabbaabbaabababaabbabbbabbbaaabaaaabbabaabaaabaaabbbbaaaababbaabaaaaabbbbaabbaabaaababbabaabababbabaabbbaaabbbbbabbbaabbbaabaaaabbabbbabaaaabaaabbbbaabbaabaaaabaaaaaaabaaaaaabbbbbababbbbbbbabbabbabbbaaababaabbabbbabbababbaaabaababbaaaaabbabaabaaabbabbbaaaabbbbbabaabbaabbbbabbbaaabaabaabaababbbaabaaaaababbbaaaaaaabaabababbbbbbaaaabbbbabbaaabbababbabaaaabbbabbabbaababbbaabbbbaaaaabbababbbbaabbababbaaaababababaaabbbbaaaaabbaaabbaaaababbaaabbabaabbaabbbbabbbabbabbababbaaabbbaaabaaabbbbaabaabaaaaaabaabbaabbaaabbabbbaabaabaabbbababbbababbbbababbabaabbbbbaaaaabbaababaaababaaaabaaaababbbbbaaabaaaaabbabaaaabbbbbabbbabaaaaabaabbbababbabbabbabbaaaaabaaababbbababbbbbaababbbabbababaaabaaaaaaaabaabbaababbbbbbbbbaaaaababbaabbaabaabaaabaabbaabaabbbbabbbbabaabbbababbaaaabaaaabbbaaabaaaaabbbaabbababbabaabbbaabbaabbabbbaaaaabbaabbabbabaaababbbbbbbaabbabaababbaabbbbbaaaaababababaabbbbbaaabbbabbbaabbbbbaaaababbbbaabbbabbabbbbbbabaaaabbabaabaaabbbaabbbbbababaabbaaaabaababbbababbababbbbbabbaaaaabaaaaaababbbabbabbbabbabbbabbaaabbaabbbabbabbbaabababbbabbabbaaaaaaabbbaaabbabbabaabbabbaababababaabbaaaabaaabbbaaabbabbbbbaaaaaaababaabbaaaababababaababbabaabbaaabbbabbbaabaabbabbbbbaabaabbababbaaabbababbbbbbbbaabbbbabbbabaababaabaaabaababbabaaaaaaaaabbabbbbababaabaaabaabaaaabaaabaaaaaaabbbbabbbababaaabbaaabaabbaaabaababbaabbaaaabbaaaaabaabababababbabaabaaababbbbaababaababbbaaaabbababbbbbbbabbbbbbabaaaababbabbbbbbaabbbabbbbabaaababaaabbaabbabbabbbabbbaaabbabaabbbababbbbababbbbaaabaaabbaabbbbaabaaaaaaabaaabbbabaabbababbbabbaabbabbbbabababbbbabbbbbbaababbaaaaaabbbbbabaabbaaaabbababaaababaabbabaabaaabaaabaabaabababababaabaababbbaabbabbbbbbabbaaaababbbbbabababaabaababbaaaabbababbbbaaabbabbbbbaaaaabaabbabaababaababbbbababbbbaaabbbbbbbbbbbaababbabbbaaabaaaaabaaabbaabbbabbabbbbbabbbbababbbaabbbbbbbaabaabaaababbbaabaaabbbbbaabbbbaaaababbaaabbabbbabbabbaaaabbbaabaabbbaaabbababaaabbbaaaabbabbbabaaaaabbaabbbbbbbaaaaaaabaaabaabaaabaabbabbabaabbbbbabaaabbabbbbbbaabaaaaaababbabbabbbbabbaaaaabbbbaaabbabbbabaabbabaaabbaaaaabaabbbababbabbbaabbbaabbababaaaaaaaaabbbabbaababbbabaabaabbbbabaaababbbbaababbabbabaabbbbbbbaaabbabbababababbbababaabbabbabaababbaaaaabbaaabaabbbbabbbabbabbbbbaaaabbbaaababbbaabaaababbbaaaabaaaaaabbaaabaaaabbababaaabaabbbaabaababbbbabbbbbbaababaabaaaababbbbbaaabbbaaaabaaabaabbaabaababbaabbabbbbbbababaabaaabbbaabaababbababaababbabbbbaaaaaaaababaaaababbbbaaabaabbbbbabaaabbaabbbbbaaabaabaaabbbbbbaabbbbbbabbabbaabbabbaaababbbbaaaaaaababababbaabaaababbaaaabaaabbabbaabbbabaababbbbabbaaaaabbabbbaababbabaababababbbbbbbababbabaaaaaabaaaaaaabaaababbbbaaabaabbbabaabbbbbabbbabbabababbaaaabaabbbaaababbaabbbbbbbaaabbbabbabbbabbaaabaabaababbabbaaaaaaaaaaaabaabaabbaaabbbbabbabaababaaabbaaaaabaaaaababbbaabbababbaaababaabaaababbbababaaababbbbabaabbbbbabbbbbabbbbbbbababbbbaabababbababbaababaaabbbbbaaaaaabababaaababbabbbaababaaabababbaabaabaaabbbbbaaaabbbaababbaabaabaaabaaaaaabaabbbbbaaaabbabaabaaabaaaabbbababaaaaaababbaabaaaaaaaabbbbaaaaaababbbaabaaaabbbbbbbbaaaabaaabababaaaaabbbbbbabaabbaaaaabbaaabaaaabbbaaabbaaabaababbabbababbbbbbbbabababbbabaabaaaaabababbbbbabbbbaaaaaaabbbaabaaababbaaaabbaabbababababaabbbabbbabaaaaabaaaabbabaabaaaabbbababaababbbaaaaaabbaaaabaabbbaaabbabbaabbaaaaaabaaaabaabbabbbaaabbababbababbbbabbbabbbbbabbbbabbaaabaaabaabaabbbbbbbbaaaaabaabaabbbbaaabbbababbaabbbaaaabaabbaabbaabbabbabaabaabbabababaabaabaabababaabbbaaabbbbbbabababbabbaaaaababaaababbbbabaaaaaabbababababbbababbbababbabbbbbbaaaaaaabbabbbbbaaaabbbbabaaaabaaababaaabababbabbbabaabaabbbbaaaaaabbbaabaaaabbaababaaabbbaaababbabbaaabbaabbbabaabababbbbaabbaaabbaababaaaaabaabbbbabaabaaabbbaababbabbaaaaaaabbaaababbaaabababbbabaaaabbbabbabbaabaaabaabbbbabaaababbabaabaabbbabbabaaababbbabaaababaabaabaaaabbbabbaaabbaabbabaaaaaaaaaabaababbaaaabbbabbaaaaaabababaabbbaababaabbaababbaabbbabbbabbabaababaaababaabbbbbaaabaaaabbaaabbaaabaabbaaaabbaabbabbbbbababbaaabbbbaabbabbaaabbababbbaaabbbbbabaabbaaaaabbabbbbbabaaaaabababbbabaabbaaabaaaabaaaabbbababbaabaaaaabaaaaaabbaabbbbbbabaababbbbaaaabbaaabababbabaaaaaabbbbbaaabbbbbaabbaabaabaaaaaabbabbaaaaaababaabbaabbbabbbaabbaaabbbababbabababbaabaababbaabbbaaababaabaabbbaaabbbaaaaabaaabbababaaaaaaabaaabbbababbaaaabbaaaabaabaaabaabaaababbaabaaabaaaabaabbabababbbbaaaabbabbaabbaaabbabaababbbaabaaababbbaabaaaababbbababbaabbaabbababbbbbbabbbabbaababaaaaaabbabbaaaaabbabaababbaabaabaaababababbbbbbabaaaaabaabbabbaaababaaabaabaaaabbaaaaaaaaabaabbbbbbbbabaabbaaaabaaaaaaaaaababbbaaaabbababaaaabaaaabaabaabaaaabbbababbababbabbaababbabbaabaabaabaabbaabbaabaaabbbbababbbabbbaaabbaabaababbaabaababbbaabbaabbaaaaaaababbaaabbaaaaaabbabaaabaabbaabbaabbbbbbbaababaaababbaababbaaaaabbabbbbaaaababaabbbbaaababbbaabbbaababbbbbbaababaaababaaabbabaabbbabaabbaaababababbbabbaaaaabbbbbbabaaabaaaabaabbabbaabaaababaababbbbbbbabbaaabbaaabbbbbabaababaabbaaabaaaabaaabaabbabaaabaaaaaabbbbbabbbbbaaabbbaabaaaabbbbbbbaababbbabaabbaabbabaaabababbabababbbabaabaabbbbbababbabbabbabbababbbaababbbbbbbbbabbabbaaabbaababbbaaaaabbaaabbababbbabbbbbaababbabaababbbbbaabaabbabbababaabbbababbbabbbabbaabababaaaabbaabbbaabbaabbaaabbbbababbabbaabababaababbbaaaabbbbbbaabbbbbaabbaaababbabaaabbababbaaabbbabaaaaabbaaaabbabbabbabbbbaabaaababbbbbbbbbababababaaaabababbaabbbabbabababaaaaabbabababaaaabbbbbbbbbbbaabaabbbbaaabbabaaaaabbbaababbbabbbbabaabaaaababbbaabbaaabababbbaaaaaaabbbbaababaaababbabbbbaabbabaaaabbabaaaaaabbaaaaaababbbbababbaababbaabaaaaabbababaaaaabbaabbbbaabbabaabbaaaababaaabbbaababbaabababbabbaaababbaabbaababababaaababbabbbbbaaabbbaabaabbbabaabbaaaabbaabaababbababaabbbbbabababbbbbababaaabbaaaaabbbbaaabababaabababbaabaaaaaabbaabaabbaaaaabaabababaabbaabbbaaaaaabbaaabaaabbbbaabababababaabaaabababbaababababbbaaaabbaabbabbbababbbabbabbabbbbabbaabaaabbbabbabaabaababbbbababbabaaabbbbaababbaabbbaaaaaabbbbbbaaaabaabbbbababaabababbbabbabaaabbabaaaaabaabbbaabbabaaaaabbabaaabbbbbababaaabbaaabaababbabbbbbaaaaabbabaabbbbbbbbabbbaabbabaabababababaabaabbabaaaaabaabbbbbbabbbabbbaaabaaaaaaaaaaaaabbaaababbbaaaababbabaabbbabaaababbbaabbabbbbbaababaababaabbbbbaaabbababbbabbbabbbbaababbabbbbaabbbbabbbbbaabaabaababbababbbbabaaabbaababbaaaabbbabaabbabbaabbbaaaaabaabbbbbabbbbaaababbababbabbaaaababaabaaaaabaabaababbbaaabababbbaaabbbbbabbabaabbbabaababbbabbbabbababbbabaabaabbabaaabbbabbaabaababbaaabaabaabbabbbabaaabbbbabaaabbbbbbbbababaaabaaababbbbabbabbaaaaaaaababbbabbbbabbbaaaabbbabbabbbbbbaaabaaabaaabbbbabaabaabbbbaababbbaababbbbabbbaaababbbbbababbbaaabaabaabaabbbbbbabbabbaabbabaaababbbbabbaaaaaabbabaaaabaabbbaabbbabbaaaabbababababbabbababaaaababababbbabaababbabbaaabaabaaaaababbbaababbbbabaabbbabaaaaababbbbaabbaababababbabbbbbbbaaaaabbaabaaabaaaaabaaaaabbabaabaaababbbbbabbbabaabbbbabaabbaabababbbabbbabbbbababbaabbabaababbbbbabbaaabbbababaaaaabaabbbbbaaaabababbaabbbbababaabbbaaabaabbbababbbbabbbbaaabaabbaabbabaabbbbbabbaabbbbbbbaabbaabbbbbbbababbbababaaabaabbaaababbbbaabbabbaabaaabababbbabbaaabaaabaababbabbbabbaaababaabaaabbabbabaaabaabbaabbaabaabbbabbaaaabaabbabbaabbababbbabaabaabaaaaabbabbbbbbbbbaaabbbbbbbaababbabbaaaaabbbababbaababbbbaaaaaaaabbaaaababbabababaababababaabaabbababbabaaababbbabbabbbbbbabbbabaaababababaababaaaabbbaaabbbaababaabaaaabbbaabaaaaaaaabaabaaabbaaaaaaaabaaaabaabaaaabababaaabbaaaaabaababbabbabaababbbbbabababbabbbabbaaaaaabbbaaabbbbaabbbbbabaaababaaaababbbbaaaaababababbbabbaabbabbaabaabbbbbbabaaaabaabbbbaaaabbabbaaabbabaabbabaaaaaabaabbaababbabbbaaabaabbaaabbabbbaaaaabaabbbabaababbabbabbbbbaaaababbaaabaabbababbbbabaaaaaaaabaaaaabbbabababbbaababababbbaaababaabababbbabababaaaaaabbbabaaababaabbbbbaababaabbbbaaabaabbaaaabbbababbbabbbbbbbabaaabbabbbaaaabbaabaababbbbbaabaaabbaabbababababbaaabaabababbabbbabaaaabbbabaabbbaabaaabaaaaaaababababaaaabbbbabbaabababababababbabaaababaabaaaaabaaaaabbbabbbbbbabbaaaabbabbabbbbbabbbbabbbbbbbbaabaabaaaababbbabaababaababababaaaaabababbbbababbbbabbaabbbabbbbbbaabaabaaaaababaaaaabababaabbaabbabbbaabbbabaaaaaabaabaabbaaabaabbabbbbbabbabbaaabbabaababbbaaababaaaabbaaaabaaabbaaabaaaabaababaabababaabbaabababaaaaaaaaabbbbababbabababbbaababaabbbbbbbbabbbaabbbabbababbbaababababababbabaabababaabbbbbaabaaabaababaaaabaabbbabbbbbbbbbabaabbbaababaabbabbbabbbaabbbababababbbbbaaabaababbabbbaabababbbabaabaabbbbaaaaabaaabbababbbbbbbaabbaabbbaaabaaabaaaababbabbbabbbbbaabbbabaabaabbbabaababbaaaaaabbaababbbaabaaaabbbbaaabbabbbbbaabbbbbaaabbaaabbbaaabbbbbbaabbabbaabbaabaabababbbabaabbabaaabaaabababbaaaabaababbbabababaaaaabbaaabaabbabababbabbbababbabaabaaabbabbbbabaabababaababbaabaaabbbabbaabbbbbaaabaabaaabaabaabbabaaaabbbbaaaaaaaabbbbbbbbababbbabbaababaabaaabaabbaaaaabbaababbbbbbbaabbbbabaaabbbabbaababbabbbabababaaabaabbbababbabbbaaaabbaaabaabbbaaaaaabbaabaaaabaabbbaabababbabbaaaabbaaabababbbabbaaaaababaababaabaaabaaabbbbaaaaaababbaaaabaaabbababaaaabbababbabaabbaaaababbaaaabaabbaaaaababaaaabaabaababbaaabbbaabaabaaabbbabbbabaabaaaabbbabbbbbbbbbabbbaaaabaaaababbaabbbabbbbbabaabbbbabbaabbbababaaaababaababbababbbbaabaabababaabaabbabaaabbabbaabaababbbaaababaabbbbbbbbbbabaabbbabbabbbbbaaabaababaaaaabbbaabbbaaaabababbbbaabbbbaabaabababaaabababbabbaabbbabbbbbbbbbbababbbabbbaabbabbbabbbbaaaabbbabbbbabababbbabaaabbabaababbbbbaabbbbbbbaaababbaabbabbabbabababbaabaaabbaaaabababaaabbbaaaaaabbbababaaabaaabaabaaabaaaabaaabaaaabbbbaaaabbaaabaabbaababbbbbbababababbbbbbbaaabbabbbabbbbbaabbbbaabbabaabbbbbbbbaabaaabbabbbbbbaaaaaabbbaababbaaaababaabbababaaaaaaaababaabaaabbaaaabaaabaabbbbbbaababbabbbbbabbbbaaabaabbbbaaaababaabbbabbabbaaabbabaabbababbbbaaaaaabaaabababbabbbbbbbbbaaaaaaaaaabaabababbaabbbabbbbbbbbbbbbabbaaabbbabaaaaabbababbabbbabaabbbaaabbbaabaaaaabbbabaaaabbaaabbaababbababbabababbbabbabababbbabaabbbaaabababababaaaaaababbababaababaabbbaaaabbbbabbabaabaaaaabbbbbbaaabbbbbbabbbbaababaaaabababaaabbbaaaabaaaabaaabbbbbbbbbaaabaaaaabbbbbabbababbaabbaabbabbbbababaaaabababbbabbaababbbaaabbbaabbbbabbbaabaaabaabbabbbaabbbbbbbbaabbabaabbabbbaaaababbbbaabbabbbbbaabbbabbabbbaababbabbbbabbbbbbbaabbababbabbbbaaaaaabbaaaabbbabbbbaaabbaaabbbbaaaabbbbbabbaababbabbabababaabbaabaabbbaabbabbababababbbbaabbbbababbabbababbaabbabbabbbaaabaabbabbaabaaaaaaaabaaaababbbaabababaaaababbbaaababaaaabaabbbbbbbaabaabbbabbaaabbaabbbbaaabbaaabbbabbabababaabbaaababbbababaababbbabbabbbbaabbbbbaabbababaaaabaabbbaaaabbababaababbababaaabbbaababbabababbbaaabababbbbbabbabababaaababaaabbaaaabaabbabaabaaaabaabbaaaabaabbabbbbbbbabbaabbabbbbabbbaaababbbbaabaaaaababaabaabbbabababaabbabaaabbbabbbbaaaaaabbaaabbababbbaabaaaabbbbaabbbabbaabbbaaaaabbbabbaababaaaaaabbaaabaaabbbaabbabbabbabbbaaaaaabaababbaababbababbbaaaaabaaababbabbaaaaaabbbbaabbaabababbbbbbbabbbbabaabaaaababbbabbbbbbababbbaabaababbaabbbabbabaabbbabababaaaaababbbabbabbbaaabaaaabbbbabbaaabbabbbabbaaaabbababbabbaaabbabaaabaaaabaaababbaabbbabaabbbbbabaabbabaaabaabbbbbabbbababbbaaaaaaaaabbabbabbbbaabababbbabbaaaaaabbaaabaaabbaabaabbbababbababababbabababbabbabbaaabbbbabaabaabaabaabaabaaabaaaabbbbbaaaaaaabaababbbaaabaababaabaaabaababababbabaabbabbabababbababbabbaabbbbbbbabbbbbbaaaaaaaabbbabaaabaababbabbabbbbbbababbabababbabaaaaabbbbaababaababbaaabababbaabbababababaaaabaababaababbbabaabbbabaabbaababaaaabaabbbbbaabababaabbbbabaababaaabaaabaaaababbbbaabbabaaabbaaabbaaababbabaabbbbbaaaaaababbaabbbaaabaabbaaabbbbbbbbbbabbbaaaabaaabaaaabababbbbabaabaaaabaaababbbbbbaaaabbbbbabbababbaabaabbbbabbbbbabbaabbaaabababbaaabaabaabaaababaabbbbaabbaaabbbbbabbabaaaaaaabababaaabbabbbbbbababaaaaaabbbbabaabaaababbaabbbbaaaabbabbababbabbbaaaabbbabbaabaabbabbbbaaaabaaaaaaabbababbaaaabbbaaaaabaaaaaaaaaabbabaabbaaababaaaababbabaaabaababbbbbabbaaabaaaaabaaabababbaabbbababababbabbaaaaaaabaabababbbbabbbbaabbbbbbbbbabbabaababbbbabbabbbababbabababaabaabaaaaabbbaabbaaabbbaaabbababbbaabbaaababbaabbabbaaabbbbbbbbababbabbababbababbbaababaabbbbabbbbbaabaabbaabaabbbbbaabbbabbbabbbababbabbbbbbabbaabbabbaabbbbbaaaabaabbabbaabbbabababaababbabbbbbaaabbaaaabbabbabababbbababababbaabaabaababaaaabbababbaabaaabababbababbababaaabbaaabbbabaabaababbaabbaabababbaaaabaaabbaaaaaabaababbaabbbababbbbbbbbabbbaabbbbaababababaabbbabbbaaababbabbbaaaabbaaaaabbabaaababaaabaaabbabbbaababbbbbabbaaaaaabbaaaabbbbbbababbbbbbbaabbaaaaababbbbbbbabaaaaaaabbbbbbbabbbaabaaaabaaabbabbabbaaaabaabababaaabaabbbababbababbabbabbabbabbbbaaaaabbbaaababaaaaabbbabaabaaabbbbbababababbbaabbbbbabaaaabbbaabbbaabbabaaabaabbbbabbbabbaabaabbbabaaaababbbbaaabbbbbaababbaaababbaaababbbaababbbbaabbbbabbaaaabbbaaabbbbbbabababbaabbababbaabababaabaabaaaabbbaaaaabbababaaababababaabbbbbbbaabaabaabbbabababbbbbbbbbbaabbaabbbbbbabaaaabbbbaaaaabbbbbbbabbbababaaaababaabaaabaabaabaabaabaabbaabbbbbaabbbbaababaaabababaaaaaabababbbaabbbbbaaababbaabbbbbbabbaaaabbbaaaababaaababaabaabbbbbabbabababbbbabbabaabaaaaaaabbaabbaaabbbabaaabaabbbbbabbbaabaabbababaaabbabababbaabbaaabbbaaaabaaabaabbbbabbabbaaaabbaaaaaabababbbbabaabaaaaabbabbbbabbaaaaaabababaabbbbbbbbbbaabaabbbaaaaababbaaabbbabbbbabaaaaababbababbabbbaabbaaaaaaabababaaabaabbaaaaabbbbaabbbbbbaaaabababbbabbaaaaaaaaabbaababaaaabbbabbaababababaaaabbbbbbaabaababbbbabaababbbbaaabbbbbabaabbabaabbabbabaaaaaaaaabaaabbabbbbaabaaaaabbbaabbabbabbaababbbbabbaaaabababbabbbaaaaaabaabbbababbabaababaabbbaaaaababaaaaabbabbaaaabbbababbbababbbaababaabbabbabababaaaabaabbbbbaaabbbbbabababbbaaabaaabaabbabbaabbaabbbaabbbbababbabbabaaabbbbaabbabbaaaaababbabbaaabbaaaaaaaabbababaaabababababbbbaaaabaababbbbababbaabababbbababaaababbbaaaaababbabbabababbbbbabbbbabaaaabbababbabbbabaaabbabbbabbbababbaababaababaabbbabbbabbaaaabababbababbbabbabbaabaabaaaaababbbaabbabaababbbbababbabbbababaaaaaabbbaaaabbbabaabaaabaaabaabaaaababaaabaabbaaaaaaababaabaabbbabbbabbbaaabbbbbbaaaaabbbaababaabbababaabbbabaaaababbaabaababbbaaaabbbbababbbbbbaaabbbaaabbaaabbbbbbabbaaabbaaabbaaaaaaaabbabbbabaabaaaabbbbbbbababbbbaabaaaababababaaaabbbbaaabbabbaabbaaabaaabbbbaabaabbabaaabaaabbaabaabaabaaaaabbbaabbbbbbaabbbaabbbbabbaaaabbbabaabbababaaabbbbabbabaaabbabaaaabbbbaaaabbbababbbaabbbbbaabbabbaaababaaabbaabaabbbaabbbaababababaaaaababaabbbbbaabbbabbaababbbaababaaabbbaabaaabbbbbbaabbaabbbabbaaababaaaabbaaabaaabaababbbbaabbbbaabaaaabaabbbbabaaabaaaaaabbaababaababaabbabbbbaaabaabababbbabaababbbbbaababaabbaabbbaabababbbababaababbbbaabaabaabbabbabbabbababbbaaaabbaaabababbbaabbbabbabababbbbabbaabbbabaaaabaaaaaabaaaaababbaabbbababaaaaaababbabababbbaabbbbbbbbbaabaaabbbabbaababbbaaabbabbbaabbbabbbbabaaaaaabbbabbabbabbabbababbbbabbaababbabbabbbbaaaabaaaabbbaababbaaaabaabbbabbbabbbaaabbaabababbbbababbbababbaaababbabbaabbbaaabbaaaaababaabaabbaaaabbbabaaabbabbbabaaababababaaabaabbabbaababaaababaaabaaaabbbbbbaababbbabaabbbbbbababbabaabaabbbbbabbabbbbbbaabbaaabaabbbababbbabbabbaaabaaabbabbbabaabaaababbbaaaabaaaaaabbbbababbbabbbabbbaaabbbbabbaaaaabbbaaabbbbbaabbaaabaaaaabbabababbabababbbaaabbaababbabbababbbbbbabbaaabaaabaaababbaabaaaaaaabababaabbababbabbbaabaaaaabaababbaaaababaabbababbbbbbbbabaabbbabaaabbbbbbaaaabaabaabbaabaaaaaaabbbaaabbaaabbaaababaaaabbbbabbbaaabaaaabbbbbaabbababbbaaaababababbababaababbaababbbaaaabababbabaabbbaaaabbaaaabbaaaabbaaaaabababababaaaaabbaabbabbbababbaabaaabaabaaaabbbaabaabbbabbbbaaaabababaaaabbbabaababaaababbbaaaabbbaaaaaabbaaabbaaaabaabbaabaabababaaaaaaaabbabababbabbbbbbaaaaabbaabaaaabbbbabbaabbbbababbaaabbaaababbaaabbbbbaabaabbaababaabababbabbbabaabaabbabbaaabbaaabaaabaabbbbaaabbbaabababaaaaabbabaaababbbababaababbbbabbbbbbbbbbaabbaabbaabaabbbaabaaaaabaaabbbaaaabbaabbbabaabbaaabbbaaaabaaababbaababaababababaabbabbabbaaabaaaabaaabaabbabbaabaabbabbaaabbaaabbbbbbababaabbabbbbaaaabbbbababbbabbaaaabbbbbabaabaabaabbbbabbababbbabbabbbabaabaabaaabbbbbbabbbbbabbaabbaaabbabaaabbbaababbbaabaaabbabaababbaaabbaaaaabbbabbabbaabbbbaaaabbbaaabaababaabbbaaabaaabaabbaabbbaababbabaabababababbbaabaaaabaabbbbaabaabbaabababbbbabaabaababbbaaaaaaabbaaaabbabaabbaabbbabbaabababbaabababbaababbaaabbbaaabbbbbbaababaabbaaabbbaabaabababbbbbababaaabaaaabaaababaaabbbbbbbbaabababbaabbbababaabaaaaabaaaabaabbbabbaabaaaabbbbbaaabaabbbbaaaaabbbaaabbbaabaabbbaababbbabbbabbabaababaababbaaabbaaaaabaabababaaaaabbbbaaabbbbaaabbbbbaaaaaaaabbabbabbbaaabaaababbaaabbaabaaabbabababbaaaaabbabbabaabbababbaababaabbabbabaabbbabbaaabaaaaaabaaabbbababaaaaabaabbbaaabbabbbbababbbbabbaabaaabbaaabaaababbabbbbabbbbaabbbabaabaabbbababaabbbabbababbbaaababbbababbbbbabbabbbaaaaababaabaaabbbbaabbabbbaabaaaabbbbbabbbbbababbabaababaaabababaabbbbbbaabbababaabbbaabaabbbbbaaaaababaaabbaababaaaaaaabaabaaaaabbaaaaabbaaabbbaabbbaaabaaaabaabbbbabaababaabbbababbbbaababaabbbaaaabbbaabaabaabaaabbbbaabaaaaaaaababaaaaaabbababaabaababbaabbaaabbabbabaabaabbabbaabbbbabbbaabbbaabaaabbbbbbbbbaabaabaaabbbabbbaabbbabaabbbbbbbbbbbbbbababababaabbbabbabbbaabbaaabbabbabbabbbbaaababababbbabbbabbababaaabaabbaaaaaabaabaabbaababbaaaaaaaaaaaabaaabbbbabbbbbbbabbaabbbababbababbbbaabaabbbabbaabbabbaabbaabababbabaabaababaababbbaabbababaababbaabaaabbbaabababbaaaaaaaaababbbaababaaabbbaababababbbbbabbababbaaabbbbaaababbaabbabbbaaabbabbaaaabbbababaaababbabbaababbaaaabaaabbbabababbaabbaabbaabbbbbaabbabbbabababbaabbbabaabbbbbaababbabaabbbabbbbabbaabbbbbabbbaaaaababbaabbbbbabbaababbabbaaabaababaabbbbabbabbaabababbbabbbaababbaaabbaaaaaabbabbbbababaaaababaaabaababbbaaaaabaabababbbbbbabababbabbabbaabbbbaabaabaabababbbaabaaabbabbaabababbbbaaaababababbbaaababbbabaabaabbbbbbbababbabbaaaabbbaabbabbaabaabbaabbaabbabbaabbbbaababbbabbbbaaababaaababaaabababababbbabababaaaaababbbbbabababaabbbbaaaaabaabababbaaaabbbaabbaaabababaabbbabbbabbababaaaaababbbbbabaaaabbaaabaaabbbbaaaaabababbaabaabbbbaabbaaabaababbaabbbbbababbbabbaaaababbaaabbababbbaabbbabbbabbbbaabbabbbbabbaaababbababaaabbbbabbbaaababaabaaaaabbbabbbbaaabababbbaabbababbaabbbabbaaabbaaabababaabaabbabaababaaaabbbbabaabababaabbbaaaabaabbbbaabaaaaaababbaabaabbababbaaabaababaabbababbabbbaaabaabbabaaaabbbbababaaaababbaaabababbbaabbbbabbbbbaaababbababaaaaabaaababbbbaaaaaaaaaaaabaaaabbaabaabbbbbaababbabbbabbbbaabbabaabababbbbbbbbbabaaaabababbabbbaabababbaaaabbabaabaabaaababbababbbaaaabbaaabbaaabbbbbaaabaaaaabbaabaabaabbaaabaabbabaaabbaabbabbaabbbbabaabbbabbabbbbbaaababaabbbbaabaabbbabbbbbaabaaabbaabbbbaabbabbababaaabbaaaabbbbbaaabbabbbbaaabbaaababbbabbababbbaaabbbabbbabaababbbaababaabbbbbabbaaaababbaabaabaabaababbaaabbbbbaaaaaaabbabaabbbaaaaaaabbbaabaaaabaaaababbbbbbaaaabaaabbbababbaabaabbbaaabaabbbaaababbbaaaaaabbababbababababbbbbbbaabbaababaabbbbbbbaaababaabbaababbbbbaabaababbbbaaababaaabbabbaaaabaabaaaababbaaaabaabbaabaabbababbaaabbbabbbaabbbaaabbabaaabbbabaabbbbbaaabaaaabbbbbabbbbbbabbbaabbbbaababbaabababbaabbabaaabbabababbabaaaabaabbbaababbababbbbabbabaabaababaabaaababaabbbbabbaaaababbaabbbbababaaabbababaaabababaabbbbababbaabaaabbabbbbaabbbaababbabababaabaabababbbbbbabababaaabbbbababaaaababaababaabaaabaaaababbbaaaaaababbabbbbababbababaaaaabbabbaabbaabaaabbbbabbbbbaaababbabaabbaaabbabbaaaabbbbbabaaaabaaaaababbbaababbbbbabaabbbaaaaaaaaaaabaababbaabbaabaaaababaabbaaaaaaabbbabbabbbaaaabbbbaabbbaaabbbababbabbbbbbaaabbbbabaabaabbbbbbabaaabaababbabbbbaaaabbbbaaaaabbbababbbababbbabaaabbaabbbababaaabaabaaaaaabbabbbaababbbaaaababaaabbbababbbababaaabbbaabaababbaaabbbbbabbabbabbbbbaaabababbbabababbbbbbbaababbbbbbaabbabaaabbaabaaaaaabbaabbababbababbbbbbaaababbbabbbaabaaababbaaabbabbabaabaabaababbaabbbabaabaaaabaabbbbbabbbaababbaaabababbabbbbbabbaababbbaabbabaaaabbbbbababbaabbbbbabaaaaababaaabababababbaabbaaabbbaaaabbabbbabbbbaaabaabbbbbabaaaabaaaabaaaaaabaabaaabaabaaabbaaabbabbaabaaaaaabaabbbbabbaaaaabbabaaaaabababbaaaabbbbaabbbbabbabbbbbbbbaaabaaabbabababababaabbbbbaaababaabaaabbbbbababaaaaababbaababbbbbbabbbabaabaaabbabaababaababbbabbaababaaaabbbabbbbbaaababbaabaaaaaabbabaababaaabbababbaaababbbbbaaabababaaaabbaaaaaaababaabbbbbbbaabbabbabaababababbabababbaaaaabbaabaabaabbababababaababbaaaabbbaabbaaabababbaabababbbabbababbaabbbbbaabbabaaaabbbbbaaaaabbbbbbabaabbbabbbbbaabaabbbaabaabababbaababbbbbaabbbbbbbbbaaaabaaaabaaaaaabbbabaabbaabbbbbbabaabbbbabbbbbbbabbbaabbaabababbbbabbaaabbbaaabbaabbabaabaaabbbbbabaabbaabbbaaabbaababbabbaaaaabaabaabbbabaaaabaaabbaabbaaaaaabaababbbbbaaaaabaaaaaaaabbabababbabbbaaabababaaaabaaaaaaaababaaaabbbaaabbabbbbabbbbbbaaababbbabaaababababbaabaabbbaaabaabbaabaabaabbbbbaaababbaaabbbabbabaaababaababaaaabbbabbbbaaabaabbabbbbabbabbaabbaaaabbbaababbbbbaabaaaababaababbaaabababababbbbaaabaaaaabaabbaaabbabbabbaabbabbaabaaaabbbbbaaababbababbaabbbaabababaaabbbabbbbaabbaabaabbabaaababbbbbabaababaabaaabbaabbaabbaaaaaaabbbabbbabbbbbbbabbbbabbabbababaabbaababbabbbaabbababbbbaaabaabaababbaababaabbabbbaaabbabababbbbabbaabaaaaaabbbbababaabababbabbbbaabbaabbaabaabbabbbaaaabbbabbabaaabbbabbbbaaaaaaaaabaaaaababaaabaaaaaaaaabbbbabaabaababaabababbbbbbabbaabababaabbbbabbbabbabbababaabbaabbbaaabbbbbaaaaaabbaabababaabaabaababaaabaabaababbbbaaabbaaabaaaababbabaaaabbaabaabaabababbaabaabaaaaaabbbbaaababbabbbababaababbabbbabababbbaaabbaabaaaaaabbaaabaaabaaabbabbabbbbbbaabaaabbabbbabababbaaaabbbbbabaaaaaaabbbaaaaaabbabbabbaababababbbbaabbbbabbbabaababaababaaaaabbabaaabaabbbabaababbbababbbbabaaaabbbabbbabaababaababababaaabbaababbababbaaabaaabbbabbbbbabbbbbabaabbababbbbabaabbabbbabaabaababbbabbaabaaabbbbbbbabbbaaaaaabbbbbaaabbbaaabbabbbaaababaaabaababaaabbbabaaabababaaaababaabbbbaabaaaaaabbabaabaaabbbabbabbababababaabaaaaabbaaabbaaabbaabbbaaabbaabaabbaababbaabbaabbaabaaaabbbabbabbbbbabbabaabbaaaaaabababababbabaababbaabbababbbabaaabaaaabbaababbbbabbbabbbbaabbbbbbbaabbbbaabbababbbbbaaababaabbaaababbbaabbbbaaaabbbbbaabbbbaaabaaabaabbabaababaaabaaababababbbbbaaaaabaaabbbbaaabbaabbbbbbbbaabaabbabaaabaabbbaaaabbbaaaaaabbbbbbabaaaaabababbbabaabbabbbabaababababbaaaaaabbbabbabbbbbbabaabbaabbbababbbbbbbbabaababaabbababaaaabbabbbabbaabaaabaabbbabbbaababababbbbbbbbaabbabbabaabbabaaabaabaabaaaaaabaababababbbabaaabbbbabbabaabaaabababaaaaababbababbabbbbaaaaabbbaabaabbabbbbababbaabaaabbbbabaababbbbabbbabbabaaaaabbaaaaababaabbbaabbababbabbbbbaaabababbbbabbbaaabbaaabbabaababbaaaaaabbbbbaaababababbaabaaabbbabaabababbabbabbbbbbaababbbaabbbababbbbaabaabbabbbbabbbbbabbbaaabbaabbbbbabbbaaaaaabbbbbabbabbbaaabbbbbaaabaabbaabbaaaaaabbbabaababababaaaaaabaaabbbbbabaaabaabbbbbbbababababbaabbaaaaaabbbabbbbabaaaabaababaabbabbbbbaaabbbaaaaabbbabbbbbbaaababbabbbabbabaaaaabababaaaaaaababbababababbbaabbababbbaaaababaabbbbbbabaaababababbbbaaaababaaaabbabbaaaababbbbaabbaababababaabaabbabbabbaabaaaabbbbbaaabaaaaaabababbbbabbabbbbaaaabbaaaabbbaabaabbaababaaabbbbbbbbababbbabbaaaaaabbbabbbbbaaaabbababbabaaababaaabbabbaabbaaabaaababbabbbbbbbbaaabbaaabaaaaaabbbbabaaabbbbababbaaaaabbaaaaabbbbbbaaababbbababaabbaaaaabbabbbaabbbaabababbbabbababaaabbabbabbbaabaaababbbbaabbbbbbbbabbbababbababbaaabbbababaababbababababbbabaababbaaababbabbbaaaabbbbabbaaaaaabaaabababaaabaabaabbbbabbabbbbbabbababaabbaabaabababbabbaaabbababaabbbbabaabbbaaabbabababababaaababbbbabbbaabbbaaaababbbbababbbaaabbbaaabaabababbbbaabbbaabbbaaaabaaabbaababbaabaaabababbabbbbbbabbaababbabbbaaaaabbbbaabbabbaabaabaababbabbbbbbaaabbbbbbababbabbbabbaaabbaaaaabbbababbabbbbbaaaabbbbbbbbaaabbbbbaababbaaaaababaaabbabbabbbbaaabbbbaaababaabbababbbabaabaabbabaaabaabaabbbabaabababaabbabaaabbbaaababababbaaaabaabbbabaaabbabbabbbbaabaabbbaaaaabbbbbaabaabbabbabaabaabbaabababababbbabababbababaabaaabbbababbbbaabaabbababaaabbbbbbabbbabbbbaaabbaaaaabbbbaabaabaaabbbaaabbaaaaabababbbaaabbbbaaabbaabbbabaaaabaabaabbaabaabbbaaababbaabababbaaaabaaaabaaabbaababbbbbabbbaabbabbbbaaabbaaabaabbbbabaababbabaaabbabbaaabbabbaaaababaaaabaabaabbabbababbaaaabbbaababbabbababbaababbbabbbbababbaabbbabababbaaaaabbbabababaabbbbaababbabbabaaabbbbbabaaaaaabaaababbbabaaaababbbbabaaabaaaabbbaabbbaaabbabaababbabababbabbabaabaabaaaabbbabbbabbabbaabbabbabbabaaaaaaabbbabbababaaaaababaaaabbaaaababbabaababbaaaaaabbbababbabaaaaaaaabbabaaabaabbaaaabaaaabaabaaaababaaaaabbaaaaaaabaabbbbaaaabaababbabbbbaaababbaaabbaabaabbaaabbaabaabaababbbbaaaaaaaaaabaabaaabbbaababaaabaabbababbabbbbbaaabaababaaabaaaaabbbbaabbabababaaabaababbbbbbbbbbabbabaabaabaabaaaabbabbaaababaaaaaaabbabaaaaababbbbbbaabaaababbabbbbbaaababbbbbbaabbbaabababaababbaaabbbbaaabababbbaaabbaabababbaabbbbaabaaaabaababaaaaababaabbbbababaabbabaaababbbaaaaaaaaaabbbbbabbbbbbbabbaaabbaaaabbbabaaaabaabaaaabbaaaababbbabaaababbbbbbaaabaaabbabbbaabbaaababbabbabbbbbaabbbbbbbaaaaaababababbabbbbaababbbbaaabbbabbababaabaaaaaababaababaabaabbabbaaaabbaabaabbbbbbaabbaaabaaaaaaaabababaaaabaaababaaaaaabbaaabaaabbbabaaabaabbabaaaabbbabbbababbbbabaabbaabbbbababaabaaabbabbbabaaabbbaaaaabababaaaabbbabaababbaabbbabbabbbaaabaaaabaabbabbaabbaaaabbbaababbaaaaaabbbaaaabbaaabaabbbbbbabbbababbbabbbbaaaababbaaaababbbbbaaabbaabbbaaabaaaaababbbababbbbbaaababaababbbbaabbbbbaabaabbabbabbaaabbaaaabbabaaabbbbaababbabbbaaabbaaaaabbbabaabbbabaabbbabbabbbbaabbaabababbaabbbaabbabbbbbbaaabbbabaaaabbaaaaabbbabbaababbbbbaabbbbbaaaaabbbabbababaabababaabaababbabaaabbbaaabbaabbbbbbbabbabaabaaaaabbaabbbabaaaaabbbbbbabbbaaabbbbaaaaabaabaaaaaaaaaabbaaaabbbaababaabababbbabbbabbbaaabbababbaababaabbbbbbababbbabbbbbabaaaababbbaaabbbabbbbabbaaabbbbaaaabbbbbaabbbbaabbababaabbbbbbaabbbbbbabbbabbabbabaabbbbbaabbabbbabaabbbbabbaabbbbbabbabaaabababbbbbbbbaaababbbaabaabaaabbbbaaaabbbababaaaabbbaababaababaabababaabbaabaabbbbbbbaabbaaaaaaaaaaaabbbabaaaaaabaaabbbababbabbbbbbababbbaabbbabbbbbbabaaaababababbbbaaaaababbabbbaabbbbaaabbabaaabbabababbabaaaabbabbbbaabbbbbabbaabbababbaababbaababbbababbaabaaaaaabaaaabbaabbaaabbbbbabbbbaabbbbaabaaabaaabaaaabbabababababaabababaabbaabababaababababaaaaaabbabbabaabaabbbbbbabababbabbbabbababaaaaabbaabaaabbababaaaababbaaababbaabbaabbbbabbaabababbabababaaabbbbbaabaabbbbababaabbbaababbababaaabaabbbbabbaabaabbabbbaabaababbbabbaabbbbbababaababbababbbaaaaaabbbbbaaaaabaabaaaaababbabbbabbabbaabaaaaabaabbbbaaabbabbabbaababbbbbaaaaaabaaaababababbbabbabaabaaababaaabababababaaaaaaaabbabbaaabaaabaabbbaaabbababbaabaaabbabbbbbbbaaabbbaaabbaabaabbabbbaaaaabaabbbaabbaababbabaaabbaaabbaaabbabbbbabbbabbaaaabaaabbabaabbbabaaaaabaaabaaaaaabababaaaabaaabbaabbabbabbbbbbaaabababbbbaabbbaaaaabbaabaababbbabaaabbaabababaaaabaabbabababbbbabaaaaaabbbbaabbababbbbaaababbbaaaabbbabbbbbabaababbaaabbbaabbbaaabbaaaaabbbaaaababaabbaabbbaabbababbbaaabaababaabaababbaabbaaabaabbaaaaaaaaababaabbabaabbabaabbbbabbbbbbbbbbabbbababaaaaabbbbaaababaabbbbaabbababaabaaaababaabbbaaabaabaaababbabbaabaaaabaaaaababbbbabbabbababbbaabaabbbbabaaabaabaaaabababaaababbbaaaaabbaaaaabaaabbabbababababaaaaabbababbabaabbaababaabbaaababbbbbbabbbabbbbbbabbbbbabaaaabaabbabbbaaabbaabbabbabbaaabbaabbabbabbaaabaaabbaabaaabbaabbbabbabbbbbaaaaabbbbabaaaaaabbaabbaaabbbbaabbbabaabbaaaababbabbabbabbbbaaaabbaaabbbaaaaaabbbbaaababbaaaabbababbbbabbaaabababaabbbbbbbaaabaaababaaaabaaabbbbbbbbbabbbbaaabaaabaaaabbbabababaabaabaabbbabbabbbbabbbabbaaabababbabaabbaaabbaaaabbaabbaaababbbbaabaabbabbbaaaabbabaaabbbaaabaaabaaabaaabbabaaabbbabbbabbbaaaabbababaaabbabbbaaabaabbbabaaaaaabbbaaabbbabbbbaaababaabbbbabbbabaabbabbbbaabaabbaaabbbabababaababaabbabbabababbbaababbbbabaaaaabbaaaabbbaababaaaaaabbabaabaaababbaaaaabaabbbbaabbbbabaabbbbabbaabbabababbbaaaaababaaabbabbabbaabbbaabbbbaaaaabbabbababbabbbbbaabaaabbaaababbbabbbabbabbabaaaababaaaaabbbabaabbbabbbabbbaabaabaaabbbbbababbabbaabbbbbabbaaaababbaabbababababbababbaabaababaaaaabbbbbaaabbaaabbabbababbbbaaaaaaaaabbaababaaaaaaababaabbbbabaabbbbbbbaababaabababaaabbabbabaabaabbabaabaaabbbaababbbbbaaaaabbababbaaaabaaabbbbabbbabbabbabaabbaabaaababbbaabbabbabaabbabbabababbabbbaabbababbbbbbababaaaabababbabaaaabbabbbabbbbabbbbbabbabaaaaaababaaaabbbabbbaabaaabbababababbabbaaaababaaaabbaabaabbaaabaaaababbbaabaaaabaaaaabbbabbababaaaabaaabbbbbbabbaabbbbaaaaabbbaaabaabbbababbabaaaabbbbbbabbbaaaabbbabbbbabbaabababbbbbbbabababbabbbabbababababababaaaaabaaabbaaabbbabbbabaabbabbbababaaaabbababbabaaabbbbbababbbbababbbbbaaababbbabaabaababaaabaabbbbaabbbbbaaaaabbabaabbbbaaaaabbabbaabbbaaabbaabaaaaaabaabaaabbbabbabaababbabbbabaaaabaaabbbabaabaaaabbaaaabaaabababbbabbbabaabbbababbabbabaaaaabaabbaabaabaabaabbbbaaaabaabbbaabababbbabaaabaaabbbbbaaabbbaabababaaabbababaaaabaababbababbbaabababbbbbababbaaaababbbbbbabbaaababbbaaabaaababaaaabaababbaabaababbaabbbbbbabbababaaaaaaaabaaaaabbabaabaabbaababbabaaaaabbaaaaababbbbbbaabaaabaaaabbbbbbbbbbbbaabaaaaaababbbababaaaaabbaabbabbaaabbbbabaaabbbababaabbbbbabbaaaabaaaaabababbaaaaababbabaaaabaabaaaababbaabaaaabbaabbababababbaabbbabbbbbaabbbbbbaaaabaababbbbababbaabbbbbabbaababbabaabbaaaaaaabbaaabaabbaaababababaabaaaaaaabaababaabbabbabbabbbbbabbabbbbbbabbbaabaabaabbabbabaaabaaaaabbabababbbaaabbabbabaaaabaaababababababbaabbabbbbaabaababbbbababaaabaabbbaabbbbababbbaabaaababbbbaababbbaaaaaaaabbabbbababbababaababbbabbbababbaaaaaabbabbaabaabaaaaaaaaaabaaaabababbababbbaaabaabbbbbbbbbbbbbabbbbabaabbabaabaabaaabbbbbbaabbaababaabbabbabaaaababbbaababbbbaaabbbabaababbbbabbabbbbbbaaababbabaaababaababaaaaababbaabaaabaaabaabbabbaaababaabaaabbbbbbaaaabababbbbababaaaabbbbbbaabbabaaabaaaabaaababaabbbabbbabaaaaabbbbbabbbabbabbabbabaabaababaaabababaabaabaabbabababbbabababbaababaaaabaabbaabbbbabaaababababaababaababbbbababbabaabaaababaaabbbbbbaaaabaababbbbaabaabaaababbbaaabbbbbabbbabaaabbbaabbbaabaaabababbbababbaababaabbbbbbabbbbabbababaabaaabbbababbbbbaabbbbabbababbaabaaaabaabaabaabbaabbabbbbbbaabaababbbabbbbbbbbbabbabaabbabbbabbaababababbbabbbbbbaaabaabbaaaaaaaabaabbaabbabbaabbaabbabbaaabbbbaaabbaaababaabababbabbbabaaaaababaaaaabbbbbaabaaaabababbbbbaaaababbbbbbbabbbbaaaaaaaaaabbababbaaabbbbbabbbabaabbabaaaabbbbbaaabbbabbabaaababbabbbbababaaabbabbabbabbbabbaaaaabbababbaabbbbabbaabaaababbbbabbbbababbaabbaabbaabbbaabaaaaaabbabbbbbbbaabbbbaaabaaababaaaaabaaabaaaaabbababbabababbaabaabbaabaabaabbbaaababbabbaabbbaaabbbabaaaabbabaabaababbbbaabbabbaabbaaaaabaabbbabbabaabbabbbbbbaabbbbbaaaababbaabbbbbaaaaabbbbbaabaabbbaaabbbbbbababbbaababababaaaaabbabaaaaabbbbbbbaaaaaabbbaabaabbaabaabaaaabbbabaabbaaababbbaababaabbababbaabaabaaaaabababaaabababaaababababbaabbaaabaaaaaaaabbababbbabbabbaaabbbbaaaaaabbabaabbabbabaabaaaabbaaaabbbbbbbbbbabababaabbabbbbbbbbbaaabababbabaaaaaabaabbbbbabbababaaaabbbabaaaababbbbbabbbabaaaaabbaabbaaabaaabbabbabbaabaaababbaaaaaaaabaaaaabbababbbabbabbaaababaabbbbbaaabababaaaabababbbbabbbbbaabbbabbaababbbaabaababbaabbabbbbbbabbbbbbbaabaaabaaabbaabbaaabbaabbabaabbaabaabbbbbaaaaaabbbaabbabbbbbbbaaaabbbababbbaaaaababaaabbbababaabbbbaaaabaaaabaabbbababbaabaaaaaaabaaabaaaaaababbbbbbbaaabbbabaaabbaaaabbabbaabaababbaaaaabbaaabbabbbaabbabbaabaaabababbbabaabaabbbabbaabbaaaabaaaabbabaaabbbbbabaabbbaabbbbbaaaababbabbbaaaabaaaabaaaabbbabaaabbbaababaaabaaabbbbaaabbbabaaabaabaabbbaaabaaabaaabbaabbbabbaabbbbbaaaaabbaabbbaabaaaaabbaaabbbbbaaabbabaabbbbbbbbbbaabbabaabaabbbaabbaabaaabbbbbabbbaaaabbbababbbabababbbabaabbbbbbabaaabbbaaaaababbaababbbbabaaabbbbbbbabbaababaaaabbaaaaabaaabababaabababbbabaabaabbbababaababbabbbbabbabbbaaaaaababbaabbabaabbaabbbaaaabbabbbbbbabbaaaaabaabbaabbbbabbbbaaaabaaaabbbbbbbabaaabbbababbbaaaaaabaabaaaabaaaabaaaabbbbbaaaabbbbabbabaabbabaabbbaaabbbbabbbbbbbbabbbbbbbaabbabaaabababaabababaabaaaaaababaaaababbabaabbbabaaabbbababbbbaaabaabbababbaabaaabaaabaaabaaaaababaaaabbbbabaaabbaabbaabbabbababbbbbaabaababbabaabababbabbababaabaabbababbbabbabbbabaabbaaaabaaabaaabbaababbbaabaabaabbbabbbababbaaabbbbaaaabbbabbbbbabaabbbbababbabbabbababbaababaabaaabaabbbababaaabbbbbabbaabbabbbaabbbbaabbabbaabbbabaabbbaabbbabaaabababbababbabbbaabaabbaaaaaaaaaaabbbbabbaabaaabbbbaaababbabbbbababbbababbabaabaaaaaabbaabbbabbbaabaaabbabbabababaabaaabbbababbaabaabbababbbabbabbaabaabbaaaaabbbaaabaababbaababbababbaaabaaabbbaaaabaabbbaababbbabaaababbaaaaabaaabbbbaaaabbbaaabbbbbabababbaaaaaabbaabaabaababbaaaaababbbbbbbababaaaababbaabbbbababababaababbbbbbbbbbbabbaabbbbbbabaabbbbbabbbbbbaabbaababbbaaababbbbaaaabbbbbabaaaaaaababbabbabbaaabbbabaaabbabbabbabaabbbababaababaababbabaaaaaaaaabababaaababbabbbaaaaababbaabaababaabbababbaaaaaabbaaabbaabbaaaabbaabbbaaaabbaabbbaabbbbbaabababaababaaaabbabaababbbaabbbabbabaababbbaaaaabbbbbbabaabbbaababbaaabbabbbaababbaaaaaabaaaabaaabbaabaaaabbaabbaabaabbbbaaabbbaaabababbbbbbbbabbabaaaabaabbbaabaabbabbbbbbbbbabbbaaabbabbbaabaabbbabababbaabababbbabaabbabaaabbbabaaabbaaabbbaababbaaabaaabbabbbaabbabaaababbbabaaaaabbbabbbabbaabbabbaababbabaaaaaaabaaabababaabaaababbaabbabbbbabbbbababaaabbbaababbbaabbabaaaaabbababaabbbbbbbabaaabbabbabaabababbbbaaabbaaabbbaabaabbabbbabaaaabbbaabaaaaaaaababaaabbbabaaabbbbbaababbaabbabaaaaaabababaabbabbabbabbabbbbbababbbaabbbabaabaaaabaaabbaabaaaabbaaabbbbbaabbabbbbaaaaabaabbaaaababbbabaababaababbbbbbbbbabbaaababbabbabaabaababaaabbabbbbbababbbbbabbaaaaaabbababababbbbabaabbbbabbbbbaabaababbabaabbaaaaabbaabbbaaababbbabbbaaabbbbabbabbbabbbabbbbaaaabbabbabaaabaabbbbaabbabaaabbaaababbababbaaaaaaaabbbababaaaaaabaaaaaaabbbaaabbabaabbaaabaabbbbabbbabaabbabbabbbbbbbabbabbbbaaaabbbabbaabaaaabbbbabbabbbaaaababaababaaabbaabaabaabaaabaaabaaabbbbabababbaabbaabbababbaabaabbaaabbbbabbbabbbbaaabaaaababaaaaabaaaabbaaababbbaaabaabaabbabbbbaababbbaaaaabbbababaaaaabbbbbababbbbabbbbabaaabbaaabaaaabbbaabbbbbbaaaaabbbbbaaababaaaaababaaaaaabbbabaababbbabaaabbaabbababaaabbabaabaabaaabaaaaabbbaabaaabaabababbabaaababaabbaaaabbabaabaaaabaaabbaabbbbabbabaaaabaaaaababaabbbabbbaaabbabbbaabbbabaaabaabbabababbbbabbbbbbbbbbabababbbaabaababbaabaaaabababbbbbbbbaabbabbaabababaaababbababbaababaaaaaabbbabbabaabbabbbabbbabbabbabbbbaabaaaabbaababbabbabaaabbbababaabbbbbabbabbbaabaabbbbbbbbbaabbbabababbaaaabaabaabbaabbbbbaabbababbabaaabaabbbbabbaaaaabaabbbabbaaaaaaaaabbbbabbbaababbbbaaabbbaabbbbbbbbbbbbabbbaabbbaabaaaabbaabbbabbbbaabbaabbaaaabababbbabbabaaabaabbaababbbbbbbabbaabababaabbabaabbbababaaaabbbbbaabbaabbbbbaaaabbabaabababaabbbbabbaaaababbaabbbbabbababbabaaaaaabbaababbaababbabbbbbabbbbaababbbbbaaaaaaaabbbabbaabaabaaaabbaabbaabaaaaabbbaaaaabbbbaaabaabaaaabbbbbbbababababaabbbaabaaabbbaaaaaabbabaababaabbbabbabbbabbaabbbabbaabababbbaaabbaababbbbbaabaaaabaababbbbabaabbbababbbaaaaababaaabbbaabbbbbaabbbbabbabbabababbababababbbbabbbbbababaabbbaabababaaaaabbbaaaabaaabbabbaaabaabbbabaabbbbbabbbbbabaabaabbbababbbaabaabbabbbbabbaaaaaaaaabbabaaaaababbbaabbbaaabbababaaaabbbabaabbbbababaaabbbbbaaabbabaaaabbbbbbaaaababbbabbbbbbababbabbaaaababaaababbabbabaabbabaababbabaabbbababbbbbbabbaabbababababbbbabbabbbaaaababbbbbaabbbababaaababaabbaaaaabbababbbbbabbaaaabbababbbababbabbabbbbabbaaabbaaaababaaaaaababbababbbabaaaaababaabaaabababbaabbbaaababaaababababbaabaaabaaaabbaaaabaabaababbaabbabaababbbaabbbbbbbbaaabbabbbabababbbbabbaabaabbbabbbabbbaabaabaabaabbaabbabbababbbaaaabbababbaababaaaabbbbaabbbbaababbbabbbbbaabbabbbbabbbbbbabbbbaaaaabaabbbbbabbbbbbbbbaababbabaabbbaaabbbbabaabbbabbaaababbbaabbaabbbbabaaaababbbaaabaaaaabaabaaabbbaaabbabbaababbaaabaaaabbabbaababbabbabbaaaabbbabbabbaabbabbbbbabbbaaabbbaabbaabababaabbbbabbbaababaaaabbabaaabaabaabbaaabaaaabbaabbaaaabbaababaabbbaaabbaabbbbabbaaabaabaaababaabbbababbababaaaaabbbbaaabbaabaaabaaaaabaabbabbaaaaaaabaaaaaababbbabaaabbaabbabaabababbabaaabbabbaabbababaaabaabaabbbaaabaaabaabbbaaaaabbaabbabbbababbaaaababaababaabbbababbbbbaabbabbbbbbaabbababbbababbabaaabbbbbaababbbabbaaabababababbabaaabaabaaaaaaabaabaabaabaaaabbabaaababababaabbaaaaababbbabbaaabbababbaabaabbbabbbbbbaaabbababbaabbbababaaabaabaabbaaabbababaabbabbbbbbbabbabbbbbababbbbbaababaaaaabaaaababbbbbbbaababbbbababbbbababaaabbabaababbaabbabbbbaababaabaaaaaaababaababbaababbaabaabbbbbbbaababbbabbbbbbaaaabaaaabbabbbbbbaabbaaaababbbbbaaaaabbbbbaabbababababbaabbbabaabaaabaaaabaabbbbbababbaabaabbaaabbbababaaaabaaabababbbaabbabaabbaabbabaaaaababbabbaaaaabbbbbaabaaaabaababbbbaabbababbbabbabaaaabbbabbbbbbaabaabaaaaaabaabaaaabaabaabaabbbbbabbbaaaaabaabbbaaaaaabaabbbaabbaaaabababaaaaaaaaaabbaaabbbbbbababaabbababbabbbababaaaabaaabaaaababbbaaabaabaababbbababbbbbababbabbbaaaabbaabaabaababbaaaababbaabababaaaababbabaabbbaaaabaaabaababbbababababbbbbbbbbbabaaabbabbbabbbbbabbbababaaaabbbabbabbbbabbaaaabbbbbbbbabaaabaaabbbbabaabbbbabababbaabaaabbababbbababbaabbaabababababaabbbaabbbabaababbababaabaaaaabbaababbbbaabbabbaaaabbbaaaabbbbabbaabbabbababbababbbbbaaaaabaaabaababbaaaaababbaaaabbbbaaabbbaabaaaaabbbbbabbabaaaaababbaabbbabbbabbbababbbaaaababbbbabbabbabaaabaaaaabaababbaaabababbbabbaababbbabbabbbbbbaaaaaaababaaaabbababbaabbbbbbbabbbbbababbaaaaabaabbabaabbbbbaaaabbaabababaaaabbbbabbbbbbabaabbaaaaaabaabbababbbabbabababbabaabaabbabbbaaabaaabbaabbbbbaaabbaaaabbbababbbabbaaabbabbbaabbbababbabbbaabbaabbaaaaabababaaabababbababbabbaababaabbbabbbbababaabaaaabbaaabbbbbababbbbbbaabbbbbbaabbaabbbabababbbbbbbbbaaaaabbbabababbaaabababaaaabbbbbabbababbaaaabbabbaaaabaabbababaababbbbbabaabbbbababaaaabaabbbaabaabbabbbaaaaaabababaaaaaaaabaaaabbbabaaaabbaabbabaaababbbbbabbbbabbaaaaaababaaabbbababbbbabababbaaabbaaaabaaaaabbababbabbaabbabababaaaababbabbaabbababaaabaabbbbbbbbbbbbabaaaaabbbbbabbbaabaabbaaabbababaabbbabaaaababbaabaabbbabaabaabbbabbbbbaaaabbababbbbbbaaaaaabaabababbbbbbaaaababaaabaabaababbbbbaababbbabbbbbaaabbaabababbaaabaabbaaaaabbaaababaabaaaaaaaaababaaaabbbbbbbbaabbbabbaaabababaabbaabbabbbababaabaaabbaaabaabbbaaabbbbbaabaaaabaabbababbaaabbabbabbaaababaabbbbababababbaaabbbbbbbabbbaabaaaababbbbaaabaaababaaaabaabbaabbbabababaababbbbbabbbaaabaabbaaaaabaaaabaaabbbaabbabbbaabbaabbaabbaabaabbbbaabaabbbbababbbbabaaabbaabababbababaabaabbaabababbabbaabababbbaababbaabaababababbbbabaabbaabbbaaababbbbbbaaabaabbbbabaaababaaaaabbaabbbbbabbababaabbbaaabbaaabbabbbbaaabaababbabaaababbabaabaababbbbabbbabaabbaababbbabbbaababaabbaabaabaaababaababbaabbbaabbaabaabbaaaaaaaaabbbaabbbabababbbbabaaaaabbbaababaaaabababaababbaaabbbaaabbbabbabbbabbaaaaababbbbbaabbbbbaabbaabbbabaabaaabaaaabaaababbbaaaaaaaabbaaaaabaabbababaaaaaaaaaabaababbababbaabaaabbbaabbbbaabbaabbaabbbbaabaaaaabbbbbbaaabbabbbbabbabaabbbaababbaabbaaaabbababbabbbaabaaabaaabaaabababbbbbabaaabbabaabaabaaababaababbabbabbbabbbabaaabababbabbabaaababbbbabbbbbababbbabbbbbbabaaabbaabaabbabbbaabbabbaaabbbbaabbaabbbbabaabbaabaaaaaaaaaaaaaaabaaaaabbabbaabbbbabbbbbaabbbbabbababbbbbbabbaabbbbbabbbaabbababbbbaabbababbabbbbaabbbbbbbbbaabbbabaaaaaababaaabbbbababaaababbbababaababaaabaaabbaabbbbbbabaaaabbabaaaaabaaabbaaaaababaaaaaaaabbbbbaaabaabbababbbabbbaaabaabaaabaabbabaaabaabaababbabbbbbbbaababbbabaababbbbbbbaabbbbbbbaabbabbbaabbabbabbabaaaabaabaaabbbabbaababbbbabababaabaaabaaabaabaababababbbbbabaaaabbabbabaabaaabbbbaabaabbbaabbbbaabbbbabababbababaabbbbbababababbbabbbbabbabbabbabaabbaababbabbbaabbabbabbbbabaaababababbbabbabbbabbbbbabbbabbabaaaaabbabaabaaaabbbaabbabbaabbbaabababbbababaabbbababbbaaabbbbbaabababaaabbbaaababababbaabbabbbbbbbbaabbaaabaababbaaabaaaaaaaaaaaabbbaabbababbaabbaaabbaaababababaaaabbaaaaaaabaaabaabbabbabaabbbbaaaaabbaababbaaabbbbaaaabbabaabbabbbbbbbbababbbabaaaabbbbaabbaabaaaabbbabababbbbaabababababaaabaabbabbaabbbababaaabbaaababbbbaabbabbbbbabbaaabbabbbbababaabbaababbbaabbabbbaabbbabbababbbbabaaabaabaababaaaababbbbbbaaaaabaabbabbabbbabaabbaabbabbabbbaaabbbaaaaabbbabababbaaabbaabbaaaaaabababaaabbbababbababbaabbbbababbbbaabbaaaaabbabaaaaaabbbbbaaabababaaabbabbbbbaaaaaaabaabaababababaaababbbbaabbbabaaabbbbaabaaabbabbbbaabbbbabaabaaababaabababababbbbbaabbbbbbaabaaababaabbababbbbaabaaaabbbabbabbabbababbaababbbbaaaaaaabaabbbbbbaababaabbabaaabbbbbabbabaabbbbbbaaaaabbaababbbbabbbaaaabbabaaaababbabaabbababbaabbbabbbbaaabbbbbaaabaaaabbbaabbbaaaabaaabaabaababbbbbbbbbbbbabbbababbbaaababbabaabaabbaabbaabaaaabababbbaabaaabbaabbaabbabaabbaaabbababbaaabaaaaabbaaabababaababaabbabbaaaaabbbbabaabbaabbbababbbbabbaabbbabaabbbabbbabbababbbbbaababbababbbbbaaaabaabbaababbababababaabbbabbbaaababbaaabaabbaabbaaababbaabbaaababbaabababbabbbaabbbaabaabaaababbaabaabbbbabbaabbabbbbbbaababbbbaaabaabbaaaabbbbbaaaabbbabbbababababaaaabbbbaaaaabaaaabaabababaabbaabbaabbaabaabaaababbabbbabbabaaaababaabaaaaaaaaaaabbbbabbbbbaabaabbbabbbababbababbabaaabbaabaaaaababbbabbaaaabaabaabaaabbbaabbabbaabababbaabbaaabaaaabaaabaabaababbaababaaabababbaabbbaabbabbabaaababaaababbbabbaaabbbbabbabbbbbbababbaaaaaaaaaababbabbaaaaabbabbabbbbbbbaaabbbbaabaabaaabbbabbaaabbbbababbbbaaaaabbbaaabbaaabababbaaaaabbababaaaababababbaaabaaaaabaaababaaababbabaaabaabbaaaaabbbbbbaabaababbabbbaaabaaabaabbbabbbaaabbbabbabbbabaabaabbabbbbbaaaaaabbababbabbaabbbaabaaaaaabaabaaaaaababaaabaaabaabaabbaabbaabbbbbaaababbabbabbabbbbababbaabbbaabbabbbaaabababbbbabbbaabbabaaabbaabbbbbbababababaababbbaaabbaabaabaababaabbaaabbabbaaaabbbaababbaaabbabababbabbababbbaabbbabbaababbaaaabbabbbbbabababbabbbabaaaaaaabbabbabaaaabaabbbbbababbbbbbababaabbbbabbaabbaaaabbbbbbbbbbaabbabbbaaaaaaabbbababbabababbbbbbbabaabbabbbaaaaabbbabababbaababababaaabbbababababaaababbbbbbbaaaabbabaabbabbbaabaabbabbaaaaabbabbbaaabbbabbbaabaabbbbbbaaabbaaabaabbababbbbaabaaaababbbaabbaaaaaaaabbaabbabbbbabbaaabaabaababbabbababaaaabaaaababbaabbaabbbbaaabbbabababbabbaaabaabbaaaaabaabaabababbbaaabbabaabababbbbbbbbbabaabaaabbbaaaaababbbbaaabaaaabbbbbbabbbbababbbababbbaaaaaababbaabbabaaaaabbaaaaaabaaabaaabbbbabaaabbbbaaaabbbbababbbbbbbaabaaaaabbababbbaaaabbbbbbbababaaaabaaabbaabbaaabbbaaaaaabaaaabbbbaaabbabababbbbaaaabbbbbbbbabaabbaababbaaaaabbaababbbaaabbbaaaabababbabbbababbababbbbbaaaababbaabaaababbabbaaabaababbbaabbababbbaabbaababaaaabbababaababbababababbaabbbbaaabaabaabbbbbbbaabbbbbbaaabbbbbbabbaabaaabaaaababaabaabbbaaabbabaaaaaaaaaaaabbbbaaababbbabaaaabbbaaaabaaabaabbbbabababbaaaaabbaabbbbaaaaaaaaababbbbbbbbbbbababaabbbbbbbaabaababbabbababbaabbbabaabaabbaaaabbbbabbaaababbbaabbaabbbbbaaabbbbbaababaabaaabaaaaabaaabaabbbbaabbbabaaabaabbabbbabbabbabbbbabbaaabbbbaaaabbbabbabbbbbabbbaaaaababbabbabbabbbbbbbbbaabaabbaabaabbbabaababaabbbaaaabaabaaaababbbaababbbbbbabaababaabbabaabbaabbabbaababbbaaabaaababbaaabbaaabbbaabbaaaabaabbabababaabaabbabbaabbabbbabbababaabbbabbbbaaababbaaabaaabaaaaaaababbabbbaaababaabababbbaaaaaaaabaaabaaabbbbbbabbaaaabababbaabbabaaabbbabbaaabaaabbabaababaaaabaaaaaabbaaabaababaaaabbbaaabbbbaabababbbbbabbabbbaabbababaabbbabaabbbabaabbbaababbbababaaaaabaaaaaaaabbbabbaaabbbbaaaabbbbbaabaabaabbbbaaabbbaabbbbbbaabababbaaaaabbaaaaabaaababbaaabaaabbabbabbbbbbabaabbaaabbaabbaabbaabaaaaaaabbaababbabbaababaababbbbbaaabaabbbabbbbbbbbabbababaaabbabaaabbaaaabbbababbaaababaaabaaaababbaabbbabbabbbbabaabbabbaabaabaabbbbbbbabaabaababaaaabaabaabbbababaabbbaaaabbabaaabbbbbbbabaabbbabaababbbababbaaaababbaaababaaaaaaaaabbbababbabbaaabbababbabbbabbaababbabaaababaabbaaabaabaaaaabaabbaababbabbabbabababaaaabbbabbaabbbaaabababbaabbbabbbbbbbbbbbabaabbabbabbaaababbbbbbaabbbbbbbbbaaaabbbbaaaabbbbababbabbabababaabaaaababaaaaabaabbbbbbbababaaabbbbbabbbbbbbaaaaaaabbbbbaabbabbbabaaaaabbaababaaaaaaabbabaababaabaabbaabbaabbbbaaaabbbabaaaaaaabbbabaababaabbababbabaabbbabbabbaaaaaabaaababbbbaabbbbbbababaabababbbbabbaabbaaaabbbaaababbbaabbbaabaaabaabaabaaaabaabaabbabaaababbabbbabbbabababbaaabbbbbbaaababbbaabaabaababbaaababaabbaabbabbabbabbaaaaaababbaaababbbabaabbaabbbabbbababababbababaaaaaabbabababbbbbababbaaaabbaabbababaaabbabababbbbbaabbbabbbbbababbbbbbbaaaaababbbababaaaabbabababababbaaabbabaababbbaaaaabababbbaabbbababbabbbbbbaabbbbbabbbbbaababbabaaabbaabaabaaabbabaaababbabbbbbaababaaabaababaaabaabbabbaaaaabbaabbabbbabaababbbaabaabbbabbababbbbabbbbbaabbbbabbaaababaababaaabbbbbbaabbbbaaabbbaaaabaabbaaaaaabbbaababaabaabbbabbbbbaaabbbbbababababbabababbaaaabaabaaabbaaaaaababbabaabbababbbbbababbaaabbabbbbaabbbbbabbaaababaabbaabbbababaabbbabbabaababaaabaaaaaaaabaaaaaabbbabababbaabaabbbbbbbabbbaaaabbbbaaaaaaabaababbababbaabaabbbbbbbbbabaabbbbaabbbbababaaaaaabaaabaabababbbbbabbbbbaababbaabbaababbaaaabaabbbbabbbbbabaaababaababbaababababbaabbaabababaaaaaabaabaabaaaabbbbabaaabbbbabbabbaabbabaabaaaaaaaaaabababbabbabaabaaababaaaabaabbababbabbaabbabbbbabbbaabaaaabbbaaaabbbbbababbabbbbbbbaaabbbbbaaabbbabbabbbbbbabbbbaaaabbbababbbbbbbaaabaaabbaaaababaaaaaaaaaaaabbaabbbbbbaaabababbbaaaaaabbbbaababbabbbaaaabaabbaabbabaababbaababaabbaabbbabaaaaabaababbababbbabaaababaaaabbababbaabbbaaabaabbaabbbabaaabbbaabbabbabbaabbaabaabbbbababbaababbaaaaaaaaaaabbabbaabbabaabaaaababaabaaaababbabaabbaaabaaaaaaabbaabbabaababbbbbabababababaaabbbabaabbaabbabbaaaaaabbbbbbaabaabaaabaabaabaaabaaabbaabbabbabaaabaabbabababaabaaaaaaabbbabbaabaaabbbbbbabbbbbbbaaaabaaaaabaaabababbabbbabbababababaabaabababbbababababbaabbababababbbaaaabbbabaaaabaabbaabbabbbbaabbbaababbbabaabbababaabbbaabbbbbabbbaabbabaababaaababbaaababbaabbaaaababbaabbababaaaaaabaaaabbababbbbbbbbaaabaababaabaabbababbbbbabbbaababaabbbbabaaabaabaaababbaaabaaaabaaaaabbaabaabaabbbabababbbbbbabbbbbbaaaaabababbaababbaaabbbbaabbababbbabbbaaaababaaaabaaabbbbaabaabaaaabbababababaababaabaabbabbbbaaaaabbbbaabbaabaabbbaaaaaaababaababbbababbabbababaabbbaabbbbabaababaabbaabbaaabbbaabbabbbbabbbbbaaaaaabbaabababbbbbbababaaaabbaaabbbabaabbaaaaababbaababbbaaaaabbbbabbbaaaaaaabbaabbaabbabaaaabaaabbbaaabbbaababbabaabbbababaabbababbabbaaabbbbbbbbaabbbbaaaaabaabaaababbaaababbabbaaabbbbbbabbbbbbbbabbbaaaaaabaababababaabaababbabaaabaabbabbabaaaaaaabbbbbaaabbabababbaaabbabaabaaabbbabbbaaabbbbbaaabbaababbbaaabbaaababbaaaabbaaaabbbbaababaaaaabbabbabbaabbabaaaaabaabaaaabbbaabaaabaaabbaababbabbbbbabaaabaabbbaabbbaaababbbbaaaabababbabaabbababbabbababaaabbabbbbabbaaabbabbbaaababbababbbababaaaaaaabbbbaabbbaaaabbbbbbabbabaabbbaaaaaaaaabbaabbabbbbbabaabaaabbbabaaaabbbbaaaabbbaaaaaabbaabbbbabaaaababababaabbbaabbabbbbaaabbbbbaaabaababaabbabbaaaabbaaababbbbbaabaabaaaabbbbaaabbbbbaabaabaaabaaaaababbbbbabbbabbaaaabbabaaabaaaaababbaababbbabbbaabbbaabaabbbababaabaaabbbababaabaaaaabaabbbbbaababaabaabbabaaabaabbaabbaaaaababbabaababababbbabaababbababbbbaabbbabaababaababbbbabbaabbbbbabbaaaabbabbaababbbbaababaaaabaaaababaaabbaabaaaabbbbbbaabbaabbbbbbbababbbaaaaabbababbabbbaabbaaabababaabbbababbabbbbbbbbbababbbabbbbbbaaaaaaababaaabbbbabaaabbaababaaaaaaabaaababbabbaaabababbbaaabbaaaaabbababbbbbbbbbabaaaabababaaaabaaaabbbababaaaabaabaaababbababaaabbbbbbbabbaaaaabbbaaababbabbbbbabaababaabbaabaabaabbaaabbaaabbbbbbaaabbbabbbabababbbabbaabaaaaabbaaabaabbabbaaaabababbabababbabbbbabababaaabbbbbaaababbaabaaabbaaaabaaaababbbbbbaabaabaabbabbbbbaabababbbbbbbabababababbbbabbaabbaaaabbbabbaaaabbbbabbbbbbaabbbaaabbbbaaabaabbbbabbbabbbbbaaaabaaababaabaabababbbbabaaaabbbbbbabbabbbbbabbbaaabaaaabbbabaababbbbbabaababaaaaaaaabaabaabbabbaabbbbaaaabbbaabbababaaaaabbabbbbbbbbaababaaabbaaabbbbbaaaabbbbaabbbaaaaaaaabbaaaaabbaabaaaaaabbbabbaababaabaaaaaaabaaabbabbaababbbaaaaabaaaaaaabaabbbaaabbbbaababbaabaabbababababbbbbbabbbbabbbbaabbabaababbbbabbbabbabaaabbbbbbabaabbbabbbbabbaabaabbbababaaabbaaabababbabaaabababbabbbbbabbbaabbbbaaababbaaaaabbabaababbbaaaaaabbabbbbababbaababaabbababbaabbbaabbbaaabababbabaababaababababaabbaaabbbaaaabbbabbabaabaaaaabbaabbabbbaabbabaabababbbababbbabaabaaaaabbbbaabababbbbabbababaaaaaabaabaaabbaabababaababbbaabbbbabaaaaaaabbbababbbbabaabaabbbaaabaaaaaababbaabaaaaaabbbbbabbbabbbbbbbaaabbbbbbaabaabbabbbbaabbaababbaababaaaababaaaababaaabababbabaababbbaabaaaaabaababaabababbababbbbabababaaaabbbbaaaabbbbbaabaaaaaabbabbababaabbaaababbabbbabaabbbbbabababababbbbbaaaabaababbabaaaabbbaababbaabbbabbaababaaaababaaaaabaabbabbabbaaababbbbbbbbbbaabaaaaaaabbabbbbbababaababbaabaabbaaaaaaaabbababbbaaabaabbbabbbaaaaabbbabaaaabaabbbaaaaaaabaabababbabaabababbabbbbabbbbbabbaaaabbbababbbbaabbaaaaabbbaabbaabaaaaabbbbaabbaaaabaababbababaabababaaabaaaabbbaaaaaabbaaaabbbbababbbbbaabbaabbabbaabababbbaaababbbaabbbbbaabaaabbaabbbaaabbbaaaaabaaabbabbbabaaaabaaababaababbaababbaababaabaaabbbbbbbabaabbbababbbaababbabbbabbaaaabbbbbbbabbababbbabbbbbabababbbbaaaabaabaabbbbbababaabbbbbbaaabbaaababbabababbabbaabbaaabaababbbbbbbabbabbbbbbaaababbbbbabbbbbbbababaaaabbaabbbbabababaaabaaaaabaabaabbaaaaaaababbaaabbababbbbbbbaaaaababaabbabaaabaaabaabbbaabbaaabaababbbbababbabaaabbaaaabaaababbbaaabbbbbbaaabbaabbaaabbaaaaaaabbababaaaaabbabaaabbbababaaaaaabbababbbabaaaabaababbbbbabbababaaaaaaabbaabbababbaabbabbbaaababbabaabaaabaaaababbabbbbbaaabbababbaabaabbabbbaabbaaabaabbbabbabbaabaababbbaabbbaaababbaabbbbabbbbbbbbbaaabbbbabbbbabababaabbbbababbaababaaabbabbaaababaaaaaabaaababbaabbbbabbaabbbabaabbbbaaaaabbabababaaaababbabaabbaaaaaabbabababababbaababaabababbaabaabbabaabaaaaaaababbbbabababbbbaaabbbabaabaaabbaaabbbaabbbbbaaabababbbaabaabaabaababaabaaaabababbbaabaabaabbbabaaaaabbaaaaaabbabaabbbbbabaabaababbaaabbabbbbbaaababaaababaabbabaaaababbaabaaaaaaababaabaabaabaaaaabbbaaabbababbbaabbababbbaaaaaabbbabbbabbbabaaaababbabbbbabbbbabbaabaabaaabbbaaabaaaaaaabbbabbbaababbababababbaaabbbbabbbaaaabbabaabbaabbabaaaabbbbbabbabaabbabababaaabababaabbbabbbbaaaabbbababbbbbbbabbbbaabaabbbababbbaabbbaababbbabaaaaaaaabababbaaabaaabbbbbbbbbbaabbaaaaabbbbbbaaaaababbabaaabbabaabbbbbababbabbbbaaaabbaabbbaababbababbbbabaababaababbbaababbbaabaabaaaaaaabbababbabbaaabbbbababaaababaabaabababbabbabababbbbabaaabaaaaaaaababababbbbaabbbbbaaaabaaabaaabbbaababaabbaabbababbaabbaabbbabbababaabbbabbabbabaaabaababbabbaabbabbbbbbabaaaabbabababaababbaaaababbabaaaaabbbabbbbaababbababaababababbbabbbabbababbbbbbbbbbaaaaaaabbbaaabbaabbabbabababbaabbbbabbbbaabbababababaabbbaaaaaababaaabbbabababaabbbbbaabaabbbbbaababbaabbbbbbaabaabbbabbbaababaababbbbabaababbababbaaabbbbbababbbaabbbbabaaaaabaabbabbaaaaabaabaabaabaaababbabbaaaaabaaaabbaabaaabbabbbbabbbabbbbaaaaaaaaaababbbaaaaaaaababbbbaabbaaaabbbabbaaaaabbbabbbbaaababbaaababaaaabaabbbaaaaaaabbaabbbabbbbaabbabbbbaaabaababaabbbaaaababbbaabababbababbabbaaababbbaabababaaabababababbaaabbbaaabbabaabaabaaaaabbbbbabbaaaabaabaaaabbaaabaabaabaaababaabbbbbbbbbbbbaaaaabbbbbbbbbaabbaabbbbbbbabbbaaabbababbbababaaabbaaabaaabababaabaababbbbbbaabbbaaabaaaaaabaaaaababbaababaabbbabbababbaabaaabaaabbababbabbaababbaababbabbaaabbaabbabaabababaaaaaabaabbaabbabaababbbbaaabaabbbbbbabbbabbaaaabbabbabbabbbaabaaabbbaabaabbbabbaaabbbaabaabaaaaaaaaaabaababababbaaabbbbaabbaabaaaabbababbabaababbaabbaaabbaababbbabaaabbbaabbabaabbabaaaabaaabbaabbaabaabbbbabbbabbbaaaabbaabbaabababbaabbbabbaaabababbaabababaabbabaaababaabbabbbbaabbaabbabbbabaababbabbababaaabaaaabbbbbaabaabbbaababbbabaaaabaaababababababaabbabaaabababababbbabbababbbaabbbabbbaababbbbbbabbbbaabbaababbabaaabbbabaabbbbbabaabbabbbaaabaababbababaaaababbbbbababbbaabaabbbbbaabbaababbababaabbbbbbbbbaaabbbbaabbbbaaabbbbbbbaaaaaaabbaabababbbabaaaaaababbbaabababaabbabaaabbabaaaaaaaaaaabbbbbaabbabbaaaababbbbaababbbaabbbbabbbbbabababbabaaaaabbaaabaabbabbbbaaabababbbaabbaaabaabaabbbabaabbaabbbabaaaaaaaabbabaabbbabbbbbabaaabaabaaabaaaaaaabbaabaabbbaabaabaaabbbbababbbbbbbbbbaabbbbaababbaaababbbbbaaaabbbaababbbbbbabbabbaaaabaaabaabbaaaabaaabaaabaaabbabababbaabaaabababbabbbaabbbabaaabbaaabbaabaabbababbbaaababbbbbabbaabbababbbbbaabbbbbbbaabaaabaabbaabbbbaaababbbbaaabaabbbbaabaaaababaababbbbababbbbaaabbaababbbbabbbabbbbbababbbbaaaabbababaababaabaabbbabbaaaabbaababbabaabbaaababbabbabaaaabaaabbbaabaaaabaabbaabbabbbaabbbbbbabbabababbbaabaaabaabbaaaaababaaaababababbbaaabaabbaababaaaabaabbabbabbbbbaaaababbbbbbabbabbbbbaababaabaaaababbbaabaabbbbbabaaabbabbbbabbaabbbaababbbaaaabaaaaababaabbbaabaabaabaabaaaaabbaaabbaabbbabbababaabababbababababaabbaabaaaabbabaaabbbbabbabbbabbaaabababbabaabbabbabaaaabbabbaaaaaaaababaababaaabbabaaaabaaabaaabaabaaabaababbbbaabbbbbbabbbbaaababaabbbabbbabbababbbbbbbabbbabaaaaabbababaabbaabbaaabaabaabaaaabbbbbabbaabbbaababbbbbbaabaabbabababaababbbbaabaabbbaaabbbabaababbbabbbabaababbabbbbbaaaabaabbabaabbababaababaabbbbbbababaababbabbaaaababababaaabbaabbabaabbaaabbababbabababbbababababbaaaabaaabaabaaabaaabbbaaaaaaabbbabbbaaaaaabababbbbabbaabaabaabbbbbaabababbbababbbbaababaabbabbbaabbbbbbbabaaaaababbbabaabbbbabbbaaabaaaabaaaabbabababaaaaaaaaaababbbbbbbaabaabbaaabbaaaababbbaabbbaaababbaaaaaabbababbaabbabbbbaaabbababbabaaabaababababababaabaabaaaabaabaabaababaabbabbabababbbaababaaaaaaaababbbbabbbabbbbbaabbbbaaaaabaababababbbbabbabbabaaaaaababbaabbbababbbabababbaaaabaaaababbbbbbbabbbbabaabbaaaabaabbbabababbabbaabbbaabbaaababbaababaaabbabbbaaaabbbababaaabaababbaabbaabaabbbaabaabbabbbbbbaaaaaabbbbaaabaabbbbababbabaaabaababababaaaabbabbaaabbaabbababbbbbabbbaabbabaabaababbbabbaabbaaaababbbaababaaaabaabaaaabbbbaabaabbbbbababbaabaabaaabaaabbaababababababaabbaabbbaaababbaaabbbaaabbabbabbbaabbbbaaaababbbbabbbaaaaabbbaababbaabbbaabbabbbaabaaaababbabbbbaabaabbbaaababbbbababbabbbbbaabaaaabaaaaabaabababbbbaaabbbbbaaababbaaabbbbbbbbbbbaaaabaababababbbbbbbaaaaababaabbbaaabbababaaabbbaaaabbabbabbbbbaaabaaaaabaaabaaababaaabaaabbbaabbbaababbaaabbbbababaabbbbbbbababbaaaaaabbbbbabbabbaaaaaaabababbbbababbaabbbbbbbbababbaaaabaaaabaaaaabaabbbbabaababbababaabbababaaaabbbbabbbbabbaabbaaabbbbbaaababbbbbbababaaaabababbbabbbbabbaabbbbbbbaabbaaabbabbbbabbbbbbbbaaaabbabaaaaabbaabbaaabbabbbbabbbabaabaabababbaabaabababaabababbbaaabaaaabbabaaababbbaaabaaabbbbbbaabbbbaabbbbabaaabaabaabaabbaaabaababbbaabbbbbabaabbabbbaabbbbbbaabbbbbaabbaaaabababaaaaaabaabbaaaabaaababbbabbababbabaabaabaaabbaaababbaababaaabaaabbbbaabaabbaaaababbabbaaaabbbaaaababbaabaabaababbbaaabbbbbbabbbaabaaabbbbbababaabbaabaababbbaabbbbaaaabbbbaababbaabbabbbbabaabaabaabbabaabaababbbbbbabbbabbaaabbabaabbbaaabaabbbbbbbabaaababbabbbbbbbabbbabaaaabaabbabbbaabaabbaabbbaaaaabbbababababaaaabbbabaaaaaaaababaaabababbbbaabbaabaababbbabababababaababbbbbbbaababbbbababbbaabbaabaaaabbabbbaaababaaaababbaaababbbabbbababbbbaababbbaabbbaababbaabbabbaaabbabbbbbababbaabaaaaababaaaabbaaabaabbabbaaabbbbbbbbaabbbabbabaabbaaaabaaabbbaaabbaabbabbababbaabaaaaabaaababbaabbbbababbabbababbbaaaabbbaaabbababbabbababbabbaaaaabbabbaaabbbbbababbaaaaaaaaaaabbaaaaababaababbbabbababababaababbbababbbaabbaaaaaabbbbabababaaabbaabbaaabbabbaaaaabbabaaaaaaabababbababbbbbaababbaababbaabaababaabaabbaababaaabbababaaababbaaaababaabbaaabbbbabbaabaabbbaaaaaabbbabaababbabbabaabbbbabababbbbaaabaabababbbababbbbababbabaabbabbabbaabbbaaaaabbbbaaaabaabaaabababbbbaaaaababbbababaaaababbbbbabaaaabbbbabbababbaababbbabaaaabbbaabbababbaabbbabaabbabbbabaabbbbbaababbbbabbbbababbbabbbabaaaaaabbbaabababbbaabbabbaaaaaaabbbbbabbbbbaaabaaaababaaaabbaaababbabbababababaabbbababbbaaaaaaabaaababbbabbaaaaababbbabaabaababbbabaaabbabbbbaabbbbbbabbaababbbabaabaaaaabaabbaaaaabbbaaaabbaaababbabaababaabbabbbbbbbabbaabbbaabbabbbabbabbaaaabbbaaabaaaabaabababbbbbbbaaaaaabaabbaababbbababbaabababbaabaaababbababbbbbaabbbbbbbaaababbbababbbaaaaababbbababaaaaabbabababbabbbaabbbaaabaabbbaabbabbabaabaabbbabaaaaaabbabbabbbaaababbababbbbbabaababbababbbbabbababaaaaaababaabbbbbbaababaaababbaaaabbaaaabbabaabbbbaaababaaaaaaabaaabaaaaabaabbaaaaababaaabbaabbabbbaaabbabbabaaaaaabaababaaaaaabababbbbaaaabababbabbbbbbbbaabbbbbbaaaabaaaaababbabababaaaabbbabbaabbbabbbbbbbbbbabbaabbbbaaaabaabbabbaabbbbabbaaaabbabbaabbabaabbaabbbbbbabbbbbbaabbaaababbbaaabbabaaaaababbbbbababababbbbbaabaababababbaaabaaabaabbbababaaaaaabbabbaaabbbbbbbaababaabaabbaaabaaaaaaaaaaabbbbaabbaabbaabaabaaaababbbababbabababbbbaabaaabbaababbabaabbbaaaaaaaabbaabbabbbabaabaaaabbbbabbbbbbbbabbbaaabaaababbaaaaabbaaaaaaababbaabbbbaaabbbbbaabbbbababbababaaababaaaabbbababbbabbbaabbabbaabbbaaabaabbaabababbbbbbabaaaababaaabbabababaaabaabaaaabaaaababbbbaabbaaaabaaaaaaabbaaaabbabbbaababaabbbaabaabbaabbbabbbaaaaaabaaaaabbaabaabbaabbabbbbbbbbbabaaabbbbaababaabababbaaaabababbbabbabbabbbbbabaaababbabaaaaaabaababababbababbbabbbbbbaabbbaabbbbbbbabababbbabbaaaabbababaabaaaabbababaabaaaaaaaaaabbabaababbbaaabbbbaabbabaabababaaaabaaaabbabaabababbbababbaaabbbbbabbbbbbababaabbbaabaabaaabaabababaaaabbabaabbaabaabbabbaaaabbabbbbbbbbbaabaabaabbabbbbaabbababbabababaabaabbababbbbabbaaaabbbbaabbabbabbbbaaabbbabbaababbbbbbbabbbbbaabaaabbaabbabbaaaaabababababaabbabbaababaaabbbabaaaabaabbabbbbababaaababbabbbabababaababaaabaabbbaaababaaabaabbaabbbbbbbbabbbbababababbabbabaabaaaaabbaabbbababbabaaaababbabaaaabbaaaabbabababaaaaabbbbbabbababbaabbabbbaabbbaababbbbbaababbaaabbbbabbbaababaababbaaaabbaaaabbabaabababbabbbaabbbabbbaabbaabbbbaababababaabaaaababbbaaabaabbaabbbbbbbbaabaabababababababbbbaabbaaaaabbbabaabbaabbbbbaaabbbbaaabaaaabaabbaabababbabaabaaaaaabababababbbbbbababbbabaabbaabaababbbaabaaaabaabbabbbaaababaababbaaabaaaabbabababbbbbbbababbbbbbbabababaabbaaaababbabbbbaabaabaabaaabbabbbbabaabbbabaabbabababbbbbabbbbbbababaaaaabbbbbabbaaabbabaaaabbbbabaabbaabbaaabbaaabbbbbabbbbaaabbaaabbaabbbbbaaabbabaaaaaabbaaabbbbaaaaaabbabbbbbaabaaaaabaaaaaaaababbbaabaaaaaaabaabaabbaaabbaabbabbabaaabaabbabaaabbabbbbbbbaaaababbbbaaabababbaabaaaabbbaabbababaabbbbbaaababababbabbabaabaababaabaababbbaaaaabaabaaabbabbaababbaaabababaaaaabbbaaababbababbababbabbbababbbabbbaaaabaabbbaaaaabbabbbbbabbaaabbbbbbbaabbbababbabaaaaabaabaabaaaaabbaaabaababbabbbbbabbabbababaaabbabaaaaaabaaaaabaaabbaaabaaaaabbbbabaababaaabaababbababbbbbbabaaabaabaaabaababbbaabababbbabaabbaaabababaabbababaabbababbaababaaaababbbaaabaaaababbaabaabaabbbaabbaabaaabaabaaababababbaaaaaabbbaabbbbababbabaaabbabbabbbbbbbabbbababababbabaabbaaaabbbaaabaaaababaaabaaababaababbabaaaaaabaabaabbabbaaaaabaaabaabaabbbbaaabbbbbbbabaaabbaabaabbabaaaaabbbbbababbbabbababababbbaababbbaaabbabaabbabaabbbbbabbaabaabbabaaabbbaabbbaabaabbabaaaaabaabbaababababaabbbabbbabbbbaaaababbaaabaaaabbabaaabbbaabaaabababbbabbaabbabbaababbaabbbabaabbbbabbabbbbbbbbbbabbbbaaabababbababbbbaabbaaaabaaaabaabaaabaaaaabbbbbaabbbbabaabaaaabababbababbbbaababaaaababbabababbabbbaabaaabbabaababbbaaaabbababbabbaaabbaabababaabaaababaaabaabababbbabbbaaabbbbaaaaabaaabaaabbbababbbbbaababbbbabbabbaabaaaababbabbbaaababbabaaabbbaaaababababaaabbbbaaabababaaaabbaababbbbabbaaaabaabaabbbabbaaabbaabbabbbbaaababbabbaababaaabaabbabaaababaaaaabbababaabbaabbbabababbabbababaababbabbababbbabbbbabbabbabbabaaaababbaabaabbbbabaaaaababaababaabbababaababaababababbbbbbbbbbaaaaabaaaaaabbbbbabbbbabaaababababbbaabbabbbbaabababbaabaaaaaaabaaabbaaaaabaabbaaaabaabaaaabbabbaabaabaaaaabaaaaabbaaaabbaaababaaababaababaaabaabaabbbabbbaababaaabaabbabaabaaababababaabbbababbbbabbbbbabbaabbaaabaabababaaabbabbaaaaabbababbbabbbbaabaaabaaaabbbbbababbabbbbbabbbbaabbbbbaaabbabaabaababaaabbaabaabbbbbbabbbaaaababaaaaababaabbaabbabbbbaaaaaaababaaaaaaaaaaaababaaaabbbabbaabaaaabaaaaabbabbbbababaabbaaabaaabbaabbabababbbaabbabbbaabaabbaaaaababbbbabbaabbabaabaaaaabaabababaaaaabaaaabbbbbbabbaaaabbabbabaaabbababbbaaaabbbabbabaabaabbbbabaaabaaaaaaabbabaabaabbbaaabbaabbaababaaaabbbbbbbbaabbaabbbbabbbbbbabbaaaaabbbabbbbabbabaaabaaabababaabbbbaaabbaaaabbbbaaaaabaabbabbbbaaaaabbbbabbbabaaaaaaabbbbababababbbbbbababababaaababbababbabababbabbabbaabaababbabbaabababbabaaaaabbbbbabbbbaaaabaaaaaaaaaaaaabbbaabbaaaaabbaababaabbbabbbaaabbabaababbaabbbabbbababbbbaaababbaababbabaaaaaabaaaaaabaaabaaababaabbbbababbbbbbaaaabbbbaababbbabababbbabbbbaabaababbbaabbbaabaabbbbbaabbbabaabbaaabaaaabababbabaaaabbaaaabbbababbbbbbaabbaaaaabaabbbabaabaaababbbbbbbbabbbbbbbababbbaaababbbabbbaabaaaaaaaabbabaaaabbbbbbabbbaaaaabbababaaabaabaaabbaaababaabaabaabbbaabbbabaabaaabbaababbabaaababbbbaaaaaaaabaababaabaababbaabbabaabbabbaaaaabaabaaaaabbbbbaaaabbaabaabbaaaaaabababaaaaabaababbbbbabbbaaababbbaaababbbaaaaababbaaaaaaaaaaababbbabbabbbababbbbbbbbbaaaaaaaaaabbabbbabbbbabbababaabaabbbbbbaaabbbbababbbbaabaaaababababbaaaababbabbbabababaaababbaaabbaaabbaaaaaaabbaabbbbbabbbbabababbabaaabababbaabaaabbbabaaabaabbbaaaabaaaaabbbabababbbaabaaabaaabbbaaaabaaababbbbaabbabbabbaaabaaabbaaabaabbbaabbbbabaabaaaabbababbbabbababbaabbaaabaaabbbaabaabbbbaaaaabbbabaaababbaababbabbaaabbabbaabbabbaabbbaabbabbbbbbabbaababaabbaabbaaaabbabaabaabaabaaaaaaababaaaaabaaaabbabaaaaaaabbabbaaaabaaabababbababaabaabbbbaabbbabaaabbbbaaaabaaaaaaabbaabbabaabababbbabbbbbbaaaabaaabbababbabbbaababaaabaabbaabaaababaababaababbaaabaaabaabbbbabaabbababaabbbbbbbaabbabababababaababbbbaababaababbbbbbbbbbaababaababbabbbbaabbaaabbababbabaababbabaabbabaaaababbabbbaaabbbabaabbaabbaababaaabababaaabbbbabbbabbabbbaabbbabaabaabbabaabbaaabbbabaabababaabbbaaaaaaabaabbbbbbbaaaaaabbaababaaaaaaabbbaababababbaaababbabbbbbaaaaababaaaabaaabbabaaababbbbababbbababbaababaaaabbbbbbaaaababbbabbbbabaaabbbababbabbbabaaabbabbbbbbaabbaabaaaaabbbbbbabbaabbbbbaabababbbbbbabbabaabbbaababbabbabaabbbabaaaaaabbabbbaaaaabaaaabaabaabbbbbbbbabbabbbbbbaabaabaaaababbbabbbabbabaabbabaaaaaabaabaaaabaabbaabaaabababbabaabbabbbbbbbbababbbbababbbbaaaabaaabaababbabbaabbbababbbaabbbaabbabbaabaaaaaaaabaabbabbbbbaababbbbbaabaabbaaaabbbaaaabbbabaabbbbbabbaaaabbbabbbaaabbbaabbababbbbbbbabbaabaaabbabbaaababbaabbbbaaabbaaabbbbbbabaaababbabbbababbabbabbbbaababbababbaaaabaaaababbbaabaabbbabbbbbabbbbbbabbaabbbbaabbabbbbaaaaaababbabbaaaaaabbaabbabbbbabbbbbaabbbbbbabaabaababaababbbbabaaaaaabbabaabaabbaaabaababaaaabababaaabbbbabababbbabbbabbbaabaaaaaabbbbbbabbbaabbbaabbbbbaabbaaaaabbbaaabaaaaabbaabbbaabbbbaababbabababbbbaabaabaaabbaaabbababbbbbbaaababbababbaabaaaaababbbabaaaaababbbbbbbabbaaabbbbbabbaababbaabbabbbabbaaabaaabbabbabbabbababababbbaaaaabaabababbbaabbababbabbbabbbabbabbbaababaaabaaababbaabbabbaaabaabaaaabbbabaabaaaabbbbbaababbbabababaabbbbaaaaaabaabaabaabababbbaaabbbaaaabbbbbbaaaababaabaabaaabbbaabababaabaaabbbbaaaaaaabaababaaababbbbabaaabbabbabaabbabaaaaaabaaaabbbbababbbbbbaaaaaababbaabbaaaababbaababbbabbabaababababaabaaaaabbaabaabababbababbaababbbaabbbbbaabbbababaaaababbbaabbabbaababaaaababaabababbaaaaaabaababbbbbaaabbbaaaabaabbaaaabaaabaabbaaaabbbbbabbbabbaababbbabaababbbabbababaaaaabbabbbbababbabbaabbbaabbbaababbabaaabaabbaabbbaaaabaababbabaaaaaaaababbbaaaababbabbbababaabbbaaaaabbabbbbababaabbbbabababbaaaaaaaabaababbaaabbabbaaabaaabbbabbabbbabbbabababaabbaaaaaabbabbaaaaaabbbbbaaababbbbbababbbbbabaabbababaaabaababbbbaaabaabbaaabbaabaabbbbabbaabbababaaabaaabbabaaabbbbbabbaababbbbabbaaaababbaaabbabbabbabbbbaaaabaabbbaaaaabaaabbaabbaaabbabbaaaaaaaaabbabbaabaaabbaaaaaaababbbbbababaaaaaaabaabbaaabbabbbaabaaababaabbbbbabbbaaaaaabbbbbaabbaabbaaabbbbbbbbaaabbbbbabaabbabbabbbbabbbaabbabbaabbbbbbaabbabbbabbbaabaaabbbabbabbaababbaabaababaabbabbbaaaababaababababbaabbbaabbbabaaabababbbabbabababbbaaabbaabbbabbbbbabbaabaaaabbaaabaaabbaaabbaaababbaabbaabbaabbababbbbabbbbababbabbbbabbaabbabbabababaabbaaabbbabababaaabaaaabbababababbbbbaaabbbbbaabbabbaabbbababbbbababaabbbaabbbaabbbbbbaaaabbbabbbaaaabbbabbaaabbaabbbbaabababaabbbababbbbbbbababbaabbbbbabbaababbbaaabbbaaaababbbababaabaabbbbbbbbaaaabbbaabbbaaaababaabaabbaaabbabbbbabbbaabbbaababbabaabbaaabababbbbaabaaabaabbbbaaaaababaabbaababbabaaabbabbbaabbbbbabbabbaaaabaabbabababbbabbabbbbabbbbbbaabaabbbabbaaaaaaaabbababbbabaabaabbababbaaaababbaababbbaabaababbabbabbaababaaabbabbbbbaabbaababaabbababaaabaaabaabbaaaabbaaabbbaabaaaaaababaaaaabababaabbbbaabaaaababababbabbaabbbbabbbbbbbaabaaabbbabbaaaabbbaabababbabbbbbabbababaaabbbaabaabaabbbbaabbbabbbbbbbaabaaabbbaaaabaaaabaabbabaabbbbabbbbabbabbbbbabbababaaababaaaabbbbbaabbaabababbabbbabbabbbbababbaabbbbbababbbbbbabbbaaaaabbaaabaaaabbaabbbabbaaabbabaaaaaaabbaaaaabbababbbabbaabbbbabbabbbabababbbaaaaaabbabbaaababbbbbabaaaabaaabbabaabaaabaaabbbabababaaabbaaaaabaababbabaababbbbbbaaabaaabbabbbabaabbaabaaaaaabbbbbbabbbbbbabbbbbabbaaaababbaaaababbaabaabaabababbaabababbababbabbaaabababaababaaaabababbaaaaabbbababbbbaabababbbbabbbbabaabbbbbaabaabbaabbbababaababbabbabaaabababbbbabbaaaabbabaabbbbababbbbabbabbabbabbabbabaaaaaabbbbaabbbbbabaaababaaaaababbabbababbbbabababababbabbabaabaaabbabbaaabbaababaabbaaaabbaaaabbbababaabaaabaabaabbaaabaabababbbbaababbaabbbaaaaaaabaabbbabbbabbabbabbabbababbaabbbbabbaababbbbaababbabbbbbabbaababaabbaaaaaabbbbbbabbabbabbbbaaabbbabaabbbabaabbabbaaaaabbbbbaaaaabbaabaabbaababbbbabbababaaaaababbabbbbaabbbbababaaaaaababbaaaaaaabaabbbabbabaaaabaababbababbabbabaabbabaaaabaaaababaabaaaaaaabbbaabaababababbaabbaabaaabbbaababbaabaaabaaaaaabbabbbabbbaaabababbbbbaaabbabababbaaaabbababbbbaabaaabbaabbaaaabbabababbbababaababbabaabbbbbbbbbbbbaaabaaaababaabbabaabbbabbbbbaabbbabaaabbababababaabaabbbaaababbbaaababaaaababbabbbaaabbbaabaaabaabababaabbabbbbbaaababbabaaaaaabbaababbbabbabbbabbaaababbaaababbbbabababbbabbaabbabbbbaaaaaaaabbabbbbaabbbabababbabbaaabaabbaaaabbbbabbabaabbbaabbbbabbbaaabaababbbbaabbabaaaaababbbbbbbbabbabbabaababbbaababbbbababaababbbaaabbaaabbabaaaaaaababbabbabbbbaabbabbaaaaababaaabbabbabbaabbbbbbbbabaaaabbbbbaabbbabaaaabbaabbabbaababbabaababbababbbbababaababbababbbabbaaaabbbabbbaabaaabaabbbbabbbbaaaaabbbbbaabbaabbbaabbbbabaaaaaaababbbbaabbaabbabbbabaaabaabaaabbbabbbbbbabbbbbbbbbaabaaabbbbbbbaaabbaabbbbaaabaaabbbabaabbbababbbaaabaaabbabaabbbbbababbaabbbabbababbbbaaaaaaaabaabaabaaabaaaababaaabbbaaaaabbabababaaaabaabbaaabbabbbbbabbabaaaabaabbbbbbbbbaabbbaaababaaaabaaaaabaaaaaabbaaaabaaabbbabaaababbbabbaabbaabbbaabaaaabaaaaaaaaababaababaabbaababaabaabbbbababababbbababaabbabaabaaaaaabbbbbaabbbaaababababaaaaababaaabbbbbbaabbbbbbaabbbaabbbabaabbbabbaaaabaababaabaabbbbbbabbaaabbbbbbbbabbbababbbabbaaabaaaaaaaaaaabaabbaaabbabaaaababbbaaaabbaababababbbabbbbbabaaabbaaaabbbbabbbabaababbaabbababaaaabbababaabaabaaaaabbaaababaababbbaabaababaabbbaaaaabaaabbbbbbbbbaaabaaaaabbbababbaaaaabbbababaabbbababbbabaabaaabaabbbaabbbbababaaabaaaaaabbaaaaaaaaaaaabbbabbabbbabababbbababababbaaaaabaabbaaaabbbabbbbaabbaaabaabaabababaaababbabbaaaaaabbabaaababababaabbbbaabbbbbabbabbababaaaaabbbbbbabaaaabbababbabbabaaabbbbbbbaabaabbbbabaaabbaababaaabaabbbabbbbbaabaababbabaabaabbababbbabbbaabababaaababbababaabbaabbababbabbbaabbbbabbabbaabbaabbbbbbababbaabaababbaaaabbbaabaaabaaaaaaabbabaaabaabbbaaaaaabbbaaaaaabbbaaababbaabaababaaaaaaaabbbbbaabbaaababbbbabbababbbbababbaaaaaabbbaaaaabaabbaabbabbabaaaaaabbabaabbababbbaaabaababaaaaabbabaaaabbbbbaabbabaabaabaaaabbaabbbbbabbaaaabaaaaaaabbaabbbaabaababbabbbaabbbbbbababbbabbabbbbbbbbbbabbbaabbaaaabbbbabaababababaabbbbbabbbaaabbabbbababbbaaaaaabababbaaabaaabaaaaaaaaaababbbbbbbaaaabbbabbbbaabaabaaababbbabbbbababababbbbaabaabbbabbabaaabaaabbbbababbbbbbabbaabaaabaabaaaaabbbbabbbbaaabbaaabbabababbbabaababbbabbbaaaabaaabbababbbbbabbbabaaaabababbbabaabbbaabaaabaabaaabaabbabababaabaaaabaabaabbaaaabaaaabaabaababaabbaaaabbbabaaaaabaabaabbbbbbbabaabaabbabaaababaababaabbbabaababbaababbaabbaaabbbbaabbaabaabaabbbabbaabbbaaaababababaaaaabaabbbaabbbababaaaaababbbaaababaaababbbaaabaababbabaaabaaababbababaaaabbababbbbaabbbababbbbbaabbbbbbaababaabaabbabaababbbbabbbabbabaaaababbbababbaabbaaaaabaaaabbaabbbababbbbaaabbabbabbbbabbabaaaaaaabbbabbbbabbbbabbaabbababbaaaaabbbbabbbbbbbaabbbaabbbabbaabbabbbaaaaaabbabaaababbaabbbbbbaababbbaaabbabbbbbbbbabaaaaabbabaaaabbabbababaabbaabbaaabbabbbbbababbaaabbbabbbaabaabbbaaaaaaabbbaaababbbabaaababaababababbbabaaaaababbbabbaaaababbbabbaaaabbaabbbbbabaaabbaabaaaabbbabbbabbbabababbbbbaabaaabaaabbaabbbbbbaababbbbabaababbbabbbbaabbabbbbaaababaabbaaababaabbbaaabbbbbabaabbabbbbabbaaaabbbaabbaaabbababbaabbabaaababbaabaaaabababbabbbaaabaababbbaabbbaaaaaabbabbbabbbbbabaabbaaabbbabbbaabaabaababaabbbbaabbbbbbababbbbabbaababaaaabbababbabbaaabbaabbabbbabbbbbbbbabbaaaabbbbabbbbabababbaabaaaaabbabbbbbbaaababbabababbbbaabaaaabaabbabbbaababbabaaabbaaabbaabbaaaababbabbaabbaababaaaabababbabbaaaaaaabbabbbbaabaaabbbbbabbbbaababbababbabbbbbbbbaabbbbabaabaaabaaaaabaaabbaaabbbabbabbaaaababbabaababbbaaaaaaabaabbbbbaaaabbbababbababaabaababbabaabaabbbaaababababbbaaabbaabbbabaaabbbbbaabbbbbabaabbabbbabbaaaaaabbabbbabbaaabbbbaaabaaabbaabaaaababaaabababaabbbaaaabaabbaababaaaaabaabaababbaaabababaaaabaaaaabbbabbbaababbaababbbabbaaababbbbabaaabbbaabaababbaaabbaabbaaaaaababbbaabaaaaababaabababbbbbbababaaabababbbbbbababbaabbbbabbaabbbabaabaaaaaababbbaababbaabbbbbaabbaaabaaabaabbabbbbabaaaabbbbaaabaabaaaaabbbbababbaaabbabaabababaababaabbbbabbbabbbbbbaaababbabaabaaababbbbabaaabbbbbaaabaabbbbaababbbabbbaaabbbabbbbbbbabbbaaaabaabaabbbaabbbaabbaaabbbaabbbbaaabbabaabbbbbbbbbbabbaabaabbabaabaababaabaaabbbbbbaaababbabbaabaaabaaaabbbbbaaaabaabbababaaabbbabaaaaababaaabbbbbaaabbbbaaabaabbbbaaabbbababbbbbabbababaaaabbbaaaaababaabbbaaaababbaaaaabbaaabbabbaabaaabaabaaabbbbaababaabbabbaaabbbabbaaaaaababababababbaabbbbbabbbbababaabababbbabaabbaabbabaaaabbaaabbaaaaaaaaabbbaababbaababbbbaabbaabbbbbbabbaaaabaabbabaaaaababbabaaabaaaaabbaabaabbbbaabbaabbaababbbababaaabbaabaaaaaaaabaaaabbbaabbbbbbabbbabbbabbabababbababbbbbabbbaabaabbbababbabaaabbaabababbaabaaabbababababbabbababaabbbbabbaabaabaaabbabbbaaabaaaabaabaaabbbaaababbabbbaaaaabbaabbbbabaaabbbbabaaabbbbbbbaabbabbabaaabaabbbbbaaaaababaaaaabbbbbabbbaababbaaaaaabbabaabaabbabaaaaababaabababbbababbaabbaaabbaabbbaabaaaabbbabbababababbbbbabbbbabbabaabaaabbaabbabababbbaaaaabbaaabbabaaaaaaaabbbabbababbbbbbbbaababbbaaababbbbababbbbabbabaabbaaaabbbaaabbbbbababaaaababbbbababababbbabbbbbbbabaabbbbabaababbababbabaaaababbaaaabaabbaaabaaababaabbaaabbaaaaabaaaaabaaaababaababaabbbaaabbaaaabbbbbaabaaabaabaabbaababbaabaabbababbbaababababbbbbbbbaabbbababbbbbbaabbbaabaaabbaabbaaaababbbbababbbabbbaababbaaabababaabbababaabbbbbbbaabbabbbbaaabbbaaaaaabaaabbbabaaaabbbaaaabbbababaaabbabaabbbbaaaaaabbbbababaabbbaaabbbbbaabbaabbbababbabbbaabbbbaaaababbbbabbbababbabbbaabaaaaabaababbbabaaabbbbababaababbbaabbbaabbababbbaabababbabaababbbaababbbbaabaaabbbaaaaabbbbabbaabbabaaabbbaaabbbbbaaabbbbaabaabbaaaabbbbaaaabbaabbababbaaabbabbbbaaaabbbaaabaabaaabbbaabababbbabbbabbbababaaaababbbabbabbabbbaabaaababbabbabbbaaaaaabababaabbabaaaaaabaaaaabaaaaaabbbaaabbbbbbbbbbbbbbbbaaaaaababbbbbabbabaabbababaabaabaabbbbaaaaabbabbbabaaaaabbbbabbbaabbabbaaabbbbbababbbaaaababbbbaaaabbaabaabbbaabaabbbbabbbbbaaaaababaaaabbabababababbabaababaaabbbaabbbbbbbbbbabbaaabbbababbababbbbbbaaababababbbaababbaabaabaababbbaabaaabaabbaaababbbaabbbbbbababbbbbaababbbabaababbababbbbabbbbaaabbababbbaabbbbbaabbabbbaabaabaaaabbaaabaaaaabbaabaaaabbaabbaaabbaabbababbabababbbbbabbabaabbabaaaaaabaabbbbbbbbbaabbaaaaabbbaaabbbaabaabbbababababbaaaaaabaabaabababbaaababbabbaaaababbabbbabbbbaaaabbaabbbabbababbbbaabaaaaabbbbaababbbabbaabbabbbbbbabababbbaabaabbaabbbbbaaaabaaabbaababbaabbabababbaaababaaababbbbaabbabbbababbbababbbabbbabbaaaaaaaabbabbbbbaaabaaabbbbbaabbbaabbaabaabbbbbbbbaaababaaaaabaabbbabababbabababbababaabbbbaababaaabbbbbbabababbbabbaaaaaabbbaabaabaababbbbbaaabbbbbabababbabaabbbbbababbbbabaaabbabaababbaabaaabbaaabbaaaaaabaaabbbbaabaababbbbabbbbbababbabbbbaaabaabbbaababaabbaaabbabaaaaaabaabbabbabaaabbbbbbabaabaaaaabaababbbabaabbaaabaabbbbbaabbabbaabbabbabbbbabaaaaaabaaaaababbbaaaabaaaaabbabbbabbabbaaabbbababbbbbaababaabbbbaabbbbaaaabbababbaababbbbbabbbbbabaaaabaaababaaabbbbaabaaaaabbabababbbbbaaabbabbbaaabaaaabbabaaaaabababaaabaabaabbbbaabbbabababbbaababbaababbaaabbbbabaaababaabbabbbaaabbbaaabbbbbababbbabbbabbaabaabbaabbbaabaaaaaabbaabaabbababbabaababbaaaababaababbbbabbbbaabbababaaabaaabbbbbaababbaaabababbbaaabbbbabbaabbbabbbbbabbbabbababbbbaababbbabaaabaaaaaaaaaaabbbbabaabaabbbbbbababaaaaabaaaaaabbabaababbbbabbabbaababbaabaabbbaaaabbbbabaaaababbbaabaabbabbaaaababbaaabaabaabbaaabbbbabaabababbabaababaababaaaaaaaabbabaaabbbaabbbbaababbaababbabaabaaaababaaabababbababaabbaaabbabaaabaabbbbbabaaabababbbaaababbbabbbaababaabbbaabbaabbbaabaababaabbbbabaabbbbabbbbbabbbaababbabaabbaaabbaababbbbaaababababaabbbaaabbaaaaaaababbbbbbbbbaaaaabaabbbbababbbabaabaababbababaabbaabbaabaaaaaaaaaabbbbbbbbabbabbaabbbaabbaaaaabaabababbabbbbaaabbbbbbabaaabbbaabbbbabababababaabbaababbbbbbabbaaaaaaaaababbbaabbbaaaababbaaabbabbaaaabbaaabaaaababbbbababbaaabababbbbabbaaababaaaaaabbaabbbbabbabbbbbaaaaabbabbbabbabaaababaabababaabbbbbabbababbaaaaababbaaaabaaaaaaabbbaabababbaaabbaaaabbbbbaabbbaaaabbababaaabaabbbbaaaaabbbaabbaaababbbabbabaaabaabbaabbabbbbaabbaaaabbbbabbbabbaabaaaabaaaaabbabababbbbbabbbbbabbbababbaabaabbbaabaabbbabbbababababbbbabbababaababbbabbabbbababababaaaabaababbabbbbababbbababaaaababbbabaabbbaaaaabaaaaaaaaaaabbaaabbabbaabaababaabbaaaaaaaabbabbabbbbaabbbaabbbaaaaabaaabbaaababaaabaaaaaaabaababaaaaaaaabbbbbbbbabbabbabbbbaabbaaaaaaabbabbaabaaaabbbbbbaababbbabbbabaaaaaaabaaabbbbbabbaabaababbaaaababaababbababaabbabbbbaabbbbbbbaaababbbaabbbaaabbabaaabaaaaabaabbbbababaababaaababaaaaabaababbbaaaababbaaabaabbbbbbaababaaaabbabbababbbaaababbbaabbbaabbabbababaababbabbbabbaaabaaababaaabbbbababbbabaababbbbbabaaabaaababaabbbababbaababababbabbbbabbaaabbbaaaaaabaababbabaaababbbaabbbbbabbbbbabababbabaaabbbaabbaaabbaabaababbbaabbbaaaabababbababbaababbabababbaababbbaabaabbabbababbbbababbabbbaabbbabaaaabababbabbaabaaabbbbabbabaabbaaabababbaaaaabaaaabaaaabaabbbbbabbbaababbabaaabababaabbbabbbbaabbbaaababaababbaabbaaaaaabbabbbbababbaaaabbbbbbaaaaabbbbaabbaaaaabababbbababbbaabaaababaabbbaaabbabaaaabbbaaabbaabbbbbaabaaabbabaababbaabbabaababbbabbaaaaaabaabbbbaaaabbaababaabbbabbbbbbbaabbbaaabbbababaaaabbaaaabaabbbabaabbaaabbbabaabaaabbbababaabbbabaabbaabbaabbbabaaaabbbbbbaabababaabababbbbaabbbabababbbbaabbbabbaabaaababbaabaabaabbbbbaabbbbbbaaababaabaaaabbbaaaaaabbaabaaaabbbaaaababbbaaaababbbabbbbbbbbaaabbabababbaababbaaabaaaabaabaaaabbbbabaababbaaaabbababbbbbbbaaaaaaabbbbaabaaabbaababbaabbababbbbaabababaabbbababaaaaaaaabbbbbabbaabaaaaabababbaaabaababbbabaabbabaaaaabbbbaaabbbababaaabaaaabaaaaabbbbbbbabbaaabbbaababbabbaaaaababbabaaabbbbaabbaabbbabaabbaababaabaababbabbbabbababbaabbaabbbbbababbbbababbbaaaabbabaaabbbbaabbabaabaabbbabaaaabbabbaababbabbbbbabaaaababababbbbaaababbbbabababbabbbbaaaababaabaabbababaaabaabaaabbabbbbbbbbbbbbabaabbbaabbbbbbabaababbaabbaabbbbbaaabbbbaababbbbbbbbabbbabbabbaabbbbbbabaaaabbbbaaaabbabbaababbababbbbaababbbbbaaaaabaaababababababbaabaababbbaaabaabaaabbbbabaababababaaabaabbaabbbbaaaababbaaaababbabbbabbabbbbaababbabbbaabababbaabbabbbaaaabbabbbaabbaabbbaaaaaaaaaaabbababbbbabaaabbaaaaabaabbbbaabbabbbbababaabbbbbabaabbbababaaaababaaabbbbbbabbabaaabaabbbbbbabaaaaaaaaaababaaabababbbbbaaabaaaaaababaabbbbbabababbbbabbbbabbbbbaaabbbbbababbbaabaabaaababbbabaabaabaaabaaaabababababababbbbbbaaabbbbbabaabaababbbababbbbbbbbbabbabaaabbbababbababbbaaabbaabbabbabbbbbbabbbbbaaabaabaaabababbaababaabaababaaaaababbbbabbaaabbbbbabbbbbbbaababaabbbbabbabababbabaabbbaaabaaababbbababbaababbbabaabaaababababbaaababbbaabbbbbaaaabbbaaabbabbabaaabbabaabbabaabbabaaaaabbbababbaaabaaaaabbbabbabaabbaabbbbbbbbbaabbaababababbaabababbbabababbabaabaaabbbaabbbaaaaaababbababababaaababbbbaaabbbaabbababaababaababbbaabbbbabbbbababababbabbbbababbabbbbaaabbaaabaabaababbbbbabbaaaaabababbaababbbababaaaabbbababaaaaabbbabbbabbababbbbbbbbabbabaabbaabaababaaabbbabbaaabaaaabbbbbabbbabbabbabaaaabbababaaabbbbbabbbaaaabbbbabbbbaabbababaabbbbbbbbbbaaabbbaabbabbaabaaaaabbabbbaabbbaaababbbaabbbbabbabaababbbaabaaabaaabababbbaabbbabaabbabbbabababbababbaabaaababaabaababbabaabbbabbaabaaaabbbabaaabaabbbabababbbaaabbbbababaababbabaabaababbaaaaaaaaababaaaaabbbbbaababbbbbababbababaabaabbbbabbbaaababaaabbababbbbbbabbaaabbbbbbbbababaabbbaaabbaaabbbabaabbbabaabaaabbabbababbbbbbbbabbbabbbbbbbbbabbaaaaaaabbaabbaababaabbababbabbababbbaabaaaaabaabbaabaabaabaaaaabbaababaabbaaaaaabaabaabaabbbabbababbbabaaaaabbbaababbaabaaabaabaabaabbabaabbbbabababaaabbbabbbbbbabbbbbababbabaabbaaaaaaabababaabababababbbaaababbaabaabaabbaabbabbaaabbaabaababbabbaaaabaababbababababababbbaaabaabaaaabbaaabaaaaaabbabaaaababababbbabbbaabaabbabaaaabaaaaabbabbbbaabaaaaaabbbbabbbbaaaaabaababbbbabaaabaaaabababaaabbaabbbababaabbaaababaaabaabaabaaabababaaaabaabbabbabbaaaaababbbabaaabbaaaababababbaababbababbbbaabbabbbbabbaaaaabbababbbbbaaaabbbbaaabaaabaababaaaabbaaaaabbabbbbbabbaaabaababaabababbabaaabbbbabbaaaababbabbbabbabaabbbabaabbbababbababbaababababbbbbabababbbbbbbaabbaaabaaabbbbbaabbbbbabbabbbbaaabbbbbaaaaabbbababbabbbabbaaaabaababbabaabaabaaaabbbaaaaaabbbbaaabbabaaabbbbabaaaabbaaabababaaaabbbbabbabbbaaaaaabbaaababbbaabbbbbabaaaabbabbaaaabbbbaaaabababbabbabbbabbaaaabbbababbaababababaaabbbabbbbaabbbaaabababaaabbbababaaaaaabaaabaaabaabbbaaaababbabaabbbabbbbabbbbbbbababbabbbbbbbbbaabaaaaaabbbabaaababaaaaaaaabbabbbabaababbaaabbbbbaabaaaaaabbbabbababbbbbabaabaabaaaaabbbbbbabbabaaabbaaaaabbbababbababbaaaaaaababbaababbabaaaaababbaababbaaabaabaabaaaaabbbaabbbababababbabbaabbaaaaabaaabbbbababbabbbbabbabaabbaabbabaabbbaabaaabbbaaababbbbaabbbababbaaaabaaaaaabaabababbbabaabbabaabbbbaaabbbaababbbbababaabbaabbbbabaabbababbaaaabbaaababbbaaaaaaababbaabbaaabbababbaabaaabbaaabbabababbaaaabbabbababbaabbbbabbbaababbbbaabbabaaaabbbaaaabbabbbabaababaababbababbabbbabbbbababbaaabbbbbbbbbbabbbabbbbaaaabbabbababbaabbabbaabababaabaabbaaaababbbabaaaabbaaababbbbbabaaaababbabaaaabaabababababaabaabbabbbbaaaabbaaaaaaaaaaabbbaaaaaaaaaaababbbaabbbaaaabaaaabaabaabbabbbabbabbbababbaaaabbabababaabbbbaaaababbabbabaaababbbabbbaabbababbbbaaabaaaabaabaabbabbaabbaaaababbaababbaaaabababbabababbbbbbaaaabababbabaaaaababaaabbbbababaabababbbbbabbabbaabbababaaabaaaababaaabaaabbaaaabbaaabbaaaaabababaababbbaabaabbbaaaaaabbbbabbbabababbbabbbaabbabababbbbbaaabaabaabaabbaababaaabbbababbbbababbbbbabbabbaabaaabbababaaabaaabaabaabababaaabbbaaabbbbbbbbabbbbaabababababaabaabbabababaababbababaaabbbaaaaaaaaabbbaabbaababbbbbabaabbbaabbaabaabaabbbbabbbabaabaaabbbbbbabaaabbbaabaabababaaabbaababbbababaabbaabbbbaabaaaabbaabbbbbabbabbbbbbabbbaaaaabaabbabaaaabaaaabbbabbabbbababbaababaabbaababaabbaababaaaaaaabbbabbbabbaabbbababbaaaaabaabaabaabbbabbaaabbbbbaaabbabbbaaaabbbaaaaabbaabbabbabababbbabbaabbaaabbaaaaababbbbaababbabaabbaababbbbabbaaabbabbaaabaaaaaaabaabbbbabbabaaababaabababbbbbabaabaabaabbbabbbbbbabaaaaaabbbabaabbaaababaabababbaaaaaabbbbbbaaabababababbbbbbaaaaaaababbbabaaababababbbbabbaabbabaaabbaaaaaaabbabababbaaabbaaabababaaabbbabbbabaaaababbbbbbbbbbaaaaaabaababbabbabbabbaabbaabaaaaaaaaabaaaaabbaabbabbabbabbbbbaabbbbbabbbbbabbbbabbbabaaaaaabbaaaabbaababbaabababbaaabbbaababaaabbabaaabbabababaaabbabbaababababbaababbbbaaabbbbabbbbaabaabaabaaaaaaabababababbbbbabaababbbbaabaaaabaaaaaabbbbabaaababbaaabbbabbababbbaabababaababbbbbabbbaaaaabbbaaabbaaabababbabbabbabbaaaabaaabababaaabababbaaabbbabbabbbbbabababbbabbababbbaabaabbabaaabbbaabbaaaaaababbbbabbababaabbababbbbbabbaababbbbabaaabbbababbbabbbbaaaaabaabaaaabaaaaaaaabbbbbaaabbbbabbbaaabaababbbababbbbaaaabaabaaaaabbababbabbaabbbbbbbaaabaaaabbabaabbbbaaaabababbbbbbaaabaaabababaaaaabaabbabaaaaababaabbabbabbabbabaabaaabbabaabaabababbaaabababbbaaaaabbbababaabbaabaaaaaaaabbaaaaabaaabbababaaaaaaababbbaabbbbbabaaabbaababaaaaabaaabbbabaababbbaaaaaaaabbaababbabbbbabbabbbbabbbababbabbabaababbbaaaabbbbbabaaaabbaababbabbbbaaaabbabbaabaabbbbbbbaaaabbbabbbaaabaaaaaabbbaaaaaabbabaabbaaabbbabbbbababbaaaaabbabbbbaaabbabbaabbabaaababbbbabbbababbabbababaabaababaababbaabbbbaaaabbbbbaaaaaaabbbbbbaaaaababbabaabbbabbaabbaabaaaabbaaabaababbabaaaaaabbbbaaabaabbbbbbaaaabaabbbbbaabaaabbbbabbbaabbbabbbabaababaaaabaaaabbbabbabaababaabbbabbaaaaabaaabaaababbabaababbaabbbaaaaababaaabbababbababaabbbbbbbabbaababababaabababababbaaaabbbbbabbbabbaaabbbbaaabbaaaaabaabbababbabaababbbaaaababababbbbbbbbaababbbabbaabaaabbbbbaaaabbbabaabaabaaabababbbaaaabbabaabbaaaababaabaabababaaaabbbaaababbabbbbaabbaaaaaaababbbaaaaaaaaaaaabaaaaabbbbbbaaaabbbbaaabbbbbbbaabbbbaabbababbbbbaaaabbbbaaaabbabaaabbababbabaabbbbbbbabbabbabaaaaaabaaabbaabbbababbaabaabbaaababbbabababbbaababbbbabaabbbabaabaabaabbaaaaabaabaaabbabbabaaaabaaaaababbaabbaaaaaabbbabbbabbbbbbbbbabbbbaabbaaabaabaaabbaabababaabbabbababbaaabbabbabaabbabbabbaabaaababbbbbbababbbaabbbbababbaaaabbbaaababbabbabaaaaabbabaaaaabbbbbbababaaaababaabaababaabaaaaabbaaaaaabbbabaababbaaaaabbabbbaabbbaabaabbbbaababbaaabbaabaaaabbbababababbabababbbbbbaaaaabbabbbababaaaaaabbabbaababbbaaababbbbaaabababaabbabbbabbabbabaabaaabaaabbbbaaaaaabbbbababbababbaaababababbbbbaababbababbbbaabbaabbaababbabbaaababaaabaaaabaaabaabaabbbaaababbbababbababbaabaabaaabbaabbbbaabbaababababbbbbabbaabaabbabababbaaababaabbbabaabaaabaaaaabbbbabbabbbbbbaaaaabaabbbbbbabbaaaabaaababbabbabbaabbaaabbbabaaaaabbaaabbbabbbaabbbbbaabbbabbabbabaabbabbaaaaabbababbabbbabbbabbabbabbaabbaababababaaabbabbbaaabaaabbbaababbabbbbabbaabaabbaaaaababbbbababbaabaaabbbabbbabbababaaaaabaabaaaaababbaaaabaabaabababaaabbbabbbabaaaaaabaaaaababbaabbabbaabbaaabbabbbbbbabbbbaaabbbabaabaababaabbbbbbabbbaaaaaabaaaaabbaaabaaaaabbbbabbabaabaababbbabababbbbbbbbaabaaaaaaaabababbaaabbbbabababbbbabaabbbbbaabbabaaabababbaaaaaaaababbaaaaaaaabbbbbbbaabbbbbbaabababbbababbabbbabbaabbbabbabbabaaaabbbbaaabbbbbbaaaabaabababbabbbabbbbaababbbabbbbabbbabababbbababbbaaabaababbbbbaaabbaaaabaabaaabbbaaababaababaaaabbbbbbbbbabbaaaabaababbbaabaaabaabaabbbbaaaabaaabbabaaaabaaabbaaabbaaaaabbbaabaaabbabaabaabbbababaaabaaabbaaaabaababbbbbbbabaababaaabbabbbbaabababbaaaaabbbbbaababbbbaabaababbaaababaaaababbbabbbaabbabbaabbbbaababbbbababababbbbbabaaaaabbbabaaaabbababababbaabaaabbbbbbbbaababaabbaaabbaaababaabbaaabbbabbbababbabbbabbbbbbbbabbbabaabaababbbaaabababbbbbbaaabbabaaaababbbabbbbabbbabbbaaabaaaabbaaaabbaaababababbbabbababbbbbabaaabbababaaaaabaaaaabbbbabbbaaaabbbbbbbbaaaababbbaabbabbbbbababbaaaabbbbbabbabaabbaaabababaabbaaabbbabbababaabababaaaababbabaaabbbbbbabbbaabbabaaababaaaaaaababaaaabbaaabbbbaababbaabbababbbbaabbaabbbbbabaabaabbbbbababaaaababbabaaabbababbbaabbaababbababbaaaabababbababbababbbbababbbabbaababbababbbabbbbbbbababbaaaaaaabababbbbabbaabbaaababbaaaaabaaababbbbababbababbbaaaaaababbbbbbbbabbaabbaabbaababaabbababbababbaababbbbabbbbbaaabbaaaabbaaaaabbaaaaaaaaabababaaaaababaabbaabaabbbbbaabbbbaaabbbaabbbababababbabaaaabbbaabaabababbaaaaababaaaaaaaabbbbbabaabbbaaaaaaaabaabbbbabbbbbbbaabaaabbaaaabaababbabbaababaabbbababbbaabaaabbbbbbaabbbaabababbbabbabaabbbabbaaaabaabbbabbabaababaaabaabababbbaaaaabaabbbbbaabbbbaabaaabbbbbbaabbbabaabaabababbaaabbbabbabaabababbbbabababbbababaabaabbbbabbbabbabaaaabbbabaaabaabababbaabbbabbbbbbbabbbaababbbabababbaaaaabbaabbaabbaaaaabaaabaaabaaaababaabaaabaaaaaabbaabbbaababbaaabababbbabaabbaaabbaaabbaabbbbabbaabaabbabaabaaababbabab
abbabbabbbbabbabbaabaaabbaaaababbaabaababbaaaaaaaaaababaaababbbaabaababbaaabaabaaaaabbbababbaabaababaabaabaaabaabbbbababbaaaabbbabbbbbbaabaababaabbbabbabbbaabbbbaaababaaabbbaaabaababaabbbabbabaabaaabbaaababbaabbaabbaaaaaaabbaabaabbaabbaaabaaaabbabbbababbbbaaababaaaabbaaaababbbbaaabbbbbababbababababbaabbabbaaabaaababbaaaabababbbbbabbaabbbaabbbbaabbabababaabaaababbbbaaabbabaaaabaaaaabaabbbabbabaaababaabbaabbbbbbaaaaabbbbaababaabbbaabbabbbbbbabaabbbbabbbaaababbbabababbbaaabababbaabaababbbabbbaabbababaabbabbbbbbabbbaabbabababaabababbbaaaabbaaabbabbaabbbbaaaaaabbaaabbabbbababbbbaaabbbabbaaaabbbaabaababababaaabbaabbaaabaaaaaaaaabbabbaabbaaabbabbbbabbbaaaabaaaaaabaaaabaaabbabbbbaabbbbbbaaaabababaabbabaabbabbbbabbabaaaaaaabbababaabaaabbaabbaaaabbababbbbbbaabbabbabbaabaaaaabababaababaababbbaaaaaababbababaabbbbabbaaabbaabbbbbbabbabbaaabbaaabbabababababababbbabbbbaabbaaaaabbabaaaabaabababbaabaabaabbaaaaabbbbbabaaaabaaaaaaaaaabaabbbaaabbbaababaaababbbbaaabbbbbbbaaabbbbabbbbabaaaaabbbaaabaaabbbababbaabbaaabbbabbabbbbabbabbaaaabaaabaaaaabbbabaabaabaaaabbbbabababaabaaabbbbbabbbabbbaaaabaaabbabaaabaabbabbbaabaabbbbbbbaabbabbaaaaaaababbababaaabbbbaaabbabbbbaabbbabbbaabababbabbbbbaabbabbaabbabaabaabbabaaaaabbbbbaababbbbabbaaabaababbbaaaababaabbbbbaabbbaabaaaabbbaabbabaabaaabbbbaabaabbbbbabaaaabbabaababababbaaababbabaaabbbbbabbbbaabbbbbbababaaababaabbbabababbbbaabababbabbbabbbbabbabbbaaaabbabaaaaaaabbababbabbaabbababbbabbbaaabbaaaaaabaabaabbbbabbbbbbbbaabbaababababbaabbbaaabaaaababaaaaabaaababbaaaaababbbabbabbbaaabaaabaabababbaabbbbbabaabbbaaababababababbaabaabbbbabbaabbabbabbbbaababababaaabbabbbaaaababababaababbbabaababbbaabbabbbaaabbaabbbaaabbbabaaabbbabbbabbbaabaaabaaabbaabababbbaababbabbabaababababbbbbbaaabbbaabbabbbaabbabbaaaabbaaabaaabaaabaaaaabbabaabbbbbabbbbbaabaabbbbbabbabaabbbbabbbbbabbaaaaabbabaabababaaabbbababbaabaabaabbaabbbbabababbababbabbbbbbbaabbabaaaabbbabbbbbaabbbbbbaaabbbbbbbbaaabaabbbaabababbbbbbabbbbbbabaabbabbbabbaaaaabbbbabbaaabbabbbbbabbbabbabbaababbaaababbaabbabbbbabaabbabaaabbaaaabaabbaabbbabbbaaabaaababaaabbbbaabaabaabbbbbbbbbabbbaabbbabbaabbaabbbbaaaaabbbbbabaabaabaabaabaaabaaaaaaababbbaaabbabbbbaabbabbbbababbbbbaaababbabbaabaaabbababbbbaababaaabbbbbabbaaaaabbbaaabbaaabaaaaabbaaabbaaaabbabbbbaababaababbaabababbabaaabbaabaaabaaabaaabbabbababaabaaabaabababaaabbbaabaabaabbabbbbbbabbbbaaaabbaaaabaabaabababbbbbaaaabababbbababbaabbaaaaabaaabbababbaabaaaabbbbbabbaabbaaabbabbaabbaabaabbabbbbaabaaababbabbbbbaaaabaaabaababbababbbbbbbaaababbbabababbaababaaaababaaaaaabaababbabbbababaaababaaabbbbabbabbabaaabbbbabbabbaababbabababbaabababbaaaaaabbabbaaabbbbaaababbabababababaaababaababbabbabbaababaabababababbbbabaaaabbbaababaabbbababbabbabbababbbabbabbbaabbbbabaababbbabbbbababbaabbbaaaaaaabaaabaababbabbbbabbaaabbbbbbabaabbaababbbbbbaaabaaabaabbbababaaaaaabaaaaaaabbbbaaaabbbbaabbaaaaabababababaabbbaaabbbbaabaaaaabbaabbbaababbababababbaaaababbbbbabbaaaaabbaaaabbaaabaaaababbbbbabaaabaababbaabbaabbababbaabaabaabbbbbabaabbaababbbaabaabaabaaaaabbbbaabbbaabaaabaabbbbaaaaaabaabbaababaaaababaaababbabbabbababaaaaaabbbaaabbaaaaaabababbabaaabbabaabbbbabaaaaaaaabbbbababbbbbbaaabbbbbabbaaaabbbbaaabaaaaabbaabbaaaaabaaaababbbabaaabbaabababbabababbbbaabbaababbaaabaaaabbaabaaaabbbaaababbbababbaaaaabbbbbbaaaaabaaababbbbbabbbabbbbaabbbaabaaaabbabababababbabababababbaaaabbbbbbbbbbabbabbbabbbbbbbbabaababaabbaaabbababbabaabbababbbaaaabaaabbbbaaabbbabbbbbbaaaaabaabbbbaabbababbaaaaaababbaabbbbbbabbbbaaaaabbaaaabaaabbabbabaaabaabbbbaaaaaabbbbbbbbabbaaabbabbabaabbbaaaabaabaababbaaabaabbaaaabbaaaaabbbaaabbabbbbabbaaababaababbbbbabaababbbbbaaabaabbbbbaabbbbaaaaaabaabaaaabbaabbbaabbaabababaabbbaaaabababbbbbbbaaaaaabbbbaabaaabaaaaaabbaaabaababbabbbabbbbbbaabaaaaaabaaabbbbbbbabbbbbbbaabbabbbaababbabbbbbabaababababbabaaabbbaababbaabaababbabbbbaaabaaabbbbbaabbaabbabbbbaaabbabaababbbbbbababbaabbbaaabbaaaaaabbababbbbbabaaaabbaaabbbaababbbabaaababababaaaaabaaaaabaaaaaaaaababaaabbabbabaabbaaababbabaabaaabbbabbaabbabbabbbabbabbabbbbbaaabbbbaababbbbabaababaaaababaaabbbaabaabbbababaaabbbabaabaabababbbaaaabbababbabbbbbabaaaaabbbabbbababbabbaaabbabbbbbaaaaabbbabbbaaabbbaaabaaabbabbbaabbbaaaaaabbbbabbabbbaabbbbaaaabbbbaaabbababbabaabaaabbaaaaaabaabbabbbabbaaabaabaaabaaabbabbaaaabbbabbbaaabbbabbbaaaabbabbabbaabbbbbbbabaaaaaabbbbaabbbbbaaaababbabbabbbbabaaaabbabbbaabbbbbbabbabaaaaaabbaababbaababbaabbbbbbabbbbabababbbbbbabbaababbbbabbbabaaaaaabbaabaabbabbbaabbabaaaaaabbaaaaababbaaabbababaabbaabbabaabaabababaaaababbbaaaabbbabbbbbaaababbbaabbabbbaaaabbabababaaaaabaaaaabbabbaabaaaaaaabbabbbaabbbaaaabbabbaaabbbaaaabaabbbbabaaabaabaaabbbbaabbbaabaabbbaababaabbbbbbbbabbbbbbbbaaabaaababbaaaaaaaaababbaababbbababbabaabbbbbbaabaababababbabaaaabbbababababaaaaaabbbaababbbbababbbaaababbaaaaabbbbaaabbbabababbbbaaabbaaaabababbaaaaabbbbbbbbbaaaabbbbbaabbabbabbbaaabaabbbabbabaaaabbaabbababbababaabbbbabbbaaaaababaaaaababbbbbaababaaaaaababbabbaaaaaabbbaaabbbbabaabaabaaabaababaabbabaababaabaabaabbbbaabababaaaababaabbbaaababbbabbaabbaabbaabbababababaaabbbbbabaaaabbabbaaaaababaaabaabbabababbabbaabbaaaababbabababaaaababbbbbaaaaaababababbbbbbaaabaabbabbabbaabaabbaaabbabbbbababbbababbbababbabaaabaaababbbbbbbbaaabaaaababaabbbababaaabaabbaabaaaaabbbaabaaaaaaaaabaabbbabaabbbaabaababbbaaaaabbbbabbabbabaababbbbbbbaaabbaaaabbbaaaaaabaabbbbaaaaaaabbbbbbababababbaabbbaaabaaaaaaaaabaabbbbbababbbaabbaaabaaaaaaaaabbabaababbbbaaaabaaaaabbbbaaaababbbbbbaabbaabbabaabbbbabaaaabbababbaaabbbaabbbbbabbaababbbbbbaababaaaabbaaaaaabbbaababbbabbababaabaabbbbabaababbabbbaabbbaaaababaabbbbbaabaabbabaaababbaaaaaaabababaaaaaaabbaaabababbaababbbbbabbbaabbabbabbbabaaabbaabbabaabaabbbaabababbabaaabbaabbaaaabbbbaaaabbaababaabbabaaaaaaaababaabbaabaaabbbbbaababaabbabbabbbbabaaaaabbababaabaabbbbaaaaabbbbbabbaababaabbaaabbabbaabbaaaabbabbabbbbaabbaaaaaaabbaaabaababababbabbbbbbabaabbaabababbbabaabbaaabbbbbaaaababbbbabbababbaabbaabbbbabbbabbbbbababbabbbbaaaabaaaabababbabbababaabbaababbbbbbbbababbaaabaaabaabbbabaabbbaaabbaabaabbabaababbbbabbabbbaababbbababbabbbabaabaabaabaabaabaaaabaaababbaabbbaabbaaaabbbaaaaabaababababaabababaabaabbbaaabbbaaaaabbbaaabbabaabbbbbbaaaabaababbabbaaababbaabaaabbbbaaaababbaaaabaaabbaabaabbaaababbbbababbabbabaaabbaabbaabbbbbbaabaabaababaaabbbaaaabaaaabbabbabaaabbbaabbbabaabaababbbbaabbaaabbbbabbbbbbaabaaaabbabaaaaabaaaabaaaaaabaabbbaaaaabbaaabbaaabbaabbabababbaaaabbbbbabaabbbaaaabbababaaabbbabababababaababbbababbabbaabbaabaaababbaaaababbbaabbabaaabbababaaaabaababbbbaaabaabbaaabbbbbabbabbbbbaaabaaaababaabbaabbbaabbababaababbaaabbbbbabaaaabbbbaabbababbbabbbbaaaaaaabaaabbabababbbaaaabaaaaabbabbaaaabaabbbaababbabbababbaabababaaababbababababaaaabbababaababbaaababaaabbabbabbabaabbaaaaaabbabbababbbbbbaaaabbabbbabababbaabbaaabbabbbaaaaababaabababaaabbbababbaababababbaababbaaaaababaabbbbabababbbbbbbbbabbabaaabbaaaababbbaabbababbabababbabbbbabbaababbaabaaabbaaaaabbbbaabbbbbabaabbbaabaabaabbaaababbbbaababaababbbaaabbbaababbbbabbabaababaabaaaaaaaaaaaabaabbbababaaaaaabaaabaaabaaaababbabbbaaabbaabbbbbaaaababbbbbbbbabbaababbbababbbababababbbaaaaaaababbbaabaabaaabaabbbabbbbbababaabbbabbaabbbaabbaabbaaaaaababbaabaabaaabbbabbbabbabaaabbaaaaaabaaaaabbbaaaaaabbbbabbabbaaabbbbabbbbbbabaaabbaaabbaabbaaaaabaabbaabbbbaaaaaabbabbbbabbaaaabbbaabaabbbbaaaaaaabbbabbabababbbbaaabbbabbbabbbabbbbaaaabbbbabbbbbaabbababbaabaaababbbbaabbbbaaabaaabaaabbaabbaabbbbbbbbbbabbbbbbabbaabbbbbbaabbbabaaaabbbabbabaabbabbbbbaaaabaaaabaabaaabaaaabbabbbbabbaabbababaaabbabbbaaabbabbaabbaaabaababbaaaabaaaabaabbababbaabaaabbbbbbbbaaaababbbbbabbbbaabbaabbbbabaaababbababaabbbaaaaababbaaabaabaabaaaabaabbbabababbaaaaabaaabaabbabbbaabaabaabbaaaabbabaabaabbaaaabbbbabbaaabaaaababbaababaabababbabbbbbababbbbbababbbbbbabbabbaabbbabbbbaaabbbbbbbbaaabbaaaaabbbbbbbbbbbabbbbaaabbbbbaaabbbabbbaabbbbbbaabbbabaaaaabbbaaaabbabbaabbbbbbaababaabbbaabbbbaabbaaabbaababbabababaabbababbbbabbaababaabaabbbabbababbaababbbaabbaabababbbabbbaaaaaaabbbababbabaaabbababbbbabaabaabbaaabbbbbaaabaabbbaaaabaaaaaaaabbaaaabbaabababbabbbbbababbabaabbabbbaaababbbababbbbbabaabaaaabbbaaababbbbaaaaababaabaaabaaabaabaabaaababbbaaabbaabbaabaabaababbaababaabaaaabbabbbaababbbbababbbbbbabababaaaaaababbaaaababbabaaababbaababbaaabbababbbbbbabbbbbbabababaaaaabaaabaabbabababbbbbbbababbabbbbbabbbbbbbbbaabaabbbabbaaabaabbbbabbabbaaabbbaabaababaaababaabbababbbbaaababababbaabaaaaabbabbababbbabbbbbabaaabaaaaaabbabbbaaaaaaabababaababaabababbabaaaaabbbbabbbbaabaabbbbaabbabaabbbbaababbaabaaaaaababbababaababaaaaaabbbabaabaaaabaababaabaaabaaaabaaaababbbaaababbbabbababbabaabaaabababbbaaabaabbaabbababbaaaababbbbaaabbbabbbbababbbbbbbaababababbabaabaaabbaaaabbbbabaabbbbabbaaaabbaaaabbbababaaaaaaabbbabaababbbabaaabaaaaabaabbababbbbbbbbabbabbbaaabababbabababbabababaabaabbbaabaabbbbabbbababaababbabbbababbbabbabbaabaaaabbaabbabbaabaababbbbabaabbaabbaaababbbabbaaaaaabbaaabbabbbaaaaababbaaaaabbabbbaaaabbabaaaaaabbaabbaabbbabbbaabaabbbbbaaabaabaabababaabbbbbbbbaabaaaabbbbaaaaaabaaaaaababbbabbaabaabaabbaabaabaaaabbbabbababbbabaabbaabaaababbbbaabbabbaabababaabaaaabbabababbbbbabbaabbabaaababaababbaaabbbbbbbaaaabbabababaabbbbbbbababaabbbaaabbbbbabaaaaabbbbbababaababbaaabbabbaaababbaabababaabbbabaabbbabaaabbaaabaabaabaabbbaaabbabbaaabbaababbabaaabaaaabbabbbbbbaaabaabaabababbababbbbbabbbababaabbbbabbbbaaabababbbbabaaabbbaaabbbaabbbbaabbbabaaaabaabaaabbbabbbabababbabbabbabbbbabbabbaabbbaaaabbaaabbabbabbbbbbabbaaaaaababbaababbbaabbbbbbbababbbaabbabaabababaaaaabbabbaaaaaaaabbbbbabbbbbbabaaabbaabbaababbbabbaababbbaaababaaaabbbaaaababbbbaaabaaabaababaaaabbababbbbaaaabbaaaaababaaaaababaaaabaababbaabaabbbaaababbbabbaabaaaaaabbbaabbbbabbabbaaabbbababaabbbbabaaabbbbabaaabbbbbbaabbababbaabbbaabbbaabbbbaabbababbaaaaabbbbbabababbabbaaababbbaaabababbbbaabaaabbbabbabbaaabbabbbbbbabbabaabbabaabaabbabbbaaabbbbaaaaaaaaababababbabaabaababbbaababbaabbabbbbaaaabbbaabbaaaaabbaaabbabaabbbaaabbababbabbaabbbbbbababbabbaaabbbbbbbbabbabbaaaaabbbbbaaabbaaaabbbaabababbabbbbabbbbaaaaabbabbaabbbbbbabaaaaaaabbbbabbabababababbabababbbbbbababaaaabbababbbabbabbbaababbaababaaabbababababaabbbabbbabbbaaaababaaabaaababbbaaabbbababbabbbbbbbbaabbaaabbaabbabaabaaaaabbbabbbbaaabbabbaabababaaababbbabaaabbabbababaabbbabbbababbbabaaaaaaaaaaabaaababbabaaaaaabbaababbabbbbaaaaaabaabbbbbaabaaaaaabbbbaaabbaabababbbaaaabaababbabbaaaabaaabaababaabaaaabbabbbaabbbaaabbbbbabbaabaaaabbbbabbbbaabaabaaaaabbabbabaabbbbbaabaaaababaababbabaabaabbbbbbbbbaaaababaabbabbbababaabaabababbbbaaaaabaaabbababbbbabbbabbbbabababaaabbbaabbabbbaabbbaaabaabbabbbbbbbbbbbbbbabaababababaaaabbaabaababbabaaaababaabbaabababbbaaaaabbaabaaaaabbbbababbbbaababaaabbaaabbbbaabbaaababbaaaababaaaabbbabaabbbbabaaabbabaabbbbaabbbbaababbbbbbbabbbababbaaaabbbbabbbbabaabbbbbaaaaaaaabbaabbbaaabbbbabababbbbaaabbaaaabbaabbabababaababaaaabaabaaababbbaabbbabaabbabaaababbbaabbaabbabababababaabaabaabbaaabaababbabababaaabababbabbbbaaaaabaaaabaababbaabbbaaaababaaabbabaabaabbabbbbabbbabbabaababbabaaaababbbaaaabababaaaabaaaabbbabaabbbbaaabbbaabaaababbbbbbaaaabaaaaababaabbbbbabbababbaaaabaabbaaaaaaabaabbbaaabbbbbaaabbaaaaaabbaababbbabaaaaaaabbbababbbabaaabbbbbbaabaabbaabbabbabbbababbbaabbbbbaabbabbabbabbbabbbbbabababaabababbbabaaabababbbbaabbbabbabbaaaaaaaaaabbabaaaaaaabbaaabbabaabbbabbaabbbbbabababababbaaaabaabababbabbaabaabbabbabbaaaaabbabaaabbbbaabbbaabbaabbbbaaaabbabbbbaabbababbabaaababaaababbaaabbabbbbbbabbabaaaabbbababbababbabbaabababbbbbbabbbaabbabaabaaabbbbaababaaabbbbbaaababababaaabababaababbababaaaaaabbaabbaabaabbbabbbaabbaaabbaabaabbabaaababbabbaaaaabbabbbbabaabaabaabababbbbbbaabbbabbaabbbaaabbbbaababaabaababbbabaaabbbabbaabaabaaabbaaaaaaabbbaabbbabbabbaaabbaaaaabbabaaabababababbbbaaaabbbbbabbbbbabababbbbabaabbbbbbbbaaaabaaabaabbabbbbababaabaabababbbbbabbbaaaabbabaaabbaaabaabaaabbbabaaaaaababbbabbbbbbaaabbbbababbababaaaababbbbaabaaabaabbaabbbabbbbbbbabbaaaabaaaabbabbbabbbabbbaabbbabaaaabbabbbbabaabbabbaabbbbaabbabbbbbbbbabaababbabbbabbbabbbabaabbaabaabababbaaababbabbbaabbbbabababbbbbbaabbbbaaabaabaababbaabbbbabaaabbaaabbaabbbaaaabbbaaaaabbabbbabbaababbbaabbaaabaabbbabaababaaaaabbabbaabbbbabababbbabaaaaaaabbbabaabbbbbbaaabaabaaabbaaabaabbbbbabbbaabbbbbabaaabaabaabbabbbabbbababaaabbabbbbaabaabaaabbbabbbbbabbbaaaabbabbbbbaaaabbbbbbabbababbbababbbbabbababaababaaabbbabaaaabaabbbaabaaaabbbbaaaabaaabbabbabbbbbaaaaabababaabbbbbbbbabbabaaaabbbabababbbabaabbaaabbaaaaababbbaabababaaabbbbbaaabbbbabbbbbbaaaabababaababbabbabababaaababbaaaaababbbbabbaabbbaabababbbbabbbbbbbbbaabbaabbbababaabaaaabababbabbbbababbbbaabaabaabbbbabaaaaabaaabbabbabbaabbaabbbbaaaaaabbaabbaaababaaaababaaaabbbabababbbbbbabbaaabaaabbaabaaaaaaababbbabaabaabbaaabababbaabaabbabbabbbaabaabbabaaaaabbbbababbabbbbbabababaababbabbbaaabaaababababbaabaabaabbbbabaabaaaaabbbbabaaabbbbabbbbabbaaaababbaaaabbabbaaabbababaabbbbbaaabbbbbaababbbababaaaabbaaaabaaabbaaababbbbbbbbabbaabaaabbabbbbbaabaaabbbaaaabaaaaabbbabbbbbaaabaababbabbaabbbabaababaaaabbabbabbbbaaabbaababaababbaaabaabbabbabbaaabbbababbbabbaaaaaabbaaabbbbaabbaaaaababbabaaaaabbabaabbabaaababbaabaaabaaababaaaaabaabbbabbbabbbbbbaaaabbbbabbbaabbaababaabbaaabaabbbaaababbbbbbabbababbaabbabaabbbbaabbbbaabbaaabbabaabbbbbbbaaaabbbabbaaaabaaabaabaabbbbabaababbaaaabbbbbbaabbababaaaaabaabaaabbabaababababbabbbbababbaabbbabaaabaaaababaabbbabaaabaaaaaabbbbbabbbbbbabbbbaabbaabbaababbbaaabababaaabbaaabbbbaabbbbbbababbabbbbbaaaaabbbbaabbaabbbabbababaaaaabbabbbabbabbabbbbabbbbbbbababbabbbbbababbaaaabbaaababbbbabbbabbbbbaaababbabbbbbbbbabbbabbaabbaabaabbbbaabaababaaabaaabbaabbaaabaaabaabbbabbbabababbbabbbabbbbabbaaababbbabbbbbaaabbababbbbaaaaabaaabaaababaababbabbaaabaaabaabbaabaaabaababbbabbaababbaaaaaaaaaabbbbbaabbaabbbbbbbbbabababbaaaabbaaaaaaaabaaaabbbbbbaaabbaaabbbbabbbbabaaabbaaabaabbbbbababaaababaabaababbbbbbbabbaababbbaabbaaababaaabaabaabbababbbbaaaabbaabbbbaabbabbbbababbaabaaaaabaabaaabababbbaabaaabbaaabaabaaaabbaabaabbbabaabbbaabbabaabbbbbbbbaabbbabaaaabbaabbaaabaabbbaaaabababaabbbbaaaaabbaaabaaaaabaaabbbbbababbaabaaaabbbbaaaaaaabababbbbaaabaababbbbabbbbaaabaaabbbaabbaabaabbbabbabbabbbbaabbbbbabbbabaababaabbaabbaababaaabaaaaabbbbbabbabaabaabbabbbbaabbabaaabbbbaaababaababbabbbbabbaaabbbbabaabaaabbbbbaaaaabbabbbbabbaababbababbaabbaaaaaaaabbbbaababaaaaababaabbabbaaaababbbaabaaaaaaaabaaabbababbbbbbbbaaabbaabbabbaabbababaabbbaabaaaabbabbabaababaabaaabbababaaabbbbaaabbbbabaaaabbbbbbaaaababbbbbaaabababaabbbbbbbbabbaaabbaaabaabbabbbababbbbabaaabaaabbaabaaabaabbbbbbabbbababbbbbaabaaabaaaaabbbbabababaababbabbbbbababbbabaaaaaaaabbbbabababbbbaaabbbbaaaababaabbbbaabbbbabbbaaaaabaababaaabbbaabbbabbbbbbbaababbbabbbbbabbbabbbbbbbbbbaabaabbabbabababaabbbaaabaabbabbabbbaaabaaaaaabbbbaabaaabaabbbbaabbaabbaabbbbbaabbaaabaababbbaababababababbbabaabbabbabbbbbabbbbbbbabaaaabbbaaaabbbabaaaabbaaaaaabbbbabaaabaabbabbbbbaaaabaabaabaabbbaabbaaaabbabbaaabbabbabbabbbbbbbbbaaabbaaabbbaababaaabbbbbaaaaabababbbbbaaabbabbbabbaaaabbbaabaabbbbaaaabbbabaaababababaaabbabbaababbaaaaaabbbbbbbababbbabbabbaaabbbaabaaababbaaaabbbabbbaaababbbaabaabababbbabbbbbaaabbbabbababbabaabbbbbababbabbabbbabbbbbbbbaaaabaaabbaabbabaaaaaaababaabaabaaaaaabaabaaababaaaaabbaaaaababaaabaaaabaabaabbbabbabbbabbbbaaabaaaaabbbabbaaabaaabbababaababbbbababbabbbbabbabaaabbaaabbbbbbaaaabaaaabbbaaabbbababaabbaabaabbbababaaaaaaaaabbbaaaaababbbbaaabbbbbbbbbabbabaaaabbbbabaababbbbbabaababbabaaabababbbbbabbbbabaaababbaaabaaabbaaabbbbbbaabbaaabbbbaaababbaabbabbbbabbbbabaabbababbabbbbabaaabaaaaaaababbabaaaaabbabaababbbabbbaababbbabaaaaabbababaaaaaabbbabbbaabbabbbbbbbbbbababbbaaababbbabaababbbaabaaabbabaaaaaaabbbbaaabaaaabbaabbaaabbaaaaabbbabbabbbbbbbbbabbababbbabaaaaaaaaaaababaabbabbbaabaaabaaaaababbabbbbbaaaabbbbababaabbaaaaaaabbbbbaabababbabbbaaaaaabaaababaababbaabaaabbaabaabaabaaaabbababaaabbabbbabbabbbaaaaaababbabaabbbbabbbbbbaaaabbbaaaabbababbbabbbaabbaababbababaabaabababbaaababbbbbaabaabaabaaaaabbaabbbbbbaababaaaaabbbabbbabbbbabbbbabbbabbaaabaaababbbbaaaababbbbababaaababaaaaaaabbabbabaabaababaaaabaabaababaaabbabbbbbbababbbbbaaabbaabaabaabbbaabbbababaaababbabbbbaabbbabbabbbaabbabaaababbabbbaababababaaaabaabababbaabbbabbababbbbbabbbabbaaaabbabaaabbaabbbaabbaaabaaabbbbbabbaaaaaaaaaabbbaabbababbbbbaaababaabbabbabaabbaababbbabaabbbbaaabababaaaaabbaababaabaaabbbabaaabaaaabbaaaaaaabaaabaabbbaaaaaaabbbbabbaabaabbaabbabaabababaabababaabababbaabababbabbbaabbaabbbbbbababbababbabbbbbbbbaababaaabbabababaaabbbbababbbbbbbbaababbbbbaabbaaaabbaabbaabbbbaababbbbbbbbaaababbbaabbaabababababbbaaabbaabbaaaabbbaaaaaabbbbbabbbababbbbaaaaabaabaaaabbbbaaabbaabbaabbabbaaabbbbaabbbaaaababbbbababbbabbbabaabaaabbbaabbabbaabaaabbbbbbbababababbaabaabbbbbaaabaabaaaabaaabbaaaabaaabbbaaabaaaababbbbabbaabaabbbbabaaaaabbabaaabbaabbbbbaabbbabbbababbababbabaababbbbabbbbbaabaaaaaabbababababaabbbaaaaabaaabbbabaaaabaaaababbbbabbbabbbbabbbbbbbbaaabaabaaaaabbbaabaaabbaaaaabbbaabbaaabbaabaaabbbbbabbbbbaaaababbbababbbbbaaabbbbaaaaaaabbbbbbbbabbbbababbbaabababaababbaabbbabaabbbbababaaaabaaababbababababaaabbbbbbababaaabbabaababbbaabaabababbbbbaabbbaaabaababbaabbaababbbaaababbbbbbbbaabbbaaaaabbabbabaabbbaaabaaabbabbaaaaabbababaaabababaabbbbbabbababaabbbbbaabbaabaabbabbaabbbbabaaaaabaabbaabbabbbbbbbbababbaaaabbaabababbbababaabbaabaabbbbabbaaaabbabbaabbaaabbaaabaaaaaaaabaabbbbaababbaaababaaaabaabbaabbbbaabaabaabbbaabbabbbaabaabaabaababbbabbbaaaaababaaaabbbaabbabaaaaaabaababbbaababbabbababbbaaabaaabaababbbabaaabbbabbbaaabbaaabbabaaabaaabaabbbbbbabababbabbbaaabaaabbbbbbababbbbabaaaabaabaababbbbaaabbbbbaabbbbabbbabbbbbbaabaaababbbbbaaaabbbabaaaabbaababbbbbbaabaabbbbaababbbaababbbbabbbbababaaaaaababaaaabababbbaaaaabbbbabbaaaabaababbbababbbbbaabbaaaaaabbaabababaabaaaababbbbabbaabaaababbbabaaaaaaabbbaabaabaabbaabbbabaaaabbaaaabbabaaababbbaaabaaabaabaaaabaabbaabbaaaaaaaabaaaaabaabbbababbbababbbbaababbaaaabaabbababbbabbbaabaaababbababbabbababbabbbabbabbababbbabbaaaaaabbbabbbaaaabababbbbbbababbaaaaabbbbababbaaaabbabbaabababbbabaaababbaaaaaabbaaabaaabababaabbaaababbaababaabaaaabbabbabbaabababaabbbabaabaababaaababbaabaababbaababbbabbbaaabbaababbabaaaabbbbbabbababaababbaaaababbbabbaabbaabaababababbbbbbbbbbabbaaaabbabaabaabababaabbbabaaababaaaababbbaabbaababbaaabbbbabbabbbababbbaaababbaaababbaabbaaaabbaabaaaaabbbbbbabbbaabababaaabbbbabbbabbbaabbbaaaabaabbabaabaabaaababbabbbabbaabbabbaaabbaaaabbbbaaababbababbaabbababaababbbababbbaaabbbbababbbbbbabbbbbbbaabbabaabbbabaabbbabbbbbabaabaabaababbaaaabbaabbababbbaaaababbabbbaaaaaababaabbbbbabaaabbabbabbbaaabbbababbbbaabbbaabbbbbababababbaabbaaaabbabbbabaaabbbbbabaabbbbbaaabbbbbbbabbabbbabbabbabbabababbaabbbaaaaabbaabaaabbbbbbbbbaaaaaabaaaabaaababbbaababbbbaabbabbbabbbaabbbbaabbabbbbaabbbaaabbabaabaaabaaaaaaabaaaaaabaaaaaaaababbbbbbabababaaaabaababbbbbbabaaabbabbbbaabbbabbbabbabbaaabbbababbabaabbabbabbababaaabaababaaabbbbbababbabaaaababaaaabababbbbabbabababbaaaaabbbaababbaabaaaaabababbbbababbaabbbbaabbbaaabaaaaababbbababbaabbbbbbabbbbaaabbbbbbbabbbaaaababbabbabaabaabbbabbabababbbabaababbaaabbbaaaababaaabaababbbaaaababbbababaabaabbbaababaaabaabbaaaabbaabbaaababbabbaaaaaaababbbbababaaaaaaaaabaaaaabaabbbaabaaabbbbaabababaaaaabbaaababaabbabbbaaabbbabbaababbbabaabaabbaaabbabbbbabaaababbbbbaabaaaaabaaabbbabbbbabbaaaaabaaaaabbbaaabbababaabbaabbbbababababbabbbbabbabbbbbbbbbbaababbabbbabbabaabbbbbbbbaaaabaabbaaabbababbbaabaabbaababbabbbababbaaaaabbbabbbabbbaaaababbaaababbabaababaaabaaabaaabbbbbabaaabbbabaabbbbbaabaababbababbbabbbaaaabbbbbababbabbaaabaaaabbabbbababbbbbabbbaaababaaababbbababbabaaabaaabbaabbbabbabbabbabaaababbbbbbabbabbabbaabbbabaabbababaabbaaaabaaaabaaaaaaababaabababaabbbbabbbaabbbaabaaaabaaabbababbaababbbababbabaaabaabbbaaabaabbabbaaabbaaaabaaaaaabababaababbbaababbabbbaaaabaaaaaaabbababaabbbabaabbbabbababaaabaaaaabaabaaabbbbaabbbabaaabbababbaaaaabbbabaaaaaabaaaaabaaaabbbbbbabbbaaaabbbbbabbaabbababbbbbabbababababbabbbabbbabbabbaaaaabbbbabbbaaaaababaabbbbbaabbbbaabbabababbabbaaaabbabbabbabbabbaabbabbbaaabaaabbabaaababbababbbbaabaaabbaabaaabaaabbbabbbbaabbabaaaababbaaabaaabbaabaabaababaabaabaabbbbabbaabbabbbaaabaaaabbaaaabaaaabbaabbaabbbababbbaabbbaaaabbbababaabbbbbbabbbbbabababbabaabaabbbbabbabbbbbabbabaaaaaaaaaabaabbbbbbaaabbaaaabaabaabaabbababbaaabbbabaaabaaaaabbbbbbaabababaabbaabbaaabaabaaababaaabbbaabbaaaaaaaabbabababbbbbaabaabbaaabaababaaaababaaabbbaaabbabbabaaaabaabaababbaabbbabbaabaaababbaaaaabbaaababbaaabaabaaabbaabaabaabaaababababbbabbbabbabbababaabbabbabaabaabbaababbaababbabaabaaaababbbbbabbbbaaabaabababbabbbabaabbabbbbabababbbbaabaaabbabbaabaaaaaaabbaaaababbbbabbbaaabbabaabaaabababbbbaaabbaabbbabbbbbbabbaaaabbabbbbabbaaaababbbbaababaabbbbbbbaaaaabaabbbabbababaababaabaaaabaaabbabaabaaabbabbabaaaabbaaababbababbabababbbbbaaabbabbbaabaaaaaabbabbabbabaaabbababaaabaaaabaabbabaabbaaabbbababbabaaaabbbbbababbbababbbbbbbaaabaaaaaabbbaaaabaabbabbabaababaaaaabaaaaababbbaabbbbbbbaaaaabbabaaababbaaababaaabaaababbaaabaaaaaababbabaaaaaaaaababbaabbaaabbaabbaabbabbbbbabbabaabbbbaababbbaabbbabbbababaaabaabbbabbbbbbaabaaaabaaabbaaaabaabbbabbabbbbbaaaaabbaaaabbbbaaabaaaaababbbbbbbbabababbaaabbbbbaaabbbabaaaabaaabaabbbabbbabbbaabbbbbbbbaabbabbabbbbaaabbbbbabbaabaabbbabaaababaabababbbbabaababbabaabaabbbabaabababaaaaaaabaaabaaaaaababbaaaabababaabaaaababbbabbaabbababaaaaaaabbaababbbabbbaaaaaaababbaababaaaaababababbaaababaaabbbbbbaabbaabaabbabbbaaababbababbaaabbbaabbbbbbbbababaababaaabbaabaabbbabbbaaabababbbbbaababaaababbaaabbbaaaaababbababbbbabaaaaababaabaabaabbbabbbaababbaabbaaaababbbaabbbaaabaababababbababbbbbabaababaabaaaabbbbaaabbbabaabbbbbbaaabbababbaabaabaaababaabbbaaaaabbbabaabababbabaaaabaaaaabababbababbbbabbbabbbbabaaaabaababbababbabbbabbbaabaabbabbabbbbbbbabbbaaaaaaabbbabaabbaabaaababbabbbbbbabaaaaabaaababbbbbbbbbaabbaabaabbbbbbabaabaabbbbababbaaaabbabbbbbababaaaaaabababbbaaaababbabbababbaabbbbbababaabbabbbabbaabaabbbbbbbabbabaabbbbbabbbaabaabaaabbbbabbabaabbaaabbabbabaaabaabbbbabbabbabbbbbabbabbbbbbababbabbbaaaabbaaaaabbaabbbabaaabaaaabbababbbbbbbabaabbbbaababaabbaabababababbbaabbbababbbaababaaaaabaaababbababbaaaaaababbbaabbababaabbabbaaabbbbbbbbaabbbabbaabaabaaaabaaababababababbabbabaabbbbbbaaabaaabaaabbaabababaaaababaaaaabbabbbbbbaaaaaaababaaaababbaaabaaabbbbbaaabaababbaaaaaaabbaabababbaaaabbbbbababbbababaaaabaababbaaabbbababbabbbaabbaaaabababbbbabbabbaaabbabaaabaaaaabaabbbabbaaaaabbbaabbbbaaabaabababbbaabaaaabbaaaaaaabbaaaaaaabaabaabbabbaaaabaabaabbaabbbaaabbbaabbbabaabbbabbabbbbabbbbaabaaaaaababababbaabbbbbbaabbababbababababbaaabbbaabbbbabaabaaabbaabababaaabaabbbbababbbbbaabbbbbbbaabbaaaaaababbabbababbbbbbbbabbbababaaaaaaabaabaaababbbbbbaabbbbabbabbbbbbbbaaabbababbbabbbababbbbabbbbaabaabbbbaabaabaababbababababababbaabababaaaabbabaabbbbabbbbbaaaaababaaaaaaaaaabbbbbabababaabbbbaaabbaababbbaaabbbaababbbbaaaaabaaabbbabaaabaabaabbabbbbbaaababbabbbaaabababbbbaaabbaaabbaaaababaaaababbabbbaaababababbbbbbbabaaaaabbaababbbabbbababaaabbbbaaaabbbabbabbbbabbbbbabbbabaaabaabbabbaabaabaaabaabbbbbabbbaaabbbabababbaaababbabbbbbabbaaababaaabaaabbbaaaaabbabbbaaaaaabbabaaaaaabbbbaaaabbbbbababbbaabbabaaabaabbbabbbbabbababbaababbabaabbbbabbbbbaaaabbbbbaabbbaaabbaaaaaabbaaabaabbaabaababaaaaaaaabbbbababbabbbaabbabbbaabbbbbbbaaababbbbabababbabaabbbbaaaaaabbaaabaabbaaaaabaababbabbbbbaabbaaabbbbbbbbaaabbbabaaabaaabbabbbbaababbabababababbbbbabaaaabbbabbaaabaaaabababbababbababbababbabbaaaababbbababababbbbbbbbaaabbabbaabbbbbaaabbaabbabbabbbaabaabbbbabbbaabaabbaabaaabbbabbabbaabbababbbbbabbababaaabbababbabbbbaabaababaaaaaabaaaababaaaaaababaaabbaaabbaababaaaaabbaaaaabbaaaaabbaabbbababbbbbabababbabbbbbbabbbbbbbaaaabaababbbbabbaaaaaaaabababbabaabaabababaaaababbabaabbbaaabaabaaaaabbbbaabbbbbbaaababbbbaababaaabababbabbaaaaaaabbaababaabbabbabbbaabbbbabbabaabbaabbbbabbabbbabaabbbbbbbabbabbbbbbabaaaaabbbbaababaaaaababaaabbbbabaabbaabbabaaabbbabababbabbaabaababbaaababbababaabbbbababbbbaaabbbbbabababaaaabbaabbaaaabbababbbaaabbababaabaaaabbbaabbabbbbbaaaaababbbaaaababababbbabbaabbaabbabbbaabaaabbaabbbabbbbaaaababbbaaaaababbbaabbabbbaaababbbbaabbbabbbbbbbbabaabaaabbaaababaaabaabbbbaaaabbbbbbaaababbbbbbbabbaabbbaaabaabbabaabbaaabbbaaaaabbbaaaaabbaaaabbaabbbabbbabbbaabaaabbaaababbaabaabbabaaabaaababbbababaaaaaababbbbaaabbbbabbbbbbabbbaabababbbbaaabaabaababbaabbabaaabbabababbbbbaaaabaaaabbabbaabaaabbabababbabaaabbaababbabaaabbbbbaabababbbbabbabaabbbabbbbbaabbbbaababaababbbababaabbababaabaaaaabaaaabaaaaababbaaaaaaabbabbaaaaabbaaaaaababbbaaabbbabababbbabbabbbbabbaabaaabaabababaaabbbbbaaabbabababaaabbabbabbabbbbbbbaaaabbbbabababbbabbbabbbabbbaaabababaaaabaabbababababbbbbaabaaabaaabbaabbabababaabbbababaaabaabaaaaabbbabbbbaaabbabbbbababaabbbbbaaaabaaaabbbbbbababaaabababbbabbbbabaaabbbbbbabbaabbaabbaabbabbabbaababbaabaaaabbabbabbabbaababbbbbbaababbbabababbabaaabaaaabbbbaabbbaaaaabbabbbaababaaababaaaaaaaabaababaabababbabaabbbbaaababaababaababbabaaaaababbbaaabbaabbabbaabbbaaababbabbbbabaabbabbaaabbabaabaabaabbabaabbbbbbbbbbbbbaabbaabbaaabbababbbbabbbabbbaaabbbababbbaaaababaaaabbababbbabbbbbaabbaaabbbbaabbaaabaaabababbabaabbbababbbaaaaabbbabbbbbaababbababaabaaaaabbbaababbbaaaaaabbbaaaabaabbbaabbaabbbababbaabbababababaaaabbbbbbbbaaaaabaaaaabbbbaaabbababbbabbababbaaaaababaaabaababaaaaabbbbababaaabbaabbaabbbbbabaabbaabbbabbbbabbbbbaabaabaabaaaabbabbbaaabbbaabaaababaaabbabbabaaaabaabaaabbabbbbaabbbbbbbabbaabaababbbaaabaaaaaabaababbbabbababaabbbbbbbbababaabaaaabbbbabaabaabbaaabbbabbabbaabaabbaaaabbaabaaabbbbaabaababaaabbbabaabaaaaaababaaaaababababbbbababbbaaabbbbbbaabababbabbbbbbabbababbbaabbaabbbaabaabaaabbbaabaaababbbabbbabbbaabbbaaabbbbbababababbabbbbabbbaabaaaaabbabbbbbabbaaaaaabbaaaabaababbabbaabbbabbabaaaabbabababbaaabbabbaabaaaababbbaabaaaaabababaababbaabbbaababaaabaaabaaabbaaabbaabaaaaabbbaaababababaaabbbbabbbbabbabaaabaaaaaabaaababbbbaabaaaabbbbbbbabbaabababbabbbababaaababbbbbabbaaabbbabbaabbaaaabbbbabbaaabbbabbababaaabaababbbabbaababbbabaaabababbabbbaababbbbabbbabbbbabbbbbaabbbbabbabababbaabaaaaaaabbbbbbbbbabbbabaaabbaaaaabaaaabbaabaababbaabbaababbbbaaaabaabbbbbbbbabbabbbbabbbabbbbaabaaaababbaabaabaabaaaabbbabbabbbaaabbbbabbbbbbaabaaababbaabbbbabbbaaaaabbababaabbabbbabbabababbaaaaaaaaababbabaaaaabbababbbabbabbaabbbaaabbaaabbaabbaaaabaabaabababbbbbaaaababbaaabbaabbabababbbabaaabaaaaabbaaabbaaabaaaaababbbbabbbaaaaabbbbbaaabaabbbabaabababbbbabbabaabaaaaaaaabbbbbbabbbabbababbbabaaaaaababbaaababbbbbbaabbabaabbabababbbbabaabbabaaabbbabbbaaaaaaaababbaabbabbbbbbaaababbababbaaaababbbabaabaaababbababaaaaabaaabaabaaaaabbbbabaaaaaaabaaaaaaababbbabbabaaaaabbbbbbabbaabbabbbaaabababababbbbabaaabaabaaaabbbaaabaaabbbaabbbaaaabaabbbaabaaaaabaababaabbaababbbbaabbaaaaabababababaabbabbbbbbabaaababbbbbabbbabaaaaabbbaabbbaabaaabbbaaaabbabbaaabbabbbaaababbababbbaaabbbbaaaaaabbaabaabbaabaaabbbabaabaababbaaabbbabbabaabababaabbbbbbbaaabaababbbabbbabbaabbaaababbbbbbbbbbaababbbabbaaaabbbaaaaabaaababbaaaaaaaaaaabaaaaabbbbaaabaababbbbbabaaabbaabbbaaabaabaabaaabbaaababbbbaaabaabbbabbbbaababbbbbbaabbabaabbabaabaabbbbaaaabbaaabbaababbbbbbabbbaabaabbbbabaaaabaaaaaaabaaaabbbabaaaabaabbbabbaabbaabbabaaabbaababaaabbbaaababbaabbaaaabbbaabaabaabbabbababbbaaaaaabbbbbbababbbbbbaababbbbbbaaaaabbaabbbaababbbaaabbbbaaaaaabaabababbabbbaabbbbaabababaabbbabbbbababababbbaaaaabaababaaabaaababbaaaaabaababbbbababbababbbabbaabbbaabbbababbaaaaababbaaaabbbbabbbaaabbbbbbaabbbbaaababbaabaabbbbaaaaababaaaabbbabbbabaababbaaabaaabaaaaabababbabbbbaaabababaabbbbbbbabaaaaaabaababaaaabbabbbaabbbbababaaabbbbaabbbbababbbbbabbbbabaaabbaaaabaaaabbabbabaababbabbbbbabbbabbabaabbbbaaaaabbaabbababbbbaaaaababbbbbababbbabbabbbbbabaabbaabbaabbbbbbaabaababbababaabbbbaabbaaabbabbaaabbbaaababbababbbabaabbaabbaabbbaaaaaaaababbaabbbabbabbabaaabababaabbbabaabbbabbbbaabbabbaaaabababaabbaabababbaaaabbaababbababbaabbaaababbaaabbaaabbbaabbbbabaaabaaabbbbbbbaaaabaaaabaaaabaabbabaabbbaaababbaabbbbbabaaabbbbbabbbababaabbaabbaabbaaabbbabbbbaaaaabbaabaabbabaaabbbbabbbababbaaababababbabaaabaaabaabbbbbababbbbbabbbbbbbabbbbbababababaaaabbabbabaababaababbbbbbaabaaaabbbbaabaabbbabaabaababaabaabbbbbaabbbaaabbbbbbaabbaabbbabbbaabbabaababbaaaabaabaabaabbabbabaabbbbabbbabbaaaababbabbabbabbabbbababaaaaaabaabbaaaabaaaaaaaababbabaaabaabbbaaaabbbabbaaaaaabbbbaaabababababaabbabbbbbabbbaaabbbaababbaababaaababbbabbababbbaaabaaaabbabaaaaabaaabbbbabaabaabbbbaaabbaaababbaaaabaabbaaaabbbabaabbbbaababbabbbaabbbbaabaabababaaaababbbbaaaaababababbbababbbaabbabbbabaabaabaaaaabbbbaababbbbaaaabaabbbaabbabbbaaaaaabaaabaabbaaabaaabbaabbaaabbaababaaabbbbbaabaabbbbbabbbbabbbbbbaababbbbaabababaaabbbbabababababbaaabbaaaaabbaabababbababaabbaaaaabaaabbbbabbbabbaaabbabbabbaaaaaabbbbbbbabbabaaabbaabaaabbabaabbabbababaaaabbaabababaabbabaabababbababbbabbbabaabbbababbaaabaaabbaabaababbbabaaaabbaaababababbbbbaaabbaaaabaaabaababbbaabbababbbbaababbbbaababbbaaaabbbaabbaaaababbaabaabbabbaabababbabbaaaaaaaaaaaababbababaaaaababbbbbaaaababaabaabbabaaabbabaabbbbbaaabbbaabbabababbbaabaabbaaababbabbbabbbbbababbbbaaaaabbbbbbabbabaabaabbaabaaaabbbbbbabaaaaaabbbaaaabbbbabaaabaaaaaaaabbbaabbaababbbbabbbbaabaaabbaabaabbbaaaaaaabbbaabaabbaabaaaabaabbaabbbbbabaabbabbaababbbbbabaabaaaabbabbaaababaabbbabaaababbbbaababbaaabaabaaabaabbbbaabaaababaaababbbababbbaabaaaaaaabbbbaabbbbabaabbbbbabbaaababbbbbbaababbbabaaaabaaababbbbbbbbaabbbbbbababbaaaababaaaabbbbbbaaabbbbbbabaabbbbbaaaaaaaaabaabbaabaababbbbbbaabababbbaabbbaaabaaabbbbaabbbbaababbababaaaaaababbaaaaabbaaababbabbbbababbaabbabbaaaabbbaaabaaabaaaabbbbaabbbbbaabbbaaabaaaaabbbbbaaaaaaaaaaabaaabbbbbabaabbbaababaaaaaababbaabbaabbbbbaaabbaaabaabaabbbababbbbbbbbbbbaabbaabbbaaaaaaaaaabbabbbbaaaabbabbaabababababaabbabbbbbabaaaabbaababaaaabbaababbbaabbbbbaabaabbaabbabbbbaaabbbbaaaaaaabbabbbabbbaabaababbaabbbbababbaaaabaaabaabbabaaaaababbabaabaaabbababaaaaaababbbaaaaaaababbbbabaaabbbbaaabbabaaabbbabbbaaaaaabaaabbbaaabbbbaaabbbbbbaabbabaaabbaababaaabbbbbbabbbaababbababaaabaaaaaaababbaabbbababababaabbabababbababaabaabbbbbbbaaaaaabbabaaaaabbabababbbbbbabbabbaaaabababbaaaabbbbabaabbaaabbabbababaababbbbbbabbabbabaaaabbbbaabbbbbbbabaaababbbabbbbabbbbabbbaaaabbbbbbbbaabababaaaababbbbababaaaabaaabababbaaaabbbbaaabbaaabbabbbaabaabaabaaaabbbababaaaabaabbbaaabbabbabbbbaabaabbaaaaaaaaaabbaabbabbbabbbbaabbaaababbbabbabbbabbaaaababaabaababaaaaabaaaaabbbaaaaaabaaaabbababaababbbbbbabaabaabbbbbbaaabbbabaaabbbaabbabaababaabbaabbbbbbaaabaaaabbabaaabaaaaaabaaabbbbbbaaabbbaaaaaabaabbbbabaabaaababbaaabbbbbaabaababaaabbaaaaabaaaaabaabbbbaaabbababbaaabbbbbbbabaaaabaabaaababaaaabbbbbbbabaaaabaaabbbaabababbbabbababaabaaaabbabbbabaabaabbbbaabaababaaaaabbbaaabaaabbabbabaaabbabbbbaaabbbbaababaabababbbabbabbaabaaaaabbabaaaabbaabaabaaabaabbbaaabaabbaabbaababbaaaaaaaabaaabbbabbaabbbabababbaabaabaabbaaabaabbbabababaaabaababaaabbbaababbaaaabbbaababbbbabbbaabaaaaaababbabbaaabbaabaaababaabbbababbbababaaabaabbaabbbabbbbbaaabababbaababbaabbabbabaabaabbabbbbbbbbaaaaabbaaababaababababbaabaabbabababaabbaaabbababbbabbabbaabbababbabbbaabababbbaaababbaababbbbaaabbaabaaabaaaaaaababbbbabbabababbabbabbbabbababbbabbaaaaaaaaaaaabbabaabbaababaaaaababbbaabbabbaaaaaaabbaabbbaabaabbbaabbbabbbababbabbbbbbbbababbbaabaababbbaabbbbaaabaaababaaababbabbbababaabaaaaaaabaaaabaaaabaaaaaabababbabaaaabbabbabaaabbbabababbaaaabbbbbbbaabbaaaabbaabababaabbaabbbbbabbabaabbbabaabbababbaaaaabbbaabbbaaaaaaabbaaaaaaaaaabbbbbabaabbbbbbabaabbabbbbbabbbbbbaaabbaaabbbbbabbbbabbabbabbabbbbaabbaababaaababaabaababaabaababaabbbabababbaaababaaaaabaabaabaaaaabaabbaabaaaaabbaaaaaabbaabaaaababbabaabbaabbabbbbabbbaabbabaabababababaaabaaaaabaababaabaabbbababbbbaabbbbabaaaabaaababaabbaabaabaaaabbbaaaaaaabbaaaaabbabaaaabaaababaaabaaaaaaabbaabbbbaaababaaaabbaababaabbbbbbbbbbabaabbaababbbbbbababbabbaababbababbbbbbbabababaaabbaabaaaabababbabaaaabaabbaaaaaaaaabbabbaaabbaaabbbabbaaabbbbbbbaabaabababbbababbbababbbaababaaabbaabbaabbbaabbabaababaaabaabbaaaabbbababababbbaaabbbbbababbbabbbbaabbabbababbbbbabbbabababbbbbaaaaababbbbabbbbaaaabaaaabbababbbabaababbaaabaabbbabbabbabbbabbabbbbbabaaaaabbaabbabbbbaabbaabaaaabaaaababaabbbbbbbababbbabbbaababbbabababbbbbbbabaabbababaabbaaaaabaabababaababbabbaababbaaaaabababbabaabbabbaaababbbaaababbbbbbbaaaaaaabaaaaaabaabbbbbabbbabbbbbbabbbbabbbabaaabbbabbbbbaabbabbaaaaaaaabaabbbbbababaababaabababaababbaaabbabbbbbabaabbbbbbaaaabbaaabbaaaabbbbbbbbbababaaaabaaaaaaabbbbbabbababbbaaaabbabbaabaaaaabbbaababbaabbaaabbababbaaabbabbabaaabaabbbabaaaaababbbaaabababbbaabbbbbbabbabaaabababaababaaaaaabaaabaaabbabbbabbbabaaabbbbbaabbbaabaabbabbbbaabaabaaabbbaaabbababaaaabaaabbbbabbaaaaabaababaaaaaaaababbbbbbabaaabaaababbbaabbaabbaabbabbbbbaaaababbbbabbbabaabbaabaabbaabaabbbbaabbbbaabbbabaaababbaaaaaabbaaababbabbbbabbaaababababababaabbababbbbaababaabbbbabbbabaababbbbbbbbabbaaabbbbbbaabbbaabaaababbababbbbaaababbaabbaaaaaaabbaaabbaabaabbbbaaabbbaaaababaaababaaaabaabababbabaabbbbabaabaabbbbbbaabaabaabaabbaabbbbabbaababaaabaabbababbbaababbbababbaaaabbbbaabbbbbaaaaaaaaaaabaaabbababbabbbbbbabbbaabbbbbaaabbbbaaabbbaaaaabbaaabaabaababababbaaabbabaaaabbaabbabaababaabbbaabababbbbabaababbbabaabaabbbaaaabbaababababbbaabbbabbbbbabbabbbaaabaabbabaaaabaabaabbaababbbabaababbaaababaaabaabbaaababaaabbbababbbbaabbaaabbaaaababbabbbaaaaababbbaaabaaaabaaabababaaaabaaabaabbaababbbbaaabaaaaaaaaaabbbaaabaaaabbababbabbbabaababbbaaabbbaabbabababbbabbabaabaaabaabaaaababbababbbbbaabbbbbbaaaaababbabaaaaabbabbaabbbabbabbbbaabbbbabababbbbbbaababaaababaaaaaabbbaabbbabbabbaaaabaaabbabbabbaabbbbaaabbaabbbbbbbaaabababaabbababaabbababbbabbababbaababaababbababbbabbaaabbaaabbaaabbaabababababaababababbbbbababbabaaaaaaaabbbaaaaababaaabbbbbaaaabaababaabaaaabbababaaaaababbaaaabbabaababbbbababbaaaaabbabbbabaaaabbbaabbababbbbbbaababaaaaababbabbbaaababbaabbaababaabbaababaabbabbbbbaabaaabbaababaaababbbababababbabbaabaaababbabbbaaabbabbabbbbabbababbbaabababbabaaabaaabbabaaaaaaabbbabaabaaaabbbaaabaaabbbbbbaaaabbaabbbaababbabbabbbaaaaaabbbaaaaaabbbabbabbbbbbabbbabaabaaabababaabbbbaaaabaababbabaabaababaaaababbaaaaaababaaabbababbbbbbaabbbbbbabbababbbbabaaaabbaabbbaabaaaaaababababaabbbaaabbbbabbabaaabaababbbabaabaabaabbbabaaaabbabbabababaabbbaabbaaaababaabbbaabbabbabaabbbabaaaabaaaaaaababbaaabbbabbbabbbaaaaaaabbabaabbabbbbbbbaabbbbbbaababbbabbbabaababbbabbaaabbbaabaaabaaaaabaaaabbaaabbaababaaabaabababababbabaabbbababbabbaaaaaaaababaabbababaabbabaaabaaaabaaaaaabbbabaabaababababaabbbaabbbbaabbbbaabbbaabbbaaabaaabbaabaaabbbbbabbabbababaababbbabaabaaaaabbbbaaaaaaaaaabbabbabbaaaaabbababababaaabaaaaabaabaaaaaababaabbabaababbbababbbaaaaabbaabbbabbbbbbaabbbabbbabaababbbaaaabaababbbaaaaabbbaabaaabaaabaababbaabbabbbbabbaababaababaabbbabaabbaaaabaaababbbbabbbbbaabaaabbabbaabbaaaaaababaabababbbaababbaaabbaababababbaaaaababbbbbbaabbabaabbbbaabbbaababbaaaaabbabaaababbbababbaaaabbbbbbabaabbaabbabbaababbaabaabaaaabbbbbabaabbaaabaababbaaaaabaabbababababbbbbabaaaaaabaabbababaabbbababbaaaabbaabbbbaaababababaaabbbaaabaabbbbaabbaaabbbbabbaabbbaaaabbbbbbbbaabaababaaaabbbbababbbaaabbaabbaababbaabbababaaaababbabaaaaabbaaababaaaaabbabbbbbababbaabbbbabbbaabbaababbbababababbbbabbbaababbaaaaababaababaababbbabbabaaababaaaaaaaababbaaababbbbbabbaabbbbabaabbabbbbbbbabaaaabaaaabbaaaaaabbabaaaaaabbbbabbbabbabbbbbabaabbbabaabbbababbababbbaaabbaaaaababbaaaabaaabaabbabbbabbbbaabbbbabbbbbbbbaaaaaabababbaabaabaababbabaabaaaabaaaabbaaaaabbbbabbbabaaabbbbbaabbbbbbaaaaababbbbbbbaabaabbbbbbaababbbbaabbabbaaaabaaaaaaaabbaaaaaabbaaabbaaababbbabbbbbbbaaabbbbbabbbaaababaabbaabbbbabbbbabbaabbbaaabaaabbaaababbaaabbbaaaabaababaababaabaabbaaaabbabbbabaabaabaaaaaabbaababaaababbbaaaabbbbababbbbabbbbababaabaaabbaabbbaaabbabbbbbbabaabbabbabbbaaabbbbabaabbbbbaabbaaababaabaaaababbbbabaaababbabbaabaabaabababaaabbbbbaaabbbbabbababaaabbaaabbbbbbbabababbbbaababaaababababaababbabbaabbbaababbbbbbabaaabbbabbaaaabbbbabbbababaaaabaaaabababaababbaaaaabaaabbabababababbbbabbbababaaaaabbababbabbbbbaabbbbbaaababbbbbaaababaaaaabbabaababaaabbbbbbabbaabbabbaabababbaaabbbaaaabbabbaaaabaabbabbababaaaaabaaababaababbbabaabbbbaaababaabaaababbbbbaaabaaaaaaaabaaaababbbabaaabbbbbaabbbbbbbabbbbbababbabbaaabbabaaaaabaaabbbaaaabbabababaaaabababbabbbabbbaababababaabbababbbaabababbbbbbbbbbbbbabaaaaabaaabaababbaabbaaaaaabaabbbbabaabbaaaabbabaabbbabbbaaaabababbababaabbbababbbaaababbbaabbabbbaaababbbabababbaababbaabbbbaaabaabaabbabbababbbbbbbbaabaaabbaabbbabbababbbaaabaabaaaaabbabababbbaabababbbaababbbaabbaabbababbbbabaabbbbbabbbbbbbaabbbabbaabaabbbbabbaaabbbbabbbabaabbbabbaaaaabbabbbbaaaaaaaaabababbbabbbbababbbabababaaaabaaabbbabbbbabaaabbbbbbbbbababbaabbbbbaabaaaaaaabbbbababbaaabbbbabbaaababababbaaabaabbabbabbabaabbbbabbabbbbbaabbbaaaaabaabbbbabbbbabaaaaaaabbabbababbaabbabaaabbbabbbbaaaabbabbbbbbbbbbaaabbbaababbbbbaaabbbbabbabaabbabababbbabbbbbaaabbabbaaabbbbabbababaabbbababbabaabbaabaaaabababbabbbbbbbabbabbabaaaabaaabbabaaabbaaaaabbbaaaabaaaababababbaaabbbabbaabbbbaababaaaabaabbaabaaabbaabbaaaaabaabbabbbbaababbbbbababbabaaabaababbbbbbbbabbabababbbaababababbabbbbbaabaaabaaaaaaaaaabbbaabbbbbabbabaaaaabaabbbaaabbaaabbaaaabaaababaabbbbaabaabababbaaaabaaaaaabaaabababbbbaaaabaaababaababbabbabbbbabaaabbbabbaabaabaaabbabbabaabbbbaababbabaabbaaaaababbabaabbbabbbaaabababbaaaabbbbbaabbbbbbababababbababababaabaabaababaabaabbabbababaaaaabaaaabababababbbbbabbbbaabbabbaabbbabbbbbaaaaaabbabbbbabbbababbbbbbaaabbbbabbbabbbaaaaababbbbbbaaababbaaabbbbabbbabbbbabbababbbaabaabbaabbbbbbbbbaaaabbbbbababbbabbabbbaabbbbbbabbabaabbbbbbababababbabbabababaaaabaaaabaabaaaaababaabbbabbbbbaabaaaabaabbabbaabbaaabbbaaaaabbbbabaabaaaaabbbaaaaabaaabbbaaaabbbaabbaaaabbaaababaabaabaaabbbababaabbbbbabbabbbbabbbabbaabaabbbabbbababaabbabbaaaabbbaababaaaabbaabaabbbbbbaaaabbbaaaabaaabbbbbbaaaaaabbbbaaaabbabbbbaaabbaabbaaabbbaabbbabbbaaaaaabbbaaaabbabaababababbababbbbbbbbbbaaaaabbbaaaaabbbbbababbbabbbbbbaaababbbaaaabbaaaaaabaaababbaabaaabbabaababbaabaabbbaabbbababbbabbbbabaaaaabaaaaaabaaabbabaabbbbbaabbbabbbaaaaabbabaabaababbbabbbbbaaaaaaabbaaaabbabbbaababbbabaabbabababbbaaabbaaabaabbaabbbaabaabaaaaabbaabbaabbaabbabaabbaabbbaaaaaabbabaababbbbbabbbbbbbbbabbabbaababaaabaabaaabbabbabbbbabbbaaaaabbbabbaabbaaaaaabbbabbbaabbabbaaaabbabaabaaabaababbaabaaaabaaaabbabbbababbababbbbbabaaabaabababaaaabbababbbaabaaaaaabababaaaabaabaabbbbbabbabaaabbababbaaaaabaaaaaabaaaaaaabbbababbabaaabbbababbbaababaabbbababbbbbbbababbbbbbbbabbbaaaabaaaaaabaaaaaabaaaaabaabaaababaababbaaabbabaaabaaaaaaaabbaaaaabaabaabaaaabbabaaaababbbbbabbbbaabbaabaaabbababbbbbabbababaabbabaaaaaaaababbabbbbabaabaaaabbbbaaaabababbaabababbbabaaaaabbbabbbabbaabbabbbaaaabababbabbbbbabbbaaababaaabbababababbbbabbababaaabbbbbbaaababbbbbbabbaabbaaabbabaabbaaababbabbaaabbabaaaaaababaabbbaabbbbaaaabbbbaabbbbbbabaabbbbbbabaaabababbbbbababbbbbbbbbbbabbbbbabaaaaabbbaabbabaaabbbabbbbbbaabbbbabbbaaabaaabaabababaabbbabbababbaaabaabaaabbbababaaabaababbbbbaaabbaaabaaaabbababbaaababbabbaaaaabbbaabbabbbaaababbabaaaababbaaaaabababbaaaababbabbabbaaababbbbaaabbbabaabaabbaabbababaaaaabaabaabbabbaaabbabbaabaaabaababbbbababaaaaaaabbabbabbaabbabbabbbbbaabaababbbbabaaaaabaaabbabaabbbaaaababaababbaaababbabbbaaaaaabbaabbbaaabbbaaaaaabbbbaaaabbaabaabbbbbababbbbaaabaabbbabaaababaaabbaababbabbbaabaabbabbbabbaabbbabaaabababaabaaaaaaaaaababbbbbbabaaababaaaaaaaaaabbaaabaabaababbabbabbabbbbabbabbaaabaababbbababbababbbaabbababbababaaaaaaabababbbaaabbaaabbbbbaaaaaabbbbbaabaabbbbbbbabababaabaabbaaabaaabbbbbbaababbababbaaabaabbabbbababaabbbabaaabababbbababbababbababbaaaaabaababbbbbbbbbbaaabbbbabbaabbbbabaabbbbaabbbababababbaaaaaabbbbabaaaabbbbaababbbbabbabaabbbaabababaabbaabaaabababaabbbabbbababaaaababbbabbbaaababbaaaaaaaaabaabaaababbabbabbabaabbbbaabaaaabbaaaaabbbbabbbbbbabbaaabbabaabbaababbbbaabababbbaaababaabbbaabababaabbabbabbaaaababbabaabbaaabaabbbbbbabbaaabaaaabbbabaababbabbbaaabaaaababababababbbaaababbbabababbbaaababbbabbbbbabbbaababbbaabaaababbababbbabaabbbaabbbababbbababaaabbabbbaabbaababababbbabbbbaaabbaaababaabaabbbbabbbbbbbbbaabbbabbbababbaaabbbaaabaabbaababbbbbbbbabbbbbbbaabbabbbaabbaaababaabaabbababbbababababaabbaaabbbbabbaababaaaaaaaabbaabbbbbbbaaaabbbbbbbbaabbbbaaaaababbbabbbbbbbbabaabbbabaaababbabaaaaaaaabaaaabaaaaababaabbabaaaaabaaabbbaaabbbaabbabaaabbaabbaabaaaaabbaaaaaaababaababaababababbaaabbaabbbaababaababbababaaabbbbbbbbaabbbabaabbbaaaaabaabbababaaabbababbaaaaabbbbbbbaaababbbababbaaabbaabbabbbaaabbaaabaabbbbabaaabbabbabbaabbabaaabbabbbabbaabababbabbaaabbaabaaaaababbabbbbabbababbbbbbbbbabaabbaabababbbbbaababaaababbabbabaabbbaaabaabbabaabaabaaabaababababaaabbabbbaaabaaabaabaababaaaaaaabaabbaabbaabaabaabbaababbaaabbaabaababbaaabbbbbaabbbbabbbbababbbaabbbaabbaabbababaabaaaababaaaaaaabbaaaaabaaabaabbbaabaaabbaaaababbabababbaaabababbababbababbaabbbbbbababaaaaaaabbbaaaabbaababbbbababbbbabbbbabbbbaaabababbaababbaaababbaabaaaaaaaabbbabbbbbbbbbabbaabbbabbbbaabababbaabaaaaaabbaaaabbababaaababbabbaabbbabababaabaaaaabbababbbaaabbbbabbabbaaabbbbbababaaabbbbbabbbabbaabbaabbabbbaabababaaabababbbaaaaababbaaaaababbbabaaaaaaaaaaaabaaaaabbaaabbabaabbaabbaabaabbaaabbaababbabababbaabbabbababbbaababaaabababbbaabbbaabbbaaabaaabbaaaabbababaabaababbbabbaaaaabbababaaabbaabbbaabaababbbbabbababaaaaaaabbbbabaaaabbbbaababbbbaaababbbbaabbbababbaaaabababbbbbaabaaabbabbbababbbaababbabbabbbaabbbbbbaaaabbbbaaabbabbbbbbbbaabbbaaabaabaaabbbbbbaababaabbbbbaababbbbabbabbbabbbaabbbbbbbaaabbbabaabbbaaabbbabbbbababbbaabaabbbabbbaabaababbbbbaabbabaabbaabbaabababaaabbababbbbbaaaabbaaaaabbabaabbbabaaaabaababbaaaababbbbaabaabbbbbaaabbaaaaabbabbabbbbbaabaaabababbbbababbbabaaabaabaaaababbbbababbababbabaabababbbabbaabaaabbbbaabbaababbbabbabbababbbabbaabbbaabbabaababbbbbbaaabbaabbaababbbbaabaabbabbbabbabbababaaabbaabaabababbaaaaabbaabaaaababbababbabaaaaabaabbbabbaaabbaabbbabaabbbabaaaabaabbabbabaababbbbbaababbababaabbbbabaaaabbbbbaabbbaabbbbbaabaaabbbaababaabbaaaaaaaaaababbbaaabbbaaaababbababaaababababbabbabaababaaaaaababbbbabababbbabaabaaaaababaaabbbabababbaaaaababbaaabbaaaabbbababbbbbaabababbaababbabbabbbbabbbaababaaaabbaaababaabbaaaabbbbbbabbbbaabbbaaabbbbaaabaabbbbbaaaabbbaaabbbaaababaababaaababaabababbbabaaaabaabaabbaaabbbbaabbabbbababbababaababaababbbaaaabbbbabaaabbaabbbabbbbaaaaababbbbaaabaaabbabbaabbaaabbababbbaabaaabbabaaaabbbaaaaaabbaabbabbbbbbabbabbbabbababbabaaaaababbbbbbbabbabaaabaaaaabaaababbaabbbbbababaabababbaaabbbabbbabaabaababaabaabbabaaabaabbbbaabbbbbabbabbbbabbbbbabababbbbbabababaabbbabaaabaaababbaabbbbaaaabaabaabaabbaabbbaabaabbbaaaabbaabbaabaabaababbbaabbabaabbabbbbaabbbbbbbbbbabbbaaabbbbababaaaaabbbabbbbbbbbbaaababababaababaabbbaabbababaaaaaaaaababaabbbbaabbaabaaaaaabaaaabaaaababbaaabaaaaababaabbaabbaabaaaaaabaabbaabababbbababababbbbabaabbaabbbbbbaabaabbbbabababbbabababbaaaaaabababbabbababbabbabababaabbaabaabababbaabbaabbbbbbbbaaaabbbaabababaaaabbbaabaaaabbababbbbbaaaaaabbbbaabbbbbababbabaabaaababbabababbbbbbabbbaabbaabaaaabababbbaaaaabbabbababbbbaaaabbbabababaaabbababaabababbbbbababbbabbbabaabbbabbabbabbabbbbabbaaabbabbbbbaabbababaaaabbbbbabbbbabbababababbabababbaabbababaabbabbbbaababbbbaaaabbbbaaabbaaabaaaabaaabbbbaababbbbbbaabbbaababaabbbaaaaababaaaabbabbabbabbaabbaaabababbbabbaababbaabaaaabaaabbabbbbaaaabaaaaaabaaaabbbbaaaaababbabababaaababbababbbababbbbabaaabbbababbababababbbabaaabbbabaaaaaaaababbaaaaabbababbabbbaaaabbbabbabbbbbbbaaabbbbabaabaabbabaaaabbabbbbaabaaabbaababababaaaaaababbabbaaaaababbabaaaababbbbababbbaaaabbababaabbaabaaaaabaababaaabbbbbaabbaabbaabaabaaaababaabbbabbbaaaababbbbaaaabbabaaabaabbabbabbabbaaaaabaabaabaaaaababaaababaabbbabaabbbbabbbbbbbaabaabaababbbaaaaaabbaaaabbabbbabbbbbaaabbaabbbabaababaabbbbbaababaabbabbbbbaaaabbbaababaabaaabbbaaaaababaabbbbbabababaabbaaabababaaaaaabbbbbaaabbaabaaaaabaaaaaaabaaabbaaaababbabaaababbaaabbbababbbaababaabbbbaababbbaabaababbaabbabbbababaababbaababbaababbbaabaabbabaaabbbabaababbabbbbbbabaabaababbabababbbabbbaabaaababababbaabaabbbabbabbbbabaaababaabbbbbbaabbbbbababbbbababaaabaababbbbbabbaaaabaabaababbbbbabaabbbbabaabbbbaaabbbbabaabbaabaaaabababababaaaabaabbbabbbabbabbaaabbabbbabbbbbababbabaaabbaabaaaababbaaabbbbbabbaabbababaaaababaaabaaaababbabaabbbaaabbaabaaabaaaaabbabbaabbbbabaaabbbbabbabaabbbabbabaaaaababbbbbaabbaabbaaababbbbbaabababbabaaababbbbbbbabbbabbbabababbaabbbbaaaaabbaabbbbbabaabaaaababbabbababbaabaaaaabbaabbaababababbabbaaabaaaaabbbbaaaabbaababbbaaabaabbaabbaaaaababbbbbaabaaaabababaaababbaabbaababaabbbaabbbababbbabbaaabaabbbbabbbaababbbabbbabbbbbbabbbabbbbbbabbbbbabaaaaaabbabbaababaaabbbbaabaababaabbababbaabbaabababaabbababbaabbbbbbabaabbbabbbbaabbbaaabaabbabbbaabbbbaabbaabbababbbabbbababaababbbabaababbbbbabbaaaaaaaabbaaaabbbabbbbabaaaabaaababbbbaaababaabaabababbabbababbbbabaaababaaababbaaabbaaaababbabbababaabbbabbabaaaabbbaaabbaaaaaaabaaaaabbabaaabbbbbaabbababbabbabaabaabbbaaaabbbbaabbabaababaaaabbababaabbbbaaabaaaabaabbaaaabbbabbbbbbbbbaaaabbbaaaaaabbaaaaabbaabbabbbababbaababababbbbabbbbbbabbaaabaabbbbbbabbababbaaababbabbababaabbbaaaababbbbabaababbaabbbaabbabbbbbbabbaaaaaabaabbaaababbbabaabaabababbaabaabbbbabaaababbaaaaaabaabbabaabbbbbbbbabaaaabbabaabaababbaabaabaaaaaabaababbabaaaaaaabbaabbabbbabbabaaabaabaaabbaabbaaaabbaabaabbbaaabaaabbabbbbababaaabaaabbabaaaabbaaaaaabbabababababbabababbaabaaababababbabbaaaabbbbbaabbaaabbbbaaaaaabaaabaaaabaaabbbbaababbbbbabbbbbaabbbbbabaabbabbbaaabbbbaabbabaaabaaaaababbbbabbbbbbaabbaaaaaabbbbababaaabaabbbbbbabaabaaaabbaabbbabbabbaaababbaababbbabbbbbbabbbabbaaababbbabbaaaaaabaaabbbaaabaabbabbbaaaaaaabaaaaaaabbaababbbabbbabbabbbaabbbbaabbbaaaababababaababaaaabbbababaaaabbaaaababababaaaaabaaabaaababbabbbbbbaababbbbaaabbbbbbabbabaabbabbabbbbbbbababbbaabaaaabaaabaabbaabbbbabbabaabababbaaaabaababbabababbbaabbabaaabbbbabaabbbabbbaabaaaaaaabbbbabbaabaaabaabbaaabbbbbbabbbabbbaabaaaaababaabaababbaababababbababaaabbbabbbaabbababbbaaabbabbbbbbbbaabbbbbbabbbbabbabbbaabbbabababaaabbbabaababbbaabaaaaabaaaaabaabbaabbababbbaaabaaabaabbbbabbbaabbbbbaaaaabaaabbabbbbbabbbbbabababbbaaaabbabaaaabaaabbbbababbabbaabbbaabaabbabbaaababbabaababbbabbbaaaaaaaaabaabbbabbabbbbbabbabbaaabbababbabbbbbbaabaaabaabbbabbbababaabaabbbbbbbbaababbaabbaaabbabbabbbabababbbbbbaaabbababaaabbbaabbbbbaaaaabaaaabbababaababaabbabbbbbbabbababbbbbbabababaaabaaaaabbabbaaababaaaaabbaababbabbbbbbbaaaabbabaababababbaabaabbbaaaabbababbbabbabbbaabbaaaaabbbaabbaababbbaaaaababbaabaabaaabbbaaabaababbabbaaababaaababaabbbbabbaaaababaabaaabaabbbbabbbbbbaaaabbaabbaaabbbbaaabbbabbbababbbbabaabbaaabbbbbbabaaaabaaabbbababaaaabbbabaaabaaaababaababbbbbbbabbbabaaababaababaabbababaabbbabaaaaaaaabaabaaabbaaaabbbaabbabababbabbabbababbabbaababbabaabaaaabaabaabaaaaaabaaabbaaabbaababaaabbabaaaaabbabbaaabababbbbaaabaaabbabaaaaababbaaabbbbbbbbbabababbabbbaabaaabaaaabbbaababaabbbbaabbaabaabbaababaabbaaabaabbaaaaababbaababaaabbbaabaaabababbbbbbaabaaaabbaaaabaaabbababbaabbababbabaaaabbabbbbbabaababbbabaaababbabbbbabbabbaaaabaabbbbabbaabababaaabababbbbaabaaabaabaaaaaabababbabaaaaaabbabbbabbbabbabbbaaabbbabbabbaaabbbbaaabbbaabaaaaaabbbabbbbabbbaaabbbaabbaababaabababaabaabbabbaababbbabbbbbbbbabaababaaaaaaabbabaabaabbabbbbbbbaababbabaaabaabbaaaababbaaabbbbbbbbbabaaaaabbbbaabbabbaabaaabbababbaaabbaabbaaabaaabbaaaaababaabbbabbbabbabbbbaaaabbbabaabaabbabbbabaabaabbaaabbabbbbaaabaabaaaaababbbbaabbaabaaabbabbabbaaaaabaababbbbbbbabbaaaabbaabaabbbaabababbabbababbbabbbaaaabbbababbaabaabbaabbbabbbbaabbaaabbbbbababaaabaabaaabbabaaabbaaaabbbaababababbbaabbbaabaaaaabbbbaabbaababbbaabbbbaaabaaaaaaaaaaabbabababbbbaabaaaabbaaababbabbabbbbbbaaababbaaabaabaaaabbbbaaababbaababaabaabababababababaaabbaabbbababaabbbaabbabaaaaaaabbabababbbbabbabbabbbbabaabbbaaaaaaababaaabaabbbbaababbabaabaabbbaaabbabaabbbbaaaaaaaababbaabbbbaaabaaaaabbbbbbaabababbbababbbabbaabbbbbbbbbaaaaaaababaabaaabababbbaaaaaaaabaabaabbaaaaababaaaabaaaaabaaaabbabaaabaabaabaaaabbbabbbabababbabbbbbbababbabaaabbabbbaaabbbbbbbbaabbbbabbaabaabbbaaabbbbbbaababbaababbaabaaabaaabbababbbababaaabbbabbbabbaabbabbbbaaabbaabaaabbaaabaabbbbabaabbabaabababbaabbabaaaabaabaababbbbbbaabbababaabaaaababababaaabababbbaaaabbaaabbbababbaaaaaaaaabbbababbbbaaaaabbababbababbaaabaaaaabbaaabaabababababaababaaaabbbbbaaaaabababbbaabaabaaaaaababbaabbaaabbbabaaabbabaabaaaaaabaabbbabbbbaaababaabbbabaabbbabbbaaabaabbbbbabbaaababbabaaaaabbabbbaababbabbaaabbabbabbbaabbbbababaabbaababaaaababaaaaaaaababbbaaaabbababaaaabbbaaabbabbbaabbbbaaaaabbaaabaabaaaaaaabbaaaaaaaaabbbababaaaabbbbaababaabbbababbaabbbaabbbabbaabbbbaabbaaabbaababbbbaabbbabbbbaabbbaaabaaabaababbaaaabbabbaaababbaababbbababbababaababbbbaababbabbaabbbabbabaaaaaabbbabaaabaabbbabaaaaabababaabbbabbabbbbaabaabaaababbabaabaaabbbabbabbabbaababaaabbbbaaabbbabbbaababbababaaabababbaaabbaabbbaababaaabbbababbabaabbaaaabaabbabaabbbabbaabbaabbabababaaabbbbaaabbbbbaaabaabaaaaaabbbbabbbabaaaaaabababbaabaaabaaaaaaaaaaaaaaabababbbbaabbabababaaababbbaabbbbbaaababaaabbbaabbaabbbbbaaaabbababbbbaabbbbbbababaaaabaaabbbaaaabbabbabaababaabbababbababaabbababbbaaaabbbaaabbbababaaabaababbbaaababbbbabbbbaabbbabbababbabbaabbbbabaaababbbababbbbbbbabbbbaabaabaaaabbaabbbbabbbabaaaaaaabababaabbaaaaabababaabbaaaaabaabababbbabbabbaaababababaaaabaabbaaabbbbbababaaaaaabbabbbbaabbbbababaababababaaaaaabbbbaababaabbbaabbbabbaabaaabbbbaabbaaabbbbaaaaabaabbaaaabaaaaabababbabababaabaaababaabbabbaaababbaaaabbbbaabbbabaaaaababbbbbbbaababbbbbbbabbabaaabbaabbabaaaaaabaaaaaaabaabaaabbbababbaaababbbbaabbabbbabbaaabaaabaabbbbbaaabbabaababaababbbaabaabbaabababaaaabbbabbbbababaabaabaabbaabaabababaabaababababaabbaabaabbabbbaabbbababbabababbbaaaabaabbbbabbbbbbabbbbabaabaaaaaaaabaababbbaaabbaaabbbaaababaaabaaaababaaaaabaabbbabaabbaabbbababbaaaabbabbabbbbbaabbaaabaaaaaaabbbbbabaabbababbababaababbaabbaaababbbbbbbbbbabaaaabbabababbbbabbaaabaaaabbbabababababbabbbabbbaaaabbababbabbbbabbaaabababbabbbabbabababbbabbbaaaabaaababaaabaaaaabbaaabbaaabaabaabbaaaabaabbbbbabaababaabbabababbababbabababbabbbabbbaaaabbabaaaaababababbbbabbbababababbabbbaaaaabbaaaabbaaabaabbaaabaababbbbabaabbaabaaaababbabbbbbbbabbaaabbbababbbabaaaaaaababbbabbbaaabbabbbababbbbbbbabbbabaaabaaaababbabbbbbaaaabbaabbbbaabaaabbbbbabbbbbabbabbbabbbaaaabbaabaaaaababbbabaaaabbbaaaaaaaaaababaaaaabaababbbaabbababaaaaabaaaaabaaabababbbbbbabbbbbbbaaabaaabaaaaaaaaaabbabbaaababbbbabbabbbbbabaababbbbabbaabaabbbbbaaababbbaaabbabbabaabbbbabaaaaaaabbbbabbbaaababbbaaaaababbabbbbaaabbbbbbbaaaabaababbbbbaabbabbababbbbbaaabbabbaaaabbaabaabbbabbbbbbaaaababaabaabbbaaaabbabbbbabbbabababbabaaaaaaababaaabbbbbbbabbabababaababaabbababbbbbabbbabbbabbbaabbbbabbaaababbababaaabbabaabbabbbababbbbaabbbaaabbbaaabbaabaababababbaabbababbbaaaaabaabbbbbbbabbaaabaabbbbbbbbababbbbbbabbabaabaabbaababaaaabbababaaabbbbabbabbabbbbbbbababaababaabbababaabbaaabbaabaabbaaabbaabbaaabaabbbbaabaabbbbaaaaaaaababbbaaaaabbaaabbbbbaaaabbaaaaaaababbabbbabbbaaababbaaabbbbbbabbaabbaabbaabbbabbaaabbbbaabbaabbbbbbbabababaaaaabaabababbbbaabbbaaaabbaabbbbbaaaaaaaaabaaaaabbabababbabbbabababaabbbbbbaaabbbbaaaaabababbaababbaaabbaaabbababbbabbabbbbbaaabaaabaaaabaabbabbaaabababaaaababbaababaaabbbabbabbabbbabbbbbaaaabbbabbabbbabbabbbabbbbbabbaabbabaaaababaaaaabaaaaaaaaaaaaabbbaabbbbbabaaaababaaabaaaaaaaabbbbabaabbabaaabbaaabaababbbaaabbbabbbabababbaabaaaababbbbaaababbbaaaabaabaaaabbabbbaabaaababbaabaabbbabaaababaaaaaabaabbbabbbbbbbbbbabbaababbbaaaabababaabbaababaaabbbbbbbbaabaaaabbbbabbbabbbabbaabaaabaaaabbaaabbababbbbaaaabbbabaabbabbbababbbbbbabbbaabbbabaaaabaaababbaabbaaababbaaaabbbbbaaaaabaabbabbbbbabbbbaaaabaabbbabbbaabababbbbbbaaabbbaabaabaababbaabbabaabaabaabbaababbaababbbabbaabbbbbbbbbabbbaabaaaabbabbaabaaabaaabbbabbbabababbbabbaaabbaaaabbaaabbaaaaaabaaaaabbbbbbbaabbaabbbaaababbbbbbbabaaaaaaaabaaabbbaaaaabbbabbaaabaaabbaaaaabbbbbabbbabbbbbbbbabaaabbabababaabababbbabaaabababbaaaabaaaaaabababbaaaabbaabbababbbbaaaaaaabaababbaabbbaaaaabababbabbbabbaaabbaabbbaaabaabaaabbbabbababbabaaabbabbbaabbabbaaabaaabaabaaaabbaaabbbabbbabaaabbbababbaabbbabbbbabbabaaaabbbbaabbbabaaaabbaabaabababbbbaababbaabaaaaabaabbbbaaabbabaaababaabababbbabaaabaaabaaabaabbbaabaabbbabbabbabbbbbbabbaaabbbaababbabababbbbabaabaabaaaababaabbbaababaabaabbabbabababbbbbbabbaaaaaaaaaaabaabbabbbbbbabbbaaaaaaabaaabaaabbbbbaabaaabbbaaaaabaaabaaaabbabaababbaabbababbabaabbbaabaabbababaababbaabaaabbaaabbaaabaababbbaabaaaabbaaabbaabbbaaabbabaabaaaaaababbbabbbbaaaabbabaabbaabbbbabaaaababaaabaabaaabbbbabababaabaaaababaaaaababababbbbbaaaabbabbaabbaaaaaaabaaababaabaaabbbaabbbaabaabbabbbabaaababbaaaaabbbababaaabbaaaabaabbaaabbbababbbaabaabaaabbabbaaabaababbaaabaaabbbbbbabbbababbbabbabaabbabbaaababbaabaaaabaaababbabbaaaaaaaaababbaaabbbaabaabbbbabbbaaaabaaaabaabbaabbaaababbabbaaabbbaabaaaabbabbbbbababaaaabbabbabaababbbbabbbbabbaaabbaabbaabbbbbaabbabaabbbbabbabaaababaaabbaababababbaabbaaaabbaaaabbbabbbabbabaabbbabbaaabbaaaaabbaaaabbbaabaaaaaaaaaaabbabaabababbabbabbabaaabaaaaaaabaabbbbaaabababbabaabbbabbaaabbbabaababbbaababaaaabaaabbabbaaaaabaabaabbbaaaabbbaabbbbbaabbbababaabbbaaaaaaabbabbbabaaabbbabbbbbaaaaabbbaaaababbbaaaabbabaabaabababaaaaaaaabbbabbaabbabaaaabbaaabaaabaaabbbbaaabaaababaabbbbbaaaabaaaaaabbaabaaaabbbbababaabbbbbbbabaaaaabbababaaaaaaaaaaaaaabbaaaaaabaaaaababbbbbbbaababaabbabaaabaaaaaabbabaabaabbbbbbbababbabbbababbbabbabbbabaaababbbaabababbabbabbabbabaaaaabbbbbaaaaabbabbbaaaababaabbbaaaaaababbaaabbbbbbabbbbbbbaabbaaaabababbabbabbbbbbababbbbbabaaaaabbbbaaaabbbbbabbbabbbbabbbabbaababababababbaaabaaabaaababbbaabaaababababaabbaabaaaabbbaabbbabbaaabbaaaaabaaabaaaabaabbabbbababbabbbabaaaaabaaababbbaaaababbabbbbbbbbbbaabababaaaaabbaaabbaabaabbbbabaaaabaaababbabbbabbbbaaaabbbbaaabbaabaaaaabbbbabbbbbbbbbbbabbbbbbabbbaaaaabbbaabbabbabbbaaaababbaabbbaaaabaaaabbbabaaababbaaaabbbbaabbbabbabbabbaaaaaaaabbbbbbabaaaabbabaabbabbbbbbbaaaabaaaabbbaaaabbbaabbaaaaaabbaabbaaaabbbaabbababaaabbbaabbbbabbabbbaabaaabababbababbbabbabbabbbaaababaababaaaaaababbabaaaabbaaaabaaaaabbbabaaabababbababaaaabaabbaaaabaabaaabbbaaabbababbaababaabaaaababbaaabbaaabbabbaabbbabaabbbbbbbbabbabbababbbbabababbbbbaaaaaabbaabbbbbaaaaaaabaabaabbbaaaabababbbabbabaabaaabbabbbbababbaabbaababaabaabaababbbbbaaabaababaabaaabaaababbaaaabbaaababbabaabbabbbbaababababbabbbabbbbaaababaabbaaaabbbaaaababbbbbababbaabaaababbabbbbbbabbbbabbaabaabbabaababbbaababbbabbaaaaaaaaababbaaaabbbabbbababaaaabbbabbabbbbabbaaabbabbbbbabbababbbabbabbabbaaaabaababaababaaabaaababbbabaaababaaabbaababbbbabbaababaaaaababababbbbaaabbabbabaaaababbaaaaaabbabaabbabaabbbbaaaababbabaaabbaabaabaaaaabbbabbabaaabbabbbbbbbbbbbbaababbbbababaababbabbaaababababbaaabbaabbababababbbababbababaababaaabbbaabbbabbaaaabaabaababbaabaaababbaaaaaaabbababbaababbababbaabaaabbbababaabbbaaaababbababbbbabaaabaababaabbbabaabaabbbababbaaabaaabbaaaaabbbbbaabbbbabaababababaaabbaaabaaabaaabbbabbbbabbababaabaaabbbbbbaaabbaabbabbaaaaaabbaaaaaabbbbbbbbbaababbaababbbbabbaaabbaaababbaaabaaaaabbbbbbbabababaaaaaaaaaabbabababbaaaababababbaaabaabbaababbaabaabbababbbaaaaaabaaabbbabbbbbbbbaabbbaaabaabbaaabaabbaaaabbbaabaababbabbaabbbbaabbabaabaaabbbbaabbbaaaabbabbabbbbabaaabababababbbaababbaaaaabaaaaabababbaabaaababababbbbbaaaabaababbbbabbaabbbaaabbabaaaabaabbabababbabbbaaababaabbabaaaaababbbaabbbabbbaabbaabbbbbbaabbbaaababbbbabaaabbbabaaaaaaaabbbaabbbbbbaabaaaaabababbabbbabaabbbabbbaaabbabaabaabababbabbbaaaaaaabbaababaababbbaaabbbbababbbbabbabaabbbabaaabaaaaabbaaaabbaabaabaababaaaabbaabbbaaababaaaaaabababbbbabaabaabbbaababbbaaaababaaaabbbababbbbbaababaaabbaabababbaaaaaaaababbbbabbbaabaaabbbbaabbbababbbbabbabbbbaaabbbaababaababbabbbaababaababaabbabbabbbbbaaabbbbbbbbaaabababbaababbbaaababbbababbbbabbababbaaaaaaaaaabbababbbbabaabababaaabbbbaaaababbabbbabbbbbbabaababbaabaabbabbbabbaabbbabaaaababaaababbaaabbaaabaaabbbabababaabbabaabaabaaaaabbbaaabbaaaabbbabaaaabbababbbaabbbabbabbbabaaaabaaaaabbabbbbabaaaabbbabbbaaaaaaaaaabaabbababbbbbbbbbaabaaabaaaabbaabbbabaaaaabbabbaabbbbabaabaaabbbbbabaaaaabbbabbbaabbbabbbbbbbbaaabbbbabbaaaaaababbbbabaaababbabaabbaababbbbabbbaaaaaaabbbabaabaabbabbbbaabbbaaaababbbaaabbabbaabbbbbabababbbbaabbabaaaaaababbbbabbbaaabbbaababaabaaaaaaabbbaaaaabbabbabbabbbaaabbaabbbabaabbbabbbbbbbbbabaaaaabababbabaabbaabaababbbabbaabaaaaaaaabbbaaaaabbbaabbabbabaabaaabbbaaaabbbbaaababbbabbbaabaabbabbbaaaaaaabaabbbbbbaaabaaabababaaaabbaabaaabbbbbaabababbabbbaaabbbaaaabaabbbbaaaaaaaabbabbaabbbaaaaaaabbbabaaabbbaaaabbaaabbababbbbaabbabbbaaaaaaabbaaaaabbbbabbbbbabbbbbbabbaabaabbbbabbbaaaabbbaabaaaabaaaaabbabbbbbaaabbbbaaaababbbababbbbbaaabaaaababaaabaaaababbababaaabababaabaaaabbbaaaaaabaaababaaaaaababbaaaaabaabbaabaaabbababbabaababbabaabbabaaabbaabbbbabaaaaaaaabababaaabbbaababbabaabaaaabbaaabbaabaabbbaaaaababaababbabaababbabbbaabaabbbbaaabbaaaaababbbbababbaabbaabbbaabaabbaabaabababbaabaaabababbbbabbaababaaababaaaaababbbabbbaaaaabbaabaabbaaabaabbabaaaababaaaaabaabbabababbabbbbbaaabbaaababababbbabbbbababbbbbbbaabbbbbaababababbabaabbabbbababbabaaabbbbaaabaaaaabbbbbbbbbbbabbababbbbbabaabbbbaabbbbaaabaabbabbababbabaabbaaaabaaaaababbbbbbbaabbbaabbabbbbbababbbaaaaaabbbababaabbabbababaaaaabaababbbbaaabbbbbbbbabbbaaabbababbabaaaaaabbbbaababaaaabbbbaabbabbbaaabaaabaaababbaaababbbbabbaaaaabbbbbbbbbbbabbaababaabaaababbbabbbbabbaabbbbbbbbabbaabbaabababbbbbabababababaaaabbabaaaaabbaabbbaaabaaaaabaaaababbbbaabbbbbbbabbbaaaaaabbabaabaabababbbbaaaabbabaaababbbbbaaaabaaababbbbbababaaabbabbabbaaabbaabaabbabbbbaabaabbababbbbbbbbbbabaabaaaabbaabbbbaaaabaabbaababbbbbbbbabbbbbbbbabbbaaabbbbaaabababbbabaabbaabaaaabbaaabaaabbabbabbabbbbababaababbaabbabaabaabaaabbabaaaabbbbaababbaaaaabaaabbaaaabaabbabaabaababababababbabaaaaaaaabaaaaaabbbbbbbbbababbbbaaabaaabbbbbabbaaabababbbbbaaaaaaabbababaaaaaaaabaaaaaabbabbababbabbaabbabaabbababbaabaabaaaaabaababbabbbbabaabbabbbbaaaaaaabbabbbbaaaabaabbbaaaaaaabbbaaaaabaabbabbbaaabababbbbaababaaaabbaaaaaabbabbaaabbaaabbabaaabbaaaabbaababaaabbbbaabbababababbbababbbbbbbbbbbabbbaabbbababaaababababbbbbbbbaabbbaabbaabbbaaaaaaababbababbbaaabbbaabababbbbbbbbaabbbaabbabaabbaabaabbabababbbbbbbbbbbbaabbabaaaabaaabaabbbbbbbaabbabbbbbbbbbbbaaaabbbbbbaaabaabbabbbaaaaaabababbbaababbaabaababbaaaabaaabababbbabaabaaaaabbbababbaaaaaaaababbbaaabaaaaaaabbbaaabbabbbbaabbaaaaaaaabbabbaaabbbbbabbbaaababaabbabbaabaababaaaabbbbabbbaabaaaabaabbbbabbbabbbbaabbbaaabaaaaabaabaaabaabaabbaabbabaaaaaababbbabbbabaaaabbaaaabbbbbabaaaaabbaaaababbababbbbbbbbaabaababbbbaababaaabbaaaabbaabaaabbbabaabababbabbbabbababbbabbaabbabbaabbabbabaaabbaaaaaaababbbbaaaaabbbbbbbbbaaabaaabbbbaaabbaabbbbaaabaaabaaaabbbbbbbabbbbaaaabbbbaaabbbaabbabbababbbabaaababaaaaabaaaaabbbbbabbbbbbbaabbaaaabaabbaaabaaaaabbaababbbaaaaabaaaaabbaaabbbaaabbbbbbaababaaaaabaaabbbaaabbbbaaabbbaabbaaabaabaabababbbbbbbbabaabbbbaaaababbbabaaaababbabaaabaabaabaabaaababbabbbaababbaaaaabbbabababbaaabbbabbbbbababbabbabbbaabbaababaababbabaabaaaaaaabbabbabbabaaabbbabbbbbaaaabaababbabbbabbbabbabaababbbaabbbbabbbabbabaaaabaabbabbaaabbababbaabbbbaaababaaaaabaabbbbbbabaaaabaabaabbbabbaaaababbbbbbaaaabbbabbabbbaaabbbabbaabbaaaabbbaaaabbbaaaaaaaabaababaabaabababbabbbbaabaaabaaabaaaaabaabaabbabbbbbbbbbaabbbbabbbbbbbbaababbbaababbaaaaabbababaaababaabbababbaabaababbaaaababbababbabbbbabbbbabbbbbaaaaabaaabbaaabababaabbbabaaaabaaaaaabaabbaabbbbabbaababaabbabaaaabbbaaaaaabaaaaaaabbbaaaabbaaabbaaaaaaabbbbbbaaaabbaaaabaabaaababaaaabababaabaabbaababaabbababaabaabbababaababababbaaabbaaabbaaaabbbbabaaabbaaaaaabbbbaaababaabababbbaaabbbabbaababbbbbabaaabababbbbbbababaabbbbababaaaaaaaababbbabaaaabaaaabaababababababbbbbabbabbbbbaabbbbbbabbabbaaaabbaaaaabbabaabbbaaaabbaaaaabbbbbaababbabbbbbabaabbaababbabbabaaaabaabbabbababbbaababbbbabbaaabbbbbaaaaabbbbaababbabaabbababaaabbabbbbbabbbbabbbbaaaaabbbaabaabababaabaaabbbababaabaabbaabbbaabaaabbabbaaabbbababaababbabaabbabbabbabbbbababbbbababaabaaaaababbbbaababbbbbbabaaabaaabbaabbaaababaaaabaababbbabbbaabaabbbaabbabaabbbabbabbbabaaaaabbbababbbaababbaaabaaaabbbbbbbbabbbaababbabaaabbaaabbaaaababbaababbbbabbbabaabbabbbababbbbabbababababbbbbaabbbaaaaaabbaabbaabaaaaaaaabbaaabbbbbbbaaaaaabaaabaabbbbbaabbaabbbbbabaabaaabbababbbbaababaaabbababaababaababbaababbabbbbaabbbaabaaaaaabbaaaaababaabaaabaabaaaabbababaaaaababbaabbaaabbbaaabaaababaababbababbbbbbababbaababbaaababaaaaaabbaabababbaabbbaabbaabbaabbbabbbababbbaabaaaabbaaabaabbababbaaaabbababaaaabbbbaaabaaaaaabaaabbaababaabaaabbabbbbaaabaaaaaaaabaaabbaabbbbaabaababaababbabbaaaababbaaaabbbbbbabbbaabaabbaaabbaabbaabbababbbabababbababaaaaaaabbbbababbabbbaaabaaabaababaabaabbaaaaabaaabbaaabaaababbbabbbbbbabaababbaabbbbabababbaaaabbbbababbbbbaabbaaaaababbbbbabababaabaabbabababbbbaabbabbbaababaabaabaabaaaaaababaaabbbabbabaaaaabbbabbbbbaabbbaabbbaabaaaabaabababbabbaaaabaaabbabbaaaabababbbaabababaaabaabbabbabbbbbaaabbaaaaaabbaabbbbabaabbbbababaaaabaabbbabaaaabbaabaaaaaaaabbbaaabbabaababaabbaababaaaaaabbababbbaaaabbaabaabababbabbabbbabaababababbaaabaabbbbbbaababbbaaabbbbbbaabbabaaabaababbababaaaabbbabaabbaabaaabaabbaaabbabaabaaabbbbabbaabaabaabaaaabaaababbbabababababaabbabaaabaaaaaaababbbaababbbbbbbaaabbaabbababbbaaaaabbaabaababaaaaabbaabaaaababaaabbabbbbbababbaaabbbaabaabbbbbaaaaaaaabbbbaaaabbbbabbabbaaabaaaaabaababababbbbbabababababaabaabaabbaabbabaababbabbaaaababaababaababababbbabbabbbaabbaaaabaabbbaaabbaaaaabbaabbaabbabbabaaaabaabbabbbabbaabbabababbaaabaaaaabbababbbababbbbaabbabaaaabbabababbbaabbaaaababaaaababbbbbaabababababbbbabbabbabbaaaabbbababaabbaaabaaaaaabaabbaaabaabababbbaaabbabaaabbaababbaaaaaabbababbababaaabbaababaabaaaababbababaabbabbaabaabbababbbaaaaaaabaaaababbbaabbbabaaaabbaaaaaabaaaaaaabbbaaaabaaabbbbbbbbaaaabbbbabaabaabaabbaabbbbababaaaaaaaaababaabaabaaaaabbabaabaabbaaababaababaaaabbabaaabbbbabbaaaabbbabababababaabbbbaabbaabbaababbbbaabbaabbabbaabaaabbbbbaababbbaababbbbbabaabbabbaaabbaaaabaababbbbbaaaabbabbbbabbaaaaaababaaaabaabbabababbbabaabbbaaabaaabaabababaabbabababbbbabbbbbaaabbbabbbaaabaaabbbaabbaaaaababababbaaaaabbbaaaaaabaaabbbabbbbabbbbabbabbaabbbbbababaabaababbaaabaababbbaaabbaaabaabbaabbaaabbbbbbabbaaabbabbbbaaababbabbabbaabaabaaaaaababaaaaaabbaabaaabbaaaaaabaababbababababaaaabaabbababbbabbaababaaaaabaabbabbbabaababaababbababaabaabbbabbaaaabbbbbbaaaaabbbbabbaabbabaaaaabbbbababbbbaabababbbababbabbbbabbbaaababbaabababbbbbabaaaaaabaabbabbaababbababababaaabbabbaaabbaababbbbbbbabaabbaaaabaaaabbaaaaababbabbbabbbabaababbaabbbaababbaaaaaababbabbbbaabbabaabbaabaabbbbabaaabababaababbbaabbbbabbbbaaaabaaabbaaaabbbbbbbbbaabaabbaabbababbbbbbabbbbbaaabbbbbaaabbaabbababababbaabaaabbbbbbaababbbbabaaababbabababaaaaabbababbaabaaabaabbbbbbabbbbbbaaaababbaaaabbaaaaababaaaaaaababbbabbbababbbaaaaabaaaabaaabababaabbaaabbaaaabbbabbbabbbbababbaaabbaaabbabbbabaabbbabbbabbaabbaabbababbbbaababbbabbaababababbbaabbbaaaaabbbababbbbbbabaabaababaababbaabbbbababbbbbababbbaaaaabbabbaaaaabababbaabbabbaaaaaabbbbabaabababbbbabbbbaabaaaabaababbabbaaaaababaaaabababbbababaaaaabbabaabbaababbbbbbaaaaaababababaaabbabaabaabaaabbbaaababaaaabaaabbbbbaabababbbababbbbbbbbbaaaabababaaaabaabaababbaababbbbaaaabbaababbaaabbbbbbabbbbbaabbbaaaaabbbababaaababaaabaabbbbaabbaaaaabaaabaabaaaaabbaabaaaaababbbbbaaabbbaabaaababaabaabbbbaabbaabababbbabaababbbbbbaabbaabbaabaabbbbbababbaaabaaabaabbabbababbbabababbbbbbababaababaabaabbababaaabbbaabaabaaaabbaaabbbbaaababbbaaabababbabbababababbaaabbaaaabbbbabababaabbabaabaaaaabbaabbbbaaaabababbabaabbbbaaabaaabbabababbaabbbbbbbaaabbbabaaaabababbbbbabbbaababbbabbbaaababaaaabaababbaabbbababbbabaababaaabbbabaaabbaababaabbabbabaaaababbbabaabbabbabbababbaabaabbaabbbabaaaaaaabaaabbababaabababababbbaabaababbaabaabaaababaababaababaaaabbabbaabbabbababbbbaaababbaabbbbaabbaaabbbbbbbbabbabaabbaaabbabababbbabbabaabbabbbaababbabbaaabbaaabbbbbbbaabbaaabbbbabbaaaaaabbaabaabaaabbaabbabbaabaaaaaabaababaababbbababaabbaabbbabbaabbabbbbbbabbbbbaabbbbaabbabababababbbbaaabbaabbaabbababaabbbababbbbabbbabbbaabbbaabaaabbabbabaabbaabaaabaabbbbabbaabaaaabababaabbbabaabbabaababbababbabbbababbaaaabaaabbbaaabbbabbbbaabbbbabaabaaaabbbbaaaabbaababaaabaabbbbabaaabaabaabababbaaaaabbbbabbabaababbbbbbbaaaabaaababbabbababbaababbabababbbaaababaaaaababaababbabaaabaaabaabbaaabbababbbabbaabaaababaabbbabbbbbbbbbaabaabaaabbbbaabaaaaababaaababaaaaaabbaaabbaabaaaabbaaababbabbbbaaaabbbaaaaabbabaababaabaabaaabaaabbaaaaabbaababaaababaabbabbaaabbbababaabbbbabaabbbabbaaabaabaababaababbbabaabbbaabbbaabbaaabaaabbaaaaabaaababbabbabaabbbababbbabababbaabbaabbabbabbabaabbabbbbbaaababbabbabbbabbabbbaaaabbaaabbbbaabababbbbbaaabbbbaaababaabaabaaababaaabaabbaababbabaaaaababbabbbabbbbbabbbbabababbbbabaabbbbbaabbbaaaaaaaabbbbbbbbbbbaabaababaabbbabbbaaaaaaabbbabbababbbbaaabbaaabaaabaaaababbbabbbbaaaaabaaaabbaabaaaabababaaababbbbbabaabaabababaabaababbbbaabababbaabbabbbabbababaabbbbaabbaabbbbbbbaaaaaababaabbbbabaabaabbbbaabbbbbabaaabbabbbbbabaaabaabaabaaababbabaaabaabaaaaabbbbbabbbbbaabaababbaaaabbbabaabababbbaabbbabbaabbaabbbaabbbaaabbbbaaabbbababbbababbbbbabbbabaaabbabbbbabbbabababbaaaabbbbaabaabbabbaaababbabbababbbaabbbbbabaababbabaabaabbbabbaababbbbbaabbaaabbbbabbabababbbbaabbbaabaaabaaabbbabbaaaaaabbbbbaaabbabbaabbaabbaaaaabbabbbabaabbbbaababbabbabbbaabababbbbabbbabbababbabbbaaaaaaaaabbbbaaabbbbabababaaaabbbabababaaaabaabaabbbabbbbabbabbaaaabaabaabbbabbaaabbbaabbaaabbababaaabbaabbababaabbbbaabbabbbbbaaabbbbbbbbbababbbbbbbaaaababbabaabbbaabaababbbbababbaaababbbbbabaabbabaabbbbaaabbabbbbbabbbababbbabbbbababbaababbaabbbbabaaaabbaabbbbabbaababbbbbbbaaabbbbaaaabaaabbababababaababaabbbbabababbaaaaaabbbaaaaaabbbabaababbabbbabaabbabbbbbaabbaabbbbbabbbabaabbabbbaaaaaaabbbabbbaabbbabaaaaabbbaaabaabbbababbbbbbbaaabaaabbbabaaaabbaabbbbbbbaaababbaaaaaaaabbabbaaaaabbaababbabbaabaaabbbbbbbbbabaaaaabaabbbabbbaaaaaaabbbaabbbbbaaaaaabababaabaabbbabaabbbabaababaaaaaaaaaabbabbbbbaaaabaaababbabaaaababbabaaaaaabaabbabbbbaabaabaaabbbabaaaabbbabaaaabbabbbbbbbaaaabaabbbbaabbbbbbabaababbbbaabaabbbbbbbabbabbaaaababbbbabbaabbbbaaaabaaababababaabbbaaaaaaababbbababbababbaabbbaabaaaabbbaabbbbaabbbababbabbabaabbbbabaabbabbaaaaaaababbabaabaabbbbaabaaabbaabbbbabbaabbabbbbabbbaaaaaabbbabbabbabaabbbaaaabaaaaabaaaaabbabbbbbbababbbababbabaaaabbbbabbababaababbbbbabbbbbbbbbbbbabbabbbbaaabaaaaaaaaababbbbbabbbababaaaaabababbaaabaaaaabbababaaabbabbbbbaaabbabbbbbaaaaabaabbbaabbaaaaabababbbbbbaaabbabbaaaabbaaaaabbbbabbaaaaababababbbbaaaabbababbabbbbbababaaaabababbabaabbabaababbbbababaaabbbbaaababaaaaaaabbbbaabaabbaababbaaabbabaaaaaaabaaabaaaabbbaabbabbbaabbbbbabaaaaabaaabbaabaabbbbbbaaabbbbaabbbabbaabbaabaabbaabaababbbababbabbaabbbaabbbaabaaaababbaaaaabbbabbbbabaaaaabaaaabbaabbabbbaaabbbabababbabbaabaaaaaaaaababbbabbbabbaaabbaaabababaaaaaaababaaabbaaaaaaabaabbaabaababbbbbbabbbbaabaabbaaabbbbabaaaabaaaaabbbbabbbbaaabbbbabbaaabbbbaaabaaaabbbbbaababaabbbaaabaaabbbabbabbaabaaaaabbbaaabbbbababbbaaaabaababbaabbaabbbbbbbaaabbabbabaaabaaabbabaaabababbbbbbaaaabaabbbaabbabaaaaabbbbbbaababaabaabbbbabbbabaaababbbbbbabaabbaabbbaabbbaaabbbbabbbaaababbbaabbabbbbbaabbbbaabbbbbbbbbbaabaaabaabaabaababaaabbaababaaaaabaaaabaaaabbbaaabbabbbbbbbbbbbbaabbbbaaaaaaabaaabaaababbbaababaaababaabbbbbabaabbabaabaaabababbaaaaaabbabbaaababbabbbbbbbabbabababbbabbaabbbabbaababbabaabbabbabaabbbbabbbbabaabaabaaabaababaabbbababaaabbabbaaababbaabbaaababaaabbbaababaaababaabbbaaaaaaaaaabbbabbbbaaaaaabbaabaaaabaaaaaaabbabbaabbbbbabbaaabababaaaaababbabbbbbabaaaababbaabbabbaabbbbabaabaabbbbabaabaabbabaaababbbabaababbbaabbbbabbbbabaaaabaabbabbaababaababbaabbbbabaabbaaaaabaaabbabbabaababbaababbabbbaaaabbabaaabbabaababaabaaabbbabbbaabaabaabababbbbaaaaabbaaabababbbbbbaababababaaabbabbaabbbaabaabaaaabbbabaababaabbaabbbbbabaaabbaabaaaabaabbbbbababbaabbabbaabbababbbabbaaaabbbaaabaabaabbabaaabbabbaabbaababbbbabbbababbbbabbbbbaabbabaabaabaabbabbaaaaaabbbabbabbbababbbbbbbbbbaabaaabaabaabbbbbbabaaabbaabababbaaaaabbabbabbaabaabaaababaababbaabbabababbbababbaabbbababaaaaaaaababbabababbaabbbbabbabbbbaaabbbaabaabaabaaaabbbbbaaaababbabababaaabbbabbaaababaaaaabbbababbbababbbaabaaababaaaaabbbaababaaaababbbbbaabbbaabbabababbaabababbbaabbaaaaaaaababbababbbaaaaaaaababbbbbaabaabbabaabaabbababababababbbaabbaaabbaabbbbbbabbabbbabbabaaaaaaaabababaaaabbaabaabbbaaaababaabbbbabbaaababaaaababbaabbbabaababbaaaaabbabaaaabbaabaabbbbabbaaabbbaababaaabaaababaaabbbabbaaaaaabbabbaabbbbaaaaaaabbaaaabbbaabbbbaaabaabbbbbbababaaaabbbbbabbaabbbbabaaaababbbbaabbbaabbbaaaabaaaaabaaaababbaaabbbaaababbaababaaaaaaaabaaabbaaabbbababababbbaabbbbbabbabbbababbabbaaaaaababbbbbbbabbbaaaaababababbaaabbabbabbbaaabbbaababaabbaabbbabbaaaaaaaabbbaaaaaabbaaabababbbabaaaaaaaaaaaababaabbaaaaababbaaabaaaabbabbababaabbabaaaaaaaaaaabbabbbabbaabbbbbabbbababababbabbaaaaaaabaababbababbbabbabaaabaaabaababbaababbaaaaaababbabbbbabbaaabbaaaabaaaaabaababaaaabbbbbbaabbbbbabbaaababbbbabbaababaaabbaabaaaaaaababbabbaabaaabbbbbaaaaaaaaababababaaababbbaabbaabbaabababbbabaaabbabbbaaaaaaabbbbbaaaabaabbabbaabbbbababaaababbababbbaababbbabaababbbaabbaabbbbbbaabaabaaaabbabbabaabbaaaabbbabaaabaabbabaaabaabababbaaaaabbabbbbbbabbaaaabbaaaabbbaabbabaabbaaabbaabbbbbaabbbbabbbabbaababbaabbbbaaabaaaaaabbbbbbbbabbbabaaaaabaaaabaaabbbaaabbabaababaaaaabababababbbbbbaababbbaababababaabababbbbbbaabbbaababbbaaaababbbabaaababbabbbbabababbabaabaabbabbaaaabbbbbabaaaaabbabbaababbbbaaababbbabbaabbabbbbbbbbbbabbabababbbbababbaabaaaaabbbbaabbbbbababbaabaabbbaaaababbaabbabbbbaababbaaabbabbababbabaaabbbabbbabbbabaababbbbbaaaaabbbbbbaabbabaababaabbbaaabbbbabaaabbabbbbbbaabbbbbbbbabbbaababaababaaaaabbbbabbbbbbaabaaabaaabbbbbabbabbbbaababbaaaabbbbaababbbbbaaabbbaaabbababbbabbaabbabaabaaabbbaaaaaaaabbbbbababbabbbbaabaaaababbbabbbaaaabbaabaabbabbaabbabaabbaabbbaaaaabbabbbaabbaababbbaaabbbabbbabaaabbaabbabbbbbbbbabbbbaaaaaabbabaabaaabaababbbbbbabbbababbaabaabbbaaaabaaaaaaabaabbbabaababbabaaaaaaaaaabaaababbbbbababbaabaaabaabaaabaabaabaababaaabbabbbaaaabbaabaabaaababbabbaaaababbbbaaaaaaababababbbbaaabbaaaaabababbbababaabaabaaabbababbaababbbbaabaababbaabaabbabbaaaababbaabaaaabbababbabaaaaaabaabbbaaabbabaabababbbbbbbabbaaaabbababbabbaaabaabaabbbaaabbbbbabbbabaabaaaabaabbababbbababbabaabaaabbbaaaaaaaabbabaabaababbbbabbbabaabababbaaaababaabbaaaaaaabaaabaaaabbbabbabaaaabbbbbaaaaabbabbabaabbabbbabbabbbabbbaabbabbbbabbbbbaaaaabbaaaaabbabaababaaaabbaaabbbaaabaaabababaabaaaaabbbaaabbaabaaabbaabbabbbaabaabbbbabbbaabaaababaabbabaaaaaaaaaabbbbbaaaaabaaabaabbbaababaababaabbaababbbbababbbbaabbabbbbabaaaaaaabbbabbaabbabbbbbabababbabaabbaaabaaabbbaabaaaaaabbbbaaabaabbabbbbaabaabbababbababbabbabbbabbbabaaaaaabbaaaaabbabaabaaabbbbbaabaabbabbabbaabbaaaabbababbaabaaababaaabaaababaabaaabaaabbbabbbbabaaabbaababaabbababbababbaaabbbaaaabababbabababaabbabaabbbaabbbbbbbaabbabababbbbabaababbabababbbbbabbbbababaaabbabbbaabbbbbbaaaabbbbabbbabbbbbbaaaabaaaaaabbbaaaababbaaababbaaaabbbbbbbbaaababbbaaaaabababbbaaabababaabaaaabaaabaababbaabaaabaaaaaabbbababaaabbabababbaaababaabbbabbaabaabbaaaaaababaabbaabbbbbabbbbaabbaaaabbbbabbabbbabababbbaaabaaabababbaaaabaaabbaaaabaaaaaaabbababbaabaaabbbabaaababaaaabbaabaaaabaaabbbaaabaaabbaabbabbabbabaababaaaaaaaabaaaaabbbbbbbabbbaabbaabaaabbabaabaabbbbabaaaaaabbaaaaabbbbaabaaaaaabbabbabbaaaaaaababbabbbaaabaaaabababbbbaabaaaabaaaaabbababaaaaaabbaaaabbabaabaabababbbabaaababbababbaaaaabbabaaabbabbaaabbaabbbbabbaabaabaababbaababbaabaabaabbbbaaababaababbaaaabbaabaaabbaababaaaaabaaababaaababbbbbbbbbbabaaabbaaababbabbbaaaabbabbbbbaaaaabbabaaabaaaabaabbaababaaaaabbabaaaaabbbbabbbbabbaaaaaaaabaaaabaabbaababbaaaaaababbbaabbabbaaabbaabbaaabbbabbaaaabbababaaaabbbbaabbaabbbbaabaaaaaababbaaababbababbbababaabbbbbbbbbbbaabaabaababbaaaabbbababababbaaaabbabaaaabbbbbababbabbbabaababbabbbbbbbbabbbaaababbbaabbbabbabaaaabbaabbbabbaabaabababaababbbbbaaaaaabaaababbabbbbababababbaaaaaabaaabaabbabaabababaaabbbabbbaaaaaaaaabaaabbaabaabbaaabbababbabaababbbbbabbabaaababbbbbabababababbbabbbaaabbbaabaabababbabbaaabbaaaaaaaababbbabbbbbabbaaabababaabbaaabaabbbbbbbaababaabbbaaaaabbaaabbbabbababbbbbaabbabaaabaaabbabbababbbaaaaabbabbbaabaaababbbaaaaabbbabbbaabbabbbaaaaabbaabbaabaaaaaabaabbbbaababbbbaababbbabababbbaabaabbbbabbbbabababbbabbbbabbaabaaabaaaabbbbababbaaaaabaaaaababbabbbabababaaabbabaabaababaabababbabbbbabaabaabbababbbaaabaabbaababababbbbabaaabbabaababbababababbaaababababbabaaaabbbababbabbaabbaaabbaaababaabbababbaabbbbaaabbbbaabaabbbaabaaabaabbabbbabbaaabaaabababbabbaabbbbbababaaaabbaababbaabaababbbbabbabbababbbabbaabababbabbaaababaaabaaaaabaaaaababbbbabaaaaabbbabaabbbbabbabaaababaaababaaaaaabaabbbaabbbaabaaaabbaabbaabbabaabaababbbababbbabaaabbbbabbaaaabbabaababaaaaabbbaabaaaaabbbbaaaaababbbbabbbbabbaaaaaabbbbaabbbbaabbbbaabbbbabbbabaaaaabbaababbbbabbababbaaabbbbabababaaaaabbaaabbabaababbabbabbbabbbbbaabbaaabaaabbabbaabbbbabbbbaabbbababbbbbababbbaababbbaaabbbbbababababaaabbabbabababbaaabbabbabbbbaaaaabaabbabaaaaabaabaaabbbaaaaaabaaaabbaaaabaaaaabbaaaaabaaabaaaababbabbababaabbbbbababbbabaaaaaabbbabbabbabaabaaaaaabbbabababbbabbbbabaabbabbabaaaabaaabbabbaaababaaababaabaaaaabbbababbbababaabaabaaaabbbbaaaaabbbbbaabaabbaaaababbbaabaaaababaaababababbbaaaabbabbbbbbbbabbbabababbbbbaaabbbabaaaabababaaabbaabbaaabbbbaaaaabbaabaababaaaabbabababbbbaaaababbabbbaaaaaaabaaaaabaaaababaaaababababbabbbbaaaabaaaaabababaabbbabbaababbbaababaaababbaaaabbabbaaabaaaaaaabbbbbabbaaababbaaaabbbabaaaaaaababaaabaabaabaaaababbaaaabbbbbbaaababbbbbbbaaaabbbabaababbaababababbbbaabaaababbabbaabbbabbbbbbbbaabbbabbbbbababaababbababbbaababbbbabbbbbbbaabbaaaabbabbababbabbbababbbabbabaabbbbabbabbaaabaaaaaabbbbbbababaaaabaaaabababaabbbaaaabaaabbabaaaabababababbbbbbbbaabbaaabbabaabbaaabbaaaaaabaaaaabaaaabaababababaabbbaababbbbbaaabbbbabbabbbbaabbaaabbbabaaabaaaabbbabababaababaaaabbbabbabaababbaabbaaabbabaaaaababaaaabaaaabaaababbbbbbababbbabaaababaaaababababbabbbaaaaabbbbabbbabbbabaaabbbaabaabaaabbabbbaaaababbaaaabbabbbaababaabaabaabbbbbbaababbaabaaabaaaabaabbbaabbabaaaaaaabbaaaabbabbaabbbbbbabaaaababbbababbbbbbabbaaabbaaababaaaababbbbabababbbababaaabaaaabaabbbbabbabaaaabbbaaabaabbbaaaabaaaaaababbbbbaababbbbbabbbaababaaaabaaabbaabbbabababaaabbababaaabababbbaaaabbaaaaababbbaabaaaabbaaaaabbaaaaabbabaaaabbbaaabaabbbbaaaababaabbbababbabaabbbbaaaaabaababaababaabbbaabbbbaaaabaabaabbabaabaaaaabbaaabbbbbabaabbababaabababaababbbababaababaaabababaabaaabaabbbabbaaaabbaabbaabbaaabbabbbaabababaabbbbaabaaaaaaabbaabbabbbaaabbbbabaabbbbbaababbbbbabbbbabbbbaabaaaaaaabaabbbbbbbaaaababaaabbbbbabaabbaaaaaaabaabbaabbabbbababbabbabbbaaaababbbaabbbabbbbbabaaaaabbabbaaaaabbaaabaababaababababbbaaababbabaaaaabbbbababaabaaaaabbabaabaababaabbbbbbabbaababaaabbbababbaabaaaaaaaabbababbbabaabbababbabbababbaabbaabbabbaabbbbababbbabababaaabaaaaaabbaabaaabaabbaaaaaababaabaabbbaaaabaabaabababaabaaababaabaababaaabbbbbaabaababaaaaabbaaabbaaabbaaababbaaabbabbbbabaababbbbbabbbbbbababbbbaaaabaabbbababbbababbbbbaaabaabbabbaaabaaaababbababaaaaaaababbaaabbbaabbbaabbbbbababaabbbbbaaaababaaaabbaaaaabbbababbaaaaabaaaaabbbbbababbbbbbbbabaabbabbababaabbbaababbbbbbaabbaaaabbbbaaaaabaabbabaabaaaaabbbbabbabbaabbabbaaabbababbabaaabbbababbbaaababbaaaabbbbbabbbbbaabaaaaaaaabbabababbaaabbaabaabbaaaaaabbbbbabababbbbaababbabbbbbbabaaaaaaabbbbbabbbaaabababababaaabbbaabaaabbbaabbbbabaabaabbaaaabbaababbababababbabaabaaabbbbbbabbaaaababbbbbbaaaabaaaaaaabbbaaaaaaabaabababababaaaaaaaaabbaabbaabbbbbabbababbbaabbbaaabaaabababababbbbbaaaabbaabaabaabbabaaaabaabbbbbaaabbbababaabbabbababaaaababbbaabbaaaabbabbbaaabbbaabbbababbaaababbaaabaabbabaabaaabbbbbbaaaaaabbbbabbbabbbaabbabbbabbbabbabbaaabbaaaaabbaabaaabbbaabbbabaabbbbabbbababbbababbaababbabbbbabbabaabbaaababaaabaaaaabbbaababbabbbabaabababbaababbbbaaaaababbabbabbbbbbaaabbaaababbabbaaabbbbabbbabbbbaabbbababaabbaababbabaaababaabbbbbbbbaaaaaaabbbabbaaaaaabbbaaabbababaabbabbbaabbbbaabbaabaabaaaaaabaaaaaabaabaabbbbabaababababbbbbbabaabababababbabbbaaaabababbaabbabaababbbbabaababbaaabbabbbbaaabbabbbabbbabbbbababbaabbbaaaaabbbaabababababaaabababaaaabaaaabbbbbabbbaaababbbabaaabbbaabbbbbbaaababbbbaaaabaabbaaaababaabbabbbababbbbabaababbabbbaaaabbbbaaaaaabaaabaaababbbaaaababbbaaaabbbaaabbaabbabbbbbbbbabaababbaaaaababaaabbaaabababbaabbaaabbabbaaabbbaaaabbbbbbabbbbbaabababbbbaaababbababaabaababbaaabaabbbbaabbbbbaaabbbbbaababbaaabbabaaabbbaaabbbababbabbbbbabaabbabbaaababaaabababbbabababbbaaababbaaabaabbbbabbbbabaabbaabaaabbabaaaabbbbbabbabbbbabaaabbbaabbbbbbababbabbbbaaaababbbabababaabbbbbabbaaabaaabababbbaabbbbbabbaaaaaabaabbaaaabbbaabbababaabbbbbbaabbbbababbbaabbaabbaaaabbabbbabaaaabbaaabaaaababbbbbbaaabbbaabaaaabbabaaabbbaababbbbaaaabbabababbbaabbabbaababbabbaaababababbbbaaabbbabababaababbbaaabaabbbaaaababbbaaaabbabbbbbabbaaabbbaabababbbbababbbbabbaaaababbaaaabaabaabbbbbabababaaababbaaabbaabbbabbaaaabbbbaabababaaaababaaabbbbbbababbaaaaabbbbbbbbaabbbaababbbbaaaababbbaabbbbabaabaabbaaaabbbabaabaabbaaabaabaabbaabbbbbababbbabaaabaaababababaaaabbbbaabbabbaaabbabbaabbbaaaababbbaabbbaaaabbabbbaaabbbabbbabaabaababaaababbbbbabbbaabbbbabbaaaaaabbbabbabaabbababbaabbbaabaaababbbbabbbaabbbabbbbbaabbabbbbbabaabbaaaabbaaabbababbabbaaababbabbabbabbbbaaaaaabababbbbaaaaaababababaaaabaabaaabbbaaaabbabababbabaaabbaaabbbbabbabbaaabababbbaaaaaaababbbaabaaaaaaabbaaabababbaaabbbbaaaabbbaaaababaaabbbaabaabbabaabaabaaaabbbbaabaabababbabbbbbabaabaaaaababbabbbabbbaaabbababbabababbababbababbababbbabbabbaaababbaaaaabbbbbbabbbbaabbabaababbbababaabbbaaaabbbaababaaaaababbabbaabbabaaababbbaaabbaaaabbbabababababbbbabbaaaabababaaababaabaaaaababbbaaabaaaabaaabbbababaaabaabbbaaababbbbabbaaabbababbbbbababaaaabaaabaabaaaaabbabbbbababbabbabaaabababaabbaabababbabbababaaabbabaaaaaaaaaabaaaaabbbabaaaaaaaaaabaaabbbbabaabbbbbbababaabbbaabbabababbbbbabaabaabaabaabbbbbababababaabbaaabaababaababababbbababaabbbbbbbbbbbaabbbbaaabbaababaaaaaaaabaaabaabbababbabbbabbbbbbbaabbbaaaaaaaaabbabbabaababaabbababbbababaabaabbaaababbbabbbbaabaabbbaaabbbabbbbaaabbaaabbbababbbbbbbaaabbababaaabbabbaabbaaababbbbaaabbabababbbabbaabbababaabaaababbabbabaaaabbbaababbababbabbbaabbbababbbaaabbbbbabbaababbabaaaaabbabababababababbaabbaabbbabaaaaaababaaaabbabaabbbababbbabbbaaaabaabababbbbaaabbabbbabbaaabbbababbaaaabbbbaabbbbaaababaabbbbaabbbbbbaabaaababbaaabbbbbabbabbbbbaaabbbbaaaaaabaaabbaababaababbabbbbabbaaabbbaabaabaabaabbaaabbaaaabaaaabbabaabbbaababbabbabbbbbbbaababaabaabaaaaaaabaaaaababaaabbbbabbaaabbbabbabababbbbabbbaabbababbaabbbbbaabbaaabaabaaaabaaaaaaabaabbaabbabaabaaaaababbaaabbbbaaabbaabbbabababbbbabaaaabbabaaaaaaaaabaabbabaabbabbbbbbbbbbabababbbaabaabaaabbabbabbabaabbaababaaaaabababbbbbaaaabbbaaabbabbaaababbaababbaababbbaaabababaaaaaaaaabaaabbbbabaababbbbbaaaaaaabbabbbbabbaababbbbbbabaaaaabaaaababbbbabbabbbabbbabaaaaaabbababaabaabbabbaaaaaaabbbaabbababbababababbbbbaaaaaaabbabaabaaabaaaaaababaaaabbbabaaaaabbaaaabaabbbbbaaaabababababbaabbbbbabbabbabbbbabaabbbaabbbbabbabaabbbbbbaabbbabbbbaaaaaababbbbababbbaaabaabbbaaaabbbbaaabbabbaabbaaaaabaabbabaabbbbbaaaaaabaaaaabbbaaabaaababaabbbbaabbababbababbbbbaaaaaaaabababbaabbabbbbbbbababaabbabbababbbaababbbabababbbaaaaabbbbaaaaabbbabababaaaabbaaabbbbaaaabaabaaabbabaabbbbaababbaababbaabbbaabbababaabbbbabaabaaabaaaabaabbbabbaabbbabbbbbbabaaaabaabaaabaabbbaaabbbbabbbbabbbaabaaaaaabaaabaababbabbabbbbbaaabbbbaabaaaaabaabbaabbababbbbaabbbbabbabbbbbbbabbbaaaaaabbaaaabbaababbaabaabbaaaabbabbabaabbaabaabbbbbbbaaabbababbaababababbabbbbbbbbaaaaaaabbbbababbabaaabaaaaaaabababbbbaabaaaabbbbabbabaabbbabaabbbaabbbaababbabbbabbbbbbbbaababbbbaaaababbaaabbaaaaabbbbbbbaaabaabbbbaabbbaabbbabbbaabbbaaabbbbaababbbabbbaabbaabbbbbabaaababaaaabbbababaababaabaaaaabaabababbbabaababaababbbbaabaabaabbbbbbbaabbbbbaabbabbababbbbababaababbaabbbaaababaaaabaababbabbbabbbaabaaaaabaababbbaabbbabbbbaaaababaabbabaabaaaaabbbaaabababaabababbbaabbbabbabbbbbbbbaababaabaaaabbabbbbbbaaaaaabbaaabaaabababbbabaaaabbaabbabbbbbbaaaaabbbabaaaaaaabbbbabbbbabababaaabbbbbbbbaaaaabbbaaabbababaabbbbaabbaaaabbbbaaaababbbababbbbbbbaababbabbbabaabbaaabbaaababbaaababbbaaabaaabababbabaaaabaaaabbbaabbbbabbbaabaabbaababaabbbbbaabbbbaabbabaaabbbbbbaaabbbaaabababaaaaababaabbbbbbabbbababbaabbaabaababbaaabbabbabbbaaabbbaaababbaabbbabaabaaabaaabaabbbbbbabaabbabbaaabbbbaaaababbbbabaaabbabbbabaabaababbbaaababaaabbabbbbabbbbaabbabaabaaababaabbbbababaabbabbabbbabaaabbaaabaabaabbbbaabbbbabbabaababbabbbabbbabbababaabaabaababbabbbbaaabaabaaaaaabbbbbbaabaaabaabbbabbbbbabbaaabaabbbabbbbabaaaaaababaabaabaabbbaabbbaaaabbabaabbaababbbbbbbbabaabaaabbbbababbbbabaabbbbababbababbabbabbbbababababaabbabaababaabaabbbbaaabaababbaaaabaaaabbaaabababbbbaaaaababababaabaaaabbaaaabaababaabababababababbaaabaabbaabbbbaabaabbbababbbbbbaaababbbbbbabbbbbaabbbaaabbbbbabbabbaababbbbaaabaabbbaabbababaababbaaaababaaabaababbbaaababbaabaabaaabbbaaaabbbaabaaaabbaaabababbaabbbbaaabbbbbabaaababaaaabbabaababbaababaaababaaaaaabaabaaaababbabbbbbbaaabbaaaabbabaabbabaabbabbbbaababbbbbabaaaabbbbaaabbbbaaabbbabbabbabaaaababaaababbaabbbbbbabbaaaaaabbabababbbabbabbabbaaabbbbabaabbaaabaaaaaaabbabbaabbbbbabaaaaaabaabbbabaabaaabbaaaabababaabbbaabbbbbbbbbabbbaaaabbbaabbabbbbbbbbbbaaabbbaaaaaabbabbaaaabbbaabbbbbbaabbbababbbaaabababaaaabbbaaabaabbbabbbbaabaaabaabbababbaaabbbabaaabbabbabbaaaababbbaababbbabbaaaaabaaaaaaaabbbaaabbbbbbbaaabbbbbabaaabababaababaabaaababaababbaaabaabaabaababbaaababbaaaaabbbbbaabbbbababbabbbabababbaabbbbbaaaabbaababaaabbaabbbaababbbabbbbaabababbbbabbaaabababbbbbbabaaaaabbaaaaaaabbabbabbaaababbaaabababbbbbaaaaabbbaabbbbbbbbbbbbbbaaaabbbabbbbaaabbabaaababaaaaabbbbababbabbbabbabaaababbaaaaaaabbaaabbabaaababaaabbbbababbaabbabaaaaabbbaaaaaabbaabbabbaaababbabbaaabbabaabbbbaaabbbbaabaaabbabbbabbbbbabbaabaaababbabbaaabbbbaaaababbababbbbababbbabbaabaabaababbbbbbabbaaaabbbaaaaabbabaababbaaaabbbaaabbbaaababbbbaaabbaabbabbaabaaabbaaaabaaabbbbaabbaaaaaababbbabababbbbabbabbbbaaabbaabaabaaabaabbbaabababbbbaaabbaaaabbbbababbbaaabbabbabbaaabbabaabaabaabbbbbabbabbbaabaaabbbbababbaabbaaaabbabbaabbbbabbbabbbaababbbaabbaababababaaaaabbabaaaabbbbaaabbabbbaababaaaabbabababbbabbbbaabbaaaaabaaaabaaabaabababbaaababaabbbbbbbabbaabaaabaabaabbabaabababbababbbbbbababaaaabbababbbbaaababbabaaabbaaababbbbbaabbbbbbabaaabbabaabaaaababaaaaabababbabbabaaabaabaabaabbababbbbbabbbababbabbbbbbbabbaabbbbbbbabbbbbbbbbbbbbbbbbbaabababbbaabbaabaaabbabbabbabbbabbbabbaaabbbaaabbaaaaabbbaababaaaaabbabaababbbbbbbaababbaabbaaabbabbabbaaaababaabaaabbbabbabbaabbaababbbbbaaababbaabbaaabbababbabaaaababaabbabbbabababbbabbbabbbbaabbbaabbbaabababbaaababbaababaababbaaaaaabababbbbaaabaaaabbaaababaaababaabbbaaabbbabaababbabaabababaabababaaabaabbababbabaababaababaabbaabbbbaabbababbabababaaaaababababaabbbbabaaaaabaaabaabababbabaabbbaabaabbbabbabbaaababbbbaababbbababbbbbabbbabbaabbabababbbbbabbababaaaabaababbbaaabbababaaaaababbbaabbaabaaabaabbbabbababbabbbbbabbbaabababbbaabaabaaabababaabbbabbaababbaaabbaaaababbbabaaaababababaaaaaaaabaaaaabaabababbaabaabaabaabbababbbabbbabaaaabbababaaabbaaaaababababababbbbbbaabbbbbabbbababaabaababbbaabbabbbbaaababbabbbbbbabbbabbaaaabababbbaababbbbabbbbbaabababbababbbbbabaabbbbbbbaaabaaaababbabaaaaabaabbababababbbbbbaaaaababbabbabbbaabaabbaaaabbbbaaabbbbbaabbaaabbbbbbbaababaaaabaabbaaabbbababbbbababbaabbabbbabbbbbbabaabaaabaababbaabbbaaabbbbbbbabbbabbbbabababbaaaabbbbbababbabababbbbbbaabbababbababaaababaaaababaaaabaaabbbabaaababbbabaabbababbbbbbbbbbbbbbbaaabbbabaabbaaabaaabababbbbbbabbaaabaabbabbbababbaabbabbabbbabbaabbbbbbbbbaaaaaaabbabaaabaabaabbaaabbbabaaabbabaaaaaabbaababbaaaabbabaabbbbaababaababbbbbaababaaabababbabbabaaaaabaaaaaabbabababbaababbbababaabbabbbbabbbbababbbbabbbbbbbabaaaaabbabbaaabbaabaaababbbaabaaaaaabbaabbababbaababaabbbaabbaaababbabaabbbbaaaabbbabbaabaaabaaaaababaaabbbbbabbbbbbabaaabaababaaabaabbaaaaabaaabbbababaaaaababbbbaabbbaabbbabaaababbababbaababaabbabaabbabbaaabaaabbaababaabaabbaaaabbbabbababbbbaabaababbabaaabbabbbbbbabaaaabbaabbbabaaababaabbabbbbbbbbbbaabbbabaaabbbbbbaaabbbbbbababababbaaaabbbbbbabbbababbbbabbbababaaabbaaaababbbbabbbabbaaabbbabbbbbabbabbaabbaaaaaabbaabaaaaababbaaaabbbbbbaabaababbbabaabbbbaababaaabaababbbbbbbababbabaaabbaabbbbaababaaaabaabbbaabbbababbaaabbbaaabbabaabbabbabbbbbaaabbaaaabbbbabbbbabbabbbaabbabababaabbabbbbbbababbbabbbbbabaabbaabaabbaaabbaabbabaaaaabbbabbabaaabbabbaaaababababaaaaaabbbbbbbbaababbabbabbbbaababaaabbabbabaabbbbbababaabbbabbbbaabaabaaababbaabbabaaabaaaaaabaabbabaabaaabaabbabbaabbaabbbabbbaaababbabbaaababababaabbbabbaabbaabbababbaaaabbaabbaaaabaaabbababaaaabbbbbaaabbbaaaabbaabaaaababaaaaaabaaaababbaaabbbbababbaaaabbaabaaaabbabbabaaababbababaaabaaaabbbabbaababbabbaaaabbaaaababbbaababbaabbabbaabaaabbaaabbabbbbabaaabbbbbbaaabbbaaababbaaaabaabbaaababbbaabbaaabbaaabaaabaababbbbaaababbababbbababbabababaabbabbabaabbbbbbabbbababbbabaabbbaaabaaaabbbbbbbabbbbbabaaaabaaaabbbbaabbaaaabbbabbabaabbbaaabbaabaaabbabaababbbbbabbaaaaabbabaabbbaababbabaabbbbbbbbbbaababbbbabbababbbababbbbaabbabaabaabbbbbbabbbbabaabababaaabbabbbabbbbbaabbbbbabbbabbaaabbababbababbaabbbaaababbababbbabaababbabbaaaabaaabaabaabaaabbbabaaaabbbaaaaabababbababaababbaaaabaaaababbabaabaaabaaababbabbbbbaaaabaaaaaabbababababbbbbbbbbbabaaaaabaabababaabaababaaaaabbabbbaaabbbabaabbabaaabbbabaaabbbbabbabbabbaabbbbabbbbababbabaabbbaaaababbbaaabbabbbbbaababbbbbaaaaaababbbbbaababaaabaaaababaaabbabaabbbbbbabbbabaaabbbabbbaabbaaabaaabbbaabbbbbaababbbbababbaaaabbbbbbbbaabbaaababaaabaababaabaabaaaabbabbaabaabbbbbabaaabbbaabbbbababaaabbababbaabbbbbaabaaaabbbbaaaabbabbbbababbabbbbabaabbbbababaabaabbababbbbabbaaabbbbababbbaabbabaabbaabaababbbabbaabbbbabbaaaaabababbaaaaabbbababbbaabaaaaababaabaaaaabbabbaaaabbabbbbababaabbbabaabbbaabbbaaababbbabaabaaabbbaaaabbaabaabbabbaabaaaaaabbbbababaaaaaabbabbaabababbbabbabbababaabbababbbaaaaaaaaaabbbaabaabbabbababbaabbaabaaaabaaaaaaaaaabbbaabbababbabbabbbbbbbaabaaaababaaabbaaabaababaaabbbbbbabbababaabaababaaaabbbaaaaaaabaabbaabbbbabaaaabaabbbaabaaaabaabbaaabababaaaabababbabbaaaaabbbbabbbabaaabaabaaaabbababaaaabbabbbabbabaabbababbaaabaaabbaaabbabaabbbababbbbaababbbbaabababaabbaaabbbaaabaabbaababaaaaabbbbababaabbabababbbaababaabababaabbbababaababbbbabbbabaabbaaaaaaaabaaaabbbbbababaabaaaabbbbbabbabbbaababbababaaabaaaaabbbabbbaaaabbbabbbababbbbabaabbbabaabaaaaabbaaaaabaaabaabbabbbbbabbbabbbbbaababaabaabbaabbbbbaaababaaabababbabaabbaabaabbaabbaabaabbbbabbbabaabbababaabbbbbbaaabbbabbabbabaabaaaaaaaaaaaabbaaabbbababbaaaaabbbaaaaabbbaaababbbaabbabbaababbbabaabaabbaaabbaabbabaaaabbbbaaaabbaabbbabbaabbaaaabbbbabaabbbaaabbaaaaaabbabaabbabbabbbbaabbaaababbbbbbababbbabaabbabbaaabbbabbabbaabbbaabbabaababbaabbabbabbabaaaabbbaaabaaaaaaaabbbbababbababbbababbbabbaabbabbabbbbaaabbbaabbbabbaaaababbbbbbaababbbbbabbbbababbbabbbbababbbabbabbababbbbabbabaaaabbbabbbabaaabbbaaaabaabbaaaabaababaababaabaabbbbbaaabbabbaaabbaababaaaabbbbbbbbaaabbabbbaaabbabaaababbaaaabbaaababbbbabbaababbaaabbbbbaababbbbbbbbaabbbbbaabbbaabbbaabbbbabbabbbbbbbbaabbabaaaabaabaabbbbabbbaaabaaababbbaaaaabbaabbaaababbbbaabaaabbaababbbaabbbabbbaaaaabbabaaababbbababbababbaababbabbaaababbbbbaaabbabaaabbbaaabbaababaaaaaaabbbbbbabbabbaabaaabbbbabbbaaaaababbbbbaaababababaaababaabaaabbaabababaabbbaabbbababbaabbaabbaaabbaabaaabbbbbbaababaaaaabbaabbbababababababababbababaabbaabaabaaaaabbaabaabaaabbaaaabaaabaaaabbbbabbbaabbbabbbaabaabaaabbbbbbabaaabbbbbaabbaaabababbbaaabaabbbaaaabbbaabaaabbaaabbababbbabbabaabbabaaaaaabbabbbbbababaabaaaabaaabbabaababbaaabbaabbbbbbababbbbabbaaabaaaaababbbabbbbabaaabbababaabaaabbaaababbabbbaabbbaabbbaabaaaaaabaabaabbabababbaaaabbabababbbbbabaaabababbaaaaabbbbaabaaaaaabbbbbaaabbbbabbabaabbaaabaabbabbbbaaabaaabaaaaabbbaaabaaababaaabbabbaabaaababaaaaababaaaaabaaaabbabaaaaabbababaabaaaabbbbbabaaabbbbbaaabaabaabbabaabbababbbaaabbbaaababbaaaababaabaababaaabbaaabbaaaaaaabababbabbbabbbbabaababaababbaabbababaababbbababbaabbabaaaabbbbabbbabbabbaaababaababbbaabababbaaaababbaaabaabaaababababbabbabbbabbbbbbbbbbbabbbabbbababaaabbaaabaabaabbaaabbaaaaabaaaaaaabaabbaabbaaabbaababbabababbaaaabbabbababbbbaabbabbbabbbabaaaabbbbabbaaaabbbbaabababaaabbaabbaabbbabbbaaaaaabbaaabbaaaababaaababbbaabbbbbbbbaababbbaaabbbbaaabbbaaababbbbabaaabaabababbabaababbabaaababbaaabbbbbbbaabaaaaaabbbbaaabaaabbaaaabaaaababababaaaabbabaaaababbaaabbababaaaabaabaaaaaababbbabbaaababbbaaaaabbaaabbbbbabaababaabbaaabaaabbbbaaaababaaaaaaabbbbaabbababbbbabbbbaababbaababbbaaababaaaabbabbaaabbaababbabaabbababbababbaababbbbbabbbbbabbabbbbaabbabbbbbbbaaabaabbbbaaabbaaabbaabbbbabbabaaabbabbbaabaaabaaaaaabababaababaabaabababbbbaababaabbbbabaabbaaabbbaaabaaaaaabbbbaabaabaaaaaaabbbababbaabaabaaabbababbbbbaabbbababbaaababaaaaababbbabbbaabbbbbaaabbbbbbabbaabbbbaabaabaaaaabbbbbabbbbaaaabbbbbaababaabaaabbabbbabaaabbabbbaabaaabbbbabbbaabbbabbbaaabaaabbbbbaababaababbbbbbbbaaabaaaaabbaaababababbaaaabbbbbbbbaaaaaabbbabbabbaabaaaaabaaabbabbbabbbabaaaabaabbbabbbbababaaaabaaabbbbbbbabbbbbaaabaababababaababbaabbbbbbaaabaababaaaabaabaabbabbabaaaaaabbaababaabbababbabbababaaaaabaabbabaaaabbbbbabbabbbbbbbabbaaaabbabaaaabbaaaabbabbbaaaabbabababbaaaaabaabbababbbbababbabababbbbaaaabbaaabaabbbbbabbbbbabbbaaababaaabbbbaaabaaabbbabbaaaaaabaababbaabbaaaaabbbbaaaababbabaabbbaaaaaabaabababbbababbabbbabbabbabaabbaabbaaababaababaabaabbaabbbaaaaaabbabbaaababaabbabbaabbabbabaaaabaaaabaabbbbabbaaabaabbbabaaabbbabbbbbabbbaabbabaaabaababbbbbbbaabaababaaabbaabaabbbbabbabbaabaaababbbababaabbbbbaaaaabaaaabbaabaaaabaaabbbbabbbabaaabbaaababbaaabbbbbbbababbaabbbabbaabbbbabaabbabaabaaaabbbaababaaababbabbbababaabaaaaaabaabaaabbbbabbababababbbababaaaaabababbbbbabbbaabaaabbbbaaaabaaaaaababbbbabbababababaaabaaabbaaabbbbaabbbaaaababaaabbabbabbbaabaaaababbbabbaabbbabaabbbbabbbabbaaaabababababbaabaaabbbbaabbabaaaababbaaabaabbbbbbbaabaaaaabbababaabaabbbaabaabbabbaaaabbabbabababbaabbbababbaabbbbbbabbbbbaaaabbbaabbbbaaaaaabaaaabbaabbaaabbabbbaabaabaaabbbaaaaaaaaaababbbabbabbabbbaaabbbabababbabaaaababbaababaaabaaaaaabaababbbbaaababaabbaabbbbbbaabbbaaaabbbabbabbbbbaaaaaabababaababababbbbbaabaabbabbbbabaabbbababbbaabaababbaaabbbababbaaabaabbaaabbaaababbabbbababbbabababaaaaaabbbbbabbabbbabbbabbaabbabaaaaabaaabaaababaabbbabaaaabaababbbabbaababbabbbbabbabababbabbabaabbbabbabbbbaaababbabaaababaabaabaabaabbbaabbaabaaabaababaabaaabbbbbbbaabbbbaaabaaababbabaabaabbaaaabbbbabbaaaabaaabbaaababaaaabbbabbbaaabbbabaababbbaaabbabaaabaabbbaabbaababaaaabbbabaababbaabbaabbabbaabbaabbabaababbbabbbabaabaaababbaaabbbbbabaabbabaabbaababbabbbbbabbbababbbabaaabbbaabbbbbbabbababbababbbbabbbbbaababababaabaaabbbaababbaaaabaaababbabbabbbbaabaabaaaaababbabaaabbbbbaaaabbabababaaaaabaabaaaaabababbaaabbbbbabaaabbabbaabbbbbbbabbababbaaababbabbaabbbbabbabbaabababbbaaabbbbabbbaabbaaaabaabbbbaabbbbbabaaababaabbbaaabbabababaaaabbbbbbaabbbaaaaababbbabbabaaabbaaaaaaaabbbababbbbbbaababbabbbbabaabaabaaabaaaaaaabaabbaabbbaababbaabaaabbababababbbababbabbbbaaabbababaaabbabaaaabbbababaaabababbabbaabaaabbaaaabbbbbaabaaaabbabbbabbabbaaaabababaabbbbbabbbbaabaaababbaabbbaabaababbbabaaabbbaaabbbbababaabbbbbaababbbaaaabbaabbaaaaaabbaaaabbbbabbbbbaababbbabbbabbaabbbaaabbbabbababbbabbaaaabaabaaabbbbbabbbbaaabaababbbbaaaabbaabbabbabaababbbbbbbaabbabaababbbaabbbababbbbaababbbbbabaaaaaaaabbbaaaaabababaabbbabbaabbbaabbbbabaabbbbabbabaaabaaabaaaababbbbbabbaabbbbaaabbabbabbababababbbbbbaabbbbbaaaaaaababbbaaaabaaababbbbaabbbbbbbaaaabbaaabbbabbaabaaaaaaaaabababababaaaaaaabbaaaabaaaaabaabbaababbabbbbaababaaaaabbabaabbbbaabbbbbabbbaabababbaabbaaaabbabbabbaabaabaabbabbabaaaaaabaaabbaaaabaabbabbabaabaaababbabbbababbabaaababbabaabbbbabbbaabbaaabaabbbbaaabbababaabbabaaaaabaaaaaaabbbabbababbbaabbbbabbbbabbbaaabbabaaabbabaabaaaaaaababbbabbbaabaaaaabbbabbbbaabaaaaaabbbaaaaabaabbaabababbabbaaaaaaaabaababbbaabaaabbaabbaabbabbbabaaabbaaaababbbbbabababababababbaabaaabaabaaaabbaaabaabaabbaaabbabaababbaabaabaaaaaababbaaaaabbabbbabbababaaabaabaabaababbabbabaaaabbbababbbaabbbbaabbabbababaaabbbabaabbbbaabbbbbbabbbbbabaaabaaabbbbbaabaabbaabaabbbbababbaaaabaabaaaaabbbaabbbbbaaababbbbaaaaaabbbabaabaabbabbbaaabbbabbabaaaabbbabbbaabbbabbaaaaabaabbaabaabbabaabababbabaabaaaaaaaabbabaabbbaabababaaaabaaaabbbbbabbabaabaaabbbaabaaaabbaabbaaabbbaaaabaaabaaabbbaaaababbababbabbbababababbbbabbaabbabbabaabaaabbbbbbbbbabaaabbabababaabbbbbaaabaabbbaaabbababaaaaabbbbabbabaaaabbaaaaaaabbbbaabaabbbaabaabababbaababbaaabbbbaabaababbabbabbabababaaaabaaaaabbaabbabbbbabbaaaabaaababbabbabbbbbaabaaaabbabbbababaaabbbababaaaabaabaabbabaaabbbbbbabbabaaababbaabbbaababbaabbaababbbaabbaabbbaabaaaaaaaaabbaaaaaabbaaabaaaaababaabbabbbabbbbbaabbaaaabbabbaaabbababbbabaaaaaaaabaabbbaabbbaabbaaaabbbaabbaaaabbaaaabbbaaabababaaabababbbaaabbabaaaaabbababaaababbbabbbaaaaabbababaaabbbbabaaaabbaabbbbbabaaaaaabaaabbababababaaaaaabaabbaabbbaabaaaabababaababaaabbbbabbbbaaaabbbaaabaaaaaaabbababbabbbbabbbbbaaaaaabbabbbaababbbbbbaabbbaabaabaaabaabababbaaaaabaabbbbbabbbbabbaaaababaaaaabbbbabababaaabbaaabbaabaaaababbaaaabaabbbaaaababaaaababababbbabbbababbabaabbbbaaabbababaaaabaaaabaaaababbbaaaaabaabaaabbbababbaababbaabbbbabbbbabbbbabaabababaabbaabaabbabaaabaaabababbaabbabababbbaabaababababbaaaabbaabaaababbaababbbbabbabbbbaaaaabbbbbbbbaabbaabbbaaabaaabbabbbabaaabbaababbbabbaababbaabbbbbaaaaabaabababbbbbbaaababaaabaababbababbbbaaaaabbbaaabbaaabaaaabbbbaababbbaaaababbbaaabaababbabbbaaaababaaaaabaaaaabbabaaaababbabaaabbabbabaaababbababbbaaaabbabaaababbaabaabbaaabbabbbaaabbaababaaaabbbbbaabbbaabbbabbaabbaababaabbbababbbaabbbbbbbbabbbbbbabaaabbabbabbaaabbbaabaaaabbaaaabaababbabbaababbabbbaaabaabaababbbaaaaabbbabbbbbaabbbbabaababaaabbbabbbaababbabbbbbaabbbbbabaabaaabbbbbabbababbabbabbabaababbbaabbabbabbababbaabbabaaaaabbbbabbbababbaaaabbbbbbabaabbbbabaaabababbbbabbaaaaabbbaaaaabbbaabaabaaabbabbaabbabaabaaabababbaaaaaabbabbbabbabbabaaabaaaaaabbabbbbbabbaaabbabbbabbbbbaabbaaabbaaabbbbbaababbbbbbbabbaabaaabbbaaaaababbbabaaaabaaaabaabaabbbaabbabaabaaababbbbaaaaabababbbabbbbabbabaaabaaabbbbbaabbbbbbbaabbaabbbbaabaababaaaabbbbbbbababaaaabbabaaabbabaaabaaabaaabaabaabbbaaaaaabbbbbaaaaaabababbbbbabbaababbbaabbbbbabbbaabbbaaaabaabaaaaababababbbbaaaabaabbbaaababaababaabbbbbbaabbababbbbabababaababbabbaaabaaaabbabaaaaaaaaaaabbbaaabaaabaabaaabbaababaaababaaabbaabaabbbbbbbbbbaabbbabaaabbbaababaababbbabbaaaababaabaabaaaababbabaaaaaabbaabbabbbaababaabaabaaabaaabaaabbaaabbabbbbbbbabaabbabbbbabbbbbbbbabbbbabbabaabbbbbaaababaaaabababaaaaaaabaabbaaabaababbaabbbaaabbabbaabbaababbabbbaaabbaaabaababbbbbabaaaababaabbababaabaaaaaaaaaabbbbaaaabababbaabbbaababbaaabbbbbaaabbbabaaaaabbbbabbaaabaabbaaabbaaaabbbaaabbbbbaaaaaaaaaabababaaaaababaabbabbaaaababaabababaaabbbbbaaababaabababbaabaababbaaababaaaabbbabbaaaabbbabbaaabbbaabbaaababbbaabbbbabbbaaaababbaaabbbaabbababbbaabbaaabaaabaabbbbbaabbaabbbaabbbbbaaababbabaabbaabbabbaaaaaabbabbbbbbbaaabbababbabbabbbabaaaabbbbbaaaaabaabbaaabbbabbababbbbbababbaabbbaababbbbaaaabbbabbbabababaaaabbbbaabbbbaabbbaaaaaaaaabaaaaabbbbaabbaaaabbbaaabaabbbbabbabbbbbaabababbaaabaaaababbbaababbabaabbaabaabbbabbabaabbaaabbbbaabbabababababaabbaaabbbababbaabbbbbaaaababbaaaaaaaabaabababbbaaaaabbbbbabbbbaaaabaabbabbabbababbbabbbaabaabbbbabbaabaabbabababaaaababaabbabbbbbbabbbbbaaaaaaaaabbababbaaaabbbabaabaaabbbbbbbabbaabbbaaaabbbbbbabbaaaabaabbaabbaabaababaaababbabbbbbbbbabbaaabaabaabababbabbaabbaaaaabbbbabaaaababaabbabaabbbbbabbbbaabbaabbaaaaaabbabaabbaabbbaabbababaaaabbbbbabbbbbbaabbbaaaaababbaabbbbbaabaabaabbbbbbababaababababbaaaaabbaabaabbababbbbbbabbbabaaabbabbabbababaaaaaaabbababababbbbaaaaaabbabaabaaababbbbaaabaaaaaaabaababaaaabaabaaaaabbababababaaabbaaababbbabbbbaabaabbbbbaababaaabbaaaaaabbaabaaabaaabaabbbbabaaabbaabaabaaabaabbbbbbbaaabaaabbaaaababaababaabbaababbbbbbaaabbababbbbaaaaabaabaaabbabbbbabbbbaaabbbbabbbbaaaaaabbabbaabbbbaabbbbaaaaaabbbabbbbababbabbabbaaababbaaababbbaaabaaaababbaaaaaababababbbababaaabaabbaabbbbbababaaabbbabaabaaaaabbbbbbabbbaaaabbaabbaabababbaabbbabaaaaaababbbbbbaaaabbaabaabbababaaabaaababaabaabaabaabbabbbbbaaabaaabbbaabbbabaabaababaabbabbbbbabbaabbaaabaabaaababababbbbaaabbabbabbaabaaabbbbaabaabbbbabbbabababababbabbabbbbabbabbababaabaaaaaabbaaaabaaaaaababbaabbaaaaababbbaaabbabaaaabbaabbbabaabbabababaabbaaaaabaaababaaababaabbbabbbbaabaaababbbbabaaaababbabbbabbbbabaaabaaabbbabbaabaabaaaaaabaabaaabbbbabbbaabaabbbbaaabbbbbabaabbbaaabaaabbbbbbabbbabbaaaabaabbaaaababababababaaaabbbaaaabababaabbabbbaababbbbbbbaabbbababbbbbbbbababaaaaababaaaaabaaaabaabbabbabbbbaaaabababbbabaabbabaabaaaaaabbbbaabaaaaabbaaabababababaababbbbbaaaaabaaabbbaaaaabbaaaabbbaaabababbaaaabbaaaaaaababababbabbaabaaaaaabbbbabbbbaabbbbbaaaabaaabbabbabbbaabaaabaababbaaaaaabbaababbabbbaabbbaabbbaaaaababaabbabbaaaaabababbabbaabaabbaaababbabbbbabaabaabbabaaaababababaabaaababbbbbaaabbababaabbbaaaabbaaaaaaaabaabaaaabbabbaabaaaabbababaabbabaabbabbbabababbbaabbbbabbbabbaaaabbbaaababbabbbbaabaabababbbbbabaabaababbbaaaabbaabbbbbaababaababaabbbaaabaabbabbbabbbaabbaabbbbbbabbaaaaababaaaaaababbbbbaaaaaaaaabababaabbbabbabbbaabbabaababbabbabbbbaabbaababbaababbaabbbaaabbaabbbbbababbbabbabbaabbbbbbabbbbbbaabbaabbbbbbaaaababaababababaabaabaaabbabbbbbaabbbabababbbaabbbbaaaaaaaaaaabbbbbbbbbbbaaabaaaaaabbbbbbbaaaaabaaaaaabbabaababbabababbbbabbbbabbbaaaaaaabbbabbababbaabaababbbaaaabbbbaaaaababbabbbbbbbbabaaaabaaaabbabaaaaaabaaabbbbbbabbabbabbbabbabaaabbabbbbaabbaaabbaabbbbbabbbbbabaababbbaaabbabbbbaabaababbabbbabaabbabbababababbabaaaaabbaababaabbabaababaabaaabbbbababaabababbaabbababbbaaaabaaaaaaababbabaaaabaaaaababbbaaaabbababbbbbaaababbaaaabbbaabaaababbaaabbbababbaababbabaaabbaabaabbabbbbababbabbbababbabababbbbbbbaabaaababbabbabbaaaaabababbbbbbbbabbaaabbaabbabbbbbbaabbaaabaabbabbbaaaabaabaaaabaaaabaabbaabbbbaabbbbaabababbbbbabbbabbaabbabbbaaabbababaabaaaabaaaababbababbaabbabaababbbbabaabbbbbbaabaabababaabbababaaabbabbbbbbaaaaaabbbbbabbbabbbbbbabaaaabbaaaababababbabbaaaabbababbbabbabababaaaaabbbabbabbaaaaaabbbbabaababbabbbaaabbbbbbaaaababbaaabaabbaabaabaabbaabbababbbabbbaabbabaababbaaababaabaababaaaabbabaababaabbabaaaaabaaabaabaababbbbabbaaababaabbbaaaaaaaaabaaabbbbababaaaabbbbabbbbabbbabababababaabbbbbbabaaaabbabbbaaaabbabbbbbaababaaaaabaabbaabbbbbbbbaaabbbaababbbbbbabbababbbaabbbbbbabbbaabbabbbbabbbaaaabbbbbbabababbaabababbbbabaaabaabbbaaababababababbabbaabbaabbbbbbaabaabbaabbbaaabbbbbbbbaaababbaaabaabaabbababaaaababaabbaaababaaaaaaaababaaaabaababbabbabbbbaabaaaabababbbbaaaabaaababbbbbbbbaaabbaabbabbabababbbabbbbbabaabaaababaababaabbbbaaaaaaabaaaabbabbbbbaabbabbbbabbabbbbaabbbbbbaabaabbaababaaabbaaaabaabababbabbbabbaaaabbbabababaabaabbaababbbbaaabbababbaaabbbbbabbaaabababaabbaaabababbaaaaabaaabbabbababaabbaababbbbbaabbabbaabbaabbabaaaabaaaaaabbbbabbbbbbaaabaabbaabaabbbaabbbaabbabbababbbbaabbbaaabbaaaaababbabbbbbbbbaaaabbaababbaaaaaaaaaaaaaabbbbaabbbbbbaabbbabbbaabbbaabbbaaababbabbaaaabbbaabbaaabbabbaababbabaabbabbbabaaababaaaabbaaaabaaabaabbbaababbbaabaaababbbbaaabbaabbbbbaaabaabbaaaaabaaabbbbbbabbbaaabbbababaaabbbaaabbaaaabaabbaabababaababbaaabbbababbaaabababaabbbbabaaaaabbabbababbbbababaaaaababaabbbbbbabbabaaabbabbaaaababaaaababbaabbabbabbbabbababbaabbaaaabaabbbbabbbbabbabbababaaababaaababaaabbabaaabbbabbabbaaabbabaaababaaaababaabbbabbbbabbaabbbbbaabbbbaababbbbabaaabaaaaaabababbaaabbbaaabababababaaaabbaabbaababbabbaabbabbaababaabbaaabbaababbbaabbbaabaababaaaababaabaaabaabbbbaababbaaabbabaaabbbaabaaaaabaaaabaababbbababbabababaabbabbababaabaaaaabaaabaaabaabaababbabbbabbabababbabbbbabaabaabbaaabbbabababaabbbabbbbabbabaabbbaaabaaaaabbbbbbaabbbaabaabaaabaaaababababbaaaabaabababaaaaabbaabbbbabaabbaaaaabaababaaaabbabaaaaaaaaaaaabbaaabbbaabbaaaaabbaaabaaabbaaabbaabababbabbbaaaabbaaabbaabaaaaabbabababbbbbbbababbbababababaaabbaababaabbbbbaaaabbbababbbbaabaaaaaababaaaaaaaaaabbabbaabaababbabbbbababbabbbbbbabaababaaaaaaabbaaaaabbbbbaabbaaabbbaabaababbbabaaababababbbaaaaabababaabaaaaabbaaaababaabaabbababababbbabbababbbbaababaaaabaabababbaaaaabaaaaaabbbaabbbababbaabaaababaabbabaaabbaabbbaabababaaabbbaabbbbababbbabaabbaaaaabbaaababaaabbbabbaabbbabbbbaaabbbaababbabaaaaaaabbbaaaabaaaabbaaabbbabbabbababbaabaabbbbaaaaabbaaaaabaaaaaabbaaabbabbbaaabaabababbbbabbbbabababaababbaabbaabbbaabbabbbbaaaababaabaababbababaaabbbbbabbbabbbbabbaababbbabbbababbbbbabaaaabbaaabbabbaabbaabbaababbbbabaabbabbaabbbaababbabbbbabaababbabbbaaabaabbbbabababbaabbbbaabaababbaaaabbabbbaaaaabaabaaaaaabbbbbbbbbabbbaaabbabaabababbbabbbbbbbbbbaabbabaaaabaaaaaaabbaabbbbbabbbbbaababbbaabbaabbabaaabbbabaaabbaababaabaaababbbabbbbbabaaaabbbbaabbaaaaaabbaababbabaabaabbbbbaababaaababbbbbaabaaaaabaaaabbabaababbbbbababbbbaaababbaabbbaaababaabaaabbbbabaabbbabaabbaaaabbabbbababaabbaaaabbbababababbaabbaaabbaabbaaabbaaaaabbabbabbbaaabbaaabbaababbbbbabbaaabababbbbabaaababaabbabaabaabaaaaabbbbbaaaabaabbbbabaabbbbbaabaaabbbbababaabaaaabbbabbaabbaaabbaababbbbbaaabbbbbbabbabbabaabbbbbbababbbbabbbaaabaababbbbaabbbaababaabbaabbaaaabaabaaabaaabbaabbbaabaabababbbbabbbbaaaabababaabbbbbbbbaaaaaabbbbbbbbbbaaababbaaabaabaabaaaababaabbbbbbbaaaabababaaaababbabaabbaabbabbaaaabbabaaabbbbbaabbbbaabbbaaaaaabbbbabbabbbbabbaababaaaaababaaaaabaabbaaaaaaaabbbbabbbabbabbabbbabbbbaabbabababbabbabbabababbaaabbbabababbaabaabbbaabbaabbaabbaabaaabaaaaabaabbbbaabaaabbbababbbbaaabaaaaabbabbbbbaaaaaaaababaaaaabbabbaababbabbbabbaababbabbaabaaabbbabaaaaaabbbbbbbabbabbbbaababbbbbbbbbaabbbaaabaabbbbbbabbbaababbbbbaabbbabbbbbaabbabbbaaabababaababaaaabaaabbbbaabbaabbaabbababbaabaabbaabbaababaaabbabbababbaabababaaabaabaaabbaababaaaabbaaaabaabbabbbbbabbbbaabaaabaabbabbbabbbbaaabaababbaabbabbbbbabaabbbbabaabbabaaabbababaaabbabbaababbabbabbabaabababbbbbaabbaabbbbabaaaaaaabaabababbbabaaaaaabbabbbabbbbbaaabbbabaabbbbbaaabbaababbaaabbbababaabaabaabbabbababaabbbbaaaabbbbaabababababbabaabbabbaaabbabaaaaabbabbaabbabaabbabbaabbbaaaaababaabbbbbaabbbbaaababaabbbaabbabaabbbababaaaaaababaabbabbbaaaabaabbbababaabbababababbbaabbaabaaaaaaababaabaabbbabbbbbababbbaaababbaabbbbaabbaaaaababaabaabaababaaaaabbabbabaaababbbaabaaaabbbabbbaaabaabaabaaabbabaaaabbbabbaaaaaaababaaabaaabbbbaaababbbbbbbbababbbaaaaaabbbaaaaababaaabbbabababababaabbabbbaaabaabbaabbbabababbababbbabbaabbaaabbbbabbbbbbbbaabbaaabbbbabaaababaabaaaaaababbabbabbbababbaaaaabababaabbaaabaabbababbbbaaababaabababaabaababbbbabaaabbbbbabababbaaabb
abbababbbbabaabbbaabaaaababababbabbabbaaaabbbabbabababbbbbbbaabaaaabbbbabaababbbaaaabbbbbbaabbaaaaabbbbaabaabbbaabababbbaabaabababbababababbaaaaababaabbbaabaabbbaaaabbabbbababababbbababaabbaaaaabbbababbabaaaabaaabbbabaaabbbbababaabbaaabbabbaaabbaaabababbabaaaaaaaabbbaabbabaabbbababaaaaabbbaaaaaababbaabbabbababbbaaabbbbbbaabaababbabaaaabababbbaaaaababaaaaababababbbaabbaabbbabbaabaaabaaabbbbabbababaaababbaaabbababababbbbababaaaaabaaabbaabbbbaabaabbabaaaaaabaaababababaababbaaababbbbabbbbbbababaaaaaabababbbbaabbabbbbaababbababbbbbabbbbaabbabbabaaaaaaaabaabaabbabbbbbababbbbaabbbaabbaaabbaababababbaaaabbbbbabaaaaaabababbaabbabbababaaaaaabaaaaaabbbbaaaaaababbababaaaaaabbababbabaaaabbaababaababababbbaaaababaaaaabbabaabbaaabbbaaaababbabbabbabaabbababbaabaaababababbbabbaabbaaaabaaabbbbbaaaababbbaaaaabaabaabbaaabbaabbbbababaaaabbbababbaaabbaabaaabbbbaaaabaaaabbabbbbbbaabbaababbbaaaabbaaaabaabbaaababbabbaababbbbbababaabaabaaabaabbbaaabaababaababbabaaabaaabbaabababaabbabaabbababaaabbbaabbababbbaaaababaaaabaaabbabbbabbaaaababbbbabbbaababaaabbaaabbababaaababbaabbaababaaaabbbbaabbbaababbbbbaabbabababbabababaabaabbaaabaaabbaababbaabbbabaababbbabaabbbaaabbbaabababbababababbbababbaabababaababbaaabaabbbbabbbbaabbaaaabbaabbabaaaabaabbbbabbbaabbbbababbbbaabbabaaaaabbaabbbbbbbaaabaabababbaaaabbbbabbbbbbababaabbbabbbbbaabbbbbaabbbbabbabbababbbababbbbabaaaaaababbaabaababbbababbaabaaaaabababaabaababbbaaabababaabbbaabbbaaabbbaaaabbbaabbbbbaabbbbbbaababbbbbaaababaaaabababbaaaaababbabbababbbababaaabbaabaabbbaaaaaabaabbbaaabbaabababbbbbabbaabbabbbabaaabbbabbaaaabaabbbaaabbbaaaaababababbabbbbaaaabbabaababaaabaaabbabaaaabababbbabbabaabbbbaaabbabbbaabaaababbabbbbaaaabaababbbabbaaabaabababbbabbababbabaabbbababbaaaabbabbbbbbbbbbabbbaaabbbbabbaabbbbabaabbabbbbaaaabbbaababaaaaabbbbbaaaaaaabbbbaababaaaabaaaabaabababaabbaabbbaabbababaabaabaaaabbababbaabaaabaabbaaabbababbabaabbbababaabaaabaaaabbbaabaaababababbbababbaaabaabbabbbbbbaaabbbababaabaabbaaaaabbaabbbbabbaabbaabaaaaaabaaabbabbbbabbbabbbaabbbaabbbaaaabbaaaabbaabbaabaabbbababbbabaaaaabbbaabbaabababaababbabbaaababbabbbaaabaaaabbaababaababaabbabababaaaabbbbaaaaabaabaaaabbabaabbbbaaaabbbaabbabbbaaababbbbaabbbbbaabaaaaaabaaabaaaaabababbbbabaaaaabbbbbbaabbabaaaaabbbbbbbbbbbbabbbbbbaaabbbbaabbbbbaababaabbaababbbbaaabbaaaabbabbaabbbbbbbabaaababbbbaaaaababbaabababbabbabbaaabababbababbbaabbbbbbaabababbababbbbabbabababbaaaaabaaabaaababbabaaabaaabaaabbbaaaabbbaaaabbaabaabbbbabbbbabbbaabaababbababaaaabbbaaaaaaaaaababaaabbbbaabbaababaaaaabaaabbaabbbbababbaaaaabbbbabbababbaabaaabbaabbbaaabbbbbbabababbaabbbabbbbbaaabaaaaaaababbaaaabababbbaaababbbbbbaaababbbbaabbbabaababbaaabbbbbbaaaabbababaaababbaaabaaabbaaababaaabbbbabbabbabbabbbaaabbbbbbababaaaaabbabbbabaababbbabababbabbbbaabbbbbbbbbbaaabbbabbabbabbabbababaaabbaabbabbbbbaaaabbbaabaaabbbaaaaabababbbaaaabbbabaabaabaabbbbaaaaaaaabbaabbabababaabbabbbbbaaaabaababbbabbababaaabbbabbaabbaaaaaaabaaabaaabbbabaaababbabaababbabbabaabaabaaabaaabbabbaaababbbbabbbabbbbbbbbbbaaaabbaaaabbaaaabbabbabaaabbbbaabbbbaabbaaaaaabbaaabababaabbabbaaabbbababbbabbbbabbbaabaaabbaaaaaaabbbabbabaabbaaabbaabbaaaaabbababaabababaabbbaaabbbaaaabbbabaabaaaababaaaaabbabaaabbabbbbbaabbaaabbbbabaaababaabaaaaababbbbbbaabababbbaabaaaababbbaabbbbabbbabbaababbbabbabbaabbbbabbbbaababbabbaabbaaabbabbaaababbaaaaaaaaababbaaabbbbaaabbabbaababaabbbaababbabaabbabbaabbbbbaabbabbbbbbbbabbaaaaaaababbbabbbbabaabaaaabababbbbbbbbbbbbbbababababaaaababaabbbbaaabbaabbaabbbbbababbabbababbaabbaaaaabaabbaaabbbbbbbaaabbbbbababaaaabbbaaaaabaababbaaaabaabbbbaabbbbabbbbaabbbbabaababbbbbaaabaaaaaaabaabababbbaababbabaaababaaababbaabbabbbbaaaabaaaabbaaabaabaabbbaabbabbaaaabbbaaaaabbaabbaabbaaaababaabbbabbbaaababbaabbabbbbaaaaabbbbababaaaaaabbbbabaabaabaababaabbabbabaaaaabbaabaabbaabbbbbbbbbbabaababaabbaaabbabbbbbbbaabababaababbbabaaabaaabbbabbabbbabaabbbababbaabbbaaabaaaaababababbaaaabbabaaaaabbaaababbabbaaaabaabbabaababbaababbbbbabaaaaaaaaaabaaaabbabbbaabbaaabbbabbaabbbbbbabaabaaabbaaabbabbabbbaaabbaabaaabaabbbbbbbbaaababbbbaabbbaaaababbaabbabbbaaaaaabbbabbbabbabbaaabaababbbbbababaabbbaaaabbbaaaabbabbbabababbabaabbabaaaabbbbbaaaabbabbaaaaabbabbbbbabbaaabbabbaabaabaaaabaabbababbbbabababbbbbabaaabaaaabbabbbbbbbaabababbababaababbbbabbbbbbabbbaaabbbaabbbababbbbabaaaaaaababababababbaabababbabbbbbababbaabbbbaaabbbabbabbaababababbaaaaaabbbabbbaabbababbababababbabbababababbaabbaaaababbabaaabbbaaaaaaababbabbbaabbbaaaababbbabbbbabababbabaabbabababababaabaabbbaabaaabaabbaabbbaaababbbaabbbbaaababbbbbabbabaaaaabbabbbbbaaaaabbbbbabbaababbabbbaaaababbaaabbbababaaabbbabaaaabaabbbaabaabbbaaabbbbabbbbaababababbababaabbaaaaabbaabaabbaabbabbbabbbaabbbaababaabbaaaabbaabbaaabbabbabaaabbbbbbbbbbaabbabaababaaababaaaaabbbababbbbabaabaabbbbbbababbbabbbabbbbabbbaaabbabbabbbbbbaaaabbbbbababaaabbababbbaaaaaaabaaabbababbabbaaaaaaaababbabababbbbbbabbabbbbbbbaababaaabbabaabbbbaaabaabbaabbabbaaaaaaababbbbbbaaabaababbbbaaabbabaabbaaababaabbbbbabaabbababbbabaaababbababbaaaaaabbbbabbbabbabaabaabbabaaaabbbbbbaaaaabababaabaaabbaaababaaabbabbbababbaaaababbaaabaabbabaabbbaaababababbabbbaabbaabbbbbbbbabbbabbaaaaaaabbbaaaabbbaaababbbbaabbbbbbaabbabbabaaabbbabbbaaabaabbaababbbbababbaabaaaabbbaaaaaabbabaaaaabbaaaaaaabbbbaabbbabbaaabababbbbbaabbabbbaaababaabaabbaaabbaaaaabbbabbbaabbabbaababaabababbbbaaaabaababbabbbaaababbbabbbbaaabbbbaaaaaaaaaabbbbbababbaaaabbbaaabbbbbabbaaaaabababbabaabbabaababbbbbbbbbbaabaaabaaabbababbbbababbbababaabaaaabbbabbababbabbabbababbbaaabbbababbababababaabbbaaaababbaabbbabbaabbbabbaaabbaabaaabaabbabbbaaabababbbabbbbaaabaaaabbbbbaaabaabbbaababbaabaaabbbbabbbabaaaaabbabbabbabbabbbbaababaabaaababbabaaabababbaaababaaaaabaabbbbabbbbbbbaaaababbbbabababaaaaabbbbbbbabaaababbaaaabaaaaaababaaaaababababbaaababbabbaaabaabbbbbbaaabbaabababbbaaabbabbbbabbabbabaabbaababababbbbabaaaabbaaabaabbaaaaabbaabaabbaabaababbbbbbbbaabaaabbaaaabaabbbbabbabbbaabbabbaaaababbbabaababbbbbbbbaaababbaabbbbbababaaabbbabbabaaabbaaaabbababbbaaabaabbaaaabaaaaaabbbbabbbabbbaaaaaabaaabababbaaaaabbbabababaaaaabbbabbabbbaaaabbabaaaababbaabaaabaababaabbbabbbbaabbabaaaaababbbaaabbbababbbbabaaaaaababbbabababaaabababbaaababaabbbbaaaaabaaaabbbaaabaaabbaaaaaaaabaababbbaababbaaababbabaabbaabababaaaabaaaabaabaababbaaaaaaaaabababbbbababbbabaaaaaabbaaabbbbbabbbbaabbaaabbbababbaaaabaabaaaabbabbaaaabbaaabaaaabababbaaabaabaaababbbbaaabaababaabbaaaaabaabaaabaaabbaaabaabaaabbbabababbaabaaabaabbaaabbaaabbbaabbaaaababbabbbbababbbbabaabababbabbbababababbabbbbbbaabbbaababbbaaaaaaaaaabbbaaaaaabbabbabbbabababaababaabbaaaaabbaaabbbbaabbbaabaabbaabbabbababababaaaabbbbabaaabaabaaaaabbbbaaaaaabbbabbaaaaaabbaabbaaaabbaabaabaaabaaabaaabbbbababbbbabbbbaabbbaaabbaaaaaabaabbbaabbbbabbababbaabbabaabbaabbabaabaabbabaababbbbabbababaabbabbaabbbbbbaabbbaaababbbaabbbaaaaabbaaababbbabbaabbabaaabaabaabbaabbbaaabaabbabababbabaababaaababbbbabbabaaaaababaaabbbbababaabbbbbbabaaabbaaaabbbbabbabbbbbabababbaabbabaababbbbbbbaabbaababbababbabbbbabbaaabaaaaabbabbbaabbbbaababbbabbbbbaaaabaabaabbbbabababbbabbbaabbbabbababbaabaaaaababaababaaaabbbbbbbabbbbaabbaaabaaabbaababbbabbabbbaabbaaaabaaabababbbbabbaabbabaabaababbaabaabbabbbaaabbaaabaaaabbaabababbbaaaaabaaabbbabbbaababbaabbbbaabaabaaaaabaabbbbabaababbbbaabababaaabaabaabbababaaaabbaabbbababbababaabbbbbbabaaabbaaaaaabaabbaaaabbbabaabbbbbabababbbabbbabbabbabababaaabbbbaabbaabbaabababababbbbaaabbabababaaaaabbbbaaabbabaaabbaababbabbbaaaaaaaabbbbbbababbabbaabbbaababaaaabaabaabbabbabbbbbababbbbbabbaabaabaaaabbaaaabbabababbaabbbbbabbaaaabababababbaaabbaababaaaabbababbbbaaaabbabbbbababbabaababaaaaaaabababaaaababbbbbbbbabbaabaabbbbbbbbbabababaabbbabbbaaabaaababaaabbaababbaaabbbabbaaaabaaaaaaaabaaabbbbbaabbaaababbbababbaabbaaaaaaabbbbbbababbbbbabbbbbbabaaaababbbbabbbabbabaabaabbaabababbbbaaaaabbbbabaaaaaaaaaaabaaababbbaabaabbabbbbbbbbbaaabbbbabaaaabbbbbaabaabbabbbbbbabbbbbaabaaaaabbabbaabbbaaabbaabaabaaaaaabbbabaaaabaaaabaabababaaabaaaaabaaababbabaaaabbaabbabaaaaaabbaaababaaaaabbbbbbabbaabbaaaaababaabbbabbaabaabbbbbbbbbababbababbbaabbababbababababbaababbbaaabbbaaabbaaababbabaaaababaaabbbaaabbbbabbabababbbbbaabbabbaabaabaabbbbaaabbbaaaaabbbaaaabbbbabbabaabaabbbbbbbabaaababbaabbababbabaaabaabaaaabbaabaabbabbbaaabaaaabbabbaabbbabbabbabaabaabbbbabbabaaabbabbbbbbaababbababaababbabaaabbbaabaaabaaababbabbbbabbaaabababaaabbbaaaabaabaabaaaabbababbbbabaabaaabaaabbbbaabbbabbbabbbabaabbbbbbabaabaaababababbbbabbbaaababababbbbbabaaabbbaaabababbaaabbbaaabaabbabaaaabbbaaabaabbbaababaababbabaabbabaabaaaabaabaabaabaababbbbbbababababbbbabbbabbbabaaaaaababababaaaaaaaabbaaababababbbaaaabbabbabbbbbbbbabbbbbbbabaabbabbbbaabaabbaabaaabaababbbaabbbabbbbababaabaabbaaabbbaaaaababbbbbaaabbbabababbbabaaaababababbbbaabbabaaabbaabaaaababaaaaaabbaababbabbbbabbbaabbbbabaaabaaaababababbbbababababbabaabbaaaabbbaabbbabbbbbbbababbbaaabbbbabbaaaababbaabbbaaababbaababababaabbaaaaababaaabbbbbabaaaaabbbabbababaabababbaaabbaaaaaababaabaabaaaabbbbaaaabaaaaaaaaababbaabaaabbaaabbbaababaabaaabbbbaaaaabaaaaaabaabbbbaaaaaaaaaabbabaaaababbbaaaabbabaababaaaabbaaabaabbbbbaabaaabbbbaaaaaaaaaababbbabbbaaabbbaaababbabbababaaabaaabaaabbaaaabaaabbbbbababaaabbbbbababbaabbabababaabbabbababaabababbabaaababbabbbaaabaababaaaaabbabbababababaabbbbaaaaabbbbabbbbabbaaaaaabbabbabbabaababaabbbbbaababaabaaaabbababaababbaabbabbabaabbaaabaabbabbbbaaababbbaaaabaabbbaabbaaaaaabbbbaabaaaaaaabbbbaabbbabbabaababbaaabbaaaabbbbbaabaabbbabbaabaaabbbabbbabbbbabababbbbbbbbaabbbbabbababaaaaabbababbaaaabbaabbabbbaaaabbbbbaaaabababaaaaababaabaaabbaababbbabbbabaaaabbaabaabaabaaaabbabbbbaaabaaaabababbbbaaabaaabbbbbbaaabbababbbabaabbbaabababaaabaaaababaabbbaabaaababbabbaaaabbbabbabbabaababaababbaabbbaaabbbaababababbababaabaaabbaaabbabaaaaaaabaababbababbabbbbaaaaaabaabbbbbaaaaaaabababaabaababaaaaabbabbababbaaaaaabbbaaaaaababbabaaabbaaaaaaaabbaababbaaabbaaaaaaababababbaabbbaaaabbabbaaaaaabaabbababbbabbbaabbaabaaaababbbaabababaaaaaabbbbbababaaaaababbbaaaaaabbaaaaabaaaaaabbbabababbaabaabbbbbaabbbaaaaabaababaabbabaabbbbababbababbaaabbbbbaabababbbaaabaaaabbbaaaaabbbbbbbaabbaaaaaabbaaababaaabbbbaabaaaaaaababbbbbaaabaaaaabaaaaabbabbbaaaabaabbbaaaaabbbaabaabaababaaaaaababbbbbaabbabbbaabbabbaaabbbbbbababababbaabbbbbbbbaabbabbaaabaaabbbabbaaabababaabbaabbabbbaaaaaabaabaabababaaabbbabaabbbbbbaaaabaabbbababaaabbaabaaababababaababababbabaaaaabaaabaababbabbaaabbaabbababbbabbbbabaabbabababbaaaababababbaaabbababaabbbaaababbbbaabababaaabbbbbbbababbbabbaaaaaaaabbaaaaababbaabbbbabbbaabababaaaaaaaaaabbbaaabaaabbababbbaaababbababbbaabbaaaaababaabaaaaababaabaaaababaabbababbabbabbbabaabbbbaababaabbbaabaaabbabababbbaaaabaabaababbbbbabababbaaabaabbbaaaababbabbbabbaabbbaabbbaabbabaababaaabaabaababbaababbbbaaabaabbabbaabaaaaababbabbabbbabaaabaababbaabbbabbabbbbababaabbaabbabbabbbbabbbaabaabbbabaaaaaabbbbbababaababbaabbbaabaabbbabbabbaababaaabbbbbbbabaabbabbabbaababbabbaaaababaababbbbaabaaaaaabbaababbbbbbaaabbaabbbaabbaabbabbaababaaaaabaaaabaabaabbaabbbabbbbbaaaaaabbababbaabaaaaabbabbbabaaaabbabababbbabaabababbabbabbbabaaabaaabbaaabababbbabbbabbbbbbaababaabbaababbbbbbbabaaababbabbbabbbbbabbaabbbaabbaaabababbbaabbbaabbbaababbbbbabbbaabbbaaabaaabbbabbaabababbbbbabaaaabaabbabbabaabbaababbaabbabbbabbaaabbbababbbbbabbbababbabaababbbaabaaaabaaabbabbbbbaaabaaabaabbaaabababbbbbbbbababaabaaabbaaababbababbbaabbbabaabaaabbbabaabbbaaaabbababbaaaababaabbabaaaaabbabbababbbaababaabbbbabbabbaaaabbbaabbaabbbbababbbabbaabbaaababbbabbaaabbaaaaabaaaababbbaabaaabbabbaabaababbbbaababaaabbabaaabbaabababbaabaaababbbabbabaaaaaabbbabaaabaaaaaabbbaababaabbababbbbbbbbaabbaabababbaaaaabaaaabababaabbabbbabbbaabbaabbbbaaaaabbbbabbbbababaaabbbbaabbaabbbbabbbbbbbaababbbaaababbbbbabaabbbbbaabaabbbbaaabaababbabbbbbaababababbababaabbababbababaaababbbababbbbbbbbaaaabaaababbbbbabaaaabbbabbbbaaabababbbbbbaabbaabaababbaababaaaaaaaaababaaaabbbaabaaabbaaababbbabababbabbbbbbbaaaaaaabbabbababaabaababbaabbbaabbaababbabbbbaaaaababbaaabbbbbbabbabaaabaaababaaababbbbaaabbbabbbaabaabaaaababbbbabbbbbaabbabaaabbbabbbabaabbaabaaaababababbabaaaaaaaababbaabbabbaaaababbbbbabaaaabbaaaaabbbbbaababbbabaaaaabbabbabaabbbaabbaabaabbabbaabbabababbabbbbabbbbabbbababbbbabbbbbaaaaaabbaabbbaaaabaaababbbbbaaaabbaabbaaaabaabbaabbbbbbbaabbbbbbbbababbbbbaaaabbbbbababaaaababaababbabbbbbaabbbbbbabaabaabbbbbaaabaababaabbbbabbabbbabaaaaababbbbabaaaaabaabaababaaabaababababbbbbaaabaabbbbabbbbababababbbbbabaabbbabbbbbbbaabbabbabbbabbbabaaabaaaaaaababbabbbbbbaabbababbabbaabaababbbbaabaababaabbbbaaaaaabaababaaaaabbbaabbaababbaaababababbbbbbabaaaabababbabaababaaaaaabababaaaaaabbabbababbbbababababbbaabababbbaaaabbaabbababaabbbabbbbabbbbbbbaabbabababbababaaabaaabbbabbbbbaaaaabaabaaabbbbbabbababbbaaababbbababbabbbabaababaaabbbaaababbbaaaaaaaababbababbabbbbaababbabbababaabbbbbbaabaabbbbbaababbabbbaabbbbbbbbbababaababbbabbbbbbbbbbabbbbbabbbabaaaabaaaaababaaababbaaaababaabbaaababaaaabababababbbabbbaaaabbbabbbabbaabbaabbbaabaaaaaabbababbabaabaababbbbbbaababbbbaaabaababaabbaabbbabbabaaaabaababbbabbbabbbbaaaaabababbaaaaaabaaaabaababbbbbbbbaabbbbbbbaabbbaabbabbabaabaaabbbabaaaabbaaabaabaaaabbaababbbbaaababbbbababbaaabbbbaababbabaaaaabaaaaaabababbaabbaabbabaaabbabbabbabbbaabbababbbbaababbaaabaababaabbaaabbaaabbbaabaabbbbbaaabbbabbababbbbbbbbaaaaaababbbababababaabaaaabaababbbabaababbbaaabaabbbaabababbbbaaabbbbaabaaabbbbbbaabbabababbbbaaabaabbaaaaabbaababaaababbbbaabababaaaaabbbaaaabbbabbababaaaaaabbbababbbbbbaaaaaabbbbababbbaaababbbabbabbaaababbabbabaabbbbbbbaababbbababaaaaaaabbaabaabababbbbababababbaabbabababbbaaaaabaaaabaabbaaabbbaaabaabbbaaaabababaaabbaaaabbabaaaabaababbbbabbaababbababababbbbabaabbbaaaababaaaababbbaabbaaaababbbbbaabbababbaabbaaaaaabbabbabaaabaabbbbbaababaabbaaaaaaaabbaababbbbbabbaabaaabbaabbaabaaaaaababbbbaaaabbbababbaabbaabaabbbbbbbaabaabaabbbbaabbababaabaabbbabaaaabaaaabbbbbbbaaabaabbbababbaababaabbbaaaababbbbbaaabbabaabaabbbbaaaababbbbbababbbbabbaabbbabaababaabaabaabbbaabbababbaaabaaababaabbbbaabbbbabaabbbbbbbbaababbbabababaababbbbbabbababaabaabbabaaababbaabbababbbbbbbbbaaaaabbaabaabbaabbbaaaaababbabbabbaaaabbabaababbaaabababbaabbbaaabbbbbbbaabaaabbabaaaaaabbabbabaaaaaabbbaabbbbbababbaaaabbabaabbbabaaabaabaabbbaaabbbaaabababbaaabaaaaababaabbbbbaababbabbbaaabbabbbbaaaabbaabaabbbbbbaaabbbbbaabababbbaabbababbbbaabaabbbaabbaaaaababbbbbbabaabaaabaaaabaaabaaababbaaabbabbbbbabaabbbbaaaaaaabaabaaaaaabaabaaaaabbbaabababbbbabbaababaaaaaaabbaabbbbaabbaaaaaaaaaabaababbbaaabbabbbbbaabbaaaabbabbbbababababbbababaabbaaaabbaababbaaaaabbbbabaabaabbbabaababbbabbaaabbababbabbaaababaaaaabbaaabbbbbaabbbbbbbbbbaaababababaababbbbbabbbababaaabbbabaaaababbabbaabbbbbbabaabbbbabaaaababaaabbaaabbaaabbbabbbaaababbaaaaabababbbaaabaabbabaabbaaababbaabbbbbabbabbaabaabaababbabaaaaaababaabbabbbabaaababbbabbbabbbaabababbbabaabaabababaaabbbababaaabbaabbababaabbaababbabaabbaabbababbbabababaaabaaababaaaababaabaabaaaabababaaabbbbaabbabaabaaaaaaababababbbababbbaaaaaaaaabbbbabbaaabaabaababbaabbbbbababaaabbabbbbaaabbbababbaaaabbabbabbaabbaabaaabbaaaaabbbbbbababbabbabbbbaabbbaaabbaaababaabbabababbbabbbbbabaaabbbaaabbbbaabbbbbaabbbaaaababababababbababbbaaabbabbaaabaabaaabbabbbbbaaaababbbaabbaaaaabbaaabbaabbbbaabbaabbbbabaabbbbabaaaabaaabababababaaaababaabbaabbbaabaababbaaabbaaaaaababbbbababbabbabaabbaabbbaaaabaaaaabaaaaaababaabababbbabbbbbbbabbaababaaabbaaaababbbbbaaaaaabbbaababbbbaaaabbabbbbaabababbbbaaabbbaaababaaabbbbabababbabbbbbabababaababbbbbaababababaababaabbbaabbbaababbabbaaaabbbaabbbaabbbbbbaabbabaabbbababaaababbbbbbabaaaaabbabbbabaaabbaaabbababbaaaabaabaabaaabbbabaabbbbabaabbaabbbbabbaabbbbbaaabababbabaabbbbbabbbbabaaababbbabaaabbabbabbbababaaabaabbaabbbabaaabbaababababbababbabaabaaaababaaabaaabbaaaaaaabbbbabbabaabaaaaaabaaaabbabbabaabbbbaaaabbabaababbabbbbabbaabbabaaaaaabbbaaaaaaabaababbaabbaaabbaaabaaabaababbabbbbbaababbaabaabbbabbbbabbabbabbaaabaaaaababbaababaaabaaabbbaaababbaaaababbbaaabababbbbaabaabbbbaabababaabbbbbabbbabaaaaaaaaaaaabbbbbabaaabbaabbbbbbababaabbbabbbaababbbbabaaaaaaababababbbaababbbbabaaaaaaaaaabbbbabbbbabbbaabaababaaabbbababababbbbbbbabaabaaaaaaabbbaabbabaaaaaabbaaaaabababbaaabbbbaaaabbaaaaababaaababaabaaaabbababaaabababababbbaaaabbbbbaaabbbabbaabaaabbabbbbabaababbbbbbaaaabbaaabababbaaabbbaaaabbabbabaaaaabaabbbaabbbabbabbbbaaababbabaabbababaaabaaabababbaabbbbabbbbaaaabbababbaabbbabbaabaaabaabaabbaabbbbbbaabbbaaaabbbaaaaabaaabababbabbbabaaaaaaaaaaabaabbbabaaaabbaabaababbbbabbabbabbabbbbbaabbaababbabbbbaaabbaaabaaaabbaaabbaabbabbabbaaabbabaabbbbaaaaaabaabaaaabbaabaabbababbbaabbababbbaaaaaabbabbbbabaabbaaababababbababaabbbaabbbbbbaababbbaabaabbbaaabaabbbaaabababbbbabbabbbbbaababbbbaabaabbbabaaabbaababbabbabaaaaabaabbaaabaaabaabbbbbaabaaaaaabbabbbaaaabababaababbaaabbbabababbaabaaababbabbbaababbaaaabbbaaabbbabbabbbabbbbbaababaababbbbbbaabbbbbbaaaaabbbaaabbbabbabbabbbabbbbaabbabbbbabbbabbbaabaababaabbbababaabaaaabaaaababbaaabbaaaabaabaaabbaabaaabbbaaaababaaaaaaaaaabbbaaabbaabaaaabbbbabbbabbaabbbabaaaabbbbaaabbaaaabbabaaabbbbbabaaabbbbbbababbaaabababbbbaaaabaababaaaababaabbaaabbabbababbabbbbbbbabbbbbbabaabbaabaabbbabbaaabbbbbbaabbbabbbabaabbbaabbaabaaaaababbaababaababaabaabaaaabbababbbbabbbabbbbbabaabaabbbabbbaabaaaababababbaabbbaabaaaabababbababbabaabbabbbaaabaabababaaabbabaaaaabaababbbbababbaaababbbabbbbbbbaaabbbaababbaabaaabaabbbbbbbbbbaaaaabaaaaaaabababbbbbaabbbbbbaabbbbbaaaabbbbabbababbaaaabaaaabbbbbabaaabbabbbbbbbbaabbaabbabababbaaaabaabbbbababbaaaaaaabbabbababaaaabaabbaababbbaaabbaababbaabaabbaaabababaaabababbbbbbbaaaaaaabaabaababbbaaaabbbabaabbbaabbaaabababbaaabbbaaababbbbaabbbbaababbbaababababbbabbaabaabababababbabbbbabbbaaaabababbaabbabbbbbbaaaabaaabbabaababbbababaabaaaababbbbaabbabbbbaaaaaabbaaaaabbababbbbaaaaaaabababbaaababbbaaaabbbbbaaaababaabbbbbbbbbaabbbabbaababababbaaabbbabaaabbbbbbbbbabbbabbabbbabaaaaabbaabaaabbaabbbbaaababbbabbbbabaabbaaaabbabbbbaaabbbbaabbbbbaabbbbbaababbaaabbbbabbaaaabbaaaaaaabbaaaaabbabbbaaaababaaabaaaaaaabaabaababaaaaaabaaaaabbaabaaaaabbbabbababbbbbbbabaaababbaaababaaaababaaabbaaabaabbbaaaaaaababababbbabbbaaaabbaabaababababbbbbbaababaaaaaabbaababababbbaaabaaaababaababbabababbaabbbbbbbabababaaabbababbbaaaabbaaabaaabbabaabababaaaaaaaabbbabaababaabaaabaaabbbaaababaababbbbababbbaabbbbabaababbbbbababbbbaaabbabbababaaabaaababbbbbaaababbbabaaaaaaababaabaaabbbbbbbaabaaaaabaabaabbaaabbaaabababaaabbbbabbaaaabbbabaaaabaabbabbabbbbbbbaaaaaaabaaabaaaaaaaaabaabbaaabbbabababbaaaabbbaaabaabbabbaabbbbbaaabababbbaaaabbabbaababbabbaaaabaaabaabaabbababbbbbbabababbaaaaabaabbabaaabbbbbbabaabbbbaabbaabbbaabaaababaaabbabaabababababbbaabababababbbbbbbabbabaabababbaabbbabbbbaababbbabbaaaabbaaaaababbbaaaaababaaaababbaabbbbbbababababbbbabbabaaaababaaababbbabaabbbbbbbaaabbaabbaabbbbbbabbbbbaaaaaababaabbbbbbbbbbabbababbaabbbaababbbbaabaababaabbbbabababbaaabbaabbbbbbaabaaabababbbbaabbbabbababbbbbbbaabbbbababaaaabbaabbbbaaabbaaabaaabaaaabbaabbbabaababbababbaabaabbbbabaababaaabaabbaabbaabbaaabbbbabbabaaaaababaabbabbabbabbbbabbabaabbababaaaaaabbbbbabbbababaabaabbaaababbaaabaaabbbbaaaaaabbabbbbabbbbabbaaabbabaaaaabbbbbbbaaaababaababbabaabababbaaabbababbaaaaaaabaaaaaaaabbaaaabaabbabbbbabbbabaaaaabbbabbbabaaaabaabbbaaaaaababbbabaabbbbbaabbbaababbbbabbbabbabbabbbbbbbaaaaabbabbababbabbabbababbabbbaaabbbbbbabbbbaaabbbbbaaaababbabaabbaabaaabbabbbaaaaabbaaabbaaaabbabbabbaabaaaabbbababababbaaaaaaabbbabbbbbaaabbbbaaabbbabbabbaabbababbbbaaabaaaaaabaabbababaabaaaaaaaaaaabbbabbbabbbaaaabaaaabbabbbbabbbaabbabababbbbabababbaabababbaabbbbbaaaabaaaaabaaaaaabaabababbababbaabbbabbabaabaabaaaaababbabbbaaabababaababaabaaaabbabbbbbabaabababbaaabababaabababaabaaaaabbaababbbabbbbbabbabbbababbbaaaabbabbbbbabababababbbaaabbababaabaabaabaabbaaaabbabbaaabbaaaabbaaaaabbbabaabaabbababbbbaabbbabaabbabaabbabbbbbaabbbaaaaabababbabaabababaabbaabababbabbabaaaaabaabbbabaabbbaabaabbbbaabaaaabaabababaaabaaaabaabbabbabbababbbbbabbabbaaaababbbabaaaabaaabaaaaabbabaaaaaaabbaaaabaaababaaaababbaabbbbaabaaaabbabbbaaabaabbbaaaaabbbbabaabbaaabbbabbbbbbbbbabaaaaaaaabbabbabaaabaabbbaabbabbbabbbbbaabaaabaaabaaabbabbabbaababaaababababbbbbaaabbbabbaababaababbabbbaaaabababaabaaaababbbbaabaaababbbbbbbbababaabbabaabbbbbabbaabaaabbbbabbabbbaabaabaaabbbababaabbbbabaaaabbabbbbbbababaaaababbabaaaababbaabaaabaaababababaabbbbaaabbaaabbabababbabbbbabbabbaabbaaabababbbabaabbbabaaabbaababaabbabaaaaaaabaaaabaabbbbabbaaaaabababbbabbaabaabbbabbabbbbbbbbabbbbbaababbaababaaabbababbabbbbabbaabbabbbabbabababbbabaabbaaaabaaababbbbababaaabbaaaaaaababbbbbaababbbbabaabaabbabbbbaaababbabababbababbbaaaaabbbbaaaabaaaaababbaaaabaaababaaaaabaabababbbabbaabbaaaaaabbbbaababaabbaababbbababbbababaababaabbbbaabaaabbaabaaaabbbaabaabbbaaababaaababbabbbbabbbaababbbbbaabbbbaaaaaabaaaaaabaabababbababbabaaababbbaababbabbaaaaabbbaababbbaaabababaaabbaaaaaaaaaaabbaaaaabaabbbbababaababbbbaababababbaaababaaaabaababaabaababbaabaaabbbabbabbaababbaabbaaabaaaabbbaaababbaaaaaaabbaabaaaabbbabbbababbbbababbbbbababbaaabaabaaabaaabbbaaabaaabaaabbbaaaababbabaaaaaabbabaabbaabbabaabbbbabbbbaabbaaabaaabbbabaaaabbaaabbabbabbabbaababaabbabbaababbbbbabbabababbbbaabbbbaaaaaabbaabbaabbbbaaabbbbbabbbbaabbabbbabbbababbababbbbbbbabbaaabbabbbbbbaaaaaabbbbbabbaaabbabbaabaababbbaababbaabaaaaabbaabbbabbababaababbaabbbbaaaabaabbbabababbabbbbaabaaabbaaabbbabaaabbbaabbbbaaababbaaabaaaaaaaabbaabbbbbabbaababbbaabbbbabbaaaabbababbbabbabbbaababbaabbbbbbbbbbaabbbbababbabbbaaabaabbaabbbabbbbaaaaaababbbaaabbbabbaaabbabbbaaabbaabbbbbabaabaaaaabbbaaaaabaabaaaaaaabababbbababaababbbababababbbbbbabaabbabaaababbaabaabaabaababaaaabaaabbaaabaababbabababbbbaabaabaabbaabbbabbaaaaaabaaaabaabaaabbaababababbbbaaabaaaababbbababababaabbbbbababbbabaaabbbbbbabbbabaaaabbababbaaabaabbaaabbabbbabbbbbaaabbbabbababaabaaaabbbababbbabbabaabbbabbbabaaababbaaabbbaaababbbabbaaabaaabaaabbbbbaaaabaabaabbabbaaaababaabaaabbaababaaabbbbbbbaaabaaaaaabbabbababbbbbaabaabaaaaaaaaabbbaabaabbaaaaabbabbbabbbaaabbbabbabaabbabbbaabbaaabababbaabaaaabbabbbabbbaabbbaabbbabbbbbabbaaaabbbbbaabaabaabbaaaaababbabbbaaabbbaabbaaabbababbbbabbbaabaaaaaabbabaaaabbaabababbaabaabbbabaabababbabbabbbaababbababaabababbbaaaaaababaaabbaaaabaaaaaaabbbbababbbbbaabaaabbaaaabaabbaabbbbbabbaabaaaabaaababbabbabaaaabbbababbbbabbbbabaaaabbbabbbaabbabaabbbbbbbbbaaabbaabaabbbaaaaabababbabababbabaabaaababbabbaaaabbbbabbbbbbbbbbbaaabababababbbaaaabbbaababbababbabbaaabbbabaabbaaaabaaababbbaaababbababbbbbbabbabbbbbbaabbbbbaabbaaabbbbbbbbbabbaaabababaabbaaabaabbbbabbaaabaaabbbbaabbabbbbaabaaababababaabaaaaababbaabaaaababbbaaabbabbbaaaaababbaaaabbaababbabbbbbabaabbaaabbaabbaaabbbbbbbabbaaabbabbaabbaaababaaaabbbabaabbbaababbaabbabbbbabbabbabababbabaabaaababbaaabababbbbbbaabbbaabbbababbbaabaaabbbabbaaaabbbbaabaabaabbaaaabbaabaabbbbabbaabbaabaababbaabaabaaaabbbbbbbabbbaabaabaabbbbbbbbbabaaababaabaaabbabbbabaaababbbbababbaaaaabbbaababaabbaaabbaababaabbabababbaababaaaabaaaabbaababbbbaaabaababbbbaaaaabaaaababaaaaaaaabbaaaaabbbababaaabaabbbaaaaaabbabaabbababaaaabbbaabbbbabbbababbaabaababbbaaaaabbaaaaaaabaaaabbabbbabababababbbaaabbabbbaaaababbbbaababbaaaaabbabaaabbaaaaabbbbaabbbaabbababaaabbabbababaabaaabbababaabaaabaababaabaabbababbaaabbbbabaaababbaababaaabababaaababbbaabaabaabbbbbbabbbaabaabbababbbbbaaabbbbaaabbabbbbabbbabaabaababaaababababbabbabbabaaaabaabbabbabbabbabaaaaabababbbbbbabaabbbbbabbbbaaaaaaabbbaabaaababbbbaabbaaaaaabaabbbaabbbbabbbbbbbaaaaabbbbabaabbbbbbaabaaabbababaabaabbabbaaaaabbabbbabbbaaabbaaaaaabaaabaaabbbbaabaaabbbaaabbaabbaaabaaabbaabbabbababbababbbbaabaaaaaaaaaaabbaaabbbbaaaababbbbbaabaaababbbbaabbbabaabaaababbbaaaabbbaabbaaaaaaabaaaababbababbbabbbbababbaabbbbabbaaaababbaaababbaaaabaabaaabbabbaaaabbabaaaaabbbbaababbbaaabbaabaabaabbabbababbaaabbabaababbbaaaabaaaabbaaaababbaaaaaabaababaaaaabbabaaabaababababbabbbaaaaabbaabbaaaaabbabbaaabbaabbabaabbaaababbbbaabbbaaabbabbabaaababbabaaabbbbaaaaabbbababaababaabbaabaaabbbaabbbababaababaaababbaaabaabaababbbbbababbaaabaaabbaaabbaabbbbbbabbbababbbababbbbbbaaaaabaabaabaaaabaabbababababbaabbabaabbbaabbaaaaababbbaaaabbbbbbbaabaaabbabababbbabbbbabaaaabaaaaaabaaaaaababbaabbabbaaaabbbaaaabaaabbbabbabbbabbbbaabbabbabbbaababababaababbabaaaabaaababbabbaabaabbaabbaabbbabaabaabbababbababaaaaaaabaaaabbbbbbbabbaaaaaaaabbbbaabbbbabaababbbbaabaabbbbbbbbabbabaaaabaaaaaaaabbbabbbabbababbaaabbababaaabbbaabbaaababaabbababbbabbabbabababbababababbbbabbabaabbaaaaabaaabbaaabbabbaababbbbbbbbbabbaabbbbbbbbbbbbbaabbbbabaabaaababbbaaabbbbbbabbbbbaaaaaabbbbbbbbbabbababbbababbabbbabbababbaaabbaaaababbbbaabbbaaaabbaababbbbaabbaaaaaaaaabbabbbbbabbbabaabaaaabbaabaabbbabbaaaabababaaabbaaabbabbabbbbbabbabaaaababbaabbabbbaababbabbbabaaabaaabbbbbaaaaaabaaaaaabbbbabaaabbaabbabaaaaaaabbbaabbaabbabaaaaabbabaaaabaababbbbaababaabbbbbababbbbaaaabbbaaaaaabbaaaaababaababbabbaababbabbbbabaaabbabbbababbbbaaababaaaaabbbabbbbbbbaabbaaaaaabbbabaaabbabbabbbbbbbabaababbabaabaaaabbbbbbabbaaaabbabbaababbaabaabaaababbaabaababbbbbbaabbabbabababbbbaaaabbbaabbbaabbaabbbabaaaaababaababaabababbababbabababbabaaaabbbbbbababaaabaaabaaaabbabbaababaaaaabaaaaabaaaabaaaaabbabbaaabaaabbbbaaabbbaabbabababaabbbbabaabababbaaababbbbbaaaabbabbbaaababbaaaabaaaaaaaaaaababbaabbbaaabbabbaaabaaabbaaaaaabababababbabaabbabbbbabbbbbbbabaabbabaabaaaaabbbbaaaaaaabaaabbabbaaabbabababaaabbaaaabbabbabbaaaaabbabbbabbabaaabaabaaaaabbaaabbabaababbababaabbbbbaaabaaababbabbaabbbbabaaababbaaababbbbbbbabbbaabaaabaabaabbbabbbaabaaaaaaaaabbbabbbbaababbbabbabbbaaabbabbabbbbaaaabbaabbabbbbbabaaabaabbaaabaabbaabbbbbaaaababbaaaabbbaabaaabaaaaaaaaaaabbbaabbbaabbbbababbbaababbabaaaabbbbaabaaabbaabaabbbbabbbbbaababbabababbaabbbaaababaabaabbbaabbaaaaabbabbbbabbabbabbbaaabaaabbbababaaabbabababaaaaaaaaaabbababaabaabbabbabbbaaaaabaabbaabbbaaaaaabbbabaaaaababaabaabbaabbbbaababbbabaababbabbbaaababaaaabbabbbbabaaabbaabababbbababaabbabbaaaabbaaaaababbbaaaaaaababbbabbbbabbbbabbbbaabaabbbabaabbbababbbbbbaabaaababaaabababbabaabbbaaabbabaababaabbbbabbbabbabaaabbaaabbaaaabaabbbbabbababaabaaaaaaababbbbbbbbabbbbababbbbbbabaaaaabbbababbaaabaabbbaabbaababbababbbabababaabababbbbbbbaabbbbbbbbbaabababbabaabbaabbabaababbbaababbababbbbbbbabbbabbbbaabaabbbbbbabababbbaabbaabaabaaabbabaabbbaaaaaaabaaabbabaabbbabbbbbbabababbbbabaaaaaaabaabaaaabbaabaaabbbbbbbaabaabaababaabaaabababbabbabaabbbbaaabbaabaababbaabbababbaabbabbbaabbbaaababbaabbaabababbbaaabaaabbabbabbbababbaaabbaaaabbbbbaababbabbaaabaaaabaabbbabbabbabbbabbbbaabaaaaabbaaaabbbaaababbaabbbbbbbbaabaabbbbabbbbbbbbaabbbabbbbbabaabbbbaaaabbababbbbaaababbabbbabaaabbaabbbaabbbbbaabbbababaaababbaaabbabaaaabaabaabaaabbabbbbbbaabbaabbbaabaabaabbbababaaaaabababbabbbabbabbbbababbabbaabaabbbabbaabbabbbabbabbbaaaababbbbaaaabbabbbaabaabbabbbbbbbaaaabababaaaabbbabaabbabbbababbbbabbbbbaaabbaaaaaaabbaaabaaabbbaabbabbbbbbabbaaabbbbbaaabbababbaaaabbaaabbbabaabbaabbabaababbabbabaabaaaabbbaabaaababbbaababbbbbaabbbabaaabbbabbabababbbabbabaababbabbbabaabbbabbaaabbababbbaaabbaabbaaabaabaabbbaaabaaaaababababbbaaabbbbababaabaaabaababbbbaabaaabababbbbaababaabbaaaabaabbbbabbaabbabbabaabaabaabaaaaaabbbbbabbbbbabbbabaaabbaababbbbbbbbaabbbaabababbbaaabaaababaabaabbaabaaabbbbbabbbabababbaabaababaaaaaabbbbbbbaaabbbaabbbaaabbbbaaaababbbbbbbbaabbababbabbabbbbababbbbababbbbababbaaaabababbababababbbababababbbbaaabbbbbaababbabbaabaaaabbbbababaabbbbabbbabbbababbbbbaabaabbaaaabbabbaabbaabaaaabbbabbbbaaaaaabaabbaabbbaaaaabbbaaaabbababbbbabaababbaaabbbaaababaababaabbbababbbabbbaabbbaabaabbbaaabbbabbaaabbbabbbabbabbbbbaabbbaabbbabbaabbbaaaaaabbbaabbabbbbabababbaabbbbaababbaaaabbbbbaabbaabbbabbbababaabbbbaabbaaabaababbabbaabbbaaaababbabbbbbbbbbabbabbbbaabaabaabbbaaabbbbbaabbbbabbaaabbbbbaaaabbaaaaaabaaaaababbbababbbaaaaaabbababbabbaaabbbbaabaaaaababbbabbabbabaaaabbbabbaabbaaaaabaababbaaaabaaaaaabbaaabbababaaabbbababbbbbbabbaabbababbbaabbabababaaabaababbaaaabbabbababaaabaaaaabbbabaabbaabbaabbabbababbabaabbaabbabbbbaaabbaabaabbaaaabaaabbbabbbbbababbbaaaaaaaaaaaabbbbaababaababbababababbbbaabbbbaaaabbaababbaaaabbbbaabbbbaabaababbbbabaabbbbaaaabbabbbbbbaababbbaaabbbaaaaabbabbaabbbaaaaababbbaaaabaabaaabaaabaabababbbbbabbabaababbaabbbbbaabbbbabbbabbbbabbbabbbaabbbababaabaaabaaababaabababaaabbbbbbabaaabbabbbbaabaababbababbbababbbaabaaabbabbbbaaaababaaaabbbbaaaaabbbaabaaaababbaababbbabbbbbaaaaabbbbaabbabbababbbbbabbbabaaaabbaaabbaaabbaababaabababbabbbabaaaababbabaaaaaabbbbabbaababbabbbbbabbabbaaaaaaaabbbbaaaaabbbabbbabaaaaabbaababaabababbbbabbabbbaababbbaaaabbbbaabbabababbabaaaabbabbbbbbaabababbaaabbabbbbaabbaaabbababaaaabbabababbaababaabababaabaaaabbbaaaababaaaaabbbbabbbabbababaabbabaaabbaabbbbbaabaaabbbaaabaabaaabaabbaaabbabbaababbbababbbbaabbabbabbbbbbababbbabbbabbbabbabababbabbaabbababaaababbaaaabaabaabbbbbbbbabbabbbaabbaabbaaaaaaaaabaabbbbabbbabbbbbbbbaabbbbbabbbbbbbbbbbbbabbbabaabaabbbbabbaabbaabbaabaabaabbaabbbbaaaababbbaabababbababbabbabbaababbabaabbaaaaaaabbababbaababbaabbbabbaabbbbaaabbaabbabaaababbaababbaabbabbbaabbaabbbbbaaaaabbababbaaaaabaaabbabaaaabaaaaababaabaaabbbbabbaabbbabbaababbbbabbbabaabaaaababbbaaaaabbaabbaabbaaaaaaabbbabaabbbbbaaaabbbabaabbbbabbaaababbababbaaabaaaaabbbbbaaabbaaababbabbbaabaaaaabbbaaababbababbabaababbabbbbbaaaaaaaababbababbbabbaaaaabbaaaababbbbbaaaabbababaabbabaabbabbbbabaabbbbbbababbaaaaaabbaaabbbaabaaaabbbaaaabbbbabaabbabababaabbaaababaaaababaababaaabbaababaaababbaaabaaaaabaaabbbbbbaaaabaaaabbabaabbabababaaababbbbbaabbabbbbaababbababaaabbabbbbbbbbbbbbbbbabbbabbaabaabaaabaaabbaaabaabaaabaabaabbbabbaabaaaaaabbbbbabaabbaaaababaabaabbbabaababababaaabababaaaaababbaaaaaabbabaaabaabbabaaaaabaaaaaaaaaabbaababbabbbbbbbbbabaabaaababbbaaabbbabaababbaaaaababaaaaaaabbbbaaaabbabbbabaabbbbabbbbababbbaaaaababbabbbbbaaaaabaaabbabbaaaababbbaaabbbaabbabbaababbbbbbabbbaabbaabaabbbabbabaaabbabaaabaabbaaababbababaaaaabaabbabbbbbbababbbababaabbbbbabbabbbababbabbabbaabbaabaaaaabaaaaaababbbbaaabaaabaabbabaabaaabbaaaababbbabaabaaabaaaaababaabbbaaaabbbaabbaabbaaababbbbababbbbabababaaaaaabbaababbbbaabaaabaabbbabbbaabababaabbbaababbabaaaabbaabbbbabbbbbabaababbbaaaabaabbbaabbaaabaabaabbbbabbabbbabbaabaababbbabaaaaababbbbbbbbbbabaaaabbbabaabbababbababbababaabaaabaababbbabababaabbabaaababaababaabbaaaabbaaabaabbbbaaabbabbbaababbababbababbabaabbbaabbaaaaaaabaaabbaabaabaababbbbbbaaaaaaaaaaaabaababaababbaaababbbaaabbbabaabbbbbbbaaaabaaabaabbabbabaabbaaabaabaaabababbababaaaababbababbababbabbaaaabbbaaabbabaaabbbbabbbbabbbbabbaaaabbbaaababbbaabbbbabbbbbaaabaababbabbaabbaaabaabbabbbabbbbababaababbbbbbabaabbbabbabaaababaababbaababbbabaaabbbbbaabaababbaabbabbaabbaaabbbababaabaabbbbbaaabbbbbabaaaaaaaabbaaabaabaabbbaababbabbbbbababbabbabbbaabbbbaababbabaabbabbaabaabaaaabaaaaabbbaaaabaabaababbbbaababbaaaababaababaaabbbaaabbaaabbababbaabbbaabbabbbabaabaaabbaabbbaabaaababbaabaaabbababaaabbbbaaabbbbaabbabbbaaabbaabaaabaaaaaaaabbababbbbaaabbbaaaaaababbbbaababbbbbaaaababbbaabbbbbbbaabbaabbaabbbaaaaabbbbbabbaabbbbbaaabbbbabaaababaabbbbbbaabbbabbababbbabaabbbbaababbbabbabbbbbaababbababbbaabbbaababbbbbbabbbbbababbbbabbababbaaaabaaaababaababbbabbabbabaaaababaabbaaaabbabbaabbbababababaaaabbabaababbabbaabaababbbabbbaabaaababaaabaaabbbbbbabbabbaabbabaaababbaaabaabbbbabbbaababbbaaaaabaabbbbbbbbbaabbbbbbbabaaabbaababbaaabaabbabaabaaabaaaaaabaaaabaabbbababaaaaabbaaabbaaabbbbabbbaabaababaaabaababaaaabaaabbaabbababaaaababbaabaaaabbababbabaabbbbaabaaababaaaaababaaaaaaaaabbaabbbababababababbbbaabbbaaabbaaaaaaababbbbbbbbabaaabbbaaaaaabaaaabababbbbaaabbbababaaaabaabaabaababbbbbabbbaabbbaabaaababaaaababbabbaabaaabbaabbbbabbbabaaabaabbbbbaabbbbbaabaabbabaaabaaabbbbaabbbbbabbaababbbaaaaaabaaabaaababaabbbbaabbaaaaaabaaaaaaabbabbbbbbbaaaabbbbaabaabbbbaabbbbabbbbaaaaababbaababababbbbbabbaababbabbbababaabbbbbabaababbbbbbaaaaaaaaabababbabbaababbbbabbbaabaabbabbaaaaababbabbaaaababaaabaabbbabbaaaabaaaabbbbbbaaaaababaaaabaabbbaabababbbbbabaaabbabbbabbbabaabbbbabbabbbaaabaabbbaabbbaaababaabababbbaaabababaababbbaaaabbbabbbabbbabbbabaabaaaaaabaababbaaabababbababbbbbaababaaaabbbbbbaabbaaaaabbbaabbbbbbbaabbaababaabaaabbbabbabbaaaabbbaabaaaaabaabaababbbababbabaabbbbbbbabaaaaababbaaabbbabababbabaabbabababbbbababababbbabbaabbbbabaaaaabbbbaabbababaabbbaaabbbbbabaabababbababbbaababaaababbbbaaababbbaaaababbbbaaabaaabbbbababbbabaaabbbaaabbbbabaaabbbbaabaaaaaaaaabbabaabbabbbbbabbaabaaaabaabaababbabbbbbbabaaaabbabbbabaaabbbbaaaabaababbbbbbaaababbbbbbbbbbababbbbbabaaaabbaaabbaaaaaaaababaaabaaaaaabbbabbbbbaababbbbbbabbbabaabaaabbaabaabbbbbabaaabbbaabbbabbbbaaabaaabbbaaaaabaabaabbababbbbbaaabbbbaababbbbabbbaabbbaaaabbbbbaabbaabbbbbaabaabababaabaabaaaaaababbaaabaaaaaaabbbaaaaabbbbaabbbababbabbbbbbabbbbaabaaaaaaaabbabbbaabbaabbbabaaababbbbbbaabbabaaabbabaaabaabbbbbabbaaabbbabbbbabbbbabababaabbbbaabbaaaaabbabaabbaaaababaaabbabbbbabbaaaabaaabaaaaabbaaabbbbbaaabaaaabbabaabbbabbababababbbbababaabbbabbbaaaababbbbaabbabbabaaabaaaabaaabbaaaabbabbababaabbbbbbabababbbaabaabaaabaaaababababaaababaabbbaaaaabaaabbbbabbbaaabaabaaabbbbbabababbaaaaabbabaabaabbaabbaabaaabbbbbbabbabbbbbaaaaaabbaabaaaaababbbabbbababbabbbaaaaaaabbaaababbbbababbbaaabaaabbabbbaaabaaaabbabaababaaababbaaaaabaabaaaabbaabbbbbbbbaaaababbbabbbbbababbaabbbaabbbabbbabbabababbaabbbabbaabbabbbbbbbbaaabbaababaabaaaaabbbbaaabaaabaababaabbaababbbaaaaabababbbaabaabbbbaaababaaaabaabbbbbbbbbaabbbabaaaababbaaabbbabababbabaaabaaabbababbaaababbabbabaaaaabbbbaababbbbaabaaaababbbbbabaaabbabbbbaabaaaaaabbbbabbaabbbbbbaabbaaaaaaaabababaaabbabaaaaabaabbbaaabbbbbaabaaabbabbaabbaabaaabbaaaabbabbabbbbaabaaababbaaababbbbbbabbbaaaabbaabbbaaababaabbbbbabaaabaabaaabababaabbbbaabababbbaaaabababbbabaababaaabaaaaabaaaababbbaaabbaabbaabbaabababaaaabbaabbbbabbaaaabbbababbaabbbbbbaaaababbbabaaaabaabababbaabaababababbbbabaabbbabbabbaaaabbabbababaaabababaaababaabbbbabbabbbbbaaaabbbbbbaaabbbabbbbaaaaaababaaabbabbbbbaaaabaaaabbbabbaaaaababbbabbbabbbabbbabbaabbbbbbaababbbbbbababbababbbbbaabbaabaaaaabbbaaababababaaababbbbababaaaabaabbaaabbbbabbaaaabababaaababbaabbbbbbbabbaababbbaabbabababbaaabababbaaaaabbaaabababaabbaabbaaaaaababbbaabbaabaabbaababaabababbbbabbaaaabaabaaaabababbaaaabaabaaabbbaababababbbbabbabbbaaabbaababbbbabaababbbaaaabbabababababbabbbabaaaaaabaabbabbbabaabaabbabaaaaabbbbababaaabaaaaabbaabaaabaaabbabaaaaaabbbbbaaaaaaabbababbaabaabaaaaaaabbbbbabbbbabbabaaababaaaaaabbbaaabaaaaabbbababbbababaabaababaababbbbbabbaaaaaabbabbabbbbbababbababbbbbaaaabaababaaaababbbabaabbabbbaaabbbaabbabbaabbabbaabaabaaabbabbabababbababbbbababbbabbaabababbbbbbbaababbbabaabbbbbbabbabaababbbbbbaaaabbbbabababbbbaaababbabbbababaababaabbbbbaaaabbbaabbbaaaaabbbaaaaaabbababaaaabaabbbabbbaababbbaaababaabaabbbbbababbabbbbaaababababaaaabbbbabababbabaaabaaaabbbbabbabbaaabbbbabbabbabbbabaabababbbabbbabbababbbaaaaaaabaaaaaabbaaaabaababbbaabbaaabaaabbbabbbabbbbabbbbabbbaaabbbaaabbbaababbbbbbabbbababaaabbbbaabbabbabbababbaabbbababaaaaaaabaabaabbbaabaabbabaaaaaabbaabaaabaabbbbaabbbaaaabbaaaaaaaaabbaaaaaababaaaaaaabbbbabaaaaaabbabaaabaabbbbbabaaabbababbbbabaabbabbabbaaabababbbabaababbabaababbbbabbababababababbaaabbaabbaaaaaaabbaaabbbbbaabbaabaaaaabbbabbaababbabbbbbabbbaaabbaaabaaaaaabababbbabaababbbaaaababbbabaababababababaababbaaabbaababbbabbbabbaababaabaababaabbbbbaaaaaabaaabaaaaabaabbaaaaaaabbbbbabbabbababaabaabbaabbbbbabbaabbabbbbbbbbaabbaaabbbabbabaabbaabaabbabbbaabaaaaabbbabababbbbbbbaaaabaaaaaababbbbbbbaabbbbabbabbbababaabbaaaabaabaaaaaaabbaabbabaaabaabbbabbbaabbbaaabbbaabaaabbbabaababbbaaaaabbbbbbbbaaaaaaababbbbaabaabababaabbaaabbabbbabbabbbbaababbbbbaababbbbbaaaabbaaabaabbabbbbabbbbbabbabbabababbaaaaaaabbabbbabbbaaaaaaabaaabbbbabbbbbaabbaabaababababbbabaababbabbabbbbaaabbabaaabaaabaaabbbbabbabaababaabababbbabaabbbabaaaabbbaaabbaabbbbbbabbaabbbbbbbabbbbaaababaabaaabbbbbbbaabbababbaaabbaabaaaabbaabaababbbababbaaaaaaaaabbbaabaaaaabbbabbababbaabaabaababbbbaaabbbaaababbabaababaaabaaaababbabaabbabbbbaaaabaaaabaaaaabbbaabbaaabbaaabbaaabbbbbaaababbbaaaabbaaaabbaaaaaaabbaabbaabaaabbabbbbbbaabbbaababaaaaabbababbbbbbbaaaabaaabbaaaaaababaabaabbabbaaabbbababbbbbbabbbabaaaabbabbabbabbbbaabbabbbababaababbbbababbaababbbaabaababbbbbbbabaabbbbaabaabbbbbabaabbbbbbaabaabbbbabbbabaababaaabbaabbbabbaabbbbaabbaababbbabbbabababaaaabaaaabbaabbbbaaaababbaaaabbabbabbabbabbbbaaababbababaaababaaabbababaaabbbabbaabaaaaaaabbaabbabaaaaabbabbbbbbabaababbbaaaabbbabbabbbabababbaabbaabbaaaababbaaabbaabbbbabbbbbbbabbbbabaaabbabbbbbaaaabbaaaabaaabaabaabaabaaaabbaabbbbbbabbbabbabababaabaabbaaabbbbababababababababbbaababbabbaaaabaaabbabababbbabbaaaabaabbabaaaabaabbbaaabbbbaabbaaaaaaaababaabbabbaabababbaaaabaababbbbababbbaabaabababbaaaabbabaaaaaaababbabbaaabaaabbbabbabbabbbbbabaaaabbbbbbbbaabaabbbbabbaaabaabaaaaabaaabbbabaaaaaabaabbaababbbabbaabbaaabbbbbbaaabaababbbaabbbaabbaaaabaabaababbbbbbbbabbbabbaabbbbbababbaaaabbbbbaabbaaabaaaabbbbbbbbbaaaabaaaaaaaabaababaabbaaabbabbbaabbbaaabbababbbbbaabbbbabbabbbababbababbbbbaaaaaabbaabbabbbababbabaaaaaaaabbbababbaabaaabbbaaabaaaabbaaaabbbaabaaababaabbbaababbababaaaaaaabbbbbbbabbbbabbabaabbbbbabaaabbbbabbabbbababaaaabbbabaabaaaabbbabbaabbabbabbbaaabaabaabababaabbbaababbbabbababbbaaababbaabbbaabbbaaabbbabababbbbaabbabbbbbbbbaabbbaaaabaabbaaaababaabbaababbababbbabbaaabaaaabbaabbbbbbbbaaaabbabbbbaabaaabbbabaaabaaabaaababaaaabaabbaabbbabbabbbbbbabaaabaaabbaaaabbbbbaabaaaabbbbabbbabababbaaabbbbbbbbbaaabaabbabbaababaaabbaabbaaaaaabbbbaaababbabbbbabbbaabbbabababaaabaababbbabbabaabaaabaaabaababaababbaabbbbaabbabbbaaabaababbabbbaabbbbbaabbbaaababaaabbbbaaabbbababbbbaaaababaaaababbabbbbbabbbbbabaaabaaababbbababbbabaabbababababaabbbabbaaaaaaaaaabbaaaaaaabaabaabbbaababbaabbababbababbbabbbababbbbbbabbabbbabbbbabaababbabaabaababbbbaabababbbbabbabaabbaabaaabbabaabbabbbabbaaaaabbbbbbaabaaabbbbababaabababbbaababbbbabbabbaaaaaabaaabbbbaababaaababaaabbabbbbbbaaabaaabbbbbbbbabaabaaaaaabbbbaaabbbbbabaabababbaaaabbbbabbabaababbbbbbbabaaaaaaaababbbbabbbabaabaaabbaabbbbbbabaaaaababbaabbbaabababaaabababaaaabbaababbababaaaaabbbaaabaababaabbaabbbaabbabbaabbabbabbabbabbbbbbababbabaabbabbabaaababaabbbaaaaaababaabaaabbababaabbbbabbaaabaaaaaaabbbaabbbababaaababbaabbbababaaabbabbbbaabbbaabbaaabbbaabaaaaababbaaababaaaabbbabbabaababbbaaaabababaaaaababbbaaabbbaaabbaaabbbbaabbabaaabaaabbbabbbbabaaabbbababbababaaaaaababbaabbababbabbabaabbaaabaababababaaabaabbbbabaabbabbaabbaabbbaaabababaabababbabbbaabaabababbbbabbaaaaabbbaaaabbababbabaaaabbabbbaabbaabbbbbaaaabbaaababbabbbababaaaaaaaabbbabaabbbbbbababbbbabaaabbaababbbaaaaaaababbaabaaabbbabbaabaababaabababbbabbaabbaaabaaabaaabbbbbabbbbaaabaaaaaaaaaabaaaaaabbababbaababaabaaabbababbbabbaabbababababbbabaabbbbabbabbaaaabbbaaabababbbbbabaabaabbaaaabbbbabababbbbabbaabbbabbbbaaaaaabaabbbbaababbaababbaaaaaaabbbabababbaaaabaaaabbabaaaabaabbababaaabbababbbaaaabaabbabbbbaabbabbabbababbbaaaabaabbbbaabbaaaabababbabbaabbbbaaaabbbaababbababbbaabaabbbabaababaabbabbbbaabbbbababaabbabaabbaabbbaabababbaabbaaaaababbabbaaabbaaababbbbababaabaaaabbaaabbabbabaabababaaaabbbaaaaaaabbbababbbbabbabbaaabbbabaabbababaaabaaababbbbabbbbbabbaabaaababbbaaababbbbabbabbaaaaabbbabbbbaaabbbbaaaabbbbaaabbaaaaabaaababbaaabbabbabbbabbbaabbaabbbabaaababbaaabaabbabaabaaaaaabbaaabababaabaababaaaabbabbabbbaababbbbabaaaaaaabaaaabbbaabbbbaaabbaababaababbababbabbabbaabbababaaaabbabaaabaaaabababbbaabbababaabbbbabbbabbabbabbaaaababaabbbbabbabbbabaabbabbaabbaabbbaaaaababbbbabaabbbabbbabaabaabababababaaaaabbbbaabbaababbbaabbbaabababbaabbbbabaaababaabaababababbabbbbbabbaaabaaaabbbbaaaabbabbbbababbabbabaabaababaabbbbabbababbabbbbaabaaabbabababbaaababbbbbbbbaabaabababbabababaaaabbabbbaababbbbbabbbbbaabbbababaabbbbaababbbbbaaabbaabaabaabbbaaabaabaaaaabbaabbbbaaababbaabbbbaababaaabaabaaabbabbbbbbbaaababababbabaaaaabbbbbabbbababaabbbaaaabaabaaabaaaabaaabababbbbabbbaabbaaaabbbbabaaaaabbabbaabbaababbaababbabbbbabbbbaaabbbaababaababaaabaaaaaaaaabbaaaabbaabaaabbaabaaaaaabbbbbaabbaabaaababbbabbbaabababbaaaababaabaabbbabbbaababaababaabaabbabbabbbababbabbaaaaababbaabbbabababaaabbbabaabbbbbbbbbabaabbaaabaababbbaaaabbbaaababbaababbbbbaabbabaaabbbbaaaabbaaabbaabababaaaabbabbbbbaaababbbbabababbabaabbabbaaabbaaabbbbababaaabbaabbaaaabaaabbaaaabaabbababbbaaaabbbabbabaabbbabbbbbbbaabbababbbbbbbbbaaaaababaabaaabaabaabbabbababbaaaaaabaabbbaaaabaaaaaaaabbaabababababbbaabababbaabbaabbbbbaabbbaabababbbbbbaaaaabbbbbababaaaabaabbabababbbaaabbbaababbbaaaaaaaaabaabaabbaaababbbbbaabaaaaaabbbaabbabbbabaabbaababbaaabbaabbababbbbbbbaabbbaabaabaaabaaaababababbaaaabbaaabaaaaabbbbbaaabaaabaaaaababbbaababbaaabbabbabbaaaabaaaaababbaaabbabbaaababaaabbbbbabbaabbbabbbabbbbabaaaaaabbabaaaaaaaaabaaaaababbbbbbbbaababababbabbabbababbbaabbabaababbabbbbabaabaabbabbabababbbbbbbabbabbbbbbabababbbaabbbaaabbabbabbaabaabaaababbbbabababbaaababbbbbbaabaabbbbbbbaaaabbaababbabbbabbaaaabbabbbaaaaaaabababaabaabbaabbbbabbababaaaaaaabbabbbabaaaaaaabbababaaabaabbbaaaababbaabaaaaaababbababababbbbbaaabbbbabbaaaabaaaaaaaaabbbabbaaababbbabbaaaaaabbbbbaaaaabbbbaabbaabbaaabaabababaabaaaababbabbabbbaaabbaabbabaaabbbbabbaaaaababbaaabbaaabaabbabbaaaabaabbbabbbbaaabbaaabbaaaaabbbabbaaabbaaaabbaaaababbbabaaaaababababaabaaaabbabaaaaaaaabbbaaababaababaababaaaaababbbababbabbabbabbbbababbbbbabbbbbbaababbaaabbbbbaaaaabbbababaaaabbabbabababaabaabaabbbaabbbaababababbaabaabbaabbabbaabababaaaaabbbabaaaabababbbabbaabbbbabbabababbbaabaaabaaaaaabbbabaaababbabbabbababaabbaabababbbaaabbbbabbabababababbbbabbaaaaaabbbaabaababbaabaaabbaababaaaaaabaaaabaabbbbabbabbbaabbabbbabaaabbbaaaabbaaaababaababaaabbbbabbabaababaabbaaaaaabababbaaaabbabaabaaaaabbaaabaaaaabaabaaaaaabbbaaaaababaabaaaabbababaaaababbababbbbbaabaaaaababaabbababbbaabaaaaaabbbababbaaaaabaababbbbaabbabbabbbaaaababaaababaaabbababaaaaabbaaaabbbaabbabbbbababbabaabaaaaaabbaabaaaaaabbbbbaaabaabaaabbbbaaabaabbbbabbaababbaabbabaaaabbababbabaaabbabbaabbaaabaaaababaaaababbabaabbaaaaaababbbbbabababbaababbbbbbaaaabababbaaabbbaaaabbbaaabaabbbabbaaaaabbabbabbbbaabaabaabbbbabbbabbabbaabababaaaabbbbbbbaababbabaabbabababbaababbbbbaababbbababaaaaabbbaabbbabbbabaaaabababaababbbabaabbbbbaabbaababbbabbababbabbabaaabbbababaaabbbaabaaabbbbaaababaaabaaabaabbabbaaaaaabaababaaabaaabbbbbaabaaabbbabaabaaaaababbbbbbabbbabaabaaabbaabababaaababbaaaaabbbbaabbaaabababbaaaabbaaaabbbaabbaababbabbababaababbaaaaabbbabaabbabbaaaaababbabbbbabbabbbabaaaaabababbbababaabbbaaaaabbbbbbbaaabaaabbabbbbbbaaaaaaabaaabbaaaaabbbbaabbbaaababbabaabababbabbabbabaaababbabbbaabbaaaabbaaaaabbbabbaabbbabaabababbbbabbbbbaabaaababaaabbbbbababababbbbbababbaaabbbbbbbbababbabbbbabbabaaaababbbbbbbabaaaabbababaabbababbabaaaaabbaaaaabbaaaabbaabaabaaabbbaaabbbaaaaabaaaababbbbbabbabbabaaaababbaabaabbabaaabaabbabbaaaaaabaaabaabbabaaababbbabbbaaabaaabaabbbaaaabababaaabaaababaababaabbabababababbbaabbabbaaaabbaababaabaabbbbbaabaababaaabbbaaabbbabaaababbabaaabbabaaabaabbabbbbabbbbaaabbabbababbabbabbbbbbabbbbbabbbababbbaaabaaaabbbabaabbaaabbbbabbabaabbbbaaabbaabaaabaaababaabaabbabaaaabbabbabbabababbbaabbbbbbabbbbaabbabababbbbabbaabaabaaaabababaaaaaaababaabbbaabaababbbabbaaabababbabaababbbaabbaaaaaabaabaababbbabaababbaaabbaaabbabbbbabaabaabbbabbabbbaaababababaaaababbbaaaabababaaaabbbabbabbaaababbbaabbbabaaababbbbabaabbabbbbbbababbaaababaaaaaaabaabaaaaababbaabbababaaaababbaaaaaabbababaaaaabaaababbbbbaaaabbbabaaaaabbbbaaababaaaabaaaabbbaaaabaabaabaaaababababaaabaabbbaaaabaabbabbbbbbbbabababaaababbaabbbbabbabaabbaabbaabaaabbbabbbababababaabaababaaabbbbbababbaaabbbabababaabbbaaabbbaababaabbbaabbababbabababbbaabbbabbbbaaaabbbbababbbbbabbbbbbaababbbaaaababaaaababbaaababababbbababbbaaaabaaaabbbbabbaabaabbabbabaabbbaabbbababaaababbaaaabbaaaababbabaabaaaaabababaaaaababbbbbaaaaaaaaaabbbbbbababbabbbabaabbbbababbaabaaababaaababbabbbabbaababbabababaabbbaaaabaaabbbbaaabbbabbbaabbbbbaaaaabbbaaabbbaababbbbbbabbbabbbaaabbaaababbbaabbbbbbabbaaabbbaabaabbaabbbbabababbaaaaaabbbaababbbaaabbbaabbaaabbabbbaaaaabbaaaabbabaabbabbaaaaaaaaabbaabbaaaaababbaabbbbaaaaabaaaaabbbbabaaabaaaaabaabbababababbbbaaabbaabbbabbbbabbbbbbbbbbaaabaaabbbbbbaabbabbaabbaabbabbabbabaabbaaaaaaaaabbabbbabbaaaaaaaabbaaaabbabbbbaababbbbbbbabbaaaabaabbababaaaaaaabbabbaabbbbbbbaabaabaaabbbbbababbaaabbaabbbbbbabbaaaaaabababbaabbababbbbbbabbababaabaabbbabbabababbbbaaaaaabbbababbabbabaaabaaaaabbbaaababbabbabbbbaabaaaaabbbabbaababaabaaaabbaabaaaaababbabbabbabbaaababababaaaabababbaabbbaabbbbbbbaaaababaabaaabbbabbbabaaaaabaaabbaababaabbbaabaaaaaabababbaaabaababbbabaaabababbbaaabbbbbbaaabbbaaabaaaaababbabbabaabaabbabbabbaabaabbbaaababbaabbabbbbbabababbbbabbbaabbabaabaaabbbbbaabaaaababbbabaaaaabbabbabaabaaaaaaabaababaabbabbaaabbbbaabaaababababbbababaaaaabaababaabbabaaaaabaabaabaaabbbbaabbaabababbababbaaaaabbbbbbabbbabbbabaabaabbbaaaaaaaaaabbbabbaaababaabbbabbbababbaaabbbaabababaababaabaabbbaabbabbbbbababbaababbabaaaabbababbaaaaabaaababbbabaabbabbbbbbbbaababbababbaaabbbaabbbabbbbaaabbbaaabababbbaaaaaaabbbbaabaaaaabbbaaabbbababbbaabababaaaabaabaaabbbbaaaaaaabbbbbaaaaaaaababbaaaabbabaaabaabbaabaabababbaabaabbbaaabaaaabbabbababbbabbbaabbabbaaabaababbbabbbbabaaabbabbbabaababbabbababbabbabbbaaababbbababababababaaaaabbbabbbababbbabbbbbabaabbaaabaaababababbbbbaaaabbaabbaaabbabbabaababbabbbabababbbababbbbabaabbabbabaaabaabbbbaabbaaababbabbabbaaabbbabaabaaaabbbbbbbababababbaaaabbbbbbbaaaabbbaaabbaabaaaabbababaaababaabbbaaaabaabbbabaaaaaababbbaaababbaaababbbaabbbaaaaaaaaabbaaababbbbabbabababbbbaaaabbaaabbbababbaabaabababaabaabbaaaaabbabababaababaabaababaaaabaabaabbbaaaabbabbbbababbaaabbbbababababaabaaabaaabaaaababbabaabbbbaabbbbbaabbababbabbbaababaababbabaaabaaababbbbaabbaabababbbbbaaaabbbbbbaabbbbbbaabbaaabaababbbababbabbbbaaaabababbbbabbbabbbbbababbaaababbababaabbbbbabbbbabaabbaabababbaaaaaabaaaababaabababaabbaaabbbababababaabbaabaaaaabaabbaabbaaababaababaaabaaabbaaabbbbaaabaaaaaaabbabaabbaabbbbaababbabbbaabbabbbbbababbaaaaabbbaababbbbabababbbbbbbbaaaaaabababbbaabbaababaabbaaaaabaaaabbbabaaaaaabbaabaabbabbbbbbaaabbaabbaabaabaabbabbbbaaababbbabbbabbbbabbbbaabaaabbaabaababbbababaaaaaaabbbaabbbabbababbabbabbbaabaaaaaaaabaaabbbaabbaabaabbaaabaaaabbabababbabbababbaabbaaaabbababbaababaaaaaabbaababaabbabbaabbbbaababbabbbbaabbbaaaabbabaabaabbabbbbbaababbabbababbaaababaaabababbbaabbbababaabaabbbababbbabaababbbaabbaaababbaababaabbbabbbabbaabbaababbbaabaaaaabaabbbabaaabbbbaabbaababbaabbaaaaaabbaababaaababaabaaaaaaabbaaaababbabaaaaaaaaabbaaaabbabbbababbbbbabbbbaabababbbabaaabbaaaaababbbaabbaabbabaabbbbbaaabaabbabbaaabbabbbaabbbabaababbabaabbbabbbabbabbaabaaabbbbbbababbabaaaabbbbaababaabaabbaaaabbbaabbbaaaaabaaabaabbabaaaaabbbbaaaaaabbbbaaaabbababaabaaabbbaabbbababbbbaababbbbbbabababbaabbabbbbbbaabbaaabaabbbbbaaaaabaabababbababbbabababaababaabbabaabbbabbbaabbabbaabbaaaabababbabababbbaaabaababaabbbbbbbababbabbaababaaabababbabbaabbbbbabbbbabaaaabbaaabaaabbabbaabaaabbbbaabaabbbbbbbbaababaabaaaaaaaaaabaabababaaaaaaabaaabbaabbaaabbbbbaabbaabaaaaabaaabbbaaabbabaabbbaabbbbbbbbaabaaaaaabaaabbabbbbabaaaabbaabbbbbbbaaaaaabbaaaabaaabaaaaaaaaaababababaababaabaaaabbbaaaabbabababbabbabbaaababbbabaaaababaabaabbaaaaabbabaaababbaaababbabbaababbbbaaabbbabbbabbabbababaaabaabbabbaabbbbaaaaaabbbbbbbaaabaaaaabbbbbaaabbbbbabbbabaababbbbaabaaababbaaabbbbbbaabbabbaaabaabbbaabbbbbababababababbbaaabbabaabbbabbaabbaababbbbbbbbbbabaabbaabaabbbbbbaaaababbaabaabababbabbbbabbaabaabbababababaaaaaaaabbabababaaabaababaabbabaaaabbaababaabbabaaaaabababbaababbbabbabbaabaabaaaaaaaabaabaaabaababababbaaabbbaaababbabbaaabbbaaaaaabaabbabbbabbaaabaaaaabbaabaaaaabaabbabaababaaaaabbbabbbbbaaaabbabbabbbbbbabbbbabbbbaabababaaababbbbaabbbbaaabaaaaabaababbbaabababbbbbbaabbbbabbbbabaaaabbbababababaabbbbbabbbaaaaaababbaaaaaaaabbbbbbabbbabbbbaabaaabbbbaaaababbaabbabaaaababbababbabbabaabbabbaabbabaabbaabbbaabbbbabbbabbbbbbaabaaaabbaabaaaababaabbbbabbbbaaababaabaabbaabaaabbaaaaababbbaaabbbbbabbbbbaabababbaabbaaaaabaaaababbabbbbaabbbabbabbbaaaabaabaabababaaababaabbbbababaababbaabbaaaabaaaabbbbbbaaaaaabaabbaaabbbbbababbaababbaabaabbbabbabbabaaaaabbabbbaabbbbababaabbaaabaaaaaaaaabaaaaabaabbabaabababbabbbbbaaaaabaabbaabbbababaabbabaaaabbaaabaaaabbabbaabbbaaabbbababbaaababaaabbbbbaaaababbaaabbaaabaabbbbbabbaaabaabaababbbabbaaaaabababaabbabbabbaaababaaaabaabbabbbbbaabaaaaaabbabbbabaabaaabbaabaaabaaaaabaaaabbbbbbaabbbabbaabbbaabbaaaababbbbabababbaabaaaabbbbabbabaaaabbbaabbabaaaaaabaaabbabbbbbbaaabbaabbbabaaababbbaabaaaaaababbaaabaaaabababbabababbababbabababbbbabababaabababaaaababaaaabaabbaaaaabbbbabbbaabbbbaabbbbbaaabababbaaabbbabababaaaaabbaabababbbaabbbbaabbababaabaaabaaabbaaabbaababaaaaaaaabbaabaababbabababaaaabbbbaabbbbbaabbabbbababaaabaaaabbbaaaabbabbbbbabbabaaabaabaabbabbaaaabbbabaabbbababbbbababbabaabaababaabaabbbbbbbbabaabbbbbabbbaaaaabbbabbbbababaabbaaabaabaabababbbabababbabaaaababababbaabbaaaabbbbababbaaabaababbabaabbaabbabaabaabaaabababbbababbbbaaabaabbbabbababaabbaababaaabbabababbabaabaaaaaaababbbbbaaababaaabaaabaababaaababaaaabaaaaabababbbaaaaaaaaabbbbaabbbabaaaabbaaababbabbababaabaaababbaaababababababbabaabbaabaaaabaaaaabbbbababbbbbaaabbabbbbabababaabbbabaabaaabbbbbbaaaaaaaaababaaaabbbbbbaaabbbbabaabaabbbbabaabaabaaabbaabaabaaaababaaaabbabbabaabbbabaabbaabbbaabbbababbbbbbaababbaabbabbaaaaaaaaabbbaaabaabbbaaabbaaabaabaabaaaabbbbbbaaaaaaaaabbbaaabababbbbbbbaaaabaabbaaaaabababaababbaabbaaaabbabbbbaabababbbaaaabababbaaabbabbabbbabaaaaababaaaaababbbbbbbbbbbbbaaababbabaaaababbaaaabababbaabababbabababababaaaaabbbbbaabaabbababaabbabbaaaaababbbaabbbbaabbbbbabbaabbbaabaaabbbaaaabbbabbbbababaabbbaabbbbaabbbbabbbaabbaababbabbbabaabbbbababaaabbbababbabbbaaabaabbabbaabbbabababaaaaabaaabaababaaaababbabaaaabbbbababaabbbaabbbaabbaababbababbbbbababaababbaababbbaabaabbbbbbaaabbbbbababbaaabaaabababaaaaaaabbaaabaaabbaaaaaaabbaaabbbaababbbbabbaabbbaabbaaabaaabbbababaaaaaaabbbabbabbbbbbabbbbaaaabaaabbbabaabbbbaaabbababbbbabbaabbbbbaaababbbabbbababbbabaaaabbabbaaabaabaaabaaabaabaaaaabaaabbaaaabbabaabbbaaaabaaaabaabaabbbaabbaabaabbbaabbbabaabbbbbbabababaaaabaabababbabbbabbaabbbbababababbabbbababaabaaababaaabbbbabbabbbaabbabbaaabbaaaaababaaabaabaabbabbbbaaaaabbbbabbbbaaabbaabbaaaababaabaabbbaabaaaabaabababaaabbbbbabbbbaabaaaaababbaabbababbbabbbababbbbbbabbaaabbabaaababbbaaabaabbbbabbbaabbbbbabbabaababaaaaaabbbbaaabbbbabbabaaaabaaaaaaababaaaaaabbbaababbbabbaaaababababbbabbbbaaaaaaabaaabaaabbabbaaababaabaaabaaaaabaabbaaabaabbababbababbababbbbbbaaabababaabaabbbababababaabaaaababaabbabbaabbbabaaaaabaababbaaabbbabbbbaaaaabbaaaabbaaaaaaababaababbaabbabbbbabbabbaaabbaaabbbbbbbbbaabbbbbabaaabbbaaaaababaababaaabababbbbaababbbbbbabbbabbaaabbababbabaabaabbaaababababbbbbabbaabbaaaaabbbbabaaabababbaaabbbaababaabbbabaaaaababbaababaaabaabaaaabaaabaabbaaaaabbbbababbaaabbaabbbaaabbabaabbbbaabbbaaabaabaaaabaaabbbbaabaabbababbbbabaaabbaabbabababbbbbabbbabbabbabbbaabaabaabababbaabababbbababbbbaabbbabaaabababbababbabbbbbbbabbbaaabaaabbbbbbbbbbabbaaaaaaababaaabaaaabbbaaaabaaabbbababababbaababbaaaabbbaaabbbaaaaabbbbabaaabaaababbabaabbabaabbaaabbaabaabbbabbababbaaaabbbbabaaaabbbabbaabbbbbbabaaabbbabbaabbbbbbaaabbaaaaabaabbabbababaababbbaaaabbbaaababbbbbbaababbaaaaababbababbababbbbababbbaabaababbaabbbabababbbbbbbbababbabababaabbbbaaababbaaaabbabbaaabbbabababbabaababaabaabbbbbbaababababbabababbababaaaabbabbbabbbbaaaaaaaaaaaabbbaabbabaaabbbaaaabbbbbbaabaaaababbbbababbaaaaabbbbbbbbaaabaabbaabbaabaaaaabbbbbbbaabbaaaabbbaabbabaaabbaabbaaabbbbbaabbaabaababaaaaaabababbbaabaababaabbbbaabbbaaaaabaaabaaababbaaabbbbbaaaabbababaabbbabbaabaabbbabaabababaabaaaaababaabaabbbbabbababbaaaaabababababaaaabbbbbabbbbbababbbbaabbbbaabbbababbbbabbbbbabbaaaaaababbbbaaababbbbbbbbbaaaaaabbaabbbababbaabaabbaababaaabbabaababbaaababaababbbabbabbbabbbbbbbbaaabaabbaababbaababaaabbabbababbbabbbbaaababaababbbaaaaaaabbbabbbbabaaababbbbaabaaaaaaaaabbbbabaaabababbbbaabbbaabbabababbabaabbabbbbaaaabbaaababaaababbaaaabbaaaabbbbaaaaaaaababaabbbbabaaabbaababaaabaaaaabaaaabaabaaaabaabababaabbaabbbaaaabbabbbbababababbabbbbaabbbbbbabababaaaaabbabbbbbaabbabbabaabbbaabaababbbababbabbabaaabaabbbabbababbaaaaaaabbbbaababbbabbbaabbbaabaabbbaaababbbaabbabbaabaaaabbaaaabababbbbbbbaaabbababbabbbbbabbaaaabaaaaabbbbababbbaabaababababbbababbababaaabbbbbbbabbbbaabaabbaaaabbbbabababbbbaabbbaabbbbbabbbabbbbababaabbbbabbbababaabbabbbaaaabbaabaaaabbbaaaaaaaababaabaaaabbbbbababbbbbbaabbaababbabaaaabbabbabbabbbaabbababbbababbbbbaabbbbbababaaabbbbabaaabaaabbbabaababbaaabbbabbbbbabababbbaaaaabbbabbaabbabbbbabbbbbabbabbabababbabbbbbbbbaabbbabbabbbabbbbabbbaaaababaaaabaaabaaaaaaaaaaabaabaabaabaabbbbbabbbaabaaabbabbbaabababaaabbbabbbaaabbbbaababbbbababaabaaabaabaabbbabaabaabaabbababbbaaabaabababbbbbaababbababababbabbababaaababbaabaabbbbabbbbbaabbabababbabababbaabbaabbabbabbabbabbaababaaaaabaabaaaababbabbaaabaabbbbaababbabbaaabbbbaabbabbbbabbbaabbbaaabaaabababaabbbbbaabbabaaabaaaaababbababbaaabbbaaabbbbaababbbaabababbaabbbbaabbbabbbabbbabbbabbbabbbaaaaaaaaaaaabaabaaabaabaaaabbabbabbabababababbaabbaabbbbabaababbbbbbaaabbaababababbbbabbaaaaaaaaaabbaabbabbbbabbabbaaaabbaabbabbabbaaabababbbaababaaabbbaaaaaababbaabbbabbbaaabbaabbbbaaaaaaaaaaabaabbabbbaaaaaaabaaabbbaaabaaaaababbababbabbbababbabbabababbaaaaabbaaaabbaaabaabaabbbabbabbbbbbaabbababbbaaabbbabaaaaaaaaaabbaaabbbaaaaaaaaaaaababbbbabaaaaaabaabbaabbaababaabbaaabaaabbbbababbbabbaaaabbbbbbaaabbbabaaababaaaabaaababbaabbababbabaabbaababbbabaaabbabbbbaabaaaaabbababbaabaababaabbabaabaabbbbaabbababbabbbbaabbbaaaaaaabaabbabbbbbabbabbbbbbaabababaaaaaaabbbaaabbaabbaabaabababaabbaaabbabbbbabbaaaabaaabbbbbbaaaaaabababbbbbbabbabbaababaaaabbbababaabbabaabaababaabaaabaabbbabbbbbaabbbaaaaaababbbbaabaaababaabbbaabaaaabbabbaabbabbbaabbbbaabaaaabaabbababaabaaaababbaabaabababbaaaabaaabbaaababbbbbbbbbaabaabbaabaaaabababaaaaaaaabaabaabbbaabaabaabaabaaaabababaababbabbaaababbbbbbbabbabbaaaaabbababbbbbbbababaabbbaaabaaabbbaaaabaabaaaabbabbaaaaabababbaabbabbbabaababbbbbbbaaabbbabaabbabbbbaaaaabaabaabababaaaaaabaaaabaaaaaaabaabbaabaaaaaaabaaaaababaabbbabbabbbababababbbbbabbbbaabaaabbbabaaababbbaaaaabbaaaaaaabbbaababababbbbaabbababaaababababaabbaaabbbbaaababbbbbbaaaaaabaaaaabbbaabaababbbaaabaaaaababbaaaaababbabaaababbaabbbbbaabbbbbbbbaababbabbaabbbbbabaabaaababbabaaaaaababbabaaabbbbbbbabbabaaaaaaaaababaababaabbababaababababbababaaabababbbbaaabbbaaaababbbaaabaabbabbbbabababbaabbbbbaaaababaababbbababbaaaababababaababaaababbabbabbaaaabbaaaabaaaaababbbabbbabaabababababababbababbbabaaabbbabbbbabbabbaaaaababaababbbbbaabbaaababbabababbaabbaaaaaaababbaabbbbbabbabaaabaabbbbabbaaabbbbbaaabaaaabaaabaaabbbaababaababbbabbbbbbbbbbbaaabababbbbbabbbbabbbbbaaabbabbbabbbbababbbbbabaabbaabbbaaababaaabbaaabbaaaabaabbabaaabbbabaabbababaabbbabbbbabbbaababaaababbaaabaabaabbbaabaabaabbbaabbabaaaaabaabbabaaabaaabbababaababbbaaaaababbabbbaaabaabaaaabbaababaaaabbbabbbbbabababbaabbbaaababaababbabbabbabaaaaabbbabbbabbbbbbbaabbbbbbaabbabbbaabbabbabaaabaabbababbbaaaababaabababbbabaabababbbaababababbaaabbbbaababbbaaaaabbbaababbabbbbbaabbbabbababbbbababaabbabababbaaaabbaaaaabbbaaaabbababaaaababbbbbbbbaaaaabaababbaabbbabbababbabbbaaaababbbabbbbbabbaabbbababbbabbbabaabbabbbaaaabaabaaababbaaabbbabaabababbabbaabaaabbabbaabaaaaabaababaababbababbbaabbabbbbbabbaaabaabbaabbbabbbaaaabaabaaaaaaabababbbabbbbaaabbbabbabababbaaaaaabaaaaaabaaabbababababbaaabbabbabbabaaabaaaabbbbabbabbaabaababbbbbaaababbaabbbababaaaaaaabbbbaabaabbabbbbabbabababaabbbaaababbbbaaababbbabbbabaaaababbabbbbbaaabbbabbaaabbbbbababaaaaaabaaababbaaaaababbbabbabbaabbaaababbabbbabbbabaabbbabbbbabbaaaaaabaaaaaabaabbbbaabaaabbababbabbbbabbaabaaabbaababbabaaabaaaaababbbbbbbababbbbabaaabbababaaababbabbbababaabaabaaaaabaabbabbbbabaabbbaabaaaaaaabbabbaababaabaababaaababbababbaaabbbbababbbaabbababaabbaaaabbaabaabbbbabbbbaaababbbaaaaaaabbaaabbbaabbabbbbaabbaaaabbabaaaabababbaabbaaaababbaabbabbaaaaaaaabaabaababbaaaabbaaaaabbabaaaaaaabaaaaaaababbbbabbaabaabbababbaaaaabaabbaabaaabbbbbabbababbbbbbbbbbabaabbbbbbbabaababbaaaabbabbaabaaabababbaabbaabbbabbaaaaabaabaababbbaaabbbbbaabaabbaaaaaaababbabababaaabbaabaaabaabbbabaababaaaabbabbbbbbbbaabbbabbbbabbbabbbbbaaaaaaababbbbaaabaaabaaabaaaaabaaaaabbbabbbabbaabbabbaabbaaabbbbaaabbbbbababaababbabbbbbaaababaaabbbaaabbbabababaaaababaaabaaabbabbbabaabbbbbbaabaabbbbaaabbbbbabaababbbaabaaabaabababbbaaaaaaaaaabbabbbbbabbbbaaaabbabbabbbabbaabbbbbbabbabbbabaaaabbaababbbabaabababbabbbbaabbabbaabbabbbbabbbabbabaaababbaaabaabbbbaaaaaabaabaababaabbbbabbbababbbbbbbbbbaababbbabaaaabbbabbaabbabaababbbbbaabbbbbbaaabbbaaaaaaababbabaababaabbaabbbaaaabbabaabbaaabaaaaabbaabaaaaaaabaaaabbabbbabaaabbbbaabbaaabaabbabbaaabbaaaaaaabbaaaaabbbbbabbbababbaabbbbabbbbbbbaabaabbabbbaaabbaabbabbbbbaaaaaabbabababaababaaaaaabbaabbbaabaabbbabbabaaabbbaaaaabbbbaabaabbaaabababbaabaabaabaabbbbbabaaaabbabaaaaaaabbabaabbabbbabbbababbbaabbaaaaababaabaabaabababbbbaababbaababaabbbbbbaaabbabbbabbaaaabbababaaabbbbaaabbaababaaabaabbbbabbbbbababababbababbaaabbbbbabaabababaabaaaaabbbaaabaabbbbbbaabbbaabbaaaaabbaabaaabbabaabbbbabbabbaaabaaabaaabaabbbababbbbabbbabbbabbbbaababbaaaaaabbbbbaabaaaaaaabbbbaaaabaaababbaabbbbaaaabaabaaabaaabbbababababbababababaabbbbaabbabbaaababaaabbbbbbbbaababbabbaabbaaaababaaabaabbabbaaaabbababbbbaaaabbbaaaaababababababaaaaaaababbbaabbbabbbaabbbbbbababbabbbabaaabbabababbbababbaabbbaaabbbaaaaabbbbabbbbabbababbaaabbabbbbaabaaabababbbbabbaaababbaabaaaaabababbbaabbabbbabbbabaaaabaaaaaaaaaaabababbbaaaababbabaaabababbbbbbaabbaaaabbabababaababbabbbbbbaaabbabaaabaaabbbabbaaabaaaabaabbbbaaabaababbabbaabbbbabbababbaaaabbbaababbbbbbbabbbabbaabbabbbabbababaabbbbabbbabababbaaaaabababbbbaaaaaababbaaabbbabbabbbbabbabaaabababaaabbabbbbaababbbabbabbbbbbaaabaaabaababbbababaaabbabbabbbaabbbbabbbbabbbaaabaaabaabaaababbabbbaaababbbbabaabbaaaabaaaababbbaabbbaabababababbaaabaaababaaabbabaaaaaaabbbabbbbabbbaaabababbbabaaabbbabbababaabbaaaaabaaabaaaaaaabbbbaabbabaaababaabaaababbbbbbbbbababbbbabbbbaabbbbbbbaababaaabbbaaabbababaaabbbaabbabbbabbbaabbabbbaaababbbabaababbabaabbabababababbabbbabbbbbababababaabbabbaababbaabbaabbbbabbaabbaabbaababbabbbbbaaaabbbbabbbaaaaabaaabaabaaababbababbbbbbabaaaaaabbbbaaaabbaabbaaaaaababbabaababbababbaabbabbbbbbbbbbaabababbabbbbbbbaabbaabaaaaaaaababbbaabbaabaabaabaabbbbabaabbbaabaaabbbabbbbaaabaaaaabbbbababbbaabbaaaaaababbaaaaaabbbabbaaaabbbbbbabbabbaabbabbaaabbaaaabaaaaaabbbabababababbbabbbaaaaaababbabbbbabaabbabbbaababbabaabaabaaaaababbababaaaababaabbbababbbabaababbbaaababbbbbabababaaaaababaabbaabbabbababbbabbbaabbbbbaaaabaaabababbbbbbaaabbbabaabbbaaaabaabbabbbaabababbbbaabbbabbababbbaabbaabbabbabaabaaaababbaabbaabaaabababbaaabbbabaaaaaabbbaaababababbbabbbababaaaaabaaaababbbbaaaaababbbbaaabbbbbaabbaaabbbbbababbababaabaabbbbaaababaaaabaaabbbbaaaabbaaabbababaaaabbaaaaabbaaaabaaaababaabaabbaabbbbababbbaaaabbabaaaaaabbababaabbbabbaabbbbbaaabaabbbabbabababbbbbaaaaaaaaabbabbbbbabbbabaabaaabbbaaabbabbbababbbbbbabaaabaabbabbbbbbbbbbbbbbaaabaabbbbbabbabaaaabaaabbaaaabbaaaaabbbbaababbbaaaaabbaaaaabababbabbbaabbaabaababbbbbabbbabbbbababbaaaababbbbbbbbbbbabbbbabaaabaabaaaaabababbbaaabbabaaaaaabbaabbbbbbbabbbaababaabbbaaaaabbbbbbaabaababbaaabbaaabaababbaaababaabbababbbabaabaaabaaababbbbabaaabbbaababaaaaaabbaabbababaabbabbababbaaabaaaabbabbabaaabbabbaabaaababbbbbbabbbbbababbabaaaabbabbabbabaaabababbaabaaaababbbaababaabbabbbbabbabbbbaaaababaabababaaaabbbbabbbabaaaaaaaabbaababaabababaabbbbaaaaaabbbbaabbababbbbbbaaaabbbabaaaabbbbbbbababaababbbbbabaaaaaaaabbabaaabbaabbbaaabbabbabaaaabbbabbabbabbbabbbabbabbbaaabbaababaaabaababaaabababbaabbbaabaaaabbabbaaaaaababbbbaabbaaaabbbbaabbbbbbbbbbabbabaaaabaaaaabbbababbaabaaaababbbbaaaabbbbaaaabbbaabbaaabbbbbbbabaaabaaaaabbbbbabbbbbbbbaabbbabbbabbbbbabbbabbababaaaaabbabbaaaaaaaaabaaaaaaaabababbaababaabbbabbababbbaabababaabbbaababababaabbabbaabbbabababbbabbaaabbbbbbbbbbbabbabbaaaabaaabbbabaaabaababaabbabbabbbabaaaabaaaaababaaabbbbaabbaababababbbbbaaababbbabbbbaabaaaaaaaaabbaaaabaaabaabbbabbbbaabaaaaabbaaababaabababbbbbababbababaababbabbaaabbbbababbaaabbbbbababbbbaabbaabbbaabaababaabbbbabaabaaaabbaaaaaaababaabaaabbaaaaabbbabbaaaaabbaabaaaabaaaaabbaababbaaaaaaaaabbbbababaaaabaaabbbbbaaabbbbaabbbbaabbbbbbbbbbbbabaabbababbbbbbaabababbababbaaaaaaaabaaaaaababbbababaaabbbabbbaabaaaabbbbabaabbaaabbabaaabbbababbabbbababbaaabbabaaaaabbbaaaabaabbbbbbbaabaaaabababaaaaaababaaabbbaaabbbabbaaaaaabababbaaabaabababaabbbbbbbabbaabbabbbababbbaaabbbbbbbbbbbabaaaaabbaaaabbabbbabbbabbbbbbbaaabbbbbbbbbababbabaabbaaabaaabaaababbaaabbbbababaabaabbababaaabbbabaabbaabbabaabaaaaababaaaabbbaabbbabbbabababbabbaababbabbbababbbbababbaababaaabbaaaabaabbbaaaaaaaabaaababbbbbabababbbbabaababbbaaaabbaabaabbbbabaaabbaabbabbbbbbbbbbbbababaabaaabbbabbabbaabababbbbbababbbbbbabaaaabbababbbabbbaaababababbbbaababaabbaabaababbbbbbbbababbaabaaaaababbbbbbaabaaaaabbbbababbabaaabaabbaabbbbbbbbbababbbbaaabaababbbabbbabbbababaaabbbaabbababaabababbbbbbababbaabaaababbbaabbaaaaabbaabbbaabaabaaabbbbbabaabbbabbabbbbabbababbababaaaababaabaabaababbaababbbabbbabaaaabaaabaabababbbabbbaaababbbbababbbabababbaaaaaabbaabaaabaaaabbabbbaabbaaabbabaaabababbbbaaaabbaaaabbbbbbaabaabbbbaabaabbbaaabaabbbaaabbaaabbababaaaaabbaabbbbbaabbabaaaababababaababababbbabaababbabaabbbabbaaababaaabaabaaababababbaaaabbbabaabbaabbaaabbbbbbbbbababbabaaaabaabbaaaaaaaababbabbaabaaaabbbbabbbbbbbaaaaaaaaabaaabbabaaaaaaaaaaaabaabaabababbbaabbaabababababbbbbbbbabbbaaababbbaabababaabbabaaababaaabaaabbbbbaaabbaabaabbaabbbbabbaaaaabababbbbbbabaabaaaaabbbbbbbabbbabbaabbaaabbbbbaaaaaabbabbbaabaabaabababababbbabbaabaabbbaababbbbbbbbabbbabbaaaaabaabbbaaabbaabbaabababaabaabbaababaabaaaaababbbbaababbbabbabaaababbaabaabbbbaabbbbbaababbbbbbaabaabbaaaabbaabbbaabbbbbaaabbbaaabaaababbaabaabbaabbabbabababbbbbbbbaabaababaaabbabbbaaaabaaabbaaababbababaaaabaabbaabbabbbbabbbbbbaabbababaaabbabbbbaaabbbbababbbabaababbaabbaaaabaabaaaaabaaabbaabaaaaaaaaabaaabaabbbbbbababbabaabbbaaabbbbaabaaababbbaaabbabbbaaaabaaaaaabaaaabbaaabbabaabbbababaababbaabbbbbabbaaabbbbbbbbabbaaaabbaaaabbbabaabbabbabbbbbbaabbbbbbbababaabbbbbbabbbaabbbbbbababaabababbbabbbabbaabbbaabaababaaabbbabbaabbabbabbabbbbaaaaabbbaaabbbaaabbabbabbbabbbaabaaababaaabbaabbaaaabababababbbbaababaabbaabbaaaaabbaaaabaababaababbabaaabbabbabbaaabbabbaaaababaaabbbbaabaaababbaaabaabbbabaaaabababbbabbabbababaabbbabbbabababbaaaaaabababbbbbaabbaabababababbaabbabbbababbbbababaaabaabbbaaabbaabbabbaaabbbbabbbbbabbaaaabbaaabaaaaaaabbaababbbababaaaaabaababaababbaabbbababaaabaabaaabbaababbbbbbaabaabbbbabbbbbbbbbbbababbbbbbbababbbbaabaaabbaaaabbbbbaaaaaaababbabbbabbbbaabaaaabaaababababbbaaaaabbbbbaaabbbaabbbbabaababaabbaaabababaaaabbabbbbbbaabaabababaabbbababaaabaabbaaaabaabaabbbaabbbaabaaabbaaaabbabbbbbbbaabbbaabaaababaaaaabbaabbaaabababbaaaaabbaaabaabbaaaaababaaabbbaaabbabaaaaabbaabbbbbbaaababaaabaabaaaabbabbaabaaaabbbbbabbbabbabaabbbbabaaabbaababbbbabbbbaababbbaaaabbaaababaabbbaababababbbabbbabbabaaaaaaabbaababaaaabbbbabaababbbabaaaaabbabbaaaaaabbbaaabaabbbabbaabaabbabaaabbbbbbababbbbaababaababbabaaaabababbaaabababbbbbaabbaababaaaaaababbbabababbabbbbaaabaaaaabbabbbbbabbabbaababbabbbbbbbbabbbaabbbbbaabbbbbabbabbbbabaaabaabbaaaabbbabbbbabbbabbbbbbbababbaabbbaaaaaaaabbbbbbaaabababababbabbaabaababbababbabbaabaabbbaabaabbababbbbbaaabaabbabbabbabbbaaabaaaaaabaaabaaaaabaaabaabbbaabbbababbbabaababbabaaababbbaabbaaabbbaaabbaababbbaababbbabbbaaababbabbbbbbbbbabbaaaababaaababbbbbbaaabbbaaaabaaaababbbbbbabaabbbaabaabbbbaabbaabbbbaaaababaaaaaaababbababbbabababaaaaaabbabaabaabbabbbabbbaababbbbaabbbbbaaabbbbbabaabbbbabbabaabaaaabbbaabbbabbbbabbbabbabbbababbbabbbbbbabaaababbabaababaabbbaaabbabbbbbabbabaaabaaabaabaabbbabbbababbbbaaaabaaabaabaaaaabbabaababbbbbbbaabbbaaabaabbababaaabbbabbbbbbbaaaaaaaabbababbbbbbbabaabababbababaaaabbabaaabbababbabbaabababbabaaaaabaabbababbaabbbbbbabbbaabbbbbaaabbbabaabaaabbbabaaaaaabbbabbaabbaaabaabbaabbaabbaaabaabbbaaaaabbabababbaabbabaabbbabbbbbababbaaaabbbbaaabaaaaaabbbabaaaaaaababbbbababbbababaabbabaaabaaabbbaaabbbaaabaaabaabaaaabbaaabbaaabbbabbbbbaaababbaabababaaababaabaabbaaabaaaaaabbaababbaaabbababbababaaabbbbbaabbbbbaabaaaababbaabaabaaabbaaaaabbbaabaaabbaabbaaaaababbbbaaabbbbabaaaababbaaaabbabaabaaabbbabaabaaaababaabbabbabaaabaabbabbaaaaabaaaababbbabbbbaabbbabbbbbaaabaabbbbabaaaaaabbaaaaabbabbbaabaaabbbbabbabaaabbbbabaaaaabbabbbbbbbbbbabbabbaaaabbbbbbabaababaaaabbbabbbbaabababababbaabbbaababbababbaababbbbaaaabbbbaaabbbbbbbbaababbabaababbaaaaabbabbababbbaabbaabbaaaababbbaaaabababaaaabbbbbbaaaababbbabaabbaaaabaaabababbbbababbbabababbabbabbabaaabbbbababaaabbbaaabbbaaabbbaaabbaabbbbaaabbaaaababbbaabbbaaaabbbabababbbababaaabbaaaabbaabbbbbabbabbababaabbabbbbababbaabababbaaabaabbbbaaaaabbbabaaaaababababaabbabbaababbbbbaaaabbabaaabaaaabbaabbaaaabbaaabababbaaaaaaabaabbbababbbababbababaaaabaabaaabbbabaaaaaababbabaaaaabaaabaaabbbabbaaaaabbbaabbbaaabbaaaaababaabaabbaaabaaabaaabaabbbbaaaaaababbaaaaabbabababbbababbbaaabbabbababbbabaabaabbaaaaaabaaaabaababbabbbabaababbababaabbabbbaabbabbaabbbbaabbbbabaababbaabbabbbbbbbbbabbbaaaaababbaabbaaababbbbabbbabbbaabbbbbbabbbabbaabaabbababaabaaabbbaaaaaabababaaaabaaabaaaaabbbaaaaaaaaaabbababbaaabababaaabaabbaabababbaaabbabbbabbababbbbbbbababaababbaaabbbbabbaaababaaaabbaabaaaabbabbaaaabaaabbaabbaabaabbabbbbaabbabbbaabbaaaabbbbaaaabbbaabbabbaabbbabbbabbbbaaabbaaababbbabbabbaabaabbaabbbababaaaababbbaabaabaabbaabbbaaababbbababbaabababbbaabbababbaabbbbababbbabbbbbbbbaaaababaabbabaaababbbaabababaabbbbbbaaaaabaaaaaabaaaabbbbbbbbababbaabbabbaababaaabaaaaaabaaabbaaaabaabbbaaabaaabababbbbbbbbaabaaabaabbbbabbaababbabbabbbbbabaabbbaaaaababbbabababbaaaababaaabaabbaabbbaababaabbbabbbababababbaaabbbabaaaabbbbbaaaaabbaaaaaababbbabbababaaabbabbababaaababbaaaabbbaaabbaabababbabbbbababaaabbabaaabbbaaaaaabbbbbbbaababbababbaabaaaabaaabababaababbbaabaababbbaaabbbaaabbbababaabbbaaabbbbbaababbabbbaaabbbabaaaababbbbbbbabbabbaaaabbababbabbbabbabbababbababbbabaaaaabaabbbbbabbbbbbbabbbbbbaaaabbbabbbbbbabaabbaabbabbbaaaaaabaabaaabaababbbbbabbbaabaababaaaaaaabbbabaabbbbabaabbbabbbababbaaabbbbababaabbabababbabbaaababbbabbbbabbbaaaabbbaabbbbabbbaaabbbabababbbaaababbbbbaaabbbbabbbbbabaabbabaababbabaabbbbaabbbbbbabaaabbbbabbaabaabbabbbaaaabbbabbabbaaabbbbbbabaaaaaabbbbbbbabbaaaaaabbbbbbbaaababbbaaaabaabaaabbaaabbaaaaaaaaababbabbbbbbbbaaabbababaabababaabababaabbabbaabaaaabbaabbaaaaabbbbbbabababbbbbbbaaaabbabbabaaabbaaaaabaababbaaabbbbaaaabbbbbbabaaaababababbbaaaaaababbabbabbabaababaaabbbbbabbaabbbbababbaaabaabaaababaaabbababbabaaaaaaaabbbaaabbbbbaabbbabbaaababbababbabbabbbaabbbbbbabaabababaaaaaabbababababbbbbabaaabaaabbbaabbaababbaaabaabaabbbabbbbbabbaababbabbbabbbabaaabbbabaabbbbbbabaaaaaabbbbbbbbabbbabbbbaabababbaaaaaaaabaaababaaaaabaaaababbbbbbbbbbbabaabbabbbbbabaaaabbaaaaabbbbaaabaaabbabbbbbbabbabbbaaabbaabbbababaaaaaaaaaaaaaabababbbabaaaaabbabbaaaabbbbaabababbabaabbbbbaabbbbbaaabbbbbbbaababaabbbabaaabaababbbababbaaaabbbbabbabaabaabbaaabbababababbbabbaaaaaabbbbabbbaabbabbbabbbbbbbabbbaaaaabbaaaabbbbabbbbabbbabaaabaabbbaababbaabbaaaaaaababbbaaabbabbaaaaaaaaaabbbabbaaaaaababbabaabaaaaabbbbbbbababaaabbbbbbbbbbaaabbabbbbbbaaaaaabaaabbaaaabbabbbaabaabbaabbaaaabbbbaabbbaabbaaaabbababbaabaaaaabaabaaaaaaaaaaabbabaaaaabbbabbbbababababbababaaaaaaabaabbabbbbababaaaaaaaaabbbbbbbaaaabbbaaabbabaaaabbbbbbabaaabbaabbaaaabaababbbbbbbaabaaabbbbaaabbbaabababbbaababbbabaabaaaabaaabbaaabbbbbaaabbbbabaaabbabababababbababbabaabbaaaabaaaaaabbbaababaaaaaabbaabababbbbabbbbbbbbaaaabbbaaabaaabbaaabbaabaaaabbbbabaababbbbabababbbbaaaaabbabaabaaaabaababaaabbabbabbbbaabababaabababbbbbbaabaabbababbabaaabbaaabaabababababaabaaaabababbbbbbbbabbaaaaabbbabaabbbbbaaabababbaabababbaaaaabbaaaaaaaabaaaabbbaabbbabaaaaababbabaaabbabbbbabababbbbababbabbabaaabbbaabaaababaabbbbbbbbabbabaabaaaabaabaaabbaabbabaaaabbbababaabaaabbbbabbbabbbaabbaabaababaabaabaaaabbbaabbbaaaaaabbabbbbbbbbbbabaababbbabababbbbabbbbbabbabbabbbbabaababababbbbbabaabbabbababbaabbbbaaaaabbbabbbbabbbabaabaaaababbbabaaaaabbbabbbbbabababbabaaabbaaabaabbaaaababaabbaaaaaabbbaaabbbbaaabbaaaababaaaaababbbabbaabbbabbaaaabbaabbbbbbbabbababbabaaababaababbabaabbababbaabbabbbbaaababbbbaabaabbbabbababaababaababbaaaabaabaabbbabbbabbababaaabbbabbbabaabbaaabbaabbababaaabaabaaabbababbbababbbababbaabbbbaaabbbaaaababbaaabbababaaaaabbbabaabaaabaaaabbaaababbbbababbbbaaabbbabbaaaabababaabaaaaaabaabbaaababaaabbababaaaaababbaaabaabbbbbbbaaaabbaabbbbbbbbbbaaabaaaaaabbabbaaabaabbaaaaaaabaaaabaaabbabababbaabaaaabaabbbabbbaaabaababbbabaabbbabbbabbaabbbabaaabbabaaabbbaababbabaabbaaaaaababbaaabbbbbababaaaababbbbbaababaaabbbbbbbaaaaabbabbbabaabbbaaababbabbbbbbbaaaabbabbaabaaaabbabbaabbbbbabbabaabaabaaabbaaaaabbabbaaabbaaaabbabababaabbbbababbabababaaabaabbaabaaaabababbbbaaababbbbabbbbabbbbabaaaabababbbbbaabbbaaaabaaabbbbaabaababaaaaabaaaabbbaabaabbbabbbbbaaaaabaabbbabaaaaaabaabababbbabbaaaaaaaaababbaabaaaababaaabaaaaabbbaaaababbbbaaaaabababbbbbabbababaaabbaaaabbababaaaabbaababaaaabaababaababaaababbabaababbaababaaaabaaabaaaaabbabbabbbbaaaabbaababbbbaabbabaaaaaaababbbabbaaaabbaaaaabaabbababbabaaaaabaabbbabaaabbababaabbabbaabaaaaaabbaaababbaabababaaaaaabaaaaaaabbabbabbbabaabaaaabbbbaabbabbaabbaaabbbbbbbbabaabbababbabbaababaaaaabbaaabaabaabaaaabbaabbbbbbabaabbabbbbbabbaabbbbbbabbbbbaaabbabaabbbbaababbbbaabbbaaabababbbaaaabaaabbbbabbbbbabbaabbaabbabbbbbaabbaabbabbbaaabbabbaabbbbbbbababbbbaabaaaaaabbbbbaaaabaabaabbbabaabaababaababaaabaabbabbbbaaabbabbabbbaababbbbbbbbbaabbbabbbaaabbbbaabbabbbbabbbbabbbabbabaaabbbaaaabbabbaabbabababbaaabbbaabaabbbabaaabaabbbbbbabaabbbbbabaaabbbbababbbbababbbbbbbbaabbaabbbbaababaabbaaababaababaaaaaabbbabbbbbababbbaabbbaaabbbbbababbbabaabaabbaaaaaababbaabbaaaaaaaabbabababaabaaabbbabbaabababaaabaaaabaabbaabababbaabbabaaaaaabaaabaaaaabbaabaaaaaaababbabbabbaababaabbbaaabbbabbbbbbabaaabbbaaaabbaabaabaabbaaabababbbaaaabbbaaaabbbaaabaaabaaabababbaababbbabaaaaabbaabbaaabaaaaaababbaababababbaaaababaaaabababaababaabbaaaaaaaabbbabbbbbbbbbabaaaabbaabbaabaaababbbbabbabbbababbabaaabbaabbabaaababbbbaaabbbaabbaabbaababbbbabbabaaabababbabbbbbbbaabaabbbaaaaabaaaabbbbbaaabbbbbaaababbbbbababbbabaababaaaabbabbabbbabbaabbabbbbabaaaaabbbbbabbbabbbbabbabbbaaabbaaabbaabbbabaaaababaabaabbbaabbaaabbbbabababbaabaaabaabababbbababababbbaaababbbbbbaabaaabbaabbbbaababaaababaaabbbbbaaabababbaaaabababbbbabbbbababbaaabbbbbbbbbbbabbabbabaabaabbbbababbbbbabbbbaaaababaabbabbababbaaaaaabbbaabaabbabbaabaaabbbbbbaaaaaaabbababbaaabbababbbbababbbbbbbbbabaabaababbbaabbaaaaabaabbaabbbabaabbbbbbababbbbbabaabaabaaabbbabbaaaabaababbbbaaaabaabbaababbabbbbbabaaababaaaaaabaaaaaababbbabbbabaabbbbbabbbbbbbbaaaaaabbabbbbbaaabaabababababbbbbaaaababbbaaababaaaaaababaabbbbabababbababaabaaababababbbbaaaabbaaaaabaababaaabaabbaaababbbaababbbbbaaabbaabaaaaaabbabaaabbbaabbbaabaaaaabaabbaabbabaaabbbbbbbbbbaaaaabaaabaabbaabbbbbaababbabbbaaabbbaaabaababbbabbbababbbababbbaabbbababbaabbbbabbbbbaabbaabababbbbbbabaabbabbaabaabababbaababbabbabbbaaababbbabbabaaaabbababaabbbbbabaaabbbaaaabaaabbabbabbbabbabbbababbbaaabbbbabbabaaaabbabbaabbaaaabaabbbaaaaabaaababbabbbbabbbaaabababaabbbbabbbaabaaaaaaaaabbaabaababbabaaabaaabbbaabababbababbbbababbbaabaaabbbaaabbbaabaababbbbaaabbabaaabaaababbbabaabbabaabaabaaaaaabbababbbaabbbbaababbbbbabbbababababbbbabbbabbabaaaabbaababbaababbaabbbabbababbaaabaaaabbaaaaabbbbbbbbbaaababbbbbbaaababababbaaababbbaaaaabbbbbbbabbbaabbbaabbabbbbbbbbaaaaabaabaaabbbabababaaababbbbaaabaabbabaaabaabbbaaabbaabaaaaabbaaabbabbababaabbbaaabaabbbaabbbaaabaababaaaaabbbbbbbabbabaaababbaabbaaaaabaaaabaaabbbbabbbabaaabbbbabbabbabaaabbbabaababbbabbaabbababaabaaaabbaabbabaabaabbaaabaaaaabbbbabaaaababbbbbabbbbbbaaaaabbaababaaabbbabbababababbbabbababbaabaabaaababaaaaababbbabaabaaabaabbbbabaabbbbbbabbbbabbaaabbbabaabababaabaabbaabbbabbaaabaababbbaabbbabbbbabbbbaaababbaabbbbbbabbbbbaabbabbabaabbbbabbbabbaaabaabbbaaaaaaaabbbbbbbaaaaaaaaabbbbbbaabbaabbabaaaabbbbabbabbaaaaaaabbbbaaaaaaaaaaaaabaaabbbaabbbaabaabaabbaaaababbbaaaabaabbbabaabababbbaabbbbabbbaabbaabbabbbabaaaabaababbbaabaaababababbbabbbbbaaabaabaaaabbbbbbaabbaaababaaaaaabbabaaababaabbaababaabbbaaabaabbbabaaabbbbbbabaabaabbababaaabbbbababaaabbbbabbabaabababbbabbbaaabababbbaaabbaaabbabbbbaabbbbaabaaaaaabaabaabaabbabaabbbbabbbababbbbbbbabaaabaaabbbaabbabaaaabbaabaaaaabaabbbababbbabbbabaaabbabaabaababbbbbaaabbbabbabbaaabbbabaabbbabababbaaabaaaababaaababbbaabbaabbabbabaabbbabbbbabbbbbaaabaaabbaabbaaaaabbaaabaabbaaabaabaaaabbbbbbaabbaaaaabbbbaaaababbabababbaaabaaaabbaababaabaababbbaababbbbaabaaaabababaaaaaabbabbaabbabaaababbaaabababaabaabbabaabaaaabbabaabbabbbbbbbabababbbbabbbbbbaababbabbabbabbbbbaabbabababaaabbbaabbbaabbaabbabbbbabaabbbbbababbbababaabbbaabbaaabaaababbaaabaaabaabaaaabaaaabbbbabbaaaaaabbbabbbaabbabbabaaabaabaabbbbbaabbbbabbaaabbabbaababababbaabbabaabaabaabaaabbbabababbbaababbaabbbbbbaabbbbabababaabaaaabaaabbaabbabbaabbaaaabbaabaaababaabaaabaabbbabababbbbaababaabbabbbabaabaaaabababbabaabaabaabaaaaabaababbaaaaaaabbbbbbbbaabbababaabbaabbabbabaabbbabbbbbaabaaabbabaabababaabababbbabababbbaaabaabaaaabbabaababaaabbabbabbbbaabaabbbbabbaabaaabbaabaaaabaaababaaabbaabbbabbbbbabaaababbbbbaaabababbaaaaabbaabbbaababaaabbbbbaabbbaabaabababaaabababaaabbaaabbbbbbbaababaaaaaaababbaaabbaaaaababbbaaaaababbbbabaabbbbaaaabbbbbbbbbababbaaaabaaabaabbbbbaaaababababbbbaaaabaabaaaabbbabbbbabbaabbbbabbbaaabaabbaaaababbbabbbbbaaaaabbabababaabaabababbbabbbbbbabaaaabaabbbaabbabaabbbbbbababaaabbbbbabbbbaabaaababbabaaabbabbababbbbbababbbabbaaaaaaababbabaabbbabbbababbaaabbbbabaaabaaaaabbbaabaabbbbaaaaaabaaabbbbbbababbaabbbaaabbabaaabababbbbbbbbabaaaaaaabaabbabaaaaabbbabbbbbabbbbbabaabaababbaabaaabaabaabbbbabbbbaaabbababaabababbaaababaabbbbbbbabaabaaabaaaabbaaababaababbbaabaaabaaaabbbaaaababbabbaaaaabaabaabaaaaabbaaabbbbaabbbabaaaaabbbabaaaabbabaababbaaaaaabaaaaabbbbaababaabbbabbaaabaaaaaabaaaaaabbaabaabbaabaaababaababababbbbbaabbbaabaabaaaabbabbbaaabbabbabbbabbbbbaabaaaaaabaabbaabbbbabbabababbaabbbabbabaaaababbbbababbbbabbbbaabbbbbabbabbaababaabbbabbabbaabbbaaabbbaaabaababbbabaababbbbaabbaaabbaaaabaabbaaabababbbbaaaabbbababaaaaababbaaaabbaaabaabaabbaaaaaabbbabbaabbbbaabbabbbbbbbbaaabababbbbaabaabababbabaaaabaabababbbaabbbabbbababbaabbababaabbaaabbbaabbabbaabaabbbbabbaaabaabaaabaaababbabaababaabbaaabbabbaaabaaabbabbaaabbbabbaababbaabababaabaabbaabbbabaaaabbaabbbabaababaaabaabaaabbabbabaaababaaababbbaaabaaabbabbbabaabbabaabaaabbaaababbaabbbabbbbbababbaabbababbbabbbbababbbbbabbaababaaababbaaaababbbababaabbabaaaabbabbabababbbaaabaaababaaabbababbbbaabaabaaabbaaaabbabbbbbabababababbaabbaabaaaababaabaabaaaabaaabaaabbabbbbabaabaabbabaabbbabbbaabbbaaaaabbabbbbabbbaababaaaaababbaaabaabaababaaaabbbbbbaaabbbbaaabaababaabbaababbbbabbbbbabaaabbbbbabbbaabababbaabaabaaaababbaabbaabbbbbababbbbabaaabababbaaaaabbbaaabbaabbbbabaaabaabbbbababbabaabaaaabbbaaaaababaaabbabbaabbbaabaabbabbababaabaaabbbbbaabaabbbaabbabbababaabbbbbbbaababbabaaaababbaabbaabbabbaaabbaaaabbaabaabaabbaabbbaabbabbabbbaaaababbababbaaabbbbaaaabbabababaabababbaababaaaabbabbaabababbaabbaabaabbbaaabaabaababababbaaaaababaabaaaaaababbaaabbbabbabbaababaaaaaaaaaaaaaaabaaabaabbbbaabbbbaabaaababaabbbbaaababbbabaaaaabbbaaababaabbbbaaaabaabaababbaaababaabababababbaaababbaaabbbbababaaabbbaabaababbbbbbbabaaabaababaabababaababbbaaaabbaabaabaabaabbabaabbbabbbbaabbaababbaabaabbbaabbbbabbbabaabbbbaabbaaababbbaabaabbababbabbbbbabaabbbababbbabbababaaababbaabaabababbbbbabbbbabbabaabaaabababaabbaababababbbbaaabababaaaabbabbbabaaabaabbbbbaaaabaabaabaaaaaaaabaabbbaabaabaaaaababbabbababaabbbabaaabaabbaaabbaaabbbbbbaabaabbababbbbaabbbaaabbbbaaabbaabaaababbbaaabaabaababaaabbabbbbbaaabaabaabbbbabbbabbabbaabbbaabaabaaaababbbaabbbaaaababbbbbbaaabaababbabbabbbabaaabbabaabbaaababbaabaabbbabbaabaaaaabaababbbbaababaabaaaabbaaaaabababbbbbbbbabaaaaababaaaaabbabbaaaabaaaaaaabbbbbbababaaaaababbabbbaabbabaabbbababbabbbbababbbabaababbaabaabaabbbaabaaabaaaaabbaababaababbabbbbaabaabbababbbbabbbaabbbbaaabaaabaabbaaaabbbbabaabaaaaabbbbaaaabababbbaabaaaabbaabbabbabbbabaaaabbaababbaabaabbababbaabbbabaaaabbbbbaaaabbbbaababaabbabbbbabaabbaaaabaaabaabaabaabbabbbabbababbbbbaaaaabaaaabaaabbbababbaabababaababaaabbaaaabbaababaabaabababaaabaabbabbababaaababaabaaaaabbaaaaabbaababbabbabbabbababaaababaabbababbbbbabaababbabababaaabbbabaaabaabbababbaabbabbabbaaaabbbbabbaabbbbabaaabbabbbaabaaaabbbabaaaabbabababaabaabbbbaaaabbbbbbaaaaaaabbbaababaaaaababbbbbabbbababaaabbaaabbabaabbbaaabaababbaaabbbabaaaabbabaabbaaaaaaabbababbaababbabbaabbbbbbaabaababbbbaaaabababbbaaabbbaabaaabbbbaaaabbbbabbabbaaaabaababaabbaaaabaabaabababbaabbbbaaaabbaabaabaabbabaabbbabbaabbbababaabaaabbbbabaabbababaaaabbabaababbbaaaaabbababbbaaaaaaaabbabbaaabaaabbaabbabbbabaabbaababaabaabaabbbbbbabaaabbbbaaabbabbaabaaaabaaaaababbaaabaababbaabbbbabbbaabbabbbbbaaaaabbaababaaababaabaabbaabbbbbabaaabaabbbababbabaaabbbbbababbbbaababbabbaaaaaaababbaababbbaaabbaaababbbbbbbababbaaababbbabbbabbabaabbbbaabbabbababbbbbabbbbaababbbbbbabbaabaaabaaababbabaabbabbbaaaabbbbbbbabbabbbbbbbababbbbbbabbbbbbabbaabaaabbaaabaabbbbaabbbabbbaababaaaabbabaabbbabbaabbaaabaababbbbbaaaaaabaababaaaabaabbbbbababbabbabbababababbbbaabaabbbaabbabbbbaabaaababbbaaaabbbbbbabbbbaabbbbabaaaabbaabbababaaaaaababbaababaabbaaaabbbbabbbbbbbbbabbbaabaabbaaabbabbbbbabbbaaaabbababbbbbaabbbbbaaabbbbaababbbaabbbabbbabbbbaabaabbbabbbbaaabaaaaabaabbbaaababaaaaabbbabaaababaabbbbabaabaaabbbaabaababbaaaabbaaabbbbbbbabbbbabbabbabbabbbbbbaabbabaabababbabaabbbabaaaabaaaaaababbbaabbbaababbbaaaaabbbbbbabababababbbababaababaababaaaaabaaaabaaabbababaababaaaaaabaabbaabbabbababbaaaabbbaaabaaaaabbabaaabaabaaababaaabaaaaaabaaabbbababaababbbaaaababaabbbbabaaaabbbbbabbbbbbbbaaaaaaabbabbababbaabaaabaabbbbbbbbaababaaaababbbbbbbabababbbabbbabbabbbabbaaabbbabaaaaaaaabaaaabaaababbbbabbaaabbabaabbaabababaabbbbbabaaabaabbaaaabbbaaababbbaabbbbbaaaabaabbbaabbabaabaaaabaabbbabbbbaabbabbbaabaaabaababaaabbbbaabbababbbbabbaabbbabbbbbaaabbbbaaabaabbbbabbbbababbbaaabaaabaaabaababbabbbabaabbbabaabaabbbaaaaabbaaababaabbabaaabaababababbbabbaaaaaaaabbbbabaabbaabbbbbbabbaaaabbbaaababaabaaaaaaaabbbaaaabbaaaaabaabaabbabbabaabbaaabbabaaabbbabbababbaaaaabbaaabaaababbbababbaaaaababaaaaaabababbaabaaabbbaaabbbbbbababaabbababbaaaaaaaaaaabbbabaaaaabaabaabbbbbabaaabbbababbbbababbbbbabaaababbaabbbaaaabbabbbbbaaaaababaaabbaababbabbaaaababbabaabbbbbabbbabaababbaababbaabaabbbaaabababbbbaabbbbbaababbaaaaaabaaabaabaaaaaaabbbaaababbbbbababababaabbabaaaaaabbbaaaabbbbaaaabaabbabbabbbaaababbbbbbbbababbbabbababaaabbaabaabbbabbaaabaaaabbaabbbaabbaababaaabbbabaabaabaabaabbaabaabbbbabbaaababbabaaaaaababbabbbbabababaabababbbabbbbaabababababaabbababaabbababbabbbababaaabaaabaabbaabbabbbbbaaabaabaaaababbbbbaabababbabbbabbbabaaabbbaababaaabbabbaababaaabaaaaaaaabbabbbababbbabbabaabaaabbaababababbbbaabaaabbbaabbbaabbbbbbbababaababbbabaaaabababaabbbababbaababbbbbbabaababababbbbaabbbbabbbbabaababbbbbaabbbaabaababbababbbbbaabbababaaabaababbaaaabaaabaababbaabaabbbbbaabbbaaaabbbababbabbababaaababababbaabababbabbbabbbaabbbbaaabbabaabaaaabbbabbabbaaaababbbabaaaaabbaabbbbbabaabbbbaabbaaaaabbbabbaabbbaababbbaaaaaababbaaaabaabbabbabbabaababbbbaaaaabbabaaabbaabbbbabbbabbabbaaaabbbbaaababaababbbbaaabababababababaabbbaabbbabbbbbabbabaabbaaaababababaabbabbaaabaabbbabaababbabbababaaaaabaabbbababababbaabbabababaabaabbabaabaaaaabaabbbaabbbabaaaaaaabababaabbbaaaaaaabbaaaabbbbaaabbbbbaabbaaabaaaabaaababbabbaaaabbaabaabbaaabaabbbbaaabbabbbbabaabaabbaabbababababaabaabbbabababbbaaababbbbbabaabbabbbaabbababbaabaaabbabaaaababbbabaabbbaaabbbbbaaababbbbaaabbbbbbbabaaabbababbaabbbbbbaabbbbbbbaabbaababbbabaabaaaaaaaabaabbabbbbaabaabbabababababababbbaaabaabaababbbababbaaaaababbbbbbaabbbbbbbaabbabbbbbabbaabbaabaabaabbaabbabbbababbbbbabbbbaaaaabbbababaaaababaaaabbabbabaaaababbabbbbabbabbaabbbbbbbabbabbabbabaaaaababaabaaabaaababaaaabbbbabbbabaaaababbbaabbaababababaaabaabbaabaababbaaabaabbbbababbbaaaaaababababbbaaabaabbabaaaabbaabbbbaabaababaabaaaabbbbaabaaabbabbabaaabaabaababbbbbabaaababbbbbaabbabbbababbabbbabbaabababaababbababbaaabbaaabbbbbaaababbbbbbbbbbbaababababbbabbbbbaaaaaaabababbbbabbbbaaaaaaaaabbaaaaaabaaabbbbbbbabaabababaabbabbbbabbabbabbbabbbbabaabbaaaaabbaabbbaaaabbbbabaaaaabbbbabaabbbbaaababbbbaababaaaaabbaabababbaababbbbaaababbababbbbaabaaaabbbbabbbbbbbbbbbbabbbabaabbbbbbabbaaababaabbbaababbabbabbbababbbbbabbbaaaaabbbaaaaaaabbbbbbbbababaaaabaabbabbaabbbbbabaababababbbaababbbbbabbbabababaaaaaaaabbbababbaabbabbbabbbaaabababbbbabbbbaaaaaaabbbbabbabbaabbabbabbabbbabbbaaaababbabaaaababbbabaababaaaaaaabaaabbabaababbaaaaaabaabaabbbabbbbbabbabaababbbbbaaaabbaaabbaabbaaabbaabbabaaaaabbbbbbbabbbabbababaaaaababababababababababababbbabbabaaaaabbbaaaaabaaaaaabaaaababbaaabbaaabbabababbbaaaaaaaaaaabbaabaabbbababbabbaababbbbbbabaaaaabbabbaaabbabbbbbbaabaaaaaaabaaababbaabaababbaabbabababaabbabbaaabbabaaabbabaabbababaaababbaabaaabaaaaaaabbbabbaaaaabbaabbabbbaaaaabbbbbaabbbbaabbbaabbabaabbaababbbaabaabbbababaaababbaabaaaabbabbbbababbbabbbaabbaabaabbaabbbbbbbaaabbbbaabbaaaaaaabaabbbbbbabaabbbbaabaaaabaaaababaababbbbabaaabbaabbbaabbaabaabbaabbaaabbbbaaababaabababbbbbababaababbaaaabbabbabababbbbbaabbaababbbbbabbababbababaaabaaaaaabbbbbababaabbaabbabbabaabaabaabbaaabaababbaababbbbbaaaabbabbabbbabbabbbbbabbbabaabbbaaabbabaaaaaababaababaaaaaaaaaaababbbbbaaabababbbbaaababbabbaaabbabbaababaaabaaabaaabbaabbaaabaabbbaaaabaaaabbaaababaabaabbabbabbababbabbbababbaaaabaababbaaaabbbabbababababaaaaabbaabaaabaaaaabaabaaaabbbbaaaaaabbaaabaabbbababbbaaababbbbaababaabaaabbbbaababbbbababbbbabaaabbaaaaaabbbbbaabbbababbbaabababbbabaabaabbaabbaabaaaabbaabbbababbabaabbabababbbaaaaabaabbbbaabababbaabbbaabababababababbaabaabbabbaaaaabbbabaaabaaabababaaababaaaaabaabaabbbbbbbbbbbbaaabaaababbabbbbaabbaababbabbbaaaabbaabbababbbbaabaababaabaaaaaabaaaababaabbababbbbbbbaaabababaaababaabbbbabbbbabaaaabbabaababbbbbbbababbbaabaabaaaabbbbbabbbabbabbaaabbbbbbaabbbbababaabbbbbababbaaaaaababababbabaabbbabaaaabbababaabbbababbbbbaaababaaaaabaababbbabaabaabbbbaabbbaabaabbabbaaaabbaaaabaaaaabaabaaaabaababbabaaabbaaababaaaababaabaabbbaaaabaaaababaababaababbabaabaaababbbaaaabaaabbaabaaaabbabaaaaaabbbbbabbbbabababaaaabbbaaaababbbbbaaaaaabbbbbbababaaaaaaababbaabbaababaabbbaabaaaaabbababbbbbbbbaaabbaabaaabbababbbababbbbbbaabbaaabbabbababbbbbbabbabaabbbabbabaaaabbabbaabaababbbaabbbabbbbaaaababaaababbbbaababababaababbabbabbbaaaaabbbaaababbaaaaaabbbbabbbbaaabbabbaaabaaaabbabbabbbbbabbabbababaaaaabaaaabbabaabbaabbababbbaabaabbaaabbbaababbbbbabbbabbbaaaaabbbbaabbbabbbabaabaabbaaabbbbaabababaaabaaabababaababaabababbbaaabbbbbbaaabaaaababbaababbbbbabbaabbbbaaababaaaaabaaabbababbaabbaaabaaaabbaababbabbbbbbbbabaaaababbaaaaabaaaabbbbbabaaaaaaaababaaabbaabaaabaabbabbbabaabaabaaaaabababaaabaabbbbababbbabbabbbaaabaaaaabbabbababbababaaaaaababaaaabbbaabbabaaababaaabaaabababbaaaaaabbabbababaabbaaababbbbababbaabbbbbbababaabbaaabbbaaabbbbbbabbbbabaaabbaaaaabbabbbabbabbabbbbbaaaaaabbaaaaababbbbbabaabbaabbaabbababbbbaabaaabbaababbbaabbbabaaabbbabaabaaaabaabbabbaababbaababbbaababbaaabaaaaababaaabaabbbbbbaabbababbbaaabbaaabbbaaabaaaabaabaaabbabbaabaaabaabaaabbaababbbababbabbbbbbbbbbbbbbaabaababbbbbbabaaababbaabbbabaabaaabaaaaababbbbaabaaaabbaababbbbbaababbbbbaabbbbbbbaaabaaaabaaababbaabbabbabbbababaaabaabaabbabaababbaabbababaaababbbbaaabbbbaabababbbbababababbbbabbbbbbaaaabbbababaaaabaaabbbabbbabababbbabaabaabaabaabbbbbbaabaababbaababbbabaabbabaabbbaaaabbaabaababbbaaaaaabbabbababbaaabbaabbabaababbaabbbaababaabbbbbabbbbbbaabbabbbbbbababbaaabbbaabbababbbbbababaaaabbbbbabbbabbabaaaabbaaababbbabaabbbbaaabaababbbbbabababbaaabaabaabaaaaabaaabababaabbbaaabaaabaabaabbbaaaaaaabbaaaaabbaaaaaabaaabaaaaabababbbaabbabbbbaaaabababaabbabbabaaabbbbaabbbbbabaababbaaabaaaabbbabbaababbaaababaaabbaabaaaaaaaaabbbbbaabaaabababaabaabbbaaabbabaaabbbbaaabaaabbbabaabaababaababaaaaababbabaaabbabbaabbababbbabbbababbabbaabbabbbababbbabbaaaababbbbbabbbabaabbbabaababbabbbabbaababbbabbababbabbbbbbaababaabbabababbbbabbbbbabbaababbabbbbbabbbaaabbbaaabbbaabbbababbaabaabababbaaabbaababbaabbbbaabbbbbaabbbabbbabbaaababbbabbaabababbbbaabbbbbbababbabbaababaabbbaaababaaabbbbaaaaaabaabbbabaabbaabbaaabbbababaabaaaababbabbbabbaaabbbbabaaaababbaabbbbabbaaabababbbbbbaaaababbababaabaabaaaaaababaaaabaaabbbbbabaaabaaabbbbbbbbbbababbbbabaaaaabaaabababbbbbabbbabababaababbaaaabbabbbaaabababbbbbbaabbaabababbbbbababbbabbaabbbbaabbbababbbabbbabaabbbaaabbbbabbbaaaaabbbbbbbabbbbbbbaabbaababbbabbaababbbaaabababaabbaaabaababbaaaabbaababbbaabbbbabbbbbbbaabbbabaaabbbabbbaaabaaabbaabababbbabbbbbbabbabbbabbbbbbabbabaabaaababbaabaaaaababaabbaabbaaaaaabababbbbabaaaabbbbabbabbbabaaaaaaaababaabbbabaaaaabaaabbabbbbbbbabbababbbbabaaababbabaaaabbaaaabbbaaaaabababbababaaababbbbabbbbaabbbbbbababbaabbaabaabababbabaaabaaaabbbaabbbaabbaaaaaaababbaaaabbbbbbbbbabababbaaabbbabaabbbaaabbbbbbbbbbabaaaabababbbbbbbaababaababaaabbaabbaaaabababbabaaabaaaaaaabbabbbaaaababaaabaaabbbaaaabbbababbaaabbaabbbaabbabbbbbbbbaabbaababbababaaaabbaaabababbabbbabaaaabbaabbaaaabaaaabbbabababbababababbabaabbabbaaabbaaaababbbbbabababaababbbaaaaaabaabbbabbabaabaabbabaababaabbaababbaaaaaabbbabbbbbbaaaababbbabbaaaabababbbbaabbbbabbbbaaaaaaabaababaaabababaabbaaaaabbaaaabaabbbbababababbaaababbababaabbababbabbbbaaaaabaabbaabababbabbbbbababaabbbbababaaaabbababaaaabaabbbbaabbbabbaaababbbbbaabaaaabaabbbbbabbbbbbaaaaabaaaababbbbbabbabbbaaabbbbabaaababaaaaabbbabbaaaaaaabbbbabaabaaaabbbbbaaabbaabaaabbbaabaaabbabbaabbaaababbabbbabbbbbbbbabaabbbaabbaabaaaaaaababaaaaaaabbbaaabababbaabbabbbabbbabbabbabaaaaabbaabaababaaaababbbaaaaabbabbababbaaaaabbaabbbabbbbabaabbbaaaabaaabaaaaaaaababbbbababbbbbababbbabbaaaaaaabababaabaaaabbabbbbabbbbababbaaaabbbaaaabaaaaaaabbaaababbbbbbaaabaabbababababaababbabaaaabababbabaaaabbaaabaaaabbbbbbbbaabbabaaaabbbababbbabbaaaabaaabbbaaaabbbbbbbabaaababbaabbaabbaaaababaabbbabbbbabaababbbbaaabbaabaabbbaabbbbbababbabbabaabbabaababbbaaaabababbaaababbaabaabbabababbbabbbbabbaaabbbbaabbbbaabbaabaaabbababbbbabbabbbbabaabbaaaaabbbaaabbbbbababaababbbaaabbaaabaabbbbbbaaababaaabaaaababaaaaaaaabaaabbaaababaaaabababaababbaabbbbbaaababababbaaaabaaabbbbbaaabbbabbaaaababaaabbaabababbabbabbbaaabaaabaabaababbabbbaaabaaaabababaabbaaabbbababaabbababbabbbbbbbbabaaaabbaaaabbabbbbabaaabababaabaaababaabbbbbaaabbaaaababbbbabbabbbabaabbbbbabaabbbbbabababbbaaabaaabbbabababbabbababababbbbabbbaabbaaaaabbbbababbabababbababbbaabaaababbbbaaabbbbbabaaabbaabaaababaababbbbbabaabbbbabaabbbbaabaaabaaaaabaabaabababaabbbabbbaaabbbabbbabaaaabbaabbbaabbbaabbaaaabaabbbaabaaabbababbbaaabbbabbbaabbabbbaaaaaaaababaabbbbbabababbbaaabbbaababaabbbbaabbaaaababaaabaabababbaaaabbabbaabaabaaabababbabbbabbaaabbbbabbaabbbaaabbbabaabaabbbabaabbbbbbbababaabbbaabbabbbbababbaaabbaababbabaaaabbabaaaaaabbbabbababaabaababbaaabbbbabbbbaabbbbabbababaabaaaabbaabaabaabaaabaabababaaabaabbaaaabbaaabaaabaaaaabbbbababaaabbbbbbbbaabbaaaababbaababbbaabaaaaababbbabbbbbaaabaaabaabbbaaaaaaababbabaaaabbabbabbaaaababababbababbbbababbaaaabbaababbbbbabbaabaaaabaaababbbbaabababbbaabbaabaaababbbbabbbbbabababaabababaababababbbbaabaaaababaabbbaaabbbbbabababbbabbbbaaaaababbbbbabbbaaabbbbaaaabbbaaabababbbbababbababbbaaabaaaabbbaaabaaaaaabbaabbbaabababaaaaaabbbabbabbbababaaaababbaabbbaabababaaaaaabbbaaabbabbaaabaababbbaababaaababbbbaaabaaaabbbabbbbaaabbbaababbbbababbaaabaabbaaaabaaaabbabbaabbbbaabbbaaaaabbababbbbaaababaaabbbaaabaaabaabaaaabbaababbaaabbabbaababaabbbbaababbabaaaababababbbabaaaaaaababbabbbbbbbbaaaaaaababaaabbbbababbbaaabaaabbbbbabaabababaabaaaabababaaabaabbaaabbaababbbaaaabaabbbbbbbaabbbbababbaaabbabbbbbaaaabbbbbabaaabbbabbabaababaaabaaabababbababbabbbbaaaabaabbaabaaaababbabaabaaaaabbabbaaaaabaaaababababbbbaaababbabaaabbababbbaaabbaabaaabaaaaababbbbaaabbbaaaabaaabbabbaabaaaaaaabbbbabaabbabbaabbbbbbbbabbbababaaabaabaabaabbaabaaabaabaaaababbababbbbababbabbbbababbabbbbabaabbbbaaabaabaaabbabaaabbaaabaabbaabbaaabbabaaaabaabbabbaabbbabababaabbbabaaaaabbabaabaaabababbababbbaababaaababbabababbbaabbbaaabababbabbbbbbbbaaababaaabbaaabbaaababbbbaaabaabaaaabbbaaabbbaabbbaabbbababababbabbbbaabbaabbabaaaabaaaabbbabababbabbababbaaaababaabbbbaaaabaabbaabaabbbababaabbbbbbbabbabbbaaaaabaabaaababaabaaabbbbbbbbabbabaabaabbbaaabbbbbbabbbbababababaaabbbbaaababaaaaabbbbbaaaaababaaabbabbbabaababbbababbaabbbaaabababaaaabaaabbabaabaaaabbababbbaababbabbbbbbbabbbbbbaabaababbbaaaabaaaaabbababbbaabbaaaabbaabbbbaaaabbbbaaabbaabaaaabbabbabaabaaaaabaaabbbbaaababaabaaabbabaabbaaababaaaabababbbaabbbaababbababbbbaababbaabbabbbaaababbabbabbbaabaaaaaabaaaaaabbbbbbbabbabbbabbbbabbbbbbbaaabaababbaaaaabbbaaabababaababaaaabbbbaabbbaaaaaabaabaababaababaababababbbbaabaaababbaaabbbbbabababaaaabaabbbbaaaaabaaabaababaababbbabbabbabbabaabbaaaabbbbbbaabbbbabbaabaaabbabaaaababaaaaaaababaaaabbaababbabababbbaaaabbbbabaabbabaaababbbbbbbbaaabbababaababbbbbaabaaababaaabbabbbbbbbbabbaaabababbbaabbbbbbaababaababbaaabbababbbabbbbaaababaabbbabbaabbaaabaaabbabaababaabbabaaaaabaaaaaaaaaaaabbbabbaababbbaaabaabbbabaabaabababbbabbabbbbaababaabbbaaabbabbbbbabbababaabbbbbaaaaabaaaababaaabbbabbbbbbaababaabbbabaabaabaababaaabbaabbaaaabaabbbbbaabbabbabaabbbaabbbbbaaaabbababbbbbbbbbabbaaabbbbbbbbaaaaabaabbbbbbabbaaaaabbaaaabaabaababbbaaababababbbaaaaaabbbaababbaabbbababbbbbbbbababbababbaabbabababaababababaaaaabababbbaababaaabbabaaabbbbaaabaabbaabaabbabaaaaaababbaaabaababaabbbbbaaabbbabbaabaaaabbbbabaaababaabaabbbabaaabaaaabbaaababbbbaabaabababbbabaaabbbbbbbbabbabaaaabababababbbabaabaaaabbbbbaaaabaabbbababbbbaaaaabbbbbaabbababaabaaabaababaabbbaaaaaababbaaaaaabababbbaababbbabbbbbaababbaaaabbababbbabbbbbbabbbbbaabaaaaaababbbaabbaababbbaabbbaabaababbaabbabbabbbbabbabbbaaaaaabbbbaabbbbbbbbaabaaabbaaabbbbaaaabaabbbaabbabaaaabbbaabbaaaabaaabbbababaabaaaabaaaabbbbbbbbabaabbbabbbaabaababbababaaaabbbaaabbaabaabbabbabaababbbbababbaabbaabbababaabbaabbbaabbaaabbbaababbbbaaaabaabaabaabbbaaabbbbbbbbbabbbaabbbbbababaaaaabbbabbaabbabaaaabbbbbbbbbbbabaabbbabbbbbbbabbaaabaabbabbbbbbababbaabababbbababbabababaaabaabbbbaaabaaaaabbaaababbbbbbabbbbababbbbabbbabbabaababaaabbbbbabbabbaabbbbbbaabbaabababbbbaababbaaaaabbaababbbaabbbaababbbbbababaaabbaababbbaaabaaabbbabbbababaaabbbabbbbbaabbbbbaaabbaaaaaaaabaaababbaaabbaabbbbabbbbbbbbbabbbbabbbabbabbbbbbbababababbbabbabbbbaabbbbbbbbbbaaabbbaabaabaabbbbabaaaabaabbababbbbbbabaabbaaaababbabaaaababbbaaaaaabbbababaabbbababbaaaababaaabbbbaaabbabbabbbabaaaababbaabaabbbbbaaaabbbabbabaaaabbabbbabaabbaaabbabababbbaaabbbbababababbaaabbbaaabababbbbbbaaaaaabbbbababbaaaabaabbbaabbabbbaabaabbbaaaaaabbababababbbbaabaaabbbbbabaaaababbbbbababbaaabbbbabbaabbaabbbaabbaaabbabbbaaabaabaabaaabbabbbbabaabaabaaabbbabbbaabaabbaaaabbabaabbbbbbabbbabbbbbbabbabbabbbbbaaaaaabbbaaaaabbabbbbbabbbabbabbaabaaaaaaaabbabaabbbbbaabbbabbbbaaabaabaaabbababbaaaaaaaaaabaaaabbaabbabababaaabbabababbbababbbabababbbaabbaaaabbbbbbbabbaababbbbaaabbababbaabbbbaabbaabaaabbababbabaaaaabaaabaaabaaaabbbbaabbbabbaababbbbaaabbaabbbaaaaaaaaaababababaaaaabbbbbbaabaabbabaaaaabaaababaaabababbabbaaabaaabababababbbabbbabababaabaababbbbaaababbaabbbbbbbabbbaaabbabaabbbababaabbaaaaababaaabbbababaaabbbaaabaabbbabaabaabbaababbaabaabaababaaabbbaaabbbbbbabbabbabbbbbabbaaabaaabababaabbaabbbbaabaaabbbbaabababaaababbbabbabbbaaababbbaabbbbbabaabaaaababbaaabbaaaabbaaabbbbaaaababbaabababaaabaabbbbabababbbaababaabbaabaabbaabbaaaaabbabaabbbabbbbaababaaaababbabbababababbbaaababaabbbababbaabbabaababbbababbbabbaababbbaaababaaaabbaaabaabababbbabababaaabababababaabaaabaabbbabaaabbbbabbbabaababaaabaabaaaaabbbbbabaabababaabaabbabbbbbaaabababbaabababababaaabbbabbbababbbbababababaaababababbababbbabbabaaabaabaabaaaaaabaaabaaabbbbbbbbbababbbabbabbaaabaabaaaabbaababbbabbaaabaaabbbbbabaaaaabababaababaaaaabaababababaabbbabaaabbbabaaabaabababbaabbaaababbbbbabababaaabaaabbbaaabaaaaaabbabbbaabbababaabbbabbababbbabbaabbbababaaaabaaababbabbabaabbbaaabaaabbaaaabaaaabaabababaabaaabbbbabaaabaababbbaaababbbabaaabbbaabbbaaaabaabbababaaababbbbbaaabababaabababbababbbbbbbaabbabbbaaaaaaaaabbbbaababbababbaaababaabbaabaaaabbabaaabbbbbbabbaaaaabababaababaaaababbbbbabbabbaaaabaababbbabbaaaabaaabaaaababbaaaabaaaababaaaaaabababaabbbabbabbabbbbbaabbabbbbaaabbaaaabaaabaabbaaaaaabbbbbbbabbaaabaaaaabaaaababbbbaaaaaaabbbaabaaaaabaabbabbbbbaabbbbbbbbbabaabbaabaaaabbababbaaabbbbababbaabaaabbbbababaabaaabbaaabaaaaaabbbabaabbbababbbbaabbabaaaabbabbabaabbbbbaabbbaabbbaabaabbbaaaababaaaababbaaababaabbbbbabbaababaababaabbaaabbbabaabbbabbbbabaabbbbabbbaabbbbbaababbbbabaaaabbaaabababbbbabaabbabaabbabbbaaaababaabbabaaabaabbabbaabbaaaaabbaababbabbbabababbbbabbbbbababaaababbbabbababaaaaaabbaaababaabaabbbbababbaaabbaaabbbbbbabaabaababbaaaabaaabbabbabbaabbbbabababbabbababbaabbbaabbaaaabaaaabbbaabbbbabbaaabbbbabaabaababaaabbbbbabaabababbbbbaabaabaaababbbbaabaabaaaaabbbaaaababaabbaabbabaabaaaabbbaaabbabbbababbbaabbaabbabbbaababbabbabaaababbbabbabbabbabaaaabbbbbbaaabababaabbbbababbaababbbbabbbbbbbaaabbabaabbbbbaaabbbbbabbaaabbbbaaaabaabaaaaaabbabbbbbbbbaaabbbbaaaaaaabaabbbbbaababaaaabaaaaabaaabbaabaaababbabbaababbaabbabbbbbbabaabbbbbabbabaabaaaaabbbaabaabababbabaaabbbbbbababaabbbbaaaaaabbaabababaabbabbaabbaaabbbaaabaaaaabbabaababbbabaaaababbbbaaabaababbbabbabababbbaabbaabbaaaaaaababbbababbabaabbabaaabbbabbbbbbbaaababaaabbbbbaaabbbbabaabaabababbbaababaaaaabaaababaaabaaabaabaabbbaaaabbabbaaabbbabbbaabaababbbaaababbbbbabbabbbbbabbabbbbabbbaaaabbaabaaabbabbabbaaabaabbbbaaaaabbabbbbabaaaaabaaababaabaaabbbababbaaabbbabbababaaabaabbaabbbaabbaaabbbbababbaaaabbbabbaaababaababaaababaaabbaabbabababaaabaaaaabbbaabaaababaabbababbaaabbababaaaabaaababababbaaababaabaaabaabaaaaabbaabbabbbbbbbaaaaaaaabbaaabbabbbabaabaaababbbabbabaaaaaaabababaabbbabaababbbbaaabbbbabaaabaaaaaaaaabababbaaaabbbbbbbabbbabbababbbabbbbbbababbbbaabaabbbabababaabbbaabbbbbabbbababaabaabbaaabbabbbaababbbbaaabbaaaaabbbaaaaabababbbabbabbbabbaababbbbababbbabbbaabbabbabaabaabbababbbbabbaaababbaabbbbababababaabbbbaabababababbaabbbabbbaabbabababaabababbbabbbbabbbbabbbaabbbabbababbabababbabbbabbbbaabaaabbbbbaaaaabbaabababbababbaababbaaabbabbaabaaaaabbaaababaaabbababaaaaaabaabaaabaabbbbaabbbbabbabbbbbaaaabbbbbbaaaaaaabababbbbbabbbabbbabbbbabbbbbbaabaabbaababbbbaabaabababbaabaaabbbaabaaabbbaaabbaababbaaabbabaabababbaaaaabbbbbbabbaabaabbbbabbabbaabbababaabababbaabbaaabaabbbaaaaababbbbaabbbbbbaabababbbaababbbabbbbbbbbbbbbbaaabaabbaaaabbbbaabbbabbaaaabbabaabbbbaabbaabaabbbbbaaabbabababbbbbbaaaaabaabbbbaabbbaaabaababbbaaaabbbbaabaaabbaabbaabbaaaaaabbbaababbabbbbbababbababaaaaababbaabbaaaaaaaaabbbaabaabbabbbbbbababaaabbbbabbabbabbabaaaaaaabbabbaabbaaabaaabaaaabababbbaabbabbabaaababbbbaabaaabbaaabbbaababbabaabbbbbaabbbbbabbbaaababaaababaaababbabaaabbbaaabbaaababbbababbaaabababbaaaaaaabbaaaabbaaababaabbababbaababbbaabaabbbabbabbbbbabbbabbbaaabaaaaabbbababababbbbbabaaabaababaababaaaaabbabbbbaabbaabbaaaabbaaaabaaabbaaaabbbaaaabbababaabbbbbbbbbbabbabbbababaaabaaaabbaaaabbbaabbbbabbbbabbbaababbbaaababaabaaaaaabaabbbaabbabaababbbbbabaaabbbaaaaabaaaabaaaaaaaaaaabbaabaabaaabababbbbaaaaaaaabbbaaabbababbaabababaabababaaaabababbabbbaaaaaaabbaabbabaabbbbbaababaaaabbaabbbabbbaaababbabbabbaaaaaaabaabaaabbbbbaaababbbaaabbbabaabbbabaaabbbaaabbbabbbaabbaaaaaabaaabbaababbababaabbaaabaababbabbabbaabaaaabbaaaaaaabaabbbababbbbbbaabbbabaaabbbabbbabababbbbbaaabbbbbabbaabaaabbbbabbbababbbbabbbaaabbbaaaaabaabbbaaabbaaabbbabbbaabbabaaabbabbabaaabbbaabaababbbbbbbabbbbbaabbaabaaabbaabaaabababbbbaabbbbabaabaaaaabbbbbaababbbbabbaabaabbabbbbabbabbbabababaaaaaababababbbbabbabbbababbbbaaabbaababaababbbaaaabaabbaabbbbaaabbaaabaabbabbbaababbbabbaabbabbbbabaaaabbaababbbbbababbabbaabbaabaaaaaaaababbbabaaaabaaaabaabaabbabababbbbbbaaabbabbbbbaaaabaaaaaaabababbabbbaaaabbbaabbbbbababbbaaaaabbaababaabaaaaaaaababbbbbaabaabaabbabbabaabbaaaabaaabbbaaababaabbaaabbaabbaaaaababbaababababaababaaababbaaaaaaaaababbbbbbaabaabaabbaabaababbbbabbaabaaaaaaaabaabaabbababaaabaaaaabaaabbbbababababaabbbbbbaabbbaaaaaabababbbaabbbaabaabaabababbababaaabbabaaabaaabbaababbabbbbbbabbababaabbbabababbaaabbababbaabbbbababbbbaaababaabaaaabbbbbababbaaabababbbbbbbabbbbbbabaabaaaababbbaaabaaaabaabbaabaaaabaaabababaaabbaaaabbbabaaaaababbabbabbaababaabbbbaababaaaaaaaabaaaabbbbbbbabbbbabbbbabaaaaababababaabbbababbbbaaaabbbaabbaaabbabbaababbbbbabaabbbbbaabbbbbbaaabaabbabbaabaaabaababaaabbbbbabbaaabbbbbabaaaabbbbababaaaaabaabaaabbabaaabaaababbbbbabaabbbabaaababbaaaaabbbabaaaababbbababaaabbbbabaabbabaabaaabbaabaabbbabbbababbbabbbbabbbbbaaaabbbbbabbaaaaabbaaababaaabbbababbbaababababababaaababaaababaaaabaaaaaababbbabbabaabbbbababbbbbabaababaabbbabbabaaababbbaabbbbaaabbbaabaaaaaabaababbabaababaabaaabbaaababaaabababaaababbbbabaaabbbabaabababbbbbaabbbaaabaaabbbabbbbbbbbbabbababababbabbbabbabaabbbbabababbbbbabbbaaabaabbbbbaaabbabaaaaabbbbaaababaaabbaaaaaaabbbaaaaaabaaababababbbaaababbabbaabbaaaabaabaabaabbbbababaaaaabbaabbaaabbbaaaaababaabbaaababbabbbbbaabbbbaaabbbbbaaaabaabaaaabbabbaaaaaababbbaabbbbbaaaabbabbabbaababbbababaaaabaaabaaaaaaababababaaaaababbabbaaaabbbbaaabababaaaababbabbabbaababababbbabbbababaabababbbbabaababbbbaabababbabbabbbbababbabbbaaaaaaaaaaaabaabaabbbbababbbbbaabbabbabaaabababaaaabaaabbbbabbabbbbabbabaababbaaaaabbabbbbbbbbaaabaabaabaabbaababbaabaaabbaabbaaaabaaaabbbaabbbabbaabbbbbabbabbababaaaabbabaabbbabaaabbababbbaababaaaabbaabaaababbbabbabaabbbbaaaabaabababaababbbbbaabaabababbbaabbaaabaabbbaaaabbaaaaaababbbbbbbaaabbabbbaaabbbaaababaaaaaaaabbababbabababababbbbaabbbabaabbaaaababbbabbaabaabaaabbbbbababbbbaaaabbbbbbbababbbababbabababaaababaaabbbbbabbbabaaababaaaaabbbaaabbbabbbabbbbbabbbbbbbaabbaabaaababaabbbbbababababbbaabaaabbabbbbabaaabbbbaabaaaaaaabbbaababaababbbbbbbbbbbbbaaaaabaaaaaabbbbbaaabbababbbbaabaaabaabbbbbbbaaaaaabbbbabbabaabbaababaababbbbbababaaababaabbbbabaabbbaabaabbabababaaabbbaabbabaaaaabaabbbaabbbaaababababbabababbaaabbabaaaaababbaabbaaababbbaaaabbaabaabbbbbabbbaaabbbababbabaabababbaaabaabbbbbbabaabbaabbbbbbaaaababbaaaaabababbbbbaaabbbaabbaababbabaaaaaabbbbabbaaabbaababaabaaabbbbbaabbbababbbbaabbabbbaaabbababbbaabbaaaaabbaaabbbabbbbbbbaabbbbbaaaababbabbaaaaaabaabababbbabaaabbaaabaaababbaaaababaaaaaabbabbababbaaaababababbabbbbabaabaaabbaabaabaaaabaaaaababbbbbbaabbaababaaabababbbbbaababbbabbaaaababbababababbbaabbbbbabbabaaaaababaabbabababbbbbaabbabaababbababaaabaabbababbbaaababbbaabbabaaabaabbabbbaaaabaabbaabbbabababbabaabaabbbbaababaaaabbaababaaabbababbbaaaabababbababbabbaababbababaabaaaabbbaabaaababbbbabbbbbabbaaaaaabababbabbbaabbbaaaaababbaaababbaaababbbabbaabbbaabaabbbabbbbbaabbabbbaabababababbbababbbbababbaabbbbbbbbbabbbbabaaabbbbbbababbbabbbbbabbaaabbaaaabbaaabbaabbbbaaabbbaabbbaaaaaabababbbbabbababbbaaaaaabbaabaabaabaaabbabbbbbbbaabbbbbbbaaababbbabaaaabbabbbaabbbaababaabaabbbaababaababbbaaaabbaaaabbabbbabbbbbabaabbbbbbababbaabbaaaabaabbbbbbaabbbaababbabbaaabaabbaaabbaaaaabaaabbaaaabbbbbabbababbabbbbababababbaabaaabaaabbabbbbabaabbabbababbabababaabbbaabbabbbaaabaaabbbaaaaababababbabaabaabbbbabaabbaabbbaabaaaaaaababaabaaabaabbabaaabbabbbaabaaaabbaabbaabbbbaaabbaababbbbababaabbbbbbbaaababbababbbbbbaaabaabbbabbbabaaaaaaaaaaaabbabaaababaaaaabbaabaabbbaabbabbbaabbaabaaaaabbaaaabbbbbabbaababbbbbaaabbaaababababbbababbbbabaaaabbbabbababbabbabaabaaaaabbbababbabbbabbbbabbbaaabababbabbaababaaabbbaaabbaabbbbabaabbaaabbbabaabbbabbbbabaaabbababaababbaaabaaaabaababbbabbaaabbbabbbababaaabaaabababbbbaaaabbabbbbaababbbbaaaababaabaaabaaaaabbaaabbbaaaaabbbbaaabaaabbabaababaaaaabaaabbbabbababbaabbababbbbbababaababbaaaababbbbbabaababbbabbaabbbbaaabbabababaaaaaabbaababbbbbbaabbbaababbaaabbbabbbbabaaaabbabbbbbaaababaababababbbabbbbbbabbaabbbbaabaabbbbaaababbaabaaabbbbaaaaabbaabbabbbbaabbaaaaaaaabbabbabaaaabbbabbabaabaaabbbbbaabbabbbbbaabaaababbbabbbabbabbbbbaabbabaaabbababaaaaaabaabaaaaabaababaabbabaabbbbaaaaaaaabbbaababaaaabbbaaaaabaaaaaaabaaaaababaaabababaaabbaaaaabbaababbbbbabbabaaaabbbbabaaabaabbaabaaabbbbbbbbbbaaababbbaaaaabbaaabbabbbaabaabbbbbaaababbbaaabbbabaababaabbbabbaabbaabbbabbaababaaabbbabbabbbabbbaaababbaaabbbbaaaaabaaaabbbbbbaaaabbabaaababbbaabbbabbbbabbbaaaabaaaabaabaaabbbbabbbababaaababbbbaababbbbbaabbaaabbabbbaababaaabbabaaaabbbbaaaaaabbabbbabbbbababbababaabbbabababaabbbbbabbbbbbbbbbaaaabaabaaaaabaabbababaabbbbaaaaabaabaaaaaaaabbaabbbaaaababaabaaaabbbbbbaaaabaaabbaaaabbbbbabbbbbaabaabbababbaaabaaaaabbbbaababaaabbababbaaaabaabbaaaaaaabbbababaababababaaaabaaabaaaaabaaabbabbbabbbbbbababbbbbaabbaaabaaaababaaabbbbbaababbbbbaaaabbaaaabbabbbbbaabababaabaababbbaaaabbabbaabbbaababbaabbbbaababbaaaabbaaaaaaaabbaabbbbbabbbababbaabaaabbaaababbaaabbbbbbaabaaaaabbbbaabbbababaababbabababbaabbabaababaabaabbbbbbaaabbbabaaaabababaabababbbbbabbaaaabbabbbbbbbaabbbbbbababbbbaababbbaaabababaabbbbbbabbaaabbbbaababaaababaabaabbababaababbbbbbbaaabaaabaababbabbaaaaaabaaaaaaababbaabababaaabbbabbbabaabbaabbaaaaabbabbaababbaaaaabbaababaaabbbbabbbbababbaabbbbbbbabaabbbaabaaaaabaaaabaabbbbaaabbbaabbbbaabbabbaaaabbbaaabbaabababbbabbbbaabbbbabbaaabbbaabbbbbbbabbbaaaaabaaaabbabbbbbabaaabbbaabbbababbbaabaababbabbabaabbabababbbbaabbbaaabbaaabababbaabbbbaaababbaaabbbaabaabbbbbabbaabaaababbbaabaaabbbbabaaabbbbbbbbbbaabababbaabbbaaabababbbbaababaababaabbaaabababbbaabbbabbbbabbbbabaaaaaaabaaabaaabaabbaabaaabbaabbbbbbabaabbbbbbaaabbbaaaabaabababbbabaababbbabaabaaaabbbbbbbbbbbbabbbbaabbabbaabbabbaaaaababaaabbbbaabbaababbbaababbabbbabbababbbaabaaabaabaaabaaababbbbbaabbbaaabaabbabbbaabaaaaabaabbabaabbaaabbaabbabbababaabbbbabababaaaabbbabbabaaaabbbabbabbaabaaabababbaaaaaaabbaabbbbabababaabbaababaaaaabbabbbaaabbbababababbbabbbababbbabbaaaabbbbaaabaaaabaabaaabaabbabaabbbabbbbabbabbabbaaabbbaabbbbababaaabbbbaabbaaabaaababbbaabaaaabbababbbbbbbbaabaaaabababbbbabbabbbbabaabaababbbaabbbbaaaabaabbaaabbabaabbaaaaaabbaaabababaabababbbbaaaaabbbaaaabaababbbaababbabaaaabaaaaaaaaababbaaaabbbbabbabaaaaaaaabbababbabbababbbaaaaaaaaaabbaababbbbbabbaabaaabaabbaababaaaabbabbbaabaabbaaabababbbbaababaabbbbbbaabbbbababaaabbbbbbbbaabbaabbbabbbaabbabbbaabbbbbaabbbbaababbbbbaaaaaaabbabbbbbabaaabaaababaababbaabaabbabaabbbabbabbaabaaabbabaaaaaabbbbbbaaabbbbbabbbbaaabaababaabbbbaaaabaaaabbaaabbbaabbabaaaaabaaabbbababbbaaabbbabababaababaaaaaabbbaabaabaaaaaabbbababbbaaaabababbbaababaaabbaabbabbbbbbbbabaababbbbbbbbaaababaaaabab
aabbbbabbababababaaabababbaabababbaabbbbbbbabaaabaabaaaaaaabaaaaaaaaabbbabbabbaabbaabbabbbbbabbbaaaabaabaabaabaabaaabaabbabaaaaaaabaaaaaabaaababaaabbaaaababbaabababbabbbabaaaabababaaaabaabaabbbabababbabbbabaaabaababaabaaaaaaabaabaaabaabbbabbaabbabbbaabaabbbbabaabbaabbbbbbababbbaabbaababbbbbaaaababbbbbaabbbbbaaaaababaaabbbabbbbbaaaabbababaaaabbabbabbbbaabaabbbbbbabaaaaaaabaabaaabbbbbbbbabbaabbaaababaaaabaabaaababaaaaabbbbbbaaaababbbbabbbbaaaabbaabbabbabbaaabbababbaabbbabbaabbbbabababaabbabbaaaabbbaababbbaaababbaabbaabaabaabbbbababaababbbbbabbababbaabaabbbabbabbababbaababbbaaabbababbabbbaababababaaaababbababbbaaabaaabbaaaabbabbaababbbbaaaaababbbababbaabbaabbbaababaaabababababbbbaaaababbbbabbbbbbaabbbabaaababababbbaabbaabaaabbaaababbbbbbbaabbbbaabbaaababbaaabbabbbbabbbbaaabbabbaabbaaaaabbbababbabaaaabaaaaababbbaaaaabaabbbabbbabbaaabaaababbbbbabbbbbbabaabbbbaababbaaaaabbaabbaabbabbbbaabbabbaaaaabbababbababbbbabbabbaaaababbaabbbaabaababbabaaaaabaabaabbbaabaaaaabaaabaabbbababaabbaaaabaaababbabbabaaababbbababbabaaaaaaabbabbbaaabbbbabaabbaabbbbbabbbbbbabbbabababbbbaabaabbbbabbaabaababbbababbbaaababbbbaabbabbbbbbbbababbbbbaaabbbaaabbbbbabaaabababbbababababbbaababbbbbbababaaabbbabaabbabbbbaabbbbbbaabaaabaaaababaaaaaabbabaaabbbabbbaaababbbbabaaabababbbbbbbaabbababbaabaabbbbabaaabbaaaabbabbabbbbabbbabbabbbbaababbbbbaabaaaaabbabaababbbbabababbbabbbabaabaaaabbbabbbbabbababbbbabaaaaabbababbbaababbabbbbababbabbbbabaaaaabbbbabababaaaabaaabbabaababbaababababbbaabababaaaabbabbabaaabaabaabbababbabbbbbbaabbbbbbabaaaaababababbbbbbabbaabaaaababbaaabbbababaaabbbbbaababaabbaabaabbbabbbaababaabbbaaaaaabbbababaabababbaaabbbababaabaaabbbbbabbaaaaaaaabbabaabbaaababababaababaabaaabaabbaabbaabbabbaababbaabaaaabbaaabbaaaabbaaaabababbaaababaaaaababaaabaabbbaaaaabaaabbaabbbbaaababbaababaaabbaaaabaabababbbbbbbbbabaaaaaaababaabbbbabaaaababbaabbbbaaabaaabbaaabbbbbaaaabbaabbbababaaaaabbbaabaababbbbaaaabbbbabbaaababbabaabaaabbbbaaaabaabbbaaaaabbaabbaabbbaababbbbbaabbbbbbabaaabbbabababbaaaabbabbaaaaabbaaabaaabbabaabbbbabbbaabbaabbaabababbababbabbaaabbaabababbabbbabaababaababbbabbababaabbabbbbaabbbbabbaaaabaabbbabaaabbbabaaaabbbabbbabbbaaabbababaababbbabbbbbbabbbababaabaabaaabbabbabbbbbbabbabaabbbbaabbabbbbbbbbabbbaabbabbbbbabababbaaabaababaaabbbbbbbbaabaababbbabbaabbabbabababbaaabbabbaabbaabbbbbbbaabaaaaabbababbbaaabaabbbbaaaabbaabbaaaabbabbbbaabbababbababaabbbabbbbbbabbaabababbabbbababbabbabbabbbabbababbabbbbaabbaabababaaaabbabbabaaaabbbabababbabbabbabbaabaaababbabbbbaabbbbbaabbabbbaaaabaababbbabababbaaaabaabaabbbabaabbabbbbbbabbabaaaaabbaaababbbaaaaaaaaaaaabbaabbabaaabbaabbbaaaabbabababaaababbaaaaaaababbaaabaaaabaabbbbbaabaabbabbababbbbbaaabbaabababbbaababbbaababaaaababaabaaabaaabbbaaabaaababbaabaabaabbaabaabaaaaaaaaabbbbaaaaabaabaabbbaabaabababbaabbabbabbbaaabbbbbaabaabaaababbbabababaaaabbaabbbbaabbbaabbbbabbabaabbaaaaaaababaaaabbbbbbbababaaabaaabbaaaaaabbaaabababbabbababaaaaabbabbaabababbabaabbaaaabbabababaaabaabbbaaaabbbbbaaaabbbaaaaaaabaababbbbbbaaabbaabbbbbbabbaabbbaabbabbbbbabababaabbbaababaabbabbaaaaabbbbaabbbbabbaaaaabbaaabaaaaabbbbbbaabbababaabaabbaaaabaaabaabaabbabbabbbbabaabbaaaababbbabaaababababbbaabbbaaabbaabbaaaaabbbbbbbbabbbbabaaaabbaaababbbbbabbbabaaaaabaabaababbbbbbbbaaaababaaababbaabaabbbababbababaaaaabababaababbaabaabaabbabbbbababababbbabababaabbbaabaabbabbabbbbbababbaabbaaabbbaabaaaaaaabaaabababbbaabaaaaabbbaaabaaabbabbbbaaababbbbbabbaaababbaaabbbaaababaaaababbbbaaaaaabbaaabbbaaabbababbababaabaabbbbaaabbbaaabbabbaaaabbabbbaaabaaabbbbababaaaabaabaaabbbaabbbbbbabbbbabaababbbbbbabbaaaaaabbaabbababbaabbaabbaabbaaabaaabbbbabaababaababaaaaaaaabaabababbaaababbbbbbbbbaaabbabbabbaabbbababaabbbbaababaaaaaabbbbaabababaaababbabbbababaabbababbbbbaaaaaababaaabbabababbabbbababbbaaaabbbbbaaaaabbbabaaaabbbbaabaaaaabbbababbaabbbaaabbabbbaaabaaaaaaaaaaabbaabbbabbbaaaabaaaabbbaababaaababbaababbbaabbbabbbabaabbaaabababaaabaabbaaaabbbabbaaaabbbbbabbaabbbaaababbabbbbaaaaaabbaaaaababaababbbbbbbbbbbbbaabaabbababbabaaabaababbbaabbbbbaababaabababbbbbbbbabbaababaaaabbbabaaabbbbbaababaaaaabbbaabbabaabbaababaababbabaabbbbbbbbbaaaaaabbbbbbbabbbaaabbaaaabaaaaabbbbbaabbaaaaaaababaabbabaaabbaabaabaaaabbabaabbabbabbbbbabbaaabbbbabababbaabbaabaaaaaababaaabaababaaabbbbabaaabababaabbbbbbbabaaabbaabbbabababbbaababbbaabbbaaabbabaababbabaaabaabaababaaaaababbbbbaaabbaabaababbaaabaaaaabbbbbaababbabbbbbaaaaabbaaaabbabbabababaaababbaabbabbbabbaabbbbabbaabbabbabababbaaabbababbbaabaaaaaaaaabaabaaabbbaaaaaaaaaaabbbabbaaaaabbaaabbaabbabbaabbabaababaababbaababbbaaabababbbaabababaaababbaaabaaaaabaababbbbbbbaabbbbbbaaabbbabbbabbbabaaabbabbabbbbbaababbaabaabbbbbbbaaaaaaabaaababababbbbaabbaaaabbababaabbabbabbaabbbbaaabbbaabbaaaaabbbaabbaaaabaaaaabbbbababbbababbabbabbbabababbabaaaaababbabbbbabbabaabaabbbbbaabbaaaaaaaabaaaabaababaabbaabbaaaaaaabbbbababbaaaaaaaaabbabbaaaaaabbabbbbababaaabaababaabbbbbababbbabbaaabbbaaaabbbaaabbbbabababbaaababaaabbbbbaaaaaaabbbbaabbababbbbaaaabbaabaaabaabbabaaabbabaaaabaaabaaabaabbaabbaabbbaaababbbbabbbbaaaabaaabaaaabbabaababaaabaaaabaabbaabbababaabbbbaabababababaababaaabaabbbaabbaabbabbabbbbbbabbbaaaabbbbabbababaababbababbbaaaabbabaabbbbbaaaaaaabaaaabbaaabbbababbaababaaaabaaabbabababbbabbaabbbbaaabbbbbbbbbbaaabaababababaabababbbbbaaabbbabbbaababbbbbbababbaababbaabbaabaabababbbaabbbaabbabbabaaaaaaabaabaabaaaaaaabaaaabbaaaaabaaaaabbbaaaabbbbbbabaaabbbabababbaabbabaababbaabaaaabbbbbbbabbaababaabbbbbbbbbaabbaaabbabbabbabbabbbbabaababbbababbbabaaabbabaabbbaabbaaaaabaabbaababbaabbbbabbaabbaaabbaaababbbabbbbbabaabababbbbaabbabbabaaaabaaaaabbabbabbbaababaabaaaabaabbababbaaabaababaabaaaabbbbaaaaaababbbaaaabbabbaaabbabbaaabaabaabbabbaababbaababaabbaabaaaabbbbabababbbbabbbbbbaaaababbbaababbabbababaaaabbbabbaabbaaababaabaababbabaaabaababbabaabababbabbbbbaaababbaaaaabaababbabaabbabbaabbabaaaaabbaabbbbaababbbbabaaaababbaaababbbbbbabbbababaaabbbbabaabbaabbabaaaabababaaabbbaabbabaabaaaabaaababbbabbbabbabbaabaaaaaabbbbbababbaaabbaababaaabbaabbabbbbbaaababababbaaabbbabbabaabbabbbaabbbbabbbbaabaababababbaabaabbbaaaaaabbababbaaaaaababbababbbaabaaaaaaaaaabbbaaabaabbaababbbaaabbbaaababbbbbabaaaabbbabbbbbabbabaaaabbaaaaabababbaabbaaaaaaaabbaaaabbaabaababbbbbababbbaaabbaababaababaaaaaaabbbbabbbaabbabbabbaabbbbaabaababbbbbabababbbbbaabaabbbaabaaabbbabbbbbbaaabbaaababbaaababbbbababbbaaabbababaaaaaabaabaabaaaabaaaaabbabbabbaababbbabbaabbabbbbabaaaabaabbbbaaabbabbaababbbbbbabaaababbbaaaabbbabbbabbbabbabbbbaaaaabbabbbaabbabaaaabababaaababaaabbababaabbbbababbabaababbbaaabbabbabbabaabbababbbbbbaaababbaabbbbababbaabbbbbaaaaaaaaaabaabbaaabbabbaabaaabbaaaaabababaaaabbbabbaabbbbbabbbaaaaaaabaabbaabbbbaaaaaaabbbaaaaabaababaababbabbaabaaaaabbabbbabbbaaabbbbbabaabababbbabbbbbaaaabaaababbabbbbbaababbaaabbbbababaaabababbbbaaaabbbbbbaaabbbbbaabaaababababaabaababbaabbbbababbabbbbbbaaabaabaabbbaababaabaabaabaabaabaaaaaabbbababbababbbabbababbbbbbabbaababaabbbabbbbaaabbabaaaabbbabababaaaabbaaaaabbababaabbbbabaaaaabbbbbbaabbbbababaaaaaabbabbaababbbbbbbaabbbabbabbbbbaaaaaaaabaaabbbbaabaaabaaaaaaaabbbaabaabbbabbabbbbabaaaaaabbbaabababbabaabaabaaabbabbaaaabaabababbababaaabbbbbbbbbbabbbabbbaaaaababababbbaaaabaaababababaaababaabaaabbaabbbaaaabaaaaaaababbaabbaaaaaabbabaabbabbaaaaabaabaabaababbbbabbaaabbaabaabbaabaabbaabababbabbbbabbaabababbbbbbbababaaababbabbaaaababbaaabbbbaaabbbaaabaababbababbaabbbaabaabbaabaaaabbabababaaaaabbaaabbabbaabbaaaaaabaabaabbbbaabbbaaaaaaabababbbbbbaaabaababbbaaabbbabbabaabaaabbaaabbabbbbabaaaaabaaaababbbbababbbbaaaaaabaaaaaabbbaaaababbbbbbbbbbbbbabbaabaaabaababaabaaabbbaaaaabbaaaaaaabbabbbaaaabababaabbaabbaabbabbbabbaabaabbababbbaabababaaaababbbabaababaabaaababaaaabbabbabbaabaabbaabbbabaabbabaababbbaabbabbbaabbaaabbabbabbababaaabbbbaaabbbabaabbaaaabaabbbbaabaaaaaabaaaabbbbabababbabbababbbaabaaabaaababbbbbbbbbabbababbbbbbabaaabbbbababbabaaababbbbbbbbbbababaabaaababbabbabababbabbbaabaaaabbbbaabaabbbabbbabbbbabbabaababbaabbbbbaabbaaabaabbbbaabbbabbbaaaaabaabaabbaabbaabbabbbaabbababbabbaababaabbaaabbaaababbbaababbaaaabaaaaaabbabbbbaaaabababababbbbabaabbbaaabbabaababaaaaaaaabbabaabaabbbbaabbabbabaabaaaabaababbabaaababbabbbabaabaaaaaaaababaababaabbbabbaababbbbbbbabaaabaabbabaaabbbbbabbbbaaaaabbbabbbaaabaababbbbbbbaabbbbabbaabbbbaabaaabaaabbaabaababbabababbbabbabbaabbbbbabaababbbaaabbaaaaabbaabaaaabbbabaaabbaabaaabbaabbbabaaabaaabaaabbababaababbaaaabbbbbaabaaabaaabbbaaabbbbabbbbaabbbbbbabbbaaabaabbbaaaabbabaaaabaaaabaabbababbbbabbaababbbaababbbbbbabaabaabaabbbaaabaabbbbaabbbababbabbbbbbbbbaaabaaabaababbaabababbaaabbbabbaabaababbbababbababaabaababbaabbbbaaaabababbbbababaabaabbabbbaababaabbbbbbaabaaabbbabbbbbbbbbbaabbbbabbbbaabababaaaabbabbaabbbbbaaababababaabbabbabaababbbabaaaabaabbbbaabbbbbbbbbbaaababbaababbbaaabbabaababbaaaaaabaaabaaaaababbbabaabbabababbbbbaabaaaabbbbaaaaaabbaaabaabbababababbabbbbbaabaaababbababbbbaabaaabababbbaabbbbbbbaaaababaababbaabaabbbaabbabbabbbaaaaabbaababbbaabbbabbabaaaabaabbaabbbaabaaababbaabaabaabaaaaabbbabbbbabbaaaaabbbbabaaabaaabaabaaabbaabbabbaaabbaaaabbbababaaabaabbaabbababbbbbbbaabaabbbaaaabababbabbbbaaaababaaaaaaaaaaabbbbabbaabaaabaaaaaaaaaababbaaaabbabaaababbaaaabaababbbbbababaaaaaaaabaaaaababaabbbbbbabbbaababbabbbabaabaabaabbaaaaaaaaabaaaabbaaabaaaabaabbbaababaaaaaaaabaaaaabaabbbbbbabbbbaaaaababbbaaabbbbbaaabaabbaabababbaabbaaabaabbbabaabbaaaaabbaaaaabbbbaaaaabababaababbbaababbaaaabababbabbbabaaabbbbaabbbbabbabbabaaabbbbabaababbbbbaaababaababaabbbbaaabbbbbaabaaaabaaabbabbbbbbbaababaabbabababaabbbabaaaabbbabaaaaaababbaabaabbabbbaaabbbbaabbabbabaabbaabbabbaaaabbbaaaaaaabbbaabbabbabaaaaabbaaabbabaabbbabbbbabbbaabbaabaabbabbaabbaabaabbbaababaabbaabbbbbabbbbaabbaaabbbbbabbbbaaabaaaababbbababaabaaaababaaaaaaabbbaaaabaabaaaababbaabaaaabaaaabbaabbbabbaaabaabbbbbbbbabababbbabbaaaaabaaaabbbbaabaaabbabababbaaaabbabaaabbbababbabbbabababbbbbabaaabbbaababaabbabaaaababbbabbaabbbabbbbaaabaaaabbbbaabbbababaaaabbbbabaabbaabababbbabbbbaabaabbbaaaabbbaababababbbaabbabaaaabbbaaabaaaaabbbbaaaabbabbaaaabaaabbaabbabbbababaabbbbbbbaabaabbbabababbabbbbababbbabbbabababbbbaabababbbbaabaabbbabbbabbaaababbbbbabaaaaaabbaabaaaaababbababbbbababaabbababbbabaaababaabbaaaaabbaaababbbaaabbbbabbaaabbbabbabbbbbbbabbbaabaabbbaaababababaabbbaabbbabababbbbbbbbabbbabaababaabaaababababbbbabaaabaababbbabbabbbbbababaabbbbbaaabbbaabbbababaaaabbabbbaabaabbababaaaababaababaaababaaaaaabaaabbaababaababbbaaabbbbabbaabbbaabbaabaaababbbabbababaabbabbabbaabbaaabbabaaaaabaaababaaaaaabbaababbabbabbbabaabaabaaaabbbabbababababbbbaaaabbbaaaabaaabaaaabaaaaaaaaabbabbababbbbbaaababaaababbbbabbabaaaabbababbbbabbababbaabaabbbaaabbbbaaabaaabbbaaaaaaaabbbbabbaaaaababaaababbbabaaaabaaabbbababbbbabababbbabbbbabbabababaabbbabaababbbbabaabbbbbbbbabaabbbbbaaabaabbbaabaaabbbbbaaaaaaaaaabaaaabbbaabbbabbababbaaababbbabbbabbbbbababaaababaabbbbbabbaababbababbbbbabbbabbabbbaaabbbababaabaababbaaabbbaabababbaaabbaaaaaaabaaaaabbaabaabbaababbbbabbbabaabaaabaabaabbbbababbbababaaaabaabbabaabbbbaabbbaabaabbaaaaaaabbaaaaabaaaaabbbbbbbaababbbaaaaaabbbbabbabbbbabaaaabaabbaababbabaaababbaaaaababaaaababbbaaabbaaabbbbbaaaaabababbaabaabbbaababbbbbbbabbaabaabaaabbbbaaabbbaaabbaaabbbaaaaaaabaabbabaababbbbbbbbabbbabaaabaaaabbbaabbaabaabbbabaaaabaabababaabbaaabbbabbaabbabbbaabbbbaaaabbbaabbbbaabbabbaabbbaabbabbaaaaabbaaaabaabaaaaaaabaabaaaabaabaabbbabbaabaaabbababbaaaabbaabbaaaaabbbbabaabbababbabbaaabbbaababaaaaababbbabbaabbbabbaababbbbbababaabbaaaaabbabbabaabbbbbbbababbbabbbbbbbbabbbbbbbabbaababaabaaaababaaabaaabaababaababababbababaabaaababaabaaababbbaababaababbbaaaaababbbbaabbaaabbbababababaabbbabbaabbababbbabbabbabbbbabbababbbabaabbbababbabbbabbbabbbbbbaabbbbaaababbababbbbbaaaaabbbabbbbabababbbbaaaabbbbaabbbaaabbbaabaaabaababbaaaabbaabaaabbbababbabaabbaaababaaabbbbaabaabbaababbbaababbbbabababaabbaabbbbbbbbaaaaabababbaabaaabaaaabbbabbaabaaabbbaaaaaaabbbbbaaaababaabaabbbbaaabaaaabaaababaabbaaaaabaabbaabbaabbbbabaabbaaabababbbbbbababbbaaabbbbbbbbbaaababbbaaabaaabaaabbbabbbbbbabaaaaababbbbaaaabbaaabaabbabbbbbabbaaaaabbbaaaaaaaabbaaabaaaabbbaabababbbbaabbbbaaabababaababaabbaaabbbbaaaaababaaabababbabaabbaaabaaaaabababbbbbbaabbbbaababbabababbbbbbbbbbababaaabaabbbbabbbbbbabbabaabababbbbabbbbbbbaababaaaabababbababbabbbbaaabbbabaabbabaaaaaabbbabaaabbabbaaaababbbbabbaaabaababbaababbabaabbbabaaaabbbbbababbaabbbaabaabbaababbbbbaaabbbbaaabaaabbabaaaaabaaabaaababbbabaabbabababbbabbaaaaaaaabaaabbabbaabbabbbabbaabaabbaabbbbaaaaabaabaabaaabbabaaabbbabbabbbabaaabababbababbbbabababbabbbaabbabbaabaaaaababaaaababbbbaaaabaababaabbbbbbaabaabaaabbbbaabbbaaaabbbabaaababbbbaaabbaabaaaaabbbbabababbbbbbbaaabaaaaababbabaaaaababababaaaababbababbbaaabbbabbaaabbaabbbbbababbbabbbaaaabbbbbabbaabbaaabababbbbbbababbbabbbbbaabaabbbbaaabaaabaababbbabaabbbbabababbabbbbabbabbbaaabbabaaabbbabaaabbababaaababaaabbabbbabaaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaabbaaaaaabbbababaaaaaababbaabaaababbbbbaaabbbbbbaaaaaaaabaaaaaabbbaaaababaabbbbabbabaabbbaababbbabbaaaaaababbbaaabbaabbaaaaaaaabbbaabbbabbbababbbababbabaababbbbbaaabbbbaaaabaabaababababbbbabbabbaaaabaabbaaaaaabbbabbbabaabbabbaaaabbaaabbaababbbaabaaabbaababaaaaabaaabaabbbbabaaaaababaabaaaaabaaabbaaaaababbbaaabaaabbbaaaabbbaabbbabbbaabaababbaabbbbababbaabbbaabbaaaaabaabbbbbabbaababaaaabbbabbbbbbbbaaaabbbbabababbbbbbabbbabbbabbbababbabbabbbbaaabbbbbaabbabbbabababbaabababbbbbaabaabbbbabbbabaaaaaaabbbaabaabbababbaaabaaaabaababbbabbaaabbabaaababbabaabbbaabbaabbbabaaaaababaabaaababbbabaabbbbbbbabbbbabbaaabaabbbbaaaabbbaabbaaaababaabaabbababaaaabbaababababaaaabbbbbbbabaaabaaaabbbaaaaaaaaabababaababbbabaaababbbaababbbaabbaaaabaababbababaaaabbbaaaaaaabbbabababababaababbaaabbabaaaabbaabbaabaabaabaaaabbbabbbababaaabbabababaabbbaaababbaabaabbbbaaabbbbbababbababaabbbabbbbabbbabababbbbbbbbaabaabbabaabbbbbaabbbbbabababaabbaababbbbbbabaabbaaababbaababbaaabbbaaabaabbbabaaabaabbbaaaabaaaabbbbbbaaaabaaaababbaaabbaababbabbaababbaabbbababbaabababbabababbbbaaaaabbabaababaababbbabbbbbaaabaaaabbbbbbbabbabbaaaabbbbabbababbbbaabababaababababaabaabbaabaabbbbababbaaaaaaaabbababbbbaaaababbbabaabbbabbbaaabbbaabaaabbaaabbbabbababbbbbbbbababbaabbabbabaabbaaabaabababbbabbaabaabbbbabaaaabbbabbabbabbbbaabbababababababbbaabababbbabbabbaaabaaaaaaabbbaaabbbabaabababababbbbabbabbbbaabbababbabaabaaabababbbaaabbababbbababbbaaaabbbabaaabaabaaabbabbababaabbbaabbaabbbbaaabbabbbbbabbbbabababbabaaabbabbabbaaaabaabaaabbabaabaabbbaaaaabaaabbbaabababababbbabbaabbbaaabbbababbbbaabaabaabaabaaaaaabbbbbababbbbbbbabaabbabababbaaabaaaabbaaaabaabbabbbbbababaaaaabbababbabaaabaababaaaabaaaabbabbbbabaabbbbbbaabbbabbbbababbaababbaaabaaabbabaaababaabbabbaabaabaaabaabbbbabbabbaabbbaabaaaaaabaababbaaabbaabaabaabaabbabbaabbbaaabbabbbabbabbaabaaaaaabaababbaaaabbbbbabbbbababaaaabbbbaabbbbbaaabaabbabbabbababbbabaabbbbbbbbaaaababbbbabbababbaaaabaaaaaaabaabaababbaaabbaababbbaaababaaabaaabbbbbaaabaaaabbaaababaabaabaaaabbbaababbaaaabaaabbaaaaabaaababbbabaaaabbaabaabbbababaabbbababbababbaababaaabababbbbabababaabababbabbbabaaaababaabaaaaabbaabbbabbbaabababbabbbbabbaaaabbaaaabbabbbbabbabbabbbbbaaaabbabaaabbaaaabbabbbaabbabbbaabbabaabbbbaabbabaabbaabaabbbbabbbbbaaaabbaabbabaaabbbabbaaaaaabbbaabbababaaabbaabaabbbbbaabaaabbabaaabbbaabbbabaabababaabaaababbbabaaabbbaaabbbbaabbbbbbbbbbabbbaaaaaabbbabababbaaabbbbbbbaaaabaabbababaabbaaabbbbbbbabbbbaabaabbbbbbaaabbbabbabbaaaaaaaabbaaabbaaaabbaaaaabbabaaabbabbbbbaabaaaabaabbaaabaababbbababaaabbbbbaaaabbbaababbaaabbbabbbabbabaabbbaaaaaabbbaaaaaabbababbbbaaaaaababababbbbbabaaabaaababbbabbbaabbbbaabbbbabaabababaabbabbbaaabaaabbabababababbabbbbbaabbbababbaaabaabbaaaaaaaabaabbabbbbabbaabaabbbbababbabababababbababbbaaabaaabaaaaabbaabbbabaabbbabbbbaaabaabbbbabbaabbabbbababaabababbbbbaabbbaaaaabbbababbbaabaaaaaabaabbbaaaabaaabababaabbbbaabbababbabbaaaaaaabbaaaaabbbbbbaabbbaabaaaabbbaababaaaababaaabbabbabbbaabbbaabaaabbabaaaaaabaabbaaababbbabbaabbbaabbbababaaababbaaaababaabaaabbbbabaababbabbbababbabbbbababaaaabbbaaaaaaabaaaaaaababbbbababaaaaaabbbaabbbaabbbbbbabaabbbabbaaabbaaaaabaabbaaabbabbabbabbbbabaabbabbbbaabaaabbaababbaababababbbbabaaaaabbbbaaababbaaaabaaaababbaabbbbaaababbabbabaabaaabbbaaaaaabaaabbbabababaababbbabbbababbababaabbabbbabbabbbabaabbaaabaaaabaabbbbbbaabbbbaabaaaaabaaaaababbbbbabbbaaaaaababababbaaaabaaabbbaababbaababaabbaababbbabaaaaababbaaaabbabaaaabbbbababbabbaabbababbbbbbabaaabaaabbbbbaabaaabbaaaaaaaabbabbbaababbbbaabbaabaabaaaaabbaababaaabaaababaaaaabababaaaaaabbbabbbbaabaaaabaaabaabaaaababababbaabbaaababbbbabbabaaabbbbbaaaabbabaababbaabbbbbbbbbaaaaabbbbbabbaaaaaaabababaabbabaabababbbaabbabbababbbbbbabbabaabbbbababbabbbababaaaababbbaabbbbaaaabbabbbbabbaababbabaaaabbbabbbaaaababaaaabbbabaabaaaaaaabbaabbbaaaaabbbabbbaabaaabbababababaaabbaababbbabbaaababaabaabaaabbbbbaaabaabbababbabbbaaaaaaababaaabaabbbbababaabaaabbbbaabbbbbbbbaaabbbbbabbaaaabababbbbbbbbbababbbaabaaaaaaababbaababbbabababaaaaaabbaabaaaaaabababbbbabbbbbaaabababbbabbbbbaabaaaaaababbbabbaaaabbbbabbabbbaaaaababbabbabaabaabaaabaabbbabbbabbbabbaaaaabaabbaaaabbaabaaaabbaabaaaabaabaabaaabbbaabaabbababaabbaaabaaabaabaabaaaaaaaabbababbabbbabbbaabbbabbabbbaaababbbbaabababbabaaabbabaabbbabaabbbbbabbaaabbbbbbaabaabaaabbbbaaaaaaaaababbbbbaabbbaabbabaabababbaaabaabaabbbbbaabaabaabaabaaaaaabaaaaaaaababbababaabbaabbbbbbbabaaabbbbabbbbabbbbaaabaabbaabababbaaaaaabbaaaaaabbaabaabaaaaaaabbaaabaaaaaabaabbabaabaaaaaabbbabbaabababbaabaaabbabaabaabbbaababbaabaaaaabbbbbbaababbaaabbaabababbababbbaaabaabaaabbbaababbababbbbabbabaabbbbabababbbabababbaabbbbaaabbabbbbaaaabbabbabbaabbbbabbbabbbabababababaabbbbbabaaababaaaabbabaababbbbbabaabbabbabbbbbbbaabaaabbbbbaabbbbbbababbbbbaabbbaababaaaabababaabbaaaaaaaaabbbbbaaaaaaaaaaabbaaaaaabbbbaabaabaabaaaabbbaaabbbbbbbaaabbabaaabbaabbabbabbaaaabbbabbabbabbbabaabbaabaabaababbbbaabbaabbbaaaaaabaaaabbbaaaaabbaabababbaaabaabababbbbaaabbaabbbbaaabababaabaabbaaaabbabbbbbbbbaaaabbaaaabbabbbabbbabbaaabbaabaaabbbbababbabbaabbbabaaaabababbbaaaabbbbabaabbaaaabbaabababbbaaaabaaaaaaaabbaaabaaaabaaababaaaaaabbbabaaaabbabababaaabbbbabbaabbbbabbababbbbaabbbbbabbbbabaaabaabbabaaabaabaabbbabbabaabbabbbbbbaabaaabbaaaaaaaaababbaabaaabababbabaaabaabababbbbaaaaaaaaaaaaaabaabbabaabbabaaabbababbbabbabaabaababbbbbaaaabbabaabababbbbbaabaaaaabbbaabbababababbabaaabbbbabababaababbbbbaabababbabaabbaabababbbaabbbbbbaababbbbbaabababaabbbabbbbbbabaabababaabbbbabababbaabbbabbbbaaabababbbbaaabbabbabbbbbbbbabbbabbbbbbbababaabbabbbaaabaaabbaaaaabbbbbaaaababbaabaabaaababaaabbabaaabaabaaaaababbaaababaaabaababbabbbabbaabaabbbbbabbbbaaaabaaaaabbaabbbbaaabbbbbababababbaabbabbabaaaababababaabbaabaaaaaabbbbbaabaababaaabbabbaababaabbbbaaaaaaaaababbaaaaabaabaaaaaaaabbabaabaaaaabaabbabaaaababbaaabbaabbabbaabaaabbbbbaaaaababbababbaabbaaababbbbbbaababbbaaaababbbabbbbababbababbbabbababaaabaabaabababaaabaabbababbbbbabbabbabbabaaababaabbbbaaabaaaaaabbaaaabbbabaaaaabbbabbbaababbabbbabaaaababababababaaaababaaaaababbbbbabaaaabababbabaaaabaaabbbaaaaabbbbabbbbaabababbbbbaaaabbbaaaabaaaaaabbbaababbbbaaabaababaaabbbababababaabaaabaabbaaaabbbbbbaaabaaaabbabbbabaabbbbabbaaaaaabbaabbbabababbabaababaabaabaaaabbbbbbaaabbbaaababaabbabaabaaabbabaaababbaaabbbbbabbbbbaaababbbbbabbaababbbaabaaababbabababbaabaabbaaabaaabbabaaabbaabaabaaabbbbbbabbabbabababbbbbabababbababbbaabaaabaaaaabbaabbbababbbbababbabbbbbaababbbabaabaaaabbbbbbaaabbbabbbabbaaababbaaaabaabbabbbbabbbabaaabbabbabaabbbbbabbaabbbaababaabbbbababaabababbbbbbabbbbabababbbbabbbbbbbaaaabababaaabaaaabbabbbaababbbbabaaaaabbbabaaaabbbabbabaababaaaaaabbabbbbabbbbababaaaabbbaaabababaabaaababbaaaaababbababbbabaabaababbbabaaabaabaaabbabbabaaabbaaaaabbabbbaabbbaabbaabaababbabbbaaaababbbabbbbababbabbbbbbbbababbabbabaabbaabaabababbabbabbababaaaaaabbaabaabbbbbaaababbbaabbbabaaaabbabbaabbbbabbbaabbaabaabbbaabbaaababababaaaaaababbababaabaaabaababaabababbbabbabbbababbbbbaabababbabbabbbbbaabbbbababbabbbaabbbbababbabbbabaaaabaaaaaabbaababbbbbaababbabaababbbbbaabbbbbaaabbabbbbbbbaaabaabaaaabaaaaaaababbbbbbabaaababbabaabbbaaabaaaaababaabaabbbabbbababbbabbbabbaabaaaaaaaaaabbbbaababbbaaabbbbaaabaaaaabbbbabababaaaababbabbaababababbaaabbbbabbbbabaabababaabbbbabaaaabbabababbbbbabbbabbabbbabaabaabaaabbaabbbbabbbbbbbabbbaababbaaabbbbaaabbaabaababbabbabaaaaabaaabababbbbaabbbababbabbbabbabbbabbabbbbaaaaaaaabbbaaabbbabbabbbbababaabaaabbaaaaabaababbabbaabaaababbaaaababaababbbabbbbbabbaaaaabbbabbaaabaaaabbbbaababbabbbbababbbbbbaabbababbabaaabaaabaabbbbababbabbbabbbaaaaaabbbaabbbabbbaaabaabbabaababbbbabaaaababaaabaaaaabbaaaababbbbbabbabbbaabaaabbbbaaaaaabbaababbbaaabbbaabbababaaaababbbabbaababbabaabaaaaaababbabbbabbbaabbababbabbbaabbabbabaababbbbaabbbbbbbbabbaabbabbbbbbbaaabbbbbabaabbbbbbbaaababbaabaabbaaaabaabaabbbbbababbbbbaababbabaaabbbbaabababababbbaabbaabbbbaaaaabababbbbabbbbaaaabaabbbbbbbbababaaabaabaabaabbaaaaaabbbaaaaabaaabbababbabaaaaababaababbbbbabbbaaabaaaaaaaabbaabaabaaabaaabaaaaaababaaababbaabbabaababbaabbbabbabbaabaaaaaabbbababaabbbabaaaaabaabbbababaaabbbbabaabaaaaaabbaabababababaaaaabaabaaabbbabbbbbaabaaaabbaabbbabbbbabaababaaaabaaabaaabbaaabaaabbbbabbbaaaaabbbabbbbababbbaaababbababaaabbabbabbbabbaababbabbbbbaababbbaababbbbabbababbbbaabbabbbbaaaaabbbbabbbaaabababbaabaabbbaaabbbabbbbbabbbabbabbaaaababbbaabaababaaabababbabbbbbbbbbbababbabbaabbaaabaaabbabbbbababababbabaabbaaaabaabaabbbbabbbabaaabaabaaaababaaabaabaabbbbbabaaaabbbbbabbbbaababaaabababaaaaabbbabbabbbaaabaaabbbaaabbaabaaabbaabaaaabbabaabbbaabbbbbabaaababaaabbaaaabaaaabaabbabababbbbbbaaaabbbabbaaaabbabbaaaabaaaaababbabbbabbaabaabbbabbabbbaaabbbbbbaaaaaaabaaababbbbaaaabaabaabbabbbbbbabaabaaabababbababaabaaabbbababbbabaabaabaabbabbbaabbaaaabaaaabbababbabaaabbbbbbababbbbbbababaaabbaaaababbbbaaaabababbbaabbbbabababbbbabbbaaaaaaabbabbbbbaabbbbaaabaabbbbbbbaaaaaaaaaaaabaaabababbaabbabbbbabbabbbbbaabbbabbbaababbaabbbabbbbbbbbbbbababbaaabbababaaabaabbbabbbaabbbaababbbaaabbbaaaaaaaaaaabaaabababaaaabaabbbababbaaabaabbbbbabbababaaaabaabbababaaaabbbaabbbaaabbbbaabbabbababbabaabbbbababaababaabababaaaaabbaabbbbbabbabbbabaabbabbaababbabbaaabaababbaabbbaabbabbbabaaabbabaabaabaaaaaaabaaabaaaaaaabbbbabbabbbbbabaaaabbababaababbabaabaabaabbbbbbabbbaaabaaababaaaabaaabbbabaabbababbabaababbbbbbbbaabbbbabbabbbbbbbababbbaaaaaababaabaaaaabbaabaaabaabbbaabbaababbbbaaabaabaababaaaaaabbbabaabbabbaaaaabbbaabaabaabbababaabbbbbaaabbbaaabaaabababbbbbaaabbbbbaaabaaababaaaaaaabaabbbbabaabbaaababaabbabbbbbbaaababaabaabaabbaabaababaabaaaaabbaabababbaaabbabbaaabbbbaabaabbaaaaabbbbabbaaabbbaaabbababaaabaabbaaabbaabababbaabbbbbaaabaabbbabaabaaabaabababbbbabbbbbbbaabbbabbaabbaabbabbbabbaababbaaabaabbbbbbaabbaabbbabbabaaababbaabbaabbabbabbabbabbbaababaaabaaabaababbababaababaabbbababaaaaaaababbbaaabbbbabbbaabaaabbbbabbabbbbbbaabaaababbabbbbabbbbabbbbbbabaaabbabbabababbbaaabbaabaaabbbbbaabbababbbaabbabaaabaababbababbaabbabbaabbbabaaabaabbbbaabaaaaaaaaaabbbaaabababbabbabaabbbbababaabaaabbaaabbbbaabbbbabaaabaaaaaaaaaabbabababababaabaabbaaaabbbaaaabaabababaabbababaababbbbbabaaabaababbbbbbabbabbbababababbbabaaabaaaaabbbaabbbbabaabbbbbabbaaabbabbaabaabbaabaabbaaabbbbabbabbbbbabaaaabaaaaaabaababaaabbaaabbaaabbbabbbaabaaaabaabbbaaaaaababababababbaabbabbbaabaababbbaaababaaaaaababbababaaaaababbbbbbabaababaabbbaabaaaabbbaabababaaabaabababbbaaabbabaaabaaaaabaabaaaaabbabbbabbaabbaabbabbabbbbbaaaabbabbbbaabaaaabbaabaaaaabaabbababbaaaabababababaaabaaabbaababaabababababaaabaaabbaaaabbbaabaaaaaababababaabbaaaaaabaaabbbbbaaabbababbbabbbbaababbabaababbbababbabbbaabaabaabbaaabababaaabaabbaaabaaaabbbbabbabbabaabaaababbabaaaababbabbaaabababaabbbaabbbaabaabbabaabbabaaababbaaaabbaaabbaaaaabbaaabbbbbaaabbababaaaaaaabaaabababbaabbaabbabaababababbaaabbabaabaabbbabaaabbbaaabbbbbaaabaabaaaababbaaabbaabbabbbaababababaabbaabbabbabbbbbaaaabbbaaaabbabbbbbaaabbbabbbbbbbbababbaaabbbbaaabbbabaababbaabbbbaaaaabaabababbabaaaaaaaaabaababbabaabbbaabbaabbbaaababaabbaabbbbbabaaaabbbaabababbbaaabaabaabaaabbbaabbbbbbbaaaabbbabaababbabbaaaabaaababaaaabaaababbaaababaababbbabbabaaaaaabababbaaabaaaababbaaaaababbbabaaaabbaaabbbbbbaaabbabbbaaaabbbbbbaaaabbaabaaabbbaabbbbbabbbbbabbabbbbaaaaaaabbbaababbababbabbabbbabbbbaaabaaabbbaaaaaaaabababaaabaaabbbbbaabbbaaabbbaaaabaaabaabaabbbbaaababbbbbaaabbbbabbaaaabbbbbabbbaaabbbbbabbbbbaabababbbababbaaaabaaaaababaabaaaabbbbbababbbaaabababaaaabababaaaaaabbbabbbbabaaaaaabaabbaaaaabbabbbbbbaabbbbabbbaaaabbabbaababaabaaaaaabaabbbabaabbaababbabaabaabbbababababbaababaabbbbaaabbabbaabaaaabaaaaaaababaabaabaaaabbaaabbaaabbbbbaababbabbaaabbbabbbbbabbbbbabbbaabaaaaabbbaaaaaaabbbabbabbaabaaaaababbbaaaabaabbbbbbbaababaabbabbbaaababbaaaaaabbabaabbaaabaabababbaabbaababbaababaaabbababbbaababaabbababaaaabaabbababbbaabaaaabbababbabaaababaabbabbaaaaababaabbbbbaaabbbbababababbbbbaabaaabababaababbaaaabaaabbaaaabbbbaabaabaaaabbbaaaabaaaaaabaababbbaabbbbbabaabababbbbbaaabababbbbbaaabbaaaaabbbabbbabbaaaaabaababbaabbaabbbbbbabaabababaaababbabaaabbbbbbbbbabbabbababaaabbaaaabbaaababbababbbaabbaabaaaaabbbaaaabababbaaababbaaababbaaababbbbaaaababbbabbabaabaabaaabaaabababaaabbbaabbbaaabababaabaababbabaabbbababbbbbaabaaaaabbaabababbbabaabbabaaaaaabbaabbabaabbaaaaaabbaaaaabbabbbbbbbbabbabaabaaabbbbabaabababaaabbbbaababbbaaaabaaabbbbaaaaaabbabbbbbbbbbbabbaabbbbabbbbaabaaabbbbaabbabaaabaaabbbbabbbabbaaabbbbbabbbaaabbbbbbbabbbbaaaaabbaaabaaabaabaabbbbbaabbbaaaababbbbbabaabaaabbbbbaaababbaaaabaaabababaabbbaabbaaaabaaabbbaaaabbbbaabbabaabbaabaababbabbbbababbbaaabbababaaabaaaaaabbaaabbaaababbbbbaabaaabaabaabaababaabaaaaabbbbbbabbaababbabaaabbbabbaaaaaabaaabaaabbbaaabaaababbbbbbbaabaaababbaaaaaaababbaaabaaabbabbbbbabbaaaababaaaabaabbabaabbabbabbaababbbabbabbaaaaabbabbaabaaaababaaabbaaabaaabababbbbabbababbbabbbbabbbaaaababbbaabaabaaabbbbabbabaaaaaaaaaaaabaaaaabbbbbbaaaaabaabbabababbbbababaabaabaaababbbbbabbbaaaaabbbbbbbbbbababaaaababaabbbabbbbababaabbbbbbaabbabaabbabbaabababbbabaaaabbbabbbabaababaaabbaabbbbabaabaabbbaaabbbabaaabaaabaaabbaabbbabbabbabbbaaaabbabbababbaaaabbabbbbbbaaabaaaabbabbaaaaaaaababababbbaaabbababbbabababbbabababbaaabaaaabbaabababbabbababbbbbabbbabaabbbbabbbbbbabbabbabaabbaaaaaaabbbbabbaabbaabbabbbbbbabbbbbbbbaaaaaabbabbbabbbbbaababbaabbaabbbbabbbaabbbabaabbbaabaaaabaaabbabababaabbaaaaaababbbaabbbaaabaaaabbbbbabbabababaababbaabababaaabaaaabbbaababbaabaabbaabbbabbabbaaabaabbbabbbbbaabaaabbbbbbbbaaabaabaabaaabaabaabababbbbababaaabaabbbaabaaaaabaaabbaababaaababbabbabababbbababababbababbbbabaababbabbaaabbbbbaabaabababbbbaaabaaaaabaabbbabbbbabbaabbbaaabaaababbbbababbbaaabbaaabbbbabbbabbaaaababbabbabaabaabbbbababbabaaababbaaabaaaabbabbbababbbaaaaaaababbbaaaabaabaabbbaabaababbaaababaaaaabaaabbabbaaabbbabaaabbbaaaaabbbaaababbaaababbabbbbaaabbbbbaabbaaaaaabaabaaaabbabbababbabbabbbaabaaaabaabbaabaabbaaaabaabbbaaabbbbabaabbababbaabababaaabbbbababababbbbbabababbbbbbabbbaaabaaaaabbbaabababaabababbbabbbbaaabbaaabbbaaabbaaaabaaaabbbaaaaabbaabaaaaababbabbbbabbaababaaabaaababaababbbbbbbbaaaabbabbaaabaabbbbbaabbbaabbaaabbbabbaaabaabbbaaabaaaaaabaaaabababaaabbabaaabbaabbaabaaabbaaaaabababababbbbbaaaaaabaaabbaaaabbbbbabaaabaaaaabaabaaaabbbbbbabababaaaababbbbbbabaaabbbabbaaabbbbaaaabbbaababbabbaaabbaabbaaababababaabbabbabbabbaabaaabbabaabaaaabbbbabbaaaaaaabbbabbbaabaaaabbbabbbbbbabbbbabababbbbabbbabbabbbaababbababaabbbababbabbabaaababaabbbaabbabababbaabbaaaaaaaababbaaabbabbbbabbababbbbaababbbbbaababbbaaabababbbbbbbbabaaaaaabababbaaaabaaababbabbabbbababaaaaabaabbbababbabbbbbaabbaabbaaabbaabbababbaaabbbabbbabaabbbbaaababbbabbbbaaabbbbbabbabaaaaabaababbbbbabbababababbbbabaaaaaabbababaabbbbbababbaabaaaabaabbaaaabaabbbbbabbbaaaabbaababbbabaabaababbbabbbbabbbbabaabbabbbbbaaaabaaababaabbaaaaaaaaabbaabbabaaabbbbaababbabaaaaaaaaababbbaabbababbabbbbabbabbabbabaabaaabaaaabbbbabbbbabbabaaabbabbaaaaabaaabaabbabaaabbbabbaaabbaabbbababbabaabbaabababbbababbbbababaaabbaababaabaabaabababababbabaabbaaaaaaabbaabbabbbbbaaaababbaababaabbbababbbabbaaabaababbaaabbbbabbbabaabbbbabaaababbaabbbabbaabbbababbababbbaabaabbabbbabaaaaabaaabbaaabababaaaababbaabbbaaabaaaababbbaaabbbbabaabbabbabaaabaabaaabaabbbbabbbbbaababbaaaabbabbabbbbbbaabbbabbabaaaaababbbbbbbaaaaabbbaaaabaabbbaaabbbaaaaaaabbbbbabbaaaaaaabaaaabaaabbaaaabbabbbbaaabbbbbbabaaaababbbbbbababbaaabbababaabbbaaaaababbbbabbbabaaabaaaabaaaaabaaaabbaaababaabbbbaabbbabababbabbbabbababbaabbbabbbbbbbbbbaabababbbabbbabbaabababbabbabbaabaaabaaabaabbabbbaababbbabbabbabaaabbbaababaaaabaaaabbbabbbbaabbbbbbaabbbbbababbabbbbaabbabbaababaaaaaaaaabbbabaababaabbaabbbabaababaaaaaabbbbaababaaaabbaaabaabbbbaabbaaaabbbabbabbabbabaaaaaababbaaaababbbbbbbbaaabbabbaaabaaabaaabbabbbabaabbbababbabababbaaaabbbbaaaabbabbbbbbbabababbbbbbbaaabbabbbbabbbaaaaaaabaaabaababbaabbaabbbbabbbbaabbaababaaaaabaababaaabbbbababaaabbabaabbaabaaaabaaaaabbababaaaaabbbabaaabaabaaaaabababaaabbbbbaabaaabaaaabbaababbaaaabbaabababbbbbababbababaaabbbbbaabbaaaaabbbabbabbbbabaaabaaababbabbabbbabaabababaababbabbbabaaaabaaabbabbbbbaaaababbabbaabbbbbbbababbbbaabbbbbaaaaabbbbabaaabaabbaaabababaababaabbabbaaaaaaaabaabaabbaababbabaabbbbbabaabbbaaaabbabbabaaabaabbbbbaabbbbbbbbbabbbbbbbabaaaaabbabbaaaaabbabbbbbaaabbabaaaabbabbbbaaabaaaaabbbbbbbbbbbabbaabbbbaaabbbbbababababbbababaaaaaaaabbaabbaaabbbabaabbbaabbabbbaababaababbbbbbbababbaaaaababaabbaabbbbaabbbbbaaabbbbaababbababaaabbbbababbaaaabbabbbaaabbabaaabababbaaaabbbaababaaaaaaabaaabbbaaabbabbbbabbaabbbaaababbbaabaabaabaaaaaababaaaababbbbaabbabbbbbabbabbaaabaaaaababbbaaabaaabbaabaababbabaaabbabbbbaabababbabaabaaababbbaabbaabaabbabbababbabababaabbaababbbababbaaaaaabbbbaaaaaabaaabaabbababbbaaaaaaaaaaaaabaaaaaaabaabababbbabbbbbaababbbabaabbbababbaaabaaabbabababbabbbababaaabbabbbbabaabababbaabbabaabbbaaabaaaabbaaabaaaabbabbabababbabbbbabbaabbabbbabbbabbaaaaaaabbabbabaabbaabbaaabbbbbbbbaababaabbbaaababbbbbbaaaaaaaababaabbbabbbaabbabbbabbbbbabbaabbaaaababbaabbbbbbabaaababaaaababababbbbaaabaaabaaaabbbabaaaaabababbaabbbbbbbababbaabbbbbbbaabaaabababaabbababaaabbaabaaaabaaabbbbaaaaabbabaabbaabaaababbbabbbaababbbbbbabaaabaaaaaababaaabaaaaaabbaabababbbaaabaabaabbaabaababbbabaababbaaabbbaababaababbbbaaabbbbaababbbbbabaaababbaababbbaababbbabbbbaabbbbabbbbabbabaaaabbbbbabbabbabbaababbabababaaaaaaabbabbababaabaaabbbabbbabbbaabbbbbbaabbaabbbbbbbaaababbbbbabbbababbbabbbbaabbbaabaababababbbaaababaaaabbaaabbbbaababbbababaabbaababbaabbaababbbabbabbabababbbabababbaaaababbabaabbbaabaaabbbaaaaaaaaaaababaabaaaaaabbabaaaaabaabaaabaaabbaaabaababbbbaababaaaabababbbbbabaaabbabbbbbbabaababbababbbbabbbbbbbbabaabbbbababababaabbaabaaaabbbabababaabaabaaabbaaabbababbabbabbabbaabbbbabbbbbbaabbbbbbbbaaabbbbbaabbbbabbbbbaabbbbabbaaabababaabaaaaaaabbbbaaababababbbabbababaaaaabbabbbaaabaabbbbabbbbabbaaabbbaaaabbbbaabbbabbabababbbaaaabaabaaabbbaaabbaabbaaaaabbaababaababbababbabbbababbbbbbbababaabaabbbbaaaaaabbbaababaaaaaabbbbabbaaaababbaabaabbbaaababaaabbaabaaabbaaaababaabaaababbaaabbabbabaaabbaabbbaaaabbbaaaaaabbaabbbababbabbbaabbbbbbbaabbababaaababaabaaabbbaabaaaabbabbaabbaaaaabababaabaaabaabbaaabbababbbbbaababbbaaabbbbbabababbabbbaaabababaaabbaabababaababbabbbbaabaaababababbaaabbbbabaaabaabbbbbbbabbbabbbaababbaaababbbababaabaaabbbabababbbbbaabbabbaabbbaaaaaaabbabbabaaaaabababbbabbbbbaaabbbabaabbaababbbbababbababbaabaabbaabbbaababbbbbaaaaaaabbbabbbababbaababbbabbbbbbabbbbbabbabaaabbbabaabbbbbbabbaaaabbaaabbbabaaaabbbaaabaabaabaabaababaabbbabaaabaaaaabaabaabbbbbbaaabaaababbabbaaaabbabaabaaaabbababbbbbbbaaababbbbbbabaaabbabaabbaabaaaabaabbbbaabbaabbababaabbbbaaabbabaaabbbaaabbbababbbaababbbbbbaaaaaaabbbaaaaaababbbabaababbabbaabababaabbbbbabaaabbaaaabbaabbbbbaabbbabaaabbababaaabbabbaaaaabbaabaababaaaaabbbabababbabbbaaaabaabbbbabaaabaaabbababbaaaaabbaaabbbbbabaaaabaaabaababaabbababbaaababbbbabaabbabaabaaaaabbbbbabbabababbabbbabbbbaabbaabaaabbbbaabbbaabaaabbbabbabbbbbbabbbbbaaaabaabababaaababaabaabaabbabbabbabaaaabaabbbbabbaaaaaabaaabababbbbabbbaaaaabaaabbbbbabbbabaaaaaaabaaabbabbbabbabbaaaaabbababbbbbbabbbabaaaaababbbaaabaabbbbbbbbabbabbbbbbababbbababababbbababbabababbbbabbababbbbaabababbabbbaaabbbbbaabababbabaaaaabbbbaaaabaabaaaaababbbabbaabaababbbbbaaabaaabbbbaaaaabbaaaabbbbababaaaaababbababbabbababaababbbaababbaaabbbabaabbbbbbbababababbbbabaabbbabbaabababbbababbababaaabaaaaababaabbbbabaabaababbabaaaaabbabaabbbabbababbaabbaaabaabbbabbaaaabbaaaabaabababbaaabbbabbbbbbababbaaaaabbbaaababbbbaaaaabbbaaaabbbaaaabbaabaaaaaaaaaabbaaabbbaabababaaaaaaaabaaabbaababbaabaabaaaabbaabbaaaaabbabbaaabbaabababbbaabaaaababaabaabbababaababababababbaababbaabaabaaabaaabbabbaaaabbbbaababaaaabaabbbbbababbbbabbabaabbbaaaaabaabaabbababababababbbaababaaabbaaabaaabbabaaaaaaaaaaabbabbabbbbaaaabbbbabaaabbbbbbaaaababbbbaaababaaabbbbbaaaaaaaabbabbaababbaaaabbabaabbbaabbabbbbabaabababaaababbabbbbbaaaabbabababbbbaabaaaaaaabababaabbaaaaabababaaabaabbaaabaaababaaaaaaaabbbbababbabaabaaabaaaaabbaaaaabbabbbaaabababbbbbbabaaaaabaababbaaaaaaaabaabbbbabbbaabaaaaaababbbbaaaaabbbbabababbabaababaaaabbaaababbaabbaaaabbbabbbaabbbbbabbaabaabbbabaabaaabaaabbaababbabbabbaaaaaaababaaabbaabbbaaabbaababbbbbbaababbbaabaaaabbbaaabbbabbbbbbaaabaabaaabaaaaaabbaaabaabababbababbababbbbbaabbabaababaaabbbabaaabbbbbabbbaababbaaaaabbbbbaaaaababbabaaaaaaaaaabbabbbaabaaabbbbbbbbbbabababaaaaaaabbabbbaaaaabbbbbbbaaabaaabaabbbaaabaaaabbabaabbaabbaabababbbbaabababaabaaaabbbaabbabbbbbbaabbbbaabaabaaaaabbaabababaabbbbbabbabbbbaaabbbabababbbabbbabbababbaaaaabbbbbbbbaabbababbbabaabbaaaabbbabababbbbaaaaaababbaabbabaaaabaababbbaabbbbbbaaabababaabbbabbabbabaaaaaaabbabbabbaabbaaabaabbbbaaaaabbbbabbaababbabbaabbabbaababababbaaababbaaabbbaabaaabbaaaabbababbbababbbabbabbbaaaaababbaabababbabaababaabbaabbbaaaaabaabbbbabbbbbabaabaaaaaaaabaaabbabbbabbabaaababbbabbbbbaabbabababbaabaabbbbaaabbbbbaaabbababbbabaaabbbabaabbabbababaabbbabaaabaaabaaaaabbaabbbbbaaababbaabbbaabbbababbbbbbababbabaaababbaaaaabbababaaabbaaabbababbaaaaabbabbaaaabbbbbbaabbbabbaaababbabababababababababaaabaabababaaabbaabbbababbbaabaaabbbaaabbbbabbbbaaaababbbabaaaababbaaababababaaaaaaaaaababbbbabbbbbaabaabbbbbbaabbbabbbbabbabaaaaabbaabaaababbbaaaabbabaaaabaabbaaaabbbbbaaaababbbbbbababaababbbabaababababbaabbbbbbbaaaababbabbababbbabbaaabbbaaaabbbaabaaabaabbbbabababaabbbaabaabbbbababbababbabaabbaababbbaaaaababaababbabbabbabbaabbbbabbaabbbaabbbbabaababaabaaabaabbbbaabbbbabbbaabbabbbabbaaaaaaaababaabaabbbabbabababbbaaaaabaababbbbabaaababaaaabbbbbaaaabbabaaabbaabbaabaaaababbbbaabababbabbabaaabaabaabbaaaaaaaabababaababbbbbaaaaaababbaabaabbaabaaaaaaabbbabababbbaaabbababaabaabaabaabbbabaaaabbabbbababaabbaaaaaaaabaabaabbbaaabbbaaababaabaabbababbbbaabbbbbbaaaabbaabbaaabbbabaaaaabababbabbbbbabbabbaabbabbabbbabaaababbababbbabbbbabababbaaaaaabbaabaaaabbbbaaaabaabbbbabaaaaaaaabbbabbaaabbbbababbbbaabbbbbaaaaabbaabaabababaaaababbaabaabbbabaaabababbbaabaaabbaaabbbaaaabaaabaaabbbbbaaaaaabaabaabaabababaaaabaabbbbaaabbaaaabbbbaaaabbbaaabbababaaabaaaabbaaaabaaababbabbaaabaabbbaaabbaabbbbabaababbababbbbababaaaaababbaaabbbbbbbbabaaaabaaabbabbbaababababbaaaabbbaabababaaabbbbbaaababbababbabaaaaababaababbbbbaaaaaaaaaaaabbbbbbaabbbbbbabbbbabbbbaabaaabaaaaabbabbaabbbbabbbaababbbabababbaaaaaaaaabaabbbabbbbbababbabbbbbbaaaabbbbbabbbbaaabaaabbaabaabbbbaabbbbaababbaabaababaaabbaaabbbbbababaaaaaabababbbaaaababbbbbbbbbbbbabbaaaaabaabbababbbbbbbaaabaaaabbaabbbabaaaabaaabababbbaabbababbbaaabaabbbaaaaababbbbaaabbabaabbaaaaaabbbabbbabbbbbaabbabbaaaabbbabbbaabbbabaaaaabbaabaaabaabbabbabbaaababaaaaabbbbabbbaaabbbbaabbababbbabbaaabbbabbaaaaabaaaabbabaaaabbbbaaabbbbbbaaababbbaabaabababbababaabbbaaaaaabaababbbabbabbbababaabbbbaabababaaababbbaaaabbbbababbaaaabaaaabbaabbabbabbabaaababbbabaabbbababbbaabababaabbaabbabaabbabaaaabbaaababaaabbaabbababaabbbbbbbaaaabaabbaaababbbabaabbaababbabbbbbabaababababababbbabbabbbaaabbababbbabbabbbaabababaabbbbabbaabaaababaababaaabbbbbbababaabbaababaaabbbbbbbababbbababbbababbbabbbbbbaaaabbaababaaabbabbbaabbabbbbbabbbabaaababbbbbbbaabbaabaabbabaabbabbbbbbabbabaabbabaabbbbbbaaaaaabbababbaabbababbababbbaababaabbabbabaabbbaaabbbbbbbaaaaaabbabbaaaababbbbabbbaaaaaabaaabaaaabbbaaaaababbbabbabababaabbbaaababbbbababbababaaaaababbaaaaabaabaaabaabbbabbbaabbbbbabbabbaaaabbaabbbaaabbaaabaaaabbaabbaaaabaabbbabbbababbababaaaaaabaababababbbaabaaaabaaabaaaaabbbaabababbbaabaabaaaabbbbabbbbaabbbbbaaaaaaaaaabbabaaaabbbaaabbbaabbbbbabbbbbbaaababaabbaabbaabaaabbabbbabbabaabbbbaabaaaabbaaabbbabababaabababaaaababaaabaabababaaabbbabbbbaaababbbbbbbaababaaaaabaabaaabaabbbaaaabaabbaaabbababbabaaabaaabbabaabaabbbbabbbbaabbbaabbabaaababbbbbbbababaabaabbbbbaabbbbbbbbababaaaababbbababababbbbbaabbbaaababaabbabaababaaaaaabbabbbabbaabababaaaaaaaabaabbaabbbbbababaabbbaaaaabbbabbbaababbbbbabbbabbabbabbbbbbabbabababaabaabaabaabbbaabbaabbabababaaabaabbabaaaaaabbaabaabaaaaabaabbabbbbabbbaababbaabaaababbababaaabaaaaabbbabbbbababaababababbaaaabaaaaaabbbbabbabbbbababbbbbbbaabbabbababababaababaabaaaabababababababbabaaaabaaabaaabaabbababbaaaabababbbbabababbbbbbbbaababaababbaaabbabbaabaaababaaaabbaabbaabbbbaabbbaaabbaababaaabbababbabbaaabaaabaaabbbbababbabbbbabaabbbabbaaaaababababaabbbaaababaabaabbbbabbbabababaababbbabaaabbbaaaaaabaaaaaaaaabbabbbabaaabbabaaabaaabaaabbaaabaabbbbaaabbbbabaabbbababaaaaabaaaabbaaaaabbbbabbaaaaaaababababaaaaabbabbbbbbabbaaabbabbbbababababbbaabbbbaababaaaaaababbbaaaabbbbbabbabbabababbabaabbabbbbbaaaababbbbbbbabbbaabaabbabbbabaaaabbabaabbbaaabbbbabbabbbabbbbababbbabbaaaababbbaaabbaababaabbabaaaaababbaabbaabbbbabbbaaaabbaabbaaabbabbaaaabaababbbaabbabbbabbbbbbbaabbaabaabbbaaaaaabbbbbbabaaabbabaabbaabbbababbaabbbbbbbaaabbbbabaabbbbabaaabbaaaababbbbbabbabbaaabbbbbbaaabbbbabbbaaaaaaabaabbaabbaaaaaabbaaabaabbbbababbbbaabbabbabbbbaaabbbbabbbabaaabbbaaaabbababbaabaabababaaaabababaabbbaabaaababbbbbaabbbaaaaabbabbaaabbbabbbaabbbbbaababbbababaaaabbbbabaaaabaaabbbabaaabababaabbbbbaaabbaababaaababbbaabbababbabbbaababaaaaaaabaaabaabbaabbababbbababbaaababaababaaabaaaabbbabbbbbbaaaabaaaabababababbabbaaabaaaaaabbbbbaabaaabbabbabbbaababaabbababaaaababbaaaaaaaabbabaabbaabaabaabaaaabaabbababbbbabbbaabbbbabaaaaabaaaaaaaabbaabbbbbabaababaaaabaabbabbaabbbabbababaabbbbbaaaaabbabaabababbaaababbbababbbabbaabaabbabbbbababaabbbaabbbabbabbaabbbaaabbababaabbbbbbbbabbbaaaabaabbbbbaaabaaaabbabaaabaabbaabbbbbbbbbbabbabaabbabaabbbaaaabaabababaabaabaaabbbbbaabbbaaaabbaababbaaaaaaaaabbbaababbbaaababaaabababababbaabaabbaaababbbbabbbaabaabaabaababbbbbbbbaabaaabaabaabbbbabaaabaaabbaabbbbbbbbbaabbaabbbabbbbbabbbbabbabbaaaaabaabaaaabbbbbabbbbabaabaaabbbbabaabbabababaabaaaabbaaabbaaabaabbaabaabbaabbaaaabbbabbbaabbbabaaabaaabbbbbbbbbababbabbaaabbaabbbbbaaaabbbababbaaaaabbbabababbababaabaaabbbabbbabbaabaaaabbbbabbabaabbabbaaaabbbbbbabbbaaaababaaabaaaaabbababababababbaabbbaaabbabbbaabbbabbbbababbbbababbbaaabbaaabbbaabbbbbabbabbbabbaaaababbaabbbbababbaaaaaabbbaabbbabaaaabaabbaaababaabbaabbbbabbabbaabbbabbababaabaabaaaabbbabbbababbaaabababbaaaaababbbaababababbaabaaaabaabbbaaaababbabbbbabaabaaabbbbabaabaabaabbaaaabbbbabaaaaaabbbaabbbbbbbbbabbaaaababbbbbababbbabbbbababaabaabbabbbbabbbbbaabbaabbabaabbbbaabaaabbababbaaaaaabaaabbababbbabbbaabbabbbaabbbbbbabaaaabbbaaabababbbaaabaabbbaababbbaabaaabababaaabbabaaaaababbbbbbabaababbbbbbbabbbbbabbbbabababaaababbbaaaaabababbaaaaabbbabbbaabbaaabbbbaabbaaaaabaaabbabbbababbaaaabbbaabbbaaabbabbabbbabbbaaaabaaabbbaabaabbaabaaaaaabbbbbabbbbbabbbbabbbbbaaaabbaabbbbaaaabbbbbabbbabbbaababababaaaaaabbaaababbabbbbaaababbbbabbbaabbaaababbbaaabbbababbabaaababaaaaabbbaaababbabaabbaaaababbbaabbabbaaaaabbbababaabbbbbbaabbbabbaababbabbbaabbabbabbbbababaaabababbaabbbbbaaabbbaaababbaabaaabaaaabbbbaaaaabbabbbaaaababaababbaabbaabababbaabaabbaaaababbbbbaaaabaabaaaabbabbabbbbabbbaabbbbbaabaabaabbaabbababbaaabbbaaaabbaababababaabababaabaaaaabaaaaababbbbbbbbabababbbabaabbabaaaaaaababbabababbbbabbbbaabbabababbabbaabbbbbbaabbabbbababaabbaababbaaaabaabbbaabbaaaabbbaaabbbababbbaaabbbbbaaabbabbbbaabbaabbabbababbaabbababaabbababbaaaaababbbbbbbbabbbaaaaababaaabbaaaaabaaaaaabaaabbbabbaaaaaaaaaabbaaabbbbbaaabaabbbbbbbaaaababbabbabaabbabbababababbabaabbbaabbabbbbaaabbbbaaabbbbbaababababbbbaaabaabbaaaabbbaabbaabbbaabbaaaabbababaaaaabababaaaaaaaaabbbaaaabaaabbaabbaabbbababaaabbabbaaaabaabbaabbbababbbbaaaabbabbbbbbaabbbbabbaaaaabbaabababaaabababbaabbbbbabaabaabbbbbbaabbababbbbbbaabbaaabbaabbaaababaabababaabbaaaaaaaaabaabbbaaaaabbabbabbabaabababbbbaaabbbabaaaabbbbbabababbbaabbbbbbaabbabbbbbababbbababbbbbabbababbbbbabbbbaabbaaaaaababbabbabbbabbbbbbabababbaabbabbbbbbaaaaabaaaaaaabbbabbaabaababbaaaabbaabbbabbaaabaaaaaaabbbaaaabaababbbaaaaaaabaaaabaababbaaabbbbbbbbabbababaabbbbaaaaaabaabaababbbbababbbbabbbaababaabaaabbbabaaaabbbabaabaaaaaaabbabbaabbabaabaaabbbaabbababbbbababaabaaaabbbaaabbbabbbabbaaaabaabaaaaaaaaababbabbbaabaababbabaababbbbaabababbaabbabaaabbbbbbaaaabbaaaabbabaabbaaabaabbababbbbaabbabbabbaaaabaaaabbaababbbbaabaabaaaaaabaaaabbbaababababbbbbbbbabbbabbabbabbbbabbbaabbaaabbbaabaabbbbaaabaababaabbaaaaabaaaabababbbbaaaaabbaaaaabaaaaaabbabaaaaabbaaaaabbabbbaabaaabbaabbbabbababbabaaaaaabbaababababbabbaaaaaabaaaaabbbabaaaababbabbaabaabbabababbaabbabbaaaaababaabbbaaaabbabaabaaaaabaabbabaaabaaabaaabbbababbaaabaaaabababbbaabbaabbbbaaaabbabaabbaabbbbababbabababbbaaabbbabaaabaababbaabbaaaaabbaaabbbabbbbaaaabaaabbbaaaabbbbabbabbbbabbbaabaaaabaaabbababbaaaaabaaaababbabbbaabbbaababbaaababbaabbbabbbabbbaabbabbaababbaabaaabbaaaabaaaaaabbbbaaaababbbaabaaabbababaabaaaabbabbaaaaabbbabbbbaaaabbaabbbbbabbababbabbabaababbaabbaabbabaaabaabbaaabaaababaaabaaababaaaaaaaababbabbabaaaaabababaaabaaabbaaaabbbbbabaaaabbbaabaabaaaaabbabbbbbbbaabababbbabbaabaaabbabbbbbbabbbbabbababbababbaaabaabaababaabaabaaaabaaaababaaaaaabbbbabbbbbbabaabbbaabbaabaaabaabbbaababbbabbaabbabaaaaaababbbbbabbbaabbabbbbabaaaaabaaabaabaabbbbababababababbabbaaabaaaababbaabbaaaabaababaaabbbbbbaaaabbbbabbbabbabaaaabababaabbaaabaababbabbbabaabaabbaabaaaabbbabbababbbbabbbabbbbaaabaabababaabbaaaaabbabbaababbaabbaababbbbbbbaaabbbabbbbbbbbaaabbabbbbabbbababaabbabaaabbbaaaabbababaabbbbbabaaaaaaaaabaaababaaaababbabbabbababbababbaaababaaabbbbaabbbbbbbababbaabbbababaababbaabbbaabbbbaaaababbabbaabbbbbaaabaaabbabaabababaaababbabaaabaabaabbbbabbaabababaabbbbaabbababbbabaaaababbabaaabababbbbaaabaababaaabbaabbabaabaaababbaaaabbabbbabaabaaaaabbaaabbabaabbaaabaabbbaaaaaaabbbbbaaabbbabaaabaaaabbbbbaaaababbbbbbbabbaabababbabbbbbbbbbbabbbabbbbababaabaaaabbabbbabaabbbbaabbabaaaabbbababbbbaaababaaaaaaabbbabbbababaaabaababbaaabababbbbaaabaabbaabbbabbaabaaababaabbbaabaaaabbabaaaaababbbababbbbabaababbbbbbbbbabbbaabbbbbabaaabaaaabaaaaaaabbbabbaaabbaabababbbbbabaabbbaaaaaaabbabbbbbabbaabbababaababaaabbabaabbbaabababbbaaaaaaabaaabbbbbbabbaaabbabbababbbaabbababaababbbbaababbababaabbabbbbbabbbabaaaaaababaaaaaabaabaaabbbbbbababbaabbaabbbabbbbaabbbbbababbbbaaaaaaabababbbabaababaabbbabbabaaababbaaaaaaaaabbaaaaabbaabbaaababaabbababbaaaaababbabababbaaabbaaabaabaaaababaababbbbaaaabbbbababaababaaaabbaabaaabbaabbabababbababaaaaaabababbabbaabaababaabbbaabbaababbbabbbbbbbbaaabbababbaaabaaaabbabaabbaaaaaabbbabaabaaaaabaababbaabaabaaaaaaaaaababbabaabbaaababaababaabaabaababaabbbbbbbabaaaaabbaaaabbaababbbaaaaaaaaabaaaababababbaabbaabbabbbbaaabaaabababaabbbabbbbababbbabbaabbaabbbabbbbabbaaaaabbabaaabbbbbbaabaaaabbaabababababaabaaabbabbbaabaabbabbabaabbaaaabbababaaaaaabbabbbbbaababbabbbaaabababbaabaaaaaababbabbababaabbbbabbaabbaabaabbbababbbabbbabbbabaabbaabbaaaabbbbabbaaaaababababbaaabababaaaabaaaaababaabaabaabababbabaaabbbaabaabaabbbaabbbabbaaabbbaaaabbaaaabbabbaaabaabababbabbabaaabbbabaabbbbbbaaabbbabbaabaababababbbbabaaaaaababbbbaabbabaabaabbbbaaabbaaaaabbaaabbaabaaabaabababbaabbabaaabaaaabbbaaaaaabbbbbabbbbbbbbabbaaaaaabaaaaaabbabaaababbaaabbbbaaabbbabababbbbaabbbaaabbbaabbbbbbaababbbbbabbababaaabbabbaabaabbabbaabbababaaaabbbaaaaaabaaabbabaaabaababbbaaaabbaabbbbbbabaabbabbbbbbaabbbaaaaabbabbbaabbbababababaaabaabaabbbbaabbabbabaababbabbababbabbaaabbbbababbaababbaaabbaabababbaaaaaabaabbbbbabbabbbbbbaaabaaabaabbababaabaabbbbbaabaaabbababaababbbaaabbaabababaababbbabbababbaabaaaababaaaaabababaabbabbaaababbaabaababaaaaaabbabbbbbbbbababbbabbaabaaaabbbabababababaababbbabaaaaabbaabbbabaabbbbbbbaabbbbbbabbbaaabaabbbaaababbabaaaaaaabbbbbabaababbababaaababbaabbbbbaaababaabbbaaabaabbbabbaaabbabaaaaaaaaabaabbaaaabaabbaabaabaababaababbbaaabbabbaaabaabbbbbabbbbbaaabbbbbbbbbbbbababababbaaabaaababaaaaabbbaabbbbbabababbbaabaaaabbabbabababbbabbaaaaabababaabbaaaaaaabbabbaaaababbabbababbbbaabbabababaaaaaaaabaaabbabbaaaaaaabbbaabaaabababababbbabbbaaaabaaabbbbaaabaaababbaabbaaabbaaabaababaaababbbaabbaabbbaaabaaaabaababbbabbbabaaababbabaaabbabbbabaaaababbbbbaaabaabbbbaaabbaaaabbaaaaabbabbbbabaaaabbaababbababbabababbbabaabaaabaabaaaaabbbbbaaaabbbbbbaaabaaabaabababbabbbabababbabbbbbbabaaaaabbaababaaaabaabbababaaaabbabbaaabbbaaaaabbbabbaababbabaabaabbbababbabbabbabaaaabbabaaaaabbabababbbaaaabbaaaaaaaaabbaabaabbbbbabbababbbbaabbaabaaaaaababaaabbbabbbabababaaabbbbbbaabbaaababbabbbaaaababbbbbabbabaaaaabbabbaaaaabbbabaabbaabaaabbbababbababbabbbaabaaaabbbbbabaaaabbbaaabbbabbbbababbabaaabaabbbbaabbaaaabbbbbbabbbaaabaaaaabbbbbbbbbbabababaababbbbababbabbbbaabaaaababbabababbaaaabbbbaaaabaaaabababaabaababaababbabbbabbbbaababbbbaaaababaaaabaaaababaabaabbaaaaaabbbaaaaabaaaaabbabbbabaaaababbbaaaaaaabbaaaaaabaaabaababbabaabaaabbbaabbaabbaaaaababababaaaaaabaaababbbabbababababbbbbbabbabbbbbababbbbabbababbbabbabbabbbaaabbaabaababbbabbaababbabbaabbbbbbbbabbaabaaaaabaaabaaaabbabbbbbbaaaabaababaabbabbbabaaaabababaabbbaababaaaaaababbabbaababbaababaabbabababaaabbabbaabbbababbbbbabbaababbbabaabbababbaaaabbbbabaabbbbbbbaaabbbaaababaaaabbaabaabbbbaabbabaaabbbbabababbbabaababbbbabaabaaaabbbbabaabbaabbbaabaabaaaabbaaaaaababaabbbabbbaaabaaaabbbbaaaabbbaabaabaababbbabbbabbbaabbbbabbbbbaabbaabbbbbbaaabbbaabbbbbabbbbabbbbaabbaaaaaaabbaaaaaababaaabaabaaabbbaaabbbbababbabbbabbbbaabbabaabaaaaaaabbabbbbbbbaabaabbabbaabaababbbaabaaabbabbbababaaaaabaaabaaaaabbbbbabbbaabbbaababaaaabaaabbbbbababababbabababbabbababbabaaabbabbabbaaabaaaabaababbbaabbbabaababaaabbabbababbaabaabbbbbababaabbbaabbaabaababababbbbaabbabbbbbbabbabaabbbaaaababbaaaabbabbaabbbabaabaaaaabaababbaabababbbaaababbabbabbbabbabbabbbbaababbbaaabbbabbabbbabaaaaabaabbbbabaabbbabbabaaaabbabababbbbabababbbbabbaaabbbbaabbabbbaabbababbbaabbbbabbbaabababaabaababaabbaaaabbabaaaaaabbaabbbabbaabaaababbbbaaabbbabbbabababababbbabaaabbbaaaaaabababaaaaabbababbbaabaaabbaabbbababbabababababaabbbaaaabbabaaabbaaabbababbbbaabbbbaaabababaabbbabbaabbbabbababbbabaabaabaabbbaababaabbaabaabbbaabbbbaababbbabbaabbbbbabbaaabaaabbbbbbababaaabbbabbabbbbaabaaabaabbbbbabbbbbabababbbbbbabbbbbbaaabbabaaabababaabbaaabbbababaaaabbaaabbabbbaabbababaaabbbbaabababaabaaaabaaabaabaaabbabbabbbaabaabbabaabaababbabbbbaababbaabaaaababaabbabababbbaabaabbbbbabbabaabbbbbbbbbbabbababababbbbabbaabbbaaabbbbaababbababbbbbabababbbbabbaaaabbababbbaaabababaaabaababbbaabbbbbbbaabbbbbabbbbbaabbaaaababbbaaaaabbbabaabaabbbbbbbbaaaaaababaaabaabbbbaabaaabbbabbbbbabbaaabaaaaaaaababbaaabbaaaabbabaaaaabbbbbaabbbaabbaabbabbbbabbbaababaabbabaabababbbbbababbbbbaabbbbbbbbbbaaaabbabbaaabbaabaaabbbbaabbaabaaaabbabaaabbbbaabbabaaaabbabbaabaabaabbbabaabaaabaabaabaaabaaababaababbaaaaababbbabbbabbbbbabbaabbaabbbbabababbababaabbabbbababbbbbbababaabbbbbbaabbabbaabaababababbabbaabbaaababaaabbbbbbaabaabbaaababaaababababaabbbbaaaabbabbabaabaababbbbaabaabaabbababaaaaaaabaababbbbabbababbbabababaaabbbabbaaabbabbbbbababaabbaaaabbabbbbbabaabbabaabbbaabbbbbbaaabbbaaaabaaababaabbabbaaababbababbbbbabaabbaaabbaabbaaabbababbbbbaababbababaabbababbbabababbabbbabaaababaababbabaabbbbbbbaabbabbbabbbabababbabababbbbbabbababbaaaaabaabaaabbbabbbaaaabbaabbabbbbaabababbbabbbbabaaaaababaaaaaabbaaaabababaabbabbbbaaaaaaababababbbaaaaaaaaababbababbbaabaabaaabbbbabbbababbbbaabbbbbbbaababbabbababbbabbabbbaaaaababbbbaaabbaaababbabbbbaabbabbabaababbaaabbaaaababbbbaababaabbaaaabbabababbabaaabaababaabbbbbabbaaaaabbbbabbbbbaabbbaabbbabbabbbbbbaaaabbbabbbbbabbaababbaabbabaabababbaabbbabbaabbbbbbbbaaabaaabaaaabbaaabaaaabbababaababaabbbaababbbabbaaaabbbbabbbaabbaaaabbabbbabaabbaaaaaabaaaababbbabbbaaabbbbabaaaabaabbaabaaabbbaaabaababaaaaaaaaaaabbbaabbabbaabaaaaaabaabaaaabbabaaababaabbbaaaaababbababaaabbbbbaaaaaaabbababaabbbabbbbbbabbbbbabaababbbaaabbbbababbaaabbaabbbbbbbbabbbabbaababbbaabbbabbabaabaabbaabbbabbababaaaabbaaabbabaabbababbbaabbabbaaabbbbaabaabaaaaabbbbaaaabaabaabbbbbaabaaaaaaabbaaabbbabaabbbbabaaabbbbaabbbbaababbbaabbaabbaaabaaabbbbaabbaaaabbbaabaababbbabaaababaaaabbbaabbaaababbaabbaabbbaaaabbbaaaaabbbabaabababaababaaaaaababaaababbaaaababbaabbaabbbbaabbbabbbabaabaaaaabaabbababbbabaabbaaabbaabaabbbbabbaaabbabaabaabbaababbbaaabbabaaabaaababbbaabaabbaaabbabbbabbbaabababaaaaabaaaabbaaabbabaababaababbbbbabbbbabbbabbbbbbbabbabaababbaaaaabaaabbbabbaabbbaaabbabbaaaaaaaaabbbbababaaabaabbbababbbabbbbbbbbbbbaaaabbaabbbbbabbbaabbbabbbbaabaaaaabbbbabaaabbbbabbbbbaaaabbababbbabaaaabaabbbbaaababbaababaaabbbaabbaaabbbbabbabbaaababaabaaaabbaabbbabbbbbbbaaabbabbaababbbbaaabbbbbbaababbbbbabbbbbbbabbaaabbbbbbabbbbaabbaabbaaabbbbbaabbaabbabbbaaabaabbbbbbbabaababababbbabbbbabaaabbaabaaaaabbbbaabaabbabbaaabbbaaaabbaababaabaababbbbaabbabbabaaaaaaabababaaaabbbaaaaaababbbaabbabbabbbababbbbbabbabbabbabaabbaabbbabbbbbabbbbabbabbbaabbaabbabaabbbbabbaababaaaabbaaabbababbbbaaaabbbababbaaaabbbbaabaaabbaaaaaababbaaabbababbbaabaababbaabababbabbababababbbbbbabbbabaabbbbaaaabbaabaabaaaabbabbabbaabaaababbbaaabbabaabababaabaabaabababbabaaaaaaaaabaabaabababbaabbaaaaabbbbabbbabbaaaabbbaaaabbbababaaabbaaaaabbbabbabbbbbbbbababbbababbababaabbbbabababbbbabbbabaababababbbaaaabbbabbbbbaababbaaaabbaababbabbaabbaababaaaabbababbaabbabababaababbaaabbabaaabbbaababbbbabbbaabaaabbababbbbabaabbaaabbbbaabbbbaabababaabbabababbbaabbbbaaabbbabaaaabaaabbaaabbababbaabbbbaaabaabaababbbababbbabbaaabaaaababaabbbaabbbbbbaaabbaaabbaabbaaabaababbbbabbabaabbabaaaaabbbbaababbbbabaababbbbaabbaabaaaaaabbaabbaaabbbbaaaabaaabbabababbbbbbbbbababaabbbbbbaaabbbabaaaaabbbbabbbbaabbbabaaaaaabbbbabbbaabbbbbbbbaabbabaaaabbaabbbabbaaaaabbaabaababbbbbbaababbabababaabbbababbaaabbaabbbbbbbbababaaaaaabbbbaaaabaabaabaabbabbbbbabaabbbbaabbaabbbbaaabaabaaabbabbbbbbabababaaaaabababbbbaabababbbaabbbbabaabbabbabaabaaaabbabaaaabbbaababaabaaaaabababaabaaabaaabbaabbbbbabbbaabbabababbaaabbbbbbbbbaabaabbabababaaaaaabbbaabbabbbbaaaaabbbabbbabbaabbaaaaaababbbbaaaabbaaaabaaaaabbbbaaaaaaaabbaabbbbbbbbabbaaabbabbbaabaabbbabbbabbabbbabbbbaabbaaaaabaaabababaabbabababaaaaaaabaabaabbaabaabbabbbbaababaabbbabaaabaabaaaaaabaabbaabbaabbbbaabbbbbbbaaabbbbbbbbaababbbbabaaababaababababbabbbababbabbbbaabbaaabbaaababababbbbabaabaaaaababbbabaabbabbbaabaababbabbabaaaabbbabaaaaabbaaaaaaaababbabbabbabbbaaaaababbabbabbabbaabbaaabbbbaaabbababaabbbaabaabaaaabbabababbbababbabbabaaaaabbbbbbaabaaabbbaaabbabbbbbabbaaababaaaaaaaabaabbabaabbaaaaabbabbbbabaababaababbaababaaaaaababaaaabbabbbbbababbaabaaaabbbabaaabaabbaaabbbbaaababbbbaaabbabbbabbaabaabbabaabbaaaaabbabbabaabaaaaabababbabaabbbaabaaababbabbaabbaabbaabababbbaaaaabbaaaaabbbbaaaabaabbabbabaaaaabbbbbabaaaabbbbaaaabbbbaaaabbbaababbbababbbabababaaababaaaaaabaabbbaabaaabbababaaaabaabbaabaababbababaabbaabaabbaaaaabaaaaaabbbaabbabbabbbaabbabaaaabaaaabbbaabbabbabaaaaabaabbabaabaababaaaabababbbbbabbaaaabbbababbbbbbbabaabaababbababbbabbabbbbbabbababbbbabbabaabbaaabbbabaaaabbaabbbbaabaaabaaabbabaaaabaaaabaaaabaaabaabaaabaaaabbbbababbaaababbbbbabbbaabababbababaababaaabaabbabbbaabbabaababaaaaaaabbbbbbbabbbbbbabaaaaaaababbbabbabaabbbbabbbbbaabbbbabbbababbbababbaababaabaabbabaaabbbaaaabbbaabbbaabaaabaaaabbbaabbbbaaabaabbbabaaabbbabbaaababbaabbababbbbbbbbababaaabaababbabbbbbaababbbbaaaaabbababbaabbbababbabbbbabbbabbbbbbababaaaaabababaabababbbabbababaabbbabbbbabbbabbaaaaaaaaaaaaabababbbaabaaaaaabaaaabbabbaabbababbabaababbbaaaabaababbaabbabbbabbaabaabaaabbaaaaaaabbaabbbabbabaabaaaabbaabbaaabababbbbaaabbbbbaaaabaaabbbbbaabbbaabaaabbaaabbababbabaaaaababbababbbbaaabbaabbbaabaaabaaababbbbbabbbaabaaabbaaaaaabaabbbaabaaabbaaababbabbababbaabaaaabaaaaaabbabbaaaabbbabbaaaaaabaaabbaaaabaaaabaaaaaabbaaaaababbabbabaababaabaaaaabaaaaaaabbaabbbbabbaaaababaaababbbbbaabbbbbabbaabbaaabaaabaababbbaaaababbbaababbbbbaaaaaaaabbbaaaabbaabbabaaabababbbaaabaabaaaaabaabbbaaababbbaababbaaabbaabbbbaabaaaaabbbaabaaabaabaaabaabaabaabbaaabaababbbabbaaaaaaaaababaababbbbbbbbbbbaabbbbabbaaabbbbababbababaabbbaababbbbbbabbaabaaaaaabbaaabbaaaabaabaaabbaaaaabbbaabaaaaaabbabbbabaaaabaabbabaabbbbbabbbbabbbbaabaababbbbbbabbabbbababababbbbbbbbaabaabbaabbaaaaaababbabbabaababaabbbabbabaabaabababaabbbaababaababbbabaaaababbbbaaababbaabaaabbbaabbbbaaaaababbaaaaabababbbababbaaabaabbbbbaabaabaabbabaaaaaabaabbbaaaaababaaababbababaaababaabbbbaaaabaaaabaaaaabbabbaabababababaaaabaabbabaababbbaaaaaababbbbbaababaabaabbbabaaabbabbbbaaaabaabbbbbbbbbbbbaabababbabbabaaabbabbbbbbaabaabbaaabaaaabaaabbbaaaabaaaaaaaabbbababaaabbaabaabbaaaababaaaababbababaaaaabaababaaabbbabbbaabaabbbaaabaabbbbaaabababbabbbbabbabaaabaabaaaaaababaaabbabbbbbababbabbbaaaabbababaabbabbbbabbbaabbabbbaaabaaaaaaabbbbbbababbbabbaaabaabbaaabbbabaaabbbabaaaaaabababbbaabbbaabbbabaababababbbabababbbbaaabbbbbaabababaaabaaabaaabbbbbbaaaabaabbaaaaabbabbbabaaaaababbbabbabaabbabaababbabbaabaabbbbbbbaababaabbabaaababbaabbabaababbbaabbbbbbbabbabbaabbabbbbbbbbbbbaaaaabbbbaaaaabaababaabaaababbababbaabbbbabbbabbabbbbabaaabbaabaaabbabaababaaababaaabaaabbbbaabababaabbbbabababaabaababbbaababbbbabbabbbbabaaaabaaaaaaaabbaaabbbbbbaaaabbbababaaabbbbbbbbbabbabbaabbaaaabbaababbaabaaabbbabbbbabbabbbaabbbbabbbaabaabbaabaaaaaabbaababaaabbaabaabbaababbabaaaabaabbaabbbabababbbababaabababbabaabbabbababbaaaaabbababaaabababaaabaabbaaaabbbabababbabaabbabbaababaaaaaababaabaabbbbbaabbbababbbabbbbbbaaabbabbaaaabbbabbbbaabaabaabaabbaaabbaaaaabbbaabaaabbaabaaababaaaabbbabbabbbbabbabbababbaaabbaaaabbbbbbbaabababaaabbaabaaabaaaaabbaaaaaabbbabbbbbaaabbbaabbaaabababababbbbabbabbaaaabbabbaabaabaaaaabaabaabaaaaabbbbbabbbbaaaabbaaaababbbbbaaabbbaaababbbabbbabaaaaaabbbbbabaabbaabbaabbbababaabababbbbbbabbbaabbbaabbbaabaababaabbabbbbbbbaabababbbbaaabbabaabaaabbaabbbabbaabbaaabbbababaabbabbbaabbabaabababbbaaabbaaabbabaaaaaabbbaaaaababaaaaaabbabbaabbabbbaaaabababababbbaaaaabbbabaaaaaabaaaaaabbbbaaababababaaaaabbbaabaabaabbabababbbbbbbbabaababbbbabaabbaabbaababbbabbbaaabbaabbbababbbbabbaabbbaabbaabaaabaabbaaabbbbbbaaababbaaabaaaababbbbaabaaabbaaabbaaaabaaaaabbabbbaaabaabbbbbbaaabbaaababababababbbbbbbaabbabbbaababbababababbabbaaaaabbbbbabaaabaaaabbbbbaaaaababababaaababbbaaabaaabbaababbbbbbabaaaabaaaaaabbabaabababbaababbababababaabbbbbbaaabaabbabbbbbbbaabbaaaaabbabbbabbbbbbabaabbabbbbbabaabaaabbabbabbaaaaaababaabbaaaabbabbbbbbbbabbbabaabbaaabbbbaaaabbabaabbabaabbaababaabbabbaababbbbaaaabbababaabaaabbbbbbabbbbbabbaabbbabbbaaaabbbbababbbaaababababaaaababbababaaaabaaaabbbbaaaabbaabbabbaaaaabaaaababaaaababaababbababaaaabbaaabbbabaabaabbbbbbbbbabbbabbababbaaabababbabbababbaabaaaaababbaaaaaababbbbbbbbabaaaaabbaaaabbbaaaaabbbbabbbaababaabababbbbabbbbbaabbaababbbaaabaabaaaabbaaabababaaabababaaaaaababbbaabaabbaabbbbaabaabbaaabbbbaabbabbaabaabbbbabbbaabbaabbabaababbbbaabaaabbbaaabbababbbaaaabbbbbaabbabaabbabaaabbbaababaabbbbaaaaaaabababaababbabaaaaaabbaababbabaaaabbaaabbbbaabbabaaaaaaaabbabbbbbbabbaabbbabbbaaaababbbabbbabbbaaaabbababaaabbbaabbbaaaaaaaaabbbbabbbbbababbbabababbbabaaababbaaabbababbaababababbbbababbabaabaabbabaaabababbbbbaaaabaaababbabbaaabbbaaaaababbabbbababbaaaaaababbaaaabbabaababbabbbbabaabbbbaaabbbabaaaaaababaaabbbaaabaaabababbbabaaabaaaaaabbbabbbbbabbababbbbbbbabbbabababbbbaaabbabbaaabaabbbbabbaabbbabaaaabaabbbababbbaaaaabaabbbbbaabbaaaaabaaaabbbaaabaababaabbbaabbbabaaaaaabbbaaabaababbbaabaaaaabaaababbaabaaaaabbaabaaabbbabaababbaaabbababbbabbbabbbbbbbbaabaabbaaabaabababbaaaaaaabbabbbbbbbaaaabaabbaaabbaaabbaaabbabbaaabaabbaaababbabbabaaaababbaabbbaabbabbbabaababaaaabbbbaaaaabaabbbbaaaaabbaaabbbaaaabaaaabaabbababaaabaaaabbaaabbbaaaabababaaaababaabaabbabbabaaabbbbbbaababbaaabaabbbbabababbaabababbbbbabaababbabbbaabababbabaabaabababaabbbabababbbbbabaabbbbaaaabbabababbabbabbbabaabababbbaabaaaabbbbabaabaabaaaaababababbbbbbabbbbabbbabaabbbabababaaaababaaaabaabaaaabbababbbbbaabaaaabaabbbbbaaaabbbabababbbbbabbaaabaaaabbbbaabababbbaaaababbabbbaabaabbaaaaaaaaabbbaabbabbbbabbaabbabbbaaabaababbabaaabaabbabbbbbabbbaabaaabaaaaaababaaabbaaaabbabbbbbababbbbbaabaaaabaabbaaabaabbaabbbbababbaaabbabaabbbaaabbbbbaabbbbabaabbbbbbaaaabaaababbaaabaaabbbabbaabbababaaabaabaaaaabbabbbabababbabaabbbaaabaabbabaabaabbbbabbbbabbbbbbbbabaabababbabbbbbbabbbabaaaaababaaabbabababaaaabbabaabaabbbababbababbbaabbaaabbbbababababaabbaaaabbabbbaaaababaaababaaabaabaaaabaabbbaabbaabbabaabbaabbabbbaaaabbabbbbbaababbabbabbbbaaababbbbbababaaaaaabbbbbbaaabaabaaaabbbaaaaaaaabaabbbababaaaabbaabbabaababaaabbabaaabbaaaaababababbbaaabbabbbbbbaaaaabaababababbbbaabaabbbbaabbbabbbabbbababaabbababbabbbbbbbbababbbbabababbbabaabaabaaabbabbababaabaaaabbbbbabaaabbbbabababbababbabbbaaabbbbbaaabaaaabbaaaabbababababbbaabbababaabbaaaaabbbaabbababbaabbaaababbaabaabababbbaaaabbbaaaaaabbabbbbaabbabaaabaaababaabbbbabbabbbbabbbbaaabbbabbbbaaaaaaaababbaababaabbabaabbabbaabbbaabbbabaababbaaabaaaaabbbabbbababbbabbbbbbbaaababbaababaaababaababaabbbbaabbbabbbbaabaaabbbaaaaabaaababaaaaabaabaababababaaaaabbbababbbbabaabbababaaababaababbabbbaababbaabbbbbabaabbabaaaabaabbabbaaabbbbbabbbbbaaaaaaaaabbbbaababbabbbbabaabbabababbabababbabbaaababbaababaaabbbaaaaabaababbaababaaaabbaaabbabaabaababbaaababaaaabbabbaabaabbabbaabbabababbaaaaababbaabaabbabbbbbaaaaaabbaaaaaaaabaabbabaabaaaabbaabbababaaabababbbaaabaababbabbbbaaabbbabbbbbbbabbaaaabbabaaaabaaababbaabaaaabbbbbbbbbbbbbababbaabaabbbabbbaabaabbbbbbbbbbbbaaabbabbbaaaabbaaabaababbbbbaaabababaaababbbbaabbbabababbaaabaaabaabbbbabbbbaaabbaaaaaabbabaabbbbbabbbaabaabababaaabababaabbaaaaaabaaabbababbabbbaabbaabbaababaaabbbbbbbbaaababbaaabbababbaabbbbabaaaabbbbbbaaabbabaababbbbbaabaaaabbabbbabbabbbbabbaabababbaaaaaabbbaaaaaaaabbabbbabababaaabaabaaabbabababababbbabaabbabbbbbbbbbabbbbabbabababbaababbababbbaaababbbabbbbaaaaababbbaaabaabaababaabbabbabbbbbbbbababbbabaabaaaaababbbbbbaabaaababbbbbbaaaababbabaabbbabbaaaabababbbbaabaaaaababbaabbbbbabbabaabaababbbbaaabbabbbbbbaaaabbbbaabaabbbabaababbbabaaababbabbbbaaababaaabbabaaaaaabbbbaabbabbabaaaabbbaabbaaaabaabbbbaabbbbabababbaaaababbbbbbbabbbbbbaabbaaabbaaababbaabababaaaaaaaabaabaabbbabaabbababaabaaabbabbbaaaaabaabbaaabaaabbaabaabaabbabbaaaaabbaaabbbbbaaabbbbbabbabaaabbaabbbbaabbbbbabbabababbaabbababbaabbaaabaaaabbbbaabaabbabbbbaaabbaaabbbbabbbabbbbabaabbaaabaaaababbbababbabbbbbaabaabbbababbaabaaabbbbababbbaaaaaabbbbbbabaaabbbabbbababaabbbababbbabaaabbbbababababbabaaaaabaaaabbaaababbbaaabbbbabbbbaabaabbabbbaaababbbabbaaaaabaaaaabbbaababaaaabbbbbbabaabaaabababbbaaaaaababbbbbaababaaababbabbbbbaaaaaabaabaaababbbaababbbbaababaabbabbaaababbabbababbbaabaabbaababbbbbaaaaaabaabbbabbaabbbbabbbabbabbabbbbbaabbaabaabbababaaaabaabaabaababbbabbaaabaaabaabbbaaabaabaaaaaaabaaaaaaaaababaabbaaaabbababaaabaaabbbaababaabbabbabbaabbabaaaaabbabbaabbabbbbabaabaabbbbbbbbbaabbabbbaababbabaaabbaababbaaabbbaaaabaabbbabbabababbbbbbaaaabbabbababababaabbbbbbbbbbbabaaaabaaababbbbbbaabbbaaababbababbbabbaaababbbbaaaabbbbababaaabbbbbbbbaaabbbbabaaababbbabbaabaaaabbabaabbbaabbbbbbaabbbbabbaabbaababbbaabbbabbbaaaabbaaaabaaabaaaaaabaababbbbabbaabbaabaabbbbaaaabababaaabbaaaaaaababbbbaaabaaababaabaabaaaaaaaababaaabbbaabbbaabbaaabbbbbaabbaabaababbbbbaaabaaaabaaabbbaaaabbbbabaaabababaababbbbabbabaaababaabbabaabbabbbbaaaaabababbaaaaabbbbaaabaabbbbbbaabbbabaabbbabbabaaaaaaabababbaabbbbaabbaaaabaabaabaabaaabbbaabaaaabbabbbbabbbbaaabbabbaaaabbabaababbbbbabaabbaabababbabaaaaaaaaaababaabbbaaabaaaaaababbbabbaaababbbbaaabaaaaaaabbbababaabaaabaababbbaababaaaababaabaabaaaaaaaabbbaabaabbbbbbabaaabaaaaabbaabbaababbbbabbabbabababbababbaaaaaabbaababaaaabaaabbbbbbaababbaaaababaabaaaabbbabbaaaabbbabaababbbbbaaabaaabbababbbbbaabaaabbbaababababbabbbaabbababbbbaaabbabbababbbbbbababaaabbbbabaaaaaabaaaaabaaabababaabbaabbabbbbabbaabaaabababbbbbbaaaababbbbbabbbbbabbbabaabaabababbabaabababaaababaaaaaaabbabababbbabbabbaaaaabbbbaaaabaabbbbabbaabbaabbabbbbababbabaabbbaabbbbaabaaabaabbababbaabbbaabbbbbaabaaaabbabaaabaaaaabbbbabaabbaaaaaaabbbbaaaaaaaaaabbbabbabbaaaaaaabaaaaababababaaabbabaabaaababbaaabbbbbbaabaaaaaaaaabaaababaaabbbabbaabbbaaaaaabbbaaaaabaabbabbbbabbaabbbbaaabbbabaaabbabababbbaababbababbabaabbbabbbaaaaaaabbababbbabaababbaaaabaaaabbabbabbabaaaaabbbabbbababababaaabaaaaaabbbabbaaabaaabbbbbabbbbbabbbaabbbbbbaabbabababbababaabbaaabaabaabaaabababbaababbababbaaaaaabbbbbaabbbabbbbababababaabbababbabbbbaaabaaaaabaaaabaababbaaababbaabbbabbaababaabbababbbbaabbbabbbbbbaabaaaaabbaaababaaaababbabaabbbbabbbbaabbbababbbbaaaaabaaabaabaababaaabaababaaaaabbabaabaababbbbbbabaaababbbabbaaababaaaabaaabbaaabaabbbbbbbbbabbaaababbaaababbaabaabaabbabbabbaabaaaabbabaabbbbbbbbabbababbbbbbbababaaabaabbabbabbaaaabbaabbabaabbabbaababababbabaaabaaabaababbbabbbabbbabbaabbbabaaabbababaabaabaabaaababaaaabaaaaaaaaababbaabaaaaaaabbbaaabbbbbaabbbabbbbbaaaaababbbbaabaabaaaabbababbbaabaaabaaababbbabaaaaaabaababbababbbbaaaabbaabbababbaaabbabbbabbbbbbabbbababbaaaabaabbbbabbbbabbbbaabaababbbbababbaaabbbbbbbbbaabbbaaabaaabbabababbbbabaababbbbbbbbbbaababbbbabbaaabbbabbbabbbbbbaabababbbaaaabaababaabbabbabababbabbaabbabbabaababbbaababbaaaaaabaaabbabbaabbabbbbbbaaabaabababbbabbbbbaabbbbbbaabaaabababbbabbbabbbabbbbbaaaabaaabababbbaababaabbaababbbabbbbaaabbbabbbbaaaaabbbabaabaabaabaababbbbbabababaaabbbbbbbbbabbbbbbababbaabbbaababaaabbbbabaaaabaaaabaabbbbbabbbaaaabbabbbaaabbaaabaaaabbbbaaaaaaaaaabbbaabbbbbbaabaaaaababaaaabbbaabbaaaabaaabbbbbaabaaabbbaabaaabaabbaaaabbababaaaaaabbbaababbaaabaaabbbbaaababbaabbbaabbbabbbbbbbaaababbabbbbbabaaaaaabaabbbaabaaaaabbbbbbabaaaabbbbbaaaaaababbabaaabbbaaaaaabbbbaaabaabaabaaaabaaaaaabaaabbaaaaaabbbabaabbbbbbabbaabababbbaaabbaabbbaabbbaaababaaababbbaabaababbbaabbbabaaaabaababaabbbabbbbbaabbbbabbabababbabbabaaaaaabbbabbbaabbaaaaabbbbbbbaaabbaabaaaaaabaabbbbaaaabbbababbbaaaaabbabaaabbaaabbbaaaaabaabbabbabbbaaaaaaabbbbbaabaaabaabbaabababbabababaabaabaabaaabaaababaabaababbbbbbabababaababbabbaabaabaabaabbabaabbbbaabaababaabbabaabbaaaaabbabaaabaabaabaabbbaaababaaaababaababaaaaaaabbabbbabbabbbbbabbaabaabbabbbaabbabaaaabbbbaabaaababbbbbaabaaaaaaaaaabaabbbbbbaababbabbaaaaaabbbbbbbabaabbaaababbabbaabbaabbaabaaababaabbaaaabbbbbaababbabbbaaabbbbabbbabaaaaabbabababaabbbababbbaabbbbababbbabaabbabaaaabbbbabaababbbaabbbbbabbbabbaaaababbabbaaaaababbababbabbbbbababaaababaaabbbbbbbaabaabbabbabbbbbbbbabaaaaaaabbabbaaabbaabaabaababbbbbbaabbabbbaabaaababbbbbaabbbabbabaabbbbbaaababbaabaababaaaaabbaaababbbaaababbaaabababbaabaabaaababbbabbbabbaabbabbbaaabaaaaaaaaaaabaabbabbbbabbababbbbaaaabaabaaababbaaaaabbbbbabbaabaaaaabbbabbbaaabbbabbabbaabaabaabbaabbabbbaabbabbaababaabbaabbbbaabbbaababbabaaaabaaaabbaabaabbabaabaabbbbbaabbbabaaaaababbbaabaababbabbbabbbbbbbbbbabaaabbbbbaaaaabbbbaabaaaabbbbbbabbbababaaaabbbaaaaabbaaaaababaaabbababaabbbbbabbaabbbabbbbbbaaaaabaabababaaababbbabbbabbaabbaabbbababaabbaaabababaabbbbbbbbbaabaaabbaaabbbbaaaaaabaababababaabbbaabbbabbbbbabbaabbbaabbabbabaaaaabbababbabaabaabaaabaabbaabaababaababbbaabbbaabaabbaaabaabbbabbbaababbaabbaababbababbbbbbbaabaaabbaabababbabbababbbbaabbaabbabbaababbaabbbabbaabbabbbbabaabbbbabbbbabbbbabaabbbabaaabbaababaabaabababbaabaabbbbaaaabbbabbbaabbabbaaaababbbbababababbbbbaabbabaaaabbaaabbaabababbbbbbabaabbbaaabbbabbbaabaabaabababbaabababbbaaabaababbbabbabaaaaaaaabbaabababbabbaabbababbbbabbbbaaaaaabababbabaabbaaaaabbaaaaaabbbbabbbbbaabbbbabaabababbabbbbbbbbbabbbaabaababaaaaababababaaababbabaabaaaababaabbaaaaaabaabababaabaaaababaabbbbababbbaabbbbbabaabaaabaaaabaabaaaaaabaabaababbabbabbbbabaaabbabbaaaaaaabaabbbbabbbbbaabaabababbbbabaaaaaaabbaabbabaaaaababababbaaabaaaabababbabaaaaaabbbaabaaaabababbbaabbabbaaabbaababbbababbbbaabaaababbbbaaabababaaababbbbababbababbaabbaabbabbbabbbabbaaaaaaaaababbabbabaababbbaaabbbbaabbabaaabbabbbabbbabaabbbaabbaabbaabbaaabbaabbbaabbaaabaaabbbabbbbbbbabaaabababbbbbbabbabaabaabbbbaabbabaaabbabbbaabaabbbbaababababbbaabbbabbbbaaaaaaaaaabbababbaababbbbbbbbabbbaababbabbbaabbaaabbaabbbaaaabbbbbbaaaabbaaababaaaaaaaababbababbbaaababbabbaabaabbaabaabaabbaabbabbbaabaabbababaabbaaabbaabbbbaaaaabaabbbabbabbbbaaaabbbaaaabbabbabbbbbabbbbabababaabbbaaaababbbbbaabaabbbaaababaabbabbbbbbaaabaabbbaaaaaabbababbaaabaababababbbbababaaabbabaabaabbabbbabbababbbbaaaaaabbbaababaaabbbabbaabbbbaabaabaaaabaaaabaaaababbaababaaaaaabaaabbbaaabaaaababbbbaabababbbbaabbababaabababaaaabbabbbbabbbbaaaaaaabbaaaabbbaaaaabbbaabbbbbaabbaaaabababbbbaaabbabbbbbbabbbbbaaaaabbabbbbaaaaabbabbbbbbabbaaabbbbabababbabaabaaabababaaabbabbabbaaaabaaabbbaaabbbabbaaabaabbbababbaaaaabbababbaababaaabbbbabbaabbbbbbaabbbabbbbbbababbbaabbbabbababbaabbaaabababbbaaabbbaabbbababaaaabbbbabbbbbbaabaaaabbaababbabaaabaabbbaabbaabbbabaabbaaabaababbbaaabbbabababbbaabaaabbbaaababbbabbaaaaabaaaababbabbaaaabaaabbbbaababbbaabbbbbbbbaabababababbaababbabbbbbaaabaaaababbbaaabbaabbaaaaabaabaaabbaaaaabababbbbabbbabbaabbbbbbbabbbabbbabbaabbbaababbbbabaaabbabbbaaabbbabbababbabbaaababaabbbbbbaababbbaabbababababbaaaaaababbbbaaaabbababbbababbaaaabbbaabaaaabbaaabababbaaaabbbbaabaaababbbbabaabbaabaaabbbbaabaaabbabaaabaabbbaaaabbbababbaaabbbabbabbaabbabbabaabbbabaaabbababbbababaabbbbbbabababbabbaababaaabbbbbaabbbbbababaaaabbbbababbbabbaabaabaaaabbaaabbbbbbbbaaabbbbaaabbabbbabbbaaabaabbbabbbabbbbaaabbaabababaaaabbbbaabbaaaaaabababbaababaaaaabbbbbbabbabbbaabaaaaabaabbabbbbabbbbbbbabaaababbaabbabbabbbbaabbababaabbaaaabaabbaabbbbbbbaaaaabaaaabbabbaabaaabbabababbbabbbabbaaaaababbaaababaaaabbabbbbbababababbaabbbbabaaaababbbaabbaaaabbabaabbbbabbaaaabbaaaabababbbbabbbbabaabaababbaabbbaabbbbbaaabaabaaabbbabbabbaaaabbaabababbbbabbaabbbaaaaaabaabbbaabbaabaabababbabbbaabbbaaaaabbbbbabaaaaabbaaaabbbabababbbbabaaabbaaaaabbabaaabbabbbabbbbbbaaaabbaababbbbbbbabbabbbababababbabbabbabaabbbabbaaabaaaabbaabababaabaabbabbbbbaababaaabbbabbaaaaaaabbababaaaaabaababbabbbaaaabaababaabbaabbababbbabaaabaabbbababbaaabaaabaaabbbbbaaaaababaaabbabaabbaaaabbababababbbabbabbababbbbbbbbbabbabbbbbbababaaaaaaabaaaaabaabbbabaaababaabbbbbbabbaaababbaaabaaabbbbbaaabaabababbabaaaabbaababbbaaabbbbaaabaaaaabaabaaabbaaabbabaaaaaaabbaaabaaaabaaabaaabaaabbaababaaaababababababaababbbabaabbbababababaabbbabaabbbbbbabbababaaabbabaabaaabaabbbbbabaabbbbbabaaaaaabaaababaaaaabaaababaabbbaaabbbbabbbbbabaabbababbaabbaaaaaabaaaaaaabbaaabbbbaabbaabbaabaabaaaaaaabbbbababbbbabbbabaababbbbbaaabbabbabaabbaaaaabbaaaabbaababaabbbbababbabbaabaaabbbabaaabbaababbbbbaabaabaabaaabbababbabbaaaaababaababbbaabbabaabbbbaaabbababbbbaababbabbaabbbababbaaaaababbbbbabababaaaaaabbaabbaaaabaaaabaaabababbabababaabababbababbabbababbbaaabbabbbaaababaabbbbababbbabaabababbbabbbabbbbbbbabbabbbbababbaaababbaababbaabaaabbbbabbabaabbaaababbaabbabbabbaaabbabaaaabbbabbaabbbbaabbabababbaabbabaabaabbabbababbbaababaabaaaabbaabbbababababbaaabababbbabbabbaabbbbaaabaaababbbaaababbabbaabbbaaaabaabababaabaababbbbbabbbaabaabaaaababaaaaaabbbbbabaaaaaabaabababbbabbaabababababaaabbbaaabbaabaaababbbaaababaabbbabaaabbbabaababbababbbababaababbabababbbabbabaabaababbbbbbaababaabbbaabbbbaabbbbabbaaabaabbbaaaabbbbbbabaabbbbbbbbaabbbaabaabababbbbbaaaababbaaabbabaaabbaaaaaabbbabaaababaaaabbbbbaabbbbbaabbaabbbabaaaabbaabaababbaababaababaabbbaabaaaaababbaaababbaabbbabbaabbaabbbaabaaababbbbaababbbababaababbaaaaaaaaaaaaabbbababbbbbbaaabbaabbbabbabaabaaaaabababbbaaabaabbabbaabbabaaabbbababbaabbbaabbabaababbbbaaaaaabbbbaaaabbabbaabbabaabaaababbbaabaaabaaabbbbbbabbbaaabbbbababaaabbbbbbbabbbaabbbbbaabbaababababbaabbbabaababaaaabaabbabbaababababababaababaabbbbbabaaaaaabbbbaabbbbababbaaaabbabaababbbbabababababbbababbabbbabbbaababaabaaaaaabaabbbaaabbaabbabababaaaaabbaababaabbaaaaababababbaabbaabbbabbbbababbbbabaaabbbbaaabbbabbbaababbbbabbbbaaaabaabbbbbabbbbababbbbbaaabbbabbbbaaabbaaaaabbababaaaaabbabaabaababaaabbbbabbaaaabaaabbaabaaabababaababbaabbbababaabbbaabbaabbababaaaabbababaaaaaabaabababababaabbabaabaaababaaabbbbbbaaaabaaaabaabbbabaabaabbaabbbaabababbabaaaabbbbababaabbabbaaababbbabaabaabbabbabaabbaabbbbabaaaabbabbbaabaaaaaabbaaabaaabbbbababaabbbbababbbbaaabbaaabbaaababbaaaaabaaaaabaaababbaaaaaabaabbabbaaabaabaabbabbbaabaabaabbbababbbbaaaaababbabaabbaabbbabbbabbaabaabbaabaabbbaababbbaaabaaaabaabbabaaabbbbbaababbabbaabaaaabbabaaabbabbbaaaabbbbbbabaaaaabbbbabaabbbaababababbaaababaaabbababbaabbababbbbabbbaaabbaabbbaaabaabbbaaaaabbababbababbbababababbbaaaaabbaaaaababaabbbabbbbbabababbabbaaabaaabbaabaaababbabbabbbababbbabbaabbbaaabbbabbababbbaabbaabbbaabaabaaabbabbabbabbbbaabaabbaaabaaaaaabbbbbbaabbbbaababbbaaaaabbaabbaaabababaaaabbaaabbaabbbabbbabbabbbababaaaabaaaaabbaabbababaabbbabbabaaaaaabbbbbbababbabbabbbaaaaaabbabbbbaaaabbbbaabbbabbabbaabababaaaaaaaaaaaabbabaabbbbbbaabbabbbaabaabaabbbbbbbbbbabbbaaaabaaabaaabbbbabaabbaabababaababbbbaabbaababaaaabababbaaabaaabaabbabaababbaaaabbaaabbaaaabbbababbaabaabaabbabbbbbbbbbbaabaabbaaabababbbaabaabaaaaabbbaaabbaaabbbbaaababbaabababaabababbaaaaaaababbbbbabbbbbabaabbaabbaaaaaaababaaababaabababaaabaaaaaabababbbbbbbabaaaaabaababaabaaaaaabbaaabaaababaaaaaaaaaabbabaababbaabbbaabaabababaaabbbbbaabaabbaabbbabbaabaaabbbbabbbbaabaabbbbaabababaabaaaaabaabbabbabaabbbbababbbaaabbbaababbbbbaabababbaaaaabaaaabbbbaaababbbaaaababbbbbabababaabbaabbbbbaaaaaabbbabbabbbababbbabaabbbaaabbaabbbabbbabbabababababaaaabbaababbbaaaaaaaaaabaabbbbbbbbbaaabaaabaaaabaaabaabbaaabbaaabaaaabaababbaababbbbbabbaabbbbbbabbabbaabbbbbaabbbbaabaabaaaabababaabbbbababababaababaaaaaabaabbbbbaabbbbaaaaaaaabbbbaabbbaabaaabbababbbbaaabbbbbaaabbaaaabbbababaaababbaaababaababbbabbbaabbbaabbabaabaababbbbbaaaaabbabbbbbaabbbbbaabbaababbbbaabbaaabbbaaaababbbbbbaaaabbabababaababaaaaaaabbaabaabbbababaaababbbaaabbbbaabbbbbaababaaabbababbaabaaabbbaabaabbbabbbbaaaaaabbababbabbababbabaaabaabbababbbbbaaababbbbbaaaababbaaaababaabababaabbaabababbbabbbabbbbabbaabaabbaabbbbbbaabbbabaabababbbabbabaababaabbaaaabaabaabaaaaabbbbbbabbbabbabbaabaabababaabbbabbabbabaabbabaabbbbbaaaaaabaababbbbababaabaabbbaabbbbbaaabaababbbbabbbbabbabbbaababaaaaaaabbaaabaabbbaaabbbbaababbbaaababbbabaaaabbbabbbabaaabaabbbbbbabbaaabbabbbbaaababbabbaaabababaaaabaaaaaabbbbbbbabaaabbbababbbbababbbaaabbababababbabbabbaabaabbababababbbabbbbbbbaababaaaabaabbbbaabbabaaababababaaaaaaaabaabbbabbbabaabbaabbbbbababbaaaaabaabbabbbabbbbabaabbbaaaaaabaababbaaabababbbbaaaabaabaaabaabbababbbbabbbaabbbbabbbaaabaabbbabbbaabbababbbbaaaaaabbbabaaabbaabbabbabbbbbbabaabaabbbbbaabbbbbbbbbaabaaaaaababbbbbbaabbbaababaaabbbbabbaaaabbbbabaababaaaabbabbbaabbbabbaabaabbaaabaabbbaabbbabbaaaaababaaaaabbabaabaaaabaaabbbabbabaabbbbbaaaaabaabababababaabbbbbabaabababbabbbbbbaaabbabbaabbabbabbbaabababaabbabbbbaababbaaaabbbbaaaaaaababbbbaabaabaaaababaabababaabbbaaababbababbbbabbaaaabbabaababbabaabaaabaaaaaabbabaabbabaaaabbaaabbabbbbaaababbabaaaaabaabbaaaaaababbbbbaaabaaaaabbaaabbaabbabbaaaaaababbaabbaaabbbabababaabababbaaaaaaabaaabaabbabbaaaabbbbabaabbabbbbbbbabbbbaaabbabbabbaabbbaabaabaaabaabbbabbaabbaababaabbaaaaaaaaabbbaabaabbbbaabbabbbaabbabaabbbbbabababaabbabababaaaabbbaaaaabbabaaabaaabaabaabaabbbaabbaaababaabbabbbaaababbbbbbaaaaaabbbaaaaabbaaabaababaaaabababaabbbbbababbabbabbbbbbaaabbabbabbabbbabbaaaaabbbbaaabbabbaabbabbbaaabaabaaaaaaabbbbbbaababbaabaabaaaaaaaabaabbbbaabbbbbabaabbbaabbabaabbaaaaaaaabaaaabaaabbbabbbaaaabbbbaaabbabbabbbbbaabbbbbbbababaabbbaaaaabaaabaabaabbbbaaaaabababbaaabababbabaabaabaabbaaaabbbabaabbbabbbbaababbabbbbbbabbaaabaaaaaabbabbaaabbbaabbabbabbaaababaabaabbabbaabaababbaabbabbabaaabbabababbbbaabaabababbaaaaaaabaabababaaababaabaaabaabbabaabbaaaaabaaabababaaaaaaaabbbbbbaaaababbbbbaabababbbbabbabaabbabbaaaaabbaabaaaaaaaaabbbbabbaabbaabbaabaaaaaaaaaabbbbbabbbaaaaababaabbabbaabaaabbbabbbabbababbabaababbbbaababbbbaabbbabbbbabaaabbbbaaabbbbbabbaaabaabbaababbababbaaabbbbbabbbabbaaaabbbbababaaababbbaababbbaabbbaabbaabbaabbbbbbbbabbbaabaaaaababaababaaaaabaaaaaaaabbbbabbbbbabaabbaaabaaaaabbaaaaaabababbbaaabbbbbbaabbaaabaabaaaababbabbbabbababbabbaabaabbbaabbabaaababbaabaabbbbbaaabbababbaaabbaaaaaabaaaaaaaaaaababaabbbbbbabaaaabbaabaabbbaabbbbaabbbaaababbbababaabaabbbbaabababbbaabbaaaababbbaaabaabbaaababaababbabbabaabaaabaaabbaaaabaaaabaababbabbbaaabaaaabbbbbbbaababbbbaaaaaaabbabaaaaabbbababbaaababbaaababbbababbabbbbbabbbaaabaabbbaaaabbbbaaaaabaabaabbbaabaaaaabbbaaabbaababbbbbbbabbbbabaaabbbbbbbbabbabbbbaaaabbaaabbabbbabababaabbbabaabaaababbbaabababaabbabaaaaabbaabbbabbaabaaabaabaaaabbababbbabaaaababaabbabbbbaabaaabababaabbbbbabbababaaaabbbabaababbbababaaabbbbbbbabbabbbbaabababaabaabbaaababaaabbaabbaaabaaaababbabababbaabaaaabbabaaaaaabbbaabbbaaababaababbabbbbabbbababaaaabbbbaabbbbaababbabababbbbbbbabbaabbbaaabbaabbbbabbaabbbabbaababbbabbaabbbabaababbabbababbbbabbbbbaaabababbaaaaaababababbababaabababbbbabbababbaaabbabbbabbabbaabbabbbbaaabbbaabaabaaabbbaabababbabaaaaababbabaaaaaabbabaaabaabababbbbabbbbaaaabaaabababbabbaabaaaaaaabbaabababaaaabbbbbbbabaabbaababaaaabbababbbabaaaabbbaabaabbbaabaaabbabaaabbbbabbabbbaabbbbaabbbbbbbbaaabbaabaaababaaababaabbaabbababaaaaabaaaaababaabbaaaabbbaababaaabbbbaabaabbbabbabbbbaaabaaaabbaaababbababbababbbbbbaabaabaaaababbbabbabaaabbbababbbbbaaababaaaaabbabaabaabababbabaaabbbabbbabbbbaaabbbbbbaaaaabaaaababbaabbbaaaaaabbababbbbbbbabbabbbbbabaabbabaababbabbaaaaaabaaaabaabbbaaabbbbaaaabbaaabaaaabbaabaaabbbabaababaabbbaaababaabaabbababaaabbbaabbbabbbaaabaabbbbbaabbbabaabaababbabbbaaaaaabaaaaaabbaabaabbbabbbbaaabbababbabaababbaaabaababaabaabbaaaababbbbbbbabbaababbbbbabbaabaaabbbabbbaaaaabbbababbaabbbabbbbaabbbbbbbababbbababbbbbaaabbbbabbaabbabaaababaaaabbbaababbabbabbbbaabaabaababaaababbababaababaaaabbbabbababbababbbbabbbabaabbaaaabbbbbbabbbaabbbbbbbbbbbaabbbabbbabbbbababbababbbbbaabbababaababbabaabaaababbababbaabaaaaaabaaabaabbbabbababbbabaaabbbabaababbbaabaaabbbaabbbbbbbbabbbabababababbbbbbaaabaaaabbaaababbbaabaaaabaababbbabbabaabababaaabaaabababababaaabbaaaaaababbaaaaababbbbaaaaabbbbabaaabaaaabbabaaabaabaabbbbbabbabaabbbbabaabbbababbbbababbaaabbabbaaaaabbbabaaabbbbbbabbabbbabbbaababbbabbabaaabbabbabbbaaaaaaabaabbbaaaababbbabbaabaababbabaaaaaaababbbbbbbbabbbaaaabbaaabaaabababababbaabbabbaaabbabaabbbaababbbbabaabaabbaabbbaabbbbbbaabbabababbbbbaabaaaabbbbaabbbbaabaaaabbaaabbbbaaababbbaabbbbabaabbbbaabbaabaabbbbbbbbbbbaabbbaabbaaaabbbbabbabaabaabbabababbabaabaaabbbbababbbbbbbabbaaaabababaaabbaabbababbbabbabaabaababbbbaabbbbbbaaaaababbbaaaaabbabbabbbabbbbaabbaababbbbaaaababbabaaabaabbaaaaaaaabbababaaaabbababbbbabaabbbbababbaaabaabaabbbbaaaaaabbbbaaaabbabbabaaabaabaabbbababaaababaaabbaaababaaababaabaaabbbaabaaaabbabaaaababaabbaabbaabbaababababbbaabaabbababababbbababbbaabbbbbababababababbaaaaabaaabbaabbabbabbbaaaabaaabaabaaaaaaabbbbabbababbbbbabbbbaaabbaabbbaabbbabbabbabbbabaabbababbaabbabbaaaabbabbaaaababaabababaabaabababbbbaabaabaabbbbababaabbbaaaaaabababbbbabbababbbbababaababaaaaabbaaaabaaaababbababbaaabbbabbaababababbbbbbbaabaabbbbaaaabbaabaaaaababaabbaabaaaaaaaaabbbabbbaaaaabababaaababbababbaabbbabbaaababbaabbabababaaabaaaaaaaaaaabbbaaabaaaaabbbaabaaabbababbbbbbabbabbaabbaabbaaaaaabaaaaaababbabbbaabbabbaabababaaabbaaabaabaababbbabbbabbbabbababbbbbbbbaabbbaaababbaabaabbbaabbababaabbbabbbaababababaabbbbbbabbbaaabaababbaabbaabbbbbbaaaaaabbabbaabababbaababaabaaabbbbabbaabbbaabbaaabbababbbbbbaababaababbbbbababaababaabababbaaabbabbbbaabbbaabbbbbbaabaabababaaababbbbbaaabaaaaabbabbbbaaaaaabababbbbbbbaabbbbbabbabbaaaaaaaaaaaaabbbaabbabbaabababbaaaaabbaaababaabbaabbaaaaaaabbaaabaaabbbbbaaabbababababaabaabbababbabbbbbabbabbabbbabbbbabbaaabbaaabbbaabababaaaaaabbbbbbabaaaaabbbbabbabbababbaabababaaabbabbabbbabbbbbbbabbbbbaaaaababababbabaaabaaaabbbababbaabbbaababaabbababbbbabbabbbbaaaaaaabbaabababbabbaabbabaabaaaaabbbaabaaabbbbbaababbbabbababbbabaaabbbbbaaabaabaabbaabaaaabbbababababbabaabbbbababbbbbaaaababbabbbbabaabbabbaabababaaabaabbababbaabbabbbaaaabbaaaabbbbbaabbbbbbabaaabbbaaaaaabbabaaaabbbbaaaaabaabbabbbbbabbbababbaabbabaabbaabaabaaabababaaaaabbbabbabaaaaabaabbaabbaaabbbabaaaabbbbbbaabbbbabbbbbbaaaabababaabbbbbbbabaaabbbababbbbaaabbbabbabaabbbababaaabaabaaaaabaaaabbbaabababaaabababbbbbbbbbabaabbbbabbaaabaaabaababaaaaabababbaaaabbaaabaaabbbbbabaaabbbbbaabbbbabbbbbabaabaababbaaaabbbabaaabbaabbabbbaaaabbbbababaabababaaabbabbaababbbababaaaaaabbbbbbaaabbabbabababbbbbbaaaabbaabbababaabababaaabaabaaaaababaaabababbaaabbbbbabbaaabbbbaaababaaabbbaabbbaaabbbaabbaabaabbabaaaaabbbaaaabaababaabaabbbabaaabbbaaabbbabbaabababbbbbbbbabbbbbabbbababaaaabbaabaaabbaabaabbaababbaaabaabbbaaaabbbaaaaaabbaabbabaabaabaaabbbbbabbaabbaaaaababaaaaabaaaababaabaaabbaabbaabbabaabababbbbbaaaabbbbbbaabbbaabbbabaabaaabbabbaaaabbbbbbbabbaaabbabaaababbaabbbbaabbababbaabbbbbbbabbbabbbbbaabbbaaabbbabbabababbabbbbbaaabaabbabaabbbaababababababbbbabbbabbabbababbabbaabbaababbbabaabbabaabaababaabbbaabbaabaababbbaabbabaabbaabbbabbabbaaaabaaabaabaaabbbbabbbaaaaababbabaabbabbabaabbbaaabababbabaaaabaabbaaaaababbaabbbaaabbaababbbabbaaababbbaaaabaaababaabaabbbabbaaaaabaaababbbbbbbababbabbababbbbbbaaaaaabbabbaaabbaabbaaabbbbababbabababaaabaaaababaabbbbaaabbbbaaaaabbabbbbabbabababbabbbbbaabbbbbbbababaababbabaabbabbbbbabaababaabaaaababbbbabaabbbabbaaabaabaabaaaabbabbabbabbabaabababbabbaabbaaabbbaaabaabbaaaaabbaabbaaabbbaaabbbaabaabababaaababbabbbaaabaaaabbbaaabaabaaabbbbaaaaaaababbabbbabbbbabbbabbababbbaaababbbabbbaabbabbbbbaaabbbbbabbabbabaababbbbabbbbbabbaaabaaaaaaaabababbbaaaaaabaababaaaabbabbbaaaaabbaababbaabbbbaaaabaababababbbabbbbababbbbbbabbaabbbababbbbababaababaaababaaaabaabbbbbbabababbbababbabbbababbaabbbbbaaaabaabbbaabbabbababaabbbaabababaabbabbaaabbabbaaaabaabbaababaaabbbaaabaabbbbabbaababbbaaaaabaaabbbbabaaabbaaaabbbabbbaababbbaabbbabbbabbbababbaaabbabbbabbbaaabbaaaaababbbbbaabaaabbaaaaabbaaaabaabbbaaabbababababaaabbababababbaaaabbaaabbbbaabbbabbaaaababbbaaaababaaaabbaaabaababbaabbaaaabbbaabbbabbaaabaabbbabbbbaababbbabaaababbbabaababbbabbbbabbbaabbabababaaaabbbbabbbbbbbaababaababbaabbaaabaaabbbababbbaabbaaaaabbaaabbaaaaaaabaabaabaababbbbbbaababaaaababbbbbaaaabbbbbbbbabbbaabbbbbabbbabaaabbbbbbababaabbaabbbabbaaaabaabbaabbbaababbbbbababbababbaaabbaaaabbbbbbbabaababaaaabbbbbaaabbbbbaabbaabbababaaaaabbbbbbbaaabbaabaabbaabbabbbaabaabaabbaabbabaabbaabaaabbbbabaaaaaabbabaaaaababbbbababaabbbbabbabbbabbbabaabbbabbabaaaabbbbbababaabbbababbbbaaabbaabbaaabbbbabbaabaaabbabbbaaaaabaaaaabbbbabbbaabbbababbbbbabbbaaaabbbaaaabbaabaaabaaabaabbabaabbbaabbbaabaaabbbbaabbaabbbbbbabababbabbaaabbbbaabbbabbaababbbabbaabbaaaababbbababaabbbbbbabbbababaabbbbbabaabaaabbaaaabbbaabaabbbababbbaaaaabbbaabbabababbaababaaaababbbbababaabaaaabbbbbaaaaababaabaababbabbbababaabbaaabbbbaababbababaabbaaabbaabbbaaabaabbaaaabbbaaabbabaaabbbababaaaaabaaaabaaabbbaaaaabaabbaaaabbaaaaaaabbbaaabbaabaaaaababbbabbbbbbaaaababbbbabbaaabaabbaabbaababababaaaabbabbbaaaaaabaabaaababbbbababaaabababbaaabbbbabababbaaabaabbabbaabbaabbaabaabbaabaaabbaabbbaaabbbbbabbaabaaaabbaababbbbbbaaababababbaabbbabbbaabaaaaabbaababbbaaaabaaabbbabaaababaabbbbaaaaababababbaaababbabbbbabaaabbbaaaababaaabbaabbbabaaabaaabaabaabaaaaaabaaabbaaabaabaababbbabbabaaaaabababaaaaaaaaaababbbbbaaaaabbbaabbbbaaaaabbaabaaaabaaaababababbabababababbbabbbabbbaabbabbbaabbabbaababbbbbbbbbbbbaabbabaabbbbaabbabbabaaababbbaababbabbbbbaabaaabababaabaaaaabaabbaababbaabaababababbaaabbabbbaabbbaaabbbabbababaaabaaaaabaabbbbabbbaabaaabbbbaaaabbaaabaabaaaaaabaaababbaabbabbabbababbaaabbbbbbbbbabaaaabbabbbbaabbabbababababbaaaaaaabbaaabaaabbbabaaabaabbaaabbbaaabbabbbaababaabbbaaaaaababbaabaaaaaabaabbbaaababbabbaabbbbabbaabbbbabaaabaaabaaaaababaababbbbabaababbabaaababbbbaaabbbabbabbababaaabbabaabbbaabbbabaabaaaabbbabaaabbbabbbbaaaaabbbbbabaaaaaabbabbaaaaaabababbabbbbaabbaaabbbaaabbbbbbabababbbbaabababaaabaabaabaaabbbabaaabbabbbaaaaabababbbabaaaaaaaaaaaaaaababbbbbaabbbaabbabbbbabaabaaabbbaaaabbbbbabbaaaababaabaabbabbaabbabbbababaababaaaabaaabbbbbbabbabaaababaabbabbbbabaabbaabbaaabbaabaaabaabbbbaabaaaabbbbbbaabbbbaaababaaabbbbaaabaaaaabaabbbaabbaaababbabbabaabbbabaabbabbababbabababaabbaaaaaaabababaaaabbbabaaaaaaabbbababaaaaabaaaaabababbabbabbbabaaaabbbbabababbbbaaaabbbaaaababaaabbabbbabbabbbababbbaabababaababbbabbbbababbbaabbaaaaaabbaaaabaaaabbababaabaabaabbabbbaaaabbbbbbbbaabbabaaabaabaaaaabbabaaaabaababaabababaaaabbbabaabaaabaaaaabbaaabababababbaabaabbbbbabaaababbbaaaaabbaaaabbbabbbbbaabbbbaaabaababaababbbbabbbbbaabababaabbaabbbbbbabaaaaaaababbbbbabaaababbaababaaaaaabaaaaaabaababbbbbaaababaabbababaaababababbbaaaaaaabaabaababbbbabbbbabaababbabbbabaaabbabbbababaaaaaabbbbaabbbbbababababbaabababbabbababbabababbabaaaaaabaaaaaabaaabbbabbbabbaaabbbaaaababbabbaaabbaabaababbabaaaabbbaaabbaaaaabbbaaaabbabbaabaabababbbbbabbaaababaabaabbbabbbaaaaabababbaaaaaababaabababbaabbbabababbbaabbabbbbbbbabbabababbbbbbaaaababbbabaaabbbaaabaaabaaababbaaaababbbbaabbbababbbbabaabbbabbabbaabbbaaabababaaababababaabaaababbababaaaaabbabbbaabaabbbbbabaaaabbaaaaaabaaabbabaaabbbbaabbbaabaababbabbbabaababbbbabaabbbbbbabaababbbbbaaaabaaababaaaaabaabbbaaaababaaabaaabbbbbabbbaabbaaabbbbbaaaabbaabbbbbaabbaababbbbaaababaaabbbbaaaabbbaabababbbbaabbabaababbbaaababaabbaaababbbbabbaabbabbbaaaabaaabbabbababaabaaabbbbbbaabbaaababbbaaabaabbbabbbbabbabaabbbbabaababbbaaaababaaaaabbbbbabaaaababaabbbaababaaabbaaaaababbbbabbaabababbbbbbaaaaababbbbababaabbbabbabbbabaababbbaaababbbabababaabbababbabbbaaabbbbbaaabbabbbaaaabaaababbbaababaabbbabaabaaabaabbbbbabbbbbbabbababbbbbaababaaabbaabbabbbabbaabaabbabaaabaabaaababbbaaabbbabaaabbbbababbabbbbbababbaaabbababaaabaaabaabbabbabbbabaabbbaaabbaabbaaababaaabaaaabbaabbaaaabbaaabaabbbbabbabbbabaaabaaaabaaaaabaabbaabaabababbbaabbbabbaabaaaaabbaaaababaababbabaabbabbabbaaabbaaabbbabaabaaaabbbbbaabbbababaabaabbbbaabababbbbbababbaabaabbbabbababaaaaabaabaabbaabbaabbaabaabaaabbabababbaabbabbbbabbaaababaaabaabbaabababaaabababbaaaababbaaaabababababbbabbaaababaaabbabbaaaaabbaaabbbabaaaabaaabbabbbaaaabaaaaaaabbbbbababaaaaaababbbbababbababbbabababbbbbbabaaaabababbababbaababaaabbaabaaaabbbbbbabaababaababbabababbaaabbbabaabaaabaabaaabaabababaaaabbbababbababbaaaaaababbaaaaaabbabbbbbabbabaaaabababbaaaaaabbbaabbaabbbbbaabbbaaabbbbaaabbbbabbaabaaaaaabbbabbabaaaabbbbbbababbaaabbabbaabaaaabaaaaaababbababbaabbbbaaaaaabaaaaabbbbbbabaaabbaabbabababbbaaaaabaaaabbbaabbbbaaaabbabaabbababbabbaababaaabbaaababbbabbbbabbabaabaabababbbbbabaaabaabaababbbbabbbaaabaabbbbbaabbbabbbbbabbaaabababbaabaaaaaabbaabababbbbaaaabaaababaaabaaababbbababbaaabbabaaaababaaabbabaaababbbbaaaaabbaabaabbbbaabaaabbaabbababbbbbaaabbaaaabababbaabbbaababbbbaabbababaababbababbbaaaaaabaaaabaaaabaaabbaababbbabbbababbaaaababbabbbabaabbbabbbaaabbaaabaaaabbaabbbabaaaababaababbabbabbbbaaaabababaaababbbabaaabaabbbbbabbbaabaabababaaababababbbbaabbabbbabaabbbbabababbabbabaabbabaabbabababbaaabaabaababbbbaaaabbabbbaaabbbbbbabbaaabaabaabbbbbaaaabbbbabaabbaabbaaabbaaaababbabaabaabbbaabababbbabbaaaaabbaababbbbbabaabaabaaaabbbaaaababbbbabbaaabbbaabbaaaaabbbaaababbaaaabbbababaaabbaaabababbabaaaaabaabbabababababaaabbbbaaaabbaabaabbabbbbbabbabbbbbbbaaaaabbbbbabaaabbbabbbbbababaaaabbabbbbbbaabbbababbbbbbabbbbbbaabbbaaabbbabaaaaaaaaabbabaaaaabbbababbabaaaabbababbbaaabababababaabbbaaaaaaabaabaaabababbabbabbbabbbbaabbbaabbbaaaababbbbbabbaaaaaaabbabbabbbbabbaabbaabaaaaaababababbaababaabbabbababaaaabbbaaabbabaaaaabababaababbbbabbbabaaababababaabaabbbbaaaaabbaabaababbabbabbabaabbbaabaabbabbaaaabbaabbbaaababaabaabaaaaabbabaabbaababbbaabbabbaabbaaaabaaaabababaaaababaabbbbbabbaaabbaaaaababbaabaababaaabbbbaabaaaababbbabbababababaaabaababababaabaababbabbbabbaaabbbbbaabbaabbbabaababbaabbaabaaababbbaaabaaabbaaaaababbbbabbabbaabaabaaaaaaaababbaabbaabbbbaabbabbaababaababbbabaaabbbaaabaaaaabbbbbabbbabaaababaaaabbaaaabbaabaaababaaabbabbabbbbaabbbabbbabaabbbabbaaaaaabbabaabaabbbababbaabbabbaaaaabababababaaaabbababaabbabbabbbaababababbabbababaabababbaabbababaababbbbabbbabbbabbbbbbbbaabbaaabaaaaaabaababaaabbbaabbbbbbbbaababbbbaaabbaababaaaaabbaabaaabbabbabaaabbaabbabbabbbbababbbabbbbbbbaaababaaabbabbabbaababbaabaaabbbbbbbbbaaababbbbbbbaabaabbbbbbabbbbbbbaaaaabbbaaababababaaaaaaabbabbbabbaaaababbabbbbbaaababbbbabbbabaabbaaabaababbababbbbbabbbabbbaaaaaabaaabbabbaabbbbbaabaaaaaaaabbaaaaaabbbaaaabbbbaabbaaaaaaaaabbbaaaabbbbaaabbbaaaaabbabbbababbbabbbabbaaabbbbbbaaaabbabbbaaabbaababbbaabbbbbaabbabbababbababbaababaaababbbbaabbabbbbaabaaaababbbaaabbbabaaababababbbabaaaaaababbababbbbababababababaaabaaaaaababbbbabababababbbaaaabaabbaaaabbbabbbaabbababbaabbaabbbaabbbabbbbbaabbbbabaabaaaabbbbbbaabbbabbabbbababbbabbabbabaabaaaaaaaabbbaabbabaaaabbbbbbababbaabbabbababababbbaaaabbbaaaabaabbbaababaaabbbbaaabbbababbababbbbaaabbababbababaabbaaabbababbababbbabbbbbbbabaababbbaaababaaabbbabbabaaabaabbabaabbbaaabbaaabaababbabbbaaabbbaababaabbbbbaababaabaabaaababaabbbabbbbabbbaabbaaabbaaabbaaabababaababbaaaaaabaabbababbabaaaabaabaaaaabbbbbaababbaaabbbabaabbabababaaaaabbbaaabbbabbabbaaaabbabbababaabbbbbbbbababbbaababbaabbbabbabbbabbaabaaababbaabbbbaaabbbbbabbbaaabaababbaaabbbaabaaaabaabbabbababbbbbbbabbbbabbbbaababaabaaaaaaababbbaabaaaaabababaababaabbaaabbbabbbabababaaaabbabaabaaabaabaababbaababbbaaaaaabaabaababaaabaaabbbabbbabababaaabbaaabaaabbaaabbaabababbbabaababbbaaaabbabbbbaabaabaabbaaaaaabaaabbbbaabaaababaaaaaabbbababbbaaaaabaaababbbabbbabbaabaabaaaaabaabbbaaaaaaabababaaabababbabbbbabaabababbbbbbbabababbabbabbababaabbabbabbaababaaaaabbbbbbbbaaaabaabababbaabbbbbaaaabaababbaabbabbaababbbbbaaabaaaaaaaabbaabbbbbabbabbbaaababbbabaaabbaaaabaaaaabbabaaaaaabbbbaabaaababbabbaaaabbbbbbaaabbbbabababbbaabbbabaaabbaababbbbababaabbbabbaaaabbabbabbaaabbbaaaabaabbbbababbbababaabbabbaaaaabbaabaababbabaababbaaaabbbbbbbbaabaababbbbaabbbbaaabaaabbbaabbbaaababababbabaabababaaaabbbabbabaaabaabbbbaaabbbaabbaabaabbbaabaabababbabbabbaaabb
abbbabbbbbabaaaaabbaabbaaaabbaababaaabbbbaabbbbbbbaaabbaaaaabbbbbbbbaabbaabaaabaaaaaabbaaaaaaabbbbaabbabaaabbbbaabbabbbbabbaaabbaaabababbbbabbababbbaabbabbaaabbaabaabaabaabaaababbaabaaaaabaabbbabaaababbbbabbabbbabbaaaabbbababbabababaabbabaababbabbaaaaaaabbaababbabbbaabaaaabaaaabbabaaaabbabbbbbaabbaabaababbaabbbbababbaabbbababaabbbbbbaaabbaaaabababbabaabbbabbbabbbabaaabbabbbbbaaaaaabbbabbbbbbabbbabaababbbabbbbbbabbaabaababbaababababbabbbaaaabbbaabbaababbbbbbaababababaaabbabbabbbbbbabbbbabaabbbbbabbababaaaaabbaababbbaabbaaababbbaababaabbaabbbbbababbabbbbbbabaaaabaabbaabbbbabbababababaaabababbaabababbaabbbbbbbabaaabaabaaaaaaabaaaaaaaaabbbabbabbaabbaabbabbbbbabbbaaaabaabaabaabaabaaabaabbabaaaaaaabaaaaaabaaababaaabbaaaababbaabababbabbbabaaaabababaaaabaabaabbbabababbabbbabaaabaababaabaaaaaaabaabaaabaabbbabbaabbabbbaabaabbbbabaabbaabbbbbbababbbaabbaababbbbbaaaababbbbbaabbbbbaaaaababaaabbbabbbbbaaaabbababaaaabbabbabbbbaabaabbbbbbabaaaaaaabaabaaabbbbbbbbabbaabbaaababaaaabaabaaababaaaaabbbbbbaaaababbbbabbbbaaaabbaabbabbabbaaabbababbaabbbabbaabbbbabababaabbabbaaaabbbaababbbaaababbaabbaabaabaabbbbababaababbbbbabbababbaabaabbbabbabbababbaababbbaaabbababbabbbaababababaaaababbababbbaaabaaabbaaaabbabbaababbbbaaaaababbbababbaabbaabbbaababaaabababababbbbaaaababbbbabbbbbbaabbbabaaababababbbaabbaabaaabbaaababbbbbbbaabbbbaabbaaababbaaabbabbbbabbbbaaabbabbaabbaaaaabbbababbabaaaabaaaaababbbaaaaabaabbbabbbabbaaabaaababbbbbabbbbbbabaabbbbaababbaaaaabbaabbaabbabbbbaabbabbaaaaabbababbababbbbabbabbaaaababbaabbbaabaababbabaaaaabaabaabbbaabaaaaabaaabaabbbababaabbaaaabaaababbabbabaaababbbababbabaaaaaaabbabbbaaabbbbabaabbaabbbbbabbbbbbabbbabababbbbaabaabbbbabbaabaababbbababbbaaababbbbaabbabbbbbbbbababbbbbaaabbbaaabbbbbabaaabababbbababababbbaababbbbbbababaaabbbabaabbabbbbaabbbbbbaabaaabaaaababaaaaaabbabaaabbbabbbaaababbbbabaaabababbbbbbbaabbababbaabaabbbbabaaabbaaaabbabbabbbbabbbabbabbbbaababbbbbaabaaaaabbabaababbbbabababbbabbbabaabaaaabbbabbbbabbababbbbabaaaaabbababbbaababbabbbbababbabbbbabaaaaabbbbabababaaaabaaabbabaababbaababababbbaabababaaaabbabbabaaabaabaabbababbabbbbbbaabbbbbbabaaaaababababbbbbbabbaabaaaababbaaabbbababaaabbbbbaababaabbaabaabbbabbbaababaabbbaaaaaabbbababaabababbaaabbbababaabaaabbbbbabbaaaaaaaabbabaabbaaababababaababaabaaabaabbaabbaabbabbaababbaabaaaabbaaabbaaaabbaaaabababbaaababaaaaababaaabaabbbaaaaabaaabbaabbbbaaababbaababaaabbaaaabaabababbbbbbbbbabaaaaaaababaabbbbabaaaababbaabbbbaaabaaabbaaabbbbbaaaabbaabbbababaaaaabbbaabaababbbbaaaabbbbabbaaababbabaabaaabbbbaaaabaabbbaaaaabbaabbaabbbaababbbbbaabbbbbbabaaabbbabababbaaaabbabbaaaaabbaaabaaabbabaabbbbabbbaabbaabbaabababbababbabbaaabbaabababbabbbabaababaababbbabbababaabbabbbbaabbbbabbaaaabaabbbabaaabbbabaaaabbbabbbabbbaaabbababaababbbabbbbbbabbbababaabaabaaabbabbabbbbbbabbabaabbbbaabbabbbbbbbbabbbaabbabbbbbabababbaaabaababaaabbbbbbbbaabaababbbabbaabbabbabababbaaabbabbaabbaabbbbbbbaabaaaaabbababbbaaabaabbbbaaaabbaabbaaaabbabbbbaabbababbababaabbbabbbbbbabbaabababbabbbababbabbabbabbbabbababbabbbbaabbaabababaaaabbabbabaaaabbbabababbabbabbabbaabaaababbabbbbaabbbbbaabbabbbaaaabaababbbabababbaaaabaabaabbbabaabbabbbbbbabbabaaaaabbaaababbbaaaaaaaaaaaabbaabbabaaabbaabbbaaaabbabababaaababbaaaaaaababbaaabaaaabaabbbbbaabaabbabbababbbbbaaabbaabababbbaababbbaababaaaababaabaaabaaabbbaaabaaababbaabaabaabbaabaabaaaaaaaaabbbbaaaaabaabaabbbaabaabababbaabbabbabbbaaabbbbbaabaabaaababbbabababaaaabbaabbbbaabbbaabbbbabbabaabbaaaaaaababaaaabbbbbbbababaaabaaabbaaaaaabbaaabababbabbababaaaaabbabbaabababbabaabbaaaabbabababaaabaabbbaaaabbbbbaaaabbbaaaaaaabaababbbbbbaaabbaabbbbbbabbaabbbaabbabbbbbabababaabbbaababaabbabbaaaaabbbbaabbbbabbaaaaabbaaabaaaaabbbbbbaabbababaabaabbaaaabaaabaabaabbabbabbbbabaabbaaaababbbabaaababababbbaabbbaaabbaabbaaaaabbbbbbbbabbbbabaaaabbaaababbbbbabbbabaaaaabaabaababbbbbbbbaaaababaaababbaabaabbbababbababaaaaabababaababbaabaabaabbabbbbababababbbabababaabbbaabaabbabbabbbbbababbaabbaaabbbaabaaaaaaabaaabababbbaabaaaaabbbaaabaaabbabbbbaaababbbbbabbaaababbaaabbbaaababaaaababbbbaaaaaabbaaabbbaaabbababbababaabaabbbbaaabbbaaabbabbaaaabbabbbaaabaaabbbbababaaaabaabaaabbbaabbbbbbabbbbabaababbbbbbabbaaaaaabbaabbababbaabbaabbaabbaaabaaabbbbabaababaababaaaaaaaabaabababbaaababbbbbbbbbaaabbabbabbaabbbababaabbbbaababaaaaaabbbbaabababaaababbabbbababaabbababbbbbaaaaaababaaabbabababbabbbababbbaaaabbbbbaaaaabbbabaaaabbbbaabaaaaabbbababbaabbbaaabbabbbaaabaaaaaaaaaaabbaabbbabbbaaaabaaaabbbaababaaababbaababbbaabbbabbbabaabbaaabababaaabaabbaaaabbbabbaaaabbbbbabbaabbbaaababbabbbbaaaaaabbaaaaababaababbbbbbbbbbbbbaabaabbababbabaaabaababbbaabbbbbaababaabababbbbbbbbabbaababaaaabbbabaaabbbbbaababaaaaabbbaabbabaabbaababaababbabaabbbbbbbbbaaaaaabbbbbbbabbbaaabbaaaabaaaaabbbbbaabbaaaaaaababaabbabaaabbaabaabaaaabbabaabbabbabbbbbabbaaabbbbabababbaabbaabaaaaaababaaabaababaaabbbbabaaabababaabbbbbbbabaaabbaabbbabababbbaababbbaabbbaaabbabaababbabaaabaabaababaaaaababbbbbaaabbaabaababbaaabaaaaabbbbbaababbabbbbbaaaaabbaaaabbabbabababaaababbaabbabbbabbaabbbbabbaabbabbabababbaaabbababbbaabaaaaaaaaabaabaaabbbaaaaaaaaaaabbbabbaaaaabbaaabbaabbabbaabbabaababaababbaababbbaaabababbbaabababaaababbaaabaaaaabaababbbbbbbaabbbbbbaaabbbabbbabbbabaaabbabbabbbbbaababbaabaabbbbbbbaaaaaaabaaababababbbbaabbaaaabbababaabbabbabbaabbbbaaabbbaabbaaaaabbbaabbaaaabaaaaabbbbababbbababbabbabbbabababbabaaaaababbabbbbabbabaabaabbbbbaabbaaaaaaaabaaaabaababaabbaabbaaaaaaabbbbababbaaaaaaaaabbabbaaaaaabbabbbbababaaabaababaabbbbbababbbabbaaabbbaaaabbbaaabbbbabababbaaababaaabbbbbaaaaaaabbbbaabbababbbbaaaabbaabaaabaabbabaaabbabaaaabaaabaaabaabbaabbaabbbaaababbbbabbbbaaaabaaabaaaabbabaababaaabaaaabaabbaabbababaabbbbaabababababaababaaabaabbbaabbaabbabbabbbbbbabbbaaaabbbbabbababaababbababbbaaaabbabaabbbbbaaaaaaabaaaabbaaabbbababbaababaaaabaaabbabababbbabbaabbbbaaabbbbbbbbbbaaabaababababaabababbbbbaaabbbabbbaababbbbbbababbaababbaabbaabaabababbbaabbbaabbabbabaaaaaaabaabaabaaaaaaabaaaabbaaaaabaaaaabbbaaaabbbbbbabaaabbbabababbaabbabaababbaabaaaabbbbbbbabbaababaabbbbbbbbbaabbaaabbabbabbabbabbbbabaababbbababbbabaaabbabaabbbaabbaaaaabaabbaababbaabbbbabbaabbaaabbaaababbbabbbbbabaabababbbbaabbabbabaaaabaaaaabbabbabbbaababaabaaaabaabbababbaaabaababaabaaaabbbbaaaaaababbbaaaabbabbaaabbabbaaabaabaabbabbaababbaababaabbaabaaaabbbbabababbbbabbbbbbaaaababbbaababbabbababaaaabbbabbaabbaaababaabaababbabaaabaababbabaabababbabbbbbaaababbaaaaabaababbabaabbabbaabbabaaaaabbaabbbbaababbbbabaaaababbaaababbbbbbabbbababaaabbbbabaabbaabbabaaaabababaaabbbaabbabaabaaaabaaababbbabbbabbabbaabaaaaaabbbbbababbaaabbaababaaabbaabbabbbbbaaababababbaaabbbabbabaabbabbbaabbbbabbbbaabaababababbaabaabbbaaaaaabbababbaaaaaababbababbbaabaaaaaaaaaabbbaaabaabbaababbbaaabbbaaababbbbbabaaaabbbabbbbbabbabaaaabbaaaaabababbaabbaaaaaaaabbaaaabbaabaababbbbbababbbaaabbaababaababaaaaaaabbbbabbbaabbabbabbaabbbbaabaababbbbbabababbbbbaabaabbbaabaaabbbabbbbbbaaabbaaababbaaababbbbababbbaaabbababaaaaaabaabaabaaaabaaaaabbabbabbaababbbabbaabbabbbbabaaaabaabbbbaaabbabbaababbbbbbabaaababbbaaaabbbabbbabbbabbabbbbaaaaabbabbbaabbabaaaabababaaababaaabbababaabbbbababbabaababbbaaabbabbabbabaabbababbbbbbaaababbaabbbbababbaabbbbbaaaaaaaaaabaabbaaabbabbaabaaabbaaaaabababaaaabbbabbaabbbbbabbbaaaaaaabaabbaabbbbaaaaaaabbbaaaaabaababaababbabbaabaaaaabbabbbabbbaaabbbbbabaabababbbabbbbbaaaabaaababbabbbbbaababbaaabbbbababaaabababbbbaaaabbbbbbaaabbbbbaabaaababababaabaababbaabbbbababbabbbbbbaaabaabaabbbaababaabaabaabaabaabaaaaaabbbababbababbbabbababbbbbbabbaababaabbbabbbbaaabbabaaaabbbabababaaaabbaaaaabbababaabbbbabaaaaabbbbbbaabbbbababaaaaaabbabbaababbbbbbbaabbbabbabbbbbaaaaaaaabaaabbbbaabaaabaaaaaaaabbbaabaabbbabbabbbbabaaaaaabbbaabababbabaabaabaaabbabbaaaabaabababbababaaabbbbbbbbbbabbbabbbaaaaababababbbaaaabaaababababaaababaabaaabbaabbbaaaabaaaaaaababbaabbaaaaaabbabaabbabbaaaaabaabaabaababbbbabbaaabbaabaabbaabaabbaabababbabbbbabbaabababbbbbbbababaaababbabbaaaababbaaabbbbaaabbbaaabaababbababbaabbbaabaabbaabaaaabbabababaaaaabbaaabbabbaabbaaaaaabaabaabbbbaabbbaaaaaaabababbbbbbaaabaababbbaaabbbabbabaabaaabbaaabbabbbbabaaaaabaaaababbbbababbbbaaaaaabaaaaaabbbaaaababbbbbbbbbbbbbabbaabaaabaababaabaaabbbaaaaabbaaaaaaabbabbbaaaabababaabbaabbaabbabbbabbaabaabbababbbaabababaaaababbbabaababaabaaababaaaabbabbabbaabaabbaabbbabaabbabaababbbaabbabbbaabbaaabbabbabbababaaabbbbaaabbbabaabbaaaabaabbbbaabaaaaaabaaaabbbbabababbabbababbbaabaaabaaababbbbbbbbbabbababbbbbbabaaabbbbababbabaaababbbbbbbbbbababaabaaababbabbabababbabbbaabaaaabbbbaabaabbbabbbabbbbabbabaababbaabbbbbaabbaaabaabbbbaabbbabbbaaaaabaabaabbaabbaabbabbbaabbababbabbaababaabbaaabbaaababbbaababbaaaabaaaaaabbabbbbaaaabababababbbbabaabbbaaabbabaababaaaaaaaabbabaabaabbbbaabbabbabaabaaaabaababbabaaababbabbbabaabaaaaaaaababaababaabbbabbaababbbbbbbabaaabaabbabaaabbbbbabbbbaaaaabbbabbbaaabaababbbbbbbaabbbbabbaabbbbaabaaabaaabbaabaababbabababbbabbabbaabbbbbabaababbbaaabbaaaaabbaabaaaabbbabaaabbaabaaabbaabbbabaaabaaabaaabbababaababbaaaabbbbbaabaaabaaabbbaaabbbbabbbbaabbbbbbabbbaaabaabbbaaaabbabaaaabaaaabaabbababbbbabbaababbbaababbbbbbabaabaabaabbbaaabaabbbbaabbbababbabbbbbbbbbaaabaaabaababbaabababbaaabbbabbaabaababbbababbababaabaababbaabbbbaaaabababbbbababaabaabbabbbaababaabbbbbbaabaaabbbabbbbbbbbbbaabbbbabbbbaabababaaaabbabbaabbbbbaaababababaabbabbabaababbbabaaaabaabbbbaabbbbbbbbbbaaababbaababbbaaabbabaababbaaaaaabaaabaaaaababbbabaabbabababbbbbaabaaaabbbbaaaaaabbaaabaabbababababbabbbbbaabaaababbababbbbaabaaabababbbaabbbbbbbaaaababaababbaabaabbbaabbabbabbbaaaaabbaababbbaabbbabbabaaaabaabbaabbbaabaaababbaabaabaabaaaaabbbabbbbabbaaaaabbbbabaaabaaabaabaaabbaabbabbaaabbaaaabbbababaaabaabbaabbababbbbbbbaabaabbbaaaabababbabbbbaaaababaaaaaaaaaaabbbbabbaabaaabaaaaaaaaaababbaaaabbabaaababbaaaabaababbbbbababaaaaaaaabaaaaababaabbbbbbabbbaababbabbbabaabaabaabbaaaaaaaaabaaaabbaaabaaaabaabbbaababaaaaaaaabaaaaabaabbbbbbabbbbaaaaababbbaaabbbbbaaabaabbaabababbaabbaaabaabbbabaabbaaaaabbaaaaabbbbaaaaabababaababbbaababbaaaabababbabbbabaaabbbbaabbbbabbabbabaaabbbbabaababbbbbaaababaababaabbbbaaabbbbbaabaaaabaaabbabbbbbbbaababaabbabababaabbbabaaaabbbabaaaaaababbaabaabbabbbaaabbbbaabbabbabaabbaabbabbaaaabbbaaaaaaabbbaabbabbabaaaaabbaaabbabaabbbabbbbabbbaabbaabaabbabbaabbaabaabbbaababaabbaabbbbbabbbbaabbaaabbbbbabbbbaaabaaaababbbababaabaaaababaaaaaaabbbaaaabaabaaaababbaabaaaabaaaabbaabbbabbaaabaabbbbbbbbabababbbabbaaaaabaaaabbbbaabaaabbabababbaaaabbabaaabbbababbabbbabababbbbbabaaabbbaababaabbabaaaababbbabbaabbbabbbbaaabaaaabbbbaabbbababaaaabbbbabaabbaabababbbabbbbaabaabbbaaaabbbaababababbbaabbabaaaabbbaaabaaaaabbbbaaaabbabbaaaabaaabbaabbabbbababaabbbbbbbaabaabbbabababbabbbbababbbabbbabababbbbaabababbbbaabaabbbabbbabbaaababbbbbabaaaaaabbaabaaaaababbababbbbababaabbababbbabaaababaabbaaaaabbaaababbbaaabbbbabbaaabbbabbabbbbbbbabbbaabaabbbaaababababaabbbaabbbabababbbbbbbbabbbabaababaabaaababababbbbabaaabaababbbabbabbbbbababaabbbbbaaabbbaabbbababaaaabbabbbaabaabbababaaaababaababaaababaaaaaabaaabbaababaababbbaaabbbbabbaabbbaabbaabaaababbbabbababaabbabbabbaabbaaabbabaaaaabaaababaaaaaabbaababbabbabbbabaabaabaaaabbbabbababababbbbaaaabbbaaaabaaabaaaabaaaaaaaaabbabbababbbbbaaababaaababbbbabbabaaaabbababbbbabbababbaabaabbbaaabbbbaaabaaabbbaaaaaaaabbbbabbaaaaababaaababbbabaaaabaaabbbababbbbabababbbabbbbabbabababaabbbabaababbbbabaabbbbbbbbabaabbbbbaaabaabbbaabaaabbbbbaaaaaaaaaabaaaabbbaabbbabbababbaaababbbabbbabbbbbababaaababaabbbbbabbaababbababbbbbabbbabbabbbaaabbbababaabaababbaaabbbaabababbaaabbaaaaaaabaaaaabbaabaabbaababbbbabbbabaabaaabaabaabbbbababbbababaaaabaabbabaabbbbaabbbaabaabbaaaaaaabbaaaaabaaaaabbbbbbbaababbbaaaaaabbbbabbabbbbabaaaabaabbaababbabaaababbaaaaababaaaababbbaaabbaaabbbbbaaaaabababbaabaabbbaababbbbbbbabbaabaabaaabbbbaaabbbaaabbaaabbbaaaaaaabaabbabaababbbbbbbbabbbabaaabaaaabbbaabbaabaabbbabaaaabaabababaabbaaabbbabbaabbabbbaabbbbaaaabbbaabbbbaabbabbaabbbaabbabbaaaaabbaaaabaabaaaaaaabaabaaaabaabaabbbabbaabaaabbababbaaaabbaabbaaaaabbbbabaabbababbabbaaabbbaababaaaaababbbabbaabbbabbaababbbbbababaabbaaaaabbabbabaabbbbbbbababbbabbbbbbbbabbbbbbbabbaababaabaaaababaaabaaabaababaababababbababaabaaababaabaaababbbaababaababbbaaaaababbbbaabbaaabbbababababaabbbabbaabbababbbabbabbabbbbabbababbbabaabbbababbabbbabbbabbbbbbaabbbbaaababbababbbbbaaaaabbbabbbbabababbbbaaaabbbbaabbbaaabbbaabaaabaababbaaaabbaabaaabbbababbabaabbaaababaaabbbbaabaabbaababbbaababbbbabababaabbaabbbbbbbbaaaaabababbaabaaabaaaabbbabbaabaaabbbaaaaaaabbbbbaaaababaabaabbbbaaabaaaabaaababaabbaaaaabaabbaabbaabbbbabaabbaaabababbbbbbababbbaaabbbbbbbbbaaababbbaaabaaabaaabbbabbbbbbabaaaaababbbbaaaabbaaabaabbabbbbbabbaaaaabbbaaaaaaaabbaaabaaaabbbaabababbbbaabbbbaaabababaababaabbaaabbbbaaaaababaaabababbabaabbaaabaaaaabababbbbbbaabbbbaababbabababbbbbbbbbbababaaabaabbbbabbbbbbabbabaabababbbbabbbbbbbaababaaaabababbababbabbbbaaabbbabaabbabaaaaaabbbabaaabbabbaaaababbbbabbaaabaababbaababbabaabbbabaaaabbbbbababbaabbbaabaabbaababbbbbaaabbbbaaabaaabbabaaaaabaaabaaababbbabaabbabababbbabbaaaaaaaabaaabbabbaabbabbbabbaabaabbaabbbbaaaaabaabaabaaabbabaaabbbabbabbbabaaabababbababbbbabababbabbbaabbabbaabaaaaababaaaababbbbaaaabaababaabbbbbbaabaabaaabbbbaabbbaaaabbbabaaababbbbaaabbaabaaaaabbbbabababbbbbbbaaabaaaaababbabaaaaababababaaaababbababbbaaabbbabbaaabbaabbbbbababbbabbbaaaabbbbbabbaabbaaabababbbbbbababbbabbbbbaabaabbbbaaabaaabaababbbabaabbbbabababbabbbbabbabbbaaabbabaaabbbabaaabbababaaababaaabbabbbabaaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaabbaaaaaabbbababaaaaaababbaabaaababbbbbaaabbbbbbaaaaaaaabaaaaaabbbaaaababaabbbbabbabaabbbaababbbabbaaaaaababbbaaabbaabbaaaaaaaabbbaabbbabbbababbbababbabaababbbbbaaabbbbaaaabaabaababababbbbabbabbaaaabaabbaaaaaabbbabbbabaabbabbaaaabbaaabbaababbbaabaaabbaababaaaaabaaabaabbbbabaaaaababaabaaaaabaaabbaaaaababbbaaabaaabbbaaaabbbaabbbabbbaabaababbaabbbbababbaabbbaabbaaaaabaabbbbbabbaababaaaabbbabbbbbbbbaaaabbbbabababbbbbbabbbabbbabbbababbabbabbbbaaabbbbbaabbabbbabababbaabababbbbbaabaabbbbabbbabaaaaaaabbbaabaabbababbaaabaaaabaababbbabbaaabbabaaababbabaabbbaabbaabbbabaaaaababaabaaababbbabaabbbbbbbabbbbabbaaabaabbbbaaaabbbaabbaaaababaabaabbababaaaabbaababababaaaabbbbbbbabaaabaaaabbbaaaaaaaaabababaababbbabaaababbbaababbbaabbaaaabaababbababaaaabbbaaaaaaabbbabababababaababbaaabbabaaaabbaabbaabaabaabaaaabbbabbbababaaabbabababaabbbaaababbaabaabbbbaaabbbbbababbababaabbbabbbbabbbabababbbbbbbbaabaabbabaabbbbbaabbbbbabababaabbaababbbbbbabaabbaaababbaababbaaabbbaaabaabbbabaaabaabbbaaaabaaaabbbbbbaaaabaaaababbaaabbaababbabbaababbaabbbababbaabababbabababbbbaaaaabbabaababaababbbabbbbbaaabaaaabbbbbbbabbabbaaaabbbbabbababbbbaabababaababababaabaabbaabaabbbbababbaaaaaaaabbababbbbaaaababbbabaabbbabbbaaabbbaabaaabbaaabbbabbababbbbbbbbababbaabbabbabaabbaaabaabababbbabbaabaabbbbabaaaabbbabbabbabbbbaabbababababababbbaabababbbabbabbaaabaaaaaaabbbaaabbbabaabababababbbbabbabbbbaabbababbabaabaaabababbbaaabbababbbababbbaaaabbbabaaabaabaaabbabbababaabbbaabbaabbbbaaabbabbbbbabbbbabababbabaaabbabbabbaaaabaabaaabbabaabaabbbaaaaabaaabbbaabababababbbabbaabbbaaabbbababbbbaabaabaabaabaaaaaabbbbbababbbbbbbabaabbabababbaaabaaaabbaaaabaabbabbbbbababaaaaabbababbabaaabaababaaaabaaaabbabbbbabaabbbbbbaabbbabbbbababbaababbaaabaaabbabaaababaabbabbaabaabaaabaabbbbabbabbaabbbaabaaaaaabaababbaaabbaabaabaabaabbabbaabbbaaabbabbbabbabbaabaaaaaabaababbaaaabbbbbabbbbababaaaabbbbaabbbbbaaabaabbabbabbababbbabaabbbbbbbbaaaababbbbabbababbaaaabaaaaaaabaabaababbaaabbaababbbaaababaaabaaabbbbbaaabaaaabbaaababaabaabaaaabbbaababbaaaabaaabbaaaaabaaababbbabaaaabbaabaabbbababaabbbababbababbaababaaabababbbbabababaabababbabbbabaaaababaabaaaaabbaabbbabbbaabababbabbbbabbaaaabbaaaabbabbbbabbabbabbbbbaaaabbabaaabbaaaabbabbbaabbabbbaabbabaabbbbaabbabaabbaabaabbbbabbbbbaaaabbaabbabaaabbbabbaaaaaabbbaabbababaaabbaabaabbbbbaabaaabbabaaabbbaabbbabaabababaabaaababbbabaaabbbaaabbbbaabbbbbbbbbbabbbaaaaaabbbabababbaaabbbbbbbaaaabaabbababaabbaaabbbbbbbabbbbaabaabbbbbbaaabbbabbabbaaaaaaaabbaaabbaaaabbaaaaabbabaaabbabbbbbaabaaaabaabbaaabaababbbababaaabbbbbaaaabbbaababbaaabbbabbbabbabaabbbaaaaaabbbaaaaaabbababbbbaaaaaababababbbbbabaaabaaababbbabbbaabbbbaabbbbabaabababaabbabbbaaabaaabbabababababbabbbbbaabbbababbaaabaabbaaaaaaaabaabbabbbbabbaabaabbbbababbabababababbababbbaaabaaabaaaaabbaabbbabaabbbabbbbaaabaabbbbabbaabbabbbababaabababbbbbaabbbaaaaabbbababbbaabaaaaaabaabbbaaaabaaabababaabbbbaabbababbabbaaaaaaabbaaaaabbbbbbaabbbaabaaaabbbaababaaaababaaabbabbabbbaabbbaabaaabbabaaaaaabaabbaaababbbabbaabbbaabbbababaaababbaaaababaabaaabbbbabaababbabbbababbabbbbababaaaabbbaaaaaaabaaaaaaababbbbababaaaaaabbbaabbbaabbbbbbabaabbbabbaaabbaaaaabaabbaaabbabbabbabbbbabaabbabbbbaabaaabbaababbaababababbbbabaaaaabbbbaaababbaaaabaaaababbaabbbbaaababbabbabaabaaabbbaaaaaabaaabbbabababaababbbabbbababbababaabbabbbabbabbbabaabbaaabaaaabaabbbbbbaabbbbaabaaaaabaaaaababbbbbabbbaaaaaababababbaaaabaaabbbaababbaababaabbaababbbabaaaaababbaaaabbabaaaabbbbababbabbaabbababbbbbbabaaabaaabbbbbaabaaabbaaaaaaaabbabbbaababbbbaabbaabaabaaaaabbaababaaabaaababaaaaabababaaaaaabbbabbbbaabaaaabaaabaabaaaababababbaabbaaababbbbabbabaaabbbbbaaaabbabaababbaabbbbbbbbbaaaaabbbbbabbaaaaaaabababaabbabaabababbbaabbabbababbbbbbabbabaabbbbababbabbbababaaaababbbaabbbbaaaabbabbbbabbaababbabaaaabbbabbbaaaababaaaabbbabaabaaaaaaabbaabbbaaaaabbbabbbaabaaabbababababaaabbaababbbabbaaababaabaabaaabbbbbaaabaabbababbabbbaaaaaaababaaabaabbbbababaabaaabbbbaabbbbbbbbaaabbbbbabbaaaabababbbbbbbbbababbbaabaaaaaaababbaababbbabababaaaaaabbaabaaaaaabababbbbabbbbbaaabababbbabbbbbaabaaaaaababbbabbaaaabbbbabbabbbaaaaababbabbabaabaabaaabaabbbabbbabbbabbaaaaabaabbaaaabbaabaaaabbaabaaaabaabaabaaabbbaabaabbababaabbaaabaaabaabaabaaaaaaaabbababbabbbabbbaabbbabbabbbaaababbbbaabababbabaaabbabaabbbabaabbbbbabbaaabbbbbbaabaabaaabbbbaaaaaaaaababbbbbaabbbaabbabaabababbaaabaabaabbbbbaabaabaabaabaaaaaabaaaaaaaababbababaabbaabbbbbbbabaaabbbbabbbbabbbbaaabaabbaabababbaaaaaabbaaaaaabbaabaabaaaaaaabbaaabaaaaaabaabbabaabaaaaaabbbabbaabababbaabaaabbabaabaabbbaababbaabaaaaabbbbbbaababbaaabbaabababbababbbaaabaabaaabbbaababbababbbbabbabaabbbbabababbbabababbaabbbbaaabbabbbbaaaabbabbabbaabbbbabbbabbbabababababaabbbbbabaaababaaaabbabaababbbbbabaabbabbabbbbbbbaabaaabbbbbaabbbbbbababbbbbaabbbaababaaaabababaabbaaaaaaaaabbbbbaaaaaaaaaaabbaaaaaabbbbaabaabaabaaaabbbaaabbbbbbbaaabbabaaabbaabbabbabbaaaabbbabbabbabbbabaabbaabaabaababbbbaabbaabbbaaaaaabaaaabbbaaaaabbaabababbaaabaabababbbbaaabbaabbbbaaabababaabaabbaaaabbabbbbbbbbaaaabbaaaabbabbbabbbabbaaabbaabaaabbbbababbabbaabbbabaaaabababbbaaaabbbbabaabbaaaabbaabababbbaaaabaaaaaaaabbaaabaaaabaaababaaaaaabbbabaaaabbabababaaabbbbabbaabbbbabbababbbbaabbbbbabbbbabaaabaabbabaaabaabaabbbabbabaabbabbbbbbaabaaabbaaaaaaaaababbaabaaabababbabaaabaabababbbbaaaaaaaaaaaaaabaabbabaabbabaaabbababbbabbabaabaababbbbbaaaabbabaabababbbbbaabaaaaabbbaabbababababbabaaabbbbabababaababbbbbaabababbabaabbaabababbbaabbbbbbaababbbbbaabababaabbbabbbbbbabaabababaabbbbabababbaabbbabbbbaaabababbbbaaabbabbabbbbbbbbabbbabbbbbbbababaabbabbbaaabaaabbaaaaabbbbbaaaababbaabaabaaababaaabbabaaabaabaaaaababbaaababaaabaababbabbbabbaabaabbbbbabbbbaaaabaaaaabbaabbbbaaabbbbbababababbaabbabbabaaaababababaabbaabaaaaaabbbbbaabaababaaabbabbaababaabbbbaaaaaaaaababbaaaaabaabaaaaaaaabbabaabaaaaabaabbabaaaababbaaabbaabbabbaabaaabbbbbaaaaababbababbaabbaaababbbbbbaababbbaaaababbbabbbbababbababbbabbababaaabaabaabababaaabaabbababbbbbabbabbabbabaaababaabbbbaaabaaaaaabbaaaabbbabaaaaabbbabbbaababbabbbabaaaababababababaaaababaaaaababbbbbabaaaabababbabaaaabaaabbbaaaaabbbbabbbbaabababbbbbaaaabbbaaaabaaaaaabbbaababbbbaaabaababaaabbbababababaabaaabaabbaaaabbbbbbaaabaaaabbabbbabaabbbbabbaaaaaabbaabbbabababbabaababaabaabaaaabbbbbbaaabbbaaababaabbabaabaaabbabaaababbaaabbbbbabbbbbaaababbbbbabbaababbbaabaaababbabababbaabaabbaaabaaabbabaaabbaabaabaaabbbbbbabbabbabababbbbbabababbababbbaabaaabaaaaabbaabbbababbbbababbabbbbbaababbbabaabaaaabbbbbbaaabbbabbbabbaaababbaaaabaabbabbbbabbbabaaabbabbabaabbbbbabbaabbbaababaabbbbababaabababbbbbbabbbbabababbbbabbbbbbbaaaabababaaabaaaabbabbbaababbbbabaaaaabbbabaaaabbbabbabaababaaaaaabbabbbbabbbbababaaaabbbaaabababaabaaababbaaaaababbababbbabaabaababbbabaaabaabaaabbabbabaaabbaaaaabbabbbaabbbaabbaabaababbabbbaaaababbbabbbbababbabbbbbbbbababbabbabaabbaabaabababbabbabbababaaaaaabbaabaabbbbbaaababbbaabbbabaaaabbabbaabbbbabbbaabbaabaabbbaabbaaababababaaaaaababbababaabaaabaababaabababbbabbabbbababbbbbaabababbabbabbbbbaabbbbababbabbbaabbbbababbabbbabaaaabaaaaaabbaababbbbbaababbabaababbbbbaabbbbbaaabbabbbbbbbaaabaabaaaabaaaaaaababbbbbbabaaababbabaabbbaaabaaaaababaabaabbbabbbababbbabbbabbaabaaaaaaaaaabbbbaababbbaaabbbbaaabaaaaabbbbabababaaaababbabbaababababbaaabbbbabbbbabaabababaabbbbabaaaabbabababbbbbabbbabbabbbabaabaabaaabbaabbbbabbbbbbbabbbaababbaaabbbbaaabbaabaababbabbabaaaaabaaabababbbbaabbbababbabbbabbabbbabbabbbbaaaaaaaabbbaaabbbabbabbbbababaabaaabbaaaaabaababbabbaabaaababbaaaababaababbbabbbbbabbaaaaabbbabbaaabaaaabbbbaababbabbbbababbbbbbaabbababbabaaabaaabaabbbbababbabbbabbbaaaaaabbbaabbbabbbaaabaabbabaababbbbabaaaababaaabaaaaabbaaaababbbbbabbabbbaabaaabbbbaaaaaabbaababbbaaabbbaabbababaaaababbbabbaababbabaabaaaaaababbabbbabbbaabbababbabbbaabbabbabaababbbbaabbbbbbbbabbaabbabbbbbbbaaabbbbbabaabbbbbbbaaababbaabaabbaaaabaabaabbbbbababbbbbaababbabaaabbbbaabababababbbaabbaabbbbaaaaabababbbbabbbbaaaabaabbbbbbbbababaaabaabaabaabbaaaaaabbbaaaaabaaabbababbabaaaaababaababbbbbabbbaaabaaaaaaaabbaabaabaaabaaabaaaaaababaaababbaabbabaababbaabbbabbabbaabaaaaaabbbababaabbbabaaaaabaabbbababaaabbbbabaabaaaaaabbaabababababaaaaabaabaaabbbabbbbbaabaaaabbaabbbabbbbabaababaaaabaaabaaabbaaabaaabbbbabbbaaaaabbbabbbbababbbaaababbababaaabbabbabbbabbaababbabbbbbaababbbaababbbbabbababbbbaabbabbbbaaaaabbbbabbbaaabababbaabaabbbaaabbbabbbbbabbbabbabbaaaababbbaabaababaaabababbabbbbbbbbbbababbabbaabbaaabaaabbabbbbababababbabaabbaaaabaabaabbbbabbbabaaabaabaaaababaaabaabaabbbbbabaaaabbbbbabbbbaababaaabababaaaaabbbabbabbbaaabaaabbbaaabbaabaaabbaabaaaabbabaabbbaabbbbbabaaababaaabbaaaabaaaabaabbabababbbbbbaaaabbbabbaaaabbabbaaaabaaaaababbabbbabbaabaabbbabbabbbaaabbbbbbaaaaaaabaaababbbbaaaabaabaabbabbbbbbabaabaaabababbababaabaaabbbababbbabaabaabaabbabbbaabbaaaabaaaabbababbabaaabbbbbbababbbbbbababaaabbaaaababbbbaaaabababbbaabbbbabababbbbabbbaaaaaaabbabbbbbaabbbbaaabaabbbbbbbaaaaaaaaaaaabaaabababbaabbabbbbabbabbbbbaabbbabbbaababbaabbbabbbbbbbbbbbababbaaabbababaaabaabbbabbbaabbbaababbbaaabbbaaaaaaaaaaabaaabababaaaabaabbbababbaaabaabbbbbabbababaaaabaabbababaaaabbbaabbbaaabbbbaabbabbababbabaabbbbababaababaabababaaaaabbaabbbbbabbabbbabaabbabbaababbabbaaabaababbaabbbaabbabbbabaaabbabaabaabaaaaaaabaaabaaaaaaabbbbabbabbbbbabaaaabbababaababbabaabaabaabbbbbbabbbaaabaaababaaaabaaabbbabaabbababbabaababbbbbbbbaabbbbabbabbbbbbbababbbaaaaaababaabaaaaabbaabaaabaabbbaabbaababbbbaaabaabaababaaaaaabbbabaabbabbaaaaabbbaabaabaabbababaabbbbbaaabbbaaabaaabababbbbbaaabbbbbaaabaaababaaaaaaabaabbbbabaabbaaababaabbabbbbbbaaababaabaabaabbaabaababaabaaaaabbaabababbaaabbabbaaabbbbaabaabbaaaaabbbbabbaaabbbaaabbababaaabaabbaaabbaabababbaabbbbbaaabaabbbabaabaaabaabababbbbabbbbbbbaabbbabbaabbaabbabbbabbaababbaaabaabbbbbbaabbaabbbabbabaaababbaabbaabbabbabbabbabbbaababaaabaaabaababbababaababaabbbababaaaaaaababbbaaabbbbabbbaabaaabbbbabbabbbbbbaabaaababbabbbbabbbbabbbbbbabaaabbabbabababbbaaabbaabaaabbbbbaabbababbbaabbabaaabaababbababbaabbabbaabbbabaaabaabbbbaabaaaaaaaaaabbbaaabababbabbabaabbbbababaabaaabbaaabbbbaabbbbabaaabaaaaaaaaaabbabababababaabaabbaaaabbbaaaabaabababaabbababaababbbbbabaaabaababbbbbbabbabbbababababbbabaaabaaaaabbbaabbbbabaabbbbbabbaaabbabbaabaabbaabaabbaaabbbbabbabbbbbabaaaabaaaaaabaababaaabbaaabbaaabbbabbbaabaaaabaabbbaaaaaababababababbaabbabbbaabaababbbaaababaaaaaababbababaaaaababbbbbbabaababaabbbaabaaaabbbaabababaaabaabababbbaaabbabaaabaaaaabaabaaaaabbabbbabbaabbaabbabbabbbbbaaaabbabbbbaabaaaabbaabaaaaabaabbababbaaaabababababaaabaaabbaababaabababababaaabaaabbaaaabbbaabaaaaaababababaabbaaaaaabaaabbbbbaaabbababbbabbbbaababbabaababbbababbabbbaabaabaabbaaabababaaabaabbaaabaaaabbbbabbabbabaabaaababbabaaaababbabbaaabababaabbbaabbbaabaabbabaabbabaaababbaaaabbaaabbaaaaabbaaabbbbbaaabbababaaaaaaabaaabababbaabbaabbabaababababbaaabbabaabaabbbabaaabbbaaabbbbbaaabaabaaaababbaaabbaabbabbbaababababaabbaabbabbabbbbbaaaabbbaaaabbabbbbbaaabbbabbbbbbbbababbaaabbbbaaabbbabaababbaabbbbaaaaabaabababbabaaaaaaaaabaababbabaabbbaabbaabbbaaababaabbaabbbbbabaaaabbbaabababbbaaabaabaabaaabbbaabbbbbbbaaaabbbabaababbabbaaaabaaababaaaabaaababbaaababaababbbabbabaaaaaabababbaaabaaaababbaaaaababbbabaaaabbaaabbbbbbaaabbabbbaaaabbbbbbaaaabbaabaaabbbaabbbbbabbbbbabbabbbbaaaaaaabbbaababbababbabbabbbabbbbaaabaaabbbaaaaaaaabababaaabaaabbbbbaabbbaaabbbaaaabaaabaabaabbbbaaababbbbbaaabbbbabbaaaabbbbbabbbaaabbbbbabbbbbaabababbbababbaaaabaaaaababaabaaaabbbbbababbbaaabababaaaabababaaaaaabbbabbbbabaaaaaabaabbaaaaabbabbbbbbaabbbbabbbaaaabbabbaababaabaaaaaabaabbbabaabbaababbabaabaabbbababababbaababaabbbbaaabbabbaabaaaabaaaaaaababaabaabaaaabbaaabbaaabbbbbaababbabbaaabbbabbbbbabbbbbabbbaabaaaaabbbaaaaaaabbbabbabbaabaaaaababbbaaaabaabbbbbbbaababaabbabbbaaababbaaaaaabbabaabbaaabaabababbaabbaababbaababaaabbababbbaababaabbababaaaabaabbababbbaabaaaabbababbabaaababaabbabbaaaaababaabbbbbaaabbbbababababbbbbaabaaabababaababbaaaabaaabbaaaabbbbaabaabaaaabbbaaaabaaaaaabaababbbaabbbbbabaabababbbbbaaabababbbbbaaabbaaaaabbbabbbabbaaaaabaababbaabbaabbbbbbabaabababaaababbabaaabbbbbbbbbabbabbababaaabbaaaabbaaababbababbbaabbaabaaaaabbbaaaabababbaaababbaaababbaaababbbbaaaababbbabbabaabaabaaabaaabababaaabbbaabbbaaabababaabaababbabaabbbababbbbbaabaaaaabbaabababbbabaabbabaaaaaabbaabbabaabbaaaaaabbaaaaabbabbbbbbbbabbabaabaaabbbbabaabababaaabbbbaababbbaaaabaaabbbbaaaaaabbabbbbbbbbbbabbaabbbbabbbbaabaaabbbbaabbabaaabaaabbbbabbbabbaaabbbbbabbbaaabbbbbbbabbbbaaaaabbaaabaaabaabaabbbbbaabbbaaaababbbbbabaabaaabbbbbaaababbaaaabaaabababaabbbaabbaaaabaaabbbaaaabbbbaabbabaabbaabaababbabbbbababbbaaabbababaaabaaaaaabbaaabbaaababbbbbaabaaabaabaabaababaabaaaaabbbbbbabbaababbabaaabbbabbaaaaaabaaabaaabbbaaabaaababbbbbbbaabaaababbaaaaaaababbaaabaaabbabbbbbabbaaaababaaaabaabbabaabbabbabbaababbbabbabbaaaaabbabbaabaaaababaaabbaaabaaabababbbbabbababbbabbbbabbbaaaababbbaabaabaaabbbbabbabaaaaaaaaaaaabaaaaabbbbbbaaaaabaabbabababbbbababaabaabaaababbbbbabbbaaaaabbbbbbbbbbababaaaababaabbbabbbbababaabbbbbbaabbabaabbabbaabababbbabaaaabbbabbbabaababaaabbaabbbbabaabaabbbaaabbbabaaabaaabaaabbaabbbabbabbabbbaaaabbabbababbaaaabbabbbbbbaaabaaaabbabbaaaaaaaababababbbaaabbababbbabababbbabababbaaabaaaabbaabababbabbababbbbbabbbabaabbbbabbbbbbabbabbabaabbaaaaaaabbbbabbaabbaabbabbbbbbabbbbbbbbaaaaaabbabbbabbbbbaababbaabbaabbbbabbbaabbbabaabbbaabaaaabaaabbabababaabbaaaaaababbbaabbbaaabaaaabbbbbabbabababaababbaabababaaabaaaabbbaababbaabaabbaabbbabbabbaaabaabbbabbbbbaabaaabbbbbbbbaaabaabaabaaabaabaabababbbbababaaabaabbbaabaaaaabaaabbaababaaababbabbabababbbababababbababbbbabaababbabbaaabbbbbaabaabababbbbaaabaaaaabaabbbabbbbabbaabbbaaabaaababbbbababbbaaabbaaabbbbabbbabbaaaababbabbabaabaabbbbababbabaaababbaaabaaaabbabbbababbbaaaaaaababbbaaaabaabaabbbaabaababbaaababaaaaabaaabbabbaaabbbabaaabbbaaaaabbbaaababbaaababbabbbbaaabbbbbaabbaaaaaabaabaaaabbabbababbabbabbbaabaaaabaabbaabaabbaaaabaabbbaaabbbbabaabbababbaabababaaabbbbababababbbbbabababbbbbbabbbaaabaaaaabbbaabababaabababbbabbbbaaabbaaabbbaaabbaaaabaaaabbbaaaaabbaabaaaaababbabbbbabbaababaaabaaababaababbbbbbbbaaaabbabbaaabaabbbbbaabbbaabbaaabbbabbaaabaabbbaaabaaaaaabaaaabababaaabbabaaabbaabbaabaaabbaaaaabababababbbbbaaaaaabaaabbaaaabbbbbabaaabaaaaabaabaaaabbbbbbabababaaaababbbbbbabaaabbbabbaaabbbbaaaabbbaababbabbaaabbaabbaaababababaabbabbabbabbaabaaabbabaabaaaabbbbabbaaaaaaabbbabbbaabaaaabbbabbbbbbabbbbabababbbbabbbabbabbbaababbababaabbbababbabbabaaababaabbbaabbabababbaabbaaaaaaaababbaaabbabbbbabbababbbbaababbbbbaababbbaaabababbbbbbbbabaaaaaabababbaaaabaaababbabbabbbababaaaaabaabbbababbabbbbbaabbaabbaaabbaabbababbaaabbbabbbabaabbbbaaababbbabbbbaaabbbbbabbabaaaaabaababbbbbabbababababbbbabaaaaaabbababaabbbbbababbaabaaaabaabbaaaabaabbbbbabbbaaaabbaababbbabaabaababbbabbbbabbbbabaabbabbbbbaaaabaaababaabbaaaaaaaaabbaabbabaaabbbbaababbabaaaaaaaaababbbaabbababbabbbbabbabbabbabaabaaabaaaabbbbabbbbabbabaaabbabbaaaaabaaabaabbabaaabbbabbaaabbaabbbababbabaabbaabababbbababbbbababaaabbaababaabaabaabababababbabaabbaaaaaaabbaabbabbbbbaaaababbaababaabbbababbbabbaaabaababbaaabbbbabbbabaabbbbabaaababbaabbbabbaabbbababbababbbaabaabbabbbabaaaaabaaabbaaabababaaaababbaabbbaaabaaaababbbaaabbbbabaabbabbabaaabaabaaabaabbbbabbbbbaababbaaaabbabbabbbbbbaabbbabbabaaaaababbbbbbbaaaaabbbaaaabaabbbaaabbbaaaaaaabbbbbabbaaaaaaabaaaabaaabbaaaabbabbbbaaabbbbbbabaaaababbbbbbababbaaabbababaabbbaaaaababbbbabbbabaaabaaaabaaaaabaaaabbaaababaabbbbaabbbabababbabbbabbababbaabbbabbbbbbbbbbaabababbbabbbabbaabababbabbabbaabaaabaaabaabbabbbaababbbabbabbabaaabbbaababaaaabaaaabbbabbbbaabbbbbbaabbbbbababbabbbbaabbabbaababaaaaaaaaabbbabaababaabbaabbbabaababaaaaaabbbbaababaaaabbaaabaabbbbaabbaaaabbbabbabbabbabaaaaaababbaaaababbbbbbbbaaabbabbaaabaaabaaabbabbbabaabbbababbabababbaaaabbbbaaaabbabbbbbbbabababbbbbbbaaabbabbbbabbbaaaaaaabaaabaababbaabbaabbbbabbbbaabbaababaaaaabaababaaabbbbababaaabbabaabbaabaaaabaaaaabbababaaaaabbbabaaabaabaaaaabababaaabbbbbaabaaabaaaabbaababbaaaabbaabababbbbbababbababaaabbbbbaabbaaaaabbbabbabbbbabaaabaaababbabbabbbabaabababaababbabbbabaaaabaaabbabbbbbaaaababbabbaabbbbbbbababbbbaabbbbbaaaaabbbbabaaabaabbaaabababaababaabbabbaaaaaaaabaabaabbaababbabaabbbbbabaabbbaaaabbabbabaaabaabbbbbaabbbbbbbbbabbbbbbbabaaaaabbabbaaaaabbabbbbbaaabbabaaaabbabbbbaaabaaaaabbbbbbbbbbbabbaabbbbaaabbbbbababababbbababaaaaaaaabbaabbaaabbbabaabbbaabbabbbaababaababbbbbbbababbaaaaababaabbaabbbbaabbbbbaaabbbbaababbababaaabbbbababbaaaabbabbbaaabbabaaabababbaaaabbbaababaaaaaaabaaabbbaaabbabbbbabbaabbbaaababbbaabaabaabaaaaaababaaaababbbbaabbabbbbbabbabbaaabaaaaababbbaaabaaabbaabaababbabaaabbabbbbaabababbabaabaaababbbaabbaabaabbabbababbabababaabbaababbbababbaaaaaabbbbaaaaaabaaabaabbababbbaaaaaaaaaaaaabaaaaaaabaabababbbabbbbbaababbbabaabbbababbaaabaaabbabababbabbbababaaabbabbbbabaabababbaabbabaabbbaaabaaaabbaaabaaaabbabbabababbabbbbabbaabbabbbabbbabbaaaaaaabbabbabaabbaabbaaabbbbbbbbaababaabbbaaababbbbbbaaaaaaaababaabbbabbbaabbabbbabbbbbabbaabbaaaababbaabbbbbbabaaababaaaababababbbbaaabaaabaaaabbbabaaaaabababbaabbbbbbbababbaabbbbbbbaabaaabababaabbababaaabbaabaaaabaaabbbbaaaaabbabaabbaabaaababbbabbbaababbbbbbabaaabaaaaaababaaabaaaaaabbaabababbbaaabaabaabbaabaababbbabaababbaaabbbaababaababbbbaaabbbbaababbbbbabaaababbaababbbaababbbabbbbaabbbbabbbbabbabaaaabbbbbabbabbabbaababbabababaaaaaaabbabbababaabaaabbbabbbabbbaabbbbbbaabbaabbbbbbbaaababbbbbabbbababbbabbbbaabbbaabaababababbbaaababaaaabbaaabbbbaababbbababaabbaababbaabbaababbbabbabbabababbbabababbaaaababbabaabbbaabaaabbbaaaaaaaaaaababaabaaaaaabbabaaaaabaabaaabaaabbaaabaababbbbaababaaaabababbbbbabaaabbabbbbbbabaababbababbbbabbbbbbbbabaabbbbababababaabbaabaaaabbbabababaabaabaaabbaaabbababbabbabbabbaabbbbabbbbbbaabbbbbbbbaaabbbbbaabbbbabbbbbaabbbbabbaaabababaabaaaaaaabbbbaaababababbbabbababaaaaabbabbbaaabaabbbbabbbbabbaaabbbaaaabbbbaabbbabbabababbbaaaabaabaaabbbaaabbaabbaaaaabbaababaababbababbabbbababbbbbbbababaabaabbbbaaaaaabbbaababaaaaaabbbbabbaaaababbaabaabbbaaababaaabbaabaaabbaaaababaabaaababbaaabbabbabaaabbaabbbaaaabbbaaaaaabbaabbbababbabbbaabbbbbbbaabbababaaababaabaaabbbaabaaaabbabbaabbaaaaabababaabaaabaabbaaabbababbbbbaababbbaaabbbbbabababbabbbaaabababaaabbaabababaababbabbbbaabaaababababbaaabbbbabaaabaabbbbbbbabbbabbbaababbaaababbbababaabaaabbbabababbbbbaabbabbaabbbaaaaaaabbabbabaaaaabababbbabbbbbaaabbbabaabbaababbbbababbababbaabaabbaabbbaababbbbbaaaaaaabbbabbbababbaababbbabbbbbbabbbbbabbabaaabbbabaabbbbbbabbaaaabbaaabbbabaaaabbbaaabaabaabaabaababaabbbabaaabaaaaabaabaabbbbbbaaabaaababbabbaaaabbabaabaaaabbababbbbbbbaaababbbbbbabaaabbabaabbaabaaaabaabbbbaabbaabbababaabbbbaaabbabaaabbbaaabbbababbbaababbbbbbaaaaaaabbbaaaaaababbbabaababbabbaabababaabbbbbabaaabbaaaabbaabbbbbaabbbabaaabbababaaabbabbaaaaabbaabaababaaaaabbbabababbabbbaaaabaabbbbabaaabaaabbababbaaaaabbaaabbbbbabaaaabaaabaababaabbababbaaababbbbabaabbabaabaaaaabbbbbabbabababbabbbabbbbaabbaabaaabbbbaabbbaabaaabbbabbabbbbbbabbbbbaaaabaabababaaababaabaabaabbabbabbabaaaabaabbbbabbaaaaaabaaabababbbbabbbaaaaabaaabbbbbabbbabaaaaaaabaaabbabbbabbabbaaaaabbababbbbbbabbbabaaaaababbbaaabaabbbbbbbbabbabbbbbbababbbababababbbababbabababbbbabbababbbbaabababbabbbaaabbbbbaabababbabaaaaabbbbaaaabaabaaaaababbbabbaabaababbbbbaaabaaabbbbaaaaabbaaaabbbbababaaaaababbababbabbababaababbbaababbaaabbbabaabbbbbbbababababbbbabaabbbabbaabababbbababbababaaabaaaaababaabbbbabaabaababbabaaaaabbabaabbbabbababbaabbaaabaabbbabbaaaabbaaaabaabababbaaabbbabbbbbbababbaaaaabbbaaababbbbaaaaabbbaaaabbbaaaabbaabaaaaaaaaaabbaaabbbaabababaaaaaaaabaaabbaababbaabaabaaaabbaabbaaaaabbabbaaabbaabababbbaabaaaababaabaabbababaababababababbaababbaabaabaaabaaabbabbaaaabbbbaababaaaabaabbbbbababbbbabbabaabbbaaaaabaabaabbababababababbbaababaaabbaaabaaabbabaaaaaaaaaaabbabbabbbbaaaabbbbabaaabbbbbbaaaababbbbaaababaaabbbbbaaaaaaaabbabbaababbaaaabbabaabbbaabbabbbbabaabababaaababbabbbbbaaaabbabababbbbaabaaaaaaabababaabbaaaaabababaaabaabbaaabaaababaaaaaaaabbbbababbabaabaaabaaaaabbaaaaabbabbbaaabababbbbbbabaaaaabaababbaaaaaaaabaabbbbabbbaabaaaaaababbbbaaaaabbbbabababbabaababaaaabbaaababbaabbaaaabbbabbbaabbbbbabbaabaabbbabaabaaabaaabbaababbabbabbaaaaaaababaaabbaabbbaaabbaababbbbbbaababbbaabaaaabbbaaabbbabbbbbbaaabaabaaabaaaaaabbaaabaabababbababbababbbbbaabbabaababaaabbbabaaabbbbbabbbaababbaaaaabbbbbaaaaababbabaaaaaaaaaabbabbbaabaaabbbbbbbbbbabababaaaaaaabbabbbaaaaabbbbbbbaaabaaabaabbbaaabaaaabbabaabbaabbaabababbbbaabababaabaaaabbbaabbabbbbbbaabbbbaabaabaaaaabbaabababaabbbbbabbabbbbaaabbbabababbbabbbabbababbaaaaabbbbbbbbaabbababbbabaabbaaaabbbabababbbbaaaaaababbaabbabaaaabaababbbaabbbbbbaaabababaabbbabbabbabaaaaaaabbabbabbaabbaaabaabbbbaaaaabbbbabbaababbabbaabbabbaababababbaaababbaaabbbaabaaabbaaaabbababbbababbbabbabbbaaaaababbaabababbabaababaabbaabbbaaaaabaabbbbabbbbbabaabaaaaaaaabaaabbabbbabbabaaababbbabbbbbaabbabababbaabaabbbbaaabbbbbaaabbababbbabaaabbbabaabbabbababaabbbabaaabaaabaaaaabbaabbbbbaaababbaabbbaabbbababbbbbbababbabaaababbaaaaabbababaaabbaaabbababbaaaaabbabbaaaabbbbbbaabbbabbaaababbabababababababababaaabaabababaaabbaabbbababbbaabaaabbbaaabbbbabbbbaaaababbbabaaaababbaaababababaaaaaaaaaababbbbabbbbbaabaabbbbbbaabbbabbbbabbabaaaaabbaabaaababbbaaaabbabaaaabaabbaaaabbbbbaaaababbbbbbababaababbbabaababababbaabbbbbbbaaaababbabbababbbabbaaabbbaaaabbbaabaaabaabbbbabababaabbbaabaabbbbababbababbabaabbaababbbaaaaababaababbabbabbabbaabbbbabbaabbbaabbbbabaababaabaaabaabbbbaabbbbabbbaabbabbbabbaaaaaaaababaabaabbbabbabababbbaaaaabaababbbbabaaababaaaabbbbbaaaabbabaaabbaabbaabaaaababbbbaabababbabbabaaabaabaabbaaaaaaaabababaababbbbbaaaaaababbaabaabbaabaaaaaaabbbabababbbaaabbababaabaabaabaabbbabaaaabbabbbababaabbaaaaaaaabaabaabbbaaabbbaaababaabaabbababbbbaabbbbbbaaaabbaabbaaabbbabaaaaabababbabbbbbabbabbaabbabbabbbabaaababbababbbabbbbabababbaaaaaabbaabaaaabbbbaaaabaabbbbabaaaaaaaabbbabbaaabbbbababbbbaabbbbbaaaaabbaabaabababaaaababbaabaabbbabaaabababbbaabaaabbaaabbbaaaabaaabaaabbbbbaaaaaabaabaabaabababaaaabaabbbbaaabbaaaabbbbaaaabbbaaabbababaaabaaaabbaaaabaaababbabbaaabaabbbaaabbaabbbbabaababbababbbbababaaaaababbaaabbbbbbbbabaaaabaaabbabbbaababababbaaaabbbaabababaaabbbbbaaababbababbabaaaaababaababbbbbaaaaaaaaaaaabbbbbbaabbbbbbabbbbabbbbaabaaabaaaaabbabbaabbbbabbbaababbbabababbaaaaaaaaabaabbbabbbbbababbabbbbbbaaaabbbbbabbbbaaabaaabbaabaabbbbaabbbbaababbaabaababaaabbaaabbbbbababaaaaaabababbbaaaababbbbbbbbbbbbabbaaaaabaabbababbbbbbbaaabaaaabbaabbbabaaaabaaabababbbaabbababbbaaabaabbbaaaaababbbbaaabbabaabbaaaaaabbbabbbabbbbbaabbabbaaaabbbabbbaabbbabaaaaabbaabaaabaabbabbabbaaababaaaaabbbbabbbaaabbbbaabbababbbabbaaabbbabbaaaaabaaaabbabaaaabbbbaaabbbbbbaaababbbaabaabababbababaabbbaaaaaabaababbbabbabbbababaabbbbaabababaaababbbaaaabbbbababbaaaabaaaabbaabbabbabbabaaababbbabaabbbababbbaabababaabbaabbabaabbabaaaabbaaababaaabbaabbababaabbbbbbbaaaabaabbaaababbbabaabbaababbabbbbbabaababababababbbabbabbbaaabbababbbabbabbbaabababaabbbbabbaabaaababaababaaabbbbbbababaabbaababaaabbbbbbbababbbababbbababbbabbbbbbaaaabbaababaaabbabbbaabbabbbbbabbbabaaababbbbbbbaabbaabaabbabaabbabbbbbbabbabaabbabaabbbbbbaaaaaabbababbaabbababbababbbaababaabbabbabaabbbaaabbbbbbbaaaaaabbabbaaaababbbbabbbaaaaaabaaabaaaabbbaaaaababbbabbabababaabbbaaababbbbababbababaaaaababbaaaaabaabaaabaabbbabbbaabbbbbabbabbaaaabbaabbbaaabbaaabaaaabbaabbaaaabaabbbabbbababbababaaaaaabaababababbbaabaaaabaaabaaaaabbbaabababbbaabaabaaaabbbbabbbbaabbbbbaaaaaaaaaabbabaaaabbbaaabbbaabbbbbabbbbbbaaababaabbaabbaabaaabbabbbabbabaabbbbaabaaaabbaaabbbabababaabababaaaababaaabaabababaaabbbabbbbaaababbbbbbbaababaaaaabaabaaabaabbbaaaabaabbaaabbababbabaaabaaabbabaabaabbbbabbbbaabbbaabbabaaababbbbbbbababaabaabbbbbaabbbbbbbbababaaaababbbababababbbbbaabbbaaababaabbabaababaaaaaabbabbbabbaabababaaaaaaaabaabbaabbbbbababaabbbaaaaabbbabbbaababbbbbabbbabbabbabbbbbbabbabababaabaabaabaabbbaabbaabbabababaaabaabbabaaaaaabbaabaabaaaaabaabbabbbbabbbaababbaabaaababbababaaabaaaaabbbabbbbababaababababbaaaabaaaaaabbbbabbabbbbababbbbbbbaabbabbababababaababaabaaaabababababababbabaaaabaaabaaabaabbababbaaaabababbbbabababbbbbbbbaababaababbaaabbabbaabaaababaaaabbaabbaabbbbaabbbaaabbaababaaabbababbabbaaabaaabaaabbbbababbabbbbabaabbbabbaaaaababababaabbbaaababaabaabbbbabbbabababaababbbabaaabbbaaaaaabaaaaaaaaabbabbbabaaabbabaaabaaabaaabbaaabaabbbbaaabbbbabaabbbababaaaaabaaaabbaaaaabbbbabbaaaaaaababababaaaaabbabbbbbbabbaaabbabbbbababababbbaabbbbaababaaaaaababbbaaaabbbbbabbabbabababbabaabbabbbbbaaaababbbbbbbabbbaabaabbabbbabaaaabbabaabbbaaabbbbabbabbbabbbbababbbabbaaaababbbaaabbaababaabbabaaaaababbaabbaabbbbabbbaaaabbaabbaaabbabbaaaabaababbbaabbabbbabbbbbbbaabbaabaabbbaaaaaabbbbbbabaaabbabaabbaabbbababbaabbbbbbbaaabbbbabaabbbbabaaabbaaaababbbbbabbabbaaabbbbbbaaabbbbabbbaaaaaaabaabbaabbaaaaaabbaaabaabbbbababbbbaabbabbabbbbaaabbbbabbbabaaabbbaaaabbababbaabaabababaaaabababaabbbaabaaababbbbbaabbbaaaaabbabbaaabbbabbbaabbbbbaababbbababaaaabbbbabaaaabaaabbbabaaabababaabbbbbaaabbaababaaababbbaabbababbabbbaababaaaaaaabaaabaabbaabbababbbababbaaababaababaaabaaaabbbabbbbbbaaaabaaaabababababbabbaaabaaaaaabbbbbaabaaabbabbabbbaababaabbababaaaababbaaaaaaaabbabaabbaabaabaabaaaabaabbababbbbabbbaabbbbabaaaaabaaaaaaaabbaabbbbbabaababaaaabaabbabbaabbbabbababaabbbbbaaaaabbabaabababbaaababbbababbbabbaabaabbabbbbababaabbbaabbbabbabbaabbbaaabbababaabbbbbbbbabbbaaaabaabbbbbaaabaaaabbabaaabaabbaabbbbbbbbbbabbabaabbabaabbbaaaabaabababaabaabaaabbbbbaabbbaaaabbaababbaaaaaaaaabbbaababbbaaababaaabababababbaabaabbaaababbbbabbbaabaabaabaababbbbbbbbaabaaabaabaabbbbabaaabaaabbaabbbbbbbbbaabbaabbbabbbbbabbbbabbabbaaaaabaabaaaabbbbbabbbbabaabaaabbbbabaabbabababaabaaaabbaaabbaaabaabbaabaabbaabbaaaabbbabbbaabbbabaaabaaabbbbbbbbbababbabbaaabbaabbbbbaaaabbbababbaaaaabbbabababbababaabaaabbbabbbabbaabaaaabbbbabbabaabbabbaaaabbbbbbabbbaaaababaaabaaaaabbababababababbaabbbaaabbabbbaabbbabbbbababbbbababbbaaabbaaabbbaabbbbbabbabbbabbaaaababbaabbbbababbaaaaaabbbaabbbabaaaabaabbaaababaabbaabbbbabbabbaabbbabbababaabaabaaaabbbabbbababbaaabababbaaaaababbbaababababbaabaaaabaabbbaaaababbabbbbabaabaaabbbbabaabaabaabbaaaabbbbabaaaaaabbbaabbbbbbbbbabbaaaababbbbbababbbabbbbababaabaabbabbbbabbbbbaabbaabbabaabbbbaabaaabbababbaaaaaabaaabbababbbabbbaabbabbbaabbbbbbabaaaabbbaaabababbbaaabaabbbaababbbaabaaabababaaabbabaaaaababbbbbbabaababbbbbbbabbbbbabbbbabababaaababbbaaaaabababbaaaaabbbabbbaabbaaabbbbaabbaaaaabaaabbabbbababbaaaabbbaabbbaaabbabbabbbabbbaaaabaaabbbaabaabbaabaaaaaabbbbbabbbbbabbbbabbbbbaaaabbaabbbbaaaabbbbbabbbabbbaababababaaaaaabbaaababbabbbbaaababbbbabbbaabbaaababbbaaabbbababbabaaababaaaaabbbaaababbabaabbaaaababbbaabbabbaaaaabbbababaabbbbbbaabbbabbaababbabbbaabbabbabbbbababaaabababbaabbbbbaaabbbaaababbaabaaabaaaabbbbaaaaabbabbbaaaababaababbaabbaabababbaabaabbaaaababbbbbaaaabaabaaaabbabbabbbbabbbaabbbbbaabaabaabbaabbababbaaabbbaaaabbaababababaabababaabaaaaabaaaaababbbbbbbbabababbbabaabbabaaaaaaababbabababbbbabbbbaabbabababbabbaabbbbbbaabbabbbababaabbaababbaaaabaabbbaabbaaaabbbaaabbbababbbaaabbbbbaaabbabbbbaabbaabbabbababbaabbababaabbababbaaaaababbbbbbbbabbbaaaaababaaabbaaaaabaaaaaabaaabbbabbaaaaaaaaaabbaaabbbbbaaabaabbbbbbbaaaababbabbabaabbabbababababbabaabbbaabbabbbbaaabbbbaaabbbbbaababababbbbaaabaabbaaaabbbaabbaabbbaabbaaaabbababaaaaabababaaaaaaaaabbbaaaabaaabbaabbaabbbababaaabbabbaaaabaabbaabbbababbbbaaaabbabbbbbbaabbbbabbaaaaabbaabababaaabababbaabbbbbabaabaabbbbbbaabbababbbbbbaabbaaabbaabbaaababaabababaabbaaaaaaaaabaabbbaaaaabbabbabbabaabababbbbaaabbbabaaaabbbbbabababbbaabbbbbbaabbabbbbbababbbababbbbbabbababbbbbabbbbaabbaaaaaababbabbabbbabbbbbbabababbaabbabbbbbbaaaaabaaaaaaabbbabbaabaababbaaaabbaabbbabbaaabaaaaaaabbbaaaabaababbbaaaaaaabaaaabaababbaaabbbbbbbbabbababaabbbbaaaaaabaabaababbbbababbbbabbbaababaabaaabbbabaaaabbbabaabaaaaaaabbabbaabbabaabaaabbbaabbababbbbababaabaaaabbbaaabbbabbbabbaaaabaabaaaaaaaaababbabbbaabaababbabaababbbbaabababbaabbabaaabbbbbbaaaabbaaaabbabaabbaaabaabbababbbbaabbabbabbaaaabaaaabbaababbbbaabaabaaaaaabaaaabbbaababababbbbbbbbabbbabbabbabbbbabbbaabbaaabbbaabaabbbbaaabaababaabbaaaaabaaaabababbbbaaaaabbaaaaabaaaaaabbabaaaaabbaaaaabbabbbaabaaabbaabbbabbababbabaaaaaabbaababababbabbaaaaaabaaaaabbbabaaaababbabbaabaabbabababbaabbabbaaaaababaabbbaaaabbabaabaaaaabaabbabaaabaaabaaabbbababbaaabaaaabababbbaabbaabbbbaaaabbabaabbaabbbbababbabababbbaaabbbabaaabaababbaabbaaaaabbaaabbbabbbbaaaabaaabbbaaaabbbbabbabbbbabbbaabaaaabaaabbababbaaaaabaaaababbabbbaabbbaababbaaababbaabbbabbbabbbaabbabbaababbaabaaabbaaaabaaaaaabbbbaaaababbbaabaaabbababaabaaaabbabbaaaaabbbabbbbaaaabbaabbbbbabbababbabbabaababbaabbaabbabaaabaabbaaabaaababaaabaaababaaaaaaaababbabbabaaaaabababaaabaaabbaaaabbbbbabaaaabbbaabaabaaaaabbabbbbbbbaabababbbabbaabaaabbabbbbbbabbbbabbababbababbaaabaabaababaabaabaaaabaaaababaaaaaabbbbabbbbbbabaabbbaabbaabaaabaabbbaababbbabbaabbabaaaaaababbbbbabbbaabbabbbbabaaaaabaaabaabaabbbbababababababbabbaaabaaaababbaabbaaaabaababaaabbbbbbaaaabbbbabbbabbabaaaabababaabbaaabaababbabbbabaabaabbaabaaaabbbabbababbbbabbbabbbbaaabaabababaabbaaaaabbabbaababbaabbaababbbbbbbaaabbbabbbbbbbbaaabbabbbbabbbababaabbabaaabbbaaaabbababaabbbbbabaaaaaaaaabaaababaaaababbabbabbababbababbaaababaaabbbbaabbbbbbbababbaabbbababaababbaabbbaabbbbaaaababbabbaabbbbbaaabaaabbabaabababaaababbabaaabaabaabbbbabbaabababaabbbbaabbababbbabaaaababbabaaabababbbbaaabaababaaabbaabbabaabaaababbaaaabbabbbabaabaaaaabbaaabbabaabbaaabaabbbaaaaaaabbbbbaaabbbabaaabaaaabbbbbaaaababbbbbbbabbaabababbabbbbbbbbbbabbbabbbbababaabaaaabbabbbabaabbbbaabbabaaaabbbababbbbaaababaaaaaaabbbabbbababaaabaababbaaabababbbbaaabaabbaabbbabbaabaaababaabbbaabaaaabbabaaaaababbbababbbbabaababbbbbbbbbabbbaabbbbbabaaabaaaabaaaaaaabbbabbaaabbaabababbbbbabaabbbaaaaaaabbabbbbbabbaabbababaababaaabbabaabbbaabababbbaaaaaaabaaabbbbbbabbaaabbabbababbbaabbababaababbbbaababbababaabbabbbbbabbbabaaaaaababaaaaaabaabaaabbbbbbababbaabbaabbbabbbbaabbbbbababbbbaaaaaaabababbbabaababaabbbabbabaaababbaaaaaaaaabbaaaaabbaabbaaababaabbababbaaaaababbabababbaaabbaaabaabaaaababaababbbbaaaabbbbababaababaaaabbaabaaabbaabbabababbababaaaaaabababbabbaabaababaabbbaabbaababbbabbbbbbbbaaabbababbaaabaaaabbabaabbaaaaaabbbabaabaaaaabaababbaabaabaaaaaaaaaababbabaabbaaababaababaabaabaababaabbbbbbbabaaaaabbaaaabbaababbbaaaaaaaaabaaaababababbaabbaabbabbbbaaabaaabababaabbbabbbbababbbabbaabbaabbbabbbbabbaaaaabbabaaabbbbbbaabaaaabbaabababababaabaaabbabbbaabaabbabbabaabbaaaabbababaaaaaabbabbbbbaababbabbbaaabababbaabaaaaaababbabbababaabbbbabbaabbaabaabbbababbbabbbabbbabaabbaabbaaaabbbbabbaaaaababababbaaabababaaaabaaaaababaabaabaabababbabaaabbbaabaabaabbbaabbbabbaaabbbaaaabbaaaabbabbaaabaabababbabbabaaabbbabaabbbbbbaaabbbabbaabaababababbbbabaaaaaababbbbaabbabaabaabbbbaaabbaaaaabbaaabbaabaaabaabababbaabbabaaabaaaabbbaaaaaabbbbbabbbbbbbbabbaaaaaabaaaaaabbabaaababbaaabbbbaaabbbabababbbbaabbbaaabbbaabbbbbbaababbbbbabbababaaabbabbaabaabbabbaabbababaaaabbbaaaaaabaaabbabaaabaababbbaaaabbaabbbbbbabaabbabbbbbbaabbbaaaaabbabbbaabbbababababaaabaabaabbbbaabbabbabaababbabbababbabbaaabbbbababbaababbaaabbaabababbaaaaaabaabbbbbabbabbbbbbaaabaaabaabbababaabaabbbbbaabaaabbababaababbbaaabbaabababaababbbabbababbaabaaaababaaaaabababaabbabbaaababbaabaababaaaaaabbabbbbbbbbababbbabbaabaaaabbbabababababaababbbabaaaaabbaabbbabaabbbbbbbaabbbbbbabbbaaabaabbbaaababbabaaaaaaabbbbbabaababbababaaababbaabbbbbaaababaabbbaaabaabbbabbaaabbabaaaaaaaaabaabbaaaabaabbaabaabaababaababbbaaabbabbaaabaabbbbbabbbbbaaabbbbbbbbbbbbababababbaaabaaababaaaaabbbaabbbbbabababbbaabaaaabbabbabababbbabbaaaaabababaabbaaaaaaabbabbaaaababbabbababbbbaabbabababaaaaaaaabaaabbabbaaaaaaabbbaabaaabababababbbabbbaaaabaaabbbbaaabaaababbaabbaaabbaaabaababaaababbbaabbaabbbaaabaaaabaababbbabbbabaaababbabaaabbabbbabaaaababbbbbaaabaabbbbaaabbaaaabbaaaaabbabbbbabaaaabbaababbababbabababbbabaabaaabaabaaaaabbbbbaaaabbbbbbaaabaaabaabababbabbbabababbabbbbbbabaaaaabbaababaaaabaabbababaaaabbabbaaabbbaaaaabbbabbaababbabaabaabbbababbabbabbabaaaabbabaaaaabbabababbbaaaabbaaaaaaaaabbaabaabbbbbabbababbbbaabbaabaaaaaababaaabbbabbbabababaaabbbbbbaabbaaababbabbbaaaababbbbbabbabaaaaabbabbaaaaabbbabaabbaabaaabbbababbababbabbbaabaaaabbbbbabaaaabbbaaabbbabbbbababbabaaabaabbbbaabbaaaabbbbbbabbbaaabaaaaabbbbbbbbbbabababaababbbbababbabbbbaabaaaababbabababbaaaabbbbaaaabaaaabababaabaababaababbabbbabbbbaababbbbaaaababaaaabaaaababaabaabbaaaaaabbbaaaaabaaaaabbabbbabaaaababbbaaaaaaabbaaaaaabaaabaababbabaabaaabbbaabbaabbaaaaababababaaaaaabaaababbbabbababababbbbbbabbabbbbbababbbbabbababbbabbabbabbbaaabbaabaababbbabbaababbabbaabbbbbbbbabbaabaaaaabaaabaaaabbabbbbbbaaaabaababaabbabbbabaaaabababaabbbaababaaaaaababbabbaababbaababaabbabababaaabbabbaabbbababbbbbabbaababbbabaabbababbaaaabbbbabaabbbbbbbaaabbbaaababaaaabbaabaabbbbaabbabaaabbbbabababbbabaababbbbabaabaaaabbbbabaabbaabbbaabaabaaaabbaaaaaababaabbbabbbaaabaaaabbbbaaaabbbaabaabaababbbabbbabbbaabbbbabbbbbaabbaabbbbbbaaabbbaabbbbbabbbbabbbbaabbaaaaaaabbaaaaaababaaabaabaaabbbaaabbbbababbabbbabbbbaabbabaabaaaaaaabbabbbbbbbaabaabbabbaabaababbbaabaaabbabbbababaaaaabaaabaaaaabbbbbabbbaabbbaababaaaabaaabbbbbababababbabababbabbababbabaaabbabbabbaaabaaaabaababbbaabbbabaababaaabbabbababbaabaabbbbbababaabbbaabbaabaababababbbbaabbabbbbbbabbabaabbbaaaababbaaaabbabbaabbbabaabaaaaabaababbaabababbbaaababbabbabbbabbabbabbbbaababbbaaabbbabbabbbabaaaaabaabbbbabaabbbabbabaaaabbabababbbbabababbbbabbaaabbbbaabbabbbaabbababbbaabbbbabbbaabababaabaababaabbaaaabbabaaaaaabbaabbbabbaabaaababbbbaaabbbabbbabababababbbabaaabbbaaaaaabababaaaaabbababbbaabaaabbaabbbababbabababababaabbbaaaabbabaaabbaaabbababbbbaabbbbaaabababaabbbabbaabbbabbababbbabaabaabaabbbaababaabbaabaabbbaabbbbaababbbabbaabbbbbabbaaabaaabbbbbbababaaabbbabbabbbbaabaaabaabbbbbabbbbbabababbbbbbabbbbbbaaabbabaaabababaabbaaabbbababaaaabbaaabbabbbaabbababaaabbbbaabababaabaaaabaaabaabaaabbabbabbbaabaabbabaabaababbabbbbaababbaabaaaababaabbabababbbaabaabbbbbabbabaabbbbbbbbbbabbababababbbbabbaabbbaaabbbbaababbababbbbbabababbbbabbaaaabbababbbaaabababaaabaababbbaabbbbbbbaabbbbbabbbbbaabbaaaababbbaaaaabbbabaabaabbbbbbbbaaaaaababaaabaabbbbaabaaabbbabbbbbabbaaabaaaaaaaababbaaabbaaaabbabaaaaabbbbbaabbbaabbaabbabbbbabbbaababaabbabaabababbbbbababbbbbaabbbbbbbbbbaaaabbabbaaabbaabaaabbbbaabbaabaaaabbabaaabbbbaabbabaaaabbabbaabaabaabbbabaabaaabaabaabaaabaaababaababbaaaaababbbabbbabbbbbabbaabbaabbbbabababbababaabbabbbababbbbbbababaabbbbbbaabbabbaabaababababbabbaabbaaababaaabbbbbbaabaabbaaababaaababababaabbbbaaaabbabbabaabaababbbbaabaabaabbababaaaaaaabaababbbbabbababbbabababaaabbbabbaaabbabbbbbababaabbaaaabbabbbbbabaabbabaabbbaabbbbbbaaabbbaaaabaaababaabbabbaaababbababbbbbabaabbaaabbaabbaaabbababbbbbaababbababaabbababbbabababbabbbabaaababaababbabaabbbbbbbaabbabbbabbbabababbabababbbbbabbababbaaaaabaabaaabbbabbbaaaabbaabbabbbbaabababbbabbbbabaaaaababaaaaaabbaaaabababaabbabbbbaaaaaaababababbbaaaaaaaaababbababbbaabaabaaabbbbabbbababbbbaabbbbbbbaababbabbababbbabbabbbaaaaababbbbaaabbaaababbabbbbaabbabbabaababbaaabbaaaababbbbaababaabbaaaabbabababbabaaabaababaabbbbbabbaaaaabbbbabbbbbaabbbaabbbabbabbbbbbaaaabbbabbbbbabbaababbaabbabaabababbaabbbabbaabbbbbbbbaaabaaabaaaabbaaabaaaabbababaababaabbbaababbbabbaaaabbbbabbbaabbaaaabbabbbabaabbaaaaaabaaaababbbabbbaaabbbbabaaaabaabbaabaaabbbaaabaababaaaaaaaaaaabbbaabbabbaabaaaaaabaabaaaabbabaaababaabbbaaaaababbababaaabbbbbaaaaaaabbababaabbbabbbbbbabbbbbabaababbbaaabbbbababbaaabbaabbbbbbbbabbbabbaababbbaabbbabbabaabaabbaabbbabbababaaaabbaaabbabaabbababbbaabbabbaaabbbbaabaabaaaaabbbbaaaabaabaabbbbbaabaaaaaaabbaaabbbabaabbbbabaaabbbbaabbbbaababbbaabbaabbaaabaaabbbbaabbaaaabbbaabaababbbabaaababaaaabbbaabbaaababbaabbaabbbaaaabbbaaaaabbbabaabababaababaaaaaababaaababbaaaababbaabbaabbbbaabbbabbbabaabaaaaabaabbababbbabaabbaaabbaabaabbbbabbaaabbabaabaabbaababbbaaabbabaaabaaababbbaabaabbaaabbabbbabbbaabababaaaaabaaaabbaaabbabaababaababbbbbabbbbabbbabbbbbbbabbabaababbaaaaabaaabbbabbaabbbaaabbabbaaaaaaaaabbbbababaaabaabbbababbbabbbbbbbbbbbaaaabbaabbbbbabbbaabbbabbbbaabaaaaabbbbabaaabbbbabbbbbaaaabbababbbabaaaabaabbbbaaababbaababaaabbbaabbaaabbbbabbabbaaababaabaaaabbaabbbabbbbbbbaaabbabbaababbbbaaabbbbbbaababbbbbabbbbbbbabbaaabbbbbbabbbbaabbaabbaaabbbbbaabbaabbabbbaaabaabbbbbbbabaababababbbabbbbabaaabbaabaaaaabbbbaabaabbabbaaabbbaaaabbaababaabaababbbbaabbabbabaaaaaaabababaaaabbbaaaaaababbbaabbabbabbbababbbbbabbabbabbabaabbaabbbabbbbbabbbbabbabbbaabbaabbabaabbbbabbaababaaaabbaaabbababbbbaaaabbbababbaaaabbbbaabaaabbaaaaaababbaaabbababbbaabaababbaabababbabbababababbbbbbabbbabaabbbbaaaabbaabaabaaaabbabbabbaabaaababbbaaabbabaabababaabaabaabababbabaaaaaaaaabaabaabababbaabbaaaaabbbbabbbabbaaaabbbaaaabbbababaaabbaaaaabbbabbabbbbbbbbababbbababbababaabbbbabababbbbabbbabaababababbbaaaabbbabbbbbaababbaaaabbaababbabbaabbaababaaaabbababbaabbabababaababbaaabbabaaabbbaababbbbabbbaabaaabbababbbbabaabbaaabbbbaabbbbaabababaabbabababbbaabbbbaaabbbabaaaabaaabbaaabbababbaabbbbaaabaabaababbbababbbabbaaabaaaababaabbbaabbbbbbaaabbaaabbaabbaaabaababbbbabbabaabbabaaaaabbbbaababbbbabaababbbbaabbaabaaaaaabbaabbaaabbbbaaaabaaabbabababbbbbbbbbababaabbbbbbaaabbbabaaaaabbbbabbbbaabbbabaaaaaabbbbabbbaabbbbbbbbaabbabaaaabbaabbbabbaaaaabbaabaababbbbbbaababbabababaabbbababbaaabbaabbbbbbbbababaaaaaabbbbaaaabaabaabaabbabbbbbabaabbbbaabbaabbbbaaabaabaaabbabbbbbbabababaaaaabababbbbaabababbbaabbbbabaabbabbabaabaaaabbabaaaabbbaababaabaaaaabababaabaaabaaabbaabbbbbabbbaabbabababbaaabbbbbbbbbaabaabbabababaaaaaabbbaabbabbbbaaaaabbbabbbabbaabbaaaaaababbbbaaaabbaaaabaaaaabbbbaaaaaaaabbaabbbbbbbbabbaaabbabbbaabaabbbabbbabbabbbabbbbaabbaaaaabaaabababaabbabababaaaaaaabaabaabbaabaabbabbbbaababaabbbabaaabaabaaaaaabaabbaabbaabbbbaabbbbbbbaaabbbbbbbbaababbbbabaaababaababababbabbbababbabbbbaabbaaabbaaababababbbbabaabaaaaababbbabaabbabbbaabaababbabbabaaaabbbabaaaaabbaaaaaaaababbabbabbabbbaaaaababbabbabbabbaabbaaabbbbaaabbababaabbbaabaabaaaabbabababbbababbabbabaaaaabbbbbbaabaaabbbaaabbabbbbbabbaaababaaaaaaaabaabbabaabbaaaaabbabbbbabaababaababbaababaaaaaababaaaabbabbbbbababbaabaaaabbbabaaabaabbaaabbbbaaababbbbaaabbabbbabbaabaabbabaabbaaaaabbabbabaabaaaaabababbabaabbbaabaaababbabbaabbaabbaabababbbaaaaabbaaaaabbbbaaaabaabbabbabaaaaabbbbbabaaaabbbbaaaabbbbaaaabbbaababbbababbbabababaaababaaaaaabaabbbaabaaabbababaaaabaabbaabaababbababaabbaabaabbaaaaabaaaaaabbbaabbabbabbbaabbabaaaabaaaabbbaabbabbabaaaaabaabbabaabaababaaaabababbbbbabbaaaabbbababbbbbbbabaabaababbababbbabbabbbbbabbababbbbabbabaabbaaabbbabaaaabbaabbbbaabaaabaaabbabaaaabaaaabaaaabaaabaabaaabaaaabbbbababbaaababbbbbabbbaabababbababaababaaabaabbabbbaabbabaababaaaaaaabbbbbbbabbbbbbabaaaaaaababbbabbabaabbbbabbbbbaabbbbabbbababbbababbaababaabaabbabaaabbbaaaabbbaabbbaabaaabaaaabbbaabbbbaaabaabbbabaaabbbabbaaababbaabbababbbbbbbbababaaabaababbabbbbbaababbbbaaaaabbababbaabbbababbabbbbabbbabbbbbbababaaaaabababaabababbbabbababaabbbabbbbabbbabbaaaaaaaaaaaaabababbbaabaaaaaabaaaabbabbaabbababbabaababbbaaaabaababbaabbabbbabbaabaabaaabbaaaaaaabbaabbbabbabaabaaaabbaabbaaabababbbbaaabbbbbaaaabaaabbbbbaabbbaabaaabbaaabbababbabaaaaababbababbbbaaabbaabbbaabaaabaaababbbbbabbbaabaaabbaaaaaabaabbbaabaaabbaaababbabbababbaabaaaabaaaaaabbabbaaaabbbabbaaaaaabaaabbaaaabaaaabaaaaaabbaaaaababbabbabaababaabaaaaabaaaaaaabbaabbbbabbaaaababaaababbbbbaabbbbbabbaabbaaabaaabaababbbaaaababbbaababbbbbaaaaaaaabbbaaaabbaabbabaaabababbbaaabaabaaaaabaabbbaaababbbaababbaaabbaabbbbaabaaaaabbbaabaaabaabaaabaabaabaabbaaabaababbbabbaaaaaaaaababaababbbbbbbbbbbaabbbbabbaaabbbbababbababaabbbaababbbbbbabbaabaaaaaabbaaabbaaaabaabaaabbaaaaabbbaabaaaaaabbabbbabaaaabaabbabaabbbbbabbbbabbbbaabaababbbbbbabbabbbababababbbbbbbbaabaabbaabbaaaaaababbabbabaababaabbbabbabaabaabababaabbbaababaababbbabaaaababbbbaaababbaabaaabbbaabbbbaaaaababbaaaaabababbbababbaaabaabbbbbaabaabaabbabaaaaaabaabbbaaaaababaaababbababaaababaabbbbaaaabaaaabaaaaabbabbaabababababaaaabaabbabaababbbaaaaaababbbbbaababaabaabbbabaaabbabbbbaaaabaabbbbbbbbbbbbaabababbabbabaaabbabbbbbbaabaabbaaabaaaabaaabbbaaaabaaaaaaaabbbababaaabbaabaabbaaaababaaaababbababaaaaabaababaaabbbabbbaabaabbbaaabaabbbbaaabababbabbbbabbabaaabaabaaaaaababaaabbabbbbbababbabbbaaaabbababaabbabbbbabbbaabbabbbaaabaaaaaaabbbbbbababbbabbaaabaabbaaabbbabaaabbbabaaaaaabababbbaabbbaabbbabaababababbbabababbbbaaabbbbbaabababaaabaaabaaabbbbbbaaaabaabbaaaaabbabbbabaaaaababbbabbabaabbabaababbabbaabaabbbbbbbaababaabbabaaababbaabbabaababbbaabbbbbbbabbabbaabbabbbbbbbbbbbaaaaabbbbaaaaabaababaabaaababbababbaabbbbabbbabbabbbbabaaabbaabaaabbabaababaaababaaabaaabbbbaabababaabbbbabababaabaababbbaababbbbabbabbbbabaaaabaaaaaaaabbaaabbbbbbaaaabbbababaaabbbbbbbbbabbabbaabbaaaabbaababbaabaaabbbabbbbabbabbbaabbbbabbbaabaabbaabaaaaaabbaababaaabbaabaabbaababbabaaaabaabbaabbbabababbbababaabababbabaabbabbababbaaaaabbababaaabababaaabaabbaaaabbbabababbabaabbabbaababaaaaaababaabaabbbbbaabbbababbbabbbbbbaaabbabbaaaabbbabbbbaabaabaabaabbaaabbaaaaabbbaabaaabbaabaaababaaaabbbabbabbbbabbabbababbaaabbaaaabbbbbbbaabababaaabbaabaaabaaaaabbaaaaaabbbabbbbbaaabbbaabbaaabababababbbbabbabbaaaabbabbaabaabaaaaabaabaabaaaaabbbbbabbbbaaaabbaaaababbbbbaaabbbaaababbbabbbabaaaaaabbbbbabaabbaabbaabbbababaabababbbbbbabbbaabbbaabbbaabaababaabbabbbbbbbaabababbbbaaabbabaabaaabbaabbbabbaabbaaabbbababaabbabbbaabbabaabababbbaaabbaaabbabaaaaaabbbaaaaababaaaaaabbabbaabbabbbaaaabababababbbaaaaabbbabaaaaaabaaaaaabbbbaaababababaaaaabbbaabaabaabbabababbbbbbbbabaababbbbabaabbaabbaababbbabbbaaabbaabbbababbbbabbaabbbaabbaabaaabaabbaaabbbbbbaaababbaaabaaaababbbbaabaaabbaaabbaaaabaaaaabbabbbaaabaabbbbbbaaabbaaababababababbbbbbbaabbabbbaababbababababbabbaaaaabbbbbabaaabaaaabbbbbaaaaababababaaababbbaaabaaabbaababbbbbbabaaaabaaaaaabbabaabababbaababbababababaabbbbbbaaabaabbabbbbbbbaabbaaaaabbabbbabbbbbbabaabbabbbbbabaabaaabbabbabbaaaaaababaabbaaaabbabbbbbbbbabbbabaabbaaabbbbaaaabbabaabbabaabbaababaabbabbaababbbbaaaabbababaabaaabbbbbbabbbbbabbaabbbabbbaaaabbbbababbbaaababababaaaababbababaaaabaaaabbbbaaaabbaabbabbaaaaabaaaababaaaababaababbababaaaabbaaabbbabaabaabbbbbbbbbabbbabbababbaaabababbabbababbaabaaaaababbaaaaaababbbbbbbbabaaaaabbaaaabbbaaaaabbbbabbbaababaabababbbbabbbbbaabbaababbbaaabaabaaaabbaaabababaaabababaaaaaababbbaabaabbaabbbbaabaabbaaabbbbaabbabbaabaabbbbabbbaabbaabbabaababbbbaabaaabbbaaabbababbbaaaabbbbbaabbabaabbabaaabbbaababaabbbbaaaaaaabababaababbabaaaaaabbaababbabaaaabbaaabbbbaabbabaaaaaaaabbabbbbbbabbaabbbabbbaaaababbbabbbabbbaaaabbababaaabbbaabbbaaaaaaaaabbbbabbbbbababbbabababbbabaaababbaaabbababbaababababbbbababbabaabaabbabaaabababbbbbaaaabaaababbabbaaabbbaaaaababbabbbababbaaaaaababbaaaabbabaababbabbbbabaabbbbaaabbbabaaaaaababaaabbbaaabaaabababbbabaaabaaaaaabbbabbbbbabbababbbbbbbabbbabababbbbaaabbabbaaabaabbbbabbaabbbabaaaabaabbbababbbaaaaabaabbbbbaabbaaaaabaaaabbbaaabaababaabbbaabbbabaaaaaabbbaaabaababbbaabaaaaabaaababbaabaaaaabbaabaaabbbabaababbaaabbababbbabbbabbbbbbbbaabaabbaaabaabababbaaaaaaabbabbbbbbbaaaabaabbaaabbaaabbaaabbabbaaabaabbaaababbabbabaaaababbaabbbaabbabbbabaababaaaabbbbaaaaabaabbbbaaaaabbaaabbbaaaabaaaabaabbababaaabaaaabbaaabbbaaaabababaaaababaabaabbabbabaaabbbbbbaababbaaabaabbbbabababbaabababbbbbabaababbabbbaabababbabaabaabababaabbbabababbbbbabaabbbbaaaabbabababbabbabbbabaabababbbaabaaaabbbbabaabaabaaaaababababbbbbbabbbbabbbabaabbbabababaaaababaaaabaabaaaabbababbbbbaabaaaabaabbbbbaaaabbbabababbbbbabbaaabaaaabbbbaabababbbaaaababbabbbaabaabbaaaaaaaaabbbaabbabbbbabbaabbabbbaaabaababbabaaabaabbabbbbbabbbaabaaabaaaaaababaaabbaaaabbabbbbbababbbbbaabaaaabaabbaaabaabbaabbbbababbaaabbabaabbbaaabbbbbaabbbbabaabbbbbbaaaabaaababbaaabaaabbbabbaabbababaaabaabaaaaabbabbbabababbabaabbbaaabaabbabaabaabbbbabbbbabbbbbbbbabaabababbabbbbbbabbbabaaaaababaaabbabababaaaabbabaabaabbbababbababbbaabbaaabbbbababababaabbaaaabbabbbaaaababaaababaaabaabaaaabaabbbaabbaabbabaabbaabbabbbaaaabbabbbbbaababbabbabbbbaaababbbbbababaaaaaabbbbbbaaabaabaaaabbbaaaaaaaabaabbbababaaaabbaabbabaababaaabbabaaabbaaaaababababbbaaabbabbbbbbaaaaabaababababbbbaabaabbbbaabbbabbbabbbababaabbababbabbbbbbbbababbbbabababbbabaabaabaaabbabbababaabaaaabbbbbabaaabbbbabababbababbabbbaaabbbbbaaabaaaabbaaaabbababababbbaabbababaabbaaaaabbbaabbababbaabbaaababbaabaabababbbaaaabbbaaaaaabbabbbbaabbabaaabaaababaabbbbabbabbbbabbbbaaabbbabbbbaaaaaaaababbaababaabbabaabbabbaabbbaabbbabaababbaaabaaaaabbbabbbababbbabbbbbbbaaababbaababaaababaababaabbbbaabbbabbbbaabaaabbbaaaaabaaababaaaaabaabaababababaaaaabbbababbbbabaabbababaaababaababbabbbaababbaabbbbbabaabbabaaaabaabbabbaaabbbbbabbbbbaaaaaaaaabbbbaababbabbbbabaabbabababbabababbabbaaababbaababaaabbbaaaaabaababbaababaaaabbaaabbabaabaababbaaababaaaabbabbaabaabbabbaabbabababbaaaaababbaabaabbabbbbbaaaaaabbaaaaaaaabaabbabaabaaaabbaabbababaaabababbbaaabaababbabbbbaaabbbabbbbbbbabbaaaabbabaaaabaaababbaabaaaabbbbbbbbbbbbbababbaabaabbbabbbaabaabbbbbbbbbbbbaaabbabbbaaaabbaaabaababbbbbaaabababaaababbbbaabbbabababbaaabaaabaabbbbabbbbaaabbaaaaaabbabaabbbbbabbbaabaabababaaabababaabbaaaaaabaaabbababbabbbaabbaabbaababaaabbbbbbbbaaababbaaabbababbaabbbbabaaaabbbbbbaaabbabaababbbbbaabaaaabbabbbabbabbbbabbaabababbaaaaaabbbaaaaaaaabbabbbabababaaabaabaaabbabababababbbabaabbabbbbbbbbbabbbbabbabababbaababbababbbaaababbbabbbbaaaaababbbaaabaabaababaabbabbabbbbbbbbababbbabaabaaaaababbbbbbaabaaababbbbbbaaaababbabaabbbabbaaaabababbbbaabaaaaababbaabbbbbabbabaabaababbbbaaabbabbbbbbaaaabbbbaabaabbbabaababbbabaaababbabbbbaaababaaabbabaaaaaabbbbaabbabbabaaaabbbaabbaaaabaabbbbaabbbbabababbaaaababbbbbbbabbbbbbaabbaaabbaaababbaabababaaaaaaaabaabaabbbabaabbababaabaaabbabbbaaaaabaabbaaabaaabbaabaabaabbabbaaaaabbaaabbbbbaaabbbbbabbabaaabbaabbbbaabbbbbabbabababbaabbababbaabbaaabaaaabbbbaabaabbabbbbaaabbaaabbbbabbbabbbbabaabbaaabaaaababbbababbabbbbbaabaabbbababbaabaaabbbbababbbaaaaaabbbbbbabaaabbbabbbababaabbbababbbabaaabbbbababababbabaaaaabaaaabbaaababbbaaabbbbabbbbaabaabbabbbaaababbbabbaaaaabaaaaabbbaababaaaabbbbbbabaabaaabababbbaaaaaababbbbbaababaaababbabbbbbaaaaaabaabaaababbbaababbbbaababaabbabbaaababbabbababbbaabaabbaababbbbbaaaaaabaabbbabbaabbbbabbbabbabbabbbbbaabbaabaabbababaaaabaabaabaababbbabbaaabaaabaabbbaaabaabaaaaaaabaaaaaaaaababaabbaaaabbababaaabaaabbbaababaabbabbabbaabbabaaaaabbabbaabbabbbbabaabaabbbbbbbbbaabbabbbaababbabaaabbaababbaaabbbaaaabaabbbabbabababbbbbbaaaabbabbababababaabbbbbbbbbbbabaaaabaaababbbbbbaabbbaaababbababbbabbaaababbbbaaaabbbbababaaabbbbbbbbaaabbbbabaaababbbabbaabaaaabbabaabbbaabbbbbbaabbbbabbaabbaababbbaabbbabbbaaaabbaaaabaaabaaaaaabaababbbbabbaabbaabaabbbbaaaabababaaabbaaaaaaababbbbaaabaaababaabaabaaaaaaaababaaabbbaabbbaabbaaabbbbbaabbaabaababbbbbaaabaaaabaaabbbaaaabbbbabaaabababaababbbbabbabaaababaabbabaabbabbbbaaaaabababbaaaaabbbbaaabaabbbbbbaabbbabaabbbabbabaaaaaaabababbaabbbbaabbaaaabaabaabaabaaabbbaabaaaabbabbbbabbbbaaabbabbaaaabbabaababbbbbabaabbaabababbabaaaaaaaaaababaabbbaaabaaaaaababbbabbaaababbbbaaabaaaaaaabbbababaabaaabaababbbaababaaaababaabaabaaaaaaaabbbaabaabbbbbbabaaabaaaaabbaabbaababbbbabbabbabababbababbaaaaaabbaababaaaabaaabbbbbbaababbaaaababaabaaaabbbabbaaaabbbabaababbbbbaaabaaabbababbbbbaabaaabbbaababababbabbbaabbababbbbaaabbabbababbbbbbababaaabbbbabaaaaaabaaaaabaaabababaabbaabbabbbbabbaabaaabababbbbbbaaaababbbbbabbbbbabbbabaabaabababbabaabababaaababaaaaaaabbabababbbabbabbaaaaabbbbaaaabaabbbbabbaabbaabbabbbbababbabaabbbaabbbbaabaaabaabbababbaabbbaabbbbbaabaaaabbabaaabaaaaabbbbabaabbaaaaaaabbbbaaaaaaaaaabbbabbabbaaaaaaabaaaaababababaaabbabaabaaababbaaabbbbbbaabaaaaaaaaabaaababaaabbbabbaabbbaaaaaabbbaaaaabaabbabbbbabbaabbbbaaabbbabaaabbabababbbaababbababbabaabbbabbbaaaaaaabbababbbabaababbaaaabaaaabbabbabbabaaaaabbbabbbababababaaabaaaaaabbbabbaaabaaabbbbbabbbbbabbbaabbbbbbaabbabababbababaabbaaabaabaabaaabababbaababbababbaaaaaabbbbbaabbbabbbbababababaabbababbabbbbaaabaaaaabaaaabaababbaaababbaabbbabbaababaabbababbbbaabbbabbbbbbaabaaaaabbaaababaaaababbabaabbbbabbbbaabbbababbbbaaaaabaaabaabaababaaabaababaaaaabbabaabaababbbbbbabaaababbbabbaaababaaaabaaabbaaabaabbbbbbbbbabbaaababbaaababbaabaabaabbabbabbaabaaaabbabaabbbbbbbbabbababbbbbbbababaaabaabbabbabbaaaabbaabbabaabbabbaababababbabaaabaaabaababbbabbbabbbabbaabbbabaaabbababaabaabaabaaababaaaabaaaaaaaaababbaabaaaaaaabbbaaabbbbbaabbbabbbbbaaaaababbbbaabaabaaaabbababbbaabaaabaaababbbabaaaaaabaababbababbbbaaaabbaabbababbaaabbabbbabbbbbbabbbababbaaaabaabbbbabbbbabbbbaabaababbbbababbaaabbbbbbbbbaabbbaaabaaabbabababbbbabaababbbbbbbbbbaababbbbabbaaabbbabbbabbbbbbaabababbbaaaabaababaabbabbabababbabbaabbabbabaababbbaababbaaaaaabaaabbabbaabbabbbbbbaaabaabababbbabbbbbaabbbbbbaabaaabababbbabbbabbbabbbbbaaaabaaabababbbaababaabbaababbbabbbbaaabbbabbbbaaaaabbbabaabaabaabaababbbbbabababaaabbbbbbbbbabbbbbbababbaabbbaababaaabbbbabaaaabaaaabaabbbbbabbbaaaabbabbbaaabbaaabaaaabbbbaaaaaaaaaabbbaabbbbbbaabaaaaababaaaabbbaabbaaaabaaabbbbbaabaaabbbaabaaabaabbaaaabbababaaaaaabbbaababbaaabaaabbbbaaababbaabbbaabbbabbbbbbbaaababbabbbbbabaaaaaabaabbbaabaaaaabbbbbbabaaaabbbbbaaaaaababbabaaabbbaaaaaabbbbaaabaabaabaaaabaaaaaabaaabbaaaaaabbbabaabbbbbbabbaabababbbaaabbaabbbaabbbaaababaaababbbaabaababbbaabbbabaaaabaababaabbbabbbbbaabbbbabbabababbabbabaaaaaabbbabbbaabbaaaaabbbbbbbaaabbaabaaaaaabaabbbbaaaabbbababbbaaaaabbabaaabbaaabbbaaaaabaabbabbabbbaaaaaaabbbbbaabaaabaabbaabababbabababaabaabaabaaabaaababaabaababbbbbbabababaababbabbaabaabaabaabbabaabbbbaabaababaabbabaabbaaaaabbabaaabaabaabaabbbaaababaaaababaababaaaaaaabbabbbabbabbbbbabbaabaabbabbbaabbabaaaabbbbaabaaababbbbbaabaaaaaaaaaabaabbbbbbaababbabbaaaaaabbbbbbbabaabbaaababbabbaabbaabbaabaaababaabbaaaabbbbbaababbabbbaaabbbbabbbabaaaaabbabababaabbbababbbaabbbbababbbabaabbabaaaabbbbabaababbbaabbbbbabbbabbaaaababbabbaaaaababbababbabbbbbababaaababaaabbbbbbbaabaabbabbabbbbbbbbabaaaaaaabbabbaaabbaabaabaababbbbbbaabbabbbaabaaababbbbbaabbbabbabaabbbbbaaababbaabaababaaaaabbaaababbbaaababbaaabababbaabaabaaababbbabbbabbaabbabbbaaabaaaaaaaaaaabaabbabbbbabbababbbbaaaabaabaaababbaaaaabbbbbabbaabaaaaabbbabbbaaabbbabbabbaabaabaabbaabbabbbaabbabbaababaabbaabbbbaabbbaababbabaaaabaaaabbaabaabbabaabaabbbbbaabbbabaaaaababbbaabaababbabbbabbbbbbbbbbabaaabbbbbaaaaabbbbaabaaaabbbbbbabbbababaaaabbbaaaaabbaaaaababaaabbababaabbbbbabbaabbbabbbbbbaaaaabaabababaaababbbabbbabbaabbaabbbababaabbaaabababaabbbbbbbbbaabaaabbaaabbbbaaaaaabaababababaabbbaabbbabbbbbabbaabbbaabbabbabaaaaabbababbabaabaabaaabaabbaabaababaababbbaabbbaabaabbaaabaabbbabbbaababbaabbaababbababbbbbbbaabaaabbaabababbabbababbbbaabbaabbabbaababbaabbbabbaabbabbbbabaabbbbabbbbabbbbabaabbbabaaabbaababaabaabababbaabaabbbbaaaabbbabbbaabbabbaaaababbbbababababbbbbaabbabaaaabbaaabbaabababbbbbbabaabbbaaabbbabbbaabaabaabababbaabababbbaaabaababbbabbabaaaaaaaabbaabababbabbaabbababbbbabbbbaaaaaabababbabaabbaaaaabbaaaaaabbbbabbbbbaabbbbabaabababbabbbbbbbbbabbbaabaababaaaaababababaaababbabaabaaaababaabbaaaaaabaabababaabaaaababaabbbbababbbaabbbbbabaabaaabaaaabaabaaaaaabaabaababbabbabbbbabaaabbabbaaaaaaabaabbbbabbbbbaabaabababbbbabaaaaaaabbaabbabaaaaababababbaaabaaaabababbabaaaaaabbbaabaaaabababbbaabbabbaaabbaababbbababbbbaabaaababbbbaaabababaaababbbbababbababbaabbaabbabbbabbbabbaaaaaaaaababbabbabaababbbaaabbbbaabbabaaabbabbbabbbabaabbbaabbaabbaabbaaabbaabbbaabbaaabaaabbbabbbbbbbabaaabababbbbbbabbabaabaabbbbaabbabaaabbabbbaabaabbbbaababababbbaabbbabbbbaaaaaaaaaabbababbaababbbbbbbbabbbaababbabbbaabbaaabbaabbbaaaabbbbbbaaaabbaaababaaaaaaaababbababbbaaababbabbaabaabbaabaabaabbaabbabbbaabaabbababaabbaaabbaabbbbaaaaabaabbbabbabbbbaaaabbbaaaabbabbabbbbbabbbbabababaabbbaaaababbbbbaabaabbbaaababaabbabbbbbbaaabaabbbaaaaaabbababbaaabaababababbbbababaaabbabaabaabbabbbabbababbbbaaaaaabbbaababaaabbbabbaabbbbaabaabaaaabaaaabaaaababbaababaaaaaabaaabbbaaabaaaababbbbaabababbbbaabbababaabababaaaabbabbbbabbbbaaaaaaabbaaaabbbaaaaabbbaabbbbbaabbaaaabababbbbaaabbabbbbbbabbbbbaaaaabbabbbbaaaaabbabbbbbbabbaaabbbbabababbabaabaaabababaaabbabbabbaaaabaaabbbaaabbbabbaaabaabbbababbaaaaabbababbaababaaabbbbabbaabbbbbbaabbbabbbbbbababbbaabbbabbababbaabbaaabababbbaaabbbaabbbababaaaabbbbabbbbbbaabaaaabbaababbabaaabaabbbaabbaabbbabaabbaaabaababbbaaabbbabababbbaabaaabbbaaababbbabbaaaaabaaaababbabbaaaabaaabbbbaababbbaabbbbbbbbaabababababbaababbabbbbbaaabaaaababbbaaabbaabbaaaaabaabaaabbaaaaabababbbbabbbabbaabbbbbbbabbbabbbabbaabbbaababbbbabaaabbabbbaaabbbabbababbabbaaababaabbbbbbaababbbaabbababababbaaaaaababbbbaaaabbababbbababbaaaabbbaabaaaabbaaabababbaaaabbbbaabaaababbbbabaabbaabaaabbbbaabaaabbabaaabaabbbaaaabbbababbaaabbbabbabbaabbabbabaabbbabaaabbababbbababaabbbbbbabababbabbaababaaabbbbbaabbbbbababaaaabbbbababbbabbaabaabaaaabbaaabbbbbbbbaaabbbbaaabbabbbabbbaaabaabbbabbbabbbbaaabbaabababaaaabbbbaabbaaaaaabababbaababaaaaabbbbbbabbabbbaabaaaaabaabbabbbbabbbbbbbabaaababbaabbabbabbbbaabbababaabbaaaabaabbaabbbbbbbaaaaabaaaabbabbaabaaabbabababbbabbbabbaaaaababbaaababaaaabbabbbbbababababbaabbbbabaaaababbbaabbaaaabbabaabbbbabbaaaabbaaaabababbbbabbbbabaabaababbaabbbaabbbbbaaabaabaaabbbabbabbaaaabbaabababbbbabbaabbbaaaaaabaabbbaabbaabaabababbabbbaabbbaaaaabbbbbabaaaaabbaaaabbbabababbbbabaaabbaaaaabbabaaabbabbbabbbbbbaaaabbaababbbbbbbabbabbbababababbabbabbabaabbbabbaaabaaaabbaabababaabaabbabbbbbaababaaabbbabbaaaaaaabbababaaaaabaababbabbbaaaabaababaabbaabbababbbabaaabaabbbababbaaabaaabaaabbbbbaaaaababaaabbabaabbaaaabbababababbbabbabbababbbbbbbbbabbabbbbbbababaaaaaaabaaaaabaabbbabaaababaabbbbbbabbaaababbaaabaaabbbbbaaabaabababbabaaaabbaababbbaaabbbbaaabaaaaabaabaaabbaaabbabaaaaaaabbaaabaaaabaaabaaabaaabbaababaaaababababababaababbbabaabbbababababaabbbabaabbbbbbabbababaaabbabaabaaabaabbbbbabaabbbbbabaaaaaabaaababaaaaabaaababaabbbaaabbbbabbbbbabaabbababbaabbaaaaaabaaaaaaabbaaabbbbaabbaabbaabaabaaaaaaabbbbababbbbabbbabaababbbbbaaabbabbabaabbaaaaabbaaaabbaababaabbbbababbabbaabaaabbbabaaabbaababbbbbaabaabaabaaabbababbabbaaaaababaababbbaabbabaabbbbaaabbababbbbaababbabbaabbbababbaaaaababbbbbabababaaaaaabbaabbaaaabaaaabaaabababbabababaabababbababbabbababbbaaabbabbbaaababaabbbbababbbabaabababbbabbbabbbbbbbabbabbbbababbaaababbaababbaabaaabbbbabbabaabbaaababbaabbabbabbaaabbabaaaabbbabbaabbbbaabbabababbaabbabaabaabbabbababbbaababaabaaaabbaabbbababababbaaabababbbabbabbaabbbbaaabaaababbbaaababbabbaabbbaaaabaabababaabaababbbbbabbbaabaabaaaababaaaaaabbbbbabaaaaaabaabababbbabbaabababababaaabbbaaabbaabaaababbbaaababaabbbabaaabbbabaababbababbbababaababbabababbbabbabaabaababbbbbbaababaabbbaabbbbaabbbbabbaaabaabbbaaaabbbbbbabaabbbbbbbbaabbbaabaabababbbbbaaaababbaaabbabaaabbaaaaaabbbabaaababaaaabbbbbaabbbbbaabbaabbbabaaaabbaabaababbaababaababaabbbaabaaaaababbaaababbaabbbabbaabbaabbbaabaaababbbbaababbbababaababbaaaaaaaaaaaaabbbababbbbbbaaabbaabbbabbabaabaaaaabababbbaaabaabbabbaabbabaaabbbababbaabbbaabbabaababbbbaaaaaabbbbaaaabbabbaabbabaabaaababbbaabaaabaaabbbbbbabbbaaabbbbababaaabbbbbbbabbbaabbbbbaabbaababababbaabbbabaababaaaabaabbabbaababababababaababaabbbbbabaaaaaabbbbaabbbbababbaaaabbabaababbbbabababababbbababbabbbabbbaababaabaaaaaabaabbbaaabbaabbabababaaaaabbaababaabbaaaaababababbaabbaabbbabbbbababbbbabaaabbbbaaabbbabbbaababbbbabbbbaaaabaabbbbbabbbbababbbbbaaabbbabbbbaaabbaaaaabbababaaaaabbabaabaababaaabbbbabbaaaabaaabbaabaaabababaababbaabbbababaabbbaabbaabbababaaaabbababaaaaaabaabababababaabbabaabaaababaaabbbbbbaaaabaaaabaabbbabaabaabbaabbbaabababbabaaaabbbbababaabbabbaaababbbabaabaabbabbabaabbaabbbbabaaaabbabbbaabaaaaaabbaaabaaabbbbababaabbbbababbbbaaabbaaabbaaababbaaaaabaaaaabaaababbaaaaaabaabbabbaaabaabaabbabbbaabaabaabbbababbbbaaaaababbabaabbaabbbabbbabbaabaabbaabaabbbaababbbaaabaaaabaabbabaaabbbbbaababbabbaabaaaabbabaaabbabbbaaaabbbbbbabaaaaabbbbabaabbbaababababbaaababaaabbababbaabbababbbbabbbaaabbaabbbaaabaabbbaaaaabbababbababbbababababbbaaaaabbaaaaababaabbbabbbbbabababbabbaaabaaabbaabaaababbabbabbbababbbabbaabbbaaabbbabbababbbaabbaabbbaabaabaaabbabbabbabbbbaabaabbaaabaaaaaabbbbbbaabbbbaababbbaaaaabbaabbaaabababaaaabbaaabbaabbbabbbabbabbbababaaaabaaaaabbaabbababaabbbabbabaaaaaabbbbbbababbabbabbbaaaaaabbabbbbaaaabbbbaabbbabbabbaabababaaaaaaaaaaaabbabaabbbbbbaabbabbbaabaabaabbbbbbbbbbabbbaaaabaaabaaabbbbabaabbaabababaababbbbaabbaababaaaabababbaaabaaabaabbabaababbaaaabbaaabbaaaabbbababbaabaabaabbabbbbbbbbbbaabaabbaaabababbbaabaabaaaaabbbaaabbaaabbbbaaababbaabababaabababbaaaaaaababbbbbabbbbbabaabbaabbaaaaaaababaaababaabababaaabaaaaaabababbbbbbbabaaaaabaababaabaaaaaabbaaabaaababaaaaaaaaaabbabaababbaabbbaabaabababaaabbbbbaabaabbaabbbabbaabaaabbbbabbbbaabaabbbbaabababaabaaaaabaabbabbabaabbbbababbbaaabbbaababbbbbaabababbaaaaabaaaabbbbaaababbbaaaababbbbbabababaabbaabbbbbaaaaaabbbabbabbbababbbabaabbbaaabbaabbbabbbabbabababababaaaabbaababbbaaaaaaaaaabaabbbbbbbbbaaabaaabaaaabaaabaabbaaabbaaabaaaabaababbaababbbbbabbaabbbbbbabbabbaabbbbbaabbbbaabaabaaaabababaabbbbababababaababaaaaaabaabbbbbaabbbbaaaaaaaabbbbaabbbaabaaabbababbbbaaabbbbbaaabbaaaabbbababaaababbaaababaababbbabbbaabbbaabbabaabaababbbbbaaaaabbabbbbbaabbbbbaabbaababbbbaabbaaabbbaaaababbbbbbaaaabbabababaababaaaaaaabbaabaabbbababaaababbbaaabbbbaabbbbbaababaaabbababbaabaaabbbaabaabbbabbbbaaaaaabbababbabbababbabaaabaabbababbbbbaaababbbbbaaaababbaaaababaabababaabbaabababbbabbbabbbbabbaabaabbaabbbbbbaabbbabaabababbbabbabaababaabbaaaabaabaabaaaaabbbbbbabbbabbabbaabaabababaabbbabbabbabaabbabaabbbbbaaaaaabaababbbbababaabaabbbaabbbbbaaabaababbbbabbbbabbabbbaababaaaaaaabbaaabaabbbaaabbbbaababbbaaababbbabaaaabbbabbbabaaabaabbbbbbabbaaabbabbbbaaababbabbaaabababaaaabaaaaaabbbbbbbabaaabbbababbbbababbbaaabbababababbabbabbaabaabbababababbbabbbbbbbaababaaaabaabbbbaabbabaaababababaaaaaaaabaabbbabbbabaabbaabbbbbababbaaaaabaabbabbbabbbbabaabbbaaaaaabaababbaaabababbbbaaaabaabaaabaabbababbbbabbbaabbbbabbbaaabaabbbabbbaabbababbbbaaaaaabbbabaaabbaabbabbabbbbbbabaabaabbbbbaabbbbbbbbbaabaaaaaababbbbbbaabbbaababaaabbbbabbaaaabbbbabaababaaaabbabbbaabbbabbaabaabbaaabaabbbaabbbabbaaaaababaaaaabbabaabaaaabaaabbbabbabaabbbbbaaaaabaabababababaabbbbbabaabababbabbbbbbaaabbabbaabbabbabbbaabababaabbabbbbaababbaaaabbbbaaaaaaababbbbaabaabaaaababaabababaabbbaaababbababbbbabbaaaabbabaababbabaabaaabaaaaaabbabaabbabaaaabbaaabbabbbbaaababbabaaaaabaabbaaaaaababbbbbaaabaaaaabbaaabbaabbabbaaaaaababbaabbaaabbbabababaabababbaaaaaaabaaabaabbabbaaaabbbbabaabbabbbbbbbabbbbaaabbabbabbaabbbaabaabaaabaabbbabbaabbaababaabbaaaaaaaaabbbaabaabbbbaabbabbbaabbabaabbbbbabababaabbabababaaaabbbaaaaabbabaaabaaabaabaabaabbbaabbaaababaabbabbbaaababbbbbbaaaaaabbbaaaaabbaaabaababaaaabababaabbbbbababbabbabbbbbbaaabbabbabbabbbabbaaaaabbbbaaabbabbaabbabbbaaabaabaaaaaaabbbbbbaababbaabaabaaaaaaaabaabbbbaabbbbbabaabbbaabbabaabbaaaaaaaabaaaabaaabbbabbbaaaabbbbaaabbabbabbbbbaabbbbbbbababaabbbaaaaabaaabaabaabbbbaaaaabababbaaabababbabaabaabaabbaaaabbbabaabbbabbbbaababbabbbbbbabbaaabaaaaaabbabbaaabbbaabbabbabbaaababaabaabbabbaabaababbaabbabbabaaabbabababbbbaabaabababbaaaaaaabaabababaaababaabaaabaabbabaabbaaaaabaaabababaaaaaaaabbbbbbaaaababbbbbaabababbbbabbabaabbabbaaaaabbaabaaaaaaaaabbbbabbaabbaabbaabaaaaaaaaaabbbbbabbbaaaaababaabbabbaabaaabbbabbbabbababbabaababbbbaababbbbaabbbabbbbabaaabbbbaaabbbbbabbaaabaabbaababbababbaaabbbbbabbbabbaaaabbbbababaaababbbaababbbaabbbaabbaabbaabbbbbbbbabbbaabaaaaababaababaaaaabaaaaaaaabbbbabbbbbabaabbaaabaaaaabbaaaaaabababbbaaabbbbbbaabbaaabaabaaaababbabbbabbababbabbaabaabbbaabbabaaababbaabaabbbbbaaabbababbaaabbaaaaaabaaaaaaaaaaababaabbbbbbabaaaabbaabaabbbaabbbbaabbbaaababbbababaabaabbbbaabababbbaabbaaaababbbaaabaabbaaababaababbabbabaabaaabaaabbaaaabaaaabaababbabbbaaabaaaabbbbbbbaababbbbaaaaaaabbabaaaaabbbababbaaababbaaababbbababbabbbbbabbbaaabaabbbaaaabbbbaaaaabaabaabbbaabaaaaabbbaaabbaababbbbbbbabbbbabaaabbbbbbbbabbabbbbaaaabbaaabbabbbabababaabbbabaabaaababbbaabababaabbabaaaaabbaabbbabbaabaaabaabaaaabbababbbabaaaababaabbabbbbaabaaabababaabbbbbabbababaaaabbbabaababbbababaaabbbbbbbabbabbbbaabababaabaabbaaababaaabbaabbaaabaaaababbabababbaabaaaabbabaaaaaabbbaabbbaaababaababbabbbbabbbababaaaabbbbaabbbbaababbabababbbbbbbabbaabbbaaabbaabbbbabbaabbbabbaababbbabbaabbbabaababbabbababbbbabbbbbaaabababbaaaaaababababbababaabababbbbabbababbaaabbabbbabbabbaabbabbbbaaabbbaabaabaaabbbaabababbabaaaaababbabaaaaaabbabaaabaabababbbbabbbbaaaabaaabababbabbaabaaaaaaabbaabababaaaabbbbbbbabaabbaababaaaabbababbbabaaaabbbaabaabbbaabaaabbabaaabbbbabbabbbaabbbbaabbbbbbbbaaabbaabaaababaaababaabbaabbababaaaaabaaaaababaabbaaaabbbaababaaabbbbaabaabbbabbabbbbaaabaaaabbaaababbababbababbbbbbaabaabaaaababbbabbabaaabbbababbbbbaaababaaaaabbabaabaabababbabaaabbbabbbabbbbaaabbbbbbaaaaabaaaababbaabbbaaaaaabbababbbbbbbabbabbbbbabaabbabaababbabbaaaaaabaaaabaabbbaaabbbbaaaabbaaabaaaabbaabaaabbbabaababaabbbaaababaabaabbababaaabbbaabbbabbbaaabaabbbbbaabbbabaabaababbabbbaaaaaabaaaaaabbaabaabbbabbbbaaabbababbabaababbaaabaababaabaabbaaaababbbbbbbabbaababbbbbabbaabaaabbbabbbaaaaabbbababbaabbbabbbbaabbbbbbbababbbababbbbbaaabbbbabbaabbabaaababaaaabbbaababbabbabbbbaabaabaababaaababbababaababaaaabbbabbababbababbbbabbbabaabbaaaabbbbbbabbbaabbbbbbbbbbbaabbbabbbabbbbababbababbbbbaabbababaababbabaabaaababbababbaabaaaaaabaaabaabbbabbababbbabaaabbbabaababbbaabaaabbbaabbbbbbbbabbbabababababbbbbbaaabaaaabbaaababbbaabaaaabaababbbabbabaabababaaabaaabababababaaabbaaaaaababbaaaaababbbbaaaaabbbbabaaabaaaabbabaaabaabaabbbbbabbabaabbbbabaabbbababbbbababbaaabbabbaaaaabbbabaaabbbbbbabbabbbabbbaababbbabbabaaabbabbabbbaaaaaaabaabbbaaaababbbabbaabaababbabaaaaaaababbbbbbbbabbbaaaabbaaabaaabababababbaabbabbaaabbabaabbbaababbbbabaabaabbaabbbaabbbbbbaabbabababbbbbaabaaaabbbbaabbbbaabaaaabbaaabbbbaaababbbaabbbbabaabbbbaabbaabaabbbbbbbbbbbaabbbaabbaaaabbbbabbabaabaabbabababbabaabaaabbbbababbbbbbbabbaaaabababaaabbaabbababbbabbabaabaababbbbaabbbbbbaaaaababbbaaaaabbabbabbbabbbbaabbaababbbbaaaababbabaaabaabbaaaaaaaabbababaaaabbababbbbabaabbbbababbaaabaabaabbbbaaaaaabbbbaaaabbabbabaaabaabaabbbababaaababaaabbaaababaaababaabaaabbbaabaaaabbabaaaababaabbaabbaabbaababababbbaabaabbababababbbababbbaabbbbbababababababbaaaaabaaabbaabbabbabbbaaaabaaabaabaaaaaaabbbbabbababbbbbabbbbaaabbaabbbaabbbabbabbabbbabaabbababbaabbabbaaaabbabbaaaababaabababaabaabababbbbaabaabaabbbbababaabbbaaaaaabababbbbabbababbbbababaababaaaaabbaaaabaaaababbababbaaabbbabbaababababbbbbbbaabaabbbbaaaabbaabaaaaababaabbaabaaaaaaaaabbbabbbaaaaabababaaababbababbaabbbabbaaababbaabbabababaaabaaaaaaaaaaabbbaaabaaaaabbbaabaaabbababbbbbbabbabbaabbaabbaaaaaabaaaaaababbabbbaabbabbaabababaaabbaaabaabaababbbabbbabbbabbababbbbbbbbaabbbaaababbaabaabbbaabbababaabbbabbbaababababaabbbbbbabbbaaabaababbaabbaabbbbbbaaaaaabbabbaabababbaababaabaaabbbbabbaabbbaabbaaabbababbbbbbaababaababbbbbababaababaabababbaaabbabbbbaabbbaabbbbbbaabaabababaaababbbbbaaabaaaaabbabbbbaaaaaabababbbbbbbaabbbbbabbabbaaaaaaaaaaaaabbbaabbabbaabababbaaaaabbaaababaabbaabbaaaaaaabbaaabaaabbbbbaaabbababababaabaabbababbabbbbbabbabbabbbabbbbabbaaabbaaabbbaabababaaaaaabbbbbbabaaaaabbbbabbabbababbaabababaaabbabbabbbabbbbbbbabbbbbaaaaababababbabaaabaaaabbbababbaabbbaababaabbababbbbabbabbbbaaaaaaabbaabababbabbaabbabaabaaaaabbbaabaaabbbbbaababbbabbababbbabaaabbbbbaaabaabaabbaabaaaabbbababababbabaabbbbababbbbbaaaababbabbbbabaabbabbaabababaaabaabbababbaabbabbbaaaabbaaaabbbbbaabbbbbbabaaabbbaaaaaabbabaaaabbbbaaaaabaabbabbbbbabbbababbaabbabaabbaabaabaaabababaaaaabbbabbabaaaaabaabbaabbaaabbbabaaaabbbbbbaabbbbabbbbbbaaaabababaabbbbbbbabaaabbbababbbbaaabbbabbabaabbbababaaabaabaaaaabaaaabbbaabababaaabababbbbbbbbbabaabbbbabbaaabaaabaababaaaaabababbaaaabbaaabaaabbbbbabaaabbbbbaabbbbabbbbbabaabaababbaaaabbbabaaabbaabbabbbaaaabbbbababaabababaaabbabbaababbbababaaaaaabbbbbbaaabbabbabababbbbbbaaaabbaabbababaabababaaabaabaaaaababaaabababbaaabbbbbabbaaabbbbaaababaaabbbaabbbaaabbbaabbaabaabbabaaaaabbbaaaabaababaabaabbbabaaabbbaaabbbabbaabababbbbbbbbabbbbbabbbababaaaabbaabaaabbaabaabbaababbaaabaabbbaaaabbbaaaaaabbaabbabaabaabaaabbbbbabbaabbaaaaababaaaaabaaaababaabaaabbaabbaabbabaabababbbbbaaaabbbbbbaabbbaabbbabaabaaabbabbaaaabbbbbbbabbaaabbabaaababbaabbbbaabbababbaabbbbbbbabbbabbbbbaabbbaaabbbabbabababbabbbbbaaabaabbabaabbbaababababababbbbabbbabbabbababbabbaabbaababbbabaabbabaabaababaabbbaabbaabaababbbaabbabaabbaabbbabbabbaaaabaaabaabaaabbbbabbbaaaaababbabaabbabbabaabbbaaabababbabaaaabaabbaaaaababbaabbbaaabbaababbbabbaaababbbaaaabaaababaabaabbbabbaaaaabaaababbbbbbbababbabbababbbbbbaaaaaabbabbaaabbaabbaaabbbbababbabababaaabaaaababaabbbbaaabbbbaaaaabbabbbbabbabababbabbbbbaabbbbbbbababaababbabaabbabbbbbabaababaabaaaababbbbabaabbbabbaaabaabaabaaaabbabbabbabbabaabababbabbaabbaaabbbaaabaabbaaaaabbaabbaaabbbaaabbbaabaabababaaababbabbbaaabaaaabbbaaabaabaaabbbbaaaaaaababbabbbabbbbabbbabbababbbaaababbbabbbaabbabbbbbaaabbbbbabbabbabaababbbbabbbbbabbaaabaaaaaaaabababbbaaaaaabaababaaaabbabbbaaaaabbaababbaabbbbaaaabaababababbbabbbbababbbbbbabbaabbbababbbbababaababaaababaaaabaabbbbbbabababbbababbabbbababbaabbbbbaaaabaabbbaabbabbababaabbbaabababaabbabbaaabbabbaaaabaabbaababaaabbbaaabaabbbbabbaababbbaaaaabaaabbbbabaaabbaaaabbbabbbaababbbaabbbabbbabbbababbaaabbabbbabbbaaabbaaaaababbbbbaabaaabbaaaaabbaaaabaabbbaaabbababababaaabbababababbaaaabbaaabbbbaabbbabbaaaababbbaaaababaaaabbaaabaababbaabbaaaabbbaabbbabbaaabaabbbabbbbaababbbabaaababbbabaababbbabbbbabbbaabbabababaaaabbbbabbbbbbbaababaababbaabbaaabaaabbbababbbaabbaaaaabbaaabbaaaaaaabaabaabaababbbbbbaababaaaababbbbbaaaabbbbbbbbabbbaabbbbbabbbabaaabbbbbbababaabbaabbbabbaaaabaabbaabbbaababbbbbababbababbaaabbaaaabbbbbbbabaababaaaabbbbbaaabbbbbaabbaabbababaaaaabbbbbbbaaabbaabaabbaabbabbbaabaabaabbaabbabaabbaabaaabbbbabaaaaaabbabaaaaababbbbababaabbbbabbabbbabbbabaabbbabbabaaaabbbbbababaabbbababbbbaaabbaabbaaabbbbabbaabaaabbabbbaaaaabaaaaabbbbabbbaabbbababbbbbabbbaaaabbbaaaabbaabaaabaaabaabbabaabbbaabbbaabaaabbbbaabbaabbbbbbabababbabbaaabbbbaabbbabbaababbbabbaabbaaaababbbababaabbbbbbabbbababaabbbbbabaabaaabbaaaabbbaabaabbbababbbaaaaabbbaabbabababbaababaaaababbbbababaabaaaabbbbbaaaaababaabaababbabbbababaabbaaabbbbaababbababaabbaaabbaabbbaaabaabbaaaabbbaaabbabaaabbbababaaaaabaaaabaaabbbaaaaabaabbaaaabbaaaaaaabbbaaabbaabaaaaababbbabbbbbbaaaababbbbabbaaabaabbaabbaababababaaaabbabbbaaaaaabaabaaababbbbababaaabababbaaabbbbabababbaaabaabbabbaabbaabbaabaabbaabaaabbaabbbaaabbbbbabbaabaaaabbaababbbbbbaaababababbaabbbabbbaabaaaaabbaababbbaaaabaaabbbabaaababaabbbbaaaaababababbaaababbabbbbabaaabbbaaaababaaabbaabbbabaaabaaabaabaabaaaaaabaaabbaaabaabaababbbabbabaaaaabababaaaaaaaaaababbbbbaaaaabbbaabbbbaaaaabbaabaaaabaaaababababbabababababbbabbbabbbaabbabbbaabbabbaababbbbbbbbbbbbaabbabaabbbbaabbabbabaaababbbaababbabbbbbaabaaabababaabaaaaabaabbaababbaabaababababbaaabbabbbaabbbaaabbbabbababaaabaaaaabaabbbbabbbaabaaabbbbaaaabbaaabaabaaaaaabaaababbaabbabbabbababbaaabbbbbbbbbabaaaabbabbbbaabbabbababababbaaaaaaabbaaabaaabbbabaaabaabbaaabbbaaabbabbbaababaabbbaaaaaababbaabaaaaaabaabbbaaababbabbaabbbbabbaabbbbabaaabaaabaaaaababaababbbbabaababbabaaababbbbaaabbbabbabbababaaabbabaabbbaabbbabaabaaaabbbabaaabbbabbbbaaaaabbbbbabaaaaaabbabbaaaaaabababbabbbbaabbaaabbbaaabbbbbbabababbbbaabababaaabaabaabaaabbbabaaabbabbbaaaaabababbbabaaaaaaaaaaaaaaababbbbbaabbbaabbabbbbabaabaaabbbaaaabbbbbabbaaaababaabaabbabbaabbabbbababaababaaaabaaabbbbbbabbabaaababaabbabbbbabaabbaabbaaabbaabaaabaabbbbaabaaaabbbbbbaabbbbaaababaaabbbbaaabaaaaabaabbbaabbaaababbabbabaabbbabaabbabbababbabababaabbaaaaaaabababaaaabbbabaaaaaaabbbababaaaaabaaaaabababbabbabbbabaaaabbbbabababbbbaaaabbbaaaababaaabbabbbabbabbbababbbaabababaababbbabbbbababbbaabbaaaaaabbaaaabaaaabbababaabaabaabbabbbaaaabbbbbbbbaabbabaaabaabaaaaabbabaaaabaababaabababaaaabbbabaabaaabaaaaabbaaabababababbaabaabbbbbabaaababbbaaaaabbaaaabbbabbbbbaabbbbaaabaababaababbbbabbbbbaabababaabbaabbbbbbabaaaaaaababbbbbabaaababbaababaaaaaabaaaaaabaababbbbbaaababaabbababaaababababbbaaaaaaabaabaababbbbabbbbabaababbabbbabaaabbabbbababaaaaaabbbbaabbbbbababababbaabababbabbababbabababbabaaaaaabaaaaaabaaabbbabbbabbaaabbbaaaababbabbaaabbaabaababbabaaaabbbaaabbaaaaabbbaaaabbabbaabaabababbbbbabbaaababaabaabbbabbbaaaaabababbaaaaaababaabababbaabbbabababbbaabbabbbbbbbabbabababbbbbbaaaababbbabaaabbbaaabaaabaaababbaaaababbbbaabbbababbbbabaabbbabbabbaabbbaaabababaaababababaabaaababbababaaaaabbabbbaabaabbbbbabaaaabbaaaaaabaaabbabaaabbbbaabbbaabaababbabbbabaababbbbabaabbbbbbabaababbbbbaaaabaaababaaaaabaabbbaaaababaaabaaabbbbbabbbaabbaaabbbbbaaaabbaabbbbbaabbaababbbbaaababaaabbbbaaaabbbaabababbbbaabbabaababbbaaababaabbaaababbbbabbaabbabbbaaaabaaabbabbababaabaaabbbbbbaabbaaababbbaaabaabbbabbbbabbabaabbbbabaababbbaaaababaaaaabbbbbabaaaababaabbbaababaaabbaaaaababbbbabbaabababbbbbbaaaaababbbbababaabbbabbabbbabaababbbaaababbbabababaabbababbabbbaaabbbbbaaabbabbbaaaabaaababbbaababaabbbabaabaaabaabbbbbabbbbbbabbababbbbbaababaaabbaabbabbbabbaabaabbabaaabaabaaababbbaaabbbabaaabbbbababbabbbbbababbaaabbababaaabaaabaabbabbabbbabaabbbaaabbaabbaaababaaabaaaabbaabbaaaabbaaabaabbbbabbabbbabaaabaaaabaaaaabaabbaabaabababbbaabbbabbaabaaaaabbaaaababaababbabaabbabbabbaaabbaaabbbabaabaaaabbbbbaabbbababaabaabbbbaabababbbbbababbaabaabbbabbababaaaaabaabaabbaabbaabbaabaabaaabbabababbaabbabbbbabbaaababaaabaabbaabababaaabababbaaaababbaaaabababababbbabbaaababaaabbabbaaaaabbaaabbbabaaaabaaabbabbbaaaabaaaaaaabbbbbababaaaaaababbbbababbababbbabababbbbbbabaaaabababbababbaababaaabbaabaaaabbbbbbabaababaababbabababbaaabbbabaabaaabaabaaabaabababaaaabbbababbababbaaaaaababbaaaaaabbabbbbbabbabaaaabababbaaaaaabbbaabbaabbbbbaabbbaaabbbbaaabbbbabbaabaaaaaabbbabbabaaaabbbbbbababbaaabbabbaabaaaabaaaaaababbababbaabbbbaaaaaabaaaaabbbbbbabaaabbaabbabababbbaaaaabaaaabbbaabbbbaaaabbabaabbababbabbaababaaabbaaababbbabbbbabbabaabaabababbbbbabaaabaabaababbbbabbbaaabaabbbbbaabbbabbbbbabbaaabababbaabaaaaaabbaabababbbbaaaabaaababaaabaaababbbababbaaabbabaaaababaaabbabaaababbbbaaaaabbaabaabbbbaabaaabbaabbababbbbbaaabbaaaabababbaabbbaababbbbaabbababaababbababbbaaaaaabaaaabaaaabaaabbaababbbabbbababbaaaababbabbbabaabbbabbbaaabbaaabaaaabbaabbbabaaaababaababbabbabbbbaaaabababaaababbbabaaabaabbbbbabbbaabaabababaaababababbbbaabbabbbabaabbbbabababbabbabaabbabaabbabababbaaabaabaababbbbaaaabbabbbaaabbbbbbabbaaabaabaabbbbbaaaabbbbabaabbaabbaaabbaaaababbabaabaabbbaabababbbabbaaaaabbaababbbbbabaabaabaaaabbbaaaababbbbabbaaabbbaabbaaaaabbbaaababbaaaabbbababaaabbaaabababbabaaaaabaabbabababababaaabbbbaaaabbaabaabbabbbbbabbabbbbbbbaaaaabbbbbabaaabbbabbbbbababaaaabbabbbbbbaabbbababbbbbbabbbbbbaabbbaaabbbabaaaaaaaaabbabaaaaabbbababbabaaaabbababbbaaabababababaabbbaaaaaaabaabaaabababbabbabbbabbbbaabbbaabbbaaaababbbbbabbaaaaaaabbabbabbbbabbaabbaabaaaaaababababbaababaabbabbababaaaabbbaaabbabaaaaabababaababbbbabbbabaaababababaabaabbbbaaaaabbaabaababbabbabbabaabbbaabaabbabbaaaabbaabbbaaababaabaabaaaaabbabaabbaababbbaabbabbaabbaaaabaaaabababaaaababaabbbbbabbaaabbaaaaababbaabaababaaabbbbaabaaaababbbabbababababaaabaababababaabaababbabbbabbaaabbbbbaabbaabbbabaababbaabbaabaaababbbaaabaaabbaaaaababbbbabbabbaabaabaaaaaaaababbaabbaabbbbaabbabbaababaababbbabaaabbbaaabaaaaabbbbbabbbabaaababaaaabbaaaabbaabaaababaaabbabbabbbbaabbbabbbabaabbbabbaaaaaabbabaabaabbbababbaabbabbaaaaabababababaaaabbababaabbabbabbbaababababbabbababaabababbaabbababaababbbbabbbabbbabbbbbbbbaabbaaabaaaaaabaababaaabbbaabbbbbbbbaababbbbaaabbaababaaaaabbaabaaabbabbabaaabbaabbabbabbbbababbbabbbbbbbaaababaaabbabbabbaababbaabaaabbbbbbbbbaaababbbbbbbaabaabbbbbbabbbbbbbaaaaabbbaaababababaaaaaaabbabbbabbaaaababbabbbbbaaababbbbabbbabaabbaaabaababbababbbbbabbbabbbaaaaaabaaabbabbaabbbbbaabaaaaaaaabbaaaaaabbbaaaabbbbaabbaaaaaaaaabbbaaaabbbbaaabbbaaaaabbabbbababbbabbbabbaaabbbbbbaaaabbabbbaaabbaababbbaabbbbbaabbabbababbababbaababaaababbbbaabbabbbbaabaaaababbbaaabbbabaaababababbbabaaaaaababbababbbbababababababaaabaaaaaababbbbabababababbbaaaabaabbaaaabbbabbbaabbababbaabbaabbbaabbbabbbbbaabbbbabaabaaaabbbbbbaabbbabbabbbababbbabbabbabaabaaaaaaaabbbaabbabaaaabbbbbbababbaabbabbababababbbaaaabbbaaaabaabbbaababaaabbbbaaabbbababbababbbbaaabbababbababaabbaaabbababbababbbabbbbbbbabaababbbaaababaaabbbabbabaaabaabbabaabbbaaabbaaabaababbabbbaaabbbaababaabbbbbaababaabaabaaababaabbbabbbbabbbaabbaaabbaaabbaaababab
bbaaabbbbaabbbaaabaabbababbaabbababbabaabbbbbaabbbbaaaaabaabaabbabaabbbabbabbbbababbbabbbbabbbbbbbabbabbaabbabbbaaabaaaababaaabbaaaababbababaaababbbbbababbbbbbaabaabbabbaabbbabbbabababaababbbaaaaabbabababaabbbbaabaaabaabaabababbbaaaabbaababbabababbaaaaaabbaabaaaaabbbabbbaaaaaaaaababbaabbaabbbbbabbaabaaaaabbaaabbaababbbbaabababbbababaaaaabababbbaaaabbbaababaababbbaaabbbaaaaabbaaaaabbaaabbaabbabbaababbabaaaabbabababaaaaaabbaabaaaaabbaaaababbbaabaabbbbabbbabbbabaabbbbbabbbbabaabbaabbabaabaabbababaaaabaaabaaabbabbaabbaaaaabaaaaabbbaaabaababbbbaaaaaabbababaaaabbabbaaaaabaabaabaaaaaaaabbbbaaaaaaaabbbbaabbaaabbaaabbbababaaaabaabbbbabaabababbbaabaabbaaabbaabbabbaaaaaabbaaabababaabababbbbaabbaaaaaabaaaaaaaabbaabaabbbaaababbbaaabbabaabaabaaaaaaabaababbbabababbbaabbbbbbabbbbabaaaabbbbbabbbabbaaabbabbbaaaabbaababbbbabaaaabababbabaaabaaaaaabaabaabaabababbbaaabbbabbbaabaabbaabbbaaabaabaabbbbabbaaaabaabbbaaabaabababbbbabbaabbbbaaaabbbbbaaabaaabababababbbbbbbabaaaabbbbaaaabbbabababababaaabbaabbbbabbbaaabbbabbabbbaaaabababbaabaaabbbbbabbaabababbbabaababbabbbababaabbbaabbbbbaaaabbaaabaabbbbaaabaaaaaaaabbbabbbbabaaabbaabbaaaaaaabbabbbbbabaababaaababbbabbbabbbaaabbaababababbabbabbababbabbaabbbaabbbabbbabbbbbbbabababbabbababaabbbbaaabbbbbaaababbbbbaabbbbaabaaaaaaabbbababbbaaaaaaabbbbaabababbaaabbbbaabaababbbbbbbabbbaabbaaaabbbabaabbbbaaaaaaabaabbaaaaaaabaaabbbbabaaabbbabaaaababbabbabbaabbbbaaabbbbaaaaaaaabbbbabbaabbababbbaaaaaaaabaabaaaabbbbaabaabbaabaabbaabbbaaaababaaaaaaaabbaabbbaaabababaaababbbbbabbbbbbabababbaaaaabbbaababbabbaaabbbbaabaabaaaababbababababbbaabbabbbbbaababaaaaabaaaaabbbaabbbbabaabbaaababbabbbaabaabbabbaabaabbababbbbbabaaabbbbaabbbbababbabbabaababbbbaaabbaabbaabbbbaaabaabaaaabbbaaababbaabbaaaababababbbababbbbbbabbaaaabbababaabbabbabababaaababbaaaababbbbbbaaababbbabababbaaabaaabbbbbaababbbabbaabbbaaabaaaaababbaabbbaababaabbbbbbbbbaaabbaabbaaaabaabbabbabbbbaabababaabbabaaaaaaaabaaaaabbbbbbaababaaaabbbabbbaaaaaabaabbaaaabababbaabbbbabbbbaababbabbbbabaaaababaababaababbbabababbbabaaabbabbbbbabaaabbbaabbaaabbabaaabbbbbaabaababbbbaaaabaabbbaaaabbbbbaabbbbaababaabbbbbaababbabaaaaaabbaabbaaabaaabbbabbbbbabbaaaabbbbbbaabaabbaaabaabbbbbaaabbbbaaaaaaaaaabaaabbaaaabbbaabbbabababbaaaaaabbbbaabababaabbbbaababaabbaabbabbbabaabbbbbaabbbaabbbaabbaaaaababaabaabaabbaababaaababaaaaababaabbbbaabbbbbaababbaaaaaaabbbbababbababbbbabaaaabbbaabbbabbabbaaaabbbbaaaaabbaabaabbabbbbbaabaabaaabaabbabbaaaaababbaaaababbabaabbbabbbbaaabbabaabbababaabbaabbabbbbababbbbaaaaabbabbaaababbbbbabbbabaaababaaabbbabbabaababbbbaaaabbaaabbbbbbbbbaaabbbbbbabbbbabbaaaabbbabbbababbaababbbaabbababbbabbbbbbbabbabaaaabaababaabbabababbababbbaabbaaabbabbbbbabaaababaabbaaababaabbbbaabbaaababababbaaaababbabaaabaababaaabaabaabbaabababbaabaaaababbaabbbbabaaaabbaaaaaaaaaaaaabbabbbabaaababaabaabbaabbbbbbaabbaabaabbaaaaabababaabbaaabbaabbbababbbabbbaaabaaaababaababbaaaaabababbabbaabbababbabaaabaaaaaaabababaaabababbaaaaabbbbbbbaaabbbaabbbabaababbaabbaabbabaaaaabaaaaabbbbbbababbabbbaaababbabaabbbbbbabaaaababbbaabaaabbababbbbbbbabaabbbabababaaaabababbaaababbabbbbaabbaaaaaabaabbbabbaaaaaaaabababbbbaaabbabbbbbbbabbabbaaabbababbbabbbbbbbabaaabaaaaaabbaabbbbabaabbbbabbbababaaabbaabbaaaaabbbbabbabbbaabbbaabaaabaaabbbaaaabbabaabbabbabbbbbabbaabaaabbababbbaaaaaaaaaabbabbaabbaabbbbbbabaaabbbabbaabbaabaabababbbbabababbbbaaaabbbbaaabaabbbabbaabbaaaabbabaababaababaabbabbaabbbbbbbababbabaaabaaaaaaaaababbbabbaabbabbbabababaabaaaabbaabbaabbbbbaababbabbbaaaaababbaabaaaaaaabbaabbaaaabbababaaaabbababaabbabaaabaababbababbbbaababbaabaabbabaaabbababaababaaabbbaabbababbbbababbbbaaabbbaabbabbabbabaaabababaabbabbababababbaaabbbbbbaaabaaabbaabbaaaaaaabaabbabbabaaaabaabaabaabbaaabbbbbbababaaaabbbabbbbaaababbbababaabbabbbbbbbbbbbaaababaababbabaaaabbaaaaabbbbbbbabaababaaabaababbbaabbbbabaabaabbabbaabbabbbaabbababaabbabbbababbbbabbaaaaaabaaabbbabbbababbbbabbbbbbaabaabaabbbbabbbaaaaaaababaaaaaaaaaaababbbaaaabababbaaabbbbbbaababbbabbabaaaaabbaababbbababbbaaabaabaaabbbbabaabbbbabbbbbaaabbaabbabbaaabbaabbbbbbaabaaaaabbabaaabbabbabaaabbbbbbbbabaababaaaaabbbababaabaababbbbbbaabbaaaaabbabaaabbabaaabbabaabaabaaaaababaaabbbbaabbbaabbbababababaaabaaabbababbbbabaaabbbaabbaabaaaaabaaabaabbbbbabbbbabbbbbababbaabaaaaaabaabaaaaaaabbbaabaaaaaababababbabbbaabaabbaaaaaabbaaabbbabaababbbabbaabbaababbabaaabbabbaabbbbaabababababbbaabababaabbbbaaaaaabbbaaabbbabbabbbbbbabbaaabaaabbbbbaaababbbbababbbbabaaababbaababbbbbababbaaaabbbabbbbabbbbabaaaaabbaabbabbabaaabaabaabbbbababababbabbabaaaaabaaaaabbabaaabaabbaababbabbaababbbbbbbabbabbabaaabbbbabbaabababbababaabbbbabbabaaabaaaabbaabbbabbbaabbaabbaaaababbbbbabbaabbaaaabaaabababaaabaaaabbbaaabaabaabaabbbaaabababaaababaabaaababbabaaaaaaaaabbababaaababbbababbbbabababbbabbaaaabbbbbababbabbaababbbbaabaabbaaabaaabaababaaaaabbbbabbbabaabbaaaaabbaaababbababbbabbabbabababbbabbaabbbaabbbbabaaabababbbbbbabaabaaaaabbaaaabbabbbbbbbaaabaabbbbbaababbaaabaababbaaaabbaababaaabbaaaabababaaabbabaaabaaaaaaabaaaababbabbabbaaababaaabbaaaaaaabbbaabaaabababbbabaaabbbbabaaabbabbbabbabbbaababbabaaababababaabbaaabbbaaabaaabbababbaaaaaabbbbababbaabbbaababbabbbbabaabaaaaabbbabbbabababbaaabaabababababbabbaabbbabaabbbbbbaaabbabbaaaabaaaaabbbbbbabaaaaabbbbaaaabbbbabbbbabbabaababbabaabaaaabababaabaaaabbbbababababbbabbbabaaabbaabbbbabaaabbabbabaabaababaabaaababaaabaabaababbbababbaaaabbabaabbaabbbbbbabbbbabaabbbaababbbabbbabababaaabbabbabbaabbbbbabbabbbababbabaababbbabbbbbaabbbabaaaaabbbbbababaabbabbbabbabbaaabaaaabbaaabaabaaabababaaabbabababbabbaabaabbbaababbabbababaababbbaabbaaabbbbbababaabbbbbaabbbbabbbbaabaabaabbaababbabbaabababbbbaaaaabbabaaaabaabaaabababaabbaabbabbbbbbabababbabbabababaabbabaaabababbbabaaaaaaabbaaabbabbababaaabbbaaaaaaaababbabbbbbbbbbbbbaababaabbbaaaabbbbaabaaabbbbaabbbaaaabaabbbbabaaaaabbbabbbbaabbaabbaaabbbaabbabbababbbbababbbabbbbbbababbbbbaabbababbbaababaabbabbbababaababbbbaaabbaaaabaabbabbbaaaababbbbbabababbbbbbaaabaabbbabbabbaabaaabbbbbabaaabbbbabaaaabbbbbbabbababbaaabbaaaabbabaababbbbaaaabbbabaabaabbaaaaaaaaaaaaabbbabbbaabababaabbaaabbabababbbbaaababbaaabbbabaabbababbabababaabbaaaaaababbababbbaabaabbabbaabbbababbbbbababbbaaaabbbbbabbabababbbbbaaaabaaaabbbbababbaaabaabbaabbbabaaabbabaabbbbbababbbaaabaaabababbaaabaaaaababaabbbbaabbabaaaaabbaaaabaabbabaabbbbbbbaaabbabababbbbbabababaaababaaababbbabbbbabaabaaabbabbabaabaaaabbabbaabbbbbaabaaaaabbabbabbbaaabbabababbaabaaabbbaaabbababbbbbbaaaabaabbabababbbabababbbbbbababaaaaaaaabaaaaabaabbbaaabaabbaababbabbabbbaaaaaabaaabbabbaabbaaababbaabaabaabbaabaabbabaaaababbabbabbaabbbabaaaabbbbaaaabbbbabaabbbbbabbbaaababbbaabaaaabaabaabbbbbaababababaaaabaaabaabbaaabbbbaabbaaabaabbbbbbbabbabaaaaaaabbbabababaaababaabbbaaaaabbabbbbbbabaabaaaabbabaabaaaaaaabaabaaaabaaabbaaaabaaaabaaaaaaabaabaabaabbbbaabaaaaaaaabbabbbbbbbbbaaaabaabbbbaabbbbabaaaabbaaababababbaabbbabaaabbababaaababbabaababbbbbbabbbbbbbabbaaaaaabbbbbabaabbbaababbabaabaabababbbabbaaabbbbabbaabbbabaaababbbaaabaaababaabbbbababbbaabaabaaabbbbbabbaaaabbbaaaabbaaaababaaaabbbbbaababbabaaaabbbaaabaabbbbabbaaabbaaabaaabaabbbbabbabaabaaaaaabbbababaabbbbbabbaabaaabaabbababaabaabbabbaaabaabbaababaaaabaaabbabbabbaaabbbaabababbbbabbbbbbbabbabbaabbbabbaabbababaaaaaaaabababaababaababaabababababbaaabababaababbbbbbaabbabbaaabbbbaaabbbabbaaaaabaabbbaaabbbaabbabaabbbabbbbbaaaaaabaaaaaaaababaaabbaabbaaaaabbbabbabbaaabaababbabbabbbabbbbbaaaabbbaabbaaaabbbaaabaababbbbaaaaaaaabbaabaaabaaaaaabbaaaabbbabaaababaabbabbabaaaababbababbaababbaaaaabbbbbaaaabababababbabbabaaaaabbbaabbbaaaaababbbbabbaaaaaabbbaabbabababbbbbbbabaaabbabaaaaaaaababbbbaaaababaabbaaaabaaaababaaabbaaaaabbaaaaaababbbaaababbaabbbbaabaabbabbaaabbbbabaabaababababbabbababababbbbaaababbbbaaaaaababbbaaaaaaababbaabbbabaaabababbbbaabbbbbabbabbabababbaabaabbbaaababbababbbbbabbbbbbaabaaababbaaaaaabaababbabaabaaaaaaaabbaaaaabbabbaabaaabaaaabaabbbbabbababaabaaaabbabbbabbabbaaaabbbababaaaabbaaaabbaaaaaababababbbaabaababababbaaaaaaaaabbbbbaabaaaabbbaaabbbaababaaaabbabbaaababbabaaaabbbbbaaaaabbaabaabaaaabbbaaabaabbbaabbbaaababbaabbabbaabbabbbabbbaaabbabbbbbabbbbabbabaaababbabbbabaaababbaabababababababaababaabbaabbabaababbaabbbabbaabababababaaaaaabbbabbbbabbabbaababbaaabaabaaabaabbaaaababbaaabaaaabbabaabbbaaaaabaabbaaabbabbbbabbaaabaabaaaabaababababaabbabbabbbabbaaaabbbaaaaaabbaaaaababbaabbbababbbaababaaababbbabaaabbbbabbaaabbbaaaabbbabbbabababbaabbbabaababaabbabbbabaabababaaaababbbaabbaababaaaabababaabbbbaabbaaaaaaaaabaaaaaaaaaabbbbbaaabababbbbbbaabbbaaaabbaaaabbababaaaabbbbbaabaabaaabbbbbbbbaabbabaabbbabbaaaaabbbbaaabaaaaaaabaaabaabaabababbababaabaaaabaabbbbaaabbbbababbabbaabbaaababaabbabaaaabbbababbbaaabbabaababbbbbbbbabbbaaabbabbbabbaaaabababaabbbbabababaaaaaaaaaabaabaaaababaaaabbbbabbbaababbbababbaabbbabaaabbbbbbabbbaaaaaaabababaabaabbbbbbaabbabaababbbaabbabaabaabbbbaaabbbaababbbbbaaaabbbababbabbabbbbaaababbbabbbaabbaaaabbbaabbabbbabbbabbababababbababbabbabaaaabbaabbbaaaaabbbbbaabaaabbaabbbbabbaaabbabaaabbbabbbabbbbaaaababbbaaaaaabbbbbbababbbaabaabababbaaaabbaabbbbbbaaabbbaabbabbabbaababbbbabbabbbaaababbabbbabaaabaabbaabbbbabaaaaaababbbaababaababababbbaabababbabbbabbbbabbaaabbbbaabaaaabbaabbabbaaababababbbaabbbbbaabaaabbbbabbabbbaabbaabbbaabbaabbbbababbbaababaabbbbbabbabbbaaaaaabaabbbbabaaabbabaabbbaabaaaabababbaaaabaaaababaaabbaaabbbbbabbbbababbbabbbbabbaaabbbbaabbaabbabababbabbbaaababbabbbbabababbaabbbbbbbabbababbbaabbbbbaabaaaaaabbabaaaabbbbbbbaabaabbabbaabbbababbabbbabaaaaaabbaaaabbabababbbbabaabbbababbbbbbbaaaaabbbaababaabbaabaaaababaabaaabababaaaababbaaaaaaaaaabaabbbbabaabaaabaaaabaabaabaabbabaaabbbbbbabbbbbabaaaaaabaaaaaaabbbbbaaaaabbaaaaabbabbbbbbbaababaaabbbbabbbabbaaabaaabbabbbabbbbbbbaabbaabbbbbababaaaabababbbabbaaaababaaaaabbabbbbbbaabbbbaaabbaabbabbabbaabbbbbabbbbbabbbbbabaaaaaabaabaaababaabbbbaabbaabbabbaaababababbbabaaaabbbababbaaaabbabbaabbaaaaaabbabaabbaabababaaabbaabaabbababbabbbbaabbaababbaaababababbbaabaaaaaaababaabbaabbababbaabaaabbbabaabaabbbaaabbaabbbbbaaaabbaabaaababaabbbbbabaaaaaaabbababaabbbbbbbbaaaaaaaaaabababbabbbabbababababbaaaabbaabaaaabaaabaabbbaabaaabbbaaaaabbabbbbbbabbabaaaaaabaabbababbaabbaababaaabbbabababababaabbaabbbbaaababbaaabbabaabbabaabbababbaaabbabbababaabaabaaaabbbbaababaabababbabababbbbbbaaabbaabbabababbabbbbababbbabbbabababaaabbbbababbababaabaaaaabbbabbbaababbbbaabbaaabbbaabababababbabbabbaabababaabbabaabbbbabaaabbaabbbbbaaaaaaabbbbababaaaabbaababbbaabaaabbbabbbbbaabbbabbbaabbaaabababbbabaaabbbaabababaababbbbbbbbbabaabaabaaaabbbabbaaaaaaababababaabbaaababbabbbbbbbbabbabbabaabbbabbbbbababaababbaaaabbbbababaaaabaaaabaaaabbbaabbbbababbbaaababbaaaaabaaabbbabbbaabbbababbbaababbbaabbabbabbbbaabaabbaaaabaaabaaabaabbabbbabababaaabbbabbbbbbabbaababbaaaaaabbaabaabaabbbbbaaabaaabaabaabbbbbaabbbbbbabbbbbaaaabbbabaaabbbbabbbbbabaabbababaaaababbabababababbbbbaabababababbbbbbbaabbbbaaaaaabbabaaabaabaaaabaaabaaaabbbabbbabaaaaaaaababaabaabaababbaaaaaababbaabbabbaabbaabaabbabbaaaaaabaaaaaababaabbaabaababbbaaabaabbbbbaaaaaababbaaaaabbbaaaabbbabbababbaaaabaaaabbaaabaabaabbbaabbbabababaabbababbaaabbababbaaabababababaabaabababbbbaaabbbaabaabababbaabbbaabababbabbbaabbbbabababaaabaabbbababbbabbabbababbbbabbbbbbabbabbaaaababbbabbbaabbababbaabbabbabaabbabbabababaabaaaaaaaabbbbabaaabbbabaabbaabbaababbabbaaabaaabbabbbabbbbbabbbbabbaabbbbaaaababbabaaaabaabbbbbbbaaaaabaaabbabbababababbaaaabaabbbaaaaabbaaaababbaabababaabaaabababbaababaaabbababaabaaabbababababbbbbababaabbabbaababbbaaaaaaabaaaababbbabaaaabaaabaaaababbbbabbaabaabbbabbaababbabbaaaaaabbbbabaabaaabbaabbaabaaaabbabbbbbbababbabababaabbaababbbaaaabababaababbababaaaababbaabbabbabbaaaabaababaaaabbbbabababbaaabbbbabaabbbbabaababbabbbabbbbbaabaabbaabbabbbbbbabbbaaabbbbaabbaababbbaabbabaababbbbbabababaabbbaabbaaaaababbaaabbbaaabbaabaaaaababbaabaababaaaaaaabbbaaabbaaabbabbbbbababbaabbabaabbaaaaaaaaaababbbababbbaaabaabbaaabaabbabbaababbbabbbabaabababbaababbaabbabbbbaaaabbbaaabaabbababbbbabbaabbaabbabbbaabbbbbbbaaabaaaababaabbababbaabbaabaaaaabbaabbabbbabaabaaabbabbbaabbbaaababbbbbbaaabbbaabbbabaaaaaabbbababbbabbbabbabbaaaaabaababbbaababaaaaababaaabbbbaabbaababaaaabaababbbabbaaababbaaabbabaababaabbabaabbbbaaaaabababaabbbabbaaabbababaabbabbbababbbbbbbbbabbababaaaaabaabaaaabaaabbababbbbaabaabbbbaaaaaaabbbbbbbaabaababbbbaaaaaabaabbaaabbaabbbbabbbbabbaaabbabababaaaaababaaabbbaabbbbbbabbbbbbbbabbbbbababbbaaaaaaabbbababbabaaabbbbabbabaabbabbabaababbabaababbaaaaabbabbababbabaaaaabbbbbbabaabbaaaaabbababaabaaabbbaaabaaaabbbaaabaabbabbabbbaababbabababbaaaaababaaaaabababbbaaababbabbaaabbbbaaaaabbabbabbaabbbbaabaaabbaabaabbbbbaabaabababaabaaaaaabaabbabbbbaaabaababbabbbaaabbbbbbbbaabbbbaaaabbbbabaabaabbbbbbaabababaabaaaaabbbbbbbabbabaaaaaaabbbbabbbbaaabbbbabbaaaaabbbbbbabbaaabababaaaaaabbbbbbbaaaaaabbbbbbabaabbabbabababbbabbaaabbbbbaabaababbbbbabbbbbbbbabbbabababababbaabaababbbbbbaaaaaabbabbbabbbbaababaabbbbabbaababbbbaabbbbbaaaaaaaaaaabaabbaabbbbbbaababbbbbababbbabaabaaaabbaabbbaaabbbabbaaabbaabbabbabbbbbbbbaaaaaaabbbbaababababbababbbbaaabbbbbbbbbaaabbaabaabbaabaababbbaabaaabababaababaaaaababbbbabbabaabbbabbbabababaabbbbbbabbabbaabababbbbaabaabbaaaaabbbbbbabbbbaaaabbabbbabbaababaabbabbbbbabbaaababbbaaababbaabbbbabbabbaabaabaaababbaabbaabbbbaababbababaabbbbaaaabbbabbabbbbbbabbabaaaaababbbbbabbabbbabbaaaabbbbbaabbaaabbaaaabbbaaaababbbaabbabbaabbabbbabababbaaabbabbbaaababaabababaabbabaabaabbbbbababaabbaaaaababaabbbbabbaabbbaaabaabbbbaaaabbbabaaaaaaabbbaaaabbbbaabaabbbbaaaaaaaaaaabbbbaaaabbbaababaaaababababbaaaabbabaaaaaaabaaabbaaabbababbbaabaababaaaabaaabababbaabababbabaabbbbbbbabababbabbaabaaaaabbbbababaabaababaaaaabababbbbabbbbbabbaaabbabbaabaaabaababbbbbbaaaaaaaabaabaabbbbabbabababababbaaabababbaaababaabaaaabaabbaabbabaabaaaabbabababaaaaaabbbbabababbbabaabbbabbbabbbabbabababaabbaaababababbbaababaabaabbaaaabbbabbaabababaaaaababbaaaabaababbaabbbaaababbaabaaabaababababbaababaaababbabaaaabbaabbbabaabbbaabbabbbabbbabbbbaabbaabaabbbabbabbbbbbababaabaabababbbbaaababbbaaaabbbabababaabbbbbaabbbaababbbabbbbbbbaababaabbaabbbbabbbaaabbaabababbaaabbbbabaaabaaabbababaabaabaaabbbbbaababbabbaabbaaaaabbbbbabbbbababbabaabaaabaaaabbbbbbaabaaabbbbababbabbaaabbaabbabaababbababaababbbbbbbababaaabbbaaaabababaaaaabbabaabaaabbaaaabbbbbabbbbaaababbabbaaabaababbbbaababaaababaababbabbababbbbbbabbaaaaaababbabababbaabbbbabaabbaaabaababbaabbaaabbbbabbaabbababbbbaaababbbaaabbbbbbbaaaaabbbabbabbabbabbababbbbaababbaaaaaaaaabababbbbaaaabbbabbabaaababaaaaaaabbbabbbababbabbbabbaabbabbbabbbbaaaabbaaabbaaabababbbbaabaaaabbaabbaabaabbaaabbbabaaaaaabbbaaaaabbabaaaabaaaabbbaaaabaaababaaabaaababbaabaaabbaabaaababaababbabbaaaaabaababbbbaabaaaabbaabbababaabbaabaaabababbbaabbbaaabbbbaabaaaaaaababbbabaabbbbabaaaabaabbbbbbbbaabbbababaabbaaabaababababbabababbbbbababbbbabbaabbabaaabbbbabbbbaabbbabbaabaababbbaaaaabbaaaaabbabbbaababbaabbabbbbabaaaabbabaaababbaabaaaabababababbbbbababbbbbabbbababbbaaabaaaaabbbabaababbbaaaababbbaabaabbbabbbbabbbabbbaaaaabbababababaaaaabababbbabaaaaabbbababbaabaaabaababbbbabbbbabbaabaaababbbbabbbababbbabbaabaaaabaaaaaabbaabaaaabbbbbbbbbabbbabaababbaaabbbbbbbababaababaabbababbbaaabbabbaabaaaabbaabbbbababbabbaababbbabbaabbbbabbbaabbabbbaaaabbaaabaaaabaabbbababaaabbbaabbaabbbbababaabbbbaaabbaabbbbbaabbaabbbababaabbaaaaabaaabaabbbbbababbababbababbababbababaababaaababbaaaaaabbbbbbabbbbaabbaaabbbaaaabababbaaaaabbaaaabbaaabbaabbbaabbbbbabbbbabbababbaabbabaabbaabaaabbaabaaaaabbbabbaaababbbbabbaabbaaabbbbbbbabaaabaabaabbbaaabbbaaabaaababaabbbabbbabbbbabbbbabaaabaabababbabbbababbaababbabbbbbbbbbbbabbbabbaabbaabbbbababbbbabaaaaaabbabbaabbabbbaaabaaaababbbabbbbbbabaaaababaabbbbbabaaabbaaabbbaabaaaaabababbabbabbabaababaabbbbababbbbaaaaabbabaababbbbabaaabaaabaabaaabbbbbbbbbabababbbbbaabaaabaabbabbabaaabbabaaababbbabaaaabbaaabbabbaababbabababaabbbaaabbbaaabbbababababaabbabaaabaabbabbaaababaabaaaabaaababbbabbbbaaaabbaaaaaabbaabbabbbababbbbbbabababaabbbbbaabaabbbabbaabaaabbabbaabaabbbbaaaababbabaabbbababbbabbbbbabbbbaaaaababbbbbbbbbaabbbabbbbababbaabaaaaaabbbabbbbbbaabbaabbabababbaabbbabbabaabbbaaababbaabbaabaaabaabbbaaaabbaaaabbabbaabaabaaaabababbbbbaababbbbbabbaababbbaaaaaababbbbbabaababbbbabbbaababbabaabbbbbbbaaaaabbbaabbaaaaaabaabaabaabbaabababbbabbabbbabbaabaaabbbbbaabbbbabbaabbabaaabaaabbaaaabbbabbbbbaaabaabaabaaaabbbaabbbababbbbbaaabbbaaaaabbaabbababbabbbbaabaabbaaabbaaaaaaaaababbbaabbabaaaaabbaabaabbaabaababaabbabaababbaabbbabbabbbbbbbbaaabaabbabbabaaabaaabbbbbbabbaabaaaabbaabaaabbbbbbaabbbaabbbbabaaababababbbbabbabababaababbabaaaabaababaababbababaaaabaaaaabbabbaaaabbabbbabaabbabbabbabaaabbbaabbaaabbbbaaabbbbabbbbbaaabababbbaabbbbabaababbaabbabababbabbaabbbaaaaabbbbbabaababbbababaababababbbabaaabbabbbaaaabbabaababbbaaaaaababbabaababbbbbabaabaabbbbbbbbabbabbbbbabbbabbabbbaabbaababaababbbbaabbbbaabbbabaaaababaaabaabbbbbaaaabbbaaabbababbaaabababbbabbaaaabbabbaababaaabbabaaaabbaaabaaaabbbaaabbabaaaaabaaabaaabaaaabaaabbbbababababbbaababbbbaabbabbbaaabbbabbbbababaabbabbaababaaaabaabbbbbbabbbbbbaaaaababbbbabababaabaababababaabababababbaaaaaaabbbbabaaaabaaabbbabaaaabaaaabaabababaabaabaaaabbabbbabbaabaaabbbbbaababaaaababaabaaaababbbbabbaabbaabbabbaabbbaabaabbbbababbababbbaaaaaaababaabababaaabbaabbbbaaaabbabbaababbababaaaaabbabbaaabbaaaabbbbbaaabbabbbaaabbaabbaaaabaabaaaabbbbaababbabbbabbabbbbbaabaaabbbbabaabaaaabbbabbaaaabababbbabbbbbaaabbaaabaaaabbaababbaababbbaaaaabbabbabbbbbbabbbaabbaabbbaaababaabbaabaaaababbabbabaaabbbabbaaabaabbbaabaababbaabbbaabbbaabaabaabaabbaabbbbabbabaaaaaababbabbbbaaabbaaaaaaaabbabaabaabbbbbaaabaaaaaaabababbbbbabbbabbaaaaaabbbbbbbbbaaaaabaaabbbababbbabbbabaabababaaaaabaababaabbabaabababaababaabbbabbaabaaabbabbaaabbaaabbbbbaaababaaaaabbbbbabbabbbbbaaababbaaaaabbabaabbabbaabaaababbbbbbbbaaabbabbaaabaaaababbbbaaabbabaabababbbabbaaaaaaababaaaabbaaabbabababbaababbaaababaaabbabbbabbbbaabababbbbabababbabbbaababaaaaababbabaaabaabaaabaaaabaaaabababbababbbaaababbaabaabbabaaabbababaababaaabbababaabbbbaabaabbbaaaabaaabbaaababaabbbbbaaabbabbbabbbabaabbbabbbaabbbbbabbbbaababbaabaabbbbabaabbbbbbbbaabbbbaabaaaaaabaabaabbaabbbaababaabbbbaaaaabbbabbaaabbabababaabbabbbababbbaaabbabababbbbbbaaaababaababaabaababbababaabaababaaaabaabbbabaabbaababbabaababaabbbbbabbbabbbababababbaaabbabbabbabbbaabaababbaabbbbbbaabbbbabbaabaababbbababbaabaaabbabaababaaababbabaaaabaaabbbababbbaabbababbaabbbaabbaaaabbaaababbbbaabaabbabbbbabbabaabbbabaabbbbbabaababbabaababbbaaaaabbaaaabbbabbbbbbaababaababababaaaabbbabbabbbaaabaabbabbabaaaaababbaaaababbbbaaaababbbaabbaabbbbbaaabbbbaaabababababbaabbaaaaaaaabbabbbabababababaababbbbaaababbbabaaaabaabbabbaababaaaaababbbababababbbbababababaaabbaabaababbbbbbbababbbbababaaaaabbabbaaabbbaabaaaaaaaabaaaaaabaabbbbbaaaaaaababaabaaabaabababaabaaaabbababbaaabbbabbabbabbbbababbaaabbbaabababbabbbbaaabaabaaabbaabbaabaabbabbbaaababbbaaabaababbbaabbaaabbababbbabbabbbaaabbabaaaabbaaaabaabbaabbaaabbababbbbabbababbabbaabbbaababbabaababaababbbbbbbabaabbbbabbbbbbbababbbbbabaababbbaaaabbabbbbbababbbabbabbabbababbbaaabaabaabbabaaababaabbbbaaaaabbbabbaabbaaababbaaaaababaaababbabbaababbaaabaabbabbbaabaaaaaaabbbbbbbbbababbbabaaabbabababbbaaaaaababaaabbabbaaaabbaaababbabbbabaababbbaabbabbaaabbababaabbbabbababbaabbbbbbaababbbbbbbbaabbbbbbaaaababaabaabbaabbbabbabbbaaaaabbbabbabbbbabbababaabaaaabbababbaaababbbbbabbaaabaabaabbbababbbbaaaaabbbbaaaabbaaaabbbaabaabbaababbabbbbaaabbbbaaaaaabbabbbbaaabaaabbbaaabaabaaaaabaabbbbaaabbbaaaaaabbbbbbabbabbbbaabbbaaaaabababababbbaaaabababbaabbbbbaaaabaaabbaaabbabbbbbaaababbababbaabbabaaabbaabaababaabbbaabbaabbaabaabbabbbaaaaaaaabaaabbbaaaabaaaaaabbaaaaaaaabaaaaababbababbabbbbbbabbaaaabbbbbbabbbbaaabbabbbbbabbbabbabbabbbabbbbabbababaaaabbabaabaabababababbbabaaabaabbbabbabababababbbaabbbbaaaaaabaababbbbababaababbbaabbbaaabaaaaabbbbbaabaaabaababbaababbbbbbbabaaaaababbabbaaabbabbabbbbbaaaabaabababaababbaaaaabbbbabbbababaabbbbababaabbabbbaaababababbbaaabbaabbaaaaaaaabbababaaabaababbabbabaaaabababbbbbaabbabbbaababaabbabbbbabbbbbbbbababaaaabbbabbaabbabbabaaabbbbbbabbaabaabbbbbbbaabaabbabbbaaabaabbaabaabbaaaaabbabbbaaaabbaaaabaaaababbaabaabaaabababbaabaaaabaaabaaababbbbbabababbabbbabaaaaabaabbababaabbbabababbabaabbaaaaaabbababbbbaabaabbbabaababaabaaaababbbabbbbabaaabaabaaaabbaaaaabaaaababbaabaababababaabbbaaaababbaaababbbabbbbabaababababaaaabaaabbbbbbaaaaaaaaababaabaaabaabbaaaabaabaaabbbbabaabbbbbbbababbabbabbbabbbbaababababababbababbbabaaaabaabbbabbaababaaaabaaaababababaabbbbbbbaaabbbbaabaaaababaabbbbbbbabaabaaababaabaaaabbbbabbbbababbbaababababaabaaabaabbaaababababaababbbabaaababaaabaaabbababbabbababbbbaaaaababbbabbbbbabaabbabbbbabbbbabaababaaabbaaaaaabaaaababaaaaabaabaaaabbbaabaabbbbbbbbaaabbabaaababaaaaabbabaabbaabbabbbabbaabaaaabaababbaaabaabbbaabbaaaabaaabbabbbbbbbabaabbbaaaaabbaaaabaabababbababbbaabaababaaabbaabbabaababaaabbbbbbbbabbbbbabbaaabbabbbbabaabbabaaaabaabbaabaaabaaaaabbabaaabbabaaababaababbabaaaabaaaaabaabaaaababaabaabbaabaaababbaabbabbabaaaaaabbabbbbbbbbbbbaabaaaaaababbbaabaabbbbaaaababaaaaaaaabbabbbabbbbaababbabababaaabababbbaaaabbabaaabaaaaabbaaaaaaaaaaaaabbbbaaaabaabbbaababbaaabaabbbabaabbaaabbabbbabaaabbaabbbbbaaabaabbbbabbabaabbbbbabbaababbabaaababbabbabbaabbaabaabbabaaaabbbaabbabbaaababaaabbbbaabaaaabaababbbbbaabababbabbabaaabbbbabbaaaaabbaaaaaaaababbabbaabaaabaaaaabbbbbbaaabababababbbabbaababaaaabaaaabbbbbaaabbabaabaababbaabbaabbbbaabababaababbbabbabbabbbbbbbbbbbaaaabbbaaaaabbaabbaabaaaaaaaaabbbbabbaaaababbababbababbbaaaabbbabaaabbabbbbaaaabbbaaaaabbaabaababbabbabbbababbabaabbabababaaaaaaaabbabbbaababbbaaaaababaaabbaaabaaaaaaabaabbbbbaabbababaababbaaabbaaaaaabbbabbaaaaabbabbbabbbbbbbabababaaaabaaabaabaabbaaabbbbababaabbbabbbabaaaabaaaaababaaabbbabaaabaaaaaabbaaabbabbaabbbaaaabbabaaabbaaabaabbaabbbbbbbabbbababbaababbbababaabaaabbabbbbbbababbbbbabbabbbababbbbaaabaaabaababaaaabaabbbaabaabbaababababaaababaaaabbaabbaabbabaabbbbabbbbaaabaaabaaabbabaabaabaabbbbaabababaaaaabaabaabaabbbbaabaabbbabbabbaaaaabbbabbaabbbbaababbaaaabbbabbaabababbaababbaabbaabbaaabaaabaaabbbababaabbaababbbbbbabbbbbabaaabbabbabaabaaaabababbabababbabbabbabaaabbbabbbaaaabbabababababaabaaabababaaabaabbbaabbababbbbbbbbbababbbabaaabbbbbaaaaababbaabbabbbbaabbbabbaababbabbabbaaaaaababbbaaabbaaaaababbaabaabbbababaaabbbbabbbbbaabaaababaaaabaabbababaababbbbbbbabaaaabbaabaabbbaababbaabababaaabaabbabaabababbbbababbaabbbbbabbbaaaabbabbabaaababaaaabaabababbbbbaabbabbbaabababbabbaabbabbabaaaaaabbaabaaaaabaabbaaaabbabaabababaaaaabbbabbabbbbbbabbbbaabbabbabbabaaaaababbbaabbbbababbbbabbaaababbaaaabaaaaaababbabaaabbbbabaaabbaabbbbaaabbabbabbaaabbabbaaaaababaabaabbabbabbbbbababababaaaaabbbbbbbaaababaaababbaaaababbabbbababaabbaabaaabbaababbaabbbaaaabbbabbbabaabbabababbbbbaababbbbbbbbabbabbbababbaaababbbbabababaaaabbbabaabbbabbbbbbaaaaabaabbaabbbaaaaabaabaaababbbabaaabaababbbaaabababbbaabaaaabbaabbaabaababbbbbbbbbabbabaaabababbaababbaabaababaabbaabbbabbabaababaababaaabbaabbaaababbaabbbabbabaabbbabbbbbbaabbabbabbaaabbabbaaaaaaabbabaabbabbabaababbbaaaaaaaaababbbababbbaaaabaaabaabbbabbbabaabbababaaabaaaaababababbaabaabbbaaabbbbbbbaaaababaabbbbaabbaabababaababbabbabbabbbbaaaababaaaabbbbbbaaabbababaabbabbbabbaaaababaabababbbbaabbbaaaabbbbababbbbbaaababaabbbabbbbbbbabaaaaabbbbaaabbbabbbbbbaaababbabbbbaaaaaabbbbaaababbaaaabbbbaaabbabbaabbabaabbaaababbbaaaabaabbabaabbbabaaaabaabbbbabababbaabaaabaaabbababababaaabababbabbbabaaabaaabaabaabbabaabbabababbaabbbabaabbabaabbabaaabababbbaabaaaaaaaabbbaaaaabbabbaabbbbababaaaabbaaaababbaaaabaaabbababaaaabbbbbbbababaaaaaaabbaaababaabaabbabbbaabbbbbabbbbaaaababbbaabbbabbbbbbbbaaaabaaabaabaabbbaabbbbaaaabbababaabaabbabbbaaaaaabaaabaababbaaaabaaaaabbbabababaababbabaabbaabbaaabaaabbabbaabbbabbbbbbbababaaaababbbaabaabbaababbbbaababbaaaabaabaaabbaabbbaaaabbaaabbbababbaababbabaaaaaaabaabbbbbaabbbaababbbabbbababaaaaaabbbaababbaabbbabaabbaabbbbbbbbabaabaababbbbaababababaaaabbaabbabbbaabaababbbbbbabbababababababaababaabbbaaabbbaaaaababaaabbbaabbbabbbbbabbaaabbabbbababbabaaaaabaabaabbbbabbbaabbaabababababaabbbababaaaaaaaaaabbaabbaabababaabbaabbaabbabbbbaaaaaabbababbabababbbabbbbabbbaaaabaaaabbaaabbbaabbabbabaaaaabbbbbbaaabbabbbbbaaaabbbbabbaaaababbbbaababaabbbbaabaaabaaaaabaabababaaabbaabbaaabbaaaabbbabbbbaabbababaabbaaaaabaaabaabbabababaaabaabbaaabbbbabaabbbbbbabbbbbbaaaaabaabaaababbbabbaabbbbabaaababaababbbbaaabaababbaababbbbbababbbbabaabbaabaabaaaabbaaaaaaabbabbabbaaaabaabbabaaabaabbabbbbababbbababbbbbbbbbabbabbbbabbbbbbaababaaabbaaabaaaaaababbaaaaababbaabbbababbbbaabbaabbbbaaaabbbbbaabbbabababbabbabbaabbaabaaabaabbabaaabababbabbbbaaaabbbbbbabbabaabbaaaabbabbabababbabaabaabbabbabbbabbabbbabaabaaababbbbbabaabaaabbaabbbbaaababbbbaabaaaaabaababbbbaabaabaababaabbbabbbbabbbbabaaabbbbaabaaabababbbbbbbabaaabbbababbaaaaaaabaaababbbabbbaabababababaaabbabbaabbbbabbbbbabbabbaaabbbbbbabababbbabbbabbababbababaababaabababbbababaababababaaabbbaabaababaabbbaababaabababbabbbaabaaabbbbbbababbbabbbbabbbaaaaaabaaabababaabbbbaaaabbbbbbaaaaabbbabaabaababbaaabbabababbbabbbbbabbaabbbbaaabbbbaaababbaabbabababbaababbaaabbabbbabbbbbabababbabbbababbbbbbababaababaaaaaabbabbaaababababababbaabaaaaaaabbbbbaaabbbabbbababbabaaabbababbaabbaabbbabbbbbbababaaaababbaaaabbaaabaaabbaabbbbbaaaaaaaaabbbbaabbaaaaaabbbbabbbbaabbbaaabababbbabbbbbbabbababbabbbabbaaaabbababaaabbbabbbbbaaababbbbbbaababbbabbbabbaaabbabbbbabbabbababbaabaabbaabaabaaaaaaabbbaababbbaaabbbaaabbbbaaaaabbbabbaabbabaaabbaabbaabbaababaabbabaababaababaabbbaaabbabaababbbaaaababaabbbbaaabbabbaabbbbaabaabbababaabbbbbabaabbbaaaabaabaaaaaabbaaababbaabbaabbbaabaabaaaabbbaaabbbbabbaabababbabbbabbabbbbbbabbbaaaaabbbababaabbbabaaaaaaaaaababababaaaabaaaaabbaaababbbbbaaaababaabbbbbbaaabaaabaabaabbbabbbbaababaabbababbbbbbbabbabaabaabbabbaabaaabbbababbbaababbbbbaaaaababaabbbaaaaaaaaaababbbabbbabbabbabbababaaaabbbbaabaabaaaabababbbabbaaaaabaaaaaabaabbbaaabbbbbbbbbaaabaaabbbbbbabbaaaaabbbaaaaabbbbabbbbbababbabbbbabbbbabbbbabbbabbbaabaabbabaabbbabaaaabbbaabbbaabaaaabbbababbaababbbbaaaaaaaaabaaaabbbbaabaaaaabbbabbaabaabaaabbbabbbbbabbbaabbbaaababbabbbbaabbbbbbbabbaabaabbbbbabbababbabaababaaababaaabbbabababbabbaabababbabbaabbabbaaaaaabaaabaaaabbbbbbbaaabaabaaaababaaabbbaabbbabbabbaaaabaabbbbaaababbabbbababaabaabaaabbaaabaaaaabbbaaabbbabaaaabbaabababbbbbaabaabbbababbaabbbbbbbaabbbababaaabbbaabbbabaababaaaaababaababababbbbabbbabababbababababababaababbbabbaababbbbbbaabbbaaaaabbbbbbaaaaaabbaabaaaabbaabbaabbabaabababbbaaaaabbabababbbbaaabababaaabbbabbabbbaababaaabaabbababaabaaababbaaaaaabbaabaabaaaabaabbabbbababbaaabbbbaabaabaaababaaaaabbaaaaaabbabbbaabaaabbabbabaaabbbabbbbbaaaaabbbbabbaaaabbbaabbbbabaaabbabbaabbaababbbaabbbbbbaaaabaabababbbabbabbaababaaaaabbbaabbbbabbbabbbaabbbbaaababbababbbaabbabbbababababbbbbbbbbaaabbabbaabbabbaabaababaaabbbbbbabaaaababbbababaaababbaaababbbbbaabaababbbabbababbaaababbabbaabbabbbaaabbbabababbabababbaababbbbabbabbabaababbbbbabbbabaaaabbababbababbaabababbbaabaaaaaabbaaabbabbabbaaaaaaabbabaaaababaababbbbabbbaabbbaabbaabbbbbabbabbbbababbbabbaaaabbbbabbabaabababaabbabbbaabbabaababaaabababababaaabbabbaaabbabababbbabbbaaaabaabbbbbaaaabbbabababaabbbabbabaaaababbbbbbabbabbaaabbaaaababaaabaabaabbaabbbbabbaabbbabaaaabbaaabbbabbbabaaaaabbbaaabbaabaabaabbbbaabaaabaaaaaababbabbbabaabbbbbaaabbbaababaaabbbabbbbaaaaabababbabbabaaaaabbaabbbbabaabaabbabbababaaabababaabbaaabaaabaaabababaabaaaaabbaabbbaababbaaabbabaabbabaaabbabaaabaabaaabbaaaaabaaaaabababbbaaabbabbbbaaaabbbbbaabbaabaabbabababbbabbabbabaaababbbabbbaaabaaababbaabaabbababbbabaababaabaabbbaababababbbbbaababaababbbbababbbbabbaaaabbaaaabaabaaaaabbaaababababbbaabbaaabababbbbaabaaabaabbbabbbbbbbbbabbbabaabbbaabbbabaaaabbabbbabbabbbaabbaaabaabaaabbbbaabbaaabbbbbbbbbabbbbabaaababbbbaaaabababaaaababbbaabbbaabaabaaabaabbabbabbaababaabaabbaabbabbbbbbabbbbbabbbabbabbaabbabbabaababaabababaaabbbaaabbbbaaabbaaaabaabbbabaabaabababbaaabbabbabaaabbbabbbbbababaaabbbaaaabababaaabaababbbabbaabaaabbbabaaaabaaabbbaabaabaaaaaabbabababbaaabaababbabbbabbbabaabbbbbbabbbaabbaaaabbabbbbbbabbababbbbaaabbbaaabaabbbabbbabbaababbbabbabbbbaaaaaababbbaaabbaaaaaabbaabaabaaabaabaaaaaabbbbbabbbbbaabbbaabbabaaaabbaaaaaabaaaabababaababbaabbabaabaaabbaaaaabaaabbabaabbaabaaaabaaaabbbbbbaaabbabbbabaabaababbbaaabaaaaababbabaaaaabbbabaabbbaaaababbaabbaabbababbaabaabbbbbaaaabbbaabbabbbbabbabbaabaaabbabaaabaabbbbbaababaabbaaabbabbbaabbabbbaabbbabbababbaabaaaaaabbaabbabbabbbaabbbaabaababbbababaaababbababaaabbaabababaaabbbabbaabaabbbaaaabbabbaaaaaabaababaabaaabbaabbbbbaaabbaabaaaabbabbbaaabbbabbaabbbaabaaaaaaaaababbaaaaabbaabbaababbababbaabbabaaabbbaabbbabbbbbababaababbabbbaabaabbabaabbabbbbabbbbbbaabaabbababbaababaaabbbabbbabaaaababbaaababbbbbbaaabbbaaaaabbbaabbabbabbaaaabaabaabbaaabababbbabababababbabbabaabaaaabaababaaaababbbbabbbaababababaabbabbabaabbbbabaabbbbaaababaabaabbaaaababaaabbbbabaabaababbabaabbbababaababaababbabaabaaabbabbabbaabababbaaabbabbbabbabaaaabaababaabbabaabbabbaabaaaaaaaabaaaaababbbabbbabbbaabaaabbaaaaabbaaaaababaabbabaabaabbbbababbbaabbbababaabaabbabbabbababbababbbababbaabaaaaabbaaaaaaababaabaaaaabbbbbbabaababaabbabbbaaaaaabaaabbabaabaababaabbaabbbabbbbbabababbababbbbbbbbbabaaaababbbabbaababbbbabababbabbabbababaaabbbbabaaabbbabbaababaaaabbaabbbabaababbbbabbbaaaaabaaabaaababbbaaabbaabbabbaaaababbaabaaababbbabbabaaabaababaaaabaaababbbbaaaababbbbaaabbbabaababaababaaaabbabababaabaabaaababbaaaababaaabbaaaababaaabbaaabbabaaabbbbbaabbaabbaababbbbabbabaaaaaaababbbbbabbbbbbaaabaabbabaababaabbbbbabbbbbaaaababbabbababbbbababbaaabbbbbaabbaaabaabbabaabbabababbaabbbbbbabaaaaaabababbabbababbbaaaaaaabbabaababbabaabbabbaabaaaaabbabaabababbabaabbbabbaabbbbbbbbbbbaabbbbbbbbbabbaaaabbababaabbaabaaaabaaabbaaababababbbaabababbabbabbbbababbaaababbbbbaabababbaabbbbbbbbaababbababbaabbabababaaabbaaababaaaabbbbbaaabaababaaabbaaaaabbabbbbbababababbbbbbbaaaabbbaababbbbaabbabbbaaabbaaabbaabbbbbaaaaabbbbbabbaaabbbaaabbbaaababbaaabbabaaaaaaaabbabbabbbaaabababaaaaaababbbbbbaabaaaabaaabbaaabbabbbaaabababaaabbbaabbbbbabbbbbbaabbbbabbbaabababbabbabababbababaabbbaaaabaaaabbabaaabbabbbbabbbaaaaabbaaababaabbbbabaaabbababaababbbaababababaaabbababbabbabaaaaaaabbbbaaabaabababbbbbababbabaabbaabbbaaaaabaababaabbabbaabaabbbbaababaaaaabbbaaaaaabbababababbbbbaabbaabbaababbababbbbaaaabbaaaababaabaaababbbababbaabbabbaaaaabbbbbabababbaaabaabbaaaaabbaababbababaabaaababbbababbabbbbbaaaabbaaaaabbabbbabbbabbabbaabbabbabbaabbbabbabbabaaababaaaaabbbbbababbababbbaabbaaabbaabbabbabbbaaaaaaaabbaabbaabbaaabbaabaaaabbaabaaababbaaababaaabbbbabbababaaaabbbabbbabaaaabbabababbabaabbbabbaabbaaaababbabaaababbaaabaababbbabbaaabbbabaaaabbbabbbbabaaabbbaaabbbababaabbaaaabbbbbaabaaabbbbaabbbbbaababaaaaaaabaabaaaabbbbaaabababbababbbaababbbbbaaabbbbbaabaabbbaabaababbabbbababaaababaabbbbababaabbaaaabaaabbbaaaaaaababababbaabaaaabaaaaaaabbaaabbbaabbaaabaaababbbbbbabbbabbbaaaabababaabbbbabbbbaaaaaaababaaabbaabbaaabbbbaababbaaababaababaabbaaaababbabbaababaaabbaaabbabababababaaabbaabaaaaabbbbaaabbabababbbaaabbabababaaabbaaaabbabaaababbabbbbbabbbaababaabaaabaabbbaaaabbabbabbbabbaabbbbabbbbabbababaabbbababaabaaaaabaaabbbbbaabaaaabbbbaabbabaaaabbabbbbabbabbbaabaabaaabbaabbabbbbaaaabbaaabbaaabbbbaababbaaaaaababbaabababbbbbbaabbabaaabbabababaaabbababbbbabaaaabaaaabaaaaaaabbaaabaabbabaabaababbabbbbbaaaabbaabbaaaababbbbbbbaaabaabbbbaabaaabbabbabababaaabababbbbbabaaaaaabaababbaabaaabbbaabababbabbaababbbabababbababaaababbababbababbbbabaaaabbabbbbaababaababaabbbaaaaabbaaaabbaababbbaaaaaabababbbbbababbababaaaaabbbbabbabaaaaaaaabbaababaababbabbbbbbabbbbbbbbaabaabbbbbabbaababaabbbabbbbbababbabbaababbaabaaabbbaaaaabababbbabaaaaaababababbbbbaabbbbabaaaaaaabababaababaaaababaabaaababababbaaabbbbabaaabbaabababbbabababaababaababaabbaabaaabaaabaaaaabbbaaaabbaababaabaaaaaabbabbaabbbbbaabbaaaaababbaaabbaaabbbbbbbababaabaaaaabbabbaabbbbabababbaabaaaabbbaabbbbbaababbbbabbaaaabbaabbabababbbababaabbabaaabbaaaaaabababaaaaababababbaaaabbbaababaaabbbbbbbaaababaaababbabbbaabbabbaabbbbbbbabaabbbababbababababbabaaaabbabaaabbaababaaaabbbaaaaabaaaabaababbbabbbaabbababbbbbababbabbabaabbaabababbabbbbaababbaaaaaaabbbbbabbbaabaaabbababbabbaabbbbbbbbbbbbbabbbabbabbabababbbaabbaaababaabaabababaabaabaababbbbbbbbaaabbabbaabbaababaabbaaaabbaaabaabaaababaaabbbbaaabababbbaaaaaaaabaaabaababbbbabaabaaabbbabbaababbbabbbbbaaaaaaabaabaaabaaabaaaabbaaabbababaaaaaabbaababbaaaababbbabaaabaabbaababababbabaabbbbabababaabbbaababbaabaaaaaaabbaabaaabbbbbabbabbaaabbabbabbbaaabbbbaabababaaaaabbaaabbbbbaabbbbababaaabababaabababbbaababbbbaaababbbabbbaabbaaabababbaaaaabaaabababaababbabbbbbbaabaaaabbbbbbabbbbbaaaabaabaabbabbabaabbbbbaababbabbabaaababbbbabababbbbbaaabbbbabaabbbaaabbabaabbbbaabbbabaaabbbbbbaabbaabababaabaaabbbbabbaabbbbaaabaabaabaaaaababaaaaabbbbbaabbbbabbbbaababaabbbaaaaababaabbbabbabababbbbbabaaabbaaabbaabbbabbabbabbbbbbaaabaabbaaababbbabbbbaababbaabbababbababbbbabaaaaaaabababbaaabbaaabbabaaaabaababbbabbbbbabababbbaabbaaaaaabbaaaababbaaababababbbbbbabbbabbbaaabaaaabaaabbababaaabaabbaaabbbaabbbbaabaaabbbbbabbbaaaabababababaabbbbbababaaababbababaaabaaaaaaaaabbbbababaaabbabbbbaabaababaababaaabaaababaaababaababbbbbaabaaabbbaababbaaaabbaabbbaaabaaabaaaabaabbbaabbaabbbaabbaaaaaababbaabbbbbaababbaabbabaaabaabbbbaaaabbbbbbabaaabaaababaaaaaabbbaabbbbbbbaabaabbbbaabbabbbabbbbabababbbabbaaababbbabbbbaabbaabaababbbabaaabbabbbabbbbaababbabaabbbbaaabaaaaaaabaaaabbbbbbbbbbaaaabbaababbbbbabbbbbbabbabbaaaababaababbaaaaaaaaababaaaabababbaaabbabbbbbaababbabaaaaabbbbbbbababbaaabababbbaaaabbbabbbbbabaaaaaabaabbbbbbbaaaaabbbbbbabaabababbbaabaabaabaabaababaabababaaabbbbaaaaaabaaabaaabbbbbbbaaabbabbbbaabaabaaaabaaabaabbabaaabaabbaaaaaaaabbabbababbabbbabbabbbaaaaaaaaaaababbabaababbbaabbbabbaaabbbaabaaabbaaabababbabaaabaaaaaababbabaaabbbbaababaaaabbabaaabbaaababbbababaabbbbaaaabbabbaaaabbbbbbbabbbabbabbbbbaaaaaabbababbbbaaabaaabbaaabbbbabaaaaaaaaaabbaabaabbbaaaaaaabbbbbaabbabaabbaaababbaabbbabaaabbbbbaabaabbbabaabbbbaabbaabbaabbaaabbabaaaabbabbbaabaabbbbababbbbbbbabbababbaabbbbaabaaabababbbabbbabbabababaaaabbbbaaabbaabbbaaababbabaababaaabaaababaabbabbbbbbbabaabababbaabaabaaabaaaaababbabbaaabaaabbbabaaaaababaabbbabbbbbbabaabbaaababaaabaabaaaaabbaaaabababaabaaaaaabaababaaabaaababaababbbabaaaabaababaabbaabababbaabbbbbbaababbbaabbbbabaaabbbbaaabaaababbbbbbaabaaabbababbabaabaabbbaabaabaaabbababaaabbbababbbbbaababbababaababaaaabbbbababbabaabbbabaabababbabaabbbabbbaaabaaaabbbabaaabaabbbabaaaaaabababbaabbabbabbbaaabaababaabaaaaababbbbaaaaaaabbbaabaababbbbbbaabaaabbbababaabbabaaaabaababaabaabbbbbbabaaabababbabababbbabbbbbbbbababaababbaabaaaaaabbbbabbbbbabaabbaabababababbbababababbbbaaabbaabbbbaaababbaaaaaaaaaabaababbbabaabaaaaabaaaaaabbbaabbbababbbaaaabaabbbaaabababbabaaabbbbbbbbbbabbababaabaaaaaaababbbbabbabbabbbbabbbbbaaaaababaaabbbbaabbbabbbababaabbbbaabaaaabbabbaabbbaaaabaaaabbabbbaaabbabbabbaababbbbaaaaaabaabaababbbbaabbaaababaabbabbaabaaabbabbbbbababbabbbababbbbaaabbbabbbaabaaabaaaababbbaaababbaabaababaaaaaabaabaabaababbabaabbaabbabbaaababbbbababaaaabbbbbbababbbaaaaaaabbbaabbababbbbababaaaaababbabbbbbababbbaaaaaaabbbababbaababbaabababaaabbbbbbabbababbbaaababaabaaabbaaaaaabbbbabbababaabababaabbabbaabbbabbbbbbbbbbaaaabbabaaabaaaabaaabababbaabbaaabaabaabbabbbabbaaabbbababaabaaabbabbbabbaabaaabbaabaabbbaaaabbababaabaababbababbbabababababaaabaabaabbaaaaabaababaababaabbbababbbbaaaabbbbaabbabbbabababbbbababababaaaaabbabbbabbbaaabaabbababaaaaaabababbaaabaaabbaabbaaababbabaaaabababbaabaababbaaaaabbbbaaaabbabbbaaaababbbaabbbabaaaabbbbbbabbbabaababbabbaabaabbabbaaabbbaababaaabbbaaaaaabbaabbbbabaabbbbbbbaaaaaaababbabaaaaabbaaabaabbbaaabaaaaaaabbbabbaaaaaaabbbabbbababaaaaabbbbaababbbbaaaabaaabaabbaababbaabbabaabbbaabaabbabbaabaabbaaabbaabbaabaaaaabbaabbbaabbabbbbabbabbaaaabaaaaaababbaabababbabaabbbbaaaaabbbbaabaababaaabbbaabbbbabaaabbaaababaabbaaabaabaaabbabaaabaabbbababbbababbbbabbbaabaabbabaabbbbbabbbababaaaabaaaabbabaaababaaaaabbbbababaaababbbababaabaaabaaaaabbbbababaabaaaaabbaabbbabaabbaaaabaaaaabbaabaaaabbaabbbabbababbaaababaaaabbababbbababbbabbbbbabbbaaabaaababbbababbabaaaaaabbabbbaaaabbbababbaaaaabbabbabaabbabbabbaaaaabababababbaabaaabaaaaabababaababaabaabaaabaaaaabaaaaabbbbbabaabaaaaaaaaabababbaabaaabbabbbabaaabaabaaaaabaaaaaaabaabbbaabbbabaabababbbbabbababaaabbaabbbbbababbbbaabbbbabbaabbaaabaaaaababaaabaabbbaaababaabababbbbabbabaaaabababaaaaabaaababbabbabbaabaabaaababaaabbaaabbaaaabaaaaaaabaababbaababbabaabbabaababbbbabbaababbbbaaabaaabbaaaaabaababbababaaaaaaabbababbaaaaaabaabbbbbbbabbbababaaaabababbbbbabaaaaaabbabbaaaabaabaabaabbaabbbaababbbaababbaabbbaababbbabaabbaaaababbababababaaaaaabbaaaababaaabaaabbbbbaaaaaaabaaabaaababaabbabbbaaabbbaaabaaabbbabaaaaaaaabbbaaaaaabbabaabbbbabbaabaababbaabbaabbaaabbbbbbabbbaaabbbbbababbaaaababbaaababbbaaaaabaaababaababaabbababbbabaabbaaabababaaabaabaabaabbabbbaaaaaababbaaabaaaaaabbabaaabbbbbbbbbaababaabbbaabbbaababbabbaaababbabaabaaababaaabbbaaaaaabbbabaabaabababbabbababbabaaaaabaabbabaababaababbbabbbbaabaaabbaababbaaababababaaabaababbbbbbbabbbaabbabbbbaaabbbbbaabbabbaaaabbbbaabbbbabbbababababbbbbabbabaabbaabbbbaabaaabbabbbaaaaabbaabbaababbbbabbbabaabbaaabababbbaaaaaaaabbaaabbbbaabaabbbaaabbbabaaabbaaaabbbbabbbaabbbbbbbabbbabababaaabbabbbbaaaabaabaaaabaabbaaabbbbabaabaabbbbabbaaabbabbaaaaabbbabbabaabbbbabbbbbabaaababbaabaabababbbbaabbbaabbbbaaababbbaaaaabbbbabbbbaaaabaabbaaabaabaabaaaaabaaababbbbaabbaababaababbbbbaababbaabbbaaaaaaabaabbbbbabaaabaababababbbbbbabaabaabaabbabbabbbbbaaaababaaabbaaababababbabaaaabaaaaaabbaaaaabbabbabaabbbabaaabbaabaabbaaabaaababaaabaaababababbbaaabaabbaaababaaababbaabbbbbbabbbabbabbbaaabaaabbabaabbaaabbaabababbaabbbbbaabaaaabaaaaabaabbabbabbabbababaaabbbbaabbaaaaaaabbbbbababbbbaaaaabbabbbababbbbababbbbbbababbabbaaaabababbbbababaabbbbbabbaaaabaaabaaaababbababaabbaabbaaabbbabbbaaabaaabaabaaaabababbaaababbaabbaabbbababbaabbaaaaaaabbaabbaaabbaabbbabbbbaaaaaaabaaaabaaaaababbbbabbabaabbaaaaaaaaababbaaabbbaabaaabbaaaabbaababbbabbbbaabbbbbbbabbbbaaabaabaabaaaaaabbbabbbbbbbbaabaabbabaaaabaabbabababaabbbbaababaabaababaaaabaaaabbbbabbabaaabbaaabababbbababbabbbbbaabbababaaaaaabbbaaaabbabbbbbbaaabaabbabaaaabbbbabaabaababbbaabbabbbabbbbbaabbbbbbbabbbbaaabbaabbabaaabaaabaaaaaaabbaaaabbbbbaabababbaababbabbbabbbabbbbbbbbbabbbbabaababbbbbaabaaababbabbbaabbabbabbbbabaababbaabbabababbaabbabaabababbbbbbbabbaabbbabaababababaabaaaaabbbbaabbaaaaaabbbbbbaaabbbbbbabbabbbbbabbbbaaaaaaabaaabbbaabbaaaaabbbbbbbaabbbabbaabbababbbbababbbbaabbaaaaababababababbabbabaaaabaaaabaabaabaababbaaaaabbbabbbbbaaaabaaaaababbabbbbababaaaaaaabbaaaabababaaababbabbbababaabbaaababaaababbabbabbbbaababbabbbbbabbbabbbbbbbabbbaaaaabaabababbababaababbaabbabaaabbaaaabaaaabaabaaabbbaabbaaabbaaaaababbabbabbaabaaaaaababbabbaaaabaaaabbaaaaaaaaababbaaaaaabbbbababbbababbbbaabbbaaabaababbbabaababbaabbababababaabaabaaaababbbaaabbbaaababbabaabbbaaaababaaaabaaaaaabaabbaaaaabaaaababababbabaaaaaabbbabaabbaabbbbbaaabaaaababbabbababaaababbabbabbbbbbabbbbbaababaaabaabbbabbaababbbbbbabbabbaabaaabaaabaabaaaabbbbbabaaabaaabaabaaabaaaaabbaaaabaabaabbbabaabbbbabababbbbbaaaababaaabbbabbabbbaaaaaaaabaabbbababbbbbbbbbaaabbbbbbabaaaabaaaaababbbaaaaaaaaaaaaababbaabbabbbbabbbaaabaabbaaabbaaaaabbbaaabaaaabaaaaaaabbaabbbaaababbbaaaabaaabbbaabaaaabbaabbabaabbbbbbaaababbbbbbabbbbbbbbaabaabbbaaaaabbaabbaabaaaabbbaaababaabbaabbbaaaaaaaababaabbbbaaabaababbbbbbbaabbbbbaaaaabaaabbbaabaabaabbaaabbbbabababbbabababbabaaaaabababbbbababbaabaaababaaabbbababbbaabbabaabbaabbbbaaabbabbabbababbbbbbabaabbbaaaabbbbabbbaabbabbbbbbbbbbaabbbaaaaabaabbaaaaaabaaabbbabababbbbbbbababababaababaaaaabaaaaaaabaabaabbaaaabaaabbbbaaaaaabbababbbbbaabbaababbbbbababbbabbbaaaabbbabbbbabbbabaabbaaabaaababbabbababbaabbaaaaaabbbbababababbbbbbbbbbababababaababbbbabbaaabbbababbbbbbaabbabaaababaabbabaabbbabbbabbbbbababbbaaaabbbaaababaaabbbabaaabbaabaaaaaaababbabbaababbabaaaabaabbbbbaaabbbbaaaabbbaabbabbbbabaabaabbaababbabbabbbabaabaabaababbbabbaaaaaaababaaabbbbababbbbaaabbabbabbbbaabbababbaabbaaababbabbabababaababbbbaaababbabbbbaaabababaababbababbabbaabaaabaabbaaaabaabbaaaaabaabbaababbaaaaabaaabbaaaababaabaabbaabaabbbababbaaabaababbbbaaabababababaaababbaabaababbabaabbbbbaabaabbabababaaaaabbbaabbabaababaaaabaababaabbaaaaaaaaabaaaaaaaabbbbaaabaaabbbaabbbbaaaaaaaabbabababbbbaaababbbbabaaaabaabbbbababbababbabbaababbbbabaabbbabbababababbbaaaaababbaaabaabbaaaabbaaaaabababaabababaaaaaaaabbaabbbabbbbaaabaabaabababaaabbabaaabbaaabaababbbaababababbabaaababbbbaabbabbbbbbaabaaaaabbaabbabaaabbbbbbaaabaabbbbbbbabaaaaabaabaabababbabbaabaabaababbababbaabbbbbabbabaaaabaaaaaaabbbaaabaabaaaabbaabaaaaababbabbbbbabbbaabbaabaabbbbbbaaabbbabbabaabbababbaabbbbbbbbabbbbbbabbbaabaaababbbbaabababaaababbaabaababbbbbaabbabaabbaabaababbbbabbbbaababababaaabaaababababaaababaababaaaaabbbbbbbbbabbbbbababbaababaabbbabbbaaabbbbbaaabbbaabbbbabaabaabbaaabbaabaaabaaaabbabaabbbabbbbbbabbababaaabbbbbbaaabbbbaabbbabaabbabbababaaababababaabaaaaaaabbbaabaaabaaabababaaabbbbaaaaaaaaababbaabaababbababbabbabbbaababbaabbaabababaabaaaabbbbaaaaaaabbaaababbbbabbbbbaabaabbaaabbaaabbaababbbbbbaabababaababaabaaabaaabbbbaabaaabaaaabaababbabaabababbabbbaabaaaaaaababbaaababbbabbbababbabbbabbbbabbabbaaaabbaaabaaabaaabbbaaababaaaaabaaaaabbbabbabbabbaaabaabbababaaaaabbbbabbbaaaaaaaaaaabbbababbaabaaaabaabbbbbbbbaabaabbabbbabbaabbbbaabbaabaaababbbaabbbaabbbbbababaabaaaaaaaaababababbbaaabbbbaabbbaababbbbabbbbbbabaabbbaaaababaabbababbabbbbabbbbbaaaaababababaabbbabaababbabbaaabaaaababaaababbbbbbbbbbaaaaaabaababbaabaabbabbaababababaaaaababbaabbbbaaabaaabbbabaabbaaabbbaabbbabbabaabababbbaabababaaaaabbbbbbaabbbabaababababbabbabaabbaaaaaaaabbbaabbbababbbaabbbabaaaaaaabbbbaabaaabababbabbaaababaaaaaabbbabaabbaabaababbababbaabaaaabaabbbbaabbabbabbaaaababaaabababaabbaaaaaaaababaabbbaabaaaaabbabbbbbaaaabbbabbabbabaabbabbbaaabbababbaaababbaabaaaababbaababbaabbaabbbbbbaaababbbbaaabbaabbbaabbaabbaaaabbbbababbabaaaabbababaaabbabbbbbbabbaaabababbbbbbaabbbabbabababaaabbbaabaabaaaaaaabaabbabababaabbbbabaaabbaabbaaababbbbbaaaabbaaababaaabbaabaababaaaaabababbaaabbbabbbbabbaabbaaabbbaababaabbabaaaaaaababbabbbbaabbabbaabbbaaaabbabbaaaaaabaaabbbaaabbbbbaabababbaaaaabbbbabaaaaaaabbaabbbbabbbbaabaabbbbaaaabaaabbaaaaabbaababaabbbababaababaabaaababaaaaaaababbbabaababbbbbabbaaaabbbaaabaabaabaabbaabbbababbababbbbbbbbbbbabaaaaaaaabbaaaabbaaabbbaaaababbabbbbbaaaababbabaaaaaabbabbaaaabaaabaabaaaabbababbaabbbaaaabbabaababbbaababbbbaaaaaabaabbbaabbabbabaababaabbbababaabaabaabbaaabbabbabaaabbbbbabbbaabbbaabbbbaabbbbbbbbbaababbbbaaaabbbababaabbaabaabbabababbbbbaaababaaaabbababbaaaabbbabbbaababaaabaaaabbababaaabaababbbabbbaaaaaaabaabbbbababbaaababaabaababbababbbbaaabbbbbaababbbaabbaaaaaaaaaabbbabaababaaabaaabbbbbaababbabababaaabbaaaababaababaababaaaababbabaaabaababbbaabbbbaababbabbbaabbabbbbaababaaaabbabbaabbabaaabbbabbaababbaabbbabbaaabaabbabababbabababbaaaabaabbaababbbabbbbbabbbabbbbbaababaabbabaaaabbaaababaabaaabaaaabaaaaaabbaabbbaaaabaaabbbabaabbbbbaaababaaabbaabbabbbaaabbabbbbbbabababaaaaabababaaaababbaaababbbbabaaaaaaaabaaaabababbabbabaabababaabbbbaabbaababaaabbbabbbbbaabaaaabbbbabbbbbbaabbbaababbabbbaaabbaabbababaaaaabaababaaaaabaaaaaabbaabbbaabababbbabbabaabaaabbbabbbbbbbabbbbbabbbbbabaabababababbabbaaaabaaabababaababbbababaabaaabbbbababaaababbbaaaababbabbaabababbbbabaaabbbabbaabaaabbababaabbbaaaaaaabbbaabbbaaaaaabaabaaabababaabbababbbbbbaabbbbaabaabbabbbaaaabaaaaababbbabbaabaaaabbaaaabababbbbaaaababaababbaabaabaabbaaabbaaabaabaabbbbabbaababbbbaaababbaabbaaaaabbaabaababaabbaaabbaabbabbaabbabbaaaabaaabbaaabbaaaaaaaabbababaaabbbbababbaaaabaaaabbbbbababbaaabbaabaaaabbbabbabaaababbabbbaabbbaabababbbaaaabbabaabbaaaaaabbbbabbbabaabbaabaaabbaababaabaaaaabbbabbaaabababaabaaabaaabbaabbaaabbababbbbabbbbbabababbbaaaaaababbbbaabbabaabbbbaaaaabbaabbbbbaaababababbabbabbaaabaabbbbaaabaaabbbabbabbbabbbbabbbabaabbaabaaaabbaababababbbbbbabbbbabbbbbabbaabbbbabbaabbabbbbbbaaabaabaaaaaabaaabbbaaaaababbbabbabbaabbababbabbbabbabbbabaabaabbbabaaababbababbabbbbbbbaabbaaabbabbababaaabbabbbababbaabbabbbaaababaaababbababaabaaabbaaaababbaababababbababaabaaababaababbababaaaabbbbbabbabbaabbaaaabababbbaabbababababaabbaaabbaaababaabbaababbbbbbbaaabababbabbbaaaaabbbabbaaaabababaaabbbaaaabbbaababaaaabbabbbaaaababaabbbababababbaabbbabbbababbabaabaabbbabbaabbabbabaaaabbbbabbaaabbbbaaaabaaaabbababababbabbbbbaabbbbaaaabbabbbabbaabaaababaabbbbabbbbbaabbbbbaaabbababbbaaabbbabbaaabbaabababbbaaabbbbbaabbabaaababaabbaaabaaaaaabababbababaabaabaaababbbbbbaaaababbbabbbbbabaaababaaaabaaabbbbbabaabababaaaabaaababbabbaabbbbbbbbaabaaababaaabaaabbabaabaabbabaabbabaaabbaabaaaaababbbabaabbbbbabaabbabbababbbaabbabbabaaaaaababaaaabbbbaaabaabaabaabbbabbbbbaabaaababbaaaaabbbabaabaabbbababbaaabaabaaaabababaaabaabaaaabbaababbaaaaaabbabbaabaaabbaabbaaaaabbaaaaabaabbabbbaababababbaaaabbbbbaabbaabbbbbbbbabaaaabababaababaaabaabbbbbbaabbabaabbaaabbababbaaabbaababbaaabaaabbbbabaaaaaaabaabaabaabbaabaabbbaababbbaabbababababbbbbbbabbaaabaaaabaabbaabbbabababbbbaababaaababbbbabbababbabbaaaababbbbbbaabbaabaaabaaaaababbaabaabbaabbabbabaaababbabaaabaaaabbaababaaaabaaabaabaaaabababaaaabbbbbabbababbaaababbbaababbabababbbaabbbbbaababbaabaaabbabaaabaabbbbabaaabbbaaabaabababaababaabbbaaabaaaababaaaabbbbaabbbbabbbbbbababbbababbbabbbaaabbabbaabbbbbaaabbaababbbbaabbabbaababbaaabbbbaaaabbabaabbbabbbabbbbbbbbbabbaaaaabbbabaaabbbaabbbaabbaaaabbbaabbaaabaaabbbabbaabbbbaababbababaaaabbbabaaaabaabaabbbbbbbaabbabbbaaaaabbababbbabaabbaababbabbbaaaabbbbbbbababbbbbabbaaaabababaabaababbbbbbbbbaabababababbababbabbbaabbbabbbbbbaabbbbbbabbabaabaabbbaabaabbababaaabbaabbbaabbbaabbaabbbabaaaabbbabbabababababbbaaaabaabaaabbabbaabbbabbaababaaaabaaababaabbabbaaabaaaabbbaabbaaabbabaaababababaabbbbbbbaabbaaabaaaababbabaabbabbaaaaaababbaaaababaababaabababaabbbbaabaaabbabbbbaabbbabbabaabbbababaabbbbbaaabbbbababbaaaaaabaaabbbbbaaabaabaabbaaabaaabaaababbbbaaabaaaabbbabbbabbbbbabbbbbbbaaabaababaabbbbabbbbbabbaaababbbabaabaabbbbabaaabababbbbaabbbabbbaaabbbababbbbbbbbaaaaaabbbbababaaaabbabaaabaaabaababbbbaabbbabbabbbbaabbbabaababababbbbabaabbababbbbabbbaaabababbbababaaaabababababbbabaaabbabaababbabbbbabaababbaaaaaaabaaabbbabbbbbaaabaabbbaaaababaaabaabaabbbaaabbaababbabbbabbbbababbbbabbabbaaaaaaabbbbaaaabbbaaaabbbabbbaabaaaababababbabaaaaaabbbaaaabbbabbaababababbabbbbbabbabaabbabaaaabaaaababaabbbaaabababaabaaaababaababbaaabbbbbbbaaaaababaaabbbaabbbabbaaaaabaaabaababbbbbbaaabababbaabbbabbbabbaaabbbbbabababbaaaabaaaaaababbbbababbaaabababbbaababbaabbbbaababaabaaaabbbaabbbbabaabaaaaababababbbaabaabbbbabbbbbbabaaaaababbbabbaabababaababbbabbbaaaaabbaaaababbaabbbbbbbbaaabbbaaaababbbaababbaaabaababbbbbbabbbaababaabaaaaabbabbababbbababbabbabaabaabaaabbababbbabbbaaabbbbbabbabbabababbabbabbbbaabbaabbbbbbaabbaaaabbaababbbbababbbaabbaaabbaababbbbbabaabaaaabbaaaabbbbaabbaababbbbbababbbaaabbbbaaaaaaaaabbaaabbaaaaaabaabbaababbabbbbaababbbbbbbbaaaabaababbabbaabaabbaaaaaabaabbaabbbbabbbabbabbbababbaaaaabbababbaaabaaabbbabbaabbabbbaaaababbbaaabbbbaababababbaaabaaabbbbbbabaaabbbabbbbaaaababaaaaaaaaabbaaaabbaabbbbabababbbaabbabbaabaabbbbabbabaaaaabaaabbababaabbababbaababbbbaaabaabbbaabbbbababaaabbbabbbabaabbaaabbaabbbbaaaaaababaabbbbabbabbabbababbbabbaaaababaaaaabbbaaabbbbbaaaabaababaaabbbbbaaaabaaabaabbbaabbbbababaaaabbabbbbabbaaabbababbbbbbbbaaaaaabbaaaaabbabaabaaaabbabaabbbaabababbbbaabbbaaabbbbabbbbbaaaaabaaaabaababbbaababbaabbabbabbbaababbaabaaabbaabaaaabaaaabbaaaabbbaaaabbbbabbbbabbabbbabbbabbabbaabbbbababbabaaabbaaabbabaabababbabbabbaabaaaaabbbaabbbbaababbbbaaabaaabaababaabbaabbababbbbaabbaabbaaaaababbaabbaabbabaabbbabaabbbbbbaaabbbbaabbaaaabbaabaaababbabababaaabbabbaaaabbaaabaabbbbbabaaaabaabaabaabbbaababbbbbaaabbbabaaaaabbbbababaabaabbabbbbbaabbaaabbbbaaabbaaaababbbbbaabaaababbaabbaabbbbbababbababbbbbbabbbbaabbaaabbbabaabaabbbabbabaababbbbaaabbbabbbaabbaabbabababbbbabbbaaabababaabaababaaabbaababaabbbbababaababababaaabbbbabbababbbaabaaabbabbbbabbbaabaaaaabbbaaaaabaaabaabbbabbaababaaaababaaaabaaababaabbaabbaaaabaaaabbbbbbabaabbbaabababbabbababaaaaabbbababbbabbaaaaaabbbabbbabababbbbaaaaabbabbabababbababaabaabbaaaabababbabbaabbaaabbabaababababbabbaaaaabbabbbaabbaaaaaabbbaaaaaaabbbababbbbabbbbabbbabbbbaabaabaaabaabaaaabbbbbaaaabbabbabbababbaaaaabbabaababbababbaabaaabaaaaabbbbbbbaaaaaababbaababaababaaaabaabaaaaaabaaabaabaabbbaaaaaabaaabaaaaabbbbaaabababbabababbbabbbaababaabaabaabaabbaababaabababaabaabbbabbabbbabbaabbabbbaabaaaababaabaabbbbaabababbbbabbabbbbaababbbaababaabbabbaababbabababaaababbaaaaaaaababaaabaabbbbbabaabaaaaabbabaabaaabbaaabbabaaaaababaaaabbaabbabaabaabbbbbaabaaababbbbaaabaaaabbbabaaabaabaababbbbbbbaaaababbbbababababbbbabbabbbaaaaabbababbbababbaabbababaababbaaaaabaaaababaaaaaabbaaabababbabbbbbbbbbbbaabaabbababbbbbaaaaaaabbbbbbbbaababbaababbaaaabbbaabbbabbbbbaabaaaabaababbabbbaaaaaabbbbabaaabbbbaabaabbbbbaaaaabbbabaaaabbbabababaababaabbaabaababbbbaabbaaaaaabbaabaaabbbabbaaaaabbbabbbabbabbbabbbabaabbabbabbbabbabaabbaaababbbaabbaaaaabaaaaababaababaaaaaaaabbbbababaaaabbababbbababbbbabbabbbbabbbabaabaaaabaabbabaaaabaaaabbbbbabbbaabaababbaaaabababaababbabbbaaaabbbbbbbababbbbbbaaaabaaaabaabaaabbbbbabbabababaabaaaababbabbbbbbabaabbabaaaabbabbbaaabbbbbbbbaaabbabbaaabababbabaabbabbbaaabbabababababababbaaaaaababbbbbbabaaabaabbbbababbaaababbbbabbaaaaaabaabbbaaaababbbabaabbabbaaabaabbaaaaabbbaaabbbbaaaaaaabbbbaabbbabbababaaaaababbbabbbaaabbbaabbbaabbbbabaaaaaaaababbaabbabaabbbbbbabbaaababaabaaaabbaabbbaabbaaabaabbbabababbaaabbbabbabaabaabababbaabbbbaaaaabbaabaabbababbabbbaaaabababbbbbaaabbbbbbabaabaaaababbbaaabababababaaaabaababaabbabbabbbbbaababbababbaaababbbbabbbbbaabbbabaabaabbaaaabbbababaaaababbabbbaaaabbbaabbbaaaaaaaabbbbbaaabaaaaaaabaaaaabababbabbbbbbabbaabaabbababbababbbbbaabababbbabaabbaabbabbbbbaaababababbbabbbaaaabbbabaaaababbaaababaabbabaabbaabaabaaababbabaabaabaaaabbbaaaabababaaabababaabababbbaabaaabaabbababbbbbbbaabaabbabbbabbbbbabbbbababbaabbbbabaaabbbbabaabbaababbbababbbaaabbabbabbbbbbbabaaababaabaabbabbabbbbaaaabbabbabbabaaaabaaaaabbbaaabbbababbababaaabbabaaabbbbaaaabaaaaababbabbabbabbabaaaaabaabbababaabbbabbaaabaaababaaabababaaaaaaabaabbbaabbbabaabbaabbbabaaaabaaaaabbaababbbabababaabbabbaababbbaabbbabaaaabaabaabbbbbaaaaababaabbababbaaaaabababaaaabbbababbabbaaaaaaaabaabbbbbababbaabaaaabbabbabbabbabbaabaabbaababaabbbbaaaabbabbbabaabbbbbbbbaabbabaababbababaabbaababaabbbbaabbbaabbabbabaaabaaaabbbbabaabaaaaaaabbaaabbabaaaababbaaababaaabbbaabaabbabaabbbbbaaaaabbaabaabbaaabaabbababbbababbbaabaababbbaabbaabbbbbbaaabaabaabbaabababbabaababbbbabbaababbabbbbbbaaabaaaabbbabbbaabbaabaababababbaabbbabbaabbabaabaabbbbbbbbabbaaabbababbbaababbababbabbbbbbabbabaabbaabaabababaabababbaaaaababbaababaabababbabbabbbabaaaaaaabababbbaabbabaaaaabaaabbbabaaaabaaaaababbbbaabbaabababbbababaabaaabbbabababbbaabbbbbbabbbbbbbaabaaaaabbbaaaabbbaabbababababbbbbaaabbabbabbbbaaaaabaaaabbbabbaabaaaaaaaababababaaaabbbabaaaaabbbbaaaaabbbbaaaabbbaaabbbbabbbbbaaaaaabbabbababbbaabbbbaabbaabbaabbbbbbbabaababbbaaabbbbbabaaaaabaaaababaaabbbaababbbbabaababbaaaaabbbbbabaabababbbaaabbbabbabaaabbbabaaabababbbabbbbbbbaaaabaaabababbbbbbbbbabaaaaaabbabbaaaabbbabbabbbbbbabbbbabaaabbaaaababababbbabbabbaaabababbbabbaabbbbababbaabbbabbbbaababaabaaaaabaaaabbbbabbbaababbababaabbaabbaabaabbbabbbaabaaaaababbaaabaababbaabbbababbababaabbabbaaababbbaabaaabbbabaaabbbbababbabbbbabaaababaaaaaabaababbbaababbbabaaabbbabbaabbbbbaabababbbaabbbbbaabaaaaabababaabbaababbaabbaabaababbaaabaabbbbbabbbabbaaaabbbaaabbaaabbbabbbabbaabbabaabaaaaaababbabbbbaababbbabbbabbaababbababbbababbaabbbbabbabbbaaabbaabaaaaaabbaabaabbabaaaaaababbbbbbaabbabababbaababaababbbbbbbbababbbbbabaabbaaabbaaabbbbbbababbbaaaaaaaaabbbaaabbaaaaabbaaaaabbabababbabbabaabbaaaaabbabbaaaabbaaababbababbbabaabbaaabbbaaababbbbabbbbaabaaabbbabbbabbaaaababababaabaabbbaaaaaaabaaabbbabbababbabbbababbbabbbabbbaabbaaabbababbbaabbbbaaaabbaaabbabbabbaaaaabaaaaabababbbbaabbabbbbaaababbbbbaabbaaabaabbbabababbaaaaaabbabababaabababbbabbbbbbbabbaaabbbabaaabaababaabaababaaaaaabbaabaaaaaabbbaaabaaaaababbbbbbbbbaaabbabbabaababbbabbbaabaabaaaababbaaaabbbbbababbaaaaabababaabbbbbaababaabbbbbabaaabbbabbbbabaabbaabaaaaabbabaaabaababbabbabbbbaabaabbaaabbbbaabaaabaaabaabbbaabbabaabaaababaaaabbaabbbbaaababbbbaaaabbababababaaaabbaaabaaabbabbbbbbbbbabbaaabbbbbbbabbbaababbbaabababbababbbaababbaabbbabaaaaaabbbabaabaababbbaaaababaabbbbbbbaababaaabaababbabbbbbbbaabbaaabaaaaabaaabbbbabbbbabbbabaaabaaabbabababbbaaaababababbabbababbababbabaaababbbaaaabaabbabababbaaaababaaabbabbaabbbabbabbbabbbaaaaaabaaaaabaabbbbaababaabbabbbbabababbabbabbbaabaabbaaaabbabaabaaabababaabaabbabaaabbabbbabbaabababababbababbbbababbbbabaababbbaabbbababababababbbbabaaabbabaabaaabababbbabaababbbaababaaaababaaabbaaabbbaabbaaaaabbaaabaaabaababbaaababaabbbbaaabbabbbababaaaabababbbaaababaabbbabbbbaaaababbaaabbababbaaabaaaabbbaabaabaaabbbaabaababbabbaaaabbaaaaaaabaabababbaabbbbaababaaaaabbaabaabbaaabaababaaabbbaaaabbabbbaaabbbababaaaabaabbaaaaaaabbbbabbabaaaabaaabbbabbaabbaabaabaabababbaaabbaaabababbaaababaababbaabaabaaaaabbaaaababbabbabbbabbabbbbabbaaabaabbbbaaabbbaabbaaabbbbbabaabaabbbaaabaabbaababbbabbbbbbbabbabbaaaaaaabbaaabbabaabababaaaaaabaababbbaabababbaaabbbbaababbbaabbbaabbaababaabbbabaaababbbaaabbbbabbabbababaabbbbbbabbababbabbbabbabaabaabaabbbbaabbaaaaaabbabbbbabaabbaababbabaaaabbbabaaaaabbbbbbbabbbaabbbbbababbaaabbaaaababbbbabbbaabaaaaabaaabbbbbaababaaaabaaabaaabbbaabbbababbabbbbbbbaaabaabaaabbbaababbabbaaaabaaababbbbbaababbbbbababbbbaaaaaabaaaababbbabaaabbaaabababbbbbabaaaabbbbaababbbbbaaaaabbabaaabbbaaaaabaababbabaabbbbaabaabbbbbabbababbaaabbbababbabaabbabaaaaaaabbbbababaaabbabbaabaabbababbabbababbabaabababbaabbaabbbbabaaababbbbaabaaaaaaabaabaabbbbaaaaababbbbbaaabbabaabaabbaaabbaabbbababaaabaababbbabbbbbbaabbbabbababbbaaabbbbbbabbbbbbbbabbbbaababbaaabbaaaaaabbababbbbbbaaaaaabbbaaabbbbabbababaaaabaaaaaababbbbbaaaaaabbabbabaaabaaabaaabaaaababababbbbababbbbbbababbbaabbabababbbbbababaaaaaabaabbbbbbabaaabbbbbababbbabbaaaabaaaababbabbabaaaabbbaaaababaaaaaabbbaababaaaababbbaabababbbaababbababbabaabaaabbaabaaaabaabbbbbababbabbbaabaaaaababababbbababaaaabaaabbbaaaabaaabaaaaabaabbbbaabababaabaaaabbaabbaaaaaaaaababbabaabbaaaaaabbaaaabbabbababbababbbaabbaaaaaabaabbaabaabbaabbabbaababbbabbabaabaaabbbbaaaaabaabaabbbbaababaabbbbbabbaabbbbaabbbbbaabbbaabbababbbabbaabbbaaabbaaaaaabaaaaababbbababbaaabbbbabbaabbbbbaabaaababaaabaaaaabbbabbabaaaabbbabbaaaaaaabbbbaaaabbbaaaaaabbbabbbabababbaaabbbbaaabbbbbbbaaaabbabbbabbbaaababaaaabbbbabaabaabbbbbaabbbabbabababbbabbaababaaaabbbbbbabaaaabaaabaaaabbabaaaabaabbbbaabbbabbaaababbaabbbaaaaaabbbabbbbbabaaabbabaabbabababbbaabbbaaabbaaaaaaabbbabbaabbbaaaabbaababbbbbaaaaaabaaabbbbbbaaaaabaabbbbbbbaababbaaaaababaababbbaaabaaabbbabbbaaaaabbbbaabbbbabbbababaaaaaababbbababaababbabaabaababababaababbaaabbaabbbababbaabbbbaabbaaaabaaaababbbabbbaaaabababbababbabaaababaaabbaaaabbaaabaabaabaaaabbbbaaaaaaaaaababbbabbbbabbbabbaaabaababbbabbaaaabaabbbbaaaaabbababaabbbbbbbbaabbbbbbabbaababbababaabbabbaaaaaabaabbbabaaaababbaaaaaaabaaabbbbbbabbbbbabbbaaaabbabaabbbaabaabbbbbaabaaaaabaaaabbbbababaaaabbbabbabaabaaababbaaaabbbababaabaaaaabbbbbbaabbaaabbbaaabaabbaabbbbabaaaabbbabbaabaaabbbbabbbbbbbaabababbbbbbaaaaaababbbbabbbbbbabaabababbababbabababbbaabababbaaababbaaaabaaaabbbbbabaabaababbbbbaaababbaababbabbabbaabbbbbbbaaabbababbbbbabbabbbbabbbaaaabaabaabbaaabaaaaababbbbabbbababbbaababaabbbaaaababbabaaaabbbbabbaabbaaaaabbbbaaabaabbbbaabbaaabaaaabaaabbabbbbabaabaaabbbabababbabaaabbabaabbbbabababbabbaaabbaaababbbbbbbaabaaabaababaaaaaabbaaaabbaabbbbbbaabbaabbbabbbaababaaaaabbaaabbbbabaaaabbabaabbabbbbababaaabbaabbbbabaaababababababbbbbababaaaababbaaabaaabbaabaabbbbaabaaaabbabbbababaabaaababbabbabbabbbbbaabbabbbaabaaaaababaaabababaababaaaabbaaabbbabbbabbababbbbbabaaaaaabaaaabababbabbbabaaabababaaaabbaaabbabbaabbaaabaabbbbaaaaaaaaababbbababbbaababaabbbabbabaabaabbaabaaababbbbbbbbbbabaabbabbbabbabaaaabaabaaabbbaababbaababaababbaabbabaaaaabbbbbbaababbabaabaaaabaaabbabbabbbabaabaaaabbaaabbbbbaaaaaaabbabbabbbbaabbbbbbbbbbbaabbabaaababaaaaaabbabbaabbabaaaabaaabbbbbaaaaaaababaabbbabbbabbababababbabaaaaabbabbabbbabbaaaabaabbabababaaababbabbaaabbbbbabaabbabbbbaababaabbbbbbbabaabbbaaabaaaabaabbaaaaaaababbabaaaaabbbbbbbbabbbbbabbabbbababbbbbabbababbbbaabbbaaaaaaaaaabaabaabbabbbaaabbabbbaaaabbbaabbbaabbbabaaaaaabaababaabaabbaabaaaabaababaaaabbbabbaaabbaaabbaaaaaaaaabababbbababaaaaaabbababbbaaaabbabbbbaabaabaaaaaaabbbbbbbabbbaaabbbbbaabbbbaaaaaabbbbbbaaabbaaabbbaaabaabbaaaababaaabbabaaabaababbababaabbaabbaabbbbbaaabaabbbbbbbbbbabbaabbbbbbbbbaaabbaabbabbaabbabaaaaabaaabbabbbbaaaabbababbbbbbbabbaaaabaabbbbaaaababaaabbababbbbaabaabaababbaababbbababbababaaaaaaaabababaaabaaabaaabaabbbabaaaaaabaaabbaabaaabaabaaabaababaaaaabaabbbbbbbbbbbaaaabaaaabbabaababbaaababbbaaabbabbaabbbababbaabbabbabbbbaaaaabbbabbbabababaaaabaabbbbaabbaabbaaabaaaaabbbaaaaaaabbbaababababbabbbbababababbaaaaabaabbbbbabaabaabaaabbabbbababbaabaaababaabbbbbabbaababaaababbbaabbbbbabbaabbaabbbbbaaababbabbbaabbbbbabbababbabaaabbaaaaaabbababaabbbaabaabbabbabbbbbbbbbbbbbabbabaaaaabbbabbbbbbaabaabbbbabbbbabbaabbbbaaaabbaaaaaaabaaaabbababbbbaabababbaaaaabbaababbabbaaaabbaababbbaaaabaabababaaabbaababbbabbaaabaabbbbbbbaabbbbbbaaaaabaabbbbbbbbabababbabbaababaababaaaaaababbbbaabaaabbabbaaaababbaaaaabaaababbaababbabbbbbbaabbaababbbaaababaaaaabbbbbabbbbabbabaaaababbaaababaabbbababbabbbaaabbbbbaabbbbbbaaaababbabbbbabbbabbaaabbabaabbbbabbababaabaaaaaaaabaabaabbabaaabaaaabbaaaaabbabaabbababaaabbbbbbabbbaabbaabbbaabbbbbbbbbabbaabbabbbaababbababbbbaaaaabaabbbabbbaaaaababbbbababaaabaababbbbabbabaababbbabbbbaababaabaaaaabababaaababbbbbabababaabbabaaabbbabbbaabbaaabababbaabaaaabbbbababbbbaabbbbbabaabbaaaaaabbababbabbbbbaaababaabbaabaaaabbbaaababbaabababaababbbabbbbbaabbbaaaababbabaabbabbbbababaabbabaababbaaaabbbaababbbbbbbaaaabbbaaaabbbaaaabbabbabbbabaabbbbabbbbbabbabaabaababbbbaaaabbbbabbabbbabbabbabaabaaaaababaaaaababaabbababbaabaabbaaaaabbababbaabbababaaabaaabaabbbabbaaaabbaabaaaabababbaabaaaabbbbbbaaababaabbbbbabbbbbbabbbabaaaaabbbaaabbabaaabbbaabbaabbabaabbbaaaababaaaaaabaaaaaabaabaabbbababaaaaabbbbabbbbbbababbaabbbaaabbaababbbbababbaaaabaabbbaaabaababaaaaabbaababaabbbaabbbbabbabaaaababababbaaaabaaabbbaaabbaabbaabbbbaababbabbbabaabbaaaabbaabbaabbabbabbbbaaaaabbbabbabbbbbaaaababababbaaaababbbabaaababaaababbaabbbabbaabbaaaabbaaabbbaabaaaabaabbbaaaaabbbbbaaaababbabaaababbbabaaabbaaaaaaabbabbabbabbbaaabbbababaabbaababbababbbaaabbaaabaaabaaaabbaabaabbbaabbabababababbabababbaaaababaaaabbbabaaabbbaabbbbaaaaaaaabbbbbbbaaabbbbabbabbababbbbabbaabbabbababbbbbbaaaaabaabbabbaaaabbaabbbbaaababbaabbabbbbbbaabbbbabbbbbbaabaaababbabaaaabaabbaabaababaaababbaabbaaabbbabbaabaaaabbabaaabbbaabaaaabaabbababbabbabbaaabbaaabaabbabaaabaaaaabbaaabbbabbbbababaabbbaababbbbaabbbbbbbaabaababbabbbaaababaabbbaababbabbabababbabbbabaaaabbaaaabaabababbbbbbaabbabbaababababbaaabaaabbbbbbbbababbbabaaabaaaaabbabaaaaaaaaababbbbaaaaaabbabbabbabbaaababaabbabbbbbbababbbbbabbabbbbaaaabbbaaabbbabaaabbbabaabaabbbaaaababaabbabbbabbababababbbababbaaaaabaabaababaabbbaabbbbbbabbaaabbbbbbaabaabaaaabbabababbbbbabbbabbaaabaabbabaaaabbaaaaaaaaabaabaaaaabbababaabbaabaabababbbbbabbbbbabbbaaaaaabbbbaaaabaaaabaaaabbbabaaaabbbabaabaaabbbabbaabbabbabbaaabababababbbaababbbabbaaaabbabababaaaaababbbbbbaabbaaaaaaabbbaaabbbbaababbabbaababbbbabaaaaaaaabbabaabababaaababaaaababaabbabbaabbabbaabababaabaaabbabababbaababbbaabbbaaaaababbbabbaabaabbbbaabaabbabbbaaabaaabaaababbaaaaaaabbaabbabbbbbbaaabbaabaabbabbababbbaaaaaabaaabbbabbaaaaaabaabaaabbabbbabbaaaaaababbbbbbabababbabbabbbbbaaaabbabbbbbbbabbbbbbbbbbabaabaaaabbabaabbabbbaabbbbaaabbbaababaaaaaaaabbabbaaaabaabbbabbbabbabbbaaaababbbabbababbababbaaabababaaabaaabaaababbbbbbbaababbaabbaabaabaaabababaabaaaaababaabaabbbbaabaaaaaaabaabbabbabbababbbbbbbbababbabbabaaababbaaabaaababbabbbbabbbababababaabbbbbbbbbabaaabaabbababaabaaabaaabbbbaabaabbaababbaabbaabaabbbababbabbbabbbabaaaaaaababbbbaaabaabbbbabbbaaabbbaabaabbbbaaaaabbaaaabbbbaaabbabababbabbbabaababaabbaaabaaaaabbbbbaaababaaaababbbabaaaaaabaaaabbabbbbbaaabaabbbabbaaaaaaabbaaabbaabababbaaaaaabbaabaaabbbbbbaabababaababbbaabbbbabbaabbaaaabaaaaabaabaaabaabbbbbabaabaabbabbbbababbbbbbabbbabbbaabbababbabbbbabbababbabababaababbbaabaaabaaaabbbbabaabbaabbabaabaabbbbababaaabbbbbabbbbabaababababbbabababbabbabbbabbaaaababaabbbbabbbaaaaaaaaaabbbababaaababbbaababaabaabbbaababbaaaaababbabaaaabababbbaaabbaaabaaabbbbaaaaaaaabaaaabaaaaaabbbbbbbabaaaaaababbbabbbbaaabaabbaaabaabaabbbbbbbbabbaababbaabbaabbaaaababaabbabbaaaabaabbbbabababbbbbbaaabababbbbbbaabbbabaabbbbaabbbabbbbaabaabaaabbaabbbbabbbbaaaaabbabbabbbababbbabbbbabbbabababbabbbbaabbbaaabbaabbabbabbababbbbbbabbbabbababaaabaaaaaabaabaaaaabbaaaabbabababaaababbbaababbaaababbbbbababbaabbaabbabaaaaababaabaaabbbbbbbaabaaabbbaaabbbaabaabbabbaabbbabbbabaaaabaababbabbbaabbbbaabbaabbabaaaaabbbbbaaabaaabaabbbabaaabbbaaaaabaababaabbbbbbbaaabbaabbaababbababbbbaaabbbabbbbbababaaaaaaababbbabaaabaaabababbababababbaaababbaabbaabaaaabbabbabbabbaaaaabaabababaabaaaaabbabbbaabaabbbababaaaaaabbbbabbbabaaababbbbbaaabaaabaaabbbbaababbaaabbbbbbbabbaaabaababaaabbbbbaabababaaaabababaaaababaababbaaabbabaabbaabaabbbabbbabaaaabbbbbbbbbabaaabbaabbbbabbaababbaaaaaaabbabbaababbbbbababbabaabbbabaabaabbabaaaababababaababaaababababbbababbaabbaabaaabbaaabbaaabbbababbabbabbbaaababbbbaaabbbaaaabbaaabbbaaabbabaababbbaaaabbabbbababbbbbaaaababaabbaaaaabbaabbaaabbbbababbbaaabbbabaaababbbaaabaabaaabbbaaaabaaabbaabbaabaaabbabbababbbaaabbaaaababbaabbababaababbabaaaabaaaabbbbaabbabbbabaaaaabbabbaabaaaaabababaaaaaabbabbbaaaaaababaaaaaaabaaaabbbbbaabbaabbbaabbbbbabbabbaaabbbbaabaabababaabbabbbaabaaabaabbabbaababaaabbabaaaabaabababababbbbbbbbbabbababbbbabaabaaaaaaabaaaabaaaababbbaabaaabaabaabbabaaaabbbbabbabaabababbaababbabaaaababbbbbaaababababbbbababbabbaaababbababbbabaaabbbaaababaabbabaababaabbabaabbbaaabbbabbbaaaaabaaabababbbabbbababbbaaaaabbbbaabaaaaabaaabaabaabbbbbaaaabbabaaabbbaabaabbbbaaaaaaaaaabbbbabbabbababaabaabababbaaaaaaabbaabbbbbaabbbaabbabababbbabaabbabaababbabababbababbbabbbaaabbabbaaabaabbabbaaabbababbabbabbbbaabababaaaabbabbbbabababbabbbbbbaaabbaabaaababbbaaaabaabbaabaaaabaabbbbbabaaaabbbbaabaaabbabbaabbbbbaabbababaaaabababababbabababbbabbabbaaaababbbbbaaaabbbbbaabaaaaabababbbbbbbbbbabbabaaabbaabbbbabbbbbbabaaabaaaaaababbbbbaabbabbabbaaaaababbaaaabbaabaababbababbabbabababbbbaaaaaaaabbbababbaabaabaaabbabbaabbaaabbaabbbbaabaaabbbababbabbaababbbbbbbbbbaaababbababaaaababbbaaaababbbabbaabbbaaabbabaabaabbbaaaabaaaababbabababaabbbabaabbbbbbbabaababaaaaaaabababababbbabbaabbbaababbababbbabaaaabaabbabbababababbbaababaaabaabaaaaaaabaabaaabaabaaabbaabababbbabaabbbbbaaabbbaaaaabaababbaaabbaababbaabaababaabbbbbaabbbabaaabbbabababbbbbbbbbbaabaaababbabbaaabababbabbbbaabaababbabaaaabbbbaaaabababbababbbababbabaaabbaaaabbbaaababbbbabaabbaabbbbbaaabbbaabbbabaaaaaabbbbabbaabbbbababaabbaabbaaaababbabbabbabaaababbaaabaabbbabbbbababbabaabababaaabbaababbbbbaabbabbbbbbabbaaaaababaababaaabbababbbaabaabbabaabbbbbbbababbbaaabababbbbbbbabbabbbaaabaaabbaaabaaaabaaabbaaaabaabaabbbabaabbbbbbaaaaabbbababbaababaabaababbbbaaabbabaabaaaabbbabbabbbabbaabababbaabaabababababbbaabbbbaaaaabbabaaaaabbbabbabaabbbbbabbabbaaaabbabbabbbbbbabbabbbbaaaabbbbaabbaabbabbbbaabbaaabbababaababbabbaaaaabbbbabaaaaababaabbaabbabaababababbabaababbbaabbaaaabaababbaabbabbbbabaabbbaaabbbbaabaabbabbbbbbaaaaaabbbabababaaaabbbbbbaabbabbbbaaaabbabababbbbbbaaabaaaabaaaaababbbaaaaabbababaaabababbbbababbababbbababbbabaaaabaabbaaaababababaaabaababaaabbbbbbabbbbaabbbbabaaabababaaaabbabbbabbaabbaaabaabbabbbbbaabbbababbaababaaaabaabbaabbbbabaaabbababbbbbbbbaabbaaaaaabaababbbbabaaabbaabbabbaaaabbbaaabbbaaabbbbbbaabaaaababbbaaaabaaaaabbabbbbbabbaabababbaabbbabaaabbaabaabaaabaaabaaaaaabbbaaaaaabaabbbabbbaababaabaaabbabaabaaaabaababbbaaaabbbaababbaabaabbaaaaababaabbbbaabbbbabababbbbbbbaaaabbbbabaabbbaababbaaaaaaabbbbaaabbabbaabbbabbbaabbbbbbbbabaaababbbbbbbaabbaaaabbbabbbaabaabbaaaababbababbbabaabbababbabbbabbaabbabbaabbaabaababbabbaaabaaabbababaababbabbbaabbbbabbabaaabbaaababaabbbbaabbababbbabababaabaaabaabaaaaaaabaaabaaaababbaabbbabbabbabaaabbbaabbabaaabbbaaabbaaabbbabaabbbaaababaabbaabaaaaababaabbbbaababaababbbbaabbbbabbbbabbaaabaabaaabababbaabaaaaaabaabaaaaaabbbaaabbaaaabaaaaaababbbabaabbababbbbbbaaabbabaabababbbababaabbabaabbbbbbbbbaaabbaaabaabababbbbabbbabaaabbbababbbaaabbbaaaaabbaaaabaabbbbabaaababaabbabaabbbaaaaaababbbbbabaabbababaaabaabbbaaaaabbbaaababaaaabbbaaaaabbaaabbaaabababbbbababbaababbbbabaaabbbaaaaaabbaaabbbbaaababbabbbababaaabbaaaabbbababaabaaaaabbaaaaabbbabbbbbaabbbbabaaababaabbabaababaaaaaaabbabaababbbaabababbabbababaaaababbbbabaabbaabbaaabbaaaaaabaaaababbaabbbaaaaaabababaaabbaaaaabbbbbaaabbabbbbbbaaaababbbabbbbbbbaaaaaaaababaababaabababababaaaaaaaaabbbbabaaaabbbbababaabbabaabaabbbbbaabbbbbbaababbbbabbbbbbbaabbaabaaaaabaababababaababbabbbbbaabababaaaaabaaaababbababbbbbaaabbaaabbaaababbababbababbbabbaabbaaaababbbababbbababbaabaaababaababbbabbaabaaaabbaabaaabaabbaabababaababaaaaababbbbbaabbbbaabaaabbabbabaaabbabbaaababbbaababbbaaaabbabbabbaaaaabaaabaabbbababaabbbbbbaaabbaaaaaaaabaaaababbaabbbbbaaabaabbbbaaabaaaaaabaaaaababbbbababaabbbabababbabbbaabbabbaaabbbbaaabababaaaabaaaabbbabbbbabbabaaaaaaaaabbbaaabbbbaabbaabbbaaabbbaababaabbabababbbbbaababbbbaaaaaaaabbabbaaaaaababaabbaaaaaabbabaaaabbaaaaabbbabbbabbaaabbbaabbaabbabbbbabbabbbabaaabbaabbabbbaabbaabaabaabbbbababbbbbbabbabaaabaabaababaaabbaababaaaabaabbbabbbaaaabbaabbababaaabaabbbbaaaabbaabbbaabbababaabaaababaaabbaaaaaaaaabababbbaaababaaaaaabbbaababaabaaabababbaabbaabbababbbabbbaabbaabbabaaababaabbaaaabbbbbaaabaabbabbababaababaabbbabaaaaaabbaabaaaaabbbbbaabbababbbaaabababbaabbaaaabbabbbbabaaaaabbaabaaabbabbabaababaabaaaaabaabbabbbbaaabaabaaabbbbbbbbabaababaabbbbbbbaaaabaaabbbbbbbabbbaabbbababbbbbaaaabababbbbbbbabbbbaabbaabbaaabaaaaababaabbabbabbaaabbabbbbbabbbaaaaabaabbaaabbbabaabbbababaaaaabbbabbabbaaabbbbbaaaabbbabaabbaabbbbaababbbbabbbbbaaaabbabaabbabbabbaabbaabbbbbababbbabbaabaabaababaaaabbaaaabbaaabbaaaabbbbbaababaabaaabbbaabbababaaabbaabababaabbaaaabbbaabbbaabaaabbbbabbabaabbbabababbaabbabaabbbabbababaabababbabbaaabbabbbaabababaaaaabababaabaabbbbaaabbbaaababbbbaababbbbbaabbababababbababbbbababaabaaaaabaabbaabbaaaabaabaaabbbbaabaabaaabbbbbbbababaabbaaaabbabbbababbbaaaaabaabbbbabaabbbabbbababaaaaabbbaabaababbbbabbaabbbababaababbaaabbabbaaaabaaabbbbaabaaabbbbbabbabbbbaaabababaaaabaabaaaaababbbaababbababaaabbbaaaaabbbaabbaaaabbbaaabbaaaaabbaaabbbbbbbbbaabbaaaababababaabaabbaabababaabbaaabbbbaaaabbbabaabbbbababaaaababbbbbbabbabbbaababaabaabaabbbbbbabaababbaabbbbabaaabbaaababbaabbabaaaaaababbabaabaabbbbbbaabaabbbaaabaababbbbababbbaaaabababbaababbabbabaaaaaabbaabbbababaaabbabbaaaaabababaabaaaaabababbbabbabaaaaaababbaabbbbaaaaaaabbaabaaabaabbbbabbaaaabbbbabaabababbbbbbbbbbbabaabbabbaabaaabaaabaabaaaaaaabbbbbbbaabaabbaabbbbbbabbaaabaaaaaababababaaaaababbbabbbbabbbbbaaabbbabbbbbbbababaaabbabbabbbbbbbabbaaabaaababbbaaaaaabbabaababbbaababbbbabbbbbbbaabababbbaabbabababaabaabaaabababbbaaaaaabbabbbbbbaaababbbbbbbbbaababaabaabbbbabaabbabbaabbbbabaabaabaaabbababbbbbaaaababaabbabaababbaaaabaaabbaaaaababaaaabbabaaabababbbbaaabbbaabbaaaaabaaabbbbabbabbaaabbaabaaabaaaababbbbaaabbbbaababaabbaabbbabaaaaaaaaaabbbaaaaaabaababbbbbaabaababbabbbbabaaaabbbabbabbaaaabababbbabaaabbbbaabbbbababbbaabaabbabababaaaabbbabbaabaaaaabbaababbabbbbbbbbabbaaaaabbabbaaaaababababababaabaaabbbbaabbaabaabaaababababaaaabbabbaabbaaabababaababbbbaaaabbbbaaaabbaababbbbabbababbaaababbbaaabaababbaaababaababbaaaababaaabbbbaabbbbaaaabbabbbaabbbbaabaabbbbbbbbabbabaaaaabaaaaabbabaabaababaaaaaaabbaaabbbbbababbaaabbabababababbaaaabaaabbbbababaabbbbbababababbbbbbabbbabbabbbbabbaababbabaabbbbbbbbabaaabbbabbabbabbaabbbabbbabbaaabaabbabaabbbabaaabaaababababababbbaabbaabbbbbabaabbbbbaabaaaabbaaabbbbbbabbaaaababbbabaabbabbbbbaabbaaabababbbbaaaaaaaabbbaaaabbaaabbbbbabaaabbbbaabaaababbaaaaaaabbabaabbaaabbbbaabaabababaaaabbbbababbaaaabbaabaaaabaabbbaaaaabbabbaababaabbabaabbbbbbbabaabbabbbbaaabaaabbaababbababaaaabbaaaaaaabbbbaabababbaabbbbbbaaabaabaaabababbaabaaabbabbbbabbaabbbaaabbaaababaabbabaabbbbbabaabaaaababbabbababbababaaaaabaaaaaaabbbabaabbbbbaabbaaaaaaaaabaabababaabbbaabbbaabaaabbbbabbbbbbbaabaaaaaaabaaabbbbbbbabbaabaabbaabbbbabaabaabbbaabbaaabaabbbaabaabbababbaabaaabbbabbbaabbaabbbbbababbaabababaababbbbabaabbabbabbabaabaaababababbaaaaaabaaabababbbababbaabbaabbaababbbbbaaabaabbbbabaaaabaaaabbabbbbaaaaabaaaaabaabaaaababbbabbaaaaaaabaaabaaaaaababaabbaabbaabbbbbbaaabbbbbaabbbaaaabbabbababbbbaaaabbbbaaaaabaaaababbbaaabaabbaaabaabbaaabbbbaaaaaaaaabababbbbaabaabaaabaabababbbbababbbbbaaabbaabbbaababbaaaabbbbbaaabababaaaabaaaabbabaabaabaababbbbbbbaabababaabaaababababbaaaabbbbbbaaababbbabbbbbbabaaaabbbabaaaabbbaaabbaaabbbaabbbaabaaabaababaaaaaaaabbbaabbbaabaabbbbaababbbbababbababaaaabbabaabbbbabbabbbaabbbbabbbbbabbaaaaaaababbaabbaaaaabababbbbababbbbabbbabaaabaaabababaabbbbabbbbbabababbbbabbbaaaaaaabababbabbaabbabbaaaaabbabbbabbaabbbaabbabababbbbaaaabaaabaababaaabbaababaabaababbababaababbbbbbbabaabbbbaababaabbbbbabbaabbaaaaabaabbbbabbbaaabbaaaababbbbaaaaaaaaabbbabbaaaabaababbababbabbbababbbabbabbbaaababaabaabbbabbbbbbbbaaaaaaaababbabbabaabbabbbaababbababbaabbabababbabbbaaaaaaaabbbbaabaababaaabababbabbabbbbbbbaabaabaaaabbbaaabaababbabbaababaabaaabbbabaabaabbbbaabbbabaabaaababaaababbbabbaabbaaaaaabaababaaaababbaabbbabbabbbabaabbaabaababbaabbbababbababbabaabbbbbaabbaababbbbaababaabaaaabbaaababbaaabaabbaabaababaaabbabbbababaaaaabbabbabaaabbbabbbbbbaabbbabbbaaaabbbbababaaababbbbaaabbaaabbabababaabaabbbbbbbbbbababbbbbaabaaaaaabbaaababaaaabaaabbbbaabaababbababbaaabbabaabbbbbabbbbaabbabaabbabbbababaabaabaababbaabbbaaabaabaaaabaabaaaaaabaabaabbbabaababaaabaabababaababaabbaaaabbbaababbabaabbaaabbbabaabbbbbbaaabbbabbaaaabbabaabbabbababbbaabaabaaaabbaabbaabaababbaababababbbababbaabbabababbbbbaaabbaababbabbababaaabbaabaabaaaabababbbbbaabbababaaabbbaabbabbbbabbbbbaabaaabababbbabbabbaaabaaabbbaaaaaabbbbababaabaaabbabababaaaaaabbbaabbabaabaabaaabbaaaabbababbbbbaabbabbaabbbbaaabaabbaabbbbaaaaabbabaaabbbababbbbbbbbababbbbbbababbbbbbabaaaababbbabbabbaabababbabbbbbaababbbbbabaaabaabbbaabbaabbaababbabbaabbabbbbbabaaaaabbbabaaaabbbaabaaababbbbbbbbbbbabbabaaaaaaabaababaabbbbaaabaaababaaabbaaaabababaabaababbbbbbaaabaaaabaabbbbbabbbaabbbaaababbaabbabbbabbaaabbabbbbaabbbaaaaabaabaabaaabbaabbabbaababbbbaaabbbabaabbabbabbbaababaabbaabaaaabaaabaababaabbaababbaaaaaabbbabbbbbaababababbabbbbbbaaaabbabbabbabbaababbbbbbaabaabbbbbaababaaabaabbaabbaabbbaaaabaaabbabbaababaababbbabbaaaabbaaabbbababbaaaaabaabbbbbaabaaaabaabbbaabbbbbbbabaababbbbbbabbababbbbabbaaababbababbbbaaaaaaababaabbabaaabaababbababbbaaaaaaabbaaabbaababbbabaabbbbbabaabaaaaaaaaabbaabbbbbbaaaabaabbaabbabbbabbbbbbbbaaabbbbbabbbbbbbbabbaabbbbaaabbbaaaabaaaaaababbabaabbbabaaaaabbabaabbabbabbbbbaababbababaaababbaaabbbababbababbbbbbaababbbaabaaabaabbaabaabbbbabaaaaabbaaabbabaaaaaaababaabbaaaaaabbaaaaabaaababaaaaaabbbbbbbaababaabaabbaaabaaabaaaabaabaaaaabbbabbbaaababbbbaaaabaaaabbabbbaababbbabbbbabbbbaabbbbbbbaabbaaaababbbaabbaabbbbaaabbabaaabababbaababbbbbbbbabbabbabbbaaaaaaaaabbbbbbabbaaaaaaaaaabbaaabaaabbbbaaaababaaaabbbbbbabbbbaaabbaabaaaaaabbbabaaabaaaaabbbabaaaaaabbbbbaababbbbbaababbaabbaaaaaabbabbbabaaaabbbbbaabbaaaabaaabbbaaababaabaabbabbaabbbbabaaaabaaaabbaaabaaaaabaaabaabbbbaabbababaabbabaabaaabbababaabaaaaabababaabbbabaaaababbabbaaaaaaaabaaaaabbabaabbbbabbbbbaabbaabbbbbbbabbbbabbbbababbbbaaaabbbabbaababbaaababbababbbaabababbbbaaabbbbbababbaabaaabbabbaaaaaaaaaabbabababbbababaabbbbaaabbababbaaabbbabbaaaabbbbaaaabaababbaaaaaaaaaababbbaaaabbbababbbabbbbbbbaaaabaaaabbabbbbaabaaabbaabbabaaaabaabaababbbabaabababbbbbbbbbaabbbabaaabbbabbbabbaaabbbbbabaaaabaabbbbbbaaaabbaaaabbaaaabaababababaabbaaabbaababaaaabaabbabbabaaabbbbabaaaabbabaababbaabbabaaabaaabbabbbabbaabbbbaabbabababaaaaaabbaaabbbabbbabbbbbbabaababbbabaabbbbbbbbabbaaaabaaaaaabbbaabaaabbabaaabbbbbbbbbababaaabaabbbabaaabaaababbbabbaaabaaaaaabaabbabbbbbbbbabbbaabbbbbbaaababababababbabbbabbbaaabbbbbabbbabbaababbaaabbbbabbbaabababbabaaaabaaaababbaaabababbbabbaabbbbaabbbbabbaabbababbaaaabbabbabbbaabababbbbaaaabaabbabbbbbbabbaabaabbbaabbbababbabaaaabaababaabaababaaabbbbbbababbabaaabaabaaabbbaabbbaabaabaaababaaabbbbaababbaababbbbbbabbaaabababaaabbabaabbbbbaababbbbaabbabbabbaabaaaaaababaabaababbababaababbbbbabbabaabaababbbbabbaabbabbabbabbbabaaababbababbbabbbaabbaaabbababbaaababbaaaabaabbbbabbbababbabaaababbaabbbbbbbabaabbbaabaabbbbabaabaaabbaaaaabbaabababaaaaaaaaababaabaaabbbaaabbbbabbbbbbaaabbaabbbbbabaababbbabaaabbbabbbbabaabbbababbbbbabaaabaaabbabbabbbbbaabbbbaaabbaabaababaabbaabaabbbabbbabaabaaabaaabaaaaabaabaaaaabbbbbaabbbaabaaaabaabaaababbbbaaabbabbbabababbababbabbaaaaaaaabaaaaabbabaababbbbbababbbbabbbbbaababbabbaaaabbbabbabbaaaaaabababaababbbaaaabbabaabababbaababababbbaabbabababbababababbabbbabaaabbaaabbbaabbaaabababbbabbbaabbabababbaaabaabaabbaabbbbabbbbabaaaabbbbbbbaabbbaabababaabbaabbaaabbaaaaabbbbbaaaaabababbabbaaaaababbaabbbbbbaaaabababbaabbabaaabaaaabaabaabbbabbbbaabaaaaaaaaaaaabbbabbbbaaabbaaaaabaaabbaabbabaabbbbabbabbaaababbbaaaaabbabaababababaababaabbbaababaabbbabaababaaaabbaaabbbabaabaabbaaabaaababbaabaaaabbaaaaabababaabbbaaaaaaabbbbbbbbbabbabbaababaaabbbaababaaaabababababbaaabaaabaababaabbabbabaaaababaaabaabbbbababbabaabbbaabbbbabbabababbbaaaaaaaaababaaabbaabababbaababbaabbaabaaaaaaababbbbbbabbbababababbbbabbaabbbbabbbaababaababbbbbbaababbbabaaabbbbabbbabbabbbaaaabbaababaabaabbbbaaaaabababaababaababbbabbabbbbbaaababaaaaaababbababaababbbbbbaaaababbabbaabbbbbbbbbbabbbbababaabaabaababbbaabbababbbaabaabbbaabbbbbabbbbaaabaababbaaaaabaaabaaaaabbabaaabaabbbbabababbbababaabbbabbbaaaaababbbaaabbbbabababbbababbbaaaaabbbbbbabaaaababaaaaabbbaabbbabaabbbbbaabbaaaabaabbbaaaaabbaababbababbbbbabbbabababababbabaaababbbbbbaabbbaaaabbabababaabbababbaaabaabbaabbbbbbbaaabababaabaababbaaabaabababababaabaabaababbbabbabbbbaababbaabababaabbbaaaabaababbabaabaabbbbaabaaaabaaaabbbbbbabbabbaaababbababbbabbaabaaabbabbbaaaaababbabaabaabaabbbabbabbabbbaaaaabbbbabababbaaaabbababbbbbaaaaabbaababaabbaaaababbbabbbbbabbbabbaabababbbbabbbbaaabbbbaabbbaababbbbbabbababababbaabbbbabbaaababbbbbabbaabaabbabaabbbbbbaabbaaabbaabbbaaabbbabaabbbabaaababbabaabaabbabbaaaabbbaabbaaaabbaabbbbaabababbbaababaaabbabbabababbbabbbaabaaaabaabbbabbbbbabbaabbbbbaabbaaabbbbaabaaaabbbbabaabbabaabaaababbbbbababbabaabbabbbaaaaaaaaabaaaaaabbaaaababbaabaaaaaabbaaabaabbbaabbaabaabbbbbbbaaababbaaababbababbbaaababaaaabbaaaabababaabbabbbbababbaaababaabbabbbabaaabbaabaabbbaababaabbbabbbbaaababbaaaabbabbaaababbbbabbbababbbbabaaaaabbbababbabbbbbbbaaaababbabbabbbaababbbbbbaaaaaaaabbababbbabababbbabbbabaaabaabbabbbabbbaaabbbbabbbbaaabbabbbabababbaababaabaabbababbaaabbabbaabaabaababbbaaabbabbbbaabbbaaaaababbaaaabaaababbbbaaaaaaaaababbbbbaabaaabbabaaaabbbaabbabbabbbbbbbabbbbabbaabaaaaabbbabbaaaaaabaabbbaaaabbbbabbbbbaaabbaabbbaababaaaaabbabaaaaaaabaaabaaaabababbabbbabbabaabbbbbaababbbaabbaabbbabaabaaabbaaaaaaaaabbbababbbaaabbaabbbaaabbbabaabbbaabbbabbbbaaaababaaabbbabbaabbbaabbabbaabaabaabbaabbaaabbbaaaabbbbbbbabbababbbabaaaaababbababaabababababbaaaabbbaaaababbabbabbbaaaababbbbaabbabbbaaaabbbaaabbaabbbaaaaaabaaabbabaabbbbbaaaaabbbaaabbabaabbabaaaabbbababababababaaabbbaabaaaaabbaaaababaaabbaababbbbabaabaaababbbaabaaabbbbababbabaabaaaabbbaabbbbaabbbbbbabaabaabbbaaabaabbabbabbbbbbbaabababaaabbbbabbabbbbaababbbabaabaabbaaabbababbaababaabaaaaaaababbabaabbaaaabaaabbabaaaabaabbbabbabbbbbbbbbbabbbaabbabbababbabbbabbabbaaababbbbaabaababbabbbabaabbbbaabbbbabababbababaaaaabaabbabbbabaaabbaaabaaabaabaaaabbabaaabaabaaaaaabbabaabbaabbbaaaaaabbbbbabbbaaabbaaababaaabbbabbabbbbababbabbbaaaabbababababbabbbabaaaaabbabababbabaaaabbbabbaaaabbbaaaabbabaaaaaababbbaababbbbabbbabbabaaabbaaabbaabaaaaababaaabaaabbbaabaaaabaababababaabbaaabbababaabaababbabbbabbbaabbbabbbababbbbbabaaabbbbbbbbbbbabbbbbbabbaababaaababbabaaabbabaabaaabaabbaabbbaabaabaaababaaabababbbbaabbbaaabaaababaaabbbaaabababbabbaabaabaaabbabbababbbabbbbabbbbbababaabbbabbabaaaaabaaabbabbbbbbbbbbabaaabbbaabbababbbaaaabaaabbabaababbaaaabbaabbbabaaabaabbbababbabbbaababaabaaabbbaaabbbabaaaabaaaaabababaabaabbaabbbababababaaabaabaabbabbbaaaaaabbaaabbbaabbbaaabbbbbbaabbabbabaabbbabbbbbababbaaababbaabbbaaaaabaaaabababbaabbbbbbbaaabbaaabbbbbbbababababaabbaaababbaabbbaaabbbabaaabbbabbabaaaabaababaaaaaaaabbabaaabbbbabbbbbbbabaabaaabbbabaaabbbabbbabaabaaaaababaaaabaabaaabbbabbababbabbbbbbababaaabbbbaaaaabbaaaababbababaabbaababbbbaaababbbabbababbaaaaababbabababbbabbaabaabbbbbabbbbbababaaaabaabaaaaabbbbbbbaaababaaabaababbbaabbabbabbabaabaaababaaabbbbbaaaabbaabbbaabbbbbbbbabbbbbbababbabbbaabbaababbabbabaabbbabbabaabbabaaabbbbbbbaaaabaabaaaaaaabababbbbaaaaaaaabbbaababaababbbaabaaabbaaababbabbbbbaabbbabaaaaaabaabbaaabbbababaaabbbbbbabaabaaabbabbababaaabbbbaaabbabbabbabaabaababbaabbbbaaabbaabbabaaaabbababaaabbaabababbabbabbbbaaabbbabbabaaababaaaabbaabababbababbbbababbaababbabababbbabbbaaaababbbaabaabbaaaaababbabbaaaabbbbbaabbbbabbabbaabaaabbaababababaabbaabaaaaabaaaabbbbbbbabbaaabaaaaaabaabbbabababbaabbabaaabbbbbbaabaaaabaabbbbabbaaaaaaababaabaaabbaabbabaaaaaabbbaabbabbabaaababbbaaaaabaaaabbaaababbbbaabbbbbabbbabbbbabaaababaaabbaabababbaabaaabababaabbababbbabbaaababbbbaabbabaaaaaabbbbababbaababbabaabbbaaaaaabbbbabbbbbbaaabbbbbaaaaaababbabaabbbbaababababababbabbbbaabbbaaabaabaaabbaabbaaaaababbababaaaaaabbaaabbaaaaaaaaabbabaaabbbbaababbabababbabbbbbabbbaabbabbbababaabbbaaaaabbbbababbbbaabaaaabaabbbbbbaaabaabaaababaabbbabbbbbabbbbbbaabbaabaaabbababaabbabababbababaaabbabbabaabbabbbbbaabbbbbbbaaaabaabaaaaaaaaaabbaaaabbabbbabaababbbabbaabbabbabababaabbbbbabbbababbbbbbabbbbbbbaabbabbbaabbabbbbbaaababaaaabababbbababababbbaabababbabbaabbbbaabbaaababaaabbaaaaabaabbbaaaababaaabbbabbabaabaaabbbabbabbabbabababababaaaabbaaaaaaabbbaababaabbabbaababbbaaaabbbbbbaabbbbabaabbbabaaaaaaabbaabbbbbabbabaaababaababbbaaabbabbabbabbbaabbbbbaabbbbaaabaaabbbbbababaaabbbbabbbaabbbbaaaabaaabaabbbbbabaaabbbaaabbababaaaaaabaaaaaabaabbabbbaaaababaababbbbbabababbaabbbabbbbbbbbbbabaaabbbbbaabbbbabbaabbababaabaaaababbaabaabbaaababbaaababbabbbbabbbbbababbabaaabbababaaabbbaaabbbababbbabbabbbbaabbbbaaabbbbbabbbababbababaabbabbaaabbaaaaababaaabbbaabbaaaaabababbbbbbababbbbababbbaaaabbbaaaabaababbababaabbababbaaaaaaaaabbaabbabaaabaabbababaabaabbbbbababbbabbabbaabaabbbbbabbbaabbaababbbaabbbababbbaabbbababaaaababbbbbbbabaabbbabbbbbabaabbaababababbabaaabababbaaabbaabaaaaaaabbaababbbbbaaababbabbababbbaaabaabaaabbaabaaabaabaababbbbbaaaabaabbababbbbabbbbbbbbaaabbabaaaabaaaaaaabaaaaabaabbbaaababbbbaaabbbabaaabaaabbaaabbaaababbabbabaaabbbaaabaabbbbbaaabaabbaababaababababababbbabbbbaaabbaaabbbbaaabaabaabbababbbbaababbaaabbaabbbaaabbaababbababbbabbbbbaabbbaabbabbaabbabaaaabaabaaaabaababbbbababbbabbbbbaaababbababbbbaabbaabaaabbbabbbbbbaabbbabaaabbbbbaabbbbbababaabaababbbaaabaababababbaaaaabbaaabaabaabaaaaabbbbbabaaabaaaabaabbbbaaaaaaaaabaababaabaabaabbbbbababbbbbbaabbbbabbbaababaaababbbaaaabababbbaaaaabaabbbbbbbbabbbaabbabbaabaaaabababaaaabbabaabababbbaabbbabbaaaababababbbbaababaabbaaabababbbaabaaabbabbabbaababaabaaaaaaaaaaaaabaabbbbbaaabbabaaaabbbaaaabaaabaaaabbaaababbbaabbbaaaaaaaabbbabbababaaabbbaabbababaabababaababaababababbababaaaabaaaaabbbbbbaabbbbbbbbababbaabaaabbaaababbabaaaabbaaabbabaabbabbabbabbaabbabbbabbababbabaaaaaabbababbbababbaababbbbbaaababaabbbaabbabbaababbabbbbbaabbbabababaabababbabbabbbaabbaaaabbabaaabbaababaabbababbababbbababbbababbbaabbabaaaabaabbaabbabbaabaabbaaabbaabbabbbabaaababbaabaabaaabbbaabbbabbbaaabbabbbabbbbababbaaabbababababbaaabbbbbabbbbbbbbbbaaaaabaabaabbbbbbabbababbbbaabbbaabbaabaaaaaabaabbababbbbabbaabbbabbaabbaaabbaabbababbabbbaaaaaabbbaabaaabbbababababbbabbbabbabaaabbbbabaabbbbbbbbababbaabbbbbbbbbbbbaababaaabaabbbbaaaabbbbbabbbbabbabaaabaaaaabbbaaaabbbbbaabaaaaababaaaaaababbabbbbaabbbbbaaabbabababaabbabbaaaabaaabbababbaabbaaaaabbbababababababbabbabbaaabbbabbaababbaabaababaababbaaaabaaabaaaabbbbbbbbbbababbaaababbabaaaabbaababaaaabaaaaaabbabaaabbbbabaaaaabaababbbaabababaaaaaaabbbbabbbaabbbabaabbabbbaaabaabaaabaaabaabaaabaaaaaaabbbbbbaabbaaaabbbbbaabbbbaabbaabbabaabbbbaabaaaabbbabaaaababbaaaaabbbaaabbabbbaabbbbbabaabaaaabbaaaabababbbbaaabaabbabaababbaaabbababbbaabaabaaabababbbbaabaaaaaabbabbaabbabbabbbaabbaababbbaababaaabaaabbbbbaabaabaaaaabbbbbbaabbaaaabaababbabbaabbabbbababaaaabaabaababbbaaabaaabaabbaaabbbaaaabbbabbabbaababbbabbaaabaabbbbbbabbabaaaaaaabaaabbabbbbbbbaababaaaaabbaabbabaaabbaaaababbbabbaaaabbbaababababbabaaababbbabbababaabbaaababaaabababaabbabbabababbbaabbbaaaabbababaababbaaaaabaabbbabbaabababaaaabaaabbababbababbaabbabaaaababaabbabababababbbaaabbbbbbabbbbbbbaaaaababaaabaaababbabbbbaaaaababbababbbbbbabbbaaaabbaabbbaaaaaabaaaabbbaaaaabbabbbbababbabbabbabbabbaabbbaababbababbaaababaaababbaaaaaabaaaaaaaababbaababbabbabbabbbaaababababbbabbbaaaababbabbabaabbbbaaabaaaabababaaabababaabaaabbbbbabbabbbbaabaabbbaabbbbaabaaaabababaaabbaaababbbaabbbabbbabbbaaabbbbbbaaaabbabbbaaaaabbbabababbabbbbbbabbbaaabbbabaaaaabbbbbbbbbbbabbaababbabbabbaaabbabbaabbaabbbbbbbbaaaabaabbbbaabbbbbabbabbabbaaababbabaabbbbbbaabaababbbbababbaaaaabaaabbabaabbababbbbbabaabaaabbbbbbabbbaaaaabbabbbabbaaabaaabaaababbabbbaabaabbbbbababaaabaabbbbaabbbbababaaaabbbbbaabbabbbbbababaaaabaabbabbbaaaabababaababbbbbaaaaaaaababbbbbaababbbaabbbbbababbababbabbbbaabbbaaaaaabbaaabaabbabbaaabbabbaabbbbbabaabbbababaaabbaaaababbbbbbabbabbbaaabbbbbbbbbbbabbbabbabbabbaababaababaabbaabbaababaaabbbbabbabbaabaabaabaabbabaaaaabaabbaabaaaaaaaababbbbaabbabbaabaabbbbabaaaabbbababaabaababaaaabaaabababaabbaabbaabababbaaaabaabbbbbabbaaaabaaabbbabaaaaabaaabbbbbbbabbbbaabbabbabbbbabbaaaabbbbababaabaabbaaabbabbbbabbbabaaabbabaaaababbaabbbbbbabaaaababaabababbabbaabbaaabbbbbaaaabbbbbbbaabbaabbaababbabbbbbaaaaaaaabbbaabaaaaabbabaabaaabbaaabaababbbabbbbaabbababbaabaaabaababbabaabbbaababbbabaaaaabbbababaabbbabaaaabaaabaabaaaabaaabbbbabaabaaababaabbabbbaaaaabbabbbabbaababbbbbababbbaabbaaababaabaabbabbabbbaaabbbaabaaaaaabbabaababaaaabbbbaabbabbbabaabaaabaabababaaaabaabbaaabbbbabaaaaaabbbabbabaabbbabaabaabbbbbbabaabbbbbabbbabaaabbbabbabaaabaabbbaabaaababaabbbababbbaaaababbaabbababbbaabaaaabbabbaaaabaabaabaabaabbbbaabaaabbbabbbbbaababaaaabbaabbbaabbaaaabababababbaaabbaaaaabbabbbabbabaaaabbbbababaaaaababaaaabbbaaaababbbababaaababbaababaababababbbbbaabaabbaababbababaabaaabbaabbbbaabbabbbbaabaabaaaabbbaaabbbababbabaababbabaaaaabaabbabababbaababbaaababbaaabbababaaabbababaabaabbbbabbbaaabaaabbaaababbaabaabbaaabbaaabbbbbbbaaaabbbabbbbabbbabaaabaaababbaaabbbbbbabbaaaabaabbbaabaabaabbaabababbbbabbbbbbaabbaabbabaababaaaabaaabbbbababbaaabaaaaaabaababaabbbaaababbaabaaaaaabbbbabaabbbaabbbabaabaaaababbaabbbbaaaabaaababbbabaaaaaaaabaaabaabaabbabbaaaaabbababbbbaabaababbabaabaaabbbabbababaabbaaaaaaaabaaababbbaaaabbbbbaabbbbbbbabbbbabbaaababbbbababbabababbabbaaaaabaaaaaabbababbabbbabaabaaaaababbabaabbaaaababaaaabbababbbabbbbbaababaaaabbbabaaabbbbaaaaabaaabbbbbbaaababbbaaabbbabbabbaabaaabaababbbaaaaabaabbaababbbabbbbabbbbbbaaaabbaabaabaaaababbabaabbbbabbbabbaabbbbaabababbbbaabbbaaabaaabaaaaaabbbbbbbbbabbbbbabbabaaaaabbaaabbaababbaaabaaabaabbbabbbababbaaaabababbbbaabbbabbbbbbabbbbbbbaababaaabaaaabbababbabbbabaabbbbbbaaabbbbbabbaaaabbabbaabaaaabbabaabaaaaaaabbbabaaabbbaabbbaabbbbbbbbabaaabababbbbbabaaabbbbaaabaababababaabababbaaaabbbabbbbbbbaaabbbabbabbabaabbbbababbabbbaabaaaabaabaaabbbaabaaaabbaabbbbbabbaaaabbbabaaabbaaaaaabaabababbaaaabaabbbabababbabaababbbbabbababaabbaabaaaaaabbabababababaaaabaabbbbbaabaabbbbbbbbbabaaabbababaaababbaabbbaaabaaabbabaaabbbbabbaabbaabaaaaaabbbbabaabbbabaaabaabbbbbaaabbabaabbabbbbaabaaaaabbbaabaaaabaabbabbabababaabbbaabaabababaaabbbbabbaabbbbbaabababbbbabaaaaababaaabbbaaabbbababbaabbaaabbbaabbbaabbabbabbaabbbbbbaabaabbaabbaaababbabbbababababbabaababbbaaabbbbbbababaabbbbaaaaaaababbbabaababaaababbbaaaaaabbaabbbbaabbababaabbbaabbbbbbbbabaaabbababbbbbaabaabbabbbbbaaabbbbbbabbaabbbaabaaabbababbaaabaaabbbbababbabaaabbbbbaaababbbaaababaaabbbabaabbababaaaaaabbbbaaaaaabbbbaaababbbbabaaaaabbaabaaaababbabaabaabbaabaabbbabaaaaababbbbaabbababbbbaabaabaaabaabaabaabbbaabbbbbaaaabaabbbabaabbaabbabbbaabaaabaababababaabbabaaaaaabbbbbbbaabbbbbabaaaabbabbaabababbabbaaaaabbbabbbabaabaabbabbbaababababbaaaaaaabbaabbabbbbbaababaabbababaaabbbaababaabbbabbbbaabbabbaababbbbaabbabaababbbaabbbbbbbabbaaaabbabbaaaaabbbbbababaaaabbabbbabbbababbaaababababbbbaabbbaabbaabbbabaaaaabababbabbabbabababbbbabbababbaaaabaaababaaabbbaabbbbabaaabbabaaaabbaaabababbabbbababbaabbbbabbbabbbbaaaaabbaaabababababaababbbbbbbbaabaabbabaaaaabaabbbaabaababaaaaaabaababbbbababaaaaaaababbbabbabbabaabababaabaaabbbbaaabababaababababaababaaaaaaaaabbabbbbaaabbbaabaaaabbbbbabaabaaaaaaabababbbaabbbbbaababababbabaaaabbbaaabbbbaaaababaaabbbbaaabababaabababbabaaabaabaaabbbbbabbaaabbaaabbaaababbaaabbabbaaababaabaaaababaaaabababbbabbbbbbbbbabbaabbbaabbbabbaaabbbabaababbbabbaabbbabbabbabaabbbababbababbabbaababbaabbabbbbbbbaabbaabbaaaabbbabbaabbbababaabbbaabbababababaabaaabaababaabbbaaabaaaabaabbaaabaabbabaaaaabaaaababbbbabbaaabbabbabaaabbaaaabaaabaaabaaabbbbbbabbaaababbaabababbbaaaaaabaabbbabbaaabbaabbaaaababbababbaabbbaaaababbbabababaaabbabbbbaabaaabbbbababaabbbbaaabababbabbbaabaabaababaabbbabaababaabbabbaaabbababbbbaabaabbbaabaaabaaabbaababbbaabbabbaaaabbaabbaaaabbaaababbbaaababbbbaaabbaaaabaabbbbaabbaaabbbbaaaaababaabaaaababbabbbbaabaaababaababbaabaaabbabbabbaabababbabbabaabbaabbbaabaaaaabaaabaaaababaababaaabaabbbaababbaabbabbbaababaabbaabbaabaaaababaaabaaaaabbabaabbabababbbaaaabbbbbbbababbabbbababaaabbbbbaabaabaaabbbbbabbbbaababaabbabbaabbaaaaaaaabbbaabbbbbbabbbbaaabbbabbbbbaabbabbabaaaaaaabbaaababbababababbbabbabaabbbabbbaaababbbaabbabbabababababaaaabaaaabbaaabbababbbabaaaaaabbbaaabbaaaaababaabbbbaaabbaabaaaabaaaabbaabaaaaaaaaabbaabbbabbaabbbabbbaababbabbabbaabbbbbaabaabbbabbbbbababaaababbabbbbbaabbabaabbabaabbbababaabaabbaaaabbbaaabbaaabaaaaaaaabbbaababbababbabbabbbaaaaabababbabbbbbbabbbbbbbbababaabaaaaaabbbababbbaaaabbbbbbaaabbbaababbbbbbaaaaaabbaaaabbbabaabababaaabbabbaabaaabaabbaaabbaabbbabaabbbabbabaaabbbbbabbababbabbbbaabaabbaabbaaabbabbbbbbbaaabbabbabaaaaaaabbbbbabbabababbbbaaabbbbabbbbaabbabbbaaababbbaababbabbabaabbbabbaaabbbabbabaabaabaaabbababbabababaaaabbababaaaababbaaaabbbaaaababbbbbbabbabbbabbbaaaaaababbbaababbbbbaabababbbbabbbabbbabaaaabbbbababababaababbbabaababbbbbbabbbbbaaabaabaaababbbbaababbbaaabbbbabbbabbbaaaabbaaaaabbaabbaabaaabaabbbbabbabbbaaabaaababbaabaaaababbbbbbbababaaabbaababbbbabbbbbbbaabababbaabbababaababbbabaabbabbabaaaabaababbbbbaabaaabbbabaababaabbabababbabbabbbaabbaaabbbababbbbbaabaabbababaabaabaaabbaabbabbbbabaaabbababbbbbabbababbbaabaabbbbabbbbaabaabaababaabaaaaababbbaaaaabaabbaaaaaabbababaabababbabbbaaaaabbbbbabaabbaaabbbabaababbabbabbaabaababbaabaaabbaaaabaabbbbabbaaaabaaaaaababbaabaabbbaaaaaabaabbababbabababbbababbbabbaababbbbababababababbbaaaabbababbbaabaabaaabbbabbbaabbbabaabaabaaababbbbabbbaaaaabbaabbbabbabaabbaaaabaabbbaabbbbaabaabbaaababbababaabbbbbababaabbabaabbbabaabbabababaabaabbbbaababbbaababaabbaaabbbabbaabaaaaabbbaabbbabababababaabbabaaabbabbbababbbabbbbabbbbbbbbbaabbabaabbaabbbababbaabbaaabaabbbaaaaabbabbbaaaabbbabbabbbbabbbababbababaabaabaabbbaabbaababbbabbbbbbabaaababaabbbbbbbbbbbbbabbaabbabbabbbabaaaabbbbbabbabbaaaabbbaaaaaabaabaaabaaabbabbbaaaaaaaabaabbbabaabbbaaabbbbaaaaabaabbbababbaaababbabaabbababaababbbaabaabaaabbababaaababaabaaaabbbaaabaaabbabbabbaaaababaabbaabaabaaabaabbabbaabbaaabbbabbabaaabaaaabbbababbaabbbbaabbababaababbaabbbabbbbabbbbbaababbbaaabbabbbbbbbbbbbbababaabbbaabbabbbabbbaababaaaabaaabababbbbbbababbaaaabbbabbababbbabbababaabaabaaaabbbabbbbabababbabaaaaabaaaaabbaabbabaabbabbbabbababaaabbaabaabbabbababbabbbbaaaabbbbbbbbbababbaabaabbbbaaaabababaaabbabbaaaabbbbbbabbbabaaabbbaababaabaabaaabbabbbababbbabbabbbbaaabbbbbbabbaaaaaaaaaaaaaabbbbbaaabaaaaaaaaaabbbbbaabbbbbabaabbbbaaaaaaaababbbababbabbbabbbbbabbabababbbbabababbaabbaaabbabbbbabaaabaaaaaabaaaababaaabaabaaabbaabbabbaaabbaaaababbbbbababbbabbbabbbbbbbabbbabaababbabbaabaaaaaaaaaababaaaababbbababaaabaaaabbbabbbabbbbaabbbbbaaaabbbaaaaaaaabbbaabbabaaababbabababbaaababbbaabaabbbabbbbaababaaabbbbabaabbbaabbababaaababaaaaaabbaaabaababbbbabaabbbbbabbaaaabbaabbbaaabaaabbbbabababbbbbaaabbabbababaababbabbabbaabbaaaabababaaabaabaabbbbaaabbabaaaababbbbaababbbabbaaabbbabbababababbaabaabbbbbaaabbbababbabaabbbaabaaabaaaababbbabaababbababbbbaababbabbbabbbaaabaaabbabbaabbabbaaabbbbabaabbaaabaaaaaabbbbbbbbaaaaaabaaaaabbbbaaaabbabbaaabaababbabaaaababbbaaabababbabaaaababbbbbaaababbbbaaaaabbaaabbaabbbbbbbbbbababbabaaaabbbbabbbbbabbaabbabbbbaabbbbaaabaababbaaabbbabaaaaaababbbaaabbbbabaabbabaabaabbabbbbaabaabbabbbabbababaaabbbaaabbbbaaaaababaabbbaabbbbbbbaabbbaaaaabaaaabbaababaabaabbbbbababbbaaaabababbbaaabbbbabbaabbbbaababaabbbbbbbbababbbaaaaaaaaabababbbbabaabaababaababbabbbbbababababaabaaaaabaabbbbabbababbbabbbbbbbabbabbabbbbbaaabbabbbabbbbbabaaabbabbbbaabaabbbbaaabbaaaaabababaaabbaabbabababbabbabbabbabbbabaabbbabbbbabaabababaaaaabaabababaaaaaaabaabbbaababbaaaabababbababbaaabbabbabbaaaabbaaaaababbbabbbaabbbababbaababbbbbbabbbbbabababbaaabaababaaabaaaaaaaaaaaabaabbbbbbabbbaaababaabbbabaabbabbabbabbabaababbaabaaabbbbaabbbaaabbababbbbbaaaaaaaaaabaabbaaabbaaaaababaaabbaabababbaabaabbbbababbbbaaabbaabaabbbbbbabbabbbabababababbbbaabbbbbbbababbbbabaaaabbabbabbbaaabaabaaaabbbbbababaaaabaabaaaababababbabbaababbbbbaabbabbaaabbaababaaababbbbbababbbbababbaaaaabababbbababaaababaababbaabaabbbbbaaabbabbbaaabbbabbabaaaaabaabbbbabbaababbabababbabbbabbbabbbbbaababbbabaababaaaabbaabaabbbabbbabbabbaaaaaabaaaaaaaaaabaabaaabbaaaabbaabbbbbabababbbbbaabbbaabbbbbabbbabaababaaaabbbaabaaabbababbaababbbaaaaaababbaaabababaaabbaaaabbabbaaabaabbabbaabaabbbaabaaaaababbbbbababbbaaabbbababbabaabababbbbabbbabbabbabaaabbbbabbbbbaabababbaabababbabbaabbabbbaaababaabaaabaabbaaabaabaabaabbaaaabaabaabbabaabbaaabaabbbbbbbabaababbaaabaabaaabbabbbabbbbaaabaaaaabaaabbbabbbaabbaabbbbbaaabbaaaaaabbbabbabaabaabbbababbaaabbababbbbbabbbabababbaaabaabbabbbbabbaaaababbbaabaaaababbaaababbbaabbbabbabaababaaabbbababaababaaabbaaaabaaabaaabaaaabbbaaaabaababbbaababbbbbabaaaaaaaabaaaababaabbbabbbabbbaaaabbbaaabbbbaabaaaabaabaaaaababbbabbabaabbbabaabbabbbabaaabbbbbaabababababbabbaababaaabaabbaababaaabbabaabbbbbbabaabaabbabbaaaabbbabbaaaaaabaabbbbaaabbababbbbaaabaabababaaaaababaabaaaaaaabbbbaabaababaaaabaaaabbbabbbbabababaaaabbbabbabbbbbbabaaaabaabbaabbbbbbaaaaabbbbbabbababaabbbbabbabbbbbabbbbbbbababaabaaaabbbabbbaaaabbbbaaabbaabaabbbbabaaababaabaaaabbbbbbabaabbbbbbbaaabbbababbbaaaaabbbbbbaaaaabaabbabbababbaaabbbabbabbbabaaabaaababbbbbaabbabbbbbbaabbaaabbbbbbaaaaabbbababaaaabbbabaabaaabbaabaabbbbaababbaabbaabaababaabbaabaabbabbabbbbbaabbbabaabbbabaababbbbbbbbbbbbabbabaaababbbbbbbaaaabbabbabaababbababaabbaaabaaabababbbbaababaaaaaaabbabbbbbababbbbaabaabbabaabbabbbbabbabaabbbbabbbaababaaabbbbbabaaabbaaaaaaabbbbbaabaabbbbaaaababbbaaabbbbbbbabbabaabbabbababbabababababaababbaaaabbaaaabbbbaaabaabbbbaababbbaabababbaabbbaabbaaaaabbbababababababbbbababaababaaaabbbaabbaababaaaabbbaababbbaabbbabaaaabbbaaabbaaaaaabaabbaababaabaabbababaaabbaaabbbbbbbabbaabbaabbbaabbbaaaaaaaaaababaabbabbbbbbaaababaababbbaabbbaabbbbbbbaaabaaaabaaabbaabaaabaaaaaabbabaaabbabbababbbbaababaabbbabbbabababbaabaaabbbbbabababaabbbababbbbbabbaabbbaaaabbaabaaabaaabababaaabaabaaaaababaaaaaababbaaaaaaabaaaabbabbaaaaaaaaabbbbbbabaaaabbaaaaabbaabbbaaaabaabaaabbbbababaabbbbaabababaaaaaabbabbbabaaabaaaaabbabababaaaabbababbaaabbbabbaaabbbabaababbbabaaaaabbbabbbbabaabaabaaaabbaababbbbbbaabbabbbbbbbbbbaaaaaaaaabbbaaaaaaaaabababbaabaabbaabababaababaaaaabaabababaabbabbbabbaaabbbaabbabaabbababbbbbbabaaaababaaabbbbabbbbbababaaaaaabbbbbabaaaababbbbbabbaaaaaaabbbbaaaababbaababababababbbabaaaaabbaabbaababbbaabaaaababbbbaabbbabababbbababbabbabbbaababbaaababbbbbaaabbbaaababbabbaabbaabbbbbbbbaababbabbaabbabaabbaaaaababbaaabbbaabbaababbabbaaaababbbbbaabaabbbaababaabbbabaaabbbbbbbbbaaabaabbbbbabbbbaabbabbbbbbaaaababaaabaabbabababaabbbabbbabaaabbabbbbbababbbaabbbaabbaababbabaaabaabbbbbbbabaabbbbababbbaaaabbbabbbbaababbbaaabbabababbbbbbbaaaaabbaabaaaabbaaaaabaababbbaaabbbbbbbabbabbabbabbbaababaabbbabbbabbaabbbbaaababbaabbabaabababbbaababaabaaababbbbaababbbbbaabbbaaaabbbbabbbaabbaabbbbababaababbbbabaaaabbbbaaabbaaabaaabaababbaabbaababaababbbbaaaaababbbbbbaaabbbbbaaaabbbbaabbbabababaaaabbbbabaabbbbabaabbbabababaabbbbaaababbaababaaaaaaabbbbabbbbabbbaabbaaaaabbbbbaabbababbbbbbaabbabababbbabbabbabbbbbaaaaaabbaaababaabbbbabababbbabbabbababbaaaaababaaabbaaabbbaaaaaaabaabbababaabbbaaabbbabaaaaabbaaabbbbbbbbbabbababbbaaabaaabbbaabbbbbbbabaababbbbababaaabbbbaabaababaabbbbabababaaabbaabbabbaabababbbbbbbaaabbabbbbbbbbabbababbabbbabaabaaaabbababaabbabbbaabbabaaabbbbaabaaabbaabbabbbabbbbabbbbabbbababbbabaabbabaabaabbaaabbbbbaaabbbbbbbbbbaabbaababbbababbbabbababbaaabaaabbaaaaaabaabaaabbaaabbabbabaaabbababbaabababaabaaaaaababaaaababaabbaaaabaaaaabbaaaaababaaaabaaaabbbbbbbbabbbaaaaabababaabbbabaabababaabbabaabbaaaaaaaabbaaabbaaaabbbbabaaabaaaaaabaabbabbbbbabaababaabbabbababbabbaababaaaabbaabababbbaaababbbababbbbabaabbbbabbbaabaabaaabaaaaabbaabbabbbabaabaabaaaabbbbbaaabaabbaaabbabbbbaabbaaabaaaaabbaaaaaabaaaababbabaaaaaaaabbbbabaabaaaabbbbaabaaabbaabaaabaaaabaabaaabbbabaaaabaabbbbaabbabbabbaaababbabbbbbbabbbabaababbbbbbabbaaaababbabbabaaaababbabaabaabbabbbaabbaaaaaaaaabbaababaaaabaabaaaabaabaaabaababbaababbabbbaaabbbbaabbaaababbbbabaabbabababbabbbabbaababaaababbbaabbbbaaaabbaaaababaababbbbaaabbabbaaabaabaabbabababbaabbbaaababbaaababaabaaabbbbaaabbabaaabaabaabaaaaabbabbabaabbabbbbbbbbababbabaaabaaabaaaabbabbbaababbabababbabbbbbaabbaabbbbbbaaabbbbbbbaaaabaabbbabbaaababaabbbaaaaaabaababbabbbabbaababbbbbabbaaabbbbabababbabbbbabbbbbbbababaaaaabbbbabbaabbabaaabaaabbaaabbbaabababaaabaaaabbaaaabbbbbaaaaaabaabbbaaaabbbabbaabaabaabbaaaaabaabbbaabbbbabbbabbbbbababbbabaababbbbabbabbbabaabaaabaababaabbababbaabababaaaaabbabaabaaabaabaaabaabaababababaabaabbbbaaabbaaababaaaaaabbbbbbabaaaaabbaaabbbaababbaaabaaaabababbababababbaabbbbbbaabaaabbbbbbbbbbbbababbbababbaabbababbaaaaaabbaabaabbaabbabbbbbaaaaabbbaabbaaaababbbbbabbbabbbaabbaabbaaabaaabbbabaaabbbaaabababaabbaaaaaaabbbaabbbbabbbbbaabbabbbbbabbbbabaabbabbbaababaabbbabbbbbabaabbabaabbbaabbabbaaabbaabababbabaababbbababaaaabbbbaabbaabbaaabbbaaaaabbbaaaabaaaabbabaaabbbbaabaabbabababaababbaabaaaabaaaaaababbaabbbaabbbbabbabbababbbbbbbabbabbabbbbaaabbaaabaabaaabaabaaaaaabbbbbbbbbbbbbaaaaabbaabbbaabaababbaabbaaabaaabbbbabbaababbabaaabababaaaababbaaaaabbababbabaabbabbbabbababbbaababaaabbaaabaaaaaababbbaaabbbbbabaaaaabaaababbaaaabbbbabbbbbaaabbaaaaababaababbbbaabaaaaaabbaaabaaaabbbbbbabbaabbabaabbaaababbbbbabaaaaaaabbaabbbbaaababbbabbbbabbbaaababaaabbabbbbbbbaabbbaaabbbbaaabbbbabbbababbbbabbaaabbaaaaaababbaaaabbabababababbababbabbabaaabbabbbabbbbbbbaabaaabaabababbaaaabbbbaaaabbbabbaaaabbaabbaabaaabbbbaaabbaaaabaaaabbaababaabaabababbbaaabbbabababbaaabbabaabaaaaababaabbabbababbaaababaabbbbbaaaaabbababaaaaabababaabbbabaaabbbaababbaaabbbbbbbabbabaabbaaaaaababaabbbaabababababaaaabbbbbbabaaaaaaabaababbbbbbabaabaababbabbbbbbbbaabbbabbaabaaababaabbabbbbabbbaabaaaababaabbbbabaabbababbababbbbaabababbaabaaabbaabbbabbaabbaaaaabbabbbbbbabaabaaaaaabbaaabbbabbabbbababaabbbaaabbbabababbaaabaabbabaabababababbbbababbaaaaaaaaaaabaababaabaaaababaabbababbbbbabbbababaabbbbababbbbbbababbaabaaaaababaababbaaabaaaaababaaaabbaaaabaaaaaaabaaabbabbabaababbbababaabbbbabbbbabaaabaaaababbbbbaaaaabbbaabbbbaabaabaaaabbaaabaaabaabaababaababbababbaabbbabbaaabbabbbababbbbaabbabaabbbaaaabaabaaabbaaaabbabababbbaaabbabbbbaaabbaababaabaaabbbbabbaababababbabbbabbabbaabaabbbbaabbabbbaabababbabbbaaabababaababaabbaabbabbaaaabbbaabbbbbaabababbaaabaabababbbabbbaababbabaababbababbbbabbbbabbbaaabbbbabaabaabbbaabbaabbaaaabbbaabbbabbbbabbbbbaaabbabaaabbbabbaaaabbbbabbaaaaaaabaabbbbbbaaabaaabababbaabbbbaabbbaaabaaaabaaaaababbbaabbabbabaaabaaaabbbabbaabbaababbbaaaababbaabbbaabaaababbbbabbaabbbbbbaaababbaabaaaaaaaaababbababbababbbaabbbababbbbaaababbbbbbaaabaaaaabaababbbbababbabbabaabaabababbbabbababbaabbabaaabbaaaaabbbaabbaabababbbbaaabbbaaaaabaabbabaaaaababbabbabbbaaabbbbabbaaaababbabaaaaaabbbaabbaaaababaaaaaabaaabbabbabbbbbaabbbbbabbbbabbabaabbbbabbbaabbaaaaabbbbbbaaaabbaaabbbbbaaabbabbbbbabbbabaabbbbabaabbbaaaaabbabaaaabbaaabbbaaaabbaabaaabaabbaaaabbbbbbbaabaaabbabaaaabbbabababbbaabaaaaaaaabbabbaaaabbbababaabbaabaababbbbaabbaabbbbbbaaaaabbbbabbbbaabaaaabaaabbbabaaabaababababaabbabaabaababaabaaabbaaabaabbababaababaaaabaabbaababbbabbbbabbaabaaaaababababbbababaaaaaabbabaabbbaaabababaabbbbaababbaaaabbbbbbabbaabbbbaabaaabbabaabbbaaabababbbabbaaababbaabbaaababaaabbbaababbbbaaaabaaabbabaabaabaabaabaabbbaabaaabaabaabbaababbbaabbabbbbbabbbbababbbababbbababaabbaabbabbbaaaaaaaabaababbababbabababbabbaabaaaaabaabaabbabaababaabbabaaaaabbbbaaaaaabbbaabbabbbbbaaabaabbbababbbbabbbaaaabbaabaaaaaabaaaabbbbbaababbbabbaabaaababaabbbbaaaaaaaaababaaaabbaaaaabbababbbbaaabaaabbbaaababaabbabaabbbbbabababaaaabbbbaabbbaabbaabbbbaaabababbaabaaaabbaaaabaabaaaabbbababbbbaaaabbbbabaaabbabbabbaaabaaaaaaabbabbaaabbbbbbbaabaaabbbaabaababbabbabbbbbaabaaabbbbbbabbaaabaababaaabbbbaabbaabaabbbbbaaaababbababaaabbabbbaaabaaaabbbabababaaaababaabaaaaaaabbaaaaaabbaabbaaaabaabbbbaaabbbbababaaabbbbabbbabbababbbaabbaabbaaaaaabbabbbbabbbababaaabaabababbaaaaaaababbabbbabaaaaabbbabaabbbbabbbbabbabbbaaabbaabaaababaaaaaaabbbbbabbbabbbaabbaaaabaaaabbaabbbbbbbbbaaaaabaaaaabbbbbaabbbabbbabaabbabbaaaabbbaaaaaaabbababbabbbbabbabbbbababaaaabbabaaaaaabaaaaabababaaabbaabbabbabbbbbaaaaaabbabbaaabbbaabbbbabbabbaaaabbbbbbababbbbbbbabbababababbbabbbbbbabaabaaabaaabaababaaabbaabaaaabbbaabbbababaabbabbbaababababaaabaaabbaabaabbbababaabababbaabaabaaabbabbbbabaaaabbbabbaababababbbbbabbbbbaabaabbababbbbaabaabaabaababbabbaaaaabbbbbababbaaabaaabaabbabbbbabbbbbaabbabaabbaaababbabaaaabbbaababaabaababbbbababaaabaaabbbbbbababababaaabbbaabaababbabbbabaabbabbbbbaababbabbbabaaaaaabbbbababaabbbbbaabbbbababaaabbbaabbaabbbbbbaaabbabaaabaabbaaabbababbbaabbabbbbabbbabbbabbbbabbabaababbbbaabbbbbababbaabbaabaabaaabbababbbaaaaaaabbbababbbabaabbaabbabbaaababababbaabaabaaababbabaabbbabaabaaaabbbabbaaaabbbaaaabbbbbababababbaabbbbabbababaaabbaaabbaaabababbabaaaabbbaabaababbabaabbbabbaaabaaabaaabaaababbaaabaaaaaabababbbaaababaaaabbaabbaaabaabbaaaaababbaaaaabaaabbbaaaabbaabbbababbaaaaabbbbbaaaabbaaabbababbaaabbbbbbaabbabbaaaabbaaababababbababbabbaaaaaabbbabbaaabbbaaaaaabaabbababbaababbaabbabbababbbaababbaabbaabbabaaabaaaabbbababaaabbbaabbbbaaaaabaabbbaabbbbabbbaababaabababbbbaabbbbbabbaabbaaabbaabaababbaaabbabaaaaaaaabbbbbbaaaaaabbbaaaaaababbaaabbaaaaabbbaaabbabbbabbaabbaababbababaaaaaaabbabbaaabaaaabbbaaabaaaaaabbbbaabababababbaabbaaabaaabbbabbaabbbbbabbbbaabbaabaaaabbbabbaabababbabbbbbabaababbabaabbbaaaaaababbbabaabaaaabbabbaaaaabaaaabbbbbabaaaabbbbbaabbbababbabaaaaaabaaaabababbababbbbaaabaaabbbbabbbbbaaabbbbbaabbabababababaabbaaababbabbababbbabaaabbabaaaaaaaabaabbabbbabaabbaabaaaaaaababaaaaabbaabbabbbbabbabaababbbbbabbbaabbbabbbabaabbbabaaaabaabbbaabaabbabaabababababbabbbbaaaaabbbaababaabbbabbbabababbbbbaababaabbbabbaababbbbaaabbaaaaabaabbbababbabbbaababaabbabaaaaababbbaabbabababaaaabaabbbbaabbaaabbbaaaabaabaabaaaabaabbbbababbbbbbbabababababbababbaabbababaaabbbaabaababbbabababbbbabbabababbababaababaaabbaaaaabaaaaabaababbaababbababaaaabbbabbabbaaaabbbbabbbaaaabbaabbabbbbaabbbaaabbaabaababbbaabbbaabbabaabaabbabaaaaaaaaaababbaaabbbaaaabaabbbaababaababbbabbaaababababbaabababaabbbabaaaabaaababbabbbabaabaababababbabaaaaaaabaabbbbbababbbbaaaabbaabbabaabbabaabaaababbaabbbaababaaababaaaaabbabbabbbabbabbbaaaabbbabbaabaaaababaaaabbbbabbbbbababbaabaaabbaaababbbaabbbbbaabbababaaaaabbbbabbbbbbabbbaababbababaaabbbbabaabbabaabaaabbabbbbbbbabaaabbababaaaaaaabaaaaababbaabaaaabbabbabbaababababbababbaaabaaabbbabbabbaababaaaabaababababbabbaaabbaaaaaabbaababbbabaaabaaaaaabbbbabbaaababbabaaabaabbbabbaaabaabaaaabbbbaaaabbbbaabbbbabaaaabbbaabaababaaaababbaaaabbbbabbaababaaaaaaabbbbaaaaabbabbbaabbabbabaaabaababbbbabaabbababbaabaaaabababbaaaaababaababbbbbabaabaabaaaaabaabaaabaaabbabbbbbabababbbabbaababbabbabaaabbaababbbabbababbbaaaaaabaababaabbaaaabaaabbbabaaabbbbbbaabbaaabbabbbabbbababaaabbbabbabbabbaabaabaaabbbbbbaababaabbaaaababababbabaabababbbaaaabaaabababbbaaaaaaaabababaaabababbababbaaaabaaaabbaabaababaaaaabbbababbabaaaabbabbaaaaabbbbabbaabaaabbabaaabaabbabaabaaabbabaabaaaaabbbbaaabaabbbabbabbabbbbbbbbbbabaaaaabbbaaaabbbbbabaabbabbabaaabbababbbabbbbabaaaabbaaabaababbaaabababbbaabababbabbbbbaaababaabbabaabaabbaaababbbbaaaaaaaabaabbaabaaababbaababbaababaaabaaaabbbaaabaababbbabaaababaabaaabaaaaabbaaaabbaabababaaaaaaabbaaaabbbbbaabbaaaaabbbbbababababaabaaaaaabbaabbbbaaaaaaabaaaaabbabababbbaaaaaaabaabbaaabbabbabbbaabaabaaaabbbbbabbbbabaaababaaabbbaababaaabaababbbbbaababbabaabaababaabbababbaaaabbaaabbabbbbbbaabbbbbbbbbbaabaabaaaabbabbbbabaababaabbbabbabababbbababbaaabaaaabbaabaabaabbabaabbabaababaababbabbbababaababbbaaabaaaaaabaaabbbbbbbbaabbbbbabaaabaabbaababbaabbaaabbbabbaaaaaabbaaabbaabbababbaababaababbbbbbbbaaaaababbbbbbbaabbbabaabaababbbbaaababaaabababbabaabaaababbbabbbaaabbbbbbbbbaaababaaaaabbbbbbbbbababbaabaaaabbaabbbbabaabbabbaaaabbaabaaabbbbabaaaabaaaabaaaaabbbaababbbaabaabbabaabbbbabababbaaaabbbbaababaabaaabbaaababbbbaaaaababbaaababbbaaaaabbaaaababbaaababbaababbbbaabbbbaababbaabbaaababbbaaaaabbbbababbaababbbbabababbbbbbababbaaaabbbbabbabbabbabbabbababbbbbbaabaababbabaaaaaabaaabbbbaaabaabaabbbaaaaabaabaabbaaabababbabbbbbbbababbaabababbaabbbbabaabbaaababbababbbbbababaaababbabbabaabaaabbaaaabbbaaabbbbbaabbaabbaabbaabbabbaabbaaaabbbbbaabbbaaabbbbbabababbaaaaaa
ababbaabbbaaabbabbbaabbbabbbbababbbbababbbaaabbaaabbbaabbbbbabbabbbabbaaaababbaabbbbababbaaaaaabbbaabbbabaaaabaabbaaababaabbaabbbbabbabbaabbbabbababaabaabaaaabbbabbbababbaaabababbaaaaababbbaababababbaabaaaabaabbbaaaababbabbbbabaabaaabbbbabaabaabaabbaaaabbbbabaaaaaabbbaabbbbbbbbbabbaaaababbbbbababbbabbbbababaabaabbabbbbabbbbbaabbaabbabaabbbbaabaaabbababbaaaaaabaaabbababbbabbbaabbabbbaabbbbbbabaaaabbbaaabababbbaaabaabbbaababbbaabaaabababaaabbabaaaaababbbbbbabaababbbbbbbabbbbbabbbbabababaaababbbaaaaabababbaaaaabbbabbbaabbaaabbbbaabbaaaaabaaabbabbbababbaaaabbbaabbbaaabbabbabbbabbbaaaabaaabbbaabaabbaabaaaaaabbbbbabbbbbabbbbabbbbbaaaabbaabbbbaaaabbbbbabbbabbbaababababaaaaaabbaaababbabbbbaaababbbbabbbaabbaaababbbaaabbbababbabaaababaaaaabbbaaababbabaabbaaaababbbaabbabbaaaaabbbababaabbbbbbaabbbabbaababbabbbaabbabbabbbbababaaabababbaabbbbbaaabbbaaababbaabaaabaaaabbbbaaaaabbabbbaaaababaababbaabbaabababbaabaabbaaaababbbbbaaaabaabaaaabbabbabbbbabbbaabbbbbaabaabaabbaabbababbaaabbbaaaabbaababababaabababaabaaaaabaaaaababbbbbbbbabababbbabaabbabaaaaaaababbabababbbbabbbbaabbabababbabbaabbbbbbaabbabbbababaabbaababbaaaabaabbbaabbaaaabbbaaabbbababbbaaabbbbbaaabbabbbbaabbaabbabbababbaabbababaabbababbaaaaababbbbbbbbabbbaaaaababaaabbaaaaabaaaaaabaaabbbabbaaaaaaaaaabbaaabbbbbaaabaabbbbbbbaaaababbabbabaabbabbababababbabaabbbaabbabbbbaaabbbbaaabbbbbaababababbbbaaabaabbaaaabbbaabbaabbbaabbaaaabbababaaaaabababaaaaaaaaabbbaaaabaaabbaabbaabbbababaaabbabbaaaabaabbaabbbababbbbaaaabbabbbbbbaabbbbabbaaaaabbaabababaaabababbaabbbbbabaabaabbbbbbaabbababbbbbbaabbaaabbaabbaaababaabababaabbaaaaaaaaabaabbbaaaaabbabbabbabaabababbbbaaabbbabaaaabbbbbabababbbaabbbbbbaabbabbbbbababbbababbbbbabbababbbbbabbbbaabbaaaaaababbabbabbbabbbbbbabababbaabbabbbbbbaaaaabaaaaaaabbbabbaabaababbaaaabbaabbbabbaaabaaaaaaabbbaaaabaababbbaaaaaaabaaaabaababbaaabbbbbbbbabbababaabbbbaaaaaabaabaababbbbababbbbabbbaababaabaaabbbabaaaabbbabaabaaaaaaabbabbaabbabaabaaabbbaabbababbbbababaabaaaabbbaaabbbabbbabbaaaabaabaaaaaaaaababbabbbaabaababbabaababbbbaabababbaabbabaaabbbbbbaaaabbaaaabbabaabbaaabaabbababbbbaabbabbabbaaaabaaaabbaababbbbaabaabaaaaaabaaaabbbaababababbbbbbbbabbbabbabbabbbbabbbaabbaaabbbaabaabbbbaaabaababaabbaaaaabaaaabababbbbaaaaabbaaaaabaaaaaabbabaaaaabbaaaaabbabbbaabaaabbaabbbabbababbabaaaaaabbaababababbabbaaaaaabaaaaabbbabaaaababbabbaabaabbabababbaabbabbaaaaababaabbbaaaabbabaabaaaaabaabbabaaabaaabaaabbbababbaaabaaaabababbbaabbaabbbbaaaabbabaabbaabbbbababbabababbbaaabbbabaaabaababbaabbaaaaabbaaabbbabbbbaaaabaaabbbaaaabbbbabbabbbbabbbaabaaaabaaabbababbaaaaabaaaababbabbbaabbbaababbaaababbaabbbabbbabbbaabbabbaababbaabaaabbaaaabaaaaaabbbbaaaababbbaabaaabbababaabaaaabbabbaaaaabbbabbbbaaaabbaabbbbbabbababbabbabaababbaabbaabbabaaabaabbaaabaaababaaabaaababaaaaaaaababbabbabaaaaabababaaabaaabbaaaabbbbbabaaaabbbaabaabaaaaabbabbbbbbbaabababbbabbaabaaabbabbbbbbabbbbabbababbababbaaabaabaababaabaabaaaabaaaababaaaaaabbbbabbbbbbabaabbbaabbaabaaabaabbbaababbbabbaabbabaaaaaababbbbbabbbaabbabbbbabaaaaabaaabaabaabbbbababababababbabbaaabaaaababbaabbaaaabaababaaabbbbbbaaaabbbbabbbabbabaaaabababaabbaaabaababbabbbabaabaabbaabaaaabbbabbababbbbabbbabbbbaaabaabababaabbaaaaabbabbaababbaabbaababbbbbbbaaabbbabbbbbbbbaaabbabbbbabbbababaabbabaaabbbaaaabbababaabbbbbabaaaaaaaaabaaababaaaababbabbabbababbababbaaababaaabbbbaabbbbbbbababbaabbbababaababbaabbbaabbbbaaaababbabbaabbbbbaaabaaabbabaabababaaababbabaaabaabaabbbbabbaabababaabbbbaabbababbbabaaaababbabaaabababbbbaaabaababaaabbaabbabaabaaababbaaaabbabbbabaabaaaaabbaaabbabaabbaaabaabbbaaaaaaabbbbbaaabbbabaaabaaaabbbbbaaaababbbbbbbabbaabababbabbbbbbbbbbabbbabbbbababaabaaaabbabbbabaabbbbaabbabaaaabbbababbbbaaababaaaaaaabbbabbbababaaabaababbaaabababbbbaaabaabbaabbbabbaabaaababaabbbaabaaaabbabaaaaababbbababbbbabaababbbbbbbbbabbbaabbbbbabaaabaaaabaaaaaaabbbabbaaabbaabababbbbbabaabbbaaaaaaabbabbbbbabbaabbababaababaaabbabaabbbaabababbbaaaaaaabaaabbbbbbabbaaabbabbababbbaabbababaababbbbaababbababaabbabbbbbabbbabaaaaaababaaaaaabaabaaabbbbbbababbaabbaabbbabbbbaabbbbbababbbbaaaaaaabababbbabaababaabbbabbabaaababbaaaaaaaaabbaaaaabbaabbaaababaabbababbaaaaababbabababbaaabbaaabaabaaaababaababbbbaaaabbbbababaababaaaabbaabaaabbaabbabababbababaaaaaabababbabbaabaababaabbbaabbaababbbabbbbbbbbaaabbababbaaabaaaabbabaabbaaaaaabbbabaabaaaaabaababbaabaabaaaaaaaaaababbabaabbaaababaababaabaabaababaabbbbbbbabaaaaabbaaaabbaababbbaaaaaaaaabaaaababababbaabbaabbabbbbaaabaaabababaabbbabbbbababbbabbaabbaabbbabbbbabbaaaaabbabaaabbbbbbaabaaaabbaabababababaabaaabbabbbaabaabbabbabaabbaaaabbababaaaaaabbabbbbbaababbabbbaaabababbaabaaaaaababbabbababaabbbbabbaabbaabaabbbababbbabbbabbbabaabbaabbaaaabbbbabbaaaaababababbaaabababaaaabaaaaababaabaabaabababbabaaabbbaabaabaabbbaabbbabbaaabbbaaaabbaaaabbabbaaabaabababbabbabaaabbbabaabbbbbbaaabbbabbaabaababababbbbabaaaaaababbbbaabbabaabaabbbbaaabbaaaaabbaaabbaabaaabaabababbaabbabaaabaaaabbbaaaaaabbbbbabbbbbbbbabbaaaaaabaaaaaabbabaaababbaaabbbbaaabbbabababbbbaabbbaaabbbaabbbbbbaababbbbbabbababaaabbabbaabaabbabbaabbababaaaabbbaaaaaabaaabbabaaabaababbbaaaabbaabbbbbbabaabbabbbbbbaabbbaaaaabbabbbaabbbababababaaabaabaabbbbaabbabbabaababbabbababbabbaaabbbbababbaababbaaabbaabababbaaaaaabaabbbbbabbabbbbbbaaabaaabaabbababaabaabbbbbaabaaabbababaababbbaaabbaabababaababbbabbababbaabaaaababaaaaabababaabbabbaaababbaabaababaaaaaabbabbbbbbbbababbbabbaabaaaabbbabababababaababbbabaaaaabbaabbbabaabbbbbbbaabbbbbbabbbaaabaabbbaaababbabaaaaaaabbbbbabaababbababaaababbaabbbbbaaababaabbbaaabaabbbabbaaabbabaaaaaaaaabaabbaaaabaabbaabaabaababaababbbaaabbabbaaabaabbbbbabbbbbaaabbbbbbbbbbbbababababbaaabaaababaaaaabbbaabbbbbabababbbaabaaaabbabbabababbbabbaaaaabababaabbaaaaaaabbabbaaaababbabbababbbbaabbabababaaaaaaaabaaabbabbaaaaaaabbbaabaaabababababbbabbbaaaabaaabbbbaaabaaababbaabbaaabbaaabaababaaababbbaabbaabbbaaabaaaabaababbbabbbabaaababbabaaabbabbbabaaaababbbbbaaabaabbbbaaabbaaaabbaaaaabbabbbbabaaaabbaababbababbabababbbabaabaaabaabaaaaabbbbbaaaabbbbbbaaabaaabaabababbabbbabababbabbbbbbabaaaaabbaababaaaabaabbababaaaabbabbaaabbbaaaaabbbabbaababbabaabaabbbababbabbabbabaaaabbabaaaaabbabababbbaaaabbaaaaaaaaabbaabaabbbbbabbababbbbaabbaabaaaaaababaaabbbabbbabababaaabbbbbbaabbaaababbabbbaaaababbbbbabbabaaaaabbabbaaaaabbbabaabbaabaaabbbababbababbabbbaabaaaabbbbbabaaaabbbaaabbbabbbbababbabaaabaabbbbaabbaaaabbbbbbabbbaaabaaaaabbbbbbbbbbabababaababbbbababbabbbbaabaaaababbabababbaaaabbbbaaaabaaaabababaabaababaababbabbbabbbbaababbbbaaaababaaaabaaaababaabaabbaaaaaabbbaaaaabaaaaabbabbbabaaaababbbaaaaaaabbaaaaaabaaabaababbabaabaaabbbaabbaabbaaaaababababaaaaaabaaababbbabbababababbbbbbabbabbbbbababbbbabbababbbabbabbabbbaaabbaabaababbbabbaababbabbaabbbbbbbbabbaabaaaaabaaabaaaabbabbbbbbaaaabaababaabbabbbabaaaabababaabbbaababaaaaaababbabbaababbaababaabbabababaaabbabbaabbbababbbbbabbaababbbabaabbababbaaaabbbbabaabbbbbbbaaabbbaaababaaaabbaabaabbbbaabbabaaabbbbabababbbabaababbbbabaabaaaabbbbabaabbaabbbaabaabaaaabbaaaaaababaabbbabbbaaabaaaabbbbaaaabbbaabaabaababbbabbbabbbaabbbbabbbbbaabbaabbbbbbaaabbbaabbbbbabbbbabbbbaabbaaaaaaabbaaaaaababaaabaabaaabbbaaabbbbababbabbbabbbbaabbabaabaaaaaaabbabbbbbbbaabaabbabbaabaababbbaabaaabbabbbababaaaaabaaabaaaaabbbbbabbbaabbbaababaaaabaaabbbbbababababbabababbabbababbabaaabbabbabbaaabaaaabaababbbaabbbabaababaaabbabbababbaabaabbbbbababaabbbaabbaabaababababbbbaabbabbbbbbabbabaabbbaaaababbaaaabbabbaabbbabaabaaaaabaababbaabababbbaaababbabbabbbabbabbabbbbaababbbaaabbbabbabbbabaaaaabaabbbbabaabbbabbabaaaabbabababbbbabababbbbabbaaabbbbaabbabbbaabbababbbaabbbbabbbaabababaabaababaabbaaaabbabaaaaaabbaabbbabbaabaaababbbbaaabbbabbbabababababbbabaaabbbaaaaaabababaaaaabbababbbaabaaabbaabbbababbabababababaabbbaaaabbabaaabbaaabbababbbbaabbbbaaabababaabbbabbaabbbabbababbbabaabaabaabbbaababaabbaabaabbbaabbbbaababbbabbaabbbbbabbaaabaaabbbbbbababaaabbbabbabbbbaabaaabaabbbbbabbbbbabababbbbbbabbbbbbaaabbabaaabababaabbaaabbbababaaaabbaaabbabbbaabbababaaabbbbaabababaabaaaabaaabaabaaabbabbabbbaabaabbabaabaababbabbbbaababbaabaaaababaabbabababbbaabaabbbbbabbabaabbbbbbbbbbabbababababbbbabbaabbbaaabbbbaababbababbbbbabababbbbabbaaaabbababbbaaabababaaabaababbbaabbbbbbbaabbbbbabbbbbaabbaaaababbbaaaaabbbabaabaabbbbbbbbaaaaaababaaabaabbbbaabaaabbbabbbbbabbaaabaaaaaaaababbaaabbaaaabbabaaaaabbbbbaabbbaabbaabbabbbbabbbaababaabbabaabababbbbbababbbbbaabbbbbbbbbbaaaabbabbaaabbaabaaabbbbaabbaabaaaabbabaaabbbbaabbabaaaabbabbaabaabaabbbabaabaaabaabaabaaabaaababaababbaaaaababbbabbbabbbbbabbaabbaabbbbabababbababaabbabbbababbbbbbababaabbbbbbaabbabbaabaababababbabbaabbaaababaaabbbbbbaabaabbaaababaaababababaabbbbaaaabbabbabaabaababbbbaabaabaabbababaaaaaaabaababbbbabbababbbabababaaabbbabbaaabbabbbbbababaabbaaaabbabbbbbabaabbabaabbbaabbbbbbaaabbbaaaabaaababaabbabbaaababbababbbbbabaabbaaabbaabbaaabbababbbbbaababbababaabbababbbabababbabbbabaaababaababbabaabbbbbbbaabbabbbabbbabababbabababbbbbabbababbaaaaabaabaaabbbabbbaaaabbaabbabbbbaabababbbabbbbabaaaaababaaaaaabbaaaabababaabbabbbbaaaaaaababababbbaaaaaaaaababbababbbaabaabaaabbbbabbbababbbbaabbbbbbbaababbabbababbbabbabbbaaaaababbbbaaabbaaababbabbbbaabbabbabaababbaaabbaaaababbbbaababaabbaaaabbabababbabaaabaababaabbbbbabbaaaaabbbbabbbbbaabbbaabbbabbabbbbbbaaaabbbabbbbbabbaababbaabbabaabababbaabbbabbaabbbbbbbbaaabaaabaaaabbaaabaaaabbababaababaabbbaababbbabbaaaabbbbabbbaabbaaaabbabbbabaabbaaaaaabaaaababbbabbbaaabbbbabaaaabaabbaabaaabbbaaabaababaaaaaaaaaaabbbaabbabbaabaaaaaabaabaaaabbabaaababaabbbaaaaababbababaaabbbbbaaaaaaabbababaabbbabbbbbbabbbbbabaababbbaaabbbbababbaaabbaabbbbbbbbabbbabbaababbbaabbbabbabaabaabbaabbbabbababaaaabbaaabbabaabbababbbaabbabbaaabbbbaabaabaaaaabbbbaaaabaabaabbbbbaabaaaaaaabbaaabbbabaabbbbabaaabbbbaabbbbaababbbaabbaabbaaabaaabbbbaabbaaaabbbaabaababbbabaaababaaaabbbaabbaaababbaabbaabbbaaaabbbaaaaabbbabaabababaababaaaaaababaaababbaaaababbaabbaabbbbaabbbabbbabaabaaaaabaabbababbbabaabbaaabbaabaabbbbabbaaabbabaabaabbaababbbaaabbabaaabaaababbbaabaabbaaabbabbbabbbaabababaaaaabaaaabbaaabbabaababaababbbbbabbbbabbbabbbbbbbabbabaababbaaaaabaaabbbabbaabbbaaabbabbaaaaaaaaabbbbababaaabaabbbababbbabbbbbbbbbbbaaaabbaabbbbbabbbaabbbabbbbaabaaaaabbbbabaaabbbbabbbbbaaaabbababbbabaaaabaabbbbaaababbaababaaabbbaabbaaabbbbabbabbaaababaabaaaabbaabbbabbbbbbbaaabbabbaababbbbaaabbbbbbaababbbbbabbbbbbbabbaaabbbbbbabbbbaabbaabbaaabbbbbaabbaabbabbbaaabaabbbbbbbabaababababbbabbbbabaaabbaabaaaaabbbbaabaabbabbaaabbbaaaabbaababaabaababbbbaabbabbabaaaaaaabababaaaabbbaaaaaababbbaabbabbabbbababbbbbabbabbabbabaabbaabbbabbbbbabbbbabbabbbaabbaabbabaabbbbabbaababaaaabbaaabbababbbbaaaabbbababbaaaabbbbaabaaabbaaaaaababbaaabbababbbaabaababbaabababbabbababababbbbbbabbbabaabbbbaaaabbaabaabaaaabbabbabbaabaaababbbaaabbabaabababaabaabaabababbabaaaaaaaaabaabaabababbaabbaaaaabbbbabbbabbaaaabbbaaaabbbababaaabbaaaaabbbabbabbbbbbbbababbbababbababaabbbbabababbbbabbbabaababababbbaaaabbbabbbbbaababbaaaabbaababbabbaabbaababaaaabbababbaabbabababaababbaaabbabaaabbbaababbbbabbbaabaaabbababbbbabaabbaaabbbbaabbbbaabababaabbabababbbaabbbbaaabbbabaaaabaaabbaaabbababbaabbbbaaabaabaababbbababbbabbaaabaaaababaabbbaabbbbbbaaabbaaabbaabbaaabaababbbbabbabaabbabaaaaabbbbaababbbbabaababbbbaabbaabaaaaaabbaabbaaabbbbaaaabaaabbabababbbbbbbbbababaabbbbbbaaabbbabaaaaabbbbabbbbaabbbabaaaaaabbbbabbbaabbbbbbbbaabbabaaaabbaabbbabbaaaaabbaabaababbbbbbaababbabababaabbbababbaaabbaabbbbbbbbababaaaaaabbbbaaaabaabaabaabbabbbbbabaabbbbaabbaabbbbaaabaabaaabbabbbbbbabababaaaaabababbbbaabababbbaabbbbabaabbabbabaabaaaabbabaaaabbbaababaabaaaaabababaabaaabaaabbaabbbbbabbbaabbabababbaaabbbbbbbbbaabaabbabababaaaaaabbbaabbabbbbaaaaabbbabbbabbaabbaaaaaababbbbaaaabbaaaabaaaaabbbbaaaaaaaabbaabbbbbbbbabbaaabbabbbaabaabbbabbbabbabbbabbbbaabbaaaaabaaabababaabbabababaaaaaaabaabaabbaabaabbabbbbaababaabbbabaaabaabaaaaaabaabbaabbaabbbbaabbbbbbbaaabbbbbbbbaababbbbabaaababaababababbabbbababbabbbbaabbaaabbaaababababbbbabaabaaaaababbbabaabbabbbaabaababbabbabaaaabbbabaaaaabbaaaaaaaababbabbabbabbbaaaaababbabbabbabbaabbaaabbbbaaabbababaabbbaabaabaaaabbabababbbababbabbabaaaaabbbbbbaabaaabbbaaabbabbbbbabbaaababaaaaaaaabaabbabaabbaaaaabbabbbbabaababaababbaababaaaaaababaaaabbabbbbbababbaabaaaabbbabaaabaabbaaabbbbaaababbbbaaabbabbbabbaabaabbabaabbaaaaabbabbabaabaaaaabababbabaabbbaabaaababbabbaabbaabbaabababbbaaaaabbaaaaabbbbaaaabaabbabbabaaaaabbbbbabaaaabbbbaaaabbbbaaaabbbaababbbababbbabababaaababaaaaaabaabbbaabaaabbababaaaabaabbaabaababbababaabbaabaabbaaaaabaaaaaabbbaabbabbabbbaabbabaaaabaaaabbbaabbabbabaaaaabaabbabaabaababaaaabababbbbbabbaaaabbbababbbbbbbabaabaababbababbbabbabbbbbabbababbbbabbabaabbaaabbbabaaaabbaabbbbaabaaabaaabbabaaaabaaaabaaaabaaabaabaaabaaaabbbbababbaaababbbbbabbbaabababbababaababaaabaabbabbbaabbabaababaaaaaaabbbbbbbabbbbbbabaaaaaaababbbabbabaabbbbabbbbbaabbbbabbbababbbababbaababaabaabbabaaabbbaaaabbbaabbbaabaaabaaaabbbaabbbbaaabaabbbabaaabbbabbaaababbaabbababbbbbbbbababaaabaababbabbbbbaababbbbaaaaabbababbaabbbababbabbbbabbbabbbbbbababaaaaabababaabababbbabbababaabbbabbbbabbbabbaaaaaaaaaaaaabababbbaabaaaaaabaaaabbabbaabbababbabaababbbaaaabaababbaabbabbbabbaabaabaaabbaaaaaaabbaabbbabbabaabaaaabbaabbaaabababbbbaaabbbbbaaaabaaabbbbbaabbbaabaaabbaaabbababbabaaaaababbababbbbaaabbaabbbaabaaabaaababbbbbabbbaabaaabbaaaaaabaabbbaabaaabbaaababbabbababbaabaaaabaaaaaabbabbaaaabbbabbaaaaaabaaabbaaaabaaaabaaaaaabbaaaaababbabbabaababaabaaaaabaaaaaaabbaabbbbabbaaaababaaababbbbbaabbbbbabbaabbaaabaaabaababbbaaaababbbaababbbbbaaaaaaaabbbaaaabbaabbabaaabababbbaaabaabaaaaabaabbbaaababbbaababbaaabbaabbbbaabaaaaabbbaabaaabaabaaabaabaabaabbaaabaababbbabbaaaaaaaaababaababbbbbbbbbbbaabbbbabbaaabbbbababbababaabbbaababbbbbbabbaabaaaaaabbaaabbaaaabaabaaabbaaaaabbbaabaaaaaabbabbbabaaaabaabbabaabbbbbabbbbabbbbaabaababbbbbbabbabbbababababbbbbbbbaabaabbaabbaaaaaababbabbabaababaabbbabbabaabaabababaabbbaababaababbbabaaaababbbbaaababbaabaaabbbaabbbbaaaaababbaaaaabababbbababbaaabaabbbbbaabaabaabbabaaaaaabaabbbaaaaababaaababbababaaababaabbbbaaaabaaaabaaaaabbabbaabababababaaaabaabbabaababbbaaaaaababbbbbaababaabaabbbabaaabbabbbbaaaabaabbbbbbbbbbbbaabababbabbabaaabbabbbbbbaabaabbaaabaaaabaaabbbaaaabaaaaaaaabbbababaaabbaabaabbaaaababaaaababbababaaaaabaababaaabbbabbbaabaabbbaaabaabbbbaaabababbabbbbabbabaaabaabaaaaaababaaabbabbbbbababbabbbaaaabbababaabbabbbbabbbaabbabbbaaabaaaaaaabbbbbbababbbabbaaabaabbaaabbbabaaabbbabaaaaaabababbbaabbbaabbbabaababababbbabababbbbaaabbbbbaabababaaabaaabaaabbbbbbaaaabaabbaaaaabbabbbabaaaaababbbabbabaabbabaababbabbaabaabbbbbbbaababaabbabaaababbaabbabaababbbaabbbbbbbabbabbaabbabbbbbbbbbbbaaaaabbbbaaaaabaababaabaaababbababbaabbbbabbbabbabbbbabaaabbaabaaabbabaababaaababaaabaaabbbbaabababaabbbbabababaabaababbbaababbbbabbabbbbabaaaabaaaaaaaabbaaabbbbbbaaaabbbababaaabbbbbbbbbabbabbaabbaaaabbaababbaabaaabbbabbbbabbabbbaabbbbabbbaabaabbaabaaaaaabbaababaaabbaabaabbaababbabaaaabaabbaabbbabababbbababaabababbabaabbabbababbaaaaabbababaaabababaaabaabbaaaabbbabababbabaabbabbaababaaaaaababaabaabbbbbaabbbababbbabbbbbbaaabbabbaaaabbbabbbbaabaabaabaabbaaabbaaaaabbbaabaaabbaabaaababaaaabbbabbabbbbabbabbababbaaabbaaaabbbbbbbaabababaaabbaabaaabaaaaabbaaaaaabbbabbbbbaaabbbaabbaaabababababbbbabbabbaaaabbabbaabaabaaaaabaabaabaaaaabbbbbabbbbaaaabbaaaababbbbbaaabbbaaababbbabbbabaaaaaabbbbbabaabbaabbaabbbababaabababbbbbbabbbaabbbaabbbaabaababaabbabbbbbbbaabababbbbaaabbabaabaaabbaabbbabbaabbaaabbbababaabbabbbaabbabaabababbbaaabbaaabbabaaaaaabbbaaaaababaaaaaabbabbaabbabbbaaaabababababbbaaaaabbbabaaaaaabaaaaaabbbbaaababababaaaaabbbaabaabaabbabababbbbbbbbabaababbbbabaabbaabbaababbbabbbaaabbaabbbababbbbabbaabbbaabbaabaaabaabbaaabbbbbbaaababbaaabaaaababbbbaabaaabbaaabbaaaabaaaaabbabbbaaabaabbbbbbaaabbaaababababababbbbbbbaabbabbbaababbababababbabbaaaaabbbbbabaaabaaaabbbbbaaaaababababaaababbbaaabaaabbaababbbbbbabaaaabaaaaaabbabaabababbaababbababababaabbbbbbaaabaabbabbbbbbbaabbaaaaabbabbbabbbbbbabaabbabbbbbabaabaaabbabbabbaaaaaababaabbaaaabbabbbbbbbbabbbabaabbaaabbbbaaaabbabaabbabaabbaababaabbabbaababbbbaaaabbababaabaaabbbbbbabbbbbabbaabbbabbbaaaabbbbababbbaaababababaaaababbababaaaabaaaabbbbaaaabbaabbabbaaaaabaaaababaaaababaababbababaaaabbaaabbbabaabaabbbbbbbbbabbbabbababbaaabababbabbababbaabaaaaababbaaaaaababbbbbbbbabaaaaabbaaaabbbaaaaabbbbabbbaababaabababbbbabbbbbaabbaababbbaaabaabaaaabbaaabababaaabababaaaaaababbbaabaabbaabbbbaabaabbaaabbbbaabbabbaabaabbbbabbbaabbaabbabaababbbbaabaaabbbaaabbababbbaaaabbbbbaabbabaabbabaaabbbaababaabbbbaaaaaaabababaababbabaaaaaabbaababbabaaaabbaaabbbbaabbabaaaaaaaabbabbbbbbabbaabbbabbbaaaababbbabbbabbbaaaabbababaaabbbaabbbaaaaaaaaabbbbabbbbbababbbabababbbabaaababbaaabbababbaababababbbbababbabaabaabbabaaabababbbbbaaaabaaababbabbaaabbbaaaaababbabbbababbaaaaaababbaaaabbabaababbabbbbabaabbbbaaabbbabaaaaaababaaabbbaaabaaabababbbabaaabaaaaaabbbabbbbbabbababbbbbbbabbbabababbbbaaabbabbaaabaabbbbabbaabbbabaaaabaabbbababbbaaaaabaabbbbbaabbaaaaabaaaabbbaaabaababaabbbaabbbabaaaaaabbbaaabaababbbaabaaaaabaaababbaabaaaaabbaabaaabbbabaababbaaabbababbbabbbabbbbbbbbaabaabbaaabaabababbaaaaaaabbabbbbbbbaaaabaabbaaabbaaabbaaabbabbaaabaabbaaababbabbabaaaababbaabbbaabbabbbabaababaaaabbbbaaaaabaabbbbaaaaabbaaabbbaaaabaaaabaabbababaaabaaaabbaaabbbaaaabababaaaababaabaabbabbabaaabbbbbbaababbaaabaabbbbabababbaabababbbbbabaababbabbbaabababbabaabaabababaabbbabababbbbbabaabbbbaaaabbabababbabbabbbabaabababbbaabaaaabbbbabaabaabaaaaababababbbbbbabbbbabbbabaabbbabababaaaababaaaabaabaaaabbababbbbbaabaaaabaabbbbbaaaabbbabababbbbbabbaaabaaaabbbbaabababbbaaaababbabbbaabaabbaaaaaaaaabbbaabbabbbbabbaabbabbbaaabaababbabaaabaabbabbbbbabbbaabaaabaaaaaababaaabbaaaabbabbbbbababbbbbaabaaaabaabbaaabaabbaabbbbababbaaabbabaabbbaaabbbbbaabbbbabaabbbbbbaaaabaaababbaaabaaabbbabbaabbababaaabaabaaaaabbabbbabababbabaabbbaaabaabbabaabaabbbbabbbbabbbbbbbbabaabababbabbbbbbabbbabaaaaababaaabbabababaaaabbabaabaabbbababbababbbaabbaaabbbbababababaabbaaaabbabbbaaaababaaababaaabaabaaaabaabbbaabbaabbabaabbaabbabbbaaaabbabbbbbaababbabbabbbbaaababbbbbababaaaaaabbbbbbaaabaabaaaabbbaaaaaaaabaabbbababaaaabbaabbabaababaaabbabaaabbaaaaababababbbaaabbabbbbbbaaaaabaababababbbbaabaabbbbaabbbabbbabbbababaabbababbabbbbbbbbababbbbabababbbabaabaabaaabbabbababaabaaaabbbbbabaaabbbbabababbababbabbbaaabbbbbaaabaaaabbaaaabbababababbbaabbababaabbaaaaabbbaabbababbaabbaaababbaabaabababbbaaaabbbaaaaaabbabbbbaabbabaaabaaababaabbbbabbabbbbabbbbaaabbbabbbbaaaaaaaababbaababaabbabaabbabbaabbbaabbbabaababbaaabaaaaabbbabbbababbbabbbbbbbaaababbaababaaababaababaabbbbaabbbabbbbaabaaabbbaaaaabaaababaaaaabaabaababababaaaaabbbababbbbabaabbababaaababaababbabbbaababbaabbbbbabaabbabaaaabaabbabbaaabbbbbabbbbbaaaaaaaaabbbbaababbabbbbabaabbabababbabababbabbaaababbaababaaabbbaaaaabaababbaababaaaabbaaabbabaabaababbaaababaaaabbabbaabaabbabbaabbabababbaaaaababbaabaabbabbbbbaaaaaabbaaaaaaaabaabbabaabaaaabbaabbababaaabababbbaaabaababbabbbbaaabbbabbbbbbbabbaaaabbabaaaabaaababbaabaaaabbbbbbbbbbbbbababbaabaabbbabbbaabaabbbbbbbbbbbbaaabbabbbaaaabbaaabaababbbbbaaabababaaababbbbaabbbabababbaaabaaabaabbbbabbbbaaabbaaaaaabbabaabbbbbabbbaabaabababaaabababaabbaaaaaabaaabbababbabbbaabbaabbaababaaabbbbbbbbaaababbaaabbababbaabbbbabaaaabbbbbbaaabbabaababbbbbaabaaaabbabbbabbabbbbabbaabababbaaaaaabbbaaaaaaaabbabbbabababaaabaabaaabbabababababbbabaabbabbbbbbbbbabbbbabbabababbaababbababbbaaababbbabbbbaaaaababbbaaabaabaababaabbabbabbbbbbbbababbbabaabaaaaababbbbbbaabaaababbbbbbaaaababbabaabbbabbaaaabababbbbaabaaaaababbaabbbbbabbabaabaababbbbaaabbabbbbbbaaaabbbbaabaabbbabaababbbabaaababbabbbbaaababaaabbabaaaaaabbbbaabbabbabaaaabbbaabbaaaabaabbbbaabbbbabababbaaaababbbbbbbabbbbbbaabbaaabbaaababbaabababaaaaaaaabaabaabbbabaabbababaabaaabbabbbaaaaabaabbaaabaaabbaabaabaabbabbaaaaabbaaabbbbbaaabbbbbabbabaaabbaabbbbaabbbbbabbabababbaabbababbaabbaaabaaaabbbbaabaabbabbbbaaabbaaabbbbabbbabbbbabaabbaaabaaaababbbababbabbbbbaabaabbbababbaabaaabbbbababbbaaaaaabbbbbbabaaabbbabbbababaabbbababbbabaaabbbbababababbabaaaaabaaaabbaaababbbaaabbbbabbbbaabaabbabbbaaababbbabbaaaaabaaaaabbbaababaaaabbbbbbabaabaaabababbbaaaaaababbbbbaababaaababbabbbbbaaaaaabaabaaababbbaababbbbaababaabbabbaaababbabbababbbaabaabbaababbbbbaaaaaabaabbbabbaabbbbabbbabbabbabbbbbaabbaabaabbababaaaabaabaabaababbbabbaaabaaabaabbbaaabaabaaaaaaabaaaaaaaaababaabbaaaabbababaaabaaabbbaababaabbabbabbaabbabaaaaabbabbaabbabbbbabaabaabbbbbbbbbaabbabbbaababbabaaabbaababbaaabbbaaaabaabbbabbabababbbbbbaaaabbabbababababaabbbbbbbbbbbabaaaabaaababbbbbbaabbbaaababbababbbabbaaababbbbaaaabbbbababaaabbbbbbbbaaabbbbabaaababbbabbaabaaaabbabaabbbaabbbbbbaabbbbabbaabbaababbbaabbbabbbaaaabbaaaabaaabaaaaaabaababbbbabbaabbaabaabbbbaaaabababaaabbaaaaaaababbbbaaabaaababaabaabaaaaaaaababaaabbbaabbbaabbaaabbbbbaabbaabaababbbbbaaabaaaabaaabbbaaaabbbbabaaabababaababbbbabbabaaababaabbabaabbabbbbaaaaabababbaaaaabbbbaaabaabbbbbbaabbbabaabbbabbabaaaaaaabababbaabbbbaabbaaaabaabaabaabaaabbbaabaaaabbabbbbabbbbaaabbabbaaaabbabaababbbbbabaabbaabababbabaaaaaaaaaababaabbbaaabaaaaaababbbabbaaababbbbaaabaaaaaaabbbababaabaaabaababbbaababaaaababaabaabaaaaaaaabbbaabaabbbbbbabaaabaaaaabbaabbaababbbbabbabbabababbababbaaaaaabbaababaaaabaaabbbbbbaababbaaaababaabaaaabbbabbaaaabbbabaababbbbbaaabaaabbababbbbbaabaaabbbaababababbabbbaabbababbbbaaabbabbababbbbbbababaaabbbbabaaaaaabaaaaabaaabababaabbaabbabbbbabbaabaaabababbbbbbaaaababbbbbabbbbbabbbabaabaabababbabaabababaaababaaaaaaabbabababbbabbabbaaaaabbbbaaaabaabbbbabbaabbaabbabbbbababbabaabbbaabbbbaabaaabaabbababbaabbbaabbbbbaabaaaabbabaaabaaaaabbbbabaabbaaaaaaabbbbaaaaaaaaaabbbabbabbaaaaaaabaaaaababababaaabbabaabaaababbaaabbbbbbaabaaaaaaaaabaaababaaabbbabbaabbbaaaaaabbbaaaaabaabbabbbbabbaabbbbaaabbbabaaabbabababbbaababbababbabaabbbabbbaaaaaaabbababbbabaababbaaaabaaaabbabbabbabaaaaabbbabbbababababaaabaaaaaabbbabbaaabaaabbbbbabbbbbabbbaabbbbbbaabbabababbababaabbaaabaabaabaaabababbaababbababbaaaaaabbbbbaabbbabbbbababababaabbababbabbbbaaabaaaaabaaaabaababbaaababbaabbbabbaababaabbababbbbaabbbabbbbbbaabaaaaabbaaababaaaababbabaabbbbabbbbaabbbababbbbaaaaabaaabaabaababaaabaababaaaaabbabaabaababbbbbbabaaababbbabbaaababaaaabaaabbaaabaabbbbbbbbbabbaaababbaaababbaabaabaabbabbabbaabaaaabbabaabbbbbbbbabbababbbbbbbababaaabaabbabbabbaaaabbaabbabaabbabbaababababbabaaabaaabaababbbabbbabbbabbaabbbabaaabbababaabaabaabaaababaaaabaaaaaaaaababbaabaaaaaaabbbaaabbbbbaabbbabbbbbaaaaababbbbaabaabaaaabbababbbaabaaabaaababbbabaaaaaabaababbababbbbaaaabbaabbababbaaabbabbbabbbbbbabbbababbaaaabaabbbbabbbbabbbbaabaababbbbababbaaabbbbbbbbbaabbbaaabaaabbabababbbbabaababbbbbbbbbbaababbbbabbaaabbbabbbabbbbbbaabababbbaaaabaababaabbabbabababbabbaabbabbabaababbbaababbaaaaaabaaabbabbaabbabbbbbbaaabaabababbbabbbbbaabbbbbbaabaaabababbbabbbabbbabbbbbaaaabaaabababbbaababaabbaababbbabbbbaaabbbabbbbaaaaabbbabaabaabaabaababbbbbabababaaabbbbbbbbbabbbbbbababbaabbbaababaaabbbbabaaaabaaaabaabbbbbabbbaaaabbabbbaaabbaaabaaaabbbbaaaaaaaaaabbbaabbbbbbaabaaaaababaaaabbbaabbaaaabaaabbbbbaabaaabbbaabaaabaabbaaaabbababaaaaaabbbaababbaaabaaabbbbaaababbaabbbaabbbabbbbbbbaaababbabbbbbabaaaaaabaabbbaabaaaaabbbbbbabaaaabbbbbaaaaaababbabaaabbbaaaaaabbbbaaabaabaabaaaabaaaaaabaaabbaaaaaabbbabaabbbbbbabbaabababbbaaabbaabbbaabbbaaababaaababbbaabaababbbaabbbabaaaabaababaabbbabbbbbaabbbbabbabababbabbabaaaaaabbbabbbaabbaaaaabbbbbbbaaabbaabaaaaaabaabbbbaaaabbbababbbaaaaabbabaaabbaaabbbaaaaabaabbabbabbbaaaaaaabbbbbaabaaabaabbaabababbabababaabaabaabaaabaaababaabaababbbbbbabababaababbabbaabaabaabaabbabaabbbbaabaababaabbabaabbaaaaabbabaaabaabaabaabbbaaababaaaababaababaaaaaaabbabbbabbabbbbbabbaabaabbabbbaabbabaaaabbbbaabaaababbbbbaabaaaaaaaaaabaabbbbbbaababbabbaaaaaabbbbbbbabaabbaaababbabbaabbaabbaabaaababaabbaaaabbbbbaababbabbbaaabbbbabbbabaaaaabbabababaabbbababbbaabbbbababbbabaabbabaaaabbbbabaababbbaabbbbbabbbabbaaaababbabbaaaaababbababbabbbbbababaaababaaabbbbbbbaabaabbabbabbbbbbbbabaaaaaaabbabbaaabbaabaabaababbbbbbaabbabbbaabaaababbbbbaabbbabbabaabbbbbaaababbaabaababaaaaabbaaababbbaaababbaaabababbaabaabaaababbbabbbabbaabbabbbaaabaaaaaaaaaaabaabbabbbbabbababbbbaaaabaabaaababbaaaaabbbbbabbaabaaaaabbbabbbaaabbbabbabbaabaabaabbaabbabbbaabbabbaababaabbaabbbbaabbbaababbabaaaabaaaabbaabaabbabaabaabbbbbaabbbabaaaaababbbaabaababbabbbabbbbbbbbbbabaaabbbbbaaaaabbbbaabaaaabbbbbbabbbababaaaabbbaaaaabbaaaaababaaabbababaabbbbbabbaabbbabbbbbbaaaaabaabababaaababbbabbbabbaabbaabbbababaabbaaabababaabbbbbbbbbaabaaabbaaabbbbaaaaaabaababababaabbbaabbbabbbbbabbaabbbaabbabbabaaaaabbababbabaabaabaaabaabbaabaababaababbbaabbbaabaabbaaabaabbbabbbaababbaabbaababbababbbbbbbaabaaabbaabababbabbababbbbaabbaabbabbaababbaabbbabbaabbabbbbabaabbbbabbbbabbbbabaabbbabaaabbaababaabaabababbaabaabbbbaaaabbbabbbaabbabbaaaababbbbababababbbbbaabbabaaaabbaaabbaabababbbbbbabaabbbaaabbbabbbaabaabaabababbaabababbbaaabaababbbabbabaaaaaaaabbaabababbabbaabbababbbbabbbbaaaaaabababbabaabbaaaaabbaaaaaabbbbabbbbbaabbbbabaabababbabbbbbbbbbabbbaabaababaaaaababababaaababbabaabaaaababaabbaaaaaabaabababaabaaaababaabbbbababbbaabbbbbabaabaaabaaaabaabaaaaaabaabaababbabbabbbbabaaabbabbaaaaaaabaabbbbabbbbbaabaabababbbbabaaaaaaabbaabbabaaaaababababbaaabaaaabababbabaaaaaabbbaabaaaabababbbaabbabbaaabbaababbbababbbbaabaaababbbbaaabababaaababbbbababbababbaabbaabbabbbabbbabbaaaaaaaaababbabbabaababbbaaabbbbaabbabaaabbabbbabbbabaabbbaabbaabbaabbaaabbaabbbaabbaaabaaabbbabbbbbbbabaaabababbbbbbabbabaabaabbbbaabbabaaabbabbbaabaabbbbaababababbbaabbbabbbbaaaaaaaaaabbababbaababbbbbbbbabbbaababbabbbaabbaaabbaabbbaaaabbbbbbaaaabbaaababaaaaaaaababbababbbaaababbabbaabaabbaabaabaabbaabbabbbaabaabbababaabbaaabbaabbbbaaaaabaabbbabbabbbbaaaabbbaaaabbabbabbbbbabbbbabababaabbbaaaababbbbbaabaabbbaaababaabbabbbbbbaaabaabbbaaaaaabbababbaaabaababababbbbababaaabbabaabaabbabbbabbababbbbaaaaaabbbaababaaabbbabbaabbbbaabaabaaaabaaaabaaaababbaababaaaaaabaaabbbaaabaaaababbbbaabababbbbaabbababaabababaaaabbabbbbabbbbaaaaaaabbaaaabbbaaaaabbbaabbbbbaabbaaaabababbbbaaabbabbbbbbabbbbbaaaaabbabbbbaaaaabbabbbbbbabbaaabbbbabababbabaabaaabababaaabbabbabbaaaabaaabbbaaabbbabbaaabaabbbababbaaaaabbababbaababaaabbbbabbaabbbbbbaabbbabbbbbbababbbaabbbabbababbaabbaaabababbbaaabbbaabbbababaaaabbbbabbbbbbaabaaaabbaababbabaaabaabbbaabbaabbbabaabbaaabaababbbaaabbbabababbbaabaaabbbaaababbbabbaaaaabaaaababbabbaaaabaaabbbbaababbbaabbbbbbbbaabababababbaababbabbbbbaaabaaaababbbaaabbaabbaaaaabaabaaabbaaaaabababbbbabbbabbaabbbbbbbabbbabbbabbaabbbaababbbbabaaabbabbbaaabbbabbababbabbaaababaabbbbbbaababbbaabbababababbaaaaaababbbbaaaabbababbbababbaaaabbbaabaaaabbaaabababbaaaabbbbaabaaababbbbabaabbaabaaabbbbaabaaabbabaaabaabbbaaaabbbababbaaabbbabbabbaabbabbabaabbbabaaabbababbbababaabbbbbbabababbabbaababaaabbbbbaabbbbbababaaaabbbbababbbabbaabaabaaaabbaaabbbbbbbbaaabbbbaaabbabbbabbbaaabaabbbabbbabbbbaaabbaabababaaaabbbbaabbaaaaaabababbaababaaaaabbbbbbabbabbbaabaaaaabaabbabbbbabbbbbbbabaaababbaabbabbabbbbaabbababaabbaaaabaabbaabbbbbbbaaaaabaaaabbabbaabaaabbabababbbabbbabbaaaaababbaaababaaaabbabbbbbababababbaabbbbabaaaababbbaabbaaaabbabaabbbbabbaaaabbaaaabababbbbabbbbabaabaababbaabbbaabbbbbaaabaabaaabbbabbabbaaaabbaabababbbbabbaabbbaaaaaabaabbbaabbaabaabababbabbbaabbbaaaaabbbbbabaaaaabbaaaabbbabababbbbabaaabbaaaaabbabaaabbabbbabbbbbbaaaabbaababbbbbbbabbabbbababababbabbabbabaabbbabbaaabaaaabbaabababaabaabbabbbbbaababaaabbbabbaaaaaaabbababaaaaabaababbabbbaaaabaababaabbaabbababbbabaaabaabbbababbaaabaaabaaabbbbbaaaaababaaabbabaabbaaaabbababababbbabbabbababbbbbbbbbabbabbbbbbababaaaaaaabaaaaabaabbbabaaababaabbbbbbabbaaababbaaabaaabbbbbaaabaabababbabaaaabbaababbbaaabbbbaaabaaaaabaabaaabbaaabbabaaaaaaabbaaabaaaabaaabaaabaaabbaababaaaababababababaababbbabaabbbababababaabbbabaabbbbbbabbababaaabbabaabaaabaabbbbbabaabbbbbabaaaaaabaaababaaaaabaaababaabbbaaabbbbabbbbbabaabbababbaabbaaaaaabaaaaaaabbaaabbbbaabbaabbaabaabaaaaaaabbbbababbbbabbbabaababbbbbaaabbabbabaabbaaaaabbaaaabbaababaabbbbababbabbaabaaabbbabaaabbaababbbbbaabaabaabaaabbababbabbaaaaababaababbbaabbabaabbbbaaabbababbbbaababbabbaabbbababbaaaaababbbbbabababaaaaaabbaabbaaaabaaaabaaabababbabababaabababbababbabbababbbaaabbabbbaaababaabbbbababbbabaabababbbabbbabbbbbbbabbabbbbababbaaababbaababbaabaaabbbbabbabaabbaaababbaabbabbabbaaabbabaaaabbbabbaabbbbaabbabababbaabbabaabaabbabbababbbaababaabaaaabbaabbbababababbaaabababbbabbabbaabbbbaaabaaababbbaaababbabbaabbbaaaabaabababaabaababbbbbabbbaabaabaaaababaaaaaabbbbbabaaaaaabaabababbbabbaabababababaaabbbaaabbaabaaababbbaaababaabbbabaaabbbabaababbababbbababaababbabababbbabbabaabaababbbbbbaababaabbbaabbbbaabbbbabbaaabaabbbaaaabbbbbbabaabbbbbbbbaabbbaabaabababbbbbaaaababbaaabbabaaabbaaaaaabbbabaaababaaaabbbbbaabbbbbaabbaabbbabaaaabbaabaababbaababaababaabbbaabaaaaababbaaababbaabbbabbaabbaabbbaabaaababbbbaababbbababaababbaaaaaaaaaaaaabbbababbbbbbaaabbaabbbabbabaabaaaaabababbbaaabaabbabbaabbabaaabbbababbaabbbaabbabaababbbbaaaaaabbbbaaaabbabbaabbabaabaaababbbaabaaabaaabbbbbbabbbaaabbbbababaaabbbbbbbabbbaabbbbbaabbaababababbaabbbabaababaaaabaabbabbaababababababaababaabbbbbabaaaaaabbbbaabbbbababbaaaabbabaababbbbabababababbbababbabbbabbbaababaabaaaaaabaabbbaaabbaabbabababaaaaabbaababaabbaaaaababababbaabbaabbbabbbbababbbbabaaabbbbaaabbbabbbaababbbbabbbbaaaabaabbbbbabbbbababbbbbaaabbbabbbbaaabbaaaaabbababaaaaabbabaabaababaaabbbbabbaaaabaaabbaabaaabababaababbaabbbababaabbbaabbaabbababaaaabbababaaaaaabaabababababaabbabaabaaababaaabbbbbbaaaabaaaabaabbbabaabaabbaabbbaabababbabaaaabbbbababaabbabbaaababbbabaabaabbabbabaabbaabbbbabaaaabbabbbaabaaaaaabbaaabaaabbbbababaabbbbababbbbaaabbaaabbaaababbaaaaabaaaaabaaababbaaaaaabaabbabbaaabaabaabbabbbaabaabaabbbababbbbaaaaababbabaabbaabbbabbbabbaabaabbaabaabbbaababbbaaabaaaabaabbabaaabbbbbaababbabbaabaaaabbabaaabbabbbaaaabbbbbbabaaaaabbbbabaabbbaababababbaaababaaabbababbaabbababbbbabbbaaabbaabbbaaabaabbbaaaaabbababbababbbababababbbaaaaabbaaaaababaabbbabbbbbabababbabbaaabaaabbaabaaababbabbabbbababbbabbaabbbaaabbbabbababbbaabbaabbbaabaabaaabbabbabbabbbbaabaabbaaabaaaaaabbbbbbaabbbbaababbbaaaaabbaabbaaabababaaaabbaaabbaabbbabbbabbabbbababaaaabaaaaabbaabbababaabbbabbabaaaaaabbbbbbababbabbabbbaaaaaabbabbbbaaaabbbbaabbbabbabbaabababaaaaaaaaaaaabbabaabbbbbbaabbabbbaabaabaabbbbbbbbbbabbbaaaabaaabaaabbbbabaabbaabababaababbbbaabbaababaaaabababbaaabaaabaabbabaababbaaaabbaaabbaaaabbbababbaabaabaabbabbbbbbbbbbaabaabbaaabababbbaabaabaaaaabbbaaabbaaabbbbaaababbaabababaabababbaaaaaaababbbbbabbbbbabaabbaabbaaaaaaababaaababaabababaaabaaaaaabababbbbbbbabaaaaabaababaabaaaaaabbaaabaaababaaaaaaaaaabbabaababbaabbbaabaabababaaabbbbbaabaabbaabbbabbaabaaabbbbabbbbaabaabbbbaabababaabaaaaabaabbabbabaabbbbababbbaaabbbaababbbbbaabababbaaaaabaaaabbbbaaababbbaaaababbbbbabababaabbaabbbbbaaaaaabbbabbabbbababbbabaabbbaaabbaabbbabbbabbabababababaaaabbaababbbaaaaaaaaaabaabbbbbbbbbaaabaaabaaaabaaabaabbaaabbaaabaaaabaababbaababbbbbabbaabbbbbbabbabbaabbbbbaabbbbaabaabaaaabababaabbbbababababaababaaaaaabaabbbbbaabbbbaaaaaaaabbbbaabbbaabaaabbababbbbaaabbbbbaaabbaaaabbbababaaababbaaababaababbbabbbaabbbaabbabaabaababbbbbaaaaabbabbbbbaabbbbbaabbaababbbbaabbaaabbbaaaababbbbbbaaaabbabababaababaaaaaaabbaabaabbbababaaababbbaaabbbbaabbbbbaababaaabbababbaabaaabbbaabaabbbabbbbaaaaaabbababbabbababbabaaabaabbababbbbbaaababbbbbaaaababbaaaababaabababaabbaabababbbabbbabbbbabbaabaabbaabbbbbbaabbbabaabababbbabbabaababaabbaaaabaabaabaaaaabbbbbbabbbabbabbaabaabababaabbbabbabbabaabbabaabbbbbaaaaaabaababbbbababaabaabbbaabbbbbaaabaababbbbabbbbabbabbbaababaaaaaaabbaaabaabbbaaabbbbaababbbaaababbbabaaaabbbabbbabaaabaabbbbbbabbaaabbabbbbaaababbabbaaabababaaaabaaaaaabbbbbbbabaaabbbababbbbababbbaaabbababababbabbabbaabaabbababababbbabbbbbbbaababaaaabaabbbbaabbabaaababababaaaaaaaabaabbbabbbabaabbaabbbbbababbaaaaabaabbabbbabbbbabaabbbaaaaaabaababbaaabababbbbaaaabaabaaabaabbababbbbabbbaabbbbabbbaaabaabbbabbbaabbababbbbaaaaaabbbabaaabbaabbabbabbbbbbabaabaabbbbbaabbbbbbbbbaabaaaaaababbbbbbaabbbaababaaabbbbabbaaaabbbbabaababaaaabbabbbaabbbabbaabaabbaaabaabbbaabbbabbaaaaababaaaaabbabaabaaaabaaabbbabbabaabbbbbaaaaabaabababababaabbbbbabaabababbabbbbbbaaabbabbaabbabbabbbaabababaabbabbbbaababbaaaabbbbaaaaaaababbbbaabaabaaaababaabababaabbbaaababbababbbbabbaaaabbabaababbabaabaaabaaaaaabbabaabbabaaaabbaaabbabbbbaaababbabaaaaabaabbaaaaaababbbbbaaabaaaaabbaaabbaabbabbaaaaaababbaabbaaabbbabababaabababbaaaaaaabaaabaabbabbaaaabbbbabaabbabbbbbbbabbbbaaabbabbabbaabbbaabaabaaabaabbbabbaabbaababaabbaaaaaaaaabbbaabaabbbbaabbabbbaabbabaabbbbbabababaabbabababaaaabbbaaaaabbabaaabaaabaabaabaabbbaabbaaababaabbabbbaaababbbbbbaaaaaabbbaaaaabbaaabaababaaaabababaabbbbbababbabbabbbbbbaaabbabbabbabbbabbaaaaabbbbaaabbabbaabbabbbaaabaabaaaaaaabbbbbbaababbaabaabaaaaaaaabaabbbbaabbbbbabaabbbaabbabaabbaaaaaaaabaaaabaaabbbabbbaaaabbbbaaabbabbabbbbbaabbbbbbbababaabbbaaaaabaaabaabaabbbbaaaaabababbaaabababbabaabaabaabbaaaabbbabaabbbabbbbaababbabbbbbbabbaaabaaaaaabbabbaaabbbaabbabbabbaaababaabaabbabbaabaababbaabbabbabaaabbabababbbbaabaabababbaaaaaaabaabababaaababaabaaabaabbabaabbaaaaabaaabababaaaaaaaabbbbbbaaaababbbbbaabababbbbabbabaabbabbaaaaabbaabaaaaaaaaabbbbabbaabbaabbaabaaaaaaaaaabbbbbabbbaaaaababaabbabbaabaaabbbabbbabbababbabaababbbbaababbbbaabbbabbbbabaaabbbbaaabbbbbabbaaabaabbaababbababbaaabbbbbabbbabbaaaabbbbababaaababbbaababbbaabbbaabbaabbaabbbbbbbbabbbaabaaaaababaababaaaaabaaaaaaaabbbbabbbbbabaabbaaabaaaaabbaaaaaabababbbaaabbbbbbaabbaaabaabaaaababbabbbabbababbabbaabaabbbaabbabaaababbaabaabbbbbaaabbababbaaabbaaaaaabaaaaaaaaaaababaabbbbbbabaaaabbaabaabbbaabbbbaabbbaaababbbababaabaabbbbaabababbbaabbaaaababbbaaabaabbaaababaababbabbabaabaaabaaabbaaaabaaaabaababbabbbaaabaaaabbbbbbbaababbbbaaaaaaabbabaaaaabbbababbaaababbaaababbbababbabbbbbabbbaaabaabbbaaaabbbbaaaaabaabaabbbaabaaaaabbbaaabbaababbbbbbbabbbbabaaabbbbbbbbabbabbbbaaaabbaaabbabbbabababaabbbabaabaaababbbaabababaabbabaaaaabbaabbbabbaabaaabaabaaaabbababbbabaaaababaabbabbbbaabaaabababaabbbbbabbababaaaabbbabaababbbababaaabbbbbbbabbabbbbaabababaabaabbaaababaaabbaabbaaabaaaababbabababbaabaaaabbabaaaaaabbbaabbbaaababaababbabbbbabbbababaaaabbbbaabbbbaababbabababbbbbbbabbaabbbaaabbaabbbbabbaabbbabbaababbbabbaabbbabaababbabbababbbbabbbbbaaabababbaaaaaababababbababaabababbbbabbababbaaabbabbbabbabbaabbabbbbaaabbbaabaabaaabbbaabababbabaaaaababbabaaaaaabbabaaabaabababbbbabbbbaaaabaaabababbabbaabaaaaaaabbaabababaaaabbbbbbbabaabbaababaaaabbababbbabaaaabbbaabaabbbaabaaabbabaaabbbbabbabbbaabbbbaabbbbbbbbaaabbaabaaababaaababaabbaabbababaaaaabaaaaababaabbaaaabbbaababaaabbbbaabaabbbabbabbbbaaabaaaabbaaababbababbababbbbbbaabaabaaaababbbabbabaaabbbababbbbbaaababaaaaabbabaabaabababbabaaabbbabbbabbbbaaabbbbbbaaaaabaaaababbaabbbaaaaaabbababbbbbbbabbabbbbbabaabbabaababbabbaaaaaabaaaabaabbbaaabbbbaaaabbaaabaaaabbaabaaabbbabaababaabbbaaababaabaabbababaaabbbaabbbabbbaaabaabbbbbaabbbabaabaababbabbbaaaaaabaaaaaabbaabaabbbabbbbaaabbababbabaababbaaabaababaabaabbaaaababbbbbbbabbaababbbbbabbaabaaabbbabbbaaaaabbbababbaabbbabbbbaabbbbbbbababbbababbbbbaaabbbbabbaabbabaaababaaaabbbaababbabbabbbbaabaabaababaaababbababaababaaaabbbabbababbababbbbabbbabaabbaaaabbbbbbabbbaabbbbbbbbbbbaabbbabbbabbbbababbababbbbbaabbababaababbabaabaaababbababbaabaaaaaabaaabaabbbabbababbbabaaabbbabaababbbaabaaabbbaabbbbbbbbabbbabababababbbbbbaaabaaaabbaaababbbaabaaaabaababbbabbabaabababaaabaaabababababaaabbaaaaaababbaaaaababbbbaaaaabbbbabaaabaaaabbabaaabaabaabbbbbabbabaabbbbabaabbbababbbbababbaaabbabbaaaaabbbabaaabbbbbbabbabbbabbbaababbbabbabaaabbabbabbbaaaaaaabaabbbaaaababbbabbaabaababbabaaaaaaababbbbbbbbabbbaaaabbaaabaaabababababbaabbabbaaabbabaabbbaababbbbabaabaabbaabbbaabbbbbbaabbabababbbbbaabaaaabbbbaabbbbaabaaaabbaaabbbbaaababbbaabbbbabaabbbbaabbaabaabbbbbbbbbbbaabbbaabbaaaabbbbabbabaabaabbabababbabaabaaabbbbababbbbbbbabbaaaabababaaabbaabbababbbabbabaabaababbbbaabbbbbbaaaaababbbaaaaabbabbabbbabbbbaabbaababbbbaaaababbabaaabaabbaaaaaaaabbababaaaabbababbbbabaabbbbababbaaabaabaabbbbaaaaaabbbbaaaabbabbabaaabaabaabbbababaaababaaabbaaababaaababaabaaabbbaabaaaabbabaaaababaabbaabbaabbaababababbbaabaabbababababbbababbbaabbbbbababababababbaaaaabaaabbaabbabbabbbaaaabaaabaabaaaaaaabbbbabbababbbbbabbbbaaabbaabbbaabbbabbabbabbbabaabbababbaabbabbaaaabbabbaaaababaabababaabaabababbbbaabaabaabbbbababaabbbaaaaaabababbbbabbababbbbababaababaaaaabbaaaabaaaababbababbaaabbbabbaababababbbbbbbaabaabbbbaaaabbaabaaaaababaabbaabaaaaaaaaabbbabbbaaaaabababaaababbababbaabbbabbaaababbaabbabababaaabaaaaaaaaaaabbbaaabaaaaabbbaabaaabbababbbbbbabbabbaabbaabbaaaaaabaaaaaababbabbbaabbabbaabababaaabbaaabaabaababbbabbbabbbabbababbbbbbbbaabbbaaababbaabaabbbaabbababaabbbabbbaababababaabbbbbbabbbaaabaababbaabbaabbbbbbaaaaaabbabbaabababbaababaabaaabbbbabbaabbbaabbaaabbababbbbbbaababaababbbbbababaababaabababbaaabbabbbbaabbbaabbbbbbaabaabababaaababbbbbaaabaaaaabbabbbbaaaaaabababbbbbbbaabbbbbabbabbaaaaaaaaaaaaabbbaabbabbaabababbaaaaabbaaababaabbaabbaaaaaaabbaaabaaabbbbbaaabbababababaabaabbababbabbbbbabbabbabbbabbbbabbaaabbaaabbbaabababaaaaaabbbbbbabaaaaabbbbabbabbababbaabababaaabbabbabbbabbbbbbbabbbbbaaaaababababbabaaabaaaabbbababbaabbbaababaabbababbbbabbabbbbaaaaaaabbaabababbabbaabbabaabaaaaabbbaabaaabbbbbaababbbabbababbbabaaabbbbbaaabaabaabbaabaaaabbbababababbabaabbbbababbbbbaaaababbabbbbabaabbabbaabababaaabaabbababbaabbabbbaaaabbaaaabbbbbaabbbbbbabaaabbbaaaaaabbabaaaabbbbaaaaabaabbabbbbbabbbababbaabbabaabbaabaabaaabababaaaaabbbabbabaaaaabaabbaabbaaabbbabaaaabbbbbbaabbbbabbbbbbaaaabababaabbbbbbbabaaabbbababbbbaaabbbabbabaabbbababaaabaabaaaaabaaaabbbaabababaaabababbbbbbbbbabaabbbbabbaaabaaabaababaaaaabababbaaaabbaaabaaabbbbbabaaabbbbbaabbbbabbbbbabaabaababbaaaabbbabaaabbaabbabbbaaaabbbbababaabababaaabbabbaababbbababaaaaaabbbbbbaaabbabbabababbbbbbaaaabbaabbababaabababaaabaabaaaaababaaabababbaaabbbbbabbaaabbbbaaababaaabbbaabbbaaabbbaabbaabaabbabaaaaabbbaaaabaababaabaabbbabaaabbbaaabbbabbaabababbbbbbbbabbbbbabbbababaaaabbaabaaabbaabaabbaababbaaabaabbbaaaabbbaaaaaabbaabbabaabaabaaabbbbbabbaabbaaaaababaaaaabaaaababaabaaabbaabbaabbabaabababbbbbaaaabbbbbbaabbbaabbbabaabaaabbabbaaaabbbbbbbabbaaabbabaaababbaabbbbaabbababbaabbbbbbbabbbabbbbbaabbbaaabbbabbabababbabbbbbaaabaabbabaabbbaababababababbbbabbbabbabbababbabbaabbaababbbabaabbabaabaababaabbbaabbaabaababbbaabbabaabbaabbbabbabbaaaabaaabaabaaabbbbabbbaaaaababbabaabbabbabaabbbaaabababbabaaaabaabbaaaaababbaabbbaaabbaababbbabbaaababbbaaaabaaababaabaabbbabbaaaaabaaababbbbbbbababbabbababbbbbbaaaaaabbabbaaabbaabbaaabbbbababbabababaaabaaaababaabbbbaaabbbbaaaaabbabbbbabbabababbabbbbbaabbbbbbbababaababbabaabbabbbbbabaababaabaaaababbbbabaabbbabbaaabaabaabaaaabbabbabbabbabaabababbabbaabbaaabbbaaabaabbaaaaabbaabbaaabbbaaabbbaabaabababaaababbabbbaaabaaaabbbaaabaabaaabbbbaaaaaaababbabbbabbbbabbbabbababbbaaababbbabbbaabbabbbbbaaabbbbbabbabbabaababbbbabbbbbabbaaabaaaaaaaabababbbaaaaaabaababaaaabbabbbaaaaabbaababbaabbbbaaaabaababababbbabbbbababbbbbbabbaabbbababbbbababaababaaababaaaabaabbbbbbabababbbababbabbbababbaabbbbbaaaabaabbbaabbabbababaabbbaabababaabbabbaaabbabbaaaabaabbaababaaabbbaaabaabbbbabbaababbbaaaaabaaabbbbabaaabbaaaabbbabbbaababbbaabbbabbbabbbababbaaabbabbbabbbaaabbaaaaababbbbbaabaaabbaaaaabbaaaabaabbbaaabbababababaaabbababababbaaaabbaaabbbbaabbbabbaaaababbbaaaababaaaabbaaabaababbaabbaaaabbbaabbbabbaaabaabbbabbbbaababbbabaaababbbabaababbbabbbbabbbaabbabababaaaabbbbabbbbbbbaababaababbaabbaaabaaabbbababbbaabbaaaaabbaaabbaaaaaaabaabaabaababbbbbbaababaaaababbbbbaaaabbbbbbbbabbbaabbbbbabbbabaaabbbbbbababaabbaabbbabbaaaabaabbaabbbaababbbbbababbababbaaabbaaaabbbbbbbabaababaaaabbbbbaaabbbbbaabbaabbababaaaaabbbbbbbaaabbaabaabbaabbabbbaabaabaabbaabbabaabbaabaaabbbbabaaaaaabbabaaaaababbbbababaabbbbabbabbbabbbabaabbbabbabaaaabbbbbababaabbbababbbbaaabbaabbaaabbbbabbaabaaabbabbbaaaaabaaaaabbbbabbbaabbbababbbbbabbbaaaabbbaaaabbaabaaabaaabaabbabaabbbaabbbaabaaabbbbaabbaabbbbbbabababbabbaaabbbbaabbbabbaababbbabbaabbaaaababbbababaabbbbbbabbbababaabbbbbabaabaaabbaaaabbbaabaabbbababbbaaaaabbbaabbabababbaababaaaababbbbababaabaaaabbbbbaaaaababaabaababbabbbababaabbaaabbbbaababbababaabbaaabbaabbbaaabaabbaaaabbbaaabbabaaabbbababaaaaabaaaabaaabbbaaaaabaabbaaaabbaaaaaaabbbaaabbaabaaaaababbbabbbbbbaaaababbbbabbaaabaabbaabbaababababaaaabbabbbaaaaaabaabaaababbbbababaaabababbaaabbbbabababbaaabaabbabbaabbaabbaabaabbaabaaabbaabbbaaabbbbbabbaabaaaabbaababbbbbbaaababababbaabbbabbbaabaaaaabbaababbbaaaabaaabbbabaaababaabbbbaaaaababababbaaababbabbbbabaaabbbaaaababaaabbaabbbabaaabaaabaabaabaaaaaabaaabbaaabaabaababbbabbabaaaaabababaaaaaaaaaababbbbbaaaaabbbaabbbbaaaaabbaabaaaabaaaababababbabababababbbabbbabbbaabbabbbaabbabbaababbbbbbbbbbbbaabbabaabbbbaabbabbabaaababbbaababbabbbbbaabaaabababaabaaaaabaabbaababbaabaababababbaaabbabbbaabbbaaabbbabbababaaabaaaaabaabbbbabbbaabaaabbbbaaaabbaaabaabaaaaaabaaababbaabbabbabbababbaaabbbbbbbbbabaaaabbabbbbaabbabbababababbaaaaaaabbaaabaaabbbabaaabaabbaaabbbaaabbabbbaababaabbbaaaaaababbaabaaaaaabaabbbaaababbabbaabbbbabbaabbbbabaaabaaabaaaaababaababbbbabaababbabaaababbbbaaabbbabbabbababaaabbabaabbbaabbbabaabaaaabbbabaaabbbabbbbaaaaabbbbbabaaaaaabbabbaaaaaabababbabbbbaabbaaabbbaaabbbbbbabababbbbaabababaaabaabaabaaabbbabaaabbabbbaaaaabababbbabaaaaaaaaaaaaaaababbbbbaabbbaabbabbbbabaabaaabbbaaaabbbbbabbaaaababaabaabbabbaabbabbbababaababaaaabaaabbbbbbabbabaaababaabbabbbbabaabbaabbaaabbaabaaabaabbbbaabaaaabbbbbbaabbbbaaababaaabbbbaaabaaaaabaabbbaabbaaababbabbabaabbbabaabbabbababbabababaabbaaaaaaabababaaaabbbabaaaaaaabbbababaaaaabaaaaabababbabbabbbabaaaabbbbabababbbbaaaabbbaaaababaaabbabbbabbabbbababbbaabababaababbbabbbbababbbaabbaaaaaabbaaaabaaaabbababaabaabaabbabbbaaaabbbbbbbbaabbabaaabaabaaaaabbabaaaabaababaabababaaaabbbabaabaaabaaaaabbaaabababababbaabaabbbbbabaaababbbaaaaabbaaaabbbabbbbbaabbbbaaabaababaababbbbabbbbbaabababaabbaabbbbbbabaaaaaaababbbbbabaaababbaababaaaaaabaaaaaabaababbbbbaaababaabbababaaababababbbaaaaaaabaabaababbbbabbbbabaababbabbbabaaabbabbbababaaaaaabbbbaabbbbbababababbaabababbabbababbabababbabaaaaaabaaaaaabaaabbbabbbabbaaabbbaaaababbabbaaabbaabaababbabaaaabbbaaabbaaaaabbbaaaabbabbaabaabababbbbbabbaaababaabaabbbabbbaaaaabababbaaaaaababaabababbaabbbabababbbaabbabbbbbbbabbabababbbbbbaaaababbbabaaabbbaaabaaabaaababbaaaababbbbaabbbababbbbabaabbbabbabbaabbbaaabababaaababababaabaaababbababaaaaabbabbbaabaabbbbbabaaaabbaaaaaabaaabbabaaabbbbaabbbaabaababbabbbabaababbbbabaabbbbbbabaababbbbbaaaabaaababaaaaabaabbbaaaababaaabaaabbbbbabbbaabbaaabbbbbaaaabbaabbbbbaabbaababbbbaaababaaabbbbaaaabbbaabababbbbaabbabaababbbaaababaabbaaababbbbabbaabbabbbaaaabaaabbabbababaabaaabbbbbbaabbaaababbbaaabaabbbabbbbabbabaabbbbabaababbbaaaababaaaaabbbbbabaaaababaabbbaababaaabbaaaaababbbbabbaabababbbbbbaaaaababbbbababaabbbabbabbbabaababbbaaababbbabababaabbababbabbbaaabbbbbaaabbabbbaaaabaaababbbaababaabbbabaabaaabaabbbbbabbbbbbabbababbbbbaababaaabbaabbabbbabbaabaabbabaaabaabaaababbbaaabbbabaaabbbbababbabbbbbababbaaabbababaaabaaabaabbabbabbbabaabbbaaabbaabbaaababaaabaaaabbaabbaaaabbaaabaabbbbabbabbbabaaabaaaabaaaaabaabbaabaabababbbaabbbabbaabaaaaabbaaaababaababbabaabbabbabbaaabbaaabbbabaabaaaabbbbbaabbbababaabaabbbbaabababbbbbababbaabaabbbabbababaaaaabaabaabbaabbaabbaabaabaaabbabababbaabbabbbbabbaaababaaabaabbaabababaaabababbaaaababbaaaabababababbbabbaaababaaabbabbaaaaabbaaabbbabaaaabaaabbabbbaaaabaaaaaaabbbbbababaaaaaababbbbababbababbbabababbbbbbabaaaabababbababbaababaaabbaabaaaabbbbbbabaababaababbabababbaaabbbabaabaaabaabaaabaabababaaaabbbababbababbaaaaaababbaaaaaabbabbbbbabbabaaaabababbaaaaaabbbaabbaabbbbbaabbbaaabbbbaaabbbbabbaabaaaaaabbbabbabaaaabbbbbbababbaaabbabbaabaaaabaaaaaababbababbaabbbbaaaaaabaaaaabbbbbbabaaabbaabbabababbbaaaaabaaaabbbaabbbbaaaabbabaabbababbabbaababaaabbaaababbbabbbbabbabaabaabababbbbbabaaabaabaababbbbabbbaaabaabbbbbaabbbabbbbbabbaaabababbaabaaaaaabbaabababbbbaaaabaaababaaabaaababbbababbaaabbabaaaababaaabbabaaababbbbaaaaabbaabaabbbbaabaaabbaabbababbbbbaaabbaaaabababbaabbbaababbbbaabbababaababbababbbaaaaaabaaaabaaaabaaabbaababbbabbbababbaaaababbabbbabaabbbabbbaaabbaaabaaaabbaabbbabaaaababaababbabbabbbbaaaabababaaababbbabaaabaabbbbbabbbaabaabababaaababababbbbaabbabbbabaabbbbabababbabbabaabbabaabbabababbaaabaabaababbbbaaaabbabbbaaabbbbbbabbaaabaabaabbbbbaaaabbbbabaabbaabbaaabbaaaababbabaabaabbbaabababbbabbaaaaabbaababbbbbabaabaabaaaabbbaaaababbbbabbaaabbbaabbaaaaabbbaaababbaaaabbbababaaabbaaabababbabaaaaabaabbabababababaaabbbbaaaabbaabaabbabbbbbabbabbbbbbbaaaaabbbbbabaaabbbabbbbbababaaaabbabbbbbbaabbbababbbbbbabbbbbbaabbbaaabbbabaaaaaaaaabbabaaaaabbbababbabaaaabbababbbaaabababababaabbbaaaaaaabaabaaabababbabbabbbabbbbaabbbaabbbaaaababbbbbabbaaaaaaabbabbabbbbabbaabbaabaaaaaababababbaababaabbabbababaaaabbbaaabbabaaaaabababaababbbbabbbabaaababababaabaabbbbaaaaabbaabaababbabbabbabaabbbaabaabbabbaaaabbaabbbaaababaabaabaaaaabbabaabbaababbbaabbabbaabbaaaabaaaabababaaaababaabbbbbabbaaabbaaaaababbaabaababaaabbbbaabaaaababbbabbababababaaabaababababaabaababbabbbabbaaabbbbbaabbaabbbabaababbaabbaabaaababbbaaabaaabbaaaaababbbbabbabbaabaabaaaaaaaababbaabbaabbbbaabbabbaababaababbbabaaabbbaaabaaaaabbbbbabbbabaaababaaaabbaaaabbaabaaababaaabbabbabbbbaabbbabbbabaabbbabbaaaaaabbabaabaabbbababbaabbabbaaaaabababababaaaabbababaabbabbabbbaababababbabbababaabababbaabbababaababbbbabbbabbbabbbbbbbbaabbaaabaaaaaabaababaaabbbaabbbbbbbbaababbbbaaabbaababaaaaabbaabaaabbabbabaaabbaabbabbabbbbababbbabbbbbbbaaababaaabbabbabbaababbaabaaabbbbbbbbbaaababbbbbbbaabaabbbbbbabbbbbbbaaaaabbbaaababababaaaaaaabbabbbabbaaaababbabbbbbaaababbbbabbbabaabbaaabaababbababbbbbabbbabbbaaaaaabaaabbabbaabbbbbaabaaaaaaaabbaaaaaabbbaaaabbbbaabbaaaaaaaaabbbaaaabbbbaaabbbaaaaabbabbbababbbabbbabbaaabbbbbbaaaabbabbbaaabbaababbbaabbbbbaabbabbababbababbaababaaababbbbaabbabbbbaabaaaababbbaaabbbabaaababababbbabaaaaaababbababbbbababababababaaabaaaaaababbbbabababababbbaaaabaabbaaaabbbabbbaabbababbaabbaabbbaabbbabbbbbaabbbbabaabaaaabbbbbbaabbbabbabbbababbbabbabbabaabaaaaaaaabbbaabbabaaaabbbbbbababbaabbabbababababbbaaaabbbaaaabaabbbaababaaabbbbaaabbbababbababbbbaaabbababbababaabbaaabbababbababbbabbbbbbbabaababbbaaababaaabbbabbabaaabaabbabaabbbaaabbaaabaababbabbbaaabbbaababaabbbbbaababaabaabaaababaabbbabbbbabbbaabbaaabbaaabbaaabababaababbaaaaaabaabbababbabaaaabaabaaaaabbbbbaababbaaabbbabaabbabababaaaaabbbaaabbbabbabbaaaabbabbababaabbbbbbbbababbbaababbaabbbabbabbbabbaabaaababbaabbbbaaabbbbbabbbaaabaababbaaabbbaabaaaabaabbabbababbbbbbbabbbbabbbbaababaabaaaaaaababbbaabaaaaabababaababaabbaaabbbabbbabababaaaabbabaabaaabaabaababbaababbbaaaaaabaabaababaaabaaabbbabbbabababaaabbaaabaaabbaaabbaabababbbabaababbbaaaabbabbbbaabaabaabbaaaaaabaaabbbbaabaaababaaaaaabbbababbbaaaaabaaababbbabbbabbaabaabaaaaabaabbbaaaaaaabababaaabababbabbbbabaabababbbbbbbabababbabbabbababaabbabbabbaababaaaaabbbbbbbbaaaabaabababbaabbbbbaaaabaababbaabbabbaababbbbbaaabaaaaaaaabbaabbbbbabbabbbaaababbbabaaabbaaaabaaaaabbabaaaaaabbbbaabaaababbabbaaaabbbbbbaaabbbbabababbbaabbbabaaabbaababbbbababaabbbabbaaaabbabbabbaaabbbaaaabaabbbbababbbababaabbabbaaaaabbaabaababbabaababbaaaabbbbbbbbaabaababbbbaabbbbaaabaaabbbaabbbaaababababbabaabababaaaabbbabbabaaabaabbbbaaabbbaabbaabaabbbaabaabababbabbabbaaabbaaabaaaababaaaaababaaabbbbaabbaabaabaaabbbbbbaabbbabbbaabbbbbabbbbbabbaabaaabbaabbbbbabaababbababbabbbbbbbaabababbaaabbbbaaaabaabbaababbaaaabbbabbabbabbaaaababbabababaabbbbbbabbbbabaabbaaaabbaaaabbbbbbbabaababbabbbbbaabbbaabaabaabbabaaabbbabaababbabbbbabbaabbbaaababbabbaaaabbbbabaababaaabbabbbabaabbaaabaaababaabbbbbababbbaaaaaabbbaababaabaabbbababaaaabbbbbbabbbaaaabbbbbaabbabbbaaaabaababababbabaaaabbbababaaaababbababbbabaaabaaababababababbbaabbbaabaaaabaabaabaaabbbaababaaaabbbaabbbbaaabbaaaabbabaaabbabbbabbaaabaaababbaaaabbbbbababaababaabbabbbbabaababaabbbababbabababbbbbbabbabbababbbaabbbababbaaabbaabaabbaaaaaabbbaaababaaabaaaababaabbaabbaaabbaabbaaaabaabaaaaaababbbbbbaaabaaaaabaabbbaababbbababbabbbbbabbbbaaaabbbbaabbbbaabbbaabbabbabbbbbbaabaababaabbbbabbaaaabaababaaabbaaaabbbabbbbaaaabbbaababaaaabbabaabaaaaaaabbababbababbaabbbbbababbaabaabaabbbbbbaaabbbabaaabaabababbaaaaabaabbabbbbabbbbabbababaaabbababbabbaabbaabbabbabbbaaabbbabbbbbabbabbbbbbaaabbbabaabaaababbbbbbabbabbbbabaabbaabaabbababaaaaaaaabbaaabaaababaabbaabaabbbbabbbababbaaabaaabbaabbababbbaaabababbbbbbbaaaababbabaaabaaaaababaaabbababaaaaaaabaababbaabbabaabbabbaabaaabbaaabaabbabbbabaababaaaaaaabbbaaabbbbbbbbbbaabbaababaaaabaaaabababbbbbaaababbbbbbabaabbabaaabaababbbabbbabaaaabbbbaaabbabbaaababaabaabaaaaabaabbbbbbbbabbaabbabaabaabaababbabaababbaaabbbaabaaaaabbaabbaabbababbabaababaababaaaababaabbababbbbbaaababbaababbabbababbaababbbababaaaabababaaaabababaaaabbaabbababbabbaabaabbbabbabbaaaabbaaaaabaababaaabbaababaabbbabbbbabaaabbbbabaaaaabbaabbaaabbabaaabbaaabbbbabbabaabbabababbbbbaaaabbbaaaabbaabbababbaabababbbbabbabbabbaabaaaabaabaaabaabbbbababbbbbaabababbbabaaabbabbbababbaaababbaaabbaabaabbbbbbaaaaaaaaaabaaaaababaaabbbabaaabaababaabaabababbbbabbababaaaaabaaabbbbbbabbbaaabbabaaababbbabaabbabbbaabbabbabbababbbbaababbabbbabbaabbbabbaaaabbaaaababbabbabbbaabababbbbabbbbbbabaaabaaabbbaababbbbbaaaabaabbbbaaabaaaababbabbabbbbababbaabbbabbbaaaabaaabaaaaaaabbaabbabbbbaabaabbabababbbabbbabaaaabbabababababbbaaabbbababbbbbbbabababababbaaabaababbaabaabbababbbababbbabbaababaabbbbabaaababbaaabbaabababbbbbabababaabbabaabaabbaabbbaabaaabbbabaaaabbabbbaaaaabbabaabbaaabbaaaabaabababbbaaababaaabbabbaaabaaababaaabbbabbaaaaaabaabaaabbababbbaababbaabbbabbaabbbabaabbaabbbbbbabbbababaaabbbaaabaababbbbbaabaaabaaaabbbbaabbbbabababbbbabababababbaabbabbbbababbbbabbababaaabababbbbbaaaaaababbaaaababaabaabababbbaaabbaaabbaaaabbaababbaabbaabbbaaababaabbbaabaaabbabbababaaababaababbababbaabbbbabbbbbaababaabaaaaaaaaaaababbbbbbbaabbaabaabbaabbaabbaaabbababbabbabbaaaabbbbbbbababaabbbabaababbbbbaaaabababbbbbbbabaaabbababaaaabaaaaabaababaaaabbbbabbbbaaabababbbbabaaabaabbbabaababbbabaabbababbabababbbaaaabaababaaaaababaaabbbbbbaabbbaaaaabaaaabababaabaabaaaaaababbbbbaabbaabbbaabbbaaaabbbaabbbbababbaaaaaaaababbababaaaabbaaabbabababbbbabbbababbaabaabbbabbbabbbaaabbaaaabaabaaaabbbbbbabbaabbbabababaaaaaabbbbbaaaababbbbaaaabbaaabbbbaaabaaaababbbbabaaaaababaaabaabbabaaabaaabaabbabbbbbaabbababaaaababbbbbaabbabaabbababaaabbbabababbbaaabbabaababbaabaababaaabbababaaaaababaaabbabaabbaaaaaababbbababaaababaaaabbbbbbbbbbbbaabbbbbaabbabbabaaabababaaaaabaaaabbbababaaaabbbbbaabbbbbabbbbbbbabbaababaabbaabbbaabbabaaabbbabbbaabbaaabbbbbabbbabbbabbbbaabbabbaaabbbabbaaabbbaabbbababbbbbaaababaaabbbaababbabbaabaabaababbaaabbbbbbabbbaabaababbbbbaabaaaaaaabbabaabbbaaaababbaabbaaabababbaaaaaaababaaababaaabaaabbbaabbabbaabbaabaaaabbbaabbaabbbabababbaabbbaaabbbaabaaaabbbaaaaaabaabaaaabaabaabbbbaabbbaaaaaabaabbabaaaabaaababababaaaaabababbabbbaaaaaaaaababbbaaaabbaaabaabaaabbbaababbbabbabaabbaaaaabbabbbbbabbbabaabbbbabbbbabababbbabaabbabbbabababbbbbaabbbbabbbabababbaabbaaabababbaabaaabbaabbaaabbbababbbaabbbabbabbbbbbaaaabbbbababbbabaaababbbbbbaababaaaabbaabbaaaabbabbbabbabbbbbaabaabababaabbaaaabbbbaabababbbbbaabbbaaaaaabbabbbaabbabababbbbbbbbbaabaabababbaabaabaabaaabbbbabbbaabaabaabbababbaabbbaabbbaaaaaaaabaabbabaabbaabbabbbaabbbbbbbbaabbbbbbabbaabbabbabbbbaabaababaaaabbaaaababbaabaabbbaabababbaaababbbbabbbbbaababaaaabaaabbbbbbbbabaabbabaabaabbabbbaaabaabaaaabaabaabaaabbbabaaabbbabbbbbbaaaabaababbabaaaabbaabbabbbabbababaababbbabbaaaaaaaabbaabbbaabbbbabbbbabbbbbabaabbbbabaaababbabbbaaaabaabababbabbbaabbbaabaaabaabbabbabaaaababaaabaabbbaabbbabbaababbaababaaabaaaabaabaabaababaabaaaaababaaabbbbaaaabbbbabaaabbbaaaabbaabbbbbbababaabaabbbbbbbbabaaaabbbbaaaaabbbabaababbabbbbaaaabaabaaaababababaaaaaabbbbaaabbaaabbbbabbaaabbabababbbbababbbaabbbbbbbaaababbaaababbabaaaaabbabbbaaaabbabbbbabbbabbbbabbbabbbabaababbaababababbbaaaaaaabbbbbbbabaaaabaabbabaabaabababaabaabaaabbbabaaaaaabaaabaabbabaaababaababbbabaaaaabaaabbaabababbaaaaabbababaabbaabbabaabbaaabbaabbaabbbbbbbbaaababaaaaaabbaabababbaababbaabaaababaaaaababaaababbbabbbaaaaaababbbbabaababbbaabbbbbbabbbbbaabbabbaaaabababbbbbbbaaabbbaaaaabaaaababbbabaabaabbbabaabbbaabbbbbbaabbaababbaabaaaaaababaabbbabaaabbbbbbabbbabbabbbbbbbaaabbababaaabbbbbabaabbababaaaaaaabbbaababbaaabaaabaabbbaaaaaabbababbbbbaabbaabaabbbaabababbbbbbbabaabbbbabbbbbabbbbabaabbababbbbbabbaababbbabbbbbabbbaababbbabbaaabbbbaaabbabbbbaabbbbbbababaaaaaabbabbbaaabbaaababaaaaaaaaaaabbbababbaaabbbababaaaabbabbabbaabbabbbbbbbbaaababbabbbbabaabbaabababbbbbbaabaabbbababaabbbbbabbabbabbaaaabbabbabaabbbbbbbbaabbaabbbbbaabababbbbabbaaaaabababbbaaaaaaaaabaaabaabaaabaabaababaaaabaabbabbaaabbbaababbbaaaaababbababbaaabbaaababababbabaababaaaaabbbaabbabaaabababbbaabbbbaaabababbaabaaaaabbbababaababaaaaabbaabbbaabbababbaabaababaaabbaabaabaabbaabaabaaaabbbbabbbaabaabbbabbabbbbaabbbbbbaaaababaababaabbbbbbbaaabbabbaabbbbababbaaababbbbabbbbaabbaabbbbaaabbaabbabbabaabaabaababbabbbaaababbbabaabbaababababaaabbbaabbbababbaaaabababbbabbaabbaabaabbbaaaaabbaaababbabbbbaaabbababbbbaabbaaabbaaaaabbaaabbaaaabbbbbbabaaaabbbbbaaabaabbabaabaaabababababaaaaaabbbabbbbbbbaaabaabbababbbbaaabbbbbababbbabaaaaabbabbaaabbabaaababbbaaabbaaaaabbbaaaaaabbaaaabaabaaabbbbbaaaabbbaaaababbbbabbbbaabbabaabaababaabbbabbaaaabbbbbbbaaabbaababbbababaaaaabaababbbbaabbababaababbbbbabbaaabaabaabbbaaabababbabbabbbbabababbbabbabbabbababbbbaaaabbaaabaaabbbbbabbbaaaabbababaabbaabaaaabbabbaaabababaabbbaaabbaaababbabaabbababaaabaaaaaabbbaaaabbaabbbbbabaaaaaaaabbbbbbbaababbbbaabbabbababbabbbaaabababaababaabaaaabbbaabaaabababbbaaaabbabaababbabaabbbababbbaabaabbbbababbbbbabaaaabababbbbaaaaabbbaabaabababbabbbaaababbabbbbbbabbbaaababaabbbabbbabbaaaababaabbbababbbbaabbbaaaaabaaaaababaaabaabbbbbbbbabbabbbbbbbbbabababbbaaabbbbabbbaabbbbbbababbbbbaabbbbbbbaaabaaababbbabbbabbaaabbaaaaaababaaaabbabbabbabbbabbaaababbaaababaaabbbaaaaabbbbbbabbaaabbbbbbababbbbbaaaaabbbabaaabbaaaabbaaaaababaaaaabbbabbabbaaaabaabbaabbaabbbbabbbaaabaaaabaabbababbbbaabbababbbaaabaabaaaaaaaaababbaabbbaaababbaabbbabaaaaaaabbaaabbaabaabbabababaaaabaaaaaaabbaaababbbbababaaaabaababbaaabaaabababbbbbbbbbbaaabbabbababbbabbbaabbabababaaabbaabbabaabbbbbabaabbababbababbbabbabaaaaababbaabbabbbaabbbababbaaabaabbbbbbbbbbaaaaababbabbbabbbababbabbbbaaaaaaabbbbbbabbbbbbbbbaababaaaabbbaababaabbbbbbbbbbbbbbabbabaaabbbbaabbbababbaabbabbbaaababbabaabbaababbbbabbaabababbaababbaabbbbabbaaaabbbbbbbbaabbbbaabbbabbabaaaabbabbbbbaabaabaabbbabaababbabaabaaaabbbabaaabbabaababbbbaaaabaabbbaaaabbaabbababbbabbabaababbbababbbaababbabababbabaaaabbabbbaabaabbbbaabbabbababaaabbbbbaaaababaabbbbabbbbababaaabbaaaaabaaabbaaabaabaaaaaaaabaaaabababbaabbbbbbbbbabaabaaaabababaaaaaaaaababbabbbabbaabbaabbbabbbabaababbbabbbaaaabbbaaababaaaabababaaabbabaababaaababbbbbaabbbaaabbaaaabbbaababbaaabbabbbababbbabbabaabbbaabaaaaabbbaaabbbbbbbaabbbbababbaaabbababababbbbaaabaaabbbbabbabbababababaabaaaaabbaaaabbbbbbbaabbaaaaaaaabaababbabbbaaaababbbbbbbabaaabbbbbaabaaaabbababbabbbabbaababababaaabbaaabbbbbababbbbabbababbabbabbaaababbaaaaaaaaaaaaabbabbabbabbbabbbbbababbaaaabbaabbbaaaabaaabbbbbbbbababaabbbbabaabbaaabbababaabaaabbbabbbbbbbbbbaaababaaaabbabaaaaaababbbbbabbabaabbbbaaabbaabbabbaabaabaaabbababbaaaaaaaabababbaaabaaabbbbbbbbbababaaabbaabaaaaabbabbbbabbabaabbbbabbbabbaabbaaabaabaaabbbbbabbaaababbbbaaabaaaabbbaaaaabbabbbabaaaabaabbbbabaaababaaababbaaaaabbbbbabaaabbbbbabbbbaaabbbabababaaaaaabababbaaabbabaabbbaaabaabaabbababaaabaabaaaaabbabaababaaaabbbbbabbabaababababaaababbabbabaabbaababbbaabaababaaaababbaabbabbabbbaabbabaaaaaaabbaabbbbabbbabaaabbabbbbbaaabaaaababbbabbaaaababaaaaaabaaabbbabbbbbabbbabbaaaababbbaabbabbbbababbbbbabbbbbbaaaaaabaaababaabbabbbbabaaababaabababbbabaababbaabbababbaabbbbababbaabbaaababbabaababbabaaababaabbbbbbbabaabababbbaababbbbababbbabbabaaaabbabaaaabbbaabaaabbbbabbaaabbaabbbbbbbaaabbaaaaabbbabbbbbaaabbaaabbabbababbaabbabaaabbbbbbbbbabaabbaababbbbbababaababbabbababaaaaaababbbbbaaabaaabbaababaaabaabbaababbbbaabaaabbaabbbaabbbbabababaaaabbbaaaabaabbbababaaabbbbbbbbaaabbababaaabbaaaabbabbbabaabaabbbbabbabbbaaabbababbabbabaaaabbbaaabaaaababbbbaabaabbabababbbbabbabbaaababbbababbaabbabbabbbaaababbaabbbbbababaaaababbababaabaabbbbabaabbbbbbaaaabbbbbabaaaabbabaabbbbabbbbbaabaabbaaaaaaaabbaaababababbabaabaaabbabbababaabbbbbbbbbabbbabbabbaabbbabbaabbbaaabaabaabbbbaabababbbaabbbaabbaabbaaabaaabbbbbabbbbaabaababaaaaaaabababaabaabbbbaaababbbabaaaaaababaaabbaabaaaaaabbbbbaabbbaaaaaabbbbabababbbabbbabaabbbaabbbbbbbbaaabbbbbaaabbabbbbbbbababbbabbbbbabbaaababbabbaabaaaaabbbbbbbbbbabbbbbaaaaaabbbbbabbaaaababbbaababaaabaabaaaaaaaabaaabaabbbaabbbbbbbaaabbbbaaaaabaaabbabaababababaaaaaaabbbbababaaaabaababaaabaaaabababaabbaaabaabbaabaabababaaabaaabbabbbbabbaaaabbbbbbaabbaabbbbbaaababaabaabbbabaabbaaaaaaababbabaabbbaaaaababababbbbbbbbbaababaabaaabbaabababaabbaaababbabbbaababbbbbbaaaabaaaaaaabbabbaabbbaabbbabbbbabbaabbbbabaabaaaaabababbbabbbabababaaabbaaaaabaaaaaabbbbaaaaaabbbbabbbabbbaababbaabbbbabaabbaaabaabbbaaabbbbbaababaabbabababbbabbabbbbbbabbaaaababaaabaaababbbbbbabbabbbbabbbaaabbbbbababaaabaababaaaabaabababaababbbbabbaabaabbaababbaaabbaababbaabbbbaabbbbabbaaaabababbbaabaabaaabbaaabaabbbabaaaabbaabaababaabbbababababbbbbbaaabaabbbaabbabbaabaaabbbabbbabbbabbbaabbaaabaaaababbaaabbbbaabbaaababbaababababbbbbbbbbaabaabbaaaaabbbbbabbbabaaaaaabbabbaaaaabbbaaabbaabbbbbbbbabbaabbabbaaababbbbbbaaaaabababababbbbbbabbaaaaaaaabaaaabaaabaaabaabbabbbabbbbbbababaababbbabababbbbababababbaaabbaababbabbaabaababaabbaaaabaaaaabbabbbaababaaabbbaabbabaaaaaabababaaabbbabbaabbababbbabaaabaaaaaabbaabaaabbabbbbbbbababbbbbbbbbaaabbbaaabbbbababababbbbbaaabababaaaaabbaaaabaabbaaaaaaababbbbabbababbabbabababaaabbababaababbababbbbabbaabaaaaaabbbabababbabaaabbaaaaabbabbabbbabbababababababbaaababbbbabaaaabbbbabbbabbaaaaabbabaabaaabbbaaaaaaababaaabbabbaaababaabaabbabbbabbbaaaaaaaaaabbbbbbaabaaaabaaabaaababbaaaaabaabbaaabaaabaaaaabaabbabaabbbabaaababbbaabbbbbaababbbabaabbbbabababbaababbbbababbbbbaababbbbababaaaaaaababaabaabaaabbaabbaabaaabbbababbbbbbbbaaabbbabbabaabababbabbaaabbabbbbaababbabababbbaaaabaabbababaababaaabbaaabbbbbabbbabaaaaababbbbabaabbbabbabbaaabbaaabaabaababaabbbbaaabaababbbbbbabbbaaabababbababbbaabaaababaababaabbaabbbbaabbbaabaababbaabbbaaaaabbbabbbaabbbbaaabbbaabbbaaaabbbbbababaababaaabbbbbbaaabbaabaababaabbaabbbaaaabbbbbabaaabbaabbabbbababbaaaaabaaababaabbbbaaaabbbabbbbbbbabaaaabaaabbbbaabbaaaababbaabbbabbabbbabbabbaaaababbaabbbbbaabaabababaabbabaaaaabbbababbbaaaabbaaaaabbbababbaabaababaaaaaabbbbaaaabaaaaaaaaaabbaabaaabbabbbabbaaabbabbaabbbbabbbaaabbabbaaaaaabbbabbabbbbabbaabbbbabaabbaaabbbbbababaaaabaabbaababbbaaabbaaaabbabaaababbabbbbbbaabababbaabbbbabbaaabaaababaabbabbaabaabbbabaaaaaababbababbabaaaaaaabbabbbbabababababbbbaabbaaababbaaaababbababaaabbababbbaabbaaaaaaabbbbaabbabbbbaabaaabbbaabbbbaaaabaabaaaababbaaabaabaaabaaaababbabbbbabaabbaaaaaabaabbabbabbababbbababbabaaaaabbaabbababbabaaabaababaaaaaabaabaabaabbababaaababaabbabbabbbbaaaababbbaaabbbababbabbbbabaabababaaabbbbbaabbabbabaaabaaaabbbbbbababaabbbbbaabaaaabbabaabaabbaabbbbbbaaaabbabaabbababbbbbaabbabbabbbabbbaaabbaabababaaaaabaaaaaabbbaaaabbbabbabbabbabbbbabbaaabaabbbaaabbbbaaabbbaababaababbaaaabbabaabaababaabbabaaaaaabbaaaaaaaaabbabaaaabbbbbababaabbaabbbbabaababbaabbbabbaabbabbbbbaabbbaabbabbbbbbabbbbababbbbbbbbaabbbabaaaaaaababaaabbaabbbbbaababbababbabaabbbbabbbbbbbbbbbbbaababbaaaabbbabbbbabbbbbbbaabaabbabaabbbaabbbaaaabbbbbabaaabababaaaabaaaaaabbaaaabbaaaaaabbabbaabaabaabbbbabbabbbabaaabbabbabbababbbabbbaabababbbbaabbaabbaaaaabbaaaaabaababbaaaaabbbbabaababbbbbbaabbabbbaaaabbbbbabbaaabaaaaaabbbbabaabaaaababbaababbabbbbbbbbbbabbbaabaaababbbbabaababbaabbbbaabaaabbaaabababbbabaaababaaaaabaaaaaabbbbbbbabbbbaaaabbbbaaababbabbbbaabaabaaaabaababbaaaaababbbabaaabbbabbbabaabbbabbabbabaabaaabaabbaaabbabbaabaaaaabbbbaabaaaaabaabaababababbabbabaaaabaababbbbbaaaabbaaaabbabbbbbabaaaaaabaababbababbbbbabaabaaababbabababaabababaaaabaabababbbbabbabaaabaababbaaaabbbabaabbaaabbbbbabbbaaabbbaaaaaabaabbabbaaababbbbbaabbaaabbbabbabaaaaabbbabbaabaaabbbbabaaaabaabbbaababbbbabaaaababbbaaaaaaaabaaaabbbbbbaaabaaabbaabababaaaabbababaabbabbaababbabbbaaaaabababbbbbbbabbbbaaaabbbaaaabbabaabaaaababbabbabaaaaabbabbaaaaabbabbbabababaabaababaabaabaaababaaabaaabbbbaaaababbbabbabaaaaaabbbbbbababbbbaaaabbbabbbaaabbbbabaabaaabaabbabaabbbbabaaababaaaabbabbaaabbabbababbbabbaaaaaaabbabababababbbabbabaaababaabbabbbababbbbabbbabbbaabbbaaaaababbbabbababaaaababbbbaaabbbabaaabaaabbbaaabaaaaabaabbaaabbbbabbabaabaababbaabaaabbbbabbabbaabbababbabbabbababbbabbabbbaaaaababababaaabaaaaabaaabbbaabaaaabababbaababaabaabaababbbbbbbbbaababaabaabbbbbbaabbabbbbbaaaabbaaaabbababbbabaaabaabbbbbaababaabaaabbbbabbbbabaabaaaaaabaaabbaabababbaaabaaaaaabbaaabbbbabaabababbbaaaaabaabbabbbaaabaaaaabbbbaaaabbbbbaabbbbaaaabbabbaaaababaabbbaabaaaaaabbbbaabbaabbbaaaabbbbaaabbbabbaaabaaabbabaababbbbbaaabababbbabababbabbbbabbbababbaabbabaaabbababaabbababaabbabbaababababbabbbabbbbbbbaaabbabbaabbabbbabaabbbaabbbbabbaaaabbbaaabbbbabbaabbbabbbbababbabbaaaabbbabbabaababbbbaabbaabaaabaabaaaaaaabbbbaaabaaaaabbbbbabaaababaaaabbababbbbaabaaaaabbababaaabaabababbabbaaabaabaaaaabaaaababaabaabaabbbbabaaabbaaaabaabaaaabbbaababbaababbaabbbabbbabbabbbababbbbbbabbbbababababbabbaaaabbaaaabbbbaabaabaaaababbaabbaabbaaabbbabaabbaababaabaaaaaabbabaabbbbbbabbbaaaabbabbbaaaaaabbabbbbabaabbbababbababababbabaababbbbbaaaaaaabaabbaababbaaaababaaabbbbbbbaabbaaabbbbababaabbbbabbbabaabbaabaaabbbbbbbabaaaabbbbbbaababbbbbbaabbbabbabbbaaabbaaaaabbababaabaabaababaabbabbbbbbbabbabbabbbabbaaababaabbaaaaaababaaabbbbbbbbabbaaaabaaababbabaaabbaabbbaaababbbababaaababaabbabbbaabaabbabbbbbbbbbabaabbaabaababbbbbabbabaaabaaabbbbaababaaabaaabbabbbaaabababbabbabbbababbaabbbbbbbaaabbababbbbaabbbbbbabababbbbbbabbabababbbbabbbaababaaaaababaaabaaaaabbaaaaababababbabbbbbabbaaabababbaabbbbabbaaaaabbaababaaabbaaabbbaabaabaaaababbbababbbabaaababbaababaaaabbabaaaababaabbaabbbbababaaabababaabaabbabbaaaabaaabaaaababbabaabbbbabbabababaaaaabaabbabaaabbbbabbabbbabaaababbabaabaabbbabbaabbabbabbabaabbbbbabbbbaabbabbbaabaabbabbabbbbabaababbbabbaabaaabaabbabababbbbbbbabbbbabaabaaaababbbabaabbbaaaaaaaaaaaaaaabbbaabaabaaabbabbabababbbbaaabaabbaaabaabbabbbbbaaabbbbaaabbbaaabaaabaaabbabbabaaaabaabbbabbabaaaabaabbbbaaaaaababababbbaaababbababbbaabbabbaabbababbabbabbabbababbbababbbaabaaaaaaabbaabbbaaabbbababbababaabbbbaababaabbaaabaaaaabbabaaabbbbaaaaabbaabbabbaabbbbabbabbbbbaaababbbbbbabaabbbabbbbbbbababbabbbaabaabbababbaaaaaaaaaabbbabbbbbbbabaabbaaaababbaaababaabababaaaabababbbbabababbbaaabbaaabbabbabbbbbaabbbaaababaabbaaaaaaabbaaaabbbbaabbbbbaabbbabbbaaabbaaaabbabaababbbbaaabbbbbbaabaabababaabbbabbbbababbababbbbabbaabbaaabaaababaaababbabbaaaababababaabbbbbbbaaaaabababbaabbaabaabbbbababaaabbbbbabbaaabbbbbabaabaabaabaababaabbbabaaaaaabbbabaababbbaaaabbaaaaabbbbabbabababaabaabbaabaabbbbaaaaaababbaaaaabaaaabaabaabaabbaaabababbbababbbababbaaabaabaaabaababbabaabbbabaaaababaabaaaaabbabbabbbaabaaabaaaababaabbabaabaaaaaaaaaabaaaaaabbaababaabbabaaabbbabaaaabbaababbbbbaaabbaabababbbaabbbbaaabaabbabaabaabababbaabbbbababbbabbaaaabbbaaaabaababbaababaaabaabbabaaaaaabaababaaababababbaabaabbaabbaaaababaabaaaaabbabaaaaaababababbaaaabbbbbaabbbaabbbbaaababaabaabbbbabbabaaaaabbaabbaabbabaaaaabbbabbbbabaababbbabbbbaababbbbbbabbbbaababbbabaaaaabbabababaabbabbaabbaaabababbabbaaabbbbaababaabbaaaabbbabaaabbbababaabbbaaaabbbbabaaaabbbaabbaababbbbaaaababaabababbaabaabbaaaababaabbbaabbaaabaabbabaabaabaabaababbaababbbbbaabbbbbabbabbbbbabaaabbbaaababbabbbaaabbbabaaaababbbbaabaaabbabbbbabbbabbabbabbbbaaaaababaaaaabaaabbabbababaaabbaaabbbbbaaabbbbbabbaaaabaabbabababbbabaaabaaaababbbbaabababaaaaabbbabbbababbbababbaaabbbaababbabbbaabaaababbbbaabbaaaaaabbbbaaabbaabbaabbbabbabbbabbbbbabbabbabbabaabaaaaaabababbabbbbbaaabbbbbaaabaaaaabbabbbabbabbabbaaaababaabbaabaabbaabbbbabaaaabaabaaaabaaaaabaaaaaaaabbaaabbbbbababaaabbabbbaaaabaabaaababababaabbbabbaabbabbabbaabaabaaabbabaaabaababbababaaaababbbaabbabaabaabbababaaaabaabaabababbbabbaabbbbbbaababbbabbbaaaabaabaaababaaabbbaaaaabaaaaaabbbaaabbbbabbbbaabbbaabbaaabaaaabaaaabbaaaabbabbaabbaaaabbbaabbabababbbaaababbbabaabbbaaaaaababaaabbaabbababaabbaabbabbbaabbabbabbababaaababbaabbaaabbabaaabbaababbabbbbbaabaabbbaaabaababbababbaabbaaaaabbbaababbbaaaaaaabbbabbaabaababaabbabbbbaaabbabaabbabbabababaaaaaaabababaaabaaaabaabbaabababbaabbaabbbaaaabbbbbbbababbbabbbbabbbabbaaabbaaabbbbaabbaaabbaaaabababbbbabbbbabbbaaaababaaaaaaabababbbbbaabaaababaaaaaaaaabaabbbbbbbbbaaaaaabbaaaabbbbaaaabaabaaabbaaaabaabbbaabbaabaabababaaaaabbbaabaabbbbbababaabaabbaaabaaaaababbabaaaabbbaaabbaaaabbabbbbabaabbbbbaabbbabaababbbbabaaaaaaabaaabbaaabbaaababbbaabaabbabaabbaaaaabbabbbaaaaaaaabaaaaaaabaaaaabbbaaababbbbaaababbbbbababaaababbbbbbbbaaaaaababbbabbbbaabbabbbabababaababbaaababbbbbabbabbaabaaaaaaababbaabbaaababbabbabaaabbbbbaababbbabababbbbababaaaabbbbaaabaaababababaaababbbababaaabbaabbaabaabaaabbbbbbbaaaaabbbababbbbbaababbbbbbabbbbabbababaaabaabaaaaabbbaaabbabbbbabbbbbbaababababbaaaaababaaaaaabaaababbbbbbbaaabbaaaaabaabbbbaabbbaabaaaababbbbabababaaabaaababaaaabbabbababaabaaaabbbbabaaaaaabababbabbbababbaababababbaaabaabaaaababaaaaaaaaabaaabbbbabbbaaabbaabbabbaabbabbbbbbbaaaabaabaabbbabaabbbbababbbababaaaabbbabbbbbbbaaaaabbaaabbbababbbaabbbabababaaaaaaaabaabbabbababbbbaabbbbbbbbbabaaaaabbbabbaabbabbaaabbbbbaaaaaaaaabaaaaaaababaabaaaabbbbbabbaaabaabbbababaaabbbabababaabbabaaabbbaaaaaaaaabbbaabbbbbbbaabababbbbaabbbbbbbbaabbababbaaabbbabbbbaabbabaaaaaabbaabababbaaaaaaaabbbaabaababaabbaabaaabbaaabaabbbababaaaabbabbbabbbaaaaaaaababbbbbababbbbabbaababbbabbabaabaaaabaababaaaababababababbbbabbaaabbabbbaabbaabaabaaababbbaaabbbabababaaaaababaabbaaababbbbabbbbbbaaaabbbbaabbbaabbaaabaababaabaaababbabaaabaaaabbaaaababaaabaabbaaabaaabaaaabbbbbabbabbbbbbabbaababbabaabaabaabbaaaaabbaaabbbbbbaabaaaaabbabababbbbaaaabbabaababbbbababaaaaaaaaabaabbbbbaabbbabbabbbbabbaaaabbbbabaabbbbbbabbabaabbaabbabbaaaabbaaabaabaabbaaabbaabbbababbbaaaaaabbabaababbbaabababbabbbbabbaabaabbabaabbabababaaabaaabaaabbabababbbabaaaaabbaaaaabaaabbabaababbababaabaabbabbabbbbabbabaababbabaaabbbbaaabbaaabaaababaaaababbbbbbaabababababaabaaababbaababbabbbbbaaaaabbbbbaabbbbaaaaaaaaaabbaabbbaaaabbbabaaabbbbaabaaabaaabaabbbbbabababbbbababbbbaabbbaaabaabbbabaababaabababaaababaabbbbbabbbaaabaaabaabaaaabaabbabbbbbaaabaaaaabbabbaaababbabaaabbababbbabbabbabbababbabbbabbabbababbbbbbaaabbabaaababaabaaabbbaabbbbaabbbbbabbabbabbbabbaaababaaabbaaaaabbbabaaabbbababbbbabbbbbbbbaaaabaaabaaaaaabaabaaabaabbbbbaaabbaaabbaabbbbbabbaabbaaaabaaabbaabbaaabbbbbbbabbabaaaabaabbbaaaaaabaabbabaabbaaabbababababaabbbbbbbaaaabaababbaaaaaaabbbbbaabbbbbbbaabaaabbaababbabaabbabbbaaaabbaabbbbbaaabaababbababbbaaaaaababbbabaaabbaabbbbbbababbabaaaaabbbbabababbabbbbaaaabbbbabaabaaaaaaabbbbbbaababaaabbbaaaabbabbbabaabaaabaababababbbbabbbababaabbaabbaababbbbbbabbbbaabbbbabbbabaaabaaaabbaaaabbbbaaaababbabaabaababaabaabbbbabbbbbabaaaaababababaabbabaaaaaabbbbbababaabbbabbaaaababbbbbabbbaabbaabbaaababbabaabaaaababbbaababaaabbbbbabbaaaabbabbaaabaabbbbbbabaabbaabbaabaabbaaaabbabaaaaabbbbbbbaabaabbababbbabbbaabaabaaaaababbabbabaabbbbbabaaabbabbbababbabbaaabababbaaabbbaaabaabaaababbbabaaaabbabbbaaababababbabbaabbabaaabbbababbabbaabbaabbbbbbbbbaaaabbbabbbaaabbbbbbaaabbaabaabaaaabaabaaabbabaababbaaabababaaaabaabbbababbababbabbaaaaaaaabababbbaabbaaaabbabbbabbbaabbaaabbbbabbababbaaaaaababababbababbaaaaabbbaaabbbbabbaaabaabaabaabbbaaabbaaaabaabaaabbbabbbbbbaabbabbbbaabbabbabbaabaaaaabbbaabaabbbaabaabbaaaaaaabaabbaaaabababbbbabbababababbbaabbbababaaabaaaaabaabbaabbbaaaaabbbbabbbbabaabbbaaaababbaaaababbbbaaaaaabaabaababaaababbabbbaabaaabbabaabbbaaaaabbabbababababaaaabaaabbbababbabaabbbbaabaababbaaaabbbaaabababbbabbbbbaaababaabaaabbbaababbaabababbbaaabaaabbbababbaaababbbaaaaaababaaaaaababbbaabbbbabbabbabbbaabbaabbbaababaababbaaabababaaaabbabbaaabbabbaabababababbaabababaabbabbabaaabaaaaabbaaabbbaaaababaabbabbbaabaababbbaaaaaaaaabaabbabababaaababbabaaabaaaabaaaababaaabaaabbbbbaabbbbbbababababbbababbabbbababbbabbaaabbaaababbbbaaaaaaabaabbaababaaaabaaabbbaabaaaabbbbaaabbabaabaabbababbabbaaaabbaaabbaababbabaaabbaababaaabbabaabbbbabbaaaaaaabaabbabbbabbbaaaababaaaaaaabbbbabababaabbaabbababaaaabbaababaababaabbabbaaaaaabaaabbbabaabaabbbabbabaaaabbababbbbaabbbaaaaaabaabaabbabaaaaaaaaabaaabbaaabaabaabbbbaabababababbaaaabaabaabbabbbbaaaabaabbabbbaabaabaaabbabbaaabababaaababaabbbaababbabaabaaabbbbaabababbbabaabaaabbaaaaabbbbbbbbaaabbbabaabababbabaaaaabababaaabaabaaabaabbbbabbbbaaaababababbbaaabbbababaabbabbbbabaabbabbaabbbbaaabaaaababababaaabbabababaabababbabbaabbbaabaaabbaaaaaaaaabaaaababbbbabababbaababbbbaaababaaaaaaabbbababbbbabaaaaabbaaabbabaaaaaabbaaabbabaabbaaaabbbabbbbbababaaabbabbbbabbbbbaaabaabaabbabaaabababbababbbbaabbbbbababbbbbbbbaaaaababaababaaabbaaaaabbbaaaaabbabaababaabbaabbbbaaabbbbabbbbbbabaabbabababbaaabaabbabbabbabaababaaabbbabbaabbaaaaaabbbabbabbbaaabbababbbbbbabbabaabbabbaaaabbaabbbaaaabbababaabbbbabaaabaabbbbaabaabaabbbbbaababbabaaabbbbabbbaabaababaabbabbbbbbbbabbbbabaabbbbaabbaabaabbbbaabaaaabaaababbabbabbbaabbabaaaaaabbaabbbbbabbbbaabaabbaabbbabbbaabababaababbaabbbabaabbabaaaaabbaaaabaabbaababbbaabbbaabaabbbabbbbbbbbabbbaaaaaaabbabbbababaabbaabbbabbbaabbbbbababbbbaabbbababaaaabbbbaabbaabaaaaaaabbaaaaaaaaaaabbbbbbaaaaaababbbbbabbbaabbbabbabbabaababbbbabbabaabaababbaaabaaaaabbabbaaaaabbbbbaababbbbaaaabaaaaaabaaaaaabaaaabbaaababbbabaabbbbbaababbaabaaabaababbbabbbabbbbbababbbabbbbbbbbbbaaaababbaaabbbaabaaababbabbbabbabaaaabbbaaaabbbbbbabaaaabbbbbaabbabbaababbbaaaaabaaaababaaaaabbbaaaabaaaabaaaababbabbbbbbaabbbbabaaabbababbaaaababaaaababbaabaaabababbbabaaaaabbaabaaabbabbbbaaabbbabbababaaaabbaabbbbbaabaaabaaababbaabbbaabaaaaaaababbabbbbbabaabbabbbbaaabbaabaabbbabbbbaaababbabbaabbbbbaaaababbbaabababbbaaabbbaabbabbabaabbbaaabbabbbabbabbbaaaabbabbaababababababbabbabaaabaaaaabbabaababbabbbabaaabbabbbabbabaaaabbaabaaaaababababbaaabbabaabbbaaaabbbaabbbabaaababbbbbabaaaabbbbbaabbbaaabbaaaaababbbbabababbabbbaabbaaaabbaaabbbbaaabbabbbaabbbababbbaaababbbbaaaabbbaabaaaaaababbbaabbbbaaabbbababaaaabaabbabaaabbabaabaaaaabaababbabababaaaaabaaabaabaabbababbabaaaaaabbaaaaaabbaaaabaaabbaaaabbaaaababaaaabbababbabaaaaaaabbbabababbbbbbabaabaaaababbbabbaabbbaabaaaaabbaaabababbaabbabaaababaabbaaabbaaaabaaaababaababbbabbbbbaaabaabaabbbaaaabbbbabaabbbbbbbabaaababbababbaaaabbbbabaabbaaaaabababbbbababbaabbaababbbabbaababbaabbaabababaaabaabbbaaaababbabbbaaabbbbaaaaababaabbaababaaababbabaaaabbaaabbaabaabaaabaabaabbaaaaaabbbbaabbaabbaababababbbbabaaaaaabbabbbaabaababaaaaababbbabbbbabaabbabaababbbbaaabbababbaaabbababbabbaaabaaabaaabbbbabaabbbaabaaabbabbabaaaaaabaababaabaaabaaabbaabbbbbaaabbbabbabaaabbbaabbaaaababaaabaabaaaabbaabbaabbabbababaababbabbaaababbaaaaaaaabbbbbbbabbbbaaaaabaabbbbababbaabaababaaababababbabbbbababaabbbbbabbabbabaabbbabbababbaababaabbabbaaabbbabababbbbbbaabaababababbaaabbbaabbabaababbaaaaabaaaabbaaaababbabbbbbbaaaaaababbabaabbbaabbaaabbbaababbabaaabbaabbabbaaaabbbaaabbbbbaabbbbbaaaaaabbabaaaabababbabbbabaabbaaaaabbbabbbaaabbaabbabbaabbaabbaaababbbabaaaabbaabbbaaabaabbbaaabbbbbbababbbababaaabbbababbbaabaaabababbbaaabaaabbbaabaaabaabbababaaaabbaabbbaababaaabbbabbabbbbabaaabbbbbbbaabbaaabaaabaaababaabaaabbaaaabaaabaaaaabbaabaaababaabaabbbaababbbababababaaabbbaababaabbabbababbbabaaaabbbbbabaaaaababbababbaabababaaabbaabababbabbaabaababaabaabaabbbbababaaaabbbbbbaaaaaabbbababbabbbabbbbbbababaabbaabaabaababaabbaabaabbbaabbabbbbbbbabbaaababaabaaabaababbbbbaaabbbbabbaaaaabbabababaabaaaabbaababaaaabaaababababaaabababaaaabaabbbabababaabbbbaaabbaababbbbbbbaaabbbaaaababbbabbababbbabbbababaaabaababbababbbbbbbbbabaaababaabbaaaababbabbbbabaabbbbbbbaaabbabbabbaababbbbaaababbbbaaabbbabbaaabaaaabbbbbbabaababbbaaaaaababbbaababbaaabbbbaabbababbaabbbaaabbaaaabbbbaabaaabbabababbababbbbbbbaaabaaaababaabaabbaabaaaaababbbbabbabbbaabaabaababaababbbabaaaabbbabbbabaabaaabbabbabbbaaaaaaabaabababababbbbbaaaabbaaabbabaaababbabbaabbaaabbaababbbbbbaaaababbabaaaabaaabababbaabbbbbaaaababaabbabbabbbaabbabababbbaabaabaaaabaaaabababbbaaabaabaaaabbaaabbababbaabbbbaaaaaaaaababaabaabaaabaabbbaababbaabaaaabaaaaabaabaababbbbbaabbbbababbbabbbbabbbbabababbaabaabaabaababbabbbaaaaaabbbbabaaabbaabbbbaaabbababababbabbbaaaabbbaabaaaabbbbbababababbbabaabaabbabaababababbaaabaabaaababaaabbbbbbaabababbbabaabbaaabbbbaababbabaabbabbaaababbbbbbababbbbababbbabbaababbabbabaabbbaabaabbabaabbbababaabbbababbbbbaaaababbaababaabbbababaababbababaaaaabaabbaaaaaaaababbbbbbaaaababaabbbabaaaabaaaabaabaabbbbababbbaaabbbaababbaabaabaaabbaaababbbabbaaaaabbabaabbbabbabbbaaabaabbbabbbbaabbababbabbbbabbaaaababbaabbabaabaaaaaaaabbaabaaabbbabbbabaaaabaabbabbabbbabbbaabbababaaababbbbabbabbbabbbabbbabbbaabbabbaaabbbabbbaaabababbaaaabababbbbabbaababaabbbbabbbbbbbbabbaaabbbbbabbaabbabbababbaaaaaaabaaaabbaaaabaabbabaabbaaaaabbaabbbaabbaababaaaabbaaabaaaabaaaaabaababbbaaabbabbbabaabababbaabbbaaabbbbbbbbaabbabbabbaabaabbaabbbbbabbabaaabbaabababaabbabbbabbbabababbaabababababaaabaababbbbbaaabbbaabbaaababaabababaabbaabaabbaabbbaaaaaaaaaababbaaaababaabbaabbbbbabbabbabbbaabababbbaaaabbaababaabaabaaabbabaaababaaabaabaaabaaaaabbbaaaaaabaabbbbbabbaaabaaabaabbbbabaaaaababbabbabbbaaaaaabbabaaabaaaaaaabaabbabbbbbbbbaabbbaabbbaaabbaaabbbbaababababaabbaaaaaabbbabababaaaababbbbaabbbbaabbaabaaababbabbbbbabbabbababbbabaabbabababbaaaaaaaaaaaaaabaaaabbbbabbbaaabaabbaaabbbbabbaababaaaabbaabaababbabbababababbbaabaababaaaabbbabbbbabbbaaababbbabababbabbababaabaababbbbbaabababbbababbaabaabbaabbabbbabbbaababababbbabababaaabbabbaabbaaabbaabbbaababbbbaabababbabaaaaaaabbbbabbaaaaaabbbaaaaabbbabbaabbbbbaaaaababbaabaababaabaabbbbbaabbbaabbabaaabbbabaabbaabbbaababbbabaabaaaaabaabbbabaabbabaabbabbbaaaaabbababbbabaaabbabbbbaababababbababbabbabbbbaaabaaabbbbababbaaaabbbbaabbbaababaaaaaabbbbabbbbabababaaabababbaabbabbbbaabaaababaabbaababbbaaaaabaaaabaababbbabababbbbabbaaaabaabbabababaaabaaaabbbababaabbbaabbbbbaaaabbaabbbbbababbbbababbbababaaaaabbbaaaabbbaabaaaabaabaaabaabbbbbabbbabaabaababaaaaaabababbaaabbbaaaaaababbaaaabbbababbaababbbbababaabbbaaaabababaabaabbbaaabbaaabbaababaaabbabbbbbabaabbbbbbaaaaaababbabbbaababbbbbbabaaaaabbbaabbabbabbaabbaababaaabaabababaabaaaabbbabbbbbabbbbaababaaaaaabbabaaabbababbaaaabbbbabababbbabaabbabbbaaaaabbbabbaaababbbbabababaabbbbbaabbabbbaabbbabbabbabaaaaaabbbaaaaabbbaaabbababaababbaaaaabaabababbbbbabbaaaaabababbbbbbabbbaaaaababbabbbabbaabbabbababaaaaababbabaababaaaaaabbbabababaababbbababaababbbabbabbababbaabbaaaababbbabbaabaaaabbaabbbaaaabbbbaaababbbaababbbabaaaaaabbbaabbbbabaaaabbaabbabbaaababbaaababbabbbbabbaaababaaaaababaabaaaaabbaaabbbbbbbbaabbbaabaaababaabaabbabbbabbbaabaaaaaaaaaabbbbbabaaabbbaaabbabbababbbaabbababaaabbbbbabaabbaaaaaabaaabaababaabbbbbbbbabbbaabbabaaaaabbbbbbababbababaabbbbaaabbbbbbbbbbabbbbaaabbbbababbbbbbaabbbbabababbbaabaabbabbaaababaaabaaabaababbaababaababaaababababaabbbbbbabbabaabaabbaabababbbabaabaabbbabbabbbaabbbaaabbabaabbbbababbbaababaababaaaaabbbbabaabbbbaaabaabbabaabababbabaabbabababbbabababbbaaabbabaaaabababababbaabbbabaabaabaababaaaaaabaaababbabbbaaabbbbbaaabaaabbbbbbaabbaababaaabaabaabbbabbaabaaaabaaabbbbbabababaaaabaabbbbbaaabaabbaaabaabbbaabbbbbaaababaaabbbbabbbabbaabbbbabbababbbbbaaaabbbbaabbbbbbabbbabbaababbbaabaaaabaaabbaaabaaabaababbabbbabbabababbabbabaaabbbbbbbbababbbaabbbbabababbbaabbbaaabbbababbbabaabbaaaababaababaabbbaabbabaaaaaabbabbabababaababbabaaabbbbbbaabbabaaabbaaabaabababaabaabaaabababbababbbbbbbaabbbabababaaaaababaabbbbbaababbbaaaababbbababbaaabaabbaabbbbabababbbbababaabbbbbababbbbaaabababbabbbabbbaabaabbabbabbbaaaabbabaabbabbbbbaaaaabababaaaaababbabababbbaabbbabbaaabbabbaaabbbbababbbbabbabbbaaabbabbabbabaaaababaababbbbbbbbbaaaaaaaabaaaaaaabbaaababbbaaaaabbbbbabbaaabaabbaabbabbbbaabbbabaababbbbaaaaabbabbabbaaabbaaaabaaabbbabbaaaabaabaaaaabaaaaabaabbbaaaaaabbaabaaaabaababaaaaaaabbbabababbbababbabababbbbabaabababbbbaaaabbbbbabbabaabbabaabaaaaaaaaaaaabaaabbabbabaaaabbaabbababaabbabaabbabaaababbaaabbabbbaabbbaaabbabaababbaabaaabbaabaaababbabbbbbaaaababbabbaaaabaaaabaabbabaabbaabbabbabaabbbaabaabaaaaaaababaaabbbbbbaaaaababaaabbabaaabaababbaababbbbbaaababbabababbaaaabbbaababbbbbabbaabbbaabbaaaabaabbbaaaabbaaabaaaaaabbbabbaabbbaaaaabbbabbbabbabaabbbabaabaabbababaaabbbbbbbbaaaaabbbaabbaaaaaaaaaababbaababaaaaaababbabbbababaaabbbbbaabbaabbbaabbbabbbbaababbbaaabbbbbabbbabbaabbbbabbaabbaabbbbaaaabbabbbbbaaabaaaaabbbabbabbbbbbababbaabababaaabaabbaaabbaaaababaabbbaaabbabbbbababaabbaabbabababaabbabbabaabaabaabbbaaababaabbbbbabaaabaababaabbbbaaaabbabbbabbaabababbbbabbaaabbabbabbbabaabaabababaaaabbababbababbababbaabaabaabbbbbbbaaaababbbabbbaaaaaabaabbaaabaabbababbbabaaaaabbabaaabbbbbbbbaaaaaaabbbaababbbabbbbbaaaaabbbbabbbbaaabbabbbabbaaabbabaaabaaaabbbbbaabaabbaabbabbbbabaaaababbbaababaaabaabaaaaababaaabbaabaaabaaaaabababbbbabbbaaabbbbababbaabaababbabbbabaabaabbabaaabaabbbaaabbbbaabababaaaabbaabbaaaabaaabbabbbabbabbbabaababbabbabbabbbabaaabbbabbbbaaabbbbbabbaaaaabaabbbbaabbbaaabbbbbbabababaabbabaaaababaabbabbabbabbaaabaabaababbbbabbabbaabaaaababbbaabbbbbbbbabbababaabaabbabbbaababbabbbbaaabbbabaababaabbaabbabbabbabbbbbbbabaabbbabbababbbbbbaaabaababbabbbaabbababbaaabbababbabaaabababaabbbaabbbabbbabbaabaabbbbbaaabababaaabaabbabaababbaaababbbabbabbabaaaaaabbbabbababbbaabbabbabbabbabaabaabbbabbbbbabaabbababaaabbaaababbbbbabbabbbbbbaabbbbbababbbbaaaaaaababbaaaaabbabbaabbaaababbbaabbbabbaabbabbaaaababbbababaabaaabbbbabbabbbabaaababbbababbaabaabbabaaaaaabaaaaaaabbaaabbbababbbaabbaaaaabbbbabbababbbabbabaabbaabbabaaabbbbaaaabbbbaabbbbbabbbbbabaaaabbaabaaaaabbbaabbababaababaaabaaabbaabaabbaabaabaababababbabaaaaabaaabbaaaaaabbaaabaaabaabaaaabbabbabbbbbbaaaabbbbbbbbaabbbabbbabaaabbbbaaababbababaabababababbababbbaabbaababbaaaaabbbaaaaaaaabbbababaabbaabaabbaabbabbababbbaaaaabbbaaaaaaabbbabbbaabaabbbbabaaaabbbbabbbbabbbaaababbbbbaabaaabababaabbbaaaabaababbbaabbabbaabaabbbababbababababaabababbabbbbbbaaabaaabbaaaaabaababbbbabbbababbaabbbabababbaabbbbbbaaabbabbbabbbabbabaabbabaabaaabbabbaabbbbbbabbbabababaabaaaaaaaaaabbbabaaaababbabbabbbbbaaaabaabbabbbbbbabbbabbaaabbbaaaababbaaababbbababbaaaabbbabaaabaabbaabaaabaababaabaaabbbbabbaabbbbaaaabaaaabaabbababbabbbaabababaaaabaaaabbbbaaabbbabbbabaaababababbababbaabbabbbbabababbbbaaabbbbbbaaababbbababaaaababaaaabbababaababbaaaaaaaaabaabbaaaaaabbbbabaaaaaaabaabbabbababbabbaaaaaabbbbbabaabaabbbbbaabbaabaaabaabaaababaaaabaaaabbaabbbabbbbbaabbbaabbbbbbaaabbaabbbbabaabaabaaabaaaaabbbabbabbabbabbbbbaababbababaabbabbabbababaaaabbabaababaabbabbbaaababbbaabbbbbabbabbaaabbbbabaaaaababbbabbbbaaabbbaaaaababbbbbaaabaabaaabaaaaaabbaaabbabbaabbbaabbbbaaaabababbaabbaaabaaabaabbaaaabbababaabaaabaabaaaaaabbbabbbbabaaaaabaabbaababaababbabbbbabbaabbabbabbbbbbaaabbaaaababaababbabababbababaaaaababbbaaaabababbababbaabbaabababbbbabbbaaaaabbababbaaababbaabaaaaaabababaababaabbbaaabbbaaabaaaaaaabbbababbbbbaaabababbaaabababaaaaaaabbbaabababaaabababbbbabababaabbabbaaaaaaabbbababaaabbababbbbbababaaabbbbbabbbbbbaaabaaababbaababaabbbbbbaaabbbbbbaabbabbbbaaabbaaaaabbabbbbbbbabbabbabaaababbaabbbbabaabbbbabbaaabaaabbabbbbaabaaababbbaabbabbabbbaaabbabbbbbabaabbbabaabbaababaaabbabbbbbbbabbbababbaaabbbbbbbabbaaabbbabbaaaabbabaaaabbaabbaabaaaabbbbabbababbbbbaabababaaabbbbaaaaabbaabbbbbbbaabbababbbbbabababaabbaabbbaabaabbbabababbaabbbbabbaaaaababaaabbaaabbabbbabbbbbbaabbbbabbbabbbbaabaaaabbbabababbabbbbabbbaaaaabbbaabbbaaababbababaaabbabababaaaaabaaaaabbbbabbbbaabbbaabbbbbaaaaaabbaabbabaabababaabbabbaabaabbaaabaaaabaabbaaabaaaabbbaaababbbabaabbababbbabaabaabaaabbbbbaaabaaabbbbabaababbabbbbabaaaabbabbaabbbaaabbbbbaabbbbaaababbaabaaaabbaabaaaabaabbbbbbbbbbababbbabbbbbbaabbabaabbabbbbabbbabbaaaababbababaaaabbaaabbbbbbbbbbbaabbabbabbabaaaabbabaabbaaabbbaaaabbababaabababbbabaabaaaaababbabbbabbaabbaabbababbabaabbaaabbaaaaaaabaaaaabbbbabbbbbbbbaabbbaaaabbbaaaaaabaaaaabaaaabbbbaabbababbbbbbaabbaabbabaabaaabbbbaaababbabbaaaaababbabaabbaababbbbaabbabbbaaaaabababbababaaaabaaaabbaaabbbbbbbbbbabbbbaabaabaabbbbaabaabbbbbbbaababbabbbabbababaabbabaaabbbbbaaaaabbaabababbbbbabbbaaaaaaaababbbaabbbbbababaaabaaaaabbbaaabaabbaabbbbaaaaaaabbbbababbbabbabbaaaaabbabbbbabbaaabbbababbbaaababbbabaaabbbbbbabaabbaababaabbbbbbbaabaaababbbaababbabaaaabbbbaaabbbbaabaaababbbababbaabaaaabbbbabbaababbaaaaabbbbaabaaababaababaabbbbbabbaababbabbbaabaaababbaaabaaaaaaaabbabbabbabaabbabbbbaaaaaaabaabbbbaaaabbaaabbbaaaabbbabbbaaababbbbaabbbaabbbaabaaaabaaabaabaabbbabbaaaaaababbabbbbbbabaababbaaabaabbbabaaabaababbbabababbababbbabbaaabbababaabaaabbbabbabaaaababbbbbaaaababbaabbbaabababbabbbababaaaaaabaababbbaaaaabababbabaabbbaaabbabaabbabbaaaaaabababbbbbbaaababbbbabbaaabaaabbbabaaababbabbaabaaababaaaaaaaabaaababbbbaaaaaabaaaabbaabaabaaaabaaabbaaabbabbbbbabbabbaabababaabaabbbbbbabbbababbbbabbaabbaaababbababbaabaabbbbbaaaababababbbabbabbaaabbabaaababbbbaabbbbabbabbbaaaaaaaaaababbaaaaabbbbbbaabaaabaababbbbaabbbaabaababbbbbabababbbbaabbbbaaabaaaabbbaabaaababbababbaaabbbabbbbbabababababaababbaaaabaaabbaabbababbaabaabaababaaaabbababbbbbaaaabaaabaabbaaaaababaabaabbabababbababbaababbbbaaababbabaaabbbabbabaabbbbabbbbabaaaabaababaabbbbbabbbbbbabababababbbaabaaaaabbbbaaabbbbbbabababaababaababaabbaaabbbbabbbababaabbaabbaabbabbabbbabbabbbbbbaaabaabaabbbbbbbbbbbaabbabaabbbbaaaababbabaabbbabaaabbabbaabbabaaaaaaabbbabbabbabaabaaaaaaaaabbbbbabbbbaabbbbbaabbabbbaaaabbabaababbbabbaaabaabbabbbabbaaabaaaaabaaaabaabbbbbbaaaabbbbbaaaabbabbbbaaababaaabbababaabaaaababbabbaaabbbaabbaabababbabbaaabaabbbbbaaabbbaaabaaaabbaababbbabababbbbaaaaaabbaabbaaaaababbaabaaaaababaaaaabbababbaaaabbbbbaabaaaabaaaaabbbbbaabbaaabaabababbbabababaabababbbbaaaaababbabbbbaababbaaabbbbbbbaaaaaaabbbaaaaaaaaaabbbabbaaabbbbaabaaabbbabaaaababbbabbababababbabaabbabbabaabbbbaaaababababbbbaaaabbabbaaaababaababaaaaaabbaaabbaabbaabbabbabbaaaaababbbbbaabaaabaaaabbaabbaaaaaabaaabababbbbabbabbbbaaabbbbabbbaaabbaaabbbbaaabbabaababbbabbaababbababbbbbababaabbbabbaaaabbbbbbaabbbbaaabbbbbbaabaaabbbabababbbbbbbbbbaabaaabaabbbbaaaaaabababbabbbbababbbaababaaaaabbbababaaaaabbabbbbaaabbbabbbaaaaabaaaabbbbaaaabbbbaaaaabbbbabaaabbbbabbaaabbbaabbaaabbbababababbbbbbbaabbabaababaabaaabaabbbaaaaabbbaaaaaaabbaaabaaaabaaaaabababaaaabaabbbbabaabbabbbaabbbbaabbaaaabbaababaaabaabaabbbbbaabaaabbbbbabbbbbbaababbbaabbaabbbbaabbbaabbbbbaabbbaabbaaabababbbaabbbababbbbbabaababbabaabbaabbbabaaabbbbbabbaabbbbbaaabbbbaabaaabbabaabbaabbabaababaaabbbbabaaabaabaabbaaaabbbabaabbaaaabbaaabbabbaaababbbbbaaabaaaabaabbaabaababababbbaabbbaabbbabbaabbbabbababaabbabaaabbbabbabbaabaababbbabbbbaabbaabbbaaabbbabbabaaabbbbbbaaabbbabbbbaaabbbabbbabaabbaaaabbababaabaabaabababaabbbbabaaaabbabbbabbbbbbbbaabbbbbababababbabaabaaaabbaabbaabbbababbabbabbbbbbaabaaababaaabbbababababbaabbbbaabbbaaabbbaabbbabaabbbaabaaabbbaaaaaabbbbababbbaabaabaababbbabbaaaababbbbababaabbbbaabababbabbbaababbbbabbabaababaaaaabbbabbabaababbbaaaaaaababbbbbaabbbbaabaaababaaaabbbababbabbbaabababbabaaaababaabbabbaaababaabbbabbbbbbaaaabaabbbababaaaaabaabbbbbbbbaaabaaababbbbaabbaabbaabaaaaaaabbababbbaabaaabbbaaabbbabbaaaaabbabaababbbabababbabbabbbbabbabbaaaaabbbbbbaabbabbbbaaaaaabbabaabbabbbbbaabaabaaabababababbabbbbabaaaabababaaaaaababbbbaabbaabaabbbbabbbaabbbabababbabbabaabbbaabbababaabbaabbaabbabababbbabaaababbaaaabaaababaabbbbabbbbabbbaabbaabaabbbbbaabaababbaabaabbbabbbaabbabbbbabbbbabbabbabbbbbabbbbabbaaaaababababbbbbbbaabaaaaabaaaaaabbabbabbbbbbabbbbbabbabbabbaabbaaaaaabbaaaaababbabbbabbbbaaabbaaaababababbabbbbababaababbbbaababaabbabbbbbbaabbaababbbaababbbbababababbbbbabbaaabbaaababaaaabbabaabbbbaaabbbaababbbbbbabbaabbaabbabaaaabbbbabbbbababbabaaaaaabaabbbaabaaabaaabaaabaabaababababaabababaaabbaabbabababbbaaababbbaabaabababbababbbaabaababbabbaaaababababaaababbabbabaaabaaabbabbaabbabaaaaaabababaaababbbbbbabbaaabbbbabbaaaaaaabbbababbaaaaaaabaaaaabbbabbbbabaaaaabaaabaabaabaabbbabbaabbaaababaaaaabaabbbababbababbabbabaaabbabaaaabaabbaabbbbaabbaaabbababaabaaaabbaabbaabbbbaaaaaababbaaaaabbaabbabbbababbbabbabbaabababaaaabbbbbabbbbbbabbaaaabababbaaaabbabaaaaaaabbaaabababaabbbababaabbbaabaababbbbbbbaaabaabababbbabaaaabbbabaabaaaabbbbaabaaaabaabaabbbbbabbabbbbbaabababbbbaaabbaabbbbbaaabaabababaaaaaabbaaabbbabbbbbababbabbaaabababaaabaaaababbaabbbbbaaabaababaabbabbabababababaaaabbaaaaabaabbbbbbbaaabaaabbbbbabbaabbabaaaaabbbbbbaaaababbbbababbbabbbbaabaabbabbabaaabbabbaaaaaaaabaaababbbbaaaaabbabaabbbabbaaabbbaaaabaabbbbbaaaabaabbabbabbbbaabbaabbbbabababbabaababaabbbbaaabbaaaabaaabaabbaababbbbbababbbbbbbababbaababbbaabaaababbababababaabbaabaaaabaaaaaabaabaabbbbabaabaaabbaababbaabaaaabaaaabbbbbaaaabbbbbbbbbaabbbabbbaababababaaabaabbbbbbbabaababbbbbaaabbbbaabbbbbabbaababbababbbabaabaabbaabbbabbabbbaaabbbabaaabbababbbaaaaabaabbaababbbbaaabbbaababbbaaaaabaaaaabaababbaaabaaaabbbbaabbaabaaabbabaabaabbabbaaabbabaabbababbaabbaabbbbaaaabaaaabbabbbbbaaaaaabbaaabaabababbabaaaabbabbaabbaabaabaaaaababbbabababbaaaabbabbbbbbabaabaaabababaabbbbbabbabbababababababaaabaababbbbaaabbbaaaaaabaabaaaaabaabbabaaaabaababbaaaabbbbbbaaaabaabaaabbaabbbbbabaabababbaabaabaabbaaaaaabaabaababbbbabbbaababbabbbbbabaabbbbabbbbbbaababbbbbbabaaaabbaaabbbaaabbbbbbaabbbabbaaaabbaabaabbabababababaaababababbbbaababbbaabaaabbaaababbaabaabbbaaabbbbbbbababbbabbbabaabaabaabaaaaabbaabaababaabaaabbbbaabaabaaaaabbbabababbabababbbbbabbaaaaaaabbabbabaabbbabaaababaabbabaabbbbbabaabbabbabbbabaaabbbbaabbaaaabababaababbbaaaaababbbabbaaabbbbabbbababaabbbabaabbbbabbaababbabaaabbaabbabaabababaabbbbbbaabbaaaabbbabbabaabaababbaaaaaaababbabbabaaaaaabbbaaaababababbbbaabbbaabbbaaaabbbbbbaabaaaaabaabababaaaaabbbaaabbaabaaabbbbaaabbbbaaabbbaaaababbabbaaaaaabbaaababbabababaaaababbbaabaaaababbbabbaababbababbababbbbaaaaaaababbbaabaabaabababbaaababbaaaabababababbbabbbabbbabbabaaaaababbabbbbaabaaaaaabaabbaaababbbabbabaaababbbbabaaabaabaaabbaabbababbbabaabbbbbabaabbbaababababbabbbbabbaabbbbbbbbbbaabbbbabbbaabbabaaabbaaaaaaaabbaabaaababbbbbabbabbababaababbabbbababbabbabaaabaabaaaaaaaabaabbbbaaaaabababbaaabbaaabababbbaabbbbbbabbabbaaaaaaabbabaababbaaaaaaaabbaabaabaababbbabababaaabbbabbaabbbabaababbabbbababbaaaaaabaaabbbbbabaaabaabaabaabaaaabbbabaababbaaababaaabbbbababababaabbbbbbabbabbaabbaabaabbbbbbbaabababbabaaabbbaababbbabbbbaaaabbbabbababbabaabbbbbbbbabbaabaabaababaaabbbaaaabbaaaaaaabbbabbbbaaabbaaababbbaaaabbabaaabbabbbaaaabbaaabababbbabbaaababaababbbbbaabbbbabbbabbabbababababababaabbbbbbbbaaaaaabbabbabaabbaaaaabababaaababbaabbbbaaabbabababaabbabaaabaaaabbbaaaabaabbabababbabbababaabbbabaababbbaabbabbbaabaaaaabaaaabaaabbbabbaaabbaaabbabbbabaaababbaaabbbaaaaabbbaaaabbaaaabbabbaabbababbabbabaaabaabbabaabaabbbbbbabbabaabbbaababaaaaabbbbaabbbaaaabbabaababbbabbaabbbaaaababbbaaabaaaaaabbbbaaabbbaabbababbaabbabbaaabbbaabbaabbababbbbbabbababbabbaababbbbaabbbaaabbbbbbaaaabaaaaaaaaababababbbbaaaaabaaababbaabbaaaaabbabababbaabababbaaababbbbbbbbbbbababbbaabbabbabbabaaabaaaaaaabaaabbaaabbabbabbabaababbaabbbbaaabbabaabaabaababaababbbabbabbbbbbaaabaaaaaabbabaaabaaabbabaaaabbaabbaababbbbbbbababbabbabbbabbbbabaaababaabbabbbbababaaababaababaaabbaabbbbababbabaaaaaabbabaabbbaabaababbbbaabababbaaaaabaabbbaaabaaabaaabaaaaabbbbaaaababbabaababbbbbbaaababbabaaabbaaabaaaabbbabaaabaababbbbabaabaabaabbaababaaaaaaabbabaababbbaabaaaaabaabaaabbbbbabbbabbbbbbabaababbabababaaabaaababaabababbabaaaabbabbbababaaaabababbabbaaabbabababaabbbbbabbabaaabbbaaaaaaaaaabbabbaabaaabbbabbaaaaabbbbaaabbabbbbabbaabbbaabbbbabaabbaababbaabbaaabbaabaababbbbaaaaaaaaababbabbabaaabaabaabaabbbaaaabababbbbaabbabbbbaaababbaaaabaaabbaaaabbbbaaaaaaabbababbbaabbabbabbabbbbbabaaaabaaaabababbbbaaabaabbaaabbbabbabaaaabaabaaababbbbabbabaabbabaaabaabbabaabbaababaabaaabaabababbabaababbbaaaabbbaaaaabbababbbaaabaaabbbbaabababbabbbbbabaabbbaababaaaabaaabaaabbabbaabababbabbabbaaabbbaaaababaaabaaaabbabbaabaabbbbbaaabbabaaaabbbbaaaabaabbbabaabbbabaaababbbbbbbaabbababababbaaaabbaaaabbbaababaaaaaaaabaaaaaaaaabaabbbbbabbbaaabbbbaabbbaabbbababbbbbbbabbaaabbbbabbbbbabaabbbbbabaaababbaababaaaabaaabaaabbabbbbbaabaaabaabababbaabababbbbaabaaaababaaabaaabaabaaaabbabbbaabbbaaabaabbbaaabbabbbaabbababbabbbaaabababbbbababaabbbababbbaabbbbbbabbbbabaaaababaaaaabbbaabaaaabaabbabbababbbbabaabaaaabbbababaaaabaababbabbaaaaabaabaaaaaabaaaaaaabaababbbbaaabaaaabbbabbabaaaababaabbbabbbbbabaaabaaaabababbbaabaaabbbbbabbbaababaaaabaaaaaabababaaabbabbaaaabbabbbbbbbbbbbbaaabaaababbbbabbaabbbaabaaabbbbabaaaaaabbabbbbbaabbbbaabaaababbabbaaabababbbabaabaabbaaaaababbbabbbaabbbababbaabbaaababaabababbababbbbaaaaaaabbbbbbbababbbaaabbbbaaaaabbbbbbabbbbbaaabaabbbaabaabbaabbbabbbabbbaabaabbaaabbbbababaabaabbabbbababbabbaabbaaabbabaaaaaabbabbbbbbbbbabbaaaaaabbbabbbbbaaababbaabaaaaababbbaaabaaaaabbbbabababbabbbaababbbaababbabbaaabbbbbbbbbbbabbaaababbbbbabbbbaaaaabbaabbbbabaaaaaabbbabaaabaaabaabbbbabbabababababbabaabaabbbabbbbabaabbbbbbbbaabbbabaabbbabbabbbbbbbbaaabaabababbbbaabbbbabaabbbbbabbaaabbaababbbaaabbbaaaaabaabbbbbaaabaabababbbaabbababbbbababbbbaaaaabaaababaabaabbbbbbabaaaabbaabaaabbabbbaaaaaabbabbbbbbbbbaabbabaabbabbbbabaabbabbaabaabaababbbbaaabaaaabbaaabbbaabbabaabaaaabaaaaabbbbbabaaaabbbbabaabbbbbabbbabaabaaaababbaaaabaaaaaabbaababaaaababaaaabaabaabbbaaababbaabbbbabaabbbbbbaaaaaabaaaaabaababaaaaaaaabbbbaabaaabbbaabbbbbababbbbbbbaabbbaabaaabababbaabbbabbbbbaababababbbbababbaababbbbabbabababbbbbbbbbaaabbbbaabbbaabaabbbbababbbabababbbbabbbaabbabbbbbbbabbabbabbaaaaabbbbababbbbabaababababbaabbaaaababaababbabaabaabbaabbbaaababbbabaaaabaabbbbbaabbaaaaabbbabbababaaabbbaababbaaabbaaaaababaababababbaabaabaaaababababaaabbbbbaababbbaaaabaaabaaaaabaabbbbbbabbbabbabbaaaababbabbaabbbaababbaabbbabbbbaaabaabbabaabababbbbabbabbbbababaabbbaaaaaaababbaabaabbbabaaabaabbaaaaaaabbaabababbbbababaaababaababaababaaaabbbabbbabbaaabbababababbabaabbbaaaabbbbaabbbbaabbbabaaabbabbbabaaaabbbaaabbabaabbabbbbbbabbbababaaabbbaabbabbababbbabbaabaabbbaabbaabbabaaaababbbabaaaaabaabaaaabbbabbbaababaabbbaabbabbbababbbbbabbbaabbbbabbaababaaabbbbbabbbaaaaaabbbabababbabbaaaabaaabbaaabbbaabaabbbabbbbabbbbaabaabbaaabbabbabbaaabbaabaabbabbbbbbabbbbbabbaababaaaabbaabbbbbbaaaababababaaabbabbbabbabbbbaaaaaaaabbabbbabaababaabbababababbbababbaaaabbaaabaaaabbaaaabbbbaaaabaabbaaababbabaabbbbaababaaaabbbbbbaabbaababaabbabbbbbbbaababaabbabaaabababbaaaabababaababbabaabbbbabaaabbbbabaaabaabaaabbbababbbbbabababaaabaaababababaabbbabaaabbabaaababababbbbaaabbbbbabaabbaaaababbababaabababbbbaaababbbbabbabbababbbbaababbaabbbaabbaaaabaaaaabbbbbababbaababaaaaaaaabbbaaabbbbabaabababbaababbbabbaabbbbbabaababbbaaaaababababababbbaabbababbbaaabbbaabaaaabbbbbaaabaaaababbbaaabaaabbbabaaabbaaaabbbabbabbababbaaabbaaaaabbabbaabaaabaaaaabbbbbabaabbbbababbbababaabbaaababaabbababaababbbbaabbbaabaaaaaaabbaaabaaabbabbabbabaabbbbaabbbababaaabaaaaabaaaabaaaabbabaaaabaaabbbaabbaabbbbaababbbbaaaaabaaabbaaabaabbbabbabbbabababbaaaababbbbbbaaaaaabbbbbbbabaabbaaaabaabbbabbabaaaabaababababbaabbbbbbbaababbabaabbbaabbbbabbbbbbababbbbabaaaaabbaaaaabaaabbabbbbbabbabaabbbbbbbbbbabababaababbaabaaabbbabaaabaaaaabababaabaaababaaabbbaaaabbbbbaababaabaaaabbaaababaaabbbbbbabababbbaaaabbbbaaaababbabbababbbaababbbbbabbaabbabbabababaaaabaaabbbabaabbbbbaabaaabbbaaabaaabaabbbabbbbbabbababbabbaaabaababaabaababaabbabbbabaaababbaabbbbaabaabbbabaaaabbbabbbbbbbababbababbaabbbbaaababaaabababaabbbbababaaaaaaabbaaababaabaaaabbabbaaabaaaaabbbabbababaaabbabbbaaabaaabbbaaaabababaabaababaaabaaaababbabbbbabbbababbabbbbbbabbaababaaabbaabbbaabbabbbabbababbbbbbabaabbbbabbabaabbbbaaababaabaabbbaabbbbbaabbababaaaabbbababaabaabbabbbbaabaaabaaabbababbbbabaabbababbaabaaababbaabbbbabbabbaabbbaababababaabbbbbaaaababbaabaaaabaabbaaababbbbbabbbbbabbabbabbaaaaabbbbbabaabaaabbabaabaaaabaaabaaaabbbaaaaabaaaabbbaababbbaaabbbbbaaaabbbaabbabbaaaabbbbabbbbbaabaabaabaaaabaaaabaabbbbaaaabababaababaababababbbbaabaabbabbbaaaaaabbaaabaaaabaaabbbbbaabaaaaabbbbabbaaaaabaaabbbbaabaabababaabaaabaaabbaaabaabbbabbbbaaaabababbababbbbbababbbbabbaabbbbbabaabbaabaabbabaaabaaabbabbbaababbbbbabbbaaabbbabbbaaababbaaabbababbabbbaabababababbbbbbabbaabaabaababbbbbaaabaaababababbbbbbaabaabbbbabbbabbbbbabaaaaabbbaaaabaabaabbbaaabaaabaaaaababbbaaabaaabbaaabbbababbaaaabbbbbbaabbbbaabbbaabbbbaaabbbaabaaabbbaabbbbaabbaaababaaabaaabaabababbbaabbaabbbbabbbabababababaabbabbababbaabbabbabbabbababbbaabaaabaaababbbbaaaabaababbabbbaababbaabababbaabaababbbaaabbaababbbbaabbbabaaaaaabbbaaabbbbbabaaabaaabbababbbbbababbbababaabababbbbabababbbbababaaabbaaaabaaaabbabbbbbaabaabaabbaaaaaabababbbaaabababbbaabbaaabbbbbbaabbaababbbaabbbbbbbaaabbabbababbaaaabbabbabbbaabaaaababbbababaaaaabbbbaabababbababbaaaaabaaaabbabbbbaabaabaabababbaaabbbbbbabaaaabbaaabaaabaabbbaaababababbababbabbababbabbaabaabbbbaabbbaaaaabbbaabaabaaaababbaabbabaabbbbaaaaaabbbbaabaaaaabaabbbbbbaaabababaababaaabbbababaaababbbbababaababbabbbaaaaaaaabaaaaabaabababaababbbbabaababaaabbbbbabbaaaaabbbbaabbaabaaabaababbbabbaabaabaaaaaaabbaaaaabababbaaabbabbbaaaabaaaaabbaaabaababaaabaabbbabbaaaaabababaaabbaabbabbbaabbbbaaabbaaabbbabbaabbbaaabaaabbaaaabbababaaaaaabbaaaaabababbbbababbbabbbaaabbaaaaabbabbbabbabbbbbaaabbaabaabaabaaaaaabbaaaabbaabaabbababaaabbbaaababaabbbbaaabbaaaaababbbbbaaabbabaaaabaabbbaaababbabaaaabaaabbbbbabbabaababbbabbabaabbbabbaaaaaabbaaaaaabbaaabaaabaaabbabaabababbbaaaaababbababaaaababbbaabbbbaabbbaaaabaaaaaaabababbbababaaaaaaaababbaabaababbabaababbbbbabbbaabbbaaabbababbbababbbbbaaaaabbaaaabbbbbbaabbbaabbbaabaaaabaaabbaaababbbabbbbaababaabaaabaaabbbbabbabbabbaaabbbaaabbbbaaaababbbaababaabbbbbaabbbbbaaabaabaabbaabbaabababbbbbbababaaaaabbbbabaabababaaaabbabaaaabbbaabbaaabbaababaabbaabbaaabaaabaaaabaaababbbbabaaaabbaababbaabaaaabaabbbbaaabaababbaababbbaabbbbbabaaabbabbaabbabbabaaababbaababaabbaabbbbababababbbbbababbabbabbabbbabababbababaaabaababababbaaababaabbaabbbbaabbbbbbbabaaabbababbbbbaabbaaaaabbabbbaabbbabbbbaaaabbbbaabbabababbabaaaababbaabbbabaaabaaababbbababbaabbabbbabaabaaabbbbaaabaaababbaababbaabbababaaaaababaabbaabbbbabaaabbbbbabbababaaabbaababbabaabbaaabbabbaabbbaaabbaaabaabbbbbbababbabbbbbabbaaaaaabbaaaaabaabaababbabbaaabaababbaabaaaaabaababbbabbbaabaabaaabaabbaabababbbaabaabbbabaaabbaaabbbabbaaababaaabaabaababbbaaaabbaaaabbaaaaaaaaabbaaaabbbaabbbababbabbabbbbabbabbbabbbbbabbbaabbaabbbbbaaaababbabbbbbaabaaabbbaabbbbbaaabaabaaabababbbbaabbabbbbbbbabbbbabbbbabaabaabbabaabaaaaabbbababbbbbbaaabbaaaaababababbaababbbabbaaaabbaabbaaaaaabbbaaabbaabbbabbbaaababbabaaaabaaabbababbabaabaabbbaaaaabaaabbababababaaaabbbbbaaabaaaaabaabaaabbaababaaabaaababaaaabbbbbabbbaaaabaabbaaababaababbabaaaabaabaaabbabaabbbababbabaaaababbaaabbaabbbbbabbabbbabbaaaaabbabbbbbaaaaabbbbabbbbbbbbbaabaababbaabbbbbabaabbaaaaabbabbabbbbbbbaaabaaabbbababbaabababaabbaabaaaaabbbbabbabaabaabbbbaaaabaabbbbaabaaaaabbbababbabbaaabbabaaabbbbbbbaaaaaabaabaaaabababbababaaaabaaaabbbbaabaaabbaaabaabbbbabaabaaaaababbaabbbbbbaaaaababbbbbbbabbbbaabbbabaaabbbababbbbbabaabaaaababaabaababbbbaabbbabaaaabaabbbbbbabaabaaabaaabbbaaaaaabababbaaaaaaaaabaaabaaaaabbaaabaabbaaaabbabbabbbbbaabaaaaaaaabbbaaaaaabbbabaabaababaaababbbbbbaaaaaabaaaabaaabbbaaabbbbbbabbbaabbabaaaabbbabaabbbaaaaabbabbbabbbbaabaaabbaabbbabaaabababbaaabaaabbabbbbbbaababbbbbbbbbbbbbababbbbbbabaabaaabbbbbaabbbabababbbaabbbbaabaaaabbabbbabbbbbabbbaabaaabbaaabbabbbabaaabaabababaaaaabbbaabbbbbbbaabbabbaababbbabbaababbbbbbbabbaaaababaabbaaaaaaaaaabbaabbbbabaaabaabaabbabbbbaabaabbabbbbbaabaabbaaabaabbbabaabaaaaabbaabaaaababbabbabaababaabaaaababbaaaabbabbaaabaaaaaabbababbbbbaabbbbbaabbbbbbbaababbaabaabaaaababbbbbbabbabaaaabbbbabbbbaaaaabbbbabaaababaaababaaabbbaababbabbbbbbbbbbaabaababbbabbaaabbbabbaaabaaaaaababbbaaaabaababaaabaaaaaababbbabbabbbbababbbaaabbababbaabaaabbbbbbaaaababaaababbababbbababbabaaabaaaaabaaaabbbaaabbbbabbaabaabbbbabaabbaabbabbbabbbbbbababaabaaaaabbbabbababbaaaababbbabababbabbabbbbbbabababbbbabaabbaabbbaaaabbbabbbaaabaababbbbaaaaaaaabbabaaababbbabbbbbabaabbababaaaaaabbbabaaaabbaaabbbbabaaabaaaaaaabaabbaabababbbabbbaaabbababbbbaabbbbbabbbaababbbababababbaabaaabbaaaaaabbbbabbabaaaabababbbaabbaababaaabaabbbbbabaababababbaabaabaababaabaaaaaababaababbabbabaaaaabbbaaabbabaabbabbababaaaababbabbbbbbababbabbabbbaabbaaaaabbaabaaabbbbbaaaabbbabbbbbabbbbbbabaaaaaabbaabbbababbbabbbaaaababbbabbbabbababbbabababbbaabaabaabbabbbabbaaaaaabbaaababbbbabbbaabbababbaaababaaaaabbbabbbaabbbabbababbabbabbbbababababbbabbaababaaaabbaaabaaaabbbbbabbbbbbabbbaabbabaaaaababbbbbbabaaaabaabbbbabbbbbbaaaabbaabbbbbaaababbabbababbbbbbbaabaaaaaabaabaabaababbbbbbabaaaaabbbbbbaaaabbbabaababbbbababaabaaaaabaaabbbbaababbaabaabbaaabbbaaabaababbbbaabbababaabaaaaabbbabbbabbbbabbabaaabaaabaabbababaabbaaaaaabaaaaaabaabbaabaababbbbababbaabbbbbababaabbbbbbabaaabaaaababaaaaababbbabababbbabbbaaaabababbabbbaababbbabaaaabbbbbbabbabbbabbbabababbababaaabaabaaabbababbbabababaaaababbababbbabbbabbbbbbababbaaaaababaabbbabaaabaabbabbbaabbbbaaaaaaabbbaaaababababbbbaabaabaaaabbaaaabbbbbabbabaaaaaabababbaaaabbbaaaababaaaaabaaaaaabaabaaabaaabaabbbbbababbbbaaabaabbaababbbbbbababaaaaababaabbaaaaabbbbbbabaaaaababaaababbaabbbbababbaabaabaabbbaababbabaababaaabbbaabbbaabbbaabbbbabbbbbbaaaabaababaabaabbabaaaaabbababbbbbabbbaabababbaaababaabaabaabbbaaababbbbbbbaabbaaabaaaaababaaabbaabbabbbbbabbbaaaaaabbbbbabaaaabbaabaabbbbbbabaababaabaaaabbbabbaaababbaaabbbbaabbaaabaabbbabbbbbbabbaaaaaabaaabbbbaabbababbbaaaaabbbbbbaabaaaabaaaabaaabbabbbaabbbbabbbbbabababaaabbbaaabbaaaabaaabbaaaabbbbaaababbbbbaabababbaabbaaabbaabbabbabbabaababababbababaababbababbabbbbababaaabaaaababbabbbbaabbabbbabbaababbaaaabbaaaaaaabaabbabbbabaaaaabaabbbbabbbbbaabaabaaaabaaaaaaabaabaaaabbbbbbabaaaabbabaaabbababbbabaabaaabbbbbbaababbabaabbabbbabbaaaaabbabbaabaaababaaaabbabbabbabbaabaaaaaababbbbbbbaaabbaaabbbaaaaaaaabaaaaababbaaaaaabbabbbaabbbaaabbbbabbbaabbbbbaabbaaaabbaaaaabbaaabaababbbaababaabaaabbababaababaabaababbbaabbaaaaabaaaaabaaaaaaababbabbbabbbbbaaaabbaaabaabbbbaabbbbaaaabbaaabbbbbbaabbbabaabbaaaabbbbbbbabaababbaabbabbbabaabababbaababbbbaaabaabbaababbbaababaaaabbabaaabaabaaaaaaaabababbbabbbabbabbaaaabbaaaaaaabbaaaabbaaababaaaaaaabaabbbbabbabaaaaabaaababaababaaabbababaabbaabbaaabbbbabaaabaabbbbbababbbbbbaabbabbbaaaaaabaaababbabbaabbbabaaaabaaaaaabbbaaababbbaabbbaaaabbbbabbababababbaaaabaabaabaaabaabaaabaaaaaaabaababbbabbbbaabbbaabababbbabababbababbbbaaababbbabbaababbbaaaaabaaaaabbababbaababaaaababaabbaabaababbababbaabaaabbababaababbaaababaabbaaabbbbbbbaaaabbbaaaabbabbabbbbabbabbaabaaabbaaaababbaabaababbaaaaaaaaaababaaababbbaabaababbaaabaabaaaaabbbababbaabaababaabaabaaabaabbbbababbaaaabbbabbbbbbaabaababaabbbabbabbbaabbbbaaababaaabbbaaabaababaabbbabbabaabaaabbaaababbaabbaabbaaaaaaabbaabaabbaabbaaabaaaabbabbbababbbbaaababaaaabbaaaababbbbaaabbbbbababbababababbaabbabbaaabaaababbaaaabababbbbbabbaabbbaabbbbaabbabababaabaaababbbbaaabbabaaaabaaaaabaabbbabbabaaababaabbaabbbbbbaaaaabbbbaababaabbbaabbabbbbbbabaabbbbabbbaaababbbabababbbaaabababbaabaababbbabbbaabbababaabbabbbbbbabbbaabbabababaabababbbaaaabbaaabbabbaabbbbaaaaaabbaaabbabbbababbbbaaabbbabbaaaabbbaabaababababaaabbaabbaaabaaaaaaaaabbabbaabbaaabbabbbbabbbaaaabaaaaaabaaaabaaabbabbbbaabbbbbbaaaabababaabbabaabbabbbbabbabaaaaaaabbababaabaaabbaabbaaaabbababbbbbbaabbabbabbaabaaaaabababaababaababbbaaaaaababbababaabbbbabbaaabbaabbbbbbabbabbaaabbaaabbabababababababbbabbbbaabbaaaaabbabaaaabaabababbaabaabaabbaaaaabbbbbabaaaabaaaaaaaaaabaabbbaaabbbaababaaababbbbaaabbbbbbbaaabbbbabbbbabaaaaabbbaaabaaabbbababbaabbaaabbbabbabbbbabbabbaaaabaaabaaaaabbbabaabaabaaaabbbbabababaabaaabbbbbabbbabbbaaaabaaabbabaaabaabbabbbaabaabbbbbbbaabbabbaaaaaaababbababaaabbbbaaabbabbbbaabbbabbbaabababbabbbbbaabbabbaabbabaabaabbabaaaaabbbbbaababbbbabbaaabaababbbaaaababaabbbbbaabbbaabaaaabbbaabbabaabaaabbbbaabaabbbbbabaaaabbabaababababbaaababbabaaabbbbbabbbbaabbbbbbababaaababaabbbabababbbbaabababbabbbabbbbabbabbbaaaabbabaaaaaaabbababbabbaabbababbbabbbaaabbaaaaaabaabaabbbbabbbbbbbbaabbaababababbaabbbaaabaaaababaaaaabaaababbaaaaababbbabbabbbaaabaaabaabababbaabbbbbabaabbbaaababababababbaabaabbbbabbaabbabbabbbbaababababaaabbabbbaaaababababaababbbabaababbbaabbabbbaaabbaabbbaaabbbabaaabbbabbbabbbaabaaabaaabbaabababbbaababbabbabaababababbbbbbaaabbbaabbabbbaabbabbaaaabbaaabaaabaaabaaaaabbabaabbbbbabbbbbaabaabbbbbabbabaabbbbabbbbbabbaaaaabbabaabababaaabbbababbaabaabaabbaabbbbabababbababbabbbbbbbaabbabaaaabbbabbbbbaabbbbbbaaabbbbbbbbaaabaabbbaabababbbbbbabbbbbbabaabbabbbabbaaaaabbbbabbaaabbabbbbbabbbabbabbaababbaaababbaabbabbbbabaabbabaaabbaaaabaabbaabbbabbbaaabaaababaaabbbbaabaabaabbbbbbbbbabbbaabbbabbaabbaabbbbaaaaabbbbbabaabaabaabaabaaabaaaaaaababbbaaabbabbbbaabbabbbbababbbbbaaababbabbaabaaabbababbbbaababaaabbbbbabbaaaaabbbaaabbaaabaaaaabbaaabbaaaabbabbbbaababaababbaabababbabaaabbaabaaabaaabaaabbabbababaabaaabaabababaaabbbaabaabaabbabbbbbbabbbbaaaabbaaaabaabaabababbbbbaaaabababbbababbaabbaaaaabaaabbababbaabaaaabbbbbabbaabbaaabbabbaabbaabaabbabbbbaabaaababbabbbbbaaaabaaabaababbababbbbbbbaaababbbabababbaababaaaababaaaaaabaababbabbbababaaababaaabbbbabbabbabaaabbbbabbabbaababbabababbaabababbaaaaaabbabbaaabbbbaaababbabababababaaababaababbabbabbaababaabababababbbbabaaaabbbaababaabbbababbabbabbababbbabbabbbaabbbbabaababbbabbbbababbaabbbaaaaaaabaaabaababbabbbbabbaaabbbbbbabaabbaababbbbbbaaabaaabaabbbababaaaaaabaaaaaaabbbbaaaabbbbaabbaaaaabababababaabbbaaabbbbaabaaaaabbaabbbaababbababababbaaaababbbbbabbaaaaabbaaaabbaaabaaaababb
babbbbabababaabbababbabaaaaabbabaabbbaaabaaabbbbbabbbabbabaaaabbbaabbbbbbbbbaaabaaabbbaaaabaabaabaabbbabbaaaaaabbbbbaabbbbbaaabaaabababbbaabaaababbbbababbbaaabaaaaaabaaaaababaabbabbaabbabababbbaaababaabababbbbbbbbbbbaababbaabbbabbbaaaabaabaaababaaaaaababbabbabbbbbaabbbbababaaaabababababaaaabbbbabbabbbaabaaabbbababbaaaaaaabaabbabbbaabbbaababbbbbababbbbbaababbaababbabbbbabbbabaaaabbabbaabbaaaababbbbabaaababbabbbbbbbababbabbbabbbababaababbaaabaababbaabbaaabaaaaaaaaaabaaaaabbbaaaaabaaaabbbbababaaabbbbbbabaaabbbaaababbaaababbbbbaaabbbaabbbbaaababaabaaababaabbbbbaaabbaaaabaaaaabaabbbaaabbbaaababbabaabbbbabbbbabaaababbaaabbababaaaabaabaababbaaaaaaabaabaaabbababbaaabaabbbaaaabbabaaaabababbaaabbbaaabbabbaaaabbababbbaababbbabaabaaaabbabaabbbbababbaaaaabbabaaabbbbabbbababaaaabaabbbaaababaabaabaaabbbbaababaabbbbbbabaaabbaababaabbabbaaaabbabbbabbbaabaaabbaaaabaaababbbaaabbabaaaaababbbbbbaaabababbaaabbbaabaabbabaabaaaabbbaaabbbbbbaabbbbababaaababbaabbaababbbabaaabaaaabbbbbababbbabaaaaabbbbaaabbbbaabbbbbbbbaaabaabbaaabbabbbbbbbbbabbaabababbaabbaabbaaababbaabbbabaababbabaababbaabbbbbaaaaaabaaaaaabababaabaabababaaaabbbbbaaabaaabaaabaaabbbbbabbbaabbababbaababbabbababbbaaababaabaaaaaaaaabababbabababbbbababababaabaababaabbaabaaaaabbaabbababaabbabaabbbaabbaaaaaaaabaabbbbbbbbabaaaaaabbbbabbaaaaaabbabaaabaaaabaabababaaaaabaabbbbabbbbbbaababaabbabbbbabbaabbbbbbbbbbaaabbbbababbabbaaabaabbaababaababbbabbaaaaabaaabaaabaaabaabbabbabaabaaababaabbbbaaaaabaabbbbbbbabbaaaaabaababbbaabbabbaabaaaaaaaabbaaabaabbbabaabaabbaaabaabaabbbabbababbbbbabbabaabbbbabbbbbbbbbabaabaaabaaaaaaaaaaaabbbaaaabbaaabbaaababbbbaabbabbbbaabbabbbbababaabababbbbbbaabaabbaabaababaabbabbbabbaabbbabababaabbbbbabaabababaabaabbbabbaabaabbbbbaaabaabbababbababbababbaabbbbbaaaabbaaaaabbabaababbbabbbbaaababbbaaaaaababbaababaabaabbbbbababaaabababbbaababbabbbaaabbbbbbabbbbabbbbbbaabbbbbbbaabbabbaaaaaabbaabbbaabababbbaaaaaabaaaabbabbababbbabaabbbaaabbbbaabababaaaaaabababbbaaaaabaabbabaaaabbbbababaabbabaababaabaabaaabbbbbbabbaaaaababaaaabaabbbabbbbabbbbabbbbabbbabbaaaababbbabbbbbbabbbabaababaabbababbbbbbbbbbabbaaababbaabbbaaaaaabaaaabababbaababbabbbaaabbabababbbbbbbbaabaabbbabbbbbbbbabbabbaabbbababbbbbababbbabbaababbabbaabbaaabaababbabababbaabbaaabbabaaaababbabaaabbabbbbabbbbaaabbabbabbabbaabaaaababaabbbabbabbbaaaabaabbabaababbababbbbbaaababbbbabaababbababbbbabbaaabbbbbabbbaabaababaabbbabbbaaabaaaabbbbaaaabaabaabbabbbbbbabaabbababbabbbbababbaabbaabbababababaaabbaaaabaaaaabbbbaabbbaaaabaaaabbabbaaaababbbbbbbabbbaababababbbaaabaaaabbaaaaababbbbbbbbaabbababaabbbabbaaaabbababbabaabbbbaaababbaaababbbaababbbabaaaaaabbabbbbbbaaaaaabbbbaabaaabbaabbaababababbbbaaabbabaaaabbbaabaaabaabababbbbaabaaaaabaabbbababbabaabababaabbbbbbabaaaabbbaabbaababaababbaaabbaabbabaaabbaabbaaaabbbbbabbbaabbaabaababbaaabaabbbbbbbaabbbabbaaabbbbbabbbbabbabbaabbbabaabbbaaaabaabbbbaabaabaaabaaaabbabbabbabbaabbbbababaabababbbbbbabbbabbbaaabbbabababaaababbbabaaaabbaababbbaabbaababaaaabbbbaaabbaaabbbaaaabaabbaabbaabbbbaabaabbaaaaabbbabbbbbaaabbabbbbaaaabaaabaaaababaabbbbaaaaaabaabbbbaabbbababaabbbaabaaaaaaaaababbaaaaaabbabbaabaababbabbbbabbbbbaaaaaaabbbaaaaabbaaabbababaaabababbaabaabaaabaabaabbbabbbaababbbbababaababbbbaaababbbabbbbaaababaababaaabbbbabaaabaaaabbbabaabaaaabbabbbabaabaabbbabaabbbbabababaabbaababbaaaabbbaabababaabaaabbbababababbbbabbbbbababbbabbabaaaaaabaaaabbbaabbbbaabbaabbbbabababbbbabbabbababbbabbbbaaaaabbbaaabbaaabbaabbabbabaabaaababbabaaabbbabbaabaaabbbbbabaabaaaaaaaaababbbbbbababbaabaaaaababbababbabbaabbaaababaaabaabbabbbbbbaabbbbbbaaaababaabbbbbaabbbbabbbababaaabbbbaabababbaabbaabaaaabaaaababbaaaaaabaababbababaaaaaaabbabaabaababbbbabababbaabbabbabbbbaaaabaaabababbabbaaaabbbaababbbaabaaabaaaabbabbaababaabbabbaababbabaababbbabbbbbbbbbbaaaaabaaaababbbaaaaaaaabbaabbbaaaaabaaaaabbbbaaaababaabbabbabbbabbababaabbbaaabbbabbabbbbbbbbbababbababababaaabaaaabbabbbaaabbbaabababbbbaaababbbababbababbbbaabaaababababbbbabbbabbbabaabbabababaabaabbabbaabbbaabababaabbbaabaaaaabbaaababaabbbbabbbbaabaabbaabbaabbaababbabbbababbbbbbaaabaaaaaabbbbaabbaabbbbababbbbbbaaabbbabaaaaaaabababbbbaababababbbabaaabbbbabbbabbbabbbbbaaaaababbabbaaaabbabbbbaabbbbaaaababbbbbababbbbbbbababaaabbbaaabbaabbbbbabbaababbbabababbabbabbababbabaabbaaaaaababababababaaabaabbbaaabbabaaababbabbaababababbabbbbabbbababbbbbaaaabbbbabaabbbabaaabaababaabbaabaabbbaaaaaabbaabaababbaababbaabbaabbabbabbabbbabbbabbaababbabbbbababbaaaabaabbbaabaaabaabaaaaaabbaabababbaaababbababbabaababbbabababaababababaabbabbbababaabbbbbbabaaabbbbababbaabababbaaaaabaababbbabbaababbbbabbababbbabaabbbbbbbaababbabbbbbabbbbababababbbaaaaaabbabaabbaabbababbaaababbbbaabbbbbaaababbbaaaaaaababaaaaabbbbbaababaababbbaaaabaaaabbababbbaabbbaabbaaaabbaaababbaabbbbbbbabbabbbababbaababaaaaaaaaaabaaabbaabaaabbbbababbbbaabbbabbaaabbbaaaabbbaaabbabbaaabaaabaaaabbaabaaaaabababbbbaabbababaabbababbbaaababbaabbbabaaaaaaabbbabaabaaabaaababbabaabbaaababbbababbbbabbaabbababbabbbaabaabaabaaabbbbabaabbbaaaabababaabbabbabbbabbabbabbbbbbaabaaaaaabbbaabbabaabbaaabbbbbbbababbbabaabaabbabbbbbaabbbbbbbaabababbbabbabbabababbbbabbbbbaaaabbbabaabbbbbbabbbbaaabbababbbaabaaabbaabaabbbaaabbbaababbbaaabaababbbaaababaababaabbbbbbaababbbabbbbababbbbaaabaabbabababaabababbaababbbaabbbbaabaabaaabbaaabbbbabababbbbbbbabbababbbbaabbabbaabaabaaaabababbaaabaabaabaabbaabbaaaababbaaabababbaababaabbbbabbaabbabbabbabbbbbabbabbbabbaaaabababbaabbbbbbbbbbaababaabaabbabbabbbbbbaaabbababbaabababaabbbbbabaaaaaaabaabbabaaaababbbbbbabaaaaaaabaaabbbbabbabababbbaaabaabbbaabbbbbbbabbabbbbaababbbaaabababbabaababbbbbaaaabaababaabbbaabbbbabbaaaababbbbbabaaabbabbbabaabbababaaaababbabaaaababaaaaababbaaaabbbbabbbbbbaaababaababbbbabbbababaaabbaaabaaaabaaaaaabbbabbabaaaaababbbaaababaaabbabbaaababbaaaabbbbbbbaabaaaabababaabbaabbabbbaaababbbbaababbbaaaababaaaabaaabbbabbabaaaabbbabbabbaabababbbbabaabaaababababbbbababbaaabbbabaaababaabbbbabaabbabbbabbbbbaaaaabbbaabaabbbaaaaabaaaaabaabaaaabaabbaaabababaaabbbabbaaaababbaabbbbabbabaabbbbaaababbbbbbabbababbaaababbbbababbabbbbbabababbabbbaaaaabbabaaabaaabbbaaaababbbbabbbbabbabaabaabbabababbbabbaaababaaabbabbaaabbbaaaaaaababbabaababbbaaaabbbbababbbaabbaaabaabaabababbbbbababbabbbababababaaabaaabaabbabaaabaaabbaaaabbaababababbbaabaaabaaabbbbabbbababbababababaabbbbaabbabaabbabbbbabbbabaaaabbabababaababbbbababbbaaabababaaaaaabbbbbbaabbbbbaababbabbbaaaabbbabbabaaaabaabaaaaabaabbbaababbbbbbaabbbababababaabbbbbaaabaabababaaaabbbaabaabbababaaabbaaaaabbbabbaaababbbbababbaabbbabbaaaabaaabaababaabaaaaababbaaaaababababbbaababaabaaabbbaabbaaaaababaabbbaabaaabbbbabbbaababaaaabbaabaaabbababbbabbbaaaaababaaabbaaaabbaabbbbabaaabbaaaabaaabbabbababaababbabaabbaaaabaabbbbbabbabbabaabbbbaaabbbbaaabaabbaaabaaabbbabaababbabaababaaabbbbbaabaabbbaabbaabababaaaaaaabababaaaaababbababbaabaababbbaababbbaababbaaaaaaabbaaabbbbbbbbaabaaababababbbaaaabaababaaaaabaaabbaababbbbaabbababababbababbabababababbabaabbababaabbbabaaabbaaababbbabaaaaaaaabbaaabaabbaabaabbbbbaabaabbabbaaaabbaaabaaaababbbaaabbbaaabbbabbbbaababbaaabbaabbababbbbbaababbbbabbaaabbbaaabaaaaaaaabbaaabbbbbaabbbbabbbaabaaabbaaaaaabbbaaabbabbbbaaaaababbaaabaabaaabaababbaabaabaaabbbbbaabbbbbbbabaaaabbaabbbaabbbbaaaaabbaabbabbbbabaabbbbaabbaababbbabbabbaababbbabbaabaabbaabbaaaabaababababababbaabaaabbabbbbababaaababbbbaabaaabbbabbababbbbbababbbabaaaabbabaabbbbaabababaaabbabbaabbbbabaaabbabbaaabaabaaabbaaabababaaababbbabbaaababbabbaabababbbaabaaabaabbbaaabbbaabaababbaabbbabaaaaababaaababaaabbbbabbabbbaabaaababbbbaaabababbaabbbbbabaaabbbbbbbbbbababbbabbabbabbabbaaaabbaaaaababaaaaabbaaabababbaabaabbbaaaaaabaabbbbaabbbaabaaabaaabbbaaabbabbaabaaaababbaababbbbbbababababbaabbaaababaababababbbabbbbbbababbaaabbbbababbbbbbbabaabbbbbababaaaaabbaaabaaababbbaababbababbababbaaabbbbaaabaababbabbaabbaaaaababbbbbabaaabbaaaaabbaaabbbababbbabbbabbbabbaaaabaabbaaabbaaaababbbbbaabbbaaaaababaaaaababbbbaaabbbaaabbabbaababbaaaabbabaaaabbbababbbabbababaaaaabbaaabbbabaababbbababbbabaababaaaababbbbabbabbbaaabaabbbbabbbaababbabbababaaaaabaaabbababaababbbaabbaaabbbaaabaaabbababaabaabbbaaaaaabaabbbbbaabaabaabbbbbabbbbaaaaaabaabbbaabbbabaabbabababbaaabbaaaabbbabbbababaaababaabaaabbabaaaabbbbababbbbbabbbbbbababaababbababbaabaaabaaaaaabaaaaababbababbaaababbbabbabababbabaaababbbaaaababbabababbbaaabbbabbaababbbabaabababbbaabababbaababbaabababaabaaabaabbabbbababaabaabbaabbbbbbaaabbababaabbbaabaaaabaabaabbabbaabbabababbbbaabbabbabaabbababbbaaaaaababbabbbaaaabbababbababaaabbbbbabaabbaabbbaabbbbabbbababbbbaaabbbabbababbbaaabaaabbbaaabababaaaaabbbaabaaabbbbaaabbaabaaaabaaaabbabbbabaaabbbbabaaabaaaaaaaaaaabbabbababbbababaabbabbabbabaaabababbbbbbbbaaaabbabababaaaabbbbbaaaaababbbbbabbbabaabbbbabaabbbbaaababababbbbaaaaabbbaaaaaaaaaababababaaababaaaaabbaabaabaaaaaaabbaabababbababaababaaabbbbbabaabbbbabababaaaaaabbabbaaaaababaabaababaabaabbbaabaaaaabababbbbaabaababbababbabbabbabbbbabbababaabbaaaabbbbaaababaaaaabbabbababbbabbabbabbabbabbbbabbbababbbbbabbbabbaaaabbabaaababaaaaaababbaaabbbbbabbababbbaabaaababbbababaaabbbbbaaabbbbbababbbabbbabbbbbbabababbabbaabaabaabbabbbaaabababbbaababababbaabbabbaabbabbaababbbabbbabaaabaabbabababbabbbbbaabaabbbbbbbaaabbababaaabbbbabbbbbaaaabbabbabaaaaaabaaabbabbaaaaaaabbabbabbbabaabbbababaaabaaabbbabbabbbabbaabbbaabaabababbbbbbbbbbbbbbaaabbbbabbababaaabbbababaabbababbbabaabbaaababbbbababaaaabaaaababbbabbaaababababbabaaaaabbabaaababbbaabaaaabbabbbbaabaaaabbbbaabaaaaaaaaabbaaabaabbbaabbbbaaaaabaabaabbababaabbbabbaaabbbaaaabbabbababbbabbaaaaabaabababbaabaabaaaababaaaaabababbbbaaaabbaaaabaaabaababbaabaaaaaabbaaabbbababbabbbbbbbaabbbbaaabaababaaabbababaabaabbaaaaababababbbaababbbababbbabaababaaabbbabbbbbbabbbbaaabaaabaabbaabbababbababbaaaabaaabbaababbababbbaabbbbaaaaaaaabbbbabaaaabbbbabbaaaabbbbbbbabaabbababbaabbaababaaabbbababbabbaabbaaaabbaababbabbbbbaabbbbaaaabbbababbaaaaababaaaabbbbbabbababbbaaaaabbbbbbbbbbbbaaabbabaaaabbaaabbbbbbabaaaaababbbaabaaababbbbbbbaaaaaaaaaaababababbbbaaabbbabbabbbbaaaaabbabbabbaaaabbabaaabaabbabbaaabbaaaaaaaababbbaabbabbaaabbaaabbbaaaabababbaabbabbabbbbbabbababbabaabbbaaaaabbaabbbbbbbaaabbaababbaaabbbbababbbababaaabaabbbaaaaababababbbaaaaabbababbbbabbbaabaabaababaaaaaaaaaababbbbbbaababbbabbaabbababaabbbabbaabbaaaabbbbabaabaabbaaabbbaababbbbabbaabbaabaabbbabbbbbabbaaaabaabaababaaaaabbabbbabaaabaabbabaaabbbabaaaaabaababbbaababaababbbabaabbabbaabbabbbabbbaaaabbbaaababbbbaababbbaaabbbbbaaaabbaaaaababbaaaabaababbaabbbbbabababbbbabbbbaaaaaaaabbbabbbbabbbaaabababbaabbabbbbbbababbabbbbbbbabbaabaaabbbabbabbabaaaababaaaabaaabbabbbbabaaababaabbbaabbbaababbabaaaabaaaaaabbaaaabaaabaaaabaaaaaabbbaaababaaabbbabaababbbbbaaaabbbaaabbbabaabbbbbaaababbabbbbabbabbaabbaaaababbababbbaaabbaaaabbaabbbabaababaaaaaaabbbbbabbaabbaaabbbbbbababaabbaaaabababbabaaabbbaaaabbbaaabaabbaababbbbabababaaababbbbaababaaaabbabaaababbbababaababababbabbabaabbbbabaaaaaababaababbbbbaaabbbbaabbaabbbaaaaaabbbabbaababbbbbaabaabbabbaabbbababbbaaaabbbabaabbaabaabaaabbbaaaabbbaaabaabbbababaabbbaabbbbbbaaabaaabbabaaaababbaabaabaaabaabaaaaaaaaabbaabbbbbbbabbababaaaaaabbbbbbbaabaabbabbaaaaaaaabbaabaaaaaaaaabaababbbaabbbbaaababbababaaababaabbababbaabbbabbbaabaaabbabababbbabbbbabaabaaaaaaabaaaaaaabbbbbababbabbbabaaababbaabaabbabaaaaaabbaaaabbbaaabbabaaababbaabbabbaabaaaabbabbaabbbaababbababbaaaaababbabbaaabaaaabbbaaaaabbababbaabbaaaaaabbbaabbabbabaabbaabaabaaababbbbabbabbabbaaaabaabaaabbbbbbabaaabbaaaaababbaabbbabbbbaabaabbabbbbaaaaababbaaaabbbbaabbbababbabbbaaababaabaabaababababbbbbbabbaaabbababababaabbbbbbaababaabaabbabbababbabaababbaaaaabbbbbaabaababbaaabbaaaaaabaabbaabbababababaaababaaaaabaababaaabaabaaabbabbaaaaaaabbabbaababaaabbbaaababbbbbbaabbaabaabbabbbaabbaabaabbbaaabbabbbbaababbbaaabaaabababaabbaabbaabaaababbaababbbaaabaaabbbbaabbbbbbbbbaaabbbabaaabbaaaaabbabbbaababaabbabaabbbaaabbbababababbbaabbabbbbababbbabbbabbbaaabbbaabbaabaaaabbbbaaaabbbabababaaababaabaabababbaabbbaaababbaababaaabbbaabaababbabbabababaabbaaababaabbbbabababbbbbbabbaaaababbabaaaababababababbaaabbbaababbbabaaaaaaabbbaababaaaaabbaabaaaabbabaaababbbbaabaababbaabbabbbbaaabbaaabbbaabaabbaaaabbbaabbaababaaaabaabbbbbbbbbbbbaaabbabaabababbaaabababbbaabbaababbaaabbbabbaaabbabbbaaabaabaabaabababbbbbbaabaababaaaababaaaabbababbabaaabbaaabbaabbaaabbaaababbbabaaaabaabbabaabbbabaaabaaabbbaaabaabbaabaabbabbaabbbabbaaaabbbbbbbaaabababaabbabababbaabaaaaababbaaaaabbababbaabbbbaaaaabbaaabbbabaaaaabbabbabbbababbaabbabbaaaababbbbaaaabbbababbbaababbbabbbbbbaaabaababbbaabbababaabababaaaabbababbbbbbbababbbabbabaabbbbbbaabaaabbabbabaabababbaabbbababaabaaababbabababaabbabababbbabbaaaababbabaaaaaabababbabbbabaaaaaaaabbaabbabaabbabaabaabbbbbbbbbabbaabbbaabbbaaabbbabaaaababbbaaaabbbabaaaaababbababbaaabbbabaaaabbaababababaabaaabaabbbabaababbbabaaabaababbbabaaabbbaaabaababaaabaabbbababbaaabbbbbbaaabbbabbbbaabababaababaaaaaabbbbbabbaabbaabaabaabbaabbbaaaabbaabbababababbaabbbaabaabaaababbabaabbbbaabababaaaaabbbabbbaababaaababbabbbabaaabbabbbbbbbbbbabbbbabbbababaabbbababbabaababbaabaabbbbbbaaaabaaabbababbbaaaaabababaaaabaaababbbbaabababbaabbbabbaaabbabbbbbaabaaaaaabbbabbbbbbaaabbabbaabaaabbaabbbababbbaababababbaaaaaabbaabbbabaaaaaabaaabababbaaababbbbbabaabbaaababaaaabaabbababbbababbabaaaabababaaabbbbbbbbbbbbbabbbaaabbbaaaaabababbbaaabbababbabaaabbabaabbbbabaabbbbbaabaaabaababaaabbababaababbaaaabaaabaaabaaaababbabbbbbbbabbaaaaabbbabaaabaabaabbbabbbaabbabbbbabbaabaabaaabaabbbbbbabaababbbbabbbbbbaaaaaabbaabaaababbaabbbabaabbbbabbbabbbbaaaaaabbbbaaaaabbbbabbbaaabbbbaaaaaabbaaaabbbbaaaababbbabbbbbaaabbaabaaaaaaaababbabbaaaabbaabaabababaaabbbabbabbbaaaaabbaaababbbbbabbababbbbaaaabbabababababaabaaabbaaaaabbbbbbaaababaaaabaaabbbaaabbbbbbbabbaabbabbaaaaaabbbaaaaabaaabbaabaaabbbaabbaaaaabbbaabababaaabbbabaaaaaabbaaaaabbaaabbbabbaaaaabbaabbabaababaaabababaaababbbbaaabbaabaaabbaaaaaabaaaabbbabbbbbababbbbbbbbaababbbbbbbabbabaaababaabbbaaaaaabbbbbbabaabbaaababaaaabbbabbbbbaaabbaababababababababaabaaababbababbabababbaaaabababbbabbbbbaaaaaabaabbababbaababbabbaaaabbabbababbabbbabaabaaabbbababaabbbbbbaaaaaabbaaabbbabbbbbbaaabababbbabaaabababbbbbaabaabbbbbabababaabbbbaaaabababbbabbaaaaaaabbabaaaaaabaaaaabbaaabaabaabaaababbababbabbaaabbbbaababbbababaabbbaaaaaaabbaaababaabaabaaaabbbbbbbbbbababaaabaaabaabbabbabbabbaaaaabababbbaaababbbbabbbaababbbaabbabbbabbbbbababaabbbabbaaabbabbbbabbbbaabbbabbbbbbaababbbabbabbabbaaaabbabbbabbbbbaabaabaaaababbbbaaabbbbbbabbbbaabaaaababbbbababbabbabaabaabaaaaabababbabaaabbaaaabbbbbbbaabbbbabbbbabaabaabbbaabbbbabbbbaaaabaababbabbaaabaaabbbabababaababbabbbbabbbabbabaaabbaaaaaaaabbabaaabaaabbbabaabbbbbbababbaabaabbaaabbaaaabaaaaabbaababbaaabbbaaaabbaabbabbaabbbbabaaaaaaaaabaabbbbbbaaaaabbaabbbbaaabbbababbabaabaabbbbbababbbbbbabaabbbaaaaaabbbabbbbaaabbbaabbbbaaabbbaaabaaaaaaaababbbababbbaabbaaaabbbbbbaabababbbaaabbaababaabbbaaaaabababaaabaaaaaababaaaaaabbbabbbaaaaaaabaababaabbbbabbbaaaaaababbbbbbbaaabbbbaaabbaaaabbbbabbaaabbbabbbbbbaababbabaabaaababababaaaababaabbabababbbbbbbbababaabbbbaabbabbbabbbababbaababaaaaaababbabaaaaaabbbbbbbaababbbbbaaaaaabbbbbaababbbaaabbbabbbaabababbbaaabbababaababbabababbbbbbaabbbbbaaaabbbbbbaaabaabbabbbbaaaabaaaaaabbaabaabbbbaabaabbbbbbabaababaaabbbbabbabbabbbbbaaabbbaabbabbababbbbbaabaabbbbbabaabbbabbbaaababbaaaaaababbbabbaaaaaaabaaababbbaabbbbbaaabaabbabbbaaabbaaaabbbbababbaabbbbbbaabbaabaaabbaaabaaababbbaaaabbabababbbbabaabbbaaaaabbabaabbbbaaabaaabaabaaababaabbaabaaaababababaaabbabaabababbbbbbaababbaababbbbbbbbabbaababbbbabababbaabaabaabbbbaababaaabaaababababaabbbaaaaaaaaabbbbbaaaaaabaabbabaababbbabaabbbaabbaaabbbaaabbababaaabbabbaabaababbaaabaabbbbaabbbabbabbbabbbabaaaaabbbaabaaababbbaaaabbababaabaaaaaabaababaaaabbabbbaaabaaabbaabbaaaabbbbbbbaabbaababbbaaaabbaaabbbaabaabaaaabbabbbaababaabbbabaabbabaaabbaabbbabbbbbbbababbabbbbabababbaabbabbaaaaababbaaaaaaaaabbabbbbbbbaababbbbaabbabbbaababbbababbbbabbbaaaaaaabbabaaaaabababbbbbaaabbaabaabbbaaabbbbbbabbbabbababbbbbababbbbbbbbababbbbbabbbabbbabbabaaaabbaabbbaabbbaaaabbbbbaaabababbbbaabaaaaaabbabaaaaaabababbbaaabbaababababaaaaabababbbbababaaabbbbbbaaaaabbbbaababaaabaabaabaaaaaaaabbaaaababbaabababbbbabababaaaabbabbbababaaababbbbabaabbbbaababaababaabbbababbbbbbbbbbbbaaabbabbbbbaaabbabbaababaaabaaabbabaababbaaaababaaabaabaaababbbbaabaababbbababbaabaaaabbbaaabaaaababaabbbbababbabbaaaaabbbaababbbbbbbaaaababaaaaaaababbbababbaabbaaaabbbabbbbbbbbabbbaaabaaababbaaaababaabaabbbbbaabaaabbbbbbbaaabbababababbabbabaabaaabbaababbabbbbaabaaababbaababbbbaabaababaabaaaaaababbbbbaaabbaababbababbbaaabbabbababbabaaaababababbbabaaaabbaabbbbbbaabaababbabbbaabbabbabbbaaabbbbabbbbbbabbabbbbaaaaaabbaaabbaaaaabbabababaaaabbbbbbbaabbababbbbabaaaababbabbaababbbbbaaabbbababaaabaabbabbbababaaaabbbabaaaaaababaaaabaaabbbaabaabbabababbbaaabaabbabbbbbababbaabaabaaaabababaaabaababbbabbaababbabbabbabbaabbaabbaabbaabbababaabababbbbbaaaababbbabbaaababbbababaaaaaaababababbbaabaabaababbbabbbabaabbbabbaaaabbbababbabaababbbbabbaabaaaabbbbabbaaababaababbababbbbbabbaaabaabbabaaaabbbbbbbabbbbabbaaabbababbbbbaaababbbbbabaaabbabbaabaabbbbbababbababaabaaaabaabaaabbbababababbaaaaaaabaaaababbbabaaaabaaabbbbbaabbbaaaaaaabbbaababaabbabaabaaaabaaabbabbaaaabbbbaabbabaaabbbabbabbabbabbbbabbbbbbabaaaaaaaaabbbbbbabaabbaaabbbabaaaaabbbabbabbabbbabbbabaabbabbbaaabababbabbbaabbbbabbabaaaabbbbbbbbaabaaabbbaaaabbabaaababbabaaabbbaaaaaabbababaaaabbaabaababbabbbabababbbaaabbabbabbbabbaaaabbaaaabbbbaabaabbaabbaaaaaabbbbbbaabbbaaaaabaaaababbabaababbbabbabaaabbaabbaabaaabbbbababbbbabaababaaaabbbbabbbbbaaabbaaaabbbbbbbbbaaabbbbaababbaabbbaabbaababbbbbaaabbbbaabaaabaabbbbbabbabbbaabaaababaababbbabbbabbabbbbbaaabbbbabbbabaabbabbbaaabbbaaaabaabaabaabaaaaaaaaaabbabbbbababaaabbbabaabbbbbaaabbaabbbbaabbabbbabbbbabaaaababbaabbaaaaabbbabaabbbaabbabaaaababbaaabbbaabbbaabaaabaabbbaabaaaaaaabaaaaaaabbbbabaaaaaabbababaaabbaaaabbababbbbbbabbaabbbbaabababbbbbbbabababbbbaabbbbbaaaaabbbbaaabaababaaaabababbbbbabbbaaabbaaaabaaaaabaabbabbbabbabbabbbaaabaaabaabbbbbababbbaabbbaabaaaaaabbbaaabbababababbbbbaabbaabbbaaabaabbbbaaaabaaaaaabaaaabaaaaaaaabbbbbabbaaaaaaaaabbaaabbbbbabaabaaaaabbbabbbaaabaabbbbaaaaabbababbbabaabaaaaabbbbaaabaaabababaabaaabbbbaabbbaaabbbbababbbabaaabaaaabbaaaaaabababaaabbabbbbababbbaaabbbbbbaaabaababbaabbbabbaabababbababbaaaaaaaabbabbabaaaaabbbbbbbbbaabbbabaabbbbbbbbabbababbbaabaaaabbaaaaaabaabbabbabaaababbbbbbaaaababbbbbbbbbbbabbbbbbbaaaaabbaaaabbbbabbbbbaabaabbabbbbbbbbbaababbaaabbbbabaabbaababbabaaaabababbabbbaaaababaaaaaaabaabaaaaaaabaabbbaabaaaaaabbbbaaabaabbaaaabbabaaaabbbaabbbabaabaaaaaaabbbabababaaaaaaaababaabaababaaaabaabbbaaaabababbabaaaabbbbabbbabaaabbabaaabbabbbabbbbaaababababbabbaabbbbbbaaaaaaabaabbaababbaababbbabaababbaababbbaababbbbbabaaaabbaabbbabbbaaababababbababbbaabababbabbbabababaaaabaababaaabbbbbbbaaaaaaaabaabbabaabbaaaaaabaabbbaaabaaabbbbaaabaababaaaabaabababaabbbbbaaabababbbabbababaabaabaabbbbbbbaaaababbaaaaaababbababaaaabbaaabaababaabbababaaaabbbbbbbaabbabbaaaaaaaaabbbbbaababbabbabbaaaaabaabbaaababababaabbaabaaaaabaaaabaabbaabaaababbabaabbaaaabaaaabbabbbbabbbabaabbaabbaaaaaabbaabbbabaabbbabaabaaaababbbbbaabbbabaaaaaabbbbaabaaabbabbaaabaaabbaaabbbaaaaabbbbaabababbaaaaabbaaabbbaaaaaaaabaaababbbabbbbbaabaaabbbbabbaaaaaabbaabaabbbaaabaaaaabaabababbbabbbbabababaabaaaaabaaabaabbabbbbabbbbbbbaaaabaaaabbabaabbaabbbabbaaaaabababbbabbabbababaabbbbbbbabaabbabbbabbaaabaabbaaabaaaabbaabaabbbbbbbbabbbbabbbabaaaaabbabaabbbbbaabbabbbaaababaaaababbaababaaabbbbbbaaabbbbbbaaaabbaaabaabbbabbbabaaaabbaabbaaaaaababbaabaabbbbbabbaaaabbbbabbbbbbabbabbbbabbbbbbaaabbaabbbaaabbaaabababaaaaabbaaaabbbaabbabaabbabaaabbaabbbaabbbabbabbbbbbababbaaaaabbbbbaaabaabbbababaabbabbaaabaaabaabbaaabbabbbbbaaaaaaabaaabbbababbbbbbabaabbabbbabbaaabaabbbbbabaaaabaaaaabbbbaababbbabaaabbaabbabaabbbbbbabaaaababbbbabbaaaaaaaabbaaaaaabbaabbabbabbabbbabaabbbbbaabbbaabbbabaabaababbaabbbbbaabbbaaabaaababaaababbaaabbababaabbbaaaaabbbbaaabaaabbbabbbbabbbbbbbbbababbababbbabbbabaaaababbbababbaaabbbbbbbabaabbaaaabbabbaababbabbaaabaabbbbbbaaaaaaaabaabaabababaaababaaaababbbababaabaababaaaabbaabbabbaaaabaaaaaabbaaaabaaababaaaaaabbaaaaaaabaababaabbaababababbabbbaabaababaaaaaaaabababababbabbbbbaaaabaabbabbaaabaaabbaabbbaaaaaaabbbaaabbbbabababbaabbbbababaaaabbababbaaabaaabababaabaababbaabbbaaaaaaabaaabaaabbaaaaabbabaabaabbabbbbbaaabaabbabbbbbbbbaabaabbaaaaabaabbaaabaaaaabaabbbbbbaabbaaababaababbbbaaaaabbaabbbaaabbbaaabababbaabaabbaabababbaaaabababbaababaabaaabaaabbbbabaabbaabaabaaabbababbabaaaabbaabbabbababbabbaaababaaababbbbaabaaabbabaabbabbaababbbbbabaabaaabaabbbaaababbbabbbaaaabaabaaabbababbabaaababaaaabaabbabbbaaaaaabaabbaabbababaabaabbabbabaabbaabbbaaabababbbaabaabaaaabaabbabbbbbaabbbaabbbaaaabaaaaaababbbaabbbbaaaaababaabaaaaaababaaabbbaaaabaabaabbbbbababababbabbaabbbaaabbbbabbbbabaabaaabbabbabaabbaaaaaabbbabbaabaaabbaaabbaabaaababbbbbabbbabaabaaaabbbbbbababababababaaaabaabbaaaabbabbbbaaabababbbbbbbaabaaaaababbabaabbabaabaaabababbaaaabaabbabaabbbbbaababbbaaaabaaaababbbaaaabbbaabaabbabbaabaabbbbabaabbaabbaaaabaaababbbbbaaabbaabbababaabbbbbbbbbbbaabaaababbabaaaabaabaaaabbabbaabbbbbbababbababaababbabbaabbbbaaababbaaaaaaaaabbababbaabbabbbbababbabbaaaabbbbbbbaabbabbaaabaaababbbabbbaabaababbbaaaababababbbaabbbbbbaaababbbababbaaaaabbbbaababbbbabbbbbabaaaaaabbaabbbbabaaaabbbabaaabbbbbbaabaabbbbabaabbaabbbabaaabbabaaaaaabbbbaaaababaaaaaaababababbabbabbbaaabaaabaaaabaabaabbabbabaaaabbaabbabbaabbababaabaabbaabbaabbbaabbabaaababaabbbbbbbbbaababbbbabbabbaabbaabbbbaaabababbaaabbaabaabbaabbabbaabbabaaabbbabbaababbabbbaabababbbbaababbababbbbababaabbaaabbaabaaabaaabaabaaaaaababaaaaabbabbaababbabbbbababaabbbbaaabbbabaaaabaabababbbbbbababbbbabbaabbbabaababaaaaababbbaababbaaabbbbbabaaaabbaaabaababbababbaaaaaabbbabaaaabaabababbbbaaaaaabbbabbabbaabbbaaaaabaaaabbabbbabbabbaaabbbbaabbaabbabbabbabbbabbbbbbbabbaaaaaaaaabbaaaaabbababaaaaaabaabbbbbbabbbabaababbbaaabbababaabababbbbaabbbaabbbaaaaabbaabbabbabbbbbbabaabbbbaaaabaabbbbbbbabbbbbbbbaaaaababaabbbaaaaaabbabbbaabbababbaababbaaababbaaaaaababbaaaaaaabbbbabaaaababbabbaaaababbaabbbbbbaabaabbbbabaabaabbaaaaabbabaaaababbbbbabbaabaaababaaaaabbbababaabbaaabbbaabaaabbabbbbaaaabababaaaabbaabababbaaaaabbabaaaabababaabbbaaababababbbbaaaababaabbbbaaaabbbabbaaababbabaabbababbaaaabbbbbbbbbababbabababbababaaaabbabbaabbbabbbababaaaaababbaabbaaaabaaaabaabbaabaaabbbaaabaaabbbbaaabaabbababbbaabababbaaababbbabbbaaabaababbbbabbbaaabaaabaaababaababababbaabababaaabaaabaaabbaaabaaababbabababbabaaaaaaaabaaabaaababbabbaaaabbaababbaaaaaabaaaaabbaabaaaabbaaaabaaaababaaababbbbbbbaaabababaababbbbbbbabaaabaabaaaaababbbbabbaabaabbabbbabbabbababaaaaabaabaaabbabbabaaaaaaababaabbbbbababbaababbaaabbaabaabbaabbaaaababababbaaabbbaaabaaaaabbaabaabbaabbbabbabbbbbbaaaababababaaaaabbbababaabbaabbbaabbbaabbababbaabaabbaabbbbaababaaaaaabbbabaaabbbbababbaabbabbaaabbbbbabababbaabbabbbabbbabaabaabbabbbbbbaaabaaaabaabbaaabbaaaabaabbbbbaabbbabbaaabbaaaabaaaaaabbbbabbbbabbbabbbabbbbbbbabababbabaaabbababbbbaaaabbbaaaabaaaaaabbbbbbbabbababaababbabaabbbaababbbaabbbbaabbbaaababbabaababbbbabbbaaabbbbabaaabbbaabababbbabaaabaabababbbaabaaabaabababbababbbbbbaaabbabbabaaababbbababbaabbabaababaabbbbbbbaaababababababbbaaaabaabbaaaaabaaabaabaaaabaabbbbbababbbbaaaaaabbbaaababbbabaaaababbabbbaabbbaaabbbabbbababaaaaaaabbbbbaaabbbbaaabbbababaabaaaabbaabaaaabaabaaabbabaabbbbbabaababaaaaaaaabbaaabbbabaababbabaaabbbbaabaabababbbbaababbababaabbaabbabaaabaabbaabaaabbaabbabbaabaaabbaabbaaaabbbbbbababaabababbbbbabbbbbaababaabababababbbbababbaabbabbbbbbaabbbbaabbbbababbabaababbababbaabaabaaaabaaababbaabaaaaaababbbabbabbabbbabbaababaababbbbbababaabbbabbabababbaaabbaaaaabaaabbbaaabaabaaabbbbaaabaabaaaaabbbbbaaabbbabaaaaaaababaaabbabbaaaaaababbaaaababbbbabbbbabbbbbbaaaabbbbbababbabbbbbbabbaaabaaabbbbaabaaabaaaabaabbabaabbbaabaaaaabbbbbabbbbaabababaabbbaaaabaaaaabaaabababbbabbbbbbababbaababbaaaabaababbbaababbbbbbbaabbbabbbaabbababaaabaababbbaaaababbbbabababababbaaaabbbabbabaabbaaaaaabbbbbbababbbaabaabababaaabbbababaababaaabbaaabbbaaaabaabaaaaababaaaaababbbabababbbaabaaabbaabbaaabababbbbaababbabbaabaaaaabbbbaaabababaaabababbbabbbababbababaabaabbababaaabbbabaaaabbbaaaaabbbaabbbbaabbbabababbaaaaaaaabaabbaabaabbaabbbabababbaabaababaabbbbbaaabbbbbbabababbabababbabbbaababbaabbaaabaababbbabbaababbabbaaaaabbbbabbbaaabbbabaabbaaaaabbbbbabababbaaaaaaabaabbaabababababaaaababbaababbaababaabbbbaabbabbbaaaababbabbbabaaaaaaaaabbbaaababaabaabbbaaaababbbbabbbbbaaabbabbbabbaabbbbabababaabaaaabaaababaaaaabababaaabbabaaabbbaaaababbbbbbaabbbabbbaaababbbababababbabbbbbbbabaabababaaabaabbbbbbabbbbaababbabaaaaaaababbabaabbaabaabbaaaaabbbaaabaabaababbabbaaaababbaabbaaabbaaababaaabbaaabbababbbabbbbbbabbaabbbabbbababaaaabbbbbaabaabbbabbabbbaababbbabbaabbbbaaaabbaaaaaabbbaabababaabbabaaaaabaaaaabbbbaabbbaaaabbabbabaaabbabbabbabbbaababbaabbaabababababaaabaaaaabaabbbabbaabbbbabbbaabababaaaababbbaabbabaabbbabbaabbabbbbaaaaaaabbaabbabaabbaabbabaababbbaabbaabbbbaababaabbaaaabaabaaaaabbbaabbbbbbbaabaababaaabbaaaaabaaaabaabbabbabbbabaaaaababbbbabbaaabbaabaabbbbaabbbbabbbbabaabbabbbbaabbaabbaaababaaaaabbaabbbababbbabbabaababbabaababbabababaaaaabababaabaababbbabababbaaabbbbaabbbbbbabbbbbbbababbbbaaabbbaabbaaaabaababaabababababbaabbbabbbabbaaaaabbbaaaababaaabbabbbaababaaaaaabbaaabbabbbabbaababbbbbbbbababbbbbbababababaaababaaababbabbbaaabbbbabbabababaabbabaaabbaaabbabbbbbababaaabaababbaabaaababbbbbbbbaaaabbabaaaabbbbaaabbbabaabababbabbbaaaaabbbbaaaaabbbbbbaabbbbaaaabbbbbbbaaaabbbaaaaabbabbabaabbbbbbbbbbbbaaabaabababbbbbaaaaaaabaaaaabbababababaabbbbbabbabbabababababbaabaaaabbbabaababbbbaababbbbbababbbbbabaaabbbababbbabaabbaababaaababbaabababbbaabaabaaaababbaabbbabaababababbbababaaaabbabaaabaaaaabbbbabaabababbabbbbbbaabaaababbabbaaabbbbaabbbbaaabababbababaabbbbabaababbaabbaaaabbabbabbbbaabaabaaaaabbaababbbbaabaabaabbabaaabbabababaabaabaabaabbaaaabaabbbbbbbaaaaaaaaaaabaaaababbbababbbbbbbbaaaabbbaaabaabbaaabaabaabbabbaaabbaaaabbaabaabbbaaaaaabbabaaabbbabaabbaabbabbbbbbbbbaaabbaabaaaababbbbabbaabaaaaaababababaaabbbababbbbabbaaaababbbaabbbbbbaabbbbbabbbbabaaaaaaabababaaababaaabbaabbbaabbaaaaabaaaabaababaaabbaabbbbbaababbbbbababbbbbaabbbbbabbaabbabbabbbaababbabbaababbabaaaaabaabababbaaaaabaaaaabaaababbbabaabbababbabaaaaaaabababbaaabbaabbabababababababbbaabaaaabaaaaaabbaabaaaabababbbbababbaabaabbabbbbbabbaaababaaabbabbbaaaaabbbaababbbaabbabaaaababaabbbbbababaaaababbabababbaaaabbbaabbbbbbaababaaabbbbbababbababbabbabbbbbbbabaaaabbbbabaaaabbaaabbbbbaaabbaabbbaabbbaabaaaababbbbbbbabaabbaababaababaababbaaaaababaabaaabbbaabaabaaababaaabaabbbabbabaaabbababababbabbbbbaaabaabbbabbbbababbbabaaaababbbbbaababbababbbaaababbbababababbbbaaaabbbbbbbababbbaaababbaabbbbbbabbbbbbaaaabbbabaabababaabaaababbaaaaaaaaaaaabbbbaabababaabaabbbbababaaabbbababbbbbaaababababaaabaabbbaaaaabbaabbbbbabbabbabaaaababbabbbaaaabbaabbbbbabbabbbaabaaabbbaaabbaabaabbbbbaababbbbbbbaabbbabaaababbbbaaabbabbbbbbbaaababaababaaaaaaaaaabbbbbbaababbaababbabaaababaaaaabbaaaabbabababbaabbabbbaabbaaabbbaaaabbaaabbbbaaabbababbbaaabbbaaababaaabbbababbababaaabbaabbabbbbbaaabababbbbbabaabaabaaabababbbaaaaababaabbbabababbaabbbaababbbabaabbbabbabababbaaaabaaabbbabaaaabbababbaababbaababaabbbbbaaaaaaabaaabaababaababbbaabaabaabbbaaaababbbbaaaaaaabbbbabaabbbbabbaaababbbabbaabbabbbabaaaabbabbabaabbababaabbbababbbababbababbbabababbababbbaaabababbaababbaabbabbbbaabababaaabaabaaabaabbbaabbaaabaaabbaaaabaabbaababbbaaaaabbabaaabbbbabaabbaabbabbababbaabaababaaaaabbbaaaabbaabbabaabababaabaaabbaabababbbabaaaabbababaaaaaaaabaaaaabaababbaababaaababaaaabbbababaaabbaabbaaaababaabaaabbabaabaabaabbababbabababababbbaabbaaababbaaabbaabbbaabaaaaababbbaababbbbaabaaaabaabaaabbaaaabbababbbaaaaaaaabbbababaabaaabaaababbbbbaaabbabbaaaaabbaababaabbabbbaababbabbbaaaabababbbbbbaabaabbbbbbbabaaaabbababaaaabaaababaabbbbbabaaabbaabaababbababaabbbbaaabababbbababababbaaaaaabbaaaabbabaabbabaabaabbabbbbaababaababbbaaaabbaaaaabbabbaabbbabbbaaababbaaaaabbaabaaabaaaababaabbaabbabaababbbbbabaabaababaaaaaaabbbbaaabbbbabbaabbaabbaabababaaabbbaabaaabbbbaabbabbbabbababbaabbbabababbaabbbbabaabababbaaabbbabbbabbababbbbabbaabbaaaabbabbabbbabbbaaabbbbbababbaababbaaabbabbbabbbabbabbbabbabbbabababbabababbbbaaabbbbbabbababbbbbaaaabaaabaaabbaabaabaabbabbbaabaabbabbaaabbbbabaaabbbaabbabababbbbbbbbbabbaabaaabbbbabababaaabbbbabbbabbbbabaabaaaaaabaabbbabbaaabababaaaabbbbbbbbbabbabbbabbbabbaaaaaabaabaaaabbaaabaaabbabbaabaaaaaaabaababbaabaabbbbabbabbaaaababbbababbaaabaaaaaababbaabbabaaabbabaaabbaababababbbbabbbabbbbaaabbbbbabbaaabbbaaaababababbbbababababbbbbabaaabababbbaaaaaababbaaaabbaaaabbaababbbbbababbbbabbabbaaaabbaabaabbbbbbbbabaabaaaaaabaababaabaaaaaababaaaaabbbababbbabababbabbbbbbbabbabbbbabbbbabbbbbabaaaaaabbaabbbbaabaabbbaabaabaabbbbbababbabaaabbbaabbbbbaaaababbbaabbaabbababbbaaaabbbabbabaaabbbaaabbbabbabbababaabbabababbaaaabbbaabbabaabaaabaaaabbbabaaaabbaabbbabbbbaababbbbaabaaaabbbababbaabbbbabaaaabaaaabaaaabababbbbaabaaabaaabbabbbabbbbaabababaababbaabbbabbabbabbbbaababbabaaabbabbbbaaaababbaaabaaababbaaababaabaabaababbaabbaaabaaaabbabaababaaabaabbbaabbababaaaaabaabbbbabbbaaabbaabbabaabaabaaabbaabbabbbabbbbbbbababbaababbabbaabaaaaaaabbaaabaabbabbabaababbabbbbbbababaabbaabbbabaabbbbaabaabbbaaaaabaabbaabaaaaaaaaabaaabbabaabaaabbabaabaababaabbbaaababbbabaaaaaaaababaaabbbabaaabababbbbaaaaababaaabbaababbabbabbaaaabbbaaabababababbbaababaaabbaaaabaabbbbaababaaaaabbabbababbabaabbbabaaaaabbbbbabababbaabbabaaabaaaabbaaabaababbaaaaabababaaaaaaaaaababbbaaabaaabbbbaaaaaabbaabbbbbbbbababaaabaabbbabaaabbbaaabbbbabbaabaaaababaaaabaaaaababbaabbababbabaabbbabbabbbaaabbaabbaabbabbabbbaaabbbbaaabaabbaaaaabbbbbbbaabbabbbaabbabbbabbbbbbabbaabababababababbabaabababbaabababbbbbabaaaabaabaaaaaaaabaaaaaaaababaaaaabbbbaabababbbaaaaaaabbababaaaaaabbabbbaabbbbababbbaabbaaababbbbaaabaabbabaabaaababbbbabababaaabbabbaaaabaaaaaaabaaaabaaabbbbaaabababbbaabbbbbabababbabbaaabbaaabaaabaaabaabbaaababbaaaabaaabaabaabbbaabbabbabbaaaaaabbbbaaabaaabbbabbabbaaabaaaabaabbaaabbbabaaaabbababbbaaababbabbababbabbbbababaabaabbbaaaabbbbbbbabaabaaaaabaabbabbaaabbaaabababbaabbbbbaaababbaabaabbabbabbbbbbababbbbbaabbbababaabbbbbbbaaabaaabbbaababbaaabbaabbbbaaababaabbaabaaababbabbabbabbabaabbbbbaaaabbabaaabbabbbbbababaaaaabaababbabbabbbabbabaaababbbabbbabaaaabbbbaaabbbbbbaabaaabbabababaaabbababbaabaaaabbaaabbbbbbababbaabbababbbabaabbbaabababbbaaababababaaabaaaaaababaabaaabbaabaaaabaaaababaabbbaaaaaaaaabaabbababbabababbbaaaaababbabbaaaaaabbaaabbbabbaaaababbbaababbaaababbaaababbbbbbabaaaaaabbbaabbbbabaaababbababaababbbaaaaabababababbaabbbbbbbabbbaaabaaabbbabbbabbaaabbabbbbaaabbaaaaaababbbbababaaaabbababaaaabbbbaabbabbbabbbbbaaabbbaaaabbaaaaaaaabbbabbbababbbabbaaaaaabababbbbbabaabaabaaaaaababbabaaaabbabaabbbbbbbbbabbaaababbbabaaabaababbbabbbbaababbabaaabbaabbabaabbaaababaaabbaaaababaaaababbaaaaaaaaabaabbbbbabaaaaaabbbaaaaabaabaaabbbbbbaaaaaaaababaaabbaabbabbbbbaaabbabaababbbaabbaaaabbaaaaaaabbaababaabaababaaabbaaaaabaaaabaabbbaaababbbbbabbabbababbaabbbaabbaaabbababbabbabaaabbbbbbaabbbababbaabbabaaabbabbbbaaabaaaababaabaabbbaaaaaabbababbaaabbaaaaabbaabbbaaaaabbbbbbbabbaabbbbbabbababbaabaaaabaabaabaaabbaaabaaababbababbbabbbbbbaaaabbaabaaaaabbbabbbabababaaaababbbabbaaaababbbbbaaaaababaaabbbabbaaabaaabbabbbaabbaaaabbaaaaabaababaaaaaaabbbabababbbaababbababbbababaaababaabbababbaabbaabbaabbaababbaaabaaabaaabbabbababbababaabbbbaabbabbbaabaabbbbbabaabbaabaaabaaaaabbbaabaaabbabaaabaaaaabbabbaabbaaaababbbbbbbaabbbabbbaabbaaaaaabbaabbabbabbbbaaababaabbabbbaaaabbbbbaababaababbbabbbabbbababaaaaabbabbbbbabbabbabbbaabbbbaaabbbabaaabaaabbbbbbabaaaabbabaabbabbaaaabaaabbbbabbaabaaabbbbbbbbabbbaababbbbbaabbbaabbbbbaabaaaaaaaabaabbbbbbbbbbaaaabaaabbbbabaaababaaababbbaabaaaabbaabaababbbbbbaaaaabaabbbbbaaaababbbaabaababbabababbabababaaaaabbaaaabbaabaaaaaababaaabaabbaababaaaaabbabbabaaaabbbbaabaabaaabaabbabaababaabbabbaabaabbbbbbaabaaabbaabbabbbaaababababaabaabbbabbbababbbbbaababbbabbbbbababbaababaaababbbaaabbabbbbbbbabbbbbbbabaabaaaaababbaababaaaaaabaabaaaababbababbababbbbabbabaaaabbabaabbaaaaabbaaaabaaaaaaaaabbaabaabbbbbabbbaabbbbaaababaaaaabaaaaabaaababaabbbabbbababababbabaaabbabbabbababbbbaabbbabaaabaabbabbbabaaaabaabbbbaabbaaabaaabbbbaababbbaabbbababbbbbbabbaaaaaaaababaabbbbabbbbaaaaaaaaabaababbaabbaabbabbbaabbbbbbbaabbaaabababbbbbabababbbaaaabbbaaaabbbabbaaabbbababaabaabaabbabbbbaaabaababbababbbaaabbaaaaabaaabbababaaabbbabbababbaabbbaababaabbabababbabbbaaaaaaaababaaabbabbbaabbaabbbbaabbaaababaababaaaabaaababbbbaababaaabbaababbbbbabbbaabbbbababbbaababaabbbabaaaaabaabbbbababaababbbbbaaababbaaabbabbaabaababbbbbbabaaabababbbbbbaabbaaaabbabbaabaababbabbbaaaabbbbababababbbabbabbbaabbbbaabbbaababaabbbbaaabbbabbaabaaaabaaabbaabbbbbbaabbabbabbaaabbbbbbaaabbaabbbaabaababbbbaabbabbabaaaababaaaaabaabaaaabbbbababbbbbbabbabbbbabbbbabbbababbaaaaabaabbabbbbbaaaabbabbbaaabababbaaabbbabbbaaaaaabbabbaaabbbaabaaaaabbaabbabbababbaaaaabaabbbbbbbbabbbabbaaaabbbaaaabbaabbbbabbbaabaabbaaaababababbbbaabaaaaabbbbabbbaababaaaaaabbbabaabaaaabaaabaabbaaaaabbabbbbbabbaabababaababaabbbbbbbbbaabbaaaabbbbaabaaabbbbbbaaabaabaabbbbaaaabbbbabaabbbbbaaabbaaaaaabbaababbabbabbabaabbbbabbbaaabaaababbabbbbabbaaabbabaabbbbaababbabbbbbabbbabbbbbbbaaaabaabaaabbbbaaabbbabbabaaaaabaaaabbaabaaababaaabaaaababbbabbbabbaaaaabaabbabbabaabaaabaabbbaababaabaabaabbababababbaaaabbbaabbabbababaaabbbabbabaaabbbbaabbbabbbbbbbabbbbbbaabababaaababbaaababbabaaababaabbbbaabbbbbbbaaaababbbbbabbbbaabababaabbabbabaaaaabbbaaababbbabaaaaaabbabbbbaaabaabaabbbabbaaababbaaaaaabbbaaaaaaabaaaaaabababaabbbabaabaabbaabbbbaabbabababbaaabbaaaaaaaaabbaabbbaabbabbabbaaaaaaabbbbbaabababbaaababaaaaababaaabaaabbbbbababaaabbabbbabbababaaababababbababaababbabbabaabaababaaaaaabbbabbaaabaaaababaabaaabababbaabbabaaababbaaabaabaabbaaabaaaabbbaaabaabaabaabaababbbbaababbaabbbaaaabababbababbaabaaabbaabaabbbbbbaaaabbabbaabbbbaabaababbbbbababaabbbbbbabbbabbbbbaaabbaabbbaaabaababbbaabbabbbbbabbbaabbbbabbbbabaaaaabbbbabbaaaabaabbbbabbabaaababaaaaaabaabababababaaaaaababaabaabbbabbbababaabaaaaaabbaaaaaaabbaaababaaaaaabbbaababaabaaaababbaaabbaaaaabbbaaababbbabaabaaaabaaaaaaaaabaabaabbbaaabaabaabbbbaababaaabbbbaaabbbbbbabbbbbabbabaabbabbbaaabaabbaabaaaabababaaabababaababaaababbabaaaababbbbbbbbbababaababbbababaababbbabbbbabbaaabaababbaabbbbbbbbababaabbbbbabbbaabbbbabaabbbbbababbbabbaabbbaaaabaaaaaaaaaaaaaabaabbbaabbbaabaaabbbbaaaaaaababaababaabbababbbaaabbaaabaaaaabbaabbbbaaabaabaabbaabbabbaaaaaaaaabbbbaaabaababababaabaaabaaababaabbbaabaaababaaabbbbabaaabbaaaabababaaaabbbabbaabbaabbbbbaababaaaababbaaaabbaaababbabbbabaaababbbbaaaababababaabbbabaaaaaaaabbbbabbbabbabbbbabaaaabbabbbbbbbbaababaaabbbbbaaaabbaaaabbbbabaabbaabbababababaabbabbbbbbbaaaaaaaaabaabaaabbabbabbbbaaabbabaaaababbbbbaaababaabbababaaabaaaabbabbbabaabbaabbbbbaaaabbbbaabbbbbbbbbabbaabbbabbaabaabbbaabbbabababbabababaaabaababaaabaaabaaabaaaabbbababaabbabbbabbababbbaaaabaabbabaabaaaabababbaabbbabaabaabbabaaabababbaaabbbbbbaabbbbbbbaabbabbbbabaabbabaabbbbabbbbabbaaababbabbbaaaaaaaaabaabaabababaabbbabbaabbbaabbbbaaaaaaaaababbbbabbbaabbbbaabaaabbbbabbbbbbbabaaababbabaaaaabababbababaabaaaaabaaaaaaabaaabaababbbbbbbaaabaabaaabbbaaabaabaaaabaabbbaaaaaabbabbbabaaabbbbabbbbbbaababaabaaaaaaaabaabbbaaabbaabbbabbaaaababaaaabbbbbbaaaaaabaabbbaabaabaaabababaabaabaabbbbababababaaabaabbababbbaabbbbbabbbaabbaaababbbabbbabbabbabaaaaaabbbaabbaaababbbabaaabbbaabbaabbaaaaabaaabaaaaabbbbbaaabaabbbbabaaaaaaabaaabaabababababbaaabbbabbbbbbaaaabaaaabbbaaaabbbbabbbabaabaaababaabbaaaaaabaaaabaaabaaababbbabaaaabbaaabbaababaaaaabaaaaaaaabbbbababbbbaaaaaaabaaaaabababbaabaaabbbaaaaabbbbbbaababbaaabababbabaababbbababbbbabbbbaaaaabaabababbaabbabbabbabaabbababaabbababbaaabbaaabbbaabaaaaabaababababbabbbbbbbbaababaabbaaaaabbbbbaaababbabaabbbbabbabbbaaaabaaabbaabababaabaabaabababbaaaabababaaababbbaabbabaabbbbaaababbaaabababbbabbabababbabaabbabaabbbabbbbbabaaaababbabbbbbbabbaaaaababbbbaababbabbabbbbbababaaabbbbaababbbbbaabbbabbbabbaaababbaabbabaaabaababababbaaabbababaaabbbaababbabbbbbabbababbabbbbabbaaabbbbbbbabbababaabaaababaababbaabbaaabbaaaaaabbbbbbbbbbabbbabaabbabbabbbaaaabbaaaababbabbaababababaaaaaabaaaaaaaaaaaaaaaaaaababaababaabbabbbabababbbbbbbbbbbbbaabababbaaabbbabbaaabbbbbbbbbabbbaabbabbbaaabaaaabaaabbaabbbbbbbaaaaaaabababbbbabbbbbaaaaaaabbaabbaabbaabbbabbbbbabbbabaabababaabaaaaabbbaabaababbbbbabaabbbababbbabbabbaababbbbbaabbabbabbababaaaaaababaabbbabababaabbaabbaaaaabbaaaabbbabbbabaaaaabaabbbaaabbbbaabbbaabbaaabbaabaabbabbaaaaabaaabbaabbabbbabaaabaabaaaabaabbabbabbbbaabbbaaababbbaaabaabbbbabaaaaabbbaaabaabbbaaaabbaabbbabaaaaababaabbbabaabbbaaaaaaaaaabbaaaabaaabaabbabbababbbbbabbbaabbaaabbabaaabaababbaabbbbabaabbbbbabaaabaabbaaaabbbabaaaababbabbaaaababbabaaaaabbaaababbbbbababbbabbbaababbbbaababaaaababbabbbbabbabaabbbaababbbabaaaaabbabbbbbabbbabbbabbabbbbbbbbabaaabbbabbaaabaabbababbaaaaaaabaaabaaabbbbaaaabababbbbabaabbaababbaaabbbbbaaaabbabaabaaaababaaaababbaabababbabbbabbbabbaabaaaabbbaaabbbabbbaaabaaaaabbabbababbbbaabbabbabbabbbaaabbbaaabbbaaaababbabbabaaaaababaabbbbbbaababbbabbabbbbaabaaabbbababbbbabaabababaabaaabbabaabbaaaabaababbbaaaaababaaaaaaabbabaabbaaababababaaaababbaabbbaabaaaabbbaaabaaabbaabababaabaabaabbababbbaababbbbbbababbabbaabaaabbabbbbbabaaaabaabbbbaaaaabaabbbabbaabaabbbababbaaaababaabaaabbababbaaaabbbaabbbbbaaaabbbaaabababbbbbabbbabbbabbaaabbbbaaababbaabaaaabbbaabaabbbbabbbbbaabaabaababababbababaaababbaaabbbaabbaababbbaaababbaabaaaaabbaabbbbbbaaaaaabaabababaabbbbababbaaabababaabbabbbaabbaaababaaaabababbaababaabbbaabbbaaaabaaaaaaabbbaaabbbaaaabbbaaabbaaabaaaaaabbbbaabbaaabaabbbbaaaabbaabbbababababbbaaaabbaaabbbbbbababbabbbaaaabbaababbbaabbabaaaaaabbabbbbbbbbbbaabaaaaababaaaaaaaaaaaaaabaabaaabaaaababbaaaababababbbbaaabbbabaababbbaaaaaabbbbaaabbbbbbabaabaababbababaabaababaaabbaaaaaaabaabbaaaaaaabbbaaabbbbbbaaabbbbaaabaaabababaaaaaababbbaaaabbaaaabababbaababaaababbabaabbbbbabaabbaabbabbababbaabaaaaaabbbbbbaabababaabbbaaabbbababbabbababaabbbbbaaaaabababaababbbaaaaaaabbbbbbbaaabaabaaaabbabbbaaabaabbbbbaababababbbbaabaaabbabbbbabaababbbbabbabbbabbbabaaabaabbbaaabaabbaaabbaaabbabaaaaaaaaabababbaaabaaaaaaaabaabaaabaaabbbbaaabaabbabbabbaabbaabaabbbabaaabaabbabbbbbaabbabbbbbababbbbaaabbbbabaabaaaaaaabaabaabbaabaabaaababaabaabbbabababbbbaaabbabbbbbbbbababaaabaabbbaabbabbabbbaaaaabbabaabbaaabbbabbaabbaaaabbbbaabaabaaabbaaabbabaaaaabaabaabbbaaaabbabbaabbbabbbbbababbaabaaabaaabbabaaababbaabbbabaabbaabbbbbabaabaaababbabababbaaababbbbbaababababaabaaabaaaabaaaaabbbabaaabaabbaaaababababaaabaabbaabbbababbaaaaaabbaabababbbbbbaabaabaabaaaababbbaabbbabbabaabbbaaabbbbabaaaababbaabbbabbababbbaaaaabaabbaabbbaaabbbbaaaabababbbbbabbbbbbbaaaabbabaaaabbabbbbbababaabbbabbaabbbbabaaabbabbbbbaabbabbbaabaabaaabaababababbbbaaababbbbbbabaaababaaabbababaaabaababaaaaabbbabaaabbaaaaaaabbaabbabaaabbabaaaabaabaaaaaaabbbabababaabbbababaabbbbbbbbbbaabbaabaaabbbbbabababaaaaabbbbabababaaaabbaaaaababaabaabaabababbbbbbababababbabbaabbaabaabaabbabababaabaaaaabbaaaaabaaaaababbbaababaaaaaabbaabbaaaabbaabaabaabbabbabbaaaabaababbbbbabbabbbabbaabbabbabbabaabbaaaabbababaaaaaababbaaaaabbbbbaaababbbbabbbabaaababbaaaabbbabaaaaabaaaaabbbbbbbabababbbbbaaaaaaabbbaabbbbbaabbbbbaaaabaaaaabbbbbbbbbaaaabbbabbabbbaabbbabbbbbbababaababbbaaababaaaaabbbbbbbbbbbababbbbbabaaabbbbaaaaaaabbabbaaabaabbbbbabaaaababababbaaabbaaaaabbabaaaaabbabbaaaabababbaabbabaabbbbaababababaaaaabbabababbababaaaabababababaabbabbabaaaaabaabbbabbaaaababaababbabaaaaaaaaaaabbaabbabbbbaababbbabbabaabbaabaabbabbaababaaabbbbbaabbabbabaabaabababaaaaabbababbabababbaabbabaabbbaaaaababbaabbabbbbabbaaabbabbabbabbaaabbbaaaabaaabbaababaabbbbaabaabbabbaaabaabababbabbbbbbbbabbabaaabaaaaaabaabaaaabbbbbbaaababbbbaababbbabbbabaabaaababbbaaabbbaabaaaabbabbbbbbbbbbbbabbabaaaaaabbbaabbabbbbababbbababaababbbbaabaabbbbaaabbbaaaaaaabbaaaaaabbbbababaababaabaaaaabababaaaaaaaabababbaabbbaaabbabaaabaaabaaaabbabbbaaaabbbabbabbbabbbbabbababaaaabbabbbaabaaaaaaabaabbaaaaabbbbbbbabaaabbababababaabbabbaaabababaaaabaabaabbbabaaababbbbabaaaabababbbbaaaaabaabaababbabbbbbbbaaabbaabbbbbbaaaabbaabaabaabaababbabbbaabababaabbbaaababbbabbbbbbababaaabaaaabaabbbaabbbaaaaabbbbbaaabaababbabbaaaaabbaaaaaaaaabbabaaaaababbabbbabaababaaaabaababbaabbbaaabaabbbbbaaaaabaaaaabbbababaababbbbbbabaabaaabaababbaaabbbaabaabbbaaabaaabaababababbbabbabaabaaabaabbbabbbabaabbaaaaaabaabbbbbaababababaaaaaababbaaabbabbaabbbbbbbbabaaababbaaaabbabbaababbbabbbaaabababbbaababbbaabbabbaabababaaaabbababaabbbbbaabbaaabaaababbabbbbbbaababbabbaabbabbbaabaaabbaaababaababbabaaaabbaababbaaaaababbaaaabbaaaabaabbbbaaaaaaababbaababaabababaabbbabaaabbbabaaaabaaaaaabbbabbaababbaabaabbbabbbbaaabbaabbabaabbabaaabaabbbbbababbaaaaaabaabbababbbbbaaaabaaabababbabbaaabbaabaabbbababbaaaababbbbbabbbbbbababbbbbbbabbbbbbaabbbabbbababbbbababaabaabbabaaabbababbaabbbbaaabbbbbabbaabaabbbabbbabbaaababaabaabbbbbabbabababbabaaaabbbaaaabbabababbabbbbaabababaaaabbaababbbabbbbaabaabababbabaaabababbbaabbbaaabbbabaaaabaabaabbabbaaaaaaabbbaabbaabbabbbaabaabbbabbbbbaaaabbbbbabbbaabbbaabbbbbbaaabbabbbbaababbbabbbbaaabbbbaaaaaabaaabbbbbbababbaaababaabaaaaababaaaaaaaaaabbaababababbaaabbabbabbbababaababaababbbabaaabbbababbbabbbababaabbbaaaabaabaabbbaaabbbaababbbaaabbaaabaaaabaabbbbbbabaaabbbabababbbbababaabbaabbbababaabbbbbaaaaabaabbaabaaababbabbbbaaabaaabbaabbbbbaabaaaababbbbbaaabbbabbbbbbaabaabbaaaababababbaabbbbabaaaabaaabaababaaaabbaaabaaaababbbbababaababababababbbabaaaababbaabbbbbbabbbabaaaaabbaabaabaaaabbbbbbababbaabaababaaaaaabaabbbabbbbaaaabbbabbbbbbbabbbaabbbbbabbabbaabbbbabbaabbbbabbaababaaabaabbaaaaaabbababaaabbbbaabbabbbbaaabaaaaabbababaaabbbbbbbaabaaabbaabbaabbbabbabaababbaaaabbbbbabbbbbaabbbaaaaabaaabbbababbababbaaabbbaabaaababababaabaabbaaababbabaaabbbbbbaaabbabbbbaabaaaaaababbbaabbabbbaaaabaaaabbaabbbbababbbaaabbbbaabbbbbbabbbabbaabbaabbabbbbabaabaaabaabbbbbbbbabbbbbbaabbaaaaabaaaabbbbaaabbabbbaabbabbabbabababbabaabababbbabababbababbaabbabbbbbbabaaaabaaaaaabababbbabbbabaabbaabbabaabaaaabbaaabaabbbbaaabbaabbbaabbabbbbbababaaabbaaabaabbbaabaababbbbabababbaaaababbabbbaaababababaabbaaabaabbabbaaabbaaabbabbaabaaabbabbabbaabaaabbbbbabbabbaaaabaabaababbbaaababbbbbbbabbaaaaaaaabbaababaababbababbabbabbbbaaaabbbaabbbbabbaaabbbbaabbaaabaaabbbbbbaaabbaaaaaaaabaabbbbaaaaaabaaabaabaaabbabbaaaaabbbaaaaaababbabbbbaaabaabbbabaabababbbbbbbbbaabbbbbabaaaaaabbaabaaaaaabbaaabaaabaabbbabaabbbaaabbaaababaababbaaababaabbbabaabbabbaabbbbbbbbbbabbbabbbbaababaabaaaabababbbababbbababbabbaaabbaaaaaaabaaababbaaabbaabaabaaaabbababbbabaaabbbbaabbaabbabbabbabbbbabbbbbbaabababbbbabbbaaaaaaabaaaabbbbaaaabbbbbbabbabbbbbbbbbaaaababbbaaaababbaaabbbaabbbaaabababbbbabbbbbaababababbabaaaabababbbbbaababbabbaaaaaaaaabbbaaaababbbbababababbaaaabbaababaabbbbabaaaaabbabbbabbbaabbaaabababaabbbbbababbbbbaabbbbabababababaabaaababbabaaaabbbabbabbbababaaaaabbabaaaabbbbbbaaaabaabbbbbabaaabbabbbabbabbabaabbabbbbbbabbbaaaaaaababbabbaabbababaaaaabbabbaabababbbaabaabbabbbaabababababbbbbbaaaabbbaabbbabaabbbaababbbabaabababaaabbabababbaabbbbaaaaababaabbabaaabbabbbbababbbababbbbabbbaabbbbbaaaababbbabaaababbaabbaaabbaabbbaabaaaaabbbbabababaababbbabbbabbbbbbabaaaabababababbabbbbbaaabaaaaaaaaaaaabaaabababbbabaabbabaaaabbbaaabbababababaabaabaabbaabaaabbabbbbbbbbbaabbbababbaaaabbbaababbbaababbababbbbaaababbbabbaaaaaabaabbbaabbbabbbabbaaaaaaaabbaababbbaaabaabbabbaaaaaabbabbaabbbbbbababababaaabaaabaabbababbbaaabaaabaabbbbaaababbaaaabababaabbbaabbabbbbbbbabaabbabbabaaababbaaaabbabababbbabaabaabbaaababbaabbbaaabaabaabbaaaabaabaabbbbbabaababbaaababababbbaaaaabbaabbbaaabaabbababbbbbabbbabaababbabbbbbaabaababbababaaaaaaabbbbaabaaabababbbaaabbaaabbbbaaabbabbaaabbabaaabbaabbbbabaaabbbaabaabaaabbaaabaaaabaabbabbaaabbbabbaabbababbabbaaabbbabaabbbbbbaabaaaaaabbaabbbaaaaabaabbaabaaaababbabaabbbbbabbabaababbbaaabbabbababbaaabaabaaaabababbabbabbbbabaabbbabbbabbbababaaabbaaaaaaaabbaaaabbaabbabbaabbabababbaababbbbababaaaabbaaabbabbbbaabbabbbaabaaaaaaabbbbaababbabaabababaaaaabbbabbaaababaabbbbbbbaabbaaabbaaabbaabbabbaaabbbaaabaaabababaabaabbbbaaabaaabbbbaabbabbbaaaabbaaaaabaabababbababbbbbabbbbbababbbabbbbbababbbabbbbaaabaabbabbbabbaaabbbaababaaaababbbbbaabababaaabaababababaabababaaabaaaabbaabbabbabaaabaaaababaaaabbabaabaabbaabababaaaabaabbaaabbbabbbbaaaabbabaababbaaaababaaaabbabbaabaaaaababaaaabaaabbaabbbbaababaabbaabaababbabbbbbabbbabbabbbbaabbaaabbbbbbbabbabbbaaabababbaaaabbbbbbabbaaaaaaaaaabbabaaaabbabbbaaababbbaaaaabbbbbabaaaababbabbbbbaaabbbababbaabbaabbbabaabbabababbbaaaaabbbbbaaabababbabaaaabaabaabbaabbaaababaaabbaaaaabbbabbaabaabbbbbbabbababababbabababaabbabaabbaaabaaabaabbbabbbbbbbaabaabbbabaaaabbbaabbabababbaabbaababaaabaabbabbbbaaabaababbbbaababababbbabbbbbaabaabbbababbbaaaabbbaabaabaaaabbbbaaaaabaabbbabbababbbbabbaabbbbbbabbbaaaaabbbabbbababbbbaaaabbbbaababbbbaabbaaabbbabaaaabbbaaaaabaaaabbbabababaaababaabbbbabaabbbbbbbabbaaaaabaaabaaaaaaaabababababbababbbbbabbaaabbaababbababababbababaabaabbbaaababaabbbbbbaaaaabbaaabbbaababaaaababbbbbbaabbbaababaaababbbababbbabbbabbbababbbbbbbbabbbbaabbbbbbaaabbabbabbabbbbbbaabbabaababababaaaaabbaababaaabbbabaaaabaaababbbbbaaaaaaabbabbbbbbabaabababbabbbbbaabaabbabaabbbaabbbabaabaababababbababbaabababaabbbbababaaaababbbabbbbbbabaaababaaaabaaabababaaabaabbbbaaaabaaababbbaaabbbabbbabaaaabbbbbbbaabaabbaaabaabbaaaabbabbbaabaababbaababbbaabbabbabaaaaabbbaababbababbbaabaabaaabbbbbaaababababbaaaaaaababababbbbabababbbbbbabbabbaababbbaaaaaabaaabbabbaaaaabbabbbabaaaabbbbaaaaababbbbaababbabbbaaabbbbaabaaabbabbaaaaaaabbaabaababaababbaaaabaababbaabbabbbbabaabbbbbababbbabbababbbaaaaabbbbbabaaabbbababababaabbaababbbbbbababababbabaaaaaabbbaabbbabbbaabbbbabaabbbbbaaaabbaabbaabbbaabbaabaaaabaaabbababaabaaaaaaabaabbaabbbabaaabbaabaabaaabaababaaabbbababbbbbbaabbaabbbbbaabbbbbbbaaabababaaaaaabbababbaaaaababbbababaaabbbbaaaaababbbbbabaaaabaabababaabbbbabbaababbabbbbbabaaaabbbbabbbbaaaaaaaababbbbabaabbabbbababbbbaaaaabbbabaabaaabbabbabaabaabbababbbbbaaaaabbbbabbbabaaaaabbaaaaabbbbabbbaabaaaabaabaaabbababbbbbbabababbbabbaababbbbbaabbbaaabaabbbaaaabaaabbabaabbabbbababbbaabaaabbaabbbbababaaabaabaababaaababbbabaabbbabababaaaabbbbabbaabbababbbaaaaaababbababaaababaabaababbaaabbabaabaaaaabbaababbabaaabaababababbaababaabaabbabbbbbaaaabbabbaabababaaaabbbabbaaabaababaaaaabbabbaababbaabbaaabbababbbbbaaaaabbbbbaabbbbababaaaabbbbabbaaabbbbbaaabaabbbbababbbbaaaaaabbabbbbbbabbaabbabbaaabababaabbbbaaabaabbabbabbaaaaabbabbaabbbabbbbabbbabbbbabbaaabaabbaabbbaaabbabbbbaaaabbbaabbabbbbbbbabbbabbaabbbbbbaababbbabbbaaaabbbbbaabaaabbaaabababbbbabbababbbbbbabaaaabaabbabaabbaabbababbabbaababbbabbbaabbabaaaaaaaaaaaabbbbbbababbbbaabbbbbbbbbabbbabbaaabbaaaabbababababbaaabbababaaabbbbbbbaaaabababbbababbaaaaaaaaaaabaabbaaabaabaaabaabaaabaaaaaaabaabaabaaaababaaabaaaaabaababaabbababaaaabaabbbaabaabababaababaaaaabbaababbbababbbbbaaaaababaabababaababbbabaababbabbbabbabaaabbabbabbbaababbababaaabbaaaababababaaaaabbaabaabbabbabaaaababbabaaababbababbbbaaabbaaabbaaabababbbbbabbabbbaaabbbababbabbabbabaabbbaabbaaabbbaabbaabbbaaabaaaaabaabbbabbabaabaaababbbababaaabbbbbbabbaababaabaaababbababbaabaaabababbbbbbbbababbbabbbabaaaaaabbaaaaabaaaaabbaaabbbbababaababaaabbabbabbabbaabbbaaababbaaaaaaabbbababbbabbaaabbaabbbabbaaababbbabbbaababbbbbbbaabaaaabbaabbbabaaabbbbababbbaaaaababbaaabbbbbbaaabaaaaabbbbbbbaabbbabaaabaaabababaabbabbbabbbaabaaaaababbbbbabbbbbaabaabbbaaaaaabaabaabbabbaababaaabbabaababbaaaabaabaabbbaaaababbbababaaaabababababaaaaaababbbbaaabbabaaabababbaabbbbabbabbbbaaaaabaabbbabaaabbbbbaaaabbbaabbaaababbabaabbabaaabaaabababaabababaaabaaaaabaababbaaaabbaabaabbbbaabaaaaabaabbabaabbbaaabbbabbbaaabbabbabbbbbabbbbbaababababaaaabbbaabbababaaaabbabaabbaababbbbaaaaabaaabbbbbabaaabbbaaabbaabaaaaabbabaabaaaababbabbaababbaaabbaaaaabbbaabbaaaaabaaaabbbaaabbabbabaaabaaaaabbabbaaaababbbbbbabaaaaaaaabbbbabbbbaaabbaababbbababbbbbbbbbaababaabaababbabbabbbbaabaabaabaaaabbabbabbbbaabbbaabbbbbbbaaababbaaababbbaabbababbaaabaaaaaaaaaabbbbaabaaaaaababaabababbabbaababbabbbaaabbbbaaabbababbbababbaaabbbabaabbabaaabbbaabaaaaababaaaaaaabaaaaaaaabababababaabbbbbbabababbbbaaabababaabbaabbaababbabbbbabaaaaabbbbabaababaaaaaabaabbbbbaabbbaaabbaabbbbbbbbaabbaabbbbabaaaaaabababbaababbbbaaaabbabbbababbaababbbabaabbabbaaaabbabbbabbababbbbabbbabaababbbababbbabbaabbaaababbbbabaabbbaabaaaaaabaabbbabbbabbaabbaabaababaaabaabbbbaababaaababababababbaaabbbabbabbbbbbbbaabbbababbabbaabbaaaababbaabaaabbbababbababaaabbbbaaabaabababbbbbbaaaabbbaaabbbbaabaaaabaaaaaabbabaabaababbbaababaaabaaaabbbabbbbbaabaabaaaabbbabbbaaaaaabbabababbbbabbaaaabaababbabbbbbbbbbaaaabbbaaaabaaaaaaaabbbabbababbbbaabbbbaaaabababaaaaabaababbbaababaabaaaababaabaaabaababbbaaabbbbababbabababaaaaaabbbbbbbabbbaabbbababaaaabbbbaaaaabbbbbbbaabbaabaaabbaabbbbbabbbbbbaabaabaaabbabbaaaabbaaaaaabaabaabbbaabbbbabababbbbabbbbbbbabbbaaabbbbabababaaabbaaaababbbaaaabbbbbaabaaabaabaaabbbaaabbaabbabbbbbaabbabababbabaaabbbaabaaabbaaabaaabbabbaaabbbabbbbbbabbbbbabaaaabbaabaabaaaaababaababaaabababbbbabababababaaabaabbbbababaabbbbbbaaaabbbaabababaaabbabbabaabababaabababaaaaabaaaaabaabbbaaaabababbabaabbbbaabababbbbaabbaaabaaaaabbaabbbbabaaabbbaababababababaaabbbbbbababbbababaabbbaabbaaabaabaaabaabababaaaabbbababbaaaabbaabbbaaaaabababaaabababbabababbbaabbbbbaaabaaaaabaababaaaababbbbababbaabaababbaaabbaaaaaabbaaaabbabbbbabbaabbaaaabbabbbbbbaaabbababbbbbbbbbbbabbbbababaaaabbbbbbabbbbabbababbbbabbbababbbabaaaabaabbbbababbaaabbaabbbabaaaabaabbaaaabbaabbababaabaabababbaaabbbbaaabbaaabbbbabaaaaabaabbababaabbbbabaabbaaabaabaabbbaaaaabbbbabaaabaaaaaaaabaaaababbabbbaababbaaabbabbbbbabbaabbbbabaaaabbabaaabbbbabbaabaabbbbbabbbbbbbabbbaabbbbabaababbbbaaaaabbbabbbabaabaaabaaabbbbbbaaaabbaabbaaabaabbaaabaabbabbbbbaaaaaaaaaaabaabaabbbbabaabababbabbbbbaaaabbaababbaaabababbabbaabaabaaabaaaaabbbaaabbaaaaabaaaaabbbbbbbababbaaaaabaabbbaaabbabbabaabbabbbbabbbaaaabbabaaabbbbabaaaaabbaaabbbaaabbaabbaabbaaabbabbababbaaaaaaabbaaababaaabbbaababbbbabbbbaabbababaaabbbaabbabbbabbabbbbbbabbabbabbaaaabbaaabbbaaaabbbbabaaabbbabbbabbbbbaabbabaabbababaabaaababbbbabbaabbaaababbabbababaaabbabbbabaabaabaabbbbbaaabbbbbbaababbabababaaabaaaabaaaabbbaaaaaabbabaaaaaaabbbaabaababbabbababbabaaabaaaaaabbbaabbbbbbbaaaaabbababbabbbaabaabbaabbbaaabaababbbaaabbabaabbbbaaaaaabbbbbbbabbaaaababbabbaaabbabbbabbbaababbbaaababaaaaabababbbabaabbaaaabbaaaaaaabaaaaabbbaaaabaababababaabaabbaabaaaabbbbaabbababbbbaabbbbbaabaababaabbabbababbabbbababbabbababbbbbabbaaaabbabbaaaabbabbbbabbbaaabbbabaababaabaabbaaaababbabababbbaabaabaaababaaaabbaababbbbababaabbabaaababaabaaababababaaabbaabbbabbbbbbbbaabbabbababbbbabbbaabaaabbaaabababaababbaaaaaabaabaaaabababaabbbababbbbbabaaabababababbbbbabababbaabbbabbbabbababbaaaabababaaabbaaabaabbabbabbabbbbbabaabaabbbabbabaababaaabbbabbbaabbbaaaabababbbabbababbaabbabaabbaaabaababaaabbabbbbbbbababbbabaaaabbbbabbbaababbababbbbbaaabbbababaaababaababbbbaabbaababbbabbbbaabbabbbbbaababbbaabbbaabbbbaaababababaaaaababaaaaabbbbbabababbbbbaabbbabbbbbbaabaaaaaabaabbaaabaababaababaaaaabbbabbbabababaabbbaabbbaaabbbbbbbaaabbbababbaaabaaaaaaaaaaaabbaaaaaaaabaabbabbbbbabbababbabaaabbbbbbabbabbbbbababbababbabaabbabaaabbbbbabbbaabaabbaaabbbbabbbbbabaaabaabbbaababbaabaabbbbbbbabbaabbbabaaaababaaaababaaabaababaabbbabbbbaaaaabaabbbabaabbbaaaaabbaabbaaabbaaaabbbbbabbababababbbaabaabbbbabbbbbaaabbaaaabbaaabaabaabbaababbbbaabbaaaaabbaaaaababaabaabaaabbaaabbbaaabaabaabbabbaababbaaabaaaaaabbbbbbabbaabbaaaaababbababaaabaaaaababaabbabaaababaaababbaaabbbbbbbbaabababbbbaaabbbbbbaaabbabbaaabbabbbbababbbbabbbbabbbaaaaaaabaaabbaabbaaabababaabbaabbbbbbaabbbbbbabbaaaabababbabababbaaabbaabbbaabbbaaabbaaabbbbaabbabbaaaababaaabbabbbbbaababaabbbabbabaabbabbbaabababbbbbbaabbaabbabbaabbaaabaaaabaabbbabbababababababbaaaabbababaabbabbababbbaaaaaabbbbaaabbababaaabbbabbaaabaaaababaabaaaabbaaaababaaaaabbbabaababbaabaabaabbbbbbbaababaababaabaabbbababaabbbabaabbbabbabaabaabaababaaababbabbaabababbbabaaaaaabbabbbbabbaaababbbbabaabbabababbaaabaabaababbbbbbbabaabaaababbbababbbbabaabbbabbbbbaaaaabbababbaaaaaaabbbabbabaaaabbbbbbaababbbaaabaabaaaaaaabbaaabbbbaabbababbaaabbabbabababababbbbabbaaaaaabbbabaaaababaaaaaaabaaaaaaababbbbaaabbbbbbbbaaaabbabbaaabaababaabaabababbabaaaabaabaaaabbabbbabaaaababaaaabbaabbbaaabaabaaabaaabbbaabbaaabaabaababaaaababbbbbabbaaaaaabaabbabaaabaaaabbbbbbbabbaabbbabbabababbbaaaababaabaaaaabbabababbbaaabaababaabbbabaaababbabbaabaaaababaabbaaaabaaaabbababbbbbbaabaababbabbabbbaaaaababaabaabbbbbbabbbbaabbaabbbbaaaaabbabbbabbaababababbabbbbaababbbaaabbababbaabbaaabbbababbaabbaabbbbababbaabaaabababbabbbbbbaaaaabbbbaaaaaaabbbbbabaaaabbbbabaabbbbaabbaaababbababaababbaaabbaaabbabbaaabbabbbabbaabbbbaabbbabaaaaaabaaaaaabbbababaabbabbbaabaabbaaabaaaaaabbbbbbaababbabaabbaabaaababababaabaabbaaabbabbbababaaaaaababbbbabaabaabbbbbababababbbaaabbaaabbbbabbaababbbabaaaabbaabbababababaaaabbbbaaabbbabaabbaabaabbabbaaaaaabababaabbbbbabbabaaaabbbbaabbaaabbbabaabbaabaaaabbaabaaaaaaabaaaaaabbbabbabbbbaabbbabbaaaabaabbababaaaababaaabbababbbabbabbbbabbbababbbbaaaabbabaaaaababaaaaabbbbabbbababbaabaaaaaaaaaabbaaababaaabbabbbbbaababaabbbbbabbabaaaaabbabaabababbaaaabbaabaaabaabaabbbabaaabbbbabaaabababababaabbaabbbaabababbaabbaaaaabbabbbbbbabbaaaababaaabaabaaaabbabbbbaaaaaaabbababbabaabbaaaababababaaabbababababbaabbbbbaaabbbbaabbabbbaabbabaabaabbaababaaaaabbabaabbabbbabaaabbabbbbbaabaaabbaabbbaababbbbbaabbaaabaaaaabbbabababbabbbabbbbaaaababbbbabaabbbaabaaaaabbaabbbbbabbabbaaaabbbaabbbababbbaabbbabbaababbaaaaabbabaaaaaabbaaaabaaababababbaaabbbbaabbabaabaaaaaababbbaaabaabbbbbaabaaaaaabababababaaabaababbbaabbbababbababaabbababbaabbabbaabbbabbabbabaabbbbaaabaabbbabaabaababababbabaaaaababbbabbbbbbaabababababbbabababaaabbabbbabaaaaaabaabbababaababbabbbbbbabababbabbbbaabaaabbaaaaaaabbaaaabbaababaaaaabbaaaaaaabbbababbababbabbbabbbabaaaaaaabababaabbbabbbbbbaaabbbbbbaabaaaaabbaaababaaaaabbbbbbabaabbabbababaaaababbbaabbaabaabababbabbbbababbbaaabbbaaabaabbaabbbaaaaabbaaabaababaabababbbbbbbaaabbabababbbbbaabbbaababbabbbbaaabbabbbaabaaabababaabbaaabbabbababbbbabbabaabbbababbbabaabaaabaabaaababbbabbbbaaabbbabaabbabbbbbaaaabbaabaabaabbaabaabbbbabbabaabbabbbaaabaaabababbaaaabbbabbbbabbabababaaabbbabaabbabbbaabbbaaababbbbbaabbbabaaaababaaababbabaaabbbbbbaabaabaabbbbbabbbbbbbbaabbbabbbbaaaabaababaababaababbbabaababaaababaabbbaabaababaabbaaaaabababbbbabaaabaaaabbaaabbbababaabbbbabababababaaababbaaabbabbaababababbabbaabbabaabbaaaabaabbbbaabaabbaaabaaaaababbaabbbabbbbbabbabbabbabaaabbaaabaaaaaaabbbaaabbabbabaaaabababbbaabbbaaabbbbbbabaabababbbbabbabbababbbaaaaaaabbbbabbbaabaaaaaaabbbaaabaaabbbbbaabbabbabbaaaabaabbbaabbbaaabbbabababaaaaabbabaabbbaabbabbbaabaaaabbaabbabbbabbbbaaaabbbbbbaabaababbabaababababaaaabaaaaaabaaabbababaabbababaabbaaaabbbbbbababbaababaaaaaaabbaabaaabaaaaaaaababaababbbabaaababaaaaabaaaaabaaaabbbbbaabaabaabababbaaaaaabbabaaababbbbbaababaabbabbbbbbabbabaaaabababaabbababbbaabaabaabbbbbabaaabaababaababbabbbbaabbbbbaababbbaabaaabaababaaaaabaaabbabbaaabbbbbabbbaaaabbbababaaaaababbbaaababbbaaaababababbabaaabbbbaabaaabbaaabbabbbbbbaabbbbbaabaababbbbbabbbaabaabaababbaaaaaaabbabababaabbbabbbbabaababaaaaaabbaaaaabaaabbbbbbbbbabbaabaababaabbbabbbbbabbaababbbbaabbaaabaababaabbbbbbbababaaaaabbaabbbbabbbaababbabbbbbaaaaabaaabaabaabbbabbaabababaabbabababbbaaaabababababaaaababbaabbabbbabababababaaabaabbabaabaababbaaabaaabaaaaaaabaabababbaabbabaaaaababbababbabbbabbbbababbbbaaaabbbbbaaabaabbaababbaabbaababbbbbbabbabbbbaabbababbbbbaaababaaabbbbbbaaabbbaaabbaaaababaaabaabbaaabaaaabaabbbabababaabbbbbabbbaabaababbaabbaaaaabababbaababaabaaaaaaaaaaabbabaabbabababbabbbbbaaaabaabbbbaaababbbbbaaaaabaabaabaaaaabbaaaabbbababbbaabaabbbbbaabbaababaaaaaabaabaababaaabbabaababbabaabbbbbbbbbbbabaabaabababbbabbaaaaabbbbabbbababbabbbaaabbababaaabbabaabbabbbabaaaaabbabbabbbaaabaaababbaaaabbbabbbbbbbaababbbbaaabbbbaabbbaaabaabbababbaabbababbabaabbbbbaabbbbaaaaabaabaabbabaabbbabbabbbbababbbabbbbabbbbbbbabbabbaabbabbbaaabaaaababaaabbaaaababbababaaababbbbbababbbbbbaabaabbabbaabbbabbbabababaababbbaaaaabbabababaabbbbaabaaabaabaabababbbaaaabbaababbabababbaaaaaabbaabaaaaabbbabbbaaaaaaaaababbaabbaabbbbbabbaabaaaaabbaaabbaababbbbaabababbbababaaaaabababbbaaaabbbaababaababbbaaabbbaaaaabbaaaaabbaaabbaabbabbaababbabaaaabbabababaaaaaabbaabaaaaabbaaaababbbaabaabbbbabbbabbbabaabbbbbabbbbabaabbaabbabaabaabbababaaaabaaabaaabbabbaabbaaaaabaaaaabbbaaabaababbbbaaaaaabbababaaaabbabbaaaaabaabaabaaaaaaaabbbbaaaaaaaabbbbaabbaaabbaaabbbababaaaabaabbbbabaabababbbaabaabbaaabbaabbabbaaaaaabbaaabababaabababbbbaabbaaaaaabaaaaaaaabbaabaabbbaaababbbaaabbabaabaabaaaaaaabaababbbabababbbaabbbbbbabbbbabaaaabbbbbabbbabbaaabbabbbaaaabbaababbbbabaaaabababbabaaabaaaaaabaabaabaabababbbaaabbbabbbaabaabbaabbbaaabaabaabbbbabbaaaabaabbbaaabaabababbbbabbaabbbbaaaabbbbbaaabaaabababababbbbbbbabaaaabbbbaaaabbbabababababaaabbaabbbbabbbaaabbbabbabbbaaaabababbaabaaabbbbbabbaabababbbabaababbabbbababaabbbaabbbbbaaaabbaaabaabbbbaaabaaaaaaaabbbabbbbabaaabbaabbaaaaaaabbabbbbbabaababaaababbbabbbabbbaaabbaababababbabbabbababbabbaabbbaabbbabbbabbbbbbbabababbabbababaabbbbaaabbbbbaaababbbbbaabbbbaabaaaaaaabbbababbbaaaaaaabbbbaabababbaaabbbbaabaababbbbbbbabbbaabbaaaabbbabaabbbbaaaaaaabaabbaaaaaaabaaabbbbabaaabbbabaaaababbabbabbaabbbbaaabbbbaaaaaaaabbbbabbaabbababbbaaaaaaaabaabaaaabbbbaabaabbaabaabbaabbbaaaababaaaaaaaabbaabbbaaabababaaababbbbbabbbbbbabababbaaaaabbbaababbabbaaabbbbaabaabaaaababbababababbbaabbabbbbbaababaaaaabaaaaabbbaabbbbabaabbaaababbabbbaabaabbabbaabaabbababbbbbabaaabbbbaabbbbababbabbabaababbbbaaabbaabbaabbbbaaabaabaaaabbbaaababbaabbaaaababababbbababbbbbbabbaaaabbababaabbabbabababaaababbaaaababbbbbbaaababbbabababbaaabaaabbbbbaababbbabbaabbbaaabaaaaababbaabbbaababaabbbbbbbbbaaabbaabbaaaabaabbabbabbbbaabababaabbabaaaaaaaabaaaaabbbbbbaababaaaabbbabbbaaaaaabaabbaaaabababbaabbbbabbbbaababbabbbbabaaaababaababaababbbabababbbabaaabbabbbbbabaaabbbaabbaaabbabaaabbbbbaabaababbbbaaaabaabbbaaaabbbbbaabbbbaababaabbbbbaababbabaaaaaabbaabbaaabaaabbbabbbbbabbaaaabbbbbbaabaabbaaabaabbbbbaaabbbbaaaaaaaaaabaaabbaaaabbbaabbbabababbaaaaaabbbbaabababaabbbbaababaabbaabbabbbabaabbbbbaabbbaabbbaabbaaaaababaabaabaabbaababaaababaaaaababaabbbbaabbbbbaababbaaaaaaabbbbababbababbbbabaaaabbbaabbbabbabbaaaabbbbaaaaabbaabaabbabbbbbaabaabaaabaabbabbaaaaababbaaaababbabaabbbabbbbaaabbabaabbababaabbaabbabbbbababbbbaaaaabbabbaaababbbbbabbbabaaababaaabbbabbabaababbbbaaaabbaaabbbbbbbbbaaabbbbbbabbbbabbaaaabbbabbbababbaababbbaabbababbbabbbbbbbabbabaaaabaababaabbabababbababbbaabbaaabbabbbbbabaaababaabbaaababaabbbbaabbaaababababbaaaababbabaaabaababaaabaabaabbaabababbaabaaaababbaabbbbabaaaabbaaaaaaaaaaaaabbabbbabaaababaabaabbaabbbbbbaabbaabaabbaaaaabababaabbaaabbaabbbababbbabbbaaabaaaababaababbaaaaabababbabbaabbababbabaaabaaaaaaabababaaabababbaaaaabbbbbbbaaabbbaabbbabaababbaabbaabbabaaaaabaaaaabbbbbbababbabbbaaababbabaabbbbbbabaaaababbbaabaaabbababbbbbbbabaabbbabababaaaabababbaaababbabbbbaabbaaaaaabaabbbabbaaaaaaaabababbbbaaabbabbbbbbbabbabbaaabbababbbabbbbbbbabaaabaaaaaabbaabbbbabaabbbbabbbababaaabbaabbaaaaabbbbabbabbbaabbbaabaaabaaabbbaaaabbabaabbabbabbbbbabbaabaaabbababbbaaaaaaaaaabbabbaabbaabbbbbbabaaabbbabbaabbaabaabababbbbabababbbbaaaabbbbaaabaabbbabbaabbaaaabbabaababaababaabbabbaabbbbbbbababbabaaabaaaaaaaaababbbabbaabbabbbabababaabaaaabbaabbaabbbbbaababbabbbaaaaababbaabaaaaaaabbaabbaaaabbababaaaabbababaabbabaaabaababbababbbbaababbaabaabbabaaabbababaababaaabbbaabbababbbbababbbbaaabbbaabbabbabbabaaabababaabbabbababababbaaabbbbbbaaabaaabbaabbaaaaaaabaabbabbabaaaabaabaabaabbaaabbbbbbababaaaabbbabbbbaaababbbababaabbabbbbbbbbbbbaaababaababbabaaaabbaaaaabbbbbbbabaababaaabaababbbaabbbbabaabaabbabbaabbabbbaabbababaabbabbbababbbbabbaaaaaabaaabbbabbbababbbbabbbbbbaabaabaabbbbabbbaaaaaaababaaaaaaaaaaababbbaaaabababbaaabbbbbbaababbbabbabaaaaabbaababbbababbbaaabaabaaabbbbabaabbbbabbbbbaaabbaabbabbaaabbaabbbbbbaabaaaaabbabaaabbabbabaaabbbbbbbbabaababaaaaabbbababaabaababbbbbbaabbaaaaabbabaaabbabaaabbabaabaabaaaaababaaabbbbaabbbaabbbababababaaabaaabbababbbbabaaabbbaabbaabaaaaabaaabaabbbbbabbbbabbbbbababbaabaaaaaabaabaaaaaaabbbaabaaaaaababababbabbbaabaabbaaaaaabbaaabbbabaababbbabbaabbaababbabaaabbabbaabbbbaabababababbbaabababaabbbbaaaaaabbbaaabbbabbabbbbbbabbaaabaaabbbbbaaababbbbababbbbabaaababbaababbbbbababbaaaabbbabbbbabbbbabaaaaabbaabbabbabaaabaabaabbbbababababbabbabaaaaabaaaaabbabaaabaabbaababbabbaababbbbbbbabbabbabaaabbbbabbaabababbababaabbbbabbabaaabaaaabbaabbbabbbaabbaabbaaaababbbbbabbaabbaaaabaaabababaaabaaaabbbaaabaabaabaabbbaaabababaaababaabaaababbabaaaaaaaaabbababaaababbbababbbbabababbbabbaaaabbbbbababbabbaababbbbaabaabbaaabaaabaababaaaaabbbbabbbabaabbaaaaabbaaababbababbbabbabbabababbbabbaabbbaabbbbabaaabababbbbbbabaabaaaaabbaaaabbabbbbbbbaaabaabbbbbaababbaaabaababbaaaabbaababaaabbaaaabababaaabbabaaabaaaaaaabaaaababbabbabbaaababaaabbaaaaaaabbbaabaaabababbbabaaabbbbabaaabbabbbabbabbbaababbabaaababababaabbaaabbbaaabaaabbababbaaaaaabbbbababbaabbbaababbabbbbabaabaaaaabbbabbbabababbaaabaabababababbabbaabbbabaabbbbbbaaabbabbaaaabaaaaabbbbbbabaaaaabbbbaaaabbbbabbbbabbabaababbabaabaaaabababaabaaaabbbbababababbbabbbabaaabbaabbbbabaaabbabbabaabaababaabaaababaaabaabaababbbababbaaaabbabaabbaabbbbbbabbbbabaabbbaababbbabbbabababaaabbabbabbaabbbbbabbabbbababbabaababbbabbbbbaabbbabaaaaabbbbbababaabbabbbabbabbaaabaaaabbaaabaabaaabababaaabbabababbabbaabaabbbaababbabbababaababbbaabbaaabbbbbababaabbbbbaabbbbabbbbaabaabaabbaababbabbaabababbbbaaaaabbabaaaabaabaaabababaabbaabbabbbbbbabababbabbabababaabbabaaabababbbabaaaaaaabbaaabbabbababaaabbbaaaaaaaababbabbbbbbbbbbbbaababaabbbaaaabbbbaabaaabbbbaabbbaaaabaabbbbabaaaaabbbabbbbaabbaabbaaabbbaabbabbababbbbababbbabbbbbbababbbbbaabbababbbaababaabbabbbababaababbbbaaabbaaaabaabbabbbaaaababbbbbabababbbbbbaaabaabbbabbabbaabaaabbbbbabaaabbbbabaaaabbbbbbabbababbaaabbaaaabbabaababbbbaaaabbbabaabaabbaaaaaaaaaaaaabbbabbbaabababaabbaaabbabababbbbaaababbaaabbbabaabbababbabababaabbaaaaaababbababbbaabaabbabbaabbbababbbbbababbbaaaabbbbbabbabababbbbbaaaabaaaabbbbababbaaabaabbaabbbabaaabbabaabbbbbababbbaaabaaabababbaaabaaaaababaabbbbaabbabaaaaabbaaaabaabbabaabbbbbbbaaabbabababbbbbabababaaababaaababbbabbbbabaabaaabbabbabaabaaaabbabbaabbbbbaabaaaaabbabbabbbaaabbabababbaabaaabbbaaabbababbbbbbaaaabaabbabababbbabababbbbbbababaaaaaaaabaaaaabaabbbaaabaabbaababbabbabbbaaaaaabaaabbabbaabbaaababbaabaabaabbaabaabbabaaaababbabbabbaabbbabaaaabbbbaaaabbbbabaabbbbbabbbaaababbbaabaaaabaabaabbbbbaababababaaaabaaabaabbaaabbbbaabbaaabaabbbbbbbabbabaaaaaaabbbabababaaababaabbbaaaaabbabbbbbbabaabaaaabbabaabaaaaaaabaabaaaabaaabbaaaabaaaabaaaaaaabaabaabaabbbbaabaaaaaaaabbabbbbbbbbbaaaabaabbbbaabbbbabaaaabbaaababababbaabbbabaaabbababaaababbabaababbbbbbabbbbbbbabbaaaaaabbbbbabaabbbaababbabaabaabababbbabbaaabbbbabbaabbbabaaababbbaaabaaababaabbbbababbbaabaabaaabbbbbabbaaaabbbaaaabbaaaababaaaabbbbbaababbabaaaabbbaaabaabbbbabbaaabbaaabaaabaabbbbabbabaabaaaaaabbbababaabbbbbabbaabaaabaabbababaabaabbabbaaabaabbaababaaaabaaabbabbabbaaabbbaabababbbbabbbbbbbabbabbaabbbabbaabbababaaaaaaaabababaababaababaabababababbaaabababaababbbbbbaabbabbaaabbbbaaabbbabbaaaaabaabbbaaabbbaabbabaabbbabbbbbaaaaaabaaaaaaaababaaabbaabbaaaaabbbabbabbaaabaababbabbabbbabbbbbaaaabbbaabbaaaabbbaaabaababbbbaaaaaaaabbaabaaabaaaaaabbaaaabbbabaaababaabbabbabaaaababbababbaababbaaaaabbbbbaaaabababababbabbabaaaaabbbaabbbaaaaababbbbabbaaaaaabbbaabbabababbbbbbbabaaabbabaaaaaaaababbbbaaaababaabbaaaabaaaababaaabbaaaaabbaaaaaababbbaaababbaabbbbaabaabbabbaaabbbbabaabaababababbabbababababbbbaaababbbbaaaaaababbbaaaaaaababbaabbbabaaabababbbbaabbbbbabbabbabababbaabaabbbaaababbababbbbbabbbbbbaabaaababbaaaaaabaababbabaabaaaaaaaabbaaaaabbabbaabaaabaaaabaabbbbabbababaabaaaabbabbbabbabbaaaabbbababaaaabbaaaabbaaaaaababababbbaabaababababbaaaaaaaaabbbbbaabaaaabbbaaabbbaababaaaabbabbaaababbabaaaabbbbbaaaaabbaabaabaaaabbbaaabaabbbaabbbaaababbaabbabbaabbabbbabbbaaabbabbbbbabbbbabbabaaababbabbbabaaababbaabababababababaababaabbaabbabaababbaabbbabbaabababababaaaaaabbbabbbbabbabbaababbaaabaabaaabaabbaaaababbaaabaaaabbabaabbbaaaaabaabbaaabbabbbbabbaaabaabaaaabaababababaabbabbabbbabbaaaabbbaaaaaabbaaaaababbaabbbababbbaababaaababbbabaaabbbbabbaaabbbaaaabbbabbbabababbaabbbabaababaabbabbbabaabababaaaababbbaabbaababaaaabababaabbbbaabbaaaaaaaaabaaaaaaaaaabbbbbaaabababbbbbbaabbbaaaabbaaaabbababaaaabbbbbaabaabaaabbbbbbbbaabbabaabbbabbaaaaabbbbaaabaaaaaaabaaabaabaabababbababaabaaaabaabbbbaaabbbbababbabbaabbaaababaabbabaaaabbbababbbaaabbabaababbbbbbbbabbbaaabbabbbabbaaaabababaabbbbabababaaaaaaaaaabaabaaaababaaaabbbbabbbaababbbababbaabbbabaaabbbbbbabbbaaaaaaabababaabaabbbbbbaabbabaababbbaabbabaabaabbbbaaabbbaababbbbbaaaabbbababbabbabbbbaaababbbabbbaabbaaaabbbaabbabbbabbbabbababababbababbabbabaaaabbaabbbaaaaabbbbbaabaaabbaabbbbabbaaabbabaaabbbabbbabbbbaaaababbbaaaaaabbbbbbababbbaabaabababbaaaabbaabbbbbbaaabbbaabbabbabbaababbbbabbabbbaaababbabbbabaaabaabbaabbbbabaaaaaababbbaababaababababbbaabababbabbbabbbbabbaaabbbbaabaaaabbaabbabbaaababababbbaabbbbbaabaaabbbbabbabbbaabbaabbbaabbaabbbbababbbaababaabbbbbabbabbbaaaaaabaabbbbabaaabbabaabbbaabaaaabababbaaaabaaaababaaabbaaabbbbbabbbbababbbabbbbabbaaabbbbaabbaabbabababbabbbaaababbabbbbabababbaabbbbbbbabbababbbaabbbbbaabaaaaaabbabaaaabbbbbbbaabaabbabbaabbbababbabbbabaaaaaabbaaaabbabababbbbabaabbbababbbbbbbaaaaabbbaababaabbaabaaaababaabaaabababaaaababbaaaaaaaaaabaabbbbabaabaaabaaaabaabaabaabbabaaabbbbbbabbbbbabaaaaaabaaaaaaabbbbbaaaaabbaaaaabbabbbbbbbaababaaabbbbabbbabbaaabaaabbabbbabbbbbbbaabbaabbbbbababaaaabababbbabbaaaababaaaaabbabbbbbbaabbbbaaabbaabbabbabbaabbbbbabbbbbabbbbbabaaaaaabaabaaababaabbbbaabbaabbabbaaababababbbabaaaabbbababbaaaabbabbaabbaaaaaabbabaabbaabababaaabbaabaabbababbabbbbaabbaababbaaababababbbaabaaaaaaababaabbaabbababbaabaaabbbabaabaabbbaaabbaabbbbbaaaabbaabaaababaabbbbbabaaaaaaabbababaabbbbbbbbaaaaaaaaaabababbabbbabbababababbaaaabbaabaaaabaaabaabbbaabaaabbbaaaaabbabbbbbbabbabaaaaaabaabbababbaabbaababaaabbbabababababaabbaabbbbaaababbaaabbabaabbabaabbababbaaabbabbababaabaabaaaabbbbaababaabababbabababbbbbbaaabbaabbabababbabbbbababbbabbbabababaaabbbbababbababaabaaaaabbbabbbaababbbbaabbaaabbbaabababababbabbabbaabababaabbabaabbbbabaaabbaabbbbbaaaaaaabbbbababaaaabbaababbbaabaaabbbabbbbbaabbbabbbaabbaaabababbbabaaabbbaabababaababbbbbbbbbabaabaabaaaabbbabbaaaaaaababababaabbaaababbabbbbbbbbabbabbabaabbbabbbbbababaababbaaaabbbbababaaaabaaaabaaaabbbaabbbbababbbaaababbaaaaabaaabbbabbbaabbbababbbaababbbaabbabbabbbbaabaabbaaaabaaabaaabaabbabbbabababaaabbbabbbbbbabbaababbaaaaaabbaabaabaabbbbbaaabaaabaabaabbbbbaabbbbbbabbbbbaaaabbbabaaabbbbabbbbbabaabbababaaaababbabababababbbbbaabababababbbbbbbaabbbbaaaaaabbabaaabaabaaaabaaabaaaabbbabbbabaaaaaaaababaabaabaababbaaaaaababbaabbabbaabbaabaabbabbaaaaaabaaaaaababaabbaabaababbbaaabaabbbbbaaaaaababbaaaaabbbaaaabbbabbababbaaaabaaaabbaaabaabaabbbaabbbabababaabbababbaaabbababbaaabababababaabaabababbbbaaabbbaabaabababbaabbbaabababbabbbaabbbbabababaaabaabbbababbbabbabbababbbbabbbbbbabbabbaaaababbbabbbaabbababbaabbabbabaabbabbabababaabaaaaaaaabbbbabaaabbbabaabbaabbaababbabbaaabaaabbabbbabbbbbabbbbabbaabbbbaaaababbabaaaabaabbbbbbbaaaaabaaabbabbababababbaaaabaabbbaaaaabbaaaababbaabababaabaaabababbaababaaabbababaabaaabbababababbbbbababaabbabbaababbbaaaaaaabaaaababbbabaaaabaaabaaaababbbbabbaabaabbbabbaababbabbaaaaaabbbbabaabaaabbaabbaabaaaabbabbbbbbababbabababaabbaababbbaaaabababaababbababaaaababbaabbabbabbaaaabaababaaaabbbbabababbaaabbbbabaabbbbabaababbabbbabbbbbaabaabbaabbabbbbbbabbbaaabbbbaabbaababbbaabbabaababbbbbabababaabbbaabbaaaaababbaaabbbaaabbaabaaaaababbaabaababaaaaaaabbbaaabbaaabbabbbbbababbaabbabaabbaaaaaaaaaababbbababbbaaabaabbaaabaabbabbaababbbabbbabaabababbaababbaabbabbbbaaaabbbaaabaabbababbbbabbaabbaabbabbbaabbbbbbbaaabaaaababaabbababbaabbaabaaaaabbaabbabbbabaabaaabbabbbaabbbaaababbbbbbaaabbbaabbbabaaaaaabbbababbbabbbabbabbaaaaabaababbbaababaaaaababaaabbbbaabbaababaaaabaababbbabbaaababbaaabbabaababaabbabaabbbbaaaaabababaabbbabbaaabbababaabbabbbababbbbbbbbbabbababaaaaabaabaaaabaaabbababbbbaabaabbbbaaaaaaabbbbbbbaabaababbbbaaaaaabaabbaaabbaabbbbabbbbabbaaabbabababaaaaababaaabbbaabbbbbbabbbbbbbbabbbbbababbbaaaaaaabbbababbabaaabbbbabbabaabbabbabaababbabaababbaaaaabbabbababbabaaaaabbbbbbabaabbaaaaabbababaabaaabbbaaabaaaabbbaaabaabbabbabbbaababbabababbaaaaababaaaaabababbbaaababbabbaaabbbbaaaaabbabbabbaabbbbaabaaabbaabaabbbbbaabaabababaabaaaaaabaabbabbbbaaabaababbabbbaaabbbbbbbbaabbbbaaaabbbbabaabaabbbbbbaabababaabaaaaabbbbbbbabbabaaaaaaabbbbabbbbaaabbbbabbaaaaabbbbbbabbaaabababaaaaaabbbbbbbaaaaaabbbbbbabaabbabbabababbbabbaaabbbbbaabaababbbbbabbbbbbbbabbbabababababbaabaababbbbbbaaaaaabbabbbabbbbaababaabbbbabbaababbbbaabbbbbaaaaaaaaaaabaabbaabbbbbbaababbbbbababbbabaabaaaabbaabbbaaabbbabbaaabbaabbabbabbbbbbbbaaaaaaabbbbaababababbababbbbaaabbbbbbbbbaaabbaabaabbaabaababbbaabaaabababaababaaaaababbbbabbabaabbbabbbabababaabbbbbbabbabbaabababbbbaabaabbaaaaabbbbbbabbbbaaaabbabbbabbaababaabbabbbbbabbaaababbbaaababbaabbbbabbabbaabaabaaababbaabbaabbbbaababbababaabbbbaaaabbbabbabbbbbbabbabaaaaababbbbbabbabbbabbaaaabbbbbaabbaaabbaaaabbbaaaababbbaabbabbaabbabbbabababbaaabbabbbaaababaabababaabbabaabaabbbbbababaabbaaaaababaabbbbabbaabbbaaabaabbbbaaaabbbabaaaaaaabbbaaaabbbbaabaabbbbaaaaaaaaaaabbbbaaaabbbaababaaaababababbaaaabbabaaaaaaabaaabbaaabbababbbaabaababaaaabaaabababbaabababbabaabbbbbbbabababbabbaabaaaaabbbbababaabaababaaaaabababbbbabbbbbabbaaabbabbaabaaabaababbbbbbaaaaaaaabaabaabbbbabbabababababbaaabababbaaababaabaaaabaabbaabbabaabaaaabbabababaaaaaabbbbabababbbabaabbbabbbabbbabbabababaabbaaababababbbaababaabaabbaaaabbbabbaabababaaaaababbaaaabaababbaabbbaaababbaabaaabaababababbaababaaababbabaaaabbaabbbabaabbbaabbabbbabbbabbbbaabbaabaabbbabbabbbbbbababaabaabababbbbaaababbbaaaabbbabababaabbbbbaabbbaababbbabbbbbbbaababaabbaabbbbabbbaaabbaabababbaaabbbbabaaabaaabbababaabaabaaabbbbbaababbabbaabbaaaaabbbbbabbbbababbabaabaaabaaaabbbbbbaabaaabbbbababbabbaaabbaabbabaababbababaababbbbbbbababaaabbbaaaabababaaaaabbabaabaaabbaaaabbbbbabbbbaaababbabbaaabaababbbbaababaaababaababbabbababbbbbbabbaaaaaababbabababbaabbbbabaabbaaabaababbaabbaaabbbbabbaabbababbbbaaababbbaaabbbbbbbaaaaabbbabbabbabbabbababbbbaababbaaaaaaaaabababbbbaaaabbbabbabaaababaaaaaaabbbabbbababbabbbabbaabbabbbabbbbaaaabbaaabbaaabababbbbaabaaaabbaabbaabaabbaaabbbabaaaaaabbbaaaaabbabaaaabaaaabbbaaaabaaababaaabaaababbaabaaabbaabaaababaababbabbaaaaabaababbbbaabaaaabbaabbababaabbaabaaabababbbaabbbaaabbbbaabaaaaaaababbbabaabbbbabaaaabaabbbbbbbbaabbbababaabbaaabaababababbabababbbbbababbbbabbaabbabaaabbbbabbbbaabbbabbaabaababbbaaaaabbaaaaabbabbbaababbaabbabbbbabaaaabbabaaababbaabaaaabababababbbbbababbbbbabbbababbbaaabaaaaabbbabaababbbaaaababbbaabaabbbabbbbabbbabbbaaaaabbababababaaaaabababbbabaaaaabbbababbaabaaabaababbbbabbbbabbaabaaababbbbabbbababbbabbaabaaaabaaaaaabbaabaaaabbbbbbbbbabbbabaababbaaabbbbbbbababaababaabbababbbaaabbabbaabaaaabbaabbbbababbabbaababbbabbaabbbbabbbaabbabbbaaaabbaaabaaaabaabbbababaaabbbaabbaabbbbababaabbbbaaabbaabbbbbaabbaabbbababaabbaaaaabaaabaabbbbbababbababbababbababbababaababaaababbaaaaaabbbbbbabbbbaabbaaabbbaaaabababbaaaaabbaaaabbaaabbaabbbaabbbbbabbbbabbababbaabbabaabbaabaaabbaabaaaaabbbabbaaababbbbabbaabbaaabbbbbbbabaaabaabaabbbaaabbbaaabaaababaabbbabbbabbbbabbbbabaaabaabababbabbbababbaababbabbbbbbbbbbbabbbabbaabbaabbbbababbbbabaaaaaabbabbaabbabbbaaabaaaababbbabbbbbbabaaaababaabbbbbabaaabbaaabbbaabaaaaabababbabbabbabaababaabbbbababbbbaaaaabbabaababbbbabaaabaaabaabaaabbbbbbbbbabababbbbbaabaaabaabbabbabaaabbabaaababbbabaaaabbaaabbabbaababbabababaabbbaaabbbaaabbbababababaabbabaaabaabbabbaaababaabaaaabaaababbbabbbbaaaabbaaaaaabbaabbabbbababbbbbbabababaabbbbbaabaabbbabbaabaaabbabbaabaabbbbaaaababbabaabbbababbbabbbbbabbbbaaaaababbbbbbbbbaabbbabbbbababbaabaaaaaabbbabbbbbbaabbaabbabababbaabbbabbabaabbbaaababbaabbaabaaabaabbbaaaabbaaaabbabbaabaabaaaabababbbbbaababbbbbabbaababbbaaaaaababbbbbabaababbbbabbbaababbabaabbbbbbbaaaaabbbaabbaaaaaabaabaabaabbaabababbbabbabbbabbaabaaabbbbbaabbbbabbaabbabaaabaaabbaaaabbbabbbbbaaabaabaabaaaabbbaabbbababbbbbaaabbbaaaaabbaabbababbabbbbaabaabbaaabbaaaaaaaaababbbaabbabaaaaabbaabaabbaabaababaabbabaababbaabbbabbabbbbbbbbaaabaabbabbabaaabaaabbbbbbabbaabaaaabbaabaaabbbbbbaabbbaabbbbabaaababababbbbabbabababaababbabaaaabaababaababbababaaaabaaaaabbabbaaaabbabbbabaabbabbabbabaaabbbaabbaaabbbbaaabbbbabbbbbaaabababbbaabbbbabaababbaabbabababbabbaabbbaaaaabbbbbabaababbbababaababababbbabaaabbabbbaaaabbabaababbbaaaaaababbabaababbbbbabaabaabbbbbbbbabbabbbbbabbbabbabbbaabbaababaababbbbaabbbbaabbbabaaaababaaabaabbbbbaaaabbbaaabbababbaaabababbbabbaaaabbabbaababaaabbabaaaabbaaabaaaabbbaaabbabaaaaabaaabaaabaaaabaaabbbbababababbbaababbbbaabbabbbaaabbbabbbbababaabbabbaababaaaabaabbbbbbabbbbbbaaaaababbbbabababaabaababababaabababababbaaaaaaabbbbabaaaabaaabbbabaaaabaaaabaabababaabaabaaaabbabbbabbaabaaabbbbbaababaaaababaabaaaababbbbabbaabbaabbabbaabbbaabaabbbbababbababbbaaaaaaababaabababaaabbaabbbbaaaabbabbaababbababaaaaabbabbaaabbaaaabbbbbaaabbabbbaaabbaabbaaaabaabaaaabbbbaababbabbbabbabbbbbaabaaabbbbabaabaaaabbbabbaaaabababbbabbbbbaaabbaaabaaaabbaababbaababbbaaaaabbabbabbbbbbabbbaabbaabbbaaababaabbaabaaaababbabbabaaabbbabbaaabaabbbaabaababbaabbbaabbbaabaabaabaabbaabbbbabbabaaaaaababbabbbbaaabbaaaaaaaabbabaabaabbbbbaaabaaaaaaabababbbbbabbbabbaaaaaabbbbbbbbbaaaaabaaabbbababbbabbbabaabababaaaaabaababaabbabaabababaababaabbbabbaabaaabbabbaaabbaaabbbbbaaababaaaaabbbbbabbabbbbbaaababbaaaaabbabaabbabbaabaaababbbbbbbbaaabbabbaaabaaaababbbbaaabbabaabababbbabbaaaaaaababaaaabbaaabbabababbaababbaaababaaabbabbbabbbbaabababbbbabababbabbbaababaaaaababbabaaabaabaaabaaaabaaaabababbababbbaaababbaabaabbabaaabbababaababaaabbababaabbbbaabaabbbaaaabaaabbaaababaabbbbbaaabbabbbabbbabaabbbabbbaabbbbbabbbbaababbaabaabbbbabaabbbbbbbbaabbbbaabaaaaaabaabaabbaabbbaababaabbbbaaaaabbbabbaaabbabababaabbabbbababbbaaabbabababbbbbbaaaababaababaabaababbababaabaababaaaabaabbbabaabbaababbabaababaabbbbbabbbabbbababababbaaabbabbabbabbbaabaababbaabbbbbbaabbbbabbaabaababbbababbaabaaabbabaababaaababbabaaaabaaabbbababbbaabbababbaabbbaabbaaaabbaaababbbbaabaabbabbbbabbabaabbbabaabbbbbabaababbabaababbbaaaaabbaaaabbbabbbbbbaababaababababaaaabbbabbabbbaaabaabbabbabaaaaababbaaaababbbbaaaababbbaabbaabbbbbaaabbbbaaabababababbaabbaaaaaaaabbabbbabababababaababbbbaaababbbabaaaabaabbabbaababaaaaababbbababababbbbababababaaabbaabaababbbbbbbababbbbababaaaaabbabbaaabbbaabaaaaaaaabaaaaaabaabbbbbaaaaaaababaabaaabaabababaabaaaabbababbaaabbbabbabbabbbbababbaaabbbaabababbabbbbaaabaabaaabbaabbaabaabbabbbaaababbbaaabaababbbaabbaaabbababbbabbabbbaaabbabaaaabbaaaabaabbaabbaaabbababbbbabbababbabbaabbbaababbabaababaababbbbbbbabaabbbbabbbbbbbababbbbbabaababbbaaaabbabbbbbababbbabbabbabbababbbaaabaabaabbabaaababaabbbbaaaaabbbabbaabbaaababbaaaaababaaababbabbaababbaaabaabbabbbaabaaaaaaabbbbbbbbbababbbabaaabbabababbbaaaaaababaaabbabbaaaabbaaababbabbbabaababbbaabbabbaaabbababaabbbabbababbaabbbbbbaababbbbbbbbaabbbbbbaaaababaabaabbaabbbabbabbbaaaaabbbabbabbbbabbababaabaaaabbababbaaababbbbbabbaaabaabaabbbababbbbaaaaabbbbaaaabbaaaabbbaabaabbaababbabbbbaaabbbbaaaaaabbabbbbaaabaaabbbaaabaabaaaaabaabbbbaaabbbaaaaaabbbbbbabbabbbbaabbbaaaaabababababbbaaaabababbaabbbbbaaaabaaabbaaabbabbbbbaaababbababbaabbabaaabbaabaababaabbbaabbaabbaabaabbabbbaaaaaaaabaaabbbaaaabaaaaaabbaaaaaaaabaaaaababbababbabbbbbbabbaaaabbbbbbabbbbaaabbabbbbbabbbabbabbabbbabbbbabbababaaaabbabaabaabababababbbabaaabaabbbabbabababababbbaabbbbaaaaaabaababbbbababaababbbaabbbaaabaaaaabbbbbaabaaabaababbaababbbbbbbabaaaaababbabbaaabbabbabbbbbaaaabaabababaababbaaaaabbbbabbbababaabbbbababaabbabbbaaababababbbaaabbaabbaaaaaaaabbababaaabaababbabbabaaaabababbbbbaabbabbbaababaabbabbbbabbbbbbbbababaaaabbbabbaabbabbabaaabbbbbbabbaabaabbbbbbbaabaabbabbbaaabaabbaabaabbaaaaabbabbbaaaabbaaaabaaaababbaabaabaaabababbaabaaaabaaabaaababbbbbabababbabbbabaaaaabaabbababaabbbabababbabaabbaaaaaabbababbbbaabaabbbabaababaabaaaababbbabbbbabaaabaabaaaabbaaaaabaaaababbaabaababababaabbbaaaababbaaababbbabbbbabaababababaaaabaaabbbbbbaaaaaaaaababaabaaabaabbaaaabaabaaabbbbabaabbbbbbbababbabbabbbabbbbaababababababbababbbabaaaabaabbbabbaababaaaabaaaababababaabbbbbbbaaabbbbaabaaaababaabbbbbbbabaabaaababaabaaaabbbbabbbbababbbaababababaabaaabaabbaaababababaababbbabaaababaaabaaabbababbabbababbbbaaaaababbbabbbbbabaabbabbbbabbbbabaababaaabbaaaaaabaaaababaaaaabaabaaaabbbaabaabbbbbbbbaaabbabaaababaaaaabbabaabbaabbabbbabbaabaaaabaababbaaabaabbbaabbaaaabaaabbabbbbbbbabaabbbaaaaabbaaaabaabababbababbbaabaababaaabbaabbabaababaaabbbbbbbbabbbbbabbaaabbabbbbabaabbabaaaabaabbaabaaabaaaaabbabaaabbabaaababaababbabaaaabaaaaabaabaaaababaabaabbaabaaababbaabbabbabaaaaaabbabbbbbbbbbbbaabaaaaaababbbaabaabbbbaaaababaaaaaaaabbabbbabbbbaababbabababaaabababbbaaaabbabaaabaaaaabbaaaaaaaaaaaaabbbbaaaabaabbbaababbaaabaabbbabaabbaaabbabbbabaaabbaabbbbbaaabaabbbbabbabaabbbbbabbaababbabaaababbabbabbaabbaabaabbabaaaabbbaabbabbaaababaaabbbbaabaaaabaababbbbbaabababbabbabaaabbbbabbaaaaabbaaaaaaaababbabbaabaaabaaaaabbbbbbaaabababababbbabbaababaaaabaaaabbbbbaaabbabaabaababbaabbaabbbbaabababaababbbabbabbabbbbbbbbbbbaaaabbbaaaaabbaabbaabaaaaaaaaabbbbabbaaaababbababbababbbaaaabbbabaaabbabbbbaaaabbbaaaaabbaabaababbabbabbbababbabaabbabababaaaaaaaabbabbbaababbbaaaaababaaabbaaabaaaaaaabaabbbbbaabbababaababbaaabbaaaaaabbbabbaaaaabbabbbabbbbbbbabababaaaabaaabaabaabbaaabbbbababaabbbabbbabaaaabaaaaababaaabbbabaaabaaaaaabbaaabbabbaabbbaaaabbabaaabbaaabaabbaabbbbbbbabbbababbaababbbababaabaaabbabbbbbbababbbbbabbabbbababbbbaaabaaabaababaaaabaabbbaabaabbaababababaaababaaaabbaabbaabbabaabbbbabbbbaaabaaabaaabbabaabaabaabbbbaabababaaaaabaabaabaabbbbaabaabbbabbabbaaaaabbbabbaabbbbaababbaaaabbbabbaabababbaababbaabbaabbaaabaaabaaabbbababaabbaababbbbbbabbbbbabaaabbabbabaabaaaabababbabababbabbabbabaaabbbabbbaaaabbabababababaabaaabababaaabaabbbaabbababbbbbbbbbababbbabaaabbbbbaaaaababbaabbabbbbaabbbabbaababbabbabbaaaaaababbbaaabbaaaaababbaabaabbbababaaabbbbabbbbbaabaaababaaaabaabbababaababbbbbbbabaaaabbaabaabbbaababbaabababaaabaabbabaabababbbbababbaabbbbbabbbaaaabbabbabaaababaaaabaabababbbbbaabbabbbaabababbabbaabbabbabaaaaaabbaabaaaaabaabbaaaabbabaabababaaaaabbbabbabbbbbbabbbbaabbabbabbabaaaaababbbaabbbbababbbbabbaaababbaaaabaaaaaababbabaaabbbbabaaabbaabbbbaaabbabbabbaaabbabbaaaaababaabaabbabbabbbbbababababaaaaabbbbbbbaaababaaababbaaaababbabbbababaabbaabaaabbaababbaabbbaaaabbbabbbabaabbabababbbbbaababbbbbbbbabbabbbababbaaababbbbabababaaaabbbabaabbbabbbbbbaaaaabaabbaabbbaaaaabaabaaababbbabaaabaababbbaaabababbbaabaaaabbaabbaabaababbbbbbbbbabbabaaabababbaababbaabaababaabbaabbbabbabaababaababaaabbaabbaaababbaabbbabbabaabbbabbbbbbaabbabbabbaaabbabbaaaaaaabbabaabbabbabaababbbaaaaaaaaababbbababbbaaaabaaabaabbbabbbabaabbababaaabaaaaababababbaabaabbbaaabbbbbbbaaaababaabbbbaabbaabababaababbabbabbabbbbaaaababaaaabbbbbbaaabbababaabbabbbabbaaaababaabababbbbaabbbaaaabbbbababbbbbaaababaabbbabbbbbbbabaaaaabbbbaaabbbabbbbbbaaababbabbbbaaaaaabbbbaaababbaaaabbbbaaabbabbaabbabaabbaaababbbaaaabaabbabaabbbabaaaabaabbbbabababbaabaaabaaabbababababaaabababbabbbabaaabaaabaabaabbabaabbabababbaabbbabaabbabaabbabaaabababbbaabaaaaaaaabbbaaaaabbabbaabbbbababaaaabbaaaababbaaaabaaabbababaaaabbbbbbbababaaaaaaabbaaababaabaabbabbbaabbbbbabbbbaaaababbbaabbbabbbbbbbbaaaabaaabaabaabbbaabbbbaaaabbababaabaabbabbbaaaaaabaaabaababbaaaabaaaaabbbabababaababbabaabbaabbaaabaaabbabbaabbbabbbbbbbababaaaababbbaabaabbaababbbbaababbaaaabaabaaabbaabbbaaaabbaaabbbababbaababbabaaaaaaabaabbbbbaabbbaababbbabbbababaaaaaabbbaababbaabbbabaabbaabbbbbbbbabaabaababbbbaababababaaaabbaabbabbbaabaababbbbbbabbababababababaababaabbbaaabbbaaaaababaaabbbaabbbabbbbbabbaaabbabbbababbabaaaaabaabaabbbbabbbaabbaabababababaabbbababaaaaaaaaaabbaabbaabababaabbaabbaabbabbbbaaaaaabbababbabababbbabbbbabbbaaaabaaaabbaaabbbaabbabbabaaaaabbbbbbaaabbabbbbbaaaabbbbabbaaaababbbbaababaabbbbaabaaabaaaaabaabababaaabbaabbaaabbaaaabbbabbbbaabbababaabbaaaaabaaabaabbabababaaabaabbaaabbbbabaabbbbbbabbbbbbaaaaabaabaaababbbabbaabbbbabaaababaababbbbaaabaababbaababbbbbababbbbabaabbaabaabaaaabbaaaaaaabbabbabbaaaabaabbabaaabaabbabbbbababbbababbbbbbbbbabbabbbbabbbbbbaababaaabbaaabaaaaaababbaaaaababbaabbbababbbbaabbaabbbbaaaabbbbbaabbbabababbabbabbaabbaabaaabaabbabaaabababbabbbbaaaabbbbbbabbabaabbaaaabbabbabababbabaabaabbabbabbbabbabbbabaabaaababbbbbabaabaaabbaabbbbaaababbbbaabaaaaabaababbbbaabaabaababaabbbabbbbabbbbabaaabbbbaabaaabababbbbbbbabaaabbbababbaaaaaaabaaababbbabbbaabababababaaabbabbaabbbbabbbbbabbabbaaabbbbbbabababbbabbbabbababbababaababaabababbbababaababababaaabbbaabaababaabbbaababaabababbabbbaabaaabbbbbbababbbabbbbabbbaaaaaabaaabababaabbbbaaaabbbbbbaaaaabbbabaabaababbaaabbabababbbabbbbbabbaabbbbaaabbbbaaababbaabbabababbaababbaaabbabbbabbbbbabababbabbbababbbbbbababaababaaaaaabbabbaaababababababbaabaaaaaaabbbbbaaabbbabbbababbabaaabbababbaabbaabbbabbbbbbababaaaababbaaaabbaaabaaabbaabbbbbaaaaaaaaabbbbaabbaaaaaabbbbabbbbaabbbaaabababbbabbbbbbabbababbabbbabbaaaabbababaaabbbabbbbbaaababbbbbbaababbbabbbabbaaabbabbbbabbabbababbaabaabbaabaabaaaaaaabbbaababbbaaabbbaaabbbbaaaaabbbabbaabbabaaabbaabbaabbaababaabbabaababaababaabbbaaabbabaababbbaaaababaabbbbaaabbabbaabbbbaabaabbababaabbbbbabaabbbaaaabaabaaaaaabbaaababbaabbaabbbaabaabaaaabbbaaabbbbabbaabababbabbbabbabbbbbbabbbaaaaabbbababaabbbabaaaaaaaaaababababaaaabaaaaabbaaababbbbbaaaababaabbbbbbaaabaaabaabaabbbabbbbaababaabbababbbbbbbabbabaabaabbabbaabaaabbbababbbaababbbbbaaaaababaabbbaaaaaaaaaababbbabbbabbabbabbababaaaabbbbaabaabaaaabababbbabbaaaaabaaaaaabaabbbaaabbbbbbbbbaaabaaabbbbbbabbaaaaabbbaaaaabbbbabbbbbababbabbbbabbbbabbbbabbbabbbaabaabbabaabbbabaaaabbbaabbbaabaaaabbbababbaababbbbaaaaaaaaabaaaabbbbaabaaaaabbbabbaabaabaaabbbabbbbbabbbaabbbaaababbabbbbaabbbbbbbabbaabaabbbbbabbababbabaababaaababaaabbbabababbabbaabababbabbaabbabbaaaaaabaaabaaaabbbbbbbaaabaabaaaababaaabbbaabbbabbabbaaaabaabbbbaaababbabbbababaabaabaaabbaaabaaaaabbbaaabbbabaaaabbaabababbbbbaabaabbbababbaabbbbbbbaabbbababaaabbbaabbbabaababaaaaababaababababbbbabbbabababbababababababaababbbabbaababbbbbbaabbbaaaaabbbbbbaaaaaabbaabaaaabbaabbaabbabaabababbbaaaaabbabababbbbaaabababaaabbbabbabbbaababaaabaabbababaabaaababbaaaaaabbaabaabaaaabaabbabbbababbaaabbbbaabaabaaababaaaaabbaaaaaabbabbbaabaaabbabbabaaabbbabbbbbaaaaabbbbabbaaaabbbaabbbbabaaabbabbaabbaababbbaabbbbbbaaaabaabababbbabbabbaababaaaaabbbaabbbbabbbabbbaabbbbaaababbababbbaabbabbbababababbbbbbbbbaaabbabbaabbabbaabaababaaabbbbbbabaaaababbbababaaababbaaababbbbbaabaababbbabbababbaaababbabbaabbabbbaaabbbabababbabababbaababbbbabbabbabaababbbbbabbbabaaaabbababbababbaabababbbaabaaaaaabbaaabbabbabbaaaaaaabbabaaaababaababbbbabbbaabbbaabbaabbbbbabbabbbbababbbabbaaaabbbbabbabaabababaabbabbbaabbabaababaaabababababaaabbabbaaabbabababbbabbbaaaabaabbbbbaaaabbbabababaabbbabbabaaaababbbbbbabbabbaaabbaaaababaaabaabaabbaabbbbabbaabbbabaaaabbaaabbbabbbabaaaaabbbaaabbaabaabaabbbbaabaaabaaaaaababbabbbabaabbbbbaaabbbaababaaabbbabbbbaaaaabababbabbabaaaaabbaabbbbabaabaabbabbababaaabababaabbaaabaaabaaabababaabaaaaabbaabbbaababbaaabbabaabbabaaabbabaaabaabaaabbaaaaabaaaaabababbbaaabbabbbbaaaabbbbbaabbaabaabbabababbbabbabbabaaababbbabbbaaabaaababbaabaabbababbbabaababaabaabbbaababababbbbbaababaababbbbababbbbabbaaaabbaaaabaabaaaaabbaaababababbbaabbaaabababbbbaabaaabaabbbabbbbbbbbbabbbabaabbbaabbbabaaaabbabbbabbabbbaabbaaabaabaaabbbbaabbaaabbbbbbbbbabbbbabaaababbbbaaaabababaaaababbbaabbbaabaabaaabaabbabbabbaababaabaabbaabbabbbbbbabbbbbabbbabbabbaabbabbabaababaabababaaabbbaaabbbbaaabbaaaabaabbbabaabaabababbaaabbabbabaaabbbabbbbbababaaabbbaaaabababaaabaababbbabbaabaaabbbabaaaabaaabbbaabaabaaaaaabbabababbaaabaababbabbbabbbabaabbbbbbabbbaabbaaaabbabbbbbbabbababbbbaaabbbaaabaabbbabbbabbaababbbabbabbbbaaaaaababbbaaabbaaaaaabbaabaabaaabaabaaaaaabbbbbabbbbbaabbbaabbabaaaabbaaaaaabaaaabababaababbaabbabaabaaabbaaaaabaaabbabaabbaabaaaabaaaabbbbbbaaabbabbbabaabaababbbaaabaaaaababbabaaaaabbbabaabbbaaaababbaabbaabbababbaabaabbbbbaaaabbbaabbabbbbabbabbaabaaabbabaaabaabbbbbaababaabbaaabbabbbaabbabbbaabbbabbababbaabaaaaaabbaabbabbabbbaabbbaabaababbbababaaababbababaaabbaabababaaabbbabbaabaabbbaaaabbabbaaaaaabaababaabaaabbaabbbbbaaabbaabaaaabbabbbaaabbbabbaabbbaabaaaaaaaaababbaaaaabbaabbaababbababbaabbabaaabbbaabbbabbbbbababaababbabbbaabaabbabaabbabbbbabbbbbbaabaabbababbaababaaabbbabbbabaaaababbaaababbbbbbaaabbbaaaaabbbaabbabbabbaaaabaabaabbaaabababbbabababababbabbabaabaaaabaababaaaababbbbabbbaababababaabbabbabaabbbbabaabbbbaaababaabaabbaaaababaaabbbbabaabaababbabaabbbababaababaababbabaabaaabbabbabbaabababbaaabbabbbabbabaaaabaababaabbabaabbabbaabaaaaaaaabaaaaababbbabbbabbbaabaaabbaaaaabbaaaaababaabbabaabaabbbbababbbaabbbababaabaabbabbabbababbababbbababbaabaaaaabbaaaaaaababaabaaaaabbbbbbabaababaabbabbbaaaaaabaaabbabaabaababaabbaabbbabbbbbabababbababbbbbbbbbabaaaababbbabbaababbbbabababbabbabbababaaabbbbabaaabbbabbaababaaaabbaabbbabaababbbbabbbaaaaabaaabaaababbbaaabbaabbabbaaaababbaabaaababbbabbabaaabaababaaaabaaababbbbaaaababbbbaaabbbabaababaababaaaabbabababaabaabaaababbaaaababaaabbaaaababaaabbaaabbabaaabbbbbaabbaabbaababbbbabbabaaaaaaababbbbbabbbbbbaaabaabbabaababaabbbbbabbbbbaaaababbabbababbbbababbaaabbbbbaabbaaabaabbabaabbabababbaabbbbbbabaaaaaabababbabbababbbaaaaaaabbabaababbabaabbabbaabaaaaabbabaabababbabaabbbabbaabbbbbbbbbbbaabbbbbbbbbabbaaaabbababaabbaabaaaabaaabbaaababababbbaabababbabbabbbbababbaaababbbbbaabababbaabbbbbbbbaababbababbaabbabababaaabbaaababaaaabbbbbaaabaababaaabbaaaaabbabbbbbababababbbbbbbaaaabbbaababbbbaabbabbbaaabbaaabbaabbbbbaaaaabbbbbabbaaabbbaaabbbaaababbaaabbabaaaaaaaabbabbabbbaaabababaaaaaababbbbbbaabaaaabaaabbaaabbabbbaaabababaaabbbaabbbbbabbbbbbaabbbbabbbaabababbabbabababbababaabbbaaaabaaaabbabaaabbabbbbabbbaaaaabbaaababaabbbbabaaabbababaababbbaababababaaabbababbabbabaaaaaaabbbbaaabaabababbbbbababbabaabbaabbbaaaaabaababaabbabbaabaabbbbaababaaaaabbbaaaaaabbababababbbbbaabbaabbaababbababbbbaaaabbaaaababaabaaababbbababbaabbabbaaaaabbbbbabababbaaabaabbaaaaabbaababbababaabaaababbbababbabbbbbaaaabbaaaaabbabbbabbbabbabbaabbabbabbaabbbabbabbabaaababaaaaabbbbbababbababbbaabbaaabbaabbabbabbbaaaaaaaabbaabbaabbaaabbaabaaaabbaabaaababbaaababaaabbbbabbababaaaabbbabbbabaaaabbabababbabaabbbabbaabbaaaababbabaaababbaaabaababbbabbaaabbbabaaaabbbabbbbabaaabbbaaabbbababaabbaaaabbbbbaabaaabbbbaabbbbbaababaaaaaaabaabaaaabbbbaaabababbababbbaababbbbbaaabbbbbaabaabbbaabaababbabbbababaaababaabbbbababaabbaaaabaaabbbaaaaaaababababbaabaaaabaaaaaaabbaaabbbaabbaaabaaababbbbbbabbbabbbaaaabababaabbbbabbbbaaaaaaababaaabbaabbaaabbbbaababbaaababaababaabbaaaababbabbaababaaabbaaabbabababababaaabbaabaaaaabbbbaaabbabababbbaaabbabababaaabbaaaabbabaaababbabbbbbabbbaababaabaaabaabbbaaaabbabbabbbabbaabbbbabbbbabbababaabbbababaabaaaaabaaabbbbbaabaaaabbbbaabbabaaaabbabbbbabbabbbaabaabaaabbaabbabbbbaaaabbaaabbaaabbbbaababbaaaaaababbaabababbbbbbaabbabaaabbabababaaabbababbbbabaaaabaaaabaaaaaaabbaaabaabbabaabaababbabbbbbaaaabbaabbaaaababbbbbbbaaabaabbbbaabaaabbabbabababaaabababbbbbabaaaaaabaababbaabaaabbbaabababbabbaababbbabababbababaaababbababbababbbbabaaaabbabbbbaababaababaabbbaaaaabbaaaabbaababbbaaaaaabababbbbbababbababaaaaabbbbabbabaaaaaaaabbaababaababbabbbbbbabbbbbbbbaabaabbbbbabbaababaabbbabbbbbababbabbaababbaabaaabbbaaaaabababbbabaaaaaababababbbbbaabbbbabaaaaaaabababaababaaaababaabaaababababbaaabbbbabaaabbaabababbbabababaababaababaabbaabaaabaaabaaaaabbbaaaabbaababaabaaaaaabbabbaabbbbbaabbaaaaababbaaabbaaabbbbbbbababaabaaaaabbabbaabbbbabababbaabaaaabbbaabbbbbaababbbbabbaaaabbaabbabababbbababaabbabaaabbaaaaaabababaaaaababababbaaaabbbaababaaabbbbbbbaaababaaababbabbbaabbabbaabbbbbbbabaabbbababbababababbabaaaabbabaaabbaababaaaabbbaaaaabaaaabaababbbabbbaabbababbbbbababbabbabaabbaabababbabbbbaababbaaaaaaabbbbbabbbaabaaabbababbabbaabbbbbbbbbbbbbabbbabbabbabababbbaabbaaababaabaabababaabaabaababbbbbbbbaaabbabbaabbaababaabbaaaabbaaabaabaaababaaabbbbaaabababbbaaaaaaaabaaabaababbbbabaabaaabbbabbaababbbabbbbbaaaaaaabaabaaabaaabaaaabbaaabbababaaaaaabbaababbaaaababbbabaaabaabbaababababbabaabbbbabababaabbbaababbaabaaaaaaabbaabaaabbbbbabbabbaaabbabbabbbaaabbbbaabababaaaaabbaaabbbbbaabbbbababaaabababaabababbbaababbbbaaababbbabbbaabbaaabababbaaaaabaaabababaababbabbbbbbaabaaaabbbbbbabbbbbaaaabaabaabbabbabaabbbbbaababbabbabaaababbbbabababbbbbaaabbbbabaabbbaaabbabaabbbbaabbbabaaabbbbbbaabbaabababaabaaabbbbabbaabbbbaaabaabaabaaaaababaaaaabbbbbaabbbbabbbbaababaabbbaaaaababaabbbabbabababbbbbabaaabbaaabbaabbbabbabbabbbbbbaaabaabbaaababbbabbbbaababbaabbababbababbbbabaaaaaaabababbaaabbaaabbabaaaabaababbbabbbbbabababbbaabbaaaaaabbaaaababbaaababababbbbbbabbbabbbaaabaaaabaaabbababaaabaabbaaabbbaabbbbaabaaabbbbbabbbaaaabababababaabbbbbababaaababbababaaabaaaaaaaaabbbbababaaabbabbbbaabaababaababaaabaaababaaababaababbbbbaabaaabbbaababbaaaabbaabbbaaabaaabaaaabaabbbaabbaabbbaabbaaaaaababbaabbbbbaababbaabbabaaabaabbbbaaaabbbbbbabaaabaaababaaaaaabbbaabbbbbbbaabaabbbbaabbabbbabbbbabababbbabbaaababbbabbbbaabbaabaababbbabaaabbabbbabbbbaababbabaabbbbaaabaaaaaaabaaaabbbbbbbbbbaaaabbaababbbbbabbbbbbabbabbaaaababaababbaaaaaaaaababaaaabababbaaabbabbbbbaababbabaaaaabbbbbbbababbaaabababbbaaaabbbabbbbbabaaaaaabaabbbbbbbaaaaabbbbbbabaabababbbaabaabaabaabaababaabababaaabbbbaaaaaabaaabaaabbbbbbbaaabbabbbbaabaabaaaabaaabaabbabaaabaabbaaaaaaaabbabbababbabbbabbabbbaaaaaaaaaaababbabaababbbaabbbabbaaabbbaabaaabbaaabababbabaaabaaaaaababbabaaabbbbaababaaaabbabaaabbaaababbbababaabbbbaaaabbabbaaaabbbbbbbabbbabbabbbbbaaaaaabbababbbbaaabaaabbaaabbbbabaaaaaaaaaabbaabaabbbaaaaaaabbbbbaabbabaabbaaababbaabbbabaaabbbbbaabaabbbabaabbbbaabbaabbaabbaaabbabaaaabbabbbaabaabbbbababbbbbbbabbababbaabbbbaabaaabababbbabbbabbabababaaaabbbbaaabbaabbbaaababbabaababaaabaaababaabbabbbbbbbabaabababbaabaabaaabaaaaababbabbaaabaaabbbabaaaaababaabbbabbbbbbabaabbaaababaaabaabaaaaabbaaaabababaabaaaaaabaababaaabaaababaababbbabaaaabaababaabbaabababbaabbbbbbaababbbaabbbbabaaabbbbaaabaaababbbbbbaabaaabbababbabaabaabbbaabaabaaabbababaaabbbababbbbbaababbababaababaaaabbbbababbabaabbbabaabababbabaabbbabbbaaabaaaabbbabaaabaabbbabaaaaaabababbaabbabbabbbaaabaababaabaaaaababbbbaaaaaaabbbaabaababbbbbbaabaaabbbababaabbabaaaabaababaabaabbbbbbabaaabababbabababbbabbbbbbbbababaababbaabaaaaaabbbbabbbbbabaabbaabababababbbababababbbbaaabbaabbbbaaababbaaaaaaaaaabaababbbabaabaaaaabaaaaaabbbaabbbababbbaaaabaabbbaaabababbabaaabbbbbbbbbbabbababaabaaaaaaababbbbabbabbabbbbabbbbbaaaaababaaabbbbaabbbabbbababaabbbbaabaaaabbabbaabbbaaaabaaaabbabbbaaabbabbabbaababbbbaaaaaabaabaababbbbaabbaaababaabbabbaabaaabbabbbbbababbabbbababbbbaaabbbabbbaabaaabaaaababbbaaababbaabaababaaaaaabaabaabaababbabaabbaabbabbaaababbbbababaaaabbbbbbababbbaaaaaaabbbaabbababbbbababaaaaababbabbbbbababbbaaaaaaabbbababbaababbaabababaaabbbbbbabbababbbaaababaabaaabbaaaaaabbbbabbababaabababaabbabbaabbbabbbbbbbbbbaaaabbabaaabaaaabaaabababbaabbaaabaabaabbabbbabbaaabbbababaabaaabbabbbabbaabaaabbaabaabbbaaaabbababaabaababbababbbabababababaaabaabaabbaaaaabaababaababaabbbababbbbaaaabbbbaabbabbbabababbbbababababaaaaabbabbbabbbaaabaabbababaaaaaabababbaaabaaabbaabbaaababbabaaaabababbaabaababbaaaaabbbbaaaabbabbbaaaababbbaabbbabaaaabbbbbbabbbabaababbabbaabaabbabbaaabbbaababaaabbbaaaaaabbaabbbbabaabbbbbbbaaaaaaababbabaaaaabbaaabaabbbaaabaaaaaaabbbabbaaaaaaabbbabbbababaaaaabbbbaababbbbaaaabaaabaabbaababbaabbabaabbbaabaabbabbaabaabbaaabbaabbaabaaaaabbaabbbaabbabbbbabbabbaaaabaaaaaababbaabababbabaabbbbaaaaabbbbaabaababaaabbbaabbbbabaaabbaaababaabbaaabaabaaabbabaaabaabbbababbbababbbbabbbaabaabbabaabbbbbabbbababaaaabaaaabbabaaababaaaaabbbbababaaababbbababaabaaabaaaaabbbbababaabaaaaabbaabbbabaabbaaaabaaaaabbaabaaaabbaabbbabbababbaaababaaaabbababbbababbbabbbbbabbbaaabaaababbbababbabaaaaaabbabbbaaaabbbababbaaaaabbabbabaabbabbabbaaaaabababababbaabaaabaaaaabababaababaabaabaaabaaaaabaaaaabbbbbabaabaaaaaaaaabababbaabaaabbabbbabaaabaabaaaaabaaaaaaabaabbbaabbbabaabababbbbabbababaaabbaabbbbbababbbbaabbbbabbaabbaaabaaaaababaaabaabbbaaababaabababbbbabbabaaaabababaaaaabaaababbabbabbaabaabaaababaaabbaaabbaaaabaaaaaaabaababbaababbabaabbabaababbbbabbaababbbbaaabaaabbaaaaabaababbababaaaaaaabbababbaaaaaabaabbbbbbbabbbababaaaabababbbbbabaaaaaabbabbaaaabaabaabaabbaabbbaababbbaababbaabbbaababbbabaabbaaaababbababababaaaaaabbaaaababaaabaaabbbbbaaaaaaabaaabaaababaabbabbbaaabbbaaabaaabbbabaaaaaaaabbbaaaaaabbabaabbbbabbaabaababbaabbaabbaaabbbbbbabbbaaabbbbbababbaaaababbaaababbbaaaaabaaababaababaabbababbbabaabbaaabababaaabaabaabaabbabbbaaaaaababbaaabaaaaaabbabaaabbbbbbbbbaababaabbbaabbbaababbabbaaababbabaabaaababaaabbbaaaaaabbbabaabaabababbabbababbabaaaaabaabbabaababaababbbabbbbaabaaabbaababbaaababababaaabaababbbbbbbabbbaabbabbbbaaabbbbbaabbabbaaaabbbbaabbbbabbbababababbbbbabbabaabbaabbbbaabaaabbabbbaaaaabbaabbaababbbbabbbabaabbaaabababbbaaaaaaaabbaaabbbbaabaabbbaaabbbabaaabbaaaabbbbabbbaabbbbbbbabbbabababaaabbabbbbaaaabaabaaaabaabbaaabbbbabaabaabbbbabbaaabbabbaaaaabbbabbabaabbbbabbbbbabaaababbaabaabababbbbaabbbaabbbbaaababbbaaaaabbbbabbbbaaaabaabbaaabaabaabaaaaabaaababbbbaabbaababaababbbbbaababbaabbbaaaaaaabaabbbbbabaaabaababababbbbbbabaabaabaabbabbabbbbbaaaababaaabbaaababababbabaaaabaaaaaabbaaaaabbabbabaabbbabaaabbaabaabbaaabaaababaaabaaababababbbaaabaabbaaababaaababbaabbbbbbabbbabbabbbaaabaaabbabaabbaaabbaabababbaabbbbbaabaaaabaaaaabaabbabbabbabbababaaabbbbaabbaaaaaaabbbbbababbbbaaaaabbabbbababbbbababbbbbbababbabbaaaabababbbbababaabbbbbabbaaaabaaabaaaababbababaabbaabbaaabbbabbbaaabaaabaabaaaabababbaaababbaabbaabbbababbaabbaaaaaaabbaabbaaabbaabbbabbbbaaaaaaabaaaabaaaaababbbbabbabaabbaaaaaaaaababbaaabbbaabaaabbaaaabbaababbbabbbbaabbbbbbbabbbbaaabaabaabaaaaaabbbabbbbbbbbaabaabbabaaaabaabbabababaabbbbaababaabaababaaaabaaaabbbbabbabaaabbaaabababbbababbabbbbbaabbababaaaaaabbbaaaabbabbbbbbaaabaabbabaaaabbbbabaabaababbbaabbabbbabbbbbaabbbbbbbabbbbaaabbaabbabaaabaaabaaaaaaabbaaaabbbbbaabababbaababbabbbabbbabbbbbbbbbabbbbabaababbbbbaabaaababbabbbaabbabbabbbbabaababbaabbabababbaabbabaabababbbbbbbabbaabbbabaababababaabaaaaabbbbaabbaaaaaabbbbbbaaabbbbbbabbabbbbbabbbbaaaaaaabaaabbbaabbaaaaabbbbbbbaabbbabbaabbababbbbababbbbaabbaaaaababababababbabbabaaaabaaaabaabaabaababbaaaaabbbabbbbbaaaabaaaaababbabbbbababaaaaaaabbaaaabababaaababbabbbababaabbaaababaaababbabbabbbbaababbabbbbbabbbabbbbbbbabbbaaaaabaabababbababaababbaabbabaaabbaaaabaaaabaabaaabbbaabbaaabbaaaaababbabbabbaabaaaaaababbabbaaaabaaaabbaaaaaaaaababbaaaaaabbbbababbbababbbbaabbbaaabaababbbabaababbaabbababababaabaabaaaababbbaaabbbaaababbabaabbbaaaababaaaabaaaaaabaabbaaaaabaaaababababbabaaaaaabbbabaabbaabbbbbaaabaaaababbabbababaaababbabbabbbbbbabbbbbaababaaabaabbbabbaababbbbbbabbabbaabaaabaaabaabaaaabbbbbabaaabaaabaabaaabaaaaabbaaaabaabaabbbabaabbbbabababbbbbaaaababaaabbbabbabbbaaaaaaaabaabbbababbbbbbbbbaaabbbbbbabaaaabaaaaababbbaaaaaaaaaaaaababbaabbabbbbabbbaaabaabbaaabbaaaaabbbaaabaaaabaaaaaaabbaabbbaaababbbaaaabaaabbbaabaaaabbaabbabaabbbbbbaaababbbbbbabbbbbbbbaabaabbbaaaaabbaabbaabaaaabbbaaababaabbaabbbaaaaaaaababaabbbbaaabaababbbbbbbaabbbbbaaaaabaaabbbaabaabaabbaaabbbbabababbbabababbabaaaaabababbbbababbaabaaababaaabbbababbbaabbabaabbaabbbbaaabbabbabbababbbbbbabaabbbaaaabbbbabbbaabbabbbbbbbbbbaabbbaaaaabaabbaaaaaabaaabbbabababbbbbbbababababaababaaaaabaaaaaaabaabaabbaaaabaaabbbbaaaaaabbababbbbbaabbaababbbbbababbbabbbaaaabbbabbbbabbbabaabbaaabaaababbabbababbaabbaaaaaabbbbababababbbbbbbbbbababababaababbbbabbaaabbbababbbbbbaabbabaaababaabbabaabbbabbbabbbbbababbbaaaabbbaaababaaabbbabaaabbaabaaaaaaababbabbaababbabaaaabaabbbbbaaabbbbaaaabbbaabbabbbbabaabaabbaababbabbabbbabaabaabaababbbabbaaaaaaababaaabbbbababbbbaaabbabbabbbbaabbababbaabbaaababbabbabababaababbbbaaababbabbbbaaabababaababbababbabbaabaaabaabbaaaabaabbaaaaabaabbaababbaaaaabaaabbaaaababaabaabbaabaabbbababbaaabaababbbbaaabababababaaababbaabaababbabaabbbbbaabaabbabababaaaaabbbaabbabaababaaaabaababaabbaaaaaaaaabaaaaaaaabbbbaaabaaabbbaabbbbaaaaaaaabbabababbbbaaababbbbabaaaabaabbbbababbababbabbaababbbbabaabbbabbababababbbaaaaababbaaabaabbaaaabbaaaaabababaabababaaaaaaaabbaabbbabbbbaaabaabaabababaaabbabaaabbaaabaababbbaababababbabaaababbbbaabbabbbbbbaabaaaaabbaabbabaaabbbbbbaaabaabbbbbbbabaaaaabaabaabababbabbaabaabaababbababbaabbbbbabbabaaaabaaaaaaabbbaaabaabaaaabbaabaaaaababbabbbbbabbbaabbaabaabbbbbbaaabbbabbabaabbababbaabbbbbbbbabbbbbbabbbaabaaababbbbaabababaaababbaabaababbbbbaabbabaabbaabaababbbbabbbbaababababaaabaaababababaaababaababaaaaabbbbbbbbbabbbbbababbaababaabbbabbbaaabbbbbaaabbbaabbbbabaabaabbaaabbaabaaabaaaabbabaabbbabbbbbbabbababaaabbbbbbaaabbbbaabbbabaabbabbababaaababababaabaaaaaaabbbaabaaabaaabababaaabbbbaaaaaaaaababbaabaababbababbabbabbbaababbaabbaabababaabaaaabbbbaaaaaaabbaaababbbbabbbbbaabaabbaaabbaaabbaababbbbbbaabababaababaabaaabaaabbbbaabaaabaaaabaababbabaabababbabbbaabaaaaaaababbaaababbbabbbababbabbbabbbbabbabbaaaabbaaabaaabaaabbbaaababaaaaabaaaaabbbabbabbabbaaabaabbababaaaaabbbbabbbaaaaaaaaaaabbbababbaabaaaabaabbbbbbbbaabaabbabbbabbaabbbbaabbaabaaababbbaabbbaabbbbbababaabaaaaaaaaababababbbaaabbbbaabbbaababbbbabbbbbbabaabbbaaaababaabbababbabbbbabbbbbaaaaababababaabbbabaababbabbaaabaaaababaaababbbbbbbbbbaaaaaabaababbaabaabbabbaababababaaaaababbaabbbbaaabaaabbbabaabbaaabbbaabbbabbabaabababbbaabababaaaaabbbbbbaabbbabaababababbabbabaabbaaaaaaaabbbaabbbababbbaabbbabaaaaaaabbbbaabaaabababbabbaaababaaaaaabbbabaabbaabaababbababbaabaaaabaabbbbaabbabbabbaaaababaaabababaabbaaaaaaaababaabbbaabaaaaabbabbbbbaaaabbbabbabbabaabbabbbaaabbababbaaababbaabaaaababbaababbaabbaabbbbbbaaababbbbaaabbaabbbaabbaabbaaaabbbbababbabaaaabbababaaabbabbbbbbabbaaabababbbbbbaabbbabbabababaaabbbaabaabaaaaaaabaabbabababaabbbbabaaabbaabbaaababbbbbaaaabbaaababaaabbaabaababaaaaabababbaaabbbabbbbabbaabbaaabbbaababaabbabaaaaaaababbabbbbaabbabbaabbbaaaabbabbaaaaaabaaabbbaaabbbbbaabababbaaaaabbbbabaaaaaaabbaabbbbabbbbaabaabbbbaaaabaaabbaaaaabbaababaabbbababaababaabaaababaaaaaaababbbabaababbbbbabbaaaabbbaaabaabaabaabbaabbbababbababbbbbbbbbbbabaaaaaaaabbaaaabbaaabbbaaaababbabbbbbaaaababbabaaaaaabbabbaaaabaaabaabaaaabbababbaabbbaaaabbabaababbbaababbbbaaaaaabaabbbaabbabbabaababaabbbababaabaabaabbaaabbabbabaaabbbbbabbbaabbbaabbbbaabbbbbbbbbaababbbbaaaabbbababaabbaabaabbabababbbbbaaababaaaabbababbaaaabbbabbbaababaaabaaaabbababaaabaababbbabbbaaaaaaabaabbbbababbaaababaabaababbababbbbaaabbbbbaababbbaabbaaaaaaaaaabbbabaababaaabaaabbbbbaababbabababaaabbaaaababaababaababaaaababbabaaabaababbbaabbbbaababbabbbaabbabbbbaababaaaabbabbaabbabaaabbbabbaababbaabbbabbaaabaabbabababbabababbaaaabaabbaababbbabbbbbabbbabbbbbaababaabbabaaaabbaaababaabaaabaaaabaaaaaabbaabbbaaaabaaabbbabaabbbbbaaababaaabbaabbabbbaaabbabbbbbbabababaaaaabababaaaababbaaababbbbabaaaaaaaabaaaabababbabbabaabababaabbbbaabbaababaaabbbabbbbbaabaaaabbbbabbbbbbaabbbaababbabbbaaabbaabbababaaaaabaababaaaaabaaaaaabbaabbbaabababbbabbabaabaaabbbabbbbbbbabbbbbabbbbbabaabababababbabbaaaabaaabababaababbbababaabaaabbbbababaaababbbaaaababbabbaabababbbbabaaabbbabbaabaaabbababaabbbaaaaaaabbbaabbbaaaaaabaabaaabababaabbababbbbbbaabbbbaabaabbabbbaaaabaaaaababbbabbaabaaaabbaaaabababbbbaaaababaababbaabaabaabbaaabbaaabaabaabbbbabbaababbbbaaababbaabbaaaaabbaabaababaabbaaabbaabbabbaabbabbaaaabaaabbaaabbaaaaaaaabbababaaabbbbababbaaaabaaaabbbbbababbaaabbaabaaaabbbabbabaaababbabbbaabbbaabababbbaaaabbabaabbaaaaaabbbbabbbabaabbaabaaabbaababaabaaaaabbbabbaaabababaabaaabaaabbaabbaaabbababbbbabbbbbabababbbaaaaaababbbbaabbabaabbbbaaaaabbaabbbbbaaababababbabbabbaaabaabbbbaaabaaabbbabbabbbabbbbabbbabaabbaabaaaabbaababababbbbbbabbbbabbbbbabbaabbbbabbaabbabbbbbbaaabaabaaaaaabaaabbbaaaaababbbabbabbaabbababbabbbabbabbbabaabaabbbabaaababbababbabbbbbbbaabbaaabbabbababaaabbabbbababbaabbabbbaaababaaababbababaabaaabbaaaababbaababababbababaabaaababaababbababaaaabbbbbabbabbaabbaaaabababbbaabbababababaabbaaabbaaababaabbaababbbbbbbaaabababbabbbaaaaabbbabbaaaabababaaabbbaaaabbbaababaaaabbabbbaaaababaabbbababababbaabbbabbbababbabaabaabbbabbaabbabbabaaaabbbbabbaaabbbbaaaabaaaabbababababbabbbbbaabbbbaaaabbabbbabbaabaaababaabbbbabbbbbaabbbbbaaabbababbbaaabbbabbaaabbaabababbbaaabbbbbaabbabaaababaabbaaabaaaaaabababbababaabaabaaababbbbbbaaaababbbabbbbbabaaababaaaabaaabbbbbabaabababaaaabaaababbabbaabbbbbbbbaabaaababaaabaaabbabaabaabbabaabbabaaabbaabaaaaababbbabaabbbbbabaabbabbababbbaabbabbabaaaaaababaaaabbbbaaabaabaabaabbbabbbbbaabaaababbaaaaabbbabaabaabbbababbaaabaabaaaabababaaabaabaaaabbaababbaaaaaabbabbaabaaabbaabbaaaaabbaaaaabaabbabbbaababababbaaaabbbbbaabbaabbbbbbbbabaaaabababaababaaabaabbbbbbaabbabaabbaaabbababbaaabbaababbaaabaaabbbbabaaaaaaabaabaabaabbaabaabbbaababbbaabbababababbbbbbbabbaaabaaaabaabbaabbbabababbbbaababaaababbbbabbababbabbaaaababbbbbbaabbaabaaabaaaaababbaabaabbaabbabbabaaababbabaaabaaaabbaababaaaabaaabaabaaaabababaaaabbbbbabbababbaaababbbaababbabababbbaabbbbbaababbaabaaabbabaaabaabbbbabaaabbbaaabaabababaababaabbbaaabaaaababaaaabbbbaabbbbabbbbbbababbbababbbabbbaaabbabbaabbbbbaaabbaababbbbaabbabbaababbaaabbbbaaaabbabaabbbabbbabbbbbbbbbabbaaaaabbbabaaabbbaabbbaabbaaaabbbaabbaaabaaabbbabbaabbbbaababbababaaaabbbabaaaabaabaabbbbbb
aaaabbabaabbaabbbabbaabababbaabababbaababbaaabbbaaabbbbbbaababaabbaaabbbaabaabababbbbbababaaabaaaabaaababaaabbbbbbbbaabababbaabbbababaabaaaaabaaaabaabbbabbaabaaaabbbbbaaabaabbbbaaaaabbbaaabbbaabaabbbaababbbabbbabbabaababaababbaaabbaaaaabaabababaaaaabbbbaaabbbbaaabbbbbaaaaaaaabbabbabbbaaabaaababbaaabbaabaaabbabababbaaaaabbabbabaabbababbaababaabbabbabaabbbabbaaabaaaaaabaaabbbababaaaaabaabbbaaabbabbbbababbbbabbaabaaabbaaabaaababbabbbbabbbbaabbbabaabaabbbababaabbbabbababbbaaababbbababbbbbabbabbbaaaaababaabaaabbbbaabbabbbaabaaaabbbbbabbbbbababbabaababaaabababaabbbbbbaabbababaabbbaabaabbbbbaaaaababaaabbaababaaaaaaabaabaaaaabbaaaaabbaaabbbaabbbaaabaaaabaabbbbabaababaabbbababbbbaababaabbbaaaabbbaabaabaabaaabbbbaabaaaaaaaababaaaaaabbababaabaababbaabbaaabbabbabaabaabbabbaabbbbabbbaabbbaabaaabbbbbbbbbaabaabaaabbbabbbaabbbabaabbbbbbbbbbbbbbababababaabbbabbabbbaabbaaabbabbabbabbbbaaababababbbabbbabbababaaabaabbaaaaaabaabaabbaababbaaaaaaaaaaaabaaabbbbabbbbbbbabbaabbbababbababbbbaabaabbbabbaabbabbaabbaabababbabaabaababaababbbaabbababaababbaabaaabbbaabababbaaaaaaaaababbbaababaaabbbaababababbbbbabbababbaaabbbbaaababbaabbabbbaaabbabbaaaabbbababaaababbabbaababbaaaabaaabbbabababbaabbaabbaabbbbbaabbabbbabababbaabbbabaabbbbbaababbabaabbbabbbbabbaabbbbbabbbaaaaababbaabbbbbabbaababbabbaaabaababaabbbbabbabbaabababbbabbbaababbaaabbaaaaaabbabbbbababaaaababaaabaababbbaaaaabaabababbbbbbabababbabbabbaabbbbaabaabaabababbbaabaaabbabbaabababbbbaaaababababbbaaababbbabaabaabbbbbbbababbabbaaaabbbaabbabbaabaabbaabbaabbabbaabbbbaababbbabbbbaaababaaababaaabababababbbabababaaaaababbbbbabababaabbbbaaaaabaabababbaaaabbbaabbaaabababaabbbabbbabbababaaaaababbbbbabaaaabbaaabaaabbbbaaaaabababbaabaabbbbaabbaaabaababbaabbbbbababbbabbaaaababbaaabbababbbaabbbabbbabbbbaabbabbbbabbaaababbababaaabbbbabbbaaababaabaaaaabbbabbbbaaabababbbaabbababbaabbbabbaaabbaaabababaabaabbabaababaaaabbbbabaabababaabbbaaaabaabbbbaabaaaaaababbaabaabbababbaaabaababaabbababbabbbaaabaabbabaaaabbbbababaaaababbaaabababbbaabbbbabbbbbaaababbababaaaaabaaababbbbaaaaaaaaaaaabaaaabbaabaabbbbbaababbabbbabbbbaabbabaabababbbbbbbbbabaaaabababbabbbaabababbaaaabbabaabaabaaababbababbbaaaabbaaabbaaabbbbbaaabaaaaabbaabaabaabbaaabaabbabaaabbaabbabbaabbbbabaabbbabbabbbbbaaababaabbbbaabaabbbabbbbbaabaaabbaabbbbaabbabbababaaabbaaaabbbbbaaabbabbbbaaabbaaababbbabbababbbaaabbbabbbabaababbbaababaabbbbbabbaaaababbaabaabaabaababbaaabbbbbaaaaaaabbabaabbbaaaaaaabbbaabaaaabaaaababbbbbbaaaabaaabbbababbaabaabbbaaabaabbbaaababbbaaaaaabbababbababababbbbbbbaabbaababaabbbbbbbaaababaabbaababbbbbaabaababbbbaaababaaabbabbaaaabaabaaaababbaaaabaabbaabaabbababbaaabbbabbbaabbbaaabbabaaabbbabaabbbbbaaabaaaabbbbbabbbbbbabbbaabbbbaababbaabababbaabbabaaabbabababbabaaaabaabbbaababbababbbbabbabaabaababaabaaababaabbbbabbaaaababbaabbbbababaaabbababaaabababaabbbbababbaabaaabbabbbbaabbbaababbabababaabaabababbbbbbabababaaabbbbababaaaababaababaabaaabaaaababbbaaaaaababbabbbbababbababaaaaabbabbaabbaabaaabbbbabbbbbaaababbabaabbaaabbabbaaaabbbbbabaaaabaaaaababbbaababbbbbabaabbbaaaaaaaaaaabaababbaabbaabaaaababaabbaaaaaaabbbabbabbbaaaabbbbaabbbaaabbbababbabbbbbbaaabbbbabaabaabbbbbbabaaabaababbabbbbaaaabbbbaaaaabbbababbbababbbabaaabbaabbbababaaabaabaaaaaabbabbbaababbbaaaababaaabbbababbbababaaabbbaabaababbaaabbbbbabbabbabbbbbaaabababbbabababbbbbbbaababbbbbbaabbabaaabbaabaaaaaabbaabbababbababbbbbbaaababbbabbbaabaaababbaaabbabbabaabaabaababbaabbbabaabaaaabaabbbbbabbbaababbaaabababbabbbbbabbaababbbaabbabaaaabbbbbababbaabbbbbabaaaaababaaabababababbaabbaaabbbaaaabbabbbabbbbaaabaabbbbbabaaaabaaaabaaaaaabaabaaabaabaaabbaaabbabbaabaaaaaabaabbbbabbaaaaabbabaaaaabababbaaaabbbbaabbbbabbabbbbbbbbaaabaaabbabababababaabbbbbaaababaabaaabbbbbababaaaaababbaababbbbbbabbbabaabaaabbabaababaababbbabbaababaaaabbbabbbbbaaababbaabaaaaaabbabaababaaabbababbaaababbbbbaaabababaaaabbaaaaaaababaabbbbbbbaabbabbabaababababbabababbaaaaabbaabaabaabbababababaababbaaaabbbaabbaaabababbaabababbbabbababbaabbbbbaabbabaaaabbbbbaaaaabbbbbbabaabbbabbbbbaabaabbbaabaabababbaababbbbbaabbbbbbbbbaaaabaaaabaaaaaabbbabaabbaabbbbbbabaabbbbabbbbbbbabbbaabbaabababbbbabbaaabbbaaabbaabbabaabaaabbbbbabaabbaabbbaaabbaababbabbaaaaabaabaabbbabaaaabaaabbaabbaaaaaabaababbbbbaaaaabaaaaaaaabbabababbabbbaaabababaaaabaaaaaaaababaaaabbbaaabbabbbbabbbbbbaaababbbabaaababababbaabaabbbaaabaabbaabaabaabbbbbaaababbaaabbbabbabaaababaababaaaabbbabbbbaaabaabbabbbbabbabbaabbaaaabbbaababbbbbaabaaaababaababbaaabababababbbbaaabaaaaabaabbaaabbabbabbaabbabbaabaaaabbbbbaaababbababbaabbbaabababaaabbbabbbbaabbaabaabbabaaababbbbbabaababaabaaabbaabbaabbaaaaaaabbbabbbabbbbbbbabbbbabbabbababaabbaababbabbbaabbababbbbaaabaabaababbaababaabbabbbaaabbabababbbbabbaabaaaaaabbbbababaabababbabbbbaabbaabbaabaabbabbbaaaabbbabbabaaabbbabbbbaaaaaaaaabaaaaababaaabaaaaaaaaabbbbabaabaababaabababbbbbbabbaabababaabbbbabbbabbabbababaabbaabbbaaabbbbbaaaaaabbaabababaabaabaababaaabaabaababbbbaaabbaaabaaaababbabaaaabbaabaabaabababbaabaabaaaaaabbbbaaababbabbbababaababbabbbabababbbaaabbaabaaaaaabbaaabaaabaaabbabbabbbbbbaabaaabbabbbabababbaaaabbbbbabaaaaaaabbbaaaaaabbabbabbaababababbbbaabbbbabbbabaababaababaaaaabbabaaabaabbbabaababbbababbbbabaaaabbbabbbabaababaababababaaabbaababbababbaaabaaabbbabbbbbabbbbbabaabbababbbbabaabbabbbabaabaababbbabbaabaaabbbbbbbabbbaaaaaabbbbbaaabbbaaabbabbbaaababaaabaababaaabbbabaaabababaaaababaabbbbaabaaaaaabbabaabaaabbbabbabbababababaabaaaaabbaaabbaaabbaabbbaaabbaabaabbaababbaabbaabbaabaaaabbbabbabbbbbabbabaabbaaaaaabababababbabaababbaabbababbbabaaabaaaabbaababbbbabbbabbbbaabbbbbbbaabbbbaabbababbbbbaaababaabbaaababbbaabbbbaaaabbbbbaabbbbaaabaaabaabbabaababaaabaaababababbbbbaaaaabaaabbbbaaabbaabbbbbbbbaabaabbabaaabaabbbaaaabbbaaaaaabbbbbbabaaaaabababbbabaabbabbbabaababababbaaaaaabbbabbabbbbbbabaabbaabbbababbbbbbbbabaababaabbababaaaabbabbbabbaabaaabaabbbabbbaababababbbbbbbbaabbabbabaabbabaaabaabaabaaaaaabaababababbbabaaabbbbabbabaabaaabababaaaaababbababbabbbbaaaaabbbaabaabbabbbbababbaabaaabbbbabaababbbbabbbabbabaaaaabbaaaaababaabbbaabbababbabbbbbaaabababbbbabbbaaabbaaabbabaababbaaaaaabbbbbaaababababbaabaaabbbabaabababbabbabbbbbbaababbbaabbbababbbbaabaabbabbbbabbbbbabbbaaabbaabbbbbabbbaaaaaabbbbbabbabbbaaabbbbbaaabaabbaabbaaaaaabbbabaababababaaaaaabaaabbbbbabaaabaabbbbbbbababababbaabbaaaaaabbbabbbbabaaaabaababaabbabbbbbaaabbbaaaaabbbabbbbbbaaababbabbbabbabaaaaabababaaaaaaababbababababbbaabbababbbaaaababaabbbbbbabaaababababbbbaaaababaaaabbabbaaaababbbbaabbaababababaabaabbabbabbaabaaaabbbbbaaabaaaaaabababbbbabbabbbbaaaabbaaaabbbaabaabbaababaaabbbbbbbbababbbabbaaaaaabbbabbbbbaaaabbababbabaaababaaabbabbaabbaaabaaababbabbbbbbbbaaabbaaabaaaaaabbbbabaaabbbbababbaaaaabbaaaaabbbbbbaaababbbababaabbaaaaabbabbbaabbbaabababbbabbababaaabbabbabbbaabaaababbbbaabbbbbbbbabbbababbababbaaabbbababaababbababababbbabaababbaaababbabbbaaaabbbbabbaaaaaabaaabababaaabaabaabbbbabbabbbbbabbababaabbaabaabababbabbaaabbababaabbbbabaabbbaaabbabababababaaababbbbabbbaabbbaaaababbbbababbbaaabbbaaabaabababbbbaabbbaabbbaaaabaaabbaababbaabaaabababbabbbbbbabbaababbabbbaaaaabbbbaabbabbaabaabaababbabbbbbbaaabbbbbbababbabbbabbaaabbaaaaabbbababbabbbbbaaaabbbbbbbbaaabbbbbaababbaaaaababaaabbabbabbbbaaabbbbaaababaabbababbbabaabaabbabaaabaabaabbbabaabababaabbabaaabbbaaababababbaaaabaabbbabaaabbabbabbbbaabaabbbaaaaabbbbbaabaabbabbabaabaabbaabababababbbabababbababaabaaabbbababbbbaabaabbababaaabbbbbbabbbabbbbaaabbaaaaabbbbaabaabaaabbbaaabbaaaaabababbbaaabbbbaaabbaabbbabaaaabaabaabbaabaabbbaaababbaabababbaaaabaaaabaaabbaababbbbbabbbaabbabbbbaaabbaaabaabbbbabaababbabaaabbabbaaabbabbaaaababaaaabaabaabbabbababbaaaabbbaababbabbababbaababbbabbbbababbaabbbabababbaaaaabbbabababaabbbbaababbabbabaaabbbbbabaaaaaabaaababbbabaaaababbbbabaaabaaaabbbaabbbaaabbabaababbabababbabbabaabaabaaaabbbabbbabbabbaabbabbabbabaaaaaaabbbabbababaaaaababaaaabbaaaababbabaababbaaaaaabbbababbabaaaaaaaabbabaaabaabbaaaabaaaabaabaaaababaaaaabbaaaaaaabaabbbbaaaabaababbabbbbaaababbaaabbaabaabbaaabbaabaabaababbbbaaaaaaaaaabaabaaabbbaababaaabaabbababbabbbbbaaabaababaaabaaaaabbbbaabbabababaaabaababbbbbbbbbbabbabaabaabaabaaaabbabbaaababaaaaaaabbabaaaaababbbbbbaabaaababbabbbbbaaababbbbbbaabbbaabababaababbaaabbbbaaabababbbaaabbaabababbaabbbbaabaaaabaababaaaaababaabbbbababaabbabaaababbbaaaaaaaaaabbbbbabbbbbbbabbaaabbaaaabbbabaaaabaabaaaabbaaaababbbabaaababbbbbbaaabaaabbabbbaabbaaababbabbabbbbbaabbbbbbbaaaaaababababbabbbbaababbbbaaabbbabbababaabaaaaaababaababaabaabbabbaaaabbaabaabbbbbbaabbaaabaaaaaaaabababaaaabaaababaaaaaabbaaabaaabbbabaaabaabbabaaaabbbabbbababbbbabaabbaabbbbababaabaaabbabbbabaaabbbaaaaabababaaaabbbabaababbaabbbabbabbbaaabaaaabaabbabbaabbaaaabbbaababbaaaaaabbbaaaabbaaabaabbbbbbabbbababbbabbbbaaaababbaaaababbbbbaaabbaabbbaaabaaaaababbbababbbbbaaababaababbbbaabbbbbaabaabbabbabbaaabbaaaabbabaaabbbbaababbabbbaaabbaaaaabbbabaabbbabaabbbabbabbbbaabbaabababbaabbbaabbabbbbbbaaabbbabaaaabbaaaaabbbabbaababbbbbaabbbbbaaaaabbbabbababaabababaabaababbabaaabbbaaabbaabbbbbbbabbabaabaaaaabbaabbbabaaaaabbbbbbabbbaaabbbbaaaaabaabaaaaaaaaaabbaaaabbbaababaabababbbabbbabbbaaabbababbaababaabbbbbbababbbabbbbbabaaaababbbaaabbbabbbbabbaaabbbbaaaabbbbbaabbbbaabbababaabbbbbbaabbbbbbabbbabbabbabaabbbbbaabbabbbabaabbbbabbaabbbbbabbabaaabababbbbbbbbaaababbbaabaabaaabbbbaaaabbbababaaaabbbaababaababaabababaabbaabaabbbbbbbaabbaaaaaaaaaaaabbbabaaaaaabaaabbbababbabbbbbbababbbaabbbabbbbbbabaaaababababbbbaaaaababbabbbaabbbbaaabbabaaabbabababbabaaaabbabbbbaabbbbbabbaabbababbaababbaababbbababbaabaaaaaabaaaabbaabbaaabbbbbabbbbaabbbbaabaaabaaabaaaabbabababababaabababaabbaabababaababababaaaaaabbabbabaabaabbbbbbabababbabbbabbababaaaaabbaabaaabbababaaaababbaaababbaabbaabbbbabbaabababbabababaaabbbbbaabaabbbbababaabbbaababbababaaabaabbbbabbaabaabbabbbaabaababbbabbaabbbbbababaababbababbbaaaaaabbbbbaaaaabaabaaaaababbabbbabbabbaabaaaaabaabbbbaaabbabbabbaababbbbbaaaaaabaaaababababbbabbabaabaaababaaabababababaaaaaaaabbabbaaabaaabaabbbaaabbababbaabaaabbabbbbbbbaaabbbaaabbaabaabbabbbaaaaabaabbbaabbaababbabaaabbaaabbaaabbabbbbabbbabbaaaabaaabbabaabbbabaaaaabaaabaaaaaabababaaaabaaabbaabbabbabbbbbbaaabababbbbaabbbaaaaabbaabaababbbabaaabbaabababaaaabaabbabababbbbabaaaaaabbbbaabbababbbbaaababbbaaaabbbabbbbbabaababbaaabbbaabbbaaabbaaaaabbbaaaababaabbaabbbaabbababbbaaabaababaabaababbaabbaaabaabbaaaaaaaaababaabbabaabbabaabbbbabbbbbbbbbbabbbababaaaaabbbbaaababaabbbbaabbababaabaaaababaabbbaaabaabaaababbabbaabaaaabaaaaababbbbabbabbababbbaabaabbbbabaaabaabaaaabababaaababbbaaaaabbaaaaabaaabbabbababababaaaaabbababbabaabbaababaabbaaababbbbbbabbbabbbbbbabbbbbabaaaabaabbabbbaaabbaabbabbabbaaabbaabbabbabbaaabaaabbaabaaabbaabbbabbabbbbbaaaaabbbbabaaaaaabbaabbaaabbbbaabbbabaabbaaaababbabbabbabbbbaaaabbaaabbbaaaaaabbbbaaababbaaaabbababbbbabbaaabababaabbbbbbbaaabaaababaaaabaaabbbbbbbbbabbbbaaabaaabaaaabbbabababaabaabaabbbabbabbbbabbbabbaaabababbabaabbaaabbaaaabbaabbaaababbbbaabaabbabbbaaaabbabaaabbbaaabaaabaaabaaabbabaaabbbabbbabbbaaaabbababaaabbabbbaaabaabbbabaaaaaabbbaaabbbabbbbaaababaabbbbabbbabaabbabbbbaabaabbaaabbbabababaababaabbabbabababbbaababbbbabaaaaabbaaaabbbaababaaaaaabbabaabaaababbaaaaabaabbbbaabbbbabaabbbbabbaabbabababbbaaaaababaaabbabbabbaabbbaabbbbaaaaabbabbababbabbbbbaabaaabbaaababbbabbbabbabbabaaaababaaaaabbbabaabbbabbbabbbaabaabaaabbbbbababbabbaabbbbbabbaaaababbaabbababababbababbaabaababaaaaabbbbbaaabbaaabbabbababbbbaaaaaaaaabbaababaaaaaaababaabbbbabaabbbbbbbaababaabababaaabbabbabaabaabbabaabaaabbbaababbbbbaaaaabbababbaaaabaaabbbbabbbabbabbabaabbaabaaababbbaabbabbabaabbabbabababbabbbaabbababbbbbbababaaaabababbabaaaabbabbbabbbbabbbbbabbabaaaaaababaaaabbbabbbaabaaabbababababbabbaaaababaaaabbaabaabbaaabaaaababbbaabaaaabaaaaabbbabbababaaaabaaabbbbbbabbaabbbbaaaaabbbaaabaabbbababbabaaaabbbbbbabbbaaaabbbabbbbabbaabababbbbbbbabababbabbbabbababababababaaaaabaaabbaaabbbabbbabaabbabbbababaaaabbababbabaaabbbbbababbbbababbbbbaaababbbabaabaababaaabaabbbbaabbbbbaaaaabbabaabbbbaaaaabbabbaabbbaaabbaabaaaaaabaabaaabbbabbabaababbabbbabaaaabaaabbbabaabaaaabbaaaabaaabababbbabbbabaabbbababbabbabaaaaabaabbaabaabaabaabbbbaaaabaabbbaabababbbabaaabaaabbbbbaaabbbaabababaaabbababaaaabaababbababbbaabababbbbbababbaaaababbbbbbabbaaababbbaaabaaababaaaabaababbaabaababbaabbbbbbabbababaaaaaaaabaaaaabbabaabaabbaababbabaaaaabbaaaaababbbbbbaabaaabaaaabbbbbbbbbbbbaabaaaaaababbbababaaaaabbaabbabbaaabbbbabaaabbbababaabbbbbabbaaaabaaaaabababbaaaaababbabaaaabaabaaaababbaabaaaabbaabbababababbaabbbabbbbbaabbbbbbaaaabaababbbbababbaabbbbbabbaababbabaabbaaaaaaabbaaabaabbaaababababaabaaaaaaabaababaabbabbabbabbbbbabbabbbbbbabbbaabaabaabbabbabaaabaaaaabbabababbbaaabbabbabaaaabaaababababababbaabbabbbbaabaababbbbababaaabaabbbaabbbbababbbaabaaababbbbaababbbaaaaaaaabbabbbababbababaababbbabbbababbaaaaaabbabbaabaabaaaaaaaaaabaaaabababbababbbaaabaabbbbbbbbbbbbbabbbbabaabbabaabaabaaabbbbbbaabbaababaabbabbabaaaababbbaababbbbaaabbbabaababbbbabbabbbbbbaaababbabaaababaababaaaaababbaabaaabaaabaabbabbaaababaabaaabbbbbbaaaabababbbbababaaaabbbbbbaabbabaaabaaaabaaababaabbbabbbabaaaaabbbbbabbbabbabbabbabaabaababaaabababaabaabaabbabababbbabababbaababaaaabaabbaabbbbabaaababababaababaababbbbababbabaabaaababaaabbbbbbaaaabaababbbbaabaabaaababbbaaabbbbbabbbabaaabbbaabbbaabaaabababbbababbaababaabbbbbbabbbbabbababaabaaabbbababbbbbaabbbbabbababbaabaaaabaabaabaabbaabbabbbbbbaabaababbbabbbbbbbbbabbabaabbabbbabbaababababbbabbbbbbaaabaabbaaaaaaaabaabbaabbabbaabbaabbabbaaabbbbaaabbaaababaabababbabbbabaaaaababaaaaabbbbbaabaaaabababbbbbaaaababbbbbbbabbbbaaaaaaaaaabbababbaaabbbbbabbbabaabbabaaaabbbbbaaabbbabbabaaababbabbbbababaaabbabbabbabbbabbaaaaabbababbaabbbbabbaabaaababbbbabbbbababbaabbaabbaabbbaabaaaaaabbabbbbbbbaabbbbaaabaaababaaaaabaaabaaaaabbababbabababbaabaabbaabaabaabbbaaababbabbaabbbaaabbbabaaaabbabaabaababbbbaabbabbaabbaaaaabaabbbabbabaabbabbbbbbaabbbbbaaaababbaabbbbbaaaaabbbbbaabaabbbaaabbbbbbababbbaababababaaaaabbabaaaaabbbbbbbaaaaaabbbaabaabbaabaabaaaabbbabaabbaaababbbaababaabbababbaabaabaaaaabababaaabababaaababababbaabbaaabaaaaaaaabbababbbabbabbaaabbbbaaaaaabbabaabbabbabaabaaaabbaaaabbbbbbbbbbabababaabbabbbbbbbbbaaabababbabaaaaaabaabbbbbabbababaaaabbbabaaaababbbbbabbbabaaaaabbaabbaaabaaabbabbabbaabaaababbaaaaaaaabaaaaabbababbbabbabbaaababaabbbbbaaabababaaaabababbbbabbbbbaabbbabbaababbbaabaababbaabbabbbbbbabbbbbbbaabaaabaaabbaabbaaabbaabbabaabbaabaabbbbbaaaaaabbbaabbabbbbbbbaaaabbbababbbaaaaababaaabbbababaabbbbaaaabaaaabaabbbababbaabaaaaaaabaaabaaaaaababbbbbbbaaabbbabaaabbaaaabbabbaabaababbaaaaabbaaabbabbbaabbabbaabaaabababbbabaabaabbbabbaabbaaaabaaaabbabaaabbbbbabaabbbaabbbbbaaaababbabbbaaaabaaaabaaaabbbabaaabbbaababaaabaaabbbbaaabbbabaaabaabaabbbaaabaaabaaabbaabbbabbaabbbbbaaaaabbaabbbaabaaaaabbaaabbbbbaaabbabaabbbbbbbbbbaabbabaabaabbbaabbaabaaabbbbbabbbaaaabbbababbbabababbbabaabbbbbbabaaabbbaaaaababbaababbbbabaaabbbbbbbabbaababaaaabbaaaaabaaabababaabababbbabaabaabbbababaababbabbbbabbabbbaaaaaababbaabbabaabbaabbbaaaabbabbbbbbabbaaaaabaabbaabbbbabbbbaaaabaaaabbbbbbbabaaabbbababbbaaaaaabaabaaaabaaaabaaaabbbbbaaaabbbbabbabaabbabaabbbaaabbbbabbbbbbbbabbbbbbbaabbabaaabababaabababaabaaaaaababaaaababbabaabbbabaaabbbababbbbaaabaabbababbaabaaabaaabaaabaaaaababaaaabbbbabaaabbaabbaabbabbababbbbbaabaababbabaabababbabbababaabaabbababbbabbabbbabaabbaaaabaaabaaabbaababbbaabaabaabbbabbbababbaaabbbbaaaabbbabbbbbabaabbbbababbabbabbababbaababaabaaabaabbbababaaabbbbbabbaabbabbbaabbbbaabbabbaabbbabaabbbaabbbabaaabababbababbabbbaabaabbaaaaaaaaaaabbbbabbaabaaabbbbaaababbabbbbababbbababbabaabaaaaaabbaabbbabbbaabaaabbabbabababaabaaabbbababbaabaabbababbbabbabbaabaabbaaaaabbbaaabaababbaababbababbaaabaaabbbaaaabaabbbaababbbabaaababbaaaaabaaabbbbaaaabbbaaabbbbbabababbaaaaaabbaabaabaababbaaaaababbbbbbbababaaaababbaabbbbababababaababbbbbbbbbbbabbaabbbbbbabaabbbbbabbbbbbaabbaababbbaaababbbbaaaabbbbbabaaaaaaababbabbabbaaabbbabaaabbabbabbabaabbbababaababaababbabaaaaaaaaabababaaababbabbbaaaaababbaabaababaabbababbaaaaaabbaaabbaabbaaaabbaabbbaaaabbaabbbaabbbbbaabababaababaaaabbabaababbbaabbbabbabaababbbaaaaabbbbbbabaabbbaababbaaabbabbbaababbaaaaaabaaaabaaabbaabaaaabbaabbaabaabbbbaaabbbaaabababbbbbbbbabbabaaaabaabbbaabaabbabbbbbbbbbabbbaaabbabbbaabaabbbabababbaabababbbabaabbabaaabbbabaaabbaaabbbaababbaaabaaabbabbbaabbabaaababbbabaaaaabbbabbbabbaabbabbaababbabaaaaaaabaaabababaabaaababbaabbabbbbabbbbababaaabbbaababbbaabbabaaaaabbababaabbbbbbbabaaabbabbabaabababbbbaaabbaaabbbaabaabbabbbabaaaabbbaabaaaaaaaababaaabbbabaaabbbbbaababbaabbabaaaaaabababaabbabbabbabbabbbbbababbbaabbbabaabaaaabaaabbaabaaaabbaaabbbbbaabbabbbbaaaaabaabbaaaababbbabaababaababbbbbbbbbabbaaababbabbabaabaababaaabbabbbbbababbbbbabbaaaaaabbababababbbbabaabbbbabbbbbaabaababbabaabbaaaaabbaabbbaaababbbabbbaaabbbbabbabbbabbbabbbbaaaabbabbabaaabaabbbbaabbabaaabbaaababbababbaaaaaaaabbbababaaaaaabaaaaaaabbbaaabbabaabbaaabaabbbbabbbabaabbabbabbbbbbbabbabbbbaaaabbbabbaabaaaabbbbabbabbbaaaababaababaaabbaabaabaabaaabaaabaaabbbbabababbaabbaabbababbaabaabbaaabbbbabbbabbbbaaabaaaababaaaaabaaaabbaaababbbaaabaabaabbabbbbaababbbaaaaabbbababaaaaabbbbbababbbbabbbbabaaabbaaabaaaabbbaabbbbbbaaaaabbbbbaaababaaaaababaaaaaabbbabaababbbabaaabbaabbababaaabbabaabaabaaabaaaaabbbaabaaabaabababbabaaababaabbaaaabbabaabaaaabaaabbaabbbbabbabaaaabaaaaababaabbbabbbaaabbabbbaabbbabaaabaabbabababbbbabbbbbbbbbbabababbbaabaababbaabaaaabababbbbbbbbaabbabbaabababaaababbababbaababaaaaaabbbabbabaabbabbbabbbabbabbabbbbaabaaaabbaababbabbabaaabbbababaabbbbbabbabbbaabaabbbbbbbbbaabbbabababbaaaabaabaabbaabbbbbaabbababbabaaabaabbbbabbaaaaabaabbbabbaaaaaaaaabbbbabbbaababbbbaaabbbaabbbbbbbbbbbbabbbaabbbaabaaaabbaabbbabbbbaabbaabbaaaabababbbabbabaaabaabbaababbbbbbbabbaabababaabbabaabbbababaaaabbbbbaabbaabbbbbaaaabbabaabababaabbbbabbaaaababbaabbbbabbababbabaaaaaabbaababbaababbabbbbbabbbbaababbbbbaaaaaaaabbbabbaabaabaaaabbaabbaabaaaaabbbaaaaabbbbaaabaabaaaabbbbbbbababababaabbbaabaaabbbaaaaaabbabaababaabbbabbabbbabbaabbbabbaabababbbaaabbaababbbbbaabaaaabaababbbbabaabbbababbbaaaaababaaabbbaabbbbbaabbbbabbabbabababbababababbbbabbbbbababaabbbaabababaaaaabbbaaaabaaabbabbaaabaabbbabaabbbbbabbbbbabaabaabbbababbbaabaabbabbbbabbaaaaaaaaabbabaaaaababbbaabbbaaabbababaaaabbbabaabbbbababaaabbbbbaaabbabaaaabbbbbbaaaababbbabbbbbbababbabbaaaababaaababbabbabaabbabaababbabaabbbababbbbbbabbaabbababababbbbabbabbbaaaababbbbbaabbbababaaababaabbaaaaabbababbbbbabbaaaabbababbbababbabbabbbbabbaaabbaaaababaaaaaababbababbbabaaaaababaabaaabababbaabbbaaababaaababababbaabaaabaaaabbaaaabaabaababbaabbabaababbbaabbbbbbbbaaabbabbbabababbbbabbaabaabbbabbbabbbaabaabaabaabbaabbabbababbbaaaabbababbaababaaaabbbbaabbbbaababbbabbbbbaabbabbbbabbbbbbabbbbaaaaabaabbbbbabbbbbbbbbaababbabaabbbaaabbbbabaabbbabbaaababbbaabbaabbbbabaaaababbbaaabaaaaabaabaaabbbaaabbabbaababbaaabaaaabbabbaababbabbabbaaaabbbabbabbaabbabbbbbabbbaaabbbaabbaabababaabbbbabbbaababaaaabbabaaabaabaabbaaabaaaabbaabbaaaabbaababaabbbaaabbaabbbbabbaaabaabaaababaabbbababbababaaaaabbbbaaabbaabaaabaaaaabaabbabbaaaaaaabaaaaaababbbabaaabbaabbabaabababbabaaabbabbaabbababaaabaabaabbbaaabaaabaabbbaaaaabbaabbabbbababbaaaababaababaabbbababbbbbaabbabbbbbbaabbababbbababbabaaabbbbbaababbbabbaaabababababbabaaabaabaaaaaaabaabaabaabaaaabbabaaababababaabbaaaaababbbabbaaabbababbaabaabbbabbbbbbaaabbababbaabbbababaaabaabaabbaaabbababaabbabbbbbbbabbabbbbbababbbbbaababaaaaabaaaababbbbbbbaababbbbababbbbababaaabbabaababbaabbabbbbaababaabaaaaaaababaababbaababbaabaabbbbbbbaababbbabbbbbbaaaabaaaabbabbbbbbaabbaaaababbbbbaaaaabbbbbaabbababababbaabbbabaabaaabaaaabaabbbbbababbaabaabbaaabbbababaaaabaaabababbbaabbabaabbaabbabaaaaababbabbaaaaabbbbbaabaaaabaababbbbaabbababbbabbabaaaabbbabbbbbbaabaabaaaaaabaabaaaabaabaabaabbbbbabbbaaaaabaabbbaaaaaabaabbbaabbaaaabababaaaaaaaaaabbaaabbbbbbababaabbababbabbbababaaaabaaabaaaababbbaaabaabaababbbababbbbbababbabbbaaaabbaabaabaababbaaaababbaabababaaaababbabaabbbaaaabaaabaababbbababababbbbbbbbbbabaaabbabbbabbbbbabbbababaaaabbbabbabbbbabbaaaabbbbbbbbabaaabaaabbbbabaabbbbabababbaabaaabbababbbababbaabbaabababababaabbbaabbbabaababbababaabaaaaabbaababbbbaabbabbaaaabbbaaaabbbbabbaabbabbababbababbbbbaaaaabaaabaababbaaaaababbaaaabbbbaaabbbaabaaaaabbbbbabbabaaaaababbaabbbabbbabbbababbbaaaababbbbabbabbabaaabaaaaabaababbaaabababbbabbaababbbabbabbbbbbaaaaaaababaaaabbababbaabbbbbbbabbbbbababbaaaaabaabbabaabbbbbaaaabbaabababaaaabbbbabbbbbbabaabbaaaaaabaabbababbbabbabababbabaabaabbabbbaaabaaabbaabbbbbaaabbaaaabbbababbbabbaaabbabbbaabbbababbabbbaabbaabbaaaaabababaaabababbababbabbaababaabbbabbbbababaabaaaabbaaabbbbbababbbbbbaabbbbbbaabbaabbbabababbbbbbbbbaaaaabbbabababbaaabababaaaabbbbbabbababbaaaabbabbaaaabaabbababaababbbbbabaabbbbababaaaabaabbbaabaabbabbbaaaaaabababaaaaaaaabaaaabbbabaaaabbaabbabaaababbbbbabbbbabbaaaaaababaaabbbababbbbabababbaaabbaaaabaaaaabbababbabbaabbabababaaaababbabbaabbababaaabaabbbbbbbbbbbbabaaaaabbbbbabbbaabaabbaaabbababaabbbabaaaababbaabaabbbabaabaabbbabbbbbaaaabbababbbbbbaaaaaabaabababbbbbbaaaababaaabaabaababbbbbaababbbabbbbbaaabbaabababbaaabaabbaaaaabbaaababaabaaaaaaaaababaaaabbbbbbbbaabbbabbaaabababaabbaabbabbbababaabaaabbaaabaabbbaaabbbbbaabaaaabaabbababbaaabbabbabbaaababaabbbbababababbaaabbbbbbbabbbaabaaaababbbbaaabaaababaaaabaabbaabbbabababaababbbbbabbbaaabaabbaaaaabaaaabaaabbbaabbabbbaabbaabbaabbaabaabbbbaabaabbbbababbbbabaaabbaabababbababaabaabbaabababbabbaabababbbaababbaabaababababbbbabaabbaabbbaaababbbbbbaaabaabbbbabaaababaaaaabbaabbbbbabbababaabbbaaabbaaabbabbbbaaabaababbabaaababbabaabaababbbbabbbabaabbaababbbabbbaababaabbaabaabaaababaababbaabbbaabbaabaabbaaaaaaaaabbbaabbbabababbbbabaaaaabbbaababaaaabababaababbaaabbbaaabbbabbabbbabbaaaaababbbbbaabbbbbaabbaabbbabaabaaabaaaabaaababbbaaaaaaaabbaaaaabaabbababaaaaaaaaaabaababbababbaabaaabbbaabbbbaabbaabbaabbbbaabaaaaabbbbbbaaabbabbbbabbabaabbbaababbaabbaaaabbababbabbbaabaaabaaabaaabababbbbbabaaabbabaabaabaaababaababbabbabbbabbbabaaabababbabbabaaababbbbabbbbbababbbabbbbbbabaaabbaabaabbabbbaabbabbaaabbbbaabbaabbbbabaabbaabaaaaaaaaaaaaaaabaaaaabbabbaabbbbabbbbbaabbbbabbababbbbbbabbaabbbbbabbbaabbababbbbaabbababbabbbbaabbbbbbbbbaabbbabaaaaaababaaabbbbababaaababbbababaababaaabaaabbaabbbbbbabaaaabbabaaaaabaaabbaaaaababaaaaaaaabbbbbaaabaabbababbbabbbaaabaabaaabaabbabaaabaabaababbabbbbbbbaababbbabaababbbbbbbaabbbbbbbaabbabbbaabbabbabbabaaaabaabaaabbbabbaababbbbabababaabaaabaaabaabaababababbbbbabaaaabbabbabaabaaabbbbaabaabbbaabbbbaabbbbabababbababaabbbbbababababbbabbbbabbabbabbabaabbaababbabbbaabbabbabbbbabaaababababbbabbabbbabbbbbabbbabbabaaaaabbabaabaaaabbbaabbabbaabbbaabababbbababaabbbababbbaaabbbbbaabababaaabbbaaababababbaabbabbbbbbbbaabbaaabaababbaaabaaaaaaaaaaaabbbaabbababbaabbaaabbaaababababaaaabbaaaaaaabaaabaabbabbabaabbbbaaaaabbaababbaaabbbbaaaabbabaabbabbbbbbbbababbbabaaaabbbbaabbaabaaaabbbabababbbbaabababababaaabaabbabbaabbbababaaabbaaababbbbaabbabbbbbabbaaabbabbbbababaabbaababbbaabbabbbaabbbabbababbbbabaaabaabaababaaaababbbbbbaaaaabaabbabbabbbabaabbaabbabbabbbaaabbbaaaaabbbabababbaaabbaabbaaaaaabababaaabbbababbababbaabbbbababbbbaabbaaaaabbabaaaaaabbbbbaaabababaaabbabbbbbaaaaaaabaabaababababaaababbbbaabbbabaaabbbbaabaaabbabbbbaabbbbabaabaaababaabababababbbbbaabbbbbbaabaaababaabbababbbbaabaaaabbbabbabbabbababbaababbbbaaaaaaabaabbbbbbaababaabbabaaabbbbbabbabaabbbbbbaaaaabbaababbbbabbbaaaabbabaaaababbabaabbababbaabbbabbbbaaabbbbbaaabaaaabbbaabbbaaaabaaabaabaababbbbbbbbbbbbabbbababbbaaababbabaabaabbaabbaabaaaabababbbaabaaabbaabbaabbabaabbaaabbababbaaabaaaaabbaaabababaababaabbabbaaaaabbbbabaabbaabbbababbbbabbaabbbabaabbbabbbabbababbbbbaababbababbbbbaaaabaabbaababbababababaabbbabbbaaababbaaabaabbaabbaaababbaabbaaababbaabababbabbbaabbbaabaabaaababbaabaabbbbabbaabbabbbbbbaababbbbaaabaabbaaaabbbbbaaaabbbabbbababababaaaabbbbaaaaabaaaabaabababaabbaabbaabbaabaabaaababbabbbabbabaaaababaabaaaaaaaaaaabbbbabbbbbaabaabbbabbbababbababbabaaabbaabaaaaababbbabbaaaabaabaabaaabbbaabbabbaabababbaabbaaabaaaabaaabaabaababbaababaaabababbaabbbaabbabbabaaababaaababbbabbaaabbbbabbabbbbbbababbaaaaaaaaaababbabbaaaaabbabbabbbbbbbaaabbbbaabaabaaabbbabbaaabbbbababbbbaaaaabbbaaabbaaabababbaaaaabbababaaaababababbaaabaaaaabaaababaaababbabaaabaabbaaaaabbbbbbaabaababbabbbaaabaaabaabbbabbbaaabbbabbabbbabaabaabbabbbbbaaaaaabbababbabbaabbbaabaaaaaabaabaaaaaababaaabaaabaabaabbaabbaabbbbbaaababbabbabbabbbbababbaabbbaabbabbbaaabababbbbabbbaabbabaaabbaabbbbbbababababaababbbaaabbaabaabaababaabbaaabbabbaaaabbbaababbaaabbabababbabbababbbaabbbabbaababbaaaabbabbbbbabababbabbbabaaaaaaabbabbabaaaabaabbbbbababbbbbbababaabbbbabbaabbaaaabbbbbbbbbbaabbabbbaaaaaaabbbababbabababbbbbbbabaabbabbbaaaaabbbabababbaababababaaabbbababababaaababbbbbbbaaaabbabaabbabbbaabaabbabbaaaaabbabbbaaabbbabbbaabaabbbbbbaaabbaaabaabbababbbbaabaaaababbbaabbaaaaaaaabbaabbabbbbabbaaabaabaababbabbababaaaabaaaababbaabbaabbbbaaabbbabababbabbaaabaabbaaaaabaabaabababbbaaabbabaabababbbbbbbbbabaabaaabbbaaaaababbbbaaabaaaabbbbbbabbbbababbbababbbaaaaaababbaabbabaaaaabbaaaaaabaaabaaabbbbabaaabbbbaaaabbbbababbbbbbbaabaaaaabbababbbaaaabbbbbbbababaaaabaaabbaabbaaabbbaaaaaabaaaabbbbaaabbabababbbbaaaabbbbbbbbabaabbaababbaaaaabbaababbbaaabbbaaaabababbabbbababbababbbbbaaaababbaabaaababbabbaaabaababbbaabbababbbaabbaababaaaabbababaababbababababbaabbbbaaabaabaabbbbbbbaabbbbbbaaabbbbbbabbaabaaabaaaababaabaabbbaaabbabaaaaaaaaaaaabbbbaaababbbabaaaabbbaaaabaaabaabbbbabababbaaaaabbaabbbbaaaaaaaaababbbbbbbbbbbababaabbbbbbbaabaababbabbababbaabbbabaabaabbaaaabbbbabbaaababbbaabbaabbbbbaaabbbbbaababaabaaabaaaaabaaabaabbbbaabbbabaaabaabbabbbabbabbabbbbabbaaabbbbaaaabbbabbabbbbbabbbaaaaababbabbabbabbbbbbbbbaabaabbaabaabbbabaababaabbbaaaabaabaaaababbbaababbbbbbabaababaabbabaabbaabbabbaababbbaaabaaababbaaabbaaabbbaabbaaaabaabbabababaabaabbabbaabbabbbabbababaabbbabbbbaaababbaaabaaabaaaaaaababbabbbaaababaabababbbaaaaaaaabaaabaaabbbbbbabbaaaabababbaabbabaaabbbabbaaabaaabbabaababaaaabaaaaaabbaaabaababaaaabbbaaabbbbaabababbbbbabbabbbaabbababaabbbabaabbbabaabbbaababbbababaaaaabaaaaaaaabbbabbaaabbbbaaaabbbbbaabaabaabbbbaaabbbaabbbbbbaabababbaaaaabbaaaaabaaababbaaabaaabbabbabbbbbbabaabbaaabbaabbaabbaabaaaaaaabbaababbabbaababaababbbbbaaabaabbbabbbbbbbbabbababaaabbabaaabbaaaabbbababbaaababaaabaaaababbaabbbabbabbbbabaabbabbaabaabaabbbbbbbabaabaababaaaabaabaabbbababaabbbaaaabbabaaabbbbbbbabaabbbabaababbbababbaaaababbaaababaaaaaaaaabbbababbabbaaabbababbabbbabbaababbabaaababaabbaaabaabaaaaabaabbaababbabbabbabababaaaabbbabbaabbbaaabababbaabbbabbbbbbbbbbbabaabbabbabbaaababbbbbbaabbbbbbbbbaaaabbbbaaaabbbbababbabbabababaabaaaababaaaaabaabbbbbbbababaaabbbbbabbbbbbbaaaaaaabbbbbaabbabbbabaaaaabbaababaaaaaaabbabaababaabaabbaabbaabbbbaaaabbbabaaaaaaabbbabaababaabbababbabaabbbabbabbaaaaaabaaababbbbaabbbbbbababaabababbbbabbaabbaaaabbbaaababbbaabbbaabaaabaabaabaaaabaabaabbabaaababbabbbabbbabababbaaabbbbbbaaababbbaabaabaababbaaababaabbaabbabbabbabbaaaaaababbaaababbbabaabbaabbbabbbababababbababaaaaaabbabababbbbbababbaaaabbaabbababaaabbabababbbbbaabbbabbbbbababbbbbbbaaaaababbbababaaaabbabababababbaaabbabaababbbaaaaabababbbaabbbababbabbbbbbaabbbbbabbbbbaababbabaaabbaabaabaaabbabaaababbabbbbbaababaaabaababaaabaabbabbaaaaabbaabbabbbabaababbbaabaabbbabbababbbbabbbbbaabbbbabbaaababaababaaabbbbbbaabbbbaaabbbaaaabaabbaaaaaabbbaababaabaabbbabbbbbaaabbbbbababababbabababbaaaabaabaaabbaaaaaababbabaabbababbbbbababbaaabbabbbbaabbbbbabbaaababaabbaabbbababaabbbabbabaababaaabaaaaaaaabaaaaaabbbabababbaabaabbbbbbbabbbaaaabbbbaaaaaaabaababbababbaabaabbbbbbbbbabaabbbbaabbbbababaaaaaabaaabaabababbbbbabbbbbaababbaabbaababbaaaabaabbbbabbbbbabaaababaababbaababababbaabbaabababaaaaaabaabaabaaaabbbbabaaabbbbabbabbaabbabaabaaaaaaaaaabababbabbabaabaaababaaaabaabbababbabbaabbabbbbabbbaabaaaabbbaaaabbbbbababbabbbbbbbaaabbbbbaaabbbabbabbbbbbabbbbaaaabbbababbbbbbbaaabaaabbaaaababaaaaaaaaaaaabbaabbbbbbaaabababbbaaaaaabbbbaababbabbbaaaabaabbaabbabaababbaababaabbaabbbabaaaaabaababbababbbabaaababaaaabbababbaabbbaaabaabbaabbbabaaabbbaabbabbabbaabbaabaabbbbababbaababbaaaaaaaaaaabbabbaabbabaabaaaababaabaaaababbabaabbaaabaaaaaaabbaabbabaababbbbbabababababaaabbbabaabbaabbabbaaaaaabbbbbbaabaabaaabaabaabaaabaaabbaabbabbabaaabaabbabababaabaaaaaaabbbabbaabaaabbbbbbabbbbbbbaaaabaaaaabaaabababbabbbabbababababaabaabababbbababababbaabbababababbbaaaabbbabaaaabaabbaabbabbbbaabbbaababbbabaabbababaabbbaabbbbbabbbaabbabaababaaababbaaababbaabbaaaababbaabbababaaaaaabaaaabbababbbbbbbbaaabaababaabaabbababbbbbabbbaababaabbbbabaaabaabaaababbaaabaaaabaaaaabbaabaabaabbbabababbbbbbabbbbbbaaaaabababbaababbaaabbbbaabbababbbabbbaaaababaaaabaaabbbbaabaabaaaabbababababaababaabaabbabbbbaaaaabbbbaabbaabaabbbaaaaaaababaababbbababbabbababaabbbaabbbbabaababaabbaabbaaabbbaabbabbbbabbbbbaaaaaabbaabababbbbbbababaaaabbaaabbbabaabbaaaaababbaababbbaaaaabbbbabbbaaaaaaabbaabbaabbabaaaabaaabbbaaabbbaababbabaabbbababaabbababbabbaaabbbbbbbbaabbbbaaaaabaabaaababbaaababbabbaaabbbbbbabbbbbbbbabbbaaaaaabaababababaabaababbabaaabaabbabbabaaaaaaabbbbbaaabbabababbaaabbabaabaaabbbabbbaaabbbbbaaabbaababbbaaabbaaababbaaaabbaaaabbbbaababaaaaabbabbabbaabbabaaaaabaabaaaabbbaabaaabaaabbaababbabbbbbabaaabaabbbaabbbaaababbbbaaaabababbabaabbababbabbababaaabbabbbbabbaaabbabbbaaababbababbbababaaaaaaabbbbaabbbaaaabbbbbbabbabaabbbaaaaaaaaabbaabbabbbbbabaabaaabbbabaaaabbbbaaaabbbaaaaaabbaabbbbabaaaababababaabbbaabbabbbbaaabbbbbaaabaababaabbabbaaaabbaaababbbbbaabaabaaaabbbbaaabbbbbaabaabaaabaaaaababbbbbabbbabbaaaabbabaaabaaaaababbaababbbabbbaabbbaabaabbbababaabaaabbbababaabaaaaabaabbbbbaababaabaabbabaaabaabbaabbaaaaababbabaababababbbabaababbababbbbaabbbabaababaababbbbabbaabbbbbabbaaaabbabbaababbbbaababaaaabaaaababaaabbaabaaaabbbbbbaabbaabbbbbbbababbbaaaaabbababbabbbaabbaaabababaabbbababbabbbbbbbbbababbbabbbbbbaaaaaaababaaabbbbabaaabbaababaaaaaaabaaababbabbaaabababbbaaabbaaaaabbababbbbbbbbbabaaaabababaaaabaaaabbbababaaaabaabaaababbababaaabbbbbbbabbaaaaabbbaaababbabbbbbabaababaabbaabaabaabbaaabbaaabbbbbbaaabbbabbbabababbbabbaabaaaaabbaaabaabbabbaaaabababbabababbabbbbabababaaabbbbbaaababbaabaaabbaaaabaaaababbbbbbaabaabaabbabbbbbaabababbbbbbbabababababbbbabbaabbaaaabbbabbaaaabbbbabbbbbbaabbbaaabbbbaaabaabbbbabbbabbbbbaaaabaaababaabaabababbbbabaaaabbbbbbabbabbbbbabbbaaabaaaabbbabaababbbbbabaababaaaaaaaabaabaabbabbaabbbbaaaabbbaabbababaaaaabbabbbbbbbbaababaaabbaaabbbbbaaaabbbbaabbbaaaaaaaabbaaaaabbaabaaaaaabbbabbaababaabaaaaaaabaaabbabbaababbbaaaaabaaaaaaabaabbbaaabbbbaababbaabaabbababababbbbbbabbbbabbbbaabbabaababbbbabbbabbabaaabbbbbbabaabbbabbbbabbaabaabbbababaaabbaaabababbabaaabababbabbbbbabbbaabbbbaaababbaaaaabbabaababbbaaaaaabbabbbbababbaababaabbababbaabbbaabbbaaabababbabaababaababababaabbaaabbbaaaabbbabbabaabaaaaabbaabbabbbaabbabaabababbbababbbabaabaaaaabbbbaabababbbbabbababaaaaaabaabaaabbaabababaababbbaabbbbabaaaaaaabbbababbbbabaabaabbbaaabaaaaaababbaabaaaaaabbbbbabbbabbbbbbbaaabbbbbbaabaabbabbbbaabbaababbaababaaaababaaaababaaabababbabaababbbaabaaaaabaababaabababbababbbbabababaaaabbbbaaaabbbbbaabaaaaaabbabbababaabbaaababbabbbabaabbbbbabababababbbbbaaaabaababbabaaaabbbaababbaabbbabbaababaaaababaaaaabaabbabbabbaaababbbbbbbbbbaabaaaaaaabbabbbbbababaababbaabaabbaaaaaaaabbababbbaaabaabbbabbbaaaaabbbabaaaabaabbbaaaaaaabaabababbabaabababbabbbbabbbbbabbaaaabbbababbbbaabbaaaaabbbaabbaabaaaaabbbbaabbaaaabaababbababaabababaaabaaaabbbaaaaaabbaaaabbbbababbbbbaabbaabbabbaabababbbaaababbbaabbbbbaabaaabbaabbbaaabbbaaaaabaaabbabbbabaaaabaaababaababbaababbaababaabaaabbbbbbbabaabbbababbbaababbabbbabbaaaabbbbbbbabbababbbabbbbbabababbbbaaaabaabaabbbbbababaabbbbbbaaabbaaababbabababbabbaabbaaabaababbbbbbbabbabbbbbbaaababbbbbabbbbbbbababaaaabbaabbbbabababaaabaaaaabaabaabbaaaaaaababbaaabbababbbbbbbaaaaababaabbabaaabaaabaabbbaabbaaabaababbbbababbabaaabbaaaabaaababbbaaabbbbbbaaabbaabbaaabbaaaaaaabbababaaaaabbabaaabbbababaaaaaabbababbbabaaaabaababbbbbabbababaaaaaaabbaabbababbaabbabbbaaababbabaabaaabaaaababbabbbbbaaabbababbaabaabbabbbaabbaaabaabbbabbabbaabaababbbaabbbaaababbaabbbbabbbbbbbbbaaabbbbabbbbabababaabbbbababbaababaaabbabbaaababaaaaaabaaababbaabbbbabbaabbbabaabbbbaaaaabbabababaaaababbabaabbaaaaaabbabababababbaababaabababbaabaabbabaabaaaaaaababbbbabababbbbaaabbbabaabaaabbaaabbbaabbbbbaaabababbbaabaabaabaababaabaaaabababbbaabaabaabbbabaaaaabbaaaaaabbabaabbbbbabaabaababbaaabbabbbbbaaababaaababaabbabaaaababbaabaaaaaaababaabaabaabaaaaabbbaaabbababbbaabbababbbaaaaaabbbabbbabbbabaaaababbabbbbabbbbabbaabaabaaabbbaaabaaaaaaabbbabbbaababbababababbaaabbbbabbbaaaabbabaabbaabbabaaaabbbbbabbabaabbabababaaabababaabbbabbbbaaaabbbababbbbbbbabbbbaabaabbbababbbaabbbaababbbabaaaaaaaabababbaaabaaabbbbbbbbbbaabbaaaaabbbbbbaaaaababbabaaabbabaabbbbbababbabbbbaaaabbaabbbaababbababbbbabaababaababbbaababbbaabaabaaaaaaabbababbabbaaabbbbababaaababaabaabababbabbabababbbbabaaabaaaaaaaababababbbbaabbbbbaaaabaaabaaabbbaababaabbaabbababbaabbaabbbabbababaabbbabbabbabaaabaababbabbaabbabbbbbbabaaaabbabababaababbaaaababbabaaaaabbbabbbbaababbababaababababbbabbbabbababbbbbbbbbbaaaaaaabbbaaabbaabbabbabababbaabbbbabbbbaabbababababaabbbaaaaaababaaabbbabababaabbbbbaabaabbbbbaababbaabbbbbbaabaabbbabbbaababaababbbbabaababbababbaaabbbbbababbbaabbbbabaaaaabaabbabbaaaaabaabaabaabaaababbabbaaaaabaaaabbaabaaabbabbbbabbbabbbbaaaaaaaaaababbbaaaaaaaababbbbaabbaaaabbbabbaaaaabbbabbbbaaababbaaababaaaabaabbbaaaaaaabbaabbbabbbbaabbabbbbaaabaababaabbbaaaababbbaabababbababbabbaaababbbaabababaaabababababbaaabbbaaabbabaabaabaaaaabbbbbabbaaaabaabaaaabbaaabaabaabaaababaabbbbbbbbbbbbaaaaabbbbbbbbbaabbaabbbbbbbabbbaaabbababbbababaaabbaaabaaabababaabaababbbbbbaabbbaaabaaaaaabaaaaababbaababaabbbabbababbaabaaabaaabbababbabbaababbaababbabbaaabbaabbabaabababaaaaaabaabbaabbabaababbbbaaabaabbbbbbabbbabbaaaabbabbabbabbbaabaaabbbaabaabbbabbaaabbbaabaabaaaaaaaaaabaababababbaaabbbbaabbaabaaaabbababbabaababbaabbaaabbaababbbabaaabbbaabbabaabbabaaaabaaabbaabbaabaabbbbabbbabbbaaaabbaabbaabababbaabbbabbaaabababbaabababaabbabaaababaabbabbbbaabbaabbabbbabaababbabbababaaabaaaabbbbbaabaabbbaababbbabaaaabaaababababababaabbabaaabababababbbabbababbbaabbbabbbaababbbbbbabbbbaabbaababbabaaabbbabaabbbbbabaabbabbbaaabaababbababaaaababbbbbababbbaabaabbbbbaabbaababbababaabbbbbbbbbaaabbbbaabbbbaaabbbbbbbaaaaaaabbaabababbbabaaaaaababbbaabababaabbabaaabbabaaaaaaaaaaabbbbbaabbabbaaaababbbbaababbbaabbbbabbbbbabababbabaaaaabbaaabaabbabbbbaaabababbbaabbaaabaabaabbbabaabbaabbbabaaaaaaaabbabaabbbabbbbbabaaabaabaaabaaaaaaabbaabaabbbaabaabaaabbbbababbbbbbbbbbaabbbbaababbaaababbbbbaaaabbbaababbbbbbabbabbaaaabaaabaabbaaaabaaabaaabaaabbabababbaabaaabababbabbbaabbbabaaabbaaabbaabaabbababbbaaababbbbbabbaabbababbbbbaabbbbbbbaabaaabaabbaabbbbaaababbbbaaabaabbbbaabaaaababaababbbbababbbbaaabbaababbbbabbbabbbbbababbbbaaaabbababaababaabaabbbabbaaaabbaababbabaabbaaababbabbabaaaabaaabbbaabaaaabaabbaabbabbbaabbbbbbabbabababbbaabaaabaabbaaaaababaaaababababbbaaabaabbaababaaaabaabbabbabbbbbaaaababbbbbbabbabbbbbaababaabaaaababbbaabaabbbbbabaaabbabbbbabbaabbbaababbbaaaabaaaaababaabbbaabaabaabaabaaaaabbaaabbaabbbabbababaabababbababababaabbaabaaaabbabaaabbbbabbabbbabbaaabababbabaabbabbabaaaabbabbaaaaaaaababaababaaabbabaaaabaaabaaabaabaaabaababbbbaabbbbbbabbbbaaababaabbbabbbabbababbbbbbbabbbabaaaaabbababaabbaabbaaabaabaabaaaabbbbbabbaabbbaababbbbbbaabaabbabababaababbbbaabaabbbaaabbbabaababbbabbbabaababbabbbbbaaaabaabbabaabbababaababaabbbbbbababaababbabbaaaababababaaabbaabbabaabbaaabbababbabababbbababababbaaaabaaabaabaaabaaabbbaaaaaaabbbabbbaaaaaabababbbbabbaabaabaabbbbbaabababbbababbbbaababaabbabbbaabbbbbbbabaaaaababbbabaabbbbabbbaaabaaaabaaaabbabababaaaaaaaaaababbbbbbbaabaabbaaabbaaaababbbaabbbaaababbaaaaaabbababbaabbabbbbaaabbababbabaaabaababababababaabaabaaaabaabaabaababaabbabbabababbbaababaaaaaaaababbbbabbbabbbbbaabbbbaaaaabaababababbbbabbabbabaaaaaababbaabbbababbbabababbaaaabaaaababbbbbbbabbbbabaabbaaaabaabbbabababbabbaabbbaabbaaababbaababaaabbabbbaaaabbbababaaabaababbaabbaabaabbbaabaabbabbbbbbaaaaaabbbbaaabaabbbbababbabaaabaababababaaaabbabbaaabbaabbababbbbbabbbaabbabaabaababbbabbaabbaaaababbbaababaaaabaabaaaabbbbaabaabbbbbababbaabaabaaabaaabbaababababababaabbaabbbaaababbaaabbbaaabbabbabbbaabbbbaaaababbbbabbbaaaaabbbaababbaabbbaabbabbbaabaaaababbabbbbaabaabbbaaababbbbababbabbbbbaabaaaabaaaaabaabababbbbaaabbbbbaaababbaaabbbbbbbbbbbaaaabaababababbbbbbbaaaaababaabbbaaabbababaaabbbaaaabbabbabbbbbaaabaaaaabaaabaaababaaabaaabbbaabbbaababbaaabbbbababaabbbbbbbababbaaaaaabbbbbabbabbaaaaaaabababbbbababbaabbbbbbbbababbaaaabaaaabaaaaabaabbbbabaababbababaabbababaaaabbbbabbbbabbaabbaaabbbbbaaababbbbbbababaaaabababbbabbbbabbaabbbbbbbaabbaaabbabbbbabbbbbbbbaaaabbabaaaaabbaabbaaabbabbbbabbbabaabaabababbaabaabababaabababbbaaabaaaabbabaaababbbaaabaaabbbbbbaabbbbaabbbbabaaabaabaabaabbaaabaababbbaabbbbbabaabbabbbaabbbbbbaabbbbbaabbaaaabababaaaaaabaabbaaaabaaababbbabbababbabaabaabaaabbaaababbaababaaabaaabbbbaabaabbaaaababbabbaaaabbbaaaababbaabaabaababbbaaabbbbbbabbbaabaaabbbbbababaabbaabaababbbaabbbbaaaabbbbaababbaabbabbbbabaabaabaabbabaabaababbbbbbabbbabbaaabbabaabbbaaabaabbbbbbbabaaababbabbbbbbbabbbabaaaabaabbabbbaabaabbaabbbaaaaabbbababababaaaabbbabaaaaaaaababaaabababbbbaabbaabaababbbabababababaababbbbbbbaababbbbababbbaabbaabaaaabbabbbaaababaaaababbaaababbbabbbababbbbaababbbaabbbaababbaabbabbaaabbabbbbbababbaabaaaaababaaaabbaaabaabbabbaaabbbbbbbbaabbbabbabaabbaaaabaaabbbaaabbaabbabbababbaabaaaaabaaababbaabbbbababbabbababbbaaaabbbaaabbababbabbababbabbaaaaabbabbaaabbbbbababbaaaaaaaaaaabbaaaaababaababbbabbababababaababbbababbbaabbaaaaaabbbbabababaaabbaabbaaabbabbaaaaabbabaaaaaaabababbababbbbbaababbaababbaabaababaabaabbaababaaabbababaaababbaaaababaabbaaabbbbabbaabaabbbaaaaaabbbabaababbabbabaabbbbabababbbbaaabaabababbbababbbbababbabaabbabbabbaabbbaaaaabbbbaaaabaabaaabababbbbaaaaababbbababaaaababbbbbabaaaabbbbabbababbaababbbabaaaabbbaabbababbaabbbabaabbabbbabaabbbbbaababbbbabbbbababbbabbbabaaaaaabbbaabababbbaabbabbaaaaaaabbbbbabbbbbaaabaaaababaaaabbaaababbabbababababaabbbababbbaaaaaaabaaababbbabbaaaaababbbabaabaababbbabaaabbabbbbaabbbbbbabbaababbbabaabaaaaabaabbaaaaabbbaaaabbaaababbabaababaabbabbbbbbbabbaabbbaabbabbbabbabbaaaabbbaaabaaaabaabababbbbbbbaaaaaabaabbaababbbababbaabababbaabaaababbababbbbbaabbbbbbbaaababbbababbbaaaaababbbababaaaaabbabababbabbbaabbbaaabaabbbaabbabbabaabaabbbabaaaaaabbabbabbbaaababbababbbbbabaababbababbbbabbababaaaaaababaabbbbbbaababaaababbaaaabbaaaabbabaabbbbaaababaaaaaaabaaabaaaaabaabbaaaaababaaabbaabbabbbaaabbabbabaaaaaabaababaaaaaabababbbbaaaabababbabbbbbbbbaabbbbbbaaaabaaaaababbabababaaaabbbabbaabbbabbbbbbbbbbabbaabbbbaaaabaabbabbaabbbbabbaaaabbabbaabbabaabbaabbbbbbabbbbbbaabbaaababbbaaabbabaaaaababbbbbababababbbbbaabaababababbaaabaaabaabbbababaaaaaabbabbaaabbbbbbbaababaabaabbaaabaaaaaaaaaaabbbbaabbaabbaabaabaaaababbbababbabababbbbaabaaabbaababbabaabbbaaaaaaaabbaabbabbbabaabaaaabbbbabbbbbbbbabbbaaabaaababbaaaaabbaaaaaaababbaabbbbaaabbbbbaabbbbababbababaaababaaaabbbababbbabbbaabbabbaabbbaaabaabbaabababbbbbbabaaaababaaabbabababaaabaabaaaabaaaababbbbaabbaaaabaaaaaaabbaaaabbabbbaababaabbbaabaabbaabbbabbbaaaaaabaaaaabbaabaabbaabbabbbbbbbbbabaaabbbbaababaabababbaaaabababbbabbabbabbbbbabaaababbabaaaaaabaababababbababbbabbbbbbaabbbaabbbbbbbabababbbabbaaaabbababaabaaaabbababaabaaaaaaaaaabbabaababbbaaabbbbaabbabaabababaaaabaaaabbabaabababbbababbaaabbbbbabbbbbbababaabbbaabaabaaabaabababaaaabbabaabbaabaabbabbaaaabbabbbbbbbbbaabaabaabbabbbbaabbababbabababaabaabbababbbbabbaaaabbbbaabbabbabbbbaaabbbabbaababbbbbbbabbbbbaabaaabbaabbabbaaaaabababababaabbabbaababaaabbbabaaaabaabbabbbbababaaababbabbbabababaababaaabaabbbaaababaaabaabbaabbbbbbbbabbbbababababbabbabaabaaaaabbaabbbababbabaaaababbabaaaabbaaaabbabababaaaaabbbbbabbababbaabbabbbaabbbaababbbbbaababbaaabbbbabbbaababaababbaaaabbaaaabbabaabababbabbbaabbbabbbaabbaabbbbaababababaabaaaababbbaaabaabbaabbbbbbbbaabaabababababababbbbaabbaaaaabbbabaabbaabbbbbaaabbbbaaabaaaabaabbaabababbabaabaaaaaabababababbbbbbababbbabaabbaabaababbbaabaaaabaabbabbbaaababaababbaaabaaaabbabababbbbbbbababbbbbbbabababaabbaaaababbabbbbaabaabaabaaabbabbbbabaabbbabaabbabababbbbbabbbbbbababaaaaabbbbbabbaaabbabaaaabbbbabaabbaabbaaabbaaabbbbbabbbbaaabbaaabbaabbbbbaaabbabaaaaaabbaaabbbbaaaaaabbabbbbbaabaaaaabaaaaaaaababbbaabaaaaaaabaabaabbaaabbaabbabbabaaabaabbabaaabbabbbbbbbaaaababbbbaaabababbaabaaaabbbaabbababaabbbbbaaababababbabbabaabaababaabaababbbaaaaabaabaaabbabbaababbaaabababaaaaabbbaaababbababbababbabbbababbbabbbaaaabaabbbaaaaabbabbbbbabbaaabbbbbbbaabbbababbabaaaaabaabaabaaaaabbaaabaababbabbbbbabbabbababaaabbabaaaaaabaaaaabaaabbaaabaaaaabbbbabaababaaabaababbababbbbbbabaaabaabaaabaababbbaabababbbabaabbaaabababaabbababaabbababbaababaaaababbbaaabaaaababbaabaabaabbbaabbaabaaabaabaaababababbaaaaaabbbaabbbbababbabaaabbabbabbbbbbbabbbababababbabaabbaaaabbbaaabaaaababaaabaaababaababbabaaaaaabaabaabbabbaaaaabaaabaabaabbbbaaabbbbbbbabaaabbaabaabbabaaaaabbbbbababbbabbababababbbaababbbaaabbabaabbabaabbbbbabbaabaabbabaaabbbaabbbaabaabbabaaaaabaabbaababababaabbbabbbabbbbaaaababbaaabaaaabbabaaabbbaabaaabababbbabbaabbabbaababbaabbbabaabbbbabbabbbbbbbbbbabbbbaaabababbababbbbaabbaaaabaaaabaabaaabaaaaabbbbbaabbbbabaabaaaabababbababbbbaababaaaababbabababbabbbaabaaabbabaababbbaaaabbababbabbaaabbaabababaabaaababaaabaabababbbabbbaaabbbbaaaaabaaabaaabbbababbbbbaababbbbabbabbaabaaaababbabbbaaababbabaaabbbaaaababababaaabbbbaaabababaaaabbaababbbbabbaaaabaabaabbbabbaaabbaabbabbbbaaababbabbaababaaabaabbabaaababaaaaabbababaabbaabbbabababbabbababaababbabbababbbabbbbabbabbabbabaaaababbaabaabbbbabaaaaababaababaabbababaababaababababbbbbbbbbbaaaaabaaaaaabbbbbabbbbabaaababababbbaabbabbbbaabababbaabaaaaaaabaaabbaaaaabaabbaaaabaabaaaabbabbaabaabaaaaabaaaaabbaaaabbaaababaaababaababaaabaabaabbbabbbaababaaabaabbabaabaaababababaabbbababbbbabbbbbabbaabbaaabaabababaaabbabbaaaaabbababbbabbbbaabaaabaaaabbbbbababbabbbbbabbbbaabbbbbaaabbabaabaababaaabbaabaabbbbbbabbbaaaababaaaaababaabbaabbabbbbaaaaaaababaaaaaaaaaaaababaaaabbbabbaabaaaabaaaaabbabbbbababaabbaaabaaabbaabbabababbbaabbabbbaabaabbaaaaababbbbabbaabbabaabaaaaabaabababaaaaabaaaabbbbbbabbaaaabbabbabaaabbababbbaaaabbbabbabaabaabbbbabaaabaaaaaaabbabaabaabbbaaabbaabbaababaaaabbbbbbbbaabbaabbbbabbbbbbabbaaaaabbbabbbbabbabaaabaaabababaabbbbaaabbaaaabbbbaaaaabaabbabbbbaaaaabbbbabbbabaaaaaaabbbbababababbbbbbababababaaababbababbabababbabbabbaabaababbabbaabababbabaaaaabbbbbabbbbaaaabaaaaaaaaaaaaabbbaabbaaaaabbaababaabbbabbbaaabbabaababbaabbbabbbababbbbaaababbaababbabaaaaaabaaaaaabaaabaaababaabbbbababbbbbbaaaabbbbaababbbabababbbabbbbaabaababbbaabbbaabaabbbbbaabbbabaabbaaabaaaabababbabaaaabbaaaabbbababbbbbbaabbaaaaabaabbbabaabaaababbbbbbbbabbbbbbbababbbaaababbbabbbaabaaaaaaaabbabaaaabbbbbbabbbaaaaabbababaaabaabaaabbaaababaabaabaabbbaabbbabaabaaabbaababbabaaababbbbaaaaaaaabaababaabaababbaabbabaabbabbaaaaabaabaaaaabbbbbaaaabbaabaabbaaaaaabababaaaaabaababbbbbabbbaaababbbaaababbbaaaaababbaaaaaaaaaaababbbabbabbbababbbbbbbbbaaaaaaaaaabbabbbabbbbabbababaabaabbbbbbaaabbbbababbbbaabaaaababababbaaaababbabbbabababaaababbaaabbaaabbaaaaaaabbaabbbbbabbbbabababbabaaabababbaabaaabbbabaaabaabbbaaaabaaaaabbbabababbbaabaaabaaabbbaaaabaaababbbbaabbabbabbaaabaaabbaaabaabbbaabbbbabaabaaaabbababbbabbababbaabbaaabaaabbbaabaabbbbaaaaabbbabaaababbaababbabbaaabbabbaabbabbaabbbaabbabbbbbbabbaababaabbaabbaaaabbabaabaabaabaaaaaaababaaaaabaaaabbabaaaaaaabbabbaaaabaaabababbababaabaabbbbaabbbabaaabbbbaaaabaaaaaaabbaabbabaabababbbabbbbbbaaaabaaabbababbabbbaababaaabaabbaabaaababaababaababbaaabaaabaabbbbabaabbababaabbbbbbbaabbabababababaababbbbaababaababbbbbbbbbbaababaababbabbbbaabbaaabbababbabaababbabaabbabaaaababbabbbaaabbbabaabbaabbaababaaabababaaabbbbabbbabbabbbaabbbabaabaabbabaabbaaabbbabaabababaabbbaaaaaaabaabbbbbbbaaaaaabbaababaaaaaaabbbaababababbaaababbabbbbbaaaaababaaaabaaabbabaaababbbbababbbababbaababaaaabbbbbbaaaababbbabbbbabaaabbbababbabbbabaaabbabbbbbbaabbaabaaaaabbbbbbabbaabbbbbaabababbbbbbabbabaabbbaababbabbabaabbbabaaaaaabbabbbaaaaabaaaabaabaabbbbbbbbabbabbbbbbaabaabaaaababbbabbbabbabaabbabaaaaaabaabaaaabaabbaabaaabababbabaabbabbbbbbbbababbbbababbbbaaaabaaabaababbabbaabbbababbbaabbbaabbabbaabaaaaaaaabaabbabbbbbaababbbbbaabaabbaaaabbbaaaabbbabaabbbbbabbaaaabbbabbbaaabbbaabbababbbbbbbabbaabaaabbabbaaababbaabbbbaaabbaaabbbbbbabaaababbabbbababbabbabbbbaababbababbaaaabaaaababbbaabaabbbabbbbbabbbbbbabbaabbbbaabbabbbbaaaaaababbabbaaaaaabbaabbabbbbabbbbbaabbbbbbabaabaababaababbbbabaaaaaabbabaabaabbaaabaababaaaabababaaabbbbabababbbabbbabbbaabaaaaaabbbbbbabbbaabbbaabbbbbaabbaaaaabbbaaabaaaaabbaabbbaabbbbaababbabababbbbaabaabaaabbaaabbababbbbbbaaababbababbaabaaaaababbbabaaaaababbbbbbbabbaaabbbbbabbaababbaabbabbbabbaaabaaabbabbabbabbababababbbaaaaabaabababbbaabbababbabbbabbbabbabbbaababaaabaaababbaabbabbaaabaabaaaabbbabaabaaaabbbbbaababbbabababaabbbbaaaaaabaabaabaabababbbaaabbbaaaabbbbbbaaaababaabaabaaabbbaabababaabaaabbbbaaaaaaabaababaaababbbbabaaabbabbabaabbabaaaaaabaaaabbbbababbbbbbaaaaaababbaabbaaaababbaababbbabbabaababababaabaaaaabbaabaabababbababbaababbbaabbbbbaabbbababaaaababbbaabbabbaababaaaababaabababbaaaaaabaababbbbbaaabbbaaaabaabbaaaabaaabaabbaaaabbbbbabbbabbaababbbabaababbbabbababaaaaabbabbbbababbabbaabbbaabbbaababbabaaabaabbaabbbaaaabaababbabaaaaaaaababbbaaaababbabbbababaabbbaaaaabbabbbbababaabbbbabababbaaaaaaaabaababbaaabbabbaaabaaabbbabbabbbabbbabababaabbaaaaaabbabbaaaaaabbbbbaaababbbbbababbbbbabaabbababaaabaababbbbaaabaabbaaabbaabaabbbbabbaabbababaaabaaabbabaaabbbbbabbaababbbbabbaaaababbaaabbabbabbabbbbaaaabaabbbaaaaabaaabbaabbaaabbabbaaaaaaaaabbabbaabaaabbaaaaaaababbbbbababaaaaaaabaabbaaabbabbbaabaaababaabbbbbabbbaaaaaabbbbbaabbaabbaaabbbbbbbbaaabbbbbabaabbabbabbbbabbbaabbabbaabbbbbbaabbabbbabbbaabaaabbbabbabbaababbaabaababaabbabbbaaaababaababababbaabbbaabbbabaaabababbbabbabababbbaaabbaabbbabbbbbabbaabaaaabbaaabaaabbaaabbaaababbaabbaabbaabbababbbbabbbbababbabbbbabbaabbabbabababaabbaaabbbabababaaabaaaabbababababbbbbaaabbbbbaabbabbaabbbababbbbababaabbbaabbbaabbbbbbaaaabbbabbbaaaabbbabbaaabbaabbbbaabababaabbbababbbbbbbababbaabbbbbabbaababbbaaabbbaaaababbbababaabaabbbbbbbbaaaabbbaabbbaaaababaabaabbaaabbabbbbabbbaabbbaababbabaabbaaabababbbbaabaaabaabbbbaaaaababaabbaababbabaaabbabbbaabbbbbabbabbaaaabaabbabababbbabbabbbbabbbbbbaabaabbbabbaaaaaaaabbababbbabaabaabbababbaaaababbaababbbaabaababbabbabbaababaaabbabbbbbaabbaababaabbababaaabaaabaabbaaaabbaaabbbaabaaaaaababaaaaabababaabbbbaabaaaababababbabbaabbbbabbbbbbbaabaaabbbabbaaaabbbaabababbabbbbbabbababaaabbbaabaabaabbbbaabbbabbbbbbbaabaaabbbaaaabaaaabaabbabaabbbbabbbbabbabbbbbabbababaaababaaaabbbbbaabbaabababbabbbabbabbbbababbaabbbbbababbbbbbabbbaaaaabbaaabaaaabbaabbbabbaaabbabaaaaaaabbaaaaabbababbbabbaabbbbabbabbbabababbbaaaaaabbabbaaababbbbbabaaaabaaabbabaabaaabaaabbbabababaaabbaaaaabaababbabaababbbbbbaaabaaabbabbbabaabbaabaaaaaabbbbbbabbbbbbabbbbbabbaaaababbaaaababbaabaabaabababbaabababbababbabbaaabababaababaaaabababbaaaaabbbababbbbaabababbbbabbbbabaabbbbbaabaabbaabbbababaababbabbabaaabababbbbabbaaaabbabaabbbbababbbbabbabbabbabbabbabaaaaaabbbbaabbbbbabaaababaaaaababbabbababbbbabababababbabbabaabaaabbabbaaabbaababaabbaaaabbaaaabbbababaabaaabaabaabbaaabaabababbbbaababbaabbbaaaaaaabaabbbabbbabbabbabbabbababbaabbbbabbaababbbbaababbabbbbbabbaababaabbaaaaaabbbbbbabbabbabbbbaaabbbabaabbbabaabbabbaaaaabbbbbaaaaabbaabaabbaababbbbabbababaaaaababbabbbbaabbbbababaaaaaababbaaaaaaabaabbbabbabaaaabaababbababbabbabaabbabaaaabaaaababaabaaaaaaabbbaabaababababbaabbaabaaabbbaababbaabaaabaaaaaabbabbbabbbaaabababbbbbaaabbabababbaaaabbababbbbaabaaabbaabbaaaabbabababbbababaababbabaabbbbbbbbbbbbaaabaaaababaabbabaabbbabbbbbaabbbabaaabbababababaabaabbbaaababbbaaababaaaababbabbbaaabbbaabaaabaabababaabbabbbbbaaababbabaaaaaabbaababbbabbabbbabbaaababbaaababbbbabababbbabbaabbabbbbaaaaaaaabbabbbbaabbbabababbabbaaabaabbaaaabbbbabbabaabbbaabbbbabbbaaabaababbbbaabbabaaaaababbbbbbbbabbabbabaababbbaababbbbababaababbbaaabbaaabbabaaaaaaababbabbabbbbaabbabbaaaaababaaabbabbabbaabbbbbbbbabaaaabbbbbaabbbabaaaabbaabbabbaababbabaababbababbbbababaababbababbbabbaaaabbbabbbaabaaabaabbbbabbbbaaaaabbbbbaabbaabbbaabbbbabaaaaaaababbbbaabbaabbabbbabaaabaabaaabbbabbbbbbabbbbbbbbbaabaaabbbbbbbaaabbaabbbbaaabaaabbbabaabbbababbbaaabaaabbabaabbbbbababbaabbbabbababbbbaaaaaaaabaabaabaaabaaaababaaabbbaaaaabbabababaaaabaabbaaabbabbbbbabbabaaaabaabbbbbbbbbaabbbaaababaaaabaaaaabaaaaaabbaaaabaaabbbabaaababbbabbaabbaabbbaabaaaabaaaaaaaaababaababaabbaababaabaabbbbababababbbababaabbabaabaaaaaabbbbbaabbbaaababababaaaaababaaabbbbbbaabbbbbbaabbbaabbbabaabbbabbaaaabaababaabaabbbbbbabbaaabbbbbbbbabbbababbbabbaaabaaaaaaaaaaabaabbaaabbabaaaababbbaaaabbaababababbbabbbbbabaaabbaaaabbbbabbbabaababbaabbababaaaabbababaabaabaaaaabbaaababaababbbaabaababaabbbaaaaabaaabbbbbbbbbaaabaaaaabbbababbaaaaabbbababaabbbababbbabaabaaabaabbbaabbbbababaaabaaaaaabbaaaaaaaaaaaabbbabbabbbabababbbababababbaaaaabaabbaaaabbbabbbbaabbaaabaabaabababaaababbabbaaaaaabbabaaababababaabbbbaabbbbbabbabbababaaaaabbbbbbabaaaabbababbabbabaaabbbbbbbaabaabbbbabaaabbaababaaabaabbbabbbbbaabaababbabaabaabbababbbabbbaabababaaababbababaabbaabbababbabbbaabbbbabbabbaabbaabbbbbbababbaabaababbaaaabbbaabaaabaaaaaaabbabaaabaabbbaaaaaabbbaaaaaabbbaaababbaabaababaaaaaaaabbbbbaabbaaababbbbabbababbbbababbaaaaaabbbaaaaabaabbaabbabbabaaaaaabbabaabbababbbaaabaababaaaaabbabaaaabbbbbaabbabaabaabaaaabbaabbbbbabbaaaabaaaaaaabbaabbbaabaababbabbbaabbbbbbababbbabbabbbbbbbbbbabbbaabbaaaabbbbabaababababaabbbbbabbbaaabbabbbababbbaaaaaabababbaaabaaabaaaaaaaaaababbbbbbbaaaabbbabbbbaabaabaaababbbabbbbababababbbbaabaabbbabbabaaabaaabbbbababbbbbbabbaabaaabaabaaaaabbbbabbbbaaabbaaabbabababbbabaababbbabbbaaaabaaabbababbbbbabbbabaaaabababbbabaabbbaabaaabaabaaabaabbabababaabaaaabaabaabbaaaabaaaabaabaababaabbaaaabbbabaaaaabaabaabbbbbbbabaabaabbabaaababaababaabbbabaababbaababbaabbaaabbbbaabbaabaabaabbbabbaabbbaaaababababaaaaabaabbbaabbbababaaaaababbbaaababaaababbbaaabaababbabaaabaaababbababaaaabbababbbbaabbbababbbbbaabbbbbbaababaabaabbabaababbbbabbbabbabaaaababbbababbaabbaaaaabaaaabbaabbbababbbbaaabbabbabbbbabbabaaaaaaabbbabbbbabbbbabbaabbababbaaaaabbbbabbbbbbbaabbbaabbbabbaabbabbbaaaaaabbabaaababbaabbbbbbaababbbaaabbabbbbbbbbabaaaaabbabaaaabbabbababaabbaabbaaabbabbbbbababbaaabbbabbbaabaabbbaaaaaaabbbaaababbbabaaababaababababbbabaaaaababbbabbaaaababbbabbaaaabbaabbbbbabaaabbaabaaaabbbabbbabbbabababbbbbaabaaabaaabbaabbbbbbaababbbbabaababbbabbbbaabbabbbbaaababaabbaaababaabbbaaabbbbbabaabbabbbbabbaaaabbbaabbaaabbababbaabbabaaababbaabaaaabababbabbbaaabaababbbaabbbaaaaaabbabbbabbbbbabaabbaaabbbabbbaabaabaababaabbbbaabbbbbbababbbbabbaababaaaabbababbabbaaabbaabbabbbabbbbbbbbabbaaaabbbbabbbbabababbaabaaaaabbabbbbbbaaababbabababbbbaabaaaabaabbabbbaababbabaaabbaaabbaabbaaaababbabbaabbaababaaaabababbabbaaaaaaabbabbbbaabaaabbbbbabbbbaababbababbabbbbbbbbaabbbbabaabaaabaaaaabaaabbaaabbbabbabbaaaababbabaababbbaaaaaaabaabbbbbaaaabbbababbababaabaababbabaabaabbbaaababababbbaaabbaabbbabaaabbbbbaabbbbbabaabbabbbabbaaaaaabbabbbabbaaabbbbaaabaaabbaabaaaababaaabababaabbbaaaabaabbaababaaaaabaabaababbaaabababaaaabaaaaabbbabbbaababbaababbbabbaaababbbbabaaabbbaabaababbaaabbaabbaaaaaababbbaabaaaaababaabababbbbbbababaaabababbbbbbababbaabbbbabbaabbbabaabaaaaaababbbaababbaabbbbbaabbaaabaaabaabbabbbbabaaaabbbbaaabaabaaaaabbbbababbaaabbabaabababaababaabbbbabbbabbbbbbaaababbabaabaaababbbbabaaabbbbbaaabaabbbbaababbbabbbaaabbbabbbbbbbabbbaaaabaabaabbbaabbbaabbaaabbbaabbbbaaabbabaabbbbbbbbbbabbaabaabbabaabaababaabaaabbbbbbaaababbabbaabaaabaaaabbbbbaaaabaabbababaaabbbabaaaaababaaabbbbbaaabbbbaaabaabbbbaaabbbababbbbbabbababaaaabbbaaaaababaabbbaaaababbaaaaabbaaabbabbaabaaabaabaaabbbbaababaabbabbaaabbbabbaaaaaababababababbaabbbbbabbbbababaabababbbabaabbaabbabaaaabbaaabbaaaaaaaaabbbaababbaababbbbaabbaabbbbbbabbaaaabaabbabaaaaababbabaaabaaaaabbaabaabbbbaabbaabbaababbbababaaabbaabaaaaaaaabaaaabbbaabbbbbbabbbabbbabbabababbababbbbbabbbaabaabbbababbabaaabbaabababbaabaaabbababababbabbababaabbbbabbaabaabaaabbabbbaaabaaaabaabaaabbbaaababbabbbaaaaabbaabbbbabaaabbbbabaaabbbbbbbaabbabbabaaabaabbbbbaaaaababaaaaabbbbbabbbaababbaaaaaabbabaabaabbabaaaaababaabababbbababbaabbaaabbaabbbaabaaaabbbabbababababbbbbabbbbabbabaabaaabbaabbabababbbaaaaabbaaabbabaaaaaaaabbbabbababbbbbbbbaababbbaaababbbbababbbbabbabaabbaaaabbbaaabbbbbababaaaababbbbababababbbabbbbbbbabaabbbbabaababbababbabaaaababbaaaabaabbaaabaaababaabbaaabbaaaaabaaaaabaaaababaababaabbbaaabbaaaabbbbbaabaaabaabaabbaababbaabaabbababbbaababababbbbbbbbaabbbababbbbbbaabbbaabaaabbaabbaaaababbbbababbbabbbaababbaaabababaabbababaabbbbbbbaabbabbbbaaabbbaaaaaabaaabbbabaaaabbbaaaabbbababaaabbabaabbbbaaaaaabbbbababaabbbaaabbbbbaabbaabbbababbabbbaabbbbaaaababbbbabbbababbabbbaabaaaaabaababbbabaaabbbbababaababbbaabbbaabbababbbaabababbabaababbbaababbbbaabaaabbbaaaaabbbbabbaabbabaaabbbaaabbbbbaaabbbbaabaabbaaaabbbbaaaabbaabbababbaaabbabbbbaaaabbbaaabaabaaabbbaabababbbabbbabbbababaaaababbbabbabbabbbaabaaababbabbabbbaaaaaabababaabbabaaaaaabaaaaabaaaaaabbbaaabbbbbbbbbbbbbbbbaaaaaababbbbbabbabaabbababaabaabaabbbbaaaaabbabbbabaaaaabbbbabbbaabbabbaaabbbbbababbbaaaababbbbaaaabbaabaabbbaabaabbbbabbbbbaaaaababaaaabbabababababbabaababaaabbbaabbbbbbbbbbabbaaabbbababbababbbbbbaaababababbbaababbaabaabaababbbaabaaabaabbaaababbbaabbbbbbababbbbbaababbbabaababbababbbbabbbbaaabbababbbaabbbbbaabbabbbaabaabaaaabbaaabaaaaabbaabaaaabbaabbaaabbaabbababbabababbbbbabbabaabbabaaaaaabaabbbbbbbbbaabbaaaaabbbaaabbbaabaabbbababababbaaaaaabaabaabababbaaababbabbaaaababbabbbabbbbaaaabbaabbbabbababbbbaabaaaaabbbbaababbbabbaabbabbbbbbabababbbaabaabbaabbbbbaaaabaaabbaababbaabbabababbaaababaaababbbbaabbabbbababbbababbbabbbabbaaaaaaaabbabbbbbaaabaaabbbbbaabbbaabbaabaabbbbbbbbaaababaaaaabaabbbabababbabababbababaabbbbaababaaabbbbbbabababbbabbaaaaaabbbaabaabaababbbbbaaabbbbbabababbabaabbbbbababbbbabaaabbabaababbaabaaabbaaabbaaaaaabaaabbbbaabaababbbbabbbbbababbabbbbaaabaabbbaababaabbaaabbabaaaaaabaabbabbabaaabbbbbbabaabaaaaabaababbbabaabbaaabaabbbbbaabbabbaabbabbabbbbabaaaaaabaaaaababbbaaaabaaaaabbabbbabbabbaaabbbababbbbbaababaabbbbaabbbbaaaabbababbaababbbbbabbbbbabaaaabaaababaaabbbbaabaaaaabbabababbbbbaaabbabbbaaabaaaabbabaaaaabababaaabaabaabbbbaabbbabababbbaababbaababbaaabbbbabaaababaabbabbbaaabbbaaabbbbbababbbabbbabbaabaabbaabbbaabaaaaaabbaabaabbababbabaababbaaaababaababbbbabbbbaabbababaaabaaabbbbbaababbaaabababbbaaabbbbabbaabbbabbbbbabbbabbababbbbaababbbabaaabaaaaaaaaaaabbbbabaabaabbbbbbababaaaaabaaaaaabbabaababbbbabbabbaababbaabaabbbaaaabbbbabaaaababbbaabaabbabbaaaababbaaabaabaabbaaabbbbabaabababbabaababaababaaaaaaaabbabaaabbbaabbbbaababbaababbabaabaaaababaaabababbababaabbaaabbabaaabaabbbbbabaaabababbbaaababbbabbbaababaabbbaabbaabbbaabaababaabbbbabaabbbbabbbbbabbbaababbabaabbaaabbaababbbbaaababababaabbbaaabbaaaaaaababbbbbbbbbaaaaabaabbbbababbbabaabaababbababaabbaabbaabaaaaaaaaaabbbbbbbbabbabbaabbbaabbaaaaabaabababbabbbbaaabbbbbbabaaabbbaabbbbabababababaabbaababbbbbbabbaaaaaaaaababbbaabbbaaaababbaaabbabbaaaabbaaabaaaababbbbababbaaabababbbbabbaaababaaaaaabbaabbbbabbabbbbbaaaaabbabbbabbabaaababaabababaabbbbbabbababbaaaaababbaaaabaaaaaaabbbaabababbaaabbaaaabbbbbaabbbaaaabbababaaabaabbbbaaaaabbbaabbaaababbbabbabaaabaabbaabbabbbbaabbaaaabbbbabbbabbaabaaaabaaaaabbabababbbbbabbbbbabbbababbaabaabbbaabaabbbabbbababababbbbabbababaababbbabbabbbababababaaaabaababbabbbbababbbababaaaababbbabaabbbaaaaabaaaaaaaaaaabbaaabbabbaabaababaabbaaaaaaaabbabbabbbbaabbbaabbbaaaaabaaabbaaababaaabaaaaaaabaababaaaaaaaabbbbbbbbabbabbabbbbaabbaaaaaaabbabbaabaaaabbbbbbaababbbabbbabaaaaaaabaaabbbbbabbaabaababbaaaababaababbababaabbabbbbaabbbbbbbaaababbbaabbbaaabbabaaabaaaaabaabbbbababaababaaababaaaaabaababbbaaaababbaaabaabbbbbbaababaaaabbabbababbbaaababbbaabbbaabbabbababaababbabbbabbaaabaaababaaabbbbababbbabaababbbbbabaaabaaababaabbbababbaababababbabbbbabbaaabbbaaaaaabaababbabaaababbbaabbbbbabbbbbabababbabaaabbbaabbaaabbaabaababbbaabbbaaaabababbababbaababbabababbaababbbaabaabbabbababbbbababbabbbaabbbabaaaabababbabbaabaaabbbbabbabaabbaaabababbaaaaabaaaabaaaabaabbbbbabbbaababbabaaabababaabbbabbbbaabbbaaababaababbaabbaaaaaabbabbbbababbaaaabbbbbbaaaaabbbbaabbaaaaabababbbababbbaabaaababaabbbaaabbabaaaabbbaaabbaabbbbbaabaaabbabaababbaabbabaababbbabbaaaaaabaabbbbaaaabbaababaabbbabbbbbbbaabbbaaabbbababaaaabbaaaabaabbbabaabbaaabbbabaabaaabbbababaabbbabaabbaabbaabbbabaaaabbbbbbaabababaabababbbbaabbbabababbbbaabbbabbaabaaababbaabaabaabbbbbaabbbbbbaaababaabaaaabbbaaaaaabbaabaaaabbbaaaababbbaaaababbbabbbbbbbbaaabbabababbaababbaaabaaaabaabaaaabbbbabaababbaaaabbababbbbbbbaaaaaaabbbbaabaaabbaababbaabbababbbbaabababaabbbababaaaaaaaabbbbbabbaabaaaaabababbaaabaababbbabaabbabaaaaabbbbaaabbbababaaabaaaabaaaaabbbbbbbabbaaabbbaababbabbaaaaababbabaaabbbbaabbaabbbabaabbaababaabaababbabbbabbababbaabbaabbbbbababbbbababbbaaaabbabaaabbbbaabbabaabaabbbabaaaabbabbaababbabbbbbabaaaababababbbbaaababbbbabababbabbbbaaaababaabaabbababaaabaabaaabbabbbbbbbbbbbbabaabbbaabbbbbbabaababbaabbaabbbbbaaabbbbaababbbbbbbbabbbabbabbaabbbbbbabaaaabbbbaaaabbabbaababbababbbbaababbbbbaaaaabaaababababababbaabaababbbaaabaabaaabbbbabaababababaaabaabbaabbbbaaaababbaaaababbabbbabbabbbbaababbabbbaabababbaabbabbbaaaabbabbbaabbaabbbaaaaaaaaaaabbababbbbabaaabbaaaaabaabbbbaabbabbbbababaabbbbbabaabbbababaaaababaaabbbbbbabbabaaabaabbbbbbabaaaaaaaaaababaaabababbbbbaaabaaaaaababaabbbbbabababbbbabbbbabbbbbaaabbbbbababbbaabaabaaababbbabaabaabaaabaaaabababababababbbbbbaaabbbbbabaabaababbbababbbbbbbbbabbabaaabbbababbababbbaaabbaabbabbabbbbbbabbbbbaaabaabaaabababbaababaabaababaaaaababbbbabbaaabbbbbabbbbbbbaababaabbbbabbabababbabaabbbaaabaaababbbababbaababbbabaabaaababababbaaababbbaabbbbbaaaabbbaaabbabbabaaabbabaabbabaabbabaaaaabbbababbaaabaaaaabbbabbabaabbaabbbbbbbbbaabbaababababbaabababbbabababbabaabaaabbbaabbbaaaaaababbababababaaababbbbaaabbbaabbababaababaababbbaabbbbabbbbababababbabbbbababbabbbbaaabbaaabaabaababbbbbabbaaaaabababbaababbbababaaaabbbababaaaaabbbabbbabbababbbbbbbbabbabaabbaabaababaaabbbabbaaabaaaabbbbbabbbabbabbabaaaabbababaaabbbbbabbbaaaabbbbabbbbaabbababaabbbbbbbbbbaaabbbaabbabbaabaaaaabbabbbaabbbaaababbbaabbbbabbabaababbbaabaaabaaabababbbaabbbabaabbabbbabababbababbaabaaababaabaababbabaabbbabbaabaaaabbbabaaabaabbbabababbbaaabbbbababaababbabaabaababbaaaaaaaaababaaaaabbbbbaababbbbbababbababaabaabbbbabbbaaababaaabbababbbbbbabbaaabbbbbbbbababaabbbaaabbaaabbbabaabbbabaabaaabbabbababbbbbbbbabbbabbbbbbbbbabbaaaaaaabbaabbaababaabbababbabbababbbaabaaaaabaabbaabaabaabaaaaabbaababaabbaaaaaabaabaabaabbbabbababbbabaaaaabbbaababbaabaaabaabaabaabbabaabbbbabababaaabbbabbbbbbabbbbbababbabaabbaaaaaaabababaabababababbbaaababbaabaabaabbaabbabbaaabbaabaababbabbaaaabaababbababababababbbaaabaabaaaabbaaabaaaaaabbabaaaababababbbabbbaabaabbabaaaabaaaaabbabbbbaabaaaaaabbbbabbbbaaaaabaababbbbabaaabaaaabababaaabbaabbbababaabbaaababaaabaabaabaaabababaaaabaabbabbabbaaaaababbbabaaabbaaaababababbaababbababbbbaabbabbbbabbaaaaabbababbbbbaaaabbbbaaabaaabaababaaaabbaaaaabbabbbbbabbaaabaababaabababbabaaabbbbabbaaaababbabbbabbabaabbbabaabbbababbababbaababababbbbbabababbbbbbbaabbaaabaaabbbbbaabbbbbabbabbbbaaabbbbbaaaaabbbababbabbbabbaaaabaababbabaabaabaaaabbbaaaaaabbbbaaabbabaaabbbbabaaaabbaaabababaaaabbbbabbabbbaaaaaabbaaababbbaabbbbbabaaaabbabbaaaabbbbaaaabababbabbabbbabbaaaabbbababbaababababaaabbbabbbbaabbbaaabababaaabbbababaaaaaabaaabaaabaabbbaaaababbabaabbbabbbbabbbbbbbababbabbbbbbbbbaabaaaaaabbbabaaababaaaaaaaabbabbbabaababbaaabbbbbaabaaaaaabbbabbababbbbbabaabaabaaaaabbbbbbabbabaaabbaaaaabbbababbababbaaaaaaababbaababbabaaaaababbaababbaaabaabaabaaaaabbbaabbbababababbabbaabbaaaaabaaabbbbababbabbbbabbabaabbaabbabaabbbaabaaabbbaaababbbbaabbbababbaaaabaaaaaabaabababbbabaabbabaabbbbaaabbbaababbbbababaabbaabbbbabaabbababbaaaabbaaababbbaaaaaaababbaabbaaabbababbaabaaabbaaabbabababbaaaabbabbababbaabbbbabbbaababbbbaabbabaaaabbbaaaabbabbbabaababaababbababbabbbabbbbababbaaabbbbbbbbbbabbbabbbbaaaabbabbababbaabbabbaabababaabaabbaaaababbbabaaaabbaaababbbbbabaaaababbabaaaabaabababababaabaabbabbbbaaaabbaaaaaaaaaaabbbaaaaaaaaaaababbbaabbbaaaabaaaabaabaabbabbbabbabbbababbaaaabbabababaabbbbaaaababbabbabaaababbbabbbaabbababbbbaaabaaaabaabaabbabbaabbaaaababbaababbaaaabababbabababbbbbbaaaabababbabaaaaababaaabbbbababaabababbbbbabbabbaabbababaaabaaaababaaabaaabbaaaabbaaabbaaaaabababaababbbaabaabbbaaaaaabbbbabbbabababbbabbbaabbabababbbbbaaabaabaabaabbaababaaabbbababbbbababbbbbabbabbaabaaabbababaaabaaabaabaabababaaabbbaaabbbbbbbbabbbbaabababababaabaabbabababaababbababaaabbbaaaaaaaaabbbaabbaababbbbbabaabbbaabbaabaabaabbbbabbbabaabaaabbbbbbabaaabbbaabaabababaaabbaababbbababaabbaabbbbaabaaaabbaabbbbbabbabbbbbbabbbaaaaabaabbabaaaabaaaabbbabbabbbababbaababaabbaababaabbaababaaaaaaabbbabbbabbaabbbababbaaaaabaabaabaabbbabbaaabbbbbaaabbabbbaaaabbbaaaaabbaabbabbabababbbabbaabbaaabbaaaaababbbbaababbabaabbaababbbbabbaaabbabbaaabaaaaaaabaabbbbabbabaaababaabababbbbbabaabaabaabbbabbbbbbabaaaaaabbbabaabbaaababaabababbaaaaaabbbbbbaaabababababbbbbbaaaaaaababbbabaaababababbbbabbaabbabaaabbaaaaaaabbabababbaaabbaaabababaaabbbabbbabaaaababbbbbbbbbbaaaaaabaababbabbabbabbaabbaabaaaaaaaaabaaaaabbaabbabbabbabbbbbaabbbbbabbbbbabbbbabbbabaaaaaabbaaaabbaababbaabababbaaabbbaababaaabbabaaabbabababaaabbabbaababababbaababbbbaaabbbbabbbbaabaabaabaaaaaaabababababbbbbabaababbbbaabaaaabaaaaaabbbbabaaababbaaabbbabbababbbaabababaababbbbbabbbaaaaabbbaaabbaaabababbabbabbabbaaaabaaabababaaabababbaaabbbabbabbbbbabababbbabbababbbaabaabbabaaabbbaabbaaaaaababbbbabbababaabbababbbbbabbaababbbbabaaabbbababbbabbbbaaaaabaabaaaabaaaaaaaabbbbbaaabbbbabbbaaabaababbbababbbbaaaabaabaaaaabbababbabbaabbbbbbbaaabaaaabbabaabbbbaaaabababbbbbbaaabaaabababaaaaabaabbabaaaaababaabbabbabbabbabaabaaabbabaabaabababbaaabababbbaaaaabbbababaabbaabaaaaaaaabbaaaaabaaabbababaaaaaaababbbaabbbbbabaaabbaababaaaaabaaabbbabaababbbaaaaaaaabbaababbabbbbabbabbbbabbbababbabbabaababbbaaaabbbbbabaaaabbaababbabbbbaaaabbabbaabaabbbbbbbaaaabbbabbbaaabaaaaaabbbaaaaaabbabaabbaaabbbabbbbababbaaaaabbabbbbaaabbabbaabbabaaababbbbabbbababbabbababaabaababaababbaabbbbaaaabbbbbaaaaaaabbbbbbaaaaababbabaabbbabbaabbaabaaaabbaaabaababbabaaaaaabbbbaaabaabbbbbbaaaabaabbbbbaabaaabbbbabbbaabbbabbbabaababaaaabaaaabbbabbabaababaabbbabbaaaaabaaabaaababbabaababbaabbbaaaaababaaabbababbababaabbbbbbbabbaababababaabababababbaaaabbbbbabbbabbaaabbbbaaabbaaaaabaabbababbabaababbbaaaababababbbbbbbbaababbbabbaabaaabbbbbaaaabbbabaabaabaaabababbbaaaabbabaabbaaaababaabaabababaaaabbbaaababbabbbbaabbaaaaaaababbbaaaaaaaaaaaabaaaaabbbbbbaaaabbbbaaabbbbbbbaabbbbaabbababbbbbaaaabbbbaaaabbabaaabbababbabaabbbbbbbabbabbabaaaaaabaaabbaabbbababbaabaabbaaababbbabababbbaababbbbabaabbbabaabaabaabbaaaaabaabaaabbabbabaaaabaaaaababbaabbaaaaaabbbabbbabbbbbbbbbabbbbaabbaaabaabaaabbaabababaabbabbababbaaabbabbabaabbabbabbaabaaababbbbbbababbbaabbbbababbaaaabbbaaababbabbabaaaaabbabaaaaabbbbbbababaaaababaabaababaabaaaaabbaaaaaabbbabaababbaaaaabbabbbaabbbaabaabbbbaababbaaabbaabaaaabbbababababbabababbbbbbaaaaabbabbbababaaaaaabbabbaababbbaaababbbbaaabababaabbabbbabbabbabaabaaabaaabbbbaaaaaabbbbababbababbaaababababbbbbaababbababbbbaabbaabbaababbabbaaababaaabaaaabaaabaabaabbbaaababbbababbababbaabaabaaabbaabbbbaabbaababababbbbbabbaabaabbabababbaaababaabbbabaabaaabaaaaabbbbabbabbbbbbaaaaabaabbbbbbabbaaaabaaababbabbabbaabbaaabbbabaaaaabbaaabbbabbbaabbbbbaabbbabbabbabaabbabbaaaaabbababbabbbabbbabbabbabbaabbaababababaaabbabbbaaabaaabbbaababbabbbbabbaabaabbaaaaababbbbababbaabaaabbbabbbabbababaaaaabaabaaaaababbaaaabaabaabababaaabbbabbbabaaaaaabaaaaababbaabbabbaabbaaabbabbbbbbabbbbaaabbbabaabaababaabbbbbbabbbaaaaaabaaaaabbaaabaaaaabbbbabbabaabaababbbabababbbbbbbbaabaaaaaaaabababbaaabbbbabababbbbabaabbbbbaabbabaaabababbaaaaaaaababbaaaaaaaabbbbbbbaabbbbbbaabababbbababbabbbabbaabbbabbabbabaaaabbbbaaabbbbbbaaaabaabababbabbbabbbbaababbbabbbbabbbabababbbababbbaaabaababbbbbaaabbaaaabaabaaabbbaaababaababaaaabbbbbbbbbabbaaaabaababbbaabaaabaabaabbbbaaaabaaabbabaaaabaaabbaaabbaaaaabbbaabaaabbabaabaabbbababaaabaaabbaaaabaababbbbbbbabaababaaabbabbbbaabababbaaaaabbbbbaababbbbaabaababbaaababaaaababbbabbbaabbabbaabbbbaababbbbababababbbbbabaaaaabbbabaaaabbababababbaabaaabbbbbbbbaababaabbaaabbaaababaabbaaabbbabbbababbabbbabbbbbbbbabbbabaabaababbbaaabababbbbbbaaabbabaaaababbbabbbbabbbabbbaaabaaaabbaaaabbaaababababbbabbababbbbbabaaabbababaaaaabaaaaabbbbabbbaaaabbbbbbbbaaaababbbaabbabbbbbababbaaaabbbbbabbabaabbaaabababaabbaaabbbabbababaabababaaaababbabaaabbbbbbabbbaabbabaaababaaaaaaababaaaabbaaabbbbaababbaabbababbbbaabbaabbbbbabaabaabbbbbababaaaababbabaaabbababbbaabbaababbababbaaaabababbababbababbbbababbbabbaababbababbbabbbbbbbababbaaaaaaabababbbbabbaabbaaababbaaaaabaaababbbbababbababbbaaaaaababbbbbbbbabbaabbaabbaababaabbababbababbaababbbbabbbbbaaabbaaaabbaaaaabbaaaaaaaaabababaaaaababaabbaabaabbbbbaabbbbaaabbbaabbbababababbabaaaabbbaabaabababbaaaaababaaaaaaaabbbbbabaabbbaaaaaaaabaabbbbabbbbbbbaabaaabbaaaabaababbabbaababaabbbababbbaabaaabbbbbbaabbbaabababbbabbabaabbbabbaaaabaabbbabbabaababaaabaabababbbaaaaabaabbbbbaabbbbaabaaabbbbbbaabbbabaabaabababbaaabbbabbabaabababbbbabababbbababaabaabbbbabbbabbabaaaabbbabaaabaabababbaabbbabbbbbbbabbbaababbbabababbaaaaabbaabbaabbaaaaabaaabaaabaaaababaabaaabaaaaaabbaabbbaababbaaabababbbabaabbaaabbaaabbaabbbbabbaabaabbabaabaaababbababbbbbbaababbbbabbabaaabbaabaabbababbbaabaaabbabbabbaaabaaabbbbbbbbbababbaaabababaaabaababbbaababbbbbbbbbbbaaaababbbbabbabbaabaaabbbaabbbbbababbbabbbaabbaaaaababbbbbababababbabbababbaabbbababbabaabaabbaabbbabbbbabbabbabaaabababaabbaaababbbbbbbabbaaaaaaabaabaabbababbaababbabaabbbbbbabbabaabaabbaaabbaaabbbbbbaabbbabbbabaaabaabbaabbabbbabbaabbababaaabbabbbababbaaaaabbabbbabaaaabababbbabbaababaaabbaaababbaaaababaaabaabbbabababababbbbabababbabbbabbbbbbabbbababbbaabaabbaabaabaaaabaabaabbbbbbabbabbaaababbbbbaabababaabbaabababbaabaaababababbbbaababbabbbaabaabaaaabbabbbbabaabaaababaaaaaabbababaaababbbaababababaababbababbabaabbbbabbabaabbaaabababababbabbbbabbabbbaabbbaabbabaabbbabaabbbbbabaaababbbbabbbbaabaaababbbababaabbaaabbbaaabbababbababababbabbabbbbbaabbbbbaaaaaabaaababaaaabbabbabbaaabbabbabbaabbbabaaaaabbaababaaaabbaaaabbababababbbbbabbaabbabaaabbbbbbbbbababaabaabaaabaaaaabbababbbabbbaaaaabbaaaaaabbabbaabaaababaaaaabbaaabbaabaabaaaaaabaaabbabbababbabbaababaaabbbbbbaabaaaabaaaabbaabbbabbabbbababbbbabbbbbbaaaabbabaababbbbabaabbbbabbabbbabbbaababaabaabaaabaababababababaababaabaabbaaaaaaaabbbaaaaabbbabbabbbaaabbabbaababaabbbbaabaaaabababbbbbabaaabbabababbababbbbaaabbbabaaabaaabaaabbbbabbabaabbabbbbababbabbabbbbbbbababaabbbabbabaaaabbabbaabaaabbabbaaaabaabbaabbbbbbaaababbbbaabbaabbaabaaaaabbbbbbabbbabaabbaabaaababbabbbaaabbaabaabababaaaabbabaabababbaababaababbabaaaabbbaabbabaabbbaaaabbaabbbaabaabaaaabaaaaababbbbababababbbabbaaaabbbbaabbbaababaaababbaaabbbbbbbbababaaabaaaabbbaaabaaaaabababbbabaabababaaaabaababbbbbbabbbabaabaabbbaaabaabaaabaaaaabaabbbbaabbbababbaaabbabbaabbbbaabababaaaaabbaaaaabaaaabaabbbbabaaaaaaabaaabaaabaaabbbababbbaabababaabbbabbbababaabaabababababbbaaababbbbbbaaabaaabbbaaaaaaabaabaabbaaabbbbaaabbbaabaaababbbabababbabbbabbabbaababbbaaabbabaaabbabaabbaabaaaaaaabbbabbaaabbaabbababbbabbbbbbabbbbbbbaaabbaababbabaabbaaabaababaaabbaabbbbaabbbbabbaaaaaaabaaaabaabbabaabbbabbaaababaabaabaabbbbababbbabbabbbbbabbaabbbbbbbbabbbabbbabbbabbbaaaaaabaaabbabaababbabbbaabaabbaaababbbababaaabaaaabaaaabaaaabaaabbbababaabbaabaababbaabbaaaaabbaabaababbaaababbbaabbaaabaababbabbaaaabaaabbababaaabbbbababbabbaabababbababaaaababbaabababbbabbaaaaaabaababaabbabbbbbaabaabababaaabaaaabbaaabbaababababbbabbaaabbaaaabbabbaabbbaaaabbaabbbbaabaaaabaaabaaabaabbbbaaabaaabbaaababaabbbbbaaaaaaabbabbabbbbaaabbaaabaaaabbabaabbabaaabaabaaaaaaaabaaabbbaaaaababaababbbabbababbaabbababababaaabbbabbbbbbabbabbbbbabbbabbbbbbbbbabaaababaaaababbbbaababbabaabbbaabababbbabbaabbaabaaabababbbaabababaaabaaabbbbbbbaaabbbbabbbbabbabbbaaaaababbbbabaabbbabbbabbbbabaabbbbabbbabbbabbabbababbbbaabaabbaaabaaababaabbbaaababaaabbabbbabbbbbbbaaaabaabbabbaaaaabbbbaabaaabaabbbbbabaaabaaaabbbbbbbaababbabaababbbaaabbbbbbabbbaabbbaaaaaabbabbabaaabababbbbbbbbaaaabbaabaabbaaababaaaaababaaabaaabbbbaaabbaabbbabababbbbbaabaaaaaabaabbbbbbabaababbbbbabaabbbaaaaabbbaabaabaabbbbbbbbbabbababbabaaaabbbbababbaababbaabaaaabbbbaaaaabbbabbbaaaababbaaabbaababbaabababbaaababaaaababaabbbbabababbbbabbaabbbaababbbababbababaaaabaabaabbbaaabbaabbbbaabbbabaaabbbbbaabaaaaaaaabababbbabbababbbbbbbbbbbaaabbbbababbaababbaabbaaaaabbbaababbbbbabbabaabbababaaaababaabaaaababbabbbaabababaaaabbaaaaabbbaababaaaabaabaaaaababaaabaaabababaaaaaabbabaabbbbbbaaaabaababaaaaaabbababaababbbaabaabaaaaaabbaabbaaaaabbbaabaaabaaaabaabaaabbabbaaaaabbbababaaabbabbbbbaaabbabbbaaabbaabbabbbbababaabbbaababaabaaaaaaabbaabaabbaabbbbabaaaabbabaababbbaaaabaabaaabaaabbbaaaabbaabaababaaabbbaabbbbbabbbbaabbbbbabbbbaabbbbabaaabaabaababbbaaaabbabbabbaaabaaaaaabaaaaaabbbbbbaaaabbbbbabbbbbaaabababbbbbabbbbbbabaaabbbabbbbaaabbaaaabaababbbaabaaaabaaaaaabbabaaababbbaababaaabababbaaabbbbaabaababbababbabbbbabbbaababbaaabbabaaaaaaaaabbabbaaaaabaabbbaaaabbaaaaabbbbaababbbbbaabaabaabbbbbabaabaabbaabbbbabaaabaabbaaaababbbbaaabaabbbababbaabaaabaabbaabbbaabbbbbbbabbbbaaaabaabaabbbbbabbbbbbaaabbaabbaabbaaabbbabbbbbabaabbbaaabbbbbbabbabbbaabbaabbbabbbbaabbabababbbabaaaabbbaaabbabbbbbbabbabbaaaaaababbaabbbabaababbbbbabaabaabaaabbbaabbbaaabbbbbaaabbbabaaabbaabbbbabbaabababbaabaabbabbbaaabbbbbbbbbbbabbabbaaaabaaaaaabaaaabbbbbabaaabbbabaaababbbababaaaabababbbababaabbaaabaabaaabababaaaabbaababaaaaabababbbbabbbababababaaaababbbbbaabababababababbbababbaaaabaabbbbbaaababbaababbbbaaaabaababaaaabbabaabaaabbbbbabbbabbbbaabbbababaabbbaababbbaaaabbaabbbbaabbaabbbabbbabaabaaaaabbbbbaaabbabbbbabaaaababbbabaaaaababbbaaaabbbbbbabaababbbbbbaaaaaaabaaaaaabbabababbbabababbababaaaabaababababaabbbbbaabbabaaaabbabbbbaaabbbbaababbbbabbbbabaabaabbbbbbaabbbbaaabaabaababaababbababaaaabaabaaaabbbabbabbbaabaaabbbbababbabababbabbbaaabbaaabababaabbbbbbbaababbbaabaaaabbbbbababaabaabaaabbaaaabbaabbaaaabbbaabbbbbaabbabbbabbaaabbbbaaaababbaaabaabbaaabaaaabbabbbaaaabbaaaabaaaaaaaabbababaaabaababbaaaaaaaabbaaabbaabaababbabaaabbbbbbabaabaababaaaaaaabaababbabbaaaaabbababbaaaaaabbbabbbbabbbbaaabababbaabbbaaaabaaaabbbaaabbabaaaabbaaabbbabbaaabaaabbabbbbaabbbbbabababbbababbbababbababaaaababbbbaabbbbbbaabababbbbbbaabbbbabbabbabaaaabbbabbabababaabaaaaabbaaabababaababbbabbbabaaababbbaaabbbabbbaaaabbabaabaabbabbaabbaabaaabbbbabaaaabbbbabaabbaaabbbbbaaabaaabbbbaaababaabaaaaaaabbbababbbabaaaaababbbababbabaaabaaabbbbaaaaababbaabaababbbabbbabbabbabababbabbbaaaabaabbbbabbbbabababbbbaabbaabaabbabbaaabaaababbabbbbabaabbbbaaaaabbabbaabbababbaababbabbaaababbaabbbabababaaaababbbabbbabaabbababbababbabbaaabaabaaaaabaababaababbabbabaababbbbbbbbbbbbbababbbabaabbbbbabbaabababbbabaaaaabbaabbabaaaaaabaababbabbbbbaabbaabbababaaaaabaaaaaabbababaaaaaaaaabbabbabaaaabbbaabbaaabaaaaaabbbaabbaaabbbaabaaabaabbaaababbaaaabbbaababaabbbbbaabbbbaabbabbababaaababaaabbbbaaaabbabaaaaabababaabbbaabaaabbbbaabbbaaabaababbabaabaabbbaabbbbbbaaaabbbbabaaabbbabbbbbababbaabababbabbbbbbbbaaabaaaabaaabbbbbbabbaabbbbbabbbaabbaababaabaabababbaaaabbbbbbbaaaaaabaabaabaabaabbabbbbbabbbaaaaaaabbaabababaabbabaabababababbabbbbabaaaabbabaabbbaaaabbbbabaabbabbbbaabbbbaabbaaaaabaabaaabbabbbabbbbaaaabbaaabbbaababbabababbbbbababbbbababaaaababaababaababbbaaabababbabbaaabbbabbbababbaaabbabaabaaabbbbbbaabaaabaabbaabababbaabbbbaaaaaaaaaaabbbaabaaaabbabbbababbbbbaaaaaaabbaaaaaaaababaaaabbabababababaabbaaaaabbbbbbbabbbbaaaaabbaaaaabaaababbbbaaabaaababbabbbaaabbabaabbabbaaaabbbabaababbaabbbbbbabbbbbabbbababaaaaaaaababbabaabaaaaababaaaaaaaaaabbabbabbaaaababaaabbaabbbbaabbbaaaababababaaaaababbabbabbbbbbabbbabbaabbababbaabbbaaaaabaaababbbabaaababababaaaababbbbabababbbbbbaabaaaaababbabaababbbabbbbbaabaabbbabbabbaaabbaabbaabaabaabaabbaaabbbbabbbbaaabaaabaaaabaaabaaaaabaabbaaababaabbbabbbbabaabbabbaaaabbbbbbbabbabbabbbaabbbababbababaaaaaabababbbbaaabbaabaaaabaaaaabbbaaaabbbaababbabbababbbabaaabababbbababababbaaaabababaabbbbabbaabbaabbbabbbbbbabaababaaaabbbbbbaabbabbabaaabbbbbaaababbbababbbabbaaabbbbababaaaaabaabaabbbbabaabbaaaaaabaabbaabbbabababbbabaabaababbbbbababbaaabbbaababaabbaaaaabbaabbabbbababbbbabaabbbaabaababbaaaaabbababbbbabaabababbabbaaaabaabbbabbbbbabaaaaabbaabbaaaabbaababaaabbbbaabbbbbbbaaabbaaaaabbbbbbbbaabbaabaaabaaaaaabbaaaaaaabbbbaabbabaaabbbbaabbabbbbabbaaabbaaabababbbbabbababbbaabbabbaaabbaabaabaabaabaaababbaabaaaaabaabbbabaaababbbbabbabbbabbaaaabbbababbabababaabbabaababbabbaaaaaaabbaababbabbbaabaaaabaaaabbabaaaabbabbbbbaabbaabaababbaabbbbababbaabbbababaabbbbbbaaabbaaaabababbabaabbbabbbabbbabaaabbabbbbbaaaaaabbbabbbbbbabbbabaababbbabbbbbbabbaabaababbaababababbabbbaaaabbbaabbaababbbbbbaababababaaabbabbabbbbbbabbbbabaabbbbbabbababaaaaabbaababbbaabbaaababbbaababaabbaabbbbbababbabbbbbbabaaaabaabbaabbbbabbababababaaabababbaabababbaabbbbbbbabaaabaabaaaaaaabaaaaaaaaabbbabbabbaabbaabbabbbbbabbbaaaabaabaabaabaabaaabaabbabaaaaaaabaaaaaabaaababaaabbaaaababbaabababbabbbabaaaabababaaaabaabaabbbabababbabbbabaaabaababaabaaaaaaabaabaaabaabbbabbaabbabbbaabaabbbbabaabbaabbbbbbababbbaabbaababbbbbaaaababbbbbaabbbbbaaaaababaaabbbabbbbbaaaabbababaaaabbabbabbbbaabaabbbbbbabaaaaaaabaabaaabbbbbbbbabbaabbaaababaaaabaabaaababaaaaabbbbbbaaaababbbbabbbbaaaabbaabbabbabbaaabbababbaabbbabbaabbbbabababaabbabbaaaabbbaababbbaaababbaabbaabaabaabbbbababaababbbbbabbababbaabaabbbabbabbababbaababbbaaabbababbabbbaababababaaaababbababbbaaabaaabbaaaabbabbaababbbbaaaaababbbababbaabbaabbbaababaaabababababbbbaaaababbbbabbbbbbaabbbabaaababababbbaabbaabaaabbaaababbbbbbbaabbbbaabbaaababbaaabbabbbbabbbbaaabbabbaabbaaaaabbbababbabaaaabaaaaababbbaaaaabaabbbabbbabbaaabaaababbbbbabbbbbbabaabbbbaababbaaaaabbaabbaabbabbbbaabbabbaaaaabbababbababbbbabbabbaaaababbaabbbaabaababbabaaaaabaabaabbbaabaaaaabaaabaabbbababaabbaaaabaaababbabbabaaababbbababbabaaaaaaabbabbbaaabbbbabaabbaabbbbbabbbbbbabbbabababbbbaabaabbbbabbaabaababbbababbbaaababbbbaabbabbbbbbbbababbbbbaaabbbaaabbbbbabaaabababbbababababbbaababbbbbbababaaabbbabaabbabbbbaabbbbbbaabaaabaaaababaaaaaabbabaaabbbabbbaaababbbbabaaabababbbbbbbaabbababbaabaabbbbabaaabbaaaabbabbabbbbabbbabbabbbbaababbbbbaabaaaaabbabaababbbbabababbbabbbabaabaaaabbbabbbbabbababbbbabaaaaabbababbbaababbabbbbababbabbbbabaaaaabbbbabababaaaabaaabbabaababbaababababbbaabababaaaabbabbabaaabaabaabbababbabbbbbbaabbbbbbabaaaaababababbbbbbabbaabaaaababbaaabbbababaaabbbbbaababaabbaabaabbbabbbaababaabbbaaaaaabbbababaabababbaaabbbababaabaaabbbbbabbaaaaaaaabbabaabbaaababababaababaabaaabaabbaabbaabbabbaababbaabaaaabbaaabbaaaabbaaaabababbaaababaaaaababaaabaabbbaaaaabaaabbaabbbbaaababbaababaaabbaaaabaabababbbbbbbbbabaaaaaaababaabbbbabaaaababbaabbbbaaabaaabbaaabbbbbaaaabbaabbbababaaaaabbbaabaababbbbaaaabbbbabbaaababbabaabaaabbbbaaaabaabbbaaaaabbaabbaabbbaababbbbbaabbbbbbabaaabbbabababbaaaabbabbaaaaabbaaabaaabbabaabbbbabbbaabbaabbaabababbababbabbaaabbaabababbabbbabaababaababbbabbababaabbabbbbaabbbbabbaaaabaabbbabaaabbbabaaaabbbabbbabbbaaabbababaababbbabbbbbbabbbababaabaabaaabbabbabbbbbbabbabaabbbbaabbabbbbbbbbabbbaabbabbbbbabababbaaabaababaaabbbbbbbbaabaababbbabbaabbabbabababbaaabbabbaabbaabbbbbbbaabaaaaabbababbbaaabaabbbbaaaabbaabbaaaabbabbbbaabbababbababaabbbabbbbbbabbaabababbabbbababbabbabbabbbabbababbabbbbaabbaabababaaaabbabbabaaaabbbabababbabbabbabbaabaaababbabbbbaabbbbbaabbabbbaaaabaababbbabababbaaaabaabaabbbabaabbabbbbbbabbabaaaaabbaaababbbaaaaaaaaaaaabbaabbabaaabbaabbbaaaabbabababaaababbaaaaaaababbaaabaaaabaabbbbbaabaabbabbababbbbbaaabbaabababbbaababbbaababaaaababaabaaabaaabbbaaabaaababbaabaabaabbaabaabaaaaaaaaabbbbaaaaabaabaabbbaabaabababbaabbabbabbbaaabbbbbaabaabaaababbbabababaaaabbaabbbbaabbbaabbbbabbabaabbaaaaaaababaaaabbbbbbbababaaabaaabbaaaaaabbaaabababbabbababaaaaabbabbaabababbabaabbaaaabbabababaaabaabbbaaaabbbbbaaaabbbaaaaaaabaababbbbbbaaabbaabbbbbbabbaabbbaabbabbbbbabababaabbbaababaabbabbaaaaabbbbaabbbbabbaaaaabbaaabaaaaabbbbbbaabbababaabaabbaaaabaaabaabaabbabbabbbbabaabbaaaababbbabaaababababbbaabbbaaabbaabbaaaaabbbbbbbbabbbbabaaaabbaaababbbbbabbbabaaaaabaabaababbbbbbbbaaaababaaababbaabaabbbababbababaaaaabababaababbaabaabaabbabbbbababababbbabababaabbbaabaabbabbabbbbbababbaabbaaabbbaabaaaaaaabaaabababbbaabaaaaabbbaaabaaabbabbbbaaababbbbbabbaaababbaaabbbaaababaaaababbbbaaaaaabbaaabbbaaabbababbababaabaabbbbaaabbbaaabbabbaaaabbabbbaaabaaabbbbababaaaabaabaaabbbaabbbbbbabbbbabaababbbbbbabbaaaaaabbaabbababbaabbaabbaabbaaabaaabbbbabaababaababaaaaaaaabaabababbaaababbbbbbbbbaaabbabbabbaabbbababaabbbbaababaaaaaabbbbaabababaaababbabbbababaabbababbbbbaaaaaababaaabbabababbabbbababbbaaaabbbbbaaaaabbbabaaaabbbbaabaaaaabbbababbaabbbaaabbabbbaaabaaaaaaaaaaabbaabbbabbbaaaabaaaabbbaababaaababbaababbbaabbbabbbabaabbaaabababaaabaabbaaaabbbabbaaaabbbbbabbaabbbaaababbabbbbaaaaaabbaaaaababaababbbbbbbbbbbbbaabaabbababbabaaabaababbbaabbbbbaababaabababbbbbbbbabbaababaaaabbbabaaabbbbbaababaaaaabbbaabbabaabbaababaababbabaabbbbbbbbbaaaaaabbbbbbbabbbaaabbaaaabaaaaabbbbbaabbaaaaaaababaabbabaaabbaabaabaaaabbabaabbabbabbbbbabbaaabbbbabababbaabbaabaaaaaababaaabaababaaabbbbabaaabababaabbbbbbbabaaabbaabbbabababbbaababbbaabbbaaabbabaababbabaaabaabaababaaaaababbbbbaaabbaabaababbaaabaaaaabbbbbaababbabbbbbaaaaabbaaaabbabbabababaaababbaabbabbbabbaabbbbabbaabbabbabababbaaabbababbbaabaaaaaaaaabaabaaabbbaaaaaaaaaaabbbabbaaaaabbaaabbaabbabbaabbabaababaababbaababbbaaabababbbaabababaaababbaaabaaaaabaababbbbbbbaabbbbbbaaabbbabbbabbbabaaabbabbabbbbbaababbaabaabbbbbbbaaaaaaabaaababababbbbaabbaaaabbababaabbabbabbaabbbbaaabbbaabbaaaaabbbaabbaaaabaaaaabbbbababbbababbabbabbbabababbabaaaaababbabbbbabbabaabaabbbbbaabbaaaaaaaabaaaabaababaabbaabbaaaaaaabbbbababbaaaaaaaaabbabbaaaaaabbabbbbababaaabaababaabbbbbababbbabbaaabbbaaaabbbaaabbbbabababbaaababaaabbbbbaaaaaaabbbbaabbababbbbaaaabbaabaaabaabbabaaabbabaaaabaaabaaabaabbaabbaabbbaaababbbbabbbbaaaabaaabaaaabbabaababaaabaaaabaabbaabbababaabbbbaabababababaababaaabaabbbaabbaabbabbabbbbbbabbbaaaabbbbabbababaababbababbbaaaabbabaabbbbbaaaaaaabaaaabbaaabbbababbaababaaaabaaabbabababbbabbaabbbbaaabbbbbbbbbbaaabaababababaabababbbbbaaabbbabbbaababbbbbbababbaababbaabbaabaabababbbaabbbaabbabbabaaaaaaabaabaabaaaaaaabaaaabbaaaaabaaaaabbbaaaabbbbbbabaaabbbabababbaabbabaababbaabaaaabbbbbbbabbaababaabbbbbbbbbaabbaaabbabbabbabbabbbbabaababbbababbbabaaabbabaabbbaabbaaaaabaabbaababbaabbbbabbaabbaaabbaaababbbabbbbbabaabababbbbaabbabbabaaaabaaaaabbabbabbbaababaabaaaabaabbababbaaabaababaabaaaabbbbaaaaaababbbaaaabbabbaaabbabbaaabaabaabbabbaababbaababaabbaabaaaabbbbabababbbbabbbbbbaaaababbbaababbabbababaaaabbbabbaabbaaababaabaababbabaaabaababbabaabababbabbbbbaaababbaaaaabaababbabaabbabbaabbabaaaaabbaabbbbaababbbbabaaaababbaaababbbbbbabbbababaaabbbbabaabbaabbabaaaabababaaabbbaabbabaabaaaabaaababbbabbbabbabbaabaaaaaabbbbbababbaaabbaababaaabbaabbabbbbbaaababababbaaabbbabbabaabbabbbaabbbbabbbbaabaababababbaabaabbbaaaaaabbababbaaaaaababbababbbaabaaaaaaaaaabbbaaabaabbaababbbaaabbbaaababbbbbabaaaabbbabbbbbabbabaaaabbaaaaabababbaabbaaaaaaaabbaaaabbaabaababbbbbababbbaaabbaababaababaaaaaaabbbbabbbaabbabbabbaabbbbaabaababbbbbabababbbbbaabaabbbaabaaabbbabbbbbbaaabbaaababbaaababbbbababbbaaabbababaaaaaabaabaabaaaabaaaaabbabbabbaababbbabbaabbabbbbabaaaabaabbbbaaabbabbaababbbbbbabaaababbbaaaabbbabbbabbbabbabbbbaaaaabbabbbaabbabaaaabababaaababaaabbababaabbbbababbabaababbbaaabbabbabbabaabbababbbbbbaaababbaabbbbababbaabbbbbaaaaaaaaaabaabbaaabbabbaabaaabbaaaaabababaaaabbbabbaabbbbbabbbaaaaaaabaabbaabbbbaaaaaaabbbaaaaabaababaababbabbaabaaaaabbabbbabbbaaabbbbbabaabababbbabbbbbaaaabaaababbabbbbbaababbaaabbbbababaaabababbbbaaaabbbbbbaaabbbbbaabaaababababaabaababbaabbbbababbabbbbbbaaabaabaabbbaababaabaabaabaabaabaaaaaabbbababbababbbabbababbbbbbabbaababaabbbabbbbaaabbabaaaabbbabababaaaabbaaaaabbababaabbbbabaaaaabbbbbbaabbbbababaaaaaabbabbaababbbbbbbaabbbabbabbbbbaaaaaaaabaaabbbbaabaaabaaaaaaaabbbaabaabbbabbabbbbabaaaaaabbbaabababbabaabaabaaabbabbaaaabaabababbababaaabbbbbbbbbbabbbabbbaaaaababababbbaaaabaaababababaaababaabaaabbaabbbaaaabaaaaaaababbaabbaaaaaabbabaabbabbaaaaabaabaabaababbbbabbaaabbaabaabbaabaabbaabababbabbbbabbaabababbbbbbbababaaababbabbaaaababbaaabbbbaaabbbaaabaababbababbaabbbaabaabbaabaaaabbabababaaaaabbaaabbabbaabbaaaaaabaabaabbbbaabbbaaaaaaabababbbbbbaaabaababbbaaabbbabbabaabaaabbaaabbabbbbabaaaaabaaaababbbbababbbbaaaaaabaaaaaabbbaaaababbbbbbbbbbbbbabbaabaaabaababaabaaabbbaaaaabbaaaaaaabbabbbaaaabababaabbaabbaabbabbbabbaabaabbababbbaabababaaaababbbabaababaabaaababaaaabbabbabbaabaabbaabbbabaabbabaababbbaabbabbbaabbaaabbabbabbababaaabbbbaaabbbabaabbaaaabaabbbbaabaaaaaabaaaabbbbabababbabbababbbaabaaabaaababbbbbbbbbabbababbbbbbabaaabbbbababbabaaababbbbbbbbbbababaabaaababbabbabababbabbbaabaaaabbbbaabaabbbabbbabbbbabbabaababbaabbbbbaabbaaabaabbbbaabbbabbbaaaaabaabaabbaabbaabbabbbaabbababbabbaababaabbaaabbaaababbbaababbaaaabaaaaaabbabbbbaaaabababababbbbabaabbbaaabbabaababaaaaaaaabbabaabaabbbbaabbabbabaabaaaabaababbabaaababbabbbabaabaaaaaaaababaababaabbbabbaababbbbbbbabaaabaabbabaaabbbbbabbbbaaaaabbbabbbaaabaababbbbbbbaabbbbabbaabbbbaabaaabaaabbaabaababbabababbbabbabbaabbbbbabaababbbaaabbaaaaabbaabaaaabbbabaaabbaabaaabbaabbbabaaabaaabaaabbababaababbaaaabbbbbaabaaabaaabbbaaabbbbabbbbaabbbbbbabbbaaabaabbbaaaabbabaaaabaaaabaabbababbbbabbaababbbaababbbbbbabaabaabaabbbaaabaabbbbaabbbababbabbbbbbbbbaaabaaabaababbaabababbaaabbbabbaabaababbbababbababaabaababbaabbbbaaaabababbbbababaabaabbabbbaababaabbbbbbaabaaabbbabbbbbbbbbbaabbbbabbbbaabababaaaabbabbaabbbbbaaababababaabbabbabaababbbabaaaabaabbbbaabbbbbbbbbbaaababbaababbbaaabbabaababbaaaaaabaaabaaaaababbbabaabbabababbbbbaabaaaabbbbaaaaaabbaaabaabbababababbabbbbbaabaaababbababbbbaabaaabababbbaabbbbbbbaaaababaababbaabaabbbaabbabbabbbaaaaabbaababbbaabbbabbabaaaabaabbaabbbaabaaababbaabaabaabaaaaabbbabbbbabbaaaaabbbbabaaabaaabaabaaabbaabbabbaaabbaaaabbbababaaabaabbaabbababbbbbbbaabaabbbaaaabababbabbbbaaaababaaaaaaaaaaabbbbabbaabaaabaaaaaaaaaababbaaaabbabaaababbaaaabaababbbbbababaaaaaaaabaaaaababaabbbbbbabbbaababbabbbabaabaabaabbaaaaaaaaabaaaabbaaabaaaabaabbbaababaaaaaaaabaaaaabaabbbbbbabbbbaaaaababbbaaabbbbbaaabaabbaabababbaabbaaabaabbbabaabbaaaaabbaaaaabbbbaaaaabababaababbbaababbaaaabababbabbbabaaabbbbaabbbbabbabbabaaabbbbabaababbbbbaaababaababaabbbbaaabbbbbaabaaaabaaabbabbbbbbbaababaabbabababaabbbabaaaabbbabaaaaaababbaabaabbabbbaaabbbbaabbabbabaabbaabbabbaaaabbbaaaaaaabbbaabbabbabaaaaabbaaabbabaabbbabbbbabbbaabbaabaabbabbaabbaabaabbbaababaabbaabbbbbabbbbaabbaaabbbbbabbbbaaabaaaababbbababaabaaaababaaaaaaabbbaaaabaabaaaababbaabaaaabaaaabbaabbbabbaaabaabbbbbbbbabababbbabbaaaaabaaaabbbbaabaaabbabababbaaaabbabaaabbbababbabbbabababbbbbabaaabbbaababaabbabaaaababbbabbaabbbabbbbaaabaaaabbbbaabbbababaaaabbbbabaabbaabababbbabbbbaabaabbbaaaabbbaababababbbaabbabaaaabbbaaabaaaaabbbbaaaabbabbaaaabaaabbaabbabbbababaabbbbbbbaabaabbbabababbabbbbababbbabbbabababbbbaabababbbbaabaabbbabbbabbaaababbbbbabaaaaaabbaabaaaaababbababbbbababaabbababbbabaaababaabbaaaaabbaaababbbaaabbbbabbaaabbbabbabbbbbbbabbbaabaabbbaaababababaabbbaabbbabababbbbbbbbabbbabaababaabaaababababbbbabaaabaababbbabbabbbbbababaabbbbbaaabbbaabbbababaaaabbabbbaabaabbababaaaababaababaaababaaaaaabaaabbaababaababbbaaabbbbabbaabbbaabbaabaaababbbabbababaabbabbabbaabbaaabbabaaaaabaaababaaaaaabbaababbabbabbbabaabaabaaaabbbabbababababbbbaaaabbbaaaabaaabaaaabaaaaaaaaabbabbababbbbbaaababaaababbbbabbabaaaabbababbbbabbababbaabaabbbaaabbbbaaabaaabbbaaaaaaaabbbbabbaaaaababaaababbbabaaaabaaabbbababbbbabababbbabbbbabbabababaabbbabaababbbbabaabbbbbbbbabaabbbbbaaabaabbbaabaaabbbbbaaaaaaaaaabaaaabbbaabbbabbababbaaababbbabbbabbbbbababaaababaabbbbbabbaababbababbbbbabbbabbabbbaaabbbababaabaababbaaabbbaabababbaaabbaaaaaaabaaaaabbaabaabbaababbbbabbbabaabaaabaabaabbbbababbbababaaaabaabbabaabbbbaabbbaabaabbaaaaaaabbaaaaabaaaaabbbbbbbaababbbaaaaaabbbbabbabbbbabaaaabaabbaababbabaaababbaaaaababaaaababbbaaabbaaabbbbbaaaaabababbaabaabbbaababbbbbbbabbaabaabaaabbbbaaabbbaaabbaaabbbaaaaaaabaabbabaababbbbbbbbabbbabaaabaaaabbbaabbaabaabbbabaaaabaabababaabbaaabbbabbaabbabbbaabbbbaaaabbbaabbbbaabbabbaabbbaabbabbaaaaabbaaaabaabaaaaaaabaabaaaabaabaabbbabbaabaaabbababbaaaabbaabbaaaaabbbbabaabbababbabbaaabbbaababaaaaababbbabbaabbbabbaababbbbbababaabbaaaaabbabbabaabbbbbbbababbbabbbbbbbbabbbbbbbabbaababaabaaaababaaabaaabaababaababababbababaabaaababaabaaababbbaababaababbbaaaaababbbbaabbaaabbbababababaabbbabbaabbababbbabbabbabbbbabbababbbabaabbbababbabbbabbbabbbbbbaabbbbaaababbababbbbbaaaaabbbabbbbabababbbbaaaabbbbaabbbaaabbbaabaaabaababbaaaabbaabaaabbbababbabaabbaaababaaabbbbaabaabbaababbbaababbbbabababaabbaabbbbbbbbaaaaabababbaabaaabaaaabbbabbaabaaabbbaaaaaaabbbbbaaaababaabaabbbbaaabaaaabaaababaabbaaaaabaabbaabbaabbbbabaabbaaabababbbbbbababbbaaabbbbbbbbbaaababbbaaabaaabaaabbbabbbbbbabaaaaababbbbaaaabbaaabaabbabbbbbabbaaaaabbbaaaaaaaabbaaabaaaabbbaabababbbbaabbbbaaabababaababaabbaaabbbbaaaaababaaabababbabaabbaaabaaaaabababbbbbbaabbbbaababbabababbbbbbbbbbababaaabaabbbbabbbbbbabbabaabababbbbabbbbbbbaababaaaabababbababbabbbbaaabbbabaabbabaaaaaabbbabaaabbabbaaaababbbbabbaaabaababbaababbabaabbbabaaaabbbbbababbaabbbaabaabbaababbbbbaaabbbbaaabaaabbabaaaaabaaabaaababbbabaabbabababbbabbaaaaaaaabaaabbabbaabbabbbabbaabaabbaabbbbaaaaabaabaabaaabbabaaabbbabbabbbabaaabababbababbbbabababbabbbaabbabbaabaaaaababaaaababbbbaaaabaababaabbbbbbaabaabaaabbbbaabbbaaaabbbabaaababbbbaaabbaabaaaaabbbbabababbbbbbbaaabaaaaababbabaaaaababababaaaababbababbbaaabbbabbaaabbaabbbbbababbbabbbaaaabbbbbabbaabbaaabababbbbbbababbbabbbbbaabaabbbbaaabaaabaababbbabaabbbbabababbabbbbabbabbbaaabbabaaabbbabaaabbababaaababaaabbabbbabaaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaa
abaababaabbababbbaabbbabaaaaabaaaaaababbaaabaababbababbbbbaaabaaaabbbbbabaababaabbbaaaabaabaababaaaaabbbbbbabbaabbaababbbbbbbaabaabbaaaabaabbabbaabbaaaabaaaaabbabbaabababbbabaababaaabbabaababababbbbbaababbabaabbbaaabbaababaaabbbbaabbababbbbaabbaaabaabbaaabaaaabbbbaabbbbbbaaababbabbabaabbbabaaabababaabbabaabbaaaaabaaababaabbabbbbbaabbabaaaabbaabbbbaaaaaaaabaaabbaaabababbbbbbaaabaababbaabaabbaabbabbaabbaabbbabaababaaaabaaababababbbabbbbabbbaababaababababbbaaaabaaabaababaabbaabbaaaabbabaabaaabbababbabaaaaabababbbababaaabbbbbbabaaabbbabbbbabaabbbaaaaabaababaabbbaaaabbababbbaaabaabbbbbabaaabbbabaabbaabbbabababbababbabababbbaaabaaabbabbabbaaaaabaabbbbabbababaabaabaaaaababaabbaabaababbbbbbbabaabaabababbaabbbaabbabbabaabbaaaabababaabbbabbbbaaaaababababaabbababbabbbabaaaaaabbbbabbbbaabbabaaaabbbbaaaaaaababbbaabaaabbbababaaabbbbaabbbbabbaaaabbaababaabbabbbbbbabbaaaaababbbbabbbbabbaaaabaababbbbaabbaaabbbbabbbaaaaaababababbbbabaababaabaabaaaaabbbbabbaabbbbaaaabaababaaabbaabbaabaaaaabbabaabaabaabbbabbbaaaaaaabababbababbbaaabbaaaabaaababaabaabaaaaabbabbbbaabbbababbaaaaababaabbbbaabbbabbababaaabaababbbbbbaabaabbbbbaabaaabaaaabbbbbaaaaaabbababbbbbbaabbbaabbbbbaababbbbabbabbabbbbaabaaababaaabaabbbbbaaabbaaababbaabababbbbabbaabbaaabbbabbbabbbbababbbbaababaabbabbbbabbaaaabaaabaaabaabaaaaabaaaabaabbbbabbbabaabbaababbaabababbbbbbaaabababbbbbbaabbababaabaabbaaaaaaaabbbbbbabbabaaaabbbaaaabaabaaaaababaaababaabbbbbaababbbabababbbabababaabbbbaabbaaaaaaaabaabaaabbbbaaaaabaaabbabaabbabaabaaaababaabbbaaabbaaaaabbbbaaabaabbabbaababbabbababbaabbaabbbabababbbaaaaaabaababbbbabbbbbbbbbaaababbabbbaaababbaaabbbbbaabbbabbbababbabbbbaabaabbabbbbabbbbababbaaabbbabbaaaabbbbbabbbabaaabbbbbaaabbbaaaaaabaaababbabaabaaabababaababbaabbbbaaaabbbaabbbbbaababbbaabaababbababaaababbbabbbaabbbaaaabaabbbaaabbbababbaabaabaabaaaabbabbbbbbbaabbaabbbaabbababaaaaababbbbbabaababaaaababbaabaaaaabbaabbbbabbaaaaabbbababaabbbabbbaaaabaabbbbababbbbababbbbaaaabaaababbbaabbaaabbbaaaaabaabaabbbbaaababbbabbbabbabaababababbabaaababababaababbaababaaaababbbaabbbbbaaababbbabababaaaaaabbbaabbbabbbabbabaaababbaabbaaaaaabbbaabbaababbabaaaabbbabbbbaaabbaabbaaabbbabbbbbbabbaabbaaaababaaaabbbbabaaabbabbbbbabbaaaaabbbbaaaaaaaabbabbaaabababababbbabaababbabbaaabbabbbbabbaaabbaabbaaaabaabababaabbbababbaaaaaabbbbabbabbbabbaabbbbbbababbabbbbbaaaaabbbaaaabbbbbaababbbbbabbbabbababbabaababbabbabaababababababbbbbbbababaaaaaabbabbbaabbaaabbaabababaaabbaabababaaabbaaabbabbbaaaaabaababbbabbaabbaabbabaabababaaabaaabaaabaaaaabbbbabbbbababbabaabaaabbbaaaabaaabbbabbabaaababaaabbababbababbbaabbbaaaaaaabaaaaabaaabbbbabababaaabaaabbbaabbbbbbbababaabaababbabbabababaaabababbaabbbabaaabbbbabbaababbbaaabbbaabababbbababbbbbabbbabbbbbbbbababaaaabbabababbabbbaaabbbbabbbbbbbbbbaaabbaababbbababbabababbaaaabbaaaaabbbaaaabbbababaabbbbaaaabbaaaabaaabbabbbabbaaabbabaababbbababbabbababbbabaabbaababbbaaaabbbabbbbaaaabbabbbbbaabaaabbbbbaabbabbbbbbaaaaaababaabaabbbabaaabbaaaaaaaaabaabaaaababaaabaabbabaabbaaabbbabbbbbbabbabbbaaabababbaaaabbabbbbabbabbbbabbabbbabbbabaabababbbbbaababbbaaababbbbaaabbbbbababbbbaaabbaaaabbaabbaabaaaaabaabbbaaaaabbabaaaaaaabbabbbbbaabbababaaaaababbaabbbbbabbbbbbaaaaabbbabaaaaabaabaababbabbbbbababaaabbbaabbaaabbaabbbaabbaabbbaaababaaababaaabaaabababaaaabbbaaaabbbbbbabaaabbbbaabbabaaaababaabbbaabbabaabaabaababaaaabaaabbaabbabbbbbabaaaaabbbabbabbbabaaababaaaaaabbbaabababababbbaaaaaabaababaababbbababaabbabbbbaabaaabaaaaabaabbabaabbbbbabbbabaaabbabbaabbabaabaaabbabbabbbaabbbbbbaaaaaabaaaaabababaabbaaabaaabababbaababbabaaaaaaabaabbbabbbbbaabababbbabababbaabbabbbbbaaabaaaaaaabaababbbbbbabaabbbaabbbbbaababbabbbbbabbbaaabbbbabaaabaabaaaaaaababbaabbbaabaabbaababbbabbbbabbabaabbbabaaababababaaababbaababaabbbbababaaaabababbbbabababbaabaaaabaaabaabbabbaabbbabbababaaabbaabbbbbaaaaabbbabaabaabbbbaaabbbabbaaaaabaaaaabaaabbaaaaaaabbaabababbaababaababaaaaaaaaaaabababbabbaabababbabbbaabaabaaaababbaaababbaaaaababbbabaaabbbabaaabaaaaabbabbabaabaaaababbabababaabbbbbaababbaaabbabbbbaaabbbbbbabbabbababbbabbabaaabaabbaaaaabaaabbbbbbbaaaaabbbaaaababbbaabbbabbbabaaabbabbbaaaaaaaababbbbbaaaabaaabbaabbaabaaabaaaabbbababaabbabbbabbaabaaabaaaabbaaabaaabaabbaaaaaaabbaaaaaaabbbaaabbaabbbabbabbabaababbbbaaaababaaaaabbabaabbaaabbbabaabbaaaababbbbbabbbababbbabbbaaaaababbbbbbaababaaaaabbbabbbbbaabbbbaababbbabbbaabbbbbbabbbbabaaabaaaaabaabbbbaaabbbaaaabaaaaaabbbaabbbaabaaababbbbbaaabaaaabaaaaabbbaabaaabbbabbbbabaabababbaabbbaabaaabaaaabbbaaabbbbbaaaaaabaababbaaabbbbbbbbababaabababbbbaababaaaaaababaabbaaaabababaaaabaaababbbbbbaaaaaaabababbbbaababbbabbabaaababaabababaababababaaababbbaabbabbbabaaabaaababbbaaaaabaaaababaabbaaabbbabbababbabbaababaabbbbbbbaabaabbaababaaabaabaababaabababaabbbabababbbbaabbbaaaaaaabaabbabaababbbaabbbabbbababbbbbbbaabbaabbabbbbaaaabaabbbaabaaaabaababababaabbababaabaabbaabaaaaababbabaababbabbabbabbbaaaabaaabbaaabaabbbbaababababbabaababbbaaaabbbbbaabbabbbaaabbbaabbaabbaaaababbbbabaaaaabaaaabbabaabaaababbaaaabaaaaaabaaabbabbbbabbabbbaaaaabbbbbabbbbaaabbababababbabbbbabbabaaabababaaaabbaabaabbaabaabbabaaababbabaabaaabaabbbbabbaaabbaaaabaabbbaaaaaaaabbabaabaaabbaabbbaaaaabaabaabbbabaabbabaabaabbababbbbbaaaabbabbabbababaaaaaaababababbbababaaaababbbabaabaaabbbbaabaababaaaaabbbabaaaabbaabbaabbaaabbbbbabbaaababaabaaaabbbbbabbabaaaaaaabababbbaaaaaabababaabaaabbaaaabbaaaaaaaabbaaabaaabbaababaaaaabbababbbabbbbaabaabbbbababbbaaabaabaabbbbaaabaabaaabbbbbbaaabbbbbbbaabbbabbababbabaabbbaaaabbabbbabaaabbabaaabaaaaaabbbbaabaaabaaaabbabbababaababababaaabbababbbabaabaaabbbbabaaababbabababbaabaabaabbbabbbbbababaabababbbaababbbaaabbbbbbaaaaaabbbaabbabbbabbbbbbaabaabbaaaaabbbabbababaabbaabaaabbabaabbbbbabbbbaabbbbaaabbbaababaabbbbbaaaabaabbabbabbbbabbabaaaabbaababbbaabbbbabbbbbbaabaaabbaabbaabbbbabbaabababbbbabaabababaabbbababbaabbbabbbbbabaaababaabbbaabababaaabbaabbaabaabaaabbabbbaaababbaaabaaaaaaabbabbbaabbaabbbbbaabaaaababbaaababaabaabbaaabbbbaaaabababbbaaabbabbaaabababaababbbababaabaaababaaabbbaaabaaaabbbbabbaaaabbaaabbabababababaababbababbaaabbbaaaabbabaababaabababaabbabbbabbaabbaababbaabbaaabbbabababbababbabbabaaabbabaaabbbbbaababbabbabbabaababbbaabbabbaaaabaaabbbaababbababbbabaaaababbbaabbabaaababbabbbabaaabbbabbaaaaabbbababaaaabbaabbaabaaaaaababaaaaabbabbaabaabaaabbbaabababbbbabbbaabbabababbbbabaabababababababbbbaaaaaaaaababaabbaabaaaabaabbaabbaaaabaababbaaaaaaababbbababbbaaaabaaaabbbaaaaaaaabaaaabbaaabaabaaabaabaaabbbaaaaaabbabbaaabaabbbaaaabaabbbbabbababbbbbaaababbbabbbbaabbabababbbbabaabbaababaaabbbabababbaabbababbaaabaabbbbaaabaabaaabbaababbbaaabbbbbbbbbababbabbbbababaabbbbbbaaabababaaaabbabbaabaababaaaabbbbabbbaaabbbabbabbbbbaaabbbbabbbbbbaabbbbabaabbbabaaaaaababaabaaaababababbbbabababaaaaabaabbbbbabbabbbaaaaabbaaaabbbababbbbbbbbbbbabbbbaababbbabaababbaabbabbbabbbabbbaaabbbbababaaaaaababbbabaababaaaaababbbabbbbbbabbbbbaaaababbababbaabbabbbbbaaabaaaabbabbbaaabbbaaabaaaaabbabbabbbbbbabaabababbbabbbbaaabbaabababaabbbbbbbabbbaaaababaabbbababababbaaaabaabbbababababaaaabbbbbababbbababbbbbbbaababbabaabababaabbabbaaabbaaaabbabaabbbbbbabaababbbbbbaaaaabbbbababbbaaabbbabaabbbbbaababbbaaabbbbabaabbbabaabaababbbabaaababbbaaabbbaabaabbbbaaaaaaaaaabbaaabbbaaaaabbabbabaaabababaaaaaabaaababaabbbabaabababbaabbbaababbbabbbabbabbbababaabbbababbbbabbbbabbbaabbabaaaabaabbbaaaabbbabaaababaabbaabbbaabbbbbbbbbabaabaaababaabababbaaababaaabababaaaabbabbaaaababaaaaaaaaabbaaabbbababaabaabbbabaaaabaaaababbbbbaaaabbaabaabaaaababbbaaaaaaabababbbbaaaaabbbaaababbaaaaabbbabaaaabaababaabbbbabbbbbaaabbaababbaaaababbbbaaaaaaabbbbbbbababaabaabbabaababbaabababbbbbbaabaabbbaaaaabaaaababbbabaaaaaabaababaabaaaababbabbaaababbbbababaabbabaabbabaaabbbabaabbaabbaabbababaabbabaaabbaaabbaaabbabaaabbabbaaaaaaaababaabababaaabbaaaaaababbbbbaaaaaabbbaaaabaaaabababaabababbaabbaaaaaaaaaaababbbaaaabbabbababbaaaaabbbbbbbaabaabababababaaaabbababbbbaababaaaababbaaabbababbababbabbbbaabbaaabaabababaaababbbabbabbaabaabbabaaabbaabbaababaaaababaabaababababbbaaaabbbababbabaabbbaababbbbbabbaaabaabbabaaabbaabaaababaaabbababbaabbabaababbbabbbbaabaabbaaaaabaaaababbaaaaaaabaababababaababbbaabaaabaabbbbaabaabaaaaabbababaaababbaaaabbbaababbbaaabaaaaabbabbbbababbbaaabbbaababaabbaabababaabaababbabaaaaaaaaabaabaabaaabaaabbaabababababbbbbabbaaaaaabababbbababbabbabbbabbaabaabbaabaaabaaabbabaabaaaababaabbababbbbabbbaaabbabbaaaabbbbaabaabaaaabaaaabaababbaabaaabaabbaaabbbaabaabbbbabbabaaaaaababbbaabbbaaaabbaabbaabbbabbbaabbaaababababbabbbabaaabbaaababababababaaabbaaabababbbabaabaaaabaabbbabababbaabababbbbbbbbbaabbaaaaabbabaabbabbbbabaabbabbbabbbbababbbaabbababbaabababbbababbbbbaabbaabaaaabbabaaabababbabaababbbabbbaaabbbabaaabbbaaababaabbbaabaabbabbaabaababbbbbaabaabbabbbbaabbaaabbbabaaababbbbaababbaabababbaabbbaaababaabbbbbbbbbbbabbbababbbaababbaaabbbabbaaaaaabbbabaaaaaaaababbabababbababbabbbabbaaabbbbaaaabababababbabbbbbbaabbbaabaabaaaaabbbaabbaaaaabbbaabaaabaabaaaabbbabbbabaaabababababbaabaaabaaabbbbaabbbbabaaabbbaabbaabbbabbbbabaababaaababbbbbaaaaabbaabaaabaabaaaabbbaaaabaabbbaabbaaaabbaabbaabaababbaaabababbabbbaabaabbaababaabaababbbbbbbbbbbabbbbaabaababaabaabbabaaaabbaabaabaabaaabbaaaaabbababbabbbaababaaaabaaabbabaabbababbbbabaabaaaaaaaababaaaaaaaaaaaababbbaabababaaabaabbabbbbabbbbabaabbabaaaabbbabbbbaaababbbbbbaaaaaabbbababbababbbaabbbaabbaabaaabaabaaaaaaabaaaaaaaaaabbabababaabbbaaaaaababababbbabbbabbabbbaaabbababbbabbaabbbbabaabaabaaabbabbbbaaaaabbbaaabbbaaaaaaabbaaaaaaaabbbbbbaaababaaaaababababbbabababbbabbaaaaabbaaabababbbbabbbbbaabbaababaaababbaababaaabbbbbbaabababbbbaaabaabbaaaaaaabbabbbbbbbabababbaabababbbaabbbaabababbababbbbabbaabaaaaabaaaaaabababbabaaaabbbbaaabbbabbbbabbbaabbbbabaabbaaabbbbbbbbaaaabbbbaaaababbabbaaababbababbbababbaaababbaaabbaabbbaaaaaabbabababbaabbaaaababbbbababababaabbabbabbaaabbabaaababababbabbabbbbbbaaaababbbbaaababaabbbbabbbbbbbbabbabaabaaabaabaaabbbbabaabaaabaababbbababbaaabbbbabaaabbaabababbbaaaabababbbbaaabbaabbaaaaabaaaabaaaaaababaababaaaaabbbbaaababbabbabaaaabbbaabaaaabaaaabbabbbabbabbabbaaaababbaabbabbaabbabbaababaabbabaaaabaaaaabbaabbaaabbbbaababbaaabaaabbbaabaaabbababaaababbbaababbbbaaaaaaabbbaaabaababbbabbababaaaabaaabbabbaabababbbbbaababaabbbbbaaaababbbbabaabaabbbbbabaaabaabbbbaaaaabbbabbbaaabbaabbbbaabaabbbbbaabaabbaabbbbbaababaaabbaaaaaaababbbbbbababababbbaabbabbbaabbbabbaaabaabbbaaabaabaababbabaabbabbbaabbababaaabbbbbaabbbabaaaabbabbbaaabbababbabbbbbabbabbaaabbbaaaaababbababbaaababaaaabaaabbabbabaabaaaabaaabbaaabaaababaabbabababaabbaabbbabbbbbabbbabaababaaaabaaaababbababaabbbbaabaabbbbaaabbbbabaabbabbbababaabbbababbaabaabababbaabbabbabbbbbaaabaaaaabbaabbbbaabbaaaaabbaabbabbabbbbbaabbbbbaaabbaababaaaaababaabababbaaabbabbbbaaaaaabbaabbbabaaabaaaabababbaaabbaaabbbabbaabaaaaaabababbaaababbbababaaabbbabaabbabbbabaabbabbbbaaabaaabbabbaabbbaaaabbbaaabaababaaaabbabaaaabbbbbbbabbabaabababaabbbbaaaabbababababaaaaabaabbbababbaabbabbabbbbaabbbbaaababaaaaaaaabbaaabaabaaabaabbbaabaabbababbaaababbaaaabbbabbbaaabaaabaabbbbbbabbabaaaabaaaaaaaaaaaabbaaaabaabababbaaaaababaaaaaabbbbbbaababaaabbbbbaaaaaabbbaaabbaabbabbaaaabaaabbbabbbbaaababaaaabbabbbabbabaabaaaabbbbabaaaababaaaaaabbaaababbabaaabbbbaaabbbbbbbabaabbaabbbbabaaabaababbbbaaaabaaababbbbabbbaabbbbbbababbbabaababaabbaabbbababababaabbababbbabaababaabbbaabababbababaaaaababbbaaaabbbabaaaaaababbabbaaabbabbbbbbaaababbbabbababaababbaabbaabaababbbabbbbaabbbbaabbbabbbaababaaababbbbbaabbbabbabaababbaaaaababbbaabababbbaaaaabbbbaabababababbbaababbababaaababbbabaaababaabbabbaaababaaabaabbbaaaaabaaabbbbabaabaaababaaaaaaabbaababbaaaaababababbaaabaaabbbbaabaabbabbbbbaaababaaabaabababaaaaaabaabaaabbbaabaaabaabbbbbbbbaabbaabbaabbbabaabbababaaaababaaaaabaabbbababbbbbbbbbabbbbabaaabbaababbaabbaabababbabbaabbabbaaababaabababaaabbbabbbabbaabaaaaabbaaaaaababbababbbaabbaabaababaaabbbbbbababbababbbbabbbbaaabaaaabbbbaabbaaabbbbaabbaabbaabababbaabaabaabbabbabbabbbabaaaabbbabbbaabbababbaabbbbaaabaabbaababaabbaaaabaaabbaaaabbaabbbaaabbaaaabbbaabababababbabababbbaaaaabbaabbbbabbaabbbbabbbaabaaababbabababbbababaaabbaaaaababbbabbababbbbaaabbbbbbbbbbaaabbbabaabaaaabbabbabbabaababbbbbbbabbbaabbbabbbaaaabaaabbbaaabaabababaabbbabbabbaaabbbbabbaabaabbbbbbbaaaaaabbabbbbbbabaabababbaaaaabbbbbaaaaabaaaababababaaabaabbbbbaabbbbaaabbbbaabbbbbbbabaaababbbbababbbaaaabbbabaabaaabaabbaaabababbbaabbbbbaabababbbbabbaabaabbbabbabababaababbaabaabbbabbababbaaabaabaaaabbaaaabbbababbbbaababaabbbbbbbbabbabaababbbaaabababaababbaabbbbbbabbbbababaababbbabbbaaaaaabaaaababbbbbabaababbbaabbbaaabbabbaabbaabbbababbabbbbbababbaabaaabbbaabbbbbbaaabbbbababbaabaaabbbababbaabbbbaabaabbabbbbbbaaaabaaaaabbabbbbababbabababaaabbbbaaababbbbbabaaabaaaaaaabbabababbaaabababaaabbabbababbbaabbbbbbaaabababbaaaaaabbaaababbaabaabbaabbabbbababbbbbbbbbbbbaaaaabaabbabaaaabbbabbbbbaabaabababbababaaaabaabbbaaabbabbaabaabababaaaababaabbbbabaaaaaabaaababbababbbaabaabbbbabaaabaaabbbbaaabbbbaabbbbbbbbaababbbbbaabbbbbbbbbbbaaaaaabaaaaabaaabaaababbbbbabbabbaabbababbbbbaabaaaaabbbbabbbbbabbbbbbbaaaabaabbbbabbababaabaababbbababbaaaaaaaaaaaaaaaabbaaabaababbaaabbbaaababbabaababaaaaabababbaaabbaabababbbbaabbababbabaaaaaabbabbaabbaaaaabbbabbaaaaaaabbaabbabaaaabbaaaabbaababbababaaabbbabaabbabbbababbabbabbbbbabaaabababaabbaababaaabbabaaaabbbbabbbbabbbaabaaaabbaabbabbabbabbbbbbbababbbbbbabbaaaababaabbbbbbaabaaaabaabaaabbabbaabbbbbbbababbabaabaabaabbbaaaabbabaaabaaabaaabababaaabbabbaaabaabbabbbbbaabbbbababbbabbbababaaaaabaabaabaaababababaaaabababbababbaabbababbbaaabbaabaabbabbbbaabababbaababbbaaabbabbbabaababbbabbabbabbbabbbbaaaabaabbbaaabaaaabaaaaabaabbbbbbbaaaabbabaaabbaabaabbbbaaaabaabaaababaabbbbaaabaabbabaaaabaaababaababbabbbbbabababababaaaaaaaabbaaaabbaaabaaabbaaabbbabaaabbbbbababaaabbbabbbababaabaabbaaabbbbababaaababaaabaabbaabaaaababaaaaaaaabababbabababababbbaabbababbabababbbaababaaabbbbbaabbabaaabaababbabababababaabbabaabbbabbabbbaabbaababbbbabaaaabbbbabaabbbbbaaabbabaaaabbbbbabbaaabaabbbabababbaaabbaaabaabaaaaabbaabaabbabbabbaabbabaaaaaabbaabbbabbbbbbababbbaababaabbbbaaabbaaaabbaabbaaabaabaaaaababbbbabbaabbaaababbaaabaaaaaaaabbabbaaaababaabbabababbbaabababababaabbbbabbbabaabbbbaaabbaaabbbbaabbbababbbbbbbbabbbbabbaabbbbbbabbabbaabbbbabbaabaaababaababaababaaabaaaaababaaaabaabaaababaaabbbbbaabababaaaabbabbabaaababbaaabbaaababababbbbbbbabaababaababababaabbbabbbabbbbabbabbbbababaaaaaaabaabbbbabaabaaababababaababbbaabaaaaabbabbaabbbbaabaaaaaaabbbbabaabaababaabbbabbaabbbaaaaaababbbbaabaabaaaaaaabbbbbaabbababbaaaabababbaabaabbbbababbbabaabaaaaababbbbabbabaaababaaababaabbbbaababbbbbbaaaabaaabbabbaabaabaabaaaabaaaabababbbaabaaabbaabaaaabbaabbbbaaabaaabbaabbaabaabaaabaaaababaabaaaabaabaababbbbabbbbbaababbaabaaabaaaabbaaababbbbaabbbbabaabbabaaabaabbbaaaabaabaababbbbabaabbbaabbabaaaabbabaabaabbabbabbabbaaaabaaaabbbaaaabbbbbbbabbbbabbbbbabbbaabaaaababaaabaabaabbabbbaaabbaaaaaaabbaababaaaabbbabbabbabbaaaaaababbabbaabbabbaaaaabaabbaaababbbbbaabababbbbaaabaaaabbaabaabbbbbbabababbaababaaaaabbaababbaabbbabababbbaababbbbababaabbabbbababaabaaaabababbbabaaabbbabaaababbbaabaaaabbbbbbabbaabbbaaaaabaaaabaabababbabbbaababbbbbabbbbaabaaaaababaababbabbbbbababbaabbabbbaaaababbbabaababaabbabaababbbaabbbbbbabbbaabbbababaabaababababbabaaabbaaaababaaabaabbaabbbabbabbaababaabbaababbbbbaababbaabaabbbaaaabbababaababababaabaabaaaaaaabbababaababaaabbbbaaaababaaabbaaabbbabbbabbbbabaaabbabbbaabaababbbaaabbaaabbbbbbaababaaaabbabbababaabbbbbabbaabbbaaababbbbbabaabbababaabbaabbaaabaaabbabababaaabbbaaaababbbaaaaaababbaabaaaababaaaaababaababbaaaaabbbbaaaaaabbaaaabaabbbbbbbabbaabbbbbabbababbbbbbaaaaababbaaababbaabbbabbbbabababaaaabaabaaaabbbbaaababbabbaabbbbbbabbabbbbbbbbbbabbabbbaabababbbbaabaabaababbaaaabbbbababbbaabaabaaabbbababbaaabbaabaabaaabababbabbabaabbbbbbbabaaababbbbaaabbaaabaabbabbababbabaaabbabababbaabbabbabaababbbbbbbbabbbbabaaaabaaaabbbbaabaabaaabbbbbaaaabaabbabbabbaaabbbabbabbaabbbbbbabbbababbaaabbabaababbabbaababaaabbbaabaaaaaaabbbbbbbbaaabbaabbaaaabbaaaabbaaabaaaabbbbababbbbaaababbbaababbaabaabaaabbbbbbbaabbaaabbabbbbaabbbbabbabbaababbabaaabbbbbbaabbbaaabbaaabaabbbbbbaaabaaaaabbbaababbababababaabbabbbaabbbbbbabababababbbbabbaabbaaaabbbabbaaabbbbbbabbaaabbbbaaaabbbabbbaaabbbababbaabbabbabaabbaaaaaaababbbbaabababaaabbbbbbaaaabaaaaabbaabbbabbbaaababbbbaabaabbbaabbabababbbbbabbaaabbaabbbbbbabbaabaabbbbabbbbaababaabababbbbaaaaabaabbbaabbaaaaabaaabbbaabbbabbaababaabbbabaabbbaabbbbabaaabbbbaaabbbaabbaaaaabbbabaababababaabbaabbabaabbaabbaabababbbaabaaabbbbababbaabaaababbbbbaabbbabbaaabaaabaababbbbababaababaabaababbbbaabbaabaaaaaaaaababbaaaaaababaaabbabbaaaaabaaababbbbbbbabbbbbabbaabbbaabbaabbbbbaaababaababaaabaababbbabaabbbabbbabaabbbbbbbabbaabbaabbbabaaababbabbbaabbaaaabbaabbababaaabaaaabbbbabbaaaabaaaaaaaabababbabbbabbbabaaaabbbbaaabbbbabaaaabbaabaabbabbbbbbabbbabbbbabaaaaababababbabbabababbbabbabaaaaaaaabbbbaaabbabaaababbaaababbbaaabaabbabbaaaabbabababbbaaabaabbaabaabbabaaabaabaabaaaabaaaabaaaabbbbbabaaabababbaabbbabbababbbbaaaabaaabbabaaabbaaababbaaaababbbaaababaaaaaababbbabbbaabbaabaabbaabbbbaabbbbababbbbbbabbbaaaabababaabbbabbababaaabbaaabbabbbababbbbaaabaaaaabbbbabaaaaabbabbbbbaaabbbabbaabbbabbababbababbbabbbbbbbbabababbabaabaaabbababababbaaaabbaaabaaaababbabbaabbabbabaaaaaaababaababbaaabbababaaababbbaabbbbbbbbbbbbbbaabbaaaabaaabbababaabaaabbabbbaaabbaabababbbabbbbaabaabaaaabaaaaaaaabababaaaabaaababaababbbbaaabbaababaaaaaaabbbbbbaabababbbbbabaababbababbaaaaaabababaaababaabaaabbbbababbaaabaaabababbbbbbaaabababbbbaabbbabaaaabbbabbbaaaaaabbbaaaababbabbbbaaaabaabbbaabababbbabaabbbaaaabaaabaaabbbaaabaaabbabbabbbababbbbaabbaababaabaababbaabbbabaaabbababaabbabbabbababaabaabababbaaaabbbaaaaaabaabaaababaaabaabbbbbaabbabbbbabbbbbaaaabbbaaabbabbaaababbbbbbabbabababaaabbbaaabaabbabbbaababbaaaabbabaaabbaabbabbbbbbabbbbabababaabaabbbabbbababbaabbbbabbaaaababbbbbbaaaabbbbbbbaabbaaabbbbbaaabbbabbbbababbaaabaaababbbaaabaabaaaabbabbbaaabbbbaabaabaabaaabbabaabbbaababbabbabbbabaaaaaabaabbabbaabbaabbbbbabbaabbbbbaaabbabaabbaabaababaabbabbaabbaaaababababbabbaaaabbbbaabaabbbabbabaabaaaaaabaababbbabaabaabbbbbbbbababbaababaaabaaabbabbaaababbbababaaaabaabaaaababbbbabababbaababaabbabbaaaaaabababbbabaabbabbabbaabaaabbbaaabbbaaababaaaababaababaababbbbababaaaaaabbbbbbbaaaabbabaaaababbbaababababbbbbbababbabbaaabbbbbbaaabbaaaaabbaabbaaaaaabbbbbbbabbabbabbaabaaabbabababaaababbbabaaaaaaaababaabaababbbbabbaaabbaabaaaaaabbababbaaabababbaabbbbabababbabaaabaaabababaaababbbaabbabbaababbbaabbbaaabbbbababbaaababaabbbaababaaababaaababababababbbaabbaabaaabaaaaaaaabababbabbabaaabbbaababbaaaababaaabbbbababbbabaaababbabbbaabbbabbbaabbabaaabbaabababababbababaaaabbaaababbabbbaaaabaababbbabbabaaaaabbbabbbaababaaaaaaaaaaaaabbbaaaabbbbbbaaaabbbbbbaabbbaababbbababbbbabbbbbbabbaaaaabbaababbaaaaaaabbbabbbababaabaaaaabaabbabbabaaaaababaabbaaabbaabaaaabaabbbabbbbbaaaaaabbabbaabbaabbabbababaabbabbaabbbbaabaaaabbbbabbbababbbaaabbabaababbbbbaaaaabaaabaaaaaabbbbaabbabaabbbbabbabaaaaaabbabbaaabaabaaaabbababbbbbabbbbaabbbaaabababbaabaaabbbaabbbabbaabbaabababbababaaabaababbabaaaabaaabaababaaaabbabbababbaabbbbbbaaabaaaaaababaabbbaabbabaabaabababbbbababbbbbabaabbbaaababababbaabbbbbaababaabaaaaaaaaababbbabbababbbabbaaaabbbbbbbbabbabaaaabaabaaaabbbbbabaabaaaaabaababaababbbabaaabbaaabbbaaaabbabababaabbabaabbbbabaabbbbaabbbabaabbabbbbbabaabbbbbbbbabaabbabaabaaabaaaababaabbabbbbbababbbaabaaabbaaaaaababbaaaabaaaabbbababbbbabababababbaabbaababbbbabbaaabbbaaabaaabaabaaaababababaaaabbbabbbbbaabaaababbaaabbabbabaaabbaaababbbbbaabbaabbaabbababaaabaaabbabbabbbaabbbbaabababbbaaababababbaabbababbaabbababbbabbbbabaababaabaaaaaaaaabbaabaaababaabbaabbabbaabbbbbbbababababaaaabaabbbabbbabaababbabbbbabababbaaabaabaaababaabbbaaaaaaaaaaabbbaabbbbbbbabbaabbabbabbbaabbaabbaaaaaabbabbabaaababbabaaabbaaabbababbbabbbbaaabbbabbaaabaaaababbbababaaaababbabbabaabaaaaabbaabbaabbaaaaaaaaaaaaaabaabababbaababbaaabbbbaaaaabaaabbbaaaabaabaabaababbbaaaaaababbaaabbababbababaaaabbbaaaaababaaaabaaabaabbababababaabbaabaabbbbaabbabbaaabbaabababbbbbabaabbababbabaaaabaaaaabaaabbbaababbaabababbabbbabababaabaaaaaaabbbabbaabbbbabbbaaababbaaabbaababbbbababaaabbbaababbababbaaababbbabbaabababbbababaabbbaaabbaababbbbabbabbbaaabababaaaaaaabaaaaabaaabbaaaaaaabbababbabbbaaaaaabaabbbbbbababbabbaabbbaaaaaaaabaabababbabbbaaaabaaaabbabaaaaaabbbaaaaabbbaabbbbaababababaabbaababbaaabbabbabaaaabbabaabbababbbabaaababaaabbaabaaaababbbaabaaabbbbbbaabbbbaaabaabbbaaabbbbaababababaaaaabababbbabaaaabbabbbaabbbabbabaabbbabbbbaabbbabbabbbaaaaaababbaaabbbbbbbbaaabbaaaaabbaaaabbbbaabbaaabbbaabbbbabbabaabbaababbbababbabbaabbaabababababbabbbabbbaaabaabbabbaabbaaaababbbabbbaaaabbbaaaaaaaababaabaababbaaaabaaababaaaabbaaababbaabbbbbbbbabaabbabaabbbaabbbbbbbabaaaabababaaaaababbbaaaaaaaaaabaabbaaaabbbbbabbabaabbababbbbbaababbaabaababbbbaabbbbabababbaababbabaabababbbaaaabbbabaaabbbbabbbaaaaaaaaabaaaababaaabababaabaabbbabbaaababbbabababbaaabaababbaaabbbabaabaabbabaabbaaabbaabaaaaaaabbbabbaaababbbbbbaabaaabbaabaaaaaabaababbbaababaabababbbabaaabaaaababbaabbababbabaaabaaaaaaabbabaaabbaabbbaaabaababbbabaaabbbbababbaabbbbbaabaabaabbbbbbaabbaabbbbabbbaaabbabbbaaabbbabababbbbbabbbabaabbabbabaaabbbbbaaabaabbbbbabbbbaaaabbbabbaabbabbbbabaababbaaababaaabbabbbbbabbabaaaaababbaabbababaaabbaaaaabaaabbaaaabababaaabaabbbaaabaaabbabaaabbbaaababbbabbbbaaaaaabababbaabbbabaaabbbaabbbbbbabbbbaaaabbabbaaababababbabbabbabaabbbbbabaabbababaabaabaabbbbabaaabbbabbbaaaababbbbbaababaabaababbbbababbaaaaabbbaaaaaabbabaabbbbbbbbbabbaaaabbaabbabababaabaaabbbabbabbabbbabbaabbbabbabbabbabbabaaabaaaaaabaaabbbabaabababbbbbbaaabaababbaaaaaaaaaababbbbbabbababaabbbbbbabaaababbaaaaabbbaaababaaabaabbaabbaaaabaababaababaabaaaaabaabbbaabaabbbbaaaaabbbbabaaababbbabbabaaabbbbbaaaaaababbabaabbbaaaababaabaabbbababbabaaaababbbaaabaabbababbbaabaaaabaabbaabaaaabbaaaababbaaabbaabbababaabbaabbbaaabbbbaaaaaabbbaaabbbababbaabbababbbaaabbbabbaaabbaababbababbaaaabbaabaababbaaaaaaaabbaabaabbbbaababbbabaababaabbabbbaaaaaaababbaaaaabbbbababbaaabbaababbbaaaaabbbabaabaaababaaabbbbbaabaaabbbabbaabbaaaabbabababbaaaabbaaabaaabaaababbaabbbbbabababbababbbbabaabaabbabaaabaaabbbaaabbbaababbbbbabaabaaabaabbbbaabbbbbaabbababbbbbababbabbbbaaaabaaabaabbababbbbaabaaaaaaaababbaabbbaaaaaabbabbaabbabbbababaaababaabbabbbabaaabbbbbbaaabababaaabbbbbbaabbabbabbbaaaabaabbabababbabaaabbbbbbaaaabaaaaaababbabababaabaababababaaaabaabaaaabbaaababbabababbbbbbaaabbbbbabbbbbabaaabababbababbaabbabaababbabaaaaaaabbbbaaaaaaaaaabaabaaabababbaabaaaaaaaaabbaabbaaabbaabbbbbabaabbaaaaaabaaaaaaababbbbabbabbabaaabaaababbaaaabbbaaaaabaaaaaaaabaabaababaabbabbaabbbbababaaaaabbbbaaabbbbaabbbbbbabaabaaaaabaabbaabaabaaabaaaaaaababaaaaabbabababbaaaabbbbbbaabaabbbbbabbabaabbaaaabaaaaaaabbbababaabababbaabbabababababbaaabbababbabbaabbbaaababbaaabbbabbbbaababaaaaaabbabbaabbbaabaaabaabbbbbabbbbabbbbabaaaaaababbabaabbbbaababbbbbbaabbbabbaaaaaabaaaaabaabbbbabaabaaaaaabbabbabbbbabababbaaababbaaabaaaabbababaaababaabbabbbbbabbbabbbbabbaaaabaababaaaaabbaaabbbbbbbababbbabaabbbababaaababbaabbaabbababbbbbabaabbaababbaabaaaabbababbababbbaabbabbbabaaabbbaabbbabbaaabababbaabbababbbbbbaaaababbabaababbbaaaababaaabbbaabababbbabbbbbaabababbaabbbbbabbabbbabbaabbaaaaaaabaabaabbaabaababbaabbaabbabbbbbbbabbbbaaabaabaaabbaaabaabbaaaababbabaabbabaabbabaabbabbabbbaaaabbbaaaaaabbaabaabababbabaaaaaaaabababaabbabbbbbaabbbababbbaaabaabaabaabaaaabaabbaabaabbababaabbaaabbabaaaaaaaaaabbbbbbbbbbbaabbbaabbaaaabbabbbaabaabbaaabbabababaaabababbbaaaaaaabbbabaaabbabbabbaaababbbbabbabbbbabbbaaabbbabaabbabbabbabbababbababbaababbbabbbbaaabbabaabbaaaababaabbaabbbbbaababbaaaabbbaaabbbabbbaababbabbbababbaabbbabbabbaaabbbbbbbaababbbaaabababbbaabaaabbbababaaabbbbabbaabbbabbbaababbbbaaabaaabbbbabbabbbbaababbbbaabababbabaaabbbbabbabbbbbababbabbbbabababbbbabaaaaaaabaaabbaabaabbbaaaabbbaaababbabbbaabbaaaababaaababababaabbaaabbababaaabaaaabbbabaabbaaabbaaababbbabaaaababaabbababaabaaabbabbbaaaababbaaabaaabaaaabbbbbababbababaabbbbaaabbaaaaabaaaababbbbbaabbaaaabbabaabbaaaabbbbbbbbbbaaaaaabaabbbabbbbbabaaabbbbbaabaabaabbbabbabbbbbabaaaaaaabbbaaaaababbabaaaaabbbbaabaaabbaaababababaabaaaabababaaababababaaaaabbabbbaabababaabaabaabbbabbaabaaaababbababbbaabbabbaabbbbbbaaaabbbbaabaaaababaabbbabaaabaaaaaaabbabbbaababababbabbababaaaabbabababaaaabbbbbbbaabbbbbabbbabaabbbbabaabbbabbabbaaaabbabbababbaabbabbaabababaaabaababaaaabaabbbabaabaaabbbbbbaaaabbabbbabaaaabaabbbbbbbbaabbbaaabaaababbbbbbaaabbaabbbaabbbbaabaababbbbaabaabaababbabaaababbbbbbbbababaababababbbaaabbaabbabbabbbbabbbbbbbbababbaabaaaabababbaabaaaabbbaabaaaaaaaabbbaabbaabbbbabbbbababbaaabbaabbababbaababaaabaaaabababaabbbabbabaabbabaabaaaababababaaabbaababbaabbbbbabbbbaaabbbbbabababbabbaabbbbaababbaaaabbaabbababaabbaabbababbbbbbbababaaabbbbaaaaabbabbbaabaabaaaaaabbbabbbbaabbbabbabbaaabbbbaabaabaaaaabaababbbaaabaaaabbbabbaaaababaaaabaaaabbaaabbaaaababbbababababaaaaaabaabbaaaabbbabbaaaabbaaaabababaabbbbbbaaaaaabaaabbbabbababaabbbbabaaaaabbaabbbbabaabaabababbbaaaababaaabbbabbabbababbbbbbbbbbabbabbaabbbababbbabbabaababbbababbbbbbaaabbababababbaabaaaabaaaabaaabbbabbbbaaaabbbaaabbbabaaaababbaaababaaababbaabbabbbbbaaabbababaaababbbbabbaaabbababababbbbaaaaababbaaaaaaaaaabaaaabaabaababaaabbabbbbaaababbaabaaabaababbbaaaabbaaabaababaabaaababbabababbbaaaabababbbbaabbabababbbbbbbaaabbaabaaaaaaaaaaaabaababaaabbabaaaabbbaaaaabababbaabbbbaaabbababaaaaabbbbaababbababbbbabbbaabbbbabaabbabaabbbbbaaabbababbabbaabbbaababaabbabbbbbbaabbbbbabababaaaabbbababbaabbababbbaababaabaababaaabbbbbbaabaaabbaabaaaabbbbbbababaabababaabbabbbabbaaabaaabababaaabaabaabaaabaabaaababbbababaaabaabaabbabaabbbbaabbabbaaabbbabbabaaaaaabaabaaaabbaabbabaabbaaaabaabaaaaabbbabaabbaaaabaabbbbbbabababaaababaaaabaabbbaaababbabaaaabaaabaaaaabbaabbbabaaaaaaaabaaaabaabbbbbaabbbbbaabbbbaababbbababaabbbbbbbbbababbbbbbaaababbaaabababbbbbbbbbbabbababbaaabbbabbabaabaabbaaababbbabbababbaaababaababaaabaababbaaaaaababbaabaaabbbababbababbaaaabbaaabbababbbbbbabbbaababbbbaaaaabbbabbabbabababbbabababbbaabaabbabbabbbbaaaaababbbbbabbbabaaabbabbbbbbabbbbbbbaabbbbbbbbaaababaaabaabaabaaabbaabbaababbbaaaaabbabbbabaabaaaaabbbbbaaabaabbbbaaaababbbabbbaaaaabaabaaaaaababbbbbabaaabababaaabbbbabaaaabbbabaaaabaababbaaabbbaaaababbbabbabaabbaaaaaababaaabbbaabbbabbbaaababaababbabaababbbabaabababbbaaabbbbaaaabbaaabaaababbbabbbabbbaaaabbabbbaaaaaaabbabababbbbbbbaabaabbaabbbabbbabbabaaabaabbaababbbbaaabaababbbbabbaaababbbbababbbaabaaaaabaabbbaaaaabbbabaaabbaabaaabbbbaaaababbbaababababaaabaabbabbaababaabbbbaabbbbaaabbaabaaaababaaabaaabbbaaaaaaabbbbabaaaabbbbaaabaaaaaababbaaaababbabaabbaababaaabbbbababaaaaabbabbaabaaaaaabaababaaaabbbbabbbbaaaabaabbaababbaabaaaaaabaababbaabaaaababbbbaaabbbbaaabbbbabbabbabababbaaaabaabaabbabbabbabbababbbabbbbbbababaaababbbabbbbabaabbabbbabbabbababbabbbaaabbababaabbbbbaabbaabbabbaabaaaabaabababaabbaaabbaabbaabbababaabbbbaaabaaababababbbbbbbbabbabaaabaaaabababaabaababbabaaabaabbabaabbaabbabbbaabaabbabbbabbaabbbaabbaaabbbbbabbbbbbaaabbbbabaabbaaaaaabbbbbbbbaaaaaaaaababbababbabbbababaaaabaaaababbaabbaaabbbabbbbaaabbbaaaabbbababaabbaababbaaaaabbabbaaaaaabaabababababbbbaabbababababbabbabaaaabbabaabaababbbabbbbbbbaabbbaabbabbabbbbbabaaabbaaaaaabbbabbaabbaaababbbbbbaaaaaaabaaaaaaaaabbaababbbaaabaabbabbbbaaababbbbaaabbaaabbbaaaaabaaabaabbabbaababababbbbaaabaabbbbabbbbbbaaababaaabbbbbabbbbaaaabbbbbabbabbbaabbbbabbabbababbaabaababbaabaababaabbabbaaaabbbbbabbbabaaaabbabbbbaaaabbbabbabaababaaabbabbabbbbaabaabbbaaabaabbaaaaabbbbabbabaaaabbbbbaabbbbbaaaabbbabaaaaabbbbbababbabbbbabaaabaaaababaaabaaabaaaabaaabaabaabbababababbbbbabaaaabbbbaabababbabaabaabbaabbabaabaaabaaabbbaabaaabababbabaababbabababababaaaabbaaabbababbaabaaabaaabbbaababbaabaabbbabaabbbbbbabbaaababababaaaaaabbbaababbabbbbbbabbbabbbababbabbaaabaaabaaaaaabbbaaabbbbabbababbaaabaabbbbbabbbbaababaaabababbbbbabaabaabaabbabaabababbbabbabbbbaabbbbbaabbbbbaabbbbbabbbbbbaaaabbbbbbbbbbabaabbaaabababbabbbbabaabaaaabbbabbaaababaaabaaabbababaabaabaaabaabbbbbaaaaabaaabbaaabbabbabbabbbbbbabbbaabbbababababaabaaaabbaaabaaaaaababbbbabbbbabbbbbabaaaaaababababbaaabbaaaabababbbaabababababbbaabaabbabababababbababababbaabbaaaaaabbbbaaaaababaaabbaaaabaaaababaabbbabbaaabaaabbbbbbaaabbaabbbbabbaabaaabbabababbaaaaaabaaaababababbaaaaaaaaaabbaaabbabaabbbbaaaabaabbaaabaabbbababababbbbabbbbababaaaaaabbabbbabbaabbabbbbabbababbbbbbbbaaaabaabbbbaaababaabbbbabbbaaaaaaaabbaabbabaaabbbbaababaabbbbaabababbbbbabaaababababaababbaaabbaaaaaabababbabbbbabbaabbaaaabbbbaabbbbabbabbabbaabbababbbbbabaaaaaabbababbbabbaababbaaabaaababaaababbbbbbbabaabaababbaababaaaaabbbbaaaabbbabbbabbaabbababbbababaabbbaaabbababaaaaaaabbaaabbaababbaabbababaaababababbbaaabbabbbabaaaabaababbbabaaaaabbaaababbbaabbbbbaaababababbbbababaabbbbaabbaaabaababbaababbbababaabbabbaabbbbbbbbababababababbbaabaaabaaababaabababbaabbbbbaabbaaabbbabbbaabaabbbbaababaaaabbbabababbbaaabbababbabbaabaabaabbbbaaabaaaaabbbbaabbaababababbaaabbababbbbaaababbbabbaabbabaaaaabaabbbbbbabababbabbaaababbaabababaaaaabbbbbbabbababbaabaaabbbbbababababbbbbbbbbbbbabbabaabbbbbaaaaaabababaaababbbaabbaaaababbbaabbababbbbaaababababbbabaaabbaabaabbbbbaababababbbbbaaabbbabbabaabbbaabaabbbbaababbabbaabaaabbabababbabbbbbbbbbbbabbbbabbaabaaaabbbbaabbabaabbbbabaaaaaabbabbbbbbbaabbabaabbbabbabbbbbbabbbabbabbabbbbbababbabaaabbaabaaaabbaabbaabababbbbaaaaaaabaaabbababbbbbbaaabababababbbbbbaabbaabbabbbbaaaabbaaaabaaaaababaaaabbbababbababaaabbaabbababbaabbbbbabbababbabaabababbbaabbabaaabaaaababababaaaaaabbaabaaabaabbabaaabaabaaaabbbabbabbbabaaabbbaabbbaaaaaabbaabaabaaabbaaaaabbbbbbabbabbbabbbabaababaabbaabbbbaababaaabbaabbabaaabbbbababbbbbaaaaababbbaaaaaabbbaaabbbbaabaabaabbbbaaaaabbbbbabbaabaabaabbbbabaaaabbaabaaabbaababbabbabbaaabbabbbababbbbbaaababaabaaabaaaaabaababaabaabbaaaabbaaaaabbbaabaabaabbbaaabaaababbbbbabbbbbaabaabaabbbabbbaababbabaaabbabaaaababbaaaaaabbbbbbbbaabaaaabbaabaababaaaaaabbabbbbabbbbaababbaabbaaaabbbababbbabaabaaabbbbbabbaaaaabbabaaaabaaaaaabbbaaaaaaaabbabbbaabbbbbabbbaaabbaabbaababbabbbaaaaaabbbabaabbbbbbaabbbaaababbabaaaabbbaabbabaaaaabaaabaaaabaabbbaabbaaababbababbbaaabbbbbabbbaaabaaabbbaabaaabbbbbabaabbaaaabbbbbaaabbbbaaabbbbbabbbbaaaabbbabbaaabaaaaaabbbbabbaaababbabaaababbbaaaaaabbaabbbbabaabaabbbbabbbaabbbaababbbaabbababbbabbbabbbaaabbabbaabaaaabbabbbbbabaaabbababbbbabbbaaabaabbaabbbbabbaaaaaaaabababbbbabbaaaabbbababbabbaaaabbbaababaababbbaaaaabaabaaabaabbbbaaabbaaabbababbbaabbbaabbaaabbabbbbbabaabbaabaaabababbbabbbbbbbbbabbbbbaabaabbbbbaaaabababbaaaaaabbabbabbbbbbaaabbbbaaabbbbbababbaabbbbababbabbbabaababaabbaaaababaabbbabbaaabbbbaabaaabaabbbbbaababaaaaaaabaaaababbabbbabbaabaababbbabbbbaabaabaabbabbbbaababaabbaabbabbbaababbabbbbbbbababbbaaabbbbaaabbbbaabbaabbbabbaaabaaaaabbbabaaaaabbbbbbabaababaabbbbaababaabbbbbabbbaababbbabaaaabaaaabbbbabbabbbbbaabbabaaaaaabaabbaaaaaabaaabbaabaaabbaabbabbabaabaaaabaabaabbbbbbbbbaaaaabbbbaabababbababbbbaabbbaaaaabaabbabbabbaabaabbaabaabaaaaaabbaabaaababbaaabbaaaaabaaababaabababaaaabababaaaabbabaabbbbaaababbbabbbaaababbabbaabbbabaabbabbbbbabababbbbababbaaabbaabaaababaaababbbbaaaabbabbbaabaaabaaaaaabaaaaabaaaaaaabbbabbbbaaabbabaabbabaaaaaabbaabababababaabbaabbaabaabbbabbaaabbababaaabbbabbbbbbbabaabbabbbbaaabaaabbbababbbbaaabbaaaaaaaaaaabbaaabbbaaaaabbbbaababbaabaaabaabaaaaaabbbbbabbbbbaabaaaabbbbbabbbaaaabbaabbaabbbbbaabbbbbaabaaaababaabbaaabbaabbaabaaaabaaaabaababbbbbbbbbaaabbbaaaabbbbabbbbbbbaaabbbbaabaaaababbababababababbaaaabaaabbbbbbababbababbabbbaaabbbbbaaaabaabaaabaabbabbbaaabaababaabaabaabbbaaabaaaabaabbbabbabaabbbbbaaaabbbbbbaabababbbbbbbabababbbbbbbabababaabbbbabaabaabaaaabbbbaaabaabbbabaaaaaaaaaabbbbbabaaaaaaaababababbbbababbaaababbbabababbbbabaababaabbabaabaabbaaabbabaaababaaaababaaaababbaabaaabaaaaababaabaabaababbabaaabbabaabaabbbbbbaaabbbaabababaabaaabbbbbbbabbabaaababababbbaabaabbaabbbbbaabbbabbbbbbbaaabababbbbabaababaabaabbababbbbbbabbabbabbaaabbbaababaaaabaaaababbbbabbaaaabbbaabbbbbbabbbbbabababbaaaabbaababababbbbbaabaabaabbbbbbabbbbbaabaabaaaaabaaabaaaabbbbbbbabbbbaabaaabaabaabaaabababaaabbabaaababbbbaabbababaabbaababbaabbabaaaabbbabaaaaaaabbabbbaaaabaaaaaabaabbbbbaabbbababbbababaaaaaababbbbbababbbbabbbabbbbbbbbabbbabaababbbbbaaabaabaaaabaaaabbaaabbabbabbbabaabbbbaababbabaaabaaaaabaababaaababaabbaababbabbabaaabbabaaabbaababbbbabaaaaaababbabaaabbbbabaaabaabaabbaabaaabaaabbababbababbabbaaabaaabbbaaaabbbbbbbaaaaabbaabbbbbbbaaaabaaabaabaabbaaabaabbaaabbababbaaaaabbbbbaabaabbbbbaabaabbaabbbbbabbababbbaabbbbabaabbababaaaabbbbababbbaaabaaabbabababaabbbaaabbbababbbababbbbabaabbabbbaaaaaaaabbaabbaaaaabbbbbbbbababbbabaaabbaabaabaaabbbbbbbbbbaaabbbaabaaabbabbbbbbababbabbabbabbbbbbaabababaabaaabaababbabbaaabbbbbaaabaaaabbbbbaaaababbbabbbaabbaabaabbbbabaaababbbabbbabaaaaaaaabbaababaaaababbbaabababababbbbbbabbbaaaabbbbbbbaababbaabababaaababbbaabbaabbbaaabaaaaaaaaaabbbbbabbbbbbababaababbbaaaaababbbbaaabbabbbbbaabababbbbbabaababbaabababbaaabbaaabaaababaaaabaabaabbaaababaaaababaaabbbbaabbabbabbbabaaaababbaabbaabaaaaaaaababbbbabbbaaaabababaabaabbabbaaabbabaaabaaabbaaaaabaabbababbbbbababababaabbabaabbbababbabbbaaaabbbabbaaabbaabaabaabababbbbbabaabbbbaaaaababbbaaaabbabbaaaaababaaaabbbaabbbaaabaabaabbbababababbaaababaabaaaaaaaabaababbbbbababaabaaababbbabbbbaabaaaabbbaabbbabbababbabbbbabaaabbaaabbabbbbbabbaabbaabbaabaaaabbaabaabbbaabbbaaaaabaaabaaabbababbbaabbaababbaababbbbbababaaaaabbababbbbabababbabbabbabbbbababbbbbababbbaabbabbababbbabaaaabaaaaabaaaaabaaaaabbbaabbabababababaaaaabbaaaabaaaaabababaabbbbbbbbbbaababbbbaababbaaaaaaabbaaaaababaaaaababababbabbbbaaaababababbababaaaaaabbabbbababbaabbbabbbbbabbbaaabbaaaaaabbaabbbaabbaabbbbabaaabbaabaabbbbabbbbbbbbaabbaabaaaababbabbbbbbabaaabbaaaabaabaaaaabbaababbbabbbbaabaaaaabbaaaabbabbbabbbaaaabbaababaaabaaaabbabbabbbbbabaababaabaabbaaabbbbaabbbbabaaaababaabbabbbbbbbaaabbbbabaabbaabbbbbbabbabbbbbaaababbabaababbbbaabaabbbbabbaaaaabbbabbbbbabbbbbaababaabaababbbaabababaaabaabaaabaaaaaabababbbaabbbabaaaaaaaababbbaaababbbbbbaabbbaaaabbababaabaaabbabbaabbabbaaabbbbbbabaabbbabbbaaaababbabbbabaabbabaabbbbabbbbbaaabbabaaaaaaaababababaababbbaababaabaabbbbaaaabaaaaabbabbababaabbabbbbbbaaabbbaaaabbabbababbbbaaaababaaaaabbabbabbbababbabbabbaabababbabaaababaababbbaabbaaabbbbaaaaaaaabaababbbabbabaabaabaabaaabbaabbabaaaababababbaaaaababbbaaaababbbbaaabaabbabaabbaaababbaaaabbbbbaaaaaaaababaaabaaabbabbbbababbbaababaaaababbbabaaabaaaababbaaaaaaaaabbbbbabaabaaaaabaababaabbaaabababaabbbbbbaababaabaaaaababbaabaabbaaaaaabaaabbbbaaababaababbaaabbbaabbaaababaabaaaaaaaabbabbbaabbbbabbaaaabbaaaabbabbaaabaabaaabbbbaabaababbaaaabbababbbbabaabaaaabaababbabbaabbbabaabaaaaababbbbbbabbabaaabbbbabaaaaaabbaabababbabbbaabbbabbbbaaabaababaaabbbaabbabababbbbbbaabaabbbaababababbabbababaaabbbbababbbaaaaabbabaababbbabbbbbbabbabaaaaabbabbbbbbabaabbabababbaaababbbaaaaabaabaaabaabaaabbbabaabbbabaabbbaabaaabababaabababbbabbbbabbbaaabaabbaaabababbbbbbabbaabbabaaababaabababaaaaaaaaabbaaabababaaabbbababbbaaaaaabaaaababbbbaabbaaabababbbbbbaabbabbabbbabaaaaaaaabaabbaaaabaaaabbbbbbbabaabbbbababbababaabbaaaaaabbababaaaabaaaabaabaaabaabbababababbbaaaaaaabbabbaaabbbabaabbaaaabaaaaaaaabbbabbabaaaaabbaaaabaabbbbaabababbbabaabbbababbababaaababbababbbbaaaababbaabbbbaabbababaabbaaaaaababababbbaabbababbabaaabbbabaababbabaabababaaaaaaababbbbbaabbbbbbbaaaaaaaaaabbaaabaaaabaabbbbaaaabbbabaaabbbabaaabbbbaabbbbaabbbbabbbbbbbbabaaaabaaaaaaaaababababbbbbbbabbbabbbbbaaabababaaabbabbababbbaaabaabbbbbabbbabbabbbbbbaaabaababaaabaabaabbbaabbbaabaabbbabbaaaababaabaaababaaaabbaabaabbbababaaaaaabbabaaaaabbaabbaaaaabbbbbbaabbbbaaaaaaaaababbbbabaaabbaaaaababbbabbabaaaabbabbbbabbabbaababbbbabbabbaaabaaaaabbaabaaaaaaabaaaabbabbbaaaabaaabbbbabaaabbaababbbababbbaaabbababaaaabbabaaababbbaaabbaaabbabbabbbbbabaabaaabbababaabbbbbabbbbaaababaabaababaaaaabaaaabaaabbaaaaabbababbaabaabbbaabaabbbbaababbababaaabbaabaabbabbaabaababbaaabbbaabbabaabbababbaaaabbbaaaabababbaaababbbbbbbabbaaaaababbbaabbaababbaaabaababbabbbaabbbaabbabaabbabababababaaabbaaabbbbabaabbabaaaaabaabaabaaaabbaabaaabbbabbaabbbbbbbaabababaabbabaabaabaaababaabbabbbbbaabbabbabbbabbaaaababbbabbababbaaabaabbabbbaaabbaaabbabbabaaababaababbaababbbaaababbabbaaabbbaabbbbbbababababbbabaabaaabbabbaaaabbababaabaaabbbaaabbababababbaabbbababbbabaababbbbababaabababaaaaabababbabbbaabbbbbabbbbabbabbabbabbbabbbaabaaabbbbaabaaabbabbaaababaabaabbabbbaaaaaaaaabaabaaabbabbbbbaabbabbbaaaaabaabbbbbbbbabbbbbabaaaabaababbaaabbbbabbabbabaaababbaabaabbabbaabaaaabbbbbababbbbbbaababbababbaabbaaaabaabbaaaabaabaaabbbbbababababababbaabbbbbabababbbabbaaababaabbbbabababaabababababbaabbabbaabbaaaabbbababaabbbbabaabbabbbbbaaaababbbbbbaabbbabaabbbbbbbbaaababbabbbbaabaabaaabbbaabaaabbbbabbaabaabababaaabaabababbbabbaaaabaaaabababababbababbbbababbbabaabaaabbabbabbbaababbabaaabbabbbbaaaaaaabbbaaabaaababbaaaaabaabbbabbbaaabaabaaaaaaabbaabbaaabaaaaabaababbaaaaaabbaababaabbabbabaaababaabbbabaaaaabbbabaabaaaabaaaaabbabbabbabbbaaababbbaabaaaababbabbaaaaaaabbaababababaaaaabababbaaababbabaababbaaababbabaaaaabbababbaabaabbaaaabaaaaaaabaaaabababaabababaaabaaaababaabbbabbabbabbaaaaaabbabaaabbbaaaabaabbaaabbabbbbabababbbaababbaabbaabbbbbbabaaaaaaababaaababbbbbbbbbbaabbabaaaaabbbaababbbabaabbaaabbabaaabaaabbabababbaaaabababbbbaaaaaaaaaaabbbabbbbbababbabababaabbbabbbbbaaabaaabbbbababababbbbababaaabbbbbbabbbbabbaabaabaabaaaaabbababababaaaaaaaabaaaababbaabbaababbbbaabbbabaaaabaabbabbbaabaabbabbbabbaaabaababaabbbbbaaabaabaababababbababbbaaaaaaabbababaabbababbababbbaaababbbaaaababbbbaaabaabbbbbbbabbaabaababbbbaaaabaabaaabbabababbbbaabbaabaabaabababaabbbbbbbbaabbaabbbbbaababbabbabaabbbabaaaaababaaaabbbaabbbaababbbaaabaabbaaaaaabbababbbbaabbaaabbbabbbaabaabbabaabbaabbbbaabaaaaabbbbbbbaabaaaaabaabbabbaabababaabbbabbaabbaaabaaaabaaaabbbbbaababbabbabaabaababababaababbbbabbaaabaaaaababbbabbaabaaabbbbaabbaaaabababaabbbbaaaabbbbbaaababbbaababbbbaaaabababbbbbabbbaabbbaaaaabbbbbbbbaabbbaabababaaaabbbbbabaaaabbbaaaaaababbaababaabbbbababbbaaabaaabbaaababababbaaaaabbaaaaababbababbabbbbabbbaabbaababababbaabbaabaabaabbbbabaaaabbbbbbaabbababbabaabbabbbaaabaaabababababbaababbbabbabbabaabaabaaaabaaabbbaabaababaaabaabbbababbabbaaabbbabbaaaababbbbbaabbaabbbbbabaababbbabaabbaabaaababababbbabababaaaaaabaaaababbbabababbbbbbbbbabbbabbbababbbbabababababaabbaabbaabbababbbabbbbaaaaabaaabaaaaabababababbabaabbababbaaaaababbabbbbbaaaaaababbbbaabbaabaabaaaaabaabaabbbbaababaabbbabaaababaaabaaabababaaaaabaabaaabbbababbbbabbbbaaaaaaabbbababababbaaaabbabbaaaabaaaaabbabbaaaababbbbbabaabbbaaabbaaababbbabbbbbaaaaabbbaababbababaabbbabbbaababbbaababbaabaaaaaaaaaabbabbbbbababbbabaaaaaaababbbbbabbabaaaaabbbaabbaaaaaaaabababaabbababababbbaaaababbabbbbbbbabaabbaabaaaabbaaabbbaabbbaabababaabbaabbbbbbaaabaaababbabbbbbabaabbabaaaabaaaabbaabbababbbbbaaabbbaabbaaaaaaabaababbaababbaaaabbbbabbbbbbabababbbaaabaaaababbabababbbbaababbaaaabaaaabbaabbaabbababaababbaababaabaaabbabaababbbbaaaabbabbabbabbbbaababbaaaaaabbabaabbbbabbbbbabbbaabbbbabaabababbabbaabaabbaaaaabbbbbababaabbbabaabbbbaaaabaabaaaababbbbaababbaaaabbbabbaaababbbaababbabbaaabbbaaaabaaaaababababaaaababaaaabbbbbbbababbaaabababbaabaaaaabbbbaabaaaaaaabbbabaabbbabaaabaaabbabaabbabaabaaaaaaaaaaaabaaabaabaababbbbabbaaabbaaabaabbaaabbbaaaabaaabbaabaabbaabbbbaaaaaababbabaabbbbaabaaabbbaaababaabaaababaabbabbbbbbaaaababbaaabbbabbbaababbaababbbabbababbabbbbbababbababbbabaaabbbabaaaaababaababbabbaaabbababaabbabaabbbbaabaaaaaabbbbbbbbaabababbabbbaabaababbabbaaaababbbaaabababbabbbabbaaababbaabaaaaaabaaaabbaaabbbabbbbabbbbabbbaaaaaaababbaabbbbaabaaabbbbbabaabbbbababaababbbaaabaaababbaabbababaaabaaaabbaabaaabbabaaabbaabaaabbababbbaabaabbaaabaabbaaaaabbbabaabbbaaabbaabbbbabbababababbababababaaaaaabaaaabbaaabbabbbaabbaabbabaababbaaababbbabbbbbbabbaabaabbbabaaaaaabaababbababaabaaabbbbbbaabaaaababbaaabbbbababaabbaabaabbaaaaaaaaababababbabbbbbabbbaaabbabaaabbbabbaaabbaabbaaaaaabbababbaabaaaabaaaaaaaabbaabbaabaababbababaaabbaabababbbabbbaaabbaabbbbabbbaaabaababbaabbbbabbbaababaabbabababbaabaabbaabaabbaabbabaaababaabaaabbaabaaaabbaaabaaabaaababaaaabbabaaabaaaaabbaababaabbaaaabbbbbabaabbaabbaaaabaaaababbbbbaaababbababaabbbaaabaabbaabbbabaaababaabbaaabbbbaabbabbabbbbbbababbabbbbaaabaabaaaabbbaaaaaababbbabbbbbbbabbaababaaaaababbbaaaabababbbbbaaaaabaabaaababbbbbbabaaaabbaaaaaaaaaaaaaabbbabaabaabbabbabbbbbabbbaaaaabbaabaababababbbaabbbbbbbbbabbaaaabaaaaabbabbbbbaaabbbabaabbababaabababbbaaabbaaabbaabbbabbabbabbaabaabbbaabbbabbababbabbbbaaaababbabaabaaabaaababbabbbbaaaabaaaaabbaaabbaababbbaaababbaaaaabaaaabbbaaabaaaabbabbbbabbababbaabaabbaabbbabaababaabaabbabbaaaabaabbaabbabbabbaabaabbbaaaaabbbaaabbbabaaababbbbabbaabaababbaabaaabbbaaaaaababbabaabbababbbbaaabaaabaababbbbabababaaaaaaabbabbababbbabbababbabbbbaababbaaaabbabaabbbbbbaaaababbabbabbaaaaaabaabbaabbbbbaaaabbaabaabbabbbabaabbababababbaaaaaaaaabbbbaabbaaababbaaabbabaabbaabbbaaababbbabaababbabbababaaaaaabbaaabaabbaaabbabbabbbabbaabbbbaaabaaaababaaaabbbabbbabbbbababaababbababbbbbababbabbaaababaabaababaaaaabaaaaaababbbbaaabaaabaabbaaabaabaaaaabbaabaaaabbabbbbbaabbbbbaababbabbaabbaaabbaabbbabbbbbabbaaabbabaabaabababbbbaabaaabbbabaaaababbaabbbbbbabbabbaabbabaabbaabbabbbabbbbaaabaaaaabbbabbaaaabbbaabaabaabaababbbaabbaabbabaabaaaabbbbbaaaaabbbaaababbbaababbbbabaabaabbbaababbaabbabbaaaabbabbbbbbbaaaaaabbbababbabaabaabaaaabbbbbbabbbaabbbbabbbbbbabababbabaabbabaababaaaaabaaabaaaababaababbaababaaababaaababababaabbbbbbabbaabbaabbbabaaaaaaaabaababababababbaaabaabbbbbbabbaaabbbaaabaabbabbababbbaaaababababaaababbabbaabbaabbbbbbabaaaababbbabaaabababbaabbabbbaabbbbbabbbbbbbbbababaabbabbbbbbbaabababbbabbbbbabaaaaababaabbbaaababbbabbabaababaababbabbababbbbbbaabbaaaabbbabaaaaabaabaabbaabbabbaabaaaababbbbaabaaabaabbbbabbabbbabbbbaabbaabbbbababbabbbaaabbbbbbabbabaabaabaabbbbbabaaaabaaaabbbbbaaaaabaababbaababbbbabbaaaabbbbabaabaabbbabbabbaabbbabbaabbbbaaabbabbbabaaabbaabaaabaababaabbaaaaabbbabaababababbaabbaabbabbbbbaababbbbaabbaabbabbabaabbbabaabbaabbaaabbaababbbbbbabaabbaababaaabaabbababbbbaaabaaaababbbbabaabbababbabaabababbbbbbaabbbbbaaabbbbbbabbbbbabaababababbbaaabbaabaaababaababbbaaaabbababaaaaababbaabbbbbaaabbbaaabaabaabbbbaababaaabaaabaaabbbbaaaabbaabbbbabbabbabbbbbbaabaaaabaaababbaabaabbaababaaaabbbaaaaabaabbaabaabbbbbabaabbabbaaabbabaabbbbbbaaaaabbbbabaabbbaababaabbbbabbbbabbbababaaabbbbbabaabbaabbbbaababbaababaabbbbbbbabaabaaabbbabaaaabbaabaaabbbaaabbbaaabbbbbbabbbaaaaabbbbaaabbabbaabaaaabbbbaaaaabbaabbbaaabbbaaabaaabababbaabbabbaaabababbaabbbababbbabaaaababbbaababaabbaaaabbbbbabbaaabbbabaababbaaaaaaaaaabbabbbbaaaaaababaaabbbbbabbabababbbabaabababababbbbabaaabbaaababbaabbbababbbbaaaabaabaaaabbaaaaaaabbbaaaaaaaabaabbbbbabbabbbbbbaaaaaababbbaaaaaaaaabbaaaaabbababbababaabbbabbabaabbbbbaaaabbaabaaaaabbbaabbbbbbaaaaabaabaababbababaabbaaaaabbababaabbbabbaababaaaaabbbabbabbabaaaaaaaaaaabbbaaababbbaabbaabbbbaaaabbabbbababaababaabbaabbabaabaabbaaabbabababaaabbaabbabaaabababaaaabbabbbbbbaaabbbbbaaababbbaabababbbabbaabbaababbababbbaabbaaaaabbbbabbbbaabbababbbaabaaaabbbbabbbbaabababaaaaabbbbbaaababaaaababbaababbbbbabbbbababbaababaaabaabbbbaabbabaababbaaaaaabbbabbabbbabbabbbbabbabbababbbbbbababaaaaababababaaaaaaaabbbbabbbabbbabbabaaabaaaabbabbbaabbbbbababbbabbabaabbbbbbabbbaababbbbbaaabaabbbabaaabbbaabaababaabbaabbaaabaaaabaaaababbbbbaaabbaaabbbaaaababaaabbbbaaabbbaabbbbbbbaabbbbababbbabbaabbabbbbaabaaaaaabbbabbaaaababbbbabaabbabaaaaabaababababbbaababbbaaaaabbbbbaabaabbaabbbabaabbaabbabaaabbabaaaaaababaabbaabbbbabaabbbbabbabbbabaabbabbbbbbbbbaabbbabbababbbaaababbbaaabababbbbbbbbbbbbbabbbbaabaabaaaaabbbabbbbbabaabaabbbaabaaabbabbabaaabbbbaaababaaaaababbbabababbaabbbabbbbbaaaababbbbabbbbbbbbbbbaabababaabbbbbaaabbbaaaabbaababbbaaababababaaaaabbababbabababbbbbbbbabaabbaababbbbaabbabbabaaababaabbbaababbaaababbaaabababbaaaaaaaaaabbbbaabbbabababbbbbabbbbbaabaabbbababaabbaabbaabbbabbabababaabbaabababbbbaaabbaaaaabbaaaabaabbbaabbbababbbbaabbbbbbabbaaabbaaabaababaabbbaaababaaaabbbbaabaaaabbaaaaaabbabbaaabbabbbbbababbabbaaaaababbababbabbbabaabaaaaabbabbaababbabbabaaaaabbaabaaaaaaabababbbbaaaaaabbabbababbbabbbababbabbbaabaaaaaaabbbbababababbbaaaaaababaaabbbabbaaaaaabbabbbabaaaababababbbbbabbbaaabbbabbaababbabbbbbbbabaabbabaaababababababbbbbbabaabbbabbabbbbbbaabaabbbabbabaababbbbbabbaababaabbbbabaababaabbabaaabbbbbabababaabbbabababbaaabbbbaabbaaabbbabbbbbbaaaaaabbbbbaaabaabbabaaabbbbbbababbbaabbbbbaabbbbaaaabbbaaaabbbaaaababbabbbbbbabaabaabaaaabbabbaabbbabbabababbbbbaaabaabbaabaabbbabaababaaabbbbabbbaaabbbbbbbaaaabbabbaaaaabbaabaaaaaabbbaaabbaababaaaaaaaaaababaaabbbbabbbbbbaababbbababbbbaaabaabbbabaaabbbaabbbbaaababaaaabaabbaabaaaababbbbbbbaababbaabbbbaaababbbaababaabbbbaaaaabbababaababaabbbaaaabaaaabaaaaaaaabbbabbaabbbabbbaabaabbabbaabbabbbabbbbbaaaaabbbbbbbbabbaabbaaababaaabbbabbbabaabaabbbbbbbbababbaabbabaabaaabaabaaaaaabbabababaaaaaabaaabababbbababbbbababaaaaaabaaabaaaaabaabbbbaaabbaabaaaabbbaabaaabbbbbbaabbabbbabbbbababbababbaaabbbaababbaaaabbbbbbbaabbaabaabbaaaabbababababababbaababbbbbaabaabababbabbababbababbabaaabbababbbbbbbbbabaaaaabbaabaaabbaabaabbabababbbaabbababaabaaabbbabaabbbabaabaabbbbbbbaabaabbaabbaababbabaaabbbbababbbbabbbaaaabaaababbabbbaabbbbbbbaababababababaaaabababbbbabbaabababbbbaabbabaabbaabaaabbabbaabbaababaabbababbbaabaabaababbababbbbaaaaabbabaabaaabbbbaabaabaaaabababbbbbabaaabbaaaaaabaabbbabbababbababababbaabaabbababbababbbabbbbabbbaaababbbbbbaabaaababababbabbbbaabaabaaabbaabbbabbababababaabbbbaabbbababbababbbaaaabaaaabbaaaabbababbbbabbaabbbbbabababaaabbbbbbabbabbaaaabbaabaababaaabaaaabbbbaabbbabaaaaaabaaababaaabaabaabababaaababaaabaabbbaababbaaaabaaaabbaaaaaaabbabaaabbaababaabbaaababababbbbabbbbbabbbaaababbaababbbbbbaaabbbaaabbbbbaabbabababaaababbbbbbbabbbaabaaabbabbbbbabbaabbaabaaabababbabbbbabbbbabbbabaaaaabababbaaaaababbbbbbaaaabaababbabbabaaaabbaabaababababbbabaaaabaaaaabaababaaabbaababbabbbabbabbaaaabbaaabbbabbabbabbbaababbaaababaabbbabaaabbabababaabbbbaaababbbaaaaabbaaaabbaababaabbaaaabbaaabbbbabbabbabaabababababbbaababaaabbababababbbbbbabbaabaaabbabaabaababaabbabbbbaaabaaababbbbbbaaabbaaaaabbabbabbabbaaabbababaabbbababbbbaabbababbbbabbaabbabaababaaababbabaabaaabbbabaabbababbabbaabbbbbbbbbabbaabababbbbaaabaaaaaababaababbbbabbbbbbbbaaaaabaaaabbbbaabaaaaaabbbbbaaabaababaaaabaabbaaabbaabaabaabbaabaaabbbbbabaababbbababaaaabbbaabaabbbabaaabbabbabbbbabbbabbaaababbabbaababbaaaaaababbbbbbaabaaaabababbabbababaaababababbbbaaabbbbbabbabbbbaababbabaaabbbbbbaaabbbaaaababbbbabbbababaaabbbaabaaabbabbbbabbaaaabbbaaaabaaabbbababaaabbbaaababbabababbaabbbabbaababbaababaaaabaabbaaabbaabbabbbaaabbaaaababababbbbbabbbababaaabbabaaababaabbbbabbbabaaabaababaaaaabbbbababbbaaabbbaababbbabbabaabbbbabbaaaaaabbaaabbbaabbbaabaaababbbbabababaabbabaabbbabbaabaaabbababaabaabaaababaabaabaabbaaaaaabaaabbababbbbbababbabbaabbaaaababbabaaabaaabbababbabaaabaaabaaaabbbbbababbbaababbbaaaabbabbabbbaababaaaabbbbaabbaababbbbaabbbbbbbabbbbbbaaabaaabbabaabaababaaabbbaabbbaaabaabbaaaaabababaabbbaaaaaaaabbbabaaaababaabababbaabbaaaababbaaaababaababbbaaabbaaaaababbbbabbaabbaaaaabbbaabbabaaabababbaaaaaabbbbbbaaaabbaabbaababbababaaabaaabbaaaabaabaaabaabbbabbbbbababbbbbaabaaaaaabbbbbaaaabbbbbbbababaabbababaaaabaaabbaabaabbaabbaababbaabaabaabbaaabaababbbaababbaabaababbabbbaaaabababbbbbbbaabaabbbbbbbbbbbaabbbbaaabbabaababbaaabbbbababaabaababbbabbababbaabbbaaabbaabbbbbabbbbaabbabaaaabaababbabaabbaaabbbbaaabaabaaaaaaaaaabababbaabbaaaababaabaaabaaabababaababbabbababbabbaabbabababbbbbbbabaaaabababbbabbabbaabaaaaaaaaabbabbaabbbbaabaabbbaabbaaaaabbabaaabbaabbbaaabaaabababbbbaabaabaababbabbaabbabbaaabbbbbabababbbbabbabbbbbabbbbbbbbaaaabaaababbaabbbababbbababbabababaaabaaaaaaabaabbaaaababbbabbbababaaabaaaaababbabbbbabbabaaabaababbbbabaabbbbabbaaaaabbbaabababaabaaaabababaabaababbaaaabbabaaababbbbbbababaaabaabaaabbbbbabbbbaaababaaabbaabaaaabbbbbbaabababbbaaaaaaabaaaabbaaabbbaaabbababbabababbbbbbabbbbbabaaaaaaaabaabbabbaabaababbababbbabbbbaabbabababbbbbbbaabaaabbbaabbabaaaaabaabaabababbaabbbabaaabbaababbbbabbbbaabaababbbbabbaaaaaaaabbbbaabaabbabababaaaaabaaabaaabaaaaabbbbbbbababbbabbabaabbaaabbaabababaabbbbbaabbbbbaaaababaaaaabbbaabbbbabababababbabaabababbbabaaaabaaabbbbbababaabababaaababbabbbabaaaaaaabaabbbbabababbbabaabaaababbaaabaaaaaabbbaaaabbbabbaabbbaaababaabaaabbaabbabbbaabbbbbbbbbabaababaaabbabbbbabababbbbbaaaaaaabbaaabbbabbabbaaabbaabbbbaabaabbabbbbbbabbbbaabbbabaababaababbaabbbabbaaaaabaabbaaabbaaaabaaaaaaabbbababaaaaabbabaaabbabbbabaabbbbbbbaababababababaaaababbababbbbaaababbababbabbabababaabaabbbaababababaabbbaabaabbaaabaaaaaabaaaaaaaabaabbbbbbaaaaaabbabbaabbbbabababbbaaabaabbababbabbaababbaabbbbbababababbbbabaabbabaaaabbbabaabbabbaabbabbaabbaaaabababaaababbbbbabaaaaaaababbbaabbbaabaabababbabbbaaabbaaabaaaaaabbaababbbaaabaabbbabaaabaaaabaabababbbbaaaaaabaababbabaaaabaaabbbbabaaaaaabbbbabbbbbbabaaabaabbaabbbabbaaaaabaabbbababaaabbbabaaaaaaabbaaabbaabaaaabbbaabbbabbbabbbaaabaabbaababbbabaaaaabbabbbbabbabbaabaabbbbaaabbbbbbbababbbaabbbbaabbbbbbbaaabbabaaaabbbaabaaababbaabaaaabbbbbbabbbbabbbabbbbbbaabaaabbabbaabaaababbaabaabbabbabbaabababbbbbabbbaabababbbaabbbaaaaaaabbabbababaabaaaaaabbabaaabababbabbaaaaaaaabbbabaaaabaaababbbaaabbbbbaaabbbaabbbabbabbbbbabaabbabababbbbbbbabaaaababbbaabaabbabbbabbabaabbbbbababbbbababaaababbbbbabbaabaaababbbbbaaabbbabbbbbbbaaaabbaaabababbaabaaaaaabbaaaabbaaabbbbbabbabbbbbaaaabaaaaaaaababaaaaaaaaabaaaaababbabbaaabbbbbabbbbbbaababaabbbbbbaaaabbaabaabaaaabababaaabbabbabbababbbababbbbbababbaababbbabaabbaaaaaababaaaaababbababbbbaababbaaaabbaabbababbaabbbbbbbaabbaaabaaabbabbaabababaaabaaabbbaabababaaabbabaaababaaaaababbbaaabbbbbaaabaabbbbaaaabbaabababbabbababbaabbaabbaababbbabbaabbbbabaababbbaabbbaababaabaabaabbabbbbababbbbbaabbbabbabbabaaaababbbbababbababbabbbbbbbbaabbbabaaabbabaaabbabaaaabbbaabbaabaababaaaaaaabaabbbbbbababaababaabbbbbaabbbaaaaabbbbabbabbbababbbaaabbbbbabbbbbaaabaaaaabbabbabaabbaabaabaababaaaaaaaabbbaababbbbbaaabbbbbbbbbaabbbbabaaaabbabaababaaabaabbaabbaaabbbaabababbbbbaabbaabababbaabaaabaabbbabababaaaababaabbbbabaaabbabbabbaaababbbbaabaabbbaaabaaaabbababaabbbaabbaabbbaaabbaababbabbababaaababaabaabbaabbbabaaababbbbbbbbbaaabbaaaabbbabaabbabaaaaaabaabbaaaabaaaaaaaabbbbababbbaaababbbabbaaaababaaabbbababababaaabaaabbbababaabbbbaaabaaaabbaaaaaaaaaaaabaaaaabbaabababbbababbbaaaaaababababaaabbbbbbaababaabbaabbaabbabbbaaaaabbababbbbaabbaaaabbabaabbaababbbbbabaaaaaaaabaababaabbbbabaabbaabbabbaaaaabbaaababababbaaababaabbaaababbbabbabababbaaabbbabaaaabbbababababababbbaababbabaabaabbaaabaaaabbabbabaaaaaabbbbabaabaaababbbabbabbababbbaaabbaaabbbaaabbbbbbbbbbbaaaababbbbbababaabbababaabaabaaaabaaaabbbabbbaabbabbbababbbaaaababbbbaabbbabbababababbbaababababbbbbaaabbababbbabbbbbbbbbabbaaababbabbaaabbaabbaababbbaababbaabbabbbbaaabbbaabbabbbbaabbbbaaabbbaaabaaabaaaabbaaababbababaabbbbaabbbabbababaabbaaaaaaaabaababbabbbabbbaabbaaabbaaabbbbbbbaaaaabbaaaaabaaaaaaaabbbabbbaaaaabbbababbabaaaaabbbabbbabaabaabaabababbababbabbbbbbaabbaabaabbababbababbbbbbaababaababaabbaaaaaaaabaabababaabbababaabaabaaabababbbbbbbbbbaabaabaaabaaabaaabababbabaabaaabbbabbbabababbbabbbbabbbaaabababaaabaabaabbabbbbbaabbaaaaaabbabbabbaabbbbaababaaaaababbabaabbbabaaaaababbabaabaababbaaababbaaaaababbbbaaabaaaabbbbababababbbaaabbbbaaaaaaaaababbaaabbabbbbaabaabaaaaaaaaaaaaabaaaabbabbbbaaaabbabbbbbbaabbbbaaaaaabbaabaaaabbbbbbbbbbaaabbaabbabbaaababbbabbbabbbbbbaabbabbbabbaaaaaaabaaabbaabaabbaaaabbbabbaaabbbbbababbbabaaaaabaaaaabaababbabbbbabababbaababbbaabbabababbaaabbabbabaabbabbabbabaaabbabbbbbaaabaaaabababbaaaaababaaaaabaababaabaaaabbabababbaabbbabbaabbababbaabaabbbbbbbbbabbabbaaabbabaaaaaaabbabbbbabbaabbabbbbbbbbabbaaabababbbaaabaaaaabbbbabbbbaabbaaaaaaabaabaaabbababbbabbaaabbbaababbbbaabaabbaaaabbbababbaaabbaabaabbaaaabababbbbababbbbbabaaaabbaaaabbbbbbbababbababbababbaaaaaabaaaabbaabbbbabbaabababaababbbbabbabaaabbbbbabbabaaaaaabbbbbaaaaaaaabbaaaababaaaabaaabbbaaabbaaababbbaabaabaaababaabaaaaaabbababbbbbbababbaabbbbaaaaabbbabbaaaaabbaaababbbaaabbbbababaabbbbabbabbbbbbaabaabaaabbaaaabbbbabbabaabaabababbbbbbababbbbabaabbabbababaaababbababbbaabbababbbaaaaabaaabbbbbbaaaabbababbabababbbbaabbaaabbabababaaaaababaabbaabbabbbbbbbaaabbaabbbaaabbaaaababaabbbbbbabaaaabababaaaabaaaaaabaaaabbbbabaababbbabaaabbbbbbaabaaaabaaabaabbabababaaaaabbaabbabbbbbbbbbaaaabaaabbababbabbaaaaaaababbbbababbbbbbaaabbbbbaabbaababbbbaabababbaababbbbbbaaabbababbbbbbaabbababaaabbbabababbabbaaaabababbbbbaabbababaaabbabaabbabbaaabbabbbaabaaaabbbaaabaababbbaaaababbabbbbbbabbababbbbbababaaababbaaabbababaaabbaabbbaaabaaabbbbbaaabbbaabbbaababaabbbaaabababaabbaaaaabbabbbabababbbaaabbabababaaaaabbaaabbabababbbbbaaaababbbaababaaabbaaaabaabaaabbbaabbbbbbbabbbaaaababbbabbababbbbabababaabaabaaabaaaaaababbbbaaaaaaaabaaabaaaabababbbbaabbbbbbabbababbbabbbaabaabaaabbaaaabaabaabbaabbbaabbbbbabbaabaabaaaabababbbaaabbbbbaabbbabbbabbaaababaaabaaabbaabbbbaabbaaaabababaaabbabbbabaaaabbaababaaaabbbbbbaaabaaabaabbabbabaaababbbbaaabbbaaaabbbbaaaaaabbaabaabbabababaaabaababbbbbaabaaaabbbbaabbaaaaabbaabbaaaaaababbaaaaababababbababbbaabbabbbababaababbbbbaabababaabbbabaaababbaaababbababbaaaabbbaabbaabbbabbbbabababaabbababbabaaaaabbabaabbbaaabaaabbbbbabbbabbabaaaabbbaabbbbbbbbbaaabaaabbbaaaabaabaabaabbbabbaaaaaabbbbbaabbbbbaaabaaabababbbaabaaababbbbababbbaaabaaaaaabaaaaababaabbabbaabbabababbbaaababaabababbbbbbbbbbbaababbaabbbabbbaaaabaabaaababaaaaaababbabbabbbbbaabbbbababaaaabababababaaaabbbbabbabbbaabaaabbbababbaaaaaaabaabbabbbaabbbaababbbbbababbbbbaababbaababbabbbbabbbabaaaabbabbaabbaaaababbbbabaaababbabbbbbbbababbabbbabbbababaababbaaabaababbaabbaaabaaaaaaaaaabaaaaabbbaaaaabaaaabbbbababaaabbbbbbabaaabbbaaababbaaababbbbbaaabbbaabbbbaaababaabaaababaabbbbbaaabbaaaabaaaaabaabbbaaabbbaaababbabaabbbbabbbbabaaababbaaabbababaaaabaabaababbaaaaaaabaabaaabbababbaaabaabbbaaaabbabaaaabababbaaabbbaaabbabbaaaabbababbbaababbbabaabaaaabbabaabbbbababbaaaaabbabaaabbbbabbbababaaaabaabbbaaababaabaabaaabbbbaababaabbbbbbabaaabbaababaabbabbaaaabbabbbabbbaabaaabbaaaabaaababbbaaabbabaaaaababbbbbbaaabababbaaabbbaabaabbabaabaaaabbbaaabbbbbbaabbbbababaaababbaabbaababbbabaaabaaaabbbbbababbbabaaaaabbbbaaabbbbaabbbbbbbbaaabaabbaaabbabbbbbbbbbabbaabababbaabbaabbaaababbaabbbabaababbabaababbaabbbbbaaaaaabaaaaaabababaabaabababaaaabbbbbaaabaaabaaabaaabbbbbabbbaabbababbaababbabbababbbaaababaabaaaaaaaaabababbabababbbbababababaabaababaabbaabaaaaabbaabbababaabbabaabbbaabbaaaaaaaabaabbbbbbbbabaaaaaabbbbabbaaaaaabbabaaabaaaabaabababaaaaabaabbbbabbbbbbaababaabbabbbbabbaabbbbbbbbbbaaabbbbababbabbaaabaabbaababaababbbabbaaaaabaaabaaabaaabaabbabbabaabaaababaabbbbaaaaabaabbbbbbbabbaaaaabaababbbaabbabbaabaaaaaaaabbaaabaabbbabaabaabbaaabaabaabbbabbababbbbbabbabaabbbbabbbbbbbbbabaabaaabaaaaaaaaaaaabbbaaaabbaaabbaaababbbbaabbabbbbaabbabbbbababaabababbbbbbaabaabbaabaababaabbabbbabbaabbbabababaabbbbbabaabababaabaabbbabbaabaabbbbbaaabaabbababbababbababbaabbbbbaaaabbaaaaabbabaababbbabbbbaaababbbaaaaaababbaababaabaabbbbbababaaabababbbaababbabbbaaabbbbbbabbbbabbbbbbaabbbbbbbaabbabbaaaaaabbaabbbaabababbbaaaaaabaaaabbabbababbbabaabbbaaabbbbaabababaaaaaabababbbaaaaabaabbabaaaabbbbababaabbabaababaabaabaaabbbbbbabbaaaaababaaaabaabbbabbbbabbbbabbbbabbbabbaaaababbbabbbbbbabbbabaababaabbababbbbbbbbbbabbaaababbaabbbaaaaaabaaaabababbaababbabbbaaabbabababbbbbbbbaabaabbbabbbbbbbbabbabbaabbbababbbbbababbbabbaababbabbaabbaaabaababbabababbaabbaaabbabaaaababbabaaabbabbbbabbbbaaabbabbabbabbaabaaaababaabbbabbabbbaaaabaabbabaababbababbbbbaaababbbbabaababbababbbbabbaaabbbbbabbbaabaababaabbbabbbaaabaaaabbbbaaaabaabaabbabbbbbbabaabbababbabbbbababbaabbaabbababababaaabbaaaabaaaaabbbbaabbbaaaabaaaabbabbaaaababbbbbbbabbbaababababbbaaabaaaabbaaaaababbbbbbbbaabbababaabbbabbaaaabbababbabaabbbbaaababbaaababbbaababbbabaaaaaabbabbbbbbaaaaaabbbbaabaaabbaabbaababababbbbaaabbabaaaabbbaabaaabaabababbbbaabaaaaabaabbbababbabaabababaabbbbbbabaaaabbbaabbaababaababbaaabbaabbabaaabbaabbaaaabbbbbabbbaabbaabaababbaaabaabbbbbbbaabbbabbaaabbbbbabbbbabbabbaabbbabaabbbaaaabaabbbbaabaabaaabaaaabbabbabbabbaabbbbababaabababbbbbbabbbabbbaaabbbabababaaababbbabaaaabbaababbbaabbaababaaaabbbbaaabbaaabbbaaaabaabbaabbaabbbbaabaabbaaaaabbbabbbbbaaabbabbbbaaaabaaabaaaababaabbbbaaaaaabaabbbbaabbbababaabbbaabaaaaaaaaababbaaaaaabbabbaabaababbabbbbabbbbbaaaaaaabbbaaaaabbaaabbababaaabababbaabaabaaabaabaabbbabbbaababbbbababaababbbbaaababbbabbbbaaababaababaaabbbbabaaabaaaabbbabaabaaaabbabbbabaabaabbbabaabbbbabababaabbaababbaaaabbbaabababaabaaabbbababababbbbabbbbbababbbabbabaaaaaabaaaabbbaabbbbaabbaabbbbabababbbbabbabbababbbabbbbaaaaabbbaaabbaaabbaabbabbabaabaaababbabaaabbbabbaabaaabbbbbabaabaaaaaaaaababbbbbbababbaabaaaaababbababbabbaabbaaababaaabaabbabbbbbbaabbbbbbaaaababaabbbbbaabbbbabbbababaaabbbbaabababbaabbaabaaaabaaaababbaaaaaabaababbababaaaaaaabbabaabaababbbbabababbaabbabbabbbbaaaabaaabababbabbaaaabbbaababbbaabaaabaaaabbabbaababaabbabbaababbabaababbbabbbbbbbbbbaaaaabaaaababbbaaaaaaaabbaabbbaaaaabaaaaabbbbaaaababaabbabbabbbabbababaabbbaaabbbabbabbbbbbbbbababbababababaaabaaaabbabbbaaabbbaabababbbbaaababbbababbababbbbaabaaababababbbbabbbabbbabaabbabababaabaabbabbaabbbaabababaabbbaabaaaaabbaaababaabbbbabbbbaabaabbaabbaabbaababbabbbababbbbbbaaabaaaaaabbbbaabbaabbbbababbbbbbaaabbbabaaaaaaabababbbbaababababbbabaaabbbbabbbabbbabbbbbaaaaababbabbaaaabbabbbbaabbbbaaaababbbbbababbbbbbbababaaabbbaaabbaabbbbbabbaababbbabababbabbabbababbabaabbaaaaaababababababaaabaabbbaaabbabaaababbabbaababababbabbbbabbbababbbbbaaaabbbbabaabbbabaaabaababaabbaabaabbbaaaaaabbaabaababbaababbaabbaabbabbabbabbbabbbabbaababbabbbbababbaaaabaabbbaabaaabaabaaaaaabbaabababbaaababbababbabaababbbabababaababababaabbabbbababaabbbbbbabaaabbbbababbaabababbaaaaabaababbbabbaababbbbabbababbbabaabbbbbbbaababbabbbbbabbbbababababbbaaaaaabbabaabbaabbababbaaababbbbaabbbbbaaababbbaaaaaaababaaaaabbbbbaababaababbbaaaabaaaabbababbbaabbbaabbaaaabbaaababbaabbbbbbbabbabbbababbaababaaaaaaaaaabaaabbaabaaabbbbababbbbaabbbabbaaabbbaaaabbbaaabbabbaaabaaabaaaabbaabaaaaabababbbbaabbababaabbababbbaaababbaabbbabaaaaaaabbbabaabaaabaaababbabaabbaaababbbababbbbabbaabbababbabbbaabaabaabaaabbbbabaabbbaaaabababaabbabbabbbabbabbabbbbbbaabaaaaaabbbaabbabaabbaaabbbbbbbababbbabaabaabbabbbbbaabbbbbbbaabababbbabbabbabababbbbabbbbbaaaabbbabaabbbbbbabbbbaaabbababbbaabaaabbaabaabbbaaabbbaababbbaaabaababbbaaababaababaabbbbbbaababbbabbbbababbbbaaabaabbabababaabababbaababbbaabbbbaabaabaaabbaaabbbbabababbbbbbbabbababbbbaabbabbaabaabaaaabababbaaabaabaabaabbaabbaaaababbaaabababbaababaabbbbabbaabbabbabbabbbbbabbabbbabbaaaabababbaabbbbbbbbbbaababaabaabbabbabbbbbbaaabbababbaabababaabbbbbabaaaaaaabaabbabaaaababbbbbbabaaaaaaabaaabbbbabbabababbbaaabaabbbaabbbbbbbabbabbbbaababbbaaabababbabaababbbbbaaaabaababaabbbaabbbbabbaaaababbbbbabaaabbabbbabaabbababaaaababbabaaaababaaaaababbaaaabbbbabbbbbbaaababaababbbbabbbababaaabbaaabaaaabaaaaaabbbabbabaaaaababbbaaababaaabbabbaaababbaaaabbbbbbbaabaaaabababaabbaabbabbbaaababbbbaababbbaaaababaaaabaaabbbabbabaaaabbbabbabbaabababbbbabaabaaababababbbbababbaaabbbabaaababaabbbbabaabbabbbabbbbbaaaaabbbaabaabbbaaaaabaaaaabaabaaaabaabbaaabababaaabbbabbaaaababbaabbbbabbabaabbbbaaababbbbbbabbababbaaababbbbababbabbbbbabababbabbbaaaaabbabaaabaaabbbaaaababbbbabbbbabbabaabaabbabababbbabbaaababaaabbabbaaabbbaaaaaaababbabaababbbaaaabbbbababbbaabbaaabaabaabababbbbbababbabbbababababaaabaaabaabbabaaabaaabbaaaabbaababababbbaabaaabaaabbbbabbbababbababababaabbbbaabbabaabbabbbbabbbabaaaabbabababaababbbbababbbaaabababaaaaaabbbbbbaabbbbbaababbabbbaaaabbbabbabaaaabaabaaaaabaabbbaababbbbbbaabbbababababaabbbbbaaabaabababaaaabbbaabaabbababaaabbaaaaabbbabbaaababbbbababbaabbbabbaaaabaaabaababaabaaaaababbaaaaababababbbaababaabaaabbbaabbaaaaababaabbbaabaaabbbbabbbaababaaaabbaabaaabbababbbabbbaaaaababaaabbaaaabbaabbbbabaaabbaaaabaaabbabbababaababbabaabbaaaabaabbbbbabbabbabaabbbbaaabbbbaaabaabbaaabaaabbbabaababbabaababaaabbbbbaabaabbbaabbaabababaaaaaaabababaaaaababbababbaabaababbbaababbbaababbaaaaaaabbaaabbbbbbbbaabaaababababbbaaaabaababaaaaabaaabbaababbbbaabbababababbababbabababababbabaabbababaabbbabaaabbaaababbbabaaaaaaaabbaaabaabbaabaabbbbbaabaabbabbaaaabbaaabaaaababbbaaabbbaaabbbabbbbaababbaaabbaabbababbbbbaababbbbabbaaabbbaaabaaaaaaaabbaaabbbbbaabbbbabbbaabaaabbaaaaaabbbaaabbabbbbaaaaababbaaabaabaaabaababbaabaabaaabbbbbaabbbbbbbabaaaabbaabbbaabbbbaaaaabbaabbabbbbabaabbbbaabbaababbbabbabbaababbbabbaabaabbaabbaaaabaababababababbaabaaabbabbbbababaaababbbbaabaaabbbabbababbbbbababbbabaaaabbabaabbbbaabababaaabbabbaabbbbabaaabbabbaaabaabaaabbaaabababaaababbbabbaaababbabbaabababbbaabaaabaabbbaaabbbaabaababbaabbbabaaaaababaaababaaabbbbabbabbbaabaaababbbbaaabababbaabbbbbabaaabbbbbbbbbbababbbabbabbabbabbaaaabbaaaaababaaaaabbaaabababbaabaabbbaaaaaabaabbbbaabbbaabaaabaaabbbaaabbabbaabaaaababbaababbbbbbababababbaabbaaababaababababbbabbbbbbababbaaabbbbababbbbbbbabaabbbbbababaaaaabbaaabaaababbbaababbababbababbaaabbbbaaabaababbabbaabbaaaaababbbbbabaaabbaaaaabbaaabbbababbbabbbabbbabbaaaabaabbaaabbaaaababbbbbaabbbaaaaababaaaaababbbbaaabbbaaabbabbaababbaaaabbabaaaabbbababbbabbababaaaaabbaaabbbabaababbbababbbabaababaaaababbbbabbabbbaaabaabbbbabbbaababbabbababaaaaabaaabbababaababbbaabbaaabbbaaabaaabbababaabaabbbaaaaaabaabbbbbaabaabaabbbbbabbbbaaaaaabaabbbaabbbabaabbabababbaaabbaaaabbbabbbababaaababaabaaabbabaaaabbbbababbbbbabbbbbbababaababbababbaabaaabaaaaaabaaaaababbababbaaababbbabbabababbabaaababbbaaaababbabababbbaaabbbabbaababbbabaabababbbaabababbaababbaabababaabaaabaabbabbbababaabaabbaabbbbbbaaabbababaabbbaabaaaabaabaabbabbaabbabababbbbaabbabbabaabbababbbaaaaaababbabbbaaaabbababbababaaabbbbbabaabbaabbbaabbbbabbbababbbbaaabbbabbababbbaaabaaabbbaaabababaaaaabbbaabaaabbbbaaabbaabaaaabaaaabbabbbabaaabbbbabaaabaaaaaaaaaaabbabbababbbababaabbabbabbabaaabababbbbbbbbaaaabbabababaaaabbbbbaaaaababbbbbabbbabaabbbbabaabbbbaaababababbbbaaaaabbbaaaaaaaaaababababaaababaaaaabbaabaabaaaaaaabbaabababbababaababaaabbbbbabaabbbbabababaaaaaabbabbaaaaababaabaababaabaabbbaabaaaaabababbbbaabaababbababbabbabbabbbbabbababaabbaaaabbbbaaababaaaaabbabbababbbabbabbabbabbabbbbabbbababbbbbabbbabbaaaabbabaaababaaaaaababbaaabbbbbabbababbbaabaaababbbababaaabbbbbaaabbbbbababbbabbbabbbbbbabababbabbaabaabaabbabbbaaabababbbaababababbaabbabbaabbabbaababbbabbbabaaabaabbabababbabbbbbaabaabbbbbbbaaabbababaaabbbbabbbbbaaaabbabbabaaaaaabaaabbabbaaaaaaabbabbabbbabaabbbababaaabaaabbbabbabbbabbaabbbaabaabababbbbbbbbbbbbbbaaabbbbabbababaaabbbababaabbababbbabaabbaaababbbbababaaaabaaaababbbabbaaababababbabaaaaabbabaaababbbaabaaaabbabbbbaabaaaabbbbaabaaaaaaaaabbaaabaabbbaabbbbaaaaabaabaabbababaabbbabbaaabbbaaaabbabbababbbabbaaaaabaabababbaabaabaaaababaaaaabababbbbaaaabbaaaabaaabaababbaabaaaaaabbaaabbbababbabbbbbbbaabbbbaaabaababaaabbababaabaabbaaaaababababbbaababbbababbbabaababaaabbbabbbbbbabbbbaaabaaabaabbaabbababbababbaaaabaaabbaababbababbbaabbbbaaaaaaaabbbbabaaaabbbbabbaaaabbbbbbbabaabbababbaabbaababaaabbbababbabbaabbaaaabbaababbabbbbbaabbbbaaaabbbababbaaaaababaaaabbbbbabbababbbaaaaabbbbbbbbbbbbaaabbabaaaabbaaabbbbbbabaaaaababbbaabaaababbbbbbbaaaaaaaaaaababababbbbaaabbbabbabbbbaaaaabbabbabbaaaabbabaaabaabbabbaaabbaaaaaaaababbbaabbabbaaabbaaabbbaaaabababbaabbabbabbbbbabbababbabaabbbaaaaabbaabbbbbbbaaabbaababbaaabbbbababbbababaaabaabbbaaaaababababbbaaaaabbababbbbabbbaabaabaababaaaaaaaaaababbbbbbaababbbabbaabbababaabbbabbaabbaaaabbbbabaabaabbaaabbbaababbbbabbaabbaabaabbbabbbbbabbaaaabaabaababaaaaabbabbbabaaabaabbabaaabbbabaaaaabaababbbaababaababbbabaabbabbaabbabbbabbbaaaabbbaaababbbbaababbbaaabbbbbaaaabbaaaaababbaaaabaababbaabbbbbabababbbbabbbbaaaaaaaabbbabbbbabbbaaabababbaabbabbbbbbababbabbbbbbbabbaabaaabbbabbabbabaaaababaaaabaaabbabbbbabaaababaabbbaabbbaababbabaaaabaaaaaabbaaaabaaabaaaabaaaaaabbbaaababaaabbbabaababbbbbaaaabbbaaabbbabaabbbbbaaababbabbbbabbabbaabbaaaababbababbbaaabbaaaabbaabbbabaababaaaaaaabbbbbabbaabbaaabbbbbbababaabbaaaabababbabaaabbbaaaabbbaaabaabbaababbbbabababaaababbbbaababaaaabbabaaababbbababaababababbabbabaabbbbabaaaaaababaababbbbbaaabbbbaabbaabbbaaaaaabbbabbaababbbbbaabaabbabbaabbbababbbaaaabbbabaabbaabaabaaabbbaaaabbbaaabaabbbababaabbbaabbbbbbaaabaaabbabaaaababbaabaabaaabaabaaaaaaaaabbaabbbbbbbabbababaaaaaabbbbbbbaabaabbabbaaaaaaaabbaabaaaaaaaaabaababbbaabbbbaaababbababaaababaabbababbaabbbabbbaabaaabbabababbbabbbbabaabaaaaaaabaaaaaaabbbbbababbabbbabaaababbaabaabbabaaaaaabbaaaabbbaaabbabaaababbaabbabbaabaaaabbabbaabbbaababbababbaaaaababbabbaaabaaaabbbaaaaabbababbaabbaaaaaabbbaabbabbabaabbaabaabaaababbbbabbabbabbaaaabaabaaabbbbbbabaaabbaaaaababbaabbbabbbbaabaabbabbbbaaaaababbaaaabbbbaabbbababbabbbaaababaabaabaababababbbbbbabbaaabbababababaabbbbbbaababaabaabbabbababbabaababbaaaaabbbbbaabaababbaaabbaaaaaabaabbaabbababababaaababaaaaabaababaaabaabaaabbabbaaaaaaabbabbaababaaabbbaaababbbbbbaabbaabaabbabbbaabbaabaabbbaaabbabbbbaababbbaaabaaabababaabbaabbaabaaababbaababbbaaabaaabbbbaabbbbbbbbbaaabbbabaaabbaaaaabbabbbaababaabbabaabbbaaabbbababababbbaabbabbbbababbbabbbabbbaaabbbaabbaabaaaabbbbaaaabbbabababaaababaabaabababbaabbbaaababbaababaaabbbaabaababbabbabababaabbaaababaabbbbabababbbbbbabbaaaababbabaaaababababababbaaabbbaababbbabaaaaaaabbbaababaaaaabbaabaaaabbabaaababbbbaabaababbaabbabbbbaaabbaaabbbaabaabbaaaabbbaabbaababaaaabaabbbbbbbbbbbbaaabbabaabababbaaabababbbaabbaababbaaabbbabbaaabbabbbaaabaabaabaabababbbbbbaabaababaaaababaaaabbababbabaaabbaaabbaabbaaabbaaababbbabaaaabaabbabaabbbabaaabaaabbbaaabaabbaabaabbabbaabbbabbaaaabbbbbbbaaabababaabbabababbaabaaaaababbaaaaabbababbaabbbbaaaaabbaaabbbabaaaaabbabbabbbababbaabbabbaaaababbbbaaaabbbababbbaababbbabbbbbbaaabaababbbaabbababaabababaaaabbababbbbbbbababbbabbabaabbbbbbaabaaabbabbabaabababbaabbbababaabaaababbabababaabbabababbbabbaaaababbabaaaaaabababbabbbabaaaaaaaabbaabbabaabbabaabaabbbbbbbbbabbaabbbaabbbaaabbbabaaaababbbaaaabbbabaaaaababbababbaaabbbabaaaabbaababababaabaaabaabbbabaababbbabaaabaababbbabaaabbbaaabaababaaabaabbbababbaaabbbbbbaaabbbabbbbaabababaababaaaaaabbbbbabbaabbaabaabaabbaabbbaaaabbaabbababababbaabbbaabaabaaababbabaabbbbaabababaaaaabbbabbbaababaaababbabbbabaaabbabbbbbbbbbbabbbbabbbababaabbbababbabaababbaabaabbbbbbaaaabaaabbababbbaaaaabababaaaabaaababbbbaabababbaabbbabbaaabbabbbbbaabaaaaaabbbabbbbbbaaabbabbaabaaabbaabbbababbbaababababbaaaaaabbaabbbabaaaaaabaaabababbaaababbbbbabaabbaaababaaaabaabbababbbababbabaaaabababaaabbbbbbbbbbbbbabbbaaabbbaaaaabababbbaaabbababbabaaabbabaabbbbabaabbbbbaabaaabaababaaabbababaababbaaaabaaabaaabaaaababbabbbbbbbabbaaaaabbbabaaabaabaabbbabbbaabbabbbbabbaabaabaaabaabbbbbbabaababbbbabbbbbbaaaaaabbaabaaababbaabbbabaabbbbabbbabbbbaaaaaabbbbaaaaabbbbabbbaaabbbbaaaaaabbaaaabbbbaaaababbbabbbbbaaabbaabaaaaaaaababbabbaaaabbaabaabababaaabbbabbabbbaaaaabbaaababbbbbabbababbbbaaaabbabababababaabaaabbaaaaabbbbbbaaababaaaabaaabbbaaabbbbbbbabbaabbabbaaaaaabbbaaaaabaaabbaabaaabbbaabbaaaaabbbaabababaaabbbabaaaaaabbaaaaabbaaabbbabbaaaaabbaabbabaababaaabababaaababbbbaaabbaabaaabbaaaaaabaaaabbbabbbbbababbbbbbbbaababbbbbbbabbabaaababaabbbaaaaaabbbbbbabaabbaaababaaaabbbabbbbbaaabbaababababababababaabaaababbababbabababbaaaabababbbabbbbbaaaaaabaabbababbaababbabbaaaabbabbababbabbbabaabaaabbbababaabbbbbbaaaaaabbaaabbbabbbbbbaaabababbbabaaabababbbbbaabaabbbbbabababaabbbbaaaabababbbabbaaaaaaabbabaaaaaabaaaaabbaaabaabaabaaababbababbabbaaabbbbaababbbababaabbbaaaaaaabbaaababaabaabaaaabbbbbbbbbbababaaabaaabaabbabbabbabbaaaaabababbbaaababbbbabbbaababbbaabbabbbabbbbbababaabbbabbaaabbabbbbabbbbaabbbabbbbbbaababbbabbabbabbaaaabbabbbabbbbbaabaabaaaababbbbaaabbbbbbabbbbaabaaaababbbbababbabbabaabaabaaaaabababbabaaabbaaaabbbbbbbaabbbbabbbbabaabaabbbaabbbbabbbbaaaabaababbabbaaabaaabbbabababaababbabbbbabbbabbabaaabbaaaaaaaabbabaaabaaabbbabaabbbbbbababbaabaabbaaabbaaaabaaaaabbaababbaaabbbaaaabbaabbabbaabbbbabaaaaaaaaabaabbbbbbaaaaabbaabbbbaaabbbababbabaabaabbbbbababbbbbbabaabbbaaaaaabbbabbbbaaabbbaabbbbaaabbbaaabaaaaaaaababbbababbbaabbaaaabbbbbbaabababbbaaabbaababaabbbaaaaabababaaabaaaaaababaaaaaabbbabbbaaaaaaabaababaabbbbabbbaaaaaababbbbbbbaaabbbbaaabbaaaabbbbabbaaabbbabbbbbbaababbabaabaaababababaaaababaabbabababbbbbbbbababaabbbbaabbabbbabbbababbaababaaaaaababbabaaaaaabbbbbbbaababbbbbaaaaaabbbbbaababbbaaabbbabbbaabababbbaaabbababaababbabababbbbbbaabbbbbaaaabbbbbbaaabaabbabbbbaaaabaaaaaabbaabaabbbbaabaabbbbbbabaababaaabbbbabbabbabbbbbaaabbbaabbabbababbbbbaabaabbbbbabaabbbabbbaaababbaaaaaababbbabbaaaaaaabaaababbbaabbbbbaaabaabbabbbaaabbaaaabbbbababbaabbbbbbaabbaabaaabbaaabaaababbbaaaabbabababbbbabaabbbaaaaabbabaabbbbaaabaaabaabaaababaabbaabaaaababababaaabbabaabababbbbbbaababbaababbbbbbbbabbaababbbbabababbaabaabaabbbbaababaaabaaababababaabbbaaaaaaaaabbbbbaaaaaabaabbabaababbbabaabbbaabbaaabbbaaabbababaaabbabbaabaababbaaabaabbbbaabbbabbabbbabbbabaaaaabbbaabaaababbbaaaabbababaabaaaaaabaababaaaabbabbbaaabaaabbaabbaaaabbbbbbbaabbaababbbaaaabbaaabbbaabaabaaaabbabbbaababaabbbabaabbabaaabbaabbbabbbbbbbababbabbbbabababbaabbabbaaaaababbaaaaaaaaabbabbbbbbbaababbbbaabbabbbaababbbababbbbabbbaaaaaaabbabaaaaabababbbbbaaabbaabaabbbaaabbbbbbabbbabbababbbbbababbbbbbbbababbbbbabbbabbbabbabaaaabbaabbbaabbbaaaabbbbbaaabababbbbaabaaaaaabbabaaaaaabababbbaaabbaababababaaaaabababbbbababaaabbbbbbaaaaabbbbaababaaabaabaabaaaaaaaabbaaaababbaabababbbbabababaaaabbabbbababaaababbbbabaabbbbaababaababaabbbababbbbbbbbbbbbaaabbabbbbbaaabbabbaababaaabaaabbabaababbaaaababaaabaabaaababbbbaabaababbbababbaabaaaabbbaaabaaaababaabbbbababbabbaaaaabbbaababbbbbbbaaaababaaaaaaababbbababbaabbaaaabbbabbbbbbbbabbbaaabaaababbaaaababaabaabbbbbaabaaabbbbbbbaaabbababababbabbabaabaaabbaababbabbbbaabaaababbaababbbbaabaababaabaaaaaababbbbbaaabbaababbababbbaaabbabbababbabaaaababababbbabaaaabbaabbbbbbaabaababbabbbaabbabbabbbaaabbbbabbbbbbabbabbbbaaaaaabbaaabbaaaaabbabababaaaabbbbbbbaabbababbbbabaaaababbabbaababbbbbaaabbbababaaabaabbabbbababaaaabbbabaaaaaababaaaabaaabbbaabaabbabababbbaaabaabbabbbbbababbaabaabaaaabababaaabaababbbabbaababbabbabbabbaabbaabbaabbaabbababaabababbbbbaaaababbbabbaaababbbababaaaaaaababababbbaabaabaababbbabbbabaabbbabbaaaabbbababbabaababbbbabbaabaaaabbbbabbaaababaababbababbbbbabbaaabaabbabaaaabbbbbbbabbbbabbaaabbababbbbbaaababbbbbabaaabbabbaabaabbbbbababbababaabaaaabaabaaabbbababababbaaaaaaabaaaababbbabaaaabaaabbbbbaabbbaaaaaaabbbaababaabbabaabaaaabaaabbabbaaaabbbbaabbabaaabbbabbabbabbabbbbabbbbbbabaaaaaaaaabbbbbbabaabbaaabbbabaaaaabbbabbabbabbbabbbabaabbabbbaaabababbabbbaabbbbabbabaaaabbbbbbbbaabaaabbbaaaabbabaaababbabaaabbbaaaaaabbababaaaabbaabaababbabbbabababbbaaabbabbabbbabbaaaabbaaaabbbbaabaabbaabbaaaaaabbbbbbaabbbaaaaabaaaababbabaababbbabbabaaabbaabbaabaaabbbbababbbbabaababaaaabbbbabbbbbaaabbaaaabbbbbbbbbaaabbbbaababbaabbbaabbaababbbbbaaabbbbaabaaabaabbbbbabbabbbaabaaababaababbbabbbabbabbbbbaaabbbbabbbabaabbabbbaaabbbaaaabaabaabaabaaaaaaaaaabbabbbbababaaabbbabaabbbbbaaabbaabbbbaabbabbbabbbbabaaaababbaabbaaaaabbbabaabbbaabbabaaaababbaaabbbaabbbaabaaabaabbbaabaaaaaaabaaaaaaabbbbabaaaaaabbababaaabbaaaabbababbbbbbabbaabbbbaabababbbbbbbabababbbbaabbbbbaaaaabbbbaaabaababaaaabababbbbbabbbaaabbaaaabaaaaabaabbabbbabbabbabbbaaabaaabaabbbbbababbbaabbbaabaaaaaabbbaaabbababababbbbbaabbaabbbaaabaabbbbaaaabaaaaaabaaaabaaaaaaaabbbbbabbaaaaaaaaabbaaabbbbbabaabaaaaabbbabbbaaabaabbbbaaaaabbababbbabaabaaaaabbbbaaabaaabababaabaaabbbbaabbbaaabbbbababbbabaaabaaaabbaaaaaabababaaabbabbbbababbbaaabbbbbbaaabaababbaabbbabbaabababbababbaaaaaaaabbabbabaaaaabbbbbbbbbaabbbabaabbbbbbbbabbababbbaabaaaabbaaaaaabaabbabbabaaababbbbbbaaaababbbbbbbbbbbabbbbbbbaaaaabbaaaabbbbabbbbbaabaabbabbbbbbbbbaababbaaabbbbabaabbaababbabaaaabababbabbbaaaababaaaaaaabaabaaaaaaabaabbbaabaaaaaabbbbaaabaabbaaaabbabaaaabbbaabbbabaabaaaaaaabbbabababaaaaaaaababaabaababaaaabaabbbaaaabababbabaaaabbbbabbbabaaabbabaaabbabbbabbbbaaababababbabbaabbbbbbaaaaaaabaabbaababbaababbbabaababbaababbbaababbbbbabaaaabbaabbbabbbaaababababbababbbaabababbabbbabababaaaabaababaaabbbbbbbaaaaaaaabaabbabaabbaaaaaabaabbbaaabaaabbbbaaabaababaaaabaabababaabbbbbaaabababbbabbababaabaabaabbbbbbbaaaababbaaaaaababbababaaaabbaaabaababaabbababaaaabbbbbbbaabbabbaaaaaaaaabbbbbaababbabbabbaaaaabaabbaaababababaabbaabaaaaabaaaabaabbaabaaababbabaabbaaaabaaaabbabbbbabbbabaabbaabbaaaaaabbaabbbabaabbbabaabaaaababbbbbaabbbabaaaaaabbbbaabaaabbabbaaabaaabbaaabbbaaaaabbbbaabababbaaaaabbaaabbbaaaaaaaabaaababbbabbbbbaabaaabbbbabbaaaaaabbaabaabbbaaabaaaaabaabababbbabbbbabababaabaaaaabaaabaabbabbbbabbbbbbbaaaabaaaabbabaabbaabbbabbaaaaabababbbabbabbababaabbbbbbbabaabbabbbabbaaabaabbaaabaaaabbaabaabbbbbbbbabbbbabbbabaaaaabbabaabbbbbaabbabbbaaababaaaababbaababaaabbbbbbaaabbbbbbaaaabbaaabaabbbabbbabaaaabbaabbaaaaaababbaabaabbbbbabbaaaabbbbabbbbbbabbabbbbabbbbbbaaabbaabbbaaabbaaabababaaaaabbaaaabbbaabbabaabbabaaabbaabbbaabbbabbabbbbbbababbaaaaabbbbbaaabaabbbababaabbabbaaabaaabaabbaaabbabbbbbaaaaaaabaaabbbababbbbbbabaabbabbbabbaaabaabbbbbabaaaabaaaaabbbbaababbbabaaabbaabbabaabbbbbbabaaaababbbbabbaaaaaaaabbaaaaaabbaabbabbabbabbbabaabbbbbaabbbaabbbabaabaababbaabbbbbaabbbaaabaaababaaababbaaabbababaabbbaaaaabbbbaaabaaabbbabbbbabbbbbbbbbababbababbbabbbabaaaababbbababbaaabbbbbbbabaabbaaaabbabbaababbabbaaabaabbbbbbaaaaaaaabaabaabababaaababaaaababbbababaabaababaaaabbaabbabbaaaabaaaaaabbaaaabaaababaaaaaabbaaaaaaabaababaabbaababababbabbbaabaababaaaaaaaabababababbabbbbbaaaabaabbabbaaabaaabbaabbbaaaaaaabbbaaabbbbabababbaabbbbababaaaabbababbaaabaaabababaabaababbaabbbaaaaaaabaaabaaabbaaaaabbabaabaabbabbbbbaaabaabbabbbbbbbbaabaabbaaaaabaabbaaabaaaaabaabbbbbbaabbaaababaababbbbaaaaabbaabbbaaabbbaaabababbaabaabbaabababbaaaabababbaababaabaaabaaabbbbabaabbaabaabaaabbababbabaaaabbaabbabbababbabbaaababaaababbbbaabaaabbabaabbabbaababbbbbabaabaaabaabbbaaababbbabbbaaaabaabaaabbababbabaaababaaaabaabbabbbaaaaaabaabbaabbababaabaabbabbabaabbaabbbaaabababbbaabaabaaaabaabbabbbbbaabbbaabbbaaaabaaaaaababbbaabbbbaaaaababaabaaaaaababaaabbbaaaabaabaabbbbbababababbabbaabbbaaabbbbabbbbabaabaaabbabbabaabbaaaaaabbbabbaabaaabbaaabbaabaaababbbbbabbbabaabaaaabbbbbbababababababaaaabaabbaaaabbabbbbaaabababbbbbbbaabaaaaababbabaabbabaabaaabababbaaaabaabbabaabbbbbaababbbaaaabaaaababbbaaaabbbaabaabbabbaabaabbbbabaabbaabbaaaabaaababbbbbaaabbaabbababaabbbbbbbbbbbaabaaababbabaaaabaabaaaabbabbaabbbbbbababbababaababbabbaabbbbaaababbaaaaaaaaabbababbaabbabbbbababbabbaaaabbbbbbbaabbabbaaabaaababbbabbbaabaababbbaaaababababbbaabbbbbbaaababbbababbaaaaabbbbaababbbbabbbbbabaaaaaabbaabbbbabaaaabbbabaaabbbbbbaabaabbbbabaabbaabbbabaaabbabaaaaaabbbbaaaababaaaaaaababababbabbabbbaaabaaabaaaabaabaabbabbabaaaabbaabbabbaabbababaabaabbaabbaabbbaabbabaaababaabbbbbbbbbaababbbbabbabbaabbaabbbbaaabababbaaabbaabaabbaabbabbaabbabaaabbbabbaababbabbbaabababbbbaababbababbbbababaabbaaabbaabaaabaaabaabaaaaaababaaaaabbabbaababbabbbbababaabbbbaaabbbabaaaabaabababbbbbbababbbbabbaabbbabaababaaaaababbbaababbaaabbbbbabaaaabbaaabaababbababbaaaaaabbbabaaaabaabababbbbaaaaaabbbabbabbaabbbaaaaabaaaabbabbbabbabbaaabbbbaabbaabbabbabbabbbabbbbbbbabbaaaaaaaaabbaaaaabbababaaaaaabaabbbbbbabbbabaababbbaaabbababaabababbbbaabbbaabbbaaaaabbaabbabbabbbbbbabaabbbbaaaabaabbbbbbbabbbbbbbbaaaaababaabbbaaaaaabbabbbaabbababbaababbaaababbaaaaaababbaaaaaaabbbbabaaaababbabbaaaababbaabbbbbbaabaabbbbabaabaabbaaaaabbabaaaababbbbbabbaabaaababaaaaabbbababaabbaaabbbaabaaabbabbbbaaaabababaaaabbaabababbaaaaabbabaaaabababaabbbaaababababbbbaaaababaabbbbaaaabbbabbaaababbabaabbababbaaaabbbbbbbbbababbabababbababaaaabbabbaabbbabbbababaaaaababbaabbaaaabaaaabaabbaabaaabbbaaabaaabbbbaaabaabbababbbaabababbaaababbbabbbaaabaababbbbabbbaaabaaabaaababaababababbaabababaaabaaabaaabbaaabaaababbabababbabaaaaaaaabaaabaaababbabbaaaabbaababbaaaaaabaaaaabbaabaaaabbaaaabaaaababaaababbbbbbbaaabababaababbbbbbbabaaabaabaaaaababbbbabbaabaabbabbbabbabbababaaaaabaabaaabbabbabaaaaaaababaabbbbbababbaababbaaabbaabaabbaabbaaaababababbaaabbbaaabaaaaabbaabaabbaabbbabbabbbbbbaaaababababaaaaabbbababaabbaabbbaabbbaabbababbaabaabbaabbbbaababaaaaaabbbabaaabbbbababbaabbabbaaabbbbbabababbaabbabbbabbbabaabaabbabbbbbbaaabaaaabaabbaaabbaaaabaabbbbbaabbbabbaaabbaaaabaaaaaabbbbabbbbabbbabbbabbbbbbbabababbabaaabbababbbbaaaabbbaaaabaaaaaabbbbbbbabbababaababbabaabbbaababbbaabbbbaabbbaaababbabaababbbbabbbaaabbbbabaaabbbaabababbbabaaabaabababbbaabaaabaabababbababbbbbbaaabbabbabaaababbbababbaabbabaababaabbbbbbbaaababababababbbaaaabaabbaaaaabaaabaabaaaabaabbbbbababbbbaaaaaabbbaaababbbabaaaababbabbbaabbbaaabbbabbbababaaaaaaabbbbbaaabbbbaaabbbababaabaaaabbaabaaaabaabaaabbabaabbbbbabaababaaaaaaaabbaaabbbabaababbabaaabbbbaabaabababbbbaababbababaabbaabbabaaabaabbaabaaabbaabbabbaabaaabbaabbaaaabbbbbbababaabababbbbbabbbbbaababaabababababbbbababbaabbabbbbbbaabbbbaabbbbababbabaababbababbaabaabaaaabaaababbaabaaaaaababbbabbabbabbbabbaababaababbbbbababaabbbabbabababbaaabbaaaaabaaabbbaaabaabaaabbbbaaabaabaaaaabbbbbaaabbbabaaaaaaababaaabbabbaaaaaababbaaaababbbbabbbbabbbbbbaaaabbbbbababbabbbbbbabbaaabaaabbbbaabaaabaaaabaabbabaabbbaabaaaaabbbbbabbbbaabababaabbbaaaabaaaaabaaabababbbabbbbbbababbaababbaaaabaababbbaababbbbbbbaabbbabbbaabbababaaabaababbbaaaababbbbabababababbaaaabbbabbabaabbaaaaaabbbbbbababbbaabaabababaaabbbababaababaaabbaaabbbaaaabaabaaaaababaaaaababbbabababbbaabaaabbaabbaaabababbbbaababbabbaabaaaaabbbbaaabababaaabababbbabbbababbababaabaabbababaaabbbabaaaabbbaaaaabbbaabbbbaabbbabababbaaaaaaaabaabbaabaabbaabbbabababbaabaababaabbbbbaaabbbbbbabababbabababbabbbaababbaabbaaabaababbbabbaababbabbaaaaabbbbabbbaaabbbabaabbaaaaabbbbbabababbaaaaaaabaabbaabababababaaaababbaababbaababaabbbbaabbabbbaaaababbabbbabaaaaaaaaabbbaaababaabaabbbaaaababbbbabbbbbaaabbabbbabbaabbbbabababaabaaaabaaababaaaaabababaaabbabaaabbbaaaababbbbbbaabbbabbbaaababbbababababbabbbbbbbabaabababaaabaabbbbbbabbbbaababbabaaaaaaababbabaabbaabaabbaaaaabbbaaabaabaababbabbaaaababbaabbaaabbaaababaaabbaaabbababbbabbbbbbabbaabbbabbbababaaaabbbbbaabaabbbabbabbbaababbbabbaabbbbaaaabbaaaaaabbbaabababaabbabaaaaabaaaaabbbbaabbbaaaabbabbabaaabbabbabbabbbaababbaabbaabababababaaabaaaaabaabbbabbaabbbbabbbaabababaaaababbbaabbabaabbbabbaabbabbbbaaaaaaabbaabbabaabbaabbabaababbbaabbaabbbbaababaabbaaaabaabaaaaabbbaabbbbbbbaabaababaaabbaaaaabaaaabaabbabbabbbabaaaaababbbbabbaaabbaabaabbbbaabbbbabbbbabaabbabbbbaabbaabbaaababaaaaabbaabbbababbbabbabaababbabaababbabababaaaaabababaabaababbbabababbaaabbbbaabbbbbbabbbbbbbababbbbaaabbbaabbaaaabaababaabababababbaabbbabbbabbaaaaabbbaaaababaaabbabbbaababaaaaaabbaaabbabbbabbaababbbbbbbbababbbbbbababababaaababaaababbabbbaaabbbbabbabababaabbabaaabbaaabbabbbbbababaaabaababbaabaaababbbbbbbbaaaabbabaaaabbbbaaabbbabaabababbabbbaaaaabbbbaaaaabbbbbbaabbbbaaaabbbbbbbaaaabbbaaaaabbabbabaabbbbbbbbbbbbaaabaabababbbbbaaaaaaabaaaaabbababababaabbbbbabbabbabababababbaabaaaabbbabaababbbbaababbbbbababbbbbabaaabbbababbbabaabbaababaaababbaabababbbaabaabaaaababbaabbbabaababababbbababaaaabbabaaabaaaaabbbbabaabababbabbbbbbaabaaababbabbaaabbbbaabbbbaaabababbababaabbbbabaababbaabbaaaabbabbabbbbaabaabaaaaabbaababbbbaabaabaabbabaaabbabababaabaabaabaabbaaaabaabbbbbbbaaaaaaaaaaabaaaababbbababbbbbbbbaaaabbbaaabaabbaaabaabaabbabbaaabbaaaabbaabaabbbaaaaaabbabaaabbbabaabbaabbabbbbbbbbbaaabbaabaaaababbbbabbaabaaaaaababababaaabbbababbbbabbaaaababbbaabbbbbbaabbbbbabbbbabaaaaaaabababaaababaaabbaabbbaabbaaaaabaaaabaababaaabbaabbbbbaababbbbbababbbbbaabbbbbabbaabbabbabbbaababbabbaababbabaaaaabaabababbaaaaabaaaaabaaababbbabaabbababbabaaaaaaabababbaaabbaabbabababababababbbaabaaaabaaaaaabbaabaaaabababbbbababbaabaabbabbbbbabbaaababaaabbabbbaaaaabbbaababbbaabbabaaaababaabbbbbababaaaababbabababbaaaabbbaabbbbbbaababaaabbbbbababbababbabbabbbbbbbabaaaabbbbabaaaabbaaabbbbbaaabbaabbbaabbbaabaaaababbbbbbbabaabbaababaababaababbaaaaababaabaaabbbaabaabaaababaaabaabbbabbabaaabbababababbabbbbbaaabaabbbabbbbababbbabaaaababbbbbaababbababbbaaababbbababababbbbaaaabbbbbbbababbbaaababbaabbbbbbabbbbbbaaaabbbabaabababaabaaababbaaaaaaaaaaaabbbbaabababaabaabbbbababaaabbbababbbbbaaababababaaabaabbbaaaaabbaabbbbbabbabbabaaaababbabbbaaaabbaabbbbbabbabbbaabaaabbbaaabbaabaabbbbbaababbbbbbbaabbbabaaababbbbaaabbabbbbbbbaaababaababaaaaaaaaaabbbbbbaababbaababbabaaababaaaaabbaaaabbabababbaabbabbbaabbaaabbbaaaabbaaabbbbaaabbababbbaaabbbaaababaaabbbababbababaaabbaabbabbbbbaaabababbbbbabaabaabaaabababbbaaaaababaabbbabababbaabbbaababbbabaabbbabbabababbaaaabaaabbbabaaaabbababbaababbaababaabbbbbaaaaaaabaaabaababaababbbaabaabaabbbaaaababbbbaaaaaaabbbbabaabbbbabbaaababbbabbaabbabbbabaaaabbabbabaabbababaabbbababbbababbababbbabababbababbbaaabababbaababbaabbabbbbaabababaaabaabaaabaabbbaabbaaabaaabbaaaabaabbaababbbaaaaabbabaaabbbbabaabbaabbabbababbaabaababaaaaabbbaaaabbaabbabaabababaabaaabbaabababbbabaaaabbababaaaaaaaabaaaaabaababbaababaaababaaaabbbababaaabbaabbaaaababaabaaabbabaabaabaabbababbabababababbbaabbaaababbaaabbaabbbaabaaaaababbbaababbbbaabaaaabaabaaabbaaaabbababbbaaaaaaaabbbababaabaaabaaababbbbbaaabbabbaaaaabbaababaabbabbbaababbabbbaaaabababbbbbbaabaabbbbbbbabaaaabbababaaaabaaababaabbbbbabaaabbaabaababbababaabbbbaaabababbbababababbaaaaaabbaaaabbabaabbabaabaabbabbbbaababaababbbaaaabbaaaaabbabbaabbbabbbaaababbaaaaabbaabaaabaaaababaabbaabbabaababbbbbabaabaababaaaaaaabbbbaaabbbbabbaabbaabbaabababaaabbbaabaaabbbbaabbabbbabbababbaabbbabababbaabbbbabaabababbaaabbbabbbabbababbbbabbaabbaaaabbabbabbbabbbaaabbbbbababbaababbaaabbabbbabbbabbabbbabbabbbabababbabababbbbaaabbbbbabbababbbbbaaaabaaabaaabbaabaabaabbabbbaabaabbabbaaabbbbabaaabbbaabbabababbbbbbbbbabbaabaaabbbbabababaaabbbbabbbabbbbabaabaaaaaabaabbbabbaaabababaaaabbbbbbbbbabbabbbabbbabbaaaaaabaabaaaabbaaabaaabbabbaabaaaaaaabaababbaabaabbbbabbabbaaaababbbababbaaabaaaaaababbaabbabaaabbabaaabbaababababbbbabbbabbbbaaabbbbbabbaaabbbaaaababababbbbababababbbbbabaaabababbbaaaaaababbaaaabbaaaabbaababbbbbababbbbabbabbaaaabbaabaabbbbbbbbabaabaaaaaabaababaabaaaaaababaaaaabbbababbbabababbabbbbbbbabbabbbbabbbbabbbbbabaaaaaabbaabbbbaabaabbbaabaabaabbbbbababbabaaabbbaabbbbbaaaababbbaabbaabbababbbaaaabbbabbabaaabbbaaabbbabbabbababaabbabababbaaaabbbaabbabaabaaabaaaabbbabaaaabbaabbbabbbbaababbbbaabaaaabbbababbaabbbbabaaaabaaaabaaaabababbbbaabaaabaaabbabbbabbbbaabababaababbaabbbabbabbabbbbaababbabaaabbabbbbaaaababbaaabaaababbaaababaabaabaababbaabbaaabaaaabbabaababaaabaabbbaabbababaaaaabaabbbbabbbaaabbaabbabaabaabaaabbaabbabbbabbbbbbbababbaababbabbaabaaaaaaabbaaabaabbabbabaababbabbbbbbababaabbaabbbabaabbbbaabaabbbaaaaabaabbaabaaaaaaaaabaaabbabaabaaabbabaabaababaabbbaaababbbabaaaaaaaababaaabbbabaaabababbbbaaaaababaaabbaababbabbabbaaaabbbaaabababababbbaababaaabbaaaabaabbbbaababaaaaabbabbababbabaabbbabaaaaabbbbbabababbaabbabaaabaaaabbaaabaababbaaaaabababaaaaaaaaaababbbaaabaaabbbbaaaaaabbaabbbbbbbbababaaabaabbbabaaabbbaaabbbbabbaabaaaababaaaabaaaaababbaabbababbabaabbbabbabbbaaabbaabbaabbabbabbbaaabbbbaaabaabbaaaaabbbbbbbaabbabbbaabbabbbabbbbbbabbaabababababababbabaabababbaabababbbbbabaaaabaabaaaaaaaabaaaaaaaababaaaaabbbbaabababbbaaaaaaabbababaaaaaabbabbbaabbbbababbbaabbaaababbbbaaabaabbabaabaaababbbbabababaaabbabbaaaabaaaaaaabaaaabaaabbbbaaabababbbaabbbbbabababbabbaaabbaaabaaabaaabaabbaaababbaaaabaaabaabaabbbaabbabbabbaaaaaabbbbaaabaaabbbabbabbaaabaaaabaabbaaabbbabaaaabbababbbaaababbabbababbabbbbababaabaabbbaaaabbbbbbbabaabaaaaabaabbabbaaabbaaabababbaabbbbbaaababbaabaabbabbabbbbbbababbbbbaabbbababaabbbbbbbaaabaaabbbaababbaaabbaabbbbaaababaabbaabaaababbabbabbabbabaabbbbbaaaabbabaaabbabbbbbababaaaaabaababbabbabbbabbabaaababbbabbbabaaaabbbbaaabbbbbbaabaaabbabababaaabbababbaabaaaabbaaabbbbbbababbaabbababbbabaabbbaabababbbaaababababaaabaaaaaababaabaaabbaabaaaabaaaababaabbbaaaaaaaaabaabbababbabababbbaaaaababbabbaaaaaabbaaabbbabbaaaababbbaababbaaababbaaababbbbbbabaaaaaabbbaabbbbabaaababbababaababbbaaaaabababababbaabbbbbbbabbbaaabaaabbbabbbabbaaabbabbbbaaabbaaaaaababbbbababaaaabbababaaaabbbbaabbabbbabbbbbaaabbbaaaabbaaaaaaaabbbabbbababbbabbaaaaaabababbbbbabaabaabaaaaaababbabaaaabbabaabbbbbbbbbabbaaababbbabaaabaababbbabbbbaababbabaaabbaabbabaabbaaababaaabbaaaababaaaababbaaaaaaaaabaabbbbbabaaaaaabbbaaaaabaabaaabbbbbbaaaaaaaababaaabbaabbabbbbbaaabbabaababbbaabbaaaabbaaaaaaabbaababaabaababaaabbaaaaabaaaabaabbbaaababbbbbabbabbababbaabbbaabbaaabbababbabbabaaabbbbbbaabbbababbaabbabaaabbabbbbaaabaaaababaabaabbbaaaaaabbababbaaabbaaaaabbaabbbaaaaabbbbbbbabbaabbbbbabbababbaabaaaabaabaabaaabbaaabaaababbababbbabbbbbbaaaabbaabaaaaabbbabbbabababaaaababbbabbaaaababbbbbaaaaababaaabbbabbaaabaaabbabbbaabbaaaabbaaaaabaababaaaaaaabbbabababbbaababbababbbababaaababaabbababbaabbaabbaabbaababbaaabaaabaaabbabbababbababaabbbbaabbabbbaabaabbbbbabaabbaabaaabaaaaabbbaabaaabbabaaabaaaaabbabbaabbaaaababbbbbbbaabbbabbbaabbaaaaaabbaabbabbabbbbaaababaabbabbbaaaabbbbbaababaababbbabbbabbbababaaaaabbabbbbbabbabbabbbaabbbbaaabbbabaaabaaabbbbbbabaaaabbabaabbabbaaaabaaabbbbabbaabaaabbbbbbbbabbbaababbbbbaabbbaabbbbbaabaaaaaaaabaabbbbbbbbbbaaaabaaabbbbabaaababaaababbbaabaaaabbaabaababbbbbbaaaaabaabbbbbaaaababbbaabaababbabababbabababaaaaabbaaaabbaabaaaaaababaaabaabbaababaaaaabbabbabaaaabbbbaabaabaaabaabbabaababaabbabbaabaabbbbbbaabaaabbaabbabbbaaababababaabaabbbabbbababbbbbaababbbabbbbbababbaababaaababbbaaabbabbbbbbbabbbbbbbabaabaaaaababbaababaaaaaabaabaaaababbababbababbbbabbabaaaabbabaabbaaaaabbaaaabaaaaaaaaabbaabaabbbbbabbbaabbbbaaababaaaaabaaaaabaaababaabbbabbbababababbabaaabbabbabbababbbbaabbbabaaabaabbabbbabaaaabaabbbbaabbaaabaaabbbbaababbbaabbbababbbbbbabbaaaaaaaababaabbbbabbbbaaaaaaaaabaababbaabbaabbabbbaabbbbbbbaabbaaabababbbbbabababbbaaaabbbaaaabbbabbaaabbbababaabaabaabbabbbbaaabaababbababbbaaabbaaaaabaaabbababaaabbbabbababbaabbbaababaabbabababbabbbaaaaaaaababaaabbabbbaabbaabbbbaabbaaababaababaaaabaaababbbbaababaaabbaababbbbbabbbaabbbbababbbaababaabbbabaaaaabaabbbbababaababbbbbaaababbaaabbabbaabaababbbbbbabaaabababbbbbbaabbaaaabbabbaabaababbabbbaaaabbbbababababbbabbabbbaabbbbaabbbaababaabbbbaaabbbabbaabaaaabaaabbaabbbbbbaabbabbabbaaabbbbbbaaabbaabbbaabaababbbbaabbabbabaaaababaaaaabaabaaaabbbbababbbbbbabbabbbbabbbbabbbababbaaaaabaabbabbbbbaaaabbabbbaaabababbaaabbbabbbaaaaaabbabbaaabbbaabaaaaabbaabbabbababbaaaaabaabbbbbbbbabbbabbaaaabbbaaaabbaabbbbabbbaabaabbaaaababababbbbaabaaaaabbbbabbbaababaaaaaabbbabaabaaaabaaabaabbaaaaabbabbbbbabbaabababaababaabbbbbbbbbaabbaaaabbbbaabaaabbbbbbaaabaabaabbbbaaaabbbbabaabbbbbaaabbaaaaaabbaababbabbabbabaabbbbabbbaaabaaababbabbbbabbaaabbabaabbbbaababbabbbbbabbbabbbbbbbaaaabaabaaabbbbaaabbbabbabaaaaabaaaabbaabaaababaaabaaaababbbabbbabbaaaaabaabbabbabaabaaabaabbbaababaabaabaabbababababbaaaabbbaabbabbababaaabbbabbabaaabbbbaabbbabbbbbbbabbbbbbaabababaaababbaaababbabaaababaabbbbaabbbbbbbaaaababbbbbabbbbaabababaabbabbabaaaaabbbaaababbbabaaaaaabbabbbbaaabaabaabbbabbaaababbaaaaaabbbaaaaaaabaaaaaabababaabbbabaabaabbaabbbbaabbabababbaaabbaaaaaaaaabbaabbbaabbabbabbaaaaaaabbbbbaabababbaaababaaaaababaaabaaabbbbbababaaabbabbbabbababaaababababbababaababbabbabaabaababaaaaaabbbabbaaabaaaababaabaaabababbaabbabaaababbaaabaabaabbaaabaaaabbbaaabaabaabaabaababbbbaababbaabbbaaaabababbababbaabaaabbaabaabbbbbbaaaabbabbaabbbbaabaababbbbbababaabbbbbbabbbabbbbbaaabbaabbbaaabaababbbaabbabbbbbabbbaabbbbabbbbabaaaaabbbbabbaaaabaabbbbabbabaaababaaaaaabaabababababaaaaaababaabaabbbabbbababaabaaaaaabbaaaaaaabbaaababaaaaaabbbaababaabaaaababbaaabbaaaaabbbaaababbbabaabaaaabaaaaaaaaabaabaabbbaaabaabaabbbbaababaaabbbbaaabbbbbbabbbbbabbabaabbabbbaaabaabbaabaaaabababaaabababaababaaababbabaaaababbbbbbbbbababaababbbababaababbbabbbbabbaaabaababbaabbbbbbbbababaabbbbbabbbaabbbbabaabbbbbababbbabbaabbbaaaabaaaaaaaaaaaaaabaabbbaabbbaabaaabbbbaaaaaaababaababaabbababbbaaabbaaabaaaaabbaabbbbaaabaabaabbaabbabbaaaaaaaaabbbbaaabaababababaabaaabaaababaabbbaabaaababaaabbbbabaaabbaaaabababaaaabbbabbaabbaabbbbbaababaaaababbaaaabbaaababbabbbabaaababbbbaaaababababaabbbabaaaaaaaabbbbabbbabbabbbbabaaaabbabbbbbbbbaababaaabbbbbaaaabbaaaabbbbabaabbaabbababababaabbabbbbbbbaaaaaaaaabaabaaabbabbabbbbaaabbabaaaababbbbbaaababaabbababaaabaaaabbabbbabaabbaabbbbbaaaabbbbaabbbbbbbbbabbaabbbabbaabaabbbaabbbabababbabababaaabaababaaabaaabaaabaaaabbbababaabbabbbabbababbbaaaabaabbabaabaaaabababbaabbbabaabaabbabaaabababbaaabbbbbbaabbbbbbbaabbabbbbabaabbabaabbbbabbbbabbaaababbabbbaaaaaaaaabaabaabababaabbbabbaabbbaabbbbaaaaaaaaababbbbabbbaabbbbaabaaabbbbabbbbbbbabaaababbabaaaaabababbababaabaaaaabaaaaaaabaaabaababbbbbbbaaabaabaaabbbaaabaabaaaabaabbbaaaaaabbabbbabaaabbbbabbbbbbaababaabaaaaaaaabaabbbaaabbaabbbabbaaaababaaaabbbbbbaaaaaabaabbbaabaabaaabababaabaabaabbbbababababaaabaabbababbbaabbbbbabbbaabbaaababbbabbbabbabbabaaaaaabbbaabbaaababbbabaaabbbaabbaabbaaaaabaaabaaaaabbbbbaaabaabbbbabaaaaaaabaaabaabababababbaaabbbabbbbbbaaaabaaaabbbaaaabbbbabbbabaabaaababaabbaaaaaabaaaabaaabaaababbbabaaaabbaaabbaababaaaaabaaaaaaaabbbbababbbbaaaaaaabaaaaabababbaabaaabbbaaaaabbbbbbaababbaaabababbabaababbbababbbbabbbbaaaaabaabababbaabbabbabbabaabbababaabbababbaaabbaaabbbaabaaaaabaababababbabbbbbbbbaababaabbaaaaabbbbbaaababbabaabbbbabbabbbaaaabaaabbaabababaabaabaabababbaaaabababaaababbbaabbabaabbbbaaababbaaabababbbabbabababbabaabbabaabbbabbbbbabaaaababbabbbbbbabbaaaaababbbbaababbabbabbbbbababaaabbbbaababbbbbaabbbabbbabbaaababbaabbabaaabaababababbaaabbababaaabbbaababbabbbbbabbababbabbbbabbaaabbbbbbbabbababaabaaababaababbaabbaaabbaaaaaabbbbbbbbbbabbbabaabbabbabbbaaaabbaaaababbabbaababababaaaaaabaaaaaaaaaaaaaaaaaaababaababaabbabbbabababbbbbbbbbbbbbaabababbaaabbbabbaaabbbbbbbbbabbbaabbabbbaaabaaaabaaabbaabbbbbbbaaaaaaabababbbbabbbbbaaaaaaabbaabbaabbaabbbabbbbbabbbabaabababaabaaaaabbbaabaababbbbbabaabbbababbbabbabbaababbbbbaabbabbabbababaaaaaababaabbbabababaabbaabbaaaaabbaaaabbbabbbabaaaaabaabbbaaabbbbaabbbaabbaaabbaabaabbabbaaaaabaaabbaabbabbbabaaabaabaaaabaabbabbabbbbaabbbaaababbbaaabaabbbbabaaaaabbbaaabaabbbaaaabbaabbbabaaaaababaabbbabaabbbaaaaaaaaaabbaaaabaaabaabbabbababbbbbabbbaabbaaabbabaaabaababbaabbbbabaabbbbbabaaabaabbaaaabbbabaaaababbabbaaaababbabaaaaabbaaababbbbbababbbabbbaababbbbaababaaaababbabbbbabbabaabbbaababbbabaaaaabbabbbbbabbbabbbabbabbbbbbbbabaaabbbabbaaabaabbababbaaaaaaabaaabaaabbbbaaaabababbbbabaabbaababbaaabbbbbaaaabbabaabaaaababaaaababbaabababbabbbabbbabbaabaaaabbbaaabbbabbbaaabaaaaabbabbababbbbaabbabbabbabbbaaabbbaaabbbaaaababbabbabaaaaababaabbbbbbaababbbabbabbbbaabaaabbbababbbbabaabababaabaaabbabaabbaaaabaababbbaaaaababaaaaaaabbabaabbaaababababaaaababbaabbbaabaaaabbbaaabaaabbaabababaabaabaabbababbbaababbbbbbababbabbaabaaabbabbbbbabaaaabaabbbbaaaaabaabbbabbaabaabbbababbaaaababaabaaabbababbaaaabbbaabbbbbaaaabbbaaabababbbbbabbbabbbabbaaabbbbaaababbaabaaaabbbaabaabbbbabbbbbaabaabaababababbababaaababbaaabbbaabbaababbbaaababbaabaaaaabbaabbbbbbaaaaaabaabababaabbbbababbaaabababaabbabbbaabbaaababaaaabababbaababaabbbaabbbaaaabaaaaaaabbbaaabbbaaaabbbaaabbaaabaaaaaabbbbaabbaaabaabbbbaaaabbaabbbababababbbaaaabbaaabbbbbbababbabbbaaaabbaababbbaabbabaaaaaabbabbbbbbbbbbaabaaaaababaaaaaaaaaaaaaabaabaaabaaaababbaaaababababbbbaaabbbabaababbbaaaaaabbbbaaabbbbbbabaabaababbababaabaababaaabbaaaaaaabaabbaaaaaaabbbaaabbbbbbaaabbbbaaabaaabababaaaaaababbbaaaabbaaaabababbaababaaababbabaabbbbbabaabbaabbabbababbaabaaaaaabbbbbbaabababaabbbaaabbbababbabbababaabbbbbaaaaabababaababbbaaaaaaabbbbbbbaaabaabaaaabbabbbaaabaabbbbbaababababbbbaabaaabbabbbbabaababbbbabbabbbabbbabaaabaabbbaaabaabbaaabbaaabbabaaaaaaaaabababbaaabaaaaaaaabaabaaabaaabbbbaaabaabbabbabbaabbaabaabbbabaaabaabbabbbbbaabbabbbbbababbbbaaabbbbabaabaaaaaaabaabaabbaabaabaaababaabaabbbabababbbbaaabbabbbbbbbbababaaabaabbbaabbabbabbbaaaaabbabaabbaaabbbabbaabbaaaabbbbaabaabaaabbaaabbabaaaaabaabaabbbaaaabbabbaabbbabbbbbababbaabaaabaaabbabaaababbaabbbabaabbaabbbbbabaabaaababbabababbaaababbbbbaababababaabaaabaaaabaaaaabbbabaaabaabbaaaababababaaabaabbaabbbababbaaaaaabbaabababbbbbbaabaabaabaaaababbbaabbbabbabaabbbaaabbbbabaaaababbaabbbabbababbbaaaaabaabbaabbbaaabbbbaaaabababbbbbabbbbbbbaaaabbabaaaabbabbbbbababaabbbabbaabbbbabaaabbabbbbbaabbabbbaabaabaaabaababababbbbaaababbbbbbabaaababaaabbababaaabaababaaaaabbbabaaabbaaaaaaabbaabbabaaabbabaaaabaabaaaaaaabbbabababaabbbababaabbbbbbbbbbaabbaabaaabbbbbabababaaaaabbbbabababaaaabbaaaaababaabaabaabababbbbbbababababbabbaabbaabaabaabbabababaabaaaaabbaaaaabaaaaababbbaababaaaaaabbaabbaaaabbaabaabaabbabbabbaaaabaababbbbbabbabbbabbaabbabbabbabaabbaaaabbababaaaaaababbaaaaabbbbbaaababbbbabbbabaaababbaaaabbbabaaaaabaaaaabbbbbbbabababbbbbaaaaaaabbbaabbbbbaabbbbbaaaabaaaaabbbbbbbbbaaaabbbabbabbbaabbbabbbbbbababaababbbaaababaaaaabbbbbbbbbbbababbbbbabaaabbbbaaaaaaabbabbaaabaabbbbbabaaaababababbaaabbaaaaabbabaaaaabbabbaaaabababbaabbabaabbbbaababababaaaaabbabababbababaaaabababababaabbabbabaaaaabaabbbabbaaaababaababbabaaaaaaaaaaabbaabbabbbbaababbbabbabaabbaabaabbabbaababaaabbbbbaabbabbabaabaabababaaaaabbababbabababbaabbabaabbbaaaaababbaabbabbbbabbaaabbabbabbabbaaabbbaaaabaaabbaababaabbbbaabaabbabbaaabaabababbabbbbbbbbabbabaaabaaaaaabaabaaaabbbbbbaaababbbbaababbbabbbabaabaaababbbaaabbbaabaaaabbabbbbbbbbbbbbabbabaaaaaabbbaabbabbbbababbbababaababbbbaabaabbbbaaabbbaaaaaaabbaaaaaabbbbababaababaabaaaaabababaaaaaaaabababbaabbbaaabbabaaabaaabaaaabbabbbaaaabbbabbabbbabbbbabbababaaaabbabbbaabaaaaaaabaabbaaaaabbbbbbbabaaabbababababaabbabbaaabababaaaabaabaabbbabaaababbbbabaaaabababbbbaaaaabaabaababbabbbbbbbaaabbaabbbbbbaaaabbaabaabaabaababbabbbaabababaabbbaaababbbabbbbbbababaaabaaaabaabbbaabbbaaaaabbbbbaaabaababbabbaaaaabbaaaaaaaaabbabaaaaababbabbbabaababaaaabaababbaabbbaaabaabbbbbaaaaabaaaaabbbababaababbbbbbabaabaaabaababbaaabbbaabaabbbaaabaaabaababababbbabbabaabaaabaabbbabbbabaabbaaaaaabaabbbbbaababababaaaaaababbaaabbabbaabbbbbbbbabaaababbaaaabbabbaababbbabbbaaabababbbaababbbaabbabbaabababaaaabbababaabbbbbaabbaaabaaababbabbbbbbaababbabbaabbabbbaabaaabbaaababaababbabaaaabbaababbaaaaababbaaaabbaaaabaabbbbaaaaaaababbaababaabababaabbbabaaabbbabaaaabaaaaaabbbabbaababbaabaabbbabbbbaaabbaabbabaabbabaaabaabbbbbababbaaaaaabaabbababbbbbaaaabaaabababbabbaaabbaabaabbbababbaaaababbbbbabbbbbbababbbbbbbabbbbbbaabbbabbbababbbbababaabaabbabaaabbababbaabbbbaaabbbbbabbaabaabbbabbbabbaaababaabaabbbbbabbabababbabaaaabbbaaaabbabababbabbbbaabababaaaabbaababbbabbbbaabaabababbabaaabababbbaabbbaaabbbabaaaabaabaabbabbaaaaaaabbbaabbaabbabbbaabaabbbabbbbbaaaabbbbbabbbaabbbaabbbbbbaaabbabbbbaababbbabbbbaaabbbbaaaaaabaaabbbbbbababbaaababaabaaaaababaaaaaaaaaabbaababababbaaabbabbabbbababaababaababbbabaaabbbababbbabbbababaabbbaaaabaabaabbbaaabbbaababbbaaabbaaabaaaabaabbbbbbabaaabbbabababbbbababaabbaabbbababaabbbbbaaaaabaabbaabaaababbabbbbaaabaaabbaabbbbbaabaaaababbbbbaaabbbabbbbbbaabaabbaaaababababbaabbbbabaaaabaaabaababaaaabbaaabaaaababbbbababaababababababbbabaaaababbaabbbbbbabbbabaaaaabbaabaabaaaabbbbbbababbaabaababaaaaaabaabbbabbbbaaaabbbabbbbbbbabbbaabbbbbabbabbaabbbbabbaabbbbabbaababaaabaabbaaaaaabbababaaabbbbaabbabbbbaaabaaaaabbababaaabbbbbbbaabaaabbaabbaabbbabbabaababbaaaabbbbbabbbbbaabbbaaaaabaaabbbababbababbaaabbbaabaaababababaabaabbaaababbabaaabbbbbbaaabbabbbbaabaaaaaababbbaabbabbbaaaabaaaabbaabbbbababbbaaabbbbaabbbbbbabbbabbaabbaabbabbbbabaabaaabaabbbbbbbbabbbbbbaabbaaaaabaaaabbbbaaabbabbbaabbabbabbabababbabaabababbbabababbababbaabbabbbbbbabaaaabaaaaaabababbbabbbabaabbaabbabaabaaaabbaaabaabbbbaaabbaabbbaabbabbbbbababaaabbaaabaabbbaabaababbbbabababbaaaababbabbbaaababababaabbaaabaabbabbaaabbaaabbabbaabaaabbabbabbaabaaabbbbbabbabbaaaabaabaababbbaaababbbbbbbabbaaaaaaaabbaababaababbababbabbabbbbaaaabbbaabbbbabbaaabbbbaabbaaabaaabbbbbbaaabbaaaaaaaabaabbbbaaaaaabaaabaabaaabbabbaaaaabbbaaaaaababbabbbbaaabaabbbabaabababbbbbbbbbaabbbbbabaaaaaabbaabaaaaaabbaaabaaabaabbbabaabbbaaabbaaababaababbaaababaabbbabaabbabbaabbbbbbbbbbabbbabbbbaababaabaaaabababbbababbbababbabbaaabbaaaaaaabaaababbaaabbaabaabaaaabbababbbabaaabbbbaabbaabbabbabbabbbbabbbbbbaabababbbbabbbaaaaaaabaaaabbbbaaaabbbbbbabbabbbbbbbbbaaaababbbaaaababbaaabbbaabbbaaabababbbbabbbbbaababababbabaaaabababbbbbaababbabbaaaaaaaaabbbaaaababbbbababababbaaaabbaababaabbbbabaaaaabbabbbabbbaabbaaabababaabbbbbababbbbbaabbbbabababababaabaaababbabaaaabbbabbabbbababaaaaabbabaaaabbbbbbaaaabaabbbbbabaaabbabbbabbabbabaabbabbbbbbabbbaaaaaaababbabbaabbababaaaaabbabbaabababbbaabaabbabbbaabababababbbbbbaaaabbbaabbbabaabbbaababbbabaabababaaabbabababbaabbbbaaaaababaabbabaaabbabbbbababbbababbbbabbbaabbbbbaaaababbbabaaababbaabbaaabbaabbbaabaaaaabbbbabababaababbbabbbabbbbbbabaaaabababababbabbbbbaaabaaaaaaaaaaaabaaabababbbabaabbabaaaabbbaaabbababababaabaabaabbaabaaabbabbbbbbbbbaabbbababbaaaabbbaababbbaababbababbbbaaababbbabbaaaaaabaabbbaabbbabbbabbaaaaaaaabbaababbbaaabaabbabbaaaaaabbabbaabbbbbbababababaaabaaabaabbababbbaaabaaabaabbbbaaababbaaaabababaabbbaabbabbbbbbbabaabbabbabaaababbaaaabbabababbbabaabaabbaaababbaabbbaaabaabaabbaaaabaabaabbbbbabaababbaaababababbbaaaaabbaabbbaaabaabbababbbbbabbbabaababbabbbbbaabaababbababaaaaaaabbbbaabaaabababbbaaabbaaabbbbaaabbabbaaabbabaaabbaabbbbabaaabbbaabaabaaabbaaabaaaabaabbabbaaabbbabbaabbababbabbaaabbbabaabbbbbbaabaaaaaabbaabbbaaaaabaabbaabaaaababbabaabbbbbabbabaababbbaaabbabbababbaaabaabaaaabababbabbabbbbabaabbbabbbabbbababaaabbaaaaaaaabbaaaabbaabbabbaabbabababbaababbbbababaaaabbaaabbabbbbaabbabbbaabaaaaaaabbbbaababbabaabababaaaaabbbabbaaababaabbbbbbbaabbaaabbaaabbaabbabbaaabbbaaabaaabababaabaabbbbaaabaaabbbbaabbabbbaaaabbaaaaabaabababbababbbbbabbbbbababbbabbbbbababbbabbbbaaabaabbabbbabbaaabbbaababaaaababbbbbaabababaaabaababababaabababaaabaaaabbaabbabbabaaabaaaababaaaabbabaabaabbaabababaaaabaabbaaabbbabbbbaaaabbabaababbaaaababaaaabbabbaabaaaaababaaaabaaabbaabbbbaababaabbaabaababbabbbbbabbbabbabbbbaabbaaabbbbbbbabbabbbaaabababbaaaabbbbbbabbaaaaaaaaaabbabaaaabbabbbaaababbbaaaaabbbbbabaaaababbabbbbbaaabbbababbaabbaabbbabaabbabababbbaaaaabbbbbaaabababbabaaaabaabaabbaabbaaababaaabbaaaaabbbabbaabaabbbbbbabbababababbabababaabbabaabbaaabaaabaabbbabbbbbbbaabaabbbabaaaabbbaabbabababbaabbaababaaabaabbabbbbaaabaababbbbaababababbbabbbbbaabaabbbababbbaaaabbbaabaabaaaabbbbaaaaabaabbbabbababbbbabbaabbbbbbabbbaaaaabbbabbbababbbbaaaabbbbaababbbbaabbaaabbbabaaaabbbaaaaabaaaabbbabababaaababaabbbbabaabbbbbbbabbaaaaabaaabaaaaaaaabababababbababbbbbabbaaabbaababbababababbababaabaabbbaaababaabbbbbbaaaaabbaaabbbaababaaaababbbbbbaabbbaababaaababbbababbbabbbabbbababbbbbbbbabbbbaabbbbbbaaabbabbabbabbbbbbaabbabaababababaaaaabbaababaaabbbabaaaabaaababbbbbaaaaaaabbabbbbbbabaabababbabbbbbaabaabbabaabbbaabbbabaabaababababbababbaabababaabbbbababaaaababbbabbbbbbabaaababaaaabaaabababaaabaabbbbaaaabaaababbbaaabbbabbbabaaaabbbbbbbaabaabbaaabaabbaaaabbabbbaabaababbaababbbaabbabbabaaaaabbbaababbababbbaabaabaaabbbbbaaababababbaaaaaaababababbbbabababbbbbbabbabbaababbbaaaaaabaaabbabbaaaaabbabbbabaaaabbbbaaaaababbbbaababbabbbaaabbbbaabaaabbabbaaaaaaabbaabaababaababbaaaabaababbaabbabbbbabaabbbbbababbbabbababbbaaaaabbbbbabaaabbbababababaabbaababbbbbbababababbabaaaaaabbbaabbbabbbaabbbbabaabbbbbaaaabbaabbaabbbaabbaabaaaabaaabbababaabaaaaaaabaabbaabbbabaaabbaabaabaaabaababaaabbbababbbbbbaabbaabbbbbaabbbbbbbaaabababaaaaaabbababbaaaaababbbababaaabbbbaaaaababbbbbabaaaabaabababaabbbbabbaababbabbbbbabaaaabbbbabbbbaaaaaaaababbbbabaabbabbbababbbbaaaaabbbabaabaaabbabbabaabaabbababbbbbaaaaabbbbabbbabaaaaabbaaaaabbbbabbbaabaaaabaabaaabbababbbbbbabababbbabbaababbbbbaabbbaaabaabbbaaaabaaabbabaabbabbbababbbaabaaabbaabbbbababaaabaabaababaaababbbabaabbbabababaaaabbbbabbaabbababbbaaaaaababbababaaababaabaababbaaabbabaabaaaaabbaababbabaaabaababababbaababaabaabbabbbbbaaaabbabbaabababaaaabbbabbaaabaababaaaaabbabbaababbaabbaaabbababbbbbaaaaabbbbbaabbbbababaaaabbbbabbaaabbbbbaaabaabbbbababbbbaaaaaabbabbbbbbabbaabbabbaaabababaabbbbaaabaabbabbabbaaaaabbabbaabbbabbbbabbbabbbbabbaaabaabbaabbbaaabbabbbbaaaabbbaabbabbbbbbbabbbabbaabbbbbbaababbbabbbaaaabbbbbaabaaabbaaabababbbbabbababbbbbbabaaaabaabbabaabbaabbababbabbaababbbabbbaabbabaaaaaaaaaaaabbbbbbababbbbaabbbbbbbbbabbbabbaaabbaaaabbababababbaaabbababaaabbbbbbbaaaabababbbababbaaaaaaaaaaabaabbaaabaabaaabaabaaabaaaaaaabaabaabaaaababaaabaaaaabaababaabbababaaaabaabbbaabaabababaababaaaaabbaababbbababbbbbaaaaababaabababaababbbabaababbabbbabbabaaabbabbabbbaababbababaaabbaaaababababaaaaabbaabaabbabbabaaaababbabaaababbababbbbaaabbaaabbaaabababbbbbabbabbbaaabbbababbabbabbabaabbbaabbaaabbbaabbaabbbaaabaaaaabaabbbabbabaabaaababbbababaaabbbbbbabbaababaabaaababbababbaabaaabababbbbbbbbababbbabbbabaaaaaabbaaaaabaaaaabbaaabbbbababaababaaabbabbabbabbaabbbaaababbaaaaaaabbbababbbabbaaabbaabbbabbaaababbbabbbaababbbbbbbaabaaaabbaabbbabaaabbbbababbbaaaaababbaaabbbbbbaaabaaaaabbbbbbbaabbbabaaabaaabababaabbabbbabbbaabaaaaababbbbbabbbbbaabaabbbaaaaaabaabaabbabbaababaaabbabaababbaaaabaabaabbbaaaababbbababaaaabababababaaaaaababbbbaaabbabaaabababbaabbbbabbabbbbaaaaabaabbbabaaabbbbbaaaabbbaabbaaababbabaabbabaaabaaabababaabababaaabaaaaabaababbaaaabbaabaabbbbaabaaaaabaabbabaabbbaaabbbabbbaaabbabbabbbbbabbbbbaababababaaaabbbaabbababaaaabbabaabbaababbbbaaaaabaaabbbbbabaaabbbaaabbaabaaaaabbabaabaaaababbabbaababbaaabbaaaaabbbaabbaaaaabaaaabbbaaabbabbabaaabaaaaabbabbaaaababbbbbbabaaaaaaaabbbbabbbbaaabbaababbbababbbbbbbbbaababaabaababbabbabbbbaabaabaabaaaabbabbabbbbaabbbaabbbbbbbaaababbaaababbbaabbababbaaabaaaaaaaaaabbbbaabaaaaaababaabababbabbaababbabbbaaabbbbaaabbababbbababbaaabbbabaabbabaaabbbaabaaaaababaaaaaaabaaaaaaaabababababaabbbbbbabababbbbaaabababaabbaabbaababbabbbbabaaaaabbbbabaababaaaaaabaabbbbbaabbbaaabbaabbbbbbbbaabbaabbbbabaaaaaabababbaababbbbaaaabbabbbababbaababbbabaabbabbaaaabbabbbabbababbbbabbbabaababbbababbbabbaabbaaababbbbabaabbbaabaaaaaabaabbbabbbabbaabbaabaababaaabaabbbbaababaaababababababbaaabbbabbabbbbbbbbaabbbababbabbaabbaaaababbaabaaabbbababbababaaabbbbaaabaabababbbbbbaaaabbbaaabbbbaabaaaabaaaaaabbabaabaababbbaababaaabaaaabbbabbbbbaabaabaaaabbbabbbaaaaaabbabababbbbabbaaaabaababbabbbbbbbbbaaaabbbaaaabaaaaaaaabbbabbababbbbaabbbbaaaabababaaaaabaababbbaababaabaaaababaabaaabaababbbaaabbbbababbabababaaaaaabbbbbbbabbbaabbbababaaaabbbbaaaaabbbbbbbaab
baabaaabbbabbaabbabbabbbabbabbabbbbbaaabbbbaababbbbabaababaaaababaaabbbaabaabbbababaaabbbabaabaabababbbaaaabbababbabbbbbabaaaaabbbabbbababbabbaaabbabbbbbaaaaabbbabbbaaabbbaaabaaabbabbbaabbbaaaaaabbbbabbabbbaabbbbaaaabbbbaaabbababbabaabaaabbaaaaaabaabbabbbabbaaabaabaaabaaabbabbaaaabbbabbbaaabbbabbbaaaabbabbabbaabbbbbbbabaaaaaabbbbaabbbbbaaaababbabbabbbbabaaaabbabbbaabbbbbbabbabaaaaaabbaababbaababbaabbbbbbabbbbabababbbbbbabbaababbbbabbbabaaaaaabbaabaabbabbbaabbabaaaaaabbaaaaababbaaabbababaabbaabbabaabaabababaaaababbbaaaabbbabbbbbaaababbbaabbabbbaaaabbabababaaaaabaaaaabbabbaabaaaaaaabbabbbaabbbaaaabbabbaaabbbaaaabaabbbbabaaabaabaaabbbbaabbbaabaabbbaababaabbbbbbbbabbbbbbbbaaabaaababbaaaaaaaaababbaababbbababbabaabbbbbbaabaababababbabaaaabbbababababaaaaaabbbaababbbbababbbaaababbaaaaabbbbaaabbbabababbbbaaabbaaaabababbaaaaabbbbbbbbbaaaabbbbbaabbabbabbbaaabaabbbabbabaaaabbaabbababbababaabbbbabbbaaaaababaaaaababbbbbaababaaaaaababbabbaaaaaabbbaaabbbbabaabaabaaabaababaabbabaababaabaabaabbbbaabababaaaababaabbbaaababbbabbaabbaabbaabbababababaaabbbbbabaaaabbabbaaaaababaaabaabbabababbabbaabbaaaababbabababaaaababbbbbaaaaaababababbbbbbaaabaabbabbabbaabaabbaaabbabbbbababbbababbbababbabaaabaaababbbbbbbbaaabaaaababaabbbababaaabaabbaabaaaaabbbaabaaaaaaaaabaabbbabaabbbaabaababbbaaaaabbbbabbabbabaababbbbbbbaaabbaaaabbbaaaaaabaabbbbaaaaaaabbbbbbababababbaabbbaaabaaaaaaaaabaabbbbbababbbaabbaaabaaaaaaaaabbabaababbbbaaaabaaaaabbbbaaaababbbbbbaabbaabbabaabbbbabaaaabbababbaaabbbaabbbbbabbaababbbbbbaababaaaabbaaaaaabbbaababbbabbababaabaabbbbabaababbabbbaabbbaaaababaabbbbbaabaabbabaaababbaaaaaaabababaaaaaaabbaaabababbaababbbbbabbbaabbabbabbbabaaabbaabbabaabaabbbaabababbabaaabbaabbaaaabbbbaaaabbaababaabbabaaaaaaaababaabbaabaaabbbbbaababaabbabbabbbbabaaaaabbababaabaabbbbaaaaabbbbbabbaababaabbaaabbabbaabbaaaabbabbabbbbaabbaaaaaaabbaaabaababababbabbbbbbabaabbaabababbbabaabbaaabbbbbaaaababbbbabbababbaabbaabbbbabbbabbbbbababbabbbbaaaabaaaabababbabbababaabbaababbbbbbbbababbaaabaaabaabbbabaabbbaaabbaabaabbabaababbbbabbabbbaababbbababbabbbabaabaabaabaabaabaaaabaaababbaabbbaabbaaaabbbaaaaabaababababaabababaabaabbbaaabbbaaaaabbbaaabbabaabbbbbbaaaabaababbabbaaababbaabaaabbbbaaaababbaaaabaaabbaabaabbaaababbbbababbabbabaaabbaabbaabbbbbbaabaabaababaaabbbaaaabaaaabbabbabaaabbbaabbbabaabaababbbbaabbaaabbbbabbbbbbaabaaaabbabaaaaabaaaabaaaaaabaabbbaaaaabbaaabbaaabbaabbabababbaaaabbbbbabaabbbaaaabbababaaabbbabababababaababbbababbabbaabbaabaaababbaaaababbbaabbabaaabbababaaaabaababbbbaaabaabbaaabbbbbabbabbbbbaaabaaaababaabbaabbbaabbababaababbaaabbbbbabaaaabbbbaabbababbbabbbbaaaaaaabaaabbabababbbaaaabaaaaabbabbaaaabaabbbaababbabbababbaabababaaababbababababaaaabbababaababbaaababaaabbabbabbabaabbaaaaaabbabbababbbbbbaaaabbabbbabababbaabbaaabbabbbaaaaababaabababaaabbbababbaababababbaababbaaaaababaabbbbabababbbbbbbbbabbabaaabbaaaababbbaabbababbabababbabbbbabbaababbaabaaabbaaaaabbbbaabbbbbabaabbbaabaabaabbaaababbbbaababaababbbaaabbbaababbbbabbabaababaabaaaaaaaaaaaabaabbbababaaaaaabaaabaaabaaaababbabbbaaabbaabbbbbaaaababbbbbbbbabbaababbbababbbababababbbaaaaaaababbbaabaabaaabaabbbabbbbbababaabbbabbaabbbaabbaabbaaaaaababbaabaabaaabbbabbbabbabaaabbaaaaaabaaaaabbbaaaaaabbbbabbabbaaabbbbabbbbbbabaaabbaaabbaabbaaaaabaabbaabbbbaaaaaabbabbbbabbaaaabbbaabaabbbbaaaaaaabbbabbabababbbbaaabbbabbbabbbabbbbaaaabbbbabbbbbaabbababbaabaaababbbbaabbbbaaabaaabaaabbaabbaabbbbbbbbbbabbbbbbabbaabbbbbbaabbbabaaaabbbabbabaabbabbbbbaaaabaaaabaabaaabaaaabbabbbbabbaabbababaaabbabbbaaabbabbaabbaaabaababbaaaabaaaabaabbababbaabaaabbbbbbbbaaaababbbbbabbbbaabbaabbbbabaaababbababaabbbaaaaababbaaabaabaabaaaabaabbbabababbaaaaabaaabaabbabbbaabaabaabbaaaabbabaabaabbaaaabbbbabbaaabaaaababbaababaabababbabbbbbababbbbbababbbbbbabbabbaabbbabbbbaaabbbbbbbbaaabbaaaaabbbbbbbbbbbabbbbaaabbbbbaaabbbabbbaabbbbbbaabbbabaaaaabbbaaaabbabbaabbbbbbaababaabbbaabbbbaabbaaabbaababbabababaabbababbbbabbaababaabaabbbabbababbaababbbaabbaabababbbabbbaaaaaaabbbababbabaaabbababbbbabaabaabbaaabbbbbaaabaabbbaaaabaaaaaaaabbaaaabbaabababbabbbbbababbabaabbabbbaaababbbababbbbbabaabaaaabbbaaababbbbaaaaababaabaaabaaabaabaabaaababbbaaabbaabbaabaabaababbaababaabaaaabbabbbaababbbbababbbbbbabababaaaaaababbaaaababbabaaababbaababbaaabbababbbbbbabbbbbbabababaaaaabaaabaabbabababbbbbbbababbabbbbbabbbbbbbbbaabaabbbabbaaabaabbbbabbabbaaabbbaabaababaaababaabbababbbbaaababababbaabaaaaabbabbababbbabbbbbabaaabaaaaaabbabbbaaaaaaabababaababaabababbabaaaaabbbbabbbbaabaabbbbaabbabaabbbbaababbaabaaaaaababbababaababaaaaaabbbabaabaaaabaababaabaaabaaaabaaaababbbaaababbbabbababbabaabaaabababbbaaabaabbaabbababbaaaababbbbaaabbbabbbbababbbbbbbaababababbabaabaaabbaaaabbbbabaabbbbabbaaaabbaaaabbbababaaaaaaabbbabaababbbabaaabaaaaabaabbababbbbbbbbabbabbbaaabababbabababbabababaabaabbbaabaabbbbabbbababaababbabbbababbbabbabbaabaaaabbaabbabbaabaababbbbabaabbaabbaaababbbabbaaaaaabbaaabbabbbaaaaababbaaaaabbabbbaaaabbabaaaaaabbaabbaabbbabbbaabaabbbbbaaabaabaabababaabbbbbbbbaabaaaabbbbaaaaaabaaaaaababbbabbaabaabaabbaabaabaaaabbbabbababbbabaabbaabaaababbbbaabbabbaabababaabaaaabbabababbbbbabbaabbabaaababaababbaaabbbbbbbaaaabbabababaabbbbbbbababaabbbaaabbbbbabaaaaabbbbbababaababbaaabbabbaaababbaabababaabbbabaabbbabaaabbaaabaabaabaabbbaaabbabbaaabbaababbabaaabaaaabbabbbbbbaaabaabaabababbababbbbbabbbababaabbbbabbbbaaabababbbbabaaabbbaaabbbaabbbbaabbbabaaaabaabaaabbbabbbabababbabbabbabbbbabbabbaabbbaaaabbaaabbabbabbbbbbabbaaaaaababbaababbbaabbbbbbbababbbaabbabaabababaaaaabbabbaaaaaaaabbbbbabbbbbbabaaabbaabbaababbbabbaababbbaaababaaaabbbaaaababbbbaaabaaabaababaaaabbababbbbaaaabbaaaaababaaaaababaaaabaababbaabaabbbaaababbbabbaabaaaaaabbbaabbbbabbabbaaabbbababaabbbbabaaabbbbabaaabbbbbbaabbababbaabbbaabbbaabbbbaabbababbaaaaabbbbbabababbabbaaababbbaaabababbbbaabaaabbbabbabbaaabbabbbbbbabbabaabbabaabaabbabbbaaabbbbaaaaaaaaababababbabaabaababbbaababbaabbabbbbaaaabbbaabbaaaaabbaaabbabaabbbaaabbababbabbaabbbbbbababbabbaaabbbbbbbbabbabbaaaaabbbbbaaabbaaaabbbaabababbabbbbabbbbaaaaabbabbaabbbbbbabaaaaaaabbbbabbabababababbabababbbbbbababaaaabbababbbabbabbbaababbaababaaabbababababaabbbabbbabbbaaaababaaabaaababbbaaabbbababbabbbbbbbbaabbaaabbaabbabaabaaaaabbbabbbbaaabbabbaabababaaababbbabaaabbabbababaabbbabbbababbbabaaaaaaaaaaabaaababbabaaaaaabbaababbabbbbaaaaaabaabbbbbaabaaaaaabbbbaaabbaabababbbaaaabaababbabbaaaabaaabaababaabaaaabbabbbaabbbaaabbbbbabbaabaaaabbbbabbbbaabaabaaaaabbabbabaabbbbbaabaaaababaababbabaabaabbbbbbbbbaaaababaabbabbbababaabaabababbbbaaaaabaaabbababbbbabbbabbbbabababaaabbbaabbabbbaabbbaaabaabbabbbbbbbbbbbbbbabaababababaaaabbaabaababbabaaaababaabbaabababbbaaaaabbaabaaaaabbbbababbbbaababaaabbaaabbbbaabbaaababbaaaababaaaabbbabaabbbbabaaabbabaabbbbaabbbbaababbbbbbbabbbababbaaaabbbbabbbbabaabbbbbaaaaaaaabbaabbbaaabbbbabababbbbaaabbaaaabbaabbabababaababaaaabaabaaababbbaabbbabaabbabaaababbbaabbaabbabababababaabaabaabbaaabaababbabababaaabababbabbbbaaaaabaaaabaababbaabbbaaaababaaabbabaabaabbabbbbabbbabbabaababbabaaaababbbaaaabababaaaabaaaabbbabaabbbbaaabbbaabaaababbbbbbaaaabaaaaababaabbbbbabbababbaaaabaabbaaaaaaabaabbbaaabbbbbaaabbaaaaaabbaababbbabaaaaaaabbbababbbabaaabbbbbbaabaabbaabbabbabbbababbbaabbbbbaabbabbabbabbbabbbbbabababaabababbbabaaabababbbbaabbbabbabbaaaaaaaaaabbabaaaaaaabbaaabbabaabbbabbaabbbbbabababababbaaaabaabababbabbaabaabbabbabbaaaaabbabaaabbbbaabbbaabbaabbbbaaaabbabbbbaabbababbabaaababaaababbaaabbabbbbbbabbabaaaabbbababbababbabbaabababbbbbbabbbaabbabaabaaabbbbaababaaabbbbbaaababababaaabababaababbababaaaaaabbaabbaabaabbbabbbaabbaaabbaabaabbabaaababbabbaaaaabbabbbbabaabaabaabababbbbbbaabbbabbaabbbaaabbbbaababaabaababbbabaaabbbabbaabaabaaabbaaaaaaabbbaabbbabbabbaaabbaaaaabbabaaabababababbbbaaaabbbbbabbbbbabababbbbabaabbbbbbbbaaaabaaabaabbabbbbababaabaabababbbbbabbbaaaabbabaaabbaaabaabaaabbbabaaaaaababbbabbbbbbaaabbbbababbababaaaababbbbaabaaabaabbaabbbabbbbbbbabbaaaabaaaabbabbbabbbabbbaabbbabaaaabbabbbbabaabbabbaabbbbaabbabbbbbbbbabaababbabbbabbbabbbabaabbaabaabababbaaababbabbbaabbbbabababbbbbbaabbbbaaabaabaababbaabbbbabaaabbaaabbaabbbaaaabbbaaaaabbabbbabbaababbbaabbaaabaabbbabaababaaaaabbabbaabbbbabababbbabaaaaaaabbbabaabbbbbbaaabaabaaabbaaabaabbbbbabbbaabbbbbabaaabaabaabbabbbabbbababaaabbabbbbaabaabaaabbbabbbbbabbbaaaabbabbbbbaaaabbbbbbabbababbbababbbbabbababaababaaabbbabaaaabaabbbaabaaaabbbbaaaabaaabbabbabbbbbaaaaabababaabbbbbbbbabbabaaaabbbabababbbabaabbaaabbaaaaababbbaabababaaabbbbbaaabbbbabbbbbbaaaabababaababbabbabababaaababbaaaaababbbbabbaabbbaabababbbbabbbbbbbbbaabbaabbbababaabaaaabababbabbbbababbbbaabaabaabbbbabaaaaabaaabbabbabbaabbaabbbbaaaaaabbaabbaaababaaaababaaaabbbabababbbbbbabbaaabaaabbaabaaaaaaababbbabaabaabbaaabababbaabaabbabbabbbaabaabbabaaaaabbbbababbabbbbbabababaababbabbbaaabaaababababbaabaabaabbbbabaabaaaaabbbbabaaabbbbabbbbabbaaaababbaaaabbabbaaabbababaabbbbbaaabbbbbaababbbababaaaabbaaaabaaabbaaababbbbbbbbabbaabaaabbabbbbbaabaaabbbaaaabaaaaabbbabbbbbaaabaababbabbaabbbabaababaaaabbabbabbbbaaabbaababaababbaaabaabbabbabbaaabbbababbbabbaaaaaabbaaabbbbaabbaaaaababbabaaaaabbabaabbabaaababbaabaaabaaababaaaaabaabbbabbbabbbbbbaaaabbbbabbbaabbaababaabbaaabaabbbaaababbbbbbabbababbaabbabaabbbbaabbbbaabbaaabbabaabbbbbbbaaaabbbabbaaaabaaabaabaabbbbabaababbaaaabbbbbbaabbababaaaaabaabaaabbabaababababbabbbbababbaabbbabaaabaaaababaabbbabaaabaaaaaabbbbbabbbbbbabbbbaabbaabbaababbbaaabababaaabbaaabbbbaabbbbbbababbabbbbbaaaaabbbbaabbaabbbabbababaaaaabbabbbabbabbabbbbabbbbbbbababbabbbbbababbaaaabbaaababbbbabbbabbbbbaaababbabbbbbbbbabbbabbaabbaabaabbbbaabaababaaabaaabbaabbaaabaaabaabbbabbbabababbbabbbabbbbabbaaababbbabbbbbaaabbababbbbaaaaabaaabaaababaababbabbaaabaaabaabbaabaaabaababbbabbaababbaaaaaaaaaabbbbbaabbaabbbbbbbbbabababbaaaabbaaaaaaaabaaaabbbbbbaaabbaaabbbbabbbbabaaabbaaabaabbbbbababaaababaabaababbbbbbbabbaababbbaabbaaababaaabaabaabbababbbbaaaabbaabbbbaabbabbbbababbaabaaaaabaabaaabababbbaabaaabbaaabaabaaaabbaabaabbbabaabbbaabbabaabbbbbbbbaabbbabaaaabbaabbaaabaabbbaaaabababaabbbbaaaaabbaaabaaaaabaaabbbbbababbaabaaaabbbbaaaaaaabababbbbaaabaababbbbabbbbaaabaaabbbaabbaabaabbbabbabbabbbbaabbbbbabbbabaababaabbaabbaababaaabaaaaabbbbbabbabaabaabbabbbbaabbabaaabbbbaaababaababbabbbbabbaaabbbbabaabaaabbbbbaaaaabbabbbbabbaababbababbaabbaaaaaaaabbbbaababaaaaababaabbabbaaaababbbaabaaaaaaaabaaabbababbbbbbbbaaabbaabbabbaabbababaabbbaabaaaabbabbabaababaabaaabbababaaabbbbaaabbbbabaaaabbbbbbaaaababbbbbaaabababaabbbbbbbbabbaaabbaaabaabbabbbababbbbabaaabaaabbaabaaabaabbbbbbabbbababbbbbaabaaabaaaaabbbbabababaababbabbbbbababbbabaaaaaaaabbbbabababbbbaaabbbbaaaababaabbbbaabbbbabbbaaaaabaababaaabbbaabbbabbbbbbbaababbbabbbbbabbbabbbbbbbbbbaabaabbabbabababaabbbaaabaabbabbabbbaaabaaaaaabbbbaabaaabaabbbbaabbaabbaabbbbbaabbaaabaababbbaababababababbbabaabbabbabbbbbabbbbbbbabaaaabbbaaaabbbabaaaabbaaaaaabbbbabaaabaabbabbbbbaaaabaabaabaabbbaabbaaaabbabbaaabbabbabbabbbbbbbbbaaabbaaabbbaababaaabbbbbaaaaabababbbbbaaabbabbbabbaaaabbbaabaabbbbaaaabbbabaaababababaaabbabbaababbaaaaaabbbbbbbababbbabbabbaaabbbaabaaababbaaaabbbabbbaaababbbaabaabababbbabbbbbaaabbbabbababbabaabbbbbababbabbabbbabbbbbbbbaaaabaaabbaabbabaaaaaaababaabaabaaaaaabaabaaababaaaaabbaaaaababaaabaaaabaabaabbbabbabbbabbbbaaabaaaaabbbabbaaabaaabbababaababbbbababbabbbbabbabaaabbaaabbbbbbaaaabaaaabbbaaabbbababaabbaabaabbbababaaaaaaaaabbbaaaaababbbbaaabbbbbbbbbabbabaaaabbbbabaababbbbbabaababbabaaabababbbbbabbbbabaaababbaaabaaabbaaabbbbbbaabbaaabbbbaaababbaabbabbbbabbbbabaabbababbabbbbabaaabaaaaaaababbabaaaaabbabaababbbabbbaababbbabaaaaabbababaaaaaabbbabbbaabbabbbbbbbbbbababbbaaababbbabaababbbaabaaabbabaaaaaaabbbbaaabaaaabbaabbaaabbaaaaabbbabbabbbbbbbbbabbababbbabaaaaaaaaaaababaabbabbbaabaaabaaaaababbabbbbbaaaabbbbababaabbaaaaaaabbbbbaabababbabbbaaaaaabaaababaababbaabaaabbaabaabaabaaaabbababaaabbabbbabbabbbaaaaaababbabaabbbbabbbbbbaaaabbbaaaabbababbbabbbaabbaababbababaabaabababbaaababbbbbaabaabaabaaaaabbaabbbbbbaababaaaaabbbabbbabbbbabbbbabbbabbaaabaaababbbbaaaababbbbababaaababaaaaaaabbabbabaabaababaaaabaabaababaaabbabbbbbbababbbbbaaabbaabaabaabbbaabbbababaaababbabbbbaabbbabbabbbaabbabaaababbabbbaababababaaaabaabababbaabbbabbababbbbbabbbabbaaaabbabaaabbaabbbaabbaaabaaabbbbbabbaaaaaaaaaabbbaabbababbbbbaaababaabbabbabaabbaababbbabaabbbbaaabababaaaaabbaababaabaaabbbabaaabaaaabbaaaaaaabaaabaabbbaaaaaaabbbbabbaabaabbaabbabaabababaabababaabababbaabababbabbbaabbaabbbbbbababbababbabbbbbbbbaababaaabbabababaaabbbbababbbbbbbbaababbbbbaabbaaaabbaabbaabbbbaababbbbbbbbaaababbbaabbaabababababbbaaabbaabbaaaabbbaaaaaabbbbbabbbababbbbaaaaabaabaaaabbbbaaabbaabbaabbabbaaabbbbaabbbaaaababbbbababbbabbbabaabaaabbbaabbabbaabaaabbbbbbbababababbaabaabbbbbaaabaabaaaabaaabbaaaabaaabbbaaabaaaababbbbabbaabaabbbbabaaaaabbabaaabbaabbbbbaabbbabbbababbababbabaababbbbabbbbbaabaaaaaabbababababaabbbaaaaabaaabbbabaaaabaaaababbbbabbbabbbbabbbbbbbbaaabaabaaaaabbbaabaaabbaaaaabbbaabbaaabbaabaaabbbbbabbbbbaaaababbbababbbbbaaabbbbaaaaaaabbbbbbbbabbbbababbbaabababaababbaabbbabaabbbbababaaaabaaababbababababaaabbbbbbababaaabbabaababbbaabaabababbbbbaabbbaaabaababbaabbaababbbaaababbbbbbbbaabbbaaaaabbabbabaabbbaaabaaabbabbaaaaabbababaaabababaabbbbbabbababaabbbbbaabbaabaabbabbaabbbbabaaaaabaabbaabbabbbbbbbbababbaaaabbaabababbbababaabbaabaabbbbabbaaaabbabbaabbaaabbaaabaaaaaaaabaabbbbaababbaaababaaaabaabbaabbbbaabaabaabbbaabbabbbaabaabaabaababbbabbbaaaaababaaaabbbaabbabaaaaaabaababbbaababbabbababbbaaabaaabaababbbabaaabbbabbbaaabbaaabbabaaabaaabaabbbbbbabababbabbbaaabaaabbbbbbababbbbabaaaabaabaababbbbaaabbbbbaabbbbabbbabbbbbbaabaaababbbbbaaaabbbabaaaabbaababbbbbbaabaabbbbaababbbaababbbbabbbbababaaaaaababaaaabababbbaaaaabbbbabbaaaabaababbbababbbbbaabbaaaaaabbaabababaabaaaababbbbabbaabaaababbbabaaaaaaabbbaabaabaabbaabbbabaaaabbaaaabbabaaababbbaaabaaabaabaaaabaabbaabbaaaaaaaabaaaaabaabbbababbbababbbbaababbaaaabaabbababbbabbbaabaaababbababbabbababbabbbabbabbababbbabbaaaaaabbbabbbaaaabababbbbbbababbaaaaabbbbababbaaaabbabbaabababbbabaaababbaaaaaabbaaabaaabababaabbaaababbaababaabaaaabbabbabbaabababaabbbabaabaababaaababbaabaababbaababbbabbbaaabbaababbabaaaabbbbbabbababaababbaaaababbbabbaabbaabaababababbbbbbbbbbabbaaaabbabaabaabababaabbbabaaababaaaababbbaabbaababbaaabbbbabbabbbababbbaaababbaaababbaabbaaaabbaabaaaaabbbbbbabbbaabababaaabbbbabbbabbbaabbbaaaabaabbabaabaabaaababbabbbabbaabbabbaaabbaaaabbbbaaababbababbaabbababaababbbababbbaaabbbbababbbbbbabbbbbbbaabbabaabbbabaabbbabbbbbabaabaabaababbaaaabbaabbababbbaaaababbabbbaaaaaababaabbbbbabaaabbabbabbbaaabbbababbbbaabbbaabbbbbababababbaabbaaaabbabbbabaaabbbbbabaabbbbbaaabbbbbbbabbabbbabbabbabbabababbaabbbaaaaabbaabaaabbbbbbbbbaaaaaabaaaabaaababbbaababbbbaabbabbbabbbaabbbbaabbabbbbaabbbaaabbabaabaaabaaaaaaabaaaaaabaaaaaaaababbbbbbabababaaaabaababbbbbbabaaabbabbbbaabbbabbbabbabbaaabbbababbabaabbabbabbababaaabaababaaabbbbbababbabaaaababaaaabababbbbabbabababbaaaaabbbaababbaabaaaaabababbbbababbaabbbbaabbbaaabaaaaababbbababbaabbbbbbabbbbaaabbbbbbbabbbaaaababbabbabaabaabbbabbabababbbabaababbaaabbbaaaababaaabaababbbaaaababbbababaabaabbbaababaaabaabbaaaabbaabbaaababbabbaaaaaaababbbbababaaaaaaaaabaaaaabaabbbaabaaabbbbaabababaaaaabbaaababaabbabbbaaabbbabbaababbbabaabaabbaaabbabbbbabaaababbbbbaabaaaaabaaabbbabbbbabbaaaaabaaaaabbbaaabbababaabbaabbbbababababbabbbbabbabbbbbbbbbbaababbabbbabbabaabbbbbbbbaaaabaabbaaabbababbbaabaabbaababbabbbababbaaaaabbbabbbabbbaaaababbaaababbabaababaaabaaabaaabbbbbabaaabbbabaabbbbbaabaababbababbbabbbaaaabbbbbababbabbaaabaaaabbabbbababbbbbabbbaaababaaababbbababbabaaabaaabbaabbbabbabbabbabaaababbbbbbabbabbabbaabbbabaabbababaabbaaaabaaaabaaaaaaababaabababaabbbbabbbaabbbaabaaaabaaabbababbaababbbababbabaaabaabbbaaabaabbabbaaabbaaaabaaaaaabababaababbbaababbabbbaaaabaaaaaaabbababaabbbabaabbbabbababaaabaaaaabaabaaabbbbaabbbabaaabbababbaaaaabbbabaaaaaabaaaaabaaaabbbbbbabbbaaaabbbbbabbaabbababbbbbabbababababbabbbabbbabbabbaaaaabbbbabbbaaaaababaabbbbbaabbbbaabbabababbabbaaaabbabbabbabbabbaabbabbbaaabaaabbabaaababbababbbbaabaaabbaabaaabaaabbbabbbbaabbabaaaababbaaabaaabbaabaabaababaabaabaabbbbabbaabbabbbaaabaaaabbaaaabaaaabbaabbaabbbababbbaabbbaaaabbbababaabbbbbbabbbbbabababbabaabaabbbbabbabbbbbabbabaaaaaaaaaabaabbbbbbaaabbaaaabaabaabaabbababbaaabbbabaaabaaaaabbbbbbaabababaabbaabbaaabaabaaababaaabbbaabbaaaaaaaabbabababbbbbaabaabbaaabaababaaaababaaabbbaaabbabbabaaaabaabaababbaabbbabbaabaaababbaaaaabbaaababbaaabaabaaabbaabaabaabaaababababbbabbbabbabbababaabbabbabaabaabbaababbaababbabaabaaaababbbbbabbbbaaabaabababbabbbabaabbabbbbabababbbbaabaaabbabbaabaaaaaaabbaaaababbbbabbbaaabbabaabaaabababbbbaaabbaabbbabbbbbbabbaaaabbabbbbabbaaaababbbbaababaabbbbbbbaaaaabaabbbabbababaababaabaaaabaaabbabaabaaabbabbabaaaabbaaababbababbabababbbbbaaabbabbbaabaaaaaabbabbabbabaaabbababaaabaaaabaabbabaabbaaabbbababbabaaaabbbbbababbbababbbbbbbaaabaaaaaabbbaaaabaabbabbabaababaaaaabaaaaababbbaabbbbbbbaaaaabbabaaababbaaababaaabaaababbaaabaaaaaababbabaaaaaaaaababbaabbaaabbaabbaabbabbbbbabbabaabbbbaababbbaabbbabbbababaaabaabbbabbbbbbaabaaaabaaabbaaaabaabbbabbabbbbbaaaaabbaaaabbbbaaabaaaaababbbbbbbbabababbaaabbbbbaaabbbabaaaabaaabaabbbabbbabbbaabbbbbbbbaabbabbabbbbaaabbbbbabbaabaabbbabaaababaabababbbbabaababbabaabaabbbabaabababaaaaaaabaaabaaaaaababbaaaabababaabaaaababbbabbaabbababaaaaaaabbaababbbabbbaaaaaaababbaababaaaaababababbaaababaaabbbbbbaabbaabaabbabbbaaababbababbaaabbbaabbbbbbbbababaababaaabbaabaabbbabbbaaabababbbbbaababaaababbaaabbbaaaaababbababbbbabaaaaababaabaabaabbbabbbaababbaabbaaaababbbaabbbaaabaababababbababbbbbabaababaabaaaabbbbaaabbbabaabbbbbbaaabbababbaabaabaaababaabbbaaaaabbbabaabababbabaaaabaaaaabababbababbbbabbbabbbbabaaaabaababbababbabbbabbbaabaabbabbabbbbbbbabbbaaaaaaabbbabaabbaabaaababbabbbbbbabaaaaabaaababbbbbbbbbaabbaabaabbbbbbabaabaabbbbababbaaaabbabbbbbababaaaaaabababbbaaaababbabbababbaabbbbbababaabbabbbabbaabaabbbbbbbabbabaabbbbbabbbaabaabaaabbbbabbabaabbaaabbabbabaaabaabbbbabbabbabbbbbabbabbbbbbababbabbbaaaabbaaaaabbaabbbabaaabaaaabbababbbbbbbabaabbbbaababaabbaabababababbbaabbbababbbaababaaaaabaaababbababbaaaaaababbbaabbababaabbabbaaabbbbbbbbaabbbabbaabaabaaaabaaababababababbabbabaabbbbbbaaabaaabaaabbaabababaaaababaaaaabbabbbbbbaaaaaaababaaaababbaaabaaabbbbbaaabaababbaaaaaaabbaabababbaaaabbbbbababbbababaaaabaababbaaabbbababbabbbaabbaaaabababbbbabbabbaaabbabaaabaaaaabaabbbabbaaaaabbbaabbbbaaabaabababbbaabaaaabbaaaaaaabbaaaaaaabaabaabbabbaaaabaabaabbaabbbaaabbbaabbbabaabbbabbabbbbabbbbaabaaaaaababababbaabbbbbbaabbababbababababbaaabbbaabbbbabaabaaabbaabababaaabaabbbbababbbbbaabbbbbbbaabbaaaaaababbabbababbbbbbbbabbbababaaaaaaabaabaaababbbbbbaabbbbabbabbbbbbbbaaabbababbbabbbababbbbabbbbaabaabbbbaabaabaababbababababababbaabababaaaabbabaabbbbabbbbbaaaaababaaaaaaaaaabbbbbabababaabbbbaaabbaababbbaaabbbaababbbbaaaaabaaabbbabaaabaabaabbabbbbbaaababbabbbaaabababbbbaaabbaaabbaaaababaaaababbabbbaaababababbbbbbbabaaaaabbaababbbabbbababaaabbbbaaaabbbabbabbbbabbbbbabbbabaaabaabbabbaabaabaaabaabbbbbabbbaaabbbabababbaaababbabbbbbabbaaababaaabaaabbbaaaaabbabbbaaaaaabbabaaaaaabbbbaaaabbbbbababbbaabbabaaabaabbbabbbbabbababbaababbabaabbbbabbbbbaaaabbbbbaabbbaaabbaaaaaabbaaabaabbaabaababaaaaaaaabbbbababbabbbaabbabbbaabbbbbbbaaababbbbabababbabaabbbbaaaaaabbaaabaabbaaaaabaababbabbbbbaabbaaabbbbbbbbaaabbbabaaabaaabbabbbbaababbabababababbbbbabaaaabbbabbaaabaaaabababbababbababbababbabbaaaababbbababababbbbbbbbaaabbabbaabbbbbaaabbaabbabbabbbaabaabbbbabbbaabaabbaabaaabbbabbabbaabbababbbbbabbababaaabbababbabbbbaabaababaaaaaabaaaababaaaaaababaaabbaaabbaababaaaaabbaaaaabbaaaaabbaabbbababbbbbabababbabbbbbbabbbbbbbaaaabaababbbbabbaaaaaaaabababbabaabaabababaaaababbabaabbbaaabaabaaaaabbbbaabbbbbbaaababbbbaababaaabababbabbaaaaaaabbaababaabbabbabbbaabbbbabbabaabbaabbbbabbabbbabaabbbbbbbabbabbbbbbabaaaaabbbbaababaaaaababaaabbbbabaabbaabbabaaabbbabababbabbaabaababbaaababbababaabbbbababbbbaaabbbbbabababaaaabbaabbaaaabbababbbaaabbababaabaaaabbbaabbabbbbbaaaaababbbaaaababababbbabbaabbaabbabbbaabaaabbaabbbabbbbaaaababbbaaaaababbbaabbabbbaaababbbbaabbbabbbbbbbbabaabaaabbaaababaaabaabbbbaaaabbbbbbaaababbbbbbbabbaabbbaaabaabbabaabbaaabbbaaaaabbbaaaaabbaaaabbaabbbabbbabbbaabaaabbaaababbaabaabbabaaabaaababbbababaaaaaababbbbaaabbbbabbbbbbabbbaabababbbbaaabaabaababbaabbabaaabbabababbbbbaaaabaaaabbabbaabaaabbabababbabaaabbaababbabaaabbbbbaabababbbbabbabaabbbabbbbbaabbbbaababaababbbababaabbababaabaaaaabaaaabaaaaababbaaaaaaabbabbaaaaabbaaaaaababbbaaabbbabababbbabbabbbbabbaabaaabaabababaaabbbbbaaabbabababaaabbabbabbabbbbbbbaaaabbbbabababbbabbbabbbabbbaaabababaaaabaabbababababbbbbaabaaabaaabbaabbabababaabbbababaaabaabaaaaabbbabbbbaaabbabbbbababaabbbbbaaaabaaaabbbbbbababaaabababbbabbbbabaaabbbbbbabbaabbaabbaabbabbabbaababbaabaaaabbabbabbabbaababbbbbbaababbbabababbabaaabaaaabbbbaabbbaaaaabbabbbaababaaababaaaaaaaabaababaabababbabaabbbbaaababaababaababbabaaaaababbbaaabbaabbabbaabbbaaababbabbbbabaabbabbaaabbabaabaabaabbabaabbbbbbbbbbbbbaabbaabbaaabbababbbbabbbabbbaaabbbababbbaaaababaaaabbababbbabbbbbaabbaaabbbbaabbaaabaaabababbabaabbbababbbaaaaabbbabbbbbaababbababaabaaaaabbbaababbbaaaaaabbbaaaabaabbbaabbaabbbababbaabbababababaaaabbbbbbbbaaaaabaaaaabbbbaaabbababbbabbababbaaaaababaaabaababaaaaabbbbababaaabbaabbaabbbbbabaabbaabbbabbbbabbbbbaabaabaabaaaabbabbbaaabbbaabaaababaaabbabbabaaaabaabaaabbabbbbaabbbbbbbabbaabaababbbaaabaaaaaabaababbbabbababaabbbbbbbbababaabaaaabbbbabaabaabbaaabbbabbabbaabaabbaaaabbaabaaabbbbaabaababaaabbbabaabaaaaaababaaaaababababbbbababbbaaabbbbbbaabababbabbbbbbabbababbbaabbaabbbaabaabaaabbbaabaaababbbabbbabbbaabbbaaabbbbbababababbabbbbabbbaabaaaaabbabbbbbabbaaaaaabbaaaabaababbabbaabbbabbabaaaabbabababbaaabbabbaabaaaababbbaabaaaaabababaababbaabbbaababaaabaaabaaabbaaabbaabaaaaabbbaaababababaaabbbbabbbbabbabaaabaaaaaabaaababbbbaabaaaabbbbbbbabbaabababbabbbababaaababbbbbabbaaabbbabbaabbaaaabbbbabbaaabbbabbababaaabaababbbabbaababbbabaaabababbabbbaababbbbabbbabbbbabbbbbaabbbbabbabababbaabaaaaaaabbbbbbbbbabbbabaaabbaaaaabaaaabbaabaababbaabbaababbbbaaaabaabbbbbbbbabbabbbbabbbabbbbaabaaaababbaabaabaabaaaabbbabbabbbaaabbbbabbbbbbaabaaababbaabbbbabbbaaaaabbababaabbabbbabbabababbaaaaaaaaababbabaaaaabbababbbabbabbaabbbaaabbaaabbaabbaaaabaabaabababbbbbaaaababbaaabbaabbabababbbabaaabaaaaabbaaabbaaabaaaaababbbbabbbaaaaabbbbbaaabaabbbabaabababbbbabbabaabaaaaaaaabbbbbbabbbabbababbbabaaaaaababbaaababbbbbbaabbabaabbabababbbbabaabbabaaabbbabbbaaaaaaaababbaabbabbbbbbaaababbababbaaaababbbabaabaaababbababaaaaabaaabaabaaaaabbbbabaaaaaaabaaaaaaababbbabbabaaaaabbbbbbabbaabbabbbaaabababababbbbabaaabaabaaaabbbaaabaaabbbaabbbaaaabaabbbaabaaaaabaababaabbaababbbbaabbaaaaabababababaabbabbbbbbabaaababbbbbabbbabaaaaabbbaabbbaabaaabbbaaaabbabbaaabbabbbaaababbababbbaaabbbbaaaaaabbaabaabbaabaaabbbabaabaababbaaabbbabbabaabababaabbbbbbbaaabaababbbabbbabbaabbaaababbbbbbbbbbaababbbabbaaaabbbaaaaabaaababbaaaaaaaaaaabaaaaabbbbaaabaababbbbbabaaabbaabbbaaabaabaabaaabbaaababbbbaaabaabbbabbbbaababbbbbbaabbabaabbabaabaabbbbaaaabbaaabbaababbbbbbabbbaabaabbbbabaaaabaaaaaaabaaaabbbabaaaabaabbbabbaabbaabbabaaabbaababaaabbbaaababbaabbaaaabbbaabaabaabbabbababbbaaaaaabbbbbbababbbbbbaababbbbbbaaaaabbaabbbaababbbaaabbbbaaaaaabaabababbabbbaabbbbaabababaabbbabbbbababababbbaaaaabaababaaabaaababbaaaaabaababbbbababbababbbabbaabbbaabbbababbaaaaababbaaaabbbbabbbaaabbbbbbaabbbbaaababbaabaabbbbaaaaababaaaabbbabbbabaababbaaabaaabaaaaabababbabbbbaaabababaabbbbbbbabaaaaaabaababaaaabbabbbaabbbbababaaabbbbaabbbbababbbbbabbbbabaaabbaaaabaaaabbabbabaababbabbbbbabbbabbabaabbbbaaaaabbaabbababbbbaaaaababbbbbababbbabbabbbbbabaabbaabbaabbbbbbaabaababbababaabbbbaabbaaabbabbaaabbbaaababbababbbabaabbaabbaabbbaaaaaaaababbaabbbabbabbabaaabababaabbbabaabbbabbbbaabbabbaaaabababaabbaabababbaaaabbaababbababbaabbaaababbaaabbaaabbbaabbbbabaaabaaabbbbbbbaaaabaaaabaaaabaabbabaabbbaaababbaabbbbbabaaabbbbbabbbababaabbaabbaabbaaabbbabbbbaaaaabbaabaabbabaaabbbbabbbababbaaababababbabaaabaaabaabbbbbababbbbbabbbbbbbabbbbbababababaaaabbabbabaababaababbbbbbaabaaaabbbbaabaabbbabaabaababaabaabbbbbaabbbaaabbbbbbaabbaabbbabbbaabbabaababbaaaabaabaabaabbabbabaabbbbabbbabbaaaababbabbabbabbabbbababaaaaaabaabbaaaabaaaaaaaababbabaaabaabbbaaaabbbabbaaaaaabbbbaaabababababaabbabbbbbabbbaaabbbaababbaababaaababbbabbababbbaaabaaaabbabaaaaabaaabbbbabaabaabbbbaaabbaaababbaaaabaabbaaaabbbabaabbbbaababbabbbaabbbbaabaabababaaaababbbbaaaaababababbbababbbaabbabbbabaabaabaaaaabbbbaababbbbaaaabaabbbaabbabbbaaaaaabaaabaabbaaabaaabbaabbaaabbaababaaabbbbbaabaabbbbbabbbbabbbbbbaababbbbaabababaaabbbbabababababbaaabbaaaaabbaabababbababaabbaaaaabaaabbbbabbbabbaaabbabbabbaaaaaabbbbbbbabbabaaabbaabaaabbabaabbabbababaaaabbaabababaabbabaabababbababbbabbbabaabbbababbaaabaaabbaabaababbbabaaaabbaaababababbbbbaaabbaaaabaaabaababbbaabbababbbbaababbbbaababbbaaaabbbaabbaaaababbaabaabbabbaabababbabbaaaaaaaaaaaababbababaaaaababbbbbaaaababaabaabbabaaabbabaabbbbbaaabbbaabbabababbbaabaabbaaababbabbbabbbbbababbbbaaaaabbbbbbabbabaabaabbaabaaaabbbbbbabaaaaaabbbaaaabbbbabaaabaaaaaaaabbbaabbaababbbbabbbbaabaaabbaabaabbbaaaaaaabbbaabaabbaabaaaabaabbaabbbbbabaabbabbaababbbbbabaabaaaabbabbaaababaabbbabaaababbbbaababbaaabaabaaabaabbbbaabaaababaaababbbababbbaabaaaaaaabbbbaabbbbabaabbbbbabbaaababbbbbbaababbbabaaaabaaababbbbbbbbaabbbbbbababbaaaababaaaabbbbbbaaabbbbbbabaabbbbbaaaaaaaaabaabbaabaababbbbbbaabababbbaabbbaaabaaabbbbaabbbbaababbababaaaaaababbaaaaabbaaababbabbbbababbaabbabbaaaabbbaaabaaabaaaabbbbaabbbbbaabbbaaabaaaaabbbbbaaaaaaaaaaabaaabbbbbabaabbbaababaaaaaababbaabbaabbbbbaaabbaaabaabaabbbababbbbbbbbbbbaabbaabbbaaaaaaaaaabbabbbbaaaabbabbaabababababaabbabbbbbabaaaabbaababaaaabbaababbbaabbbbbaabaabbaabbabbbbaaabbbbaaaaaaabbabbbabbbaabaababbaabbbbababbaaaabaaabaabbabaaaaababbabaabaaabbababaaaaaababbbaaaaaaababbbbabaaabbbbaaabbabaaabbbabbbaaaaaabaaabbbaaabbbbaaabbbbbbaabbabaaabbaababaaabbbbbbabbbaababbababaaabaaaaaaababbaabbbababababaabbabababbababaabaabbbbbbbaaaaaabbabaaaaabbabababbbbbbabbabbaaaabababbaaaabbbbabaabbaaabbabbababaababbbbbbabbabbabaaaabbbbaabbbbbbbabaaababbbabbbbabbbbabbbaaaabbbbbbbbaabababaaaababbbbababaaaabaaabababbaaaabbbbaaabbaaabbabbbaabaabaabaaaabbbababaaaabaabbbaaabbabbabbbbaabaabbaaaaaaaaaabbaabbabbbabbbbaabbaaababbbabbabbbabbaaaababaabaababaaaaabaaaaabbbaaaaaabaaaabbababaababbbbbbabaabaabbbbbbaaabbbabaaabbbaabbabaababaabbaabbbbbbaaabaaaabbabaaabaaaaaabaaabbbbbbaaabbbaaaaaabaabbbbabaabaaababbaaabbbbbaabaababaaabbaaaaabaaaaabaabbbbaaabbababbaaabbbbbbbabaaaabaabaaababaaaabbbbbbbabaaaabaaabbbaabababbbabbababaabaaaabbabbbabaabaabbbbaabaababaaaaabbbaaabaaabbabbabaaabbabbbbaaabbbbaababaabababbbabbabbaabaaaaabbabaaaabbaabaabaaabaabbbaaabaabbaabbaababbaaaaaaaabaaabbbabbaabbbabababbaabaabaabbaaabaabbbabababaaabaababaaabbbaababbaaaabbbaababbbbabbbaabaaaaaababbabbaaabbaabaaababaabbbababbbababaaabaabbaabbbabbbbbaaabababbaababbaabbabbabaabaabbabbbbbbbbaaaaabbaaababaababababbaabaabbabababaabbaaabbababbbabbabbaabbababbabbbaabababbbaaababbaababbbbaaabbaabaaabaaaaaaababbbbabbabababbabbabbbabbababbbabbaaaaaaaaaaaabbabaabbaababaaaaababbbaabbabbaaaaaaabbaabbbaabaabbbaabbbabbbababbabbbbbbbbababbbaabaababbbaabbbbaaabaaababaaababbabbbababaabaaaaaaabaaaabaaaabaaaaaabababbabaaaabbabbabaaabbbabababbaaaabbbbbbbaabbaaaabbaabababaabbaabbbbbabbabaabbbabaabbababbaaaaabbbaabbbaaaaaaabbaaaaaaaaaabbbbbabaabbbbbbabaabbabbbbbabbbbbbaaabbaaabbbbbabbbbabbabbabbabbbbaabbaababaaababaabaababaabaababaabbbabababbaaababaaaaabaabaabaaaaabaabbaabaaaaabbaaaaaabbaabaaaababbabaabbaabbabbbbabbbaabbabaabababababaaabaaaaabaababaabaabbbababbbbaabbbbabaaaabaaababaabbaabaabaaaabbbaaaaaaabbaaaaabbabaaaabaaababaaabaaaaaaabbaabbbbaaababaaaabbaababaabbbbbbbbbbabaabbaababbbbbbababbabbaababbababbbbbbbabababaaabbaabaaaabababbabaaaabaabbaaaaaaaaabbabbaaabbaaabbbabbaaabbbbbbbaabaabababbbababbbababbbaababaaabbaabbaabbbaabbabaababaaabaabbaaaabbbababababbbaaabbbbbababbbabbbbaabbabbababbbbbabbbabababbbbbaaaaababbbbabbbbaaaabaaaabbababbbabaababbaaabaabbbabbabbabbbabbabbbbbabaaaaabbaabbabbbbaabbaabaaaabaaaababaabbbbbbbababbbabbbaababbbabababbbbbbbabaabbababaabbaaaaabaabababaababbabbaababbaaaaabababbabaabbabbaaababbbaaababbbbbbbaaaaaaabaaaaaabaabbbbbabbbabbbbbbabbbbabbbabaaabbbabbbbbaabbabbaaaaaaaabaabbbbbababaababaabababaababbaaabbabbbbbabaabbbbbbaaaabbaaabbaaaabbbbbbbbbababaaaabaaaaaaabbbbbabbababbbaaaabbabbaabaaaaabbbaababbaabbaaabbababbaaabbabbabaaabaabbbabaaaaababbbaaabababbbaabbbbbbabbabaaabababaababaaaaaabaaabaaabbabbbabbbabaaabbbbbaabbbaabaabbabbbbaabaabaaabbbaaabbababaaaabaaabbbbabbaaaaabaababaaaaaaaababbbbbbabaaabaaababbbaabbaabbaabbabbbbbaaaababbbbabbbabaabbaabaabbaabaabbbbaabbbbaabbbabaaababbaaaaaabbaaababbabbbbabbaaababababababaabbababbbbaababaabbbbabbbabaababbbbbbbbabbaaabbbbbbaabbbaabaaababbababbbbaaababbaabbaaaaaaabbaaabbaabaabbbbaaabbbaaaababaaababaaaabaabababbabaabbbbabaabaabbbbbbaabaabaabaabbaabbbbabbaababaaabaabbababbbaababbbababbaaaabbbbaabbbbbaaaaaaaaaaabaaabbababbabbbbbbabbbaabbbbbaaabbbbaaabbbaaaaabbaaabaabaababababbaaabbabaaaabbaabbabaababaabbbaabababbbbabaababbbabaabaabbbaaaabbaababababbbaabbbabbbbbabbabbbaaabaabbabaaaabaabaabbaababbbabaababbaaababaaabaabbaaababaaabbbababbbbaabbaaabbaaaababbabbbaaaaababbbaaabaaaabaaabababaaaabaaabaabbaababbbbaaabaaaaaaaaaabbbaaabaaaabbababbabbbabaababbbaaabbbaabbabababbbabbabaabaaabaabaaaababbababbbbbaabbbbbbaaaaababbabaaaaabbabbaabbbabbabbbbaabbbbabababbbbbbaababaaababaaaaaabbbaabbbabbabbaaaabaaabbabbabbaabbbbaaabbaabbbbbbbaaabababaabbababaabbababbbabbababbaababaababbababbbabbaaabbaaabbaaabbaabababababaababababbbbbababbabaaaaaaaabbbaaaaababaaabbbbbaaaabaababaabaaaabbababaaaaababbaaaabbabaababbbbababbaaaaabbabbbabaaaabbbaabbababbbbbbaababaaaaababbabbbaaababbaabbaababaabbaababaabbabbbbbaabaaabbaababaaababbbababababbabbaabaaababbabbbaaabbabbabbbbabbababbbaabababbabaaabaaabbabaaaaaaabbbabaabaaaabbbaaabaaabbbbbbaaaabbaabbbaababbabbabbbaaaaaabbbaaaaaabbbabbabbbbbbabbbabaabaaabababaabbbbaaaabaababbabaabaababaaaababbaaaaaababaaabbababbbbbbaabbbbbbabbababbbbabaaaabbaabbbaabaaaaaababababaabbbaaabbbbabbabaaabaababbbabaabaabaabbbabaaaabbabbabababaabbbaabbaaaababaabbbaabbabbabaabbbabaaaabaaaaaaababbaaabbbabbbabbbaaaaaaabbabaabbabbbbbbbaabbbbbbaababbbabbbabaababbbabbaaabbbaabaaabaaaaabaaaabbaaabbaababaaabaabababababbabaabbbababbabbaaaaaaaababaabbababaabbabaaabaaaabaaaaaabbbabaabaababababaabbbaabbbbaabbbbaabbbaabbbaaabaaabbaabaaabbbbbabbabbababaababbbabaabaaaaabbbbaaaaaaaaaabbabbabbaaaaabbababababaaabaaaaabaabaaaaaababaabbabaababbbababbbaaaaabbaabbbabbbbbbaabbbabbbabaababbbaaaabaababbbaaaaabbbaabaaabaaabaababbaabbabbbbabbaababaababaabbbabaabbaaaabaaababbbbabbbbbaabaaabbabbaabbaaaaaababaabababbbaababbaaabbaababababbaaaaababbbbbbaabbabaabbbbaabbbaababbaaaaabbabaaababbbababbaaaabbbbbbabaabbaabbabbaababbaabaabaaaabbbbbabaabbaaabaababbaaaaabaabbababababbbbbabaaaaaabaabbababaabbbababbaaaabbaabbbbaaababababaaabbbaaabaabbbbaabbaaabbbbabbaabbbaaaabbbbbbbbaabaababaaaabbbbababbbaaabbaabbaababbaabbababaaaababbabaaaaabbaaababaaaaabbabbbbbababbaabbbbabbbaabbaababbbababababbbbabbbaababbaaaaababaababaababbbabbabaaababaaaaaaaababbaaababbbbbabbaabbbbabaabbabbbbbbbabaaaabaaaabbaaaaaabbabaaaaaabbbbabbbabbabbbbbabaabbbabaabbbababbababbbaaabbaaaaababbaaaabaaabaabbabbbabbbbaabbbbabbbbbbbbaaaaaabababbaabaabaababbabaabaaaabaaaabbaaaaabbbbabbbabaaabbbbbaabbbbbbaaaaababbbbbbbaabaabbbbbbaababbbbaabbabbaaaabaaaaaaaabbaaaaaabbaaabbaaababbbabbbbbbbaaabbbbbabbbaaababaabbaabbbbabbbbabbaabbbaaabaaabbaaababbaaabbbaaaabaababaababaabaabbaaaabbabbbabaabaabaaaaaabbaababaaababbbaaaabbbbababbbbabbbbababaabaaabbaabbbaaabbabbbbbbabaabbabbabbbaaabbbbabaabbbbbaabbaaababaabaaaababbbbabaaababbabbaabaabaabababaaabbbbbaaabbbbabbababaaabbaaabbbbbbbabababbbbaababaaababababaababbabbaabbbaababbbbbbabaaabbbabbaaaabbbbabbbababaaaabaaaabababaababbaaaaabaaabbabababababbbbabbbababaaaaabbababbabbbbbaabbbbbaaababbbbbaaababaaaaabbabaababaaabbbbbbabbaabbabbaabababbaaabbbaaaabbabbaaaabaabbabbababaaaaabaaababaababbbabaabbbbaaababaabaaababbbbbaaabaaaaaaaabaaaababbbabaaabbbbbaabbbbbbbabbbbbababbabbaaabbabaaaaabaaabbbaaaabbabababaaaabababbabbbabbbaababababaabbababbbaabababbbbbbbbbbbbbabaaaaabaaabaababbaabbaaaaaabaabbbbabaabbaaaabbabaabbbabbbaaaabababbababaabbbababbbaaababbbaabbabbbaaababbbabababbaababbaabbbbaaabaabaabbabbababbbbbbbbaabaaabbaabbbabbababbbaaabaabaaaaabbabababbbaabababbbaababbbaabbaabbababbbbabaabbbbbabbbbbbbaabbbabbaabaabbbbabbaaabbbbabbbabaabbbabbaaaaabbabbbbaaaaaaaaabababbbabbbbababbbabababaaaabaaabbbabbbbabaaabbbbbbbbbababbaabbbbbaabaaaaaaabbbbababbaaabbbbabbaaababababbaaabaabbabbabbabaabbbbabbabbbbbaabbbaaaaabaabbbbabbbbabaaaaaaabbabbababbaabbabaaabbbabbbbaaaabbabbbbbbbbbbaaabbbaababbbbbaaabbbbabbabaabbabababbbabbbbbaaabbabbaaabbbbabbababaabbbababbabaabbaabaaaabababbabbbbbbbabbabbabaaaabaaabbabaaabbaaaaabbbaaaabaaaababababbaaabbbabbaabbbbaababaaaabaabbaabaaabbaabbaaaaabaabbabbbbaababbbbbababbabaaabaababbbbbbbbabbabababbbaababababbabbbbbaabaaabaaaaaaaaaabbbaabbbbbabbabaaaaabaabbbaaabbaaabbaaaabaaababaabbbbaabaabababbaaaabaaaaaabaaabababbbbaaaabaaababaababbabbabbbbabaaabbbabbaabaabaaabbabbabaabbbbaababbabaabbaaaaababbabaabbbabbbaaabababbaaaabbbbbaabbbbbbababababbababababaabaabaababaabaabbabbababaaaaabaaaabababababbbbbabbbbaabbabbaabbbabbbbbaaaaaabbabbbbabbbababbbbbbaaabbbbabbbabbbaaaaababbbbbbaaababbaaabbbbabbbabbbbabbababbbaabaabbaabbbbbbbbbaaaabbbbbababbbabbabbbaabbbbbbabbabaabbbbbbababababbabbabababaaaabaaaabaabaaaaababaabbbabbbbbaabaaaabaabbabbaabbaaabbbaaaaabbbbabaabaaaaabbbaaaaabaaabbbaaaabbbaabbaaaabbaaababaabaabaaabbbababaabbbbbabbabbbbabbbabbaabaabbbabbbababaabbabbaaaabbbaababaaaabbaabaabbbbbbaaaabbbaaaabaaabbbbbbaaaaaabbbbaaaabbabbbbaaabbaabbaaabbbaabbbabbbaaaaaabbbaaaabbabaababababbababbbbbbbbbbaaaaabbbaaaaabbbbbababbbabbbbbbaaababbbaaaabbaaaaaabaaababbaabaaabbabaababbaabaabbbaabbbababbbabbbbabaaaaabaaaaaabaaabbabaabbbbbaabbbabbbaaaaabbabaabaababbbabbbbbaaaaaaabbaaaabbabbbaababbbabaabbabababbbaaabbaaabaabbaabbbaabaabaaaaabbaabbaabbaabbabaabbaabbbaaaaaabbabaababbbbbabbbbbbbbbabbabbaababaaabaabaaabbabbabbbbabbbaaaaabbbabbaabbaaaaaabbbabbbaabbabbaaaabbabaabaaabaababbaabaaaabaaaabbabbbababbababbbbbabaaabaabababaaaabbababbbaabaaaaaabababaaaabaabaabbbbbabbabaaabbababbaaaaabaaaaaabaaaaaaabbbababbabaaabbbababbbaababaabbbababbbbbbbababbbbbbbbabbbaaaabaaaaaabaaaaaabaaaaabaabaaababaababbaaabbabaaabaaaaaaaabbaaaaabaabaabaaaabbabaaaababbbbbabbbbaabbaabaaabbababbbbbabbababaabbabaaaaaaaababbabbbbabaabaaaabbbbaaaabababbaabababbbabaaaaabbbabbbabbaabbabbbaaaabababbabbbbbabbbaaababaaabbababababbbbabbababaaabbbbbbaaababbbbbbabbaabbaaabbabaabbaaababbabbaaabbabaaaaaababaabbbaabbbbaaaabbbbaabbbbbbabaabbbbbbabaaabababbbbbababbbbbbbbbbbabbbbbabaaaaabbbaabbabaaabbbabbbbbbaabbbbabbbaaabaaabaabababaabbbabbababbaaabaabaaabbbababaaabaababbbbbaaabbaaabaaaabbababbaaababbabbaaaaabbbaabbabbbaaababbabaaaababbaaaaabababbaaaababbabbabbaaababbbbaaabbbabaabaabbaabbababaaaaabaabaabbabbaaabbabbaabaaabaababbbbababaaaaaaabbabbabbaabbabbabbbbbaabaababbbbabaaaaabaaabbabaabbbaaaababaababbaaababbabbbaaaaaabbaabbbaaabbbaaaaaabbbbaaaabbaabaabbbbbababbbbaaabaabbbabaaababaaabbaababbabbbaabaabbabbbabbaabbbabaaabababaabaaaaaaaaaababbbbbbabaaababaaaaaaaaaabbaaabaabaababbabbabbabbbbabbabbaaabaababbbababbababbbaabbababbababaaaaaaabababbbaaabbaaabbbbbaaaaaabbbbbaabaabbbbbbbabababaabaabbaaabaaabbbbbbaababbababbaaabaabbabbbababaabbbabaaabababbbababbababbababbaaaaabaababbbbbbbbbbaaabbbbabbaabbbbabaabbbbaabbbababababbaaaaaabbbbabaaaabbbbaababbbbabbabaabbbaabababaabbaabaaabababaabbbabbbababaaaababbbabbbaaababbaaaaaaaaabaabaaababbabbabbabaabbbbaabaaaabbaaaaabbbbabbbbbbabbaaabbabaabbaababbbbaabababbbaaababaabbbaabababaabbabbabbaaaababbabaabbaaabaabbbbbbabbaaabaaaabbbabaababbabbbaaabaaaababababababbbaaababbbabababbbaaababbbabbbbbabbbaababbbaabaaababbababbbabaabbbaabbbababbbababaaabbabbbaabbaababababbbabbbbaaabbaaababaabaabbbbabbbbbbbbbaabbbabbbababbaaabbbaaabaabbaababbbbbbbbabbbbbbbaabbabbbaabbaaababaabaabbababbbababababaabbaaabbbbabbaababaaaaaaaabbaabbbbbbbaaaabbbbbbbbaabbbbaaaaababbbabbbbbbbbabaabbbabaaababbabaaaaaaaabaaaabaaaaababaabbabaaaaabaaabbbaaabbbaabbabaaabbaabbaabaaaaabbaaaaaaababaababaababababbaaabbaabbbaababaababbababaaabbbbbbbbaabbbabaabbbaaaaabaabbababaaabbababbaaaaabbbbbbbaaababbbababbaaabbaabbabbbaaabbaaabaabbbbabaaabbabbabbaabbabaaabbabbbabbaabababbabbaaabbaabaaaaababbabbbbabbababbbbbbbbbabaabbaabababbbbbaababaaababbabbabaabbbaaabaabbabaabaabaaabaababababaaabbabbbaaabaaabaabaababaaaaaaabaabbaabbaabaabaabbaababbaaabbaabaababbaaabbbbbaabbbbabbbbababbbaabbbaabbaabbababaabaaaababaaaaaaabbaaaaabaaabaabbbaabaaabbaaaababbabababbaaabababbababbababbaabbbbbbababaaaaaaabbbaaaabbaababbbbababbbbabbbbabbbbaaabababbaababbaaababbaabaaaaaaaabbbabbbbbbbbbabbaabbbabbbbaabababbaabaaaaaabbaaaabbababaaababbabbaabbbabababaabaaaaabbababbbaaabbbbabbabbaaabbbbbababaaabbbbbabbbabbaabbaabbabbbaabababaaabababbbaaaaababbaaaaababbbabaaaaaaaaaaaabaaaaabbaaabbabaabbaabbaabaabbaaabbaababbabababbaabbabbababbbaababaaabababbbaabbbaabbbaaabaaabbaaaabbababaabaababbbabbaaaaabbababaaabbaabbbaabaababbbbabbababaaaaaaabbbbabaaaabbbbaababbbbaaababbbbaabbbababbaaaabababbbbbaabaaabbabbbababbbaababbabbabbbaabbbbbbaaaabbbbaaabbabbbbbbbbaabbbaaabaabaaabbbbbbaababaabbbbbaababbbbabbabbbabbbaabbbbbbbaaabbbabaabbbaaabbbabbbbababbbaabaabbbabbbaabaababbbbbaabbabaabbaabbaabababaaabbababbbbbaaaabbaaaaabbabaabbbabaaaabaababbaaaababbbbaabaabbbbbaaabbaaaaabbabbabbbbbaabaaabababbbbababbbabaaabaabaaaababbbbababbababbabaabababbbabbaabaaabbbbaabbaababbbabbabbababbbabbaabbbaabbabaababbbbbbaaabbaabbaababbbbaabaabbabbbabbabbababaaabbaabaabababbaaaaabbaabaaaababbababbabaaaaabaabbbabbaaabbaabbbabaabbbabaaaabaabbabbabaababbbbbaababbababaabbbbabaaaabbbbbaabbbaabbbbbaabaaabbbaababaabbaaaaaaaaaababbbaaabbbaaaababbababaaababababbabbabaababaaaaaababbbbabababbbabaabaaaaababaaabbbabababbaaaaababbaaabbaaaabbbababbbbbaabababbaababbabbabbbbabbbaababaaaabbaaababaabbaaaabbbbbbabbbbaabbbaaabbbbaaabaabbbbbaaaabbbaaabbbaaababaababaaababaabababbbabaaaabaabaabbaaabbbbaabbabbbababbababaababaababbbaaaabbbbabaaabbaabbbabbbbaaaaababbbbaaabaaabbabbaabbaaabbababbbaabaaabbabaaaabbbaaaaaabbaabbabbbbbbabbabbbabbababbabaaaaababbbbbbbabbabaaabaaaaabaaababbaabbbbbababaabababbaaabbbabbbabaabaababaabaabbabaaabaabbbbaabbbbbabbabbbbabbbbbabababbbbbabababaabbbabaaabaaababbaabbbbaaaabaabaabaabbaabbbaabaabbbaaaabbaabbaabaabaababbbaabbabaabbabbbbaabbbbbbbbbbabbbaaabbbbababaaaaabbbabbbbbbbbbaaababababaababaabbbaabbababaaaaaaaaababaabbbbaabbaabaaaaaabaaaabaaaababbaaabaaaaababaabbaabbaabaaaaaabaabbaabababbbababababbbbabaabbaabbbbbbaabaabbbbabababbbabababbaaaaaabababbabbababbabbabababaabbaabaabababbaabbaabbbbbbbbaaaabbbaabababaaaabbbaabaaaabbababbbbbaaaaaabbbbaabbbbbababbabaabaaababbabababbbbbbabbbaabbaabaaaabababbbaaaaabbabbababbbbaaaabbbabababaaabbababaabababbbbbababbbabbbabaabbbabbabbabbabbbbabbaaabbabbbbbaabbababaaaabbbbbabbbbabbababababbabababbaabbababaabbabbbbaababbbbaaaabbbbaaabbaaabaaaabaaabbbbaababbbbbbaabbbaababaabbbaaaaababaaaabbabbabbabbaabbaaabababbbabbaababbaabaaaabaaabbabbbbaaaabaaaaaabaaaabbbbaaaaababbabababaaababbababbbababbbbabaaabbbababbababababbbabaaabbbabaaaaaaaababbaaaaabbababbabbbaaaabbbabbabbbbbbbaaabbbbabaabaabbabaaaabbabbbbaabaaabbaababababaaaaaababbabbaaaaababbabaaaababbbbababbbaaaabbababaabbaabaaaaabaababaaabbbbbaabbaabbaabaabaaaababaabbbabbbaaaababbbbaaaabbabaaabaabbabbabbabbaaaaabaabaabaaaaababaaababaabbbabaabbbbabbbbbbbaabaabaababbbaaaaaabbaaaabbabbbabbbbbaaabbaabbbabaababaabbbbbaababaabbabbbbbaaaabbbaababaabaaabbbaaaaababaabbbbbabababaabbaaabababaaaaaabbbbbaaabbaabaaaaabaaaaaaabaaabbaaaababbabaaababbaaabbbababbbaababaabbbbaababbbaabaababbaabbabbbababaababbaababbaababbbaabaabbabaaabbbabaababbabbbbbbabaabaababbabababbbabbbaabaaababababbaabaabbbabbabbbbabaaababaabbbbbbaabbbbbababbbbababaaabaababbbbbabbaaaabaabaababbbbbabaabbbbabaabbbbaaabbbbabaabbaabaaaabababababaaaabaabbbabbbabbabbaaabbabbbabbbbbababbabaaabbaabaaaababbaaabbbbbabbaabbababaaaababaaabaaaababbabaabbbaaabbaabaaabaaaaabbabbaabbbbabaaabbbbabbabaabbbabbabaaaaababbbbbaabbaabbaaababbbbbaabababbabaaababbbbbbbabbbabbbabababbaabbbbaaaaabbaabbbbbabaabaaaababbabbababbaabaaaaabbaabbaababababbabbaaabaaaaabbbbaaaabbaababbbaaabaabbaabbaaaaababbbbbaabaaaabababaaababbaabbaababaabbbaabbbababbbabbaaabaabbbbabbbaababbbabbbabbbbbbabbbabbbbbbabbbbbabaaaaaabbabbaababaaabbbbaabaababaabbababbaabbaabababaabbababbaabbbbbbabaabbbabbbbaabbbaaabaabbabbbaabbbbaabbaabbababbbabbbababaababbbabaababbbbbabbaaaaaaaabbaaaabbbabbbbabaaaabaaababbbbaaababaabaabababbabbababbbbabaaababaaababbaaabbaaaababbabbababaabbbabbabaaaabbbaaabbaaaaaaabaaaaabbabaaabbbbbaabbababbabbabaabaabbbaaaabbbbaabbabaababaaaabbababaabbbbaaabaaaabaabbaaaabbbabbbbbbbbbaaaabbbaaaaaabbaaaaabbaabbabbbababbaababababbbbabbbbbbabbaaabaabbbbbbabbababbaaababbabbababaabbbaaaababbbbabaababbaabbbaabbabbbbbbabbaaaaaabaabbaaababbbabaabaabababbaabaabbbbabaaababbaaaaaabaabbabaabbbbbbbbabaaaabbabaabaababbaabaabaaaaaabaababbabaaaaaaabbaabbabbbabbabaaabaabaaabbaabbaaaabbaabaabbbaaabaaabbabbbbababaaabaaabbabaaaabbaaaaaabbabababababbabababbaabaaababababbabbaaaabbbbbaabbaaabbbbaaaaaabaaabaaaabaaabbbbaababbbbbabbbbbaabbbbbabaabbabbbaaabbbbaabbabaaabaaaaababbbbabbbbbbaabbaaaaaabbbbababaaabaabbbbbbabaabaaaabbaabbbabbabbaaababbaababbbabbbbbbabbbabbaaababbbabbaaaaaabaaabbbaaabaabbabbbaaaaaaabaaaaaaabbaababbbabbbabbabbbaabbbbaabbbaaaababababaababaaaabbbababaaaabbaaaababababaaaaabaaabaaababbabbbbbbaababbbbaaabbbbbbabbabaabbabbabbbbbbbababbbaabaaaabaaabaabbaabbbbabbabaabababbaaaabaababbabababbbaabbabaaabbbbabaabbbabbbaabaaaaaaabbbbabbaabaaabaabbaaabbbbbbabbbabbbaabaaaaababaabaababbaababababbababaaabbbabbbaabbababbbaaabbabbbbbbbbaabbbbbbabbbbabbabbbaabbbabababaaabbbabaababbbaabaaaaabaaaaabaabbaabbababbbaaabaaabaabbbbabbbaabbbbbaaaaabaaabbabbbbbabbbbbabababbbaaaabbabaaaabaaabbbbababbabbaabbbaabaabbabbaaababbabaababbbabbbaaaaaaaaabaabbbabbabbbbbabbabbaaabbababbabbbbbbaabaaabaabbbabbbababaabaabbbbbbbbaababbaabbaaabbabbabbbabababbbbbbaaabbababaaabbbaabbbbbaaaaabaaaabbababaababaabbabbbbbbabbababbbbbbabababaaabaaaaabbabbaaababaaaaabbaababbabbbbbbbaaaabbabaababababbaabaabbbaaaabbababbbabbabbbaabbaaaaabbbaabbaababbbaaaaababbaabaabaaabbbaaabaababbabbaaababaaababaabbbbabbaaaababaabaaabaabbbbabbbbbbaaaabbaabbaaabbbbaaabbbabbbababbbbabaabbaaabbbbbbabaaaabaaabbbababaaaabbbabaaabaaaababaababbbbbbbabbbabaaababaababaabbababaabbbabaaaaaaaabaabaaabbaaaabbbaabbabababbabbabbababbabbaababbabaabaaaabaabaabaaaaaabaaabbaaabbaababaaabbabaaaaabbabbaaabababbbbaaabaaabbabaaaaababbaaabbbbbbbbbabababbabbbaabaaabaaaabbbaababaabbbbaabbaabaabbaababaabbaaabaabbaaaaababbaababaaabbbaabaaabababbbbbbaabaaaabbaaaabaaabbababbaabbababbabaaaabbabbbbbabaababbbabaaababbabbbbabbabbaaaabaabbbbabbaabababaaabababbbbaabaaabaabaaaaaabababbabaaaaaabbabbbabbbabbabbbaaabbbabbabbaaabbbbaaabbbaabaaaaaabbbabbbbabbbaaabbbaabbaababaabababaabaabbabbaababbbabbbbbbbbabaababaaaaaaabbabaabaabbabbbbbbbaababbabaaabaabbaaaababbaaabbbbbbbbbabaaaaabbbbaabbabbaabaaabbababbaaabbaabbaaabaaabbaaaaababaabbbabbbabbabbbbaaaabbbabaabaabbabbbabaabaabbaaabbabbbbaaabaabaaaaababbbbaabbaabaaabbabbabbaaaaabaababbbbbbbabbaaaabbaabaabbbaabababbabbababbbabbbaaaabbbababbaabaabbaabbbabbbbaabbaaabbbbbababaaabaabaaabbabaaabbaaaabbbaababababbbaabbbaabaaaaabbbbaabbaababbbaabbbbaaabaaaaaaaaaaabbabababbbbaabaaaabbaaababbabbabbbbbbaaababbaaabaabaaaabbbbaaababbaababaabaabababababababaaabbaabbbababaabbbaabbabaaaaaaabbabababbbbabbabbabbbbabaabbbaaaaaaababaaabaabbbbaababbabaabaabbbaaabbabaabbbbaaaaaaaababbaabbbbaaabaaaaabbbbbbaabababbbababbbabbaabbbbbbbbbaaaaaaababaabaaabababbbaaaaaaaabaabaabbaaaaababaaaabaaaaabaaaabbabaaabaabaabaaaabbbabbbabababbabbbbbbababbabaaabbabbbaaabbbbbbbbaabbbbabbaabaabbbaaabbbbbbaababbaababbaabaaabaaabbababbbababaaabbbabbbabbaabbabbbbaaabbaabaaabbaaabaabbbbabaabbabaabababbaabbabaaaabaabaababbbbbbaabbababaabaaaababababaaabababbbaaaabbaaabbbababbaaaaaaaaabbbababbbbaaaaabbababbababbaaabaaaaabbaaabaabababababaababaaaabbbbbaaaaabababbbaabaabaaaaaababbaabbaaabbbabaaabbabaabaaaaaabaabbbabbbbaaababaabbbabaabbbabbbaaabaabbbbbabbaaababbabaaaaabbabbbaababbabbaaabbabbabbbaabbbbababaabbaababaaaababaaaaaaaababbbaaaabbababaaaabbbaaabbabbbaabbbbaaaaabbaaabaabaaaaaaabbaaaaaaaaabbbababaaaabbbbaababaabbbababbaabbbaabbbabbaabbbbaabbaaabbaababbbbaabbbabbbbaabbbaaabaaabaababbaaaabbabbaaababbaababbbababbababaababbbbaababbabbaabbbabbabaaaaaabbbabaaabaabbbabaaaaabababaabbbabbabbbbaabaabaaababbabaabaaabbbabbabbabbaababaaabbbbaaabbbabbbaababbababaaabababbaaabbaabbbaababaaabbbababbabaabbaaaabaabbabaabbbabbaabbaabbabababaaabbbbaaabbbbbaaabaabaaaaaabbbbabbbabaaaaaabababbaabaaabaaaaaaaaaaaaaaabababbbbaabbabababaaababbbaabbbbbaaababaaabbbaabbaabbbbbaaaabbababbbbaabbbbbbababaaaabaaabbbaaaabbabbabaababaabbababbababaabbababbbaaaabbbaaabbbababaaabaababbbaaababbbbabbbbaabbbabbababbabbaabbbbabaaababbbababbbbbbbabbbbaabaabaaaabbaabbbbabbbabaaaaaaabababaabbaaaaabababaabbaaaaabaabababbbabbabbaaababababaaaabaabbaaabbbbbababaaaaaabbabbbbaabbbbababaababababaaaaaabbbbaababaabbbaabbbabbaabaaabbbbaabbaaabbbbaaaaabaabbaaaabaaaaabababbabababaabaaababaabbabbaaababbaaaabbbbaabbbabaaaaababbbbbbbaababbbbbbbabbabaaabbaabbabaaaaaabaaaaaaabaabaaabbbababbaaababbbbaabbabbbabbaaabaaabaabbbbbaaabbabaababaababbbaabaabbaabababaaaabbbabbbbababaabaabaabbaabaabababaabaababababaabbaabaabbabbbaabbbababbabababbbaaaabaabbbbabbbbbbabbbbabaabaaaaaaaabaababbbaaabbaaabbbaaababaaabaaaababaaaaabaabbbabaabbaabbbababbaaaabbabbabbbbbaabbaaabaaaaaaabbbbbabaabbababbababaababbaabbaaababbbbbbbbbbabaaaabbabababbbbabbaaabaaaabbbabababababbabbbabbbaaaabbababbabbbbabbaaabababbabbbabbabababbbabbbaaaabaaababaaabaaaaabbaaabbaaabaabaabbaaaabaabbbbbabaababaabbabababbababbabababbabbbabbbaaaabbabaaaaababababbbbabbbababababbabbbaaaaabbaaaabbaaabaabbaaabaababbbbabaabbaabaaaababbabbbbbbbabbaaabbbababbbabaaaaaaababbbabbbaaabbabbbababbbbbbbabbbabaaabaaaababbabbbbbaaaabbaabbbbaabaaabbbbbabbbbbabbabbbabbbaaaabbaabaaaaababbbabaaaabbbaaaaaaaaaababaaaaabaababbbaabbababaaaaabaaaaabaaabababbbbbbabbbbbbbaaabaaabaaaaaaaaaabbabbaaababbbbabbabbbbbabaababbbbabbaabaabbbbbaaababbbaaabbabbabaabbbbabaaaaaaabbbbabbbaaababbbaaaaababbabbbbaaabbbbbbbaaaabaababbbbbaabbabbababbbbbaaabbabbaaaabbaabaabbbabbbbbbaaaababaabaabbbaaaabbabbbbabbbabababbabaaaaaaababaaabbbbbbbabbabababaababaabbababbbbbabbbabbbabbbaabbbbabbaaababbababaaabbabaabbabbbababbbbaabbbaaabbbaaabbaabaababababbaabbababbbaaaaabaabbbbbbbabbaaabaabbbbbbbbababbbbbbabbabaabaabbaababaaaabbababaaabbbbabbabbabbbbbbbababaababaabbababaabbaaabbaabaabbaaabbaabbaaabaabbbbaabaabbbbaaaaaaaababbbaaaaabbaaabbbbbaaaabbaaaaaaababbabbbabbbaaababbaaabbbbbbabbaabbaabbaabbbabbaaabbbbaabbaabbbbbbbabababaaaaabaabababbbbaabbbaaaabbaabbbbbaaaaaaaaabaaaaabbabababbabbbabababaabbbbbbaaabbbbaaaaabababbaababbaaabbaaabbababbbabbabbbbbaaabaaabaaaabaabbabbaaabababaaaababbaababaaabbbabbabbabbbabbbbbaaaabbbabbabbbabbabbbabbbbbabbaabbabaaaababaaaaabaaaaaaaaaaaaabbbaabbbbbabaaaababaaabaaaaaaaabbbbabaabbabaaabbaaabaababbbaaabbbabbbabababbaabaaaababbbbaaababbbaaaabaabaaaabbabbbaabaaababbaabaabbbabaaababaaaaaabaabbbabbbbbbbbbbabbaababbbaaaabababaabbaababaaabbbbbbbbaabaaaabbbbabbbabbbabbaabaaabaaaabbaaabbababbbbaaaabbbabaabbabbbababbbbbbabbbaabbbabaaaabaaababbaabbaaababbaaaabbbbbaaaaabaabbabbbbbabbbbaaaabaabbbabbbaabababbbbbbaaabbbaabaabaababbaabbabaabaabaabbaababbaababbbabbaabbbbbbbbbabbbaabaaaabbabbaabaaabaaabbbabbbabababbbabbaaabbaaaabbaaabbaaaaaabaaaaabbbbbbbaabbaabbbaaababbbbbbbabaaaaaaaabaaabbbaaaaabbbabbaaabaaabbaaaaabbbbbabbbabbbbbbbbabaaabbabababaabababbbabaaabababbaaaabaaaaaabababbaaaabbaabbababbbbaaaaaaabaababbaabbbaaaaabababbabbbabbaaabbaabbbaaabaabaaabbbabbababbabaaabbabbbaabbabbaaabaaabaabaaaabbaaabbbabbbabaaabbbababbaabbbabbbbabbabaaaabbbbaabbbabaaaabbaabaabababbbbaababbaabaaaaabaabbbbaaabbabaaababaabababbbabaaabaaabaaabaabbbaabaabbbabbabbabbbbbbabbaaabbbaababbabababbbbabaabaabaaaababaabbbaababaabaabbabbabababbbbbbabbaaaaaaaaaaabaabbabbbbbbabbbaaaaaaabaaabaaabbbbbaabaaabbbaaaaabaaabaaaabbabaababbaabbababbabaabbbaabaabbababaababbaabaaabbaaabbaaabaababbbaabaaaabbaaabbaabbbaaabbabaabaaaaaababbbabbbbaaaabbabaabbaabbbbabaaaababaaabaabaaabbbbabababaabaaaababaaaaababababbbbbaaaabbabbaabbaaaaaaabaaababaabaaabbbaabbbaabaabbabbbabaaababbaaaaabbbababaaabbaaaabaabbaaabbbababbbaabaabaaabbabbaaabaababbaaabaaabbbbbbabbbababbbabbabaabbabbaaababbaabaaaabaaababbabbaaaaaaaaababbaaabbbaabaabbbbabbbaaaabaaaabaabbaabbaaababbabbaaabbbaabaaaabbabbbbbababaaaabbabbabaababbbbabbbbabbaaabbaabbaabbbbbaabbabaabbbbabbabaaababaaabbaababababbaabbaaaabbaaaabbbabbbabbabaabbbabbaaabbaaaaabbaaaabbbaabaaaaaaaaaaabbabaabababbabbabbabaaabaaaaaaabaabbbbaaabababbabaabbbabbaaabbbabaababbbaababaaaabaaabbabbaaaaabaabaabbbaaaabbbaabbbbbaabbbababaabbbaaaaaaabbabbbabaaabbbabbbbbaaaaabbbaaaababbbaaaabbabaabaabababaaaaaaaabbbabbaabbabaaaabbaaabaaabaaabbbbaaabaaababaabbbbbaaaabaaaaaabbaabaaaabbbbababaabbbbbbbabaaaaabbababaaaaaaaaaaaaaabbaaaaaabaaaaababbbbbbbaababaabbabaaabaaaaaabbabaabaabbbbbbbababbabbbababbbabbabbbabaaababbbaabababbabbabbabbabaaaaabbbbbaaaaabbabbbaaaababaabbbaaaaaababbaaabbbbbbabbbbbbbaabbaaaabababbabbabbbbbbababbbbbabaaaaabbbbaaaabbbbbabbbabbbbabbbabbaababababababbaaabaaabaaababbbaabaaababababaabbaabaaaabbbaabbbabbaaabbaaaaabaaabaaaabaabbabbbababbabbbabaaaaabaaababbbaaaababbabbbbbbbbbbaabababaaaaabbaaabbaabaabbbbabaaaabaaababbabbbabbbbaaaabbbbaaabbaabaaaaabbbbabbbbbbbbbbbabbbbbbabbbaaaaabbbaabbabbabbbaaaababbaabbbaaaabaaaabbbabaaababbaaaabbbbaabbbabbabbabbaaaaaaaabbbbbbabaaaabbabaabbabbbbbbbaaaabaaaabbbaaaabbbaabbaaaaaabbaabbaaaabbbaabbababaaabbbaabbbbabbabbbaabaaabababbababbbabbabbabbbaaababaababaaaaaababbabaaaabbaaaabaaaaabbbabaaabababbababaaaabaabbaaaabaabaaabbbaaabbababbaababaabaaaababbaaabbaaabbabbaabbbabaabbbbbbbbabbabbababbbbabababbbbbaaaaaabbaabbbbbaaaaaaabaabaabbbaaaabababbbabbabaabaaabbabbbbababbaabbaababaabaabaababbbbbaaabaababaabaaabaaababbaaaabbaaababbabaabbabbbbaababababbabbbabbbbaaababaabbaaaabbbaaaababbbbbababbaabaaababbabbbbbbabbbbabbaabaabbabaababbbaababbbabbaaaaaaaaababbaaaabbbabbbababaaaabbbabbabbbbabbaaabbabbbbbabbababbbabbabbabbaaaabaababaababaaabaaababbbabaaababaaabbaababbbbabbaababaaaaababababbbbaaabbabbabaaaababbaaaaaabbabaabbabaabbbbaaaababbabaaabbaabaabaaaaabbbabbabaaabbabbbbbbbbbbbbaababbbbababaababbabbaaababababbaaabbaabbababababbbababbababaababaaabbbaabbbabbaaaabaabaababbaabaaababbaaaaaaabbababbaababbababbaabaaabbbababaabbbaaaababbababbbbabaaabaababaabbbabaabaabbbababbaaabaaabbaaaaabbbbbaabbbbabaababababaaabbaaabaaabaaabbbabbbbabbababaabaaabbbbbbaaabbaabbabbaaaaaabbaaaaaabbbbbbbbbaababbaababbbbabbaaabbaaababbaaabaaaaabbbbbbbabababaaaaaaaaaabbabababbaaaababababbaaabaabbaababbaabaabbababbbaaaaaabaaabbbabbbbbbbbaabbbaaabaabbaaabaabbaaaabbbaabaababbabbaabbbbaabbabaabaaabbbbaabbbaaaabbabbabbbbabaaabababababbbaababbaaaaabaaaaabababbaabaaababababbbbbaaaabaababbbbabbaabbbaaabbabaaaabaabbabababbabbbaaababaabbabaaaaababbbaabbbabbbaabbaabbbbbbaabbbaaababbbbabaaabbbabaaaaaaaabbbaabbbbbbaabaaaaabababbabbbabaabbbabbbaaabbabaabaabababbabbbaaaaaaabbaababaababbbaaabbbbababbbbabbabaabbbabaaabaaaaabbaaaabbaabaabaababaaaabbaabbbaaababaaaaaabababbbbabaabaabbbaababbbaaaababaaaabbbababbbbbaababaaabbaabababbaaaaaaaababbbbabbbaabaaabbbbaabbbababbbbabbabbbbaaabbbaababaababbabbbaababaababaabbabbabbbbbaaabbbbbbbbaaabababbaababbbaaababbbababbbbabbababbaaaaaaaaaabbababbbbabaabababaaabbbbaaaababbabbbabbbbbbabaababbaabaabbabbbabbaabbbabaaaababaaababbaaabbaaabaaabbbabababaabbabaabaabaaaaabbbaaabbaaaabbbabaaaabbababbbaabbbabbabbbabaaaabaaaaabbabbbbabaaaabbbabbbaaaaaaaaaabaabbababbbbbbbbbaabaaabaaaabbaabbbabaaaaabbabbaabbbbabaabaaabbbbbabaaaaabbbabbbaabbbabbbbbbbbaaabbbbabbaaaaaababbbbabaaababbabaabbaababbbbabbbaaaaaaabbbabaabaabbabbbbaabbbaaaababbbaaabbabbaabbbbbabababbbbaabbabaaaaaababbbbabbbaaabbbaababaabaaaaaaabbbaaaaabbabbabbabbbaaabbaabbbabaabbbabbbbbbbbbabaaaaabababbabaabbaabaababbbabbaabaaaaaaaabbbaaaaabbbaabbabbabaabaaabbbaaaabbbbaaababbbabbbaabaabbabbbaaaaaaabaabbbbbbaaabaaabababaaaabbaabaaabbbbbaabababbabbbaaabbbaaaabaabbbbaaaaaaaabbabbaabbbaaaaaaabbbabaaabbbaaaabbaaabbababbbbaabbabbbaaaaaaabbaaaaabbbbabbbbbabbbbbbabbaabaabbbbabbbaaaabbbaabaaaabaaaaabbabbbbbaaabbbbaaaababbbababbbbbaaabaaaababaaabaaaababbababaaabababaabaaaabbbaaaaaabaaababaaaaaababbaaaaabaabbaabaaabbababbabaababbabaabbabaaabbaabbbbabaaaaaaaabababaaabbbaababbabaabaaaabbaaabbaabaabbbaaaaababaababbabaababbabbbaabaabbbbaaabbaaaaababbbbababbaabbaabbbaabaabbaabaabababbaabaaabababbbbabbaababaaababaaaaababbbabbbaaaaabbaabaabbaaabaabbabaaaababaaaaabaabbabababbabbbbbaaabbaaababababbbabbbbababbbbbbbaabbbbbaababababbabaabbabbbababbabaaabbbbaaabaaaaabbbbbbbbbbbabbababbbbbabaabbbbaabbbbaaabaabbabbababbabaabbaaaabaaaaababbbbbbbaabbbaabbabbbbbababbbaaaaaabbbababaabbabbababaaaaabaababbbbaaabbbbbbbbabbbaaabbababbabaaaaaabbbbaababaaaabbbbaabbabbbaaabaaabaaababbaaababbbbabbaaaaabbbbbbbbbbbabbaababaabaaababbbabbbbabbaabbbbbbbbabbaabbaabababbbbbabababababaaaabbabaaaaabbaabbbaaabaaaaabaaaababbbbaabbbbbbbabbbaaaaaabbabaabaabababbbbaaaabbabaaababbbbbaaaabaaababbbbbababaaabbabbabbaaabbaabaabbabbbbaabaabbababbbbbbbbbbabaabaaaabbaabbbbaaaabaabbaababbbbbbbbabbbbbbbbabbbaaabbbbaaabababbbabaabbaabaaaabbaaabaaabbabbabbabbbbababaababbaabbabaabaabaaabbabaaaabbbbaababbaaaaabaaabbaaaabaabbabaabaababababababbabaaaaaaaabaaaaaabbbbbbbbbababbbbaaabaaabbbbbabbaaabababbbbbaaaaaaabbababaaaaaaaabaaaaaabbabbababbabbaabbabaabbababbaabaabaaaaabaababbabbbbabaabbabbbbaaaaaaabbabbbbaaaabaabbbaaaaaaabbbaaaaabaabbabbbaaabababbbbaababaaaabbaaaaaabbabbaaabbaaabbabaaabbaaaabbaababaaabbbbaabbababababbbababbbbbbbbbbbabbbaabbbababaaababababbbbbbbbaabbbaabbaabbbaaaaaaababbababbbaaabbbaabababbbbbbbbaabbbaabbabaabbaabaabbabababbbbbbbbbbbbaabbabaaaabaaabaabbbbbbbaabbabbbbbbbbbbbaaaabbbbbbaaabaabbabbbaaaaaabababbbaababbaabaababbaaaabaaabababbbabaabaaaaabbbababbaaaaaaaababbbaaabaaaaaaabbbaaabbabbbbaabbaaaaaaaabbabbaaabbbbbabbbaaababaabbabbaabaababaaaabbbbabbbaabaaaabaabbbbabbbabbbbaabbbaaabaaaaabaabaaabaabaabbaabbabaaaaaababbbabbbabaaaabbaaaabbbbbabaaaaabbaaaababbababbbbbbbbaabaababbbbaababaaabbaaaabbaabaaabbbabaabababbabbbabbababbbabbaabbabbaabbabbabaaabbaaaaaaababbbbaaaaabbbbbbbbbaaabaaabbbbaaabbaabbbbaaabaaabaaaabbbbbbbabbbbaaaabbbbaaabbbaabbabbababbbabaaababaaaaabaaaaabbbbbabbbbbbbaabbaaaabaabbaaabaaaaabbaababbbaaaaabaaaaabbaaabbbaaabbbbbbaababaaaaabaaabbbaaabbbbaaabbbaabbaaabaabaabababbbbbbbbabaabbbbaaaababbbabaaaababbabaaabaabaabaabaaababbabbbaababbaaaaabbbabababbaaabbbabbbbbababbabbabbbaabbaababaababbabaabaaaaaaabbabbabbabaaabbbabbbbbaaaabaababbabbbabbbabbabaababbbaabbbbabbbabbabaaaabaabbabbaaabbababbaabbbbaaababaaaaabaabbbbbbabaaaabaabaabbbabbaaaababbbbbbaaaabbbabbabbbaaabbbabbaabbaaaabbbaaaabbbaaaaaaaabaababaabaabababbabbbbaabaaabaaabaaaaabaabaabbabbbbbbbbbaabbbbabbbbbbbbaababbbaababbaaaaabbababaaababaabbababbaabaababbaaaababbababbabbbbabbbbabbbbbaaaaabaaabbaaabababaabbbabaaaabaaaaaabaabbaabbbbabbaababaabbabaaaabbbaaaaaabaaaaaaabbbaaaabbaaabbaaaaaaabbbbbbaaaabbaaaabaabaaababaaaabababaabaabbaababaabbababaabaabbababaababababbaaabbaaabbaaaabbbbabaaabbaaaaaabbbbaaababaabababbbaaabbbabbaababbbbbabaaabababbbbbbababaabbbbababaaaaaaaababbbabaaaabaaaabaababababababbbbbabbabbbbbaabbbbbbabbabbaaaabbaaaaabbabaabbbaaaabbaaaaabbbbbaababbabbbbbabaabbaababbabbabaaaabaabbabbababbbaababbbbabbaaabbbbbaaaaabbbbaababbabaabbababaaabbabbbbbabbbbabbbbaaaaabbbaabaabababaabaaabbbababaabaabbaabbbaabaaabbabbaaabbbababaababbabaabbabbabbabbbbababbbbababaabaaaaababbbbaababbbbbbabaaabaaabbaabbaaababaaaabaababbbabbbaabaabbbaabbabaabbbabbabbbabaaaaabbbababbbaababbaaabaaaabbbbbbbbabbbaababbabaaabbaaabbaaaababbaababbbbabbbabaabbabbbababbbbabbababababbbbbaabbbaaaaaabbaabbaabaaaaaaaabbaaabbbbbbbaaaaaabaaabaabbbbbaabbaabbbbbabaabaaabbababbbbaababaaabbababaababaababbaababbabbbbaabbbaabaaaaaabbaaaaababaabaaabaabaaaabbababaaaaababbaabbaaabbbaaabaaababaababbababbbbbbababbaababbaaababaaaaaabbaabababbaabbbaabbaabbaabbbabbbababbbaabaaaabbaaabaabbababbaaaabbababaaaabbbbaaabaaaaaabaaabbaababaabaaabbabbbbaaabaaaaaaaabaaabbaabbbbaabaababaababbabbaaaababbaaaabbbbbbabbbaabaabbaaabbaabbaabbababbbabababbababaaaaaaabbbbababbabbbaaabaaabaababaabaabbaaaaabaaabbaaabaaababbbabbbbbbabaababbaabbbbabababbaaaabbbbababbbbbaabbaaaaababbbbbabababaabaabbabababbbbaabbabbbaababaabaabaabaaaaaababaaabbbabbabaaaaabbbabbbbbaabbbaabbbaabaaaabaabababbabbaaaabaaabbabbaaaabababbbaabababaaabaabbabbabbbbbaaabbaaaaaabbaabbbbabaabbbbababaaaabaabbbabaaaabbaabaaaaaaaabbbaaabbabaababaabbaababaaaaaabbababbbaaaabbaabaabababbabbabbbabaababababbaaabaabbbbbbaababbbaaabbbbbbaabbabaaabaababbababaaaabbbabaabbaabaaabaabbaaabbabaabaaabbbbabbaabaabaabaaaabaaababbbabababababaabbabaaabaaaaaaababbbaababbbbbbbaaabbaabbababbbaaaaabbaabaababaaaaabbaabaaaababaaabbabbbbbababbaaabbbaabaabbbbbaaaaaaaabbbbaaaabbbbabbabbaaabaaaaabaababababbbbbabababababaabaabaabbaabbabaababbabbaaaababaababaababababbbabbabbbaabbaaaabaabbbaaabbaaaaabbaabbaabbabbabaaaabaabbabbbabbaabbabababbaaabaaaaabbababbbababbbbaabbabaaaabbabababbbaabbaaaababaaaababbbbbaabababababbbbabbabbabbaaaabbbababaabbaaabaaaaaabaabbaaabaabababbbaaabbabaaabbaababbaaaaaabbababbababaaabbaababaabaaaababbababaabbabbaabaabbababbbaaaaaaabaaaababbbaabbbabaaaabbaaaaaabaaaaaaabbbaaaabaaabbbbbbbbaaaabbbbabaabaabaabbaabbbbababaaaaaaaaababaabaabaaaaabbabaabaabbaaababaababaaaabbabaaabbbbabbaaaabbbabababababaabbbbaabbaabbaababbbbaabbaabbabbaabaaabbbbbaababbbaababbbbbabaabbabbaaabbaaaabaababbbbbaaaabbabbbbabbaaaaaababaaaabaabbabababbbabaabbbaaabaaabaabababaabbabababbbbabbbbbaaabbbabbbaaabaaabbbaabbaaaaababababbaaaaabbbaaaaaabaaabbbabbbbabbbbabbabbaabbbbbababaabaababbaaabaababbbaaabbaaabaabbaabbaaabbbbbbabbaaabbabbbbaaababbabbabbaabaabaaaaaababaaaaaabbaabaaabbaaaaaabaababbababababaaaabaabbababbbabbaababaaaaabaabbabbbabaababaababbababaabaabbbabbaaaabbbbbbaaaaabbbbabbaabbabaaaaabbbbababbbbaabababbbababbabbbbabbbaaababbaabababbbbbabaaaaaabaabbabbaababbababababaaabbabbaaabbaababbbbbbbabaabbaaaabaaaabbaaaaababbabbbabbbabaababbaabbbaababbaaaaaababbabbbbaabbabaabbaabaabbbbabaaabababaababbbaabbbbabbbbaaaabaaabbaaaabbbbbbbbbaabaabbaabbababbbbbbabbbbbaaabbbbbaaabbaabbababababbaabaaabbbbbbaababbbbabaaababbabababaaaaabbababbaabaaabaabbbbbbabbbbbbaaaababbaaaabbaaaaababaaaaaaababbbabbbababbbaaaaabaaaabaaabababaabbaaabbaaaabbbabbbabbbbababbaaabbaaabbabbbabaabbbabbbabbaabbaabbababbbbaababbbabbaababababbbaabbbaaaaabbbababbbbbbabaabaababaababbaabbbbababbbbbababbbaaaaabbabbaaaaabababbaabbabbaaaaaabbbbabaabababbbbabbbbaabaaaabaababbabbaaaaababaaaabababbbababaaaaabbabaabbaababbbbbbaaaaaababababaaabbabaabaabaaabbbaaababaaaabaaabbbbbaabababbbababbbbbbbbbaaaabababaaaabaabaababbaababbbbaaaabbaababbaaabbbbbbabbbbbaabbbaaaaabbbababaaababaaabaabbbbaabbaaaaabaaabaabaaaaabbaabaaaaababbbbbaaabbbaabaaababaabaabbbbaabbaabababbbabaababbbbbbaabbaabbaabaabbbbbababbaaabaaabaabbabbababbbabababbbbbbababaababaabaabbababaaabbbaabaabaaaabbaaabbbbaaababbbaaabababbabbababababbaaabbaaaabbbbabababaabbabaabaaaaabbaabbbbaaaabababbabaabbbbaaabaaabbabababbaabbbbbbbaaabbbabaaaabababbbbbabbbaababbbabbbaaababaaaabaababbaabbbababbbabaababaaabbbabaaabbaababaabbabbabaaaababbbabaabbabbabbababbaabaabbaabbbabaaaaaaabaaabbababaabababababbbaabaababbaabaabaaababaababaababaaaabbabbaabbabbababbbbaaababbaabbbbaabbaaabbbbbbbbabbabaabbaaabbabababbbabbabaabbabbbaababbabbaaabbaaabbbbbbbaabbaaabbbbabbaaaaaabbaabaabaaabbaabbabbaabaaaaaabaababaababbbababaabbaabbbabbaabbabbbbbbabbbbbaabbbbaabbabababababbbbaaabbaabbaabbababaabbbababbbbabbbabbbaabbbaabaaabbabbabaabbaabaaabaabbbbabbaabaaaabababaabbbabaabbabaababbababbabbbababbaaaabaaabbbaaabbbabbbbaabbbbabaabaaaabbbbaaaabbaababaaabaabbbbabaaabaabaabababbaaaaabbbbabbabaababbbbbbbaaaabaaababbabbababbaababbabababbbaaababaaaaababaababbabaaabaaabaabbaaabbababbbabbaabaaababaabbbabbbbbbbbbaabaabaaabbbbaabaaaaababaaababaaaaaabbaaabbaabaaaabbaaababbabbbbaaaabbbaaaaabbabaababaabaabaaabaaabbaaaaabbaababaaababaabbabbaaabbbababaabbbbabaabbbabbaaabaabaababaababbbabaabbbaabbbaabbaaabaaabbaaaaabaaababbabbabaabbbababbbabababbaabbaabbabbabbabaabbabbbbbaaababbabbabbbabbabbbaaaabbaaabbbbaabababbbbbaaabbbbaaababaabaabaaababaaabaabbaababbabaaaaababbabbbabbbbbabbbbabababbbbabaabbbbbaabbbaaaaaaaabbbbbbbbbbbaabaababaabbbabbbaaaaaaabbbabbababbbbaaabbaaabaaabaaaababbbabbbbaaaaabaaaabbaabaaaabababaaababbbbbabaabaabababaabaababbbbaabababbaabbabbbabbababaabbbbaabbaabbbbbbbaaaaaababaabbbbabaabaabbbbaabbbbbabaaabbabbbbbabaaabaabaabaaababbabaaabaabaaaaabbbbbabbbbbaabaababbaaaabbbabaabababbbaabbbabbaabbaabbbaabbbaaabbbbaaabbbababbbababbbbbabbbabaaabbabbbbabbbabababbaaaabbbbaabaabbabbaaababbabbababbbaabbbbbabaababbabaabaabbbabbaababbbbbaabbaaabbbbabbabababbbbaabbbaabaaabaaabbbabbaaaaaabbbbbaaabbabbaabbaabbaaaaabbabbbabaabbbbaababbabbabbbaabababbbbabbbabbababbabbbaaaaaaaaabbbbaaabbbbabababaaaabbbabababaaaabaabaabbbabbbbabbabbaaaabaabaabbbabbaaabbbaabbaaabbababaaabbaabbababaabbbbaabbabbbbbaaabbbbbbbbbababbbbbbbaaaababbabaabbbaabaababbbbababbaaababbbbbabaabbabaabbbbaaabbabbbbbabbbababbbabbbbababbaababbaabbbbabaaaabbaabbbbabbaababbbbbbbaaabbbbaaaabaaabbababababaababaabbbbabababbaaaaaabbbaaaaaabbbabaababbabbbabaabbabbbbbaabbaabbbbbabbbabaabbabbbaaaaaaabbbabbbaabbbabaaaaabbbaaabaabbbababbbbbbbaaabaaabbbabaaaabbaabbbbbbbaaababbaaaaaaaabbabbaaaaabbaababbabbaabaaabbbbbbbbbabaaaaabaabbbabbbaaaaaaabbbaabbbbbaaaaaabababaabaabbbabaabbbabaababaaaaaaaaaabbabbbbbaaaabaaababbabaaaababbabaaaaaabaabbabbbbaabaabaaabbbabaaaabbbabaaaabbabbbbbbbaaaabaabbbbaabbbbbbabaababbbbaabaabbbbbbbabbabbaaaababbbbabbaabbbbaaaabaaababababaabbbaaaaaaababbbababbababbaabbbaabaaaabbbaabbbbaabbbababbabbabaabbbbabaabbabbaaaaaaababbabaabaabbbbaabaaabbaabbbbabbaabbabbbbabbbaaaaaabbbabbabbabaabbbaaaabaaaaabaaaaabbabbbbbbababbbababbabaaaabbbbabbababaababbbbbabbbbbbbbbbbbabbabbbbaaabaaaaaaaaababbbbbabbbababaaaaabababbaaabaaaaabbababaaabbabbbbbaaabbabbbbbaaaaabaabbbaabbaaaaabababbbbbbaaabbabbaaaabbaaaaabbbbabbaaaaababababbbbaaaabbababbabbbbbababaaaabababbabaabbabaababbbbababaaabbbbaaababaaaaaaabbbbaabaabbaababbaaabbabaaaaaaabaaabaaaabbbaabbabbbaabbbbbabaaaaabaaabbaabaabbbbbbaaabbbbaabbbabbaabbaabaabbaabaababbbababbabbaabbbaabbbaabaaaababbaaaaabbbabbbbabaaaaabaaaabbaabbabbbaaabbbabababbabbaabaaaaaaaaababbbabbbabbaaabbaaabababaaaaaaababaaabbaaaaaaabaabbaabaababbbbbbabbbbaabaabbaaabbbbabaaaabaaaaabbbbabbbbaaabbbbabbaaabbbbaaabaaaabbbbbaababaabbbaaabaaabbbabbabbaabaaaaabbbaaabbbbababbbaaaabaababbaabbaabbbbbbbaaabbabbabaaabaaabbabaaabababbbbbbaaaabaabbbaabbabaaaaabbbbbbaababaabaabbbbabbbabaaababbbbbbabaabbaabbbaabbbaaabbbbabbbaaababbbaabbabbbbbaabbbbaabbbbbbbbbbaabaaabaabaabaababaaabbaababaaaaabaaaabaaaabbbaaabbabbbbbbbbbbbbaabbbbaaaaaaabaaabaaababbbaababaaababaabbbbbabaabbabaabaaabababbaaaaaabbabbaaababbabbbbbbbabbabababbbabbaabbbabbaababbabaabbabbabaabbbbabbbbabaabaabaaabaababaabbbababaaabbabbaaababbaabbaaababaaabbbaababaaababaabbbaaaaaaaaaabbbabbbbaaaaaabbaabaaaabaaaaaaabbabbaabbbbbabbaaabababaaaaababbabbbbbabaaaababbaabbabbaabbbbabaabaabbbbabaabaabbabaaababbbabaababbbaabbbbabbbbabaaaabaabbabbaababaababbaabbbbabaabbaaaaabaaabbabbabaababbaababbabbbaaaabbabaaabbabaababaabaaabbbabbbaabaabaabababbbbaaaaabbaaabababbbbbbaababababaaabbabbaabbbaabaabaaaabbbabaababaabbaabbbbbabaaabbaabaaaabaabbbbbababbaabbabbaabbababbbabbaaaabbbaaabaabaabbabaaabbabbaabbaababbbbabbbababbbbabbbbbaabbabaabaabaabbabbaaaaaabbbabbabbbababbbbbbbbbbaabaaabaabaabbbbbbabaaabbaabababbaaaaabbabbabbaabaabaaababaababbaabbabababbbababbaabbbababaaaaaaaababbabababbaabbbbabbabbbbaaabbbaabaabaabaaaabbbbbaaaababbabababaaabbbabbaaababaaaaabbbababbbababbbaabaaababaaaaabbbaababaaaababbbbbaabbbaabbabababbaabababbbaabbaaaaaaaababbababbbaaaaaaaababbbbbaabaabbabaabaabbababababababbbaabbaaabbaabbbbbbabbabbbabbabaaaaaaaabababaaaabbaabaabbbaaaababaabbbbabbaaababaaaababbaabbbabaababbaaaaabbabaaaabbaabaabbbbabbaaabbbaababaaabaaababaaabbbabbaaaaaabbabbaabbbbaaaaaaabbaaaabbbaabbbbaaabaabbbbbbababaaaabbbbbabbaabbbbabaaaababbbbaabbbaabbbaaaabaaaaabaaaababbaaabbbaaababbaababaaaaaaaabaaabbaaabbbababababbbaabbbbbabbabbbababbabbaaaaaababbbbbbbabbbaaaaababababbaaabbabbabbbaaabbbaababaabbaabbbabbaaaaaaaabbbaaaaaabbaaabababbbabaaaaaaaaaaaababaabbaaaaababbaaabaaaabbabbababaabbabaaaaaaaaaaabbabbbabbaabbbbbabbbababababbabbaaaaaaabaababbababbbabbabaaabaaabaababbaababbaaaaaababbabbbbabbaaabbaaaabaaaaabaababaaaabbbbbbaabbbbbabbaaababbbbabbaababaaabbaabaaaaaaababbabbaabaaabbbbbaaaaaaaaababababaaababbbaabbaabbaabababbbabaaabbabbbaaaaaaabbbbbaaaabaabbabbaabbbbababaaababbababbbaababbbabaababbbaabbaabbbbbbaabaabaaaabbabbabaabbaaaabbbabaaabaabbabaaabaabababbaaaaabbabbbbbbabbaaaabbaaaabbbaabbabaabbaaabbaabbbbbaabbbbabbbabbaababbaabbbbaaabaaaaaabbbbbbbbabbbabaaaaabaaaabaaabbbaaabbabaababaaaaabababababbbbbbaababbbaababababaabababbbbbbaabbbaababbbaaaababbbabaaababbabbbbabababbabaabaabbabbaaaabbbbbabaaaaabbabbaababbbbaaababbbabbaabbabbbbbbbbbbabbabababbbbababbaabaaaaabbbbaabbbbbababbaabaabbbaaaababbaabbabbbbaababbaaabbabbababbabaaabbbabbbabbbabaababbbbbaaaaabbbbbbaabbabaababaabbbaaabbbbabaaabbabbbbbbaabbbbbbbbabbbaababaababaaaaabbbbabbbbbbaabaaabaaabbbbbabbabbbbaababbaaaabbbbaababbbbbaaabbbaaabbababbbabbaabbabaabaaabbbaaaaaaaabbbbbababbabbbbaabaaaababbbabbbaaaabbaabaabbabbaabbabaabbaabbbaaaaabbabbbaabbaababbbaaabbbabbbabaaabbaabbabbbbbbbbabbbbaaaaaabbabaabaaabaababbbbbbabbbababbaabaabbbaaaabaaaaaaabaabbbabaababbabaaaaaaaaaabaaababbbbbababbaabaaabaabaaabaabaabaababaaabbabbbaaaabbaabaabaaababbabbaaaababbbbaaaaaaababababbbbaaabbaaaaabababbbababaabaabaaabbababbaababbbbaabaababbaabaabbabbaaaababbaabaaaabbababbabaaaaaabaabbbaaabbabaabababbbbbbbabbaaaabbababbabbaaabaabaabbbaaabbbbbabbbabaabaaaabaabbababbbababbabaabaaabbbaaaaaaaabbabaabaababbbbabbbabaabababbaaaababaabbaaaaaaabaaabaaaabbbabbabaaaabbbbbaaaaabbabbabaabbabbbabbabbbabbbaabbabbbbabbbbbaaaaabbaaaaabbabaababaaaabbaaabbbaaabaaabababaabaaaaabbbaaabbaabaaabbaabbabbbaabaabbbbabbbaabaaababaabbabaaaaaaaaaabbbbbaaaaabaaabaabbbaababaababaabbaababbbbababbbbaabbabbbbabaaaaaaabbbabbaabbabbbbbabababbabaabbaaabaaabbbaabaaaaaabbbbaaabaabbabbbbaabaabbababbababbabbabbbabbbabaaaaaabbaaaaabbabaabaaabbbbbaabaabbabbabbaabbaaaabbababbaabaaababaaabaaababaabaaabaaabbbabbbbabaaabbaababaabbababbababbaaabbbaaaabababbabababaabbabaabbbaabbbbbbbaabbabababbbbabaababbabababbbbbabbbbababaaabbabbbaabbbbbbaaaabbbbabbbabbbbbbaaaabaaaaaabbbaaaababbaaababbaaaabbbbbbbbaaababbbaaaaabababbbaaabababaabaaaabaaabaababbaabaaabaaaaaabbbababaaabbabababbaaababaabbbabbaabaabbaaaaaababaabbaabbbbbabbbbaabbaaaabbbbabbabbbabababbbaaabaaabababbaaaabaaabbaaaabaaaaaaabbababbaabaaabbbabaaababaaaabbaabaaaabaaabbbaaabaaabbaabbabbabbabaababaaaaaaaabaaaaabbbbbbbabbbaabbaabaaabbabaabaabbbbabaaaaaabbaaaaabbbbaabaaaaaabbabbabbaaaaaaababbabbbaaabaaaabababbbbaabaaaabaaaaabbababaaaaaabbaaaabbabaabaabababbbabaaababbababbaaaaabbabaaabbabbaaabbaabbbbabbaabaabaababbaababbaabaabaabbbbaaababaababbaaaabbaabaaabbaababaaaaabaaababaaababbbbbbbbbbabaaabbaaababbabbbaaaabbabbbbbaaaaabbabaaabaaaabaabbaababaaaaabbabaaaaabbbbabbbbabbaaaaaaaabaaaabaabbaababbaaaaaababbbaabbabbaaabbaabbaaabbbabbaaaabbababaaaabbbbaabbaabbbbaabaaaaaababbaaababbababbbababaabbbbbbbbbbbaabaabaababbaaaabbbababababbaaaabbabaaaabbbbbababbabbbabaababbabbbbbbbbabbbaaababbbaabbbabbabaaaabbaabbbabbaabaabababaababbbbbaaaaaabaaababbabbbbababababbaaaaaabaaabaabbabaabababaaabbbabbbaaaaaaaaabaaabbaabaabbaaabbababbabaababbbbbabbabaaababbbbbabababababbbabbbaaabbbaabaabababbabbaaabbaaaaaaaababbbabbbbbabbaaabababaabbaaabaabbbbbbbaababaabbbaaaaabbaaabbbabbababbbbbaabbabaaabaaabbabbababbbaaaaabbabbbaabaaababbbaaaaabbbabbbaabbabbbaaaaabbaabbaabaaaaaabaabbbbaababbbbaababbbabababbbaabaabbbbabbbbabababbbabbbbabbaabaaabaaaabbbbababbaaaaabaaaaababbabbbabababaaabbabaabaababaabababbabbbbabaabaabbababbbaaabaabbaababababbbbabaaabbabaababbababababbaaababababbabaaaabbbababbabbaabbaaabbaaababaabbababbaabbbbaaabbbbaabaabbbaabaaabaabbabbbabbaaabaaabababbabbaabbbbbababaaaabbaababbaabaababbbbabbabbababbbabbaabababbabbaaababaaabaaaaabaaaaababbbbabaaaaabbbabaabbbbabbabaaababaaababaaaaaabaabbbaabbbaabaaaabbaabbaabbabaabaababbbababbbabaaabbbbabbaaaabbabaababaaaaabbbaabaaaaabbbbaaaaababbbbabbbbabbaaaaaabbbbaabbbbaabbbbaabbbbabbbabaaaaabbaababbbbabbababbaaabbbbabababaaaaabbaaabbabaababbabbabbbabbbbbaabbaaabaaabbabbaabbbbabbbbaabbbababbbbbababbbaababbbaaabbbbbababababaaabbabbabababbaaabbabbabbbbaaaaabaabbabaaaaabaabaaabbbaaaaaabaaaabbaaaabaaaaabbaaaaabaaabaaaababbabbababaabbbbbababbbabaaaaaabbbabbabbabaabaaaaaabbbabababbbabbbbabaabbabbabaaaabaaabbabbaaababaaababaabaaaaabbbababbbababaabaabaaaabbbbaaaaabbbbbaabaabbaaaababbbaabaaaababaaababababbbaaaabbabbbbbbbbabbbabababbbbbaaabbbabaaaabababaaabbaabbaaabbbbaaaaabbaabaababaaaabbabababbbbaaaababbabbbaaaaaaabaaaaabaaaababaaaababababbabbbbaaaabaaaaabababaabbbabbaababbbaababaaababbaaaabbabbaaabaaaaaaabbbbbabbaaababbaaaabbbabaaaaaaababaaabaabaabaaaababbaaaabbbbbbaaababbbbbbbaaaabbbabaababbaababababbbbaabaaababbabbaabbbabbbbbbbbaabbbabbbbbababaababbababbbaababbbbabbbbbbbaabbaaaabbabbababbabbbababbbabbabaabbbbabbabbaaabaaaaaabbbbbbababaaaabaaaabababaabbbaaaabaaabbabaaaabababababbbbbbbbaabbaaabbabaabbaaabbaaaaaabaaaaabaaaabaababababaabbbaababbbbbaaabbbbabbabbbbaabbaaabbbabaaabaaaabbbabababaababaaaabbbabbabaababbaabbaaabbabaaaaababaaaabaaaabaaababbbbbbababbbabaaababaaaababababbabbbaaaaabbbbabbbabbbabaaabbbaabaabaaabbabbbaaaababbaaaabbabbbaababaabaabaabbbbbbaababbaabaaabaaaabaabbbaabbabaaaaaaabbaaaabbabbaabbbbbbabaaaababbbababbbbbbabbaaabbaaababaaaababbbbabababbbababaaabaaaabaabbbbabbabaaaabbbaaabaabbbaaaabaaaaaababbbbbaababbbbbabbbaababaaaabaaabbaabbbabababaaabbababaaabababbbaaaabbaaaaababbbaabaaaabbaaaaabbaaaaabbabaaaabbbaaabaabbbbaaaababaabbbababbabaabbbbaaaaabaababaababaabbbaabbbbaaaabaabaabbabaabaaaaabbaaabbbbbabaabbababaabababaababbbababaababaaabababaabaaabaabbbabbaaaabbaabbaabbaaabbabbbaabababaabbbbaabaaaaaaabbaabbabbbaaabbbbabaabbbbbaababbbbbabbbbabbbbaabaaaaaaabaabbbbbbbaaaababaaabbbbbabaabbaaaaaaabaabbaabbabbbababbabbabbbaaaababbbaabbbabbbbbabaaaaabbabbaaaaabbaaabaababaababababbbaaababbabaaaaabbbbababaabaaaaabbabaabaababaabbbbbbabbaababaaabbbababbaabaaaaaaaabbababbbabaabbababbabbababbaabbaabbabbaabbbbababbbabababaaabaaaaaabbaabaaabaabbaaaaaababaabaabbbaaaabaabaabababaabaaababaabaababaaabbbbbaabaababaaaaabbaaabbaaabbaaababbaaabbabbbbabaababbbbbabbbbbbababbbbaaaabaabbbababbbababbbbbaaabaabbabbaaabaaaababbababaaaaaaababbaaabbbaabbbaabbbbbababaabbbbbaaaababaaaabbaaaaabbbababbaaaaabaaaaabbbbbababbbbbbbbabaabbabbababaabbbaababbbbbbaabbaaaabbbbaaaaabaabbabaabaaaaabbbbabbabbaabbabbaaabbababbabaaabbbababbbaaababbaaaabbbbbabbbbbaabaaaaaaaabbabababbaaabbaabaabbaaaaaabbbbbabababbbbaababbabbbbbbabaaaaaaabbbbbabbbaaabababababaaabbbaabaaabbbaabbbbabaabaabbaaaabbaababbababababbabaabaaabbbbbbabbaaaababbbbbbaaaabaaaaaaabbbaaaaaaabaabababababaaaaaaaaabbaabbaabbbbbabbababbbaabbbaaabaaabababababbbbbaaaabbaabaabaabbabaaaabaabbbbbaaabbbababaabbabbababaaaababbbaabbaaaabbabbbaaabbbaabbbababbaaababbaaabaabbabaabaaabbbbbbaaaaaabbbbabbbabbbaabbabbbabbbabbabbaaabbaaaaabbaabaaabbbaabbbabaabbbbabbbababbbababbaababbabbbbabbabaabbaaababaaabaaaaabbbaababbabbbabaabababbaababbbbaaaaababbabbabbbbbbaaabbaaababbabbaaabbbbabbbabbbbaabbbababaabbaababbabaaababaabbbbbbbbaaaaaaabbbabbaaaaaabbbaaabbababaabbabbbaabbbbaabbaabaabaaaaaabaaaaaabaabaabbbbabaababababbbbbbabaabababababbabbbaaaabababbaabbabaababbbbabaababbaaabbabbbbaaabbabbbabbbabbbbababbaabbbaaaaabbbaabababababaaabababaaaabaaaabbbbbabbbaaababbbabaaabbbaabbbbbbaaababbbbaaaabaabbaaaababaabbabbbababbbbabaababbabbbaaaabbbbaaaaaabaaabaaababbbaaaababbbaaaabbbaaabbaabbabbbbbbbbabaababbaaaaababaaabbaaabababbaabbaaabbabbaaabbbaaaabbbbbbabbbbbaabababbbbaaababbababaabaababbaaabaabbbbaabbbbbaaabbbbbaababbaaabbabaaabbbaaabbbababbabbbbbabaabbabbaaababaaabababbbabababbbaaababbaaabaabbbbabbbbabaabbaabaaabbabaaaabbbbbabbabbbbabaaabbbaabbbbbbababbabbbbaaaababbbabababaabbbbbabbaaabaaabababbbaabbbbbabbaaaaaabaabbaaaabbbaabbababaabbbbbbaabbbbababbbaabbaabbaaaabbabbbabaaaabbaaabaaaababbbbbbaaabbbaabaaaabbabaaabbbaababbbbaaaabbabababbbaabbabbaababbabbaaababababbbbaaabbbabababaababbbaaabaabbbaaaababbbaaaabbabbbbbabbaaabbbaabababbbbababbbbabbaaaababbaaaabaabaabbbbbabababaaababbaaabbaabbbabbaaaabbbbaabababaaaababaaabbbbbbababbaaaaabbbbbbbbaabbbaababbbbaaaababbbaabbbbabaabaabbaaaabbbabaabaabbaaabaabaabbaabbbbbababbbabaaabaaababababaaaabbbbaabbabbaaabbabbaabbbaaaababbbaabbbaaaabbabbbaaabbbabbbabaabaababaaababbbbbabbbaabbbbabbaaaaaabbbabbabaabbababbaabbbaabaaababbbbabbbaabbbabbbbbaabbabbbbbabaabbaaaabbaaabbababbabbaaababbabbabbabbbbaaaaaabababbbbaaaaaababababaaaabaabaaabbbaaaabbabababbabaaabbaaabbbbabbabbaaabababbbaaaaaaababbbaabaaaaaaabbaaabababbaaabbbbaaaabbbaaaababaaabbbaabaabbabaabaabaaaabbbbaabaabababbabbbbbabaabaaaaababbabbbabbbaaabbababbabababbababbababbababbbabbabbaaababbaaaaabbbbbbabbbbaabbabaababbbababaabbbaaaabbbaababaaaaababbabbaabbabaaababbbaaabbaaaabbbabababababbbbabbaaaabababaaababaabaaaaababbbaaabaaaabaaabbbababaaabaabbbaaababbbbabbaaabbababbbbbababaaaabaaabaabaaaaabbabbbbababbabbabaaabababaabbaabababbabbababaaabbabaaaaaaaaaabaaaaabbbabaaaaaaaaaabaaabbbbabaabbbbbbababaabbbaabbabababbbbbabaabaabaabaabbbbbababababaabbaaabaababaababababbbababaabbbbbbbbbbbaabbbbaaabbaababaaaaaaaabaaabaabbababbabbbabbbbbbbaabbbaaaaaaaaabbabbabaababaabbababbbababaabaabbaaababbbabbbbaabaabbbaaabbbabbbbaaabbaaabbbababbbbbbbaaabbababaaabbabbaabbaaababbbbaaabbabababbbabbaabbababaabaaababbabbabaaaabbbaababbababbabbbaabbbababbbaaabbbbbabbaababbabaaaaabbabababababababbaabbaabbbabaaaaaababaaaabbabaabbbababbbabbbaaaabaabababbbbaaabbabbbabbaaabbbababbaaaabbbbaabbbbaaababaabbbbaabbbbbbaabaaababbaaabbbbbabbabbbbbaaabbbbaaaaaabaaabbaababaababbabbbbabbaaabbbaabaabaabaabbaaabbaaaabaaaabbabaabbbaababbabbabbbbbbbaababaabaabaaaaaaabaaaaababaaabbbbabbaaabbbabbabababbbbabbbaabbababbaabbbbbaabbaaabaabaaaabaaaaaaabaabbaabbabaabaaaaababbaaabbbbaaabbaabbbabababbbbabaaaabbabaaaaaaaaabaabbabaabbabbbbbbbbbbabababbbaabaabaaabbabbabbabaabbaababaaaaabababbbbbaaaabbbaaabbabbaaababbaababbaababbbaaabababaaaaaaaaabaaabbbbabaababbbbbaaaaaaabbabbbbabbaababbbbbbabaaaaabaaaababbbbabbabbbabbbabaaaaaabbababaabaabbabbaaaaaaabbbaabbababbababababbbbbaaaaaaabbabaabaaabaaaaaababaaaabbbabaaaaabbaaaabaabbbbbaaaabababababbaabbbbbabbabbabbbbabaabbbaabbbbabbabaabbbbbbaabbbabbbbaaaaaababbbbababbbaaabaabbbaaaabbbbaaabbabbaabbaaaaabaabbabaabbbbbaaaaaabaaaaabbbaaabaaababaabbbbaabbababbababbbbbaaaaaaaabababbaabbabbbbbbbababaabbabbababbbaababbbabababbbaaaaabbbbaaaaabbbabababaaaabbaaabbbbaaaabaabaaabbabaabbbbaababbaababbaabbbaabbababaabbbbabaabaaabaaaabaabbbabbaabbbabbbbbbabaaaabaabaaabaabbbaaabbbbabbbbabbbaabaaaaaabaaabaababbabbabbbbbaaabbbbaabaaaaabaabbaabbababbbbaabbbbabbabbbbbbbabbbaaaaaabbaaaabbaababbaabaabbaaaabbabbabaabbaabaabbbbbbbaaabbababbaababababbabbbbbbbbaaaaaaabbbbababbabaaabaaaaaaabababbbbaabaaaabbbbabbabaabbbabaabbbaabbbaababbabbbabbbbbbbbaababbbbaaaababbaaabbaaaaabbbbbbbaaabaabbbbaabbbaabbbabbbaabbbaaabbbbaababbbabbbaabbaabbbbbabaaababaaaabbbababaababaabaaaaabaabababbbabaababaababbbbaabaabaabbbbbbbaabbbbbaabbabbababbbbababaababbaabbbaaababaaaabaababbabbbabbbaabaaaaabaababbbaabbbabbbbaaaababaabbabaabaaaaabbbaaabababaabababbbaabbbabbabbbbbbbbaababaabaaaabbabbbbbbaaaaaabbaaabaaabababbbabaaaabbaabbabbbbbbaaaaabbbabaaaaaaabbbbabbbbabababaaabbbbbbbbaaaaabbbaaabbababaabbbbaabbaaaabbbbaaaababbbababbbbbbbaababbabbbabaabbaaabbaaababbaaababbbaaabaaabababbabaaaabaaaabbbaabbbbabbbaabaabbaababaabbbbbaabbbbaabbabaaabbbbbbaaabbbaaabababaaaaababaabbbbbbabbbababbaabbaabaababbaaabbabbabbbaaabbbaaababbaabbbabaabaaabaaabaabbbbbbabaabbabbaaabbbbaaaababbbbabaaabbabbbabaabaababbbaaababaaabbabbbbabbbbaabbabaabaaababaabbbbababaabbabbabbbabaaabbaaabaabaabbbbaabbbbabbabaababbabbbabbbabbababaabaabaababbabbbbaaabaabaaaaaabbbbbbaabaaabaabbbabbbbbabbaaabaabbbabbbbabaaaaaababaabaabaabbbaabbbaaaabbabaabbaababbbbbbbbabaabaaabbbbababbbbabaabbbbababbababbabbabbbbababababaabbabaababaabaabbbbaaabaababbaaaabaaaabbaaabababbbbaaaaababababaabaaaabbaaaabaababaabababababababbaaabaabbaabbbbaabaabbbababbbbbbaaababbbbbbabbbbbaabbbaaabbbbbabbabbaababbbbaaabaabbbaabbababaababbaaaababaaabaababbbaaababbaabaabaaabbbaaaabbbaabaaaabbaaabababbaabbbbaaabbbbbabaaababaaaabbabaababbaababaaababaaaaaabaabaaaababbabbbbbbaaabbaaaabbabaabbabaabbabbbbaababbbbbabaaaabbbbaaabbbbaaabbbabbabbabaaaababaaababbaabbbbbbabbaaaaaabbabababbbabbabbabbaaabbbbabaabbaaabaaaaaaabbabbaabbbbbabaaaaaabaabbbabaabaaabbaaaabababaabbbaabbbbbbbbbabbbaaaabbbaabbabbbbbbbbbbaaabbbaaaaaabbabbaaaabbbaabbbbbbaabbbababbbaaabababaaaabbbaaabaabbbabbbbaabaaabaabbababbaaabbbabaaabbabbabbaaaababbbaababbbabbaaaaabaaaaaaaabbbaaabbbbbbbaaabbbbbabaaabababaababaabaaababaababbaaabaabaabaababbaaababbaaaaabbbbbaabbbbababbabbbabababbaabbbbbaaaabbaababaaabbaabbbaababbbabbbbaabababbbbabbaaabababbbbbbabaaaaabbaaaaaaabbabbabbaaababbaaabababbbbbaaaaabbbaabbbbbbbbbbbbbbaaaabbbabbbbaaabbabaaababaaaaabbbbababbabbbabbabaaababbaaaaaaabbaaabbabaaababaaabbbbababbaabbabaaaaabbbaaaaaabbaabbabbaaababbabbaaabbabaabbbbaaabbbbaabaaabbabbbabbbbbabbaabaaababbabbaaabbbbaaaababbababbbbababbbabbaabaabaababbbbbbabbaaaabbbaaaaabbabaababbaaaabbbaaabbbaaababbbbaaabbaabbabbaabaaabbaaaabaaabbbbaabbaaaaaababbbabababbbbabbabbbbaaabbaabaabaaabaabbbaabababbbbaaabbaaaabbbbababbbaaabbabbabbaaabbabaabaabaabbbbbabbabbbaabaaabbbbababbaabbaaaabbabbaabbbbabbbabbbaababbbaabbaababababaaaaabbabaaaabbbbaaabbabbbaababaaaabbabababbbabbbbaabbaaaaabaaaabaaabaabababbaaababaabbbbbbbabbaabaaabaabaabbabaabababbababbbbbbababaaaabbababbbbaaababbabaaabbaaababbbbbaabbbbbbabaaabbabaabaaaababaaaaabababbabbabaaabaabaabaabbababbbbbabbbababbabbbbbbbabbaabbbbbbbabbbbbbbbbbbbbbbbbbaabababbbaabbaabaaabbabbabbabbbabbbabbaaabbbaaabbaaaaabbbaababaaaaabbabaababbbbbbbaababbaabbaaabbabbabbaaaababaabaaabbbabbabbaabbaababbbbbaaababbaabbaaabbababbabaaaababaabbabbbabababbbabbbabbbbaabbbaabbbaabababbaaababbaababaababbaaaaaabababbbbaaabaaaabbaaababaaababaabbbaaabbbabaababbabaabababaabababaaabaabbababbabaababaababaabbaabbbbaabbababbabababaaaaababababaabbbbabaaaaabaaabaabababbabaabbbaabaabbbabbabbaaababbbbaababbbababbbbbabbbabbaabbabababbbbbabbababaaaabaababbbaaabbababaaaaababbbaabbaabaaabaabbbabbababbabbbbbabbbaabababbbaabaabaaabababaabbbabbaababbaaabbaaaababbbabaaaababababaaaaaaaabaaaaabaabababbaabaabaabaabbababbbabbbabaaaabbababaaabbaaaaababababababbbbbbaabbbbbabbbababaabaababbbaabbabbbbaaababbabbbbbbabbbabbaaaabababbbaababbbbabbbbbaabababbababbbbbabaabbbbbbbaaabaaaababbabaaaaabaabbababababbbbbbaaaaababbabbabbbaabaabbaaaabbbbaaabbbbbaabbaaabbbbbbbaababaaaabaabbaaabbbababbbbababbaabbabbbabbbbbbabaabaaabaababbaabbbaaabbbbbbbabbbabbbbabababbaaaabbbbbababbabababbbbbbaabbababbababaaababaaaababaaaabaaabbbabaaababbbabaabbababbbbbbbbbbbbbbbaaabbbabaabbaaabaaabababbbbbbabbaaabaabbabbbababbaabbabbabbbabbaabbbbbbbbbaaaaaaabbabaaabaabaabbaaabbbabaaabbabaaaaaabbaababbaaaabbabaabbbbaababaababbbbbaababaaabababbabbabaaaaabaaaaaabbabababbaababbbababaabbabbbbabbbbababbbbabbbbbbbabaaaaabbabbaaabbaabaaababbbaabaaaaaabbaabbababbaababaabbbaabbaaababbabaabbbbaaaabbbabbaabaaabaaaaababaaabbbbbabbbbbbabaaabaababaaabaabbaaaaabaaabbbababaaaaababbbbaabbbaabbbabaaababbababbaababaabbabaabbabbaaabaaabbaababaabaabbaaaabbbabbababbbbaabaababbabaaabbabbbbbbabaaaabbaabbbabaaababaabbabbbbbbbbbbaabbbabaaabbbbbbaaabbbbbbababababbaaaabbbbbbabbbababbbbabbbababaaabbaaaababbbbabbbabbaaabbbabbbbbabbabbaabbaaaaaabbaabaaaaababbaaaabbbbbbaabaababbbabaabbbbaababaaabaababbbbbbbababbabaaabbaabbbbaababaaaabaabbbaabbbababbaaabbbaaabbabaabbabbabbbbbaaabbaaaabbbbabbbbabbabbbaabbabababaabbabbbbbbababbbabbbbbabaabbaabaabbaaabbaabbabaaaaabbbabbabaaabbabbaaaababababaaaaaabbbbbbbbaababbabbabbbbaababaaabbabbabaabbbbbababaabbbabbbbaabaabaaababbaabbabaaabaaaaaabaabbabaabaaabaabbabbaabbaabbbabbbaaababbabbaaababababaabbbabbaabbaabbababbaaaabbaabbaaaabaaabbababaaaabbbbbaaabbbaaaabbaabaaaababaaaaaabaaaababbaaabbbbababbaaaabbaabaaaabbabbabaaababbababaaabaaaabbbabbaababbabbaaaabbaaaababbbaababbaabbabbaabaaabbaaabbabbbbabaaabbbbbbaaabbbaaababbaaaabaabbaaababbbaabbaaabbaaabaaabaababbbbaaababbababbbababbabababaabbabbabaabbbbbbabbbababbbabaabbbaaabaaaabbbbbbbabbbbbabaaaabaaaabbbbaabbaaaabbbabbabaabbbaaabbaabaaabbabaababbbbbabbaaaaabbabaabbbaababbabaabbbbbbbbbbaababbbbabbababbbababbbbaabbabaabaabbbbbbabbbbabaabababaaabbabbbabbbbbaabbbbbabbbabbaaabbababbababbaabbbaaababbababbbabaababbabbaaaabaaabaabaabaaabbbabaaaabbbaaaaabababbababaababbaaaabaaaababbabaabaaabaaababbabbbbbaaaabaaaaaabbababababbbbbbbbbbabaaaaabaabababaabaababaaaaabbabbbaaabbbabaabbabaaabbbabaaabbbbabbabbabbaabbbbabbbbababbabaabbbaaaababbbaaabbabbbbbaababbbbbaaaaaababbbbbaababaaabaaaababaaabbabaabbbbbbabbbabaaabbbabbbaabbaaabaaabbbaabbbbbaababbbbababbaaaabbbbbbbbaabbaaababaaabaababaabaabaaaabbabbaabaabbbbbabaaabbbaabbbbababaaabbababbaabbbbbaabaaaabbbbaaaabbabbbbababbabbbbabaabbbbababaabaabbababbbbabbaaabbbbababbbaabbabaabbaabaababbbabbaabbbbabbaaaaabababbaaaaabbbababbbaabaaaaababaabaaaaabbabbaaaabbabbbbababaabbbabaabbbaabbbaaababbbabaabaaabbbaaaabbaabaabbabbaabaaaaaabbbbababaaaaaabbabbaabababbbabbabbababaabbababbbaaaaaaaaaabbbaabaabbabbababbaabbaabaaaabaaaaaaaaaabbbaabbababbabbabbbbbbbaabaaaababaaabbaaabaababaaabbbbbbabbababaabaababaaaabbbaaaaaaabaabbaabbbbabaaaabaabbbaabaaaabaabbaaabababaaaabababbabbaaaaabbbbabbbabaaabaabaaaabbababaaaabbabbbabbabaabbababbaaabaaabbaaabbabaabbbababbbbaababbbbaabababaabbaaabbbaaabaabbaababaaaaabbbbababaabbabababbbaababaabababaabbbababaababbbbabbbabaabbaaaaaaaabaaaabbbbbababaabaaaabbbbbabbabbbaababbababaaabaaaaabbbabbbaaaabbbabbbababbbbabaabbbabaabaaaaabbaaaaabaaabaabbabbbbbabbbabbbbbaababaabaabbaabbbbbaaababaaabababbabaabbaabaabbaabbaabaabbbbabbbabaabbababaabbbbbbaaabbbabbabbabaabaaaaaaaaaaaabbaaabbbababbaaaaabbbaaaaabbbaaababbbaabbabbaababbbabaabaabbaaabbaabbabaaaabbbbaaaabbaabbbabbaabbaaaabbbbabaabbbaaabbaaaaaabbabaabbabbabbbbaabbaaababbbbbbababbbabaabbabbaaabbbabbabbaabbbaabbabaababbaabbabbabbabaaaabbbaaabaaaaaaaabbbbababbababbbababbbabbaabbabbabbbbaaabbbaabbbabbaaaababbbbbbaababbbbbabbbbababbbabbbbababbbabbabbababbbbabbabaaaabbbabbbabaaabbbaaaabaabbaaaabaababaababaabaabbbbbaaabbabbaaabbaababaaaabbbbbbbbaaabbabbbaaabbabaaababbaaaabbaaababbbbabbaababbaaabbbbbaababbbbbbbbaabbbbbaabbbaabbbaabbbbabbabbbbbbbbaabbabaaaabaabaabbbbabbbaaabaaababbbaaaaabbaabbaaababbbbaabaaabbaababbbaabbbabbbaaaaabbabaaababbbababbababbaababbabbaaababbbbbaaabbabaaabbbaaabbaababaaaaaaabbbbbbabbabbaabaaabbbbabbbaaaaababbbbbaaababababaaababaabaaabbaabababaabbbaabbbababbaabbaabbaaabbaabaaabbbbbbaababaaaaabbaabbbababababababababbababaabbaabaabaaaaabbaabaabaaabbaaaabaaabaaaabbbbabbbaabbbabbbaabaabaaabbbbbbabaaabbbbbaabbaaabababbbaaabaabbbaaaabbbaabaaabbaaabbababbbabbabaabbabaaaaaabbabbbbbababaabaaaabaaabbabaababbaaabbaabbbbbbababbbbabbaaabaaaaababbbabbbbabaaabbababaabaaabbaaababbabbbaabbbaabbbaabaaaaaabaabaabbabababbaaaabbabababbbbbabaaabababbaaaaabbbbaabaaaaaabbbbbaaabbbbabbabaabbaaabaabbabbbbaaabaaabaaaaabbbaaabaaababaaabbabbaabaaababaaaaababaaaaabaaaabbabaaaaabbababaabaaaabbbbbabaaabbbbbaaabaabaabbabaabbababbbaaabbbaaababbaaaababaabaababaaabbaaabbaaaaaaabababbabbbabbbbabaababaababbaabbababaababbbababbaabbabaaaabbbbabbbabbabbaaababaababbbaabababbaaaababbaaabaabaaababababbabbabbbabbbbbbbbbbbabbbabbbababaaabbaaabaabaabbaaabbaaaaabaaaaaaabaabbaabbaaabbaababbabababbaaaabbabbababbbbaabbabbbabbbabaaaabbbbabbaaaabbbbaabababaaabbaabbaabbbabbbaaaaaabbaaabbaaaababaaababbbaabbbbbbbbaababbbaaabbbbaaabbbaaababbbbabaaabaabababbabaababbabaaababbaaabbbbbbbaabaaaaaabbbbaaabaaabbaaaabaaaababababaaaabbabaaaababbaaabbababaaaabaabaaaaaababbbabbaaababbbaaaaabbaaabbbbbabaababaabbaaabaaabbbbaaaababaaaaaaabbbbaabbababbbbabbbbaababbaababbbaaababaaaabbabbaaabbaababbabaabbababbababbaababbbbbabbbbbabbabbbbaabbabbbbbbbaaabaabbbbaaabbaaabbaabbbbabbabaaabbabbbaabaaabaaaaaabababaababaabaabababbbbaababaabbbbabaabbaaabbbaaabaaaaaabbbbaabaabaaaaaaabbbababbaabaabaaabbababbbbbaabbbababbaaababaaaaababbbabbbaabbbbbaaabbbbbbabbaabbbbaabaabaaaaabbbbbabbbbaaaabbbbbaababaabaaabbabbbabaaabbabbbaabaaabbbbabbbaabbbabbbaaabaaabbbbbaababaababbbbbbbbaaabaaaaabbaaababababbaaaabbbbbbbbaaaaaabbbabbabbaabaaaaabaaabbabbbabbbabaaaabaabbbabbbbababaaaabaaabbbbbbbabbbbbaaabaababababaababbaabbbbbbaaabaababaaaabaabaabbabbabaaaaaabbaababaabbababbabbababaaaaabaabbabaaaabbbbbabbabbbbbbbabbaaaabbabaaaabbaaaabbabbbaaaabbabababbaaaaabaabbababbbbababbabababbbbaaaabbaaabaabbbbbabbbbbabbbaaababaaabbbbaaabaaabbbabbaaaaaabaababbaabbaaaaabbbbaaaababbabaabbbaaaaaabaabababbbababbabbbabbabbabaabbaabbaaababaababaabaabbaabbbaaaaaabbabbaaababaabbabbaabbabbabaaaabaaaabaabbbbabbaaabaabbbabaaabbbabbbbbabbbaabbabaaabaababbbbbbbaabaababaaabbaabaabbbbabbabbaabaaababbbababaabbbbbaaaaabaaaabbaabaaaabaaabbbbabbbabaaabbaaababbaaabbbbbbbababbaabbbabbaabbbbabaabbabaabaaaabbbaababaaababbabbbababaabaaaaaabaabaaabbbbabbababababbbababaaaaabababbbbbabbbaabaaabbbbaaaabaaaaaababbbbabbababababaaabaaabbaaabbbbaabbbaaaababaaabbabbabbbaabaaaababbbabbaabbbabaabbbbabbbabbaaaabababababbaabaaabbbbaabbabaaaababbaaabaabbbbbbbaabaaaaabbababaabaabbbaabaabbabbaaaabbabbabababbaabbbababbaabbbbbbabbbbbaaaabbbaabbbbaaaaaabaaaabbaabbaaabbabbbaabaabaaabbbaaaaaaaaaababbbabbabbabbbaaabbbabababbabaaaababbaababaaabaaaaaabaababbbbaaababaabbaabbbbbbaabbbaaaabbbabbabbbbbaaaaaabababaababababbbbbaabaabbabbbbabaabbbababbbaabaababbaaabbbababbaaabaabbaaabbaaababbabbbababbbabababaaaaaabbbbbabbabbbabbbabbaabbabaaaaabaaabaaababaabbbabaaaabaababbbabbaababbabbbbabbabababbabbabaabbbabbabbbbaaababbabaaababaabaabaabaabbbaabbaabaaabaababaabaaabbbbbbbaabbbbaaabaaababbabaabaabbaaaabbbbabbaaaabaaabbaaababaaaabbbabbbaaabbbabaababbbaaabbabaaabaabbbaabbaababaaaabbbabaababbaabbaabbabbaabbaabbabaababbbabbbabaabaaababbaaabbbbbabaabbabaabbaababbabbbbbabbbababbbabaaabbbaabbbbbbabbababbababbbbabbbbbaababababaabaaabbbaababbaaaabaaababbabbabbbbaabaabaaaaababbabaaabbbbbaaaabbabababaaaaabaabaaaaabababbaaabbbbbabaaabbabbaabbbbbbbabbababbaaababbabbaabbbbabbabbaabababbbaaabbbbabbbaabbaaaabaabbbbaabbbbbabaaababaabbbaaabbabababaaaabbbbbbaabbbaaaaababbbabbabaaabbaaaaaaaabbbababbbbbbaababbabbbbabaabaabaaabaaaaaaabaabbaabbbaababbaabaaabbababababbbababbabbbbaaabbababaaabbabaaaabbbababaaabababbabbaabaaabbaaaabbbbbaabaaaabbabbbabbabbaaaabababaabbbbbabbbbaabaaababbaabbbaabaababbbabaaabbbaaabbbbababaabbbbbaababbbaaaabbaabbaaaaaabbaaaabbbbabbbbbaababbbabbbabbaabbbaaabbbabbababbbabbaaaabaabaaabbbbbabbbbaaabaababbbbaaaabbaabbabbabaababbbbbbbaabbabaababbbaabbbababbbbaababbbbbabaaaaaaaabbbaaaaabababaabbbabbaabbbaabbbbabaabbbbabbabaaabaaabaaaababbbbbabbaabbbbaaabbabbabbababababbbbbbaabbbbbaaaaaaababbbaaaabaaababbbbaabbbbbbbaaaabbaaabbbabbaabaaaaaaaaabababababaaaaaaabbaaaabaaaaabaabbaababbabbbbaababaaaaabbabaabbbbaabbbbbabbbaabababbaabbaaaabbabbabbaabaabaabbabbabaaaaaabaaabbaaaabaabbabbabaabaaababbabbbababbabaaababbabaabbbbabbbaabbaaabaabbbbaaabbababaabbabaaaaabaaaaaaabbbabbababbbaabbbbabbbbabbbaaabbabaaabbabaabaaaaaaababbbabbbaabaaaaabbbabbbbaabaaaaaabbbaaaaabaabbaabababbabbaaaaaaaabaababbbaabaaabbaabbaabbabbbabaaabbaaaababbbbbabababababababbaabaaabaabaaaabbaaabaabaabbaaabbabaababbaabaabaaaaaababbaaaaabbabbbabbababaaabaabaabaababbabbabaaaabbbababbbaabbbbaabbabbababaaabbbabaabbbbaabbbbbbabbbbbabaaabaaabbbbbaabaabbaabaabbbbababbaaaabaabaaaaabbbaabbbbbaaababbbbaaaaaabbbabaabaabbabbbaaabbbabbabaaaabbbabbbaabbbabbaaaaabaabbaabaabbabaabababbabaabaaaaaaaabbabaabbbaabababaaaabaaaabbbbbabbabaabaaabbbaabaaaabbaabbaaabbbaaaabaaabaaabbbaaaababbababbabbbababababbbbabbaabbabbabaabaaabbbbbbbbbabaaabbabababaabbbbbaaabaabbbaaabbababaaaaabbbbabbabaaaabbaaaaaaabbbbaabaabbbaabaabababbaababbaaabbbbaabaababbabbabbabababaaaabaaaaabbaabbabbbbabbaaaabaaababbabbabbbbbaabaaaabbabbbababaaabbbababaaaabaabaabbabaaabbbbbbabbabaaababbaabbbaababbaabbaababbbaabbaabbbaabaaaaaaaaabbaaaaaabbaaabaaaaababaabbabbbabbbbbaabbaaaabbabbaaabbababbbabaaaaaaaabaabbbaabbbaabbaaaabbbaabbaaaabbaaaabbbaaabababaaabababbbaaabbabaaaaabbababaaababbbabbbaaaaabbababaaabbbbabaaaabbaabbbbbabaaaaaabaaabbababababaaaaaabaabbaabbbaabaaaabababaababaaabbbbabbbbaaaabbbaaabaaaaaaabbababbabbbbabbbbbaaaaaabbabbbaababbbbbbaabbbaabaabaaabaabababbaaaaabaabbbbbabbbbabbaaaababaaaaabbbbabababaaabbaaabbaabaaaababbaaaabaabbbaaaababaaaababababbbabbbababbabaabbbbaaabbababaaaabaaaabaaaababbbaaaaabaabaaabbbababbaababbaabbbbabbbbabbbbabaabababaabbaabaabbabaaabaaabababbaabbabababbbaabaababababbaaaabbaabaaababbaababbbbabbabbbbaaaaabbbbbbbbaabbaabbbaaabaaabbabbbabaaabbaababbbabbaababbaabbbbbaaaaabaabababbbbbbaaababaaabaababbababbbbaaaaabbbaaabbaaabaaaabbbbaababbbaaaababbbaaabaababbabbbaaaababaaaaabaaaaabbabaaaababbabaaabbabbabaaababbababbbaaaabbabaaababbaabaabbaaabbabbbaaabbaababaaaabbbbbaabbbaabbbabbaabbaababaabbbababbbaabbbbbbbbabbbbbbabaaabbabbabbaaabbbaabaaaabbaaaabaababbabbaababbabbbaaabaabaababbbaaaaabbbabbbbbaabbbbabaababaaabbbabbbaababbabbbbbaabbbbbabaabaaabbbbbabbababbabbabbabaababbbaabbabbabbababbaabbabaaaaabbbbabbbababbaaaabbbbbbabaabbbbabaaabababbbbabbaaaaabbbaaaaabbbaabaabaaabbabbaabbabaabaaabababbaaaaaabbabbbabbabbabaaabaaaaaabbabbbbbabbaaabbabbbabbbbbaabbaaabbaaabbbbbaababbbbbbbabbaabaaabbbaaaaababbbabaaaabaaaabaabaabbbaabbabaabaaababbbbaaaaabababbbabbbbabbabaaabaaabbbbbaabbbbbbbaabbaabbbbaabaababaaaabbbbbbbababaaaabbabaaabbabaaabaaabaaabaabaabbbaaaaaabbbbbaaaaaabababbbbbabbaababbbaabbbbbabbbaabbbaaaabaabaaaaababababbbbaaaabaabbbaaababaababaabbbbbbaabbababbbbabababaababbabbaaabaaaabbabaaaaaaaaaaabbbaaabaaabaabaaabbaababaaababaaabbaabaabbbbbbbbbbaabbbabaaabbbaababaababbbabbaaaababaabaabaaaababbabaaaaaabbaabbabbbaababaabaabaaabaaabaaabbaaabbabbbbbbbabaabbabbbbabbbbbbbbabbbbabbabaabbbbbaaababaaaabababaaaaaaabaabbaaabaababbaabbbaaabbabbaabbaababbabbbaaabbaaabaababbbbbabaaaababaabbababaabaaaaaaaaaabbbbaaaabababbaabbbaababbaaabbbbbaaabbbabaaaaabbbbabbaaabaabbaaabbaaaabbbaaabbbbbaaaaaaaaaabababaaaaababaabbabbaaaababaabababaaabbbbbaaababaabababbaabaababbaaababaaaabbbabbaaaabbbabbaaabbbaabbaaababbbaabbbbabbbaaaababbaaabbbaabbababbbaabbaaabaaabaabbbbbaabbaabbbaabbbbbaaababbabaabbaabbabbaaaaaabbabbbbbbbaaabbababbabbabbbabaaaabbbbbaaaaabaabbaaabbbabbababbbbbababbaabbbaababbbbaaaabbbabbbabababaaaabbbbaabbbbaabbbaaaaaaaaabaaaaabbbbaabbaaaabbbaaabaabbbbabbabbbbbaabababbaaabaaaababbbaababbabaabbaabaabbbabbabaabbaaabbbbaabbabababababaabbaaabbbababbaabbbbbaaaababbaaaaaaaabaabababbbaaaaabbbbbabbbbaaaabaabbabbabbababbbabbbaabaabbbbabbaabaabbabababaaaababaabbabbbbbbabbbbbaaaaaaaaabbababbaaaabbbabaabaaabbbbbbbabbaabbbaaaabbbbbbabbaaaabaabbaabbaabaababaaababbabbbbbbbbabbaaabaabaabababbabbaabbaaaaabbbbabaaaababaabbabaabbbbbabbbbaabbaabbaaaaaabbabaabbaabbbaabbababaaaabbbbbabbbbbbaabbbaaaaababbaabbbbbaabaabaabbbbbbababaababababbaaaaabbaabaabbababbbbbbabbbabaaabbabbabbababaaaaaaabbababababbbbaaaaaabbabaabaaababbbbaaabaaaaaaabaababaaaabaabaaaaabbababababaaabbaaababbbabbbbaabaabbbbbaababaaabbaaaaaabbaabaaabaaabaabbbbabaaabbaabaabaaabaabbbbbbbaaabaaabbaaaababaababaabbaababbbbbbaaabbababbbbaaaaabaabaaabbabbbbabbbbaaabbbbabbbbaaaaaabbabbaabbbbaabbbbaaaaaabbbabbbbababbabbabbaaababbaaababbbaaabaaaababbaaaaaababababbbababaaabaabbaabbbbbababaaabbbabaabaaaaabbbbbbabbbaaaabbaabbaabababbaabbbabaaaaaababbbbbbaaaabbaabaabbababaaabaaababaabaabaabaabbabbbbbaaabaaabbbaabbbabaabaababaabbabbbbbabbaabbaaabaabaaababababbbbaaabbabbabbaabaaabbbbaabaabbbbabbbabababababbabbabbbbabbabbababaabaaaaaabbaaaabaaaaaababbaabbaaaaababbbaaabbabaaaabbaabbbabaabbabababaabbaaaaabaaababaaababaabbbabbbbaabaaababbbbabaaaababbabbbabbbbabaaabaaabbbabbaabaabaaaaaabaabaaabbbbabbbaabaabbbbaaabbbbbabaabbbaaabaaabbbbbbabbbabbaaaabaabbaaaababababababaaaabbbaaaabababaabbabbbaababbbbbbbaabbbababbbbbbbbababaaaaababaaaaabaaaabaabbabbabbbbaaaabababbbabaabbabaabaaaaaabbbbaabaaaaabbaaabababababaababbbbbaaaaabaaabbbaaaaabbaaaabbbaaabababbaaaabbaaaaaaababababbabbaabaaaaaabbbbabbbbaabbbbbaaaabaaabbabbabbbaabaaabaababbaaaaaabbaababbabbbaabbbaabbbaaaaababaabbabbaaaaabababbabbaabaabbaaababbabbbbabaabaabbabaaaababababaabaaababbbbbaaabbababaabbbaaaabbaaaaaaaabaabaaaabbabbaabaaaabbababaabbabaabbabbbabababbbaabbbbabbbabbaaaabbbaaababbabbbbaabaabababbbbbabaabaababbbaaaabbaabbbbbaababaababaabbbaaabaabbabbbabbbaabbaabbbbbbabbaaaaababaaaaaababbbbbaaaaaaaaabababaabbbabbabbbaabbabaababbabbabbbbaabbaababbaababbaabbbaaabbaabbbbbababbbabbabbaabbbbbbabbbbbbaabbaabbbbbbaaaababaababababaabaabaaabbabbbbbaabbbabababbbaabbbbaaaaaaaaaaabbbbbbbbbbbaaabaaaaaabbbbbbbaaaaabaaaaaabbabaababbabababbbbabbbbabbbaaaaaaabbbabbababbaabaababbbaaaabbbbaaaaababbabbbbbbbbabaaaabaaaabbabaaaaaabaaabbbbbbabbabbabbbabbabaaabbabbbbaabbaaabbaabbbbbabbbbbabaababbbaaabbabbbbaabaababbabbbabaabbabbababababbabaaaaabbaababaabbabaababaabaaabbbbababaabababbaabbababbbaaaabaaaaaaababbabaaaabaaaaababbbaaaabbababbbbbaaababbaaaabbbaabaaababbaaabbbababbaababbabaaabbaabaabbabbbbababbabbbababbabababbbbbbbaabaaababbabbabbaaaaabababbbbbbbbabbaaabbaabbabbbbbbaabbaaabaabbabbbaaaabaabaaaabaaaabaabbaabbbbaabbbbaabababbbbbabbbabbaabbabbbaaabbababaabaaaabaaaababbababbaabbabaababbbbabaabbbbbbaabaabababaabbababaaabbabbbbbbaaaaaabbbbbabbbabbbbbbabaaaabbaaaababababbabbaaaabbababbbabbabababaaaaabbbabbabbaaaaaabbbbabaababbabbbaaabbbbbbaaaababbaaabaabbaabaabaabbaabbababbbabbbaabbabaababbaaababaabaababaaaabbabaababaabbabaaaaabaaabaabaababbbbabbaaababaabbbaaaaaaaaabaaabbbbababaaaabbbbabbbbabbbabababababaabbbbbbabaaaabbabbbaaaabbabbbbbaababaaaaabaabbaabbbbbbbbaaabbbaababbbbbbabbababbbaabbbbbbabbbaabbabbbbabbbaaaabbbbbbabababbaabababbbbabaaabaabbbaaababababababbabbaabbaabbbbbbaabaabbaabbbaaabbbbbbbbaaababbaaabaabaabbababaaaababaabbaaababaaaaaaaababaaaabaababbabbabbbbaabaaaabababbbbaaaabaaababbbbbbbbaaabbaabbabbabababbbabbbbbabaabaaababaababaabbbbaaaaaaabaaaabbabbbbbaabbabbbbabbabbbbaabbbbbbaabaabbaababaaabbaaaabaabababbabbbabbaaaabbbabababaabaabbaababbbbaaabbababbaaabbbbbabbaaabababaabbaaabababbaaaaabaaabbabbababaabbaababbbbbaabbabbaabbaabbabaaaabaaaaaabbbbabbbbbbaaabaabbaabaabbbaabbbaabbabbababbbbaabbbaaabbaaaaababbabbbbbbbbaaaabbaababbaaaaaaaaaaaaaabbbbaabbbbbbaabbbabbbaabbbaabbbaaababbabbaaaabbbaabbaaabbabbaababbabaabbabbbabaaababaaaabbaaaabaaabaabbbaababbbaabaaababbbbaaabbaabbbbbaaabaabbaaaaabaaabbbbbbabbbaaabbbababaaabbbaaabbaaaabaabbaabababaababbaaabbbababbaaabababaabbbbabaaaaabbabbababbbbababaaaaababaabbbbbbabbabaaabbabbaaaababaaaababbaabbabbabbbabbababbaabbaaaabaabbbbabbbbabbabbababaaababaaababaaabbabaaabbbabbabbaaabbabaaababaaaababaabbbabbbbabbaabbbbbaabbbbaababbbbabaaabaaaaaabababbaaabbbaaabababababaaaabbaabbaababbabbaabbabbaababaabbaaabbaababbbaabbbaabaababaaaababaabaaabaabbbbaababbaaabbabaaabbbaabaaaaabaaaabaababbbababbabababaabbabbababaabaaaaabaaabaaabaabaababbabbbabbabababbabbbbabaabaabbaaabbbabababaabbbabbbbabbabaabbbaaabaaaaabbbbbbaabbbaabaabaaabaaaababababbaaaabaabababaaaaabbaabbbbabaabbaaaaabaababaaaabbabaaaaaaaaaaaabbaaabbbaabbaaaaabbaaabaaabbaaabbaabababbabbbaaaabbaaabbaabaaaaabbabababbbbbbbababbbababababaaabbaababaabbbbbaaaabbbababbbbaabaaaaaababaaaaaaaaaabbabbaabaababbabbbbababbabbbbbbabaababaaaaaaabbaaaaabbbbbaabbaaabbbaabaababbbabaaababababbbaaaaabababaabaaaaabbaaaababaabaabbababababbbabbababbbbaababaaaabaabababbaaaaabaaaaaabbbaabbbababbaabaaababaabbabaaabbaabbbaabababaaabbbaabbbbababbbabaabbaaaaabbaaababaaabbbabbaabbbabbbbaaabbbaababbabaaaaaaabbbaaaabaaaabbaaabbbabbabbababbaabaabbbbaaaaabbaaaaabaaaaaabbaaabbabbbaaabaabababbbbabbbbabababaababbaabbaabbbaabbabbbbaaaababaabaababbababaaabbbbbabbbabbbbabbaababbbabbbababbbbbabaaaabbaaabbabbaabbaabbaababbbbabaabbabbaabbbaababbabbbbabaababbabbbaaabaabbbbabababbaabbbbaabaababbaaaabbabbbaaaaabaabaaaaaabbbbbbbbbabbbaaabbabaabababbbabbbbbbbbbbaabbabaaaabaaaaaaabbaabbbbbabbbbbaababbbaabbaabbabaaabbbabaaabbaababaabaaababbbabbbbbabaaaabbbbaabbaaaaaabbaababbabaabaabbbbbaababaaababbbbbaabaaaaabaaaabbabaababbbbbababbbbaaababbaabbbaaababaabaaabbbbabaabbbabaabbaaaabbabbbababaabbaaaabbbababababbaabbaaabbaabbaaabbaaaaabbabbabbbaaabbaaabbaababbbbbabbaaabababbbbabaaababaabbabaabaabaaaaabbbbbaaaabaabbbbabaabbbbbaabaaabbbbababaabaaaabbbabbaabbaaabbaababbbbbaaabbbbbbabbabbabaabbbbbbababbbbabbbaaabaababbbbaabbbaababaabbaabbaaaabaabaaabaaabbaabbbaabaabababbbbabbbbaaaabababaabbbbbbbbaaaaaabbbbbbbbbbaaababbaaabaabaabaaaababaabbbbbbbaaaabababaaaababbabaabbaabbabbaaaabbabaaabbbbbaabbbbaabbbaaaaaabbbbabbabbbbabbaababaaaaababaaaaabaabbaaaaaaaabbbbabbbabbabbabbbabbbbaabbabababbabbabbabababbaaabbbabababbaabaabbbaabbaabbaabbaabaaabaaaaabaabbbbaabaaabbbababbbbaaabaaaaabbabbbbbaaaaaaaababaaaaabbabbaababbabbbabbaababbabbaabaaabbbabaaaaaabbbbbbbabbabbbbaababbbbbbbbbaabbbaaabaabbbbbbabbbaababbbbbaabbbabbbbbaabbabbbaaabababaababaaaabaaabbbbaabbaabbaabbababbaabaabbaabbaababaaabbabbababbaabababaaabaabaaabbaababaaaabbaaaabaabbabbbbbabbbbaabaaabaabbabbbabbbbaaabaababbaabbabbbbbabaabbbbabaabbabaaabbababaaabbabbaababbabbabbabaabababbbbbaabbaabbbbabaaaaaaabaabababbbabaaaaaabbabbbabbbbbaaabbbabaabbbbbaaabbaababbaaabbbababaabaabaabbabbababaabbbbaaaabbbbaabababababbabaabbabbaaabbabaaaaabbabbaabbabaabbabbaabbbaaaaababaabbbbbaabbbbaaababaabbbaabbabaabbbababaaaaaababaabbabbbaaaabaabbbababaabbababababbbaabbaabaaaaaaababaabaabbbabbbbbababbbaaababbaabbbbaabbaaaaababaabaabaababaaaaabbabbabaaababbbaabaaaabbbabbbaaabaabaabaaabbabaaaabbbabbaaaaaaababaaabaaabbbbaaababbbbbbbbababbbaaaaaabbbaaaaababaaabbbabababababaabbabbbaaabaabbaabbbabababbababbbabbaabbaaabbbbabbbbbbbbaabbaaabbbbabaaababaabaaaaaababbabbabbbababbaaaaabababaabbaaabaabbababbbbaaababaabababaabaababbbbabaaabbbbbabababbaaabbabababbbbababbaabbbababbabababbbbbbbaababaabbababbabbabbbbbabbbbaaaaabbabaaabbbababbaababbaabababbabbabababbaababaababaabbaaaabbbbbaababbbbbbbabaabbaaaabababbbaaabbaabbbbbabbabbaaababbbbbabaaabbababaabbbaaaabbbaaababbaaaaaaaabaabbbbbaabaabbbaabbaabbaabaaabbbaababaaaababbbbbaaabaabbbbbbabaabaaaababbbbbbaaabbbbaabbbbababbbbaababbbbabaaaababbbbabababbbaaaabaababbbaaabaaaaaabbaaababaabbbaaabbbabaabaaaababaaababbbaababbaaaaaabbabaabbaabaaaaabbabbbbabbbbbaabaaabababaabbaabbabbbabbababbbaaaababbaabbbbbbaabaaaaaaabbbaaaababaababaabaabbbbabbbaababaaabbbaaabbaabbaaaabbaabbabbabbabbbbbabaabaabbabbbbbbaaaaaabaababababbbbbbbabbbabbaaabaabbbbabbabbabbabbbbbbaaabaaabbaaaababaabbbbaaaababbaaaabaaabaabaaaaaabbaaabaaabbbaaabaaababbbaabbbbbaababbbbbbaabbbbbaababababbbbbbabaaaababbaaaaabaabbabaabbabbaaaabbaababbbabaaabaabaabaabaaabbabbbabbabbbabbaaababbbbbaaaabbaaaababaababbbbbbabbaaaabbabbaaaabbaaabbbbaaaabbbaababbabbababbbbababaababbbbaabbaabaaababbbbaaabaabbaabbbabbbabbbabbbbabbbaabbbaabbbababbaaabaabaaaabaaaabbaabbbaabbaabbababbbbabbbbbbabbbaabbbababbaabbbababbbbbaabaabbabbaaaaaaaaaaabbabbaabbbbbabbabaaaaabaabbaabbaababbbbabaaabaabbaaaaaaabaabababbababbaaaaaaabbaabbbbaaabaabaabaaaabbabbbbabbbaabbbabbabababbaabababaaaabbaabbbaabbbbaabaaaaababaaabaabbbbababbbbaaabaaaaaaaabbbababaabaaababbbbbabaabbaababbaaabaabbabaabaaabbbabaababaaabaaaaabaabaaaabbbbbaabaabbbbbababbbbbbbbbbabbbbaabaabbabbababbaabababbbbbabbbababbababbabaaaaabbbbbbababbbaabbabbaaaabbaaaaabbabaabbbababbaaaaaababbbaabbbbaaaaaaabbbaaabbaababbabababbababbbaaaaabbaaabbaabbabbabaaaabbabbabbabaaabaaabababbbaababbbbbaababbabaababaaaabaabbbbaaababababababababbabbabbababbbabbbbaabbbbaaababbaaabbbbaabaabaaabbabbababaaabababbabababbbbbaabaabbbabbbaabbbbbaaabbaaabaaaaaabbababaaabbabaaaabbbbaaaaaaaaabbbbababaabbbbaaabbbbbabababbababababbbababababbaaaabaaabaaaaabbbaabbabaababbbabbaaabbabbbbabbbbbbbaaabbbaaabbabaaaaaabbbbbbbbaabbaaabbabbbbaabbaaabaabbbaaaaabaaaabaaababbabbaaabaabbaaaabbbbababaabbbabaababbbabaaaaabbbababbbabbaabbbaaaaabaaabaaabbbbaabbbabbaaaababbabbbaabbabbaabbababbbaabaaababababaabbaaaababbbabaaabbbaabbbbbbbabbabbbaabbabaaaaabaaaabbabbaaaabbbaaabbbabbbaaaaabbbaaabaabbabbbabbbbbababbbbbaabaabbbabaaaaaabbbabaaabbbaabbbaaababababbabbaabaababbabbababbaaaabaabbbaaabaababaabbabbabaaabaaabbbaabbaaabaaaabbbbbaabbaabbaaaabaabbbaaaabbbbbbbabbaaaaabaaaaaaabbababbbbbababbbaabbababbaaaabbbababaaaabaaaabbabbaaababbaaabaabbbabaaaabbbabaabaabaaababbaabbaabaaaaababbababbaaaabbaabbabbaabbbbaababbbbbbababbbbababbbabbaaaababaaaabbabbaabbababbbaabaabbbabaabaaaabbabababaabbaaaabaababaababaaaaaaaaaaababbabbabbbaaababbbbabbbbababbabbaaaaaabaabbabababaabaabbbbabbbbbbbababababaabbbbaaaaababbaabbbbbaaaabaabaabbaaaaaabbbbabaabbbbaabaaaaabaabaabbbbaaaaababaababbbaaaaaaabbbbbabababaabbaaabbabbbaabaaaabaabbbbbbabaabbabbbabbbabababbbbaaabbbaabbaaabbbbaabbbbabbaaabbbabbaaaaababbaaaaabaabababbbbbbaaabbbababbbbababaaabaaaaabbbabbababbaabbbbbbaabbaabbbabababbbbabaabaaabbababababbbbbabaaabbbaabbaabbabbaaaabbbababaaaaabaabbbabaaaababababaaabbbbbaaaabbaaabbaaaabababbbaabbabaabbbbbbaaaaabbabbbabaaabbabbbbababaabbbaaaaabbabbbaababbababbabbaabaaabbbabbaababaabaabbbbabbbabbbabaabaababbaaabbbbaaabaaabbbaabaabaaabbaaabaaababbbaababbaaaabbabaaaaaabbabbbbbabbbbaabaababaabbbaabbbbabbaaaaaaabaaaaaababbabababbbaaabbbabbbbaaabbabbaabaabbbabbabbaabbabbaaababbaaabbaaaaabbaaaabbaabaaababaaaaaababbbabbbbabaabbbbaaabbbababbbbbaaaaaaaaaabbaabbbaabaabbaabbbbbabababbbbbaaaaabbbbabaabaabaaaabbbabbaabbabaabbaabbaaaaaabbaaabbbabbababbabbabaabbbbababaabaabbabaabbbaabbaaabbbabbabaaaaababbbbbbbabababbababbbaaabbabbbbaabbaaaabbbabbbbaaaaaabaaabaaabbaaaabaaaaababbabbbbaabaababababbaaaaabaabaabaabababbaaabaaabababaabbbaaabaabbabbaaababbbbaabaabaababbaaaabaabbabbaaabbabbbabaabbabaabbaababaaaabaabaababbbabaaaaaaabbababbbbbabbbababbabbabbabaaabaababaa
abbaabbaabbaabbbbbaabbabbbabababbaabbbabaabbbbbaababbabaabbbabbbbabbaabbbbbabbbaaaaababbaabbbbbabbaababbabbaaabaababaabbbbabbabbaabababbbabbbaababbaaabbaaaaaabbabbbbababaaaababaaabaababbbaaaaabaabababbbbbbabababbabbabbaabbbbaabaabaabababbbaabaaabbabbaabababbbbaaaababababbbaaababbbabaabaabbbbbbbababbabbaaaabbbaabbabbaabaabbaabbaabbabbaabbbbaababbbabbbbaaababaaababaaabababababbbabababaaaaababbbbbabababaabbbbaaaaabaabababbaaaabbbaabbaaabababaabbbabbbabbababaaaaababbbbbabaaaabbaaabaaabbbbaaaaabababbaabaabbbbaabbaaabaababbaabbbbbababbbabbaaaababbaaabbababbbaabbbabbbabbbbaabbabbbbabbaaababbababaaabbbbabbbaaababaabaaaaabbbabbbbaaabababbbaabbababbaabbbabbaaabbaaabababaabaabbabaababaaaabbbbabaabababaabbbaaaabaabbbbaabaaaaaababbaabaabbababbaaabaababaabbababbabbbaaabaabbabaaaabbbbababaaaababbaaabababbbaabbbbabbbbbaaababbababaaaaabaaababbbbaaaaaaaaaaaabaaaabbaabaabbbbbaababbabbbabbbbaabbabaabababbbbbbbbbabaaaabababbabbbaabababbaaaabbabaabaabaaababbababbbaaaabbaaabbaaabbbbbaaabaaaaabbaabaabaabbaaabaabbabaaabbaabbabbaabbbbabaabbbabbabbbbbaaababaabbbbaabaabbbabbbbbaabaaabbaabbbbaabbabbababaaabbaaaabbbbbaaabbabbbbaaabbaaababbbabbababbbaaabbbabbbabaababbbaababaabbbbbabbaaaababbaabaabaabaababbaaabbbbbaaaaaaabbabaabbbaaaaaaabbbaabaaaabaaaababbbbbbaaaabaaabbbababbaabaabbbaaabaabbbaaababbbaaaaaabbababbababababbbbbbbaabbaababaabbbbbbbaaababaabbaababbbbbaabaababbbbaaababaaabbabbaaaabaabaaaababbaaaabaabbaabaabbababbaaabbbabbbaabbbaaabbabaaabbbabaabbbbbaaabaaaabbbbbabbbbbbabbbaabbbbaababbaabababbaabbabaaabbabababbabaaaabaabbbaababbababbbbabbabaabaababaabaaababaabbbbabbaaaababbaabbbbababaaabbababaaabababaabbbbababbaabaaabbabbbbaabbbaababbabababaabaabababbbbbbabababaaabbbbababaaaababaababaabaaabaaaababbbaaaaaababbabbbbababbababaaaaabbabbaabbaabaaabbbbabbbbbaaababbabaabbaaabbabbaaaabbbbbabaaaabaaaaababbbaababbbbbabaabbbaaaaaaaaaaabaababbaabbaabaaaababaabbaaaaaaabbbabbabbbaaaabbbbaabbbaaabbbababbabbbbbbaaabbbbabaabaabbbbbbabaaabaababbabbbbaaaabbbbaaaaabbbababbbababbbabaaabbaabbbababaaabaabaaaaaabbabbbaababbbaaaababaaabbbababbbababaaabbbaabaababbaaabbbbbabbabbabbbbbaaabababbbabababbbbbbbaababbbbbbaabbabaaabbaabaaaaaabbaabbababbababbbbbbaaababbbabbbaabaaababbaaabbabbabaabaabaababbaabbbabaabaaaabaabbbbbabbbaababbaaabababbabbbbbabbaababbbaabbabaaaabbbbbababbaabbbbbabaaaaababaaabababababbaabbaaabbbaaaabbabbbabbbbaaabaabbbbbabaaaabaaaabaaaaaabaabaaabaabaaabbaaabbabbaabaaaaaabaabbbbabbaaaaabbabaaaaabababbaaaabbbbaabbbbabbabbbbbbbbaaabaaabbabababababaabbbbbaaababaabaaabbbbbababaaaaababbaababbbbbbabbbabaabaaabbabaababaababbbabbaababaaaabbbabbbbbaaababbaabaaaaaabbabaababaaabbababbaaababbbbbaaabababaaaabbaaaaaaababaabbbbbbbaabbabbabaababababbabababbaaaaabbaabaabaabbababababaababbaaaabbbaabbaaabababbaabababbbabbababbaabbbbbaabbabaaaabbbbbaaaaabbbbbbabaabbbabbbbbaabaabbbaabaabababbaababbbbbaabbbbbbbbbaaaabaaaabaaaaaabbbabaabbaabbbbbbabaabbbbabbbbbbbabbbaabbaabababbbbabbaaabbbaaabbaabbabaabaaabbbbbabaabbaabbbaaabbaababbabbaaaaabaabaabbbabaaaabaaabbaabbaaaaaabaababbbbbaaaaabaaaaaaaabbabababbabbbaaabababaaaabaaaaaaaababaaaabbbaaabbabbbbabbbbbbaaababbbabaaababababbaabaabbbaaabaabbaabaabaabbbbbaaababbaaabbbabbabaaababaababaaaabbbabbbbaaabaabbabbbbabbabbaabbaaaabbbaababbbbbaabaaaababaababbaaabababababbbbaaabaaaaabaabbaaabbabbabbaabbabbaabaaaabbbbbaaababbababbaabbbaabababaaabbbabbbbaabbaabaabbabaaababbbbbabaababaabaaabbaabbaabbaaaaaaabbbabbbabbbbbbbabbbbabbabbababaabbaababbabbbaabbababbbbaaabaabaababbaababaabbabbbaaabbabababbbbabbaabaaaaaabbbbababaabababbabbbbaabbaabbaabaabbabbbaaaabbbabbabaaabbbabbbbaaaaaaaaabaaaaababaaabaaaaaaaaabbbbabaabaababaabababbbbbbabbaabababaabbbbabbbabbabbababaabbaabbbaaabbbbbaaaaaabbaabababaabaabaababaaabaabaababbbbaaabbaaabaaaababbabaaaabbaabaabaabababbaabaabaaaaaabbbbaaababbabbbababaababbabbbabababbbaaabbaabaaaaaabbaaabaaabaaabbabbabbbbbbaabaaabbabbbabababbaaaabbbbbabaaaaaaabbbaaaaaabbabbabbaababababbbbaabbbbabbbabaababaababaaaaabbabaaabaabbbabaababbbababbbbabaaaabbbabbbabaababaababababaaabbaababbababbaaabaaabbbabbbbbabbbbbabaabbababbbbabaabbabbbabaabaababbbabbaabaaabbbbbbbabbbaaaaaabbbbbaaabbbaaabbabbbaaababaaabaababaaabbbabaaabababaaaababaabbbbaabaaaaaabbabaabaaabbbabbabbababababaabaaaaabbaaabbaaabbaabbbaaabbaabaabbaababbaabbaabbaabaaaabbbabbabbbbbabbabaabbaaaaaabababababbabaababbaabbababbbabaaabaaaabbaababbbbabbbabbbbaabbbbbbbaabbbbaabbababbbbbaaababaabbaaababbbaabbbbaaaabbbbbaabbbbaaabaaabaabbabaababaaabaaababababbbbbaaaaabaaabbbbaaabbaabbbbbbbbaabaabbabaaabaabbbaaaabbbaaaaaabbbbbbabaaaaabababbbabaabbabbbabaababababbaaaaaabbbabbabbbbbbabaabbaabbbababbbbbbbbabaababaabbababaaaabbabbbabbaabaaabaabbbabbbaababababbbbbbbbaabbabbabaabbabaaabaabaabaaaaaabaababababbbabaaabbbbabbabaabaaabababaaaaababbababbabbbbaaaaabbbaabaabbabbbbababbaabaaabbbbabaababbbbabbbabbabaaaaabbaaaaababaabbbaabbababbabbbbbaaabababbbbabbbaaabbaaabbabaababbaaaaaabbbbbaaababababbaabaaabbbabaabababbabbabbbbbbaababbbaabbbababbbbaabaabbabbbbabbbbbabbbaaabbaabbbbbabbbaaaaaabbbbbabbabbbaaabbbbbaaabaabbaabbaaaaaabbbabaababababaaaaaabaaabbbbbabaaabaabbbbbbbababababbaabbaaaaaabbbabbbbabaaaabaababaabbabbbbbaaabbbaaaaabbbabbbbbbaaababbabbbabbabaaaaabababaaaaaaababbababababbbaabbababbbaaaababaabbbbbbabaaababababbbbaaaababaaaabbabbaaaababbbbaabbaababababaabaabbabbabbaabaaaabbbbbaaabaaaaaabababbbbabbabbbbaaaabbaaaabbbaabaabbaababaaabbbbbbbbababbbabbaaaaaabbbabbbbbaaaabbababbabaaababaaabbabbaabbaaabaaababbabbbbbbbbaaabbaaabaaaaaabbbbabaaabbbbababbaaaaabbaaaaabbbbbbaaababbbababaabbaaaaabbabbbaabbbaabababbbabbababaaabbabbabbbaabaaababbbbaabbbbbbbbabbbababbababbaaabbbababaababbababababbbabaababbaaababbabbbaaaabbbbabbaaaaaabaaabababaaabaabaabbbbabbabbbbbabbababaabbaabaabababbabbaaabbababaabbbbabaabbbaaabbabababababaaababbbbabbbaabbbaaaababbbbababbbaaabbbaaabaabababbbbaabbbaabbbaaaabaaabbaababbaabaaabababbabbbbbbabbaababbabbbaaaaabbbbaabbabbaabaabaababbabbbbbbaaabbbbbbababbabbbabbaaabbaaaaabbbababbabbbbbaaaabbbbbbbbaaabbbbbaababbaaaaababaaabbabbabbbbaaabbbbaaababaabbababbbabaabaabbabaaabaabaabbbabaabababaabbabaaabbbaaababababbaaaabaabbbabaaabbabbabbbbaabaabbbaaaaabbbbbaabaabbabbabaabaabbaabababababbbabababbababaabaaabbbababbbbaabaabbababaaabbbbbbabbbabbbbaaabbaaaaabbbbaabaabaaabbbaaabbaaaaabababbbaaabbbbaaabbaabbbabaaaabaabaabbaabaabbbaaababbaabababbaaaabaaaabaaabbaababbbbbabbbaabbabbbbaaabbaaabaabbbbabaababbabaaabbabbaaabbabbaaaababaaaabaabaabbabbababbaaaabbbaababbabbababbaababbbabbbbababbaabbbabababbaaaaabbbabababaabbbbaababbabbabaaabbbbbabaaaaaabaaababbbabaaaababbbbabaaabaaaabbbaabbbaaabbabaababbabababbabbabaabaabaaaabbbabbbabbabbaabbabbabbabaaaaaaabbbabbababaaaaababaaaabbaaaababbabaababbaaaaaabbbababbabaaaaaaaabbabaaabaabbaaaabaaaabaabaaaababaaaaabbaaaaaaabaabbbbaaaabaababbabbbbaaababbaaabbaabaabbaaabbaabaabaababbbbaaaaaaaaaabaabaaabbbaababaaabaabbababbabbbbbaaabaababaaabaaaaabbbbaabbabababaaabaababbbbbbbbbbabbabaabaabaabaaaabbabbaaababaaaaaaabbabaaaaababbbbbbaabaaababbabbbbbaaababbbbbbaabbbaabababaababbaaabbbbaaabababbbaaabbaabababbaabbbbaabaaaabaababaaaaababaabbbbababaabbabaaababbbaaaaaaaaaabbbbbabbbbbbbabbaaabbaaaabbbabaaaabaabaaaabbaaaababbbabaaababbbbbbaaabaaabbabbbaabbaaababbabbabbbbbaabbbbbbbaaaaaababababbabbbbaababbbbaaabbbabbababaabaaaaaababaababaabaabbabbaaaabbaabaabbbbbbaabbaaabaaaaaaaabababaaaabaaababaaaaaabbaaabaaabbbabaaabaabbabaaaabbbabbbababbbbabaabbaabbbbababaabaaabbabbbabaaabbbaaaaabababaaaabbbabaababbaabbbabbabbbaaabaaaabaabbabbaabbaaaabbbaababbaaaaaabbbaaaabbaaabaabbbbbbabbbababbbabbbbaaaababbaaaababbbbbaaabbaabbbaaabaaaaababbbababbbbbaaababaababbbbaabbbbbaabaabbabbabbaaabbaaaabbabaaabbbbaababbabbbaaabbaaaaabbbabaabbbabaabbbabbabbbbaabbaabababbaabbbaabbabbbbbbaaabbbabaaaabbaaaaabbbabbaababbbbbaabbbbbaaaaabbbabbababaabababaabaababbabaaabbbaaabbaabbbbbbbabbabaabaaaaabbaabbbabaaaaabbbbbbabbbaaabbbbaaaaabaabaaaaaaaaaabbaaaabbbaababaabababbbabbbabbbaaabbababbaababaabbbbbbababbbabbbbbabaaaababbbaaabbbabbbbabbaaabbbbaaaabbbbbaabbbbaabbababaabbbbbbaabbbbbbabbbabbabbabaabbbbbaabbabbbabaabbbbabbaabbbbbabbabaaabababbbbbbbbaaababbbaabaabaaabbbbaaaabbbababaaaabbbaababaababaabababaabbaabaabbbbbbbaabbaaaaaaaaaaaabbbabaaaaaabaaabbbababbabbbbbbababbbaabbbabbbbbbabaaaababababbbbaaaaababbabbbaabbbbaaabbabaaabbabababbabaaaabbabbbbaabbbbbabbaabbababbaababbaababbbababbaabaaaaaabaaaabbaabbaaabbbbbabbbbaabbbbaabaaabaaabaaaabbabababababaabababaabbaabababaababababaaaaaabbabbabaabaabbbbbbabababbabbbabbababaaaaabbaabaaabbababaaaababbaaababbaabbaabbbbabbaabababbabababaaabbbbbaabaabbbbababaabbbaababbababaaabaabbbbabbaabaabbabbbaabaababbbabbaabbbbbababaababbababbbaaaaaabbbbbaaaaabaabaaaaababbabbbabbabbaabaaaaabaabbbbaaabbabbabbaababbbbbaaaaaabaaaababababbbabbabaabaaababaaabababababaaaaaaaabbabbaaabaaabaabbbaaabbababbaabaaabbabbbbbbbaaabbbaaabbaabaabbabbbaaaaabaabbbaabbaababbabaaabbaaabbaaabbabbbbabbbabbaaaabaaabbabaabbbabaaaaabaaabaaaaaabababaaaabaaabbaabbabbabbbbbbaaabababbbbaabbbaaaaabbaabaababbbabaaabbaabababaaaabaabbabababbbbabaaaaaabbbbaabbababbbbaaababbbaaaabbbabbbbbabaababbaaabbbaabbbaaabbaaaaabbbaaaababaabbaabbbaabbababbbaaabaababaabaababbaabbaaabaabbaaaaaaaaababaabbabaabbabaabbbbabbbbbbbbbbabbbababaaaaabbbbaaababaabbbbaabbababaabaaaababaabbbaaabaabaaababbabbaabaaaabaaaaababbbbabbabbababbbaabaabbbbabaaabaabaaaabababaaababbbaaaaabbaaaaabaaabbabbababababaaaaabbababbabaabbaababaabbaaababbbbbbabbbabbbbbbabbbbbabaaaabaabbabbbaaabbaabbabbabbaaabbaabbabbabbaaabaaabbaabaaabbaabbbabbabbbbbaaaaabbbbabaaaaaabbaabbaaabbbbaabbbabaabbaaaababbabbabbabbbbaaaabbaaabbbaaaaaabbbbaaababbaaaabbababbbbabbaaabababaabbbbbbbaaabaaababaaaabaaabbbbbbbbbabbbbaaabaaabaaaabbbabababaabaabaabbbabbabbbbabbbabbaaabababbabaabbaaabbaaaabbaabbaaababbbbaabaabbabbbaaaabbabaaabbbaaabaaabaaabaaabbabaaabbbabbbabbbaaaabbababaaabbabbbaaabaabbbabaaaaaabbbaaabbbabbbbaaababaabbbbabbbabaabbabbbbaabaabbaaabbbabababaababaabbabbabababbbaababbbbabaaaaabbaaaabbbaababaaaaaabbabaabaaababbaaaaabaabbbbaabbbbabaabbbbabbaabbabababbbaaaaababaaabbabbabbaabbbaabbbbaaaaabbabbababbabbbbbaabaaabbaaababbbabbbabbabbabaaaababaaaaabbbabaabbbabbbabbbaabaabaaabbbbbababbabbaabbbbbabbaaaababbaabbababababbababbaabaababaaaaabbbbbaaabbaaabbabbababbbbaaaaaaaaabbaababaaaaaaababaabbbbabaabbbbbbbaababaabababaaabbabbabaabaabbabaabaaabbbaababbbbbaaaaabbababbaaaabaaabbbbabbbabbabbabaabbaabaaababbbaabbabbabaabbabbabababbabbbaabbababbbbbbababaaaabababbabaaaabbabbbabbbbabbbbbabbabaaaaaababaaaabbbabbbaabaaabbababababbabbaaaababaaaabbaabaabbaaabaaaababbbaabaaaabaaaaabbbabbababaaaabaaabbbbbbabbaabbbbaaaaabbbaaabaabbbababbabaaaabbbbbbabbbaaaabbbabbbbabbaabababbbbbbbabababbabbbabbababababababaaaaabaaabbaaabbbabbbabaabbabbbababaaaabbababbabaaabbbbbababbbbababbbbbaaababbbabaabaababaaabaabbbbaabbbbbaaaaabbabaabbbbaaaaabbabbaabbbaaabbaabaaaaaabaabaaabbbabbabaababbabbbabaaaabaaabbbabaabaaaabbaaaabaaabababbbabbbabaabbbababbabbabaaaaabaabbaabaabaabaabbbbaaaabaabbbaabababbbabaaabaaabbbbbaaabbbaabababaaabbababaaaabaababbababbbaabababbbbbababbaaaababbbbbbabbaaababbbaaabaaababaaaabaababbaabaababbaabbbbbbabbababaaaaaaaabaaaaabbabaabaabbaababbabaaaaabbaaaaababbbbbbaabaaabaaaabbbbbbbbbbbbaabaaaaaababbbababaaaaabbaabbabbaaabbbbabaaabbbababaabbbbbabbaaaabaaaaabababbaaaaababbabaaaabaabaaaababbaabaaaabbaabbababababbaabbbabbbbbaabbbbbbaaaabaababbbbababbaabbbbbabbaababbabaabbaaaaaaabbaaabaabbaaababababaabaaaaaaabaababaabbabbabbabbbbbabbabbbbbbabbbaabaabaabbabbabaaabaaaaabbabababbbaaabbabbabaaaabaaababababababbaabbabbbbaabaababbbbababaaabaabbbaabbbbababbbaabaaababbbbaababbbaaaaaaaabbabbbababbababaababbbabbbababbaaaaaabbabbaabaabaaaaaaaaaabaaaabababbababbbaaabaabbbbbbbbbbbbbabbbbabaabbabaabaabaaabbbbbbaabbaababaabbabbabaaaababbbaababbbbaaabbbabaababbbbabbabbbbbbaaababbabaaababaababaaaaababbaabaaabaaabaabbabbaaababaabaaabbbbbbaaaabababbbbababaaaabbbbbbaabbabaaabaaaabaaababaabbbabbbabaaaaabbbbbabbbabbabbabbabaabaababaaabababaabaabaabbabababbbabababbaababaaaabaabbaabbbbabaaababababaababaababbbbababbabaabaaababaaabbbbbbaaaabaababbbbaabaabaaababbbaaabbbbbabbbabaaabbbaabbbaabaaabababbbababbaababaabbbbbbabbbbabbababaabaaabbbababbbbbaabbbbabbababbaabaaaabaabaabaabbaabbabbbbbbaabaababbbabbbbbbbbbabbabaabbabbbabbaababababbbabbbbbbaaabaabbaaaaaaaabaabbaabbabbaabbaabbabbaaabbbbaaabbaaababaabababbabbbabaaaaababaaaaabbbbbaabaaaabababbbbbaaaababbbbbbbabbbbaaaaaaaaaabbababbaaabbbbbabbbabaabbabaaaabbbbbaaabbbabbabaaababbabbbbababaaabbabbabbabbbabbaaaaabbababbaabbbbabbaabaaababbbbabbbbababbaabbaabbaabbbaabaaaaaabbabbbbbbbaabbbbaaabaaababaaaaabaaabaaaaabbababbabababbaabaabbaabaabaabbbaaababbabbaabbbaaabbbabaaaabbabaabaababbbbaabbabbaabbaaaaabaabbbabbabaabbabbbbbbaabbbbbaaaababbaabbbbbaaaaabbbbbaabaabbbaaabbbbbbababbbaababababaaaaabbabaaaaabbbbbbbaaaaaabbbaabaabbaabaabaaaabbbabaabbaaababbbaababaabbababbaabaabaaaaabababaaabababaaababababbaabbaaabaaaaaaaabbababbbabbabbaaabbbbaaaaaabbabaabbabbabaabaaaabbaaaabbbbbbbbbbabababaabbabbbbbbbbbaaabababbabaaaaaabaabbbbbabbababaaaabbbabaaaababbbbbabbbabaaaaabbaabbaaabaaabbabbabbaabaaababbaaaaaaaabaaaaabbababbbabbabbaaababaabbbbbaaabababaaaabababbbbabbbbbaabbbabbaababbbaabaababbaabbabbbbbbabbbbbbbaabaaabaaabbaabbaaabbaabbabaabbaabaabbbbbaaaaaabbbaabbabbbbbbbaaaabbbababbbaaaaababaaabbbababaabbbbaaaabaaaabaabbbababbaabaaaaaaabaaabaaaaaababbbbbbbaaabbbabaaabbaaaabbabbaabaababbaaaaabbaaabbabbbaabbabbaabaaabababbbabaabaabbbabbaabbaaaabaaaabbabaaabbbbbabaabbbaabbbbbaaaababbabbbaaaabaaaabaaaabbbabaaabbbaababaaabaaabbbbaaabbbabaaabaabaabbbaaabaaabaaabbaabbbabbaabbbbbaaaaabbaabbbaabaaaaabbaaabbbbbaaabbabaabbbbbbbbbbaabbabaabaabbbaabbaabaaabbbbbabbbaaaabbbababbbabababbbabaabbbbbbabaaabbbaaaaababbaababbbbabaaabbbbbbbabbaababaaaabbaaaaabaaabababaabababbbabaabaabbbababaababbabbbbabbabbbaaaaaababbaabbabaabbaabbbaaaabbabbbbbbabbaaaaabaabbaabbbbabbbbaaaabaaaabbbbbbbabaaabbbababbbaaaaaabaabaaaabaaaabaaaabbbbbaaaabbbbabbabaabbabaabbbaaabbbbabbbbbbbbabbbbbbbaabbabaaabababaabababaabaaaaaababaaaababbabaabbbabaaabbbababbbbaaabaabbababbaabaaabaaabaaabaaaaababaaaabbbbabaaabbaabbaabbabbababbbbbaabaababbabaabababbabbababaabaabbababbbabbabbbabaabbaaaabaaabaaabbaababbbaabaabaabbbabbbababbaaabbbbaaaabbbabbbbbabaabbbbababbabbabbababbaababaabaaabaabbbababaaabbbbbabbaabbabbbaabbbbaabbabbaabbbabaabbbaabbbabaaabababbababbabbbaabaabbaaaaaaaaaaabbbbabbaabaaabbbbaaababbabbbbababbbababbabaabaaaaaabbaabbbabbbaabaaabbabbabababaabaaabbbababbaabaabbababbbabbabbaabaabbaaaaabbbaaabaababbaababbababbaaabaaabbbaaaabaabbbaababbbabaaababbaaaaabaaabbbbaaaabbbaaabbbbbabababbaaaaaabbaabaabaababbaaaaababbbbbbbababaaaababbaabbbbababababaababbbbbbbbbbbabbaabbbbbbabaabbbbbabbbbbbaabbaababbbaaababbbbaaaabbbbbabaaaaaaababbabbabbaaabbbabaaabbabbabbabaabbbababaababaababbabaaaaaaaaabababaaababbabbbaaaaababbaabaababaabbababbaaaaaabbaaabbaabbaaaabbaabbbaaaabbaabbbaabbbbbaabababaababaaaabbabaababbbaabbbabbabaababbbaaaaabbbbbbabaabbbaababbaaabbabbbaababbaaaaaabaaaabaaabbaabaaaabbaabbaabaabbbbaaabbbaaabababbbbbbbbabbabaaaabaabbbaabaabbabbbbbbbbbabbbaaabbabbbaabaabbbabababbaabababbbabaabbabaaabbbabaaabbaaabbbaababbaaabaaabbabbbaabbabaaababbbabaaaaabbbabbbabbaabbabbaababbabaaaaaaabaaabababaabaaababbaabbabbbbabbbbababaaabbbaababbbaabbabaaaaabbababaabbbbbbbabaaabbabbabaabababbbbaaabbaaabbbaabaabbabbbabaaaabbbaabaaaaaaaababaaabbbabaaabbbbbaababbaabbabaaaaaabababaabbabbabbabbabbbbbababbbaabbbabaabaaaabaaabbaabaaaabbaaabbbbbaabbabbbbaaaaabaabbaaaababbbabaababaababbbbbbbbbabbaaababbabbabaabaababaaabbabbbbbababbbbbabbaaaaaabbababababbbbabaabbbbabbbbbaabaababbabaabbaaaaabbaabbbaaababbbabbbaaabbbbabbabbbabbbabbbbaaaabbabbabaaabaabbbbaabbabaaabbaaababbababbaaaaaaaabbbababaaaaaabaaaaaaabbbaaabbabaabbaaabaabbbbabbbabaabbabbabbbbbbbabbabbbbaaaabbbabbaabaaaabbbbabbabbbaaaababaababaaabbaabaabaabaaabaaabaaabbbbabababbaabbaabbababbaabaabbaaabbbbabbbabbbbaaabaaaababaaaaabaaaabbaaababbbaaabaabaabbabbbbaababbbaaaaabbbababaaaaabbbbbababbbbabbbbabaaabbaaabaaaabbbaabbbbbbaaaaabbbbbaaababaaaaababaaaaaabbbabaababbbabaaabbaabbababaaabbabaabaabaaabaaaaabbbaabaaabaabababbabaaababaabbaaaabbabaabaaaabaaabbaabbbbabbabaaaabaaaaababaabbbabbbaaabbabbbaabbbabaaabaabbabababbbbabbbbbbbbbbabababbbaabaababbaabaaaabababbbbbbbbaabbabbaabababaaababbababbaababaaaaaabbbabbabaabbabbbabbbabbabbabbbbaabaaaabbaababbabbabaaabbbababaabbbbbabbabbbaabaabbbbbbbbbaabbbabababbaaaabaabaabbaabbbbbaabbababbabaaabaabbbbabbaaaaabaabbbabbaaaaaaaaabbbbabbbaababbbbaaabbbaabbbbbbbbbbbbabbbaabbbaabaaaabbaabbbabbbbaabbaabbaaaabababbbabbabaaabaabbaababbbbbbbabbaabababaabbabaabbbababaaaabbbbbaabbaabbbbbaaaabbabaabababaabbbbabbaaaababbaabbbbabbababbabaaaaaabbaababbaababbabbbbbabbbbaababbbbbaaaaaaaabbbabbaabaabaaaabbaabbaabaaaaabbbaaaaabbbbaaabaabaaaabbbbbbbababababaabbbaabaaabbbaaaaaabbabaababaabbbabbabbbabbaabbbabbaabababbbaaabbaababbbbbaabaaaabaababbbbabaabbbababbbaaaaababaaabbbaabbbbbaabbbbabbabbabababbababababbbbabbbbbababaabbbaabababaaaaabbbaaaabaaabbabbaaabaabbbabaabbbbbabbbbbabaabaabbbababbbaabaabbabbbbabbaaaaaaaaabbabaaaaababbbaabbbaaabbababaaaabbbabaabbbbababaaabbbbbaaabbabaaaabbbbbbaaaababbbabbbbbbababbabbaaaababaaababbabbabaabbabaababbabaabbbababbbbbbabbaabbababababbbbabbabbbaaaababbbbbaabbbababaaababaabbaaaaabbababbbbbabbaaaabbababbbababbabbabbbbabbaaabbaaaababaaaaaababbababbbabaaaaababaabaaabababbaabbbaaababaaababababbaabaaabaaaabbaaaabaabaababbaabbabaababbbaabbbbbbbbaaabbabbbabababbbbabbaabaabbbabbbabbbaabaabaabaabbaabbabbababbbaaaabbababbaababaaaabbbbaabbbbaababbbabbbbbaabbabbbbabbbbbbabbbbaaaaabaabbbbbabbbbbbbbbaababbabaabbbaaabbbbabaabbbabbaaababbbaabbaabbbbabaaaababbbaaabaaaaabaabaaabbbaaabbabbaababbaaabaaaabbabbaababbabbabbaaaabbbabbabbaabbabbbbbabbbaaabbbaabbaabababaabbbbabbbaababaaaabbabaaabaabaabbaaabaaaabbaabbaaaabbaababaabbbaaabbaabbbbabbaaabaabaaababaabbbababbababaaaaabbbbaaabbaabaaabaaaaabaabbabbaaaaaaabaaaaaababbbabaaabbaabbabaabababbabaaabbabbaabbababaaabaabaabbbaaabaaabaabbbaaaaabbaabbabbbababbaaaababaababaabbbababbbbbaabbabbbbbbaabbababbbababbabaaabbbbbaababbbabbaaabababababbabaaabaabaaaaaaabaabaabaabaaaabbabaaababababaabbaaaaababbbabbaaabbababbaabaabbbabbbbbbaaabbababbaabbbababaaabaabaabbaaabbababaabbabbbbbbbabbabbbbbababbbbbaababaaaaabaaaababbbbbbbaababbbbababbbbababaaabbabaababbaabbabbbbaababaabaaaaaaababaababbaababbaabaabbbbbbbaababbbabbbbbbaaaabaaaabbabbbbbbaabbaaaababbbbbaaaaabbbbbaabbababababbaabbbabaabaaabaaaabaabbbbbababbaabaabbaaabbbababaaaabaaabababbbaabbabaabbaabbabaaaaababbabbaaaaabbbbbaabaaaabaababbbbaabbababbbabbabaaaabbbabbbbbbaabaabaaaaaabaabaaaabaabaabaabbbbbabbbaaaaabaabbbaaaaaabaabbbaabbaaaabababaaaaaaaaaabbaaabbbbbbababaabbababbabbbababaaaabaaabaaaababbbaaabaabaababbbababbbbbababbabbbaaaabbaabaabaababbaaaababbaabababaaaababbabaabbbaaaabaaabaababbbababababbbbbbbbbbabaaabbabbbabbbbbabbbababaaaabbbabbabbbbabbaaaabbbbbbbbabaaabaaabbbbabaabbbbabababbaabaaabbababbbababbaabbaabababababaabbbaabbbabaababbababaabaaaaabbaababbbbaabbabbaaaabbbaaaabbbbabbaabbabbababbababbbbbaaaaabaaabaababbaaaaababbaaaabbbbaaabbbaabaaaaabbbbbabbabaaaaababbaabbbabbbabbbababbbaaaababbbbabbabbabaaabaaaaabaababbaaabababbbabbaababbbabbabbbbbbaaaaaaababaaaabbababbaabbbbbbbabbbbbababbaaaaabaabbabaabbbbbaaaabbaabababaaaabbbbabbbbbbabaabbaaaaaabaabbababbbabbabababbabaabaabbabbbaaabaaabbaabbbbbaaabbaaaabbbababbbabbaaabbabbbaabbbababbabbbaabbaabbaaaaabababaaabababbababbabbaababaabbbabbbbababaabaaaabbaaabbbbbababbbbbbaabbbbbbaabbaabbbabababbbbbbbbbaaaaabbbabababbaaabababaaaabbbbbabbababbaaaabbabbaaaabaabbababaababbbbbabaabbbbababaaaabaabbbaabaabbabbbaaaaaabababaaaaaaaabaaaabbbabaaaabbaabbabaaababbbbbabbbbabbaaaaaababaaabbbababbbbabababbaaabbaaaabaaaaabbababbabbaabbabababaaaababbabbaabbababaaabaabbbbbbbbbbbbabaaaaabbbbbabbbaabaabbaaabbababaabbbabaaaababbaabaabbbabaabaabbbabbbbbaaaabbababbbbbbaaaaaabaabababbbbbbaaaababaaabaabaababbbbbaababbbabbbbbaaabbaabababbaaabaabbaaaaabbaaababaabaaaaaaaaababaaaabbbbbbbbaabbbabbaaabababaabbaabbabbbababaabaaabbaaabaabbbaaabbbbbaabaaaabaabbababbaaabbabbabbaaababaabbbbababababbaaabbbbbbbabbbaabaaaababbbbaaabaaababaaaabaabbaabbbabababaababbbbbabbbaaabaabbaaaaabaaaabaaabbbaabbabbbaabbaabbaabbaabaabbbbaabaabbbbababbbbabaaabbaabababbababaabaabbaabababbabbaabababbbaababbaabaababababbbbabaabbaabbbaaababbbbbbaaabaabbbbabaaababaaaaabbaabbbbbabbababaabbbaaabbaaabbabbbbaaabaababbabaaababbabaabaababbbbabbbabaabbaababbbabbbaababaabbaabaabaaababaababbaabbbaabbaabaabbaaaaaaaaabbbaabbbabababbbbabaaaaabbbaababaaaabababaababbaaabbbaaabbbabbabbbabbaaaaababbbbbaabbbbbaabbaabbbabaabaaabaaaabaaababbbaaaaaaaabbaaaaabaabbababaaaaaaaaaabaababbababbaabaaabbbaabbbbaabbaabbaabbbbaabaaaaabbbbbbaaabbabbbbabbabaabbbaababbaabbaaaabbababbabbbaabaaabaaabaaabababbbbbabaaabbabaabaabaaababaababbabbabbbabbbabaaabababbabbabaaababbbbabbbbbababbbabbbbbbabaaabbaabaabbabbbaabbabbaaabbbbaabbaabbbbabaabbaabaaaaaaaaaaaaaaabaaaaabbabbaabbbbabbbbbaabbbbabbababbbbbbabbaabbbbbabbbaabbababbbbaabbababbabbbbaabbbbbbbbbaabbbabaaaaaababaaabbbbababaaababbbababaababaaabaaabbaabbbbbbabaaaabbabaaaaabaaabbaaaaababaaaaaaaabbbbbaaabaabbababbbabbbaaabaabaaabaabbabaaabaabaababbabbbbbbbaababbbabaababbbbbbbaabbbbbbbaabbabbbaabbabbabbabaaaabaabaaabbbabbaababbbbabababaabaaabaaabaabaababababbbbbabaaaabbabbabaabaaabbbbaabaabbbaabbbbaabbbbabababbababaabbbbbababababbbabbbbabbabbabbabaabbaababbabbbaabbabbabbbbabaaababababbbabbabbbabbbbbabbbabbabaaaaabbabaabaaaabbbaabbabbaabbbaabababbbababaabbbababbbaaabbbbbaabababaaabbbaaababababbaabbabbbbbbbbaabbaaabaababbaaabaaaaaaaaaaaabbbaabbababbaabbaaabbaaababababaaaabbaaaaaaabaaabaabbabbabaabbbbaaaaabbaababbaaabbbbaaaabbabaabbabbbbbbbbababbbabaaaabbbbaabbaabaaaabbbabababbbbaabababababaaabaabbabbaabbbababaaabbaaababbbbaabbabbbbbabbaaabbabbbbababaabbaababbbaabbabbbaabbbabbababbbbabaaabaabaababaaaababbbbbbaaaaabaabbabbabbbabaabbaabbabbabbbaaabbbaaaaabbbabababbaaabbaabbaaaaaabababaaabbbababbababbaabbbbababbbbaabbaaaaabbabaaaaaabbbbbaaabababaaabbabbbbbaaaaaaabaabaababababaaababbbbaabbbabaaabbbbaabaaabbabbbbaabbbbabaabaaababaabababababbbbbaabbbbbbaabaaababaabbababbbbaabaaaabbbabbabbabbababbaababbbbaaaaaaabaabbbbbbaababaabbabaaabbbbbabbabaabbbbbbaaaaabbaababbbbabbbaaaabbabaaaababbabaabbababbaabbbabbbbaaabbbbbaaabaaaabbbaabbbaaaabaaabaabaababbbbbbbbbbbbabbbababbbaaababbabaabaabbaabbaabaaaabababbbaabaaabbaabbaabbabaabbaaabbababbaaabaaaaabbaaabababaababaabbabbaaaaabbbbabaabbaabbbababbbbabbaabbbabaabbbabbbabbababbbbbaababbababbbbbaaaabaabbaababbababababaabbbabbbaaababbaaabaabbaabbaaababbaabbaaababbaabababbabbbaabbbaabaabaaababbaabaabbbbabbaabbabbbbbbaababbbbaaabaabbaaaabbbbbaaaabbbabbbababababaaaabbbbaaaaabaaaabaabababaabbaabbaabbaabaabaaababbabbbabbabaaaababaabaaaaaaaaaaabbbbabbbbbaabaabbbabbbababbababbabaaabbaabaaaaababbbabbaaaabaabaabaaabbbaabbabbaabababbaabbaaabaaaabaaabaabaababbaababaaabababbaabbbaabbabbabaaababaaababbbabbaaabbbbabbabbbbbbababbaaaaaaaaaababbabbaaaaabbabbabbbbbbbaaabbbbaabaabaaabbbabbaaabbbbababbbbaaaaabbbaaabbaaabababbaaaaabbababaaaababababbaaabaaaaabaaababaaababbabaaabaabbaaaaabbbbbbaabaababbabbbaaabaaabaabbbabbbaaabbbabbabbbabaabaabbabbbbbaaaaaabbababbabbaabbbaabaaaaaabaabaaaaaababaaabaaabaabaabbaabbaabbbbbaaababbabbabbabbbbababbaabbbaabbabbbaaabababbbbabbbaabbabaaabbaabbbbbbababababaababbbaaabbaabaabaababaabbaaabbabbaaaabbbaababbaaabbabababbabbababbbaabbbabbaababbaaaabbabbbbbabababbabbbabaaaaaaabbabbabaaaabaabbbbbababbbbbbababaabbbbabbaabbaaaabbbbbbbbbbaabbabbbaaaaaaabbbababbabababbbbbbbabaabbabbbaaaaabbbabababbaababababaaabbbababababaaababbbbbbbaaaabbabaabbabbbaabaabbabbaaaaabbabbbaaabbbabbbaabaabbbbbbaaabbaaabaabbababbbbaabaaaababbbaabbaaaaaaaabbaabbabbbbabbaaabaabaababbabbababaaaabaaaababbaabbaabbbbaaabbbabababbabbaaabaabbaaaaabaabaabababbbaaabbabaabababbbbbbbbbabaabaaabbbaaaaababbbbaaabaaaabbbbbbabbbbababbbababbbaaaaaababbaabbabaaaaabbaaaaaabaaabaaabbbbabaaabbbbaaaabbbbababbbbbbbaabaaaaabbababbbaaaabbbbbbbababaaaabaaabbaabbaaabbbaaaaaabaaaabbbbaaabbabababbbbaaaabbbbbbbbabaabbaababbaaaaabbaababbbaaabbbaaaabababbabbbababbababbbbbaaaababbaabaaababbabbaaabaababbbaabbababbbaabbaababaaaabbababaababbababababbaabbbbaaabaabaabbbbbbbaabbbbbbaaabbbbbbabbaabaaabaaaababaabaabbbaaabbabaaaaaaaaaaaabbbbaaababbbabaaaabbbaaaabaaabaabbbbabababbaaaaabbaabbbbaaaaaaaaababbbbbbbbbbbababaabbbbbbbaabaababbabbababbaabbbabaabaabbaaaabbbbabbaaababbbaabbaabbbbbaaabbbbbaababaabaaabaaaaabaaabaabbbbaabbbabaaabaabbabbbabbabbabbbbabbaaabbbbaaaabbbabbabbbbbabbbaaaaababbabbabbabbbbbbbbbaabaabbaabaabbbabaababaabbbaaaabaabaaaababbbaababbbbbbabaababaabbabaabbaabbabbaababbbaaabaaababbaaabbaaabbbaabbaaaabaabbabababaabaabbabbaabbabbbabbababaabbbabbbbaaababbaaabaaabaaaaaaababbabbbaaababaabababbbaaaaaaaabaaabaaabbbbbbabbaaaabababbaabbabaaabbbabbaaabaaabbabaababaaaabaaaaaabbaaabaababaaaabbbaaabbbbaabababbbbbabbabbbaabbababaabbbabaabbbabaabbbaababbbababaaaaabaaaaaaaabbbabbaaabbbbaaaabbbbbaabaabaabbbbaaabbbaabbbbbbaabababbaaaaabbaaaaabaaababbaaabaaabbabbabbbbbbabaabbaaabbaabbaabbaabaaaaaaabbaababbabbaababaababbbbbaaabaabbbabbbbbbbbabbababaaabbabaaabbaaaabbbababbaaababaaabaaaababbaabbbabbabbbbabaabbabbaabaabaabbbbbbbabaabaababaaaabaabaabbbababaabbbaaaabbabaaabbbbbbbabaabbbabaababbbababbaaaababbaaababaaaaaaaaabbbababbabbaaabbababbabbbabbaababbabaaababaabbaaabaabaaaaabaabbaababbabbabbabababaaaabbbabbaabbbaaabababbaabbbabbbbbbbbbbbabaabbabbabbaaababbbbbbaabbbbbbbbbaaaabbbbaaaabbbbababbabbabababaabaaaababaaaaabaabbbbbbbababaaabbbbbabbbbbbbaaaaaaabbbbbaabbabbbabaaaaabbaababaaaaaaabbabaababaabaabbaabbaabbbbaaaabbbabaaaaaaabbbabaababaabbababbabaabbbabbabbaaaaaabaaababbbbaabbbbbbababaabababbbbabbaabbaaaabbbaaababbbaabbbaabaaabaabaabaaaabaabaabbabaaababbabbbabbbabababbaaabbbbbbaaababbbaabaabaababbaaababaabbaabbabbabbabbaaaaaababbaaababbbabaabbaabbbabbbababababbababaaaaaabbabababbbbbababbaaaabbaabbababaaabbabababbbbbaabbbabbbbbababbbbbbbaaaaababbbababaaaabbabababababbaaabbabaababbbaaaaabababbbaabbbababbabbbbbbaabbbbbabbbbbaababbabaaabbaabaabaaabbabaaababbabbbbbaababaaabaababaaabaabbabbaaaaabbaabbabbbabaababbbaabaabbbabbababbbbabbbbbaabbbbabbaaababaababaaabbbbbbaabbbbaaabbbaaaabaabbaaaaaabbbaababaabaabbbabbbbbaaabbbbbababababbabababbaaaabaabaaabbaaaaaababbabaabbababbbbbababbaaabbabbbbaabbbbbabbaaababaabbaabbbababaabbbabbabaababaaabaaaaaaaabaaaaaabbbabababbaabaabbbbbbbabbbaaaabbbbaaaaaaabaababbababbaabaabbbbbbbbbabaabbbbaabbbbababaaaaaabaaabaabababbbbbabbbbbaababbaabbaababbaaaabaabbbbabbbbbabaaababaababbaababababbaabbaabababaaaaaabaabaabaaaabbbbabaaabbbbabbabbaabbabaabaaaaaaaaaabababbabbabaabaaababaaaabaabbababbabbaabbabbbbabbbaabaaaabbbaaaabbbbbababbabbbbbbbaaabbbbbaaabbbabbabbbbbbabbbbaaaabbbababbbbbbbaaabaaabbaaaababaaaaaaaaaaaabbaabbbbbbaaabababbbaaaaaabbbbaababbabbbaaaabaabbaabbabaababbaababaabbaabbbabaaaaabaababbababbbabaaababaaaabbababbaabbbaaabaabbaabbbabaaabbbaabbabbabbaabbaabaabbbbababbaababbaaaaaaaaaaabbabbaabbabaabaaaababaabaaaababbabaabbaaabaaaaaaabbaabbabaababbbbbabababababaaabbbabaabbaabbabbaaaaaabbbbbbaabaabaaabaabaabaaabaaabbaabbabbabaaabaabbabababaabaaaaaaabbbabbaabaaabbbbbbabbbbbbbaaaabaaaaabaaabababbabbbabbababababaabaabababbbababababbaabbababababbbaaaabbbabaaaabaabbaabbabbbbaabbbaababbbabaabbababaabbbaabbbbbabbbaabbabaababaaababbaaababbaabbaaaababbaabbababaaaaaabaaaabbababbbbbbbbaaabaababaabaabbababbbbbabbbaababaabbbbabaaabaabaaababbaaabaaaabaaaaabbaabaabaabbbabababbbbbbabbbbbbaaaaabababbaababbaaabbbbaabbababbbabbbaaaababaaaabaaabbbbaabaabaaaabbababababaababaabaabbabbbbaaaaabbbbaabbaabaabbbaaaaaaababaababbbababbabbababaabbbaabbbbabaababaabbaabbaaabbbaabbabbbbabbbbbaaaaaabbaabababbbbbbababaaaabbaaabbbabaabbaaaaababbaababbbaaaaabbbbabbbaaaaaaabbaabbaabbabaaaabaaabbbaaabbbaababbabaabbbababaabbababbabbaaabbbbbbbbaabbbbaaaaabaabaaababbaaababbabbaaabbbbbbabbbbbbbbabbbaaaaaabaababababaabaababbabaaabaabbabbabaaaaaaabbbbbaaabbabababbaaabbabaabaaabbbabbbaaabbbbbaaabbaababbbaaabbaaababbaaaabbaaaabbbbaababaaaaabbabbabbaabbabaaaaabaabaaaabbbaabaaabaaabbaababbabbbbbabaaabaabbbaabbbaaababbbbaaaabababbabaabbababbabbababaaabbabbbbabbaaabbabbbaaababbababbbababaaaaaaabbbbaabbbaaaabbbbbbabbabaabbbaaaaaaaaabbaabbabbbbbabaabaaabbbabaaaabbbbaaaabbbaaaaaabbaabbbbabaaaababababaabbbaabbabbbbaaabbbbbaaabaababaabbabbaaaabbaaababbbbbaabaabaaaabbbbaaabbbbbaabaabaaabaaaaababbbbbabbbabbaaaabbabaaabaaaaababbaababbbabbbaabbbaabaabbbababaabaaabbbababaabaaaaabaabbbbbaababaabaabbabaaabaabbaabbaaaaababbabaababababbbabaababbababbbbaabbbabaababaababbbbabbaabbbbbabbaaaabbabbaababbbbaababaaaabaaaababaaabbaabaaaabbbbbbaabbaabbbbbbbababbbaaaaabbababbabbbaabbaaabababaabbbababbabbbbbbbbbababbbabbbbbbaaaaaaababaaabbbbabaaabbaababaaaaaaabaaababbabbaaabababbbaaabbaaaaabbababbbbbbbbbabaaaabababaaaabaaaabbbababaaaabaabaaababbababaaabbbbbbbabbaaaaabbbaaababbabbbbbabaababaabbaabaabaabbaaabbaaabbbbbbaaabbbabbbabababbbabbaabaaaaabbaaabaabbabbaaaabababbabababbabbbbabababaaabbbbbaaababbaabaaabbaaaabaaaababbbbbbaabaabaabbabbbbbaabababbbbbbbabababababbbbabbaabbaaaabbbabbaaaabbbbabbbbbbaabbbaaabbbbaaabaabbbbabbbabbbbbaaaabaaababaabaabababbbbabaaaabbbbbbabbabbbbbabbbaaabaaaabbbabaababbbbbabaababaaaaaaaabaabaabbabbaabbbbaaaabbbaabbababaaaaabbabbbbbbbbaababaaabbaaabbbbbaaaabbbbaabbbaaaaaaaabbaaaaabbaabaaaaaabbbabbaababaabaaaaaaabaaabbabbaababbbaaaaabaaaaaaabaabbbaaabbbbaababbaabaabbababababbbbbbabbbbabbbbaabbabaababbbbabbbabbabaaabbbbbbabaabbbabbbbabbaabaabbbababaaabbaaabababbabaaabababbabbbbbabbbaabbbbaaababbaaaaabbabaababbbaaaaaabbabbbbababbaababaabbababbaabbbaabbbaaabababbabaababaababababaabbaaabbbaaaabbbabbabaabaaaaabbaabbabbbaabbabaabababbbababbbabaabaaaaabbbbaabababbbbabbababaaaaaabaabaaabbaabababaababbbaabbbbabaaaaaaabbbababbbbabaabaabbbaaabaaaaaababbaabaaaaaabbbbbabbbabbbbbbbaaabbbbbbaabaabbabbbbaabbaababbaababaaaababaaaababaaabababbabaababbbaabaaaaabaababaabababbababbbbabababaaaabbbbaaaabbbbbaabaaaaaabbabbababaabbaaababbabbbabaabbbbbabababababbbbbaaaabaababbabaaaabbbaababbaabbbabbaababaaaababaaaaabaabbabbabbaaababbbbbbbbbbaabaaaaaaabbabbbbbababaababbaabaabbaaaaaaaabbababbbaaabaabbbabbbaaaaabbbabaaaabaabbbaaaaaaabaabababbabaabababbabbbbabbbbbabbaaaabbbababbbbaabbaaaaabbbaabbaabaaaaabbbbaabbaaaabaababbababaabababaaabaaaabbbaaaaaabbaaaabbbbababbbbbaabbaabbabbaabababbbaaababbbaabbbbbaabaaabbaabbbaaabbbaaaaabaaabbabbbabaaaabaaababaababbaababbaababaabaaabbbbbbbabaabbbababbbaababbabbbabbaaaabbbbbbbabbababbbabbbbbabababbbbaaaabaabaabbbbbababaabbbbbbaaabbaaababbabababbabbaabbaaabaababbbbbbbabbabbbbbbaaababbbbbabbbbbbbababaaaabbaabbbbabababaaabaaaaabaabaabbaaaaaaababbaaabbababbbbbbbaaaaababaabbabaaabaaabaabbbaabbaaabaababbbbababbabaaabbaaaabaaababbbaaabbbbbbaaabbaabbaaabbaaaaaaabbababaaaaabbabaaabbbababaaaaaabbababbbabaaaabaababbbbbabbababaaaaaaabbaabbababbaabbabbbaaababbabaabaaabaaaababbabbbbbaaabbababbaabaabbabbbaabbaaabaabbbabbabbaabaababbbaabbbaaababbaabbbbabbbbbbbbbaaabbbbabbbbabababaabbbbababbaababaaabbabbaaababaaaaaabaaababbaabbbbabbaabbbabaabbbbaaaaabbabababaaaababbabaabbaaaaaabbabababababbaababaabababbaabaabbabaabaaaaaaababbbbabababbbbaaabbbabaabaaabbaaabbbaabbbbbaaabababbbaabaabaabaababaabaaaabababbbaabaabaabbbabaaaaabbaaaaaabbabaabbbbbabaabaababbaaabbabbbbbaaababaaababaabbabaaaababbaabaaaaaaababaabaabaabaaaaabbbaaabbababbbaabbababbbaaaaaabbbabbbabbbabaaaababbabbbbabbbbabbaabaabaaabbbaaabaaaaaaabbbabbbaababbababababbaaabbbbabbbaaaabbabaabbaabbabaaaabbbbbabbabaabbabababaaabababaabbbabbbbaaaabbbababbbbbbbabbbbaabaabbbababbbaabbbaababbbabaaaaaaaabababbaaabaaabbbbbbbbbbaabbaaaaabbbbbbaaaaababbabaaabbabaabbbbbababbabbbbaaaabbaabbbaababbababbbbabaababaababbbaababbbaabaabaaaaaaabbababbabbaaabbbbababaaababaabaabababbabbabababbbbabaaabaaaaaaaababababbbbaabbbbbaaaabaaabaaabbbaababaabbaabbababbaabbaabbbabbababaabbbabbabbabaaabaababbabbaabbabbbbbbabaaaabbabababaababbaaaababbabaaaaabbbabbbbaababbababaababababbbabbbabbababbbbbbbbbbaaaaaaabbbaaabbaabbabbabababbaabbbbabbbbaabbababababaabbbaaaaaababaaabbbabababaabbbbbaabaabbbbbaababbaabbbbbbaabaabbbabbbaababaababbbbabaababbababbaaabbbbbababbbaabbbbabaaaaabaabbabbaaaaabaabaabaabaaababbabbaaaaabaaaabbaabaaabbabbbbabbbabbbbaaaaaaaaaababbbaaaaaaaababbbbaabbaaaabbbabbaaaaabbbabbbbaaababbaaababaaaabaabbbaaaaaaabbaabbbabbbbaabbabbbbaaabaababaabbbaaaababbbaabababbababbabbaaababbbaabababaaabababababbaaabbbaaabbabaabaabaaaaabbbbbabbaaaabaabaaaabbaaabaabaabaaababaabbbbbbbbbbbbaaaaabbbbbbbbbaabbaabbbbbbbabbbaaabbababbbababaaabbaaabaaabababaabaababbbbbbaabbbaaabaaaaaabaaaaababbaababaabbbabbababbaabaaabaaabbababbabbaababbaababbabbaaabbaabbabaabababaaaaaabaabbaabbabaababbbbaaabaabbbbbbabbbabbaaaabbabbabbabbbaabaaabbbaabaabbbabbaaabbbaabaabaaaaaaaaaabaababababbaaabbbbaabbaabaaaabbababbabaababbaabbaaabbaababbbabaaabbbaabbabaabbabaaaabaaabbaabbaabaabbbbabbbabbbaaaabbaabbaabababbaabbbabbaaabababbaabababaabbabaaababaabbabbbbaabbaabbabbbabaababbabbababaaabaaaabbbbbaabaabbbaababbbabaaaabaaababababababaabbabaaabababababbbabbababbbaabbbabbbaababbbbbbabbbbaabbaababbabaaabbbabaabbbbbabaabbabbbaaabaababbababaaaababbbbbababbbaabaabbbbbaabbaababbababaabbbbbbbbbaaabbbbaabbbbaaabbbbbbbaaaaaaabbaabababbbabaaaaaababbbaabababaabbabaaabbabaaaaaaaaaaabbbbbaabbabbaaaababbbbaababbbaabbbbabbbbbabababbabaaaaabbaaabaabbabbbbaaabababbbaabbaaabaabaabbbabaabbaabbbabaaaaaaaabbabaabbbabbbbbabaaabaabaaabaaaaaaabbaabaabbbaabaabaaabbbbababbbbbbbbbbaabbbbaababbaaababbbbbaaaabbbaababbbbbbabbabbaaaabaaabaabbaaaabaaabaaabaaabbabababbaabaaabababbabbbaabbbabaaabbaaabbaabaabbababbbaaababbbbbabbaabbababbbbbaabbbbbbbaabaaabaabbaabbbbaaababbbbaaabaabbbbaabaaaababaababbbbababbbbaaabbaababbbbabbbabbbbbababbbbaaaabbababaababaabaabbbabbaaaabbaababbabaabbaaababbabbabaaaabaaabbbaabaaaabaabbaabbabbbaabbbbbbabbabababbbaabaaabaabbaaaaababaaaababababbbaaabaabbaababaaaabaabbabbabbbbbaaaababbbbbbabbabbbbbaababaabaaaababbbaabaabbbbbabaaabbabbbbabbaabbbaababbbaaaabaaaaababaabbbaabaabaabaabaaaaabbaaabbaabbbabbababaabababbababababaabbaabaaaabbabaaabbbbabbabbbabbaaabababbabaabbabbabaaaabbabbaaaaaaaababaababaaabbabaaaabaaabaaabaabaaabaababbbbaabbbbbbabbbbaaababaabbbabbbabbababbbbbbbabbbabaaaaabbababaabbaabbaaabaabaabaaaabbbbbabbaabbbaababbbbbbaabaabbabababaababbbbaabaabbbaaabbbabaababbbabbbabaababbabbbbbaaaabaabbabaabbababaababaabbbbbbababaababbabbaaaababababaaabbaabbabaabbaaabbababbabababbbababababbaaaabaaabaabaaabaaabbbaaaaaaabbbabbbaaaaaabababbbbabbaabaabaabbbbbaabababbbababbbbaababaabbabbbaabbbbbbbabaaaaababbbabaabbbbabbbaaabaaaabaaaabbabababaaaaaaaaaababbbbbbbaabaabbaaabbaaaababbbaabbbaaababbaaaaaabbababbaabbabbbbaaabbababbabaaabaababababababaabaabaaaabaabaabaababaabbabbabababbbaababaaaaaaaababbbbabbbabbbbbaabbbbaaaaabaababababbbbabbabbabaaaaaababbaabbbababbbabababbaaaabaaaababbbbbbbabbbbabaabbaaaabaabbbabababbabbaabbbaabbaaababbaababaaabbabbbaaaabbbababaaabaababbaabbaabaabbbaabaabbabbbbbbaaaaaabbbbaaabaabbbbababbabaaabaababababaaaabbabbaaabbaabbababbbbbabbbaabbabaabaababbbabbaabbaaaababbbaababaaaabaabaaaabbbbaabaabbbbbababbaabaabaaabaaabbaababababababaabbaabbbaaababbaaabbbaaabbabbabbbaabbbbaaaababbbbabbbaaaaabbbaababbaabbbaabbabbbaabaaaababbabbbbaabaabbbaaababbbbababbabbbbbaabaaaabaaaaabaabababbbbaaabbbbbaaababbaaabbbbbbbbbbbaaaabaababababbbbbbbaaaaababaabbbaaabbababaaabbbaaaabbabbabbbbbaaabaaaaabaaabaaababaaabaaabbbaabbbaababbaaabbbbababaabbbbbbbababbaaaaaabbbbbabbabbaaaaaaabababbbbababbaabbbbbbbbababbaaaabaaaabaaaaabaabbbbabaababbababaabbababaaaabbbbabbbbabbaabbaaabbbbbaaababbbbbbababaaaabababbbabbbbabbaabbbbbbbaabbaaabbabbbbabbbbbbbbaaaabbabaaaaabbaabbaaabbabbbbabbbabaabaabababbaabaabababaabababbbaaabaaaabbabaaababbbaaabaaabbbbbbaabbbbaabbbbabaaabaabaabaabbaaabaababbbaabbbbbabaabbabbbaabbbbbbaabbbbbaabbaaaabababaaaaaabaabbaaaabaaababbbabbababbabaabaabaaabbaaababbaababaaabaaabbbbaabaabbaaaababbabbaaaabbbaaaababbaabaabaababbbaaabbbbbbabbbaabaaabbbbbababaabbaabaababbbaabbbbaaaabbbbaababbaabbabbbbabaabaabaabbabaabaababbbbbbabbbabbaaabbabaabbbaaabaabbbbbbbabaaababbabbbbbbbabbbabaaaabaabbabbbaabaabbaabbbaaaaabbbababababaaaabbbabaaaaaaaababaaabababbbbaabbaabaababbbabababababaababbbbbbbaababbbbababbbaabbaabaaaabbabbbaaababaaaababbaaababbbabbbababbbbaababbbaabbbaababbaabbabbaaabbabbbbbababbaabaaaaababaaaabbaaabaabbabbaaabbbbbbbbaabbbabbabaabbaaaabaaabbbaaabbaabbabbababbaabaaaaabaaababbaabbbbababbabbababbbaaaabbbaaabbababbabbababbabbaaaaabbabbaaabbbbbababbaaaaaaaaaaabbaaaaababaababbbabbababababaababbbababbbaabbaaaaaabbbbabababaaabbaabbaaabbabbaaaaabbabaaaaaaabababbababbbbbaababbaababbaabaababaabaabbaababaaabbababaaababbaaaababaabbaaabbbbabbaabaabbbaaaaaabbbabaababbabbabaabbbbabababbbbaaabaabababbbababbbbababbabaabbabbabbaabbbaaaaabbbbaaaabaabaaabababbbbaaaaababbbababaaaababbbbbabaaaabbbbabbababbaababbbabaaaabbbaabbababbaabbbabaabbabbbabaabbbbbaababbbbabbbbababbbabbbabaaaaaabbbaabababbbaabbabbaaaaaaabbbbbabbbbbaaabaaaababaaaabbaaababbabbababababaabbbababbbaaaaaaabaaababbbabbaaaaababbbabaabaababbbabaaabbabbbbaabbbbbbabbaababbbabaabaaaaabaabbaaaaabbbaaaabbaaababbabaababaabbabbbbbbbabbaabbbaabbabbbabbabbaaaabbbaaabaaaabaabababbbbbbbaaaaaabaabbaababbbababbaabababbaabaaababbababbbbbaabbbbbbbaaababbbababbbaaaaababbbababaaaaabbabababbabbbaabbbaaabaabbbaabbabbabaabaabbbabaaaaaabbabbabbbaaababbababbbbbabaababbababbbbabbababaaaaaababaabbbbbbaababaaababbaaaabbaaaabbabaabbbbaaababaaaaaaabaaabaaaaabaabbaaaaababaaabbaabbabbbaaabbabbabaaaaaabaababaaaaaabababbbbaaaabababbabbbbbbbbaabbbbbbaaaabaaaaababbabababaaaabbbabbaabbbabbbbbbbbbbabbaabbbbaaaabaabbabbaabbbbabbaaaabbabbaabbabaabbaabbbbbbabbbbbbaabbaaababbbaaabbabaaaaababbbbbababababbbbbaabaababababbaaabaaabaabbbababaaaaaabbabbaaabbbbbbbaababaabaabbaaabaaaaaaaaaaabbbbaabbaabbaabaabaaaababbbababbabababbbbaabaaabbaababbabaabbbaaaaaaaabbaabbabbbabaabaaaabbbbabbbbbbbbabbbaaabaaababbaaaaabbaaaaaaababbaabbbbaaabbbbbaabbbbababbababaaababaaaabbbababbbabbbaabbabbaabbbaaabaabbaabababbbbbbabaaaababaaabbabababaaabaabaaaabaaaababbbbaabbaaaabaaaaaaabbaaaabbabbbaababaabbbaabaabbaabbbabbbaaaaaabaaaaabbaabaabbaabbabbbbbbbbbabaaabbbbaababaabababbaaaabababbbabbabbabbbbbabaaababbabaaaaaabaababababbababbbabbbbbbaabbbaabbbbbbbabababbbabbaaaabbababaabaaaabbababaabaaaaaaaaaabbabaababbbaaabbbbaabbabaabababaaaabaaaabbabaabababbbababbaaabbbbbabbbbbbababaabbbaabaabaaabaabababaaaabbabaabbaabaabbabbaaaabbabbbbbbbbbaabaabaabbabbbbaabbababbabababaabaabbababbbbabbaaaabbbbaabbabbabbbbaaabbbabbaababbbbbbbabbbbbaabaaabbaabbabbaaaaabababababaabbabbaababaaabbbabaaaabaabbabbbbababaaababbabbbabababaababaaabaabbbaaababaaabaabbaabbbbbbbbabbbbababababbabbabaabaaaaabbaabbbababbabaaaababbabaaaabbaaaabbabababaaaaabbbbbabbababbaabbabbbaabbbaababbbbbaababbaaabbbbabbbaababaababbaaaabbaaaabbabaabababbabbbaabbbabbbaabbaabbbbaababababaabaaaababbbaaabaabbaabbbbbbbbaabaabababababababbbbaabbaaaaabbbabaabbaabbbbbaaabbbbaaabaaaabaabbaabababbabaabaaaaaabababababbbbbbababbbabaabbaabaababbbaabaaaabaabbabbbaaababaababbaaabaaaabbabababbbbbbbababbbbbbbabababaabbaaaababbabbbbaabaabaabaaabbabbbbabaabbbabaabbabababbbbbabbbbbbababaaaaabbbbbabbaaabbabaaaabbbbabaabbaabbaaabbaaabbbbbabbbbaaabbaaabbaabbbbbaaabbabaaaaaabbaaabbbbaaaaaabbabbbbbaabaaaaabaaaaaaaababbbaabaaaaaaabaabaabbaaabbaabbabbabaaabaabbabaaabbabbbbbbbaaaababbbbaaabababbaabaaaabbbaabbababaabbbbbaaababababbabbabaabaababaabaababbbaaaaabaabaaabbabbaababbaaabababaaaaabbbaaababbababbababbabbbababbbabbbaaaabaabbbaaaaabbabbbbbabbaaabbbbbbbaabbbababbabaaaaabaabaabaaaaabbaaabaababbabbbbbabbabbababaaabbabaaaaaabaaaaabaaabbaaabaaaaabbbbabaababaaabaababbababbbbbbabaaabaabaaabaababbbaabababbbabaabbaaabababaabbababaabbababbaababaaaababbbaaabaaaababbaabaabaabbbaabbaabaaabaabaaababababbaaaaaabbbaabbbbababbabaaabbabbabbbbbbbabbbababababbabaabbaaaabbbaaabaaaababaaabaaababaababbabaaaaaabaabaabbabbaaaaabaaabaabaabbbbaaabbbbbbbabaaabbaabaabbabaaaaabbbbbababbbabbababababbbaababbbaaabbabaabbabaabbbbbabbaabaabbabaaabbbaabbbaabaabbabaaaaabaabbaababababaabbbabbbabbbbaaaababbaaabaaaabbabaaabbbaabaaabababbbabbaabbabbaababbaabbbabaabbbbabbabbbbbbbbbbabbbbaaabababbababbbbaabbaaaabaaaabaabaaabaaaaabbbbbaabbbbabaabaaaabababbababbbbaababaaaababbabababbabbbaabaaabbabaababbbaaaabbababbabbaaabbaabababaabaaababaaabaabababbbabbbaaabbbbaaaaabaaabaaabbbababbbbbaababbbbabbabbaabaaaababbabbbaaababbabaaabbbaaaababababaaabbbbaaabababaaaabbaababbbbabbaaaabaabaabbbabbaaabbaabbabbbbaaababbabbaababaaabaabbabaaababaaaaabbababaabbaabbbabababbabbababaababbabbababbbabbbbabbabbabbabaaaababbaabaabbbbabaaaaababaababaabbababaababaababababbbbbbbbbbaaaaabaaaaaabbbbbabbbbabaaababababbbaabbabbbbaabababbaabaaaaaaabaaabbaaaaabaabbaaaabaabaaaabbabbaabaabaaaaabaaaaabbaaaabbaaababaaababaababaaabaabaabbbabbbaababaaabaabbabaabaaababababaabbbababbbbabbbbbabbaabbaaabaabababaaabbabbaaaaabbababbbabbbbaabaaabaaaabbbbbababbabbbbbabbbbaabbbbbaaabbabaabaababaaabbaabaabbbbbbabbbaaaababaaaaababaabbaabbabbbbaaaaaaababaaaaaaaaaaaababaaaabbbabbaabaaaabaaaaabbabbbbababaabbaaabaaabbaabbabababbbaabbabbbaabaabbaaaaababbbbabbaabbabaabaaaaabaabababaaaaabaaaabbbbbbabbaaaabbabbabaaabbababbbaaaabbbabbabaabaabbbbabaaabaaaaaaabbabaabaabbbaaabbaabbaababaaaabbbbbbbbaabbaabbbbabbbbbbabbaaaaabbbabbbbabbabaaabaaabababaabbbbaaabbaaaabbbbaaaaabaabbabbbbaaaaabbbbabbbabaaaaaaabbbbababababbbbbbababababaaababbababbabababbabbabbaabaababbabbaabababbabaaaaabbbbbabbbbaaaabaaaaaaaaaaaaabbbaabbaaaaabbaababaabbbabbbaaabbabaababbaabbbabbbababbbbaaababbaababbabaaaaaabaaaaaabaaabaaababaabbbbababbbbbbaaaabbbbaababbbabababbbabbbbaabaababbbaabbbaabaabbbbbaabbbabaabbaaabaaaabababbabaaaabbaaaabbbababbbbbbaabbaaaaabaabbbabaabaaababbbbbbbbabbbbbbbababbbaaababbbabbbaabaaaaaaaabbabaaaabbbbbbabbbaaaaabbababaaabaabaaabbaaababaabaabaabbbaabbbabaabaaabbaababbabaaababbbbaaaaaaaabaababaabaababbaabbabaabbabbaaaaabaabaaaaabbbbbaaaabbaabaabbaaaaaabababaaaaabaababbbbbabbbaaababbbaaababbbaaaaababbaaaaaaaaaaababbbabbabbbababbbbbbbbbaaaaaaaaaabbabbbabbbbabbababaabaabbbbbbaaabbbbababbbbaabaaaababababbaaaababbabbbabababaaababbaaabbaaabbaaaaaaabbaabbbbbabbbbabababbabaaabababbaabaaabbbabaaabaabbbaaaabaaaaabbbabababbbaabaaabaaabbbaaaabaaababbbbaabbabbabbaaabaaabbaaabaabbbaabbbbabaabaaaabbababbbabbababbaabbaaabaaabbbaabaabbbbaaaaabbbabaaababbaababbabbaaabbabbaabbabbaabbbaabbabbbbbbabbaababaabbaabbaaaabbabaabaabaabaaaaaaababaaaaabaaaabbabaaaaaaabbabbaaaabaaabababbababaabaabbbbaabbbabaaabbbbaaaabaaaaaaabbaabbabaabababbbabbbbbbaaaabaaabbababbabbbaababaaabaabbaabaaababaababaababbaaabaaabaabbbbabaabbababaabbbbbbbaabbabababababaababbbbaababaababbbbbbbbbbaababaababbabbbbaabbaaabbababbabaababbabaabbabaaaababbabbbaaabbbabaabbaabbaababaaabababaaabbbbabbbabbabbbaabbbabaabaabbabaabbaaabbbabaabababaabbbaaaaaaabaabbbbbbbaaaaaabbaababaaaaaaabbbaababababbaaababbabbbbbaaaaababaaaabaaabbabaaababbbbababbbababbaababaaaabbbbbbaaaababbbabbbbabaaabbbababbabbbabaaabbabbbbbbaabbaabaaaaabbbbbbabbaabbbbbaabababbbbbbabbabaabbbaababbabbabaabbbabaaaaaabbabbbaaaaabaaaabaabaabbbbbbbbabbabbbbbbaabaabaaaababbbabbbabbabaabbabaaaaaabaabaaaabaabbaabaaabababbabaabbabbbbbbbbababbbbababbbbaaaabaaabaababbabbaabbbababbbaabbbaabbabbaabaaaaaaaabaabbabbbbbaababbbbbaabaabbaaaabbbaaaabbbabaabbbbbabbaaaabbbabbbaaabbbaabbababbbbbbbabbaabaaabbabbaaababbaabbbbaaabbaaabbbbbbabaaababbabbbababbabbabbbbaababbababbaaaabaaaababbbaabaabbbabbbbbabbbbbbabbaabbbbaabbabbbbaaaaaababbabbaaaaaabbaabbabbbbabbbbbaabbbbbbabaabaababaababbbbabaaaaaabbabaabaabbaaabaababaaaabababaaabbbbabababbbabbbabbbaabaaaaaabbbbbbabbbaabbbaabbbbbaabbaaaaabbbaaabaaaaabbaabbbaabbbbaababbabababbbbaabaabaaabbaaabbababbbbbbaaababbababbaabaaaaababbbabaaaaababbbbbbbabbaaabbbbbabbaababbaabbabbbabbaaabaaabbabbabbabbababababbbaaaaabaabababbbaabbababbabbbabbbabbabbbaababaaabaaababbaabbabbaaabaabaaaabbbabaabaaaabbbbbaababbbabababaabbbbaaaaaabaabaabaabababbbaaabbbaaaabbbbbbaaaababaabaabaaabbbaabababaabaaabbbbaaaaaaabaababaaababbbbabaaabbabbabaabbabaaaaaabaaaabbbbababbbbbbaaaaaababbaabbaaaababbaababbbabbabaababababaabaaaaabbaabaabababbababbaababbbaabbbbbaabbbababaaaababbbaabbabbaababaaaababaabababbaaaaaabaababbbbbaaabbbaaaabaabbaaaabaaabaabbaaaabbbbbabbbabbaababbbabaababbbabbababaaaaabbabbbbababbabbaabbbaabbbaababbabaaabaabbaabbbaaaabaababbabaaaaaaaababbbaaaababbabbbababaabbbaaaaabbabbbbababaabbbbabababbaaaaaaaabaababbaaabbabbaaabaaabbbabbabbbabbbabababaabbaaaaaabbabbaaaaaabbbbbaaababbbbbababbbbbabaabbababaaabaababbbbaaabaabbaaabbaabaabbbbabbaabbababaaabaaabbabaaabbbbbabbaababbbbabbaaaababbaaabbabbabbabbbbaaaabaabbbaaaaabaaabbaabbaaabbabbaaaaaaaaabbabbaabaaabbaaaaaaababbbbbababaaaaaaabaabbaaabbabbbaabaaababaabbbbbabbbaaaaaabbbbbaabbaabbaaabbbbbbbbaaabbbbbabaabbabbabbbbabbbaabbabbaabbbbbbaabbabbbabbbaabaaabbbabbabbaababbaabaababaabbabbbaaaababaababababbaabbbaabbbabaaabababbbabbabababbbaaabbaabbbabbbbbabbaabaaaabbaaabaaabbaaabbaaababbaabbaabbaabbababbbbabbbbababbabbbbabbaabbabbabababaabbaaabbbabababaaabaaaabbababababbbbbaaabbbbbaabbabbaabbbababbbbababaabbbaabbbaabbbbbbaaaabbbabbbaaaabbbabbaaabbaabbbbaabababaabbbababbbbbbbababbaabbbbbabbaababbbaaabbbaaaababbbababaabaabbbbbbbbaaaabbbaabbbaaaababaabaabbaaabbabbbbabbbaabbbaababbabaabbaaabababbbbaabaaabaabbbbaaaaababaabbaababbabaaabbabbbaabbbbbabbabbaaaabaabbabababbbabbabbbbabbbbbbaabaabbbabbaaaaaaaabbababbbabaabaabbababbaaaababbaababbbaabaababbabbabbaababaaabbabbbbbaabbaababaabbababaaabaaabaabbaaaabbaaabbbaabaaaaaababaaaaabababaabbbbaabaaaababababbabbaabbbbabbbbbbbaabaaabbbabbaaaabbbaabababbabbbbbabbababaaabbbaabaabaabbbbaabbbabbbbbbbaabaaabbbaaaabaaaabaabbabaabbbbabbbbabbabbbbbabbababaaababaaaabbbbbaabbaabababbabbbabbabbbbababbaabbbbbababbbbbbabbbaaaaabbaaabaaaabbaabbbabbaaabbabaaaaaaabbaaaaabbababbbabbaabbbbabbabbbabababbbaaaaaabbabbaaababbbbbabaaaabaaabbabaabaaabaaabbbabababaaabbaaaaabaababbabaababbbbbbaaabaaabbabbbabaabbaabaaaaaabbbbbbabbbbbbabbbbbabbaaaababbaaaababbaabaabaabababbaabababbababbabbaaabababaababaaaabababbaaaaabbbababbbbaabababbbbabbbbabaabbbbbaabaabbaabbbababaababbabbabaaabababbbbabbaaaabbabaabbbbababbbbabbabbabbabbabbabaaaaaabbbbaabbbbbabaaababaaaaababbabbababbbbabababababbabbabaabaaabbabbaaabbaababaabbaaaabbaaaabbbababaabaaabaabaabbaaabaabababbbbaababbaabbbaaaaaaabaabbbabbbabbabbabbabbababbaabbbbabbaababbbbaababbabbbbbabbaababaabbaaaaaabbbbbbabbabbabbbbaaabbbabaabbbabaabbabbaaaaabbbbbaaaaabbaabaabbaababbbbabbababaaaaababbabbbbaabbbbababaaaaaababbaaaaaaabaabbbabbabaaaabaababbababbabbabaabbabaaaabaaaababaabaaaaaaabbbaabaababababbaabbaabaaabbbaababbaabaaabaaaaaabbabbbabbbaaabababbbbbaaabbabababbaaaabbababbbbaabaaabbaabbaaaabbabababbbababaababbabaabbbbbbbbbbbbaaabaaaababaabbabaabbbabbbbbaabbbabaaabbababababaabaabbbaaababbbaaababaaaababbabbbaaabbbaabaaabaabababaabbabbbbbaaababbabaaaaaabbaababbbabbabbbabbaaababbaaababbbbabababbbabbaabbabbbbaaaaaaaabbabbbbaabbbabababbabbaaabaabbaaaabbbbabbabaabbbaabbbbabbbaaabaababbbbaabbabaaaaababbbbbbbbabbabbabaababbbaababbbbababaababbbaaabbaaabbabaaaaaaababbabbabbbbaabbabbaaaaababaaabbabbabbaabbbbbbbbabaaaabbbbbaabbbabaaaabbaabbabbaababbabaababbababbbbababaababbababbbabbaaaabbbabbbaabaaabaabbbbabbbbaaaaabbbbbaabbaabbbaabbbbabaaaaaaababbbbaabbaabbabbbabaaabaabaaabbbabbbbbbabbbbbbbbbaabaaabbbbbbbaaabbaabbbbaaabaaabbbabaabbbababbbaaabaaabbabaabbbbbababbaabbbabbababbbbaaaaaaaabaabaabaaabaaaababaaabbbaaaaabbabababaaaabaabbaaabbabbbbbabbabaaaabaabbbbbbbbbaabbbaaababaaaabaaaaabaaaaaabbaaaabaaabbbabaaababbbabbaabbaabbbaabaaaabaaaaaaaaababaababaabbaababaabaabbbbababababbbababaabbabaabaaaaaabbbbbaabbbaaababababaaaaababaaabbbbbbaabbbbbbaabbbaabbbabaabbbabbaaaabaababaabaabbbbbbabbaaabbbbbbbbabbbababbbabbaaabaaaaaaaaaaabaabbaaabbabaaaababbbaaaabbaababababbbabbbbbabaaabbaaaabbbbabbbabaababbaabbababaaaabbababaabaabaaaaabbaaababaababbbaabaababaabbbaaaaabaaabbbbbbbbbaaabaaaaabbbababbaaaaabbbababaabbbababbbabaabaaabaabbbaabbbbababaaabaaaaaabbaaaaaaaaaaaabbbabbabbbabababbbababababbaaaaabaabbaaaabbbabbbbaabbaaabaabaabababaaababbabbaaaaaabbabaaababababaabbbbaabbbbbabbabbababaaaaabbbbbbabaaaabbababbabbabaaabbbbbbbaabaabbbbabaaabbaababaaabaabbbabbbbbaabaababbabaabaabbababbbabbbaabababaaababbababaabbaabbababbabbbaabbbbabbabbaabbaabbbbbbababbaabaababbaaaabbbaabaaabaaaaaaabbabaaabaabbbaaaaaabbbaaaaaabbbaaababbaabaababaaaaaaaabbbbbaabbaaababbbbabbababbbbababbaaaaaabbbaaaaabaabbaabbabbabaaaaaabbabaabbababbbaaabaababaaaaabbabaaaabbbbbaabbabaabaabaaaabbaabbbbbabbaaaabaaaaaaabbaabbbaabaababbabbbaabbbbbbababbbabbabbbbbbbbbbabbbaabbaaaabbbbabaababababaabbbbbabbbaaabbabbbababbbaaaaaabababbaaabaaabaaaaaaaaaababbbbbbbaaaabbbabbbbaabaabaaababbbabbbbababababbbbaabaabbbabbabaaabaaabbbbababbbbbbabbaabaaabaabaaaaabbbbabbbbaaabbaaabbabababbbabaababbbabbbaaaabaaabbababbbbbabbbabaaaabababbbabaabbbaabaaabaabaaabaabbabababaabaaaabaabaabbaaaabaaaabaabaababaabbaaaabbbabaaaaabaabaabbbbbbbabaabaabbabaaababaababaabbbabaababbaababbaabbaaabbbbaabbaabaabaabbbabbaabbbaaaababababaaaaabaabbbaabbbababaaaaababbbaaababaaababbbaaabaababbabaaabaaababbababaaaabbababbbbaabbbababbbbbaabbbbbbaababaabaabbabaababbbbabbbabbabaaaababbbababbaabbaaaaabaaaabbaabbbababbbbaaabbabbabbbbabbabaaaaaaabbbabbbbabbbbabbaabbababbaaaaabbbbabbbbbbbaabbbaabbbabbaabbabbbaaaaaabbabaaababbaabbbbbbaababbbaaabbabbbbbbbbabaaaaabbabaaaabbabbababaabbaabbaaabbabbbbbababbaaabbbabbbaabaabbbaaaaaaabbbaaababbbabaaababaababababbbabaaaaababbbabbaaaababbbabbaaaabbaabbbbbabaaabbaabaaaabbbabbbabbbabababbbbbaabaaabaaabbaabbbbbbaababbbbabaababbbabbbbaabbabbbbaaababaabbaaababaabbbaaabbbbbabaabbabbbbabbaaaabbbaabbaaabbababbaabbabaaababbaabaaaabababbabbbaaabaababbbaabbbaaaaaabbabbbabbbbbabaabbaaabbbabbbaabaabaababaabbbbaabbbbbbababbbbabbaababaaaabbababbabbaaabbaabbabbbabbbbbbbbabbaaaabbbbabbbbabababbaabaaaaabbabbbbbbaaababbabababbbbaabaaaabaabbabbbaababbabaaabbaaabbaabbaaaababbabbaabbaababaaaabababbabbaaaaaaabbabbbbaabaaabbbbbabbbbaababbababbabbbbbbbbaabbbbabaabaaabaaaaabaaabbaaabbbabbabbaaaababbabaababbbaaaaaaabaabbbbbaaaabbbababbababaabaababbabaabaabbbaaababababbbaaabbaabbbabaaabbbbbaabbbbbabaabbabbbabbaaaaaabbabbbabbaaabbbbaaabaaabbaabaaaababaaabababaabbbaaaabaabbaababaaaaabaabaababbaaabababaaaabaaaaabbbabbbaababbaababbbabbaaababbbbabaaabbbaabaababbaaabbaabbaaaaaababbbaabaaaaababaabababbbbbbababaaabababbbbbbababbaabbbbabbaabbbabaabaaaaaababbbaababbaabbbbbaabbaaabaaabaabbabbbbabaaaabbbbaaabaabaaaaabbbbababbaaabbabaabababaababaabbbbabbbabbbbbbaaababbabaabaaababbbbabaaabbbbbaaabaabbbbaababbbabbbaaabbbabbbbbbbabbbaaaabaabaabbbaabbbaabbaaabbbaabbbbaaabbabaabbbbbbbbbbabbaabaabbabaabaababaabaaabbbbbbaaababbabbaabaaabaaaabbbbbaaaabaabbababaaabbbabaaaaababaaabbbbbaaabbbbaaabaabbbbaaabbbababbbbbabbababaaaabbbaaaaababaabbbaaaababbaaaaabbaaabbabbaabaaabaabaaabbbbaababaabbabbaaabbbabbaaaaaababababababbaabbbbbabbbbababaabababbbabaabbaabbabaaaabbaaabbaaaaaaaaabbbaababbaababbbbaabbaabbbbbbabbaaaabaabbabaaaaababbabaaabaaaaabbaabaabbbbaabbaabbaababbbababaaabbaabaaaaaaaabaaaabbbaabbbbbbabbbabbbabbabababbababbbbbabbbaabaabbbababbabaaabbaabababbaabaaabbababababbabbababaabbbbabbaabaabaaabbabbbaaabaaaabaabaaabbbaaababbabbbaaaaabbaabbbbabaaabbbbabaaabbbbbbbaabbabbabaaabaabbbbbaaaaababaaaaabbbbbabbbaababbaaaaaabbabaabaabbabaaaaababaabababbbababbaabbaaabbaabbbaabaaaabbbabbababababbbbbabbbbabbabaabaaabbaabbabababbbaaaaabbaaabbabaaaaaaaabbbabbababbbbbbbbaababbbaaababbbbababbbbabbabaabbaaaabbbaaabbbbbababaaaababbbbababababbbabbbbbbbabaabbbbabaababbababbabaaaababbaaaabaabbaaabaaababaabbaaabbaaaaabaaaaabaaaababaababaabbbaaabbaaaabbbbbaabaaabaabaabbaababbaabaabbababbbaababababbbbbbbbaabbbababbbbbbaabbbaabaaabbaabbaaaababbbbababbbabbbaababbaaabababaabbababaabbbbbbbaabbabbbbaaabbbaaaaaabaaabbbabaaaabbbaaaabbbababaaabbabaabbbbaaaaaabbbbababaabbbaaabbbbbaabbaabbbababbabbbaabbbbaaaababbbbabbbababbabbbaabaaaaabaababbbabaaabbbbababaababbbaabbbaabbababbbaabababbabaababbbaababbbbaabaaabbbaaaaabbbbabbaabbabaaabbbaaabbbbbaaabbbbaabaabbaaaabbbbaaaabbaabbababbaaabbabbbbaaaabbbaaabaabaaabbbaabababbbabbbabbbababaaaababbbabbabbabbbaabaaababbabbabbbaaaaaabababaabbabaaaaaabaaaaabaaaaaabbbaaabbbbbbbbbbbbbbbbaaaaaababbbbbabbabaabbababaabaabaabbbbaaaaabbabbbabaaaaabbbbabbbaabbabbaaabbbbbababbbaaaababbbbaaaabbaabaabbbaabaabbbbabbbbbaaaaababaaaabbabababababbabaababaaabbbaabbbbbbbbbbabbaaabbbababbababbbbbbaaababababbbaababbaabaabaababbbaabaaabaabbaaababbbaabbbbbbababbbbbaababbbabaababbababbbbabbbbaaabbababbbaabbbbbaabbabbbaabaabaaaabbaaabaaaaabbaabaaaabbaabbaaabbaabbababbabababbbbbabbabaabbabaaaaaabaabbbbbbbbbaabbaaaaabbbaaabbbaabaabbbababababbaaaaaabaabaabababbaaababbabbaaaababbabbbabbbbaaaabbaabbbabbababbbbaabaaaaabbbbaababbbabbaabbabbbbbbabababbbaabaabbaabbbbbaaaabaaabbaababbaabbabababbaaababaaababbbbaabbabbbababbbababbbabbbabbaaaaaaaabbabbbbbaaabaaabbbbbaabbbaabbaabaabbbbbbbbaaababaaaaabaabbbabababbabababbababaabbbbaababaaabbbbbbabababbbabbaaaaaabbbaabaabaababbbbbaaabbbbbabababbabaabbbbbababbbbabaaabbabaababbaabaaabbaaabbaaaaaabaaabbbbaabaababbbbabbbbbababbabbbbaaabaabbbaababaabbaaabbabaaaaaabaabbabbabaaabbbbbbabaabaaaaabaababbbabaabbaaabaabbbbbaabbabbaabbabbabbbbabaaaaaabaaaaababbbaaaabaaaaabbabbbabbabbaaabbbababbbbbaababaabbbbaabbbbaaaabbababbaababbbbbabbbbbabaaaabaaababaaabbbbaabaaaaabbabababbbbbaaabbabbbaaabaaaabbabaaaaabababaaabaabaabbbbaabbbabababbbaababbaababbaaabbbbabaaababaabbabbbaaabbbaaabbbbbababbbabbbabbaabaabbaabbbaabaaaaaabbaabaabbababbabaababbaaaababaababbbbabbbbaabbababaaabaaabbbbbaababbaaabababbbaaabbbbabbaabbbabbbbbabbbabbababbbbaababbbabaaabaaaaaaaaaaabbbbabaabaabbbbbbababaaaaabaaaaaabbabaababbbbabbabbaababbaabaabbbaaaabbbbabaaaababbbaabaabbabbaaaababbaaabaabaabbaaabbbbabaabababbabaababaababaaaaaaaabbabaaabbbaabbbbaababbaababbabaabaaaababaaabababbababaabbaaabbabaaabaabbbbbabaaabababbbaaababbbabbbaababaabbbaabbaabbbaabaababaabbbbabaabbbbabbbbbabbbaababbabaabbaaabbaababbbbaaababababaabbbaaabbaaaaaaababbbbbbbbbaaaaabaabbbbababbbabaabaababbababaabbaabbaabaaaaaaaaaabbbbbbbbabbabbaabbbaabbaaaaabaabababbabbbbaaabbbbbbabaaabbbaabbbbabababababaabbaababbbbbbabbaaaaaaaaababbbaabbbaaaababbaaabbabbaaaabbaaabaaaababbbbababbaaabababbbbabbaaababaaaaaabbaabbbbabbabbbbbaaaaabbabbbabbabaaababaabababaabbbbbabbababbaaaaababbaaaabaaaaaaabbbaabababbaaabbaaaabbbbbaabbbaaaabbababaaabaabbbbaaaaabbbaabbaaababbbabbabaaabaabbaabbabbbbaabbaaaabbbbabbbabbaabaaaabaaaaabbabababbbbbabbbbbabbbababbaabaabbbaabaabbbabbbababababbbbabbababaababbbabbabbbababababaaaabaababbabbbbababbbababaaaababbbabaabbbaaaaabaaaaaaaaaaabbaaabbabbaabaababaabbaaaaaaaabbabbabbbbaabbbaabbbaaaaabaaabbaaababaaabaaaaaaabaababaaaaaaaabbbbbbbbabbabbabbbbaabbaaaaaaabbabbaabaaaabbbbbbaababbbabbbabaaaaaaabaaabbbbbabbaabaababbaaaababaababbababaabbabbbbaabbbbbbbaaababbbaabbbaaabbabaaabaaaaabaabbbbababaababaaababaaaaabaababbbaaaababbaaabaabbbbbbaababaaaabbabbababbbaaababbbaabbbaabbabbababaababbabbbabbaaabaaababaaabbbbababbbabaababbbbbabaaabaaababaabbbababbaababababbabbbbabbaaabbbaaaaaabaababbabaaababbbaabbbbbabbbbbabababbabaaabbbaabbaaabbaabaababbbaabbbaaaabababbababbaababbabababbaababbbaabaabbabbababbbbababbabbbaabbbabaaaabababbabbaabaaabbbbabbabaabbaaabababbaaaaabaaaabaaaabaabbbbbabbbaababbabaaabababaabbbabbbbaabbbaaababaababbaabbaaaaaabbabbbbababbaaaabbbbbbaaaaabbbbaabbaaaaabababbbababbbaabaaababaabbbaaabbabaaaabbbaaabbaabbbbbaabaaabbabaababbaabbabaababbbabbaaaaaabaabbbbaaaabbaababaabbbabbbbbbbaabbbaaabbbababaaaabbaaaabaabbbabaabbaaabbbabaabaaabbbababaabbbabaabbaabbaabbbabaaaabbbbbbaabababaabababbbbaabbbabababbbbaabbbabbaabaaababbaabaabaabbbbbaabbbbbbaaababaabaaaabbbaaaaaabbaabaaaabbbaaaababbbaaaababbbabbbbbbbbaaabbabababbaababbaaabaaaabaabaaaabbbbabaababbaaaabbababbbbbbbaaaaaaabbbbaabaaabbaababbaabbababbbbaabababaabbbababaaaaaaaabbbbbabbaabaaaaabababbaaabaababbbabaabbabaaaaabbbbaaabbbababaaabaaaabaaaaabbbbbbbabbaaabbbaababbabbaaaaababbabaaabbbbaabbaabbbabaabbaababaabaababbabbbabbababbaabbaabbbbbababbbbababbbaaaabbabaaabbbbaabbabaabaabbbabaaaabbabbaababbabbbbbabaaaababababbbbaaababbbbabababbabbbbaaaababaabaabbababaaabaabaaabbabbbbbbbbbbbbabaabbbaabbbbbbabaababbaabbaabbbbbaaabbbbaababbbbbbbbabbbabbabbaabbbbbbabaaaabbbbaaaabbabbaababbababbbbaababbbbbaaaaabaaababababababbaabaababbbaaabaabaaabbbbabaababababaaabaabbaabbbbaaaababbaaaababbabbbabbabbbbaababbabbbaabababbaabbabbbaaaabbabbbaabbaabbbaaaaaaaaaaabbababbbbabaaabbaaaaabaabbbbaabbabbbbababaabbbbbabaabbbababaaaababaaabbbbbbabbabaaabaabbbbbbabaaaaaaaaaababaaabababbbbbaaabaaaaaababaabbbbbabababbbbabbbbabbbbbaaabbbbbababbbaabaabaaababbbabaabaabaaabaaaabababababababbbbbbaaabbbbbabaabaababbbababbbbbbbbbabbabaaabbbababbababbbaaabbaabbabbabbbbbbabbbbbaaabaabaaabababbaababaabaababaaaaababbbbabbaaabbbbbabbbbbbbaababaabbbbabbabababbabaabbbaaabaaababbbababbaababbbabaabaaababababbaaababbbaabbbbbaaaabbbaaabbabbabaaabbabaabbabaabbabaaaaabbbababbaaabaaaaabbbabbabaabbaabbbbbbbbbaabbaababababbaabababbbabababbabaabaaabbbaabbbaaaaaababbababababaaababbbbaaabbbaabbababaababaababbbaabbbbabbbbababababbabbbbababbabbbbaaabbaaabaabaababbbbbabbaaaaabababbaababbbababaaaabbbababaaaaabbbabbbabbababbbbbbbbabbabaabbaabaababaaabbbabbaaabaaaabbbbbabbbabbabbabaaaabbababaaabbbbbabbbaaaabbbbabbbbaabbababaabbbbbbbbbbaaabbbaabbabbaabaaaaabbabbbaabbbaaababbbaabbbbabbabaababbbaabaaabaaabababbbaabbbabaabbabbbabababbababbaabaaababaabaababbabaabbbabbaabaaaabbbabaaabaabbbabababbbaaabbbbababaababbabaabaababbaaaaaaaaababaaaaabbbbbaababbbbbababbababaabaabbbbabbbaaababaaabbababbbbbbabbaaabbbbbbbbababaabbbaaabbaaabbbabaabbbabaabaaabbabbababbbbbbbbabbbabbbbbbbbbabbaaaaaaabbaabbaababaabbababbabbababbbaabaaaaabaabbaabaabaabaaaaabbaababaabbaaaaaabaabaabaabbbabbababbbabaaaaabbbaababbaabaaabaabaabaabbabaabbbbabababaaabbbabbbbbbabbbbbababbabaabbaaaaaaabababaabababababbbaaababbaabaabaabbaabbabbaaabbaabaababbabbaaaabaababbababababababbbaaabaabaaaabbaaabaaaaaabbabaaaababababbbabbbaabaabbabaaaabaaaaabbabbbbaabaaaaaabbbbabbbbaaaaabaababbbbabaaabaaaabababaaabbaabbbababaabbaaababaaabaabaabaaabababaaaabaabbabbabbaaaaababbbabaaabbaaaababababbaababbababbbbaabbabbbbabbaaaaabbababbbbbaaaabbbbaaabaaabaababaaaabbaaaaabbabbbbbabbaaabaababaabababbabaaabbbbabbaaaababbabbbabbabaabbbabaabbbababbababbaababababbbbbabababbbbbbbaabbaaabaaabbbbbaabbbbbabbabbbbaaabbbbbaaaaabbbababbabbbabbaaaabaababbabaabaabaaaabbbaaaaaabbbbaaabbabaaabbbbabaaaabbaaabababaaaabbbbabbabbbaaaaaabbaaababbbaabbbbbabaaaabbabbaaaabbbbaaaabababbabbabbbabbaaaabbbababbaababababaaabbbabbbbaabbbaaabababaaabbbababaaaaaabaaabaaabaabbbaaaababbabaabbbabbbbabbbbbbbababbabbbbbbbbbaabaaaaaabbbabaaababaaaaaaaabbabbbabaababbaaabbbbbaabaaaaaabbbabbababbbbbabaabaabaaaaabbbbbbabbabaaabbaaaaabbbababbababbaaaaaaababbaababbabaaaaababbaababbaaabaabaabaaaaabbbaabbbababababbabbaabbaaaaabaaabbbbababbabbbbabbabaabbaabbabaabbbaabaaabbbaaababbbbaabbbababbaaaabaaaaaabaabababbbabaabbabaabbbbaaabbbaababbbbababaabbaabbbbabaabbababbaaaabbaaababbbaaaaaaababbaabbaaabbababbaabaaabbaaabbabababbaaaabbabbababbaabbbbabbbaababbbbaabbabaaaabbbaaaabbabbbabaababaababbababbabbbabbbbababbaaabbbbbbbbbbabbbabbbbaaaabbabbababbaabbabbaabababaabaabbaaaababbbabaaaabbaaababbbbbabaaaababbabaaaabaabababababaabaabbabbbbaaaabbaaaaaaaaaaabbbaaaaaaaaaaababbbaabbbaaaabaaaabaabaabbabbbabbabbbababbaaaabbabababaabbbbaaaababbabbabaaababbbabbbaabbababbbbaaabaaaabaabaabbabbaabbaaaababbaababbaaaabababbabababbbbbbaaaabababbabaaaaababaaabbbbababaabababbbbbabbabbaabbababaaabaaaababaaabaaabbaaaabbaaabbaaaaabababaababbbaabaabbbaaaaaabbbbabbbabababbbabbbaabbabababbbbbaaabaabaabaabbaababaaabbbababbbbababbbbbabbabbaabaaabbababaaabaaabaabaabababaaabbbaaabbbbbbbbabbbbaabababababaabaabbabababaababbababaaabbbaaaaaaaaabbbaabbaababbbbbabaabbbaabbaabaabaabbbbabbbabaabaaabbbbbbabaaabbbaabaabababaaabbaababbbababaabbaabbbbaabaaaabbaabbbbbabbabbbbbbabbbaaaaabaabbabaaaabaaaabbbabbabbbababbaababaabbaababaabbaababaaaaaaabbbabbbabbaabbbababbaaaaabaabaabaabbbabbaaabbbbbaaabbabbbaaaabbbaaaaabbaabbabbabababbbabbaabbaaabbaaaaababbbbaababbabaabbaababbbbabbaaabbabbaaabaaaaaaabaabbbbabbabaaababaabababbbbbabaabaabaabbbabbbbbbabaaaaaabbbabaabbaaababaabababbaaaaaabbbbbbaaabababababbbbbbaaaaaaababbbabaaababababbbbabbaabbabaaabbaaaaaaabbabababbaaabbaaabababaaabbbabbbabaaaababbbbbbbbbbaaaaaabaababbabbabbabbaabbaabaaaaaaaaabaaaaabbaabbabbabbabbbbbaabbbbbabbbbbabbbbabbbabaaaaaabbaaaabbaababbaabababbaaabbbaababaaabbabaaabbabababaaabbabbaababababbaababbbbaaabbbbabbbbaabaabaabaaaaaaabababababbbbbabaababbbbaabaaaabaaaaaabbbbabaaababbaaabbbabbababbbaabababaababbbbbabbbaaaaabbbaaabbaaabababbabbabbabbaaaabaaabababaaabababbaaabbbabbabbbbbabababbbabbababbbaabaabbabaaabbbaabbaaaaaababbbbabbababaabbababbbbbabbaababbbbabaaabbbababbbabbbbaaaaabaabaaaabaaaaaaaabbbbbaaabbbbabbbaaabaababbbababbbbaaaabaabaaaaabbababbabbaabbbbbbbaaabaaaabbabaabbbbaaaabababbbbbbaaabaaabababaaaaabaabbabaaaaababaabbabbabbabbabaabaaabbabaabaabababbaaabababbbaaaaabbbababaabbaabaaaaaaaabbaaaaabaaabbababaaaaaaababbbaabbbbbabaaabbaababaaaaabaaabbbabaababbbaaaaaaaabbaababbabbbbabbabbbbabbbababbabbabaababbbaaaabbbbbabaaaabbaababbabbbbaaaabbabbaabaabbbbbbbaaaabbbabbbaaabaaaaaabbbaaaaaabbabaabbaaabbbabbbbababbaaaaabbabbbbaaabbabbaabbabaaababbbbabbbababbabbababaabaababaababbaabbbbaaaabbbbbaaaaaaabbbbbbaaaaababbabaabbbabbaabbaabaaaabbaaabaababbabaaaaaabbbbaaabaabbbbbbaaaabaabbbbbaabaaabbbbabbbaabbbabbbabaababaaaabaaaabbbabbabaababaabbbabbaaaaabaaabaaababbabaababbaabbbaaaaababaaabbababbababaabbbbbbbabbaababababaabababababbaaaabbbbbabbbabbaaabbbbaaabbaaaaabaabbababbabaababbbaaaababababbbbbbbbaababbbabbaabaaabbbbbaaaabbbabaabaabaaabababbbaaaabbabaabbaaaababaabaabababaaaabbbaaababbabbbbaabbaaaaaaababbbaaaaaaaaaaaabaaaaabbbbbbaaaabbbbaaabbbbbbbaabbbbaabbababbbbbaaaabbbbaaaabbabaaabbababbabaabbbbbbbabbabbabaaaaaabaaabbaabbbababbaabaabbaaababbbabababbbaababbbbabaabbbabaabaabaabbaaaaabaabaaabbabbabaaaabaaaaababbaabbaaaaaabbbabbbabbbbbbbbbabbbbaabbaaabaabaaabbaabababaabbabbababbaaabbabbabaabbabbabbaabaaababbbbbbababbbaabbbbababbaaaabbbaaababbabbabaaaaabbabaaaaabbbbbbababaaaababaabaababaabaaaaabbaaaaaabbbabaababbaaaaabbabbbaabbbaabaabbbbaababbaaabbaabaaaabbbababababbabababbbbbbaaaaabbabbbababaaaaaabbabbaababbbaaababbbbaaabababaabbabbbabbabbabaabaaabaaabbbbaaaaaabbbbababbababbaaababababbbbbaababbababbbbaabbaabbaababbabbaaababaaabaaaabaaabaabaabbbaaababbbababbababbaabaabaaabbaabbbbaabbaababababbbbbabbaabaabbabababbaaababaabbbabaabaaabaaaaabbbbabbabbbbbbaaaaabaabbbbbbabbaaaabaaababbabbabbaabbaaabbbabaaaaabbaaabbbabbbaabbbbbaabbbabbabbabaabbabbaaaaabbababbabbbabbbabbabbabbaabbaababababaaabbabbbaaabaaabbbaababbabbbbabbaabaabbaaaaababbbbababbaabaaabbbabbbabbababaaaaabaabaaaaababbaaaabaabaabababaaabbbabbbabaaaaaabaaaaababbaabbabbaabbaaabbabbbbbbabbbbaaabbbabaabaababaabbbbbbabbbaaaaaabaaaaabbaaabaaaaabbbbabbabaabaababbbabababbbbbbbbaabaaaaaaaabababbaaabbbbabababbbbabaabbbbbaabbabaaabababbaaaaaaaababbaaaaaaaabbbbbbbaabbbbbbaabababbbababbabbbabbaabbbabbabbabaaaabbbbaaabbbbbbaaaabaabababbabbbabbbbaababbbabbbbabbbabababbbababbbaaabaababbbbbaaabbaaaabaabaaabbbaaababaababaaaabbbbbbbbbabbaaaabaababbbaabaaabaabaabbbbaaaabaaabbabaaaabaaabbaaabbaaaaabbbaabaaabbabaabaabbbababaaabaaabbaaaabaababbbbbbbabaababaaabbabbbbaabababbaaaaabbbbbaababbbbaabaababbaaababaaaababbbabbbaabbabbaabbbbaababbbbababababbbbbabaaaaabbbabaaaabbababababbaabaaabbbbbbbbaababaabbaaabbaaababaabbaaabbbabbbababbabbbabbbbbbbbabbbabaabaababbbaaabababbbbbbaaabbabaaaababbbabbbbabbbabbbaaabaaaabbaaaabbaaababababbbabbababbbbbabaaabbababaaaaabaaaaabbbbabbbaaaabbbbbbbbaaaababbbaabbabbbbbababbaaaabbbbbabbabaabbaaabababaabbaaabbbabbababaabababaaaababbabaaabbbbbbabbbaabbabaaababaaaaaaababaaaabbaaabbbbaababbaabbababbbbaabbaabbbbbabaabaabbbbbababaaaababbabaaabbababbbaabbaababbababbaaaabababbababbababbbbababbbabbaababbababbbabbbbbbbababbaaaaaaabababbbbabbaabbaaababbaaaaabaaababbbbababbababbbaaaaaababbbbbbbbabbaabbaabbaababaabbababbababbaababbbbabbbbbaaabbaaaabbaaaaabbaaaaaaaaabababaaaaababaabbaabaabbbbbaabbbbaaabbbaabbbababababbabaaaabbbaabaabababbaaaaababaaaaaaaabbbbbabaabbbaaaaaaaabaabbbbabbbbbbbaabaaabbaaaabaababbabbaababaabbbababbbaabaaabbbbbbaabbbaabababbbabbabaabbbabbaaaabaabbbabbabaababaaabaabababbbaaaaabaabbbbbaabbbbaabaaabbbbbbaabbbabaabaabababbaaabbbabbabaabababbbbabababbbababaabaabbbbabbbabbabaaaabbbabaaabaabababbaabbbabbbbbbbabbbaababbbabababbaaaaabbaabbaabbaaaaabaaabaaabaaaababaabaaabaaaaaabbaabbbaababbaaabababbbabaabbaaabbaaabbaabbbbabbaabaabbabaabaaababbababbbbbbaababbbbabbabaaabbaabaabbababbbaabaaabbabbabbaaabaaabbbbbbbbbababbaaabababaaabaababbbaababbbbbbbbbbbaaaababbbbabbabbaabaaabbbaabbbbbababbbabbbaabbaaaaababbbbbababababbabbababbaabbbababbabaabaabbaabbbabbbbabbabbabaaabababaabbaaababbbbbbbabbaaaaaaabaabaabbababbaababbabaabbbbbbabbabaabaabbaaabbaaabbbbbbaabbbabbbabaaabaabbaabbabbbabbaabbababaaabbabbbababbaaaaabbabbbabaaaabababbbabbaababaaabbaaababbaaaababaaabaabbbabababababbbbabababbabbbabbbbbbabbbababbbaabaabbaabaabaaaabaabaabbbbbbabbabbaaababbbbbaabababaabbaabababbaabaaababababbbbaababbabbbaabaabaaaabbabbbbabaabaaababaaaaaabbababaaababbbaababababaababbababbabaabbbbabbabaabbaaabababababbabbbbabbabbbaabbbaabbabaabbbabaabbbbbabaaababbbbabbbbaabaaababbbababaabbaaabbbaaabbababbababababbabbabbbbbaabbbbbaaaaaabaaababaaaabbabbabbaaabbabbabbaabbbabaaaaabbaababaaaabbaaaabbababababbbbbabbaabbabaaabbbbbbbbbababaabaabaaabaaaaabbababbbabbbaaaaabbaaaaaabbabbaabaaababaaaaabbaaabbaabaabaaaaaabaaabbabbababbabbaababaaabbbbbbaabaaaabaaaabbaabbbabbabbbababbbbabbbbbbaaaabbabaababbbbabaabbbbabbabbbabbbaababaabaabaaabaababababababaababaabaabbaaaaaaaabbbaaaaabbbabbabbbaaabbabbaababaabbbbaabaaaabababbbbbabaaabbabababbababbbbaaabbbabaaabaaabaaabbbbabbabaabbabbbbababbabbabbbbbbbababaabbbabbabaaaabbabbaabaaabbabbaaaabaabbaabbbbbbaaababbbbaabbaabbaabaaaaabbbbbbabbbabaabbaabaaababbabbbaaabbaabaabababaaaabbabaabababbaababaababbabaaaabbbaabbabaabbbaaaabbaabbbaabaabaaaabaaaaababbbbababababbbabbaaaabbbbaabbbaababaaababbaaabbbbbbbbababaaabaaaabbbaaabaaaaabababbbabaabababaaaabaababbbbbbabbbabaabaabbbaaabaabaaabaaaaabaabbbbaabbbababbaaabbabbaabbbbaabababaaaaabbaaaaabaaaabaabbbbabaaaaaaabaaabaaabaaabbbababbbaabababaabbbabbbababaabaabababababbbaaababbbbbbaaabaaabbbaaaaaaabaabaabbaaabbbbaaabbbaabaaababbbabababbabbbabbabbaababbbaaabbabaaabbabaabbaabaaaaaaabbbabbaaabbaabbababbbabbbbbbabbbbbbbaaabbaababbabaabbaaabaababaaabbaabbbbaabbbbabbaaaaaaabaaaabaabbabaabbbabbaaababaabaabaabbbbababbbabbabbbbbabbaabbbbbbbbabbbabbbabbbabbbaaaaaabaaabbabaababbabbbaabaabbaaababbbababaaabaaaabaaaabaaaabaaabbbababaabbaabaababbaabbaaaaabbaabaababbaaababbbaabbaaabaababbabbaaaabaaabbababaaabbbbababbabbaabababbababaaaababbaabababbbabbaaaaaabaababaabbabbbbbaabaabababaaabaaaabbaaabbaababababbbabbaaabbaaaabbabbaabbbaaaabbaabbbbaabaaaabaaabaaabaabbbbaaabaaabbaaababaabbbbbaaaaaaabbabbabbbbaaabbaaabaaaabbabaabbabaaabaabaaaaaaaabaaabbbaaaaababaababbbabbababbaabbababababaaabbbabbbbbbabbabbbbbabbbabbbbbbbbbabaaababaaaababbbbaababbabaabbbaabababbbabbaabbaabaaabababbbaabababaaabaaabbbbbbbaaabbbbabbbbabbabbbaaaaababbbbabaabbbabbbabbbbabaabbbbabbbabbbabbabbababbbbaabaabbaaabaaababaabbbaaababaaabbabbbabbbbbbbaaaabaabbabbaaaaabbbbaabaaabaabbbbbabaaabaaaabbbbbbbaababbabaababbbaaabbbbbbabbbaabbbaaaaaabbabbabaaabababbbbbbbbaaaabbaabaabbaaababaaaaababaaabaaabbbbaaabbaabbbabababbbbbaabaaaaaabaabbbbbbabaababbbbbabaabbbaaaaabbbaabaabaabbbbbbbbbabbababbabaaaabbbbababbaababbaabaaaabbbbaaaaabbbabbbaaaababbaaabbaababbaabababbaaababaaaababaabbbbabababbbbabbaabbbaababbbababbababaaaabaabaabbbaaabbaabbbbaabbbabaaabbbbbaabaaaaaaaabababbbabbababbbbbbbbbbbaaabbbbababbaababbaabbaaaaabbbaababbbbbabbabaabbababaaaababaabaaaababbabbbaabababaaaabbaaaaabbbaababaaaabaabaaaaababaaabaaabababaaaaaabbabaabbbbbbaaaabaababaaaaaabbababaababbbaabaabaaaaaabbaabbaaaaabbbaabaaabaaaabaabaaabbabbaaaaabbbababaaabbabbbbbaaabbabbbaaabbaabbabbbbababaabbbaababaabaaaaaaabbaabaabbaabbbbabaaaabbabaababbbaaaabaabaaabaaabbbaaaabbaabaababaaabbbaabbbbbabbbbaabbbbbabbbbaabbbbabaaabaabaababbbaaaabbabbabbaaabaaaaaabaaaaaabbbbbbaaaabbbbbabbbbbaaabababbbbbabbbbbbabaaabbbabbbbaaabbaaaabaababbbaabaaaabaaaaaabbabaaababbbaababaaabababbaaabbbbaabaababbababbabbbbabbbaababbaaabbabaaaaaaaaabbabbaaaaabaabbbaaaabbaaaaabbbbaababbbbbaabaabaabbbbbabaabaabbaabbbbabaaabaabbaaaababbbbaaabaabbbababbaabaaabaabbaabbbaabbbbbbbabbbbaaaabaabaabbbbbabbbbbbaaabbaabbaabbaaabbbabbbbbabaabbbaaabbbbbbabbabbbaabbaabbbabbbbaabbabababbbabaaaabbbaaabbabbbbbbabbabbaaaaaababbaabbbabaababbbbbabaabaabaaabbbaabbbaaabbbbbaaabbbabaaabbaabbbbabbaabababbaabaabbabbbaaabbbbbbbbbbbabbabbaaaabaaaaaabaaaabbbbbabaaabbbabaaababbbababaaaabababbbababaabbaaabaabaaabababaaaabbaababaaaaabababbbbabbbababababaaaababbbbbaabababababababbbababbaaaabaabbbbbaaababbaababbbbaaaabaababaaaabbabaabaaabbbbbabbbabbbbaabbbababaabbbaababbbaaaabbaabbbbaabbaabbbabbbabaabaaaaabbbbbaaabbabbbbabaaaababbbabaaaaababbbaaaabbbbbbabaababbbbbbaaaaaaabaaaaaabbabababbbabababbababaaaabaababababaabbbbbaabbabaaaabbabbbbaaabbbbaababbbbabbbbabaabaabbbbbbaabbbbaaabaabaababaababbababaaaabaabaaaabbbabbabbbaabaaabbbbababbabababbabbbaaabbaaabababaabbbbbbbaababbbaabaaaabbbbbababaabaabaaabbaaaabbaabbaaaabbbaabbbbbaabbabbbabbaaabbbbaaaababbaaabaabbaaabaaaabbabbbaaaabbaaaabaaaaaaaabbababaaabaababbaaaaaaaabbaaabbaabaababbabaaabbbbbbabaabaababaaaaaaabaababbabbaaaaabbababbaaaaaabbbabbbbabbbbaaabababbaabbbaaaabaaaabbbaaabbabaaaabbaaabbbabbaaabaaabbabbbbaabbbbbabababbbababbbababbababaaaababbbbaabbbbbbaabababbbbbbaabbbbabbabbabaaaabbbabbabababaabaaaaabbaaabababaababbbabbbabaaababbbaaabbbabbbaaaabbabaabaabbabbaabbaabaaabbbbabaaaabbbbabaabbaaabbbbbaaabaaabbbbaaababaabaaaaaaabbbababbbabaaaaababbbababbabaaabaaabbbbaaaaababbaabaababbbabbbabbabbabababbabbbaaaabaabbbbabbbbabababbbbaabbaabaabbabbaaabaaababbabbbbabaabbbbaaaaabbabbaabbababbaababbabbaaababbaabbbabababaaaababbbabbbabaabbababbababbabbaaabaabaaaaabaababaababbabbabaababbbbbbbbbbbbbababbbabaabbbbbabbaabababbbabaaaaabbaabbabaaaaaabaababbabbbbbaabbaabbababaaaaabaaaaaabbababaaaaaaaaabbabbabaaaabbbaabbaaabaaaaaabbbaabbaaabbbaabaaabaabbaaababbaaaabbbaababaabbbbbaabbbbaabbabbababaaababaaabbbbaaaabbabaaaaabababaabbbaabaaabbbbaabbbaaabaababbabaabaabbbaabbbbbbaaaabbbbabaaabbbabbbbbababbaabababbabbbbbbbbaaabaaaabaaabbbbbbabbaabbbbbabbbaabbaababaabaabababbaaaabbbbbbbaaaaaabaabaabaabaabbabbbbbabbbaaaaaaabbaabababaabbabaabababababbabbbbabaaaabbabaabbbaaaabbbbabaabbabbbbaabbbbaabbaaaaabaabaaabbabbbabbbbaaaabbaaabbbaababbabababbbbbababbbbababaaaababaababaababbbaaabababbabbaaabbbabbbababbaaabbabaabaaabbbbbbaabaaabaabbaabababbaabbbbaaaaaaaaaaabbbaabaaaabbabbbababbbbbaaaaaaabbaaaaaaaababaaaabbabababababaabbaaaaabbbbbbbabbbbaaaaabbaaaaabaaababbbbaaabaaababbabbbaaabbabaabbabbaaaabbbabaababbaabbbbbbabbbbbabbbababaaaaaaaababbabaabaaaaababaaaaaaaaaabbabbabbaaaababaaabbaabbbbaabbbaaaababababaaaaababbabbabbbbbbabbbabbaabbababbaabbbaaaaabaaababbbabaaababababaaaababbbbabababbbbbbaabaaaaababbabaababbbabbbbbaabaabbbabbabbaaabbaabbaabaabaabaabbaaabbbbabbbbaaabaaabaaaabaaabaaaaabaabbaaababaabbbabbbbabaabbabbaaaabbbbbbbabbabbabbbaabbbababbababaaaaaabababbbbaaabbaabaaaabaaaaabbbaaaabbbaababbabbababbbabaaabababbbababababbaaaabababaabbbbabbaabbaabbbabbbbbbabaababaaaabbbbbbaabbabbabaaabbbbbaaababbbababbbabbaaabbbbababaaaaabaabaabbbbabaabbaaaaaabaabbaabbbabababbbabaabaababbbbbababbaaabbbaababaabbaaaaabbaabbabbbababbbbabaabbbaabaababbaaaaabbababbbbabaabababbabbaaaabaabbbabbbbbabaaaaabbaabbaaaabbaababaaabbbbaabbbbbbbaaabbaaaaabbbbbbbbaabbaabaaabaaaaaabbaaaaaaabbbbaabbabaaabbbbaabbabbbbabbaaabbaaabababbbbabbababbbaabbabbaaabbaabaabaabaabaaababbaabaaaaabaabbbabaaababbbbabbabbbabbaaaabbbababbabababaabbabaababbabbaaaaaaabbaababbabbbaabaaaabaaaabbabaaaabbabbbbbaabbaabaababbaabbbbababbaabbbababaabbbbbbaaabbaaaabababbabaabbbabbbabbbabaaabbabbbbbaaaaaabbbabbbbbbabbbabaababbbabbbbbbabbaabaababbaababababbabbbaaaabbbaabbaababbbbbbaababababaaabbabbabbbbbbabbbbabaabbbbbabbababaaaaabbaababbbaabbaaababbbaababaabbaabbbbbababbabbbbbbabaaaabaabbaabbbbabbababababaaabababbaabababbaabbbbbbbabaaabaabaaaaaaabaaaaaaaaabbbabbabbaabbaabbabbbbbabbbaaaabaabaabaabaabaaabaabbabaaaaaaabaaaaaabaaababaaabbaaaababbaabababbabbbabaaaabababaaaabaabaabbbabababbabbbabaaabaababaabaaaaaaabaabaaabaabbbabbaabbabbbaabaabbbbabaabbaabbbbbbababbbaabbaababbbbbaaaababbbbbaabbbbbaaaaababaaabbbabbbbbaaaabbababaaaabbabbabbbbaabaabbbbbbabaaaaaaabaabaaabbbbbbbbabbaabbaaababaaaabaabaaababaaaaabbbbbbaaaababbbbabbbbaaaabbaabbabbabbaaabbababbaabbbabbaabbbbabababaabbabbaaaabbbaababbbaaababbaabbaabaabaabbbbababaababbbbbabbababbaabaabbbabbabbababbaababbbaaabbababbabbbaababababaaaababbababbbaaabaaabbaaaabbabbaababbbbaaaaababbbababbaabbaabbbaababaaabababababbbbaaaababbbbabbbbbbaabbbabaaababababbbaabbaabaaabbaaababbbbbbbaabbbbaabbaaababbaaabbabbbbabbbbaaabbabbaabbaaaaabbbababbabaaaabaaaaababbbaaaaabaabbbabbbabbaaabaaababbbbbabbbbbbabaabbbbaababbaaaaabbaabbaabbabbbbaabbabbaaaaabbababbababbbbabbabbaaaababbaabbbaabaababbabaaaaabaabaabbbaabaaaaabaaabaabbbababaabbaaaabaaababbabbabaaababbbababbabaaaaaaabbabbbaaabbbbabaabbaabbbbbabbbbbbabbbabababbbbaabaabbbbabbaabaababbbababbbaaababbbbaabbabbbbbbbbababbbbbaaabbbaaabbbbbabaaabababbbababababbbaababbbbbbababaaabbbabaabbabbbbaabbbbbbaabaaabaaaababaaaaaabbabaaabbbabbbaaababbbbabaaabababbbbbbbaabbababbaabaabbbbabaaabbaaaabbabbabbbbabbbabbabbbbaababbbbbaabaaaaabbabaababbbbabababbbabbbabaabaaaabbbabbbbabbababbbbabaaaaabbababbbaababbabbbbababbabbbbabaaaaabbbbabababaaaabaaabbabaababbaababababbbaabababaaaabbabbabaaabaabaabbababbabbbbbbaabbbbbbabaaaaababababbbbbbabbaabaaaababbaaabbbababaaabbbbbaababaabbaabaabbbabbbaababaabbbaaaaaabbbababaabababbaaabbbababaabaaabbbbbabbaaaaaaaabbabaabbaaababababaababaabaaabaabbaabbaabbabbaababbaabaaaabbaaabbaaaabbaaaabababbaaababaaaaababaaabaabbbaaaaabaaabbaabbbbaaababbaababaaabbaaaabaabababbbbbbbbbabaaaaaaababaabbbbabaaaababbaabbbbaaabaaabbaaabbbbbaaaabbaabbbababaaaaabbbaabaababbbbaaaabbbbabbaaababbabaabaaabbbbaaaabaabbbaaaaabbaabbaabbbaababbbbbaabbbbbbabaaabbbabababbaaaabbabbaaaaabbaaabaaabbabaabbbbabbbaabbaabbaabababbababbabbaaabbaabababbabbbabaababaababbbabbababaabbabbbbaabbbbabbaaaabaabbbabaaabbbabaaaabbbabbbabbbaaabbababaababbbabbbbbbabbbababaabaabaaabbabbabbbbbbabbabaabbbbaabbabbbbbbbbabbbaabbabbbbbabababbaaabaababaaabbbbbbbbaabaababbbabbaabbabbabababbaaabbabbaabbaabbbbbbbaabaaaaabbababbbaaabaabbbbaaaabbaabbaaaabbabbbbaabbababbababaabbbabbbbbbabbaabababbabbbababbabbabbabbbabbababbabbbbaabbaabababaaaabbabbabaaaabbbabababbabbabbabbaabaaababbabbbbaabbbbbaabbabbbaaaabaababbbabababbaaaabaabaabbbabaabbabbbbbbabbabaaaaabbaaababbbaaaaaaaaaaaabbaabbabaaabbaabbbaaaabbabababaaababbaaaaaaababbaaabaaaabaabbbbbaabaabbabbababbbbbaaabbaabababbbaababbbaababaaaababaabaaabaaabbbaaabaaababbaabaabaabbaabaabaaaaaaaaabbbbaaaaabaabaabbbaabaabababbaabbabbabbbaaabbbbbaabaabaaababbbabababaaaabbaabbbbaabbbaabbbbabbabaabbaaaaaaababaaaabbbbbbbababaaabaaabbaaaaaabbaaabababbabbababaaaaabbabbaabababbabaabbaaaabbabababaaabaabbbaaaabbbbbaaaabbbaaaaaaabaababbbbbbaaabbaabbbbbbabbaabbbaabbabbbbbabababaabbbaababaabbabbaaaaabbbbaabbbbabbaaaaabbaaabaaaaabbbbbbaabbababaabaabbaaaabaaabaabaabbabbabbbbabaabbaaaababbbabaaababababbbaabbbaaabbaabbaaaaabbbbbbbbabbbbabaaaabbaaababbbbbabbbabaaaaabaabaababbbbbbbbaaaababaaababbaabaabbbababbababaaaaabababaababbaabaabaabbabbbbababababbbabababaabbbaabaabbabbabbbbbababbaabbaaabbbaabaaaaaaabaaabababbbaabaaaaabbbaaabaaabbabbbbaaababbbbbabbaaababbaaabbbaaababaaaababbbbaaaaaabbaaabbbaaabbababbababaabaabbbbaaabbbaaabbabbaaaabbabbbaaabaaabbbbababaaaabaabaaabbbaabbbbbbabbbbabaababbbbbbabbaaaaaabbaabbababbaabbaabbaabbaaabaaabbbbabaababaababaaaaaaaabaabababbaaababbbbbbbbbaaabbabbabbaabbbababaabbbbaababaaaaaabbbbaabababaaababbabbbababaabbababbbbbaaaaaababaaabbabababbabbbababbbaaaabbbbbaaaaabbbabaaaabbbbaabaaaaabbbababbaabbbaaabbabbbaaabaaaaaaaaaaabbaabbbabbbaaaabaaaabbbaababaaababbaababbbaabbbabbbabaabbaaabababaaabaabbaaaabbbabbaaaabbbbbabbaabbbaaababbabbbbaaaaaabbaaaaababaababbbbbbbbbbbbbaabaabbababbabaaabaababbbaabbbbbaababaabababbbbbbbbabbaababaaaabbbabaaabbbbbaababaaaaabbbaabbabaabbaababaababbabaabbbbbbbbbaaaaaabbbbbbbabbbaaabbaaaabaaaaabbbbbaabbaaaaaaababaabbabaaabbaabaabaaaabbabaabbabbabbbbbabbaaabbbbabababbaabbaabaaaaaababaaabaababaaabbbbabaaabababaabbbbbbbabaaabbaabbbabababbbaababbbaabbbaaabbabaababbabaaabaabaababaaaaababbbbbaaabbaabaababbaaabaaaaabbbbbaababbabbbbbaaaaabbaaaabbabbabababaaababbaabbabbbabbaabbbbabbaabbabbabababbaaabbababbbaabaaaaaaaaabaabaaabbbaaaaaaaaaaabbbabbaaaaabbaaabbaabbabbaabbabaababaababbaababbbaaabababbbaabababaaababbaaabaaaaabaababbbbbbbaabbbbbbaaabbbabbbabbbabaaabbabbabbbbbaababbaabaabbbbbbbaaaaaaabaaababababbbbaabbaaaabbababaabbabbabbaabbbbaaabbbaabbaaaaabbbaabbaaaabaaaaabbbbababbbababbabbabbbabababbabaaaaababbabbbbabbabaabaabbbbbaabbaaaaaaaabaaaabaababaabbaabbaaaaaaabbbbababbaaaaaaaaabbabbaaaaaabbabbbbababaaabaababaabbbbbababbbabbaaabbbaaaabbbaaabbbbabababbaaababaaabbbbbaaaaaaabbbbaabbababbbbaaaabbaabaaabaabbabaaabbabaaaabaaabaaabaabbaabbaabbbaaababbbbabbbbaaaabaaabaaaabbabaababaaabaaaabaabbaabbababaabbbbaabababababaababaaabaabbbaabbaabbabbabbbbbbabbbaaaabbbbabbababaababbababbbaaaabbabaabbbbbaaaaaaabaaaabbaaabbbababbaababaaaabaaabbabababbbabbaabbbbaaabbbbbbbbbbaaabaababababaabababbbbbaaabbbabbbaababbbbbbababbaababbaabbaabaabababbbaabbbaabbabbabaaaaaaabaabaabaaaaaaabaaaabbaaaaabaaaaabbbaaaabbbbbbabaaabbbabababbaabbabaababbaabaaaabbbbbbbabbaababaabbbbbbbbbaabbaaabbabbabbabbabbbbabaababbbababbbabaaabbabaabbbaabbaaaaabaabbaababbaabbbbabbaabbaaabbaaababbbabbbbbabaabababbbbaabbabbabaaaabaaaaabbabbabbbaababaabaaaabaabbababbaaabaababaabaaaabbbbaaaaaababbbaaaabbabbaaabbabbaaabaabaabbabbaababbaababaabbaabaaaabbbbabababbbbabbbbbbaaaababbbaababbabbababaaaabbbabbaabbaaababaabaababbabaaabaababbabaabababbabbbbbaaababbaaaaabaababbabaabbabbaabbabaaaaabbaabbbbaababbbbabaaaababbaaababbbbbbabbbababaaabbbbabaabbaabbabaaaabababaaabbbaabbabaabaaaabaaababbbabbbabbabbaabaaaaaabbbbbababbaaabbaababaaabbaabbabbbbbaaababababbaaabbbabbabaabbabbbaabbbbabbbbaabaababababbaabaabbbaaaaaabbababbaaaaaababbababbbaabaaaaaaaaaabbbaaabaabbaababbbaaabbbaaababbbbbabaaaabbbabbbbbabbabaaaabbaaaaabababbaabbaaaaaaaabbaaaabbaabaababbbbbababbbaaabbaababaababaaaaaaabbbbabbbaabbabbabbaabbbbaabaababbbbbabababbbbbaabaabbbaabaaabbbabbbbbbaaabbaaababbaaababbbbababbbaaabbababaaaaaabaabaabaaaabaaaaabbabbabbaababbbabbaabbabbbbabaaaabaabbbbaaabbabbaababbbbbbabaaababbbaaaabbbabbbabbbabbabbbbaaaaabbabbbaabbabaaaabababaaababaaabbababaabbbbababbabaababbbaaabbabbabbabaabbababbbbbbaaababbaabbbbababbaabbbbbaaaaaaaaaabaabbaaabbabbaabaaabbaaaaabababaaaabbbabbaabbbbbabbbaaaaaaabaabbaabbbbaaaaaaabbbaaaaabaababaababbabbaabaaaaabbabbbabbbaaabbbbbabaabababbbabbbbbaaaabaaababbabbbbbaababbaaabbbbababaaabababbbbaaaabbbbbbaaabbbbbaabaaababababaabaababbaabbbbababbabbbbbbaaabaabaabbbaababaabaabaabaabaabaaaaaabbbababbababbbabbababbbbbbabbaababaabbbabbbbaaabbabaaaabbbabababaaaabbaaaaabbababaabbbbabaaaaabbbbbbaabbbbababaaaaaabbabbaababbbbbbbaabbbabbabbbbbaaaaaaaabaaabbbbaabaaabaaaaaaaabbbaabaabbbabbabbbbabaaaaaabbbaabababbabaabaabaaabbabbaaaabaabababbababaaabbbbbbbbbbabbbabbbaaaaababababbbaaaabaaababababaaababaabaaabbaabbbaaaabaaaaaaababbaabbaaaaaabbabaabbabbaaaaabaabaabaababbbbabbaaabbaabaabbaabaabbaabababbabbbbabbaabababbbbbbbababaaababbabbaaaababbaaabbbbaaabbbaaabaababbababbaabbbaabaabbaabaaaabbabababaaaaabbaaabbabbaabbaaaaaabaabaabbbbaabbbaaaaaaabababbbbbbaaabaababbbaaabbbabbabaabaaabbaaabbabbbbabaaaaabaaaababbbbababbbbaaaaaabaaaaaabbbaaaababbbbbbbbbbbbbabbaabaaabaababaabaaabbbaaaaabbaaaaaaabbabbbaaaabababaabbaabbaabbabbbabbaabaabbababbbaabababaaaababbbabaababaabaaababaaaabbabbabbaabaabbaabbbabaabbabaababbbaabbabbbaabbaaabbabbabbababaaabbbbaaabbbabaabbaaaabaabbbbaabaaaaaabaaaabbbbabababbabbababbbaabaaabaaababbbbbbbbbabbababbbbbbabaaabbbbababbabaaababbbbbbbbbbababaabaaababbabbabababbabbbaabaaaabbbbaabaabbbabbbabbbbabbabaababbaabbbbbaabbaaabaabbbbaabbbabbbaaaaabaabaabbaabbaabbabbbaabbababbabbaababaabbaaabbaaababbbaababbaaaabaaaaaabbabbbbaaaabababababbbbabaabbbaaabbabaababaaaaaaaabbabaabaabbbbaabbabbabaabaaaabaababbabaaababbabbbabaabaaaaaaaababaababaabbbabbaababbbbbbbabaaabaabbabaaabbbbbabbbbaaaaabbbabbbaaabaababbbbbbbaabbbbabbaabbbbaabaaabaaabbaabaababbabababbbabbabbaabbbbbabaababbbaaabbaaaaabbaabaaaabbbabaaabbaabaaabbaabbbabaaabaaabaaabbababaababbaaaabbbbbaabaaabaaabbbaaabbbbabbbbaabbbbbbabbbaaabaabbbaaaabbabaaaabaaaabaabbababbbbabbaababbbaababbbbbbabaabaabaabbbaaabaabbbbaabbbababbabbbbbbbbbaaabaaabaababbaabababbaaabbbabbaabaababbbababbababaabaababbaabbbbaaaabababbbbababaabaabbabbbaababaabbbbbbaabaaabbbabbbbbbbbbbaabbbbabbbbaabababaaaabbabbaabbbbbaaababababaabbabbabaababbbabaaaabaabbbbaabbbbbbbbbbaaababbaababbbaaabbabaababbaaaaaabaaabaaaaababbbabaabbabababbbbbaabaaaabbbbaaaaaabbaaabaabbababababbabbbbbaabaaababbababbbbaabaaabababbbaabbbbbbbaaaababaababbaabaabbbaabbabbabbbaaaaabbaababbbaabbbabbabaaaabaabbaabbbaabaaababbaabaabaabaaaaabbbabbbbabbaaaaabbbbabaaabaaabaabaaabbaabbabbaaabbaaaabbbababaaabaabbaabbababbbbbbbaabaabbbaaaabababbabbbbaaaababaaaaaaaaaaabbbbabbaabaaabaaaaaaaaaababbaaaabbabaaababbaaaabaababbbbbababaaaaaaaabaaaaababaabbbbbbabbbaababbabbbabaabaabaabbaaaaaaaaabaaaabbaaabaaaabaabbbaababaaaaaaaabaaaaabaabbbbbbabbbbaaaaababbbaaabbbbbaaabaabbaabababbaabbaaabaabbbabaabbaaaaabbaaaaabbbbaaaaabababaababbbaababbaaaabababbabbbabaaabbbbaabbbbabbabbabaaabbbbabaababbbbbaaababaababaabbbbaaabbbbbaabaaaabaaabbabbbbbbbaababaabbabababaabbbabaaaabbbabaaaaaababbaabaabbabbbaaabbbbaabbabbabaabbaabbabbaaaabbbaaaaaaabbbaabbabbabaaaaabbaaabbabaabbbabbbbabbbaabbaabaabbabbaabbaabaabbbaababaabbaabbbbbabbbbaabbaaabbbbbabbbbaaabaaaababbbababaabaaaababaaaaaaabbbaaaabaabaaaababbaabaaaabaaaabbaabbbabbaaabaabbbbbbbbabababbbabbaaaaabaaaabbbbaabaaabbabababbaaaabbabaaabbbababbabbbabababbbbbabaaabbbaababaabbabaaaababbbabbaabbbabbbbaaabaaaabbbbaabbbababaaaabbbbabaabbaabababbbabbbbaabaabbbaaaabbbaababababbbaabbabaaaabbbaaabaaaaabbbbaaaabbabbaaaabaaabbaabbabbbababaabbbbbbbaabaabbbabababbabbbbababbbabbbabababbbbaabababbbbaabaabbbabbbabbaaababbbbbabaaaaaabbaabaaaaababbababbbbababaabbababbbabaaababaabbaaaaabbaaababbbaaabbbbabbaaabbbabbabbbbbbbabbbaabaabbbaaababababaabbbaabbbabababbbbbbbbabbbabaababaabaaababababbbbabaaabaababbbabbabbbbbababaabbbbbaaabbbaabbbababaaaabbabbbaabaabbababaaaababaababaaababaaaaaabaaabbaababaababbbaaabbbbabbaabbbaabbaabaaababbbabbababaabbabbabbaabbaaabbabaaaaabaaababaaaaaabbaababbabbabbbabaabaabaaaabbbabbababababbbbaaaabbbaaaabaaabaaaabaaaaaaaaabbabbababbbbbaaababaaababbbbabbabaaaabbababbbbabbababbaabaabbbaaabbbbaaabaaabbbaaaaaaaabbbbabbaaaaababaaababbbabaaaabaaabbbababbbbabababbbabbbbabbabababaabbbabaababbbbabaabbbbbbbbabaabbbbbaaabaabbbaabaaabbbbbaaaaaaaaaabaaaabbbaabbbabbababbaaababbbabbbabbbbbababaaababaabbbbbabbaababbababbbbbabbbabbabbbaaabbbababaabaababbaaabbbaabababbaaabbaaaaaaabaaaaabbaabaabbaababbbbabbbabaabaaabaabaabbbbababbbababaaaabaabbabaabbbbaabbbaabaabbaaaaaaabbaaaaabaaaaabbbbbbbaababbbaaaaaabbbbabbabbbbabaaaabaabbaababbabaaababbaaaaababaaaababbbaaabbaaabbbbbaaaaabababbaabaabbbaababbbbbbbabbaabaabaaabbbbaaabbbaaabbaaabbbaaaaaaabaabbabaababbbbbbbbabbbabaaabaaaabbbaabbaabaabbbabaaaabaabababaabbaaabbbabbaabbabbbaabbbbaaaabbbaabbbbaabbabbaabbbaabbabbaaaaabbaaaabaabaaaaaaabaabaaaabaabaabbbabbaabaaabbababbaaaabbaabbaaaaabbbbabaabbababbabbaaabbbaababaaaaababbbabbaabbbabbaababbbbbababaabbaaaaabbabbabaabbbbbbbababbbabbbbbbbbabbbbbbbabbaababaabaaaababaaabaaabaababaababababbababaabaaababaabaaababbbaababaababbbaaaaababbbbaabbaaabbbababababaabbbabbaabbababbbabbabbabbbbabbababbbabaabbbababbabbbabbbabbbbbbaabbbbaaababbababbbbbaaaaabbbabbbbabababbbbaaaabbbbaabbbaaabbbaabaaabaababbaaaabbaabaaabbbababbabaabbaaababaaabbbbaabaabbaababbbaababbbbabababaabbaabbbbbbbbaaaaabababbaabaaabaaaabbbabbaabaaabbbaaaaaaabbbbbaaaababaabaabbbbaaabaaaabaaababaabbaaaaabaabbaabbaabbbbabaabbaaabababbbbbbababbbaaabbbbbbbbbaaababbbaaabaaabaaabbbabbbbbbabaaaaababbbbaaaabbaaabaabbabbbbbabbaaaaabbbaaaaaaaabbaaabaaaabbbaabababbbbaabbbbaaabababaababaabbaaabbbbaaaaababaaabababbabaabbaaabaaaaabababbbbbbaabbbbaababbabababbbbbbbbbbababaaabaabbbbabbbbbbabbabaabababbbbabbbbbbbaababaaaabababbababbabbbbaaabbbabaabbabaaaaaabbbabaaabbabbaaaababbbbabbaaabaababbaababbabaabbbabaaaabbbbbababbaabbbaabaabbaababbbbbaaabbbbaaabaaabbabaaaaabaaabaaababbbabaabbabababbbabbaaaaaaaabaaabbabbaabbabbbabbaabaabbaabbbbaaaaabaabaabaaabbabaaabbbabbabbbabaaabababbababbbbabababbabbbaabbabbaabaaaaababaaaababbbbaaaabaababaabbbbbbaabaabaaabbbbaabbbaaaabbbabaaababbbbaaabbaabaaaaabbbbabababbbbbbbaaabaaaaababbabaaaaababababaaaababbababbbaaabbbabbaaabbaabbbbbababbbabbbaaaabbbbbabbaabbaaabababbbbbbababbbabbbbbaabaabbbbaaabaaabaababbbabaabbbbabababbabbbbabbabbbaaabbabaaabbbabaaabbababaaababaaabbabbbabaaabababaababbaaabababbbbaaaabababbbbbabaaababababaaabaabbabbbbbaaaaaaaabababbbaabbabaabbbabbabbabaaabbaabaaaaababbbbabaaaaaaabbaaaaaababbaabbbabbbaaaabbaabbaababaababaabbbbaaaabbbbaaabababbbbbabbbbbbbababbabaababbbbbaaabbababaaaaaabbababbababbabbaaabaaabbaabbbaaaabbaaabaabbbabababbabaaaaabbbababbaabbbbbaabaaabbbbaabbaabbbbababbabababbabaabbababababbbaababbbaabaaaababaaababbabaabaaaaaaaabbbbbbabababaaabbbbabaaaaabaabbaabbabbbaaabbabbaaaaaabbaaababaaaabbabaabbabbbabaaababbaaabbbabbabbbbaaabbbaaabaaaabaaabbaaaabbaabaaaaabaabababbbaaabababaaaaabaaabbbabaaaaaaababbabaaabbbbabaabbbbbbabbbaabababaaabbaabbaabaabbababbbabbbabababbbbbbabbbbbababababbaabbbaaabbababababbababaaabaaabbabbabaaaaabbaababaaaabaababbbbbabaaabbaaabababbbbbbabaaabaaaabbbaaaaaaaaaabbbbbabababbaaaabaaabbbbbabbbabbababaaababaaaabbaabbbbababaabaabaabbbbbbbabababbabbbaababbaabbbaababaaaabbbabbbabaabbbbabaabaaaababaaaababbbaaaababbababbababbbaabbbaabaabababaaaabaabaaabbabbaaaabbababaabbbabbaabbbbaabbbbabaaaababbbbaababbabbababaabbaaabaaaabaabbaabbbaaabaaaabbaabbabbbbabababbaaaabbbbabbabbaaabbbbbbabaabbaabbaaababbbaaaaaabbabaabaabaaababababbabaaabbbbbabbabbbbbaababbbabbabbababaabbbaabbbbbaaabaaaabbbbbaaabbababaababaaabaaabbbaaaaabbaabbabaabbbabbbbbabbbbabababaaaaababbaaaaabbabaababaabababaabaabbabbbbbaabbbaaabababbabbbaabbabbbbbaaabaaaabbbbabbaabbabbbabbbbaabbbaababbaababbbabaabbbbababbabbababbabbbaaaaabbabaaaabbbbaaaabaaaababbbbbabaaaabaaaaabbbaabbbabaabbbbaaaaaababababbabbabbbaababbbaaababaabbaaaaaaaaaaaabaabbbbabaabbbabababaabbbbbabbbaababbaaabbbababbaabbbaaabaabbaabbbbaaaabbabaaabbbabbbbbabbbababbaabbbababbbabbaabbaaaabbbabaaaaaabababbbbaaababbabaaabababbbbbaaabaaaabbabaaabaaaaaabaaaabbababaaaabbabbbbaabbabaaaaabbbaabaabbbaaaabababbaababaaabaabbbaabaaabbbbabaababbbaababbababbabbbbbbbabaabaaaaabbabbbabaaabbaaaaaabbbaabbbbaaaabababbaabbbbbaabaaaaaabaaababbbbbbbbbbaabaabbbaababababaaabbaababaabbbababbbbbabaabaabaababaabbabaaaaabaaaabaaaabaabbbbbaaabbbaabaabbbabaabbabaaaaababbbaababaababbbaabbababaabaabbabbbaabbbabbbbabaaaabababaabaabaaaabaabaaaabbbaabbbabbbaaaabaabbbabababbbaabaabbbbabaaabbbbaaaabaabbbabaaababababababbababbbaaaaabababbabaaabbbbaabaaabbbababaaabaaabaabbaaabaaabaaaabbaaaaaaaabbaaaababbbbbbaaaabaaabaaaabbbbbbabababbbbabbabaaababbabbababababaababbabaaabbabaaaaabbbbbbababaaabbbbabababababbabbbaabbabaaababbabbbbaaabbbbaabaaabbbbbaaaabaabbbbbbaaaaabbbabbbaaabbaabbbbbaaababbbbbababbaabbabbabbabbaaaaababaabaabaaaaababaaabbbbaabbbbbaababaaaaaabbaaaabbabbabaaaaaabbbbaababaabbabbbaaabbaabababbbbbbaaabaaaabbbbabbaaaaaabbaaabbbaabbbbbbbbaabaabaabababbbaabaaababbbaabbbaaababbaabbbaabaabbbabaabbbaabbbababaaabaaaabaabbbabbaaaaaaaabbaaabaaabbbababababbbabbbbaaabbbbbabbbaabaabbbababbbaaabbbaaabaabbaabbbabbabbaabbbbabaabbaabaaabaabbabababaaaabbbbabababbaaaaaaaaaabbababaaabaabaabaaabbabbababaaabbabbbaababaababaaabbaababbabbabaaabbbabbbabaababbbbbbaaaabbbbbbabaaababbaaaaaabababaaabbabbbbaabbaabbabaabaaababbababaaababaaaababbabbaabaaaaabbaabbabaabaabaabbaabbabaaaaababababaaaaaaaababaabababbaababbbaabbbbbbabaababbbaababaababbaaabbbbabbbababaabaaaaababbbbbbbabbbbbaabaabbbbaabaabababbbbbabbabbbbbbbaaaaaabbbbaabbbabbaaabaaaaaababababbabaabbbabaabaabbaaabbabbabaaaaabbbaabaabababaaaaabbbaaabababbababababbbbaaabbaaabaaaabbabaaabbaaabaabaababaabaabaabbbaaabbbbbaaabaaabbbaaabbabbaaabbabaaababbabbababbbaabaababababbabaabbbaaaaaaabbaaaababbabaaabbaaababababbbaaaaabbaabbabbaababbbababaabbaaabbbbaabbbbbbbbabbbbabbbabbbbbaabaababbababbaaababbabaaababababaaabbbabbababbababbbbbbababbabbabaaabbbbabaabaaaaabbbabbbbbaaabbbbaababaaaaaabbaaabaabaabbabbbaaabbbbbbaabbabbabababaaaaaabbbbbbbbbbbbaabaabbbbbaaaabaabbaabaabbbbbbbbabaaaaaaaaabbbaabbbbaabbabaaabbbabaabbbaababbbaaaaaaaabbababababbbbbabbbbbaabababaaababbbbabbabbbabababbaaaaabbbaabbbbbabbaabaabbbbbaabaaabaaabaaaabaabbbaabaaaabbbaabbaaaaaaababbbbbabbbaaaaababbaaababbaabbabbabbbbbabbabbababbbabaaaabbaaabbbbaaaaabbbabbababaaabbbbbababbbbabbaaaaaaaabaabbabbbbaaabaaabbabbbaabababbaaaabaaaabbbbaababbabbaaaaaaabbabbbbaabaaabbbaabababbaaabbbbababbbbaaabaaabaaababababbaabaabaaabbbbabaabaabaaaaabbbaabaabaababbbbaabaabbbabbbababbabbbaabbbbabbbaababaabbbbabaaabaaaaaaaaaababbbbbbbaabbbaaaaababaabaabaabbabbbbbaaaabbabababaabaaabaaaababbaaaaabbbabbaabbaaabbaaaaababaabbababbbaabbaabbbbabaabbbbbbaaabbbbbaababbbaabaabaabaaaaabbbaaabbbaabaaaaaabbbbbababbbbbbaaaababaaaaabaabbabaaaabaabbaaaaabaabababaabaabbbbabbbaaababaabbabaababaababbabaaabbaababbbbbaaabbaabbabbbaabaaaaababbbbbabbbababbaaaaababbbabbabbaaaaaabaaaabbbabaaabbbbbbbbaabbaaaaaaaabaaaabbaaabbaaabababbbaabbaaabbbbabaababbbbbababbaaababaabbbaaaaabaaaabababaaabbbaabbbbbbbaaaabaaaaaaababaaaabbbbbababaaabaaaaababbaaaaabbaaaaabaabaababbbbababbbaaaaaababababbabbabaabbaababbaaaaabbaaaaabbbaababbbaabababbbbbabaaabaabaaabbbaabbbaaaaababbabaaaabaabbbbbabbabbaaaaababaaaaaabbababbbbabaababababbbbabababbabaabbababaaabbaababbaababbababaaababaaaaabbababbbabaaabbbbaaaabbbababbaaabaaababababababbbbbbbabaabbaabaabaabbbbabababbabbbabbaaabaaabbbbaabbaaababbababbbabaaaabaaabbbbaabbaabaaabbabbbbbabbbbabbbbbabbbaaaaababbbaababaaaabbbaababbbabaaaaaaaabaabaabaabbbaaabbbabbababaaaabababaaabaaabbbaaaababbbababbaabaabaabbbabbaaaaaaaaaaabaabbaabbaabbbbbbabaaaabbbbaaabbbbababbaabbaabaaabbbaabaabbbaabaababaabaaaabbabbbabbbababaaababbbbbaaabbabbbbbbbbbbabaaaaababaababaabbbaabaaabaabbabaabbbbabaaaaaaaabaaababaaababbbbaabbbabaabaaabbbababaabbaaabbabbbbbababbbaababaaaaaaaaaaabaaababababaabbbbabababbbbbbabaabbabababbaabbbabbbbbbabbbaabababbabbabaabbaaabbaabbaaabbaabbababaababaabbaabaabaabbbaabbbaabbbabbabbbbbbbbaaabbaabbbbabbabaabaaaaabbaaaaaaabbabbbbabaaaaaaaaaabbbabbbaaabbbabbabaabbbaabbbaaaabbbabbabbbbbbabaabaaabaabaababbbaaaaabaabbbbaaabbababaabbaababbbabbaababbaabbbbbabbbaaabaabbabbbaabababbaaaaabaaabbabaaaabaaabbaaaabbabbbabbaaabaababbaababbbbbabbababbaabaabaaaabbbababbabbbbabbbaabaaabbbbbaaabbaaaabbaabaabbaaabbaabbabaabaaaaaabbbbabbaababaabbbbbabaabbabaaaaabbbbabbabaaabaabbbbbabaaaabaaabaabaaaaaabbababbbbbabbbbababbbbbbbabaaabaaababbaabbaabaabbaaabbbabbaaabaababababbabbbbaabbaabbabaaababababaaabababbbbbaababbbabbbbbbaabbbbabbbbabaaabaaaabbababbababaaaaaaaabbabaaaababbaaaabbabbbbbabbabbbbabaabbbbaabbbabbaaaaabbbaabbabbaabbbabbbabaaabaaababbbaaabaaaaaababbabbbababbbbabbaabaaaaabbbbbabbaabaaabbaabaaabbabbaaababaababbaaaabbbabababaabbababaabbbbbaaaaabaabbbbaabbbaaabbbbbaaaabaaaaaabbbbaaabaaaabbbbbabbaabbbaaaabbabaaaaabababbbbbabaabbbbbababaabbbaaababaabbaaabbabaaabbbbabbbbababbabbabaabbabaaabbabbbaabbabbbababbbababababbbababbbaabbbaaabbaaabbbaabaababaabaabaaabaaabaababbbaaabbaabaaaabaaabbaabbbbaabbbbaabaaaabbbbbbbaaaabaabaabbbbbabaabbabbbabbbaaaababbaabbabbabababbabbaaaababababbaabaaaaaabbaababbbbaabbbabbabbbbaaaababaaababaabaabaaaabbbbbbaaaaaaabaabaaaabaaaababbaabbabbbabaabbbaabaabbbabbabbabaaaabbabbaaaabbbabbaabbaaaaabaaaabbaababbbbababababbbaaaaabaaabababbaabbbaabbbbbbabbaabbbabbabbbaaaababbbaaaabaabbababbabbbabbbbbbbaaaaaababbbabbaaabbaaabbaabbaabaaababbabbbbbbabbbbaababbbaabababbbaabababaababaabaaaaabaaaababaabbbabababbababbbabbaababaaaaabaaabaababababbaabbbabaabbababaabbabbbbbbabaababbaaaaaabbbaaabaaaaabbbbbaabaaabbababbaaaabaaababbbbbbbbababaabaabbaabbbbaaaaabaabaabbbbbaababbabababaaaaaaabaabbbabbbbabaabbaaaabababaababaaaaaaaabbbbbbaabbaabbbbbaabababbbbbbabababbabaabbaabaabbbabbbaabbbbaabbbbababbabbbbababbaabbbbbaabbbbbababbbaabbbaaaabababbbbabbaaabaabaaabaabbaababababbbbabbbbbabbaabaaabaaababbabbaabbabaababaabbbbaabaabbaababaabababaabaabaabbbaabbbaaabbababaabbabbabbaabbaaaaabaabababaabbabaabbabaabaabbaaaababaabbaabbbaaaaababbbaaababbaaaaabbbbabaaaaababbbbabaaabaaabbaaababbababbabbababbbabbaaababbbbbaabbaababbbbbbbbbbbabbbaabbabbbbbbbbaabbbbabbabbababababaababbbbbaaababbaabaaaabbbbaaabaabbaabbababbbabbbbabbaaaaabbbbaaaaaaabbbabbabbbbabaaabaabbbbbbaaaabababbaaaababbabbbaabaabbbbbbabbaaaaaaaaabbbbbbbbabaaabbbabaaabbababababbbaaaaaababaabbabbbaaababbbbbbabaababababababaabbaababbaaabaabaaabbabbaabaaabbaaaaabbbababbbbbbbbbababaabaaababababbbbbbbabbbbaaaabbbbbaaaaaabbbbbababbbbabbbaababbababaaaabbaabaaababababaaaabbbbabbaabbabababbbbbbabbbaabaaaababbabaabbbabbabaaabbbabaabaaaabbbbabbbbabbbbabbaaaaaaabbaababababbabbaaabbabaaaaabaaabaabababaaaababababbaaaabbabababbbbaaaabaabbaababbbbbababbbbbaabbbbbbbbbaabababbaabbbbbaabbbababaaaabbaaabaabababaaabaabbaaabbbaabbbaabbbbbababbababaabbaaabaabaaaabbabaaabbabaaabaaabaabaabbabbabbbbbaabbbbababaaabaabaaabbbbbbbaabaaabaaaabbbbabbbaaabbbaabbabbbbbbbbbabbbabaaaabaaababbaaabaaaababbbabbbbaabbbaabbbbaaaabaabaaabaaaaababbbbbbbbaabbbbabbabbaaabbababbbaaaaabaabaabbaaaaababaabbbabaabaababaaaaaabbbbabaabaaaabbababbbaabbabbaabaaabaaabbaabbbbaaaababbaaaaaaaaaabaabaabbabbabbabbbaaabbbaaabaababbbbabbbbbbbababababbababaaaaaababaaabbbbaaabbbaababbabaababbbababaaaaababbabbaaaaabbbababaaaaabbabbabbabbababaabaabaababaabbbaaababaaaaabbbaaaabbbabbbbbbbaababbabbbaabbababaaabaabaaabaaaabbaaabaaabaaabbbbabbbaaabaaabbaaabbbbbbabbabbbaaaaabbbabbabbaaaababbbaabababbabbabbabbbbbaaaaaabbbbabbbbbbbababbaaaabaabaabaabbbbbabbabbaabababbabbaaababbabbaaabbabaaabbbabaabbaaababaaaaaabaabbbaabaabbbbbabaaaababbaabbaabaaabbabababbaaaaaabbabbabbaaabbaaaabaabaaabbbaabababbaabbbabaabbaababbabbbabbaababbbaaaabbbabbbbbbaaaabbbaaaabaaaaaabbbbaaabbaaabbabbabbbbbbabbbbabaaabaabbbabbaaaababaabbabbbbbbbbbbbaaaabaaaaaabaababaaaabaabbbabbababbabbbaabaaabbbbaaababaaaaabaaaababbaabbbbaaabaabaaabaaaabbbabbabbabbbaaabbbaaabbabababaababababbbabaaabaaabbaaaaabbaaabbabbbabbaababaababaaabaabbabbbabbbbbaabbabaabaaaabbabbbbbbbbaabaababbaabaabbaababaaaaabbbaaaaaaabbaabbbbabababababaaabababababbaaabbbbbaabbbbbaabbababaababbaaabbbaababbabaabbbbababbbaaabbbaababbbbbbbbabbbbabbbaaaaaabbbabbaaabababaaababbaaaaaabbbaaabaaabaabbaaaaaababbabbaaababbababbbabbbaaaaabbaababaababababbbaaabaabbbbbbbaabbabaabbabbaaaabaaaaabababbbabababbbababaabaaabbaabbbaabaaabbbabaabbbaabaabbaabaababaabbaaaaaaabbaaaaababaabbaaabbabaababaababbaabbbaabbaaabbaabbbbbbbabbaaaabaaabbbaabaaababaaaaabbbbabbbabbabbbbbbaababbabbbaabbbbbabbabaabbbabbababaaaaaabaabbbaaabbbbbaabbbabaabaaabaabbaabababbabaababbbbabaabaaaabbabbaaaababbbbbbabaabbabbababaabababaaaaabaabbbbaaabbababaaaabbaabbabbaaabbbbbbabbbbaabbaabbbbaaaaabbbbabbaabbaaabbbbbbbabababababaabaabbaabaaaaabbaaaaabbababbabaaabbabbaabbabbabbabababbbabbbabaaaabbaabaababbbaabaabbbbbbaaaababaaaabaabaaabbaaabaaaaabaaabbabbaaaabbbaaababbbbabbbaaabbbaabaaaaaaaaabbbbbababaaabbbabbaaaabbbbbabbabaabbbbaabbbbaababbbabbbaaaaabaabbbbaabaabaabbbaabbbaaabbbbaaaaaababbbbababaaaabbabbaabbaabbbbabaababbbabbbbabaabbabaabaabaabbababbaaabbaabaaaaabbabaaabababbbaaabaaaaababaaabbaaabbbbbbabbaaaabbbbaaaabbbababbabbaababbaaaaaaabbbababbabaabaabbbbbaabaaaabaaabaaabbbaabbabaabbbbaabababbabbaaaabbbaaaabababbabbabbaaaaababbbbaabbbaabaabbbaaaabaaabbbaababbaaaaabaaabbaaaabbaaaaaaaaaabababbbabbbabbbaabbabbababbababbababaababbbbabaaaabbbbbbbbbaaabbabbbaabbbbabbbabbabaababbabbaaaabbabaabbaabbbbaababbbaaabbaababababababbbbbabaaaaabbbaabbabbababababbbbaaaaabaababaaaabaaaaabbaaabbaaabaaaaabaabbaababbababbababaababbbbaabbbabababbaabbbbabaaaabaaabababbabbabaabbbabbaabbaaaaabbaabaaabbabbabbbabbabbbbbbaabaaaabbbbbbbaaaaaaaabaaabbbabbababbbbaaabbbbabbaabbbababababbabbabbaabaabbaabbababbababbbaabbabbaabababbaaabaaabaabaababaaabbbbaaababababaababaababbbbaaabbabaabaaaaaabaabbaabaababaaababaaaaababbbbbbaaabbbaaaaaabbababbabbababbbbaaabbaabaaabababbaaaaaaaaabababaaaaabaaabbabbaabaabaababaaabbbaabbbaabaaabbbbabbaabbbaaabbbaaabbbbbbbabbaabababababbaaababaaabbabaaabaaabbbbbbbbbbaaaababbbbaaaabbaaabbbbababbbbaaaabbbbabbbabbaabaaabbaaaababaaaaababaaaabbabbaaaaabbaabaaabbaaaaabbbabaaaaabaabbbbbbbbabbbaabaabaaaabbbabbbbbbbbbabbaaabbbaabbbbaabbabbaabbbbabbaabaaababaaaabbaababbbababbaaabaababbbbabbabababbbbbbbaaaaabbaabaabbbbaaaabbabbbaababbbbbabbbbabaaabaaabbbabaaaaaabaaaabaabbababaaaabbaaababaabaababbabbbaabbbabaaaabaabaababaabaababbaabbaabaabbbaababbaaabbbbbabbbbbaaaabbaaabaabababbabbaabbbaaababbbabaaabbaaaababbabababaabbabbbbaabbbbabababbbabbbbaaabaaaabbbaababbbaababaabaaababbbaabbbbababbabbbbaaaabaaababaabbbbbbbabbabbbbbabbabababbbaaababbabaabbbbbaababbabbaaaaabbaabbbbababbabbaaabaabbabbbbbabaabaaaabaaaaababaaaabbaaaaabbbbbbbababbbabababaababbababaaaaaaaabababbbabaaabbabaabbaabbabbbbaaabbbbabbbbabaaaaabaaaaabbabbbbabababbaaababaaababbaabaaaababbababbbbbbbbbaaabbabbbaaababaaaaabbbbaabbabbaabbaaaababbbbabbbbbbaabababababaabaaaaaaabaaababaabaaaaabbbbbbaaabababababbbabaaabababaababbabaaababbbabaaabaabaabbaabbaababbaabaabbaaabbbbbabbbaaababbbaaabaabbbabbaabbaabababbaabbbbabbabbbabaaaabbaabbbaabbabbaabbbaaabaabbabbaabaaabbabbbabaabababaabbabababaaababaaabababaaaaaaaaaabaabbbaabbaabaaabaabbabaaaaaabbbabababababbabbaabbabbbbbbabababbaabbbbbabbaaabaabbabbbaabbaabbbbbbbaabaabbbbbababaabaaabaaaaabbbbbbaabaaaabaabaabbaabaaaabaabbaaabbbbaaababbbbbaaabbaabababbababbabbaaaababaaabbbbabbaaaaaaaaabbbbbaabaaababbaabababaaabbbababbaaaabaaaabaaaababaaaabaaaabbbaabababbaabbaaaaaaaaaaaaababbabaabaabbbbabbbbbaaabababbbbbbbabbbbaaaaababaabbaabaabaaababbaabbababbbbaababbabababbaabbbbaaaababbabbabbababbabbabbbaaabbbabaaaabbabaababbabaaabbbaabaaabaaabbaabbaaabbababbbabaaabbbbaaaababbaaabbbbaabaaaabaaaaaababaaababbabaababbaabbbaaaababbbabbbbbaababbbbabbabaaaaabbbabbbabbbabbbabaabababababaaababbabbaaaaaabaaabbbbbbbaaabbbbbbbbabbbbbbbabbababbaabababbaaabbbaabbabbabaabbabbabaaababbabababababaaabbbaaaabbbabaaaabbabbaaabaaabbababaaaaaaaabbbbbabaaaaababbababaabbababababbabaaabbbaabaabaaaaabbbbbbaaabbabbbaabbbabbbbbabbaaabaabaaabaabbbabbabbaababbbbabaaaaabbbaaaabaabbbabaaabaaabbbbabbbbbaabbaabbaaaaabaabbbbbabbbababaaabbabaabbaabbbbabbaaaabbbbaaababbaabbaabbbababaaabbbaaaaaababbbbabbabaabbbaaaabbbbbaabbbbbabababaabaabaaaaabbbbbabbbaababbbaabbabaaabbbaaaabababaabbaabaabaabbbaabbbbaaabbbbbabaababbbbbbbababababaababaabababbaaabababaabbbbaabbbbbbaabbbbabbabbbaabababbbaabbabbaaaaababaaaaababbabbbabbaaabbbaabbbabbbbbbbaabaaabbaaaabbaababbbbabababbbabaaaabbbbabbababbaabaaabaaabbbaabaaaaabababaabbbaaababababaabaabaabbbbabbabaaaaaaababababbaaaaabbabbbbbbbaabbbaaabbaabaabbabbbaaaabbbaaabbbaabbbaaaaabbabbaaaabaaabbabbababbbbbabaaaaaabbbbbbabaaababbbbbbbbbbaabbabbaabbbbbabababbbabababaaabaabbababbaababbabaaaaabbbbbabaabbbaabbbabbbbaabaabbbbbbaaaaaaaababaaabbabbbbaaaaababbbbabaaabababbaaaaabaabbbbabaababaababbaaabbbaabbaababbabaababbbbbbbabababaaabbbbbbabaabaabbbbbbbbaaaabbabbabbabaaaababbbbabaaababbbabbbaaababbbbabaaabaabbaaabbababbaabbbbaaabbbabbabababaababaabbaaaabbabbabbbbbabbbbbbbbbaaabbbbabaabababbbabbaabbabaabaababbbbaabbbbabbabbbabbabbbabbbaaaabaabbbbabababaaaabaabbabaaabbbabbabbabbbaaabaaababbaaababbbaabbabaabbaabababbabaaaabbbbabaabaaaaabbababbbaabaabbbabbbbaabaababbbaaabaabbaabaababaababbbaabbbbaabbabbbaabbaaaababaaabbbabbbbabbbbaaaaaaabbbbaaabbbbbbaaabbbbabaabbabbabbaabbaabbaabaaabaabaaabbbaabbbbbaaabbbababbbbaaaaabbaabaabaaabbababbbbbabbabaabaaabbbaabbbabbbaaabbaabbbbbbbaabaaabbabbbbbbbbbaababbbbbabaaabbabbababaaabbbbbaabbaabbbbabababaaaababbbbbbaabbababbbbbaaaababbaaababaaaaaaaabaaaababbaaaabbaaababbaaabbaaaaaaaaabbbabaabbabbababbbabbabbbbabbbaaaabbbbabbbbbbabbbabbbbbaaaabaabaaaaababaaabababaabbababababbabbbabbbbabaaaabbbabaabaaababbabbababbbbbaabaabbaabbbaaaaabbabbabbababbababbbbaabbbabbaabbbabbaaabababbabbbaaabbababbaaababaababaaabbababbaaaababbbabbabaabbabbabaaabbbbbabaaaabbaaaaabbaabbbbbbabbabbbaabbbaaaaaabababbbbabbaabbababaaabbaababaaaaaabbabaabbbaaaababbababbbbaaabbaabbbabbbbabbbbababbabababaaababbaaaabaaaaaabbbbaaababbabbbbbbbababbbbbbaababbbbbabbabbababaaabaabaabbaaabbbbababaabbbaabaaaabbbbabbabbbaabbbabababaaabbbbbbaaaabaaabaaabaabbaaaaabaabababaabbbbbbaaabbbaaababaabbababaaaababaabaaaaaaabbbbbbabaaabbaabaaabbaaaaaabbbbbbaabbabaaaabbabaabbaaababbaababbbbbabaaabbbabaaaabaabaababaababaaaabbbabbaabbabbbbaaaabaaaabbaaaabaaaabababaabaaaaaaaaaaababaababbaabaaababbabaaababbbabababbababbababaababababbbaabbbababbbbaabaaabaabbbbabbababbbbbbbaaaabbaaaaabaabbbbabbbbababababbaaaababbbaaaaabbbaabbbaabaaabaabbbbbabbbbbaabbaaaaabaabbbaaabaaababaabbbabbabbababaababbaaabbbabbbbbabbaabbabbbaaabbaaaaaabbbababaaaaaababbaabaaababbbbbaaabbbbbbaaaaaaaabaaaaaabbbaaaababaabbbbabbabaabbbaababbbabbaaaaaababbbaaabbaabbaaaaaaaabbbaabbbabbbababbbababbabaababbbbbaaabbbbaaaabaabaababababbbbabbabbaaaabaabbaaaaaabbbabbbabaabbabbaaaabbaaabbaababbbaabaaabbaababaaaaabaaabaabbbbabaaaaababaabaaaaabaaabbaaaaababbbaaabaaabbbaaaabbbaabbbabbbaabaababbaabbbbababbaabbbaabbaaaaabaabbbbbabbaababaaaabbbabbbbbbbbaaaabbbbabababbbbbbabbbabbbabbbababbabbabbbbaaabbbbbaabbabbbabababbaabababbbbbaabaabbbbabbbabaaaaaaabbbaabaabbababbaaabaaaabaababbbabbaaabbabaaababbabaabbbaabbaabbbabaaaaababaabaaababbbabaabbbbbbbabbbbabbaaabaabbbbaaaabbbaabbaaaababaabaabbababaaaabbaababababaaaabbbbbbbabaaabaaaabbbaaaaaaaaabababaababbbabaaababbbaababbbaabbaaaabaababbababaaaabbbaaaaaaabbbabababababaababbaaabbabaaaabbaabbaabaabaabaaaabbbabbbababaaabbabababaabbbaaababbaabaabbbbaaabbbbbababbababaabbba
ababbaabbbaaaabaaabbaaababbbabaaabbbbaaaabbbaaaaaaaaaabbabbababbbaabbaaaaaabbabbbbabbbbaaaaabbabaaaaabaaaaaaaaaaabaabaabbbbbbbbabaabbabbabbbaabbaaabaabababaaaabbbabbbbabababaaaabbbaabbbbbbbbbbbabbababaaababbabbabbabbbbbbaabbbbaaabaabaaabbbabbbaabbbababaabaaaabaababaabaaabaababbbbaaabbaaaaabaaabaabbababbaaaaabbbaaabaaabbbbbbaaaababbbabaabbbaaabbbbbbbababbbbabaababbabbabbbabbaaaaabaaabbbaaaababaaaabbabbabaabbbbaaaaaaababbbbaaabaababbbbabbbbbaaabaaababaabbbaabbbbbbbbbbbabababaabbbabbaababaabbbaabaababbbabbbabbbbbbabbabaabaaabbaaabbaababbbabbbaaabbababbaababababababaaabaaabbbbaaabbbbaabbbaaaaaabaaabbbaaabbbaabaababaababbbabaabbabbabaaaaabbaaabaabbabbabaabababbbaaaabaaaaabbaaaabbaaaababababbabbaaabbbaaaabaabaaaaabbaabaabababaabbbbbaaababaabbabbbaabbbabbbaaaaabbaababbbaababbbabbbbbbbbaabbbabaababbaabbbbabbabbababbaabbabbaaabbababbabbbbabaabbaabaaabbbaaaaaaabbaaaaaaaabbbbbbabaabbbaaaaaabaaabaaabaabbaabaabaabbbabbaabaaaabbababbabbabaaabbbabababbbbaababaababbbaababbaaababbabaaabbbbaabaabbaaaaaabaabaaabbbbabaaababbbbabbbbabbaababbaabbbbabbbbabababbabbbabbbbbabbabaabbaaabbbaabaaaabbbabaabaaaaabbabbbbbaabbaabbbbbbbbbaaaabbbbabbaaaabbaaaabaabababbaaabaabbabbaaabbbbababbababaabaaabaaaaabaaabbbaaabbbbaababbaaaabaaaaaaabbaaabaaabbbbbbbbbaabaaabbabaaabaabaaabaababaabaaababababbbabbabbaabaaaaaabaabbaababbbbbbbbbbbabbbaaaaaabbbbaababbaaaabbabaaababbbbbbabaabbabaabaabbabaaabaabbaaabbaaaabbbbbabbbabaaabababaababaaabbabbbbaaaabaabbbabbbaababbbbbbaaaaaabbbabbbaabbbabaababbbaabbababbaabbaaaabaaaaabbabbbbababbaabbbbbbbbbbbabbaaabaabaaaababbaabbbaabaaabbabaaabbbbabbababaabbaaaabbbabaabaabbbabbabbabbabbbaabbbbabbbaaaabaaabaababbbbabbbbabbbbbaabbbababaaaaabaaaabbbbbbabbbabbbabbbabbbbbbbaaaaabababaabbbabaabaaaabaaaaabbbbbbaababaaabbaababbababaaaaaabbabaababbbaabababbbabbbbaababbbaabbbabaabaaababababbbabaabbaabbbaabbabbabbbbabababbaaaabbaabaaaabbbabaabbabbaaaaaaaabababbbbbaabaaaaaaaaabaaabbaabaababaaaaaaaabbbbaababbabbbabbabaabababaabbabaaabbaaaaabbbbbbbbaaababbbbabbabaaabbbabaaaaabbbbbaabbbaaaababbbbbababababaabbbabbababbbbbababaaaabaabbababbbbbbabbabbbaabbbbababbbbbbbaababbaaababbaabbabaaabaabbbaaaaabbabaaaaabbbaaaaaaaaaabbbabababaabbbaabaaabaabaababaaaaaaabababbbabbbaabbaabbaabababaabbaaabbbbaabbabbbbbababbbbbbabbabbbabbbbbabbaabbaaaabbaaaaaababbbbbbbaaabbbaaaaaabbaaabbabababbaabbaaaaaabababbbbbbabababbbabaabbabbbbbbbbbbaabbbaababaababbbbbaababbbabbabbbababbbbabbbabaaaaaabbbaabbbabababbbbbbabbbabaabaaababbaababaaaabaabababbbabbbaabbbabaabbbbbabaabbbababbbbbaabaaababaabbaaaabbbbbaabbabbbabbabaabbaababbbbabbbbbaabbabababbaaaabbaabbbaabbabaaaabbabaaababaaabbabbaaaabbbabaabaaaaaaababbaabbbbaaabaaaaaaaabbbaabbbbaaabbbaaabaaabbabbbababaababababbbabaaaabaaababbbbbbabbabbaaababaaaaaaaaaaabbaabbaaaaaabbbaabaaabbabbabbabababbabaabbababbbbabaaaaabbbaaabaaababaaaaabbaaaaababbabbbbbbabaaaabbabbbaabaabaababaabaabbbbababbaaaaabbbbbbaababbbaabbaababaabbababbabbabababbbaaabbbaaabbbbbbbabbbaaabaaaaaaabaaabaababbaaababbbaabbbaaabbaaabaabaaabaabababbabaaabbbbabaaaaaabbabaabbbabaaaaabbbabaaabbababbababaabbbaaabaabbbaaaabbbababbbaaabbabbabaabbaabababbbbbaabbbbabaabaabbbbbaaaaabbbabbbbbbaaabaabbaabbaabaabbaaabbbabababaabbabaaabaaabbabbababbbbbabbbaababaaaababbbbbaaabbbabbbaaabbbabaababbaababbaaaaaabbabbabaabbaaaaabbabbaabaaaaaaaaaaabbbabbbbaaaabbbbbbbbbbbaaaaaaabaaaababaaaabbbaabbaaabaabaaabbbaaaaaabbbbaaaaabbbaabaabbbbbabaabbaaabbabaababababbbbababbbabaaaabbbbbabbbabbaaaabbababaababbababbaabaaabbbbaaabaabbbaaaababbabbababbabaabaabaabaaaabaaabbaabbbbaababaabbabbaaabbbbbaaaaabaabbabaabbbbabbbbbbabababbbaaabaaaabbaaaaabbbaaaabababaaaaaabaabaaaabababbaabbbabaaabaaabbaabbbbaabbababbaabbaaaabbbabbbaaabababaababbabbbbbaabaabbabbbaabbababaababababaaaaabaaabababaaababaabbbabaaabababbbabbaaabbaabbaabbbbaababbabaaaaaaaaaaaaabbbaabaaabaaaaabaaaaabbaababbabaababbbaaabaaabbaaabaabbbbabbababaaabaaabbabbbaaabaabababbaaababaaaaaaabbbbbbabbaabababababbaaaaabaabaabaaabaabbbbabbbbbaaabbabbbaaaaababbaabbbaabaababaaaaabbaaabaaaabbaaabaabbabbbbbbabababbaababbbbbbabaabbabbbbaabaabbaababaaaabbbaaaabbababbbabbbbaabbaabbabbababbbabbaabbabbbbbababbaaabaabbbaaaaabbbbaabbbbbaaabbbababbbaaababbbababbbaabababbabbbabbabbaababaabaabbbaabbbaaababababababaabbbbabbababbaabaaaababbabaabbaaabaaaaaaaaabaabababababbbaaabbabbaaaabbbbaaaaabaabbabaababaaaabbbaababababbbaababbbabaaaaaababbaaaababababbaaabbaaaaabaaabbbababababaaabbaaabbabaababbabbabaabbbbbaaabbaabaaaaababbbbbaabbaaaaaaaaabbbabaabbbaabaababbbbbbabababbbabaaaaabbbababbababbbaaaaaabbaaabaabbbbbababbbabbaaaabaabaababbbbabaabaaaababbbbbbaaabaaaaaabbaabbabaabaaababbabbbaaaaaaabbbbbbbabbbbbbaabbaaababbbbaabbbbabbaaaaabababbaabbbabbaaaabbababbabbaaaaaabbababbaaaabbabbbababbbbabbbbabbaaaaabaaaabbaabaabaaaababaabbaaaaaababaabbbbabbababbbbabbbaabbabaaaababbbbaaaabbbbaabbbbbaabaabaaaabbbabaaababaaabaabbbaababbbbaaababbababbbbbbbabaaaabbbbbaabbaaababbabbaaabbbbaaaabbabbbaabbbaaabbabbaaaaabaaaaababbaabbabbaabaaaaababaababaaabbbabababaabbaaabaabaaabbbbababbaababbbbbaabbaabaaaaaabaabababbabbbaabbbbbaabbbabaaababaaaaabbbabaaabbaaaababaabaabbabbbaaaabbbbaabbaabbbaaaaaaaababbaababbaabbababbabbabaaabbbbabaaabbabbbababababbaaaabbabaaaabbbabaaaabbbabbaaaabbaaabbabaabbbaaaaababbbababbabbbbaabbbabbbabbbbaabaabaaabbabbaaaabbbaabababaabaabbaabaaaabaabbabbbaababbabbabbbabbbaaabaaaaababbbbbaaaaaababbaababaabbaaaabbbbbbabbbbababaabbaabbaaabbbaababaabbaaaabbbaaababbabaaabbaababaaabaabbbbabbbabbaababaabababaaababbabbbbbabbbbaabaaabbbaaaaaabbaaaabbbabbabbabbbbbabbaabaababaababaabbbbbbabbbbaabbaabbabaabbaabbabbbbbabbbaaaabbaabbbaaabbbbbabbaabaaabaaabababbaaaabaababaaabbbbaaaaaaabbaaaababbbababaabaababaaabbbaabaaababbbabbabbbaabbbbbbbaaaabbabbabbbaababbababaabbbbabbbbaaaaaabbaaabbaaaabaabbbbaababaaaaaaaababbababbabaaabbabbbabbbaabbaabbaaaaabbbabaabbbbbabbbbaababbbbbbababbabaaaabbbbaabbbbbbbbabbbbbaaababbabbabbabababaabbabababbbaaaabbabbaabaaaabbbbbababbbbbaabbbbbaabbbbbababbbabbababbaaabbbbaaaabbaababbbbbabbababbabaabbabbabbaabababaabaabbbbaababbaabaaaaabbabaaaabbabbbaabbbaabbbbbbbbbaabababbaaaaabbabbabbaaaaabbaababbbbaabbaaaaaaaababaaabababaabbaababbbabaabbbbabaaaabaabbaaaabbbaaaaaabaabaabaaabababaabbbaababaabbaaaabaaabaaababaabbabababbaababbbbaababbbbabaabbbbbabbabaaaaabbabbaabababbabbbabbabbbbababbbaaababaaabaabbbaabbbbaaababbbbabababbaabaaaaabbbabbbbaababbabbbbbbbbbaabbaaabbabaaaaabababaaabbbbbaabaabbbabaaaabbbbababababaabbbabbbaabaabbaababbbabbaaaabbaaaabbbbaabaaabbabababbaaaaabaaabaaabbaabaaababaabbbbbaaaaabbaaaaaababbbbbbbaabbaaababaabbbabbbbabbbaabbbbabbaabababaaabaabbbabaaaaaababbbaabaabbaabaababbbaaababbbabbbbaabbbbbaabbbababababaaababbabaababbaaabbbaaabaabbbabaabababbaaababbabbaaabaaabbabbbbbababbbababbababaababbaabbabbbbbaabaababaabaaabbaabbbbabaababbabbabbabaaaaababbabbbaaabaababbabaabaabbbabaabbbbabbaababaaabbbaaabbabbbaaaababbaabaababababbbbaababbbbbbbbabbaabbbbaaaabbabbababbbaabbabbabbbababaaaababaababaababbbbbabbabaabaabbbaaaabaabababbbabbabaaaabbaaabababaabbbabbbabbabbbbbbaabaabbbabbbaabaaaaabbabbbaaabbaabbbaabbbbbbbbbbbaababbabaababbabbbabbbabaabbbbbabbabbaabbbbaaaaaaaabbbbabaaababbbaaabaabbabbaaaabababaabbaabbaabbabbababbbbaaaababbbbaabbaabbabbbbaaabbabbaabaabbbbbabbbabbbbaaaaababbbabbbabbaaaaabbaaabaaaaabababaabaaabaababaaaababbbaabbaabbaabbabbabababbaabbbbbbaabbbaaaaaabaababaaabababbbaaabaabbabbaabbaaaaaabbababbbbaababbbaaaabbaaaabbbaabbababaabababbbabbabaaaabbbaaaabaaaaaaabaabbaaababaaaabbabaaabbbabaaaabbbbababbbbabaaaabbaaabaabaababababaabbbbbaaabaaabaabaaaaabaaaaaaaaaaaabbabababbbbaaabbbaaababbababaaaaabaaabaabaaaabababbbbbaabaaabbbabbbabaaababbbbaaabbaaaabbbbaaabababaaabaabaabbabbababbbabbababaabbbaaabbbabbbbbbbaaabbaabaaabbbbabbabaaabbbabbaaababaabbaaabaaaabbbaabbaabbaaabaabbbbabababbbbbaabbbbabbbbbabbbabbabbaabaabaaaababaabaababababaabababbbbbabbbaaaaaabbaabaabbbbbbababbbaaabaabbbabaaaababbaaabbbbbbaaabbbbbaaaaabbabbabbbbabbaaabaabbbbaababbbbaaaabaaabbbbbbabababaabaaabaabbbbabababbbababaabaababbbaaaabbaaaabbaabbbaaabbbbbbbbbbbaabbaaaaaababaababaaaaaaaabbbbbbbbbbbabbbbaabbabbbbabbbaabaababbbaaabbaababbabbabbabaabbababbbbbbbaababbbaabaabaabbbababbbaaabbbbbabbababbababaaaaababbabbaababbbbabbabbabbabbabaabbbababbaabbbbbbaababbbaaababbaabaabbaaababbabbbaaabbabbbaaaabbabababbabbbabbbbbaaabababbabbaabbabaabbbbabaaababaaababbbaaababaabbbbaabaaabaaaababbababaabbababaababbbbbabbbaababaabbbaaaabbabbbabaaaabaabaaaaababaabbbbbbaaababbbaabababbbabbaabbbabaabaaabbbbaaabaabbbbabaaabaaaabbbaaabaaaaabbbaabbabbbaaaababbababaabbbaabbaaaabbbbabaabaabbababaabbbaabbbbababbaaabababaabbbabaabbbbaaaaababbbabbaaabaaaabbaabbaabaaaabbaaababbbabaabababbbabbabaabbaabbbbaabaaababbabaaaaabbabaaaaabaabbbbaaabbbaabbaababbbbabbbabbbabbbbabbababbbbbbbbbaabbbbaabbbbbabbaaabaababaabababababbbaabbababbababbbababbaababbabaaababaaabaaababaabbabbbabaabbabbababaabbbaaabbbbababbbbbabaaaabaabbbabaabbaabbbbaabbbbabbabbbbbbabaaaabbaaaababaababbabbabbaabbabaaababaabbababbbabbbabbbabababaabbbbbbbbbbabbbababbbbabbbbabbbbbaababaaaabaabaabbbbabbabaaaaaabbabbbaaaaababbabbaabaababbaabbbaabaababbabbabbbbababaabaababbbaabaaaabaababbababbabbaabbabbbaabaaabaaababaabbbbbbbaabaabaababbbbaababaaaabbabbaaabbbbbaabbababaababbabbbaabbbbabbbbaabaaaabbbaaababbababbbabababbbabbbaabbbbabaabbbbaabbbbabbaaaaabbbbaaabaaaaabbabbaabaaaabaababbbbaabbbbbaababaaaaaabbbbabbaaabbbbaaabbbbabbababbbbbaabbabababbaabaaaabaaaabaaaaaabaaaaaabbbaaabbabbbabbbabbbaabaababaaababaabbabbaababaaabaaababababaabbbaabaaaaaabbababbbbaabaababbbabababbabbaaabbaaaabbaabaaababbaabbaabaaabbabbbaaabaabababaaaaaaabbbaaaaabaabbbaaaabbbbabbbabbbbaabaabbbabbabaaabababaabbbbbbbaaabbaaaabbabbaabababbbabaaababbaabaabbbaabbabaabaabaaabaaabababaabaaabbaabbabbbbbaabababaaababaabbbaabababbbababababbbbababbaaabaaaabaaababbaabbbbabbaabaabbbbbbbaaaabaaaaaaababbaaaaaabaabbabaaabbaabbababaaabababbbaababbababaabbbababbaaaaabbaabaabaabbaababbbaabababbaabbababaabaababaababbbaaabaabbbbaaabbbaaaabaaabaaaabaaaabbabbabbbbaaaabaabaaabbbbabbbaababbabbbaaabbbbababbabbaaabaabaabbaaaabbabbaababababbbbaabaabaaabbaabaabaabababbbbaababaababaabbababaabbbabbaababbbbbbaabaabbbbbbaabbbbabbbaaabbaaaabaaababaababbbbabbbaaabaabbabaabaaaaabbabbaaabbbabaabbbaabbbabababbaaababaababbabbbbbabaaaababaabaababbaabbabbbabbbbaabbbaaabbabaabbbabababbbbaaabbbaabbaababababababaaaaaaaaaabaabbababbaaaabaaaaaaaababaabaabbaaaaababbbababbaaaaaabaaabbbabbbabbbbbbaabababbabbbbabaaaabaabbbbababbabaabbaaaabaabbbaabaaabbbbbabbabbbababbbaaabaaabaaababbabbbabbaabbbaaaaabbabbbaaabbababbbaabaabaaabbbabbabbabababaabbaaabaaababbbabbbbabbaabbaaabbabbabbbaaaaaaaaaabaaaaabaabbaaaabbbababbbbabbaaaabbbbbabbabbaabbbababaaababbbbbbabbbbbababbbbbababbbabbbbbaaabbabaaabbaababbaaaabbbbaaabbaabbabbaaabbbbbabbabbbbabbbaaabbbbbbbbabbbbbbbaabbaababbaabbbabaaaabbabbbabbabbbbaabbbbabbabaaababbabaaaaaaabbbbbbbabaaaabbbbbbabaaaaabbaaaabaaaaaaaaabbabbbbaabbaaabbbaaaaaabbbbbabbaababbbbaabbbabaabbbaaaabaabaaaababababaaabaababbbbbbaabaabbaabaaaabbbaabaabbabbbabbbababbababbbbbaaaaaaabbbabaabaababaabababbaabaabbbbbbbaabbbbbabababbbaabbbaaaabbababababbbabbabbbbaaabbaaaabbabbaababaaabaaababbabbaaaabbbabbbbbbababaabbbabbaabbbbbbbabbbaaaabaabaababaaaabbabbabbbaaaabbaabaabaaaabbbabbbbabbaabbbaabababbababbaabaabbaaaaaabaabaaaaaabaaabababbbbbaabbbaababbbabbaabaabbaababbbabbbabbaaaaaaaabababbaababaaaaabaababbaabbaaaabaabbaababbaabbabaaaabbabbaaaabaababababababbbbabbbababbaaaaaabbabaabaaabbaabbabbbababaaaaaabbbbbaaaaaabaabbbabbbbababbbabaaaaaaababbabaabbbaaabbbbabbaabbbbbabbbaaabaabbbabbbbabbbaabaabaabbaabbbabbabaababbaaabbababbabaaababbbbbbaabaabbaaabababbababbbbabaaabbabbaabbabbbaabaabbabaabaaabbbbabbbaabbaaaaaabbaabaabbbaaaaabaabbababababaaabbbbaaabbababaabababbbabbaaaabbabbbbabbbaaaabbbbaaaabbaabaabbbaaaabbbbbbbbbabbababbabaababbabbbbabaabbbabbbbbabbabbaaaabaaabaaaaaabbbbabbbaaaabaaaaabaaaabaabaaaaaaababaababbbbbabbbaaababbaaaaaabbabbaaaaaaaabbbbbababababaaabbabaabbbbbbbabbbabbabbbbababbabaabbbbbababaaaababbbaabbbaabaabbaaaaababbbaaabaaabaabbaaaaabaababbaababaabaaabbbaaababaababbbbabaabbbaabbbbbbbaabbbabbabbababbaaaaaabbaaaababbbbaaaaaaaaabaaaaabbaaaabbbaababaaaabaabbaaaaababbbbabbaaaabbbabaaaaabaaabaabbbbbbbababaaaaababbababaabbbbbaabaaabbaaaabbbababbabbbbbaabaabaabbabbabaaaabbbaabbbbbaabababbaabbababaabbbaabbbaaababaabbbbabbabbbbaaaababbbaaabbbbbbaaabbbbbababbbaabbbbabaabaaabbbababbbbbbbbabaaaaaaabbbbaaaaaaabbabbaabbaabaaababbbaabaaabbbbbabaaabbababbabaaabaabaaababaaababaabbababaaaabababbaaababbabbabaaaabbbbababbabababbaababbbabaabbbaabbaabababbbabbbabababaabbaaabbbbaaabbaaaabaaaaaaaaabaaaabbbaababbaaabaaaaababbbabbababbabbabaaaabbbbbabbabbaaabbbaaaaabbaababaaaaabbbbbbbbbababaaabbbbbbababbabababbbbaabbabaaaaaaababbaabbbbbaabbbbaaabaaabbabbbaabaabaabaababababbbbbbbabaaabbabbbbaabaaaababbaabbababbbaababaaabbbaaabbaabbababbbbbbbaaabbbbbabbbbabaaabaababbaaabbaabbaaabbabbabaaaaabbbabaaabbaabbbbbababbbaaababbaababbaabaabaabbbabaaaaabbbbabaabbbbbbbbabbaabaaabababbabababbabbaaabbbbbabbbabbaaaaabbbbbaaabababaaaababaabbabbababaabaabbbbbabbbbabbaaabbabbaabaaaaabbaabaaabbaaababbabaabbbbaababaababaababaaabbbaabbaaaaaaabbbbbabaabbaaabbabbaabbbbbbbaaabaaababbbbabaababaaabaaaaababbbababbaabbbaabababaabaabbbbbbabbbabbababbbabaabaabbaabababaaabaababbababaabbbaaabbbbabbaabaabbbbabaabbbaaabbbbbaabbbaabaaaabbaaaaabaaaabbbbabbabbbaaaababaabbabaaaabbaaabaabbbbabaaabbaabbbbbbbabaababaabaabbbaaababbbabbaababbabbaabbbabbbaabaaaabbaaaaaabbbaaababbaaaababababababbaaaabaabbabababbabbaabbbabbaaaaabbaaabbaababaaaaabbbabbabababbbaabbbabbbabbaaaabaababbbbaaaabaaabbbbaababbbabbabaaaaabaabbbababbbabbbabaabbababbaaaabababbaaaabaababbbaaababbabbbaaabbabaabbaabbbababbaabaaabaabaaabaabbaabababababaababbbbbabbbbbbbbabbaababbaaababbaaaaabaabbbabbbaaaabbaaaaabbbaabaaabaaabaabbabbbaaaabbabbbbaaabaababbababbbabbbbabbaaababaaaabbbbbaaabbbababaabbbbbaaaaabbbabbbaaaabaaabbbaaababbbbbabbabbbbbaaaabaaaabbbaabaabbbbabbaabbbaababbaababababaaaaabababaabbaabbabbabbabbaabaaabbaabbbabaaabaabaabaabaaabaaaaaaabbbbaabaababaabbbbaababbaabbaaaaabbbabbaaababbabbbaaabbbaaaaabaabaabbbaabaabbabaaabaaabbbabbaababbbabbbbabbabbbbbabbabbaababbbaaaabbabaaaabbaaaaaabaabbbbaababbbbaaaaaabaabbbbbbabbbaaaababbbbbbaaabbabbbabbababbbbbbbababababbbababbbbbbabbbbabaababbbbbbaabbabbaaaaaaaaaabbbabbbbaabbabbaabbaaaaaababbababaabbabbabbaababbababaabbaabbaabaabbaaaabbbaababbbabbbabaaabbbabaaaabaaaababbaababaaaabbaaabbbbababbaabbbababaaabaabaabbabaababbaababbbaaaababbabababaabbbaaaaaaabbbabaaabaaabaaaabbabbbaabaabbabbabaaabbaababababbaaaaaaabaabbaaaaababbaabaaaaababaaaabbbbbbbbbbaabaaabbbababaabababaabbbababbabbabbbaaaabbaabaaababbbabababbaaaabbababbaaabbbbaaabaaaaaaababbbabaabbbbbaaabbabaabbbaabaabaabbabaababaaaaaaaaaabbbaaaababbbaababbabbababbaaababbaaabaaabaaaabbaabbbabaaababaaaaabbbabbbabaaabaaaaaaaababaaabaaabaaabaaaabbabbaaabaaaabbbbaaabbbaabbbabbbbabbbabbbbaababbbbaabbabbbbbabababbabbbababbbbaaabbaabbaaaabababababaaaabaababbaaaabaabaabbbabaababaaabaabababaaaaabbababaababaabababaaaaabbbaaabbbabaabaaabaaabbbbbababbaabbabaababaabbbabaabaababaabbabaaaaabbaababbaaabababbabbbbbbabbaaaabbabbaababaaabaaababaaabaaaabbbabababaabbbaaabbbababbabbaabbaaabaabbaaaabababaabaaaaaaaabaabaaababaaababbaababaabbbbaaaabbaaaaababbaaaaababbababaabaabababbbbbabbbbbaaabababbaabbabababbabaaaaabaaaabbbbaaabababbbaaaaaaaaabbbaaaabaabbbaabbabaaaabbbaaaaaabaaabaabbabbabaaaaabaaabbbbbbbababbbbbabaabbbbbbbbaaaabbbaaaaaababaaaaaabbaabbbbabbbbaabbbbabbaabbababbaaaaaaaaabbbabbabbbbabbbbbabaabbaabaababbaaabbaaabbaabbaaabbbabbbbaaababbaaabbabaaaaabbababaabababababaabaabbbbbbababbaabbbbaaaaaabbaabbbbabaaaabbbabbbababaabaabaaabaaababbaaabbabbababbabbbaabaaaaaaabaaabbbbbbbbaaabbbbabbaababbbabbbaaababaaaababaaabbbbaababaaabbabbbaabaabaabbabbaaaabaabbaaaaaaabbabbabbbabbbbbaabbababbabbbaabbbbbaaabbbabaabaaababaaaabbbabababbabbbaababaaabaababaabaaabbbbbbaababbbaaabaabbaaabbabaaabbababbababbbbaaabbaaaaabbaaaaaabbbbabbabbabbaaaaaaabaaaaabbbaababbbabbabbabbaaabaaaababababbababaabaaaabbbaababaaaabbbaabbaabbbabbabaaabaaababbbbabaaaaabbbbaabbabaabbbbbaaabbabbbabbbabbabbbbaababababbbaaabaabbbbaaabbaabababaaababbababbbaaabbaabababaaaaabababababaabaabbbbaabbababbaaababbbbbbaaabaaabababaababbaaabaaaaaaababbabaabbbbbaaaaaabbbbabaaabaaaababbabbaaaabbbaaaabbbaabaaababbbabaaababaababababbbabbaaaababbabbaababaaabbbaaabaaaaaaabaaabababaabbbaababbaaabbbabaaabababbbabbababbbaaaabaaababbabaabbbbaabbaaababaababbabbaaaaaababaababababbbbaaabbbababbabaaaaaabbbbbbbababaaaaaabaabbbaaababbbabbbbaababaabaabaabaabaaabababbabbbbbabbabbabaababbbbaaaabbaabbbabbbababbaaabbaabbbbaaaaaababbabbabbababbaaababbbaabaababbabbaabbabbbabbbaabbbbbabbabbaaaabbaabbbbbabbababaaaaabbabababaaabbbabaaaabababaaababbbbbbabbbbbabaabbabbbabbaabababbaabbabbabbbabaaaaabaabbbaaaabbbababbabababaabaaaabbaababbabbabbaaabbaaaabbbbabaaabbbbbbbbbabbbbbabaaaaaaabbababbbbaabbababbbbaaaabbaabbaaaaabbbbbababbaaaababaaaabbabaabbaaaaaaabaaabbbababbabbaabaabbbbaababbabaaaabbaabaabaababababbaabbbbabaaaaaaabbaaaaababaabbbabbabbbbbbabbaaabbabbabbaababbbbbabaababbabaabababbabaaaababbaaababbbbabbbbababaabbbabbaaabbbbaaaaaababbbaabbbbaaaabaaababbbbbbbbaababaababbaababaabbabbaabbbababbbbbabaabbbbbbabaaabababbabbabaabaabbbaabbbaabaabaababaaaaaabbabaababbaabbaaabaabbbabbabbbaabaababbbbaababbbababaaabbbababababbaaaaabaabbbabaabaabbabbbbabbaabaaaaaabaaaabaabbaaabbaababbabbaabaaabbbbababbaabaabbababbabaaabaaabaabbabaabbaabbaaabbabbababbabaaabbbbababaaabbabbababbbaaaabababaabbbbababaaabbbbbabbaababbaaababbbaabbbaaaaaabbbbaaaabaaaabaaababaaabbbaababbabbbbbbbbbbbbbabbbabaabbbbbbaaababaaababaaaaabbbbbaabaaabbbabbabaaabaaabbabaaabbbbbbaabbbbbbbaaaababaaaabaabbabbbbbbaabaaaaababaaabbabbbbbaababbababbbaabaaaabbaaaababbaabababababbabababaabbabaaaaabbaababbaaabbabbababbabaababaababbaaabaabaabbbbaaabababbbaabaaabbbabbbaaabbababaabbabaabaaababbbbaaabbaabbbbabbbabaabbaaaababbaaabbabbaaaaaaaaaaabbbbbbbaaaaaabbbbbaababaaaaababbabaabbaaabaabababbbabaabbabbbbbbababbbabaabaababbaabbbbabbabaabaabaababbbbbaabaabbbaaaabaabaabbbbbbbaabaababaaaaaaaabbaabbbaabbaaaaaabbbbbbbabaaaaabbabbbaabbbbaabbbbbaababbaabbbaabababbbaababaaabaaaaabbbbabbabbaabbaaabbabbaaabbaabaaababbbbaabaaaabaabbbbaaaabbbbbaaabaabbbbabbbaabbababbababbaaaaaaaaabbbbabbabbabaabbbaaaaaababbbbababbbbabaaababaaaababbbbabbbabbbbababbbabbabaabaabbaabaaababbbaabbbaaabbbbbaaabaaaabababaababbababababaabbababababaababbabaaabbbabaabbaaaaabbaaaaaaaabaaabbbbbbabaabbbbabbaaaabbbaabbbababbababbaabaaabbabbbbbbaaaabbabbabbabbabbbbaabbaaabaabbaaabbbababaababbaabbbaaababbbbbabbaabbaababbbaabbabaaababbaaabbabaabaabbbbbbbbabbbaaababbbaaabbbabbbbaaabbbaabbbbabaabaaabbabbabbaaababbabababaabbabaaaaababababaaaaaabaaababbbababaabbaababaaabbabbabbabbbaabbbababbabbabbbbbaaabbbabbaaaabaaabaabbabaabaaaabababaabbabbaaaaababaabbbbbbaabaaabbabbaaaaababbababbbaaabbabaaababbabbaaabaaabaababbabaaaaaaababbaaaaababababbabaaaabbbababbaaabaabbbaaabbaabbaaaaaaabbbbaabaaaaabbbaaaababaaabaababaabbaabbaaababbabbbabbabbbabbabababbaaaaaabbbbaabbbbbaaabbbabaabbbbbbaabaababbaaababbbabbbbbbbabbbaababbbabaaaaababbabbbbbabbabaababaaaaabababbababbabbbbbaaabaababaaabaaaabaaaaaaababbaababbbbbabababbbbbabbabbbabbbbbababbaaabbaabbabbbababbbbbaaaaaabbaaabbaaabbbabbaabbabbbbbaabbbaababbaaabaaabbbbabbabaaaabbbbababbaaabbaabbaabaababbbaabbabbabbaaabbabaaaabaabbaaabbaabbaaabbbababbabaaabbbabbbbabbbbbbabbabbbbbababbbabbababaabbbbbbbabbbaaaaaabaabbabbaababbaabaabababbbaabbabababbaabbabbaabaaabbabbbbbbaaaabaababbaaabbaabababbbabbbabbbaababbaaaaabaaaaabbbbbbbababaaababaababbbbbbbbbabaababbaabaaaabbbbaababaaaabababbbbbbbbabbaabaabaaaababaaaaababbbabaaaaabaaaabbaabbbaabaaabaabbaababbabababbbbbbbabbabaaababaaaaabbbababbabbbaabaabaaaaaaaababababaabbabbbbbabbbbaabababbbaaababaaaaabaaabbbbaaabaabbababbaabaabaaaaabbabbaaababaaaaaaabaaabababaaabbabbbbaabbababbbaabbaabababababbbbbbabbaabbaabaabbbbaaaaaababbbbbaabbbbbbbbbaaabbbbbabaababaabbbbbaabaabaaaaaaabaaabbaaabbbbaabaabbababbaabaaaaaaabaabaabbaabaaaabbaababbbabbbbabbaaababaaaabbbaabbbbbbaaaaaabbbaaaaabbbbaaaabaabbbaaabbabbaaababbbbbbbbaabbbaaaabbbbbbbbbaaaaaaabbaaabbbbbaaabbaabbbaababaaaababbaaaaaababbbbabbbbbaaabaaabbaabbaaababbaabaaabbababbbbaaababbbaaabaaaabbaabbaabaabbabaabbabaaabbaabbabbababbaabbabaaaaaabaaababaabbaabbaabbaaaababbaabbbaabbabbbabbbbbaabaabababaaabbaaabaabbbabaabaababaabbbaabbababaaaaabbbbabbbbaaaabbbabababaaabbaaaaaaaababbbababaaabbabbbbaabaababbabaaaababaaaaababbaaaabbaabaababbbaaabbbbabbbbbbbaaaaaaaaabababbbbaaabaabbbabbaaaabaaabaababababaabbbbbbbbaabaaabbbbaabbbbaabbbaabbabbbbaabababbbbabbbbaaaaabbaaabbababbabbbaababbabbbabbbababbaabbbbbaabaabaaabbbaabbaaaaabababbabbaaaabbabbabbabababaabaaaabaabababbaabaaaaabaabbbbbaabaabbbbbaababbbbbbababbbaabbbbaabaabaabaaababbaaababbababbabababbababaaaaababbaaaaabbabbbabaaaaaabbbbaaabbbbaabaabaaabbababbabbbbbababbbbaaaabbabbabaabaaaaabbbbabaabbabaaabbbaabaaaababbbabababbabababaaaabbaaaabbabbaabbbbaaabaabbaaabbbbabaababbaabbbbbbbabbbaababbabbbbbabbaabbbbabaaababaabbbbaaabaaabaabbabbbabaabbbaabaabbaaabaaaaabaabaabbbbbbaaabaaaabaaabbabbbbabbbabbababbbababaabbaababaaaababbaababbbabbabbabbbbbaabbabaaaaabaabbabbaaabaabbbbabaaaabbabbabaaababbaabbbaaabaaabbaaabbbaabbabbabaabbbabbbbababbbbabaabbabababaaabaabbabbabbaabbaaababbbbbabaaaaaabaabaaababaabbbbbabbbaaaaaabbbaabaaabaabbbaaababbbbbaaabbbaabbaabbbbabaaaabbbaabbbabbaabaaaabbaababbbbaababbbbbbaabbbbbbaaabbbbbbbbaaaabbaabbaabbabbabababbaaababaabbbbbbbbaabbaabbaabaabaababbbbbabaaaaaabbbbbbbaabbabaaaabbaaabbbaabaababbabaaaababababbbababbbabaabaabbaabbabbaaaabbaaaaaaabababbbbabbababaaaaaaabbabbabaaaabbbbbaabaaabbbaaabbbbbbbaabababbbbbaaaaabababababbaaaabaaabaabbabbaababaaababbbbabbbaaababaaabbaabbaaabbaabbabbbababbbabbabaababaabbbaaabbaabbabbbaabaaababbabaaabaabbaaababaaababababbbabbabaaabaababaaaaabbaabaabbababbabaaaabbbabbbbabaaababaaaabababaabbabbaabbaaabbbbaaabababaabbbbbbabababbbbbbbabbababbbaabbababbabbabbbabbbbaababababbbbaaababbbaaaaabbababbaabbbbaabbaaabbbbaabaabaaaaaabaabaabbbbbbababaababbaaabbaabbaabbababaaabaabbabaabaaababbabbbbaaababababaaabaaaabbbbbabaaabbabaabaabbbaaaababbbbabaabaabbbaababbaaabbbbaababbbabbbabbbabbbbabaabbaabbabaaabbbaabbbbabbaababaaaababbbaabbbbaabaaaaaabbabbabbbaaaaaabbabbabbaaaabaabaabbaabaabaaaabaaaaabbbaaababbabbbabaabaabbabbbbbbabbbbbbbaabaaabaaabababbaababbabbabababbaabbababbbbbabaababbabbbaabaaabbabbababaaaababbbaabababbabbbabaabaabbaabbbaababbbabbabbbaabaabbaababbabbbaaaabaaabbaaaaaaabbaaabababbbababaabbbaaabbabaaaabaaaabaaabbababbbaaabbaabaabaaaaabaabaabbababaaaabbabbaaababaabaabbabbbabaaabaaabababbaabbbabbabaababbaaaaabbbbaaaabbbaaaabbbbbabababaabbabbaabaabbabbbaaabbbbbaaaabbbbaaabbabbabbaaabababaababaababababaabbbbaababbababbbbbbbbaabaaabbbaabbabbbaaaabbbbaaaabbaaaabaabbabbbaabaabaababbbbbbbbabbbbaaaaaaaabbbbbbaabaaabbabbbbbbbababbbbaaabbabaaaabbaaabbaabababbbbbabbabbababaaaabaabbabaabbbababababbbabababbabbbbaabbbbabbbababbaabaababbbaababbbaaabaaaaabbabbabbabbbbabbbabbbabaaaabbabbbababbbabbababbabaaaaaaababbabbaaabaababaababbbbbbbaaaababbabbbbbaaabababaababbbbbbabbbbbbbabaaaabaaabbaababbbabbaaabbabbaaaaaaabbbbbbbbababbabbbbbbbbaaabbaaabbababbaababaaabaabbbbbbbbbbabbababbbbbbabbababaabbaaaabbbabaababbabaabbababbabaaaaababaabaaababbaabaaabbbbabbaaaabaaaaaabaabbabbbabaabaabaaaaabbaaababaaaaabbbabbbbbbaaaaaababaabbababbaabbaababbbabaaabbbbbaabaaabbbaaabbbaabbaabaaaaaabaaabbaabbbaababbaaabbabaaabbbbaabaabbbbabbbaaabbbbbbbabaaabbbbabababbabbaabaaaabbaaaaabbaaabbabbbbbbaaabbbaaaaaabaaaabbbababbbbabbaabbaabaabbbaabbbbaabbaabbabbbaaabaababbabaaabaababaaabababbbbbbbbabbaaabaaaaaaaaaabababbbabaabbaaabaaabaababbaaaaabbaabaaabbaaaaabbaabaaabbababbaaabbbbbbaabbababbbbbabaaaabaaabbbbbbbababbbaaabbabbbaabaaaababbabbabbbbaabaabbbaaaaababaaaaaaabbbbbbbabbabaaaaababbabbabbbbaaaaaabaaaabaaaaabbaaaabaabbbababaaabbbbbbaaabaaababbbaaaaabbabbababbaaabaaaabaababbbbabbaaaabbbbbabbbaaabbbaabbbbaaabaabaabaaaabababababaaabbbbbaaabbabbbaaabaabbbabbbbabaabbbababbaabbbaabbabaaaababaabbababbabbabbababbabaabbbbbabbababbbabaaaaaabbbaaaabbbaabbaababbbababaaaaaaaababbabaaabababbbbaaabaababaaabaabaaabbbbbabbaaaabaabaabbaababbbaabababbabaabbbabbbabaababababbabbaaabbababaaaabbbababbaabaababaabbaaabbbabbaabbaaabababbaabababbbabbbbbbabbababaaaaabbbabbaaaaaaabbbabbbaabaaabababbbaabbaabaaabaaaabbbbaabaaaabbbabbbabbbaabbaabbbbaaaaabaabbbaaabbabbbbbaababaababbabbaabbbbbbabababbbaaaabbbaaabbaaabbbabaaaabbaabbbbabaaabbbaabaabbaaabaaaabbbbbbbabbaababaabaabbaababaaaaaababbbabbabbaaabbbbabaabaabbbabababbbaaaabababaababaaaabaabbaabbaababbbaabbbbbaaabaaababbbabbbbbaaaabbabaaaabababbbbbabbaabbaaaaaaababaaabbabbbbbaaabaabbbaabaaaaaabbbbababbbbbbbbaabbaaabaaabababaabababaaaaaaaababbaaaabaaababbaaaabbaaabbaaabbbaabbabbabbaaaaaaaabbbbbaabaababaabbbabaabbabaabbbbbabbaabbaaababbaabaaabbabbabababbaabbbbbabbaabbbbabbbbaabbbabbbabbbbbbbbbaabbaaaabbabaaabbaabbbbbbbaabababbbaaabbbabbbbbbbbbabbbabbaabbabaaabaabbbbabbbbbaabbbaabbbbaaababaaaabbbababaaabbbbabbababbababababababaabbbabbaaabbaaaaaaabbbababbbababbabbaababbaaabbbbbaabaabbabbaabbbabaababbabbaaaabaaaaaaaaabbbbbbaabbaaabaababbbabbbaabbbbbabbabbaaaaabababaabababbbbabbbababbababaabaaabaabaabbbbbbbababaaabbabaaabaaababbbaabbbbbaababaabababaaaababbbabaabbaaabaaabbaabaabbabbabbabaaaaabbbabababaaabaaaaabbbbababbaabbbbaabbaabbbaaababbabbabbbbaaaabaababaaaabaabbbbbabaaaabbbabababbaaaabbabbbbabbbababbaabaaababababaaaaaabbabaabaaaaababbaaaaaaabaaabaaabaabbaaaaababaabaaabbaaaabbaaaaabbaabbababaabaaaabbababbbaabaaababbbaaababaabbbaaababbbbababbabbbaabaabbaababbabaaabbaaaaabaabaabaaaaaaabbaabbbbaaabaabaaaabbbabbaaabaabbbabbbbaabbaaabbababaaabbababbbbbbbababbbbababbabbabbbaabaabaaaabaaaabababababbaabbbabbbbbbaaabbabbbbbabaaaaaaabaababaaabbbaaaaaabaaabbbabbbbabbbaabbbaababbbaaaabbaabbaabaaabbbabbaabbabaababbbbbbabababbbbababbabbabbbbaaabaaaabaaaaabaaaaaabbabbbabbbaabbaabbbabaaabbbaaabbbabbaaababbbabaaabbaaaaaabbbaaaabbaaababbaaaabaaaaaaabbaaaaaaabababaaaaababbabbbabaaaababbbaabaababbababaaabaabaaaaaaaaabababababbbbaaabbbaababbaabbbabababaaaababaabbbaaaababbbabbaaabababaabaaaaabbaabbbbbaaaabaabababbabaaabbbbbbabbbbabbbaabaabbabbbabbbaaabbbabbaabbaabbaaababbbababaaabbabaaabaaabbababaabbbbbababaababaaababbabaaaaaaaabbbbbbaaabaabbbbbaaabbbabbabbabbbbbaaabaabababbaaaabbaababbaaabbbbabaaaaabbaabaabbabababaabababaabababbbbbaaabbbbbbaababaaabaaaaaabbbbabaaaabbaaabaabaaabbbbbbbbaaabbbbaabbabbaaaaabaabaabaaaaaababbaabbababaaaabbbbbbabbbbaababaaabbaaababbabbbabbaabbbababbaabaaaaaaaaabbbbabbaaabbabbabababaaaabaabbababbbabbbaaabababbbbbbabaaabaaabbbbbbabaabbabaaabbabbabaabbabbaabbbabbababaaaabbbaaabbbbaababbbbaaaabbbbbbbbbbabababbbaabbbbbbabaaabbbaabaaaaaabababbbaabbaabbbbaaababababaaaaabaabaababaaaaabbbabbabbbbbabbbbbaaabaabbaaababaaaababbabbbbbabbbbbaaabbbbabbbaababaaaabbabaabbbbbbabaababababbbbaabbaaaaaaaababbaabbaaabaaaaaaabbbbbaaaabbaabbbbbbabbbaabbabababaaabbaaabaaaaabaaabbabbabaabbbaababbabbaaaaaaabbbaaababbabaabbbbaabaabaababbbbbbababbaaaabbabaabaabbaabbababbabaaababbbaabbaabbaaabaabbababbbbababbaabbbaaabaaaabaabbbabababbababbabbaaabbabbbbbbaaaaaaaaabaaaaaabbabaaaaaaaaabaabbabaabbbaabaababaabaaabaabbaababababbbabbaaaabbaabbabbbaaaabbaababaabaabababaaaaaaabaaaaabbbabaaababbaaaabaaababbbabababbabbbbbaababbbaabababaabaabbabbabaaabbabbbaaaaaaaabababbabbabaababbbbaaabbaaabaabaabaabaaabbbabbbbabbbbbbbaaabbabbaabaabbbabbbabbbababbaaabbabbbbbbbaaabbbabaaaabaaaaabbbbbbbbbbbbabbbbabbbbabbbbbbbaaababbaaaabbbabbabbbaabbaabbaaaababaaaabaaabbbaaababaabbabbabaabbbaabbbabbaabaaabaabbbaaabbabaababbababaabaabaabababbbabaaabaabbabbababbaaabaaababbbbbbbbaabaabbaabbbbabaaabbabaaaababbaaaaaabaabbbbabaaaabbaabbbaaaaabbaaaabbaabaaaababaaabaaaaaababbbbaaababaaaaaaaaaabbbbaaabbbbbbabaaabbabaaaabaababbaababbbaabbbaaabbaabbabbaaabbaaaabbabababbaaababbaabbbaaabbabbbabbaaaaabaaababbbaabaabaabaabaabababaabbbbbbaababbabbabbbbbabbababbaaaaababbaabbbbabbaabbabaaababbbaabbabbabaabaaabbbaaabaaaabbaaabbbbaaaaaabbbbabbbbbbaaaabbaaabbabbaaaabaaababbaabbbabaaabbbbbbabababaabbbbbbbbbbaabbababaaabbbabbaaaaaaaabbbaabababbbbbabbaabbbbabbaabaabaababababbbbababaabbbabaabbababbbabaaaaaabaaaaaabbbababaaaabaaabbbbbbbbbabbbbabababbbababbaabababbabbbababbbbabaababbbababaaabbabbbbbaaaaaabbbbbbabaaabbabbbaaaabababbaababababaaaaabaababbbbbbbbabbbaabaaaabbaabbbabaaaabbabbbbbabbbabbabaaabaaabbbaabbabbabbaababaabbbabbabaaabbbabaaabaabbbbaabbbbabaaaaaababaabaaabbbabbbbabbbbbbaaaabaaababbaaabbababbaababbbbbaabbbaabaabaababbbaabababbabbbabbbabbbabaabaabaabbbaaaaaabbaaaaababababbababbbaaabababbabbaaabaaabaabbbababaababaaabbabbbbabbaaaabababaaaaabbbbbbabaabbbaababababbbbbabbbaaaaabaabbbaabbaaababaaabaaabbaaaababbaaababbbaabaabbbbaabbbabbaabbababaababbabaaaaaabaaababbbabbaababaaabaababbbbababbababaaaabbaaababbbbbbabababaabbaaababaababaabbaabbaaababbbbbbabaabbaababbabbbabaabaaabbabbaaaabaaabaabbaabbbaaababbabbbaabbaababababaababbaababababaabbbbbbabaaabaababaababbaaabbaabababababbbababbabbabaaabbaabaababbbababbbababbabababbabaaaaabbbbaabbaabaaaaaaabbaaaabababbbaabaabaaaaababaababbaabaabbaaababbbbaababbababaabbbbbaabaaaabbaabbbbbbbbbabbaaabbaaaababaabbbabbbaabaaaaaababababaaaabaaaaabaaabaaabababaabababbbbbbbbbbabbbaabbbababbbbbabaaabbaabaabbaaaababbabababbabbabbabababbbbabbabbaabaaaaaabbbaaababbababbabbaaabbabaababbbbaabbbaaabbabbabaabaabbabbaabaaabaabababbbabababaaabbabbabaaabababbabaaaaaabbbbbbaaabbbaaaabaabbabbbabbabaababbaababaaabaabbaaaaababbbbbaabaabbbbbbabaaabbbbbaaabaaaababbabaabbaaabababaababbbababbaabbaaababbaababbababababbaaaabaaaaaaabaababbabbbaaababaaaaaaabaaaaabaabbbabaabaabaabbabaaabbaaababbbbabaaaabbabbbbbabbaaaabbbbbabaaaaaaaaababababbabaaaabaaaabbaaaabaaababbbbbbbaaaabaabbbbbbaababaaaaababbaaabbabaaaabaababbababaabbaaaababbaabaabbbbbbaaabbabbaabbababbaabbaabbaababbbbabaaababaabababbaabbaaaaabbaaaabbbbaaaaaaaaaaaaaabbbaaaabbababbbbabbaaaabbbbbbabbaaabaabaababbaaaaaaabbbababaaababbbbabbabaabaaaabaaabbbaaaababaaabaaabababababbbabbabababbabababbbbbabaaaaabaaababbbbbbaaabbabaabbababbbaaabaaaababbbbbbbbabbaabababbbaababbaabaabbababaaaaabbabbaaababbbbbabaabaaababbabaabaaaababbbaaabbbaaaaaaabbbaabbbbbabaaaababbaaaabaabaaaaabbaaabbbbbabbabaabbbabbaaabababbaabbabaabbbbbabbbaaaaabbbbabbbaabaabbabbbbbbbbabaabbbbaabaabaaababaabaaababaaaaabbaabaabbaaaabbbaaaabbbaababaabbababbabaaabaaabbbbbaaabbabaaabbbabbbbabbbaaabbaabbbabaababaabbabbbbaaabbbabababbbbbabaaaabaabbabbbaabbababbbababbbabaababbbbbbbabbabbbbaabbabaaaabbaaaabaaaabaabbbbbaabbababbaaabbabbbaabbbabbaaaabaaabaaaabaabbbaaaababaabaabbaaaaaabaabbbbbbaaaabaabbababbaaaaabbbbbabbbbabaaaabbbaabbbaabbababaaababababbaaaaaabaabbbbbbabbabaabbbababbababbabbabbaaabaaabbabbabbbaaaaabbbbabbbbaaabababbaaaaabbbbbbbababaaaabaaabababbaabaabbbabbaaababbbbababbbbbbaabbabaabbaabbbabbbaabababbbbbaaabbbbbabababbbabbabaabbabbbbbbbaabbaabaabbbbbbabbbaaaabbbbbbbbbbbabbaabaaabbbbbabbbabbaaababaaabbbbbaabbbabbabbabbabaababaaaaababbabbbbaabbaabbbabbabbbaabbaaabbbababaabababbaaaaabaabbabaababbbbaabbaabbbabbbaababbabaabbbababbbbbaabbababaaabbbababaabaabbbababaabbabaaabaaabaabaaabbbabbabbabaabbbabbbabaabbbbbbbbaaabbbbbbbbaabaaaababababaababbaababaababbbbbaabaaaaaabaaaaababbbbabbabbabbaaabbbbbababbabbbbabaababbbabaabaabababbaabaabbaaabbbabbaaababaaabbabbabbabababaabbbbbbabbaaabbababbbbabababbbaaabbbbbaabbabababaabababbabaabbabbaabbbbaabbababaababaababbabbabaaaaaaabbababbbbababaababbbabaaaabaaabaaaaaababbabbabbbaaababbbbbbbaaaabaaababaaaabaaabbaaaaaaababbbbaabaaababbabbbababbabbaabbabbabbbaabaaaaabbaaaabaabbababaaaabaabbaaababaabaabbaaaabaaaaabaaaaabababbbbabaaaaaaababbaabababbbaaababababbbbababaabaababaaababababbabaababbaabaaaabaaaabbbaabbabaabbbbabaabbbabbababbbabbbbbaabbaaabaaaabaabbbabaaaaaabaabbbabaababaabbbbbaaabbbabbabbbaabbbabbbaaabaaabbaaaaababababbbabaabaabbbbbbabaaabaaabbabbbabbbaababbaaaabbaaaabbaabaaabbbaaaaabbbaaaaaaaaababbbababaaabaaaabaabbbaabbbbabbaaaaaaaaabbaaaabbbbabababaaabbababaaabbabbbbaabbabaabbbabbabaabbbbbbababaaabababbaabbbaabababbbbabaaaabbbbaaaababbbaaaabaababbbbbbbbbababbbbabbabbbbababbbbabbabaaabaabbaaabbabbbabbabaaabaaabaaaabbaaaabbababaabaaabaababbaaabbbbaabaaabababbbabbbaaaabababbabbaaabbbaaabaaababbbbabbaaaaaabbabbbaaaaaabbabababaaaaabbbababaababbabababbbbbbabbabbabbaabaabbabaaababababbaabababbabbaaaababbabaaabababbbbbaaababbabbabaabbababbbbaabaabbbbbaaaaaaaaaabbabbbababbabbbbabbbbbabaabbbabbabbababbababbbbbabbaaabaaabbaaaabaabaaaababababbbaababbbbabaabbbbabbbbabaabbabbabbbabbabaababbaaabbbaaabbbaaabbababbbbababbaaaaabbbabbbbaaabababaaaabaababbaabaaaaaaaabbaaaaaabbabaabaabababbaaabbaaababaabaaaaabbaaaaabbabbbabaabbbaababbbbbaaaaaabababaaaaaaabbbabbbbbbbbbabaaabbbbaaaabbbbaaabbababaaaabbabbbaaabbaaabaabbbaabaaabbabbabbababbbababbbabbaabbbbaababbbbbaaaabaaaaaabaaabbbaababbabbbaababaaaaababbabbababbbabbbbbababbabbabaaaabbbbbbaababbaabbbaaaaabbbaababababbbababbbbaabbbbbaabbaaaaaaabaababbbabbbbbbbbabaaabaaabbaabbbbaaabbbbbaabbbaabbbaaabbaaaabaaaabbaabaaaabaaabbaababbbaaabbbbabbabbbbaababbbbaabaabbabbbbaaaabbbbbababaabbbabbaaabbbbaaabaaabbabbbbaaaabbbbbabbaababbabaabbaabbbabaabbbabbaabbbbabaabababbbbbabbbababaaaabbbbbbbbabaabbbbbaaaababaabababbbaaabbaaaabbaababaabaaababaaababbbbababbabaaaaabbaabbaabababbaaaaabbbbbbabbbbababaabababbabaaabbbaaababbbbabbbaaaabbbbbbbbaaaabaaabbaabaabaaaaaabbbaaabbaabababbaabaaaaabbaaababbaabbbbbabaaaaabaaabbaaaabbbbbbababbaabbaabaabaaaabbbbbaabaabababaababbabbbbaaabaabaaaabbabbabaaabaaaaabbabbbaaaabbbbbaaaaaaabbaaaababbaaaaaabaaaaababababbabbababaaababbaaaaabaabbbaaaababaaaabaaaabbbbaaabaabaababbbbaaaabaaabaabbaabbbbabaabaaabababaaaabbbabbbaabbaababbabaaaaabbaaaaaabbbaabaabbabbbbaabaabbbaabaaaabbaabababbbaabbbbaaaaaabaabababaabaaaabababababbabaabbabbabbabaaabbbbabbbbbbaabbabbaabbabbbbaaabaabbabbbbaabaabaaaabbbbabaabaaabbaababbbbabaaaaaaabbbbbbaabbbabbbbabbabbbbaaaaaabaabaabbbabbbbaabaabbbababaabbabbababbbbbbbabababbbbababbaabbabbaaabbbbbababbaaabbbbaaaaaabbbaababaabbabababbbbabbababbbbbbaabaaababbbbabbbbabaabbbabababaaaaabbabbaabbbabbbababbaaababbbaabaaaaabaaabbaabbbabaabaabbaaababbbbabbaabaabaabbbbabbbbbaabbbbaaababaabaabbbababaabbbaabaaabaaaaaabaabaaabbbabaaabaaabaaaaabbbaaaaaabbbabaaabbbabbabaaaabbabaaaababbbbaabbbabbaaabaabbaaaabbaabaababbabaabbbaabbbbabaaaaaaaaabbaaabaaaaaaaabbbbaabbbaaabbaaaabaaabbbbabbabaaabbababbbbbaabbaaabbbabaabbababbbbbbababaababbaaababbbbaabbaaabbaababaabaababbaababababbbaaabaabbaaaaaaabbaaaaaabbbaabaaababaabbaaabaabbaabbbbababaaaaaabbaabaabbabaabbaaaaabbabaabbbaabbbbbbbbabbbabbaaaababaaaaaaaaaaabbbbabaabaaabaabbaababbabbaababaaaabbbababaabbaaaaaabbbbabbbbaaaabaabbbbaaabababbbabbabbbbbaaaaabaabaabbbbabaababababbbabbababbbababbaaababaabbaabbabababaababbabbbaabbbbbabbababbabaababbbabbbbbababbbbabbbbaabbbaaabaababbbabbabbbaabbbaabbaaababaababaababbbbbbaaaababababbabbbbabaaabbabbbabbbbabbabaabaababbbaabbbbabbbbbbbabbaabaaabaaabaabbbbaabbbaabbbbabaaabbababbbbabababaabbbabbabbabbabbabaabaaaabbbbbaaaabbabbabbaabbbbaabbbbbabbbabbabaabbabababbbbbbbbbbaaaabaababaabbababbbbaababbbbbbababaaaababaaaababaabbbabbbaabababaabbabbbbbbabababbbbabbaabbabbaabbaaaabaababbbbbabbabbbaabaabbbbabbaabbbaaaaabbbbbbbbbbbbbabbaabaaababbbbabbbbbbbbbbaaaaaababbbaaababaabbaaabbbbabbaabababbbbbbabaababbbbbbbabbbbaabbaabababaaaaaaaabbaabbbbababaaaaaaabbbbbababbbaaaabbbabaabbabaaaabaaabababbabbbbbbaaabbbbaaaabaaabbbabbbabbbbbaaabaaaabaaaaabbaaababaaabbbbababaaabbaababaababbbaaaaaaabaabbaabbbbaaabbbababaabbbbbabbabaabababbabbbbaaabbbabaababbababbbbaaabaaaaabbababbbaaaaaabababbaababababbbbbaaabaaaabbabababaabaababaababaaabbbbaaababbbbaaabbbaaaaaaaabababaabaaabaabaabbaabbaabaababababbaabbaaabbbbbabbbaaaaabbababbbbaabbabbabaaabaabaaaaaaababaabaaaaabbaabbaabbaaabaababbbabbabbabababaaababbaabbaabbbaaaabaaaaabbabbaabbaabaabaaaaaabbbabbabbaaababaaaabbaaaabbabbbaaabbbabaababaabbabbaaaaaabbbbaababaabbababaabababababbaaabbababbbbbbbabbbbabbbbaababbabbaaaaaaababbabbbbaabbbbbbaabaabbabaaabababababababbaabaaaaaabbababbaaaabaaabbbabbbaabaabababbbaabbaabbbabbabaaaabababbabaabaabaababababbaababbabbaaaabbbbaabbbbaaabaabbbbababbbbbaababbaababaababbbabbabaababaaaabbbaaaababababbbabbabbaaaaabbabbaaabbbbbbbbaabaabbbbbbbaaabaaabbababaaababbaaaabbaaaabbaaaabaabbbabbabbabbababbbabbbbaababbbbbbabaaaabbbbaabababbababababbbbbabbbaaaaaababaaababaabbbaaabaaabbaabaabbababbaaaabaaaabaaababbbaaabaaababbbabbbabaaaabbbbbababbabbbbbbaaabaaabaabbbaaaababaaaabbbbbbababbabaaabbababbabaaaabbbbabbbabababbabaabbbabbbaababbabaaabbaabbabbbabababbaababbaabbaaabbaabbaaaababbabbaabbababaabbabbbaaaaabbbabaabbabbabbbabaabaabaaabbabaabaaaaaabbbbaabbbabbabbbabaabaabaaabababaabbbaabbaaabbbbabaaaabbabbaabaaaabaaabbaaaabaababbbbbbbbbbaabaaabbabbbbaabbabbaaabaabaababaaabaabbbbabbbaaaabbbbabbabbbaabbaabbaabbbaabaaabababbbbbabbbababbabbbaabbbaababbababaaabbaabbaabbaaaabbabaababbaaababbbaabaababbabbabaaaababababbbaabaabbabbbaaaaaaabbbaabbbababbaaabaababaabbaabababaaaabbabbbababbaaababaabaaababbababbbbaaaaabaaabaaaaababbababababababababbbaaabbababaaaabbbabbbbbbaabbababbbbbbabbbaababaaaabbbaabbbbbbabababbbbaaaaababaaaaabbabbabaaabbbaaabbabaabbbaabbaaaaabbabbaabaaaaaaabbbbbabbaababaabbabbbbababbababbaaabbbbbabbaaabbabbababbaababbabaabbbbbabbbbabbbbbbbbaaaaabbabbaababbaaaabbabbbbbaababbbbbaababbbaabaaabababbaaaaababbabaabbaababababbaaaabbbabababbbaaaabababaaabbbaabbababaaabbbbaabaaabbabbababbaabbaabbaaababbbabaaabbbabaaababababaaababbabaabaaaaabaabaaaaabbabaaababbaababaabbbaaababaaabbababababbbbabbbaaaabaabbbabbbabbbaaaabaabbbbbabbaaabaababbbbbbabbbaaabbaababbbbbbbbabaaaaabaaabbaabbaabbbbbaababaaaababbabaaabbabaaaababaaabbbabbbbbabaabbaaaabbbbbaabbbbbaaabbbaabbabbbbabbbaabbaabbbabbababbabbbaababaabbbaabaaaaabaabbaabbbabaabbaabbaabaabaaaababbaabaababbaabaabaaaaaaaabbbaabbbbaaabaaabaabbbaaabbaabbbaaaaaaaabbaaaaabbbaaaabbaabaabbabaabaaabaaabbbabbaabaaabbaabaaabbbbabbaababbabaaabbbbbbabbaabababaababbbaababababbabbbbbaabaabaaabbbaabaabbbabbbababababbababaaaababbaabbaaaabbbbabbababbaababbabbabbababababaaabbabbbbbaababbbabaaaaabbaabaabaaababaabababbbbabaababbababaababaaabbabbbabaaababbbbabbbbbbabbbaaaabbaaababbbbaababbabaabaabbbaaaabaaaaabbbaabbabaabbaaaababaaaabbbaaaabaababbabaababbbbbbaaabbbaaabbbaabbbbaaababbaabbabaaaaabaaabbbaabaaaababaabbbbbabbbbaabbbbbabbabaaaabababaabbaabbbaabbaabbbaaabbbabbaabbbaabbbabbaaabbbaaabaaabbbbaababaaabbaaabbaaaabbabaabaaabaaaaaabababababbaabbbababaabbbbbbbaabbbababababaaababaabaabaaabbbbaabbbbbbabaabaaaaabaabaababbaabaabaaababbaaabaabbbbaaababaaabbaaaaaabbaaaabaabbaaaabababbaaabbabbbaaaaaaabbbabaaaabbababbbabaaaabababbaabbbbaaaaabbabbbabbaabbbbbbbbabbbaaaaabbbbaaabbabaababaaaababbaaabbbaabbbaabbaaabaabbbabaabababbabbaaaaaababbbabbbaaabbababbbabbbbbbbabbbbbbaaabaaaaaabbaaabababbabbbbaaabaabaaabbbbbbaabaabbbaababaabbbbbbabbbabaaababbaabbaabbabbababbbaaaabbabbabbbbbbbbabaaaabbababaaaaababbaabbaababababaababababbababbbabbabaabbbbbaabbaaababaaabaabaaaababaaabababbbaaaaabbbbbbabbaabaabbabbaabbbaaabbbaaabbbaaaaabbbaaabbbbaaaabbaaabaaabaabbbbaaaaaabaaaaabbaababaababaabbbbabaaaaabbbbbbbababbbbbababbbaabaaaaabababaaababababababbbabaaaababababababbaaaabaaabbaaabaabbbbbabaaabbbbabbbbbbabababbbbaabaaabaaabaaababaabaabbaaabbaaabbaabbabababbaaaabbbbaabaaabaaabbabababaabbbaaaabbbabbabbabaabbbaaaabababaabbabbabbaababbbbabbaaaaaaaabbbbabbbbbbabbabbabaaaababaaaabababbbbbbaaaabababaabaaabbbaaabaabaaabababbaaaaabbaaababbaababaaaabaababbbaaabaabaaabababbababaaaaaaaabbaabababbbbbbaababaabbbabbaabbaaaaaaabbabbababababbbbbababbabbbabbaabaababaaabbabbaaaabaaaaabbabbbbbabbbbbaabbbbaaabbabbaabbaaaaabbbbaabbaaaabbbbbbbaaabbbbaaaababbbbaabbbaaaabbbaabaabbabaaabaabbbbaaaabbabbaaaabababaaaaaaaabbaabbbaaabbbbaabbabbbabbbbabbbbaaabaaabbbbbababaaaaabbaaababbababbabbbaaaaaababababbbbbbbbbabbabaaaaabbbababbbabbaabaaababaaabbbbabbbbabbbbbabbabbabbabbbababbbbaaabbaaabaaaabbbbbbbabbaaababababaabbaaabbababbaababbabbaabbaaaabbbaababbbabbabbbabbaaabaaaababbabbbaaaaababbbbbaabbbabbbaaaababbaababbaaaaaabbbbabaababbbbbabbbbbaaabbbbaaabaaabaaabbaaabbbbabaaabbababaabbabbbbaabaaaaaabbbbaaabaaababbaabbaaabaabaabbababbbabaabbabbbabbaaabbbaababbaabababbaabbbbbabaaabababbabbbababbaaabbaaabaaabbabbbbbbaabbbabaabaabbaaabaabbaaaaabababaabaabbbabbbaaabababaaabbabbbbaababaabbbbbbbabbaabbbbbbbabaababaabbbbabaaabbaabaaabbaaabbbababbbaaaabbabbaabbabaababbabbbbbbababaabbaabbbabababbabbbabaaababbabaababbaabaaaabbaabababaabbbbbaababaaaabbaaaaaabbabbaaabbababaababbabbbaabbbabababaababbbaaabbbaaabaababbaaaabbaabaaaaabbbaabbbbabbaaababaaabbababbbababbaaabbabbabbabbaaabaaabbaaabababaababbbbbaabaababababaabaabaabbbabaabaaaababbaaaaabbbaaabaaabababbaabababbbbbbbbaaaaababaababaaabbbaabbabaabaaaaabaabaabaaabaabaaaababaabbbbbbabbbbaabbabbbabbbbbaaabaabaaaabaaabababaabbabaaabaaabbbbbbabbabaaabbbbababbbabaaabbbbaabbaaabbbbbbbabbbaabaaabaaaaaaabbaababaaaaabaaaaaaabbbababbbbbbbababbaaabaabbabbbbbaabbaabaabaaaaaababbbabaabbbbaaabaabbaaabbbbabbaaabbbbbbabbabaabbbbbbbabbbaaabbbbababaaaaabababaabaaabbaabbaaaabaababbaaabbbabbbaaabaabaaabbbbbabababbbbbbaaaaababbbbbaababbbbabbabaababbbbbaaaaabaaabbaababaaabbabbbabbaaabbbbbbaaaaabababbbbbabababbabbbaabbbbabaabababbbbbaaabbbaaabaaababbbababbbbbaabbbbaaabbbbabbaaabababbbaaababaaabbaabbbaabaaabbaaaabbbbbbabaaaaabbbabbabbbbbaaabbbbababaaaaabbabbaaaababbabaababbaaaabaaababbbbaabbbabaababbbbbaabbabaaabbbbabababaaabbabbabaabbbbaaabaabbabaabababbabbbaaabaabbbbaaaaaabbbbabbaabbbbababaabababbaaaabaabaaaabaaabbababababbbaaababaaabbaaaaabbbbbabbbaabaababaabababbabaabbaaababbabbabbaabbabbbbbaabaaabbbbbbbaabaaaaabbaabbabbaabbaabbabbbbbbbabaabaaabaaababbbaababbabbababababaaababbaabaabbbabbbaaabaaaaabaabaabababbbbaaabbaaabbbabababbbbabbaabaababaabbbbaaabaabaabbabbbbbaaabbbabaabbaaaababbbbabababbbaaaabbaaaabbaabbaaaabbabbbbbabbabbabaabbbaabaaabaaaabbbaaabaaabbbaabbbabbaabbaabaabbbabaaaaababbbabbbababaabaabbbaabbbbabbbabaaabaaaabaabbbabababbaaabbbaabababbaaaaaabbbbbbbbbabbbbbabbbbbabaabbbabbaabbbabaaaabbbbbbaaabaabbbbaabbbbbbabababaaabaaabbbaabbbaabbabbabaaabababbabaabbaaaaaabbaaaaabaabbaababaabaabbbabbaabbabbabbabaabaabbabbbabaabbaabaabbabbabbbbbbbaabbbbabaaabbabbaaaaaaaaabaaababbabaaababaaabaabbbbaaabbaaaabaaaaabbaabbabaababbbaababbbabaabaaaabaaabbaabaabaababbabababababbbbaaabbabbaababaababbabbbabbbbabababbbababaaaabbbbbaabbbabaabaaaababbbaababbbbaaaaaaaabbbaaaaabaaabaaababaabbbabbaabbbbabbbbbbabaaaabaaaaaaaabbaaabbbaaaaabbbbaabbaaaaabaababaaaabbaabbbbabaaaaaaabababbbaaabbbbbbbbabbabaabbaababbabbbbbbaaabaabaabaaaaabbbaabbbbbaaabaabbbabbabbabbabbbabaaabbabbbabbbbabbabaabbbbbbbaabbbaaababaabbabbbbaaaababaabbbaabbbabbabbaabaaabbbbbabaabbbaaabababbaaaaabaababbaabbbabaababaaaaabbbaaaababbaabbaaaababaababaabbbbbbbaabbaababbaababbbabaabababbababbbaabbbbaabbbaabbbabbbabbabbbababbaabbabbbbaaabbaaababaaaaabbabaaababbbbabaaabaaabbbbabbbaaababaaabbababbbababaaaabaabbabbbbbbaabaabaababbaabbbabbabbaaaabbaaabbbbbbbababbabbbabbabbaaaaaaabbaaabaabbbaaabaaaabababbbbababaabbbbbababbbbaaabaaaabababababbaaaaaabaababbabaaaababbabbaabbbbbbbaabbabbaaabaabbbaabababaabbbbaabbaaaababbaaabbabbbababbabbbabaaaaabbaabaaaaabaaaaaaaabbbaaaabaabababbbbbaababbaaabaaaaaabbbababbabbaaaaababaaabbbbbaabababbbabababaabaaaabaababaaabbbbabaabbbbbaaaaababbabbbbabbbababbaabaaaaabbbbbbbbaabbbbbbbaaabaabaabbabbbabbaabaaababbabbabbabbabaababbbababaabaabaaaabaababaabbbabbaabbaaaaabaaaababaaaaaabaaababbabbbbabaaaabbaaababbabbaabaabbbabbaababaaababbabaaaaabbbabbbbaabbabbababbbbbbbabbaabbbabbbbbaababababbbaaaabbbbbabbbbbabababbaaabbbabaaaaabbbbabbabbaabaaababaabbabbaabaaaabaaabbabababbbabababaaabaabbbaaaabbbaaaabbbabbabbababbaaaabbbabaaaabbabaaabaabbabbabababababaaabaaaabbaaaaaababbaaaabbabababbabaaaaabbbaabbaaaabbaaabbaababbbaabbaabababbaabbabaabaabaabbabbbaaabbbabbabbaabaababbaaabbabbabababaabbaaaaaaaaabaaaababbbababaabaabbbbbbbaabaabbababbaaabbabbabababaabbbbbbbbababbbbbaaabaaaaaaaabbaaaaabbbabaaaabaaaabbabbbababaaaababbabbbbbaabbaaabbbabaabaaaaabbbbabbabbababbbbbbabaaabbaababbaababaaaaaaabbbbbbbababbbababaaabbaaabbbbaabaaabbbaabbbaabbabbabbbbababaaababaaaaaababaaababbbbabbbbbbaabbbbbabaabaababaaababbbbabaaaabbabbabaaabbbbbaaababbababbbbaaaaabaabbbabababababaabaabbaaabaaabbbbaababbbaabaabbbbabaaaaabbbabbbbabaaabbaaabababbbaabaaaabbaabaaaaabbabbbbabbbbbbbaaaaababaaaaabbbbabbabbaaaaaaaabbaababaaaabbaaaabbabababbababbabaaababbbbabababbbbbbaababaaabbbbbaabaabbbaaabbabbaaaaabbbaabbaabbaaabbbaabbaaaaaaabbbbbabbaaaabbbbbbbbbbaaabbababbbbaabaabbababbbabbabbaabaabbbbaaabaabaabbababaabaabbbbbbaaaaaabbabbbabbbbbabaaabbbbbabaabbbbbbabababbaabaaabbaaaabbababbbaabbabaabbbaababbbbbabbbabbabbaaababbaabbbbbaabaabbbbabababaabbbaabaabaaabbbabbabbabbababbbbbbaaaaaaaaaabbabaaaabbabbbbaaabaaaaaabbabbbbbaababaabaaabaabbbabbbabbabbabbabaabaabaabbbbbbbbbbbbbbabbbaaaaaaabaabbaabaabbabaaaabbbbbabaaabbbbabbbbaaabbbbabaaaaababbaaaabbbaaababbbbababbbbbbbabaaaabbbabbabbbabbaaaaabbababbbaaababbabbbbabbaabbbababbbababbbaaababbaabaaabababbaabbababaaabaabbbbaabaaaaaaaabaaaaabaaabbbabbaaaaabbabaabaaabaababaababbaaabbbbbbaaababbbbaabbbaaaaaababbababaaaabbababbbbbbbbaaabbaaaaaababbbbabbaaaababaaabbaabaabbbbbabbaababbaaabababbabbaaaaabaabbaaabbababaaaaabbababbbabaababbaaabbabaaaabbaaabbabaaabbbbabbbaababaaabbbaababaaaababbabbabaaabaaabbabababababbaaaaabbbabbbbbabbbbaabbabbbbbbabbabbbababbbaabbbbbbaabbabaabbaaaaaabbbaababbbbbbabbabaababbbaabbaabaaabababbaaaaaaaabbbbbbababaababaabaabbababbababbaabbaaabbbaabababbbbbaaaabbbababbbbaabaaaabaaababbaaaaaaabababbaaabbabbaabbbbaaabbbaabbbbabaaabaaabbababaaaabababbaabaaabbbbbaaaaababaaaababbbbbbbbabaaababbbbabbbababbbabaaabaabaaaabbabbaababbbabababaabbababbbababaaaaaaaaabbabababbbabbabaaabbabaabbbaabbbbaaaaabaaababbbaabbabbbaaaaabbaabababbbbababbaaaaababaaabbaabbaaabbbbbaabaaaaabbbbbabaaaabaabaaabbbabaaababbaaaaabbbbbababaaaaaababaababaabbbabbbaaabbaaaaabbbbbabbbabbbababbaababbbbbaaabbaaaaababaaabbabababbababbaabaabababbbbbbaaaaabbbabbbbbaaababbbaababbbabbbbbaababbabaaababbababbabaaabaababaabbbababaabbbaabaababaababaaaabaaabbaabaaabbabbbbbabababbababbaaaababbbbaabbbbabaabbaababaabbababbabaabbbbaabbbaaabbbbaabbaaababaabbaabbbbabbababbabbbbabbbbaaaaaaabaabbabaabbaaaaabbbbaaabaaababbabbabbaababaababaaabbabaabaaabaabaabaaababaaaaabbbbaaaabaabbbaababaabbaaabaabaaaaaabbaaaabaaaaaabaabaabababbbbaababbababbbaabaabbbbabbababbbbbbaabaaaaaaaaaabbabbaaaabaabbaaabaabababaabbbbaababbbabaabbbaabaaabbabbaaaaaaaaaabbabbabbaaababbababbbbabababbbabaaababaaaabbbbbaaaaabbbbabbaabbabbaababbabbabbaaabbabbabaaabaababababbbbabbbaaabaaaabaababbbbaaaaabaabbbaaaabbabbaaabbbbaaaaaabaaaabaaaabaabbbbababbbaaaabababbbaaababbbbabbabbababaababaaabbbbaabbbbabaaabaaaaaabaababababbabbabbbaaabbbbabbbabbbaababbbabbbababaabbaabbbbabaaaabbabababaabaabaabbabbbabbabaabbaababbabbbbaaabbaaabbabbbaaabbabababababaabbaaaaabaaaaababbabaabbbabbbabbbabbabbbbbabababbbababaabbbbabbaaabababaaabaaababaaababaabbbabbabbbbbaaabaabaabbababbabaabaaaaabaaabaabbbbaaababababaabbababbabaaaaaaabbbaabababbaabaabbaaaaabbbbbbaaaabbbbbaabbabbabbbaabbabaabbaababaabbbbbaaaaaabbabbbbbababaababbbabaabbbbababababbabaaaaabbbbaaaabaababbaaaababaaabbaabbbabaababbbaabaaaabababaabbbabbaaaaabaaaabaaabbabbbbabbbaababbbbbbbaababbbaabbbbbababaababbaaaabaababaababbaabaabbbaaabbabaababaaabbbabbabbbbababbbbaaaababbbbababbbbbaaaababbbaaabababbbbabaaaaaaaaaaabbbbbabaabbabbabbabaaaababaabbbbababbabbaabbaababbaababbabaaababababbbaababbaaaababbbabaaaababbbababaaabaaaabaaabbabbbaaaabaaabbabbbbbabbbbaaabaababbabaabbbbabbaabbabaaabaabaabbaabaabaabbbbababbaabababaababababbaabbababababbaabababbaababbbabaabbbbabbbbbaaaabaaabaabaabbbaabaabababbbbbbbbbaabbabbaabaaaaaaabababaabbbbabaaaabbaaabbbbbbaaabaababaaabaaaabbbbaaabababaabbabaaaaabbbbaaabaaabaaabaaabbbbbbaaabbaababbabbbbbababbaaaababbbaabaaaabbababbababbbbaabbaababaababbbbaabbbababbbbbbbaaaabbabaabababbbabbabbbaabababaaabbababbbbabbaaabbbaaabbbbaaaabaaaaaabbbabaaababbaaabbaaaabbbbbabaaaaabbbaaabaabbbbaaabbabbaabbbaabbbbaababaaaaaabbabbbbbbbabababaaaaaaabaaababbaaaaaaaaababbbababbbbaababaabaaaababbababbbaabbbbbabbabbbbababbbabbbbababbabbaabaaaabababbaaabbbbbbaaabaabbabbbbbaaabbabbbababbbabbbabbabaabbaaabbbbbbbbbaabaaababbabaaabbbaababbaabbbbbaababbbabaaaababbbbabaaababababbabaabbbaababbbbabbabaabbbbbaaababbaabaabbbbbabaaaaabbaabbbaabaaabaaaaabbababbbbbbabbbbbbabbaaabababbbbbaaaaaabbabbbabaaabbbababbbbbaaababbbaabbaababbbbaabababbabaababaaaabaaaabbbabbabaabbabbbabaabbbbaaaababbabbbaabbabbaabaaabbaabbaabbaaaabaabbbbbaaaabbaabaaabbabbbabaaaabaaabbbbabaaaaabbaaabababbbbbbbbaababaaababbbbbabbbaabaaaabbbaaabbbaaabababaabbaaabbaabbabaabbabababababbabbabbababbbbbababbabaababaabbbbbaaaaabbbbabbbababbbbbbabaabbbabaaaabaaaabaabbaaaaabbaaabaaaaaaabaababbaaabaabaaaaabbbaabbabaaaaaaabbaaaaabaaabbaaababaaaaaabbabbabbbbaaabbabababbaaabbbbaaaaabbaaaababaabababbaaababbabaabbaaaaabababaabbababababaababaabaaaabaababbbbaabbbabbbbbaaaaabbbbaabababbabbbaabbbababaabbaaaabbbbbabbabbababbbbaabbbbabbbbbaaabbbabbaaabbbbaababbbbaaaabaaabbbaaaababaaabaabbababababbbbbbaababbbaaabbbbbaabaababbbbbbbaaababbababbbbbaabbbabbaaabbaabbbbaabbabababbaababbbaaababaabbaabbaabbbbbaabbbaaababaaabbbabbabbabbbbbbbbbbabaabbaabbbbababbbbbbababbabababaaaaaabbbabababaaaaaabaababaaaaaabaabbbaabbaaabaabbbbbaabbbabbaabbbababbbbbababbabaabaaaaaabbababbbababbabbbaabaaaabaaaaaaaabbabbabaabbaabaaababbbaaabbbabbbaabbaaaaaabbbbbaabbbabababbabbababbbaabbaaabbbbababaaababbabbabbaaabaaaabbababbbaaaababbabbbaabaaabbbababbabababbbabaababaaaababababbaabaaabbbabaabbbbabbabbabaabbabababbababbaabaabbababaababbbbbbbbaabababbababbbaaabbabaabaabbbbaaaaaabbaaaababaaaabbbbaabaabbbaabbabaababaaaaaaabaaababababbbbbaabaabababaaaaaaaaabbababbabbabaababaaaaaaabbbbbaabbaaaaabababbaabaaaaababaaabaababbabbbbaaaaabbbaaabbbabbaaaaaabaaaaaaabaabbbabbbaabbbbbabbbbaaaabbbaaabbbaaababbbbbbababbabababaaaaaabaabababbbaabaabbbaaabaaaabbabbbabaabaaabababaaabbaabaabbaaabbbbbabbaaaabbbaaababbbabbbbaabbbabaababbaaaaabbababaababbaabaabbbbaaabbbaaabaabbbabaaabababbbabbaaabababaababbaababaabaabababbabbbabbaaaabbababababbbaabbbababbbbaabbbbbbabbabbbbbabbabbabbaaaabaabaaaabbbaaabaabbbabababaaabababbaabbbaaababbbababaabaababaabbababbabaaaaaaaabababbbbabbabaaabbbaaaabbaabababaababbabbbababaabbaaabbbabbaabaaaaabaababaaaabaabbaaababbbbabaababaaaaababbaabbbabbbbbabaabbaaabbabaaabbaababbbbbabaabaaaaabbbababababbbbbbabbaaaaaabaaaaabaaabbabbaabbaaaaabaaaababbbaaaabaaaababbbbabbbbbbbaaaabababbabababbbbaaabaaabaabbbaababbbbbabaaababbbbaabaabababbbabaaaaaaababbabbbbbaaabbaaaabbbbabaabbbbaabbabbabbbbbabbaaaabbaaaabbbabaabaabaaabbaaabbabaaabbaaababbbaababbbababaaaabbbabbbaababbaaabaababaaaabbbbababaaaaaababaababababbabababaaaabaabbababbaabaaababbaaabbbbaaabbbabbababbabbabbbabaabaababbbabbbaabababbabbaabbaaababbaaababbbbabbaababbbaabbaaabaabbabababbbbaaababaaaaaabbbbabbbbabaaabaababbbaaaaababbbbaaaaabbbbbabbbabbbbbbbaabaaabbaababbbbbbbbaaabbaabababaaabbaabbbaaaabaaaabbbababaababaaaababbaababbababbbbababaaabbbababbabbaababbaabbbababbbbabbbbbbabaaaaaaaababbbbabaaababaabaaaaabbbabbaaabbaabaaaaabaaaababbabababbaabaaababbaababbbabbaaabaababbbabbaabbababbbaababbbbbabbabbbaaabbbaabbaabbababbabbbabaaabbbbbbbaababbbabaaabbaabbababbbbabaaabbbaaaabbababbaababbbbaabaaaaaaaaababbabbaababaabaaabaaababababbaaaabbbabbbababaaabbaaaababbabaabbbbbbaabaaabbbbbabaabbaabbaaabbabababbaaaaaaabaabbababbabaabaabbaabaabbbbbbaabaababaaabbbabbbabbbbbbaaaaababbabbbbbababaabaaaababbbaaabaaaaabbaabbbbaaaaabbbbbbbaaaaaabaabbababbaabbbaaabaabbbbbbbaaaabaaaabaaabaaaabaabbababbaabaaabaaabbbaaabbbbabbabaababaaaaaaababbabaabaaaabbbbabbaaaaaaaaabbabbbbbbaaabbaaabababbbbaabbabbbbaabbbbababaaabbbbbababbbabaaaabbaababababbbabaabbbaabbbaaaaaaaabbaaaabbaababbababaabaababbbbaaababbbabbbabbbaaabbbabaaaaaabaabaaabbaaabaabbbaaabbabbaabbbbabbbabaabababbababbababbaabaabaabbabbbaabbbbababaabbaabaaabbaaabbaaabaabbbbbbbaaaabbaabbaababbbaabbababbbaaaabbaaaabbbbbbbbbabbaabaaababababaaaababbabaaaababbbaaaaaabbababbabaabababaabbbbababaaabaaababaaaaababbbabaabaaaaaaaabbbbbabaaabaaaaaabaaaababbbbaabababbbbbaabbbababbababbbbabbaabaaabbabbabbabaaaaabbbaaabbababbbaaaababbbabbbabaabbaaaabbaaaabbbabbbabaabaababaaabbbbabaabbbaababbbbbbabaaaabaaabbbabbbbaaababaabbabbbbaaabbbbaaaaaaaabbbbaabaabbabbababbabababbbabbaabbbaaaaabaaabaaabbbbbaaaaaaabaaabaabbbabaabbbaaabaaaaaabbbaabbabaaaaabbabbbbaaaaaaaaaabbababbbaaababababaabaaabaabbbaabaaaababbababbaabbaaabbaaababbbbbbaababbaabababbaaabbbaababbbabaabbaababbaaaabbbbabbaabbabaaaabaaaaaababbbabaabaabbaaabababbaaabababbababbaabbaaabaabbbbbaabbbabbbbabbbaabbbbbbaababbaaaaabaaabbabbabaaabbbaabbababbaaaababaabbbabaababbbabbabbbababbbabaaababaaaabababbabaaaaabaaaaabaabbbbbbabbbbaababababbaababbbbbbbbbbabaaabaabababaaababbbabaabaabbbbbaaababaaaaaabbabbbabbabaababbabababaabbababbbaaaabaabbbaabbbbbbaabbabbabbabababbababbbbababbbbbbabbbaabbbabbbbbaabbaaaabbbbbbaabbbabbaaabbaaabbababbbaaaaaaaaabbaababaababbbaaaaaabbbbaabbaababbbbbaabbbbababaaaaabaaabbaaabbbaabaaaaabbabbaabababaabbbbbbabababaabbbabbabbbbbbbabbaaabbbbaabbbbabbbaaabbbbbbaabbaaaabaaaabbabbaabaaabbabaabbaaabbbbabaaabaababaabababaababababaababbbabababbbbbbbabbbabbbbaabbbbaababbababbabbbaababababbabbaabbaabbaababbbbbaabababbabbbbbbaabbbaabbaabbabbbbbabbabaaabbaaababbaaaabaababbbbbbabbaaaaaabbababbbaaaaaaabaaaaaabaabaaaabbbbababaaaaaabbababbabbaababababaaabbbbbbbbbbbababbbaaabbabbababbbbbbbababaaaabbbaaaababaabaabaaaabbaabaaaaaababaabbbaabaaaaaabbbabbbabbbabbbaaaaabaababbbbaaabbbabaaabbbbbababababbbabbabbbabababaababaabbbbaabaaaaabbbabbbbababbaaabbaababbbbbabbaabbabaabaaaabaababaababbabaabbbaaabbbabbaababbbaaabababbababbbabbaabbaabbaaaabbbaababaabaababbbaabababaaabbbaabbbabbbaabababababbaaabababaaaaabaabbababaaaaaaabaaaababbbbaaaabaaaaaabaabaaaaabaaababaabbbbabaabbbbabaaabbbaaababbabbababbbabbaaaababbaaaabaabbbabbbbbaaabbbbabaaabbababbabaaabbbbbabababbaabaabaabbabaaababaaabaababbbbaababbababbabbbababaababbaaaabaabbaabbbbababaaaabaaabbabbbbabbbabaabbabaabaabbbaaaabbbbbbaabaababaabbababbbaabbbabaaaaabaaaaaababbaaabaababbababbbbbaaabaaaabbbbbabaababaabbbaaaabaabaababaaaaabbbbbbabbaabbaababbbbbbbaabaabbaaaabaabbabbaabbaaaabaaaaabbabbaabababbbabaababaaabbabaababababbbbbaababbabaabbbaaabbaababaaabbbbaabbababbbbaabbaaabaabbaaabaaaabbbbaabbbbbbaaababbabbabaabbbabaaabababaabbabaabbaaaaabaaababaabbabbbbbaabbabaaaabbaabbbbaaaaaaaabaaabbaaabababbbbbbaaabaababbaabaabbaabbabbaabbaabbbabaababaaaabaaababababbbabbbbabbbaababaababababbbaaaabaaabaababaabbaabbaaaabbabaabaaabbababbabaaaaabababbbababaaabbbbbbabaaabbbabbbbabaabbbaaaaabaababaabbbaaaabbababbbaaabaabbbbbabaaabbbabaabbaabbbabababbababbabababbbaaabaaabbabbabbaaaaabaabbbbabbababaabaabaaaaababaabbaabaababbbbbbbabaabaabababbaabbbaabbabbabaabbaaaabababaabbbabbbbaaaaababababaabbababbabbbabaaaaaabbbbabbbbaabbabaaaabbbbaaaaaaababbbaabaaabbbababaaabbbbaabbbbabbaaaabbaababaabbabbbbbbabbaaaaababbbbabbbbabbaaaabaababbbbaabbaaabbbbabbbaaaaaababababbbbabaababaabaabaaaaabbbbabbaabbbbaaaabaababaaabbaabbaabaaaaabbabaabaabaabbbabbbaaaaaaabababbababbbaaabbaaaabaaababaabaabaaaaabbabbbbaabbbababbaaaaababaabbbbaabbbabbababaaabaababbbbbbaabaabbbbbaabaaabaaaabbbbbaaaaaabbababbbbbbaabbbaabbbbbaababbbbabbabbabbbbaabaaababaaabaabbbbbaaabbaaababbaabababbbbabbaabbaaabbbabbbabbbbababbbbaababaabbabbbbabbaaaabaaabaaabaabaaaaabaaaabaabbbbabbbabaabbaababbaabababbbbbbaaabababbbbbbaabbababaabaabbaaaaaaaabbbbbbabbabaaaabbbaaaabaabaaaaababaaababaabbbbbaababbbabababbbabababaabbbbaabbaaaaaaaabaabaaabbbbaaaaabaaabbabaabbabaabaaaababaabbbaaabbaaaaabbbbaaabaabbabbaababbabbababbaabbaabbbabababbbaaaaaabaababbbbabbbbbbbbbaaababbabbbaaababbaaabbbbbaabbbabbbababbabbbbaabaabbabbbbabbbbababbaaabbbabbaaaabbbbbabbbabaaabbbbbaaabbbaaaaaabaaababbabaabaaabababaababbaabbbbaaaabbbaabbbbbaababbbaabaababbababaaababbbabbbaabbbaaaabaabbbaaabbbababbaabaabaabaaaabbabbbbbbbaabbaabbbaabbababaaaaababbbbbabaababaaaababbaabaaaaabbaabbbbabbaaaaabbbababaabbbabbbaaaabaabbbbababbbbababbbbaaaabaaababbbaabbaaabbbaaaaabaabaabbbbaaababbbabbbabbabaababababbabaaababababaababbaababaaaababbbaabbbbbaaababbbabababaaaaaabbbaabbbabbbabbabaaababbaabbaaaaaabbbaabbaababbabaaaabbbabbbbaaabbaabbaaabbbabbbbbbabbaabbaaaababaaaabbbbabaaabbabbbbbabbaaaaabbbbaaaaaaaabbabbaaabababababbbabaababbabbaaabbabbbbabbaaabbaabbaaaabaabababaabbbababbaaaaaabbbbabbabbbabbaabbbbbbababbabbbbbaaaaabbbaaaabbbbbaababbbbbabbbabbababbabaababbabbabaababababababbbbbbbababaaaaaabbabbbaabbaaabbaabababaaabbaabababaaabbaaabbabbbaaaaabaababbbabbaabbaabbabaabababaaabaaabaaabaaaaabbbbabbbbababbabaabaaabbbaaaabaaabbbabbabaaababaaabbababbababbbaabbbaaaaaaabaaaaabaaabbbbabababaaabaaabbbaabbbbbbbababaabaababbabbabababaaabababbaabbbabaaabbbbabbaababbbaaabbbaabababbbababbbbbabbbabbbbbbbbababaaaabbabababbabbbaaabbbbabbbbbbbbbbaaabbaababbbababbabababbaaaabbaaaaabbbaaaabbbababaabbbbaaaabbaaaabaaabbabbbabbaaabbabaababbbababbabbababbbabaabbaababbbaaaabbbabbbbaaaabbabbbbbaabaaabbbbbaabbabbbbbbaaaaaababaabaabbbabaaabbaaaaaaaaabaabaaaababaaabaabbabaabbaaabbbabbbbbbabbabbbaaabababbaaaabbabbbbabbabbbbabbabbbabbbabaabababbbbbaababbbaaababbbbaaabbbbbababbbbaaabbaaaabbaabbaabaaaaabaabbbaaaaabbabaaaaaaabbabbbbbaabbababaaaaababbaabbbbbabbbbbbaaaaabbbabaaaaabaabaababbabbbbbababaaabbbaabbaaabbaabbbaabbaabbbaaababaaababaaabaaabababaaaabbbaaaabbbbbbabaaabbbbaabbabaaaababaabbbaabbabaabaabaababaaaabaaabbaabbabbbbbabaaaaabbbabbabbbabaaababaaaaaabbbaabababababbbaaaaaabaababaababbbababaabbabbbbaabaaabaaaaabaabbabaabbbbbabbbabaaabbabbaabbabaabaaabbabbabbbaabbbbbbaaaaaabaaaaabababaabbaaabaaabababbaababbabaaaaaaabaabbbabbbbbaabababbbabababbaabbabbbbbaaabaaaaaaabaababbbbbbabaabbbaabbbbbaababbabbbbbabbbaaabbbbabaaabaabaaaaaaababbaabbbaabaabbaababbbabbbbabbabaabbbabaaababababaaababbaababaabbbbababaaaabababbbbabababbaabaaaabaaabaabbabbaabbbabbababaaabbaabbbbbaaaaabbbabaabaabbbbaaabbbabbaaaaabaaaaabaaabbaaaaaaabbaabababbaababaababaaaaaaaaaaabababbabbaabababbabbbaabaabaaaababbaaababbaaaaababbbabaaabbbabaaabaaaaabbabbabaabaaaababbabababaabbbbbaababbaaabbabbbbaaabbbbbbabbabbababbbabbabaaabaabbaaaaabaaabbbbbbbaaaaabbbaaaababbbaabbbabbbabaaabbabbbaaaaaaaababbbbbaaaabaaabbaabbaabaaabaaaabbbababaabbabbbabbaabaaabaaaabbaaabaaabaabbaaaaaaabbaaaaaaabbbaaabbaabbbabbabbabaababbbbaaaababaaaaabbabaabbaaabbbabaabbaaaababbbbbabbbababbbabbbaaaaababbbbbbaababaaaaabbbabbbbbaabbbbaababbbabbbaabbbbbbabbbbabaaabaaaaabaabbbbaaabbbaaaabaaaaaabbbaabbbaabaaababbbbbaaabaaaabaaaaabbbaabaaabbbabbbbabaabababbaabbbaabaaabaaaabbbaaabbbbbaaaaaabaababbaaabbbbbbbbababaabababbbbaababaaaaaababaabbaaaabababaaaabaaababbbbbbaaaaaaabababbbbaababbbabbabaaababaabababaababababaaababbbaabbabbbabaaabaaababbbaaaaabaaaababaabbaaabbbabbababbabbaababaabbbbbbbaabaabbaababaaabaabaababaabababaabbbabababbbbaabbbaaaaaaabaabbabaababbbaabbbabbbababbbbbbbaabbaabbabbbbaaaabaabbbaabaaaabaababababaabbababaabaabbaabaaaaababbabaababbabbabbabbbaaaabaaabbaaabaabbbbaababababbabaababbbaaaabbbbbaabbabbbaaabbbaabbaabbaaaababbbbabaaaaabaaaabbabaabaaababbaaaabaaaaaabaaabbabbbbabbabbbaaaaabbbbbabbbbaaabbababababbabbbbabbabaaabababaaaabbaabaabbaabaabbabaaababbabaabaaabaabbbbabbaaabbaaaabaabbbaaaaaaaabbabaabaaabbaabbbaaaaabaabaabbbabaabbabaabaabbababbbbbaaaabbabbabbababaaaaaaababababbbababaaaababbbabaabaaabbbbaabaababaaaaabbbabaaaabbaabbaabbaaabbbbbabbaaababaabaaaabbbbbabbabaaaaaaabababbbaaaaaabababaabaaabbaaaabbaaaaaaaabbaaabaaabbaababaaaaabbababbbabbbbaabaabbbbababbbaaabaabaabbbbaaabaabaaabbbbbbaaabbbbbbbaabbbabbababbabaabbbaaaabbabbbabaaabbabaaabaaaaaabbbbaabaaabaaaabbabbababaababababaaabbababbbabaabaaabbbbabaaababbabababbaabaabaabbbabbbbbababaabababbbaababbbaaabbbbbbaaaaaabbbaabbabbbabbbbbbaabaabbaaaaabbbabbababaabbaabaaabbabaabbbbbabbbbaabbbbaaabbbaababaabbbbbaaaabaabbabbabbbbabbabaaaabbaababbbaabbbbabbbbbbaabaaabbaabbaabbbbabbaabababbbbabaabababaabbbababbaabbbabbbbbabaaababaabbbaabababaaabbaabbaabaabaaabbabbbaaababbaaabaaaaaaabbabbbaabbaabbbbbaabaaaababbaaababaabaabbaaabbbbaaaabababbbaaabbabbaaabababaababbbababaabaaababaaabbbaaabaaaabbbbabbaaaabbaaabbabababababaababbababbaaabbbaaaabbabaababaabababaabbabbbabbaabbaababbaabbaaabbbabababbababbabbabaaabbabaaabbbbbaababbabbabbabaababbbaabbabbaaaabaaabbbaababbababbbabaaaababbbaabbabaaababbabbbabaaabbbabbaaaaabbbababaaaabbaabbaabaaaaaababaaaaabbabbaabaabaaabbbaabababbbbabbbaabbabababbbbabaabababababababbbbaaaaaaaaababaabbaabaaaabaabbaabbaaaabaababbaaaaaaababbbababbbaaaabaaaabbbaaaaaaaabaaaabbaaabaabaaabaabaaabbbaaaaaabbabbaaabaabbbaaaabaabbbbabbababbbbbaaababbbabbbbaabbabababbbbabaabbaababaaabbbabababbaabbababbaaabaabbbbaaabaabaaabbaababbbaaabbbbbbbbbababbabbbbababaabbbbbbaaabababaaaabbabbaabaababaaaabbbbabbbaaabbbabbabbbbbaaabbbbabbbbbbaabbbbabaabbbabaaaaaababaabaaaababababbbbabababaaaaabaabbbbbabbabbbaaaaabbaaaabbbababbbbbbbbbbbabbbbaababbbabaababbaabbabbbabbbabbbaaabbbbababaaaaaababbbabaababaaaaababbbabbbbbbabbbbbaaaababbababbaabbabbbbbaaabaaaabbabbbaaabbbaaabaaaaabbabbabbbbbbabaabababbbabbbbaaabbaabababaabbbbbbbabbbaaaababaabbbababababbaaaabaabbbababababaaaabbbbbababbbababbbbbbbaababbabaabababaabbabbaaabbaaaabbabaabbbbbbabaababbbbbbaaaaabbbbababbbaaabbbabaabbbbbaababbbaaabbbbabaabbbabaabaababbbabaaababbbaaabbbaabaabbbbaaaaaaaaaabbaaabbbaaaaabbabbabaaabababaaaaaabaaababaabbbabaabababbaabbbaababbbabbbabbabbbababaabbbababbbbabbbbabbbaabbabaaaabaabbbaaaabbbabaaababaabbaabbbaabbbbbbbbbabaabaaababaabababbaaababaaabababaaaabbabbaaaababaaaaaaaaabbaaabbbababaabaabbbabaaaabaaaababbbbbaaaabbaabaabaaaababbbaaaaaaabababbbbaaaaabbbaaababbaaaaabbbabaaaabaababaabbbbabbbbbaaabbaababbaaaababbbbaaaaaaabbbbbbbababaabaabbabaababbaabababbbbbbaabaabbbaaaaabaaaababbbabaaaaaabaababaabaaaababbabbaaababbbbababaabbabaabbabaaabbbabaabbaabbaabbababaabbabaaabbaaabbaaabbabaaabbabbaaaaaaaababaabababaaabbaaaaaababbbbbaaaaaabbbaaaabaaaabababaabababbaabbaaaaaaaaaaababbbaaaabbabbababbaaaaabbbbbbbaabaabababababaaaabbababbbbaababaaaababbaaabbababbababbabbbbaabbaaabaabababaaababbbabbabbaabaabbabaaabbaabbaababaaaababaabaababababbbaaaabbbababbabaabbbaababbbbbabbaaabaabbabaaabbaabaaababaaabbababbaabbabaababbbabbbbaabaabbaaaaabaaaababbaaaaaaabaababababaababbbaabaaabaabbbbaabaabaaaaabbababaaababbaaaabbbaababbbaaabaaaaabbabbbbababbbaaabbbaababaabbaabababaabaababbabaaaaaaaaabaabaabaaabaaabbaabababababbbbbabbaaaaaabababbbababbabbabbbabbaabaabbaabaaabaaabbabaabaaaababaabbababbbbabbbaaabbabbaaaabbbbaabaabaaaabaaaabaababbaabaaabaabbaaabbbaabaabbbbabbabaaaaaababbbaabbbaaaabbaabbaabbbabbbaabbaaababababbabbbabaaabbaaababababababaaabbaaabababbbabaabaaaabaabbbabababbaabababbbbbbbbbaabbaaaaabbabaabbabbbbabaabbabbbabbbbababbbaabbababbaabababbbababbbbbaabbaabaaaabbabaaabababbabaababbbabbbaaabbbabaaabbbaaababaabbbaabaabbabbaabaababbbbbaabaabbabbbbaabbaaabbbabaaababbbbaababbaabababbaabbbaaababaabbbbbbbbbbbabbbababbbaababbaaabbbabbaaaaaabbbabaaaaaaaababbabababbababbabbbabbaaabbbbaaaabababababbabbbbbbaabbbaabaabaaaaabbbaabbaaaaabbbaabaaabaabaaaabbbabbbabaaabababababbaabaaabaaabbbbaabbbbabaaabbbaabbaabbbabbbbabaababaaababbbbbaaaaabbaabaaabaabaaaabbbaaaabaabbbaabbaaaabbaabbaabaababbaaabababbabbbaabaabbaababaabaababbbbbbbbbbbabbbbaabaababaabaabbabaaaabbaabaabaabaaabbaaaaabbababbabbbaababaaaabaaabbabaabbababbbbabaabaaaaaaaababaaaaaaaaaaaababbbaabababaaabaabbabbbbabbbbabaabbabaaaabbbabbbbaaababbbbbbaaaaaabbbababbababbbaabbbaabbaabaaabaabaaaaaaabaaaaaaaaaabbabababaabbbaaaaaababababbbabbbabbabbbaaabbababbbabbaabbbbabaabaabaaabbabbbbaaaaabbbaaabbbaaaaaaabbaaaaaaaabbbbbbaaababaaaaababababbbabababbbabbaaaaabbaaabababbbbabbbbbaabbaababaaababbaababaaabbbbbbaabababbbbaaabaabbaaaaaaabbabbbbbbbabababbaabababbbaabbbaabababbababbbbabbaabaaaaabaaaaaabababbabaaaabbbbaaabbbabbbbabbbaabbbbabaabbaaabbbbbbbbaaaabbbbaaaababbabbaaababbababbbababbaaababbaaabbaabbbaaaaaabbabababbaabbaaaababbbbababababaabbabbabbaaabbabaaababababbabbabbbbbbaaaababbbbaaababaabbbbabbbbbbbbabbabaabaaabaabaaabbbbabaabaaabaababbbababbaaabbbbabaaabbaabababbbaaaabababbbbaaabbaabbaaaaabaaaabaaaaaababaababaaaaabbbbaaababbabbabaaaabbbaabaaaabaaaabbabbbabbabbabbaaaababbaabbabbaabbabbaababaabbabaaaabaaaaabbaabbaaabbbbaababbaaabaaabbbaabaaabbababaaababbbaababbbbaaaaaaabbbaaabaababbbabbababaaaabaaabbabbaabababbbbbaababaabbbbbaaaababbbbabaabaabbbbbabaaabaabbbbaaaaabbbabbbaaabbaabbbbaabaabbbbbaabaabbaabbbbbaababaaabbaaaaaaababbbbbbababababbbaabbabbbaabbbabbaaabaabbbaaabaabaababbabaabbabbbaabbababaaabbbbbaabbbabaaaabbabbbaaabbababbabbbbbabbabbaaabbbaaaaababbababbaaababaaaabaaabbabbabaabaaaabaaabbaaabaaababaabbabababaabbaabbbabbbbbabbbabaababaaaabaaaababbababaabbbbaabaabbbbaaabbbbabaabbabbbababaabbbababbaabaabababbaabbabbabbbbbaaabaaaaabbaabbbbaabbaaaaabbaabbabbabbbbbaabbbbbaaabbaababaaaaababaabababbaaabbabbbbaaaaaabbaabbbabaaabaaaabababbaaabbaaabbbabbaabaaaaaabababbaaababbbababaaabbbabaabbabbbabaabbabbbbaaabaaabbabbaabbbaaaabbbaaabaababaaaabbabaaaabbbbbbbabbabaabababaabbbbaaaabbababababaaaaabaabbbababbaabbabbabbbbaabbbbaaababaaaaaaaabbaaabaabaaabaabbbaabaabbababbaaababbaaaabbbabbbaaabaaabaabbbbbbabbabaaaabaaaaaaaaaaaabbaaaabaabababbaaaaababaaaaaabbbbbbaababaaabbbbbaaaaaabbbaaabbaabbabbaaaabaaabbbabbbbaaababaaaabbabbbabbabaabaaaabbbbabaaaababaaaaaabbaaababbabaaabbbbaaabbbbbbbabaabbaabbbbabaaabaababbbbaaaabaaababbbbabbbaabbbbbbababbbabaababaabbaabbbababababaabbababbbabaababaabbbaabababbababaaaaababbbaaaabbbabaaaaaababbabbaaabbabbbbbbaaababbbabbababaababbaabbaabaababbbabbbbaabbbbaabbbabbbaababaaababbbbbaabbbabbabaababbaaaaababbbaabababbbaaaaabbbbaabababababbbaababbababaaababbbabaaababaabbabbaaababaaabaabbbaaaaabaaabbbbabaabaaababaaaaaaabbaababbaaaaababababbaaabaaabbbbaabaabbabbbbbaaababaaabaabababaaaaaabaabaaabbbaabaaabaabbbbbbbbaabbaabbaabbbabaabbababaaaababaaaaabaabbbababbbbbbbbbabbbbabaaabbaababbaabbaabababbabbaabbabbaaababaabababaaabbbabbbabbaabaaaaabbaaaaaababbababbbaabbaabaababaaabbbbbbababbababbbbabbbbaaabaaaabbbbaabbaaabbbbaabbaabbaabababbaabaabaabbabbabbabbbabaaaabbbabbbaabbababbaabbbbaaabaabbaababaabbaaaabaaabbaaaabbaabbbaaabbaaaabbbaabababababbabababbbaaaaabbaabbbbabbaabbbbabbbaabaaababbabababbbababaaabbaaaaababbbabbababbbbaaabbbbbbbbbbaaabbbabaabaaaabbabbabbabaababbbbbbbabbbaabbbabbbaaaabaaabbbaaabaabababaabbbabbabbaaabbbbabbaabaabbbbbbbaaaaaabbabbbbbbabaabababbaaaaabbbbbaaaaabaaaababababaaabaabbbbbaabbbbaaabbbbaabbbbbbbabaaababbbbababbbaaaabbbabaabaaabaabbaaabababbbaabbbbbaabababbbbabbaabaabbbabbabababaababbaabaabbbabbababbaaabaabaaaabbaaaabbbababbbbaababaabbbbbbbbabbabaababbbaaabababaababbaabbbbbbabbbbababaababbbabbbaaaaaabaaaababbbbbabaababbbaabbbaaabbabbaabbaabbbababbabbbbbababbaabaaabbbaabbbbbbaaabbbbababbaabaaabbbababbaabbbbaabaabbabbbbbbaaaabaaaaabbabbbbababbabababaaabbbbaaababbbbbabaaabaaaaaaabbabababbaaabababaaabbabbababbbaabbbbbbaaabababbaaaaaabbaaababbaabaabbaabbabbbababbbbbbbbbbbbaaaaabaabbabaaaabbbabbbbbaabaabababbababaaaabaabbbaaabbabbaabaabababaaaababaabbbbabaaaaaabaaababbababbbaabaabbbbabaaabaaabbbbaaabbbbaabbbbbbbbaababbbbbaabbbbbbbbbbbaaaaaabaaaaabaaabaaababbbbbabbabbaabbababbbbbaabaaaaabbbbabbbbbabbbbbbbaaaabaabbbbabbababaabaababbbababbaaaaaaaaaaaaaaaabbaaabaababbaaabbbaaababbabaababaaaaabababbaaabbaabababbbbaabbababbabaaaaaabbabbaabbaaaaabbbabbaaaaaaabbaabbabaaaabbaaaabbaababbababaaabbbabaabbabbbababbabbabbbbbabaaabababaabbaababaaabbabaaaabbbbabbbbabbbaabaaaabbaabbabbabbabbbbbbbababbbbbbabbaaaababaabbbbbbaabaaaabaabaaabbabbaabbbbbbbababbabaabaabaabbbaaaabbabaaabaaabaaabababaaabbabbaaabaabbabbbbbaabbbbababbbabbbababaaaaabaabaabaaababababaaaabababbababbaabbababbbaaabbaabaabbabbbbaabababbaababbbaaabbabbbabaababbbabbabbabbbabbbbaaaabaabbbaaabaaaabaaaaabaabbbbbbbaaaabbabaaabbaabaabbbbaaaabaabaaababaabbbbaaabaabbabaaaabaaababaababbabbbbbabababababaaaaaaaabbaaaabbaaabaaabbaaabbbabaaabbbbbababaaabbbabbbababaabaabbaaabbbbababaaababaaabaabbaabaaaababaaaaaaaabababbabababababbbaabbababbabababbbaababaaabbbbbaabbabaaabaababbabababababaabbabaabbbabbabbbaabbaababbbbabaaaabbbbabaabbbbbaaabbabaaaabbbbbabbaaabaabbbabababbaaabbaaabaabaaaaabbaabaabbabbabbaabbabaaaaaabbaabbbabbbbbbababbbaababaabbbbaaabbaaaabbaabbaaabaabaaaaababbbbabbaabbaaababbaaabaaaaaaaabbabbaaaababaabbabababbbaabababababaabbbbabbbabaabbbbaaabbaaabbbbaabbbababbbbbbbbabbbbabbaabbbbbbabbabbaabbbbabbaabaaababaababaababaaabaaaaababaaaabaabaaababaaabbbbbaabababaaaabbabbabaaababbaaabbaaababababbbbbbbabaababaababababaabbbabbbabbbbabbabbbbababaaaaaaabaabbbbabaabaaababababaababbbaabaaaaabbabbaabbbbaabaaaaaaabbbbabaabaababaabbbabbaabbbaaaaaababbbbaabaabaaaaaaabbbbbaabbababbaaaabababbaabaabbbbababbbabaabaaaaababbbbabbabaaababaaababaabbbbaababbbbbbaaaabaaabbabbaabaabaabaaaabaaaabababbbaabaaabbaabaaaabbaabbbbaaabaaabbaabbaabaabaaabaaaababaabaaaabaabaababbbbabbbbbaababbaabaaabaaaabbaaababbbbaabbbbabaabbabaaabaabbbaaaabaabaababbbbabaabbbaabbabaaaabbabaabaabbabbabbabbaaaabaaaabbbaaaabbbbbbbabbbbabbbbbabbbaabaaaababaaabaabaabbabbbaaabbaaaaaaabbaababaaaabbbabbabbabbaaaaaababbabbaabbabbaaaaabaabbaaababbbbbaabababbbbaaabaaaabbaabaabbbbbbabababbaababaaaaabbaababbaabbbabababbbaababbbbababaabbabbbababaabaaaabababbbabaaabbbabaaababbbaabaaaabbbbbbabbaabbbaaaaabaaaabaabababbabbbaababbbbbabbbbaabaaaaababaababbabbbbbababbaabbabbbaaaababbbabaababaabbabaababbbaabbbbbbabbbaabbbababaabaababababbabaaabbaaaababaaabaabbaabbbabbabbaababaabbaababbbbbaababbaabaabbbaaaabbababaababababaabaabaaaaaaabbababaababaaabbbbaaaababaaabbaaabbbabbbabbbbabaaabbabbbaabaababbbaaabbaaabbbbbbaababaaaabbabbababaabbbbbabbaabbbaaababbbbbabaabbababaabbaabbaaabaaabbabababaaabbbaaaababbbaaaaaababbaabaaaababaaaaababaababbaaaaabbbbaaaaaabbaaaabaabbbbbbbabbaabbbbbabbababbbbbbaaaaababbaaababbaabbbabbbbabababaaaabaabaaaabbbbaaababbabbaabbbbbbabbabbbbbbbbbbabbabbbaabababbbbaabaabaababbaaaabbbbababbbaabaabaaabbbababbaaabbaabaabaaabababbabbabaabbbbbbbabaaababbbbaaabbaaabaabbabbababbabaaabbabababbaabbabbabaababbbbbbbbabbbbabaaaabaaaabbbbaabaabaaabbbbbaaaabaabbabbabbaaabbbabbabbaabbbbbbabbbababbaaabbabaababbabbaababaaabbbaabaaaaaaabbbbbbbbaaabbaabbaaaabbaaaabbaaabaaaabbbbababbbbaaababbbaababbaabaabaaabbbbbbbaabbaaabbabbbbaabbbbabbabbaababbabaaabbbbbbaabbbaaabbaaabaabbbbbbaaabaaaaabbbaababbababababaabbabbbaabbbbbbabababababbbbabbaabbaaaabbbabbaaabbbbbbabbaaabbbbaaaabbbabbbaaabbbababbaabbabbabaabbaaaaaaababbbbaabababaaabbbbbbaaaabaaaaabbaabbbabbbaaababbbbaabaabbbaabbabababbbbbabbaaabbaabbbbbbabbaabaabbbbabbbbaababaabababbbbaaaaabaabbbaabbaaaaabaaabbbaabbbabbaababaabbbabaabbbaabbbbabaaabbbbaaabbbaabbaaaaabbbabaababababaabbaabbabaabbaabbaabababbbaabaaabbbbababbaabaaababbbbbaabbbabbaaabaaabaababbbbababaababaabaababbbbaabbaabaaaaaaaaababbaaaaaababaaabbabbaaaaabaaababbbbbbbabbbbbabbaabbbaabbaabbbbbaaababaababaaabaababbbabaabbbabbbabaabbbbbbbabbaabbaabbbabaaababbabbbaabbaaaabbaabbababaaabaaaabbbbabbaaaabaaaaaaaabababbabbbabbbabaaaabbbbaaabbbbabaaaabbaabaabbabbbbbbabbbabbbbabaaaaababababbabbabababbbabbabaaaaaaaabbbbaaabbabaaababbaaababbbaaabaabbabbaaaabbabababbbaaabaabbaabaabbabaaabaabaabaaaabaaaabaaaabbbbbabaaabababbaabbbabbababbbbaaaabaaabbabaaabbaaababbaaaababbbaaababaaaaaababbbabbbaabbaabaabbaabbbbaabbbbababbbbbbabbbaaaabababaabbbabbababaaabbaaabbabbbababbbbaaabaaaaabbbbabaaaaabbabbbbbaaabbbabbaabbbabbababbababbbabbbbbbbbabababbabaabaaabbababababbaaaabbaaabaaaababbabbaabbabbabaaaaaaababaababbaaabbababaaababbbaabbbbbbbbbbbbbbaabbaaaabaaabbababaabaaabbabbbaaabbaabababbbabbbbaabaabaaaabaaaaaaaabababaaaabaaababaababbbbaaabbaababaaaaaaabbbbbbaabababbbbbabaababbababbaaaaaabababaaababaabaaabbbbababbaaabaaabababbbbbbaaabababbbbaabbbabaaaabbbabbbaaaaaabbbaaaababbabbbbaaaabaabbbaabababbbabaabbbaaaabaaabaaabbbaaabaaabbabbabbbababbbbaabbaababaabaababbaabbbabaaabbababaabbabbabbababaabaabababbaaaabbbaaaaaabaabaaababaaabaabbbbbaabbabbbbabbbbbaaaabbbaaabbabbaaababbbbbbabbabababaaabbbaaabaabbabbbaababbaaaabbabaaabbaabbabbbbbbabbbbabababaabaabbbabbbababbaabbbbabbaaaababbbbbbaaaabbbbbbbaabbaaabbbbbaaabbbabbbbababbaaabaaababbbaaabaabaaaabbabbbaaabbbbaabaabaabaaabbabaabbbaababbabbabbbabaaaaaabaabbabbaabbaabbbbbabbaabbbbbaaabbabaabbaabaababaabbabbaabbaaaababababbabbaaaabbbbaabaabbbabbabaabaaaaaabaababbbabaabaabbbbbbbbababbaababaaabaaabbabbaaababbbababaaaabaabaaaababbbbabababbaababaabbabbaaaaaabababbbabaabbabbabbaabaaabbbaaabbbaaababaaaababaababaababbbbababaaaaaabbbbbbbaaaabbabaaaababbbaababababbbbbbababbabbaaabbbbbbaaabbaaaaabbaabbaaaaaabbbbbbbabbabbabbaabaaabbabababaaababbbabaaaaaaaababaabaababbbbabbaaabbaabaaaaaabbababbaaabababbaabbbbabababbabaaabaaabababaaababbbaabbabbaababbbaabbbaaabbbbababbaaababaabbbaababaaababaaababababababbbaabbaabaaabaaaaaaaabababbabbabaaabbbaababbaaaababaaabbbbababbbabaaababbabbbaabbbabbbaabbabaaabbaabababababbababaaaabbaaababbabbbaaaabaababbbabbabaaaaabbbabbbaababaaaaaaaaaaaaabbbaaaabbbbbbaaaabbbbbbaabbbaababbbababbbbabbbbbbabbaaaaabbaababbaaaaaaabbbabbbababaabaaaaabaabbabbabaaaaababaabbaaabbaabaaaabaabbbabbbbbaaaaaabbabbaabbaabbabbababaabbabbaabbbbaabaaaabbbbabbbababbbaaabbabaababbbbbaaaaabaaabaaaaaabbbbaabbabaabbbbabbabaaaaaabbabbaaabaabaaaabbababbbbbabbbbaabbbaaabababbaabaaabbbaabbbabbaabbaabababbababaaabaababbabaaaabaaabaababaaaabbabbababbaabbbbbbaaabaaaaaababaabbbaabbabaabaabababbbbababbbbbabaabbbaaababababbaabbbbbaababaabaaaaaaaaababbbabbababbbabbaaaabbbbbbbbabbabaaaabaabaaaabbbbbabaabaaaaabaababaababbbabaaabbaaabbbaaaabbabababaabbabaabbbbabaabbbbaabbbabaabbabbbbbabaabbbbbbbbabaabbabaabaaabaaaababaabbabbbbbababbbaabaaabbaaaaaababbaaaabaaaabbbababbbbabababababbaabbaababbbbabbaaabbbaaabaaabaabaaaababababaaaabbbabbbbbaabaaababbaaabbabbabaaabbaaababbbbbaabbaabbaabbababaaabaaabbabbabbbaabbbbaabababbbaaababababbaabbababbaabbababbbabbbbabaababaabaaaaaaaaabbaabaaababaabbaabbabbaabbbbbbbababababaaaabaabbbabbbabaababbabbbbabababbaaabaabaaababaabbbaaaaaaaaaaabbbaabbbbbbbabbaabbabbabbbaabbaabbaaaaaabbabbabaaababbabaaabbaaabbababbbabbbbaaabbbabbaaabaaaababbbababaaaababbabbabaabaaaaabbaabbaabbaaaaaaaaaaaaaabaabababbaababbaaabbbbaaaaabaaabbbaaaabaabaabaababbbaaaaaababbaaabbababbababaaaabbbaaaaababaaaabaaabaabbababababaabbaabaabbbbaabbabbaaabbaabababbbbbabaabbababbabaaaabaaaaabaaabbbaababbaabababbabbbabababaabaaaaaaabbbabbaabbbbabbbaaababbaaabbaababbbbababaaabbbaababbababbaaababbbabbaabababbbababaabbbaaabbaababbbbabbabbbaaabababaaaaaaabaaaaabaaabbaaaaaaabbababbabbbaaaaaabaabbbbbbababbabbaabbbaaaaaaaabaabababbabbbaaaabaaaabbabaaaaaabbbaaaaabbbaabbbbaababababaabbaababbaaabbabbabaaaabbabaabbababbbabaaababaaabbaabaaaababbbaabaaabbbbbbaabbbbaaabaabbbaaabbbbaababababaaaaabababbbabaaaabbabbbaabbbabbabaabbbabbbbaabbbabbabbbaaaaaababbaaabbbbbbbbaaabbaaaaabbaaaabbbbaabbaaabbbaabbbbabbabaabbaababbbababbabbaabbaabababababbabbbabbbaaabaabbabbaabbaaaababbbabbbaaaabbbaaaaaaaababaabaababbaaaabaaababaaaabbaaababbaabbbbbbbbabaabbabaabbbaabbbbbbbabaaaabababaaaaababbbaaaaaaaaaabaabbaaaabbbbbabbabaabbababbbbbaababbaabaababbbbaabbbbabababbaababbabaabababbbaaaabbbabaaabbbbabbbaaaaaaaaabaaaababaaabababaabaabbbabbaaababbbabababbaaabaababbaaabbbabaabaabbabaabbaaabbaabaaaaaaabbbabbaaababbbbbbaabaaabbaabaaaaaabaababbbaababaabababbbabaaabaaaababbaabbababbabaaabaaaaaaabbabaaabbaabbbaaabaababbbabaaabbbbababbaabbbbbaabaabaabbbbbbaabbaabbbbabbbaaabbabbbaaabbbabababbbbbabbbabaabbabbabaaabbbbbaaabaabbbbbabbbbaaaabbbabbaabbabbbbabaababbaaababaaabbabbbbbabbabaaaaababbaabbababaaabbaaaaabaaabbaaaabababaaabaabbbaaabaaabbabaaabbbaaababbbabbbbaaaaaabababbaabbbabaaabbbaabbbbbbabbbbaaaabbabbaaababababbabbabbabaabbbbbabaabbababaabaabaabbbbabaaabbbabbbaaaababbbbbaababaabaababbbbababbaaaaabbbaaaaaabbabaabbbbbbbbbabbaaaabbaabbabababaabaaabbbabbabbabbbabbaabbbabbabbabbabbabaaabaaaaaabaaabbbabaabababbbbbbaaabaababbaaaaaaaaaababbbbbabbababaabbbbbbabaaababbaaaaabbbaaababaaabaabbaabbaaaabaababaababaabaaaaabaabbbaabaabbbbaaaaabbbbabaaababbbabbabaaabbbbbaaaaaababbabaabbbaaaababaabaabbbababbabaaaababbbaaabaabbababbbaabaaaabaabbaabaaaabbaaaababbaaabbaabbababaabbaabbbaaabbbbaaaaaabbbaaabbbababbaabbababbbaaabbbabbaaabbaababbababbaaaabbaabaababbaaaaaaaabbaabaabbbbaababbbabaababaabbabbbaaaaaaababbaaaaabbbbababbaaabbaababbbaaaaabbbabaabaaababaaabbbbbaabaaabbbabbaabbaaaabbabababbaaaabbaaabaaabaaababbaabbbbbabababbababbbbabaabaabbabaaabaaabbbaaabbbaababbbbbabaabaaabaabbbbaabbbbbaabbababbbbbababbabbbbaaaabaaabaabbababbbbaabaaaaaaaababbaabbbaaaaaabbabbaabbabbbababaaababaabbabbbabaaabbbbbbaaabababaaabbbbbbaabbabbabbbaaaabaabbabababbabaaabbbbbbaaaabaaaaaababbabababaabaababababaaaabaabaaaabbaaababbabababbbbbbaaabbbbbabbbbbabaaabababbababbaabbabaababbabaaaaaaabbbbaaaaaaaaaabaabaaabababbaabaaaaaaaaabbaabbaaabbaabbbbbabaabbaaaaaabaaaaaaababbbbabbabbabaaabaaababbaaaabbbaaaaabaaaaaaaabaabaababaabbabbaabbbbababaaaaabbbbaaabbbbaabbbbbbabaabaaaaabaabbaabaabaaabaaaaaaababaaaaabbabababbaaaabbbbbbaabaabbbbbabbabaabbaaaabaaaaaaabbbababaabababbaabbabababababbaaabbababbabbaabbbaaababbaaabbbabbbbaababaaaaaabbabbaabbbaabaaabaabbbbbabbbbabbbbabaaaaaababbabaabbbbaababbbbbbaabbbabbaaaaaabaaaaabaabbbbabaabaaaaaabbabbabbbbabababbaaababbaaabaaaabbababaaababaabbabbbbbabbbabbbbabbaaaabaababaaaaabbaaabbbbbbbababbbabaabbbababaaababbaabbaabbababbbbbabaabbaababbaabaaaabbababbababbbaabbabbbabaaabbbaabbbabbaaabababbaabbababbbbbbaaaababbabaababbbaaaababaaabbbaabababbbabbbbbaabababbaabbbbbabbabbbabbaabbaaaaaaabaabaabbaabaababbaabbaabbabbbbbbbabbbbaaabaabaaabbaaabaabbaaaababbabaabbabaabbabaabbabbabbbaaaabbbaaaaaabbaabaabababbabaaaaaaaabababaabbabbbbbaabbbababbbaaabaabaabaabaaaabaabbaabaabbababaabbaaabbabaaaaaaaaaabbbbbbbbbbbaabbbaabbaaaabbabbbaabaabbaaabbabababaaabababbbaaaaaaabbbabaaabbabbabbaaababbbbabbabbbbabbbaaabbbabaabbabbabbabbababbababbaababbbabbbbaaabbabaabbaaaababaabbaabbbbbaababbaaaabbbaaabbbabbbaababbabbbababbaabbbabbabbaaabbbbbbbaababbbaaabababbbaabaaabbbababaaabbbbabbaabbbabbbaababbbbaaabaaabbbbabbabbbbaababbbbaabababbabaaabbbbabbabbbbbababbabbbbabababbbbabaaaaaaabaaabbaabaabbbaaaabbbaaababbabbbaabbaaaababaaababababaabbaaabbababaaabaaaabbbabaabbaaabbaaababbbabaaaababaabbababaabaaabbabbbaaaababbaaabaaabaaaabbbbbababbababaabbbbaaabbaaaaabaaaababbbbbaabbaaaabbabaabbaaaabbbbbbbbbbaaaaaabaabbbabbbbbabaaabbbbbaabaabaabbbabbabbbbbabaaaaaaabbbaaaaababbabaaaaabbbbaabaaabbaaababababaabaaaabababaaababababaaaaabbabbbaabababaabaabaabbbabbaabaaaababbababbbaabbabbaabbbbbbaaaabbbbaabaaaababaabbbabaaabaaaaaaabbabbbaababababbabbababaaaabbabababaaaabbbbbbbaabbbbbabbbabaabbbbabaabbbabbabbaaaabbabbababbaabbabbaabababaaabaababaaaabaabbbabaabaaabbbbbbaaaabbabbbabaaaabaabbbbbbbbaabbbaaabaaababbbbbbaaabbaabbbaabbbbaabaababbbbaabaabaababbabaaababbbbbbbbababaababababbbaaabbaabbabbabbbbabbbbbbbbababbaabaaaabababbaabaaaabbbaabaaaaaaaabbbaabbaabbbbabbbbababbaaabbaabbababbaababaaabaaaabababaabbbabbabaabbabaabaaaababababaaabbaababbaabbbbbabbbbaaabbbbbabababbabbaabbbbaababbaaaabbaabbababaabbaabbababbbbbbbababaaabbbbaaaaabbabbbaabaabaaaaaabbbabbbbaabbbabbabbaaabbbbaabaabaaaaabaababbbaaabaaaabbbabbaaaababaaaabaaaabbaaabbaaaababbbababababaaaaaabaabbaaaabbbabbaaaabbaaaabababaabbbbbbaaaaaabaaabbbabbababaabbbbabaaaaabbaabbbbabaabaabababbbaaaababaaabbbabbabbababbbbbbbbbbabbabbaabbbababbbabbabaababbbababbbbbbaaabbababababbaabaaaabaaaabaaabbbabbbbaaaabbbaaabbbabaaaababbaaababaaababbaabbabbbbbaaabbababaaababbbbabbaaabbababababbbbaaaaababbaaaaaaaaaabaaaabaabaababaaabbabbbbaaababbaabaaabaababbbaaaabbaaabaababaabaaababbabababbbaaaabababbbbaabbabababbbbbbbaaabbaabaaaaaaaaaaaabaababaaabbabaaaabbbaaaaabababbaabbbbaaabbababaaaaabbbbaababbababbbbabbbaabbbbabaabbabaabbbbbaaabbababbabbaabbbaababaabbabbbbbbaabbbbbabababaaaabbbababbaabbababbbaababaabaababaaabbbbbbaabaaabbaabaaaabbbbbbababaabababaabbabbbabbaaabaaabababaaabaabaabaaabaabaaababbbababaaabaabaabbabaabbbbaabbabbaaabbbabbabaaaaaabaabaaaabbaabbabaabbaaaabaabaaaaabbbabaabbaaaabaabbbbbbabababaaababaaaabaabbbaaababbabaaaabaaabaaaaabbaabbbabaaaaaaaabaaaabaabbbbbaabbbbbaabbbbaababbbababaabbbbbbbbbababbbbbbaaababbaaabababbbbbbbbbbabbababbaaabbbabbabaabaabbaaababbbabbababbaaababaababaaabaababbaaaaaababbaabaaabbbababbababbaaaabbaaabbababbbbbbabbbaababbbbaaaaabbbabbabbabababbbabababbbaabaabbabbabbbbaaaaababbbbbabbbabaaabbabbbbbbabbbbbbbaabbbbbbbbaaababaaabaabaabaaabbaabbaababbbaaaaabbabbbabaabaaaaabbbbbaaabaabbbbaaaababbbabbbaaaaabaabaaaaaababbbbbabaaabababaaabbbbabaaaabbbabaaaabaababbaaabbbaaaababbbabbabaabbaaaaaababaaabbbaabbbabbbaaababaababbabaababbbabaabababbbaaabbbbaaaabbaaabaaababbbabbbabbbaaaabbabbbaaaaaaabbabababbbbbbbaabaabbaabbbabbbabbabaaabaabbaababbbbaaabaababbbbabbaaababbbbababbbaabaaaaabaabbbaaaaabbbabaaabbaabaaabbbbaaaababbbaababababaaabaabbabbaababaabbbbaabbbbaaabbaabaaaababaaabaaabbbaaaaaaabbbbabaaaabbbbaaabaaaaaababbaaaababbabaabbaababaaabbbbababaaaaabbabbaabaaaaaabaababaaaabbbbabbbbaaaabaabbaababbaabaaaaaabaababbaabaaaababbbbaaabbbbaaabbbbabbabbabababbaaaabaabaabbabbabbabbababbbabbbbbbababaaababbbabbbbabaabbabbbabbabbababbabbbaaabbababaabbbbbaabbaabbabbaabaaaabaabababaabbaaabbaabbaabbababaabbbbaaabaaababababbbbbbbbabbabaaabaaaabababaabaababbabaaabaabbabaabbaabbabbbaabaabbabbbabbaabbbaabbaaabbbbbabbbbbbaaabbbbabaabbaaaaaabbbbbbbbaaaaaaaaababbababbabbbababaaaabaaaababbaabbaaabbbabbbbaaabbbaaaabbbababaabbaababbaaaaabbabbaaaaaabaabababababbbbaabbababababbabbabaaaabbabaabaababbbabbbbbbbaabbbaabbabbabbbbbabaaabbaaaaaabbbabbaabbaaababbbbbbaaaaaaabaaaaaaaaabbaababbbaaabaabbabbbbaaababbbbaaabbaaabbbaaaaabaaabaabbabbaababababbbbaaabaabbbbabbbbbbaaababaaabbbbbabbbbaaaabbbbbabbabbbaabbbbabbabbababbaabaababbaabaababaabbabbaaaabbbbbabbbabaaaabbabbbbaaaabbbabbabaababaaabbabbabbbbaabaabbbaaabaabbaaaaabbbbabbabaaaabbbbbaabbbbbaaaabbbabaaaaabbbbbababbabbbbabaaabaaaababaaabaaabaaaabaaabaabaabbababababbbbbabaaaabbbbaabababbabaabaabbaabbabaabaaabaaabbbaabaaabababbabaababbabababababaaaabbaaabbababbaabaaabaaabbbaababbaabaabbbabaabbbbbbabbaaababababaaaaaabbbaababbabbbbbbabbbabbbababbabbaaabaaabaaaaaabbbaaabbbbabbababbaaabaabbbbbabbbbaababaaabababbbbbabaabaabaabbabaabababbbabbabbbbaabbbbbaabbbbbaabbbbbabbbbbbaaaabbbbbbbbbbabaabbaaabababbabbbbabaabaaaabbbabbaaababaaabaaabbababaabaabaaabaabbbbbaaaaabaaabbaaabbabbabbabbbbbbabbbaabbbababababaabaaaabbaaabaaaaaababbbbabbbbabbbbbabaaaaaababababbaaabbaaaabababbbaabababababbbaabaabbabababababbababababbaabbaaaaaabbbbaaaaababaaabbaaaabaaaababaabbbabbaaabaaabbbbbbaaabbaabbbbabbaabaaabbabababbaaaaaabaaaababababbaaaaaaaaaabbaaabbabaabbbbaaaabaabbaaabaabbbababababbbbabbbbababaaaaaabbabbbabbaabbabbbbabbababbbbbbbbaaaabaabbbbaaababaabbbbabbbaaaaaaaabbaabbabaaabbbbaababaabbbbaabababbbbbabaaababababaababbaaabbaaaaaabababbabbbbabbaabbaaaabbbbaabbbbabbabbabbaabbababbbbbabaaaaaabbababbbabbaababbaaabaaababaaababbbbbbbabaabaababbaababaaaaabbbbaaaabbbabbbabbaabbababbbababaabbbaaabbababaaaaaaabbaaabbaababbaabbababaaababababbbaaabbabbbabaaaabaababbbabaaaaabbaaababbbaabbbbbaaababababbbbababaabbbbaabbaaabaababbaababbbababaabbabbaabbbbbbbbababababababbbaabaaabaaababaabababbaabbbbbaabbaaabbbabbbaabaabbbbaababaaaabbbabababbbaaabbababbabbaabaabaabbbbaaabaaaaabbbbaabbaababababbaaabbababbbbaaababbbabbaabbabaaaaabaabbbbbbabababbabbaaababbaabababaaaaabbbbbbabbababbaabaaabbbbbababababbbbbbbbbbbbabbabaabbbbbaaaaaabababaaababbbaabbaaaababbbaabbababbbbaaababababbbabaaabbaabaabbbbbaababababbbbbaaabbbabbabaabbbaabaabbbbaababbabbaabaaabbabababbabbbbbbbbbbbabbbbabbaabaaaabbbbaabbabaabbbbabaaaaaabbabbbbbbbaabbabaabbbabbabbbbbbabbbabbabbabbbbbababbabaaabbaabaaaabbaabbaabababbbbaaaaaaabaaabbababbbbbbaaabababababbbbbbaabbaabbabbbbaaaabbaaaabaaaaababaaaabbbababbababaaabbaabbababbaabbbbbabbababbabaabababbbaabbabaaabaaaababababaaaaaabbaabaaabaabbabaaabaabaaaabbbabbabbbabaaabbbaabbbaaaaaabbaabaabaaabbaaaaabbbbbbabbabbbabbbabaababaabbaabbbbaababaaabbaabbabaaabbbbababbbbbaaaaababbbaaaaaabbbaaabbbbaabaabaabbbbaaaaabbbbbabbaabaabaabbbbabaaaabbaabaaabbaababbabbabbaaabbabbbababbbbbaaababaabaaabaaaaabaababaabaabbaaaabbaaaaabbbaabaabaabbbaaabaaababbbbbabbbbbaabaabaabbbabbbaababbabaaabbabaaaababbaaaaaabbbbbbbbaabaaaabbaabaababaaaaaabbabbbbabbbbaababbaabbaaaabbbababbbabaabaaabbbbbabbaaaaabbabaaaabaaaaaabbbaaaaaaaabbabbbaabbbbbabbbaaabbaabbaababbabbbaaaaaabbbabaabbbbbbaabbbaaababbabaaaabbbaabbabaaaaabaaabaaaabaabbbaabbaaababbababbbaaabbbbbabbbaaabaaabbbaabaaabbbbbabaabbaaaabbbbbaaabbbbaaabbbbbabbbbaaaabbbabbaaabaaaaaabbbbabbaaababbabaaababbbaaaaaabbaabbbbabaabaabbbbabbbaabbbaababbbaabbababbbabbbabbbaaabbabbaabaaaabbabbbbbabaaabbababbbbabbbaaabaabbaabbbbabbaaaaaaaabababbbbabbaaaabbbababbabbaaaabbbaababaababbbaaaaabaabaaabaabbbbaaabbaaabbababbbaabbbaabbaaabbabbbbbabaabbaabaaabababbbabbbbbbbbbabbbbbaabaabbbbbaaaabababbaaaaaabbabbabbbbbbaaabbbbaaabbbbbababbaabbbbababbabbbabaababaabbaaaababaabbbabbaaabbbbaabaaabaabbbbbaababaaaaaaabaaaababbabbbabbaabaababbbabbbbaabaabaabbabbbbaababaabbaabbabbbaababbabbbbbbbababbbaaabbbbaaabbbbaabbaabbbabbaaabaaaaabbbabaaaaabbbbbbabaababaabbbbaababaabbbbbabbbaababbbabaaaabaaaabbbbabbabbbbbaabbabaaaaaabaabbaaaaaabaaabbaabaaabbaabbabbabaabaaaabaabaabbbbbbbbbaaaaabbbbaabababbababbbbaabbbaaaaabaabbabbabbaabaabbaabaabaaaaaabbaabaaababbaaabbaaaaabaaababaabababaaaabababaaaabbabaabbbbaaababbbabbbaaababbabbaabbbabaabbabbbbbabababbbbababbaaabbaabaaababaaababbbbaaaabbabbbaabaaabaaaaaabaaaaabaaaaaaabbbabbbbaaabbabaabbabaaaaaabbaabababababaabbaabbaabaabbbabbaaabbababaaabbbabbbbbbbabaabbabbbbaaabaaabbbababbbbaaabbaaaaaaaaaaabbaaabbbaaaaabbbbaababbaabaaabaabaaaaaabbbbbabbbbbaabaaaabbbbbabbbaaaabbaabbaabbbbbaabbbbbaabaaaababaabbaaabbaabbaabaaaabaaaabaababbbbbbbbbaaabbbaaaabbbbabbbbbbbaaabbbbaabaaaababbababababababbaaaabaaabbbbbbababbababbabbbaaabbbbbaaaabaabaaabaabbabbbaaabaababaabaabaabbbaaabaaaabaabbbabbabaabbbbbaaaabbbbbbaabababbbbbbbabababbbbbbbabababaabbbbabaabaabaaaabbbbaaabaabbbabaaaaaaaaaabbbbbabaaaaaaaababababbbbababbaaababbbabababbbbabaababaabbabaabaabbaaabbabaaababaaaababaaaababbaabaaabaaaaababaabaabaababbabaaabbabaabaabbbbbbaaabbbaabababaabaaabbbbbbbabbabaaababababbbaabaabbaabbbbbaabbbabbbbbbbaaabababbbbabaababaabaabbababbbbbbabbabbabbaaabbbaababaaaabaaaababbbbabbaaaabbbaabbbbbbabbbbbabababbaaaabbaababababbbbbaabaabaabbbbbbabbbbbaabaabaaaaabaaabaaaabbbbbbbabbbbaabaaabaabaabaaabababaaabbabaaababbbbaabbababaabbaababbaabbabaaaabbbabaaaaaaabbabbbaaaabaaaaaabaabbbbbaabbbababbbababaaaaaababbbbbababbbbabbbabbbbbbbbabbbabaababbbbbaaabaabaaaabaaaabbaaabbabbabbbabaabbbbaababbabaaabaaaaabaababaaababaabbaababbabbabaaabbabaaabbaababbbbabaaaaaababbabaaabbbbabaaabaabaabbaabaaabaaabbababbababbabbaaabaaabbbaaaabbbbbbbaaaaabbaabbbbbbbaaaabaaabaabaabbaaabaabbaaabbababbaaaaabbbbbaabaabbbbbaabaabbaabbbbbabbababbbaabbbbabaabbababaaaabbbbababbbaaabaaabbabababaabbbaaabbbababbbababbbbabaabbabbbaaaaaaaabbaabbaaaaabbbbbbbbababbbabaaabbaabaabaaabbbbbbbbbbaaabbbaabaaabbabbbbbbababbabbabbabbbbbbaabababaabaaabaababbabbaaabbbbbaaabaaaabbbbbaaaababbbabbbaabbaabaabbbbabaaababbbabbbabaaaaaaaabbaababaaaababbbaabababababbbbbbabbbaaaabbbbbbbaababbaabababaaababbbaabbaabbbaaabaaaaaaaaaabbbbbabbbbbbababaababbbaaaaababbbbaaabbabbbbbaabababbbbbabaababbaabababbaaabbaaabaaababaaaabaabaabbaaababaaaababaaabbbbaabbabbabbbabaaaababbaabbaabaaaaaaaababbbbabbbaaaabababaabaabbabbaaabbabaaabaaabbaaaaabaabbababbbbbababababaabbabaabbbababbabbbaaaabbbabbaaabbaabaabaabababbbbbabaabbbbaaaaababbbaaaabbabbaaaaababaaaabbbaabbbaaabaabaabbbababababbaaababaabaaaaaaaabaababbbbbababaabaaababbbabbbbaabaaaabbbaabbbabbababbabbbbabaaabbaaabbabbbbbabbaabbaabbaabaaaabbaabaabbbaabbbaaaaabaaabaaabbababbbaabbaababbaababbbbbababaaaaabbababbbbabababbabbabbabbbbababbbbbababbbaabbabbababbbabaaaabaaaaabaaaaabaaaaabbbaabbabababababaaaaabbaaaabaaaaabababaabbbbbbbbbbaababbbbaababbaaaaaaabbaaaaababaaaaababababbabbbbaaaababababbababaaaaaabbabbbababbaabbbabbbbbabbbaaabbaaaaaabbaabbbaabbaabbbbabaaabbaabaabbbbabbbbbbbbaabbaabaaaababbabbbbbbabaaabbaaaabaabaaaaabbaababbbabbbbaabaaaaabbaaaabbabbbabbbaaaabbaababaaabaaaabbabbabbbbbabaababaabaabbaaabbbbaabbbbabaaaababaabbabbbbbbbaaabbbbabaabbaabbbbbbabbabbbbbaaababbabaababbbbaabaabbbbabbaaaaabbbabbbbbabbbbbaababaabaababbbaabababaaabaabaaabaaaaaabababbbaabbbabaaaaaaaababbbaaababbbbbbaabbbaaaabbababaabaaabbabbaabbabbaaabbbbbbabaabbbabbbaaaababbabbbabaabbabaabbbbabbbbbaaabbabaaaaaaaababababaababbbaababaabaabbbbaaaabaaaaabbabbababaabbabbbbbbaaabbbaaaabbabbababbbbaaaababaaaaabbabbabbbababbabbabbaabababbabaaababaababbbaabbaaabbbbaaaaaaaabaababbbabbabaabaabaabaaabbaabbabaaaababababbaaaaababbbaaaababbbbaaabaabbabaabbaaababbaaaabbbbbaaaaaaaababaaabaaabbabbbbababbbaababaaaababbbabaaabaaaababbaaaaaaaaabbbbbabaabaaaaabaababaabbaaabababaabbbbbbaababaabaaaaababbaabaabbaaaaaabaaabbbbaaababaababbaaabbbaabbaaababaabaaaaaaaabbabbbaabbbbabbaaaabbaaaabbabbaaabaabaaabbbbaabaababbaaaabbababbbbabaabaaaabaababbabbaabbbabaabaaaaababbbbbbabbabaaabbbbabaaaaaabbaabababbabbbaabbbabbbbaaabaababaaabbbaabbabababbbbbbaabaabbbaababababbabbababaaabbbbababbbaaaaabbabaababbbabbbbbbabbabaaaaabbabbbbbbabaabbabababbaaababbbaaaaabaabaaabaabaaabbbabaabbbabaabbbaabaaabababaabababbbabbbbabbbaaabaabbaaabababbbbbbabbaabbabaaababaabababaaaaaaaaabbaaabababaaabbbababbbaaaaaabaaaababbbbaabbaaabababbbbbbaabbabbabbbabaaaaaaaabaabbaaaabaaaabbbbbbbabaabbbbababbababaabbaaaaaabbababaaaabaaaabaabaaabaabbababababbbaaaaaaabbabbaaabbbabaabbaaaabaaaaaaaabbbabbabaaaaabbaaaabaabbbbaabababbbabaabbbababbababaaababbababbbbaaaababbaabbbbaabbababaabbaaaaaababababbbaabbababbabaaabbbabaababbabaabababaaaaaaababbbbbaabbbbbbbaaaaaaaaaabbaaabaaaabaabbbbaaaabbbabaaabbbabaaabbbbaabbbbaabbbbabbbbbbbbabaaaabaaaaaaaaababababbbbbbbabbbabbbbbaaabababaaabbabbababbbaaabaabbbbbabbbabbabbbbbbaaabaababaaabaabaabbbaabbbaabaabbbabbaaaababaabaaababaaaabbaabaabbbababaaaaaabbabaaaaabbaabbaaaaabbbbbbaabbbbaaaaaaaaababbbbabaaabbaaaaababbbabbabaaaabbabbbbabbabbaababbbbabbabbaaabaaaaabbaabaaaaaaabaaaabbabbbaaaabaaabbbbabaaabbaababbbababbbaaabbababaaaabbabaaababbbaaabbaaabbabbabbbbbabaabaaabbababaabbbbbabbbbaaababaabaababaaaaabaaaabaaabbaaaaabbababbaabaabbbaabaabbbbaababbababaaabbaabaabbabbaabaababbaaabbbaabbabaabbababbaaaabbbaaaabababbaaababbbbbbbabbaaaaababbbaabbaababbaaabaababbabbbaabbbaabbabaabbabababababaaabbaaabbbbabaabbabaaaaabaabaabaaaabbaabaaabbbabbaabbbbbbbaabababaabbabaabaabaaababaabbabbbbbaabbabbabbbabbaaaababbbabbababbaaabaabbabbbaaabbaaabbabbabaaababaababbaababbbaaababbabbaaabbbaabbbbbbababababbbabaabaaabbabbaaaabbababaabaaabbbaaabbababababbaabbbababbbabaababbbbababaabababaaaaabababbabbbaabbbbbabbbbabbabbabbabbbabbbaabaaabbbbaabaaabbabbaaababaabaabbabbbaaaaaaaaabaabaaabbabbbbbaabbabbbaaaaabaabbbbbbbbabbbbbabaaaabaababbaaabbbbabbabbabaaababbaabaabbabbaabaaaabbbbbababbbbbbaababbababbaabbaaaabaabbaaaabaabaaabbbbbababababababbaabbbbbabababbbabbaaababaabbbbabababaabababababbaabbabbaabbaaaabbbababaabbbbabaabbabbbbbaaaababbbbbbaabbbabaabbbbbbbbaaababbabbbbaabaabaaabbbaabaaabbbbabbaabaabababaaabaabababbbabbaaaabaaaabababababbababbbbababbbabaabaaabbabbabbbaababbabaaabbabbbbaaaaaaabbbaaabaaababbaaaaabaabbbabbbaaabaabaaaaaaabbaabbaaabaaaaabaababbaaaaaabbaababaabbabbabaaababaabbbabaaaaabbbabaabaaaabaaaaabbabbabbabbbaaababbbaabaaaababbabbaaaaaaabbaababababaaaaabababbaaababbabaababbaaababbabaaaaabbababbaabaabbaaaabaaaaaaabaaaabababaabababaaabaaaababaabbbabbabbabbaaaaaabbabaaabbbaaaabaabbaaabbabbbbabababbbaababbaabbaabbbbbbabaaaaaaababaaababbbbbbbbbbaabbabaaaaabbbaababbbabaabbaaabbabaaabaaabbabababbaaaabababbbbaaaaaaaaaaabbbabbbbbababbabababaabbbabbbbbaaabaaabbbbababababbbbababaaabbbbbbabbbbabbaabaabaabaaaaabbababababaaaaaaaabaaaababbaabbaababbbbaabbbabaaaabaabbabbbaabaabbabbbabbaaabaababaabbbbbaaabaabaababababbababbbaaaaaaabbababaabbababbababbbaaababbbaaaababbbbaaabaabbbbbbbabbaabaababbbbaaaabaabaaabbabababbbbaabbaabaabaabababaabbbbbbbbaabbaabbbbbaababbabbabaabbbabaaaaababaaaabbbaabbbaababbbaaabaabbaaaaaabbababbbbaabbaaabbbabbbaabaabbabaabbaabbbbaabaaaaabbbbbbbaabaaaaabaabbabbaabababaabbbabbaabbaaabaaaabaaaabbbbbaababbabbabaabaababababaababbbbabbaaabaaaaababbbabbaabaaabbbbaabbaaaabababaabbbbaaaabbbbbaaababbbaababbbbaaaabababbbbbabbbaabbbaaaaabbbbbbbbaabbbaabababaaaabbbbbabaaaabbbaaaaaababbaababaabbbbababbbaaabaaabbaaababababbaaaaabbaaaaababbababbabbbbabbbaabbaababababbaabbaabaabaabbbbabaaaabbbbbbaabbababbabaabbabbbaaabaaabababababbaababbbabbabbabaabaabaaaabaaabbbaabaababaaabaabbbababbabbaaabbbabbaaaababbbbbaabbaabbbbbabaababbbabaabbaabaaababababbbabababaaaaaabaaaababbbabababbbbbbbbbabbbabbbababbbbabababababaabbaabbaabbababbbabbbbaaaaabaaabaaaaabababababbabaabbababbaaaaababbabbbbbaaaaaababbbbaabbaabaabaaaaabaabaabbbbaababaabbbabaaababaaabaaabababaaaaabaabaaabbbababbbbabbbbaaaaaaabbbababababbaaaabbabbaaaabaaaaabbabbaaaababbbbbabaabbbaaabbaaababbbabbbbbaaaaabbbaababbababaabbbabbbaababbbaababbaabaaaaaaaaaabbabbbbbababbbabaaaaaaababbbbbabbabaaaaabbbaabbaaaaaaaabababaabbababababbbaaaababbabbbbbbbabaabbaabaaaabbaaabbbaabbbaabababaabbaabbbbbbaaabaaababbabbbbbabaabbabaaaabaaaabbaabbababbbbbaaabbbaabbaaaaaaabaababbaababbaaaabbbbabbbbbbabababbbaaabaaaababbabababbbbaababbaaaabaaaabbaabbaabbababaababbaababaabaaabbabaababbbbaaaabbabbabbabbbbaababbaaaaaabbabaabbbbabbbbbabbbaabbbbabaabababbabbaabaabbaaaaabbbbbababaabbbabaabbbbaaaabaabaaaababbbbaababbaaaabbbabbaaababbbaababbabbaaabbbaaaabaaaaababababaaaababaaaabbbbbbbababbaaabababbaabaaaaabbbbaabaaaaaaabbbabaabbbabaaabaaabbabaabbabaabaaaaaaaaaaaabaaabaabaababbbbabbaaabbaaabaabbaaabbbaaaabaaabbaabaabbaabbbbaaaaaababbabaabbbbaabaaabbbaaababaabaaababaabbabbbbbbaaaababbaaabbbabbbaababbaababbbabbababbabbbbbababbababbbabaaabbbabaaaaababaababbabbaaabbababaabbabaabbbbaabaaaaaabbbbbbbbaabababbabbbaabaababbabbaaaababbbaaabababbabbbabbaaababbaabaaaaaabaaaabbaaabbbabbbbabbbbabbbaaaaaaababbaabbbbaabaaabbbbbabaabbbbababaababbbaaabaaababbaabbababaaabaaaabbaabaaabbabaaabbaabaaabbababbbaabaabbaaabaabbaaaaabbbabaabbbaaabbaabbbbabbababababbababababaaaaaabaaaabbaaabbabbbaabbaabbabaababbaaababbbabbbbbbabbaabaabbbabaaaaaabaababbababaabaaabbbbbbaabaaaababbaaabbbbababaabbaabaabbaaaaaaaaababababbabbbbbabbbaaabbabaaabbbabbaaabbaabbaaaaaabbababbaabaaaabaaaaaaaabbaabbaabaababbababaaabbaabababbbabbbaaabbaabbbbabbbaaabaababbaabbbbabbbaababaabbabababbaabaabbaabaabbaabbabaaababaabaaabbaabaaaabbaaabaaabaaababaaaabbabaaabaaaaabbaababaabbaaaabbbbbabaabbaabbaaaabaaaababbbbbaaababbababaabbbaaabaabbaabbbabaaababaabbaaabbbbaabbabbabbbbbbababbabbbbaaabaabaaaabbbaaaaaababbbabbbbbbbabbaababaaaaababbbaaaabababbbbbaaaaabaabaaababbbbbbabaaaabbaaaaaaaaaaaaaabbbabaabaabbabbabbbbbabbbaaaaabbaabaababababbbaabbbbbbbbbabbaaaabaaaaabbabbbbbaaabbbabaabbababaabababbbaaabbaaabbaabbbabbabbabbaabaabbbaabbbabbababbabbbbaaaababbabaabaaabaaababbabbbbaaaabaaaaabbaaabbaababbbaaababbaaaaabaaaabbbaaabaaaabbabbbbabbababbaabaabbaabbbabaababaabaabbabbaaaabaabbaabbabbabbaabaabbbaaaaabbbaaabbbabaaababbbbabbaabaababbaabaaabbbaaaaaababbabaabbababbbbaaabaaabaababbbbabababaaaaaaabbabbababbbabbababbabbbbaababbaaaabbabaabbbbbbaaaababbabbabbaaaaaabaabbaabbbbbaaaabbaabaabbabbbabaabbababababbaaaaaaaaabbbbaabbaaababbaaabbabaabbaabbbaaababbbabaababbabbababaaaaaabbaaabaabbaaabbabbabbbabbaabbbbaaabaaaababaaaabbbabbbabbbbababaababbababbbbbababbabbaaababaabaababaaaaabaaaaaababbbbaaabaaabaabbaaabaabaaaaabbaabaaaabbabbbbbaabbbbbaababbabbaabbaaabbaabbbabbbbbabbaaabbabaabaabababbbbaabaaabbbabaaaababbaabbbbbbabbabbaabbabaabbaabbabbbabbbbaaabaaaaabbbabbaaaabbbaabaabaabaababbbaabbaabbabaabaaaabbbbbaaaaabbbaaababbbaababbbbabaabaabbbaababbaabbabbaaaabbabbbbbbbaaaaaabbbababbabaabaabaaaabbbbbbabbbaabbbbabbbbbbabababbabaabbabaababaaaaabaaabaaaababaababbaababaaababaaababababaabbbbbbabbaabbaabbbabaaaaaaaabaababababababbaaabaabbbbbbabbaaabbbaaabaabbabbababbbaaaababababaaababbabbaabbaabbbbbbabaaaababbbabaaabababbaabbabbbaabbbbbabbbbbbbbbababaabbabbbbbbbaabababbbabbbbbabaaaaababaabbbaaababbbabbabaababaababbabbababbbbbbaabbaaaabbbabaaaaabaabaabbaabbabbaabaaaababbbbaabaaabaabbbbabbabbbabbbbaabbaabbbbababbabbbaaabbbbbbabbabaabaabaabbbbbabaaaabaaaabbbbbaaaaabaababbaababbbbabbaaaabbbbabaabaabbbabbabbaabbbabbaabbbbaaabbabbbabaaabbaabaaabaababaabbaaaaabbbabaababababbaabbaabbabbbbbaababbbbaabbaabbabbabaabbbabaabbaabbaaabbaababbbbbbabaabbaababaaabaabbababbbbaaabaaaababbbbabaabbababbabaabababbbbbbaabbbbbaaabbbbbbabbbbbabaababababbbaaabbaabaaababaababbbaaaabbababaaaaababbaabbbbbaaabbbaaabaabaabbbbaababaaabaaabaaabbbbaaaabbaabbbbabbabbabbbbbbaabaaaabaaababbaabaabbaababaaaabbbaaaaabaabbaabaabbbbbabaabbabbaaabbabaabbbbbbaaaaabbbbabaabbbaababaabbbbabbbbabbbababaaabbbbbabaabbaabbbbaababbaababaabbbbbbbabaabaaabbbabaaaabbaabaaabbbaaabbbaaabbbbbbabbbaaaaabbbbaaabbabbaabaaaabbbbaaaaabbaabbbaaabbbaaabaaabababbaabbabbaaabababbaabbbababbbabaaaababbbaababaabbaaaabbbbbabbaaabbbabaababbaaaaaaaaaabbabbbbaaaaaababaaabbbbbabbabababbbabaabababababbbbabaaabbaaababbaabbbababbbbaaaabaabaaaabbaaaaaaabbbaaaaaaaabaabbbbbabbabbbbbbaaaaaababbbaaaaaaaaabbaaaaabbababbababaabbbabbabaabbbbbaaaabbaabaaaaabbbaabbbbbbaaaaabaabaababbababaabbaaaaabbababaabbbabbaababaaaaabbbabbabbabaaaaaaaaaaabbbaaababbbaabbaabbbbaaaabbabbbababaababaabbaabbabaabaabbaaabbabababaaabbaabbabaaabababaaaabbabbbbbbaaabbbbbaaababbbaabababbbabbaabbaababbababbbaabbaaaaabbbbabbbbaabbababbbaabaaaabbbbabbbbaabababaaaaabbbbbaaababaaaababbaababbbbbabbbbababbaababaaabaabbbbaabbabaababbaaaaaabbbabbabbbabbabbbbabbabbababbbbbbababaaaaababababaaaaaaaabbbbabbbabbbabbabaaabaaaabbabbbaabbbbbababbbabbabaabbbbbbabbbaababbbbbaaabaabbbabaaabbbaabaababaabbaabbaaabaaaabaaaababbbbbaaabbaaabbbaaaababaaabbbbaaabbbaabbbbbbbaabbbbababbbabbaabbabbbbaabaaaaaabbbabbaaaababbbbabaabbabaaaaabaababababbbaababbbaaaaabbbbbaabaabbaabbbabaabbaabbabaaabbabaaaaaababaabbaabbbbabaabbbbabbabbbabaabbabbbbbbbbbaabbbabbababbbaaababbbaaabababbbbbbbbbbbbbabbbbaabaabaaaaabbbabbbbbabaabaabbbaabaaabbabbabaaabbbbaaababaaaaababbbabababbaabbbabbbbbaaaababbbbabbbbbbbbbbbaabababaabbbbbaaabbbaaaabbaababbbaaababababaaaaabbababbabababbbbbbbbabaabbaababbbbaabbabbabaaababaabbbaababbaaababbaaabababbaaaaaaaaaabbbbaabbbabababbbbbabbbbbaabaabbbababaabbaabbaabbbabbabababaabbaabababbbbaaabbaaaaabbaaaabaabbbaabbbababbbbaabbbbbbabbaaabbaaabaababaabbbaaababaaaabbbbaabaaaabbaaaaaabbabbaaabbabbbbbababbabbaaaaababbababbabbbabaabaaaaabbabbaababbabbabaaaaabbaabaaaaaaabababbbbaaaaaabbabbababbbabbbababbabbbaabaaaaaaabbbbababababbbaaaaaababaaabbbabbaaaaaabbabbbabaaaababababbbbbabbbaaabbbabbaababbabbbbbbbabaabbabaaababababababbbbbbabaabbbabbabbbbbbaabaabbbabbabaababbbbbabbaababaabbbbabaababaabbabaaabbbbbabababaabbbabababbaaabbbbaabbaaabbbabbbbbbaaaaaabbbbbaaabaabbabaaabbbbbbababbbaabbbbbaabbbbaaaabbbaaaabbbaaaababbabbbbbbabaabaabaaaabbabbaabbbabbabababbbbbaaabaabbaabaabbbabaababaaabbbbabbbaaabbbbbbbaaaabbabbaaaaabbaabaaaaaabbbaaabbaababaaaaaaaaaababaaabbbbabbbbbbaababbbababbbbaaabaabbbabaaabbbaabbbbaaababaaaabaabbaabaaaababbbbbbbaababbaabbbbaaababbbaababaabbbbaaaaabbababaababaabbbaaaabaaaabaaaaaaaabbbabbaabbbabbbaabaabbabbaabbabbbabbbbbaaaaabbbbbbbbabbaabbaaababaaabbbabbbabaabaabbbbbbbbababbaabbabaabaaabaabaaaaaabbabababaaaaaabaaabababbbababbbbababaaaaaabaaabaaaaabaabbbbaaabbaabaaaabbbaabaaabbbbbbaabbabbbabbbbababbababbaaabbbaababbaaaabbbbbbbaabbaabaabbaaaabbababababababbaababbbbbaabaabababbabbababbababbabaaabbababbbbbbbbbabaaaaabbaabaaabbaabaabbabababbbaabbababaabaaabbbabaabbbabaabaabbbbbbbaabaabbaabbaababbabaaabbbbababbbbabbbaaaabaaababbabbbaabbbbbbbaababababababaaaabababbbbabbaabababbbbaabbabaabbaabaaabbabbaabbaababaabbababbbaabaabaababbababbbbaaaaabbabaabaaabbbbaabaabaaaabababbbbbabaaabbaaaaaabaabbbabbababbababababbaabaabbababbababbbabbbbabbbaaababbbbbbaabaaababababbabbbbaabaabaaabbaabbbabbababababaabbbbaabbbababbababbbaaaabaaaabbaaaabbababbbbabbaabbbbbabababaaabbbbbbabbabbaaaabbaabaababaaabaaaabbbbaabbbabaaaaaabaaababaaabaabaabababaaababaaabaabbbaababbaaaabaaaabbaaaaaaabbabaaabbaababaabbaaababababbbbabbbbbabbbaaababbaababbbbbbaaabbbaaabbbbbaabbabababaaababbbbbbbabbbaabaaabbabbbbbabbaabbaabaaabababbabbbbabbbbabbbabaaaaabababbaaaaababbbbbbaaaabaababbabbabaaaabbaabaababababbbabaaaabaaaaabaababaaabbaababbabbbabbabbaaaabbaaabbbabbabbabbbaababbaaababaabbbabaaabbabababaabbbbaaababbbaaaaabbaaaabbaababaabbaaaabbaaabbbbabbabbabaabababababbbaababaaabbababababbbbbbabbaabaaabbabaabaababaabbabbbbaaabaaababbbbbbaaabbaaaaabbabbabbabbaaabbababaabbbababbbbaabbababbbbabbaabbabaababaaababbabaabaaabbbabaabbababbabbaabbbbbbbbbabbaabababbbbaaabaaaaaababaababbbbabbbbbbbbaaaaabaaaabbbbaabaaaaaabbbbbaaabaababaaaabaabbaaabbaabaabaabbaabaaabbbbbabaababbbababaaaabbbaabaabbbabaaabbabbabbbbabbbabbaaababbabbaababbaaaaaababbbbbbaabaaaabababbabbababaaababababbbbaaabbbbbabbabbbbaababbabaaabbbbbbaaabbbaaaababbbbabbbababaaabbbaabaaabbabbbbabbaaaabbbaaaabaaabbbababaaabbbaaababbabababbaabbbabbaababbaababaaaabaabbaaabbaabbabbbaaabbaaaababababbbbbabbbababaaabbabaaababaabbbbabbbabaaabaababaaaaabbbbababbbaaabbbaababbbabbabaabbbbabbaaaaaabbaaabbbaabbbaabaaababbbbabababaabbabaabbbabbaabaaabbababaabaabaaababaabaabaabbaaaaaabaaabbababbbbbababbabbaabbaaaababbabaaabaaabbababbabaaabaaabaaaabbbbbababbbaababbbaaaabbabbabbbaababaaaabbbbaabbaababbbbaabbbbbbbabbbbbbaaabaaabbabaabaababaaabbbaabbbaaabaabbaaaaabababaabbbaaaaaaaabbbabaaaababaabababbaabbaaaababbaaaababaababbbaaabbaaaaababbbbabbaabbaaaaabbbaabbabaaabababbaaaaaabbbbbbaaaabbaabbaababbababaaabaaabbaaaabaabaaabaabbbabbbbbababbbbbaabaaaaaabbbbbaaaabbbbbbbababaabbababaaaabaaabbaabaabbaabbaababbaabaabaabbaaabaababbbaababbaabaababbabbbaaaabababbbbbbbaabaabbbbbbbbbbbaabbbbaaabbabaababbaaabbbbababaabaababbbabbababbaabbbaaabbaabbbbbabbbbaabbabaaaabaababbabaabbaaabbbbaaabaabaaaaaaaaaabababbaabbaaaababaabaaabaaabababaababbabbababbabbaabbabababbbbbbbabaaaabababbbabbabbaabaaaaaaaaabbabbaabbbbaabaabbbaabbaaaaabbabaaabbaabbbaaabaaabababbbbaabaabaababbabbaabbabbaaabbbbbabababbbbabbabbbbbabbbbbbbbaaaabaaababbaabbbababbbababbabababaaabaaaaaaabaabbaaaababbbabbbababaaabaaaaababbabbbbabbabaaabaababbbbabaabbbbabbaaaaabbbaabababaabaaaabababaabaababbaaaabbabaaababbbbbbababaaabaabaaabbbbbabbbbaaababaaabbaabaaaabbbbbbaabababbbaaaaaaabaaaabbaaabbbaaabbababbabababbbbbbabbbbbabaaaaaaaabaabb