abbbbabaabaaaabbbabaaabababaabababbbabbabbababbabbaaabbabaaabaaaaababbbbbababaaabaaaababaabaababbbbaaabaabbaabbaaaabbbaabaaaaaababbabbbabbaaabbbbbaaabaaaabbbbabbaaabaabbbbaaababbbbaabaabbbbbbbbbaabaaabaabbbbaabbaaaababaaaababbbaaaaabbbaabaabbabababaaababbbbbbabaaabbabbbbababbaabaaaaaabbaaabaababbabaabbaaaabbaaabbaababaaaabaaabaabbbaabbbbaaabaabbbabaaaababbbbaabaaabbaaababaabbaabaababaabbbbabbabababaabbaaabababbabbbbaaabababbaaaabbaaabaaababbabbaababababbbbabbbaabbabbbbbababaaabbbbbbababbaaaaaabaaababbaaabaaabaabababbbbabaaabbbabbabaababbbaaaabbbaaaabbbababbabaabbbbaabbaaabaaabbaabbbbaabbbbabaaaabbabbbbababbbaaaaabbbbaaababbabaabaaaabbaabbaaababababaabbababbbbabbaabaaabaaaaababbaabbbbbbbaaaabbaaaabbbbabababaaabaaababaabbbabbbabbababbabaabababaaaabbaaabbabbaaabababbbabbbaaaababbabaabbaabbaabababbbaabbaaabababbbabbabaaababaaaabababbbbbbbbaaabbbbbbbbbaabbababaabbbaabaaaaaabbabbbabaaabaaabbababbbaaababaabaabbaabaaaabaabaabaaabbbbaabbbabaaababaaabbaaaaaaaaaabaabbabaababbbaaaaaaabaabbbbabbbaabbabbabbbaaababbaabbbabbaaabbbbbaaaabbbababaababbaabaaabbaaaaabbaaaabaababbababbbbaabbabaaaabbbbbababbabbabaaaaaaabbabbaababbbbbbaabbabababaaaaaaaaabababaaabbaaabaabbaaabbbabbaaaaabbbabababbbbaabbbbbbaabbabababbaababaabbabbbbbabaaababaabaaabbaaaabaaabbbbabbabababaabbabaabbabbabbaabaaaaabaababbbbaaaaabbbbabaabaabbbbaaabaababaaaaabbabbaaaababaabbbabbbaaabaaabbbabbababbaabbbbbabaabaaaaaaabaabbbbabababbbababbaabbaaaabaaaaabbbaabaabbababbbabaabaaaabaabbbabbbbbabbbbbbbbbaababbaababbabbbabbababaaaaaaababaaabbaabaabbaabbaabbbaabbbaabaabbabaaaaaabaaaaabbbabbababaabababbabbaabaababbbbbaabaabbabbabbabaaabbabaaaabbbbbbbabbbaaababbaaabbbababababbbbbaabaabaaababbbbbbbbabbaaaaabbaaaabbaabbbbbbabaabaaaabbaabbbabaaaabbabbbbbabbaababbabbaaaabaabaababbbaaababaababbbaabbaaababbaabaaababababbaabbbaabbbbaaaababbababbabaababbbbaabbbaaaabbbbbabaaaabbabbaababaaabaaaaababaababbbbabaabaabaabbabbaabbabbaabbbabbbbaaabaaaaabbabababbbabbbbbabbaababbbaabbaaaaabbbaabbabbbabbbaabbabbbababababaabbaaaaaaaaaaaaaaabaaabbbabaaababbaaaabbbbbaabbaaaababbaabbbbaaabbbaabaabbabaaaababaaababababbbabbaaaabbbbaaaabbbaaababbbabbabbbabbbabbbabbaabbbabbababbbbababbaaaaabababaabaaabbbabababbbabbbabbbababaababaaaabbbababbaaaabbbbabbaababbbaababbbabaaaaababababaabbabbbbababbabbababbabbababbbaabbababbabbbaabbabaabaaaaabbabababbbbaabbaabaabbaaaaaaaaabbaaabaababaababbbbabababaababbaabbaaababbabbabbabbbbbbabbbaabbaaaaabaaabbbbaaabbaabababbabbbabaabbbabbaabaabababaaaabbababbaabbbaaaabbbbababbbbabaabaaaabbbabbabbaabbbbbbaabbaabaababababbaaaaabbabbbaaabaaaabbbaabaababbbabaaaabbaababbabbbbabaabaaaaaabaaaabaabbbbbbabbbaabaabbbaabbabbbbbbaaaabbbbabbbababbabbbaaabbaaaaababbaababbbabbbaabaaaabbabbbaababbabbbabbbaaabaababbbbbabbbaabbabbbbaaaaabbbbbbbababaabbaaaaabbaaabaabbbbaababaaabaabaababbabababaaaaaaabaabbaaabbaaabbaaabaabbababaabbaabbaabbaababaabaaaaababbaabbabbaababbbaabbbabbbbabababbbaaaaabbbaaaabaaabaabbabbababababaabbbaaabbbbbaababaabbabbaababaaaabaabbaababaabbabbaaababbabaabbbbababaabbabbbbbaaaabaabaababbabbbaaabbbaabbbbbbbbbbbbbbaabaaabbbaaababaabbabbabbababababbbaabbbaaaaabbbababbbbbabaabbaababbabbbabababababbbaabaaaaabbabbbaaaababaaaababaaabaaababaababbbbababbbbbaababaaaabbababbbabaaaaaabbbabbbbbbabbababbbbbbabaaabbaaabbbbbbababaababaabaabbabbbabbababbbbaababaaabababbbbbbbbbabbabbabbbabbababaaabbaabbaaaaababbbababbaabbababaaabababaaaabaabbbaaabaabbabababaabaabaabbabbaababababbaababbbbaaaabaabaababababbababbbaabbaabbabaaabaabbbaaaabbaabaabbbbababbbabbaaaabbabbaaabbbabaaabbbabbbbbaaabbbaaabbaabbbbabbbaaababbbababbbabaaababbbbbabababbbbbabaabaaababbbbbbbbabbaabbbababbaaaabbababbaaabaaaaababbaaabbaabbabaabbababbababbaabaaabbbaaabbababbaabbbbbababbaabaaaaaabbbaabababbaabaabbaabbaabaaababbaaaaabbbabbababaaaaaaaabbbbaabbabbbbbaaababbbbbaabbbbbaaaabbaaabaaaaaabbbabbabbbbabaabaaabaabaabababbaaabaaabbaaaabbbbbbaabaabbbaaaaabbaaaabbabbaababbbbaaababbabbbaabaaaaababbabbaaaaabaaababbbbbbababbbabaabababbaaaabaaaabbababaaaaaaaabbbababbaaabbaababbbbbabaaaaabbaaabaaabbababaaabbbabbaaaaaababbbbbbbaaaabbbbabaababbbbbabaabbbbbaabbabababaaaaabbaababbbababbabababaaaaabaaababbaaabaabaabbbbbaaaabbbbbbabaabbbaababbbbabaaababbbbbaaabbbabaaabbaabaabbbaabababbbababbbbaaaabababbbbaaabbbaabaabbaaabababababaaababababaabbabbbabbbaabbbaabbbbabaababbababaababbbaaabbabbababbaababaababbbaaaaabbbabbababaababbabbaabaaabbaaaababbaabaaabbabbbababbbabaabbbabaabababaabbbabababbabababaabbaaababaaaaabaababbabbbaaabbbbbaabbbbbbbbbbaaabaabbbaaabbabaababbaaabbaaabaabaaabababbaaababaaabaaaabaabbbaaaabbbbbbbbbabababbbbbbabaabbabbabbbaaabbbabbababaabaabababbabababbbbaabaaaaabbbababaaaaabaabbbbabbbbaabbabababbbabbaaabbabbabbbababbabaabbaababaaaaabbbbbabaabababbbbabbbabbaaababbababbbbbaaaaaabbbabbbbabaaaabbbbbbababaaaaaabbbbbabaabaabbbabaaaaaabbabbaababaabaabbabbbbbbbbaaababbaabbbabbbbbbbbbaaaaabbbbbbaababababbbbbabaabbabbbaabbaaabbaabbbabaabbbbbbabaababbaabbbbaaaababbabbaaaaaabaabbababbbbbaabaaabaabbbbaaaaabbabbbbaaabbabbaabbbbbabaaabbaaaaaabbbbaaabbaabbbbabbaaaaabbbbaabbbabbaaaaabbbaabaabbbbabbaabbbbbaaabababbbabaabbabbbaabbabaaababaabbbbbbabbbabaaaaaaaabbbabbbabbbbaaaaaababaabaabbaaabbbaabaaaaaaabbbabaabbabbbbbbaaaaaababbabbabbaaaababaabbaaabbbbbbbaaabbbbbbaabbaabbbbbbaaaaabbaaabaababaaabaaaababbbaaaaabbbaaaaaabbbabababaaaabbababbaaaaaaabbaabaababababaaabbaababbbbbaababbabbbaababaaaaaababababbbabababbbaaaaababaaabaaabbbbbabbbbbbbbbabbbbabbaaabbbbabbbababaaababaabbbbabbababbabaaaabbbaaaabbabaabbbabbabaaaaabaabaaababbbbaaabbbaaaabbaaaaabaabbbaaaaabbabaababaaaaaabaaaabbbababaabbaabbabaababbbaaabbbabaabbabbbbabababababbbabaabbbbaaaaaaabaabbbaababbbabaabaabbbbabababaaabaaabbbaabbbabbbabbaabbabbbabbabbbababaaaabaabbabababbbbbbabbbbbaaaaaaabaababaabbabaaaabbabbaabbbbaaaaaabaababbbabbabbaabbbbabbbabaaaaaabbbbbaabbaaaabbbbbababaaabaabbbbbbbabaaaababbbaabaaaababbbaaabbaaabbabbbabaaaaaababbabbabaaabaaaaaaaabababaabbbbabbaaaabbbaababaaabbbbabaaabbbabbbbbabababaabbbbbbbababaababbbaabaaabbbbababbabaabbaabaabaaaabababbbbbabbbbaabbbaabbbaaaabbbaabaabbbababababbaaaabbbbbbabaaabababbaaabbaabbbaababababaabaababbaaababbbaabbbbbbbbbaaaaabbbbaababababbbabababaaabaabaabbaaabbbabbabaaabbababbbbbaabbbbbabbaaaaaabbbabaabbbbaaabaabaabbababbbbbbbbbbbababbaaabaabababbbbbbbbaabbaabbbabbabbbbbabababbbbaabaaaabaaabbabbabaaaaaabbbbbbbbbbbbbaaaabbaaabaabbaaabbbaaaabbaaabaabbabaabbbbabababaabbbabaaabbabbababbbaaaabbbbbaababbbaabaaaabaabbbaaababbbabbabaabaaaabaaaaaabaaabaaaabaaabbbaababbaabbaababbaababbbbabaabbabababbaaabbbbaaabbbabbabbaaaabbabaabababbabbaaabaababaababaaabbbaabaaabaaabbbbbbbaabaababaababababbbbaabaaabbaaaabbbbaabaaaabbbbabaaabbbbbbbbaaabbabaaaaabbbaabbbabbbaabbabaaaaabaabbbabbaaaaaababbbababaababbbbbabbbaabaabbbababbbaabbbbbababaabbaabbabababbaababbabaababaaabbbabaabaababbbaabbbbbabaabbbbabbbababbababbabaabbbbbaabaaaabbbbbbbababbababbbbabbbaaaabbaabbbbbbbaaaaaaabaaababaaaabaaaabbbbbbaaabbbbbababbabaaabbbaaaaabaaaabbabbbabbbaaabaaaababbababaaabaabbabbbababaaabaabbbabaabaabbabbbaaaaaabbbbabbaaabbabbaaaabababaaaaaababbabbbbaabaabbbbababbababbaaabaaaabaaaababbaabbabbbbabbabbaabbababaabbabbaababaaababbbaaaaabbaabaabaaaaaaabababbaabaaababbbaabbbbbbababaabbbaabaabbaaabbbabbbaabbababbaabbabbbaabbbabbaabaabaaaabaabbbbbbbabbbaaabbbbbaabbaabbababbabbbabbbbbababbabaababbaabaaaabbaaabbbabaaaabbabaaaaabaababbbbbabbbabababbbbaabbbaaaabaabbaabbbbbaaaaabbaabbbabbbaabbbbbbbabaabaaabaaababaabbbbbbaaababaaaabababbaabaaabbabaabaabaaaabbaabbbababbbabbababbbaaaababababbababababaaabbabbbaabaababbbbbbbababbabbabbaaabaababbbbaaabbabbbbaaabbbabbaaaabbbabaabbbabbabbbabbbbbbaababababbabbaaabbbaabaabbabaababbabaaaabbbabbbbababbbbbbbaababbbbbbbbaabababbbaabbbbaaabaaaabbbbbabbaabbabbbbbabbbbabbbbbbabaabaaaabbbbbaababaaabbbbbaaabaabbabbaabbaaabbabababbbbbabbbabaabbbaababaabbbaaababbaaabbbabbabbaabababbbbaabaabaababbbbababaaabbaababaaaabbbbbaabbbbababbbaaaabbabaaabbabbaabbbbaabaaaaaababbbbaabbbbbbbabbbbababaaaabbbabbbababbabaabababbbbabaababbabbbbbbaababaabbbabaaabbbbbbbbbbaaaaabbbbabbaabbabbabbabbabaaaabbbbaaaababaabbbabaaabababbbaabbabaabbbabaabaaabbabbbaaababbaabbabbaabbabaabaabbbbaabaabaaaababbaaabaabbbbbbbbbbaaaabaaababbabbaabbbbbbabbbabbaababaaaaaababbbaaaaabaaaabaabbbbababbbbbaababbaaabbabbbabbbabaaaaaaaaabbaabbbbbbaaaabaabbbbabbbaababaaaaaabaabbbbababaabbbbaaaabbbbabaaabaaaaaaaaaaababbbbaababaaaaaababbabaaaaababbbbabbabaaabaababbabaabaabbbaabbbbbabbbbababaababbabbbabbbbaabbaabaaababababbabbabaaabaabaabbbabbabbbaabaaaaabbbbaababbabababbaaababaaababababbaaabbabaaaabbaababababbabaaaaaaaaabbbbaaababbaaabbbbbaaaaabaabbabbaabababaababbbbbbbaaabbabbbbbbaaaaabbbbaabbabbaabaaaaaaabbbabbabaaabbbbaabaaaabbaabababbbaabbbaaaaaabbbbbaaababaaabaabbababaababbbbbbabababbbbaabbbbbbbaabaabababaaabbbbababaabbbbbabbbbaaabbbabbbaabbaaabaabbbaaaabbbbbbabbbbabbaabbbaabbaaaabaababbabaabbbbaaaabaaababbbaabbabbaaaabbaabbbabaaabaabaabbbabbaaaabbaaabaabbaaabbbbaabbbbabbbbaababbbbaababbbaabbaaabbbaaaabaabbbbbbbbaaabbbbabaaabbbbbababbaaabaaaabaaabbbaabababbaaaabbbabaaaaababbbabaaaabbbbbababbbaababbbaababaaabbaaaabaaabaaaabaaaabbabbabbaabaabbbbbbabaababaaaabbaabbabbbbaababbaabaaaabbabbababbaaaaabaabaabaaabaaaaabbababbbabaabaababaaabbbababbababaabababaabbabbbaaaaaaababababbaaabbbbabbbbbbbbbabbbaabbaabbbabaaabaaaaabbbbbabbaaaaabaaabbbababbbbbbbbbbbabbabbababaaaaabaabbabaabbabbbaababbababbbbaaabbbbbbaababbbabababaabaabaababbbaaaabbbbaabaaaaabbaaababbbbababaaaaabbabaababbabbbabaabbbbbbabbbbababbbaabbaabaaabbbaabbbbbbabbbbbbaababbaabbbbbbabaaaaabaaabaaabbabbbabbaabbaaabbaaaaaabbbbbbbbbbbaabbbabaaaaaaabbbaaaababababbababbaababaaaaabbabbabbbabaaababaaababbbabbaabbbbbabaaabbbbaaabbaabaabbababbbaabababababaabbabbbababaabbaabaabbbbabbbbbbaaabbabbbaabaababbabbbbbaaabbbabababbaabbabbabaabaabaaabababaabbbbbaabaabaaaaabaabaaaabaaabbaabbbbaabbbbaaabbabbaabbbbaabbbbabbbbaabbababaabababbababababbbaaaaaabbbbabbbabbbaabbaaabaaabbaabbbbaabaaabbaaaaababbbbaababbbbbbababbababbbaabbabbaabaabbaaabbbabaaaaababaababbbbabaaaaaabbbbbabaabaabaaababaaabbbaaaabbaaaabbbabbababaaaaaabbbbbbabaababaabaabbaaabbaaabaabaaaaabaaabbbbbababbbbaababbbbbaabbbbbbabababbbbbabaaaaaabaabaaabbbababbbaaabbbbabbbbbaababaaabbbabbbbbbbbabbaaabbaabbabbbaaabbaabaaabaaaaaaabbbbbababbaabbbaababbaaababaaabbaaabbbaaabaaaabbabbbbaaabbbaaabbaabaaababaaaabbababaabaabbbbaaaabbaaabbbbbabbbbabbbabaaaabbbbababbbabaaabbabbbabbabababbbbaaaabbbbabbabaaabbbbabbbbbbbabaaaaabaaabbaaaabbbaaabaaaababbaaaabbbaaaabaabbbbbbaabaaabaaabaaaabbaaaaababbbbbabbbaaabbababbabbbaaaabbabbaaabaabbabbabbbbbbbabaaaabbbabbbababbabaaababaaaabaaaaababbbabaabbbababbbbabababbbaaaababbbbaaaaabbbbabbbbaaaabaaaaaaabaabaabaaaaaabababbaaabaabbabbabbbbaaabababbaabaaaabaabbbabbbabbbaaabbbbbbbaababbababaaaabbbbabaabaaaabbbaaabbaaaabababbaaaaababbaababbbabbabaaaaabbabaaaaabaabbabbbbbbabbbbbbababbbabbbabbbbbbaaabbbbbbbaaaabaaabbbbbaabbbbaabaabbbabaaaaabababbabababaabbbaababbabbaaaaabaaaaababbabbbbaaaabbaaabaabbbbbbbaabababbbaaaaaaaaabbababbabbabaababaaabbbbaaabbbbbaabbbabbaaaababbabbaabbbbabaaaababbaabababbbbabbaabaabaabbbbbaabbbbbbaabbbbbaaaaaabbbaabbaaaabaaabbbaaaabbbbaaabbbabaabbbbababbabababbaabbaaababbabbbbbabbabaaaabbabaaaaaabbbbababaababaaaabbaabaabbbabbbbbbbbbababbbaabbabbbbaababaaabaaaaaabaaabbabababbabaaabaabbabaaabaaabaabbbbabaaabababaabaaabbbbaabababbbbbbababbbabbaababaabaabbaabababaabaaabbbabbaababbbbaaabbbbbbbaaaaaaaaaabaaabbbbbaabaaabaabababaaabbaaabbbaaaaaabababbbaaabbbbabbbaaaaabbbbbbbaaaabababbbababbabbbaababaaaaaaabaaabaaaabbbbaaabaabaaabbabaaababbbaaabbaababbaabbbbbaaabbaaaaaaaabbbaaaababbababbbaaabababababaaaababbaaabaaaababbabbaabbbbabbbaabbbbbabaabbbbaabbbababbbabbabbbaabbababbbaabababbaaaabaabbababbbbbaabaababbabaababaaaaababaaaaabbbaabbaababbabbabaaabababbabbbaaaaaababbabaaabbaabaaababaaabbababaaaaababaabaabbabbbabbababbaaabaaabbababbaaaaaaababaaabbbbabbbbaaaaaaabaaaaababaabbaabbbbabbaaabaabaabbaabaabaababaaaaababbaabbababbbbbaaabaabaababaaabbaabbababaabbabaaaaaabbbabaaaabaaabaabbbbabbbbbabbbaaaaabbaaabababbbbbbaaaaabababaaabbaaaabbababababbbabbabaabbbaaaaabbbbbaaaaabbaaaabaaaabbbbbababaabaaaabaabbbbabbabababababaaaaaababbaababbababbabaaabbaabbbbaaabaabbabbbabbbbbbbbabaabbbbbbaabaaabbbbabbabaabbbabbbbaabbabababaaaaabababaaababaaaababaababababbaabaabbbaababaaabaaabbababbbbbbbabababbababaabaababbaabaaababbbaabbabaabaabaaaaaaabbababaabaaabbbbbababbabaabbaabaaabbbbbaaabaaaabaabbabaabbbbabbaabbbbbbaaaababbaaaaabbbabbaaaaaabaababbaabbabaaabbbaababbbabbaababaaabbaaaabbaabbaaabaaaaabaaaaaabbaabbbabaababaaaabaabbaaaaabababbbabbbbaabaaaaaaabaabaaabbaaaabbabababaaabaaabaaaaababbaabbaaabbbaaababaaaabbbaababaaaaabaaabaabbbbaabbbbbbababaaababbbababbbbaabbaaabaababbaaaaaaabababababbbbabbbbabbabbbbbbabbababbbbbbabbaaaaabbbaaabaabababbbbaaaabbbaabaaaababbaaabbbbabaaaabbaaababaabaaaaabbbbabaabbbababbbaaabaaaabbbbabbabbbaaababaabaabbbabbbaaaaabbabbabababbbaaabbbbaabbabaabbbaaaabbaaabbbbaaaaaababbabbbbaaaaabaaabbabababababbaaaabbbbbbaabbabaabbaaabbababbbaabbabaabaaaaaabbabbbbbaabbabbbbabbabbaaaabbbbaabaababbbaabaabaabbaabbbbbaaaaabbbbbbbabaaababaaabbbbbaabbbbbbbabaababbbbabbbbbbaabbaabaabbaabbaaabaaaabbaabaabbaabababababbbbbbaabbbaaaabbabaababaabaaabbababbbbabababaaaabbabbbbaaaabbababbbaababababbabbbaabbaabbbbbaaaaabaabaabbabaabbbabbaaaabbbbabaaabbbabbbaaaaabaaababaabbbbababaaabaaabbbabaaababaabbbaababbaaabbbbaababbaabbaaababbabbaaaaaababbbbbbbabbbbbbbabbabaababaaabbbbaabaabbaabbaaabbababbabbaabbbaabbbababbaabbbbaaababbaabaabaaaabbbabbaabbbaabbbababaabbabababbbbbbbaababaaabbbbabaabbababbbababaaabbbbaababbaabbaabbaaabbabababbbbabbbaabbbaabbbbaababbbbaaabbbbbbbababbbbaabbabbbabbbbaaaaababaaaaaaaabbaaaababbbbbaaaaabababbbbabaabaaabbbaaaaaabbaaaabbabbabaababaaabaaaaabbbaabaabbbababbbabaababaabaaaaaabbbabaabbbbabbbbaaaaabaabbababbbbbababbbbbbbbaaababbbbbababbaabaaaaabaabbbbababababbbbaabaaabbbbabaabaabbbbbaaaaaabaabbbbaaababbabaabaabaaaaaaabbabbbbabbaabbbaaaaabaaabbbababaabaaabaabaabaaabababbbaabbbaabbaaaabaabbabbbabaaaabbababaaaaabaaaaabbabbbaabbaabbbbbabbaabbbbbababababbbbaaaabaababbbbaaaababbabbaabaabbabbaabaaaaababaababbbabbbaababbaabaaaabbbbaabbbaabbabbbbbbaabaaaaabbabbbbaababbbababababbbaabbaaababbbbbababbaaaaabbbbaabbbababbaabaabbabbbaaaabbaaabbabaabbaaaaabbbbaaaabbbaaabbabbbabbabbbabbbbaabbabbbbaabbaaababbbaababaababbbbaabababbbbbbaabababbbabaaaaaabababbbaaabbbbbaabbabbaababbaabaabaaaaababaaabaaaaababaaaabbbbaaaaaababbabbbbbbabaaaabbabbabaaaaaaaaaaaaaaababbabaabbabaabaaaaabbababaababaabbaababbabaaaaaaaaabaabbbaaaaaaaaaabaabbaabbbabbbbbabaaabbbaabaabbaabbaabaabbabbbbbababbbaaaababbaaabababbabbaabababbbaabbabaaabaaabbbbbbbaababababaaaaaaaabaabaabbbabaaaabbbaaabbbababbbbabbbabbbbbbbbbababbaaabbbbbaabaaaababaabaaaabaabbbaaabaabbbbbaabbbbabbabbbbbaaaababababbaaabababbbbaaabaaaaaababbaaaaabbaaaabbbbaaababababaabbaaabbbbbababbbabbbaaaaaaababbabababbaaabbababaaababaabaaaaaabbaaabbaabbbabbaabaabbababbbaaababababbabbbabbabbbabaababaaabbbbaaaabbbbbaaaabbaababbbbbaaaaabbaaaababbbaabbbbabbbbababaabaababbaabaaaabaaabbbaaaaaaaaaabbabaabaaababaaaaabbbaababababababbbbbababbaabaabaabaabbbbbbbaabbabbbabaaabbabbbaaabbbbbbabaabaaaaaaabaaaaabbbbbbbbabaababaabbbabbabbbbaaaabbabbabababbbaaaabaaabbabbbaababbabbbbaabbabbbaababaababbaabbabbabaaaaaaabbbaabaaaabbbbbbabbbababbaabbaaabbbaaabaabbababbabbbaaabaabaaabbbbabbababbabababaaaaaabaabaaaababaaaaabaaaabbaaaabbabaaaabbabbabbabbabbabaabbabbaaaabaaaaabaabbbababababaabbabbabbabaaaabbbbbaaaababaaabaabbabbbaaababaababbabaaaaabbabbaaababbbabaabbaaaaabaaaaabbbaaabaabbbbbbbbbbabbaaababaaababaabaaabaaabbbbaaaaaabbaaaaabaabbaaaabbbaababbaaaaaaaabbaaaababbbabaabbbabaabbaaabaaaaababbbabaaaaabbabababbbbababbabbbbaaabbabbbabaababbabaabbbabaaaaabbbbabaababbaaabbbbaababbabaaababbabbbbaabaabababbbababbbbbbbabbbaaaabbaaababbaaabbabbbbbbaabbaabbbbbbabbababbaabaabbbbaabaaaaababbbbabbbbbbbbaaabbbbbbabbabbbabbabbbabaaabbaababaaabaaaaaabababbabbaabaabbbbaaaaabaabbabaababbaaaabbabaaaaaabaababbaabbbabaaaaaaababaaababbbbaaaaaabaabbabbaabbbbbbbaabaaaabbbaaaaaabaaaabbaaabaabbbabbbaabaabaabaabaaababbabbbabaaababaabbbbbbabbaabbabbabbbbbababaaababbabaabbaaabbaababbaaaaabbabbabaabaaababbabbbaaaababbbbaaaabbbbbabbbabbababbbbaabaaaababbbbabbbbaaaabaabbaaaaabbaaaaaaaabaaabbbabbaabbabbbbbbababbabaaaaababababbbaaaabbbbbbbababaaaaabbbbbbbaabbabbaaabaaabbabbabbbbabbabbabbbbabbaabbabababbaababbbabaaababbabbbbbbbabaaabababaabaaabbbbabbbbabaabaabbbabbbbaaabbbbbabbaabaaabaaabaabaabaaabaaabaababbaabbabaaabbabaababbbabbababbaabbaaabbbbbbabaababaaabbabbbabbaaaabbbbbababbaaaaaabaaaabaabaaaabaaabbbbabbababbbaaaaabbaaaabaaaabaaabaaabbbaaababbbaababbaabaaaaabbbaaaabaaabaaaaaaabaabbbaabaababbbabaabaabbababaabaaaaaaaaabbaababbbabbaaabaaabaababbbaabbaabbbbbabaabbaaaabaaabababbaabaaabaabbaaaaabaabbaaabaaaabbabaabbbbbbaaababababbabaaaabaabbaaabaabaabababbabbbbbabbbbabbaaaaaabbabbaababbabbbabbabbbbaaaaabababaaaabbbbabbaababbbaabababaaaaabababbbaaabaabaaabbbaaaabbbababbbabaaababbbaaaabbbbaabbaabbbbabbabbbbbabbaabbabaabbbbabbaaabbbabaaabbabababaabaabaabaaabbaabbababbbbbbabbabbbbabbabbbbaabababbaabbbbaababbbbabaababbaabbbbbabbaababaaabbabababbabaabbbbbbaababbbabaabaaaaabaabbaabaaaabaabaaaabbbaaaabbbaaabaabbbbaababbaaaaaababaaaabaaabbbaaaaaababbabababababbbabbaabbaabaabbabaaaabbbabbbbbabbbbaaabbbbbaababaabbbbbaababbababaabbbabbbaaaaaabbbbaabbbabbbbababaaaabbaaaababbaaaabbabbbbbbbaaaabaabaabbaabbbbbabaaaabbbbaaaabbabbaabbababbabababbbaabaabaaabaabbabbabaababaaabbabaababbbabaaababbbaaabababbbabaaabbbaabbbabbbbabbbaabbabaaabbabbbabbbabbbabbbbaaaaabbbbbbaaabaaabbbaaaabbbaabaabbaaabaaaaaaaaabbabbbabaabaaaaaabaabaababbbbaababbbaabaabaabbaabbababaabaabbabbabaabbabbbaaabaaaabbbaabaaabbababbabababbaaababbaababbabbaabaaaabaababbaaabaaaaababaaaabbbbaabbaabaaabbbbbbaabbbbaabbbaabbbbbbbaabbaababbbaaaabbbaaabbbaaabaaabaaabbababbaaaabbabbabaaabbabbaaabbbbbabaababbabaaaabbbbabbabbaabaaababaaaabbabbaaabbbababaaabaaabbaaaabbbabababbaabbbbbbaabbabbbbbabababbabbbaaabaaabbbabaababaaaababbbabbbbbbabababababaaabbbabababaabaabbbbbabababbabbbabababbababbbbbbbbaabbabbabbaabbabbbaaaababbaaabaaaaabbaabababaababaaabaaaaaabbbbaabbbbaabaaaaaabaaabaaabaababbabababbaababaabbaabbabbaaabaabbabaaabbbbbaababbababaaaabbbabaaaababbbbbaaaaaaaababbbababaabbbabaabbbaabbbabbbbbaabbbabbbbaaabbbbabbbaabbbbaabababbaabaaaababababaababababbaaaaaaaabbabaabbbbaaabbabbbaabbbaabababababbbbbbbbbbbaaabbbabbbabbbaaabababbaababbbbabbbbbbababaabbaabbbabbabaaaaaaabaaaaababbbbaabbbbaaaabaabbabbabbabbbabbababbbaabaaaaaaabaaaabbbabbbababbbbbabababbaaabaaaabbbbabaaabbbabaabaaabbbbbabbaababaaaaaababbbbbaabbaabaaaababbabbabbbbbbabbbabbbbbaabaaaaaaababbbabbbabaaaaabaababbbbababababbbabbababbababbbbbbaaabbbaaabaaabaabaabbbbbabaaaabaaababaaabbaabbbaaaabaaaaabababbabaababaabbabaabaababbabbaabbbbaabbbbbaaaabbabaaabbbaaaabaababaaaabababbabaabbabbbabaaabbabaabbababbabbaaabbbbaababbaabbbbaabaabaaaaabbbaaaaabbbbbabaaabbabaaabbabaaabbabaaababbaabbbaaababbbabbaabbbabbbababbbabbbaaaabbbaaabbbabbabbbababbababbaababbbbabaabbabaabaaaabaabbabaabaaabbbabbaabaaabbbbbaaaaababbbaaabbaabbabbabbbabbbbabbbaabaaaabbbaaaaaaaaabaabbabaaabbaaabaababaababbbbbababaabbbbbbbaabbbaabaababaababaabbaabbbbabaaabababaabaaabaabbbbaaababaabbababababaabaabbbabbaaaaaabaaabaabbabaababaabbbbbaaabbaaaababbaaabaaaabbabbabaabaaaabababbabbbbaabbabaabbabbbbaabaabbabbaababaaabbbaababaabbaaabbbabbbabaabbbbbaaabaaaabbbbbaabbaabababbbabbababaabbbbabaabbabbabbbbbbbbaabbbaabaaaaaaaaabaabaaaaabbaaaababbbbaabaabbabaabbbbaaabbbbabbabbbbaabaabbabbabbbaabbaabaaabaaabaabbababbabbaabbabaaaaaabbabbbbabbaaaabbabbaabbbababbbaaaabbabbbabbbaaaaaabbbaaaabaababbbbbaabbbbbbaaabbbabbbabbbbaaababbbbbaaaaaabbbbabbbaaabaabbbaababbbbabaaaabababbbababaaabbbbaabbabbabbaaabaaabbabaaaabbbbbaaaabbaabbbbabbbbbbbabaaaaaaaaaaaababaababaabbbaaabbabbbaabaaabbaabbababbbaabbababbabaaaabbababaabaaaababababbaaabbbbbaababbabbbbbababbabbaaababbabbabaabaababaababbabababaaaaababbbabbbbabbaabbabaaaaaabaabaababbbaaabaaaaabbbaaaaabbbbbbaabbbbbaababbbbababbbaaabbbbbabbabbbbbaaaabbabbbbabbaaaaababbbbbbabbbabbbabaababaaaabaaaabbbaaabbbbaaabaabaaaabbababbabababbabbaabbbaaaabababaababaaababbbabbbababbbabbabaabaaababaabbabbbbaabbabbbbbbbbaabbbaabbbbbbbbbbaaabbaaabbabbabababaaabbbaabaababababbbbbaaaaaaaabbaaabbaababbbaaaaaabbabbbbbbaaabbabaabaabababbabababbbbabaaaabababbbabaaaabaabbaabaababbbbaaabbabaabbbaabbaabaabababbbaaaabaababaabbbbabaaababbabababaababbbabaaabababbabbbbaabaabaaaabaaababbaaabaabababbbbbbbbbbbababaaaababbbbaaaaababaabaabaabbbaabaabbbaaababbbabbaaaaaabbbaaabbaaabbbbbbbaaababaaaabbbbbbbbbaabaaabbaabaabbaaabaaaaaaabaabbababbbbaaabaaabbaaaabbbabbabbbaabaaaaaaabbaababbabbbbbabbabaaaaabaabbbbbbbbabbbbaaabaabbaabbabbabbbabbabbbbbabaaaaabbbabaabbbaaaaaaaaabbbbaabaabaababbbbabaabbaabbbbbbbbbbaabbaabbaababbbaabbabbbaaabaaaaaaaababaabbbbbaaabbbbbbabbbbbbbaababaabaaababbbababbaabbabbbbbabbbabbaabbbabbaababaaaabbabaaaaaaabbbaaaabbabbbbbbaaaabaabaaabbbbbabaabaabbabaaaaabaaaaabaabababbbaabbabbbaababbbbbbbbbbbabbabbaabbaabaaababbabaaabaaabababaaababbbbaaaabbbbbaabaabaababaabaabaaaaabaababbabbbababbaabbbbaabaaabaaabaaaaaaaabbaabbbbaaabaaabbbaabbbbababbbaabaabbbabbbabbababbabbbbaaaabbabaaaaaaabaababbaaaabbaaabbabbabbaaaaaaabbabaaabaaabbbababbbababababbaabbbbaabaaabbaabaaabaabbbaaaaaabbababbaabaaabbaaabbabbaababbababbbaaabbbbabaabaababbbbbaabbbaabbabaabbababbaaabbbaaaaabbaaaabaaaaaaaababbbabbbaaaababaaababaaaaaaabaaaaaaaaaaaabaabbbaabbbaabbaaaababbabbbbbbbaaabbbbbababbbabbbbaaababbabbbbbabaabbbabbababaaaaaabbbbaabbbbabbbaabaabbabbabaaaaaaabbbabababbbbbaaaaababababaaaaabbbbbaaabbabbbaabbababaabaaabbaaaaabbaabababaabababbbabbaabaababbababbbbbbbabaaaabbababaabbbbaaaabaabbaaababbbababbaaaaabbaaabbbababbbbababbaabbaabbbbbababbbbabbaabaaaabbaabababbabaaabbbbbbbbabbbbaabababbaaabbbababaaabbabbababaababaabbaabaabbaabbbaababaaabbbaabbbababaaaabbabbaaabaabbaaabbaababbbabaababaabaabbbaabaababaabaabbbbbabaaabaaababbbababbbabbabbbbabaaaabaaaababbaabaabbaaaababbabbababbabbbaabbbabbbbbbbbbbbabaaaabbaaaabbbbbbbbbabbabaaabababaababaaabbbabaabaaababbabbbbabbbbababababbaaababbaabbabbabaaaabbaaaaaaabbbababababaabaababbbabbbbbababbbbbbbaaabbababbbaaabaaaabbbbbbbbabbaaabbababbbabaabaabbbbbabaabaaaaaabaabbaabbaabbababbaabaabbbbaaaaabbbbabbaabababaabbababbbbaabbabbaaaaaaaabaaaaaabbaabbbbbbaaabbbaaaabaabbbabaaaababaaababbbbabbabbbbaaabbaaabaabaaaaaaabbaaaaaaabaababbbbabababbbbbbaabbaabaabbaabbbaaaaaaabbbbbbbbabaaaabababbaabaabbbabbbbbabaaabbaababbbbaaabbbabbaaabaabaaabababaaaabaaabaabbabbbaabbbbbbabbbabaaaabaaaabbaabbaabbbaabbaabbbbababbaaabbaaabbaaabbbbabbbaabababbbbbaababbbbaaabbbabbbaaaaabbbbaabaababbbababaaababababbaaaabbabbbaaabbbabbaaabaaababaaaaabbababababaabaabbbaaabaabaabaaabbabbabbbbbbbbabaaaabaabaaabaaaaaabaaabbabaababbababaabbabbbbabbbbaabbbbbbbbbbbbabbbbabbbabbbbbbaabaabbbbbbabaaabaaaabbbabbabbbbaabaabbabaaabbabbaabaaaaaaaaaabbabaababaabaaaababaaabbabbabaaabaaabbaabbabbaaaaabbaaabbbbaaaabbaaabbbbaabaabababaabbbbaabbabbbbbaaaababbbaabaaaaaaabaaabbabbaabbbabbaababaabaaaabababbbabababbbbabbabbbbaaabababbbabaaababbabbbbbbaabbabbabbabbbbababaabaabbaaabbaaaaabbbbabbaabaabaaaabababbbbbaaababaabababbaaabbbbaabbbaabbaaaaaababbbabaaabaaabbbaaaabaabbbababbabaabaabababbabaabaaaabbbbabaaaabbbaaabbabbabaaabbbaaaabbabaaaababaababbbabbbabbabbbbabaabaabaaaabbbbabbbbababbabaababaaaababababababbbabaabababbababbbbabbaabbbbbaaabbabbbababababbbabaabbbbbaabbaaabbabaabbbbabababaabbbaaaabbababbbaababbbbbbaabaababbaabaabbbaabaabaaabbbbbbabaabbbabaaaabbbbabaaababaabababaabaaabaabaaaaababbbbbbbbaabababaaabaabaaaaaaabbbabbabbaaaaabbbaabbabbaababaabbbbaabbaaaaaaaabaaaabbabbaabbaaaabbaabbbbbaaabbbababbabbbaabbbabaabbbbaabbaabbbaabbbaabbbaaababababaabaaababbabaaabbbbbbbaabbaaabbaaabbababaaaaaaaaaaaabaaabbaaaabbabbabbbabbabababbbbaababbababaababaabbaaaabbaaaaaaaabbaaaabaaaabbabbbbaabbabaaaaaabbbaabbbbababbbbbabaaabbaababbaabababaaababaabbaababaaaaababbbabbaabaaaaaabababbbbabbaaabaabaabbabbbbababbbabbabbbababaaaaabaababababbbaabaabaababbbbbababaaaaababbbbbabbbaaabaaabaabababaababbaaaabaaaabababbbaaababababaaabbbbbaabbbbbababbaabbabbabbbaaabaaaabbabbbbbbababbaabbbbbaabbaabbbaabaaabbaabaaabbbaaabbbabbbbaabaabbabbabababbabbabaabababbabbbbabbbaaaabbabbaaaaabbbbababaaaabbbbaaabaaaabbbbaabaababbbabaabbbaabaaaabbbbaaabbaaaabbaaaabbbbabbaaabaaabaaaaababbbbbbbaaabbaaaabaabbbabbabbbaaabaabbabbabbbaaaabbabababaababbabbabbabbaabbabaababbaaaabbbbbabaababbbabbaabbaababbabbaabbaaabbbbaabaababbabbbbbabbabbbbbbaaabaabbabbbabababbaabbbbbaabaababaabbaaabbbaaabbabababababaabbaabbaaabbbabababaabaabbaaaabaabbababaabaaabbaabaabbbaababaabbabaabbaabbabaaabaabbbbbbabbbbaabbabaaaabaaabababbbaaabbbbbbaabbbbababbbbbabababbaaaaabbaaabbabaabbbababbababababaababbaaabbaaaaaaaabbbbaaaababbbbbbabaabbabbbaabbabbaaaaaabbaaabaaabbaaabaabaaabaaaabbaabbaaabbababbbbbabbbaabbbabbabbbabbbabbbbbabbbbaaabbbbaabababbbbbaababbaaaaabaababbbbaabaabaaabbabaabbbbbaaaaabbaabbabbbaababbbbaabaaabbabbaababbababbbaaaabbbbabbbaaaabaabababbaaaabaaabaaababbbbbbabbabaaababaabaaaaabaababbaaaaaaabaabbaababababaaaabbabbababbbbbbabbbbbabbabababbbbbababaabbbbbaababaabbbaaabaabaaabbaaaaaaaaababbaabbabaaaabbbbababbaabbbabbbbabbaabbbabaaaabbbbbabaabaababbaabbabaabababbabbababababbaabbbababbbbbababaabbbbbbbabbbbabbaaababaabbabaabaabbaaaaabababaabaaaabbbbbaaabababbabaaabababbbababbabbabbbbbabaabbbabbbbbbabbbabbbbaababbaaabbabbabbaabbaaaabbababbbbabbbaaaabbaaababaabaaabababababbbbbbabaaaaabababaaababbbbbaaaabaabbaabbaabbaaaabbaabbaabbabaaaaaaababbaaabbabaababaaabbbbabbbbaabbbbabbbabaaaaaaaabbabbabaabaabbbbbababaabbbabaabbabaaabbaabbbaaabaaababaabbbababbaababbbbaaaaaaabbbabbbaabbabbababbbababbababbbabaababbbbbbbbabbbaabbabaabababbabaaababbbbbbbaabaababbbbaabaaaaaabababbbbbbaaaaaabbabbabbaababaabbbabababaabbbaababababbbaaabbbaaaaabaaaabaaabbaababbbabbbaabbaabbbabaabbabbbbaaababbabbababababbabbbbbbbbaabbaaabaaaabaababbaabbaaabbbbbbbbbbabbababbbaabbbabbabbababaaaaabbbbabbaaaababbaaabaaababbaabbaaaabaaaabbaaabaaabbabaaaabaabbbaaababbaaaabaaabaaabaabbbaaabbbbbaabbbabbbabaabaabbaabbaabaaabaabbbabbbabbbbabbbbababbbbababbaaaaaaabbaabbabaabbbbbabaabbbaaabbababbbaabaaabbbabbaabbbbbbaabbbabaabbbaabbbaaabbaabaaababbabaaabaabbbabaabbaaaabaabaabaaaabaabaaabbabaababaababababaabbabaabbabbbaaaaababbbababbbaabaaababaababbbababbabbbaababaaaababbaabbaabbaaabbabbaabaabbbaabbaaaababaaaaaabbaababababbaabbbabbabbbbaaabbababbaaaaaaaaaaabaabbbabaabaaabbbbaabbbababbbaabbbabaabbababaaaaabbbbbaabbabbbaabaabbbbbaaabaaaabbbabaaaaaaabbbbbaaabbbabaabaaababababaaabbbbbaabababababbaabbbaabbbaabbbabaaaaabbabbbbbaabaabbaaababbaabaaabbaaaabbaabbaabaaaababababbbbaabaabaaaaaababaabaaabbabbaabbbbbabbaabbbabbbaabababaabbabaababaabbaaabbabaaabbbaaabababbbaaaaaaabaababaaabaababbbaababaababbbbbbbbbbabbabbbbbabababababaabbbbbbaabbbaababbbabaabaaaaabbabbbaabaaabababababaaababbbabbbababbaabaaabaaaabbaaabbaaaabaaaabababbbaababaaaaaabbbaaaababbaaababaabaabaabaabbaababbbbbbabbabaaaaaabaaaaaabbaabbaabbbbbbaababaabbbaaabbbaaababbaaaabaaaaaabaaabaaabaababababaaabbbbabbaababaaabbaaabaababababaaaabababaaabbbaaabbaaabbaaabbaabbbbaababbaaaaaaaaabbababbbaaabbaaabbbbaabbbabbbaaaabbaaaaaaabbbaaabbbbabbaaaaaabbabbaabbabbabbbbbaababaaaaababaabbaabbbbabaaabaaabaabababaaabaaababbabaabbaababbbbbabbbabbaababbbaabbbaaaabaaaaaaaabaaaaabbaaabaabaaaabaabaabbbabababaabbbaaaababbbaababaaabaaaaaaaaabbbabbbbabbbbaaaaaabbbabbbaababbbaaabababbaabbbaaaababaabbbababbbbbabbbbaaababaabbabbbbabbabbbbaaabbbbbabaaaaaabbabaaaaabaaababbabbbaaabbbbbabaabbabbbbababbaaabaababbaabbaaabaaaaababbbaababbaabbabbaabbaaaabaabababbaabbababababbbbbbbaabbbababaaabbbbaaaabaabaaaaaabbbbabbabaaaabaabbbbabaabbbaabababbaabaabaaaabbababaabbababaabbbabbabbababbaaaaaabaabbbbbbbbbbbabaaaaaaabababbbabaaaaaaabbaaababbbbbabababbbaababbbababbabbbbbaaaabaabbbabbaabaaabbaaaaabbabababaabbbabaaaaaabbbabaabbaaaabbaaaabaabbbbbbabaaaaabbbbbaaabaaaababbbbaabaabaaabababbabbbbbabaabbbbbbaabbaabbbaaabaabbbabaaaaaaaaabbbaaabbbbbbbbababbbaabbbbabaaaabaaabbbbbbbbbbaaababbaaabbaaabbabbaabaaabbaabbbabaaababbaabbbbabbaaabaabaabbbaabaabaabbaaababaaaaaabbbbabababbbaabbbbabaaabaaababbbbbbabbbbbbaabaababaabbbbaaaaaabaabaaaababbaaaaaaaaaabbaaababaabbababababbaaaabababababababbaabbbabbbaabbaabbaababbaaaaabbbbaababaabaaaabbbabbbababaaababaabbaaababbabbaaaaabaaaabbbbaabababbbabbaaabbabbbaabbabaababbabbbaabbaabaabbaabaaaaaabbbbbaabbbbbbbabbbaaaabaababbbabbabbabbbabaabaabbbabbbbbababbaaaabaababbababbbbbabbababaabbbabaababbababbaabbaabbabbabbbabbaabbabaabbabbababbabbababbbababbbbbaaaaaababbbbaaabbbbababbabaaaabbaabbbabbababbbababaaababbabbbaabbbbababbbaabaabaaabbbaababaaabbbbbaabaababbababbabaabbabbbbaaababababaaaabaaaaaaabaaabaaaabbbabbbbbbaabaaaabaabbaabaaaaaaabaaabaabaaaaabbaaabaabaaaaabbbbbbbbabbaabaabaabaaababaaaabbaabbbbabbbabbaaaabbbaabbaabaabaababbabbbbaaaaaaabaaaaaaabbbbaaaaabbabbaabbbababbbaaabaabbabaaabaaabaaaabaaaabbabababaaababbabbaaaaaaaaaabaaabbaabbbbbaabababaabaabbbababbaaabbbbaaabbaabaabbbabbabbbabbaaabbabbbaaabaabaabbabaabbabaaaaabbbbaaaaaabbaabbbababbaaaaaabaabaaaabaababbbabaabbaaaaaaabaabbabaaababbbabbabaabbbababaaaaaaabbabbbabbbaaaabababbabbbaabbaabaababbbaaaabbabaaaaaababbaabaabaaabbbbbbbaabbabbbbaaaaabbbbbbbbbbaaabbbbaabbababbabbaaaabaabababbaabbbbbbaaaabbabaaabbaaabaabaabababbaaabaaaabbaabababbbbabaaaabbbabbabbbbabbabaaaabbabbabaaabbaaababbbbabbabaaaabbaabbbbbbbbaababbaaababbaaaaaaaaaabbbaaaabababaaaabbaaabaabbbaababbbbbaabbbbaaabaababbaabbaabaabaaababaabaaaaaabaaabbabaabbaaaaabbbbbbbbbbbabbbaabbbbbbbaaabaaabbabbaaababbaabaaaaababbaaaaaaaabaaaabbaababbbabbababaabbaabababbbbbbabaaaabbabababbbabbaabbbbbbaaabaabababababbbaabaababbaaabbaaabbabbbaaaaaabaaabababbbbbaabbbabaaabaaaabbbbbabaabbabaabaaaaabaabababbbbbbaabbbabaaaaabbbbbbbaabaabbababbaabbaaaaaaabbbbbaaabaaabaaaaabbaaaaaaaabababbaaaabbaabaababbbbabbabbabbaabbaaababbababbbababaaaaabbbabaabbbabbbabbbbbaaaaaabbabaaaabababaabaaabaaabbabbaaabaabbaabbbbabaaaaaabbbaaababbbbbabbaabbbaaaaaabababbaaaabaabbbbaabbbbbbabbabaaaaaababbbbbbaabaaaaaabbbbaabbbbaaababbbaabbaabaaababbaaabbabaabbabbabbabaabbaaaaaabaaaaaabbaaabbababbabaabbaaaabaabbabbaababbbababbababababaaabbbabbbabbbbaababbbaaabaaaababbbbaaaabababbbbabbaaabaaabbaaaaaaabaaabaaabbbaaabaaaaabbbabaaababbabaabbbaababbbababbbaabbbbbabbbaaaaaaabaabaaaababbaabbbabaababbababbbaabaaaabbaababababaaababbaaabbbaaabbababbbababbbaababbabaaabaababbabbabaabaaabaaabbaabbaabaabbaabbbaabababbaabbbbbbbaaaabbbbaabbaabbaaababbbabababaaabbabbabaabaaaababaabbbabbbbbbbbabaababababaaaaaabbbbabbbbabaaabbabbaabbabaaabaabaaaababbaaaabbaabbbababbaaaabbabbbaaabbaabbaaaababbabaaabbbbbbababbbbaaaaabababbbbbbbbbbabbaabababaabbbbabbbbbbaabaabbbbaaaaabbbbbbababbbaabbbbbbbbbbbaaabaabbabbabaabbbbabababbbbbbbabbbbbbbaaabbaaabbababbaabbbbabaababbbbaaaabaaabaabbbabbbbbbbbbbaabbbbabbaaabbaababbbbbbbabbbbbbbbababbbbaabbbbbaaabbbbbbaababbaaaaaababaabaabbabbaabaaabbbaabbababaabababaabaabbabbaabababababaaaaaaabbbaaaaabbaaabbaaabbabbaaabbbaaaabababbabaabbbbaabaabaababaaaaaaabababaabbaaaaaaaaababbbbabbbabbbababaababbbbabaaabbabaaaaaabbbbaabbbbbbbaaababbbababababababaabbbabababaaababbbbababbbabbbababbbbababbbbbabbabbbabaaababbbaababbaabaabbaaaaaaaaaabbbabbaababaaaaaabbaaaabbaaaabbbbaaaaaabbababbbbabaaaabbbbbaabaabbaababaababbbbbabbbabbaaaabaabbbaaaabbabbaababbbaabbbbabbbbbbbabbbabbbabaaaabaaaababbbbbabaabbabbbbbababaaaaaaabbabbaaabaaababbaabaaabaababbbabaababbbabbbbbbbbabbabababaabbbaaaaaaaabbbaaaaaabaababbabbaaaabbaabbbbbaaabbabaabaaabbaabbbababababbaaaababaabbbbbbbbabaabaabbababbbaabaabababbbabbabaababbaaaaababaaaaabababbbaabbbabababaabbbbaabaaaababaaababaaaaaababbbbaaaaabbaaaababbbabbabbbaaaaaaabaaabbabbaaaaabaaabbbbabaabbbabababbbabbabbbaaaaaaaabbabaaaabbbbaaababbabababbababaaaaaabbbbaabbbbabaabababbabaabbabaabababbabaaaabbbaabbbbaaaababbabaabaababbabaabaabbbbaaaabababbaabbbabaababbabbbaaababbbaaaabbbbbbbbaaaaaaaababbbabbabbbbaaaaabbbbbbabbbabaabbaabbbaaababbbbbaaaaaaabbbabaababbbabaaaabbaaababbaababbaababbbaababbbbbbbbbabaabbbbbabbaabbbbababbaabbabbbababbaabbaaabbbbabbaabbbbabababbbaaaabbaaaababaaabaaababbabababbaabaaaabbbbbbabbabbbaaaaababbabaabaabaabbbaabbbbabbbabbbbabbabbbbbbababbbbbaabbbbbbbababaaaaabaabbbabaaabbbbababbaaabbabaabbbbbababbbaaabaaabaabbaaabaaabbaababaabbbabbbabaabbbaaaabbaabaaaabbabbbaaabbabbaabbabaabaaabbbbbbaaaababbaaabbabbaabaaaaaabbbbaaaababbabbabaabbbababbaabbababaaaabaabbabbbaaabaababaaaabbbababbbbbaaababbbabaaababaaababababaabaabbbaaabbbbbaaaaabbbbbaababbabbbbbababaabbbaabbbbbbbbbaabbbaabaabbbabbaaabbbaabaaaababbaaaababbbbabbbbbababbabbaabbbabbbabaaaabbbabbaabbbaabbbaaaaabbaabbbabbaaaabbabbbbaabbbbbbaababbaababaaaaababbabbbaabbbbbbbaaabbaaaabaaabbbbabbaaaabbbaaabbbbaaaaaabaaabaabababbabbbaaaababbabbabbbabbbaaaaaaabaababaaaaaaababbbaaaaabbababbababaaaabbaabaaaaababbbbbabbaabbabbaabbabaaabbabbaaabbaababbbaabbaabbaaaabaabbbaababbaaabbbbaaabaaabbaaaabbbbaabbbaaabaaababbbabbbabbaaaabbababbabbaaabaababbbaaabaabababbabbaaaababbabbabbbabbabbabbbabbaaaaaaaaaababababaaaaabbbaabababbbaabbaababbbbaababbbbababbbbbbbabbbbaabbbbabbaababbaaaabaabaaabaaabbabbbbbabbbababaaabbaaaaaabaababbaaaabbbaabbabbabbaababbbaababbababaaaabbbaabbbbabaabbbaabaaaabbaaaabbbbaaabbabbaabbaaabbbbaabbbaaabbbbbaaaaaaabaaabbbbaaaaababaaaabababbaaabbbbaaaababbabbabababbababbaaabbabaabbabaabaabaabbbabbbbaabbbaabbbbbbbbabbaaaabbabbbaabbbbaaabbbabababbabbaabbaabbaababbbbbaabaaabbabbabbabbbabbbabbabbaaaababbbbbbbabbbbbbbbbaaababbbbaabbbbababbbabbabbabbbabababbbabbabbbbabababbbabaabaaaababbbbbabaaababaabbbbababaabbabaaabaaabbaaaabbbbbbbbaabbabababaabbaaabaaabbaaaababbabbabaaababbbbaabaaaabbaabaabbbbababbbaaabbababbbabbbbbabbaabaabbaabaabaabbbaabababbbaaabaaaaabbbbbaabbbbbbbbabaabbaabbbbaabbbbabbaaaabbbbbbbbaabbbabaabbaaaabaababbabababbbbabbaaaaaaabababbabbbbabbababbaababaabbaabababbabbbbaabbaaabaababaabaababaabbaaabbbbaaabbaaaabbbabbaaaaabbbbabaabbbababbabbbbaaabaababaababbbbaaababaaabaaaababbbaabababaabbbbbaaaaaababbaabababbababaaaabaaaaaabaabaaaabbbaabbaaabaababbbabbbabbaaabaababbbbaaabbbbbaaababbbababababbaaabbaabaabaaaabbabbaabababbbabababbbbbabbbaaabaaabbbbbbbbabbbaabaaabbaababaabbbabababbbaaabaabbbabbaaabbbaabbaaaabaaaabbabbbaabaabababaaaabbbaaabbabbabbbababbbbbbababbbbabbbbbbaaaababbaabaabbbabbaabbaaaabbabaabaaabbbaaabbabbaabbabaabbbbababbbaaababaaababbbabaaaabbbaababaaabaabbbaabaabbababbababaababbbbaaabbbbaababbbabaabbbaaaabbababaabaabbbbbaabaabaabbaabbbbaabaaababaabbbbabaaabbabaaaabaaabbbaaaaaaaabbabbbbabbbaaabbbaaaaabbabaaabbabababbaaaaabbaaaababababbabbaabaabbbbbbbbaaaaababbaaaabbababbbbbaabbabaabababaabbbaaaabbaabbbaabaaaaaaaaaaabaabbaaaaaaaaaaaaababbbbaaaaabbaabbaaabbaabbabaaaabbbabbbbabbaaabbbababaaaaabbbbbbbaaababbbbbbabbbababbaaaabbbbabaababaaaabbaabbabbbabaabaaabaaaabaababbababbbaaaabaaaabbbbabaaabbaabbabbababbaabaabaaabbabbabaababbaabababababbbabaabbaaaabbbaaaabababaaaabaabaabaabababaaabaaaaababbaabbbbbbbbbbbbbabbbbbbaabaaaaaabbabaaaaababaabbbaaaaaaababbbbaabaabbabbbaabbbaabbbbbbbbaaaaabbbaaaaabbaababaabbaaaababaabbbbbabbbbabaaabbbaaaaaababbbaabbaaaaabaababaaaabbabbbabbbbaaaababbbbaabbbaabbabaababbbabbaabbbbbbabbababaaabbbabaabbabbbbaabbabbabaabaababbaababbaababaabbbaababaaabaabbbaabbaaaabaababbaaabbbbaaaabbbabaaabbbbabbbababaaababaaaabababaaaaabbabbababbbbaabaaabaaaabbbbabbbababaababababbaabbbaabbbbbaaabbbbbaaabbabbaabbbbabbabaababababbbbbaabbababbaabbabbaaaaabbbbbabbbbbbbaabbaababbbbabbababaaaababbaaaabbaabbaaaaaabbbbbaaaabbbababaaababbabaaababbbbbbaaaabbbababbaababaabbababbbababaabaababaaabaaababbbabbaabaaabbbabbbaabaaababbbaaaaaabaabaabbabbabaabaaaaabaabbabaaabbbabbbaaaababaaabbbbababbabababbabaabababbaaaaaaaababaababbaaabababbaaaaaaabaaabbaaabbabbabaabbbbbabaabbbabbbabbbaaaabaaaabaabaabbaabbabbaaabababbaabababbabbaabaaabaaaababbbbababbaabbaaaabbabbaaaabaaaabaaaaaabbbbbbaaaaababbaaababbababbabbbabaabaaabbbbbababababbabaabbbabaabaabbbbbbbabaabbaabbbbaaaaababbabaabbaabbbbbbbbbaabbabbbabbbaaaaaabbbababbaabbabaaaaaabbbaaaabbbababbbabbbaaabbaabbabbbbababaaaaaabbaaaaaaababaabaaaabbabbababbbbabbabaabababbabaaabbabbaabaaaabaabbbaaaabbbbbbbaabbaaabbbaababbbbaabbbbababaabbaabbabbbbabaaaabbaaababbbaababaaabbbaababababbbbabaaaaaaaaaabbaaaaabbaabbbbbbaaababaabbaababbaaabbabbabbaababbbabbaaabbabbbababbbaabbbababaaabaabaababaababaaaaaaaabaaaabbbbbaaaaabaabbabaaaaabaabaabaaabbbbaaaababababababbabaaaababbbbaaaaaaabaaaabaaaabaababbbaabababaababaabaaabaabaaaaaabbbbbabbbaaabaaaabaabbbabbbabaabbabbbabaaaabababbababbbababaabbaababaaaaaababbaabaaababbaaaaaaabaababaabbbbaaaaabbaaaaaabbaaabbabbaababbbbaaaaababaaaabbbbabaabbaabbababbabbabbaababababbbbbbabbabbbbbabbbbabbaabbbbbaabbbabbabaaaabaababbbaabbabaabaaababaaabbabbaabbababaaabbabaaaabbaababbabbbbabbaababbbbbbabaaaaaaaababbbabaaabbaaaababaaaaabbaabaaabaabababbbababbbaabbbabaabbaabababbbbaabaabbbbbabababbaaaabbbabbbaabbbbaabbaabababaabbaabbaabbbbaaabbbbaabbaaaaabababbaabbbaabbababbababbaaaaabaababbbbaabaaabbbaaaaabaabaaaabbababaaabaabbabbbaaababbabaabaaabaababbaabaaaaaaaabaabbbabbaabaaababaabbbbbabbababababbaaabababaababbbabaaabbabbabaaaabbaaaababbbababaaaabbbabaababbbbabbaaaaabaabbaaaaababbaabbbaabbabaabaaaababbbaabbbbabbaaabbbbbbbaabbbbaabbbabbbaaaabbbaabbaabbbbabaabaaabbaaaabaabbbaaaabababbabbbabaaababbbbbababbaaababbaabbbbabbbbbbbbbabbaaaabbbabaaabbababbabaabbbabaaabbaaabbaabbabbabaaaabbaaabaabaaaabaaabbabaaababaaabbababbaabaabbaaaabbbbabbbaabbabbbbabbbabbabaabaabaabbbaaaabbbbababbbbbabbbabbbaaaaaaaabaabaaabaaaabaabababbabbbbabababbbabbbbabbbababbaaabbaaabababbbababaabaabbababbbbbbababaaabaaabbaaaaaaabaaaabbaababbbbabbbaaabbbaaaaaabbbbaaaabbaabbbbbbababbbbbabbbababaaaaabbababbabaaaaaaaabaaababbabaaaabaaabaaaaaaabbababababbbbababbbabbabbabbbbaaabbaababababbabbabaaabaaabbbabaabaaabbabbbabbaaaaaaaabbbabbaabaabbbaabbbbaabbabbbaababbbaababbabbbaabbaababbbababaabbbabbaaabaabaabbabaabbabbbababbbbaabaabbbbabababaababaababaaabaaababbaabaabbbaabbbbbbaabbbbbaabaaabaaaaabbbbbaabaaaabaaabbaaabaaabbabbbbbaaababbbbabbbabbbaaaaabaababbaabaabbabbaabaaabaaabbbbbaabababbbbababaaabbbabbbaabaabbababababbbaaaabaabbababbaaababbabbabaaaabbbabaabbbbbbabaabbabbbbbabbbaaaababbaabaabbbbaabaabbbbbaaabbbaaababababbaaabbababaaaabbbaaaaabbababaaaabaaabbbbbaabbabaaabbaababbbababaaabbbbbaaabbababaaaaabbaabbabbaaaaaaabbababbbabaabbbbbabababbaabbaaabaabbabababbaababaaaabbbabbbaaaababaabbbbabbaaaaaabbabaabaabbaabbababaaabbaabbaabababbbbaabbababbabbbabbabaababbabbbbbaabaababaaabababaabaaabbbbbaaaaabbabaaaabaabbbbbbaababbabbbabbaabbbbaaaaaaaabababbbaaabbbbbbbabbabaaaabbbaaaaaaaabaaabaababbabbbababbbaaabaaaababbbabbbabaaabaaaabbabbabbbbbbabbabababbbbaaabbbaaaababbaabbbbbaaabbaaabbbbaabaaabababbaababbaaabbbbbabbbaabbbabababbbaabababbbaaabbabaaaababbaabbbbabaaabaaabbbbbbbaaabaabbbbbbaabbabababaabaabbababaaabaaabbabaabbabbbabbbbababaabbbabaaaabaaaabbbaababaabbbbaabaabbbababaabbaaababbababbbaaaabbabbbbabbbbbbbaabababababbaabaaaaaaaababbbabbbbbaaabaababbbababbaaaaabbbbbaaabbaababbababbaabbababbaababbabbaaaabaabbbaaababaabbababbaabbbbbbababaabbaaaababbababbbbaaaaabbbabaabbababbaabbbabbbbabbaaabaabaaaaabbaaabbaabbaaaaabbaaaabbbbbbabaabababbbbbaaabaabaaabbabaababbbbabbaabababaabababaaaaabaaaaaaabbbbbbaaababbabbaaaabbabaabbaababbabbababaaabbaabbaaaaabaabbabbbaaaababbabaaabaabaabababbabbabbaaaabababaaaabaabbabbaaaaabbbbbaabbbaabbaababbabbaaabbbbbbbbabbbabbabbaaabbabbabbabaaabbbaabababaabaaaaababaabaabbabbaabbbabaaaabaaabaabbbababaabbabaaabbbbabbabbababbaabaabbababbbbaaaabbaaaaabbbbaabbbbababbabbbaabbaababaabbbbbababbbbbbaabbbbbbbbbaabaabbbbaabbabbbaaaaaabababbaabaaaabbaaaaaabaababababaaabbaabaababbaaaabaabaaaabbaaabbbababbabbbaaaabbbbbbbaaabbbababbabaabbbbabbababbabbbbabbaaaaabbabbbabaaababbbabaabaaaaabbbaabaaabbbbbaabbaaabbbaaabaaaabbabbbaaabbbaabaaabbaabaaaabbababaabaaaaabaaaababbbaaabbaaaaabbbbbaaaaabbaaaaaabaaabaaababaaabaaaaabaaabaabbbbbabbbbbbaababaaaabbabbaababbbbabbbaabaabbabaabbababbbbbabababaaaababbbaaaaabaaabbbbbababaaaaaababaababaabaaaaaaaababbaaabbababbaaabbbabaaaaaaabbabbabababbbaabbbaaaaaaaabbabbabaaaabbabbaaabaaaabaaabbbbbbbbbbabaababbabbbbaaabaabbaabaabbbabbaabbaaaaaabaaaaaababbbbabbabbbabbabaabbaabbbaaabaabaaaaabbbbabaababbaabbabaaaabbbaabbbbaabbbaabaabaaabaabbabbbababbbbabaabababbbbbababaabaabaabbbbbabbaaabbbabaabaaaaabaaabbabaabaabaababbbbbaabbbbbababaaabbbaaabbaabbbbabbbbabbababbbbaaabbaaaabbaabbbbbaababaababbaabbaababaabbababbbababbabbaabaaababbbaabbbaaaaabbbbbbbbaaaaabbbabbbbbbbaababaaaabbaaaaaababaaabbbbabbaababaaaaabaaaabbabaabbaabaaababbbbaabaabaabaabbbaabbaabbbababbaabbaaaabaabbbaabaabaaabbabbaabababababbaaabbaabababbababbaaabaabbbbbaaaaabaabaaaaaabbbabbbabbaababbabbabaabbbaabbbabbbbbbbabbaaabbbbabbababbbabababbaabbbabaabbbbbaabbbbaabbabaaaaababaaaaaaaaabbaaabaababaaaababbabbbabaabaabaabbabbaababababaabbaaabbabaabbaabbbbaabaababbabaabaaaabaababbbbbaabbbabbabbaabbbabbbbababbaababbbabbababbabbaaaaaaabbbabbabaabbbababbabababaabaaaabbaabaaabaaababbaaaabababbbabbbbbbaababaaabbbbbaaabaaaabbababaabbbabbbaaaabbabbbbabababbbabbbaaaabbbaabbaabbbbaaababbabbbbaabbbababbbbaabaabbaaaababbabbbababbabbabbaaabbbbbbabbbabbbaaaabaabaabbbbabbaaabbbaabaaababbabaabaabbaaabaaababaaabbbabaaaabaabaabbbabaaaabaabbbbbbabbaaabaaaababaabbabbababaaabbbbaaabbbbaaaababbabababaaaabbbaababaabbbbaaabbbaabaabbaabbababbbbbabaaaabbbbbabbbaaabaabaaaababbbaabababaabaaaabbaaaabaaaaaaabaaabaaabbababbabbbbabbaaaaaabbabaaabbbbabaaaabaabbbbaababaaabaaababaabbabbabbbabbbaaabbaaaabaababbbabbaaabbbbabbbbbbaaababababaabbbbbbbaababababbaaabaaaabbaabaabbbbabbbabaabbbbaaabbaabbbaabaabbaababbbbabaaaababababbbbaaabbabbbbababababbbbabbbbbbabababbaaaaaabaaababbbabababbaabbaaabbbabbbababaabaaabaabbbbbaabbbababbbbaababbbaabbbbbaabbabaaabbbaabbbbaabbbbaabbaaabbbaaabbabbaaaaabbabbbabbaabbaabaaaabbaaabbbbbbbbaaaaaababaaaabababbaababbabbabbababababababaaaaabbaaaaaabbaabbabbabbbbbaabaaaaabbabbabaaabababaaabbabbabbbaababbaaaaabaaababbaaaaaaaaaababbbabbaaababaaabaaabbbabaaaaabbaababbaabbaabaaabbaaabbbaababaababbbbbaaabaaababbbbbabaabaabbaabaabaabaabbaaaaaabbbbbbabbaaaababbbaabaababaaaaaabbbaaabbaaabbaabbabaaaabbbbbabbbaabaabbbabaabbababababbabbbbaaababbabbbbbaaababbaaababaaabbabaaabbbababaaabaaababbbababbababababbbababbbabbbaabaaaaaaabbabbabaabababaababaabbbbbbbbbbabababbababbaabbbbaaaababbaabbabaabbabaaabaaabbbabaaabaaaabbbbbbaaaaaabaaaaaabbaaaaaabbbabbaaabaaaaaababaabbabbaababababbbbbbbababbbbababaaabbbbaabbbabbbbaabbaabaaabaabbabbbaaabbbaabbbaaababaaaaaaaabbbaabbbbbaabaabbabbaabababaaaaabaaaabbaabbabbaaaabaababbbbaaaaaaababaabbaaababababbbbbbbaabbbbbbbabaababaaaaaabbbbbbababbabbbaaaaaaabbaabbbaabbaaaabaabbaabbbbbbbbabababbababbaabbbabababaabbbaababbbbaababaaabbaabbbabaabbaaaaaabbabaaabbaabbabbbbbabbbbbababbabaaabaaaaaabaaaaaabaabaabbbabbaaabbbaabbbbaaaaababbabaaaabaaabaabbbaabbbbbbbabaaababbbbbbabaaaabaaaabaaabbabbaabaaaabbbbaaaabbabaabbbbababbbbaabaabaabbbaaabbbaaaabaabbbbbbabbaaaaaaabbbbabbabbbaabbabbababaaababbabbbbaaaaaaababaaababaaaaaaaaabbbaaaaaaababbaaaaaaabbbaabaabbabbaaaabaababbabaaabbabaabaaaaabbaaaababaababbabaaaaabaaaaaaaaaaabbabaaaaababbabbbbbabababaabaaaaabaaaabaabaabbaaaaaabbbbabaababbbbbababbbabbabbbbbabbbabaabbabbabbaabaabababbbbaababaaabbbbaabbbaababbbabbaaaaabaababaabaabbabbabbbbbabbbaaaaababaaaaaabaaaabbabbbbbbbbbabaabaaaabbaaaaababaabbababaaabaabaaabaabaaaabaaabbbaaaababaaaabbababbaaaababbbabaaabbabbaaabbbaabababaabaaaabbbabaabbaabbabbbbbbaabbabbbaababbabbbabaabbbaaababbbbaaaaabbbaaaaaaaabaaabaaaabbababbbababbbabbabaababaaabbbaaaaabababbbbbbaaaabbabaabaababaabbaabababaaabbbaabbaaabbaabbbbaaabbbabaaaaababbaaabaaababbabbaabbbbabbbaabaaaabbbbbbbabbbaabbbbbbbbaabaabbaaaabbabbbbbaabaaaaaaabbaaaaababbbaaaababbaaabababaaabaababaabbbbbbabababbbbababbabbaabaaaabaaaaaaababbbaababaabaababbbabbaaabaaabbbbabaaaabbabaabaaababbbabbbabaaaaaaaaababbbbabbaabbbaaabaaaaaaaabbbabbababbabaababbbaababaaabaaabbaaabbbbbabbbabbaabbbaaabaaababbabaabbababbabbabbbaaabbbaabaabbaababaabbbaaabbbbbbbabbaabbbabbbaaabaaabbbbbbabbabaaabbbbaabbabaabaabbbbbabbbaaabbaaabbabbabaaaaaaabaaaabaaababbbbbbbbbbabbabaaabbaaabbbababaabaabbaaabaabbabaaabaabababaabaabaaababbbaababbabbaabaabaaaabbaababaaabaaabbaaabbaaaaaaaababaaaaababaaabbaabbbbababbbbaabaaabbbaabbbbbaaaabaabaaabbbbaaabbababbbbaaaabbaaababaabaabaabbbabbaabbbabbabbaaaabaabbaabbbbabbbbbbbbababbbbbbabbbbaabaabbbaaababbabbaababaaaaaaaaababbbbbabbabaaaababababbbababbaaabaabaaababaababbaabbaabaaabbaaabaaabaabaaaabbbbabaababbbbbbbaababaabbaaababaabbabbaaaaabaaaabbaabaaaababbbbabbababbbbababababbaabbbabbbaabaababbbbbbbbbbbbabbabbbaaababbbabbaabbabbbaaaaaabaaaaaabaaabbaabaababbabbabaaaaabaaaaaaabaabbbbabaaabbbbbbbaabbabbbaabaabbbbabababbababbabaaaaabbbaabbaaabaababbabbababbbabaabbbabaabbaaaaaaaaababbbabaaaabaaaaabababbabbabbaaaaaaabababbababababbaababbababbaababbbbabababbababaaabbabbbaaabbaabbbaababbbbabbaabaaaabbabbaaaabbbbabbbabaababbaaaabbabbabbbaaabaabaabaaabaaaabbabbabbbbbbabbbabbaaabaabbbbbaaaabbaabaabbbabbbabbbbbaababbabaabbaaaababaabbbbaabbaabaaabbaabbabbbaaaabbbbaabaabbaaaaabaabbaaabaabaabbbbbbaabbbbababbabaabaabbabbabbabaaaaaaaaabaaabbaababbaabbbbaababaaabbabbbbabbabaabbaaabbaabbaaabbaabbbaaabaabaaaaaaabaaaabaababaabaaaabaabbbaaaabaabbbbbabbabbaaaabaabbbaaaabaabbbabbbbbabbbbabaaaabaaaababbbbbbaaabbbababaaababbbabbaaaabbbaababbbabaaabbaabbaaabbaabaaabbbbbaababbbabbbbbbbaabbaabbabbaaababaaabbbbaabaabbbbbaaababbbbaabaabaabbabbbababbbaaababbbbbbabbbabbababaaaababbaabbbbaabaabbbaabbaabaababbbbababbabbabababbbabbaabaabbaaabaaabbabbabaaabbabbbabaabaaabaabbaaaabaabbbbabbaabbbbbbabaaaaaaaaabbababbabbbbabbbaaabbbabbbaababbbaaabbbabbaaaaababbbbaabbabbbababababababaaababbbaaaaabaaaabaaabbabbabaabaabbababababaaaabbbbbabbabbaabbbabbbbbbaaaaababbbbaaababaabbabbaaabbabbababbbabababababbabbabbbaaababaabbbabaabbaaabaabbabaababaabbbaaabbbbabbbaaaabbbabaababbbbbbbabbbbbabbbaaabbbaaaaaabbabbbaabbababbabbbaaabbabbbaabbabaabaaaaababbbbabababbbbbbaababaaababbababaaaaaabaaabbaabaaaaaabaababbbbbaababbbabbabbbabaaabababbaabbbaaabbbaababaabaabbaaaaabaabaabbbbbaabbbbabaaabbababaababbbabbbabbaaaaaabbabaabaabaaaaabbababaaabbabbabaaababaabbabbaabababaaaabbaaaababaaaaaaabbaaabaabaaabaabbbbbabbbbbbbbaabbabbabbbababbabaabaabbaabbbaabaabaaaababbababaaaaabbbabbbbbbabaaaaaaaaababaaabbbbaaaaabaababaaaabbbaaabbbaabbbaaabaaaabbbbbbbaababbabaaaabaababaaababaabaabaaaaabbaaababbabbabaaababaaaabbbaabbbabbbbbaaaabaaaabababbbabaabaabbbbbbbabaaabaaababbabbaaabbbaaaaaaabaabbbbaaabaabbabaabaaababbbbaabaabbabaaaaaabbabbaabbabbbabbbaaaaababbbbabaaaabababaabbabbbbaabbabbbaabbbbbbabaabbaabaabaabbaaabbbaabbabbbbabaababaaababababababaaaabaabbabaaaabbaaaabbbbaaabbabaabbbbaababbabbababbaabaaaaaaabbbaaabbababbabaabaabababababbbbabbbaaaababbaaababbaababaaababbabbbbaaabaaababbabbabababaabbaaaaaaaaabbbaaabaabaababbababababbaabbbbaaabbababbabbbaabbbbbaaaaabaaaabbbbabaaabaabababababbaabaabbabaaabbababababaaaabaabbbbababaabbbbbbabbbbbbaaababbbbabbbbbbbbbaabbbbaaabaaaaaabaaaabaabbbaabbbbbbbaaaabbabbbaaabaaabbaabababbababbaababaababbbbabaaabbabbbbabbbbbbbaaabbabababaaabbbbabaababbaabaaabbbbbaababbbbbbbbaaababbbaaaabaaabbbbaabaabaabbaaaababbaabbaababbabbaabbbaaaababbbabbabbbaaaabbaaabaababbbbabbabaabbaabbbaabbbaabaabababbabaabababaaababaabbbabaabbbabbaaaaabbbbabbaaabbbabbabbbaaaaabababbabbbababaaabbbbaabaaaabaaaaaaabbaabbbaabbbbbbaabbaaabbababaabbabbabbabbababbabababbabbaaaabbbbaabababaabbbaaabaabbabaababbababbbbbabbaababaaabbbaabaaabbbababbabaabbbaabbaababaabbbbbbaababaaaaaaaaababbbbbbabbabbabbbaaababbbbabbbbbaabaababbbbababbaaaababbbbbbaababbaaababbbbbbabbabbbbaababbabbaaabbaaaababbababbbaaaabbbbabababbababbbaabaaaabbbaaaabbbbaabaaaaaabaaaaaaaabbabbabaaaababaababbbbababbbbbbabaababaaaaabbbaaaaabbababbaababbbababbbaabbaaabbbbaaaabbbaaababaabaabaababbaabbbbabbbaaabbabaaaaaaaaabbaabbabaaaaabbabaababbabbbaaabababbabababbabbbaaabababbbabbbbababbbbaabaaaabaabbabbbbaabbaaaabbbaabababbbaaababbaaababaaababbaaaaabbbabaaaabbababbbababbaabababbaabbaabbbbaaaababbababbbbbbbababaabaaaabababaaaaaaabbbbaaababbababaababbaaabbbabbbabbbbbbaaabbbbababaaabaabababbbbabbbbababbbabbababbbaaabaababaaaabaabbbbbabbabbaaababaaabaabbbbaabaaabaabbaaabbbbababbaaabbbaabbbaaaabbbabbbaabbbabbbbbbbbabbbbbaaabababbaaababababbbaaaabbbbbbbbbbaababbaaabaabbababababbababbaabababaabbbbbbaaabbbbbbbbbaaaaabaabbbabaaabaabbbbbaabaaabbbaabbabbbbbaaababbaaaaabbbaabaabaababbbbababaabaaaaaababaabaababbbbbabbababbaaabaabaabbaaaababababbbababbabbbbabbabababbaabaababaabaabaababbbbbabbaabbbbabbabababaaabbabaabaabbbaabaaaabbbaaaaababbaaaaabbaaaaaabbbabbabbbbaababbaabababbbbbabbaababbaababababbabaabaabaaaaaaaaaaaaabbabbabbbbbaaaaaabbbabbabaaaaababaabbabbbaaaaabbbabbbbbbbaabbbabaaabbaaabbaabbbaaaabbababaaaaababaaaaababbaabaabaaabbabaabbbabaabbbaabbaabbbaaabaaaaabababbababaaabaababbbabbabababbbabbabababbbbababbbbbbabbbbbabababbabbbabbbaabbabaaaabaabaabaabbaaaaaaabbaabbabbabbbabbabbabbaaaaabbbbabaaaaaabbbaaaabaaaaababbbaabaababbaaaabaaabbbbbbabbbbbbaabbbbbaabbaabaabaababaabbabaababaabaaababbbbbaabbaabbabbbbbbbbaaabbabababaabaaaabbbaabaaaababaabababbbabbbbabbabbabaaababbbbbbbbabbaaababaaababbbbaabbbbbbabbbaabbabbbaabbaaaaabbbabbbaaaaabaaababaababbaabbbababbaaababbabaaaabaaabaabbbbababababaaabaababbaaaabaabaaaaabbaaababbaababbbbbababbabbbabbbaaabbbbaaaaaabaaaabababaabaabbbaabaaaababbabbabbabbabababaabbbbaaabbbbaababaaaabbbbbaaaabbbbabaaaaaababbbabababaabaaaaaaabaababbaabaababaabbabbaaabaabbabaabaaaaaabaabaababaabaaabbaabbaaabbabbbabaabbaaabbbabbabaaabbababbaabbbaabbababbabaaaabaaaabaaaaabbbbaaaabbbbabbabbbbbbbabbbbabaabbbbababaabbaabbbaababbaabaaaaabaaabbbbabaaabaabbaabbaaabbbaaaabbbaabaabbabababbbaababbbabaabaaabbababababbabaabbabbabbaabbabbbaabababbbbabababaabaabbaaabbbbbabbabaaabaabbbbbbbaaaabbaababaaabaaabababbbbbbabbbaaaababbabbbbbbababaaabbbabababaabbbbababaabbbbabababaaabbbbabaaaabaaababbaaabbbabababaabaaabababbbabababbabbbaabbbbabaaabbaaaaaabaaaaabbbbaaaababababbabbababbabbbaabaabaaabbabaababbabaaababbbabbabbabaaabaaababaababababaaaabbbabababaaaabbbbabababaabaabbaaaaaabbbbabbabababbbababbbbabaaabababaaabababbbaaaaabbabaaaaabbababbbaaabbaabababbaabbabaabbaaaabbbbbbababababbbabbabbababbabbbbbaaaabbbaabababbbababaabbbbbbaaabbbbbbaabbaaabbbbabbbaaaabbaabaababbbbabaabbabbbaababbbbababbaababaaaabbbbabbbababbbabbaaaaabbbabbaabbbbabbbbbabbbbbababaaaabababaabaaabaaaaaaaaabaababbabbaaabbaaaababbbaababbbaabbababaabbbbbabaaaabababbbbbaaabbbaaabbaabaabaabaabbbaaabbabbbabaabaaaaaabbbaaaabbabaabbaaabababbbaaabbabbabbbbabbababaaababbbaaabbbaabbaaabaaaaaababaaaabbbaabbbbbabaaabbbabbbaaaaaaaabaaaabaabababbbabbbabbabababbaabbababbbaaabbbbbbbbaaabaabbbabbabbbbbbaabbabaaaabbbbabaabbabbbabbabababbababaaabaaabaabaabbabbbaaabbaabbbbaaaabbabababaababaabbabbbbabbbaaabaabbabaaaabbabababaaaaababaababbbaababbbbabbbabbbbbababbabbabbbbbaababababaababbbbbababbbaaaaabaaabbaabaaaabbabbbbbabbbabababbaaaababbaabbbababbbaaabbabaaaaabaabaaabbabaaaababaaaabaaabababbbbaabaaaabbaabbbbababbbabbbbbbabababbaabbabbabbbbbbbaabaaabaababaabbabbaabaabbbababaaaaabaaabbabbabbaaababbbbbbbbabaaaaabaabbbabbbbabbbbaaaaaaababbaaaaabbbabaababaaaabaababbababaabbabbaaabbabbabbaabbaababbbbbbaabbaaabbbbaaababbabaaabaaaabbaabbbbaabbabbbaaaabaabaabaabababaaababbaabaabbbaaaaabbbbbabaabbabbbbbbbbaabbaaababaaabbbababbabaabbbaabaabbbbbbabbbabaaababbaabbbbbbbabbbaaaaaababbbababaabaabbaaabaaaabbbabababaaaaabaabbaaaabbbaabbbabbbaabbababbbbabababbbbbbbbaababbaaaaaaabbbaaababaaababbababbbabbaaaaabaabbaaaaaaabaabaaabaabaabbbaabaabbbaabbbbbaabbaabbaaaaabaabbabbaabbaaabaaaabaaaaaabbbaabaabaaaabbbbbbaabbbaabbabbbbbabbbaaaabaabababbabbbaabbbbaabaabbababaaaabbababbabbbaababbabbaaabaababbaaabbbaabbbbbbbabababababbbaabbabababbabaabababaabaaaaabbabbababbbaaabaabaaabbabaababbabbbbbaabbbbbabaaabbaaaaababbabbabaababababbbbababbabaabbbaaabbbabaaabbbbbbbaababaaaabbbbaaabababaabbbaaaababaababaaabbbaababbababaaabaabaabaabbbaabbbbbbbbaaaabbbbbaababbbaaaabbabbabbabbabbbbbababbbbbbbbaababaaabbabaaababbaabbbbbbbbbbaaabbaabbabbbaaaabbaabbaabbbabaabaaababbaabbaaaaaaaaaaaabbbbbaabbbbabbbababaaabbabaaaaaabbabbbaabbbbabbbbaaaabbbaaabbbabaabbabaabbbbbbbbbaaabababbaabbbbbaaababaaababaaabaaaabbaababbbbbaabbabbabaabbbbbbaaabaabbabbbabbaabbbaaabbbaaabaaaaabaaabbbabaaabaaaabbbaaaabbbabaaabaaabbaaabbaaaabbababbababbaaabbbbbaaabbaaaabbbabaaaaaabbbaaaaabbbaabaababbbbbbbaaabaabaaabbaaaababbaaaaaaaaaaaaaaabbaabaaaabbaabbaaabbabbaabababbaaaababaaaabbabbbbbaabaaabbbabaabbbababaaaaaaaabaabbabbababbbbbbbaabbbbbabbbaaaaabbaabbabbabbbaabaabaabbbaaabbbaababbabaaabaabbabbaabbaabbaabbbbbbaaababaabbabbabababaabbaabbabbaaaabbababbababbbbababbbbababaaaaaabbabababbaaaababbbbbaabbbabbabaababbbababbbbbbbbabaaaaabaababababbaababbaaaaaaabaabbbabaaaababbbbbbbbbbbbaabbbbbabbbaaababbabbbabbbbbaaababaabbbabbaaaabbbaaaaabbaaaababbababbbaaaababbaababbbabbabaaabbbbaabbbaabbabbbabbaaabbbbaabaabbbbbbbabbbaabaaabaabbbbaabbaaaaaaaaaabbbbbabbbbabaaaaabbbabbbaaaabababbabbbaaabbbbababaaaabababaaaabaaaabaaaababbaabbaaaabbbbabbbaaaababaaaaaabaaaaaaaaaaabbbababaabbaabbaabbaaabaabbaaaabbbababbabbbaaababbaaabaaabbbbbbbaaababaabbbbbaaabababbaaabababaabaababbbbbbabbbbbbbbbbaabbbbbbabbaababbaaaabaabaabbbabaabbaaaaaabbababbaabbabaaaabbbabaaabbabbbbaababbbabaaabbabbababbabbabbbbaaaabababbbabbabaaaababbaabbaababaabbaababbaabababbbaababbbbbaababababbaabababaabbaabaaababbabbbbbbababbabababbabbaaabbbbabbbbabaabaabbbbbabbbbbbaababbaaaabbbbbaabbbbaaaaaaabbbaababababbbbbbbbaabbaaababbabbbbaabbabaabbbbbaaaabbabbbbbaabbbabbabbbbabaaaabbbbaaaabaaaaababababaaaababbaabaabbaaabbbbabbabbbbaabaaaaabbbbbaaabbbaaabaabbaabbaabbbabaaaabaabababbaaaabbaabbabbbabaaaabbaaaabbbbbbbabbbbbbbababaabaaaaaaabbbbbbbabbababaaabaaabaaaaabbababbbabbababbaabaababbbaabbabbabbabbabbababaaabbbaaaaabbbbaaababababaabbbbabbbbbababbaaaabababbabbbbabaaababbbbbbaaabbabbaababbabbaabbababbaabbbbaabbbaabbbbabbaabababbaabbbbaabaabbabaaababbaabbbbbbbababaaaabbbaaaaaaaabbabaabaaaabaabaaabbbaaaaabaaababbaaaababbbabaaaaabababbbaaaabbbabbbaaabbbbbbaabbabbbbaaaaababbabbaabbbaaaaaaabbbabbabbbabbabbabbbabbaaabbaaaaababaababbbbaabbbbabaaabbaaabbaabbbabbbaabababaaaabbabaaaaabaaabbababbaabaabaabbabbaabbbabbababbbbabaaaababababbbabbaaababaabaabbbbbababbaaabbbbaaaabbaababaabababbabbaabaababababbabbbbbbabbbbbbaaaababbaabaaabbbaaabaaaaababbaabbaabbaaabbbbbaaabbbbbabbabbbaaabaaaabbaababbaaabaabbbbbbaababbaaaababbbabaaabbababbbaababbaababbabaabbbaabbabbbabaaababbbabbabbaaaaababaabbababbabbbbbbabbabbbbaabbbbbbababbbabaabbbbabbaabababaaabaabbbbbaabbbbaabbaabbabbabbbaaaaababaababbbbaabaababaabbabbbbbbaaaaabbbabaaaababaaabbabaabbaabbbaababaaabbaababaababaabbababbbbabaaaaaabbabababaaaababaabababaaabbaababbababaaaabbbabaabaaabaaabbaabbbbaabbbbaabbabaabbaaaaabbaabaabbaabbabaabbababbabbaabbbbaaaaabaabbbbbabababbbbbaabaabbaaababababaabbbbbbaaaababbaababbbabbbaabbaababbaaaabaaababbabaaabbbbbbaaabbaabbaaabaaabaaaaabaababaaaabbbbaabbaaabbbbbbbbaabbabbbbbbbababaabbbbbabaaabbbbabbababbbbabbaaaaaabaaabaabababbaaaaaababaaabbababaababbbabaabbbbabbbbbbbbaaaabbbbbbabbabbbaababababbaaabaaababbbabbabaabbbaaaabaabaabaaababaaaabbabaabaabaaabbababbabbbaababbabaabaababaabaabbaababaaabaaabbbaabbaaaabbabbbabbaabbaabaaaabaababaabbbbbaabbbbababababbaabbababbabbbabbabbabaaababbbabbbbabababaabaabababbaabababbbbaabbbaabaabbaabbbaaababbabbabaaaaaababaaaabababbaaababbbabbaabbaababbababaaabbbabbbbbbababaabaabaabbaabaaababbabbbababbbaaabbbbaabbabbbabbbababbaaabbbabbbbaaababbababbbbbabbbababbabbbbbbbaabbaaababaaabbaaabbaaaaabbaaabbabababbbbababbbbbaabaaaaaaaabbababababbbbbabbabbaaabbbaabaabababbaaaabbaabbabbabababaaabbbbbabaabaabbabbababbbaaabbabbbbaaaaaabbaaaababaabababaaabababababbbbbbabaaaaabbaaabbaababbbaaabaaababaabaaaaaababbbbbabbbaaaabbbabaaaabbaaaababaaababaabaababaaababbaaababbbabaabababaabbbaaabaabbbbabbaaababbbbabaabbababbbbaabbabbababababbabbbbbaabbbaaabaaababbabbbabbaababaaaaabbaaaababbbbbaababbbbaabbbabbabaabbaabaaabbababbbbbaabaabbbaaaabbabbbaabababbbbaabbbabbabaaababbaaaaaabbbabbabbbbabaaababbaaaaaabbabbbababbabababaaaaaaaabbabbababbaabbbabbaababbbaaaaabaaaabaabbabbabaaababaabaaaaaabbbababaabbbbbbbaababbbabaabbbbaaaaaaaabbbbbbaabaabbbbabbbaabbbaaaabbbababaabbbabababbbbbbabababbaabbaababbababbbaabbaabbababbabbbbbabbbaabbbaabbbbabbbabbabababaabbbbaabababbaabbababbaabbbabbabbaabaaaaaabaababbbbbabbbaabbbababbabbababbbbaabbbabaabbaabaabaabbbbbabbabaaabbaaababababbabbaabbbaabbaababbabbbaabababbbbaabbbaaabaabababbbbbbaaababbaabbaaababaaabaaabaabbababbaaaaaaababbababbaaaabbbabbababbabbbabbbabbbabaaaabbabbbbaabaaaaaabaabaabbabbbaabbbababbbaabbabbbbaaaabbbbabbbabbabbabaaababbaababaaabaabbbbbabbabbabbbaababbbbbababbabbbababbabaabbbabbababbaaabaabaabbaaabaabbaababaababaaabaabbabbaaaaabbabbbaaabbaababbbbbaabaabbbbaabbbbaabbbabaababaabaabaaaaabbbbabaabbaaaababaabbabbbbabbaabbbbabaaabbaaaaabaaabaaababbbabbbaaabbbbaaabbbbbaaabbbabaabbbaaaaaaaabbaaaabbabbabaabbaaaaabaabaabaaabbaaabaababbbaabaababababaaaabbaaaaaaabbabaaabaaababaaaaabababbabbbbabaabbabbaaaabbabababaababababbabbbaaaabababbaaaaabbbbaabababbabababaaabbbaaaaaabbababbaabbaababababbaababbaabaaaabaaabaababbbbbbbabbbbbbbaaabaaababaaaabbaababaabaababbaaabbbbaaabbbaaaabbbbbaaababbbaabaababbaaaaabaaabaabbbaaabbbabbbaabbabbaaaabbbaaabaaaaaaababaaabbbabaabbaaabbbbabbbbbbabbbbbaabbaaaabbabababbaaaaaabaabaabbabbbbbaaababaabbabbbaaabbaabbaabbabbababbabbbabbbbaabbababaaaababbbbbabbaabaabaababbbbabbbaaaaaababbbbbbabbbabbababababbaabaaaabbaabaaabbababbabbbaababaabbaabaaaabbbababbbbbabbbaabbbaaaabbbaabaaaabbbbaaaabbabbbabbabbbbabaabbbaabaaabbaabbaaaabaabbbbbaaabbaabbaaabbaaaabbaabbabbaabbbabbbaabaabbaabbabaabaababbabaaaaaabaaabbbaaaaaaaaaababbabbabbaaabbabaaaababbbababbabaaababbabababbbbbaaaaaaaababbabababbabababbbbababaaabbabbaabaababbbbbbabbbbbabaabbbaabaaaabaababaaaabbabbbabaabbbaaaaabaaaaabaaabbbabbbabababbabbaaabbbbbbabbabbaaabaaaabaabbbabaabbbaabbbbabaabbbbbaabbabababaabbbabbbbababbbbaabaaababbbbaaabbabbabbaabaaabbbabaaabaaaababaababbbaabaaabbbbabaababbabaaaabbabaaabbabbabaabbbbaaaaaaaabaaabbabbbababbaababaababaabbbbbbaaaabaaabaabbaaabaabaababbabbaaabababbaaaaaaaababbbbababaaaaaabbbaaaabbbaabaaaaaaababbaaaabaabbaabbbbabbbbabbaaabbbbbaaabaabaaaabbbaaaaabbbbbaabbabbbbbaaaaaabbabbabaaaabaaababaaabaaabbaaabababababaaaabbbbababbbaabbababaaaaabbbabbbaaabbababbabaabbabbbbbbaababbbabaabababaaabababbabbbbabbabbbabaaabbabaaaabbbabaabaaaabbaaaaaaaaababababaabbbbaaabaabbabbabbababababbabaaaabbaaababaabbabbbbaababbbabaabbbbbaaababaabaaabbaaabbbbaaabbbaabbbbababbabaaaabbbbbbaabaaababaabbbbbbbbabbbbbbbbababbbbaabbbbbabbabbabbabaaabbbaaaababbabaaabbbaabbbbaaaaabbbabaabbbbabaabaaaabaabbbabbabbbabaaaaabaabbaabbbbabaaaaaabbbbbbbaaaaababbbabaaaaabaaabbbbbbababbababaaabbbabbaababbbaaababaaabbbbbabaabbaababaabbabaaaabbbaaabbabbbbaabbbbbabbbbbbabbbbaabaaabaaaabaabbaabbbbbbababbaaabaaaaababbabbabbabbabaabbaabbbbbabbabaabaabbaabaabbbaaaaabbbaabaabbaabbababaaaabaaabbbbbaabbbbabbaabbaabababaabaabbaaababaaaaabbbababbaaabbbaaaabaaabaabbbbbabbaabbbbbabbaaabaabaabbbabbabaaaabbaaabbbbbbbbbaaabbaaaabbabaaabaabbabbbabbababbbbababaabababbaabbabbaaabbbbbaaabaabbbbaaabbababaaaaabbaabbbbaaabbabababbaaaababbabababaaaababbaababbaababbbaabaaaababbbbaaabbbaababbbbbaabbaaaabbabababbabbbbbaabaabbabbabaaabbabbbaaaabaaabbaaababbaabaaaaabbaabbabaaaabbababaabaaaaabbaabababababbbaaaabbabaaaabbaaaabbaabababbbaaaabbaaababaaaaabbaaaaabababaaabbaaaaaabbbbaaaabbbbbabaaababaababababbabbbbabbbababaabaabaabbaabbbbbababaaaaaababaaaabaaabaaabaabbabaabbaabbbabbbaaaababaababbbabbabababbabbabaabbbbabaabbbabbababaabaababbbabaaaaababbaabbabbbabaaabaabbaaabbbbabaaaaababbabbaaabbbaababbababbbbbabaaabbbabaababbbbaaabbbbababbabbbaabaaabaabbbbbbabaaabaaabbbababaaabbaabaababbabbababbbaaabaaaabbbbaabbabbaaaaaaabbaabaaabbaabbababaaaababbbabbaaababbaaaaaaabaaabbbbabaaaabaaaabaababbbbbabbbbaaabbaaabbbaaaaaaaaababaaabaababbaaababbbabbaabbbbaaaaaaabbaaabababbbaaaaabaaaabbaaaabaababbbabbbbbaaaaaabbaabbabbabbabbabaaaaaabbbaaaaabbbbbaaaabbabbabbaababbbbaaababbaaaaababababaaabbaaabbaaabbabbbabbbabababbabaabbababbaabaaaaabaaababababaaaaababbbbabbbaaaaabbbabbaaabaabaaaaaababbbabbbaaabbbbaabbabaabaabababaabbbbbaababbbbbbabbabbaabbababaabbaaabaabababbaabaabaababababaababbbbbabaabaaaaaababababbababbabbaabababbbbbabbbabaabbbabbbbabbabbbaaabbbaaabbbbaabaaaaabbbbbbaaababaabbaabbbbbbabababbaaabaaababaaaaaaababaaabaabaababaaabbaaababbababaabaabaabbbabbbaaaabababbabbaabaaaaabbbbaabbaabaabaaabbaaabbbbaababaabbaabbaabbbbbaabaabbbababbbbaaaabbbabaabababbaabbbbbbbabaabbaababaabaaabbbaabaaaabbaaabaabbaabaaaaabbaabbbaabababaabbabbaaabaabbababbbabbbbbabbbabbaabbababbbaaaaabbabbaabaabbabbbbbbabbbbbaababbbabababbabababbbbbaaaaabbaaababbabbbbabbaabbabbbbbaabaaabababbaabababbaabbbaaaaaabababbaaababbabbababaabbbabbabaabbaabbaaaababaababbaabbaabbaabbbababbaaabaabaaabaabaaaaabbbbbbbabaabbbbbbaaaaaabaabbbbbabbbbaabbabbbbabbaababaabaaaabbbbabbababbabbbbabbabaabbbbaabbbbabbbbababaaababababbbbbbbaabbbbabaaaaaababbbabbaabbbbbbbaabaaabaababbbaabbabbabaabbabbababaabaaaaababaaaaabbabbababbabababbbababbbbbabababbbbabaabababbbbbbbabaabbaababbabbaaaabaaabababbaaabaabbbabbababaababbabababaabbabbaababbabaaabababbabbbbbaaaaababaaaaabbbbabbaabbbbabbbbaabbabbbaabababbabbbbaababaaaaaabbabbababbbbaaaabbbbbabaaaaabaaabbbbbabbabaaaaabaabbbaababababbbaaaaaaababaabaabbaabbaaaaaaaaabaaaabbbabbbbbbababbbbbaabababaaaaabaabaaaabbabbabbbbbbbaabbbababbbaaaabaababbbaababbbababbbbbaaababbabababaaabbbbabaabaaabababaaabaaaabababaaaaaabbaabaaaabaabaaaaaaabaaabbbaaabbbbbabbbabbabaaabbbabaababbabaabbababbaaababbbaaaaabaaaabbabbbaaaaabaaaaabbaaaaaabbaabaaabbabbababbabbaabbaaaaababbaababbababbbbaababbabaabababbbbbbaaabaababababbbbabbbbabbbbaabaabbbbbabbbaabbaabbbabbbaabaabbababbaaabaabbaaaabbaaabbbbababbabbaabbaaaababaababaabbaaabbaaabbbaabbbbbabaabaabbaabaaaaababababbabbababbaaaabaaabbbbaaabbabaababbbaaabaabbbbbabababbaabababaaaaabaababbaaabaabaabababbabbbbbabbaabbaababaaaaaabbbaabaaaaabbaabaabbaaaaabaaabababaabaaaabaaaaaaaaabbbbaabbaaaabbbaabababbbabbabaaaaabbaabbababaaaababaabbaababaabbabaaabbabbbabbaaabbabbaaaabbaaabbababaabaaaaaaaaabbaabaaaabbbabababbaabbbaabbbbbaaaaabbbbabbaabbbaaaaaabaabaaabaabbbaaabaabbbbabbabaababbaabababbbbabbbababbaabaaabbaabaabaabbaababbbaabaaabbbbaabbaabbabbbabaaabbbbabaabaabbaabbaaaabaaabbabbaaaaaabbabbaababbbabbbbbaabbbbbaaaaaabbaaababaabbaaabaababbaaaaababaabbababbababaaabbbaaaaaabbabbaabbbaaaabaaaabaaabbbbabbabbbbbaaabaabbababbaaabaaabbababbaabaababbabaaaaabbabaaabbababababbabbaaabaaaabbbbaabbaaaabbbabaaaaaaabbbbabbabaabbabbbbaabaaaaabbbbaaaaabbbbbbbaabababbaaaaaababaaabaabbabaabaabbbbbbbbaaaababbbabaaabaabbbbbaababbbaabbaabbaabbbaabaaababbbabaaabbbbbbabbaaabaaabbbababbaababababaabbababababababaaabaaabbaaaabaabbabaabbbbabaabbababbbbabaababbabbababbaaabbbabbbbbaaabaaabbabbbbbbaaaaababaabbbabaaabbabbaabaaaabaaababbaabaaaaababbaaaaabaabbbaababbbabaabbbaabbabaaababbbaabbaabbbbabbabaabaabaababaababbabbbaaabbbbbaababbbbbbbbbbbabbababababbbaaaaaaaaaababababaabaaabababbbaabaaabbbaababaabbbabbabbbaabbbbbabbbbaaabbaaabaaabbbbaaabbbbbbbbababbababbbabbabbabaaaababaaababbaababbaabbbbababbbbbaabaaaabbbbaabababababbbabababbbbabbbaabbaabbbabaaabaaaabaaaaaababbabbbaabaaaaaaababbaaaaabbababaaaaabbbbaaaabaaabaaababbabaaababaaaaaabbbabbbbabbaabaabbaaaaabaababbbbabaabbaaaaaababbbabbbaabbaaabbaaaabababbbbabaaaaaaaabbbbaabbababbaabbabbbbaaaabaababbbaabaabbbbbbabbbaaabbabaaaabbbababaaabaabababbbbaaaaabaabbbbbaabbaaabaabbabaabbbaaaaabbbbbbaabbaabbbbbabaabbbbaaaababbabbaaabaaaaaaaabbbbbbbbbaaabbbabbbbabbaaabaabbaaaabaabaaaabbbbabaababbbbbabaabaababbbbabbbbababbbbbaabaaababaabbaabbabababbbabbaaaabbabaaababbbbbbabbbabbabababbbbbbbaaabbbbbabbbaabaaabbabbbaaabbbabababbbbaaaaaabbaabababaabaaaababaabbaaaabbbababaaababaaabaaabababbbbbbbbaaabbababaababaaababaaaaaaaaaababbbbaabbbaaabaababbbbabababbbbbbaabaaaabbbbbaaabbbaabbbabaaabbbbbbbbbbbbababbbbabaaabaabbababaabaaababbbbaabbaababbbbaaaaaaaaaabababaabbaababaaabbabbbaaaabbabbbbaabbbbbbaaababbbaaaababbaabbbbbbbbbbaaabaaabbbbbbababbbbbaabaaababbbabbababbaaabaabbbaaabbbabaabbababbaabbabaabbabaaaaabbaaabaaabbbbbabbabbaaabaabbbbabbabaabbabaabbbbaaabaabbbbbaabaaabbabbbaaabbababaaabbbaaaaaababbabbababbababbbbabbabaabaababbbbbbbbabaabaabbbabbabaaaabaaabbbbabbabbaabbaabbbabaaabaabbbbaabbababbbabbabbbbbabaabbabaaabbbbabbabbbabaaabbabbbaababbbbbbabaaabbabaaaaabbabaaaababbabaaababababbababbbabbbababaaaaabbaabbabaaaaaaaabbbaabaaabbaabbaaabbaaabbaabababbbabbbabaaababaaababbaaabababaaaababbbabababbaaabbbaaaaabbaaaabbbbbabaaaaaabbaabaaaaaaababaaababbabbabaabababaabaabaaabababaaabbaaabbbababbbbbabbbbbbbbabbaaaabaaaababbaabababbbbbbaabbaabbaabaabbbaabbabaababbbbbbbbbaaaaaaabaabbabaabbaaabaababbaabaabaabbbabaabbabbbaaababaabaaabaaaaaabaaaaabbbabaabbbbbabbbbbbbbbbbbbabaaaaabaaabaabaababbabbabbbbbaabbabbaaaaabaabaabaabbaaabaabbbbaaabbbabaaabbabaaaababaaaaaabbbaabbabbbbaabbbbbabbbbaaababaaaabaabbbaabbbaababaaaaabaababbbbbbabbbabbabbbaabaaaaabbbababbaabaaaabaaaabbababbbaaaabaaaaabbbababbabaaaabbabaabbabbaaababbbaaabbbaaaaaaababbababbbbbbaaaaaabaaabbbaaaabbaaabaabbaabababbaaababbababaabababbbbaabbbbbababbbabbbbbbbbaabbbbbaaabbabaaabbbaabbbaaabbabbbbbaaabbbaaabaaabbabaaaaabbbaaabbaabbbbaabbbbaaaabbbabaaabbabbaababbbabbabaaaababbbbbabaabbbbabbaaabbbbaabbabaabbbbbababaabaaabbbabaabbabbabaabaaaabbabbbbbaabababbbaababbbbbbabbbbbbaabbaaaabbbaaabbbababaabbbaabbaaaababbbaabbaabbaaabbbabababaaabaaaaaaabaaabbaaabababaaababbaabaabbbbaaaaabaabbbbbbbabaaaaababbabbabbaaabaababaabababbbaaaabbbbabbbaaaaabbaaabbbaabaabbaaabaababbabbaababaaaabaaabaaaabbabbbabbaaabbbaaabababbababbababbbbabaababbaabababbabababbbaaaabbbbaabaabbbbabbaabaabaabbaababaaababababaaaaaabbbbbbabbbaabbaaaaaababbbbaabaaabbbbaabbabbbbaaaabbaaaabaababaaaaabbabbbbbaaaababbabbbbbbbbabbbbbabbbaaababbbabbabbbabaaabbabbabbaaabaabbbabbaabaabbbbaabbaaabbbabbabaabbaaaaabbbabaabbbbbbbbaabaaababaaaabaaaababbabbbaaabbbbaaabbbabababbbaabbbaaaaabaabbbbabbaaaabbbabbbbbbaababbbaababbbaaaaababaaababaaaabbaaabaababbaabbaaaaaaabaabbbbbbbbbbaababababaababbbbbaaabbbaabaaaaabbbabbaaabaabababbbbabbbabbbbababaaabbabbabababbaababbbabbaabaabaaaabbbbaababbbaaaabbbbbababbbbabbabaababbbababbaabbbbbabbbaaababaabbbaaababbaaaaabbbaaaaabbaaabbbbbaaabaabbbbaaaaaabbbbbabaaaabbabbbbabbbbaaaaabbbbbbbabaabbabbabaabaaaabaabbaaaaaaaabbababababaaaabbbbbbbabababababbaaabbbabaabaabaaaabbaaabbbaaabaaaaababaabababbbabbabbabbabaaaaabaaaababbbbabbabbabaabaabbbbaabbabbabbbbbabaabaabbabbaaababbaaaabbababaabbaaabbabababababbbbbababbbaabababbbbabbababbbaabbbbbbbbaabbabbbaaababbbbbbbaaaaaaaaabbaabbaabbbbaabbabbabbabbbabbbbbbbababaabaaabbaababbaaaaaababbabaababaababbaabaaabbbbbbbaaaabbabbbaaabababbbbbaabbbaabaabababaaaaaaabbabbaaaabbabbababaaabaabbbbbbabaaabaabaabaaabaababaabbbbbbbbabaabaaaaaabbaaaabbbbabaabaabbabababaaaaaabbabbbaabbbaaaaaabbbbabaaaabaabbbaaabbbabaaabaabababbbbaabbaabaaababaaaabababbaaabbaabbbbaabbbabbabaaabbbbbbaabaabaababaaaabbababbbaaaabababbbbbaaaaabaabbbbbabbbaaabbaaabbaabbabbaaaabbababaaabaaaabbbbabbaabbbaaabbbbabbbbaaaaaaaabaaaaaaababbbbbbaaaaabbaabbaaaababbbbaabaaabbababaababaaabbabaabababbabaabbbbaabaaababaaabbabaaabaababababbababbbabbabbbbbbbbbaababbaabbabaaabbabbabaabbbabbbbaabbbaabaaaabbbaaaababaabaabababaabaabaaaaababaabbababaaababaabaabababaaabbbbaabbbbaabaababaabbbaaaaabaaaaaabbabaaababaaaababaabaaabbbbbaabaaabaaababaaaaababaabbbbababaabbbbaaaaaaaaaaabbbabaabaababaaaaabbbabbabbbaaababababbabbbaaaabaaaabbbabbbababaaababaabbbaabbbaaabaabbbabbbbaaaabbbabbbaaabaabbaaabbbaaaaabbbbaababaabbaabbbbaaaaaaabaaabbbbaaaabaabbaaaaaabbabbbbbabaabbaaabbabaabbabaaababababbaaababbbbaaabbbaabbbbbaaaabaaaababbbbabbabbaaabaaaabbabbabbbaaaaaabbaabbbababbbaaabaaaaaabbbbaaaabaaababaabbaabbaabbabaaabababbabbabababbbbabbaaaaabbabbbbaaabbabababababbbaabaaabbabbaabbaaaaaaabbbbaabbbbabaabbaababbbbbaabbbbabbaababbbaaabaaabbaabaababbaabbbabbbababaabaaababababbbbaabaaabaaabbbabaabaabbaaaaaababbbbaaabaaaabaababaaaabbbabbbabaaaabbbbabaabaabbaabababbaaabaabababbabbabbbbbaabbbbabbbbbbbaaababaaabbbaabaaabaabbbabbbabbbabbaabbaaaaabbbabbaababbbbaababbabaabbaaababbaabbbabbbbabaaaababaabbbababababbbbaabbabaabaabbabaaabbbaabbabbabbbbabbababbbbaaaabaabaabbbbbbaaababaabbbabbbaabaabbbbbabbbbbbaaaaaaabaabababbbaaabaaaaabaababbbbbabbaaabaabbbaababaabbbbaaabbabbabbaaaababaaababbabaabbaabbabbaabbaaaaaabbabaaaabaabaabaabaabaabaaabaaaabbaaabbbbabbaaabbaabbaabaabaaaaaaabbaababaaaaaabbababbaabbbaaaabaaabaabaaaaaaabbbbabbaaaaaababaababaaabaaabbbabbaaaaaaabbbababaaaabbbbbbbbbbbbbabbbaaabbbbbbbabbbbbabbbbbbbaaaababaaabbaaaabbabaaabbabaaaabbabaaabababbbbbbbaababbbbbbaaaabbababbabbbaabbbbbbaaaabbaabbabbbabbabaababbaabbbaaababbabbabababababaaaaabbbbbbaabaabbababbaababaaababbaababbabaabbabbbbaaababbaaabaabbabaabbabbbabbbabbbbbabbaaaaaaabaaaaabbaababbbbaabbaabbbabbababaabababbbbbbaaababbbaabaabaaaaaaabaabbbabaaabbbbbbbbbaaaaaaabbbaababbaaaabbabbaabbbabababababbbabbaaabbbaaaaaaaabbaaaaaaabbbaabbbbabbbbbabbbbabaabaababaaaaaaaababbbabaaaaabbbaabbaaaaababababaabbabbbbabbbbbaabababaaabbabbabbaaaaaaaaabbbbaabbbbbaaaaabbbbbaaaabaababbabababbabababaabbbaaabbbbaababbbbbaabbbaabaabbbbbbaaabbbaabaabbaabbabbaabbbbbbbaaabaaaaabbaaaabbabababbabbbbababaabaaabaaaabaababbababaaaaabaabbaaabbaaaababbaababaababaaabbaabbaaabbabbaaaaabbabbbbbabbbbabbbbabababbabbaabbaababbbaaabaabaaaaabbaaaabbbbaaaaaaabaaabaabaabbbababbbbaabbbabaaabaaabbbbbaababbaaabbaaaabaaaaabbaaaaaababbbababbbbbbaabbaaaabbbababbbbbbbbabbbaababaabaabaabbbbaabaaabbbbababbaaabbbaababaabaaabbbbaabbbbbabaaaaabbbbaabababaabbbaabababaaaaabbaaabaabbbabaababababaaaaaaabbbbbbabaabbaababbaabbbbbaabbabbaababbbaabaaabbababbbbaaabbaababaabaaaaaaaaabbabbabbabbaaaabbaaaababaaabaaabbabbbbbabaabbabbabaaabaababbbbabbbbbbbbbaaabaabbbbbaaaaabbababaabbaababababaaabbbbbaaabbaaaabaabbaaabbababbaaabaaabbaaaabaaaaaababaaaaababbbbbbbabbbbbbaaabababababaabaabaabbbbbbbbabbaabbbaababbbabbabbbbaaabbbaababaaabbbbabbbaaaaabbaaababbbbaabbbaabbbabaaaabbbbbbbbaaabbbbbaabbbaabbbaabbababaabbabbbaaaabbaabbabbbbabbabababaaabbaaaabaabbaaaabbbabbbabaabbbaaaababaaaaaababaabbaabbababbabbaabbbaaabbbaaaabaaabbbababbababbbbbaaabbbbababbbbbabbbbaabbbbabaabbabbaabaababaaabaaaababbabbbabbabbabaaabababbaababaaababbbbabbabbbabbbbbaabbbababbbbaabaababaabbbbaabaabaabaababaabbaabbbbbababbbaabaabaabbababbabbaaaabbaabaabbaabbaaabbaabbabaaaaaaababaaaaabbaabbbbbbaaababaaaaababaabaabaabbabbaaabbaaaaaabbbbbbababababbbbabbbbbabbbabaaaaabbabbaaabaabaaaababaabbbbabaabbbababaabbaabbbbbbbaabbabbabbbababbbbbbbaaaaaabaabaaaaabbbbaabbababbababbbaabbaaabaabaaaabaabaabbabaaabababaabbbbbbbabbabbbbbbaabababbbabaabaabaaaabbababbababaababaabababbbbbabbababbbbabbbbbbaaaabbbaabbbbabaabbabbbabbaababbbbaaababaaabababaabbbbbaabbabbbababaaabbabbaabbbaabaabbabbbbbaabaaabbbaabababbbbaabbbbbaabbaabbabaabbaabbbbbbbbbaaabbbaabbbabababaaaaabbabababbababbbbabbbababaababbbabbbaaabbaaabbbbbabaabbbbaabbbbbaaaaaababbbababaababbaabbbabaaabbaababbbbbaaabbbbbabbbaaaaaaabaabbabbbbababbbabbbbaaababaabbaabbabaabbbababbbbbbbabbbbababaaaaaabaabbaabbbbbbbabbabababbbbbabaabababbbaabaabbbabbbabbabababaaababbabababbbaaaabaaabbaababbbabbbbbabababaabaabaaaaabbbaaabbbaabaaabbaabbaabaaaaaabbbbbababbbaaaabbababbabbabbaabbababbabbbaaaabaaabbabaaabababbbabbabaaabbbabbbababbbbaabbabaabaaaaaabbabbaaababaaababbabbbabbaabbbbbbaaaaaabbababbbababaabbaabbabaaaababbbbbabbabbbabbbbaabbaaabaabbabaabbbbabaaabbbbabbaabbbbbbbaaaabaaaaabbbbaaabbaaabbbbbababaaabaabaaaaabbbbabaaabbbbaabbbaabbaabbbbbaabababaaababbababababbbbabbababababbbaaababbabbbbbbbaaabaababbbaaabaaaabaabbaabaaabaaabaaaaaaabbabbaabbbbaabaababbabbaabbaaabbbbbbbbbabaabbabaaabbabbbabbbbababbbbbaaaabaaabbbbbbaaaaaaaaaabbabaabaaabbbaabaaaaaabbabbbbbabbbaababbabbabaaabbaaabaabbbabaaabbaabaaaabaababbabbaaabaaaaababbbabaabbbbbbbaaaaaabbbabbaaaabaabaabbabbaabbabbbbbbabaabaabbbbababbababaaabbbbabaababbbaaabaaaaaaabaaaaabbbabbbabababbbbbbbaabbbaaaabaababaaaaaabaaaaaaabbabaababbabbabbabaaaabbaabaaaaaaaababaabbbaaababbbbbabababbabaabaabbbabaabaaaaaabaaaabbbbababbabbbbbbabbbababbabbbbabbabaabbbbbabbbbaaabaaabaaaabbbabaabbaabaabbbbbbbbabbaabaabaabbbbaaabaaabaaaabbbababbbbbabaabbababababbbbabbabaaabbbbbabbaabababbbbbbbabbbbbbabbabaaabaaaaabbaaaaaaaaabaababbbbabbbababbabaaaaabbbaabbbbbbabbaabbaaababbababbbaabbbabbabbbabbabbaaaabaaaaabaaaaabaaaabbbbbbbbbabbabbbbbbbbbabaaabababaabaaaaababaaabababaabaabaabbbaaaabbababaaaaabaabbbbabbbabbbaaabbbbabbbbbbbbaabbbabbbbbbbaaabbbabaaaabbbabaaaababaaaabbaabbabaababbabbbababbabbabbbbaabaabbbbbababababbabbbbabbababaabbababbbaabbabbabbbababaaaabaaaaabaaaaaabaaaaabbaaabaaaaaabbaabababbaaaaaabbabbababaabbabaaabbbaaaabaaaababababababbabbabaaabbbbaaaaaabbbababbbaaaabbbbaabbbbbaaaaaaaaabbbabbbabbbbaaaabbbaabababbaabbbabbaabbbaaaaaabbbaaababbaaaabbabbaababbaabbabbaaaaabbbaaaaabbabaaaaabbababaaabbbababbabaabbbaaababbbbabbbaabbabbbbbbbbbabbbaaabababbbababbbabbbbbbaabaaaabbbababaabbbbaaaaaaabbbbbbaabababaaababbbbbbbbbabaababaaaabaaabababbbbaabbaaabaaabaababbaabbabbabbbbabbbbbaaabbababbaabbabbababbabbabbabbbabbaaabbbaaaabaaaabaabbbaabbabaaabbbabaaabaaabbbbbbaaaabaaabbaabbaaabaaabaaaabaabaaabbabbaabaabaababbbabbabbaabababaabbaabbabbbabbbabbbbbbabaaabbabbabaaaaaabbbbaabbaaabbaabbbbbbaabaaabaabbaaababbabbbabbbbbbbbabbaabbbabbabababbbaabaabbabbbabbbabbabbbaaababbaabbbaabaaabaaabbaababbaaabaaaaababbaaabaaaabaaaababbbbaaaaabbabbabbbbaaaabaaaaaaaabaabbbabababababaabbabaabbbbbabaabbbaabbbabbabbabbbabbbabaaabaababaaabbbbaabbbbbabbbbbaababbaabbababaabbaaabbbabababaababbbbbaaaabbbaaaaabbbbbabbbaaabaaaaaaabbabbabbabbabaabbaabaabbabbbbaabbbaaabbbaabbbababaaaaaaaababaabbbabbbabbabbbbabbaabbbabbabaaabbaaabbababbbbaababbaabaaaabbbabaabaaaaabbabbaabbbabaababababaabbabbaaabaaabbababbaaababbabaaaaabbabbababbbbbbbaabbbaabaaaabaabbaaaaabbabbaabababbbabaaabaaaaaabababaaaabbabaabbbaaabaaabaabbbbababbabbbbbbabaaaabbbbaaabaaabbbbbaabbaabbabbabbabaabaaabababbabbbaaaaabaabaabbbaaabbaababaaaaabaaaabbbaaaabbbabbabbaaababbaaabbbbabaababbaaaaababababbbabbbababbabaabbbbabbbabbabbbabaaabaabbaaabaaaaababbabaabbbaaabaaaaabbbabbaaaaabbaaaabbaaaabbbbabbbabbbaaabaabababbbababbababbbbbbbaabbbababaaaaaaabbbbabaaababababbabbbbaaabbabaaabaaaaababbaaabbbababababbaabbaaabababababbbababbbabbbaabbababbaabaaabbabbaaaabbaabaaaaabbaabbaaabbbbabbaaaababbaabaaaabaaabaaabaabaaaabaabbabbaaaabbaaababbbbbbbbbbaaaaaaaababaaabbaabababababaababaaaababaaaaabbaaabbabaabbbaaaaaabaaabbaaabbaaababbababbbbbbbbabaabbaababbbaabbbbbaabbbbbbbaabaabbaabbabababbbbabbababaaababaaaaabaabaaabababababbababbbbbaabbbaaaabaaabbbababbbbbbabbaaababaaababbbbabbbbabbbbaabaaaabbaabbababbbabbbababaaaaaabbaabaabbbabaabaaabbbaaabbbaabaababbbababaaaaabaabbbabbbaabbaaabaaaaaababbbabaaababaaabaabaaaabbaaaabbbaababaaaabbaabbaaabbbbbbaababaaabaababbbaabaaababbaaaaaabbbaabbbabbaaaaababbaabbbbbbbaaaaababbbbaaaaaaaaababbbbbbbabaaaabaaabbbaaabbaaaaabbbaaaabababaabbaababbabbaababbbabbabaabaaabbbbaaaaabbababbbabbbaabaaaababbaaaabbbababbaaaaaabaaababaabaaaaaabaabbbbababaaaabaabaaaaabbabbbbababaabbaababbbabbaaaaaababaaaaabaabbaaabbabaababaaaabbaababaaabaaabaabbaaaaaabababaaaababbaabaaaaaaaaabaaababbbbaaaabaabbabbaabaaabbbbbaabbbbbabbbabbbbbbbbabbbbabababbaabbababbaababbbaaabaabaabbabaabaabbbabababbabbabbbbaabbaabbbabbbaabaabbbaaabaaaaabbabbbbaaaabababbbabaabaaabbaabbbaabbaabbbbaabbababbbaabbbaaabbabbaabaaaaaabaaaabbbaabbabababbbaaaaaabbabbaaabbbbaababbaabaaaaaabbbbbaaaabaabbabbbbabaabaaabbaabaaabaabbbabbbbbababbaaaaabbabbbaababaabaabbbaaaabbabbbabbababaabbaabbaaaabbaabaaaaaabaaaaaaabbbbaaabbaaabaabbbaaaaababbbaaaabaabbababbaaabbbbbabbaabbabbaabbaababaabaaaaaabbabbabbbabbbbaaaabbbbbbbbbbbbbaabaabaaaabbabbbaabbbbaaaaaaaabbbbbaababbbbababbbabaabababbbabaababbaababaababbbabaabaaaaaaabbbababbbbbbaabbbabaaabaababaaaaabbaaabababababaaabbaababbbbaabaababbbaaaaaaababbbaaaaaaaaabbabaaabbbabbabbbbbbababbaabababbaabbaaababaaaabbbbabbabbabbaabbbabbaaabaaaaabaababbbbbbbabaababababaababbbbbbbbababaabbbbaaaabbaaabbbbbabbabbababbabbbabaaaaabaaabbaababbabbbaaabbbbabaaaababbabbaabaaaaaaaaaabbababbbaabbabaababaaababbbaaaabaaaabababaaaabaabbbaabaabaababaaaaabbabaaaaaaababbaaaaabbbbaabaabbbabbbbbaaabbabbbaababbaababbababbabbbaabbaabaabaabaababbaabbaaababaaaababaabbaabababaaaabbbbaabaabaabaaaaabbaaaaabaaaabbabbaaaabaaaabbbabaabaabbabababbaababaaabbaaaaabbaaabbaababbabbbaaaababbbabbbaaabbbaaababbabbbabbabababaabbbaaaaaababbbaaaaabbababbaaabbababababaaababaaabbaaabaaaaaabbbbabbbbbbbbabaaabbbbaababaaabbabbbbbababbbabbbaababababbbbaabbabbabbabaabbabbbbbbabaaaabaababbbabbabbabbbaaaaaabaabababbbbbaaaaabbaabaabaaaaaabaabbbbaabbabaabbbabbbabaaabababbabbbaaaaabbaaabaaaaabaaabbabbaabbabababbbbbaabaabbbababbbaaabbbbaababaaaabbbabbaaaabababbbbbbaabbbaaabbbbaaaabbaaaaabaaaaaabaabaabbbabbbbaaabbabbaabbbbaaaabababbbbbbbaaaaaaaaabababaaaabbabbaabbbabaaabaabaaaaabbaaabbabbabbaabbbbbbbbaaaaaaababaabbbabbaaaabaaaabaabbaaababaabbbbabbbaabbbbbbaabbabaabbababaababababbaababbababababaaaaaaaaaabbabbaababbbaaaaaaaabbbabbbaabbabbabbbbbbbbaababbbbbabbbabbbbabbbaababbaaabbbabbabaabaaaaaaabbabaaaaabbaabbbaabbbaaababbbbabaaabbbbaaabbabbbabbbbabbbaaaababaaaabbbbbbaabaabbaaaaabbababbbbbaaaabbbbabbabaaabbaabbbbbbaabbababaabaabbaabbaaabababaaabaaaaaaaaaabbbabbaaaaababaaabaaaabbabbbbbbbaaaaababaaaaabbabaaabaabbbaaaabaabbabbbabaaaabbbaaabbababbaaabababbbbbbbaaaaabbbaabaabaaaabbabbbbaababaabbaaabbbbbabbabababaabbbbaaaaabbabbabbabababaaabbabaaaaaababaabbabaaaabababaababbabbbabaaaaabbbaabbbbaaaababababbbbbaababbabbabbbbbbabbbbabbaabbbbabaaababbaaabbababbaabbaabbabbbbbbabbbabbbbaaabbbabaaabbbbbbabbbbabbbbabbaaaabaaabaabbbaaabbaababbbbabaabbbbbbaabaaaabaabaaaaaaaaabbabbaaabbabaababababbbbaabaaababbaaaaabbaabbbaaaabaabbabbaabbababbabaaaaaabbaabaabaabbbbbbaaaaaabbaaabbbaaaababbbbaaaaaaabbabaaababbbbabbbbabbbabaabbabaaaaaabababbaaaabababbbabbbabaaaabaabbabababbbbaaaaabbaaabaabbabbbbbbbabababaaaaabbabaaaaaababbbaababbbaaababbaababababbbbabbabbbbaaabbbbbaabbbababbaabbabaaaaaabbbabbabbaabbbbbaaabbbaaabbabaabbabbaababaaaabaaabbbaaaaabbabbbbaabbabbbbaaabbabbbabbbbaaabbbbaaaaaabaababbbbbbbbabbbbbbbabbababbbbaabaaabbbbaabbabbaaaaabaababbbababbabbbabbbaaababababbbabaabbaaababbabaaaababaabaabbbaabbabbabbaabababbabbbbaabbbaaabaabbbaaabbabbbabbbaaaabaaaaababbabaababbabbbabbaaabaaaabaaabbbbabaaabbabbbabaabbaabaaaabaaaabbbaabbababbbabbabaaabbabbbabbaabbbbbaabbbbabbbbaabaabaababbabbbababbbabbaaabbbbaaababbbabaaabbbabbbbabbbaabbaaaabaabbabbabaabaaaaabaabaabbaaaaaaabbabbabaababbaaaaaabbaabbbbaaaaaabaaaabaaaaaaaababaabbabaababbbbabaabbbabaaabbbabaaababbbabbaaaabababaaaaaababaabbaaaababbaaabbaaaaabbbabaaabbabbaaababaaabaababaabaaabbabbbaabbbbaababbabbbbaaabbbaaabbaaabbbabababbaabaaabaaababababbaaaabbbbbabbbaabaabbabbabbbabaababbaaaaabababaabaaaaababaababababaaabbbabbaaababbbabbaaabaababbaababaaaaaabbabbababaabbbaabbabbabaabaababbbbaabaabbabbaabbabbaaabbbbbbaaabbaababbaababbaababaaaaabaabbabaaabaaabbbbaaaaababaaaaabbbaaaaaaaaabaaababbbbabaabaabababbababaaaabaaaaabbaaaababbabbbbbbbaaabaabaaababbabaaabbababbbbababababaababababbababbaaababbababbaaaabbaaababbbabbaabbbbbaaaabaabaaaabbbbbbbaaababbbbabaabbbabaabababbabaaabbbaabaaaabaabbaabbaaaaabaaabaaaaaaabbbbaaabbbbbaaabbabbaabababbbbbbaaaabbbbbbabbbaaaabababbabbbabbaaaabbbabbbbbbabbbbbbabbbbaabbabaabaabbbababbbaabbbbbbbaabbbbabbbaababbaababbabbabaabbbaaaaababbbbbbbbabbbbbbaaabaabbbbabbaaabbaaabbaabbaabaaabbaababbbbbaababaabbbbababbaaabaabbaabbbbbabbbbaabbbbbbaabbbaaaabbbbaaabbabbbaaaabbbbbabaaaaaaaababaabbaabaaabbaaaabaabaababaababbaaabbaaaaaabbbbbbbbbbabaabbaababbbbabbaaabbaabaaaaaaabbbabababababababbabbababbabbababbaababaaabbabaaaaabbbbbaabababaaaabbaaaaabbaabaabaaaabbaabbabbabaababababaaaaabaabaaaabbabbbbabaaaaabaababbbaaabbbaabbabbabaabbbababbbabbabbbaaabbabbbaaaaaaabbbbbbabbbaaabbababbbbaababbbbbaabaaabbbaabaaaababbaaabababbbaaabaaaabbbabbbbababaaaabbabbabbbbbbbbbaaababbabbbaabbbbbbabbbaabaabbbabbaabaabbbabbabaabbbbbaaaaaaaabbbbbbbaaabababaaaabbbaabaabbbabbbbbabaaabaaaabbbaaaaababbabaaababaaaababbabbaababaaababababaababbbbaabbbaaaabaaaabbbaaabaabbabbbaaaaababbbbbbbabbbbbbaabbababaaaabaaaaaaaabbbaababbaabbababbabbbabbbbaaabbbbababaababbbbbbbbaababaabbaaababababbbaaaabbbbabbabbababbabbababaabaababaaabbabaabaaabababbbbaabaabbbbbbbaabbabaaabaabbbbbaabbbabaabaabbabbaaabbabbbabbbbaaabbbbabbaaaabbabbaaababaabbaaabaabaabaababbaabbbbaabbaaabbabaaababababaaabbbaaabbaabbaabababaaababbbbabbaaabababbabbbaabbaabaabbaaaaabbabaabababbaaabbbbabbbaaaabaaaaaababaaaabaaaabaaabbaaabbbbbbbabababbbaababababaababbbaaaaabbabababaababbaaabbabbaabbbaabbbbbaaabbaaaabbabaaabaabaaababbbaabbbbaaabbbababaabaaababbabbaaaababbabbbaaabbbbaaabbabaabaaaaabbabaaaabaaaabbabbabbabbabaaaabbbbabaabbbaaaaaaabaabbaaabbabbbabababbababaabbbbbbababaabaabbbbbbbbaaabbaaabaaaaaabbbaababbabaaabbaaaaaabbbababbabaababbabaabaaabbbabbaaabbbbaaaabaabbbaabbabababbababbaaabbbaaabbabbbbbbbaabaaabbaaaabaaabbabaababbaabbbbbbbbbbaabbabaababaabbbbabbabbaaaaabbbbbbabbbbbabbbbabaaababaabbabaaaaaaaaaaabaabbabbbbaabaaabababaaabaaaaaabbababbbbbaabbbababbaaabbabbaaaaaaaabbbbaabbbbbbbbbabbbaabbaaabaaababbabbbaabaaabaaaabbbabbabbbbbaaaababbaabaabaaaaaaabaabbbbbababbbbabbbbaaaabbbbaabbbaabbababaabaaabbaabaabbbabaaaaabbbabbabaabaabaaaaaababbbbbabaababbbaaabaaabaaaaaabababbbaaababaaabbababaaababbbbababaaaaaabaababbaabaaaabaaaabbababaaabbbabbabababbaabaaabbaaabbbabbabbbaabbbbbbbaabbaabaabaabababbaabbaabbaaaaaaaabaabbaababaabaaaabbaaabababbabaaaaabaaaabaaaabbbbbbbabbbaabbaababbbbbbabbbbbbabaaabbbbbaabbabaaabbabbaaabbbbababbbabbbbbbbbababbbbbabbabaabbaabbbbbbababaababbbaaabababaaaabaaabaaaaaaaababbaaabbabbabaabaabbbbbaaabbbaabababababbaaaaababbaaabbaaabbaaababbbabbbaaaabbababbbaabaabbaabbbbbabbabbabbabbaaabbaaaaaabbabbabbbbabbabbaaabaabbabaaaababbababbbaabbbabbaabbbbaaabbbaaabaaabaabaaaaaaabaaaabbbbaabbbbababaaaaaaaaaaabaaaabaabababbbababaabbaaabaaaabababbbbbaabbbbabbbbabbabbbbbbaabbaaaababbbbbbbbbaabbbaaabaaaaaabbaabbbabaababbbbbabbabbbbababaaaabaaabaaaaaabaaaaabbbabbaaaabaababbbbbaabbaabbaaaabaabbabaababbbaabaaababaaaaabababbbbabbbabbbaabbbbaababbbaaababaabbbabaabbaaabababaabbbabbbaabbaaaaaaabbabbabaabbbaabbabababaabbbbbbaaaabaabaababbaaaaaaabbaabbbaaaaababbbaaaaaababaabbaaaababaaabbaababababaaaababaabaaaababaabbabbaaaabaabaababbbabbbbaabaaaabbabbabababaaabbbaaaaabbbaabbbabbababbaaaaababbabbbbbbabaababbbaaabbabaaabaaabaaabbabbabaaaaaaabababbaaabbaabbbabbabaaaabbbabaabbbaaababaaaabaaaaabababbabbbaabbbabbbabbbabbaaabaababbaabbbbbabaabbaaaabbbbbabaaaababbaaaaabaaabbabbabbbbbbbaaaaaaaababbaabaaabaaabbbabaabaaabaabbababaabbababbbabaaabbaabbaababbabaaabbabaaaaababaaabbabbbaabaaabbbabbbaaaaabbbbabbabaabbabaababaaaabbababbbaaabaaaabbababaabbaaaabbabaaaabbbbbbbbabbbaababaaaaaaababbabbbbabbabaabbbaaaabbbbbbbaabaaaababbbbbbaabbabbaaaaaaabbabaabaaababbbabbaaaabbaabbbabbbbaabbbabbbbabaabbaabaaaabbabbabbaaaaabbbabaabaaaabaabbbababaaaabbabbaabbbbbabaabbbbbbbbabaabbaabbaaaaabbaaaababbbbabaabbabbabaabbbabbbabaababaabaabbaabbabbabbbbbbababaaaabaaaabbbaababbaabbbbbbabaaabbbabbaaaaabbbbbbbbbbbaaababbbaabaabbbbababbabaabbaabbbaaaabbabbaabbaabbababaaabababbbabbbaaababbababbabababaaaabaaaababaaababaabbabaabababababababababbbbabaaabaaabbababbbaabaaabbbbaaaababbaaaaaabaabbaabababbabbabbbabaaabbaaaabbbbabbbbabaaaababbbabbbbbbbbababaabababaaabbaababaaaabbabaabbbaaabaabbbabaabbaaabbbbbbaabbaabbbaaabbbbaabbabababbbaabbbbbabbabaabbbbabbbabababbbaababaaabbaabbabaabaabbbabababbbbaabbaaaaabbaaababaabababbbababbaaabaaaabaabbabbbabbbabbabaaaababbbbbbabaabbaabbbababaabbbababbbaababababbaaaabbbbbbababbababbaabaaabbbbabbaaabbababbabbaabbaaababaabbbbbbabaaaaabaababbaabbbaababaaaaaababbbabaabaababbbabbaaabaaabaabbabbabaaabaaaabbabbababbaaabbbbabbabbbbaabbababaabaabaabaaabbbaabbbbaabbababbababaaaaababbabbaababbbbaaabbabbaaaaaabbabbababbabbaabbaaabbbbabbabbabaabaabbbbbbbaaaabbbaaaaababababbabaaabbbbabaabbaababaabbbbbaaaaaabaabbbbabbbbabababbaabaabaaaabbbbbabaaabaaabbbaababaababaaaababbbaabaabbaaabbabbbaabaababaabaabbbbbbaababbaabbaabbbbbbbabaaaababababaabaaaabababbaaabbaaabaabaabbbbababaaaaabbabbbbaabbaabaaaababbbbaaabbbaaabababababbbbbbaaabbbabbaaababbbbabaabbbaaaabbbaabbbaaaaaaaabbabbbbbbabababababbbbbaabbabbbabbabaaaaaaaababaabaababbbaaabaaabbabaabaaabbaabbabaababbaabbbaababbabbabababaaaabbbbbaabababaabbaababaaaabbbbabbaaaaaababbbbbaabbbbabbaabbbbaabababbaaabbbabbbaaaabaabbaaababaabbbbbabbaaaabbbbaabbabbbbaabbaababaaaabaaabbbaaababababbbaaaaabbbababbabbbbbbabaababbbaababababbbbabbabababbaaaabbbbbaaababbaabaaaaabbaaaaaababaababbbabbabbbbbabbabbbababababbaabaaabbababbbbaaaaaaababaabbabaaaaaabaaabaabbaabaaabbbbbbababbbaabaaabaaaaabaabaabaababbabbbbabbaaabbababbbbabaaababbaababbababaababbabaaabbaaaabbbbbaaabbabbbbbbabbbaabababbabbbabababaaabababaabaaababbababaaabbaabbabbaabbaaaabaabbbbbababbbaabababaaabbababaabaaababbbbbabbbbbabaabbbbabaabbabbbabaabbbabababaabbaabbbabbbabbbabaabaaaabbbbaabbbbbbaabbbababbbbbbbabbbaabbabbbaabbaaabbaabababbbbbabaababbabbaaaabbabbabbabbaabbaaabbabbaabaaaaaabaabbbbbabaaababbbaaabababbbbbaaabaabaabbbbbbbabbaabaabbaabaabaabbbaaabbbaaabaabbbbbbaabaaabababbbbbaaabbaaababbaabbbbbbbbbbbaaaaabbbbbaabaaabbabbbbababaababbbbbaabaaaaaaabbaabaabbbaabbbbabaabbabababbbabaabbabbaaabaabaabbaaaaaabbabaabbbababaabaaaabaabababaaababbbaabbaababbbabaababbbabbbbaaababbabbabaaaabbbbaabaaabbbabababaaaabababaababbbbbabababbababbaabaaabbbbbababbbabaababaababbabbabaaabaabbbabbaaabbababbabbbabaaababbababbabbbabbabbbaaaaaaaabbabbbbbbbababbabbbaaaaaaababababbbbbbbbaaabbaaababbbababaabbbbabbaabaababaabbbbbabbbaababbbbaaabbbbaababaaababaaabbabbbbabbabbbaaaabaabaabbbabaabababbbababbbbabababaaaaabbbbaaabaabbaababbabbbababbaaabbbaaabbabaabbbaaaababaabbabbaababbbbbaabaaaaaabababbbbaaabbbbbaaababaababbbbbbbbbbbabaabbaabbaababbbbabaaaaaabaabaaabababbaabbababbbbbaaaabaaaababbababaabbbbaaaababaabaabbabbaabababbbbaaabbbbbbbbbabbbbbbababbaaababbbaaaabbbabaabaabbabbabbabababbaaabbbbbaabbabaaababbbaabbabbbaababbaabbbababababbbbbababbabaabbbbaaabbabaaaabbbabaaabbbaabaaabaaababaaaabbabbaaabbabaabbaabaabaaaaabbaabbaabbababaabbaabbbabaabbabaaabababbbaababbabaabbbbaababbaabbbaababbbbbabbabaaaaabaabbbaababbaaabaabbabbaaaaaabaaabbaaabbaaaaaabababbbaaaaabbbabbabbaaaababbbaabaaaabbabbaabbabbabaabbaabbbbbabaaabaabbabbbbabbaabbbaaabbaabababababbbbabbbbabbabaabababbbbbbbbabaaaaaaabaaaaabaaabbbaabbbbabaabbaabbaaaabaabbaabaaabbaaababaabaabababbaabbaaaaaabababbbabbbaabaabbaabbabaababaaababbabaabaababababbaabbbaaaabbbabbbbaababbaabaaabababbaaaaabaabbbbaaababaabaababaabbaababababaababbaaaaaaaaaababbbaabbbabbbbbbaaaabbbabaaaaaaabaaaabbbbbbabbaaaabbbbbbbaaababababbbabbbbbbaabaabaaabbbbabaabbabbbaabbbaabbbababbaabaabaaabaabbaaaabbbabbababbabaabababbbabaaaababbaabaaaabaababbabaabbbbaababbbbbbabbabaabbbababaaaaaabaabaababababbababaabbbbababbaabbbaaabbababaabbaabbaaaababbbbaaaaaabbbbabbaabaaaabbbabbbbbaabbbbbbabaaabbbabaababbbbaabaabababaaaabababbabaaaabaabbbbbbaabbabaababaaaabbaaaabababbbbabaaaababbaabbbbbbaaaaaaabbbbabbaabbbababbaaaaaaabaaaaaababaabbaaaabaabaaaaabbbbbabbabbaabbbbbabbbabbbababbbbbababaabbbaaabaabbababbbabbbaabaaabbaaabaaaabbbaaabaaabbbabaaabaabbaababaaabbbabbabaaaaaaaaababbabbbabbaaaaaaaaaabaabbbabbaabbabaabbbbbbaaabaaaabaabbababaababaaaabbaaababaabaabaaaaaaaaabbbabbaabaabbaaabbbbababbaaaaabbabbbbaabaabbbbbbababaabbbbbbabaaababbaababbaabbabbbabaabababbbbabaababaaaabbabbaababaaababababaaaabaaabbbabaaabbbbbbbbabbbaababbabbabbbabaabbabaabbabaababaababbaabaababaaabbaaaabaaaaaabbabbaaaaabaabbbbbbbbbbaaaaabbabaaababaaabbbaabaaaaabaabaaababbaaaababbabbbbbbbabbbbbabbabaaaabbbaaaababbabaababaaaaaaaabbaabbbbababbababbbbbababbaaabbaabbabbabbababbaaaababbabaabbbabaaabbbbbbababaaabaabababaaaabbbaabbbaabbaaabababaaabbbabbbbbbaabaabbbaababbbbabbaaaaabaabbabaaaaabbbbaababbbabababababababbbbbbbbbaaabbbaaababbabbabbbaaaabaababbabbabbbbbaaaababbbbbbbbababbbbaaaabbbaabbabbaabbaaaaabbbbaaabbaaaababaabbbbbaaababbabababbaaabababaabbbaabbbabbaaababbbbbabbbabbaabbaabbabaaaaababbbabbbbbbaaabbaaaaaabbbabababaaabbbbbbbaabbbbaabbaaabbbbaaabbaaaaaaaaabbaaabaabbbbaaaaaabbbbaaaabababaabbbabbbbaaabababababbaabbaaaabaababbabaabbbaabbaaaabbabaabaaaaabababaabbaaaaababbbbabaaabababaabbbaaabbaabbbaaaaabbbababbaaabaabababbbbabaabbaabbbaaababaaabbaaaabaabbabababbabbbbbaaababbabbaaababaabaaabaabbabbaabbabababbaabbaababaababbabbbabbbabbaaabbbbbbbbaaaababbbbaaaabbbbaabaabaaaaabaabbaabbabbbbbbabbaaababaababababaaababbabaaaabaabbbaabaabaaababababbababbbaaaaabbabbbaabaaaaaabababababababbbbbaabbbbabbbbbbaaabbbababbaabbababbbaaabbbabaaaabbabbabaabbbbaaaaaaabbbbbaaaaababbbabbbbabaabbaaaaabbbabbbaaabbaabababbbbbbbaaaabbaabbbbbbabababbbbbaabbabbabbaaabaaaababababaababaababaababaabaaabbabbabbaaaaaabbbabbbbaabaaabaaaabbaaababbaaabaaabbbbabaabbaabaaabaabababaaabaabbbbbaabbababaaabbababaabbabaabaaabbbbbbbababaaabbaaaaaaaaabbbbaaaaababbababbbbbbbaabbaabbabbbababaaaaabbabbaabbaaabbaababbbaaaabaabbabbbbabbabbababaababababbabbbabaaabbbabaaabbbaababbbbbabbaabbaaabbaaaaabbbabaabbabbababbabaaaaaababbbaaaaabbbaaababbabaaaabbbbaabaaaaaababababbbaaaaaabababbbabaaabaabbbaaababaaaabaaaabbaaaaabbabbbaabbaabbabaaabbabbabbbbaaabbbaaaababbaababbaaabbbabbaaaabbabbbbbababbbabaabaabbababababaaaaabbbbbaabaaabbbbaabbabbabbabaaabbbabbbaabbaabbbaaabbaababbbbbaababbbbbaabaabaababaababbaabbaabaabaaabaabaabbabababbaabbaabbbbaabaaabbababbbabbaabbbbababbabbbbbabaaabaababababbbbbabaaabbbbaaababbaaaaabbbbbaaabbabbbbababbbbabbaabbabaaabbbababbabbbbaaaaabaabbbabbabbabaaababbabaaaabbbababababbababaabbbbabbaabababbbbabaabbbbbbabaabbbaaabaaabbabaaabaabbaaaaababaaabbabbaabbabbaababaaabbbabaaaabbaababbaabaababaabaaababaababaabababbaaabbbabbaabbabaaabbbaaaaabbaaabbaabbbababbaaaaaabbaaaaaaaaaaaabbbaaabaaaabaaaaabaaaababababbabaaabababaaabbbaababbababbaaabbbbabbaaaaaabaabaabbababbbababaabaabaaabbabaabbaabbbaabbaaaababbbbababbaabbbabaabababbababbbbabbaaaabaaabababbabaaaaababbaabaabaaababbbbbbbbbbbbababbababbabbabbbabababbabaaaabbbbabababbbbabaabbabaabaaabaaaaabbabbabbaaabbbbabaaabbabbbaabaababbbbaaabaabbababababbaaababbabbbbaabbaabbabbbbbbbaabbaabbbaabbbaaaaabbaaabababbabaabaabbbababaaaaaaaababaaabbbbbabaabbbbbbbababababababbabbaaaaaabbbbaabababaaababaaaabbbbbbbbaababaabbbaababbbabbbbaaaabbabababababaabbaabbabbaaabbabaabaaabbbabbbabbabaabbaaabbbabaaabbabbbbaabbaaabbaababbbbbbbbbbbaaaababababbbaaabbaabbbbbaababbbbaaabaabaaabbabbaaabbabbaaaaaabaabababbbbaaaabbaaaabababaabaaaaaaaaaabbbbabaaabbaaabbabbbabbbaaabbaaaaaaaababaabaabbbaabbaabaaaabaabaaabbbabbabbaabbbbbabbabaaaaaababbaabbbbbaabaabbbaabbabaaabaaaaabaabbababaaaabbbbbbbbaabaababaaabaababbaabababaaaaaaabbabbbbbababaabbaaababbabaaabbbabbbbabaaaaababbababaaaaabbbababbbbababbaabaaabbbaababbaababbaababaaabbbbbbbbaaabbaaaaaabaababaabaabbabbbbaabbabbaabbaabaaaaaaabaaabbbaabbbbabaaaaabaaababaaaaababaabababaaaaababaabbbbbabaabbbbbaababbaaaaaaaabbaaaabbabaabaabbababbaaaaaabbabbbabbababaaaabbabaaaaaababbbabbaabbbaabaaaabaabababbaabaaababbbbaaaaaababbaaaabbaaaaaaaaabaaabaabbaaaaabababbbabbababbbbbbbaaabbbbaaabaabaabbabbaabbababbaabbabbbaaabaabababbaabbabaabbabaaaabbabbabaabaabababbbaabaabaaababbaaabbbbabbaabaaabbbabbabbaababbabaabbabbaabababbabaaaabaaababbbabbaabababababaaababaabbbaaaaaaabaaabbbabbabaaaabbaaaabaaababbaabbaaaabbbbbaaaaabaaabbbaabaabbabbbaabbbaababaaaaababaaaaaaabaaababbbbabbbaaabaaabbabbabbbbabbabbabaaaaabaaabaaabbbababaabbaababbbbabbbaaaaaaaaaababaabaabababaabbaabbbababaababaabbababbbaabbaabbbabbbaaaaabbaaabaabababbaaabaabbbaaabaaaaabbaabaabaababaababbbaabbbaaaabbbabbbaabbbbbbbaaaaaaaaaabbaaaabbbabababbbababbabbabbbaababababbbbbbababbbabbaabbababbaaaabbaababbaabababbbbababbbaabbbabaaaabbaaaabbaabbaaaabababaabbbabbabababbaaabbbabaaaaabaaabaaababbbababaaabbbbababbbabaaabababaabbabbabaaabaabbbabbbaabbabbbaababaaababbbababaaabbaababaababbaabbababaaaaababababbaabbabaaaaaaaabaaaabaaabaabbaaabbabbbababbababaaaabbbbabaaaabaaabaaabbbabbbabaaaaababaabaabababbbbbbbaaaabbaaaaaabbbaaabbabaabbaabaababbbaaaabbaabababaabbabababbbaababbaaabbbbaaaababbaaabbbbabbaabaaaababbaababaabbaaabbbbabababaabaababbbbbababbabbabaaabaaaaaabbabbbbabbbabbbabaaaabbaababbabaaaaabbabbbbbaaabbabbaaaabbaaabbaababaaaaaabbbabaaabbabbabbbabbbbaabaaaaabaaabaabababaabbbbbabaaaabaaababbbabaabababbaabbaababbbbbbabbbbbabbbbbababbbabbaabbbbbaaababbabbaaababbabbbaaababbababaaabbbbababbbbbbaababaabbababaabaaaabbaabaaababbaaabaabbbaabaaababbaabbaabbbabbababbababbaabbbaabbaabbaaaabaabbbbababbbabbabbaaaabbabbbbbbababaababaaaaabbbababbbbaaabbabbababbbbabbbaabbabbbaaabababbbbaabbbabaabaababbabbaaaabbbbaabbabbbbabaaabbabbaaabaaaababababaaaabbbbabbaabbaaabababbbbbaabaababaaaabbaababbaababbbabaaaaabbaaaabaababbaababbababbabaaabbbabbaaaababbabbabbaababbaaabbaaabbaabaaababaaabbbbabbbbbababaaaaabbbaaaabbbbbbabbbbbaaaaabaaaaabaabbbaaabaabaababbbbbbabaababaabbaaaabbabaababbbaabbbbababbbaabaabbababaabbaaababbaaaabbabbbaabbbaaaaabbaabbbbbbaaabbbababaaabbbbaaabbbaaaaaaabaaabaabbbbaabbababbaabbbaaaababbabbbbababbaaabbaabbaabbabbbabbabbbabaaabaabbabababbbbbabbabbaaaaabaabbaabaaabbaabbaaabaabbbbaabaaabbaaaabaabbbaaabaabababbaabaabaaabbbabbaaabaaabaaaabaabbabababbbbabbaabbbaabbbbaaaaabbbbabbabababaabbbababaabababbbababbaaaaabaabbbaabababbbababaaaaaaabbbbbaabbabababbabbbabaaabbbbabbabbbabaaaaabaabbabaabababaaaaaabababbbbaaababaaabbababbabbabbbabaabaaaaaaaabbbaaaaabbbaaaabaaabbababbbaabaababaaaaabaaabbbbaaaabbbbbbbbaabbbbbaaabbbbaabaaaababbbbaaaaaabbbbbbbaabbaabbbbbbbababaabbaababaaabbbbbbaaabbaaaaaababbbbaaabaabbbbaabaabababaaaabbbabbbaabbbbbbabaaabaababbaaabbaabbbabaabbbbaabbbaabbaaababbbabbabbababbabaaabbaaaaaabbbaaaabbbabbbbaabbababaaaaaaababaabbbaabababababaabaaabbbbbaaabaababbabbabaaababbbaabbbaabababbbbabbbabaaabbababbaaaabbaaaaaabbaaaabbabaabbbaabbabbaabbaabbabaababbbaaaaaabbbbbabbbbbaabababbbbaaaabbabaaabaaabbaaabbaabbbbabaabaabbabbbbabbababaaabbaaabaababaabbbaaaaababbaaabaababababbabbabbabbbaaaaaabbaaaaababbaaaababbbbbbbbbbbbbaaaabbaabaaabaabbbabaaaaababbbbbbaabbaabaaaabbababbaaaaaababbbbabaabaaaaaababaaabbabbbaababababbaababaabaabaabbbaabaaabbbaaabbabababaaaaabbbbabbababaabbbabbbbabaaababbababbbbbbbabaaaaabbbaabbbbaaaabaaabaabaaabbababbababbbababbbbaaaababaaaaababbbbbabaaaabbbabaaaaaabbabbbaaabaaaaaabaaaaabaababaaaabaabbaabbaaaabbaababbaabaaabaababbbbaaaabbaabaabbbaaaaaabbaabbabaaaaaaababbbaabbbabbbbbbaaaababbabbbababbabaababaaaababbbaabaaabbabaaabbbababaabbababbabaabbbbaabbbbaaabaabbbababaabaaaabaaabbabaabbabababbabbaabaaababaaabbaaabbbbbbbaabbababbaaabbababbaabbaaaaababbaabbbbaaaabbaabababbabbaaaaaaaaabbbbbbbabaababaababbbabbaabbabaaaaaabaababaaaaaaaaabbabbbbbabbaaabbbabababbbbabbbababbbbbbbbabbaababaaabbbbbbabbbbbabbaaabaabbbbbbabaabaaabbaabbbabbabbbabaababbabbbbabbbabbabaabaaaabbabbabaaabbababbbababaabbababbbbabbabaaaaaaabaaaabbbbabbbbaaaababbbaaaaabbbaabbbaabbabaaaaababbaaabbbbabbabbababaabbbbbbbbaabbbabbaabaabbbaabbabaaabbaaaaabbbabbbbaaaabaaabbabbbbaababbbbbabbbabaaabbbaabababbbbbbaabbaaabbbbbbaabaabbabbabbabbbbbabaaaaaabaabbbaabababbabbbabaaaaabbabababbbbbaaabaaaabbababaaabbaaaaabaabaabaabaabaaaaabababbababababbbabbbbbaaabbbaaabbbabbbaaaabbbbbbbbbbaabbbababbbaabaaabaaaabbaababbbaabbaabaaaaaaabbaaaaaaaaabbaaabbbaaabbababababaabbbbaaabbabbbabaaaabbabaababaaaaabbbabbbaababbaaaaabbbbaaaabbaaaabbbbbbbbbaabbbabaaabbbabaaaaaaaabaaabbbbaaaabaababbabbbbabababababbabababaabaabbbbabaabbbbaababaabaababbabababbbabaaaaaaabbaabbababbbabbbaabaabababbabababbabbbbabbaabbbaabaaaaababbbabaaabbaababbbbabaababbabbbaabababbaaababbabbaaaabaaabbbabaabababbabbaabaaaabbabaaabaaaaabbbbbaaabbaaaaaaabbabababbbbabbbbbbbbabaabbababbaaabaaabbbbbabbbababbaabababaabbbabbaaababbbaabaaaaababbbaabbaaaabbabbabbaaaaabaabbbbbbabbaabbbbabaabbaabaabbaababaabbaabaaabbbbbabababaaaabbaabbaaaaaabbabaabbabbabbabbbbabbbbbbbbaabaaaabababbaabbbbbabbaaabbbabbaaaabbaaabbbaaababbabbabbaabbabbabbbbaababaabaaabaaaababaabaabbbbbbbabbbbbbaaabbabbbbbbaabaabaaababbaabaaabbaababbbbaabaaaabbbabaaaababbaaabbaabbaaabbaabbaaaaaabaaabaabbaababbbbbbabaabbbbbbbbaaaaaaabbbbabaaaababaabbbbaabbbbaabbbbbbbaababbbbabbabbaaaabaabaaabaaabaabaabbabbabaaabaaaaabbaaabbababbababaabbbabbbababaabbbabaabbaaababaaaaabaabbbabbabbbbaaaaabbbababaabaaaabababbababaaaaababbbbabababbaabbbbabbbabaabbaababbaaaababbbbabaaababaaabababaaaaaaababbaabbaababaabbaababbaaabbabbaabbbbabbbaaabbbbaababbaaaaaaabaaabbaabbaaaaabaabbbbbbbabbababbaaaabaaaabbbbaababaabbbaabbababbabaabaaabbbbbaaabaaabbabbbbbbabaaabbaabbabaabaabbbaabbbababbbababaababababbbbabbbbabbaabababbaaaabbabaabbbaabaaabaaaabbabbaaaabbababaabbaaaaabababaaaaabbbaababaaaabbaaabbbbaaaabbbbabababbababababbbababbbabbaaaabbbbbabbbabaabbabaababbbaababaabbbbbbabaabababbbbbbabbbbbbbbabbabbbbaaababaaabaabbaabbbaaabbbbaabbbbabbbaaaaaabaababababbbaabbaaabbaaabbabbbbaabbaabaaaaababbbabbbbabbbbabababaaaabbaaabbbaaaabbbbaaababbbaaabbaaababaabbaabbbbbbaaabbbaabbbbbabbaabbaaabbbbaabbbabbbbbbaaaababbababaabbaaaaabbbbbaabbaaababbbbaaaaaabaaaabbbabbbbabbabbbababbababbaabbbaabbabaaabbbbabaabaaaaaabbaabaabbbbaaabababbbaaaaabababaabababbbbbabaaabababbbaabbbbbbbaababaaaaabaaabaaababbaaabaabbaaaaababbbbaabaabbaababaabababaaabbbababbbbaabaababbbaababbaba