abbbabbbbababaababababbabbababbbbabbababbaaaaabaabbabaabbbabbaabbbbbaaabbbbabbbabbaabaabbbbaaababbabbbaababbabaaabaababbabaaaababababaabbbbabbabbaabbaababbbbaaaaabbbaaaabbababbabbabbbbabaaaabbbaaabaaabababbaaabbaaaabbaababbabababaaaaaaaaaababaabbbbbaaaaabbaabbbbbbbbbaaabababaababbababbababbbbbababaaabababaabbbaabbaaaababaababaaaaaabaaaaabaabbabbbbbbabbaaabbaaaabaaaabbbaabbababbabaaaaaabbaaaababbbabaabbbbababaababbbabbabbbbbbaababaabbaaabaabaabbbbababbbababbabaababaaababaaabbbabababbabbabbbaaaababbabababbbbbbbabaabbaababaaaaaaaaabbabbbbabbbababaabbabaaaaabaaabbbbaaabbbaabbaaababbabaabababbaaabbaaabbbabbbbbaabbaababbabaaabbbaaabaababaaabbaabbbaaaaabbabaabbaababbabbababbaabbbbbabaababbbaaababbabbaaabbbaaabbbaaababaaabaaabaabbabaaabbbabbbbaaababbbbbaababbbabaabababbaabbbaaaabbaababbbaaaabababbbabbaaababbaabbbababbababbbaabbbbaabbbbbabbbababaaabaaaabbabaaabaaaabbabaabbbabbbbaabaabbaaaabbaabababbbbbbaaabbbaaaabaaabbbbbabaabababaaaaaaaabaaababbabaabbbabaabbaabbabbbbbbabbabaaaabbaaaabbaabbbaabbaaaaabbabaaaababbabbbabbbbaaaaaaaabaaabbbaabaaaababaabbaabbbaaaaabababababaabaabbbbabaababbabbbaaababbbbaabaaabbaabbabbababbabbbabbabaaaaaabbbababbaabababbabbaaaaaaaaaabaaaabbabbbbbabaababbabbabbbabbbaababbbbaabbbabbabbabaaabaaabbabbababbaaabaabbbabaababbabaabbabbaabbbabbbbbaabaabaaaaabbaabbababbbbabbaaaabaaaabbaababbaabbbbbbbabbaabaaabbbbbabbaabbbbaabaabbabaaabbabababbbabbbbaaababbbaaabbbaaaabbaaaaabaaaabaaaaaabaababaaabbabaaabbbbabbbbbbbaaababbbbbabaaabbbbabaaaaaaabaaabbbaaaaabbabbabbabababaaabaababaabaabbbaabbbbaabbbbaababbbbbbabbaaababaaaababbbbaabbbbabbabbaabaaaabbabaabaaaabbbaabbaabbabbbabbabbabbabbaababbabababababbbaaabbbbabbabbbaabababbaaaaaabaaabbaaaaabbbbbaaabbabbabababaaabbaabbaaabbbaabbbbbabbbbbabaababaabbaaabbabbbaaaaabbaabbbaabbaabbabbaaaabaaaabbabababaaabaaaaaababaabbbbabbbabbbbaabaabaabbbbbababaaabbabbbbaaaabaababbababbaaababababaaabbaabaaabaababbabbbabbaabbbbaaabbaaaaabababbabbaabbbbabbbabbabbbabbbaabbabbbabbaaaaabbbbbbababbaabaabbabbabaabbbabbabbaabbbaabbabbbbabbabbaaaaabbbabaaabaaabaaabbbaabbaaabbbaaabbaabaabaababbbaababbbbaabbababaabababbabbbbbababbbbaaabababbbaabbbbabaaabaaaabaabbbbbabaababaaabaabbaabbbababbababbbaabbbbabbabbabaaabbbbabbababbbabaaabaaaababaaaaabaabaaaabaaababbbabbbbaababbaabaaababaaaaabbaaaabaaababbababbabbaaabbbbaaaaaaaabbbaaaabbbbbbbaaaabbabbbbabbaabbbbbaabababbaaabbaabbbbbabbababbbbbbabaababaaaabbababaaabaababaaaababaabbabbababbbabaaaaaaaababaababbbbbbbaabbabababaaaaabaaabbbbbabbbbbbbaabbbbaabbaaaaababbaabaaaaaaabbabbbaabaaabbaababaabaabaabaaababaaaaaaaaabbaaaabaabbaababbabbbbaabbbabbbaaaabaabbbbbabaaababbaaaaabbabbaabbabbabbaaabbbbbbbabbbbbababaabbabbbbababbabbbbbaabbaabbabababbabbbababbbabbaabaabbaaababababbabbabbbbbaabaabbbbbbabbabaabababbabaabbbbaaaabbbbbbbbbbaaaabbbbbbabababbbbbababbabbababaabababaabaaaabaaabbbababaaabbbbaaabaabbbaabaababaabbbaabbbbbbbbaabababbaabbaaababaabbaababbaaabababbbbabaabbabaaabbbbbbbabaaababbbaabbbbaabbababbbbbaabbabbbbbabbbbababaabaaabaabbaaaaababababbaaaaaaaaaabaababbaaabbbbaabbbbaaaaabbaababaabaababbbbabbaaabbaabaaaabbabbabbbaaababaabbaabaabbaaabaaabababbbbabbaabaabbababaaabbabbbaaaaaaabbaaaaabaaaaaabbbabbbababbabaaabbabababbababbabbababbbabababbaabbabababaabababbbabbabbabaaabbabbbbbbbabaaababaaaabaaabbbbaaabaaabbaaabbbaabaaaaaabbbabbbaabbbabaabaaaabbbbbababaaaaabaabbaabbaabbbabaabbaababaababaababaaaabbbabbaaaabaababbabbbaabaaabaaabbbbaaababbabaabbbabbbbabbbbbbababaabbbaaaababbbbbbaaaabaabaabbabaababbbabbabbbbbaaabbbbababbbbabaabbbaaaaababaabaabbbabbbabbbabbbbbbbbabaababbaaaaabaaabbabbbaabaababbabbbbbabababaaabbaaaaababaaabbbbbbababbaabaabababbaabbabaaaabababbbababbabbbabbabaabaaababbaaaaababbaabababbaaaaaabbababbaaaaaababbbbbabbabaabaabbbaabbbabbbbbbabaaaababbabbbbbaababaabaaaabaaababbaaaabbbbbbbaabaaabbbbbbbbbbaabbbbaabababbbaaababbabaabaaabbbaabaaaaabbbbaabbbbbbaabaabbbbabbbabbaabbaaabbbbabbabbabaaaaaaabbbaaabbaabaaaabaabababbbaabbababbaabaaabbaabaabaabaaaabbbaabaaabaabaaabbbbbbbaabaaababaababbbabbbabbbaabaabbbbbbbabaaaaabbbaaaabbbbbbaaaabbabbaaabbabbbbabbabbaababbababababbabbabbabbbbbbaabbabbbbabaabaabaaabaabbabbaaaabbbaaaabaabaabbbaaaabbbabbbbaaaabababaaabaabbababbbbbbbaaabbbabaaaababaabaabaaabababaabaaabbaababbbbaababbbabaaaaaababbbbaaabaabbbabbababbaaaaaababababaaaaaaaabbabbbbabababaabbbbbbaaaaaaabbbbaabaabbaabbaaabaabaaaabbbbbbaababaaaaababaababbabbbaaaaaaabaabbbbababbaaabaababababaabbabbbabbbabbabaabaaaabbaaaababbaabaabbbbbbbbbaaaaababaabaabababbaabbabbabbbaabbababababbabbbbbbbbaaabaaaaabaaababbbbbbbaaabaaaabbaaaabaaaababbabaabaabbbbababbabbabbbbababbaabbababaaaabbaabbbaaaabaabbbabababbbbbaaaaaabaaabababbabaaaababababaabbababaabbabbaaabaaabaabbaababbbabababaabaabaaaaaabbaabaaaabaaaaabaabbbabaaaaabaaaaaababbbaaababbbbbbabbbbbabbbbbabbababbaabbaaaabababbbbbbaaabbbabbbbaaabaaaabbbabbaababbaaabbabaabbbaaabaabbbabbbbbabbbababaaabbbbbaabababbbbaabaaababaaabaababbaaabbbbaabbbbaaaaabbaaaababbbabbbabbabaaaabbaaaabbbbababbbaabaaaaabaabbbaababbbbabbabaaabaaabbbbabbaaaabbbbbaaaabababbabbabaabaaaabbbabbabaabbaabaaababaabbbbbaabbaaababababbbaaaabaaaabbbbbabaaaabaaabaabbbaaabaabbababbbbbbaababbbbabaabbbaabababaaaabaababaabaaaabaaaababababbbaaaabbbbbbbbaabaababbaaaaaabaaabbbbaabbaababbabaabaaaaababaabaababbbbabaabbbaabaababbabaababbaaaababaabaaabababbbababaaaabbaabaabbaababaabbbaabaaabbaaabbabbaaababbbabaaababbaaaaaaaaabbbbabbabaabaaabbbbbabbbbbbabbaaaabbabaaaababaabbbbbbabaaabaabbabbabaabaababaaaabbbbbbbbbbbbababaabbaabbbbbbbbbabbabaaaababbaabaabbaaababaabbababaabbbbbabaaaaabaababaabbaaaaabbababbaababbbabbaabbbbaaabaabbaabbabaababbbabababbaaaaaaaabbababbbbaaaabaabbbbaababaababaabababbabbbbabbbbbaaaabbbbaaaabbbbaaaaaaaaabbabbbbbbaaaaabbaaaabbbbbbaaabababbaaaabbbaabababbbabbaabaabbbabbaabbbbaabbbabbabbbbaabababbbabbbababaabbbbbaaaabbbaaaabaaabbbaaaabbbbbbbbbaababbbabbabbbbbabbbabbbbbbaabbabaababbbbbaaabbbbbbababbabbaaabbbaabbbbbaabbaabbabbaaabbbabaaaabbabbabaabbbabaaaaabaababbabbaaabaaaabbbbabaaaabbbabaabaabaabaabbbaaabbbabbaabaabbaabaabbbaaaaaabbbabaabaaaaaabbabbabaaaabbaaabbaaabbaaaabababbbabbbbabbaaabaababbaaaaaaaababbaaaaabbabbaabbbbaabbbbabbabbabbbababababbabababbbbaababbbbbbbabbbaaabaaaaaababaaaaaabababaaabaaabaaaababbaaabbbaaabbbbabbabaabaaababbbbaaabbbbbaabbbbabaaabbbbaaabbbbbbbaaaabaababbbaaaabaaababaabaabbaabbaaaaababbbbabbbbabbbaabaaababbaaababbaabbbbbbbbaababbabbabbbbbabbabbbbbbaabbbaabbaabbabababaaabbaaabbabbbababbbbabbbbbbbbabbababaabbbbbbaaaabaaaaabaaaaaaaaabbbbbbbabaaabbabababaaaaaaabaaaaaabbbaababaababbaabaabbabbababbbabbaababaaababbbbabbababbbbbbbbbbaaaabaaaaabaaabbaabbabbaabbaaabbaabaababaababaabbaababbbbbbabbaaabaaabaaabaaaabaaabbabbaaaababaabbbbbabbbabbabaababbaaababaabbabaaaaabaabbbabbbbbaaababaaabbaabaaaaaaaabaabababaaabaabababbabbbaaabbababbbababbbbbbaaaabbbbbbabbaababbaaaabaaabaaabbbababaaaabbbaabaaabababbaaabbbabbbababbbababaabbbabaaaabbabbbbaaaabaabbbabbabababababbbbabbbbababaaabaabbaabbaaabaaabaaaababaaabbbbbbbabbbbaabbbabbbbbbbbbbaabbbaababaababbbabbbabaabaaabaaabbbbbbbbbbbabaaaabaabbaababbaaabaaaaabaabaaabababaabaabbbabbbaaaababaabaabbbababbaababbaaabbbabbaaaaaaaabbbbbabbaabbbbabbabaaaaabaaaababbbbabbbbbbaabbabaaabababbbaabaabababbbbaabbababbaabababbbabababbbaabbabbbaaabbbbbabaaaabbbbaabbbbbbaabbbbaababbabbbbaabababaaababbbaababaaaabbbabbbaabbbababaaaabbaaababbaabbabbbabababaabbbaababbbbbbbbbaaabaababbabaabbaaabbaaaaaabbbabaabaabbababbabaabbabbbbbbbbabababbbaabbabaaabaaabaabbbbabaabbabaabaaababaabbababbbaaaaabbbbaababbbbbaabaaaaababbbbaaababbaaabaabbabaabaaabbaabbbbaaaabbbbababbbaaabaaaaababbbaabaaababaababbbbababaabaabbbbbaaabaabbbaaabaabababaaababaaaaaaaaaabbaabbbbbbaabbabbabaabaaaaaaabaabbabababbbbbaababbbbbabaabaabbabbbaaabaabbaaaabaaababaaabbababaabaabbabbbaabbababbaabbabbaaabbaabbbababbbbababbabaabaabbbbbbaaaababaaabbbbbabbaababaababaaaabbbaaabbbbbbbababbaababbabaaababaaaabbbababaaaabbabaabaabbbabaaaaaaababbbbbabbaabbabaaabbabbbaaabaaaaaabbaaaaaaabbbbababaaabaaaaabaaababbabbbbbbbbbbabbabbababababababbabbababbbbbabbabaababaaaaaabbabbbbabbbbabababbaaabaabbbabaaabbbababaababaabbababbabbaaaabaaabbabaabbbbababbababbbababbaabaabbabbbaaabaaaabbbabaaaabbbbbaababbabbababbbbbaaabbaaabaabbbbababbababbabaabbbbbbaaaaababbaaabbbbabaaabbaabaabaaaabbaababbbbbbaababbbbaaabaaabaabbaababbaaaabbbbabaabbabababababaabbbbbaabbabbaabaaaaaaaabbabaaaabbbabbaabbaaabbabaaaabbbbaaaaaaabbbaaabbbbabaabbbbbbbaababbbbabaababbaabaabaaaaaabaabaaaabbbbababaaabbaabbaaababbbbaababaabaaaaabaabbbaabaaabbbbbbabbabbbbabaaabbaabaabaaabbbaaaabbbbabbbaabaabaaaabababbbabbabbbbabaaaabaabaabaabbaaababaaabbbbbbaaababbaaaaabaabbbbbabbbbbbabbabbabbabaababaabaabaaaabbaaaabaaabbaabababaaaaaabababbbaabbababaababbbbabaaababbbaabaaaabababbabbaaaabbbbbaaaaabaababaabbbbbbbaaaaaaaabaaaaaaabbbabbaabababaaabaabbaaaabbbbabababababaaabaabbaababbaaabbbaabbbbabaaaaaabbbaabababaabaabaaababaaaababbbabbabbbaaabbbbabaabbbaaaaaaaaababaaabbaababababbbbabbbabbbbbbaabbbabaaaaabababaabaaaabbaaaaaabbababbbabbababaaaababbbbbbabbbbabbbbaaabbaaaaabaaaaaaaababbaaaababbbbbbaaabababbabaabbabaabaaabbaabbbabbaaabaabaabbaaabaabbbabbbbbbaaaaaaababaaabbaaabababbbbaaaabbbaaaababababbbaaaaabbbbaaaababaabaaaaabbaabbbababbbabbbababbaaabaabbbaaabbbaaaabbbbaaaabbbabaabbbbbbbababaabaabaaaabbabaaaabbbbbbbbbbbabbaaababbbbbbbaababababaabababababaababaabbaabaabbabbaaabaabbbbabaabaaabaababbaabababaabbbaabbbaaaabbbaabbbbaababbbbbaabaabbaaaabbbbbaabbbbbbabbbabbaaaaaababbabbaaabbbababbaabaaaaababbbaabababbbaaabbabbaabaaabaaababbabbbaaaabbbaaabbaabbaaaababbaabbbbbabbabbaabbabbbbbabbbbabbbbbbabbbaaabbabaabbaabbbabaaaaaaabbbbabbababbaaaaabbaabbaaaaabbaabbabbbbbbaababaaaaabbababbaaabbabaababaaabbbbbaaabaabbaaababababbabaabaaaaaaabbbbababaaaabababaabaabbbaaaabaaaabbaaabababbabbbbabababababababababaaabaaabaabaababaaaaabbbabbaabbabaaabaaabababbbaaaabbbaaaaaaabbbbabbbaabbbaabaabaabbabbbbaabbabaaabbbaabbbbbaabababbbbbbbabbaaabaabaaabaabbbbabbabaaababababbbabbbbbbabbbbbabbababaaabbaabbbababbaaaababbbbaaaaaaaaaaabbababbabaabababbababbbbabababbbbbbbbbaabbaaabbabbabbbabaaabbbaababbaaaabbbbabaaababbaaabbaaaababababbbbaaabaabaabaabbabaaaabaaababaaaaaaababaaabbaaaabbbabbbabbbbbabbbbbbbbbaabbaabbbbaaabaaaabaabbabaaaabaabbbbaabaaabaaaababbababbabaaabaabbbaaaabbbbababaaabaabbbababbaaaabbaabababbbabbbbabaabaaabbbbbaaabbaabaaaabbbbaaaabbaabbbababaaabbabbaabbabbbababbbabaabaabbbbbababababaaababbbbbbaababaaabaaabbaabababbaabbbabaababababaaaaaaabbbbbbbaabababbababbaaabbbbabbabbaabbaabbbbabaabaabbabaaaaaaaabaaaabbbbbbbbabaababaaaaaaabbbaaababbbababaaaabaaabaaaababbaabbaabbababbbaaabbbaaaabaabbabbbabbaabaababaaabababaaaabaaabaababaaaabbaaaabaaabaaabbbbbabbabbabaabbbbbabbaaaaabbbbabaaababaabbaaababaaaaaaaaaaaaabbabaaabbbabbabaaabaabbbbabbbabbabbabababbaaababbabababbabaaaaaabbabababbbbabbabaabababbbbbbbbbbababbaabaaaaabaaabaaaaabaaabbabbbababbbbabbaabbababbbbbbaaabbbbaabbababbababbbaaaaabbbaabaaabbbaaabbbaababaaabbaabbbabaaababbbbaaabbbbbabababaabbaaabbbbbababababbbbaaababbbbaaabababbaaaaaabbaaaaabbabaaababbbaabababbbaaabababaabbbaabaabaaaabaaaaabbabababaababbbabbbaabababaabaaabababbbbbabbaabaabbabbbbaaaabbbabababbbbbaabaabaabbaaabaaaabababbaabbbababbaabbabbbbaabababaaaaaabbaabaaababbbaabaabaaabbbabaaaaabaaaabaabbbaabbbbabbbaabbabababbbbbbbaabababaababbaaabbaababbababaaaabbabaabbaabbabbaabbbaabbaaaabaaabaabbabababbaaabbaaaababaabbaabaababaabaabbaaababbbbbbbbbbaaabbbbbababaaaaabaabbbbaabababbbbbaaababbbaaabbaabbabbbaaaabaabbbbabbbaaabaaababaaabbbaabbabaabbbabaaababbabbaaaabbaaabbbaababbabbabaabbaaabbaabbbababbbbbbbbbaabaaabbababbababaabbaaababbbbbaabbaabbbbbaabbbbabaabbbabbbaaaaabbbbbbabbbbaaaabbabbbbabaaaabbbbabbbabbbaaabbbbaaaaaabbaababbabbbaabbabbbbbabbbbababbbabbbabbbabababbbbbbbbababaabbabbaaaaaabaababaaaaabbbbabbaaaaaabbaabbabbbbbbaaabaabaaaaabbaaaabaabbaababaabbaabbbbabaababbbbabbbbabaaaaababaabbaaaaaaaabbabbbaabbababbbbaaaaabbbabaabaabaaabbabbbbabaaababaaaaaaababbababababbbabbbbabbbaaabbaabbbaababbbbaabaabbaabababbbbbaaabbaabbbbbbababaababbaaabaabaaababaaabbabbaabbabbbbaabbbaaaaaabbabbbabaaaaaabaababaaabbbbabaaaaaabbabbbbabbbababbbbabaabbaaabbaaaababbbaabaaabbbaabbabbaabaabbbaababaaaabbabaabaaabbabbaaaaabaaabbbabaaaaaaaaaaaabbbabbaaabbbabbababaabaaaabaaabaaaaaabbaabbbaaabababbababbabababbaaabaaaaaabaabbabaaaaabbbaabbbbbabbaabbaabaabababbbabaabbabaababaaababbbabaababbbbababbaabaabbabbabaaabaaaaaabaababbaabbbabaaaaaaaabbaaaaabbbababbaaabaaaaabababbaabaabaababbaababbabaabbabaabaaaaaaaaaaababbaaabaaabbbbaaabbabaabbabbabbbababbbabbaaaababbbbbaabaaaabaaabbabaabbbabbaaaabaaaabbaabaabaaabaababababaaabaaaababbbababaababbbbbbabbaabaababbaababaaaaaababaaaaabbaaaaabbbabbbbaaabbabaababbabbbbaaabbababbbabaaabbbbaaabaaababbabbbabaaababaababaababbbbaababbbabbbaabbaabbbaaabababbbabaabbbabaaaabbbbbabbaabbbbbbbbababbababaaabbaaaaabbbabaabbbabababbbbbbaababbaabbaababbabaabbbbaaaaabbbbaaabbbbbaaaabbbbababbaaaabaaaaabaabababaaabaabbbabaabbababaabaabaaabbabaabbbbabbbababbaaabbbbabababaababbbbbbaababbaabbababababbbbaabaaababaabbabbaaabbbbaaaaaabbabaaabaaabbbbabbaaabbababaabaaaababbaaaababaaabbbabbaaaabbbbbbabbaababbbabbaaaaaaabbbaaaababbabbaabbaababbaaabababaaabaabababbbaaaabaaabbabbbbbbaaabaababbbbaababbbaaaabbbbbabaabababbaaabbbbbbbabbababbbaabbbaabbbabababbbaabbabbbababaaabbabaababababbbbabbaabaabababbaaaabaaabbabbaabbbaabbaaabaababbbaaaabbbbaababbabaaabbbabaaabbabbaababbabaaabbabbbbbabbbaaabababbabbbaaaabbbaaabbbabaaabaabbababaababbabbbbaabbabbbbbbaaaababababbbabbaaaaabaababaaabbabbabbaabaabbaabbabbaaaabbabbbabbaaababbbaabbaaababbabbabaaabaaabaaaababbabbababbabbababbabaaaaabaababbabbbbbaabbbbbbabaaaababbababababbaababbaabababbabaaaabababbbaabbaaaabaabaaaaabaababbabaabbbbabbabbaaaaaabbaaababbbaabaaabbbbabbbbbbbaaaaabbbbaaaaaabaababaaabaaaaaabababbbaababbbbbbaabbababbbaaabaaaaaaabbaabaabbbaaaabbaabbaababbbbbbababaaaaaabbaabbaabaaaabaabbaabbbbbbbbaabbbbbbbbaabbbbbbbaabaabbbaaaaabbbbabaabaaaaaabbababbbbababbababbaabaabbbbbaaaaaabaabbaaaabbaabbabbbababbbbbbbbabbabaababbbabbabbbaaaaabaabbaaaaabaaabbabaaabaabbaaaaaaaabbbaaaaaabaabaabaabaaaabbaabababaabbbabbaababbbabababbabaaaabababababbbaaaabbaabaaabaaaabbabaabaabbaabbbabbababaabbaaabbbababbaabbaabbbbbaabbbbabaabaabababbbbbaabbbababbaaabaababaabababaaaabaababaaababbbbabbabbbaaaabbbaabbbbbbbabaabbbaababbbaabbbaaababbbaabaabbbababbaababbbbbababbaaabbabbabbabbbaaabbaabaaaabbabaabbbbbabaabbbababbbbabaaaaaababbabababaaaaaaababaabaabaabbaabbbbbaaabbbabaaaabbaaaaaaabbaaaababaaaaabbbbbbbabaabaabababababbbbaabbaabaaabbbababaababbabbbbbbaabbbbbbababaaaaaabbabaabaababababababaabbbababaaaaabbbaabaaabaababbababbaabbaabbbaabbabaaababbbaaaabaabbbaaaaababaaabaaaaabbaabbbababaaaaababaabbaaabbbbbaababaababaabbabbbbaaabaaabbabbabaababbababbbbbbaaababbababbbaaaabbaaabbabbbabbababaaabbababaabbbbaaabbaaabbaabbabaaabaabbaaabaaabbbaaaabbbabaabbbaababaaababbaabaabbbbbaaabaabababbbbaababbbaabbaaabbbaaaabaaabbabbbbaababbbbabbaaababbbabaababaabbbaababbbbbbbbbaaabbbaaaabbbaaaaababaaaaaabaaabaaaaaaaaabbbabbbbaaababbaabbabaaabbababaababbbabbbbabaababaaabbaaaaaabaaabbabaabbabbbaaaaabaaaabbaaababbabaaaabaaabbbaaababaabbaabbbaababababababbbaabaabbbbaabaaaabbabababbbbbababababbaabbaabbabaaababaaaaaaaabbbabababbbbbbbababaaabbbbabbbaaaaabbabaabbbbabbabbbaabaaababbbabbabbbaaabbaabaaaaabaaababbbbbbbbabaaabaaaaabbabaabbaaaaabaabbbbabbbaaaababbaabaaababaaaaabaaaabbaaaaabbababaababbaaaabaaaaaabbbaaabaababbabaaaabaabaaaababaaaaabbbbabaabbbaabaaabaababaabaabababaaabbbbaaabbbabbabbababbbbaaabbababbabbbabbbbbbabaabbbbabaaaaaaabababbbaababbbababaabbaabaaabbbbbabaaabababbbbababbbbbaaaaabbbbbabaaaaaabbabbabbababaaaaabaababaaaaaaaabbaaaabaabbbbaaaababbaaaaabbbaaababbababaababbabbabbbababbabaabbbbaabbbaabbaababbbbbabbbababaaabaaaaaaaaabbabbbabbbbbbbaaaaabbaaabbaabbbabbbbbbababbbbbbbabbabbbabaabbabbaababaababbbaabbbbbbaabbbaaaaabaabaabbaabbbaabaabababbbabaabaabbbbaabbabbbaababababbbaabaaababbbabaaaaaaaaaaabbabaaaaaaaaaabbabbbbbaaaabbabbabaabbaaabbbababbaaabaabbbbbbabababbbaababbabbbbbaaaabbaaaaabaabbaabababbaabaaabbabbbbbaaaaabaabbbaabaaaabababbaaabbbbabbaabaaaaaaaabbbabbaabbabaaabaabababababaabaabbabbbbaabbbbbaaabbbbbbbabbbbbabbbabbbbaaababbabbabbbbabbabbbbbabaaaabaaaabbaaaabaaaaaabbbbababbaaabbbbbabbababababaabbbabbababaaabaabbaabaabbaabbabbabaaababbbaaabaabaaaabbababaababbabaabababbbbbababbbababbaabaababaaabbabbaaaabbbaabbabaababaaabbbbbbaababbaabbabbabbbabbaaabbababbbbaaaaabbaaaaaaabbbaabaabaaaabbabbaabaaaaabaaaabbaaabaaabaaabaabbababbabbabbabbaabbaaabababbbbbbbbababaabbabaabaaabaabaaaaabbbbbbbaababaaababababbbbaababbaaabbbabbbaabaabababbabababbbabaaabbbaaabbaababbabbabbbbbabbaaaabbabbbbaababbbbabaabaaababaaaaabbbaabbbaaaaaabaabbabbababbbbbaaaaabbaababaaabababbabbbbbaabaabbabbbababbbaaabaabbbbbababbbbbbbaaabbbabbbbabbbabbabaaabbaaaabbaaababbbaabababbbababbbabbabaabaaaaaaabaabbbaabaabbaabbbaaaaaabbaabbbbbbabaababaaaaabbbbbbbabaabbbbbbbaababbbabbbbaaababbabababbababaababaaabbaababbaabaabbaabbabababbaababbbabbabbbbbbbabaaaaabaaabbbbabbbbaabababbaaaaaaabbabbaaabbabbbabbaaaaababbaabaabbbbababbbababbbbbbbbbabbbaaaabbaabbbbababaaaabaabaaaaaabaabababbbaabbababbaaaaabbbabaabbababaaabbbbabaaabababbbabbbbaaaabbaaaabbbbaabbbbbbbbbbabbabbabbaaabbbaaabbaabbabbbbbababbabbaaabbbabaabbaababbaabaaabbaabaaaaaabaabbbabaabbbababbababaaabbbaabbabbbaabaababaabbaabbbbbbabbaabaaabbaaabbaababbbaababbabbbabbaaabbabababbbbbaabbbaabababaababaabaaaaaabbababaaabbbbaabbbaaaaabbabaaabbabbaabababbaababbbbbaabbbbbbabbbbababbbabbbabbbbaaabaabbbaaaaaaabbbbbbaabaaaaaabbbbbbbabbbaabaabaaabbbababbabbabbabaabbaabbbbbababababbabbabbbabaaabaaabbbbbaaaababbaabbbaabaaaabbbabbbaaababbbaabaaababbabbaabbabababbabbbaaababababbbbbbababababaabbabbabaabaabaabbabaabbbbaaabbbaaababaaaabbabbbbaaabbbbaaaaaabbaabbbababaabbaabaaababbbabbabbabbbaabaababaaabababbbbabbbbbabaaabbbababababbaabaaabbbbabbbaaabaabbbbababbbaabababaaaabbabbbaaaaaabbbbbabbabaabaabbabbaabbaabbbbbaaabbaabaaababbbbbaaababbbababababbaaaabbbbbaaabaabaaabaaaabaaababbbbaaaababbbbaababbbbabaabaaabbaaaaabbaababbbababababbaabaabbbaaaababbaaabbbbaabbbabbbaaaaaaaaabbbaaabbaaababbabababbaaaaababbbabbabbbaabababbbbbbbaaabbabbaabbabbbabbaaaaaabbabbbaabaabbaaaabbbabbabaabaabbbababbbabbbbabbbbbbbbabaaababbababbbbaabaaabbbaabbabaabbaabaaaabaabaababbabbbabaabaaaaabaaabbaaaaabababbbabbabababaaabaaabbaaabbabbbabbabbbaaabbabbbaaababbabaaaaaabbaabbabbaaababaaaaabbbabbabbaababbaabbabbbbabbabbaaababaababbababaababbababbaababababbabbaaaaabbbaaabbbabbabbaaaaaaaaababaabbabaaaaababbbabbabaabaabbbababaabbbababbababababbaabaaabbabaaaabbbaabbaaabaaabbbabaaaaaabbabaaaaabbabbbbbbaaaaababababaabbbbaaaabbaababbababbbbaaaaaaaabbabababbaaaabbaaaaabaabaabbbbaaaabbabaaaaabbaaabbaabaaabbabbbbaaabbbbabaababaabbbabbabbbbabbaabaabaababbabbbababaaababaaaaaabaabbbabbbabbabaaabababaabbbbbbbababaaaabaabbabbbbbbbbaaabaabbbbabaaaaabbbbaabaaaabbabbabaabbbabbabbaabbbbbbabbaaababaabababaaaabaabaaaaabaabbaaaabbbaaaabaaaabbbbabaaaababbbababbaaaaaabbbbabbaabbbabbbbbbbaabaabbbbaaaabbaaaabaabbaaaaaaabbabababbaabbaababbaabbbbbbbaaaaaabbabbababaaabbbbabbbabbaabbaabaaaabbbbaabbbaaabaaaabbaabbaaaabbabbaabaaaaababbbbaaaaabaabbbbaababbaaabbbaabababaabbbabbbabbabbaabababbababbbbaaaabbbaabbaabaaaabbaabbaabaaaababbbaabaaaaabbbbaabbbbbaabaabbabaaabbbbabbbbbabaabbbabbaaabaababbbabbaaaaaaaaabaaabababaabbbababbbabbbaabbbaaaabbabbabaaaaabbaaababababbbbbbababbbbababbabaabbbbaabaaaabbbbaabababbabaaabbbbbabbbaaaabbbababababaaababbbabaaaaabaaababaaaaababbaabbaaaaabbaabbbaaaabbbbaabaabaaabaabbaabbabbabbaabababaaaaabaabaabaaaaaaaaaababaabaabbaaabbbbbbabaaabbabbabbbabbbbbbbaaaababbabbbaabababaabaababbabbabaabaabbabbbaaaababbbbaaababbaabbbabbabaabaabbbaababbaabbaabbaabbabaabaabbabbababbabbbaabbbabaabaabaaabbbbaaabaaaabababbbabaabbbbbabbaabbabbbababababbbabbbbbabaababbaabbbbaababbaabaabbaaaaabbaaaaababaabbaaabaaaaaaabbabbbbbbababaaaaaababbbaabbbbbbaabbbaabbbaaabbbabbaabbbbabbabbabaaaaaabbaabbaaaaaaaaaabbbaabaababbaaaaabbabaaabaabaaabababbababbbaabbbabbaaabaabaaaababbbbaaabbabbbbaaabbbababbbbbaabaaabbbbbababaabaaaaaaababababbabbaabaabbabaaabaaabaabbbbaaabaaaabaaaaababbabbababbaaabbbbaabbbabbaabbaabbaaaaaabbbbaababaababbbbbbbababbbaabaaaaabbbabbbaaabababbbbbaaabaaaabaabbababbbbbbaabaaaababaabaabbbaabaaaabaaabbabbaabbabbabbbbbaaaabbabababbaabbabbabaaabaabbbbbbbaabbbabbbabbbaaaaababbbaabbbaaabbabbabaabaabbbaaababbababababababaabbaaabbbaaabbaabaabbabbaabbbbbabbabbbabbbaaaabbabaaaabbabbbabaaaaabbbaaabbbabbaabaabbbbbaaababbaaaabbbbbbabbbbabbabbbabaaaaaaaaabbaaabbbbbaabaaabbaababbbabbaaaabbaaabaaaabbbbabbbbabbababaaabbabababbabbbbbbbbbaaabbaabbaaaaabbbababbabbaabaaabaabaabaaabaabaabbababbaabbbaabababbbbabbbbbbaaabbaabaababaababababbbbabbaabaaaaabbbbaaaaabaaabbbbaabaaabaabaababbbabababbaaababbabbabababbababaaaaaabababbbbababbaabbbbbbbbbbaaabaaaaabbbabbbaaaabbaaaabbabababaabaabababaababbababbbbbaaaaaaabaabaabbaaaaaaaaababbbbabbabbabaaaaaaaaaaaaababaabbaabaaaaaaabbbaabbaaabaababaaaaaabaaababababaaaabaabaaabaabbaababaaababbabaaabababaababbabaaabaaaababbbbabbaaababbbaabbbaabaaabbababbbbaabbbaabbabaabbbaaaaaababaaabababaabababaabaababbbbbbbababaaabababbaabbbbaaaaabaababbaaababbbbbabaabaaaabbbaaaabaabbbaabaabbabbaaaaabaaaaaaaababbaaaabbabbabbbbbabaaabbbabbaabbbbbabbbabbabbbabbbbbabbbbbbbaaabbababababbaaabababbbabaababbababbbbaababbaabaaabbbabaabaaaaababaabaabaaaabbaaaaabaaaabbaaaaabababbbaaabaaaabbbabbbaaaabbaabaababbaaaaaabbaaaabbbbbabbabbabbaaaaaabaaaabbbaaaaaaaabbbaabaaababbaabbbbbbbabbabaaabbabbbabbababbaabaaabbabbbaabbaaabaabbbbbbbaaabaaaabaaabbbbbbbaaaaabbbbabbabbbaaabbbaaaaaaabbaabbbbbaabbbabbbabbababbaaaaabbaabbbbaaaabbbbbbaababbaaabbbbabbabbbaabbbbaabbbbaabbbaababbbbabaaabababbaabbabbaaaaabbaabaabbbbabaaaaaabbabbbababababbbbaabbaabbababbaabbaabbbaaaaabbabbbabbaababbabbaabaabbabaaababbaaabbbbbbbaaabbabbaabaaabbaaaaaabbbbbbbbbbbababbaabaaaaaabbaabbabbbabaabbbaaaababaabbaaabbabbababbbbababbbaabbbbabbbbbabbbbbabbaabaabbbbabbababaababbbabbaaaabbababaabaaaaabbabaabbabbbbbaaabbabbbabbabbbbbabbaaabbaaabbbbbaabaabaaaababaaabaabbabaabbababaaaabbbaaabbbbbbabbbabaabbaabbaaaaabbbbbaaaabbabababababbbbbaababaababbabaaaaaabababaaaabaaaabbaabaababaabaabbabbabaabbaabbaaabaaaabbbabaababbbaaaabababbababbabbaabbbbbbbbbabaaaabbabaabbabbbbabbbbaabbabbbabaabbaaaaabbababaababbababaabbbbbaabbaaaabbbbbabaaababbbbbaaabaaaabbbbbbaabbbaabbbaabbaaaaababaabbaabbbaabbabababaaaabbbbaaaabaaabaabaaabbaabbbaaababababaaaaaabbbaaaabbaabbabaaabbbbbabaaaaabbbabbbabbbbaabbbbbbaaabaaaaaaaaaaaabbbbbbbabbabbabbbababaababbabaabbababbabbabababbaabbabaababaabbabbaaabbbabbbaaaababbaaabbbbbbbbaababbaaabbabbabaababbbaaaabaabbabaababbbbbbbbabaabbaabaaabbbbabbbaaaaaaaaaaaaaaabaaaaabbbabababbbbbabaababaaabbbbbbaabbaabbbababbbbaabaabbaaababaaaaaabbabbabababaaabaaabaabbabbbbbbabbabaaabababbbbaaabbbbabaaababaabbabbbaabbaaabababaaabbabaabaababaaababababaaaaababbbaababbbaaaaaabaaaabababbaabaabbbaaaababbbabbaaabababbbbbbabaaabbbaaaaabbaaabbaabbbbaaabababbaaabbbbbababbaabbbababaaababaaaabaaabbabbbaaabbaaabababbbbbaabbbabababababbbaababbbbaababbaabababaaaaaababaaabbbbabaababbabbbbababbbabbababbabaaaaabaaaaaaabbbaabaaababaabbbbbabbbaaaababbbaaabbabbbbbbaabbaaabbbbabaaabaaabababaabbbbbaaabaababbaabaaabbaaabaabbabaabaaaaabaaaababbabbbaaabbaabbaaabbbaabaaaaaababbaabbaaabaabbaaaababbaaaabbaababaabbabbabbbaaabaaaabbaabbbbababaaaaabaaababbaabbbabaaaabbbbbbbbaabaaaabbbaabbbbaaaaabbbbbbabbbabaabaabbabbaabbaabaabaabbbbbababbbaaaaaaabbaabbabaabbbbaaabbabaabaaababaaaaaabbbaaabbaaaaaaabbbabbaaabababaaabbababbabbbbabbabbabaaabbaaaaabbbaabbbbbabbaabababaababbbaaaabababababbaabbabbbaabaabbbabaaaaababaabaaaaabbaabbabbbbabbbbbaaabaaaaabbaabababaabbbabaabaababbbbbabaaaabbbaabbbaababbbbbbbaabaaabaaaaaabbaaabbaabaabbbbaabbbbbbaabaaabaabbaababbaababababbbbabbbbabaabbaabaabbabbababbbaabaababababbaabbaababbbbabbbabbbbabbaabbbaaababaaabaabbbbbaaabbaaabbabbbaabaababaabbbbbabbbbaaabbbaababaabbbbaabbabbbaabbababaaaaabbaaaaaabaabaabaaabbaabbbbabbbbaababbabaabaabbbaaaabbaaaabbababbbaaaabbbabbaaabbbaaaaabaaabbbabaabbaaaaabbaaabbaaabbbbaabaaabbbbaabbababbaaabbbbaabbbaababbbabaabbababbaabbbabababaabbbaabaabbbaaaabbbbaabaaaaabaaabababbbbaaabaaabbbaaabbababbabbabbbaabaaabbbbbbbbabbbaabbaabbbaabaaaababaaaababbbbababaabaabbbbabababababaaabbbbabaaaabaaaabbaaaabaabbaabaaaabbbbabbbabbabaabaabbaaaabbbbabbbbbbabaabbabbbabaabaabbbaaaabbbbbaaabaaababbbbbbaabbbbabaaabbabaabbaababbbbbaabaaaabbbbabbbaaaabaabbaaabaababaabaaaaabaaabbaaaaababbaabbbbbbbbbabbabbbbabababbaaababaaabaaaaabaaabbbababaabaaaababbbbabbaaabaabaaaaabbbabbababababaabbbbaaababbbababbaabaabaaaaababbaabbbabaabbbaaabaaaabababaaabbaaaaabbababaaaaabbbaaaabaaabbababbababbbbbaaaaababababbbaabbbbbabaabaaaabbababaaabbbbaabaaabaabbbabaaabbaaaabbaaabaababbabaaabbabbaaaabababaabaabbbbaabaabbabababbbbabaaabaaaaabbbbbaababaabbaaabaaabbbbabbababaabbbaaababbaaabaabbbbbabaabaabbbaabbbbabbababbabbbabbbababbbabbbbabaaabbbbaaababbaabbbbabbbaaababbbbbbaabbbbbbbaaabaaabbabaaaabbabbabbbbababaaaaaabbbbbbbbabaabaabbbaabaaaaabaaabaaaaababbaababbaaabbaaababbbaaaaababbabaabbbbabbbaabbbabaaaaababbbaabbabaabaabbababbaaaaababaababbbbbbbbaabbbababbabbbabaabbaabbbabbbabbabbabaababaaababbaaababaabababababbabbaabbaababbabaabbbabbbbbbabbabbabbaaababbbbbabbaaaabbbbaaaaababbbabbaabbbabbaabbbbbabbbaabbbaababbbaabbaabbaabbabaabbbbaaaababaabbababaabbbaaaabbbabaaaabbaababbbbabaaababaaaaabaabbaaaababbbaaabbabbabaabaabababbaaaabbbbbbabaaabaaabbaaabbaabbaababbaaaabaabbabababbababbbbbbbabbaaabbabbaaaaabbababbbbabbbbabababaaabaababbaabbbbbbbabbaaaabbabaaaaaabbbaababbaabaaabbbbbabbbaabababbabbbabbbaaabbaaabbababbabbbbabbbbbbaaaabbaabaaaababbabaabbbbbbabaabbbaabbabbaaaaaabbaaabaaabbbaabaaabababaaabbbbabaaaabbaabaaabbaabbabaababababbbbbabaaabaaaaaababbabaaabbabbbaabaababaabaaaabbabaabaaabbbaabbbabbaaabbbbabbaaaaaabbababaabaaabaabababbbbbbabbbaabaaabbbbbababaabbbbaabaaabaabbaaabbabbbaaabbbaaaaabbabbabbbbaabbaaabbbbbbababbbbbbaababaaaaabaaabbbbababaabbaabaaabbabbbbbabbbbbbabbbababaabaabbaaabbabbabbabbabbabaabbaabaaabbaabababbaaababaaababbabbaabbbaabbbabaabbabbbaaaaababbbabaabbaabbabaabababaabaaaababbaaabbabbaabbbaabbbabaabbbabbaaaaabaabbbabaaababbaabaababbbbbbbbabaabbabaabbababbababbbbabaabbbbbbabbaaababbaabaabaabbbbaabbbbaababaabbaabbbabaaaabababbbabababbaaababbabbbabbbbbaaaabaababbabbbbbaaaaaabababbabaababbbaaababaabbbbbabbbbbbabbaabababbbbbbbabaaaaaaaabbababbbaaabaaababbabbbbabbbbbabbababbaaaaaaabbaaabababbaaaaaabaabaabbbaaabaabbaaaababbaababaababbbaababbaabbbaabaaabaabbababaaaabbaabbbbbbaabbbbaaaabbabbbabbaaabaaabbaabaabaaabaabbabbbbaaaabbaaaabbbbbababbbababbabaabbabaababbbbaaabbbbaaabaabbabbbabaababbaababbbaaaabbbaaabbaaabbbbababbbaaabbbabbbabbbbbbabaaababaaaabbabbbaabaaaabbbababbbaaaabbabbbabbaabaabbaabbbababbaababaabbbabbbbbabbbbabababbabbbababababaaabaabaabaabaaaaabababbabaaaaaababaaaaabaabbbbabaaabaaabbbbbbaaabbaabbbbaabaabaaabbbbbaabbabbbabbbabbabbbbaabababaaabbabbbabababbbabbaabbbbaaababbbbaaabbbabbbabaaabaaaaaabaaabbbbaaaabbbabbaaabbabbabbabbbbabbbbaabbbabbabaababbbbaaababaabaaaaabbabaababbbbbaabaabbbbbaabaaaaaabababbabbaaaabbbababbbbbabaabaaabbabbbbabbbbbababaaabbabaabbaababaabbbabababaaaaaabaabababbbbabaaaabbababaabaabaaaababaabababbbabaabababbbaaaabbaaaaaabaabbbbbbaaabbbabaaababbaabbaabbaabbbababbbbaabbaaabababbaabbaababbbaaabbbaaaaabaabbaaabaabbbababaaaabbabaabbbaababbbaaabbbabbabaaaaaabaabaaaabbabaaabbbaaabababbbababaabaabbbbaabbbbbabaaabaabbabbbaaabbbbbaabaababbaabbbaababbababaabbbaababbbbaabaabababbbbbaababbbbbaaaaaabbbbbaabbbbbabbaaaaabaaaaaabbbabbbbbbaababbbbbabababababaaaabbaaaaaabaabaabbaaabbbaaabbbbbabbabbaaabaaabaaababaababbabaabbbbbaabababaababbbbbabbbaabababababaaaabababbabaabbbbaaabbaaaababaababbbbbaaabaabbaaababbbababbbabbbababaaabbbabaaabbaababbabaaaababbaabbabbaaaabbbbaaaabbbaabbbabbabbaaabbaaabbbbbbbabbbabbabaaaabaaababaaabaabaaaaaaaabaaababababbaaabbabbbaaababbbaabaaabbbbaabbaabbaabbbababbaabbbabbbabaaaabaababbabaabbbbbaaabaaaabbaaaaaabbaabaababbabaabaabbbabbbbabaaaaaabaaaababbaaabbbabbbbbbbbaaaabbaaaabbbbbbbaabbbbabaababababbabaabaaabbabaaaabaaaaaabbbababbbaabbbaabbbbabbaababbabaaabbbabbaabaaaaabaabbbaababbabaabababbbbbaabbbbbababaaabbabbbbbbbbbabaaaaaaabbbaaaaabaabaaabaaaaaaaaabaabbbbbbbaababaabbabaababaababbaaaaaaabaabbaabbabaaabaaabaaaaaaabbbbaaabbbaabaabbabbbabbabbbaaabbbababababbbbaaabaabaabbbbaabbbbbabbabbbbaaaabbabbabaabbaabbbbaaababbbbaabbbaabaaabbaababababbbabbbbababaabbaaabaabbbaaabbbbabbbbbbbbabbbababbbaabbaaaaaabbabaaaaababbbbaabaaabbababbaabbaaabaababbbbbbbbaabbaaabaabaabbaabbabbbababababaaaaabbabbbaabaabbabbabbaabbaababaabbbbabaaabaaaabaabaabbbaabbaabbababbababaaabbaabbababaabaababbbaaabbaabbabaaaaaabbbaabaaabaaabbabaaaaaaabbbaaaaabbbabababbabbbaaabaababaababaaabaabaaabaaaabaabbbabbababbabbbaaaababbbbababbabbbabbbbbbaaabaabaabbbbbbbabbbabbabaaabbabababbabbaaabbaababbaababaaababbabbaabbbbbbbabbaaaabbabbaaabbabbbabbabaaababbbbbbaabbaabbbbaabbaabbaabbabbabbabaaaababbbaabbaabbaaabbabaabbbbbababbababaabaabababaaaaabaabaaabbbabbbbbabaaabbaabbbbabbaabbbabbbaaabaaaaabbabaabaabbaaaaaaaabaaababaabaababbbaabaaaabababbbbabababbaabbbaabababbaababaabbbbbbbabaaaaaabbabaabbaaaaabbbaaabbbbbaaabaaaabbabbababbaaaabbabaabbabababbaaaababaaabbbbbabbbababaababababaabaabbbabbababaabaababababaaabbbbabbbababbaabbabbbaabbaabbbaaabbbababaabbaabababbaaababaabbabbaabbaaabababbabbbbaaabbbbbaaababbbbbbabaabbbbaaabaaabbaabbbbaabababaabbaabaaabbbaaabbbabbbbbabababbbbbaaabbababaaaaaaabbbabaabaabbbaababbbbbabbaabbbaaabaababbaabaaaabaababbbaabbbbaabaaabbbaaababaaaaabbaaaaaababbaabbbbbbbbabaaaabbbbaaaabbaabbbbabbbbabbbabbbabaaaaababbbbaabababbbabbabababbaaabaaabababbabbbabbababbbabbaabaababaababababbababbbababbbabaaabaaaabaaaaabababababaaaabbbaababababaabaaaaabaaabaaaabaabaababbbabbbbbababaabaabababaaaaaabaabbbaabbabbababbbbaaabbbbbabbababbabbabaabaaaababbabbbbabbaabaaabbbabbabbaabaabbabbabbaabbaaaaabaaababbaaaabbbaabaaaabbbbabaaababaaaaaaabaabbababbaaaaababbbbabbbbbaaabbaaaabbabbbbabbabbabbabbabaaabaababaaabbabbbbabaaabbaabbabababbbbabaabbbbbbaabbaabbbbbbaaaabaababaaabaababbbbaabbabbbbbababaaaabbbaabaaabbababbababbababaaaaabbbaabbbabbbaaabaabbaaaaabaaaaaabbbbbbabbbaabbaaabaaaababaaabbbabababbbaabbbbababaaababababbaaabbbaaabaaabbabbabaabbaaabbbababaaaabaabaabbbbbabbaaabbbbabbbaabaabbbbaaaabbbaaaaaababababbabbbabaabbabbaabaaabbaaabbaaaabaaabbabaaaabbbbbbbaabbbbabbbabbaabbaabbabababbaaaabaabbabbaabbbbbabbbbaaababaaabbbbabbaabbbabababbbbaabaaabbaabaabbbaaabbbbbbababaaabbaabbabaabababbaaaabbaabaabbabaaabababbaabaaabaaaabaabaaaabaaababbabaaaaaaabbbbbabbabbbbbaaabbaaabbabaabbababaaabababbabababbbabbabababbababbbbababbbabaaaabababbabbbbbbabbababbbbbaaaabbaabbbbbbbaabababbbbbbbaabbaaabaababaaabbbabaabaaabbabaaaababaaabbaabbaaaaabbabbbbaabaabbabbababbabbaaaaabbabaabbabaabbbababbaabaaaaaaabbabababaaababbabaabababbbaaaaabbbabababaaaabbbbbbabbbaaaabbbabbaabbabbababbabaabaaaaaabbaabaaaabababaaaaaaaaabaabbaabababaaaaaaaaabbababaaabbbabaaaabbabaaabbbbaaabbbbbaabaaaabbbbbaabbabbabbbabababbababaabbbbaaabaabbbbabaabababaabaabbbbbbbabababaaabaaabaabbaaaaabbbabaaaabbbabbbbabbabbabbbaabbbbaababaabaabaababbaabbbbaababbababaaababaabaaaabbabbbabaabbabbbaaaababaaaabaabababbabaabbabbbbabbaabbbaababaabababbabaaaaabbbbaabbbbbaabbbbabbaabbaabbaaabbabaababbaabaaabaaaabbbbababbaaabbbaaabbabaabbbabbaaabbaabbaabbbbbbbbbbbabaabbbabbaaabbababbababbaaabababbabbabbbbbababaaababaabbbaabbaabaabababaaaaaaabbbbabaaaabaabbabbabbbabaabbaaaaababaaababbaaababaaaaaabbabbaaabbbababababaaabbbaaababbbbaaababbababbaaabaaaaababbbbabbbababaabaabbbbbbbababaabbbabababbaabbbbbabbabbabaaaabbaaaaaabbaababbabaaabbbabaabaababbbaabaabbbbababaabbbabbabbaaaaaabbbabbbbabbaaaabbbabbababbbabaaabababaaaaabbaabbaabababaabbaaabaaaababbaaabaabaabbbbbbaaaabbabbaaababbbabaaabababbbaaaabbaaaabaaaabbabaabbabaabbbaababbaabaababababbbaababbabbbabbbbbbababaabbabaaaaabbbbabbababababbabaabbaaabbbbaaaabbaababbaaaababbaaaababaabbabaabbabbaaaaabbaabbabbbbaabaaabbaababbabbbaababaababbbbaabbbbaaaaaaaababbbbbaabbbaaaaaabbbaaabaababaaababbbbbbbbbbababbabbabaaaabbababaaabaababbbaababbbbbbabbaabababbbbbaabbbabbbbaabbbabbaabbbaaaaaabaabaabbabaabaabbaabbabbabbbbababbaababaababaabaaaaaaaabbabaababbbbbbaabbbabaabaabaaaaabaababbabbbbbbaabbabababbaabaabbaabababbaaabbababbaaaaaaababbabaaababbabbabaaaaaaaaabaaabbaabaaabaabbbabababbaaabaabbbaaaabbaababbababaaababbbabbbbbaaaabbabbbbabbbabbbbbaabbbabbaaabbbbaaabbabbaababaabbaabbbbbaabbaababbabbbbababbaabababaabbaaaaaaabbabaaaabbaaaaabbabbaaaabbbbbabbabbaabbbaabbbbabababbbbabaabbbaaaabaaaaabbbbbabababbababaabaaaaaaabbbbaabbabaabbbbbababbbbbbaabbbbbbbaabbabbbbbbabaaabbbababbaaaabbbaaabaabaabbaabaabbaaaaaabbabaabbaaababbaaabbabbbbbbbbaaaaaabaaabababbabbabbaaabbabbbbabbbabbabaaababaaabbbabbbabbaababaaaaabbbaaaabbbbaabaaaaabaaabbbbaaaaaabbbbbaababaaaabbaabbaabbbabababbbbaaaabaaaaaabbbbbabaabaabbbbaabaaaaabbbbaaabaaabbaabbabbbbbabbabbaaabbbaabbabaaaaaaaaabbabaaaababbaababbabbbaababbbabaabbababbbbbbbaaabbbbabbbbbbbbaaaabaabbbaaabbbbbababbababbbbbbabbbababbabbbabbaaaaaabbbaabbbabbbbaaabaaaaabbaaaabbbaababaabaababbaabbaabbbababbbbaabaabbbaabbaaabbbbbbaabaababababbabbbaaaaabaababaababaaabbabbbaaaababbaaabbaababaabbabaaaabbbbbabaaaaabbbbababbbbbbaaabbbbabbabbbababaabbabbbbbaaaaaaabbbaaaababbababaababbbabbaabbaabaababbaabaaaaaabababbbaababaaabaababbbbaaabbaaabbbbabaabaabbaaabaaabaababaabbabbbabbbaaabababbabbbabaaaaaaababababbbaabbaabaaabbaababbbabbbbbbaaaaabbbabaaababbbabbbaabbbbabbaaabaaabbbbbabbbbaaabbbbaabababaaaabbabbabaaabaabaabaaaaabbaabaabaaaaaabaabaaaabbababaababbbbbaaaababababbbabbbbbbabaababaaababbaaaabbaababbbbbaababbaaababbababababaabaaaababbaaabbbbabbbbabbabbababaabbbabbbbababaabbabaaaabaaaaababbbabbbbbaabbaabaabaaaabaaaabbbaabaaaabaabbababaabaaaabbbbbaababbbbbababbbaaabbaabaabbabbbbbaaaabbbabaaababbababbbbbabaabbbabbbaaaabbaabbbabababbbababbbbaaaaaabbbaaabbbabaabbbbbbbaaababaaabbabbaabbbabbbabaabbaababbaabaababbaaabbaabbabbaababbaaaaabaaaababaabaaaabaaaaaaaaaabbaabaabaaabaaabaaaaaaaaabbbaaabababbbaaababbbbaaaababaabbbaaaababbaaaaabbbbaabaaabbbbaaabaabaabbbaabaabbbaaabbaabbabbaababbbbaababbaaaaaabbabbaabbbbbbabbaaabbbbabbaaabbaababaababbbabaababbabaabbbbbbbaabbabbbaaaabbaabbabbbbaaaabaababaaaabbaabaabbbaaaabaaabaabbaaabaabbbabaabaaaabaaabbababbbababbabbbababbaaabababaaaabbbaaabbbbbbabbbbbabbabbaabbbaaabbbababbababbbaababbbbaaabbbbababbbbbaaaaaaaaaaabbaaabbbabbaaabbabaaabbaababbaaaaaaababbabbaaababababbbaabbababbbbbbbbbbbaaababaabbbabbaaaabbbbbbbaaababaaaabbaabbaaabbabbbabbbaabbaaaababbabbabaaaaaaaabbaaaaaabaaaabaabbbabbababbaaabaaaaaaabbabbbbabbabbabbbaabbbaabaabbabaaabaabbbaaabaababbaaababababbabbabbbbbbaaaaabbbaaaabaabbbbaaaaabbbabaaaabbaaaaabbababbabbbabbbbbabbbbbbbbabbbbbaababbabbaababaaaaaaaaabbabababaabababaabbabbaaabaabbabbabbbabbbbaabababbaaaaaabababbaabaaaababbaaabbbbaaaaaabbbabbbbaaababbabaabaaababbaaaabbabaabbbbaabaababbbbbbbbaabbbababababbabbabbabbbaaabaaabbaabbaaaabbaaaababbabbbbbbbaaaabaaabaabababbbbaaaaababbaaababaaaababbbbbbbabbabaabbaabbbbbbabababbaaaaabbababbababaaababbabbaaaabaabbbbaabbbbabaaaabbababbaaababaabbbaaabaabbbaabaaabaaaababbaaabaababbbaaaabbbaaaaabaaabbabbabbbabbbaabbbabbbabaabababbbbabaaaabbbababbabbabbbaaabbbbabbabbbbbabbabbbabbaaababbabaabaaaaaabbbaaaabaaaabababbababbbaaaaababaaababaaabbbaaabababaaababaabaabbbaabbbbbbbbbbaabbbbaaabbbbbbbababaababbabbabbaabbbbabaababbbbabbaababaaaaaabbbaaabaaaaabababaaabaabaabbabbbbbabababbababaabbbbaaaaaababbbaaabaaaaaababaababbbbbbbabbbaaabbbaababaabaabaaaabbbaaabaababbbaabbbabbabbaaaaababaaaaababbaaabaabaaaaababbbabbbbaabbbbaabaaaaaabbbbabbbbbabaaaaaabbaaaaabbbbaabbaaaabaaaabababbabbbabbbbaabaabbbaaaabbbabbabbabbbaababbabbbabababbbbbaabbaababbbbbbbbbbbbabbabbabbbbbbaabbbabaaaaabbabababaaabaaaabbababaabbabbbaaabbbababbabaabbaabaabbbaaaababaaaaababaabbabbbabbbbaaaaaaababbabbaabababbaaaabbbbaaaabababababaaabbababbbaabbbbaababbabaaabbbababbaabbaabbbabaabbaaabbabbaaaaababbbbbabbbabbbaabbababababbaabaaaabbbbaabbbabbaabbbbababbababbbbabbaaaabbbbaaaaabbbababbababbabbbbbbabababbbbaabbabbbbbbbabbabbaababbbaaaabaabbaaabaaaabbaabaababbaaaaabbabaaabaabababbbababbbabaabbabaababbbabaaaaaabbbaaabababbbaabbbbabbaababaabbbaabbbbbabaabbaabbaabbbbbbaaaaaaabbbabaaabbaabaabbababbbbbbabaabbaababbbbbabaabbabbbaaabaabbaaabaabaabbbabbbabbaabbbaababbababababbababbabbaabbabbbabbaababababbaabaabaaabaaaaabbabababaaaabbabbbaabababaaabaaaaabaabbabbaaaabbaababbaabbbbaabbbaabaaaabbbababbbbababaabababaababbbbabbbbaaaabaabbbbbbabababababbaababbbaabbabbaaaabaaaaabaaabbabaabbaababbaabbaababaaaabbababaabbbbabaaaababbababaaabbabbabbaabababaaababbbabaaabbabbaaaaabbbbbabaababbbbabbbbbabbbabbabababbababbabaabaababababbaaabbbabbbabababbabbbaaaababbabaaaabaaabbbbbaaaabbaaaababbabaabbaaaabaaaaaaabaaaabaaabbabbbaaaabbbabaabbbbbaabaabbababbaaaaaaabbbbabbababaababbbbbbbbaaababbbbababaabbbbbbbabbabaababbbbababbbbbabbaaabaabbbbbabbabababaabaabbabaaaaabbbbbbaabbaaaabaaabbaaabbabbaabbbaaaaabbaabbaaabaaabaababbaaaaaaabbbaaaabbababbbbaabbabaaababbbbbbbaaababbbbaaaaaaabababbaabbaaababbaababaababaabbbbbababaaabaaaaaabbaababbabbbabbaabbabbbaabbbaabbabaabbbbbaaaabbbaabbbbbaaaabbbababbbaaabababbbaaababaababaaabbbabbbbaaababbaabbabbbbbbbbbbbaaaababbabbbbabababaabaabbabaaabbaabbbaaaaababbbbbabaaaaabababbababbabbaabbbabbabaabababbbaaabbbabbaabbbbaaabbbaabbaaaabaabbbabaabbbbabbababbbbaaaaabbaababbabbbbaabbabbbbaaaaabbbabbaababbbabbbabbbbbbaaabaababbaaaaabbababaaabbbaaabbabaaaaabaabaaabbaaababababbbabaaaaabbaabbaaabbaabbaaababbbaaabbbabaaaaaababbaababbabbaaaaaabbbababbbbabbbaaaaabaaaababababaabaaaabbbababaaaaabbbbbaaabbababaabbabbbababbabbabbababbbaababbaabbbaaabbabbaabababbbaaaaabbbbabaaabbabbbbaaaabaabaababbabbabaababbaabbaabbaabbabbbabaaaaabababbbabaaaabbbbbbbbbbaaabbaabaaaaaaabaaabbbbaababbabbbabbbaabaaaaaabbbbbbaabaababbababaaaabbbaaabbbababaabaabbbabaaaabaabaaabaabbaabaaabbaabababbbaababaababbaaabbbbbbbbbbaaabaababbaabbabaaaaabbbabababaaaabaaaaaaaababbabbabbbbbabaabbbbbbabbaabaaabbbbbbaaaabbaabbbbbbaababaabaaaaaaabbabbbaababaaabababaabaaababbbbabaabababbbaababbbabbabbaabaabbabbbaabbaabbbbabbabbaabbaaaabbbaaababbbaaaaabbbbbabbbbbabababbaabbababaabbaaaaaaabbbbbbbaabbabaabbababbababaaabaabbbbbbbbbbbbbbababababbbaabababbabbaabbbabbabaaaababaaaababbaabaabababbbbabaaabaabbbaaaaabbbabbbabbaaaababbbabbababaaaaabaaabbaabbaabaabaababbabaabaaabababbbaabbbaaabaabbabbaabbaabbbaabaaaaabababbabaaabaabbbabaaabaaaabbbaabbbaabbbabaaabaaabbbabbbbbaaaaabbbbbbabaabbaabbabaabbbbabbbbbaaabaaaabbaabbbbabaababbaaaabbbbababaaababaaaabaabbbabbaaabaaababbbbbaaababaaaabaaaaababababbabbbbaaabababbaabbbababbbbababaabbababaabbaabaabbbbabbbbabbaabaaabaababbabaaabbabaaabbbbaabaabbbbbbaabaabbbaababaabbbbaabbaabaababbbbbbabbaabbabbbabaaaaabbbaababbaaabbabbaaaaabbbbbaabaaaaaaaaaaabaaababaabbbabaaabbbabaaaaabbaabbaaababbababbbaaaaaaababbbabababababaaabbaaababbbabbbaaabbaaabaaaaabbbaaaabaaaaababbaababaaaaaaaababbbbaaabababababbaababaababaaabbabbabbbbabbbaabbaaabbbbbababaabbbaaabbababbabbbaabaaabbbaaabbbaaaaaabbaaabbabaababbababbababbaaaababbbabbaabaaabaababababbabbbaabbababababbbbbaaababbaaabaabaabbbaababbbabaabbbbaaaabababaababbbbbabbaaabaaabbaabbabbaabababbbaababbaabbabbbabbabbbaaaaaabaaababbabbabbbaabababbbabbbbbbbabbbbababbaaaabbbbbbbabbbaaabaaaababbabaabaaabaaabaababbabbaaababaaabbaabaabbbbaaaabbbaaaaabbbaababbbbababbaabbaaabbbabaaaaabbabababbaaaaaabbaabbabbbababbaabbaaaabbaababaaabaabbbabaaaaabaabaabbbabbbbabaaaaaababaaabbbbabbaabaaabbbbaaaaabababbaaaabaabaababbbaaaaababaaababbbbaaabaabbbbbabbbababaabaababaaaaaababbbabaabbbbbbabbbbaabbbbbbabbbabbbbbabbaaaabbaababbbaabaaababbabbbaaabaabaabaaaababababababaaaaaabbbbbbbaabaaaaabbbbbabaabbabbbbaabababbbaabbaabaabbabaaabababaaaaaaaababababbbaaaabbbababaaabbabababbbbbbbababaabbabbaababababbaabbbbaabbbbbabbaabbaaaabababbabaaaababbabababbbabbbbbaabaabaabaaaaabbbabaaaabbbabbabbabaabaabbbaabbbaaaabbbabbaabaaabbabbaaaabbaaaaaaaaabbbbaaabbbabbbbbbbbbabbabaaabbbbabababaabaabababbbaabbbaaaabaaabbabbababbbbababaabaaaabbaabbbaabbabaaabbbaaabbaaabbbabbbbabbbbaabbbabbababbbbbaaaabbabbabbabbaabaaabbaabaababbbbbbaaabaaaabbbbbbbaabbbbbbaabbaababbabbbabbaabaabbbaaaabbaaabbbbbbabaaaabaaaabbaabababaaaaabbaabbabbabaababaababbbaabbbbaaaaababbbbabbbababbbbaaaaabababbbaaabbaabbbaaababababaabbabbaabbaabaabbbbbaabaabababbaabaabbbabaabaaababbbaaabbbbabbbaababaabbbbaabaabbaabbaababbabbaaabbbbaaaababbabaabbbababaaaabbbababaaaabbaaabbababbabbaaabbaaaabbabbbbabaababaaaaabbabbbbbaaaabbaaabbaabaabbababbaaabbbbabaabbabbaabbabaabbbababbbbbbabbbbbababbabbabbaaaababbbbaabbbbaaaabbabbaaabbbabbbbbbaababaaaabaaabbbbabbababaabbabbbbaababaaabababaaaabbbbabbaabbaaaabbbbaaaaaaaaabbbbbaaabaaaaaabaababbbbbabbabbabaabbabaababbbbbababbababbbabbbaababbaaabbbaababbababbaaabbbaaaaaabbabaaaabbaababbaababbaabbbabababbabbabaaaaaabaababbaaabbaaababababaaaabaaaaababbaaabbbaabbbbababbabbaabaaaabaabbaabaabbaaaabbbaabaabababbbbbaabbbababbbbbaaabaaaabaabababbaaaaabaaabbaaaababaaaabbbbaababaababbabaabbaaaaaaabbabbabaaaaaaaabaabaabbbaabbaabbbbbaaababaabbaabbababaaaaaabbbbbbbaabababaabbaabbbbbabbaaaabbbaabababbaabbabaaaaaaabbbaabbbaabababaaaaaaaaababaabbaabaaaaaabababbbbabaabaababbaaabaababbbbbabbaaaaaaaabaabaaaabbaaaababbababaaabaabbaaabaabaaaabaaabbaaabbabbabbbbbbbbabaaaabaaaaaaababbabbaabbaaabbbabbbbbbabaabaaaaaababaaaaabbbababaaaababaaaaabaaaaaabbbbbbaaabaaaababbbabbbbbbaabbbbaabbababaabbaabbbaaabbbaaabbabbabbaabbbbaaaaaaabbaabaaaabbabbababbbbaaabbabbbbababbaaaaabbbbabbabbbbbbbaaaaabbaaaaababbaaababbbbbaababbbaaaababbbbbbbaabbbbbaabbaaababbaabababbbabaabbbbbbbaabbaaaaaaabbabaaabbaaaabbaabbabbbabbaabbabaababababbabaaaabaaaabbbbbaaaaaabaabbabbbbaaaaabbaaaaaabbbbaababaaabaaaabbbababababbbabbbbbbaababaabbabbbaabababbbaaaababbbbbbaaabaaaaaabaabbbbbbababbbbbbaaabbabbbabaaaabbaabbbababaaababbababbbbaaaaaaabababaabaaaaaabbabaabbaaaabbabbaaabaabbaabababbbbbabbaabbaabbbaabaabbbbbbaaaaabbaabbbbaabbbbababbbababaaabababaaaabaabbaabbabaaaabbaabbbaaaabbbabaabbabababaaaabaaaabaababbaaaababbbaaabbbabbaaabbbbbbbaaabaaababababbbabbaaaaabbbababbababbbabbbaaaabaaaaaaabaaaabababbbaabababbabbbababababbbbaabbaaabbabaabababaaabbababaaabbbabbaaaabbaaabaabbabbabbbaaaaababbabbbaaaaabaaaaaabbabaabbaabbaabaaababaaabbbaaababbbaabbaaabbbbabbaabaaabbaabbbabaabbaaaaaaaabaaaabbababaabaababbbaabaabbaaabbbbbbbbaaababbbbbaabababbbbabbbabbababbbabbabbbbbbabaabbaabaaabaabbbaaaaaababbaaabaaabbaaabbaaababaaababababbaaabaaaaaaabaababaabbaaaaaaababaababbabaabbbabaaaaababbaaabaabaababbbaaabbabaabbbbbababaaaaababababbababbabbbabbbbbbbabbaaabaaaabbababaabaababbbaabbbbaaababbaabbbabbbbbbbabbaaababaaababaaaaaabbabaababbbbbbabaabbaabbbabbbbbabaaaabbaabbaaaaaabaabbabababbbaababababbbababababbaaaaabaabbababbbababbaabaababbabbbaabbabaaaabbaaabbabbbbaabaababaabbabaaaaaababbbaaaababbabaabbbabaababbbaabbaabaaaabaaaabbbbabaabbbbaaababbabaababaaabbaaaaaaaaaaabababbbaaaaabaabbbabababbabbabbaabbabbbabbabbabbbbbbbaabbabaaaaaababbbbaabbaaabababaabbabbabaaaaabaabbaabababaaabbabbabbaabaaabbbbabbaabbbbbbbaabbbaaaababbaabbabbbbbbbbabbbaabbaababaaabbaaabaabaabbbbbbabaaaaabaaaabaaaabbababbabbababaabaabbababaabbbbbbaaabbbbbbaaabbaaaabbbababbaabababbababbbabbbbbbababbaabaaabaaababababababbbbbabaababbbabbaabbaababbaaaababbbbaabbbbbbabbaaababaababaaabababbaaabbabaababbaaaabaaaaaaabaabbbbbabaabababbababbbaabbabbaaaabbbbbabaaaababbabaababbabbbbbaaaaababbbababaabbabbabbbbaabbabaaabbabbaabaabbbbabaaaabbaabbaabaabbbaabbbabbabababaaaababababbbbabbbabbbaaabaaababbaabababbbbbbabbabbbabbabaababbabbbbbaaaaaaaaaabaabababbbaaabaaabaaabbaaaaabaabbbababaabbabaaababbabababaaabbbbbababbbabaaaabaababaabbabbabbabaabbaabbbbababbabbbaaabababbababaaaaabbabbaabbaabbaabaabaaabaaababbabbaabbababbaaabbbabbbbbbbbbabbbbabbbabbababbabaaaaaaababbaaaababbaababbaabaaaabbbabbababaabbbbbbabbaaaabbaababbaaaabaaaaaaaaaabbbabbbaaabaababbaaabbbabaaaaaaaabbbaaaaaabaabbbabbaaabaaaabaaabbbabbbbabbaababbaabaaaabbabaaabbbbbababbabbaabbababbabaabbbababbababbbabbbbaabbbbbababbbaaabbbbabbaaaaaaabaaaaababbbaabbbbabbabaabbabbbbaaaabbaabababababbabbbabbbaaabbababbbbbbbbbbabababaaabaaabaaaaabbaabbbabaabbaaaabbaaaabbbaababbbbbbaabaaaabbbaabbbbbbbaabbaaaaabbabaaaaaabbaaabababbbaabbbabbbbabbbbaabbabababaaaabababababaabaaabaababbbabbababbbbabbbabbabaabbababaabaaaaabbabaaabbbbabbaaabaabaaaaaabaaaaababaabbbabbabbabbaabbbbbabaabaabbbbaabbabbbbaaaabbbbbaababaaaabbbbabbbbbbbabbaaabaabababbbbbaabbaaabaabbbbabbaabaabbbaaaaabbbbabaabbbaabaaaababaabbabbabbabbababaaaababbabbbaaabbabbaabaabababaaaaaaabbbaaaabbaabbabbaabaabbaaaababbababaaabbabaaabaabbbbbbaaababababbbbaaabbaaaaabababbbbbaaababbbaaaaabaaaababbbaabbbabbabbabbabaaabbbaababbbbbaaabbaaaaababbabaabababbbbaababaaaabbbaabbaaaabaabbaabaaaabaabbbbabbbbbaabbbabbbaaabbbaabbbaabaaababbbbabababaabaabbaabaaaaaabbaabbbbbbbbababbbabbbbbbaababbaabaabbbbbabbaaaabbbbbabbaaaaaaababababaabbbabbbaaabbabbabaaaaabbaabbaabbbaabbabaaaaaabaabaaababaabaaababaabbaabbbaaaabaaaabaabaaabbababbabaababbbbbbaabbbaaaabbbbabbabaabbaaaabaabbaaabbbaabbbbaabbabaaababaabbaaabbbabaaabbaaaabaabbaababbbbbaaaaabbabaaabaaaaabbaaaabbabbaababbbabbbabbababaaaaababaabbabbabababbbbaabbaaaaaabbbbabbbaabaaabbabaaabaaababbbaaababaababbabaaaaaaababaababbaaabbbaaaaabbaaabbbbbabbbababaabbbaababbbaababbaabaababbababbaabbababaaababbaababbaababbabbabaaaabbbbbbbaababbaabbbaabbbbbaabbbaababaabbaaabaaaaaabaaabbbaabaaabaaabaaaabaaaabababbabbaabbababbbaabbbaaabbababababbaabbbbaaababbbaaaaaaaabbabbbabbbabaababbbabaabbbabaabbabbaabbabbbbaabbbabaaaababaabbaababaaaaaababbbbbabbaabbaaaabbaaaaabaaaaaabbabbbabaabbabaabaabaaaabababaabbbaaabaabbaabbbaaaabaaaabbabababbabbbabbabbbbbbaabaabaaabaabbabaabaabaabbbaabbbaaaaaaaababaaabaabbababaabbabbbabbaaaaaaaaabababaaababbbbabbabbaabbaabbababbbbabbabababbbbabbbbbaaaaabaaaaabaaaabababaabbbaaababbaabaaabaabbabbbaaaaaabbaabbbbaabbbbabbbaabababaaaabaabbbabbbaaabbabaaaabbabaaababbbbbbaaabbabaabbbbbbaaaabbabaabababbaabbabaaababaaaabaabaaabbabaabbbabbaabbaabbabbabaaaababbbbbbbbbaaababbaaabaaaaababbbbababbaaaababaabbbaaaababaabaaababababbaaabbbababbbababaaaaabbaaaababaaaababbaaabbbabbbaaabaaabaabbbaababbbbbbbbaababbbbaabaabaabbaaaaabaabaabbbbbaabbabaaabaabbbababaaababababbbbabbbbababbbbbaaabbabbaababbbabbbbaababaaabaaaabaabbaaabaaaaabaaaabbabbbaaaabaaaaabbabbaaaabaaaaabbbabaaaaabaaaaababbaababbabbabbabaabbbbbbabababaaaababaabbbabaaabaabbbbbbabbabbabbbaabbabbaaaaabbbabbbaabbbbbabaabaaaaabbabaaababbabbabbbbbabbaaabbabaaabbbaaaabaaaaaaabababbaaaaababbababbababaaabaaabaaaaaababbbbbaaaaaaaaabbabbbaaaababaabaabaabbaaaaaabbbaabbbabaabbabaabbbbbaabaabaaabaaabbaaabbababaaababbaaabbaabababaabbbbabababaabaabaabaaaaabbbaaaaabbabbaabbababbbbbaaababaaaababbaaaaaabbbbabaaaaaaaabbabaabbabaaaabbaabbbbbbabbabbaaaabbaaabbaabaaabaaaaaabbbbabbbabaaabbababbaaaaaaaaaaaaaaaaaababbaaaaabbbbabbbaabbaabaaabbabaabaaaaaabbaaaaaabbaabaabaaababbabbaaabaabbbabbbaabababbaaaaaaabaabaabaaabbbbaabbabbbaaaabaabababbababaabbabbbababbbaabaaabbaabbaaaaabaabaaababbaaabaaabbbbaabbababaabbbbbabaabbabababbabababbbbabaaaabababbaaaaaaabaaabaabbababaaaaaabbabbbbabaabababbabbaaaaabaabaababbaabbbbaaabbbbbabbbaabbaabbaabbaabbabbaabaabaaabaaaaaaabbbaabbabaabaabaabbaababbaaaabbabbaaabaaabaabaaabaaaaabbabaababbbabaabaababbbbaabbababbbaaabababbbabbaabbbabbabbaaababbabaababbbbbababbaabbababbaaaabaaababbabbaabbabbaaabaabbbbbbbbaababbbaababbbabaaaabbbaabbaabbbabbbbaaabbbaaaaaababbaabbbbaaaabaaaaababbbabbaaabbbbaabbbbaabbabaaabaaaabbababaaaababbbaababbbbbbaabaababaaabbaaabbbbaabbbaabaababaababaabaaababaabaaabbabababbbbbbaababaaabaabaaaaaababaaabbabbbbabbabbbbaabbbbabaabaaaabbbabbbabaabbaabaaaababbbbabaabaaabbaabbbabaabaaababbabbaabbaaababbbaaaabbaabbabbaaaaabbaaaaabbaaaaaabbabbaaabaaabbbaabaaaabbaaabbbbabbaaaaaabaababaabababbbabaaabbaaabbaabbabbbabbabaaababababbaaabbaaaabaabbaaabbabbbbbbaabbbaababaabbabaabaaaaabaaabbaaabaaaababbbaaaabbababaabbbaaabaaabbbaaaaabbabbbaaaaaababbbababaabbbbabaabaaabbbbbaaabbbabbaababbabaaaaabababbaababababbbabbbbbbbbbabbbbaaaabbbaaababaaaabaaaaabbbabbbababbababababbbbabbaababbbbbbbbabbbabaaabbbbbbabbabaabbbaabbbaabbaaaaaaabbababbbaaaabbbaabaabbababbabbaaabbbabaaaabaabaaababbbbbbbaabbbaabaaabaaababaabaaaabbaaaababbbbaaababaababaaababbbaaabaaaabbaababbbbbbbbbbabbabbababbbbbbbbbaabbaaaabbbbaaaababaabbababaaaaabaabaabbbabaabaabaabbabababababaabbbbababbaaaabbaabbaaabaaaaaaabbbbababbbaabaabbabaabbabbabaaabbbbbabbbbbaabaabbbbaabaaaaabaaababbabbaaabaaaabaabbababbbaaaabbabbabbaababbabaaabbbbaaaabaaabaaaaabababbabbbabbbabbbabbaabaaabbabbbaababaabababbabbabbbababbabbbbabababbbbabaaabbbbbaabbaabbaabaaabaabbaabbabbbaababbbbababbbabaabaaaaabbbbabbaabaaabbabababbaabbabaaabaababaaabaaababbababaaaaabaababaabbaababbaabbabaaaaabaaabaabaaabaaababbaabbaababaabbabbbbbbbbaaaabbbaababaabbbababaaaaabaaaaaaaabbbabbbbaabababbbababbabaaabaaabbbaabbaaaaabbabaabbbbbaababbaaabbaaaaabbabbaabbaaaabbbabbabbbbbaabaaaaabaabbbbababababaaaabbbababbbababaaaaababaaaaabbbaabbaabbbaabbbbbbbaabaaaabbaaaababaaabaabaabaabaaaaaabaaaaaaaaaaabbaaaabbaabbbaaaaaabbaaaabbaaabaabbbbbabaababaaabbaaabbbbaaabaabbaabbbaaaaabaaaaabaabbaabbabbaababaabbabbbbbaaabbbbabaabbbbaaabaaabbaaabbaabbaaaabbaaabbbaaabaaaabaaabbabaababaaabaaaababbaababbabbbbababababababbabaaabaaaaabbbaabaabbaaababababababbabbbbbaabbaabbbbbbabbbabaabbababaababbbbbbbbaaabbabaaaabaabbaabbbbabaababbbaaaabaaabaabaaaaabbbbbabbbaabbbababaabaaabaaababaabaaaababababaaaaaababbababbabbbbbbbbabbbababbbbbaaaabbbbbaababbababbabbbaaaaaaaaababbaaabbbbbaaabbbabaababaabbbbabaaaaabaaaaabaabaaaabaabaaabbaabbabbbbaaabbbabbbbaabbbbbbabbbaaabbbabbaaaabbbbbbaaaaabbbaaabababaaabbababbbabbbaabbabaaaababbbaaabbbaaaaaabbabbabbabbbbaaaaabaabaaababaabbaaababaabaabbbaaaabaabbabbaabaabbbaaaababbbaabbabbbaabaabbbbbabaababaaabababbabaabbabaababbaaaabbabbbaabaababbabbabababaabbbaabababaabaaabbabbbbbbaabaabaaaaabbabababbababbaabbbbbbaaabaaaaabbbbabababbbbbbbbbabbbabbbababbbababbbaaaaaabbabbabaaababbbaabababbbaabaabaaabababbbbabaabbaabbbabbbbbabbaabbaaaabbbbbababaabbbbbbbaaaaaabbbbaaabaaabbbbbbaabaaaabbaabbbbaabbbbaabbababbababbbbbbaaaaaaababbabbababbababbaaaabbabbaababaabbbaaaabbbaabbbaaaaabbaaabababaabababbabaaaabbbabbaabbbbabbabaababbaaaabbaabaaabbabbabaaaaaaabbababbbbababbaabaababbabbaabaabaaaaabbabababababaaabbbaabaabaabaaaabaabaabbbbbbbaabbbbaaabaaabbaababaaabbaaaaaabababbabbaaababbaabaaabababaaabaaabbbababbbaaaaaaabaaaaabbbbbabbabaaabababaaabbaaaaabaaaaaaabbbaabbaaaabaaabbbabbbbbbaaabaabbbabbbabbbaabbaaabaabbbbabbbbbbbbaaaabbababbababaaabaabbabbbbaaaaaabbbbababbbaaaaaabbbabbabbabbbbaaababababaabbaaabaabbbabaaabbababababaaabbbbaabaabbbaaabbbbaaabbabbbbbbbabbabbbbbbbaaabbaabbaaabbbbabaaaaaaabbbababbbabbababbababaabbbbbaababbbaabbbbbaaaababbbbbbbaaaabbbbbaabbbbabaaabbabbbaabbabbbbabababababbbbbbabbbbaaaabbbabababaabaaabbabbbabbbaabaaaaabbabaaabbbbababbbabaabbbbbabbabaaabbbbabbababbaabaabbbbabaabbabaaabbaabaababaabbbaabbaaabbaabbabbaaabbbbbbbbabbbbababababbabbbbabaaabaaabaaabbabbaaaaaabbaabbbbabbaabbbababbaaaabaaaaaabbaabbaababaaabbabababbabaabaaaababaaaabbabaaababbbbbabbababbbaaaaabbbabababbaabaabbbabaabaaababbaaaabbbbbaabaaabbaaaabaaaaabbaababbbbbbbbbaaabababababaaaaababbbaababaaabaaaaabbbbbbbabbaaabbaabbaabbbaabaaaaaaaaabbbbaaaaaaabaaababababaaaabbaabaaaabaaaaaaabaabaabbabaaabbaaabbbbabbbbbaaaabbbbbaababbabbbbbabbabaaaaaaaabaabbaabaaaabbaaaaaaabbbbababbabbaaaaabaaabababbbaabbbabbbababbbaaababbaabaabbaabbbbbabbaabbbabbbbabbbabbbaabbabbbbaabaabbbaabaabaabaaabababbbaabaaaabbbaaabaabbbabbbabaababbbbbaaabbbbaababbbbbbbababaaaabbabaaaabaaabaabaaaaabbbabbababaabbbabbbbaaaaababbbabbaaaaabaababbabaababbbbbbabaabbbaaabaaabababbaaaabbabaaaabaaaabbbabbbbbabbbababbabbababbbaaabbbabaabbbaabaabaabababbabbaaabaabbbaabbbaabbbbaaabaabababaababbabbbabbbababaaaabbaabbbaaabbbabbbabbababababbababaaaabaabbabaaaababaabaababbabbbbbbbbabababbababbabbabbaaabbaaabbbbbabababbabbaaaaabaababbbbbabbbbbaabaaaababbbabbbbababbbabbbbaabbaaaabaaabaabbbabaababbaabaabaabaaabababbaaaaaabbbbbaaabbbbababbabababaabbaabaababbaabbbbbaaaabbabbabaabbaabbaaabaaabaababaaaabaababbaaaaaaaababaaabaaaabbbababbababbaabbbbababaaaabbbabbbabbababbaabbbaabbbbaabbbbaaabbaabbaaabbbbaaababaabbbabbabaabaaabaabbabaabaaabababaaaabbbaaaabababbbabbbbaabababababbbaaababbbbaaababbabbbaabbbabbabbbbbaaaababbabbabbbabbbaaaabaabbaaaaaabaaababaaabbbaabbabbabaabababbbaabbabbbbbaabbaabbbaaaaaaabbbbbaaabababaabaaabbbbabbaabaaabaabababbabbbabaababababbaabbabbabbaaababababbaaabbbaaaaaaabbbbabbbabbabaababaaaababaabbabaaaaabaabbabbaabbaabbbbaababbaabbbaaabbababaabababbbabbabaaabbababbaabbbaaaabaaaababaaabaabaaaabbababaaaaabaabbaaabbabbababaaaababbbbaabbabaababbbaabaababbbaabbaabaaabbbabbabaabbbbbbbabbbbaaabaaabaaabbaabbaaabaaabbbaabbababbaabbbbaabababbaaaababbaaababbaaaaabbaaabbaabaaaabbaaabaaaaaaaabbaaabbbabababbaaaaababbaaabbbbbaaaaababaabaabbaaaaaabaaaaaaabbbaabbabbaaaabbbaabbbabaaabaababbaabbaaaabbbababbbbabbbbabbbabaaaaaaabbbaabbbabbaababaabbaaaabbabbbbbbbaaaaabbbbababbbabbbababaaaababbababaabaaaaababbababaababbaabbbbababaabbbaabaaaaabbabaaaabbbbaaaaababaaaaabaabbbbabababbbbaaaaabaabbabaabbaaabaaaaabaabbabaaaabbabaaabbbbaababaababaaabaabaabbbbababbaabbbabbbbbbbababaabaaabbbbaabaabaabbababaaabaabbabaabbbbabaabaaabababbaaaaaaabababaabaaaaaababababbbbababbbaababbbaaabbabbaaabbabbbbbabbaabababaababaaaaabbbbbabbbaabbaabababbbabbaaabbabbabaaaaabbbaaaaaabaaabaabbababbaababaaabbabbabababbabbababaaaaaabaababababababbabaaaabbbbbabaabaabbaaaabaababbbbbaaabababbabaaaaababbbababbbbaababbaaaabbbabaaabbbababaaabababaaabbbbbbaabbbaaabbbbbbbaaaabaabbbaaabbbbbabbbabbbbabbbbbabbbabbbbbbbbbbbbaabbbabbaabbbabbabbbababbbbabaaaabababbaaabababbaabbbaaaabababaabaabbabaaaaaaaabaaaaabababbbababaababbbbbaabbbbabbaabaabbbaaaababbbbaabaaaaabbbabaabbaaaabaabbaabbababababaababbbabaabbbbbbbaaababbbbabaaabaaaaaabaabaaaaaabbabbbbabaaaabaaaaaaabbbbaabbababbaabaababbababaabaaaaababbaaababbababbbabbbbabbaabbbabbaaaaaaababbaaabaaaabaaaaaaabbbabbaabaaaaabbbbaababaaaaabbaabaabbbaabbaaaabbaaaabbabababaaaabbaaabaabbababbabbbbbabbbabbbbbbbbaaabababbaaabbaababbaaaabbabbbaaaaaaaaaaabababaaabbbbabaaabbbbaabbbbabbbbbbabbbbbaaaaabbbbbbabbbbbaaabbbbabbaabbbbbaabbbbabaaabbabbaaabaaababaabbabbababbabbabaabbaaabbbbababbaababbbaabbbbababbabababaababaabbbbaabbbbababbbababaabbabbbabbbaaabbbbbbbbabbbaabbbaaaabbabbaaabbbaaabbbbbababbbbbbbabbaaaaaaabbbbaabbbbabbabbababbabbabbabbbbaaaaaaabaababababbabbaaabbbabbbbaabbbaaabaaabbabbaaabaabbbabbbbbbbbabbaabbbbbaababbabaabbbbbaababbabbbabaabaaabbbbbaabbaaababababaaaaaababbababbabbabbabaaaabaaabaababaaaaaabaabaababaabbbabbabbbbbbbbbbbaaabbababababbbaaabaaaabbabbbaaaabaabababbabbbbbabababaabbaabbbbbbabbaababaabbababbbaababbaababbbbabbbabbaaaaabababbaabababaabbbabaaaababbbbaaaabababaaababaabaabaababaaaaabbbbababaabbaaabaaaabbbaabaaabbbbbbabaaababbbabaaaaabaaababbbaaabaabbbbabbabaababbbbaabaaaaaabaabbbbbbabbaabbbbaaaababbbabbabbaaabbaaabababbbbaaaaababbabbbaabbababaabbabbbbbababaababababbababbbabbaabbaabbbabbbabaaaaaaababaabbaababbbabbbbabaaaaaabaaabbbabbabbbaabaaabaabbbababaaaaabaaaabbabbaabbaababbabbaaabbbabaaaaaabbabbabbaabbbbbaabbbbbaaaaabbbaaaababbaababbbbbbbabbaaaaababaabbaabbbbabaabaaaaabbbaabbabaaaababbabbbaaaabaababbaabbaababbababbaaababbbababababaaabbaabababbababbabbaaaaabaabaaaabbbbbabaaaabbbaaabbabbbbbbabbbbbbbababbbabbbbaabbbbaabaaaabbbaaababbbbbabbabbababbababbbbbbaabbabaaababaabababbbabaabbbbbaaaabaababbaaaabaaabbbaaaaabaababbaabbaabbbbbbbaababababaabbaaaababbbaabbabbbababaababbaabaaababaabaaabbbaaaabaabaabbbbbaaabbabababbbaaababbbbbababbbabaaabbbbbbabbaaabaabbbaaaabbaababaaaabbaabbbabbbaababbbabbbbabaabbbaababbbbbbabbaaabaaabababbababbaaaaaaabbabbbbaaaabbbaaabbbbaabaaaabbabbabbbabaabababbaaaaaabbbaaaabbaababbaabbbbbbaaaaababbbabaabbabbbabaaabbbbabbaaabaaabbaaababbabaababbaabbbbbbabbbaabbabbaabaababaababbaaabaabaabaabaabbabbaabbaaabaaaaaaabbbbabababaaababbabbbaabbabbbabbbaababbbababaabaabbbabbbbaabbaaaaaabaaaabaaababaabbbabbaaabbbabbaaaababbbabaaabbbaabaababaaaaabbbbbabaaabbbaaabbaaaaabbbbabaaaabbbaaabaabbababbabaabaaababbabababbbbbaaaabbbbabaabaabbbbababaabababbaabaabbaaababbababaababbbbaaaaaaaabbbbbabbaabbbaaabbaaabbabbbbaaaabbbabbbbaabbabbaaababbabbaabaaaaabbbbbbbbaabbaaaaabbbabaaaaaabbbbbbaaabbaaaaabbbabbbabababbabbaaabbbabaababaabbbabbaabaaaaaaabbbbabbbbbbaaababbaaabaabbaaaaabaabbaaaaabaaaaababbbabbabaabaaababbbbaaaabbbababaabbbabbaaaaabbbbbbbabaabbaaabaababbbbabbaabbbaaaaabaaaaaabababbbbaaabbaabbbaaababbaaabaabaaabbbbbbbaaabbababbaaabaabbbbabbabaabbbabbbbbbaaabaabaabbabbbbbbababaabaabbababaaaaaaaabbbbbaaaabbababbbabbbababbbbaaabbabaaabaaaaaaaabaaaaabaabbabaaaaabbaabaabbababaabaaaaaaabbaaaabaaaaabaababbbabbaabbbaabaaaabbaabbaabbabbbbbbabbaaabaaabaabaaabaabaabaaabbbbbabababbbababbbaaaabbbbaabaababaaabbbaaabababbbbbbaabbbbababbbaabbaabbaaaabbbabbbabababbbabbabaaabababaabaabababbbbbabaabbabaabbbbbaabbbabbbbbaaaabbbbaaaaaaaaabbaabbbabbabbbbbabbbabbaaababababaaabaabbabaabababbabbaababaaababbabbabbaaabbbabbbabbaabbababbbbbbabaaaabbbabababaaabaabaabbaabbaabbbbbaaaabbabaabbababaabaabaaaabaabababbaabbabaaabbbbaabaaaaaaabaababbbbbaaaaaaaaaaaaabaaababbbabaabbbabbbaabaaaaaabaaaabaaabbabababbabbaaabbbbaabbbabaabbbababbbaabbbbbaaabbbbbbaaaaaabbabaabbaaabbbabaabbabaaababbababbaaaaaababbabaaaabbababbbabababbbbbbabababaababbbaaaaababaababbbaabbaabbaaaabaababaabaabbabbbabbabaaababaaaaababbaaaabababaaabaabbbababaabbabbbabaaabbbbbabbabbbaabbabbbababbaababbabbaaaaababbabbabaabbaaabbbbbaaaaaabbaabbbabaaaabbaabbaaaabbbabaabaaaaaabaaaaabbaaabbbaaaabbaaaabbbbbbababaabaabbbbaababbbababbabbaabaaaabbbababbbabbbaabbbaaaaaaaabbaaaababbababbabbbbbaababbaaabbaaaaaabbabbabbbababbabbabbbabbbabaaabbababbabbabbaabbbbaaaaaaabaabaaaaabaaaabbabbbbbabbbbabaaabbbaaabbbbabaaaababbbaaabbbababbbbabababbbabbbabbbbbbaaabbbabaaaabbbbbbaabaaaabbbaaaabaaababbbaababaabaabaabaaababbabbbaabaabbbaabbbaaaaabbaabbaabbaaaabbabbabaaaabaaabaaaaabbabbbbababaabbbbbbbaabbbbbbabaababbbababbbaaabbabababbabababbabbbbababbaaaaaabbabbaaabaaaabaaabbbbbbbbabbaaababaaaaabbbbabbaabbbaaaaabbbbbbaabbaabaabaaabaaabbbbbabaaaabbabbababbababbbbbabababaabbabbbbaaabbbbbabbabbbbabaaabaabaabbbbbabbaabbbbbbaabaabbaaabbaaabbabbabaaaaabaaabbbaabbbbbbaabbabbbabbbbabaabababababbbbaaabbbabaaabbaaaaaaabbbaababbabaaababbbbbaababababbbbbbbbaaabababbaabbbaabbbbbaababaaaabbabbabbaabbbbbaababbaaaabaabbabaaabbbababaabaabaabaabaaabbbaabaaababbaabbbbbaabbbaabaaababaababababbbbabbbbbbaababbbbaabbaaabaabababbbbabbabbbaaababbaabbabaaaaabbabbbbbabaaaaaabbaababaaabbbbaabbabbbabbabaaaabbbbaabbbbaaaabaababbbaabbbabbabababababbaaaabbababbabbbbabaaabaababababbaaaabbbaabbbbbaaaaabbababbabaaababbabbaabbbbbaababaabaaaaaabbaaabbaaaabbaabbbbbbbbbaaabbabaabbabbbaababaabbbaaabbbabbbbbbababbbaabbbababbbbbabbbaabbabaaababbbaaabbabaabbbbbbbbaaaabaababaaaaabbbaabaabbababaaaaaaabaabbaabaaababbabbaaaaaaababbaababbabaabbbbabaaaabbababaaaaaababbaaababababbbabbaaabbabbabaababaabbaaabbaabaaaabaaaaabbbbaababbaaababaaabbbababababbbbbbbaabbbbbbbabbbbbbbabbbabaaaabababaaaaaabbababbaaaababbabbbabaaaabbabaabaaabaaaabbaaababbabaabbabaababbbabaaaabbaabbbabaabaabaaabaaaaabbbbabaababbaabaaaaabbabaaabbaaaaaaaaaabaabbaaababaabaaababbabaababaababababaabbbbbaaaaaababbbaaabaababbaababaaabbbbabbabbbabbaaaabbabbbaabaabbbbbbaabbaaaaaaaaabaaaaabbaaaaababaabbbbaaaaababbabbbbaababbababbaababaaababaaaabaaabbbbbaabbaaaaaaabbabbbaabaabaabbbbaabaaabbababbaaabaabbaaaabbaaabaaabbaaaabababbbaaaabbaaaabbbbbaabbaaabbabbbabbaaaabbababbbbabbbbbabbaabbabbabbbaabaabbabaaaaaaaababbaaabbabaabaabbaabababbaaabbabbbaaabbbabbbabbbbaaaabbbbaabbaaabaababaaaabbbabbaaababbabbabbbbbbbaaaabbabbbababaaaaabaaabaaaaaaabbbaabbbbaabbbaabbabbabbaaaaabbbbababbabbabbaabbaabaabaabaabaaabababbabbbaaaabbabaaabbaababaababbaabbbbabaabbabaaabababaaaaaaabaaabbababbaaaaabbbaaaabbbabaabaabaababbbababbabbbabbbbbbbabbabbbbbbababababbbbbbaaaababaaabbaaababbbbbabaaabaaabbaabaabbbabbbbbaabbaaaaaaabbabbbaabbbbababbbbbababbaabbaaaababbababaaaabbbbaaabababaaabbbbaabababbbbababbabbbbbaabbaaaaabbbbbaabaaababababbbabbabbbbaabbaabbababbabbbaabaaaaaaabbaaaabbabbbaabbaaabbbbbababbabaaaabaabbabbbabbbbbbbbbabababaaabaaaabbaaabbbbaabbbbaababaababbaabbbabbabbbabbbbbaaabaaaabaababbbabbbaaabaaaabbabbaabbbbbbabaaaaabbbaabaaaaabbbaabaaabbbbabbbbbabbaabaaabaaabbbbbaabbabaaaabbbbaabbbababbababbbabbaabaabbbbababbbbabaaaaaabbbbaababaaabbbabbaaabbbaabbbaaabbaaabaaabaaaabbbbbbaaabaaabbbaaabababbababbbabaabbaaaabbaaabbbabbaababaaaabaabbaaaabaaaaabbaaaaabbbbabbbabbbbabbababbabaababaababaabaabbabbaaababbabaaaaabbaaabaabababaabaaaabbababaaabbbabaaabbbbbabbaabababaabaabaaabaaabbbbbbaaaaaabbaaabbabababbaaaabbabaabbaaaaababbbababbaabaaaaaaaaaaababbabbababbaabbababaaaabbaaaabaababaaaaabbbbbbabaaaaabaaaabbabbabbbbabababaaaabbabbbabbbaaaababaaaaaabbbbbbbbaababbaababbbabbbabbabaaabbaabababbaaaaaaaababaaaaaababbbbabbaaaaababaaaabaaaababaaabbbabbbaabbabaaaaabbabbababababaaabaaabbbabaabaaaababbbbaaaabaaaabababbabbaabbbbaabbabababbabbbbbbbbbbaaaabbaaabaabbaaaaabbababbbabbaaaabababbbbbabbaabbabaabbaabbbbbabbabaaaaaabbaababaaabaaaaaabaabbbbbbabbbbabababbbbbbaababbbbbbabbababbaabaaabaabaaaabaaabbbabaaaaabaaabbbbababbbbbbbaabbaaaaabababbababaaaabbabaaaabbababbbabababbbaaaabbbaabbababaaaaaabbaaabbaababbaaaabbaaaaaaaaaaaabaaaabbbaaaaaaabbbaaaabbababaaaabaaabbababbbbabaaabaaaaaaaabbbbbaaaabaaaaaaababaaababbbbaabbbaaaabbabaabbabbaaaaaaaabaabaaababbaabbaaaaaabaabbaabbabbaaababbaababbaaaaaaaabaaaabbbbbaabbabababbbabbbabababbabbabaabbabbbabbaabbabaababaabbbbbbababaaababaaaaaababbbabaaaaababbbaaababbbbbababbbaabaababaaaaabbaabaaaaababbbaaaaaabaabbabbbaabaaaabaabaaabbbabbbababbaaaaababbaababbbbaabbbababbbaababababaababababaaaababbaabababaabbbaaaaabbbbaaaabbbaabaaabbaabbbbbbbbbbbaababababbbbbbbbabbbaaabbaaaaabaaabbbbbbabbabbabbababbabbaabbabbaabaabbabaabababbababbbbaaabbaabbabbabbaaabbabbaaabbbaaaaaababbabaabaaaaababbaabbbabbbaaaaaabbbbbbabaabbbaaabbbbbaaabaaababbabaababaabababbaabbbbbbababbabbaaabbbabbbababbbaabbbaaababbbbbbabbbbbbbbbababbbbabaabbabbbbabbbbaaaabaaabababbaaabaaaaabaabaaaabbbaaabbabbaabaabaabbbabaaaabababbababaabbbababaaabbbaaaaaaabbbbabbbbbaabababaaababbabbbaaabaaabaaaabaabbabaaaaaabbbbababbbbbbbbbbbabaaaabababbbbbabababbbaabbbaaabaabaababababbbaabaaaaaabaaabbabbbbbabbaaaaaaaabababbabbaabbabbaabbbbbabaababababbaabbbaabbababababaaaabbabaabbaabababbbbabbbbababbbabbbbbabbaabbabbbaabbabaaaaaababaabbbbaaabbaaabbaabbabaababbbbbaaabababbabbababababbbabbbabbaabbabbbbaaabaaaaaaabababaababbaabbbabbaaaaabbbaabababbbaababaabaaabaabbaabbbbbbaabbbbbabaabbbaaabbababbbabbabababbababaabaaabbbbababbabaabaaaabaaabbaabbaababbbabababbbabaaaababbaabbababbaababbaababaabbababaabaabbbaaaabbaabbaabbbbababbaabaaaaaaabbbbabaaaaaaabbbaaabbaaabbabbabbbabbbababbbaaababbbbbbbbababaaabaabaabaabaababbaabababbbabababbbbbbbabbabbbaabbbabbaaababaaaabbaaaabbabbbababbabaaababbbbbaabbbbaaababbaaabbbbbabbabababbbababbbabbbaaaabaaababbbbabaabaababbbbaababbabbababbabbabbbaaabbbbbbbabaaaabbabababbabaabbbaabbbbbbbbaababbabaabaabbbbbbbabbababbbabaaaababbabaabaabaabababbbbbaaaababaaaaaaabbabababbbbaababaaaabaababbaababbbbbbbababbbaabbabbbaaabaaabaababbabaabbbbbaaabbabbbabbbbabaaaabaabbbbaababaabbbababaabbbbaabbaabaaabbaabaaaaabbababaaababbababababaaababababbbbaabbaaabaaabbababaaaaaabbbbaabababaaaabbbabaaabbbaabbbbabababababbabbbaaabaaaababbaaabbabbbbabbaabaabbbbabaaabababbbabbbbabbaaaabbbabbabbbaaaabaaabaabababbabaabbaaaaaaabaaaabababaaaababbaababbabbaaaabbbbbbaabbaaabaabbbbaaabaabbaaabbbbabbabaabbbabbaabaabbaaababbbabbbaabababbbbabbbaaabbbabaababbbabbbbababbbabaaaabbaababbbabbbaabaabaaabbabaabbaaabaabbbbbbabbaaabaaaaababbbabaaaabaaaaaabbbabbbbbaaabbbaabbbaabaabbbbaaabbbbbaaaabbabaaabbaaabbbabbbbbbbbbbbbbbaabbbbbbbbbbbbaaaababbabbbaaabbabbaaaababbbabbbbbabaaaabbbbbabbbbababaaaabbaabbbbababbabbaaabbbbababbbaaaaabaaaaaaaabbbaabbbbbbaaabbabbabaabaabbaaaabbabbaaaaaabaababaaaaaaabbabababbbbbaabaaabbaaaaabbbabbbbbbaabbaaaabaababaaabaaabaabbbaaabbbbbbaabbabbaaaaaabbbaaabaababbbabaabbbaabbbbabaaabbababbbbbaabaabbbaaaaabbababbbabbbabbabbababbabababbababbaaaaaaabbaabaabbaabbababbabaaaaaaabbbaabaaaabbbababbbbbaaaaaababbbbabaabbabaaaabbaaaaabaaaababbbaabbbaaabbbbbaaaaaabbaaabbaaabbaabaabbbbaabbabbbabbaaababbbbaabbababbbbaaaabbaaabbabbbbbbaabaabaabbabbaaababbabbaaabbaaababbbabbbabbaaaaabbabbbbaaababbbbbbbbabaaababaaabbabbaabbbbabbbabababaaabbabbababbbaabbbbbbbbbaaaaabaabbbbababaabbbaaaaaabbabaaabbaabababababbabaababbbbbbabababbaaaaabbbaabaaaabbbabbaaababbaabababbbbbaabbaababaaabbbbbaabababbbaaabbababbaaabaabbabbbaaaabbbaababaaababaaabaaaababbbbbbaabbaaabaaabbbbbabbaaababbabababbbbaabaaababbbbbaabbabaaaaaabbabbbabaabaabababbaaaaabbabbabababaaabababaaabaaabbabbabababaabaabaabaabababbabbaabaaabbbabaaababaababbbabaabaaababaabbbaaabbabbabababbaabaaaabbbabaababaabbbaaaaababbabbbabaabbbbbbbbabababbbbabbabbabaaaaabaaabbbbbaaabbbaaabbbaabbababaaabaabbbbaababbbbbbaabbbababbbaaabbbabbbaabbaaabababaaabbbbbbababababbaaaabbbbaaababaaababbababaabbbaabababaaabbaaaaabbabaaabbbbbbabaababababaabbaabbbaabbabbbabbbbbaaaaaaaabaaaabaaabbbbbababababbaaabbaaaaababbabbbbaababbaabbabbaaabbbbbaaaabbaabbbbbbbbbaabbababbbaaaaaaaaaabaabbbbbaababaaaaaabaabbabaabaabbabbabbbbbabaabbabbaaaabbabbaaabbabbabbbbbaabaaabbababaabbabbabbbabbabbababaabaababbababbbabbaaabbaaaaabbbaaabbbabbaabaabaababaabaabbbbaaaabaabbbbbbbaaaaaaabbbaaabaaabbabaaaaaaaaaabbbaabbbababbbbaaababbbbaaaabbaabbabbaaaabaaaaabbabababaabbaaaabbaabbaaaabbbbbbbaababbbbaabbbbaabaababbbabaabbbbaabbaabbaaaaaababaabbbbaabbaababbabaaaaaabbbbbababbaaaaaababaaaaaabbabbbbbaaaaaaabbaaababababbaaaaaabbbbabaabaababbabbbbbbabbaaaaabababbbababaababaaaababababbbaaababababaabbbbabbbaaabbbbbbabbabbaaabaaaabbbabbbabaaababbabbbaabbaababaabbbbbbabaaaaababbabaaabaababaabababaaaaababaabbbaabaabbaabbaababbabababbbbbbabbbabaabbabababaababaababbabaabababaababbbbaabbababaaaaaababbbabaaabbabbbaabbbbbaabbbbbbbbbbbabaaaaaaaaabbaababaabbbaabbabbaaaaaabbbaabbbaababbabbaabaababaabbababbaababaaaaabbabaabbaaaaaaaabbaabbbaaabbabbaaabbbabbabaabbaaaabbbbbbbbaabababbabbbbbabbabaabbaaaabbbabbbaaaaaaaaaaaaabbbbbbaabaabbbbbaabaaaabaaaaaabaaaaaabaaabbabbbbaabbabbaababbbbabaaabbbbabbabbabbaabbabaabaaabbbbabaabaabbababbbaabaaaaabaaabbbbaaabbaaabaabbbababbabbbbbbabbbbaabbaabbabbbbbabaabababbbbbaabbbaabaaabaaaaabaaababbaabbbbbbababaabababaaababaababbbbababbaabaaabbaaaabaabbaaaaabbbabaababbbabaaabbbbbbaaabaaabbbbaabbaaaaabbabbbabbaaaababbabbababbabbbaabaaaabbaabbabaaababbabaabababababbbaabbbabaaaabaaabbababbababbbaababbabbabaaaaabaaabbabababbaaabbbabaaaaaababbababababbaaaabbabbbaaabbbbbaabaabaaaabaaabbbabababbabbbbaaaabbbaababbbababbbbaaabbbbbbabbaaaaabbbbbaaababbbabbbabbaabbabaabaabaabbbabbaaaabbaabbbabbbbbbbbabbabababbaabbbababaaabbaaaabbbabbabaabbaaabaaaabbbaaabaaaaabaaaababaababbbbabbababbbbbbbbaababbbbbababaaaaabbbbaaaaaabaaaaabaaabbababbabaababaabbbababbbbbaaabaaabaabababbbbababbaabbbbabaabbbbabbaaaabbaababbaaabaaabbabbbbbbbaabaababaabbabbabaaabbbaabaaaaaabaaaaabaaaabbababaabaabbbbbbaaaaabaaabbaaabaaabaaaaaaaaabbbbbbbaaaabaababbabbbaaaababbabbaabbbbabbbbbbabbabaabbaabbababbabbbababbbaaabbabbaaabbbaaaabbbaaabbbbbaaaaabbbabbbbabaaabbbbabbaaabbabababbbbbbababbbbaabaaabaaaabaabbabbbbabbabbabaaabbababaabbbbabbbababbbbbabbbbbbaabaaaaababbbaababbabbababbbbaaaababbaaaabbabaabbbbabbbabaaabbbabbabbbaababbbbbabaabaaabbaaaabbbaaaaaaaaababaabaaaabbabbaaaaaabbbaababbbbababaaabaaabbbabaaabbabaabbabaaaabbbababbaaaaabbbbbaabbabbababbbbbbbabaaabbbbbaaabbbbbbabbabbabbbaaaababaaabaaabbaaaaaabbbbbaabbababaaabbaaaaabababbbbabababbbbabbaababbabaabaabbabaabbabbbbaaabbaababbaaabbabbabaabbaaababaabaabbaaaaabbaabaababbaaabaaaabbbbbabbbbbabbaaabaabbaaaaaaaaababaabaabbbaabbbabaaabbbbbaababbbabbabbabaaabababbbbaababbabbaabbbaaaaaaaabbbbaaaaabaabbaababaabbaaabbaaabbbbbbbaabbabbababbbaabbbbabbbabbaabaaabaaaabbabbbbaaabbbbabababababaaaaaaabaaababababbbaaaababbabaabaabbbbbaaaaababbbabbaabbaabababbbbbabbaaaabaaaaaaabbbaabbaabbbbbaabbabbaaaaababaabaabaaabaabaaaaaaabaaabbaababbbbaabbbbbbaababbbaabbbababababaabbabbabbbaabbaababbaaaaabbbbabaaaaababbaaabbaaaaaaabbabaabaabbabbaabaabaabbabbaaaabbaaaabbaabbbaaabbbababbababaabbbbbabbaaababbaababaaabbaababbbbaabbaabbbbbababbbbabaabbaaababbaabaaaabbaaabbaabbbabaabbbaaabbabbaaaababbbbbababbbbbabbbaabaaaabbbbababaaababbbbbababbaabbaaababbabbaaaabaaaaababababbabaabbabaabbbabbbbbaababbabbabaaabbbabbaaaaaabbbbaaaaaabbabbbbbbbbaabaabbaabbaabaaabababaaaaaaabaabbbabaabaaabaabaaabaabbabbaaabaabaaaaaababaaaaabbabbbbaabbaabaaaaaababaabbaabbbbbaaabaababbabbbbbabbbbbbbbbaababbaabbbabbaabbaaabaaabaabaaababbbabbabbabbbbbbbaaabbbabbbabbbbbbaabababaaaaaabbbbaabbabbbaaaabbbbbbaaabbabbbbbbbabaaabbabababaabbaaaabbabbbababaababaaaababbbabbabbaaaabbabbabbabbbbbabbbbaababbbbabaaaabbaaaababaabaabbbaabaabbaaabbaaabaabaabbbbaaaabbbbbaaababaaaabbbaaaabbbababbbabbababbbabaabaabbababbbabbabbabbaabaababbbbabbabbabbbaaaaabaaabbbbaaabaabbbbabbabbbbbabbbbabbbbbaabbbbbbbabaaaaaaaabababababbabbbbaaaabaabbbbabbaabaaaabbbbabbaaabaabababaaaaaabbbbbbbbaabaaabbababaababbaabaaabaabababaaaabbbbbbbaaabababaabaaababaaaaababababaaabbbbabbbbbaaaaaabbaaabaaaabababbbbbababbbbbaabaabbbaaaaabbbababababbbabaaabbbaabbaabbabaabbaaaabbbbabbbabbaabaaabababbbaaabababbababbabaaaaaabbabaabbbbbababababaaabbbbabbaabbbbbbaabababbaabaaabbbbbaabbbbbbbbbaaaabbbabaaaaabbbbaaaaababbaabbababbbabababaaabbbaabbbbaaaabaaabaabaabbbbabbabbbbabbbababbabababaabababbabbbaaaabaabbaaabaabbabbbabaababaababbaaabaabaabbbabbabaabaaabbbbbbaaabababbbababbaabababbaaabbaabaaaaaaabaabbabaabaabbabbabaaaabbaaaaabbaaaaaaababaaababbabbababbbabaabbaabbaababaaabbaabaaabbbbbbbbabbbabbabbbabaabbabaabbaabbbabbbbaabaababbabaaabaaabbabababbbbaabbababbaababbbbababbabbbabbbbaaabaaaabaaabaabaaabbababaaababaabbbabaababbbaabbaaaaabaaaaaabbaabbabbaababaabbbabbabaabbbbaabaabbbabbabbabbbbaabaabaaabbbbaaabaaaaaaababbabbaabbbaaabbbabbbaaabbabbaabaabbbabbbaaabbababaaaabbbbbaaaabaaaaaababaaaaabbbbabaabbabbbaaaababaabaaababaabbababaaaabbaababbabbabbbabbababaaababbbaabbaabbaaaaababaaababbbaabbabbaaabbababbabbabababaabbaaaaabbaaaabbbaabbaabbbbabaabbbbbbaabbaaabbabbabaabbaaaaababababaaaaaaaaaabbaabababbabbabbbbabaaaaabbbbababaabbbbbaaabbbaabaaabaabaabababbbbababbbbabaabaabaabbabbabababababbbabbbababbbbaabbbaaabbaaabaabbbabbaaabbaaabbaababbbabbbbbabbbbbabbbaaabbaababaaababbaabbabbaabbbbaaaababababbaabbabbabbaabababbbaabaababbbbbbababaababaaabaabbabbababaabbabbababbaaaababbbbaaabbaabbabaaaaaabaabaabbbaaabababaaaaaaaaaabaaaaaabbbbbabbababaabbabaaaaabbbabaaababaaaabbaababaaabbbbaabaaabbabababaaaabaabaaabbbaaabaaaaababaabababaabaaaaaabbbabaaaaaaabaabbabbbbbaaaaaaaababaaabaabbaababaaaabbbbbaabaaababbabbabaabaaaaabababaaaaabbababaabbbabbbababaabbbabaaababaabbaabaaabaabaaababbaababbbaaabaabaaabaabaaaababababababbabaabbbababaabbbbbabbbabbbabbabbaaaaabbabbaabbabaabbbaabababbbbbaabbaabbaaaabababaabbbabbbbabaaaaabbbbbbbabaaabbbbbaaabbaabbbbbaaabbababbaabaaabbaabaaabbabaaababaaabaaabbabbaababbaabbbbbbbabbbbaabbbbbbaabaaaabaabababaaaababbaaabaaabbbaaaaaababbabbaabbabbbbabbaabbbbaaaaababbaaaaabaaababbababbbbababbbaabbbbbabbbbbbbababbaabbaaababbbbbabaaaabaaabbabaabbabaaabaabbababbabaababbbaaaabaaaaaabbbaabbababbbbbabbbaabababaaabbabbbbbabbaaabbbabaabaabbbbabbbbbbbbabbaabbaaaabaaaaabbaabbbbabbaababbbbbbabbbbbaaaaaaaaabababbbbabaaaaaaabaaababbabbbaaaaababaabbaaababbaaaaabaaabbbaaabbbbbbaabaabbaaabbbbaaabbabababaabaaaababababbbabbaabbbbbbaabbababaaabbabbaaaabaabaababbababaaabaabbaabababbbbbbaababbabaaaababaaabaabbaabaaaaabababbabbbaababaaabbaaaaabaabbabaabaaaabbaaabbabaabbaaaaaabbabbaaaaabbabbbaabbbabbbbbaabbaabaabbbbaaabaaabbaaababbabaabbababaabbbbbabbaabaabbaaababaabaaababaabbbbababaaaabbbbbaaabaabaabbaabbbabaaabbaabbbaaaabaabababbaaabaaaaaabbaaabbaabaaaabaaaaabaaabbbaabbbbbbaaaabbabbaabbbabbbaaabaaabaaaaabaabbabaaabbaaabbabaabbabbabaaabbabaaaaaaaabaabaaabbbabbbabbbbaabbabaaabbababaabbbabbaabbbabaaabbaabaaabbabaaaaabaaaabbbbbbabaabaabaaaaabaaaabbabbbabbaaabbbabaaababaabbbbaabbbbaaaaababbbabbbbababbbababaabaabbaaaabbababaaabbbaaabbbbbbaababbaaaababbaaaababbababbabbbabbabbaabbaaaaaababaaabbbbabbaaaabababbbbaabbbaaaaaababbaaaabbbaaaaabbbbbabbaabbbbaabaabbaaaababbbbbababababbabaabbbbabbbbbbaaababbbaabbaababbbaaabbbbbbbbabaaabbbbbabaababbababaaabbabbabbabbaababaabaabbaabababbbbbababababbabbbabbaababbaabbbbbabbbbabbbbbbaaaaabbbaabbbbbaaaabbaaababbaaaaaabbbbbaaabbbbabbbabababbbaabbbababbbbbaaaaaabbaabaaababaaabaaaaaabababbabbaababaabbabbaabaabaabbababbbaabaaaabbbaabbbaaaabbaabbaabaaaababbaaabaaabbbababbaabbbbaaabababbaabbbbaabababababaaaabaaaabbabbabbaabbbbbbbaabbaabbabaabaabaaaababaababaaabbbbaabbbbbbbaaaaaabbabbaabbbaababababbababbbabbbababbaaaabbabaabababbaaababbbabbabbababbabaaababaababbbaaabaaabbbbbaaabbbaabbaabbabaaababaaababbaabbaaaaaaabbbbbababbbbaabaabbaababbbabababbbabbabbbabbababbababbbababbaababbbbbababaababaabaaaaabaaabbabaaabaaabbbabbabbabaaaabaabbaaabbaabaabbaaababaaaaabbbaaabbabbabbbbaaabbaaabbaababbbbabbaabbabbbaabbabbbbaababbbabbaabaaabbbababaaaaaaabbbabbbabbaaababbababaabbbaaaabbbaaabaaabbbbaaaababaaaaabbbaaaaaabababaabbaaaaabbbaaaabbbbaabbbbbaabbaaaabaabaabaaaabbbababababaabbabbbaaabbbaaabbbbaaaaaaaabababbaabbaaaabbaabbababbabaaaaabbaabbbbaabbabbbababaabbaaabbaabbaabababbbaabbabaabbbbabbbbbaabaabbbababaabaaabbbbaabbabbbabbbabaabaaabbaababbbbbbabababbbaabababaaaaaababaabaababbbbbabaaaabbaabbababbbbabaaababaaabababbbabbaabbbaaaaaaaaaaaabbabbbabbaabaaabaaabbabaaabaaababbabaaabbabbaaabbbbbbbaabbbbaabaaaaaaaaaababbbabaababbbababbaabbbbaaabbbbabbabbaaaabbbbabaabbbabaabbaabaabbbabbbbabbaababbbbaabaabbabbbbabaaabbbbbbbaaabbaabbabbabbaaababbbaaaabbaaabaababaaaaabbabbababbbabababbbaababbbbaabbabbbabaabaabbbbabbbabbaaabbabaabaaabaabbabaabbaababababaabbaaaaababaabbbaabbabaaaaaaaabaaaabbabbabbbbbbaabbaabbbbabbbabababbaaaababbabbababaaaaaabbaabaabbaababaaaabaabababbbbaaabaaaaabbbababaaaabbaaababbaabaabbbbaababaaabbababababbbbbaabbbbbabaabaaababbbaaabaabaaabaababbabbabaabbaabbbaaaaaabbaabbbabbaaabbbbbbabaaaabbaabaaabbabbbbbbbaaaabbabbabbabbabbabababbaabbaabbaaaaaaabaaabbbaababbbaaabaaabbabaaabbaabbbaaabbaabbbababababbbbbaaabbbbbbbbababbbbbbababababbbabbbbbababaabbabaaaabbbbbbaaabbaaabbbaaaaabbbabababaaaaababbabbbbbabbaabbbbbbaaaaabbbaaaabbbbabbaabbabaaabbbaabababaabbabbaaababbbaaabbbabaaabbbbaaabaaabbaaaabaaaabbbbbabbabbabbbababbbaaaababbabbabbababbabaaabbbbbabbbbaabaabaaaabbbbbbabaabbaaaababbababaaabbaabaabaaaaaaabbbabbbbbabbaababababaabbbaaabbbbbabaaaaababaabbaaaaabaaaaabbbabbbbbbbbbabbaaababaabbabaaababbbaaababaaaaaabbaabbbaaabbbaabbaababaaabbbbbaaababaaaaaaaaaabbaabbaabaababbbaaabbbaabbabbaababbbaaabbaabbbaaababbbbabaabaabaabbaaabbaaaababbbaaaabaaaaaaababaaabbbaabaaaabbbbabbaaaabaaabbabbaaabbbbbaaababbbbabbbabbabbaabbababaaaabbabaaaaaababbabaaaabbbabbbaaabbaabbabbaabaaababaaabbababababbabbaabbababaaabababbbaaababbbaabbbaaaaabbabaaabaaabaabbabaababbbbaababaaaaabaaaabbbbbbabbabaaaabaabbaaaaaaabbaabbaabbaabbbabbabaaabaaaabbabaabaabababbabbbabbbbababbabaabbabbaaabbababaabaaaabbbaabaabbbabaabbaaabaaabbbbbaaabbaababbbaabaabbbabaabaababababbbaaababababaaaaabaaaaabbababbabaaabbbbbbbbaaaaabababbabaabaaaabbaababbabbbbbaababbaaababaaabbbbbaaabaabbbbabaaabaabbbbbbbbababaaaaabbaabbbabaabbbbabbbbabbbaababbbabaaabbbbaaaaaababbbabbaaabbaabbaabbabbbbaaaaabaabbbbbbbbbbabaabbbaaabaaabababaabbabaabaaaabbbabababbbaaabbaabbaaaaaabbaabaabbaabbbbbabbaaaaaababbbabbaaababbbabaabbbbbabaaaaabaaaabababababbabbbbbabbbabbbaabbaabbababaabbbbbbbbababbabababbabbaaaabbbabaaabbabaaaaaabaaaababaaabbbaabaaabbbaabbaababaaabaaaababaabaabbaababbbababababbaabbaaaabbababaabbbbaaaaaabbaababbaabbbbabbaaababaabbababbbabbbbabbbabbbaabaaaaaaaaaababaabaaabbbaababbbbaaaababbaabbbbaaabbabbbaabbbbaaaaaaabbabbababaabbbaabaaabbaabbaababbbbaabaabbbaabaabbbabaaaaabbabbbaabaababbbabbbababbbbbbabbbbbbabbbaaabbbbaabbabaaababababaaaaabbbbabbbbbaaaabbaabaabbababbaaaabaabbbabaaaabbabbaabbabbbbaaaabaaaabbbbbbaaabbaababaaabaabbbababaabbbbbbabbabaaababbaabbbbbbbaaaaaaabaababbaaabaaaaabaababaaaabaaaaabbabaaaabbbababbaababbaababababbaabaaababaababaaaaababbbbbabbabbbbaabaabbabaabbbaababbbbabbbbaaaabbababaabaababbbbaabaaabababbaaaabbbbaaabbbbbabaaababbbbbbabaabbabbababaaaabbbbbabbbbaaabbaabababaabbaabbaabaabbabbbaabbabaabbbaaaaaabbbabbaababbababbbabbbabaaabbbaaaaabbababaaaaabbbbbbbbbbaaaaaaaaabaababbaaaabbababbabaaabbbbaabbbbaaaabaabbabbbabbbbabaabaaabaabbaaaaaaaaaaabbaaabbbbaaaaabbbbbbaaaaabaaaabbbbababbbbaaaabbaabbbbbaabaabbaabbabaababbbbbbabbbabaabababbbbbaabbbbbabbaabbbabbaaaaaabbbbaabbbbaaabbbabaabaabbabbbbbaabaaaababbbabaabbbbbbbbabbabbbabababaaaabbaaabbbbabbbababbbbbaabbababbbbbaababbbaaaababbbaabbbbbbabaabbaabbabbbaaaaabbbabbbbbbbbaaabbaaabbabaaaaaaabaaaaabbababbaaaaababbbbabaabbbbbababaababbbabbabaaaaabbbbaabbaabababababaabbbbbaaabbaabbaabbababbbbbbbbbabaaaaabbababbbbababbabaaababbbbbbbabaabbbabababbbaaaabaababaabbaaaaaabaaabbaabbbabaaabaaabbbaaaaababaaabababaababbbbabbaaaababababaabbabbbbbbbaabbbaaababaaabbaabbabaaabaabababbabbbbabbabbbbbaaababaaaaabbabaaaabaabaaabbbbbababbbbabaaaaabbbbaababbbabbaaaabbbabababaaabaaaabbababbbaaaabbaabaabbabaabaabbbbbaabbabbaabaaaabbaabbbaabbaabbbbbbaaabbbbababbaabbbbabaaaaabaaabbbababbaaabbbbaaaaabbaabaabaabababaabaaaaabbbbabbaaaabaababbbbaaaaabbbaaabbbbbaabbbbaabaabaaaaaabbaabaababbaabaabbbbbaaabbaabababababbabbbbbaababaababbabbbababaaaaaaabbbbbaabaabaaaaaaaababbabababbabbaaabababaabaabbabbbbaaaababbaaabbbabbabbbbbbbabbaaabaabababaaabbabbbbbbabaabbbbaaabaaaaaababaabbaaaabbbabbabaababaaababbbbbabbabbbaaaaaabaabababaaabbaabaabaabaaabbbbbbabbaaabaaabbabababbbbbaaaaabaaabbabbaaabbaaaabbabbabbaabaaaaaaaaababbaaaaaababaaaabbbbbbbbbabbaabbaaaaaaaababbaabbbabbaaabaabbbaaaaaabbbbbbaabbababaabaabababbaaaaaababaabaabbabbbbaaabbababbbaababbaaabbbbabbaaaaabbababbbbabbaabbbbbaaabbbbbaaabababbaaaababbbbaabbbabaaaaaabbabaabaabaabababaaabaaaaabbbbaabbaaaaaaabbabbaaabbbbabaaaabaabaabaaabaabbbaaababbaabbaaabbaabaabbaaaaabababbaabbabbaabbabbbabababbaabbaabaaabbbbaabbaabbbaaabbbbababbaabaabbbbabbababbaaaaabaaabaabbaabbbbaaaabaabaabaababbbbabbaaaabbbbbaababbbbbaaabbbabbabaabbaaaababbbaabbbbbaabbababbaabbbbababaaabbbbaabbbabaababbbabaabbbaabbaaabbaababaaaaabbbbbaaabababbabbababaaaaabbbabbbabaaabbbaaaababbbbaabaabbabbababbbbbbbbbbbaabaaaaaaaaabaaaaabaabbbbbabaaaabaabbbbbbababbaaabbabbbbababbabbbbbbabbbabababaaaaababaaabaabaabbaaabbbaaaabaababbbababbaaaaaaaaaaaaabaaabbabbbababaabaabbbabbaabaababbabbabbaababaabbbaabbbbabaaabbaaabaababbaabaabbbbaabaabbaaaaaabababbbaabbbbabbbbbababaaabbbbbbabaaaabababaabbbbaaaaababaabbaaabaababaaaabbaabbabbaababaaaababbbaabbaaaaaaaaaabbaaaabbbbaaabababbbbaaaabaaabababbabaabbbabaaaabbabaaababbabbbabbaaabbaabbabbabbaabbababbbbbabaaaaabbabbbbaaabaaaaaababbaaaabababbaabaaaaaaabaaabbabbbabababaaaaabbbabbbabbaabaaabaaabbaabbaaababaabbbabbaabaabbbababbbabbaaababbabbbbaabbbaabaaabaabbabbbaaaabbaaaaabbbbbaaaaaabbabaaaabababbbbbabbaaaaaabbbaabbbbbbbabababaaaaaabaaababaaaabbbabbabbbbabbaabbbbbabbabbbbabaabaaabaaabaaaababaaaaabbaabaabbaababababbabbbabbbabababbaaabaaabbbaaabbbbbababbabaaabbabbaaabaaababaaaabbbbabaabbbbaaabaaaabbbbabbbaaababbbaaaababbaaaabaaababbbabbaaabbbaaababbabbbbbbaaababaaaababaaabaababaabaabbbabbbbbabbabaaabbbabbaaabaabbbaaaabbbbbabbaaabbaabbbaaababbbbbaaaabaababbaaabbbabbbbbbbaabaabbabbbbabababbbabbaaabbbbbbabbbbaaabaaabbabbbbbbbbaabaabbabbbbabbabaaaaabaabbaabbaabbabbababbbabaaaaabaaaabaaaababaaaabbbbabaabbabbaabaaababaabababbabbabbbbaabbabaaabaaababbaababbaabbaaaabababbabbaaaaaabbbbbabaabaabaabbbbbaaabbbaabaaaabbbaabbbabbbaababbabaaabbabbabbbbaabbbaaaabaaabbabaaabbaaaaabbabbaaaaabbbbaaaabbbaaaabaababaabaaaaaaabbbababbbaaaaabaabbbbbbaaaababbbaabbbaabaaabbabaababbbbbbbbaabbabbbbbaabbaabbbaaaabaaaabaababbabaaaaabbaabababbbaababbbbbbabaabaaaababbaabbabbabbabbbbbabaaababbabaaaababababbababaabaaaabbbbaababbabbabbbbbbbabbbabaaaabbbbaaaaaabbababaaababaabbabbaaabbbbaabababbabbabaaabbbabaaaabbaabaabaabbaabaaaaaaaaababaaababaaaaabbaabbbababbaaabbaaaaaaabbbaaaabbaaaaaaaabababbbbaabbbaaabbaabbabbaabaabababababbbbbbbbabbbaabbaaaabaabbbaabbbbabaabbabbaaababaaabbbbbbaaaabbaabbbbbbaaaabaaaabbabbabbbaaabababaaaaaabaabaaaababbbabaaabaabababababbbabaabbbabbbbaabaaababaabbbabaabbbaaababbbbaabaababaabbaababbaaaabaaaaabaaaabaababbabababbabbaabbbabbabbabababbaabbbabbabaabaaaabbbaabaabaabaababababbbbabbbbaaaabaaabaaabbaababbbbbbbaaabbabaaaaabbbbbbaaabbabbaabbbbbaaabaaaaabbababbbabbabbbbbbbbabaababaaababbabbabaaababaaaaabababbbababbaabbbbbaabbaaaaaabababbbbbbababbabaabbbabaaaaabaaaabbbaabbaaaaabbbbabbabbaabababbbbaaabbbbbaabbbababaabbbaaabbaaaaaabbabaababbbbbbaaabbabbbaabbaabbbbbabbaabbbaaaabbaaaabbabbbbbaaabbbbbbabbababaaaaabbabaabaaaaaaabbabbbaaabbaaaabbaaaaaababaaaabbbbabababbbaabbbbabbabbabbbbbbabaabbaabbabaaabbabaabbbbbababaabbbabaababbbbbabbabaabbbbbbbbbbbabaaaaababaaaaaaababbaabbabbbbaababbbbabaaababbaaaaaabaababbbaaababbbababbbbbabbbaaababbabbbbabbaaabbaaabaabaaaababbbbbaaabbbaaaaaabbababbbaabbbbbabababaababbabaababaabbbaabaabababbabbbabbaaababbbaaaabababbabaaaabbbbabbabaabbaaabaabaabbbaabaabbababbbababbbbbabbbbbababbbaabbbababbaaaababbabbaaaaabbababbbababbbaabaaaabbaaaaababbbabaabaaababbbabaabbbbbabbbabbbaaaabbaabaaaabbbbabaababbbbaaaaaaaaaaabbbbaaaaabbbbabaaabbbaabababbabbbaabaabababbbbaabababbaababbababbaaaabbabaaaabbbaaaaaabbbbaaaabbbaabaabbaaaaaabbabbaaabbabababaaaabaaaaaababbabbbbababaaabbbabbbaabbbbbaababbabaaaabbbbbaaaaababaabbbbabbaaabaaabaababababaaabbbbbaaababaabaabbbabbaaabbabbabbabbbaaaaaaaaabbaababbbaabbbbbaaaaaaabbbabbbaabaabaaabaabaaaaabbaaabaababbbbbbbaaabbbbaaabbbbaaaababaaabbabbababbbbbbabaaaabbaabaabaaabbbaaabbbbbbaabaabbbbabaabababbbaabbbbbbabbbbaabbaaababbababababbabaabbabbaaaaaabababbbababbababbbaaabbabaabbbbaaaaaabbabbbaababaaabbaababbaaabbbbabbbbabbaaabbabbbbabbbbbbbbbaabbaabbababaabbabbbbabbbbabbbbbaaababaabbbabaaaabababaabbaaaabaaaaaababaaaaabbbabaabababaababbbbbbaaabbaabbaababababaabaaaaaaababbaaabbaaabaaaabaaabbbabababababbbabaabbbbabaabaabbbbbbaaaaaaababaaababbbaabbbabbbabaabbbbbababbbaaabbaabaaabababaabbbbbbbbaabaaabbbabbababbbbaaabbaabaaabbababbabbabbbababaabbbbbabaabbaabbaabbaaaababbbbbaaabaaabbaabbbbaaabbabbbaabaabbaaabbabbababbabaaabaaabbababbaaabaaaaabbabbaaabbbbaabbaaaaaabbbbaaaabbaaababbbbaaaaaabababbbaaabbabbaabababaaabaaaabbaababaaaababbaaaabbbbaababababaaabaaaabbabbbbabaaabbbabaababbababaaaabbbbbbaaabbbaaabaaaaabbaabaababbbabbbbbabaabbabbbbababbaababbaaabbbabababbaabbaabaabbaaabbbabbbbaaaaabbbbaaabbbbaabbababaabbbbabbbabbbbbaababbbbbabababbbbabaaaababbaabaababbbbbbbabbbaaabbbababbaaabbbaaabaabbabbabbabaaabbaaaaaaabbababababababbbbbbabbabaabbaabbabbabbaababbaaaaabbbbbaabaaabbabbaabbbbaabaaaabbaabbaabbbaaababaababaabaaababbabbabbbabbaaaaaaaaababababbbbaababaaababbbbbaababaababbbabbbbabaabaababaaabbabaaababaabbbbbbabaabbbbbbbbabbaaabbbbbbbbabaabaaaaabaabbaaabaaabaaabaabaaabbbbababbaaaaaaababaaababbabbabbaaabbaababbbaabaaaaaabbbbbbaababbaaaabbbababaabbbabaabaabaaaaabbbbabbaaababbaabababaabbaabbaaabbaaaabbbabbaaabababbbaabababbbbbbabaabbabaaaabbbabaabaaaaabbbaaaaabbaabbbbabababbbaaabaabaababbaaababababbabaaaaaabbbaaabababbbaaaabababaababbabbbaaaabababbbaabaaabbababaababbaaababbbbaaabbbbabaaabbabaaaaabaabababbbbbbbbabbbabababbaabbbbababaaaabbaabbbaabaaabaabbaaabbbbbbbabaabbbaabbbbabaabbaaaaaabbbbbbbbbabaaaabaaabaaabbabbbbaabbbaaaabbbababbaabbaabbaabaabbbaaaabbaaabbbababaaabbabbbbaabaaabbaaabbbabaaaababbaaabbaabaabababbabbaababaababbaabaaababbbbbbbaaaaaaabbabbbaabbaabaaabbbbaaaaababaaaaaaabbaabaaababbbbbbababaaaaaabbabaabbabaaababbabbbabaaaabaabbbabaabbababbbbbaaaabbbbabbabbbaabbabaabaaaaaaabbbbabbaaaaabaababbbabbbaabaaababaabaabaabbaabbbbbaaaababababaaabaabaaaabbaababaababaabbbababbabaabbbbbbbaaababaaabbabbabbababaaabbabaaaabaababbaabbbbaababaaaabbaaaabbaabbbaaabaabbabbbbbbbaabbbbbbbaaaaabbaaaaababbbabbbabbabbaabbbbabaaabababaabaaaabbbbaaabbbababbaaabbaabbbbaaabaabbaabaaababbaabbabbbaaabaabaaabaaaabaabaabbbbbabbabbabbbaaabaaaaaabbbabaabbbbaaababbaaabaaabaaababbaabbbbbbbbbaaabaaaabbababbbaaabbbbbbaaabbaaaabaaabbbaaabbaaabababbbbabaabaababbaaaabbaabababbbbbbbaabaabababbaaababaabababaaababbababbbbabababaaabababbaaaabbaababaaaaaabaaaabbabbbabbabbaabababbabbabaaaaabbaaabbabbbbaabbabaaabbbbbbaaabaaabbbaabbabaaabaabbbbbbaaaaaabbbaabbbaaaabbbaaabbbabaaaabbaaabaaaaaaabbabbbababbbbabbbabbaabaaaaaaababbbbbaabbbbabaaabababbaaaaaabaabbbabaaabbbaaabbabaaaabbabaaabaabbbbaabbaaabbabaabbbaaaabababbabbaabaabaaaabababaabbbaaaaabaabababababbaaababaabbbbbaaabaabbbabbaaabaaabaaabaaaaaabababbbbaaabaabbaaaaabaabaababaababaabaabababbabbbabaaabbaaababaaaaabbaaaaaabbbbaabbaabbaabbabbabaaaabaaabbbbbaabababbaaaaabbabbbaaaaabbaaaaaaaaabbabbabbabbbbaabbaaabaaabaabaabbbaaaabbabaaabbabbabaabbabbabbabbaaaaaabbabbabbaabbabbbbbabbbbbbaabbbbbbbabaaabaaabbbaababbabbababbaaabaaababbabbbaabbababababbbabbabbabaabbbaaaabbaabbbbaaabaaaabaaaaabbbbbbbabaabbabbabbaabbabbabaabababaabaaabbbabaabaabbbbbbaabbaabababaabaabaaaabaaaabbaabaaaabbaabbaaabbbaaaabbbaabbbaabbbbbabaabbbaabbbbbabbbbbabbaababbbbbbaaaabbbabbbaaabbaababbbaaaaaabaaaaababababbbbaabbabbaaaabbabbbbaabaaaabaaaaababbabaababaabaaaababbbbbaabbbbbaaaaaabbbaaaaaabbbbbaabbaaabaabaabbbaaabbbbbbaabaaaababbaabbabbabbbbbbbabababbabbbbbabaaaaababbbaababbaaabbaabaaabaabaaaabbaabbabaaaabaababaababaaaaabbabbabbbbabbaabaaabaabbaabbbbababbbabbabaaaaaabaaaaababbbabaababbabbaaaabbaabbabaaabbaabababbbaaaaabbaaaaaababaabaaabaabaabbbabbbbbabaababaaaaaaabbbababbbbababbbabbabbaabbbabaabaaabbbbabbbbaabbbaaaaabbabababbaaaabbabbbaabababaabaababaabaaabaabbbaabaaaabaaabbaaaabbbbabaababaababababaaaaaaaabbbabaabaaababbbbbbbbbaabaabbaaabaababaabbaababaaaaaabababbbaaabaaabaaabaaaababaaaaaaabbbbabaaabbabbaaaabbaabbaaaabbababbabbaabaaaabbaabaabbabbabaababbbbbaaaaabaabaaabaababbbabaaaabaabaaaaababbabbabbbabbabbabbaabaabbbbaaaabaaabababaabbabbbbaaabbaaabaaabaababaaaabaaaabaabbbbaaaabbbaabbaabaababbabbbbaabbaaaababbbbbbbabbaaababaaabbabbbbbbaababaababaabbbbbaaaabbbabaababaaabaabbabaabaabbbaabababaaabaabababbbabbaabbbabaabaaababaabaabbbabaaaaaabbaabbaabbababababbabbabbaaaabbaaabbbbaaabaabaabbabaabbabaaabbbbabaaaabbbaaaabbbaabbaaabbbbabbaababaababaabbaaaababbaaabbbabaabbbbabbaabbaabbabbaabaababbbbaaaabbbabaabbabbaaaaabaaabbabaaabbabbaaaabaabbbabababababaababbabaababaabbbabbababbabbaabaaabbbbabbbaabbaaababbbaabbbbaaabaaabbbbbabbababbbabaababbbbaabbbabbaabbbabbbababbbabbbbbbabbabbabaaaaababbabbabababbaaaaabbbabbaabaabaaaaababbbbbabbabbbbababaaababaaabbbbaaabbaababaabbbbbbaaabaababbbabbaababbbbaabbbbbbbabbababaabaaababaaaaababaaababbaabaabbbbabbbbbbaaabababaabaabbbbaababababaaaaaaaabaabbbaaabaabaabbabbaaaaaabaaaabbbbbbabaabababbbabbaaaababbbbaaabaabaaabaababaaaaabbaabaaaaabbbbaaabbaaabbabaababaaaabaabbabbbbabbabbbbbabbbabaaaaaaabaaabaaabbabbbbbabaaaabaababaababbaaaabbbaaabababbbabbbbbbbabaabaaabaaababbabbaaaabbbbabbbbaaabbaaabbbabbaaabbabbbabbbaabbbbbbbabbbbbbaababaabbabababaaabbababaabababbaababababaaabbbababababbbaabbbabaaabbaababbaabababaaaabbaabbbbbbaaaabababaabbbbbbabbaabaaabababbbaaaaabaaabaaabbbbbaaabbbbaaaaaabaaaababababbbbbbbababbbaaabbabbababaaabaaaaaabbbabaababbaaaaaaaaaabbbaaabbabbbbaaaabbabbabbababaabbbaabbbbaaaabbaabbabbaaaaabaabaaabababaaababaabbbbbaabaabbaaabbbbaaaabbababbbbbbabbbaabbbaababaaaaabbbabaaabaabaaababaabaabaabaaabaabbbaaaaaaabbbbaababbbaabaabbabbbabababbaaaabbababbbbbbbbbabbaaabaaaaabaabaabbaaabaaabbbbbbbbaabbaaabaaaaaababbaabbaabaabbaabaabaaababaabbababbbbabbababaaabababbaaaabbaaaaabbaaababbbbabaaabaababaababbaaababbaaabaaabbaaaabbabaababbaabaabbbbaaabaabaaabaabaabaaaaabbaabbaabaaabbbababababbbbbbbbabbaabbabababbaaabaabbbbabababaaabbabaaaaabbabbbbaabaabbbaabaaabbaaabbbbababababaabaabbbbaaabaaabaabaabaabababbbbbaaaabbaaabaaabaabaaabbaababbbaabaabbaaababaaababaababbbbaaaaabbbaaababbbaaaabbbbbababbbbaabababbbbaaaabbbababbbbbabbaabaaaaaababaabaaabbbaaababaabaabbbbbaabaabbababaaaaabbababababbbababbabaabaabbabbbaabbaababbbaaaaaaaabbbaaaaaabbbaabaaabaabbbbaaabbaaaaaaaaaabaabababaababaaabbbaabbbbbbbbabaabaaababaaaaaababaabbaaabbbaaabbbbbbbbaabaaabbbababbababaabbbaabbabbaaaabaababababbabaabbabbababbbbabbabababbbbaaabaababbbababaabaaabaaaababaabbaaabbbabaabaaaabbbbaababababbabaaaabaaabaabbaabaaaaabbbababbbaaaaaabaaaaaabaababbaababbbabbbbabbabbababbabbabbbbbaabaaabbabbabababbabaaaabbaabbbaaabaabaaabaaababbbbaaaaabababbbababbbbbababbbbbbbbaaabbaaaabbbbbbababbabaabaaaaaabbbbbaababbaaabbaaabbaabbbababbbaabbaabaaaaaababbbabbbaaababbbbbbabaababbbbbaabaaababaababbbbbbbbbaaaabaaababbbbaaabaabbbaababbaabaabbbaabbaabababaaaaaababbbaaabaabaabbabaabbbbabababaabbbbbaaabbbbbbabbbaaaabbaaaaaaaabbbbababaaabbbabaabaababbaabbaaaaabaaaabbaaaabbbabbbbaaaaabbbaabaaabbaaaababaababbaaaabaaababaabbabbbbbbaaabbbbbbabbabbabaaaababababbabababababbbbbbbaaaabbbaabaabaababbbbaaaaabbbbabbabaaaabaabaaaabbaabbaabaabaaababaaabaababbbbbabaabaababaabbaababbaabaaaabbaabbbbbaaaababbabaaaaaabbbabbaaabbaabbbbaabaaababbbbbaabbaaaaaaababaabaaabbbabaaaabaabaaaaabbbabbaaabbbbbbaabbaaabbbabbbaabaaabbaaaaaaababaababbbabaabbbbbaababababbbaaabaababaaaaaababbaabbbaaabbababaabbbbbaabaaaabababbbbbbbaababbbaaabbabbabaaaababaaababbaababbbaabbbababbabaaabababbabaaababbabaabbababbbbababbbbbbaabaabbbbaabababaababbbbabaaaaaababbabbbbbbaaaaabaaaaababaaaabbabaaabbaabbaabbabbbaabbbabbaabbbbbaabbbbaaabbabbbabaaabbbbabababbaaaaabaababbaabaaabbababbbabbaabbaaabbaaaaabaaabbbbabaabbbbabbabababbbaaabbaabbbabbaaabbabaabaababbababaaababbbbbbbbaabbbbabaabbbaaabbbbaabbabbabbababaabbabbaabbaaaabbbbabbbaaabbbbaaaaaaababaabbabbabaaabbbabbbababaabaaabbbbbbbbaaabbbabaabaabaabaaababaaabababaababaababaabaabbbababbababbbabaabbbbbbbaaaabbbbababaabababbbabbbbaababbaabbbababbbaaaabbbbbbbbbbabbbbbaababbabbbabaababaaaaabbaabbbabbbabbbaaaababbbbaaaaaababababbbbbaabababbabbaaaaababbabababbbabaabbbabbbbaabaababaaabaaabbbabaaabaababbbbbbaabbbaaabaaabaabaabbabbbaaababaabbbbaabbbbaaaaaababaaaabaabbbaaaaaaabbaabbbbaabaaaabababaaaabbbaaabaabbbbbbaaabbbbbabbbbbaabbbaabbbbaaaaaaaaaaabbaabaabbabaaaaaabbaaaaabbababbbaaabbbbbababbaaababbbbbabbabbbabbaaabbabaaababaaaabaabbbababaaaaaabaabbbbbbbbbbbbbabaabbaabbbbbbaaaaaaababbababaabbabbbbbbbababbaabaabaaaaabbbabaabaabaabbbbbabbbaaaababaaaabaabaaabbaababababaaabaaababbbbbaabbbbbbaababbbabbbbbabbaaaabbbaaabaaaaabbaaabaabaaaabaabaaaaabbbababbbabaaaaaabaaaabbbbbabbbabaaaaaabbababbabaaaabbaababababaaaaaabbbbabaaaaabbbbbaaabbaaabbaababbaaaaabbaababaabaaabbbabbaaaabaaabbbaabbbbbbbabbabaaabbbbbbaaaaaaaabaaaaabbaababaababbaaabbbbbababbbbabbabaaabbaababbabaabbbaababbbababbabbaaabbbbabaaabbbabaabbabbaaaaaaaabaabaaabaabbbbababbaababbaabababbaaabbbbaabbaaaabaababbaabbbabaabaababbbaababbababaabbbabbbaaaabbaaabbbbbabbaabbbbabaaaaaababbaabababaaaabbaaaabababbbbababbbbbbbaabaaaaabababbbbbaabbbaabaaabaabaabaaabaaaabaabaaabbbaaabbababbabaaabbabaabbaaababbbbaababaabbbbbbbaabaaabbbaaabbbbbbabbbbbaababbbababababbbbbbbaaabbbbbbbabaaabbabaabbaabaaababbbbaabaabababbaaababbbbbaaabbbabbbbbaabbbaaabbbbaababbbbbbaaabaabbaaaaaaaabbabbabbabaabbababbbaaaaaaabbbaaabbbaabaabababbababbaabbbbbbabbaaaaababbbaaaaabbaaababbbaabbaaaaaaaaaabbabaaaabbaaaaabbbababbabbabaaaaabababbbbaaabbbabbaabaabaabbbbababbabbaabaaaaaabaaabaaabbbbabbaaaaabbabaaaabbababbbabaaaabbaabbababaaaaaabbbabaabbabaaaabbabbababbaaaaabbababaabbaaaaabbaaaaaaabbaaaaabaabbabbbabaababababbabaabbabbbbaaabbbbbaaaababaabaaaaaaaaabaaaabbbbbbbbbbbbbabbbbbbabbabbbbbaabaabbabaababaababaaabbaabbbbaabbaaaabbbbaaabbbbbaaabbbbbababaaababbbbabbbabbaaabaabbbaabbbbaabbaabaaabbbaababbabbaabbaaabbbabaabaabbaaaaabaaabbababbbabbbbaaaabaaaabaaabbababbaaaaaabababbaaaabbabbbaaaaaabaabbaabbbaaabbabbbabbbbbbbaaababbabaaabbbaabbaaaababbbabaaaaabbaabbabaaabbbaaaaaababbabaaabbaababbaaabaaabbbaaaabaaaabaabababbbabbaaaababbabaaabbaaaabaabbaaaababbbbabbaabbbbaabbbaabbabaababbaaabbaaaabaaabbbbbabbbaaaaaaabababbaaabbaaaaabbbabaababaabaabbaaabbbbabbabbabbbaabbaabbaababbababbbaaaaaabababababbbabaabbaabbbabbbababbaabbabaabbaabbaaaababaaabaaaaabbaaaababbabbbabbaabbababbabbbabbaaaaaabbabbbaabaaabbbaaaabababaabbbbaabbaaaabaaabbaaabaaaabbaabbbbbbbbabbababbbbabbbbbaaababbaaaaaaaabbbbaaabbaabbbaabbbbaaabababbbabbaabbbbbaaaabbbbbabaaaabaabbbabaaababbbbbaababaaaaaabbaaaaaabababbbbbbbbbbbbbaaabbabaaaaabbababbbbaaababbabaaabbbaabaabbbbbbaaaabbaaabbbaabbbbabbbbbbbbaaabbaaaaababbbaaaabbbaabbbabbbbaaaabbbbaabbbbbbababababbbbbabaabbbbabbaabaababbbabbbaabbbabbbbbbbbababababbaaabbbaaabbabaaaaaabbbaabbaababbababbbbbaabbaabbbaabbbbaabbbabaaaaaaabaabaababbaabbbbbababaaabaaaabbbbbbaababaabbaaababaaabababbaaabaabbbaaabbaabbbbbabbaaaaabbbaabbabbbaaabaabbbabaabbaabbbbbbaabaabaababbaaaaaaaaabaaaabbbabbaabaaaaabaababbaabaababbababaaaabaaabaabbbabbabbbbabbaabaabaaaabbbaaaabbbabbbababbabbabaaabbaabbabaaababbabbaaabbaabaababaaaaabbbabaaabaabbbababbbabbaababbbaaaaaabaaaabaabbabbaaababbabaaabaababababbaabbaaabbabbbabbaaaabaaabaabaababaaabaabbbabaaabbaaababbbabbbabaaabaaabbbbbbaabaaaababbbbaabbabbabbabaababbaabbabbbaabaaababaaaaabaaabaaaababbabbaaaabbaabbaabbbaabaabbbabaaaaaabaababbbabbaabbabbbbbbbbaaaabbababaabbbabbbbaaaabaaabaaabbbaababaabbabbabaaaabbabbbbabbaaabababbbaabaaaababbaaabbaaabbaaabbaaabbabaabbabaaabbbbaaaabbbbbbbbabbbabaabbababbbaaaabbababbbbbbabaabbbbbababbbabbbabbbbbaaabbbabbbaababbbababbabbaaabaaabaabbabaaababaabaaabbababaaaaababababbbababbbabbbbaaaabbbbaaababbabbbbaaabbbaaabbabbabbbbabaaabbbaaaaaaabbaaaabbabaaaaabbbbabaababbbababbaabbababbababbaabbbaababbaabbbaabaaabaababaaababaaabbbbabaabbaaabbbbbbbaabababaaaaabbaabaabaaababbabbbaabaaabbbabbbbbbbbabababbbbbbabbbaabbbabbbaabbbbbbbaabbaaaabaabbbabbaaaaaababaabbbbaaababbaabaaaaaabbabbbbaaaaaaaababbabaaababbabbbbbaabbbbbabbaaabbbababbaaaababbbabbaaaabaababbaabbbabbbbbaabbaaaaabbabbbbabababbababbbaaabaaaaaababbaabbababbbabbabbbbbabbbbababababbaaabbaaaaabaaaabbbbaabbbbbaaaaababbaababaababbbbaabbaaaabaababababbabbabbabbbbbabaabababbaabaabbaaaabbaababaabaaababbbaaaaaabaaababbbabbaabbaababbababbaaabaababbababbaabbbabbbabbbbabaabbbabaabbbabbbbbabbabbaaaabababbbaababbabbaaababbabaabbbbabaabbbaaaaaababbbaabaabbbaaaaaaaaaaabbbaaabbbaaaaabbabaaabbaababbaaaaaabbbabaaabaabbbbbbbaaababaaababbaababbbbabbabaaabbaaabaaaaaaababbabaaaaaabaaaaabbaaabbbaabababaaabbababababaabbbbabaaaabbaaabbbaababbabbaabaaaaabbbbbabbbabaaabbbabbaaabababbaaabbbabbbababababbbaabbaabaaabaaababbababaabababbbbbabbbaabaaabababbbbabbbaabaaaaaabaabaabababababaabbaabaabbbababbbabaabbabaaabababbbaabbaaaaabbaaabbbabaaaaabbabbaaaabbaaabaaabbbaabaabaaababaabaaaaaaaaaaaaaababaabbbababaaabbaaaabbbbbbababbbbbaabbaaababaabaaabbbbbaababaababababbabbbabbbbabbbabaaababbbbababaaaababbbbbbbbaaabbababbabbaaababaaaaaaaaababababbbbbbbbbabaababbababaaaabababbbaaaaabbaabababbbbbbbbbababaabaabaaabbbbabbaaabbbbbaababababaabbabbbabaabbabaaabbaabbaaabbabbaaaaabbbabbbaaaaabbaabbbbbabaaababaababbbabbbaabbabaaabbbaabbabaabbabbaabbabbbbaabbbabaabbbabaaaaabaabbbbaabbaabbbbabbabbbaabbabbbbbabababbbaabbbbaabbaababaabbaaaababbabababaaabbbbbaabbbabbbaabbabaabaaaaabbbbabbbbbbaabaabbabbabbabbbbbbababbbababbaabbbbbbbbabbabbbaaabbbabbaaababbaaaaaabbbbabbbaaabaaababbbaaaabaabbabbbabaabababbabaaaaabaaaababbaabbababaaaababbbabbbabbaaabbabbbbabbbaabaabbbbbabaababbaabaabbbabbabbaababbaaababbababaaabaababbababbaaaabbaaababbabababbaaaabbabbbabaabbbbbaabbbbbbaabaabbaaabbbabababaababaaabababbbabbaaabbabbaaabbaaaababababaabbabaaaabaabaabbaaabaabaaaabaaaaababbbaabaaaabbaaababbabbababaabaaaaaaaaabbbaaabababaaaaaaaabbbbabaaabbbbbaabbbbaabbbbbbabbabbaaaaabaaabaabbabbbabaaababbbbbbbbaaabaaabaaaababbbaaabbbabbbabbababbbabaaaaaabaabaaabaaaabbabbabbbbbabbabbaabbbaaaaabbbabbaaaaaaaaaaaaaabaaabaabbaaaabbabaaabbbbbaababaaababbbababaababaaaabbaabaabbbbaaaabbabaaaababbabbbbaaaabaaaaaaaaabbbbaababaaabaabaaabaababbabaabbbababbbaaaabbbaabbababbaabbaabbbaabbababaabbbbbbbaabbabbbbbabaaaaaabbabaabbbbbaaaabbaaabbbbbabbbabbabaabaaaabaaaaabaaababaababaaabbaaaabaaaaabbabaabbababbabaaabbaabbbbbbbbaaaabababbbabaabaaabbabaaababaaabbbaabbaaabbaababbbabbababbabbbbbbbabaabbbaaaabaabbaaaaaaabaabaababaaaabbbababaabbbaabbaabbabaaaababaabbaaaababababbabaaaaabaaaabbbbbabaaaabaaabbbbbabbabbbaaabbbbbaababaaabababbababaaaababbabbabbaabbbabbabaabbbbbbababbbbbababaabbaabbabbabbbaaabbbabaaabbaababbbabbabbabbbababbabbaabbbaaababbbababaabbbaaabbbabbabbbabbaaaaaabaaabaaaaabababbbbabbaaaaaaababababababbbabbababaababbaabbbaabbabbaaabbaabaabbbbbbabbaababbababbbaabbababaabbaabaaabbabbaabbbabbaaabbabbaaaabbbaaaaaaaaaabaaabaabaabbaaabaabbaabbabbabbaababaaabbbbaaaaaaababbaaaabaabaaaaabbabbaabaababbbbaabbbbbabbbbbaaaaababbaababaabbaababaabbabbbbbbaaaaaaaabbbaaaabbbbaaaabbbbbbabbabbbabbaabbbbabbaababaaaaababbababbabbbaabbabbbbbbaaabbaaaaabbaaabbabbaaaabbbbaaabbbaabbaaabaabaaabaaaaababaaaaaabaabbabbbababbbbbabbbbabbaaaabaaabaabbbaaaaabbaaaaaabbbbabaaabaabababbaaabbabbabbbbabbbbaaaababbabaabbabaaaabbaaaabaabbaabbbababbabbbaaaabaaaabbbbbabbaaabbabbbabababbbaaabbaabaaaaababbaabbabbabbbbaaababbabbabbbbabaaaaaabaababbbbabbabaabaabaababbbbabbbbabaaaaabbbabbaabbbbbbbababbbaaaabaaabaaababbbbabababbbaaaabaabaaaabbabbbbbaabbaabaaaabbabbbabaaaaaabaabbaaabaaaabbbabbabaababbbaaaabbaaabaabbbbabbababbbbabaaabbabbbbaaaabbbbabbbbabbbababbaaaabaaababbbaaabababbbaaaaababbbbbaabaaabbbbbbabbbabaaaabbbbbbaaaabbbaaaabababbababbaababbbaaaabbbaabaabbaabaabbbaabaabaabbaaabaababbbbabaaababbbbbbabbbbbabbbaaabbabbbbaaabbaaaabaabaababbaabbbababbaaabbabbaaaaaaaaaababbababbbbbabaababbaaababaabbabababababaabbaabaabbbbbaaababaaabaababbbbabaaaabbbaaabbbbaaabbabaabaaabbaababaabbbbabaababbbabbbaabbaabababaabbbaaabaaaabaabbaababbabaaabbaaaabbaaaaaabbaabaaababaaaaaaabaaababaaababaaabbbaabbbabaabaabbbaaabaaaaaaabbaaaaabaabaaabbbabbabababbaaabbababbaaabbbbbaabbbbbbaaaaabbbaaabbbaabbabbbbabbabaababbbaababaabaabaaabbabababaaaaaaaaaabbaabbbaabbaabaabbabbaababbabaababbbabaaabaaaaaabbaaabbbbaabaaabbbabbaaabbbbaabaaabbaabbababaabbbaababaaabbbbabbbbbbabbaaaabaaaabbabaaababaaaabaabbbbabbabbabaaabbbaabbbbabbbabbababaaaabbbbbabababaaabbaabaabbaaaaababbabbaaabbaababaaaabaabbabbabbbbbbbaabaababaaabbaabababbbaabbaabbaabbbabbbababbbaabbaabaaaabbaabbbababbabbabbbabbabaabababbababbaaabbbabbabaabbbaabbaababbbbaabbabbbbbabaabbabaaabbaababaaaabbbbaababbbaabbabbbbabbbabbaaaabaababaabaaabbbaaababababaaaaaabbbbbabbaaabbabaaabbaaabaaabbbbaaabbaaabbbaaaababaaabaaabbabaababbaabbbaabaaaabaaabbaaababbbabbbaabbabbbbbaaaaaabbbbabbabaabbaaaaabaaabbaaaababbabbbbabaababbbbbaababbbbbabbaaabbaabababbbaabaaabbabaabaabbabbabbaaaababaabaababababaaaababaabbbabbabaaabaabbbbbaabbaaabaaaababaaababbbbbababbababaaaabbaaaaabbababaabbaaabbabbabbaabaaabbbaaabbababbaaabbbbabbbaabaabbbaaabbaaaabaaaabbbabaabaaabababaabbbababbbabaabaabaaaabababbabbabbbaaaaabaababbaabbabbbbbaabaabbbbbbabaaaaaababbbaaaababbbbbabaaaaababbbabbbababbabaabababbbbaabbabbababaaabbbbbaaababaaabaabaaabbbbbbbabbbbbbbbbaababbbbbabbbabababbababbabbbbbaaaabbbaaaaaababbabaabbbaabababbbbaaaaaaabbababbaaabbbbbbaaaaaabaabbbaabbbbbaababaaabbbbbbabbbaaababbabbaabbbabbbaaaababbbaaabbabaaabaabbbbababaaaabbaabbbbbbabababaaaabaababbabaabaaaaabbaaaaabaabbbbbaabababaabababaaabbababaaaabbabababbbbbabbabbaabbbbababaabaaaabbaaababaababababbbbbbbababaaaabbbaababbabaaababaabbbbaaaaabaaaabaabaaaaababaabaaaababbbabbbbbbabbaababbbabbabaaaaaaaababaababbaaababbaabbaaababbababbabababbabbaabbbaaaaaaaabbbbbaaabaabaaaaaabbaaabbbaabbbbbaabababaaababaaaabbbbabbabbbabbababaabbbbbbaabbbbabbbbbbababbbbbaabbababbaabababbabbbbabbabaaaaaaaabaabaabbaaabababbaabbabaaaaaabbbaaaaabbbbbaabaabbaaaaabaabbbaabbababbbbbabbababbaaababaaaaabbaabababbbbbbbbaaababababbbbabbaaababaabaaaaaaaaabbabbbbababbabaabbbbababbaabbabaaababaabbaabaaabaaabbaababbbbababbababaaabaaababaaaabaabbababaaaaabaabbbbaaabbabbbabaabbbaabaababbaaaaaabbbaaaaaabbbaabbbbbabbbbbaaabbbbbababbbabaaababaabbaaabbbabbabbababbbabbaabaabaaaaaababbaabaabbbbabaaabababaababbabbabbabbababbaaaabbbbaabbbababbbbbaaaaaaaababbaaaabbaaabaababaaabaaaababbabbbbbbabbabaabbabbaaabbbaaabbbabbabbbaabaaaaabbbbbabababbabbaaaabaabbaababbaaaabaaabaabababbbabaabbaaabbaababbabbaaaababbaaaaabbababbaaaaaabbaabbbababababbaabaabaaaababbabaabbbbabbaabbbababbabbbbbababbabbbaababbbbababbbbbbbbbaabbabbbababababaabbbbababbbaabbabaaaaaaabbabaababbbbbaababaaabbbbaabaababaaaabbbbbabaabababbbbaabbaabbbbaabbbaabbababbaabbbbbbbbbabbaaabbbbbbbabbabbbbababbbaaaabbbabbbbbabbbbbbbbbabbbababbbbbbbbbaaabbabababbbabababbababbbbaababaababbbbbbabbaaabbaabaaaaaaaabbbababbaabaabbabbbabaabbbabbbbbbaabbbaaaaabaaabbaababababbbbabbbabbbaabbabbababbbababbaabaaabbbbbaaababbabbbbabaabbbbbbababbabbbabababaabbbababbbabbaabaabaabaabbbbabbbaabaaabaabbbbbbbabbabaabbbabaabbbaaabbaabbbbbbaaaabbabbbbbbbbbabbabbabaaabaaaabbbbbaaaaabbbabbbbbbbabbbbbbbbbabbbbbbbababbaabbaabbaaaabbbbabaabbbabbaabaabaabbbabbbbbabaaabaaaaaaabababaaaaabaabbabbabbaaaaabababaaaaaaababaabaababababbbaababaaabbabababaaababaabaaabbabaaaaaabaaabbaaabbbbaaabaabbababaabbbabaaabaaaaabaabbabbaaaaaabababbbbbbababbaaababbbbaabaabaabbaababbbaaabababbabbbaaabbbaaaabbbbababbbaabababbbabaaaabbbbabbaabababbababaaabbbabbbaaabaaababaaabbaaaaababbaaaabbbbabaaaabaaabbbbbbaabaaaaabbbaababbbabbbbabbaabbaaaabbaababbabaabaaabbbaaaabababbbaabbabaabbaaaabababbabaabbaaaaaaabaaabbbbabaababababbbbbaaaabaaaaabaabbbabaabababbabbbbbababbbbaaaababaaaaaaababbbababbbbaabaabaaabbaababaabaaaaabbbbaaaaabbbabbaaaaabaababbbbbbbbbbbbbaaaaaabbabaaaabbbabbbabbbbabaabababbabbbaaaabaaaaabababbaaabbbbaaabbabbbabbbbaabaabbbaaaabbbabbbbbabbaababbaaababaaabaaaaaaaaabbaaabaababbabaaaaabababbbbabaabbaaaabbbaaaaabbabbaabbbbabbaaaabbbabaababbaaaaaaabababaaaabaabbabaabbbbabbaaabaababbabbabbabbabbaabababababbaaaaaaaabbbabababbabaabbbbbabbbbaaabbaaaababbbaabbbaababbbbbaaaabbbbaabbbbababababaaabaaabbbbaabaabbaabbbbaabaaaaaaaaaaababbabaaababababbbbabaabbbaabaaaaaaabaaaaaaaabaaaabbbabaabbabbbbbbbaabbabaaaaabbbbbbaaaababaaaaabbbbbbabbabbbbbbbbaabbbababaababaababaaababbbbbabbbbaaaabaaabbabbaababaaababbbababbbbabbabaabbabbaabaabababaababbabbbaaabbbbaaabbaabaabbbabbaabaabbaaabbbaabbbabaaaaabbbbbabaaababbbbbbabaaabbaaababbababbbaaaabbabaaaaaabaaabbbaabbbaabaabaabbbbbaabaaaabbbbabaaabbbaaabbaabaababaabbabbbabbaabbababbababaababbbaaaaaaaaaababbbbaaaabaabbbbbabaabaaaaabaaabbbabbaaabaabbaabbababaabababbbbbbaaaaabbaabbbbaabaabbbbaabaaaabbbbbaaaababababbbbababbbbabbbbbaaabaabaabababbbaaabaaabbbaabbabbabaaabbaabababbaabaabaabaabbbbaabbbbabababaaababbabbaaaaabaabbabbaaabaaabbbbaabbbbbbababbbbaaaababaabbbbbbbabbbbaabaaaabbaaabbaabbaabbababaabbbbbbabbaabbbbaaababbaabbaaabaabbabbabbbbbaabbbbbabbbabaabbaabbababbaabbabbbaaabaaaabaababbbaabbbabbbabaabbabbbaaaaaaaaaaabbabaaaaaaaaaababbbabababbbaabaaaaaabbaaaaabbbbabbbaaabbaaabbbbaababaababbaababaaabbbabbbaabbbababbaabbbbaaabaaababaaababbabaabaaaababaaaaaaaaaaabbababbbabaabaaaaababbaaababababbaaababbbaaabaabbabaabbabbbabbaabbbbaabbaaababbaaabbaabaaaaaaabbbabbababbabbaabbbbabbaaaaaababbbbabaaaaaaabaaaaaabbbaababbbabbabbbbabbbbbaaaabaabaababaaaabbaababaabaabbabaabaabbababbaaabbbaabaabbbabababaaabaaaabaabaabbbbaaabaaaababbaaabbbaaaaaaaabaabbbabbababaabaababbbbbabaababbaabbbaaaaabaaaababbbabababbbabaaabbbbaaabbbbaababaababaabbabbabaaaababbaaaaabaaabaaaaabaaabbbbbababbaaaabbabbaaabbbaaaaabbaaababbbbbbabaaabbbbaabaaaabbbbbbabaaabbaababbabbaaabababbabbbaaaaabbbbabababbabbbaabaabbaababbababbbaababbabbaaabbbabaaabbaabaabbaababbbabbbabbaaabaabbabbaabbaababaabbabaabaaaabaaababaabaabbbbabbbbaaaabababbabbbbabbbbbbaabbbbaabbbbaababbbbabaaaaabbaabbbabaaabaaaabaabaaaaaaabbbbaabbbbaaaabbbbbbbbaabaaabbaabaaabaabbaababaabaababaabaaaaaabaabaabbbbaabbbbabaababaabbbbababbbbaabaaaaabbbbaabaabbabaabaaaababbaabaabbbaabbbaaaaabbbbbaaabaabbbaabbbabaabaaaaabbbaababbaaabaabbbabbabbaaabaaaabbbbaabbaabbbbbbbabababbbaaabaabbbbabbabbaabbababaaaaaaaaaabbabbaaabbbaabbabaaaaabbbbbbbabaaaaaababbbabbabbababbaaabaaabbbbaaaabbababbababbabbbaabbabaaaabbaaaaaabbaabaaaaabababbababaabbaaabaabbaaaaabaaabaabbbababbaaabbbbbbbaabaaaaababbbbabaababaaabaaaabbbababbbbbabaababaabbbabbaabbbbabbbabbbbabbabaababbbaaabaabababaaaabbbaaabbbababbbbbbbabbbbabbbaabaabbaababbbaaaababbbaaaaabaaaabbbbabababaabbabbbbaaababbababbaabaababbbbbbbababbabbaaabaababbaaaaaaaaabbabbabbaababbbaabaabaaababbbbabbabababbbbbabbbbbaaabbbbabbaaabaabababbbaaabbbabaabaaaaaaababbababababbabaabababababaabbaababbbbbababaabbbaabbbabbabaababbabbaaabaabaaabaaaabbabababbabbaabaaaabbabaabaababbbbbaabaaaaabbbaabbabbaaabaababbbbbbaabbbaaabbbaaababababaabbbbbaabbbababaaabaababababbbbbbaababbabbaabbbaabbbbbaabaaaabaabaaaabaaaaaaaabbbababbaaaabbbbbbbababaabbaaabbbbabbabbbbaaaabbabaaabbaaababbbaaabaaabbabaabbababaabaabbbabbbabbaabbbbabaababbbbababaabbaabbbaabbabbbabaabaaaaabbbbababbbaabbbbaabbabbabbaabaabaaaaababbabbbaabbbabaabbaaabaaaaaabbaaaabaabbababbbabbaabbbbababaaabbbabbabbbababbabbbabbaaaaaabbabaababaaabbbbabaaabbababbbbababbabbbabbaabaaaaababbbabbaaababbbabbbabaababbabbbbaababbaabaaabaaabaabaaaaabababbbaaabbbbbaaabbbaabaaaabbaaaaaaabaaaaabbaabbaababbaabaababbabbbbaaababbbbaaabbaabababaaaabbbaabbbaaaabbabaaaabaaaabaaabbbaababbaaabaaaabbbabbabbbbaaaaabaabbaaabaaabbbaabaababaababaababaabbbbbaabaaaaaabbbbbbabaaabbaaaabbabaaabaaaabbaabaababaabbbaabbbbbbabababaabbabaaaabbabaabbbaabaabbbabbbbaaababbaababbbbbbbbaaabaaabababbbbaabbabaaaabaaaaabbbabbbbbabbbbbbaaabbbabbbbabababbaaaaabbbbbbbaaaaabbbbaababaaaaaaaaaaaaaababaaaaabbabbaaabbaaaabbaaabbbaaaaabaababbbbabbbbbbabaaababababaaaabbbaabbabbabbbbabaabbbaabbbbbbbbbbbaaabbababaababaaabaaabbbaabbaabaaaaaababababbaabababbbbaabaabbbbaababaabababbbbaabbbbabaaababbbbbbbabaabbabaabbababbbababbaabaaabaaabaabbbababaabaaaabaaabaaabbaabbbaaaaaabbabbaaabaaabbbbaabbabbabbbaaaaaaabbababaabaabbbaababbaababbbaaabaababaabbbabbaabbabababbaaabbabbabbbaaaaabbbbbbbbabbabbababaaabaabaabbbaaaabbbbbbabaaabaaaaababbbbaaaaababbbaabbabaababababaabbbaaaabbbbbbbbbabaabbabaababbbbaaaabaaabbaaaabbabbbabbbbbbbbabbaabaaaabaabbababbaabababbbaaaaaaababaabbaabbaaabbbbaababbbbbaaabbbababaabbbaaabbababbaabaababbbbbbaabbbbbbbbabbbabbbbabbbaaabaabaabbaabbbbbaabaaabaaaabbaabbaababaabbbabaaaaababaababaabaaaabbbaaabbaaabaabaababbbbbabaaabaababbabaabbbabbbbbbbabbaabaababbbabbbbaabaaabbbabbbabbaabbaaababbbbbbbababaaababbaabbbababbbbaabbbabaabaaabaaaabbaaaaaabbababaabaabbaabaabababaaabbaabbbbbbbbbbbabbbabaaaabbabbbaaaabaabaababaabababbbbbabbbbbbabaabbabbbbaaabbbaabbbababbabbbaaabaabaaabababbabaabbaaaaabbaaabbbbbbbabbabaabbbbaaababbbbbabbbbbbbbbaabbabbaaabbabbbaababaaaababbabbbbbbabaabbabababbbbbbbaabaababbbabaaaaaababbbaabaabbbabbbaabbaaaababbbaaabaabbbabaabaaababbbaaabababaabbabbbababbabaaaaaaababaabbbbabbabbabbbaabbabbbaaabbbababaaaabbaabbbabbaabaabaabbbbbbabaaabbbbbbbaaaababbbaaaaaabbaabbaaabbbaaabbaaaabbababbaaaabbababbbbabababaaaabaaaabbaabaaaabaaabababbababbbbbbabaabbbbaabbbaaababbbaabbbbabaabababbabaabbaaaababaabaabbbbaabaabbbbaaaabaabbbaabbbaabbbabaaaaabbbaabaaaaaaaaabaaaabaabaaaabbbabbbbbabbaabbaaaaabaabababbaabbbbababaababbaaabaaabbababbababbbaabaabbbbbbbbbabbbbbabbbabbbaababababaabbbbabbabababaaaaabaaabbbabaaabbbabbbbaaabbbabaababaaaaaababaaababbbabbbaaabababaaaabbaaaaaababbaabababaabbabbaababbbababaaaabaabbaababaaabbbbaaaababbbbaaababbabbbababbbbaabbababbaaaabbabbababaaabbbaababaaaaaababaababbbaaaaaaaabaaaaabbaaabbbbababaaabbbbbbaaaaaabbaaababbbbbaabababaaaaabaaaabbbabaabaabaaaabbaaabbaaaaabbabbbbaabaaaaabbaaababbaabbbbbbbbbaaabbbbaaaaabbbaaaaaabbaaaaaaaaabbbbbabbabbbabbbaaabbbabaaabbbaabbbabbaaabbaaababbbaabbabbbabaaaaaabbbababaaaaabbaaabbbabbaabababababbbbbbbbabbbaaababbbaaaababbbaabaaabbababaaaabbbbaabbbbaaaabbababbabaaabbbbbabaaaabaaabaaaaaabaabbbbbabbababbaababbabbabbabaabababaaaaaaaaaabbbbaaababbbababbaaababbaabbaabababbbaaaaaababbbaabbbaaabbbaaababbababaaaabaaaaabbbabbabaaababbbabbaabaaabaaaabaaabaaabaaabaabaaaababbbbaabbaababbbbabbbbbaabbaababbbbbbaaabbaabaaaaabababbbabbbaaababbbabaaabbbbaaaaaaaabaabababbbaabaabbbbbbbbbabbbbbaaabababaabbbaaabbbbaaaaabbabbbbbabaaabbbaaababaababbabbbbbbbbaababbbabbaaabbbabaaaababababaabbbabbaabbbbaababaaabbbaabaaaaaabbbaabaabbababbbaaabbaabaabaabbbbbababbababbabbaabaabbbbbababaabbaabaabaabbbabbaabbbabaaaaaaaaababbbbaaaaabbababbbbabbabaabbabbbaabababbaaaabbbaabbababaabababaaabbbbbbaabaababbaaabbbabbbbabbbbbbbaabaabbabababbbbabbabababbbaaabbbaaaaabaabbabbaabaabbaaaabababaaabbbaabbabaabaabbbbabbaaabbbaababaabbaabbbaabaabaaaabbbbbaabbbbaaababbbbbabaabbbbbabaaabbaabbaaababbaabbbababbbbaabaabaabaabbaaabbaaabaabbbababbabbbbbbbbbabbaabbaaabbbbbabaaaaababbabaabaaaabbaaabbabaaaabaaaabbabbaabaaaabaaabbaaaaaabaaabbbbbaababbbababbbbbbabaabbbaaabababbaabbbbbaabbaaabaabbabbaaabaaabaaaabbbbabbaabaaaabbbbabbaabbaaabaabbbabbaabbbbbabababaababbaaaaabbbbbbabbabbababaaaabbbaabbababbbaababaaaaaaaababbaaaaababbbbbbabbabbbbbbbaaabaabababbbbbabbbbabbabababaaabababbbaaaababbabbbabaaabbabbbbbbaabbaaaaaababbbbababaaabaababbbabaababbaabbaababbabababbabaaabaaabbabbbbbbaaaabbbbabaabbbaabbaaabbabaaaabaaabbbaabaabbaabaabaabbbabaabbbaaaabaaabaaabbbbabbbbaaaaaaabaaaabaababaabbbaabbaaaaababaaaabaaabaaaabbbabbbaaabbbabbbbbbbbaababbbbaabaaaabaaabbbabaabbaabbbaaaaabababbbbbbaaabaabaaaaabbaaabbbbabbbabaababbaabaabbababbabaaabbbababaabaabbbbaaaabbaabbabbbabbaababbbaaaaabbaabbbaaaabbbaaabbaaabbbbbbabaababbbbaaaababbaaababaaabaabbabbabbaabaabbbaababaabbbbabbbbbabababbaaabbbbbaaaaabbabbbbbbaaababbbabbbbabababbaaabbaababbbaaaabababbabababbaabbbbabbababaaabaababaabbaabbaababbbbaabaababaabaaababababababbabbbaaaaabaaabbbbaaabaaabbabaaababbbbbbbaababbababaababaababbaabbaabbaaaaaabaaaaaaaaabbaaabbbbabaabbabbbaaabbbbbaaaabaabababbbabbbaaaababbaabbbabaabbababbaababbabbbaaabbabbaababaabbbaababbababbbaaaabaabbaaaabababaabbbbbababaabaaaababbbaabbbbbaaaaaabaaabbbabbbaaaababaaabbaaabbbbbbbaababaabaabbbbaabbabbabbbaabbbaaabaabaababbaabbaabbabaabaababbaabaaabbabbbbbaaaabbabbbaabaababbaaabbbbbaabbabbbabaaaabbababaabbaaaaaabaabbbaababbbabaaababaabaababbabaababababbabaabbaabbbbaabaabbababbbbaabbaaabbabbaaabbbbabbbaabaaabababaaaababbabaabbbaaababbbaabbbbabaaaababbaaaabbaabbbabaaaabbababaabbbbbababbbbbaaaaababbabbbbbabaaababbbbbbbaaaababbaabaaaaaababbabababaaaaababbaaabbbbbbababbaabbbbbbbbaaaabaabbbaaaaabbaaaaabbbabababaabbbaaaabbaaaaaaabaabbbabbabaabbbbbababbaabbabbbbaababbaaaaabbabbbbbbbaaabbbbbaabaabbabaabbbbaaaaaabaababaabaaabbbabbabaaabababbbbbabbbbababaaabaabbbaaaabbaaabaaaababbbaabaaaaabbbaabbbaaaababbabbbaaabbaaabaabbbabbabbbbaaaabbaaabaababbabababbabbaabbbbbbaababbbabbbbabbbaaabaaabaaabbabbbaaaabababbbabbaabbaaaabbbbaabbaabaaaabbabababaaaabaaaabbbbbbaabaaabaabbababaabaabbbbbaaaaaabbbaaabbbbbbbbbbababbbbbaabababaabababbbbbbaaaaabbabbbbaaaaaababaabababbbabbaaabaaaaaaaaabbbaabaaaabbaabbababaababbaabbaaabaabbabaabaabbbbbabaaaabaaabaaabbbbbaabaabaabbaaaabbabaabbababaaaabbbbaababbbabbbabbbabbabbaabbbabbabbbaabbabbbbbbabbbbbbbaaabaaaabaabbbabababaabaaaaaabbabaabbabaababbbbbbbbabbbbbababababaabbbabbbbbbabaaaababbbaabaabbbbabbaabbabbabaaaaabbbbabbbaabbabbbaaabbabbbbbabaaabaaaaaaaabbabbbabaaabbaaaaabaabbbbaaabbbbbaaaaabaabababbbbabbababbbababaaabbaaabbbbbbbabaaabbbbaaaaaabbaabababaabbabaaabbaabaabaabbaaabaababbabaabbbababbaabaabbaabaabbaaabaaababbbbaabbabbaaabaaabbbbbbabaabaaaaababbbaabbabbaabbabbabaabbbaabbbbbabbbbaaabaaabaaabbaaabbabbbbbaabaababbaabbabababaabbaabbababaaaababaaaaababaaabbababbaabbaababaaababbbbaaabaaaaabbaaaabbabbabaabaaaabbaabaaaaababaaaaaaabbbabaaaabbaaabaaaabaababababbbaaabbaabaabbaaaaaabaabaabbbaabaaabababababbbabbbbabbabaabbbaabbbaaaaaaabbaaabbbbaabaabbbbbbbbbbabbababababbbaababbbababbbbabaaabababbbabbabaababbbbbbbbbaaaabaaabaaababbbbbbbaaabaabbbbbabbababbaaababbbbabaaaaabbbabaabbaaaaaabbaabababaaaabbbbbaabaaabbababbabbaaaaababbbabbaabbbaabaaababaaababbbbaabbbaaaaabaaaabababbbbabbababaabaabbbaabbabbaaaabaaabbaaaababbaaaabbbaabbbaabbaabbbbbaaabaabbabababaaaabbbaaabaababbbbbbbbaabaabbbbaaaaaabaabbbbabbaaaabbbbabbaaaaaaabaabbbbababbbbbaaabbbaabbaaabbaababaabbabaabbabbabbbaaababaaababbabaaabbabbabbabbabaababbababbaaabbabaaaabbbbbaabaabbabbbbbbbabbaaabaaaaaaababbaabaaabbaabaaabaaaabbbabaaabaababbbaabaaabaabbaabbbbabbabbaabbbbaabaababbabbaaaababbabbbbbaaabbaaaaabbaababbabbaaabaabaabaaababaaabbbbbabbaaabaaaaaaaaabaabaaaababbbaaaabbababbaababaabbbbabbaabaaaaaaaabbbaaabbbabaabaababbaaabaaabaaabababbababaabbabaabbbbaaaabbaabaababaaaabaabababbbbbabababababbbababbbbbaabaaaaaaabbbabbbaababaaaabaaaabbaabbaababaabbbbaababbababaabaaabbaaababaaabaaaaaaaaaaaabbbbbabbbbbababaababaabaababaabaabbbbaaaaaaaaababbbbaaabbababbaababbabaaaaaaabbabababbbbaaabaaaaabbbbbbabaabaabbaabbaabbbaaaabbabbbbabababababbbababababababaabababbaaaaabaaabaababbbbabaabbbaaabbbbaabababaabaabbbbbbabbbaabbbbbababaabaaaabbabaabbbaabbabbbbabaaabbaaaaaababbbaabbababbaaababbaabaaabaaaabaaababbaaababaabaaabbbaabababababaaababbaaaababbabbaabaaabaaaaaabaabbbbabbbbaaaaabbabaabbbababbbabaaaabbbaaabbaababaaaaaabbbaabbbaaaaaaababaabbaabbbbbbabaabbbbbbbaabbbabaaabbabbaabbbbaabbbbbbababababaababbbbbaaaaaababbbbbbabbbababbabbabbbaababbabbbaaaaabbaaaaabbbabbbbbbaabbaaabababbabababbbaaaabbaaaaabaababbaaaaaababaaaaabbbbbbbabbbabaabbabbbabaaaabbbbbbabaaabbaaabbabababababbbbaabababbaabbabbaaaabababbbbaabbaabbbababbbababaabbbababbbbbabbababababbaaabbbbbbbbababaabbaabbaaaaaaabbabbaaabaaaaabaabaaabbabaaababbabbbabaaaaaaabaaabaaabbabbbaaaaaaaabbbababaaaaabbbbbaaaabbbbbbaabbaaaaabaaaaabaaabaabbababbbabbbbbababbbabbbbaaabbbabaabaabbbaababbababbbabbabbababbbaaaabbbbbaaaaaaaabbbaababbbaababaaabbabbabaabbaaabaaababbbabbaaabbbabbbbabbbbabbbaaabaabbaaabaabbabbabbabbabbaaaaaabbabbaabbaaabbaaabbbbababbaabaabbaaaabbaaabbabaaabaabbbbabbbabbbbbbbaaabaabaabbaabaaabaabbaabaabbababaaabbaababbbaaabbababbbbbabbbabaaaaabbbbbaabbbababaaababaaabbbbbaababaabbababbaaababaaabbabbbabaabbaaaaaaababbbbabbaaabababbababbabaababababbababaaabaabbbbbbabbbaaaabbabbbaabbbbababaabbbbabbbbabaaabbaaababaaaababbbaabaabaaaabaabbaabbbaaabababaabaaabbbbbbaabababbaabaabababbababaaaabbaaaaabbaaabaabbbbbabbbbabaaabbaaaaaaaaaaaabaabbbabbbbabaabbbbbabaaababaabababbababbbababbabbbbaaabbbbababbbaaabbbabaaababbbababaabaabbbaabaabbababbbabbaababaaaaabaaaaaabbaababaaababaabaababbaababbabbababbabbaaabbbabaabbaaabbaaababbbaabaababaaaaabbbaabbaabbaababbbaaaabababbbbbbbaaabaabababbaabaaabbbbbaabbbbbbbaaaabbbaabbbaaaabaaabaabaaabaaaababaabaabbbaaababbabaabaaaabaabbbbaabbbababbbbbabbaaaaaaababbbabbbabababbbaabbabbbabbaabaaababbaaabbaabaaabbbabababbaabbbbbaabbabababbbbbababaabaabbbbaabbaaabaaababbabbbbbaaaaabaaaaaaaaaaabaabaabbbbbbabaabbbabbbbbbaabaabaaaaabbbabaabbaaabaababbbbabbabbbbbbbbabbbaaaaaaaaabaabbaaabaabaabbabbbbababaabaaabbbabababbaabbbbabababbabbbbbbaabbbabbaababaabaabaaaabbaaabbbbbaaabbbbbbbbbaaabbbbaabbbbaabbbbaabaaabaaabababbabbabababbabbabbbbbabbbbbbbbabaabbabababaabbbbaaabbbaaaaaababbbaaabbbbabaabbbaabababaaabaabaaaaabaaaabaaabaabbaaaabbaaaaaababababbbaaabaaaabaabbabbbbbbbaaaaaaaababaaaaaababbbbaaababaabbaaaaaaabbbaaaaabbabbabbabaababaaaaaaababbbbabaaabbbbbaabaababbaaababbbbaaabbabbaaaaabbbbbbbabbbbababababaabbbaaaaababbaababababbaaabbaabaabbabaababbaabbbbbbabbabbabbaaabbbbabbaaaababbbbbaababbabbabbbbbbabbbababbbbababababaaabbaaababbaaababbbbabababbabbaaabbbabbababbaabaabbbaaabababbbbaaababaabbbbbabaaabaabbaabbbbbabbabaaabaaaaaaabaaaabaabbbbbbbbbabbbaaabbabbababbaabbabaababbaaabbaabaaaaaaabaabbbabbbaaababbbbbaabbbababbbbbabbabaabaabaaaabaababbbbaabbaaaaababababababaabaabbbbababbbabbbbbbaaaaabbbaaaaabbbbbaabababababbbbaababbbababbaabbabbabbabaaaaaaabaabbabbbbbbaabaabbbababbbaaabbbbabbaabaabbbaabaabbabaabbbbaabbbaabaaababbabbbbbaaaabbabbababaabaaabababbbabbabbbabbbbaaaaaaaabaaaabbaababaabbabaaaaabababbabbaababbbaabbbaabbbbaabbabbbbbbbaababaabbbaabbbbaabbbaabbaaaababbaabababababbbaabbabbabbaaaabaabbbbbaaaabbabaababbbbbaabaabaaabbabbbabbaababbababaabbbbbbaaaabbbabaababbaabbaabbbabaabbaabaabaaabbaabababbbbaaabaaaaaabaaabaabbbbaabbbbaabbbaababaabaabaabbbaaababbbbaabbbbababababaaabbbabaabababaababaaabababbabbababbbbbbbbbababaababbbabaaaaaaabbbbabaabaaaaaabaabaaabbaababaaaababaaaabaaaabaaabaaabaabbbabbbabababababbaaaabbbabbbbbbbbbbbaaababbaaabbaabbbbaabbbbabbbabbabaaaabaaaabaaaabbabaaaaabbbabaababbaaabababaaaaaabbabbbbbbabaaababaaabbbabbabbbbbbaabaababaabbbabbbabbababbabaaaaabbaaabbbabbbabbbaaaaaababbabababaaabbabababbbbabaabaaaabaaaabaaababbaaabbbababbbbabbabaaaaaaabaaaabbbababaabbabbbbbbbabbbbabbbababababbbabbaaaabbbababbbaaababbaaabaaaabababbaaabbabbbbbabbaaabbbbbaaaaaababaabbbbbbaaaaaaabbaaaabbababbbbaaabbaaaabbaaaabbbbabaababaaaaababbbbbababbbbaaaabbbabbbaaaabbabbaabbababbbbaaaababaabaaababaabababbbbabbaaabbbbbbaabaaabbbbbbbaababbabaabbaaaabbbbabbabbaabbbbbbbaabbbbbbbbabaabbabaaabaabbaaabbaabbbaaabbabbababbbababbbbbababbaaaaaabaababbaabbabaabaaababaabbbbaaababbaabababbbbbbbabbbbaabaaabaabbbabaababbbaaaaabababbaabbbbaabaabbbbbababaaaabbabbababbbaaabbbaababaababaaaabaaaabbaaabaaaabbbabbaaaaaabaabbbbbbabbaaaaabbbaabbababbbaabbaabbabbabbbbaaaaaabbbbbaabaabbabaabbbbbabbababbaabbabbbabbaaaabbaaaabaaaaaabbbbbbbaaaabbabbaababaaaabbbaabbbaabbaaababbbbbabbbbbbabaaabbbabbbaaaaaaababbbbbbbaaababaaaabaaaaabaabaaabbbbabbaaabbabbbbabbbaaaabbabbbaaaabaabaaaababbaabbbbbbbababbabababaaababbabbbbbabbaaabaaaaaaababbaaaababaaaabbbbabaabaababbbaabbbbaabbbbabbbbbbbbbbbaabbbbbaabaabbabbbaaaaabbabbababaabbaaabaaabbbabbbbaaababbababaabbbaaaaababaaabbabaaabababaabbababbabbbbaabaaaabababbabbbabbbbbabaaaabbbbbbabbaabaabbbabbbabbabbbbabbbabaaaabaaabbbbabbbaabababbbbbbababaaaaabbbbbaaaabbabbaababbaaaabaaabaabbbabbabaabbbbbbaabbbabbbaaababbabbabbbbbabaabbbabaaaaaababaaaaababbbabbbaaaabbbbabaababaabbaabbbbababbbabbbabaaabababbbaaabababbabbababbbbaabaaaabbaabbbbbbaabbaabbbbbbabbabbabbbbbbbabaaaaababbabbbaababaababaabbbbbabaabaaababaabbabbbbbbbbabbbbbabbaaaabbbabbbbbbaabbbbbbaabbabbbababbbbbbbaaaabaabbaaabaabbaaababaaababbbabbbaaabbabaaabbaaaaabbabababbbbabaabbabbbaabbbbbaaaabbabbbbbabababaaabaabbaaababaabbbabaabbabaabbbbbbbbbabaabbbbabaababaaabbabaaaaaaaaabaabaabbbabaaabbbaabbbbaaaaaaaaaabaaabababbabaabbbbabbbbbabbbabbabaabbbababaabbbabaabbabbabaaaabbbaababaaabbbbbbbbaaababbaabbabaabbbabababbaabaaaababbababbaabbbbabaaaaabbbababbbbaabaabbaaabbabaabbbabbabbbbabaaabaaaaaababaabababbbaabbbaaababbababbbaaabbaaababbbbbabbbabbbbbabbabaaaabbbaabaaabaabbbbabbbbbbaaaabbaaabbbbabaababbbbbaababaababbbabbabbbabbababbbbbbbbbbaaabaabaababababbaaabbaabbabbabbbbaabaaababbbabbaaaababbabaabababbbbabbabbbbababbaaabaaaaaaabbabbaabbaaabbbaabbbabbbbaaaaabaaaaaaabbbabababbbbaabaabaaabaaaaaabaaabaabababbbaababaaabaabbaaaaaaaaaaaaaabaaabbbbbaaabaababbaabaabbbbabbbbbbaaabababaaabbbabaabaabaaaaaabaaabbbaabababbababaaabaababaaaaababaaababbabbabbbaaaaaaaababbbaaaaaaabbbabbaababaabbbabbbababbabaaaababaaabaaabbbababbbbabaabbbaaaaaabbaabbbbabbaababbababbbababbaaabaaaaaababbababaaabbbbaabbbbabaaabaabababbbaabbaabaababaaaaaaaaaaaaabbbbaaaaabaabbbababbbabbaaabaaabaaabbbabbbabaabbabbbaabababaabaaababbbbabaaaaaababbbaaaaaaaabbaabbaabbababbbbabbabbababbaaabbbbbbbaabaabbbabaaaaabbaaaaabbbabbabaaabaaaaabaabaaabbaaabaaaabaaaababbaabbbbbabbbbbbababbbbbbbbaaaababbbbabbbbaabbabaabbbbabbababaaaabababbbaabbaabaaaaaaaaabbaaabaaaabbababbbbbabbababaababbaabbbbbbaabbaabbaaaaaaababbbbbaabaaaabbaababaabaabbaaabababaababbbaababbabbaabbaaabbbbbaabbaaaabbbaaaabbababbbaabbbabbabbbaaabbbbbabbababaaaaabbaabaaaababbaabbababaaaaabaabbbbabbaabaaabaabbbbbabbaaabbbaabbbaabbbbaabbabbabbbbaaaaaababbbbaabbaaaaaaabbbaaaabaababbbaabaaabbbabbabaabbabbabbbbbbaabbbbbbaabbabaabbbbbbbbababaabbbbaaaabbaaaabaabababbabbaaabbabbbbbbaaaaabababbaabbabababbababbbbaabbaabaabbbbabbbbaabbaabbabbbaaabaabbbabbbbbbbbabaababaaabababbabaaababaaabbaababbabbabbabaaababbaabababbaabaaabaabbbbbabaaaabbabbbaaaaabaaabbabbbaaaabbaaababbbbbabbabbabbbaaabaaabaaabaaabababbbabaabaaaabaaabbbababaabaabaababbabaaaaabaabbbbabbabbbbbbbbaabbbaabbabbbaaabaababbabaabbabaaaabbbaabbbaabaaaabbbaaabbabbabbabbbbbabbaabaabbbabbabbabbbbabbbaaaaaaaababbbbbbbbaabbabaaabbaaabaababaababbbbbaabaababaaaaaabaaabaaababaaaaaabaaaabbaaabbaaabbabbbaaaaaabbbababaabbbaababaabbaabbbabbbaaaaaabbbbbbbaabbbabaabaababbabbbabbaaaaabbbaabaabaaababbaaabaaabbbabbbabbbbaaaabbbaaababbabbabaababaaaaaaaaaaabbbaaaabbbbbaaabbbaaabaabbbabbbabaababbaaabaaabbaababaabbabbabbaaaaabbbbaaabababaaabaaaabbbbbbaaaabaaaaaaabbbbbbabababaabaaabbaabbabbaabbbabaabbaababbababbabaaaaabbaaaabbbaabbbabbabaaaaabbababaaabbbbabaaaaaabbababbaabbbbbaabbaaaababbbbbbaabbaabaaaaabbbabbababaaabbbbabababbabbababbabbaaabbbaabbbbabbabababbaabbaaaabababbbbabbbbaababbaaaababbaaaaaaaabaabaaabbbabaabbaaaaabaaaaababbbabaababaabbbabbababbabaabbbbaaabbbbbabbbbbababbabaaaaaaabbbaabaaaaaabaabbbbaaabaaabaaaabaabbbabbbababbaabbbabbaaaabbbabaaaaaabaaabbabbaabbbababbaabbbbbaaaababbbababaaabbbbabbaaababaaababbbaaababbabaabbbbabbbaaaaabbaabbaaabaababaabababbbaabbbaaabbaabbbaabababbaaabbbabbbbbababbbbabbbaabaaaabbaabaabbbaaaabbbaababababaaabbabbbbaaabaababaabaaaabababaaabaabbaabaabababbabababaabbaababbaabbaabbabaabbababbaaaaaabaaaabbbbababbaabbbababaaabaaaaaaabababaaabaaaaaabbababaaaaaabaaababaaaaabaaabbaababbaaabbbabaabbaaaaababbaabbababbbbbababaaabbabbbaaaaababbaaaaaaaababbabaaababaaabbbaaababbaabababbabbabaaabbbaabbbbbbbbaaaababbbbbabbabaaabbaababbbaababbbbaaaabbaabaabbbaabaaaababbbababbababbaaaaababaaaaabbaaaaabbabaaabbaaabaabbaaaababbaaaabbbbbaaabbaaabaaaabbbbbbbbaaaaababaaabbaabbbabaaaabbbabaabaabbbbbbaaaabaabbaaaaabbabababaababbabababbbbbbbbbabababaabbaaabbaababbbababbbbbbbbaabbbaabbbbbaaaaaaabbabaaabbbbbbbaabbaabaaaababaabbaaaabaaaaaabbbbaababbbababaaabbaababbabbabbabbaaabaaabbabaaabaaabbbbbaabbbaabaaaabbaaabaaaabbabbaaaaababaabbabbbabbbabbbaaaabbbbabaaaaaabbabbaabaababababbaabbabbbabababaaaabbbaabbbbaaabbaabaabbabababbabbaabbbbabababbbbbabbbabaaaababbaaababababbbbbbaaabbaabababbaabaaabbabbbbbababbbbaaabababbbabaaabababaabbbbbbababaaaaabbaabbbbbbbbbaaaabbbbaaaabbabaabababbbbabaabaabaabbaababbbbabaaaaabaababaaaaaabaabbaabbabbabbabbaababbbaabbaaaaaabbbaaabaaabaaaaaabbaaabbbabaabbbaaababaaaabbaabbbbaabaabbaabbbbaababbaaabbabbabaabbbaaabaaababbabaaaabbbbbabaaaaaabaaabbaaaaabbababbaaaaaababbabbabbaabaabaaabaaaaaaaaabbbbbabaabbbabaaabbababbabbaaaaaaababbabbabbbbabbababbbababbaaaaabaabaaabbbaaaaabbabbbaaaaababaaaabbabaaabaababbabbaaaaababbbaaaabbbabbbaaabbabbaabbaaaaaaabbababaabbbbabaabbabaaababaabbbbbbbbababbabaaaababababababaabbbabbabaababbbbbabbaabbaaaabbbbabbaababbbabbaaabaaaabbaaaaaabaabbabbbabbabbabaabaaabbbbbbbbaabbaababbbbbaaabbbbbabaaabbabaabbaaabbabbaabbbbaaabaababaabbaaababaababaabaabaabaabbbaabaaabbaaaaabbbabbabaabbbbabbabbaaaababbbaaaabbababaaabbabbababbbbababaaaabbabbabaaabbabaaabaababbbaaaaabbbabaababbaababbbbabaababaaabbbaaaaaabaabbabbababbaababaaaabaabaaabbbbaaaaaaabaaaabbbbbbbaaabaabaabaababbaabaababbbbbbbaaabbabaaabbabbbabbbbaaababababbaabbbbbaabbbbabbababbbbabbbbbbbbabaababaaabaabaaaaabbaaabbbbbaababbabaaabaaabababaabbabbaaabababaabaaabbbaababbbababaaabbaaaaabbbabbabaabababbaabbbbbaaabbbaaabbaaabaababbbbbaaabbbabaaabbababbabbabaababaaabbbababbbaabaaaabbaabaabaabbbbbabaaabbabaaabaaaababbabbaababaabbaaaaaaabaaabbaaaaabbabbbbbaabbaaaabbbbbababbbabababaaabaaabbaabaabbbaaaabababaaaabaabbbbaaaabbabababbabbbabbaaabaabbbaabbabbaaaabbbaababbaabbbbaaabbaababbbabababaaaabaababbaaababaaaaaaababbabbabbaabbaaababbbbabababbaaabaabaabbaaabbababbaaababbabbaabbbababbabbbaaaababbabaabaabbababbabbabbbabaaaaabbbbaababbbbbabbbbaaababbbaaaaaaaabbbbabaaababbababaaaaaabbaabbaaabbaabbbbaaaaabbaabaababaabbabaabbbbbbbbabbaaaaabbbbaaaaaaabaaaaabbabbbbaaabaaaaaababaaabbaaaabbbaabaaabaabaabbabaabbbaabbbbabbbababbbabbbabbabbbabaaababaabbabbbaaaaaababbbbbbababbabbbaabbabbaabbbbabaabbaabbabaabaabaabbaabbbabababaababbbabababababbaaabbbbababbaaaababbbaaaaaabaabbbabbbaaababbbbababaabbabaabbabbbaaabbbabbbaabaaaaabaaababbababbbbaabbabbaababbaabbaabbaababbabbaaaabaabbbbbaaaabaaaabababbabbaaaaaababaaababbabbaababbaaaabaaaabaaabaaababbaabaaabbabbaababababbbbbbbababaaabaababaabbabaabaabbbabaaaaabbbbaababaabbababbbbbabbbbabaabbbaabaaaaabbaabbbabbababbbaaabaabaabaaabbaabaaabaabaababaabbabbabbbaabbbabbbbabaabbbaababbbabbaaaabbbabbabbaaaabbabbabbbaabbbabaaaababbabbbbbabbbaabbbbaabbbabbaabbbababbaabbabbbbbbaabbbbbbbabaabbabbabababbabababbaaaaababbaaaabbbbbbbabaabaabaababaababbbaababbbabbbbbbbaabbbbbbaabbbbbabbabbbbbabbbbabbbbabaaaabbbbbbbaaaaaababbbabbaaababbbbbbbabbbaaabbaaaaababaababbabbabbabaabbaaabbbbbbbbaababaabbbaabbabababababbbbbabaaabbaabababaaaabbaaaaababbbbbaaabbabaababbbbaaaababbbabaaaaabaaaabbbabaaabbabaaabbaaabaababbbaaabbbbbbbabbbaabaabaababaabbbbbaaabbbbbaabaaaababababaaaababababbbaabbbabbababaabaabbaabaabbabaaabaaaaabababbbabbbbbaabaaaaababbaababaaabaaabbbababbbaaababaabbbaaaabbbbabababababbaaaabaaabbaabaaaaabbaabbbabaabaabaabbaabaaabbbbabbbabbbbaaabaabaaaaabababaaabbaabababbbbaabaabbbabbaaabbaaabaaaabbabaaaabbbbbaaabababaaaaaabbaabababbbabbbbbbbbbaabbaaabaaaabaaaaabbbbbaaaabbbabaabbbbbbbbaaaaaabbaabaababaabbabaababaabbaaabababbababbabbabbbabbbabbbabaabababaabbbbbaabbbbabbaaaaabababbaaaabbaaaabbaabbaababaaababbaabaababbbababaaabaababababbbbbbabaaababaaabbaabbbabbbbaabbaaaabaaaaabaabbbababbbaabbbbbaabbaabbbaabbbbabbabbbbaaabbaaabbbbaabbbbbbaaaaabbbabaabbabbaaaababbabbabababbaaabaabbbbababaaabbbaaabaabaaababbbaabaababaabaaaaabbabbabbbbbbbaaababaaaaaabaaaabbbaaabaababbabbabbbbaaabaaabbbaabbaaaabaaababbabababbabbaaabbaaaaaaaabbabaabbbbabaaaabbbaabbabbabbabbabaaaaabaaabaaaaabbbbbbabbbababbbabbbaaabbaaaabbbabaabbabaaaabaabbbababaababbaaaabaababbaababaabbaaabbbbabbbbbaaaabbbaaabaaaaabaabbbabbbabbaababaabbbaabababaaaabbbbbbabaaabbbaaaabaabaabbaabbabbaaabaabbabababaaababbaabbaaabaabbbaaaababbabaabbbabababbbbababbbbaabbbaaaaaaabbaabbbaaaaaaaabababbbbbabbbbbababababababaaabbbabaaaaabaabaabbbbbbabbbbaaabaabaabaababbababababbabbabbbbbbaaabbabababbabbaabbbaaaabaabaabaaaababaabbbbbbababbbbbabbabbaabbbabbbaaaabbaabaabbbbaaaaabbbabaabbbbbbbbbabbaabababbbbabbbbbbbaaabbabbbbbaabbbabbabbbbabbbbabaababbabaabbbbbbabaaaaabbbabbbbabababbabbbbabababababbbaabbbaabbbabbaabbbaaaabbbbbaaababbaababaaaabbbbaabaaaaaabbabaaaabbbbabbbaababbaabababbaaaaaababaabbaaaababaabaaaabaaaabbaabaaaaaabbbbbaababbbabbaabbabbaabbbaabbbbbabbababbaaabaaaabbbbabbaaababaabbbabbbbabbabaabbbbaabaaaababbaabbabbbaaaaaaababaaabbabbaaaaabaaaaababbbaaababbbbbbababbaababbabbbbbbabbabbababaabaabbbbbaabaababbbaaaababbbabbabbbbaabababbabaaaaabaaaaababaabbbbabaabaabbbabbbabbbaabbaaaabbaaabbaaaabaabaaaaaaaabaabbaabaaaaabbaaabbbbabaaaababbbbbbabbaabbbaabaabbaaabbaaababbbbbbaabbabbbbabbbbbbbbabbaaaaaabaaaaaababbababbaababaaaabbbbbbbabbabbbbababbaababaababaabbabbaabbbaabbabbabbbbbaabbbababbabbbabbbbabbaababaabababaaababbbbbababbabaaaabbbbbabbbaaabbbaabaabaabaabaabbbabaabaabaaabbbaaaabbbabaabaaaabaaaaaababbaaaabbaabababaaabaabababaaaababbaabaaaababaaabaabaababbbbaabaabbaaababbaabaaabbbaababbbbbabbbabaababaabaaabaabbbbbabbbabaabbaaabbbbbbaaabbbbabbabaababbaaaabaaabaabaabbabbbbbababbbbbaabbbbaabaaababbbbaaaabbaabaaabbbbbbbbbaaabbbbbabaabaabaaaaabababbbbaabababaabaaabbbabbbaaaaababababbbabbbbbababaababbaabbabbababbbaabbbbbbbbaaaabaabbabaaabaabbaaabbbabbaaaabaaaabbabbbbbabaaaabaaaaabaaabbabbbaaabbbaaaaaabbbbbbaaabaaaababaaaabbabbbbbbbabbababbbababbbaababbabaaaaabbbbaaaaaabaababaaabbaabbbbaabaaaaabbaaababbbbaababaabaaabbbbaabaaabbbbbaaaaaabbbbaaaaabaaabaaabaabbbaababaabbaabbbbbababaaabaaabaababbbaabbbbbbbbabbabbbbbbbbbbbbbbabaaabbbaabbaaaaabbbabbabbabbaababbabbaabaababaaabbababbaaababbaabbbbaabbabbaaabbababaababbbbbbaaaaabbaaababbabbbbabaaaabbbbbababaabbaaabbbbaaabbbbabbaaababababbbaaabaaabbbaaaabbbbbbaaabbaaaabbaabaaaaabbbaababbbabbbbbbbbaaaaabbbaaabbaabbbbbbbabaaababbbababbbbababbaaaabbabaabaababbbaabbbbabbbaabbbaaabaaababaababbabbabbabbaaaaabbbbaaaabbbabbbbaaaabbbaaaabbbbbababbababaaabbaabbabbabbbbaabbbbbabababaabbaaababababbbababababbbabaaabababaaababababbabbbbaabbabbaaabbaaaabbabbbbbabbabbabbaabbbaaabbabbbabbaabaaabbabaaaabbabbabaabbabababaabaabbabababaabbabbbbbabbaaaabaaaaabbabbababababbbbbbaabaaabbbbbbaaaaabbabbbbbabaaabbbbaabbbbbbbbaaaaaaaabbbbaaaababbaaaaaaabbaabaaabbaabbbbabbbbaaabaaabababbabbaabbabababaaaaaaaabbaababbbaaaaaabbbaababbbababbbbaaabbababbbaabaaabbabbaaaaaabbaababaabbabbabbababbabbbbaaabaaabaaaaaabbbababaaabbbbbaabbbababbaaabbbbaaabbababbbbbbabbbabbbbabbabbbaabbabbaaabbbaaababbbbbbbbaaaababaabaaaabbabaabaabbbaababbbbbbaabababbbabaababbbaaabababbbbaaabababaababbbababbbbabababbaabaaaabbbbabbbbabbbaabbaaabaabbaaaabbababbabbbbbaaabbbaaaababbbbbaabababaabababbbabbbabbbabaabaaaabbaaabbbbabaaabaabbbabbabbaaababbbaabbbbbbaababbbabaabababbbbaaaaabbbaababaabaaaababbababbaabbababbbabaabaaabbbbaaabaaaabbbaaabbbbbaabaabbaabaaabaaaabbbbbbbabaabbaaababbaaaabbabababbbbabaabaaabbaaabbaabbaaabaaabbbabbbbaababaaaabbaaaabbbbbaabbaababbaaaabbaaaabbbaaaabbbaabbabbbbbbbbaaabbabbbaaabaaabaabababbbbbaaabaaaabbaabaaabaaabbbaabbabbaaaaaabbaaaaababbababaabaaabbaababaababbbbbaababbbaaabaaabbabababaaaaabababbabbbaabababbbabbaabaaaaabbbababbbaabbbaaababbbabaabbbbbaaaabbabbabbbbabbabaabbbaaaaabaaababababbaaaabbabbbaaaaaabbabaabaaaababaababbaaabaabbbaabaabbaabbabababaababbaaabaaaaabaaababbbbababbaaabbabbbaaaaabaabbbbababababaaabbababbbababbaabaaababbbaaabbbbabbabaaaaabbaaaaaabbabbbaaababbabbbbbaaabbabbbaaabababbbbbabbbababaabbabbbbaababababaababababbbabaaabbbbabbbbabaabaaaaaababbaabababbbbaabbbbbabababbbaababbababbbbabbaaaaaabbbabaaababbbbbbaaaabaaababbbbbbaabaaaabaababaabbabbbabbbaabaabbaaabababbaabaaabbaababababbabbaaaaabaababaabbbabbbbabaaaabaaabbaaaabababaababbbbaabbaabaaabbbabbaaaaaaaabbbbbbabaaabaabbabbabaabbaaaaaabbabbbaabaabbaabbaaabbbabbbbababaaaaabbbabbaaaaabababaabbabbaabbbbbaaabbaaaababbaabaabbababbaaabbabaaaaaaaaabbbababbaababbabababaabbaaaabbbbbabbaabaabbabbabaaabababbaaaababbbbabaaaabbaaabbbaaabbababbabbbabbbbababbabaabaaabbbabaabbbbabaaaababaaaabaaabaabbbbabbaabbbabbaabaaaabaababbaaaababbbbabbbbbabbbbbbaaaaababaababbabababbbbabbabbaabbbbbbbababbbbbaababbbbabaaabbbaabbbababaaabaaaaabbaabbabbbaabbbbbaaaabbbbbbbbaabababbbbaabaabbaaaababaabababaabbabaababbaaaaaabbbabbabaabbbbaabaababbbaaabbbbbaabaaabbaaababbbbbbababbbbbbabaabaaaabbbaaabaaaabaaaabbabbbabaababbbaaaaaabbbabbaaaabaabbaaaabbbbbaababbaaabbbbbabbbbabbbaaabaaaaaabbbabbbaababbaaababaaaaaaaaaaaaababbbbbbbaaabbbbbaaaaababbabbbabbbaaaabbaabaabbbababbbabaaabbaaaaaaaabaaaaaaaabababbabbaabbabaaaabaaaaaaaabababbbbaabbbabbaabaabbababbbbbbabaaabbbbaaaabbbbabbaaababbabababbabbabababaabbababbbbabaabaababbabbaababbbbbaaabbbbbbbbbaabbbbbabbbaaaabaaaaaabaaabbabbaabbabaababbaaaaaaabaabbbbababbbaaaaababbababbbbaaabbbabaabbbbbaababaabaaababbbbababbaababbbbbaababbaababbabababaabaaaaaababbaabbabbbabbbbbaabbababbbbabaaaababbaabbabbabbabaabbbabaabbabababaaaaaaabaaaababbbabababbababbbbbabaababbbaaabababababaabbbbabaababbaaabaababbabbaabaababbaaaababaabbaabaabaababaabbbaabaaaabbabbbbbaaaabaaabbbaababbaabaaabaaababaabbbbabbabbbababaabaaabbbbbbaaaabbababbbbaaaabaabbabbbaababababaabbaaaababbabbababaabbaaababbabbbbaabbbbabaabaabbaabbabaaaaaabbbbbbbbaaabababaaaabbbbbaaabbbaaaabaabbaabbbbbbabbbbbbabababbabaabaaabababbabbbabbabbaabbabababaaabbababbaabbbbbabbaabababbbbbabbbababaaabaabaabbbbbbbaaaaaabbbababbbbababaababbbbbaabbbaaaaababbbbbaaaaaaabbaabbbaabbabbabaaabbabbaaaabaaaabbaaabbbbabaabaaabbbababbaabaabababababbaababbbabaabaabbaabaabbbaaaaaabbaaabbbababbbabbababbbaababaaaababbbbbaaaabbbbaababaabaaabaabbbbbabbbabbabbbaababbbababaaaaaabababbababaababbaaabbababababbaababbbbabaabaabaabaabaababbbabaababababaabbbaabbaabbbaaabbaabaabaabbaabaaabaabaaaabbbbbbaaabaabaababbbaabaaaabaabbababbabbbbbababbabaabaabbabbbaaaaaaabababaabababaaabaabbabaaaaababaabbabababbabbaaaaabbbaaababaabbaababaaabbaaaaaabbabaaaaababbbbabaabbaaaabbbbabaababbabababaaababbaabbbbbbaaabbbaabbbababbabbbabaabbbaabbbbbabababababbbbbaabbabbbbaabababababbabaaabbbbabbbbaabbbabbbbabaaaabaabbbabbbbbbbabbbbbaaabbaabbbbbbbbbababaabbbababbbbaababaaabbaaabaabbaaaabbbabbbbbbabbbaaaaabaaabbabbbaababbbabbaaaabbaabbabbabbbbaabbbbababaaaaabbaaaaaabbbbaaaabaabaababbaaabbaababaababbbabbbaabbabbabbababbaababbbbaabaabaaabbbbaababbbbabbabbbababbbaabbbbbbabbabbbbbabbbbbaaaabbbaaabbbbabbbababaaaabbaababababaabaabbbbbbbbbbbaaabbaaabaaaabbaaaaaaabbabaaaabaaabaaababbaababbbbbbbbbabababaabbbabaabbbabbaaababababaababaaaaabaaabbbabbabbabbabababbaaaaabaaaabbbbababbabbbababaaabbaabaaaaaabbbabbaabaaabaababbbaaabbabbabbbbaaaabaabbaabaababababbaabbaaaabbabbaabbbbbbbaaaabbbaaababbbaabbbbbaabbaaaaabbaabbaaaaabbaabaababbbaaabbbabaabbabababbbbabbaaabaaababbbbbbababbbabbbbaababbbabbabbbbbaaabbaabbbabbbaaaaaababbabbbbbbbabaaababbbbbaababaaaababaaabaabbaabaabbbabaababbbbabbabbbbaabbabaabbaabaabbabaababbabbabbbabbbbbaaaabbbbbbbbbbbaaaababbbaaabaabaaabbabbabaaaaaaaabbbbaabbbbaabbabbbaabbaabbbbabababbbbaaaabbaabbbaabaaaaaabbbabaaaaaababbababbbbaabababbbbababbabbbaabbaabbabbaaaaababbaabaaaabbaaaabbabbbbaaababaaabaabababbabbbabababababaabbababbababbabaabaabbaababbabaababbabaababbbbbaabbbbbaaaaababbbbbaabbabbaabaaaaaababaabbababbaabbbaaabaaababbbabaabaabbbbabbaaaaababbbaabbaaaaabaaabbbabaabbabbbabbbbbaabbbbbabababbabbbbabbbabbabaabbbbaababbaabbaabaaababbbaabaaaaaaaababababbbbbbaaaabbabbabbbbaaabbbbabbabaaabaabbabaabbabaaababbbaabbbbbababbabaabaababababaabababaaaabbaabbabaaaaabbbbaaababbabbaaabbbbbbbabbaaabbbabaabaaaabbabbbbbabaabbbbbbabbbbbbbbbbbabbbbaaaabaabbbabbabaababbabaabbbaaabbbabbaababbaabbbbaaaabbbabbabaaabaabbbaaabbbbbaabaabbbbbbbababaabbaabbbbaaabaaaaaaaaaaaabbaabbbbbbbaabababababbbababbaaaaabbbbaaabaaababaabbabababbbbbbababbabbabbbabbbabbabbbbabaabaabbaaabbaabbaabaababbabbabbbababaabbabbbaaaabaabbaababbababbbbabbbbbbbabbaaabaabbaabbaabababbbbabaabbababbbbaabaababbabbbaabaabaabbaaaabbbbbbabbaaabbbaabbaabaabaabaabbabbbaaabaaaaabbbbbabaababaaaababaabaabbaaaaabbaabbbaaaaaaaaabbbbaabaabbaabaabbbbabaabbabbabaababaabaaabbaabbbbbababaabbbbaaabbbbaaababbbaabaaabababbaaaabaaaabbbbaabbbababbabbaaababbbabababaabaabaabaaaabaabbbabaaaaaaabaaabbabaaaaabbabaaabbabbaabbaababbabaabbbbbbbabbababbbbbbbababbbbabababbababbbabbababbaaaaaaaabaabaabbaaaababbbabbaababaaabaababaabaabaaaaabaaaabaabbabaabaababaaabaabbbaabaababbaabbbaaaabababbabbaaabaababaaaaabbbababaabbbabbaabaaabbaabbbbaaabbbbbabaaabaaabbaabbababbbaaabbbababbaabbaaaaaaaaabaaaaabbbbbbbbababaabbaaaababbaababbbbaababbaabbbbaaaaaaaaaabbbaabbbbbbabbbbaaaabaababbbbbbbabbaaaabbbaababbbbababaaaabbbbabbabbbabbaaabbbbaaaaaaabaabbaabbbbaaaabaaaabbbbbabaaabaaaababaabbbbaabaaaaabaaabaaaabaaaabaaabaabbbbaaababaabbaaaaabbbbbabbbbbbababbaabbaabaaaabababbbbaabbbbbaabaabbaabaaaaabaaababbaaabaabbbabaababbbaabbbabbaaabbbbbbbaabbbbabaaaababbbabbbabaaababaabaaababbaaabbaaabbaaaabbbabaaababbbbbabbabaaabbbbbbbbaaaabbbababababbbababbbbbaaababababbaabaaabbbbabbbbbabaaaaabbbbbbabbabaaababbabbaaabaaabaababbaaaaabbaabbbbbbbababbbaabbbaaabbbbbbabbbaaabaabbababbaabbbabaaabbaabaaaaababbabaaabbbaabababaaabbabaaabbbaaabaababbaaabbbaababaaaabbbababaaabababbbbabbbabababbbbbbaabaaabbbaabababaaabbaabbbbbbaaabaabbaabaababbaaaaababbbbaababaaaaaabbbbbaabaabababaaabbabbaabaabaabbababbaaaabbabaabaabaaabaaababaabbaabaaaaaaaabbaabbabbaaabaaabbbbbabaaabbbaabbbbbbbaaaabbbaabbbbabababababbbaabbbabbbaaababaabbbaabbaaababbaabbbbaabbabbbabaabbbbabbbbababbabbaaababbabaaabbabaaaabbbabbbbbbababbbaaabbbbbbbabaaaaabbbaabababbbaaabbbbbabbabbabbbbbaabababbbbabbaaabbaabbaaabaaabbbabababbaaaaaabaabaaabbbbbbabbbabaabbbabbbabbbbaabbabbbabbababbaabaabbaabbbabaabaabbbaaaabbbbaabbbabbbbaabbabbaaabbabababbbbbbbaababbbbbbaababbbaabbbaaabaaabbabbbabbababbbbaaabababaabbbbabbabbbbbbaabbbaabaabaabaabaaaabbbaaaabaaaabbbbabbbababbbbbaaabaaaaabbaabaabbbabaaabbabbbabbbbababbaaaabbababbbbabaaabaababbbbbbaaaaabbbabbababbbbbabaaaababbaaaabbaaaabbaababaaabbabababaabbaababaabbaabbbabbabbbbabbbbbabaababbaababaabaaaaaaaabbbaabbabababaabbababaabbababaaaaaabaabaaaaaaababbbbaaabbbabbbbabaaaaabbabbabbbaaaaabbbabbaababaaabbbaaaabbabbbbaababababaaababbbabaaabbbbaabaaabbaaaabbbabaaaaabbabbaaabbbabbbbbabbaaaabaaaababaaababbaaabbaabababbbbababbaaaabbbaabaaabbabababbbababaaaababbaaabbabbaabbaabbabbabbaaabbababaaaabbbabaababbbaaaabbbabbbbabbbaabbbbabaaabbbbbabbbbababbbaabbbbabbbbbaabbaabaaabaababaaaabbaabababaaaaaaaabbaabbbaaaaabbbaaababbabababaabaabaabaaabbabbbbaaaaabaabaaabaaabbaababbbaaaabbbabbbbbababbbbaabbbaaababbbbabbabaabbabbaabbbbbbaabaababababbbaabbababbaabaaabaabbabaaabbabbaababbabbbbabbaabaaabbbaabaaabaabababbbbababbbbaaabbaaabbbbbbaaabaabaaabbbbbbbbbaaaaaabaabbaaabbaaaaaababbaaabababbbbababbbbaabbbbbabaabbaabaaaabbbbababaabbababbbabaaaaabbababbbbbabbabbbabababbbbaaabbaaaaaaababbbbabbaaabbbabaabbaaaabbbaabbbabaaaaaabaaaaababbbaabaababbaaabbbbbabaaababaaabbbabbaaaaabbbbaaaaaababbaaabbbbaaabbbaaaaabbbaabbbbbbaabbbbabaabbabaaaaabbbbbababbbaabaaaaababaaaabbbaaabababbbbabbaabbababababbbbbabaaabbaaabaaaababaaababbaabaabababaababbaaababaababbbbabbaaabaabbabaaabbbbbaaaabaaabbbbbaabaaabbaaabbbbbabaababaaaaaaaaabbbaabbbabbbbbaabbabbbbaabbaaaabaaaaaaabbabaabaaaaaaabbababaaaaaaaaaaaaaababbababbaabbabaaaabbaabaaabaabaaaabbbbaabbaaaabbababaaabbbaabbbbbbaaaaabbbababbaabbbbbbabbabababbabbbabbaabaaaabbbabaaababbbbabbabbbbbabbaaaaaaabbbabbbbababbaaaaaababbbbababababaaabaaabaabaaaababbaababbaaaaabaabbaaabbaaaabbbaaabbaabaabaabbbbbbbbababaabaababbbbbababaabaababaaabbbabbaabaaabaabbaabaabbbabbaaabbbaabaabaaabbabbbabaabbbaaabbaabbaaaabbbabaaababbaaaababbaaabbbababbabaaaabaaaabbbaababbbabbbbabbbbabbabbaabbababababaabbaabaaababbaabbbbabbabaabbbababbbabbaaabbaabbbaabbaabaabbaaaababababbaaabbbabaaabbbbaababaaaaaabaababbabaaaabaaabaaabaabbbbaaaababaabbbaaabaaaaaabbaabaabbbbbabbbbabbabaaabbaabaababaaabbbabbbabababbbbbabbabbbaabbabaabbbbbbbaaaabbbbbbaababbaabbabbbabbbbbbaaaabaaababbbbabbbababaaabaabbbabbbbaababbbbbbaabbbabaabbaaaababaaabbbbbaabaaabbabababbbabbabababbabaababbbbabbaabaaababbbbbaaabbbaabababbaabbabbbababbabbbbbbabbbabbbbababbaaaabbbabaabbbbbbaabbbbbaabaaabbbbbbaaabbbbbbabaabbbbbaabababbabbaaaabababbababbbaaaaabbbaababbaabaabaaaaaabbbabbbbbbabaaaaaaabbaaaabbbbabbaabbbbbbbbbbabbbbabaaaaaababaaaabbbababaaaababaaababbbaaaaaabaabbbbaaabbbbababbabbbabbabbababaabaaaaabaabbababbaabbbbbbaabbbaabbbbbaabaaaaaaabbbbaaaabbabaaaaaabbaaabbaaaaababbbbbbaaabbababbbbbabbbbaaababbaababababababbbaababbbbaaabaaabbbaabbabbaabababbaaabbaabaaaaaaaabbaabbbbbaaabbbbbabbaabbaababaaabbaababaaaabaaababaaabbabbaabbaabbbbbabbbbbaabbabbbbbbbbbbbaaabbaabaaabbbaabbbaabbbbaaaaaababbbbaabbbaabaaabaabaaaaababbabbbabaabbbbbabbabaaabbabaabbbabbbababababaabbbbbaabbbabaabaaabaabaabababbaabaababbabbababababbbbbbaaaaabaaaabbbaabbbabaabaababaabababbababaaabaabbaababaabbaaabaaaabaaaaaaaabbabbaaaaabbbabaaaabababbaaaabaaabbbaaaababaaabbbbabbababbaabbabaaaababaaaabbaabaaabbbaaaaabaaabababbaaaababbaababbbaaabbaabbaabaabaaaaabbaaabbbaabbaabbbaababbaaababbbababbabbaabaabaaabbaaabbabbabaaababbbababbabaabbbbabbbbaaaaababbbbbaabababaaabbabaabbbaaabaaabbbabbabbaababbbabbaaaabbbbabbaaabbababbbaabbabbbbbbabbaaaaabbababbabaaabbbaabbbaaabbbaabbbaaaabbbaaabababbbabaaaabaaabbbababaaabbabbabbabbaaababbbbbaabababbbabbbaaabbbbbbbbaaabbbababababaaaabaabaaabbbabaaaaaabbbabaaabbbaaabbabbbabaabbaababbabbabbabbabbbbbbbaaabbababaabaaabaaabbbaababbaabbabbbaababbbbabbaaaaababbababaaaabbbaababbbbabbababbbbbaaaaaaaababbaabbbaaabbbaabababbababbabbbbbabbaaabababaabbaabababbaaabbaabbbbbbbaabbaabbbabaabbabaababbbbababaaababaaabaababaaabbbaaabaabbaaabbbaababbbaabbbaababbbbababbbabaababbabbabbbbaaaabbaaabbbbbaaaabaaababaababbbaaaabaaabbaababaaaaabaabbbbaababbabbaabbaabaabbbaaaaababaabaabbbbbaabaaabbbbabbbabbabbbabaabbbbbaabaabbaabaaabaaabbbbababaabbbbababaabbbaaabbbabaabbbbbabbbbabbabaababababbaaaababbbaaaaabbbaaaaabbaaaabaabaaaaaabaaaabbbaaaababbbbaaabbaaabaaaaabbbbbaabbbaabaabbbaabaaababbbbaabbabbbabbabaaaaaabbaaaababbababbbbabbaaabababbbbabaaabbabbbbbaaababaaaabbabbaabbbbabaabaaabaabaaabbaababbabbbbabaababbaaabababaaababbbababbabbbbbbaababbaaababababbabbabbaabababbaaaabbbbabababaaababbabbbaaaabbbaaaababbabbbbbababaaabbaabaaaabaabababbbabaabababbbbaaababaaabbabaabbabbaaaaaababbbbaaaababaaaababbaaabaabbababaaabaababbbaaaaaaaaaabaaabaaaaabbabbabbaaabbabbabababaaabaabbbabbbbbabbbaaaaaabbaababaaabaabbabaaaaaabababbbbababababaabbbaababbbbaaaabbbaaaabbabababaabaaabbbaaababbbbbbbababbbbbbabbbbabababababbabbbaabaababbbbaaaaabababaaababaababbabbabababbbabbbaabababbbabaabbabababaabbbbbaaaaabbbababbabaaaaaabbbbbbabbabbaabbabbabaaaaaabbbbabbbaaaaabaaabbbbaaaaabbaabbbbbbaabababaaababbaaaabaabbaabaabaaabbaababbaaabbabbbbaabaaaabaabbababaaaaabaabaaabbabbbbbbaababaaaaaaaaababaaaaababbababbbbbaabbbaabbbababbaabaabaaaaababbbabaaaabbbaabbbbaaaabbaaabaaabbaaaaaaabbabbaaaaabbbababaaabbbabbaaabaaaabaaaabbbbabbababababbababbaabaabbbbbbbbbbbbbbbbabbbaababbaababbbbababaaabbbaabbbabbbaaabbbabbaabbaabaaabaaababbabbabaaaabbaaabbaaaabbbaababbbabaabaababaaababbabbbaababbbbbbaaabbabaabababbaaaabbbabbbbaabbabbbbbabaabbabaabaaababbbaaaaabaaababbbabbbbabbabbbbaabaaabaabababbbaabbbabbbaabaabababbaabaabbbbababaababbaabbababaaababaababbabbabbaaabbaaabbaabbbbbbaabaaaaababbbbaabbaababbbaaaaaabbaabbaaaaaabbabbbabaabaababaababbbaaabbbbabaaaaaaabbbbababaaaabbaaaabbabbbbbabbaaabbbabbabaaabbbabbbbbabababbbbbbabababbabbbaaaababbaabababbaaabbaabaabbbaabbbbabaabbaabaabbabababbabbabbbaaabbbabbaaabbbbaabbbbaabbaaaabbbaaaaababbbaaabaabbaaababababbbbababbbbaababbbaababbabbaaaaaababbbaabaaabbbbaaaabbbbabbbbbbaaaabaaabbbaaaabbbbbaabaaabababaaabbbaaaaaaaabbaabbbababaabaaababaabbbbabbbbaaaababbabbabbbbbbbbbbabaaababaabbbbaaabbbbbbbbabbbbabaaabbaaabbbaaabababaaaaaabbaaabbabbaaabbbabaabbaaaabaabbaababaabbaaaaaaabbbbaaabbbbaabbbbbaababbbbbbbaabbabbabbabaaaaabbabbaaabaabbaaababaabaaaabbbaaababaabbbbbbaaababbaabbbabaaaabbabbbbaababaabbbababababaaaababbaabaabbbaabababaabbbabaaabbaabbaaaabbabbabbababbbaaabaabbbabaabbbbbbbbaabaaaaaabbabaaabaaabababbaabaaaabbababaaabaababbbaabbababaabbaaabbbaaaabbbbbaababbabbaababaabbaaabaaaabaabaabbbbabaabbabababaabbaababbaabaababbabaabbbbbbbabaaaabbbbaabbabbaabbbbaabbaaaaabaaabbbbaababbabababbabababbaabbaabbbabaababbaabbbabbbababbabababbbaaababbbbbbababbbaababaababaaabaaabababbbbbaabababbabaaaaabbbaabbababababaabbaabaabbbaabbaaaaaaabaaaabbbbaaaabbbbabbbbaabbabababaaaabbbbaaaaaabbbbbaaababaaaabbbababaababaaaaaabbbbabbabbbbaabaababaaabbbaabbabbaaababbaaabababbaaaaabaabbabaabbabbbaaaabbabaabbbbaaaababbbbababbbabbbbbaabababbababbbabbababaabbbaaaababaaaaababbabaaabaabbbabbbbbababbaabaaabbbbbaabbabbbbabbababbababbbbaaaabbaaabbbaaabbbaaabbaaaaaabbaabbbaababbbabbaababbaabbbbbbaabababbbbbbaaababababaabababbabbabbbabaaaaabbabbbabaaabbaaaaaaaaabbbaaaaabbbbbabbbabaabaaaababbbababaaabaaaabaaabaaabbbaabbabaaabbbbaaababbaaabababaababbbbbaababbaabbbbbbababbababbaabbabbbbbbaabaabbbbabbaabbaababbaaababbababababaaaabaabaaaaaaaabbaaababbbbaabbaaabbaabbababbabbaabbaaaabaabbaaababbabbababbabbbabaaaaaaababaaabbabbbbbbbbbbabaaabbbbaababbbbbbbbbbababbaaaabaabaabaaaabbabbbaaabaaaaababaabbbababaaabbbbabbaaaabaabaabaabbbbaabaababaabbbabaabbbbaabbbbbaabbbababaaaaaabaaaaaaababaaabbbbaaaabbbabaabaaabaaaababaaababaaabaababaababbbbbbbaaaaaaaaaaaaaabbbbbabbbaabbbbbabbaaabbaabbbbababbaaaabaaaabaabaabbbbbbbabbbaaaaaaaaabaaaaabaabbabaabbaababbaabaaaaabbabaabbaaabababaaabbababababaaabbbbbaabbababbbbbaabaaaabaaabbbaaaaaaabbababbabbabbbbaabbaaaaaababaabbabbabbabbabbbabbbaaabaaaabaabbaaaabbbaabaabababbaaabbabaabaaabbbbbbababaababbabaabaabbaabbabbababaaaaaabaabaaababaabbbbaabaabbbbbbabbbbbababbbbbbabbbbaaabbaabbaabbbbbababaaaaaababbbbaabbbaabbbbaaababbbbbbbabbbbbbbbababbabbaabbabaababaabbbaabaabaabbaabbaaaaabbaaaabaabbbbaaabaaabbaabbbbbaabbabbbbaaaaabbbbbbbbabbbbbabbbaabbbbaabbbbbaabbbaaababbbabbabaaaabbbaabbbaabaabbababaaababaabbbaaaaaaabbbaabaabbabbaabbaabbbaababaabababbbbaabaaaaaaabbaabbababbbbbaaaaabbbbabbababbbbbabbbaabbababaaabbababbaaaabbbbabbabbbabbbaaababbbbabbbaaabbabaabaaaabaaabbabababbabbabbbbbabababbaababbabbbabbbaaaaabaaabaabbbaaabbbbbbabaaaabbbaaaaabaaaabbaabbbbabaaabaaaabaaabbabbabbbababaaabbaababbbababaaabaaaabbbbaaabbaaabbaabaaaababaabbbababbbbabaababbbabbbbaaabbbbbbbaabaabaaaaaaaababaabbbbaabbababbbbababbaabababbabbabbbbbaabbabaaaabbbababaaabaaaabbbbabaabbaabbbabaaabaaabbbbbaabaabaaabababbaaabbaabbbbbabaababaabababaababababbaabaabbaabababaabbbbbaaaaaaaaaaaabbbbaaaabbbbababaaabaabaaaabababababbbbbbbbbaabaaabbaabaaaabbbbabbababbaaababababaabbbbbabbababaaabbbabbbbabbbbbaaaaaabaaaaaaaaaabaaabaabbbbbabbbbaaaabaababbabaaaaaabaabbbbaaababbabababbbbaaababaabbbabbabbaaabbbabababaaaaabababaabaaabaaaaababbaaaabbbbbababbbbbbbbbbbaababaaaabbaabbaababbbabaabbbbaababababbaabaabbbbababaaabbbababaaabbababbabaababababbaabbaabaaaabaaabababbbaaaababbbbbabbbbabbaaabababaaaabaabbbababbaabaababbbbaaabaabbaabaababaabbaaaabbaaaababbabaabababbbbabbbabaabbbaaabbbbaababbbaababaaababbbabaaaabaaaabbabbaaaabbbbbbaababaaaabaabaaabaaaabbbbbbbbababbbbabaabbbbbbabbbbaabbbbbbaaabaabaaaababaaaaaaaabbabbbbaabbababbbbaaabaaababababbabaababaabbbbabaabbbaabaabbbabbaaabbbaababaaabbbbbabbabbbbabbbaabbaaaaaaabbbbbbabbbaaaababbabaaaabaaaabbaabaaaabbaaabaaaaabaaababbabbaabbbbbabbbaaabaaaabbaaababaaabaabbababbaaaaabaabbababbaababaabaababbbababbaaabbaabbbbbaabbaabbabbbbbabaaabbbbabaabbabaaaabbbaaababbbabaabbbbbbbbabbabbabbaabaaaaabaababbbaaaabbabbaaaaababbbabaaabbabbbaaababaabbabbbabbabbaabaabababaaaaabbbabaabbbbababbbaabbababaaabbababbbbaabaaabaabababbbabababaabbbaaabbbbbbaabbabbbabbabaabbaaabaabbabbbaaabaaabbbbbbabbabbbabbaabbbaabbaabbbbbaaaababaaabaaabbbbaaaabbaabaabaaaabbaaaaaaabbbbaaaaaabbbabbabbabbbbbaaaaababbbabaabbaabbbbabbbaaabaaaabbbbaaaaaaabaabaaabaaaabbaaabbaaaabababbabaabbaaabbababaabababaababbbbaaaaabaaaaabbaaaabbabbaabbabbaabbabbabbababbbbbbbaabbbaababbaaabbbbbaababaabababbaabaabbbaaaaaabaabaaabbabbababaabbaabaaabbababaabbabaababaabbbbbabaababbababbababbbabbbaabbaaaabbbbbbabbabbabaaabbbbaabaaabbbaaababbbbababbbbbaabbabaabbaaabababaaabbabbabbababababbaaababbbbaaaaaabbbaaabaaabbaaaaabbbabaabbabbaabababbbabababbaababbabaabbbbaaabbbbbbabaabababaabbaaabbbabbabbabaabaaaabababbaababbababbbabbbaaaaabbaaabababbaaabaaabababaaaabababaabbaaaaababbbabbaaababbbaabababaaabbaaaabaabbababbaaababaaabbbbaabaaabaaabbbbbaaaaabbbabbbaababbbabbbabbaaaaabbbaabbbaaabaaaabbbabaabbaaabbbbabababaaaaabbabbaaaabbbbbbaaabaaaaabbbabaaaabaabbabbaaaabbbbbbbbbabbabbababaaaaabbbbbaaaaababbbbbaaaaabaaaababbbbbababbbbbabbabbabbbbaaababbabaabaaaaababababaabababbaaabaaaabbaababbbbbbaabbbbbaaabaababbaaaaabbbaaaababababbaabaaaaaabababbabaaabbbbaabbaaabbabbbabbaaabaabaababbaabbababaabbabaaababbbaaabbabbbbaaabbabbabababbaabbbababbbbababbababaaabaaabaaaababaaaaaaabbabbbabaabbbbaabbbabbbaabbabbaabaaaababaabaabaaabaaaabaaaabababbaabbababbabaabaaabaabaaaabaaaabaabaabababaaaabababaaabaabbabbabbbaaabaaaabaaabaabaaaabbababbaababaaabbaaaababbbbbaaaababbbababbbaababaabbbbbabbbbababaababbbabaaaabaababaaabbaaabaaabbaabbbbbaabababbabaaaabaabaaababaabaaabbbaaabaabaaaaaabbababbabaaabaabbaaaaabababaaabaaabaaabaabbabababbbabababbbbbbaabaabbbaaabaabaabbbbbbababbbbbbbaabaabbbaabbabaaaaaabbabababbaabbbabababbbbaabaaabaaabaababaabbbabababababaabaabbabbbbbbabbbaabbabaabaabbabbabbbbbabbaaabbbbbbabababbbabbaaaabaabaabaabbabababbaaabbabbbabbbaaaaabbbababbbabbabbbabbaabbbaaaaabbbaaaabbbbbbabaaaaababbababaaaaaaabbbabaaababbbabababababbbabbbbbbabbabbbaababbabbbabaabbbbabaabbaaaabaaaabaababbababbababbaabaabbbaabbababaaaaaabbaaaabbabaabaaabaaabaababbbaababbbbbaaababbaababaabaaabababaabaaabaaabbabaabbbbbabbbabababbbaaaabaabaabaaababaaaabbaaabbbbaabbaaaabbabbbbaabaabbbababbbbbaaaabbaaabababbbbbabbababbabbabbbabbbaaababababbabaaaababaaaabbaaaabbbabababbbaabbaababbaaaabbaaaaaaababbaabaaabbaabababbbbbbaaababbbbaabaabbaabbabaaaababbabbabbabaabaabbbababbbbbbbbaaababbabbababbbbabbababbbbbbaabbaaabaaaaaabbbabbbbaaaaaaaaabbbbbbbbbbaaaabbababbaaababaaababbaaabbbbaababbaaabbabbaababaabbbababbaabbabaaaaaaaaaaaabbaaaabbbbabbbaababaaaabaabbbabaaabbaabababbabbaabbbbabaabbabbaaababbbbaaaaabbbaaaabbabaababbabbbaabaabbaababbaaaabbbababbababbbaaabbabababbbabaabbbabbbababbbaababababbabaaabbabaaaabaaaabbabbbababbabbabbbaabaabababbaabababaabbbabaaaabbababbbbabbbaabbaaabbbaabbbbaabbbbabababaabbaabbababbababaaabbabbaabaaaaabaaabbaaabaabbbababaababbabbaabbaaaabaababbbabbbbabaababaabbabbabbaaaaaaabbbbabbbbabbbabbbbabbbabaabaabaabbbababaabbabbbbaaaababbabbbaabbaababaabaabbbababbbbbbabbaaaabbababbbaaababbbaabaabbbbbaabaaabbaababbbabaaaaabaaaabbbaaaaaabbbbaabbaaaaaaaabaaaaaaaabbabababbbbbbabbabbbaabbaaaababbbbbaabaaabaababbbbbbbabbbbaaaabbaabbbaabababaabbbabbaaaaaabbbbbabaaabbabaabaaabbbaabbabaaaaaaabbbaabbaaaabbabaaaabbabaabbaababbaaaaabaabaabbaabbbbaabaababaabbaaaaaaababbabbbaaaabaababaabababbbbbaabaaabbabbaaaabaaaababbbbbbabbbaaaabaabbbbbbaaababbbabbbbbaaaaababbaabbabbbbaabbbbabaaaaaaabbbbbbbbbababaaabbbbbababbbabbabbbbbabbbabababbbababbaaabababbabababaaaababbaababbbbbaababbababaababaabaabaaaababbabbababbbbaaabbaabababaababaaababaabbaaababbbababbbabaaaabbbbaabbabbbaabbbbabaabbaabbbbbbbbbbbaaabaaabbbbbaaabaaabbababbbaaaaababbaababaabbababbbbabbbabaaabaababaababbaaabbababbbbabababbaaabbbbaaaabaaaabaabbabbbbaabaaaabbababbaaaabaabbbbbbaaaabaaabbbaaabaaabaaaaaaaabbaaaabbbaabaaabbaababbbbbbbabbaabbabaabaaababababaabbbbbbbbbbababbbababaaaaababaaaaabababbabbbabbabbbbbaaaaaaabaabaaababbbbbbbbbbaaababbaababaababbbbbaabaaabbaababaabbaaaababbbbbababaaabaabaaabbabaaaaabaabaaaabaabbabaabbbbbbabbabbabaaaaaabaabbbaaabaabbbabbabaabaaabbbbbabbaaaaaaababbbaabbbbaabaababbabaaabbabbaaababbaaabbbbbabbbbababbbaabbbbbbaaaaaabbabaabaabaabababaaababababbbbbbbaaaabaababaaabaaabaaabbaabbaaabbaaabbbbaaaaaaabaaaabaababbababaaabaabaababbaaaabaabbbabaababababbbbbbabaaaaabaabbabbabbbbbababbbbbabbabbaaababaabbaaaaababbbbaaababababaabbabbbbbbbabaaaabbbabbabbbabaaababababbbbaababbaabbabbbaaabbabbbabaabbbaabbaaaabbbbabaabbbaabaabaaabaabaababbaaabbbaabbababbababbababbabbbaaaabbaaaabaaabbbabbbaabaaaababbabbbbabaababaaabbaabbaaaabbaaaaaabbbbbbbabaaababbbbaaaababbbaabaabaabbaabbbabaabbabaabbaaaaaabbabbaabaabaabbbbbabbabbbbabbbbbbaabbaaaaaabaabbaaabbbbaabbabbaaabbaabababaaabaaaaaabbbbbbbababbbaaaaaaababaaaaaaabbbababaabbbabaabaabbaaabbaabbaababbbabbbbabbabbbaaabaabbbabbaabbbabbbababbaaaababbbbbabaabaaaabbababaaabbaabbaaaaabbabaaaaaabaabaaabbabaaaaabaabaaaababbbbaabaababaabbaabbbaaabbabaabbaabbabbbbabaaabababaaababaababbaabbaabababaaaaaaabbabbbbababaabbabaaaaaabaabbbaabbababaabbabbabaababbbbaaaaaaabbabaabbaaaaabababaaaaaabbbabaaaabbbbbabaaabbbbabaabbaabbbbaababaabbabbababbbbaabbaabbaaabababbaaaabaaaababaabbbabbaabababbbaabaabaaaaabababbbaabbabaaaabbbbaababbbbbaaabbbbabbbbabbabbbaabbaababababaabaaaabbaabababbababaababaabbaabababbaabbabbbbbbbaaabbbbaabbbaaabaabaababababaaabaaababaababbabaaabaaabbabaaaaabaabaaaabaabaabaaaaaabbbbababaabaaaaaaabaabbbbbababaabbaabbabaabbbaaabaabbaaaaaababbbbabbabbaabaabbbaaabbbbabaaabbbbbbababbbabbaaabaabbbabaaaaabbababbbaabbbbaababaaababbbbbaabbaaabbbbbabbaaaaabbabbaabaaabaababbabbbabaaabbaabbbabaaaabbbbbbbbababaaabbabaaaaababbabbbbabbbbaabbbbabababbaabbaaaabbbaaaaaaabbbaabaaaaabbabaaabababbbabaabbabbabaabaaaaabbabaaaaabbbbbabbabbaaabbbbbbbbbbbaaabbbaaaaaabaaabbbabbbbbaabaaaabbbbbbbbaaababaaaabbbaabbbbababbabbabbbabbaaabbbaabbbbbbbaaaabaabbbbbabbbaabbbbaaaabaabbbaabaaababbbbabbbbaaabaabaababbbaabbbaabbabbbabbbaabbbaaababbbaaaaabaabbbabbaaabbbabaabbaabababaaabaaaababaabaabbaaaaaababaabbaabaaaababbaaaababababbbaabbabbbbabbaaaababaaabaabbbabababaaabbaaabbbbbaababaabaabbbabbbbbaabbbbbbbaaaabbbababbaaababbabababbbbaaaabbaabbababbaaaabbabbbbbaabbaabbbbbbaaabbbabbbbbabbabaaaaabbaabbbabababbbbbbbaaaaaaabbaaaaabababbabbaabbbbbaabbbbbbbaaabaaabaaaabbbbbbbbabaabbabaaabbbbaaaaabaababaaababbabbbababbbabbabbbbbbbaababbababbaabbbbbababaaabbbaababbaabaabbbbabbbbaabbbaabababbaababaaaabbbbaabaabbababbaabbaabaabbaaaabaaaaaaaaaabbbbbbbbababbabababbbabbabbbbaaababbbbbbaaabaababbbabbbbaaababbbbbbabbaabbaabbbbabbaaabababaabbbaabbaaaabaaabbbbbbbbaaaaabbababbbabbababaaabbaabbbaababbbaabbbbbbaaababaababbaabaababababbbaabaaaaaabbababaaabbabababaaababbbbbbabbbbaabbbaaaaabbbbaabbbabababbababbaaabaaaaabaabaabbbaaaabaabababbbababbaabbbbabbaaaaababbbbabaaaaaaababbabbbabaabaabbbabaaabaaaababbabbbbaabbabbbbaabbaabbbbabaababaabaabbaabbbbbbbbabbbbbbbaaaabaaaaaabbbaabaaaabaabbaaaaaabbbabaaaaababaabaabbbbaaabaaabbaabbbaaaaabbbaaaaaaabbabaabbbabbaaaaaaaababaaabaaababababbbaaaabaabababbbbbbabaabbabbbbbbbbbaabbaaaaaaabbaabbbaabbbbaabaabbabababbaabaaaaabaabbaaaaaabbaabaabaaaaabbaaabbaababaabbabaaaaaababbbbbaababaabbbbababbbbbbaaaabaabbbbbaabbaabbbbbaabbbabaaaababbaabaabaaaabababababbabbbabaaabbbabaabbabbbabababaababaaaabbbaaabbbbbaabaabaaaabbbaabbabbbbababaabaabbbaabbbbaaabaabaabaabbbbabbaababbabaaabaaaaabbbbababababaabbabbbbbbabaabababbbaaaabaababaabbababaaabbbbbbabbabbabbbbababbaaababaaaabbbaabbababbaabbbababaaaaabbabaaababbbaaabbabababaaaaaabbbaabaabbbbbbbbabbbbbbaaabbbbabbaabaabbabbbaabbaaababbbababbaabbbbabaabbbaaabbbaabaaabbabaabbaabaaabaaaabbbaabaabbbaaaabbbaabaabbbaaaabbaabbaabbaabbabbbbbbbbbbaabbbabbbbbbbbbbbaaabaaaabbbababbbabbabbbbbabbbbbbabaabbaabababbababbbbbbbaababbbabaabaaaabbaabbbbaaaaabbbbaabababbabbbabbababbbababbabbabaaabbaabbbaabbbbaaabaabababaabbaaaaaaababbbaaaabbaaaaabbbabaabababbaabbaabbbbbbbbabaaaaabbbbabbbabbbbbabbbbbabbababbbbaabbbbbbaabaaaaaaabbbbaababbababababaaabbbbbaababbabbaabbababababaaabaabaabbbbaabbaaaaaaabbbbabbaaaaaaaabaaabbbabababaabbaaabbbabaaabbabbbaaababaabaaabaabbbbbbaaaabbaababbababbbabbbabbbaaabababaababaaabbbaabaaaaabaaaaaaabbbbbaaabbbaababbbaabaababbabaaaabbbbaabaabaabbaabaababaabababbababbabaaabbabaabbbbabbabbaabbbbabbaaabbbbbaaabbbbbabbbbbaabbbbbaabababbbaababaaabbbbaabbaabaabbabbbbbbbaabababbbbabbaaaaaaaaabbbaaabbaabaabbaaabbabbaaabababbbbbaaabbabbaabbabaabbbbbbbbabaabaaabbbbbbaaaaaabaaabbbbbaaabbabababbbbabaabbababbaaabbbaaaabbbbabbbabaababbbbabaaabaabbbabbbbabaaabbbbabaabbbabababbabaaaaaabaababbaaaaababbabbbbaababbaaabbabaabbaaaabababbbbbaabbbababbbbabbbaaaabbbabbbbaabaaaabbabbaabbabbbaaaaaababbaaababaaaaabaabbbaaabbbbbababbabbabbbbaaaaabaabbababbbbabaaaaabaaabbabbaababbaabababaabbaaababaaabbbaaababbaaaababbbabbbaaaaaabbaaabababbbbbaabbbabbabaaaaaaaabbbbabababbbaabbaaabbaabbabbabbbababbbabaaabbabababababaababbabababaaaaabbaaabbbbbaaaaaaaabaaaaabaaaaabbaaaabbbabaaaaaaaaabbbbbbabbabbaaabbaaaabaaabaabbaabbabbbaabaabbabbbaaaaaabbbaaababbabbbbababbaaaababaabbabbbababbaabaabbabbbbabbaaaaabbbaaaaabaaaaaabbabaabbbaaabbbbababbabbbbbababbabbbbabbabbaababaaaaabababbaaaababbabaaaabaabaaaaabaabaabaabaaaabaaaaabbaaabababababababbaabbaaabaaabbaaaabbbbbbbbbbaababbabbbaababbaabaabababbbabaababaaaabbaaabaabaaabbabaabbaabbaaaababbbabbabaabaaaaaabbbbabbabbbaababaabababbaababababaabaabbaabbbaaaaabbaaaababbbaaabaaabbabbabbaaaaaabaaaabbabaaaaabbabbaaabbabbaaaabbbaabbaabababbabaaabbbbbaaaaabbbbbaabaaabbabababaaaabbaabaababbabbbbbbbaababbbabbbaaabbabbaaaabaaabbbbabbaaabbbaaabbbaaabbaaaabaabbbbbbbbbaaabbbaaaabbabbabababaabbaaabbaabaabbbbbbbabababbbaabaaaaaababbaabababbabaaabaabbbbabbabbabbbbaabbbbaaabbaabbabbbaababbaabaaabbbbbabbbaabaabaababababaabbbaababaaabababbbaababaabbabbbbabbbababbbbaaabbbaaabbbabaabbaaaaabbaabaabbabaabaaabbabaaabababbaaaababbaabababbbbaabbbaaaaaaaaaaabbaabbbbabbaababbbaabaaabbabbabbabbbabaaabbbaaaaababbaababbaaabbbbaabaaaabaaabaaaaababaaaabbbbbabaabaabababbbababaaabaabbbabbbbaabaaaaabbabaaaaaababbaabababbaaabbbbabbbbaabbaaabababaaaabbbbababbaabbbbbbabaabbabbbaaabaaabbbbabbabaaabbababbaaabaababbbbabbabaaaaaaabaabbaabbabaaabbbabbbbaaaaaabbbabababbbbabaababaaaaabababbbbbabbabaabbbababbaaaabbaabaabaaaaabbbaababbbabaaabbabaaabaabababbbabaabbabaaabaaabaaababaabbbbbbbbbaabbabbaaabaabbbabaabbabbbaaabbbaabbbabbabbbabbaabbaaabbbbbabbbaaabababaaaaabaaababbaabbaabbbaaaaaabbbbbaaabbbbabbbababaabababaababbbaababbbbbbaabbbbbbabbbbaabbbbabbbaabaaaababbaabbbbaabaaaabbbbbaabababbabaaabaaabaababbbaabaababbabbbaaaabaaaaababaabbbabbabaaababbabbabbabaaaabbabbaabaabbaaaaaabbabbbababaababbaabbaababaaaaaabbbabaabaaabaabbbbaabbaaabbabbabbbaabbaaabaaababbaabaaababaaabbbaabbabaaaaabbaaabbaaaaababbbbbaaaaaaabbbabbaabaababbabaabbbbabbbbaaaabbbbbbbbbabbbbaabaabaaaababbabbabbabbbaabbbbbbbbbabababbabaaabbbaabbababbbabbabbabaabbaaabbaaabaaabbabbbbbabaabbaabbaaaabaababbbbbabaabbaabbbaabbbbbabaabbaaabaabbbabaaaabbaabbbabaaaabbabaabbbabbbbbabbabbaababbababbabaabaabaabbbbabaabaabbbabbbbaaaaabbaaabbabbbabbaaaababbbaaababbbabaaabaabbbbaababaabbbbbaabbabbaabbbbbaaabaaaabbaaaaabaababbbaaabaaaabbabbaaababbbbbaabaabaabababbbbbbaabbbabbaaaabbbbbabbbbbabbaabaabbaabaaabaaaabbbbaabaabaababbaababaabbaaabbabaaaabbabbbbbbbbbbabbbaaaaabbababbaababbbabbabbababbbabbabaabbbbbbabaabbbaaabaaaaaaaababaabbbabbbaabbabbaababbbbbaabbbbbbbabbababbbbbbbabaaaaabbabaaabbabbabbbabbbbaabaabaaaabbabbaaabbbaaabbabababbbaaaaaabaababbbbbaabbbbbabbaabbabaabbbbaabbababbbbbbaaababaaaaaaabbbbabaabaabbbbaabababbbaaaaaababbabaaaabbabbabaaaabbbabaabaabaababbabbbbbabbbabbbabbabaabaabbabababbbaaabbbabaabababaaaaaaabaaaabaaabbbbaabaaabbbabaabbbabaaaaaaaabbbbaaaabbbbbbabaaaaaaaaaabbbbabaaabbaaaaabbbabbbbbbaaaabababaaabbbabbabbabbbaabaabbbabaaaabbabbbbababababbbaaabbbbabbaabaabababaaababbabababaabbbbabbaaaababbababababbabbabbabbbabaaaaabaababaabbabababbaabbbbabaaaababbabbaabbaabaaabaaabaabaaaaaabbbabaabbbabaabbbabbaabbbbabbabbabbbbbbababbbbabbbbbaaabaaaaabbababababaaaaaaaabbbaabaaabbbaababaaaabbbababbabbbbbaaaabbaaabbaaabbababaaabbabaabaabbbabbabbaababbaababbaabaabbbbabaabaaaabbbabbaaaabbaaaabbbaabbabababbaaabababbbbaabaabbbabbabbbabbabbaaabaaaabbbbaabaababbaabbabaabbaaaaabbbababbaaaabababbaaabaaabbabbbbaabbabbbbabbabaaabaaaaaaaabbbbabbaababbaabbbbbaaababbbaaaaabababaaaabbbbbaababaabbbabbababaaababaaabbaaabaaababbaabbaabaaaaaabaabaaaababbabbbaaaababbbabaaababbbbbabababaababbbbbaaababaaaabbbabbababbbaabaabbbaabaaababaaabaaaaaaaababababaabaaaaabbaabbaababbababbaaaabaabbbbaaabbaaabbbbabaabbbbaabbabbabbbaaaaabbbbaaabbbbbabaabbbabaaabbbababbabababbbbbbbabaabababbbbaaaaababbbabbaabababbbababaabbababbbbabaaaabababbaabaabbbabaaabbbbbbaaaaabababbabaabbabaabbabbbabaababaabaaaaaaaaabbbbbbaaabaaababaabbbabbaabababbaaaabaababbababbabaaabbaabaaaabbbbbbbaabbbababbbabbababababaaaaaaabaaaabaabbbbaabbbababbbabbbabbababbbbbabbbbbbbaabaabababaaaaaaabbbaaaabbabbbabababaabbbbbbbaaabbbabbbaaaaabbbbbbbabbaaaabbabbaaabbabbbaaabaabbbbbabaaabaabbbbbaaaabaabaabbaaaaaaaaabbbbbbaababbabbaaabbabbbabbbababbbbbbbaaaaabababbaaabbbaaabbabaabbbabbaaaabbabaaabaabaabbaabbabababaaaaaaaaabaabbbbbabbabbbaaaaabaaaaaabbbaaababbabbbabbbbabbaabababbbabaaabaabbbaabbaaabbaabbbbaaabbbaabaaaababaabbbaaaaabbbabbbabbabaabbbbabaabaabbabbabbbabaaabbabbbababbbbaaaaababbbaabaabbbaababbbbbbabaaabbbbaaababaaabaabaabaababaaabbbbaabbbbbaaaaababaababbabbbbabababbbabaababaabbaabaabaabbabbaaaabbabbababaabbababaabababbabbbbaaaabaaabaabbaababaaaaaaaaaababbaabababababaaabbabbbbbababbabbabababaabbaaababbbbabaabbbbbbabbbbaaabbababbaabaaabbaabababbbaaabaaaababbbabbbbabbbaabaaaabbbabbabbbbbababbaaaaaabbbbbababbbbababaaaaaaaabaaababbbbbbbbbaaabbabbbabbbbbbbabbaaaababbabbaabaaaaaaabbabaabaaaabbabbababaababaababbbaabaaaabaababbbbabaaaabbaaababbabbbaaabbaabaabbaabaabbabaabaabaaabaaabbbbbbaaaaabbbaaabaabaaabbbbaabbbabaaaabbababaaaabaaaaaababaaabaababaabaaabbbabbaaaabaaabbabbbbbabbbbabbbaabababaababaaaabbaabbbbaabbabbaabbaabaaabababbaaaabbabbbbbbbbaabbaabbaaababbbbaabaaaabbaaababbbaaabbaaabbabbaababbaaababbabbbaabbabaabaabaaaaabaababbaaabaabbabbabbbbabaaabbbababaaabbaaabbbbbabbaaabbbbbbaaabbaaababbbbbbaababbaaaaabaaaaabaababbbbbabaaabbabbaabbabaabababbbaabbaabaaabbabbabbbabaaabaaaaabbbaaaabaababaaabbaabbabbabaaababaaaababbabbabbaaabbabbabbaabababaabaabbabbabaaaaaaaaabbaabbababbabbabbbbbababaaaababaabaaaabababbbabbaaaaababbaaabbbbabbabbabababbbbbaaaaaaaabbbaaabaabbaabbaaaaababbababaaababbaaaaabaaabbbaabbbaaababbbbbbaabababaabbbabaabaabaabbabbababaaaababbbbababbbabbbbbbaaabbababaabaaababaabbabaababbaaababbaaaaabbbabbbabaabaaabbaabbbbbbbabbaabaaabbbaababbbaaaaaabbbbababbbabbaaaaaaabbbbbbabbbabaaaabaabaaabaaabaaabbaaaaabaaaaaabbbabaababbbbbbaaabaababbabbabbbbaaaabbbbbaabbaaaaabaaaabbabbbbbbbabbbbbaaabaababaaaabbbbabaaabbbaabababbaaabbaaaaabbbaabaaabbbbbbabbaaabaabbbbaabaaaabbbbbbababbbbbababbbaaabbaaababaaabaaabbbbaaabbaababbaabbababbbabaabbbababbbbabababaaaaaaabaaabbbbbbbbabbabbaaaaabaabbbbabbaababababbbababaabbabbbbaabaaababaabbbaaaaabbaabbbbbaabababbbabaabbaabbaaabbabbabababaaaaaaaabbabaaababbbaaabbaabbaaaababbaabaaaabbabbaabbbbaaabaabaaaaababaabbaababbbabaaaabbbaabbabbabbbaabababbbabaababababaabaabbbbbaaaababababbabbabaaabbbabbbabbbabbbaaabbbabbaababbbabaabaabaaabbababaaaabbbababaababbbbaabbbabbaaaaaabbbaaaabaabbababbbabaababbbababaabbabbababbbaabaaaaaabaaabbaabaaabbaabaabbababbbaabbbbbabbbaaababbaababbbaabbabbbbabaabbbabbaabababbbabbaabbbabbbaaabbbbabbbbabbbbbabbabbbbaaabaababbaaabbbbbaabbbbbbabaaabbbbbbabbababaaababbaabaaabbbabaaaaabbbbaaaaaabbabbabababbabaaaaabaababbaabaabbaabbbbabaabababbbabbaaababbaabbaaabbaaaaabbbbbaabaaabababaaaababbbabaaaababbaabbbabbababbbabbbabbaaabbbaabbababbbabbaaabbabbbbbabbaabaaaaaaaabbbaababbaabbbbbbbbbbabababaaabaabababaabbabbbbabaaabababbbaababbbaaababaaaaabbaabaaabbbbabaabbababbbbaabbbaabbbbaabbbababaaaaabbababbabbbbbbbbbaaaaababaaaaababbbbabbaaaaaabbaabaabbabbabaaaabbbaabaaabbbbabaabaabbbbbbbbabbbabbaabbabbbbabbbaaabbababbaababbbaabaaaabbbbbbaaaaabbabbbbbbbababbbabababbabbbaabbabaaaabbabbaaabbaaaabbaababaaabbabaabbbaabbbababbbabbaabbababbbbbaabaaabbbaabaaaaaabbaaabaaababaaabbbaaaaababbabbaabaabbbabbababbabbaababababbaaababbbaaaaabbababbbaaaaabaaabbbabaaabbbbababaabbbbbbaabbababaaabaaabbaaababaaabaabbabaababbbaaaaababaabbbbabababbbbbaabbaaabbabbaaabbaaaabbabaabbbaaaabbaabbbbabbbbbaaabbaabbbaabbbabaaaaababababbababababbbbaabaabbbbbbbbaaaaabbaaaaabababbabbaabaababaaababbbbbabbaababbaaaabbaababbabaaaabbbbbbbaaababaaabbbbbababbaaabbbabaaabababbaabaaabbabbababbabababbbbbbabbaabaabbabababaaaaaaabbbaaabbaababbbbbabbabbaaaaaaabbabaabbabababbaabbabaaaaababaaaaaababaaabaaabaababaaaabbbbaabbabbabababbabbabbbaababbbbbaaabbaabbbabaaaaaabaabaabaaabaabbaaaaabaabaabbabbbaaababbbbaaaaaaabaaaabbbabaaababaaaabbaaaabbbbababbababaabbbaabababababaabbbaaaabbabbbbabbbbaaaabbaaabbbbbbabbbbbaaabaaaababbaabbaabbbababbabaabbbaabbaaabaaaaabbabbabaaaabbbbbbbbbbaabbbaaaaabaaaabaaaabaaababbabbaaababbbbabbaaaaaaabbbbbbbbabaabbbbaabbaabaabbabaababaabbbbabbbbaaaaabaaaaababbbabbaabaababbbaabbbaaaababbababaaababbbbbbababbbbaaabbabbbbbbbaaaabbbabbaababbbbbbaabbabaaaabbabbbbbbabbbbababbbabbbbabbbbababaabaabbaabaabaaaababaabaaababbbababbbbabbababababababbabbbbababaaabbbbabbaababaaababababbbbabbbabbbbbbababbaabbabbbbabbbbbaabaaaaaabbababbbbaababbbbabbabbaaabaaabababbbaaaaaabbaabbaaaaabbbabaaabbabbbbaaaaaababaaabbbbaabaaabbaaabaababbbaaabbabbbabbbbbaaabaababababaabaabbabaabbaaabaaaabaabaabaaabbbabbbbabaaaabbaaaaabaabbbaaabbbbbbbababaaabbabbaaabbbabbbaabbbaaaababaababaaabaaabaaaaaabaaaaababbbbabaaabbbbabbaaabbaabbbbabbabbbbababaabbaaababaaaabbabbaaaaabbabbbaababaabbbaaababaababbabbbaabaabbaaaabaabababbbbbbbbbbbbbaababaabbbbaabbbbbbbabbabbaaababaaabbabbbabbabbaaababaabbbabbabbbbaabbaababaaabbbaabbbababbaabbbabbabbaaaaaaabababaaabaaababaabbabaabaababaaaababbbbbaaaababbbababbbbbbaaabbbabaaababbabaaabbaabababbbaabaaabbbbbabaaaaabaaabbbaaaaaabbbaaabaabbabbbabaaaaaababbaaaabaabaabaababbaabaabbbabbabbbbbaabababababbbabbababbbababbbbabbbabaabaabbabbabaabbbabbaabbaabbbabbbabbbbbabbbbaaabaabbbbaabaaaaaabbabababbabbababbbaabbbbabbabababbabaaabbbabbaaabababbbbbbbbbbabbbaabbaaababaaaaabbababaaabbabbaaaaabaabaabaaabbaabaabaabbbbbbabaabbaaabaabbabababbbbabbaaaaaaaaabbabbaaaabbbababbaaaabbbbbbaababaabababaababbbbbbbbbbbabaaaabaaabababaabbaaaaaaabaaaabbabbabaabbabbbbaabbbabbaabbbabbaaaaaaabbaaababbabbbbabaaaaabbaaaabbbaaaabaabaabababaaabaabbbbabbbbbabbabbbbbbbababbbaabaabbaabbbbabbbbababbbbbbbbbbbbaaabbaabbabbaababbbaaaaaaaaabbbbabaaaabaaaababbbbbbabbbbbbabaaabbbabbbbbbbaaababbababbbabbaaabaabbbbbbbaababbabbaabaaababbbabbabbbabaabbbbaabbbbabbabbbabaababbbbbabbbaabaabbbaaaaabaaaaaabaaaababbbabbabaabbbbaabbbbbbbbaabbabababbaabaabbbbababaaaababbbbbababaabaaaababaaaaaabbbaaaaaabbbaaabbabaaaaababbaaaaaabbabbaababbabaaaaabaaaabbbbaaabbaabaaabbbbaabbbbabaabbbbabbabbbababbbabaaaaababbaaaaaabaaababbbabbbbaaabbbbbaaabbabaaabbaaaaabbbbabbbababbaabaabaabbbbbbbababaaaaaaaababbbabbaaaabaabaababbabaabbbaaaaabbaaaaaaaababbaaaaabaaabaaabbbaaababbbbababbaaababaaabbbbaabaabababbbbaabbbabbbababaaabaabbabbbbabaabbbbbbabaaaaaabaaabbbbbaaaabaababababaabababbbabbbbbbbbababbababababbbabbbabbbbbbbabbabbababaaabbbbabaabaaaaabbbaaaabaaaababbbbabaababaaabbabbaaabbbbaaababbbabaabaabaaaabaaaabaaabbbbabbababaababbbabaabababaabaabbaaababbbaabbaaaaababaaabbababbabbabaaaabaabaabbbbbaaaabbbababbabaababbbaaaaaabbbaabaaaaaaaababaabaabbaaaabbbbaaaaabaabbabbababbabbbbbbbabaaaaaabbbababaabbaaabbbbbbbaaaaaababababbbbbbabaabbabbaaaababaabbaaaababaaaaaababaabbabbababbaabbbaabaaaabbaabaaababbabaaaabbbbbbaabbbbaabaaabaaababaaaaabbaaabbabbbaaaabbbbbbbbabbaaaabbabbababbaaabaaaaabaaabaabbbabbaabaaaaaaabbababbbabbababbbabaaaaaabbabbaabbbbbababaaaabbabababbbabbabbabaaaabbababbabbabbbabaabbabbabaaaabbbababbababaabbbabbbabbbabbbbaabaabbbbbbaaabbaaaaaabbabaabaabbbbbbabbbbabbabaabababbbabaabababbbbabaaaabbabababaaaabbbaababbaaabaaabbbaaabaabababbabaaaaababbababababbaaaaaabbaaabaabababaaaaabbaaaaababbbabbababbaaaabbbbaaabbaabaabaaababbabbabaaabbbbbaabaaaaaabaaabbbaaababababbbbbaabbbabaabaababababbabababaabbbabbbabbbbbbababbaabbbbbbbabbaabbbaaababaababbababaabbaaabbbaaaabbbabbbabbbaaaababbaababaaabbbbbbabaaaabbaaabbabaaaaaabaaabbabbbabaaaabbbaaaababaabbababababababaabaaaabbabaabbabbbaaaabbabababbbbaaaaabaaabbabbabababbbbbaaabaaabbbbaabbbaaabaabaaabaaaabbaabaaabababababbbbbaababaaababaaaaababbaabbaabbaaaabaabbbabbabbabbbbbbbaababbbbbaaabaaabbabaabaabbbaaaababbbaaaababaaaaaabaabaabbabbbbabaaababbabaaababaaabaababaabbbaabaabbbabbbbaababbbaabaababbaabbaaabaabbbabbabaaabbabbabbbbaabaaaabbabbaabbbaaaaabaaabbbaabbbaaaabaaabbbbbbabbabbbabbbbabaaaaaaabbabaaaabbbaaabbabaabababbaabababbaaabaabaababababbbbbbaaababaabaabaabaaaaabaababaababaabbaaabaaabbbabababbbbbabbaaabbababbaaabbababaaababbababbbbbbabbbbabbbabbbababbbbabbbabababbbabbbbaababaababbaababbbabbaabbbabaabbabbabbbaabbabababbbabbbabbbbbbabbbaaabbabaabaabbbbabababbbaabaaaaaaabbaaabaabbbabbaabbbaaabaabababbaaaaabbabaababaabbbbaaaaaaaabbbbababbaaababbaabaaaaaaaababbaaababbbbbaabbaabbaabaabababaabaababaaababbababbbaabbaabbbbbababbaaaabbaababbababbaabbabbaaaaaabbbbabaabaaabbabbaabaabaabababaaaabbbbabbbbbbaaaaabababbbbabaaaabbaaabbbababbbbbbbbbaaababbbbabbabbbaabaaabbbaabaabbbaabaaaabbabbabaababbbbabbbaaaabaaaaaaaabbbabaabbaabaababbbbabaabbbaabbabbbaaabbababbbaabbaabbaabbbaabaaababbaabbaabababbabbbaabbaabbbbabababbbabbbaaabababbbbabbbaaabbbaabbaabaaabbbbababaabaabaabaaabbabababbaaaaabbbbbbababbbbbbbbbaababababbaaababaababbbbbabaabbaaabbbaabaabaaaababbaabababbbabbbaaaabbabbaabbaaabbbbbbbababbabbbabbaababbaaaababbbabaabbbabbbbbaaabaabbabbaaabbaababbbbbbaaaabaaaaabbbababaaababaaababbbbbbbaaaaabaaaaaaaabbbbababbabababbbbabbbabbbaabaaaaabbabbbaabaababbabbbabbabbabbababababbaabaabbabbbbabaabaaabbbabaaabbbabaabbbbaababaaaabbbaaaaabbababbbbbbbbaaabaabbaabbbabbbbbbabaaabbaaabbbabbaaabaabaaababaabbbbbbababaaaaababbbaabbababbaabaabaaaababbabbaabbbaaaabbbaababbaababababbabbaaabbababbbbabababaabaabbabbabbababaaaaabbabbbbababbaabaaabababbbaabbabaaaaabbbbbaaabaabbabbbabbabaabbaaabbbabaaaabbbabababbbbabaabbabbababbaaaaaabababbaaaaaaaabbbbabbaaabababbbaabbbbaabbabbabaaaaabaaabaabbaaaababbaaaabaababbbabaabababaaaababaabababbaaaaaaababbbbbabbaababbbbababaabbabbabbabaaabaaabababbabbbbbbbaabbbbaaababbaababbaaaabbbbbabbbaababababbabaaaabbabbabbabbabbbbaabababababbaaabbbbabaaababbaaaaabaaaabbbaaaababababbabaaaaabbabbabbbabbbbbbbabbaabbbbbaaaaabbaabaaabaaabaaabaabbbabbbabbaababaaaabbabaabaabaababbaabbaaaabaaaabaabbaabababaaabbaabbababaabbbaaaaabbaaaabaabababbaabaaaababbbaaaaababbbaaababababaaaabaababbaaaabbbbbbbaaaabbabbaabbbabbbbbaaabababbabbbabbbabbababaabaababbaaabbabbaabaaaabbaabaabaaaabbbaabbbbaabbbabababaabbababbaabbaababbbaabbaaaababbabbbbabbbbababbaaababaaaabbabbbaababbbaababaaaabbbbababbbbababbbbaabbbabbaabbaababbbbabbaaaabaabbaabbabbababbaabbaaaaaaaabbaabbbababbbaaababbaabaabaaabbbbabaaabbbbbbbbababbabaabbbbaaabaabbbabbaaabbabababaaaaaaaabaabbaabbaaabbaabaaaababaabaabaaaaabaababbbabbababbbaaaabaaababbaabbaabaabbbabbaaabbaaaabbaaabaaabbbabbbababbaaaaabaaabababbbabaabbbbbaabababbababaaaabaabbaaaabaabbaaaaaaabbabbbbaaababaaaaabbbaaabbbbabbbbabbbbabbbaaaababbbaaaaaaabbabaabbbbabaabaabbbbabababbabbababaabbaaababaabbbbabbabbabbabbababbbbbaaaabaabaabbaaaababaaababaabbbaabaabababababbabbbaaaaababababbaabbbbaaaabaabbababbbbbbbaabbbaabbabbaaabbbbbbbaaabbabbbababababaabbaaaaabbabbaabbabaabbbababbabbbabbbbaaaaaaabbaabbabbabaaabbbbbabaaabababbbbbaabbaababaaabbbababaabaabbaababbbabaabbaaaaabbbbabbbabaabbbbabbaababbabaababbaabbbbbaaabbbababbbbbbaaaabababaaabaaababbaaaaababbaaababababbabbbbabbabbaabbabbaaaababbbbbaabbabaabaaaaababbbbaaaaabaaaabbbbabaabababababaabbaabbabbbaabaaaabbababaabbbbaaabbaaaabbababbaaaabbbabbbabbabbaaabaaabbbbabaaabaaababbabbbbaaabaabaababbbbbababababbbabbbaababbbaaaabbbbaaabbaabbaabaabbbbbbbbaababaaabaaaaaaabbbbbbbabaabbababbaaababababbababbaabbabbaaababbbabbbbbbbbbaabaaaabbaaaabbaaabbbabababaababaabbaaabbbbabaaabbbbbbabbabbabbbabaabaabbbbbbbabbabbababaabbbbbbaaaababbbbbbbabaabbabababbbaaaaaabababaaabaaaaaabaaabbabbaabbabababaaaabbaaaabbbbbaaababaabaaabaaabbaabbabbbababbbabbbbaabbaabaabaaababbbabaaabbbabbabaaabbaababbbaaaaabbbaaaaabbbabbbabaaabaaaabaabbaabaaaaabbbbbaababbaaaaaaaababaabbbbbbbbbaababbbababbaaabbaaaaababaaaaabbabaabaaabbbaabbabbbabaabbabbbbbabaaabbbbabaaaabbaaaabbaaaababbbaaabaabbbabbbabbbabababbbbabaabbabbbaababbabbabbabbaababbbbbabababaaaabaaabaaaaaabbabaabbbbaaaabbbaababbabbbbbaaabaaabbabaaaaababaaaabaaaabbaababbbbbbabbaabbbbbbbabbbbbbababaabbbbaaabbaabaabababbbbabbbaaabbababaaabababbaaabbbabaaaabababbabaabbababbbaabbabbbaaaabbbbbaababbaabbaabbabbaababbaaaaabbababbbbbbababaaabbaabbaaaababbabbbbbabbabbbbbbbbaabbababbbaabaabbbbabaabbabbbabbbbaababbaaaabbaabbbbaabbaaaaaabaaababbabbbaababaabaabaababbbbbbaaaabababbabbaaaaababbabaaabaaaaabbbbaabbbabbababaaabbabbbbabbbaaabbaaababbbabbbaabbbbaaaabbbabbbaabaaabbbbbbaabbbabbbbabaaabbabbabbaabbaabbabbbbabbbabaabbbbabaabaabbbbbbbbbabbaabbababbababaaabaabaabbbbbabbbabbaaababbbbbaaabbbabbabbababbaabbbababaabaaabaabbabababbbabaabaaababbbabababaabaabbbabbababbbabbaaabbaabaaabbabbaaaabbabbaaabbaabbbbbabbaabbaaababbbbababbbbaaabaababaaabbbbbbaabaaababaaaabbaaaabbbbbaabaabbbababbbbbaabaaaaababbaaabbbabbbaabbaaabaaaaaaabbbaaababbbbaaabbababbaabbabbbbaaabbbbbbabbbbaabbababbababbabbbbbbbababaabbaabaaaaaabbabbbbbbbbbabaaaaabbbababaabbbabbbabbabababaababbbbbaaaabaabbbbbbababbaabaabababbaabbababbaaaaabaabaaabababbbabbbaaabaababbbbaaaaaabbbabaaaabaaabbbbabaabaaabbbaaaaabbbaaaaabbbbaaababbaabaabababababaaaabbaaabaababbabbabbbababbabbbabbbabbbaabbbbaaaabbaaabaabbbaaabaabbaabbabaaaaaaababababbbababababaabababbaabaaababaabbaaabaaaabaaabababaaaabbabaabaabbaaaaabbabbababaaaaaaababbaabaabaabbbbaaabbbbaabaaaabababbabbbbabbabababbaaabbbabaaaabbbbabbbaaabaaabbbbbbabaaabbbbaabbaabaaabbaababbabaaabbbbbaaaaabbbaababaaabbabaaaabbbaabbabaaaaabbaaaabbbbaabaabababbaabaabababaaaabbbaaabaababababbabaabbbabbabbbbabaabbabbaaaabbababbbaaababbbababaabbaabaabbbabbbbabbaabaaabbaaaaabbbabbbbbbbbaaabaabbbabbbabbbbaaaaabbaaabaaaaabbaabaabbaaaaabbabaaaabbaaabaabaabbbbbaaababbbabbaabaaaabababaabbbaabbbabaaabbbbaaabaaabababaabbbbabaaabbbbaababbbabaaabbbaababbbbbabbabbbaabbbbabbaaaabaabababaaaabaabbabaaaabbbaabaaabaababaabbabbaabbabbabbbaaaababbaabaabaaabaaaaababbbbbbbabbabbaabbabbbaababbbbbababaabaabbaaaaaaabbaaaaabbbbbbbbabbababbabbaabbbaabaaabbbbabbbabbaababbbbbbbabbbbbababbabbbaaaaaabbbaaaababaabbbbabbaabaabbaababaaabbbbabbbbbbbabbbbabbbbabaaaabababaaabaaaababbbababbbaaabbababababbbbabbbbaaababbaaaabbbaabababbbbbaabaaaababbbbaabaababbababbabababababbababababbaabaaaabbbbaaaaabbbbbabbabaaaabaaabbbaababbbabbbaabaaaabbaaaabbaaaaabbabababababbabbabbabaabaabbabbaabbaaaaaababaaaabaaabbaaaababababbaababbbbbbbbaababbabbbbababbbabbaabbbbbbbabbbbababbbbbaabbbababbabaabaabababbbbabbabaaaaaaaaabaabbbaabbbabaaaaaaaaaaaaabbaabaaaabaabbbbbabaaaaabbaabbabbbbbbbbaaabaaaaaabaaaaabbbbbbaaaabbbaabbaaaabaabaabaaabbbabbbabbabaabbbabbabaababaaabbbabaabaabbbbabaaaaaabbabbabbaaabaaabaaaaaaaabbbbaaababaabbbbbbbabaaaaaaaabbbabbbbaababaaababbaaaaabbabbbabbaababaaaaaaaaabaaabbaaaaaabbababbaaababababbabaabbababbbabbbbbbabaababbaaababbbbbabbbbaaaaabbbaaabbabaaabaaabbaaaabbbaabbaaabbbbaaababaabaababababaabaaabbbabbbbaaabaabaabbbabbbbaabbabbbbbabaababaabbbbaaabaabbabbaaaabaabbbabbaabbbaaaaaaababbabbbabbbababbbabaababaaabababbbabbaababbaaabaaababbaabbbababaaabbabbbbabbabbaaabbaababbbaababbbbbbbaaabaabbbbbabababaaabbaabaabbaabaaaaabbbaaaabaabaabbbbaaabaaaabbabbbabaaaabaabbbbbaabaabbaaaabbbbbbbabbbbabbbbbbbbaabbbaaabbbaabbbbababbababbbababbbbbbabababaaabababbabaabbaabbaabaabbbbaabababaababaaaababbabbabbaaaabbbbaabbbabbabaaabbabaababbbabbbabbabaabbabbaababbbababaaaabbbbbababbbabaababababbaaaaabbbbaaabbaaaabbbaaaabbabbbabaaaaabbbabababbbababbbbabbbbaabaabbbbbabaaabaaabbaaaabaabbabbbbaabbbabbbbabaabaaaaabbaaaaaaaabababbbbabaaabbbabbbaaabbabbaaabaabaababaabbabaabaaabaaaaabbbbbabbbaabbabbbaaabaabbbbabbabaaaaabaabbaabaababababaaababbbababbbaaababbbabbaaabababbabbaaababbabbaaaaaaaabbabbaaabbaaabbaabbaaaabbaabbbbaabbbbbabaababbaabbbbbbabbbbaaababbbabaaaaaababbbbbababababbaaabbbbabbbabaaaaaabbabababaaaaaabbabaabaaaaabaabbaaaabbbaabbababaaaaaabbbabbaabbabaabaaabbababaaaabaabaabbbbbabbbbaabaaaaaababaaababbbaabbababbaabbbaabbbababaabbaababbabbababababaaaaababbbaababbaabbbaabbbaaaababaaaaabbabaaabbababbbbaaaababaaaabaabbaabbbbbaababbaabbaaaaaababaaabbbbabbbabbbaabbaaabbbbabbbabababaaabbbbabaababbbbababbababbabbbbbbabbbbbbbbbaababbaabaabbababbababaaabaaababaabbaaababaabaabbbbaaababaaabaaaabbabaabaabababbbbabaababababaaaabbbbabaabbabaaaabbbaaabbaabbbaaababaababbababbbabbbbbbbbaaaaababbaababaaabaabaabaabaaabbbabbbaaabababbaabaabaababbaabababbabbababaabbabababbababbabbaabbbbbbaaabaaabaaaabbabbaaabbabbbbbbaaabbabbababaabbabbbababbabbbbaaaabbababbaabbaaaabaaaaaaaaabbbaaaaabbaabaaaabbaaabbbaaaabaaabaaaabbbababbababababbaaabbaabababbaaaababaaaaaaaababaaaaaaaaaaaababababaabaabbbbaaababbaaaaaaabbbbaaababaabaabbabbbbbbabbbbabababaaabbbabbbabbabbaaaaaabbbaabbababaaabaabaabaabbbbbabbabbbabaaaaaaaababaaaabbbbabaabaabaaaaabababaaabbbbbaabbbaaaababbbbabaaabaabbbababbbabbabaabbbbaabababbbbaabbabbaabbbaabbaabbbbabbbbbaabaababbbabaabbbbbbbabbaaaabaaaaabababaabababbabbbbbbababbaabaabbaababbaababbbabbaabbbbbbaaaaaabaaaabbabaabaabbbababbaabaaabababbabbbaabaabaaabbaaaaabbbaabaaababbbaaaabbbaaabbbbbbbbbabaaabbbbaaaabaaababbbabbbaabaabbaaaababaaabbababaaabbaababbbbaabaaabbbbbaaabbbabababbababaaaaaaabbaaaaaabaabbaabbaabaaaaabbbbaaaabbbbbbababbbbbaabaaaaaaabbbaaabbaaabaaaaaababaaaaabbabbbabbbabbbbbabababbabbabaaabaaababbbabababbbbaabababaabababaaabbaababbbbabbbbbbabaabbbaaaababbabababbaaabbbaaabbaabbbbbaabbababbaaaabbbbaaaaabbaabaaabaabaaaaabbbabbabbbababaaaabaabaababbaabbbbaaaabaaababaaababbbabbbbabbbabbbaabababbbbbbbabbbbaaabbaabbbbbababbabaabaabbaabbabaaaababbaababbbbaaabbaaabbbababaaaaaaabbbaabaabaaaaaaaaaabbbbbbaaaabbaaabbaabbaaabaababbbaabaaabbbbaaaaaabababbbaaaabbbbbaabbaaababbababbaabbbbbaaaabbbaabbbbabaaababaabbbbabbaabbbaaabbbbaaabaabaaababbbbbaaabbbaabbaabbbaababaaaabbbabbbbaaaaaabbabbbbaaaabbababbbabbabaaaaaababbabbaabbbbbbbaaabaaaababbabaabbaaaaaabaabbbaabaaababbabbbbbaabbabaaabbababbababbaaaaabaababaaabbbbaaabaaaaaaababbbbbbbbbaabbaaaabbbbaaabaaababaabbaaaabaaaababbaabbaaaabbabbbbbbbbabbbaabaaabababbbababaabbbbabbbabbbbabbabaabbababbaababaabbbbaaaaaabaaaabbbbabbbbabaaabbabbaabbbbababbaaaabaabbbbbabbbbaaaabbbabaaaaaabaaabaaaabaabbabababababaabaaabababbababaaaabbbaabbaabbbaaabaaabbaaabbbbababbbaaaabbbaaaabababaaaaaaabbbababbaabaabbabbabbbaaababaaabbaaabbabbaabbbbbabbaaababbbbaabaaaaabaaababbbabbbbbabbaabbaabbabbbbaaabababbbbbbabbbbbababbbabbabababbbababbabaaabbaabaabababaabaabaaaaaabbaaabababbaaaaababaaaababbababbabaabbaaaabaaaababbbabbabbababbbababbababbaaabbbbaaabbbabbbaababbbabaabaabbbbabbbbbbaaabbbbababababbbabbaabaaabbababaabbbabbbabbaabaababbbabbaaaaababababaababbbbbaaabaababababbbaabbaababbbabababbbbaabbbbbabbbabbaaaaababaaabbbabaabaaaaaababbaaabbbaabaabbabbbbbabbaaaabaabaabbbaabbaaabbbbbaabbabababbbabbbbaabaaaabbabbabbbabaabbaaabbbbbaaaaaaaaababaaaaabbbabaaabababaababaababbbbbbbaabbabbbabaabbbbababaaaaabbaaabaaabaababbbaaaabbaaaaabbbbbbbbbaabbbababaaabbbaaaaaaaaabababaabbabbbabababbbbbaaababbbbbbbaababaaaaaabbabaaabaaaaaaababbaabbbbbbbbaaabababbbaaabbabbaaaabbbaaababbabababaaaaabbbababaaabababaaaabbabababbbbaabaabbbaaaaaaabbbabaabaaabaaabaabaabbbbabbbaabbbbbbabaaababbaabbbababbbbaabbbbbabaababaabbbaaababaabbbbaaaabbaaabbabaabaabbbaaaaaaaaabaaabaabaaabbbbaaabaaabbaaabbbbbbabbaaabbabbbaaaaaaabbaaaaaabaaaabbaaababaaaaaaaaababaaaabbaababbabbbbabababbbaaaaabbabaaababaaaaabaabababbabaabaabaabaaaabbaaaabaaaaababbbbaabbaabaaaaabaaaaababaaaababaaabbaabbaabbbabbabaaaaabbbbbabbabaaabbbbbaaabaaaaaabbbbbbbbbaabbbabaaaabaaaabaababbabababaabbbaababbbabababbbababbbbbbaabababbbbbababaaaaabbabaababbabbbbbabbabbbababaaabbbbabbababaaaaabbbbaabaabbabababbbaaaaabaabbababbaababbaabbabbaaaaababbabbbbbbabbbabababbaaaababaabbbbbbbbababaabbaabbbbaababbabaaabaabbaabaaaaaabbabbbbbabababaaabaabaabbbabaaaaabbaababbbbbbabbbaaabbabbabbababaaababababbbabaabaabbbaabbbababbbbbbabbabbbabaabbbbbbabbaabbbbbbabaaaabbabaababaababbaababaaabbbaaaabbabbbabaabbaabababbaaabbaaaaaaaaaababbaaabaabaabaaaabaaaababbbabbaaaabababbabbabbabbbbaabbbabaabbabbabbbbaabbbabababbbabbbabbbbbabaaaaaabaabbbababbabbbaabbbabbababbaaabbabaaaaaababaaabababababababaaaaabbaaababbabbabaabbbbabaabbbababbaabbbaaaaabbbbaaaabbabbabaabbbbabbbbbabbbaabbbbbbbbbbbabaabbaabbbbbbbbbaabaabbaabbaaaaabbaaaaaabbaabbaaabaaaaabaabbabaaaaabbbabbaaaabaaaababaabababbaabaaaaababbbabababaaaabaaabbbabbabababaababbbabbbaabbbabbaaababbbbbbabaaabaaabbabaaaabaaaaaaaaaaaabababbabababbaaabaaabababbbababaaabbaaabbbaabbbbbbbababbaabbaaaaabbbbbabbabbaababaabbbbababbbbabbabbbaabbbabbaaabbbbaababbbabaaaabbbabbaabaabbaabbbbbaaaabbabbbbbabbaaaabbaabbbaabbaaaabbbababaabaaabbaaaabbbbaabaabbabbaaababaabbaabbbbaabbbbaababbabbaaabbabaabbaabaabaaabbabbaabbaaabbbbbbaaabbaaabbabbaaaabaaaabbbaabbbbabbbaaaaaabbbbbbbabbbbaaababbbabababbabbbabaaabbaabbaabaaabbbabbbbabbbbaaaabbbaaaaaaabbbabbbbbaaababbabaaaaaabababaaaaaabaabababbabbbaaabaaaabbbbabbbbabbaabbaaababaabbaaaaaabbbabbbabbaabababbbbaabaabbbbabaabaaaababaabaababbbabaababbbabaababaabaaabbaabbaabaaaabaaabaaabababaaababbababaaaabaaaababaabbabbbaababbbbabbbabaababbbbabbaabbababbabbabbbbabaabababbaaaaaaabaaaaabaababbbaabbaaaabaaaaababaabbbbaabbbbbababbbabbaaaaaabaaababaaabaaaaabbabaaaaababaaabbbabaabbbaabaaaaaaababaaabaaaaaabbbbbaabbababbbbbababbabbbbabbbbaabaababbbababababbbabbabbbaababaaabbbbaaaaaaabaabbbabaaabaaaabababaabababbabbbbbbaababbaabaaabbabaaababbaaaabababbbabbaababbbabbaabbbaaabbbbabababbbaababbabbbaabbbaaabbabaabbbbaababbabbabbbabbabbaaabbabaaabbbbabababbbbabbbabbbaaabababbaaaaabaaabaabbabaaaaaaaabbabbababaabbbaabbbaaabbabbbaabaabaabbabaaaabbabaaabbbbabbbbaabbbbbabaabaabbaabaaabbbabbabbbbbabbbbaaaaaaabaababbbbbaabaababbbaaabbbbaaababaaabbaabaabbabaabbbabbbabbabbbbbbabbbabbabbbbbababbbaaaabbbabbbaaaaaababbaabbbabaabbabaaaababaabababbbbbaabaaaaababbbabaaabbbbabaabbaaabababbbaaaabbabaaaabbabaaababbaabbbbaabaaaaabbbaaabbaaaaabbababaabababaabaabbaabaabbbbabbaababaaaaaabbbaaaababbababbaabbaaababbbbabbbabbbababbabbbbbaabaaabababbbaaabbabbabaabaaaaaabbbbaabbaabaaaabaabbbbbabaabbabaabbabbbaabaababbabaabbbbabbabababaaaaaaaaababbaabbabaabbaababbabbaaaabaabaaabbaababbbbaabbbbabaabaaaabbabbaabaababaabbabaaabaaababaabaabbaaaababaaaaabaaaaaaabbbbabababbababbaabbbaabbababbbaaaabaaaaaaaaaabababbbbabbbbabababbbbabaaaaaaabbbaabbbabaabbaaabababbbabaaaaaabaaaabaabbaaabbbaabaaababaabaabbabaabbabababaaababbbbbababaabbabbaaababbabbbabbabbbbaaabbaaaaaaabaaaabbbbabbaabbbaabbbabbaabbabbababaaaabaaaabbbbbbbabbbabaaaabbbabaababbaabbbbabaabbbaabbbbabaabbabbbbaababbbbbbabbbbbabaaaaabaabaabbbbbbbababaabbbbaabbabbabbbbbababaababbbabbabaabaabababbabbbbaaaaaaaabbbbaaaabaababbaaabbabababbaabbabababaaaaaabbbabaabbabbbbbabbbababaabbbbbbaaaabbabbbbabaaaabaabbbabbbbbaaabaabaababbaabaabbbbbbbabbbaaaababbbbababaabbaababaaabbabaaaaaabaaaaaaabbbabbbabaaabaaabbaabbbabbababaabaababaaaabababbabaaababaabbbbaabaabaabbabaabbbabaabaaaabbbbabaabbaaaababaabaaabaabbbabbbabbbbbbbbaaaabababbaabbabbaabaabbabbabbbbbbabaabbaaaabaabaabbaabababaabbababbababbabbaaaabbaababbaabbaabbaabbbaaaabbbabbaabaabaabbaaaaabbbbbbbbbbabbbaababbbabbababbaabbbabaabaabbbbababaabbabbaabbaabbbabbaaaaababbaaabbaabbaaabaaaaabbbbabaaaaaababaaaabbbabababbaaababaaabaabbababbabbababaabbaaaabaabaabbaababaababaababaaaaaaabaabaabbabbababbbaaababaaaaaabaabbbbbabbbaabaabbaaaaabaabaaabbabababbbbbabbbbbbaabaabbaabbaaabaaaaaabbaaaaabaabbbaabbbbbbbbbbbaaababaababaaabbabbbbabbabbaabbaaaaababbbaababaaabababababaaaabaabaaababbbabbbabaaabbababaabbaaaabbbbabaabaaaaaaaaabbbbbaababbabbbabababbabbbbabbaaaaaabbabbaabbbabababbaaabaabaaababaabaabbabbbaabababababababbbbbaaaaabbaaaaabaabbbbbbababbbbbbbbaababaaaabbbbbabbaaaaababababbaaaababbaaabbbaababbaabbabbbbbabaababaaabbaabaabbaaaaaabbbbbbabaabbabbabbabbabababaabaaabbbbbaabaabbaabbabaabaaabbabbaaaabbabbaaaabaababbabbbbaaaabbbaaabbbabaaaabaababaaabaaaaababaaabaabaaababaabaabbaaabbbbababbababbabbaaababbaaababbbabbaaababaaaaaabaabaaabbbbbbbaaaabbaabbbabbbbaaaaabbbaabbababbabbabaaabaabaaabbbabaabbbbbaababbbabbaabaaaaaabbabaabaaaabaaaaaabaabbaabababbababaaaaababbaaababbababbaabaabbabbabbbbabbaaaaaaabbbbbabbbbbbabababaaaaaabaababbbbbbbbbbaaabbbabbabbbabbaabaaaaaabbaabbaabbbabbaaaabaabaaaababbbaabbbaabaabbbaaaaaabaaabaabbbbbababbbaababbbbbabbbbbaabaaaaaababaaabaaaaabaaabaaaaaababbabaaaabaabbbaababbaababbbabbbabbbbbabbaabbaaaababbbaaaaaabaabaaaabbbbabbbbbbababbbbbbbaabaabbbbbbbbbaaababaaaaaabaabaaabbbbabbababbbabaabbbabbaabaaaabaababbaabbbaababbabbaabbbbabbbbbabaaaaabbababbbabbbbbbbabbaabbbbaaaabaaabbbabbabbabaaaabbababaabbabaabaabbbbababbabaaaabbabbbbbababbabaabaababbababbabbabbabaabbaaaaaabbabaabbbaaabbabbbbaaabaababaaabbababaabbbabbbbabaaabbbbbababbaaaabaabbbbabbbbbabababaabaababaaaaabbbabbabaaaaaaaabaabbbbbaaaaaaabbabaaaababbbabbaabaabaaaaabaaaaabbabbaaabbaaababbabbbababbaaaabaabaabbaaaabaabbbbbaababaaabbbabbababbbbaaabbbbabababaabbaaabbbbaaaaaaababbabbbbabbabbaaababbaaaaaaabaabaabaaaaabbaaabaaaaaaaabababaabbabbbaabaabaaaaabbbbbabbbabbbabbbbabbbaaabbaababbabaaabaaaabababbababbabbbabaabbbababaaabaaababbbabbabbbbbababaaabbaaabbbabbbababbbbabaabababaaaabababaabaabbabbbaaaababbbabbabbbabaaabaabbaaabbbbabaaaabbabbbbbaabababbbbaaaabbbabbaabbabaaaabaababaababbbaabbbabbbabababaabbabaabbaaaabaaabaaaabbbbbaabaabbbbaabbbaaaababaabaaababaababbabbbbabababbabaaabaaaaaaaaaabbaabbbbbbbbbbbabbbbbbabababbaabbbbaaabaabababbaaabbabaaababbbabbbabbaabbbbaaaabbababbbbbbabaabbabaaabbaabbbabbabaaabaaabbaabbabaaaabababaaabbbaaaaababbbabbaababbbbbbabbbbbaaaaabaabaaabababaaabaabbabbbaaabbaabbbaaaaaaabbbbbbbbbbababbbbababbabaabaaaababbabbaaaabababababbbaaaabbbbbaabaaabbbbbababababbbbbaabaabaababbaababaaabbbbbbbbbbbabbaabaaaaaabaaaaaabbbbabbbbababbbabaababaabbbbabbabbbbbbbbbabbbbaaabbababbaaaabababbbbababbaabbabbbbabbbbbaababaaaaaaabbababbbbbbbbabbaabaababaabbabbabababababbbaabaabaaabaaaabbabaabbaaabaaaabaaabbbaaaaaababaaaabbabbbbbabbbbaabbbbababbbbabbbbabababbababaababbbaababbaaaabbaababaababbbbbababaababbbbaabababbaababbabaabaaabbababbababaabbbaaaabaabababbabababaababbbbaaababaaabbbbbbabababbbaababbaabbaaabaabbbaababaabaabaabbaaaaababaabbbbbbbaababaabbaaabbaababaabbaababbabbbbababbaabababbababbbabbbbbaaaababbbbbbbbbaabaaaaabababbbbaaabaaabbbbbabbaabbbbbabbbabaaaabaaabaabbababbbaabababbaabbaabaaaabbbababaabbbbaabaaaabaabbbbbaaabbbaabaaabbbbbbabbababaabaabbbbbaaabbaaabaabbbaaabaabbabaaaaabbabbabbaaabaaababbaabbbbbaabaaaaabaabbabbabaabbbbaabababbabbbaaabbbbbbbaaaaaaababaabbaabbaabababaaabbbababaabaaaabababbaabababbbbabbbaabbaabaaabbaaaababaabbbbaababbbaabaababbbbbbbaababaaaaababbabaababbaaaaabbabbaabbbbabaabbbbbbaaaaaaababbabaaaabababbbbbabbbabbaabaaaaaabbababaabbabbaababbbabbababaabbbbaabbbabbaaaabbbbabababbbbbbbbaaaaaaaaaabbababababaaaaabbabaaaabaababbababaabbababaabaabbbaaabbbbaabbbaaaababbaababbbabbabbabbbbbbabaabbabaabaabbaaabbbabbabbabbababaabababababababababbbabbbbbabaabbbbabbaaabbbbabaaababaaaaaaabbbbbabaaabbabababbaaabbaaaabaabbabaababbbababaabababbaababbaaababbbaaaabbabbbbbaaaabaaabbbabaababbabbbbbbabbabbabbaaaaaaabaabbbaaabbbbaabaaabbbaabbbaaaabbbaabaababaaabababbabaaaaaaaaabbbaaabaaaabbbbbabbaabbbabababbabababababbbbaabaabbbabbbbbbbbbaabbabbbbbbbbaaabaaaaabbabbabbbabaabaabbbbaababbbbbaaaabaaaabbabbabbbbbbbabbabbabbbaabaabbababaababbbaababbbbbbababbbaababbaabaabbbbbbbbabbaabbbaabbababbbababbbbbbabaaaabbbabbababbbabbbaabaabbbbabbbbbbbabaabaabaaabbbaabbabbbbabababbaaaabbaababaababaaaabbabababbbbbaaaabaaaaabaaabababaababababbbbbbbbbaaabaaaaababbaabababababababbaabaaaabbaaabaababbbbabbbbaabbbabbbababaabbaabaaabbbbaabbbbaaaabbbbabaaabaaaaaabaaabbbabbbababbaaabbbaababababbabaababaabbaaabbaaabbbaaabbaabbabbaaababaabbaaabbabaaaabbaaabbbbabbbabaabbbaaabbbabaabaabbaababaabbbaabbabbbaabaababbababbabbbbbabbbaabaaabbababbbaabbaaaaaabbababaaaaabbabbbbaababaababbbaaabbabbabbbaabbaababbbbabaaaaaaaabaaabaaaabbbbbaabbbaabaabaaaababaabbbaabbbabaaaabbbbabaababbabbbbaaaabbabababaaababbabbbbbababbbbababbaabbbaaaabbabaabbbbbabbabbbabbbabaaabababababaaaabbaaaaabaaaabaaabaabaaababbbaabbbbbbbbbabaabaababaabaabbbbbabbbbaabbabbbabbbaabbbbbbbabbbbbabbbaaaabbababbbabbbbabbaaabbabbaaaaabaaaabaabaababababbbaabaaaaaabaaabbbabaaabbbbaabbabababaaaababbaaaababbbabbabbbaabaaabaaaaabbbaabbaabaabbabbaaabbbabaaaaabbbabaaaaaaabbbabbbbaabaabbababbabbabbabbaaabababababbaabaabbbbbbabababaaabbaaaaabbbbbabbabbabaaababaabbabbbababbbbaabbbbbbbbbababaabaaaabbabaaabbababaababaaaaabaababbaabbaabbbaabbaaabbaaabababbbabaaaabbbbaaababbbaabababbbbabbbbbbaababababababaaaabbaaaabaabbaabaaaaababbbbbbabbbbbaababbbabaaabababaabaabbababaabaababaabbbababbbaababbaabbaaababababaaaabbaabbbabbbbbaababbaabaabbaabbabababbbbbbbbabaaaabbababbabaababaabbaaabaaabaabbaabbbbbbbbababababbbbbbabaaabaaaababaabbabbbbbabbabbbbaaabbbbbbaabbaaaaabbbaaaabaaabbbbbbabaaaabbbbaabababbbabbaabbbbabbbbbababaaaabaaaaabbbbaaabbbbbbbaabbaaaaaabbabbabbabaababababaababbbaaaababbaabbbaabbbbaababbaabaaaabaabbbbaaaabbaaabaaabaababaaaaaababbaabababbababbaaaabbbabbaabababbababbaaabaaaabbbbaababaabbaabaabaababaabbbababbaaaabaaaaaaabbbbabaabaabbaaabaaabbabbabbaaababbaaababbbaaaaaabaabbbbaabbbabbaaabbbabaabbbbbbaaaaaaabbbbabbbaaaabaaaabbbaababaababaaabbaabaaabbbbbbabaabbabbaaabaaabbbababbaaaaabababbbaaaababbaaabaaababbbababbbabaabbbaaaabbbbabbbababbaabaaaabbaabbaabaabaabbabbbbbbababaaaaaabaaabaabbbbbaababbaababbabaabaaabbababaaaaaabbabababaaaabbabbbbaabaabaabaaabbbbaabaabbaabbbabaabbbbbaaaaabbbabbaabbbbaaabbbbababbaaaaabaaaaabaaabbaabbabbbbabbabbaababbaaababbbabbabbababaabaaabaaaababababaababbabbbbababaabaabbbbabaabaabbbabbaabaaabababbaababaababbaabbabbbbaaabaabbbbabababbbbbabbabbbabbaaaabbabbaababbabbbbbbaaaabbbbbbaaaabbabaabbaaaaaabbbbaabaabaababaaaabaabaabababbbabbbbbaaabababbbabbbbbaaababababbaaababbabbbbbbbbbababbbababaaaabbbaaaabbbbbbbbbbabbaaaaaabaaaababbbabbbbbbaaabbbabbbbbabbbbabaaaabbbbaaabbabbaabababbabbaaabbababaaabaaabbbbabbaaaabbbababbaaaaababababbabbabaabbbabbbabbabbbaaabababbbabbbbbabbababbbababbbbbabbbbabaaaaaaabaabbabbabbabbabaaabaaaaaaababaaabababbabbaabbbbbababaaaabbbbabbbababbabbbbbabbbbaabaaabbbbbbbaababaaababbbaaaabaabbaabbbbababbbbaababbbaabbbaababbbaababbabbaabbaaaaaaaaaaaaaaabaabbbbaababbabbbbabbbbbbbabababbaabbbbabbbabaaababbbabaaaaabaababababbbbbbbbbbaababababbaababbbbbabbabbbbabaaabbbabbabbbaabbbbbbbabbbbabbbbbbbbabbabbabaaaaababbaabaaaababbaababababaabaaaaabbababbbaababbaaababbababababaabbbabaaaabaaabaababbbabbbaaaaaaabbbbbbbbbabaabbabbbaabbabbbaabbbabaaabaabbbabbaaaaaaaabaaabaaaabbbbabbabbabbbaaaaaaaaaabbaaaababbaaaababbbbbabaaaabbbabbbbbabaabaabbaaabbbaabaaababbbaabaabaabbaaaabbabababaabaaabbbbaabbababaabbbaababababbaaaabbababaaaaabababaabbbaaaaababbbbaaabbbabaababbaabaabbabaaabbaabababaaabababaaaabaaabbabababbabbabaaababaabaaaaaaababbbabaaabaababaaaaabaaaabababbaaabbbaabbbbababbababbabbabbbaabaaaabaabbabbbbaaabbabbbbababaaaaabaaaaaabaaaaababaabaabaabaabbbbbaabaabaaababbaaaaaabbaabaabbaaababaabbaabbabbaaaabbbababbabbbabaabbabbaabaaaaaaaabbaaaaaaaaaaaaaaabbbbababaaaaaababbbbbaaabbabbababababaaaaaabbaaaabaaabbbabbbbbaaabbaabbaabaaabbabbabbababbbababbaababbabbbabbbbaabbabbababbaabaababbbaaaaabababaaaabbbbbaaaaaababaaaaaabbbabbbabaaabaaaabaabbbbaaabababaaaaaabbbbbaababbaabbaaababbbbbbbbaabbbabaabbbababbababbabaabbbabbbbbabbbababaabbbbbaaabbaaaaabababaababaabbabbbbabbbaababbbabababbaaabaabaabaaabbabbabbbbbabbabababaaaabbbbabbbbbbaaabaaaabbaaaabaaabbbabbbbabababbbbbabbbbabbbabaababababababbaabbabaabbababababbbbabbbaabaaabbbbbbaabbababbaaaaababaaaaaababaaaabbabbbaaaaabbbbababaabbabbbabbabbababbaaabbabbbbbbabaabbaabaaaabaaaabbaabababaabbabaabbbaaabbabbbaaaabaaabbbbbaababbaaaabaaababbaaabbababaaaabaababaabbbabbaaabbaaaaabbaaababbabaaabaaababbbababbbbaaaaaaabbabbbbabbaabbabbabaabaaaabbbaaaababbbabbbaaababaaaabbbbaaabbbbbabbaaabbaaabaabaababaaabababaababbaaaaabbbbbabbabaaaaaaaabbbbabaababbaababaabbabbbbbabbbabbaabbabaaaabbbbababaaaaabbabaaaabbabaabaaabaaabaaaabaaabaaaaaaabbabababaaaabaabaabbbbbbbbbaaaaaaaaababaabbaaabaabaaaaabaababbbaababaabaaaaaaabbabbbabbaababbaabbaaabababbabbabaaabbbbbabaabbbaabbaaaaaabbbbbbbababbbaabbaaaaaabaaaabaaabbbababbbbbabbababaabbbbaaabbabaaaaabbbbbbbbbbbaaaaababababbaabbaaaabaabaabaabaabaaabaaaaabaabbaabbabaabbaaaababbbaaabbaabbbabbbbbaaabbbbaabbbbbbbabababbbabaababbabbbbaabaabaaaaabaabbaabababbababbbabbabbbaabbaabbaaaaaaaaaabbbabbbbbbaababaaabaaaaababaaaaaabbbabbababbbaaaabaaababbabbababababbbabbbbbabbaabaaaababbaabbabbbabaaaaabaaababbbaaabbbabbaaaaabbbbaaaabbaaaababbbabbbabaaaabababbababbbbbaaaaabbbaaabaabbababbaabababbbbababababaabbabbbabaabaabbaaabababaaaaaaabaabaaabbaabbbbaaaabbbaabbaabbbbbbbbaabbbbaaabbbbbbbaabaabbbbbaababbbbbabaabbbaababbbabbbaaaaaaababaaabbabbaaaabbbababaaaaaaababababbabbbababbbbaaabbaabbaaabbabbbbbaabbabbbbababababbbbabbbbbbaaabababbbaaabbaaabbaaabaababaaabbaabbaabbbbbbaabbabbbbaababaaabbaaaaaabaaaabbaaabbaaabbaabbaabbbbbaaaabbaabbbbbabbaababbbabaaaaaaababbaababaabaaababaabbbaabaaabbbbabbababbbabbbababbbaababbaaabbbbbaaabbbbaabbbbabaabbabbabababbababbaaaabaaaabbabbbababbabbaaabbaababbbaabababbbbbbbabbbaaabbababbbbabbabaabbbababaabbaabbbaaaabbaababbaabbbabaabbbaabaaaabababaaaabbaabbaabaabaaabaabbbaaababbbbabbabaaaabaabbababaabbbababbbbaaabbabababbbbbabbbbbbbabbbabbbbaabbaababbbbaaabbbababbabbbbaaabbabbababaababbaaaabbbbbbababbbbababaabaabaaabaaaaabbbaaaaaaabababaaabababbaabaaabbaababbbbbaabababbbbabbaaabaabbabbbaabaaaaababaabbbabaabaabbabaaabbaabaaaaaabbbbbaabbbaaaabbbabaabaaabbabbababaaaaabbaaabababbabaabaaabababbbbbbbabaabbbabababbaaabaaabbbabbaabbabbbbbaababbbbbbaabbaabbbabbbbbaaaaababaabaaabbaaabaaaaabbabbbabaaabaaaabbabbbbbbbabaaaabbbababbaaabbabbabbbabbabbababaabaaabbababbbaababbbaaaababbbbaabaabbbbbabaaaabbaaaabaabaaaaabaabaaabbbbabaaababbaaaaabaaaabbaababbbbabaaabbabaaabababbabaaabbbbababaaaabbbbbbbabbbaabaaaaabbaabbaabaaababbbbbbabbaaaababbbbbbababbaaababaabbaababbabbaaababaaaaabaaabbababbbababbbababbbbababbbabababbbbbbbbbbabaaababaaabaaaabaabaaaaabbbaabbbbbaabaaaaabbabaaabbbaaaaabbbaabbbbbababaaabababbbbababbabbaaaaabbabbbabbbbaaaaaaabaaaababbaaabaabbababbbbbaabaababbbbbbbabaabbaababbabbaaababbabbabaaabbbabaabaabbababbaabaaaaaabaaabbbbbabbbbabbabaabaababbbaabaaabaaaabbbbabbbaaaababaabaabbbababbababbbaabbbbabbbabbabbbbbbbbbaaabbaabbbbbabbbbabbbaabababbbaabbbbbaabbbaabbaaaaabababababababbbaabbaabaababbbaaabbabbaaaaaabbabaaababbbabbaaababbaabaaaaaababbaaababaabbaabbaaabbbaaabbbbbbbbbabaaabbaabbaaaababbbbabbabbaabbbabbbaabbabaabababbabaaaabbbaababbaabbababbabbabaabbbabbaabaaaaabbaababaaaabbabbabababaaaabaaaaaabbbbaabbaabbaaabbababbbbabababaabaababababbababbbaaabaaaaababbaababbaababbbbaabaabbbbbbbaabbbbbabababaabbbaabbbabaaababaaabaaababbbaabbaaabbbaabbaaaaaabbabbaaabaabbabbbababbabaaabaabbabaaabbbbaaabbaaaaabbbabababaaabbbbabbababbbbaaabbabbbbabbbbaaaabbbbbbabbbabbbaabbabbbababaaababaaabbbbaaababaaaabaabbabbaabababbaaaabbaabbabbaaaaaabbaababbabaaababaabbababbbbaaaaabaabbaaaaaaabbaabbbbbababaabbbaabbaaabbabaaabaaaaaabbaaaaaababbbaababaaaababbbabbbbbbbbbbaaaabbbaabaaaababaabaabbabaabbabbbbaabaabbbbaabbaaaaabaabbbaaabbabbabaaabbbbbbbbbaaaaabbbaabbbabaabbbbbaaabbabbbbabbabbababbabbaabbaababababaabaababbaabbabbbbaaabbabbaaabbbbaabbaaababaaababbabaabbabaaaabbabbbbbbbbbbbaaababbbabbbabbbabbbaaaaabbbabbbaaabaabbbbaaabaaaabbabbbbbababaaabaaababbabbbbbbbaaaabbaabbabaabbbbbaaababaaabaaaabbbbabbbaaabaabbbbabababbaabbbaaaaaabbabbbaaabbaaaaaabaaaaabbabbaaaababaababbababbaabbbbbbbabababaaabbbabbaabaaaabaabbbbaabbbbbbbaaababbbaaabaabbbaaabbbaaabbababbaabaaaabbbbabbaaaabbbbbaabbabbbabbabbbbaaaaaaaaaabbbbbbababbbbabbabbaabaabbabababbbbaababbaabaaabbbbbaabbaabbaaaaabaabbaaaabbbabbababbaaabbaaaabbabbaaaabbabaabaaaaababaaabbabbbbabaaaabbabbabbabbaabbaabbabbabbababaaabaabbbabbabbbbbbababbaaababaaabababbbbaaaaaababaabbbabaabbaaaaababbaaababaaaaaaabbaaabbbabaabbbaaaabbbbababababaabbabaabaaabaaaaaabbababaabbbabbabaababbababaabaabbaabaabaabbbbabbaabaabbabbabbbaaaabababbabbbabbbbbabbbaabaaabbaaaabbbbaabbbaaaababbbbaaaabbbaaabaaabbbbbbabbbbabbabbababababbbabbbaabaabbbaaaaabbbabbbbbababbbbabbbbaaaaabaaabbbabbababaababaaababbbbaaaaaaabbbaabbabbbbaabbaabaaabababbbbbbbabaababbabbbaababbaaaabbabbabaaabaabaaaabaaaaaabababbbabbabaabaaaaaabaaaaaaabbaaaaababaaaaababbbabaaabbbbbbbbbaaaababaabaaababbbbaaabbaaabbbabbaabbabaabbaaabbabaaaaaababbbaabaaaabbaaaaaaaaabbbabaabaabbbabbbabbbbaabaaababbbaaabbabaabbababaaabbbabaaaababbbbbabbbabaabaababaaabbaaaabbbbbbabaaaaabaabbbbaaaababbababbaaabbbabbaaaaaaaaaabbabbbbbaaababbabaaababbabbabbaaabaaabbbababbabaabbababbaabbbbaabbbbabbbaabbbabbbbaabbabbbabaabbaabbaaaaabababaababbbababaaaabbbabbbaaaaabbaabaaaaaaabababbbbbbaabbaaabbabaabaaabbaaabbabaaabaabbbbbababbabbaababbaabbbbabbaaabbaaaaaaababbaaababbabbbabbababbaabaabbbbbaababababbabababbabbabbabbbbabbaaababbbaabbaabababbbbaabaaaaabaabbaaabaabbaaaaabbbbbbbababbbbbbababababbbababbbaabbbabaababbbbbaabbbbbaaaaababbabaaaabaaaabbbbaaaabbbbabbbabaaabbaabababaaabbbbbbbbbaaaabababaabaabaaaabbbbaaabbbbbaaabbbaababbbbabaabaaaabbbaaabbabaabbbbbbababbbbaaabaababbaaabbabbbbbbbababaaabbbaabbbbabaababbabaaaaabbbaabbaabbabbaaabaaaababbabbbbbaabababaabbaabaaababbbbbaaabbbbbaabaabaabaaaaaaabbaabbaaabbabaaabaababababbababbbbbbbaaabbabaabbabababaaaabbaabaabaababbbaabbbbbaaaaababbababbbbabaaabaaabbbbabbbaaaabbabababaababaabbbbbaababbaaabbbbababaaaaaaababbbabbaaaabababbabaabbaabaabbaaaababbabaaababaaabaabaabababbbbabababbbbbbaaabaababbaaaaabbbbaabbabbbbbbaaaaabbbbababbbabbbbaaabaabbbaabaaabbaaabaaabbbbbaaababbbbabaabbbabaabbbaabbabaabbabbaaabbbabababbbaababbbbbbaaaaaabbbabababbaababaababbabaababbbabbaabbaaabbaabbaaababaabbaabaaabbbbbbbabbaabaabbbaabbababbbaaaabaabbabbabbbaaabbbbabbabaaabaaaababbbbabaabbbbbbbabbbbbabaaababbaabaabaaaaaababbbabbbabbaaabbabbbbaabbbababbababbabaaabbaabbabbabbbbbabaaababaabbbaaabbbbbaaaabbbaabbaabababaababababbbabaabbaabbbbbabbabaaaabaababbbabbbbaaaaabbbababababbaaaabbaabaaaaaaabaaabbbabbbbabbbabbbaaaabaabbbbbbbababaabbaababbabbbbbbbbaaabbbbaabbaaabbbaaaaabaaabaaabbabaabaabbabbababaababaaabbababaaabbbababaabababbbabaabbbaaaabbbbbbababbabababbbbbbbaaaababaabbaabbbababababaabababbababbaabbaaaabbbababaaabbaabababbbbbbabaaabbaaaabaabbabbababbbbabbbabbbbbbabaaabaaabbababbaababbabaaaaabaaaabaabbbaaababababbabaaababbaaababaababaaababbaabbaabbaaabbbaaaaaabbabaabaaabbbbbbabaaababaaabbaababaabbaababaaaaabbabbbbabaaabaaabbbabababbaaabbaaabaaabbbaababbbabbaaababababbaaabaaaabbbbaabbbbbbaabaaaabaabbaabaaabaabbbbbaaaaabbbbbbbbaabbababbabaaaaaabbbabababbaabbbbbbbbababbbbbbbbaabaaababbbbaabbaaabaaabaaaabbababbabbaabbbabbabbbabaababbabaaaaaaaaaabbaabaaaabbbaabaabababbbaabbbaabaaabbbaababbabbaaabbbbababbbbabaabababbbaaaabbabaabaabaabbbbbaaababbbbbaabbbabaaabbabbbbaaaaabbababaaaaabbabbaabbaababbbbaaabbabbbaaabbbaabbbabbaaaaaabbabbbbbbbbaababaaabbbaaaabbaababbbababbabbabaabbbaaabbbabbbbabaababbaaaabaabababbbabbbabbbabbabababbbabbbbbbaabbbaaabaabbbbaabaabaabaaaaaabbbbababaabbbbaaabbbabaabbbbabaaababaabababbbbbababbaabbbbababbabbabbbbbbbbbbbbbabbbaabbbbabbaaaabaabbaabbbaaabaababbaaaaaaaaaaabbababbbabbabbabbaabaabbaaabbabaaabaaaabbbaaaabbbabbababbaaababaaabababbaababbbabbbaabaabbbabbaaaaaaaabaaaabbbaabbbbabbbbbaabbaaabbbbbbbababaabbbbbbaabbbbbaaabababbbabaabbbbaaaaabaabbbbbaabbbabbbaaabbaabbbbbbaababbbbbaaabbabbaabbaabaaaabaaabbaaaaaabbbbabbabbabaaaaaaaabaabaaaabbaaabbaaaaaaabaabbbbbbabaaaababaaaaabbbabbbbabbaaabbaaaaabbaaaababbaaaaababababbababaabaababbaaabaabbabbaaaabbbaaaabaaabbabbaabbabbbaaababbababbbaaaaababbaaabbbbabbbbaaabbaaaaaabbbabaaaabbbaabbbaabaaababbbaabbbaabaabbbabbabaaaaabbbbabababbaabbbbbbbbbabbaabbbaababbbbababbaaaaaabbabbabababbaabababbbabaababbbaabbbbaaababbabbababaaabbabbbaaaaababababbbbbababbbbabbabbaaaabbabbabaabaaaabababaababaaabbaababbbaababbbaaabaabbbaabbbaaaaaaaaabbbbbbababaabbbbabaabaaaaababaaaabaaaaaababbbbabaaaaabbbbabbbbabbaaabbbaaaabaaaabaabaababbabaababbababaabaaabbbaaabaabbaaaabbbbaaabaabbbaaabbbaaaaababaabbaabaaabaabbbbabbbabbbbababababbbaabbbbbbbabaabbbbbabaabaaaababbaabbbbbaabaababbabaabaaababaabababaaabaaabbbbbaabbaaaabaabbabbbbbaaaabbbbabbbbbbaababbbbabbaaaaaabbbaabaaabaabbababbababbbabaaaaaaabbbabbabbabbabbaaaababbbabbbabbbaaaababaabbbbbababaabbaabbaabababaaaababababbbbbbbbbabaababaaabbabbabbbaaabbabbbabbbbaabbaababbbbbaababbabaabaaabbabbaabaabbababbbabbaabbbababbbbabbababbabbbbbabbababaabaabaabaabbabaaaabbbababaaaabbbbbbbabaaaababbbabaaaababbabbaaaaabbabaabbababaabbaabaabbabbaaabbbabababaaabaabaaaabbbbbbaabbababbbabbbbaaaababbbabaabaaaabbbbbabbbabbaabaaabbbbaaaaabaababbabbaaaabbabbbabbabaabbabbbbbaaabbbbbabbaaabaabaaaaaaababbabbababbbabbbbababbbbaabbabbbabbaabbaaabbbaaabaaaaaaabbababaaababbbaabaaaababbbbbaaabbbbbabababbababbbababbabbbbabbbabababaaabbaaaabbaabaabababababaabaababbbabbabaabbbaabbaaabaaabaaabbbbbabbaabbaaabbaabbbbabbababaabaaaaababbaabbabaaabbbaaaabbbbaaabbaabbaababbaabbababbbabbbbbabaabbbbbaaabaaaaababbbaaabbbbaaaabaaaaaaaaabbaaaaabbbaabbbabbababbbaaaabbbbaabbabbbbbababbbbabbabbbabbbbabbabbbbbaaabbaaababbbabbaaaabbabbbbaaaaaaaaabbababbbbabbababbabaaabbaaaaaabbbabaababbabbaaaaaababbbbabbbabbbaabbabaaabababababaaabaaabbaabbaabbaaababbababbabbaabbbbbaaababaaabaaabaabaabaabbbaaaabbababbaabbbbbbbbabbbabbbaaaaaabbaaaabbbbbbaaaabbbbbbbbbaabbbbabaaabbabbaaaabbbaaabaaababbaaaababbaaabaabaaabbaaaabbabbbabbababaaaabbaaaaababbbbaaababbaaabaabbaaaabbababbbaaaaabbbbbababbaabbbaaaaaaabbababaaabbaaaaabaaaababbbaaaababababbaabaaaabbaabbabaabbbbbbababaabbbabbbaaabbbbaaabbabbaaabaaababbaaababababaabaabbbaabbbbbbabbbbabaababaabbbbaaaaaabbbaaabbabaaabbaaaaaaabbbabbaaabbbbbaabaabababbbaaabbabaabaaaabbabaaabababbbbaaaababaababaaabbaabbbaaabbabbbaabababbbbaabbbababbabbaaabbbbaabbaaaaabaaaaaabbbababaabbbaaaababbaaabbabbbababaabaaaabbabbaaabaaabbbabbabbaabababaabaabaabaababababbabbbbbbababaaaaabaaaaaaabaabaabbabbaabbbbbbbbbaabbbbabbaaabbbabbbbbabbbaababbbaabaaaaabbbbbbabbaabababbbaaabaaaabaababababbabbaaabaabbbabbbbaabababbabaaaababbabbbabbaabaabaaaaaaabaabbabbbbbbbaabbabaaaabbababbbaaabbaaaaabbabbaabababbabbaabaabaabbbabbaabbbabbbaabbbababbaababababbbaaaaaabbbaababbbbabbbbbbbbbbbbbbabaabaabbabbabbbabbbaabababbbbabbbbaaabaabbaabbaaaababbbbbbbbbbbbbabaabbaaaaabbaaababaabbaaaabbaabaaabbbaaababbaaabbaaaaabbbbbaaaabbaabbbaaaaabbaaaaabbbaaababbababbabaaabbbbaaabaabbbaaaaabbabaababaaababaaaabbabaaaaabaababbabaabbababaababbababaabababaaababaaabbaabbbbaaaabbabbabbbaaaaaabbbbbbbbaaaabaaaabbaaaaabbaabbaabbbababbaabaaabbbbabaababaababaababaaaaabbaabababaabababaaabbabbbbbaaaaabbbbababbbabbbbbaabbbaababababbaaaabaabbabaabbbbababbabaaabaaabaabbaabaabbabbabbaaaabaaaaabbbababbbbababbaabaaaaaaabbbabbbbabbbbabbbabbbaaabbaaaabbaabaabababaaababababababbbbababaaaaaabbabbbaababaaaaabababaabaaabaaababbabbbaaabbabbbbababbbababbbbabaaabbabaababababbbbaabaababbabbabbaaaaabbaabbaaaaaabbbaababbaaaaaabaabbababbaababbabbbbbbaaabbbabaababbabbababaabbbababababbaabbababbbbbaabababaaabbabbbaabbbabbbaaababbaabbaabaabaabababaabaababbbababbabbbbbbbbaaababaabbaaabbbaabaaababaababbbababbbbbabbbbabbbbaabaabaabbbabaabbabbabbbbbaabaaabbabbaababaaabbaaaabaabbbbbbabbbabaaabaaabaaaaabbbbbbbbaababbbbbbbbbbbabbabbabbbabbaababababbaaaabaaaaaabbaabbbababbaaababbababbababbabbbbbbbaabbababaaaabbaabbababbaaaaaabbababbaaaababbaabbbabbaabbbbbbbbbbbbbbbbbababbbabbbabbabaaaabbbaaabbbabaabaaabbbabbbbbbbbabbabbaaaabababaababaaaababaabababaaaabbbbbabbbbbaababbaabbbaabbaabbababbaaabbaabbaaabbaaaaabbabaabababbbaabbabbabaababaabababaabaabaabbbbbaababbbbabaaababaabababbabbbaaaaaabbbaaabbabbbabaabaabbaaaaaabaaabbaaabbbababababaaaabbbaaabaaabaabbbbabbbaababbbabbabaaaaaaaabababaaabbbaabaabaaaabbbababbbbababbbbbbbaaabaaaaaaababaabaabbabbabbbaaaaabababbbbbabbbabbaaaabbbbbabbbabbababaabaabaabbbbbbbaaabbbaabbbbbaabbbbabbabbaabbaababbbabaaabbababbbabbbaabaaaabaaabaababaabbabbbababbbabbbababbbbaabaaaaaaababbbbaabbabbabbababbbaaabbabaabbbbbaababababbbbbbaabaababbbbababbbabababbabbbabaaaabbababababbaaabaaaabaaabaabababbbbaaaababbbabbbbbbabaababbbaabbbabbbbbaaabababababaabaaaabababbabaababbaabaabaabbbaabbbbaabbababbaaaaaaaaaabbaabaabbabbabaaabbabbbbaaabbaaababbbabbaabababbbaaaabbaabbabbbbbaabababaaaababbbbaaabbabbbabbaaaaabaabaaaaabbbababaababaaabbbabbaaababaababbaabbbabbabbbbbababbbaabbbbaaaaaababbabbbbabbbbbababbbbbaabbaabbbbaababbbabbababbbaaaabbaababbabbbaaaabaabaaaaaaaabbaabbbaaabbbbabbaabbbbbbbabbbbaaababaaaabbabaabaaababbbabbbaaabababbababbaabababbbabaaabbabbbbababbabaabbaaabababbbabbbbaaaabbbbaabbbbaaaabbbaabbbbaababbbabaaaaaababbbabbabbbbbaaababaabbbabbbabbbbbbaaaabbbbaababbbaaaaabaabbabbbabbbbbaabbbaabbbaabaabbabaabaabbbaaaaaaabaaabaabbbbbbabbbaabbaaababbbabbbaaaabaabbabbbbbabbbbbbaabbaabaaabbaaabbaabaabbbbbaabbbbabbbaaabababaabbabaaaaaabbbaaaaaababaabbbbaaaabbbabaaabbabbababbbbaabababbbbababbbbbabbaabbabaababaaabbbbbabbbabaabaabababaaabbaabaaaaabbbaabbaabaabaaaaababbbaabaaaabbbbbbaabaaaabbaabbbabaaabbaaabbaabbbabbababbababaababbaaaaabbabbbabaaaabaabbbaabbbaaabbabaabbbabaabbbabbbaaaababbaaabaabbbaabbbbaaaabaaabbbabaabbaaabbbaaaaaabaaaabaaaaababbabbababbbbababbaaaaabbaaababbbaaabaaabbbaaababbbbaaabbaabbaabaaabbbabbbaabbbababbbbaabbbbaaabaabbababbbaabbbbbaabbbaaaabaaaaaaaaaababbabbbaabbbababbbbbbbabbbabaaabbaabbaabaabbaaaabbbbabbabbbbababbabaabbbbbabbaabaaabbababaabbaaaaaababaaaaaaabbbaabaabaabbabbabbaabababbbbaabbaabbabbaaaabbaaabaaabaaaabaaabababaabbbbbbaaaaaaabababbbbbabaaaaabbbbaabbbbaaaaaababbbaababbabaabbbaabaabbaaaabbaabbbbaabbaaaabaaababaaaabbbabbbababbaaaabaabaaaabbbbabbbbbaaabbaaabbabaabbabbaaaabbbbaaababaaabbbbabbbbbabaabbbaaabbabaaababbabbabbbbaabbaaaabaaabaababbbaaaabbbbbbbaaabaababbbbabaaaabbabbbbbbbabbababaaabbbbababbabaaababbbabbabaababbaaabbbbabaababbbbbbbbbababaababbabbbbbaabaaaaaaabaabbbbbbbaaaabaaaaaabbbbbbaaababbbbbaaaabbbbabbaabababbaabbaabaabbabaaabaabbbbabaaababbbbabaabbababbbabaabbaaabaabaaaaabaababbaaaabaaabbbabaaaabababaabaaabbabbaababaabababaabbabaabaabbaaaaabbbbaabbbbbbaabbaabbbbbbabbbbaababbbaaabbabaaababbbbabbbbaaabbababbabbbbabaababbbababaabbabbbaaabbababbbaaaabaaabbbaababbababababaaaaaaaaabaaabbbbabaaabbbbbbaabbaabbbabaabbaabaababbbabbbaaaaabbabbaaabaaabababaabbbaaaabbbbabbabbaabbbaabbbbbbbbaabbbbbbbbabbbabbaabbbbbbabaaaaabbaaaaaabaaaababbaaaababaaababbabbbaababbbaaabaabababbbabbbabaaababbabaaaabababbbaaabaabbabaaabbbaabbbbaaaaabaabbbabbbbbaabaabaaababaaaabaabaaabaabbbabbaaabbbbbbbbbabababbbbaaaaaabbbbbaabbbababbaaaabbbbbbaabaabbbabbaabbabbbaabbbaaaabaababbbbbbbbaabbaaaabbbaababaaabbbabaaabbbaabbbabaaaabbbbbbaabbaabbbabbbbaabaabaabbababbbaabbbaabaabaaabaaaaabbabaaabbbabbbbbbbbbbbbbaaaabbaaabaababbbaaaababbbbabaaaababababaaaabbbabaabaabbaaababbbbabaabaaabaaaabbbbbaaaaabbbbabbababaaaababaababbabbabbabbbbaaabaaaaaaaaaabbabaabbbbbabbbaaaaaabaaababbbbabbabbaaabaabbbaabaaabbbbaabaabbbbabbbbbbbaabbaabaaabababbababbaaabbbbaababaabbbababaaaaaababaabababaaabbaaabbaabbbbbabbbbaababababbabbabaabaabbbbabaababbbbaabaaaabbaaabababaababaabbabbbaabbbaabbbbbbabbaabbbaaaaaaabaaababbabaabaabbabbaaaaaabbbaaaaaaaabbbabbabbbabbaabbaaababaaaaabbaaaabababbabbbaabbaaabbaabbaabbbaaaabbabaaaabbabababbaaababaabaabbbbbbbbbbabbaaabbbaaaabbbbbbaaabbbaabbbaababaabbbbaaabbaaabbbbaaaabaaaaabbbaaabbbbababaaaabaaaaabbaaaabbaaaaababbbbbabbbbaaabaabbbabbaabbabbabaabaabbaaabbbabbaabaaabbabaababababaaabbbbbabbbbabbbbbaabbabbaaaaabaabbbaababbbbabbbbbbbabbabaaabbbbabaaabaaabbababbabbabaaababbabbbaabaaaababbabaaaabbbaabbababbababbabaaaabbbaababbbabbb
aaabaaababbabbaabbaabaaabaaabbaabbbbaabbbbaabaaabababbbbbbabaababaaabbbababbbaaaaababaaaabbaabbaaaabbbbaabaabaaababbaabbbbaabbaaaaabbaabbbababaaaaaabaabbabbbbaabbaaaabbbbbababaaaaaaaababbabaaaababbbbaabbababbaababaababbababaaaabaabaaaaababbaaabbaaabbbabbaaaabbaaababaabbabbaabbbaaababaababbbbbaaaababaabbabaabbaaaaaababbbaababaabbbaaaabababaaaaababbbabbbbabaabbbabbbbbbabbabbabbaaabbbaabababaabbabbbbbbaaaabaababaaaaabaaaaaabbabaababbababaabbbabbbbbabbbaaaabbaababababbbbabaaaababbabbabaaabbaabbbbaabbaababbabaabbabbbaaaaababbaababaaababaaabaaaabaabaaaaaaabbbabbbabbaabbabaaaabbbbaabbbbbbababbaaabbbbaaabbbbaabbaabbbaabaababbbaaabaabaabbaabaabbbbaabaaabaabaabbaaaababaabbbbbabbbbabbabaaabbbbababbababaababaaabbaabbbabbaaaaaaaaabaaaaabaaabaaabbbaaababbabababbbbabaabbaabaabaabbaaababbbaabaababaaabaabbaababbabbbbaababbbbbbabababbbbaaabbabbabbabaaaababbaaababbabbbbaaabaabbabaabbaababbabaaabbbbbaabaaaabaaaaaabbabaaaaabbaaaabbabbabbbaaaabbaabababaabbbbbbbabbbaaaaaaaaabbbbbaaababbbaaaaaaaabaabbbbabaababbbbbaaaaababaaabbbbabaaabbbbbbbaabbaaaaaabababaababbabbababbbaaaaabaaabbabbaabaabababbaababaaaaabbbbabaabbbbbbbabaababbabbbabbabbbbbabaababbbaabbababbbbbbbaaabaabbbbabbaaabbabbaaaababbbbabbbbbaabaaabbabaaabbbbbabbbabbaaabbbbaabaaabababbabababbabbbbabaabbaabbaaabaaaaaaaabbbbbbbababbabbaabbababababbabbababbabbaaaaabbabbabbbbaabbaaaabbbaaababaabbbabbbbbbbbbabbbbaaaaaababaaabbbbabaaaabbabbababbbaabababbaaaaaaaaaaabbabbabaaababbbaaabbababaaaabaabbabaababaaabaaaababbbabbbaaaabaabaabbbbabaaabaabbaababaaaababaabaaaaaabaaaaaaabbabbbabaaabbbbaaabaaaaabaaaabababbbaaabaaaabaaabbbbbbbbaabaaaabbaabbaaabaaabbbbabaababaabaabbaababaababaaabaababababbaabbbabbbbbaabaaabbbaabaabbabbabbbaabbaabbbbabbbbabbaabaaaaabaabbabbaabbaababaabaabbbabaaabaabababaaabbaaaabbabbbabbbbbaababbbaabbbababbabbbbababbbbbaabbbaaababbabbaaabbbbaabaabaabaaabbaaaaabbbaaabaabaababaabaabbbabbbbaabbabbbaaaababaabbababaaabbbbaaaaaaabaabbbbbbabbbababbbaabaabababaaaaabbaabbbaaabbabbbabaabbaabaaababbbbaabaaaaaabbbaaaaabbabbbbabaaabbababbabbbbabbaaabbabaaaabbbaababababbababbbaaabbabbbaaaaabbaababaaabaaababbabbabbaabbbbbbaababbabbabbbbbaababbbabbabbbaabbbaabbabaabaaaabbaabbbbababbbbbbbabbbaabbabbabbababbbbbbbbabbaabaabbbbbaabaaaaaaaabaababbabbaabaabbabababbbbabbbbbabbbaababaaaaaababbaabbabbbbbaaabaaaaabbbbababbbaababbbbabbaabbaabbbbaaaaabaabaaabaaabbbabbabaabbbaaababaabbbbbbbaaabbbbabbaaabaabbaaabaabbbaaaabaabaabbbaabbababaaabababaababbaaaabaaaaabbabaababbbbabaaaabbaabbbaaabbaaaaaaaabbbaaabbaabaaabaabaabaabaaaaaaabaaabbaaaaaabbabaaababbaabbbbbaabaaabbbababbbbaaabbbbbbabaabababaabbbabaabaaababaabaababaaaaaabbbbaababaaaabbbabbbbababaaaababbaaaabaaababbaaabaaabaaaabbababbaabbbbabbbbbbaabababaabbbbabaaabaabaabaabaabaababbbbabbbabaaaabbbbabababababbbababbabbabababbbbaabaabaaaaabbabbbbabbbbaaaaaaaabbbbababababbabaababbbababaaaaaaaabaabbaaaabaaaaabbbbaaaaabaaaaaaaaabbabaabbaabaabaabbbbbaaabbabbbaababaabbaaabbbaabbabaabbbaaabbbbabbaababbbabbabaaabaaaabbaaabbaaaabbaaabbbbabbabbababbbbaabaaabaabababbaaabbababaaabaabaabbbabbbbbabaabbaababbababaababaabbbbbaaaababbbabbbbaabbbbbaababaaabbabaabaabbaabbbbbbbbaabaababbbaababbbbbbaaabbabababbabbababbbbabbbabbababbbbbaabbabbbabaabbbaabaabbbabbabbaaabaabaaaaaabbabaaaaaabaaaabbbababbbabbaaaaabababbbbaababaaaaaaabbaaaaaabaaababbabbabaabbabbaabbaabaaabaabbbbbbbbaabbbaaabaaaaabbaaaababaaaaaaabaaaabbbaaaabaaaababbbabbbaabbabbbabbbaaaabbbbbaabbbababbbaaabbaaabaaaabbabbbaaaaaabaaaabbabbbaabbaaaababbaaaaaabaababbaabbaaaaabbaabaaaabaababbaaabbaaabaababaabaaaaaabbabbabababbaaaabaabababaabbbabbabbbbabbaaababaaabababbabbaaababbbabbaabaaaabbbbbababbbbbaaabbbaaaabbaabbabbbbbaaabaaabaaabaabaaaaabaaaaaabaabbbaaaaaabaaabaababaababbbbbbbaabbbbbbaabbbaaabababaabababababbbbabaaabbbabaababbbaabbbaabaaababaababbaabbabaababbbaaaabbbaaabaabbbbabbbabaaabaaababbbbaabaabbbbabbbbbabababaaabaaabaaaababaabaaabbabaaaaaabbababaabbaababbabbaaabaababbabaaabbaaaaabbabababaababbbbbaaaababbaaaaaababaaaabaabaaabaabbbbbabaababbabbbaabaabbbaaabbbbbbbabbbaaaabbaaabaaaaabbbaabaababbbbaabbbabbbbbaaabbaaabbabaaaabbbabaabbababbaabaaabaabbbabaabbabbaababbbbbbbabaabaaabaaabaababbbbbbbabbabbbbaaabbaaaaabbbaabaabbbbabbbaabbbbaabbabbaaaaaababaaabbababbababbbbabaaabbaaababbabaaababbbaabbabbbbbabaabaaabbaaababbbabaabaaabaaababbbabbbaabbababbaaababbbbaaabaaaaaabaabaababbaaaaabbabbbbbabbbaabbabababbaabbbbaaaaababbbbaaaaabbaaaaabbaabbabbabbbbababbbabaaaababbabbabbbbbaaaaaababbaabbbbabbabbbabbaababbaaaaaabaabbabbbabaabaabaabbabaabaabbbaabbbbaababaabbaabbaabbbbbbbbabbaaaababbabbbabaabbabbbabaaaabaabaabaaaabbabbbbaaaababaabaaaaabbaaabbbbaaababbaaabbabaabaabaabbbbabbaabbbbabbaabbabbbaaaaabababbbababbbabbbaabbabbbbabababbbabbaaaabbbaaabbbbaababaaabaaababbbabbbabaaabaaababbbaaababbbababbbbbababaababbbbbbbabababbbaaaaabbbabaabbbbaabaaaababbbaabaaababbabaaaaabbaaabbaabaabababbaabbaaabaaabbbaaaaaaaaaabaabbabbaababaaaabbaaaaabbabbbaabbabbbbbbbababaabaaabbaaaaababababbbaababbababaaaababaaaabbbaabbbbbbabbbbbbaabbbbbbbbbbbbaaabaabbbabbbabbaabaabbbbbaabaaaabbababbabaabababaabbabaaabbbbaabaaababbbaaabbbabaaabbababaabbbbaabababbbababababbaaababbaaaababbabbabbbabaabaaabbbbaaabaabaaabbaaaabbabaababaaabbabbbbbbaabbaabbbabbbaabbbbbbbbbbababbaaabbbaaaaababbbbbbbbabbaaaababbabaabbabaababbabbbaabaabbaaabaaabaabbbbaabaabbaaabbbbbaababaababbbbabbaaabaabaabaaaababbabaabbaaabbbaabaaaababaabbabaaaababaabbbbabbaaaaabaaaababbbbaababaaaabababbabbbbbabbbabbbbbaabaaaaaabaabbbbabaabbababbbaabbabbaaabbbaaabaaabaaaabbabbbbaaabbbbbabaaaaababbbbbaabbabbbabbaabbbbbabababbbbaaabbbabbbaaaaaabbbbabbabaabbabbbabbbbabaababaaaabaabaaabbaaaaabbabbbbabaabbaaaaabaaabaabbbaababaaabbbbbbabbbbbbaabbaaabbbaabbbbbabaaaaabaabbabbaaaabaaabbbaabbababbbaaaabbbaaaabaaaababaaaabbaabbbabbaabbaabbababaabbaabbbbbbbbababbbaabaabbbbbbbbabbbabaabbaaabbabaabbbbbbaabaaabbbbbaabbbbabbbabaaaaaabbabbbbaababbbaaaaababaaabaaabaabbaaaababbbaaaababbababbabaaaaaaabbbaabbabbabbbababaabbbbabbaabaababbbaabbbaabbaaabaaababbbbabbaaabaaabaaabbbabbbaaabbabababaabababaaaaaabbbabaabaabbbbaaaaaaaabbbbabaaaaabaabbbbaaaaaabaaaabaaababbbabbabbbaabaaaaabbbabaaabbbbabbbabaabbabbaabaaaabaabbbbbbbbabaaaababbbabaabbbaaabbbaababbbabbaaaaaaaababbbbaaaabbababbbbbbaaabbbbaababbbaaabaabbbaabbbabaaaabababbabbbabbbaaaaababaaaabbbaaaaabbabbabbbabbbababbaaaaaaaaabbabbbbbaabbbbabababbbaababbbbbabbaabbabbbbbbbaabababbaababaaaabbbbbbbababaababbaababbaabbbbabbbbbbbaaaababbbbbbbbbabbbbabbbaaabbaaababbbbbabbbabbabbabbaababbbbbbaabaaabbbbaaaaababaaabbbbbabaaaaaabaaaaaaabababbaaabaaaabbababbbabbbbbbbabbbbababaababababaaabbabaabbabbaababaababbabbaaaaaaaaabbababaabbabbbbbbaaabbaaabaaaababbbaaaabbbbaabbaabbababaaaabaaaaaaabbbbabababababaabaababbbbaaabbabaaabaaaabbbbbbbbbabaaabaaaaaabbababaaaabbbaaaaaabbabbbababbabbaabaabaaaababbababaabaaabbbaaaaabbaaabbaaaabbbbabbabbbababbaabbbbbbabbbaaaabaaaaababbabbbbbbbababaaaaaababbbbaabaabaabbaabbbabbaabbbbaaaaabaabbbaabababaabbbaabbbabbbbaabaaababbbaabbabbbbaabbaababababbabababaaaababaabbbaaaaaababbbabbababbabababbabaabaaabbbaababaaaaabbaaaabbbaaaababaaabbabaabbababababaaabbaabbabaababbabbababaaaababbaaabbabbaaabbbabbbbbababbabbbbbbaabbbaabaaabbabaaaaaaabbabababaababbabaaaabaaaababbbaabbababbbabbaaaababaaabaabaabbbaaabababbbbabaabababbbabbbbaaabbbbbababbabbbabbbabbbbbabbabbabaaaaabaabbabbaaaabbbabbaaaababbaaaababbabaaaabbbbaababababaababaaabbbaabbbabbabbbaabbbaaababaabbabbabaaaaaababbaaaabaabbabbaabbbabaaabaaababbabbbaababbabbaaabbbaabbaabbbabaaaaababbbbabbababbbababbaaabaabbaaaaaaaaaaaaababbaaaabaaaaaaabbababbabaabbbbaaabbbbbbaaaabbbaaabbbbbbababaabbbaabbaaabbaabbbaabbbbbabbbabbbabbabaaaabaabbaabaaaaaaabbbabbaabaabaaabbbabbbbbaaabaabbbabbbaabbabbbabbbbbbabbabbaaabbaabbaaababbaaabaaabbaaaabbaaabaaabaabbbbbbabbaaabbbabbbbbabbbbbabbaaabbaaabbbbababbbbbabbabbbabbaabbbbbaabaaabbbbaabaabbabaabaaabbaababbbbbbbbbaabbaabbabaabbaaaababbaaaabbbaababababaaaababbababaabbbaababababbbabbababbbbabaaaabbbaaaaababbbbbabbbbbabbbbaabbababbbbabababbabbabababaaaabbabbaababaaabaaabbbabbbbbabbaabaaaaabababbbabbbbbaabaabaabbabbaaabaaaabbababbbbbaabbbababaabbbbabbabaabbbaaaabaabbaaaaabaaababbbaabbaaaabbaaababaababbabbababbaaabababbbbaabbbabaabaaaabbaaabbbaababbbbabbababbaababababaaaaabbaababaabbbabbabbbaaabbbabaabbbbaaabaabbbababaaabaababbaaabbabbaaabbbbbbaaaaabbbbbabbaaabbaaaaabaaabababaabbaabaaaabaaababbababbbaaaaaabaabbbaaaaabaaaabababaaaabababbaaabbabbaabbbababbabbabaabababbabababbabaabbbabbabbaaaabbbabaabaabbabbbaababbbbabbaaaaaababaaabaaaaababbabbabbbabbababaaabbabbaaaabaaaabbbaaabaabaababbbbbbbaaabbaaaabbbbbbbabababbbabbbbbabbbbabbbbbaabaabaabbaabaaaaaabaaaaaaaabbaabbbabaababaaaaaabbbaaaabaabbaaabbbbabbababbaaabaaaaabbbabbbaabbbbbaaaabaabaaabaabaaaabababbbbbaaaaabbaaaabbaabbaabaaaababaabbabababaabaaaabbbabaabbaabbbabbabaabbabaabbaaaababbbbbbaababaabababbbbaaabaaababbbbaabaaabbbabbabbabaaaaabaabbbbbbbabaabababaabababbabbbbabbaaaabbbaaabbaabbbbabbbbbabaabbbaabbabbaabababbbbbbaabaabaabaabababbaaaaaabaabbbbaaabbaabbbababaaabbaababbbbaaaabbabaabaaabbaaabbbaaaabbbaaabaabaababbaaaabababaaabaaabbababbabbaaaabaabaaaabaabbbbaaabaaaaaabbaabbbbaabbaabbaaabbbaaaabbabbaaaaababbbbaaaabaaaabaaabbabbbabbabbabbaaaababbbbbbbbbbabaabbababababaabbaababaabbaabaaabbaaaabbbbbaabaabbaaaabaaabbaaabbbbbbbaabbbaabbbabbaabbbbaabbaabaaaaabbbaabbaabbababaababbaaababbabaabaabbabbaabbbbaabaabbaababaabbbabbbabbbbbaabbaababaaaabbbbbabbbbbbbbbabbbbbaababababbababaabaaaabbbaaabaabbbbbaaaabaaabaabbbaaaaaaaaaaaaabbbbbbbbabbabaaaabaabaabbbabbbababbabbabbbbbbbabaababbabaababbbbbaabbbaaaabbabaaaaaaabbaaaabababaabaaabbbababbbabbaaaaaaaabbbabaaaababbaabbabbabbbabaabaabaaabbbbbbaabbbababaaaaabbaabbbaabaaaabababbabbbabaaabbabaaabbaaababbaabbbbaaabbaababababaababbbbaaabbabababbaaaababbaaabbababaabbbabababbbababbbbaaaaaabaaabaaaaaaabaabbbbabaaaabaaaababbbbbbabbaaababababbbabbabaaabaabbbbababbabbabbbabbbbaaaabbbabaaaababbbbababaabbbabaaabaababbababbbaabaaababbababbaaabaabbabbababbbbabaaababababbbbabbaaaabbbababbbabababbaaabbabaaabbabaabbbababbbbaabbbabbbaabbbaaabaababaaaabbabbaabbaabababbabbbabbaaabaababbabbaaabbbaabbaabababaaaabaaabababbaaaabbbbaababaaabbbababaabaabaaaababaaaaaaabbabbbbbabbababaaaaaaaaababbabaaabbababbaaaaabbabbbbbaabaaabaaabbbaaaaaabaaaaaaaababaabbbbababaababaaaabaabaaabababbbbbbabaaabbbbaabbabbbabbbabbaabaaabbbbabbbaaaababaaaaaaaabaaaaabaaabbaabaabbbbaabbaabbaaababbabbaabaabbbbbabbabaaaabbbbaaabbbabbaabbaababbabbaaabbbbaaabaaaaabababaabaaaabaaaaabbbbabbaaababbabababbabbbaaabbaabbbaabaabaababbbaabbbababbbbbbbabbabbabbaaababaaaaaababbaaabababbaabbaabaabbbbbababaaabaabbaaabbbbbbaabbabbbaabbaabbaaabbbaababbbbbbbaabaaabaababaaaababbabbbbabbbbbabababbabbaababbbbaaabbbbbabbaaaababbbaaaaabaabaaabbabaaaabaabbbaabbaababbbbabaabbbabbabbaaaababaaaabaaabaaaaabababbaaaabbabbabbbaaaaabaaaabaabaabaaabbbaaabbaaaaabbbaabbbaaabbbabababbabaabbabbbaababbbabaababbbbabaababbabbaababababbbabbabbabbaabaaabbbbbaaabababbbaaaabbaabbabbbaabbabaababbbaabbbabbaaaaabaaabbbabbababaaababaabababbaabbbaababaaaabbbabbbbbaabbaabaabbabababaababaaabaaaaaaaaabbaaaaabaaaaaaaababaabbaabbaabaabbaabbaababbbbbabbbabaabaababaaabbababbaabbbbbbbbbbaabbbabbaaaaaaabbababbaaabaaaaaabaaabbabbabbbababbaaaaabbbbbbbbabaaabbbaaabbababbbbbabbbabbaaaaabbabbbabaababbabbaaabbbbbbbaababababaaaabaaabbabbbabbbbbbaabbbbbaabbaabbbbabaabbbbbaabaaaaaaabbbbbbbbabbbaaabbabbaaaaabbaabbaaabbabbbbbaaaabaabaabbbbbbabaabbabbbbababbbabbbbbbbbbabbaaaabbbbbabbaabaabbbbaabaabbbaabbabbaaaaabaaabaaaaabaababbbabbbabbabaaabaabaaaaaaaabaaaaaabababaaaabbababbaabaababbabbaabaabaaabbbaabbabababaaabaaababaabaabbbbaaaabbababaabbbaabbbbabababbaaababbbbabababababaabababbaabaaabbaabbbbbbbabbbbaaaabbbbbbbaaabbbaabbaabbabbabababaabbaaabbaabaabbbbaaaaaaababaaabaababaaaaababaabbbbbbbabaaaabbbaaaababbbaaaababbbabaababbbabaaaabaabababaaaaabbbaaaababaabbabaaaaaabbabaabbababbabbbbbbbbaaaaabbbbabaaabbaaaaaababbabbaabaaaababaaaaababbaaaabbabbbabbbabbaaababaabbababaabaaaaababbbbaabbbbabbbabababbababbbbaaabbbaababbababababaaaabaabababaababbbabbabababaaaaabbaaabbbbaabababbabbbbbbbabbbabbabbbaabbababbaabbbaaabaabbabaaabbbbbabaabaaaababaaababbaaabbaaaabbbbaababbbaaaababbbabababbaabbbabbaababababaabbabbbbbbaaabaaaabbbbbbbabbbbbabbabbaaaaababbbaabbabbabbbbaabbabbababbabbaabbbbbabaabbbbaaabbaaaabbaabbbabaaaaaabbaaabaaaabbbababaabbbabbabbaaaababababbaaaabbbaaaabbabaaaaabaabbbaaabababbaaabbbaabbbabbbbbabaabaabbaabbaaaababbabbaabbbaaaaabaaabaabbababbababbabbabbbabababbbbbabaabbbababbaabaabaaaaaaabbabbbbbbbbaaabbabbaabaabaaaabbaaaabbbbaaabaaabbbaaaaabbabbaabaabbabaaaabababbaaabbababaabbabaabbaaababbbbabbbbaabbabbbaababbbaaabbbbababbaaabaababaababbbababbabbbbaaaaaaaaaabbabaabbaaabbaabbaaaabbabbaaabaabbbbabbaaaaabbbbabbaabbaaaabbaababbababaaabbabaabbbaababbbbaaabbabaaabbaaaabbabbabbbaaaaaaabbbbbbbaabaabbbaaaabaaaaabbaababbbaaaaaaaaaaabababbaaabbbbbaaabaabbababaababbbabaaaabaabaaababaabaaabbaaabaabaababbbbbabbbababababbbabbabbbaaabbbbbaaabbaaaabaabbaaabbbbaabbaabaaabbbbabbaabbbababaabbaaabbbaabbbbbaaaabbbabaabaabbbabaabbbbbaabbbaaaaababaabbabababaaababbbbbbbbabaaaabababbaaaaabaaabaababaabaaababaabbbbbababbaaaaaabbbaabaaaaaabbbbababababbaabababaabaaabbbbbbbabbabaaabbaabbaaaabbbaabaabbbaababaabbabaababbabbaaaaaabbabaaabbaababbababbaaabaabbbbbaabaababbaabbaabaabbaaaabbbaaabababbbbbbbbbbabbabaabaaababbaabbaabbaaabbabaaaaabaaabbbaababbbababbababaaabbababaabbaabbaabbbaaaabbaababbbaababbbaaabbbbbabbaaabbaabaaabaaababababbaababbaabbbbabbabaabbabbabbbababbbabbabbaaabbaaaababbbbaaabbbaaabaabbbbbabbbbaabaababbaaaabbbababaaabaaabbaaabbaabaaabbaaabaaaaabbaabbaaabaaaabbaaaabbabaaaaabbaabaababaaaabaabbbbabababaabaabbaabbaaaabbabbaabbbbbabaaabbabbaababbabbbabbabaabaaaababbbababbabaaabaabaaaabbbaaaabaabbbbaaabaaababbbbaaaaaabaabaaababbbaababbaabbbbaaabbbabbabbaaaabbbbbbbababababbbbaaabbabbbabbbabbbbaaabaaabbbbbaaaaabbabaabbbabbbbabbbaabbbabbaaababbbbbbabbababaaaabbabbbaaabbbaabababbabbbbbabaaababbbbaababaaabbbbaabbbbabaabbbbbbbbbbaaabababbababbbbaabaabbaaaabbaaabbbabaabbabbababaabaabbababbaaaababbabaabbaaaabaaaaaabbbbaaabaaaabbabababbbaaabaababaabababaabaabbbaabbbaababbabbbaabbaababbbbaaaabbaabbbaaaabbbaabbabbaabaabaaaabbaabbbbaaaababbbaaaababbbbbaaabbbaababbaabbbbabaaaaaabaaabbbbabbabaababababbbbaaabbabbbbbaabbaaabbabbaaaaaaabaaabbaaaabaaaabbaaaaabaaababaabbbabbbaaaabababbaaabbbabababaabababaaabaaabbababbaaabbaabbabaaaaabbbbaaababbbbbbbbbbaaaababaaaabbbaaaaaabbabbbabbaaabbabababbabaaabaaabaaabbababbaababbabbbbbbaabababbabaabbabbaaabbabbbaabaaaabbbbbbbbabbabbbaabbaaababbbaabaabbabaababbbababbaababbbaaabbbababbabbabaaabaabbbaaabbaaaaaabbbbbbbaaabaabaababbaabbabaaaabbbbabbbbbbbaaaaabaabbaaabbababbbaabbbaababaabbbaababbababbbbbaababbaabaaaaaaaaabbaaaabbbbaaababababababaabbababbbbbabaabbabbaaabbaaabaabaaabbaaabaaabaaabaabaabbbaaababaaaaaaaaaaaabaaaaababaaaaabbbbbabbbbbabbaaaaaabbbaabaabbaabaaabbbbbaaabaaaabaabbbbaaabbaabaaaaabaaaababbaabababbbabbabbabaaabaabbaabbabaaababababbabaabaabaabbaabbbabbabbbbbbabbbabbbbbbbabbaaababaaaababbbaababbaaaaaabaaaabaaabbaabaabaaaabbbabaababbbabbaaabbbbbaabaaababaabaabbbbbbaabbabbaaabbbaaababbabbababbbabbbbabbaabbaaabbbbbbbaaabbaabbbabbbabbaaababaaabbbbbaaaaaabbbbbbababbbababbaaabbabaabbaaabbbaabbabbbaaaaaaababbaabbabbaaaabababbaaababbaabababbbbbbabbbbaabbbabbbabbaaaababbbbbabbbaabaaabbbaaababbbbbabbaaabbaaabbaaabaaaabababaaaababaaababbbbbabbaaaabababbabaabbbaababbbabababbbabbababbaaabbbbbaaaabbaaaaabbabbbaabababbbbaabaaaabaaabbaaababababaaaabababbaabaabbbaaaabaabaaaaabaababbbababbaaaaaaabbbabbababbaabbabbbbabbaaaabbaabbbbaaaababbbbabbbbbbbabbaaabbbabbababbbaaaaabaabaaabbbabbabbbabbabaababbbbbbabbbaaababbbbabbababaabaabababababbabaaaaaabbaabbabaabbbabbabbabbbbbabbabbbbbaaabbbaabaaabbaabbabbbbbababbaaaaabbaabaababaaabaaabbbbababbbbbbaaabaabbbabbbbabaaaaaabaabbabbabbabababbbabaaaaabaabaaaaaaaabbbbaabaaabbaabbbbaabbabbabaabababaaaaaaaaaabbbabaaaabaaaabbbaabbbbaababaaababbbaaabbbbbbabaababbababbbaaabaaabbbabbaabababababbbbabbbabbaabaabbabbaabbbbbbabbaaabbaaabbaaaabababbabbbbbbaabbababbbbbbabbbabbaaabbbaaabbbabbbabaaabaabbbbbbababbaababbababbabbbabababbbbaaaababababababababbaaaabbaaaabaaaabbbaabbbbbbbaababaabbabbbabbbbaaaabbbaabbabaabbaabbababbbabaabbbababbbabbaaaaaaaabaaaaabbabbbbbaaaaaaaabbaabbabababbabbabababaababaabaaaaabbbabbbabbaaaaabbababbaaaabababaaaababbbaabbbbaabbaabbababbabbabaaabababbabababaabbabbbbabbabbbbbabaabbaabaabbaabbbaabaaabbaaabbabbaabaaaaaaabbbbabbabaaababaababaaaaabbbaabbbaabbaaabbbbabbbbababbabbbbbbbbbaaabbbabaaabbbbababbbbbaababbabbaabaaabaabbbbaababbabbaabbbaaaabbbbbabababaaababbbaaaabbbbbaaabaabbababbbbbaabaabbbaaababbbaababbabbbaaababbbabbbbabbabbabbbaabababaaabbaaabbbaaaaabbaabbababbbaaaabbbabbaaaabbaaaaabbaaaabbababbaaabababaaaaaaabaaaabaabaababbbabbaabababbabaabbbaabbbbabbbbbbabaabababaaaaababbbbbabaaaabbbbbaaaaaaabbbbbbaabaabbaababbabbaaabbaabababaaabbbabababaaabbaababbbabbabbbbbbaabbbabbbbabaabaabaabaabbbabaabababaaabababbaabbababaaaaaaababaaabbabbabababbbaaabbbabbbbaaabaaaababbbaaaaaabaaaaaabbbabbabbababaabaaabbbbbbbaabaaaaabaabbbbbbbbabbabbaabbbaaaabaaabbabbbaaabababaaabaaabbbbaaaabbbbbbbabbbababbbbbaaaabaabbbbaaaaaababbbaabbabbbabbbbbbbbabbbabbbbbaaabababaaaaaabbbaabbaaabbaabaaabaaabbaaaaaabbbbabaabbbbbbbaaabbabaabaabbabbbabbaaabaaababbabbbbabaaabbbaaaabbaabbabbbbaababbabbbaabbabaaaabaababbabaaabaaaaabbbbbabbbbbbbbbabaabbabaaabababbbaaabaaaaababbbbaabbabbabbaabbabbbbabaaabbaababbabaababbaabbbabbbbababaabaababaaaaaabbabbbbabbabababaabbbaaababbbbbbbaaabaaaabababbaabbbabbabbabbbabbaaabaabaaaababbabbbababbaabababbabbbaababaaabbbbbaaabbaaaaaabababbaababaaababaabbbaabbaababbaabbabbababbbaababbaababbaabaabbbaaabaaababbaaabbbabbbbbaabbabaaaabaabbbbbabbaaaaaabaababbbabbbbaaaaaaaababaaabbabaabaaaabbabbbaabaaaabbaaaabbbabbbbbaababbbbabbbbbbbabbbbbaaabbbaaabbbbbbaabbababbbbbabaabbbababbabaabaabbaababbbbaabbaabbbbabbabababaababbbabbababaabaaaabaaabbabababbaaabbaabaaaabbbbbbaabbbbbabbbbabbaababbaaaaaaaabaabbbababaabaaaaabaabababaaaababbaaaaabbbbaababaaabbbbababbbaabbabaaababbaaabbaaaaabbbabbbaabbbbaabaaaabbbbbbbaabababaaaaaabbabbbbaaaaababbbbabbabbaaabbabbbbbbabbbbabbabbbabbbabbbabbaabaaabbabbbabbbabbabbaaabaabbbbaabbbaaaabaabababbabbbbbbababaabaababbbaaabaabbbabababbaabaaaabaaaababbaaabaababaabababbaabbaaaaaabbbbbbbbabbababbbbbabababaabaababaabaaaabbababbaababbabbaaaaababaababaabbabbbabababbbaababaaabaaabaabbaaabbbbabbabbbbababbbbbbbaabaaaababaabaababaabaabbababbbbabbaabaabbabbbbbababbaababbbaabbbabbaababababbaababbbbbabbbaaabbababbaaaaabbababbaabbbbaababaaabbaababaabababbabaabbabbbbbbbabbabaabbbaabbaababbbbababbbabbbbbabbbbababaababaabaaabbabaababaabbbbbabbbbaabaaaaabaabababbaabbbabbaaabbaababbabbaaabbaababaaaabbbababbaabbaaaaaaabbbaaaaabbbbbabababaabbaaabaaabbababbabbbabbbaaababbaabbbaabaabbababababbabaabbaabaabbbaabbbabbbbabaaabababbaabbbaabbbbaababbbabbabbbbbabababaaabaabbbbbbababaaabbabaabaaaabbaabbabbbbaabaabbbbababbbbbaaabaababbaaababaababbaabaabbbabbaabbbabaaaabbaaaaabaabaabbbbbbbaabbabaababbaaabbabbbaabaabababbaabaabbbbaaaababbaaaaaabbaaabbbbabbbaaabababbbbbabaaaaabaaaaabbbaaabbabaaaaabbabbaabaaaabbbaaaaababaabaaabaaaabbababaabaaaaabbbbaabababbbbabbbaabbbabbbabaaaaaaabbaaababbaababaaabaabbabaaaaabbaaaababbabbaabbbbbbbbbaabbbbaabbabaaaaaaababbbbbbbaaaabaabbaabbabaabbaabbbbbbbaabbabaababbbaaaaaaaaaabbbabaabbbabbabbbaabababaaabbabbababaaaaababaabbaabaaabaaaaaabbaabbbbbaabbbbaaaabaaabbbabbabbbabbbbababaabababbbaaaababbaabbbaabaaaababbbaabaabbaababbaabaaabbbababaaaaababbbabbbbabbbbbbaaabbbaabbabababbabbababbabbaabaaabbbabbabbaababaabaabaabaabaaabaabbbbabbabaababababbaaaaaababaaaaabbaabbabaababaaaaabbaaaaaaabbbbabababbaaaababaabbaabaaaaaabbaaabaaabaaabbbabbbbaaabbaabbbbaabaaabbbbaaabaaabaabbbbbbaaabababbbabababababbbbbaaaaaabbbabababaaabbababbabaabaabaaaaabbbaaabbbabaaabbbababbbbababbbbbababaabaabaaaaabaaabaabababaaaabbabbaaaaabbbbbaabbbabbbbaaababbbbbabbabbbabbbbbbaaaaabaabaabaababaaaabbbbbabbaaabbbbaaaabaabbabbbbbaaabbbbbbaabbaaabaabbbbabaaaabaabbbaabbbbababababbabbbaabbabbababaababbbbaabbbbbbbbababbbbabbababaaaaabbbbababbbababbabbbbabbaaabaabbaaabbabaabbabbbaaaabaabbbbabaaabaabbaaabaabaaaaaaabaaaaabbbaabbbbaaaabaaaaabbbbbbbbabbbbaabaabbbbaabbbabbababbaabaaaabbaabaaabbaaabbbbaabbbaaaaaaabbbabaabababaaaabbbbbbbbbabbbbaaabaabbbbbbbbaaaaaabbbabbaaaababbaaaaabbbbaaaabbabababbbbbbaaaabbbaaababaaabaabbaaaababaabbbabbbaabbbbabaababbbbbbbabaabaaaaabaabbaabaaaabbbbaababbbababbaabaabaaabaabbbbbbaabbaabbabbaaabbaaabaabbaaabbbaaaaabaabbaabbbaaaabbaaaabaaabbaaaabbbbbaabaababbaabaababbbbbbabbabbbaaabbbaaaababbaaaaabaabbabaababbbaaabbbbabbbabaaaaabbbbbabaaaabbababaabbbbaaaabbbaaaaaaaabbaababbababbbababbaababbbbbbbababaababaabbabbbabababaaababaababbabababbababaaaabaabaabaaabaaabbbabbbbbbaabababaaababbbabaaabaababababaaabbbbabbbbaabababaabbbaaaababbbbaaabaaabbbbbbaabbaaababbbaabbbbbaabbababaabbbbabaabbaaaaaaaaabbaabbaaaaabbaabababbaaaaabbabaaaaabaabbaabbaaababbbaabaaaaabaabaabaaaababbabbbabbabbabaabbaabaaabaaaabaaabbaaaabbbabbaabaababbaaabababaaaaaabababbbbbbabaaaaababbbbbbbabaabbbbabbabbabbbbaaaaabbabababaaabaaaabaaabaabaaaaaaabbabbaaaaababaaaababaabaabbababababaaaaaabaaabbbaabbbbabaaabaaabbaaabbbabbabbbbaaaaaabaabbaaaabbabbaaaaaaabaabbaaabbaaabaabababbbbbabbbbbbbbabaabbbbbabaaabaabbaabababbabaabaaababbbbbbaaaaaaaababbabbaababaaabbaaabaaaabbbbabbaababbaaaababaabbaaaaabaaabbaabbaaabbababaabaababababbababaaababababaaaabbbbbbaaabbbbaaabaaabbabbababababbbabbabbbaaababababaaabaaaaaababaaaababbbbaaabaababaabaabbabbbaababababaaabbababaaabbbaabaabbaabbaabbbaabbababbbbabbaaaaabbbbaaaabbbabbabaaabbaababbaaababbaaaaaababbaabbaaaabaaabbbaabaabaaaaaaabbaabbaabbbabbbabaabaaaaaaaabaabaabbbaabbbbbaaaabbabababbaabaabbabbabbaaaaaabaababaaabababaaabbaaabbaababaaaabaaaaaaaaaaaaabaaaabaabbaaaaabbabaabbabaabbbbabaaabbaaabaaaaababbbbabaabbbbabbaabbaabbabaabbbabababaaaaabbbaabababaababbababbaaaabbabbbabaabbbaababaaabaabaabbbaaaaaabbaaabaaaabbabbabbaaabbababaabababbbaaaaaabbbababababbbaababaaabbbaaabbaaabaabbaabaabbabaaaabbbbbabaaababaaababbaaabaaaabbabbaabbbabaaaabaabbbaabbaabbabbaabaaabaabbbbababbbbaabaaaababbababababaaaaabbbaabaabbbbaabbaabbaaabbbbbbbaabbaabbbbbbbaabbaabaaaabbbbabbaaabbaabbbaaaabaabababbaaaabbaaaabaababaabbbbabbbbaaaabbbabbabbaaaabaabbbbabaaabbbabbabaaaabbabbbbabbbbaaabaabaabbbaaabbbabababbbbabbbbabbbabbaabbabaababbbabbbabbbababbbbabbabbaaabbaabbbbabbbababaababbbabaabbbabaabaabbaabaabbbbababbbbaaaababbbbabababaaabbbbabbaaabaababbbbabbabaababbabbbbabbbbbaaaabbabbabbbaaaaabbabbbaaaabbbaaabbbbabbabbbbbbabbabbaabaaabaabaaaabbaabbbabbbaabbbbbababbaababaaaaaaababbbaababbbbaabbaabbabbaaaaaababbbaabbaabbbaaaabbbbbbbbaaaaaaabababababbaaaaabaaaabaaaabbabaababaaababbababaabaababbaabaabbbababaaababbabbbbabbaaaaaabaaaabaaaababbabbbabbbaabbbaababbabaababbaabbabbbbbbabaaabbabbababbabaabbbabaababbabaababbbaabbbababbaaabbabbaabbbbbbbabbbaabbababababaabbaababbabbabababbbaabababaaaaaabaaabbbaaabbaabbbabbaaabbbaaabaabbaababbabbbabbbbbaabaaabbabbabababaaaaababbabbabbabbaaabbbbbbbabbbbbaaabbbaaabbaabbbaaabbbbbbaabaaababaaabbbaaaaaaaabbbbbabaaababbaaabbbaaabbbbbbabaabaaabaababbabaababbbaabbabaababaaabbaabbaabbbaaaaaaaabbabbaaabaabbaaabbabaabbaababaababaabbbbbaaaaaaaaaabbbabbbbabbaaababbababbbbbaabaabbbbabaaababbabaabbabbaabbbbbbabbaabbaababaabbbabaabaaabbbbaabbaaaababaabaaabbbaaaababaabaaaaaaabbababbaabbbaaababaabbbaaaabaaabbbabaabbbabaabaabaabaaaaaabbabaabbbabbaaaaaabbbaaaababbaaaaabbbaaabaaababbabbbbbbbaabaaaaabbbbaaaaabbabbaaabaabbabaaaaaaabbabaaabbbabaaaaaabbaabbbbbbaaababbabbbabbbbbaaaaababababaabbaabbbabbaabaaabaaababbbbbabaaabaaaabbbbbaabbbaabbbbabbabbababbaaaaabaaaaabababababbbabbbaaababaababaaaaaababbabbbbababbaabaaabbbbbaaababbaaabbbabbbbaabbbbaaabaaaabbabaababbabbabaabbabbabbbbbaabbaabbbabbbabbbabbbbbbabbaabaabbbabaaaaabaababaabbaabbaaaabababbbbbaabaaabbaaabbababbbababaaaaaaabbabbbbbbbbbababaabbababbaaaabbbabbabaaabbabbaababaabaaaaaaaaaaaaabbbbbbabababbabaaabbbababbbbbbbbaaabbbabaaabbabbbaaaaaabaabababbabbbaaabbbaabbaabaabbbbbbbabbabaabababbbaaabbbbabaabbbaabbabaabababbabbaabbababbaaaabaabababbaabbabaaaaaababbbbbaabaaaaaaaaaaabbabbbaaaababbabbbaaabbbbabaaaababaabbbaabbabbabaabbabababbbbbabbabbbbaaaabaabbaaaabaabaabbaababaaaabbaababaaabaababaabaabbbbbaabbaaabbbaaabbaaaaababbababbaaabbabbaaabaaabbabbbbbababbaabbbaaababbaaabaabbbbabbbaabbbabbaabbaaaaaababaaaabbabaaabbabaaaaaaabbaabbabbabbaabababbaaaaabbbaaababbabaabbbbbabbaabbaaabbabbbaabbbaaabaaaaabbabbbaaaaaaabbaaaabaaaabababbaaaabbbbbabaabaaaababbaabbabbbbbabbaaabbbbbbaabbbbababaaababaabbabbabaaaaaaababbbabbbabaaababbabbababbabbbaabbababaababbbbbaababbbbabbaaabbabaabbaabbaabaababaaabbbabbaabbbaabbababaabbaabbabaaaaaabaaabaababaabaaabbabaaabbabbabbbbbabbaaabaaabbbbabbaabaaabaaaabaaaabbbbaaabbbabbbbaabaaaababaaaaaaaaabbaaabaabaaaaaabbbbabbabbaaabbbababbabbabbaaaababaaabbaabaabbabbbaabbbabaabbaabbabbabbbaaaababbbbbaaabbbaabbbbaabbabaabababbabaabbbbaabbabbababaabaaabbbaabbbaaaabbaabbbabbaaabbabbbbabbababaaababbbbbababaabbaaaaabaabaaabbabbbbabbbabbbabaaababbbbbabaabababaaaaaaaaabbababbbbabaaabbaabbbbaaabbbaaaaaaabbabbabbaaabbabbbbaababaabbbababababbababbaabbbabababbabbbaaababbbbbabbbbababbabaaaabaabaabbababaabbabbbabbbaabbbbabbabbbbaabbbbbabaaaaaaaababbbbaaaabaaabbbbabbaaaabbbbbabbabbabbbbbaaaaaabbabbbbbbbabababaababaababbbababbaabbbbaaaabbbabbabababbaaabbbabbbaaabaaaaaaabbabaabbaababbabaabbabababbaaabbabbbabaabaabbababaaaababababbbabaaaaabaaaababbababbaaaabbabbbbbababbabbabbabaaaaaababbabbaaabbaaabaaaaabbabaababaaabababbbaaababbbbbbbababaabaabbabaaabaabbaaaaabbabaabaabbaabbababaababaaaaaaabaaabbbaaaababaaaababbaaabaababaabbbababaabaabbbaabbbbbaaaaabbabbabbabbbaababaaabaaababaabbabbbbababaabaabbbaaaaabbbaaabbababbbaaaabaaaaaaababbbbbbbaabbaaababbabaaaabbbabbaaaaabbbbaababbbbbaabbaabbbaabaaaaabbaabbbbbaaaaababbabbabbbbbababbabbabbaaaaaaaaabbbaaaabaabaaaabbbbbaabbabaabaabbbbababbbbbbbbabbbbaabbaaaabbaababbbabaababbabbbbbbbaabaaabababbabaaabbaaaaabbabbaababaabbababbbabbbaabaaababbababbaabbbaaababbabaabaaaabbaaabaababbaaabaaaababbabbaabbbabbbaabaaaabbbbaaabaababaabaabaaabbbbabaaabbaabbababbbabababbabaaabbbbaaaabababaabaabbaaaaaaabaabbaabbbabbbaababbaabababaabbaaabaaabbbababbbbaaaaaaabaabbbabbabaababbabaabbbbbabbbbabaabbbaababbbabaaabbabbbbbbaaabbaabaaabaababaaaaaaaabbaaaabbaababbbbabaaabaabbabbabbbbaabbbbaababbabaaaabbbaabbabbbbbbbbaabaababaaababaabbbbaabbaaaaaaabbbabbbbbbaababbabaaabbaabaababaababbabaaaaababbaaabababaaaaababbaabbababbabbbaabaaababaabbabaabbaabaababbaaaaabaabaaaababbabbabbaaaabaababbaabaabbbbbbbbabbaaaabaabaabbbaabbaaabababbbaaabaababaaabbaabbbbbbbbbbabbabaaabbbabaaabbaabbbaaaabbabbbaaabbbbaabbaaaabbaababbabbaaaaaaabbaaaabbabababaabbbaaababababbabbabbabbbbaaaaaaaabababaabbababababbaababbbabaaaaaabaaababababbbbbbbaaababaaaaababbaaabaaababaababaaabbbabbabbbbabbaaaaaaaababbbbaabaaabbbaabbbababaabbbbbbaaababaaabbbbabbaabbbbabbbabbaabbabbbaaabaaabbbbbabaabbbbaaabbbaabbabbbbabbabbbaaababbbaaababbaaaaabaabaaabbbbbabaabababbbabaaaabbbbabbabbbabbaabbbbaabaabababbaababbbaaaabaabbabaabbababbbabbbabbababbbbbbbaaabaabababbbaababbbbbaabbaaaaabbbbbbbbbbbaabbaabbaaaaabaaaaaabbaabaabbbaabaabbbbaaababbbbaabbaabbbbbbbabaaaabaaaabbbbabaaabbaaaaababaaabbaababaabbbababbbaaaabaabaaaabbaaaabbaabaaaabbabbbabababbbbbababaaabababbaabaabaabbbbbaabbabbbbbbabbaabbbaaaabaaaabbabbbaaaaabaaabaaababaaabbaababaabbaabbbaababbaaabbaaababbbaaaaabaabbbbbaabbbbabbabaabbbbabbbabbbbbabbbbaaaabaabbabaabaaaabbbbaabaababbbbaaabbabbaabbbbaaababbbbabaabbaaabbbabaababbbbaaababbaababaabbbabbabbababababababbabbbabaaabbaabaabbabbbaaabbaabaaaaaaababbaabbbabbaaababaaaaaababaaaababaabbbabbabbaaaabaababbbbaaabbabbbbbbbbbbaababbabbbbbabaaabaaabababaaabbaabbababbbababababbbaaaabbabaaabbbbbbbababbbbababbbbabaababbbaabbbabaabbaababbbbbaabababbabbbabaaaababaaabaabbbbaaabbabaabbbbbbaababbaabbbabbbabaababbaabbaabbbabbbbabbabbaaabaabbabbaaaaaabbbaaaaabbbbbbabbababbabbbbbaabbabbabaabbaabaaabbbaabbbaaabbaaaaaabaabaaaabbbbabbbbbababaaaaabbaabaaabaaabbaaaaabaabbabbbbabbbabaabaaabbaaabaaaaaaabbaaaaaaaaaabbaaaaabbaabbabaabbbababaabaaaabbabaabbbabbbaaabbabbbaabbbabaababbbbbbbababbbaaaaabbbabbabaaaabaaababbabbbbbababbaababbabbaabaabaabbbbbabaabbababbaabbbaaaaabaabaabbbbabaabababaababbabbabaabaaaaaaaabbaabbababbbbbabbaaabbbbaabbbabbbaaaabbababbbababbaaabbbbababbaaabbababbbababaaaaaaaabbbbbbbbabaabbbaaabbbbbaababbbbabbbabbbbaababaaaaaaaabaaabbbbbabababbabbbbababbbbabababaabbaabbaaaaabbbbaaabababbaaaabaaababbaaaaaaabaaabaaabaaabaaaaabbbaabbbabbbabbaabbbaabababaaaabaaaaaabababaabaaababaabbaabbaaaaababbababaaabbbaababbbbaabababbbbaabbabaaaaaaaaababaabaabbabbaabaaaaabbbabaaabbbabaabbbaaabbbaaababbabbbbbbbaababbababbaabababbbaaabbbaabaabbaabaabaaaaabbababbbabbaaaabaababbbbaaaaaaaaaababaabbbbbbbabbbaabbbabbbaababaaaaaaaabbabbbbbbbbbaaababbaaabbbaabaabbbaaabaaaabaabababbabbaabaaaaabaaaaaababbababbabaabbbabaabaababaabbbabababaabaaaabbabbaababbabbababbbbaaaaaaaabbbbaabbaaaaabbaababbbbbbbbbbabaabaaaabbaaaababaababbbaabaabbbbaababbbabbaaaaaaabbaaaabaabababaaaabaabbaabbbabbabbaaaaababbbabaabaaababaabaaaabaabbbbaaaababbaaaaababbabbabaabbaaabaaaaabbbbaabababaaaabaaaaaaabaabbabbbaabaaabbbbbabbababaaabaaaabbbaaabbaaabbbaabbaaabbbbaaabaabbabbabbbbbaabbaabababaabababababbbbabaababbaaabbbbaabbaaabbbabaabbbabbbababbbaabbaaaaababaabaaaaabaaabbbabaababbaaaabbaaaaaabababaabbbabbaaabaabaaaaabbababbbaababbbbaababbbbbbabababbababbabababbbbbababbabaabaabbbbbaabbaaabbbbaababbbbababaabaaaaabbbbaababbbababaaabaabbabaaaaaaabbaabbabaaaabbbbbbababbabbabababababababbbabbabaabaaaaaabbbbbbaabaaabbaabaaaaabbbaaaabababbbababababaaabbabbbaabbaaaabaaabbaaababbaaabbbaaaaaaaaaaabaaaababbabbabbababaabbbbbaabbbabbaabaabbabbaabaaabbababbaaaaabbabbbaaabbbabbbabbaababbaaaaababbaaababbbbaabbabaaaabbbababaabbaaabaaabaaaabbbbbabbaabaaabaababbaabbaabaaabbabbabaabbbaaaaabbaaaaaabbbabbbaabbbbaabbbaabbbabbbbabaabaaabbbbbbbabaaaabbabaaaabbbbbabbaabbaabbabbabaabbabaaabbababaabaabaaabbbabbababaaaaaaabbbaababbbababbaaaabaaababbbbbbbbaabbbabaabbbbabbabaababbababbaaaaaaabababbbbbbbbbaaaaabbbabaabbaabbbbaaaabaaaaaabaabbaabbbaaaabbababaabaababbbbaaaabaaaabbbaaabaaabaaaababababaaaabbabbbababaaababbabababbaaaabbbbaaababbbabaaaabbbaaaababbabaabaaaabbbbbbaabbbbbbabababbaabaaabbbababababbaabaabbbaaabaabaaaaaababbaabbaabbbababbbbbabaaaabababbbbbabbaaabbbabbbbaaaabaaabaabbbaababaaabbaaabaabaaaabbbbbbaaaabababbbabbaabbabbbaababaabbbaaaabbaaabbbbbbbbbabaaabbaabaabbaaaababbbbabbabbaabbbababbbabbaaaabbabaabbbaabbabababbabaaaababaabbbbaabaabbbbaaabbabbbaaaaaaaabababbbabbbababbaababbbabbaabaaabaaaabbbbbabaabbbaabbbbaabbbbbaaabbaabaaaaabaabbaabaababbbbbaabbbbabababbaaabbababbabbbaaabbaaababbbbbbbbaaaaabbbbaabbbabbaabaaabbabbaaabbbbbabbaaabbbbbaabbabbabaaabababbbaaaabbabbababbbbaaabbbbbbbabaaabaabaabbbaaaabbabbbbaababbabaabaabbbaaabaaaaababaaabaabaabbabbbaababbbaabababababbababbaabbabaaababbababaaabbbabaabbaababaabbbbbbaababbabaaabbbaabbabaaabbaabbabaabaaabbaaabaaaabaababababaabbbabbabababaabaaabababbbaaaabababaabbbabbaaabababbaabaababababbaaabbabbaaaaaaaabaaabbbbbbaaabbbbbaabbbbaaaabaaabbbbbbabbaaaabbbaaaaaaababaabaaabbaabababababbaaaabbbaabababbaabaabbaaaaabbbabaabbbbbaabbaaaaaabaabbabbaabbbbbabbabbabbbbababaabbabbbababaabababababaababaaabaaabaabaaaabaaaaaabaababbbaaaabbbaabbbbabbbbbaabaabbabbbbababbabbbbbbabbbaaaabaaaabaaabbaabaaaabbbaabbababbbaabbbbbabbbabbbbaabbaababbbaaaaabaabbaaaababaaabbbbaaabbaaaaaabaabaaabaaabbbabaabababbbbabbbabbabbaaaaaaabaabaababababbaabaaabbbaaabaaaabbbababaabaaaaaabbbaaabababababaaaababaaaabaaabaababaabaabaaaabaababaabbbbababaabbababbabbabbabaabbabbabaabbbabbaabbaaababaababbaababaababbbaabababbbababaaabaabbbaaabbaaababbabaababbbaaaabbabaabababbbaababbabababaaababababbbabbaababbababbabaabababbbaaaaabbbabbaaaabbaabbbabaaaaabbababaaaaaaabbaaabbababbbbaabbabbaaabbabaabbbbabbaaaabbabaaababbaabbbabbabbbbabaaaabbaabbbbbababbaaaaabbbbaabababaaabbbbaabaaabaabababaabaaabbbabaabbaabaaababaabbaaaaaabbabaabaaaaabaabbbababbabaabaaabbaabbaabbbaababaaaabaaaababbbabababbbaabaaaabaabbabaaaaabbabbbaaaabaababbaaabaabaaaabaaabababbabbbabbabaaaaabaaaaababbbabbbaaaabaaabaaabaabbabaaabaababaabbaabaabbaaaabbbbaababbaabbababaabbbbababbabbababaaaaabaabaaaaaaaaabaaaababaabbbababbabbbabbbbbbaababbbaaaaababbabbaabbbbbbaabaaaaabbbbabaaabbabbbababbbaaaaabaaabbabaaababaaabaabbbaabaaaaaaabaaaaaaabaaabababababbabbbbbabbababaaababbbaabaabbbbaabbbbababbaabbbabbbabbbbbbaaabaaaabbaabaabaaabaabbabababbbbabaabababbbbabbbababbbabaaabaabaaaababababaabbaaabbbaaabbabbabaabaaaabbaabaabbaaabbbaaabaabbbbbbaaababaaabbababbbaababbaaaaaaaabaaaaabaabbbbaaabaababbaabbaababbbbaabaaabbbabbaaaaaaaabababbbabbabaaaabaaabbbbbaaaaaabbababaaaaaabbaababaaaaaaaabaabbabbaaabbbabbbabbabaaaaaabbababbbbbbbabaaabaabbbaabaaabbbabbbbaaaaaaabbbbabbbbbbbbaabbabababbaabbbaaaabbaabbabaaabaaabbbabbbbbbabbaaabbabababbaabbabbabbaaaaaabbbbabbababaababababbaabaabbabbbbaabaaaabbbbaaaabababaabaabbababaaaababaaabaaaabbababbababaababbabaaababbbbababaaabbaaaaababaabbaaaaaaaabbaabaaabababbbbbabbbabbaabbabbbbbbaaaababababbbbaababbababababaababaababbabaaaaabbabaababaaaabbaaaaaaababbaababaaabbbbabbabbaabbabbbbaabbbaabaabbaabbababbaababaabaaaabbaabbbbaaaabbabbaabaaabaabbbbbaabbabbaabaabaababaabbabbbabababaabbaabaaabababbaabbbbaaabbababaaababbbbabababbbbbbabaaaababbbaabbbbbaaabbaabbaaabaaabaabaababbbabbabbbbabaaabaabbabbabbabbbbbbbbbababbababaaaababbbabaaabbbbaaaababaaabbaabbbbaabbbbbaaabbabbbbbbbaaabaaaabaaabbbaabbbbbaabbaaabbabbaaabaaabbbabaababaaabbbabbabaabbbbabbaaabaababbaaabbabbbbaabbbbbaaaaaabaabababbabaaaabaababaabaaabbabababbbabbaabaabbabbbbaaabbbaabaaaabbabaaabaabbabbbbbaaabaaabbabbabbaaaabbabaaabaabababbaaabbbababbaababbabbabbababbbaaabaabaaabbabaabaabbaaaabbbaabbbaaaaabaaabababbaaabaabbbababbbbbabbabbaaaaababaabbaaabbbaaababbbbbbabbbabaabaaaaababbabbbaabbbbabbbabaabbabaaababbabaaaababbaaababaaabababaaaaaabaaabaabbabbabbbabaaabbbabbababbbbbbaaababbaaaabbbaabbaaababaaaaaababbaaaabbabbaababaaaabbabaaababbaababbbaaabaaababaabbbbaaaabbabaabaaababaaababaabaabbaaabbbbbbbbabaaabaabbaabaabaabbbabaaaabbabbaababaaaaaaaabbbaaaabbbabbbababbbbbaaabaaaaaaabaaaabababaabaabbabaaabaaabbbbbbbaaabbababbabababbbabbaababaaabababaabbbaaabababbaaabbbbababaaaaababaabbbaabbbbbaabaaababbabaaaaabbbbbaababbabbbababaaaabaaabbaabbbbbbbbbababbbaaabbbbbbbbabaaaaababbbabaaaabbbaaaaaabbbbabaabaabaabbabbbbbabaababbbaaabbbbbabaabababbaabbbababbabbbabbabaabbbaaabaababbababbabbabbbbaaaabbbababbaabaabbabbabaaabbbbbbaababbbbabaababbaabbabaaaaabbabaaabbbbbabbbabaababaaaaabbbababbaabbaabbabbbaaaabaaaabbbabbbbaabbaabbabaabbaaabbbbaaabaabbbaaabaaaabbbaabbbbbbbbabaaaaabababbabbbbbbaaabbabaaaaabbaaaababbbbbbabbbababaabbabbabbbbaaababaababbabbabaabaababbbaaaaabbabaabbaaabaabaaaabbbaabbababaaaaabbbbbabbbabaabbbbaaabaaabbaaaaaabaaaaabaabaaaaabbabaabbbaabbabaaababbaabaababbbabbbaaabaababaabbbbaaaaabbababbbbbaaaaaaabbbaaaabbbbbaabbbaaabbaaabbaabbabababababaaaaababaaaabbabbaababbbbabbbbbaababbbbbabaaabbbbabaababbbbbbbaaababaaaaabbbababbabababbbaaaabbaababaaaabbbabbbbbababbaabaaababaaaabaabbbbaabaaababaababaaaaaaaaabababaabaaabababbabbbaaabaaaabbaabbbababbaabbbaabbabbabbaaabbabaaabaabbbaabaaaaaaabbaaaaaaaabbabaabbbbabaababbabaabaaaaababbbbbaabaaaabaabbaabbbbbaaababbaababbbabaaabbaaaabaaabaaabbabaaaaaabaabbabababbaababbaababbaaabbbabaaabbababbabaaaababbabababababbbbbbbbbbbabababbaababbbaababaabbbaabbbaaaababbbababbbbaababbbbbaabbabbbabaaaaababbbbaabbaabbaababbbbaaaabbaabbbabbbbbaaabbbabbaabaaaabbaabaaaabbbaaababaaaabaaabaabbababaaaaaaabaaaabbaaababbbbbaabaabaaabbabbaaabbabaabbbabaabaaabaaaabaaaabbbbabbaabbbaabaabbbbabaaabbaaaabbabbabaabbbabbbabbaaabbababbbbbaaababbabaabbbaaabbaaabbabbbabbaaaabaaabbaabaabbabaababaabbaaaabbbaaababaabbbbbbbbbabbbaabbaaaaabaababaabaabaaaabbbaaababbaabaaaabababaabababababbbbaaabbbaaaabbbbabaaabbbaaabbbbabaabbbbababbbbabaaabaabbbaaaabaaaaaaababbaabbbbbabaabbbaabbabbbbbabbaaababaaaabaaaaaaaababbaabbbabaabbbaaabaabbabbabbbabbababbbbbababbbbbbaabaababaabbaababaababbbabbbaaabbabbbaabbabbaaabbaaaaaabaaabaabaaaabbbbabbababbaaabbabaababaabbabbbaaaabbabbbbbaababbaabbabbbabbabaaaabbbbbaabbbbbbbaabbabbbabaabbaabbabababbabbaaaabaababaaaaaaabaabaaabbabababbabbaaaabbbbbaaaabbaabbbabbababbabaaaaabbaaaabababababbbabbababbaabaaaababbbbabaabbbbababaabbbbbbbbaabbaabbabbabbbaabaaaaabbbabbababaaabbbbaabaababbbbabbbbbaaabaaaaaabbabaaabbbaabaababaaabaababbbbaaabbbbbbabbabaabbbabbaaabbabbbbbaaaabababbabbbabbaababbbaaaaaabbbabbbbaaababbaaabbbabbbbbbababbbabbaabbbabbbbbaabaababaaaaabbaabaababbbbababbbbbbaaaaabbababbaaaaaabaaababbbaaaaaabbbbaaababbbaabaabaaaaabbababbababbaabbbbbaabaaaaababababaabbabbbababbbaabbbbbbbbbaaabbabaababbaaaabbabbbbaababbbaababbabbabbbbabbaaabbabaabbabbbaaaaaabaaaabbabbbaaabbaaaaaabbaabbbbbbbbaaabbbbaabababbaaaaaabbbbbbaaaabbaaabbbabbaabbababababaaaaaaaaaababaaaaabbaaabbbaabbbaaabaaaaaaabababababbbaaaaaaabbababbbbbababaababaaaabaaababbbabbaaaaaababbbaaabbbbabbbbbabbbbbabaabaabaaaabbabbbbaaaabaabbbbaabbaaabababaabbababaabbbabababbaaabbbaabbbbbabbbbaaaabaabaabbabaaaaababaaaaaaabbaaabbaabbbbbaababbaabbabbabaaababaababaaaababaaaabaabaaabaaabbbaabbabbbaaabbbbbabaaababaabaaababaaabaaabbbababaaaaabbaabaabbaabbbbabbbbaababbabbabaaababbbaabbaabbabbbabbbabaababbbbbabaaabaaabbaaaababbbbbbbbaaabbabaaaaaaabaabababababbaabbbababbbaabbbbaabaaaabbaabababbaaaabababaaaabbaaaabaaabbbaaabbabababbbaaabbbbabaaaabbabbaababbabbababaabaaaaaabbabababbbabbaaabbabababbabbbabbaaaabbbbaababbabababaababbaaabababaabaaaaabbbabbaaabbababaaabbaababbbbbabbbbabaabaabaabbbbaababaababbbbaaaaaaaaaababaaaaaaababbabaaabbabbbbabbabaaabbabaabbbabbabaababaabbbbbabbbaaaabbbbbababbaabbabbbaaabbbbaaaabbbbbabbabbbbaaababbbaaabbbbbbbbbbbabbaaabaababbbbaaaabaaabaabaabaaaaaabbababaababaaabaaabaababaaabbaaaaababaaababbbbbbaababaabababbababaababbabaabaaabbbbbbaaaabbbaababbbaabbbaaaaaaaaaaabaaaaabbabbbbabbaaabbaaaabbababbabbbbbbaaabababaababaaabaabbbaaabaaabbabbababbaaabbabaaaaaaaaabbabbabaaabaaabbbaaababbbbbbabaaaaabbaaabababbaaabbbaaabaaaaaaababbaabbaabaaabaababababaabbabbbbabaaaaababbbaabbababaababbbbabbbaababbbbaaabbbbbbbbbbabaaabbbbbaaababbbabaababbabbaaaabbababbbbbbababbaabbababababbbbbbaababbbbbbbbaabbbabbabbabaababbaabbabbbbbbaabbabbbababbbbbaaaaaaaabbbbabbbababbabaababbbaabbbbbbabbbbaababaabaaababbbabaabaaaababaaabbabbbababababbbaabaabaabababbaabbaaaaabbaabbaaaabbabaaabababbababababbbbababbbabbbbbabaaaabbbbbaaabbabbabaabababaabbaabaaaabbbaaabaaabbbbabbbabbbaaaaaaabaabbababaaaaabaabbabaaaabbbbaaabaabaababbbabbbbaabbabaababbababbabaababbbbbbbbbbabbaabaabaaaaabaaababbaabaaaaaabaaabbabbbaaabbbabbabbaaabbbaaaabaabbbbbbaaababaaaaababbbbbbababbaabaabbbabbaaabbbaaaaabbbabbabbaaabbbbaaaaabaabbabbbababbabbaaaabaabbababbbbaababbabbabbbbababaaabbbbabaaaaabaabbaababaaaaabbbbabbabababbbbbbbabbaaaabaaabbbabbabbabababbbaaaabaabaaaaaabbbabaaaaabbbbbbaabbbabaabbaabbbaabaabbabbbbababababbbaabbaaaabbbbababbaabbabaaabbaaaaaaabaaabbbbbaaaaaabaabbaabaaaaabaaaabaabaaabbabbbabbbbabababbbbaabbbabaababbbabbaabaaabbbaaaaabbababbbbaaaabbaabaabbbaaaabbabbabababbbabababbbbbbaaaabbababaaabbbbaaabbaababbbbbaaaabaabaaaabbaabbabababbbbbbbabbaaaabbabbaabaabaaaabaabaababababaaaaabaaaaabaabbaaababbabbaabababbababbbbbbbbbbaaababbbaabaaabbbaabbaaabaaaabbbabbaabbbaabaaabbaabaabaabaaabababaabbbaaaabbaababaabaababbaabbbaaaabbabbbaaabbbbbababbbbbabbaabababaaabbabbbbbbbabbbabbbbabbabaabbbbbaabaabbbabbabbabbbaabaabbabbbabaabbaabaaaabbbabbaaaaabbaabaabbbabaabbbabababbabbbaaaabbbbbabbaaaabaaabaaababbaabbaabbabaaaaabababbbbabbabaabbbbbbabababbaaaaaabaaaabbabbabaabbbaabaaaabbabaabbbabbabaaaaaaabbbabbaaababbbbbbbaaaaaabababbbaaaabbbbababbaabbbaaabbabbbaaaabbabbababbaaababbbaababbbbabaaabbaabbbbbbaaababbbbabaababbababbaabbbaabbbbbaaaaaababaaaaaaaaabaabbbbbbbaaabaaaaabaabbbaaabbaaababbbabaabbaabbabaaaaabaaabbbabbbaaaaababbbbbbbbabaababaabaaaaaaaababbbaabbbbaababaaabbbabaaaaabbaabbababaabaabbaabbbabbbbabbaaaababbbababababaabaaabababbbbbbbbaaaaabbbbbbababbbbaaabaabbabbabaabbaabbabbbaaababbaaabbaaabaabbababbbaaabbaababbaaaaaaabbbbaababbbbbbaaababbaababbabbaaaaababbaaabbabbaabaabbbabbbaabbbabaaaabbbbabbbbbbbababbbabbbbbabbababbbbaaabbabaaabbbabbbababbabbaabbaabbbabbbaaabbaabbbbaaaaabaababababaaaababbabbababaaaabaababaaaaabbabaaaabbbbabaaabaabbbaaaabaaabbaaaaaaaaabbbbaaaaaabbaaaababaaaabaabbbaabbbbbbaabaaaaabbabaaaaabaababbabaaabbaaabbaabbabababbababaaabbbaaabbabaabbabbbbbababaabbbaaabaabbbabbbaabababaababbaabaababbbbbbbaaaabbaaabaaababbaababaaaaabbbaaabbbbababbaaababaaabbbabaababababbabbabaaaabbbbbbaaababbaaabaaabaaabaaabaaababababbbbbaaabbaabaaaabaabbaaabbbabbbabbbabaabbbbbababaaababaabbbaaaaaabbabbbabbbabbbbaaaabaaaaaababbaabaababbabaabababbbbbaaabbbbaababbbbbababbbbababaaaaaabbabbabbbbbabbaabbaaabbbababbabababbbbaaaabaababbbaaababbabbabaabaaaaaaaaaababaaabaaaaabbaababaababababbbbaabaaababbaaabaabaabbbbabbaabbbabaaaaaaabaababbaabbbabababaaaaaaabaaaabaabbbaabaaabbbaabbababaaaabbbabaabaaaaabbbbaabbbabaabaabaaabbaaaabaabbaaaabbbbabbbbabbaabbbaabbbbabbbbabbaaababaaabbbbbbaaaabbaaaabbaaaaabbabbbbbaaabbbaaaababbbabaaaaaaaababbbaabbbababbbbbbabababaabaaababbaabbbbbbbababaabbbbaaaaaabbbbabaabababbbaababbabababababaabaaabbabbbbaabaabbbaabbbaaabaaaabbaaabbabaaaabbabaabbaabaaaabababbbaaaababaaababbabababaabbbaaabbbbbbbbbabbaababaababbaabaabbbaabaaaaaaaabbbababababbbaaabaaabbbbbbbbaaaabbbabbbbbaababaabbbabbbabbbbaabbaabaaabaabaaababbbbababbbbaabaaabaaababaabbbaaaababbaaabbaaababbabbbbabbbbbbbaaaaaabbbbabaabbbaabaaabaaabbabaaabaabaaababbabaabbbbbbabbababbaababaabbaaabababaaaabbaaaabaaabbabababbbbabaaaabbaaababbbbbbbabababbabaabaabbabbbaabbbbabaaabbbaabaaababaaabababbaabaababbbababaaaabbaabbabbababaaaaabbababaabaabababaababaaaaabbbabbbbbbaababababbbabbbbbbaaabaabaaabbbbbbabaabbbaabbababbbbaaabbbbabaababaaaaaaaababbababaaabbabbbbbababbabbbabbabbbaaaaababababbaaabbbababaabbababbabaabaaababababbbbaabbaaabbaaabaabbaabbbbbaaabaababbbbaaaaabaaaaababaabaaababababbbbaaababaaaaaaaabaaaaabaaaaabbababbbaaababbbbbabaabaaabaababababbabaaaababbbaababbbbbaaaaaaabbaaabbbaaaabbbbabbaaaabaaabbbaabbaabaabbaaababbaabaabbaaaabaabbaaabaabaabbaaabaaaabaaaabaaabbaababababbababbbbababbbabbbbbbabbbaabaaabaaabbbbababaaabbbbbabbbabbabbbaabaaaaaaaababbbbaaaaabaaaabbaabbaabbababaababaaabababbabbbbabbabaaabbbabbbabaaaababaaabaabaababaabbbbbaabbababababbaaabbbbaabbaaaababbbbaabbaabaaabbaaaaabababbaaabaaabbabbbaabbabbbbbbbbbaaaabbbbababaabaaaaaaababbbbbabaaabababbaaabababbbaaabbaabbabbabbbbabbbabbaaaaaabababaabbbbbabbaabbbbababbbbaaaaaabbbbbbabbaaabbbbbbbbaababbaaaabaababbababbaabbabbabbababbbbaabaaabababbabaaaabbabaabaabaaaaaababbaabbbbaababbbbbaaabababbaabbaabbbabaaababbabbbbaaaabbabbbaababbaabbabaabaaabbbbbaaaabbbabbaabaabababaababaaabbaaabaabbabbabbababbaabbbbaaabaabbaabbaaaaaaababbaaabaabbbabbabababaabbbbbaaaabbaabbaabaabbaaaaaababbabaaabbaaaaababaabaabbaaaababaaaabbabaaabbaaaaaaabbbababbbbbabbbbaabbbbabbbabaabbabbaaaaaaaabbababbabbabbaaabbabbbbaabbbabaaaababbabababaabaabaaaaabaabbbbababbbabbabbababaaababaaababababbbabaaabaaabbbbbababbbbaaaaabbabaaaaaabaabababbbaababaaabaaaabbbbbaaaaabbbaabbbaabbbaaabaaabbbbabaaabbbabbabbabaabbbabbaaaabaabaaabbaababaababbbbabbbababbaaaaaaabababbbbbbbaaabaabaaababbabbbbbbbbbabababbbbbbbbbaaaabaabbbbaababbaabaabababbabaabababaabaabababbaabababbbabaabababbababbaaaabbbbbaaaabbabaaabbaaaaaabbbababbbbabaabbaabbaabbaababaabaaaaababbbabbabbbbbabbaaabbbabababbaabbbaabaaabaaabbababaabaaabaabaababbbaababaaaabbbbbbababbaabbbabaaabbbbbabbaababbbbbbbaabbbbabababaaabbaabbbbabbbaababbabbbaaaaaaabbababbaaabababaaaaabaaaaabbabaabaaaabbaabaaaaabbaaabaaabbbbabaabbaaababbababaababbababbbabbabbabbbabbaababbabaababbaabbaabaabbbabaabbabbababbbaaaababbaaaaaaaaabaabbbaaaaaaabbbaabaababbababbabaaaabaababbbababbbbaaaaabaaabaabaaabbabababaabaabbbabbbbbaababaabaabbabaabbababaabbaabaabbabbbbbbbabaaaabababaabaabbbbbbbaaaabaabbabbbbababbbaaaaabbaabababbabaababbbaababaaaaababbaaabbbbbbabababaaabaabababbbbabbaababbbabaaabbabaabaabbbbaabaabbaaabaabaaaaaabaabbbbbabaaabaaabbababaabbabaaababbaabbbbaaababaaaabbaabaabaaaabbbaabbabaabaaaaababbaababaabbbaababbbbababaabbbabbbbbabbabaabbaabababbbaaaabbbbaaabbaabbabbbabaabbabbabbabbaabaaaaabbbbbbbbabaaababbbabaababbbbbbbababbbbbbaababbbbabbbbbbabaabbaabaaabaabababbaaaaabbbabababbbbbbabaabbababbbabbbbbababbabbaaaaabbaabaabbbabbbabbaabbaaaabbbbabaabaaaababaaaaaababbbabbbaaabbabbaababbabbababbaabbaababbabbbaaababbbbbbbaabbaaabbbbabbabbabbbababbbaaabbbbaaabbbbbbbbababababbabbbaaabaaabbaaaaaabbbbbbabbabbbbabbbbabbabababbabbbababababaabbaabaabbbaaabaabbabbabaaaabbbbaaabbababbbabaaabaabbaaababbaabbbabbbbbbbbbbbbbbabbbbabbaaaabaabaaaabbaabbabbbabbabbabaabbababaababbabaaabbabbaabaabbaabbabbababbbbbbaabbaabbabbaaaaababaaababbababbaaabbabbbbbbbaababaaabbababbbbbaabbbabbabbaabababbbababaaaabaabbbbbaabbaabbaaaaaaabbbabaababaaaaabaaabaabababaababbabaabaaabaabaababaaaabbabbbabbbaaaabbbbbaababbabababababababaaabaabbbbababbaaababababaaabbaaaabbbbbbaaabbabbbabaaaaabbababababaabaabaaabaabbbbabbaaaaabbaaababbbabbbbabbabaabaabaabaabaaaabaabbbaaabbbbaaaaaaabbaabaaababbabbaaaaabababbaaaabbbbaaaaababaaaaabbabbbaababbbaaaabbaaaaabaababababbbbababbbabbbabaaaaabaabbbabbaabbbbbaaaabbaababaaabbbbbabbababbbabbabbbaabbaababbbbaababbbbabbaaaaabababbbaaabababaabbabaaaaabbabbaaaabbaabbbbbabbbbbbaabbabaabbbbabbbaabbaaaabbabbbaaaaababaabaabaaaaaaabbbbabbbbabaabaababababababbabaaabbabbbabaabbaaabaaaaababababbbaabaabbabbaaaabbbbaabaabbbbabbababaaaabaaabaaaabbbbaaabbaabaababbbaabababbababaabbabaabaaaaaaaaaaaaabbbababbbaabbabbbbaaabbaabbabbbbbbaabbaabaabaabbbabaabbbabbbbbbaaaaaaaabaaabaabbbbabaababbbaabababbaabbababaabaaabbaaaabbbabaabababaaaaababbaabbaaaabaaabbabbaabbbbbbabbbbbababbabbaababaabbababbabbbabbbbbabbabbabaabbabbbbaabbaabbbbbabbbbbaaaaaaaababbbbbbabbaabababbaaaaabbaabbababababbaababbbaaabbaabbababaaababbabaaabbbbbabbaaabbaaabaaabaaaabababbaabbbaabbaababbaaababbaabaaaabbbbbbbbaabbbaabbaaabaababbbbabbbaaabbbaaaabababababaababaabbabaaabbaababaabaaaabaabababaabbbaabbbbababbabbbbaabbbaababbabbbaaabbabaababbaabbaaabaabbbbbabaabbabbaabbbabababaaabbabbaaababaaabbaaaababaabbaaaaaabbabbbabaaababbabbbbbbabbbabababbabbbbababaabababbbbbbbbaaaaabaabbbabbbbaaaabaaabbbaabababbbaaabbbbaababaaababbabbabbabbabaaabbaabaaaabaabaabbbaabababaaaabbbabbaaaaaaabbaabababbbabaabbbbabaaaabbaabbabbbbbbbaabbaabaabbabbbaaabbbabaaabbbaabbabbbabaaabbbabaaabbbaabaababaaaabbabbbbabababbbabbbbbaaabaabbbbbbbbaabbaabbabbaababaabaabbabababaaabbabbbbabaabbbbabaabababbbbbbbaaaabbabbbbaabaabbbabababaaabbabaaaababbbbbabbabbaaabbabbbbbbbaaaaaabaaaaaaaaaabbbbbbbbaaaabbbabbababbbbbbbbbbbbbabaaaaababbbbbaababbaaabaaabaabaaabbbaaabaaaaababaabbaaabababbaaaaabbaababbbaaaaaaaaaabaabaaabbababbaaaaababababbbbaabaabbbaabbababbaabbbaabbbbbaaaabbaaabbabbbaaaababbbaaaaaabbabbaaabbaaaaaaaabaaaaaaaabbaabaabaabbbbabaaabbbabaabaaabaabaaabbaaabbbabbbaaaabaabababaabbbbbbabaaaaabaaaaabbbaabbaaaaababbabbbaaabababbabbabaabbababaaaabaaabababaabbbbbbbabaabbaabbbaaabababbbbaaabbbaababaaabaaaaaabaabaaabbaaaabaaaabbbaaaaaaaaabbbaabbbbbaababbbaaabababbabbabaaabbbbabbababbbbabbabababaaaaababababaabbaababaaabbaabbababbaaaabbbbbbbbbaaabaaaaabaabbabbabababaababbabbbbbbbbbaaaaababbaabbbabbbaabaabaabbabaaabaaabbaaaabaaabaaaabbababaaabababbbabbabababbaaabbbababaabbbbbabbbbbabbbaaabbaaaabbaaaabaabaaaabababbbbabababaabbbbbbbbaaaabbabaababaabbaababaaababbbabbabbababbaaabaaabbbbbbabbabaaabbbbabbaaabababbbbaaaababbaabbbaabbbbbabbaabbbaabbaaababbbaabbaabaaaabbbabbababaaabbaabbbbaabbbbaabaaaabbbbbbaaabaaaabbbabbaaabbaaaababaaaabbabaaabbbbbbababaaabbbaaaabbbbaabbaabbbbaababbbbabbbaababbbbaaabbbbabbaabbbabababababaaaaabaaabaaaabaaababbbababaaaaaaaabbbaababbbbabbabbaababbaabababbbaababbaaaaaaabbaaababbbabaaaaabbabaaababaaaabbbbbaababbabaabbbaaaabbbbabbbabbbbaaaaabaaabaaabbaabaabbbaaabaaabaaabbabaaabaabaaabbbbbbabbaabbbabaaabaabbbbbbaabbaabbaaabaaabaaababbaaaabaaaabaaaabbbabaabaaabbbbabbbbbbbabaabbaaabaaababbaaababaabbaaabaabaaababbbbbbbbababbbbbaabaaabbbbabbaabaaabababbbabbbbbabaababaaabbaaabbbaaaaaabbbbbaabbbbaaaabaaaaaabaabaaabbabbbabbbbaaaaabaabbbabaaabbaabababbabaababaabbaaabbaaaabbbbbaaaabbbabababaaaaabaaaabaabaaaaaabbaaaababababbaaabbaabbababbbbbabbbaababbabbbabbbabaabbbabbaabbbaabbabbabbbaababaaabbbbabaaaaabbababbbbbbababbaabababaaabbababbaaaababababaabababaabababbbaabaabbaaabbabaaaaababbabbbbbbbabbbaaababbbaaabbaababaaababbaababbbbbaaabaabbabaababbbbaaababbbaaaaababbabababbbabbbbabbbbbabbbbbabbbbbaabaaaababaabbbabaababaaabbbaabbbaaaaabbbaaaaabbbbbabababbbabaabaaabaababaaabbaaababababbaaaabbabbaabaabababaaabbabbabaabbabaababbbbbaaaababbaaaabbbabbabbabbaaabaaaabbbaabbbbabbbaaabbbbabaabaaabbaaaabaaabaaabaabaaabbaabbbbbbbabbaabbbbabbbbbbbbbabbaababbbbaabaaabbaaaabbbaaabbbbababbaaabaababaaabbbbbbbababaabbaabbbbbbbbbaaaabbbabaabaabbaababaaabbabbbaaaaabbaaaaaaababbbaababbaabbbbaabbbbabbbaabbbaaaabbbaaabbbbaababbbabbbabbabbbaababbbbababbabbabbbbbbabaabbbbabbaababaababbbbaabaaaaaaabaabbabbabbbbabaabaabaabbbbaaababbabbbbabbaabaabbabbaaabaaaaaabaabbabbabbbbaabbbbabbbbbbbabbabbbbabbababbbbbabbbaabbabbbbbaabbbabaaabbbbaabbaaabbabaababbabbbabaaaaabbbaaabbaaaabaababababababbaaababaababbbaaabababbbbaaabbbbaaabaaabaababbbbbaaaaababbabbbabbbbaaaabaaaabbaaaaababbbaabaaaabbaaaaababaabababbaaababbaaabaaaabbbaaaabaaaabaabbaaaaaabaabbaabbaabbabaabbaaaabaabababaaabaabbabaaabbaaaaabbababbbbabbabaaabbbaaaababbababbbabababbababbbbbbaaababbbbaaaaaaaabbbbbbaaababbbaabbaabbbbababaaaaabbaaabbabbabaabbbabaababaaabbabbaaaaaabbababaaabbaabaaababababaaaabaaaababbabaaabbaaabbaabaaabaababaaaababbaabbbbbbabbbbababbaabababbaaaaabbaaabbabbbbbabaaabbabbbbaaaaababbaaaabbbababaaababaabbaabbbaabbbabbaabbbabaaaaaabbaaabaabbbaabaabaabababaaabbbababbbbaaaabbbbbbaaaaabbbbbbaabaaaabbabbbbabbbabbbbaabaaabbbaabbaaaaabbabbbbababbaababababaabaaaaabababaaabbabbbbbbbaabbaabbbaabbbbabbbabbabbaaaababbbaabbaabbbabaaabbbaabbbbbbaabbbaaabbabbbbbbaaaaabbabaabaabababaaabbbbabbaababaabbababbbaaabbbbabbbbababbbabbbaabbaaabbbabaaababaaababaaaaabbaabaaaaaababababaaaabbbaaaaaabbbaabababbbbabbbaaabbaaababaabaabbbbabbbbbabaabaabbabbabbabbabbaaabbbaaabbbabababaaabbaaabbabababaaaabbabbbbaabaaaaababababbaabababbaabababbaaabaaabbbbabaabbaaabaabbbbababbabaaaabaaabbbbbbbabaabbbabbbababbababababaaaaaaabaaaababaabbaaaabaabbbbbaabbaabaabaabbbbabaababbbbbabbbabbbaabbbbbbbaabaabaabaaabaaaaaabbabababaababbbbbbabaabaaabbabababbbaaabbbabbbbabbaaabbaaabbbabbbbbaabbaabbaabbbbabbabaaabaaaabaababbabbbbabbbbbabbbbaaaabbabbbabbbaabaababbaaabbaaabbaaabaaaabaaaaaaaaabaabaabababbbaababaabaaaaaababbbabaaaabbabbbbbbaaababaaaaaaaabbabbbaabaaabbaababaabbbbaababababaabbbaabbabaaaaabaaaabbabbbbaaaabbbabbababbaaaaaaababababbbaaaababaabbbbbbbaabaabbabaabbabaaaabaaaaaabbbabbaabbbaabaaaaabbbabbbbbbaaaaabaaabbbabbababababababbabbbabababaaabbabaaabbaabaababaaabbbaabbaaaabaabababbbabbbabbbbababaababaaababbbababbaaaababbaaaaabbabbbbbaaaaabaaababbbaaaaaabababbbababaaabbaaaabbbbabbaaabbaaababaababababaaaabbabaaaaabbaabaabbbbbabbbabaaaabaaaabbbaabaabbbbaaabaabbbabaabbabababbaabbababbabbaaaabababaababaabbababaabbaaaababababbaaabbbbbabbaabbaababbbababbbaabaaaaaaabbaaaaaababaabbbabaaabbbbbaabbbbaaaaabaaabbbababbbbbabaabbbbbaaaaababaabaaabbbabaabaaabbbbbabaabbabbbbaaaaaaaaaaaabbbbbbabbbbaaabbbbbabbaababbbaaaaabbaabbbaabaaababbabaabbabaabbabaabbabaaabbbaaaabbababaabbbbbbbabaabbbbaaaabbbaaababbabaabbbbbabbbababbbbbaabaababbbabbaabaaaabbbbbabaaabaabbbbabbbaaabaabbababbbaaaaaabbabbbbbbaaaaaaabbabbaaaaabababbaabbabaabbaaaaaabaaaaaabbbbbbabaabaababbbbbabaaaaabaabbbababbabbaabbabaaaaaaaabbabababaaababbbaaaabaaaabbbbaababababaababbaabbabaabaaabbaaaababbaaaababbbbabbbbbbbaaaababbbbaabbbabbbbabbaabaabaabbabbbabaababbbaabbaaabbabbabbaabbaaabbabbbbaabbaaaabbbbbabaabaaabaababaababaaabababaababbabbbabababbbabababbbbbbbbbbaabbbbbababbbaaabbbabbaaaababbbaabbbbbbabbaaaaaababbabaaaaabbbaaabaaabbabbabbaabbaabbbbbabaabababbaabaaababbbaaabbaaaaaabbabaaaababbbabbbaabbabbabbaabaababababaabbbabbabaaabbbbabbbaababbbbabbbababaaabbabbabaababbbabaaaabbbaabbaabaaabbbbbaaaabbbaabbbaaaababbaabbaaaabababbababbbabaabbbbabaaabaaaabaabbabaabbaaabababaaaaabbbbbbababbbbbababaaaaaabbaabaaaaabaabbbbbaaabbaabaaaababababbbaaababababbaaaabaaaaaaaaaabbbbbaabbabbbabbbbaaaababbabaababababbabbaabbbbbaabbabbbaaaabaabaabaabbababbbabbbbbbbababaabbabbbabbbaaabaabbabaabbabababbabbaaabaaaabbbbbaaaabaaaaaaaabbbabbaabbbaaabbbbaabbaabaaababaabaabbbaababaaaaaabaabaaabbabaaabbaabbababbbbbaaabbbaababababaaaaababbbbbaaabababbaaabaabbbabaabbaaabbaaabababbbabbaaabbaababaabaababaabbabbabaabababbabbaaabbbabbabbbabbbaaaaababbababbbabaabbbabbaaaaabaaaabbaabbbbaaaabbababbaabaaababaaabbbbabaabbabaabaabbabababaaabbabaabbaaabaaabbbabaabbaaaababbbaaabbbbaaabaaabbbbabbabaababababbaabaababbabaabbbbaabaaaaaabbaaaaabbbaaaabbbbbababbbaaababbbaaabbabaaaaabbbbabababababbbbaabaaabbaabaaaabbbbbbaabbaabbbbaababbbaababaaababbbababbabaaabaabaaabababbabbaabbaabaabbbaababababbbabababbaaaabbaabbbbaaabbabbbababababbabbbbbbbbabbbaabaababbbbaabbabbbbbaaabbbaaabbaabbabbabbbabbaaaaaabaaaaaabaaaabbabaaabaabbabaababbbbbabaaaabbbaabababaabbabaabbabaaababbbabbbbbbbaabaabbaaabaabaababababaabbbaaabaaaaaabbbbbabaaaababababababbabbbabbaabbbabbbbababbaaaaabaaabbabbaababbbabbbbaaaabababaababbbbabababaabbbbaaabbbbabbaababbaaaaabaabbbbbabbbbaaaaaababbbbaaaaabaabababbaaababaaabbbbaaabaabbbbaaababbbbbbabaaaaabbaababababbbbbabbbbaaaaaabbbaaababaaaababbaababbbaaabaaaabbababbbababbbbbbaaabbbbbaabbaaabbbabaaabaaaaaabbbaabbbabbaabaaaaabababaababbabaaaaaaaababbaaabbbaaaabaaabbbbabbbbaabaaaabbbabbaabaaababaabaaabbbaabababaabababaababbbaabbbbaabababbbabbbabaaabbabbaaababaaaaaabbbaaababbabbbbabbababbaaaabbabbbabaabbbbbaababaaabaabbabaaabaaaababbbbaabaaaabbbbbbabbbbaabaababbbbaabbbaaaabbababbaaabaaaaababbaaaabbbaabbaabbabbbabaabaaabbbabaaaaaabbaabbbabaababbbbabbaaabaabbaabaabbaabbbbaaabbbbaaaaaababaaabaaabbabbabaabababaaabaaaabbbbabaabbaabbbbbbbabaaabaaaaaaaabbaabbaababaaaaabbaaababaaaabbbaaabbaaabbbbabbababaabbaaaabbbbabbbbbaabaabbbaababbababaaaabaabbbababbaaaaababbaaaaababbaabbaabbabaaabbabaabaaababaaaaaabbaaaabbbabbbbaaaaaaabbbaabbaaaabbbbaabaaaabbaaabaaaaabbaaabaaabbbabbbaabbbababaaabbaabaaaaabbbababbabbabbbbabbbabbaaaaaaabbbaaaaaaababbabbaaaaabbaabbbbaaaaaaaaabbababaabababbbabaaaaaabbabaaaaabaaabaaaabbabaabaaaabbbbabbaabababbababaabbbaababaaaaabbbbbabaabbaaaaabbabbbbaaabbbbaaaabbabbaaabbaaabbbabbabbaabaabaaaababaabababbbbbaaabbbaaabababaababaaabaaabbbababbabaaaaaaaabaaabaaabbabaabbaaaabbabbbbabbbbabaaabaaabbaabbbbbabaababaaabaaabbabbbaaaaaaabaaaaaaabbbabbbaaabbabbbbaaaabaaaaaabbaabbbaabaaabbbbbaaaaaabababbaaaaababababaaababbbabbabaaaabbbbbbbababbabbbbababaabbabbabaabbaababbbabaabbabbabbabbaabaabbaabbbbaabbaabbabbbaabbbbbbabbbabababbababaabbbbaababaaabbababbabaabbbaabaaaaaabbababbbbababbbbbaabaaabbabbabbaabaaabaababaaababbababaabaabaaababaababaabbbbbbbbabbaaaaabbababaaababaaaabbabbabbbababbabbaabbabaaaaaaabbbbbbbaaabbbaababaabbaababbaaabbbabbabbbbaabbbabbbbabbababbaaaaaaabbbbabbababbaaabaaabbababaaaaabbabaaaabbaaaaabababbabaaabaababaaaaaaabbaabbbbbaaaabbbbabbbbbaabbabaaababaabbbaabbaabbabbababbaabbbabbaabbaaaaabbaaababbaabababababbaabbabaaaabaabbaababbabbaabbbbbabaaabbbaaabaaaabbabbbababbbaababbabbabaabaaabaaaabaaaabbbbaaababbbbbbbababaaabbbaababbaaaabaaaaaaabbabbabaaabaaabbabaabaaabbaaabbaabbbaabbbbabbbabbbabbaaaaabbbaaaaabaaabaaabbaaaabbaabbbaaabbbaaabababaabbbbbbaabbbbbabaaaaabbbbbbabaababaaaaabbaaaaabbabaabbaabbbbabbaaaaabbabbbabbbbababaaaabababbbbabaabbababaaaabaabbbaaaaabbbabaaabbbababaaabaaababbabbbaaababbaabababaaaaabbbbbbaaabbbaaabaabbbabbbabbbaabaabbabbababbaaabbaaabbaabababbabbbbaabbbaababbabbbaaabaaaaabbababbbbababaaabaaaaabbabbbaaaaaaaabbbaabababbababababababbbabaababaabbabaabbbbbbabbbabbbbbbaabbbbbbbbaaabbaaabaaabaabbbbbaabbabababbaaaaaaababbbbbbbaabbabaabbbababaaaabbabbabbbaaaaabbaabbbbabbbaaaaaabaababbabaaaabbaaaabbaabbaababaabaabbababbaaaaaabaaaaabbaabbbaaaaabababbabbabbabbbbaaababbaaabbababaabbbabaabbbabaaabaabaaabaaabaabbbababbabbbbbabbbaaabababbbabaabbaabaaaabaabbabababbbaaababbbbabababbbabbabababbbbaabbbaabaaaabbabaaababaabaaabaabbbbababbbbabbaaaaaaaababbabaabaabababbbaabaabbbbababaaaababaaabbabaabbbbaaabbaababbabbababaabbbbbbbbbbbaaabaaabbbaabbaabbaabbbaaababbbbabbbabbbaababaabaabaaaaaaaabbaaaaabaaaaaaabbabbbbabbbbababbabaabababaababbaababbbaaabababaabbababaabbbbbbabbbaaabaaaaabbbababaabbabaaabbabbbabaabbaabbbbbaaabbbbabaaaabbbbbababaabaaabaabbaaaabbaabbbabbbaaabbbaaaabbbbbbabbaabbbabaabbabbaabaaabaaaabaaaabbaaaabbbbaaababbbbbabbbaabaaababbbaabaababbbaaaabaaaaabbbabbabaaabaaabbbabbbbaaaabbbbbbabbbaaaabbaabbbbbababbabbbaaabbbbbabbbbabaaabaabbababbbababbabbabaabbabbabbbaabbbaaaaaaabbbbabbbbbabaabaabaaaabbabaaaaaabbbbabaabbaaaabbabaabbbaabababbaabababaabbabbbaabbaabaaaaaaabbbaabbababaaaabababbabbbbbbaaabbbbbaababbabbabbaabbaaaaababbbaababaaababaaabbabbabbabbbbbabababbbbbbababbbaaabbabaabbbabbababababbababbbabaabbbaaabbbbabbabaabbaabaaaaaaabbbbaababaabababaabbabbbbaaabaabaabbabaababaaaababbaabbbaaabaaababaaaaaaabbbaabbaabbbabaaaabbbabbbaabbbbbbabababbbbbaaababbabbbbbbaababaabbbbaababbbaababaaaaabbaaabbaabbbbaabaaababbbbabbabbbbbbaabaabababababbabbaabaabaaabbbbaaaaabbaabbbaabbbaaaababbabaaabbbabaabbbbbaababababbabbabbabaababbabaabaabbabbaaabbbaabbbaaaaabbababbababbbbababbbaabbbabbababaabbbbbbbbbabbbbbbbbbbabbabaabbabaaabaabbbbabaababbbbaabaaabbbaabbaabbaabaabaabaaaaaabaaabbabaaaabaaabababaababaabbbbbabaabaabbbaabaabaababaabaaaabbabbbbbbbabbababaaabbbaaabaabaabbbbaaabbbababbbbbbaabbaaabbaabaabaabababbbabbaababbbabaabbabbabbbaabbbaaaabaabababaabaabbabbababbabbaaaabababbbbbbaaabbbbaabaabbaaaaabaabaaabbabbbbbabbbbaababaaababbabbbbbbaabbaababbbbbabaaaaaaaabbbbbaaaaaaaabbbabbbbbbaabaabbbbbaaaabaaaababbabaabbaaabbababbabababbbbabababababbbaabbaabaabbbaaaabbbaaabbabbaabbbbbbbabbbbabbbbbbaababbabbbbabaabbabbaabaaaaabaaaaaabaabbabaabbabaaabbbbababaaababaaabbbbaaaaababaabaaabaaaababababaabaaaaaaaababbaabbbaaaabaabbbaaabbbaaaabbaaabaababbaaabbbaaababbabbbbbbaaaaaaabaaaabbbbababbabaabbaaaabbbaabbaababbababbbbbbbaabaaaabbabaaabbbabbbabababbaabbababbaaaaabbbbaabaabbabbabbbbabbabbbabbaababaaaaaabbbaabbabbbaabbbabbaaaababaababbabaaababaaababbbbbabbaabbababbbbbaaaaabaaabbbbaabbaaaabbaaaaaaabbabbbababbbabaabbbaabaaaabaaabbbababbaaababbbbabaaabbbabbbababbaabaaababaaaaaaaababaabbbaaaaaabaaabbaaaaaaabaabaabbbbabbabbaaabbbbaabbbabbaaaabaaaababbbbaabbbbbabaaaabbabababbbababbaabaaaabbaaabbaabbabaaabbaaaaababbaababbabaabaaaabbbaabbaaaababbbbaaababababbbbabaaaaabbabbabbbabbaabbaabbaabbababaaaaabaabbbbabbbabbbbabaaabbaaabaabaaabaabbabbbbbbbaaabbbbbbaaaaaaaaaaaababbbbbabbaaabbbabbbabbaabaaaababbabaabababababaaaaaababbaabaabbaabbaabaabbababaababbaaabbbaababbaaababaaababbbbaabbaabbaaaaaabbaaabbbbaababbbbaababbbbbababaabbabbabbbbbaaaabaaaabaabbabbbbaaaaaaaaaabbaaabaaaabaabbbababaaabbbaababaaaabbbbbababbaabaabababbaabbabbaaababbbbbaababbabbabbaabbbbabbbbbbbabbbbbbbabaabbabbbabbbbababababbaaabaabbbabaabbaababaaabbbaaaabbbaaaaaabbaababaababbbbbaaaaabbaaabbbbbbbaaabaabbabbbabbbbbbabbbaabbbbabbaaaaabaababbaaabbbbbaabaabaabaaabbababababbabaaaabbbbbabaababbbabbabbaabbaaaabbabbbabbabbbbbabaabaaababbbbbababbbbabbaabbababaabbaaababbbbaaaabababbabbbbababbaaabaaaabaababbbabaaabbabbaabbaaaaabbaabaabababaaaaaabbaaaaabbbbaabaaabbbabbbbbabbbabbabbaaaaaaabbbbbbaabaaaaaabbaabbabbaaabbbaabbbbbbbbbababbabbbabbbaabbbaabbaabaabababbbbabbbbbaaababbababaabbbabbabbbbbaaabbbaabaababbbbbabbababbbabbaabbbbbbabbaabbbbaaaaabbbabbbaaaababbaaaabbabbbabbaabbabbabbaaabbabbbbbbabbbbababbbbbbabbbababbaaabbabaabbaababbbaabaabbaababbbbbbaabaaaaaaaaaaaaaaabbabababbabaabbbbbaabbaaabbabbbabaaababbabbbabbbaabaababbaaaaaabaabababaaababaaaabbababbaababbabaabbabaaabbaaaabbabbbabbbbbaabababbaaaabbbbabbaaabbbababaababaaabaabaaabababbbaaaaabaaababbabbbbbbaaabbaaababbbabbbbabbaabbbbabbaabbbbbbaaaaaababbabbaabbbbbbbbaaabaabaabaabaaabbbbaabaabaabbaabaaabbaabbaaaabaaabbaaabaababbaabbbaababbaaabbaaabaaaaaabaabaababbbaabababababbbbbabbbbbbbbaabbbababbbbbaaaaabbbbbaaabbaaaababbaaabbbaaaabaaabbabbbabaabababbbabbaaaaaaaaabaaabbbaabaaabbaaabaaaababbabaabaaaaabbbaabbbaabbaaaaaaaaaaaabbbbbaabbbbbbbabaaabaaabbbaabbbababaabbabbabaabbababaababababbbbbbababbabaabbbbaaabbbaabaaaaaabbbaabaabbaabbaabaababaaabbaabaaababaaabbbabaaaaabababbaabababbbaabaabbaabbbbabbaabbababaaaaabaabbaabbbaaaaabbababaabbaabaabbaaabbabbbbabbbbbbbabbbababbbbaababbabaaaaaabbabababaabbbabaabaaaaaaabaaabaaabbabaaaaabaaaabbbbbbabaabaaababababbaaabbababaabbbbbbaaabaabbbbababbaaabbbbbababaabbabaaaabbbaaabaabbbaaaabbaaaaabaaabaabbbbbbbaaabbaaabbbbabbaaaabbbbbbbbbabbbbbbabbbababaabababbbbbababbabbbabbaababbbabaabbbaabbbbbbbaabbabbbbaaaaaaabbbbbbbaabaaaabbababbbaabbbbbbbabbbbabaaabbaaabbabbaaabbabaabaaabababbababbaaaabaaabbaaaababaaaabaaaabaabaabbabbbbababbbbaaaababbbbbbbaababbbaaaabbaaaabababbabaababbbbabbbaaabaabbbbbbabbbbbaaabbbaaaaabaaaaaabbabbbaabaaabbbbbababaaaaabbbaabbbabaabbbabbbbbaaabbaabaabbbaaaaabbbabababbbaabbbbbbbbbbaaabbabbbabbabbbaabbababbababbbabbbaabaaaabaaabaaabbbbabbaabbabaaabaabbaabaabababbbaaabbbbbbaabbaabaabaabaaabbaaabbbbbabaaaabbabbaaaaabbbabaabbbbbabbbbbbbbbbbbbaababaaabbbbababbbbbbaaabaabababbbbbbbbbabbaabbbabbbbaabbbbbabbbbaaaaaaababbababaabbaaaababbbaaaabbabababbaabbbbbbabbbaabbbbababbaabbaabaabbabbaaaabababaaaaaababaabbabbaaaaaababbbaaaabbaaabbbaaaaaabaaabbaaabbbbaababaaaaabbbaabababbbbababbaabbbaabbbabaaababaabbbabbabbaaababbbabbbabbaabbbbbbbbbabaaabbaaaabbaabbbaaabababbabaaabbaaabbaaaaaaabbbbaaaaabaababaaabaaaaabbbababbaabbbbbabbbbabbababbbabbbbaabbabbababbbbabaaaabbabbaababbabbbabbbabbababbbbbbbabababbbabbabaabbabaaaaaaaaaabaaaaabbabbbbabbaabbbbabaabaababbbabbababbaaaaaabbabbbbbababbababaaabbbaabbaaabbbaabaabbbaaaaababababbaabbbbbbaabaaaabaabbabbababaabaabbbbaabababbabbabbbabbbbbbabbbbbababaaaabbbbababaabaaaabbbaaabbabbbbbabbaaaabbaabbaababaabbbbbbbabbbbbbabaaabaabbbbbaaabbabaaaabbaabababbbbbbbbbaabaabaabbbbbabaaaaaabbbabaaabaabbabababbabbbababbababaaabaabbaabaabbabbbabbaaabbbaaaaababaababbaabbabbbabaabbababbaaabaaabababaabbbbaaababbaaaababaaabbaababbabbabbababaabbbbbbbbababaababaabbbababbababbaaabbbabbababbbbbbababaababaaabbaaaaababbaababababbaaaabbbabbbababbaaaaabbababbaabaabbbabbbbaabaabbaaaabbaabbbabaabbaaaabbbabaabaaabbbbabbaabaaababaaaabaaaaabaaabbaabbaabaaabbbabaaaabababbabaabaababbbaaababbbbaabbaabaaabbbbaabbabaaabbabbbbaaabbbaabaababbaaababbaaaaabaaabbbbabbbbabbbaabaaabbbaabaaaabbababaabaabbbbbababaababbbbaaaaaaababbbaaaababbababaaabbabbabbbabbaaaabaabaabbabbbbbababaaabbabbbbabaabbabbabbabababbbbaabaaabaaaabbabbbababaabbaabbababaabbbaabababbabbaaaabaaabbaaaabbaabbbabbbbbaabbaabaabaababbabbbaabaabababababbbbbaababaaaaaaaaaaaabaaabbbaabaaaabababbbbabaabbaabbbbaaabaabbaabaaabbaaabbaaaabaaaaaaababaaabbaaabaabbabbbbbaabababbabbaaaabbaaabbaaaaabbabaabbaabaaaabaabbbbbaababbabbabbaaabaaabbbabbbbbabbababbabbaabababbaabbbbaaababaaaabbbaaabbabbbbbbbbaabbabababaabbaaabbbbaaabaaabaabbbaaaaaaabaabaabbbaaaaaaaaabbbaaaaaabbbababaabaaabbbaaabaaabaabababaaaaababbbaaaaaaaaabaabbbaababbbabaababaaaababbaaabbbaabbbbbaaaabbabbaabaababbaabbbababbaaaaaaababbbaababaaababababaabbbabbabaaabaaabbaabaaababaabbbabaabaababbabaabaababbabbbabaaabababaabbaaaabaababbbabbbabaaaababbbbabbbabbbaabaabaaabaaaaababbabbababbbbbbbaababbbaabbbbabaababbbaabaababaababbabaabbbbbbbbabaabbabbbbaababbabbaabbbbaabbbabaabbabbabbaaaaaaabbbabbbabbaabaabbbaabaabaabbbbaabaabbaabaabbbbbbbbbabaaabbbbbabbaaaababbabbaabbbbabaabaabaaaababbbbbbbbababbbbabababbaabbabbaaaabaabbbbbaabbaabbabababbaabbbabaabbaaaaababbbabbbabbbaaaaababbbaaaaaabbabaabbaabbababbabaabbaabaaaaaaaaabbbaabababbaaaabaaabaaabbabaabaababbbbaabbaabaaabababbabbabababbbabbbbaababaababbbaabababbababaabbaabbbbbbbaabbabaabbbbaaaabbbaababababbbaaaababaabaaabababaaababbbaababaaaababbaaabbabaabbbbbabbbaabbabbabbaaaabbbabbbbbaaabbbabbaabbaabbaababbbaaaaaaabbabbbabbaabaabaabaaaabaababbbbbbbbabbabaaabbabbaaabbababbbaaaabbbbbbbbbbaababbabaabababbbbabbaaaaabababbaaaabaaaaaaabbaabababbbaabbabababbaaaabbabbabbbbbabbabbabaaabbbbbbabababbbbbaabaaaaabbbbaabbababbbbbbaabbbbaaaaaababbaabbabababaaabbbbbbaabbabbbbbabbaaabaaabbaabbbabaaaabbaababbabbaabaaabaabaabbaaaaaabbbbaaaabbababbbaabaababbbabaaaabbbabbbaabaaabaabbaabaababbbaabbbbbbbbbbababbbbbaababababbbaaaaaaabbabbaabbabbaaabbbbbbaaabaabaaaabbbabbbbabaabaaababaababaaabbbbbbbbbababaaaaabbbabaaaababbbabaaabbbaaaabbbbbbbaabbabbbabbabbbabababbabaaabaaaaaabaabbbabbbabababaabbabbabaabababaaaaaabaaaababaaabbbabbbbbaabaababababaabaaaaaabaaababbbbbaaaabbbababbabbbbabaaabbabaaabaaaaaaaabbabaabbbbabbabaaaaabbaababbbaaaabaaaaaabaaabbbbabbaabaaabbbbabbbbaabbbbaabaaaabaaabbabbabbabbbbabbabbbaabbbbbbbabbabaabbbabbaaabbabbbbbabaaaabbaaaababaaaaaabababbaaaaabaabababbbbabbbbbbaabaababaaabbaaaababbaaabbbaabbbbabbaaaababbababbbbbbaabababbbaaabaaabaabbabaabbbabaaababbaabaaaaababaabababbbbbbaaaabbabbbababbabbbbabbbabbbaabaabbbbabbabbabbbaaabaaabbbbbbaabaababbbaaabbaabaabaaabaaabbabbabbbabaabbbbbbaabbaababbabbaaababbabbabaaabbbbaaabbaabbbbbaabbbababbabaabbbbababbbbbaaabaabaaabaababaabaabbbbaaaabaabbaaaabaabbababbaababaabbabbbbaaaaababaabbbabaabbaaabbbabbbbababaaaabbaaababbababababbaababbabaaaabbaaabbbaaababaabbaabaabaababbaababbabbaaabaaaabbaabbaababababaabbbabaabbbaaabbabaaabbababaaaaaababbabbaabbabaababbbaababaabaaabaaababaaabababbabaabbbbaaaaaaaaabbbabbabbabbaabbbaabbaabbbbbaabbaabbabaaabbbaaaabbabbaabbaabbaababbbbbabbabbbabaababababaabbaabbabababbbababaaaaaaaabaaaabbabbaaabbabbbbabbbbabbaabbbbaaabbbabbaaaabbbaaaabaabaabaaababababababaabababbbbaaaaaaaababababaaaaaaabbbbabaaababbaaaabaabaaaabbbabaababbabbbaabaababaabbabaaabaabaaaabbabababbaaaabbbabababbbbabaaaaaabbaaabaaaaabababaabbabaaababbabaabaaababbababbbaaaaabaababbbbbbaabbaabaabbaaaaababbaabbaabbbbbaaabababbaaabbabaaaabbabbaaaaaaabaabaabbbbbabaaaaaaabbbbabaabbbaabbbaaaababaabbababbbaaabbabbabbbabaaaabbbbabbababbbaaabbbaabbbbbbaabbbbbbabababbbabbbabaaabababbaabbabaabbbabaaabaaabaabbbbaabaaabbabaaaaaabbbbbabaaabbabaabbbbbabaaaaaabaaaaabaaaaaabbbbbabbbbbbbabaabbaababaabaabaaaabbabaaaaabaabbbababbbbabbbababaaabbbaaaaaabbbaababbbbbbbbbaaaabbbbabaaaaaaaabbbababaabbbaaabaabbabaaababaaabaabbbaabbbabbabaaabbbaabbabaaabbaabbaaaabbbabbbaaaaabbabaabababbbbbaaaaabbaabbbaabaababababaabbabaaababaabaabbbaaaabbaabababbababaaaababaaabbabbbbbbabbbbbbababaabbaaaaaabbababbbabaaabbbabbbbbababbabababababbbbaaabbbaaaababbabaababaaaabbbbaabaaababaabaabbaabaabaababaaababaabababbbbaabaaaabababbbbbbabaaaabbbbbbabaabbaaabbbbbbababbabaababaababaabbabaabababbbbabbabbabbbabaaaaabbaababbbbabbaababababbabaaabbaabbaaabbbaabbbaabbbabbbbbaabaababaabaababbbabbbabbaaaaabbabbaaabbababaabbabbabababaabbabaabbbababaababaaabaaaabbaabbbaaabaaaaabbaabababaaaababbbababaabbabaabaabbbaaaababbaaabaaaaababbbbbabbabbaabbbaaaababaabbbaabababbbabaabbaabbbbaabbbbbbabaabaababaaaaabababbaabaababbbbaaaabbaaababbbaabbbabbababbbababbbbbaaabbbabbbbabbbaaabbaabababbababaabbbbaabbabbbabbbbbaaabbbababababbabaababbabbbabbbaaabaaabaabababaababbaabbaabababbbabbbbabbaababbaaabbbaaaabbaabbbaabbbbabbbbbbababaabaabaaabbaaaabbaabbbaabbbbabbabbbbbbbaababbababbabbaaabbababaaaaaaaabbbbaabaaaabbbabbababbbababbabaaabaaabbaaabbbababbbbbbbbabaabbbabbaabaaabbbbbbababbbbaaabaaababbababbaaabbbaaabababbbaaaabbbbabbababbabbaaaabbaaaabbbaaabbaabaabaabbbabbbaabbbbabaabaabbbaababbabbbaaaabababbbbbabaabbaabbabbababaabaaaaabbbbaababaabababbaabbbbbbbaabaaaaabaaabbbbaabbabbbbaabbaababbabbbaaaabaabbbbaabbaaaaababbbaabaabbaaaabbbbaabaabbabaabababbbababbabaaaabbaabbbbabaaaabbbabbbabaabbabbbbbaabaaabbbbabbaaaaabbaabbabaaaaabbbabababbbbbaaaabababbaabbaaaaabbbabbbaaaaaaabababbbaaabaaaabbbabbababababaaaaabaababbabbbbaabaabbbababbaaaabbaaaabbaaaabbbbbbbbbaaaabababbbbbababaaabaaababbbbaaaaaaaabaabbabbbbbbbbaabaaabbbaabbbaababbababaabaaabbbaaabbabbabaabababaabbaaabbababbaabbabbaaabaaaababbbaaaaaabaabbaabbaaabbabbaabaabbbbbababaaabbbaabaababbaabaaabaabaaaaabbaaabaabaababaabbbbaabbabbaabbbbbababaaaabbbbbabaaabbaaabbaaaabaaabbaabaabbbbbabababbbabaabaaababaaabaaaabbbbbbbbaaaaabaaabaaabbbbabbabbaabaabaaaaabbaabbabaaaaabbabbbaaaaaaaaaabbababaaababbabbbbbbaaaabaababbabaaabbbabbabbaabbbbaaabbbbbaaabaaaabaaabababbbaabbbbaababbabbbaaabababaaaababbabbbbbbbababbbbaaabbaaababbaabbbbabbabbabbabbbaaababbabbabababaaaabababaaababaaabaabbbabbabaaaabbbabababaabaababababbbabbaaabaabbbaabababbaaaaabaabbabaaabbbababbbabbaaaabbabaaababbababaababbbbabaaabbaaabaabbabbbaaaaabaaabaaaaaabaabbbbaabbbabbabbbbbabaabaaabaaabaaaaabbbaaabbaabbbaaaababbaaabaaabaabaabaaaaaabbaaaaabaaababbababaaaabbbabbbbbaaabbaaaabbabaaaaaaababaaaabaaaaaaaaaaaaaaaabaaaaaabbbbbbbbbaabaabaabaaaabababbbabbaabbbaabbabaaabbbbaabbabbaaabbabaabbbbaabbbaaabaaaaabaabababababbaaabaaaabaabbbabbabababbabbbaababaababbbbaaaabbbababbbbbaaaaababababbbbbbbaabbaabbababaaabbabbaababaabaaabbabbaaabbaaaabbaabaabababbaabbaababababababbababbbaaabaaaabaaaabbababaaababbbabaaabaaababbabbbaaaababbaabaabbabbbabaaaaaabbbabbbabbaaabbabbbababaababbabaaaababbbaaaabaabaaaabbbbbaaabbbaabaababbabbbbbbabaaaabaabaaababbaaaaabbabbaababbbaaabbbabbabaabbaaabbaababbbbaaaabaabababaaaabbbbaabaabbabbaabbabbbaaabbbbaabbabaabbaaaaababbaaaabaaabbaabaabbaababbaabbababbaaaababbaabaabbbaabbabbbbababababbabbaabbbbabbbaababaabbbbbbababbbbbabbabaabaabaababbaabaaaabbaaabaaabbabaaabbbababbbbabbbaaaaaaababbabababaabbbaaaaabaaabbaaababbaaaaabbaaabaaabbabbaabbbbbabbabbaaabbbaabbabbabababbbbbbaabbbababbbbbaababaabbbbbabaaaababaaaaabaababbbbaaabbbbaabbbbabbbbbababbaabbbaabaabbbabbabaabbababbbbbbbabbbbababbbabaaaabbbbabbaaabbaaabaabaaababbbabaabbaaabaabbbaaababbaabbabbbbbbabbbabbaaabbabababbababbaabaaaaabbabbbbaabbbbbbaaabbabbbbbbaaababbaabbababbbbaabbbababaababbbaaaaabbaabaabaabbbbabaabbbbbbababbbbabbbababaabbbbbaaababababbbabbbbbabbbabaaaabbababaaabaabbbaabababaaabaaaabaababbbaabbbbabbabbbbbaabbbaabbbabbabbabbbbabbabaabbbabbabaabaabbabbbbbaabbbaabbbbaabaaabaaaabbabababbabaaaaabbbbaaabbbbabbabbbbbbbbbababaaaaababaabaabbbbbbbbababbabbbaabaaabbabaabaaababbbbaabbaaaaabaabaabbabbbbbbbbaaabababbabbabaababaaaabaaabbabbbbbbabbbaabbbbbaabaaabaababaaaabbbabbaaababbbbabbbbaababbbbbabababbbbbbbbaaabbbaaaabaabababababbbabaabbabbabbbbaaaabbbabbaaaaaabaaaabaababbbabababaabaabbaaabaaababbaabbababbabaabaaababbaaaaaabbbabaaaaababbaaababababbbbbabbaaaaaaabaabbbaaaabababbbbbabbbbbbabaaababaabbaabbbbbbaaaaabaaabbbaaababababaabaabbaabbbbaabaabbbbabbbaabaaaabbaabaabbbabbbaabbbbaabbbaababbaaabaaaaabbbaabbbaaaabbbbbababbbbbaabbaabaaabbaababaabaabbbbabbbbaabbabbabababbaabaabbaababaababbbabaaaabbbaaaabaaaababbabaababbbbbaaabbbaaabbbbabbaabbbabbabbbbabbbbaaaabbbbaabbabbaaabbabbbbbbbbaabaaaabbaabbbbaabbbabbbaabbababbbbbabbabbbbbbbaaaaabababaababbaababbbabaaaabaabbaabaababaabbbbabbabaabbbbaaaabbabababaababbaabbbbababbabbbbaaabbaaabaaaaaaaaaaabbaabbabaabbbaabbbaabaabbabaabbbbbbbaaabaabaaabbaababbbbaabbbbbabbaabbbbbaaaaabbbbbaaaabababbbaabbbaaaabbbabbabaabaabaaabbaaababaaabbaababaababaabaaabaabbabaabbabbabbabaaaaabbbababababaaaabbbbaabaababbabaaaabaaaabbaaabbbabababaabbbbabaabbbbbaaaaabbbaabbbbabaaaabbaaaabaaaabababaaaabbbabbabaaaaabaaaaababbababbbbbbabaaaaabbbaababaaaaaaababaaaabbbbbaabbababbaabaaababbbabbabbbaababaaaaabaabaabaaabaabaabaababbbbbbbbbbbabbabbbabbbaabbaaabbbabbaaaabaaaaaababaababaaababbbbbaabaaabbbaaaabbbbaabaabaaaababaaaababbbbaaabbbabbbaabbababbabbbabbbaabbbbaaaabbabababbabbbabbabbbbabbaabaabaababbbbaaabaaaaabbaababbaaaabbaaababbababbbbbabaabbaabaaaaababbaabaaabaabbbbabbbbabaaabbaaaaaaabaabbbbabaabaabbaabaababbbabbabbbbbaaaabbbbaaabbababbbbaabbbaaabababbaaabaaabbabaababbbababbabbaaabbbbaaabbbaabbabbabbababbabaabbaabbabbabaaabababaaaaaaaaabaaabbabbabaaabaabbabbabbbbbaaabbaaabbbbaabbbbbbbababbaabbabbabbabbaababbaababbbababbbbbababbbbbbbaaaaaabaaaaabbbaababababbbbbaabbabaaababbbaabaaaaaabbaaabaabbaaaaabaabbbabaaababaaabaaabbababbabbaabbababaaaaabbaaabbbbababbababbbaaabaaaaaabaaaaabbbaaaabababbbaaaabaaabbaaabaaaabbbbbabbbbbbbbbaaabbaabbbbaaabbbaabbabbbbbabbabbaaaaaababbaabbbabababbbbaaabaaabaababaabbbbababbbbabbaabbaababaabbbbbbaabbbaaabababbbabababaabaaaaaaaabbbbbababaaabbaabbabbbbbabaaabbaaaabbbbabaabaaabaaabbbabbbabaabbbabbabbbaabaabbbaabbabbbbabbaabaaaabbababbbabaaaabbbabaaaabbbbbbaaabaabaaaababbbbbbaaaabaaabaaabaaababbbaabbaaaaaabaaaabaaaabbaaaabbaabbbaababbabaabbbabbbbbbbaaabbbabbaaabababbbbaabbbabbbaaabbaaaabbabaaababababbaabaabaabbaaabbbabbbbaabaaabbbababbbbbaabbabaaaaaaabaaaaaaabbaabbabaabbaabbaabbaabbbbaaabbbbaabbaabbbabbababbbabbbbbbabbbaabaaaaaaaabbaaaabbabbbaabaababbbbabbbaaababbbabbbaaabaabbbbabbbbbbbaaaabbabbbaababbaaabababbbaaaaabaaaabbbbbbabbaabaaabbabaabababaaabbbaaaabbbbaabbaabbbaaaabbabbabaabaabababbbbbbbabaabaababaaaaaaabbabbbbbaaaaaaabbbbbbbbbabbbbabbaabaabbbbbbbbbaaabbaaaabbaaaabbbaaabbaaababbaaaabaaabbbabbaaaabbbabbbbbbabbbaaabaabbabaaaabababbbbabaaaabbbababbabbabbaababbaaaaaabbbbaabaaaabbabbaaaaaaaabaaaaaaababbaabaaabbaababbbbaabbabaabbbaababababbabbaabbababbbaabbbabaabbaabaababaaaaababaababaabaaabaaabababaaaaabaababbbabababbaaaabbaaaabbbaabaaaabaababaaababbbbabbaaaaabbbababbbbaaaabbbbbbaababaaaaababbbbaaaabaaaaabaaaabbbbaabbbbaaabababaaababbbaaabaabaaabaaaaabbbaabaaaababbbbbbabbbaabbababababaabaabbbaabaabbaabaaabbaaabaabbbabbbbbaaaabbaaababaaaabababaaabbbabaaaabbaaaababbaaabbbbbaaabbaabbabababaaaaaaaabbaabbbbbbabbbaabaaaabbbabbaababbababaaaaabaaababaabbbaaababbbaabaaaabbabbbbbaaabaabaabbabaabababaababababaababbbaaaabbaababbaaabaaabaaabaababaabababbbaabbababaaababbabaaababbabbbabaaaabbbaabbaabaabaaaaabaaaaaabbbaabbbbababbbbbaaababaababaabababbbbbabbaabaabaabaabaabbbabababbabaabaaabbaabbbbaaabbbbaabbbabaabaabaabbaaababbabbbabbababababbabbaabbbabbaabbaabaaaaabbbababbbaaabbaaabaabbbbbbbbbabbababababbbaababbbaaababbabaabababbaababbaaabbaabaabaababaabbbbbababbbaabaababbaabbbabbaaabbbbabbabaaaaaaabbababbbbbbbaabbbbbaaaabaabbaabbbbbbbbaaabbbbbbabbbaaabbaabbabbbabababaabbbabaaaaabaaaaabaabaababaaabbababaaaabaaaabbbabaabbbabbaababbaabaababbbaaaabbbabbbaaaabaaaababbbbbaaaaaaaabbabaabaabbaaaaaabbbaaabbababbabaabbababbbbabbaabbbbbabaaabbbaaaaaaaaaababbabaaababaabbbabaababbbaaabbbabbaabaaaaabaaaaaababbabbaaaaaabbaaaababbabbbabbababbabbaabaababbbaabababbabbbbabababaaabbababaaaabababbabaaabbaabbbbbbbaabbabbababbbaabbbabbabababaaaaabaabbbabaaabaabaaabbbbbbbbabbaabaaaaababaaaabbbbbaabababaabbbbaabaaababaabbbbbbabaaaabbbbaabaaaabbbabaaababaaaaaabaaaababaaabbbbbbbabaabbabaaaaaabbabaaaabababaaaaabbbbabaabababbaaaabbbbabaaaaababaabaaababbabbbaabbbbbabababaabbbaababbaaabbababaaabbaaaababbaabbabbaaaaaaabaaabbabbbbabaabaabbabbbabbaabaaabaaabbbbbbbaaabaaabbaabbaaabbababababbaaabaabbbaabababbababaaaaabaabbaabbabbbbbbabbaababaabbababbaaababbaababaaaababaaabaabbaabbabbaabaabbbaabbbbabbaabbbbbaabaabbaababaaabaabababaaaaabbabaaabbbbaabaaabaaabaabaaabbaabbaaabbbbbabbbaabbbbbababbbbbbaaaabababaabbbbabbabbbabaababaaabbbbaaaaabbabbbbaabbbaaaaabbbaaaabbbbabbbbabbabbbaaabbbabbbbababaaaabaabbbabbaaabbaabaabaabbbaabababbabaabaaaabababaaaaabbbaaaaaaabbbabaaababbaabaaabbbabababbbabaaaaabbbbaaabaaaabbbbbaaaabababbaabbbaabbabbbbaabbbabababbbabbabbbbabaabbabbbabbbabbbbbbbaabbaaabaaabbbabaaabbbababbababaababbbabaabaaabaabbaabaaabbabbbbaaabbbbbbbaabaaaaaabaaabaabbbabbbbbababaabbbbabaaabbbabaaaaabaaaabaaaabbbaaaaaaabaabaabaaabababaaaaaabbabbbbaaabbbabaababbaababbababbababbbbabbbaababbbbbbabbbbbbaabbaaabbababbbbbaababaabababbabbaabaaaabaabababbabababbbaababbbaabaabababaaabbbabbbabbbaaaaabaabaaabbbababaabababbbbbbbbaaaaabbaababababbbaabbbbababbabbbabbbbbbbabbbaabbabaabbaaabaababaabbbbababaabaabbbaaaaaaabbbbbaaaababbaabbbbabbaaabbaaabaabbaabbaaababbbbbaabbababbabbaaaaaabbaaaaabaaabaababbbaabbababaabbbbbbbaaabaabbaaababbbbbaaabbabbbababbbbbababaaabbaaabbabbaaaaabaaabaababbbaababaaaabbabbabbabbabbaaaaaaababaaaabaabababaaabbaaabbbabbabbaabaaaabaaabbbaabbaaaabbbababaababbbbabbabaabbabaaaaabbbabaababaabbaaaaabaaabbbbbaabababbababbaabbabbaaabbbaabbbabaabbbbbaaabaaabaaabbbaabbabaabaaabbabbabababbabbbbbaabbbaaabaabbbaaaaaaaaaabaabaabbbbbbaabbaaababbbaabbabaaababbababbabbabaabaaabbbaabbbababbababaabaaabbbaaaabaabbbaabbbabbbbaabaaabbbbaaabababaaaabaababbbabaabababaabbaabbbababbbbabbbabbbbbbbbbaaaabaabaabbbbbaaaabaaabababbaaaaabaabbaabbbbaababbbbaabbaaabbabbbaabbbabbaabaaaabbaaabbbaabbbaababbaabbabbaabbbbaabbbbbaababaabbbaabababaaabbaabababbaaaabaaaaabaaaabaabbbbbaaaabbababbbaabaabbabbaaababbabbbbabababbbbabaaaaaaabbbbabbaaaabbbabaaaaababaababaabbbaabbabbaababbaabbbbbbabbabbbbaabababbaaaaaaabababaabbbaaabbbbbbabbababababbbaaababbbbbbaaaabbbbbabaaaabbbbabaababbbbbabbbbbbbabbbbabbabbbaababbbabbaababbababaaabbbbabaabbaaaabaababbbbabbbabaabaabbbbaaabbbaabbababbbbabbbbaabbabbbaabbababaaaaabababaaaaaaabababaaaabbbaaabbaabbaaaaabbbbbabbbbbbbabbbaaababbbaaaabbbbbaabbbbaaaaabbabbabbbabbbaabaabaabbbbbbbbaaaabbbababbabbbabbbbbabbbbbabbaaababbbaaabaababaaaabbaabaaaabbbaaabbaababbbabababbbbbbbabababbbaabaababaaaabbabaabaabaabaabbabaababababbabbabbbbbbaababaababaababaabbabaaabaabbbbaabbbaabaabbbabbbbbabbabaababbababbbbabbabababbaabaaaabaababaaaababbbbbababbbabbabbbaabbabaabaaaaabababaababbbabbababbbbaaabbabaabaabbbaabaabbbbbabbabbbaabbbaaabaabaabaaabbbababbaaabaaaabaaaaaabaaaaaabbabbbaaabbaabbbaabbbaabbbabbaabbaabbaaaaabbaabbaaabbaabaaabbabbababbaababbabbabbbbbaaaabbaabbaaaabbaaaaaaaabababbabaabbbabbbbbbaabaabababaaaaaaabbaaabbbbaabbabbbbbaabbababbbaabbaaaabbbbbaaaaabaabaabbababbbbbbbaabbabbbbbabaababbbaaaaaaaaababaaabbaabbaabbbbbabbabbabaaaababbabbbababaabbabbaaaabaabbbabaaababababbaaaabbbaababbababaaaaaaabaaabbaaabbbbabbbabaaababaaaabbababababbabaabababaabaaaaabaaaabbbbabaabbbababababbababaabbbbabbabaabbaabaabababaababbaaababaababbbbaabbbaaaaaababababbabbaaaabababbbabaabaabbaabbabaabbbbbaaaaabbbaaabbababbaababbaaaaabaabbbabbaaaababaababbbbbaabaabaaabaabaaabbababbabbbaaaaaabaabaabbbabbbaaaaaaabaabaaabaaaaabbbbbbaabaaabaabaabaaabaaaababbaaabbbaaaaaaabbbaababaaababaaabbbbabbbabaaabbbaaabbbabbbbaaabaaaaaaabbababbabbabbbaabaaaaaabababaabbabbbbbbabbbabbbabbabbaabaababaaaabbbbaaabbbbbababbbbbbbbaabbaaaabaabbaababaabaaaabbbbbabaabbbbaababbbbbbbbbbbabaaaabbbbaabaabaaabaabaabbbbbbbbabbaababaaabbbabbabaabaaabbabbaababaabbaaaabbbaabaaabbaaabaaabaabaabbbbbaaaabbabbbbabaaabbbbabaaaaaabbabaaabbababbbbbbaaabaabaabababbbabbbbbaabaaabaaaabababaaabbababbaaabbbbbbbababbbabbbaabbabbabaababababaabbaababbabbbabbabbbbbabaaababbbaaaabbaaaabbabbbbaabaaaabaaabbbbbbbbbaaaababbabbaaababbbbababaaaaabaabaabaaababbabaaabbabbbabaabaabaaaaabbaabbbaaabaabbbabaabbbabbabaaaaaaaaabaabbaaaababbabbbababaabaaabbabbaabaabaababababaaabbaaababbbbaabbbbaabbabaaababbbaaaabbaabaabaaaabbbaaaaabaaaaaaaaaaaaabbbbbbaaaabaabaaaaaabababbaabbabbbbaabaaabaababababbaaaabababbaabbabaababbababaaaaabaaababbbbaaabbbaaaabbbaaaaaaaabababaabbbabaabbbbaaabbabaabbabbabaaabaaaaababababaabaaaaaabbbbaabbaaaabaabaaaaabbbabaaabbbbbaaabbabaaaabbabbaabbababbbbabbbbaaabaabababaabbbbaaaababbbbaabbbbbabaaabaababbabaaaababababbabaabbababbbabbaababbabbabbaaaabaabbbbaabbbbbbabbbbbbaaaababbabaaababbaaaaabababbbababbbababbbaabbaababaababaabaaaababbbabbabaabbbbbabaabbaabbbbbaaaababaabbbbbaabaabbbabbbabaabaabaaaaabaabbaaabbbaabaabbaabbaabbbabbbbbbbaaabaaaaaabbbabaaaabbbababbaababbaaaaabbbaabbbaabaaabbaababbabbbbaaabbbaaaababaabaabbbaaaaaabaabbbbbbbbbabbbaabaabbaaaabbbbbbabbbabababaabaabaabaaabaaaabbaaaabbabbbbbbbaabbbaabbbaabbbabaabbbbababbbbbbbbabaababbbaabbabbbababaaabaaabbaabbbabbbbbababbabaaaaababbbabaaaaaabbabbbaaaabbbabababbbbbaababaababbaabbaaaabaaaabbaabbbbbababbabbbabaaaabaabbaababbaaabaabbabaabbbabaaabaaabaaaaababbaabbabaaaababbbaababbbaababababbaababbaaaababbbbababbbbbaabaaabbbbabbbbaabbbbbabbabbbbaabbabaabbaabbabbbbaaabbbabbababbbaabbabaaabbabaaabababbaababbaabbaaabbaaabaaaababbaabbabaaaabaaabaabaababaaaaaaabbabaabbbaaabaabbaaabbbbbbbaabaaabbbbbbabababbaaabbbabbbabaaaabbbbbabaabbbaabbbaaaaaabbbabaaabbbaaabbbbbabababaaabbbaabbababbbabaaabbaaaabababbbbbabbabaabbabababbbbabbbbabbaabbabaabbaababbabbbbaaaababaabaaabaaababbaaabaaaabaaabababbabbbbaababbabababbbaaabbaabaaaabaababaaaabbabbbbaabbaabbbababbbaababaababbbabbababbabababbbababbaabbabbaabbbbbabaababbabbabbbabbaabaabbbbbbabbaabbabbaaaaababbaaabaabbbaabbaaababbaabbbaabbaaaababbaabaababbbbaabbababbaaaaaaaabbaabbbbbaaabbbbbaaabaaababbaaaaabaabaaabbaababbabbbabbabbaaaabbbaababbaaababaaabababbbabbbbaabaabbbababbbbbbbbbabaabbbabbaaaabaababbbaabababababaaaabbabbaaabbbbaababbbaaabaabbababababbbbabbaaabaabbbaaaababaaaabbbbaabbababbbabaaaaabababbaaaaabbaaaababbaaaabaaaabbaaaaabbaabbaabbabaaaaaaaaabbbaababbaaaaabbaaabaabbabbaaaaababbbbabbbabaabaabbaabababbabaabaaaababbbbbabaabaabbbbbababbaaaaababbbabbbaaabaaaaabababbbabaaaababbaabbabbaaabaabbabbabbbaaabbabaaaaabbabaabbaabaaabababbbaaaaabbababaabaabbababaaabbbabaaaabbaaabbabababaaaaaababaaaabbbabbbbbaabababbaabbaababbabbbbaaaabbbabababbaababbabaabaabbaababaaaaaaabbbbaaaabaaaabbbabaabaabbabbbaabbaaaabbbaaaabbababbaaabbaababababababbaabbabbaababbbabaabaaaabaaaaabaababbbbabbbbbaabbbaabbaabbbabababaaabbabbbaabbaabbbabaaaabbbbabaabaabaaaaabbbbaabbabbbbbbbbaababbabaaaababaabbbaabbbbbbbaaaaaabbabbabaaabbaababbbaaaaaaaaaaabaaaabaaaabaaaaabbabbaabbaababababbbaaabbaaabbbabaabaaaabababbbbbbaabbbabbabbbbaababaaabbbababbbbbbaabbbaaabbbababababbbaabbbbabbbbabbaabbbaaabbbabbbaaaabbaabbaabaaaaaabbbbbbaabbabbaabaababbbbbaabaaaaabbaabbbbabaabaaaaaaaaaabbababaabbaaaaabbaaabaabbbbbabababbaabaabaabaababbbbbaaaababbaaaaabbabaabbaaabbaabbabbabbbbbbabbaaabbbabaaaaaaaababbbbabbabbbbaaabbbabbbbaaabbaaabbbababaaabbabaabaabaaabaaabbbaaabbabaaaabaababbbbbbaabbbaaababbabbaabbbbabbabababaaabababababbababaaaabbaababbbaabbbbbbaabbbabababbababbbababbabaaabbbbaabaaabbbababababaaabbbbababbababababbbbababbbabbaaababaaabaaabaaaaaaaaabaabbaaabbaaaabaaabbabbbbbabbbbaabbbaabaaaababaabaaabaabbbabaabbaabaaaaabaaaabbbbbabaaabaaabababaaaababbabbbbababaabaababbabbbabaababbaaababababababbbaabbabbbbbbaabbaabbababaabaabbaaaaababaababbaaaabbaaaaaabbbabbbbabaababbbbabbbbabbbaabaaabbbbabbababbbaababbbbabbaabbabbaaaabbbbabbaaaaaaababaabbababaabaababbaaabaababaabaaaaabbbbbabbbabbbbbaabbaabbaababaaaabbabbaabbaababbaaabaaabbbbbaabaabbbabbabaababbbbbaabbbaababbbbbbaabaaabaaaababbbbaaababbbabaaaaaaabbbbaababababaabaaaaaabbbaaaabbbbaaabaaaaaabbbaabaaaababaaaabbbbbbbbabbaaaababbbababbbbaabbaaaaaaababbbbbbabbbaaaaaaabbbaabbbabaaabbaaaaabaaaabbbabbbbbbaabbababaabaabaabababbbabaababbbaaababaabbaaabbabbbaaabababababbbabbababaabaaabaaaaaaabbabbbbaabbbbbbaaaaaabbabbaabaaaabbaaaababaababaabababababbabaaabaaabbbbababbbbbbbabbababaaabbaabbabaabbbbbbaabbabbaabbaaabbbbaabbabbaababaaabbbabaabbbabbbbbbbabbbbabbbbaabaaabbbababaabbbbbbbabaababbabbaabbbaaaaabbbaabbaabbaabaaaababaaaabaaabbbbaaabbaaababaaababaaaaaababbaaabbbaaabaababbbaaabbabbabbbbaaababbbababbbabaaaaabaabbbaaababababbbbbbabbbababbaabaaabbaaaabbabbaabbbabbbbaabbaaaaabbaaaaabaaaaababbbbaababaababbbaaaaabbbbabbababaabbbbabaaabbbabababbabbbbaabbbbbabbbbaaabbaaabbababaaaaabbbbbbbabbbaaaaaaaababbbabaaababbababaaaaaaaaaaaaaaabaaabaaaaaabaaaabbbababababbabaabaabbabaabbaabbaabbbaaababbabbbbaaaaaaabbbbbababbaababababbabbbbbbababbbabbbbbbbbaabababbbaaabaabaaaabbbbbabbbabaabaabbbbaaaaaaababbbaaabbbbbabbbbbbaabaaabababbabbbbaabbaaabbaababbaaaaaabbaaababaaabbbbbbbbbaabbababbaabaabaaaabbbabaabbaaabbbbabaabbabbababaaabbabaaaaaaabaabbaaaabbababbaaaabbbaabbabbbbbbbabbbabbbaaabaaaaabbabaaaaaaabbaabbbbbbaabbabbabbabbbabaaabbbbaabbaabbabbbbabbaabbbbbbaabbabbbbaabbbaaababbbabbbabbabaabbbbaaabbabbbaaaaabbbbbbaabababbbbbbaababbaaaaaaaabaaabbabaaaaaababbbbaabbbbabababaabbbaabbbbbabaabbabbabababababaababaaabaaababbbaabbbaaaaaabbaaaaabbbaaabaabaaabbbbbbbababaaabbbbbbabbbbaabaabaaaaaaabbbbbbbbaaaaababaabbbaabbaaaaaabbbaaabbbaaaabababbbbbbbbabbbaaaabbaaabbbaaaaaaaabbabbaababababbaabbabbbbbaabaababbabbbabbbaababbabaaabbbabbaabaaaabaaaababbbababbaaabbbbbaabaaaabbabbbaabbaaaaababbaabbbbbabbabaaaaababbaaaabaaababbbbabbabaabaabbbaabbbabbbbbbaabababbaababaababbbaabbbbbaabbaabbabaaaabbbabaaabbbbabbbbaaabaabbbabaabbabaaaaaababbabbaaaaababbbabaaababbbabaabbbabbbaaaabaaabaababbbbabaaaabbaaababbaaaabbbabaabaabaaaaabaaababaabababbaaabbbabbabbaaabbabaabbababaaababbbaaabbbabbbbbabbbbbbaabbaaabbbaaababbbbaaabbabababbbbabbababaababaaaabababaababbabaaaabaaaabbaababbabbbbabbbbaaaabbbaabaabbbabbabbaababbbaabbaababbbbabbaaaaabaabaaaabbbaaabbaaaaaaaabababbbbbabaabaaaabbababbaababbbbbababaaababaabbbabaabbabbbbbbbbbaaabbbbaaaaabaabaabbbbbaaaabbbabababbaaaabbbaaaabbaabbabbabaaaaaaaabaababaaaabbbbaaababababaabaabaababaabbababaaababbbbaabababbbbbababbaaabbaaaaaabaaababbaaababaabbabaaabaaababbaaaabbaabaaababbbaaaaaaaaaabbabaaaaaabbbabaababaabbabbaaabbabbabababbbbaaababbbbbbbabbaaaaaabaabaabbaaabaabbbbaaaaababbabaaabbabbaaabaabbbaaaabaababaababaabaaaabbaaabbbaabaaaaaabbaabbaabbababbaabaabbbababababaabbbabaaabbbbbaababbaabbaabababaabbabbababaaabababbabbbbbaaaababababaaabbbbbbaaaababbaaaaabbbaaaabbbbbbbabaaabaaabbbaabaabaababaaaabbbabaaaabbaabbabbaabbabbabbaaabbbaaaaaaaababaabbbaababbbbbababbbabbaabbbbbbbabbabbbbbbaabaababaaaabbabbbbbbbaaabbbabbababbbaabbabaaaabaababaaabbabaaaababbbaaabaaabaabaaabbababaaabaaaabaaaaaaaaaaaabbabbbaabaabbbbbbabbbbbabaaabbbbaaababbabaabbabababababaabaaaaaaabbbbaabaabbaaababbbababaaabbaaaababaabaabaaaaaabbabbbaaaaaabbaaaabbbbbabaaaaaaaaaabbbabaabbaabbbababbbbbabaaaaaabaabbbbaaabbabbbababbbbbbbaabaabbbababbbaabaabbabbbaababbbbbaaabaabbaabbababbbabbabbbbbabbbbbaaaababababbbabbbbbabaaaabbabbbbaaabababbbabbabbababaaaabaaabbaabbbbbbabbaabaaababbbbbbabaaabbaaaaaabaabaaabbabbbaabbabbabaaabbbabbbbaabbaabbbababaababbabbaaaaaababbababbbbbbababbababbaaaaaaaabbaaaaaabaaabbbaabaabbbbababaaababbaabbababbbbaaaaabbabbaabaaaaabbbaabbbabaaabaabaaaabbbaaabaabaabaababababbbaabababbaabaabbabbabaabbababbbbabbbabaaabaabaaaabbbbbaabaabbbabbabababbbbabbbabaabbbaaaababaababaaaabababbbbbbabbbbabbabbbbaababbabaababbaababbabbbbababbaaabaabbbbbbbbbbbababbaaaaabbbbbaabbbbabaaabaabbbbbabbaababaaabbabbbbabaabbbababbbabbbbbbabbabbbbaabbabbbabaababbbaabbbbaabbbbbababbaababbbababababbabbbaaababaaababbababbbabababababbbbabaabaaabbabbbabbaababbaabbbbbbbaaaababaabbaaabaaaaaaabbabbbbaabbbbaabbaaaaabbaabababababbbbbaabbabbaaababbbaabbbbbbaaaababaaaaabbbbaabaaaaaabbabbbaababaaaaabaaabaaabbbaaaaaaabbbbababbbaaabbabaabbabaaabbaaaababbabaaaaaaabaabbbaabbbbbbaabbbbbaabaabaaababbbbbaaabbbabbbabaabbaababbabbaaabaaabbaabaaabaaaaababaaabaaabbabbbbbababbbaaaaabaaabbbbbaabababaabaabaaababaababbaaabbbbabbabbaabbaaabbbabbaababaababaababbaabaaaaaabaababbaaababbabbbabaaabbaaaababbabbaaabbbbabaaaabbabbaabbbbbbbaabaaabbbbaaabbaaabbbbbbbbbaaabbbaabbbbbbaababbbbbaaaaaabbbbabbababbababbbbaaabaabaaabbaaaaabaabbabbaaaaabababaabbaaabbbabbabbabaaaaaabbbbaabaaaaaaabaabbaaaaabbaaabbbabaaaababaabbaabbaabbaaabbbaabbaabaaababbabbabbabbbabbaaaaaabaabbbabbaababbbabbbbabbbbbaabaaaabaabaaaaaababaabaabbbbaaabaaabbabbbaaaabbabaabbbbbbabbabbaabaaaababbabababaabbbbaababbbabbabaabbbbbaaababababbbababbabbaaabbabbaabbaaabaaaabbbbbbbaaaabbbaabaaaabbbbabbbabbabbaaabbbbbbbbaabbabaaaaabbaabbabbaaabaabaaabbaabbabbababaaabaaaabbbaaaaaabbaaaababaaaababbbababaabbbabbbbbaaaaabaabaabaabbbabbbaabbaabaaaabbbbbababbaaabbaaaabbbbaaaabaabaaaaaaabbbaabbbaabaaaaaabbabbabbbababbbbbbbbaabbaabbbbaabaaaaaaabbabaaaabbbbaabaabaaaaabbaabaabbaabbabbbbbbabbaaabbbaabbbbaabaabaaababaaabbbbbbbaaabbbbbaabbaababbaabaababbbbaabbaaaaabbbbaaaaaabaabaabbbbaaaabbabbabbbaababbaaaaaaaaaaabbbbbbaaabbbaaabaabbabbababbaaabababaababbbbaabbbabbbbabbabaaaabaabbabbaaaaaabababbaaaabaabbbbababbababbbbabbbabbbaaaaaaabbabababbaabbbbababbbaaabbabaabbbbbabbabaaaabbbbabaabbbbaaabbbabbabbaaabbbababbabbabaaaababbabbbababababbabbaaaaabababaaabbbbaaaaaaababbabbbabbaabbaaaaaababaabbbabbabaaababbababaabbaaabbabababbbbabaaaabaaaabbbbabbbaabaaaababbabaaabaababbabaabaabbabbbbaaabaabaaaaaaabbabaabbaabbaaabaabbaaabaaaababbaaaaabbbaaabbbbbabaabaababbaaaaabbbabaaaaaaabaaabbbbbbaabababbbbabbbababbbaaabbbbaababbbbbbabbaaaaabbbbabbaaabbaaabbabaabbabbbbbaaabaaabbbababaaabbabbabaabbabbaaaabbabbbabbbbaaaaaaabbbaabbbbabbbbbbbabbaabbaabababbaaababaaabbbaabbbaaababbaabbbaabbaabbaaabaaabaababbaaaaaaabbabbbbabbaabbbbabbbbbbbabbbabbbbaaabaaabaaaaabbaabbbbbbbaababbaaaaaabbabaaabbabbabbaabbababbbabaabaababaabbbaabaababaabbabbbabbabbbaaaabaaaabbabaaaabababaaabbbabbbaabbbaaabbabbabaaaabaaabbaabbbaaabbaaaabbaaaabbaabaaababbabbabaaaaabbaabababbaaabbbaaabaabbbbbbbababbbbabbbabbabbababbbbabbbaabbabbbbaabbbbababababbaaaaabbbbaabbbaabbbbaaabbabbbbabaaaaabbabbaaaababbabaabbbaaabbabbaababbaaaabbbbaabaabbbbbbbabbbaaaaaaaaabbbabababbbaabbbabaaaabbabbbababbabbbaaaabbbbaabbaabbaabaaaaabababaaaabbbababbaabbababaababaaabbbabaababbbbbabaabbbaabaababbabbaabaaaaabbabaaaababbaaabbbbbabbaabbbabbbbababbabbababbbabbbbabbabaaaababbbababbabaaaaaaaaabbaabaabbabababbaababbaaabbbbbabbbbaaaaaaaabbbbbbaaaaabbabaaababbabbabaabaabbaabaabaabbaabbaaabbbbbabbabbbbaaabbbbabbaabababbbabaaaaaaaaaaaabbbbbbbabaaabaaabbbababbbaababbbabbaaabaaabbabbbbbbabaabbbbbbbaabbabaaabbaaaaabaaababbbababbbabbaaaababaababbabbbbaabaaabaaabbaabaaabbbbbabababbbbbabbbababbbbaabaababbbbbbabbbabababbbabbabbbabbaaabaaabbabbbabaaabbaababbbbaababbbbaabbbaaaabaaabbabbabbabaaaabaaaaabbbbbbbabbaababbaaabaaabaabbabbaabaabbabaaabbaaaaabaaabababaaaaabaabbbbbbbbabbabaaaabaabbbaaababbabababaababaaabaabbbaaabbbbabbabbababbabbaaabaaaaaaaaabaababbbaabbbbaabababbabaabbaaabbbbabaaabaaaabababbabbbbbabaaabaaaaaabbaaabbabbbbaabbabbabbbaababbabbbabaabbbabbbaabbabbababbaababbaabaaaaaaabbbbaabababaaabaabbabbaabaabbbaaaaaabbaababaaabbaaaaabbbababbbbbaabbbaaaabbbbbbbaaaaababaaabaaaabbaababaabbbbabaabaaaaabaaaabbbaabbbbbbbbaabbabaaaaababbbaaaaabbbbbbabababaabbaabaaaaabbbabbaabbbaaaabbababaabaaabbbbbbbbbabbabbbabababaaabbaaabbaaababaabbaaaabbabbbbaabbbaabbbbabaabbbbbbbaaabbabababaababbabaaaababbabbbbaaabbaabaaaaababaabaaaaaaabbabbbbaaabbaabbbabaaaabbbaaababaaaabbaabaabaababbabaabbbbbaaaabbbabaaaaababbbbaabaabababbbbaabbbbbabbabbabaabbbaaabaaaaaababbbaaaaabbbabaababbbababbaaababbbaaababaabbabbbbbbaaabbabbbbabbbbbbabbbaaabaaabaabaabbbaaaaaabaaaababaaabbbbabbaaabaaabbbbaabbaabbbaabbbbababbbbbbbaaaabbaabaaababbbbbaabbbbaabababbababbaaaabbaaabbbaabbbbabbbbaabbabaabaabbbbbabaabbbaabaababbabaaababbbbbaaaaababbabaababaaabbbbbbababbaaabbaaabaaababbabbbbbaaababbaabbaaababaaabaabbbabbabbbaaaaaaaabbaabaaababaaabbbaabbbbbaabbabbabaaaaaaaabbbbbbbabaabbaaaabbabababbbaabaaaaabbbbaaabaabaaabababbbabbbbabbbabbaaabbaabaaaaabbabbabbbbbaababbbabaaaabaabbabaababbbbbbaaabbaabbababbbaaabaaaabbabbbbbbbbaaaababbbaaaaabbaabbaababababbababaaababbbaababaaabbaaababaabaabbabbabaaaababbabbaababbaabbbbabaabbbabababbbbababbabaabaaaabaabaaabbaaaabbaabaaaaabaabaabbbbbbabaabaababababbaaaabbababbabbbbbaabbabaaaabbaabaabbbbaaabbbbbababaaaaabababbaaaababaaabbbbababaabbaaababbabbabababbabbbbabaabaaabaababbabaaaabaaaabbaaaaababbbbbababababaaaaaaababababaabbaabbabbaabaababababbaabbbaaaabaaaaabababbaabbbaabaaaabababbbabbabaaaabbaaaababaaababababaaabaaabababaabbaabaaabbbbaabaaaabaaababbabbaabaaaabbabbbbbbbbaabababbabaabaaaaaababaabbabbabbaaaaabaaaababaabbbaaaaaabbaabaaaaabbabbbaabbaabaabbababbbbaababbbabaabbbbbbbaabaaabaabbbbaababbaabbaabbbaababaabbaababaabbaaaaabaaaababaaaabaabaaabaabbabbababbabbabbbbabbbbaabaababaabbbababaaaabaaabbabbabbaabbabbbababbbbaabbaaaabbbbbaaabbababbaabbbbababbbabbbbaabaaabaaabbabaaaaababbbbbbbabaabbababbbabbbabbbaabbabbaaaaabbbaaaaaabbabaaaaaaabaababbbababaabaabbbbaaaaabbaababbbbabbbbaaaaabababaaabbabaababbbaabbabaababbabbbaabbabaaabbabababbaabbbbbaaaaaaabbbbaaabbabaabababaaaaaabbabbbbbababbbbabbbbaabbbabaabbbabbbaabbbabbbaabbaaaaaaababbabaababaabaabbbbaabbaaaabbbbabaaabbabbbbbababbbabaabbaababbbabbbbbbaabbabbabbaababaabaaabbabbabbaababbbbbbaabaaaabbabaaaaabaaaabaaabbaabbbbabbaababaaabababababbbbbaabbbbbaabbaaaaabaabaaabbabaaabaaababbaaaabbaabbbaabaabbaaaabbbaabbbbabaaaaaaababbbbbbbabbbbbaaabbaaaabababbabbabbaaabbbbababbbbaaabaaaaaaabbbaabbaaabbaabbabbbaabbbabaaaaaababbbbaaaaabaabaabaaaaaaaabbaabababaaabaabbabaabbbaaaababbbbaabaaaabaaaaabbbabbbbbabbaabaabbabaaababbbabbaabbbabbabbbabbababbbaaaaabbaaaabbbbbbaaaabaaabbababbaaabaabababbbaabbaaaabaaaaababbbaabababaaaabababababaabbaabbaaaaaababaaabbabaabbababbbbaababababbaababbbbaabababbaabbababbbbbaaabaaabbabaaabaaabbaaaabbababbbaaaaabbababbbabbaababbbbabbaaababbbaaaabaaababbbaaaabaabbbbbaaabbaaabababababbabbaaabaabababbabaabbaabbaaabbabaabaabaabbaaaaaaabbabbbaaabbbbabbaabaabababbaabaaaaabbababaaaaabbaabbbabbabbaabbabaaababaaaabaabbbbaababaababbabbaabbbbaabbbbaabaababbbaabbbaaabbbaabbbabaabbababaabababbbaababababbabaabbababaaaabbbabbaaaabbabababbbbabbaaaaaabaaaabbbabbaaabaaabaabababbaabbbbaabbbaaaabaabaaaabbbbbaaabbbababaabbbaabbabababbababbaaabbbbaabbbbbabbbbbaaaabbbababbaaabbaaaaabbabaabaabaaaabbbaaaaaaabbbabbbaababaabbbbbaabababbaabbaabababbbbababaaababababaaaaababbabaaababaabbaaaababaabbabaaaaaabbbbaababaaababababbbaaabaaaabaabaaaabaaababababaaabbababbbbbbbbabababaabaaaabababbbaaabaabbbbbaaababbbbabaabbabbbabbaabbbbbbaababaababbbabbabbaaaababbabbbaaabbbababbbaabbaabbbbababaabaabbabbaabbbbbaabbaaabbbababbabababbbbbbabaabaaababababbabbbaabaababbaaaaaabaabaaabbbabababababbbaaaaabaaabbbaaaaabbbbabaabbbbbbbbabbabbabbaabbbabbbaabaababaaaabbabbbaaabaaaabbaaaabbaaaababbabbaaabaabaaabbabbbbbaabbbaaaabaabbabbaaaaabababbaaaaababbbababaaabaabababaabbbaaaabbaabaababbaababbbbabbbbaaababbbaaaaabbaaaaaaababababbabaaaaabbbababbbbbababaaaaabbbaaabababbbbaaaababbaabbbbbaabbababbabaaaaaaaaababbbaaaababbbaaabaaabaabbbaababababababbbabbabaabbabaababbbaabbaabaababbaaabaabbbabbabbbaaababaaabbbabbabbbbbbaabbbaaaabbaabaabbaababbbbbaaabbababbababaabbbbabbbbbaaaabbaabbbaabbaababbbaaababbaaabbbbaaabbbaababbbbbaaababbaabbabbbbaabaaaababababbbbbaababbbbaaaaababaabbbbbbbbaabaaabaaaaabbbaabaaaabbbbaabbbbabaabaababbaaaaabbbbaabaabaaabbbbbaaabbabbbbaabaabbbababbabbbbaababbabaabbabbbbbaabaabbbabaaaaaaabaabaaababaabbababbbabbabaabaaababbbaabbabbbbaaaabaabbbaaaaaababbbbbbababababbaabababababbabaabaaaabbaaaaababbbaababababaaaaaabaaabbaaaabbbbbaabbbbaaaaaaaaaaabbaaaaababaabaabaaaabaaaabbbbbbaababaaaaabbababbababbbababababaababaaaabaabbaaaaaaababaaaabbaabbaaabbbbaaabbabaaababbaabbbbabbbbabbbabaababbbaaaaaaabababbabbaabababbbbbbbbbabbbabaaabbaabaabbaabaabbbbbabababbabbababaabbbbabaaabaabbaabababaaababbbbbabaabbbbaaaaaabbaaabbbbbbabaabbbbaabababbababbaaabaabbaaaabaaabaabbaaaaabababaababaabbbabaabbaaaaaaaaaababbaabababaaaabbabbabbabababbbbaababaababbbbbababbbababbababbbbabbbbbbaaaabbaabbabaababbbaabbaabbbbbbabaababbbababbabababaabaababbabaaabababbaaaababbaaaaaaabaaabaaaaaabbaaababbbaabbabaababbbaabaaaabaabaaaabbbaaaabbabaaaaaaababaaaaaaabbababbbbaababbaababbabbbabaaababbbabbbabbbaababababababbbabbbabbabbbbbabbbbbbababbbaaaaabaababaaaaaababbabaabaabaaabbabbabbbbbaaabababababbabaaabbbaabbbabaabbaaaaaaaabbabbbbbbabbaaabababbabaabaabaabbaaabbbbbbabaaaababaabbabbbbabaababababbbbbaaaabbababbaabbbbabbaaaaaabbabababaaaababaabbaabbbaaaaabbabbbbaababaaaaaaabbbbabaaabbabaaabaabbaababbaaabbaababaabababbbbbaaababbabbaabaabaaabbbababbbbbababaababbaababbbbaaaaababababababbbbbaababbaaabaabbbbabbaaaaaaaabbbbaaaabaaabaaaaabaabbbaaabaabaaaabbababaaaabbbbbbabaaaababbbbabaaababbbaabbbaabaabaaaaabaababbababbaaaaaababbbbbbaaaaabbabaabbbaaaabbbabbabaababbbbbbbbbababbababbbbbbbbababbababbabbabbababaaaaabaaaabaababbbaababbbababbaaabaaabaababbbbabaaaababaabaabbabaabaababbbabbaaaaabbaaaaabbbaabbbbabbbbbbabababaaaababaaabbbbaaaaabaababababbbabaababbabaaaababaabbbbbaaabababaaabbbaabaaaaababbaaabaaabaabaababbabbbbaaabaaabaabaababbbaaababbabaaabbbbbaabbbaaaabbabbbabababaaababaabbaaaabbbaaababbaaaaaaabaabaabaaabbbabaababbbbbaaabaabbaaababbbbbbbabaaabbbabbababaaaababbabbababaababbaaababbbbbbbaabbabbbabaaaaaababbbbbbbbbbababaaabbaabbbbbbbaaaaabbaaaabbabaaabbbbabbbaabbbbababbbbaabaaaabaabbaaaabbbbabababbbbbaaaaabaabaaaaabbabbaaaaaaaabbbbbbababaabbabbabaabaaaabaaababbabbaabababbabbbaabbabaabababbaaabaaaababbabbbbbaabbbbaaaaabbbaaabaabaabbbaaabbbbaabbbababbabbbaaabaabbaaaaaabaaabaababababbbabaabababbaaabbabababbaaababbbaaabaabaaabbbabbbbaaaabbaabbaababaaaabbabbabaababbbbbbaaabaaabbababaaababbaaabbbaabbabbaaababababaabbaababaaabababbabaabbaaabbabbababbbbbaabbaaaabbbaaabbaababbaabbbbabbabaaaaabbbaaabaaabbbbaaabbbaababbaaabbaaabaaababababaaabbbbabbbbbbaaaaaababaaabbbbabbabababaaaaaaabbabbabaabbbbbaabbbbaaaabaababaabbbbbbbbaabaaabbabaaaababbbaabbbbaabbaabaaaababbaaabbaabbbbababababbaaaaabaabbaaabaabaaaaababaaabbaababaaababaabbabbbaaaababbbbaabbbaabbbababaaaabaaaabaaaabbaaaababababbabaaababbabaabbaababababbabbaaabaabbaaabbabaabbbbbbbbbbabaabababaabaaaabbbaaabbabbbbbabbabbabbbaababbbbbabbabaaaabbabbaabbaababbaabababababbabbbbbbaabaabbbbbababbbbbaaabbbbabbbbbbababbbbbbbbbaabbbabaaabbbaabbbbbaabaabbbaabababbbbabbaabaaaaaabaaaaababababaabbbaaaababbbbababaabbababaaabaabbbbbababbabbbbbaaabababbbaababaaaaaaabbabaaababaaabababbaaaaabbbbabbabaabaabaabaaababbbaaabbbaaaaaaaabbbbaabaabbabbaaabababbabaabbaaaabbabbbbbabbaabbaaaabbabbaabbaabaaaabbabbabbbabaaabaaaabbbbbbbbbbabbabbbbaabaabbaaaaaaababbbbaaababaaaaaaabababbababbbaaababbbbabaabbbbbbabaaabbbaaabbaabbabbbabaaabbaaaabbaaaaabaabbbbaaabbababbbbbababbabbbaabaabbabbbbbababaaabbbaaaabaaabbbaababbbaabbabbaaababbbaabbbaabababbbbbaabbbbabbaabababbbbabaabbbbaabababbaabaaababbaababbaabbabababbbaabaaababbabbabbaaabbbbbaabaaaaaaaabbbbabaabbbbbaabbbbbabbaaaabaababaaaabaaabaabbabaababbabbaaabbbabababbbabbabbbbbbaaabbaaaababbbabbbbaaaaabbbbaabbabbbabbbabbabaabaaaaabababbababbbbaababaaabbabaaabbbbabaaaaaaabbabababbbbabbababbaabbbaabaaaaabaabaababbabbabbabaababbaabaababaaaabaabababbbaaabaaaaaabaaabbaabaabaababbbaaabaabababbaabbbaabbbbabaaabbabaaaaaaabbabaaaabaabbbabaaaaababaaabbaabaabaababaabbbbaabbbbaabaabaabbaaaaaaaaaabbababababaaabbbbbabbabbbbbaaaabaaabbabbbbabaabbaababbbbbabbabbaabbbaaabababbbbaabbaaaabaaababaaaaababbbbabaaaabbababaabbbaaaaaabbabaaaabbbababbbaaababaababbaabbaaabbbaaaaabbaaaabaabbbbbaababaabababababbbaaaababbbbabbaabaaabbababbababbbabbbaaaababababaabbbabbaabbbabaaaabbabaaaaaabbaaabaabbaaaabaabbaaababbaaabaaaabababbbbaaaaaaabbaabaababaaababbabbbbbbbabbbbabbaababbaaabbabbabbbbbaaababbababaabbabaaabaaababbbababaaabbbabbbaaabbaaabbaaabaabbbbbababbbaabababaaaabbbbbbaababababbaabbbabaaaaaaabbbaabaabbbbbaaabbaaaababbaaaaabaabbabbbabbaaaabbababbabbbabbaabbbbbaaabaabbabbaaaaaaaababbbaabbbabaaaaabaabbbabbbbabaaababbaaaabbabbabbbabaaabababaababbbabbaabaabbbababababaabaaabaabaaabbbbaababbbbbaabbbbabbaabaabbaaaaabbaaaabaaabbaaaabbaabababaabbbabbbaabbaabaaababbaaabaabbbbaabbbbaabbbababaabbaabaabbbaaabababbbabaaabbbbbbabbbbbbbbababbaaabbabbaabbbaababbbabaaaaabbabbbaaaaaaabbbbbbababaaabbaaaabaaaabbbbaabaaabbbbabaabaababbbbabaabbabbaaaabaaaabababbaababaaababaaabaababbabaabaaaabaaaabbbaababbbaabbbbababbbbbaababbaabbabbaabbaaabaabaabaaaaaabbaabbbababaabbabbabaabaababbbaaabaaaababbababababaaaaabaabababbbaaaaaababbbbaabbbabbbbbaabaabaababbababbbaaabbaaaabbaaabbbbbbaabbbaaaaabbaaabbbbaaaaaabbabbabbbababababbbaaaabbababbaabbbbbbabaababaabababaaaaaabbababbbabbaaabaabbbabaaabbabbaaaababbbabbaaaaabbabbabbbabbabaabbbaabbbbabaabababaaabaaabbababaaabaabbbbaabaaabbbbaaabaabaaaaaaaababbaabbaaaabbbbaabbaabababaabababaabababbaaaababbbabbababbbabbababbabbbbbbabbbbaabbaabaaabaaabbababababbabbabaabbabbaaabaabababbaabbbabbaabbaabbaaabbabbbbaabaababaaaaabbabababbaabaaababaababbaababbabaaaaabbbabaabaaaabbbbabbbaaababbbbabbbaabbabbabbaabaabbbaabbbabbababbbbbaaabbbaabbbbabaabaabbbaabaabbbaaabaaabbaaabbabbbabaabaaabbbaaaabaaabbabbabbabaaabbabbbabbbabaabaabaaabaababbaabbaabaaaababaaababbbaaabbbabbbabbbbabbababababbbbbaabaaabbabbababababaaaabbabbabaaaabaabaababbaaaaababbabbbabababbbbabbbaababbbaabaaaababbbabbbbabaaabbbabbababbbabaabbabaaaaababbababbbabbbbbbbaaaaabaabbaababaababbaabaabbbaaaabbabbbababbaabaabbabbabaaabaaabbbaaabaaabaabbabaaaaaaaabaaaabbaabaaabbbabbaaabbaababbbbaabbaabaabbbbaabbaaaaaabbbbbbaaabaaabaaaaabbaaaababaaaaaabbbabbabbababbabbaabbbbbbbbbbbbbabbaaabbbabaabbbaaabbbabbbbabbbabbaabbbbabaaabaaababababbaaabaaabbbabbbbaaabbbababbbbbaabaaabbbaababaaaabbbabbbabababbabaabaaaaabababaaaabaaaaabbbbbbbabbabbaababaaabbbaabaabbbaabbbbabaababbabaaaaabbbbaababbabaabbbaabbabaabbaababbaaabbbaaaabbbabbbababaabaaaabbabaaabaaabbaaababbbbbbbbabbbbababababbbbbbbabbbaabbbaaaabaaabbabaaabbbbbababaaaabbbbbbbbababaaaababbaabbbaabaabaaabbaaaaaababaabaaababbbabaaaaabbaabababbbaabaaabaabbaabababbbababbabbbbababaaabaabaaaabbbbbbbababaabbabbbabaaabaaababababbaaababaaabbabaabbabbabaabbbbbababbbaabaabbbbbbbbababbbaaaaaaabaabbbaaabaaaabbababababaaaaaabbabababbbaabbbaababbabaaaaaaaaaaabbabbbabaabbabbaaaaabbbbaabbababaaaaababaabbbabaababaabababbababaaaabaabbabbbbbaaaabbbabbababaaaabaaaabbbaaaaababaabbabaaaabaaabbbbabababbbbbbaabbbbabbbbaaabbaababbabbaaabbbbaabaabbbaababbbaabaaaabbbbbbbbaaaaaababbbabbaababaababbbbbaaabbbbabaaaaaaaabababbabbabbabbbbbbababaabaaaaaaaabaabbbbbababaabaababbabaabbaaaaaaabbaabbabababaaabaababbbbabaaaaaaababbaabbabbabbbbabbbababbabbabababbabaabbaaabbabbbababbbabbbbabaabaabaababbbabbabbbabbaabbbabbaaaaaaabbaabbbbabbabbabbabbaabbbabbbaabbaabaaaabbbbbbbbabbababbabbbabbbaabbaababbaabbaabaaaabaaabbaaabaaaababababbababaabbbbaaabababbaababbbbbaaaababaabaabaaabbbabbaaaabbbbbbbbabbbbbbabbbbbbbbbbaaaaababbbaaabaaaabaabababababbbbabaaaaaaaaaabbbbbaaabbaabaaaabbbbbababaaabaabbbbaaaaaabbbbbbbababbaabbbbabaaaaabbbbbbaaaaabbbbbaaabaaababbabbaabbabbbbabbbaaaabaaabbbabbaababaaababbbbaabbabbabaabbbabbbabaababbabaaabaabbabbaabbaaaabaaaabaababaabbaaaabaababaaababaabbbabbabaabaabaaabbbabbbaabaabaababbaaaabbbbbaaababaaabbbaaabbbababbabbabaabaaaaabbbabbaaaaabbabaababaabababaaabbbbaaabaaaabbabbbabaabaaababbabaabbbbbbaaaabaaabaabaabaababbbabbbbbabaaabbbbbabbaaaaabaaaaabbbaabaaaabbaaabaababaabbbaabbbabaabbabababaabbbbaabaabaaaabaaaaaaaabababbabbaabaababbbabbabbbaaaababaabaaaababaaaababaaaaabaaaabbaaaaababbaaabaababbabbabbaaaaaabbaaabbabaabbabbaabbaababaababbaaaabaaaaabaababaaabbbbbbbbbabbbaabbabaabababababaabbaaababbaaaaaaabaababaaabaaabaabaababbaabbabbbbaababbababbbabbaabaabaabaabbaaaabaaabbbaaabbabbbbbbbaaaababbaababaaaaaaaabbaaaaaaabbaabbbbaaaabbbbbbaaaabaababbbaaabbbabbbaaaabaaaaaaabbabaabbababbbbbbabaabbbababaaaaaaaabbbbababbbabbbbaabaabbaaaababaabaaabaabbbbaabbababbabaaaabbbaaabbbbabbababbabbbbbbbaababaabababaaaabaabbaabbbbaabababbaaaabbbbbaaaaaabbbbbbbaabbaabbbbbaaaaaababaabaabbaababbaaabaababaababbaaabbbbbabaaaaaabababbaabbbbbbaaaaababaabaabaaaabbaabaaabbabbabaaaaabbbbababbbaaaaaaaabbbabbbaabababaaabbaababbabaabbbbaabaabaabaababbaaabaaabbbbbaabbaaabbbbbbbbbababaababbabbabbababbbbabaaaabaaaababababbabbbbbbbaaabbbbbbaabbaabbabbbabbbbbabbaaabaabaabbbbbababbaababbbaabaabbbaabaaababbbbabbbbabbabaaaabaabbbbbbbaaababababbaaabbbaaaaaababaabbaaaababbbabaabbbabaabbababbababaabbbbbababbbbabbaaabbbabbbbbbbbaabbbaaabbaabbababbababbaabbabaababaababbaabbabbbaaaaabbabaaabbbababbbaaaabbbabbbbaabbabbaaabaaaaabbbaaabbbbabbabbaaabbaaaaabaabbababbaabbabaababaaabbbabababbbbbbaabbbbbbbabababbaabaabaabbbbbaababbbbaaababaaaabbbaaaabbbaaabbbbbabbbaabbbbbbbbabababbbaabbbbbbbbaabbaaaaaaaaabababababbbabbbaabbbbbabbaaabaaababbabbabbbabbabbaaabaabbbbababababbbabbbbabbbababaababbabaabbbbbaabbabbbbbbaaaaabbbaaaababbbbababababaabbbbaaababaaaabaabbaaaabaaaaaaaabaaaaaaaabbbaabaaabaaaabaaabbbbbabaaababbbbbabaabbabbbabbabaaaaaababbababbbaaaaabbbaababbbabbbaaaaabaaabababbbbbbbaabbabbaaabbbbbabbabbbaaaabbabbbabbaaaaabababbbabbaaababbbaabbbaabbababbaaabbaaaabbbabaaaabbbbbaaaababaaabaabababbbbaaabaababababbaababbbaabbabbbbbababbaaaaabbababbbabababbababbbaaaaabbabbabaabbabbaabbbbbbbaababababbaabbbbbbabaabaabbbbbbaabbaabbbbbaaaaaaababbbbbbbaabbbababaababbbaabaaabbbbabababbabbbaabbbbabbabbbabbbababbbaabaabaabaababbabaabbaabaabbaaababaabaaabaaaaabbabbabbbbbbbbaaaaabababaabaaabaaabbaabbaaabbababaaaabbbaababbabbaaabbbbababbaaababaaababbbaaaabbabbaabbbaaaaaaaabbaabaababaabaaabaabaaabbbbaaabbaabbaabbbaabaabaabbaaabaaabababaabbbbaabaabbababaabaaabababaaaaaaabbaabaaabaaaaabaaaabbaabbabaabbaabbabbaabaaaaaaabaaababaabaaabababaaaaaaabbaabbbaabaaaaabbbbbbbbbabbbbabaabaaabaabbaaabbbbbbbaababaaaabaaaababbaabaaaabbabbbaabaaaabababbbabaaaabababaabaabaababaabaaaabaabbbbbbabbaaabbbbabbbabbbaaaaaaabaabaaababbaaaabbbbbbabaabbaaababbaaabababaababaaababbbbaaabaababbaabbaabaababbbbabbbbbbababaabbaaabbbbabbbbaabbbbabbbaabbbaaaabaaabbbabbbabababbbbbbbbbabaaabbaaaabbbaaaaababbabaaaabaaaaabaababbaaababbbababaaaaabbabbaabaabababbbbbbaaaabaabbbbbabbbabbabbabbbaaabbbbaaaaabbbbaababbbbbbababababbaababaaaaabbbbabbaababbabbbbabbbbabbaabaabbabbbbababbaaabababbbabaaabbbbbbababaaababbabbabababbababbabababababaababaaabbbabbababbabaabbbbbaaababbaaabaaaabababbbabaaabbaaabababaabaababbabbbbabbbaabbbbbabaabaaababbaaaaabbbabbbabbbabbbbaabbaaaaabaaaabaaabbbabbbbbbaaaabbaababaaaabbbababbababbabbaabbbabaaaabbbbbaabbabbbabaabababaabaaaabbbbabbbbababbaababbaabbaabaaaaaaaaabbbbbabbbbaaababbbbbbbbbbababaabbbbabaabbbaabbbabaabaaaaaaaabaabbbbaabbbbbabbbbaaaababaababababbbbbabaabbbabbbbaabbaaaaabaaaaaaaabaabbbaaabbbbaabbaaabaabbbaabbaaabaaababaaabbabbabbaabbbaaaaababbbabbbbabbaaaabbbbaabbbbbaabbbabbbbaaababbbbabababbbbbababbbbaabbabbbabaaabbbababbaabababaaaaabbbaaababbabaabaaaabbaabaaababbbbababbaaaabbbababbabbaabbbbbababbaabbbbabbbabbababbaabbabaaabbbbababbbbabaabbbaaababbbaaabbabaaabaabbbbabaaabbbbbbbbbaaababbbabbbabbbabaaabbaaaabbbbaaaabbbbbbabbaabababbbbabbabaaababbaaaababbabbaaaabbabaabbbabbaaabababababaabbabbbbabaaaaabbaababbbabbbbbbbabaabbbaababaabaabaabbaabbbbbbbabaabbaabbbbabaaabaaabbabbabbbaabbbaaababbbbbabbaaabababbbabababbabbbabbaabaaaababbbaababbbbabaabaababbbaaaaaabbbbbaaaabaabbbaabbaabbabbbabbababbaaababbabbaababbbabaabaabbbbabaaababbbbbbbbabbbaaaabbbabaabbbbbababbbabbababbbababbaaaabbbbabaaabbaaaaabbabbaabbbabaaaaaabaaaabbbabbaaabaaabbabbabaaabbabbabbaaababbabaaabbbbaabbbababaaababbaabbaabbaababababbbabbbabbabaaaaaaabbabbabbbaaabaabbbbbbbbbbbabaaaabbbbabbbbabababbaabbabbababaaabbababbababbaaaabbbaaaaabaaaabaaabaabaaaabaabbabbabbabbbaabbaaaaaaabbbabaaabaabaaaaabbbbabaaaababaaabbbbaabbbbaaabaaabbaaaaabbaabaaaabbabbbbaaaaabaaabaabaabbbaabbaabbbbbbbbbabbbbabbabaaaaaaabbbabbbaabbbabaabbabaababaababaabbbbaabbbbaabaabaabbbaabbaabaabbbaabbbbabbbabaabbbaabbbbbabbbabbaabaaaabbbbbbbbbbbaaabaaaaabaaabbbabaaaabaaaaaabbaaabaabaabbbbabbbbaabaaabbaaabaabbbbbababababaaabbabbbbaaaabbabbbaaaabaaabbaaaaaababbabaabababaabbaaabbabbbbaabaaaaabbbabaaaaabbbabbaabbbababbaaaaaabbbbbababaaababaababaaaabbbababaabbaaabbabbbbbbabbbbbaaabaaaabbbabbabaabbaabbbaaaababaaaaaabaaaabbbbaaabaaaabbbababbabbabbbababbbbbababbababaaaaabbaaabababbbbbabbbbabaababbbaabbbaababbbbaababbaaabbbbbbaaabbabaabbabaabbaaabaabbbbbabababbbabbbbbaabaababbbababbababbbaaabbaaaaabaaabababbbabababbaabaaabababaabbababaabbbabaabbaabbbaabbabaabbbbabbbabaaaabbabaabaaaaaaababbaabbbaaabaaaababbbaaaaabbbbaaabaabbaaaaabbaaabaabbababbabbaabbaabababbbbaabbbbaabbbababbaaaaaabaabaaabababaaaaabaabaaabbaabbbbbaabaaaababaabbaaabbaaabbbaababababbaaaaaaaaabbaabbbabbbbabaabbbaaababbbaababaabbaabababaabaaaabbbbbaaaaabbbbbbbaabbababaabaaaaaaaaaabbababbbababaabaababababbaabbbbbbaabbaababbabbaaabbaabaabbabbbabbaabbabaaaabbaabbbaaababbbbbbbaaababbbbababbbabbaabbbaaabbaaababaababbbbaaaaaaaaabbaaaaaaababaababbabaabbbbbabababbbaababbabbaabaaabaabaabaaabbaaaabaababbbaaaaababaaaabbbabbbabbabababaababbaaabbbaaaabaababbaabbaaaabaaaaaaaabaaabaabaaabaaabaabaaaabbbaabaabbbabaaaaababbbbaabaaabaaabbbbbaababaabbbbaaaabbabababaabbababbaabbbbbbaaaabaabbaaabaaaababaaabbbaababbabbabaaaabbababbabbaabbabbababaaaabaabbabbbaaabbbaaaaaabaabbaabaaabbabbbbaababbaabaabbbabbbbbabaaabbaaaabbbbabbbabaaabbabaaabbbabbabbbaaaaabbabaabaabbaabbbbbbbabbaabbaaabaabbaababbaaabbabbaaabbabbababbaaaaaaaaaababababaabbabaaaabbbaaabaaabbbaababaaaaabbbabbbbababaabbbbababbbbabbbabbabbabbbbaaabaabbaababbbaabbaaaabbaabaabaaababbbbaababaabaabbbaabbabaabaaaaaaabaaabbababbabbaaaaaabbbabbbabababaabbabaababababaaaaaaaaababaabaabbaabaaabbbaaabaaaaaaababababbaabbababbbaabbabababaabbaababbbaabbbbaaabaaabaaabbbbaabbbbaaaaababbaabababbaaabaabaaaababaaabbbbabababbbabbabbbaaaabaababbababaaaaaaaabaaaaaabaabbaabababbabbbbaaabbbabababaabbaaabbbabbbbabaaaaabbbaaabbaaabbabbabbbbabbabbbabbabaabbaaaaabbbbabbbbbaababbbbbbabbabbbabaaabaaabaabaabbbaaaababaaababbbbbbabbaabbbbabbbbabababaabbaabbbaaabbbababbaaaabaabbaaaabbbbabbbaaaaababbbabbaaabaaabaabaabbabbbabbbaaabbbaaabbbbabbbbbbbabbaabbaabaabaaaaaaabaaabbbababbbabbbabbababbbbabbbaaabbaaabbabababaababbbbabbabbabaaaaabaabaabaaabbaabbaababbaaabbbbaaaaababbaaaabaabababaaabaabbaaabaaaaabaabbbbabbaabbabaaaaaaaaababaabbbbbbbbbbabbbbbaabaaabaababbbabbabbaababaaaaabbaaaabbbabababaaabbaabbaaaaababaabaababbaabababaabbbaaabbaaaaababaabaaaabbbbaaaabaabaaabbbbbaaaababbaaaaabbaaaaabbbbabbabbabbbbabaaabbabbbabababaababaaabbbbbabbabaaaabbbbbbabababbabbbbabbbbbbaababbaaabbbbaabbaabbbbabbababaaaababaabbabbabaabbbbaaaaabbbabbabbaabbbbbabbbaaaaababbaababbbaaabbaaabaabbabbabbbabbabbbabbbbbaabbbbabbbbbabbaaaabaaabbbaabaaaaabaaaabababbabbabaabaaaabababbaaaaaabaaaaabbbbbaaaaabbabaaabbbbababbbabbaabaaaaaaaaabbbbababbbbbbbbabbaababbbabbbbaabaabbaababaaabbbabaaaabaabbabbbbaabababbabbbbabbabbbaabbaabaabaabbababbbababaaababaababbbabbaaaabbbbaabaabababaaaaabbbbabbbbbaabbaaabbaaabbbbbbbbabbbbbbbaababbabbaabaabbaabaaabbaaaaaaababbbaabaababbbbaababaababbbbabababaababbaabbbbabbabbabaabaaabbbbabbbbabbaaababaaabbabaaaababbaabbaaaaaaabbbbaaaabbbbbbbabbaaabbbaabbabbbabaabbbbabaaabbaaaaabbabbbbbbbabaaaabbabbbbbaabbbaaababbbbbbbbbbbbbbabbabaaabbbbbbbbabbbabaaabbbabbbbbbababaaabbabbabbaaaaaabbabbbbaaabbababaaabaaaabbaabbaababababaaaaabbbababbbabaabbbaabbaababababbaaaaaabaabbaaaabbbbabbaaaabbaaabbabbbaaaabaababbaabaabbbabababbbababbaaabbbababbbaaaabababaabbbabbabbaababbbaababbbbabbbbbaaabbaaabaaaaaaabbbbababbaababbbababaabbbabbaabbbabbaaabbbabaabaabababababaababaaaaaaabbbbbbaaaaabaaaaabbaabbabaabbbabbbabbababababaabaabababbaabbabaabbbbabaabbbabaaabbbaabbbbbbbaababaaaababbbabbbbaabbbabaabbabbbaaaaaaaabaabbbbaabaaaaaaabbbababbbbaaaaaababaababbbbaaabbbbbbaaaabaabaaaaababaaaaabbababbabbbaabbbabbbbaaabbabbbbbabbabbabaabaaaaabaabaaababaabaabbabababbbbbaabbababaababaaaabbaabbaabbababaaaaaaabaaaaababbababbaaaabbbaababbbabbababbababbaabbbbabbabbbaaaabbbbaabbbbbabaabbbbbbbbaaabbbabbaaababbbbabbbabbaabababbabbaaabbbaabaaabaaaabbabaabbbabaaaaaabaababbabbbbbbabbbaaabbaaabbabbbbabaaaaaabbabbbaaaabbaababaaabaabbbaaababbababbaaabaaaabbbabaaabbabaabbaaabaaabbabaabbbababbababaaabbbbbaabbbaaaaaaaaaabbabbbabbaaababbaababbabbabaaaaabbbbbaaaaabababaabbaabbaaaabbbbaabbbbabbabbababaabbbbabbbbbaaaaabbaaaabbbbbbbabbaaabbaabbbbbbbbbabbbabaabbaabababaababbabababbabbabbabaabbbbbabaaaababbabababbbbbaaaaabbbbaaababaaaaaaaabaabababbbaaabbbaabbabababbbaabbbaaabbbaabaaaaabaabbbbaaabbbbbbbaaaabbabbabaabbbbbaaabbbabababaaaaaabbaabaaababababbbbbbaababbbbababababbaaaabbbbaaaababbaaabbbaabbbaabbbbabbaaaaabaaaababbaaabaabbaabaaabaaaaabbaaabbabaaabababbaabbbaaabbabbbaabbabbaaaaaaaaabaaabbabaaabaaaaaaabaaaabbbabaababbababaaabaabaaaaabbabbabbabaababbbbabbaaababbbbbbbababaaaababbbbabaabbbbaaabbbabaaabaabbbbabbbaaabbaaaaabbabbabbbbbbababbbaaababbaaaabbababbaaabbabbaabbbaaabbbaabbaabaaabaaabaabbbbaabbbbbabbbbababaaaabaabbaabbbabbbababababbaabbabaaabbbabababbaabaaaabaabbaaabbbaaaaaaabaaabbaabbbaabbbaabbbbaaababbbbbbbabbaaaaaababbbbaabbbbabbaaabbaabbbabbbbbaaaaaaaaababbaababbbababbbaabbbbbbabbbbaababaabaabaabbbbabbaaababaababbbaabbabaabbbbbabbaaabbaabbaaaaababaaabaaaaabbababbaabbbbabbaaabbabbbaabaaabaaaabaabbaababbbaabbbbbbaababbaaabaabaaabbbabbbbbaaaaaaaabbaabbabaabaaabaaaabbbbbabaababbbbaabaabbaaabbbabbababbbaababbaabbbababbaaaabbaababaabbbbbbbaaaaaaabbbabaabbabaaaaabbabbababaabbbababaaaaabbabaaaabbabaaababbaaaabbbbaaabbabbbbbabaaaaabbaabbbabbbaaabaaabbbababaabbbabbbaababaabbbbabababbaabbababbaabbbababaabaaababbabbbbabaabbaababababbbaabbaabbaabaaaaababaabaaaabaaaabbbbabaaaaabbbaaaababaaabaabbaabbbabbbbabaabbababaaaaabbbbabbaabababbabbaabbaaaabbbabaabbaabbabababbabbbaaaabbaabbabbbbbbbaaaaaababbaabbabababbbaabbbababbabaaaababaabbbaabbbbbabaabbbaaaabbbabbbbabbababaabbbaaaabaaaaabababaaabaabbbaabababaabbaabbbabbbaabbbaaabbabbbaabbbabaababbaabaaaaaabaabaabbbbbbbabababbababbaabbaabaabaaaaaabbaababaaababaaabbbaabbabbaabaaabaababababababbbbbaabbabbbbbbbaabaaabbabbaabbbbabbaabbabaabaaabaabaabaabababaabababbbaaaaaabbaaabbbaaaaaaabbaababaabaabbbaaaababbbbaabbbaaaabbbaaabaabbbbbaaabbbbaababbabbaababbabaababaaaaabbbbbabbaaaabbababaaaabbbbababbbaaaaabaababbaaabbbbbababaaabbbbbbbaabbaaaabaabbbbbabbaababbbaaabaaaabbbabbbaabababaabaaabbbaaabababaaabbbaaabbbbabbabbaaabbaaaaaabbabaabaaababbbaabbaabbbaaabbbbbabbaabbbbbbaaabaaabbbbaabaaaabbbbbaaabbaabbbbbbbbbaabbababaaabaaababababababbaabaabaaaababbabbbbbababbababbabbbbbbbbbbababaaabaabaaabbbaaaaabbabbaaaaaabaababbabaabaaaaaabbaababbbbaabbabaaaaabaababbbaabbabbabababbaababbbbaaaaabaabbaabbaabbbaabbbbaaabbaabbbbabbaabbaabaabbabaaabaabbbbbbaaaaaaabaaababbbbbaabbbbaaabbaabaaababaabaababbbaaababbbbbaabbaabbbbaaaabaaabbabbababaaaaababaaabaabbabbaabbaabaaabbabaaaabbabaababbabbbbaabbabaaabababbbbaabbaababbababbaababbbbbaabaabbbabaabaaaababbbbaaabbaabbabbbababaaaaabbaaababbabbbaabababbababbbbaaabaabbbaabaabbbbabaaabababaabbabbabbbaaaaaaabbaabbbaabaaaaaabababbababbaaabbabaabbabaababbabbbbabbabbbababbbababbbaababaaaabbbaaabbbbbbbbbaaabbaaaaabababbbabbbababbaabbbbabaabbbabaabbaabbaaabaababbaababbbaaaaabbbabaabbababaaaabbaaaabaababaabbaaabbabbbbababaababbabaaabbaabbbbbbaaabaaaaabbbaaababbbaabaababbabbaabbbaaaaabbbbbabbaaabbaaabbababaaababaabbaabbabbabaaababbbabbaabbaaabbabbabaaaaaaabaababbbaabbbabaabbaaaaaababbbaaabbaaaaabbbabbababbabaabaababbaabbabababbaabaabaaaaaaababaabbbbaaaabbbbababbbabaabaabbabaababbababaaaaaabaaaabbbaabaaabaabaaabbaabbbaabbbabaaababaabaaaababbbabaabbaaabaaabbabbaaaabbbbaabbbbbabaabbabbbbbaabbabbaaabaabaabababaabbababaabbabbabaaaababaaabaaabbaabaabaaabbbabaaabbababaababbabaaaabbaaaabaabbaababbbabaaababaabbaaaabababaabbaabbaaaabaaaaaabbaabbaaaabbbaaaabbbbbbbabbaabbbbbabbaaaabbabaabbbabbbbaaabbaaaaaaaaabaababbbbbabbbababbbbabbbbbabbbaabbabbabaaaaaabbbbbbaaabaaaababbbbbbbabbbbababbbbababaaabbaabababbabbbabbabbbbbbaabbbabbbabbbbbbabbaabbbabaaabbbbbaababbaabaaabbbaaaababababbaababbabaaabbbbaaabbaabbbabbabaaabbababbbbabbaaababbbbaabaabaabaabbbaabbabbbaabaabababbbaaaaabbbbbbbaababaaaabbbbbbabaababbbaabbbabbbaaabbbaaaabbabbbbbaaaababbabaababaabaaaaaababbbabaaabababababbaabbaababaaabbaaaabaaaaabaaaaabbbababbaababbbbababbbbbbaababaaaaaaaaaababbaaabbbbababbbbaaaaaabaaaabababababaabbabbaaabbbabaaababbbabbbbabbbaabbbabbbaabbaaaababbaaaaabbbbabaabbbabbabbbabbaabaababaabbabbbbbbbbbbbaabbbbbbaaaaabbaaaaababbababbbbabaaaaaababbaaabbabababaaabbbababbaaaabbaababaabbbbabbaabbbbbbbbaabbbbbaaabbbbbbababaaabbbbaabbbbbababaababbbaabbbababaaaababababababaaabbbaaabbbaabbbbbabaaabbaaababaabbabababbaaabbbaabaabbbbbababaababbabbaaabaaaaababbbaabababbaabbababbbbbababaaaaabbbbaabaaababbaababaababbaaababbaabaaaabaaaaaabbbbbbbbbababbaabaaaaabaabbbaaaaaaaaabaababbbbbbaabbabababbbbbaabbbaaaaaabbbaababbabbaababbbbaabbabbbbbbaaaaababbaabbbaabaaaabbbaabbbbaaaabbabaabbbabababaaabbbbababbbabbababbaababaaababbbabaabaaabaaababbabbbbbaaaaaabbababaaaababaabaaabbbbababbabbbabbabbaaaaaababbabbaabbabbaaabbabbbbaaaabbaaaaabbaabbababbbabaabbbbabbaabbbbbbaabababbbbabbaababbbbabbabbbbaabaabbbabbaaaaaaaabbabbaabaaaabaabaabbabbbbaabaaabbabbababbaabbabbabbbaaabaaaababbababbbabbbabaaabbbabaaabaababbabbabbbabbabbabaabaababababaabbaababaaabbbaaabbbabbbbabbabababbababbaaabababbbabbabaabababbaaaaaaaaabaabaababbabbbbbabbbaaaababaababbbaaababaaaabbababbabbbabbabbaaaaaabbababbaaaaabbbababbbbbabbbbbbaaaabababbbbaabbbbbbaaabbabaaabbaabbabbaabababbabababaabaaaabbbbbbabbbbbaabaabbbababbabbaaabbaabbbbaabbbaaababbbbbababbabaababbbbabbbaababbaaababbaaabababbaabbabbaabaabbaabbaaaaaabbbaaaabbaabaabaaaaaababbbbaabaaaaabbaaaabbbbaabbbbabaaabaabaaabbababbbabbbabbabaaaaaaabaabbbaaababbabbaabaaaabaaabbbbababbbabaababbbaaaaaababbabaabbbaabaabbaaabbbaabbbbabbbaaabbbbabbbabbbaaaaabbbabbbababbbaabbaabbaabaaaaaabaabaabbabbaaabaaababbbabaabbabbaaaabbbaabbaababbbaaabaababbbbbaaaabaaabababaabbbbbabbababaaaababbbbbbabbbababbbababbbbbbabbaaaaabbbbabbbaaabaaabbabababbbbabaaabbbabbaaaaaaabbabaababaaaaabbbaaababbaaaabaabbaabbbabbaaaabbababbbbbbaaaaaabaabbbbbababbbaababbaabbbabaababaababaabbbababbabbaabababaaababbbaaabbabaaabbbbabaababbbbabbbbbaabaababbaaaaaabaaabbbaababbabaababbbaaababbaaabbabbaabbaabbbaabbbababaaabbabbbbabbaaaaababbbbbabaaaaabbbbabbbaabbbbbbababaabbbbbbbbbbabbbabbbabbabababbaabbaaabbbaababaaaabbaabababbabaaaaaaaaababaabaabbbbbbbaaabbbabbbbbbbaaabbbbabbbabbaaababaabaabbaababbabaabaaaaaabbbbabaababaabaaabaaaabbaaabaaabaababbbaaabbbaaaaaaababbbbaaababaaaaabbaaaabaabbbaaabaaabaabaabababbaaabababbbabaabbbbbbaabbbbaabaaaaaabababbabbaabaaabaaabbaabaaabbaaaabbbbabbbabababbbabbbaabaabbbaaaaabaababaaaaaaaaaaaaaaaabbaabbbabbaaaababbaaaabaaabbbaaababaaabbbababbbbbaababaaaaabbbbabaaaaabbbabbbbbbbaaaababbababaaabaabbaababaaaaaabaabbaabbaabbabbbbbbabaaabaabaabaabbbbabbbbaababbbbaaaabbaabbaabbababaaabbbbaabababbaabbaaabbbaababababbaaababbababaaaaabbbbbbbbbabababbbaaaabaabbaabbbaaabbaaabbaabbabbabaaabaaababbbbaaaabaaabbabbabbbbbaaababaabaaaabbabbababbabbbabbbaabbbbabaaaabaababbababaabbaaaabbbabbbbbbaaabababaaabbaaabbbbbabbaabbbbbabaaabbbabbaababababaaabababbaabbbaaababbaabababbaabaaaababaaaaaabbbabaaabbababbabbbaaabbaabbbabbabababaababbabaaaaaaaabaabbabababbbbbbbbabbbababbbbabaaaaabbbbbbaabaabbbbbabbbbaaabbabbbbbbabaabaaaaaabbbbbbaaaababbbbababbabbabbabbaababbabaabbbaaaabaaaaaabaaabbbaabbbbbababaabbabbaaabbaaababaabbabbaaabbabbabaaaabbbaabababaabbbbabaaabababbaaabaabaababaaaaabbbbbaabaaaabbabababaabaabbbbbabbbbababbaaaabbababaabbababbabaabbbaabbaaabababaabaababbaabbbbabbaabbaaaabbbbbaaaaabaabbbaabbbbaaaabbaabbabbabbbbaabaabaaaabbbabbabbbabaabbabbaaabbabaaabbbababaaabbabaaaabbabbabaaaaabbbbbabbbbbaaabaaabaabbabaababbbaabbaaaabbababaababbbbabbbaaaaabbbaaaabbabbabaaabababbbaabbbaababbaabababbabbbbbbaabbbbbabababaabbbbaaabaaaaabbbabaabbaaaabbababbbbababbaabbaaaaababbbbabaabbbabbbabbbbabaabaaaaaaaaaababaaaabababbaabaaabaaaaaababaababbaaaaababaabababbaabaaaaaabaaaabbabbabbbbbababaabaababbbbbbbbaaabababbabbbbaabbabbababbbbbbbabaabbabaaababbbbabbbabbbbaabbbababbbbbbaabababaaaababbbbbbabbaababbababaabaaabbaaaabaaabababaaababaabaaababbbababbaaabaaabbababbaabbaabaabbaaaabaaabbbaabaabbbaabaaabbbababaaababbaaabaabbbaabbabbbaaababbbaaabbabababababaaabababaaabbaabbbbbbbbaabaabaabababbbaaaaaabbbbabaaaaaababbbbaabaaaaaaaaabbbabbabbbaaaaababaabbbbbabbbbbaaaabaabaaababbababbabaabaaaabbbabbaaaabaaaaaabaabaaabbaabbbabbbbaaabbbbabbaaababaabababaaababaabaabbbaababbbbbbaabaaaabaabbaaababbbbbaaabababbaabaabbbbaababababaababbaabbbbbbbabaaaaabbabbaaabbaabaababaaabbbababbababbbaabababababaaabbbaabbabbaaabaabbabaaabbabbabbaababbaabababbbbbabaaaaabbabbabaabbaabaaaabaabaabaababbbbbababbaaaabababbbbaabbbbaaaaababababbaaaaaaaababaabbbaaabbabaabaaabaaaaaabbbabaabbbbbabbabbabbbbbbbbabaabbabaaabaabaaaaabaabbabaabaabaaabbbbbbbaaabaaaaabbbbbbbabaaaabbbaabaaabbbbbaabbbbbbbbabbbaaaaaabaaabbaaaabbbabaaaabbababaaabbabbbabaabbabbbaaabaababaabbaaaabbbbabaaaabbbbbbbaaabbabbaaabbaabaaabbbbabbababababbabbbbaaaabbbbbbbababbababbaaaabbababbaabbbbaaabbaabaababaaaabbabaabaaabbbbaaabbbabbaabbabbbaabbbbbabaabbbbbaabaabbbabbaabbaaababbbbababaaabaaababaaaaaabbbabababababbbaabbaabbbabbababaabaababbbabbabbbbaabbaaabbaaaaabaabaaabaaaabbaaaabbabaabaaabbabbaabbabbaaaaaaaaaaabbaaabbabbabaaabaaabbbabababbabbaaababbabbababbabaaabbabbababbbbbbabaabaaaabaaaaabaaaabbbbabaababaaababbaababaabbbaaabbababababaaababbbbabaaabbaababbbabbaabababbbbbbabbbabbbabaaabbbbbbbbabaabbbaaabaabaababbabaaababaaabaabaababaababbbaabaaabababaaaabbbbbbbbabaabaababababbaabaaaaabaaaabbabbaababbabbaabaabaabbabbbbbaaababbaaaabbbaaabbbbababbbabbbabbbaaaaababaabbbaaaabbbabbabbbaaaaabbbabbbaabbaaaaababaaaaabbbbabbaabaaaabaabaaaaabbbbbbbaabbbbbbabaaababbbbbbaaaabaaabbbaaaaabbaaaaaabbbaabbabaaabbbbaaaabbabbabaaaabbbbabbaaabbbaaaabbabbaaabbaabaababaaaabbbbaaaababaaaabaaaaaabbbaaabbaaababaaabbbbbbaaaaaaaaaabaaaabbbbbbbaaaabbabbbbabbabbbaaaabaaababaababaababbbabaaaabbaaaabbabbaaababbaaabaaababbbbbabaabbbbaaabbbaaaabbbbaababbbbbbbaaabbbabbbaabaaabaababaaabaabbabaabbaabbbaaabbaaabaaaabbababaabaaabbbbbbbabbbaaabaaaabbbabbaaabaabbaabaaabaaaaabaaabaaabaabbbbbbbababbabbaaaabbbbabbbbbababababbabbabbaababbbaabbababaabbaaaabbbabbbabaaabbabbaaababbabaaababaaabbabbbaabbaaaabbabababbabababaaabababbbbbbbbbaaababaaaaabababbbaaabbabbaaaabbbabbbbbabaabbbbbbababbaabbbabbabaaaababababbbbababbaaaabbbabbbbbbbbbaabbaaababbbbbaaabbbbababaaaaaabaababbababbaaabaabbabaababbbbbbbbabaaabbbababbbbaaaaabbaaaabbaabaaaababbbbbbaababaaaaaabbaababbbbabaabbbbabbabbbaaababbbabbaababbbaaabbbbabbabbbbbabbbbaaabaaaabaaabbbaabababaaaaabbbbbbaabbbbbabaabbabbbbaaaabbaabbaaabbaabbbbbaabababbabbbbabbabaabbabaaabbbabababaaaaaaabaabaabaaaaaabaabaabaabbbaabbbababaaabaaaaababbbaabaaaaabbabbaaaabababbbaabbbabbaabaaaabababaaababaaaaaabbaaabaaababbbabbbbbbbabbbbabbbabaaabbbbaaababaabbabaaabaabbbaabbbaababbababababbbaaaabaaaaaaabbbabaaabbbaababbabbbbbabbabbaababaaabbbaaaababbaababababaaababbbbaabbaababababbbbbababbbbabbaabaaabaaaaabbbabaabbaaaaabbaaaaabaaabbbaabaaaababaaababaabaabbbabaabbbbbbbabaaaabbbaaaaababababbbbabaaaabbaaaabbbaabaaaaabaaabaaabaaabababbbaaabbbbbabbabaabbbabbbaaabbbbaabbbababaaaaaabaaaababaaaaaababaaabaaaaaaabaaaabbbbaaabaaabababbbabbabababbaabbabbbbbbbbaaabbbbbbaaabbbbaaaababaaaaabbbaaabababbbaabbaabbabababbaabbbaaaaabbbbaaabbbbaaabbaaaaabbaabaaababbaabbabaaabbbbbbaabbbbabbbaabbbabaaababaaababbbbabbbabbbaabbaabbbaabbaaaaaabbaaabbbbbabbabbbaaaaaabababaabaaaaaaababaaabaaababbababaababbababbbaaaaababaaaababbbaabbaaabbababbbbaaabbaabbaaaabbabaaaaaabbabaabbbbaaabaabbababaabbbbabbbbbababbbbabbaababbbbabbbaaaaaabbaabaaaabababbbabbaaaaabaabbbbaaaababaababbbbabaabbaabaaaaabbbaaabbbaabaaababbbabbaaabaaaaaabbaabaabaabbbabbbaaaaaaaababbbabbaaabaaaabaaabbbaaaaabbaaaaabbababbbbabaababaabaabbbbabbbabaaababaaabaababaaaaaaaabababaabbbbbbabbaaabaaaaaabbabbbabaabbababaabaaaaabbababaababaaaababaaababbbbababaaabbaaaabababbbaaabaababbbbabbbabbaabbaabbbbabbbbabbaabbbaababababbbbaaaabaaabaaabbbbbabaaaaaaaabbbabaabaaaaababbabaabbabbbbaaabaaabaabaabbbabababbbabaababbbbabaaaabbbbaabbababbaaaabaaaabbaabbbaaaabbbbababaabbaaababaabbabaaaabaaabbabbbbaabaababaabbabbaababbaaaaaabaaabbbbaaabbabbaabaaabaaabbbababbbaaaabbabbabaaaaaabbababbbaaababbbbbabbabbbbbbbaaabbbbabbbabaabbabaaabbbabbbbababaabababababbbaaaaabaabaabaaabbabbbbabaababbababbaabbaaabaaabaabaababaabbababaaabaaaabbaaaabaabbaaabbbbbabbbbbbabaabaabbabababbabbaabbbaabbbaaabaabbabaaabbaaababbbbbabbbbbabaaaaabaabbaabaabbaaaabbbaaaabaabbaaabbbbaabaabbbbaabaaabbaabbaabbbbbabaabababbaabbababaabbaabbabbababaaaaabbabbbbbabaababaababbbbabaabbbbabbbabbbbaaaaaabaaaabababaabbbaababababbabaaabbaaaaaabababbbbabbaabababbabbbaaabaabaaaaabbaabbbaaabaaaabaabaaaabbababbabbabbabaababbaaaabbbabababbbbbabbaababababaaaababbabaabbababbaaaabababbaaaaaaaababaababbabbbbaabaabbabbaabbaabbaaaaabaabbaaabbabbaaabbabbabbbbbaabaaaaababbabbbabbbbbabbaaaabbaaabbbbaabbbabaabbbbaabbbbabbbaabaaaabaaabbbabaabbbabbbbbaaaaaaaabbbabbabbbaababbabbbabaabaaaabaababbbabababababbaaaaaabbbababbaabaabbabbabababbbbbaabbbabbbabaabaaababababaabbbabaabababbaabbbabbbabbbaabaabaaababbbbaabaababbaaabbbbbaaaaaabbbbbbbabbbabababbabbbababaaababbbbabbbabbbbaaabbbaaababababbbabbbbaababaabaaaabbbabbaaabababbaabaaaabbbbbbbbbababbaabbbabbababbbabbabaabaaabbbaaabaaabbbbbaabbbbaaababbbaababbaaabbbbbbbbabbbabbabaaaabbaabaaabaababbaaabaababbbbaabbbaabbbababbbbaabbababaababaabbbabbaaaabaaabbabbaabbaabbabababaababaaaaabababaaaaaabbbbbababbabbababaabbbbabaaaabbaaaaabababbbababbbabbabbbbbbbabaaabbabbabaababbbabbaaaabaaaaaabbbbaababbbaaaabaabaabbbbaaaaaaaabbbbbbbbbbabaaaabbbabbabbbbbbbbbababbbaababaaaabaababbbbbbaabbbabaabbabbbabaababbbbababbbabbbbabbaaaabbbaabaaabbabbbbbaaabbababbbaababbaabbbbaaaaabbbbababbbaaabbbbbbabbaabbbaabaabaaaabbaaababbbbbaaaaabbabbbbbbbaabaabbaaaabaabaaaaaaabababbaaabbabaabbbaabbbbabaabbabbabbbbaabbaaabbaabaaababaabbabbaaaabbabbaabaaaaaaaabbaababbaaaababbbabbbbaababaaabbbbbababaabaaaaabbababaabaabbabbabaabaaabbbabababaaabaaabbbbaabaaabaabbabbabbababbbbbbbabbabaabaabbbabababaaababbabbbbabbbabbbaabbaabbaaabaaaababaaaaaabbababbabbabbaaabababbaaaaaabbabaabbaaaaaaabbbabaabbaaaaaabbaaababbbbaaaaababbbaabbbabbbbababaabaaaaaabbabaabbaabbbabaaabbaaabaabaabbababbabbbbaaaababbbaaababbbabaabbaaabbbbaababbbabbbaabbabbbbababababbbabaaaababbaaaabbabaaababbaabaabbbbaaababaababbbaabbbaaaabbbbaababbbbbaaaabababbbabaabbbabaaaaabaabaabbbbababaaaabaaaabbbaababbabaabbbababaaaaaaaaabbabbbbbbabbbaaabbaababbbbaabbbaabababbbabaaabaaaabbabaaababbabbbaabbaabbaababaaaabbabaababbabaabbaabababbbaaaabaaaaaaaabbaaaabbbbababbaaaababbabbbbbaaabaababbaabaaaaabaaaaaabbbaabbbaaababaaaaaaaaaabababbbababbababbaaabbbabbabbaaabbabbababbabababaaabbaabababaaaaaaaababbbbbbbbaaaabbbaaaabaaaababbbaaaaabababbbbbabaaaaabaabaababbaabbbbaaababaabbabbbabaaabaabbbabbbbaababbabaaaaabbababbbbaabaababbbaaabababbabaaabbaabbaabbabaabbbaabaabaabbaaababaabaababbbbbbbbbaaabababbabbbaabbaabbbbbbababaabbbaabbbbaababaaaaaabbbbabbababbbaabbababaabbbbabbbbbbababbaaababaaaabbaababaabaabbbaabbaaababbaabbaaaababbbbbbbabbabaaabbbbbbaaabbbabaabaabbbbabaababaaaabaababaabbaaabbaabbaabbaaabaabbabaabbaabbaabbabaaaaaababbaaaabaaaabbababbaaabbaabaaababaabaababbabbbabbabbbaabbbbaabbabbaaabbababbbbaaabbaaabbbbabbbbbbabbabbbbbaaabaaaabbbabaaabbabbbbaaabbbbbbaaaaabababbaabbbbbabbbabaabbaaaabbbabaaaaaabbaabbaaabaaabbbaabbabbaaaaabbbbababbaabbbbabbbbbaabbaabbaaaabbbaabaabaabbabbaabbbabbbabbbbaaaaabbabbabbabbbbabbbaabbabbbabbaaabbababbbaaaabaaaabbaaabbabaabaaabbabbaabababbabbbabaabaabbaabaaaaabababbababaabbabaabaabbaabbabbabbbaaabaaaaababbaaabaaaaabbabaaaababbabaabbbaaabbabbbabaabbbbbbababbaabaaaaababbbbaaabaaabbabaaaaabbbbbbbbbbbabababaabaabbbbabbbababaaabbbbbabbabbbaabaaaabbabaabbabaaabbabbbaabbaaaaabaaaabbabaababbbaaabaaaabbbababbabaaabbabbabbbbbabbabbbbaabaaabababaaabbaababbabababababaabbbbaaabaabaaaaabbaaabaabaabbbabbbbbaaabbabbbbabbaaaaaabaababbaaabbbabababbaaaaabaabababaaaaaabaaaabaaaaabbbaaabbbbbababaaabababbabbaabbbbaabaababbaaabaabbbaaaabaaababbabbbbaabaabbabaababbaaaabaaabaababaababbbbabbbbababbbbbaaaaaababbabaaaaaaaababaaaaabbbaabbabaababbbbbbabbabaaaaabbaabababbaabbaaaabbbabbabaabababbababaaaaababbbababbbaabbbbbaabaaababbbaaaababbababbabbaaaaabbaabaabbbaabaabbaabbbaaababbabbbbbabaaaaababbababaabbbaaaabaabbbbbbbaaababaaabbaabababababbaabbbbabbbbabbbbbaaaaaaababbabbaabbababbabbbabbbbaabbbabbbbbbbaaabbaaabaababababbabbbbbaaaababbbbaaabbbbaaabaabbabbbbbabbbbabababaabbbabaabbabbabaabbbaabbbabaaaabbaabbbbbbbabbbaaabaaaabbabbabbaaabbbbbbbaaaabbbbaabaabbbbaabaaababaabababaaabbbbbabaabaaaabbaaaaaabaaabbbabaaabababbbbaabababbbababbaabbbabbbbababbabababaaaaabaaaabbbabaaaabbbbbabbbaaaaaabaaabbbaababbaabbaaaabaabaabbaabbbaabaabaabbbaaaababbaaaababbbbaaabbabbbabbbababbbbbbbbaabbbababbbaaababbbabbabaabbaababaaabbaabbbabbaaabbabababababbabbabababbbbbbbaaabaabaaabbabbbbabaaabbabbbbaabbbbbbbbbaaaaabbababbbaaababababbbaababaaabbbababbbabaaabbbbbabaaababaaaababaabbbabaaababbaaaabbbababaabaaabaaaaabaaaabbabaababbbaaababaaababbaaaabababbaaababbaabbbabbbaaaaaababaaaaabaababbaaababbaabbabbabbbbbbabbabbbbbabbababbabaaabbaaabbbabbabbbbbbbabbababbabaaaabbaabbbbbbaaaabbabbaabaababbababbbbbbbabaabababaababaabbbaaabbbabaababaababbbbbbaabaaaaababbbabbbbababbbabbaabaaaabbaabbbbababaaaaabaaababbbbbbaaaaabbababaababaababaabbbbaaababaabbbaabbabbbabbbaabbbaabbbabbabaaaababbbabbaaabaabbaaaaaaaaabaababbbababbaababaaababbbabbaaaaaaabbaaaababbaabbaaabaaababaabbbabaaaabbbbbabbababbbbabbabaaabbababaababaaaaaabbbababbbaababbbbaaabababaabaaababbbbbababaabbaabaaaaabaaabbabbabbbbbaabbabaaaaaaabbbbaabbaaaababaabababbabbbbabababbabbbbaaaaaabbbbabbabbbabbaaababaaaabaaaabbabbbbabababbabbbbaaaababbabbabbaaabaaabbababbabbbaabababbbbabbaaaaabbbbaabababbbaaabbbabbbbabaabbbbaabbbaaaabbbaaabbbbbabbaaaaabbaabbbbaaabbabbabaaaabbaaaabaaabababaababbbbabbababbababaaaabbababbbbbaaabaabbaababbbbbbbbbbabaababaaabaababbbbbbbaaababbababbaaaaaabaaabaabaaabbbbaaaabbbbbaaabbbbaaabbaaaabbabbabaababababbabababbaaaabaabbaaabbbbaaaabaabaababababaaaaaababbabbbbababbaababbaaabbabbbabaaababbaaaabaaaaababbbaaaabbaaabaabbaaaaaabaaaaaabaababbbaaababaaabbaabaaaabbabbaabbaabbbababaabbaababbbababbababbaaaaaaaaababaaaaaaaabbabbabbbaaabaaabaaabaaaaabaaabbabaabbbaabbabaabaaaaabbabaabaaababbaabbbaabbaaaabbaaaaabbabababaaabbababaababaaaabbbbbbbbbbbbababaabbbbabaaabbbbbbaaabbaabbaaabbaabaabbbbbaaabaabababbbaabaabaaaaababbbbaabbabaaaaaabaaabaabababaabbaababbaabababbbaabaabababbaabbbabbbabaabbababbabbaaababbaaabababbbbbbabbabbbbaababbbaababbababbbbabbbabbbbbaaabbabbaaaaaaabbaaaaababbabbaaababaaaaaababababaaaabbaabbbaabbabbaabaabaaaaaaaabaababbbbaabbbbbaabbaaaaabbbaababaababaaaabaabbaababaaabbbabbaababbbbabaaaabababbabbaaaabaabbbaaababaabbbaabaaabaabababbaaaabaaaaaabaabaabbabbbabaabbabaaaabbbabbabaaaabbabbbbaaaabbbaabbbabababbaaaaaaaabbbaaababbbbbbabaabbaaaaaababbbbbabbbaababbbbbabaabbaabaabbaabbbbbbabbaabaaabbaaababaaaaaabbaaabaaababbabababbbbaaabaababbabaabbaabbaababbbabbbbabbabbbbabbbaababbabbbbbbbbbaabbbbababaaabbabbabbaaabbbaabbaaaabaaababaaaabbbbaaaabbbabaaabaabbabbbabaababaaabbaabbbbabbbbbbababbaaabbbababaaaaabbbababbaababbbbbaabbbabbaabbbbaababaabbabbbaababbbbbbabbaabbbabaaababbbbabababbabaaabbabaabbbbbababaabababaaaababbbaabbaabaaaaabaabbabbbaabaabbaabaabbbaaaaabaabbbbabbbaaabbbbabaababbaabababbbbbababaaaabbbbbbbabbaabbababababbababbbbabbbabbaababbabaaaaaaababbbaabbbbaabbaabbabbbbbbaabbabaaabaaaabababbbbbaaabbabbaaababaaabbbababaabbaabababaabaabbaabbbabbbbbbabbbbabbbaaaabbbababbbabaabaaabbaabaabbabaaabbaaaabaaaabbabbbaaaabbabbabaabaabbababbabbbaabbaabababaababbbabbabbaabbabbbbababaaaaaabbbabbaaababaaaababaaaabbbabbbbbbbbabaaabbabbabaaaaaababbaabbbaaabaaabaaaaaababbbbabaabababbbababbbabaaaabaabbbaabaaabbaaabaaaaaaaabbbbaabbbbbbaabaaabbbbbabbaaabbaabbabaaabaaabaabbbbaabbbbbbabbbaababaabbaabbabaabbaaabbbbababaaaaaaabbbbabaaabbabaaabbbaabbbaaabbaabbaaaaaaabaaaabbbbaabbaabaaabbbabaabbbabbaaabbaaababaaabbaabaabbbbbabbaaaaababaabbaaaaaabbabbbaabbabababbbbbaabbabbbbababaabaababbabaaaabbbbaababaabbaaabbbababbbbbaabbbababaabaabaaaaababaaaabbbababaabababbbaaaabbbbbabbaabbaaaaaababaaabaabbbabbabbbaaababbbabbbbaababaaabbabbabaababbbbaabbaabbbbbbabaabbabbabbbabaabaaaabbbbbabbaaabbbbbbbbabababbaababbabbbbbbaaaabbaaaababaabbbaaaaaabaaaababaaababbaabbabbaaabababbababaaaabaabbaaababaabbabbaaaabbabbaaaabbbabbbbbabbbbababababaababbbbbabaaaababaabbabaaaaaabaababaabbabaaaabbabbbaabbbabbbababaabbabaababaabababbaaaababbababaaabbabbabbbaababaaaaabbabbaaabbabbabaaababbbabaaabbabbabbbbbababbaaaabbabbabbaabbabaabbbbabbabaaabbabaaaabbbaaabbbabbabbaabaabbabbbabbabababaabbaabbabaaabaaaaaabbaaabbababbbbbbbabaabbabababbaaaaaaaaaaaaabbbababaaaabbbbbaaabbabaabaabbaaababaaabbbababaabaabbbbbaabbbababbaaabbababbbbbbababbbbbbbabaabaaaabbabbbabbbabbaaaabbaabbababbaaaaaababbabbbabbaaaababbabbabbbbaababbaaabbbaaababbaabbbabbbaaaaabbbaaaabbbbbaaaababbaabaaaaabbbabbaaabababaabbabbaaaaabbbbbbbabaabbabaaaaaaaabababaababbbbbbbbabaaababbbabbabaaabababbbbbbbbbbaaababaabaabaabbabbbaaaabbbbbbabbbabbbbbabbbbabbaaabbbaabbbbbaabbaabababbabaabbabbbbabbaabbaabaaababbbabaaaababbaaaabbbbbbbbbaabbbababbbababbababbbbbbbbabaabaabaaabbabaaaabababbaaaaaabaaaababaabaaabbababbbaabaabbbbaabbabaaabbbabaabbabaaaabbbbbbbaababbbbabaabaaabbbbbbbaaabbaaabaaaaabbabbbabbbabbaabaaaaabbbaabbababaabbbaabbbbaababaabaabbbabaabababbaaababababbbabaaaabbbaaaababbaaababbbaabaaabbbbaaabbaabbbabbbaabbababbaabaaaaabaaaaabbbbababaabbabaaaaaabbbaaababababbaabaaaaababbbabbabbbbabaaabbaaabaaaaabbbbaabaaaabaaaababbbbbbbbbbbaabaababbaabaaabaababaababbbaabbaabbabbaaaaaabaabbbbbabbaabbaaabbbbaabbbbaabbbbaababaaabbbabbaababbbabbabaababbabaaabbbaabbaabbaaaaaaaaabbbbbaababbbaabbbaaabaaaaabaabaabbbaaaaabbabababaabababbabaabbbbbbbaaabbaabbaabaaaaaabaabbbbababaababbbbaaabbbaabbbbabbbbbaaaababbabaabbabaabbbbbaabaabbaaabaaabaabbabababbaabbaababababbabbabaabaaababababbaabaaabbbaaabaaaaaaabbbabababababbbbbbbbbaabaabbabbbaabaaabbbbbbbabababbaaabbbbabaaaaaabababaabbbaaabbaabababbbaababaaabaabbabbbbbabbaaabbbabbaabaaaabaabbababbaaabbabababaaabbbbaabbaababbabbbababbaabaababaabbabaaababbaababbabbaaababababaabaaaaabbaaaabbbaabababbabbaaababbaababbaababaaabbabbaabbbbbabbabbaaabbabaabbbbbabbaabaaababaabbbabbabaaabaaaaabaabbaaabbaaabbbbbabbababbabaabaaaaaabaabaaaababbaaabbbbaaaabaababbabbbaabababbbbbbaaababaabbbaaaaabaaaababbbbbbaabaabaababaababaabbabaababbbaabaaaabbbaaabbbaaaababaaabbaaaabaaaaaababaaaaabbbbabbbbababbbbbababaabbabaabababaabbabbaaababbbbababbaababbbbbabbbbbaaaabbaabbbbabbaabaaabaabaabbaabababbbabaaaaabababbabbbbabaaababaaabbaabaaabbbbbbbbbbaabbbbbababbbabababaaaabaabbaabbaaababababbabaabaaabaaaaabbbaaaaabaaaaabaaaabbbabbbabbabababaabaaabaabbbbbbaabbbbbbaabbaaaabbaabbbabbabbaabbbbbabaabaababbbbbbbbbbbbbbbbbbbbababbaababaabaabbbbbbababbabbaaaaaaaabbaabbbbbbbbbababbaabaaaabbabaaaabbabbaaaabbbaabbbaabbbaaabbbbabbabbbbabaaababbbabbabbabbaaaabbaabbbaabbabaababbbbabbabaaaabbbaababaabbabababbbaabaabaaabaababaabaaabaaaabbbbbbbbabbaabaabbabbaababaaaababbbbaaabbbaaaaabaaaabaaaaaaabbaaaababbaaabbaaabaabbbaabababbbbbbbbababbabbaaaabaabaaaaaabbbbbababbbbbbaaaababbabbbaababbbaaabbaaababbaabaaaabbbaaaabbabbbabbbbbbaaaababbaaaaaaabaababbababbbaaaabbabbabbbaabaaabbbaabbabababbbbbbbbbabbaaaabaaaabbababbbbbaabbbabaaabaabbabbbbbaaaababbbbaababaaaaabaabbbbbbbabbbbabbbaabbbaabaababaababbababababaabbbaaaaaabaaababbabbabbaaabbbaaababaaaabaabababbbababbabaaaabbbbaaabbaaaaaaaabaabbbabababaaabbbbabbbbbaaabaababbbaaaaababbbbbaaaaabbbabbbaaabaabaababaaabaabaabbabbabaabbbaabaaabaabbabbbbbbbaaabbbabaaaabaababaaaabbabbbaabababbaabbababbbabbbbaabbbabbbabaaabbaaaaabababaabbababbabbababaaaaaabaaaabbabbaabaaaabbaaaabbbaaaaabbbbaaabaaabbabaabababaaaabaaaaaaabbaabaabaaaaaabaabbbabbbaaaaaabaabbababbaabababaabbaabbabababaaabbabaaabbbaabbbaabbbaababbbbaabbabbaabbbbaaaabbbabbbbbaaababababaaaaabaaabbbbaababbbaababbaaaabaabbbaabbbaaaabaabaaaaababbabbaabbbbaaabaaababaaababbbaabaaaaaaabababbbbabaabbbbaaababbaabbbbaaaabbbaabaabababbababaabbbaababbbabababaabaabaabbbaababbbaaabaaaaaaababaaaabbbabaabbbbaaaaababaabaaabbbaabbabbabbbbbbabbbbbabaaababbabbbabaaabbbabababbbabbabbbaaabbaabbaababbabaabaabbbabbaabaaaabbbbaababbbaaaababbabbabbbababaaabaabbbabbbaaabbbabaaabbaabaabaababbbbaabbbbbbaababbabbbabbbabaaabbbbbbbbabbabbbbabbaabbbabbbaaaababaabbaaabaaaabbabbabaababbbabbbabababaaaaabaabbbbabbbbaabaababaaaabbabbabbaaaaababbbbaabaabbabbabaababababbabbababbaaabbaababbbbbabaabaaabbbbaabbababaaabbbbbabaaabbaabbaabaaaaabbbbaaababababbbaabbbabababbabbbbaaaaabbbbaababaabbaaaabbaabaaaabbbaabbbababbaaaaaaabaababbbabbbbababbababbaababbbbbbabaababbabaabaabbabaaaabaabaaaabbabbbbbaabbaabababbabbbbbbaaababbbabaabaaaaabbaabbaabaaababbbabbbbbabbaabbabbaabbaaabbaaaabbaaaaabbabbbaabbaabbbabbbaababababaababaabbabaaabbaaaaabaaababaaaaabbbbababbaabbaaaaabaaabbbabaaababaabbbbabaaababaaabbbbabaabbbabbbbbbaababbbbaaabbabaabbbaaaabbbaababaaaaababbaabbbbbaabaabbbbbaaaabbaaabbaaaaaaaaaaabbabbabaaaabbbbabbaaaaabbbbbabbbbabababbaaaabaaaaaaaaabbaababbabaaaaababbbbabbabaababbbabaabaaaaaaabaababbaaabbbbabaaaabaaaabbbabbaaaabaaaababbbabaababaaaaabaabaaabbaaaabbbbbababbaaabbbbbbbaababbababaabababaabaaaabaabaaaabbbbababaaabbabaabbabbbbaaaabbabbbbaaabbababbabababababbbaabbbaabbbbabbaababbaaabbbabaabbbabbbababaaaabbabaaabbabbbbaaabbbbaaaaabbaaabaaabaaabbbbbbabaabbbabaaaabbabaabbbabbabbabbbaabaabbbaabbbbbbbaabbbbabbbbaabaaaaaabbaabbaaabaabbbaabbbbbabaaaaabaaabbabbbaaaabbbbabbabaabaaabaabaabaaabaabaabbaaaabbbaababbbbbbbaaaaabaaaaaaaaabbaabaaabababaaaabbbbbabbabbbaaaabbaababbaaabaaabaaaababaababbbabbabbbbbbbbbbaaabbaabbabaaaabaaabaaabbbbbbbaaaabaababbbbabbbabaaabbbaabaaaaabaabbaaabaababbbbbbbbaaabbaabbabaaabbbbbbbbabaaababbaabaaaabaaababbbababbbabbaaababbbaabaaaaaaaaaaabbaabababbbabbabaabbaaaaaaaaabbbbaaaaaabbabbababbabaabbbaaabbaaababbaabaababaabbabbaababaaaabbbaabababbaaabbaaabbaaabbbaabaaaaaababbaaaabaaabbbaabbabbabbbaaabbbaabbbabaaabbbbabbabaaaaaabbabbbbbaaaabababbabaaaabbaaabaaabababaaabbbaabbabbaabbbabbbaaabaabbabaabbbaaaabbabbbbaaabaabbabaaabaaabbbbbbabbbbaaaabbbbaabbaabbaabbabbbaabbaabbbaabbaaaabbaaaaaaaabaaabaabbabababbbabbababaabaaaababbaaaabaababaababbbbabbabaaaabbaabbbabaabbbbbbabbaaababbabbaaabaabbbabaaaabaabaababaabaaabaabbabaaaaabaaabababbaabaabbabaababbbbbbbabbabaabbaaaaabbbaabaaaababaababbabbbbbbabbbababababbaaaaaababbbbabaaaaaababbbabbaaababbaaabbbbbbaababaabbbbbabbbaabbabababbbababbababababaabbbabaaababbabbabbbbabaaabaaabbabaaabbbbabbaaaaababbaabaababbbbaaabbbaaabbbbbbaaabbabababbabaabaabbababaaaaabbabbbbaaabbaaaabbbabbababbaaaabaabbbabbabaababbbbabbababbaabaabaaabbababbaaaabaabaaabaababbabbbbaaaaaabbbbbbbaababaaababbbababbbbbaabbabbbbabbabbaaabaabaabbbbaabbabbababbbbbbbabbababbbbababaaabbbbaabbbaaababbbbbabaaaababaaaaabaaaabababbbbaaaaaaaaaaabbbbbbaaaaabbabaababbaabbaabaaaaabababbabbaababaabbaabbabbaabaababbbaabbababbabbbbaabaababababbaabbbbbbababaabbbbbbbaaaaabaaaaaaaabbaaaaaaabbabaaaaaabaabaababbabbbababbaaababbbabaabaabaaaabbabbaaababaababaabbbbbababbabbababaaababaababaaaababbaaabababbabababbbaaaaaaaaababbbabaaaaabbabbabbbbbbaaabaaaabbaabaaaaabbbabbbbbabbbaabbaaaababaaabaabbbaaababaaaabbaabbbaaabbbbaaabaabbbbaaabbaabaaaabbaaaaabbbbabbbbbaabbbabaabbabbbbabababaaabbaabbabbaabbabbbaaabbaaabbbaababababbbabbbbabbbbbbbababaaaabbbabaaaabaababbbbabbbbabaabbaaaabaabbbabbaaaaaababaaabaabaababbbbabbbbbbbbaabaabbbabbbabaabbaaabbbaaabaaabbaaabbbbbbabbaaaabbbbabbbabbbbababaabaabbabaabbbbbbabbbbbababaababababaaababbabbaaaabababaababaaabbbbbabababbabbaaabbbabaabbabaabaabbbbbbabbbbbbbbaabaabaaaaaabaaaaabbbbbbaaaabbababaabbbaaaabaabbbbabbaaabbbabbbbaaaabaaabbababaabbbaaaaababaabbbbbbaabababbbbaaabbbabbaaaababaaaabbaabaaaababbbbabababbaababbabaabbbbaababbbbbababaaaababbabbbabbababaabbabaabbbababbbbbaaaababaababaabababaabababbbabbbaaabbaaaaaaaabbaaabaabbbabaabbbbbabbaaaabaaabbbbababaabbbaabbbbabaabaaaabababbaabaabbbabbbbaabbabaaaaaababababaaabaabbbaaaabbaaabbbbbababaaaaaabaababbaaabbbaabbbbabaabbbaaabbaaaabbbbabbababaabbaaaabaabbaaababbaabbaaabaabaaabbbabbaaabbabaaaaabaabbbbbabbaaabbaaaabaaaababbaabbaaaaabbabbaaaabaaaabbaababbbabaaababbabababbabbbaaabababbabbaababbbabbabaaabaaabaababbabaabbaabbbabababbbbabbbbbbabaaaaaabbabbbabbbbaabbbbbabaabbaabababbbaaaaababaaababaabaaababbaaababbbbbaaabbbbabbbbbbaabbbbbbbaabbbabbabbaaaaabbaabaaabaaaababbbabaababbbabbabaaababaabbabbbaabbbbabbabbbaabaababaaababbbaaaaabbbabaaabababbaaaaaabbabbabbaaababaaabaaaaabbbabaabbaaaaaabababbabbbababaabbabbabbbababaaaaaabaabbaaababaabaaabaaaaabbaaabaaaaaabbbaaabbaabbaabbbaababbbaabaaabababbbabaabbaaaabaaaabaabaabbaaaaabbaabaababbbabbbabaabbbbbaaabbaaaabaabbabaabbaabbaaabbaabbabbbabaabbabaabbbaaaaababaabaabbababaababbaaaabbbaaabaababbbbaabbbbbbaabaababbababbababbbbbbbbaabbbbaabaaaababbaabaabaababababaababbbaaabaaaaaaabababaababaabbaaabaaaaabbbaaababababbabbbbbbbabbbbbbbabbbabbbaaaaabbaaaabaabbbbaababbbbababbabababbbaaabbaababaabbabbaaaabbbaaabbaabbbbbbababbabaaabbbabbbbbababbabababbbbababbaaabbbaabbabbabbbbbbbbababbabbbaaaabbaabbbaaaaaababaaabaaaabbbbbaabaaabaaabaaabbbbabbaababaabbabbbababbabbaabbaabaabbbbbaaaabbaaaaababbababaabaaaaabbaabbaababaabbaaabbbaaaabaaabbabbaaabbababbbabababbbbbbbbaaabaaaabaaaaabaabbbaaaaabbaabaaaabaabaabbbbbbbbbbabbbbaababbbaabaaababbbbbabaabbabaaaaaaabaababaababaabbabababababbabbbabbabbabbbbabbabbbabbabbbabaabbabaaabbbbbaaaabbabbbaaabbaaabbbaababbaaaaabababbaaaabaaabbaaabababbbabaaaaabaaabbabbaabaaaaabbbabbbabaabbbababaaabbbbbabbaababbabaaaaabaaaabaabaaaababbbababbababbaaabbbabaabbaabababbabbbabbaabaaabaaabbbaabaaaaababbbbbabbbbabaaababbaababbaaaabbbbbaaaabaabbbaaaaaabbaababbabbaabababaaaaaaaaaabaabaabbababaaabaaababbaaaabbaaaaaaabbabbaaaabbabbaabaabbaaabbaaaaaabbbabbabaabababababababbaabbbbabbababbaababaaaabaaaaabbbbaaaababbbbaababbabababbababaababababbabbbababbaababbaabbabaaabbaaabbbaaaabbbbabbbbaabbabaababaababbbabaabbbabbabaaabaabaabaaabbaaaabbaaabbbbbbbabaabbaabaaaaaabaaabaabaaaababbabbaaaaabaaaaababbabbbbbaabbabbaabbabbbabaabaabbaaabbaabbbaaababaaabaababbbbaabbaaababbababbaaabbaabaabbbbabaaaababbbabababbbbbabbbbbabbaaaabbbaababbbaabababaaabbbaaaabbbbaababbabaabaaabbbaabbbbbaabbbababaaaabbbaaaaaaabaaaaabbbbabababbabaaaabababbbbabbaabaabbaaaaabbabaaaaaaababaaababaaabbaabaababbbbbbbbbaaaaaababbbbaaaaabbabaaaabbaaaaaabaaabbbbbbaaabbbbababbabaaaabbbbbaaaaaababababaaaaaaaaaababaabbbbaaabbbaaaababaaaabbbbaaaabbaababaabbaabbabbbbbabaaaabbabbaaabbbbbbbbbababbaabbbbbabbbbababbabbbbbbabaababbaabbaabbbaababbaabaaaabaaaaaabbaaaabaababababaabbbaabbabaabbbababbbaaabbbbbaaaaabaababbabaabbbaababbbaaabaababaabbbaabbbababaabbaaabaaaabbababbabbbbbbabbbaaaabbaabbbbaaabbbbabbbbbaabbaabbbaaaabbbababbaabaabbabaabbabbbaabbbabbbbabbbbbaabbbbabbabbbbaaaabbbbabababbabbaabbbabbabbaabbbbbabbbababaaabbaabaaaabbbbbaababbabaaaabaaaabbbaaabbbbbaabbbaaabababaaabbaaabbbaaaaaabbbaaaaabaabbaababbabaababbabbabababbbbbaaabbabababbbabbabaaaaaababbaabbbaabbabaabbabaabaabbbbabaababaaaabaaaabaaababaaabbababbbababbbbbbaabbaaababbbbabbabaabbabbababaabbaaababaaaabbabaabaaaabbbbaabaaaaaabaabaaaabbabbbbaabababbabaaababbbbbbaabbabbaabbbabbabbbaabbbaaaabaaabababbbabaaaabababbaaabaabababaaabbaaabababaabaaaabbaaaababbbbbabbaaabbbbbaaaaaabaabbbaabbbabbabbbbaaaabbabbaababaabaaaaabbabbbaaaabaaaaabbababaababbbbaaaababaabababbaaabbbabababaabbbbbababbbbbbabbabaabbaaaababbaabbbbbbaaababbbaaaaaaaabbbaaabaabbbabbaaabbababaababbabaabaabbbaabbbbbabaaabbabbabbabaabbbbaabaababaababbbbabbabaaaabaaababbbabbbbaababbbbabbbaababbababbbaaaaabbaaaabbaabbbbaabaabbaabaaabaaabbbabbabaaababaaaabbabbbbabbabbbbaabaababbababbbbaababaaaababbbbaaababbbbbbbaabaababaabaabbaaaaaaabbbabaaaabbaabbabbabaaaaabbbabababababbbabaabbaabbbbbbbbbabbbbbbaaabbbbbbabababaabbaaabbaabbabaaaabbbbabababaaabbbbababbbbaaaabbaabaaaabbbaabbabbaabbbbaabbbbababbbbbaabaababaabbbaabbbaaaaaabbaaabaabbbabbbbaabaaabbbabbaaabbbbbbaaabbabbabbbbabbabababbabababbbbbaabaabaabaaabbaabaaaaabbabaababaaaaaabbabbbabbabaababbaaaaaaabababaabababbbbbaabbabaabababbbabbbbababbabbbaaabbabababbabbbaabbbabaabbbabbbbabaaaabbaaababaababababbaaabaabbbaabbbabbabaabbabbaaabbababaabaaaabbbbaaabbaaaaabbabbabbaaabaaabbaabbabababbbabbabaaaaaabbbaaabbabababaaabbaaababbaaabbbababababbaabbaababbabbaaaaabbababbabbaabaababaabaaabbaababaaaabbbbaabbabbbabbbbbbbaababbbabaabaabbaababbbbaababbbbbbbbaaabbabaababbbabababbbbbabbbaababaabbbabbaabbbbababbbababbaaaabababaabbabaaabbaabbabbaaababbaaaaabaaaaabbaababbbaabaababbabbbaaaaabbbaaaaababaaaabaaabbabbaaabaaabbbababababababbaaabaabbbbabbbbabaaabbabaaabbbabbbbaaabababaaabaaaaabaaabbaabbbabaabbbabaabbbababbbabaabbaabbbabbbbbaabbbaabbaababaabaaabaaaaaabbbbbbbbbbaaaabbaaaabbaababbbaaaabaaabaaabbbbbaaabaaaaaaaaaaabaabbbabaabaabbababbabbbbbbbbbabaaabaabbbabbbbaabbbbbabbbaaabbaaaaaaaaaaaabbbaaabbabbbbbbabaaaaababbababbbbbaababbabbbabaaabaaaabaabaababbabaabbabbaabababbabbbabaabaabbaabaaaabbabaaabaabaaaaaaabbabaaaabaaaabbaababaaaaabbababbbbabaaabbbabbabaabbbbaabbbaaaaabaabaabbbaabbabbaabaabbbaabbbaaabaabbbbaabbbaabbbaaabaaaaabaaaaaabbbbbabbbbabbaabbaaaaabbbbabbbaaaabaaabbabaabbbbbbbbaabbabbaaabbababaaabababaababaabbabbbbabbbaaaabababbbababaaaababaaabbabaabbaaabaaaabaaabaababaaababbaaaababaabaababbbbbbbaaabaaaaaabbabaaabbbbabaababaabbaaaabbaababbaaabababbbbbbbababbaabbabbbabbabbbbaabbaabbaaaaabaabababaabaaabbaababbbbabaababbbbaababbbaaaaabbaaababaabbabaabbaaabbaaabbbaaaabbbbbbabababbbaabaabbbaaabaaabaabbbabbaabaabbaaaaabaaababaaabbababbabaabbbaabaabbaaaaaabbbaaabaabbabababbbbbabbbbabbabbabbaabaabaababaabbbababaaaabababbbaaaaabbabababbaabbababbbbababbbaababbaaaababbbaababbbbbbabaabbbabbaabbaabbabbbabbbaabbaabbaabbbaabbaabbbbbbaaaabbbbaaabbabbbaabbaabbbaabbabaaaabaabbbbbbbabbabbbaaaaabaaaaaabbaababbbbbaabbabababbaabbaaabaaabaaaaaababaababaabaabbaaaaabbabaaababbababbbaaabbabbbaabbbabaaababbaaaaaaaaaaabaababbaababbbaaaaabbaababbaababbbabaababaaababbabaabbaababbabaaaabbaaabaabbbbbbaaaabbbaaababbbbbbaabbaabbaabbabbaabaaabbbabaababaabbaaaabbabbbbaabbabbaabaabbbbabbbbaaaabbbaaaababbabaaaabbaaaaabbbbabaaaabbabbbaababaabaaaabaabbbabaabbbbbabbbaabbbbbaaaabbabbabbaaabbabbbabbbbaabbabaabaabbababababaabbbabbaaabbabbbbabaababbaaaaabaaaabbaaabaaabaabbbaabaabbaabbbbabbaababbbbbabaabaaaaaabababaaaaabbabaaaababbaaababbaabaabaabbaabaabababaabbaaaabaaaabaabbaaabbbbbaaababaaabbabbbbbbbbbbabbaababbabaabbabaabaabbbbbbaaababbabaabbabaabbaababaabaaabaabbaabaabbabbaababbaabbbabbaababbbaabaaaabbbbaabbbbbbbbbabbbbabbbabbabbbbabbababaaabbbaabaababbbbbaaaaababbaabbaaabbaaaaaaaabaaabababbaaabababbbbaaabaaaabbaaabaabbbbabaabbbbaaaabaabbaabaabbabbaaababbbabababbaaaaaaabababbababbbbabaababbaaabaabbabbbbbaabaabaaabaabbbbaababbbbababababbabaaaabaaaaabababaabbbbbabbbbabbbbaabbbbbbabaaaababbaabbbaaaaabaabbbababaaaaabbbbbaaabaaaaabbaababbaaababababbbbbbbabbaaaabaaabbbaabbabbabaababbbaaaabbbbaabababbabbaabbbbbabbabbbabaabaabaabbabababaaababbabbbabbbaaabaababbbabababbbbbbbaababbbaabaabaaaaaababbbaababbabbabbababaabaaabababbabbaaaababbabaaaaaaaabaabbbaaabaabbaabbababbabababbbaaaabbbbbbbbaaaaabbbbbabababaaaabbbbabbababababbbbaaaaaabaababbbbbaaabaaabaabbaaaaaabaaabbbbbbaabbababbbabbbbbabababaabaaabaaabbaabbaabababbaaaabbabbabbababbbabaaababaababaaaabbababaaababbbbababbbaababaabbaaabaaabaabaaaaababaaababaabbabaaaaaababbbaababaababbababaabaabaabbaaabbbbbaabbabbbabbbbababbbaabbbabaaaabbabbbababaaababbbabaaaababbbbaaaabbbbbbbbabbabbabbbaaaaaaabaaaababaaaabbbaaaaabbabbaabaabbaaabaaaabababbbabbaabbaaaabbbbbbbbbbbbbaabaabaabababbbababaaabababaabbaabbbaababbbbbaabababbbabbbabbbbaaaabbbbbaaaabaabbaabbbaabbababababbbbaabaaabbabaaaaaababbbaabbbababbbbabbbaabaaabbababababaabaaabaabbbaabaaaababbaaababaaababaaabbbbbabaabbaaaabaabababbaaabbbabbababaababbbbaabbaaababbabbaabababbbaaababbbbabbababbaabbbbaabbabbbbbaaabbbbaabaabaabbbbabbbabbaaaaabaabaabbbbabbabbabbbbbbaaabaabbabbabaaaababbaaaabaaaabbbbbbbabbbaabbabaabbbbabaaaabbbbaababaabbabbababbaabbbbababbbaaabbbabbababaaabbabbabbabababbabbbaabaabbabbabaaabababbaaaabaaababbaabbaaabbbbaaaabaabaaabbbbabbbbbaaabaaabbabbabbbbabaabbbabababababababbbbabbabaabbbabbbbaabbbbbaabbabbbaabbbbaaabaabaabbbaabbabaababababbaaabaababbabaabbbabbabaabaabbbbabbaabbabbbabbaabbabababaaaabaaaababbabbbbabbababaaabbabaaaabaabaabbbbabaaaabbbbbbabbaaabbbbaaababababbaabbbbbaababaaababbbbabbabbbbbaabaaabbbaabbbbaaabbabbabbbbababaaabbababaaaaababaabbbabababbbbaababbabaabaabbbaabbaaabbabbbabbbabaabbaaabbbbbaaabbaababaabbabababababaaabbbabaabaababaabbabbbabaaaaaaaabbbaaabaaababaabaaabaaabbabbaabbaababaaaabababababbbabaaabbbbaababababaabababbaababaabbabbaaababbbbaababaababbbbbbaaaaaabababbaaaaabbbbbabbbabbaaaabbbabbaaabaaabbbaabaaaabaabababababbaaaaabbaaaabbbbaaababbbabbaabbbaababbababbaaaaaaaababbbabbbaababaabbabbaabaaaabbaababaabbbbbbaaabaabbaaabaaaaabaababbbaaabbaabbaabababaaabaabbabbabbbaaaabbabbababbbabbaaabaaabbbbabababbaaaaaaababababbbaaabaaabbaaaababbbababaabbabaabbabaaaaabbbbbbaaaaaabbbaaaabbbabbaaaabbabbbaaababbbaababaaaaaaababbbbbbaaaaaaaaaabbbbbabaabbababbbaabbaabababbaaaabaabbbbaabaabbbaabbaabbbabbaaabbbaababaabbbbabbabbbababbaaaaaaabbbaaabbaaabbaaabbbaaabaaaabbbabbbbbabaababaaaabbbbabbaababbbabbaaaaabbaaabbababbaababaabbaabaabbbabaabaaaaaaabbabbabbbaabbaababaabbabaaaaaababbaaabaabbabaaaaaaabbaababbbaababbababbababaabababbabbbbbaaaabaababbbabbabbbbabbaabbabbabaabbbaababbabaaaaaaaaaabbaaaaaaaabbabaaaaabbaabbaaabbbabbbaaabbaabaaaabbbababaaaabaaaabaabbabaabbaaabbaabaaaababaaaaaabaaaaaababaaaaabbbaaaabbbbbbaabaaababbbbabaabbabbaabbaaaababbaaaabbbbababaabbbabbbaabbbbbabaaabaabbbaaaabbbaabbabbabbbabaabaabaaaaabbaaababaabbabaababbaaaabaababbabaabaabbbbbbbbabababbbabaabbababababbbbabbaabbabbababbaababbaabaababaaaabaababaabaababbaaaaaaabbbbaabbaaaaaaaaaaaabbabbbbabaababbbbbabababbbbabaabbaabaaaabbaaaabababaabaabaaababbabbbaabaabbbabbabaaabbabaaaabaababbabbbbbbbbaabbaababbaaaaabbbabbabbababbaaaababbaaabbbabaaaabaabbbbaabbbbaabaabbbbabaaabbbaabababbabbbabbabababaaababaabaaaabaaaaabaabbbaabbbabaaaabaabaabaabbaababbbababbbbbabbaaabaabbaaabaabababaaaabbaaaabbbabbbbababaaaaaaaaabbbababbbbabbabbababaabbabbaababbaabaaabbbbbbabaaabababaabaaaaaaaaabaabbaaabbbbaaaabaaababbaaaabbbababaabbabbaabbaaabbbabaaabbbbbbbbabaaabbbbabbabaababaaaabbaabaaababaabbaabaaaaaaaabaabbaabaababbabaaaaaabaabbabbbabbbababaaabbababbbbabaaababaaabbaabbababbaabaababbbaabaaabbababaabbaaabbbbbababbbaaaababbbaabbabbaaabbabaaabbaaaababbbaabbaaababaaaababbbbbbaaaabbbbbaabbaabbbbabaaabbbbaaaabbbaabbaabaaabababbaaabababaabaaabaaaaabaaaabababaabbbbbbbabbababaaabbbbbabbbaaababbabbbabaaaababbaaaaabbabaabaabbaaabbbababbaabaabbabbababbaaabbbaabababbaaabbbbabaabbabaabababbaaaabbbabbbababbabbbbaaaabaabbbabbabaaaababbabaabbabababaabababbbbababbbbbabbabbbbbaaabbbbabbabbaabaabbbbaabaaabbbaabaaaababbabbabaabaaabbaaaaabbbaabbbabababaabaabbbaabbbbabbbbbbaaabbaaababaaabaababaabaababbaabaababbbbbabaaaabbbbbababababaabbbbabbababbbaabaabbabbaabaaaaaaabbbaaababbbbabbaabaabbbbaababbabaaaaaaaabaabaaabababaaababbabbbabbaabbbbbbaabbababbbbababbbbbbbbbbabbbaaabbababbabaaabaabbaabbabbbbabbabbbbaabaabaaaaaaaabbabbbabaabbaabbaabbaaaaababbbabbbaabaabaabbaababbabbbbabbbaabbabbbabbbbabaabbbbbaaabbababaababaaaaaabbaaaabbaaaabaabaaababbbbbaababaabbbaabaaababbbbabaababbbbabbabaabbaabaaabaabbaaabababaaaababbaabbabaababaaaabbaabbaabaababaababaababaabbaaaababbaababaaabbaaabaabbbabbababaabbabbabababbbaaaabbaabbbaaaaaabbabaaaaabbbbbaaaaaaaababbbbbbabaabbbbbbbbabbabbaaabaabbabaaaaaaaaabaaababbbbabaabaababaaaabaabaabaaababbabbabbbbbbaabaaabaaabbabbbbbbaaaaaaaabbaaaaabababaabaabbbabbabbbbbbbaababbabababbaaabbbabbbbbaaabaababbbabaaabbbbaababbbababbbbababbaabbaaaaabbbbabbbabbabbabbaabbbbabbabbabaababaaaabbabbbabbbbaabbbabababaabbbbaaababbbbaabbbbbababaababaabaaaaabbaababbaabaaabbabaababbbbbbbabaaabaaabbaaabaaaabaabbbababaabbbbbbabaaaabaabaababababaabaabaaababbababbbbaababbaaabbbabbaabbababbbbaaabaaaabaabbaabaabaabaabaababbabaaaaaaaabbaaaaababaaabaaaabbbabbbbbabaaaaaabaaaabbbaaaabbbbbbbbabaabaaabbbbaaabbabaaabaaaabbaabaabababaabbbaabbbbbbbbbababbabbaaaabbbbbabbabaaababbababbaabbbbabbbaabbabbaaaabbaabbaabbbbababaaaabbbaabbbabbaaaabbbaababaaabaabaaabaababbabbbbbaababbababbaabbbbabbaaaaaabbbbbbabaaaabbbbbabaabbbbaaababbbbabaabbbababaaababbbaabaaaaaabbabaaaaabbaabbabbabbbbabaaabbabbabaaababaaabaabbbaabaaaabbaaaababbbaaabbbbbbabbbbaabbbaabaabaaabaaaabbaabbaabbabbbbaaababbbbaaabbaaabaaabaabbbaabbabbabababbabaabaaabbbbaaabaaaaaabaaababbaaababbbaaabaababbababababababaaabaaabaabbbababbbababaaaaabbabbbaaaaababaaaabaaaabaaabbbabbbbbabbaabaaaababbbaaabaaababbbabbbaaaabbababbababbbaabaaababababbbbbbbaabbbababbaaabaaaaaaaabaaabaaaababbbaabbabbbabbbbababbabbbabbbabababaabbbababbabbabbabbababaabbbaabababbbabbbbbabaabaaaababaaaabbabbbbaaaaabaabbaabbaaaaabbbabaabbbbabbbbbaaaaabaaaababaaabbaabaababbbbaabbbbbbaabaabbaababbbbbbababaaaaabaaababaabbabaaaabbabbabbabaabbbaababbbaaabaabababaabaabbbabbbbaabaabbbabbbbaaaababbabbababaaaabbaaabaaabbabbaababbababaabbbaaaabaaaaababaaabaaaaababbbabababbbababbabbbabababaaaababbbababbbbaabababbbbaaababbabababaabaabbbbabbaaabbaaaabbbbbbbbbabbaababaaaaaaabababbaaaaabbabbabbaaabaabaabbabbaabaaabbabbaabaabbabbbabbbaaabbbbaaabbbabbaaaabaaaabbababaaaabababaabaababaaaabaabbabaaaababbaaaaaaaabaaaaaaaaaabbababbaababbababaaaabbbbabbbbbbbabbabbbaabbbaaababaabbababaabbabbbaababaaabbaabbbbabaaaabbaabbbaabbbbaabaababbaabaabbbbabaaabbaaaaaabbaaababbbaabbababbabbbabbababbaaabbbabbaaababbbbbbabbabbbbababaaaabaaabbabaaaaaaaaabbbabbbbbbaabbabaabbaaaabbabababbbaabaababbbbabaababbbbabbaaaaaaababbbaababbbbbbaaaaabbbaabaaaaaababbbbbabbbbaabbababbbbbbbaabbaaaabbbbbbaaaabaaabbaabaababbabababbaaababbaabaaaaaaabaaabaabaababaaabababbabbbaababbbaaaaabaaaababbaabababbbabaabbbbabbbbaaaababbbabbaaaabbbaabbbabbaabaabaaabbbbbaaababaaaabaabababbaaaaabaaaabaaaabbbbabaabaabababaaabaabaaababbbabbabbbaabaaabbabbaaaaaaababaabbbbabbbaaaaabababaaaabbabbaababbbbbbaabbaaabaabaaabbbaabbbbabbbaabbaaaaaaabbabbbaabbaababbaabbbbbbbaaabbbbbbbabaabaaaabbaabbabbbababbbbabbbabaabbaaaaabaaabbabbbbbababbabbbabaabbbbabbababbaaaabbaabbaaaaaaaaabaabbbabaabbbabbababbaaaabbaabbbbaaabbbaaabbaabbaabbbaabbaabbaabaaaabbbabbaaaaababbbbbbbbbaabaabbbabbaabababbbbbaabaabaaaabbbabaabbbbabaaababaababaabaabbbbbbbabbabbaaabbbaabaabaaabbbabbaabbbbaaaabaaabaabbbababbabbabababbbaabbaaabbbbbaaabbabaaaaabaaaabbabbaababaaabaabababababbbbbaaaabbbbabbaabbabababbbabbaaaaabababababbbaabaaaabbaabaaaababbbbbaababbabbaaaaabaabbbaabbbaaaaaababbbbaaabbaaaababbbbaaabababaabbbaaaabaabaababbbababbbaaaaababababaaabbaababaaabaabbbabbbbbbabababbbabbbabbabababbbbabaabbabbbabaaaabaabbbabaabaaaabbaaabbaaababbaabaabbbabbbbabbbbbababaabaabaabbbababaabaaaaaaaabbabaaaaababbbababbabaaabaaabbbbababaaababababbaabbbaaabaabaababbaabaaabbaaaaabaaaaaabbbbaabbabaaabbbabaaaabaaaaabaabaababbabaaaababababbabaaabbababbabbbbababbbababababaaaabababaababaaabbbbabaabaabbbbbaababbaabbbbabbbbbaaaabaaaabbbbbbbababbbababaabaabaaaaaaaabbbbbbaabbbabbbababaaaaaaaaababaaaabbbbbaaaaaabaaaabaabbbaabbabaaabbabbaaaabbbbbabbbaabaaabbbbabaaaabbbbbaaababaaababaaaabbbbbbabaabbbbbbbbbabbbbaaaaaaaaababbbbabbbabbaabaaaabaabaaaaababaabaaabaaaaaaababaabbbabbababaabbabbbabaabbbaaabbbaaaaaaabbaababbbbbaaaaabbabbaababbabaabbbbbaabaabababaaabababbbaabbaabbababababbaabbabaabbbbbabababbbabbababbabbababbaabbabaabbabaaaabbaaaaababaaababaaabaaaaabbbabbbaaaaaabbbbaababaabbaaaaaabaaababbbabbaabbbbbaabbababababbbbbbbaabbaaaababbbabbabbaabaabbabaaaaaabaaaaabbbbabaaabaabbbbbbaabbbabbaabbbabbbbbbaabaababbbbbbabbbbaaaaaaaababbbbbbaaaabbababbbbbabbbabaaaabaaaaaababbbbbbaaaababbbaabbabaabbbaaaaababbbbaaaabaabababbabaaabaabaabbaabaabaabbbabbaabbbabbababbbabaabaabbbbbaabbbabbbabbbaaaababbaaababbaaaaabababbaaaabaababbbbbaaaabaabaabbbbaabababbabbbababbaaaabbbaaaaaaabaabaaababbabbaabaaabbbaaaabaaaaaabaabbbbabaaaaaaabbbaaaabbaabababbbaaabbbaaabbbaaaaaaabbbababbabaabababaaaaababbaabbbbbabaaabaabbaabbabbabbbbabbbaabbaababaabbabbaaaaaabaabbbbaababbbbaaaabbabbbaaaaabbaabbbabaababbbaaaababbbaabbbbabbabaabbaabababaabbaaaababababaaaaaaabbbbbbbaabbbababbbbbaaabbbabaaaaaaaabaaaaabaababbabaaabbbabbbbababababaaaabbbbbaaaaaabbbbaabbbabbbabaababbabbbbbaaababaaababaaaabbaaaababaaaabbbbbbaaaaaabbbbaabaaabbaabbabbaabaabbbabaaaababbbabbabbabbbabbabaababaaaaabababaabaaaabaaabbbbbabbaaaababaabbaaababaaabbabbabbaabbaaaabaabbbbaaabaaaabbaaabaabbabaaabbbabbbababbbabababababaabbbbbaabbbaabaabbbabbbbabbbabbbbaaababbaaabaaababbbbabaabbbbbbaaabbbbaaaaaabbbaabaaabaaaaaabaaaaabaaababaaabaabaaaabababbbabbabbbbbabaaaabbaabaabbabbbababbabaabbaaaabbabaabababaaaabbaaaabbababaaababbaaaaaabbbaaaabbabbabbbaaabaababbbbbbabaabbbabaaaaabbaabbaabaabbabbbaaababbbbbaaabbabbaabbaaabaabbbaaababbaababbbbbabaababbbbababbabbaaaababaaaabaabaaaabbaaaaabbaaabbabbbababaabbbbbbbaaaaabbabaabbaaabbbbaabbbabaababbabbabaaabbbaaabababbbaaaababbabababbbabaaabaabaaabaababbbbabbabbbababbababbbabbabaaabbbbbbbbbbaabaaaababbabbaaababaaababaabbabbabbaababaabbabbabbaaaaababbbbbabbbabbbabbabaabbbbbbbabbbaaaaabaaaabababaabababbbababbaabbaaabbabbaababbbaabbabbbaabaabbaabaababaabbbbabbaaabbbbabbabbaaabbbabbbabaabaaaaaaaabbbbbbabbbbbabbbbbbbababababbbabbbabaaabbabbbababbbbabababbabbabaaabbbaaaabbbbbabbbbaaababbabbabbbbabababababaaaaaaaabaaaabbbbaaaababbabaabbbaabbbabbaabbaabbbaabbbbbbbbaabbbbababbabbaaabbabbababbbabaaabaabbaaabbbabbaabaababbabbbbababbbaababaaabbababaababaaabbbabbabbaababbbaaaaaaaabaabbbaabbbbbbbabbbbaabbbbbbbbbbbbaaaaaababbababbabbbaaababbbabaababaaaaaaaabbabaabbabaabaabababaaaaaabababaababaaaabbaababbbbabbababbaaababbbbaabbaaaabbabaaaaaababbbbbababababbbbababbbbaaaabaabaaabaaaabaababbaaabbbbbabaaabbbbbaaabaaaaabaaaaabbabbbaaabbbbaabbaabbaababbaabbbabbbbaabbbbbabbaabaabaababaaaaabbbbbabaabbbabaabbaaaaababaabaababbbaaabbaabbbabbbbbbaaaaaabbaababbbabbabaaabababbabaaabbaaaaaabbbabababbbbbabbabaaaaabbbaabaaabaabbabaabaaaabbbabbbaaaabbbbbaaaaaabbabaaabaababbbabaabababaaaababbbabbbbbaababbaaaaaababbbaabbbbbababaaabaabaabbabaabbabbabaaabaaabbaaaaabbbbaaabbabbabaaaaaabaaabbaabbbbbbabbabbbbaabbabbbbbabbbabbabbbabbbbbaaabaabaabaaaaaabababaababaaabaabaaabbbbbaabaaaaaaababababaabababababaabbaababbbbbbaaaaabaabbbaaaaaabbbbababbbbbbabbabaabbbababaaabbaababbabbbaaaaaabaabaaaababaabababbbaabbbbbbaabbbbbbbabababbbbaabaababbbabaabbbaabbbaabaaaabaaabbaaabaabbbabaababbabababbbabbbabbabaabbbbbaaaabbbaabbaaabaaaaaaaaaabaabaaaabbbbbabbbabaaabababbbbbabaaabbbbaaaaabbbaaaaaaababbbabbaabbbbbabbbbbaaabbaaaabaabbbababaabbbbbbabbbaababbbaabaaabaaabbaabababbbaabbbabbbbaaaabbaababbaaaabaabbaaaabababbaabbbbbaaabaabbaabbaaaaaaaaabaaabbaaabbbaabbaabbaabaabababbabbbababaaaabbaababaaabbabbbbaabaaaabababbaaaabababbbabbbabbbabbbabbbbabbaaaabbaaaaabaaabbbabbabababbabbbabbabaabbaabbbabababbbbabaabbabbbabbabaabaaaabbaaabbaabbaabbabababbabaababaaaabbaababbabbbaabaabbbbabaaabaabababababbbbbabbaaaabababbabbbbabaababbbabbbbabababbaaaaaaabbaabaababaaabbbabbaabaaaaabababaabbaaaaaababaabaaabbbabababbbbaabbbbaabbabbaaabbbababbbaabaaaaaabbabbbbbabbaaababbaaaabbaabbbaaababaaababbbaaabababbaaaabaababababbaaabbbaaabbbbbbbababaabaabbabaaaaababaabaaabababaaaaaaabbbbbabbbabbbabaabbabbaaaaabaababbaaaababbbababbababbaaaabbaabbbbbbaababbabbabababbbbbaabaaababbababbabababbbbaaabbaaaabaaaabbabbabababbaabaaabbaabbbbbababaaaaaabbaababaaababbaaaababaababaaaaabbbaaaaabaababaaabaaaabbbbbabbababbbaabaaaabaaaababbaabaabbaaaaabbbbbababbabbaaaabbbabbababbbaaabbababaababbaaaaaabaabababbbbbaabbabbbbabbaababbbabaabbbbbbaaaababaaabaabbbbbbaaaabaaabaaaaabbbbbababbabbbbbaaabbbabaabbbabbbaaabaabbaaabbababbaabaaaaaabbabbbbbbbaababbbbbaaaaaaabbaaaaabbaabababababbbaaabababbabbabbbaabbaabbbbabaaabbbbabbbbbabbbababaaababbbaabbabbaababbbbaaabaabbabaabbbbbaabbbbbabaaaabbbbbbababbbbbaaaaaaaaaabaabaaaaabbbaaaabbbbbabaabbbbbababaaabbababbaababbbbaabbbbaabbbaababaaaaaababbbbaaaaababbabbbbaaababaabbbaabababaaaababbaabbbbabaabbbabaaaaabaaaabbbabbbbaabbbabababbabbaaababbbbbbabaaabbbababbaabbbbbbabaabaabaabbaaabbbbaaaaababbbaaaabaaaabbababbabbabaabbabbbaaabaaaaaaabbaaabbbababbaabababbabbaaaababbaaaaabaaabbaabbababbbaabbbabbbaabababbbaaaaaababbbbbaaabbaabbabbabaabbbbabaabbaabbabbbabbbaaaabbbabbababbaaabaaaabbbbbbabababaaababbabbbaabababbabababaaababaaabaaaaabaabbbbababbbbabbbbbaaaabbbbbabbabaababaaaabbaabbabbbabababaabbbbaaabbaabaaaaaabbbabbababaaabaabbbbbbaabbbbbbbbbbaabaaabbbabbababbbbbabbbaaaabbbbababbbbbabbaaabbabaabbbaaaabaaabbababbaabababbbababbbbbbbbbababababbabaababaaabababbaabbbabababaaababbabbaabbaaaaaabbbabababbbabbbbaaabaaaaabaaaaaaaaabaabaababbbbabaaaaabbbbaaababaabbaabaaaaaaaabbbabbaaabbbabaabbaaaaabaabababbabbbaaaabaabaabbbbaababbabaabbbbaaaaaaabbbbaaaabbbbbabbabbaabbbbaaababaaaabaabbbaabbaabaabbaabbbababaababbbaaaabbabbababbaaabbbababbaaaaaabbaaabaaaaaababaaababbaabbbaabababbabbbbabbabbbabbaabbaaabaaababbbabbbabaababbabaabbbababbaaababaaabbbbbaaaabbbbbaabbbababaabbabbaaaabbabababbbbaaaaababbababbbabbbaabaaabbaabbbbbbabbbabbababbbbbabababbaaaabbaaabaaaabbababaaaabaabbabbbaabbbbbaabaaabbaaabbbabaabaaabbabbaaabbbaabbabbaaaaabbaaaabbaabaababbbabbabbbaabbaaaaabaaabbaaababbbbbbabbbbbbbaaabaabaabaababbbbababbbabbaabaabbaaabababbbbaaaabaabbaaaabbbabbbabbbaabbbbbbbbaababbbbabbabbbbaaababbabbababbaabbbabbaababababaabbbaaabbbaaabbabbbbbaabbbabaabbaaababaaaaaaabbbbaababbbaaabbbaabbabbabbaaaaabbaaabaaaababbbababaababbabaababbbabbbbaaabaabbaabaaaaaabbaabbbabbabaaabaaaabaaabbaabbabbbabbabaaabaaabbaabaaabbaaabaabbababbaaaababaabbbbbbaabbbbabaabbbbaaabaaabbbbbaaaaababababbbbaabaababbababaaabbaaabbabaabbaaabababababbaabbbabababbbaaaabbaaabaabbbbbbabbabbbabbbabaabbbbbabbabbbababbabbbababbbabbabbabababaaaababbbbaabaabbababbbbbbbababaaaabbbbbbbbabbababaaaaaabaaabbbbbabbbbbbbbbabbabbaaaabbbbaaaababbababaababaabbbaabbbbabbbbbaabbabbbbbaaabbbaaaabbaababbabaaabaaabbbabbaaaababbbabbaaabbbbaaabbbabababaaabaabbbbbaabbaaaaabbaaabaaaaabbbababbabbbbbaaabbaaabaabbaaaabaababbaaabaabbbaaabbaaaaaababbbbabbbaabaaababbaaaaabbabbaaabaabbaabbababbaaaaaabbbbabaaabbabababbababababbabaaabbabbbbbbaaababbaaabaabbaaabaabaaababababaaabbaabaaababbaabaabbbbbabbaaabbababaaaaabaaabbbbbbbbbbbabbaababaaaabbbbbabaabababbaababbbbaabaababbabbabbbabbaabaaabbbaaaaaababbababbabababbbbabaaaaabbaaababbbbbaabaaaaabababbaaaaabbaababaaabbaaabaaaaabbababbabbabababaabababbaaaabbababbaabbbbabaaabbbabaabbbababbbbaaaaaaababbabbaabbbabbaaaababbbbaaababbaaababbbbbababaababababbbbabaabbbbbabbabbaaabbbbaabbaababaaaabbbaaaaababaabaaabaabaabbbababbbbabbaaaaaababaaaabbababbbababbbaaabbbbaaaaaabababbbbbabababbabbabaabaaabbaaaaaaaaaabbbabaabbbbabbbaaaabbabaaababbabbaaaabbababbbbbaabbbbaaabababbabbbaabbbbbaabbbaabaaaabaabbbbbabbbbaaabbaaaabababaabbabbaaaabaaaaaabbbababababbbaaabbbabaaabbbbbabaaaaaaaaabbbaaabbbbbabbbbbbababaaababbaaababbbabbaaaaababbbbaabbabaaabbbababaaaababbbbbabababaaaaabbabaaaabaabbaababbabbababaaaaaabbabbbbbabaaababbbabaaaabbbababbaaaaaabbaaababaabbaaaaaaaaabbabbbaaabababbaaabbbbabbbabaaaaaaabababbabbabbabbabbbbbabbbaaababaabbaaababbaaaaaabbaaabababbbbaaaaabbbbaaaaaabbbabaabbaaabaabaaababbaabbbaabaaababaaaabaabaabbabbbbbaaababaaabbabaaabaabbbaabaabbbbaababbbaaaabaababbbbbaabbabbabbbbabababaabbaabababbaaabbababbaabbabaaabbaabbababaaabbbaabbababbbbaaababbbabbabaabaabaabaabbbbaaabaabaaaabbababaabaabaababbabbbabbbaabababbbaaaababbbabbbbabbbaabbbaabaaabababbabbbabbbabaabbaabaabbbbbbbbbbbaabbbbbbabbbbbabbabaabbbaabbbbbaaabaaaababbaaaabbaababaaababbbababaaaabbbabbaabbaaaabbaaaaabababbbabbbaababbbbbbaababbabbabbbabbbbbbaababbaaaaaabaabaaaaabbbbbaabbaaabbabaaabbaabbbababbaaaaababaaabbaabbaabbabbbbbabaabbbbbbabaaaababbabababababbbbaabbaababaaabbbbabbbbbbbabaaabbaabababbbbabbbaabababababaaabbababbabaabbaaabaabbbababaabbbabbaaabbabbabaabaabbbbaababaabaaabbaabbababaabbaabaaababbbababbbbbbbabbabbaabaabaabbbaaabaabbaaaaaaababbaaaaaabbbbaaababababbaaaababaaaabbaaaabbaaababaaaaabbbaaababaabbbabaabaaaabaaabbaabaaabbbaabaabbbaaababbbbbaaaaaaabaaabaabbabbbbbabababbaabbaabaababaabbbbbbbbbaababbababaaaabababbaabaabaaaaabbaaababbbbbaaabbbbaabbaaabaaaabbabbbabbabbababbbabaabbbabbbabbaabaaaabbaaabbbbbabaaaaaaababababbbababaaaaaababbaabbabaaabaababbbbabaababbaabbbbabaababbaabbbbbaababbbbabababbbaababbaabaaabbbababbabbbbababbbaaabaababbbabbabababbbaabbaaabbaaabbbbbabbaababbbbaabbaabbabbbabbabaaabbbbababaabaaabbbbabbbbbabbaababbaaabbbaabbaaaaaabaaabbaabbbbbbbbbabbabaababbbbbbbaabaaaaaabbaaabbaabbbbbabbaaaabbbababaaabaabaabababbabaaabababbaaabbbbaaabbbbabbbbbabaabbbabbaaaaaabaaaaaaaaabaaabbbbabaaabbabaabaabbbaabbbbaaababbbababbbbaaaabbabbbbbaaabaababbabbaababbabaaaabbbbabaabaaaaaaaabbbbabbabaaabbbabbabbaaabbbaaabbbaababaaaabbbabbaabbbbbabababaabbbababbbabbbaababbaaababbbbababbbbbaaababbbaabababaabbaaaabbaaabbbbababbaaabbababbabaabbaaaaaabaaaaababbbabbbababbbbabbabbbabaaabaaaaaabbbabaaaabbbaaaabbbababaaababbababbaaabaaaababbabaaaababbababaababbbbaababbaababaabbaababbaabbabbaabbababbabbbabaabbbbaaababaabababaaaabaaaaaaabaaaabaaaabbaabbababaaaaaabaaaaaabbbababbaabaaaaaabbbaaaaaaabaaaababbbbababaabbbbaabbbbbaaaaabbbbaabbbbbaabababaababaabbbaaaaabbbaabaaabaabbbaababbbabaaabbbaabbaaaaabbababbbabbaabbbabaaaaababbaabababaaaababaaaaaaabbaababbbbaaabaaabaabaabbaabaabbbabbaaaaaaabbaabaaabbbbbbaabaaaabaaaabbbbbbbbbaabbabbabbbababbbbbaabbaababaaaaaaaabaaabaaababbabaaababbaaaaaabbbaabababbbbbbbbaabaabbabbbaaaaaaabaabbabbbabbbbabbaabaaababaababbaabababaaabbaaaabbabbaaaaabaabbbaabbbbbabbbaaabaabaaaaaaabbbababaabbaaabbaabaabaaaaababbabaaaaaabbbbbabbaabbbaaaabbbbaaaababbaababbbababbbaaaababbaaababaabbaababbaabaaababbababbaababbbbbaababaabbaabaababbaaaabaabaabbbabbaaaabbababaabababaabbbaaababbaabbbbabaaaabbbbabbaababbbbabbababaaabaababaabababaaabaabaabaaababbabbaaaaabababbaababaaaababababbaabbabbbaaabbbbaabaaaaaabbbbaaabbabbaaabbabaabaaaabbabaaabbaababbbaaabbabababbbaaaaaaaaaaabaaaabbaaabbabbaaaabbbbbbabaaaababbbabaabbbbbabaabbbbbbbaaaaaaabbbbbaabaaabbaaaaaaaababbaaaaaaabbaabababbbaabababbbbbaabbaaabbabbbaaaaaaabaaaabaaabbbabbaabbaabbbaabbbaababaabbabaaabbbaabbbbaabbbabbaabaabaaabaababaaabbbbababbaaaaababaabbabbbbbbababaababbabaababababbbbbbabaabbbabbbbaabbaabaabbbbbabbaabababaabbabbabbabbbabbabbbabbbbaaaaababbabaaabbaaaababbabbbbbababbaabbabbaabbaaabbbbabbbbbbaaaababbaaabbaaabbabaaabbabaaabaabbabbbaaabaaabaabbbaababbaaaabbbbbabbababaaaaaaaaaabbaababaaaabaabaababbbabaababbaababaababbabbaabaaaaaabbbbaabbbabaabbabbbbabbbbaaabaaabbbaababaabaabaaaaaabaaabbababaaabaabbaaabbbbaaaabbaabbbbbabbabbbbbbaabababaaabaabbaabbbaaaaababababababababbabaabbaabaabaaabaabbbbaabaabbbbaaaaabbbbabbabbabbaabbbbbabbbaabaabbbababbbbabbaabababababbabbabbababbbaaaabbababaabbbaababbbaabbaabbbbbbbbbbbabbababababbaaabbbbbbabaabaabbaabbaaabbaabbbaabbbaabbabbbbbbbabaababbbabaaaabbababbabbaaabaabbbbababbbbbaaabbabaababbbbabbbbbbaabbbabbaabababbbababbaabbabaababbabaaabaaabbaaaababbabbbbbababaaababaabaabaaabbbaabbabbbbabbabbaaabbbbabababbababbbbaababbaababbbbaaabaabbabbbbbbbaabbbbaaaaabababbabaabbbaababbaabbaaabbabbbaaabaaaaabaabbbbbbaaabababbabbbbabbababbbbaabbbabbaaaaaaabbbbaaabbaabaababbbbbaabbaabaaababaabbbbbbabaaaaaaaaabaaaaabaaaaaabbaabbabababbaabaaaabbababbabbbabaabaaabaabbabbabbaaaaababbabaabaabbababbbbaabababaabaabbababababbaaaababbbbbbabaaababaabaabbbaaabaabbbabbaaabbbbababbbabbbabbbabaaabbbbbabbbaabbabbaaaaabbabbaabbabaaabababbaabaaaabbbaabbbbbaaaabbbbbbaabbaaaabbaaaabbaaaaaabbbaabbbbbabaaababababaaababbbbaabbaaaaaaaababbbbbabbbbbbbaaaabbababbabaababaabbbbaabbbabbbaababbbabbaabaabaaaaabbabbbbbabbaaabbabbaaabaaabbbabaabbaabbbaababaaaabbabbaaaaaabaabababbaaaaababbbbaababaaaaabbbbbbabaaaaaabbaabbbaabbaabaabbabbababaabbaaababbbabbbbbbbaaaaaaaaaaabbbaabbaababbbaaaaabbaabaaabbaaaaabbbaaabaaaaabababbbbabbaabbbbaababbabbaabbbaaabbaaaabbababbabaaababaabaaaabbabababaaababbaabbbabbaaabaabbaaabababbaabababbbbaaabababbbaaaabbaabbbbbabaaaabaaaababbbaabaaaaabbabaaabababbbaaababbbababbaabbbbbbaabbaaabbaaabaaaababbbbbbbbabaaabaabaabaaabababaabbabbbbaabaaaaabbbabababaaaabbbbbaabaababbaaaabbbbaababbbaaabbaabaaabbbaaabbbaaaababbbbbbbaaabaabaaaaabbaaabaabaaaaaababbbabaabaaaaabaaaaaaaabaaabbababbabbbaaaabbbbbbaabbaabbabbbbaaaaaabaabbbaabbbaabaabbbbbabbbbaaaabbbbabbaaaaaaabaaaaabaabbabaaabaaabaaaaababbaabaababaababaaaabbaaaaabaaaaaabaaaabbbaaababaabbaabbbbabbbbaaababbabaabaabbbbabababbbaaaabbaaaaabbaabbbbaabaababbabbabaabbbbbaabaabbbaaaaaaaabbabbbbaabbbbabbaabbbbbbabbbbbbbbbbababaabbbbabaaababaaaabbaaaabaaaaaaabbaababbabbbaaabaabaabbababbbbabbaaaabbbababbbabbabaabaabbabaabbbbaaabbbaaaaabbaabbbaabbbbaabbbbabbbabbabbaaabaababbaaababbabbbaabbbabbabbabbbabbbbbabbabaaabbaababbbbaaaaaaaabbaaaaaabbaabaaaabababbbbbbaabaaabbaaaaaaaaaabbbababbbaabaabbbaaaaaabbbaaaababbaaaaabbbbaaabbbbbaababaaabababaababbbabbababbababbaaaabbabbbbaaabbbabaaabbbaabbaabbbababababbbabbbbbbaabbababbbbbabbababaabaaaaaaaabbbbbaaaabbabaaabbbaaaabababaabbbaaaaabbaabbbaaaabbbabbbaaabaaabbbbbbbaabbabbabbbbbaaabaaaaaaaababbabbbababaabaaabbbaababbaabababaaabbbabbabbaaaabaaabaaaabababbbbabaaabbaaabaaabbabbbaabbababbaaaaaabaabbabababbbbabbaabbabaaabbaaabaaaababaaaababababbbbbabbaaaabbaabaabbaaaabaaabbaaaaababaaaababbbabababbbaabbaaaaaaababaaaabaaabbaabababbaababaabaababbabbaabaaaaabaaabbaaaabababaaaaabbbaaabaaaabaabbbaaaaaabaabbbbbbabaaaabbaaabbbbbbbaaaaaabbaabbbabaaaababbabaabbaaabbabbabaabbbbbababaaaaaaabaaabbbbabbababaaaabaababbbbbabaaaababbbabbbbabbaaaababaaabbbbaabbaaaaabbaababbaabaaabbbaababbbaabbaaabbaaaabbaaaaabbbbbaaaaabbbbaaabbbbbbbbaabababbbbaaaabaabbbaaabababbabaababaababbaaabbbbaabbaababbbabbbabbaaaaaaabbabbbbbabbaaaaabbabbbaaabbaababbbbbaabbababaababbaabaaabbbbbaaabbbabbabaabaaababaaabbbbbbaaabbabbabaababbabaabbabbbabaababaaababbbaabbaabbbbaaabaababbbbbbabbababaabbbabaabaaaababaaaabaaabaabbaabbabaaabaabaaaaaaaaabbabbbababbbbbaaaaaaabbbbababbbaaaaaabababbbbbaabaaababaabbbaabbaaaaaabbaaabaaabbababaabbabbbaabbabbbbbbbbabbbbabaaabbbbaababbaaaabbbaaabbbaabbbbabbaabbaaaabbaabbabbbaaabbaaaaabbbbabbbbabbbaabaabaabbbabbbaabbaaababbabaababbaababbaabbbaabababaabbbbababaababbbabbaaaaabbaaaaaabbbbaabbbbaaababaaaabaabbabbbbbbbbaaaaaaaaaaabbaaabbaaaabbabaaabaababbbbabbaabaababbbaabbabaaaabbababbaaaababbbabbaabaabbaabbbbaaaabababaaabbaaabaaabaaabaaaaabbaaaabaaabbbababbaabbbbbbabbbabbbbabaaabbbbaaaaabaabaaabbabbbbbabaabbbbaabbaaabbbbbabbbaabababbbababbabaabbbaaabbabbabaaaaaaabbbbaabbbbaabbababaabbbaaababbaababaabbaabbbabbaabaababbabbbbbbaababbabbbbbbabaababaabababbbbbbbaabaabaaabababaaabbababbbabababbbbbabbbaabbbabbbabbbaaabaaaabaabbbbabaaaaaabbbaabbbbaaababbaaabbaaaababbaaaabaabbbababbbabbbbaabbabbaaabaabbaaaabbaaabbbbbbbbababbaabbaaabbbbbaabaabbabbaabaabaaabaabaaaababaabbbbabaaaaaabbabbabbbababaaababbabbaaaabbbbabbaabbbbbabaabbbbbbbaaababbabbabbbaaabbababbbbbbabbbbababbbabbaaabbabaabababaabbabbbbabbaababaabbabaaababbbaaabbabaaaaaabbaaabaaabbbbbabababababbaaababbaabbbababaabaabaababaabaaabaaabbaaabbbbbaabbbababbbbaaaababbbbbaabaabbaaaaabaabbbabaaabaaabbabbbbaabbbbaabbbbabaababaabbbbbaaabbbbbabbbabbaababbabaaaabbbaaaabaaabbbabaaababbbaabbbbbbbbabbaaaaababbaaaaababaabbabaabbabbbbbaaabbabbbababbbbbaaababbaaababbbbaaabbbbbbabaaaaaabababbabbbabbbbbbbbbbaaabbaababababaaaabbbabaabbbbaaabaaaabbaabaabbaaabaabaaaaabaaaababababbbbaaabbbbbaaaababaaaabbbaaaabababababaabbbbbaabbbbaabbaaabbbbaabababbbaaaabbbbbababbbbbabbbabbbbaabbaabbaaabababbbabbbababbbbbabaaabaaaaababbabbaaaaaabababaaaaaabbbbabbababbabaaaabbaabbbbaaaabbbbbaababbaaaaabbbaaabaaaababbbabbabbbbabbbbbabaabbaaaabababbaaabbabbabbaabbaaabbaabbbbbaabbaabaabbabaaabbbbaababbaabbabaabaaaaaabbbbbaaaaaaababaaaaabaaaabababaababaabaaabbabbaababbabaabaaaababbbbbbbaaaababbbbbaabbaabbbababbabaababbabababbabbaaabbbbababaabbbababaabbaaaabbaabababaabaabaabaabbbbbababbbbbaaabababaabbbababbabbaaaaaabbaabbbabbabaaabaabbbbabaababbabaabbbbbabaabaaaabbabbaabbabbbabbbaabbbbbbbbbbaabababbbbbbbababbbbaababaaaababbbbaaaaabbabbbabbaaaaabbbbaaaaabbabbbaaaabaaaaaaababaaabababbbabbbbabbabbaabaaabbabbaaaaaaabbaaaaaabaababaaaababbababaaababbabbabababbbabaaabaabaaabaabbbbabaabbabbbbbbbbabbbbbababbbbbbaaaabbabaaaaabababababaabbaaaaababbbaabaaaaaaababaaabaabaaaaababbbaaabbabbabbbbabaabbaabbabaabababaaababbaaabbbaabaaabbabaabbbaaaabaaaabbbbaabbbbbabaabbaabbbaaaaaaaaaabbbbbaaaababaaaaaaabbaababbaababbbbbababbbaaababbbbaaabaabaaaaaaaaaabbabbaababaababaaaabbabbaabbbbbbabbabbbaaaaabbbabaaabaabbabbabbbbbaaaaababababaaaaababbaaaababbaabbbabbbbabaabaabbbbabbababbaaaababbbbaabaaaaabababbababbababbbabbabbabbbbbaabbaaaabaaaabababbaabbbbababaaaabbbbabbaaaaabbaabaababbabababaabaaabababaaaaaaaababababbbbbabbbababbbbbbaaaabaaaabbaaaaaabbabbbabbaaabbbbaaabbbababbbbbbbaabbabaaabbbaaaabaaaababbaababbaabbaaaaaababbbababbbaabbaaabbbbabababababbabababababaaabaabbabbbaaaabaaabaaabbabaababbaaabbbbaaaaabbaaabbbabbaaaaaaaabbabbaaabaabbabbbbbabaabaaabaabaaaababbabaabbaaaaaababaaabbabbaaabaababbabaaababbaabbaabaaabababaaabbababbaabbbabbbbbabaaaaaaaaabbababbbbabaabbbbbbaaabbaababaaaabbbaaabbbbabbbabbaabbabaabaaabbbaaabbaaaaaabaabbabababbbbaaabaaaaababbbabababababbbabbbbaaaaaaabbbabaabbaabaaaabaababbbabbbabbabbaabaabaaabbabbaaaaabaaaabbababbaaabbbbbabbaabbbabaabaaaaabbbabbaabbaabaaaaabbabbbbaaabbbbabbabbabbaababbaababbaaabaaabaaabaaababbaaabbaababbaaaabbbbbaabbbbbbbabaabababbababababbaaaaabbabbbbbabaaababaaabbaaaaabaabbabaababbabbabababaaaabaaaaabaabbabaabbabbbaaabaabaabbbbbbbabaaabaabbbbabbbbabbaaabbaaababbaababbabbbaabaabbaaabaabbbaabaaaabaabababbaaababaaabaaaabaabababaaabaaaaaaabbbaabaaabbbbaabbbbaabaababbbbaababbbaaabbababbaabbaaababaabbaaabbabaabbabbbabbababbbbbabbbabaabababaabbbabbabbabaabbbbbbbbbabaabbaabbbbbaabbbbabaababbbbaaabaaaabbabbaaabbbababbaaaababbbbabbaabbaaabababaabaababbbbaababababbaaaaaaababaabbbbababaabbbabbbbaaaabaaabbabbaaaaaaaababbbaabbbbbabbbaabbbaabbbbbbabbbaabbababaabaaaabaabaabbaaaaabbbbabaababababbbabbbbaabaabaabbbbaaaabbababaaabbbabbabaaababbbbaaabbaaaabbaabbbbabbbaabbbabbabbabbabbbbbbbbbbababbaaaabbaaaabaaaaaababbbaabbaaabbbbbababbabababaaababbbabaabbaaaaabbababbabaabbaabbabaaabaaabbbbaaababbabababaabbababbabbbbbbabbbbbabababbbbabbaaaababbbaaaabbabbabaaaaababbbbbbabababaabbaaabbabaaaaaaabbaababaaabbbaabbababaabbbbbaabbaababbababbbaabaabbbabbbaabbbabbbbbbbababaabaababaababaababaaabaabbaaaaababbaababbbabbbaaaaaaabbbbabbbbaaabaaaaaaababbbbbbbbbaabaabaabbabbbaababbbbaaabbbbbababbbbbbbbababbaababbbabaaaabbabaabbbaabbabaabbabbaabbabaaabaabbaabbbbaaabaaaaaaaabbbaaaabaaababaabbbbaaabbbaabababbaabbbaabbbabbabbbbabbbabbbababababbaaaaaabaababbaaabaabaaabaaabababbbbaabbbabbbabbaaabbaabababaababbaabbbabababaabbbabbbaaaababaaabbbaaabbaaaaabbaaababbaabaaaabbabbabbabaababaaaababaaabababbabababbbbaabbaabbabbabaaaaaabbaabbabababbaababbbaababaaababaabababbabaaabaaababaababbbaaabbaabaaaaaabbbbbbabbbabbbababbbbaabaaabaabaabaaaaaaabbbbbbaabbabaaabaabababaaaabaaaabbaabbbabaababbaababbbabbaaaaaaaaabbbbbbbbbabbbabbaaabababbababaabbaaaabababbaababbbbabaaabbaabbaabaaaaaababaabbababababbbbabbbaababababbbabbabbbabbabbabbaabbabaaaababbbbaaababbabbaabbbbbaabaabbabbaabaabbbaabaabbababbaabaabbbbaabbababbbbbaaaaabaababbaaaaabaabaabababbbbbaabaabbbbbabbbbabababababaaaaaabbaaaabbbaaaabbbbabaaaaababbababbabbabbabbbbbbbababaaaaaaabbbaabbaaabbabaabaabbbaabbaaaabbabbabbabbaaaabbabbabaabaaabbbbabbbababbbabbaaabbbaabbababbbabbbbaaaabbaaaaaaaababababaabbababaaaaaabaababaaaabbababbabaabbbaabbaaabbbbaabaabbbbaababbabaaabbbbbbabaaaabaabaababbbaaaaababbaaaaabbaaabaabbbabbabbababbaaaabaaabaababaaabababaabaaaaaaaabaaaabbbbbbbbbaabbbaabaaaababbaababbbabbaabbbbabaababbbaaaabbaabbabbbabbbbbaabbbbbbbbabaabbabaabaababbaaaaaabaabbaababaabbaabbababbabababaaaaabaabbbbbbbabbaaaaaabbabbbbabbabbbababbbbaabbabbabababaaaabbbaabaabbbbbababaaaabbbbbaababaabbbbabbbaabbbbbaaabaabbabaaabaaabbbabbaaaabaabbaaabbbabbbabaabaabbbaaabbbbbbbbbabbbbaabaaabbbabaaabbaabababbbbbbaabbaaaaaabbbbaabaaaaabaabbbabbbaabaaaaabbbabbbbaaaaaaaabbaababbabbaaabaaababababbabaaabaaabbbbabbaabbbbabbbbbaaabababbabaabaabaaaabaaaaabbababaaaaabbabaaaaabbbbbbbbabbbaabbbbbabaaaabababaabbbbabbabbaaababaabbbbabbbaaaaaabbbbaabaababbabbababbabbbbababbaabbbaaaabababbbabaabbbabbaaababbabaaaabbbabaabaaabaabbbbabbbbbbabaabbabbabababbabbbaaaaaaaabbbbabbaabaaaabaaabbabbbaaaaaaabaaababbabbbabaaababbbabbbaababaaaabaaaababbaaabbbabaaabbabbbababbaaaaaaaaabbbaabbbbaaaabbbabaabbaaabbabababbbaaabbbbababbabaabbbbbaababaabaababaabbbbaabbabaaabbbbbbbbbabbababbbbabbbbabbbbbaababbaabaababaaabaabaabbaabababaabbbabbaaaabbbaaaabaaaaabaaabaabaaabbabbaabbabaabaabbbaaaababaabaaabbbaaaaaabbabababaaaabbabaaaaabbababbbabaaaabbbabbbaabbaababbbabababababbabaaaaabaabaabbbabbababbbbbabbaaabbbaaabbaabababbbbababbababbbbbbaaabbaabaaabababbaaabaaabbbbaaaaabaabbabbbbbaababbabababbaababbabbabaabbbbaababbababbbbaaabaabbbbabbbababbabbaaabbbaaaabbaaabbbbabbaaaaaabbaaabbabbbababbabbbbababbaababaaaababaaabaabbababbabaaaabaaaabbbaaaabbbbbbbbabbbabbaabaaaabbabbbbbbaabbaabaaaabbbbababababbaababbbababbbbbabbababbbbaaaababbbabbaaabbabababbabbbbbaaaabbaabbabbbbabbbbaabaaaaaabbaabaabbbababababaabbabbababaabaabbabbbabaaaabaaababbaababaabbabbbbbaababbbbaabaabbababbbbaaababaabaababaabbaababaababaabbbaabbbbbbabbbbaaaaaabbabaabbbabbbaaababbbabaabababbbbbaabababbbbaaabaaaaabbabbbbaaaabaaaaababbbabbabbbbabbbbabaaaaababbbaabbbbaaaababbbaaaaaaabbbbabbbbabbabaaabbaaabbababbabaaabaabaababaabbababaaaababaababaababbbabbbbabaabbabbaaaaaabbabbababaaabbababbbaaabaabbbbbbbaaababbbabbaababaabbbbaaaaabaaaabaabaaabbaaabbabbbabbbbbbbbaaabaaabbabbabbbbbbbabaabbabaabbbbabaaaaaaababaababbbabbaaabaabaabaababbaaaaabbaaabbbbaabbaababbbabaaaaaabbaabbbaaabbabbaaabbbbbbbbbbaaaaaaaabaabbababaabbaaaaabbaabaabbbaabbbaaabbabaabbaaaaababaabbbbababbabbaabaabbabbabaabbbaabbaaaaabbbabbbbaabbaabbbaabbabbaaabbbabbaabaabaaabbbbbaaabbabbaaababbbabaaabababababbbaabbbbbabbbbabbabaaabbaaabaaaaaabbaababaaaaaabbabaababaabbbaaababbbbabaababbbaaababaaaabbbbbbbbabbbbbaaaababbbaababbabbbabbbbbaabaaabbbabaaaabaaaabaabbbbababbabaaaaababbbaabbbaaabaaababbaabaaabbbabababbabaaababbaabaabbababbbabaabbaabbabbabaabbbbbbabbababaabaabbbbbbbbbaabbabbbbaabbbabaabaabaabbbaabaaabbbbaaabaabbaaaaababbaaabbaaaaabbaabbabbbbbabbbbaaaaababaaababaabababbabbaaaabbaaabaababbbabbbbbaabbbababbababbbbbababababaaababababaaabbaabbaababaaaabbbaaaabbaabbaabaaaaaaababaaaaabaabbaabbabaabbbbaaaaabaaaaaabbbbbaababbaaabbabbaaaaabbbbbaaaabbbbabbbbbabbbabaababaabbbbbbababababbbaabbabbbbbbaabbababbbaaaaabbabbababbaaaaabbbbbbaaaabbbaabaaabaaabaaaabaaaaaaabbaabbaabbaabbaabbbabbbbbbbabbbaabbbabaababbaabaaaabbaaaabaababbbabaaaaaaabaababaabaaababaababbaabbaaaaaababbaaaabbbbabbabaaabaaaaabbbabbabbbabbabaaababbaabbbbbbbbbbbabbababaaabaabbbbbbbaaaaabbababbaabbaaabbaabaabbabbabbaaabbbaabbbaaaaababbaabaaaabaaaabbababbbaababababbbababbbbbababaabaababbbbaaababaaabababbaaabbbbbbbbabbababbaabaabbbabababbaaabaaaaabbaabbaabaaaaaaababababaabaabbbaaaaabbbbabbaaabbbababbbbbabaababbbbbabbbbbbaabbabaaaabaabbabbaaaaabbaaaabbaaaaaabbbbbbaaaaabaaabbbabbaaabbbaaabbaabaaabbbbaaabbaabbabbaabbaaaaabababbabbbbababbaabbbbbaaabbaaabbabaaabaabababbbaaababbbbaaaaaaaabbbbaaabaaaaaabbababbabbbaabababbbbaaabbaabbbaabbaabbabbaabababbbbabbbaabbbbbababaababbbbbbabbabbbababbabababbbaabaaabbbaaaaaaaabaabaabbabaabaaabbbbabaaabbbbaabaaabbbbbbaabaabaababbabbbbabbaabaaabbaabbbaaabbabbbbabbabbbabaabbbabaabbabbabbbbabbaabbbbbaaaaabaabaabbbabbbabbbbaabbababbbabbbaabbbabbbababbabaabaabbbbbbbaaaabaaabaaabbbababaabbabababababababbbbabbaaabababbaaaaaaaaabaaabaaabbbbbbbabbabaabaaaaaaaaabaaaaabaababababaaaabaaaaabbbbbbbaaaabaaaaaababaaaabbababaaaaaabaabbababbbbbbabababaaabaabaaaabbbabbbbabbababababababbabbaaabaaaaaaaaabbbbababbababaabbbbaaabbabaaabbaababababaababbbabbbaaaaabbaabbabbbbaabbbbaaaabbbaaababbbbaabbabbabbbaaaabbabaabbbaaaaababbabbaaaaaaaaaaababbbbbabababababbbabbbaabbabbaaababbabaaaababbbbbaaabbbbbabbbbaaabbabbaabbbabaaabbbabbbbabbbabaaaabbaabbbaaabbaababbaabaabbbababbbbbaaaaaaaabbaabbbbaabbaaaabbbaaaaaaabaaabaabbbabbabaaaabaaaabbabbabbabbbaaaaabbbbaabbbbbabaabaaababaababaabaaaaaaababbabbbbbbabbbaaaaaabbbabaabaabbbabbaabababbabbabbaabaababbbbaabaabbbbbbababaaaaabbaaaababbaabbbaabbbbbaabaaabaabbababbabbbababbbbbababbabbbabbabaabbaaababaaaaabbbbaabbaaabbbaaabbaaabaababababaabbabaabbabaabaaaabbaabaaababaabaaabbbabbaaabbaaaabaaabbababbbbbbababaabbbabbbababababababbababbbbbbaabaabbbbbabaaabbaababbbaaababababbbbaaaabbaabbababbbabbabbabbbbaabbaaaaabababaaabaabaaaaabaabaabbaaaaaabaabbbbaabbaababbabbaaabaaabaaabbabbaaabbaaabaababaabaaaaabaaabbbaaaabbbaaabbbbaabababaabaabababbababaabababaabbbbbbbbabaabbaabaabbbbabbabaabbabbababbababbababaaaababbaaaaaaabbabbabbaaabbaaabbbbaabbaaabbbbabaabbbbbabaaabbbbabbabbabbaaabbbbabaababbabbabaaabbbbbbaababbababababaabaaaabaabaabaabaababbabaaaabbabaaabbbabaaabbbabbbaabbbaaaabbabbbbaaaaaaaaababaababbaabbaabaaabababbbbaaaaababbbbbabbaababbbbaabbbaaaaaaaaaaabbbababaabaaaaaaabbaabaabbaabbabababaaababbbbbbbbbabaaabbaabbbbbbabaaaaaaabaaabbbbbbabaabababbbaabababbbaaabaaabaaabaabbbbbbabbabababaaaabaaababbababaababbbaaabbbbaabbbbbabaabaaaaaaaaaabbbaaabaabababaaaaabbabbbaabaababbbabbbbabbaaaaaaabbaaaabaaabbabaaababbbbabbbaaaababaaaabababbaaaabaabaaabaaababababbabbaaaababbbbbababbbaaababaabbbababaaabaabbbbbbabbabbabaaaabbbbbbbabbabbabbbbbbaaababaaababbaaabbbbbaaaabaaababbabbbbbaaabbbbababbbabaaaababaabaabaaabbabababbbbbbbabaabbabbaabaaaababbaaabbababaaabaabbbbabaabbbabbbbbbbbbaaabaababbaabbbbbbaabbbbbabbbababbaaababaabababbaaabbababbabaabaabaabbbbbaabababbbaaabaaaabbaaaabbbaabbaabbbababbbbabaabbbbaaabaabbabbbbbaaaababababaaaabababaaabbbbabaaaabbbaaababaaabaaaaaababaaabababbbabaaabaaabbbaaabaabbabbbbbabbbaaaaaabaababaaabaabbaaaaaaabbbababbbabaaabbabbbbaabbabbbbaaaabbbbbbbaaaabbababaaaaabaabaaabbaabaabaaaaabaaaaaaabbabbbaaaabaaaabbaaabababbbbbaababbabaabbabaaabbaabaaababbbbbbbbbbabaaabbabaabbababaabbabbaabaabbbabbbbabababbbbabbaaabbaabbbaabaababababbaabaaaabbaaababbababbbbababbbbbbbbabaabbbbabbbabbaabbaaaaabaabbbabababaababbbaababaabbabbbbbbbbabbabaabaabbbabaabbaabbaaaaaaaabbbababaababaabaabbbaaaaaaabbbbbaaabaabaaaabaabbabbbabbabbababaababaabbabababbabbaababaabbababbbaaababbababbbabbaabaabbbbbababbaaababbbabbaaabbaaaaabbaabbaaaababbbbbbbbbbbaaaaabababababbbabaabbbbaabaaaaabaabbbbaababbbbbbaabababbaabbbabbabbabbabbbabaababaababbbabbaaabbaaabbbbbabaaababbbabaababbaaaaaaaababbbbbbaabbbaaababbaabbbbabbbbabbbbbbbabbbabbababbaabaabaabaabbaababbabbabbaababbaabbababbbbaaababbaabaaabaaabbabbaabbbaaaaaaaaaaaabababbaabbaaaabbabaabaaaaaabbabaaaaaaaabbbaababbbbabbbaaaaaabaaaaaababbbabaabbaaabbbbbabbabababaabaabaabababbaaabbabbbabaaaabbbbaabaaabbbbaaabaaaaaaaababbaaaababbaabbbaaaaabaabbbbbbabbbababbabbaababbbbbabbaabaabaaaabbabbbaaaabbbaababaababaabaaabbbbbbababbbabbbabbaabbaaaabaaaababbabaaabbabbaabbbaabbbabbbaaaaaabbbaababaaaaabbabbaabbabaabababbabaabbaababbabbbbabbbbaaaaabbababbbbaaaaaaaaaabbbbaabaaaabbabbabaababbbbaaababbbbabababbabbbaabbaaabbaaababbabababbabababbbabaababbaabaaaabababaabaabaabaabbbaabbbaaaabbaabbabbabaabbabababaaabbabbaababbbaabaabaabbbbbbaaabababaabaabbbaaabbababbbbabaabbabbabbaabbbbbbbabaaaabbababababaaababbbbbbbabaababbaaabaaabbaaabababaabaaabaabaaaabbbabaabbbbaabbabaaaaabababaabbbbbbabbbabbbbbbaabababbbbbaaaabbbbabbabbbbabbababbbaabaabbaabaabbbaaaaaabababaabbbaabbbabababababbbbbabbbbababbababaaaabbaaaaabababaaabbaaaababbaaaaaabbaaaababbaaabaabbabababbaaaababaabbbabbbabbabbbbbbaaaaaabbbbaaaabaabbbabbaaabaabbaabaaabbbbbabbbaabbabbbbbbbaaababbaabaaabababaaababaabababbaaaaabaababababbabbaabbaaabababbbbaabaabbabbbbaabbaaaabbbbbabbaaababbbaabbaaaaaaaaaaaaabbbbababababbbabbbaaabbbaabbaabbbbbbbbaababbabaaaaabaababaabaaaababbbbbbaaababaaabbbbbbaabbaaabbbbaaaaaabaabaaaaabbaaaabaabbbbabbbababababbbaaabbbbbabaaaabaabbbbbbabaabaabaaaaaabababbaabbaabaababbabaababaaabaabbbabbbabbabbbabbabbaaaabbabbaaabaaabbbbbbaabbbbbbbbabaaabbbaaaabbbabbbaabaaabbaabbbaaaaaabbabbbabbbbbbabaaaaabbbbbaabaabbbbbbbbabbaaaaababaaaababaababaaaaababbabbbbbaabaabaaabbaaabbbbbaaabaaabaaabaaabbabaaabbbaabaaabbbbabaabbabbabbbbababaabbaaabaabaabaaaaabbbaabbbbabbabbbabbaaabaabbbaaababbabaaaaaaaaabbbbabbbaaabaaabbababbaaababbbabaaaababbabbbbbaaaababababbaabbbbbbbbaababababaabbabbbbbabbabbbabbabbbbaaabaabbabaaabababaaaaaaabbaabbbabaabbbabaaaabaaabbaaaabaabaabaabbabbabbaaaaabaabaaaaaabababbabababaaabaababbaabaaabbbbbbaabaababbabbbbbbabaaaabbabaabbabbbbbababbaabbabbbbaabbaaabbbaabaabbaaaaaaaaabaaaaaaabbbaaaaaaabbbaaababaaaabaabbbaabbabbaaabaaabaabbbababbbaababbbababbabbababbbbbbabbaabaaabaaaabbabbbababababbbaaabaaabaaabaabbbababaabaababbbabbbabababababbbbaababaaabbabaababbaabababbbaabababaaabbabbaaabaabaabbaababbaabbbbabbbababbabbababbbbbbbbbababbbabbbabbbbabaababbbbaabbabaaabbbbbaaaaabbbbbaabbbbbbabbbbabaababbbaaaabababbbaabbbbaaaabbbbbbbbbababaabaaaaabaabbbbaaabaaaabbabaabaababbbaabaababbbbbaaaaababaabbaabbaaabbabbbaabbbabbbaaabaabaabaaabbababaaaaaabbbbababbaababbbaaabbbabaabbaaaaaaaabbaabbaabbabaabbbababaaaabbbabbabbaabbbaabbabaaabbaabababbaaaaabbabbababaaaaabbabbaaabababaaaaabaabbbbbbaabababaaaaaabbaabbaababbaabbaaababaababbaaabaabaabbbbbbbaabbaaababbaaababbbbaaaaababaabbaabbbbbbbbbbbbaabbbabbaabbbbaaaabbabaaaabababababbaababbabaaaabbabababbbaaabbabaaabbbaaababbaaabbaaaaabaaababbabbbbabbaaaababbaaaabbaaaababaaaabbbaababbabaaaaabaabaaabaaaaaabababbababbaaabaabaaaababbbbbabbaaaababbbabaabaabbbbabbbbbbbabbaaaabbababbbbaababbabbbababbbbabbbabbabbbaaabbabaaabbbaaabbbabaaabbabbabaabbaaaaaababbbbbaabaaaabaababaaaabbbabaaaababbbbabbbabaaaabaabaababbaababaabaabaababababaaaabbbaabbbbaaaaabbbbbabaaaaabbbabbabaaaaaaaaabababbbabaabbaaabbaaaabaaababaaaabaabbabaababaaabbbaaabbbaabbbabaabbabaabaabaabbbbaaabbbbbbbbaaaaabbabbaabaaaababaabaabbbbbbbabbbbabbbabababaaababbababaabbaabbabaabaaaabbbababaabbabbbbbbabaabbbbababbbabbbbbbbabbbbbbabaaaabbbabaaabaaababbabbbabbaabaaaaaabbbbababaabbbbbaabaaabaaabaaaabbababababbaabaaabaabaaaabbababbabbbaababbbbbbaaaababbbbbaababaabbbaaabbbbababbabaabaaaaaabaaababbbabbabbbbabbabaabababaaabaaaaabbbbbababababbbbabbbabaababaaababaabbbbaabaaaaababaaababbabababbababbaaaaabaaababaabaabbabbbaaaabaabbbbabaabbabbbabaabbbbaabbabababaabbbbababbbbaaabaabbaabbaaabaabbbabaaabaaaaabbbbabbbbabaaababbabbbbbbaabababbabaaababbababbabaaaaaaaaaabbabaabababbbaaabbaaaabbbbabbbbbababababababbaaaaabbabbbaabbaabbbabaaabbbbbbbbaabababaaaaaabbabbabbaabaaaaababbabaabbaabababbaabababaabaabbbbbbaaabbababbbbbbabbbbabaabaabababbabaaabbabaabaababbaaabbaabaabaaabbbaabbababbaabbbaaaabbababaababaaaabbabbbababbbaabaabbabbbbabbaababbbbababaaaaababaaabaaabbaabbbbabbbababbabbaababbaababbbaabaaaaaaababaaabaababbaaaaabbbbabbabbbabaaabbaabbbbabaabbababbababababbbbbbaababbbaaabbbaabbabbabbabaabbaabbbabaaabbaabaabbabbaabbaaabaaaaaaaaababaaababbbbbaaaababaaaabaaaaaabaabaabbbaaaabababbbbabbabaaaaabbabaaabaaabbabbababaabaaaaabbbbabababbabbababbbabaabbaabbaaababbbababbabbaabbbbabaaababbbbbbabbbababbaabaababaaabbbaabaaabababbbababbbbbaaaaaabaaabaabbbbaaaaaaabbbbbaabababaababaabbabbabbbaabaabaabababbbabaabaabaaabaaaabaaabaaaabababbbbbbbbbbabbabaaabaabbbaababbaabbbaaaabbaabaabababbbaabababaaabbbbbaabbbbaabaaaabbbbbabbbbbaababaaaaabaaabaaaabbbabaaaabbbaaababaabaabaabbabbabbbbbbbbaaaababaabbbaabbbbbaaabbbabbabbbbabbaabbbabbbbaaaabbbbabaaaabbbaabaaaaababbbaabbbbbbababbabbaaaaaababbabbbaaabaabaabbbabbbbabbaaabbaababababaaaabaaabbabaabaabbbaaabbbaabaabbbbaaaaabababbbabaababaabbaaaabababaabbbababbabaabaabbaaaaababababbbbaabaabaaabaabababbabbababbaabbaababaaaababbababbbabbbabbabaabbbbaaaabaaabaabbabbaaaabbaaaaaabababaaaaabaabbbaaabaabaabbabbbbbbbaabbbaaabababbabaaaabababbbababbbbababbbbbbabbbbbabbabbbbabbaaaabbaabaabbaabbbbbaabbabaaabbaaabbbabaaaaabbabaabbaaaabbaabaaaabbaabbbaabaaaaaababaabaabaaabbbabaabbbabbaabbbbaaaaababbbbaaabbaabababbaabaabaabbbbaaabaaababaabaabaaaabbbabbababbbaaaabbbbbbabbbabaabaaaaaaabaabbbaaabbaaabbaaabbababbbbabbabbbbbbbbbbbabaaaaabaabababaabbabbbbaabbbabbbaababaaababbaaabaabbbbbbaaabaababaababaabaabbabbbabbaababaabbabababbbaabaaabbbbaaababbbabbabbaaaabaababbababbabbbabbababaabbabbaaaabbaaabaababbabaaabbaabaaabbabababaaaabbbbbbbabbbaabaaaababaabbbaabbabbbbbbabaabaaaabaabaababbbabbbaabaaaaaabbaabbabbbaabbbbabbbabbbbaabababaaabbabbbabaabaaabbbbbbaabbaaababbbbabbababbbabbbbbbbabaabaaaaaabaaaabbabbabaabbaaaababbabaaaaaabbaabbbaabbbbbaabbbaababaabaaaabbaabaababbbbaaabbbbbabaabaaaaaaabaaabababbaaabaaabaaabaaababababaabbaabbabbabbabbabababbbababbaaabbabbabbaaaaaaaabbbaabaaaaaaabbbaabababbbbaaabaababbbabbbbaabbabbaababbbabbbbbaaaabaaaaaaaaabbaaaabbaaabababbbababaabaaaabaabbabbaabbaaaababbbabaabbbbaabbbbabbbbbaaabaababbbabbaaaababaabbababababaabbbaaabababbaabbabbbaabaaabbbbaababbaabaaaaabaaabbbbbbaabbaaabaaabaaaababbbaaabaaaaaabbabbaaabaaaaaababaaababaaabbaabbaababaaaabbbaaaabababababaaaaabbbbaabbabaaabbbabaabaabbabbbbbabaaaabbaabaaabbbaabababaabaabababbbbbbbaaabaaabaaabbababaababbabaaabaabaaabbababaabaababababaaaababbabbabaabbabbababaabaaabaaaaaabaabababbbabababbbaabbbabaaaaababaaabaaababaaabbabaaaaabaaaaabababbababbababbaaaaabbbbbababbaabaabababaababbbbaabababbabaaaabbaaabaaababababbabbbaaabaaaaababbbbbabaaabbabbaabbaabbaabaaaabaabbaabaababbabbbababaababababbabbbbaaaabbbabbabababbababaaabbbbabbbbbaaaaaabbabbbbbabababbbbababbabbababbbabaaabbabaababaaaabbbabababbbbabbabababbaaabbababbbaabaabaaaaaaaaabbbbbbbbbbaaaaaaaaabaabbaaaabbbbaabbbbbbbaaabbbbbbbbbbbabbaaabbbabbabbbabbaaaaaaaaaaaabaabbaabbbbaaaaaaaabbbbababbbaabaaaabaaabbbbbbaababaabbbaababbaabbbbababaaaaabababaaaababaaaaaababaabbabbbbbbabaabbaabbaaabaaabaaabbaabbbabbbbaababaabababaabbbaabbaaabbabaababbbbababbbaaaaaababbaabbbbbaaabbaaaabaabaaababababbababbbaabbbabbabaabbbbbaaaaaaabbababaababbaabaababaaabbabaaaaaaaaabbaabaaaaaabaaaabbaabababbaaaabababbbaaaababaaabbaababbaababbbbabaabaaaaaababbaabbbbaaabbbbbbaaaabbabbbabaabbaabaaabbbaaaabbbbabbbaabbabbbaaaabbbbbbbababaaaabbbaaabbbababbbaaabaabaabababbbabbaaaaaabbbbbbabbabbabbbbaaabbbabbabbbaabbbaaaaabbbbbaaaaaaababbaaabbbbbbabababaabbbbaabbbbabbbbbaaabbaaaabbaabbbabaaaabaababbababaaaabbbabbabaabbabbaabbaabbabaaaaaabaabaaabbbababbabbbbaaaabbbbababababbbabababaaaaabbbbaaababaabababbbaabbabaaababbabababbbbaaaabbbabaabaabaabbbaaabaaaaabaaaabbbbbbbaabbbaabbaaaaabababababbaaabaaaabbabbbabaabababbbaaababaabaabbabbaababbbbbbbaaaaabaaabbbaaabbbaaabbaaaabaababbbaabbbbbbabbaaabaabbbbbaabbbabbbabaabaaaabababaaaaaabababaabababbababaaaaabbbbbbbaaaabbbabaabaaabbababbaaabbbbaaaaaaaaaabbaaabaabbbabbababbbbbaaaaababbabaabbaaababaabbbbaabababbaababaabbbbbababbbabaabbaaabbbbabbbabaabbbbaabbbbaababbaaaabbabbaaabbabbbbbbbbabaabbbbaababbbbaabbbbbbbbbaaaababbaabbbbababbbaabbabbbbbbbbbbbbabbaaabababaabbababbabbaabababbbaaabbbbabaabbbabbabbbabbabaabbabbaabaaabbabbabbaaabaaabbbaaaaaaaaabaabbaaabbaabbaabaabababbbaabaabbbaaaaaaabaabaabaabbbabaaabbbbbabbbbbabaaaaababbbbbbababbaabbaaaaabababaaabaaababaaabaaabbbaaababaaabaabaabaabbbabaaaabbbaaaaaaaaababbbabbbaaabaaaaaabbaabaaabaaaabbaabbaaaaababbaabbbaaaaabbaababaaabbbbbbbbbbabbbbbabaaaababbaaaaaabbbbabbbababbababababbbabbabbabbbbabbbbbbbababbababbaabbaabaaabbbbabbaabbbaabaaaaaaabaaaababbbbbaababbbabbaaabbaaabaaabbabbbaaaaababaabaaabbaababbabbaabaaaaabbabaaaaaaaaabaabaabbbabaabaabaaabaababaaaaaabaabaaaabbbaaaabbabaabbabbabbabaabaaabaabbbaaaababaaaabbabbabaaabbbabbaababbbaaabaababaaaaaaaaababaababaabbbabbbbbabaaabbbababaaabbababbaaabbbabaaabaabababbabbbaaaabbaaabbbbaabbbaababaaababbabbaaaabbbbabaaaaaabbaaaaaaaaabababaaaaabbbbababbaabbaababbbbabbaabbaabbababaabaaababbabbaaaabaaabaaabaabbaaabaaaaaabbbabaabbabbaaabbabaabbbaaabbaaabbabaaaabbababaaaabaabaabaaaabbaabbababbbbbaaaabababbaaaaaaaabaabbaabbaabbbabbbbbbaaabaaaabbbbababbbbbbabbbaaabaabbbbbaaabbaabbaabbbaaabbaabbbabaaababaabbaaaabbbbabbaaaabaaabbbabaaaabbaabbaababaaabbabaabaabababbbbbaabbbbababbbbabaabaabbabbabbaaabaababbaaaaaaaababbaaabbabaaabbaaaaaabbbbbbabbaaaabbbaabaabababaababbbbbaaaababbbaabbaaabbbabababbaababaaaababbaaaabaabaabbbabbbaabbbabaabbbbbbbbbbaababbabaaaaabababbabbbbbbabaabbaababbaabbbbbbbbabababaaabbaabbaabaaabbbaabbaabaaaaabbbbbbaabaaabbababbbbabbbbabaaabaaaaabababababbbabbabbababbabababbabaabbaabbbbbbbaabbbaabbbbabaababaababbababababbabbaabbbabbbbbbbaaaabaaaababababaaababbbbbbbbbabbbaaabbababbaaaabbbbaabaabbabbbbaabbabbbbaabaaabbbbaaababbababbbaaaabaaaabbaabbbabbaaabbbbbbaabbaaabbbaaabbaababbbbaababbbabaababbaaaababababaabaaabbaabbbaabbbbbbbbabbbaaabababbbaaaabaabbbaababaaabbaaaababaaaaaaabbaabaababbaabaaabbaaaabbaabbabbbaababaabbbbaabaaababbaabbbaaabbababbbaababaaaaabbbbaababababbbbbabbaaabbbbabaabaaaabbababaaaabababaaabbabaaaaabaababaaaaaabaaaaaabaaaabababbabbaabbbbbaaaaaabaabbabbabbaabbbaabbbbabbbaabbababbbbbbababababababbbbbababbababbaaaaaabaabaabaabbbbababbaaabbbabaabbabaaaaaaabbbbbaabbaaaababaabaaaaababbaaaabaaabaaababbbaabbbbabbbaababbbabaabaaaabaaabbbbbbabbabbbbabbaaabaabaabbbaabbaaabbababaaaaaaaaabaaababaaabbbaabaaaabbbabbbbbbababaaaababbbaaaabbbabaabbbababaababbbbbbabbabbaaaaaaaaabbbaaaaaaaaaabaabbbabbabbabbbbbaaaaabaabbbabbbbabbaabbabaaaabbaabbbbaabaaaabbbbaabababaaabbaabaabbbaabaababbbbabbabaababaababbbbbabbabaaabbaabaabaaabaaaabbbbababbabbaaaababbbbbaaaaabbbbaabaaaabbbabaabbabaaaaabbbbbabaaaabbbababaabbaaaabbababaaababbbbabaaabaaabbaabaaaabbaabbaababbaaababaaabaabbbaaababbbababaabbbaaaabbaabbbababbabbbbbaaababbbababbbbaabbababaaabaabaaabbabababbbaaaabbaabbbabaaaaabababbaaaaabbbaaaabbbbbaaaababbbbabaabaabbbabaabbbabbaaaabaaabaaabbbabbbabbbbaabababaababaabaabababaaabbabbbaabaaaaabababbaabbaabaabababbbaaaaaaabbabbaabaaabababbbbaababbaaabbbabbbababbaabababbaabbabbaaaaabababbabbaaababbaabbababbababbbbbbbaababaaabbabbbabaaaababbbbbbbabbbabbbbbababaabbaabbbabbabbbbbbaaabbbababaababbabaabaaaaaabbbbbbbabbbaaaaababababbabbbbbbaaaaaababbaaaaaaabaaabbbbabaaaaaaabaaabbbabaaaaabbbbabbaabaabbaaabbbabbbbbaababbbbbbababababaababbbaabbabbbbaabbbababbabaabbbbbbbbbbabaabbabaaaababaaabbababaaaaabbbaababbabbbaaaabbbbababaababaaaaabaaaabbabaabbaaaabbbaaaabaaaaaaabbbabbbabaaababbbbbbabbbaabbaabbbaaaaaaabbbaaaaaaaaabbaaaaabbabbaabaababababbababababbaaababababbbbababaaaaabbbaabaabbabbbbabbbbbaaaabaaaabbbabaabaaaabbaaaababaabaabaaabbbbabababababbaabbbabaaaabbaabaaabbababababbabaaaabaabaababbbabbbaaababbaababaaabbbbabbbabbaaabbbabbbbbbaaaaabbbbaabaabbbbaababbbaaabbbaaabaaabbababbbaaabaaaabbbbbababaabbaabbabababaabababaaabbaabbababbabaababaababbbbbbaaaababaaaaaaababbaabbbabaaababbbaaaabbbbbabbabbbaabbbbaababaaaabbbaaaabababababbbaabaaaaababaaaabbaabaaaabaaaabaaabaaaaaababbabbabbabbbaabbbbaaababbbababbabbaaababbaaabaaaabbbaaaaabbbbabaaabaabaabbbabbbbbabaabaabababaaaaaaaaaabbaaabbabaaaaaaababbbaabbbababaababaabbaaaaaaaaabababbabbaabbabbbabbbbbabbbbabaabaaabaabbabbbbbaabaabaabaabaaabaaaabbbbaaaabababbbaabbbbbababbbababbbaaabbaabbababbbbabbbaaaaabaaabaabbaaabababaaaabbbbaaaabaabbbaaaabbbabbababaaabababbababababbbaababbbabbaabbbbaabbbbbbaabbabaaaabaabbbabbbbaaabababbbaabaabaaaabaaabaabbbbbbabbababbbabbaaabaaaabaabbbbbbbabbabbaaaabbabaaabbaabbaabaabbabbbbabaabaababbbababababaaababbbabbaaaabaaaaaaabbaaaabaabbaaaaabaaabbbaabbbaabaaaabaababbabaaabbbbabaabbabbaaaabbaaaaabbabaaaaaaaaaaabbbbbaabbaabaabbbaaabbabaaabbaaabbabababbbbaabaabaaabaabbabbaaabbaabbaaaababbbbaabaaaaaaaaabbbbaabaababbaaabababbabaababaabbbabaaaabbbabbabbbbbabbbbaabaababaaabaabbabbbbbabbaaabbbbabaabababaabaaabbbbababbaaabbbabaaaaabbaaabbbbbbbaaabaabbbbaaaaaaaabbabbaabbabaabbbbbabaabababbaabbabbbaaabbabbbbbaabbbbbbbbbbbbabbbbaaabbbaaabbaaabaaabbabaaabbbbbbaaabbaabbbbbbabbaaababaabbbbaabaabaababbababbbbbaababababbabbaaaabbaabbbabbabbbbbaabbaababbabaabbbbabbbaaaaaabbabbbbbbabbbbababbbbbaabbbbbaaaabaabbababbbbbbaabbabbabaaaaabbbbabababbaaabaaabbabbaaaaaaaabbbaaabbabaaababaaaabaabaabaabbbabbbababbbbaaaabaaabaaaabaabaabbabbaabbbbbaabababbabaaaaabbaaabaabbbbabbaababaaabaaaaabbbbbabbbabbabbbaaabbbbaabaabaaaaaabbbbabaaabbbbabbaabbbababbbbbaabbbaaabaaaaabbaabbbabaaabaabbabaaaabaabaababababbbaaaabaaaabbbbbbbbabaaabbaababaaaababaababbbaaaabbbaabbbaaaabaaabaaabbbabbaabaabbaaabbbbabaaabbabaabaaababbaaababbabaaabbaabaaaabaaaaabaabbbbbabbaaaabbababbabbbbababaaababbbaabababbaaaababaababaaaaababbabaaaaabaaabbabbabaaaaabaababababaabbbbbaababbabaabaabbaaaaaaabbaabbabaabbbaaabbbbaaaabbbbabbbabaababaaabbabaababaabaabbbbabbaaabaababbbbbbaaaaaabaabaabaaabaabaabbaaaaabbbabbbabbaabaaabababaabababaaabaaabaaaaaabbbaabbbabbabababaaaabaabbabbaaabbabbbbbbabaaabbbababaaabbbaaaabbaaaaaaabbabbabbbbbabababbaaabbabbababbbababbaabbaaabbbbbaabbabbbaabaaabababbababaababaabbbbabbbbbbbababbabbbaaabbabbaabbbabbaabbabbaaaabaaabaabbbbaaaababaabaabbbbaaaaababbbbbabababbabaaabbaababaaababbbbbaabaaaaabbaaaabbaaaabbabababababaaaaaaababbbbbabaabbbabbabbbbbaaaaabbabaabbbbabbaabbaababbabaababaabbbabbbaaabbabbbaaababbbaabbbbbbbbbbabbaaaabbabbbabbbbaababbabaababbaaabaaabababaabbaaaabaaabbaabbabaabbababbaaaaabbbbbbbaaaaababaaaabbaaaabbabaabbabbabbbaabbbbaaaabbbaaaaabaababbbaabaabbbbabaabaaabbaaababaaabbbbabbbbbbababababbaabababbbaabbabbabaaabaabbaaaabaaaaaaabaaababaaabbaaaabbabaaaabbabbbbababbaabaaaabaaaaaaaaaaabbbaaaaaaaababaaaaabaabbabbbabaabababababbbabababbbabbabaabbaaaaaaabbaaaaaaababbbabbabaabbbaabbababaababbbaaabaaabbaaabbabbbbbaaabaaabbaaabbaaaababbbbbbaabbbbabaababaaabbabbbbababbbababaabababbbabaaaababaababbbabbaaabababbbaabbbbbababbabbbbabbbbaababbbbbbabababaaaabaaabbbbbababbaabbabaaaabaaaaaabaaabbbababbbaabbbabbabbbabbabbaabbbaaababbbbbaaaaaabbababbbaabbabbbaabaabaaabaaaaabaaaaabbbabbaaabaaaaababaababbbbbabbbbbbabbababbaabbbaabbabbababbaaabababbbabaabaaaaaaaababbabbbaababbbbaababbaaabaaabababaaaabaaabbabbbbbabaababbababbaabbabbbbabbbaaabbbaaaaaababababbaababaaabaaabaabababaabbaabaaaabaaaaaaaaabbbbaabbbabbbabaababbbaaabbabbbbbabababaabaabbaaabbbbbbababbabbbabbaabbaaaabbbbababbbbaabaaaabbababbaabbaabbaabbbabbbbaabbaaaaabbababbbbababaabaaaabbaaaabbaabaabbbbaaabbbbbabaaabbbabbbbbbbabbabbaabbbbaaabaaabbababbbbbbaaaabbbabaaaaaaababababbbaaaaaabaaaaaabbaabababbababaaabbbaabaabababbbaabaabaababbbbaabbabbbbaabaaaaaaabbbbaabbaabbbbaabbaaabaaaabbbabababababaabbbbbaaaaabbaabbbbabbbaaabbaaabbaababbabbbaababbabbbbaaabaaaabaaaaaabbabaaababaabbbbabbababbabababbbbbabbaabaaaaabbbaabababbaabaabaaabaaaaaaababbaaaabbaaaabbaaaaabbbbabbbababbbabbabbbbbaaabbbabbabaaabbbbababbbaabbabbabbaababaaabbaaaababbaababbabaabaababbbbabaabaabababbbaaabbaaababaaaababaabbaabaaabbbbabbbaaabaaaaabbbbbbbaaabbbbbbbaababaaabbbababaabbbaabbaaabbaabbbaaaabbaaabbbaaababaabbaaaaaaababbaabababbababbbabbabbbbaaabbbbaaabbbabbbaaababbaabaaabaaaababaaabaaabbbbaabbaabaaababaabbbaabbaaaaaababbbaaabaabbbbaaabbbaaaaaababaaaaaabaaaababbaabbaabbbaaaabbbbbbbbaaaababbaaaaabbbbaaaabbbaaaaaabaabbbaaaaaabaabbbaababaaabbbaabbbbaabbbababababbabababbabaaaabaaaaaaaaaaabbbbabbababaaababbabbbaaaabbababaaaabaabbaabbaaaabbababaaaaabbbabbbabbaabbbabbbbbabbbababaababbbbbbaaabaabbabaabbbbaabaabbbbabaabaaaabbbbaabbbabaaaaababbaabaaaaababaabbbabaaaaababaabbabbabbbaaabbabbbbaaaaabbaaaaaaabaaaabbababaaabaaabbbaaaaabbbababbaaaaabbbbbbaaabbbbbaaabbabbbbbaaabababaaaabbabaaaabaababbbbbaaaababaabbbbbbbaababaaaabaabbbbaabbaabbabbabbbaabbbbabaaabbabaabababaaabbbbbbabbababbaaabaababbabbabbabaabbbbabbaabbaabbbabaabbbbaaababbbabaaaaaaaaababbabbabbbabbaabaabaabbabaaaaabbbaabbaaaababbaabaabababbaabbaaaaaaabaaaaabbbabababbbaababbabbbbbbaabaaabaaaabbabaabaaaababbbbaabbbaaabbaababbbabbbababbabbbbabaabbabbababbbbababbabbbbabbababbabbbbbbaaaabababbabaabbbbbbabababaabbaaabaababbabbabbbbabaaabbbbaabaabbbaababaabbabaaaaabbabbbabbbaaababbaabaaaaaabaababbaaabababaaababbaaaaaababaaabaaabbababbabababaaababaabbaabaababababababbaabaaababbabaaaaaaababaaaaaaababbaaabbbbabbbaaaaaaaaabbbaabbbaaabbabaababbabaaaaabbaabaaaabaabaababaaaaaaabaaaabaababababbbbaaabbaabbbaaabaaaababaaabaaaaaaaaababbabbbababbbabaaabaabbaabbaaaaabbaababaaabbaaaabbabbbabbaabbabbbabbbaabaaaabbbabbaaaabbbababbbabaaababbbaaabbbbbaaabbabbabbababbababbbbbbabbaabbbaabaabbbaaaabbabaababbabbbaaaabbababbbbaabaababaababbbabbbaabaababbbaababbbbbababbababababaabaaaaabbaabbabbabbaaabaaaababbabbbbababaaabbaabbbaaaabbabababbbbbaaabbbaaaaaaabbbbbbabaabbaaaabababbbabaabaababbbbbababbbbbabbabbabbbbbaaaabbaaaaaabbabaabbbaaababaababababbbbabbbbabbbaaabaabbbbbababbaabbbaaabbaaaaaaaaababbababaabbbbbaabaababbaabbaababbaabbbaabbbbabbbaabbaabbbabbbababbbaabbbbabbbbbbabaabaaaababbbbbbaabbaabbbbbbbbbabbabbbababaabbbbaababaabbaaabbbbaaabbbbaababbabbbababaabbabbababaabbbaaabbbbabbbabbbabbaaabbbbbbbbbababbbaabbaabbaaaabbbbaaabaaabbbaabaaabbabbbbbaabaabbbabbbbababaaaabbbaaabbaaabbbbbbbabbabaabbabaabaaaababababbababbabbbbaaabbbbababaaabaababaaababbbabbbbbabbbbbabbaaabbbbaabbbbbbabbbabbbabbbbbabbbaabbbbbabbabaaaabbbbaabbbabbbbbaaababbabaaaaaaaababbabbaaabaaababaabaaabababbababbaaabbaabaabbabbabbaaaabaabbbabbbbaabbabaababbbaabbbabbbabaaaaaabbbaaababbababaabbbbaabaaabbbbaaabbbaaaababbabbaabaaaabbaabaaabbbaabaabaaabbbbbabaabababaaaaaabbabbabaaaaabbbbaaaaaaaaabaaaaaabbaabbbbbbbaaaaaabbaaaabbababaabaaaaababbbabaaaaabbbaabbabaabaabaaaabaababbbbbbbbabbaabbbbabbaaaababaabbbbbbbaaabababaababbaabaabbaabbbbabababbbaabbbbaaabaaabbbbbabababbbbaaabaabbaabbbababababbbbbbaabaaaaaaaaaaaabbaabbbbbaaaaaaaababbbabbbabbaaaaabbbaababbbaaababbbabbaaabbbbaabbbbbaabaabbbabbaababbbabbbbbaaaaaabbaabaaabbbabbbbaaaabbbbaaaaaabbbbaaabaaabaaabbbbbabaaaaaabbbabbbbbaababaaababbbaaabbbbabbbabbbbaabbbbbaaabaaabbbaaababbbabbaaabaaaaabbabbaabbabbababbbaabbbbbbaaaabbaabababbbabaabaaabbbbaabbabbabbbaaaabbbbbbbbbaababbabbababaabbbbaaabbbbaaabbaaaabbbababbaabbbbbabbbbabbbababaaaaabababbabbbbbaaabbbbbbbbabbbaaaaabbbbbbabbaabbbabbaaababbbabbbababbbaababaaaabbabbaababaaabaaabbbbbabbaaaabaaaaabbbababaaaaabbabaaaaabbbbabbaaabaaababaabbababbaabbbbabaabbaabababbbabbbbbabbbababaaaabbbbbaabbabbbbaabbaaabbbbbaabbaabbabbaaaaaaabaaaaaaaabbbaaabbaaaaaabababbbbabaabbbbbbbbbbaaaabaabbaaabaaaabaabbabbbbbaaaababbaaababbabaaabbaabbabaabbbbaabbbbaabaaabbaababbaabbbbabaaabbbbbaababbabbabbbaaaaabaaaababaabaababaaaaabababbaabababbabaaababaaabbbbbbbabbabbbbabbbbbbabbbbaabaabbbbbaaaabbbbbababbbabaaabbaabbbbaaaaaaaabbbbaabbbaaabbababaababaabababaaababbbbbbabbabaaaabbbaabaaaaabbaaaaaaabbabbabaaabbabbbaabbbbbbbbabbbbbbaabaabaaababaabbbbaaaabaaaabbbbbbabaabbbbabbabbaaaabbababbbbabaabbaaaaabbabbbabbbaabbbbabaaabaabbbbbabaabaaaabbbabbabbabbbbabaaabbaababbbbbabaabbbbabaaabbbbabaabbbbabbbbbbbbaaaabbbbbabbbaabbaaabbabbbbabbaaaaaaaaabbbabababaaabbaaabaabbbbabbbababbbbabaabbbabbabbaababbaababbabbabbabaaaabaabbaabaaaabbaabababababbabaabaaaaaabbbbbbbabbbaaaaaabbabaaabaabbabbbaaaabaaabbababababbbbbaabbabbabbbabbabaaabbbaaaabbbabbbabbbbbbaababbbabbaabaaaabbbababbbabbbabaaaaaaaabaabbaabaabaabbbbabbbabaaaaaabaaaabbbbaaabbababaaaabaaabbaaaabbaababbaaaabbbaaaaaabaabaabbbbbababaabbabababbababaabbabababbaaababbbaaaabbbbbbbbbbaabaabaabaabbabaabbbbaabbbaaabaabbaaaaabbbabaabbababbbbbbaabaaaabbbabaabbaaabaaaaaaaabbabbaabbbbabaabbbaabababbbbabbaaaaabbbbaaaababbbbbbbbabbbaaabaabbaaaaabbbaaabbabbaaaababbabaabbbbbabaaaabaaabaaabaabaaaaaaabaabaabbbbabbababbbbabbbbbbbaaabaababbabbabaaaabaababaabbbabababaaaaabbaabbbbbabbbaaabbbaaabababbbbbbaaabaabaaaaaabbabaababababbbaaaabbaaababbbbbbbabbaaabbaabaaabbaaabbbaabaaababbbaabaababaababbbaabbabababbabbaaaabbaaabaaabaababababababaabbaabaababbabaaaaabbbaabaaabbabaaababbbbbbaaabbbabbabbaabababbaabaabbbaaaabbbabbbbbabaaaaabbbbabbabaabaaabbaaabbbbabbaaababbabbbbaabaababababbbabbabbbabbbbbbaabaaabababaaaaaabbabaabaaaaabbabbbabbaaaabababbbaababaaabbbaabbbabaabaaaaabbabbbbbbaababbbabaabaaababbaabbbaabaabaaabbaabaaabbbbaaaabaabbbaaaabaabaabaaaabbbbaaaaabbbbabbbaaabaaaabaaabbbbbaaabbaabbbaaaaabbabbabaaaabaabbbababbbbaaabbaaabaabaabbbaaabbbaaaaabaababbbabaaabbbaabaabbababbbababaabbbbaabbabaabbbaabbbaabbaabbaabbbaaaaabbabbabbabbbbabbbbabaabbbababaaaabaabbaaaabbababbbbabaabbbbbbabbbbabbbabbbbabababaaaababbbabaabbbabababbbaabaabababaabaaabbbaabbbabbbaabbaabbbaabbaaaaaaaaaaababbaabbbaababaaabaabaaaaabaabbbbabbabbbbbbaaabababbaaaaababababbbabbbbabaabbaabbabbabbabbaabbbbbbaaaaabbbbbababbbabbbaaaabbbbaabbabbbbbbabbbaaabbbbbaaaababbbaaababaaabaaabbaabbbababbbabbaaaaaabbbaabbbababaaaabaabbaaabbbbbaabbaaabaaabababaaabbbbaaabaaabbaaaabbaabaabbbabbabbaaaabababbbababbabaababbbaabbabababaabbbaaaabaabbababaaaabbaaababbbababbabaabbaabbbbbabbbbaabaabbbaabbabbbabaaaaaaaaaaabaabbbaabbaabaabbbbabbaabaabaabaaaababbbbabbaabaaabbbaabaaababbaababbbbbbaabbaabbabbbababbbaaaababaaaaabbbbaaaaabbbbbbabbbbbbaaaaaabbababbbbabaabbaabbbaaaabaaaabbababaaaaaaabbaabbabaaaabbabbbababbaaaababaaabbabaaababbaaaaaabbbabaaaaabaaabbbabbbbabbbbbbabababbaabbaaaabbbbbbbbbabbbbbaaaabbbbaaababbababbbaaabaababbabaabaaababaabbaaaaaabaaaaaaaabbbbabbabaabbababaaabbaabaabbbbabbaaababbbaaaabbbabbbbabababbbabbbaaaaabaaababbbaababbbbbabbabaababbaaabaaababbbabaaababaabaaaaabaababbbbbabaaaabbbabbaabaababbbbbababbaaaaaabbababbabbbbabbbbaaaabaababbababbbbabbabaaaaaaabaaaaaabaababbaaaaaaaabaabbbabbaabaabaaabbaabaaabababaabbbbbababbaabbaaaabaabaaabbbbbabbbaaababbbaabaaaaabbabbbbbbbaabbbbaabbababbbaaabbbaaaabbbaabbaaabbabbbababaabbaaabaabbbababaabbbbaaabaaaaabababbbbabbaababaabbbbaaababbabaabaabbbaaaaaabbbaabbaaaaabbbbbabaabbbabbbbbaabaababaaabbaaaabbaababaaaaaababbbbababaaabbbaaaaababaabaaaaabbabbbbbbabbabbabbbbaaabbbabbbbbabaababbaaaabbbbaaabbaaabbaabababbbbabbababbaabaabbbabaaababbbabbaaabbbaaaaabbabaabaaaababbabbaaaaababbabbbbbbabbbaaaabbaaabbaaaaaabaaaaabbabbbabaabbabaabbbbbbbabbaabaabbbababbaaaaabbaaabbabbbbbbbbaabbbbababaaabbabbabbbabbaaabbabbbbbbbaabbbabababbbaaaabbbaaaabbbbbbbbababbbaabbababaabbbaaabbabaaaabbaabaabbbaabbabbabbaaaabbbabbaabbbababbbbabbabbababbbaaaababaaabbaaababbaaaaaabaaababaaaaaababaabbbaabaababbababaabbbabaaaaaaabbbbaaabbbbbbaaabaaaabbaabbabbabbabbbaaaaaabbaaaabaaaaababaaabaaabaaaaababbbabbabbabbaabbbaaaaabbaaababbbbbbbbbaabababbbabaaaaabbbabaabaaababbaababaababbbaaaabaababbbbbbabbbbbaaababaabaabaaaabbaaaaaababaababbbaaabbbbbbbbabbaababaaabaaaabaabaaabbabbbaabbabbaabbbaaabaaabbaabaabababbabbaabbaaaababaaabaaaabbbabbaaabbbaabababaaababaaaaaabaaaababbbabbbaaabaababbbbaabbabbaabbabbabaabaaaaaabbbaaabaabbaaaabbaabbaaaabaaabaabaabbbaaaaabaaaaaababbbabaabbabbaababbbbaaabaaabaabbbabaabbbabbbabaaaababaaaaabbbabbaabaaabbbbaabbaaabaaababbaabababaabababbaaaaaabababbbabbbabaaaaabbabbbbbbaabaabbbbabbaabbbaaaaaabaaaababbababaaabababaabbbaaabbbabbaabaaabababababbbbbbaabaaaaaababbbababaabbbaaaaaaabbbbbaabaaabbbabbbbbbbbabaaabababbabbababbabaabaaabaabbbbbaababababaababbabbabbbababbbaabaabaabbbbbbbbbabbaaaabababbabaabbbaabaaabaabbbaabaababbbabbaababbbbaabaaaababaaaaaabaaaabaaabaabbabbaaaaaabbbaaabbbbaaaaaaaabababaaaaabbaaaabbbaabbabbbaaaababababbbababababbbaaaaaaabaabbabbbaaaaaba