babababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbabababbbabbbbaaabaabaaaaabaabbbaababbbaabbbbabbabbbbbbaaabbbabbaabbaabbaabbaaaabaaaaababbaaaaaabbbaaabbbbbababaaaabbbbaabaabbbbababaaabaababaabbbbbbabbabaaaaabbabbbbabbbbbabbababbabaaababbaaaabaabbaabaaaababbabbbbbbabaaabaabbababababaaababbbabbaababaaababaaaaaabaaaaaabbaaaabaaaaaaabbbbbaababbabbaaabaaaabbabbaababbaaabbaaaaaabaaaaaaabaaaaaaaaabababaabbbababbaabbbbbababaaaababbabbaabaabbaabbababaaaabaaabaaaabaabbbbbbaaabaabbbbbaabaaaaabbbbbaaabbabbbaabbaaabbbbbbabbabbbabbbbaabbaaabbbababbbbaabbabababbbaabaaaabaaabbbaaabbabbbaabababababbabbaaabaabbaababbaababbbaabbaababaabbbbaabbbbbaaabbbaaaabbbabbabbabbbaaabbbbbabbbabbabbbbabbabbabbbbaabbababaaabaaaabbaabbbaaababaabbabbbaaaaaaabaababbabababbaaabbbbabaabbaaabbabaabbbbabbbbbbabbbabbbaaaabbaaaaabbbabbbbbabbaabaaaabaaababbbbbaababbbaaaaabababbabaabbaabbabaabbbbaaaabbbaaaaababaaaabbaaaaaaaabbbaababbabbbaaabaabababaabbbababbbbbbaabbababbaaaabbbbbbbaabbbabbaaaabbbbbababbbabbbaaabbaabaabbbbabaabbabbabaaabaaaaabbbbabbabaaabbabbabbabaaabaabaabaaaabbbbaaaaaaaaababaabbbaabababababaaaaabbaabaabaaaabbbaaabbaaaabaaaaabbbbbbaaabbbbbbbbabababaaaababbbbbbbaaaabababbbabbabbaabbbabbbbbbbbbbbabbaabaaabbbbabbbaaabbababaaaabbbaababbbababaababaabbbbabbbbbaaabaababbbbbbaabbaabaaabababababbabbabaabbaabbbbbbbaaababbabbbbbbabbbbbbababbaaababbabaaabaaaaabbabaababaaabbabbbabaaabbabaabbaabbaababaaaabbaabbabaabbaabbbbaaaabbbbaaaaabbabbabbbabbaaaababababbbbbbabbabbaaaabbbbabbbbaaabbaaaabbababbbaabaaabbabbbaababbabbabbaabbbbaabaabbbbabaabbbaabbbbababbbbabbaaabbaaaabababaaabaababababaabaabbbababaaaabaaaabbbbababababbabbbbaabaababbbbaabbabaababbabaabbaabaabbaaabbbbaabababbaaabbaabaaaabbabaaaaabbaaaabaaabbabbaaaababbbaabbabbbbbaabaabbabbbaabababbbbabbabbbbaabbaabbabaaabbaabaaababababbbbababbaabaabbbbbaababababaaabbaaaaaaaabaaaaaaaabbbabbbbbbbaabbbbabaabbaaaaabbaabaababaabbbbaabbabbabaabbbbaabbaaababaabaaabbbbaabbabbababbababababaababbbbababbbaaabbbbbababbbbaaabbbbbbbbbbaaaabbabbbaabbabbaabaababbabbabaaaabbaabbbabaaaaaabbbbaaababbbababbabbaaaabaaaabbbaabbababaaaabbbaaaaaabbabbbbbabbbbabbbaabbbabbaabbbabbabbabaabaabbabaaaaaaaaaaaabbbbabaaaabaaaababbabbabbbbaabbababbaaabbaaaabbbaaabbbabaabaaabbaabbababaaabbaaabbbbbbabbabbbbaabaaabbbbaabbbaaaaabbabaabbbbbbbbbbaaaababbaabbaaabbbbaaabbaaabaababaaaabbbabaabbabbbbabbbabaababbbbbabaabbbabbaabaaabbaaabaaaaaaabaabbbaaaabababaabaaabaaaaabbbbbbbbbbbbaaaababbaaaabbaabababbabaaabbaabaababbbbbaababbbbaaabbbabbaaaaaaaabaaaabaaaaabbbabbbbabaabbbbbbbbaababaabbaaaaaaaabbbabbaababbaaabbabbbabbbaaaabaabaabbaaabbbaaaaabaabaaabaaaababbabababbbbbbabababbaaabbaaabaabbbabbabbbbaabaabbbbaaaaabbaabbaabaaabbababbbabaaabababbbabaaabaaaabbbbbaaabaaabaabbbaabbbbabbabbbabbbbbbbaabaabbbbabbbabbbaabbbabbbababababaabababaabbbaaaabbbbababbaababbbbabbaabbabaaabaabbaabbabaaaabbbabaaabaababababaabaaabaabbbababbbbbbaabaababbbabaaabaaaaabbbbaaabbababbababbbabaabababbaaabbbaaaaaaababbabaababbbabaaaabbbbaabaabbabbabbaaabbbaabbabaaabbbaababbbaabbabababbaababababaaaaababbbaabbbbbabbaaaaaabaabbaaabababbaabbaabaabbbaabbaaaaabbbbababbaaaababbaabaaabbaabbbbaabbbbaabababbbaaaaabaaababbabbbaababbaaabbbbaabbbabaabbbbbababababbabaabaabaababbaabbabaaabbbbaabbbaaababbaabaabbbbbabababbbabaaababbbabbababbbaaaaaabababababbaabbbbbabaabbbbabaaaaaaabbbabbaaababaaabbbbaabaabaaabaaabaababaabbaaaabbbbbabbbbabababaabaaababaaabbababaaabaabaaababaabaabababbbbbaaaababbababbabbbbbaaababbaaaabaabbbbbabbbbabbabbaaaababaaabbbabbabbaaaabaabaababaaabbabbaabbabaaaababbabaaabbbbaabaaabababaabbbbbabaaaabbbbaaabbbbbbbaabaaaabbabbbabbbbbbbbaaaabbbaababbabbbbbabbaabbabbbbaabababaaabbaababaaabaaaaabbbbaaabaabbbabbbabbabababbaaaaaaaaaaabbbbaaaaabaaababaabbababaabbbababbaabaabaaababaaababaabaabbbaaabaaaaabaaaaaaaabbbbabaaababbbbaaaababbabbabbabbabababbbbababaaabaabbaababaabaabababaaaabbababbabbbaabaababaabbabbabbabbaabaabbabbbbbbabaaabaaaabbbbabaabbbaabaaababbaaabbaabaababbaabbabbaabbbabbbabbbbbabaabaabbbbbabbbabaabbbbaaaaaabbaabaabaaababaaaabaaabaabbababbbabaaabababaaababbbaabbaabababbbbaabababbbabbbaaaabbaabbbbaaabaaaaaabaababaabaaababbbaaabaaabbbabaaaabaaaaababbaaaabbbaaabaabaabbaabbaabbaaabbaaabbabaaabbbabababbbaabaaababbabbbbaabababbababbaabbabababaaabbabaaabbaaaabababbababababaaababaaaabababaaaabbababbbaabbaaaababaaabaaabaaabbbabbabaaaabbbaabbaabaabbbbaaaababaaaabaaabbbabaaaaaaabbabbbabbbaaabaaabaaaaaaabbabbbaaaaababaaabbbbabbaabbaabaaaabbbbababbabbbbbaaaabbababbaababbbaaaabaaaabaabbababaaaabaaabbbbaababaabaaaabbbbbbbbabbbbbaabaabbbaabbbbbbabbbbbbbababaabbaaabbbaababbbababbaaabbbbaabbbaababbbabaababbbbbabaabbbbbbbabbababaaaaabaababbabaaababaaaabbabaaaaabaaaababbaabbbbbbabbaaaabbbaaaaababababaaaaabaabbbabbaabbbaaabababbaababaabaabbbbbabaaaabaaaaaaaababbbbbaaababbbbabababbbabbbbbababbbbabaabbbbbbbababbbaabbaaaaaaabbbbbbbabbabbaababbabbbabaabababbbaabbbbababaababbbabbbaaabaaababaaaaababbaabaabbaabaaaaaaabbabaaaabbaababbababbabbbbaabbbaaaababbbaaaabababbbbaabaaabbbbaabaaabbabbbaaaabaaabababaaababaabbabbbabbabbabababbbbbaabababaaabbbbaaabababbaabbabbabbaabbbbaababbababaababbbbaaaababbababbaaaaabbbbbbbaaaabbbababbbaaaabaabbaaaaaaaabaabbbabbaabbaaabbbaaababababaabababbaabaabababababbbbaaabbbabbbaaaabaaabbababbbbbabbaabaabbbaaabaababbbaabbbaaaabbbaabbaaaaaabbbbabbbaabbaabbaaabaaaaaabbaaabaabbbaabaaabbbaabbbaaaaababaabbbbbaaabbabbbbbabaaabbababaabbaabababaaabbabababababbbabbaaabbabbaaabbabaabbbabababbaabaaabababbbbabbabbbabbbaaaabbbaabbbbbaaaabbbbaaaaabaabababbbaababaaaaababbabbaaabbbaabaaaaababbbbabaabbbbbbaabaaaaaaabbabababbbbbbababbbbabbabbabbbbbbbabbbabbabaababababbbbbabaabaaabbbaaaabaaaaaabbbaabbaaaaaabbbbbabbabaaaaaaaaaaaaaabbabbabbbbbbabbaabbbaaaabbaaababbabbbbbaaaabaabaaaabbaaabbbaaaaaaaaababbabaababbbaabaababaabbbbabbaabbabbbabbaaaaaaabbbaabababbbabaabaaaaaabababbaabbbaabbabaaaababbabbbbbababbbaaabbbabababaabbabbaaabbbbaaaaaaababbaabbbabbbaaaabbbaabbbabbbbbaaabababaaaabbabbaabababababbbbaabaaaaaaabbababbbaababbabbaabbbbabbaaaaababaabbabbbbbabbbbbaabbbabbaaaababbababbabaaabbaabbbbbbabaaabbaaabbaababbbabbbabbbabbbaaaabbaabbbbbbbaabbbababaaabaabbaaabbaababaaaaaabaabbaaaabbbbbabbaaababbbaabbaabababababbaaabbbbbbaaabbbbbbaababaabbabbbbbabaababbaaaaaabababaaaaaababbbaabababbbbbabbaaaaaabbaaabbbaaabbaabaabbaaababbabbaabbbbaaabaaaaaaabbbbabbbbabbbaabaaabaaabbabbababbbaaaabbaaabaababaaaabaaaaaabaabaaababbaaaaaaabbabaaabbbabbbaaaabbbbaaaabbababbbbabbbbbabbbbabbbbbbaaaaaabaaabbbbabbbbabbababaaababbabaaaaaaaaabbaabaababbbaaababbbbababbabaabbaabbbbbbbaababbaaabaaabbaababaaaaabbabbbababaabbabbbaababbabbbabaababbbabbbbabbaaaabaaaabbaaaabaabbbabbbbaaabaaaaabbbabbabababbbababaabaabbbbaabbbbabbaaabaababbaabaaaababbabbaaabbbbaabaaaabaaaabaaaabbaaabbbbaababababaaaabaababbbabaaaaabbbbaaaabbabbbbbaaaabaabbaabaaabbbbabababaababababaabbbabaaabababababbbbbaaabbbbbbbbbababbbbbbaaaaaaabbbbabbbababbbbbabbbbaababbabbabaaababbababbbaabbbaabaababbabaabbaabbbbabbbabbbbababbabbbaaabbabbaabbabbbababbbaaababbbaababaabaaaababababaaabababbbaabbaababaaaaabbbbabababbabbbabbaabbbaaabbbaabbbaaaaabaaaabaabababbaaaababbbabbbbaabbbaaaaaaababbbbababbbbabababbabbaabbabbbbaaabbbbbabaababbaabaabababbabbaabababababaabbbaabaaabbaaabbbababbbbbbbaabbabababaaaaaababaaaaaaaaababbbabaaabbbabbbbaabbbaaaaaabababbbabaaaaaaaaababaabbbbaababaaabbbbaaabaabbbaabaaabababbababbbbbbaaaabbabbaaabaabbababbabbbbabbababbaababbababbabbabaaaaababaabbbababbabbabababbaaabaabbbbbaaabaabbabababbabbbbabaabbaaabbbbbbbbbbbbbabababaabbabaabbbaabaabbbabaaaabbbbabbaabbbbabbbababaaaabababbaabbbaaaabaaabbaababbbbaababbabbaaaaababbabaabbabaabaaabbbbaaaabaaaaabbbabaaaabbbaaabaabaaaabbbabaabbbbaabbbabbabbaabbbbbababbbabaaabaaaaabaabbabbbbaabbabbbbbaaaaabbabaabbbabbaabababbbaabbaaaaababbbbbaabbbababaaabbbaaaabaaaabbbbabbbaabbabbababaabbaabbaaaaabababbabaaaaabaaabaabbaababbaabbaaaabaaabababbbbbbabbbbbbaabbabaabbbbababbbaaaaababaaaabbaabbabbaaabbabbbabbbbbaaabaaabbbababaaaabbbabbbbabbaaaabbbbbabbbbbbbbababbbbbbaaabbbbbbabaabbababababaaabaababbabbabaabbaaabbabbaaabbbaabbababbaaaabaaabbababbbabbbbbbaaabbbbbaaabaaaaabbbabbabbbbbbabaaaabbbbababaaaabaaaaaabbbbbabbbaaaabbbababbabaababbbbbabbbbbabbaabbbaaababaabababbabbababaaababaaababaabaaaaaabaaaaabbabbabbbaaababaababbaaabababaabababbbbabbbaaaaaaaaabaaabaaaababaaabbaaaabaababaabababbbbabbbbaaaabbbababbaabaaabbbaabbabaaaaaababaabaababbabaabbbbabaabaaaaabbbaaaaaababbbaabaabbbaabbbbbbbbbbbbbaabbaabbababbaaababababbaabbbbbbbbaaabababbbaabbbaaaabbaaaaabbbbaabaaaaaaabbaaaabbabbbabbbabaaaaaabbbabaaababaaabaabbaabbabaabbaaaabbbababbbbabaaaaabbabbbbbaaaababababbabbbbbbbaabababaaabbbbbabaaaabbababbabbbababbbaaaabbbbaababbaabbabbababbbbaaaaabbaababaabbababbbbbbbabbbaababaabbbaaaaaaaaabaaabbaabababbbbabaaaabbaababbababbaaaaabbaaabbababaabaabababbbbbbabbbbbabbababbabbbabaaabbbabbbbbbabababbbaaaabaabaaabbabbbabbaaabbaababaababbaaabaaaabbaaaababbbbaabbbaabaabbbbabbbaaababbbbbbaababbaababbababbbbbbbaaabaaaaaabaabbabaaabbabbabaaabbaaabbbbaaaaabbabbabbaabaabaabbabbbabbbaaabbbaaaabbababbabbabbbbabaaabbaabbaabbaabbabababaabbbaabababbbaabaaaababbbbabaaabbbbabbbaabbbbbabbbbababaaabbbbabbbaaabbabbaaaaabbabaababaabbbaaaaaaaaaaaabbbbaabbabbaabbbbbababbbbbbbababbbbbbbbaabbabaabbbbbbbaabbaabbabababbaabbabaaaabbaabbabaabaaaaaabababaaaaabababbababaaababbaabbbabaaaabaabbbbaaababbbaababbbaabbbbbbbabbbabbabaabbbaaaabbbbababaababababbaabbaaaaaababaaabbaaaaabaaaaabbbaabaaaabbbaabbaababbaabaaaabbbbaaaaaabbbaabbbbbbabbbaaababbaaabbaaabaaabbbaabbabaaaaabbbaaabbaababbabbbabaabbaabbbaaaabaababbbbaabbbbbabbaabbbbbbbaaaaaababbbbabbbbaaaaabbbaababaaabaaabaaaaaaabaabbbbbabbbababababaabaaabaabbaabbbabbbaabaaabbabbabbaabbabbaaaabbaaabbaabbaababaabbabaaaaaabbaabbababababbabaabbbbbbbbaabbababaabababbbbbababaaabaabbaaabbbbbbabbbbabaaaabababaabbbababaaabbaabbbbaaaabaaaaabbabbbaabbabaababbabbaaaabbaabbaabbbbabbabbabbaaababbabbbbaabbbaaaaaabaaaababaaaababbbabaabababbbbbbbbbbabababaaabaababaabbaaabbbabbbaaaabbaaaaabbabbbbbbbbabbabaabbabbbbabbabbabbabaaaabbaabbababaaaaaaabbbabbbaabaaaabbbbbbbababbaababbabbabaaaaaabababbaaaaaaaaabbaaaabbaabbaabbaabaaabbbaaaaaabaaaaabbbbbabbbaabbbaaaaabbbababbbbaabbabbaaabbbaaabbabbabbbaabaaababbababbbbabaabbabaaabaaabbabbabaababaababbabaabaaabbabbbbbbbaabbababbbaaabbaabaaabbaaaaabbbabbaaababbbbbbaaabbaabaababaaabaaabbbaaaabaabaabaabbaaabaaaabbababbabbaabbbabaaabbbbbbbbbaabbaabaaaababaaaababababbbbaabaaaababbabbbbabaabaaaaabbaabaaaaaabaaababbaaaabaaaabbbbbbaaaaaabbbababaaabbbbaabaabbababbabaaabaababbabaababaaaabbaabaababaaaaaaaabbaaabaabaabaaabbbbbbabbaaabababbababbabbbbbaaabbabbaaabaaabbbbabbbabbabbaaabaaaaaabababbaabbaaabbbbaabbabbbbabaababbaaabbabaabbaaabbbbbabbbbbabababbaaaabbbaaababababbbbaababbabbaaaaabbababaabaaabbaaaaaabbaababababbaabaababbbbaaaaaaabbbaaaaaaaabbabaaabaaabbababbbaabbaababbbaaabaaababaaabaaabababaaabaaabbbaabbbbbbbbaabaaabbbbbbabbbbababbbabbabbbbaaaababbaababbbabaabaaaabbaababaaaaaaababaaaaabaaaabbbaaaabbbbaabbbbbabbbbbbbaabbbabbababababbbaababbaaaaababbababaabbaaababbabaabbbbbababbbbaaaaaabbbaaaaabbbbbaabaaaabaabbbbbbbaaaaabaababaaabbababbaabaabbaaaaabaabbaabaaabaabaaabbbbabbbaaaaaabbaaaabbaaaaaabaababbbaaabbaaaabbabababbabbabbbbaaabaabaababbaabbbabaaabababaabbaabbbbbaabbabbbbbbabbabbbababbbbaabaababaabbabbabbbababbaaababaabbbbbaaaaabaaaabababaabbbbbbabaaabaabbaaabbabbabaaababbababbbbbbbaababababbabaaaaaaaaaabbbbaabbabaaabbbbaaaababbbaaaaaaaababbaabababbbbbbbaababbaaaaabbbabaabbababbbbbaabaaabaaababbaabbbbbabaabaababbabbbaaaabbaabbbabbbbaaaabaaaaabbbbbaaababbababbbbbabbabaaaabaaabababaaabaaaabbaaaabbbaabaaaababbbaaababbaaaabaabbbabaababbbbbbabbababbbababbbabbabaaabbbbaabababbbabaabbabababbabbababbabbbabbaaaaabbaababaaabbbaaabbbabbabbbbbabbaabaabaabaababaaaaaaabbaabbbbababaabbbbabbbbbbabaaaaababbababababaaaaaaaabaabaaabbbbabaabbabbbaabbabbbabbbbaaabaaaabbbbabbbabaabbbbbabbbbbabbbabbbbbbabbbaaaaaaaaabbaaaaabbbbabbbbaaabbababbabbbbbaaabaaaaaaabbbaaaababababaabbababbbbbabaabbabaaabbbbbabaabaabbbaabaaaabbaabbaababbbbbbababbabbbaabbbbbabbbbabaabaaabbbaabaabbaaaabbbbbbaaabbbbbbbaabaabbbbbbbbabaaaabaaaabbbbabbaabababaabbbaaaaaabaaaabaababbaabbaabaabbbbbaabbaaaaabbaaaabbabbababbaaaabbabbabaaaaaaabbbbbaabbbbbababaaabbbbabbbaaabbaaababbababaaaabbbaabbaaabaabbabaabbbbaaabbaaaaaaababbbaaababbaaaabaabbaabaaaaaabbababbbbbabaaabbbbaabbabbababababbbaaaabbbaaabbbbbabaaaabbbbbaabaabbaaaaaaabaaabaaaaaabbbaaaabbbaabaaabbbaabbbaabbbabbbaabbabababbbabbbbabbaabbaabababaabbbaababaababaababbaaabbaaababbaaaaabbbabbbaabbbaabaabbbbaaaaabababbabaaababbaaaababaababaaaaaababbaaaabbbabbbaaabaabaaaabaababaaaabaaabaaaaababababbaabbababaaaaaaabbbabababbbabbbbaaaababababaabbaaabbabbbaaabbbabbababaababbbbaabaaaabaaaaabbaababbaabbaaabbaaaabaaabbbaababaaaaaabbaabbbbbaabbbabbbaaabababaaababbaaabbbabbbababababbbabaababbaaaaaabaaaabbabbaaaaaabaaaaababbabababbabbbaaabaaaaaabaaababaaaababbbaababbbbbbbabbabababababbbbaabaaaabbaababbbababbabbbbaaababaaabbaabaaaabbaababababbaaabababbaaaabbaaabbbaabaabbbbbbbaabbaaabaaaaabbbbbabbbbaaaaaaaababbbaaabbaababbbbbaababababbbabbbaaaabababbbaabbbabbbabbbabaaaabbbbaaaaaabaabbaabababbaaaaaaabbabbababababbabababaaababbbabbababaabbbabbaabaabbaabbaaabbabbbbbababbbbbaaaaabbaabbaabbbaabbaabbbabbbaabaaaabbbabaaaabaabaaabaaaababbabbbbbbbbbbbabbbaaabaabbbbbaabbbbbaabbbabababaaababaaabbaabbbbabbaabaaababababaaabaaabaaaabbbabbabbaabbbaaaaaaabbbbbbbbaaaababaaabbaaabbbbbbbabbbbbbabbbbbabbabbbabbbabbaaabaaaaabbaabbbaabaaabaaababbbbbbaaaababbaabbabbbbaabbaabbbbbbabaaaabbbabbbbababbbabbabbbabbbbaaaaabbabaabbaabbbaaabbaaaaabbbbbaaababbbabaababaaaaabaaabbaabbbaaaaaababaaabbabaabbbbaaabababbbbbabaaaabababbbbaabbababaabbabbbbbaabaaaaabababababbabbabaababaaababbaabaaaaabbbabbaaababaaabbaaaabaabbaabbbababaabbbabbbabbbababbbbabaaaaaabbaabaaaaaaabbbbaababaaaabaabbbbbabbbbaababbabbbababbbbaaaaaaababbbbbbaabbabaabbaabbaaaabbbabbaabbaaabaaaaaaaaabbbbabbbbbbaabaabbabbabbaabbbbaaabbbbaaaabaabbbbbbabaabaaabbbababbabbababbabbbabbbbbbaabaababaabababbaabaaaabbabbbbbbbbababaaabbbbbababbbbabbbabbbabbbabbbabaabbabbaaabbbababababbaabababaaaabbababaabbbabbaabbbabbaaabbbbbbaaabaaababbbaaaaabababbaababbbbaaabababbbbbababaabbbbababbaabababbbbabaabaaaaababbaaabaaaabbaaaabbaabbabbaaaabbabbaaabaabaaaaababaabaabbbbbbbaaaaababaabaaabbaaaabbbaaabbbabaabbababbabbbababbaabaaaabbbaaabaaaabbaaaaaaababbbaaaabbbbaaabaabaabbbabaabbbbbaaaabaaaaababbababbbaaaaabbaababaabbbabbaaababbaabbaababbbabbabbaaabbbababaababaaabababbaaabababbbaaabaabbbbaababaaaabbbbaabaaaaaaaababbbaaababbbababbbbaaabbababbaabbabbbaaaaabbbaabaaaaabbabbaabaaaaabaabababaabbbabbaaabbbbbbbabaaabbbbbabbaaaaaabbbaababababbbaabbaaaaaabaabbbbaabbbabbbaaaabaaababbbbbaaabaabbaabaaababbaababbbbabbaababaabaabbbababaababbbbbabbaaabbaaabbabaabaabbbbbbaaaaaabbaabbaaabbbabaabaabbaababaabbbabbbaababaaaaaaabbabbabbbbababbabaabbbbaabaaaaababbaabbbbaaabbaabbbbbbababbbabbaabaaabaaaaabaaaaaaaabbbaabbbbbaaaaaabbbbbbaaaabbbababaaaabababbaaaaaaabbabbbbbbababbaaaabbbbbbbbaabbbababbabbaaabbbaaababaaaabbaabaaabbbbbaabbbbbababbbabbbbabaaabbbbabaaaaabaaaaaaaaabbababbbbbbbabbaabaaabaabbaababaababbbaaaaaabbbababbbbbaabbbbbabbabbaaaaabbabababbabaaaaaabaabaabbaaabbabbbabaabaaaababbaabbaaabbbaabaaaabaaabaaabbabbbababaaabaaababaabbbbbbabababbaaaaaabbabaaabaabbbbabaabbaaabbbaababbaaaabbbaaabaababbbaaababbbbabbbbabaaaaaabbbaaaabaabbbabbbabbabbbaabbbbbbbbabbaabbaaabaabaaaababaaaaaababaaaabbbbab
