1000000 0
aaabbbabaaaaabbbaaabbaaabbabaabbbbbbbbbabababababbaabaabbbbbabbbabbbbbbababababbabaaabbbaaaaababbaaaababaababbaaababaaaaababbbaabaabaaaabaaaaabaababaabbababaabaabbaaabaaabbabbbbbaaabbabbaaaaabbbaabababababbbababbabaaaabbaabbaababaaaabaaabaaabbbbbaabbbbbabbababaaabaaababbabaabbaabbbbabbaaaabaaabbbbbbbbabbaaaababbabababbbbabbabaaabababbbbbbbabbbbabaababaaaabaaababaaababaabaaaaaaabbbbbabbbbbabaabbbababababbababbbaabbababbaababbbbabbbaabababbabbabbaabbababbabbabaabbaababaaabbbabaaabababbabbbbbabbbbababaaababbbabaaaabbabababbaaabaabababbbbaabbabbaabbaabaabbaabaaabaabbaabbbbaabbbbbaaabbbbbaaabbabababbabbbabbabbbaaaaaabbababbbbaaabaaaabaaabbabbabaaabaaaaaaaaaaaaaabaabaaabbbababbbbbaaabaaabaaaaaabbbabaabbbabbabbbaabbababbbbaabaaabbbbaabababbabbabbbbbbbaaaaaaabbaabbabaaaabaabababbabaaabaaabbbaaabababbbabbabaaabaabbbbbabbaaaababbabaaabaabbbaabbabbbaaabababaabbbaaabaabbababaabaaaababaaabbbabbabbbaaaababaabbabbbbababbaababbaaabaaabbabaaaaabaaababbbbaabbabbbbbbaabbababaabbbbababbbabaabbaabaaaaabababbbbbbbbbabbbbaaaaabaaaabaaaababaabbaaabaaaaaaaaaaaaaaabbbabbaaabaabbbbabbabbabababaabbbbbabbbabbaabbabbabbbaaabbbabbaabbabbaabbbbbbabaababaabbbabbaabbaaabbabbaababbbaabaabaaabbbbabbabaabbabababbbbaabaaabbbbbbbaaabbaaaabbbbabababbbaaaaabbaabbbbbbbaaaabbaaababbabbbbbaaaabbbaabaabaaabbbbabbabbabbbbabbbaaabbbabaaaabbabaabbbaabaabaaabbbaaababbaaaaaaabbbababaaaababbaabbabbaaabbbbbbabaaaabaaaabbbbbbbaababaaabbbbabbbaabbbbababaababababaaaaaabaaaabbbababbbbaaaabbababaabbbbbbaabbaabbaabbbaabbabaaaabbaababbababbbbbbabbbbaababbbaababbbbbbaabbaaabbbbababbabbabbbbabbababbbbabaaaabbaaaaabaababbaaababbaaaabbaaababbbbaaaabbbabbabbbabbbbabaaabbababaaababbbbbbabbabababababaabaabbbabbbbbabbbbaababaaaabbabababaabbbaaaabbabbabbbbaabaababaabaabaaaabbbabbbbaaaabaabbbabbabbbababbaaaaababbbabaaababbabbaabbaabbabbbabaabbbbbbbababbbaabbaababbaabaaaababbbbbbaaabbaabbbbbabbabaaaababaabaabaabbbaaaaabaabaababaabbaabaabaabbbbaabbaabbaabaaabaabbbabbbbbbaaaaababaababbbaaabbbabbbbababbaaaaabbaaabbabaabbbaaaaabbaabababbbbabbabaaaaabbbaabaaabababaabaaaaababaaaababbbbaabaabababbbbbbbaababbaaabbbababaabbbbabbaaababbbaaaaaabaabbbbaaababbaababbbaaabbbbbaaaabbababbaabbbbbaaaaabaaaababaabbbbbbbababbabaaababbbababbbbabaaabbaababbbbabbbabaabbaaabbabbaaabbaaababbaaaabaabbbabaababaabbabbabaaababbababaabbbbbaaabbabbbbababbabbaabababababbbababbabaaaabbaaababbaaababbaabbabbaababbaabaaaaabbbabaabbaaaabbbbababbaabaaababbaaaabbbbbbaaaaaaabaaabaababaaabbaaaaaabaaabababaabbabbaabbbaabbaabbababbaabaaaabababbaaaaababbbabaaaababaabbbabbabaaaaababbbaabbbbaaabbaaabaaaaababaaaaaaaabbaaababaabbbaababaabbabbbbbaabababaaaabaabababbbbbaaaabbbaabbabbabbaaaaabbabbbbabbbbbaabbaabaaaabaabbabbaaaabbbababaabaabbabbabaabaaaabbbbbbabbabababaaaababbbabaabbabaabababababbaabababababbabaaababbaababababaaabbbaababbbbbababbbbaaaaaabbbaaabababbbabaababbbbbabbbbabbbbbabaaaababbabbbbbbaaababaabababbaabbaabaabbbbbbabababbbabbabaabbaaabaabbbababababaabbbbabaaaaaabbbaaabbbabaababbbbbababbabbaaaabaabbbbabbaabbabbabaabaaaaabbbabababbbaaabbaaabbbbaaaaaababaaaaaaabbaaabbabaaaabbbbaaaaaaabbbbaabaabaabaaaabbbbaababbababbbababbbabbabbaaaaabbbabaababbbbabaabbaabbbaabbbaaabbbbabaababaaabaaabababaabaabbbbbbbbabaabbbbaaababababbaaaaababbbaaabbbabababbbaabbbabbabbbbaaaabaabaabbbaabababbabaababbabbaabababbbbabaabaabbabaaaabbbbbaabbbaabaaababbabababbaaabaaaabbaaababbaababbabbabbbaabbaabbaabaaaabaaabaabbababbabaabbababbbababaabaabbaaabbaaabbbbbaaaaaaaaaabbbaaababbbaabaabbabbaabbabbbabaaabaabbbbbbbabaaaabbbbaabababaabbabaaabbbbababbbabbaababbbbaaabbbaaaabbaabababbaabbaaaabaababbbbbabaabbabbaababbaaaabaaaabaaabbaaabbaabbbbbbaabbaaaababbaaabbaaaaaababbbababaaaabbbbababababbaaaabbbbaabaaaababbbbaabbbaaabaaabaabbbbbaaaabbbaabbbabbbaabbabaabaabbabaabaaaabbbbabbbbbaabbbbbabbbbabbbaabaaaabbaaababbbabaabbaaaabbaaaabbbbbbbabaabbaabbabbabbaaaabaabaabbabaaaabaaabaaaaabbbaaabbbaababbaaaabbababaaaaabaabbbbaaaababbabbbbaaabbabbbbbaabaaaabaaaababbaaabbaabbbbabaaaaabbabbbabbaaabbbbababaaababbabaaaabbaaaaaaabaaabbbaabbaaabbbbabaaaaaaaaabbbbaabbabbbbabababbbaababaaaaabbaabbabbabababbbababbbbbaabaaaabaaaaabaaaabababaaabbbaaabaabaaabbbbbabbaabbaaaabbbbaaabbaaaabaaaaaabbaaabbbaaababaaaaabbbaabbaaabaabbaaabaaaabbbbbbbaaabbaabaaaaabaaaaaabbaabababaaabaabbbbabbbbbaabbbbbaabbbaaabaaabaabbababbabababbababababaaaaabbbaaabbbabbaaabbbabbbbabbbaaaaaabaabababbbabbbbaaabbbbbbaabaaaababaabaabaabaaababbbbbabbbabaabbabbabaabbabbbbbabababaabbababbbbabbbaaabbabbaabbaaaaabbbabaaaaabaababaabaabbbabaaaaaabaabaaabbbabbbbbbbbabbaaabbbabbbbaabaaabbbbaabaabbbabbababbbabbaaabbabaaababababbabaaabbbbbbbbabaaaaabbaababbabababbaaabbbaaaaaaaaaabaabbabbababaaabbbbbbaaaaabbbbbbaababbbaababbaaaabbabaaabbbbbbababbaabaaabbababbbbbaababababaaababbababbabbaababaababaaabbbbbababbabbaabaaabbabaabbabaababaaababbaaabababbabbbbaaaabababbaabbbbaabbabaabbabbaaabbbbabbbbbaaaaabbaabbbabaaaaaaaaaaaaaababbbbaaaababbbbaabbaaaaaabbbbaaababaaabbbbaabbababbbabbbbabaaabbbaabbababababaabababaaabbabaabaaaaabbababbabaabbbabaaaabaabaaaabbbbbbababaabaabbbbaabbbaaaabbabaaabbbbabaaabbaabaabaabbabaaaaaaabbaaababbbbaabababbabbaabbababbbbaabbaabbbbbbabaabaaaaabbababbbbabbbbabaaabbbabbaaaaaaaaaabaabbbabaababbabaabbabbaaabbbabaaabaabbbababbabbabbbbbbbabbaabbababaabbabbbaabababbbaabaabbbbbbaaaabbababaabbbabbababaabbbbaababbbabaaaaabaabbbbbbbbaaabababbbbbababaaabbaaaabbaaabaabaaabbbbaaabbbabaaaabbbbbaabbbbbabbbaaaabaabaaababababbabbbaabaaaabbaabbbbabbbabaaaababbbbaaabbbaaaabbbaabbabbaabbbaaaaabaabbababaabaabbbbaaabaabbaababbaabbabaaabbabaabaaababbabbbbbabbbbaabaababaabbabbbbbaaababababbbbbabbbaabbbbbabbbbbbbaabbbbbbbabbbbabbbbbabbabbabaababbabaaaababaaaaaababbabbbaabbbbabbbaaabbaaaabababbbabbbabaaabbbbbaababbababaaaaaababbabbbbbabababbbabbabaabbbaabababbbbbbbabbaaaaaaaaabaabababbabaabbabaabababbbabaabbababbabbbbbbbbabbaaabbaaaabbbaaaaababbabaabbabbabaaaaaaabbaaababaaabbabbaabaabbbbabbababbaababbbaabbbbbabbaaabbbaaaaaaaabbabaabbabbaaaaaababbaabaababbbbbbabbabbabbbbbbbabbabbaaaabaaaababbbbbaaabaaaababbabaabaaabbabaaaaababbbbbbaaaaaaababbaaaaabbabababbaababaaabaabbaabaaabaaabbbabaaaaaabbbbbbbbbaabbbbbabbaabbaaabaaaabaababbabbaabbabaaaababbabababaaabbbbababaaaabababaaaabbabaabaaabbbbababaaaaaaaaabaababaaaaabaaabbbbaabaabaababbbaaaaababababaabaaaabbbbbabbbababbbaaabaaaaabababbaaaaaaaabbabbbaaaaaabbbbbbbaaaaaaaabbabbbaaaababbaababaaabbababbabbabababaaaaabbabbabbbaabbbabbbbbababaabbaababaaaabbbababaababbbaaaaaaaaabababbaaabbbabbaaabbbbbbbabbbbbabbabbbabbabababaaabbbaaaaababaabaabbbaaabababbbaababaaaaaabbbbaaababbbaaaaaaababbbbbabbbbbabbbbbbaababaabababaabaabbbaaabbababaaabaababaababbbabaabbaaabbaaaaaababbabaabaabaababbbaaabbabaaabaaaabbaaaabbaaaaaabaabababbbbaabababbbabababaaabaaaaababaaabbbaabbbbbaaaaababbbaaaababaababbbababbababaaaaabbbaabaabbbaabbaabbbbbaababaabaaaaabababaabaababbbabbabbbbaaaabaabbbabbabaabababbaaaaaabbbababaaabaaabbbaabaaabbbbbbbbabbbbaababaaababbbbbaaaaaaaabbaaaaabbbaaaaabaababbaaabaaababbabaaabaaababababaabbabbaaaaabbbbaaabaabababaabbbabbaabbbbbabaaabbaabaabbaabaaaababababaaaabaababaabbaabbaabbaaaabbaabaaabbbaababaaabaaaaabbbbaaaabbbaababababbaababbbabaababbbbbabaaaaabbababbbbaaaaaabaabbababaaaabaaaaabbabbbbabbabbaabbaaaabbaabbaabbaaabbaabbbababbabbaabababbaabbbbaaaabaabaabbbabaaabaabaaaaaaabbabbaabbabbaabbabbbbbbbbbbbabbaaabbaabbabbaabbaabbbababbaaabbbabaaaabbabaaabbbaaababbbbaabbabaabbbababaaaabbbbaabbbaabbaababbabaababbbbabababaabaababbbaabbabbaaababbbaaaababababbabbbaababbbabbbaaabbbababbbaaabbabbbaabbbbbbbbbabaabbbaabaaaabbbabbaababbababbbbbaabbbabbbbabbbabbaabbabbbabbaaabaaabbabbbbaabbbbaaabbaabbbbabbbbbaabbabaaabaaaabaaababaaaabbbaaabaaabababbabbbbbaaaababaaaaababbabaaaabbbbbabaaabaaaabbabaabbaabaabbaaabbbbaabbbabbbbabaaabbabaabaaabaabaabbababababbaabbabbbbbabaabbbbbbabaaaababaababaabaabbbaabbabbaaabbbaaababbaabaabbbababbbbaababbaaaaabbbbaaabaababaababbbbabaabaababbbbbaaaabbbabbaababaaabaabbabbbabaabbaabaaababbaabbababaaaabbbababbaababbabaaabaabbabbaaabaabbaabbbbbbabaaabbbabaababaaababbabbbabbaaaaabbaaaabaababbbabbbbbaaabaabaaababbabbbbbaabbabbbbaababbbbabaabababbaabaaabaaaaaaabaaaaaabbbaababaaabbbbabbaabbaababbbaaaababaaaaaaababbbbabbbababababaabbbabbbbabbbaaabaaaaabbbaaabbaaabaaabaaabbaaabbaaaababbbabbabaaaaaaaaabbbbabababaababaaabbabbaaabababaabbaaaaaabaaabbbabaabbabaaaaaaabbbaabbbaabbabbabbbaaabbaaabbbbaaabbabbaabbababbaaaabbabbabaababbbbbaaabbbbabbababaaabaabbbabbaababaaaaababbabbbabbbbbabbbababbaabbbbaababbaaaaaaabbababbabababbabbaababaaabaababaabbabbababaabbbbaaaaaabbbaabbabaaaaaaabbbaabbbabbbaabbaaababaabaaaabbbbbababaabbabaabbabbabbbabbbbabababbababbbaabbaabbabbaabababaaaabbababbabbbaababbbabbbaabaaabbaabbbaabbabbaaaaababaaaaaaaaabbbaaabaabaabbaaaaabaababababababbbbababbaababababbbaaaabbabbaababbbbabbbbbbbbbbbbabbabaaaabbaabaababaabababbbaabbbababaaaaabaabbbabbaabaaaaaabbbbbabababbbbababbabaababbbbbaaabbaababbbaaaabababaabbbabbbaababbbbaabaaaaabaaabaaaabaaabbbababbaaabbbabaaaabaaaaaabababbbaaaaaaaaababbaaabbbabbaabbbaabaaabbbbabbabbbbaaaaabaabbbbaaabaaaabbbbbbbaabbabaaabbbabaaaaaabaaabbbaaabbbbbbbbbaabababbbbaabaabababaababbbbbabbababaaaababaaabbabbabbaabbaabababbbaabbbaaabbbbaabababaaabaaabbabbbbbabaababbaabbbbaaaabaabbbabbaaabaaabbbbbaaaaabaaabaabaabaabaaaaaabaaabbabaaababbababbbbabbbabbbaaaabbbbaabbbbbababaabbabaabbbaaaaaabbaaababbbbbbbbababbaaabbaabbabbbaaabbbbbaaaaaaaaabbbbbabaaabbaabbbabababbbabbabbbabaabaaabbaabaabbabbbbbbbbbbaaabaaaabbbbbaaaabbaabbaaababbbbabbabaababbabbabbaaaaabababbaaabbbabbaababababbabababbbbabaabbbaabababbbbaaabaabbbbaababbaaabbaabbabaabbabaaaaababbaaabaaabbbbaabababaaabbababaabbbaaabaabbbbbabaaaaaaabbabbabaaabaaaaabbbbaabbbbabaabaaababaaabbaabbbbababbbaaabaababaabbbbaabaabbabbbbaaaaabaababbaabbbbaabbbbaabaabbabbbbabaaaaabababbaaaaabbbbaabaaaababbbaaabababbbbaabbabaababbbbabbaaabbabaabaabbaabaabaaabbbabbbbaaaabbabaaabbaaabbaabbaabbbbaaaaabababbbbbaabbbbbaabbabaababbaaabbababaabbaabaaabbbbbbaabbabbbaabbbabbbabaaababaaababbaabbaaaaaaabbbbbbaabbaaaaaabbabaaaaabbbaababaaaaababbbaababbabbbbabbaaabbabaaababbaabbabaaaaabababbaabaababaaaaaaabbbbabbbbbababbbbbaaaabbbbaaabbaaaaaaabaaababaaaaaaabbbabaabaababbaaabbbaaabbbbbabbaaabbbbbbbbbabbaabbabaaaaaabbaabbbbababaaabbbbabbababbbaabababaaaaababababbabababababbbbbabbabaaaaaaaaaaaaaabbabaabbbabaabbaaabaabbababbabbbaabababbabbbababaaabbbbababaabaabababbbabbaabababaaaaaaaabaaababbbbaaabbbbbaaabbbabbbabbaaaaaaabbbaaabbababbaabbbabaababbbbaababbbbabaaaababbbaabbbbabaaabbabaabbbbbaababbababbabbaaaabababaaabaabaaaaabbaabababbabaababbbbabbabaabbaabbbbbbbbbbbaabaabbaabbbaabbbabaaabbbaaaabbbbbaaaaabbbbbabbbaabaaaabbbbaabbbbabaaabbabababaaaabbbababaaabaaaabbbaaabbbabbbbbbaabbabaaabbabbaaabbbbbbabaabbaaabbbaabbbbabbaabaaaaaabbaaabbabbaabbbbbbbbbaabbbaaababbbbabbbaaabbbabbbbbaaabaabbaaabaababbbabbabaaaaaaaabbaabbabaaabbbbaaabbbaabbbabaaaabbabaababbabaababbabbbbabbababaaaaaabbbaaababaaaaabababbbabbbbbabbbbbbbbbbaaabbbabaaaabaabaaaabaabaabaaabbabbbbbbabaaaababbababaaababbbaabaaaaaabaabbbababbabbbbbbbabaabbabaabbbaababbaaaabbbbaabbaababbababababbbaabaaaababbaabababbbabababaaaaababbbbbabaaaabaaabbaaaaabbbbbababbbaaabbbaaaabaaaaaaaababbbaababbbbaaabbbaaaababbabaaaababbaabbaabbbababbbababbaaaabbabbaabbabbaaaabaabbbbaaabaabbbaabaabaabaabbbbbaabaaaaaaaaabaabbaaababbabbbbaabababbbbaaabaabbabaabbbabaababaaaabbbaaaaaaabaaababbabaabaabbaabbbabbaaaaaaabbbabaabbbbbaaaabbabbbaabbbabaaabbabbbbbaaabababbbbbbaaabbabaaabaabababaabaabbaaabababaaabaabbababbababaaabaabaabbaaaaaabaabaaaaaaaaaaaabaaaababbabbbbbaabbbbabbabaabaabbbaaababbabbbabbaaabbbaaabbabaaaabbabaaabaaabaabbaabbbbbbabbaabbbbabbbbbabbbabababaaaabaaaabbabaababbabaaaabbbbbbbababaaabbbaaabaaabaabaabbbbbbbbbbaaabbbbababaaaaabaaabbabaababaabbbababbbaabbbabbaaabaaaaabbabbaababaabbbababaaabaaaaaabbaaaabbbbabababbaaababbbbbabbbababbaabbbaaaabbbbbbaaaabaabaabaabbbaaaabaabbabbbbbbabaabaabaaaabbbbabbaabbbaabbbbbabbaaabababaabbbabbbbbbbabbbaaababababaaaaabaabbbbbbbaaaabaabaaaabababbbbaabbaabaaaabbbbabaabbbaaabbbbaaabbaabababbabaaabbabbabaabababbababababaaaabbbbbbbabbaaababaabbbabbbaabbbaaabababaabbababaabbbaabbababbabbbbbbbbaabbbaaabbbabaaaaabaabbbbbbbbaabbbaababbabbabbabbabbabbaaabaaaaabbaaabbabbabbabaaaabbbababbabbaaaabbbaababbbbbaaababbbabbbabbaababbaabbaaaaaaaaabbaaabaabbaabbbabbaaaababbbaaabbabbabbbbaabbabbabbabbaaaaaabbaaaabbbaababaaabbbabaabababababbaaabababbabbbaabaabbbbbabaaaabbbbbbabbaabaabaaabaaaabbbaaaabbbabaababbabbbbaabaabaaaabababbaaababaaaaaabbaabbaaababbbbbabaaaababbaaaaaaababaaaabbbabbabbabbaaababbbaaabaabbbbbbabaaaaabbbaababbbabbbbbbbbaabbabbabbaabaabbbbaaaaabbbaaaabbbabaabbbabbabaaaaabbaaabaabbbbbbbabbaaababbbbbabbababaaabbbbbbabbbabaaaaabaaabbabbabbbabaaaaaabbaaaabbbababbbbbbbabbababaaabaabbbaaabaabbbaabbaabbaaabbbababbabbbbabbaababaababaababaaabaabbabbbbbabbbaaabbbabaaaabbabbabaaabaaaababbabaaabaabbbbbbbbbabaaaaaabababaaabbbabbaabbabaaababbbbbaaababbbaabaaababaaaabbbabbaabbabbabbbaababaababbbbabaaababaaaaaabababbbbabaaabababbaabaaabaabaaabbbbaaabbbbaabababbaabbabaabbaaabbababbaaaabbabbbaababbaaabbaabbababaabbbbabababbbabbbbbabaaaaaabbbabbaaaaabbabbaabaabaaaababbbbbabbaababbbbbaababbabbaaabbbbaaabbabbbababbbbaaaaabbaabbaaababaaaaaabbbabababbbbbabbbbaaababaabbababbbbabaabbbbaabaabbaabbbbaabbbababbaabbbbaaabbbabbaababaabbabaaabaabaabababaaabbaabbabbaaabbaaaabababaabaaaababbaaaabababaabaaaaabababbbaabbababbbbaaababbbabaababaaaaabbabbaaaaabbbbaabbbabbbbababababaababbbbbaabbbbabaaaaabababbabbbaaaabbbabaabaabbbbaabbbaaaababbabaaabbaaaaabbbaabababaababbaaaababaaabbbabbbabaaabbabbbbbabbbbbbaaabbabbbbaabbbbababaabbaabbaaaaabaabbabaaabbabbbbaaaaabbbaaabaabbbaaabbaababbbabababaaaaababbbbaaaaaaabababbaabbababbbaaabbabbababaabaaaaabaaabbbbaabbbbaaaababbbabbbaaabaaabbaababbabbbbbabbabbaaaabababababbaaabbbabbaabbaabababbbbbaaaabababababbababaabbababaabaababbbbabbbaaababababaabbaaaabbaababbabbabbabaabbaabbaaabaababbabbabaabaabaabbbbbaabbabbaabababbabbbbbbbabbabbbabaabaabbbaabaabaabbbabaaaaabaabbbabbbbaabaaaaabaaabbbbaababbbababaabaababbabaaaaabaaaabaaabaaabbbbbaabababbbabbbbbababbbbabaaaabbbabaababaababaaabaabbaababaaababbbaaaaaaaabbbbaabaabbbbbbabbbbaaabaabbbbbabbbbbaabbbaaabbaaaabbabbaaabbbbabbbbaababababaaaaabbaaaaabababbbbaabbbbbabbbabbabbababaaaaabbaabaabaaabaababbbbbbabaaaaaabaaaaaaabaabbabbbbbabbbbaababbbbaababbbababaaaaaaaaabaaaaaababaaaabbababaaabbbbbbbbbbbabaabbbbabbbabbabbbbabbbabbabaabbabbbbaaabbabaababaabbbbbabbaabbabbabaabaabaabaabbbaaaabaaaaababababbbbbaabaabaabbbaababbaabaabaaabbbbabbbbaaaaabbabbabbaabbabbbbaaabbaaabaaaabbbaaaaabaabaabbaabaabbbbbbbbbaaabbbaabbaaababaaabbabbabbbabaababbabaaabbababbbbaaabaababbaabaabbbabbaaabbaabbbbbaaaaabbbbbbabbbbbaabababaabbabababbbbbabbaaaaabbaabaaabbbaaabaaaababbbbaaabbaaaaabbbbbbbbabaaababbbaababbaaaabbababbaabbabaabbababaababaaabaabbbbbabbbbaababbaaabaaaaababaaabaaabaabaaaaaabaaabaaaaababbbaaaabbabbaabaabbbabaaaabbbbabbaaabbbaabbbbababbbbabbaabbaaaabaaaababaabbbbababaaaabaabbaaababaaababaaabababababaabababaababaaaaaabaabaababbabaaababbbbaaaaabbbbaaabbbaabaaaabbbaabbabaabbbabaaaaabaaababaaaabbaaaabbabbbabbbabbbbbabbbaaabbbaabbaaabaaaabbbabbbaaabbaababbbbaabbbaabbbbaabaaaaabbbbbbbabbbbaaabababbaaaaabaaaaaabbabbabbabbaaaabababbbaabababababaabbababbbabababbbbbbbbaababbabaabbaaabbaaaaaababaaabaaababbabaaababbbabaaaaaaaaabbbaaabbbbbbbabaaabbabbabbabbbbabbabbbbbbbbabaaabaababbaabbbbaacbbbabbabbbababaababaabaaaaabbaabbaabbbbaabaabbbabaabbbbaabbbaaaabbbababbbabbaabababbaabaaaaaaabbbbbaaabbbaaabbbbaaaaaaaabbbbbbabbababbaaabbabbaababababbbbbaaaaaabaaaabaaabbaaaabbabaaaaabbabaaabaaabaabbaaabbaababbaabbbaaababbbaaaabbaaabbbaaaabbaaabaababbbaabaaabbaabbaaaabaabaabaaaabaababaabababbbaaaaaababbbabaaaabbabbbabaabaabbbbbabababbaaababaabbbaaabbbbbaabbabaaabaabbbbbabbbaaabbaabbaaababaaaabababbbbaaaabaabaaaaaaabbbaabbabbbaaaaabaabbaabaabbbabaabbbabbaaababbbaaabaaabaaabaabbaaabbbababbbabaabaabaaabbaabbbbbaaabbbbaaabbaabbbbbaabaabababbbabbbaaababbbbbbbbbbbaaaaabbaaaaaaabbbaaaaaababbaaababbbaaaabababababaabaaaaaaabbbababbaaaaaaaababbaaabaaabbbabaabaabbabaaabbaaaabababbaabbaabaaaaabaababbbaaaabaaababbaabbaaaaababaaaaabbbabbabbabaabaaabaabbbabaaaabaaabbbbabaabbbabbaababbbabbabbabababbbabbbaabababbababaabbaaabbbbbbabaababbbbabaaabaabaabbbaaabbababaaababbabbbaaaaabbbaabbabbabaaaabbaaaaaabbbaaababaaaaaaaabaaaaababaaaaabbaababbbbbaabbbaaababbbbabbabaaaaabaaabbabababbbbabaabbbaabaabbaaaabbbbbbbaaababaaaaabbabbbabaabbaabbaaaaabbbabbabbbbbaaaabbabbaaababbbbabaaabaaaaabaaabbbbaabaaaababbbbabbaabbbabaabaaaaaaaabaaaaabababbbbaabbaaababaabaaabababbabaabbaababbbbbbaabaaababaaabbbbaababbbabbaabbbaabaaaabbbbbbaabaaabbbbabaaaaabbaaabbbabbabbbbababbabbaabaaaababbaababababbbbbbaabaaabbbbabaaaababbbbababababaabbabbababbbaabbbbaabbababaaaabaabaabaaaababbabbbbbbabbbbabbababbaaabbaaabaabbbabbbabbbabababbabbaaaabbbbaabbbbaaababbbbaaabbaaaabbaaaaabbbbabbaaabbbbbabaaabbabbabaabbabbbabaabbaaaababbbabaaabbabbbbbabaaabbbbababababbabaaabbababaaabaabbaabbabaaabbbbaabbbbbaaaaababbbbabaabbabbbbabaababaaabaabaabbbbabbabaabbbbbaabbbabbaabaabbbababbbaaabaaabbabaabbaaaababbabababbabbaabbbbabbbabbbbbbbbbabaabaabbabbbbbabbbaabaabaaabbababbbabaaababbaababbbbaabababbababbbbbaabbaaabbbaababababbabaabbabbabbababbabababbbabaabbababbbaaababbbaabaaababbabbbabaaabbaabbaabbbbabbaabbbaaaaaaaaabaaaabbbbaabbabaaaabbabbababbbaaababbaabbaabbaabbbaaabaaaaaaaaaabaababaaabbaaaabbabaabaabaabaabaabbbabbabaaaaaabbbbbababaaaaaaabababaaaabaabbbabbaabbabbbbbbaabaaabbaaabaaabbbbbbaaabaabaaaaabbabaabaaabbbabababbbaaaababbaabaabbaabbbaaabbaaaabbbbbabaabaaaaabbabaaababbbbaabbaaaaaabbbbbaaabbaabbabababaabbbbabbabbbbbbbbabaaabbbaaabbaaaabbbabbbbaaabababbabaabbbaabaabbaabaabbabbbbaaabbbabaabbbabaaabbbbbababaababbbaaabaaabbaaaaabbaababbaabbbabaaabababbbabbaaaaababababbbbbbababababbbaaaaabbabbabbbabaabbbbbbabbbbbbbabaaabbabaaabaabbabbaabbaabaabaabbaabbbbbbbababaabbbbbaaaaabaaaaaaaabaabbababbbbbbabababbababbbaabbaababaaabbaaaabaaabaaabaabbabaaabaababbbaabbaabaaabbabaabaabababaabbababaaababbabaaaaaabbaabbabaabaaabbaabaaabbaaabbbabababbabababbaabababbbabaaababbbababbaabbbbaaabaabaaaaaaaaaaaabbaababbabaaababbabaabababbbbababbbbbabbaaababbabbbbabbaaabbbbabbabaabbabbbbabbbbabbbabaabbaabbaabaaaabbabbaaabababbbbbaabbaaaaabbabbbbaabbbbabbbbbaabbabbabaaabbbaabbababaaabbbbbaaaaabbbaababbababababaabbbbababbbbaabbabababbaaabbbbbbabbaaaaaababbabbbbaabbabaaabbabbbbbababbaaabbbaaababbbaabbabbabbbbbaabaaaaaabbabababaaabbbaababbbbabbbaaababbbbaabbbababbaabbabbaaaaababbaaaabbbbbbabbaaaababbabbababbabbaabaaaabbaabbbbbbbabbaaabbbbbbabaaabbabbabbbaabababaabaabababbbbbbaabbbbbabbaaabababbaabaabbabaababbbabbbaabbabbbbbbbababbbbaaaaabbabbbabaabbabaabaaaaabaaaaaababbabbbaaabaabbbbabbaaaabbabbababaaabaababbababbbabaababbbaaaaabbbbbaabbbbbbbaaaaabbabbbaabbaabbbbbaaabbbaaaabbbabaabbbbbbabbbbbbabaabbabbbbbabbbbaabbaabbbbabaaabbbbbbbabaabbbabaabaaabbbbabaaaabbbaaabbaababbaaababaaabaaabbbbbbaaaabbaabbabbbbbabbaabbbbbababababaabbbbbabbababbabbaabbbaabbbbabbbabbbbbbaaabbaaababaabbababbaaabbbbaaaaaabaabbababaaaabbbaabbaaabbbaaabbaabbbbbbabbabaaabbbbbaaaabbaabaabbbbbababbbaabbaaaabaabaaabbaaaabaaababbbaabbaabaaaabaabbbbababaababbbababaabbaabbbabbaaaababaaabbaabbbbbaaabbbabbbbaabbbabbbbbaabbababbbbabaaabababbbabbaabababbbaabbababaabaabaaabbbabbaaaabaaaaaabaabbababababaabbbbbbbaabbbaabababbaaabbabbbaaabbaaaaabbaaabbaabababaaaaaaabaaabaababaaabaaaaabbbabbbabaabbbbbabaabbababaaaaabbbaaaaaaabbabbabbbabbbbbabaabbbbaabaaabaaabbbbbababbaabbaabaaaabaabaababbbaaababaaababbbaaaaabaaaabbaaaaaaaaaabaabbbaaabbbbbbaabbaaaabaababbbbababbabbbbbbbabbbaaabaabaaabbaabababaabababbaaaaabababababbababbbabbaababbbaabbbbaabaaaabaaabbbbbaababaababbaaabbbbbabbaabbaabbbbbabbbabbbbabaabbbbbabbaaabbbbbbaaababbabaabaaabaaaabbbaaaabaabababbabaaabbbbabbbaaabbbabbaabaabbbbbaabaaabaabbbbbbabbbaababbbbbabbbaaaabbbbbabaababbbaaaaabbabbababbabbabbbbbbbaabbbababaabbaabbbaaaabaaaababbbbbbaabaaaabbaaabbababbaaabbaaaabbbbabbaabbababaabaaababbaabbaaaabaaabbabbaaaabbaababbaabbabbbbbbbaaaabbaaabbabbaaababaabbbaaababaabbbaaabababbaabaabbababaaaabaaabbaabbbbabbaabbaaabbbabbaaaaaabbbaabaaababaabbabbaaaabbabaabbbbbbbbababbbaaabaabaabababaabaabbabaababaaabaaaaaaaaabbbaaaabababbbaabaaabbbababbbaaaaababaaabbbbbaaababbabbabbababaaabbbbaabbabbbaabaabaaaaabaabaaaaaabbaabaabaaaabbbababbbbaabaabaababbaababbbbabbbabbbaababbbbabbbbbaabababbbaaaaaaaabaaaaabbabbbabaaabaabbbababbaabbbbbabbbbaaaabbabbbbaabababbbaabaaaaabababababaaabaaabbabaaaaabbaabaababaabababbababbabaabbabaababaaaababaabbbabbbbaabababbbabbbabbaaaabaababbaaaabbbaababababbabaaabaabbbbbabaaaaaababaabbbaaabbbaaaaaababaaabaaaababbababaaaaabaaabbbaababbbbababbabbbbaabaababaabbbbbbbabababaabbabaaababaababbbabbbababaabbbaaaabaabaaabbaaabaaaaabaaaaabbbabbbabbaabbaaabaabbaabbabaabaaaabbabaaabbaabbaabbabbbbbabaababbabbbbaabbbaaabaababaabbaaaabbababbabbaabbbaabababaaabaabaaabaaababbabbbabaabbabbbbbbaabaabbbbabababbabaaaabbbabbaaaabbbaabaaabababbabababbabbbaaaaaababbaaabbabbaaaaabaabbbabbaababbbbbbabbbaaabbabbbabaabbaabbbbbbbbbaabaabbabababbabbbaabbaabbbbbbbbbbbbbbbbaaabbabbaaabbaabbababaaabbabaaaabbbbababaabababababaabbbaaaabaaaabbabbabaabbabaaaaaaaabbbababbbbaaaaabbbaabaaaaabbabbbbabaaaabbabaabaaaabbabbabaababaabbabbaaabbabaaabbabbaaababbbbaabbbabbbbabaaaaaaababbbabbbbaababaabbabbabaabbabbbbababaaabbaabaaaababbaaaabaabbbbababaaaabbaaabbbababaabaababaaaabbababbaaababbbbaabaaabbabaabaaabbbbaaaaaabbabbabbbbaaabbaaabbbbabaaabbababbbaabbabbbbbaababbbbabaababaaaabaaabaababbaababbaabbaababbaaabaababbababaabbabbabbbbbbababbbbaaaababbbbbbabaaababbbababaaaababaaababbbbabbabbaabbbbbbbbbbbbaabababbababbbbaababbaaabaabbabaababbabaaabababaabbababaaabbabbbbabbabbaabababbabaabababaabbbaababbaabbaabbbaaaaaaabaabbabaaabbabaabbabaaababababbaabbaaaabbabbabbabbabbbabbbaaaaaaaaabababbbaaabbbababbbaaabbbbbaaaabaabbbbbaabbabaaabbabbababbbabbabbbbbaaabaabaabaabaababbbababbaabaabaabbabbbbbbbbbbabbbaabbabaaabbbbabbabbbbabaabaaaabbaababbabbbabbaaaababbabbaaabaaaaaaaaaabaababbabaaabaaabbbbbabbbbbaaaabaababbbaabaabbaabbbabbbaaaaaaaaabbbbbabaaaabbababbaababaaabaabbbbabaabbaaaabaaaaaaababbaababaababbbabbbabbbbabbbbbaabbbabbbaababaabbbbababaabaaabababbbbabbaaababaaabaaaaaabbbaabbabaaabaaabbbabbabaaabaababbaababaabbabbbbbaaaabababaabaabbbaabbabbabbbbaababbaaaabbbbbbbaaaaabbbbbabababbbbbaabbabaabbbababaabbaaaaaaabbbabaabbaaaabaabaabbaaaabbbaabaaaaabbbababaabbabbaababaabababaaaaabbbaaaaababaaaaabbabaaababbaaabaaaabbbbaabaaababbaaaababbbabaabbaaaabaabbabbababbbbabaabbaaabbabaabbabbaabbabbbaabaabbabbabaaabbabaaaaaababbabbaaabbabbbaaaababbbbaabbbbbabbaabbbabbabbbbabbaabbabaabbbbbaaabbbabbbbbaaaaaababbaababababbaabbaaaaabaababbaababbabbaabaabbaabbaababbaaaaabbbabbaaaaabaabbabbaaaaaaabababbbababbabababbbabbabbbbabbbbaaaaabbbababbbbabaabbabbabbabaaabbbbaabbbbabbabbaaabaaabbabababaaabbabaaabbaabababbbbabaabbabaaabbabaaaababbbbabbabaaaaaabbaabaabbbabaabaabbabaaaabbabbbbaaababaababbbababaabaaaaaaabbbbaabbabbbabbaaabaaabbbbabbbaabaaabbaaababbbaaaaabaaabaaaaaabbbbabbabbbbabababbbbaaaaabbbbaabbabaababaaaababbaabbaabbbbabbabaabbaabbaaabaabaabbaabbbabaabbababbaabbbbbaabbbbaaaababbabbbababbbbbabbababbabbaabaaababbabbbbbaabbbbaababaaabaabababbbababaabaaabaabbaabbbbabababababaaababbbabbaabaaabbaaababaabbaabaaababaaaaaaaaaabbabababaababbbbaaaabbaabbbabbabbbabbbaaaaaabbbbaabaabaabbbbabaaaabaabaaaaaaabbbbabbbbababaabbbaaabbbbababbbbaabaaaaaabbaaaabbbabbbaaaaaaabbaaabbaaaaaabbbabababbabbbbbaaabaaabaabbbbbbabbababaaabbbabaaabaaabaabbbabaaaaabbababbbbbbbbaaabaaabbbbbaababaaababbbababbaabaabbaabbbabaaababbabbbaaabbbaababbbaaaabaaabaabaaaaaabaaabbbbaabbbaaaabaaabbbbaaaaabbabbbabaaabbbaabbabaaaabbbbbabbbbbbbbaababbbbaaaaabbbaaaabaabbbbabaaabbaabbbabbaabbbbaaabbbbbaaaaabaaababbbbbabababaaaababaabbabaabbbababbababbbbbabaaabaabaababbbabbaaabbaaabbababaabaaaabbabbabbaababaaaababbbaaaaaaaaabaabaabaabbabaaaabbbaabaaaaaaaaaaabbbbaaaabbabaaabbbbababbabbaaaabbabbbbbbbabaabbabbbbabbbaaabbbaaaaabaabaaabbabaaabbbaabaaabbbabbabbbababbbbbabbbbaabbbbaaaaaabbbaaaabaaaaaaabbbbaabababbbbbaabbaaabaabbbaabaababbabbbbbaaaaababaababababbaaaabbbabbbbbababababbababbbbabbbbbababbbaabbabbbaabbababababbbbabbbabaaaababbbbbbbbbabbabaaabbaaababbaabaabbabaaabaabbbbaaaaaabbaababaabababbbaaabbabbbaaababaabababbaaaaabaaabbbabbaabababbaaabaabbbbaaaaabbabaababbaaaabaabaaaabaabbababbbabaaabbbaaababbbbbbbbbbabaababbababbababbaabbabbabaaabaababbaaabbbbbaababbbabbaaabababbbaaaaaaaaaaaaaaabaabbbbaaababbabbbaaaabbbbaaabbbaaabaabbaabbbabaaaababbbabbbbbbabbbaaababababbabbbaaabbbabbabbabbaabababbbbbabbaaabaaaaaabbbabaababaabbbaabbbabbbbaabbbabbaabbbbaabaaaabaabaababbaaabbbbaaababbaabbbabbbababbbbabbbaabbbaaababbbaaaaabbabaabbbbabaabaaaabaaabbbbbbabaabababababaaabbbbbaabababbaababaabbbaaabaaabbabbabbbbbbabaabaaaabbabbbaaaaaabababbbaaabaaaabbaaaaabbaaababaaabbabababbabbababbbaabbaaaabbababbabababbaabbbaaabbbbbaaabaaaaabbabaaabaaaabbaabaaabaaabbbaaaaaabaaababbbababbaabbaaababaaaabbbababbaaaababbabaabbaaaabababbbbaabbaabbbbabbbbaaababaaaabbbaabbaaabbbbaaabababbbbbbbabbbababaabbaabbbbaaabbbaabaaabbaaabaabaaaaaaabaaababaabbababbbbbabaaababbaabbbababaababaaabbaaaabbbbbbbaaaabbaaaaaabbbbabbaaabbabbbbbbbabaaabbaaabbbbbbaaababbbbbababbbaabaabababaababbbabbbbbabbabbbabbbaabbbbbbbababaabbbaabbaaabaabbaaababbaabaabbbbbbabbabbabababaabbbbbbababbabbabbabbaaaabbbbaaaababaabaaaabaaababbbaabbbbabaaabaabababbbbbaaabbababbaabbbbaaaabbbbbabbbbbaabbbabbabababbbaaababbabbaaaabbabaaaababababaababbabaabbabaababbaaabaaabaababbbaabaabbabbbabbabaababaabbaaaaabbaaaabbbbbaababbabababbabbaaabbbabbbabbababbbbbabbabaaababaaaaababbabbabbaaaabaaabbbbaaaaaaaaabbababbbaabbbbaabaababaaababaaabbbaaabbabaabaaaabbbabbaabbabbabaabbaabababaaabaababaaaaababbaaabbabbabbaaabbbbbbbbababbaaaaaaabbaaaabbbabbabababbbbbbbbbbbaaaabbaaaaabaaaaaabbbaabbaabbbabaabbaaaabaabbabaabaaabaaabbabbbbbabbabbbaabbaabaaabaaabbbbabbbaabaaaaabbabaababaaaaaabbabbabbaabbaabaabbbbbabbbbbabbbabbbaabaabababaababababbabbabaabbaaabbbbbbbbbbbbbbabbaaaababbbbbbaaaaababbabaaabababbbbaababbabbbbaaabbaabbbaabaababaabaaaaaaababbaaabbaabbbabaababbbabaaaaaabbabbaabababaaaaabbaabbbbaaabbbbaabababbabbabaababbababbbbaabbbabaaaaababababbabbabbbabaaabbaaaaaaabababaabaaaabaaababbbaaaabbabbbbbabaaabbbbbbbaaaaaabaaababbbabaabbbbbaabaabbabbaaaabbaababaabaabaabaabbaababaaaaabababaabababbaaaabbbbaabbaabaaababaababbbbbbbbababaaaabaaababaabaaaabbbaabaabbbabbaaabbababaabaaaaaaaaabaababbaababbbaabaabbaaaabbaababaaaabbababaababbaabababaababbbbbbabaaabbbbaaabbbabbbbbaababababbaabbababbbbbbbbabaaaabababbbaabbababbbbaabbaaaabbbaabbaaabaabaabbabababbaaaaabbbaabbbbaaabababbbbbaaaaaabbbbbbbabbbbbabbbabbbbbbabbaaabbabbaaabbbbabaaabaabaaabaaaabaabbbabbaabbbbbababbbbabababaaaaabbabbababbbbabaabbababbbababbbbbabababaabbbaaabbbaabbabbabbbbbabaabbbaabaaaabaabaaabaaabaaaabaaabbbbabbaaababbbbabaaaababababbbbbbbbbabbaaaaaaababaaabbbaaaabbabbbbbabbaaaaabbababbbaabbabbbbababbbaaaabbaaabababbbaaaabbababbbaababaabababaabaabbabababbbbbaabbbaabaabbbabaaaabababbaaabbbaaaabababaaabbbbbabbbbbaaababaaaabbabbbbaabbabbabaabaabbabaaabaaabaabbbabbaabaabbaaaabaabaabbaabbaabaabbbaabbaabaabaabaabaaababaaabbbabaaababbaabbaabbbbbbaabbabbbabaaabbbababaabbbbbbbaabbbaababbaaaaabbaabbaaabbbabababaabaaaabbbaaabbbbaababbbbbbbbababaaababaabaaaabaabaabbbaaabaaaabaaaaabababbaaabbbaabbaaaababaabaabbbbbbabaabbbbababbabababbaaaaababbbababaaaabbabbababaaaabaababababbabbabaaaaabbaabbababaabbabbbbbaaaaaaabaabbbbaaabaabbaabaababbbaaaabbaaaabbbbabbaaaaaabbababbaabbbaaaaabaaabbbbababababaaaaabbbaababbabbbababbbaaaaabbaaabbabababbaabaababbbabbbaaababbabaaaabbabbbabbbbbaaabbbabbaabbabbabbaabaabbaaaabbabbbbabaaaababbbaaababbbbabbbbababbbbaabbbbabbbbaabbababaabbbbbabababbaaabbabbbaaaababaabaaabababbbaaabaaabbabaabbaaaabbbaabbabbababbaababaabaaabbbaaabbbbaaaabaaabaaabbbbaabaaaaaababbbbbbbbbbbbbaaabbbbbaaaaababbbabaabbabbaabbbbbaaaababaabbabbbbbbaaabbbbababaaabbbbbaaaababaabbbaaaaabbbaaabbabaaabbbaaaaaaabaababbbabbaaaababbbabbbaaaabababbabbbbaaaabbbbbababababbabbbabbbaabaaababaabaaababbaaabaababbaabaaabbbabaaaaaaaababbaabbbababababbbaabaabbbbaaaaaaaaabaaaaababbbbaaabaaaaababbaaabbbbbbbbbabbbbaabaabaaaabaababaaaabaaabbababbbaabbbbabbbaababbbbbbbaaabbbbabbabbabbbbaabababbaabbaaaababbababaaabbaabbbbabbbbaabaabbaabbbaaabaabbbabbaabaababababbabbaabbbaabaaaabbabbabaabbabaaaaabaaaabbaabbababaaabbabaaaabaabbbbaabaaaaaaaaaaabbbbbbbaaabbabaaaababbbbaabbabbabaaabaaabaabbbbaaaaabaaaabaaaabbabababbbbbbbbaabbaabbbbbaabbbbbababbbbaababaabbaaabbaaabaabaabbabbabbbabbbbbbbbabaabbababaabbaaaabbabbbbababaabbbabababbbbbbaabbbaabbaaabaaaaabbaabbbaaabbbbbbbbbabbbbbbaaaabbbbbababaabbbbbbbbbbaaaabaabbabaaaaababbbbaaabbbaabaaaabaabababaababbbbbbaabaaabbbbababbbbababaababaaaabaaabaaababbababbbbababbaaaabbabbbaababbbbbaaaaababaabbabaaabaabaaaaababababaaaaabbabbbaabbbbaaaaaabbaaaabbbababababbbbabbababbababbababababbbabbbaaaabbbbabbabbaabbbbabbbbbbbabbabababaabbbaabbbabbbbabbbaaaaabaaabaaaabbbbbbaabaaabbaabaaababbaabbbabbbbaabaaaaaabbbbabaaabbabbaabababbbaabaaabababbbbbabaabaaabaabbaabbbabbbbabbbbababaabbaabaaaaaaaabbbbaaaaabaaababbbbaaabbbabbbabaaabababbbaaabaabbaabbababbabbaabbbaabaabbababbabbaabbbbbbbbaaaaabaaabaaabbabaaaaaaababbababaaaaabaabaaaaaabbabbabaabbaaaaabbabbabababaabaaabbababababbabbabaabbaabbbbbbbaabaabbaabbbaaabaabbabbbbbabaaababaababbaaabbbaababbbbbaabbaaabbaaaaaabaababaaababbbbababbbbaaababbbabbaababaaababbbaabbbababbaaabbbabaabaababbbbabbbbbbbaabbbaaabbbbbbaabbababbbbbababbabbbbaabbbabbaababaabbabbabbbaababaababababbababbababbbaaaabaaaababbaaababbbaaaaaabbaabababbabaabbbbbbbbbbbbaabbabbbbbabaaababaababbbbbbaaaaabbaabbbbbbbabbbbbabbabbabaababababababbbaabaaaabababbbabababababbabaabaaababbaababababbaabaaababaabbbabbaaabaaabbaababababbaabbabbabaaabaabbbabaaababbabbbbabbbaaaababbabbaaaaaaabaabaabaaaabaabaababbbanbaaabbabaaababbbabbaabaabbbbbbbaabbabbbaaabababbaaaabbbabaababbbabbaaabbababbbbabbbbaababaababbbabbaaaaaaaaaababbbabbabbaaaabababaaabbbbbbbbbbabaababaabbaababaabaaaaaaaaaabbabbbbababaabababbaabaabbbbbaabbaaabbaaaaaabaaaaabababaaabaabbaababaaababaabbaabababbbabaaaabbbababbaabaababaaabbbbaaababaababbbbbababbaabbaabbaaabaababaaabaabbbaaaababbbbbabbaaabbaabbaabbababbaaaabaababbbabaabaabaabbaaabbbaaabbbabbaabbaabaaababaaababbbbaaaaaaababaabbaabbbabbabaababbbaaaaaaaaabbbabaaabaaabaabbbabbaabbbaabbabaabababbbabaaababaaababbaabaabaabbbbbaabababaaaabbabaabaaabbbaabbaabaababaaabbbbbaaabbbabababaababaabbbaabbaaabbabbabaaaaaababbbbabaaaaabbbaabaaaaaaaabbbbabbabbabbaabaaaaaabaabbbbaaaaaabbabbbababaabbbabbaaaabbabbbaaaaaaaaaabbbabbbaaabbbabbabbababbabaaaaaaabbabaaaabbaabbbbbbbaabbbbbbbaabbbaaabbaaabbbabbbaababababbbababbabbaabbabbbbabaabbbbabbaababbbbaababbbbbbbabbbbbabbbbbaabaabaaaaababbaabbababbbbabaabaaabaaaaabbaabbbaabbabbaabaababaababbbabbbaabaabbaaabbbbbaabbbabaabaabbaabaabaabbbbababbaaaabbabaaaaaabaabbabbaaaabbbabbabbababbaabbaababbabbbbaababbbbbbbbabbabbbababaaaabbabbbabaaaabaaababbbbbbaaabaabaabbabbbaaaabaabbbbabbabbbabaabbbabbaaababbbaaaabbababbbbbbbbabbbbaabbaabaabaaabababaaaabbaaaabaabbaabbaaabbbabbababbbbbabaabbababaabaabbabbabaabbababbbbbabaaabbbabaaabbabbbbaaabbaaababbbbbaabaaabaabbbbbaaaabbbbaaabaaabaaababbbbaabbbbaabababbbbbbbaaabbbabaabbbbaababaaaabbabaaaabbaabbaaaababbabbbabaabaaabaababaabbaaabbaaaaabbbbbabbaabbabbabbabaababaabaabbbaaabbaabbbaaaaabbaaaaaabaaababbbaabbbbbbbababbbabbbabaababbbbabaaaaabbaaabbbaabbaaabbabbbabaabbabaababbbaabbaaabbbaaaaaabababaaababaabaaabbabbbaaaaaaaabaaaaaabaaaaaabbbbaabbbbaabbbaabbbabaaabaaaabaaaaaabbaaabbaaababbbbbaabaabbaababaaabbaaabbaaabbbbababbbababbaababbaaabaaabaabaaabababbaaababaaabaaaaabaabbbaaaabbbbbaabbabbaabaaaaaaabaaababababaaababbbbbaaabbaaabbabbbabaabaaabbaabbaabbbbaabbbaabbabbaabbbbaaabbbababababaabbaabbbababbabababaababbbbbabbabbbbaabbbbabbbbbabbaaaabbbbaabbabababbabaaaaababbbbbbaabababbabaabaabaaaaabababaaabaaabaaabbabbbaaaababbbbbbbbababbaababbbbaababbbbbaabbbaabbbabaabbbaaaabbbbbbababbaaabbbbaaaaaabaabbaaabaaaabbbbbaabababbbabbaabbaaabaabbbabbaaabbaaaabababbabaaaabaabbbbbbbaaabaaabbabaabbbabababababbaaaaaabbbaaabaabbaabbabbabbbbbbababaaaababaaaaaaaabbaabbabaabababbabbbaaaaababbabaaababaaaabbaabbaabaaababbbabbaabbaabbbaaaabaaaabbbbabbbbbaababbbbaabbbbabaaaabbaabaaabbaaabaabbababbabbabbbbabaaaaaabaabbaabbbaabbbabbbaabbbbaaabbaabbbaabababbbbabaaaaababbbbaababbbabaaaababbaabaabbbabababbaabbabbaaaaaabbbbbabbaaaaaaabbababbbbabbbbbbabbaaabbabbaabaabbabaabaaabbbababababbbbababbbbaaaabbbbabababbaaabaabbaaaababbbaababbbabbbabbbbbaabbabababbabaababaaaabbaabaabbaabbbabbaabbabbabaaaaaababaababaaabbbaabbbaaaaabbbabbbabaaabbbbaaaabbbbaaaababaaaabaaabababababbbabbbabaaaaaaabbabbbababbbaaaaaababaaabbbbabbabbbaaabababbbaabbaaaabbbabababbbbbbbaaabababbbababbbabbabaabaaababbbabbabaaaaaabaaaababbabbaabaabbbbabababaaabbabbbbaabbabbbababaaabaabaabaaaababaabaabaaaabababbabaabababbaababababbaaabbababbaaaabbbbbbbabaabbbbbaaaabaabbbaabaaaaabaabbabaabbbbbbbbabaabaabbbaaaaababbabaabbbbaaaabbbabaabbbbabbabbbabbbaabbaabbaabaaaabbbabbaabaabbababbaaaabaabbbbbbbaabbbaaaabbabbababbbbaabbbbbbaaabaabaaabbbaaaaaaabbaaabbbaabbbbbaabaabbbbabbbbbabbbbaabaabaaabaababaaaabaabaaabbbababbbabbbbabaabaabaabbbbbabaaaabbaababbbaaabaababbaaaabbabaaaaabaabaaabbbabaabbaaabbababbaabbabbabaaabaabbbababaabbbbbbaaaaaabbabaabaabaabbabaabaabaabababbabbabbbabbbaaabbabbaabbbbbbaaabbbbbbbbbbaababaabaaaaabaababbaaabaaaabbbbbaabaaabbbabbaaaaaaaabbaaaababbbabababbbaabaabaabaabbbaabbbaababaaaaaaabbbabbabaaabaaaaaaaabbbbabababbabaaabbbbabbbbbbabbbbbaaabbbbbabbbaabbaaaaabbabbbaaaaaabbbbbbbbbbabaaaaaaababbabbaabbbabbaaabaaababbbabbbbbbbabaaaababaaaabaaaabababbbbabaabaaabbbbaabaababaabababbabbabbaaababaaabbbababababbababbbbabbabaaababaaaaaabbabbaabaabbaaabbaabbababbbbabbbabbbaaabbbaaababababbbbbaabababbbbabaaababaaabaaababbabaababaaabababbabbbaaabbbabbbababaabaaabbbaabbaabbbbaabaabbbaabaabbabaabbbbababbbababbabbaabbbaabbabaabbbbabbbabbaabbabbbbbabaabbbbbabbaabbbbabbbbbbaaabbbaaaababaabaabababbabbbbabaabaabbaabaabaaabababbbbabaabbabaabbaaaaabaaaababbbbabbbabaabbaabbbbabbaabaaababbbbbaaaaabbbabbabbbabbbbaaaabbaabbababbabaaababbaaabaaaabbbbaababbbaabbabbbbbaababbaaabaabbabbabbbaabaabaabaaababababbaaaaababbbaabbbbabaaabbaabbabaababbbabbaabaaabababbabaabbbaabaabababbabaaaaabbaaaababbbbbaaabbbabababbaaabbbbbbbbbaabaaaaaaabbaaabbaabbbbabbbabaabbbbbabaababbbabbaabaabbbbaabaabaaababbaabaabbbaabaaaabbaaaabaabaabbaaabbaabbaabbbbbbaababababbababbbbbaabbabaabbbaabbaaabababaaabbaaabaaaababbabaaabababaabaaaaaabbabbababbabbbbbabbabaaaaabbbbaabaaaabbbbabababbbbbabbaaabaaaaabbbaabbbabbaabaaaabbaabbbaabbbbbbbbbbbbabbaababbbabbbbbbbbabaaaaaabaaabbbaabaabbbabbaabaaabbaaaaaaaaababaabbbaaaaabaaaaaaabbaaabababaabaabababbabbaaaabaababaabaababbbbbabbbabbbabbaabbaaaaabbaaabbabbabaaabbabbaaabbbaaabbabaaaabbabbaabbbaabbaabaaaaaaabbbaabbbabbbbaababbabaabbbaaaababbababbaaaaabbbaababbaaabbaabbaababbbbbaaaabaaababbabbbbbbababbbbaaaabbaaabaaaababbababbabbbaabbabbaaaaaaabbabaabbbbabbbbaaaabaababbaabaaaaabbaaaaaaaabbaabababaaaabaaaaaaabaabbbbbabbbaaabaabbabaabaabbababaabbbaaabbbabbbbbaabaaaaaabbbaabbabbbbbbbaaaabababbabaabbabbabbabbbbbbabbaababbbaaabbabaabbbaabababababbbbabbaaababbabbbauaaaaaaabaaaabaaaaaababbbbababbbabbbbaaabbaabaabbbaaabbabaaabbbabbbbbabbaaabbabaaabaaaaabababbbaababaabaabaaaabaabaabaabaaaabbbbbbaabaabbbbaabbbabaaaaababbbbabbabbabbaabbbbbaaaaabbababaaababaaabaabaaabaabaaabbaaababbabbabbbababbabbaaabaabaabbbbbbabbababbbbaabaababbabaabababbabbbabaaaaabbbbaaaaaabbaaaabababbabbbaababababbbbbabbbababbaabbaabbababbbbabaabaaabababaababbbaabbbbaabaababbaaaaaababbabaabbabbbbbbaaaaaaabaaaaaaabbabaabaababbbbaaaababaababaabbaababbbbbbbbbbbabbaaaaabaaabbaababbaababbabbabbbababaabaaabbbabbbabbbbbabbbaaabbbbbabaaaabbabaaaabbbabbbbabaaabbaabaababbabaabababaabbabbbabbbbbabbaaaaabaaaaababbbbabaabaaabaabaabbbbbbbbbbbaabbbaaabbbbbbabbbabababbabbabbbbaababaaaabaaaaaaaaababaaaababbababbaabbbaababaabbbbaaabbbbbbbaaabbaaaabbabbaaaababbababaabbbaabaabababaabbaababababbabaaabababbabaabbbbabbaaabbaababaabaaabbabbaabbaaaaaaaaabaabbbaabbaabaabaabbaabababaababbabbaaababbbaaaaabbabbaabaabaaaabbbbbbbbaabaaabaabbbbabaabbaabaaaaabbbaaabaaaabbbbabbababbbaababbbaaabbabbabbbababbbbbbbbaabbbbbbbaaabbaabababbabaabbbabbbaaaaaababbaabaaaaaababaabababbaaaabababbaaabbabaabaabbbbabaabbaabbaaaaababaaaaababbabbabaabbbabababaaaaababbbbaabbbbaabbaaaaabbababbabbaaabaabaabbaabbbbbaababbababbbbaabbbbaaabbabbababbaaaabbaaaaaabbaaaababaaaaaabbbbaaaaabbbbbbabbaabaabbbbabaaabbbbababbbabbabaabbbbabbbbaaababaabababbaaaabaaabaaaaaaaabaabbbbbabbbabbbabaaaaabbababaabbbaaaaaaaabaabbbbaabbbaabbabaaaaabaababaabbbabaaabababbaabaaabaabbbbbabbaababbbbbaaabbbaaabaaaabababbbbaabbbaaaaababaabaaaaaababababbaaaaaababbbbaaaaabbbabbababaabbbbbbaabbbbaababbabbabbbababbbaababbaabaaaabbaababbbabaaabbbabbbbbaaabbbaaaababbabbaaaaabaabbbbbababaaabababbbababbbaabaabbabbabaabaabbbaabbbaababbbababaaaaabaaaabaaaaaaaabaaabaabaaaabbbaababbbaabaabbaabbaaaaaababaabbaabbbabbbbbabaabababbbbbaaabababbbbababbbabababbaaabbbbbbbaabaabbbbabbaaabaabbbaabbbbbbaabaaabbbbbaaaaaaaabbabaabbabbababbabaaaaabbbbaaabbbaabbbababaaababbababbbaaaaaaaabbbbbaaaaabbbabbaaaaabbaabbbaabaabaaabbababbabbbbbaabbabbaababbabaabbabbbaabaaabbbbbbbababaaabbaabaaabbabbabbbbbabababaabababbaaabaabbaabababaabababbbbbaaaaaaabaabaaabaabaabbababaaaaaaababbbaaaaabababbbbbbbaabbbaabaabbbababbaabbabbbbabbbbbbaabbbbbaabbabaaaabbbbabbbbaaabbbaabaaaaabbbbabaaabbaaabaabbbababbaabbabababbbababaabaabababbbabbabaabbbbabbbbaabaaaabbaaabbbabababaabaababbbaabbaababaabaabbaabbbaaabaabbaabbaababababaabbbabbaaabbabbaabbbbbaaabaaaaaaabbaaabbaabbbaabbbbaababbaabbbaabbaabbbababababbaabaaaabaababbbbaabababbaaabbaababbaabbaaabbaabaaaaaabbbaabbababaabaaabbababbbbaabbbabaababbbbaaaabaababbabaabaaaabbbaaabaabbbabbbbbababbaaaaaaabbbaaabaabaabbaaabbaaaaaaababbaaabbbabaababbaaaabbbaabbababaaaaabbabaaaaaabaabaaabbaabababaabbbbbaaabaaaaabbaabbabaaaababaaaabbababbaaaabbbabaaaabaaaabbababbbabbabbbabbaabbabbbaaababbbbbbaaabaababaaaaabbbabbbaaababbbbaaabbbbaabababbaaabbbababbababaabbbbbbbabaaaaaabbbbabaabaaaaaabbbbbbbbabbbaaababbabbbbbbbaaaaabaaaaaabaaaaaaaabbbbbbbbbabbabbaabbabababaabaabbbabbbaabaabababbaaabbabbababababaaabbabababbaabaabaaaabbbbaaaaababbbabbbaaababbbabaaaaaaabaaababbbbababababaaabbbbbbbbbbabbabbababbabbababbbaabbbbbabaaabaaabbaababbbaabbaaaabaababbaaaababbbabbbbbbabbbbbbababbaabaabaabababbbabbbabaabababababbbbabbaaaaaaabbabbabaababaababbaababaaabbbaaaababaababaaaabababbbbbabaaaaaabaaaaaabbbabbababaabaabaabaaaaaaaabbbaabaabaaaaababbbabababaaaababbbbaaaaabbbbbaaabaaaaaaabaabaaaaaabbbbbbbaaaaaababbaabaaaabaababbabbbbaabbaaaaaaabaabbbbbaaaaabaaaabaaaabaababbabababaaaabbbaaabaabaaaabbbbbbabaaaabaabbbabbabbaaabaaabbabbbbabbaababbbaababbabaaaabbabbbababbbaaaaababbabaaaabbbabbbabbabbbababbbbaabbaabaaaabaaabbbaabaaaababaabaaabbabbaaabbaabaaaabbbaaabbbabbabaaabbbbabbbbbbabaababbabbbbabbbbbbbabaaababbbaabbababbabbbabbbabaaabbbbbabaaababaaabaaaabbababbabbaababbaabababaaaabbaabbabaabbaabbbbababbbabbaababbaaaaababaaaabaaaabbababaaabbabbbaaabbabbaaaabbbabbaaaabaaabababbbbbaaaababbabaabababaaaabaaaaaaaaaabaaabbabaabbaabbabbaabbbaabaabaaabbaabbbabbbabaaaabaabbaabbbaabaabaabaabbbbaabaabbaabbbbbbababaaabaaabbaabbaabbbaaaaabbbabbbbbaabaababbababababbbabbbabaabbbbbaaabbbbabbababbaaababbbbbaaaaaaaaabbabaabbbbaaabbbaaaaaabaabaababaabbbbaaaaabbbaabaabaabbaabbbabbababbbbbbaabbbbbabababbabaabbbabbbaaabbabaabbaababbbbbbaabbabaaaabaababbaabbbaabaaabaabbbaabaaaaaaaaaaaababbbbbabbbabbbabbbbaaabbbbaaaaabbbaabaaabaababbababaababbbbabaaabbbbabbabbbabaaaabbaabbbaabbaabbbaaaabbbabbbaababaaabbbbbbabababbababaaaaaabbaaabbbbaabbaaaaabbaabaaaabaaaabbabbbaaabaabaaabbaaabbabaaabbbabbaabaabbbaababbbababababbabbabbbbabbaabbbbbbbaaaabaabbbbabbbabaaaaabbaabbbababbbabbababbbbbaaaababbaabaabaababaabbababaabbaabbbaaabbbbbbabbababbaabbabbbbbabbbabaabbbabbbbbababbbabbbbbbbabaababaaabbbaaaaaabbbbbbaabaaababaabaaabbabbaabbaabbbababbbabaaaaaaabaabaababababbababbbabbbbbaabaabbabbabaabbbbababbaaabbaabababaaababbaabbbbbabbabaabbabaabaaabbbababbaabbbbabbaabababaababbbabababbaabbaababbbaaabaababbbababaaabbababbabababaabababbbababbbabbbbabbaabbaaaaaabbbaababbbaabbbabaabbabaaababbbabbabbbbbaaaaabaaabbbaababbbbaaaaaaaaaaaababbabbbbaabbbaabaaabaabbbabbabbabaababbaabbbbaaabbbbabbaaaaabbbbabbbabbbbbbbbbbaababaabbbaabbabaaabaaaabbabaabaaabbbbaabababbabbabbabaabababaaaabbabbabbaabbaabaaaaaabbbbaabbbbbababbbaaaaabbaaabaabaabbbaaaabbbbaabbbaabbbbbaababbbabbbabaaaaaababbbaabbbaaaabaaaaabbbaaaabaabbaaaabbaaaaababbaaabaababaabaabbbabaabbbbaabaabbbabaababbbbababbabbbbaababaaaaabaabbbbbbaabbbbababbaabaaaabbabbabbbaabaabaabaababbabaaaaaabaaabaabbbaabbbbaaabaaabbbbbabaaaababbaabbbaabaaaababbbbaaaaaabaaaaabbbbbabbaaaaaabaaabaababbabaabababbabbbbaabaabbabbaabaababbbaaabbbababaabbbabbbabbaaaabbaaaababababbbaabbababbbbbaababbbbaabbbaababaaaaabbbabbbababababaaaabbbbaabbabaababaabaaaabbbababbababbabbbbbbbabbabbabbabbbbbabbbaaaaaabbaaababaabbaabbababaabaaaaababababaaaaaaaaabbbabbaaabbbbbabbbaaaaabbaabaaaaaabbababbbababbbaabbbabbaabbaaaaaaaabababbbaabbaabbbaabbbaaabbabbbbbbabbaaabbabaababbaaaaababaaaabbbaabaabbbbbbaabbbbbbbabaababbabbbbbabaaaaabababbababaabaaaababbbbaaabbbaabbabbabbaabaabaaabaabbbabbabbaabaaaaabbbbabbbbabababbbbabbababaaabbaabbbabaaabaaabaaabaabbababbbbabaaabababaaaabbbabaabbaabaabbbbbaaaabbababaabbbbabaabbabbabaabaababbbbaabaabbabbaaababaaabaabbbabbbbbbabbbbaaaabaaaabbaaabbbbbbbbaababbbabbbaaaaabbbabbabaaabaaaabaababbabbbbabbbaabbaaaaabbbaaabaaaaaabababbbbaabaaabbaaabaabaaaabaaababbbbbbaabaababbbabbbabaabaababbaaabaaaaaaabbbabbababbababbaaabababbaaababaaabbbaabbabaaababbabbbbbbaaababaaabbbaaaaaabbababbaaaaaabbabbbbbbbbaabaabaaaaaaababbbabbaaaabababaaaaaababbbbbbabbaababababaaaaaabbbbbaabbabbbbbabbbbbbaaabaaaabaababbababaabbbbbbbabaabbbaabbbabaaabbabbbbbaababbbabbbbababbbbabbababbbaabbbaabbbaaaabbbbaaaabaabababaaabaababaabbaababaaaabaaabaaaababbabbabbababaaabaaaababbabbaaabababaaaabbbbbaabbabbabbbaabbbabaabbaabaaababbbbbbababababaabbaababaababbbbbbaaaabaabbbbbabbaabababaaabbaaaabbaabaaabaabaabbabababbabbabbbaaabbbaababbbbbbbaaabbaababbbbbbbaaaaaaabbaabaaabbbbaaaabbaaaabbbbbbabbbaabaabbbaabaaabbaabaababbbaabaabbaaabbaaaabbababbaabaabababbbaaabbabaababaaabbabbbabbaababaabaabbbaabbababaaaabaabbbabbbbaabaaaaababababaabaabbabbbbbbabaaabbbbababaabbbbaabbaaaabaaaabbbabbbaababaaabbbbabbaabbaabbabbbbbbbababbbabbbaabaabaababaababbbbbbbaaabbbabbabbababaaaaabbbaaaaaabbabababbababaabababaabbabbbbabababaabaabbbaaaabaabbbaaaaaaaabbbbaabbbaabbaaaaaabbabaabbbaaaaabbbabbababbbabbaaaabaaaaababbabbbababaaaabbaaaabababbaaabbbaaaaaabbbaabaabbaabbbbbabbbabbbbabbbbaaababababbabbabbbbbaabaabbbbbbabbabbbabbbbaabbabaababbababbaaaaaaaaabbbbbbbabbbbbabaabababbaaaabbbbbabbbabbbbbaaabbbbbbabbbaabaabbabaabbbaaabaaabaaaabaaababaaabbabbbbbabbaabbaaaaabababaaabaaaaaababbbbbbabaabbaaabbababbabbabbbaaabbaabbbaaaaabbaaabaabaababbaabaababbbbabbabbbbaaabaabaababaaabbaaabaababaababaabaabaabaabbaaaabbbababbbababaaabaabaababababbaabbbbaaaaaaaaabbbbabbabaaaaabbabaabaaabbbabbbbaaaaaabaaaabbbababbbbbbabaabbbbaabaaaaabbabbaaabbbbbbbbbabbaaabbaabaaabaaabababaabaababbabaaaabaaaabbbbbbabaaabbababbbaabbbaababaaabbababbbbabbbabbbbbbbabaaabaabaabbabaaaabaaaabaaababbbabbabaaabbbbbaababaabaaaaabbbababaabbaabbbbbabbaababbbababbaababaababbaaaabbbaaabbbaaaaabbabababbababbaaaaaabbbbbaabbbbaaaabbbbbaabbbabbaababbaabbbababaaaabbbaababbabbbbaabbaaaaabaabbabbbabbbaabbbababbabaabbbbbbaabbaabbabaababbbbbbabbababbbabababaabababbbaaababbaaaaaabbabaababaabbabbabbbbababbabaaabbbbabbbaababbaaababbbaaabaaabaaaaaabaabbabababbbbabaabbbabbbabbbababaabbbbbabbabbbaaabaabbbbbbbbabbbabaaabaabbaabbabbabbbababaabaaaaaabbbaabbbabaaabbbbaabaaaabbbbaaaaaabaabbbaaaaaaaaabaabbbbbababababaabbbbaaaaaabbbbabaaaabbbaaaaabbaaaaaaaababababababababbbbaaabaaababaaababbbbbbaabbbabbbbbbaabbabaaaabbbbbabbbaabbaaabaababbbababbbababaaaabbaaaabbbbbbaaaabbaaabbabbbbbabaaaabaababbbaaabbabbababbbabbbbbbabbabbbbabbaaabbaabbbabbbbaababbaabaabaaaaaababbabbabaabbbbbababbaaaaabbbbbaababaababbaabbbaaababbbbaaabbbabbbbaabbbbaabbbbbaabaaaaabaabbaabbaaabbbbababaaaabbaaaaaaaabbabbbbbabbbabaaaabaabababbabbbabbbabaabbbbababbabbbaabbaaaaaabaabbbaaaababbaaabbababbbbaabbabbbbbabbbabbbaabbbabaaabaaaabbabaabaaaaaababbbaaabaabababbabbbabaabbabbabaabbbabbaabbaaaabbbaabbaabbaaaaabbabaabaabbbbbabbbaaaaaabbbbbbbababaaaababbabaaabbbaababbaaaaaabbaababbbaabbbbababbabbbbbaabbaaababbababbbaaaaababbaaabbaaabbaababaababaaaabbbbaabbbbbbaababbbabababaababbbaaaaababaaabbbabbabbabaaabaaabaabbbabaaaababbbaabaabaababaaabbababababbbbaabbaaabaabbaababbaabbabbbaaaabbbabbabaabababbbaabbaabaaababbbabbbaabaaaabbabaabaabbaababaaabbaaabbaabbbbabbbaabbaabbabaaabbabbababaabaaaaaabaaabbbbabababbabababbbabbbbaabaaababbbbababaaabbbabaabababababbbbbaabbbbbbbbaaaaabaaaaabbaaababbabaaabbaaabaaaabbaababbbaaaabbabbbaabaabbbaaaaaaaaabbbabababbaabbababbbaabaabbaaabbaaaababbaabbbbbbabababbaababbabbabaababbbbbabaaabbbaaaabbabaaaaaabaababaaabbabaabbbaaaaaaababaaabbaababaabbaaaaabaaabbbbaabababaaaababbaabbbabaaaababbababaaaaababbbbbbabbababbbaabbabaaaababbabababaabbabbabbaabbaabaabbbbbbabbbbabbaaabbbabbabaabbaababbabbbbbbabababaaaabababbbbbaababbaaabababababababbbbbbbbbbbabbbbbaaaabbaaabbabbaabbabbbabbbbbbababaabbabbbaababbbbbbabaabbaabbbbbbaabbabaababbabaabaaabbbabbaaaaabbbabbbabbaaabaabbaabbbababaabbaaaaaaaaaabbbbbababababbaabbbaaaabaabbbbabbaabbaabbaabbbbbbababaabbbbaaaaabbbbababbaaaababbaabbbaaabababbbaaaaaabaaaaababbbbbbbbaaababaabbabbbbbbbaaabbaabaaaabbaabbbbaabbaaaaaaabbaabbaabbabababaabbaaabaabbbaabaaaabbbaaaabbbabbaabbbbbbbabbabaabbabbbbababaaabaababaaaaaaababbbbaababbaabbaabbbbabaaabababbbbbbbbaaaaaaabbaaababaaaaaaaababaabbaabbabbbbaaaaaababaabaaaaabbaabaaabaaaababaabbbbbbababbaaabaaaaabababbbbaaababbbabbbbaaabbbbababaababbbbbaababbaabbbabbababbabbabbbbabbbbbbbaabababbbbaaababbaaaabbaaabbbabbbbbbaaaaaabaaaabaababaabbaaabbbbabaabbaaaaabbaaabbbababbabababbababbbaabaababaaabbaabaabbbaabbaaaabbbaaabaaabaaaabbbbbbbbbabaababbaaaababbabbabbbbbbaabbaabbbabbaaabaabababbabbbbababbbaaabaaabbaaababaaaaabbaaaabababaaabababbbbbbabbabaabaabaaabbbabbbaabbaaaaaabbbbababbabaabababaababbbbaababaabbbabaabbbbaabbbaaabbbabaaabbababaabbabbababbbaaababbaabbbbbaabbababababbabbabbbbbaabaabbbabbbabbababaabbabaaabbbbbaaaabbbabababaabbabbbbbbbababaaabbabbbbaaaabbaaabbbababbabaababbaaabbababaaaabbbbaabaaaaaabbaaabbaabbababbaaabbbbaabbabaabaaaabaaaaaaaaaabaabaaabbababaabbbaaabaababbbaabbbbbbabaabbbbbabbbbabbaabaabbbbbababababbbabbbababaababbaaaaaaaabbbabbbaabbbbbabaaabaabaabbbbaabbbabaaabbbbabbbbaaabbbaaabababbbabbbaababbaababbabbbabaaababbaaaabbbaabababaabbbabaabbabbbaabbaaaabbbababbaaaabaababbaabbaaabaaaaaabababbbaaaaababaabaaabbbbbbbabbabbaabaababbaabbbabbbbabbabaabaaaabaaabbaababaaaabaabbabbbabbbbaabbbbbbbabbbbababaabaaaaaaaaaaabbbbaabbbbababbabaaaaababaabaabbaabbaababbaaaababaaaaabbbbaaaabbaabaabaaabaabaabbaababbabaababaababbbaababbbaabbbabbbabbbaababbbbbabaaaabbbbbbaaabbaabbabaabbabbbababababbaaabbbbbabbaababbabbbaaaabbbbaaabababbbbaaaabbbabbbbbaababaaaabbaaaaababaabbbaaabaababbaabaaaaabbbbabababaabbbbbaaabaabbababbbaabaaaaaaaaaababaaabaababbbaaabaaaabaaababaabbaabaabbbbbbabaabbababbbbbaaabbaabaabbbaabababbabababbabbbbabaaaaaaaaaaabaaaaabbaabbbabbababbabbaababaabbbbabbababababaabbbaabbbaababbaaabababababbbabaaaaababbbbabbbaabbaabaaaaaabbabbbbbbababbbbbabbbbbbaabaabbbaabbbbbaabaaabaabaaaababbbaaaababbabaaabababbbbbbbbaaaabbbbbbabaabababaaababbbbbaabaaabbaaaabbaaabaaabaaababababaabbbabbbabbaabbaaabbbbbaabbbabbbaaabbbaabbaaaaabbbbabbbabaabaababbbabaaaaaaabababaaababbbabbbaaaaabbbaababbabbaaabaabaaabbaabbbaababbabbabbbbaaaabbbabbbbbabaaabbbbbbbaaaabaabbbaaaaabbbaaaabbbaabbabbabaabbbbabaaabaaaaababbaabaababbaaaaabaabbbaabbbbabbabbbbaabbaaaaaababbbaaaaababbbabaabababaabbaababaabaabbbbbbabbbbaabbbbabaaababbabbbbbaabbabbaaabaabbbaaaabaaaaabbbbbbbabaabaabaaabbabaabbbbbbbbabbbabbbabaabbaabbabaaaabbbaaabbababaabbabbbaaabaaabbbbababaabbbaaaabaababbbbbaababbbbbbbbbaababbabbbbbbbabaaabaaabbaabaabbabbabaabaaaabaabaaaabbbabbbaaaaababaaaaabbabbaaabaaababbbbbbbbbaabbaaabbaaababbbaabaaabaabaabbabaababbaabaaabababbabababbaabaaabaabaabbbaaaabbbaababaabaababbabbaaabaabaabaaaaabaabababaaaabaabaaabbbbbaabbbaabbabaabbbabbbaabaabaaabbbbbabababbbaaabaabbbbbabababbababbbababababbaabbaaaaabbaaaabbbbbaabbabbbbbaaaaaaaabbabaabbbabbaaabbbbbbabbabbabaabbabbbbabbaaaabbabaaabaaaaabbbabababaaaaaaabaabbababbaabbaabaabbbbababbbabaabaabbbaaaaababbabaabaaababbabaabbaaababbabaabbbbbaabbbaaabbbaabaaababbbaaaaabbbbaaabbbbaabaaababbbbbaabababaabaaababaababababbbbbabbbbbaaaababbbaaabbabbbaaaaaaaaabaaaaabbaaaaabaaaabbbbbababaaaaabaababbabaabababaabbaabbaaaababbababaabbabbaabababbbaabbbbabbabababaaabbababbbababaabbbabbbbaaaababbbaaabaaabbaabbbabaaabbaaaaaabababbabbbababbabaabaaabaaabababbabbaaaabababbbbaababbbabababbabaababbabaaaabababbbbabbbbabbbbaabaaabaaaaabbbaaabbbaabbabbbabbbbbabbababbabaaaabbaabaaabbaaabaabbaaaaabababaaaaaabaabbababaaabababbabbbbbbbabbbabaaaaaaaababaaaabbaaaabaaabbaaabbaaaabaaaaabababbaabbabbabbababaabaabaaabaabbabaaaabaaabaabbababaabaaaaaabbbaaabababbaaaabbbbbabbbabaabbbbbbaabbabababaaabbababbbaaaabbabbbbaaabbaabbabaaababaaaababbabbbabbbbaabaabaabbbbbaabbbbabaaaaabbaabaabbaaabaaabbababaabbbabbabbababbbabaaaabbababbaababbaaaabaaabaabaaabbaabbaaabaaabababaaaaabbbaaabababaababbabaababbbaaaaabababbbbabbababaaabbaabbbbbabbababbbabaabbbbbbabbabababaaabaaabababababaabbaaababbabbbaabbaabbaaaabaababababaabbbabbbbababaababbaabbbbbaaabababbbabbbaababbbbbaaabbabababaabbbbababaaabaabbbabababaababaababbaabababbaaabababaabaaaaabbabbbbbabaababababbbaabbabbbbbbbbbaabbababbbaabbabaaaaabbbabbbbaabaaaabbbaaabaaababbbabbbbbaaaaaabbaaaaaaabbbabbbabbaaabbbaabababaabaaaaabaaaabbababaabbbabbbbaaaaabbabbbababbabbbabbabbbaaaabbbaabaaabbbabababbbbbaabaababaaababbaaaaaaababbaaabaabaabbaabbbaaabaabbbbaaaababbbbbaaabbabababbaababaaabbabaabbbaaabbbbaabaababbbbabbbabbbbaabbbbaaaabbabbbabbbbaaaaaabbabbbaabbabaaabbbbbabaaabaabbbbabaabbabbbabaaaaabbabaababbaaaaaababbaaaaaaaaababbbaaabaabbbbbaaabaabbababbbbaaaabbbbaababbaaabbaabaaaabaaaaabbabbbbababbbbbaaabbbbaaaabbaabbaabbabbabbaaaababaaaaaaaaabbbbbabbaaabaaabbabbbabaabbabbbaaaaaabbababbaabaabbabbbaabaaaabaaaaaabbabbaaaabaabbbabbaaaabaaaaabbabbaababaaabababbbaabaaabbaaaaababbaababbabaabaaaababbaabaababbbbbbabbbbaababaababababaababbbababaaabbbbaababbbbaaaaabaabbababababbababaababbaabbbaabbaaaaabaaaababaaaabbaaaaaabbaaabababbabbbbaabbababbaaaaaaaabababaaababbaabbbaababbaabaabbbaaaaaababbbababaabbabbbababbaabbbabaababbabbbaaaabbabbabaabaabaaababababbbaabbaaaabbabababbbabbabbabbabaabaabbabbbaaaababbaaabbbbabbaabaaabaaabbbbbaaaaaabbabaabaaaabaababababaababbbabaababbaabbbaabbaabbabababaabaabbbaaaaaabbbbababbababbbabbbaabbabbababaabababbaabbabbaababbbbbababbbbbaabaabaabbabaaaabbabaabaabbbabbbbaaaabbbaabaabbbaabbbaaaaabaaaaabababababbaaababbabbbbabbbaabbabbbaaababbbbabaaabbbbbababbaaaaaabaabbbbaabababaabbbbbbabbbbbbabababaababbabbbaabbbbbbababbaabaabbaabbbaabbbbaaabaababaaaaabbaaaabbaaaabbbbbbbbbbbbaaaaabaabbbbbabbaaababaabbaabaabababbbabaabababbabbbababbbababbabbbbaabbbabbabaabababbbbbaaabbbabababbbabbababbabbbabababaabbbbabaaabbbbbaabbababbabbbaabbaaaaababbbaababababaabbbbbaabbabbbabbaaaabbababbbbaabbbababbabaabbbbbbbaabbabaababaaababaaabbaabbababbbaaabbbbabbbbbbbabbbaabbaaaabbbbabaabaabbbabababbabbababbaaaaaabaaaaabaaabaaabaaaaaaabababaabbbaabababaabbaababbabbbbbabbbaabbaabaaaaaaaaabbbbbabbbbbaabbbaaaaaababababbbabbaababbbaabbaabababbaaaabaaaabbaabbbbaabababbbbaabbababbbbbaaaaaaabaabbabbbbaabbabbbababbbbbbabaabaaaabbaabbaababbbabaabbbabbabbbbbabbbbabbaaaababaaaabbbbaaaaaaaaabbbaabbbabaaabaaabaaabbbaabbbbbbbbbbaababbbbbaabbaaabaaabbaababbbbabbbbababbbaaababbaaaaabaaabbbaaabaaaabbbabbaabbbaabbbbabbababbbabbababaabbbaaababbbbabaaabbababababaaaababbababababbaaabababbaababbaaaabaaaaabbbaabbabbaaabbbbbaaaababbbababaaabbbbaabaabbabbaaabbabbaababbbbaababbababababaaaaabbbabbaabbbaabbbabaaababbaaaaababbbbaabbabbbaababbbbabbabbabaaabababbaabbabbaaabbaabbabbbbbbbbbbabbbbaabbabbbabababaaabbbaabbbaaababbbbabaabbababbbbababbabbabbabbaabbbaaaabbaaababbbababbabaaaaabbaaaabaababaaaaaabbababbbaaaabaabaabbababbbaaaaaababbabbababbbbbabbaababaabbaababbabaababbbaababbaaabaababbabaaabbbaaabbabaabbbbbaabbbabbbbabbbaaaabaabbbbabbbbababbbbabbaabbbbaaaabbbbababaaabbbbaaabaabaaabbaabbabbaababbabaaaababaabbaaabbbababaaaabbbbaabbabbaaabbaababbbaaaaababaabbabbabaabaabaaabbbaaaabaabbaabaabaaaababbbbabbbababbbababababbabbbbbbbbbbbbaabbaababbabbbbaaaabbbbbabbbbbababababbabbabaabaaababaaabbbbaaabbbbbaabaaabababaaaaabbabaaababaabbaabaaaaabbbaaaabbabbababbaabababaaaaaaababbabbaabbabbbaaabaababaababbaaabbabaaaabbabbbabaaababbaaababbabbbabbabaaabbabaaabbaabababbaaaabbaababbbbbaabbaabbaababbbabaabbababaabbbaabaaaaabaaabbaaaaaabababaaaababbbabbaabababaabbbbabbabbbabbabbabbbaaababbbbaaaabbbababbabbaabbbbaabbabababaabaabbaaaabbabaabbbabbabbaaabbbaabbbbbbaabbaababaabaabababbaabaabbbaaabaabaaaaaababaabbbbbbbbbbaabbbabaaabaaabbbbaaababbbbbaabbbbaababbbabbaabaabaabbaabbbbabbaaaabaaababbabbababaabaababbbbbabbbbbbbbabbabaabbbbbaabababababbabbaabaaabaaabbbbaaabaaaabaaaabbabbabbbbaabbaaaaaaaaaabaaaabbaaabaababbbabbabbaabbbbbabbabaabbbabaaabbbabbbaaaaabaabaabbaabaaabbbaaaaabbaaaabbabababbababbaaaaaabbbbbbbababbabababaabababbabbabaabbbaababbbabaabbbabbbbbbabbaaaaabaaaababbaaaaabababbabaababbaabaaabbbbbabaabaaabaabbabbaabaabababbababbabbbbbbabbbbbaaaaabaaaaaaaaaabbbbabaababbbbbabababbaababaabbbabbaaaabababbbabbabbbaabbabbaaaaaaabbababbabaaaabaaaaabbababbabbababaaabbbbbbbbabbbbabbbaaabbaaabbaaabaaaaabbbabababaaaabaaaabaabbbabababbaaaaaabaaabbbbabaababbaaabaabbbabbbababbbbabaabaaabaabbbabbbbbaaaabaabaaaabbbbabaaababaaabbbbbaababaababababaabaaabaaababaabbbabababababaabaabaaababbabaaaaaabababbbbaababbabbbabbaabbbbbaaaaaaaabbaabaaaaaaaabbbbaabaaababaabbbbbabbaabbaaabbbbbbbbbabaaaabbababbbaaabbabaaaaabbabbabbbaaaabbbaaababaabbaaaabbbabbbbbaababbaababababbbaaabababaababaababaaabbbaaababaabaaaaaabbaabbbaaaaabababaaabbbababaababbbbbababbbabbabbbaababbabbaabbbbbbbbabbbabbabbabbbabbbbbbabbaabbaabaabbbabababbabbbaaabbbbbbbbbbbbaaaabbabababbababababbbbbbbbbabaabbaaabbbbabaababbbaababbbaabbabaabbaabbbbaaabaaaaaababbbbababaaaaabbaababbabaabbaabbaaabbabbaaabaabbaabbbaabbabbabbbaaaaaabbbbabbbbbbaaaaabababbababbbabababbaaaaaabbbabbbbabaabababbbaaabbabbbabbbabaababbbababbbaabaaaaaabaababaabaaaababaaabaabbbbbabbabbabbabbbbabbbaaaabaabbabababbbbabaabaabbbabaaabaabaababababaabbbbaaabbbaaaabbaabaababaababababbaabaabbabababaabbbbbbabaabaabbaabbbaaabaababbaabaabbaaabaabbaabbaabababaaaabaaababbbbbaabababbbababbaaaabbbbababbbbabaaabbabbbbabababbbbabaabbabbbababaabaaabbbbabababaaababaaaabbbbbbaaabababbbaabbabaaaaaaaaaabbbaabaaaabbabbbabbbbbaaabbaabbbaabbbaaaaaaaabbabbababaaaabbaaabaabbbaabababbbababbbbbaababaabbaababaabbbaabbaaababaaabbbabaabaabaaababbabaabaabaabbbabaaabbabbababababbbbababbaaabbabbbbaaaabbabbabbbaabababbaabbaaabaabbbbaabbbabaaaababaababbbbbabababaaaaaababbaababbbabaaabaaabaaababbbabaabbbbaababababbbbaaaaabaaabbbbbaabbbbabbbaabaaabbaabbbaabaaababbaaaaabbbbbbbababbbabaabbabbbabbabbabaaababbaaaababbbbaababababaaaabaabaabbbbbbbabbaabaaabaaabaaaabbbbabaabbbaaaaababbbbbabaaabaaabbaaabbbbabaabaabbababbaabbabbaabbaabbbbbaaaabbbbaabbbabbbaabbbbbabaaaababbbbaababababbbbbaabbabbbabbbbbbabaaaaaaabababbbaaabbbaaaaabbbbabbaabbbbaaabbabbaabbabaababbabbbaabaabbaaabbbaaabbaabbbbaabbabaaabbabaababbbbaabbabbaababbabbabbabaaabaaaaabaabbbabbbbaaaabbabaaabbabaabbababbabbbbababbaaabaaaaaaaaaabaabbaababaabbabbbabbbaaababbbaababaabbbaaaabbbaababbaaabbbbbbabbbbabaaabaaabbabbababbababbaaaabbaabbbbaaaababbabbbbbbabbaaabbbabaababaaaaaaaaaaababbabaaaabbbabaabbbbaaabababbaaaaaaaabbababaaaabbbbbbaabaaaaaabbaaabbbaabbabbbbabbbbabaaabbbbabaaaaabaaaaabababbbbbaaaabbaaaaababbabababbabaaaaababbbbbbabbaaaaabbabbbbbbaaabbbbabaabaabbabbabbbabbbbabaaaaabaabbabbbaaaabbbababbaaabababbbabababaabbabbabbbbbaababbaaabaaaababbababbaabbabaabbabbabaaabaaaababababbababbaabbbababbbabbbbaabbabaaaaaabbabababbaaabaabbbabaabbbbaababbaabaaabbbbbabbbbbaabbabaaabaabbabbbaaaababbbbaaabbbaaaabaaaaaabbbbaabbbbababaabaaaaaaabbaaaabbabbaaabaaabbbabaabbbbaabbabbababaaaabaaaabbaabbbbabbabaababbababaabbabbbbaabbababbbabababaaaabaababaaaabababaabaabaabaabbabbaabaaaabaabbabbaabbababaabaaaaabaaabaaaabaaabbababababbaabbbbaaaabaaaaaabbaaaabbabbbbabaaaaaabbbbaaabbbabbbbbabbaabababbaaabbbababbaababaababababbaabbbbbbbbabbaaabbbbbabbabbbaabbbaabaaaababbbbaaaabaaaaaabbbabbbbbabababbaaaaaabaabbabaabaaabababbaaaaabaababbbabbaaaaababaababbabbababbaabbabbabbbbaaaaabaaababaaaaabbbbbbabaaaabaabbbbbbabababbbababbbabbabbabababaaaaabbaabaaaabbaababbbabbabaabaaaabaaaaabbabbbbbbbbabababaabbbbababbbaabaaabaaabaabbbbabbabbabbbbbbabbaabaabbbbaaaabbaaaabbababbbabbbaaaabbbaabbaaaabbbbabbbabbababbbabbabaabaababaababaaaaaaaabbabaaababababbbbbaabababbbaaabbabbabaababbaaabbaaaaababbbbbbbbbabaaaaabbbaaabbabbbaabbaabaabaaaabaaabbaaabbbaaabaababaabbbabaabbabababbaaabbaabbbaaaablaaabbaabbbaaababaaaabbabbaabaaaabaabbbbbbaababababbbbbaabaababbabbaabbabababababbabbabbbaabbbaabababaabaabbbbaabbabbbabbbaaaabbababbaaaabaaabaaabbaabaababbabbbabbbaaaabbaaabababaababaabaaaababaababbabaabbbabbababbabbbaabaaaaabababbbabbaabbabbabaaababaaaabababbaaababaaaaaaaabaaaabbaabaabbbaabbabbbbbaabbaabaaabaaabbbaabbbababbabbbbbaaaabbbaaaaaababbbbbababaaaabbaaaabbababbabbbaaaaaababaabbaababbbbbabbaaaaaabaabababababbbbbaabbabaabbbbbbbbabbbbbbbabbbbabaabaabbbaaaaabbbbbbbbababaabaababbabbbaabbaabbaababbabbababaaaabaaaaaabbabbabbbaabaaaabaaabbbbaaabbbbabbbbbbabaabbbaaaaabaaaaabaaabbabbbababaaaaaaabbbababbaaaaabbabbaababaaabbaabaababaabaababaaabbbbbbbaaaaabbabbabbbbbbbabaaaabaababaaabaabaaaaabbababbaaaaabbabbabbaaabaabbbbbabaaaabbbababbaaabaaabbabaabaaaababaabaabaaabbaaaaabbbbabbbbbbbbaabbbabbaaabbbbabbbaaaabababaaaababaababbabbaabbabaababaababbbabbbbaaabbbaaabbbbabaabbaaaababaaaababbaaabbabaababaabbaabaaaaabbaaabababbaaabaaaaabbbbbabbbbaaababbbbabaabbbbbabbabbaabaabbabbbbaabbbbbbbbabaaaaaabbababbabbbbaaaaaababaabbabbbaaaabbbabaaaabbbbbbbbaabbaabaaabbababbbbaaabbabaaaaaabaababbabaabababbbabbabbabbababaaababaaaababbbaabbaabbbbabbaaaaabaaabbbaabbbbaaaaaabbabbabbbabbaabbaaaaabbaabaabbbaabbbbabbaabababbbaaabaabaaaabbaabaaaabbababbbabababababaaabbabbbaabbababbaabbabbbbbabbaabaabbabaabaaabbbabaababaababababaabaaaabaaaaaaaaababbbbbaabbabbbbbaabaabaabbbaababbbaabaababbbbbaabbabbaabbaaabaaabbaabbbabbaabbbababababbaabbbababbbbbaaaaabababbabbabbbabaaabbaaaaaaaabaaabbabbbbabababababaaabbabbabbbbbbbabbaabaabaaabababaababababbabbabaabbaaabababaabaaaaaaabbbbbaabbbbaabbbaaaaabaabbbaaabaababbaaabbbbbaabaaabaabbaaaaabaaaaabbbbbaabaababaabbbaabbbaabbaababbbaaabbaaaaababbabbabaababbabbbbabaabaaabbbaabaaaababbabbaaababbabbabbbbbbbaaaabaabbbababbabbbababaaabbababbbaabaabaaaabbbbabbababbbaababaabbaabbbbaabbabbaaaaaabaabaaababbbabbabaabbbbabaabbababbaaaaabaababbbaaaaaabaaabababaabbaaabababababbbbaabbbabababbbbbaaaaaababbbbbbaaaaaaaaaababaababbbabbabaabbaabbaaaaabbaabaabbbabaaaaaaabbbabbbaabbabbabbbabbbbbbbbbbabbabbbbbabbaaabbabbbbbbaabbaabbabaaaaaaabaaabbbbbbaaabaabbbbbabaaaaabaaabaababbaaabbbbbbbababbaaabbabbaababbbbaabbbaaaabaabbaaabbbabbbbabbabbbababbbaaaaaababaaaaaabbabbaaabbabaaaaabbaabbbbaabbbbbaaababbaaababbabbaababbbaabaaaabaabababaaaaaaaababbbbaabbbbbbaaabababbabbabbbbbbaaaabbabbbbaabbabaabbaaaabaabbbabaaabbaaaabbbbbbaabababbbaaaabbbbbaabababbabbbababbaabaaaabaaababaaaabbbaaababbbbbbbabbaaaaabbaabbbbabababaabbbbaaaaaaaabbbaaaabaabaaabbabaabaaabaabbbbaaababbaabbbbbabababbabababbbbbbabbbabababaaaabbabaaaabbbbababbaaabaaababababbbbabbabbabaaaabbaabbababababbbaaabbaaaaabababbaababbabbabababaaabbbaaaaabbababaaabaabbabaaababaabbabbbababababaaababbababbaaabaaaababaababbaabaaaaaabbaabbbabbababbaabbbababaabbabaababbaabaaaabbbbbbaabbaaababbabaaabaabbbbaaabbaababaaabbaaababaabaaababbbaaababbbabbbbaabaababbabababbababbbbbabbbabaababaabaaaaaaabbbabbbabaaaabbaabbaaabbbabbbbbabaababaaababbbbbbabbbbbabbbaaabbbaababbaababbabbababbaaabbabbbbbaabaababbabaabbabaaabbaaaaaaaabbbbbbbabaaabbabbaababbbaababbbbbabaababbbbbaabababbaabbaaababbabababbaabababbbababbbaabaaaabaaaabbaabaaaaaabaaaababbbbbaaaabbabbabbbaabbbbabaabaaabaaaababbbaabbbabaabaaaabbabbbaabbbababbbaaabbbabbaaabaabbbbbaaabbbbbabababbbabbabbbbbaaaabaaabaabbaaababaabbbabaabbbaabbaaaabaababbbaabbbbbbaababbbabababbababaabbbaaaabaabbbbabbababbbabbababaababbbbababaabbbaabaaababbbabbbbbabaababbbaaabbabbbaaabababaaabaaababaababababbaabbbabbabbaaaabaabbaababaabaabbbaaabbbabbaabbabbabbabbbaaaabbbaaabbbaaaaabbababbbaabbbaabaaabbbabaaabbbbbabbaaaaabababaaabbabbabaabbbabbaaabbaabbaaaaaaabbbababbbbaabbbbbbbbaaaabbbaaabbaaaabbaabababbababbbbaababbabaaaabaaaabbbabbbabaaabaabbaabbbaaaabaabaabbbabaababaaabababbaabbaaababbbbbaaabbaabbbabaaabbbaababbbbabaaabbbabbbaaabbaabaaaabababbabaaababbaabbaaababbbabbaaabbaaabbaaaababaabbababababbbababbbbbbaaabaaabbabbaaaaaaaaababaaababaabaaaabbbaabbbbabaabaaaabbbbabbbbaaaabaaaaababaaaabbbaababbaabaaabbababbbbbaaaaabbababbbabbbaaaaababaabaabbaabababbabbbbaabbbbbaababbbabbbbaabbbbbbbaaababababababbaabbaabbbabbbbaaaabaabaaabbbaaaabaabbbaabbbaaabbaaaaaaabbbababababaaaabbaabbbbbbbabbababbabababbbabbbbabbabaababaaabababbbabbabbaababababaaaaabbaaaaabbbbabbaaaaabbaaabbbabbbbbbbabbbbbbaaabaaabbababbabaabbbbaaabbaaaaabaabbbabbbbababababaabbaabaababbaabaababaabbbbabbababbbabbaabbaababaabaababaabbaaabbabaabaabababbabbbaabbaabaababaabbababaabbbbbbbbaababababbabaaabaabbbbbabbaabaaaabbabbaaabaabaabbababaaaaababbbabbaabaaabbabaabaaabbabbabbababbabaaabaaabbbbaabbbbbaaabaaababbaabbbbaabaabbbbbabbaaaaabbbbaabbabbaabbbbabaabaaabbaaaabbbbabaabbbababbbbbbabbbbbbabbbbbaaaababaaabbbbabaaaaaaabaaabbbbbaabbbbbbbbbabaabbabbbbbbbbabbabaaabaaabbbabaaaabaabaabaaaaabbbabababbaaaaaaababaaaaabaabaabaaaaaabbabaabbbbbbbbbbabbbababbaababbabbbabaaabaaaaabaaabbbabaaaaababababbabaabbabaaabaaabaabbabbabbaaaaaaaabababbabababaaabaaaabbabbabaaaabbababbbabbabbaabaaabbbabbbbbbabbbbbabbaababbbbaaaaaaaaaaaaaaababbaaaaaabbaaabababbbabaaabaabbbbababbbbabababbbbbbabaabbbabbaabbaaaaaabaabbbaaaabababbbbbabaababbbabbabbabbbaabaabaabbaababbbabbaaaabaaaaaaaabbbaaaaabaabbbbabaaaababbbbbaaababaaababbabaaaaaabbbbababbbaaabbbaaabbbbbbbaababbbbbbaabbbabbaaabaaaabbabaabaabaaabaababbabaabaabababbbbabbabbabaababababababaaaabbbbbbabbbabaaaaaababbabbabbbaabaabbababaaabbbabaaababbbbbbbaaaaabbbbaaabbbbbabbbabbabababbaabaabbbaabaabbbabaaaaaaaaaababaabbbaaaabaabbabbababbaababaabbbbaaabbaaabbbbbbbbabaabbaabbaabaabbaaabbabbaaabaaabbababbbaabbbaaaabbaaaaabbbbbabaabababaabbbbbbbbbbbaaaabaabaaaaaaabbababbbaaabaaaaaabaaabbbababbbabbabbbaabbabbaaaababbbabbbaaaaaaabbbababbbaabbabbbabbbabaabaaabbababbaaaabbaabaaabababaaaaabaabaaaaaabbaaaabababbbaaaabbaabbaababbbbaabaabbaaabbabababbabbaaaabbabbbaaabbbnbabbababbbabbbbbbbabbbbabababaaabbaabaaabbaabaaaababaaabbabbaaaabbabbbababbabaababaaabaabbbaaaababbbaabaabbbaaabbbbabbabbaabaabbaabbaabbaababbaaabbbbabaaababaababaaaabaababbabaabbbbbbaabaaabbaababbbababbbbbabaaaaabaaabbbababbbaabaabbababbabababbabbaaaaabbbbbaabbbbaaababaabbaabbbabababbbabaabaaababbbbaaaaabaababaaabbbabbbbaaabbbaabaabaaabbabbabaabbbaaabbbbbbabaaababbbbbabaabbabbabaaaabbbbabaaabaaababaabbaaabbaaabaaabaaabaabaaaaabbaabbaabaaabaabaaaaababbbababbbabbaaaabbababbabbaaaaaaababbaabbaaababbbbaaabbabaaabbaabbabaabbbabbbaaaabaabaaabaaaabbabababaaaabbbbbaaababbabbaabbaaabaaabbbbabaabbabbbbbbaabbababababbabbbbbabaaaabaababaaaaabaabbbbaaababaaaaaababbbbbbabaaaabbabbaaaaaaaaaabbbabaaaaabaaabbabbbbbaababbaaabbabbabbabbabaabbbaaaabbbaabbbaabbabbbaabbaaaabbabaabbbabaababaabaabbaabbbaaaaabbbabbbbaabbabbbabbbaabbaabbabbaaababbaabbbaaaaabbabaabbabaabaabbbbbbabababbbbbaaabbbbbaaaabbaaababaabaabaabbbababbbbbaaababbaaabaabaabbaababbaabababbaaaabaaabbbbabaaabbabbbaaaaaabaabbbbababaababbbbbbbabababbabbaaaabbaaabaabaaababaaaabbbbbaababbaabbbaaaabbbaaabbaaaaabbbaaaabbbbabaaaaaabbaababaaabaaaaaabbaaabbbaababababaaabbbababbababbabbabaababaabbbbaababbbabaabaabbbbaaaaaababbaabaaabaabbbaaabababbaaabbababbbbaaabaabaabaaabbaaabbbaabaaaabbaaababaaaaabbababbbbbabbbbbaaabbaaabbabbabaabaabbabaaaaabbbabbbaaababbbbbabbbaabbbbaabbbbbabbabbababbbaabbbabbbaabaababaaaababbabbaabbabbaaaabaaaabbaaabbbaababaaaababaabaaabbabbbaaabbbaabaaaaabbabbaaaaaaaaaababaaaaababaababbaabbabaaabbbababaaaaabbbbaababaaaabaaaabbbaaaaabbbbabababaabaaabbbbbbaabbbabbbbaabbbbbbbaababbbbaabbababbbbbaaabaabbababababaabaaabaabaabbabbbbaaabbbbabbaabbabbabbaababbaababaaaaababaaababababaaaaabababbbbabaabaabbabbbbaabbbbaabaabbbaabbababaaaabbbbaabaaabbbbbbbabbbaaaaaababbababbabbaaabbbaabbababbbabbabaaaabaabbbbbbabbabaaaabaaababaabbbbabbaabbbbabaababaabbabaaaaaabaabbabababbaabbaabaababbabbbaababbbbbbbaabbababaabbabaabbbbbbbbabbaababbaabbbbbaaaabbbbaabbaaaabbbbbaaaabbbabbaabbaaaabbbbbbbbbabbaababbbaabbbbababbbababbbabbabbbbaaaabaaabaabbbbaaaaabbbbaaabbaababbabbabbbbbbaaababaaaabaaabababababaaabbbbbaabbabbbbaababbbabbbbbabbbbbbaaaaababaabbbabaaaaaababbbbbaabbaabaaaaababbabaaababbaaabaabbabbabaaaaabbbbbbbbbbbaabbbabbbbbabbbbbbbaabbbababbbabbbbaaaabbbabbaaabbabbabbabbaabbababaaababbbabbbabbbbaaaababbaababaaabaaababababbbabaaaaaaababbbaabbbbabbbbbbabaababaaaabbababbaabbaaababaaabaabbbbbaabaababaaaaabbbbbbbbaaaaabbabaabbbbabbbbaaababbbbbaabbbbbbbabaababbbbaababbbbbabbababbaaaabbaabbaabbbabababbbabbbbaaabbbbbbbabaabbbaaabbababaabababbbbbbaaaababaabaabbaaabaaaabaabbaaaaababbabaabaaababaabbbabbaaaabbbababbaaababaaaabbaaabbababaaaabbabbbabbababaaabbbaaabbbabbbaabbabaaababaabaabbaaabbbababaaaabbabbaaabbaabaaabaaaaabaaaaabaaaabbabbbbbabbbbabaaaaabaaabbbaaaababaaaababbaaabaaaabbabaababbaabbabaaababbaaaababaabbbabbabbbbaabaabaabbaaaabbbbaabbabaaaabaabbbabababaaaabbbbbaaabbaababababaabbabbaaaaabbaaabaabaababbaabbabbaabaaaabaaabbaaaabaaaaaababbaabbababbbbaaaaaabaaabbabbaabbabbabbabbaabbabbabbababababaaaababaaabbbababaabaabbabbaaaaaabbbabbabaaaaababbaababbbababababaaabbbbbbbbaaaabbaababbbbbbaaaabbabaababbbaababaaabbaaaabaabbbaaaabbabbababbbbbabaabbabbbbbbabaabbabbbaaababbabbbaaabbaabaaaaaabbaaabaaaababaaaabbbabababbbbbbbbbabbbaabbaabaabbbbbbaaaaaaabbabbaaabaaaabaabbaaaabbaaaaababbbbbabaaaaaabbbbbaaababaaabbbbabaabbababbbaabaaaaaaaaaabbbaaabbbbbbbbbbbaabaaaaabbabbaaaababaaaaaababbbbbbaababbbbaaaabaabbaabaaaabbbbbaaaabbbaaabbbabbababbabbbbbbbbaabaabbbaaaabbaabbaabbababbbaaaaabbbbaababaaabaaaaababaaabbbbaaabbbabaaabbbabaaaababaaaabbabaaaabbbbaaababbbaabaaabbababbaaabbbaaabbbbabbaabbbbbabaaaaaabbbbaaaaababbbbbbbabbaabaabbbbaaaaaabbabbabaabbbbabbababababbaabbabaaabbbaabbbaaabbbbbababbababaababaaabbbbbabaabbaaaaaabbaaabbaabaaabbbabaababaabaaabbbbaabbbbbbbaabbbaababaaaaabbaabbbaabbbaaaaabbabbbababaabbbbbaaaababbaabaabaabbaaaabaabbaaaaaabbaabbaaababbaaabbababbbbabababbaabbbabbbbbababababbbbabbbabbaabbbaaaabbbaababaababbaabbaaaabbaaaaaaaabaaababaaabbbababababaabbaabababbabbabbbbbbabaaabaabbbbbbbbabbabababaabbabbbaaaaaaaaaabbababbbaaaaaabaababbaaaabbaaababaabbaabbaabbbaaaaaaababbaabaababaabbbbbaabababbbabaaaaabbabbbabaaaaaaaabbabbbaaababaababbbaabbbbaaaaaaaabaaaabbaaaabbbabbaabaababaabaaaababaaababbbbababbbababbbaaababbbbababaaabbababaababaabbbaaabbbaaaabbbaabbabbbabbbaaabbabaaaaababababbbaaabbabbababbbabbababbbbabbaaaaaababbaabbaaabaabaaaaaaabbaaaaaabaaaaaabbababbabbbabaababaaabbbbabbaabbabaaaaabaabbaaaaaababaabababbbaabaaaabbabbbzabaaaaaabbababbabbaabaaaaabaababbaabbaaaaabbaaaababaabaaaabababaaaaabbbbabaaabaaabbbbbbbbabaabbbaaaababbbaabbbaabaababababaabaaabbbabbbbbababaabbabbbabbabaaaabbaaaaaaababbabbbbbaaaabaaaabaaabbaaabaaaabababbbaaababbaaababbaaababbbaabbabaabbbbabbaaaaabbaaaaabbabbabbabbbabbabbaaaaabbababbaabbabababbabbabbaaababaaabbbbaababaaabbbabaaaabbabaaabbababaababbaaaaabbbaabaaabbababbbbabbaabbbabbabaaabaaaaababbbbaabbaaababaaabbbabaaaaabaabbaaabbbbbaabaaaabbaabbabbabbbabbbbababbbabbabbaabaabbababbaaaaaaabbbaaabaaabbbbbaabaabaaababbaaaaaaabbbaabbabbbaaabbabbabaabbabbabbabaaaabbaaababbabbabbaabaabaabaabbaabaaabbbbbaaaababbbaaaabbbbaaaabbbbaaaaaaabaaabababbaaaaabbabbaabbbaabaababbabbbbbabbabaaaaaaabbbabbaaababababbabaaabbbbbabbabababbbabaabababaababbabbabbaabbabbbbabaababbbbaaaabaaabaabbbabaaabbabbaabbbbbbababbbaaabbaaabaabaaaabbabaabbbbaababbbbbbbabaaaaabbbbabbbaababaaabbaabaaababababbbbabbbbaaaabaabbabaaaaababbabbbaababbaaaabaabaabbbaaaaabbbbabaabaaababababaabbbaaababbaaaabaababbbaaabbabbababbbbaabaaabbaabbbababababbabaaabaabaabbbbbbabbaaaaaabababbaabbabbabaaabababbbaaabababaaababbaaaababbaabababbaaabaaaababaaababaaaaabaababababbbabbbababaabbababbabaaaaabbaabbbbbabaabbbbabbbaaaaababbbaaaabbbabaaabbaaaaabbaababbbabaabaabbbaabbabaabaabbababbaaaabbabababbabaabbbbabbabbaabbabaaabaaababbabbabaababbaaaaaaabbbbbbaabbbaaaaababaaabaabbbaabbbbbbbbbaabbabbaabaabaabbabbbaaaabaababbaaaababbbbabbababbabababbbabbbabbbaababaabaabbbbaaaaabbbbbbaabbbabbbbaaabbabbababbbbaaababbbbaaabbabbabbbbbaabababaaabbbaababaaaabbabaabaaaabaabbbabaaaaaaaabbabbaaabaaabbbaaaabbaababaaabaaabbbaaaaabaaabababbabbbbaaabbbaaaabbabbaabaaaabaabababaaababbbaabbbaaabbbbbabbbbbbabbaababaaaaabbbbbaaabaabbaaababababbaababbbaabbbaaaabbbbbbbaaabaaabbbaaabaaabaaababbababaabaabaaaaabaaaaaabababaaababbaabbbaababbaaaabbbabbbbaababaaaaaabaaaababbababbbababbabaabbabbbaabbbaaaababaabaaaaabbababbbaaaabbbabbbbabaababaaaabbaaaababbabbabbbbaaabaaabbbabaaabbbbabbaaaaabbbaabbabaabbbaababbaaabababbbbbaaaaabbabaabaaaaaabbaaaaabbbabbbbaababaaabbabbbabbbbbbbbbbbababaabaaaaabbababbbabbbaababbbbabaabbabbbbaaabbbaaabbbaaabbbbbbbbbaabaabaabbabaaababaaabaabaaababbbbaabbabbbbbbaaababbbabbabababaaaaaabaabbaaabbabaaabbbaaaabbbababaaabbaaaaaaaaabaaaaaabbaabbbababaaaaaaabababbabbaaaabbabaaabbabbaabbabaabaaabbbaaaaaaaabaababbabbbbaabbabababaaaabbbbbababbbbbbabbbaaabbababaaaabaaababaaaabaaabaaabbabbababbabaabbbaabaababbaabababbabbbaabababaaaabbbbabaabbbbaaabaaabbbabababaaaabbaaaababaaabbbbbaababbbaabbbbbaaabaabbaabbbabaabaaabaaabbbabababbbabaabbabbbaababbbaaaaaaabbabbaabbbaaaabbbbabbbbababbbbbbabaaaababbaababbaabbbaaabbbabbabaaaabbbabbaaaababbbbabaabbbabbababbbbbabababaabbbabbaabbabbaaababaabaaabababaabbbbabaababbabababaaabbaabaaaabaabaabaababbbabaaaaaabbabbbbbbabbbbabbbababaaabbbbaabbbbaaaaaaababbbabbaaaaaaabbbaabbbbbabaabbbaaaaababbbbbbabaaaaaabbabbbabaababbaaabbababaabbabbaaaaaaababbabaababaabbbababbabaabbaabbabbbbabbbabaaabaaabaabaaaabaaabbbaaaabbaaabbbbbabbbababaabaaaababaabbbbabbabbbabbbabbaabbabaaabbbbabbbababbbbbbbbabbbbaaababaaababbbabbabbaababaababbaababaaabababaabbbaabababbabbaaaaabaaabaaaabaabaaaaabbbaaababbbbbabbabbbbbbbbbabaabaaababaabbbbabaabbbbbababaabbaaabbbaaababbbbbaabaabaaabbbbbabbaaaaabbaabaababaabaaaabbbbababaaaabbbabababbbbbabbaaabbababbbaabbbbabbbaaaaaabaaabaabbaababaaababbabbbabaabaaaaaabaabbaabbabbazbbabaabaaabaababbaabaabbabbabaaababbaaabbaaaaaababbababbbbbabaaabbbabbbbbaaabaabbabbaababbaabaababaabbbaaabaaaaabbaaabbabaabbabbaabbbbabbbbbabbbbaababaabaabbaaaaabbbbbaabbaabbbaabbabbaabbaabbbaaabaaaaaabaaabbbbbbbaababababbaabbbbbaaababaaabbaaabbaaaaabaababaaabbbaabbbabbabbbbaabbaabbabaabbaaababbaaabbbbaabbabaababaaabbaaaaabbaabababaabbaababbbbbbabbaabbbbabaababaabaabbabbbaaaabbabbabaabbbaaababbbabbabababbbbbbbbbababbbbabbbbbbaaabbbbabaabbbbbbaaaabaaaabababbababbaaaaabbbbaabbaaaabaabbbbaabaaaababbbabbaabaaaabaaaabaaaaababbaaaaabbbbabbabaaaabbbbbbbbbabaaaaaaabaaaaaabbbbabaabbbaaaabaaaababbbbbbbaababbababbabaabbaabbabbababbabaababaabbababbbabbbbbbaabbaabaaaabbabaaaaaabaaabbbaaaaaababbbbbaabbbabbaabaababbbbaaabbbaaaabaaaaaaaaabbbabbabbaaaaaabbbaababbabbabaabbabaabbabaabbbabbbbaaabbbbbabbabbbbababbbabbbbbbbabaaaabbababababbababbbaabbaabbabaaabbbbabbbabaabaaabaaaabaaaabbbbbabbabbaabbabaabbababaabbabaabbabbbbbabbbabababbabbababbaabaababbbaabbbabababaaabbaaaaababbbbabaabababaabbababaabbbbbaabaabaaababaaaababaabbbbaabbaaaaabbabababbbbbbaabaabbbaabaababbbbabbbbaaaaaabbaabbbbaababbbabababaabbabbbaabbaaaaabbbbabbaaaabbbbaaabbabaaababaabbbbbaabbbbbabbbabbaabbabbaabaabaaabbabbbbaaaabbbbbbbbaababbbaabaabbabaabbabbaababbbbbabbaaabaaaaaaabbbbbaaabaaaaaaabaaaaaabbbabbbabbbabbbbaabaaaaababaaabbbbabbbaabababbbabaaaabbabbabbaabbabbbaabbabababbbabaaababbbaaabaabbbbbbaaaaaabbbbaabaaaabbbbaaabbbbbbbbbbaababbaaabbbaabaabaabbbabaaabbaaaaabbabbbbbabaaaabbababbbaaaaaabbbbabbabbabaabbaabbbbbaaabbaaaaaabbbabbaabbbabaabbbbbbbabbbaabaabaabbbabaabbabbbbabbaabaaaaabbbbaaabababbaaaaaaaaaaaabababaabbbaababaabbaaababaabbbbbbbbbbbbabaababbaaaaaabbaabbbabaabaabababaaababbaaababbabbbbbbbaabaabaabbabbbbbaababbaaaabbbabaaaabbbbbbabaaababaaabbababaaaaabbbbbbbbabbaabababaabbbaaaababaabbaabaaababbabbbbababbabaababbabbabbbabbbbabaaaababbabbaabbbaaaaababbbbbbbabaababaabaabbababaabbbaaabaaaabbaaaaabbbbbaaabbaabaaabababaababaabbabbbbbaaaaaabababbaaaabbaabbbbbbabbaaaababbbbaaababbbaaaaababbbbbbbaabaabbaabbabbaabaababaaaabaaaababbabbbbbabbbabbbbabbabbabbbbbabbaaaaaabbaaaabababaaaaabaaaabaaababbababaabaaabbaabbabbabaabbbbaabaabaaaaaaaabbbbabbaabbaaabaababaababbbabaabbbbbaaaaabbaaabbbaaaaaaabbbbbaaaaabbabbbbbbbabaaaabbbaababaababbbbaababbabbabaaaabaabbaababbabaabaabaaaaabbbbbbbaabbbabaaababaaaabbaaaaabbbbbaabbbbbabaaaaabbabbbaabaabaaaaabbbaabaababbbaaaaaabaaababaabbbbbabbabbbaaaabbbaababaaabababaabababaaaaabaaaaaabbaaaabbbbaabbaaabababaaaabaaaaabbababbbaabaabaaaaaababababaaabaabababbabaababbbbbbaabaabbbabbbbbbbabaaaabbbabbaabbbabaabbbbaabbbaaabaabbbabaabaabaaabbaaabbbaaaabbbbaabaabaaabbbabbaabbaaababbaaabbabbbbaaaababbbaabbbaabaabaaaaaababbaabaabbaabaaaabbaaabbbbabbbaabbaaaabbaaababbbaabaabbbababababaaaabbbbbbaabbaaaabaabaabbabaabbaaaaababaabbaaaaaabbbabbbaabaabbbaaaaaabbbbaababbbbabbaaabababbaabbababbababaaaaabbbaabbbbbaaaabbbbaaaabbaabbbbaabaaaaaaababbabababababbbababaabbbbbbabbbaaaaaaabaaabbbbababbbbabbabbbabbbbbbaaababaabaabbaaabbbbababbbbbabababaaaaaabbbabbbaaabaaaaabaabaabbbaabaabababaababaabbbbbaaaaaababbbbbbbbababaaabbaabbababbbaaabaaabbababababaaabbbaababbababbaabaaaaababbababbbbaaabbaababbbbaaaaabaababbabbabbbbbbbbabbabbaaaaaaaabbbaaabababbaabbaaaaaabbbbbabababaabaaababbaaabbaaabaaabbbbbaabbbaabbaabbaaaabbaabbbaabbbaabbbabbabbbaababbaabbbbabbbbaaababbbbaaabbbbbaababaabaabbaabbbbaababababbaababbbbaaababbbabbabbabbbabbabbbabbbbaaaabbaaaaaaababbabbaabbaaabbaaabbaabbaabbbabbbabbbbabaaaaaabbaaaabaabbbaababbbbabbbbaaaabbbbaaaabbbbbbaabaababbbabbbbaabbaabaaabaaaaaabaaaabbbaaabbbabbabbbabbbabababbabbabaabababbaaabbbabaabbaabbbbbaaaaaabaaaaabbbbaabaabaabbaababbabababaabbbabbbabbbaababbbaaabaabbbbabaaaaabaabbaaabbbabaaabaaabababaaaaaaabaababbbbbbbaabababbbbbbbbbabaabbabbbbabaabbbbabbabaaaaaabbbbbbaabbbbaaaaaabaabbaaabbbabbbababbbbbbababbbbbaabababbbabbaabbbbaabbaababbbaababbababaabaaabaaabaaaabaabaaababbabaaaabaabaababbbbabbaaabbbabbbbbbbbbabbaaaabbbaaaaabbaaabbbaabbbaababbbaabbbaaaaaabaaaaabaabbaabaaabaababbbaabbbabbaaabaaabbbaaabaababaabaaabbabbbaaababbbbaabbbaababbaabaaaabaaabbbabaabbaabaaabbaabaaababaabbbbbabaabbaabbabbbaaabaaaaaabaaabbbabaabbaaabbabbabbbbaaaaaabbbabababbabbbaabbbbaabaabaaabbaabaaaabbaaaabbbbaabaaababbaaaaaaabaabaabababaabaabbbabbabaababbbababababbbbbabbbaaaaabbabaaabaabbababbababbabbaaabbabbbbbaabaabaababbbababaaaababbaaabbaaababaaaaabbabaabababbaababbaababbabbbbabaabbaaaabbaabbaabbbbabbbababbbabbabbabababababbbaabbbabbbaaabbbababaaaabbaabbaaababababaabbbbbabaaabaabbaababbbaaaaabbaaaaabababbbabbabbbbbbaabaabbbaaaaaababbabaababaaaaaaaaabbaaaaaabbaabbbaaaabaabbabaababbabaababaaaabaabbbababaabaaaaabbabababbbbabababbbaabbaaababaaabbbababbaabaabaaaababababbbbaaababbbaaaaabaaabbaababbabaaabbbbababbbbaabbaabaabbaababbbbaababbbbaababbbbbbbbbaaabaababbbaaabababaabbbaababaaabbbbababbabbbbbbbbbabbbaaaaababbababbabaaaaabbaaaaaaaabbaaaaaaaababbaababbaaabaabbbabbbaaabaaaaabababbaaaabbabaaababbbaaabaabaaaababbbbabaabbbaabbbaabbaababaabaaaaaabbaaaaabbbbbbaabbbbababbabababbbbabbbabbaababbbaaabaaababbbbaaabaaaaaaaaabbaabbbbbabbaabaabbbabaabbbbbaaaabaaabbbbbaaaabaababbaaabaaaaaabbabbbabbbbbbbababbaabababaaaaabbbbbababaabbaaabbbbaaaabbbabaababbabbabbaabbaaabbbbbbaaabaaaaabaaaabbaababbaabbabaabbbbbababaaaaababbaabaabbbbbbbaabaabaaaaababbbababbababaabbbbbaabaabaabbbabbbbbbbbbaaabbbabbbbbaabbaaabbbbbbbbbabbbabaabbaabbbaaabbbbaaabbbbbbbbaababbbabaabaabbaaabaababaabbbabbbabbabbbbbbabaaaaabbbbbaabbaaaaaaababaababbbabbbaaabababaabaaaaabaabaaababaababaaabbabababbbaaaaaaaabbbaaabbbaabbbaaabaaabbaaababbababbaababaabaabbaabaaabaabaabbbbbbbaaabbbabaaaaabaaaabbbababbaaabaaaababababaaaaaababbaabaabbbabababaaaabbaabbaabaabbaabbabbbaaaaaabbbbbbbbabbbabababbaababbaaabbbabbabbbbabbaaaaabaabbababbbabbaaaaaaabaaaabbbabbaaaabbbabaabababbbbbbbbaaabbbaaabbababababbbbbbaaabbbaabbbbbbabbbaaaaabaabaaabaabaaababbbbbabbbaabbbabaaaaaaaabaabbbbbaaaabaababbbabbaaaaabbbbabbbbbaabaabbabbabaabbabbbbbbababaabaabbbbbbabbaaaababbaaabababbabbbbabababababaaabaababbabbaababbbababbbbbbbbbbabbbabbaaabaaaaababbbababaaabbaaabababbabbaaaaaabbaaabaaababaaababbabbbbbabbbbaabaabbbaaaababaabbaabbbbaaabaaaaaabaaabbbbbabaaabbbbababaaaaabbababaabbaabaaaabababbbbbabbbbaabbbbbbabbbaabaabbbabbbbbbbaabbabaabaaabaaabbbaaaabbbaabbbabaabaabbbbaaaaabbbbaabbbbbbbbaaabaaaaaabaababbaaaabbbbababbaabbaabbaaaabaaababaabbaabbaaaabaaaaabaaabaababbbaaaaabbabbbbbbababaababbbbbabbbbabbbbaaaabbaabbabbaabbbbaabbbabaabbbabaaabbaaaaabbaabaababababbbbabbaaabaaabaaaaabbbabbbaabbbbbabbbaaaabbabbbabaaaaabaabbabbabababaabbabbaabbabbaababaababbabaabbababbbbaabaaabbababbbbbabbababaaaaaabbbabbbbbbabbbbbabababbbbaaabaababbbbabaabbaaabbbaabbaaabaabababaaaaaaabbbbabbbabbabaaaabaabbabababbaaaaabababbbbbbaabbbbbbaabbbbbaabababbabbbbbaaaabbaababbaaaaababbaaabbabbbbababbbaaaabaabbabaabbaaaaaaabaababaaabbbaaaabbbababaabbaaabbbaabbabbabbbaaabbaaaaaabaaabaaaabaabbaabbbbbbaabaabbabaabbaaabbbababbbababbbbbaaababbababbbbabbabbabbabbaaabaabaaabaabaababbaaabababaaaabaabbbbbabbaabbaaabbbababababbbbbabbbaaaaaabaaabbbaaabababbaaaabbbbbabaababbbbbbbaabaaabbabaaabbbbabbbabbabaaababababbababbbaabbabaabbbbbabbbababbabbbbaaaaabbaaaabbbbbbabaaabaaaaaabbababaabbbabbabbaaaaabbbabbbabbabaabbbaabbbbababbaabbaaaaabaabaaaaabbababaaababbbbbabbbabbabaabbaabaaabaababbaaabbaaabbbbabbaabaabbbbaaaaabbbaabbbbababaaababababbaababbbabbaabababbaaabbaabbabbbbbababababaabaabbbbbbabbaaabbbaabbababbbbbbaabbbbabbabaaababaabbbbabbabbaababaabbbbabbbbbbababbbbaabbbbbbaaaababbbaaabbbbbbaabababaabbabbabbbaaabbabbbaabbabaababaaaaaabaaababbbbbbbbbaaababbbabbbbbbaabaabaaaaaababaabaaabaabbaaaabbaababababaabbbabaabababaabaaaabbbaaababababbbbbabababbbbabbbbabbababbbbbbbbaababaabaaaabaaababaaabababababbbabbabaabaabbbbabaaabbaaaaababbbabaaaabbabbaaababaabbabaabbbababbbbbbabaaabbbaaaabbbbaabbbbaabbabbaaabbaababbbbaaabbababaabaaaaaaaaabbaaaabbabaaaaaabababbabbaaabbbbabbaaababababbbaaabbabbaaaaaaabbaababaaabbabaaabbbbaababaabbbabbaabaabbbabbbaabbaaabbabbbbaabaaababbabaabbabbabbabbbaaaaaaaabaabbaabaaabbbbabbaababbbaaaabaababababababbaababaaabaabbbabbbbaabaababababbaaaabbbaaabaabaabaaaabaaababbbbbbbbabaabbbbbbbabbbaaaabbaabbabaaaaababbabbabbbbabaabbbbabbbaabaabaabbbaabaaabaaaabaaaababaababbabbbbbbbabaaabaaaaaaaaaaaababbbaaaaaababbbbbabbababbaabbbbaaaabbbbbbabbaaaaaaabbaaabbababaaaabbbbabbbbabaaabbbaababbbbbaabaaabbbbbbaabaaaaaabaaabaabbaaaaaaaabbbabbbbbbbbbbbbaabaaabbbbaabaaabbabbaabaababbbabaabbaaaaaabababbbaaaabbbbbbbbaaaaaaaabbababbabbaabbbabbbabbabaaaababaaabbabbaabababababababbaabaababbaabaaaabaaaababbbbabbbaaaababbbbbaabbbbbaaaaaabbaabaaabbbaaababbbaababbbabaababbabbbabbbaaaaaaabaabaaabbabbbbbbbaabbbbaabbbaaabbbabaabbbababaabbbbbbaababaabaabbbaabaabaaaaaabbbbaaaabbaababababbabaaaabbbaaabbbbaaabaabbaabaabbababbababaaabbbaaaaaaaaaaabbbababbaaabaaabaababaaaaabbbaabbaaaabaaaabbabbbaaaabbababaaababbbabbbabbbbbbbabbbaabaababbbbaaabbabbbaababbbbabaabbbababaabbabababbbbbbbbababbabbaaababababbabbbbbbbbaaabaaabbbbabbbabbbaaabaabbbabababbbabbbaaabbbbaaaabbbabbaaabaaabaababbbabbbbbbabbbabaaaaaabbbbbabaaaaaabbaaabbbaabaababbbabaababaabababbaabaabbbababbbabaabbaabaaaabaabbbabaaaabababaabaabbaaabbaaabbabababbababbbbababaabaabbbaabbaaaaabbabbaababbabbbbbabbbabbbbabbaabbbbbbaabaaabbbbabbabaabaaaabababbaabbbbbbaaaaaaaaaaaabbabbaabbaababbbbabbaabbbbabbbbabababbaabbabaaababbbabbabaabbabaaabbaababbaababbbbbbbbababaaaabbbaaaabaaabbbbaabaaaaababbbbbbabaaabbabaabbbbaaaaaaaabaabbababbbaaaaabbaabbabbaaaaabaaaaaaaabaaabaabbbabaabbbbabbabaaaaaabaaaaabbbababbabbabaabbabbbbbbababbaaabaaaaaaaaaabaaababbbababbaababaabbabbaabbbbababababbaabbbbabaaaaabbbaaaaaaaababbaaabaabbbabaabababbbbbaaababaabbbaabbaabaabaaaabbabbbabbbbabbabababbaabbbbaababaabbbababaabababbabaaabaabaaaaabbbbbbbabaababbababbbbbabbbaaabbaabbabbbbababbaaaabbbaaabbbaababbbbaaaabbbbabbbaabbaaabbbbbbbbababaabbbbbaaaaabbbaaababaabbabababababbaabaaabbabbaaaaababbbabbabbababababbabbaaaabbaaaabaaabbbabbabbbaaaababbbbabbbbaaaaaaabbaabbabbbbabbbaaaababbbabaabbbabaaaabbbabbbaababaaaaabbabbaaabaaaaababaaabbaababaabaaabbaabbabbabbaabaaaaabaaaaaabbabbbbaaabbaaabbabbbabababaabbabbababaaaabaaabbbbabaabbabaaaababaaabbaababaababbbbbbbbaababbbaaaaabbbbbabbbabbbbbaaabaaabbaaababbbabababaabbaaabbaaaabbabaabbabbbbbbbabababababaababaabbababbbbababbaaaabbbbabbbaabaaaabaaabbbaabbbaabbabaaaabaaaaabbbaabaaaabbaaaababaaaaabbbaabbbbaababbbbbaabbabaaaabbbbbabbabaabaaaaaaaaaabbbaaababbabbaabbaabbbabbbabbbbabbaabbababaaaaaabaaababbbabbbabbbbbababbbabababbbbaaaaaabbaabababaaaaaababaaababbaaabaaabbabaaabbaababbbaabbbabaabaabaabaabbbabaaaaabababaaabbaabbaababbbbabbbaaabaabaaabbbbaabaaabaabaaaabbaabbbbaaabbaaabababbbabbabbabaaaaaaaabbaabaaabababbaabbbbbaaabbaaababbabaaaabbabbbbaaababababababbababbababbaaaabbaaababbbabababbabbbbabbbbaabbbbbbbaabbbaabbbbabbbbbabbabbbbabaaababbaaaaabbbbbbbbbbaaaaabaaabbabbaaabbbababaaabaaababaaabbbabbaabababaababbbbbaaaabaabbabbbbaabbbaabaaaabbaaabbaaaabaaabaababababbaabaabbabaaaaaaaaababaaabbbaaaababbbaaabaabbaaaaabbaaabbbbbbbbabaaababbbbbababaabbabababbbaababaaabaabaababbaababaabbbaaababbaabbbbbabbabbaabbaaabaaabbbbbaaaabaababaabaabbbbbbbabbbbbbbbbbbbbbabbbabbbaabaababbbbaabababaabaababbaaaaabbaaabbaaaaaaababaabaaaaabbbabaabbaaaaabbaabaaaaabbabaabbbbaaaababbababababbabbabaaabbbabbbbbbabbaabaaaabbbbaaaaaaaaaaabaaaaaabbbaaabbaaababaabaaaabababababaabbaaaababbbbaabaabaaababaababaaababbbbbabbabaabbaaaaabbbbaabbaaabbaabbabbaabaabaaaaaaabbaaabaababbbbaaaabbaaaaabbabbbbbbaaaababaabbbaaaabababbbaaabaababbbabbaaaabbbbabbabbbabbabaaababbbbbbbaabaaabaaaaaaabbababaaaaabbbbbbaabbbaabababaabaabbaaabbabbaaaabbabbabbaabaabaaaababaaabbbbabaaaaabababbabbbbbbaaabbbabababbbbabbbbbabaabbabbbbabbabbbabaabababbbbbbbaaababbbaaaaabbababaaabaaaaabbbbabaaaaabababaabaaabbbbbbabbbbaabbbaaabbabbbabbbbabbbabbaaaaaaabbbbbaaaababbabbbabaababbabbabbabbaababaaabaaababbababbaabbbabaabababbaabaabbbabbaabaabbaabbbabaaaabaabaabbabbabbaaaaaabbbaababbaaabaaabbbaabaaaaabbbaabbaabababaabaaabbaabbaaaabbbbabbbaabbbababbbabaaabaabbbaababbbbbbaaaaaaabbbbabbbababaaabbaaabaaaabaababaabbbbbbbbbbbbaaabbbbbaaaaabaaaabbbbbbabaababababbaaabbbbbbaaabbaabaaabbaabbaaabbbbbbaabaabbbaaaabbaaaaabbbbabbaabaabbabbbbbabbabaaababaabaabbaaababaabbbababaaaaaabbaaabbbbabbaaababaaabbabbbaabaaaabbbabbbbabbababbbababbbbbababbbababaaaaaaabaaababaaabababbaaabbbbaaabaababaaabaababbbbaabaabbaababaaaabaababbabbabababbababbabababbbabbaabaaaaababaaabbbbbbbaaabaaabaaababaaabbbbbabbaaaaaaaaababbbbbbaabbaaababaabaaababbbbaaaaaababaababbaabbbaabbaaabbbbaabbbabbbbabaaabbbbbbabaabbbabababbbaaaabaabbbabbabbaababbbbbaababbbaabaabbaabbaabbbaababababaabbbaabbaabababbabbfbabbaabbbabbbbaaaaaaabaababbbabbbababbabaaababbaabaaaaabbabbabbaabbbbbbaabaabaabaaaabbaabbbabbaaaabbabbbabbaaababbbbaaabbabbbababaabaaaaabbabbabbbbaabaababbaababbabbbbaabbabbbbababababbbbbaaabbbaaabababababbbabbbabbbbaabbaaaaaaaabbaaaabababbbababababaabaabbabbabababaaaabbaaaabbbaabbabbabababaaabbbbbabbbaababbaabbbbbaabaabbbaaaababababbbabaabbbaaabbbaaabaaabaabbabbabbababaabbabaaabbbabaaaabbbaabaababbbbbaabaaaababbbabbbbbaabbabbbabbbbbbabbaaababbababbbaabaaaabbaaaabbaaaaabbbabaaaabbabbbbbababababaaaabbaababbbaabbbaabaabbbaabbbbbbaaaabaabababbabbabbaaabbaaaaaabaabbbaaaabbabababaaabbbaaaaabaabaaabababbbaaaabbbaabbbaabaaaababbabababbbaabaabbabbabbabbbaaaaabbbaabbbabbbbbbbabbaabbbbabababbbabaaabababbbbaaabbbaabbaaaabaaabbaaabaabbbbbbbaaabbabbbbbaaaabbbabaaaabbaaaabaababaabaababababbbbbababbabbaaaaabababaaabaabaaaabaaabaaaababbaabaaaababaaaaaaabbabaabbabababababbabbbaabaabaaabbbabbaaabbbaabbabbbbaabbabaaabaabaabbabaababbababbaabaaaabaaaaaaaaaabaabbbabaabbbabaabbbaababbabaaabbbbaabaaaaabbaabababbbbbaaabaaababbabbabbabbaaaabaaababbbabaaaaaabbbbabbbbbbabbbaaabbaaaabaababbabaaaabbaaaabaabbbaabbbabababaaaabbaaaabbbbaaabbbbabbaaabbabaaabababbbabbababaabaabaabbabbabaaaabbaababaabbababbaaabaabababbabbaababbaabbabaabaaabbaababaabbaaabbbaabbbbaabaaababaaaaababaaabbaaabbbabbbaabbaaaaabbaabababbabbbbbbbababaaabbbaaaaabbabbabbaabbabaaaabbbaababababbbababbbaabaaababbabbbbbaabababbbbbaababaababbabbbaababbbbababaaaabbbbabbbbababbaaaaaaaaababbbbbbbbaabbbbaaaaababbabaabbbaabbbbababbaabaaaaabbabbbbbbaaababababaaaaaabaabaababbbaaaabaabbaaabaabbaaabbbbbbbbaabbabababaaababbaabaabaaaababbbbabababaaabaaaaaaabbbaaaabbbbabbaaaaaabbbbaababaabbabbbbabaababbbbbbbabbaabbaaaabaabbaabbaaabbbababbbbbbaabbabbbaabbabbbbbaabaabbbbabbbbbbbabaaaaaabbaabbbbabbbaaabaabaabbbbaaaabaabbbbbababbaabbbbaabbabbabbaabbaabbbabbaabaabbaabbababbbbaabbaabaababbbaaaaabbababbababbbbabbbaabaaabbaaaaabaaaabababbbbaaabaabaaabaaababaabbbbbbabbbbbabbaabababbabbbaabbbababbaabbbbabaababbabaababbababbaaabbaaabaaaabbbaaabbabaaabbbaaaaababbabaaaabbabbaabbbaabaabbaabbaaabbbbbabbaaaabbbabbbbabbbbabaabbabbabababaabaaaabaaabbbbbabababababaaaababbaaababaaaaaaaaabbaaabbaaaabaababaaaaabaaaabbbbbbbabaaaababaabbaabbababbabaabbaaaabaababbaaabbbabbbaaaaaabbabbbaaaabbbbbbaaabbaabbabaabbabaaababababbbbbbbbbaabaabaaababbbbbbabbbbabbbaabbbbbabaabbbabbbbbbabaababaabaabaabbbabababbbbbaabaababbbbbbbaabbabaaabbababbbbbbaabbaaaaaaabaabbaaaaabbabbbbbababaaaabbaabaaabaababbabbaaabbababbabbaaabababaaaababbaabbaabaaabbbabbbbaabbbbabababaabaabababbbaabbabbabbabaaaaabbbbaaabbbbaaaababbaabaaaaaaaaabbaaaaababaabbbbabbbabababbbbbabbabaabaaaabbabaabaabaaaaaabbbabaaaaabbaabbaaabbbbbaabbabaaaaabbbabbbbaababbabaaabbbaababbbbbbabaaabababaababbbbaabaabaabaababababaaaabbbabbbabbaaaaaabbbbbbabaabaaabbbbbbababbbabbbaabbbabaabbababbbbbbbbbbbbbaabababbbbababaabbababbaabbaaabbaabbbbaaabbbaaaaaabbaaababababbaabbabbbabbbabaaabbbbbaabaabaababbabbbaaabbbbabaabbbbaabbaabaaaaabbaaababababaaaabbbbabaaaabababaaaaabaabbaaababbbaaaabaaaaaaabbbaaaababaaaaaabbaaaaaaaabaabaaababbbabbbabaababababbbabaabababbbaaaaabaabbabbbbaaabababaaabaaabbbaabaababbbbabbaabbbbbbaabbabbbbbbbbabbaababaabaabbaaabbbaababbbabbbbaababbbaabaaabababaabbbbbabbaabbaabaaabaaabbaaabbbbabbbabbbbabbbbabbbabbbbbbabbabbbbbaabaabbbbbbaaaaabbbababaababbbaaaaabbaaabbbaaabbaaabbaaabbaabbaaaaabaaaabaabbaaabaabaaaaabbbbaababbaabbaaaabaabbbbabbbbaabbaabaaabaabbbbbbbbabbbabaabaaababababbbbabaabbaabbabaabbaabbbbababababbbaabababaaabaabbaaabaabaabbbababbaabaababaabbbbabbabbababaabaaaaaabbbaabaaabbbaaaabbbbabbabbbbaabaababaaabbbbabbbaaababbaababbaaaaabbabbbabbabaabaaaaaaaabbbaabababbbbaaaabbbabababbbaaabaabbbbbbaabaabbbababbbaaabaaababbbbababbbaabababbbbbabbabbaaabababbbbbaabbaabbbabaabaaababaaaaaabaabababaabaababaabbbbbaabaaaabaaaaababbaabbabaababbbbbbbabbaaaaaabbbabaaabbaabbaabbabbaaababaabbbaaabbabbbbbbbbbabaaaaaababaabbbbabbbbbbabaabaabaaabaababababbbaaabbabbbbaaabaabbbbabbaaaabbbbaabbabbbbbabababbbabaabaabbaabaabaabaabbbbbbbbabaabbaabbaabaaabbabaaabaaabbaababbbabaaabbbaaabbbaabbaaababbbabababbbbbababaaabaabaabbbbaaababbbbabbabaabaaabaaaababbabaabaababaabbbbabbaabaaabaababaabbaaaaababbbbababaaabaabaaabaabbbbababbbbbaabaabbaaaabbaababaabbbababbaaaabbbaabababbabbabbbbaabbababaaaabaaaabbaaaaaabababbbaabbaabbabababbabbabbabbabbabbbbbabbabaabaabbaaaabbaaabbabaabaaababbaabaaaababbabbabbbbaaaaabaaabababbaabaaabbabababbabbbbbbababaababbabbbbaabbaabaabaababaabaababbbbbaaaababaabbaabaababbababbbabbaaababbbbabbabbbabbaabbabbbbbaabbbbbbaabaaaaabababaabbaabbaabbbbabaabaaaabbbaabbaaaabababababbaabaaabaaabbbaaabbaaaaabbaaabaabbabaaaabbbbaaabbbbaaaaaabbaababaababaaababaabaabbabbbaaaabababaabbaaabbbaabbbabbabbbbbaaaababaaabbabbbbabbabbaabbabbbbaaabaabaabbbaabbbaaabbbbababbbbaabbaaaabbabbabbababaaaaababbaabbbbbbbbbbbaabbaabaaaababaabbbaaabbabaabbbbaababbaaabaababaaabbbbbbbbbbababbbbbbabbabaaaabbaaaaababbababababaabbaaabbbbabaabababbabaaaaabbbabbbbaabbabaaaabaaabaaababbabbaabbabaababaabbbabbababaabbbaaabababbbbbabaabaabbaabaabaaabaaaabaababbabbbabbaabaaabbbabababbaaabbbabbbabbbbabaabaaaaaaaabbabbbbbbbbabaaaaabababababbbabbabbbabaaabaaaaaabbabaabaaababbbbaaabaaaabbaaababbabbbbabbbabaaababaabbbbababaabbabbaaabbbababaaabbaaabababaabbabbabbbbaaabbaabaaabbbaabbbbbbababbabaaabbaabbabababbabbbbaaaaabbbbbbbbaababababbabbaaababbbbaaaabbbabbaaabbbbbabbbbbbbbabbaaaabbabbaaaabbbbaaababbbbaaabbabaabbbabaabbaaaabbabbaaabbaaaaaababbaabbabbbbaabaaaabbbbbbbabbbbbbaaaabbaabbbbaaabaaabaababaaababbbbbbabaabbbabaababbaababbaaaabbabbabaaabaabababbbabbbabaabbaabababaaaabbbbabbabbabaabbaabbbbbbaabaaabaaabbbabbababababbbaababbabbaabbaaaaaaaaabbababbabaabbbbaabaaabaabbababbbbbaabaabbbaaaaabbabaababbbbabbbaaaaabaaabbabbbabbbababaaaababbaababbbabaaaabbbbbaababbaabaaaaababaababaabaabababbbaaaababaaabaaabbabababababbbbaabbbbabbaaabaabaaaaaabbabaabaabaabbbbababababbabababbabbabbbabbabbbbaabaababaaabbbbaababababbbaaaababbbbaabbabaaabababaaaaababbbaabbabbbbbbaaaabaaaabbbababbbaababaabbbabaabaaaaaabaabbaaabbaabbbbbababbabababbabbbaabbbababbbbbbabbbbbaabaaaaabbbabbaabbaaabababaaababaaabababbbaabbbabbbaabbababbaabaababbaabbbbaaaabaabaaaabbbabbabbaaabbbaabbabbbbabaabbbaabaaababbbbabbaaaaabbaabbbbababbbaabbbbbbbbaabbabbabbbbabbbbaaabababbaababbbbbbabbaaaaabbabaababbbbabaabbbbbabababbabbbabbbabbbbbbbbbaaaabaababbbaaaaabababbbbbaabababaabbbaaaaabaaabaaaaaabbbbabaabbbbabbbbaaaababbaaaaabbbbababbbaaabbaabaaaababbabababbbbaaaaaaaabbaaaabbaababaaaaabaaaabbbabbaabbabbbbbbabbabaaabbbbbabbbaabbababaaaaabbbabbbbbaaaaabaaaaabbaabbabbabbbababaabbbabaaabbbaabaabaabaaabaabbbabbbbbaaaaabbbaabbabbbaaaaabbbbbbabbbbaabaabbaaaababbbbabbbabbabbaabbbabaabaaaababbaaabbabbaaabbaabbaaabaaabbaabbaaabbbababbbbabbbbbbabbbbbababbabaabababaaaaaaababababbabaaababbbbbbbbaaababbabaaabbaabbabbaabaaabbbaabbaaabbaaaabbaabbbbbaaabaaaaabaabaaabababaabbababababbaaabbaaababbababbbabaaabaaaabbaaababbbbabbaabbaaabbabaabaabbabbabbbbabbabaababbbbaaabbabbbbababbabbababbbababaaaaaababbaababbbabaabbbbbbbbaaabbbaaaaaabaabbababbaaaabbbabaabbbbababbbababbaabbaaaaabbaaabaaaabbbbabbabbabaaaaabaaabaaabaabaaaaaabbabaaabbbbabbbbbabababbbaabaabbabaabaaaabababababbbaaabbaaabaabaabaaabbbbbbbaaabbbbabaababbabababababbbbabaabaabbabbbbbbaaaabaaaaaabbbbbabbbabbbaababbbbbaaaaaabbbababbabbaaabababbbaabbababaabaaaaaaaabbabbbbbaaaabbbaabaaaababbbaabaabaaaabababbabbbaaaaabbbbbaabaaaaaaabbbbbbbaaaaabbbabbabbbbbabababbbabbbabaaabbabaabbabbaaaaabbabababbbabbbaabbaabaabbbaaababaabbbabababbbababaaaaaabbaaaabaabababbbbabaabbbbbabaabbbbbabbabbabbabababbbbbababababbababbabbbaabaabbbaabbbbbabbababbaabbaabbbaababbaaabaabaaababaababaaabaaaabababaabbabbbaaaaaaabbaabaabbbababbaaaababaabbbbbbabbaabbababaaabbbbabbabbaaabbbbbaaabbbbabaaabaababaaaabaabaabbbabbabbbabaaabaaababbaabaabbababbbaaabbbaabbaaaababbbabbaaaababbaaabaabaaabbbbbbaababbaaabbbbbbbaaaabbaaabbbbbbabaaaaaababaaababaaaaaaaabbabbbaaabaaaababbaaaaababaaaaaababbaaabaabbbabbaaabbaaaaaabbabbbaaaabbabbabbaabbaaaabbaaabbbaabbabbabaabbabbbbbbbaabaaabbbbbbabaaababaababaaaaabababbababbbaababbabbbabbaaaabbabbbaaaaabababbbababaaaabaabaaabbbaaaabbaabababaabbbbabaababababbbabbbbababbaababbaabbbbabaaabbbabbaabbababaabbabbabaaabbbaaababaabaaabbabbbabbbabaabbbbbbabaabbbbaababababbbbbaaabbabababbabababaaaaaaabababbabbbababbbbaaaaababbbbaabaaaaaaabaaaabaababaabaabbaaabbabbaaabbbbbbbbbabaaabbababaaaabbabbbaaaaababaaaaabbaabbabbabbabbbbabbaaabaaababbbaababbbaabaaaabbaaabbaabaabbababbbabbbbbabbaaabbbabbbbbbbbbababbbbababbabaababaaaaabaabaaaaaaaabbbbbabbababbaabbaabaabbbbabbbaaaaaabbabaaabaaaabbbabbaabbbbbbbbaabaabaaaabababaaabbaaabbbbbaabababbaaaaaaabbbbabaaaabaaabaabaaaababaaaaababaababbbbbbbabbabbabbbabbbbbbbaabbabbababaabbbbabbbbbbabbababbbbaaaabaaabaaababaaaaaaabbabbbbaaabaaaabbaaaaabaaabbaabbababaaabaaababbbbabbbbabbaaabbbbbaabbaaaabbabbaaaaaabababbbabbaaaabaabababbaabbabbbaabbbbbabababbabababaabbabaabbbababbbbbabaaaababbaabbabbaabbabbbbbbabaaaaaaabbbbbbbaaaabaaaaabbabaaaaabaaabbbbbababbabaabaabababbaaaabbbbbbbaakbaabaabbbbbbabbbbabbbabbbbbbbabaababaababaabaaababababbbabbbabbabaabaababbaaababaabbabaabaaabbbaabbaabbbaaabbbaabbabaabbaababaabbabbabbabbabbabbabbbaaababaaababbbbaabaaaabaabaabbaabbaabbbbbbbaaabbaaabaaababaaabbabaaaabbbabaabbbaabaaabbbbbbbbababbbbaaababaabaabbabaaaaaaaaaababbbbbababbaabaabbabbabbbbbbaabaababbaabbabbababbabbaababbabaabaaabbabbaabbabbabbaabaaabbaabbbabbaaabaaabaabbaabbbabbbabbbbbabbbaaaabaabaabbbababbbbbaaabbbababaabbbbaaabaabbbbabbbbabaaaabbbbabbbbaabbbbbbbbbabbabaaaabaabaaaabaabbbbbbaabababbabaaabbabaaaaabbbbbbbbbbaaabaaaabaabaabbbabaaaaabaabaaabbbbbbbbababbbaaaaaaaabbbaabbabbaabbbabaaabbbbbabaabbbbaaaaabbaabababbbbabaabbbabbabababaabbbabaaabbbabbabbbabbbbaaabbbabaabbbbaabaababababbaaaaaaaaababababaaabaabababaaaabbababbababbabbbabbaaaaabbabbaaaaaaabbbbaabbaabaaaababababbbbbbabaaabaabababbbbaaaababbbbbaabaaaabbabaabbaabbbbbabaabbabbabaaaabaabbbbbbabaabaababbabbabaabbbabaaabbbaabbabbaabbbaaabaaabbbbbabababbabaaabaaabbbababaabababbbbaaaaabababbbbabbaabbbaaaabaabaabaababbaaaabbabbaabaaabaababbbbaabaabbbbababbabbaabaabbabbabbbbbaaabaaaaabaaaabbbaabaababbbbbbbbbabaaaabaababbaabbbbbbabbabbaababbbbbbbaabbabbaabbbbabbbbabababaaaaabbbbbaaaaaabbabaaaaaaabababbbbaaaabbbaabaaaaaabbababaaaaaaaaaabaabaabbabbabaabaaaaabbabaaabbbaabbabbabaaabaaabbabbaaaaaabaaabaaabbbbaababababaabbbaaaabaaabbbabbaaabaaabbaabaaabaabbbabbaaaabaaaaaabbbaabbbbbabaabbbbaaabaaababbaaababbaabbaabbabbbbbbbaabbbbabaabbbbaabbbbbabbbabbabbbbabababbaabaaaabbabbbaaaabaaaaaaaaaabaabbbbabbbaabbbbbbabbbbbbbbbbaabaaabbaabbbbaababbbabbbbbabaabbaaabbbbbbbaababbbbbababbbbbabbbaaaabbbabaababaaaaaababbaaaaaababbbbaabbabbbaabaabaabbaabaaabbbbaabaabbbbaababbaaaaabaabaabaaaabbabbbbbabaaababbbbbaabaaabbbbaaaabaaaaaabbabbabababbaabaaababbbabaabbaababaababaaaaabbbbaaabaaaaabbbbbbbbabaabbabababbbabbbbbbbbbbbbabbbaaabbbaabaabaaaabaabbabaabaabaabbaabaaabababbbabbbabaaabbaaabababbaabbbababbabbbbabbbaaaabaabbbbbbababbabbabbaaababbaababbbaabaaabbabbaabbbabbbabbbaababaaabaaabaabbabbaabbbbbbaabbbbbbaabbabbaaaaababbbabaaabaaabbaaabbbbbabbbaabbbbaababbababbaaaabababaabbbaabbaaabbbaabbaabaabbbbbaaabbaaaabbaababaaaaaabbbabaabbabbabbababbaaabaababababbbbbbbbbbbbaabbabbabbaaaaababababbbaabbabbabbabaabaababbbbaabbababbaaaabaaababaabbbbbaaabbbbbbabbababbabbbbaaaabaabbaabaabbabbabbbabaabaabbaaaaabbaabbbbbbbbbbbbbbbbbabaabaabbbabaaaababbaaabaabbbbabbababbbbbbbbabaaabbaababbaababaaaabbabbabbabbbbbbababbaaabaababaaababaabbbbbbbbbbbabbbabbabbaabbbabbbaabaaabbabbbaabaaabaaabaabaabbbaaaaabaaaabbbbbabaaabbabbaabbbabababbbbababbabbabbabbabbaaaababbbbabbaaaabababbabaabbbbaabbbbaabbaaabbbaaaaabbababaabaaaaabaaaaabbbbbbabbbaabbbabbabbabaaaabaabbaababaaababbbaaaabbaabbaaaaaaabbaababaabaaababbaabaaaabbaababbbabbabbbbbaaabaabaaaabaabbbabbbbbbbaaaabababaaabaababaaaaabbaaaabbaaaabaaaabbbbbbbaaababbabaabaabbbbbbaaaabbbabaaaaaaabbbbbabbbabbbbaabbbaaabbbabbbbbaaaaababbababaabbabaaabaaababbbbbbbabbabaabaaaababaaaabbaabbababaaaaabbbbabababbbbaabaaaabbabababbaaaaaaabababbbaabaaaabaaaaabaabbbaaabbbbbbbababbabbbbabbabbbbbababbbabaabbbbabbbbaaaaabbababaabbbbaaababaaaabbabbabbbbbabbaabbbbabbbbbabbaaaaaababbbbbabbaabbbabbabbababbbaabaaabababbabbbabaabbbaabbabaaababaabbabbbabbaaaabaababababababaaaabbbaabaaabaabbabbaabbabbaabaaabbabbbababbbbabbbabaaababbbabbbbbabbaaabababbaaaaaaaabababbbaaaaabbaababbbaabbbbaaaababaabaaabbaababbabbabbbbabbbabbbbaaaaabaabbbabbbbaaaababbabababaaaaaabaaababbaababbbabbaababbabbabbaaaabbaaaabbaababababbbbabaaabbbaaabbbabbaabaababbbaababbaabbaabbabbbbabaabbabbbabbababaababaabbabbbabbbbaabbabaabaabaaaaaabbbbbbabaabaabbabaabbabaababbaabbabbbabbabaaabbbaabbbbaaaaabaabbaabbbaabbbbaaabbaabbbbbabababaaabbaabbabaaaabbaaaabbabbbbaaaaababbbababaaaaaabbbaaaaabbaabababbbbbbbaabbbbabababbabbababbbbbbbabbbbbbaaaaaaaaabbabaababaaababbbabababbaaabbabbbbabaabababbbaaaaaabaaaaabababaabbababababbbabababaaabbbabbbaabbababbabbbbbaabbbbaababbabaabbbbabaaaaaabbaabbabbababaababaaaabbbbbbbbbbaaabbaaababababbabaaaabbabaaaaabaaababbabaabbbababbbaabaabbababbababbbaaaabbababbaabbaabaababaababbbababbbabbabaaaabbbbbbabaaaaaaabbbbbbaaabaaaaaaabaabaabaaabaabbaabababbabbbbaabaaabbbaaababaaaabbbbbaaaaaababbbbabaaaaaabbbaaaaabbababaabbabaaabbabaabaababbbaababaabaabaababbbbbaabbabaaabbbaabbbbaabbabbababbabbbaabbbbbaababaaaaabaabbbbbabbaaaabaabbabbbaabababaaababababababaaaaaabbaabbbaaababaaabaaaabbabbbbabaabbbbbbbaaabbaabbbabbabbbbaaababbbababababaaabaababbabaaabbabbababaaabbbbababbbababbabbaabbbabababaaabaabbaabaabaabbbbabaabbbaabbbbaaababaabaaaabbabaabbbaabababbabbbbbbbbaaabbababababbbababbbbbbabbbababaababaaaaaaaaabbbbaabbaaaaabababbbbabbaaabbababbbaaaaabbabbabaabbabaaabbbaabaaaaababbbbbbbabbabababaaaabbbaabbbbaabbabbbaaaabbaabababbaabbababaaababbbaabbbbbbababbaabbaabaaaabaabbaaababbbbabaaabaaabbabaaabaaaabaababbaaabbabaabaabaabbbbabbbaaaaaaababbbbbaaaaaabbbbaababbabababbabbaabaaaaabbababbbbabbbabbaaabbbbaababaabbbbaababbbbabaaaabaaabbbbababbabaaabbabaabaabbabbbabababaabbababbbaaabbaabbabbbabaaaaaaabbbaabbaaabaababbbbaabbbbbbbbabaabbbabbaaabbbabbbbbbaababbbbbaaabaabbabaabbbbbaabbbbaaabbbbabbbaaabbabaaabbabaabbbbaababbababbabaaabbaaabaaaaaaabbbabaabaabaababaaaabaaabababbabaaabbbbaaaabbabbbbbbbaaaaababaabaabaabbbaaabbbbaaaabbbaabaaabbabbbabbaaabbbababbbbbababaabaaababbbaaababbbbaababbbabbbbbaaaababaababbaaabbabaaabbbaabbaababbabaaaababaabbaaaabbaabbabbbaaaaaababbbbbbbabaaaabaabbbbaabbababbababbaabbbabaababbabaaabaaaaabaabbbabbaaabbbaaaabaabbaabbaaabababbbbbbbbabaaaaabaabbaabaaabaabbabaabbbbabbabbbaabababbbabbababaaaabaabaabbaabbbbbbaaabbaabbbabaaabbbaaaababaaaababbbbaabababbbbaaaaabbbbbabaabbabbaaaaababbabababbabbbaababbbaaaaabababbbbaaabbbbabbaabbabaaaababbbbaaabbbaaabaaabaabbaaabaaaaabaabbbbbababbaabaabaaaabbaabababbbaaaabaabababaabbaabbaaaabbbbababaaaabbbbbbbabbabbaabbababbbabbabbabababaaaaabbbbbbaababababaabaaababbbbbbbbbaaabaabbbbbbbbabbaaaaaaaabbbbbaabbbbbbbbaabbbbbababbaabbbbabaabbabababbaaababbbbbabaabababbabbaabbbaabbaabbbaabbbbabababaabbbbababbabababbbababbbbbbbbabaaaaabaaaabbabbabbbabaaabbaaabaaaababaabbaabababbbababaaabbbbbabbaaaabbbbaaabababbaaabaabaaaabababbababbbabbaababaababababbbabbabaababbaaaaabbabaaaabaabbbbaabbaabbaaaaabaaaaaabaababbabbbababaabaaaaaabbaaabbaaaaabababbabbbaabbabbabbabaaaaababbabbabaaaaababbbaaaaababaabbaaabaaaababbaabbbaabbbabbabbaabbbaabaaabbaabbbbaaabbbaaaaaabaaaabbabaabbaaaaabbbbabbaabaabbbbbabaaabbbababaaaaaaaabbabbbbbabbabbaabbaaaaabbbaabbbbabbabbbaabaaaababbbbaaabbaababbbababbbbabbbbabaabaabbaaaaaaabaabaabbaaabbbababaabaaaababaabbbbbbbabbbaabbabbbbbbaaaabbabbbabbabaabbbbaaaababbbabaabaabbbbaabbbbaaaababaaaabaaabbbababaaababbbaaaabaaabbaaaaababaababaaabbabbaabaaaabaabbaabbabbabaaaaababbaabaababbbabababbabaaabbaabaabbababaaabbbabaaaabbbababbaabababbabababbaabbbbaaababaaaaaaaaababbbbababbabbbaaababaabbbbabaabaabbbbbaababaababbaaaabababaababababbbbbaaaabaaaaabaababbabbabbbbaabaabbbbaabababbbbababaababababbbbbbbaaabaabababaabbbbbaabbbbbaabbaabbaabbbbabbabaababbaaabbbbabaaaababbabbaaaaaababbaaaababbabbabbbabbbbabbaabbbbabbababbaaaabababbbaababaabaaaaabbbbbabaaabbaabbbbabaabaaabaababbbbababaaabbbbaaabaababaabbababbaaaababbbaabbaaaabbabbbabbabaabbbaaaabbbbaaababbaabaaabbbabbabaaabbbababbababaaababbaabaabbababbbbbbbaabaaaabbabbbbaabbbabababaababbaabbaababaabbbbaabbbababaabbababbbbabbbbabaaaabbbaaaaaababbbbababbbababbbbabbaaababaabbabababbabbababbaaaabaaaaabbbababbbaaaaababaabaabbabbbbaababaaaaaababbaaaaabaaaabaaabaaaaabaabbabaabbbbabaaababaaaaaababbbababbabbabaababbbbbbaaaaaabaaabbbabaababaaaabbbbabbaababbbaababbaaaabbbbabbabaaaabbbbaababbaaabbbaaaaaabbbaaaababaabbbbbababaabababaaaababbabbbbbabbababaabbbabbaababbbabaabbbbbabbbbabaababbaaaaabbaaababbbbaaabaabbbbbaababbabababbabbaaabaaabbaaababbbaabaabababbabaaabbbababaababaaaaaaaabbbbbbabbbbbaabababaaaabaaaaaaaaaaabaaabbababbbbabbababbabbbabbbbabbbbabbbaaabaabaaababababaaabbbababbbabababbabaaaabaababbaabbabbbbbbbababbbaabaaabbabababaabbabbbaabbababbababbabaaabaabbbbababbbbaaabbaaaaaaaabbbbbaabbabbbaabbabbbababbbaabbbaaaaabbbaaaabaabaaabbabbbbaabbbbbabbabbbbabaaaabbaabbabaabaaabaabbbaababbbbabaabababababaabbabbbbaaaaaaaaaabbbabbaababbbaabaaaabababaaaababbbabbbaaabaabaaabbbabbbbbbabaabaababbaabbaaabbaabbaabaabaaaabbabbaabbbbababbbaaaabaabbabababbabbabaabbbaabbbabbaabaabbaabbaaaaaaabbbaabbaabbbbaaabbabbbbbbaaabaaabbbbabbbbaaaababaababaaabbabbbbbbaabababbbbabbabaababaaaabbababbbbabbbbabbbbbbbbbbaabbbbaaabbbbbababbbbababbaababababbabbaababaaaabbaabbabbbabbbbaabaaabbbbbbabbaababbaaaaabaaaababbabaabaaabaababaabbaabbbabbabbbabbaabaaabbaabaabbbababaaabbbbbaaabbbbabaabaabaabbabbababaababaabbabaabaaababbbabbabaaaaabbbaaaaaabbabbbaaabbabbbbbbabbaababbbbbaaabbabaabbaaaaaaaababbaabbaabbabbaabaaaaabaaaaaaaabaabbaababaaabbaaaaabbbabbababbabbabbbabbbabbbaaaaaaababbabbbabbbbbabbaabaaabbbababbbaabbbaabaabaaaaabaaababaaaabaabbbaaababbaabbbaabaaabbbbbbaabababbababbaabbbabbbabbbbbbbbaaaaaaabbbabbbabaaaaababaaabbbbababaaabbbaababaababbabaaaabaabbbababaaaabbbaaaaabbaabbbabbaabbabaaababbbbababbaaababaabaaababbbbaabbaaabbbbbabaaababaaaabbabaabaabaaaabbbaaaaaaaabbaabaabaababaabbbbbbaabaaaabbaabaaaaaaabbabbabaabaaaaababaabbbabababaabababbaabbaabbaaaababbbaabababababbabbaabaabbbaaaaabbaabababbbbbbababbbaabbbaabbaabbbababbbbaabbbbabbbaabbaababbbabbaabbbababbbbaaaaabaaababaabaaaabbaabaaaabbbbaabaaabbabaabababbbbbaaaaabbabbbababbaababaabbbababaababbbbaaaabbbbbabaaabbababbbabbbabbaaaabaabbaababaaaaabbabbbbaabababbabaaabaabaabaaababaabaaaaaaababaaaaabbabaabbbbbaaabbbababbbaaaabbbaabaaaaaaaaaaaaaaaaabbababbbbabbbbbbbaaaabbabbaababbbaabaabbabbaabaaabbbbbbbabbababaaababbbbaababaaabaababbaabbaabaabaaabaabbbaababbabbabbabaababaababaabaabbabbabaabbaaaabbbabaababaaaabbbabaaababbbbbbbbabbabaabaabaaababaabaaabbbbaabbbaaabbbaababbbbaaaabaaababbabbaaabbbababaaabaaababbababbbaaaabbaabbabbabbbaabbababababbabaaaabbbaaabbaaaabbbbbbabbbabaabbabbaabaababbabababbbaabbbaaaaaabaabaaaaaaaabbbaabbbbababbbbbaaaababbbabaaaabbababaaabaaaabbabbbbbababbbaabbabbbbbbababbbabbabbbbbaabaabbbaaaaaaaaaababbbbabbbbbababbaaaaabbaaaaaabbbabaaaaaaaaaabaaabbaaabbabbbabababaaababbabaaaaaabababaaaaabaabaaabbaabbbbabababaabbbbbaaaaabbabababbbbababbabababaaaabaababbbbaababaaaabaaaabbaaabaaaabbaababbabbbbbbbabbbbbabbababaaaaababaaaaabbbbbbbabbabaabbbbaaababababbbabababaabbababbbaaaaabbbaabbabbbbbaaabaabbbabaabbabbabaababababbababbaaabaababaababaabaaababababbbbbbbbbaabbaaaababaaababbbbbbbbbaaabbaaaaaabbaaabbbabaabaaaabbbabbbabbabbabbaaababaaaaabaaababaabaabbbaabbaabaababbabaaaabaabaaababbaaaaaaababaabaaaababaabbaaaabbabbbabbbabbbaabbabaabbbabbabbaaabbaaaaaabbbaabbbbabbabbbabbbbbbabbbbababbbbbbbaabaabaabbbaabbaababababbabbaabbabbaaabbbbbaabbbbbaaabaabbbababbbaabbaaaaabaabbaababbbaababbbabaabbbbaabbbabbaaaaabababbbbbbabbaabbbbabaaabbbabbbbbbbabbaabbbbaabbaaaaabbbbaaaaaabbbbaaabbaaabaaaabaaababaabbaabbaabababaaaababbababbbabbaababbbbaabaaaaababaaaaabbabaababbaabbbabbaabbabbbbababbbabbabbbaaabbabbaaabaaaaaaaababbbbbbabbbabbbaaabbabbaaabbaaaabbbababbbbbbaaabbbaabaaababaabaabbbababababbabbbaaabbbabbbaabbabbabbaaaaabaababababaababababbaabbabbababaabaababbbabaaabbbbbbbbababaaababaaababaaaababaaabaaaaabaababaababbaabababbaaabbaaaabaabbaaaaaaaaaaabababbaaaaaaaaaabsbaabaabaabbbbbbbababbbbabbbabbbabaaaaababbabaabbabbbaaababbabbababbbabbabababababababbbababbbabababbabababaaabbbababaaaaaabaabbabaaabbaabbbbbbaabbbababbbbbbbbaaabbaababaabbbbbbaaabaabababaaaaabbabbbbababbbabaabbbaabaaabbabbbaabbbbbbaaabbaaaaaabaaabababbabbaabaabaababababbabbbbbbbababbabaabbbbabbaabbbbaabbbaaaabbbabaaaabaabbbbabbaaabaabbbaabbbbbaabbbbabbbbaabbbaabbabaababbabaaaabaaaabaabaababbbaaaabaababaababababaabaaababbaaabababbaaaababbabbaabaaaabababaaabaabaabaaabbaabbaaabaaabababbbabbaabbabbabaaaaaababababababaabaabaaaaaaabaaaaabaabababbbbbabaaabbabaaaababbbababbbbaabbbaababaaaaaabaaaaabbbbaaababbbaababbbababbbbbbaaabaaaaabbaaababaaaabaabaabbbbaabbbabaababbaaabbaabbabbabbbbbabaabbbabaaaabaabbbabbbaabbbaabbabaaabbabbababaaabababbabaababbbbbabbbbbabbbabaaababbababaabbaabbabaabbbabaaabaaabbbaaabbabbabbaaaabbabbaaabbbaabaabbbbaaababbbababbbbaaaababaaaaaaaababbbabbbbbaaaabaaabaaaabbbbaababaabaabaaabbababababbbbabbabababbaababaaabbaaaababbbaabbbbbaaaaabbaabaabbabbbaaabbbabbbbabbabbaaabbaaabababbaabbbbbbbabaabbaabbbbabbabbaaabbabaabaabaaaaabbbbbbbbbbbabbaabbaabbbaabbbbababbaababababaabbabbbbaababbaaaabababaabaaaaaabaaabaaabaaabaabbabbabbbbaabbabbbaaabaaaabbbabbbabbbabbbbaababbabbbbbaaabbbbaabaabbababbbaabbaabababbaaabaabbbaabbbabbbbaaaabbababbbbaaabbaaaaaaabbbbbbbaaaaaaaaabbabaaabbbaaaabbbabaaabababbaaaaaababbabaabbbabbbabbbababaabbbaaababaaaaabaaabbaaaaabbbbbabbbbaaababababbbabaabbbbaaabababbababbabbabbaabaaaaabaababaabbaaaababbabaabbaababbaababbbbabaaabaaabbaaaaabababbaaabaaaaaabbabaabbaaabaaabbbbbababbbabbabbabaabbaabbbabbbbbbbbbaabaabbbbaabbbbbaaababbbbaababbbbbaabaaaaabbbbbaaaaaabbbbaaaaabaaabaaabababbabbaabbbbabaabbaaabbaabbabbbbbaabaaaabbbabbbabaaabbabababbaaabbaabbaabbaabbabbabaaaaabbaaababbaabbbabbbaaabbbababbbbabbaaababaabbbbbaaaaaababaabababbbbababbabbababbbabbbabaaabbababbbaaabbbbbabaaababbbaabaababbabaaaaababbabbabbbbbaaaabbabaaaabbbabaabaabbbaaabbabaaabbbababaaaabbbbabbbabbaaabbaaabaaabbbabbbbbabbbbbbabbbabababbaaaabbbaabbbbabbaaaaaabbbaabbabaababaaabbaababbaabababbaabaabaaaabbaabbabaabbaaaaaaabaabaaabbabbbaabbabaabbbbbbaabbbaabaaaabbbbabbaaabbbaaabbaaaabbbababbbaabaabbaabaabbbbbbabbbbabbaabbbbbbbabbbbbbaaabaabbaaaabaabbaaababbbababababbabbbbbabaaaaabababaabbbaabbbaabbbbabbbaaababbbbabaabbbaaababbbbaaababbabababbaabbaaaabbabbbaabbababbaabbbabbabaababbaabbbaabaaabaabbabbbabbaabaabbabbabbababbaaabbaaaaabbbaaaabbbabbbbaaaaabaabbbbbaabbaabaaabababaaabbaaabababbbbaaaaaaaabaababaabbabbababbaaabbbbaaaaababaabababbbbbabbabbbbaaabaaabbbaababbaababaabbaaaaaaabbaaaaaaabbbbaaaaaabaaaaaaabaaabaaaabbaabaaabbaaabbbbbbbaababbaaabbabaaaabbaababaabbaaaabaabbaaaaabbbabaabaaaaabbabaaaaabbabaabbbaabaaaaaabababbabbbabaaaababbbbababbabbbbbbbbbaaabbaabbbbababaabaaabbaaabbabaabababaaaaababbaaaaaabbaabbaaaabbbaababababaaaaabbbbabaaaaabbbaaabbaabbaabbbaaabbaababbabbbaaabbabaaaabaaaaaabaaaabbabbbaaaabababbbababababbbbbbaabaabbbabbbabbabbbaaabbaaaabaabbbbbbbbbababaaabaabaaaaaaaabaabbaabbbbbaaabababbbbbbabbaabaabbabaababbaaabaabbbbbabaaaabaaaaaabaaabaaabbbbbbbbbbaabaabbaaaaaaabbabbbabbababbaabaabaabaababbbaaaaabbaaaabaaaaabaabbbaababbbabbaaaaaabaaaababbbabbbaababbbaaaabbababbabbabaabbbbbbabababaabbabaabaaaabbaabbbaababaababaabbbabbaaabbaaabbababbbaaabbabbbbbabbbaabbbbbbaaabbbaabbabbbbaabaaaabbabaaabbaaaabbbaababbaaaabbbbaaaaaaaabbabbbababaaabbabaabbabbbabbabbbaabbabaabbbbabbaababbbbabbbabbaabaabababbbabaabbabbaabbabaaaaabbaababbbbbbaabbbaaaabbbbaabaaaaababbbbbbabbaabababbababbabbaaaabbbbabaabbaaabaaaaaaabaabbaabaaabbbaaabbbbbbabababababbabaabbbbbbbbaababaaabbabbaaaaabbbababaabbbbbaaaabaaaaabaaabaabbabbbaababbbbbbbbabbbabbbbbaaaabbbbbabbbababbababbbbbababbbbaabbababbbaabbaababbabbaabbabbbabababbbababaaabbaabababbbbbaabbaaababbababbaaababbabbbbaaababbbaaaaaaabbabaabaabbbbaabaaabbbababaabaabbaaababaababababaaabbbbbaaabbbbbbabbaabbababaabababbaaaabbbaababaabbbbbabaaababaaabbaaabaababbbbbbbabbabababbbaabbbababaabbbabababbababbaabbaabbaaabbaabbbbaabbbbaaababaaabbaaaababbbbaabbaabaaabaaaaabababbbbaaabaabbbaaaabbaaabbabaabbbbbbbbaaabbbbbbabaabbbaaabbbbbaaaababbbabaaabbbbbbababbabaaabbbaababbbabaababbbabaabbaabbbbbababbaabbbabbbababababbbaaabaaabbabbabbababbbbbababbbbaabbbbaababbbbbbabbaabbabbaababbabababbabbbbabbaabaaabaababaaabbbbaaabbabbbbbbabbaababbabababaaaaaaaabbabbbababbabababbbabaabaabbbbbabaabbbbabaaababbbbbababaaabbabaaaabbbbababaaaababbbaabbaaaabaabbbaababbbaabbabbbbbaaabbbbbbbbaaaabaaabaaabbabbbbaabaababaaabaaababaabbabaaaabaaaabaaabbbaabbbaaabaabbaabbababbabaabbbbbaababbabaabbbabbbaabbaaaaabbaaababbbbabbbaaabaabbaaaababbbbbbbbbbbabbabbaaabbabaaaaabaabaababaabbbababbaabababbbababbbbbbbaabaabbbbbaaaaaabaaabbbabaabbbabbbaaaabbaaaaababbbbabaaabaabbbbbaaabbaabbbbabbaabbbaaaaabaabaaaabbabbbbabbabbabaaabaabbbaabbaabbaabbbbbbaaaababaabaabbbaababbabaababbaaaabaaaabbaabbbaaaaabaaaabbbbabaababababbbaabbbaababbbbababbababbaaaabbabaabbabaabaabbabbaabbbabbaabbabbaabbbababaabbbbbbabbaabbbaababbbbabaaaabaabbababbaaaabaaaababaaababaabababbabbaabbaaaababababbbabbaababbbababbaaabaaaaaaabbbabbbbbbaaabbabaabaabbbababbabbababbaaababbababaaababbaabbbaababbbabbabbabaaaabaabbbabbbabbbbaaaabbabbbabbababaaaaaaabababbabababbaaabbbbbbaaabaababbbabbbbaaaaabbbbbbbbbabbaaabbababbaaaabbaababababbaabaabbbaaaaaaaaaaabaabbbbbababbaaabbbaabaabbaabbaababbbbaaabbbaaababbbaababaabbaabbbbabbbabbbbaabbaaaabaaabaabaaaabaabaabbbaaaabbbbbbbbbbbbababbbabaababbaaabbabbbabaabbaabbbbabbabbabaaaaabbaababaabbaaababaaababbabbaaababbabbaabbbabbaabaaaaabbaaababaabaaabbbabbababaabbbabababaababaaababbbabaabbbaabbaaaaabbbbabaaaaabbbabaaabaabbaabaabbbaaabbbbbbbababaaaaabbababaababbaaaabaabbababbaaabbbabbbbabbbbaabbbbbaaababbababaababbaaaabbaababbabbabbbbbabbabbbbbbbababbaaaabbbaaaabaabbbaaaaaaabbaabbabbbaaaaaabaaabbbaaaaaabaaaaaaababababbabbabaabababbbbaabaabbabbbbaaababbabbabaaababbbbbbbaababaabbbabaabbbbbaaaababbbbaabbaaabbaaabbbbbbbabaabbbaabaabababaabbaabaaaabbaaaabbaabaaabaababbbbbaaaaabbabbbaabbbbbbbaabbbbbaabbaaaabaabaaabaabaaabaaaabbbbaaabaabbabbabbbabaaaababaaaabababbbbbbbbbbabbaabaaaaaabaabbbabbbbabbbababbaabbabbbabbbbaabaababbabbbbabababbabbbaaaabbbbbaaabbabbaababbaabababbabaababaabbaabbbabaabbababbbababaaaaabaaababbabbbabaaaabbabbaaaaaabbabbbabbbaababaaaabbbabaabaaabbbbbababbbbaabbbbaabbbbabbaaaabbbbaabbaabaabaaabaaabbbbaabbabaabaabaaaabbbaabbbbbbababbabaabbbaabababbbababbaabbbbabbabbbaabbabbabbbaabaaabbbbababbababbbbabbbaabbbbbaabbbbabbbaabaaaaabaaabababababababbbbbbbbabbbbbbbbaaabbababbbabaaabbaabaaaabaaabbaabbaaabababaaaaabbababbaababbbbbabaaabbbbbabaaabaaaabbbaaaaabbabbbabbababababababbaabbaabbabbaabbabbbbaaaaaabaaabbabaaababaaabaababaabbabbaaaabaaababaabbbaabbaaabbbabbbbabbaababababbbababababaaaaabbbbbbbaaaaaababbaabbaababbbbbababbbaaababaaaabbaabbabaaababaabaabababbaaabaabbbabaabbababbaabbbbabbaababbbaabbbbbbaababbbbaabaaaabbaaabbbbbabbbbbaaabbabaaabbbbaaabaaababbaabbababaabbabbbbabaaaabbbaabababaabbaaababbbbaaaaababaaabbbbbaababbbaabaababaabbabbaaabbabbbabaabbabbbababaaababbabaaababbbbbbbbabaaaaaabbaaaabaaababbaabaaaabbbabbabbaabbbaaaaabababaabbbabbbababaaaabaaaaaabbbaaabbbbabbabaaaabbabbaaaabbbbbabbbabaaaaaaabababbabbbbbaabbbabbabbbbbaabaaababbbabaababbaaababbabbaababaaaaabbbbabaabaabbaaabbaabaabbaaaabaaabbaabbbabbbaaabaaaaaabbabbababbabbbaababaabbbbaaabababaaabbbabaabbaabbbbabbabbbbbaaababbbaaabaabbaaaaaaabbbabababababaaabbbabaabbbbaabbaaaabbaababababbbbaababbbaababbaaaabbbaaaaaabbabbbaaaaabbabaabaaababbbbbaaabbaaabaabababbabaabaaaaaaabaabbbbbbaaaababbbbbbababbabaaababbbabbbaababbbaaabaababbbbbbbbbbabbbaababbababbbbaaababbbbabbabaabababaaaaaabbbaaabbbababbbabbaabbaabaabbabbbbbaabbbbbbabbabbabbbaabbaaaabbaabbaaabbabbaabbbabbaabaaaaabbbbbabababbaabbabbbabbbbaaaabaaabaabbbbbabababaabaabaaaaabaabbbbabbbbbbaabaaaaaaaaabaaaaabbbbaaabbbaaaabaabbababbaabababbaaabbababbabbaaabbbaaaaaabaaaaaaabbbbbbabaaaabbbaababbabababaabbbbbaaababbbbbaaaaabaabaaaaaababbababaabbbababbabaabbaaaabbbbbaabbabbbbabaabaaaaaabaaabbabaaaaaaaaaaabbbbbbbabaaaaabbabbbbbaababbbabbbababbabbbababbbaaabbbababbababbaabaabbbbababbabaabaaaabaabbbaaaababaaaabbbaabbbaabbbbbbbbaabbbabababbbbbaaaaaababababaabaaabbbbbbbaababaabaaabbbaabaabbabbababaaabbaaabaababbbaabababbabaaaabaaabbababbbaaabaababbabbbbbbabbaaabbaababbabaaabaaabbbaabaabaabaabbaabbabbbaaabbbabbbaabaaaabbbaaabbaaaaabbababaababaaabbabaabbbbbbabaabababaaaaabaaaaabbbbbbbbbabaabbaaaabbaabaabbbaabbabbbaabaaabaabaaabbbaaabaaaaabaabaabbbabaaaabababbbaaaaabbbabababababbaabbaaabbaaaaaaaaabaaabbaabbabaaaaaabababaaababbbbaaabbbbbaabbaaaabbbabbbaabbbbbbabbaaaabababaababbaaaaaababbbabbbabbaabababbbaaabbabbaaabbaabaabbbbbaabaabbaabbbbbaababbbaaabababbaaaabaabbbbbaaaaaabbbaaabbaaaabaaaaabbbabbbbbbbaaabbbbbaabababbabaaaabbaababbbaabababaaaababaaababbbabbabbbabbaababbabbaabbbbaabababaabbbbaababbabaaaababbbbaababbbaaabbaababababbbbabbabbaaabbbabaaabbbbababababbabaaaaaabbbababaaaabbabbbababaaaaaabbabbabaabaabbaabbaabbaaaabbbaabbabbbbbababaaabbbababaabababbbbbabbbababaabaaababbbabbbababaaabbabbabaabaabbbaaababaaabbaabbbaaabbbabaaaaaabaabaaaabbbbababbbbabaaaabbabbbbabaaaabaaaaaabbbabbbbbbaabbabbabbbbaabbabbaaabababbabbbbabbaabaabaaabbbbabbaaababababbbbabaabbbabbbabbbaaaaabababaababaaabaaaaabbaaabaabaaabaabbbbbbaabbbaaaaababaaaaaaaaaaaaabbbbaabbbbbabbbaabaaabbbaaabababbaabbbbbabbaababbaaababaababbbabbbabababbbabbaabbbabbbbbabbbbbbbbaaabaabababaabbbaabaaabbabaabaaababaaabbbbaabaaaaabbaaabbabaabbbababababbaabaababbbaaaaaabaabbabbabbaaabbbbaabbbaqbaabaabbaaabbabbaaaababbbbbababbaabababaababaabbabbabbaaababbabbabaababbbaabbaaababbaaaabbaaaabbbaabbbabbabbaabababababbbaaaaaaabababbabaaaabbaabababbbaabaaabaaabbbaaaabbabbaabaabaaaabbabbbbbbbabbbbbabbbbbbaabbababbabaaaaabbbabababbbaaabababaaaaabababaaabbbbbbbbabbaababbaaabaaabbbaaababbbaabbbaabbaaaabbababbaaaaabababbbaaaabbababbbabababbabbabaabababbbaabbbbbaabbabaababbabbbaaabababaababbbaaabbabbbabaabababbbaabbbaaababbbabbbabbbbbababbabbaabaaaabaabababababbbabaaaabbbaabbabbbaaaabaabaaabbabbbaababaaabbaaababababbabaaaaabbbbbabaaabbabbabbbaabbbbabababbbaabbaabbbbaabababbaaabaaabbababaababbbabbbabbaabbbabbbbbbbaaabaaaababbbaaabbbbbbaababaababbbaababbbabbbbbbabbabaababbbbbabaaabbbpbbabbaabaababbaaaaaabbbbabbabbbbbabbbbababbaababaaaaabaaabbbabbabbaaaabbbabbbaabbaababbababaabbbaaaaaababbaabbbabbaabbbaabaabbabbabaabbabababababbbabaabbbaaaababbbbbbbbaaabbbbbbaaaaaabbaabbaabbbbaaaabaabbbbababaabbbabaabaaaabbbbaabbaababbabababbaabaaabbbbbababbbbbbaabbabaaaaaaabbbbaababaaabbbbaabbaaabaaabbbbbaababbabbaabbbbbbbbbbbaaabbbbbaabbabababbababbaababaabbbbabbabbabbbbaaaaababbaaababaaababbbabbbbabaababbaaaaabbbaaababaaabbbbbbbababbaaaaaaaabbaabaaaaabbbbabbabbababaaaabaabbbabbaabbbbaaaabbbbbbbbabbbabaabbbbbababaabaaaabbbbbabababbaabaababbaaaaaabaabbaababaaabaabbaaaaaaabaabbbbbababaabbaababbabaaaaabababbbababbaababbaaabaaabbbbbbbbbbbbbbbbaaabbbbabaaabaabbaaaaaababbbaabaaabbaaaaaaabaabbaaabbaababbaaabbbbaaaabababbabaababbbabaaabaababaabaabbaaaabbbaababbbbbbbbbbabbbabaaabaaababbbaabbabbaabaabaaabbaaabababababaabaaabababbababbbbbabbbbbbbaabaababbababbaaabbabbbbbaabbababaaababaaabbabbbaaababbaabbbbabaaaabaabababbaabaaabbbabaabbaaaaaaaabbbababbabbaaabaabababaabbabababbabaabbbbbbbabababbabbaaabaabbbaababaabbbaaabbababbabaaaaabbabbbabbaaaaaabbbaaabbaababbbabbabbbaabaaabaaabaaababbbabababbbbbaabbababababaaaaabbbbababaabaabbbaaabbbbbbaabbbaabbbaaaaabababbbbabbbbababbabbababaaababbabaabaabbaabbbaabaabbabbababbaababbbabbbbbbbbabbaabbabbbbbbabbbabbabbbaabbaababbababbabbbbbbbabaaaaaaaababaaabababbaaabababbabaaabaabbabbbbbabbaaabaaaaaaabbaaaaabaababaaaabaaabbbbabaababbabbbbaaaaaabaababbbabaaabaaaaaaabbabbbabaaaabbbbbaabbabababbababaaaababbbbbabaabaaaabababbbabababbbababaababbbbbabbbaaabbabbbabbabaaaaaabaaababbbbbbabbababbbbbbabbabbbabbabbbaaaababaabbbaabbbabababbbaabbaabbbaaababbaabbbbbaaaaabbabbbaabbaaaaabbbabbbbabaaabaaaabbabaaaaaabbbbbbbabbabbbaabbbbbaabbbbabaaabbbbbbbaabbababbabbbbbabbbaaabaabbbbabbaabbbbaaaababbbaabaaabbbbbaaabaaaabababbaababbabbbababbbaabaabbbaabbbbaabbbbbbbaabaababbaaaaabbabbbaabbabbaababbaaabbababbaaaaabaabbbbbaababbbbbbaaaaaaabbbabaabbbabbbbbbbaaababbbbbbabbbbbbabaabaabbbababaaaaabbbbabaabaabbbbbabaababaabaaabbabaaabbbabaabbbaabbabaaabaabaaaabaaaabababaaaabaabaaaababaabbbaaabababbbaaabbbaabaabaaaaabababbbaaababbbbaaababbbbaaabbbbbaabbbbabbabbbbbbaaaabababababaaaaaabbaabaaabbbaabbaabbaababaaababbbbbabaabaababababaaabaabababbabbaabaababbabbabbbbabbbbabbaaababbbbabbbbabaaabaaabaabbbbaaabaaabbababaabaaaaaaababaabaaaaaababbbbabaabaabaabababaaabbaababbaabaaabbababaaaababbbbaaababbbaaabaaaaaabaaabbaabaaababaabbbbbaabbbabbabaaaaabbbabbaaaaaaabaaabaaabaabbbbaababaabbbaaabbbbbbaabbaaabbabaabaabbbababbbbaaabaababbaababbbbaaaaabbababbbbabbabaabaabbabbabbaaabaaaaabaababbaabaaabaabbbabaabbbaababbabbbbbaabbbabaabaaaaaaaaabaabababababaabaabaabbbaaabbabaaabbaabaabaaaababbbabaaababababbbabbaaabbbbababbbbaababaabbaaabaaabbbaaabaabbaabbbaaabbbabbbabbabaabaabaaaabbaaaaaabbaabaabbbbaabababbabbabaabbabbaaaabbaaabbaabaabbabbaaaabbabbbaaabbbabaababaaaaababbbaababaaabaaaaaaabababbbabaababbbaabababaaabababaaabbbbaaaababbabaabaaaabaaaaabbbbbaabaaaaabbbbabaaaaabaaaaabbaababbabaaabaabbbababbbbbbababbbaabbaabaaabbababaabbbaaabaabaaabbabaaabbbbbbaaabbaaabbbbabbbbaabaabbbabbabaaaabbbaaaaababbabababbaaaaaaabbaababbababbabaaabaaaaababbaaabbababbabaabbabbabaaaababaababbbbabbbbaaabaaabaaaabbababbbaaabaaaabbbababaaaaaabbaabbabaaabbababbaabbaaabaaababaaababbaaaabaabababaabaaaababbbbbbaaaaaababaaaaaabbaabbbbabababbaaaaabbbaaaaabbaabbbbbababbbaabaabbabbbaabbabbbbbbabbabbbaaaaabaaabaabbbabbbaaabaaaaabbbbbbaabbaaaaaaabaaabbbaabababbababbaaaababbaabbbaaaaaababababaaaabbaabaaaaabaabaaaabababbbabbababbabbabbaabbabbbbabbbbaaaabbaaabaaabbbbbabbbabaaaaabaabaabaabbbabbabbaaabbaabbaabbabbbaababbbbaaabbbaabbabbaaaabbbaabbbbbbbabbaaaabbabaaababababbbbaabbbaababaabaaaaaababababbabbaabbaabaabaaabbaaabababbbbaaabbbabaaabababbbbbaabbaabbbbbababababaaabababbbbabbbbabaaaaabaabbbbbaaabbabbaaaabaabbabaaaabbbababaaaabbaaabaaabbabaaaaaabababbababbbababababababbabaaabbabababaaababbaabbaaaabaabaabbbaabbabaabaaaaabbbabbaabbabbbabaabbbaabbbbbbaaaaabaaabbbbbbabbaabbaabbbbbaaababbbabaaababaaabbaaabaabbbabbbbaabaaabaabbabbabbaabbbbbbbbabbbbbaaaaabbabaabaabababaaaaabbaaababaaabaababaaabaaaabbabbbbababbaababbbabbbabbaaabbabaaabbbbbbbabbbaabbabbaaababbbaabaababbaaabababaaabbaaabaabbbbababbbababaaaaababbbbababbbbabaabbabbbbbaaababaaabbaababbaaaaaaaabbaaaaaaaabbbbaaabbbabbaaaaaaaaabbbbabaabbbabbabbbaabbbaabbbaaababaababbabbabbabbbabaabaaaaabbbabbabaabaaaaaabbbbbaaabbaabbbabbaaaaabbbbbbaaaababbabaaaabbbbaabbbbaabbbabbbabaabaabbbbbababaabbaaaabaabbabaaaaabbbbbbbbabbbbaabaabaaaababbbbbbbbbaaaabaaabbaaaaaaaaabaabaaabbbbabbaaaabaaabbaaaabbaaaabbbbaaababbaaaaababbbabbaabbbaabbbaababbaaabbabbbbbbbaaabbbbabbaaaababaaabababababbbbaaaabbbabbbbbaababbbabbbaaababaabbbaaaababbabbbbbabbababaaababbabaabbbbaaabbbbbaaaaaababaababababbaaababaababbaaaabbbbbbbabbababaaaabbabbbabaabbbaaaabbbaaaabbbabaabbbbaabbbbabbbabbbaaaaaaabbbbbaaaaaaababaaaaababbaabaaabaabbaaaababbaaababaabbbbbabaabbbbbabaaabbbbbaabaabbabbaaaabbabbbbaabbbbaaaababbababbbbbbbababaaaaabbaaabaaaabaaaabbbbaabbabaaaaaaaaabbaabbbabbbaaaabbababbbaaaababbbbbaaaabbaabbaabbbbbabbbbaaaaabbaaabaaaaabbabaabbaabbbbbbbabbbbabbbbbabaaabababbbbbbababbbaababbabbaabbbabbbbbbaaaabbbaaaabbabababbbaaabaaabbbaaabbababaabbabbabbbbaabaabaababbbabbabbabbbbbaabababbabababbbbbaaabbaaababbbaabbaaaaabababbabaabbabbbbabaaabbbababbaaabababaababaaabbababbbababaaabaaaaabababbbbabaabababbbabababaabbbbababbbaabaabbbbaabbabbaabbbaaaaaabbaaababbbbabbaabbaababababaaabbaaaabbbbabababbaaabbaabbaababbbbabaaaabababaabaabbbaaabaabababbbbbababbbbbaaaaaabbbaaaababaabbbaababaababbbaabaaabababbabbaababbbabbbbbabbaaababbbbababbaaaabbbabbbbbbbbabaababbbbaabbaaaabababbaabbbaaababbbabbbbbaabaabbaabaaaaabbbaaaabaaabaaaaababbbabaaaaaaaabbbbabbbbababaaaabaaababaabaababbabaaabbbbbbaaabbbbabbbaaaabababbaaaaaababaaababbaabbaabbabaaaababbabbaabbabaababbbbaaaaaaaabbabbaababaabaabababaabaabaababbaaabbabbaababaabababaaaabababaabbbbbbaababbaaabababbbbbababbbabbaaaaaaababaababaababbbabbbbbaaaaaaaabaaaaaababbabbaabaabbbaaabababaaabbabbababaabaabaabbbabaaaaaababbbbbaabaabbbaabaabababbabbabababbababbabaaaabbbbaabbbbbabbbbaaababbbabbbabbabababbabbabbbbaaabababbaababaaabbbbbbaaaabbabaaaaabbababaababaaaaaabbbbbaaabbbaaababbaabbabaababaaaaaaabbaaababbabbbbbababaabababbbbbbaababbbbabaaabbbabbabbaabbbaaaababbaaabaabbabaabaaabbababbabaabbabbaaaababbbbbaabababbabaaabbaaabababbaabbbabbabbababbaababaabaababbaaaababbbababababbaaabbaabbaabaaaabaaaaabaabaabbbaaabbbabaaaabababbbbbaabbabbbbaaaaaabaaabaaaaabbbabaaabbbbabbaaababbaaaaababaaaaabaabaabaabbbbbaabaaaaaaaabaababbaaababbaabbbbbabbbbababaaaabababaabaabbabaababaaabaabbbabbbbababaabaaaabbbbaabbaabbaaaabbbbabbbaaababbabbbabaabbabbababbbbbabbbabbbbbabbbabbabbbabababbbbbabbbbaabbbaaaaaabbabbabaabbabaaaaaabbaababbbbbaabbaabbbbaabbbaaaaaabbaabaaababaabaabbbabbbbabbbbbaababbaabaaabbbaaaabaaabaaababaabababbbaaabbbbbbbababbbabbbbbbbbbbbbaaabbaababaaabbabaabaabbaaababbbbabbbbaaabbbaabaaabababababaabaaaaabbbaabbbbbbababbbbaaabaaabbbbbbabbbbaaabbaabbababbbbbbbaaabaababaaabbbbbabbbbabaaaababaaaabbbbbbaabbbbabbababbabbaababbbabbabaaaababbbaaaababaabbbaaaaaabbbbbbbaaaaaaaababbbbbabbbbbbbababbabaababbabaaababbabbbbaababbaabbbbabbabbbaabababbaabbbaaababbbaaabbaabbbbaaabbbabaaaabbbbbbbaabbbbabababbaaabbabbaabbbbbaabaabbbaababababbbbbaaaaabbbbbbaaaababbbabababaaabbaabbaabbbabbbaabaabbabbaabbbbaaabbbbbabbaabbaaabaaaabaaababbabbababababaababbbaaaabbaabaaabaababbabaaabbbaabaaaabbbbbbbaaabababababbbaaaabbabbbabbababbaababbabaaabbbbbbabaabbaaaaabbbaaaabaabbaabaaabbabaabbbababbababbaababaabbaabbbbabbbabaabbbababbbabbaaaabbbbbabbbabbbaaaaababababababaabababbaabbaabbaaabaaaabaaaabbbbbbbababababaabbabaabaaaaaabbbbbbbaababaababbaababbbabaababbabbbabaaababaabaabbbaaaaaababaaabbaabaaabaabbbbabababbaaabaaaaaababbaabaabbaaaaaaabaabaababbabaaababbbaaaabababbbbbbaaaabbbbaaaaaaabbabaababaaaaababbbbbbabbabbabababbaabaabaaaabaaaabaabaaaabaaababbbbbbbabbabbbabbabbbbababbaaaabababaabbaabbaaaaaaabbabbbaabbaaaabaabbaabbaabbbaabbbbbbbaaaabbbabbbababbabbbaaaaaaabbabaababaabababbbbabababbbbbabaabaaaaabbbbabbbabbbbabaababbbbabaaabaabaaaaaabaaaabaabbbabbbabbabababbaabbabbabbaaababbabbbbaaaababbbaaaababbbbaaabbaabbaaabbabbbbbbbabbbbaaaabbbbaaabbabaaaabbababbababaababaabaaaababaabaaaabaaabbbaabbbbabaaaaabbaaaabababbabbbaabbbaabbabbbbabbbbbabbababbabababbaabaabaaabbbbbaababbbbaaababbaaabaabbbbabbbabbaaaaaaabbbaaabbaaaaaaaaaaabbbbbbbbaaaabaabbbbabbaaabbabaaababaababaababbabaaabbaaababaabaaaaabbbabaaaabbabbbaaaaabababbaaabbabbabbbbabaaababbbabaabbbbabbaaabaaaababbbbbabbbabaaababaababaaaabbababbbbbaaaaabaabbbaabbabbbaabbbabaababbabbaabbabaaaabbbbabbbbbaaabbabaaababbabaaaaabaaababbabbababbbabbabaabaabbbaababbabababbaabaabbaabbbbabbbabbbaaaabbaabbabbbbbbaaabaabbbabbbaabaaababbabbabbaaaabbbbabbaaabbbbababbbbaabbababbbbabbabaabbbabbaaababbaababbaabaabbbaaaabbabbbbbabaabbbaababbaaaabaaabaabababaabaabbbbbabbbaabbabbaaaaaaabaababaaabbbbbabbbbbbabaabbbaabbaabbbbbabbbbabaaaaabaaabababbaaaaaaabababbbabbaaabbbaabaabbabbaaabbabbbbbababaaabbaabaaabbabbbbbbababbabbbbbbbbbbaaaababbbbaabbbabbaaabbbbabbbbbaabaaabaaaaaaabbbbabaaaabbbbbabbabbabaabbbabaaabbbbabbbaaabbabaabaabbaababbababbaaaaabbaabababaababaaaaabbaaaaaaabababbababbaabbaabbbabbaabbbbabbabbbaaabbaabbaaaabababbbababbbabababbababbabbaabaabbbabbbaababbaaabbaabababbbaabaabababaabaaabaaabbaaaabaaabbabaaabbaabbababbbaaaabaabbbbbbbbbabbaaaababbbbbbabbaababbbabaaababbabbabbbaaaaaabbbabbabababbabbaaaaabbbbaaababbabbbaaaabbababbbaabaaaaaabaabaaaaabbaabbaabaaaaabaabaabaabaabbaababbbbaabbbabbbaabbbabbbbbbabbaabababaaaaabbbbaaababbabaabaaaabbbabaaabaaababbbaabbbbabbbbbbababbbbabaaabaaaabaabbaaaaaaaabababbbaabbabaababbbbabbbaaabaaaabbabaabaaabaababbbaabaabaaabbbaababaaabbbbbaababababbababaabaabbbbabbabbabaaabaaabaabbbaabbbbbaabaaaabbaabbbaababaabaaaaababbbbbabbaaaabbabbbabbbbbabababbbabbbabababbbabbbbbbababaabbabbbbabbbbbbaabababbbabaabbaaabbbbabbaabababbaababaabbaaaabbbbabaaabbbbbabababbbaaaabababaabaabaaabaabbaabbbbbaababbbbabaabbabaababaababababbabaabbaabaabbaaaabababbbbbabababaabaaabbaababbaabbaaababbbbaaaaaabababaabaabbabaabbbbabaaabababbbbaaaababbabababaaababbbabbabbaabbbabbaabbabbbbabbababbaaaabaaaaaaaabbbaababbaaabbbbabbaabaaabaaabaaabbaaaabbaaabbaaaaaaabbbbababbbbbbbaaabbabbababbbbabaabaababaabbabaaabbabbabbbbaabbaaababbbabbaaaaabaaaaaaaabbaaaabaaaaabbababbabbabaabaabbbbbabaabbbaaababbbbbaaaaabaabaaaabaabbbaabbaabbbaaababbabbbbababbaabaabbaaaaaaaaabbbabaabaaabbbaabbaabaabbabbbaaaabaabbbabbbbbabbbaabaaabababaaaabbbbbbababaabbaabaaabbaaabababbbaabaaababbabbabaaabaababaaabbbbaabaaaabbbaabbbabaaabbababbabbbbaaaabbbbaabaabaaaaabbabbabbaababaaaababbbaabbaabaaabbaabaaabababbbaababbaabbbbabaabaaaaaabaaaabbaaababbbbabbbbbabbbaababaabbaabbaaabbbbbbabbaaabbbaabbabbaaabbbaaababaabbabbabbbbbbbabbaaabbbaabbaaaabbbababbaaabbabbaabbabaaababbbaababbaababbabaabaabaabbabaaabaaaabbbabaababbababbabbbabaaaababababbbaababbabbaabbaaaabaaaababaaaabbbbaabbaaaabaaaaababbbbbabbbaabaabbbbbbabaabbabaabaaababbaabbabababbaaabbbabbbabbabababbbbabaabbbbaaaaabbaabababbabaabababaaabbbbbaabbaabbaabbaabaaaababbabbaaabbabbbabbaaaabbabababbbbbbbaaabbbbabbbbbbbbababbaaaaaaaabbbaabaabababbbbaabbabbabbbaababbaaabaaabbbbaabbbababaabbbaabbababbbbbbabaabbababbabbbaaaaabaabbaaabaabaaaaababaababbaaabaaaabbabbaaaaaaaaabbabaaaaaababbbaaaabbabbbabbbbaaabaaabaababbbaabbbabbbbaabaaabbbbbbbbaabbbabbaaaaabaaababbaababaababaababbbbbbabaabaabbbaaabbababbabaaaaaabbabbaaaabbabababbbbababbabbabbabbbbaaaaaababbaabbabbbbbbaabababaabbaabbabbbbababbbbaabbabababaababbbabbbbabbabaaaaababababbaabbbbaaaaaababaababbaaaabbbaabababaabbabbbbbabaabbaaaababbabbababbabaaabaabbabaabbbbabaaaabbaaaaababaabbbaaabbbabbaababaaaabaaabaaaaabbaaababbbabbabaabaaabbaaaaababaaaaaababababbbaabbbabbbaabaaabbaababababbaababbaaaababaaabaaabbbababaabbabaaaaabaaabababbaababbababaabbabaabaaaaabbbaabaaabbbaababaabaaaaaabaaaaabbbbbaaaaaabaaababbaababbaabbbbbaaaabbaaababbaaabaabaaaabbababaababbbababbbaababbaaababbbbbbaabbaababbabbbabbaabbbbaaaaabbaabaaaaabababbbbbababaabbbababbaaabbbbbbaaababaabaabaaabbbbbbbbbababbaaaabababbabbbbaababbabbbbabbbaaabbaaaabababbaaabbaaaababaabaaaababaaababbbbaaaabbaaababaaabbaaaabababaaabaaaababbbabababbaaaaabbbbabbbbbbabbaabbbaaabaababaababaabaaaababbaaabbbbaaaabaabbababaabbababbbabbaaabbabbbaaaabbabbbbbbababbbabbbabbbbbbabbbbbbbbaabbbbbbbbbbbaabbaabbabaabaaabaaabaaabababbbababbbabaaaabaabababababbbbaaaaabbbbaaabbbbbbabaabbbabababaabbaabbabbaaaabaabbaabababbabbabbbbbbbaaaabbababababbbabbbbbbaaaaabaabaabbbabbaababaababbbbbbaaababaaaaabbbaabaaabbbbabbbbbbaabbbabaabbaabaaaaaaaaaaaaabaababbbababaaaabbaaabbbbbbaababbbbbbbbbabaaaabbbabbaaabbabbbbbabbbaabaabbbabbbbaaaaaaabaabababbabbababbabbbbaaaababaababbabbababaababbbbabbaaaabbaaabbaaabaaabbbaabbababaaababbbabbaaabababbbaaaaababaaaaaabaaababaabbaabaabaabbabbbaabaababbbbbabbabababbaabaaaaabbbabbabaabaabbbaabbaabaabaaaabaaaabaaaabaaabbbbaaabaaabaababbbbaaaaabbaaaabaaabbabaaabbbbbbbababbaaaaaabbbaaabbaaabaabaabababbabbaaabababaaaabababbbbabbbabbaaaaaaabbabbabbabbbabaabaaaaabbaaaaababaabbbaabbbababbbababababbaabbbaababbbbaaaabbabaaabababbabbbabbbaaaabaabbbbbbbaabbaaaabbaaabbabbaaabbbbbbabaabbaaaaaaaabbaabaabababbababaabbaaabbbaaaaababbbbbbaaabbaaaabaababababababbabbbbbaabaaabbabbbbabaabbabbbbbabaaaaaaabbbaababbbbabbababaaaaabababaabbababaabbaaabaabbabaababbbabaaaaabbaabbbbbbbbabbbaaaababbbababbabbaababbabaabbbaaabbababaabbbabbbbbbbabababbbaaabbbbabbaabaaabaabbaaaaaaaaabbaaabaaababbbbaababaabaaabababbbbaabbbabaababaaabaaaababbbaabbaababbaabbbbaabbabbabbbbaaabaaabababaabaaaababaabaabaabbabbabbbaabbbaaabaaaabbbbbaabababaabbaabbaaabbababaabbbaaabbbbbaaaaabbaaabbbbbbbbaabaababbabbbabbbabbaaabaabbabbababbbbabaababbabbbabbaaaaabababaabaabbbbbbabbaabbbaabbbbaaabbbabbbbbbbabbabababbaaababbbbababbbabaababbabbbabbbbbbbbaaabbaabbaababaaaaaaaaabbbbabaaaaabbaabbbbbbbabbbbabbabaaaaaaabbababbabbabbbaaabaaabbbbaabbaabbbbaabbbabbaaabbbaaababaababbbbbaaabaaabbbbaaabaabaabbaaaaabbbbabbbabbbbbaabbabbababbbbabbbbbaaabbaaabbbbabaabaaaaabaababaabaabbbbbbbbbbbabbbbbbaabbbabbaababaaabaaabbbbbbabbbabaaaaabaaabbaabaabaababaabbaabbbaababbbbbbbbbabaabbbbaaabbbbaabbbbaababbbabababaabaabbaabbbbbbaababbbabbbbbaabababbaababaaaabaabbaaaabaabaaabaaaabbabbaaabbaaabaaaaaabbbaaaabbbbabbababaaabbaaaaaabaababbbababbbabbbaaabaabaabababaabaabbbabbbaaabbaaabbabababbbaabaabababaaaabaabbbaaabaaabbababbaaaaaabaaaabaaaabbabbbbbababbaaabaaabbabbbbbbababbabbbbbbaaabbababbabaaabaabbaabbbbbbabbbbaabbbbbabaabbaabbbbabbbaababaaabaaaabaabaabaaaabaababbbbaaaaabbbbbbbbbbabaabbbbbbbbaabbaababbaaaabaabaaaaababbbbbabbababbbaaaabbbaabaababbbbbbbbabaaaabbbbbabbababbbbaabbbabbabaaaababbaaababbbaabbbbbabbbaabbaaaaabbbaaaaabbbbbbbbbaabaabbaaaaabbabbaabaaabbbbaaaabbabbbbaabaaabbbabaaaaababababbabbbbbbbaaaaaaaaabababbbbbbaabbbabbbaaaaabbbaabbabbabaababbaabbbbabbbbabbbabbabbbbaaaabbabbaaaabbabbaabaababbbabaabaaaaabaabaaababbabaababbbaaaabababbbbbbabaaaababaaaaabbababbbabaabaaaabbbababbaaaabbbbaabbabbaabaaaaaaaaaabbbabbbbbbabbabbabaaabababbbabbaababbbbaaabbbbabaabbbbbaababbbaaabaaaaabbabbaaaaaaabbbabbaaaaababbaaaabaababbabaaaaabbabbbaaaaabaabbabbabaaabaabbabababaaabbaaabaaaaabbbabbbababbabababbabaaababaababbbbaabaaabbbbbaaababaaabaaabaaaaabbbaabbbbbbabbabaabaaabbabbaaaababaaabbaababbbabbaaabaaabbabababaababaaaabbbbbbbaabaaabbbbbbabaabbbbaaabaabaaaabaaabaababbaabaaaaabababbbaababbaaabaaabbbbbabbbaaaaababbbbabbabaababababaaabbaabbabaaaabababaabbbbbbbaaababababbabbbabbbbbababaaabbbaaaaaabbbbabbaaaabbbbaabbaaabbbbaaaabbbabbabbbbaabbbabababaaaaaabbbbbbbbbbbaababbbbabbabababbbaabaaabbbabbbaababbaabaaaabaaabbaabaababbabbbbaabbbabbbbbbbbbbabbbbabbababbbbababbbbabaaabbaaaabbbababaabbaabbabababbaababaababbbaabbaaaabaaabbababbabbababaaabababaababbaababaabaabbabaaaaabbaabbabababbaabbababaaaaababbbaaaababbbbaaababaaaaababbbabbababbabbbbaabbaaababaaaaaaaaabbaaabbbabbbabbbbbbbaaabaabbbbbababbaaababababbbbaaabaabbbbbbaabaababbbbabbabaababbbbabbbbababaaaaaaaababbaabbbaaaaabbbaaabbbbbabaabaaaaabbabbaaaaabaaabbaababbaaabbbbbbbaabaaaabbaababaabaaabaabaabaaaabbabbabbbbbaabababaaaabaababbbabbaaababbbaaaaaaaabbbabaaaabbbbbbabbbaabbbaaabbbaaabbaabbbaababaaaabaabbaabbababbaaaaababbbabbabbbbabaabbaababababaabbaabaaaabaaabbabbaaaabbaabaabbaababaababbaabbbbabbbabbaababbbabaaaaaabbabbbbbbaaaaabaabbabbaaaaaaaabbabaaababbabbbbbababaaababbaabbbbbabbabababababaabababbaaabbbbabbaabaaababaaabaabababbaababbbbabbbbabaabbbbabbbaabbaaaabbbbbabaabbaaaabbaabaabbbbbaababbaaabbbaaabaaabbbabaabbaabaababaaaabbbbbbbaaabbaaabbbaaabbbaabbabaabababaaaabaaabbbaabaababbabbabbbabbbbbaabaabbaaaabbbababbbbbabbbababbabbbaaaaabbbabbbbbbbbaaaababbbaaabbaaabaaabbaaabbaabaaaabbabaabaaaaaaabaabbaaabbaabbbabaababaaabbbaabbbaaabababbbabaaabaabbbaabaabbbabbbbbbaababbabbaaaaaaababaaaabaabaabaaaaabbabaababaaabbbbabaaabbababaabaaabaaaabbbabbbababababbaabbabbbaabbbababbbbaabaababbaaabbbbaaaabbabbaaababababaaaabaaabaaabaabbaaaaabaabbbaaabbababbabbbbbbbababbabbabaababaaaababaababbbbabaaababbaaabbabbaaaabbbbababaabaaaaaaabbbabbaaabbaabbbbaaaabababbbbaabbbabbaaabababbbbbbbbbbbabaababbbabbaabbabbbbaaabbbaabbaabbbaaabaabbbaaaabaabbbbabbabbabbaaaaabbabaaaaaabbbbbabbabbbaaababaaabbaabaaabbababbbaaabbaababaaabbbbaabbaaaababbbabababaabbababbbabaababbabbaababbabbbabbbbaabaababbbaabaaaabaababbbbaaaaabbaaaabaaaabbaabbbababbbaabbababbababbbbbbaabaababaababbaababbbbaaababaababbababbbbabaabaabaabbbabbbbbabaaababaaabbaaabbabaaaaabbabaababbabbaabababbbaaaabbbbaaaabbbabbbbbabbbbbbbbbaaababaabbaaabbaaaaaabbabbbabababbbaabbbbabaabbaaabbbabbabbbbbabbaaababbabbbbbabbbbbbaababababaaababababaaaababbbaabbbabbbbabbbbaaabaaaababaabaaaaaabbbbbaababbabaaabaabaabaaababababaaababaaaababbbbabbaabaabaaabbaabbbaaaaabaabababbbbbaabababbbabbaabbaabbbaaabbaabbbbbaabaabbbbaaabaabaabaabbabbaabaaaabbababbaabbaabbbaabaaaaabbabbaabbabaabaaaaababbbabbbaabaabbababababbbaaaaaabaaaabaabaabaaabbbbbbabbbaaaabaababbbaabababbbbabbaabbbaaabaababbaaaaabaaaabbbaabbbbabbabbbbbabbbaabbaabaabaabbaaabbbbbbbbbaababbaababaababaabababbaabbabbabaabaababaabaabbaaabbbabbbaabaabaaabbaababbaaabaabbbabaaaabbbbaaaabbabbaaaaaaabbbbaaababaaabbbabaaaaaabbbbabbbbaaaabaaabaaabbbabbbabbabaaaaabaaababbabaaabbbbbbbababbaaaaaaabbabbbabbaaabaabaababbbabbbbbabbbabbabbbabababababaaabbbbbaabbbbbbaaaabbbbaabbbbbabbabbbbbaaabbabaaaabaabaabbbbaababbbbaabbbaababaaaaabaaababababbbaabbaabaabbabbabbbaabaabbbbbaaabbabbaabbaabaababaaaabaabaaaaaabbabbbbaaaaabbabbabbbaabababbabaababababbbabaabbababaaabbabbbaabaabaaaaabbaaaaaaaabbabaaabbbabaaaabaabbbaaaababbbbaaababaaaabbbababaaabababababaabaaabbababaaabbbbbbaabbbbabbaabababbabaaabbbabbaababbbbababbbbbbaabbaabaaababaaaaaabbbaabaabbbaaabbbaaabbaaaabbababababbbbbbbababbbababbabbaaaaaaabbaabbbabaaaaabbaaabbabbbaabababbabbababaaabbbbbbbaaabbabbaabbbbabaaaaaaaababbabbbbbbaaababaaaabbbbaabbabbabbaabaaabbaaabbababaaabbaabbbabbbabaabbbaababababbababaaabaaabbbbbbaaabbbbabbbabaabbaabbaaabaabbbbabbbbaaabaaabaaaababbabbaabaaaababbbbaabbbabbbaababaaaababbababaaabaaababbaaaaaaaabbbbabbaababbaabbbabbaaabbbaabaabaaaaabaabaaabaaaabbaaaaaabbaabababbaabaaabbabbabbababaabababbbbbaababbbaabbbababbaabaaaaaaababbbbbaaabbbabaabababbaabbaaaaaaaaaaaababbbabbaabbabaaabbabbbabbbbbbbababaabbbbbbabbabbbbabbbaabaabbbbbbabbaabaaaabbabbbbabbbbbbbababababbbabbbbaabbbbbaabaababaaabbbbbaaaabbaaabaabbbbbaababbbbbbbababaabbbbbbbbbabbabbabbbbaababababbbabaaaaabbabaaabbbaaaabbabababbbabbabababbaaabaabbaaaabbbbabababbababbaaaaaaabbbabbbbaabbbabbabababbbabaaabbaaaaaabaabbaabbbbaababbaabaaaabbbbbbbbaaabbaabaaaaaababababbbbbbbabbababbaaababaabababbbbbbbababbbabbaababbaabababababaaabbbabaaaaababbabababbbabbaaaaabaaabbbbaabaaaaaabbbbabaaabaabbbaaaaaabbbabaabbbabbbaabbaabbaaabaabbababbbaaabaaabbbabababbaabbabaaabbbaaaaabbaaabbaabaabaaabaaabbbaaaabbabbaaabbbabbabbababababbaaaabaaaaababaabbbbbababbababaaabbbabbbbaaaaaabbbabbaaababaaaaabbaaaababaaabaabaaabaaaabbbbabababaaabbababbaabbaaabbbabaaabaaabababaaaabbbaabbbaabbbbbbaaaaabababaabbaabbaaabbbaabbaabbbaabbaabaabaaaaaabbbbabbbbbbbaabbbaaabbbbbbabbbabaabbabbabbabbaaababababbaaaabaabaaababbaabaabababbbbbbbaabababbbbbbaaabababbabaaaabaaaababbbbbbbaabbaaababbbbbabbbbbbbababbbaaaabababbaabbabaaabbbbabbabbabbaabaababbabbaababaabaaabbbababaabababbaaabbbaaaaabbbabaaaaabbbabbbbbbabbbbbbbbabbaababbabaaabbbababbbaababaaaaabbaabbababaaaaaaababbabaaabaaabbaabababbbbbabbbbabbaaaabbaaabaabbaabbbaababbbbaaabaababababbbbabaaaaabbabbaaababbabbbbbabbaababbaaababbababbaaabbbbbbabbbbaaaabbabbabaabbaaabaaabbbbaaababbbabaabaaababbababbbabbaaababaabbaaababaababbbbabbaabababbaaaaababbabaaaabbaabaaabbbabbbaabbbaaabaaaaabaaabbbabaabaabbbaabbaababbabbbbaaabbaaabaaaaaabbbbbaabaabababaaaaaababbbbbbabbabaabaaaabaaabaaababaabbaababbaaabbaabaaabbbabbbbbbabaaaabbababaaaaaaaabbabaabbbbbababbbbababbaabaabbbababbababababaaaaabbbbaaabaabbbbbbbbbababbbabbbbbbbabbbbbbababbbababbaabbbabababaabbbaabbabbaabbbaababbababbbbbabbbbbaaaaabaababaaababaabbbbabbbbbbbabaabaaabbbbabbbaabbabbabbabbbbbbababbabaabbbababbbbbbaaabaaabaabbbababbaaabbaaabbbbbbbbbabbaaaabaaaabaaabbbbbabbbbbabaabbbbbbbbabbbabbbaaaaababbaaaaaabbbbbaababbaaaaabbbbbbaabababbbaababbbababababaaaaabaabababaaaaabbbaaaaaaabbbbabbabbaaababaabbbababaaabababaaabababbbbbabaaaabaaaaaabbbbabbbbabababbbbbbbbabbbabbbabbaabaabababbabababbbbbbbaabbbbaaabaabaabaaababaaaaaaaaaabaaaaabbaaabbaaabbbbabbbbbaabaabbabaabaababaabaaabaababbaaabaaaabbabbaabababbabbaababaabbaababbaabbabbabababaaabbbaabbbabaabbaaabbbababbabbaaabaaababaaabbbbbbaabbbbbbaaababaaababbbaababaabaabbabbbabababbbbbabbaaaababaababaababbbaabaaabababbabaaabbaaabaabaababaaaabbbaabaababaabaababbbbbbbababaabbaaaabaaaabaaaabaabbaaabaaaabbbbbabbbabaaaabbbabaaababbabbbabbbaaaaaaaabaaababbabaabbbbbaabaabbaaaaabbbbaabbbaababbbbbaaabaababaabaaaaaabbbbaabbbbbabbaabbaabaaabbaababbbbbbbabaaabbabababbbababbabbaaababaabbaabaabababaabbaabaabababaaabaababbbbbbabaaaaaaabbaabababaabbbbaaaaabaabbbaabaaabbbaaabababbabbbaabbaababababbbababbaaababbbbaabababbbbbbbbabaabaaababbbaababaabaaaaaabbbbbaababbababbbbbbbbbbaaabbaaababbabbababbabaaaaabbaabbbabaababbaabbbbbabbabaabaaababaababababbbabaabbabababbaabbaaaabababbbaababababbbaabaabbbbaaabbbbbbbaaaaaabbbbbbabbabbbaabbabababaabaaabaabaaababbbbabbababbaaaaaaabababababaabaaaabaaaabaaabbbababababbbaabababbaabaaaabbbaaababbbbbbabbabbaabbbaabaaaaabaabaabaabbaababbbaabbbbaabbbabbbaaaabbabbbabbbaaabaaaaababaaabbaabbbbaaaabbbbabababbaabbbbaaabaaaaaabaaaabaaaaaabaabbabbaaababbabababbaabbaaaababbbbbbbbababbbbabaabbabbaaabaabaabbabaabbbbabaaaaaaaabbaabbbbaaabbbbaaabbbbaaaababbbbbabbaaabababaaaaabaabaaabbaaaabaabbbabaabaabbbaaaaabbbbbababbbabaaabbaabaaaabaabaaabababbbabaaabbbbbaaabaaaabaaabaabaabaaaaabbbababaaaaabbbaabbbaabaaaabbbaabaaaaabaaababbaabaaabbabaabaabbbbbaabbbaaaabbbbabbabbabbbababbaaaaabbbbbbbaaaaaaababbbbbaababbabbbbaabbaabbbabaaabaababaaaaabababbbababbaaaabaaabbabbaaaabbbbbaabbaaabaabbabbbbbaabaabbbabaaabababbbabbabbabaaaabbbaaaababaaaabbbbaabababababbbbbbbabbabbabaabaaaabbaabbbaabababbaabbababbabbbbabbaabababaaabbaaabbbbabababaabbbababbaaaaabaaabbaabaaaaaaaababbbbbbabaaabbabaaababbababbbbaaaababaababbbababbbbaaabbaaabaabaababbababaabbabbababbaabababaabaaaababaabbaabbababaaababbaaabbbaababaaababbbaabbbbaabbbbaaababbaabaabbababbaabbabbbaabbbaaabaabaababaabbbabbabbbbabaabaabbbbbbabbaaababbabababaaababbbbaabbbbabbbbbabaaaaabaaababbbabbbbbbbbaaaabbaaabaabbaaabaababbabababababaaaabbabaababaaaaaabababaabaaaaaaaaabaabaabbaaabbbaabababababaabaaaaaababaaaaababbabaababaababbbbababaabbbabbbababbaaabbbbabbbabaaaaabbbaabbbbaabaaabbbababbaaaabbabbbbbbaaaababaaaababbbababababaaabbbaababaabbbaaaaababaaaaaababbababbababaabbbbbaaaaabbaabbbbbbaaabbbbaaabaaababaabaabbbbabbaabaaaaabbbbaaaaabbaabbbbaabaababbbbbbabbbbabbbbbbaaaaaaabbababbbaabaabaabbbabbbbabbaaabbaaabaaababbabbaabaaabaaabbbaabaabaaababaaabaaabbbbabbbaabbaabbabbaababaabbaabaabbababaaabbabababaaaabbbbababbbaabaaabbaaaababbaaaabaabbaaaababaaababbabbbababbaaaaaaabbbababbbbbabbababababbbbbbabbbbbbaabbbabbbaaaaaaabbbbbbbbbaababbbbabaaababbbbabbbbaaabbbbaaabababbbabbbaaabbabbbaabbaabbaababbabaabbbababaaaabbaaabbaababbabbaababbbabbbbaaaaaabbbbabbbbaaababbabbaabbbaaaaaabbbabaaaababbbbbbbaabbabbaabbabaaaabaaaaaaaabbbaaaaabababbbbabaaabbbaababaaabbbabbbabababbbbbaabbabbaaabbabaaabbaaaaaaaaaabbababbbbbaaababababbbbbaababbbaaabbabbbaabbbabababbaaababbaabaaaabbaabbaaababbbbaaaaaaaabaaaaaababbaaabbabababbbbbaabbabaaabbbaaabbabbbaabbaabaabaabbabbaaabbbbabbbbbbababbaababbaabbbbbbaaabaabbabbabbaabbbabbbababaabbaabbabbabbbaaaaabaabaabbabbaaabababbaaaaaabaaabbbbaabbaababbaaaababaaabaabbababababaabbabbbabbaaaaaaababaababbaaaabbabaabbbabaabbbabbaaaabaaababbbbaabaabbabaaaabbbbbabbaabbaaabbbbbbaaababaabbabbabbaabbbabbbbabbabaaabbabaabaabbbbbaaabbaabbabbbbabbaaabbbbbbbabaaabaabbbabaabbaaaabbaaabbabbbabbbababbbaababbbbabbabbbbabaabaabbaaabbaabbaababaababbaababbaabbbbbbbabbbbbabbabbbbabaabbaaaabbaaaaabaaabbaabaaaabbabbaabbaaabaaabababbabababababbbabbbabbabababaabbabbbbbbababbbbabaabbbbbbaaaabbaaabaaabbaabbbbaababaaabbbaabbabbbabbaabaaabaaaaaababaabaababaaabbbabaababaababbabbbbaabbaaaababbabaaabaabbabaaabababaaaabaaabababbababaabaaaababbbaaabbaaaabbabbabbaabbbbbabbaaabbbabaabababbbbabaaaabbbbbbabbabbbaaabbaabbababbbaaaabaaaaababaaaaabaaabbbabaaaaaaaaaabbbbaaabbbabbbabaaaababbabbaababbaaaababaaaaaaababbbbabaaaaabbbaabaabbababaabbbaabbbabaabaaaababaabbbaabbabbbbbaaaabbbabbbaaabbaabbaaabbbaaabbababbbaaabbabbbaaababbaaaababaaaaabbbbbbaaaabaaabbbbaaabababbbaaaaaaababbabaaaaabbaaabaaaabaaabbaaaaaababababbbbbabbbaabaaabbabababbaababababaaababaaabbaabaaabbbaabbabaaaabaabbbababaaaaabbbbbbaaaaaaaaaabbbabaabbbaaabbaabbabbbbbbbabaabbababaabbababbaaabbaabbbbababbbbaaababaabbbbababbababbbbaababbabaababbabbabbabbaabbbbabaaaabbbabaaabbaabaabbbbababbababaaaaabababbbbaabbaabbbabbbbabaaabbbabbaaaaabaabaaaaabbbabaaabaabaaababaabababbbbbaaaaaabbabaababbabbbaabbbabaaaaabbabbbbabaaabaabbbbabaaaababbaabbaabbbbaabbbabbbaabbbaaaabaabababbbbbaaabbabaabbaabbbabbbaababbbbbbaabababbbbabaabbababbbaabbbaaabaaababababbbababbaaabbbaaaabbabbababaabaaabbbaaabbbbaababbbaabbbbaabaabaaaaabbbaabbbababbbaabbabbbbbaabaababbbbbbaabbabbbaabaaabbaaabaabaababbbaababaababbbabaabbbbaaabbaaaaababbababaaabaabbaaabbaaaabaabbababbbbbbbbbabbbbbbabaaabaaabbabaabaaaaabbbbbbbbbbaaabbaababbbbabaababaaabbaabbbbbaaabbaaabbbabaabbbabaabbbbabaaabaabbaabbbbaababbbaabaabbaaabaabbababbabbabaaaaaaabbbbbabbaaabbbbbbababbabbabbbaababaaaaaabbaaabaabaaababbaaabbbabbababbaabbababbaabaabaaaaababaaabababbbabbabbbabbbaabbbbbaabaaababbbbbabaabbaababbaabbbaaaaabbbbbabbbaababbabaababbbbbaabababbbbbbbbababbaabababababbbabaababaaaaaaaaaababbabaaababbbbaaaaaaabbaabaababaaabababababaababaabababbbbaabbbbabbbaaaaababababbaababbbabbaababbabbbbbbaabaaababbbababbababaaabaabbaababbaaabbababaababbabaaaababbbaaababaababaabaaaabbbabaaaabbaaaaabaabbbababbbbbbbbbaaaaabbaaaaaabbbabbaabbbbababbbbababaaabbbbbaabaabbabbabaaabaabaaaabababaaabaabbabbaabaabbbabaababbbbaaaababbaaabbabaaaababbabbbbbaaababbabababbbaabbbaaaaababbabababababbbbbaabbbbaababbaabaabbaabbbbbaabababbabbbbabababbaabbbabaaabababaabbabbbaaabaaabbbaaaabaaabbbaaaabaabaabaaaaaabbbbbbbabbbbbbabaaabababaabaabaabbaaaabbbbabbbbbabbbaaaaabaaaaaabbbabbaabbbbaabbbbabaaabbaabbababaabbbaabaabbbaaabaabaabbaaabbababbbbbabbbaabbbbbbbbaaaabbababababbbaabbaababbaaaababbaabaaaabaabbabaabbabbbbaaabbbbaaabaaaabbbbbbaaaaabbbaaaabababbaaababbbaabababbaaabababaaabbbabbabaaababaaabaabbbbbaaabbabaabababbbbaaaabbabaaaaabababbaaaaaaaaabbaababaaaabbaabbaababbbbbbabbabbbabbabaaababababaababaabbbaababaaaabbaaaaababaabaabbbbabaabababbababaababbaaabaabbbabbaaabababbaaaababbaaabbabbbabbaaabbbabbbaaaaabbbaabbbbbbbaaabaaaaabaaaaaaaabbbbbbbbabaaababbbaabbbbaaaaabbabbaabbbaabbbaaabaaabbabaaababbbbabaabbbababbaaaabbaaabaababbbabbabbababbababbabbabbbbbbaabbabbabbbabaabbbabbbabbbababbabbaaabaaababbbabaabbaabbabbaabbaaabaaabbabbaabaabbabbbbbaabbbbbabbabbaaabbbaaabaabbbbbbbbbaababababbabbbababbbbaababaaaaabbabaabbbbbaaaabbbaababababbaaaababaabbbbaaaabaaaaaabaaaaabbabababaaaaaababbabaababbabbabaaababbbaaabaabbabbbbbbabbbbaaaaabaabbbabbaaabaaaababbaaaaabbaabaaaababaababababbabbaabbbbbaabaabbbbbabababababaabbaaaaaabbababababbbbbabbaaaabaaaaaabbabbaaaaaabbababaaababbabbabbbbabbbaabbbbabaaabaabbaaabbababbaaabbbbbbbaaababbbabbaabaabbababababbaaabbbbaabbaababbbabbabbabaabbbaaaaaaabbbbbbaaabaaaaaaaaababaaaababbbaababababbbaaaabaaaababbaaaabbbaabbbabbabbababbbabbbababbbbbaabbbabbaaababbbaaaabbaaabaaabbaaaabaabaababaaaabbaabbbaaaaaabbbaaababaaabbaababbbbbbaaabbaaabaaaaabbbaabbaabaaaabbbabbabbaaabbbbbaabbababbaaaaaaaaaaabbabbaababbbbbaaaabaabbbaabbaabaabbaabaabaaaabaababbbbaabababbbaababbaabaaababaaabbabaaaaaaaaaabaababbababababbabaababbabbbbbbaabbbbbbaabaabaabbbbbabbbaababbbababbaabaababbabaabbbaababaabbaabbbabbaaabbbbababbabaababaaabbbbaaabaabaabbbaabbbbbaaaababbaabbbababbabaabaaabaaabbabababababaaaaabbbaabababababaabbabbbbbaaabbaabbabbbbbabbbbaabbbbbbbbabbaaaabbabbbbababaababbbaababbaabbaabbabaabaabbbbababbabaaaababbaabbabaababbbbbaaaaabbbbbaaaabbbbbbbababbbabbbababbaaabbaababababbaaababbbbaabbabaaaabaaaabbbaaabbbaaaabaaabaabaaaaaaaabababbababaaababbbbabbbaabbaababaabababaabbbbababbbbbaaabbaabaaaabbbbaaababbabbbbabaabbbbabaaaababbaabbaaabaaabababbbbbaabbabaabababbabbbaababbababbbaabaabaaaabbaababbaaabaaabbabaabbabbbaababababbaaaaaabbabbbaaabbbaabaabbaababaaabaabbbaabaaabbbbabaababaaabbaabaaaaabbaababaaabbaaaabbabbabbaabbbaaaabbaaaaabbbbbbbabaaaabbbabaaabbabababbbbbabababaabaaabbababbbbbaaaaabaabbaaaababbbbbabbbbbaaaabaabbaababbabbbbabbbbabaabaabbbbbaaaabaababbaaaabbababbababaabaaaaaaaabbaabbaaaaabbbbbbabbabbbababbabbbbabbbaabbaaababaaabbabaaaabbabbbbbbaabaaaaaababababbbaaaabbbababaaabbaaabaaaaabbbbabbabbabbaaaabaabaabababbbabbaaaabaabbbbbabaaaaababbbaabaabbabbbbbabaababaaaabbaabbaabbbabaabbaabababbbbbabbbaaaaaaaabbaababbbaabbaababbababababbabbaaaabbbabbbbabaabababbbbbaaabaaababababbbbbbababaaaaaabaaabbbaaabbaabababaaaaabaaaabbbbaaababbaabbbabbbabbbbabbbaaaaaababbaabbaaabbabbabaaabbaabbaaaabbaaaabababbaaababbabbbbbaabbbaaaaaabbabbabaababaababbbabaaababaabbbabbbbaabbbbbbbaaaaabbbaabaabbaabbbaabababbbbaabababbbbbbbbaaabaabaabbbabbaaaababaabbabaaaabbaabbbbbbbaaaabbabbaaabbbbbaaabbbaabbbaaabbaabaaabbabaabababbabaababbaababbabbabbabbaaabaabaaaabababbaabaaaabbabaaaaabbaaabbbbaaaaaaababbbaaababbbaaababbbbbbabbbabbbbbbbabaabaabbabbbaaababbbabababbbaaabbbaabaaababbaabbaaaaaabbbbbabaaaaabbabbbababaaaaababbaabaababaaabbbbbababbbaababbbbaabbbabbbabaababbbbabababaabaaaabbbbbbbbababbabbbbaabbbbaaaabbaaabbababaaabbaaabbbabaaaabbababbbbbaaababaabbababaababbaaababbabbbbbbbaaabbabaabbbbbabbbbbababbabbabbbbbbaaaaaabbaaabbaababbababaabaabababbabaaabaabaaaabaabbabbaabbaaababbbaaaabaaaabaabaaaaaabaaaaaaaabbbaabaaabaabbaaaabaabaababbababaababaababaaaaaabbaaaaabbabbbbabaaabaaaaabbbbaabaaaabbbbbbaaaabaabaaababaabbbabababbabaabbabbbabbabaabaaaaabaabbaaaaababbaaababbaabaabbababaabaababababbabbbbaaabbbbaaaaaaaaabbbaabbabbaaaaaabaaababababbbbaabaaabbabababaabbabaabbbbbbbabbabbbaabbbabaabaaabbbabbaabbbbbababababbaaababbabbabaabbabbababababbabbbbbaaababbbaabbabbababaabbaabbbbaababbaabaaaabaabaabaaaabbabbbaabbbbbaabaabbbbbaababaababaaaababaabaaaabaabaababbbabbbbaabbaababaaaaabbaababababbbaaaaaaaababbbbaaabaaabbaabaabbababaabbaababbaabaaaabaababaaaabababbaaaaaaaabbbaaabbbababababaabbbbbabbababbbbababbbaababababbaaabbbaabbabaaaabbbbbbbbabbaaaabaaabaabaabaabaababbbaabbaaababbbbbbbabbabaababaaaabbaaabbbaabbbababababbabbbabbaaaabbbbaabbababbbbabaaababbaabbaaababbbbaaaabaabbabbbaaabbbbbabbbabababbbaabbaabbbaaabbaababaaaaaaabbabbabbaabaaabaaaaabaabbaabaabbabaabaababbaabababbababbbbaababbaaababbbbbaabbabbbaabbaaabaaaabbbbbbaabbaaaabbbbbaaaababbbbbbabbbaaaababbaaaabbaabbbabbabbaaaababaabbbaaababaababbaaaaabbaababaaabaabaabbbbbbbbaaabbababababbabbbbabbaabbaabbbaaaabbbbababbbbabbabbaaaabbbaaaaaabbbabbabaaaabbaaabbababababaababbabbbabbaaaaaabbbaaabaabbbaabbababaabbbaaaabbbbabbbaababbbbaababbabaabaaabaaaababaaaababbabbabbaabaaabababaabbbaabbabbaaaaababaaabbbbaabbabbbaabbbabaabababbabbbabbaabbbabaaababaabbabbabaabaababbbaaaabaabbbbbbbbaababaaaababbabbabaaaabaaabaaaaababaababbbabaabbbbbabaabbbababbaaabaaaabaaaaaaabbbbabbbababaaaabbabaaaaabaaaabbbbaaaaaaabbabaabbabababbaabbbabbabbaabaaaababbbaabaabaaababaaaabaabbaaaaaaaaaaaabbbaaababbaaabababaababbbbbabbabbbaabaabbabbbbbabbaaabbaabababaaaabababaaaabbbbbabaaaabbabaabbabaabbaabaaaaababbbbabaaabaaabbabaaababbbbbbbbaaaaababaabbabaaaaabaaababbabaaaaabababbabaaaaaaabababababbaabaaabbababbbaabbbbaaaabaababbaaabbbaaaabbbbaabbaaabaaaaaababaabaabbaabbbaabaabbaabababbbbbabaaaaabbbbbbbbabbabbabbabbaaaababbbbbbabbaabbabaabbaabbbbbaaaaabbbbbbabbbaabbabbbbabbaaaaabbbabaaaaabbbbabbabaabbbbbbbbbbbbbbbbabaabbababaaabbaabbaababaabbbaabbbbbaaabbaaaabbabbababaaaabbbabaabbbaaaababbaaababbaabababbbabbbaabbbabbaaabbbabbaaaaaaabaabaabbabbabababbaababbaabbabababaabaaaabbbbbabbbaababbabbaaaababbabbbbaabbbbbbabaaabbbbbabbabaababaabbabbbaaaabaaababbbbababbaaaaaabbbabaabaababbbaabaaaaabbbbababbbaabbbaabbbaababbaaabbababbbbbabbbbbbabbbbbbababbbabaababbabaaaabababbababaabaabbaababaaabaaababbbbabababaaaabbbbbbbbbbabbbaabbabbbaaaaabaabaaabbbaaabaaaaabbabbaaabbaaaabbaabbbabbbbbabbabaaaabbbabaaaaaaabbbbaaabbaaaababbabbaabbaabbbabbaabbabbabaabaabbbaaaabaaaabbabbabbaaababbababaababbabaabaaaabbabaaabababbaabaaabababbabbbaaaaabbbbabbaaaaabbabbbbbabbabababababaaaabbababbabaabababbabbbbbbbbaabababbaaaabaababaababbbabbaabaabaabbbaaababbaaaababaaabbbbbbaabbbaabaaaaabbababaababbbbbbbbbbabaabbbbaababaaaabbbababbaaabbababaaaabaabbaaaabbbabbbbaaabaaabbbaaababaaaaaabbbabaababbabbbbabbbabbbbbbbbbabaabaaabbbabbaaaabbbabaabbbaabbabbaabaaaabababaabbababbababbbbbbbabbbabbbbaaabbbbbabbbaababbbaabbbabaabaaaaaababbabbbbbaabbabbbbabaaababbaaabaaabbaabaaaababbbaabaabbaabaaaabbbabbbabababbbbbbabaabbbabbbbabbbbaaabbbbbbbbbbbbababbaabbbabbaaababaaabaababaaabbbbaabaaaababbbabbabbbbababbbbaabaabbbbaaabbbabbabbaabaaaababaaaaabababbaabaaabbabbbbbaaabbbabaaaaababababbaabbabaabbbabbbbbbabbaaaaaaabaaabbbbabbabaabbababbbbbaaababaabaaaabaaaabaaaaabbaabbababaaababbabaabbaabbaaaabaaaabaaaababbaaabbbabbaaaabaabaaaabbbabbabbbaaaabbaaababbbbbaabbabbabaababbbaaaabaabbbbaababaabbababaabbaabbaaaabbbbaabbaababbbabaaababaababbaaaabbabbaabaaabbaabaababbbbaaabbaaabbbabbbababbaaabbbabbbaaaaabbaabbbaabaabaaabaaababaaaaabaabaaaaabbbbaabaabaababbbbbbaabaaabbaababbaaabbabbbaabababaabbabaabbabaababbabaaaabbababbbbabbbbaabbaabbbbbbbbbaabaaaaabbababbbaaababaaabbbaaaaaaabaabbbbbbbabbaabbbbaaabbbbbbaaaababbbbaabbaaaaaabbbbaaabbbabaabbaabbaabaaabaaaabbaaabababaaaaaaaaaaabaaababbbabbabaaabbabaaabbbabaababbabbabbaabbbbbaaaabababbbaaaaaaaabbabaabbabaaabbbaaaaabbaabbbbbaaabaaaaabbbbbbbbbabaabbaaaaababaaabbaabbabbabaabbaaabaabbbbabababaababaaaabbaaaabbbabbbabbbaabaabababaabaaaaaaaababaabbbbabaaabababbbabbbbaaabbaaaabbaabbaaababbaaaaaabbbaaabbbaaaaaabaabbbbbaababbabaaaababbbaabbaaaaaababbbaaaaababbbabaaaabbbabababbbaabbbbbabbaabbaaabbabbabbbbabaaaabaaabaaabbaaaababbaabbabbabaaabbbaaabaaabbbbbbabaabbabbababbaababaabaaaababababbabaaaaaabbaaaaaaabbaabababaabbaabaabaabbaaaaaaaaabaaaaabbababaaababaabbaabababbabbabaaaaabbaabbbabababbbabbabaabbaabaaabababbaabbabbaaaababaababbbaaaaabaaaababbaabaaabaababbbbbaaaabbabbbabaabbabbabbbbbaaabaaabbbaabbbbbaabbaaaaababbbbbbbaabaabbbabbabababababbbbabbbababaabaabaabbbbbaaabbbaaaabbaaaaabaaabababaaaabbabababbbaaabbabbaaaabaababbbabaabbbbabababbababbbaaabbbbbabaabbaaaaaabaaaabbbababbaabaaabbbbbbbababaaaaabbbaababbbbaaaaaaababbbabbbbbabbabababbaabbbaaabbaaabbaabbaaabbbaaaabbaaabaaabaabbababaaabbabbbbbaabaaaabbabababbaaaaabaabbabaabbbabbbabaabbbaabaabaababaaabababbbbbaaabababaaaabbbbbbabaaaaaaabaabbabbbabaaaabaabbbabbaabbabbbabaabbaaabbaaabbabaabaabbbbbabbbbbbbabbbbabbaaaaaaaaabbbbaabbbbbababbabaaaaaabbbaaabbbaababbaabaaabaaaabbabbbbbbaabbbbbbaaababaaaabaaaaabaababbbbbbbabbaaaabbbbabbaabbbabbbaaabaabbbbbabaabbbbaaabaababbaabbabaabbbbbaaabbaabbbaaabbaaaabbbbabbbbabababbbbbaabbaaaaabbaabbbabbabbaabbaabbabbaabbaaabaaabaababbbbbbbbbabaabbbabbbaaaaaababaabaababaabbbbbbbbbbaabbbaababbabbabbbaabbbbaabababbaabbaaaaababbbabbabababbbbbaabbaabbabbbaaaabbbaaaaaabbabbaaabaabbbaaaabaabbaabaabababaaabaaaabbbaabaaaaaaababbabbbabababbaaabbaabababaaabbbaabaabbbbabbaabbbbaabbababbbabbaaaaabbabbbaaabaaabaaabababbabaababbaaaaaabababaaababaabbbbbbaabbbbabaaabaaabbbbaabaabababbaaabbaabbaaaaabbbaabbbabbbbababbbbaaabbaaabababaaabaaaaaaabaabbabaabbaaababaabbabbbaaaaaaabbbbaabbbabaababbbabaabbbaabbbbbabaababaaabbababaaaaaabbaaaabaaabbaabbbaaababbbbaababaabaababbbbbbabbbaabbbabaaaaabaababbaababbbaaaaabbabaabbaabbaaabbaaabaabaaabbbbbaaaabababaaaabaabbbaaaaaabbbbaaaabbbaaaaabaabbbaaabaaaabbababbbababbabaaaabbabbaabbbbbaabaabbbaabbbbbabbbaaabbabbabbbaababaabaabbaabaaabbabbaaababbaabababaaaaaabbaaababbabbaabbbbbbababaaabaabbaabaaabbabaabaaabbbaabbbabbbabbbbabbbbababbabaabbabbbaabbbbbbbbbbabbaaabbabbababbbbaaaaaabaabbaabbabbaaaabaabbbaaabbbbbaaaabaaabbaabababbbabbbbbbaabaabababbaababbbbabaaabbbbaaaaabaaabaabbabbbababaabbabbbabbababbabbabbbababbaabbbbbbbbbaabaabbaaaaabbababbbbbaaababaaaabbabbbabbbbabaababbabaaabaaaaabaabaaaabbabbaabaaaabbbbaaaabbbbaaaaabbabbabaabaaabaabbbabbbaaaabaaabbbbbabbbbaabbbaaabbbaaabbabbaababbbbabbbbbababaabaaaabaababbaaabbbaaabaabaaabbbabbaababaaabbbbbbbbbabbabbbabbabaaaaabaaabbabababbbabbaaabbaaabaaabbaabbbbbbbbabbabbbbabbbababaaabaababaabbbbbbbababbabbaababaaabbaabaaaaaaababaabaabbaabbbaabababababbbaababbabbababaaaaaabaaabbbbabaaabababbbbaabbaabaaababaaaaabaabababbaaabbbaabaabbbabbabaaabbbbbbbabbabbaaabbbbbbabaaaaabbaabaababbaabbabaaabbabaabaaabaaabbabbbbbbabbaababbabbabbbbababaaaaabaabaabbaabbbaababaaaabbbbbbbabbabababbaabbbbbbabababaaababbabbbabbbbaabbabaaaaabaabaabaabaabbabbaaaababbaabbabbbaaaaabbabbbbaaabbbaaaaabbbabbbaaabbbbabbbaaaaabbbaabbabaabbaababbbaaabbbbbbabbabbaabbbabaabbaaaaababbabbbbbbbbaabaaabaaaaaaabaababbbbabbbbaaaaabbabababababbbbbbabbbbbabbbbbbabaaabaaabbaabbaaaaabbbbababbbabbaabbaaaabbbabbbaabaabbaaabbbabbabaabbaabaaaabbaabaaaaabaaababbababaabbaaaabbabaabaabbababbbbabbbbabbbbaaaaaaaaaaabbbabbbbaaababbaabaaabbbabbbbabbbbaaaababbabaabaaabbbabaababababbbbbbaabbbbabaaaaababbaabaaabbaaabbabbbababababababbaaababababbbaabbbbbaaaababaaabababbbbabbabaabbbbaaaabaabaaaaaaabbaababbbababaaababbaabaabbabaabbbbaabaaabbbabbbbbabbabbbbabbbabbababaabbbbbabaaabbaaabbbbbbbbaaaabaaaaababbaaaabbbaaabbabbbaabbbabaababbabbbbabbaaabbbabaaababbbbbbbabbabbaabbababbbbaabaaabbbaabbabaabbaabaababbabbabbbabaaaabbababbbaabbaaaabbbaabaaabaabbabaabbaababababbabbbaababbaaaababbaaaababaaaabbbaababbbaababbaabaaaaaaabbbabbbbbaabbabbabaaabbabbbbabaabaabbabbbabaababbabbbbbbbbbaabbbabaababaaababbaabbaaabbaaabbabaababbbaaababaabbabaaaabbabaaabababbabbbaabbabaabaabbbbbabaabbaabbabbaaaaaabbbaababbababaaaabbaabababaaaaaaaabbaaabaaaabbbbaaabbabaababbababaaaaaabbaabaaaaaabababbbababbabababbbbaaaabbbaababaaaabbbbbaabbababbaaaaaabbbbbbbabbabbababbaaaababbbabbbbaabbbaabbbaabaaabababaaabbbbabbaababbaaaaabbbabbaaabbababababaaababaaabbabbbabbbbaaaaaaabbabbaaaaaaaababbaabbabbaaabbbaaababaaabaabaaabaabbbbbbabaabbabbbbaabababbabbbbbaaaabaaaabaaaaababbbababaaababbbbbaaaaaaabababbbabbaabbbbaaaaaaababbbbbbbabaabaabbbaabbbbbbaabaaaaaababbbbbababbbabababbaaaabbbabbabbabbbaaaaaaaabbabbabaabbababbabaabbaababbababbbabaabbaabbabbaaabbbabbbbbaabbbaabaaaabaabbbbbbbbbbbbbbaababbbbaaaabababaababbbaaaaababaabbbbbaabaaaaaabbabbbbbbbbaabbbabbaababaabbbbbabaabaabbabbabababaaabbbbabbababbbaaaaababaabbbbbabbbbabbabbbbbbbabababbabbaabbbaaabbbbbbabbaaaabbbbabbaabbbbbbbbbbaabbbbaaabbbbabbaaaaabaabaaaabbaaaaabbbbbaabbabaaaaaababbaaaaababababababbbbaaababababbbbbbbbaaaabbabaabbababaabaababaababaabbabbbababababaabbaaabbaaaabbaabbabbbbbbbabababbbbbbbbbaaabababaabaaabbabaabbbababaabbbbabbbabbababbaabaaababbaaabbbbbaabbaabaaaabbbabbabbabaabaababababababbbaaababbbaaababbaaaaabbabbbaaaaabababbbbababaaababbabaaaabbabaaaabaababbbbaaababbbabbaabbaabbbbababaaaaaabbabababaabaabbbabbbabbabaaaaabbbbbaaabbbbbbbabbaaabaababbaaaaabbbabbabbaaabaababbbbbaababbabbabbaaaabaabbbaaababbbbaaaaabbabaabbbaaaabbabaababaaababbbbababbaaaabababbbbbbabaabbbbababbabbbbaaabbaaabbbbaaaaabbbbaaabbbaaaabaabbbbaabaababbbaabbbaabbabbabbbababbababaaaababbaaaaabaabaababbabbabababbaaabbababbabbbbbabaaababbbbbbbabbaabaaabbababbaabbaaaaabbbaaaaabbbbbbaabaaaabbabababaabaaabbbbaaaabbbabaababaababbbbbabaaababbabbbbabbaaaabbbabbabaaaaabbbbbabaabbbaaaaaaababbbbaaabbbbbbabbbbbabbabbbaaabbbbaabbbbbbbbbbabababbaababaabaaabaaaabaababaaabaaabbaaabababaaaaaaaabbabbbaabbbaabbbabaabbaabbaabbbaabbaababbbbbbaabaaababaaabbabbabbbbbbbaabaaaabbbaababababaaaabbbaaaabbbabbababbaabbbbaaabbbabbbbbaabbaaaaabbabbababbbbaaababaaabbbabbbaaaababbabbaabababbababbbbbaaabaabbbaaabbaabbaababaaaabbbabaabababbbbabbabaabaaaaababbbaaaabaabbbbbababaaabaaabbababbabbabbbaaabababaabaaabbababaabababaaabbabbbaabbbbbbaabaabaaaababbabaabababbabbaabbbaababaabbbbabaabbbaabaaaaaabababababbabbaabaabbbbaabaabbabbbaaaaababbbbbbaabbaabbbbbbbaaabaabbbbbaaabbbabbbbaaabbaabbbaaaaabbabaabbabbaaaaaaaaaaaabbbbabbaaabaaaaaaaaaabaaaaabbabbbabbabaaababbbbaabbaaabbbbbaabaabbbaabbabbabbbbaabbabbbbbbbabbbaaabbababababaabababaabbbabbabaababaabbabbaaabaabbabaababaabababbbaabbaaaabaaababbbbabaababaabbabbabaabaaaaababbbbababbababaabaabaabbbbababababbaabbabbbaaabbbbbbaaaaaaaaaaaabbaaababbbbbabbabaabbbbaabbababaaaaabaaabbbbabababbaaabbaaabaabbbbabaaaaabaaaaaaaabbabbabababbbbaaabbababbabaaabbabaabbaaaaabaababbbaaabbababbaaabbbbabbbbbbaaaabaaaaabbabaabaaaaaaaaaabababbbaabbbababaaabbbabbaaaabaaabbbaabbbbbbbaabaabbaabbbbaaaaaabababbaababbbabbbbbbbaabaaabaaaaababbbaabbabbbaabaaabbbaababbabbabbbbbbbaababbbaaabababbbababaaaabbbbbbbabbabaabbbbbaabbaaaabbabbaabaaaababbbbabbbaabaabaabaaabbabbbbabbbbbbaabaaaaaabbabbaabbbbabababbbabbabaaaababbbabbbbbbabababbbbbbbabaabbababbabbaabaabbaaaababbaabbaaaaabababbaaaaababbaaabbaabbbbbabbbaabbabbaababbbabbbbbbaaaababaaaabaabbbaaababbabaaaabbaaabbbbaababbbabaaaababbbaaaaaaabbaaaaaaaababaaaaaabaabbbababbababbbbabbbbabbbbabbaaaaaababbababbbbbabbbaaabbbbaabababbaabbabababaabbaabbabaaaabaabbabaabbbbbaaaaabbabbbaabbaabbbaaabaaabbababbbabbababbabbbaabbaaabbaabbbabaaaaababaabababbbaaaaabbabababbbbaaabbaaabbbbababaabababaaabaaabbaabbbababbaaabbabbababbbaabaabbabbbababbabaabbbbbbbbababbbaababbbbabbabaabaabbabbbbbabaaaabbbaaaababababaaaabaaaaaaabaabbaababbaabbabaaaaaabbbaabbaaaaabaaabaaabbbabababbabbbaabababbbbbbbbaaaaaaaababbbbabaaaaabaaaabbaaaaabaabbbababbbabbbabbbaababbbbaababaaabbbaaaaabbbabababababbabbbababababbabbabaaaaaabbaabaaabbabaaaabbbaaaaababaabbbbbaabaaababaabaaabbbbbabbbabababbaabaabaaaaabbaaabaabaaababaabbbababbbbbabaabbababaaababaaaaabaaabbaaaaaabbabaaabbbbbbaabbaaabbaabbbabaaaababaabaaabbbaabaabbbbbbabbabbaaaaaaababababbbbbaabaabbbabbbaabaababaaaaababaaabaaababbbabbbbaaaaabababaabbbbabaaabaaabbabaabbbabaaabbbbbbababbbbabaabaaabaaabaabbbaaabbaaababbaabbbabaababbaababaabbbbbbaabbaabaabbbbbbaabaabbaabaaababbababaabbbbababaabaabbbbbabbbbaaaabbaabbbaabaaaaabaabababbaabbabbabbaabbabbaaabaabbabaabbbbbaaaabaaaaabbbaaaaabbbbaabaabaabaabaaabaaaaaaaabbaaabaabaaabaabaaababaaaabbbbbbaabaabaaabbbbbaaaaabaabaabbbabbbbbbabbbababaabbbabaaabbaabbbbbbaaaaaaaaabaabbabbaabaaabbaaabaabbbbbaabbbabbaaabbbaabaaabbbabbbbababbbbabaaabbbaabbababaaabbbaaabaabbabbbbabbbaabababbbaabbbbbbbbbaaaaabbabaaababbbbabbbbbabaabaababbbaabbbaaabbabbababaabbbbbabababbbababbaaaabaabaabbbabbaabaaabbaaaaaabbbbaabbaabbbbbababbbbbbaabbababbbaaabbabbaabaababbbaaabbbbbbabababaabbababababababbbbabaabbbabaabaaababababbaaaabbbabbaaaaabbbabaabababbabbbababbabaababbababbaabbbababbabbabaaaababaababbbbabaabbabaaabbbbabbaaabaabaabababbbbaabaaaabaaaaaabbbaaabbbabbaaabbaabbaaabbbabbaabbbabbabbbbaababbabbaababbbaaabaaaaabbbaaaaaabaaabaabbaaababbbbbabaabaaaabaabbabbbbaababaabbbbbbbaaabaabbbaabbaaaaabaabbabaababaabbaabbaaabbabbbaababababbabaaabbbbbaabbbbaaaaabbabbbbaababaabababaaabbbaababbaaaaabbababbbabbbbaababababababaaaaaaababbbaaaababbabbabbabaabbabbbbbabbbababababbbbabaabbbabbabbbababbbababbbbbbabbabbbaabaabaaaabbbabbaabaabaaabbbbbbbaaaaaabbaaabbabbbbaabaababbabbbbabaababbbababbabbbaababaabbbbbaaaabbbabaaaabbababbbbabbbaaaaaabbbaabbabaabbbaaaababbbabaabbabaabbabbabbaabaaabbbaabbbabbabbabababaaababbaaaaaabaabaaabbaabbaabaabbbaaaababbaabaabbabbabaaabaaabbabaabbbaababbbbbaabbbbbbabbbabbabbabbaababaabbbbbbaaabaababbbbbbbabbabaaabaabbbbbbbbaaaaaabbabbaaababbbaababbabbbaabbabbaaabbaabbabaabbaabbbbaabbbbabbbababbabbabaabbaabaaabababaabbbaabaabaababaabaaabbaabbaaabababaabbaabaabaabaabbbbaaaaaaaabbbbabbaabababbbaaabbbbbaabbabbabaaaaaaababaaabaaabbbaababbbbaabbbbbababaaababababbabaabaababbabaaaaaabbaababaabaabbaabbaababababbabaaabbbabbbabaabbaababbaabaabababbbbbaaabbabbbababaaabbbabaabaababbbbabbbbbbabbaabaabababbbaabbbaaabaabbaabbbbbabbbbbbabaabaaabbabbabbaabaaaabbbbaabbabbbaaaabbabababaaabaaabbaabbabbbaaaabbbaaabbaabbaaaaabbabbbaabbaabbbbabbabbbaaaaabaabaabbaaabbbaaaaaaababaababaababbabbabaaaabaaaabaababbbababbaaaabbaaabbbabbbbaaaababbbbbbaaabbaaaaaababbabbabbaaawbbbaabbabbbbaababbbbbaaaababbaabbbbababbabbabbbabaaaababaababaabbababbaaaaabbbbaaaaabaaababaaabaaabbbaaabbbbbbabbabbbaababbbaaaaabbbbaababababaababbaaabaabbbaaaaaaabbaaaaabbabbabaaabaabbbabaabbbabbaababbababbbaabbbbaaabbababaababbbbbbababbbbabaaabbabbbbbbabaabbbbabaaabaababaabbbbabbabbaaabbbbabbababbabaabaabbabababaabaabbbaabaabbbabaabbbbbbbaabaaaabbbaabbabbabaabaaaaabbbbbbaabbbbbbaabaaababbaaabaabaaababaaabbbabbaabbaabbaaaaabaabaaaabaaaababaaabbbbababaaaaabbabbbaaaababbbaaabababaabbaaaaabbabbbabbaaabbaaaabbbaaaaaabbbabbabbabaaaaabbbbaaabbbbaababbaaabbaabbabbabbbbabbabbbbbabbabbabbbbbaababaaaaabbbbbbbbabbabbbbaaaaaaaaabaaababbbbbabbabbaabbbaaabbbaaabbabbbbbbababbbbabaabbbbbaabbaabaaaabbbabababaabaaabaaabaaabbbbbbbabababbabbbaaababbaaabbbbaaaaabbabbbbaabaaaabaaaaaabbabbbaababbbababbbbbaababbaaaabababbbbabaababbabbbabbbabbaaaabaababbbbaababaabbabbaaaaabaabbbbaaaabbbaabbaababbaabaabaabaaaabbabbbbbaabababbbbaabaaaabaaaaaaaabbabaaabbbbbbaaaaabaabbaaabbabbabbbbababbaabbbbabbaaaaaababbbbabaababbabaaabbbabbbbababababaababbbaabbababbabbabaaaabaaaaabababbbabaaabbbaabbbbabaaaaababbbabaaaabbaabaaabbbbbabaaabbbbaaabaaaaababbbabbababaaabbaababbaababbbbabbabbaaabaaaaabaabbbbaabbaaabbababbabbababaabaaabbbabbaaaaabbbbababbbbbabbbbbababbabaabbabaabbbbbaabaaabbabaababaaabbabaaaabbbabbabbbbbbaababaaaaabababbbbaabababaaabbbbbbbabbaaababbbbbbaaabbbbbabbaabbabbbaabbaabaaabaaaabbbaabaaaaaaaaabbabaabaaaabaaabbabaaabbaaaaaabaabbbaabbbbbbbbbaabbabbaaabbabbbaabbbaabbababaaabaabaababbabbaabbbbbaaabbaaaabaabbbabaaabaaaaaabbabbabababbbabaabaabbbaabbababaaabbabbbbbbabbabbabababbbbbaababbaaaaaaabbbbaaaababaabababaababbbbabbaabaaaaaabbaaababaabbbbbbbabbbaaaaaababbbbabbbaaaabaaabaaaabbbbbababbbbbababbabaabaaabaaabbabaabaaaabbaabbabbabbabbabaabababbaabaaaaaaaaaabaaabaababbabbabbabababababbbbaabbabbbabbbabababbbbabbbbabbbabbaaababbbaabbbaabbbaabaababbaaabbbbbbaaaabaabbbbbbaababbaabbbaaaaaaaaaaabbbbabaabaabbaabbbbabbbbabbabbbaababbaaaabbbaaaabbbabbaabbaaaabaabbaabaabbbababbaabaabbababaaaabbbbaaaabbbbbabbaababaababbabbaabaababbbbbbabaaaabababaaaaaabbbaabbabbabbbaabbbaaaababbbbbbaaaababbaaabaaaaabbbaaabbbabbabbababbbbbbbbaaaabababbaaaababbbbaaabbabbabbaaaabbaaaaabbbaaaaabbabbbbbbbaaabaababaabbababbabaaaabbaabbabbbbabbbbbabbbbabbbababbaabbbbabbabbababbbababababaabbbaabaaabababbabbbaaabaaabbaabaabaabbbaabbbababaaaaabbbbbbaaabaabbaababaabbabbbbbabbaaaaabbbbaaaaabbabaabaaaababaabbbbbbaabaabaabaababaabbbbabbbabbbbbbbbbaaabbbbabbaabbaaaaaabbaaaaaabbabbbbaaabababaaaaaaabababbbaabaaabbbbbabbaaaabaabbbbaaaaaaaaaabaababbbbabbabaaabaabaababbabbaaabbabbaabbbababbabbabbbbaabbbaaaabbbababababaabbbbbbbbbbaabbbbbbaababbabaaabababaaababaaabbabbabbbbbabbbbbaaabbbababababbabbabaaaabbbbaaabbabbbbaabbaaabbbbabbabaaabaaabbababbbbaabaabbbbbbabaabbbbabbaabaababbbbabbaabaaaaabbbabbbbaabaabbababbabbbaaaabbabbbbaaababbbbbaababbaabaaaabababaaaaaaaaaaaabaaabbaabbabbbaaababbbbbbaaaabbbbababbaabaabababaababbababbbaaaabbabaaababbbabaaabaaabaabbaaaabbabaaaabbbbbababaaaababaaaabaaababaabbbaaabbabbaabaaabbbaabaabbaaabaabbbaabaabbaabbaaabbbbababbbbbbabbaaabbbabbabbaabbabbaabaaaabbbbaabababaabbabaaabbbaaaabbaabbbababaaaabaaaaabbabababababbbbbababababaabbbaaaaababbbaabbaabaabbbbaaaabbbabbababaaababbaaabaabababaabaababbbaaaaababbbbbbaababbbbabbaaabbaaabbbbbbbbaaabbabaaaababaabbbbabbabaabaabaabababaaabbaabaaabbabbabaaaabbaaabaaaaababababaaabaaabbaaaabababaaabbabbaabbbbbbabbaabbabbbbbaabbaaabababbbaaaabaaabbbabaabaaabababbbbababbaaabaabbbbaaababbbbbaaaabbbababaabbbbbbaaabbbaaabaababaaaabbaabbbbbaaababbaaabbaababbaabbbbbbbaaaabaaaababbababaabababaabbabaaabababbbbbbababbbbabaabbbbbaabbaabbababbbabaaaaabaaaaabaababbababbabbbabaababbbbaaaababbbaaaaaaababbaabaaaaaaabbbbababbbbbbabababbbabbbbabbabbabbbabaabaaabababbbbaababbaabbbababaaaabaaaaabbbbaaabbabababbbbaaaabaaaaabbbabbaaaabbbabbbaabbbarbbabaaaaaabbaaaabbabaaababaaaaaabaabbabaaaaabbbbabaaabbbaaabbbbbaaabbabbaaababbbbbbaabbbaaabbaabbbaabaabbbbaaaaababbababaabbaababbaaaaabaabaababaababbbabaaaaababbabaababbabbabaababbabbaaabaabaaabbabbbaaabbbabaababbbbbabaaababbbaabbbaababbaabababababbbbbabaaababaabbbbaaababbababaabbaabbabaaaababaababaababababbbbbbbbbaaababbbababbbbaabbbaabbabbbbbbbaabbaaababaaaabababaaabaabbaaaaabbaababababbbabbabbaaaabaababbabbabbaabaaaabaaaaaaaaaababbabaabbabbbbbaaaaaaabaaabbbbababbaaababbaaabbbbbbaaababaabbbbaaaabbbbbaabaaaabbabaababbaaaaabbaaabaaabbaaaabbbaabbbbbbbaabaaaabaabbaabaaaabbbaaaaaabbabaabbbbaaaaaabbbbbabbabababbbbaaaaababbaaaaaababbaaabababaabbbababaaaabaabaaababbbababaabbababbabbbbaaaabaababbbbabbbbbbababbaaabaabaaaabbbbbbbababbbabbaaaaaaaabbbaabaaabbaaababbaaaabbbbbbbabbbabbabbaababbaaabbbaaaaabbaaaabaababaaaaabbbbbbababbbbbbaaabababbaaaabaaabaabaabbbaabbbabbabbabbaababbbbabbbbbbbabababbbbbbbabbababbaabbbbbaabbbbaababbaabbabbbbbbbabaabbbaaaaabbbbbabbbbbbaabbbabaaabababbabbbbbaabbbabaabaaaababababaabbbbaababbbababbaaaaaabbaababaaabaabbbbbabbabbaabaaababaaabbabbabbaaabaaaaabbbbabbabababbbbbbaaabbaaabaaaababbaaaaabbabbaabababbbbaabababbabbabaabbbbabbbabbbabbbbbbbbaabbabbbabbabbbbbbabbaabbbababbaabbabaaababababaabaabbbabababbababaabbbababbabbaaabababbbbbbbbabbaababbbbaabaaaababbababbaabbaabbbbabbababbbbbbabaaabbabaabababaabaaabaaaabbababbbbbbabbabababaabbababaaaababaababbaabbaababbbbbabbbaababaabbbabbbaaabababaabaaaaabaaaaabbabaaabaabbbababbababbabbaababbaaabbabbbbaaabbbbaaabbbaaaaaaaabaabbabababaaabaaaaaaaabababbbbabbbbbbaabbabbbbabbbbbaaabaaaabaaaaabbbaaaabbabaaaaaabaaaabbabbabbabbabbbbaaaababbbababaaabbabbbbbabaabababbbabaabaaaabbbabaabaabbaabbababaaabbbbbaababbbababbbbbbbbbaabbabbaaabaaabbabbabababaaaaaaababaabaaabababaabaaaabaaabbbbbbabbbbbbaaaabaaaaaabaabaabbbaaababbaaabababaaaabaaabbaabbaabbaabaabaabbaaababbbbaababaaababbbbbaaaababbbbbbabaaaaabaabaababaabbaaabbabbbabaabbbbabbaabababbbbbabaaabbaaaababaaabbaaabbaabbbaabbbbbabbaaabbbabaabaabaabbaababbbbbababbbabbababaababbbbabbaaabbbaaabbbabaabbabababaaaaabaaaabaaaaabbbbbbaaabaaabbbbabbbaabbaababbbaabaababaaaaabaabbbbabbaaababababbababaababbbbbababbabbaaabaabbbbabbabaaabababababbabbaababbaabbaabbbbbbbbaabababaaabbaaabbabaaabbabaaabaaaaaaaabaaababbaaabbabbbaabbabbabbbabaaabbaaaaabbbabaaaababababaaaababaaaabbaaabbabbaaabbbbbaabbaaabbbbababbbbaaabbbabbbbbaaabaababbbabbabababbaaabbbbbbaabaaaaabbbbbaabaabbbbbabaaaaaaababbabbbaabbbaabbaaaaaabbbbababbaaaaabbaabbbbbbbbbbaaababababaababaaababbabaaaababbbbbabbbbabbaaaabbbbbbaaaaaaabbbaababbbabbabaaabbbbabaaaabaabbabababbbaaaaabaaabaaaaaaabbabbababbaabbaabbabaababbbaabbbababbabbabbabaaaabaaabbabaababbbbabbaaaababaaabaabbbbabbbbabaabbaaabbabbbababaaaabbbbbabbaabaababababbbbbbbbbbababbabbbbbbbabaabbbaaaaaaabbbababbaaaabaabbbaabbbababaaaabbaababbabaababbaaabaaabababbaababbbbaababaabbbbbbaabababbaabbabbaaabababbaaabbaabaaabbbaaababaabbababbbabbbbbbaaabbabaabbbabbbbbabbbbbbabbbaabaabbabbabbaabbbabaabaabbaaabaaabaaaabbbabaababaabaaaaaabbbaabbaaaababbbaabbbbaaabbbaabbbabbaaaabbaabbabaababababaabaaaaaababaaaaabaabbbbbaaaabbabbaaabbabbbabaababababbbabaaaaaaababbaaabaaabbbbabababaaaaaabaabbbbaabaaaaaaaaaaabbabaabaabbbababbbaaabaabaabbaaabaababbabaababaabbbbbbabbbbabababaaaabbbaaaababbbbbbaaaabbbbababbbababbaaabababbbaaabbabbbababbabbbaaabaabbaaababaabbbaababaaabbabaabbabbabbbabaaababbbbbaaabaabbaabababaaaabbabaababbababaaababaabaabbaaaabbaabbbbaaaaaaaaaaabbbaaaaaababaabaaaaaaaaabbbaabbbabbabbbbabbaababbbbbabbbabaaaaababbbaababaabbbaaaabaabbbbbaabaabbabbababaabbbaaaaabababbbbababbbbaaaababaababbbabbaababbbbaaabababbbbabbabaaaabaabaaabbabbabababbbbbaaabababbaaaaabbabbbbabbaababaabbbbabbababbbbababbbabaaababbabbbaaaaaabaabbaababbbababaaaababbaaabbaababababaaabbbbaaaaabbaaaaabaaaabababbbbbabbbbabbbbaababbbbbabbabbbaabbabaabaabbaaaababbbbababbabbbbaabbaaaaaabaabaabaabbabbaabbabbaabbbbabbaababbbbaaabbaaababaababbaaaaaaabaabbbbabbbbaaabbbbaababaaaaaabbbbabaaabbbabbabbaabbbaabababbaabbabbabbababbbbbaaaaaabaaabaabababbbbabbabbbbabbbbabaaabbbabbbababbabaaabaababbbabbbaaabababaaabbbbaabbabaaaaaaabbbbbaabbbaaaabbbbbbaaaabaaaabbabbaabaaabbbaabbaaabaabbbababaabaaababaaabbbabaabbbbabaabaabaabaaabbaaabbbaaaababbabbaabababbbaaaaabbaabbbbabbbbbbbababbaaaabbababbbaabbababababbbbaabbbaabbaaaababbbaabaaabbaaaabbaaaabbabbbaabaabbbabababbaabbbbabbaabaababaaabababbabbabbbbaaabbabaabbaaaaabaaaabaabbbabaaabaabbabbbaaabbaaababbabbbbbbbbbaababaaaaaabaaabbaaaabaababbaabbaaababbabbbbaaabbabbabaaabbabbbbbabaababbaaabbaaabbabbbbbbbbabbaabbbaaabaaaababbaabaaaabaababaaabbbaaabaabaaaaaaaabababbaaaababbbbbaabbbabbabbaabaabaaaabbabbbaaaaaabaaabbaabababbaabbbaaabaaababaaaaaabbaababbabaabbbbbbbababbaaaaaabbbbababaaaabbaabbaaabbbabbaabaaaabaababbaaaabbabaabbbbbabbababbbaababbabaaaabbbbaabbabaaabbbaabbabbbbaabbababbbabbaabbaabbaaaaabbbbbbbbaaababbbbaababbabbbabbaababbabaaaababbbbaabbbaabababaababbaaaaaababbbbaabbbbbabbabaabbbabaaabbaababaaabaaaabaaababaaaaaaaaaaabbaababaaaaaaabbbbbabbbaaaabbaaabbbaabaababbbabaaaabbaababbaaaaabbbabbbbabababaababababaaabaaaabbbaaabaabbbabbabaaabbaabbaaabaaabbabaabbbabbbaababbaaabaaabaabbabaabbaaababbaaaabaaaabbbbabababbaaaaababbabbabbabababababaababaabaababbabaabbbbbaababbaabaabbabbababbabaabbbaabaabaaabbaabbaaaaaabbbabaabbbbaabaaababbbbbbaaababaaabababbaababbaabbbbabaabaaaaaabbbaabbbbaababbbabbbaabababbabbbbabbababbbaabaaabbaaaabbaabbbbaabbaaabbbbabaabbbaaaaaabbbbababaababbbabababbbaaaababbaabaaabbabbaaaaabaabbbbabababaababaaaaaaabaabbabaababbbaaababaaabbbaabbaabaabaabaabaabbbbbbbababababbabbaaabbbbaababbaabbabbbababaaaaabbbaaaaabaabbaaaaaababaababbaabbbbaabbbbabaaabaaabaaaaabbbaaaabbbbaaabaabaabbaabbbbaabababbbabaababaabbabbbbaaaabababaaaabbaabaabaabaaabbabbbabbbaabbbabbabaaabaaabbabbbababaaabbaaaabbbaabababbbbabbabbbaabbbabaababbabaababaaabaaabbaabbbbaaaaabaaabbbaaaabbbabaababaaaabbaabaabaaabbbbaaabaaabaabbbbbbaabbbabbbaababaabbabbaaababbabababbbaabbbbbbbabbbabbbaaaabbbaabaaaabbbbbaabbbbbbbabbaabaabbaaaabaaabbbbababbaabaaaababbaaababbbababbabaaababbaababbaaababbabbaaaabbababaaabbbbbbbbbabaabababbbaabbbbbabbaabbababaabbaaabbaabaaabbbabaaaabbabaaabbbbbbbbabaabababaaaabbababaaabbbabbbbbbababaaabbbaaaaaabbabbbbaaaaababbbaaabaaababbaabbabbaaaaababbabbbbbaaaaababbababbabbbaabababaaabbaabaabbaabbbbbbaabbbbbbabbbababbababbbbbbabaabbbaababbaabaaaabaabaaabbbbbbaaabaaaabbabbbabaaabaabbabaaabbbabbbbabaaaaaabbaababaabbbbabaabaaabbaaabbbabbababbbbaababaaabaabbabbbbabbbabaabbabbbababbaaababbbbbbabaabaaaabababbabababaaabbabaaaaaabaaabaabbbaabbabaabaaaababbbaaabbbbbabbbaabaaababababbbbbbabbbaaaaabbbbaaaabaaaabaabbbabaabbbbbbbbaabbbaaabababaaababababbaaabbababbaaabbbbabbaaaaabaabaabbbaaabaaabaabbbbaabbbbaabbbababaabaaabaababbbbbbabbbbabaabaabbbabbaaabbbbaabbaaabaaaabbbababaaaabbbaabaaabaabbbabbbbbbabaaabbbaaaaaabbbbababbaabaaaabbbaaaabbbabbbaaaabbabbbabbbabbabaaaababbaaababbbababbbaaabbbaabaaabaabaaabbbbaaaabaaabbbaaababababaabbbabababbbbbaababbbaaaababaabbabbbaaaaabbbbaaaabaabbababbbbbbaabaabbbbbbbbbbbabbbbbaaababbabaaaabbbaaaaabaabbbabbaabaabbbbaabaaaaaaababaaabbaaaabaabbbbbaaabbbaaabbbabaabaabaabbbaababbababbbababbabbaaababbaababaababaaabbbbbbababaabbabbaaabbbaaababbabbaaabbabbbbbaaabaaabbabababaaaabaaabaababaabababbbabaabbaabaabaaababaaabbaabbbbaabbbbbbbabaabbaabbbaabbabaaaabbbbbababbbbbbbaaaabbbabaababbbbbbabababababbabbbbbbabbbabaabababbbbbbbaabbbababbbabbbaabbbbbabbaaababbaabbbaababaabbaabbabababbaaaabbbaaabbbbaabbbaaaabbbabaabaabbbaabbbbbbbbbbbababbbabaababbbbbabaaaababaaaaabaabbaabababaaaaaababaababaaaabbbaabbabbaaababbbbaaaababbbaabbbaabababbbababbbbbbbabbbbabbabbbabbbabbbaaaaabaaaaaabaabbabaaabbbbbbbaabaabaabbaaabbaabbabbbbbabbbbbbbbbabaaaabaabbbaaabaaabbbaaabaabbbabaaabaabababbabbaabbbaaaaaabaabaaabbaabbbabaabbabbaabaaabbaabbabaaaaabbabbaaaaabbaaabaabaaabbabbaabbabbbaabaaaaaaaaaaaabbbbbaababaaaaabbabbbbbababaababbaaabbbbbababbababaabaabbbbabbbbaabaaababaaabbbbabbbbbababbbbbaabbbababbbaabbbbbabbaabababbbaababaaaaababaabbababbaaabaabababbaaabababaaaaaaaabbbabaaaaabbabbaabbaaabbaabbbabbbaabbbaaaaabbbabbaaabbbbabbbbbaaaabbbbabbabbbbbbbbaaabababbbbbbaabbabaabbbaaaaabbbaababaababbaabbababaababaaaabaaabbaaaabbbabbbbabbabbaabbaaabbbbbabaaaaabaabaababbabbbbaaaabbbaaabbbbbbabbbaaaabababaaabbababbbbbaabbbbaabaaabababbbaaabbaababbaabaabbaaabbbaabbaababaaabbaabaaaabaabbbbbabbaabbaababaaaabaaaabaaababaaabaabbaabbbbabbbbabbababaaaabbabbabaabbaabababbbabaabbbbbbabaaababbbbbbaaabbbbbabbaabaaabababaabbabaabababaaabababaabbaabaaaabbaaababaaaaaaaabbbaaaaabbaabbabbbbaaaaabbabbabaaabaaaabaaaaaababbabaabbabbabbaabbbbababaabaaabaabaabaabbbbbbaabbbbbbabbabaababbabbbbaaabbaabaaaababaabbbbabaabbabababbababbbbaaabbaaabaabbaabbbababaaabbbaabbabbbabbaabbaaabaaabbbbbbabaabbaaaaaabababbababaababbababbbababbaaabababaabababbabaabbbbabaabababaabaabbabaabbbabbaaaaaabbabbbaaaabaabbbbabbbbbbaabbbbabaaabbabaababaabbbbababbbabbaaabbbabaaaaaaabbaaabbbaabbaaababbaabbbbaaabbbabaaabbbaaabbbbabbabbaaaaababaabaaaaabbbbbabbbbbabbbababaaabbabababbababbbaaabbbbbaaaababbaabbbaaabbabbbaabaababbbbbabbbaababaaabaabaaaabaabbabbbaabaaaabaabbaaabbabbbbaabbbaaaabbbbaaaabbbababababaabbbaaababbbbaaabaabbbaabaaabaaaaabababababaabaabaaaaabaaabaabababaaabaaaabbabbababybabbbbbbbaaaaaaabaaabbabbaabbaaaaabababbaaabbabbbbbaababaabbbbabababbabbbabaaabbbabbbaaabaaabaaaaaaabbbbaababababababbaabaabbbaababbaabbaaabbbaaaaababbaabaababbbbbbbbbabbabababbabbabbbabaaabaabbabbbaaabbbbbbaaaaabbbbaabbaabaabbbbbbabbbaaaababbaabaaababaaabaaababaabbbabaabaaaababaaaaaaababbaaaabaabbbbabbbaabbaaababbbbbaabbbbbaaaabbbbabaabbabbbbababbbabbaaabbbbbbbabbbbbbbabaababbabbaabaaababbaabbbbbbbaaaaaaaaababbbbaaabaaaaaaaaabaaabaaaaaabababbabbaabaabbbbabbaaaaabbbbaabaabbababbaaaabbbbabbbaabaaaaaaabbbbaababbbaaababbaabbbaabbabaaabaaaaaabbbaaabbabbbbbbbbaabbbabaaabaababbbabbaabaabaabbabaaabbaaabbabbbaaabababababbaaabbbbaaabaaabaabbabbabaabbbbaababbaaaabbaabaaabaaaabaaaabbaaabbaabbabababbaaababaaabaabaaaaabbbbabbaabaaaaaaaaababaabbbbababaaaabaabbbabaabaaaabaababbbbbbabababbbbbabbbabbbabaaabaabbabaaabaaaabaabbabbbbaaaaaabbaababbbababbbaaababaaabaabbbaaaaabbbbbaaaaaaabaaaabbbabbabbbabaaabbabaabbbaaabaabaabaaabbaabbaabbabbaabbbbaababbabaaababbbabbbbabaabbbbabaabaababababbbbabbaababbbbbbbbbaaaabbbbbabbbabaaaaababbbababbbaaaabaaabaababbabaababbaaabbbaabbbaababbabaabbaaabbbbabbababaababbabbbbbaababbbbabbaaaaababbbbbabaaabaabbabaaaaaaabaaaaaabababbaabbaabbbbaabababaabbaabaaaaaabbaabaaabbbbbabbbbbbbabbaabaaaaabaabbbbbbbabaababbbbbbbaaabbaaaaabbaaabaaaabaaaabbabbababaaaabbbabbbabbaababbabaabbbbbbabbabbbaaabaaabbbaaabbabbbbbaaaaababaabbababbbabbabaabbaaaaaaaabbbababbaabbabaaaababbbaaaaababaaababababababbaababababbaaaabbbbbbabbababaaaabbbabababbaaabaaaabbabbbbaaabbbbbbababababbbabbaaaaaabbabbaaababbaabbbaaabbabaabbabaaabbabaaabbbaaabbbaabaabaaabbbaabbaaaaababababbbbbbabbbaabaaabbbabaabaaaaababbbabbaabbabaabaaababbabbbbabbbbaabaabbabbbbbababbbbabaaaabaabababbaababbabaaabbbaabaaaaaaaabbaaaababbabbbbaaaabbaaaababbabaaaaaaaabaaabbbbbbababbbbbababaabbbaaababababababaaaabaaabbbbabbbbabbaabababbaabbbbbabbaaabbbbaaabbbabbbbabbbbabaabbbbbaaabbaabababbabbabbbbbbbaaabababbbabbababbababbbabababbaaaabaabbbabbbaaaabbbbabbbabaaabbaabbbabbabababbabbbaabbaabaabaabaabaabbaaaabbaaaabbabaabaaaaabbbbabaaabbbbaaababbaaaabbabaaababbbbbbaaaaabbbabbbbbbbbbaababaabababbabbbbabbaabbabbbbbbbbabbabbabbbbaaaabbabaaaabbbbabbabbabbaabbabaaaaaabbbababaabbaaababaaababbbaaaaaaabaabbbbbbaaaaabaaababbababaabbaaaababaaabbaabaabbababbabbabbbbaaaaabbbbabbbbbbbaabbaabbababbbbbababbaaababaabaababbabaaaaaaabababbbaabbaaaabbaaababbababbaaaabababbabbaabbabaabbabaaaaaaaaaaabbabaababbbaaababaaaabbaabaaabbabaaaaaababaabaabbbabbbbabbabaababbbbbbbaaababbaabbabbaaabaaabbaabbbaaabbbbababbaababbaaaabbbabbbbabaaaababaabbaabbaabaababaaaaaabaaaaabbaaabbababaabbabbaaaaabaaaabbabbaaaaabbaaaababaaaabbbabaababaaaabaaabbabababbbaaabbaaaaabababbaaabbbbbabbbbbaaaabbaaabbaaabbaaabbababababbaabbbaabbbbbbabbaaabbabbbabbaabaababababbbbbaabbbbbabbaabaabbabbbaaaabbbbaabbbabbaaaabbaabbbbaabbbaaabbbbbbabababbbabbaaaaaababaaabbabababbbaababaabbbaabbbbabbaabaababbbbaaabaabaaaaabbbbabababbabababbaabbbbaaabababbabbbaaabaabaaabbbbbbaaaabbbbbbababbbbabaaababbaabbbbabaaabbaaabbababbaaaababaaabaaaaaaaaaabaaababaabbbabaabaabababaabaaabaabbaaabbabbabaaaaababaabaabbbbbabbbbaaaaababbbaabbabaaabbaaababbbbabaaabaabbbaaabababbbbaaabababaaaabbbbabaaaabaaababaabaaaaabaabbaabbbaaaaaaabbbbbabaaabababbbbbaaaabaabbabbaaabbabaaababbbbbbbabbaabbbababbabbaaaaabbaaabaabbababbbbaabbabbabbabbbbaaaabbbabaaababbabaaaabaabaaaaabbababbaabaabaabababbababbabbbabaabbbabbaaaabbaabaabbababbbbbbbaabbbaaaabbaababaaaabbabbaaaaabbaaabababbbbbabababbbabaabbbaabbbbaabbbbaaabbabbababababbaaabaaabbbabbabbbbbaaabbbbabbaabbbbbaaabababbbaaabbaabbbababbabbbabbaabaabbaabaaaabbbaabbabaabaaaabbabbbbbbabaabbbaaabbbaabbababbabaaabaaaababbabbbababbbbbabbbabaaaabbbaaababbbaaaaaabbbabbbaaabbbaaabbaabbabbbbaabaabbabbbbbbabbbbbbbababbbbbabbababbbaaaabbaaaaaaaaaabbbbbbaaabbbaabababbbbbbbaabaaaaabaabababaabbbabaabaababbbbbbabaaaaaababbaaaaaaaaaabbbabbaaaaaabaaaaaaaabbbbababbbbaaaabaaabaaaababbbaaaaababbbaabbaaabbbabbababbbbbbaaabbaaaababaaabbbbababbbbbbbbbbbbaababbbababaabaaabbbbaabbbababaabbabbbbababaaabaaaabbbbababbbbbaaaabaaaaabbabbabbabaabbaaabbbababbbabaaaababbbaababbbaabbbbbababbbaaaaabaabaababbbbaaaababaabaaaabaaabaababbabbbabaaabababaababaabaabaabbbbbaabbaabaaabaaabababbaaaaabaabbaaabaaabaaabaaaaabaaababbbabbbbabbbaababbabbbbbabbbbabaaabbbaabbbaaabaaaabbabbaaaabbabbabbbbbbaaaababbabaaaaaaaabbaabbabbaababbabbabbabbaaabbaaaabaaababbababaaaaaabbaabaaabaaabbbabaabaaabbbabbaabababaaaabbaaaaabaababaabaaabbbaabbbaaaabbbbbaaabbababaabbabbbbbbbabbbaabbaaabaaaababbabbaabbabbbbabbabbbababbbabbbaabbbbbbaaababaaabbaaabaaaabaaababaabaababbbaaaababaabbaabaaaaaabbaaaabbababbbbbabbabbabbbaabbabbaaaababaaaabbbbbbabbbaaaabaabbabbaabbabaabbbbababaaaaaaabbaaabaaaabaabaaaaabbaaabbaaaababbbbaabbabaaaaababaaabaaaaaaababaaaabaabbabaabbaababbbaabaabaabaababbabbaabaaababaaabaaabbaaaaabbabbbbbaabbbbbababaaabaabababbabbaaabbbababaabbbbaaabbbabaababbaaabbaaabbaabaabbababbbaaaaabaabbaaaabaaaaababbaabbababbbabbbabababbabaabaaababbaababbaabbbaaabbaaaabaaaabbbababbabaaaabaaaabaabaaaabaaaaaabbaababbaaabbaabaaaaaaababbbbbaabbbaaaaabbbaabaaabaabbabbbababaaaaababbbaababbaaaabababbbbbabbbabaaabbbabbbbaabaaababbaaabbbabbaabababbbabbbaaaabaaaaaaababbbabbabbaabbbaabaaabbbbaabaaaababaabaaabbbbaabbbabaaaaaaaababbbbaaaabbaaaabbaaabbbaabbbbababaababbabbbaaabaaabbaabbaabaabbabaabbaaabaaaababbaaababbaabbabaabaaaaababaaaabbaaaabbbbaababaaaaababbbabbbbabaaaaabaaababbbaabababbbabbaaaaaabaaaaaabaaaaaabaaabbbbbabababbabaabbaaaaaabaaabaababbbbbaaababaaaabbbaaaaaaabbbabababbaabaaababaabbbbaabbaabaabaaabbbaaababbaaaabbababaaabbbbabbababbbabbabbbabababbbabaababbaaabbaaababbaaabbbbbaaabaabbabaaaaabbbbbbbbabbbababaaabbabbbbbabbaaabbbbbbbaaabababaababbbbbabaabbaabaaaababbbbaabbbbbabbabbabbbabbaabbabbbaabaabbaabaaaabaababbbbbbbbbbbaaababbbabbbbabbbbbaaaaababaaaabbbabbaaaabababbbbbaaabaabaaabaaabbbaaabaabbabbaabbabbaabbbbabbbbbaaaabaabbaabbbababbbabbbbbaaaaabaaabaabaaabbbaaabbbbaabbbbbbabaaabbaaaabaababaaaabbaaaaaabbaababaaabaaaabbaaaaaabbabbabbbbbbbaababbabaaaaabbbababbbaaaaaaabaaabbbbbaabaaabaabaabaabaabbaaabbbaaaabaaaaabaabbabbaabbbbaababaaabbbbbabbababbaaababbbbabaabbabaaababaabaabbaaaaabbbbbbbbaaaaababaababbabbaabaaababababbbabaaababaaaaaabbbababbbaabbaaabbaaaabbbbaabaaaaaaababbbabbbbabbabbbbbbbaaaabbabbbababbabbbaaaaaaaabbabbabababababababbababaaaababaabaabbbabaaabaaabbababaaabbaaaabbbbabbbabaabbbbbabaabbabaaaabbaababbbaaaaabababbabbaaaaaaabbabbbbaaaabbababbaaaaaabbbbabaababbbaaaabbbabbaaaabbbbaabababbaaabbabbbbbabaababaabbaaaaaabababaaaabbabaaabbababbbabbabbabaabbbbabbbabbabbbbbbbbbbabbbaabaaaaaaaaaaaaaaaaabbaabababaaabbbbaaaaaaabbaaabababaaaabbababbbbbbbaababaabaaaaabbababbbabbbaabbabbabbabaabbbbbbaabbbbaaaaabaabbabbaabbabbabbaabaababbbbaaaababbbbbbababbaabbabaababaababbaabbbabbbbaabbbbbbbaabbaabbbabaaababbaaababbaababbabbbbabababaabbaabaabbbbabbbbabbaaaabaabbaaaaaabbbabaaaaaabbabbbabbbabababbbabababababbbababbaabaaabbbaababbbbbbbababaaaabbbaaababbbaababbaaabaaaaaabbaaaabaababbababbaabaabbaaaabbaababbbbbbbabbbaabbbbabbbbbaaaaaabbbabaaabbaabababbbabbabbbbaaababbaabbabaaaababaaabbbabbabbbaaababababaaaabbabaaabbbabbbaaaabbaaaaaaabbbaaabaaaabbbaaaaaaaabbaaaaaaabbbaaabaaaabaaabaabbababbaaababbaaaababbbababbaabbaabababbaababbaabbaaabbaaaababaaabbbaabaabbaabaabbbbaaaaaaaabaaababbbabaabbaaaabbbaaaabbabbbaaaabbbabaababbabbbbbaaaaababababbbabaababbbbbaaaabbaabbaaaabaabaabaabababbbbabbaabbaaabaaaaabbbbbbaaaabababbaaaaaabaaaaaaaaabbbbaaaaabbbaaabbbababbbaabbbbabbabbbbaabababbbbbbababbaababbbabababbbbbaaabbbbabbbbbaabbababaaababababbbabaaabbabbbaaabbbabbabbababaababaabbbbbabbbaababbabbbbaabbbababbaabaaaababaaabbbaabbbaaabaababbbbabaaaabbaaaaabaaaaaababbabbaabaabaaaaaabbbaabaaababaaabbabbaaaaababaababbaaabababbbbbbbabbaaaabbbabbababbaaababaabbbbaabbbabbaabababbaaababbaaaaaaaaababbbbaabaababbabbbbbabaaaabaaabbbbaaabbbaaaaabbbbaaaabbbaababbaabaabaabbbbaaaabbaabaaabababaabbaaabbababaaaaabbabbaabababbbaaaaababbbbbaababaabbbabaababaaaaaaabaaaabbaabaaaaaaaaaaaabbabaababbaaaaabbbbabaaabbbbabbbabbaabbaaababaaaaaaaaabaababbabbababaabbabbbababaaaaaaabbbbbbbaaabaababbbaabbbbaabbabbaabaabaaabbbaaabbbaabbbabbaabbaaaaabaaabbaabbaabbbbbbbbbaabababbaaababababbaaabaaaaabbabbbabaaabbababababbaababbaaababbabbbabaaaabababbbbabaaaababaabaabababbaaaaaabbababaababababaabbbaabbbbaaaaabaaaabbbbabbababaabbabbbababababbabbaabaaaaaaaaaabaaababaaaabbbaabbbabbbaaaaabaaabbaaaabaaaabbbaaaaaabbbbbabbbaaaababbabaaababbaabbbababbabababbbbbaabbabaaaaaabbaabbbaabbbbbaaaababbabbbabaabaabaaaaaaabbbbaabbaabbaaaabaaaaaaaababbbaabaabbbaaabbbbabbabbaabbbbabbbbbbaaaabbababaabbabbabbabababbbbbabbbbbaababbababbbbabaabaabbbbbbabaabaaaaababbbaabbabbbaabbaaabababbaaabbbbbaabbabbbaaaabbaaaaabaaabbabababbbbbbabbaabbababbbbbbbabaabbabbbabaaabbaabbabbabbbbabbbbbbaaababaabbaaaabbbabbbabaaabababaabbbbabbbabbbbabbabbbbabaabbabbbabbaabbabbbaaaabbaaaabbbbbaaabbbaaaababbabbabbaaababaaabaababbaaabbbbabbabababbbbabbabbbbaabbababaaaabbabaaaaabaaabaaaaabaaaabbaabaababaaaabababaaaaaabbbbaaaaaabbbabbaabaabababbaaaabbbababbbabaabbbbbbbbbbbbaabbbbbbabbbaaabaabbbbbbbaaabbbbbababaaabaabbbaabbabbbbbabbbbaaaabbababaaaaabbababbbbbbbbbbabbaabbbbababaaabbbaaaaaaaabbababbbbbbbaaabaababaaaaaaaabbaababaaabbbabaaaabbbabbabbbbaabaabaabbbabaaabbaabbababaaaaabbaabaabbbbaaaabaaaababaabaaabbbbbaaabababaaabbabababaaaaabaabbaabaababbbbbbbabbababbabbababbabbbaaaabaabbbaabbabbbabaabaaaaabaabaabbaabababbbaaaaabaaaaaaaaaaaaaaabbbaaaabbbbbbbabbababaaaababbaaaabababababbbbabaabaababaabbabbabaababbaababaaaaaaaaabaabbaaaabbabbbabbababbbaaababbbbaabaabababbaabbaaabaaaababbaaabbbaaaabaaabbbabaabbbaaababababbabaaaaaabaabbaabaababbabbabbbabbabababababaabaaaababbaaabbaaaabaaabbbbbbbabbbabaabbbabbaaaababaaaaabaabaababaaaaabbaabaabbaababbbbbabbaabbaaaaaaaabaaabbabaabbababbbabbbbaabbaabababbbaaabababbabbbbbabbbababbbbbbabaaabbabbaabbbabbbbbabbabaabbabaababaaababbaaabbaabaabababbabaaababaaaaaababbbbaabbaaaabababaabbbaaabbbbbaabaaaabbaaababaaabbaabbaaabbbbbbbababaabbbaababaabbaabaaaabaaaaaabaaaaabbbbaaaaaaaaabbbbaaabaaabbbabaababbbbaabbbaaaababbbabbbbbabbbaabbbaaaababbbbaabaaabbbbbbbabbbbbbabaaaaaabbbaaabaaaababaaaaabbbbaabbabaaabbbababaabaaaabbaabaaaabbabababaaabaababbbabbabaaaaaaaaaabbbabbababbbaabaabaaabababaaaaabababbaaabaaaaababbbaaababbabababaabbbaabaabaabbaabbbabaaaaabbbaabaaabbbbbabbbbaaaabaaaabaabaaaaabaababbaabbabbabaabbabbbaabaabbabaabaaababbaaaabbbbaabbbbabbabbabaabaababababbbbbbbbabbbbaaaabaabbababbabaaabababababbaabbbabbbbaaabaabaaaababbabbaabababbbaaabbaaababbaaabaaaaaabababbbaaaaabababaababbbaaaaaaabbabbabaaaabbabaababbbabbabbabaaabbabaababaababbbbabbbabaaaaaabbbbabaaabbbaabbabbaaaabbbbbbaababbabaabbbbababbbbabbbbababaababbaabbabaaaaabbaaaabbbaaabaaabbaabaabaaaabaabbbbaabbaaababababaaaababaabbabbabbababbabbbbbaaaababaaaabbbbabbabbbbaaabaaababbbbaabbbbbaabbabbbbabaabbbbbabbbbbabaabaaaaaaabbbaaaabbbabbababbbbaaababbaabaabababbabaaaaaaaaabbaaabbbabaabbbaaabbaaaababbababbbbaababbaabbbabababbbaaabaababaaabaaabbababaabababbbaabbabbaaaabbabaabaaabaabaaabbbabbbabbabbabbabababbbbabbabaaaabbaabbaabaaabaaaaabababaaabaaabaabbaababbaaabbaaabaaabbbaaababbbaaaaaabbbaabbaabababaabbaaaabaabbaaabbbababaaaabbbbabbabbaaabaaabababbaabbbaaaaaaabbaababbbabaaabaaabbbabaaabbabbaaababaaababbaababbbabbaaabbbabbbabbbbabbabbaabaabbbaaabbababbbabbaaabbabbaababbabbbabaaaabbbbaabbbbbbabbbbbbaababababaaabbbaaaabbababababaabbbabbbbbabaaaabbaabbababbabbbbbbababaaaabbbbaabaaabaabaaabbbbbbbbbabbbababbbbbaabbbbbababbabbaaaaaabaaabbbabbbaabaabbbaabaaaaaaabaaaaabbabbbaaababaaaabaaaaababbbaaabaabaaaabbbbabbbbbbababaaabbaabbbaaabbabaabababbaabbaaaaabaaabaaaababbbabaabbbaabbbbbbabbbabbabbbbbabaabaaaabbbbababbaabaababbabbbbabbabaaabbbbabbbbbaababaabbaabababaabbbaabaaabbaaabaaababbabbababbbbbbbbaaaabbaabbbaaaaaababbbaaababbbaaaaaaabaaabbabbbbbaaaababbbbbbbbbaaabaabaabaababbabbaabbbbbbababaababaaabbabbababbbaaabbbbaaabbbabbabbaabaabbbbabbbaababaabbbaaaaabbbababbbaababbbababbbbbaabaaababababbbaaababbaabaabaaaababaaabbbababbbbbbbbbbbbababbabbaabaaaababbbaaaabbbbabbbbbaaabaababaaaaabaabbaaabbabbaaababababaabbbaabaaabaabaabaaababbaaabbbabbbbbbbabaaaaabbaaabababbabaaabaaabbabaabbbbabaaabbababaabaaaaaabbabbbaaaaaaabaaabababbaabababaaabaanaaabbaaabbbaaaaababbbbbababbaaabaaaaababbbaaaaaabaabbbabaabaabbabbaaabaabaaabbbbabbababaabbaaabbabbbbaabbbabbaaaabbaaabaabbbaaabbabbaabaaaabaabbabaaabaababbaabaabbbbabbbbbbabbabbbbbaaabbabaaaabbbaaaababaaabbaaabbaabbabbaababaabbbabbabbabababbbbbbababbbbbbabaabbbbbbabbaaabbbabbabbaabaabbbbbabbbababbbbbaabbabbaaaaaaaababbbbbbaabaabaaabbbbbaaaabbaaabbbabbbababaaababaabaaabbabababbaaaaaabaababbbaaabaaabaaabaabaababaaabbbabbaababaaaaaaaabbbbaababbabbabaabbbaaaaaaaabaaabababbabbaaabbaabbaabbaababaababbababbbbabaaabbababbbbbaabaabaabbbbbbbabaaaaaabbabbbbbabaaaabbaaababbaaabbababaaaaabbbbaaabbbabababbabbabbbabbbabbabbbabaaabbaaabbabbaabaaabaabababbbbbabaaabaaaabbabbaaababbbabaaababaabbbabbbababbaaabbbbaaabbaababaababaababbbabbbaaabbababbaaabaabaabaaaaaaabbaabaaaaaaabaaababababbaaaababbabbabaaabbabaabaaabbaabbbbabaaabbaaaaabbbaabbababbabaaabbbaaaaabaaaababbbbbbbabbbabaababbbaaaababaababbbaabbbbaababbaabbbabbbaabbbababbbabaaaabaabbbbbbabbbbbaaabbaaabbbabaaabbbaaaabaabababaabaabaaababaaabaaaababbabaabbababbbbbbabaaabaaaababbbbaabbabaabaaaabaabbaabbaaaaaabbabaabbbaabaabbbbaabbbbabbbaabababbbabbbbabaabaaaabbabaabaabbaaaaaabbaaaabbaabaaaabbbbbbbaaaabbabbabbabaabbbabbaaabbaabaaabbbbbbabbbabaaabababbabbaabbbabbbaaabaabbaababbabbabaabbaaabbbbbabbabbbababbbabbbaabbaabaaaaaabbbabbbaaaaabaaaabbabbbaabbababbbbbaaabbbababaaababbabbbaabbabbbbaabaaaaabbabbbabbaabbbbbaaaabbaabbbabbbaabbbabbbababbbbbbbaaabaaaabaabaaababbbaabbbabbbbaaabaababbaabbbbbaabbaabbbaaababaaaabbabbabbbaaababbaabaabaaabbbbbbaababbababbababbaabbbbbaaaaaaaaaabbbbaabbbbbbbbaabaaaabbababbbaababaabbabbabbabaaaabaabbbbaabbaaabbaaababbbaaababbbaabbaabaaabbabaaaaaaaababbbabbababbabbbbbabbbbaaabbbbbaabaabbaabbababbaaabaabbabbbbbbabbbaaabbbaaabbbabbbbbabaabbabaababbbaaabaabababbaababbaaabaabbbbbaabaaaabbbbabbaabaaaaaaabbaaaababbaabbabbabaabbbbaabbbbbabbbbbaabbbbbbbbbbbbbbbbaabaababaabbaaaabbbbabbaaabbaaababbabbabbbabbbbbabaaabbbaabaaaaaaaaabbbabaaaaabbabbaaaabbaabbbbababbabaabbabaaaabbaababaababaababbbbbbaabaababbbbabbbbaabbabbabaaabbbaaaababbababbbabaabbbaaaabababbbbbbbbaabbbaabaaabbaaababbabbbabbbaaabaabaabaabaaaabaababbbabbabbbbaabaaabbababbbbaaaabbaabbabbbbaabababbabbabbbbaabbbbaaabbaaabababaabbaaaaaabbbabbbabbaabbbbaabaaababaaaaaababbbbbababaaaaabaaaaabaaaabbbbbabbababaabbbaaabbaaaabbbbaabbababbbaabbabaaabaaabaabababaabbabababbaaababbbbbaaababaabbababbbbabaaabbaaabbabbbbbaabbbaaabaabaaababbaaaaabbbaababababbbabbbabaaaabaababbbbabaabbbbbbaaabababbbbbbabbbbbaaabaaaababbbbbbaabaaaabbbbbbbaaabbbaabaaaaabbbaabaaababaabababaabbabbbabbaaabbbabaabbbbababaaabbaaaababaaabbababaabbbaaaaaaaaaabaababbbababbaaabbabbaabbbaabaaabbaaababaababaabbbbaaaababaaaaaaaaaababbababbbbabbaaaaaaabababbbbbababbabbababaabbbabbbbabaababaabbbbbbaabbaaabbbabaaabaaabbbaabbbabaabbaabbabaababbaabaaaaabaaabaabbaaabbabaabbbabbababaabaabbabaaabaaababbabaaaabbabbbbbaabbaaabbbbaaababbabbbbaaaabbbbbbabaabaaabaababbbbabaabbaababaabaaabbbaaaaaaaaaaaababaabbaabbbabbabbbbababababbaabbbbbababbaababbaaaabaabbbaaaaaababbbbbaabababbabaaaabaabbbbbaabbaaaabbaabbabaababaabbbabaaabbbaaaababbbbbaababbaaababaabbbabbabbababababaaaaaaaabbaaabbbabbbbbbbabbababaaaabbabbaabbbabbaabbbbbaababaaaabbaaaabbbbababbbabbaababaababbabbaaabbbabababaababbbaaabaabbaabbbbabbabbaaabaaaaaaababbbababbbaaaaaaabaabbbaababaaaaabbabbbbbbaababbaabababaaabbbaababbbbabaaababbbbaabbabbaaabbbbabbbabbbbbbbbaaabaabababbbaaabbbbbbaabbaababaabbaaabbbbaabbabaabababbababaabbaaaaaaabbbaaaabbabaabbabbaaaababbbabbbbaabaabbabbaaaababababaababbaaabbbbaabbabbababaabaaabababaabbabaabaababbababbabaaababaaaababababbabaababbaaabaaaaababbabababbbaabababbabaaabaaaabaabaaaaabaaabbaaaaabbbbababbabababababababaababbabbbaabbaabbababbaaaabbaababbabaaabbbbaabaaabbabaaaaaabbbabaaaaabbbabbbbaaabbabbbbbbbbaabbabbbbbbaababaaabbabbbaabbbbaaababaaaaaaaabbbabbaabbababbbbbabbaaabaababbaaababaabbbaabbaaabbababbbabaabaaaaaabaababbabbabbbaaabbbbaababbababbaababbbaaabbababbbbbbabbaaaaaabbabaaababbbabaabaaaabbabbaaabaabaaaaaaabbbbaaabaabbaaabbabbbabaaabbbbaaabaabbabbbabababaaabbaabbaaabbaaabbabaabbaabbaababbaaaabbabbbababaaaababbbbbbaaabbbaababbaabbbaaaabbbaababbabaaaaabbababbbaabbababaaabbbabbbbbaabbbabbaaabaabaaabbbaaaaabbaaabbaaabaabbaabbaaaaaabbaabbbbbbaabababbaaabababbabaaaaaabaabbbbaaaaaaabbabaababbabbbaabbabbabbaabbabaabaaabbbbabaabbbbaabbbababaaabbababbaaaaabbabbaaabaabbaaabbbbabbabbaabababbbbbbbbbbaaabbbbaaaaabaaaabbabbaabbbaaaaabbababaabbaabbaababbbbbbbbaabaaaababbabababbbabaababbabbaaabbaaababbabababababaaabbababbaabbbaaaabbbbbaaaaabbabaababaaabaaabbaaababbbaaabbbbabaabbbbbaaabbaaaaaabbbbbaabbabaababababbaabbbaabbbababbababaaaabaaababbbbaabbbbbbbbabbbbaabbbbbbaabbbaaababaaababbbaaaabaabaababbababbbaabbbabbbbaabbbbbbbaabbbabbbbbaaaaaabaababbababbbbbababaabbabaaababbbbbbabaabbabbaabbaaaaaabbababbbbababaabaabaabbbabaabaaabbaabaaaaabbbbabbbbaababbaabaabaabbbbbbbbababbaababbbaaaabababbbbbababbbaabaabaababbbbaababbaabbbbabbaabaaabbbaabbbaaaababbabaaabababbabbaabaaabaabbbbabbabbbbaabbbaaaaabaaaabababbbaabbaabbaabbbaabaaabbbbaababbbbbaabbabbabbbaaabaaabbabaabbabbaababbbababababbabaabababaabbbbababbabaabaabbabaabaabaabbbabbabaaaaaaaabbaababababaabbbbbabbbaabbaababbaaaababbbbaaabaaababbbabbabbaabaaabbabaabaaaaabbbaaabaaaaababaaaabbbabbbaabbaabaabbbbbaaaaaababbbaaaababbabbaababbaaabaababbbbbbaaaabababbabababaabbbaababbabbaabbaabbbbaaaaababababababbbbbaaaaabababaabbbabaaaaababbbabbababaabaabbabaaaabbbbbbabaabbbaaaaababbbabaabbabaaabbaabbbbbabbaaababbabbbbbaabaaaaabbaababbbbabbaaaabaabaabaaaaaaaabbbbbabababbbbaababaabbaababaaaabaaabaababaabaabbababaaaabbbbbabbabbabbbabbabbbaaabaaababaabbbbbaaabbababaabaaaaabababbbbbbbbaabbabbbbabaababaababaababbaaaabbbbabbaabbbbaababaaaaaabbbaaabaabbaabaabbaaabbbaababbbabaabbaababbbaaabaabbbaaabbaaaaaaabaaaaaabaaabbbaababbbabbbbbaaabaaaaaabbbaabaaaababaabbaabbbbaaababaaabbbabbabaabaabaaaaababbbbababababbabaabbaabbbbbbabbbabaaaaaaaaabbaaaaaaabaababbbabbbabaabababaaabababbaaaaababaababbaaaaaabbbaaaabaaababbbbbabbabbabbaabaabaabbbbabbaaaaabbbaabbaaabaaaabbaaabaaabbababbabbbbbaaaabaababbbabbabbabbbabbaaabbbbaabbababaababaaabaaabbaabaabbbaabbbababbaabbbbaaabbaabbabababababaaaabaabbbaaabbbbbbbabaabbaaabbbbbaaabbaaabaaabaabaababbbbbbbbaabaaabbbbbbaababaaabbabababbbbbabbbaaaaabaaaabaabbbaaabababbbaaaabaaaabaaabbbaaabbabbbbabbabbabbbabbaabbbbababbbbbbabbbbabbabaabbaabbabbbbabaaababbbababbbaabbbbaababaabaabbabbababbabbbbabbababbaabbaaaaaaaabbabbbbbabbabbbaaabbbabaabbabbbababbbbbaabababbbbaaabbaaababbbaabbbbbaabbaaabaaaaabaaabaabbbbbbbbbaaabababbbaaabaabbbbabbbbbbbababaabaaaaaabbabaaabaaaaababaaabababbbabaabaabababbaabaaababbbbbbabaaabbbababbaabbbabbaabbabbabbababaaababaaaaaaaaaaaabaaababbbabaaaaabaaabbbabbbbbaabbbaababaaababaaaaababbaabbbabbbbbbaabbbaaaaabbabbbaabaaabbbaabababbbbbaabbbabbbbbababbbbaaabbaaaaaabbtaabbbaaaaabbabbbaabbbaabbbaabaabaaabbbbaaabbaabaabbabbbaabbabbababbaabbbbbbbaaaababbabbbaaaaaaabbbbbabaaaaaaaabbabaaaaaabaaabaabbabbaaabaaaaababbaabbaababaaaaababbbbbbbababbbabbaaabbabbbababbbabbbabaabbbbabbbbaaababaaaaabbbaaaaaabbaababbaababbbbaaabaaabaabbaabbaaabbbbabbaabaaabbbbaabbaabaaaaabbaabababbbabaababbabaaaabbbbabbaaabaaaaaabbbbabababbabaabbbabbaaaabaabbaaaaaaaaaabbbbaabbbbaabbbaaaabababaaaaaabaaaabbbbabbabaabababbabbaaabaaaabaaaabaabbabaabbaababbbaaaabbabaaaabbbaabaaabbbbbababaabababaababababbbbabbbababbbbaabababbabaaabbaabbbbabaaababbaaabaababaaababaaabaabaabaabaabbbbabbabbbbaabaaabbbabaaabaaaabbbbbababaabbbaaaaabbbbbaaaaaaaabaaababbababbaababaabbbbaaababbbbbaaababaababaababaaababbaaabbabaabababaaaaababaaabbbbbbababbabaabaabbbbabbbababbababaaabbbabbaabaababbaaabbaaaabaabbaaaaaababbabbababaaaaaababbbbbbaabaabbaaaabbbbabbababbabbaabbbbbaaaabbaabaaaaababbbbbabaababababbaabababaaabababababbbabbaabaabaabbabbbaaaaabbbbbababbbaaabaabbbbbaabaaaababbaaaabbaabaaabaaababbbbaabbbbaababbaaabbaabbababbbaaabbbbbbabbbbbbaabababaabbabbbbaabaabbbaababbababaaabbbaababbabaabaaaabbaaaaaabbbaabaabaaaabbababaababbaaaabbaabaabbaaaabbbbabaabbaababaaaabaabbaaabaabaaaaaaababbaabaabaabaaaaaaabbbbaaabbbaaaababaababbbabbabbaababbabaaaaaaabababbbaabbabaabbababbbabbbababbaabbbbbabbabaaaabaaabaabbaabbbbababaaaabaababbbbbabbaaaabaabbbbabbabbbabbbbbbbaaabaaaababbbbaabbbbbabaababaabbbbabbbabbabaabaaaaaaaaaaabaaaaaabbaabababbbbbbbbbabbbbbbbaaaaabbaaabaabbaaabbabaaabaabbbabbbbbaabaaaaaaababbabaaabaabbbaaababbababaaaabbbbbabbabbaaaabbbababbbaaababababbbbbbaaabbbbabababbaaababbabbaabaaaaababaaaaabaaabaaababbbbbaaabbaabaaabbbabbaaababababbaaaaababaaabaaabbbaaaabbaabbbbbbabbbabbbbabaaababbaaaabaabbabaabaabaaababbbbaababaababaabbbbaaabaaabaabbabbabaabaaaaaabbbbaaaaabbbbaaabaabbabbbbbabbaaabaaaaabbbbababbabbaaaaababbabbabaaabaabaabaaaaaaaaabbabbbaabaaaaabbbbaaaabbaaabbabaabbabaaababababbabbaabbabaabaaabababaabaabbbbabbbbbbabaaaabaaaabbaabaaaaaababbbbbabaababbaababaaaabaabbaabbbababaabaabaabbbbaaaabaababaaabbbabbabaaaababaabababaabbbbbbaaababbabbbbababbabbbaababbbbaabaabbabbbababbaabaaabbbbabaabbbbbbbbbbabbbbbaababbbbaaababbabaabbbabababbabaaaaaabbaabaabbabaabaabaabbababbababbabbabababaaaabbaaabbaababbaababaaabababababbbabaabababbbabbaaabbaaaabbbbbaaabaaaabbabbbbabaaabbbbaaabababbababaababbaabbbbbbaabbabaababaaaabbbaabbabaaabaaabaabaabbbaaabbaabbaaababaaaaaaabaabbabbbbbbaabbbaabbbbabaaaabbbbbabbaababbaabbbbaabbbbbbaaaaaaaababbaaaaaababbabababbbbaaaababbababbabbbbabbaaaaaaaabababbaabbbbbaaabbabababbabbbaabbbbbaabaabbbbabaababbaaaaaaaaaabaaaaabaabbbababaxababbbbbabbabbbaabbbbaaaaababaabaaaaabbababbbabaaababbabbaababaabbbbbbbaabbbaaaaaaaaaabbbbbabbabbabbbbaabbbbbaaaaaaaaaaaaaaababbaabbaaabbaabaabbbaaaabbbaababaaabaababbaaaabaaaaabbbaabbbbabbbbabbabbbbbaaabbabbabaabbabbbaaaabbbbabbbaaabbaaaabaaaababbabaaaabbababababaabbabbbbaaabbbbabbabbaaaaaaabaabbbbbbabaabaaabaaabaababaabababbaaababbbabaababbbabbabbbababbbabbabababbbabbaabaaabbaaaaaaaabaaabbbbbbaaabbabbabaababbaaaabbaabbbabbbbbabbabbbbbbaabaaabaaabbaaaaaaabbaaabbabbaababaaaabbbbabbaaabbababbaaaaaabbbaaaababbabaababbabbaaabbaabbbabbaaabbbbabaabaaaaabbabaabbbbbaaabbbaabbaabaaaabbbaababbbaaabbbaabbbbaabaabaabbbbaabbababbaaaabaaabbaaaaaaabaaababbbbaababbaaabaaababbbaaabbabbaaaaaabaabbabaaaaaabbaabaababaabbabbbababbabbababbbababababaababbbbaaabbaaabbbaaaaabbaaaabaaabbbbbaaabaaabbbabbababbbbbbbaaabbaaaabbbabbbbbbaabbbbbaabaabbabbaaabaaaaaaaaabbabbaaaaaabaaabbabbbaaabbabbaabaabbbabaabbabbabbbaaaabbbbbaabaaabaababaaabbbabbbaaaaaaaaaabaabaaaaaaabbbaaaabbaabaaabbaababbabbabaaabbaaaabaaaabaabbabaababbaaabbababbaaaaabbabaaabbaababbabbabbbbbbbbaabaaaabaabbaaabbabbbbaabbbaaaaaabbbababbabaaaaababaabbbbabbbabbbbbaabbbbbbabbbbbabababbbaaaabbaaabaabaaaababbbababbbbbbbbaabaaabababbabbaabbbbaaababaaaabaaaaabbbabbbaaababbaabaaabaabbabbbaaaaaabaabaabbaaabbaaaaabaaaababaabaabbaabbbbabbabababaabaaabbbaaabbbbabbabbbbbbbbbababbbbbaaabaaaaaababaabbabababbbabbbbaaaabbbabbbabbbbabbabababaaabbaaaaaabababbbaaaabaabbaaaabaabbabbbaabbbaaaabaaaaaaaaababaabaababbaaaaabbababbbbbbaaababaaabaaabbbaababbbaaabaaaabbbbaaabaabbbabaabaaaababaaaabbbbabababaaaababaaabaabaabbabbabbabbbaabaabbbbbaaaaababbbaabbbbbbbabbbbbaabbbababbbbbabaabbbaabbbbabbbaaaaabbababbaaabaaaabbbbbabbabbabbabbbaabbbbbbaaabbbaabaaabbabbaababbaabaabaabbababababbbbaaabaabaaaaababbbbabbaaabababbaababaaabbbaaabababbabbaaababaaaabbbbbbabaabbbaaabababbabaaabbbabbbaaabbbaaaaababbaabbbbabbbabaabaabaabbaaabaabababbbbbaaaaabbaaaaabbabaababbabaaababbbaabbabbaaaababbbbaabbaaaababbaabbaaaabaaabbbbbabbbabbaaabaaabbabbbbbabbaababbbbbababbaabbabaabbabbababaabaabaababaaabaaaaabbbaababbaaaaaaabaabbaaaabbbababbbbaabbbaaabaaaabababaaabbabbaaabaababbababbbbaababaabbaaaabaabbbaaabbbbaaaaaaaaaaabbababbaabbaaabaabaaaaababbbaabaabaaaabbbababbaaabbbaabbabaaaaaaabaababaaaabbbbbaaabbaaaaabaabbbbbbaabaabbabaaabbaaaabbaababababbbbbaaabbabbaaababaabababaabaaabbbaababbbabbbbbabaabbabbbaababaaaaabababbabbbbaababaabbbaaaababbaabbabbbaaaabbabbbaabbaaabaababaaaabbbaabababbbbaababbbaabbbaabbabaabaabbaabaaaaaabaabbbabbabbabbbbabaabaaaabbbbbaaabaabbbabaaabaabbabbbabaabbabbbbaabbbaababbbabaabababbbaabbbaaabaaaaabababbaaababbaababbbaaaabbaabababbbbaababaaaaaabaabaabbbbabbbaabaabbaabaaaaaababbbaaaabaaabaabbabbaabbabbbabaaabbabbbbaabaaabaababbababbabbbabababaaaaaabbbaaabbbbaabbbaaabaabaaabbbabbbbbbabbbabbaabababbabaaaaabaaabbbaaabbbababbbbbaabbbbaaababbababababaabbbbaabaabababaabbbaabaabbababbaabbabababaaaaabbabaabbbaaabbaabaaaaababbbaabbbabbaabaabaaabababababaaaaababaabbbababaaaaabbbaaabbaababaaaaaaabbbbbbbbbbbbbabbbbaabaaaaabaaaababbabbbbbbababbaaaaabbbaaaaaaaababaaaaaabbbbbbaabbbbbbaababbabbaaaabaabaaaaabbbbbabbbabbaababbbbaaabbabbbbababaaabababbaaabbbaaaabababaaaaababaababababaaabbbaabbbbabbbaaaabbbbaabbaababababbabaabbabaabbababbabbabbabaaababaaabbbaababbaabbbaaaaababaabaaabaaababbabbaaaaabaaaaaaabbaaaaabbaaababaabbbbbbaababababbbaaababaaabbbbbaabaababaabbaaaaaabbbbbbaabbbaaaaababbbbaabababbbaabaabababaababbbbabbaaaabbaabaaaaaababbbbababaabbaabbbbaaaaabbbbaaabababbbaaaaaabbbbbaaaabbbbbabbbbabbaaaabbaaaababaaababbabbbbabbaaaabaaaaaabbbbbaabbbbabbbbababbbabbaababbbbbbabbabbaabbabaaabaaaababbbaaabaabaabaabababbbabbbbabbabbababbbabbabaababaabaaaaabbbbaaaaaabbaaaaaaababbaaabbaaaabbbbabbbbbbabbaabaabaaeababaabbaababbaababbbbabbaabbabbbaaabaababbabbbbbbaaabaaabbbaaababbabbbbabaaabbaababbbbbaaaaabaabbabbaabbbabbaaabbabbbbbaaabaaabbbabababaaaabbababbabaaaabaababbaaabababaabaabaaaabaaabbaaabaaabaabaaaaaabbaabbaaabaabbbabbaababbabaabaaaabbababbbabaaabbaaaababbaaaababbbbabbbbabbbabbaaaaaaaaaabbaabbbbbbbabaabbababbbbaaaaaaaaaabaaaaababbaaaabbbbbbbaaaaabaaabababbabbbbbabbbbaaababababbbababbababbaababaabbbabaabababbabbabbaabbbbbbaabbaaabababbbbababbaaabbabababaaabaaababbbaaababbbaababaaaaabaaababbbaabbaaaaabaaabaaabbaaabbabbbbaaaabaaaaabbaaaaaaabaaaabbaaaabbaabbaaaabaaaabaaaaaabbabbababbaaababbbabbababbbbabbabbaababbababaabbbbbbbaaaabbbabaaababaaabbbabbaabbbaababbaabbbaaaaabaabbbaaababaabbaaaaaabbaaabbabbababbbababbbaabbaababbaababbaaaabbbbbbbbaabbaaaabbbbbbbbbaabababbaaabbbabbbbaaabbabbbbbaaabbbaabaabaaabbabbbaabbaabbbababaaababbaaabbaabababaaabbbbaabbabbbbaabbbabbbbaaaaaaabbbabaaaaabaaabbbaaaaaaabababbaaaabbabbbaabaababaabaabbbaaaabaabbababbbaaaabbbbbabbbbabbaabababbaaaabbbaabbbaaabaabbbbbbbbbbbaabaaababbabbaabbabaaaaabababbbbabaabbbbaabababababaabababaababbbbbbabbbaabbaaababbaabbaabaabbbaabbbaaaabbaaabbaabaaaaababababaabaaaaabbaaabbbbaabaabbbabbbabababababbbaaabbabbababaaaaaababbaabaabaabbabbababbaaabaaabaabababbbbabbbbabaabaabaaabaaaaaabababbbabbbaaaabbabbbababbbbbaabbbbaaabbaaabbbaaaaabbabbabaaaababbbbbaaabbbbabbababababababaaabaaaabaababbababbaabbbababaabbbaabbabbbbbaaababaaababbbbbbbbbaaabababaabaababababbabbbabbbaaaaabbababbabaaaaaaaaabbaabbabaabaaabbbbababababaaaaaaabbbaaabbabbbaaabbabbbabbbaabbbbbbbaabbbaaababbbaaaabbbbbbabbabbaaaabbbaababbaaaabaaaababababababababbbbbbabaabaabbbbbabbbbabbbaababbbbbbaabbbababababbbaaabbbbabbbbbabaababaabbabbbbbababbabaababbbabaababbababbaababbaaaabaabbaaabbaababaaabbaaabaaaabbaababbbbabbbbaaaaababbbbaabababbabbababbbbabaabbbabaaabbbbbbbbbabbaabbaaabbbbbbbbaaabbabbabbbbabbbabbbbbbbabbaaabbaabbbabbbaabbabbabababbabbababababbbaabbbbababbaabababbabbababbaaaabababbbbaaabbabaaaababbbbabbaabbaaaaaaaaaabbabaabbbbbaabbbbaaaababbbaabbaabbbaaaabababaabababaabbbbaababbbababbaaabbbbaabaaabaabbaabbbaaaabaabbbbbbbbababaaabaaaaabbabababaabaaabaaaaaaaaabbbaaaabbbbbbbbbbbaabbbaaaaaababbaababbaabbbbbabaabbaaabababbbababaababbbbbabbabaaabababaabbbbbbaababbaabbbbabbbbabbabbababbabbbabbbaabbabaaabbaaabbaaaaaabaabbababbabbabbbaabababbbbaabaaabbbabbabbabbbbbaaaaababbbbbbaabaaaababbbaaabaaaababbababbbababbaabaaaabbbbabbaaaaababbbbaaaabbaababaaaaababbbaabbbbaaaabbbbabaabbbaabaabaaabbbbbaabababaaababbbaabbabaaabbaaabababababaabbbbabbaabaaababaaaababbbaaaabbaabaaabaaaabbbbaabababbabaaabbaaaabaababaaabbbbbbabbababbbbbaaaabbbbabaaaababaababbbbbabbbbbabaaaaaaabbababaaaaaaabaaaaaaaabbbbbaabbaabbaababaabaabbaabaababbbababababbbabaabbbbbbbabaabbbbaabbabbabbbaaabbaaababbaababbbabaababbbababaabbabbbbaabbbbbaabbaaabbbbbabbaaaabbaabaaaabbbbbbbbabbbbaababbababaabbbbbaaaaabababbabaabaabbaaaaabababaaababaabaabbbaaaaaabbbaababbabbbbabbaabaabbaaabbaaabbabbbbbabaabbbabaaaaaaabbbbababababbbababaabbaaabbabbbababaabbbabaabaabaaaaaaaababbaaabbbbbaababaaababaabaababbaabbbabbabaababaabbbbabbbbabaabaababaabaababaabbabaabbbbbbabbabaaaabbabaabaaaabbaaaaabaaababaabbbabaaaabaabbababbbabbaabbababbbbaabbabbbbbbbaaabababbaabaabbabababaabaababababbabaaababbaabbabbaabaaabababbbabaabbaaaabaaaabbbbbababaabbabbaaabbabaabbaaabbbaaababaabaaababaaababbbbbaaaabbaaabbbaaababaaabaaaabbabbbbbbbaabbabbbbaabaabbbaababaabaaabbbabaaaabbabbaaaababbbbbbbbbaaaabaabbbabbbababbababbabbaabbabbabbaaabbbbaaabbbabaabababaaabaabbabbabaaaaabababbaaabaabbaaababbaabaabaaaaaaabaabaaabaaabaababaabbbaabbabaaabbabbbaaaaabbbaababababbabaabbbaababbbaaababbabbaabbbbbabaaaaabaaaaabababbaababbbabbbaababaabbaababaaabbbabaaaaaabbabbbbbaaaabbabaaaabaaabababababbbbbababbabbbbaababaaabaababbabaaabaabababaabaabbbbbabbaabaaaaabaaabaaababaabaaababbaabaabbaaaaabbaaabbbaaabaabbabbbbabbbaaaaaaababbabbabaabbaababbbabbbbbbaabbabababaababbbbbaabbbbababbbabbbbabaabaaaaabaaaabaabaaaaabbaaaaaabaaaabaaababaabbbbabbbaababbabbaabbabbaaabbbaaabaabaabbbababaaabbbbabbaaaabbbbbababbbbbaabbbbbbaabaaaababaabaabaabbbbbababbbbbbabbbbbaaabaabbabbbaaabbbabaaaabbbabbbbbaabbaabbaaaabbaabababbbabbbbaaaaababaaabaaabbbbbaabbbbbbababbbabaabbbbabababababbaaaaabbaababbbbaaaaabbaababaaababbaaabaaaababaabbaababaabbbbbbbbabbbbabbaababbbbaaaaaabbaaabbbbabaaaaaabbaaabbaaaaabbbbaabaabbabbbaabbaabbbababbabbbaaabbbaabbbbaabaaababbaaabbbbbbbabaabbbbbababababbabbababbabbbaaabaaaaaaaaaabbbbaaabaabbbabaaabaaabbbbaaaaabbbabaaabbbbababbbabbbabaaaaababbbbbbaabbbbaaaaaababababaabbbaaaababababbaabbbbbbbbaaabbaaabbbaabbababaaabaaabbbaababbababbbbaaabaaabaabbbbaabaaaabaabbbaababaaabaabaaaaaaabaabaaaaaaabbabbbbbbaaaabbbaabaaabaabbbbbaaaaabaabaaababaabbaabbabbabbbbaabbaaabbbbababbabaabbabbbabbbbbabbabbabaabbbabaaaabbbaabbbbaaabbbabbaabbbabbbbababbaabaaaaaabbbbbabbbaaabaabaaaaaaabaaabbbabbbabbaaabbbbaabbaabaaaabbbbbbaabbbababaabbbbaaabbbabbaaababaaaaaabaaaabababaaaaaaaaabaaaabbabbbaaaaaaabbbbababaabbbaaaaabbbababaaaabaabaabaabaababaabbbbaaabbbaababbaabbaaaaaababaabaaabbababaababaababaabaababbababbabbbbabbaaaabaaabaabaabbaabbabbabaaaaaabbabaabbababbababbaaababbbbbaaabbaabbabaaababbaaabbababaabaabbabaaaaababaaabbaaaabbbabbaaabbabaabbababbbbabbbbbbabbabbabababbbaaabbbaabbbbbaaaaabbbabbbaaabbabbbaaaaaaaaabbbbaaaababbbaaaaabbbababaabbbabbaaabaabbbaaabaabbbbbbbaabbbbbbbbbaaaabbbaaaabababaababbbbaabbbbbbbaabbbbaaaaababaabbbaabaaaaabababbaabaabbbababbaaabababababbbbbaabbbaabaaaaaaabbaaaababaaaaaaabaaaaabbbbbabbbabbbbaaaabbaaabbbabaaaabbabaabbbbbaabbabbbaaabbaaababbbaaabaaaababaabbbbaabbabababaabbaaaababaaababaaaaaaabaaabbbabbbababaabbbaababbbbabaabaaabbabaabbaaabbbaabaaababaabaabbabbbbaabaabbabbbaabaaabbbbbbaabaabaabbbababaabbabaaababbbbabababaabbabbabaabaaabbbbbabaaaaabbabaabaaaaaababbbaaaaabaabaaabbaabbaabaaabbababbbabaabababbbaaaabbbbbaabbaaaaabbabaaaaabaababbbbbbaaababbbbaabbabaabbbaaaaabababbbababababbbbabbaaaabbbaaaabaaaaaaaabbabbabaabaaabaaabbbabaaabaabbababaababaaaaabababbbaabbabbaaabaaababbaabbbaaaabaaaabbababaabbaabbaabbbbbaabbbabbbabaaabbbbabaaaabbbbbbbaaaaabbbbabbabbbaababaabbbabbaaaabbbbabbaabbaaaaabbbbaabbabbbabbbbaaabbabaabababbaaabbabaabbbaaabababaababaaaaababaaababaaaaabbbababbaaabbbbaabbbabaaaaabbbabababbabbbbbbabaabbbabababbababababbbbbababbbaabaaaaabababbbbbaabbbaabbababababbaababbaaabaababbabaabbaabbaaabaabaaaaabbbabaaabaabbbbbbbaabbabbabbababbabaabbbbbabbbababbbbbabbabbababbbbbbaaabbbaababbbbababaabbababbbbabaabaaababbabaaababbbaabababaabaaababbabbbabaabbbbbabbaaaaabbaaaaaabaabbbaaaaaabbaabbbbaaaaabbbbbbabbbabaabbbbbbbabbbabaaaabaaaababbaaabbbababababbbabbbababbabaaabbbbbbaabaaaaababaaaabaabbaabababaababaaaaababaabababaabaaabbbbbbbbbbabababbaaabababaabbaababbbababbbbbbabbbbaaabaaaaaaaaabbbbabaabaaaaabbbbaabbabbbabbabbaaabaabaabababbababbaabbbaabbaabaaaabbaaabbbbababbbbabbbabaabaabbbbaabbbabababbabbbbabaaabaabbaaaaabbabaaaaabaaababaabaaababbbabbabbbabbbaababbabbbbbbbbababbbbabaaaabaaaabbaabaaaaabaabaaabaabbbbbaaaabbaaabbbabbbbabbbbbababbaababbabbbbbaabbababbbaabbbbbbbbabaabaabbabaaaaaaabbabaaabaababbbbaaaabaaabbaababbabbbabbaababaabbaaaabbabbbaaabaabaaabbbbbabbaaaaababbaabbbbaabbbababbbbaaaababaaaaaaabbbbbbbabbaaabbaaaabbbbaaabbaaaabaabbbbaaabababbbbaaaabbbabbbbbbabbaabaaabbbababaabbaaabbbbabbbbababaaabaabbababbaabbabbbabbbabbbaabbbbbaabbaaaaabaabbaaabaabbaababaabbbbabbbbabaaaaaaaabaaabbababbbbbaaabaaaaaababaababbaabbababbbababbbaababbaaabaabaaaabaaaabbabbbbaababaabbbbaaabbbbbbaabbabbababbbaaaabbabbbbbbaaaabaaaaababaabbaaabaaaabaaaabbbbaaabbbbababbbaabbaabbaaaaabbabbbbbbaaaabbabaabaaaabababbbaabaaabbbbabbabababbababababbbbbababbaaaaaaabaaaaaaabbbabbbbaabbbabaaaaaaaabababbaaaabaaaaabbabbaabbabaababbbaaababbaabbbaaababbbbabaababbabbbaaabaabbbaaaaabbabaababaabbbaaaabbbbaababbaabbbbbaabbbaabbbaaababaababbbaabbaababbabaaaababaabbbabbaabbbabbbbbababaabbbbbbaabbbbbbaaabaaabababaabbbbbbaaaaaabbaaaabbbbabbabababaaaabbbaaaababbabbbbbbaaabbbabbbbbbbbaaaababbbababbaaaaaabbbbababbabbbbabbbbabbabbaaabbababaaabaaaaaabbbbaaaabbbbabbbabaabaabbbbbabbbabbabbaabaaaaabababababbbaabaaaababbbbabaabbabbaaabbbaabbababbbaababbaaaabbaaaaaababbbbbbbabababaabaaaaaabbaabbaababbaabaabaaaabaabaabaabbbbabbbbaabbabbbbabbbbabaabbabaaaaaaaabaaabaabbbbabababbabbaabbbabbabbababbbbbabbaaabbaabbbaaabbabbababbabaabbaabbbbbbaabbbbaaaabaaaaaaaaaabbabbaaabbbbbaaaabbababbaabaabaababaaabaababbaaabaabbaaabbbbabbabaabababbbabaaabbbbbbaabbabaaabbbaabbbbbbbbaabbaabaababbabbababbbbbabbabbaaababaaabbbbbabaababbbaabaabababaababbbbbbaaabbabaabbbbbbbaaababaaabbbabbabbbaaabaaabaababbbabbbbbbbbababbbbabaababbaaaabaabababbbaaabbaaaabbbbaaaaaaaaaababbbbbbbbabbbbaaaabbabbbbababbbabbaababbabbababbbbbbaaababaaabaababbbbbbbaabaaabbabababbabbbaabbbbabbbbbabababababababaabbbabbabbaabababbaaaaabbbabbbabbbabbbbaababababaaaabababbaaabbbbaaaaaabaaaabbabbaaaabaabababaaabaababbbbbbabaaabababbabbabbabaabaaaababbaaaaabaaaaabaabaaababaababbabbbabbabaaaabbabbabbbaabbbbaaabaabaaaaaabbbaabbabbabbabbbbabbabbabbbbbbbbbbaaabababaabbbabaaabbabaabbabaababababbbabbbababbaabbbbabbbbabbbbbbbaaabaaababbababbbbbabbbaaaababbbbbaabaaababbbbbbbbbaabbbbbbababaaabbbabaabaabbbaababbabbbbaaaabbbbbaaabbbbbabbbabaaabbaabbbabbaabbababababbaaaaaababbbababbbbabbbbbbbabbabaaaaaabbbbbaaaabbababaabbababbabbababbaababbaaabbbbbababbaababbbaabbaaaaababaaabbaabbaabbbababbaabaaabaabbaabbaaaabbbabbbababbaaaaabaabaababaabbabbbbaababbbaaabaaabbbaabbaaababaabaabbaaaaaabbbaaaabaaaabababbabbaaaaaababaabbbabaaababaaabbabbbbbabbabababaaaaabbbabbabaababbaabbabbaababbbbabaaabbbaaaaaabbbbbbabbaaaaabaabbbabbbaabbbbaaabbaaaabbbabbababbabbabbaabababaaaaababbaababbaaababbaababbbabbaabbabbabaabbaaabbbaabbabababbbaabaaabbbbabbabbaabaaabbaabbbaabbaabbbaaababbabbababbbaaaababababbbabbbaabababbbbbbbabbaabbbbbbabbababbaaaabaaabbabaabababaaaabaabbbbbbbbaabbaaaababbaabbbbabbabbbbbaaabbbabbbbbbbaabaabbbbbbabbbbabaaababbbaababbbabaaabbbbbbaabbbabbabbaabaaaaaabbbbbabbabbbbbbaabbabbabbaaaabbbabbababbbaaaaabbaabbbbabaaaaababbbbbbbbbbbbbbbababbbbababababbbbbaabababababaaaaaaabaabaaaababbabbababbaaaabbbabaaaababbaababbaaaabbbbaaabababbbabababbbbbabbaabaabaabbaaabaaababaaabbaabbaaababaabbababababbbbabbbabbaaabbbbbbbbbbbaabbabbabbbababaabbbbbbbabbbaababbaaababbbaaababbbbbaaaabbbbbababbbaaaabaaaabbbbbababbababaaaaabbaabbbbbabaabbbababbbbaabaaaabababaabaabaabbaaabbbababaababbbbbabbabaababababbababaabbababbabaaababbbbaabbaabaaabbbaabbaaabaaaaaaabbbabaabbbaabbbabaaabaabbbbbaabbabbbabbbababbbbabbaababbabbbaabaaabaaabbabaabaaabbbbbbababbabaaaabaaabbabaabaaaabbaaabababababbaaabbbababaabbbabaaaaababbaabaaaaabbbbabbbbabaabbbaaaabbaabbaababbbbbabbbbbaaaaabababaababbbabaaaabbbbbbbaaabbbbabbbbbabababbabbabbaaabaaabbaaaabbaaaabaaabbbbababbabaaaaabbabbaaaaabbababbaaabaabababbbabbbaaababbbbbabbabaaaabababobabbbabbabbbabbaaababaabaababbababaabaaabababbaabbbaaabaabbbbbabbaabbabaaaabaaaabababaaaaabbbbaababaaabbaababbbababbbbaabaaababbabbaabbbbbaabbbbbbaabbbaaabaaabbbabaabaaabaabbbabbbbbaabbabbbbbabbbababbbaabbbbababbbbaaaabbbaaaabbaabaaabaabbbbbbabbabaabaabbababbaabbbabbabbbbaabbbabaaaaabbabbbaabaabaabababbbaaabbbaaaaabbbabababbbbbbaabaabaabaababbabaabbbabbbabaabaabaaaabaaaabbbabbabbbabbabbbbaabaababaabbabbbbabbababbbabbababaaaaaaaaababbbababbbbbabaabaaaaabaabaaabaabbabbbabbabababbabaaaababbabaaabaababbbaaaabbabaaaaaaabaaabbbbbabaaabbabbbbabbbbbaaaaabaaaaaabbbaabaababaababbabbabbabbbbbbbabbaabaababbbaaabaaaaaaabbbaaaabbbbaaaababaababbaabbbbaaaababbabbaaabbbbbbbabaaabbaabbaabaaabbabaaababbabaabbabbaababbbbaababaaaabbbababbabbbabbbbabbababbabaabaabaababbbbaaabbbaaababaabbbabbaaaaabbbaabbbaabaabbbbbaabaaaabaaaabbbababaabbbbabaababaaaabababaaaabbaaaabbaaaaabbababbababaababaababaabaaaabbbbabbaabbabbaaaaabbbbbbbbbbbbabbbabaaaababaabbbabbababaaabbbabbbbaaabbbabbbbaaababababbbbabaaaababbbbbbaabbbbaababababaaaaababaabaaabbaaaabbaababbbaabaaaabbaaabbbbbbbaababbaabbaaaabbabaabbababbaabaaaababaabbaabaaababbbaaaaaabbaaabbbbbabaabbaabaabbabaababaaaabbbbbbaaaaaaaababaababbabbbaaaaaaaabbaaababaaaaabbaaaaabbbaabaaaabaaaaabaaaaaabaabbaaababbaaaababbabbbbababbbabbbbbabaaabbabbaabababababaabbbbbbabbbaaabbbbabaaabbbaaabaababaabaabaabbbbbaabaabbbbbbabbababbbbabaabbbaabaaaaababaaabbaabbaaaabbbaaabbaababaaaababbbbbbbaaabaaababbbbabaaabbabbbbbbbaababbbababaabaaabaabbbaababaababbabbbaaaaabbbbabababbaabbbaaaaabaabbabbbaabbbbabbabbabbabaabbabbbbbababbaabaabbbabaaaaaabaabaababaaaaabaaabaabbaaababbbbbababaabababbabaaaaaaaabbabaabbaababaabababbbabbaaabbaaabaababbabbabaabbaaabbbbbababbbbabaaababbaaaabbbaaaabaaaabbbbbbbbbaaaababaaaaabbaabaabbbbbbbbbbaaabaaababaaaabaaababaabaaababaaaaaaabaaaaaaabbabaaabbbbbabbabaaabbbbabbaaaabaabaabbaabbabbaaabbababbbbbbbbaabbababaaaababbabbaaaaababbababbbbabbaaaaabbbbaabbbbbbbbbbababababbbbaaabbbbbbabbabaaaaababbbaabaaababbaaababababbbbbaabaaabbaaaaabbabbbabbbababbabbabaabbbaaaabbbbabbaabaababbbababaaabbbbabababaaabbaabbbbbbbabbababbaaabbaaabbababbbabaaabaababaaabbabbbaabbbaabbbabbbaaabbbbaabaaaaaabbbaaaaaaabababbbabbaabaaabbababaaaaaaaabbabbaabbbababbbabbabbabaaabaaaabbaabbaabbaaaaabaabbbbbbaaabbabbbaaabbbabbabaaabbaababbbbbbaabaaabbbbbaababaaaaaabbbbbbbbabbbbaaabbbbabaabbabbabaaababaaababaababaabbbbabbbaabaabbbaabbababbaabaabbbbbabaabaabbbbaabbbbbaaaabbbbbbbaabbbabbabbabababababaaabbabbbababababababbaababbaabbbbaaabbaabbaabaaabbbaabababbabbbababbabbabaaababbababbbabbbaabbaaabbabbbaaaababbbabbaabbaabaaaaabbbbbbababaabbbbbababaaababbbaaaaaaaabbbbabaaabababbbbbaaaabbaaabbbaabbabbaaaabbbbbabbababbabaabbaabbabbaabbbaabaaabbbaabbabbbabababaaabaaaababaabaabaabbabbaaabababbbaaaaaaabbbaaaaababaaabbababaabaababbbabaabbbbbaabbbaaaaabaaabaabbbbbaabbbbbbaabbaababbabbabbaabbbaaabaaaaabbbabbbbabbabaaaaaabaaababbbabbaaaabbbabaabaaaabbbabaababbbbbbbbbbbaaaabababaaabbabbaaabababaaabbbbbaaaabaaaabbabababbbbbbabaababbbbaaabbabaabbbabbbbabbaaaaaaabbababababbbabababbaababbabbbabaabababababaaabbaaababbbbbbabbbbbbaaabbbbabbabbaaabbbbaabbbbaabbabbbbbbbaaabbaabababaaabbbbbbaabbbaababaaaabaabaaabaaabbabbbbbaabaabbabaaaabbabbbbbbabababaaabbbbaababbbabbaaabbbabbbbaabbbaabbaaabbbabaaabbabbbbbbbbababaabbaaabbaaabababbbbaabbbbbbbaababbabbabaaabbbaababbbbbbaaabbabbababbbaaabbbbabaabbbbaabbbbabbbabbbababbbbaabbaabbbabbbaaababaabbaabbabababbbbabaabbaabaaabbababaabbabbabbbabbbbaababbbbaaaaaaaaaaaaabbaaabaabbbbbaabbaaaabbbbaaabbababbabbbabaaaabbbbbaaabbabaaaaababbabbbaabbbababbbbabaabaaaaaabaaaabbbbababbbbaaaabaabbbabbbaabbaababbababaaaabaaaabbababaabaaababbbababaabaabbaabbaababbabbaaaababbbbbaaabbabaaaabbbaababaabbbbaaaaaaaaaabbabbbbbbaabbbabababaababaaaabaabbbabbabababbaababaaaabbababababbbaaaabbbbabbbbbbbaabbbaabbaabaabaababbabaaabaaaabbababbbbbbbbbaaaaaaaaaaaabbababbbbabbbbbabbaabbbbabbabababbbbabbbbaabaabaaaabbbaaaaaabababbaaaaabaabaabbaaaaaaababaaabaaabbbaababaabbbaaaababbbabbbbbbbbababaaaaaaabbaaaaaaaaabbaaaababbbaaabbabababbaabbbabababbabaaabbbbbbaaabaaabbbbbabababaaaaaabbabaaabbabbbbbaabbbbabbababbaaabbaaaaabaabbbbbabaabaabbbbababbbbaaababbbbaaaabaabbabbabaaaabaaabbabbababbaabbbbababaababbbbabbbbaaaaaaaabbabaaaaabbaaabbabbbbaabbabbbbabbbbbbbbbbbaababbbabaabaabbbbabaaaababaayaaaaabaaabaabbbbaababaaaaababbaabbbbbabbaaabaaaaaaaaaabbaababbababbabbaaaaabaaaaababaabbbaaaababbbbaaaabbbabaaaabaaababbababaababababbabbbabaabbabbabbabababbbbababbbbbbbababbbabbaabbbabaaababababbbbabaabaababaabaaabaaaabaababaabbbbbaaaaababbabbbaaaabaabbbbbababbabaaaabbaaabababbbbababaaaaaabbabbbabaabbbabaabababbaabbbaabaabbbbaaabbaabbbbbaaaaaaabaababaaaabbabaabbababaaabaabbababbbaabababbbbabaabbaaaabaaabbbabbbabbaabbabaaaabaabbbabababbbbbaababbbababaababaabaaaabbabaaabaaababaabbabbbaaaaabbbabababbabbabbabbbbbaabbbabbabbbaabbaaababbaabaababbaaabaaabbababbabababbaaaaabababaabbaabbbbabbaaaababaaaaaaababbbaabaaaaaaaabbaabaaaabaabbaaaabaabbabababaabbabaaabaaabaaabbbbbabaaababbaababbbbabbbaaabbabaabbbbaabbabbbbbbbbabaaabaabaabbaaaaabaaababaabbbbaaabaabaabbbababbbbaaabbbabbbababaaaabbabaaaaabbbabbbababbaaaabbabaabaaaaabaababbababbbbbbaaabaabbaababbaaabbaabbbbbbbbbabbaaaaabbbabbabaaabaaaaababaaabbabbbabababbbabbbbbbbbabaabbbaaabbaaaabbbbaabbbaaabbabbbaabaaabaaaabbbbbbaaabbbbaaaaabbbbabaabaabbbbbbabababababbbbbbaaabaaaabbbaabaabaaaabbabaaaababbabbaababaaababbbbabbabbaabbaaaaabbaaaabbaaaababbbbabaaabbabaaaaabaabbaabaaaababaaaabbbabaaaaaaabbaabbabaabbabbbbbbaababaababbbbaaabababbbabbabbbbabababbbbbabbaababbbbbbbbaaaaabaabbbbaabbaabaaaababababbababbbaababbaabaabbaabbbbababbbbabababbbaabbbaaababbbaabbaaaaaabbaaaaaababbbbaabbabbaaabbbaaabbbbabaaaaabbbaabbaabbbaababbbabaaaaabaabbaabbbababbbababbbabbaaababaabbbabbabbabbbabbabaababbbbabbbbbbbbbbbabbabbabbaabaaababbbaabbbbbababaaaaabbaaabababbaaabababbbabbbaabbaabbbababaabbbaaababbbbbbaabbabbaaabbbaababaabbaaaabbbaaaaaabababaababbbbabbaaabbabbbbababbabbbbaaaabbababaaaaabaaaababbbabbbbbbbabbaaaababbbabbaaabbaaaabbbbaaaabababaaababaabbaabaaababbabbabbbaabbaabbaaaabbaaabbabaabbbababbbabbabaaaaabaabaaabbbaaabaaabaabbababbaaaaaabbabaabbaaabaabbbbbbbaabbbbaababbbbabaabababbbbbbabbabaaabbbbababaaabaabbbbbaaaaabbabaaaabbbaabbbaaabbabbbaabaaabbabbaaabbababbaabaabaabbbbbbaabaaaaabaabaaaaabbabaaaabaaaaabbaababaaaaabaaabbbaaaabbaabbabaabbbababaaababbaaaaaabbbaabababbaaaabbbbabbabababbabbabbbabbbbaabababbbbbaabbbbbbaaabbbbaaabaaabababbaaabaabbbabbbbbaabbbbbabaabaaabaaaaababbbaaabaaaaaaaabaaabababaabaaababaaaababbbbaababaabbababbaaabbaabbbabbababbbbbbaaabbabbbaaaabbbaabbabbabbaabaaaabbaababbbbaaaaababaaabaaabbaaabbbbbaaaabbbbbbbaaaaaabaaabbaaabababbbbaaababbabbbbbaababbbbbabbbabaabbabbabaaaabaaaaababbbbbbaaabaaaaabbabaaabbabbabbaabbaaaaababbbbbbbbbbbbaaabbbabaababaabbbabababababbbbabababbabaaaababaaaabaabbbaaaaaabaaaaaaabaaabbbbabbabaabaabaaaaabbbbbbbbbbaabbbabbbaababbabaababaaabbabbabbababbaaabbaabbaabbaabbabbabaabaaabaaabbabbbaabbaaaaababbabbaaaaaabbaaaaabaaaabbbbabbaabbbbbbaababbbbabbbaaababbaababaaaaabbaabbbbbbbaaaabbbbababbbbabaababaabbbbaaababaabbbababbaabbaabbbbbaaaaaabbbaaaaabaaaabaabababbbaaabbbbbabbababbbbbabbbbabbabababbaabbbbaaaaaaaaaabaabaabababbbbabbbbbaabbabaaabaabbbbaaaaabaabbababbaaabaaaaabbaabaaabbbbabaabbaaabbaaaabbaababababbabbabaaaabbaabbbaababbabbaabaabbaaababaabababbaaababbbbbbaaaabaababbbabaaabaabaabababbabbabaabbabaaabbbbaabbbaababbbbbababaabbbaababbbabababbaababababaababbabaabbabaaababbbabaabaaaaaabbabaaaaababbbaaaabbaabbaaaabababbbbbbbbaabbaabbbbabbbbabbbaabaababaaabababbbbbbbababaabaabbbbbbaaaaaaabbbaaabaabaaabaabbaaabbaaaabbaabbaabbbaaaabbbabbaaaaababbababbbaababbaaaaaaaaaabbabbbaaaababbabababbbaabbbbbbbabbbaabaaabbabbbaabbbabaabbababbbbababaaababaaaaababaaaabababaaababaababaaababaaabbbbabbaaababbaaaaaaabbaababbbababaabaabaabbbbabbabbabaaabaaabaabbbbbababaabababbababbbbaababaabaabaaabbabbabbababaabbabababaabababbaababbaabaabbbbabbaabababaabbaabbaabaabbaaabaababbbbbaabbaaaababbbbbabbbaabbabbbbbbabaaabbabababbabaabaabbbaabbaaaabbbabaaaababaaaabbbabbbbbabbbbabbaabaaabbbbabaaabbbbaaabbbaabbababbaabbbbbababaabbaabbbaababaabaabaabbabbbbbbbaabbabbabaababaabbbbbaaaabbabaaaababbbabababaabaaabababaababbbaabaabbabbbaaabaabaabbababbaaaabbaaabbbbaabaaabbabbbaabbbaaabbbaabbabbbbaaaaabbabbababbaabbaabbabbabbbbabaaabababbaabbbbbbaaaaabbbbaabaaabaabbbabbbaaabbbbababbbaaabaaabababbaaabbabbaaaabbaaabbaaababaabababbbaaabbbbabbbbbbabbbabbbbbabbbaabbbbaabbabbabababbbbabbbaabaaaabbbabbabbbaaabbbabaabbbababbaaaabaaaababbbaabbbaababbaaaabbbaabbaabbbbabaaaaabbbabbbbbaabaabababaabbaabaababbaaabaaaaaaabbababbaabbbbbbaaaaaababbabaaabbbabaaabbbbbabaabaaaaaabbabbaaabbaaaaaababababbbabbaabbbbbabaaabaabbbbbbabbbbbaaaaaaabaaababbababbabaaabbbbaaaaababbabbbabbabbbabbaaaabaabbbababababaaaabbaabbaabbababaabbabbbaabbaabbbbaabbbababbbaabaaaabaaaaaaaabaaabbabaaabbbbabbbbaababaaabaaabbabaaaaaabbababbababbabaabaababaabaaabbabbbbbabaabbabababababbbaaabbbabaaaaabbaabbabbbabababaaababaaabbbbaababbbbbabaaabbbaaabaaaabbaaaaabababbbbbaababbbbbabbbbbbbbabbbaababbabaabaabaaabbbaaababbbaaaabbbababbbbaaababbbbbaabbabbbbbabaababaaabbabbbbaaaaaabababaabababaabbaabbbbaabbbbbababbbabaabbabababbbbaabbaabaaabbbbababaabaaaaababaabaabbbabaabbbbaaabbbabbabbabbabbabaaabaaaaabaaaaabbaabbaabbaabbaaababbbaabbabaabbabaabbbaabaabababaabaabbbaaaaabbabababaabbbaabbbbabbabbbaaabbbabbbbabaaabbbbbbababbaaababbbaabbbabbbababababaabbabbbbabbabaaabbbbababbaaabbaabababaabbbabababaabbbbbabbabbbababaabbaabbbababbbbaabbaabbbbbbabbaaabbabaaabbaabbbabbbababbaabbbaabbbbbabaaaabbbababbaabbbbaaaababbabbaabbabbbbbbbbaaaaabbbabbbabbaabbabbbbaababaabaababaaaaabbbbbabbbbbaaabbaaaaaaaaaabaaabbbbababbaababbbaaabaabbbbaababbbbaaaabbaaaaabababbbabbaabbbaaabbaaabaaabaabbbbaaaaabaaabbaaabbabbbaaabaaaabababbbabbababaaabbabbbbabaaaabababbbaaaaaaabaaababaabaaabaaabbaaababbbaabbaabbbbaaaaabaaabbabbaabaabbabababbaabababbbbbbbbbbaaaaaabaabbbbbaabbbaabaaabbbbaaababaaabbbbaabbaababbabaababaaaabaababbaaaaaaaabbbaaaabbbabbbbaababaaaaabaaababbbbabbbbbbbaababaabbbbaaaaababbaababbabaabbaaabaabbaabbaababbabbbbbbbaabaabbbbabbaaabbabbbabbabaaabbbbbbbaaabbbbbabbabbbbbbabaababbbabaaabaabbbaaabaaabaababbbbbbbbbaabbaabbbbaabbabaaaaababbbbabbabaabaabbbabbabaabbaaaabaabaaaabbbabbbabbbabbbbbaababbaabbbabbbbbabbbababaaaaaabbaaaaaaabbabbabbbbabaaabbbbaabaababbbbaabbbbabbbaaaaaabbaababaaaaabbababaaabbbbabbaababbabaabaababaabaabbbbaababaaababaaaabbbbaaaabbbbaaaaaaabbbbabaabbabaaaaaabbabbbababbbbbaabbbabbabaaaaaabbaaabbbaabbbbbbbababaaaaaaababbabaabaaaabbbbbbbaababaabaabbbaaaabbabaabbbbbbbbbbbaaabbabbabbaabaabbbbabaaababbababbabbaababbabbabbabaaaaabbbbbaaabaaaaaaabababbbababbaaabaaabbaabababbababbbaabbaababaaaaababbababbabbabbabbabbbaabaababbbbabbababbaababaaabbababbbabbabaabababaababbabbaabaabaaaaaabbbaababbbbaabbbbbaaabaaabbbabaabbbbaaaaaabaabbababbbbabbabaabbbbabbababbabaababaaabbababaaaababaababbbaaababbaabbabbbaaababbbabbbbbbaabaaababbbabaabaababbaaaaaababbbbaabaaaababbababbbabbbaabbabbbaaabbbabababbbbabaaaaaabaabbaabaaabbbaaaaaaaabbabaababbbabaabbaaaaaabbaabbaabbabbbbabbaaabaababababbababaaabaabbaabbbaaabaaababbbbababbabbbbabaababaababbbbabbaabababababaabaababbaababaabbabbbbbbbaaaaabbaabbbabbbaaaaabaaaabaabbbababbbbbaaabaaabbaababaaaabbbbabbbaaababbbbaabaaaaabaaaaabbaaaabaabbaaabbabbbbbaaabaabbbabaabaaaaaabaabbbabbbbabbbaabaaabbabaaaabbbabbbbbababbbbabaabaaabbbaababbbbbbbbabbbaaabaaaaababaabaaabbbbbabababbaabbbbabaaababaaabaaabbaababbbbbbbabbaababbabbabbbbabbbabaaaaabbabbabbabaabababbabbbbbbaabbbaaaaaaaaababaaaaaaaabaababbbbbbbabbaabaaaabaaababaabbbababbabaabbbaabaaabbbaabbaaabbaaababaabababbabbaaaaaaabaabbabbaabaabbbaaabbaabaaaaaaabaabaaaaaabaabbbbaaaabbbbbbbaabababbaabbaaabbbbbababaaaabaabbbaaaaaabbbbbbbaabaaaabbbabbabaaabbababbbabbbaaabaabbbaaaabbbbbbbbbbabbaaaaabaaabababababaaabbaaaababbabaaaabaaaababbaabbaaaaaaabbbbababbbbbbaababaaabaaaaabbbabaaaabbababbbabbbabbbbaaabbaaaaabbaabaaabaaabbbaaaaaaabbababbaaabaabbbabaaaaaabaababaaababaaabbbbaabbaabababbaaababaaaaaaaaabbaabbababbaabbaababaabaababababaabbbbbbaababbbaababbaaababaabaaaaabbbabbbabbaaabbbbbbaababbbbabbabbabbbabababaabbbaaabbabababaaaabaaaababbbbabaaabbbaaababbababbabaabaaabaabbbaabbabaaaaaabaabbbbaabababaaabaabababbabbababbbbabaaabbbbbbbbbabbbbaaababbaaaabbbbababaaaaaabababaaaabbbabbaaabaabababbbaabaababaabaabbbbababbaabbaabaabaaaaaaabbbbababaaaaabbbabbaababababbaabaaabaabbaaaababbbaabaaaabababbabaabaabbabbbabbabaaabababbbabbbbabbbbbaaabaabababbababbaaaaaababbbabbabbabaabbabbaabababbaababbbabaabbbababbaaaaaabaaabbabababbaaabbabbabbabaabaaaaaabbaabbabbbbbbbbaabaaaaaabbbbaaabbabaaabbbbababbabaaaaabbbbaaaaabaabaaaaaabaabaaabbbbaababbaababbbbabbabaabbbabbbbbabbabaaababbaabaaaabbaabbabbbbaaabbbbbbbabbabaabbaabababaabbabababaaabababababaababbaabaabbbbabbabbbabbbbabbababbbabbbabbbbaababbababababbaababbaaabbabbbbbababbbaabaabbbbbababbaaaaabbbbabaabbbbbaabbabbaaaaaaababbaabbbbabbababbaaababbbabbaababbaaabaaabaaaaabaabbaabbaababaabbbbbababbabbbbbbaabbbbbbbabbbaaababbbaaaaaaaaababaaabbaabbbbbbbbbbabbabbaaabbaaabababbbbbbaaabaababaaaaabaaaaaaababaaaaaaaaabbaaabaababbbbabbbaabbaaaababababbababbababbbbbbbabbabbbabbababaabaaabaaaaabbaababbabababbaababbaaabbaaaaabaaaaaabaaababbbabababaaaabbabbbabaaaabbaaabbabaaabaaabbaaabababbaabbbaababaababbabaababbbabbabbbaaaaabaaaabbaaabbabaaaabaabaaabbaaaaaaaabbabababbabbaaabbbabbbbaaabbaabbaaaababbaabababaabbaaaabaaababababaabbababababbaaabbbaaababbbbabbbbbbabbbbababbaaaaabbabaaabaaabaabbbabbabbabaaabaabbaabbabbbbabbbabaaaaabbabbbabbbbbabaaabbaaaaaabbbaaaaaaabaabaabbbbbbbbabaaaaabaabbabbaaabbbabaaabbbbaaabaabbabbbabbababbbaaababaababaabbbababaabaaaaabaaaaababbbbaaaabaabbbbbaababbababababbaabbabbbaaaaaabbbbbaabaaabbbbbbbbbababbbbaaaabaaabbbaababbbabbabbaaaabaabbbabababbabaabaaaaaaaabbbbbabbbabaabbabaaaaabaaaaaabbbaaaaabababbabaababbabbbbbbbbbababbaabaabbaabbababaaabaaaaabaababaaabbbbaabbbaabbaababaabbbabbbaabbbaaaabbbbbbbabbbaaaabbbaaaaababababaabaabbaaababbaaaaabbaabbabababbbbbaaabaabababbabbbaaaaabbbbababaabbbabbbbaababbababbbabaaabbbababbababbbbbbbbababaabbbbaaabbabaabaababbbabaababaabaaaaabbaabbbbbaabbbbaabbaababbabbbbbaaababbaaababaaaabbaaaabbbabbaabbbbbbbbababaabbaabaabbabbaaaaaaaaabaababbbbaaaabaabbabaaabbbabbabbabaabbabbbbbaaabbaaaaabbabaaabaaabbbbaababbababaaaabaaaabbbabbaaaababbaaabbabbabbbababbbbaaababaaababbaaabaabaabbbaaabaabaaaaaaabbaaabbaaabbabbabbabbbaabaabbabbbaaabaaabaaabababbaaabbbbaabbabaabaababbaabaaababaababaabaaababbbbbbaabbbaaabaaabaaabbabaabbbbabbaabaababbabbaaabababaaabbabaaabbaaabbbaabbbabaabaaaaaaaaabbabbbabbababbbabbabababaabbbabbaabbaaababababbabbbbabbbaaababaaaabbaabaabbaaaabbbabbaabaabaabbbbbaabaaaaabbbaaabaabbbaababbbabbbabaaabbbaaaaabaababaabbaabaabaabbbbaaabaabbbabbaabbabaababbbbababbbabbaabaaabbaabaababaaaabbbbaaabaaaabbababbababababbabbbbabaaaabbaaaababaabbbbbabaabaabbbbabbabababaabbaaaaabbbbbabbbabaaaaaababbbababbbabbabaabbaaaabbababaaabbaaaaabbbbbabbababbbbbaabaaababbbaababbababbbbabaaaababbabbbbaaabbbaaabaababbbababbaaabbaabbbbabaaaaabababbbabbbbaabbbbbbababaabbbbaabaaaabbbabbbaaabaaaaaababbbaabbbaababaababbaaabaaabaabbaaabbbaaabbbaabababababababbabbabbaaabbabbababaababaababbabbbbaabaabbbaaabbaabaaabaaaaabbbbbabaababaaabaabaabbabbabbaaaaababbbabbaaaabbbbaabababbaaaabaabaaabbbaaababbbabbbabbababbbabbabbbabaaabaaabaababababaabbbaababbbaaaaababaaabbbabbbabaabbaaabbaaabbbabbbababbaabbbbbbbaaaabbbaabaaaabaaabaaabbbbabbaabbbaaabababbabbaabbabaaaababbaabbababaaabaaabaaabbaabbaaaaaaaaaababbbaaabaabababbabaaabbbaaababbaabaaabaabbbaaabbaaabbabaababababaabbbbabaabbabbbaabbababbabbbbabbaaababbbbbaabaaababaabaaababababbbaabaabbaabaabbbbabaabbbbbbaabbaabbbabbabbbbbaabbbbaaaaabbbaaabbaababbaaabaababbbbabaababaabaaaaabbbabbaababaabaabbabaabaabbbbaabaabaaababaabaabaabbabbbbbbbaaabbbaaaaabbbaaabababaabbaaababbbbabaabbbbbbaaaabbbbaaaababaabbabbbaaaaabbaaaabbaaabbaababbbaaabbaabbabbaaaabaabababbbaaabaaababbbbaabbbabababbbabababbaaabbbaababbabbabababbbaabbbbabbaabbbbbaababaababbbaaaaaabaaaababbbbaabbbabaaabbabbabaaababbbbabaaaabaaabaababaababaababaabbbabaaabbaababaabaaabbabbbbbabbbbabaaababbababbbbabaabbbbbbbbabbaabbbabaabbbabbbbabbbbaaabbbaababbabbbbbaababaababbbbbbaabbaabababaaaabaabbabbaabaaabaaaaaabaaaaaabaaabbbbbbbabaabbabaabbbaaabaaabbabbababaababbaabaabaaabbbababaabababbbbbaaababbabbbababaababbbabaababaabababababbabbbbbbbbabbaababbaaabbbabbabbabbaabaaabaabbbabababaaabaabaaaaabaabbaaaabbabaabaabbaaaabbbbabbaaabaabbaabbbabbbbaaaaaabbaaabaababaabbbabaaaaabaaaabbaabbabbaaaabaaabaaaabbababaaaaabbaabaaabaababaaabbbabbaaaabbbbaaabaababaaaabaaaabbbaabababbbabbbabbbbaaabaaabbababaaaaaaaaaababbabababaabbaaaaaabbaababbabbbbabbbbbbabbaaabbaabbbabbbabbabbabaabbbbbbbaabbabbbababbaabbbaaaabbbbababbbaabaabaaaabababbabababbbbaaaaabbbabbaabbbbaaaabbbbaaaabbabbababababbaaaabaabaabbbaabbaaaaabbbaababaaaababababbbbbbabbbaabbbbbaabaabbbbaaababbaaaaabbaaaabababbabbbababbaabaaaaabbbaabbabbaaaabaaabaaabbbbbabbbaabbbabbbbaaabababbabababbaaabbabaaabaabbbabaaaaaabaaaabbbbbaabbbabbbaaaaaababaabbaaabbabbbaaaaabaaabbaaaaaabbbaaaaaabbabbbbaaaaaaaababaabbaaaaababbaaabaaaabbbaababababbaaabaababbbabaaabbbaaabbabababababaaababbabaabbbbaabbaabaababbbaaababababbaaaaaaabbaabbaabaaaabbbbaaabbbabbbbabbbababbaaaaaaabbaabbaaaabbbbbbaabaabbbabaabbabbabaabaaabababaaabbaabbaaaaabaaaaabbaabababbbbbbbaabbbaabbaaabbababaababbaabbaaaabaaabbbaabababaababaabbbbbaaaabbabaabbbabbbbbaaaabbbaabaabaaaaabbbbabaaaaababbaaabbbbaaabbabbaaabaabaabbabbbbabbaabbbabbbbabaaaaaaaabbbbbbbabbbababaabbbabbbbaaabbbaabbaaababaaaabaabbababbbbbbabaabbbababbbbaabbaabaabbaaabbabbabbaaaaaaaabaabbbbababaaaaaabbabbaababaababbaaabbabbaaabbbbaaababbbababaabaaabbbabaaabbbabbaabbaaaaababbbbaaaaaaabbabbbaaaaaaabbaabbaaaababaabbaabbaabbbaaabbabaaabaababaabaaaabbaabaaababbbbabaaabaababbaabbaabbbaabbaaaabbbbaabaababbbabaaaababbbbbbbbbbabaabbbabbbaabaabbabbbbbaabbabbabbbbaaaabbaaabababbaababbbabbbaabbaaabababaabaabbaaabaaabbbbabbaababbbaabaabbbababaabbbbbbaabbbaabbbbbaaabbaabababbabbbbabababaaaabbbaabbabbaaaaababaabababaabaaabaabbbbbbabbabbaabbbabbababaaabbababaaaaabbbababbbaaabbbbaabbbaaabbbabaabbbbabaaaaaaaabaabababaabbaaaababbabababbbbabaaabbaaaaabbbababbababaabaaabaabaabbbaabbabbababbbaabbaaabbaababbabbbaaabaabababbbbbbababbbbababababaabaabbababbbbabaaababbbababaaababaabbbbaaababaaabbabbabbabbaabbaabbbaaababababaabbbaabababbbbaabbbabaabababbbabaaabbaababaabaaabbbaaabbaababaaaababbbabababababbabbbabbbbaaaabaabbbbbabaababbbbbaaaabbbabbbbbbbbbbbbbbabbabbaaaabaabaaaaabbabaaaaabbaabaaababaabbbbaaabbaabababbbabbabaaaabbabbaaabbaaaabbaaabaaababbbbbbbbbabbabbbaababbabbbabaaababbababbaabbbabbababbbaaaaababaabbabbabbaababbabbaaaabaaababaaabaaaababbbbbaaabbbbabbaabaaababaaaaaaabbaababbbababbaabbaaaabbbaaaabbabaaabbabaaababbbbbbaaababbababbbaaaabbabababbbbbbaaabbbaaabbaaaaababaabbaabbabbaaababaaabbbbabbbaabbbbaaaaabaabbbaabbabaabbbabbaababbabbabaabaabbabbbabbbbabbababbbbaaababbbaabbbbaaaabbaaabbaabababbabaabaabbabbaaaabaaaabaaabaabaaabbaaabbaabbaabbbabaaaababbabaaaabaabbabbbbabaababaaababbbabbbbaaabbbabbbbbabaaaaaabaaaabbaabbbabbaabababbaaaaabbbaabbbbbaabbbaaababbaaabababaaabbbbbbabaabbaabbbabbbbbabbbaaaabbbbabaaaabbabbbaaabbbaabbabaaaaabbababaabbababbbaabbabaabbaaabaabbbabaaaaabababbbbaabbaaabbaabaaabbababbaaaabbaaabbababbabaaaababaabbbbabbaabababaabbabaabbaabbaaaaababbaabbaabbaaabbbbabbaabaaababbbbbabbabaabaaaaabbabbabbabaabbbbbbbbaaabbbaaaaabbaababbbaaabbbababbbabbbbabbbaabaaabbabaababaababaabbabbbbbbbabaabaaaabaabaabaaaabbabbabababbbbbbaabbbbabbbbbabbaabbbbaabbbaaabaabbababbbbbbbbbaabbaaabbabaaaaabbbababbbbaabaabaabbbaabbaaabbabababbbaaaaaababbbabaaababbaabbaabbbbbbbaababbbbababaabbabaaabaaabaaaababbbbaaaababbbaaabbbbbabbbbbaaaababbbabbabbbaaaabaaaabbaaaaabbababbbabbabbaababbbbabaababbbbaabbbababbbaaaabaabbabababbbaaabaabbabbbaaababaabbbbabbaabbbbaaaabaaaababbababaaabbaababaabaaababbbaaabbabbabbbbbaabbabbbbbbbabbbbbaabbaababbabbbabbabbabbbbbabbabbbaaaaabbbaabbababbbbabbbbbbabbabbbbaabaaabbbbbaaaaaabaabbbabaaaaaaaababaaaaaabbbabbbbabaaaaaabbabaaaabbaaabbabaabaabbbaaabbbaaaaaabaababbaababaabababababbbbaaabaabbbbbbbaaabbabaaaaababbbbbabaabaabababbababbaabbaaaabbbaabbaaabaabaaabbaaabbbaabababbbbbbbbbbaababaaabbbbaaababaabbbbbaabaabbaabbaabaaabababaaabababbbabbbbabaabbaabbbbabbaaaaaabbaaabbbabaabaaaababbaabbaabbabbbbababaaaabaabbaabaaababaabbbbaaabbbbabaaaabbbbabbbababaaababbbbbbbbbaaaaaabbbaaaabbbaaaabaaaababaaabaababbababbbaabbbababbbbbbaabaabbbaabbbaabbabbbaaaaaaaabababbababaabbabbabbaababbbabaaaabbababbaaabbbababbaabaaaababbaaabababbabbbababababaababbbbbaaabbbaabbabaaaaabbaabbbbaaabbbaababbaabbbbabbabbbbabaaabbabbabbbbabaaaabaababbbabbabbbbaaabbbaaaabbaabaabbabaabaababaabaabbaaaababaaaabbababbbababaaaabbaabbabbaabbbbbababababaabaabbbbabaabaaabaabaaabababbbbbaabababaaabbababaabbabababbbbaaaaaabbbabababaabbaaaabbbbbbabbaaaaabbbaaaaaaabaabbabaabaabbabbbbababbbbbabbaaabbbbbbababaaabaaabbbaabbbbbbaabaaaababaaaaabaaaabaabaabbaaaaababaabbbbabbbbbbbaababaaaabbbbaabbaaaabaaaababbaaabbaabbbabaaababbbbbaaaabbababaaaaabbbbaaaabbabbaabbaaaaaaaaabbbaabbabaabababbbbaababbabbabbbbaabbabbabbbbbbabbbabaababaabbbbaabbbaaabbbaaabbbabbabaaaaaabbabaaaaaaabbbabbabababbaaabbaaabaaabbababbbabaaababbbbbbbabbbabababaaaaabbabaaaaaabaababaaababbaaaabaabbabababbabaabbabbabbbbabaaaaabbbbbabaabbbabbbbbbbabaaaabbbbbaaaaaababbbabaaaaabaaabaabbababbbabbababbbbabaabababbbbbbbabbbaaaabbabaaaabbbbbbabaabbaaabaabbaabbbbbaababbabbbaaaabbbabaaabaabaabbaaababbabaaaabbaaaaabbaaaabaaabbbabaaabaaabbbabbbaaabbbabaaababaabaabaaabaaaababbabaaaabbbababaabbbbaabbaaaababbbbbabbbbbaaababaaaabbbababbbbbbbabaaaaabbabbbaabaabbabbbabaaabbaabbbabbbabbbabaabababbbbabababababbaabababbbbbbabbbabaabaabaababbbbbabaababbbabaaababbabbbababaabbaaaaabbbabbaabbabababbabababbbabaababbabaaabbbbaabbbaaaaaababbbaaaaaaaaabbbaabaaabaabbbaababbbbaaaabababbbabaabbbbababaababababaaabbbbaababaabababbabbbabbbaababaabaaaaabaaabaabbabbbabbbaaaaabbaaaababbabbbabaababbbaabbabaaaaaaaabbbababbaabbbaaaaaababaababaaababaabbaaaabaaabaaabbabbbaaabbabbbbabbbbbbbbaabaaabbbbbbaaabbbabbbbaaabbbaaababbbaabbbaabbaabbaabbbaaabaabbabaabbaaaabbbaabbbbbbabbaabaaababbababbaaaabaababbbabbbabbbbbbbbababbbabbaaabbabaabababaaaabbbbaababbabbbbbbabaabbbbaaaababababbbabbbabbaaaaaaabaaaababbbbbaaabaabbabbbaabbaaaaaaaaabbabaaabaaaaaababbbbbaaabbbabababaabaaaaaabaaabbabbaabababababbabbabbabbaaabbabaaabbababbababbaabbabaabbbbbaaaaaaaabbbabaaabbabbabbbabbbbbbbababaabbabbbababaaaabbabbbababaaabbbbaaabbbbbbaabaababbbbbbbabbbbaaaabaabbabbabaabaabaaabababbababaabaaaaabbababbbababaabbbbabbababaabbbbbaaabaabaababbaaaababbabaabaaababababbbaababbbabbaaabbbbabbbbababbbabaaabbaabbaabaaaababbaabbabaaaababbabbabbbaabbbbaaaaabbbaabbbbbaaabaabbabbabbbbbaaaabbbbaaaabbababbabaababaabbbbaabbbabbbbababaabaabbababababaaabbbabbaaabaaaabbabbabbababaabababbbbabbbbbbaaaaaaaabbaaabbbabababaaabaaaabaaabbaaabaaaaaaaaaaaaaabbbbaaaaaaabbbababaaaabaababbbbbaaaabbbbbbaaabbabaaaabbaababaabaaaaaaabaaaabbaaababaaabbbbaaabbbbbbbabbbbabbbabaababbbbabbbbababbabaaabaaabababaaabbaabbababbaabbbaaabbbabbbaaaaabbbbababbbaababaaabbbaaabaabbabaaaabaaaaaababbbaaabbaabaaabbbabababbabbbbaabbabbabaabaaaabaaaabbbababbbabbbbaaaababbabbabaaabababbabbaaaabaaaaabbaabaaaabbaabaababaabaabbababbaabbbbabaabaaaaabaabababbbbaaabaaaabababbbaaaabababaabbabbabbbabbbaaaaabbabbbaabaaaabbabaaaababaabaaabaabbabbbaababaabaabaabbbabbaabaabaaaaaabaabaaabbbaaaabbbaaaabbbaababbbbababbaaaaaaabbaabbbbabababaaabbbbbaaabaaabababaababbaabbbbbbbbabbababbaaaabaaaababbaaabbbbbabbbbaabaabaaaaaaababaaabbbbabaaaabbabbbaabababbaaaabbaabbbabaaababbbaaaaababaabaaaabbaabbaaababbbaabbbbbaabaabbabbbaaabbbaaaaabaaaaaaabbababaaabababababbbbaababbbababbbaaabaabbaabbbaaabaaaabbbaaaabaaabbabaabababaaababbbbbaabbabbabbabaaabaaaababbaababbbaaababaabbbaaabbabbbbabbbbaaabbbabbbbaabbbaaaabbbbbabababaaaaabbababbbbabaaabbbbbabbbaaabbbaabbbbbabbaabaaaaaaaaabbbbbbbbbaaabbbbaabbbbbbabaaabababbbbabaaaaababbbaaaabaabaaabbaabaaabbbabbaaababaababaabaababbbbabbbbaaaaababbaaabaabaaababbabbbbbbaabaaababaaaabbbaabbbabaababbbbababaabbbabbaababbaaaababbaababaababababbabbaabbabaaaabbbaaaababbbbbababbbaaaabaabbabbaabaabbbbaababbbabababbaabaabbabbaaabbabababbabbbababbabbaaaaaaaabbbbbbbabababaabbbaaababbabbabaaaabbababbbabababbaaaabbbbbbbaaaaababbbbbabbbaabaaaaaabaabbabaaaabaababbaaabbbaababbabaabbababbbaabbaabbbbaabbbbaaabbbbbabbbbabaabababbababaaababbaaaaababaaabbaaaaababbaabbaabbbabbbabbaaabbaabbaaabaabbaaababaaabbabbbabaabbaabbababbbbbaabaaaaaababbabbbbabaaaabaabbabbaaaababbabbabbaabaaaaaaabbabbbaaaabbaaababaaabbbabbbbaaaabbabaabbbabaaaababbbabbaababbbaabaabbaabbbaaabbbabbababaabbbbbbababbaaabbaababbbaaabbaabaaabbbbbbbaabbbaabbbbabaaabbbbaaaababaaabbababbaaabbbaaabbbbbbbabaabbbaababaabbaabbaaaaabbbaabbbbbbabaaaaaabaaaaaabbbbbbaaaaaaaaaaaabaaaaaaaaaaaababaaabaaaabbbaaaabbaabaaabbabbabaabaaabbaaabbaaaaabbabaaabbaabbaabbbbabaaabbbbbbaaabaaaaaaabaaaaabbbbbbaabbbbbaabbbbababbaaaabaaabbbabbbbbbbaaaabaabbbbabababbaaababbaabbaaabbbabaaaabaaabbababbbbbbbbbabababaababaaabbbbbbaababbbbabbabbaaabbababbbbbbbabaaabaaabaaaaaaaaababbbbbababbaaabbbabbbaabbaabaabaabbabbbbbbaababbbbabbbbaaaabbbaabbaabbabbbababbbbabaaabbabbbaababbabbabababbbaaabbaabbaabababbbbbaababaaabaabbaabbbbbaabbabbbbaabbaaaabababbbbbbababbabbabaabaaaabbaaabbbbaaabaaaababbaababaaaaaaaaabaabaaaaaabaaaaabbbaabaababbbabbbabbbaabbbbaaababbbbbaabababbbbbabbababaabaaabbbbaaaabaabaaaaaababbbbaaababbaaaabababbbbbbbaaabbaaaababaaaaaabbbabbabbabaabbbaaaababaaabbbbbbaaabababbbabaabbaaabbaabababbaaabaababaaabaabbbababbbababbbbbabbabbbaabbabbbbbabbabababaaaababababaaabaaaaabbabbaaababaaaaaababaaababbaaaabaabaaabbbbbaabbbaaaaaaaaabbaabbaababbbbbaaaabbaaababbaabbabaababbbbaaabaaababababbaaabababaabaaaaababaabbaaabbbabaaabbabbbabbaababaaabbbabaabaabababaaabbbaabbbaaabbaababaaaabbbaabbaabbabbabbbbaabababbbbbaaabababbaabababaaabaabbbbaababbbabbaababaabbaaaaabbaaaabbababaabbbabbbbaabbaababaababbbbbaabbbabbbaaababaababbbabbbabbbabaaabaaaabaaaaaaabbabaabbbbaabababbbbabbbabaababbabbbabbabaaaabbaaabbababbabbbbaabaaabababaaabbabbbaabaaaabababababbabbabbbbbaabbaaababbaabbabbbbbbbbbbaabbaababaababaaabbbbabbabbbaaaaabababbbaaabbbbbbabbbbabababbbababbabaaabaaaabababbaabaaaaabbbaaabbbbbbaabababbbbabababaababaaababbbabbaabaababbabbbbbbbaaabbabbbbbbaabaababababbaaabbbaabbaababababbbaaabababbbbbbbababbbaababababaabbaaaabbaaaabaababbabbababaaabaabbbabbababaaabbababbaababbabbaabbbbbbabaabaabaaabaaabbbabababbabbbbbbbabbaabbaabbbbbbbaaababbbabaaaababbbaabbbaaabbbbabababbaabbbbbbbaaabbaabbabbaaababbaaabbabbbbbbabbbbaaabaaaaaabaaaaaabaabbabaabaaabaabbbbaababbbababbabbbaaaaabbbbbbbabbaaabaaabbbaabbbabababbbbbbbabbbaaaaabaaabbbaabbbbbbbbabbbaabbaaababbbaaaaabaaabbbabbbababaabbbababbbbbababaabbaabaababbbbabbaabbbbbaabbaaaaababbbbaaaaaaabbbbaabaabbbbaaabbbaabbbaaababbbbbaaabbaaaaaaaaaaaababbbbaabbbbbbbbbbbbabbababbabbbbaaaaabbaaaababbbababbbabbbabbbaababbbabbbaaabbabaabbabbbbaaabaaabaaaaaabaababbabbabaababaabbbbbbbbababbbbbbbbabababbbbabababaabbaaaaabbabbaaabbaaaabaababbbaababaabbababbbbaabaabaaaaababbaababbabaabbabbaaabbaaababababaabbbbbbaabaaabababababbaabaaaaaabbabaababbbbaaabaaaabaaababbbabbbaaaaabaababaabbbbbbaabaabbbaababaaaabbbbabbbaabaaabbbbbabbbbbbbaabbabbbaababbbbabbaaabaaaaababababbaabaabaaaabbabbbaaaabaaabbababaaabaabaaaabbbbaaaaaaaabbbaabaaaaaababbabbbbbaabbabaabbbbaababaaababbbaaaaabbbbaaababbaabaabbbaaaabaabbabbabaabaaaaaaabbabbbbbaabbbababbbbabbabaabbaabaabaabbbbaaaabbabbbaabbbbaaaaaabaaabbbbbbabbaaabbbbbbaabbaabaabaaaaabbababababbaaababbbaaababaaabbbabaaaaaabbbbaaaabaabbaaabbaaabaaabbaaababbabbbbaaabbbaabbbabbbbbabababbbaabbabaaabbabaababbababaaaaaaababbbababbbbaaabbabbbbaaaabababbabbaababbbaaaaaabbabbaabbbaabbabbbabbbbbbaaabaaabbababababaaabbabaaabaababbababbaaaabbabaababbabaaabaabbaabababbbbbaabababababbaaababaabbbbbbaaaaaabababbaabbbbbbbaabbbbabbbabbaababbbaaabbaaaaaababbaabbbbabbbbbabaaabababaaaabbabbaaabbaaababbbbaabbbbbbbbabaabbbbaaabbababbbbaaababbbaaabbaaaabbaabbbababbbbbabbbaabbabaaaabbbbbbbbbbabbbbababbabaaaabbaaaabbaaaabaaaaababbbbbbbbabbaaaaaaabbaaaaaaaaabbaaaabbbaaaaabaababbbabbbaaabaaaaabbbbbbababbbbbaaabbbbaaabbaaaabbaabbaaaababbaaabbbabbabaaabbabaaabbbbbabbababaaaabbabaaabbaaaabbbbabbabbabbabbabbbbbbabbbababbbbbabaababbbbbbaabbbabbbabababbabbbaabaabbaababaaaabbabbbbabababbbbabaaabbabaababbababbbbbabbbbaaaaabbaaaabbaaabbabaaaaaaaabbaaaaaababbaababaaabaaaabaaabaaabaaabaaaabbabbaababababaaababbaabaaaaabbbbbaabbbbbbaaabbaaabbabbaaababaaabaabbbbabababbbbbbaabaabbbbabbabbababababbbbaaaaabbbaaababaaaaaaaaaaabbaaabbabbabbaabbbbbbaaababbbbbabbbaababaaaabaaaabaabbbbbbbbababbaabbaaababaabaaaabbaabbaabbabbbababbaabbbaabababbababbabbaabbaababaabbabbbaabaabbabababbbaabababaaaababbaaaabbbbaaabaabbabaabaabbbabaaabbbaaabaaaaaabbababbabbabbbabaaabbbabbabaabbaaababbbaabababbbbabbabbbabababbaaabbabbbbbabaababbbbaaabbbbabaabbabaabbabbaaaaaaabbaabaaababbbbbababbbbbaababbbbbaabbababbbbbbbbaabaaabbbbbbbababaaaabababbbaaabbbabaabbbababaababbaabaabbababbbaabaabababaabaabbabbabaaaaababbbaaaabaaaabaaaabbbaabbbaabbbababaabbaabbaabbaabbaabaabababaabaabbaaaaaabbaabbaabbbbbbaaaaabaabaaaababbbabbaaaaaabababbbbbbbbababaabaaabaaababaaabbababbbbabbababbbaaaabaabbaabbaaaabbbabbabbabbbbbbaaaaaabbaabaaaaaababbaaaaaabaaabababbbabbaababbbbababbaaaaabbabababaababbbbaaaabbbbaabaabaaaabbaaabbbbababbaaaaaabbbaabbbabbaababaabaababbaabbbabaabbaaaaaabaabbaaababababaaabbabbabbaabaaaaaaaaabbaaaabbbabaabababaaabbaabbaaabbbbaaabbbbabbaabbbbaababaababaaabbbbbaaabaabbaabaaabbbaabbbbbababaaaaaaaaaaababaaaabbabbaabbbaabbabaaabbabaaaaababbbabbababbbaabaababaaaababaabbabaabbaabbbabaaaababaabbbaaaabbababbbaabababbbabbbbbabaabbbabbaaabaaaababbabbababaababbaabaaaaaaaaaabbbaabaabbaaaababaababababaaabbbabbaababaaabaabbbabbabbbbabbbaabbbabbaaabbbaaababbbbaabbbbbaabaabbbbabaaababaabbbbabbaabbabababababaababaabbbabbabaaaaabababbbabaabbabababbbababbbabbaaaabbbbbababaabaaaabbaabaaabaabbaaababaabbbaababbabaabbaaaabbaababbbbabbaabbbaabbbaaaabaabbababbaababaaabbabbbaaabababbaaabbbaababaaababaaaaaaabbaaabbabaababbbbbaabaaabbbabbabababbbabbbaaaaabaabaaaaabbaaaababbbaaaabaabbbbabbbbaaaaabbaaabbbaababbaaabbbabbbbbabaabaaabaababaabbaabaabbaabbbbaabbabaaabbbbaaabbaaababababaaabbabbbabaabaababbbbbababbbbabbbabaaaabaaaabaaababbaaabbbaaabaabbabbaabbaabbbbbbbaaabbabababbbbabbbaabbbbbaaabaaabbaabaabbbaababbaaaabaabbbaaaaaabaaabaababbabbbaaaabababaabbabaabbaaabaabaabbbabbaaabbabaaababbbabbababaabbaaaaabbababbbaabbabbbbaababaaaaaababbbbaaaaababaaaaaababaaaaaabaaaabaababbabaabbbbabbabaabbaaaababbaabaaabaabaabaaabaabbbabbbbabbbaababbbabbababaaabbabaabbaaabaaabbabbabbaababbaabbbaaaabbaabababbabbababaaaaaabbaaaaaaaabbaaabaaaababbaaaaaabbabbbaaabaabbaabbbabaaabaaaabbbaaababbbabbabababbaaabbabbbabababbbbaabbababbbaabbabbbbaabbbabbababbaaababababbaabaaabbbaabaaabbababbbbaaaababbaaabaabbbbbabaabaabaabaaabaabaaabaaabbbbaaabbbbbabbabababbabbbaabbaabbababbabaababaaaabbaaababbaabababbaaaababababbaaaaababbbbbaaaabbbaaabbaaabababaaabbabbbaaabbbbbabaabababbabbbabbaabbbbababaabaaaaaaabaabbbabbabbaaabbaababbbaaabbababababaaaabaaaaabbbbaabbaabbabaabbbbbbbaabaaaabbbbabbbbaaaaabbaabababaabaaabbaaabaaaaabbbbbbaabbabbbbabaaababbbbbaaaabaabbaaabbababbbbabbbababbbabaaabbbbbaabbbabbaababbbbbbaaabbaabbabaabbaaaabbbabaaabaaaabbaabaabbaaaababaaabbaababbaabbaabbbbbabaaabbbbaabaabababaaabbbabaababaaabbaabbbabaaaababbbaabbbaabbababbaaaababbabbbbaabababbabaaabbaaabbaaaabaaaaaabbbaabaaaaaaabaaabbaaabbaaabbaaaabbaabaaababbabbbabbababbbaaaabbaaabbbbbbaaabbbaabbaaaabbababbaabaabaabaabbbaaabbbaabbabaabbbbaabaabbababababbaabaaaabbbaaababaaabaaaaabbbabaaaaaabaaababbaaaabaabbbaaabaaaaaababbabbbbaabaabbbbbabbababaaaababbbbaaaababbabbbabaabbbabaabbabaabaabbaabaabbbaababbbaabbabaaababababbabbbabbaabaabbaabbaabbbabaababbaaaabbaaaaababaabaaabbbaabaabbbbbabaabbbbbbaabbbaaabbbababbabbabbaaaaaaaaaababaaaabbabababbbabbbbabbaabaabaaaababaaabbbabbabbabbabaabbabaabaaababbaababbbaabbaabababbbbaaaaaaabaaaabababababbbabaabbbbaaabaababaaabbbaaaaabbabaaabbbabbbbaaaaabaaaababaaabababbaabaabbaaaaababbbbaaaaaaababbbbaaabbbaaaabbbababbbaaabbaaaaaabbaaabaaaabbbbababaaabbbbababbbbbbbbbaaabbaabbaaaaabbbbbbbaabbbabaaaaaaababbabbaaababaaaabaabaabbbaabbabababbbbaaabbbaaaabbbabbbbbababbaaaababbbbabbbabbbababababaaabbbbaabaabababbabaaaaabbabbbbbbbbbabbababaabaaaabbbbaabbababbbaaaaababaaabababababaaaabbbbaaaaaabbaabababbbaabababbbbabbbbbbbaabbaabbbabbbaaabbaaabaaaaababbaaaabababbbababaaaaababbaaaaabbabaaabaabbabaabbbbbbbbabbaabbbbababbbababaababbaaabbabaabbaaabbaabaaababaabbbbbabababbaababbaabbbaabbbabaaaabaabbaaaababaaaaaabaaabbaaaaabbaaabbbbbabbaabababaaabbaaabbabbabbabaabaabaababbababbbabaabaababbbbabbabababaaababaabaaaaaaabababaabbbbbbbbbaaaabbaaaabaabaaabbbbbaabbabaabbaabbbbbbabaabbabaaaababbaaabbbaabaabbaaabbbaaaababbaabaabaabbabbabbaabaaaabaabbbaaabbaabbabbaababbabbbbbabbbbbbbabbbabbaabbbbbbbbaabbbbababbaaaabbbababaabaaaaabaabbaaaaabbabbaabaaabababaaabbaabbbabbbbabbbaaabbbabbababbaaaabbbbabbbaaaabbbbbbabbabbabbababaabbbababababaabbaaabbababaabbaabbbbbabbbaaabbabababaaabbbababbbbabbbaaababaabbabaaababbbabababbbbaabbabababbaabababababbaabbbabbbabaabaabbaaaaababbabbbbbbbabbabbaababbaabababbbabaababbbbabbbbbbabaaaabbaabbbaabababaaaababbababbabaaabaabbbbaababbbbaababaabbbbbbbaabbbbabbabaaaaabbabbbbaaaaaaaaabaaabbaaaabbabaabaaaabbaababbbbaaabbaaabbbaaabaaabaaabbbaabbabaaabaababbaaaabbaaabbbbaababbbababaababbbbabaabbbbaaaabaabbbbababbbbbabaaaaaabaaabaabaabbaabbabbbbbbbbbbbbaabbbbbabaabaaabaabaaaaaabbbbaabbbbabababbbbabbaababbbabbbaaababbabbaaabbbaabbbaabaaaaaabbaaababbbabaaaaaaaabaaaaabaabbabbaaaaabaaaaaabaabbbaaababaabaababaabaabababaabbaabaaabaaabbababaaaabababbaaaaaabbababbabbaababbaaabbaabbaaaaaabbbababbbbbaababbaaaabaaabaababaaaaaabbbbbabababbaabaaaaaaaabbaaaabaaababaabaabaaabbbabaaaabbabababbbabaaabbbabbaabaabbbbbbabbbaababbaaaaababbbaaaabbbabaabaabbaaababaaaabaaabaaaaaababbabaaaabaaaaaabbabbbbbabaaaabbbabbabbaabbaaaabbbbababbbabbbabbaabbbabbbabababbabbbababaababbabbbaaabbbabbbbaaaaabaaaaababbbbbaaababaababaabaaabbabbaaaaaaaabaaababaaabbabbaaaaaaaabbabaaaabbbbbababaabbbaabbbbabbabbaababbbbabaaababaabbbbbabaabaaaaababbbaaaabaaabbaabbbbabbabbbaaababaaabbaaaabaaaababaabbaababababbaaabababbbababaaaabaabbaaaaabbaaabbbbabbbbbbabaababbbababbbaabaaabababbaaabaabaabaabbaabaaaaaaabbababbbbaaaababbabbbaababababbaababaabbbabaaabbaabbaabbaababaaabbbbaaabbaabaaababbaaaabbbbbababbaabbbabaaaaaaaabbbbabbbaabbabababbabaabababababbaaababbbbbabbbbbbbaababbbbbabbabbaabbabaaaaaabbbbaaaaaabbbaaababaabbabaaabbabaabaaabbbaabbabaaaabaaabaaaabbaaabbbbbbbbbbbabaabbbbbbabababaaaabbaabbbbbbbabaaaababbababaabbbbbbaaababbabbaaaababaaababbaababaabbbaabababbabaabbaaaabbaabbbaaaaababbaabaabaaaaaabbbabaaabbbaaabbaababbbabaabbbaababaaabbbbbaaababbaaabbbbbaaababbabbbbbaabaabaabaaabaaabbbaaabbabbabbbababaaaababbababaabaababbbbaaabaabbaabbaaaabbaababaabbbbbbabbbaaaaaabaabaababbaabaaabbbbaabbaaaabababababbababaaabbaaabbbabbabbaabbbabbaababbabaabaabbbbbababababaabaabbabbbabbbbaabbbbabbbbaaaabbaabbbbabaabbaaaabababaaaaaaaaaababababaabbaabbbaaaabbaaaabbaababbaaaabaabaabbbbaaaaaababbbaaaaaaaaababbbbabbaaababaababaaabaabaaaabbaaaaabbbbbababbbaababbaabababbababaaaaaaababaaaababbbbaaaaabbbabbbabbababaababbbbbbabaababaabbabbbaabaabababbbbbaabbababbbabbababbbabbbaaabaaaabaaabababaaabbaababbababaaaababaaaaaabbbabaabaaababaabbbaabaaabbbbabaabababaabbbabbbabaabbabbbbabbbababaabbababababbbaaabaababbbbbbabaaabbabaaaabbabababababbbabaaabbaababbaaababbaabaababaababbbbbaabbbaabaababbaababaababbaaaaabaabbababaaabaababaaabbbabbaaabaabbbbabaaaaabbbbbabababababbbaababbbbbbaababbbabbbbabaababaabaabaabbbaaabbabbabaabaabbbbbaabbaabaaabbbbabaabbbabbaabbabbaaaababbbabbaaabbbbbbaababbbaaabbaaaabbaababaaaaaaabaabbabbabaabaaaabaaaabaabbabbbaaabbbbbbbaabbabbbaabbbbabaaaaaabbaabaaaabaabababbaabbbbaaaaabbbabaaaaababbaababababaabbbbabbaaaaaababbbabbababbaaaaabaaabbabaabababbbaabaabaabaabaabbabaaababaaaababbaaaabbbaaabbababbabbabbbaaabaabbabaaaababbabbaaabbaaaabaabbbbaabbbaabbaabbbbaabbabaaaababbabbaabbbaabaabbbabaabbabbaaaabaabbaaaaaabbbabbaaabbaababbababaaababaaabbaabababaabbbbabbaaaababbbbbaaabaaabbbbbbbabbabbaaababbaabaabbabbbbabbbbaaaaaaabbbbabbabaabbaaaaabababababbbbabbabbabbbaabaaabbbabaaaaaaaaabbbbbaabaaababbabbabbababaabbabbbaabbbaaabababbabababaabbbbbbababbababbabaaabaabbbaababaabbaabbbbbbaabbbaabbabbabbaabaababbbaabbbbbaaabbaabbabbabbbbabababbaaabababaabbbbababbbbabababaabaaababbbaaaababaaabaaabbabbaabbabbbbbaaaaaababaaaabbbababbaaaabaaabbaabababbabbaabbaaababbabbaaaabbbbaaaaaaaabaabbbbaababbbabaaaaabaabaaaaababbbbaaaaaabbbbababbaabbaaabbbbabbbaabbbbbbbaaaaabbababbbabbabbaababbbaaabbabaaaaabaaabbbbaabaabaaababaaaaabbbaabaabaababbbbbababaaabbbaabaaaaaaabbabababbbabababababbaaabaaabbbaabbabbbbbbaaabbabaabbaabaabababaaabababbbbaaabaaabbaabbbaaaabbbaaabbbbaaabaabbaaababbbbbabbabbbbaaaababbbbaabaabbaabbbbabaabbbaabbaaaababbabaabaabaabbababaabbaaababbbbaabbbabbbbbaaaabababaaabaaabaababbbaaaaabababbbabaaabaabaaabbaabbbaabbbababbbbabbbbaaabbbbbaaabaabbbbbaababababbbbaaaaaaaaaabaababbbabaaaabbbaaabbbbbbababbabbabbbaaababaabbaaaaabbbbaaaaaababbbbbaabaababababaabbbabbbbabaabbabbbbbaaaabaaabbbaaabbabbababaabbaaaaaaaabbaaabbababbbabbabbabbbaabababbbbbababbaaabbaaabaaaababbaaaaabbabababbbbaaabbbbaaababbbbbbbabbbabaaabbababbbaababaaaabbbaababbabababbbaaabbaabbaaabaabababaabababbbbabaaaababbbababaabbbabbbbaaaabbabbbbbaabaabbabaabbaaaababbbbbaaaaaaabbbbababaabababbbabbbabbabaabbaaaabbbbababaaaaaabbababbaababbbaabbaaaaabbaaaababababaababbbaabbbbababaaaabbbabbabbaaabaabbaaaabbaababbaabababaaabbababbaaababbaaaaabbabaabaabbaaaaabaababaabbabbbbaaabbbababaababaabaabbbbabbbbbbbabaabbbabbbbabaaaabaabaaabaaaaabbbbbbbabbabbabbbaabaaaabbaaaabaaaabababaaaabbaaaaabaabababaabbbbbaabaaabaaabbabbbbaabbbabababaaaaaabaaababbaaaabaabaababaaaaaaaaabaabbbbabaaaababbaaaaaaabbabbaaabbbaabbbabaaabaababbaaababbaaabbaabbaaaabbabbabbbaaaaabbbaabbbbbbaabaaabaababaabbbbbaababbaabbababbabbaabaabbbaabbababababbabbaaaabaabbabbabbbbabbbbbabbbbbabbaaabaaaaabbbbbabaabbabbabbabbabaaabbaaaaqaaabaabbbbabababbbabaaabaaaaabaababbabababaabbbbbbbbabbbbababaabbaabaaababbbabaabaabbaaababaababbabaabbbaababaabbbaaaabbabbaabbabbaaaabbbbaaaabbbaababbbbbbbbbaaaabbbbbabaaaaabbaaaaaabbaaabbbaabbbbbbabaaabbaababababbaabaaaabbaaaababbbbbbababbaabaababbbbbaabbbababbbababbbaaabbaabaababababbbababbbaaababaaabbaababbabbabaaaaaabbbbabbaabbaaaaababbbaababaaaababbbbbbaabbababbbabbbaabbababbaababbbaabbaaaaabbaaabbbaaaabababaaaaabaaaabbaaaaababbbaabbbbabbbbbaaabbbabaababaaabaabaaababbbbaabbaabaaababaabbbaabaabbbbbbbabbbaaabbaabbbbaabbbababaaaabaaababaabaaababbbbbabbbaaaaaaabbbabaaaabaabaabbbbbbbaababbbaaaabaaabaabbababaaababaabbabbabbbaaaaababbaaabbababbbabaaabbbbaabbbbbbababbabbbbaaabaabbaaabbabbbabbbbabababbbabbbbbbabbaaaabbabbbbbababbabababaabababaabbabbaabbabbaabbabbbaabbbbaabbbaaababbabaabbababbaabbbaaaaabaaaaababaababbaababaabaabababbaaaaaaabbbbbabbabbaaaaaaaabbbbbaabbababbbaaaaaaaababababbabbaaabbaabaabbaabbababaaabbbabaabbbbababbbaaabbbaabbbaabaaabbababbaaaabbbbaababababbbbaabababababbbbbbaababbaabbbaabbbaaabaaabbbaababbbaababaababbaaaabaabbaabbaaaabbbaaabaabbbbbbaabbababababbbabbabaabbabbabbbaaaaaaabaaabbbbbbbaababaaabbabaaabbabbabbaaaaaaabababaabbbaabbbbbbaabbaaabaaabbbbbabbbabbaaabbbbbabaabbbbababbaabbabbaaabbaabbbbbabbbaaaababbbbbabbbabbbbabbbaabaaababbabbbabababbbaaaaabbabaaabbaaabbbababbbaabaabaabababbababbbaababaabaaaaaaaabbababaabaabababbabaababbbbbabaabbaaababaaaababbbbbbaaaaaaabbaaabaababbbbbbabaaaaabbbaaabababababababbbaaaaabaabbaaabbabbbbbbabbababaabbabbbbbabbbbaabbbbaaaababbabaabbbbbbbbbbbabaaaaaababbbabbbababaaababbbbababbbbaaabbbabbababbbabaaababbbbabaabbbbbbbbabaaabaabaaaaababbbbbbabbbbbbbaaaaaaabbaaabbbbabaaabbaaabaaaaabaabaaaaaaaaaaaaaabbbbaababaabbabbaaabbbabaaabaaabaaabbbababbbbabbaaaaaaaaababaabaaabbbababaaabbabaababbaabaabaabbbbbbabbbbaabbbabaaabbababbabbabaababbaababaaabbaabaaaaabaaabbabaabaababababbabbaabbaaabababaaaaabaabbbaaababaabbbababbabaababaaabbbbbbabbabbaabbabbaababaababaabbbbbaababbaabbbbbaabababbbaababbababababbababbbabbbaaaabbabbbbaaaabaabbaabaaaabbabbbaabaaaaababaabaaabbbbaabbbabbbbababaaaaabbabbbbbababbaaabbaaabbaaababaabbaabbabbabbbbbbabbbabbaaaabbbabbaabbbabaaaabbaaaaaabaabaabababaabaaaaabaabbaaabaaaabaababababbaabbabaaaaabaabaabaaaabbbabbbaabaabbaaabbaabbaaaabbbbbabbbaaabbbbbbaaababbbabbabababbbaaabaabababbabaaababbaabbabaabbbbbaabbababbabaaabbaabaaababababbbaaaabaaabbbbababbabbaabbaaaabaaaabababbbabbabbaabbbaabbbabaaabbbbaabbabaabaababbbabbababbbbbbabababababbbaabababaabbabababbababbaababaabaabbbababbbbababaababbbaaabbaaabbaabbbabaaaabbbbbabbbbbbbaabaaabbaaaaaababbaaababbaaaaabababaabaaaaaaaabababaabbbaababaaabaaabbbbbbbbbababbabbabbaaaaaabaabbaababbbaabbbbabaaaabaabaababbbbbbbbbabababbbbaaabaaabaabbbbaaabababbbabababaaabbbaaabaabbaabbbaaabbbaababbbababaabaaabbbaaaaaaaaabaabbbabbbabbbaaabaabbaaababbaabbbaaababaabbbabaabaaaaabaabbbbbabbbaaaaaabbbbbaaaaaabbababaabaaabbabbaaaababaaaaaababaabbaabaaaaaababbabbbbaababbbababbbabaaabaaababbaaabaabbaabaaabaabaaabaaabaabaaaabbabaaababaaababaaabbaaaaaaaabbaaabbbaaaabaaaabbabababbababbbabaabaabbababbabaaabaabbbaaaaababbbbaabaabaabaaababbbaaaaabaabbbabbaabbaabbabbbbbbbabbabaaaaaaaabbbbabbbabaaababababbbbaabaabbabababbaabbaabbabaabbaababaabbbbbbbbbabaabbbaaabaaaaaabbaaaabababaaabababbbababbbaabaaabaaaabbbbbbbabaabbbaaabaabbbabababbbaababaaaabaaabaabbaabbaaabaaabbbaababaaabbaabbbbabbbabaaabbaabbabaababaaabbaaaabaaabababbaaaaaabaaaaababbbabaabaaabbbbbababbabbababbabbaaabbabaababbbaaaaabababbababaaaabababaabaaabbabbbaaaabaaaaabbabbabaababaabbaaababbaabaaabbbabaaabababbbbbaaabababaabbbbaababababbabaabaabbabaaabaabbbbaabaababbabbbaaaaaabbbaabaaabaabbbbabbabbbababbababbaabaabbbabbabbaabbbabaaaaaabbaabbbabbbababbbbbbbaaabbabaaaaababbbabbaabbbababbaaaababbbbbaaaaabbaaabbabbabaababaabaaaaaabaaaababaaabaaabababababaaabaaababbbbabbaaaaaaabaababbaaababbbaabbbabbabbaabaabbbbabbaabaaaababbabaabbbaaabbbabaaaaaabbbabbabbaaaaabbaaabaabaaababbabbbaaaabaaabababababbbaabbbaabbbbaabbabbababababbaababbbbbaababbbabbaabbaababababababbaaaaababbaabbabaaaaaaaaabbbabaaaabaabbbbaabbabbaabbaabbbaabaaabaabbbaaabaaabbababbaabbababaaabababbbaabbbbbaabababbbbbaababaabaabbaabaabaabababbabbbbbabbbaaaaabbaababababaabbbbabbbaabaaabaabbbaabbababbabaababbabbbababbaaabaabbbaabbababaabbbaabbbbababbbaaabbaaabbbaabbbaaabaabbabaabbbabaabaaabbbaababbbaaabbaaaababaabbbbabbaaaabbaabaabbaabbabaaaaabbbbaaababaaaabbaaabaabbaaabbbbbbbbabababaabbbbaaabbabbbaabbabaabbbbabbbbbbbbaaabababbbaaabbbaaababbabaababababaabaaaaaabbbbbbaababbabbabbabbaabababaabaabaabaabbbaabbbaaaaaaaaaaaabbabbabbbabaaabbaaabbaabbbabaaaaaababbbbabaaabbabbaabbaaaabaaabaaaaabababaabbaaaaaabbbbabaabbaaabbbbbbbbaaababababbbaabababbbbbbbbaaaabbbaabbbabaaaaaabbabababbbaabbbaabaababbbbabbaabbaaaabbbbbbbabababbbaabbabbbaabbaabaaabbbbaaabbababbbababaaaabaaabaababbbbababaaabbaaabaaabbbabaabbbaaaaaaaaaaaabaabaabbaaaabbbabaaaaaabbbbaaaabaabbaaaaaabaababbabbabbbaaaabaaabbaaaaaabaaabaabbbaaaabaabababbbababaaaaaaabaaababbababaaabbbbaaaabbabaababaabababbabbbbaabbbaabaaabbbbaabbabaabaabbbbabbbbababaaababbaabbababaaabbaababaaabaabaabbabaaaabaaaaaababaaaaabbabbabaaaaaaabaaabbbaabbbbabbaabbbaabbabbbbbbbbbbbababbabbabaababbbbababbaaaaabaabbbabbabaabbaababababbaabaaabbabaababbaaaababbbbbbaaabbabababababaabababbbabbbbaabaaaabbbaaaabaabbbbaaabbaabaabaaabbbabaabaaabbbbaababaababaabaaabbaaaaaaabaabaabbbbbaaaaaaaaabbaaaabbabaabaabbbbabaaabbaaababbabbaaababbbaaabaabaabbbbababbaaabbaabaaababbaababaaaabbbababbbabaabbababbbbbbabaaabbbaaaaaaabababaababbaaabaaabaababbaabaaabbaaabbaabaabbaaababaaabaaabaaaabaababbabbabbaabaaabbbbababbbbbababbaaababbbaabaababbbaababbaababaabaabaaabaabbbbbbbabbabababbabbbaaabaabbaababaaabbaaaabaabbbbbabbabbbaabbbbbaabbaabbbaababaaabbabaaababbaabaababbbbbaaabbaaaaabbbabbbbababbbaabbbaaaaaabaaabaaaaabbabbbbbaaaabbabaabbbabaaaaaabababbabbabaabaabababbbaabaabbbbbaabbbaaaaaaababbbaaababaaaaabaaabaabababbaaaabbaaaaabaabaaababbaababbaabbabaabbabaababaabbbbbaabbaaaaabababbaaaaabbbaabbbbabbbbaabbbabaabaabbaaabbababbaababbbabbabbaabbbaabbbbaaabaaaaaabaabbabbaabbbabbabbbbabbababbbabababbaabbbbbbaababbaaaababaabababaaaabaababbbaabbbaabbaaabaabababbbabbaaaaaaabaaaaaaababaabbbabbaaabaababaaaabbbaabababaabbaabbbbbababbaabbababbbbaaaabbaabbbbbaaaaabbbbbbbbbbbaaabbabbbbababaabbababbabaababbabbbbabbbbbabbabaabbbbbbbbababbbaabbbbabbbabbbbbbaabaaaabbaabaabbbbabababbbaaabaabbabbabbabaabbaaabbabbbabaababbbaabaaabbbaabbaaabbabbbbbababaabbaabaaabbaabaabbabbbbaaabbbbaaabaaabbbabaaaaababbbaaabaabaaabbbbabbbbbaaababaaababbbbbbbbabbababaaabaabbbbaaaabbaaabbabbbabbbbbabaabbbabbabababaabbaabaaaabbbbbbababbbababbabababbbaabbbbabbaaabbaaaababaaaabbababbabaaababaaaabaaaabbaaaaaababbabaabbabaabaaaabbbbabaaaaababbbbababbabbaaababaabaabaabbbbbbbabaaabbaabaaabaabaabababbaabaabbaaaababababababaaabaaabaabbbabaaaaabbbabbbbbbbbabbaabbbabbbaabaaabaaabaaabbaabbbababaaaaabbbabaaabaaababbabaaabbbbaabbabbabaabaaaabbbaaaaabbaaabbaaabbabbbbababbaaaaabbaabaabaabbabbaabbabbaaababbabbabbbbaaababbabbbabbbabaaabaaaabbaabaaabbaaaaababaabbbabaaaabaababbaabbbbbbbaababababaababaabbbabaaaabbabbabaaabbabbaaabbbbbbaaaaaabababbbbbbaabbaabababbbbabaaababbaabaabaaabbbbbbbbaaaaabbbbbbbbabbbbababbbabaabbbbbabbbbabbbabbbabbbbbbaaaabbabbabbaaabbaabbbaabbabbbabbabbbbbaababbbaabaababaabaaaabaaaabbbbaaaabaaaaabbbbababbaaaaabbbbbbbabbaaabbabbbbabbbabaabbbbaabbbaabaaabababbabaaababbbbabaaabbaabbabbbababbbbabbabbabbaaabaaaabbbaaabbbbbabaababbaababaabbaababbabbaaaaabbbbbbaaaabbaabbabbaaabbababababaaabbabaaababbbbaaabbaababaabababaaabbbaaaaaababababbbbaabaabbabbabaabbbaababaaabaabbabbaaaabbabbabbaabbaabbabbabbaababbbaaaaaabbabaababaaababbabaabaabbabaaabbababababbbbbbbabbbbaaabbabbabaabbaaabaabbbaaabbbbababbbaaababbbbabbabbbbbabbabbaaabbbababbabaaaaabbbbabbbbaaabbabbaaaabaabbabababbabbabbbbaabbbbbbabaaaabbbbaaaabbabaaaabaabbbaabbbbbbabbabbbabbbbabaaabbabababbaaabbbbbbbaaababbabbbaaabaabbbbbbaaaabbbabaabbaaabbabaabaabbbbbaababbbaaabaaaabbbabaabbabbbbbaaaabaaabaabaabaaaaabbbbbababbaabbaabaaabbaaaaabbbbabbaaabbbabbabbbbbabbaabbbaabaaabbaaabbabbbbabaabaaaaabbaaaaabababaaabaaabbabaaaaabababbabbbbbaaaaaabaabababababababbaabbbbababaaaaaababaaabababaaabbaaababababbbbabbaabbaabbaaabaababbaababaabaabaabbabbabaaaababaababaababbaaaabbbbababbbbbaaabbbabbbabababaabababbbaabaaaaaababaaabaabbabbbaaabaaabaaaabbabbbabaabbbbabaaabaaaababbbbbaaaaabbbaaabbaabbbbaababbbabaaaababbaabaabbaaababbababaaabbaaaabbabaaabaabbbbbaabbbbbabbaaabbbbabbabaaababbaaaabbabbaababbaaaaabbabbaabbabbbbbbabbbbbbbaabbaaaabbaaabbaabaaaaabbbbaaabaaaababbaaabaabbbbbbbbbbaababbaabbaabaabbbbaaaabbbaabbabaaaaaaababababbbbaabababbbbbbbabbbbababbbbbbaaaaaaababaabbbbbabbaababbaabbbaabbabbaabababaaababaabbabbaabbbbabbaaaaaabbbababbbbabababbbbbabaabaabaaabababbaabaaaaababbabbaabbaabbaabbaabaabbbaabbbaaabaabaabbbbaabbbbbabbababaabaabaaababbbbbbbabbababbabaaaaaaababaabbabbbbbbaabababbababbbbbbabbabbbabbabbbabaaaaaabbbbbabbabaaaaaaababbabbbaaaabaabbbbaaabbaaabaaabbbbbbbaabaabaabbbbbbbbabababbabaabbbabbaaaaabbbababbaaaabababbabbbabbbabbaaabbaabaaababbaaababbbbbbaaaabbababaaaabbbabbbaabbabbaaabbabbbbbbabaabababababbaabaababbbabbabbaabaababbaabaaabbbaaababbbaaabaaaaabaabbabaabababaabaaaaababbbbabaaaabbbaabbbbbbbbbaaabababbbbababaaaabbaabbaaaaabbbabaaaabaaabbabaabaaaabbaaaababaaabaabbbaabbbbbbababbbbbababaaabaabbaaaaaaabbbabbbaaaabbbaaababbaaabaaabaaabbbabbbabbbbbbabaaaaabababbabaabbbabbbbbaaaabababababbbbaaababaaababaaaaabaaabbbbbbbaaaaaabaabbbaaababbbabaabbbbbbbabbbbaaaababaabaabaabbabbaaaabaaaabbbaabbabbabbaabaabaabaababaabbbabbbbbbbbbbaaaabababaabbaabbbababbbbbabaaabaababaaaaababaaaaabbaabaabaaababaababaaabbbbbabaaabaaabaabbbbaabbbbbbaabbbbbbaaaabbbabababbbbbabbbbbbbaabbbabbababbababaabbabbbbbbaaabbaabaaabbbbaaaaabbabaabbabbaababbaabbaababbaaaaabbababbabababbabbbaabaabababbbaabbaaabababbbabbbbaabbbbaabababbbbabbbabbbbaabbabababaaaaabbbaaaaababaabbabaaababbbababbbababbabaaabbbbbbaabbbbbbabbaaabaabbbbabaaaaabaababaabbbbabbbaaaabaabaabbabaababaaaaaaabbbbbbababbbabaaaaabaabbbaabbababbabababababbbabbababbbbbbabbabbbbbaaaabbbaaaaaababbaaaaaabbbaaabbbababbbaababaababbbbabaaabaaabbbaabbabbabbbaababaabbaaabababbbaabbbbbbbbabbbbbbabbbbbaaaabaaaabaabaabaababaababaababaabbaaabbbbaabaabbaababbaabaabbabbbbabaababbabbaabbbabbaaaabbabaaaaaabbbabbbbaaaaabaaabaabbbbbabababaaabaaabaababaabbbbabbaababaaababbbbababababababbabbbaabaaaaabaaabbbbbaaabbaaaabaabaababbbaaabaaaabbbabbbababbabbbaaabbbaabbbabababaaabbababbbaabbbabaabbbbbbbaaabbbbbababbbbabbbabbabbbbbabbbbabbaaaabbbbabbabaaaaaaababbababbabbbbabbaababaabaababaaabbabbbbbbbbabababababbbabaabbbbabbbbbbbaaababbaabbbbabbbababbbbbbbabaabaaabaaabbabaabbabaababbababbbaabbbbabbaabbbabbbabbaaabbbaaabbbbbbababbbbbbbabbabbbbbbaaaaaabbaabbbbbabbaaabaabaaababaaabbbbaaaaaaaabaabaabbababbbabbabbbbabaabbbaaababaabbaaaabbaaaababbabbbaaabbbbaabbbaababbbaababbbbaaaabbaabaaaaaabbabbbbbaababbababbababbbbabbabbbaababaabbbbabbbabbbaabbaaabbbbaaaaaabbabbbbabbaabbbbbbbaaabbabbbabbaabbabbaaaaaaabaaabbbbbabbbbbbbbaabaaabbabaabaabaabaaaaaaaabbaabbaabbbbbaaaabaaabababaaabaaaabbbabbabbbbaabaabbbababbbaabaabbbbaaabbaaaaaaaaaabaabababaaaabbbbabaabbaaaabaaaabbbaaaabababbaabbbbbaaaabbaaabbbbbbaaabaaaaabbabbbaaabbaabbbabbbbbabbbabbabbbabbabbbbabbabbbabaabaaaabaaabaabaabbbbbbbbaaaabbaabbbbbaabbbaabbaaabbabbabaabbbaabbbbbbbabbbabababbabbbbbbaaaaaaababbaaaabbabbabababbbabbbabbabbaabaaabbababbbaababbbbbaaabbabaaabbbbbaababbbbbbbbbaaaabbbbaabababaababbaaababaaaabaabaabaaabbaaaaabbbaababaaabbbabababaaababaaaababaaaaabbbaabbabaaababaabbabaaaababababbbbbbaababaabaabbbaaabaabaaaabbbbbbabaaabaaaabababaababbaabbabbbbbaaaaaaabbaabaaababbbbbaabbbbababbaaaababbbababbbbbaababbbbbbabaabaabbbbaababbbaabbabbbabaaaaababbbbbaaabaabbabaabbbaabaaaababaaaaababaaabaabbaaaaabaaabbbbbabaabbababbbbaaaaaaabaabbbabbbbabbabbaaaaabbabbbabaabbbabaabbabbbabaaaaabbabbbababbbbabaaabbaaaaaaaababbabbbbaababbabbbabbbbababaabaabbaaababbabaabbaaaabaabbbbbabbbbaaabaaaabaaaaabababbababbbaabababbabaaabaaabbabaabbbabbababbaaaaabbbbbbaaabaaabbbaababababbbaababaaaaaabaaabababaaabbabbabbbbbbbbaabbbaabbaaababaaaaabaabbaabbbabaaababababbaababbabbababbabbabbabbbaaababbbababbaabbabbbaaababababbbaabbaababaaabbaabbababbaabbbabaaaaababababababbbbabbbaabbaabbaabbbbaabbbbbaaabbaaaabababbbaabaabbaabbbbbabbbbbaaabbbbbbbbbaabaabaabbbaaabbaaaaaaaabbaaaabaaabaaaaabbaaabaabbbbbbabaabbbababbaabaabaabbbbbbbaaaabbabbabbbaaabaababbaaababbaabbbbaabbaabbbabbbbaaabbaaabaabbabbaababaaaaaaaaaabbbabaaaababbabbbaabbababbbabaaabbbbbbababbabbabbbbaaabbabaabaaaabbabbaaaaabbaaabbbbbaabbaaaaaabbaabaababbabbaaaabbabbbaabbbbbbbbbaabbaaababbabbbbbbaaababbbababaababaababbaabaaaabbbabbbbaababaaabaabaababababaabbbbaaaabbbbbabbaaaabaaaabbbabbbababbaabbbaababaabbbbbabbaaabaaaaaaaabbaababaabaaaababbabaaaabababaabaaabaaabbabaabbabbaabbbbbbaaabbbbbbaabbaabbaabaaaaababbbbbbaabaaabbbbbabbbbaaaaaababaaaaababaabbbbabaaaaabbbbbbabbabaabaaabbbbaaabbabbaabaabaaabaabaababbabbbbaaabbaaababaababaaaaabbbbabababaaabbaaabaababbabaaabbbabaabbabbaabaabbbabbaaaabbaaaaaaabbbabaaaaaaaaaabbaabaabbaababaabaabaababaaabbaaaababaabababbabbaaaaaabbbbabababaababbaaaaabbaaaaababbbbbabaabaabaaaaaaaaabaaaabbbaababbaaaabbbabaaaaabaabaaaaabaabbabaaaaabababbbbaaabaababbaabbabaaababbaaabbbbbababababbaaabaabaababaaabbabbbbbaaabbaabbbbbbbbabaabaabbbaaaaabaabbababbaaabbbbbbbaabbaabbabbbaaababbaaabaabbabaaaabaabbbbaaabababbaaabbbaabbbbabaabaaaaaabbbbbababbbbbaaabbbbbbaaaaaaaabbbababaaaaaaabbaaabaabbaabaaabbaaababbbbbaaaabbabaabaaabbaabbaabaabaabbbbbaabbbaaaabbaabababbaababbbaabbbaaabaaaababbbaabbabaabbbbaaabaaabbbaabbbaababbaaaabaabbbbbabababbbaabbabbababaaaaaabaaaabbaabbaabbbababbbabaaabbbaababbaabbababbabbbbabbbbaabababbbbaabaabaabbbbabbaaabbbaabbbbbbababababaaabababbaabbbababbaaabbbbbbaaababbbabaaaabbbabbbaaaaabaaababaabbbaabaaabbbbbaaabbbbabaabaaaabbaaaabaababbaabbaababbbbababbbbbbabaabababaabbaabbbabbbbbbbaabaabbbbabbaabbbbbabbbaaaaabaabababaabbaaabbaabbbbabbaaabbbaabaabbbbbbabaaaabbaaaabaabbbaabbaabaabbbbabababbaabababaaabbbbaaaabaaabbababaaabbababbbabbabaabbbabbbaabbaaabbaabbaababbbaaabbaaaabababaabbbbbabaaababaaababbababbaaabaababaaaaaabbabbbababbbbabbaaabababaabbbababbaabbbbabaabbabbbbbabbbbbaabbbabaababbaaaaaaaabaabbbbbaabbaababbaababbababaabbbaabbbaaabaabbaabbaaabbbababbababaababbabbbbbbaaaaabbababababababaabaababbbaaaabaabaaabbabbbbabababbabbaabbbbbbbbaababaaabaababbbabaaababaaabbbabaabaaabbbbababaaaababababababababbabaaaabbbbbbbbaaaababbaaaaaaabbaaabbaabbbbaaaababaaabbabbbbbbabbbbababababbaabbabbbbaaaabababbbbaaababaabbabbbbbbaaabbaaaaabaaabababbabbabbaaaaaabbabbbbbbaaabbbbbabbabbabbaaabaababaabaababbaabbbaabbbbbbbabbaabaaabbaabbbbbbbbbaaaabababbabaaaaaaaabaaaaabbbbaabbbbabbbbbaabababbaaabbaaabbbabbbabaaaabbbbbbaaaaabbababbbabbbbabbaaabababaaabbaabbbbabaaaabababbaabbbaabbbaabaaabababaabaabbbabbbbaabbabababbaaaabaaaaabababbbabaaabbaaabbabbababbababbbaaaabbbbaababbbaababbababbbababaabbbbbaaabababbbabaaabbabbbbaaabaaaababaabaaabbbbbbbbbaabaabbabbbbabaaabbbabbbbaabbbabbbaaabababbbbaaabbabbabaabaaabbbaaaababaababaaababaabbbbbaababbababaaababaaabbaaaabbaaababbabbaabbbbaaabbbabbbaababbaaaaaaabbaaaabbbbbababbaabaabbabbababbabbbabaababaababababaaaababaaaabbbabbbbabaaaabbbaabaabaaaabaaaaaababaababaaabababbabbbbabbabbabbaaabbbbbaaabbbbaaaabaabbaababbabbbaabaabaabaaababbbaababbbabaabbbaabbaabbaababaabbaaaaababbabbaaabbaaaaabaaaaaabaaaaabbaabababaababbbababbabbbbaaaaababbaabbabaabbbbbaaabbaabbaabaabbabababbbaabaaaabbbbbbbababbababbbaaaabbbabbbbbaaaaaaaababaaabbbaabbbbbababbabbabaaabababbaabaaabbababbbababbbaababbaaabbabbababbbbbaaababbaabbbabbbbbbbbbbbbaabbaaabaabaaaabbabbaabaaaabbaabbaaabbabbbabbaaaababbaaabbbbabbaabaaaaabbaaabaaabbbbbbaaaabaabaaaabbaaabbbaabbbbbaabaaabbaabbbaabbbababaaababbaabaaaabbababaabaaababaaaabaaabbbbbabbbbbbbbbbbbbbababbbaabbaaabbbbabbaaababbbbbabbbaaaabbaaaabaabbbaaabaaababababbbbaababbbaaababbaaabbabaabbabaabbabbaabaabaabababbbbaaabbabbbabababbbbabbbababbbbaabbbabbaababbbabbbaaabbbabbabbabbbaabbbababbbaabaaabbabbaaaabbbbaaabababbabbbbbbabbaaabbbabbaabbbbbbabbabbbababbabbbbbaaaaaabbbbbbbabababbbbaaabbabbabbbbaababbbbaababababbabbbaaabbbaaaabbbbabaaabbaaaaaabbabaaaaabaabababaaaabbbbbabbbaabababababaaababaaabaaabaaaabbbbaaaabaaabbbbabbbbabaaaaaabbabaabbbbbabbaabbaabbbbbbbabaabbbbbaaabaabbbbaaaaaaaabbbbabaababbbabbbabbabbbaaabaababbaaaaaaabbbaabbababaabbaabaaaaaaabaabbbbaaaabbaaabbbabbbbbaaabbbbbabaaaaabbababbbabbaabbbbabaababbbbbbbbbbbaabaaaaabaabbbbbabbaabbabbbbbabbaabbbbabbbbbabbababbaabbabbbaaabbaabbabaabbaabbabbaaaaabbaabbbabbaabbbaabbbbaaaaabbbbaaabbbbabababbbbaaaaabbaabaaabbbbabaababaaabbbbababaabaaaabaaabbabbbbbaabbaababaababaaaabbbbbbabbabaababbabbaabaaabbabaabaaaaabbabaaababbaabbaaabbbaababababaabaaaaabaaaaaaaababbaaaaabaabbababbbbbbabbbbbaabbaabbbbabaaabbbaabaababbbaababbbbbbbbbbabbabaaabaaaabbbabababaababaaabaabbbbbbbabaabbbbbbababbaaaaabbabbbaaaabbbbbabbaabaaaabbbbbabbaaabbbabaabbbaabbbaaabbbabbaabbbbaaabbaaabaaaaaaabbbbbbaaaaabbaabaaaabaaaabbaaaaaaaabababaaaaaaaabbbaabababaaaaabbababbaaabaaabbbbbbbbbbbabbbabbaaaaabbaababbbabbbbaaabbabbbbbabababaababaabaaaabbabbaabbbbabbbaabbabaaabaaaaaabbabbbbaaaabaabbbabbbbbbabbabbbabbbbbbbbbbaabbbabbabababbbbaaaabaabbbaabbaabaaaabbabaaaaaabaaabaababaabbbaaabaababaaaaaababababbbbbaabbaabbbabbbbbaabaababbbaaabbaaaaaaaaabbbaaabbabbbababababbbabaaaabbabbaabbbaaaabbbabaaababaaabaabaababbbbbaaaabbbababbaaaaaabbaababaabbbbaaaabbbbaaaaabbbbbabaabaabaabaaaabbbaababbabaaaabbabbababababbaaababbabbaaaaabaabbbbbbaabaaabaaaaabbabababbbaababaaabbbbabbaaaabbbbabababababaaaabaaabaabbbaaaababbabbbabaaaaabbbbbaaabaaaabaaaaabababbbaabbababbaaaabaabbaababababaabaabbbbbbbabbaaaabbabaaaaababbbbbbaababbbbbaababbbaababbaabbabaaaaababaabbbbbaabababbaabbabaaababaaabbbbaabbabbbaabbabababbbabbaaaaaababbbbababbbbababbbabaabbbbaaabbababaaaabaaaaaabaababbbabbbbbbbbabbbbabaabbbbbaabaaaabbabaabbabbbaaaaaababbbbbabbabbbbbbbbbaabbaaaabaababaaaabaabaaabbbaabbbabbbbbbabaabaabbbaabaaaabaabbabaaabbabaaaaabbaaaaabbaaaaabbababaabaababbaaabaaabababaaaababbabaababaabbabbaababaaabaaaaabbabbaaaaaaababababbbabbbabaabbabaabbabbaababaaabbbaabbaabaaabaaaaaabbbabbbbbbaabbbabbabbbaababbbaaababbbbaabbbbaaabbaaabbaabbabbabababbabababaabbaabbbabbbbbbbbbbabbabaababaaaaabababbbababababbaabbbbabaabbaabbaaabbbbaababbaaabababbaababbaaaaaabbabbbaabbaabbaabbababaabbbbbbababbaabbbababbababbabaaaaabbaaaabaaaaaabaaaaaaaaaabaaabbbbaaabbbaababaabaababbbbaaabbabaaababaaaabbabbababbabbbaaaaaababbaaababaaaabbaabababbbabbaababbabbbaaaabbbaabbabababaaaabbbbaabbbbabbabaababbabaabaaaabbbaabababbbabababababbabbbbbbabbaaabbbbababbaaaabaaaaaabbbabbbabaaabaabaaaaaaaaaabbaaabbabbbbaaababbabbabaabaabbbababbbaabbabbabaaaaaabbbaabababababaabaabbbababaababaaababbbbbbbbbbabbabbbbabbbbbaabaaababbaaaaaabaabbaababbbabbaabbbbaabbbaaabbaabbabbbbabbaaabbaaaabbaaabbaabbabbbbbbbabbbbbabbaabbbbaaabbbbaabbaabbabbbabbabaabaabbbbbbaabbaaabbbbaaaababaaabbbaaaabbbabaabbaaaaabbaaababbbabbababaaaaaababaaaabaabaababababbaaabaaaabbbaaabbaabbababaabaaabaaabbbbaaaabbaabbbbaabbaaabaaabababaaaaaababababbabaaabaaabbbaaaabbbabbbbabaabbbbbbbababaabbaaaaabbbbbbbbbbaababaababaaabbbaababaabaabbaabbabbaabbabbaabaabaaabbbbababbbbaababaaaaabbbbbabbbbbbababbbbbbbbbabaabbbbbbbbbbbbbabbbbabbaaaabbaaabbababbaaababbababbaaabbabbabbaaabbbaabbbbbbbaaabababaaaabbbaabbaabaaabbbaaabbabbaababababaabaababbbbbbabbbaabababbabbbabaaaabbaabbabbaabaaaaaaababbbbbbabbbbbaabbbbaabbababbbabbaababbbbaabbbaabbaababbbbbaabbabbabbabaaaabaaabbbbbaaabaabababbbaabababbabbbbbbbbbbbabbababbaaabababaaaabaababbbbaabbbbabbaababbaababaabbbbaababaaaaaaaabaaabbabaaaaaaabbbbababbbabbbaabababbbaabbbbbbbbbbaaaabbbaabbbaaabbbbbaaaabaababbbbababaaaaaabbbaaababaabaabaabaabbaabababbbabaabbabbabbbbbbbabbabbbaaaabbabaabbaaabaabaaabaaaabbaaaaaaaaabbaaabaabaaaaaaaaabaabaababbbbbaababbabbbaabbbbabbbbbaaabbbbabababbbbabbbbbbbababaaaabaaabbbbabaabaaaaabbaabbbbaabbabbabbbabaaabaabbbbbabbbbabbaabaaaaaaabbabbabbabbbaaabaaaaabaaaabaaabbaabbbabbbaaabbbabbbabbaabaaaaabaaaababbbaabbaaabaabbbabbaaaaababbbabaaaabbabaabbaabbaaaabababaaabaabbaabaabbbbbaabbbabbabbababaababaabaaaabbabbbabbbaaaaabbaaaabbbbbbaabaaabaaabbaababbababbabbaabbaabbaaababbbabaababbaaabbbaaaababbaabaaabaaababaaaabbabbbaabaaaaaababaabbbabaaaaaabbaabaababbabaabbabbbabababbbaaaaabaaabbbbbbabbaaababbbbaabbbabbbbaabaabaabbaababaabbbabbbabbabaaaababbbbabbbabbabbbbabaaaababbbaabbaaaaaaabbbabaaabaaabbabbaabbabbababbbbaabababbabbaaababbbabbaaabbabababbaaabababbbbbaabbbabbbbabbaabbbaaaabbaaaaaaabbbbbaaaaaaabbabbbaabbaababaabbaabbbabbaaaaaaaaaabbbabbbabbaabbaaaaabbabbbaabbababbaaabbbababbababaabbababbabbababaaaabbbbabaaabbaabbbabbbbbbbaaaabbabbbbaaabbaaaaaaabbaabbbaabbbbaaabaabababbbaabbaaaabbaaabbabaaabaaaaaaabbabbbaabbaabbaaaabaaaaaabbaaabaaabaaabaaabbabbbaabbabbbbbabaabaabaaabbabbaabbaabaaababaaababbababbabbbbaaaaaabababaabbbabbaaaabaabbababbbbbbaaabaaaaababaabaabaabbaaabbbbaabbabaabaaaababbabaabbaaaaaabaaaababbbababbabbababaababaaaaaaaaabbabbbabaabbbbbabbaabababaabbbbbababaabbbbabbabbbaababbbbbbaabababaaaaaabababbbaababbabbaaababbbbbababaaabaabaabababababbaababbbabbbaabbababbaabbabbaabbbaabbbbabaaabbabaaabbbbaabbbaaabaaaaaabbbbbbababbbbbbaabbbabaaabbbbaabbaabbbaabbabbabbbbbaabbbbbbbbabbaaabbaaabbabbbbaabbaaaaabaababbabaababaabaaaabbaabaabaaabbabbbbbaaaabbaabbbbbabaababaaaaababbbabbaabbbbbbbabaabaabbbbabbbabaabbaabaabaabaaaabaabbbaababbbaabbabbabbbbbabbbaabbbababbbbbbabaaaaaaaabbbbabaaabbbbbbabbbaaabaaabaababaabbaaabbbaaababbaaaaaaabbabaaaaababbaaabaaabbabbaaababbabaabbabaaabaabbbaababbaaabbbbabbaaabbbaaabbbabaaaabbbaababbbbbabbbbabbabbbbaaaaababbbaaaaabbbabaabbbabbbbaaaabaabaabaabaaaabbaabbabbaaabbaabbbbaabbbababaaabbbabaaaaabbaaabbabbbaabaaababaaababababbabbaabbabbaaaaaabbbbababaabbbaaaaaaababbaaaaaabaabbbbbaaaabbbbbbaabaaaaabbabaababbabbabbaabaaaabbaabbaabbababaaaabbabbababbabbaabbababbabaaabaabbbaabbbbbaabbbbbbabbaababbabbababbaabaaababbbababbaabbbaaabbbabbbabbbaaabbabaaaaaabaabababaaabaaabbabbaabbbaabbaabbaaabbbabaabbbbbbaaaaaaababbaaabbaababbbbaaaabbaabaababaabbbbbbbbbabbabaaababaabbabbabaaabbabbabababbbbbbbaabaaabaababaaaabbbabaaababbaabbbbbabbbbbbaabababbabaaabbabbaaababbaaaaaaaaaaabbbabbaabaaabaabbbaababaaaaaaabaaabbaaaaaabbaaaaabbaaaabbbaaaaaabbbbabbbbaaaabaabbbababbbbbabbabbabbaaaababbaababbbaabbaabbbbaabbbbabbbbbabbaabaaaabbbbbbaaaaaaaaababaabbabaaaabbbbaababbaababbababbbaabbbbabbaaababbabbababababababaaaabababaaabbabaabbbaaabbaabbabaaabbbabbbaabababaaaabbaaabbbbabaabaaabaaababbbabaaaaabbbbbaabbbbbbbaaabbabbbababababaaabbbaaabaabbaabbbabaabbaaabaaaaabbbbbbbaaaababababbbabbabaaaabababbbbabaababbbbbabbbaababbbbaabbbaabababaabbbbaabbbababbbbabaaaaaabbaaaaabbbbaabbabbbbababbaabbababbaaaabaabbaaaabaaaaababbaabbaaabbabbbbbaabbaaaaabbbbaabbabaaababaabbbbaaabaaabaaabaabaabbabbabbbbaabaaaababababbbbabaaaababbbaaaabaabbaabbaaaaaaababbbababbbabbababbaaabaaaababbabbabaabaabbbbbaaaaabbbbaaaabbabaabbaaaaabbaabbaaaabbbbabaaababbaababbaabaaaaabbabbbbabaaabbaaaaabbaababaabbbbaaaabaaabaabbbaaabababbaaabbaababbbbaabbabbabbbbabababababbbbababbbabaaabaabbbaababaabaabbbaaaaabaababbaabaaaaabbbbbaabbbbaabaaabbbbbaaaaaabbbbababaaaaaaabbbaaabaaaabaabbbbbbbbbbaabbaaaaabbbaabaaabbbabbbbbbbaaaababaabaababbbaaaabbbbabbabbbbbbbbbbaabaabbabbbbaaabaabaabbbabbbbabaabaabbabababbabaababaaaaababaababaabaabbbbabbbaaaaaaabbbaabbabbabbbabaaaaabbabbbbaaabbbbbaabaababaaabbbbabbabaababbbbbaaabbabbabaabbaababbbbababaaaabbbabbbbbbaaababababbbbaaaabbabbbabaaaabababbaaabaaaabaaabbbbabbbaabaaabbbabaababaaabaaaaaababbbbabbaabbbbbaabaaabbbbbaaabbaababbbbaaaababaaaaaabaabaaabbabababaaaaaabbbaabaabbaababbbbbbaabbbbaabbaabbbbbbabaabbbbababbabababbbbaaabbababababaababaabbaabaaabaabaaaababababbbbbababaaabbbbbabbbababbbaabbaabbabbbbaaabaaabbabbaaaabbbabaaaabbbbbbabbbbbbbbabbbbaaababbbaaaaaaaabaabaaabbbbbabbababbbaabaabbbabaaaaabbabaaaabbabbaaabbabbbabbbabbbabbaaababbaaabababaabbbbaabaaabbabbbababbbbbbaababaabbbbbaaabaaaabaaaabaaaababbaaababbbbabbbbbbbabaaabbbababbbabaabbabbbbaabaaabbaababbabbabbababbbbbaabaaabaababbbaaabbababaaababaaaaabbbaaaabaaabaaabbabbbaaabaabbaaaabbaaaaabababbabbaaabbaaaabbbaabababbababbaaabaabbabbbbabbaaaabababbbbbabbabbabaaaaaaababbbbabbbababbbababbabbbaabbaababaaabbaaaaaaaaaabaabbabbbbaabaabaabaaababababbababbbabaabbbbbabbaabbbababbbbbababaaababaabbbbabababbabbabbbaababbabbbaababbbbabaaabaaabababaaabaaaaabbbaaaabaaaabbabbababbbaabaabbaabaaaabaaabaaaaababaabbbabaabaabbaababababbbabaabaabbababaabaaababbabbabaaababbaabbabaabbaabaaaababbaaaababbabaaaabbbaaababbbaababbbbbababbaaaabbbbbbaaaabbbbbbabaaaababbbabbaabbbababbbaababaababbaaabbbaaababaabbabbbbaaababbbbbbaaababaaabbabbbbaababaaaabbbbaabbbabaaaaabababbaababbabbaaabbabbaaaabbbabbababaaababbbbaaabbaababbaabaabbbaabbabbaaababbbbbaaaabbbaaabaabaaaaabbababababbabababaabaaaababaaabaaaabaabbaaabaabbbabbbbaaababaaaaaabbbbbbbbbbbaaaabbbbaabbaababbababaabbbabbabaaaabaaababbabaaabbbbaabbabbabaabaabbabbbaabaaaababbbbbaabaaabbaaaaababbbaaaaaababbbbabaaaabbbbbaaaaaabaabbabbabaaaaababbbabbbaaabaabbbbbbbbabbbbbbbbbabaaaaababaaaabaaaaabbaabaababababaabbaabababbaaaabbbbaabbbabbbbababbbbbababbabbbbbbaabbbabbabbaabaabbbaabbabababbbaaaaabaaabababbabbbbaaaabbbabbaabaabaabbaabaaabababaabababbabbabaaabaaaabaaababbbabbaabbabbbbbbbaababbababaaabbbbaaaabbaabbabbababbabbbaaabbbbabaababbbabbabaabbbaaaaaabababbababababbababbababbbbbabbbbbbbaabbabbaabbbabababbabababbbbbabbabbbabbaabaaababaaaabbbabaababbaababbbbbaabbbaabaaaababbbbaaaababaaabaabaabbbabbaabaababaaaaaaabbaaaabbaaababaabbabbaabbbabababbabbabbbabbbbbbbbbbaababbbbabaabbabbbbaabbbaaabaaaaaaabbbbbaaabbbbbbabababaabaabbbaabbbaabbaabaabbbaabbaabbaaaaaaababbbbaaabbbaaabbaabbabbabbbabbababbaaabbbaaaabbbbbabababbabbaabbabbababababbabababbbaaaabaaaabbbbaaaabaaababbbababaabbbbbbbbaabbbbbbabbbbaabbbbaabbbaaaabbaaabaabaabaaaabaabbbbbbaaabbbbbbababaabaabbaaaababbaabbabaabaaabbabbbbaababaabaaaaabbbbbbbbbaabbaaaabaaabbbbbbaababaabbaabaabbbaaababaabbbbbabaababbabaabaaabbbabbbbbbbbbabaabbbaaaabbbbbbbabaabbaaabaabbabababbabbbbbbababbabbaaabaabaabbbbabbababaabbbbbbabbbbbbaabbbaabaabaabababaaabaaaabbaaaaaabaaabaaabababbabbaabaabaaabbbbaaabbbbabbabaaabbaaabbbabbaaabbabaabbabaabbbaabbabbabaaabababbbbbaabaaaaabbbbaabbbbaabbaaaabbabbaaaabaaababaaaabaaabbbbbbababbaaabbbbabbbbbbaabbbbabbaaaaaabbabaabbbaaaabaabbaaaaaaabaaabababbbbaaabbaabaaaabaaaababbbabbbabbbaabaabbbabbabbbabbabbaabbbabbaabbbaabbabaaaaaaaaaaababbabababbabbababaabbabbbababaabaabbabaaabbaaaabbaababbabbbabbaaaabaaaaaabaaaaabbbaababbbaababbabaabaabbabbabaaababbabaabbaabaababbaaabbaabbbabbbabaaaabbaababbbaaaabababbaaaabaababbbabbbbbbaaaaaabbabbabbbaababaaabaaabaababaaaababbbbbbbababbbbaabaababaaaaabbabbaaabbaabaabbbbaabbaabababaababababbaabaabbabbbbababbbaabbaaabaaaababbaabbaaabaabbbabbbaaaabbbbaabaabbababbaabbaaabaaababbbaaaaabbababbbabbaaabaabbabbbababbaabaabaaaaabbbabbbabaababbababbaaababaababbababbaaabababaaabbaababaabaabbabaabaaabaabababaabaabaabaaabbabaaaabababaabbbbabbbaaaabaaababbbbaabbaabbabbbbbbbbabbabbbbabbaaabbbbaaababaaaaaabbbaaabbbbaabbaabbbbbaabbbbbabbababababbbbbabbaaabababababbbabbbababaabbaababababbabbaaaaabaabbaaabaaaaaaababaabbbabbbabbababbbaaabbaabababaababbaaaaabbabbaaaababbaabbbaabbaabaaaaaabbbbbbaaabbabbabaaabbbbbaaaaabaaaaabbbaabaaabbababaabaaaabbbbbbbabaaaaabbbaabaabbaaaaabbbbbabbbbbaaaabaababababaabbbabbbaabaaaababbabbbbbababbabbaabbbbbabaaabaaabababbaaabbbaaaabbbbaaabaabaaaaaaaabaaabaabaaaaababbbbababbabbabbbaaaabbbababaabbbaabaabbaababaaaabbaaabbbaababbababbbbbbaabbaabababbbbaaabaaabbababbabababbbababbabababababaabbabbaabbbaaabbbabaaaaaaaaabababaaaabaaaabababbaaabaaabababbababaabaabababbabaaaabababababbaabbabaaababbbbbaabbbbabbbbabbabbababbbbbbaabbabbbababaaababaaaabababbbaaaaabaaabbaaaaababbabababbbaabaabaaababbbaabaaabbbbababababbbabbaaabbabbbbaabbbbabaabbababbaaaabbaabbaaaaabaaaabbabbabbababaabbbbbabbabbaabaaabbaabbaabbbbbbbbbaabbbbabbabaababbbabaababbaababbababbaaabbbbbbbbbbbbbbbabaaabbbaaabaaabaaababbabbbaabaabbabbabbaaaabbaaabbbbbbababbaabaababbbbbbaabbabbbaabababbbbaabbabbaabaababbbbabababbbbbabaaaaabbbabaaaabbbbbbbabbabaabaabbbbbbbabababbbaaaaabbaaabbabbbaababbaaaabaabababaabbabaababbabaababbaabbaababaababbabbabbbbabaaababbaaabbbbbaabbbabaabbbabbbbabbaabbaaaaababbabababaaaaabaaaabaabbaaabbbaabbabbbaababbbbabaababababbaaabbabbbbbaabbbaababbabbaaaaabaabbbabaaaabbbaaabaaaabbabababbabaaabbaaaabbbbabbbabaaabaabaabaaabbaaabaaaabaabbbbaabaabbbabbabbabababbbbbbabbbaaaaabaaabbabbaabbbbabbbbbbbaaabbaababaabbaabbaaabaaaaaaabbbbbbabaaabbaaaabaaaabbabababbabbbaabaaababbbabaaaabbbabbbaaabaaaabaaabaabaababaaabbaaaaabbbbbbbbabbbbabbabaabababbbaaabababaabbbaaabbabbaaaababbbaabbaaaaaabbbababbaaababbaabbaaaabaabbabbaabbbbabababbbaabaaabbaaaabbabaaaaabaabababababbaaabbbabaabbbabbaaabaaabaabbaaabbbbaaaabababbbbabbabbababbaaaabaabbabababaabaabbabbbabbabbabaabbabaaabaaabbaaaaababbaabaaabbbbbbabbababbbbbababbababaaaaabbbbaabbaabbbaaabbaaabbbbbaaabaabbbabbaaabaababaabaabbaabaabbbbabbaaaabbbbbaaaababaaaabbaaabaababbbbbbaabaaabbababbbbabaaabaaabbbbabbabbbaaababaaababbbbababbaaababbaabbbbbbabbaabaababbaaabaabbbbababaababbabaababbbababbbaabaaaabbbbabbbaabbaaaabbbbaabbbbaaaaaaaaabbabaabbbabbbabbbbbbaaaabbabbbaaabababbabbbaaaaaabababbabbababbabbbbbabbabbbbbabbbabaaabbbbbaababbababbbbbaababbabbababbaaabbaaabaaaaaabababbabbbbabbaaababbaabbaababbbbabbaaaaabbbbbbabbababbbbababaabaaabbaababbaaabbbbbaabaaaabbaaaababababbbababaabbabaabaaabbbbaaaabababbbaabbbbabaabbabaabaaabbaabaaaaabbbababaaabbaabbabababaaabaaaaaabbababbabbbabaabbaabaaabbaabbababbaabaabaaabbababaabbbbbaaaaabababbaaabbaaababbbaabbababaabaaababbbaaabbabbbbbaaababbbaabaabaababababbababbaababbbabbbbaaabbabbabbaaabaababbaababbaaaababababbababbabbaabbbabaaaababababababaaabbbaabbabaabaaaaabaaaaaaababaabaaaaabbbabbbbbabababbaabbbaaabababbabbabaaabbbbbbaaabbbbbbbaaaaabbaaaaaaababbbaaaabaaababbbabaabbaabbbbaabbbbbbababaaaabbbabbbbbbaabbbbbabbaabbbbababbbabbabaabaaaabbabbbbbaaabbbbabbaaababbabbbabbababababbbbaaaaabbbbbbabaabbbaabaabbbbbabbbaabaaaaabaabbbbbbbabaaababbbbaaaabbbaabaabaaaabaabbbbbbbabbbabbbaaabaabbbabaaaababbabbbbbaaaabaaaabbaabababbbbabbaaaabbbaabbbbaaabbbabbbaaabbbbbaabbbabaabaabababbbabbaabbbbaaababbbabaababaabbabbbbaaaabbbbaaabbbaaababbaaabbabababbbabaabaaaaabbabbbaaabbababaaabbbabbaaaaabaabababbbbabbbbbbaaababaabbbbaaaaabbabababbabbaabbbbbababbbababaabbbaaaaabbaaaaabaabbababaaaabbbbaabaaaabaaaababbaabaabbbabababbbaabaaaababaaaabbbaabbaaababaababababbbaabbaabaaabaaabbababbababbaaaabbbaaaabbbaabbbbbaabbbaabbbbabaabbaabbabababbbbabbabaaaabaaaaabbabbabaaaabbabbbaababaaabbaabbaabaaabaaabbaabbabaabbaaabbbaaaaaabaaabbaaaaababababaabbbbbabbbbabbaabbbabbbaabbaababaabababaaabbbaaaabbbbaaaabbaaabaabaababbbabbabababbbaababbaaaaabaaaaaabbabaaabaababababbbabababbbbaaaabaaaaaaaaaaaababbaaaaaabaaabbbabbbaababaaabaababaaabbbbabababaaababaababaabbaaababbbaabbbaabaaabababbbababbbbbaabbbbababaabaabbaababbababaabbbbabbbaaabababbababbbabbabbbbaaababaaabaababaaabbbbbbaabbabbabbbbabaababbbabbababaabbbabaababaaabaaaababaabbaaaaaaabbabbabbaaaaaabbbabbbaabaabbbababbabbaababbbbbaaabbbbababbabbaaaaaabbbbababbbababbabbbaabbbbbaabaaabbababbbbbababaaabbbaabbbabaababaaabbbaababaaabababaabbabaaabbbababbabbbbabaabababbbabbabaababaaaabaaaaaaabaabaabbababbabbbaaabaababbabaababbbaaabbbbabbbbbabbbbababaaaaaabbbbbaaababbabbabbbbbabbbabbbabbbbbababaababbaabbbbababbaaabbaabbabaaaabaaabbbbbbaabbabababaabaabbabaababbaaabaaaabbbaaaaaaaabbabababaaabaabbabbaabaaabbaabbbaaabbbabaabbbababaabbabaaaababababbbaaabbbbbabbaaaaabbbabaaababaabbbbababaaaaaabbbbaaaaaabbbaabbabbbbaababbbabbaabbbbaabbaaaabababaaaaaaabbbbbaaaababbbbbbaabababbaaaabbaabbaabbabbbabbabbaabbbaabaabababaabbbbaaabbbbbbaabbbbabbababbabbbabaaaabaabababaababbbbabbababbabbbaabababbbabbbbbbbabaabaabbbaaaabaabbaabbaabbbaaaaababaaaabaabbbabbaababbaaaaaaabbbbabbbaaaaaabaaaabbbbaabbbaabaabbabbaaaabbbbaaabaabaabbaaaabbbabaaaaaabaabaaabababababbaabbaaaabbabaaabbbabbbbaaabbbabbaaabbbababbbabaaabbbabbaabaabbbaaaaababbaaaabaabbbababbabaaaabaaabbabaaaaababbbaaabbbbbaaaababaabbbbabbbabbabababbbaaaabbaaabaaabababbaababababbbbabaaaaabbbbababaabbbbbabbabaaaaaaaabbbbbbbbabbaabaabaaaabaaabbaababaabaaaababbbbbabbabbbbbbbaabbbbaaaababbaaaaabbabbbbaababaabbaaababaabaaabaaaababbaaaabbbbaaaaaaabbbbabaabaabababbbbabbbaababababbbbaabaaabaabaaaaabbbaaabaaababababababaaabbabbaabaaabbabaaababaaaaabbbbbaabbabbbaabbaaaabaaaabbabababaabaabbbbabaaabbbabbabbbbababbbaaabbaaaabbaaaababbbbababaabababbbaaabbabbbaaabaaaaabababbbbbaabaabaababbbabbbbabaaabbababaaabaaaaabbbabaabaaababaabbbbbaabbbbabbabaaabaaaaabaabaabbabbbbabbbbbaabbbbabbaabbbaabbbabaababbbbaabaaaaaabbaaababbbaabbabbaaabbaababaababbbbbbaaaababbabbababaaaaabbaaaabbbaabbaabbbabbaaaababaaaaabbababbbbabbbbaaaaaabaaaaababbabbbaaababbaaabaabaabbabbbbbbbbbaaaaabbabaaaaabbaaabaabababaabaabbaabaaabbbaaabbbbaabaaaabbbbabbaaaabbbbaabbabaabababbabbaabbaaaababaaabbbbabbbabaaaabaaaaaabbaaaaabaabbbbababaaaabababaabbaaabaabbaaabbbaabbbbbaabaabbabbbaaaabbababbbbaabbbabbbbaabaaabbbaababbababbbaababbbaabbbbabbbaabbbaababbbbaaababaaabaaaabbabbabbaabbbabbabbaabbabbabaabbbaaababaabaabbbbbaabbbbbbbbaabaabababbbabaababbabbaaabbbaabbababbabbaababbaaababbbaaaaabbbbaabaababbabaaabaaaabaaaaaabbaaaaabbaababababbbabbbbaaaabaaaabbabaabaaaabbabaaaabbbbababbbabaaaaaabbbbaabbababaabbbaababbabbbaaaabaababaaabaaabaabbbbaaabaaaaaabababbbbabbabbbbaabaabaabbabaaaaaaabaabbaabbaaaabbbaabbabbaaaaabbaabbababaaaaaabbaaaaabaabaaaabbabbbababbabaaaababbabbbabbbabbaaaaababaaaababaaaaabaaababbabaaaaaaabaaaaabbbbaabaaabbabbbbbaaabbabaaaabbabbaabaabbbaaaaabbaaaaabaaaaaaabbaaaaaaababaabbbababbaaabbbbabababaabbbabaaaabaaabbaabaaaabaababaaabbbabaaabbaaaaabbbababbbbbbabbbbbbaababaaabbababbaaabaabbabaabbababbabbabbaabaabbaaababbbbaaababaaabbaaababbbababbbaabbababbaababbbbbbbabbbaabaabbbbaababaaaaabbaabaaaaaaabbbbaabaabbaababaaaaabaaaababbbbababbababaaaabbbbabbaaaabababaaabbbbaaababaaabbaaabaaabbbabbabbbbbaaaaaabababbabaabbbbbbaaaabaababbbbabaaababbbabbaaabbbbbaaabbbabaabbbbaaabaabbbaaabbbaababbbaabbabaababbbbaaaaabaaabbbabaaaabaaaabbbbbbaabaaabbbbbbabaabaaaaabbbbbaaaabaaabbbabbbaabaaaabaabababaaaaaababaaabbabbbbababbabbbbbabbabaaaaabbbaabaabbabbaababaaaaabbabbaabaababbaaaaaababbabaaabbabbabbbabbababbbabbaaabbaabbbbbbbbbbbabbbababbabaaaabbaabaaaabababaaaabbaabaabaaaabbbbabbbaaabbaabbbbabbbabbbbbbabbabbbbbbbbbbbaaabaaabaabaabbbbabbaaaaabaaabbbaaaababaabbaabaaabbbbbbaaabbaabbabbabbbbabababbababaabbaaaaabbbaabaabbaaabaababaabbaabaabbaabaabaaaaabbababaabaabbbbabbbbaaaaabababaaaaaabababbbbabbabaababaabaaabaaaabbbbbaabaababbaaaaabaaabaabbabaabbbbababbabbaaababbabaaaaabaaaaabbabbabbaaaabbabbaaabaabbabbbbbabbbabababaababbbbaaabbabaabaabaaababbbbbabaaaabaaaabbbabaaabbaababbbabbabbabaaaaabaababbbababababbbbabaabbabaaaaaaaabbbbabbabbbabababbaabababbbaabaabbaaabbababbbbbabbbaababababaababbbbbbabaabababbaabbbbabaabbabaaabaabbaabbbbbaaabbabbaababbaaaaabaababbbbbbbbbbaaabbaaabaaaababaabbbbaabbabaababaaabaaabbaabaababaabbabababaaababbabaaabaabbbbbaabbbabaababbbabbbbaaabbbbbaaabbbabaabbbabbbbbbbaaaabaabbaaabbbbbababbbbababbbbbbabbbbababababbbbaaaabaabbbaaabbabaaaabaaabbaabbaabbbaaababaabaabbaababbbbbbabbbbbbababbababaabbbababbbaabbbaababbaababaabaabaababbbaaabaaababaabbabbababaabbaabbbababbababbbbbabbbabbbabbbaabbbaaabbaaabbbabaaaabababaabaaababbbabababbbbaaabbabbabbaaabaabaaabaabaaaabaabbaabbbabababbaabbbbaabaabbaaabbbabbababbaababaabaabbbabbaababbbbabbaabaababaabbbaaaabbbabababbaabaabbaababbbaaaababbabbbabbabaabbabbaaabaaaabbbbbbaabbbbaabbbbbbaaaaaaaaabbaaabaaabbbbabbaaaabaaabbbbabababbaabaaabaaaaaaabbbbaaaabbabbbaabbababaabbaaabbabbaabaabababababbababbbaababaabbbbaaaaaaaabbbaabaabaaababaabbbaaaababbabbaabaaabaaabaabbaaabaabbbaababbbbaabbaaababaaabbabbabbaaaaaaabaaaaabbaababaaaabbbabaababbaabbaabbbaabbbbbbbbbbaabababbbaababbaabbaaabbbabbababbbaabbabaabbbbaaabbababbabbbabbbaababbbbaaababbaaabbbaababbabababaaaabababbbbaaaaaaabbaabaaabaaaababaabbabaabbbbabaabaabbababbaaabaabaababaabaaaaaabaabbbbbbbbabaababbbbbbbbbbbbbaaaabbbabbaaaabaaabbbababbbbbabbbababaabaabbaaabbabbbaaaaaabaaaabbbabbabbbbabbbaabbaabaabababbbbbbbbbabaaabbaaaabbabbbbaaabbabbabababbbabbaaabbaaabaabaabbabbbbbbbaabbbababbbababababbaababaaaabbaaaababbbaababbabbaabbbabaaabbabababababbaaaaabaaaaaaaabbabbbababaaaabbbbbaababbabbbaaabbababaaaabbbabbababbbbbbaaabaabbbabbbabaaaaababbabaabbabbaaabaaababaabbbbbbababababbbbbababbbbababbabaaabbaaaabababbaaabbbaaaaaabbbbbababaaaaabbbbbababbbaabbaaabababbabaabbbbbaababbbabaaababbabbbbabaaabaabbbbabaabbbabbbabbabbabbabababaaabbabbbaaabbababbaaabbbaababababbbbbaabaaaaabbbbbbbabaabaaabaabababaaabaaaabaaaabaaababaabbbbaaaaabaaabbabbbbabaabbbbaabbbabaaabbaababbbabbaaaaabbababababababaabaaaabaaaaabbbbbbaabaaababbbbbabbbabbabbabbaabbbbaabbbaabbbabbaaabaabaaababaabaaababababaabbbbbabbaababbbaaabaaabbaabbbbbaaaaaabaabbaaababaaababbbaaaaaabbaaaabaabbabbbbbabbbbbababbaabbbabbabbabbbababbbabbabaabaaaabbabbbaaabaaaabaabaabbbbbabbbabbaababaabaaabaaaabaaaaabaaaaabbaaaaabaaaaabababbbbaaabbbbaaaabaabaabbabbbbabaaabbaababaaaabbabbbbabbbbbbbaaabbabbaaaaabbbababbabaaabbaababbbaabbbaabbbbbaababaabababaabababababbbbababbababbaabbbbaaabaabababbbaaabbabbbaaaabaabaabaaabbbababbbbbbabaaabaaabaabaabbababbabaabbaababbbabababbbbabbaaabbbbbabababaaabbaaabbbbabbbbaaababbaabbbbaaabbababaabbaaaaaabababbbbaaaabbbaaababbaabbbbaaabbabbabbabbaaababbaaaabbabbbabbbbabbbabaaababbbbbaabaabbbbbabbbbbabbbbbabbbbbbabbbabababbabbbbbbbabaabaabbabaaaababaabbaaabababbaabbbbbabbbbbbbbbaababbabbbaaabbabbabbaaaaaaaabbabaaababbbbababbbaabaabababaabbbbabaaaaabbbabaababbabbaababaababbabaabbbbabbabaabaaaaabbaaabbbbaaababbaaaaaababbaaabaaaaabababaaaababababbaabbaabbbabbbabbaababbbababbbbbbbbaabbbaaaaaabababaabaaabababaaabbbbaabaabaabbbabaabababaabbbbbbbbaaaaabbbabaabaaaaaabbababababbaabababbabaababababaabaabbbababaaaabbabbabbbaaaabbaabbbaaabbabababbbaaababaaabbbbaabaaabbaaaaaababaabbaaaabaaaaaaabbbaaaaabbaabbbaabbaabbabbbaabbbaababbbbabaaabaabaabaabbbbbabbbbbbbaaabaabbaaabababbabaabaabababababbbaabaaaaabbaabaabaaababbbaabbaabaaabaababbaaaaaaabaaababaabababaabbabbabbaabbbababbaaabbaabbaabaaababbababbbababbbbababababbabaabbbbbababaaabaaaaaaabbabaaabaaababbbabbabbaabbaaabbbabbabbaabbabaababbababbbaabababaabaabaabbbaaabbbbaaaaaaabbbbbbbaababaabbaabbabbabbbaaaabaaabbbaaabababaaabbbaaabbabbaababbbbababababbbbababbbbaabbbaaaaaaaaabbaabaaababbaaaaaaabbaaaaabbbaabbabbabaaabbbbaababaabaaabbaaaaaababaabbbbabaababbbbbabaabababbabbabababbbbaababaabaabbaababbabbbabbabababbbabaaaabbaaabbaababaababbbbaababaaabbaababbababbabaabbaaabbbababaaaababaabaaaababababaaaaaaaaaabaaaabaabbaabbbbaaaabaabaabbbaaaabaababbbbbaaaaaaabbbbabaaabaabbaabaaabbabbaabababbbabaababaaababaababbbababaaaaababaaaabbaabbbbabaaabbbbbaabaaaaaabbaababbaaabbabbbabaaaabbbbbbabbbaaaaababbaababaaaababbaababababbbaaabbbbbabbbbbbabaabbaaabaababbaababaaaabbbaaabababbbaabbababaaabbbbaaabbaabbabaabbabbbbbabaaabbbaababbabaaababaaabaabaabbbbbababaaabababaababaabbbababbbabbabaabbababaabbaabbbabbbaaabbbaabbababaabbbbbabbbbaabbabaabbaabababababbbnbbaabbaaaababababbbbbabaabaaababbbabbaabaabbbbaaabbaabbbbbaababaaaababbbaabaabaabbbabbabababbbaabbaababaaaaabbbaabaabbaaabbabbabaabbbbabababbabaababababaaababbabbaaaaabbabbbaaababaabababbaabbbaaaaabbabbbbbbaaabaabbbababaaababbbbaaaababbabbbabbbabababaababaabbababbabababbbbbbabaabbabaabaabbbabbbbbbaaabbaaabbbabbbaababaaabbaabbbaabababaabbaababbbaababbaaaabaabbbabbbbbabaabababaabaaabaabaaababbabaabbabbbaaabaaababbababbaabbbaaaaaaaaababbabbbbbabbbaabbbbbbbbabaababbbbbbaabbabbbaabababbababbabaaaabaaabaaaababbbabbbabababbababbbababababaaaaaabbbbbbbaabaaabaabbabbaabababbabaababaabaaaaabababbbaabbbbaabbabbaabaabbaaabbaaabbbaaababbbaabaaabbbbaaabbbbabaababbaaabbaababbbbbaaaaaabaabbabbbaabbaababaaababababaaaaabbbbabbbbbbbbababaabaaabbaabbbababaaababbaaabbaabbbbbbabaaabaabababbbabababaabaabbbbabbababaaabaabbaabaaaaabaaaabaaaaabbaababbabbaabaabaaababbbbabbbaabaabbbabbababbbabbaaaaababbbbabaaabaaabaabbaaabaababbbbaaaaaabbbaabbbbbabbbbbaaabbbaabaabbabbbbbbbabbbabaaabababababbabbabaaababbbabababbbaaabaabbbababbaabababbaaaaabbabbaaaababaaaabbaabbbbaabbbbbbaaabbbbababbbbbbaaaaabaabbaaababbaaaabaaabaaaaabbbaabbabaaaabaaaabaabababaabaabaaaaaaaabbbaaabbbbaaaabbaaaabbabbbaabbbbabaabaaabaaababbbabaabbbabbbaaabbbbabbaaaaaabbabbbbbaaabbbaaabbaaaabbaabbbbbbbabbbbbbbbbbababaaababaaaabaabbbaabbbababbababbaabaaababaabaaaabbaaabbabbbaaabbbbbabbaabbaabbaabaaababaabbbabbabbbabbbaaaabbabbbbbbbaabbbbabbbabbbbaababaaaaaaaababbaababbbaabbabbabbbabbabbabbbbbabbbababbaababaabbbaaabbaabaabbbabbbbbabbbbbbabaabbabbbbbbbbaaabbbbaaabaababbaaaaabbaaaabbabbbaaababababababababbaabbaaaaabababaabbaabababbaabbbbaaabbbabaabbbbaabbabaaabaaaababbaabababbbbaabbbbbbbabbabaaaaaabaabbbababababaaaabbabbbababbbaaabbababaaaabbabbbbaaaaaabaabbaababbabaaaaaabbaabaabaaababbbbbbabaaabbbababaaabbbbaaaaabaabababbbabbaabaaabaabbbaabbabbaaabaababbababbaabbbaaabbbaababababbababbbaabbbbbbaaaababbabaaaabbaaabaaaabbaaaabaaaaabbbbbbaabbaaaaaabaaabbbbaabbbbaaabaabbbbaaabaaaaaaaabbbbbbaabbabbbaaaabbbaababbaabaabbbabbbbaabaababbababaabaabbbbaabaabaaababbabaabbabaabaababaabbaabaaabbbabaaaaabaabbbaaaabaaababaabbbbaabbabbbbababaaababbabaabbabbabbbaaabbbaabaabbaaaabaabbaabbbbabababbababaababbbbbbabaababaababaabaabbabbaaabaababaaaababaaabaaabaaabbaababbbbbbabbbbaaaaaaaaabbaaaabaabbaabbabababbabbbababbbababbbbaaaabbbabaaaaaabaabbbabbbbaaababaabbbaabbbaaabaabbaababbabbbbabbbaabaaabaaababbbabbbbbaabbbaabbbbbaaaabaaaabbabaabaabbbaababbabbaabaababbabaabbbaabaaaaaabbababaaabbbaaaaababbabbaaaabbbaabbabbabababbbbbaababbbabababbabaaababaabbabbabbbbbabbababaabaabbaaaaabbabbaabbaabababbbaabbaabaaabbbabbbbabbaaabaababaaabbaabbbabbaaaabaabaaaaaabaaababaabaaabbbbabaaaaababaabbbaababbaabbaaaaaaaabbbbbaabaaaababababbaaababaaaaaaabaaaabaaaabababbbaabababbabbbbaaabbaabaabaaaaaaaababbaaabaaaaabbabbabaaababbbaaabbbbaababbbbabbbbbbbabbbbbaabbbabbaabbabbaabbbaaabbabbabbbaabbabaabaaabbbabbabbaababaaaabbbbabaaabbbbbaaabbaaaaaaabbababbbabbaaaabbbbbaaaaababbbbabbaababbabbababaaaaaaabbbbbabababbabaabaabaababbbaaaaaabaaabaabaabbbbabaaabbaaaabbabbbbaaabbabbbaaabaabbbaabababaaaababaabbabaababbbbbaabbabbabaaaaaabaabbabaababbbaabaaaaaabbabbabaabbabbbbbaaababbbabaaaabbabaaabbbbbaaaabbbabaaababbabaabbbaaabaabbabbbbababaaaabbaaabbabbbbbababababaabaababbaabbbaabbbababbaaabbaabbabbabbaaaaaabbbbbbbbababbaabbbbbbbababbbbaababaabbaaaabababbaaaaaabbbabababbababbbbbaaabababbbaabaabaabbbaabaaabaaaabbbaaababbbaaabbaababbbbaaabaaabbbbbbbbabbaabaaaaababbabaaaaababbbababbbbababababaaaabbbaaabaabbabbbbabbaaabaabbaababaabbabababaabbbabbbbbaababaabbbaabababbabababbbabbaababaababbbbabaaaaabbbaaababbaabbbabbaababbaabbabbabbbbbaababaaaabbbbbbabbaabbbabbaababaaaaaabbbbabaaababbbbbbbbbaabbabababaabbbbbbabaabbbbbabaabbaababaaabbababaaaaabbbaabaaababaaaabbaaabaabaabbbwabbaabbbbaaaaaaaabbbbaaaaaaaaaabbbaaabbabbbaaabbababbbbaababaaabaaaaabbbabbbabbabbbbbaaaaababbbabaaaabbaaaabbbababbaabaabbbabbaabbbbabaaabbbaababbaaaaaabbaaababbbaaaaababbbaaaabaaabababbbbaaaababbbbbaabaabaaababbbabbbababaabababaaaabbbbbaaaaaaaababbaabbababaaaabbabbbaaabbbbbbbabbaaabbabbbabbaaaaabababbbaababaaaaaabaababbbaababbbbabbbbbabbbbbbabbabbbabbbbaabbbababbaaaabbbbbabaaabbbbababbbbbaaabaaaabbbbbaabbaabbbababaaabbbaabbaaaabbabababbaaabababaabbbaabbaaaabbbababaabaababbabaaaabaabbbaabaabbaababbabbabbaabbbbaaabbbbabaabbaabbbbaabbbbbaaaababaabbbbbbbaaabbbaababbabababbbbbabbabaaabbaaaabaaababbbbbbaaabababbaabbbbbabbbabbabababbaabbaaaabbabaababaabaabaaababbabbabaababababbaabbbbbbbbbabaabaaabbbaabaababbaababaabababaaaaaaabbbbabaabaabbaabaabaaabbbabbaabbbbbbaaababbaaabbbabbbbaaaaabbabaababababbaabbaaaaaaaababbabaabaababbbaabaabaaababbbbabbbbbaabbaaaaabbababbaaaababbbbbabbabbbabbbabbbababaabbbbaabbababbbbababbaaaaabaaabababababbbbabbabaaaabbbabaabaababaabaabbbbbaaabbbabaaabbaabbaabaababbbbabbbbaaaabababaabbabbbbbbaaabbabaabbbabbbabbbaaabbaabbbbbaaaaabbbbbbabbaaabbbbbabaababbbababbbabaabaaabbabaabbaababbaaaabababaaabaabaaabbbbaabaabababaabababbbbbabababbababbbabaabbbbbbbabaaaabbabbabababbbabbaaaaabbbaabbbbbbbbbbbabbbaaabaababbabaaabbbbabababaaaababbbbbabbbbabbbbaaabbbbbaabbaabbaaabaababbbababbaababbaaaabaaabaaaabaabaaabaaaababbbaabbbabbbbbabababbbbbbbbababbababaabbbbabbbbaabaaabbaaaaabbaabbaaabaaaaabbababababbbabaabbbaabbaabbbbbbbbaaaabbbaaabbaabbbbaababbababababbabbabbbbaaaaaaaabaaaabbabbaaaaaabbbaabbabaababbaababaaabaaababbabababbbabaabaabaababbabbbbabbbbbbabbbababbaabaababaaaabbabbbbaabaabbabbbaababaaabbbbabbabbbbaabbbaababbbbababbbabbabbaaaaabaaaabbaabbbbaaabbbbaabbabababbabbbbbbbbaaaabababaaaaabaabbabaaaabbabbababbbbaabbbaaababbbababaabbbbbaabaabbbbabaaaababbabbabbbbabaaaaababaaabbbbbabbabbaaaaabbbaabbbbbbabbababaabbaaababaaabbabbabaabbbbabbaaabbabaaabbbbbaaaaabababaabbbababaaabbaababbaabaaaababbbbbbbabbaaabababbaaababaabaaaabaabbabbbaabbabaabbbbabaabbbabbaaababaabaabbbabbaaabbaabbbabaaabbbbbabbaabaaabaaaaabbaabbbaaaaabaababbaabbaaabbbbaabbaabaaabaaabbbababaabbbbabaaaababbbbaabaaabaabbbbaabbbbbabbababbbaaaaabaaabbbbbabbaabaabaaaaabaaaaaabaabbaabbaaabaaababaabbaabaababbbbabbbbbbaabaaabaabbbbaabbabbbbbabbabbbbbabbaabbaabbaaaabbababaaaaaaaababbababaabbbaaaaaaabbaababbbbaababaababbaabaaabbbabbbbaabbbbbbaaaabbababbaabbaabbbaaabbbbabbbabaabbbabbbaabbababaaaaabbbbbbbaaabaaabaabbbabbaabbbaabbbaaabbabbbbbabababbabaabbaababaaabaaabbabaaabbabaaaaabbbabaaaaabbbbbaabaaababbbbbbaaabbabbababbabbababbbbaabababaaabbbbbbabbbabbaabbbbbaaaaaabbbaabaaabbaababbaaaaabaabbaabbbbaaaababaaaabaabaabbaabbaaaaaaabaaaababbbabaaababaaababbabbabbbbbbaabaaaaabbaabbbbbababbabaababbabbaaaababbbabbaabababaaababaabaabbabbbbbabbbaabbabbbbbbbabaabbbabaaaaaababaabaaaabbbabaaaaabbbaaababaaabbbbbbbbbabababbbbabaaababbbababbaaababababbbabbaaaaabbbbbabbaabbaababbaaababaaaabaabababbbabbbababbbabbaaababbaabaababbaaabbbababbabaaabbbbaabbaaabbbbbbaabbaabbbbbbabaaaaabaaaabbabaababbbabbbbababaaaaaaaaaaaaaaaaaababaabbbbaababbabbbabaabaabbbbaabaaaaaabbbabbabbbbaabaaaaabaababaabbbaababbaaaabbbbababaabbabababbbbabbbaabaaaabbabaaaabbabaaaaabababaababababaaaaaaabbabbbbaabbabbaabbabaaabbabbbbbabbbbaabababbaabababaababbbaaaababbbaaaaaabaabababbabbaaabababaabbaabbbabbababbabbbaaaabaabababbbbbbaaabababbaaaaaabaaabbbbaabaaabbababaabaaababbbbaaaaabaaaaabbaaaaabbbbbaabbababbaaaabbbaaaaabbbbbaaaaababbaabbbaaabbbabaaabbbabaababbabbbaaaabbbbbbbabaabbbbaabbababbbaababbaaaaaaaaaaabaababbbbaabababbabaaabaaabaaabbababbbaababaabbaaabbbbabbbbaaabbbaaaabbbbabaaaaaaabababbaabaabbaaaaabaaaaaaaaaabbabaababaaabababaabaaabaababbabaaabaababaaaaababaababbbabaabbaaaaababbaababababaabbbbbaaaababaaabbaabaabaaaaababbbaabaaaaaababbbbabbbbbbbabbbbabbbbbbabababaabbbabababbbbbabbabbaabaabaaaaabaaaababbbbaabaababbaaabbbbbbabbaaabaaaabbababbabaabbbabbababaaaaaaaababababbbaaabababbbbababaabaaabbabaabababababaabbbabaabbbbbbababaababababaaabababbabaabaaaaabbababbaaabbaababaaababbbabaababbbabbbbabbabbabbbabbbababbaabaababbaababaaaaabaabaaabaabaababababaaabbabaaabaabbabbbbabbbababababbabbaabbaaaabbbbabbabbabababbbababbbabbbaabbbbabbbbabababaababbbbbabbaaaabaaababbaaaaabbbbbaaababbabbaabaababbbabbbabaabbaababbaaaabbabbbaaaaababbabbaabbbbabbbbaababababbbbaabaaabbababbbaaaabbbaaabbabbabbbbbbabbbbbaababbaababbabbbbbbaabbbabbbbbaabaabbaabaaabaaabababababaabbbaabbabbababaabaabbabbaaabaaabbbbabbbaaaaaabbbaaaaababbbbbbbbbabaaaaaaabbbabbaabaabbbaababbaaaaababaaaaabaaabbababaabbaaabababaaaabaaaabbbabaababbaababaabbaaabababbabbaaabaaaaaabbbabaabbaaaabaabbbaaaabbaabbabaaabbaaaababaaaabbbababbbbababbbbbbbaaaabbbabaaaababaaaababbbbbbababbaaaababbbaaabbbaabaabaaaabaabaaaabbabaaaabababaaaaaaaaaabbabbabbbaaaaababababbbbabaaaaaaaabbbbbaaaaaababbbaaababaaabbbababbbbaaaabbababbbbbbaabbaaaababaababaaabababaabbbaaaabbbbbabaababababbabbbbbaabababaababbbabbabbbbbbbaaaaabaaaaabbbaabaaabbabbbbaababbbbaabbababababbaaaaabbabaabaaaaaababbbbaababaaababbbbbaabbbbaabbabbabbbbbaaaabbaaaaabbbbbbabbbbbbababbbabbbabbabaaaaaaaabbbbabbbaababbaabbbaababbbbbabaaabbbabbbbbaababbbaabbbbbbbaabbaaababbabbbbaaaaababaaabababbabababaaabaabbaaaaaaabababbbbabaaaaabbbbabbababaaaaaaabababaababbaabbbbaaaabbbbbbabbabbbbbbaaabbabbababbaaaabbbabaaabbbbaababaaaabbbbabbaabaababaaaababaaabbbbbabaabaaaabbbbbabaaaaabbbbaaabaabaaababbbababaaababbbaabbabbabbaabaaabbababqbbbbbbaaabbaabaaaaaabbabbabbbabaabaaaaabbbaaaaaabaaabaaabbaaaaabbabbbababbbabababaaaaaaaabababbbabbbabbbbaaaaaabbbaabaaabbabbaaabbaaaabbabaabbabaaabbababbabaabbabbaababbababbaaabaabbabbbbbaabbababbbbbaabbaabaabbbbabbbbbbabaaaabaaaaababbbababbaaaaaaabaabbabaaaabbaababbbaaabaabbbaabaaaaaabbabaaabbabaabaabbbbabababaaaaaaabbaaaaabbbabbbaaabaaabaabbbbababbbabbbaaabbbaaabbbaabbabaaaabbbaabaabbaaaaabaaaabaabbabbaabaaaaaaaabbbaaabbaaaabaabbbbaabbbabababababbbbaaababbabaabbaaaaabbbbaabbabbaaaabbabbabbaabababaaababababbbabbaaaaabaababbbabbbaababbbababbbaaabaaabbaaabaabbbbbabbaaabababbabbbabaaaabbabbbbbabbbbbbbbaaabbabbbabbbabbaabbbabbaaaabaabbbababbbbababbbbbaabaabaabbbbabbaaaaaabbbabaababbbbabbaabbaaababaabbabbbababaabbaabbaabbabbbaaabaabbababbbaaabbaaabababbaaaaaabbaaababaaaaabababbaabbbbbababbbaabbbbbaaabaabbbaabbabbaaaaaaaaaaaabaabbbbbabbbbbaabbbbabbbbbabaaabbaababbbbaaababaaaaaabbbabaaaabbaababaabbabbabbbabbbaaabaaaaababaabababbabbababbbababaaaaabbaabbaabbaaaaaabaaaaaaabbaababbbaabbbbbaabbabaabbbbabbaabbbbbaabbbbbaabaabaabbaabaaaaaababaaaabbbbbbabababbbaaaaabbabababaabaabbaabababbbaabbbbaabaaabbbabbbabbbbbbbbabbbbabbbababaabababaababbbbabbaabaaaaaabbaaaabbbbbabaaababaaaabaabaabbbbbabbbbbabaabababbaabbbbaabaaabaaaaaaabbbaaaaaabbbaabbaabababbabbbaaaababbbbaababbabaababbabaaaaaaaababbbababaaaabbaaaabaabbbabaabaabbbbbabbabbaabbbbbabbaabbaabbbabbbbbababababbbbaaabbbbbbbbbabaababbabaaabababbbabbbbbbbbbbaaababbababbbbaabaabbbbbabaabaaaaaaababaaababaabbbbbaaaaabbabbabaababaaaababaabbbbabbbaaaabbbbaaababaaaaaababbaaaaabbabbababbbbabbaaabaaaaabaabaaaabababbbabbaaaaabababbabaababbbaaabbbaaabbbbbbbbaabbbababbbbaabbabbbbaabbbabaabaabbbbbbbbbbbbaaaabbbabbabaababbaaababbaabbbabaaaaaaabbbbaabbbbababbbaabbaaabbaaaabbaabaabaabbabaaaabaabaaabaabaababbabaabaaaaababbbbabaaababaaaaabbbabaabaabababababaaaabbaabbbbabbaabbaabbbaaaaaaabaaabaabbbbbbabbbaabbaaabbbbaabaababbabbbaabbbbaababbabbbabbbbabaaabbaaababbbabbbaaabbbabaaabaabaaaabbabaabaabaabbaabbababbbaaabbaabaabbbabaababbaaaabaaaababbbabbbbabbaabaaabbbabbabbabbbbbbabaaaabbbbbbbbbaabbaabbbbabaababaaababaabbaabababbbbaaaabababaaabbaaaaaabbbbabbbabbbabaaaaaaaabaabbaaaaabbbabbaaaaabbaaaaabababaabaabbbbabbaabbabbbaaaaaababaaabaaaaaabbaababaaaabbbbbaaababaabbbbababaabaabaabbbabbbaabbabbbababaabbabbbaaaaabbabbabaabaabbabbaaabbbaaaabbbaaabbaaabbaaabababbaababaaaaaabbaaabbabaaaabaaaaababbaaabbbabbaaaaaababbbbaabbabbababbbbbaabbaaaaabbbbaabbbaaaababbaabababababbababbabbabbabababbbaabbbabababaabbbababbaaabaaaaabbabbbaabbbbabbaaabbbabbbbbbabaabbbbbaaaaaaaaabbbaaabbaabbbbbababbabbbbaabababbababbaaaababbbbabbbbabaabbabaabbbbbabbaabbaaaabababbabbababbaabbabbbabbaabbaababbaaaaaaabbbaabbbbbbaabaabbaabababaaabbabaabbbbbbabbbabbaababbabababbababbbbabaabaabbbaababbaabbababaabbbbbaaabbbbbaaaaabaaabbbbabbabbbaabbaaaaabaaabaabbbbbbbaaaaabaaaaaabbaabaabbaabbbbaabaababababbbabbabaabbababaaabaaabbaabaababaabbbbaaababbaaabbabaabbaabababbbbabbaabaabbbbbbabbaababbbaabbaaaaaaabaaaabbababbbbabbababbababaaababbabbabbaabbaabbabbaabbaaaabaaaababaaaaabbabaabbbbbaaaababbbbbabaaaabaaababbbbbabaaababbbaabaabaabbbbbabaaababbbaaabaabbaaabbbbaabaaabaabbababbbbaababbaaaabbbbabaaaaaabaaabbaaaababbbabaabbababaababbbabbaaabbaabbbbbabbbaabaaabaaaabbbabaabababbaabbbabbbbbababaababababbaaaaaaaabbababbabaabaaaaaabaababbbabbaabbbbbbababbbabbaaaaabaaaaaabbabaabbbbaaaaaaaaaabbbabaaabbbaaababbbaaababbabaaaabbbbbbbbbbabababbbbbbaaabbaaaaaaaabbbbabababbaaabababaaaaaabbaaaaaaabbabaaababbbabbbaabbbbaaabbabbaabbabaabbababaabbbabaaabbbbaabaabbbaaabbbaabbabaababaabbaaabaabaaabbaabbaabaaabaaabaabbaabaabbbaabaaabbababaaaabaabaaabbaaaaaabaaabbaaabbbbaaaabbbaabbbbaabbbbaabbbbbbbaaababaaaabaaaabbababbbbbbbabababaabbabbaaabbaaabbbbababbabbaaabbbaabaabbabaabaababbbbaaaabbaaaaabbababbbbabbaabbababbbbbbbbabbaaaabbaaabaabbabbbbababaabbbbabbaabaabbbaabababaaaaabbbaaabaaabaaabbabbbbaabbbbbbabbababaabbbabababbaaabbaaabbbbaaabaabbabbaaababaabbbbabbabbabaaabbbabbbaaabbababababbabbaabaabbababbbabaaabbbbbbaabaaabababaabbbbbabaaabaabaabbbbaaabbbbaaaaabaabaabaabbbbbabbbaaaabbaabbbbabbbaaabbbaabbbbabbbabbabaaabbbaaababaababbabbaababaabbbaaabbaaabaabbaaabaaabbabaaababaaabaababbaabbabaaabababaaaabaaababaabbbbbabaaababbabbaabbbbbaaabaaabaaabbabbabbababbbaaaaabbabbbaaabaabbbabbbabbbaabbabbbababbabbbbababbbaaaabbabaabbabaaaabbabbbababaabababbbbbabbaabbabbaababaabaababaaaaaabbaaaabbaaabbbabaabbbbabbaaaabbaaaabababbabaaabbaabbbbbbbaaaaaabbaaaaaaaabbabaabbabbbaabababaaaabbaabababbabaaaaabaaaababbaabbaababbbbabbabbabaaabbabaaaaaaaaabaabaababbaababaaabbbaaaababbaaaabaabbbbbabbbbbabaabbaaaabbbabaaaabbaaaabbbbbbabbabbbababaaababbbabaababaaaaabbbabbaabbbbabaababbbbaababaaabaaaabababbbbbabbabbabbaabbabaaabaaaabbabbaabbbaaaababababbaaaabbabbaaaaabaaaabaaabaabbbaaabaaabaababbbaababbaaaaabbbbbbaabbabaabbbbababbbbbaaaabbaaabaaaababbbbbaaaaababbbabbbbbbabaaabbaaaaababaabaabbbbbabbabaabbbabaabbbaaaabaabaaabbbbaabaaabbbabbbabbbabaabbaabaaabbbabaaabaaaabbbbbababaababbbbbbababbbabaaababaabababbabbabaabaabbabaabbabaaababababababaaaabaaabaaaabbaaaabaabababbbaaabbbbbbaaaaaaababbbababaaabababbababaabbbbbbaababbbaaabbbbabbbbaabaabbbabbbaaababaabbbabbabaaaaababbabbbabaaabababbbbbbbabaabbbbbbaababbbaaababaawbabaabbaaaabbbaaabaaabbabbbabbbaaaaabababaabbabbbbaaabaabaabbbaabbaaabbaabbaaabaababaaaabaabaabaababbaabaaaabaabbbbaaababbabaabbabbaaaabbbbabbbaabaaaabbbbababaaaabbbabbaabaabbaababaaaababaabbabaabbababbabbaaaaababbaabbabbbaaaababaaabbbabbababbaabbaababbbabbbbaabbbbbabbabbbaaababbabbbbbbabbaabababbabaaaabbbbbbababbababababbaaaaabbaaababbbbbababaabbabaababbbbabbbbbbbaaabbaababbbbabaaaaabbaabbabbbbaababaabbabaaabbaabbbaaababababbaaaaaaabaabbbbbabbbabbbabbababaabbbbaabbbaaababbaaaaabbbabaababbbabbbaaaabbbbabaaaaaabbabbaaababbbaabababbabaababaababbaaaabababbbabbaaaabaaabbaabbbbaaaaababbbbaaaababaabbbabaabaabbbbbaaababbaabbbbabbbbabbbbaabbabaababbaaabaaaabababbbbbaaababbbbbaabbabbabbbbaaaaabbbbaaaaabbbaaaaabbabbbbbbbbaabababbabbaabbaaaabababbabaaabaabaabbbaabaabbbaaaaabbbabaabbaaabaabbaabaaaabaaaabbbababaaabbbaababbaaaababaaabbbaaabbbabaaabbbbaaaaabaabaabbabaaaaaabbaaabbaabbbababaaaaabbaaaabaabbaaabbabbabbbabbaaaabbbbbabbbbaabbabbbabaaabbabbaaabbabbaabbaaabbaabababaabaaaaabbabbabababaaaaaabbbbbabbabaaabababaaaaabaaaababaaabaabbbbaabaabababaabbbbbaabbabbbbabaaabbbbbababbbaabbabaabbbbbabaaabbbaabaaaabbbabbbaabaabbababaabababbbbabbbbbbbbbaabbbaaabbaababbbabaabbaabbaaaabbabaabaaaaaaabaaabaababbbbabbabaaababbbbaababaabbabbbaaabaaaababaabababbbbbaabaaabababaabbbbaaaaaaabaababbaabbaaaabbababbbbbbbabbaabbaabbbbabbaabbabbbaaaabbbabbaabbbaabbbbaabbbaabbabbaababaaaabbabababababbabaaaaaababbbbbaaaabbaabababbbbbababbbaaaaaabbbbbabbbbabbbbbbaaaaaaabbbbaababababbbaabbaaaaaabababababbbbabbbbababbbabbaabbbbabaaaaaaaabbaabbabbbabaaabaaabbaaaabaabbbababbabbababbaabababbabaabbbabbabaabaaaabaabbabaabbbbaaaaaaabaabaababaaaabbbbaaaabaaaaaaaabbaaabbabbbabaabbbbbbbaabbbaababaaabaababbbabaabaabaaabbbbbababbbbbabbbabbabbabbbbbbaababababaaaaaabbabbaababbbbaabbbaabbaababaaaaabaabbbaaaaaababbbbbabbaababaaaaabbbaaababbbababbabbbbabaaaaabbaaabbbaabbabbbabaaabbaaabaababbaabbbaabaaabbbaaabbbbabbbbbabbbbbaababbbbabaababaabaaaaaababbaabbbababbbabbbbbbbbaaaabbbbabbbbbbabbbaabaabbabababbaabbbbbbbbbbbbabbbbababaababbbbbbabbabbabaababbbbbbbabbbabaababaaaababaaaaabbbbaaaabababbabbabbabababbaabaabbbaaabbaabbbbaaababababbababbbbbbabbbbbaabbabbaaabbabbaabbbbabbbaababaabbabaabbabbaabaabaabbabaabaaaabbabbabbabaabababbbbbbabaabbaababbbbaaabaabbabaaababaabbbabaabbaaabababbaabaabaaaaaabbaaabbbbbaababbbbaaabbbabbbbabbabaaabaabbbaaabbbbabbbbabbabaaaabbbaababababbbabbabaaabbbababababbbbabbababababaaaabbbaabaabbabbbbbabaaabaaabbabaabaabbbbaababababbbbabbabaabbabbaabababbaabbbbbabbbbabaaaabaaaaaabbaababbabbaabaaabbbabaaabbaabbbbaaaaabbbababaaabaabbaabaabbaaabaaaaababbbaaaababababbbbbbbbaabababaaabbabbbbabbaaabbbaabababbaababbbbabaababbaabbaaaababaaaabbbbbaaaaababaaaaabbaaabaabaabbbaabbaaaaababaabaaaaaaaabbbbabbbbabbaaaaaabbaaaaaaaaaaaabaaabbababbbabbaaabaabaaababaababaaabbabbbbaaaabbbbabbbaaabbaabbbabbbbababababbaaabaabbbabbbbaabaabaabababbaaaabbaaaaaaabbababaaababbaaaabbaabbabbaaaaabaabbaabbbaaaaaabbaabaabbabbaabbbabbbaabaaaaabaababbaabaabbbabaaababaaaababaababababbabaabaabbabababaaabaaaaabbaaabaabbaabbaaabbabbabaabbbbbbbbabbaaababaabbabbababaabaabaabababaaaaaaaaababbaaaababbbabbabaaabaabbbaababaabbaabbababaabbabbabbbaabbabbbabaaaabbabaabaaabbaabbbbbbbbaabaabbaaaabbaaabaaabbbaaaabbbbabbabbbabbabbaabaaaaababbabaaaabaabbbbbbaabbbaabbaaabbabbaaaaabbaabbbabbbaabbaaaabbbaaaaaaaabbbbabbbbbaababaaaaaababbaabbabbabbbbaaaababbaaabbaaabbbbbbbabbbbabbaaababaaabbbbbababbbbaabbaabaaaabaaaaabbbabbbaababbbaabaaaabaabbabbbbbaabbbbababbaababaababbaabaaababbabbbaaabbbaabaaabbbababbaaabbabababbabaaabbbbbbaababbaaabaababaabbbaabbaaabbbababaabaabaababbaaaabaababaaabbbbbabaaabbaababbbbbbbbbbbaabbbabbbabbabbaaaaabbabbbbbbaabaababaabaabaababbbaaaabbabbaabbbaaababbbaaaaabbbaababaabababbbaaaabbbabbaaababbbabaababbababbabbbabbbbbaabaaabababbbabbbbabbabaaaabbaaabaaabbbbabbabbaabbabaaaaaaaabbaabaaabaabbbbbbabbbabaabaaababbbabaabbbbbaabbabbbbabbbbabbabaaaaabbababbaaaabbbabbbababababaabababbbbaabaabbbaabbaabbaaaaaabaaabbbabbabaaaaaaabababaaaaabaaaaabbaabaaaaaaaabababbbaaabaaabbbbaabbabbaaaaaaaaabbbbbbabaaaabbaababbbaababaabbbabbbbabbaababababbbbbaababababbabaaababbabaaaababbbaabaaaaabaabaabaaabababbabaaaaabbaaabaaabbabbaabbabababaaabbaaaaaabaaabbbabbbaabbbaaabbaabbaaaabbabbbabbaaaababaabaaaaaaabbbbaabbabbbbaabababbaabababbaabbaabaaababaaabbababaabaaaababbbbbbababbabbabbbabaababbbbababbbbaaabaabbaabaabbabbabbbabbabaaaaabaabbbabbbabbbbaabbbabbbbbbaabbbabaabbababaabbaaaaabbbbbbbbbbbbabbbaaaababbaabbaabaaababbbbaaababaabaabbaaababababbabbaaabaabbbaaabaaaababbaaaabaaabbaaabbabbbaaabbbbbaabbabaaabbabaabbbbaabbabbbabaaabbaabaaaababbbbbababbbbbbaabbabbbbbbbbbbbbaaabbbbbabaababbabbabaabbbabbbabbabbaabaabbbabaabbbabbbaaabbaaaaaaaaabaabbbaababbaaabbbababaaabbabbabbbbabababbaababaabbaaaaaabaaabbbaabaabaabababaababababaabbabbbbabababaabbbaaababbbabbbbbabbbbaaababbbbbbaabababababbbabbababbaaaaaaababbaabaaaaabbbbabbababbaabaabaaaabbbbababbbaabbaabaababbaaaaabbbaaaabbaabababaabaabaabbbbabbbbbbbbabbbbabbbaaaaaaaabaaaabbbbababbabaabbabaabbbbababbaaaaaabaaaabbbaabbabaaaabbbaaabbabbababaababbbbbbaababbaaaabbaababababbbbbbbbaaaabaaababaabaaaabbbbaabaaaabbbbaaaabaabababaaabbaabaababaabaaaabaabbbbbbbaabbabaaabbbbaabbbaababbbbbbbbabaabbabbabbaabaaabbaabaababbabaabbabababbbaaabbababbaaabbbbbaaaaaaababbaaaaababbbababbababbaaababaaaaabbbbbbbaaaabaaababbbabaabbabbbbbababaabaababaaabaabaaaabaababbababbbabbbababbbababababaabaababbaaaababbbaabaaabababbabbabaabaaaaabbbababbbbabbbabbbbbbaabbaabaabbbbabaabaabbabaaaaaabaabaababaabbabbaabababaabbaabbabbaabaabbaaabaaabbabbbaaabababaababbbbaabbbbabbabaabaabababbabbbaaaabaaababbbaababababbabbaababbbbaababaababababbaababbbbaabaabbaabaaabaaaababaaabaaabaabbaaaabbbaaaabaabaabbbaabbbbabababaaabaabaabbbbbabbbababbbababbaabaabababaabaaabaababbbbbabaaabbaaaabababbabbbababaabbbababbabbbbaaaabaaaaabaaaabbaaabbbbbbbaaaabbbaabaabbaabbbaaabbaaabaabaabbabaabbabababbaaabaabbbababababbabbbabaaabbaabbaabaaaabaaaaaaabbbbbbbaabababaaaaabaaabbabbabababbababababaababaabbbbbabbaabbaaaabbababaabbababbabbabababaabaaababababbaabaaabbaaaaaabbaaabbaaaabaaaaaaaabaabbbbaabbbababbaaaabbbabaabbaaabaaaabbabbbaaaabbbabaabbababaabbabbaaaaabbaaababbabbbaababaababaaaaaaaabbbbabbaabbbabbbabaaabaaabababababbbabbabaaabbbaaabbaaaaaabababbbabbbbabbbbbaaaaaabbbbbbbabbaaaaaabbabbbaaabaabbaaaababbbbbbabbaaaaaaaaaababbabaaabaababbaaaababaabbababbbaaababbbbbabaaaaaaaaababaaaaababbaabbababbaabaabbaaabbabababaaababbabaabbbaabbbabbaabaabbaabbaaababbaaababbabbbaabbaababaabaabaaabaabaaabbaaabbaabbbabbbaaaaabbaaabbabbbbabbbbabbabbbbbaabaabbbbabaaabbababbabaabbbababababbaabbbbbbaaababaaaaabbababbabbbababbabbaaaabbbbbabababbabaaabaaabbaaaaabaaabbabaaababbbaabbbbabbaabbbbbaabbaaaaabaaaabbbbaaaaababbbabbbaababbaabbaabbbabbabbaabaababbbbbabbbbbaaababaabbbaabbaababaabaabbabbbabbbabbbabaaababaabbaabbabbbabaaaaabbbbbaaabbbaabaabbbaabbaababaaabababaaabaabbaaaaabaaabbbbaaabbaaababaaabaabaabbaaaaabaaabaaababaaaabbababbaaabbaabbbaaabaabbaabbbbababbaaaabaabbbbbbaabbbaabaaaaabbbbbbaaabbaabbbbbabbaaabbbaaaabbaabbaaabaabaaabbabaaabababbabaaaabbbabbbbbabbbbaaaaaaabaaaaaaaabbabaabbabbbbbabbbbbabbaababbbaaaaababbaababaaaabaaababbbaabbbbaabbbaabababbabbbaaaaaabaaaabbbbaababbbaaaaaabbabaabbaaaaaaabbbaaababbbabbabbaaabbaabbaaabaabbaabbaababbbbbabbabababaaaababbaabbbbabbbbbabaababababbababbaabaaaaaaaabbaababaaaaaaabaabbbbaaababababbaabbbbaabbbaababbabbbbbabbbaaaaabbaabbabbbbbaabaababaaaabababbababbaabbbbbbbaabaabbbbbbababaababbbabbaabbaaaaaababbbbababbabbaabbbabaabbbaaabbbaaababbaabbabbabbbaabaabbaabaabaabaabaaaabaaabbbbbaabbbbbbbbbbaabbababababaabbabbbaababbbbabaabbbaaababaaabbbbbaabbbbbaabbabaaaaaabaababbabbbbbbaabaaabbbaabbbabbbaaaababbbabaabababbbaaaabbabaaababbaabbbaaabaaabbbabbaaaabababbbbbbababbabaaaabaabbbaaabaaaaabbbababbabbbbaaaaababaabaabbabaaabbabababbaabbbaabbaabbbbbaaababbabaaabbabaabbabaaaabbbbbaabbbbbbbbbabababbbaabbbbbaaabbbabbbbababaaaaabaaaabaabbabbaabbbbbaabbbabbaabaabaabbabbbaabaaaabbaabbaabbaababbbabbbabbbbababaaabaaabaabaaaaabbbaabaabbababaaababbbbabaaabababbbabbbbbababaabbbbbabbaaabaabbbbaaabaaabbaabaaabbbaaaabbbaabbaaaabaabbaaabaababbbbbaababbaabbbabaabaabbbbbaabaabaabaaababbbbbaaaabaababbabbabbabbbabaabaabaabaaaaaaaaaabaabbbababbbaabbbbabaaaabbbbaaabbabbbababaaaababbabbababaaaababbababaabbbbbabbbbabbbabbbaaabaabbbaabaaabababaababababbbbaabbbabbaabaabbaaabaabbaaabaaabaababbbbaabbababaaaabbbabbaaabaaaabbbaaabaaabbabababbbbbaaaabbbbbabaaabaabbabbbbaaaababababbabaababbaabaaabaababbbaabbbbbbbbbbaaaabbaabababaaabababababaababaaabaaabbaaaabaabbbaaaaababbabbaaaaabaabbbbbbbbbabbbbaabbaaaaaababbabbbaaaabbbbabbaababbbabbababbbbbbbbababbbaaaaaabbbabbabaabababbababbbabbaaaabaabbababbbbababbbbaabaaaababbaaaaaaababaabaaabbababbaababbbbbbbbbbbabbabbbbbbaaabbbabbaababbbbabaabbaabbaabaaabbbaaabbbbbbbbabbaabaaaabbbaaaaaabaabababbbabbabaabbabaabaabaababbabaabbaabbaabbabaaaaaaababaaababbaaaababbbbbaaaabbabbaabbbbbaaaaaabababbabbaabaaaaaaabababaaabbbbbabaaababaabbbbbbbaaaaaaaaaaaaabbbabbbbababbaaabababbaaaabaabbaabbbaaabbaaabaababbbaabaabababbaababaabaaabaaaabbabbabbbababaaabbaaaabaabaabbabababaaaaaabaabbabbbababbbbaaaabbbbabbbaabbabbababbabbaabbbaaabaabbabbaababbaabaaaababaabbaabbaababbabbbbaaaababaabbbbaabbaaaaababbbbbaabaabaaabaaabbabaaaabaabbbaabaaaaabbaaaabaabaabaaabbbabbabbaaaabbbbaaaaaaabbabbbaaaabaaabaabaabbabbaaabaaababbbabbbbabbababaabbbababaaaaaabaaaabaaabbaaaabbaaaaabaabaaabaaaaaabaaaabaaababaabbabbabaabbbaabbaabbbaaabaaaaaabbbbabaaaaabaabbbbbaabbbbaaabbbbbabbaabaaabbbabaaaaabbbabaaabaaabbaabbabbbbabbabaaabbabaaabbbabbbbbbbaaaaabbabbabaaaaaabbaaaaaaabbabaaaabaaabbaaaaabaaaaaababbaabaabbaababbbabbaaababbbbababbaaabbababababbabbabaabbaabbaabbabababbabaabaaababbbaaaaaabbbbbaaaabbbaaaaaaabbbabbbbabaababaabbbaaabbaabbbaabbaaabaababbbaabbabbbabaababaaaabbbbbaaaaaaabababbababbabbaaaaabbbababaabbabbabbbbbbbbabaaaaababaababbaaabbbbbaaabbabaabbbabaabbaaabbabaabbaaabbababaaaabbabbbaaaaabbbbbbbbbbaabaaababbbabbbbbaabaabbbabaabbbbbbbaaaababaabbbbbbabbbabaaaaabbbababbbbabaabaaaaabaaababbaabaaabbbbaaabbabaaaaababbbabababababbaaaaaabaabbbbbbbbababbaaabaabbaabbababbbbbbbaaababbabbbababaaabaabbbbbabababbbbbbaabaaaaabbbaaaaaaabaabaabaabaaabbbbbbaababbbaaaaabbababababbbbababbaabbbabbbabaaabbaaaaaaabbbbaabbaabbbabbababbaabbbabaabaabaabaabaabbbabbaabaabbabbabbaaababbabaaabbbbbabbbaaababaababbbbabbaaabaaabbabbaaaaaabaabbbbbbabbaabbbabbabaabbbaaabbabbabbabaabbaaabbaababababbaaabaaabbabbbbbbaababababaaaabbabaaabaaababbaababbbbaaababbaabbaabaaabbbababbbbbaaababbbabbabbbbababaaaaabbbbabbbbbabbaabbbbaaaaaababbaabbaaaaaaabbbabbaaaabaaaabbabaaabaaaabbabaababbaababbbaabbabbababbaaaaabbbbabbbbaabbbbaabbbbaabbabbbbabbababbabbaaabbaabbabbabaaabbbaabaababbaaaaaabbaabbaaabbbaabbabbbababbbaabbbbbbbaaaabababbabbbbaaabbaaaaaabbaaaaaaabaababbbbbbaaaaaaaaaabaabbbababaaabaabbbaaaabbabaabbabbbbaaaabaabbaaabbabbaabaaaaabbbbbabbabbbbaabaababbabaaaaabbabbbbbbaabaaaaabbabbabaaabbbabbbbaaababbabaaaaabbaaabbbbbbabaaababbabababbbbaaabababbabbbbaabbbbaaaabbbbababbabaaabbbbaaabaaaabaababaaabaabababbaabbbababbabbabbaaabbabbabbaaababaabbababaaabbababaaababbabaaaaabbbaaaabbbaabbbbbaaabbbaaabbabbaaabbaabaaabaabbabbbaabbbabbbababbabbbaabaaaabbaabbbabbbabbbbabbbabbbababaabbabbbaaabbaaababaaabbbbbbaaabbaaabbbaabbbbaabbaaaabaababbbaaabaabbbbababbaaaabbbaabbbbbbbaabababbaabbaaabababbbabbbabbabaabbbaabaabbbbbaabbabbaaabbaaabbbbaaabababbbaaaabbbbbbabbabaabbbaabbabbbabbbbbbabbbbaaabbaaaaabbbbbaaaabbabbabbababababbbabaaaaabababbbbababbaabababaabaabbaaabbbbabababbbabbbbbbaabbaaaababbaaabbbbbbaabbababaabbbabbbabbbbbbbaaaabbaaaaabaabaabbaaabbabbbabababbaababbaabaaaabbbaaabaabaaabbaaabaaabbbbbabbbabbaaaaaabaaabbbaaabaaabbabbbababbabbbabbabbbbaababbbabbbaaaaaabbabaaaaabbbaaaabbaaaabbabababababaaaabbaabaaaaabbaabbbbababaaaabaabbaababbababbbaaabbaaababababaabbaaabaabbaaabbaabaabbbbaabbbbbabbbabaabbbbbaaaabbababbbbaaaabaabbbbbaabbbabbbbaabaabbaaaaaabababbbbaaaaaaabbaaababbbbbbabbaabbbbbbbabbabbbaaaaaabbbbabaaaaababbababaababbbbabbaaababbaabbbbababaaaaaabbababbbababaaaabaaabbabbaaaababaababbbbbabbbabbabbaaabbbaaabbabbbbaabbbabbaaaababbaaabababaababaaabaaaababaabbabbaabaabbabaabbabbbbbbbaaabaabbbbbbaaaabbbaababbbababbabbbabbabaabbabbabbabbbbababbbabababaabaaabaaaabaaabbbbaababbbaaaaabbbabbaaaaaabababababbbbaaaabbbbaaabaabbbbbbbbbababbaabaaaaabbaaababbaaabbbababaabaaaaabbabbaaabbabbbabaababababaaabbabaaabababaaaababbabbababbaaabaabbbbaaababbabbbaababaaaaabbabbabbaababbabaabbbaabaavbbbbbabbaabbabbbaaaaaabbbbaabbbbbaaaabbabbbaababbaabbbbabbaaaabbababbbbbaabbabbbababbabababbbaaaaaabbabbbabbbbbaabaababbabbbaabbbaabbaabbaabbabbbababbbaabaabbaaabbababbaabababaabbbabbbaaaaabbbbbbabaaababbbabbabbbbbaabaababbabbaabbbbbaabbabbbabbbbababbababaababbaabbbabbabbabbabaaaaaabbaaabbabaaabaaaaabbaabbbbaabbbbaaaaaaabaabbbbaabaaabbbaabaabbaababaaabbabaababaabbaaabaabaababababaaabaaabbabbbaaabbaaababbaaaabbbbbbbababbaaaabababaaabbaaababbaaabbabbbababbaabbababbbbbaabbaaaabababaabababbbaababbababababbabbbaabbbbbaaabbabbbbabbabbbbbbbabbabababaaabbaaaabbbabaababaabaaabaababbbabbbbaaabaabaabaabbabbbaaabaaaabaabbbbbbbaaabbbbabbbbbaabbaabbabaaaaaaabbbaabbaabaaababbabababbbaabaaabbaaabbaabaaaaabaabaaabababbaaaaaababaabaaaaabaabbbbabbabbabaaabbaaabbaabaabbbaabbaabaaabbbbbabbaaabbbaaaaaabbbaabaaabbaaaabaabbbabbabbaabaabaabbabaaabaababbbabbbbbaaaaaaaabbbabaabbbabbaabaabbaaabaabbaabaababbbaabbababbaabbaaabababbbbaabbbbaaaabaabbbaaabaabbabaabbabbbbbababbabbabbabbaabaaaaaabbabbaabbaabbaaabbaaaabbaabbabbbbaabababbaabaaaabbaaaabaabbbbbbbbbbaabbbaabaaabaaaabbbabbaababababbababbbababbbabbbababbabbbbbbabaaaabbbbaababababababbaaabaababbbabaaabaaababbbaabbabbbababbbabbbbbabbabbabbabaaaaaabbabaaaaababaaabaaaabbbbaababababbbbbbabaabbbbaaaaabbababaabbabbaababaaabbbbbaabaabbbabbabaabaabbbaabbabaaabbaaabbabbaabaaabaaababbaaaaabbbababaaabaaaabbabababbabbbbbaababbabbbbbbaaabaababbaaabbbbabbbaaaabbbabbbababbaaaaababbbabbabaababbbababaabaabababaabbaaabbabbabaaabbabbaaababbbbaabaabbbabbbbbbabbbaaaaaaabbaabbabaabaaaabbabaaaabaaaaaabaaaabbaaabbababababbabbbaabaabbbaabbbbaaababbabbbbbabbbabbbbbbabbbababbbaaabbbabaabbaaabbabaabbabbaaabbaaaabbbabaababbabbbbabaaaabaababbbbababaabbabbbbaaabaaabbaaabababbabaababaaaababbbbaabbbbbbaabababbbbababbaabbbabbabbbaabaababbaaaabbbabbabbaaababaababbbbababaaaababbaababaababbbabbbbabbabbaabbabaababbababaabbbaaabbbbbababbababbbabbbbbbaaaaabbaaabbbbaabaaaabbbaaabaaaaaaaabaabbbbbaaaabababbbabaaabaaabbbbbbbbbbbaababbbabbbbbbabababaabaabaabbaaaabbbbbbbabbbbbabababbbaaaabbaabbbbabbabbbbababbbbabbabbbaaaaabababababbaabbbbabbbaabaabbaaabbaabbbaabbbabbabbbbaabaaabbabaaabbbbbbaaabaababaabababbabbababbaaabaaabaababaaaababbabaaaabbaababaaababaabbabbbbababaababbbabbbaaaaaabaaaabbabbabaaaababaaabbbbbaabaaaaaabbbaabbbbababaaaaaaabaabbbaaabaaaabaabbbbaaaabbabbabaababbabbbabababbbabaabbabaaaaabbbbbaabaaabbabbababaabbabaabbbababbaabbaabbbbbabbabaabbabaabbbabbaabbaabaaaabbbaabbaaaaabbbbabaaabbaabbbbbbabbaaabbbabbbbaabbbbababaabababbabbabababbbbbaabbabbababbbbbabbbbaaaabbaaabbaaababbbbaaabaaabbabaaaabbaabbaabaabbbaaabbbbbabaaaabbbaabbaabaabbaabbaaaabbaabbbababbbbaabbaaaaaababbbaaabbbabababbaababbabbbbaaabbabbaaabbbbbababaaaabbbbabbbababbaabaaaabbaabbbaaabbbbababbbbbababbbbaaabbbabaaaabababbababaaaaabbabbabaabbbaaabababaaaaabbaaaabbbabbaabbabaaabaabbaabbaaababbbbbaabababbaaabbbaabbbbaababaabbbbaabababbbbbbabaaaaabaaaabbbaabbbbaabbaaabbbbabaaaaabababaabbabbbbbbaaaaabaaabbabbbbbaababbbabaaababbbbbaaabaabbbaabbbababaaaabaabbabaabababaaabbbbbabaaabbabaaabbaaabbbabaaaabababaaaabbabbaabaaababbbbabbbabababbbaabbbbbabbaababbbaaabaaaababaabaabbbbaabbbabbaabbabaaababbbbabbbaaabbaaabbbabbbaaabbaababbbbababaabbbaabababbbabbbbabbbbaabbbabaabababaaabbabbaabbabbabbabbabbaabbbaabbbbbbaabaaababbbabbbababaaaabaaaabaaaabbbabaaaabbbbbabbbbbaabbaabbbabbbaabaabaababbaabaaaaabbabaabaaaaababaaaabbaabaaabaabbaaababaaaaaaabbbabababbbbaaaaaaabbbaabaaaaaabaababababbabaababbbbbaaaaaaaaabbbbababaabaabaabbbbbaaabbbabababbbabaabaaabbaaaabbbabaababbabbbabbabbabbbbabbbabbbbababbbaabbaabbbbbbababbbbabbbbababaaaabbabbababbbbbabaaabbbaaaabbaaabbbbbaabaababaabaabbbbaababbbbaaababbbaabaababaababababbaaabaaabbabbbbaabababaabaabbbbbabbbaaabaabbbbaabbbbabbbababaaaaabaabaaabbabaaabaababaaabbaaababaaabaabbbbbaabaabaabbabaaabbabbbbabbaaabbbbaaaabbaaababbbbaabbbbaabbbaabbabbaabaaabbabbbaaabaabbbababbbbbbbaaabbbbaaabbbaaaaaaabbaabbababaabaaabaabbbaaabbaababaababababbaabbbbbbbaaaaabbbabbaabaaaabbbbababaaabbaaabaababbaaaabbabbbabbbbbaabbbababbababbbaaaaabaaababbbaaabbbaabaaaababbababaabbbababbabbbbbaaabaaaaababbabbbaabaabbbabaabaaababbabababaabaaababababbbbbbaaabbbbbbbaaaaaababbbbabaabababbbaabbbabaaaaabbbabbabbaabbbbbaaaabbbabaaabbbbabaababbbbbbaabbbabbaaaaababbabbbabbbbabbbbaaaabbbbbabaaabbaabaaabaaaaaaaabbbaaabbaaaabbbabbbabbbbbbbbaabbaaabbabbaabbababaababbaabbaaabaabaaaaaabbbaabbbbaababbbbabaababaabbabaaababbaabbbbaababaaababbaaaaabbbaabbbbabaaabbbabbbbaaaababbbaabbaababababababaaabaabbbaabaaaabaaabaabaaabbababbbbaabbbbabbaaaaabbabbbbbbaaaaaababbbbaabbaabbbbabaabaabaaaaabababbababaaaabaaaaabbbaaababbaaaaaabaaaabbbaabbaaababaaabaababbaabbbbabbbbabbbabaabbaabbbababaabbaaabbaaaababbaaaabbbbbaabaaabbbaabbaaabbbabbbabaaaabaaaabaaabbaaaabaabbbbabbbbabbbbbbabaaabaabbbababaaabaabbaababaabbbabbaababaabbbaaaaaaaabaaaababbabbababaabbaaaaaabbabbaaababbabbaaaaababaaababaaaaaaabbbbbbbbbbaaabbaaabbbbabbbbaababbaabbabbbaraabbbbbaabbaaaabaabbaaabbaaabbbbabbabbbbbaaabaaaaabbbbaababbbbababbbbabaababbbababbbabbaaabbbbbaaaaaaabaabaabaabbababaaaababaabaaabbaaaaaaaaabbaaabaabaaaabaaabbbabbaaaababbbbaaabbbbaaabbbbaaabaaabaaaaabaaaabbababbaabbbaaabababaaabbbaabbaabbbbbbaaaabbaaaabbaaababbbbbabbbbbaaaaaabbabbbaaababbbababababaabaabbbababaaabababbabaaaaaaabaabbbabbaaaaaabaaaaaabaababbbaaaaaabbbbabbbbaabbbababaaaaaaaaabaababbbaaaabaabbbbbaaabaababaabaabbbababaaabaababaabbabbabbbaababaaaababaabbbbbabbaabaabababbbbaabbaabaaabaaaabaaabaabbbbaabbaaaababbbabbaabaaabbbbabaaabaabbbbabaabbbbbaabbbbbbbbbabbabbbabaabbababbbbbbbabaaababaabababbaabbbbaaabbbababbaabbbabbaabbbababbaabbbbbaabbbbbaabbababbabbbabaabbaaaaaababbaaaaaaaaabbabbbaababbbbbabbbababaababaaaabbbbbaabaaaabbabbbaaabbaababbababbbababbaaaabababaaabbababaaabbabababbaababaaaaaabbaabbabbaaabbbbaabbaabbbbbababbbaaaaabbabaabbbbbaababbababbababbbbbbbbaabbbaaabbbbabaaaaaaabaababbbbaababbaababbbababaaabaaaabbabaabbbbbbaababbaabbbabbbaabbbabbbbbaabaaaababaaaaaaaabbbaababbabababbaabaababaabaabbabbaabaabaabbababaababbbaababbabbaabababaaababbbbbaabbabbbbbbbaabaaaaabbababbabbabbbbabaababaabaaaaabbbaaababbabbaabaaaabababaaaaabbababaabbabbbbbbbbbbaabaabaabaabababbbbbabababbabaaabaaabbbaababbabbbababbaaaabaabbbbbabbaababaaababbbaabbaabbbaaaaabbaabbbabaabbaabaaaaaababaaabbbbabaabbbbabbbbaabbaaaabbbbbaabbbbababbabaaababaabbbbbbaaaaabaaaabaaaabbabbabbaaaabaaaababbbbaabaabbbaaaabaabbbaaaabbabbaabbbbaabaababbaaabbbabbbababbbbabbabbbbaababbbbbaaaabaaaaabbbabbbbbaababababbabaaaaaabbabbaaabaababbaaababbabababbabbabaabaabbbaabbabbaabbbbbbbababbbabaaabbaaaaabaaababbabaabbababaaaabaabbababaabbbbababbbbaabbabbbbbbabbbbaaabaaababababbaaabaababbbbbbabaaabbbbabbaabbbbabbbbaaabaabaaaaaaaaaaaaaaabbbbaabaabbbaabbbbbbabbbbaaaabbaaaaaabaabaabbababbbbaabbaababbababaaaaabbabbbbaabaaabaababaabbbaabbbbbaaaabaaaabbbaabaaabbaaaabbbbababaaabababaaaaaabbaababbbaabbbabababababbbbbbababaaaababbababababbababbaabaabbababbaaabbbaaabaabaaabaabbbaaabbabaababbbabbaaabaaabbbbabaaababbaaabaababbbbbbbbababbabbbbabababaabaaabaaabbabaabbaabbababbababbbabaaaaababbabaabbbbabaabbabbbababbbaabbbbbbbbabaabaabaaabaaaabbababbbabababaaababbabbaabbaaabbabaaabbbaaaabbabaaababbaaaabbabbaabbbababaaaaababbbbbabbbabbbabaabbbbaaabbabaabaaababbbabababbbabaabaaaaabbabbaabababaaabbbabbabaaaabababbbbaabbaaababaaaabbaabbbbabbaaababaaababaabaaaababaababbbbbbabbabbabbaaabbbabbbaaabaaaabaabbaababbaaaabaabbbbaabbabbbaaabaaaaaabaababbaaaaabaabbbbbaabaaabbbabbbbaabaaabaabaaaabbbaababbaabaaabaaaaaabbabbbabbababbababababbaaaabbbaabbbabbaaaabaabbaabbabbababbbbbabaaabbabbabaaababbaabbabaaaabbaaabbaabaaaabbbaabbbbbbbabbbaabbbabbbabbaaaabbbbbbbbbbabbbabbabaaaaaabaaababbbbabbbbbaaaabbbababbbaaababbbbbbabbababbabbabbbaabbaabaaabbabaabaabaaabbbbbbababbabbbaabbbabaabaabababbababaaaabaabbabbaabbabababbbaaaabbabbbaaabbaabaaaaababaaaabbaababaaabbbaaabababababbbbbaabaabaaabbaaaabbaabaabbbaaabbbaaaabbaabaaaababaabbabbbbbababaabaabbaaaabbbbaaaaabbbbabbbbbaaaababbbbabbaaaaabaabbabaaabaabbbbaaabbabaabaaaabaaaaaaabbabbbbaabaaabaaaaabbbbaabbababaaaabaaababbbbaabaabbbbbaaabababbbbaaaaaabaabbbbbabaabbaaabaaaabbbaabbaaaabbaabbababbababababaabbabbbaabababbaabbaabababaaaaaaabbabbaaaababaabaabbababbabbbbbabbabaaaaaababbabbabababaaaababbbababbabbabbbbaabbbabbbaabbbaaababbbbaabaaababaaabbbbababbaababbaabbaabbabbbbabbbbbabbabbaaabaabbabbaaabaabbaababbbbbabaabbaaabaaababaaaaaaaaaaabaabbaaababbbbbabaaaabbbbababbbaaaabaabbbabbabbaabaababbaabaaabaaaabbaabababaabbbabbabbabbabbaabaababbbbbbabbbabbabbaaababbaaabbbbbbaabbbbbbbbaabaabbbbbaabbbbabaaabaaaaabbbaabbbaaaaabaabbabbbbaaaaaababaaaabbaaaaaabbabbaabbaaabaabababbbbbbbbbbbbbabaaaaabbaabbabbaaabbbabaababbbababbbbbbbabababaabaababbbaabbaabaaaaabbabaaabaaaaabbbbbbbaabaababbbabbbaabaabbbabbbaaaaaababababbaabbbaabbbbbaaaabaabaababababaabababaaaabbbaababaababbbaabaabbbabbbaababaababbbaababaabaabbabbabaaabababbbaababbbabbbababbbaaabbaabaaaabbaababababbbbbbbaaaaabaabbaabaaaaabbbbabbabbbbbbaaaabbaaaabaabaaaabbaaabaabababbababbabbaabbbaaabbabaabbaabbbababbaaabbbaaabaabaaaaaaabbaaabbbbbaabaabaabbaabbaabbaababaabbbaabbbbabbbabbaaabaabbabaabbbbbbabbabababaabaaaaaaaabbaabaaaaaabbaabaabaabaaabbaaaabbbbbbabaaaababbbbabaabbbaabaabbabbaababaabbabaababbbaababaaaabbbbbaababbbaaaabbaababbabbbbaabbaaaababaaaaababaaaababaababbbbbbababbabaabbbaaaabbaaabbabaaaaabaabbaabbbabbbbbababababbbbaabaabbbbaaabaaababaaaabbbababbbbabbabaaabaabbbaabbbbabbaabbaaabbbbbbaaaaaaaabaabababbaaaaaaababbbbbabaabbabbbbbbbbabbbbbaaabbbbbbbbbababbabbaabbbaababaabbbaaaaaabbabbbbbabbbbabaababbaabbabbbbaaabaabaaabaaabaabaabaaababaababbababaabbaaaabbaaaabbaabbaabaaabbbaaaaabbabababbaaaaabbbaaabbabbbbabbabaabbabbbbabbababbbababbbabbaabaabababbbaaabaaaabababbbabbaaaaabbbaababbabbbaabbbabaabbbbaaaabbabbbbbabbbabaabbabbbaabbaabaabbabbabababbabaaaaaabaaabbaabbbbbbaabbbaaaaaaaabaabbababbabbbaabaaaaabbaaabaababaabbaaaaaabaabbabbbababbbabaabbaababaaaabbabbababababbababbabaaaaaababaaaabaabaaabbabaaaababbbabbaabbabaaabbaabaaaababbbaababbababaaaaaaababbbbaabbaaaababaabaabbabbababaabbbabbaababbababbabbbbababaaaabbbababaabbaababbbabbababaaaaabbbbbbabbaaabababbbbbabaabbaaaaababababbaaaabbaabaabababbbbaabbaaaaaababbbabaabbbaaabbbaaabaaabaaaababbbabbbbbbbbbbbbaabaabbbbabaabaaabbbabbbbaaabababbbbbbbabbaaabbbbabbbbabbabaaaababbaaaaabbbaaabbbabbbbbabbaaaaabaaaabbaabbaabababbaaabbaaaababbabbaaabaabaabaabbbbbbbabababaabbbaabbbbbaaabbabaabbaaaabbbbbbbaaaaaaabbabbbbaaabaabaaaababaabbaabbbbaabaabaaabaaaabbbaabaaaaaabbbaaaaaaabbabaabababababbabbbaaaabaaaabbbaabbabbbbbabbbabbbaababababbaaaaaaaabbabababbbbabbbaaaabbaabaabababbbbbaabbbaabbbbabaaabbababbaaaabbbabbbabaaabbbbbaabbbaabaaabaababaaabaabbaaaaaabaaabbbbbabbbbbbabbbbaaabaaaaaabababaabababbbbbabaabbaaaaabbaabaabbbababbaabaabbabbbabbaaaaabbaaabbaabbbabaababbbabbaaababbbbbabbbaabbbaabbbaaaabaababbabbabaabababbbbabbbbaabababbabaabbbbaaababaaaabbaaabbbbaabbaababbababaaaaabbbabbbabaaabbaaabbaabbaabbaaabbbabbabbbabaabaabbbabbaaabbbbbbbbababaaaabababababbbabbabbabbabbaaaaaabbababaaaaaaaabbabbbbbbabbbbabaabbabaabaaabbbaaabbabaaaabababaabaaabbbaabbbbbabaabaababaabaabbbabaabbbbbbbabbbabbbbbbbbbaabababababbaaaaaaabbbababaaababbaaabbabaaababbbabababbaababbbaabbabaabbaabbaabaaabbbaaababaaabababababbbbaaabbbbabbaabaabbbbbbabbabaabbbbaabbbaaaabbabbbabbbaababbaabbabbbababbbabbabbababaabbbbbbbabaaabbbaabbaabaaabbbababbaaaaababaabaabababaaaaaaabbabaaaababbabbabaaabaaaaabaabbaaabbaabbbabbbbabbababbbabaaabbaabbabbabbbaaabaaaabaababbbbabaabaabaabaaaababbbaaabaaaaabbbbbabaaaaabbbaaaaabaabbabbaabaaaaaaabaaaababbbaaabbabbaabbbbbabaabbbbbaababababaaabaabbbbaabbbbabaabbbbbaabababbbbaaabbbabaaaaabababababbbabbbbabbbbbabaaaaaabbbbabaaabaababbbbaabbabaaaaabbbbbabababbabbaaababbbbabaabbaabaaabbabbbbaabaaabbaabaaabaabbabbbabaabaaabbbabbbaaaaaabbbabababbbaaababbbbabbabbbabaabaaaaaababbbaabbaabbaaaaababaabbbaaabbbbaabbaaaaaaabbabbbbaabaaabbababbabbaaabaaabbbbbbbaaaabbabaabababbabbabbabbbbbababbabbbbabbbbababbababbabbababaabbabababbaababbbbabbbaaaabaaaaabbaaaabbbabbbabbbabbbbbaaabaaaaaabbabbbbaaababbbabbbababbbbbbbbbabaabbaabbaaaabaabbababbbbbaaaabbabbbaabaabbababababbaaaaabaaabbbbababbabbbaaabbaabaabbbaaaabbbbbbbaaabbabbbabaaabbbaabaaabaaaabbbbbbabbbabaababbbabbaabbaabbbbbaababbbbabaabbbaaaabbbabbabbababbabaabaabbbaabbaabaabaabbaabbbaaaabbaaaaaabaaabbaaaabaabbabaaaabbbababaabbbababbabaaababbaaaabbbbabaaabbabababbaababababbababbbbabbbbaaaabbbabbbbaabaabaababbbbabababbbbaaabbabaaabaabbaaaaabaaaabbbbbaabaaabbaabbbbaaaabaababbbababbbabbbaabbbbabaaaaabbbaaaaabbbbbbbabbaabaaaababbbbabaaabbabbabaabaaabaaaaaabaaabbbabaaabaaabaaabaaaabababbabbbbaaababaaababaaabaaabaabaababbbaabaababbaaabbaaababaaabbabaabaabbbabbbabaabbaaaaaabaaaabbbaababababaaaababbbaabbaabbabaaaaaaabaaaabaabababbbbbbabbababbabbbbbbbbbbbbaaaaabbabaabaaaaaabaaabbbabababbbabbabbbbabbbaababbbbababbbaaaaaaaabaababaabaabababaaababbbababaabbbbaaabbaabaabbbaaaaabbbabbbbaaabaaaabaaaaabbbabbababbbabbabaaabaabaaaababbabaaabbaababaabbaaabaaabbaabbabaabbbaaaababbbabaabbaababbbbababaabbababababbbaababaaabaaaabaababbbaabbbaaaabababbbabaababaaabaabbaababbabaaabbaababbbaabbbaababbababbbabbabbaaaaaaaaabbbbbaaaaaababaabaabbbbaabaabbbabaaabababaaabbabaaaaaaabbabbaaaabbbbaaaabbabababbbbbabbaabbaabaababbbaaaaaababbbaaabaabaaaabbbbaabbbbbababbaaabaaababbabbaabbaabbbaaaaabaababbabbaababaaabaaaaaabbbbbbbbaabbbaabbaabaabaabbaaaaaaabaaaaabaaababbbaaaabaabbbbabbbabaaaaaabbaaababbabbaabbbbabbbababaabbaabbbbaabbabaabbbabbbbaababbabbbaaababbbababbbbabbabbaaabaababbaabbbaaabbbbabbbbbababbbabbabbabbbbaabbbaaababbaaababbbabaabbbbbbbaaaaabbabababbbbbbbbbaabbaaabbbbbaababaababbbaabbaabbbaabaaabbaabbbbaabbbabababbabbabaabbaababaaababaaaabbabaabababbaaaaaaaaabbbbaaaababaabababaabbbabbaababbbbbabbbbbbabaaabbbabbbabbababbabbbaabaabaaaababbaaabaababaabbaabbabbaaaabbbabaabbbbbbbabbaaabbbbbaaabaabbaaababbbbaaaaaaabbaaabbbbaaaaaabbbbbaaaaabbabbaabbbbabaaaabbabbababbaabaabbaaabbbaabbabaabbaaaaabaabbaaaabaaaaabbaababbababbabababbaabbaaaababababbaabababaaaabababbaabbaabaaabbaaabaaaaaaabbaaabbabbbbbaabaabaabbbbbbbbbaaababbabbbababbbaabbabaabbbabbbbaaabaaabbabbaabaaaaabaaaaaaaaabbbbabaaababababaaaaaaabbbbbbbbabbaabaabaababbbabaaaaabaaababbbaaaaabababbbbbbababbbabbbaabbaabbabaabababbabbabaaabbaabbaaaabbbabbabbbbaaabbbbaababbbbabbbbbbabaabaabaaababbbbbabbabbaaaabbbabbbbbababbabbaabbbababaabababbbaabaababbbbabbbbabaababababaaaaaabbaaaabbbbabbababbbbbabababaaabbabaaaaabbbbaaabaaaaaaabbbbaaababbbbaabbabaabbabbabbabababbbbbbbabbabbbabbbbbaaaaabbbabaaaabaababaaaaababaaaaaaabaaaabbabbababaabaabbbaabababbaabaaabaaaababbbbbababbbabbbbbaaaabbbabbbaabbbabbbabbbbabaabbbbbbbabbabaaababbaaabbbaabaabbabbabaaababaabababbabbbaabaabaaaabbabbbaabbababbaabaababaaabababaabbbababaababbaabbbaaabbbbaaabbaaaaaabbbbbbaaababbbbaabaaabbbaaaabbbaababbbbbbbaaaaabbbaabbabaaaabaaaabaababbabbaababababbbaabbaaabbabababbabaaabaabbbaabbbbabaaaaabbaabbabbaabaabababaabaaabbbbaaaaaababbbbbbaaaabaabbaabaabababaabbbbbabbbbaabbbbbbaabaabbbabbaabbabbbbbaaababbabbaabbbbaabbbabaabbabbbaaabbaaaabaaaaaaaabbbbbbbaaabbabaababbbababaabbbabbaaabaabbbabbababbbaabbbaabbaabbbabaaabbbababbaababaaababaaababbbababaabbaaabbaabbaabaabbabababaaaaaaababaaaaaabbababbaaabbbbabbabbabbbabbaaaaabbbaaabaabbababbbaaaaaaaaabaabaabbbbabaaabbabaaabaaabaaaaaabbbbbaababbabbaaaaaabbbabbabbbaaabaabbbbabbbaaaaabbaababbbaabbaaaaaababbabbababbbaaaababbababbbbabaabbbaababbbbbaaabbbbbabaababbabaabbabbabaababaaaaaaaabaabaaabaaabbbabaaaabaaaabaaaabaabbbabbabbbbbaaababaabbabaabbbaaaabaabaabaabaabbbbfbababaabbbbaabbaabaabbaaabbbababbbbaaaababbbabbabbbbabbaabbabaaabbbbabbbaaaabbaabaabbabbbbbabbabbbbbaaaabbaababbabbababbbaabbaaabbaaaaaaaabbbbbbbabababbbabbbaaaabbbaabbbbabbbbabbaaaabbbbbabaaaaababaababaaaaaaaabaabbaaabbbaaaabaaabbbaabaabbabaabbabbbabababababbbabaabbaabbaaaababbbbbbaabbabbbababaaabbbbbabbaabbbaaaaabbbbbaabbbbabbbababbbbbbabbaaabbaaabaabbabbbaabbbaaababbbaabbababaaaabbaabaaaaaaaababaaabaabbabbaaaaaababaaabbaababbabaaaaaaaabaaaaabbaababbbaaaaaaabaabaabbbaabbaababbbaabaaaabbabbbbbbaaaaababbbabbaaababaaabaaaabbabbaaaabaaabbbbbbbbbbaabbaabababbabbbbbbabbbaaaabbababbabbbaabaaababbabbbabbbabbbbabbbababbaaabbbbaaaabbababbabaababbbbaabbbaaaaaaaaabaaaababbbababbabababaabbbbbbabbbabaaabaabaaaaabbbbbabbaaabbbbabbaabbababababbbabaaababbabaababaabaabaaabbbbbaaabbababaaabaaaabbaabbaaaaabbbaaabaabbaabbaaaaaabaabbbabbbababbbbbabbabbabbbbbaaabbbabbbabbaaabbabbabaabaababaabbbbbbbbbaaaababbbaabbbbbabaaabbbabaabbbaabaabbbaabbbaabbbbabababbaaababbbaabbababbaaabbbabababbababaaababaaaaaabbaabbaababbabaabbabaabaaaaabaabbabbbaaabaaabaababbbbababababbbaaabbbaaabbabababbbabbbaabbaaaaaabaababbabbbbaaabbbaabbaababababbabbaaaaabbaaaaabbabbbbbbaaaabbaaaaababbbbabababbbabbbaaaabaabbbbbbabbbbaaaabaabbaabbbaababaabaaaaabbbaaabaaabbbbbaaaaaaaaabbbaabbbaaaababbbbaaaaababbbabababbbbbbabbabbbbaaaaabababbabbaabbbabaabbbabaabbababaabbaabbaaaaabbbbabbaabaabbbaaaababababbabbaabbabbabbbababaabbbbbaabbaaaabababbabbbbbbbaabaaababbabbaababbababbbaaaaaabbababbbbbaababaabbbaabaabaaaabbbabbaabbaabbbbabaababaaababbbaababbabbaaabaababbbabbbbbaabaaaaababaaabababaabbbbabbababbababbaabaaabbbbbbbabaabaaabaaabababbababababbabbaabaabbbabbbbabababaabbbabbabbbababbaaabaababbbababbbbbabbabbbbabaaabaaabbabaababaababbabbbaaaaaabbbaaabbbaabbaabbabbaabababbbaaabaaaaaaababbbaaaaaabaaaaaaabbabbaaababbbbababaaaabbaabaababbabaabababbbbbabbbaabbaaaabababbaabbbaababaabaaabbbababbabbbababbbaaaaaaababbbaabbaaaaaabbbabbbbbabbabbbbbabbabbaababbbaabbabaaaaabbaabaaababbbbabaaaabaabaaabbabbbabbaaabaabbbbbababbbaabbbaabbbbaabpaaaabbbaabbababababbbaabbbbabbbbbaaaabaaaaababaababbbbbbbabaaabaaaaabbababaaababbabaaaaaababbabbabbbabbbbaababbaaabaababbbaabbabbbababababbaabbaabbaaabbaaaaabbbaaaaaabbabbbabaabaaaaababababaaababaabbbaabaabbbbbbabbababbbbaabbabbbabbabaaabbbbbbaaaaaaabbbbaaabababbbaaaabbbaaaababbbaaaabaabbbbabbbbbbaaaaababaaaabaabbbaaaabaaaabbabbbabbaaaabaabaabababbbbbbbbbaaabaaabbbaabaabbaaabbaaaabbbbaababbbabaabbbbbaaabbbaabbbabbbaaaabbbababbaababbbbabbbbbbbabbaaaaaaaaabbabbabbbabbaababaaabaaaaaabbbbbbabaaaaaaaaabaabbaabaaaabbabbbbbbaabaabbaabaababbaababaabbbabaaaaaababaabaabaabbbbbbbabaaabbabbbaababbbaabaaaababbabaabbbbababbaaabbabbabbbbabbbbbabaaabbbbbabbaabababbbabbaaababbabbbaabbabbbabbbbbbbbbbabaabbbbabbbaaaaaaaabbabbbaabbbbbbbabbbbabbaabaaabababaabababaaabababbbbbaaabbbbbbaabbabbbbabbaaabbbababababbaabaaaaaabbabababbabaaabababbbbaabbbbababbbbabbabaaaabaaaaaaabababaaabbabaabbbbbbbabaaabbabaaabbabbbbbabbaabababbbbabbbabbbabbaababababbaaabbbababababaabbabaaaabaaaaabaabaabbaaabbabbbabababbaabbbbaaabaaaabaaaabbbbbbaabbaabbbabaabbabbbaabaabbbbaabaaabbaaababbabbabbabababaaabaaabbbababbaabbababbaababaaaabbaaaaabbaabaaabbababbabababbaaaabaaaabbbbbbaaaabaabbbabbabbabaaaaaababbaaaaaababbabbbabaaaabbabaaabbbbaabbbbaaabaababaabbaabaaabbabbbaabababbabaabbabbabbabaaabaabbabaabbabaabbbaabaaabbababbabaabbaaaaaabaabbbbaaabababbbbabbaaaaabbbaabababaaabbaabbaaaaababbbbabbaabaababaabaabbaababbbbbaabbbbaaaaaabaababbbbbaaabaabbbaaabbbaaabaabbbaabbabbaaaaaaaaaababbbabbbbabaabaababaaaababaaaaaababaaabbbabbaabaababbaabbbabbaaaaababbbababbbbabbababaaaaabbabaabbabbbabbabaabbabbbababbbbbaabaaabbaabbbabbbabbaaabaaababbbaababaaabababbbbaaabbabbababbbaaaaababaaababbbbaaabaabaabbabaababbbbbaababbbbbabababbbbaabaababaaabaababbbaabbbabbaaaaaaaabbabaabababbaababbaaaaabaaabbababaaaaabbbabbabaaaababbbbbababbaaaabbbbaaababbaaabbababaabaabababbbbbabbbabaaaabaabbababbabaabaaabbabababaabbabbaababbaabbbbbaabaaaaaababbbaabbabaabbbbaaaabaabaaababaabbabbbabababaabbabaaabababbbabbbababbabaaaaabbabbbbabaaaabbbbabbbbaaaabaababaababaabbbbababbbbaababbababbabaaabbaabaabaabbbababaabaaaaabaabaababbbaabaaaababbabbbbbbbabbaababbaabaaababbbbbabbbbaababbbabbbabababaabaabbbbbaabbabbbbbbabaabbbaaaaabbbbabaabbabaaaaabaaaaaaaaaababbbaabbabbbabaaabbbbbbbabbbbbabbaabaabbbbaaaabbaaaabbabbaaabbaaababbbbaabaaabbaabbbabbbabbbababbaabbaaabaaaaabbaabaabaabbbbabbababbbbaaaaabbaaaababbaaabbaaaabbbbbbaaabbaabbbaaababaabaabbaaabbbabbababbbaabbababbbaabaabbaabaaaaabbbbaaaaabbbaabbbbaabbabbbbbaaaaaabaaabababaaaabbbaaababbbbbaabaabaabbababaaaaabbaabbbbabaaaaabababaababbabbbaababbaabaaababaaabababbbababababbbababbbaaaabaaaaaaaaaabaababaaabbbbaabaaaabaabbabbaaababbabbbabaabbaabaababbbabbbbbbbbbabaaaabbabbabbbbabaaaaaaaaaabbbbaaaabbabaaababababbaabbababbbaaabbbbaaabbbaaabbaabbabaababaabbbaaaababaaaaabababbabaaababbaabbabbbbbbbaababbaabbbaabaabbbaabbbbbbabbaabaaabbbbbbaaabaabbbbbababbbbbbaabbbaaaaaabbaabbbabbababbaabaaaaaabbabaaaababbbbbaabbbbaaaaaabbaabbaaaabbababaaaaaaabbaaabaababbbaaabbaaaaaabbbabaabaaaaaabbbbabaabbabababaabbababbabbaabaaaabbbabbbaabbaabbaabaabbbbbabbbabbbaaababaaabbbbaabaaaababbbbaabbbabbbaabaabaabbbabbaaaaaabaaabbbbbabbababaaababbbbbababbaababbaabbbbbbaaaabababbbabbbaabaababaaabbbaaaaabbbabbaaabbaabbbabbaababbbaabbabbbbbbbbabaaaabbabbbaabaabbbbaaabbaaaaaaabbaabbbbaababbbabbbbababaaabaabbbbaabbbbaabbabaabbbbaababbbaabababbbaaabbabaaaabbbbbbababbbbbbbaaaaaabbbaaababbabbbbbbbaabaabbbaaabbabbbababaaabbbbbaabbaaaaabbabaabababbabbbbaababbbaabbbabaaaabbabbababaaaabaaababbabaaabaaabbbbaabbaabaaaabaabaaaaabaaabbbababbaabbbabaaababaababbbababababaaabbabaabbaaababbbbabaaaaaaababbbbaabaabbbababaaabaababbabbbaaaabaaaabaaabbabbaabbbaabbaaaabaabbbbbaabababaaabbabaaabbbabaaaaaababbbaabbaaaabaabaabbbaaabaabbababbaaaabbbbbbbbaaaabbbaabaaabbaaabbbaaabbaabbbabaaaabababaaabaaaaaaababbaaaaabbaababaabaaaabbaabaabaaababababbaaaababbbbababbbabaaaaaabbaaabbbaababaaabaabaabaaaabbbbaaaaaabaabaaabaabaabbbbbaaaabaaaabaaabbabbbaabaabbbbbabbbaabbbbbababaabaabbbbabbbabbabbaaaabaabaababbbbbabbbaabbbabbbbabaaaabbbaabbabaaaaaaababbbaaaabbabbbbabbbbaaaababbbabbabbaabbbbbaaaababaaabaaaabbbbbbabbaabababaaabaaababbbbababaababbbabaabbaaabbbaaabaabaaaabbaabbaaabbbabbaabbbbaaaabbbbabaabbbabbaaaabaababbababbbaaabaabbbabababaabaabbbbbbabbbababaabbaaabbbbbbabbabbaaaaabbababaaabbaabbababaaaaaabababbbbabbbbabaaaaabaabbaabbabbbabbbbbabbbbbbbaaaaabbaabaaababbbabbbbbbbababababaababaabaaaabbbabbbabbbabbbbaabbabbaaaabaaababaaababbaabbaabaaabbaaabbbabbaaababaabbbababbaabbbbaabbbababbbaabaabaaaabaaaabbbbaaababbbbbabbbaaabbabbabbababaaabaaaabbbbaaabbbaabbabbabbbbbbaabbababbaaaababababbbaaabbababbababbababaaabababbaaaaabbabbbaaabbbabbbabaabbaaabbaaaabaababaaabbbbaabbaaaaaaaaabaaabaaaabababbbaabbabbabbbaaabbabbbaababaaaaaaabbaaaabbabbbabbabbbaaabbaaabababaaaaaabbaabbbbbbaababaabbbababbabbbaabaabaababbaaabaabaaaabbabaabbbabaabbababbbaabbbbaabaaabaaaabbaababaababbbbababaaabaabbabaaabbaaabaabbbbbbabbaabbaabaabaaabbaaabbbbaabbbbaaaaabaaaaaababaaaaabbbbaabbaababaabbabbbabbbaabababbababbabaababaabbaabbbbaabaabbabbaabbbbababaaaabababbbabbbabaabbababbaabaabbabbabaaaabbbbaabbbabbabaabbbbaabaabbaababababbbbaabaaabbbaabaabaabbbbbbaaabbaabbbbaabaaabbaabaababbbaaaabaabbbbabbaaabbbabbbabbbaabaabbaabbaabbabbabbbbbbabbaabaaaaabbabaaababaaabaabbaabbabbaababbbaababbaaaaababababaabaaabbbaabbabababbabbbaababbbaabaababbabbabbbbabbbabaaaaaaaabbbabbbabbaabbaabbabbbaaaababababbbbaabbaaabbbbbaabaaaabbabaaabbababaaabaaababaabbbbaabaabbabaaaaaaabbaaaabbbababaabbbaaabaabababbaaaaababbaaaaaaabbaaaabababaabababbaaabbbabaabbaaaaabbbaaaaabaaaabaabababbababbabaabaabbabaabaaaababbbbaaaaaaaaabababaaabbaabbbbabbbabaaaabbbbababbbaaaababbbbabababbabbbbbbbbbbaaabaaabbbbabbbabbabbbbabaaaaaabaababaaabaaabaabbabbbaabbabbbaabbbbaaaabbabababbbbababbaabbabbababbaabaababaaaabbaaabbbbaaabbbbaababbbbabbaababbbbaaaabaaaababaabbaabbabaabbabaababbbbbbabbababbabbbabbabbbabbbababaababbabbaabaaabbabababaaabbbaabbbbaabaababaabababbaaababaaababaabbababbababbbbababaaabbaabaaabababbabbaaabbbbbbabbabaaaabaabaabaaaabaaaabbaabaababababbaaabbbbbbbabbaabbbbaaababbbbaaabaaabababbbabbaaabbbbbbbbaaaaabaabbbaaabbaabaaabbbbaabababbbaaaabaabaaaaaaaabbbaabaaabbbaaaaaabbabbbaaabbbbabababaaabababbbbbabaaaabbbabaaaaaababbbbabbbbaababbaabbbbbbbaabbbbbaaababaaaaaababbbabbaaabbbabbbbbbbabaaabbabaabbbaaaabbaaaababbababababaabababaabbbaaabaabaaabbbbbaaaaabaaaaaaabaabbbbbabaabbaabbabbabaaabbaaababbabbbaabbbabbaababbbbabbaabaabbaaaabbbaababaaabaaaabaaabaababbbbababbbbaaabaababbbbbababaabbabbbaaaabbaaabbabbaabbaaabaaabbbaabababbaaabababbbaaabbaabbbbbabaaabbaababababbabbbaaabbbaabaabbabaaaaabbaabaaabaabababbaaaabbbbbabaaabbbabbbababababaaabaaaaabbaabaaaaabbbababbbbbbbbbbababbbbabbbbbbabbbbbabaabbabbaabaabbabbbbbababbbabbbbbbaaabbbaabbabbabaabaaaaababaabaaabbabbaabaabbabbbbabaababaababbaababbaabbbbbbaabbbababbbbaabaaabbbbbabaaababaabbabababbbababaabbbbbaababaabbbabbbbbbbababaabaabbbbabbbabbaabaaabaabaaabbaaabbbabababaaaaababbaaaaaabbaaaaaabbbabaabbaaabaababaaaaaaabaabbaabbbaabbbabbaaaabababbabbbbabbaaaaaabbaaaaaabbbbaabaaabaababbbaaabbaaabbbaabaabbbbaaaaabbababbbbbabbaaababababaaaaababbaaaaaabbaabaababaaaaabbabaabaabaaabaabbababbabbbabaababaaabbbbbbbaaabbabbbbbabbaaabaaabbbbbbbaabaaaabbbabbabaabbbatabbbabaaaaabaabaabaabbabbbbbaababaabbaabbaaabaabbaabaaabaabbbbbbaababaaabbbbbbbaababbbbbabbbaaabaabbbbabbabbababbbbbaaaaabaabaabbbaaaabbaaabaabbaabababbaaabaababaabaabaabaabbbbbaabbbaaaabbabaabbabbbbbbaaaaaabbabaabababababbbabbbbbbbbabaaabbbbaabbabaabaaabbaaaaabbaabbbbbaaabaaabbaaaabbabaaabaabbbabaabaaabaaaabaababaabbababaababbbbababaaaabbaabbabababbbabaabbbbaababaabbabbaaaaaaabababaabbabaabbaabababbbbaaabbbabaaabbbbbaababaaaaaabbbabbabbbaaabbbabaabbaabbbaabababbbaabaababbabababababbbaaaabbbaaaababbbaabbbbaaaaaaabaababbabaabbabbaababbbaaaaaaabbbabaaaaaabaaababaababbababaaabbbaabbababaaabbbaaabbabbbaabaabababbabaaabbabaabbbaabaaaaaabbababbbbabaabbbabbaabbbabbbabbabbbabbababababaabbbbaaababaaabaabbbbabaaaaaaabbabbaabbbaaaabbbbaaabbbbababababaabaaabbabbbabbbbaaabaabbababbabbababaababbbbbaaabbabbbbbbaabaaabbaaabbbababbaaaaabaaabaabbababbbbbaabbabaaaababaabaaabaabbbabbabbbbabaabbbbbbbbbbbaabaabbbbbbabaaaabaaaabbbbababaababbbabbbbabbbbabbaababaaaababaaabbabbabbbbbabaaaaabaaabaababbbabbabaabaabbababaababbbbaaabbbabbaaababaaaabbaaaaaababaabbaabbaabbaababbabbaaaabbbbbbbbabbbbabbaaaabbaabbbbaababbbbbaabbbbbbbaaaaabaabbaabbbabbababaabaaaaaaaaabbbaaaabababaaabbbbabbabbbabaaaaaabbbbaabbabaaababaabaabbababaabaaababbbbbaaabababbbabbbbbaabbabbbbaababbbbabbbaabaabbaabaabbababbbbaababbbbaaabbababbaabbababbabaabbabbabbbabbabbbbbbaabbbabbaabaabababaabbaabaaabbababaabbabaabbbbaaaabbaaabbbbaabbabbbaaabbbaabbabaaababbabaabaababbaabbbbbbbabaaabaaabbbbbaabbabbabbbbbbbaaababbaabaababbaabaabaababaaabaaaababbaaabaabaaaabaabbaabbabbbabbaabbbbaabbabbbbaabbabaaaaabaabbaabbabaaababaababaabaaabbbaaababbababaaaabaaababaaabbaabaabaababbbaababbabaaababababbabaababbaaababbbbabbababbbaabaabbbbaabbbababbbaaababbbaababababbbaabaabaaaaabababbbabbbbbabbaaabaaaabaaaabababbbbaabaaaabbaabaababbbabbbaabbaababbabbbbabbabbbbbbabaabbabbabbabbabbbbaababbbabbababababbabbbaaabbbbabaabbaabaaabbabbabbbababaabaaaabbbababbbbbbbbaabbaabaaaaaabbaababaaabbbbbbaaabbabbaaabbbbbbbbaaaaaabaaaabbababaababbabaabbabbabbaaabbabbbbabbababaaaaaaabbbbbbaabaaaaaabbabbababaaaababaaabaaaabbbbaaabaabbbabbbabbabbaabaaabababaaabbabbbabaaabbabbaabbabaaaabbbbababbabaaaabaaaaababbaabbabaabaabbbabbabbabaababaabbbbbabaaaaababbabbababbababbaabbababababaabbbabbbaaaabbaaabaababaababbbababbabaabbbbbaabbabbababbbbaaabbabbaaaababbbabbabaabababaaabaaabbabaabababababaaaababbaaaaababaaaabbabbbbaaabbabbaaabbbbaababaabaaabbbabbbababbbaaaaabbbbabbbaaaabaabaaaaabbbbbaabbbabbbbabbabbabbbabbabaabbaabbabbbbabbaaabaaabaaaababbaabbbaaaaabbbbbaaabaaabbabaaabbaaabbbbabbbbabbaaabbabbbabaaabababbbabaaabababbabbabbbbaabaabbbaabbabaabbababababbaabaabbaaaaaaabbaaaababbbbaaabbbbabbbababaaabbababababaaabbbbababbabbaabaaaababababaaaaaaabbbbbaaaabababbaaabbbaaaaabababaabbaababbaabbbbbaabbaababbaabaabaaaabbababbaaaaabbbababaabaaaabbbbbaaaaabbaaaaaababbbbaaabaabbaabbaaaaaaaaaababaabbababbbabbabaaabaababaaaaaaaabbbbbbbbabbababaaabababbaabbababbababbabbabbaababbaabbbabbbbababbabbaaaababbaaaababbbaaaaabbbabbababbbabbaaabbbbababbbabbaaabbbabbbbaabaabbbbabbababbbbbbababbaabbbabaaabbbaaababaaababbaaaababbaaaaabbabbabbbaabbbbbbbbaabbabaabaaabaaaaaabbbabaabaaababaabababaaaaaabaaaababbbbaaabaababbbbbaaaaaaabbbbbabbaabbaaabbbababababbababbbbbabababbbbbbbbaaabaabaaabaabaaaabbbbaaababbaaabaabaaaaabbababaabbabababaaaaaaababaababbbbabaabbaabbabbbbbbbbabbaabbbbbabbaabbabbaababbbbbbabababaabababaabbbbaaaaaaaaabbbaabbbabbbabbbbbabbaabbbaabaabaabbababaaabbabbbaaabaaababababaabbbabababbaaababaababbaaabababaaaabaaaababbabbbaabbabaababbbabbbabababbbabaabbbaabaaaaabaabbabbaabbbaaaaabbbaabbaabbaabbaabbaababbabbbbbbaabbbaaaabababbabababaaabaaaaababaaabaabbbabaaaaaaabbabbbabaaaabbbaabbbbbababbabababaabbbaaabaabaaaabababaaabaaaababbbaaaabbbaabbabbaaaababbbaaaaababbaababbbbbbaabbaaabababaaaababbaabababbbaaaaababbaabaaaabbaaaaabaaabbabaabaaaaaabbbbbabaabbbbbbaabababaabbaaabbaababbabbabbbaabaaabbbbabbbbabbaabbbbabbaaababbbaababaabaababaaaabbbbbaababbbbbaaabbaaababbaababbabaabbbbbbababbbbaabbbbbaaaabaabbababaaaaabbbbababbaaaabbaababaabbabbabaaaabaabababbaababbbbbaaaabbbabaabaabbabbbbaabbbaabbabbbbbbbaaabaaabbbbabbaabaaaabbbaababaabaaabaaabaabbbabbaaaabaabbbbaaabbabaaaababbbababaabbbabbbaababbaabaaabbaabbaaaabbbbabbbbaaababaaababbbbaaababaabaababababbaabbaaabababaaabbaababaaabbbaaaaabbaababaaabaaabbbaaaaabbbaaaabaababaaabababaabaabbbbaabbbbbbbbbabbaabbabaabbbabababbbabbbbababbabbbaaabbabaaaabaaaabbbaabababbaabaabaababbaaaaaababbabbaaaaaabbabbbbbbbabbabaaabbabbabbbbaabbabbabaababbabbbbbbbabaabbbbbabaaaabaaabaabaaabbaabbbabbbaababbababaabbbbaabbbbbbbbabababbbabbaabaababababaaabbabbababaaaaaabbaaabaaabaababaaabbaaabbbabbabaaaaabbabaaabaabbbbabbbabbbbabbabbbbaabbbaabbabbaababaaaaabbbbaaabaaaaaabbbbabbbaababbbbaabaabbaaaababbaaabbbbabbaabbbbabbabbbbbabaaaabbbbaabbabbbbaabbbbbabaabbbabaabbbabbaaaaabbaaaaaabaabaaabaabbaaabbaabbabbbbabbbabbbabaaaabbaaaababbbabaaaabababbbbaabbbbaabbaaaaaaabaabababbabbabbaaabbaaabbaaabbabaaaabaaabbababbbabbaaabbaabaaabbaabbabbabbbabbaaabbaababaaabaaabbbbbbbabbaabbaaabbabbaabbabaababbabbbbbabbbbabaaaaabbaabaaababaabaaababbaaaaabbabbbbabbbaabaaababaaabaaabaaabbaabaaaaababbaaabbbbbabbbbaaabbaababaabbaaabbbabbbbababbaabbaaaaaabbbabaabbbbababbaababbbabbaabaabbbabababbbbbbabaaabbabbaaabbabaabaaababaaabbaaaaaabbabaabaaabbbaabbabaaaabaaaaaabaabaaabaaabbbbaabbabbbaababbaaabbbabbbbaabbabbaaabbabaabbaabbaabaaababbaaabaabaabababbbbabaaaaabaabaabbbabbabbabbaaaabbababbaabaaabbaabbbaabbabbbabbaabaaababababbaaababbbaaaaababbbabbbaaabbaabaaabaabbbabbaaaaaabbbbbbbaababaaaabaaababbbbbbbababaabbababbabbbababbbbaaaababaabababbbaaababbaaaaababababbbbabbabbbbbbbaaabababbaaaababbababbbababbababaabaabaaaaababaababbaaaaaaababaaaaaababaabaaaabbbbabbbbbabbaaaabbaababaaabbaabbaaabbbbbaabbabbbbabaabbbaaabaabaaabbabbaaababbbabbbaabaababaabaabbbabaabbbabbabbabbbbabbaaaaabbbabaabbbabbabbababaabaabbaabababbabbaaaabbbbbbbbabaabbaabbabbbbbbabaabaaababbbbaaabbaaaaaabbabaaaaabaabaabaababbbbaaaabaaaabbabaabbbbabaaababbbabbabbabbbbabbbbaaaabaaaabaabbababbabaababababaabbaaabbbabbbbaabaabababbaaaaabaaabbaaaababbabababbbabbaaaabbbababbbaabaabaaabaabbabaaaaaabbabbbaaaabbbabbaababbbbabbaaabaabaaababbbaaaabbaaabaabbbbbabbabbaaabbaaaabbbbbbbbaabaababbaaabababaaaababbabbaabbbaabbbaaabababaabbababbbabbbbbbabbabaabaababbabbabaabbbbbabbbbaabbbaaaaabbabbbaaababbaababaaabbaabaabaabbabbbaabaabaaaaabaaabaaabababaababaabaabaaabbaabbabbbaaaaaabababbbbaabbbbababbbaabbbbabaabbbababbabbabbbbbabaababababbaabababbbaaaabbbbaabaabaaababaabaaabaabaabbabbbbbbbbbababbbabbabbaabbaaaabbbabbaaabbaabbaaaabaaabbaaababaabaaaabbaabbaabbabbabbaaaaaaaaabababbbbaaababbabbaaababbbaabbabbbbabbbabbaabbbaabaaaaaabbaababaabbabbbbbbaaababbbbbaaabbaabbaaabaababbababbbabbaabbbbbbaabbbbabaaaabbbbaaabaaaaaaaaaabaabaabbaabbbabababbbaaabbbabaaaabbabbaaabbbabbbbbabaabbbaaaabbababaaaaabbaababaabbbbabaabbabaabbaaaabbabbbbaabababbbbabbaaababbaaaabbabbbaabbbbbaabbabbaaabbabbabababbbaaabbaaaabbbbbbbabbabababaabbbbbbabbbbbaaaaaaabbbaabbabababbaaababaaaaaabbbbbbbababbabbaaabaaaaaaabaabbabababbaaaabababbababaaaaaaaaaabbbbaabababbbbaaaaabbabbababaaabbabbbaaaaabbbabaaababaaaaabaaaaaaaaaabbabababbbbaababbbbaabbbabbbaaaaaaabbaabbaaaabaabbabbbbbaaabbaabbbababaababbaabbbabaaababbaaabbaaaaababaaabaaabaabbbaaaabbabaaabbbbbabaabbaaaaaaabbaaabbbbabababaabbbaabbababbbaababaaabbaaabababaaabbabbbbbabbaaaaababbbabbbabbaabbbaaabbbbbbabbababbabbaababbabaaaababbabaaaabaaabaababaabbbbaaabbbbbbmaaabbbbababbaabbbabbabbabbaaabaabbabbbbabbbaabbbaaababbabbbabaababababbaaaabbbbbbbbbbababbabbbbaabbabbaabbabbaaabaabaabbbaabbaabbbabaabbaabbabaababbbbbaaaaaabbababababbbababababbbaaabaaaaababaaaaababaabbaababababbbbbabaaaabaaaaabababaaaaabbbbbbaaabbbbbaaababbabbaabaaaaabaaaaaaabbbababaabbaaaabbabbbbbaabaaabbbbbaabbbaaabaababaabbbabbaabbbbbbbbbbbbaababababbbababbaababbbbbabaaaaabaaaaaabababbbbabaaabaaabababbbbbaabababbaabaaabaaabbabaabaabaaaaababaaaabbbabaabaaaaabaabaaabbbaababbaaaabbbbaaabbaaaabbbbaabababbbaaababbbbbabbbbbabbabbaaabaaaaaaababbabaabaabbaabaabbaaaabaabbabbabaabaaaabaaababbbbabbabbbaabaaabaabaaabaaabbbbaabbbbbaaabababaabbaabaabbbbbabaaaabbabbaabbaababbaabbaaabbbbbbbabbaaababbaaaabbabaabbaabbbbaabababbaabaaabbaaaabbbababbabbbaaabbabaaabaabbbbbbabbbbaabaababbabaabbabaaaaaabaabbbbaaababbabbaabababbbababaaaabaaaaabbababbbababaaaaaaababbababbbbabababaaababaabbabababaaabaabbaababaabbaabbabbbabaababaabaabbbbabbaaabaabbaaaababaaababbbbabbbaaabbbabbabaaabbabbbbbababbbbbbbababaabaaabbbbababababbabaaabbbababababbabbbbbbaaaaaaabaaababbbbbbbaabbbabbabbbbaaabbaabaaabbbabaaabaabaabbabaabbabaabbaabbbaababbababbaabbbabbaaabaaabbaaabbbbbabaabaaaabbbbbabbbabaabaaaaaaabbbbabaabbbabbbabbaabaabbababbbbaaaaaaaaabaabbbbaabaabababaabbabaaababbabbaabbaababaaabbbbbbababaaabbaababbbaaaabbaaaabbbaaaaaabbaabbbabababbbbaabbababaaaaaaabaaababbabbababbbbbaabbbbbabababbababbbbbbbaabbaaabbbababbabbbbababaaaabbbaaabaabbbbbabaaabbaabababbbabbbbabbbbbaaabbaaaaabbaababbbbaaabbbabaabbbabbaabaaaaabaaabbabaabbbabaaabbabbbbabbaaaabbbbbbbbabaaabbabaabaaabbbbabbbbbbaabaabbaabbbaabbabbaababaababaabbbbbabbabaabbaabbabaabaabbabaaabababbbabaababbbbbababbabbaaababbbbbbbbbabbaabaaaaabaabbbababaabaaabaabbbbababbaabbabbabbbaabaababaaabbababbbabaaaababaababaabaaaaaabbaababbbaabbabbaaaaabbbbabbabaaabbaabbabaabbaabbbbbbababbbaabbbabaaaabbaabbaaaaabbabbaaabbabaabaabbababbabababaabbababbabbababaabaabbabbbbabbbbaaabbabaabbababbbbaaaabbbbaaaababababaaaababbaaabbabbabbbbaababaaaababaabbbbababbbabbaabbaabbbbbbbaabaaababbaabababbbaababaabaaaabbbbaaababaababbaaabbbaaaabbabbabababaaaabbababaabbabaaabbabbaabbbbaabbbbbbbaabbabbbbaababaaaabbaaababaaabbbabaaabbaabbabbabbabaabbabababbbbbabbbaabaabbbbbbbabbabaabbababaabbbabbbbbaababaabaaaaabaaabaaabaaabbaabababbaaabbaaaabbabbaabababbbaaabbaabbbbaabbaababaaaaababbaabbabaaabaaabbbaaabbabbabbaaaabbaabbabbbbbbabbbbaabbbabaababaababbbababbabaabababbaabbbbaaaaabbbabbbbbaaababaaaabbaaabbbbbbabaaabbabbbaaabbaabbbaaabaaaaabbbbbbaaabababbaaabbbbaabbaabaaabbbabbbbbbabbbbaabaabababaaababbbabaababaababbabbbaaaabbbaabaaaababaabbaaaabbabbabaabaabaaaabbabaabaaaaaaabbbbababbabbaaabbbaabbbabaaabaababbaaaabababbababbaabbbababababbbaaaabbaabbaaaabbbbaabbbbabbbbabbbbaaabaababaabbbaabbbbabbbaaabbaaabbbababbaabaabbababbbabbbabaababaababaabaabaabaabbabbbbbbaabbbbbbaaabababbabbabababaabaababbbaababbabbbabbbaaaaaabbbaaabbbabbbbaababaabaababababaaabbababaaabaaabaaababaaabbaaababbbbbbbbabbaaaaabbabbbaaabbbaaaabbabbbaaababaabbabbbaaabbabbbbaababbaaabbaaaaabbbbbabbbbbababababbbbbaaabbabbbabaababbaabbababbabaaabbababbbababaabaaabababbabbbbaaababbbbaabbaabbbabaaabbababaabbbbbaabaaabbbabbaabaabaaaabbaaabbabaabbabaaabbababbbaababbbbabbaaabbaaaaabbaaabbbabaaabbbbabaaaaababbbabbaababbbbaabbabbbbaaaabaaabaaabbabbbbbabbaabbababaaabababbbabbbbbaaaaaabbaaabbbaaababaababaabbaaaabbbbabbbabaabbaabbabaaabbabbbaabaaababaaaababaabbabaaaaabaabbbbaabbaababaabbaaabbabbabbaaabbbababbaabbabbbbbbbbbbbaabaaabbbaababbaabbabaaabaabbbaaaaaabaabbbbabbaabbaaababbabbbabbbaabbaababbabbaabbaabbbabbbabbaaabaaabbaaabbabbbaabaaabbbbabbbbbbbbabbabaaaabaaaaabbbbaabababbbaabbababababaaaaaabaaaaababababbbbbbaaaaaabaaaabaabbbaaabaabaababaabbaaaaaabaaaabaabbbbbaabbbaaaabababbabaabbbbabbbaaabbbaababaaaababaaaabbbbbaaaaaaabaaaaaabaabbbabbbabbbbaaabbaaababbbabbabaaabbaaababbaaababaaababbaaababbabbaabbbababababbbbababbbbaaaabbabbaaaaaabbaaaabaabbbbabbaabaaabaaaabbaabbbbaabaabaabaabbbbbbbaaababbaaabbbababbbaaabaaabaaababbbbaabbaaaaaabbbabbabbaaababbaaabbbbaabababaaabbbbbbbbbaababbaaabbaabbbbaabaaabababaaaabaaabbbaabaababbbaabbaaabaaabbaaaabaabbbbaaabaababbbbabbbaababbbbababaababababababbbbaabbaabababbbbbbbaabbbbabbbaabbbbbbbababaababbabbaabaaabaabbbbbbbaabbaabaabbaabbbbbbbaaaaabbbbabaaababbbbaabbaabbbbbabaaaaaabaaaaaabaabaabbaaabbbbababbabaaaaabaababbabbbbabbbbabbbbbbbbbabaabaabababbaabaaaabbababbbbaabbaaaabaababbbaaabaabbbabbbbbabaaabbbbaabaaabbbbabbababbbababaaabbbaabbababaaaaabbbaaaaaabbaabbabaaaabbabbaaababbabaababbbbabbbaaabbbbbbaaaabaaaabaaaaabbaabbbabaaaabaaababaabbbaaabbabaabbaaababbaabbaaaaabaabbabbababbbbbaabaababbabbaaaabbabbaaabbbbbbbbbabaaababaabbbaabbbbaaaaabbbbaabaaaabbbbbbbbabbaaaaaabbbbabbbbbaabbbbbabaabbabbababababaabaabbababbbaabaababababbaaabbaaabaabbbababaabbbbaaabaababbaabbbabbabbaabbbabbaaaabaaabaababbaababbaaaaabbabbaabbabababbbabaaabbbbbbbaabbaaaabababbaabbbabaabbbaabababaaaabbabbbaabaaabababababbaabbaaabbbaaaaaabaababaabbaababaabbbbaaababaaabaabbbabbbaaababbaaabbbbabbababbbbaabbaaabaaabaaaaababaabbbaaababbbbabbaabbaaaaaaabbaaabbbaaaabbabababbbaaaababbbabaaaaabbaabbbbbaabababbbbbbbbbaabaaaaaabaaaaaaababbbbbbabaaabaaabbbaabaabbababaaabbbbaabbbabaabbbabbaaabbbbbbbbaaabbbbababbababbbaaaaabbbabbababaabbaabbbbabaababbababaaabbbabbbababbaabbbaabbbabbaaabbababbbaaabbbbaaabbabaaaabaabbaabbababbbaabaabaaabbabbaaaababbbabababbbaaaabbbbaababaababbababbaaaaaaabaaabaabaabbaababaabbabaabbabaaaabbbbbbabaabbaaaabbaabaabaabaababababbbaaaaababababaabbaabaaabbabaabbbaaabbbbaaabbabbabaaaaaaaabbbbbabbabababbaaaababaaabbabbbbabbaaaaaabbbbabaabbbbaaaabbbabbbbbabaaabbbbbbaaaaabaabbbbbabaaababbaabbbabbbaabababbbbbbaabbaaaaaabbbbbbabbbbabbbbababaaaaaaaaabbaabaaaabaababbaaaaabbbabbabbaabaaabbababaababababbababbbaabbaababbbaaaaaabaabbbaabaaaaaaabbabbbbaabaaaabbaaaabbabbaababaaabbabaaabbaabbbbbbbabbbbbababbaaababbbbabaababbbbbbabbabbbabbbaaaaaaababbbbaaabbabaaaabaabaabbbbaabaabaaabaaabbabbaaaabaabbbbbbababaaaabbbabbbabbaaabbbababaaabaaaabaaaabaaaabbbbbaabbabbbaaaaaaabbaababbbbbabbbaabbaabaaabbaababaaabaabbbbabaabbaaaaabaaaabbabababaaababbbabaabbabbabbbbaabababbbababaaaaabbaaabbaabaabbbaaabbabbbabbaaababaabbbabbabaaababababaababaabbbbbbabbaaababbabbbababbaabbbaababaaaabbabbabaabaabaaaabaabbabaabbbbbababbbababbbabbaabbaababaaaabbbaabaaabbbbaabbaaababbaabbbbaabaabbbbaaabbbaaaaabbabbbaababbaaabaaabaaababbbbbabbabbbbaabbbaabbabaabaaaaaaaabaaaabbabababbabbaabbabbbabbaaabbaabaabbbabaabbbabbaaabbbbbbaaababaaabbaaabaabbbbbaababbbbbaaaaabaaaababaaabbababbaabbbbbabbbbbbbbbaaabbabbabbbaaaabbbbbbbabbababbbabbbbbaabbbabaabbbaabbbabaabbbaabbbaababaaaaaaababbaaaaaabaabbbbaabbbbabbbbabbbababbbabbaabbabbbaaaaabbaabbabbbbbbbabbbbaaaaaabaaaabbaaaabaaabbbbaaababbbaaaababaabbbbbbabbabbababaaababababbbbbababaabaaabaabaaaaaaaabaabbbbbababbababbabbaabbbaababbabbaaaabbbababaaaabababaaaabababaabaaabbabaaaaaabbaabaaabaabbaabababbbabbaaabbbbabaaabbabaabaaabbabaaababababaaaabbabababbabbbbabaaabbaaaabbbababbababbaabbaaaabbababbbaabababbaabbbbbbabbaaabbbbaaaabbbbbbaabbbaabaababbbaaabbaabbbababbaaababbaaabbbbbaabbbababbbabbbaabbabbabbaaaabaaaabaaabbabbabbbbabaaaaaaaaabbbbbaaababaababaaabbabbbbbabbabbbbbbabbaaaaaaabaaababbbaaaabaaabaababababbbbbbbbbaabbaabaaaaabaaababbababbaabaababababaaababaabbbabbaabaaabbaaabbaaabbabbaaaababaabbabbabaaaaabaaabaaabbababbbbbaababbbaabbabbaaaaaababaababbaaabaaabbababbbaaabbbbabaaabbabbaabaabaababbabaabbaabbbaabbabbbbbabbbabaaaabbbbababbbaaabaabbbabaaaabaabaaabbaaaaaaaabababaaaaabbbaababaaababbaaaaaabbbabbbbbbbbbabbbbaaabbaaabaabaabbbababaaaaabbabbaaabbabaaabbbabbaaaaaaabaaaabbbbbaaabaaabbbababbaaabbaaaabaabaaaabababaaabaabbbbbbabbaaaabbabaaaaaaabbbabababbaaaabbaabababbbbbbbbaaabbbbaabbabababaabbbbabbbabababbaaaabbababbabaaababbbbbaaabababbbbababaaaaaabbaaabaaaaaabbaaabababaaababaaaabbabbbbbbabababababbababbaaabbaaaaaaabbaaaabababbaaabbbaabbbabbbabbbbbbabbbbbbaaaaaaaaabbbbbbbaabbabaabbabababaabbbabbbaababaabbbaaabbbbabaabbbaaabababbabbbbbbabbababababbababbaabbbbaabbaababbaabbbabbabaaabbaaaaaaaaaabbabaabaababbbbbaaabbbaaaaaaabaabaaabaabaaaabbaabbbbaaaaaaaabbbbaaabbbabbaababaaabaaabbbabbbaaaabaababaabbbaabbaabbaabbbabaababbabbbbabbabbaaaababbbbbbbabbabaababbaaaabbbbbaaabbabbabaabbaaabbbaabbbabbbbbaaaabababbaaaabbaaaababbbbbbabbbbbaaaaabbabaabbabbbbabababbaabbaaabbbabaababbabaaaaababaaababaabaababbbbbbbbbbbbabaababbbabbabbbbaabaaaaaabbabbbaaabaaabbbaabbbabababbbaaabbaabbaabaaabbbaabbababbabbbbbbbabbabbbbabaabbbaaaaaaabababbbabaaaabbaaabbbaabbbababaaabbbbbbbbbbaababbbbbbabbaaaaaabbbbbabbabbaaaaabaabbbababaabbaaabbbaababbbaabbaaabababaaaaabababbbbaabaabbbbaaababaaabbbabbbababaabbbaababbaaabbbbbbaaaababbabbababababbababaabbbabababbabbbabababbaabaaaaabbabbaabababababbabbaaabaabaabaaabbabaababaababbbabbbaaabaaaaaabaaaaaaaababbababbbaababbbbaaabbaababbbbaababbabaaabaaabbaababbabbbabaaaabbaabaabaaabbaabbbabababbbbaababbbbabbbabbbabaaaabbbaabbabbabababababbbbbaabaaaabaaabbbaaaabbababaabaababbabbbbabbabbaabaaaabbbaaaaaababbaabbabbbababbbababaabbaababaababbabbabbababababaabababbbaabbabaaabbbaabbaabaabaabbaaabbaaaabababbbababababaabbbabbbaaabbabaabaaaaaababbbbababababbaabaabaaaaabaababbbbbababbbbabbaaabbaaabbbababaabbbabbaabbabaaababbbaaabbbbaabababaaabbbabaaaaabbbbbbabbbbbbbaabbaaabababaabbbabbaaaabaabbaaababbbbaaabaabaabababbabaababaaabaaaababaaabbbabaabbaabbbaaabaaaabbbaabbababaaaaabaaabbbaaabbbbabbabababaaabababbabbbabbaaaaabababaaaabbabbaaababbbabbaaabababbaabbbbbabbabbabbabbbbbbbbbbbbaababbbbbbaaaabbbbabbbabaaababaaaaaababababaabbbbbabbaababbbaababbabbababaabababaaabbaaabaabbbbbbbaababbaababaabaabaabaabbabbbbbaabaabbaaaaaabaabbbabbbabaabaaabbbbaabaaaabbabbaaaabbbbbbaabbaabaabbbbbbbaaaaabaabbababaabbaabaabbbababbbbabbabbbbbaaabaaaaabbabbabababaaaaaababbabaaaaaaaaabaabbbbabbaaaaabbbbabaababbababbbabbbbbbbbabaaaaaaaaababbbbbbaaabaaabaaaaaababaababaaaabaabaaaabbabaaabaaabbbbbaaaaabababbabaaaabbbababaaababaaababbababbabaabbabaabaaabbbaabbbbbbbaabbaabbaaabbabbbabbaaaabbaabbbaaabbbabababbbbaaababbaabbabbbbabbaaabababbabbbaabbaabbbbbaaaaabbbabaaababbbabbabaaaaaaaaaaabaabbbaababbaabaaaaabaaababaaabababaaababbbbbbbabaaaabbbbbababbbaaabaaaaabbabbabaabbbaaabbbabaaaaaaabaabaababbbbbbbbbbababbaabbaabababbbaabbbaaabbabbbabbbbbaaabbbbbbbabbbbababbabbbbbabaabbabbbbbabbbbbaaaaababaabbbbbbabaabbbabbabbbbabbbaababbbbbbaabaabbabaabbbbabaabaaabbaaabababbbbaaabaababbbbaabbbbbbbbaabababbabbbbbbbabbbbbabbbabbabaaaabaabaaaababaaaabbabbaaabbabbbabaabbabaaabaaabbbabbbaaabbaabaaaaaabbbabbbabaaaaabaaaabbaababbaaaaabaababaaaaaabababbbbababbaaabaabbabaaabbbabbbbbabbabababbbaabbabbaababbaabbbababbaabbaabbaabbabaaababbabaaaaabbbbaababaaaababaabbaabbbaababbbbbaaababbbbbababbbbabbbababbababbaaababbbabbabbbaabbbbbbbabaaaaaaabbbbbbaaababbbbabaabbbabbbabbbbbabababbaababbbbaaababbaaababababbabbababaabbabbababbaaabbbbababbaababaabbaabbabbbbaabbbababaabababababbbababaaaaabaabbbaabbabbabbabbabbbababaaaaababbbbbbabbabaaabbbaaaaabbbabbbbaaabbaaaabbaababaababbbbaaababbbabaabaabbabbbbabaabbbabaaaabbaaaabaaabaaabaabbabbabbbabbababbabbabaabaabaabaabaaabbbaabbabbbaaaaabaaaabababbabaaaaaabaaabaaabbbababbaabbbabababbabbbbaababbbabaababaabbbaababbbbabbaaabbbaabbabbbaaaabbaaababbaaaabbbbbaababaababbbbaabbbaabaaabaabaabaabbaaabaabbababaaabaaabbaaabbaaabbbbbbbbbaabaaababbaabbbbbbababbaabaaababaaaabaababbaabbbbbababaabaabbbbaabbababaabaaabbaabbbababbbbbbbaabbaaaaabbbbbbbbbabaaabbaaabaabbbaaabbbababbaabbbbbbababbbbbbabaabaaabaaaabbbabbbaabbbbaaaaabbabaabbaababaaaaababbbabaaabbaaabbaabaaaabababaaabaaabbbbaaabbabaabbaabbbbbaaabaabaaaabaababbabbbaaaaabbabbaabbbabbbbababbaababbaaaabbbbbaababbabbbbbabbbabbabbababbaabbbaabaaaaabaabbaaababbbaababbbaababbbaaaaabbbbbababbbaaaabbbbaaaaaababaaaabbaaabbbabaaaababbabbbbbaabbbbbaababbbbabaabbabbabaababababaababaababababaaaababbbbabaaaabbabaabbbbababababbaaaaababaaaabaabbaabababbabbbabababbabaabbbbaabaaaabaaabbabbababbabbbbaaaaaabbbbaaababaabbbbbbabaabbaaaaabbbbbabbaaaababbbbabbbbbbbabbbbaabaabaabbbaabaababaaababababbbaaabbabbbbbaaaabbaaaaababbabaababaabbbbabbbabbababaababbaabaabbabbbbbbaababbabbbbbabbbabbabaaabbabbbbaabbbbaaabbabaaaaabaabaabbaaabaaabbabbbababaaabababaaaababbaaabaabbabaaababbaaaababbbbaaaaaaaaababaabaabaaabaabaababaabbbababaabbababbbaaabbabbababaaaabbbaaaaabaaaabbbbbbaabbaabaabaabbbbabbabbbaaaababbbbbabbabaaababbaabaaababaaaaaaabaaabababbbbaababbbbaaabababaaabababbbbbbababbaababababbabbbaabbababaaabbabbabbbaaaaabbabbabbaaabbabbabaabbabbabaaaababbbabbbbbbbaabaabaaaaaababbbaaaabbbaabbabaabbaaaaabaabaaabbbaabaabbaaaabbabaabababbabbbbaaaabaabbabaaabbbbbbbbbbbaabaababbaaaabbabbabbbbabbbbbaaaaabbababbbbbaaaabbbbaabbaabababbbbaabaabaaaaababbbabaabbaabaaaabaaabaaaaabbaabbbaabbbabbabaababbaaaababaaabaabbaabbbaaababaaaabaababbaabaabbabbabaaabaaaabbabbbaaabbbbaabbabbaaabbbaabbbbabbbaabaaabaaababbbabbbbbbabbbaabbbbbabbaabaaaabaaababbababbaaababbaabbaaabaaabbbbaaaaaabbabbaabaaaaabbabaabbbabbaabbaaabaabbbbaabababbbaaabbbbaaabbabbbbabbbbbabaaaaaaabbabbabbbaabbaaabaaaababaaaabaaababbababaaabaaaaabaabbaabababababaaaaabaaaaabbbaababbbbbabbbaaaabbaabaabbbabbababaaabbabbaabababbbbabbbababbaaaaababaabbabbbbbaaabbabbbbbabababbabbbaababbbbaabababbababaabbaaababaabbabababbbbbbaabbbaaabbbbaaababababbbbaabbbabbbaababbaabaabbbaaabaaababbbababbaaaaababaaababbbaabbbbaaababbbabababaaaaaaabbaaabbbbbbaabbabbabbbbbbbaaababbaaaabbabaabaababbbbbbbbbaaaababbabbbbbabbbabababbbabbbaaaabaaabbbaabbbabbbbabbabaabaaaaaababaaaaaaaabaababaaababbaababababaaabaabaaaabbabbbabaabbbabaabbaabbbbbabbabbaabaabbaaabbbbbabaaababaabaaabaabaabbabbabbbabaabababaaaaabababaaabbabbbbbaaabbbabbabbababaaabaaabbaabbabbbbbababbaaaababaabbbaabbbbbaababbbabbbaababaaabbabbbababaabbbaaaabaababbbaababbbabbbbaaabaaaabbaabbbbbabbbabbaaaabbbabbaaabbbaaabbbbbbabbbbbabbbabaaabbbabaaaabaabbbaaabbaabaababbbbbaaabaababbaabbbabbaaaababbbaaabaababbabaaaaabbbaabbaabbbabaabaaabbabaaabbbbabbaaabbbabbbabaababbaabbbbabaaaaabbabbbabbabaabbabbaabbabbaaababaabbbbbbabaabaababaababaabbaabbbababbabaaaaaaaabababbbaabbaabaaaaaaaabbbabbbbbabbbbaabaaabaaabaaabbabbbbbbbbabbaabbabbabababbabbababbabbaaaabbbbbbaabbaabbaaabbbabbbaabbabbabbbabbaababaaaaababaaabbaabaababaabbbbbbbbababaaababbabaaaaaaaabbbbabbbaaaababababbaaaabaaabbabaabaaabaaabababbaabababaaaaabababababababaabaaaaaaabaaaaababbbabbababbbabbbbaabaaabbabababaabbaabababbabbaaaabbaaaabbaabaaabbaaabbabaaabbaaaabbbbabbababaabaababbaababaaaabaaaaababaaaabbbbbbabbbaaaabaaababbababbaaaabbbbaaaaaabababaaaaaabbbbbbabbbabbaaabbbaaaabbabbabbaabbaababaabababbabaabbbaaabbabbabbbabbbaaaabbabaaabbabbaaabbbbaaaabbababbabbbbbaabaaaababbaabbbbbbbbbabbbabaabaaaaababbabbbaaabaabbabababbabbabababbbaaababaababaabbbaaaaaaaabaaabbabbbaabbaaabbababbababbaaaaabbabbababaaaaabaaaaaabbbbaaaabbbbabaabbbbbabbbbbbabbaaababbbbbabaabaabbbbbbaabababaabaaabbbbbbabbaaaabaaaaaaaaaababbbbbbbbbaaabbbaaaabbbbbaaaaabaabababbaaabbaababbaaaaabbbaaababbbabbaaaaabaaababbbbaaabbabbabaabababbaababababbbbaabaaaaaaaabaaaabbaabbabaabbabbbbaaababbbababaabaabbabbbaaaabababaabbbaaabbbaaaabbaabbbbbbbabbbbaaaabbbabaaaaaaabbbbbaaabaabaabbbaabbbbbabbaaabbbaaabaabbbbbbabaabbbaaaabaaabbbbaaaaaabababaababbbaaabbaaaaabbbbbbbaabbaaaabaabaaaabababbaaabbbabbbbaaaababbbbabbbbababbbaabaabbabaaabaabbbaabbaaaabbabababbaaababbbbaabaaaabbabaaaaabaabbabbaabbbbbabbababbabbaabababbabbbaaaaabbbabbaaaabaaabbababbabaabaaabababbaaaabbababbaabbabbaabbababaabbaaaaaaabaabbabaabbbababaaabbaaabbaaabbaboaaabbababaabababbababbbbbbabbabababbbbbbbabbbabababbbaaabbabbabbaaaabbaabaaabaaabbabaabbaabbbbbbabaaabaaaaabbbabbbbababbaabbbabbaaaabbabbabbaababbabaaaabaabbababbbabbabaababaabbbabbabbabaaababaabaabbaabbaabbaabbbaaababbabaaababaabbaabababbabaaabbabaabaaaabbabbbbbaaaaaabbabbababababbababbaabaaaaababbaaabbababbabaabbbbabaabbabaaaaabbabaabaabbaabaaaaabbbaaaababaabbbbbabbbabbababbaaabbabbaababbaaabbababaaabbbbabbaabaaaabababbabaaabbabbabaaabaabbaabbaabbaabaaaaabaabbabaabbaabbbbbbbbabbabaabaababbbaaaaaabbaabbababbbbbabaababbabaaaabababbaaaababbabbbabababbaaabaaaaaabbabaabaaabaaaaaababaaabbbabaabbabbaabbbababaabbbbbbababbaabaaaaababbbabbbaaabbabbbabbaaaaaaabababbbabbaabaabbbabbbbbababbaaababbbbbbaababbbaabaaaaaaaaabbaabaababbbbbaaababaaabababbbabaaababbbbabbbbbaaababbbbaaaababbabbbbbabbaaaaaaabaaaabbabaabaaabaabbaababaabaababaaaaababaabbaaaaabbbbababbaabbbbabaaabbabaaababbaabaabaabbaaaabbbaaabaabaaabbbababbabbbaabbababbaabbaabbababaaabbaabbaabaaabaababbbbbbbbaaaaabbbabbababbaabaaabbabbbabbaababbaaababaaabaababaababbbaabaaabbbbbaabaaabbaaabaaaabaaabbbbbaabbbbbbbbbbbabbbaaaaaabbbaaabaaabaaabbabbaabaaaababbabbbbabaababaabbabbaaaaababbbbbaabaaaabaabaababbbababbaababbababbbbbbbaabbababbaabbabaaaabababaabaabbbaaabaaabababbbbababbabbbaaabbabbaaaaaabbbaaaabaabaaaaaaabbbbbbabaabaaabbbabaaaabaaababbbbaabbaaabababaabaaabaabbaaabaaaaaaaaabaaaaaaabaabaaaaababababbbbbabaabaaabaaabaaaaaaabbabbbaabbbbaaabaabbbaabaaaabbaababaaabababaabbabaabaabbabbababaaabbbaababbbbbbaaabbbbbbaabbabbaaaababaaaaaaaaababaaabbbaabbabaaaabbbbbbabbbabaabaaabbbbabbbbaaabbbabbabbababbbbbbaabbbbaabbabababaaabaaaaabaaabaababbbababaaaabbbbaaaabbaabbbabbbbbaaabbabbbbbbbabaaababbbabaaaaababbababbbbaabaabbaaababbbaabbbaaababbbbabbbaaabaabbbbbaabbabaabbbaaaaaaabbaaabababbaabbabaaabbaaaabaabbabbabababbaabbbabbbbbaabbaaabbabbbabaaabaaabaaabbbbbaabaababbbabbababbbbaabbbabbbbabaabbaabaaabaabbababbaababbbbbbabbbabbabbbbaabaaaabbaababbaababbabaaaaaabbbaabaababbabababbbbaabbaabbabbaaaabbabbbbabbaaaaabababbabaabbbbabaabbaabaaaaaaabbaaaaaaaababbbbaabbbbaabaabbbaaaaaaaabbbaaababaaaabaaababbaabbabaaaaabbbabababbaabbbaabbabbabaabbbabbababbbaaabbabaaabaaaababbbbaaabbabaabaaaabaaababaaabbaababbbabaababbbabababaaabbabbabbababbaabaabbbbbaabbbbbabaabbbbbbbbbaaaabbbababbabbbabbaaaaaabaabbbaabbbaaaabababbabbbaaababaababbbbbaaaabbbaaaabaaabbababababbaaabbaabaabaaababbaaaababaababbaaaaabbabbbababbbbbaabbbbbbababbbaabbaaabbaabbaababbababaabbbbbaaabbabaaabbabbabbabaabaabbababaabbabbabaaabbbaabaaabbbaaabbbbbaaabbabaaabbaabaabaaabbaababbbbbbbbbabbababbaababaababbabbababbaabbbbbbbbaaaaaabbabbbbabbaababbaaaabbbbababbbaabaabaabaabbbababbbaababbbabaababaaabbbaababbbabaaabbbabbbbbbabbaababbbbabbabbabababababbaabbbaaaabbbabababbbbabbabbaaabababaaaaabaaabaaabababbabaabaabababbaaaababbaaababaabaabbaaabbbbbbaabbbbbaaabababbaabbabbbbbbbbaaaaabbabaabababbaabbaaabbabbabbabaaabaaaaabbabbbbaaabababaababbbaabbbbbabbaaabaabbbbbaaaababababaaabbbbbababaabaaaababbaaabbbbaaabbababaabbbbbabbababbbbaabbaabbbbbabbaaaaaabbabababbbbbbbbabaaaabbbbababbaabbbababababbbbbababaaaabbbabbaaaaaabbabbabbaaababbbabbbbabbababbbbbbaabbabbbbbabbaaababbbaabbaaabaaabaabbaaaababbbaaabaaababbbbaababababaabbbbaabaabbaaabbaaabbbaabbbabbbbbabababbbaabbbbabbbbbaaabbaabbaabaaaabaababbaabbabbbbbabaabbbaaaabababbbbaaabaaabbababbaababbbaaaaaaabaaabbababaaabbbbbbbbaabbaabbbaabbbbaabaaabbaabbbaabbbabaaabbabbababbbaaaaaabaabbbababaaaaaaaabbababbabbaabaabbabaaababbbaaabaaabbaabaaaaaabbaabbabbbbaabbbabbabbaabbbaaabaabaaabbaabaaaaaabbbbaabbbaaabbbbaaaababbbbbababaabbbbbbaabaaababbaabbbaabbbbaaabbababaabbbabaababbaabbbbabbbabbaabaaaaaaaaabbabbababababbaaaabbbbbababbaabbaaabbbbaabbabbaabbaaababbbabbbabbbabbbaaababaababbbabbbaabbabaaabaababbaaaabbaabbbaaabaaaabbbabbabbabbbbbbaaababaaabbabbaaabbbbaaabbabbabbbaaabaaaaabbbabbbaaabaaaaaaaabaabbababbbbaabbbaababbabbbbabbbbbabaaaaaaaaaabbbbaaabaaaabababaabbbbaaaabbaabababbbbabbaaaabaaaabaabbbabbbbbaaababbababbbbabbbabbababababaabbbababbaabababbabbbbbaababbaababbbabbababaaaaabaaabbbbababbaaaaaaaaabbbaaaaaaaabbbaabaabbbaaabbbbaaaaaaaababbbbbabaaaabbbbbbaabbbbaaaababababababaaabbbabbbabaaababbbaabbbaabaabbabbabbbabbbbbabababbabaabbaaaabaabaaabbaaaabaabbbaababbabbbbbbbabbabbbbbaabbabbbabaabbabbababbabbabbaabbbbbababbabbbbbbaabbabbbbaaaaababbabbbbbbaaabaabaabababbbbbbbbbabbbabaabbaaaabbbabbbbabbbbaabaabbaabbabababaababaaabababaaaaaaababbbabaaaabbbbbaaabbbbbabaabaabaababbaaaaabaaaababbbbbbabbababaabbbababbbabbaaabbabaaabababaabbabbabbaaabaaaabababaaaabbaabaabababaabbaaaabbaabbabbbbababbabaaabbbbababbbaabbabbbbbabbbaabaaabbaaaaabbabaaaabababbaaabaabbabbaaabbabbbabaabababbabaaaaababbbaaabbbbbaaaaabbaaaababababbbbabbabababbabbbababbaaaaabaabbbabbabbbbabaaaababbbbbaaabaaabababbabbaabaabaabbbabaaaabababaaaabaaabaabbbbabaabbbababbbbaababaaaaaaabaabaabbaabbaabbabbbaaabbbaaababbbabbbbabbbbbbbbaababababaabbabaaaaabbbbaaabbaaaabbbbaaabababbbabaabbaaaaaabbaababbaababbabaabaabbbbbbaabbabaabaabababababaaaabbabbabbaabbabaaabaaabbaabbbaabababbbbaaabbaaaabbbbbbaabaabbbbbbabbaabbbbbbababababbbaaaabbbbbabaabbaaaabaabbaaabbbbbabbbbbbbababbaaababbaaabbabbbababbbbabaaaabbabbbbbababbabbabbabbabaaabaabbaabbbaabbabbbbbbabbbbbbbaaabaabbbbababaabbabbababbabbaabaaababaababbbbbabaabaaabbabaabbababaabaaabbaaabbaaabaabaabbbbbabbbabbbababababbabaaabbbaabbbbbaaaaabbbbbaababaaaaaabbbbaabaaabbaaaaababbaababbbbbbbbbabaaaababbbbbabbbaabbabaabababaaababaababbbbaaababaabbabaababbbaaabbbbaabbbbbabbabbbabbaaaabbbbbaaabbbbbabbabbbbbabbbaabbaaabbabbabbabaabbabbaababbababbbabbaaababbababbbbaabaabbaabbabbbbbbbbbaaabaaaabbaababaaaabbababababbababbbbabaaaaabaababbbababbaaaababaabbbbaaabbbabaabbbaabaaababaaaabbbbabbbabbabbaaaabbbaaaaabbbaaabbaabbaababaababbabbbaabbbbbbabaaaababaabbbaabaaaaabbbaabaaaaaabaaaaaabbbaabbabbbaabbabbabbbbaababbbaaababbababbbabbaaababaaabababaaabbbbaaabbaababbbabaababbbaaaaaabbbbabaaaabbabbaaabaabaaabbbabababbbaaabbababbaabbbabaaababbaaabbbaabbabaaabaababaaabaabbbbaabbbbbabbaaaaaabbaabaababbabbabbbaaababbaaaabbabbbbbbaabaaababbaaaaaaabbbaaaabbbabaaabababbaabaabbbabaaabaaaababbbaababababaaababbababbbaaabbaabaaabbbbaabaaababbabaaabaabbaabbbbbbabbbabbbaabaababbabbbabbaabbbbbaaaabababbbbbbbbbabbbababbaaababbbbbbbbaabbbbbbbaaabbabbbabbabaaaabaabaababaaaabbabbbbabaaabaabbbababbabbbbabaabbbaaabbabbbabaaaababaabbbbbbbbbbaaabbbbaaababbababaabababbbbbaababaaabbbaabbbaaaabaaabaaabbaaaabbaabaababbbbabbbbbbbaaabbbaabbaaabbaaabbaabababaaaaabbbbaaaaabaaabaabaaababaaaaababbabbbbaaabbaabbaabaabaaaabbbbaaaabaabbabbaaababaaaaaaabbbaaaababbababaabbbaaaaabbaabbabbababaaaaaaabbabbbaababaabbaabbbbaabaabaaaaabbbbbabbaabbaaabaabbbaaaaaababaabbabbbbbbbaababaaaabbbbaabaabaaabaaaababbabbbaabaabbabbaaabaaabaabaabbbabbbbabbaababbbbababaaabaabaababbbabaaabbabbabbbabaaababaaababbaababababaabbabaabaaabaabbabbabbabbaaababaaabaabbbaabbaaaababaabaaaaaabbbabbbbbaababbbbabbbabbbbbbabbabbbaababbbbbbbabbbbbabababbaaaababababaabbaaabaaabaaaabbabbabbabbbbabbaaabbbaabbaabaaaabaaaaaabbbbbabbbabaabbbbaaaabbabbbabbbbbbabbabbbbabaaaabbbbaaabaabaabbbbabbaaabaaabaaababaaabaabbababbaabaaabbbbababbbbbaabaabbaaaaabbaabaaababaababbababaabaabbbbabbbaaaabbbaabbaaabbbbbabababbbaaaaabbbababaabbaabbbbaaaaaabbababbbbaaabbaaabbbababbaaaaabbaabbbababababaaabbababbaabaaabbababbbbbbabbbbbabbbaaabaababbbbabaabbabaaabaabbbaaaaabbbbbbbaaaabbbaabaaaabbaaaaabbaaabababbbbabbbabaaabbabaaababbaabbaaaabbbbaababbabaaabbababbaabaaabbabaabbaabbbaaababbaabbbaabbbaaabbbbbbbabababbaaaaaaabaabaabbaabbaababbabbaabaaaaababaabbaaaaabaabbbbababababaabaaaaaabaaaabaabbbbaaaaabaabbbaabbbbbaaaaabbabaababbbaaabbbbbbbaabbbbbbbabbabbaaabbbaaaabbbbbabbbbabaabbabbbaababbbbbababaabababbabbaabbabaabaaaabaaabaaaabbabbababbabaababaabbbbbbabaabaabbbabbbbbaaababbbbbabaaabbaabbaaabbababaabababaabbaaabbbbbbbbbaaabbaabbabaabababbaaaababbbabbabbaaababbabbaaaabbbbaababaabaababbbabbabbbaabbaaabbbbaaabbbabaabbbbbbabbbaaabbbababbbbbbbaaabbbaabaabbbaabaabbaabbbabbbbbaabbbaabbabbbbbabaaabbaaaabaaababbbbbababbbababaabbabbaaabaaababbbbaaaaaabbbabbbabbaaaaabbbbabaabbaabbabaabaabaababaaaaabbbaababbbbabbbbbabaaaaabababbbbbaaaaaaabbaabaabbabbaabbbbbbaaabbabbabbbbabaababaabaabbbabaaaabbababbbbabbabbaabaaaabaabaabbabbbbababbaababaaabbbaababbabbaabaabbbaaaaaabaaabbbbababbbbaaabbbbbbbaababaaabbabaababbbbbaaaaabaababaababbaaaabaababaaababbbbabbbaaabababbbaababbbaaaabbbaaabbbbababababbaabaabbbabbbbbbaababababbabbaaabbaabbbbbbabbbbabaabbaaaabbbbabaaababbaabbbababbbaaaabaabaaaabbaaabbabbaaabbbabbaaabbbbaababababbbbaaaabbababbabaababbaabaabbabbaabbbbabaaabbabbaaabaaaaaaababaaaaaabbbaabbabaabaaabbabaabaaaabbbbbbababbbbaaaaabbababababaaabaabbaabaaababbbaaaabbabababbababbbbaaabaaabbabaababbabbaaaabaabbbbabaababbbabbaaabaabaabaabbbbaaaababaaabbaababbabababbbbabbbbbbbbbbaabbbbabbaaababaaabbaaabbaaababbbbbbabbbbaabaaaaabaabaaaaaaaaabaabbabababaababbaabbabbaaabbaaabbbbbabbabaababbabbaaabaaaaaaaababbbaaabbbbbbbabbbbabbbbaababbaaaabbaabbaababbababababbbaabaaaabaabbbbaabbbabbbbbabaabaaaaabaaaaabaabbbabbabaabbababbaaaababaaaababbabbaaabbabbbaaababbbabbbbbabbbbbbaababaabaabaabbaabbbbbbbbbaabaabbbabbaabaaaababbaaaababbbaaaaabaaabbbbbabbaaaaababababaaaaaaabaaabbbbbaababbabbbaaabbbbbbbabbbababbbbabaaaaaaababbbbabbbabaabbbabababbaaaabababbaababbbbabbbbabaababbbababbbbbabaabaabbaaabbbabaabaababbbaabaabbabaaaaaababbabbaabaabbaabbbabaabbbbbbbaabbaaababbbabaaaabbaabaabbbbaaaabbaabababbbaabbabbabaabbabbaaababaaaababaaaabaaabbbbababaabaabbbaabbabbbaaaaaaabbaaaabaabbabbaabbaabaaaababbbbabbaabbaabbababbaaabaaaabaaaaaabbaabbbabbbbabbabbaaaabaaaaaaaaabbaaabababababababaabaabaaababbabbaaabbbbabbabaabaaaababaabbaaabaababbaabaaaabababbbbaabbababaaaaaabbaaabaaaaaabbaabababbbaaabbabaaabbbaabababbabbbaaaabbababaabbaababaabbabaabaaaaaabbaaaaaaaabaabaabbabaaabbbabbabbaababbaaaaabbabbaaaaabaabbbaabbbbbabbbbbabbabbaaababababbbabaababbabaaabaabbabaaaabbabbaaaababaababaabbababbaaaabababbbbbbbbbaaababbaabbabbbaaaabbabbbaaaaaaaabbbbabaababaaabbabababbbbbabbabbbabaabbabaabbbbaabbabbaaabaabaaaaaababaabaabaaababbabbaabbbaabbabbbbabbbababaabaabbbbaaaaaaabbaabbbbbabaababaaaaaababbaaaaaaabaabaaaabbbbabbbbbbbabababbaaabbbbbbabaababbabbabbaaaaaaabbaaaabbaabbaabbbaaaaaabbbabbaababbbaabaabbbaaaabbbaabbabbbabaaabaababbbabbaaaaabbbbbbaababaabbabbaabaaabbababaaaabaaabbaaabaaaaaaabaaabbabbaabaaaabbababababbbbbbabbababaaabbaaaabbabbbabaaaaaababbabaabbababbbaaaaaaabbaabbaabbbbaaaabaaababaababaaababaaaaaaaabaaababbbbbbabbaaaaaaaaababbbaaababaabaabbbbaaaaabaabbbbabbabbbbbbaabbaaabbbbabaabbbbaababaababbbabbabbabaaabbabaabbbbabbaabbaaabbabbbabbaabbbaabbbbbbababbbbabaababbababaabbbbbabaabbaabbbabbbabaaaabaaabaababbababbaabbaaabbaaaabbabaabbbabbbaabbbbbaabbbaabbaaaaaabbbabbabaabbbabbbaaaaaababaababaaabaaaabaabbbaababbabbaaabbaaaabaaabaaaabaabbabababababbbbabbabbbaabaabbaabaaabbbaaabbabbabbbaaabbababaaabbbbaabbabaaabababbaaabbbbbabaabaabaaababbaabaaaaabababbaaaaaabbbabaaababbaaaaabababababaabbabaabaaabbabbaaaabaabaaaaabbaaaabbabaaaaaabaabbaabababbaabaababbbbaaababbbabbabbbbbabbababbaaabbbbaabaaaaabbababaababaaababaaabaaabbaaababbaabbbbaaabaaabbaaabbabababbabaabbabababbbbbababaababbbaaabaabaababababaabaabaaaaabbabbbabbbbabaabbbababbabbbbaabaaabbabbbbabaabbabbbabaaaaabababbaaabbaababbaaababbaababbbbabbaaaabbbbbbbbaababbabaaabbbbaabaababaababbaabbabbbabbabaaaaabbabbabbbbabababaababbabaaaababaaaaaabbaaaabbabbbaabaabaabbbababbababbabbbaaabbabbbbaabbbbbbbaababbaaaabbbbabaaaaabbabbaabaabbbbbabbaabbaaaabaaababbbbaabaaabaabbbababbababbaaaabaabaabbbabbaabaababaababaababbabaabbababbababbbbababaaabaabbabbaaaaabbaabbbbabbabaabbabaaaaaabaaababbaaabbbaabaabababbbbababbabbaabbaababbbabaababbabaababbabbabaabbabaabbabaabbabbbabbaabbbababbbbbbbababbbbaababaaaaabbaaababbbbbabbabbbbababbbbbbbaabaabbbaabaababbabaaaabababbbbaabbbabaaaaaaababbbaabaaaabbaabaaaabababbaababbbaaaabaabbbabbbbbbababbaabbaaaaaabbbabbababbaabbbbaaaaabaabbaaaaabbaaaabbababaabbaabbabbbbbabababaaabbababbbbabbbabaabaaaabbbaaabaabbbababaaaabaaaabbaaaabbbabbabbbbababbaaabbbaabbaababbaabaaaabbaaaaababaaaaababababbabbbabaabaababaaabbaabbaabbbbbbbaabbaaabaaaaaaababbbbbaababaabbbaabbabbaaabaabaabaaaaaaaabbaababbaababbabbbbabbabbbbabbbababbabaaaaaaabbbaabbbbbbbbbbababbaaababaabbbaabbbbbbbababbbababbabaaaaabababaabbaabbaaaaabaaaaabbbbabaaaabbaabaabaaabaaababbbabaaabaabbbaaaaabbbbbbabaaaaababbbbbbbaaaaaaabbbaababbbbbbbbaaababaabbabbaabbbaaaaaabbababbaabaababbbbabaababbbabbaaaabbaababbabbaabaaabbababababbbbbbabbababbabbbbbbbabbbbbaaaaababaaabaaabaabbabbaabbbbbaaabbbbabbabaabbbabbaaabbbaabbbaabbbbabbbaaaabbbbbbbaabbbabababbbababaabbaaabbbbbababaabbbbaaabbbaabbbbaaaabbaaaaabaabaaabaaabaaabbaabbbbabaaaaaabbbaaabbaabbabaabbbabbaaaabbbbababaaabaaaaabbbabbaabbabaaabbbbababbbbbabbabbbaaabaabbaaabbaabababaabaaaaaababaaaababababababaaabaabaabbbaaaabababbaaabbbabbaabaaaaabababbbbbabbbbbbabaababaabaababaaaaababbbbaaabbbbbbbbbbbaaababbbbbaabaababaabbbbbaabbbbaaababababababbabaaaaabbbabbbaaaaababbbbaaabaababaababababbabaaaabbaaaabaaababbbabbbaababbaabbabaabaaabbbaaaabbbaaaaabaabbbaaababbbaabbabaabbabbaababababbbbababaabababbababbbabbababbbbabbabaabbaabaaabbbababbaaaaaaaabababbbbbaabaabaabaabbbababbbbabbabaabaababbbabaabbbabaaabaabaaaaabababbaabbbbbaaabbbbbaaaaabbaababaabbaabbaaaaaabaabbaaaaabbaaabaabbaaababbbaaabaaaaaabaabbbaaaabbbbabaaabbbaabbbbaaaabbaaabbabbbababbbaaaabaabbbabbbabbbbbbabbbbababaabaaaabaaaabaabbbabaaaaabaabababbbabaabbbbaaaabbabbabbaabbaababbaaaabaaababaaaababbaaababbabbabaaaaabbabaaaaababaaabababaaaabaaaabbababbbbbbbbbaaaabaaaaaabaabababaaaaababbbaaaabbbbaaaababababaabbabaabbbbbbaabbbabbabababababaaabbbbaababbbbabbbbabaababbabbaaaababbbabbbaabaaabbbababbabbaabbbaabaabbbbaaabbbabababaaaabbbababaaaaabbbaabbaaabbbbaabbbabababbbaabbbbaaaabaaaaabbaaababaabbbbbbbbbaababbabbaabbbabbaabbbbabaaaabaaababbbbaabababbabbbbaabbbaaaaaabaabbaababaaaaaababababbbabbaabbbaabaaaababbbbbabababaaabaaaabbabababbabaaabaaaaaabbaaaabaaabbbaabbbabbbbabaabaaabbabbabbbabbaaaabbbaaaabbabaaabaaaabaaabbbbbaabaaaaaabbababaaabababbaaaabaababbbbbbbbbbbbbabbbaaabbabbbabaababaaabbabaabaaaababbbbbabababbaabaababaaabaabaabbabbaaaaabbbbbaabaabaaaaaababbabbbaabbabbbababbbbbaabbababbabbaaabbaaaabbaababaaababaaaaaaaaabbaaabbbbaaaabbbaaabbaaabbbabbbaaabbabaabaaaabaaaabababaabbaaabbbabbbaaaababbabaabaaabaabaababaabbbbbababbababbbabbbabaaaabbbabaababaaaababbbaababbaaaaabbabbbbaaababaaaaaaaabaaaabbaaabaabbaabaabbaaaabbaababbbbbbaaaabbbbabbbababaababbbabbababaaaabaaaabbaaaaabaaaabbbaabbbaababaababbbaabbabbbbabaaababaaaaaaaaabbbbbabbaaabababaabbaaabaaababbabbbabbabbbbabaabaabbaabbabaaaaaaabbbababaaaababbabbaaabbbbbbabbababababbababbbbbababbbabbbbaabaaaabbaaabbbababaaaaaaabaaabbbbbbaabaaaabaabaaabbbbabaabbababaabaabbaababaabbbbaabaabaabbbbbabbaaabbbbabbbbaababaaaaaabbbbaaabbbabbaaabaaabbbaaabbbaabbabbbabaaaabaaabbaaaabaabaaabaaaabbbbbbbabbbbbbbbabbbbaaabbbbbaaaabaabbaaaabbaaaabaabaaaaabaaabaabbaaaaaaaaabbaabaaababbabbabbababaaaaaaabaaabbaaababbbbabbaabbabbbababaaaaaababbaabbbabaaabaaaaaababbabaaabaaaabaaabbbbabaabbabbabbaabababaabbbbbbabbbaaaaaaaabaaabbbbbbbabbababaaaabaaaaabaaabbbabbabbaababbbbbaababbababbabbbabbabbabbabbaababaaaaabaaababbaaababbbaaaabababbbabbbaabaaababbabaaabbabbbabbbbbbaaaaaaabbaaababbbbaaaaabbabbbaaabaabaaaabaaaaababababbaabbbaaaaaaaaabbbabaabbaaaaaaaaabbbbbbabbaaabbabbbaabbaaabbaababbababbabbabaaaaabbabbbaaababbabbabbabbabbbababbbaaaaabbbbbabbaabbabbaababaaaabaabbabaabbbbabbabbaaaaabaaaaabaaaabbabababbabbaabbaabaabbababbababaaaabaaababbbabbaabaaabbbaaabaabaabaaabbababbbbbbaaabaabbababbaabbaabbaaabbaaaababbbabbabbaaaabaaabbbaababbbbbbabbaaaaabaabaababbabaaabbbaabbababcaaaaaabbbababbabaabbabbaabbbababbaaabbabbababbaabbabbabaaaaaaaababaaaabababbbabbbbabaababbbbabbbabbbbbabbabaabaaabaaaabaaaabbbabbaabbbaabbbbbabbbaabaabaabbabbbbbbabbbabbbbbabababbabaaaaabbaaaaaaaaaabbbababaabbbbabbbabbaabbaaabbaaabaabbabbbbabbaabbaabbaaaaaaaababbabbaababaabbbbabbbaabaabaabaaababbabbbaaaabaaabaababaaaabbababaabababaaaabbaabababbaaabbaaababaabbabbaabbbbaaabaababbbbabbbaabbaabbbaaabbbaabaaabbbaababbababababbbabbaaaaabbbabbaaabbabbbaaaaaaaabbabbbababbbbabbbabbabbbbababaaabbababababbbaabaaaaababababbbabbaabababaababaaabaaabbabbbabababaaabaaabababbababaabaaaaaabaababbbbaaabbababaaabaabbbbabbaaaababbbbbbbaaabbbababbbbbabbababbbabbbaaaaabaaabbaabbbabbbbaaaabaababbbaababbaaabbbaaabbababaabbbaabbabbaababaabaabbbbbaabbbabababbbbabaababababaaabbbbaabbbaabbaabbbaaaabbbaaabababbbaabbbbbbaabbbbbabaabbabbbbbaaabaaabaaaabaaabaabbabaaababaabbbaaabbaaaabababbbbababbabaababbabbaaaaabbabbbaabbaaabbaabbbabbbbbaaaabaabababababbaaabaababbabbaaaaaabbbbbababbbabbbaaaaaaaabbbbaaabbabaaabaaabbbbbabaabaabababbabababbbbaaababbbaaabbabaaaababbbbbabbbaabbbbbbabababababaababababbaabbaaabbababbabbaaaaaabbbabbaaababbaabababaababaaaaaababbabaaaaaaabaaabbbbaabbbbabbbbbababababbababaabaaababbbbbaabbbbbabaaaaababbbbabbaaabbabbababbbbabaaababaabbabbabaabaaaabababbaaabbbbabbbabababaaabababaabbaaaabbbaabbaaaaaabbbbbbbbaaabbaababaabababbabbaabbbbaaabbababababbabbbabaabbaaabaaaabbabbabababababbabbaabbabaabababaaaabbbaaaabababababbaabbbabaaaabaaaaaababbbabaabaabbbaabaaabbbaabbabbbbbabbbbbaaababbbaaaaaaabababbbaaabbbababbbbbbababbaaaabbbabbbaabbabbbbbabaabbaaaabbabbbbaaaabbbaaababaabbaabbaaabaabababaaaaabbbabaaabnbbaabababbbbabaaaaabbbabbababbbbbbabababaabbaabbbabaaaabbbbababaaaaabbbaaaaabaaaaaabbbbbababaabaaababaabaaabbabbbabbabaaabababababababbaaabbbaabaabababbbaabaaaaaaabbababbabaababbaaabaabbbabababbbaabbbbbbabbabaaabbbbaaabbabbabaaabbbbaabbaabbbaaababbabaababbaabaaaabbbababababbbaabbbbbbbaaaabbbbabaaaaaabbababbbbbbaaabaabbbbaaaabbbabbbababaababbabbbaaabbabaabbbbbbbbbbaababbbaaaabbabbaabbbbaaaaaababbbabbbbbabbaaaaabbbaaabbababbbbbbbaababaaaabbbbaaabbbbabbaaaaabbaaaaabbbbabaaabbaabbabaaabbbababaaaabaababababaababbbabbbbababbbaabaabbaaabaabaaababbabbaaaaaabababbaabaaababbaabbbbabaabbabbabaaaaaaaabbababaabbababbbabaababbaabaabababbbaaaaababaaababbaabbabaabaaabaababbaababaaaabbbabaaabbabaaaaabbbaababbaaaaabbabbababbaabaabbaabbabbaabbaaaaaababbaaaabbabaaaababaaabbaabbbaaaabaabbbabbbaaaaabbaabbbbbbabaabaaabaabbaabaaaabbabaaaaaaaabbabbbabaaababbbabaabbbbaaababaabbbabaaabbbbbaabbbabbbaaabbbaabbaabbbbbabbbababbbaababbbaaaababbaabbbaabbbbbaabbaaaabbbbabbabbaaabbbabbbaababbbababababaaaaaaababbabbabbbabbbbaaababaababbabaabbbabaaabbbbababaaabbaaaaabbbaaaabbababaabbababaabbbbbbbaabbbbbaababbaaabaabaabbaaababaaaaaababaababbbbbbbbaabaaababbbbbaababaabababbabaabbbbbaaababbbababbbbbbababaabaababbbabbababbabaaaabbbbbbaaabbbabaaaaaabababbabbabbbbbbbbabbabbbababbbbabaaabbbabbbaabbbbaaabbbbbbbaaaaaaabaaababaabbbaaabaaaaaabaaabbabbabbbaaabbaaabbbababbaabbaaabbbbabbabaababbbababbbbaabbabaaaaabbbaabbaaaaaaabbbabaabbbaabaaaaababbabaabaaabababbbabbbabbaaabbabbbababaaababaababaaaaaabbbabaaababaababaaaaababbbabbabbbaaabbbababaabbaaabbabbaabaabbabbaabaaaaaaaabaaaabaabaabaabbaaaaababbabaaaaaaaaaaabaababbbaabbbbbaababbbbbbaaaaababaabbabaaabbbbbbbbbbbaaabbababbabaabbbbabaabbbbabbaababbbabaaabbbbbaaabbaaaabbababaaaabaababaaaabaaaabbbbbbbbaabbaabbbabbabbbabaaabbbaabaaaaabbbaaaabbbbbbabbbabbbabbabbbaabaaaabbabbbbaabbbaaaaaabaabbbbaabbababbaaabaabbabaabbbaaabaaabbbaabbabbbbbabaabababbbbbaabbbabbbbbbaabababbbabbababaaabaaabbabaaabbbabababbaaaababbbbbaabaaabbabbabbabbbaabbbaaabbabbbbbbabbabababbbaabaabbbbbababbabbbaababbbbbaabaaabbbabaaabaaaabbabbbbbbababaaaabaaaaaabbaaabbbabbbbaaabaaaaabaaabbabaaaaaaabbabaaabaabbaaaabbbaabbbbbbaababbababbbbaaababaabbabaaabbababbaabbbbaaaaaaabaaaabbabaaaabaabaaabbabbabaaabaabaabababaaababbaabaababbbbabbabababbbaaabbbbaaabbaaaaaabbbbaabbbababbbabaabbabbbbbbabbbbbbaaabaaaabbbabbaaaabbaabbabababababbaaaabbbbbaaaabaabbbbaababaabaaaaaababbbbbbbaabbbaaabaaaabaaaabbbabaaaaababaabbbababaabaabbbbbabbababaabaaababbbabbabbaaababbbabbabbbbbbbaaabbabbabababbaaababbabbbaababbabaabaabbbbbaaaaabbbbbbaabaaabbaabbabaaaaaabaaabaaabbabbaababaaaabbbbbababbabaabaaabababbaabaaaabbbababbbabbaabbababbabbbababbbbbbaababababbabbbbbbabababbbbabbbbaababaabbbbbaaabbbababbbbaabbaabbaababbbaabbbbabaaaabaaaaaabaabbbaababbbaaabaaabbbbabbababbbaaabababbaaaabaaaababbaababaaabbbbaabbbaaaabbaababbbbabbaabaaaaaabaaabbbbbbbabaababbaabaabaaaabbbabaabbbabbbbaabbbabbbbbbabbbaabbaabbbababbbbbbaaaaaabaabaabbaabaabbbbabbabbabbaabbbabaabbbabbbabbbbbbaabbaabbaabbbbbbbaaabaababbbbbababababbabbabbabbaaaababbaaabababababbabbabbabaabbababaabaaabababbabbababababaaaaabaababbaabaabbaaaabbabaababbabbbbababbaabbbbaaaabaaabababaaaaabbaaabbbaaabbbabbbbbbabbabbbababaabbabbaabaababaaaababaabbbaabbabbbabababaabbbaaaaaaababbbbababbbabaabaabaabaabbabbaababaabbbaaaababbaaabbababaaaaabbbbaaaabaabbaababaababbabaabbabaabbbbabaaaaabbaaabbababbbbbaabbbbababbbbaabaaabaabababbaaaaabbbbbaabbaaabbbaabbaaabbababababaaaaabbababaaababbaababaabbabbbaabbbabaabbaaabbaabbbaabbabaabbabbaabbbaabbbababaaababbaaabaabbbabbabbbbabbababababbbaaaabbabbaaabaabbaabaabaaaababaaabbbaabaababaaaaabbbbbabbabbaaababbaaabbbbababbabbbbbbaaaabbbbbabaabbbabababbaabbbbbbbbababbaaaababbaaabbbaaababaaaabbbabaabbabbabbbabbaaabbbbaaaaabaabaababbbbbbaabababbbabaababababbbaabababbaaabbaaaababbaaaaabbaabbaabaabbabaaaaaabbaaabbbbaabbbbbabbababaaaaaabbaaababababbbaaaaabaaababbbbaabbbaabbbbbabbbabaabaabbbbbaabaaaaabbbbbabbbbaaababbaabaabbbaaabbbaabbbaaaaabbababbaababbaababababbaaaabaabaaabaababaaabbaaaabababaabaabbaababbbbbbaabbabaaababbbaaaaaabbaaaaabaabbbbababbababbbbbaaaaabaabaabaaaaaaaabaaaaabaaaabbabaaaaaabbabbbbbabaabbababbabbaabaaaababbbbbbaabbbbbabbababbabaabbbaaaabbaaaababaabababaababaabbbabaaaaabbaaababbaababbabbbabaaababbbbaaaabbaababbaaaaaabababbaababbbaabbabbaaababbbaaaabababbabaaaabaaabababbabbabaababaaaaaababbbbababababaabaaabaaaabaaaaaaababaaabbbbababbbababbabbbaaabbaababbaaaabbaaababaabaabbbbbbabbaabbbababbbbaababaabbabbbbabaaaaababaabbbbbbababaababbbbbbbabbaaaaaabbbbabbbbbbaaabbbaababbababbbbbababbbbababbababaaababaaaababbbbbbabaabbbbbababababbabbbabbababbabaabbbabbbbaaabbabaaabbaaaaabaabaaaaaaaabaaabbbabaabbabaaabbabaaaabbababbaaaabababbabaababbaaabababbbbbabaabbbbaabaabbbabaaabbaaaabaaababbbababababbbaaabaabaaaabaabbabbbabaababaaaaabbbaaaaabaabbaabaababaaabaabbabaaabbaabbbaababbbabaababbbbaaaaabbbaababbaabaabbababbaabbbbababbaabbabababaabaabbbbbbbaaaabaabbaaaabbabaababaaababaaabbabaaabbbabbabbbabaabaabbaabababbbaabbbbaabaababbbaaaabbabbababbbaabbbabbabaaabaabaabaaaababbaaaaaaaaaaabaaaababbabaabababbabababbbbabbbbabaaaaabbaaabbababbabaaaabbbaabaaabbaaababbaabbabbbababbbbbbbaababbbabaabaabbabbaaabaabbabbbbbaaaabaabaabaabaabbbbaaaabbabbabbabababbbbabbbbbabbabaaabababaaabaabbaaabbbaabababbaaabbaababbaabaabbaaabbbbabaababbbbbbaaaaabababaabbbbaabaaaaaababbbbbbbbbbabbababababbbaabbbaababbbbababaabbaaabbbabbbbbaabaaaaaaaabaaabaaaaababaabbaaabaabaabbabbabaaaabaabbaabaaabbbbaaabbaabaababaaaaaabbbbaaabbababaaabaaaaaaaaabbbbbbaaabbaababbaaaabaaaabaabaaabbbababaababbbababaaaaaaaabbbbbabaaabababbaaaabbabaabbbabbabbabbbabbbaabaababaaaabaabaababbbbbaaaababbbbababbbbbabaaaabbbaabbabaaabbbbaababbabaababbbbbabaababbbbbaabbabaaaaaababaabaaaabababbbababbbbabbaabbbaabbaabbabaabaaabbabbabbaababbbbabababbbbbaaabaaabaaaabbbbbabbbaaabbabaabbbaaabbbbbbbbbaaabababbbabaababbbbabbbbbabbababaabababbbaaabaababbbbbabbbbbabbaabbabbbaabababaababaaababbbbbbbbbbbbbaaaaabababaaaaababbaabbaababaabbaababaababbababbaaaababbbabbaaababbaabbababaaabbaabbbbaaaaabbbbababbbbabaaaaaabbbabaaaababaaaaaaaabbbaaabbaaaaabbbabbbabbbaabbbabbaaaabaabbbabababbabbababbabbaaaababababbabaaaaabaabaaaababbbaaaabaaaababbbaabaababaabababaaabbbbaaabaabbabaaaaabbbaabaaaabbbaaaabaabbaaabaabbbbaaaabbaabbbaabababbbbbaabaaaabbbbbaabbbbbaaabababaaaaaaaabbbbabaabbaaababbabbaabaaabaabababbbaaabbbababaaabbbababbbaaaaaabbabaabbabababbaababbaaaabbababbbabaabababbabbbbbaaabbaabbbbbaaaabbbbbaaaaaaabaaaaaaabbbabaabbbaababbbbabbbbaaaababbababbbbabaaabbbaabaabbbaababbbbaabbabbbbbaabababaaabaaaabbbaaababaaaaabbabbbbabbaaaabaabababbaaaaabababbbababababbbababbaaaaababbaababbbaaaababbaabbabaabaabbbbabbabbabaaabbaababbbbbbbbbaabbbabaaaabbbababaaaabaaaaababaabaabbbabbbbbaaaaaaabaababaaabbbaabbababaaababbabaaabbabbbbbbaaabaaabbaabaabbbbbbaabababbbaaaaabbaababbababaaabbbbbbababbaaaabbababbbaaaabbbababbbaabaaabbabbabbbaabbbaaaaabaaaabaabaaababbbabbaabbbababaaaababbbaaaabbbaabbbaaabbbababbaaaaabbbbaaaabbbbbbaaabababaaaabaabbbbaabbabaaabbbaabbbbbabaabbababaaabbbaaaababbbabbabaaaaababbbabbaabaabbabbaaabbbabbaaaabbaabaabaabaabababaabbbbaabbbaabbbbbbbababbaaabbabaabbbbbaabaabaabaabbaabbababbabbaaaaaabbbbbabaabbbbabbbabaaaabbaababbabaabbaabbaabbbbabaaaababbbbabbbbbaabaaaababbbbabbaababaaaaababaabbabababaababbaaaabbabbaabaaabababbbabaabbabaabbbaaaabbbaabaaaaaaaabbababaaabaabaaaabbababbbabbbaaaababbbaaaabbaababbbbbaaabbaabaaabaaaabbabbaaabbaababaaabaababbbaabababbbaaaababbbaababaaaaaabababbabaabbaaabbabbabababbabaaaaaababaaababbabbabaabaaabaaababababbbabbabbbbbbababaaabbabbbbaabaabbbbabaaaababbbaaabbbaabbbaabababbbbbbbabbaababbbbbaaababbbabbaaaaabbaabaabaabaaaabaabbababbaabbaababaaaaaabababbaababbbaabababbbbbaabbaaabbbbbabaaaaabaabaaabbbbabbbbbaaaabbabbbabbbbbbaabbabaabababaaabbbbbabababbabbbbbaabaabababbbbbbbaabaabbabbabaabaaaaaabaaaabbabaabbabaabbbbaaaababbbaabbbbbbbbaababaababbbaabbbaabaabaaaabbbababbbaababbabababbaaaaabbaabbbabbaabbbbbaababaaabbabbbbbbabbbbaaaaababababaababbbbbbabaaaababaaabaababaabbbbabbbababababbbaaaabbbbbaabbbaaaabbbbbaabbabbbaababbaabbbbabaabaabbbbbbbaabbabbbbabaaaaababababbbbaaabaaaaaabaaabbabbbbbbbabaaaaaaabbbabbabaabaaababaaaabbabaababbbabbbabbbbbaaaabbbbbabaabbaabbababbbabbbaababbabbabbaabaababbaaaababaaaaababaaaabaaababaaabaaaaabaaaabaaababbbaabaabbabbbaaaabbababbbaabbbbabbbaabbbbaaaaabaabaaabaabbaaaabbaabbaabaabababbbababbaabbbbaabbaabababbabbbaaababbbabbbaabbbbaaabbbaaaaabbbbabaababbababbbbabaabbaaaaaababbaaaaaabbababbababbbabbabbabbaabbbaabbbaaabaaaaaaaabbababababaaaabbbbbaabbbbbbbbbbaabbaabaabaabbbaaabbbbaabaabaaababbababaaababbbbabbbbbbabaaaabababbababbababaaaaababbbaabaaaaabaabbbaabbbbaaaababbbababaababbbaaabaababbaabaaaaaabbababbbaaabbbaabbaaabbaaabbaaabaaaabbaaaababbabaababbbbaaabbabbaaabaaaaabaababababbabbbbabaaaaababaabbaaabbabbaabbbaabbbaabbbaabababbabaabbbaaaaaaaaababbabaaabababbbbbbabaaabbbaaabbabbbaaaabbababbaaabbabbabaababbaaababaabbaababaababaabaabbaabbbbaabbabbabbbbbbbbaabbaaaaabbabaaaaabaaababbaabbbbbabbabbbaaaaabaabbabbaabbaabbaaaabbbbaaabbbbbbaaaabaaabaabbaaaabbbbabbbaabbaaaabbbbbaaababaababbabbababababbbabbbaaabbababbbaaababaababbbbabbaabbaaabaaabbbbaababbaabbbbbaabbbbbababbabbabaabbbbaaaabbaaaababaabbaaaaabbabaabaaaababaaabbaababaaaaabbbbaaabbbbabbabaabbbbbaabbbabbaabaabbaaaaabbabababbaababbaaaabbabbabbabbaaaaaabbbbbaaabbabbabbbbabaabababaabbaababababbbaabbbbaabaaabbaaabababababbbaabbaabbbbabbabababbbaabbaabbaabbbabbababbbbaabaabaaaabbbababbaabbabaabababbbabbbbbabaaabbabababababababaababbaaabbbabbaabaaaaabbaaabaabbabbaaaaaaababbaaababbbabababbbaabbbababaaabaaabbbababbababbababababaabbaaabbababbbbbaabbaaabababbaabbbaabaabbabbaaaaabbbbaabaabbbaabbaaaaabbababbbabaababaaaabbaaabbbabbaabbaaaaabbabaaabbbbaaabaabbbbaababbaabbbabbaaaabababbaabbbbbaaaabaaaabaaaabbabbbbbbbaaaababbbabbabbbabbbbbabbaabbaabbbbbbbabaabaababbabbaaababababbabbaaaabaaabbaaaabbbabaaabababbabbaabbabaaaaabaababbbaaababbaaaabbaabaabbabbaabbbbababbaabbbbaabbbabbaababbaaaabbabaaaaabbaabaaaaabaabbbabbbaaabababaaabababbbaabbaabaaabaaaabaaaababbaabaaabbabababababaaabbaabbbbbbaabbbabbbbaaabbbaabbbbaabbabbababaaabbbbabbabababaaaaaabbbaabaabaabaaabaaaababaabababbbbaaaabbaabbabaaabaaaabaaaaabbbaaaabbabbababbbaaabababaababbaabbaaaabaabbbaaabaaabaababbaaabaaabababbabbbbbbbbaaaababaabaaaababbababbaabbbababbaabbaaaaaabaabababbbbbabaabbabaaabbababbbbbabbbbaaaaababaaaaaabbabababbabaabbabaaaababaaabaababaaaaaaaaabaaabaababbbabbabbbbbbabaaaaaabbaabbbababbbbabaabaabaaaabbabbbaaaabbaabaabaaababbbabbaaaaaaaabbbbabbaaaaabaaaaaaababbabbbaaabbbabbabbaabbbbaababbbbbbaaabbaaabaabbaabbaabbaabbaabaaabbaabbbbbbababaababbabbbbbaaaaaabbbbbababbabbbbabaaaaabaabbbabbbabaaaabbbabbbbababaaaaaaabaabbbaaaaabbbbbbaabababbbaabbbabbabbabbbaaabbabbbaaababbbbabaabbbabababbaaabbaababaaaaaaaaaabbabbaaaabbaababbbbaaabaabaaaabaabbaabbabbabbabaababbbaababaabbbaabbbababbbaabbbabbaababaabbaaabbbbabaabbaabbabaabbbbbbaabbaabaaaabbaabababaabababbabaaabaabaaabababaabbbaaaababaababbaabaababaabbaaabbabaaabbbabbabbbbbaabababaabbbabbbaabbaaababbaaaaaaabbaabaaababbbbaaabababbababbbaaabaababbbbabbbbbabbbbbaabbbbbababbbababbbbbabaaababaabababbbbabaabaabaaabbaaababbabbbaabbbbbbbbbabbbaaabbabaabbbbaababbababbaabaabbaaaaabbaaabaaabaaaaabbaabbaababaababbabbaaaabbbbbbbbbabbaaababaabababaaabaaabbaaaabbbbaabbbabbbbaaabbbbbbbaaaaaabaabbaabbbabbbbaabbbbaaaaabaaaaabaabbababaaaaababbbaabbaaabbaabaaaaababbbaaabaababaaaabbaabbbababaaaaabbbbbbabaababaaabababbabbabbaabaaaababbbabaababaabbaabbabaaababbababbbabbaababaababbbbaabaaaababbbaaabbbabababbbbaaababbababaabababaabaaabaaaaaababbaaaabbbabaabbabbaabaaaaabbbaaabbbaababbbaaaaaabaabaabaaabbaabbbabbbbbabababaabbbbaaabaaabbbbaabbbababbabbbababaaaabbbaabaabbaaabbbabbbaabaaaababbabbaaabbbaabaabbbabaaaaabbaaaabbaaaaaababaabaabbaabbabaabbabaabbabbbbaaaaababbbaabaababaaaabbabababbbabbaaabbabbaabaabbbababbababbaaababbabaababbaabbaabababbbbbabbbbbbbbbabbbaaaaabababbaabbaabbaaaabababbbaabaaaaabaabaabbabbbbbababaaaababaaaaaaaaabaabaaabbbabbabaabbabbbbbabbbabbaababbaaabbbbbabbaaabaaaaabbaabbaabaaabbabaaabaabbaabbabbababaababbbbabbbaabbaabaaababababbbbbbaaababbaabaaaaabbabbabbabbbaabbbbaabaabaaaabbbababbaaaabaabaabbbbbaabbbaaaabbaababaababbbabbbbaabaabababaabaabaaaababbbababbbbababbababbbaaaaabbbaababbabbbbbbabaaaabbbbbbbabaaaabbbabbaaababaababbbbbbabbbbaaaaababbbaaaabaaababbabbaabbbbababbbaabaaabaaaaaabbbaaaaabbbbbabbbababbabbaaabbabaaabaaabaaaabbabbbbaabbaaabbaababbababaaaaaabbaaaabbbbabaabbbbabaaaaababbbababababbbbbbabaaaaabbbbbbabbaaabbaabaaaaaabbaaabbbabbaaaaabaabbbabaabaaaababbbabbbbbbababaaabbabbaaabaababaaaaabbaaababaabbababbbabbabbaaaaabbaaaaaaabaabababbababbbaabaaabbbabbaaabbaababbbbabaabaabbaaaaabbbbbbaabaababaaabaabbabbbabbbbbabaaabbababababbbaaaaaaabbbabaabaababbbaabbbbbabaabababaababaaaabababbaabbbbbaaabbbbbbbaaabbbabbabbbaabbbaabaaaabaabbaabaabbaaabbbbbbbaaabbababaabbbbbaabbaabbaabbabbababbabbbaababbaaabababaabbbababbabaababaabaaabbbaabaaabbabbaaaabbabaaaaabbaabbbbbbaabababbabaabbaabbbaaabaaaaabbababbaaaabbbbbaabbbbbbbaabbabaaababababbaabbbaababbababaaaaaabbaabbbaaaaabbaabbbbbbbbbaaaabbbbaababababbababaabbbbbbbbbabbbbaababaaabaabaabbbaaaaaaaaabababaababbbbbbabbbabbbbababaaaabaabbaaaaaabababaabbbabbabbaabbaabbaabbaaaaaabbabbbbbbaabaabbbbbbbabababaabbaaaaaabaaabbbbabbaaaaababbaabbbabbbabbbaabaaaaabaaabbbbaabaaaabaabaaaaababaaabbbbababbaabababbaaaaababaabbabbaababaaaabaaabbbbababaaaabaababaabababaaaababbbababaabbbbbbbbbbbbabbabbbaaaababababaaabaabbaabaabbbaaabbaaabbaaabbaaababbbbbbababaaaabbbbbabbaabbaababbbbbaabaaababbbbaabbaaaaabbabbbaabbbbbbabbaaabababababaaabbbababbbbaabbbaaaaabbbabbabbaabaabaababbbaabaaaaabaababbbabababbabbaabbabbbbaabababbbababaaaabbbbbbbbbaaaabaaabbaabbbbbaaabbbbbbbaaabbbbbaabbaababbaabababbbabbbababbbaaababbbbbababaabbaaaabaabbaabbbabaaaaabbbbbabbbababbbbbaaaaabaabbbabbbabaaaabbbaaaaaaababaabaaaabaabbbbbabbbbaabbbabaaabbabaaaabbabaabbbbaaababaababaababbbaaaaaababbbbabaaabbbbaabbbbaabbabaaabbbbbbabbbaaabbbaaaaababaabbababbbbaababbbabbbbbabababbaababababbaaabbaababbbabbaabbababababbaaaabbaababaabbbbabbaabbbaabaabababbbbababaabababbababaababbbbaaaabbaabbbbbabbbbabaaabbabaaabbaababababbbbaaaaaaababaaaabbababababaaababababbabbbabbbbaababbbaabababaabaaabbbababaabbaabbaaaabaabaabbbaabbbbabbaaaababbaaabaababbbaabbabbbaababbaaabaababbbbbaaabbaaaaabbbaaaabaabbbabbbabaaabaaabaababbaabbbaaabababbaababbbaababbbabbabbbbabaababbaabbaababbaababaaaabaabbbbaabbbbbbbabaaababababababbbbbbabbaabbabaaabababbbbababababbbabbbababbbbbbabbabbbbaabbabbaaaaaaabaabbaaaaaaaaabbabababbbabaabbabbbabbbaabbbbabbbaaabbbbbbaaabbaababbabbbbbbbbabbabaaaaaaabbbbbaaabaabababbbbabaaaabbbbbbaaabbbabbabbaaaabbbbbabbabaabbaaabbbababaaaaaabbbbbabbbbaabbaabaabbabbaaabababbbbbaababaabbabaaaabaaaaabaaabaaaaaabbabaaaabbbabbaabababbbaabababbbababbaaabbbbabbbbaabbbababaaabbbbbaaaaaabababbabaabbabbbabababbbbababaababababbabababbbbabbaabbabaabbaabbaaabaabbabbbbbabbbabaaaabbaababaaabaabaabbabbbbababaabababbaababbbbabbbaababbababbabbbbbabbaabbbaaaabbbbaabbbabaababbbaaaabbbbbbbbbaaaaaaaaabbabbabaaabbbbaaabbbbbaabbabbabaabaaaaabbaaabbaaaaaabbbbaabaaaabbbabbaaabbbbbbaabbabbbaaaaaabbaaaabaaaaaabbbbbaabbbabbaabaaabbaaababbababaaaabbbbaababbbbaaabaabbbabbaaabababaabaabbbbaabaaabbbbaabbaaabbaaaababbabbbbbabababbaaaababaaaabbbbaaabbaaabaabaaabbbbbaabaabbbaaababaaababbaabaaaaaabababbbbabaaaaaababbabababababbbbabbbabbbaaaaabbbbabbbbaaaaabbabbaaaaaaababaaaabbbbaabbbbbaabbabaaaaaaabaaaababababbbababbabbabbbbbbbbabababbbbabaabababaaabbaaaaaabaabbabbbbaabbbbaaabbabaaababbabbaaabbaabbbbaaabaaaaabbbabbbaaabaaaabaaaaabbbbababababaaaaabbbbabbbbabbababaaabaababbbbbaaabbababbabbabbaaaabaaaaaabbabbababaabbbbbaababababbabababaaabbbaaababbaaaabbaabbbabbbaaabaaabbbbaabababbaaaababbabbbabaabbbbaabaabbbabaabaaababaabaababbababbababbaabaaabbbbbababababaababaaabaabbaaaabaababbaabababbbaabbaabbabaabbbabaaaaababaaababbbbbbbababbbbaabbababbbabaaababbbaababbbbaabaababaabbaabaaabbbbbaababbaabbbabaaabbabababaabababbabaabbbbaaaaabaabaabaabaabbabbbbabbabbabaabbbaaabbbabbbaabbaaaabaabaaababbbbbaabbbabbbbbaaababbbabbbbaabbaaaaaaabaabbbabbbbaabbbabbababbbabbaaabababbabaaababbbbabaaaaabbbaababbaaabbbaaaabbaabbbabbbbbbabaabbaabaabbaaaaabaababbababbabaaaaaaabbbabbbbbbbbbbbbaaabaabaaababbabaaababaabaaaabaaaabbabbabaaaabbaaabbababbbaababbaaabbbabbababbabbabbabababbabaaaabbaaabaaaaabbbabbabbabbaabbabbabaaaaabbaabaaaabbaaabbabaaaaaababaababbabbbbbababbbaabbaaabbaaabbbbbabbbbbbbabaaabbabbbbaaaabbbbabbaaaabbbbaabbaababbbbbbbbaaaaabbbaaabbbbbbbbbbbabaababaaaabbbaabbaaaababbaabbaabbbbbabbbabaaaabbbbbbaaaabbaabbaabaaaaabbbababaaabbaabaaaaabaaaaababbbbaabbaabbbbaababaaabaabaaabbbaabbaabbabaabbbbbabbaababbabbbababababaaabaababbbaaabababaaaaabbbaaabbaabbaaaabbabbabaabaaaabbaaaaabbbbbbbabbbaaaaaabababbbbbaaabbabbabbaabbbbbbbbabaabababaabaabbaabbaababbabababababbbbbbbabbabbabbaaaabbabbaaabaabbabaabaabaaabaababaaabaaaaaababaaaabaaabaababbbaaaabaabaaabaabbbabbbbababaaababbababbbbaabbbbaaabbbabaaabbababbababababbbaabbaaaabaaabbaaababaabbaababbababaaaabbabbbababbabbaabbaaaabbbaaaabbbababaaaaaabbbbabbaaabbabbaabbbabbbaaababbbbbaaabababaaabbbbabababbbbababbabbbaaabababababbbbbbababababbaaabbbabbbbabbbaaaabbaabababaabababaabbabaabaababaaaaaaaaaabbaaaaaabaaabbabbaabbbabbbbabbaaaaaaababbbabbbaabbaabbaababaababbabaaaababbaaababbbbbabbbbbbbbaabbabbbabbababbbaaababbabaaaaabaaaaabaaaabbaaabbaaaabbbabbbababababaaabaabbbbaabaababababbaabaababbabaaababbaaaabbbbababbababababaaaabbaabbabbbbabbbbbabbbbbaaaababbbbaabababaababbabbbbbaaaaaabbaabbbabbaaabaabbbabbbaaaabaabaabbbaabbaababaabbbbbbaaabbbbbbaabaaababaabbabbbbbbabbbbaaabbbabaaaaaaabbbaabababaabaaaabbbaabababbabbbabbabaabababbaababababbbbabbabbaabbaaaaaabbaaaabbabbabaaaababaaabaabbabbaabbaaabbbbbaabbabbbbbbaabbaabbabbbbbbaabbbbabbbbbabbababbbbabaababbbaabbbabbaaabaabbabaaabaabbbabbaabaabaabaabbbabbbabaaaaaaabbbbbabaababbbbbaaabababababbabaabbbbababaaababbbbaabaaabbaababbbaabaabbbbabbbbbaaaaaaaaabaaabbbaaabaaaaababbaaaaaabaaabbbaabaaabbabaabaaaaaabbabbbaaaaaaabaabbabbabaabbaaabaababaabbabbaaabaababbaabbaabbbbbbbbbbababaabbabaabbabbaaabbabbabaababbbbabaaaabaababaaaaaabbbaabbbaabababbaabababbbbbbbbaaababaababaabaabbbaaaaaabaabbaaabbaaababababbbabaabbabbaabbabbbbbabbaaaaabbabbbbabbbababbababbaaababbabbaaabbabbaaaabbabbaabbabbaaabbaabbaaaaababbbbaaaabbaaababbbabaaaaaaabbaaabbababbabaabbaabaaaabbbababbbbaaabbbaaabbababaaaabaaabaaabbaaabaaabbbaabbababaabbabaabbabaabbbbbabbabbbbbaabaabbbabbaabaabaababbbabbababbabaaabbabbbbabbaababbbaaababbabbbbbbbababbbbabbbabbabbabaaaaaabababbabbabaabbbbaaaabbbabbaaabbbabaaabababbabaaabbabbbbaabbaabbabbaaabbaabbabbbaabaabbbbaabaabaaabaaaaabbaabbbaaaaabaaabbaabbaaabababbabbaabababbbabaaaaaaababaabbbbaabbabbaaaabaaabbabaaabbbbbbababababbaaaaababaaabbbaabaabbaaabaabbbbbabbabbaabbabbabaabbaaabbbbbbbaabaabbbabaabaabaaabaaaaaaaababbabbababbaaabbbbabaabbbbbbaabbbaababbabaaaabaaabbabaaaaababbaabaabbbbabaabbaaaaaababbabbbaaaababbbbbabbababbbabbbabbabbaaabbaaaabaaaaabbaabaaabbabaababbaabbaaaababaabbbbababababaabaaaaabbaaabbbbababababbbaaaababaabbbaaaaababaaabbaaaabbbababbbabbbbaaabbaaabbabaaabbbbabbbabaaabaabbbaabaaaaababbabaaababbabbabbbbbbaaaababbaabbababaabbaabbbaabaaabababaabaaaaabaabbbbabbbabbbbbbbabaaaabbbabbbbbabbabbaabaabbbaaababbabababbaabaabaabbbaaaabaaababaabaaaabbbaabbbbbbbabbabbabbbbbbbbbaabababaaabbababaababaababaaabaabbbbbaabaaabbbabbaaabbabbaaaaababbaabbaaaabbabbaaaaaaabaaaaabbbbababbbbabbbbbabbbbabaababbaabbbaaabbbbbabbabababbbbaababbababaaaabbabbbaabbbbaaaabaaabbbbabbaaababbbbbabbbbbabbabbaababbaabbbaaaaabababaaaabbbbbaaaaababbbaababaaaabaabaaabbaabbbaabaabbbbbbababaaababbbbbbabaababbbaabbbaaabbbababaabbabaaaaaabaaaabbabaaaaabaabaaaaabbbaaabbbbaaaabbbaabaaabbbaabbbaabaabbbbbabbaababbbaabbbbaaaabbaabbaababaaabbaaaaaaaabbbababaaaaabababbbbbbbaabbaaaaaaaaaaaaabaabbaaabbbaaabbaabbaabbabbbbbabbabaaababbbabbabaaabaaabaababbababbabaaabaaaaaaaaabaaabbabaaaabbbbaabaabbbbaabbababbabaabbaabbaaabbaabaabaaabababbabbbaabbbbaababaaaabbbabbbbaabaabababbabaaabaabbbabaabaabbaabbbabaabbbbbabbbabbaaaaaaaabaabbbababababbbbababbaaaaabbbabababbbbbaabbaabbabbbaabbbbaabbbaaabbabbbababbabbaabbbabaabaabbbaaabaaababababbbbaaabbbababaababbaabaabbababaaabaabaababbababbbbaabbaababaaabbbaaabbaabaababbabbaabbbbbbaaaaababbbbaabbabbbabbabaaababbaabbbaaaaabaabaaabbaababbaababaaabababaaaaababaabababaabbbabbabaaabababaababbbbabbbbaabbbbaabbaaaaaaabaabaaabababbbbabbabbaababbabaaaaaaaabbbbaaaaababbabbababbbaaabbabbbbbaabbaabbabaabbaabbbaabaabbbabaabbaabbbbaabbbbabaababaababababbaaabbbababbbaababaababababababaababbaabaabbabbabbbbbaaaaababaabbbabaabbbababbbbbbbabbbaabbaaababaabaabbbaaaaaabaabaabbabbabbbbaaaaaababbaaaabbbbabbbbbbaaaabaaaabbbabaabbbbbbbbaaababaaabaaaabbaaabbbaaaaaabbabbbbbbbbbabbbbaaaaaaaaabbbabbabababbbbababaaaabbaaaabababbabbbababbbabaabbaaaaaaaaababbaaaabbbaabbbbaaabbbabbbbbabbbaaabbaababbaabbabbabaaaababbaaaabbaababbabbbaaaaabbabaaabbaabaaaababaabbbabbaabbbbabbbabaaaaaaabaabbbbaabbababbaaabbbbaabbabbbabaaabaabbabababaaaabbbaaaabbaaaaaabababbbabbbababaabbbbbbaabaaaabbaaabbababbaabbaaabaaaaabbbbbaabbabbaabbbaabbbbbaabbaabbbaabbaaababaababaabbbabbaaaabaababbabbaaabbababaaabbababbbbbabaaabaababbbabbaababbaaababaaaababaababbbbbbaababbaabaabbbbaabaababbaabaaabbabababaabaaaabaababbbaaabaaabababaaababbbbabababbbababaaababaaaaaabaaaaababaababaabbbaabbaaabababbababaaaabaabbbaaaabbbbaabaaababaaababbabbbaabaaaabbaabaaabbabbbabbbbbbbbbbbbbaabbaaaababbbbabababbabbaaabbbabbaababaaabababbabaaabaababaaaaaabbbbbbabababaaabaaaabaababbbaaaabbbabbabaaaababbabbaababbabaaabbbabbbbbababaaababaabbbbbaabaaaabaaaaaabbababaababaabbabbabaabababbbbbaabbaabbaaabbaaaaaaaaaaaaababbbbbaababbbbbbabbabbbabbaaabaababaabbbabaaabbaaaaaabababbaabbabaaabbbbbabaaababbaabbaabbaabababbbbabbaaabababbaabbaaabbaabaabbaabbbbaababbbaabbbbabbbbbbaaababaaababaabbbabbabbbabaaaabbbaabbbbbabbbbbbabbabababaaaabbaaaaaabbabbbaaabababaaaababaabbaabbabbaababbbbbabababbaaaaabbabbbabbbaabbbbabbaaabbbabaabaaabaaaaaaababbbbbaaabbabbaabbbbbaaabbabaabaababaaaaaaaabbabbaabbbbabababbaabaabbaababbbabbabbaaaababaaabababbbabaaaabbababbbbaabaabaababbaabbaabbabbaabbaababbabbaabaabbabbbabbbbbaaaabbabbbbbabbbbbbbbaaaabaabbbbbaabbaaaabaaababababaaaabbbbbbbaabaaaaabbabbabbbbbbbababaabbaaaaababaababbbaaaaaabbbaabaabaaabababbbabbaababbbbbaaabaaaaabaaaaaaaababbaaabbaabbbbbaaabaaababbaaaaaabbaabaabbabbbbaaabbbbbababbabaabaaabababbaaabbabbbbbbbbbbabbabaabbbaaabbbbabbaaababbbbabbbabbbbaabababbbbbabaabaaabbababbaabbbbbbbbbabababbabbbaaaababbbaaabbaaababbbabbababbaababaaababbaaababaababbbababaabbaabaaabaaaabaaabaaaaaaaaababbaabbababaabbbbaaabababaaaaaaaabababaaabbabbabbbababaababaaabbbaaaaabbbbabaabbbaaababaabbbaaabbbababbbaaaaaabaaababaaaabaabbbbabbabbbaabbabbbbababbbaaabaaabbbabaaababbbbbaabbbaabababaababbaaaabbabbabbbbabbababbabbaaabbababaabbbabbbababbabbaaabbaaabaaabaababbabbbabbababbaababbaabbbaabaaabbaabaaababbbabbbbbbaaaabbbabaaabbbbabaabaaabaaabaaaabbaabbaaabbaabbbabbaabbababbbabaaaabbaaaabaaaaabbaaaabbbbbabaabaaabaabbbbaabbabbbaaaaabbbbbaababaaaabbbbaaaabbbbabababbbabbaaaaababbbbbabbabbabaaaaabaaaaaabbbbbbbaabaaaabaaaabbbbabaabbbbababbaaabbbbbaaaaaabbaababaaaaaaabababababbaabbabaaabbaaabaabbababaaababbaababbbbbbaabbaaaabaabaabbabbaaabbabbbbabbaabababaabbbbbaabaabbbabaaaaaaabbbbbbaababbbbbbbbaabbbbaabbbbbbabbaaaabbbbbbbaaaaabbbbaaabababbbbbbbbbabaabbbbbbbbbbabbbabbbabbbabaabbbaaaaaabaabbbbbaabbbbaaabbabaabbbaaabbabaabaabbbbaabbbaababbaaabaaaaababbaaabbababbbaababaabbbaaabababababaabababababbaaaaaaababaabaabbbaabaaaabaaababaaaabbaaaabbbbbbabbbbbababbbaababbbaabbbaababbbaabbbbbbbbbbaaabababaabbaaabbbaaaaaababbbbaabbaabbbababbaaaaaaaaabaabbbbbbbababaabaaabbbbaaabababaaaabbaaaaaababaabbababaababbbabaabbabbbabaaaaababbaabbbabbaabaaababaaabbbabbbaabbbaabbbbbabaabbbbbababaaababaaabaaaaabbbaaabbabbababbababbbbbbbbbabbabaabbaaaaaabbaaaabbbabaaaabbbababbbbaaaabaabbaaaaabbbbbbaaababbbbbbaaaaababaaabbbaaabbababbbababababbababbabbabbaaababaaaaabbbaabbbaabaabaaabaaaabaabbbbbaaabbbbaabaabbbbaaaaaabbababbbbbbbaaaabbaaaaabbbaababbbababbabaaaaababbbbababaaaaababaabaabbaabababbbbaababbabbabaabbabbaaaaabbbbbaaaaababaaabbaaabbaababaaaabababbbabaaaabaaabbabaabbabaabbbaabbbbbabaabbaababbaabbbababbbababbbbbbaabaabaaabbbbabaabbbbbabbaaabbaabbabaaaaabbbbbbabaaababababbabaaaabaabaababbababaabaababbbaaaaababbbaabbabbaaaaaabaabbbbabbabababbaaaababbabbabaaaaaaabaabaaaaaaabababbaaabaababbabbbbbaaaaaabbbaabbaaabbbbbbabbabbbabbaababaabbaabbabaabbabaababbbaabaabaabbaaaaabbbaabbbbababbbbbbbbbbabbbabbaabaaaaaababbabbaabababbbbbabbabbbbaabbabaaabbabbbabaaaabbabbaaababaaaaaabaabbbbbabaababbabbbbabbbaabaabaaababaabaaabaaabaaabbbaabbaabbbaaaabbbabbbbbabbbbabbabbaaabaaababbbabaaabbaabbabaababaabbaaababaabbbabbabbbaabaaabbabaabaaaaaabbabaabbabaaabbabbababbbaaaabaabbaaaaaaaabbbbbaaaabaababaaabbbabaaabababbbbbbababbababbbababaabbaabbbaaaaaabbbbababbabbababababaabbbbbbababaababaabbbaaabbbaaababaaabaabbbbaaabbaabbabababaaababababbabbbabbbaaaabaaabababababbbaabbaabaaaabaabbaabbbaaabaaaaaabbabaababbbbabbaaaabaabbbabaababaabbaaaaaabaababaaaaaabbaababbaaabaaabbaabbaaabbaaaaaaabbabbbbbaabbbbbaaabbbbabbaababbaabbbbbbbaaabaaaaabaaabababababaababbbabaaabaaaaaaaaaabbbaaabbbaaabbabbaaabababbbbaaaaaabbbbbabbaabbababbabababababbababbbabbabaabbababbbabbabaababababbababbbbbbabbabaaabbababbabbbbabaaabbabbbabbbaaaaabbbaaababaabbbaaabbbbabaaaabbbbabbbbbbaaabaaabaaaaabababaabaaabbaababbaaaaaaaaaababaabaaababababbbbabbaaaaabbaabaabbbaabababbbabbaaaaabaabaabbababbaabbabbaaaaqaabbbaaababaabababaababbbbaaabbaabbabababbabbbbaaabbbababbbabaaaababbaaabbabaabbbbabbbaaabbabaabbaaabbaababaaaabbbaaabababbaabababbbbabbbabaabbabbabbababbabbaabbabaaaabbbabbaaaaabaababbbaaaaaabbbaaababbabaababaabaababbabbbabbbababbaaabaababaaabbbaaaabbbaabbbbbbbbabaaaabbbaabbbabbbabbaaabbabbbbbaababbbbaaabbaaabaabbabbababbabbbbbbbaabbaabaaabbbbabaaababaabbabbbaaaabaaababaaaabbabaabbbaaabbbbbbaabaabbbaaaaaabbbbbaabbbaababbbbbbbaaabbbbbabbbbaabbbabbaaabbbbbaabababbbbababbaabbbbbbbaaaaabbaabaabbbbbbabababaabaaaabaaabbabbaabbbaabbabaaabbababbaaaabbaaaaabbababbaaabaaabbbbaababbbaaaaabaabbababbabaabbaaaaabbbaaaaabaaaaabbaabbaaabababbbababaaaabaaabbbbaabbababbbaabbbbbabababbaababbaabaaaaabbaabbbbabbabbabaababbaabbaaababbabbbbaaababbababaabbaaaaaaabbaaaaabbbababaaaabbbbbbbbbbbbbbaabbbaaaaabbbbabaababaabaabaaabbbaabbbbbbbbbbabbbaaaaabbbaabbaaabbaaaabaabbaaabbbbbaaabbbbaababbabaaaaabbaabbbabbababbaabbbbaabbaaaaabbbaaaaaababbaaaabbbabbbbbbabaaababaaaaabbbaaaabaabaabbaaaababaabbbbbabaabaaaaaabbbbaaaaababababbbbbbababbbbbaabaabbaaaaabbbbabbababbbbaaabaabaaaaabbababababbababaababbbbbaaaaaabaaabbbaabbabaabbabbabbbaaaabaaaaabbbbababbabbbaabbaabbbbaaaabbabbaaabaaaabbabbaaaabbbbbaaabbbaaabaaaaaaaaababaabbbbaaaaabaaaaaaaabbaaaaaaababbbabbbabbaaaaabaabbbabaaabbabbabbabbaabbbbabbaabbababaabbbaabbbbaabbaaaabbabbabaaaaabaabbabbaababaabbababaabbbabbbbaabbabaabbabababaaababbaabaabbabbaaaababaabaababbbbaaaaababaabbbaabaabaababaabbbbbaabbabbabbaabbbababbabbabaabaaaabaabbaabbabbabababbbbbbabbbabaabbabaaabbbaaabbaaaaaabaaaaaaabbbbababbbbbaababbbabaabbababaabaabaabbbabbaaaabbabaabbaaaabbabbaaabbaababaaabbabbbbaaabaaabaaaaabaaababbabaabbbbbbbbbabbbabababbbaabaaabbabaaabbbbabbbbbbababbbbabaabaaaabbbababbbbababbbabbabbbaaabbaabbbbababaaabbabaaababbaabbbbbbbbbaabaabaabbbbbaabbbaabaaaabbaababbabababbaaabbabaabababbbbaabbaabaaabaaaaabbaaaabaabbabababbaabbaabbabaaaabbbabbaaabaabbabbbaaaaabbbbaababbbabaaaaabbaaabaabaaaaababbaabaaabaaabbbbabbbaabaabaaabaabababbaaabbbbababbbbbaaabbbabbbbabbaabbabbababbbbbabaababbabbbabbbbaabbbabbaaaaabbbbabbbaababbbbabaaaaababbbbbabbaabbaabbabbaababababbbaabaababaabaababbaabbaabbaabbbbabaaabbbbabbbaaababbbabbaababaaabababaababaaaababaaaabaaaaaabbabaabaaaaabbbaabaaaaabbabbbaaaaaabaaababbbaaaaabbbbbababbabbbbbaaabababaabbaabaabaababbbbaaaaabababaaaabbabbbaabbabbabbaaaabaabbbbbbabbbaaabaaaaaaaabbbabaabbabbaabababbaaaaaabababbbbbaabbaaabbbbababbbbbbbbaabbbbbbbbbbaabbabaaaabbabbaaaababaaaabaaabbbbbbabbbabbbbbbababaaabaaababbbabaabbabbabbaaabbabaaaabbbababbabaaabbaabbababaabbababbaaaabababbabaabababbbbaabaaaabbbabababbabbbbabaabbbbaabbbbabbabbbbabbbaaabbabbabbbabbbbbabbbababbabaababbabaabbabaabaaaaababaaabababbaababaaaaaabbbbbabaabbaabaaababbabbbbbaaabbaaabbbaabbabbbaaabbbabbaabbbbabbabbbbbababaaaabaaabbbbabaabaaaabaaaabbaaabbbbaaaaabbbaabaabbaaaaaabaabbbabbaababbaaabaaaaaabbabbabbbaabaaabbbbbaaababbaabbbbbbbbabaaaaaaabbaababbababaabbabbbabbbababbbbabaaabaaaaaabbabaabbabbbbaabbaaabaaaaaaaabbbabaabaaaababbabaabaaaaabbbaabaaaababababbbbaaaaaaaabaaababbbbaaabbbbbabaabaaaabbbbbabbaaaaaabbabababbaabbabbbabbabaaababbbbbaaaaaabbabbbabaabbbabbabaaabaabbbbaaaaaabbbbbbbabbabaababbbabbbbaaaaabbabaaababbaabaaabbaaabaaababaabaaaaaabbbaaaaaabbbbbbbbbabaababbaaaabbbbbabbaaabbabaabbbbbbbaabbababababbbaabaabababaaababbbaababbababbaabaaaabbbaaaaabaaabbabbbbbababbabaabbaabaaabbbaaaababababbbaaaabaaabbaabbabbabbbababbbbababbaaaabbababbbbbbbbaababababbbbaaabaabbbbaaababbbabbaababaaaaaababaabaaaaaaaabbbabbbbbbaabbaababbabbaaaaaaabbabbaaababbbabbbbbaaaaabaaaabbbbabbaaabbbbaaabbbababbababbaababbbaababaabbaaaabbaabbaaababbbaaabaabaabaabbaaababaabbaaabaabaaabbaabbbbbbabbbbbaaabbbaaabaaababbbabaabbaabababbaaaaabbabbaabbaabaaabbaabaaabbabbabbbbbaabbbaabbbbbbbbbbbbaabbbbaabbabbaaaababaababaabbbabbaabababbbbbaabaabbababbbababbaabbabababaaaaababbaabbbaabbbbbbabbbaabaaaaababaababbbbaaabaaaababaaabbbaabaaabaaabbbaababaabbabaabbaabbbbaaaabbabbaabaaababaabbbaaaabbbbbbbaabaaababaabbbaaaabababaabbabbbababaabbaababaaabbabbababbabaaabbbbbaabaaaaaabaabbbbbaaaaaaaabbbbaaabaaaabbbaaabbaababbbabaaaababbbbaaabbaaabaabbaaababaabbbabaabbbabaaaababbbbaaabaabababbbbaabbbaaabbaaabaabaabbbaababbabbbbababbbbbabbbabaabbaabaaababbbabaaaababbbababaaaaabbabaabbabaaabaabaaababbabababaabbabaaaaabababbababaabbaaabababbbabababababaaaabbbaabababaabaabbaabbabbaaabbbabbbbbaabaabaabbbbabaaaabbabaabaaaaaabbaaabbbabaabbbabbabbbbbabaababaaaaaabaabbabababbaaabbabaaaabababbaaaabbbbaabababbbaabbbaaababababbabaabbabbbbabababbababaabaabbabaaaaababaabbbbbaaaaabbaababaabbbbabbabaabaaabaabbaaabababbabbbaabbbababaabaabbaaaaabbababaaaabbabaabbabbbabaababbbabbbaaaababaabaabbaabbbabbbabaabababbabbbbabbabbabbaabbbabbbbbaaabbaabbbaaabbbbaaabbbbbbaabbbbbbbabbbabbbaababbabbbaaaabbbbbbabbbbaaaababbbbabbbbabbbabaaabbaabababaabbabbbababaaaabbababaaaabaabbabaabbaababababaababbabaababbbabbbaabababbaabbabbbaaababaaaaabbabaaaabbbaabbbaaabaaabbabbbbaaaababaaabbaaabbaabaaabbbabbabbbbbaabaabbbbabaaabaaaaaaaaaabbbbabbbaababbaabababaaabbabbbbbbbaababaaaabbabbbabaaaabbbbbaabaaababaaabbababbbabbbabaaaababbaaabbbaabaaababbbaabbbbaabbbaaabbbabbabaabbbbabaabaabbabbbbbaabaabbabbabaaaabbbbbaaabbbaabaabaaaaaabaabbbabbbbbaabbaabaabababaabaaabbbbbaaaababbabbbbababababaabbababbabbbaaababaabbaabbabbbbabaaababbbbaaababababaaaaabbbbbbaaaaabbbabaabbaabbababbabaaaabababababaabbabbbbbaabbaaababbaaaabbaabbaaaababbabbbbbbbbbbaaaababaabaababbabbbbbbbabbababbaaaabbaabaabbaabaaabaabaabbbababbabbbbbaaabbbabbaaaabbaabbbbabbabaaabbbbaaaaabaababaabaabbbbbabbbaaaaabbabbaaaabaabbabbbbababbbbabbbaaaabababaaaaaababababbabbbbabaabbbabbbaaaaaabababbabbaabababbaabbbbabababbbaabaaababbbabaababaabababbbababaabaabaababbaabaabbbabbbaaabaaaabbabbbaaaabbabbbbabbabbababbaabbbbbbababbbabaaaabaaaabaabbbaaabbbabbabaaaabababbabaaabababaaaabbbaaaabaaabbaababababbbbabababaabbbbabbabbababbbababaaaabbbaabbbbbaabaabababaaabaaaabbaaaaaababbaabaaababababbbaabbaaaababbbbaababbbabbaaaabbaaaaabaabbabbbaaabbbabaaabbbababbbabababababaaaababaabbaabbbbbabbabaaabbababbababbbabbbbbaabaaaaabaaabaabbabbaaababbabbabaabaaababaabaaaaababaaaabaabbbaababaabbbaababbaababbabbabaaaabbababbbabaabbabbabbaaaaaaaabbabbaaababbaabbaaaaaababbabbbbaabaababaaaaaaaaabaaaaabbbbaabaaaabaaaaaababbbbbbbabaababaaaaabbbaababbabaaaaabbabbabaabaaaaaaabaaabbabaabbbabbbbbabbbabbbbaabbaabaaaabbbbbbbbaabbabbaaaabbbaaabaaabbabbbbbababaaabbabbbbaabbbaaaabbbbbbbbbbbaaabbabaabbaaabbaababbabaabbbaabababbbbbabbababbbaabaabaababbbbababbaaaabaabababaaaaabbbababbbabbbbababbbbbbbbababbbabaabaaaaaabbabbabaababbaababababbababaababaabbbbbbababaaabbaabbaabababaabababbbbbbbabaabaaababababbababaabababbbbbabbababaaababbabaaaabababababbbaabbbababbabbaaaababaabbaaaaababbaabbaaaababaabbbbabbabbabbbabababababbabababbaabbbbbbaaabbbbaabbbbabaaaaaaaababbabbbabbaabbaaababbaabbbabbaaabbbbbbbbbabbbaabaabaababababaaaaababbabaaabbbabbbbbbaaabbabaaabbbaabbaabbbbabbbaaabbbbbabbaaaaabbbaaababaaababbabaabbabbabaaabaaabbabbababbabbababbbabbaabbbababaabababbbabbbaaaaaabaaabaabaababbbabbaabbaabaaaabbababbaabbabaababbabbbabbabaabaaabaabaabbbaabaabbabaabbaaabbbaaabaabababbaabbbbbaabbaaababbbbbbbaaabbbbabaabbaababbaaaaaabaaabbabaaabaabaaaaababbbbaaabababbbbabbaabbabaabbbbaaaabaababbaaababaabaabaaabaaaaabaabbabaabaababbababbbbaaaabbbaaabaabbabaabbaaabaababbbbbbbabaaabaaaabbaaababbaabbaababbbbabaabbabaababbbabbbbaaaabbaaabbabaabbbaaabbbabbbbbaaabbaabaabbabaabababbaaaabaaababaaaaaabbaababbbbaaaabbbabaababbbabbbabbaaabbaababbbabbaababbbbbbbbbbbbbbbabbababaabababbabbabbbbaaabaaaaabaababbabaababababbabbaabaaaaabbabbbaabbbbaababbabbabbbbabbbaaabaaaabaabbabbbaaaabbabbbabbaaabbbbbbaaabbabbbbbbbaaaabbbbbbbbaaaabaaaaaaaabbbaaababbaabbabbbbbabababababbbbaababaabbbaabababbbabaaabaababbaabbaabbbaaabaaabaababaaaaaabababbbaaabbbbbbbbbbbbbbaababbabbabaabbaaaaaaaaaaaaaabaaaabababababbaaabbaababbbaaaaaaabbaabaaaaaabababbbaabbabaabbbbabababbabbbbaaaababaaabbaaaaaaabababbaaabbabbbbbbabbbaaabaaabbaaabbabbabbaabaabbaabaaaaaabbabaabbbaabbabaaabbabbbbbbabbbabaaabaabbabbbbaaabaaabbbababababbabaaabbbabaabaabaaaaaaaaaababbbabbaababbbbbabaaababbbaababbaaaaabaaabababaababbabababaaaaaababbbbabaabbaabababbbbabbbabbbabaababbbabaabaaaababababaaabbbbaabbababababbaabababbabbbbbabbaaabbbabaaabaaabaaabbaaaababbbaababaababaabaaabaabbabababbabbaaabbabbbbbaabbabbbaabbbababaababbaaababaaaabbabbbbbaaabaaabbaabaabbabbaabbaaababbabaabbaaabababaaabbbabbaabbbbaababaabbbabbbbbbabbbabaaaabbaabababbbaaabbaabbaababbabbbabbabbbabbbbbbbbabaabbbbaaabbabbaabaabbbabaaabbabbbabaaaaaaaaaababaaaaaaaabababababbbabaaaabbbabaabbbbbababaaabaabababbbabbbaababbbaaabababbababbbaaabaaaabaabbabbbbaababaaaabbabbbaababbbabaaaabababaabbbaababbbbaaaabbaabbbaabababaaaaaabbaabbbaabbbbbbaaaabaaaabaaababbbbaaabbbbababbabaaaabbabbaaabbaabaaabbbbbabbbabaaaaaaaabaaaaaabaabaabaaabbbaababaaaabbababbbbaabbaaaaaaaabbabbbbbabbabbbababbbaaabbbbbbbbaaaaaabbbabbaaaaaaaabbabbbaabbbababbbaaaaabaabbbabbaaaaabababaaaabababbaabaabbbbababbaabbaabbaaaababaabbaabbababbaaabaabbaabbbabbbaaabbbaababbbabbaaaaabaabbabbbbabbaababbaabbaabaaaaabaaabbaabbbbabbaababbbaaabbbaaabaaabaababbbbabbaababababbabbaababbabaaaabaabbbbbababaaababbababbbaaabbbababbbbaaababbababaaaaabbbbbabbbabbaabbaaababaababaaabbbbbaabaaaaaabbabbbbabbbbbbababbaabbbbbbbbbaabbaaabaabbbabaababbbbabbbbbbbbbabbbbabbabbbbaababbbbabaababaabaabaabaababaabaaabaabbaabbaaaaabaaaababbbbbbabbaabbbaaaaabbaaaaaabbbaaabaaababaaabaabbaaaabbbaaabbbbaabbabbabaaaababbabbabaaaaabbaaabbaaaaabbbaabbababbbbabbabbbabbaabbbababababbbabbabbabaaababbaaaaabbbaababbbaabaaaaabbbabbbbaabbbbbaabbbaabababaabaababbaaabbbabababbbbababbbbbbbaababbabbbbbaaababaaaababaababbbbbaabababbbbabbabbbbbbbbaababababbbbbbbbaabbbbbbaabbaabaabaaabbabbaaaabbaabbaabbaabbaaaaaabbabbabbbbbabaaabaaababbbbababaabbbbbbbabbaabaabaabaabaabbabbbbbabbabaabbbbbaaabaaaaaaaaabaababbbbaaabbbabbabbbbababbababaabbbbabaabbabbaaaabbbaabbbaaabbbbabbabaabaabbbbbaabababbabaabbabbbbababbbbbaababaaabaabbbabbabbaabababababbbaababaabbaaaabbabbabababaaabbaaabaabbabbbabaaabbabababbbaaababbbbaabbbbabbbbbaaaaaababbbaabbabbbaaababbaaabbbbabbbbaaabbbbbbabbbbbbbabbabaaabaabbabaababaaabbbbbbabbaababaaaabbbaabbbbbbbabababbaabaabbbbbababbaaaabaaaaaabbabbbabbabbbabbbaaabbaabbabbbaabaaaabaabbbaabaaaabaabbbbbabbabaababbbbaaaaabbbbbbabaaabbbbbbbbbbbabbbaabbaabbabbaaabaababbaaaabbabaaaababbbbbbbabaaabbabaabaabbbbbababaaaabbabbaaabbbaaaabbabaaaaabbaaaabaababaabbbbbabababaabaaabbbbbabbabaabaaaaabbbaaabaabbbbbaaaababaaaabbbababbbaabbbababaabaababbbbbbbaaaabbbabbbbbabbaababbbbbabaaaabaabbabbabaaaabaaabbaabaababbabaababbaabbabbababaabaababbbabbbaaabbbabbbabbabaaabaaabaabaaabaababaabaaaabbabaaabaaababbbabaaaaaaabaabaabbbababaabbabbbbbbaaaabaabbaabbaaabbaaababababaabbabababababaabbaabbbabbaaababbbbaabaaabaabaabbbabbabbbbaabaaaabbbaaaaabbbabbabaababaabbaababbaaabbbbbbbbbaaababaabbbbbbabbaaabaabaaaaaaabbaaabbbbbababbbbbaaaaabbbbbaaaaaaabaabbbbbabaababaabbabaabaaabaaabababababaababababbbbabaaaabababaaababaabbaaababaaaaabaaabbbabbaaaaaaababbababaaabaabbaaabbaaabbaabbaabababaababbbbabbbaabbaaabaaababaabaabaabbbbbaaaabbbaabaaaaaaaabbaabbbabbbabaaabbbabbbbabaaaabbaaaabababaaaaaaaaaababaababbaaabababbaaabaabbababaaaaaababbbbaababbbbaababaaaababbbaaaababbbbbbaaababababaabaabaaabbbbaaabbbbaababbbababbabbbabaabbabbbabababbbbbabababaaaaabbabaaabbbbabbabbbbbbaaaaaababbababbbbaabaabbabbbaabbaabbbbabbaababaababbaaaababbbbbaaababbbbababaaaabbbbbabbabaabbabaaaabbaaaaabababbbbbbaababaababbaaaabbbababbbabaaabaabaaaaaaaaaaabbaababbbabbbabbaabaaaaaababaabaabaababbabaabbababbbbabaabababbbbabaabbaaaaaabbbbabbbbbaabbaabababababbbbbbbababaababababaaaaabbbbabbaaaaabaabaabaababbabbbabbbbaaaaabbbbbabbbbbabaabaabbaabbaaaaaaabbaaabbbababbababaaabbaabbbabaaaaaabbbbaaabbbbaabaaabaabaaaaaaaaaabbabbabbbaabbabbbaabaabaaaaabbbbbbbbabaababbbabbbbaaaababbaabababbaabbbababbaabbbaabababbabbbbbaaabaaababbbbaaaabaababbbabaabaaaaaabbbbabbabbbabbbbbaaababbbbbbbaabbabbabaaabbabbaaaaababaaabaabbabbabbabbbbaaababbbaaabababbabbabbababbababbbbbaaaaaabababbaabbbbabbbbaabaababbaaabaabbaaababbabbbaaabbbaaababbaabaaabbbbbbabbababbbbbbbbbbbbabbbbaaabbaabbbaabbaaaaaabbaaabbabbbbaaabbbababbabaabbaabbaaababbaabbaaabababbbbbaabbbabaaaababaaaababbbbabaaaaabbbabbbabaaabaabbaaaaabaaaababaabbbbbbbaaababbbbbabaabaaababbbbbbbbbbbbbabaaabbbbbaaaaabbabbaaaababbbbaaaaabbbaabaaaaaaabbaabbabbbbbaabbbbabaabababbbabbaabababababbbaaaabbbaabbbbaaabbababbbbbababaabbbababaabbabaaabaabbbbaababbaaaabbbaabaaabbbabbabaaaaaaaaaabaababaabbbabaabbabaaabbbaabaabbaabaaababaababbababbababbbbbbbabbaaabaaaabaabbbabaaababbaabbaaababbabababaabbbaaabaaabbabaabbabbaaaaaavababbbbabaaabaaabaabaababaaababbaabbbaabaaaaaabababbaaaababbabbaabbbbabaabbabbabaabaabbbbaaabbababaabaaaaabaabababbabaaabbbbbababababaabbbaabbabbaaaaababbbbaaaababbabaaaaabaabbababbbbbbaaaaaabbbbaaaabbbbaabaababaaaaaaabababaaabaabaaabbbbaaaaabbabaabbaabaababaaaabbbabbbbaaaabaaaaaaabbaababababbabbbbbaabbbababbaabbbbbabbbaabaabbbbbaabbbaaaaabbaabbabababbbbbbababbbbaababaaaabaabbbbbabaabbbbaaaabbbaaabaabbaaaabaababbaababbabbababababbbaabbbbbbbbaaaaababbbbaaaaabaabbbbbbaaaabbbbbaaaaaababaabbabbbbabbbbaababbbbbabbabbbabababbbaabbabaabbbaabbbabaabbaaabaabaabbbaabbababbbabbbbababaaabbaabbbaabbbbbaaaaabbaababbaabababbaabaaaabababbabbbbaaaabbbaaabbbbababaabaaaaaaababaaaaabaabbbaaaaaabaaabbbbbbaaaababbbabbbabaaabbaababbbababaaaaaaaaabbabaaaaaaaaaababbbaabaabbaabbaabbaaabaaaabaabbaabaabbabaababbbabbabbaabababbaabbbbbaabaaabbaaaababaabaabbaabbabaaaaaaaaabaaabaabbbbbabaaabaaaaabbabaabbaaababababbaaaabbbbaabbaabbbbbbaaaaabababbabbabbbbbbababaaaabbbabaabbabbbbbabbbbabbbabbaaabbaabbaaaababbbabbbbaaababaaababaaabbaaabbabbbabbaaaabbbaaaaaaaaaaabaabbbabbbaaaababbaabbaaaaaabbaaaabbaabbaaabbbabbbabababbabaaaaabaaabbbababbbbaaaaaaaabaababbaaaababaaaabbaabaabbaababaabaaaababbbaaabbabbababaabaabbaaabbbabaaaabaabaaaaaababbbaaabaaabbbababaabaaaabbbabbbbabababbaabbbbbbabbbababaaabbbbbaabbaabaaaabbabbbbaaababaaabaaaababababbbaabaaabbbbbbbababbaaabbaabaabbaaaababbaaaaaaababbbbaabababaababababaaaaaabbbbabbaabbbbaaabaabaaababaaaaaabaaabbbbaaaabbbaabbbabaabbbabaaabbaaabaaaabaabbbbbbabaabbabaaabbbbabbabbaaabbabbbaaabbbbbbaabaabbababbaaaababaabbabbaaabbaaaabbbababbaabababbaabaaababaabaaaaaaaaaaababbbbabbbabababbaaababaabaabaababbaabaaaabbbbaababbbbbbabaabbbaaaabbaaaaabbbbbbbaababbbabbabbaabbbaaaababbabbaabbbbbbbabbbbaaaabbabababaababbabbaaabbababbababababaaaaabaaababbaaaaabaabbbaabbabbaaaaababbaaabbbababaabaaabbbbbabbaaaabbaaabbbababababaababababababbababbbbaaabbbbbbaaaabbbaaabbbbbbbaabababaabbababaabaaabaaabbabbbabbbbaabbbbaaaaaaaaaabbbaababaaabbbaabaaabaaababbabaababbbbbbbbbbbbbbbbaabbbbbbaababbbbaaabbbbbababbbaabbbbaaaaabbbaaabbabaabaaaabbbbbabbabbaaaabababaababbaabbaabbabbabbaabbbbabbababaaababaabbbbaabaaababbbbbabbaaabbbaabbaabbaaaaabbaaabaabaababbbaabababaababaabbaababbbbaabbbabbbbbaababbbbbaabbbabbaabaabbabaabbabaaaaabaabbabbbabbabbaaabbabbbbbabbbbabbbbaabbbabbabbbabbaabbbbaaaababbaababbabaaabbbaaabaaabbbbabaaabbabbbababaabbabaabbaaabaabaaaaabbbbabaaabbbabbaabaaaaababbabbbbbbaaaaaabbbaaabababababbaaabbbababbbaaaaabaabbbaabaababbbabaababbabaaabbaaaaaaaaaaaaaaaaaabaabbaababaaabaaabababaaaaaaabaabbbabbbababbbaabbaaaabaababbbbbaabbbabaababaaabbaabbaabababbaaaaababaabbabaaaabababbbbaabbababbbbbabababbbbbababbabbbbbbaaaaaabababbbababaabbbbaababaabbbaabaaababbbabaababaaabaaabbbabbabaaabababbaabaabaaabbabbbbbabaaababbbbaabababaaaaaabbabaabaaaabbaabaababbbbabbababbababaaabbbbbbbbbabbbbbbaababbbbbbaababbbabbbaabbabbbbabababaabbbbabbaabbabbabbaabaaababbaaabbbbaaaabbabbbbaabaababbbabbabbaaaababbbabaaaaabbbaabaaaaabbabaabbbaaabbbbababbbbbabaaaabbbabaaabbabbaababaaaabbbbbbbbbbbbbbbbbbbbaababbbbaaabbbabaaabbbbabbababbbbabababbbababbabababbbbbaaaaaabbabbbbababaaabbaaabaaaababbbabbaaaaababbbbaaabaaababbabaabaabaaabbabbabbbbbabababbabbaabbbbbabbbbbbbbaabaabababaabaaaabaababbaaaaabababbbbbbabbabbaabbbbbbabbbaababaabbaaaabaababbbbbaaaaaabaaabbbabaabaabbbaaaabaaaabaaabaabaaabaaabbbaaaabbbbbaabaabbbabbaaaabbbabbbabaaaabaabbabbbbbbbbbbbaaabbabbbabbbaabbbbbabaabaaabaaaabbabbaaabaabaabbaabaababbbbbaaaabbaabaababbaaabbabbababbaabbabbaaabaaabbbbbbbbabbabaaabbbabaabaababaabaababbbbabbbbaaababbbbbababbbbaaabbbabbbabbbbbbaabbbaaaabbbbbabbababaabbbaabaabaaaaabbaaababababaabaabaabababbabbabaaabaabbaaabbaababaaababbbabbbbbbbbbbbababbaabbbbabaabbabaabbababbbabaababbabbabababbaaaaaaaabbabababaabaaaabbaaabbbbbaaaabababababababaabbaaaababaaaabbbbabaabaabaabbaaabbaaaabbabaabbbbabbbbababaaababbbaababaabbabbaaabaaaaaaaaaaabbaabababbabbaabaaabbbbaabbaabaaaabbaabbbaabaabbbaabaaababbbaabababababababbbbaababaababbbaaaaaaababaaabbbabaabbbabbbbabbaaabbaabbbbababbaaaabbbbabbaabbbbaaabaaabbaabbabbaaabbbaaaabbaaaabaabaaabaaabaabaaaabbbbabbaaaaabbbbabaaabaabababbbbaaabbaaabaababbbaabaabababbbaababbaaaabbbbababaaaabbabbbbbaabaabbbbaabbbabbbaaabbbababbbbbaabbbbbabbbaabaaaababbbbaabbabaabbaabbbbababbbababbabbbbbbabbbabbbababbaaaabaabbaabbaaaabbabbbabaaaabbbbbbbbabbbaabaabbbabbaaababbaaabbaabababbaaaaaabbababaaaabbbaaaaaaaaaabbbaababbaabaababaaabbbbabaaabbaabaaaaabbaabbabaabaaababababbaaabbaaabaaababbbababaaaaaaaabbbabbbaabbbabbbbaabbbbbbabbbaaabababaabbbabbbaabbbbabbabbaabbbaababbbbbaaababbabababbaababababaabababaababaabababbbbabbbaababaaabbbabbbbbbbabbbaaababbabaabaaaabbaaabbbbbbbaababaaaabbbbbaaaabbaaaababbaababbbbbbaababbbaabbabaabbbabbbaabbaaababbabaaaaaabbaabbabaaababbbabaabaaabaabaababaaaababaaaababbbbbaaababaabbaabbaaaaabbabbababbaaaababaabbaabaaabababbbbbbbabbababbbaaabaabaababaabbbabaaaabaababbaaaaabaabaabbbbbbbbbbbbabaabaabaabababbbbaababbbabbbbaabbbbbaabbabbabbbaabbaaaaaabbbbbaabaaabbbbbabbbaabbbababbbabaaaabbbaaaaaaabababbbbaaaaaaabaaaaaaaaaabbababbbabaabbbaabaabaaaabaabbabbbaabbbbbbaabbaaaababbaababbbabbbbbaabbbbaaabbbbababbbaabababaaaabbabbabaababbabbbaabaaababbabaabaaabaabbabaaababbabbaaababaaabbbababbbabaaaaaabaaababbaabaabbbbbbabaabbbaabaabbbbaaabaaaaabbbbbbbbbabaabbabaabbaabaaaaabbabaabaabbbbabaabbaabbbaabaabbaaaaabaabbabbabaaabbbaabbaababbaabaabaabbbaabbaaaaaabaaaaaabbaabbaabaaabaabbbbbbbababaaabaabaabbbababbabbbaaabbabababaabaabbabababbabaaababaaabbabbbabbbbabbbabaabbabbabbbaabbbaababbbbbaababaababbaabababbabbbbbaaaaababbbbaabbbaabaabbbabbbaabaabababbabbbbbbabbbbbaabaaabababaabababaaaaababaababbaaabbbbbbabbbabaaaababbabbabbabaaaaaabababaaaaaabbbbbaabbaabaaaabbabbababaabbabbababaabababbbbbaaaaababababbababaaabaabbbaabbababbaaaabaabaaaabababbbaabbbbbababbaaaaababaaaaaaaabbbbaaaabaabaaaaaabbbabbaabbabababbbaababbaabbaabbbbabababbbbabbbabbbabbbbaaaaabaabbbabaaabbbbaaaabbbbbabababbabbabaabaaabbbaababbaababbaaabaaabaabaabaaabaaaaaabbababbabbabbabbbbababbababbaaababbbababbaaababababbbabbababaababbaaaaabbbbababaaabababaabbbbaababaabbbabbbbbbbaaaaaaaabbabbaabbbbbbbaaababbbabbababbbbbabaabaababbbbbbbbabbbababbbbabaaabbabbaabaababbabbabaaaabaaaaababaaaabbbbabbaaaaabaaabbaabababbaababbaaaaabbbbbabbabbaaaaabbbbbabbbbbbabaaabbaabbbbabbbaabbabababababbbbaabbbbbbbababaaabaaababbbbbabbbabbabaababaaabbaaabbbbbbbbbbbaaababbbabbbbbbabaabaababaaababaabbabbababaaaababaababaaabbbaababbbababbabbabbabaaabaaabbbbbbbaabaaaabbabaabbaaabaaaabbaababaababaaaababaaabbaabbabababbbababaaaababbaaabaaababababbaabaaaababbaaaababbbabbaaabbbbbbbbaaabbaaaaabbbbabbbbababbaababbbaaaaaaabbbabbbaaaaabababbbbbbbbbbababaaaaabbbabbbaaaabbbbaabbbbaaaaabaabaabbbabbbbaabbababbbabaababaaabbaaaaaaabbbbbaabaaabbbbbbbbaabbbbbaababaaabbaaabababbbbabbbaaaaabababababbbabaaabbababbaabaababbaaaababbabbbabbbaabbabababbaaabaaabaabaabbaaaaabbbabbabbbaabaabbbabaabbbbaaabbabbbbaaaaabbbbbbaaaaabbaabbabbbbbbbaaabbaababbbbbabababaaaaabbabbbbbaaaabbbbbabaabbaababaabaaabbabbabbbbbaaabbbbbbaaaabbbbbaaaaabaaaabbaabbabababbbbabbbbaabbbbabbabaabbbabbabbbbbaabaaaabababbaabababbabbabbabbbabaaaabbbbbabaaaabbabbababaaaaaabbaababbabbaaabaabaaaabaabbababbbababaaabaabbabbabaaabbaababbabbaaabababaabbbbbaaaaaabaabaabaabbaabbaaaaabbaabaabbaaababbbaababaaabbbbaaaabbbbbaabbbbbaaaabbabababaababbaabbbbaaaaaaaabbbaaababaabbbababbaabaaabbbbaababbababbabbbbababbbaaabbaabbbbbbaabbaaaababaaaaaabbabbababbbbabbabbaabbaabbbbabbaabaaaaaabbbbbbaabbbbbabaaaaaaaaaaaabbbbbbabbabbbababbbaaabbbaaaababaabababbabbbaabbaababbabbbaaabaabaaababaabbaabbbbbbbbbabbaabbaababbabaabbbaababbbaabaabaaaabbbbabaaaabaaaaabaabbaabbaaaaaabaaabbababaababaaaabbabbaabababbbbabbaaaaabbaaaaaaabaababaaabbaabbabaaaaaababbaababaabaaababbababaababbbbbababbbbabaaaababbaababbbaaabababbbabaaaababbabbaaabbbaabaabbabbbaabaabaababbaaababbabaababababaaabaaababbabaabbaabbbbababaabbbaababbaaababbbbbbbabaaaaaabbbaabbbbaaaaaabaaaaaababaaabbababbabbabbaaaaabaabbababbbaababbbbbbabbbbababaaaaaabaabaaabbbababbaaabbbabbabababbabbabbaaabaaabaaabbbbbbbaabbabaaaaabbbaabbabbbabbbabbaabbaaaabaabbabbaaabbbaaababaaabbaaabbbababbbaaaabbbabaaabbbaabaabababbabababbabbbbabababbbaabbabbabababbaabbababaabbbbaabbbbaaabbbaaaaaaabaabbbbbbabbbbbaaabbbbbbabbaabaabaaaababbbababbaaaabbabbaabbababbbbababbbabbabbaababaabaaaabaaaabaabbbbabaaababbbaaaaabbbaabaababbaaaabaaabbabbabbababaabbbbaababaaaabababbabaabaabbbabbabbabbbbbbbaaababaababbaabbbbbaaabbbaabbbbaabbbbababaaaaabbbabbbabbbabbbbaaabbbaabbababaaaabbbabaabbbbabbbbbbbbaaabbbbaabbaabaabbbbbbabbababbbbbbbbbbaaaabaaaaababbaabaababbbaabbbbabbababababbabbbabbbbbabbbabbabababbbabaababaabbbbbbabbbbaaaababaaabaabbbababbabbbbbaaabbbaaaabaabaaaabaaabaabaabbbaabbaababaaaabbaaabaabbabaabbaababbababaaaabaabaaaabbbbabbbbbbbbaabaaaaabbabaaabbbbabababbaabbbbbababbbbbababbbbabaabbbbaaabbabababbabbbbbbbbaabbbabbbbababbbbbbbbbabbbbbaaababbbbbabbbbaaabaaabaaaaaababaababaabbbbaaabbabbbabbbbaaabbbaaabbbbaabaabbbbabaababbabbbaabbbbabbbbbaaaabbaaaababbaabbabaaabaaaabaababababbaaaaaaabbbbaaaabbababbabbaabbbabaababbaaababbbbbaabbabababbbbaaabbbababbbaabbaaabbbbabbabbabbbbabaabbbbbabbbaababaaaabbabaababaababaaaaaabbababbbaabaaaaaabbaabbbbbabbbbbaaaabbabbbbbbabbbabbaabbababbaaaabaababbabababbaababaaaababbbabbbbaaaaaaabaababaaabbbabababababbaababaaaaabbbaabbbbbaaaaaaabbbababaabbbbbbabbbbbbbaabbaaabbbbbbbabbabababbbababbaaaabaababbbababbabbbaabbaaabababbabbbbbabaaabbbabbbbaabaaabbbbbabaabbaabbbabababbabbaabaababbababbaabaabbababaaababaabbbbbaaabaabbbaabbbbbabaabaaaaaaabbabbababbaabbbabbbababababaaabaabbabbaabbaaaaaaababbbbababbbababbaabaabbaabbaababbabbbbaaaababbbbababbaaaabbabbaababbbbaabbababbbbbbabbbaaaaaaabaabbaabaaababbaabaaaabaabaaaabbbbbbaababaabbabbbaaababaaaaaabbbaaaaaaaabbbaabababbaaababababbbaaaaaaabbaabbbabbbabaaaaababaaabbbbbaababbaaaabbbabbaababbbabbbbaababbababaaaaaaaababbaaabbbaabbaabaaabbaababbbbbaabaaabaaabbbaaabbbbaababbabababbbbbababbbbbabbababaaabaabbbbabaaaabaaabbabaaaaaabbbabbbabbaabaababbaabaaaababababaabaababaabbbbabbbabbbbbababbabbabaaaababbaabaabbababbbabababababbbbabababbbaaaaaaaabbabaaabaaaababaaaaaaabbaabbaabbbbaabaababaaaaabbaabaabbabbbababaaabbbabbaabaabbaababbabbbbbbbbbaaaabaaaaaaabbbbbabaaaabbbbbaaabababbabaaaaabaaaaaabaababaaabbabbbabbbabaaabaabaaaaaaaaabbabaabaaabbbbbbbababbaababaaaaabbabaabbbabaaaabbaabaabbaabbaaaaabaaaababbaabbbaabaaababaabaababaabababbabababaabaaabbabbaabbaaaaabababaabbaaaaababbbabababaaabbbbaabaabaabaaabbababababaabbabbbaababbbabbbbabbaaabbabbabbaaabaaabbbabaaabaaabbbbbaaaabbababbbabbbbabbabaababbababababaaaabbabbabbbbbbbabbaabbaaaabbbabbbbbbbbaaaaabbaaabbbaababbabbbababbababbbaaabbababaaabbaaababbabaaabbbbaabbabaaababaabbbbbabaaaaaaaaaaaaababbabbbabbabbaaaaabbbbaabaabbaaaabbaabaababbbabaaaaaaaabaaaaaaaababbbaabbaaabbbbbabaababbaabbabbbabbaabaabbaabaaaaabbabaabaaabaaaaaaaabbabababbbababbaaabaabbbabbbaababbabaabaabbaaaabbabababaaaaaabbabbbbaaaaaabbababaabbababababbaabbbaaaabbabbaabaabbabaababbababaabbbababbbabbaabbabbabaabaaaaabaaabbbaabbabbaababbabaaaabaaabbaaabbabbaaaabbbaaabbabaaaaabaabbbbbababaaabaaabbaaaaaababaababbabaabbabbbababbbbbababbaaaabbabbababbaabaabaabbabbaaabbabbbaabbabbbbaaabaababbbbaabbbbbaaabbbaabbbbbabbbbaababbabbbaababababaababbaaaaaaaaabbabbbabaabbbabababaaababbabbbaaaabbaabaaaaaabbbaaababaaababbbbaaababbababbbabbbabaababaabbaaaababbbbabababbabbbbabbbbaabbbbaabbbbabbbaaababbabaabaaaaaabaaababaaaaabaabaabbbbbbabbbbaaaaabaaababbbbaaabaababbabaabababbaabbaababbabababaabaabbaababbbabaabbbbbababbabaabbbbaaababababaabbabbbaaaaabaabaababababaabbabbababaaaaabababbbbabbaaabbabbbbaaabaabbabbbaabbbbababaaaabaabbababbbbaabbbbaabbbababbabbaaabbabbbabbababbaabbabbbaabbbbbbbaaaaaabbbbaaaababaaabaabababaaabbbabbbabbbbbbbbbaabbbbbbbbaabaaaaaaabbaababbbbbbababbaabbabbaaaababbaaabbaaabbbbaaabbaabbabbaababbbbbbabbababaaaababaabbabbabbaaabbabaabbaaabbabbaaabbaaabbbbaabbabaaabaaaaaabbaaabbaabbbaaaabbabbaababaababaababaaaabbaabbaaaaaaabaaabaaabbbaababbbbabbbaaababaaaabaabbbaabbaaabaaababbabbbbbbbaababaaaabbabbaabababbabbababbbababbbbbabaabbaaabaabaaabbbbaaababbabbbaabbbbbabbabbbababbaaaabaaababbababbabbabbabbabbabaabaaabbbbbaabaabaabbbbababaaabbbbbbaabbbaaaabaababaababaaabbaaabaabbbbbbbbaabaababbbbbaaabbbabbaaababbbbaabaaabbabbabbaabbaabbbaaabbbbbaaaaabaaabbaaaabaaabaabbbbbabbbbabaaababbbaaabbbaaaabbbbbbaaabbbbabbaabbabbbaababaababaaabaaabaabaabababaabaaaabbbabbabbbabaaabbbababaaabbbaabbaaabbbabbaabaabaaababbaaabababaaaaabbaabbaaaaabbabbbbaabababbbabbabababbbbbbbbbaaabaabbaabbabbaabaaabaabaaabbbaababbbaabababbaabaaababaabaaabbbbbbbbbaaabbabaaabababbbbbabbbabaaaaabbababbbabbbababbbbbabaabbaabbbaabaabaaaaabbabaaabbaaabaababbbabbbaababbaabaabbbabbbbbbaabbabbaabbabbaabbbaababbaabababababbbbaaaaababbaabbbbbbbbbabaaaaaabaabababbabbaabbbbaabbbabbbabababbbbbbababbbbaabaaabbbabbaabbabbababaaaaaaaabbabbbaabbabaabababaaababbbbaabbaababbbbbababbaababbbaaaaaaabbaaaaaaaaaabbaababaabbbbbbabaaabbaaaabbbbbbaaaaababaabaabbaabbbababaabababaabbbaaabbabbaaababbaaabbaaabaababbbaabbbbbbbaabaabbaaaabbbabbbaaabababaaaababaaaabbbabaabbaaabaabaaaaaabbaaabbabbabbbababbaabbbabaaaabababbaaabbbababbbbaabbaabbaaababbbbbaaaaabbabbbbbbbaaaabbabaaabaababaaababaaabbabbaabbaaababaabaaabbbaaabbabbabababbaabbaabbbabbbaabaababaabbbaaaaababbbbbabbbaabbabaabaabbaaababaabbabbbabaabbababbababaaaaaaaabbabbbbbaababbbaaaaaaabbaaabaabbbaabababbbbaabbbbbbabbaaabaabbbabaaaabbabbbbbbababbabaaabbabababaabbabbbabaaabaaabbbaabbaaaabbbaabbbaabbbaaaaabbbaababbabaaaaabbbaabbaaabaaabbbbbaabbabbaaabaabbbbaaabbbaababbbbbababbbabbaabbaababbababaababbaababbbaaabbbbabbaabbbaaabaaaabaaaaaababbabaaaabaaaaabaaaaabbaabaabaaaaabbbabbaaabbbabbaaabbabaaabbaabbbaababaaabaababaaabbaabaaabbbaaaabbbbbaaaabaabaaabaabaabbbbababababaabaabbbbaababaabbbbbabaaaaabbbbaaabbbabaaaabaaabbaabbabbbbaabbbabbbbbbaaaababbababaabbbbabbbbaabbbabbbbaaabbbaababbabaabbbbaaabbabaaabaabababbbbbabaabababbabbaabbbbabbabbbbbbaaabaabbabbbabababbababbaabbaaaaaabaaabbbbabbbaabbbaabaabaabbbbbbbaaaabababaababbbaabbababaabaaaabaabababbbbaababbabbaabbbbabaaabbbbababaaaaaaabbaaabaabbbbaabbaaabbbaabbbbabaaabbbababaabaabaaabaabbabbaaabababbaaabbbaabbaabbabbbababbbbabaababaaaaaabbabaababababbabaaaaaabbababababbbaabaababbaababbaaababbbaabaaabbbaaaaaaaaabaaabaababbabaaaaaaabaabaabbaaabaaabbbabaababaabaabbababbbbbbbbabaaabaaaababababbaaaababbaabbaaababaaaaabbbabaaaaaaaaabbabbabababbbababaabaaaaaaabbbaabaabbaaabaaabbbbabbababbbbabbbaababaabaabaabaaabbbabbbabaababababbaabaababbabbaaababbbbabbbaababbabbaaabbbbbabbbbaaaaaabaabbaabaababbbbbbabaaabaaaabbababbbbbaaaaabbbbbbbbbabbababaaabaaabaaabaaaabbbaabaaaaaabbaabbabaabbbabaabbbababaaaaaabbababbaaabbabababababbbabbabbabababababbbababbabbaabaaaabbababaaabbbabaababbabaaabbbaaaaabaababbbbabbbbbabaaaaaabaabbaabbbbbbabbaabbabbaaaababaababbaaaaaabbababaabaaabbabbabaabbbaaababbaaaaaaabaabbabaaabbaaaabbaababaabbbbbabbbaabaabaaabaaaabaaaabbbbbbbabaabbaabbbbbabbbbbaaabbbabbbaabbbaaabbaabbabbabaabbbababbbaaaaabbababbbabbababbaaaabbabaabbbaabaababbaababaababbbbabbaaaabbbbbbabaaabbbaaaaabaabbbbaabacbbbabbabbbbbbbaaabaabaaaaaaababaaaabaaaaaabaaabbaaababbabbbaaabbaabbbababbbbbbbaababbaabbbaababaababbbbbbbbbbaaabababababbaaabaaabababababbaaabbababbaaababaaaabbaabaababbbabbabaabaaabaaabaaaaaaabaaaaaaaabbbbabbaabbbbaabbabbbbbbababbaabbabaabaababbbbabababbaabaaaaaaaabbbbbbbbbbbbaaaabbabaabbbabbaaabbbaaababbaaabbbbabbbabbbbabaaaaaaaaaaabbaababababaaababbbabbbbabaaaaabbabaaaaaabaabaabbaaaababbbabaaaaabbbbbbbaaaababbaabbababbbabbbbbbbbababbbbbbaabaabaabaababbbbaaabbaaababbaabaaaabaabbbaabbbabaaaababbaabbbbaaabbababbbabbababbbbaaaabbaaabbbbbbabaabaabbbbaaabaabbabbbbabbbaabaabbabaaabbabbabbaabaabaabaabaabaaaabaaaabaabaabbbaaaabaabbbaaabbbbbbaaabbaaaaaaabbaaabbabbaabaabbbbbbaaababbbabababababbabaababbabbaabbaaabbbbbbbbabbbabbbaaaabbabaaaababaaabaabbbbaaababbbababaababbbabbaabbaaaabaaabbbabbbbaabababbbbbbaaaaaaabaaabbabaaaabbbbaabbaaaaaababbbabaaabbbabbbaababbabbbabaaabbabbaabbabbbabbabaaabbaabaabbaaaabaababababaaababababbbbbabaabbbbabbabbbabaabbbaabababbabbbbabbbaabaaaaaaaabaaaabbaaabbababaaabbbabbbaaabbbaaaabaabbbabbaaabbaabbbabbbbbabaabaaabbabaabbabbabaaaabbbababbbbaaaaabbababbbbbbbabbabbbabbaabbaabbaaabbabaababbabaabbababaaabaabaaabaabbaabbaaabaabaaaabbbbbbbaaababbbbbbabbaaabbbaaababbaabbbaabaaabbbaabbbabbbbabbaabababbbaaaabbaaababaaabbaababbaaabbaaababbbbbabaabbbaaabbbaabbaaabbbaababaabbbabbbabaaabaabaabbbbbaaabababaaaaaabbababbbabbaaaabbaabbaaabbaabbaabbbaabaaaababbaababbbaabbbbabbaabbabbababbaabbbaaaabbbbbbbabaabababaaaababbbbabbbbabbbaaaabbbbbaaabababbbaabaababaababaabbbbbaaabababbaaaaababbbbbbaabaabbbbbbbbbbaaaabbbbbabaabaaaabbaabababaabaabbbabbaabbabbbbababbbbaabaabbabbabbbbbaaaaabbbbbabababbbbabbaaabbabbbbaaaababbbaaabababaaaababbbbbaabbabababbbabaabaaaaaabbabababbaabbaaabbbbabbbbbbbbbaabbbabbbaaaaaabbbbabbaababbbaabbbbbaaaabbababbbaaaabaaaababaaaaabbbababbbbabbbababababbbbabbabbbabaaaaabbababbbababaaabaaaabaabbaaabbabbbbbbbabbabbaaabbbbaaaabaaabbaabbabaabbbabbbbaaaaaabbaaabbaababbbabbaaabbbabbabbaaabaabaaabbabbabbbaabaabaabbaaaabaabaababbaabaaabbaabbbbabbbbaaabbababbabbbbbabbbbabbbaaabbbababaaaaabbbaaaabaabaabbbaaaaaabbbaaaabbaabaabbabaabaaabbbbaaaabbbbbabbbbabbabbaabbbababbbbbbaabababababaabbbbbabababbaaaaaaabbabbbababaabaaabbbbaaaaababbbbbabaababbbbabbaaaabbbbbbababaabaababaaaaabbabbababbaabaabbbababbbaabbabbbbababaaaabbbbabbaabbbbbbbbaaaaabbaaaabbabaaaaabbaaaaaabababaaaaaaabbbbbaaababbaabbbabbbbaaabaabaabaaababbaabbbbaabaaababaaaaaababaababbaaabbbabababbbabbaabbbbbbbaabaabbbbabbaababbaaabbbaabaaabbbbaaababaaaaabbaaabbbaaaabaaabaaaaababaabbabbaabaaaabababaabaabbbabbbabbabbbaaababbaaaabaabbbaaabbabbbbbabaaabaaabbaaaabbaabbbaabaabbaabbbabbabbaabaababbabbabbbabaabbbbababaabbbbbbbaaabaaaaaaaaababbbaabababbbabaaaababbbabaabbaaaabbaabaaaaaabbbabbbbabaaaaababaaabaabaabbaabbbbaabbbbbbababbabababbababbbbabaababbbaabbbbbaaabbabaababbbababbaaaaaabaabbaabbaabaabbbbabbbbbabaaababbbbabaaabbbbabaaabababbaabaaaabbbbbaabababaaaaaaaababaabaabaababbaabbaabbaaabbaaaaabaaabababbaaababbbbbaababbaabaabaaabaaabaababaaaabbabaababbbabbbaababbbbaaabbaabaaaabbaabababaabbbbbabbabaaaabbbaabbaaaaabaababbaaaaaabaabaabbaabbbababbabbabbbbaaaaaabbababbbaabbaaabbbbbabbbaabbbababbaabbabbaabbaababbaaaabbabbbbbabaabbbbaababbbbbabbbaabaaaaaabaaaaaaaaaabbaabbaaabbbbabaaabbabbaaababaabaaababaabaaaaaabbbaabbbbaaababaaabbbbbaabbbbbababaabbaaaabababaababbabbabaabbbaabbbbabaabbaaaabbabbbabbbbababaaabbbaababababaaabbbaabbbabaabbbbabbaaabbaabaababbbabaaabbbabbabaaababaaaabbabbbaaabbaaaaabbbbbbbbaaaabaabbbabbaaaaaaabbaabbbbababbbaabbbaaaaabbaabbbaaababaaaaabbbbaabbbaababababaaaaabaaaababbbbbbabaababaaaabbababbaabbbbaaaaaabababaabbaababaaaabbaaabaabbabaaababbabbababbbabbaababbaabbbbabbabaaabbbabbaaababaaababbababbbabaaabababbbaabbaabaabbaaaaaabaabaaabbbbbbbaaaaabababaaaabbaaabaaabbaabbaabbbaaaaaabbaaabbbaaabbaaaaabaaaaabbabbabaabbaababbaabbbababbaabbbbaaaabbabbbbbaabbabbbabbbabbbbabbbbbaabababbaabaabaabbaabaaabbabbbabbbaabaaabbbaaaaaabbbbaabbaaabbbbbaabaabbbbabbababbababbbbabbaabbbbabbbabbaaabbbaaababaababbbaabbbababbabbbabbbababababaababbbbbaababaabaaabaabaabbaaaaabaaabaabaaaaaabababaabbbbbabababaaababaabbabbbaaaabbabaaaaabbbabaabbaabbabaaabbbaaaaaaabaaababbbaaabbbabbabbbaaabababaaaaaaaabbbaaaaabaaabbbaaabbbbbbabbbabbaabbaababbbbaabbaabbbbbbbaaabbabaabbabbabbbaabaaaabbbaaabaabbbbabbbabaabaabbbbbababaabbbaaababbbabaabbbabbbbbabbbaabaaabbabbababaabbbabaabbababbbaaabbbbabbaabbbabbaaaabaaabbabbbaaaababaabbaaaaababaaaabaaaabbaabbaaabaabbbaabbbbbbbabbbabbabbbaaabbbbababbababbbbabaaabbbaabbabaaaabbabaabbbbaaabbbbababbbabbbabwabbababbaabababbaaabaabbbabbaaabaababaabaaababbbaaabbaaabbbaaabaaaaabbbbabaababbaabbbbbbbbbbabaabbabbbabaaabbbbabbabbabbababbaaaaaabbaaabbbabbaabbbbaaaaabaabbaaabbabbabbbabbabbbababaabababaaabbaabbabbbaabbababbbababbbabbbbaababbabbaaaabbababaaabbbbbbbaabbaaababbbaaaabaaababbbbabaababaaababaababababaabaabbabbaaaaabaabbaaaaaaaaabaabbabbabbbbbababbbaababbaaaabbaaabaaabbbabaabbbaaaabaabaaaababbbbaaabaababaabbbababbabbaaaabbbbaaabbbaaaabbbaaabbabbbaabaabbabababbababbabaabbbaaaaabaaaabbababaaabbbaaabbababaabbaaabaaabaaaaabbabaaaaabaabbbabbabbabbbaaabbbbbbabaaabbabaaaaababbabbaaaaaabaabbbaaabbabbbbbbabaaaababbabaabbabbbabaabbbaaaababaaabaabbbaabbaabbbbaababbbbababbbbaabbbbbbbbaaabaabaabbbbaababbababbaababaababbbbaaaabababbbaaaabbababbabababbabbabbbbbbaabaaabbaabbbaaabaaaabbabbbaababaaabbabbabababaaaabababaabbababaaaabaabababaabaaaaababbaaaabaabbaaaabaabbaaaaabbabbabbaaabaabaabbaaabaaaaaababbbabaababbabaabaaaaaabaababbaabaabbbbbbbaabaaaabbabbaabbbaababbaababbaaabbaabababaaaaabaabbbbaaabaabbbabaaabbaaabbbabbbaabbbabbabababbbabaaaabbaabbabaabbbbabaabbbbaabaaabbabbababaaaababaabbabababbbaaaaaabbbbaaabbababbbbaaaaaabbabbabbbabbabbbbabaaaabababbbabaaabbbaabaaabbbaaaaaaabbbaaababababaabbabbbaababaaabbbaabababaaababbabbbbbbbbababbabbbaabbabbbbaabbaaaaaaabbabaaabaaabaaaabaabbababbbabbbbabaaaabbbbbababbaabababbbbabbbaabaaabbbabaaababbbabaaabababbbaabaabbabaaabbabababbabbbabbbabaabbaabaaaababbabaaabaaaabbaabbaaaaabaaabaaaaaabbaababbbabbabbabaaababbbabaabaaaaaabbabaaabbaabbabbaaabaaabbaaabaabbaabbaababababbbbaabaabaaababbaabbaabbabbaaaaaaaababbbaaabababaaabbbabaaabaaaaabbababaabbaabaabbbabbbbbaababbabaabbbaaaababbabbbbbaabaaabababbaaaabaabbbbbbbbbbabaaaabbaabbbabbaabbbbaabababababbbabaaabaaabbabbabbbbbaaababbbaabbbaaabbaabbabaabaaaabbababaabbbaabbaaababbbaaabababbbbaaaabbabbbbabbabbbbbaababaaaaaabaabaaaabbbaaabbbababaabbaabbaaaaabaabbbbaabbbbaabbaaaabaabbabbbbaabababbbbbaababbabbaabbbabbbaaaabbbaaabaabbbbaabbaaabbaaaaaaababaabaaaaaaabaabbaabbaababbbaabbaabbbabbbbbabbabbbaaaabbaabbbbbaabbabbbbbbbaaaabbaaababababaababbabbbabbabbaabbaaabaaaabbabbbbbbabbabaaabbaaabaaaaababbabbbbaaaabbaabbbabaabababaaaabbabbababbbbbaabbabbabbabbaaabbaaaaabbbbaabbbaabbbbbabbbababaababbaaaaaaabbbababbabaaabbbabbbbbbbbbbbbbaabaaaaaaaababbbbaabaababbaabbaabaaaabababbbaaabbbaaaaabaaaaabababbaabbaaaaabaabaababbbababbaabbaabaabbaaaaaababaababbbbaaaabbbabaaababbabaaabbaaabbaaaababbbaababaabaabaaaabaabbbbabaabbaabababbabaaababaababbbbaaabbabbabbaabaababbbbbbaabababbababaaaaaaababbabaababaabbababbbaababbaabbbbbbabbaababbbabaaaaabababaaaababbaabaabbbaabbabaabbabbabbbaaaaabbbabaabaaabaabaabbbbbbabbabbabbabbaabbbababbbbbbabbbbbbaaababbbbbaabababbababbbaabababaabaaabbaaaaaabbbbbbaabbbbababbaaaabbaabbaabaaabaabbbbaabbbabbbababbabbabbbbababbbbabbabbabbaaaababbaaabababbbbaabbaaaaaaabaabababaaaaabbaaaaabbbabaabbaaababaaababaaaabaaabababaabbbaabbaabababbaaababbababbbababbbabaabaabbabaaaabaaaaaaabbaababbbbabbbbbabaaabaabbaabbababbbbabaaababbbabaaabbabbaabbbbbbaabbbbabbbaaabbbaababaaaabbaaabbbabaaaaaabbbaabbabbabaabbabbabbbbbabbabbababbabababaaaabbbaabbabbabaabaaabaabaabbabbababbbaaaabaabbaabaabbabbabbbbbbbbbbbbaaaabbbabbbbabbbbaaabbbababaaabaaabbbaaaabbaabbbababaaababaaaaaababbbabaabbbbbbbbababaaaabbbbbaaaaaabbabbbbabbabbaaaabbbababaabbabaaababaaababababbbabbbaabababbbaabaabaaabbabbabbbbabaabbbaabaaaaaababbbabbababaabbbabbbabbbbaaaababababbbaaaaaababaababababaababbabbbbbbaaabbbbaaabaaaababbaabaaaabbababbabababaabaabaaaabbbaabbaabaabbbbababbaabaaababaaabbbababbaaaaaaababbabbbbbabaaabbabababbbbaaaabbaababababaababbabaabaabaaabababababbbbabbbabbaaababbaaabbabbaabbbbaaabbaabbabaababaaaabaabbabbabbabbbababaaaabaababaababbbbbaaabaabbbabbbabbaaaababbaaabbbabbbababbbbbbaaabababbabbabababbbbaabbababababaabaaaaababaaaabababaabaaabbbaaababbbbaabaaabaaaaaaababbbbababbabbbbbbbaabbbbbaaabbabaabbabbbababaaaaaaabaabbaabbaabaaabbbbaababbbaabaabababbbaaabbababbbbaabbbabaabbabbbbaabbbaaaaaabbbbbaabababaababbabaaababaaaabaaabaaaabbbbbbaaaabbbbbaababbabbbbbababbbbbaaaabaaaaabbabbabaaabaaaabbaaabaaabbabbbbabbabababbbbbaababaabaabbaaabbbbaaabaababbabaababbbaaaabbabaaaaababbaabaaabbbabbbbaabbababaaababaaabbbbaaabbbbababbabaabaababababaabaabaaaabababaabbabbbaaabbbbbaabbbbabaababaaaabbbaaaaaaabbaabbbbabbaabbababbabababbaabbbabbbbaababaabaaabbbababbbaaaaaaabbbbbbbbaabbbaabaaaaabaabbaaabbbbbabbbabbbaababaaababbaaaabbaaaabaabbbaabbaabbbaaabaababbbbbabbaabbabbbbbaabbabaabbbabaabaabaaabaababbabbbbaaaaaabbbbaaabbbabababbbabaabaaaabaabbaababbbaabbabbbaaababaabbbaababbaabbaababbbbababbaabbbaaabbbabbaababaababbabbababaababaabaaaababababaabbabbbaababbaaabbbaabbabbbbbbbbbbaaabaaaabbabbbbbabbbababbbabaabbabbbbbbbbbbbbababbbabbaaabbbabbbaabababaabaabbbbabaaaabbbabbababbabaabaabaaaaababaaaababbaaaaaababbaabbaaabbbbabbabbaaababaabbabaaabbaaaabbbabaabaaabbaaabbbabbaaababbbbbabaabbaaaaabaababbababbbbaabbbbaaabababababaabaabaaaaaaaababaabaabbbbbaabbabababaaaaabaabbabaaabaaabaaaaaabbbbbbaaaaaabbbaaaaaaabbaaabaabbabbbaaaaaabbabbabbabbbbbaaabababbbbababbbbbabbabababbaabbbababababbababbbbbbbababbaabbababbbbabaaabaaaaabaaabbabbbabbabbbabaaaaabbbbabbbababbbbbabbbbbbabbaabbbaaaaabaaabbabbbabbabbaabaaaabaaaabaaaabaabbbaabbbabaabaaabbababbaaababababaaaaaabaaabaabaaaabbaaababaabaaababbbabaaaabbaabbbabbabbbababaabbaaabaabbbabbaabbbbaabababbbbaababaabaaaaabbbabbbabaabbbbbaabbbabbaabababaababbbbbaaabababbaabaaaababbbabbbaaabbabbbbbbbbbabababbaababbababaaabbaaaababbabababbbababbbbbbbbaabaaaabaabbaaababbaaabaabbabbaaaabbababbbabbbbaabbabaaaabababbbaababbaabaabbabbbbbababababbbbaaabaaaabbbbababaabaababaaabbabaaaaaaaaaaaabaaaabbbbaaaaabbbbabaaaabbaaabbbbbbbababaabaabaaababbaaaabaabaabbababbbaabbbabbaaabbaabababaabbaaabababaaaabbaabbaababaabbabbababaaaababababaababababbabbbbaaabbaabbbabaabbabaaabaaaaabaaaaabbbbabbbbaaabbbaaaaaabaaaabbbbaababaabaaaababbabbaababbaaaaaaaaaaabababbbbbbbbabbaabbbaaabbabaaaabbbbbaabbbaabaabaababaabbbaaabbbaaabababbababbaabbbaaaaaabababaababbabbabaaabbabbbabbbbbaaabbbabbbbaabbaabbbabbaaababbbaaabbabbbabaaababaabaaabaaaaaabaaabbbbaaaaababbaabaaabbbbbbbabbbaabbaaabababbaababaaabaababaaabbaababbabbbbbbbbbbbbbbbbbbbbaaaabbaabbababbbaabbbaaababbabaaaabbbabbababbaababababbabababaabbbbabbbbabbaababbaaaababababbaabbaaaaabbbbaaaabbbbabababbabbaaaaabbbbabbaabbbbabbabbaaabababaabaaabbbababbaabababaabbababaabaaabbbaaaaabbbabaababaabbaaaababbbbbbaabbabbbbbbaabaabaaabaabaabbbaaaabbbbabbbbaaaaaabbaabbbaaaaabbaaabaaaaaaaaabbabaaabbbbabbbabbbaaaabbaaabbaaaabbaaabababbababbaaabbbabaaabbabbbaababaabaaabbbababbabaaaabbbbabaaaabaaaababababababbaaaababbaabbbaababbbaabbbaabbabaababbababaaaaaababbbaababbbbbabaabbbabbabbbbaababaaaaaaaababbabaaaaabaaaaabaaaaabaaabbababaababbaabbbbbbabbbabbbbabbbbbbabaabaaabaaaaaaaaabaaaaaabbaabaaababababbaaaaaabaababaaababaabbabaabbaabbaabaaaabbbabbbabaaaaaaabbaaabbabaaabaabbaaabaababaababaaaababbabaaaabababbbaabaaabaaabbabaabbbabbbbabbbbbabbabaabaabaaabbbababaaaabbabaaabbbbabbaabbaaaabbabbbbbaaabbbbbabaaaaababbaabaaabbbbbaaabababbabaababaaabaabbbbabbabbababaaaabaaabaabbbbbbabbbbababbbbabaababaabaabababbbaaababaabaaaababbaabaabbabbbbbaababaaabbabbbabaaabaabbbaabbbbaaabbbaaabbaabaaaaaaabbbbaabaaaaaaaaabaabbaababaabbabaaaaabbbaaaaaaaaaaaaaaabbbabbbabbbabbabbbabbabbbbabaabaaabbbbbababaaabaababbabbbabbabaaabbaabbbbabbbabaabbbbbbbaabaabbaaaabaabbabbbbabbabbabbaabbbbaabaaabaaaaaaaabababbbabbbababbbabbabaaaabaababaabbaaabaababbabbbabbaabbaabababbabbbabbaaaaabbbabbabbaabbbabaaabaaabaaaaabaaabbaabbbbaababbbbbbbbbbaaabaabbbbaabbabbaabbbbbababbaabbaabbaabaaababaaaababaabbabababbaaabbbbabababbbbbbbaabbbbbbaabbbaabbbaaaaababbaabaaabbbabbabbbababaaabaabaabababbbbbbbbbbbabbabbbaabbbaabbaaaababbaabababbababaabaabbaaaabbaaaabbaaaabaaaaababbaabaabaaabbbabbababababababaaabaaaabbabbabbbabbbaaaabbaababbabbabbbabbbaaabbaabbaaaabbbbbbabbbbaababbabbbbbbbbbabaaabbabbbaabababaabaaaabbaaaabbaaabbbbbaaabbaaabbabaaaaabbabbbabaaabbbabbbaabaabbaaabbaaaaabbaabaaaaabbbbbbabbbaaabaaaabbaaaabababbbbaaabbbaababbababbbabbabbaabababaabaaabaaababaaaaabbaaababaaabaabaaabbaaabaabaababbbbbbbbabaababaaaabaaabaabbabbaaaabaabbbbbabaabaabaabababbbbbbaabbbbaaababaababaaabbbbabbbbabbaaaabaabbabaababbabbbabaabaabbbabbbbbaababaababaabaaababaabbabababbabbaaabbbaabbabbabbbbbabbaabbabbbaabbbababaaaaaaabbbaaabbbababbbbabbbbabbbaabaababaabbaabbbababaabbbbbbbbaababbbaaaababbbbaaaaaabbbabbabbbbbbbababbabaaaabaabbbaaabbbbabaaabbaabaabaaaabbbbababbbaabaaababbbaaabbbbbbbbaaabaaabbbbababbbbaaababbababbaaababaaaabababbbbbabbbbaaaaababbbaaabbbabaabbaabbaaaaabababbababbbbbbabaabbbbbaabbbbbbbbaaaaababbbbabbaabbaabbbaaaaabbababaaaabbbaaababbbbbaabbbaabbabaaaabbaabbbabbaaabbababaabbbababaaabaaabaabbbbbbaaababbaabaabbaabbaaaaabaabbaaaaabbbbbaababbbabababbaaabaabbaaaaababababbbaaabbbabaababaababbabbbbbbbabbaaaaaaabbbabaabbbbbbaabaaabbabbaabaaabaaabbbbbaabbbbabbbaaaaabbbbabbaabbbbabbbaababbbbaaaababaabbaaaaababaabbabbabbbaabbaabbababaabaabbabbabababaabaabaabaaabbaaabbbaaaaaabababbbabababbabaabbbbbbbbabbaabaaabaababaabbabaababbbbababbabbbaaabaabbababaabaaaaabbabbbbabbaabaaaaabbbaababbbbaabababbabaaaaaaaabbbaababbaabbaaabaaabbaaabbabbaababaabbbbbbabbbbbbababbabababbbbbbbbbbabbabaabbababbaabababababaaabbaabbabbaabababbaabbbbbbbbbaaababababbbbbaababbaaaaabbabaabbabbbbbababbbaababbbabbabbaabbabbbbbaababbbbbaabababbaabaaaaaabbbbbbbbaababbbbaabbaaabbbabababbbbbaabbbbaaababaababbabbbbaabbabbaaabbaaababbaaabbaababbbbbaaababbbaaabbaaaaaababaabbbababaababbababbabbbbabbabbbaaaaaabbabbbaabbaaaababbaaaababbbbbbbbbabbaabbabbaaababaabaababbbabaabbabaaabababbbaabbaabaaaaaaabbaabaaaababaababbbbbbababbbbaaaabababbbabaaaaabbabaaaababaabbabaaabbbbbabbaabbaaaaaaabbbbaabbbbbaabaabaaaaaabbaabbaaababaabababbbabababbbababbbbaababababbaabbbbbaaaabbababbaababbaabaaaabbbaabbbbbbabbbbbbbbaaaabbabbbaaababaaabbbabbaabbabbbbaaababbbbabbbabaababababbabbababbbaabbbbbaaabbbababbabbaabbbababbbbbabaababbabbbbbabbbabaaabbabaabaabbababbbabaaaabbbaababbaaaaaabbaaaababaabbabaaaababbaaaabbabaaaaabbbababbbaaabaabaabbabbababaaaaabbaaaaabaabbbabbbababaaabbbaabaabbbabaabababbbaabbabaaababbabbbbabbabbbbbabbbbababbabbbbbabbaaaabbaabaabbbbabbabbbbbbbbbabaababaabbbababbbbbbaaabaababbabbaabaaabbababbababbbbaabaaaabbababbbbaaaababbabaabbbaabbaaababbbbabaaabaabababbaaabbbbbbbaababaaaaabbabbbbbababaabbabaaaaaabbbabaaabbbbaaababbababbaabbbbbaaaaababbaaaababaababaabbaabaaaabababbbbaabbabbabaaaabbbabbaaaabbbabbaabbbaababaababbbababaaaaaaaabaaaabbababaaaabbbbaaaaaabbbbaaaababaaaaaaaabababaabababaaaabbbaaaababbbabbbbaabaabbaaaabbbbbabaabababaababaababaaaaaabbbababbaaaabaaaaaabaabbbbabaaabbababababaabbbbaabababaaabbabaaaaaabbabbbbbaaababbbbabaabbbaabaaaabababbaaabbabaabbbabbbaaabbbbabbaaababababaaabbaaabbbabbbabbababaaaaabaababbabaabaaaaababaabbabaaaaaaabbbbaaababaabaababbaababbabbbbabbabaababaaaaaabaaababbbbababbaabbaabbbbbbaaaababbabbbbababababbaabbbabbbabaaaabaaabababbbbaaabbabaaabbbbaababbaabbabbbaabaabababbabbbbabbbbababbbbbaababbabbbbbbaabbaaabbbbbaaaaaaaaaaabbbbbbbabaaaaabbabbbbaaaabbabbbabbaabbababbabbbabaabababaabaaabbababbbaaababbabbaaaabbaaaaaaabaaabaabbaaababaaabbabbbbbaaaaaaaaaababaaabaabbbabbbbbabaaaabbaabbbaaaabbbbaabbbaababaaaaaaaaabbbbaabaabbbbbbbbbbabaaaabbbbabaabbbababaaaabaaaaaabaabaabbabbaabbbabaaaababbbbabaaabbbaaaababbbbbbaabaabbabbabbabbbabbaabababaaabbbaaabbaaaaabbababbbbaabbbaaaaabbabbabaabaaaabaabbbbbbaabbbababaaabbbbbabababbaaaaabaababaabaaabbaabbaaaaaabaaaaaaaaaabbbbbabaabbbbaaabbbaaabbbabbababbaaabbaababbababaaaabbaabbbbbaaaaaaabaaaabbbbbbaaabbbbabababbabaabbbbbbabbabbbbbbaabbababbbbbababbababbbbaabbbaabababbbaaaaaaabaabbaaaaaaaaaabbbabbaaaaababaaaaabbbbaabababaabbbabbaabbabaababbbaaaababaaababaaaaabababbaabbabbaaaababbbaaaababbbbabaaabbbbbbabbabbbbbbbbbbbbbbbaababaabbaaaabaabbbaaaabbbababbbbbbbabbbaaaabbaaabbbabaabbaabbbaababbabaabbbbaaabaaaabaabaaababbabbabbbbabbbbbaaabbabbbabbbabbbaabbababbbbabbababaaabbbbabaabbaaabbbbbaababbbabbbabaaaaaabbbbaaababbaabaaabbabbaaababababaabaaaaababbbbbbabbabaaababaabaaaaabbaaaaabaaabbbbaaaabaababaaabbabbaabaaaababaaaabbbaaabbaaabbabaaabbabbaabbbbbaaaababaaabaabaaaaaabbababaaabbaababbbbabbabbbaabbbbaabbbabbbaababbaabbaaabaaabababbbabababbbaaabababbababaaababbbbababbabaabaabaabbabababaaabbbbbababbabbababaaabbababbbbabababababaabbbbaababaabaaaabbbbaabaabaaaabaaaaaabbabbbabbbbbbbaaaaaabaabbbaaaabbaaabbaabbbbbabaaaababbaaaabbbaabaabbabaaaaaaaababbaabaababbbbabbbbbbabbaabaaabbbbbabbbbbbbaabbbbbbbaaaabbabbbbaaabbabbbbabaabbaababbbbabbbaaabbbaaababababbbababaaabbaababbbbbbaabbabbabbabbaabaaaaabbbbaaabaaabbbbbabbbbbababaabbbabbbbbbababbbaaababbaaaaaaabaabbbbabbaaabbbaabaaaababbabbababaabbaaabaaababbabaababbbbbbbabababbbbaaabbabaaabbabbbbbaabbabbabbababbaabababaaababaaaabbbbabaaaaaaabbbababaabbbbababbaabbabababaabbbaaaabaaabbaaaaabbbbbbbbabbaaaabbaabbbbaaabbaaabaabaaaaaaabbbbababaaabaababaabbaaabbaabbabbabbababbaaababaaaaaaabbaaaaaabbbbbaaaaaabbabbbaaaabbaaaaabbaaabaabaabbaabbbabababbabbaaababaaabaaabaaabababbbbaabbabaaaaaaabbbbababbabbabbabbabaaaabababaabaabbabbbaaaaaabbbbbbabbbbbaababbaabaaaaabaaabbabbbbbbaaabaababaababbbbaaaaabaaaaabbabbabbbbaaabbaababaabbabaaababbbabbbbbaabaaabaababaaaaaabaaaabbbaaaabbbbabbaabbaabbbaababbabaaabaabbbaaaabaaababaabbbaabaaababbbaabbabaabaabaabaabbbbababbaabaaaabbbabaaaaaaababbbbaabbbbbbaaaabbaabaabbbababbbabababaabbabbaababbbbbbbaaaabbaabaaaaababbabababaaaaaababbaaaabbaaabbbaabbbabaabbbbaababbbbabaaabaabaaabbbbababababaaababbabababbbaaaaabababbbabbbababaabaababaabababbaaaabaabaaabaabbaaababababaababbbbbabaabaabbaaabaaaabbbbbbabbbbbaaabbbaaabaabbbaabaaabbbabaabbabaabbaaababbbabababababbbaabaabaabbaabababbaaaaaaaababbabaaabaaabaaaaabbababbbbbabbabbbaababbabbabaababaaaababbabbabbbbbababaabaababbbbababbababaabbbabbaaabbbbabbaabbaaaababaabababbabaabbaaababbababbabbaaabbaabaabaaaababaaabbbbababbaaababaaabaaaabbbabbbbbbbababbbabbabbaabbbaabaaabaaaababbbabaabbbbbabbabbaaaaaaaabbbbbabbabaabbabbbbbbbaabbbbaabbaabbababababbaabbbaabaabaabbabaabaabaabbbbababaaaaababaabababbabbbaaabababbbbaabbbabbbabbaaaababbbbabbbbbbaabaabbabbbabbaaababbbbaabbaabaaabbaababbabbabbaabaaaababbabbaaabababbabbabbaababbbbbabaaaaabbbabbabbababbaaabaabbbaabaaababbabaaabbbbbababbabaaabbababbbbaababbaaaababbababbabababbbbaaabaaabbaababbbaaaaababababaaaabbbababbababaabbbbbbbabbaaabbbaabbbaabaaaabbabaaaabbaababbaaababbbbabaaaaaaaabbbbbbaabaabbaabababbbabbabababbbabbaabaabaaabaabbababababbbbabbbbaaaabaaaaabaaabbbbaaabbabbabbbbabbaabbbbbbbaaabbbbababbabbaabbbbbbaaaaabbbaabbabbbbbaaaababbbababbbaaabbbbbabbabbbaaaaaaaabbbabbabaaabbbbaaabbababaabbbbbaaabbaabbaaaabbabaabbabbbbbaaabbabbbbabaaabaaaabbbbbaaabbababbabbabbabbbbbaababaaabbaababaaaaabbbbbabbaaaaabaaaabbbaabbbaaabaababbbababbabbbbbbbabbbaabbbbbbbabbabaaaabaabbbabaabaabababbaaaabbbbbaaaaabaaababbbabbabbbbbabbbbaaabbabaaababbbaabbabbbbaabbabbbaaababbaaabbbabababbbaabbbaaaaaabaabaaabbbbbaababbbaabbbaabbbababbbaababbaaaabbbbbbbbaabaaaabbbabbbbbbbaaabaabbbabbaabbaababbbbaabbabaaaabbbbbbabbbabbbbaaabbbaaaaabbbbababbaabaabaaabababbabbbbabbbaabbbabababbbbbaaabbababaaabaabbaaabbbabbabbbbabbbaabbbabbaabbaaabbbbabbabbbbaababaaabbababaaabaaaababbbaababbbbaaabbbbabababaabbbaabbaaaaabbaaaabbaabbbbbaabbabbbabaaaaaaabbabbbbaaaaaaaabaaabbabaabaabbbbababbaababaabaababbaaabaabbaaaaaabaaaabaabbbaababbabbbbabbababbbbaabababaabbbaabbabbbbbbabaabaababbbbbbabaabbbbbaabbbabbabaaaaabbbababbabbbabaaaaabaaaabbaabbbbaabbbbbbbbbababaabbabababaaaaaabbabaababbabababbbaabababbbbabababbbaaaabbbbbaaaaaaaaaaabaababbbbabbbaabababaabaaaabbaabbbbbbaaaaaabaababaabbbbbbabbaabaabababbabbaaaaabababaaabbabababbbababaaabaaaababbaaaaabbbbbbabaaaabbbabbabbabbbbababbaababaaaaaaaaababababbababbabababaaabaaabaaabbabbbabbabbabbbabbaaaabbababbabbabbaaabaabbaababababaabbabbababababbbbbbabbbbaaaaabbaabbabbaabbaabaaaabbabbbaaaaaababbbbbbbbabaababaabbbabbabaababbabbabaaabaaaaabbbbaabbbbaaaaaababaaabaaaaaababaaabaaaabaaaaabbbabbababbbaababaaaaabbbbabaaabbbbaabbaabaabababbbbbaabbabaaababbaaaabbabbaabbbbbbbaaababbabbbaabaaaabaaaaabbaaaabbaaaabbaabbbabbabbbbaaabaabaabbaaaabbabbbbaabaaaaabaabababaababbabbabbaaababbabababbbbbaabbabaabbbbbbbaabaaabaabbaababbaabbbaabbabbbabbbabbbbbaaaababaaaababbbbababbbbabbbaaabbbabaabbabaaabaabbbbbabbbabaaababbbbbababbababababbabbbabaaabaabaaaabaabaaababbaaabaaaaaabababbaabbbababbbaabaaabaabbababababbababaabababababbabbbbbbbbabbbbbabaaaaabbaaabaaabbbbababaabaababbbbbbaabaaabaababaaabbabaaaabbbaababbbabaaaabbbbaaabababbbaaabbbababbaaaabbbbabaaabbabaabaabaaaaaabababbbbabaabbbbbbabaaabbaaabbbbbaabbbaaaaaabaabaaabaaaaabbbbaaaaabbabababbbaaaabbbaabaabbababbabbabaaabbbaaaabbbbbbbbabbababbabaaaaabbabaababbabbbbbaaaaaabbbbaaaababaaababbbbbaaaabbbbaababbabbabaabaabaabaaaaaabbabaabaababaaabaabbbaaaaaaabbababaabaaababbbaabaaabbabbababbbabbabaaaabbbbbbbaabaababaababbbbabbabbbabbbabbbabbaaabbabaaaabbabaabaabaabaaaaaabaababbabbbabbbbbbaaabababababbbaaaaabaabaaaabbbbbbbaabbbbbbbababaababbabbbbbbbbaabbbaaabababaabbaaaababaababbaababbabbbbaabbababbaaabbabbbaabbabaababbabaabbaabaaabbabbaabbabbbaaaabbaabaabbbbbbabbabbababbabbaaaabbaaabaaabaabbbabbaabababbababbababaaaababbaaaabbababbbabaaabaababbbaabbaabbbabbababbabbaabaabbaaaababbbabbabbaabaababbaababaabaaabbbbbaaababbaaaabbababbbaaabbbbaabbbabbbaababbbbabaaaaaaaabbbaaababbabbbabbaaabaababaaaabbbbbbbbbbabbabbbbaaabababbaabaaabbaaaabaabaaababaabbbbbabbabbababaaabababababbabbbabbbaaabbbbababbbbbaaaabbbaababbaabbbbbabaabbbabbaabbbbaaaabaaabaabbbbbaaabaaabaabbaaababaabaabbaaabaabbbaabbaaaabbbababbaababbbaaabaabbbabaaaaaaaabaabbabaabbbaaabbabbabbababbbaabaababbbbbababababbabaabbbaaabaaabaaabbaaaabaaaaabbbaabaabaaaabbaaaabbabbbbbbbbabaabbbabbaabbabaabaaababbbaaaabaaaababaabbaaababababaabaaabababbbbbaaabbbbbbaaaaaaaabbaabbbaaababbbaaaaaaaaabbabbabbbabaabbbbaaabbaabbbbababaaabaaaaabbabbbaabbbbbaabaabbbbbbaaaaababbbabbaabaaaabababbabbabababbbbaaaaababbaaababbbaaabbbabbaabbbbabaaaaabaabaaaaababbaabbbaaababbbabaabbaabbaabbabbaaabaababbabbabaabbaaabaabbbbabaabaababbbbbaaaaaababbbbaababbbabaaabbaabababaabbbaaaabaabababbbabaabaaabbbabaaabaaaababbabbabbaaaabbaabbbaaaabaaabbbbbaaabbbbaaabaabababababbaabaabababbabbabbbabaabaabbabbbbbbbbbbabbbbbaaabaaaaaabbbbbbaabbbaababbbbaaabbaabaabbbaabbbbabbbbaaabaaaabbaaababaabbbabbaabbaabbabbbabbaaababbbbbbabbaaabaaaaaabbbaaababbbababbbbaaaaaaabbabaabaabbbaabababaaaaababaaababbbaababaaaabaaabaaabbbabbaaabbaaabaaabbabbabaaabbbaaabbbbbbbbbaaabbabbaaaaaabbbaabaabababaaaaaabbababababbbbbabbaababaabaababaabaabbabbbbbabaaabaaabaaaabbabbabbbbbaabaaaabbbbaaaaaababababbaabaababbaaabaaabbbbaaaabbaabaabababbabbbabbaabaababbbbbbbbabaaaabbbaaaaaaaaaaabbbabbbabaabaaaaababbabbbbbabbabbabbbbbbbabbaaababbaaababaabbaabaaabaabaabaaababbbabaabbbaaabaababaababbbabbababbbabababbaaaabbbabaababaababbbaabbbbaaaabbbaabbaaabbbabaaaabbbbabbabaaabbabbabbbbbbabaabaaabaaabababbbabbaaaaaaabbbbbbabbabababbabbaabbbaaaaabbbbbbbabababbbbbbabaababbaabbabbabbabaabbbbaabbaabbbbbbabbbaaababaaaabaaaaabbbabaabbabaaaabaabbbbabaaaaabbabaaabbbbbbbabaababbbaabbaabbabaaabababbabbbabbbbbbbabbabbaaaabbbbbbbabbbababaaabbbabaaababbaabaaabaaababbbaaaabbbbbbbbbaaaaaabababbabbabbaaababbbabababbbaababaaaababbabaaaaaaabaabbbaabaabbabbabbbaabbaaaaabbbbaabbabbbbbbabbaaabaaababaababbabababababbbaaabbbabbbaabbaaaabbababbbbbabbaabbababbababaaabbbabbaaaabaabaabbabbabbaabaababbabbabababababababbbababbbaaabaaaaabbbbabbabbababbbbbabbaabbaabababaababbabbaabbbbaabbbbbbaabaaaaaaabbbbbbaaaaaaaabbbbbabbbabababaabbabbbababbaabababbabbbbaaabbbbabaaabbbabbaabbbabbbabbbbbaaabaababaaababaaabaaaaaaabbbbbbbbabbbbaaaabbbaabbbbaaaabaabbaabbbaabbbbbabaaabbbbbabbbbaabbbbaaaaaaaaababaaabbbaaaabbbbaaaaabababaabbabaaabbaababbbababbbbababbbbabbaabbabbbabbbbbabbababbbbbabaaaababbbaabaaaaabbabababbababbbbbaabbabbabbbaabaabbbaabbbabbbaabababbbababaaaaabbbbbbaaaaaababbbabbababbabbbbbbbbbbbbbabaabbaaabbaaabaabbaababbbbabbaaaaabbbabaaabbababbbabbbabababbaabbabbababbbabbbbbbbabababbaaaaabababbaabbbbabbaaabaaababbbbbababbbaaabbbaaabaaaaaabaabbbaaabaabbaabaabbbaabbbbaaaaaabbbababbbbaaabbabaabaabaaabbaaabaababbaabbaabbbaabaababbbaabbabbbbbaabaaabbbbbaaaaaaabababbbbbbaabbbbaaabababbbababaabbbaaaaaaaaaaababbbababaabbaaabbaabaabbbabbaababaabbabbabaabbbabbaabaaabbbababaaaaaaababaaaaabababbbabaabbbbabaaababbbaabbaababbaabbaababbabbabaaababbaababbabaaabaabbaaababbbaaabaabaabbaabbbbbbbbaaaabbbbbabbabbbbaabbabbbabbbaabbbabbbbbbaaababaaababaaabbbaaababbaaabbbababbbbbbaaababbabbaaabaaaababaaaabbbababaaabaaaababbbabaaabbabbbbbabbbaaabbabbaabbbaababbbbbaabaaabababbbababaaabbbbabbabaaaababaabbabbabaabbbbbbbbbbbaaabbabbbaabaaabaaabababaaababaaaabbbbababbababbbaabbbbbbbbaaaababbbabbaaaaaaaaabbabababbbbbbabaaabbbaabaaabbaaabbaabbabbbbabaaaabaabbabbaababbbaabbaaababbababbabbbabbbbbabbabbbbaabbbbbbbaaaaaaaabbabaaababbababbbbbbaabbaaabaaabbabbbabbaabbabbabbababbbbbbbabbbaabbabbaaaabbbabbaababbabbbbabbababaababbbbaabaaaabbabaabbabaaabbbababbaabababbbbbbabaababbbbabbbabbaaaabbbbaabbbabbbbaabbbbabaabbabbabaaabaaabaabababaaababbbaaababbaaabababbbaababbaabbbabbbababbabababbabbaabaaabbabaaaabaaababbbbaabbbbbbababbbbabaabbaaaaababbabaaaaaababbbabbbbbbabbabbaabbbaabaaabbaaaaaaabaaaaabaabaaaaaabbbaaabbaaababaaabbbababbabaaaabaaabbbbaaabbbabbbababbabbabbbababbaabbbbbaaabbabaaaabbbbbabababaaababaabababbaabababbbbbbaabaabaabaaabbbababbbababbaababaababbaaababababbbabaababababbbbbbabaabaabaabbabbbaababaabbbbabbabaaaababbababbbbbabbababbbabbabbaababbaabaaababbbbaaaaaabbbbbbbbababbbabbababbbbbaaaaababaababaaabaabbabbbabbababbaaaaaaabbaabbaabbaaaaaaabaaabbbbababbbbaababaabbaaaabbabaababababbbaabaaababbbbaaaababaaaabbbabbbababbbabaabbbbbbaababbbbaabababaaaabbabbabbbabaabbabbbbaabababaaabbbaabbabaabbababbaaaaaabbabbabbbbabaaaaabbabbbabbabbbaaaaababbbbabbaaaabaabbbbaaaabaaaaabbbabbbbbbbbaabbbaaaabaabbabbaabbaaababbbbbaabbbbbbababbbabbaabaabaababbaaaaaabbbbabaaabaaaabbbaaabbaabababbaaababbabbabaaabbbaaabbbbabbabbabbabbbbbababbbaaabbabaabbaabbbaabbaabaaabbaaabaabbbabaaabbbbbaabbababaaabaabaabbbabbaabaabaabbaaaababbaaaabababaaabbbaaaaabbabbbabbbaabbababaaaaabaaaababaaaaaabbababaaabbabaababbbaaaabbaabbaaabbbbabbbbaabaabaaabbabaabbbbbaaaabbababaabbaabbaaaabbbbababababbbabababbabaabbbbabaababbaabaaababbbbbbbabbbababbabbaabababbabbababababbbbbbbbaababbabbaaaaababbbaaaaaaaaababbbababbaaabbabaabbbabbbbabaabaababababbabababababbaaaaababbaaabbbbabbabbaaaababaabbaabaababbaababbaaaabaabaaabaaabbababbbbbaababbababaaaaababbaabaaaabbabbaaaaaabbabbaabaabaaaaabaaabbbbababababbbbaaabbabababbabababbbbaabaababbabaabbabbaabaabaabbbbbabbaaababaababbbababaabaabbbaabbabbabbbaaaaaaababbbbaaaaaaabbaaaababaaababaaabababbaaababaaaabbbbbaabbbaabaaaabaaaabbaabbabaabbabbaabaaaaaababaabaabaabbbbbaabaabababbbaabbabbbababbaaababaaaababbaabbbbbaaabbbabaaabbaaaabbabbaaaabaaabbaaabbbabbaaaaaababbaabaabbaabaaababaabbabaaabaabbaaaabbaaabbabbabbbaaabaaabababbaabbabbaaabbbababbbaaabbbaaababbaabaabbbbaaaaaaaabbaaabbbbaabbbaabababbabbbaabaababbaababbabaaaabaaaabbbbaababaaaabbaabababaabbbabbbababbababababaaaabaaabaaaababaaaabbbbababbaaaabaaaaabbabaaabbaabbaabaabbabaaaaaaaabbbbabbbbaabaababbbaabbbbabbaababbabaabaabaabbaaaababaaabbabbbbaabbabbababbbbbbabaababbabbbbababbaabbabbabbabaaaaababbabaabbabbaabbaaabaabaabbabaaababababaabbbabaababaabbbaabaaaabbbbabbbaaaababbaaababbaababbbbbbbbbaaaaaaaaaaaaababbabaaabaaaabaabbbabbbabbbbabbbabbabbbabbbaaababbaaaaaabbbaabbbaaaaababbbbbaaabbbabbaaaaabaaabbabbbbbbabaababaaaabaaabbbabaabbbaaaaaababbbaaaabbbabbbbbaabaaaabbaabbbaaaabaabbaaabbabaabbababbaabaaaabbbbbbbbababbbaabbbbaaabababbbbabbbbaaababbababaababaaababaaaababaabaabababaabbaaaabaabbbabbabbaaabbbaabbbbabaaaababababbbabbababababaaababbaaaababbaabaababaabbbbbbabbaababbabbbbbaaabbabaabbaabbbbbaaaaaabbbbaaabaabbbabababbbaaaababbaabaabbabaaaaabbabbbbaabbaaaaaaaaabaaaabbbaabbabaaaaabbbbabababbaabbbbaaabaaabbbabaabbbaaaaabbbbbbabaaaababbbabaabbaabbbaaabaabaaabbaabababbaaaabbaaabbaabbaaaabbaababbababaababbbbbaaababaabaaababababababbbbababbbaaabaaaaabbbbaaabbaabbabaaaaaabbaabbaabaabababbbaaaaabbbbaaabaabbbbaabbabaaabbabababaaaababaaaabbbbaabbbabaabbbaabaabaabbaaaabababaabaababbabbbbabbabbaaaabbbbaaaaabaabaaabaaaaabaaabaabaaabaabbaabbbbabbabaababbbabbbaabbabbaabaabaaababbbabaabbbbabaaaaaaabaabaaabaaabaaabbabbbbbbbabbabaaabaabbaababbabaabbaaabbabbabbaabaaabaababbabaabbaaaaabbababbabbbaabbaabbaaaaabaabaaaabbabbbbbaaabbabaabaaabaabbbbbbabaaababaabbabbbabbaaabaabaababbbbbabbaaabbbbbabbbbbbabbabaababbaabaaaabaababaaaababbabbabababbabbbbbbaababbaababababbbbabbbbaabaabbbabbaaaaaaaabbababbbaabbaaaabaababbbababbabbaaabababbbbababbabaaaaaabbbabbbabaaaaababbbabbbaaabbbbabbbbaabbbbbaabaabababbbaaaababaabbbabababababbbaababbaaaaaabbbaaaaaabbaaababbaabbababbbbbaabbbbbbbaaaababbbaababbaabaaabbbaaaaabaabbbbbbaaaabbbabbaababbbaabbbabbaaaababbbabaabbbaaaabbbbbabaababbbbbaabaaabbbbbbbaabaaababbabbbbbaabaabbababbabaabaababaababbaaaaabbbbabaabbaaabbbababbabaaaabbabbaaabaaaabbbbbbbbaaaabbaaaaabbaabbbabbabbbaaabbabbaaabbbbaaaaaaababababbbbaabbaaaabaabaabaaabaabababbbbbbaabbabbaabbabaababbbaabaabaabbaabbabbbbaabbbbabbbaaaabaaabbaaaaabbaabbaababababbaaaaabbaaaaabbaaababbbbabaabbaaabbbabbabbbbbaabaababbabbabbbbaaababaaaaaabbbaaababaaabbabababbbabbbabbabbbbbbbbbabababbaaaabbabaabbaaababbaababbbbaabbbababbbbbaabbbabababaaabbabaaabaababbaaaaabbbbbaaababbbabaaaaaabbbababaaaaabbaaaabbaaabaabbaaabbabaaaababbaaabbaabbbaaaababaabbabaaaabaaaaabbababbbabaaabaabbbaababababaababbbbaaabaabababbababaaabbbbbabaaabbaababbbabaaabaababbbabaababbabbbaaaabaabbbaaaaaaabbbababbbaabaababbaaabbaaaaabbbbaabbbbabbaabaabbabbbaaaabaaaaabaaababaaaaabbbabaabbbbababaaabbbbaabbbaabaaaaaaababbbabaaaabbbaabaaaabbabaaaababaaabaaabaabaaaababaabbabbababbaabababbabaabbababbbbaaaabaabbbbbaabaaaabbabbbaaaaaabbabaaabbaabbababbabababbaababaabbbbaabbbbaabbbabbababaabbbaaabaababaababbbabbbbabaabbaabaaabbababababbaabaaaaabaaababbbaabbabbaaaababbaabbbbbbbbaabbababababaabababbaabbabaaabaabbbbbabbabbaababaabbababbbaaaaaabbbaabaabbaaababaaaaabbababaaaaabaaabababbbabaaaaaababbaabbbbabbabbababbabbabaaabbababaabbabbbabbaabbbaaaabbbbbabbaabbababaabbbbabbababbbaabbbabaabbbbaabbbaababbbbaababaabbbbbbbabbbababaaabbbbabaaaabbbabaaabaabbaabbaaaabbbaabaabbbbaaaabbbbabbabaabbaaabaabbaaabababbbaababaababaabaababbabbabbbbbbaabaaabaababaabbbaaaababbaaababababababbbabaaababbbbbbaabbbbbbabbaaababbaaaaaaabaaabaaabaaababbaaabaabbbbbbaaaaababbbbbbbaaaaaabbbbabbbbbbaaaababbabbabbbaabbbabbababababbbbababbaaabaabbbbaaaabbbbaabbbaaaabbbbbaabaaabbbbbbbbbbbaaabbbbbaaaabaaabbaaaaaababbbbaabaabbabbbbbaaaaababbabababaabbbbbbababbbaabababababbbaaaabaabaababbaaaabbabbbabbbbaaabbaaaaabbaaaabaaababaaabbbbaaaabaabbabbaabaababbabbabbabbaababbbaabbbabababbaaabbbbaaaaaaaabbabbbbbbbbabbbbaaabaaabababaabbbbbaabbbbaaabbaaababbbaaababbaababbaabaabbbaaaaababbabbabbaaababaaaaabaabaaababababaabaabbbababbbbaabbbabaaaabbbabaaababbbbbbaaaaabbbbaabbbbbbabaababaabaababaabaababbbaaaabbbaabbbaaabbababbbaaaaabbabbaabbaabbbbabbbbabbbaabbbababaabbabbabbbababaaaaaaababaaaaabbaabaaaaabaabbabbabaababababbaabaaaabaaaabaaababaabbbababbbbbabaababaabaaaaaaabbabaabaaaabbaaaabbbaabababbababbbabaaaaabaabaaaaabaabbbbaabaabaaababaababaaaabbbbabbbbaaabaaabaaaabaaaaaabaabaaabbbbbabaabbaaaaaaabbbbbbbaaaabbbaabaaaaaaaabaabaaabbbaababbbbabaabbbbabbaabaabbabaaabbbbaaabbbababbbbababbbaabaaabbaabaaaababaabaabbabbbbbbbaaabbbabbabbbababbaaabbababbabaaaabbbbaaabaabaaabaaaaabbaabbabbaaaaabbabaabababbbbaababababaabaabbabaababbabaaababababbaabbbbbaaabbbabababbaaabaabaaabbbbabaabaabbabaabbaabbabbaaabbaaabababbabababbbabaabbabaaaaaababbabaabbbabaaabaabbabababababaaababbababbaaaaabaaaabaaaabbaababbbaaabbbbaabababbbaaabababbababaabbabbabaaaababaabbaaabababbaaaaaaabbabbbbababbababababbbbabababababbbaaaabaababababaaaaaabbaabaabbbabaaababaabbbbbaabbbaaabaaaaababbbaababbbabaaaabbbbbbbaaabaababbbbbbbaabaabababbbbabaabbabbbbbaabbababbaabaaaaabbaabbabbbabbbbabbbbbababbabaaabbabbabaaaaabbabaabaabaaabbbabbabaabbabbabaaabaaaaabbabaabbaabbbbbbbaaabbabaababbaabbbabbababaaabbabababbbaaabaaaaaabbbbaabaababbaabbbbabaaaaaabbbbbbbabbabbbbabbaababaaababababaabbbbababaaabbbbbbaabbaaaaababbbaababababbbbaaabbbbbababbbabbaaabbaaababbbaabbabaaaaabaaabaababbbaabbaabaaabaababaabababbbaaaaaaaaabbbaababbaabbbabbabbaababababaabaaabbaaabbaabababaababbbabbbbbbbaabbababbbbaabbabbbaaaaaabbbabbabaaabbabbbaaabbbbbbaaaaaaaaababaabbbababbbabbbaaaabbbaabbababababbbbabbbbabbbbbbbabbaaaababbabbabaaaababaababaabababbabbaabbaaabababbababaabbbabbbababbaabaaababbabaabaababbaabbbbbbbaabbabababbabaababaabaabababaaaabbababbbbbbbabbabbbababbbaaaaabbbbbbbbbbbbbbbaaaaaabbabaababbaabbaaabbbbababaaaabbaabbabaababaaabbaaababaabbbbaaaaababbbabaaaabbbaaaaababaaaaababbabbaabaaaaabbaababbabbbbbabaabbabababbbaaaaaaabababaaabbaabbabbbabbabbaaabbaaabbbbbababbabbbabbbabbabaabbaaabbbaabbbabaabaabaaababbbabbaaaaaaaaabbbbaaaabbaaabbbabaabbbbababbaabaaaaabbaaaaabbbbaabbabbaaaaabbabbaaabaaababaaaaaaabbbabbbaababbbbabbbabbabababbaabaababbbabababbabaaababbbbababaabababaabababbaaaababbbbbbbababbaabaaaabbbabaaabbbabababbbbbbabbbbabbaaabbababbabbabbbaabbbbbaabbababaabababbaaaabaaaaaaabbbabbbaabaabbbababbbbababbaabaaaaababaaabababbababbbaaabbbbbbabbbaaababbbbaaababbaababbbbbbaababbabbbaaabbaaaaaabaabbaabbababaaabaababaabbaabbabbaabbbabbabbababbbbabaababbbbaababbaaaabbbbbaababbbaabaaababbbabbbabbabaabbabbbbbbabbabababababbbabbbbbbabbbabbbabababbaaabbbbabbbaabbbaaabaaabbababababbabaabbabababababaaaaaabbaabbbbaabbababaaaababaaaabbaabbabbbbbbaaaabbaaaabbbaaaabbaabaaaaaaabbbaababaaabbaabbbaabaaababaaabaaaaabbaaaabababaabaaabbbababbbbbbbababaabbaaaababaaaaababbbbbabbababaaaaaaaabaabbbaabbbaabbbabbaabbbbbbbaaaabaabbabbababbbaaabaaabbbbbbaabababbaabbbbabaaaaabababbbbbbabaabaaabbbbabbabbbbaabababaabaabbabaabbaaaababbaababaaabaaabaabbbbabbbbbaababaaaabbbaaaabaaaabaaaaabbabbbbaababbbabbbbaaabbabaabbaababbbbbbbaabaaabaaabbaaaabbbbbababaaaabbbabaababababbabababaababaaaabbbbbbbabbabbbaabbbababaabbaaaabbbbbaaaababbabbabaaaabbbaaababaabbbbbbabaaababaaabaabaabbbbbaaaaaaaaabbbbbbaaabbbbbaaaaabababbaabaabaababaabaabbbbaababaaaaaaaaaabbaababaaaabaababaabbbbbbbabbbbbbbaaaabbbaaaabaaaabbbbaaaabbabaababaaabaabbababbaabbbbbbbbababaabababbbbbbabaaabbabaaababbbbabababbababaabbaaaabaaabbbabbabaaabbbbbabbbbbaabbbabbbbababaaababaabbbbbbaaabbbbabbbabbaabbbbbabbaaababbbaaaaabaabaaaabbbbbbbbaaababaaabbabbbaabbbbbbaaabaaaaabbbbbbbaabbbabaaabaabbabbbbaaaaabaabbbabbbababaabbababaababbabbababbaaabbababaaabbaababaaaaabbaabbabbbbbabaabbabaabbaabaaaabbabbbbabaaabababbaabbbbbabbabaaaaaaaaaabbaaabbbbbbaaababbbaabaaabaaabbbbababbaaaaaabbbaaaabababaaaabbbbbbababbaabbbbababbbbabaababaaaabaaabbbbbbbbbbbbbaabaaaaabaabbaaaaabbbbaaabbabbababaaaaaaaabbbaabbaabaababbaaaabaaabaaabbbaaaaaaaaabbbabbaabaabaabbbbabbbbbaabbabbaabaabababbbabaaaabaaabbabbaaaaaabbbabbababbbbbbbbababbbbaabaaaabbbabaabbbabbbaababababaaaabbbbbbbbbbabbaaaabbbbaaababaaaabbbbbbaabbaabaabbbbabaabbbaaabbabbaaaaaabbabbababbabaaababbbbababbabbaabaabaaabbabababbbabbbababbbbbbbbabaaaaaabbaaabbbaaaabbbabbbbaababaabaaaaaabbbabaaaaaabababaabaaaaabbabbabaaaaabaaabbaaaaabaabbbabbabbabaaaabbbabaaaabaaaaabbbbbbbbbabbaababbabababbaabaaababbaababbaabbbbbbbaaabbbaababbabbbbbbababababbbabaabaabbaaaabbabaabbbabbbbaaaaabbabaaaaabbabbabaabbbbbabbaabbbbbbaaaaabbababbabaaabababababbaabaabbbbaabaabbabbbbababaaabbbabbaaaabbbabbbabbbaabaaababbabaabbabaaaaaabaaababbbbaabaaaabbbabbaaaaabaaaaaabbbbaaaababaabaaaababbabaaaabbbaaaabbbbababbbabaabaabbaabaabbbaababbabaabbabaaabaabbbabbaaaabaaaaaabababaaababbbabaaababbbbabaabaaabbbbbbabbabbaabbbaaaabbaaaabbaaaaaaaababaabbabababbbbbabbbaaaaabaababbbbaaaaaabbabbbbaaaaaabbbaaabbabbababaaababbaaabbbbbbbbabaaabaaabbbaaaabbbbbaaaabbababbbbaabaabbbabaaaaaabbaaabbbbabbbbaaaabbbaabababbbababaaabbbaaabbabbbbabaaababbbbbaaabbbaabbbbbaaababaaabbbbabbabaabbaaabbbbaaabbbabaabbaaaabbababbbbbabbaabbbaababaabbababbbbbbaaaabbbbaaaabbbbababbaababbaaaabbababaaaabaabbbaaaabaabaaabbabaabbbbaaaabbbbbaabaabbbbbabaaababaabaabbabbaaaabbbaababbaaabbaaabaabaabbabbbaabaaaabababaabaaaaababaababbabaabbabaaabaabbbabaabaaaababbbaaabababbbbabbbbbbbbbaaaaaaaabaabaababbaabbabbababaaaabbaabaabbbaabbbbbaababbbbbabaaaababaaaaabaabbbbbaaabbabaaabbbbbbbbaaaabaaaaaaababbbbbbbaabbbbbbbbabababaaabaabbabaaaabaabaabaabaaabaabbaaabaabaabbbababbabbbaabaabbbaaabaabbabbaabaaabbbbababbbbbabbbababaabbaabbbaabbabaabaaaabbaaaaaaaaaaabbaabbbbbaababbaaaababbbbaaababbaaaaaaabbbbabbbbbbabaababababaabbbbbaaabbbbaaaabbaabaaaabaababbbbbbbbbbaaabaaaabaaabaababaabbbbabbaaabaaaabbabbbbbbbbababbbaaababbaaaabababbaaabbbabbbaaaabbaaabaaababababbabaaabbabababababbaabbaaaaabaabaaabbbaaabaaaabbbababaaababbababaabbbaabbabababbabaaaababaaabaabbbbbabaabbabbbaaabbbbabbbbabaaabaababaaabbbbbbaababaabaabaaaabbaabbabaaabaabbbaabbbaababbbbaaaaabbbbababbabababaabbabbbbbababbbbaaabbbaaabbbaaaaabbbbbbbaababbaaabbbbbabbbbabbabababaababbaaabbaabbbbbbbaabaaaabababbaababbbbaaaabbbababbaaabaaaabababbabaaabbabbbaaaaaaabaaabbbbbabaaababbaaaaabaaabaabbababaabaabbbababbaabbaababbbbaaaaaabbbbbbbaaaaaaaaabbaaababbbbaabbabbababbbbbbbaababaabaabbabbabaababaaaabbaabbabbbabbbbaabababbbababbbabaabbabbbabaabababaabbabbbaababbabbaaababbbbabbabbbbaaabbaaabbabbabbbbaabbaaabbabaabbaaaaabaaaabbaaaabbbbaabaababbbababbbababbbaabaabababbbbabbaaabbabbbbaababaabbbbaaaabaabababaaabaabbabbaabaaababaaabaabbaabbaabbaabbbbabbbaaabbbaabaabbbabbbbaabaababbbbaababbabbaaabaabbbbbababaaababaaabaabbabbbaabaaaaabbabaaaaaaababbaabbabbbbbabbaabaababbbbbaabbbaaabbabbaabbbaabbbaaabbaabaabbbbabaabbaaaabababaabaaabaaabaabababaaabbaababbaabaabbbabbaabbaabaabbbbbabbbbbabbabbabbbbbabbaaaaabaababbbabbaaaabbabababaaabaabaabbaababbbbbbaabbbbaaaaabbbaababaaaaaabaabaababaababbaaaaabaaaabababaabababbaaaabaababaabbaaaabbbaabbabaaabbbaabbbbaaaaabbabaaaabbbaababbabbbaabaababbbabaabbaabbbbabbabbbabbbbaabbbbaabbaaaaaabaaaaababaabaaababbaaaabaababbbaaababbbabbaaababbbaaabaaababaaaabbaabbbabbbabbaaabaabababaaababbbbabbabaaaababbbbaabaabaaaabaabababaabbabbaaababbaaaabaababbabaaaaaaabaababbbbbbbababaaabbbbabbbabbabbaaaabbbbbabababbabababbbaaaaabababaaaaababbbbaaabbababababbaabbaaaabaabbaabbabbbabaabababaaaaababbbbbabaabbabbbbabbaabbbabbbaaabbbbabbbbaabababbbbbbbbaabbbababaaabaabbabbbaabbaababbbabbabbabbbbabbaabaaabbaaaabbbbabbaaaaababaabbaaaabaababaabbbbaabababaabbabaaaabaabbbbaaaabbbbbababbabbaaaaaaabbaaaaababbbaaabbbbabababababaabaabababbbababbbabababbbabaabaaabbbabbaabaaaabaababbbabbaaaabbbbabaaababaaababbabaaaaabaabaaaabbabababaabbbbbababbbbbbbbaaaaaabbabaaababaababaababbaaaabbbaabbbbbbaabbbbbaaababaabbbbbaabbbabbaababbbbabbbabaaabbaaaaabaabbabbaaabababaabbbaaababbabbaaabbababbbbbabaaabbbaabbabaabaabbbaaaabaaaaabbaababaabbbaaaaabababaaabbababababaaaaabababababaaabaabbbabbabaabababbabaaaaabbbaabbabbbbabbaaaaababbbababbaaaaabbaaaaaaabaabbaabbabbaaabbaabbaaaabbbbaaababbaaaababbaabbbaaaaabbbbaabbabbababaabbababbaaaaababbbaaabbaabaaaabbbababbbbbbabbabbababaabaabaaababbbbaaaaaaabababbaaaaabbbaabbbbbbbbaaaaababbbababbabbababbabaaaaaaaaaaabbabaaabbaababbaaabbbbbbabaaabababbbbabbabbabbbabaababbababbbabaaaaaaabbbbbabbbbbabbaaaaabababaabbababbbababbbbaaabaababaabaabaabaabaabbbababbbabbbabbbbbbaaababbaaabaababbbaabaabaaabbaabbbbbbaabbaabaabbaaaaaababababbbbabaaababaaaaaaabbaabbababbababaababbbaabbabaabaabaabaababbbababbabbababbbaabaababbabbabbbbaaabbabbbaaabbaaaaabbbbaaabaaaaabaabbbaaababbbaabababbbaaababbbababbababbabbababaabbbbababbabababbbabbbbbbbbbabbaabaabbaaaaaabbaababababaaaababbbbbbabbbbbbaabaaabbaabbabaabbabaaaabbbbbaababbbbbbbbabaaabbbbbbabaaabbabaababbbbbababbababbaabbbbaabbbbabbaababaabaaaaaabbbabaababbaabaaabaaabbbabbbbbbababaabbaaabaaaaababaabbbaababaaaababbaaabababbbaaaabbbbabbbbbababababaabaabbabaaaaabaabbabbabbbbbabbaaaaabaaabbbbbababbaabbbbabababababaababbbababaaaabbabbaaabaaaaaaababbbbabbbbaabbbbabaababaabaaaaaaabaababbbbbbbabaababbabbaaaaaabbababbbbbaabbababaaaabbabaaababaaaabaabbbbaabaabaaaabbabaabaaabaababbabaaaabbababaabaabbababbaaaabbbaabaabbbbbbababaabaaaaaabababaaababaaabbabbaaababaaabbaaabbbabbbabaabababbabababbabababaababbbabbbabaaaaabaaababbababbbbababbabbbaababbbababbbbababbbbbbbbbabababaaabaabbbbaabaaaaababbbabaaabaabbbaaaabababaabbaabaaaaaabbbbaaabaaaaaaababbabbaaaabbabaaaaaabbaaaabbbbaabaaaaaaaaaabaaabbbabbabbbabaaaaabaababbbaaababbbaaaabbbbaabababaaaaaabbabbababaaaaaabaabaaabbbbabababbbbbaabbbbabbaabaaabbabbbbbabaaabaaabbaababbababbaaabaaaabaabbbaaaaaabaabbbaaaaaaabaaaabbabbbbbbabbbaaaabbbabababbbaabbbbbabbbaabbaaababaaaabaabbbbaababbbbbabaaabbbbabbaabbbababaabbbbaabbbbabbaabaaaabaabbbbbaaaabbaaaababbbbbabbaaabbbabbabbababaaabababbbbaaaaabbabbbbabbbaabbabbbaabbbabbababaaaaaaabbbaabbbaaababaabaababbaaaabaaababababaaaabaaababbbaaabbababbaabbabababbababaabaaabbbbabbbbaabbbaaaaaaaaabbabbaabbbaabbabbaaabbbbaabbabaaabbbbaaabbabbbbbbaababbabbbaabaaababbbaaabaaaaabbabaaaabbabbbbabbbbbbabaabaabaababbaaabbbaaabbabbbaaabbbabbaabbabbbbbbbabababbbabbabbbbaabbabaabaaaaababbabaabbbaaaaabbbaaabaabbababaaaaaabaaabaabaabaabbbbbaababababbabbbabbbababbaabbbbabababaaaabbbbbabababaabbbaabaababbababaaabaaabbabaabaababaaababbaaaabbbbbbbabaababbaabaaabbabbabbabbbaaaabbbbbbabbaababaabaaabaaaaaabbbbbaababbbaabaaabbbbbaaaaaaaabaaaaaabaababbaabbaabbbaabaaaaaabbabbbbbbbbabbbbbbaaaaaaaabbaabbbbaaaabbabbbbbaabbbbaabbabbbbbbabababbaababbbbaaabbbabaabbaabbbaabbbaabaabbbbbbbaababbbbbaaaaabaabaaaabbabbabaabbbbbaaaaabbbabbaaabbbaabbaabbbbbbababaaaabababbbbbbbbbbbbaabbbbabbbabbaabaababbbbaaaaabbbbaaaabbbbbabbaabababbbbbbaaabaaaabaaaabbbbbaaabaaaababababbbababbbaabaabbaababbbabababbbabbbababbbabbaaabbbbbaabbabbbbbbababaaabababbababaaabaabbabbbbbbabbaabaaaabbaaabababbbbbbabaababbbbbaabbbaaababbaaaaabbaabaaaaabaaaabbabaaaababbababbabaaaaaaabbaaabbabbabbaaabbbabbaabbbaaaabbaababaabbbabbbbbaaabbabbabaaabbbbaababbbabbabaaaabaaabaabaaababaababbaababbaaabbbabaabbbabaabbaabbbabbabbbaababaaabbaaaababbabbaaaaaaaabbabbbaaaababbabbabbbabbbaababbababababbaabbbbababababaabaaaabaababbbbbabababbbbbababbbaaabbabbaabaaabbaaabbaaabbbaabaaabbabbaabababbabaababbbbbaabbbbbbabbabbbbbaabaaababbaabaaabbababbbbabbaaaaaaaabababaaabbbbbbaaabbbabbaaaababbbababaaaabbaabbbbaaababbaaabababaabbbaabbabbabbababaaabababaababaabbbababaababaaabbaabbbaaababaaaabaaababbbaaaabbbabaabbbbbaaabbbbaabbbbbbaabbababbbbaabbaabbbabbbbbaaabbbabbbabbababababbbaababbbaabbbababbbabaabaaabaabbabbbbaaaabaaabaabaababbbabaaaabaabbabaaaabaaababaabaaababaaaabbbbaaaabbabbaabbbbabbbabaaababaabbabbaaababaabbaabbbbbbbbbbaaabbbbaabaaaaabbbaabaaaabaaabbaaaabbaabbaaabaabaaaaabaabaaaabbbbaaaabaaaabaabaaaabbbaaabaabbbaabaaaaababbbabbbbbababbbababbabbbaabbbbbbbaaabbaabbaabaabbbbbbbbbbabaaaabbbababbbbbabababaabbabbbabbbbbbaabaabbaaabaaaaaaaaaaaaaaaabaababaaabababbababbabbbbabbbaabaaaaabaaabbabaaabaabbbbbbbaabbbbbabbabaababaaaaabaaabaaaaabbabbababbbaaababbbaaaabaaaaaabbaababbaababbbabbbabbababbaaabbaaabaabbbaaaabaabaababababbbbaabbbbabbabaababbabbaabbaabaabbbaaabbbbaabababbbbaabaaababbaabbbaabababbaabbaabbaabbaabaaabbbbbabbbbaaabaaaaaaabaaabaaaaaabababbaaabaabbabaabababbabbbabbbbbaaaabaabbabbbaaabbbabaaababaabbaabaaaabbaaabbaabbabbbbbaabbbbbbabbaaaaabbaababbaababaabbbbbbabbaabaaaaabbabbbbbbabababbabaaababbbbbbbbabbabababaaabbaaaaaaaabbbabaabbaababbbbbaabbaaabbaaaaaabbbabbbbbbbbbbbbaaabbaabbbabaaababaaabbabbbababbbbbabbbbbbaabababbbaabbbbaabaaaaaababbaabbaaaabbaaabbabababaaaabbbbbaaabbbabbaababaaaababbbbbabbabbaaabaabaabbababaabbbababaabaaabbabaabaaabaaabbababaabaaaabaaaaaababbababbbbbbaaabbbbababababbbaaabababbbbabbbaaabbaaabbbabbbabbbbbabbaaabbbbabbbbbaaaabbbbbabaaabaabaaabababbbbbaabaaaababbbaabbaaabaaabbbbababbbbababababbbaabaaabbbbaababaaaababbbbbbaaaabbaabbaaabaaaababaabaabaaabbbbbbbabaabbabbaaaaaaaaaababbbbbabbbababbaababaabaababbababaabaaabbbbababaaabaabbabbbaabaaaabbbababaaaababbbabaaaaabbaaaabbaabbabbababbbaabbbabbaabbbabababababaabaaababbabaaabbababbaaaaaaaabaaaaabbaaaabbabbbaaabaaaaabbaaaaababaaabbaaaaabbabaaabaabbbbbbababbbaabbbbbaaabaabbbaaabaabbbbbbabbaabbbabbabbbaabbbbabbbabbbaabaaaababbaaaabbaababaaabaaabbaaabaabbbbaaaaaaabbaaabbaabbababaabbabaaabaabbbbbbaaaaaaababaabbaababaaaaaaaabababaaabababbbbbabbbababbabaabbabaababaaaabbbbaabbabaaabbbaabbababbbaaabaaaaabbaaabaaabaaabaababbabaabbbabbaabaabababbaabababbaababaabbaabababbabbaaaaaaaaabaaaabaabbaabbabbaabaababbaabbabbbbaabaabbbabababaaabbbabaabaababaaabaabaaaabbbabbbabbaaabaabaabbbbbbabbbaaaabbabaabbbaaaaabbbbabbababbbaabaaaabbabbbaaabbbbabbbaaaabbabbbaaababaabaabbbbabbabbbbabbabbaaaaaabaabaaaabababaaabbbabaaabbbbbababbbabbabaabaabbabbbbbaababaabbaaabaabababbbbabbbbaabbaabaabbabbaabababaaaaaabaababbaabaaabababaabaabaaaabbbbabbabaaaaaabaaaaababaaaabbaababbbbbbabbaabbbaaaaabbbbbbbabbbabbaaabaaaabbbaaabaaaaaaaaaabbaaabbbabaabbabbbabbbaabaaaaababbbbaabaaaaaaababaabaabbaaabaabbbaaabbbbbaabbabaabbbababbaabaaaaababababbabbababbbbabaaabababbaababababaabbaaaabbbbbbabaabaabababaababbabbabbbabbabbababbbaaabaabbbbabbabaaaabbaabaababbbababaabbbbbaaaabbababaabaabbbabbabaaaaaabbaaababaaabaaaabbabaababaabbbbbbbbbaaaabbbbabbbbabbaaabbbabaaabaaabbbbbbabbaabaaabaababaababbbabbbabbbbabbbbbbbbbbaaabbaaabababbababbbbbabbbabaababaabbaaaaaaabaabbaaabbaaabbababbbbaaaabbbaaabbabbbbbaaabaaaabbabaabbbbaaaabbbabbbbaaabbabbbbabbababbbabbababbbabaabbaabaaaaaababaaaaabbaababababbaaababbbbbbabbbaabbabaabbabbabbbaabababbbaabaabbbabbababaaaabaabababbabbbbaaabbbbabbbbabbaaabaaaababbbbbbaabbbbaabaabaababbbaaaababbababaabbbaaaaabbbabbbbaabbbbbbaaaaaababbababbaababbbababbbaaaabbbaababaabaaaaabaabbaabaaabababbaabbaababbababaabaabbbbbaabaaaaabbabbaaabbababbaababaabaaabaaaaaaabaabaaababbbbbabbbaabbbabbaabbbbabbaabbbababbabababaaabababbbbbabbbbaabbbabbaabbaabbaababbabbaaabbbaabaaaabbbbbbbbaabaabbbaaaabbaaaabaabbbbaaabbaabbabaaaabaaabbaabbbaababaababbbaabbaabbaabaaaababbaaabaababbbbbaaraaaaabababbaaabbaaabbabbaabbaabbaaaaaabaabbbbbbbbbbbaaabaaabbbabbbaaabaabaabbbaabababbaaaaababbbaabbbbabbaabbabaabbbbbaaaaaabbbbabbbbbaababaaaaaabaabbbbbabbbbbbbabbbbbbbbaabaaaabaabbaababaaaabbbbabababbbbabbabbbbababaaaababaabbbbabbababababaaabaaaaabbbbbbaaabaabbbabbabbbbabbaabbbbabbaaababaabbbabbbbbaabababaaabbaaababbbbababbbbbbbabbabbabbbabbbabbbabababbabbababbabaabbababaaabbbaaabbaaaaababaaaabbbbbbbaaabaaaababaabaabbaaabaaaaaaaaaaabbbbaaaaaabababbbbbbababbaabaaaaaaabbaabbbbaabbbbbabbabbbabaababaaabbbabbbaaaaabaabbabbabbabbaaababbbaabababbababaaaaabbbabbbbaababbaabaabbbaaabaabababbabaaaaabbaababaabbaaabaaabbbaaaaabaaaaaababbaababbaaaabbbbaaabaabaaaaabaaabbabbbbabaaaaaaaabbbabbababbbaababbaaabaaaabbbbbababaaabbbaaabaaaababbbaabbabaaaaaabababbaaaaaaabaababbbaaaaaaaaaababbbaaabbbaabbaabababbaababbbababbbbabbbabaaaaabbaababbabbbbbabbaababaaaaaaabababaabaaaaaaaabbbbbbbabaabbbaabaabbbbbaaaababbbaabbbbbabbaaaaaaaabaababbbababbbbabbaaaabaaaababaababbbaaabbabaaabababbabbbbaaabbaabaaabbaaaaaaabbabababbaaabbbbbbaaabbaaaabbbaabaaabbabaabbbaaaaaaabbabbaabaabbaabbbbabbaabbbbabbababbbabaaabaabbbbbbaabbbaabbaaaaaabbaaabbbaababbbabbbbabbbbbababaabbabaabbbbaabababbbaababbbbbabaaaabbbbbabbbbbaabaaabbabbbbbaababbabbabbbmabaabaabaabaabbaabbaabbabbaabaaababaabbbaaabbaaabaaabbabbbababbbababaabbbabaaaabaaabbbabaaaabaabaaaaaabbaaabbbaabbbaaaababbbabbbabaabbbaaabbaabbaabbabbbbabbaaaaaabbaaaabaababbaaabbaabbaabaabababbbbbbaaababbaaabababbaaaabbbabbaababbbabbaaaaabaaabbbaaaabbbbbaabaaaaabbbbabbbbbbbabababbbabbaabbaabbbbaaaaaabbbbaaaabbbabbaaaaababbabbbabaaababbabbababbabbabbabbbbbbaababbbabaabaabbbabababbbababbabbbaaabaaababbabaaabbbaaabbaababbabbbbbbabbabbaabbaabbbbbbababbababaabaaabaabbaababbbabaaabbabbbbaaabaaaaababaaaaabbbabbbaaabababaaaaabbbbabbbabbaabbabbbbabbabbbabaaaababbaaabbbaaabbbaabaaaaaaabbbaabaabbaababbbbbabbbabbaaaabaaaaaabbaabbbaaabaababbaaababbababbbbbbababbabbabbbaaabaabaababaaaabaaababaaabbbbaabaaaabbbbaabbbabbabababaabbabaabbabaaabaaaaaabbbaaaabbabbabaabbbbbbbababbbbabbaaaabbabbabbbabbbbaababaaabbbbaaaaaabaaaabbababaaaabbabbbbbbbbbbabaaabaaaababaaabaaabaaaababbabbbabbbbaaabbbbbabbbbabaabbaaabbabbbabababbaabababbbababbbaabbabbaaaaabbababaabbababbabbbbaaaaabbaabbbbabaaababbbaaaabbbbaaabbaabaaabbbbbabbababbbbaabbaaabbbbaaabbaaabaaaabbbabaaaabbabbbbbbbaabaababaaaabbaababbbabaaaabbabaaabbbaaabbbabaabbaaaabbabbbababaababaaabaaaaaaababbabaaaababbbabaababbbbbaababaaaaaaaaaaaaabaaabbbabbbabaabbabbbabaababaaaabbbababbabababbbababababbababbabbaabaaabbabaabaaaaabbbabaaaabababbbbabaaaaabbaababbaababababbbbabbabaabbaababbaaababbbaabbbbaababaaabbababaaaabababbabaabbaabbabbbbabbabbaababaabbaabbaabbabbabbbbabbabaaabbbaabbaabbbbabbabaaababbabaaaaabbabbabbababbabbabaabbbbbbaabababaaaaabaababbbaabbbaaaababbababaaabbbaabaabbbbabbbbababbaabaababbababbbbbaabbbaaabbbabbabbbbaababbaabbabbaaaabbbbbaaaabbaaabbbabaabbaabbabbbbbbbababaaabbbaaaabbbaababbaabbabaaabbbbaaaaabbbbbbabaaaabbaabaaaabbbabbbaaaaaababbaaaabaaaaababbbbabaabbbabaaabbbbaababaabababbbbbabbaaaaababaabbbbaaabbabbabaabbbabababaaabaaaaabbbbbabbbbaabaabbbbabbabbabaabaabbbbabbabbbbaaabaaabbabbbabbabbaabbbababaababaaabbaaaabaabaaabbabbaaabaabbaabbbaaaaababaaaabaababbabaababaaaaaabbaabbbaabbbbbbbbaaabbbbbabbbbababaababbbababaababbababbbabbbbbaaaaabbbbbaaaaaaabaababaabaaabaaabbabbbbabbaababababbabbabaabbbbbbbaabbbbbbaaabbaabaabbabbbaaabaaabaaabaababbbababbabbaaabbabaabbbbbbaabbbabaabbbbbbababbabbaabaabaabababaabbbbbbbabbaaabbabbbababbbaaaaabbbaababaaaabbbbaaaaaaaabbabaabbabbbbbbbaaabaaabbaabbbbbaabaabbabbaababbabbabbbbbaababaabaababbbbbababbbaabbbaabaababbaaaabbbbbbaaaaabbbbaabaabbbbabbbbabaabbbbaaababaaabaaabbbbbbbbababbaaaababbbaaaaabbaaabbbababababbabbbbaaabbbabaaaaaabbbbaabaaaaabaaabaaaabbaaaaabaabaabbbbbabaaababaaaabaabbbbababbbaababbaabaabbbbbbaaaaaaaaabbabaaabaaababaaabbabbaabababababaababaaabbbbaaaabbbbbabaabaabababbbabaaababbabbbbabababbbbabbaaabbbabaaabbababbababbbabaabbabbbaaabbaabaaaaaabaabbbbbaaaaababaaaaabbbaaaabbbaabbbbbbaabaaaaabababbbbaabbabababbbbaaaabbbabbbbbbaabaaaabbbaabbbbababaaaaaababbbabbbbbabababababababbaaaaaabaabaabaabbbbbaababbaaabbaababaaabbaaabbababbbabbbbabbabaaaaaaaaaabbbbabaabbbbbbbaaabaababaabaabababaababbbbbabaaababaaaabbbaaabaabbabaabbabbbbabbababbbabaabbaaabbbbabbaababbbbbbbbbbbbaaaaaaaabbbaabbbaaabababaabbbbbbaabaabaabbabbababbaababbbbbabbaababbaabbbabbbbabbbbabbabbaabbaaaaaaaaaaababbababaaababbbbabbbbaabaaaabaabbaabbbabbbaabaabbaabbbabaabababbbabaabaababbababbbbaabababbbababbbaaaabbaabbabbaabbbabbaabaabbababaabaaabbabbbbbaaaabababbbbabababbabbababbaababbabbabaabbabababaababbaaaaababbaaabaabbbaaababbbbaabbabaabaaababbbabaabbabbbababbbbbabbbabaabbbaaabaaabbbabbaabbaabaabbbabbbbaaabababababbbaaaaaaababaabbabaaaaababbaabbbbaaababbbbbaaaababababbbababbbaaaababbabbabbbaaababaababbbaaaabaabbbbbababaabaaaaababaaaabbbbabaaaaababbbbbbaabbaaabbbbbaaabaaababbbbbbbbbaababbbababbaaabaababbaaaaabaaaabbaababbbbabbbbbbbbaabaaaabbabaaabbbabababbbbabaabbabbbbabaaabbbbbbbbaababaaaaabbabbabbbbbabbbbbbaaaabaababbbaabbbbababaabbbbbaaaaaabababbabaabaababbaaabbaaaabbabbaabbbaabbabbaaabaaaaababbbbaaaaaababbaaaabbabbbbaabbabbbababaabaaabbbabbbaabaaaaabbabaaababbaaababbbababbbbbbbbbbaaabbbbbbabbababaaababbbbbabaabbbabbaaaabbaabaaaabaabbbbbabbbabbaaaaaabbbbbababaabbbabababbbbbaaaababbbabbaaaabaabaaabaababbbbbbbaabbaaababbabbbaaaaababaabbaababaaabbbaaabaaaabbbbbabaabbbbaababaaabbbabbaaaabbbbaaaabbbabbaaaaaabbbbaabbababababaababbbbbaabbbaaabbbbbaababbaabbbabaaabbbabbabbaabbaabbbbaaaaaabbabaabbbbabaaaaababbabbbabaaabaabbbbababbbbbbbaaabaababaaaabbaabaabbaaabaabbbaaaaaababbbabbbaaaaaabbaaabbbaabaabbabaabababbbaabbbabbaababbabbbaabbbaaababbbaababbabbaabaabaaaaabbbbaaaabbbbaaaababbaaaabbabaababbbbaabaaaaaaaaaabbbbabbaabbaabbaaabaabbbbaabaabaabbbababbbbbbabbaaabababaabbbaababaaabbbaaabbabababbbabbbbaabbabbabbbbabbabbabaabbbbabbabbbbbbbbabbaabbaabbbaaaabbbbabbabaababbbabaaaaaabbbaaaabbbaababbbbaaaaaaaababababaaababaaaabbaababbaaababbbbbbbaabbabaaabbbabaabaaababbaaabbbbabbbbaabbbbbbbabbaaabaabbbaabaabbbbbaababaabbbaaaabbbbbbbbabbaabaabaaaaaababaaaabbbaaababaabbaabbaaaaaabbbabbabaaababbababaaaaababbaaababbabaaaababbbbbbbbbbaaabaaaaababbbabababbaaabbbabaaabaaabbaaaababaabbbbaabbabbbabbbaabaabbaaababaaabbaaaababaabaabaaaaabaababbbabbbaabaabaaababaaaabbabaaabaabaaaaababaaaabbababaaaaababbabbbbabaababaaabbaaabaaaaaabbbaababbbababbabbbabababaabbabbbaaaaabbaababbabaaabaaabbaabaabbbbbabbabaaaaabbbbababaaabbaaaabaaababbaabbbbbbaababbbabbbaabaaabaabbbbbababaaabaabaaabbbbaaaababbbaababbbabaabbbbabbbbaababaaabaabbaaaaaaaabaabaaabaaaaaabaaaaaaababaabababbabaababbbaaaaaabbaabbabbbabaaaabababaabaabaaabaaabbbabbababbbbbbbaabbabbbabaabbbbaaabbaabbbaabbabbabbaaabaababbbbbaabaabaaabaaaaaaaabaaababbbabbbbbbaaabbbbaabbbabbaaaaababbabbbbabbaaabaabaabbbbbbaabababbbbabbabbbbabaababbaaabbbabaaaaaabbbaaabaaabaabababbbbbabbaabaabbaaaaaabaaaaababbaaaabaabbbabaabbaaabaababbaaaabaabbababbaaabbaaaabbbbaaaabaababbbbbbaabbabbbaaaaaaabbabaaaabbaaaaabbbabaabbabaaaaaabaaabababbaababbabbaaabaababbaaaabaabbaabaaaaaaabbbbababaaaaaaaababaaaabaaabababaaaaabbbabbaababaabaababaaaabaaaaabaaaabbaabbababbbabaaaabbbaabaabaabbbbbbaaababbbbabbbaabaabaabababbbbaaaaabaaabababbababbaabbbaabbbabbabaabbbababbbbabbbababbabaabbbbbbbaabaaabbaaababbbabbabaaabbbbaababbababaabbabbababaabbabbaaabbaaabbbabbbbbbbbabbbaaabaaaaaaabbbaaaaaaaabaabbbaababaaababaabaabaabbaaaaaaaaababbbbbabaabbbabbaaabaaaababbbbbabaabaaaabaaabbbbaabbaaabaaababababbaababababaaabaaabaaabababbbbabbbbabbbabaabaaaaaaaaaabbababaaababbabbaaaababaaabaaabaabaaabbbabbbbabbbaaababbababaabbbaaabbaaabaabbbabaaaaaabbaabbbaabbabbbbabbabaaabbabaabbbabbabbaaabbaaabbbbaaaabaababbabbababababbabbbbbbaaabbaaababbaabaabbababaabaaaaaababbabbbbbaabaabaabbababaaabbaabbabaababbbbabaababaaabbbaaabbababbbabaaaaaaababbabbabaaababaabbababaabbbaabbbaabbbabaaabbbbbbaababaaaaabaabbbababbabaabaaabbabbbbbbabbbbababbabbaabbaababbaaabbbbbababababaaababbaaaabbaaaaabbbabbbbabbaababaabbbbbabababaabbbbbbaabaaabbabaabbbbababbabaabaaabaaaaaabbaaaabbaaabbaaaabbaaaabaabbbaababaaaabababbabbaaababbbabaabbbbbaaabbaabbaabbabaaaabbbabbbbabbbaaabbabaabbbabaababbbbbaabbaaaababbabbabaabbaaaabaaaabbbbaababbbbabbabababbabbaaabbaaaaaabbbaaababbabbababaabbbbbbbabaaaabaabbabababbababbbbbabbabbbabaabbbbbbaaaabbbbbabbbaaaabaabbababbaabaabbbabbbbbbabbaaabbbbbababababaabaaaaabbbababbbbabbbaababbaaabaaaabbaaaaabbabbaaababbaaabbaabbbabaaabbaaababaabbabbbbbaaaabaaabbabbaaaaaaaabbbbaaaababbaabbbababbaaaabaabbaababaabaaaaaaabaabbbaabaabbaaabaabbbabbbaababaaabaabbbaabbaabbbbbbabbbbabbbbabbbbbbbbbbaaabaabbaabbaaabbabaababaaaabbaabaaaaabbaaaababbaaaaaabbbbaababababbbbbaabbbababbaaaaabbaabaabbaababaabaababaaabbabbbbabbaabbaababbbbbabbbbabbaaabbababbabbababbbaaaaaaaaaaabbbbaababbbbbaababbbaabababaababbbbababbabababbaabbbabaaaaabbbbaababbbbbbbaabaabbaabbbabaababbabbbabbbbabaababbbaaabaabbbaabbabbabbbabbabaabbbbaabaaabbbbaabababbbbbaaaaabbaababbaabaabbbaaabbbabbabbbbbbbbbabbaaaabaababbababaaaabbbbabaaaaababbabaaabbaababaaaabaaaabbbbbaabbabaaaaabbbbabbbbaaaaaaaababbbabaaabababbbbbbbbbbaabbbbbababababbbbbbaaaabbaaaaaaabaabbbbababbabbbaaaaabbbaaabbabababaabaabbbbaaaaabaaaabbbabbbbbbabaaabbbaabbaaaaabbbabbaaabbabbabbaabbbbbaababbabbbabababbbabaaabaabbbbbabbabaabaababaaaaaabaaaaabbbbbabbababbbababbbbbbbaabbaababbbaaabbbabbaabaabbbbbbbbbbaaaaababaaaaaabbbabbabbbbbbbababbabbbaabaaabbbbbbbabbbababbaabbaabbbbaaabaabaabaaaaaaabbabaabbabbaabaaabbaaaaaaabbaabbbbaaabbbbbbbbbabbabbbaabbbabaababbbabababbbababbbbabbababbbbbabbbbbabaaabbbaaabbbaaabaababbabbababbaaabbaabaabbabbbbaaaaabaaabbbabaabbababbaaaaaaaabababaabbaaababaabbbbababaababaababbabaaaabbaabbababbbaabbbbbbbabbaaaaabaaaaaaaaabaaaaaaabaaabbabaaaabbabaaabaaaaabbbaaaaaabbaababbbbbbbaabbbaabbbaababbbbbabaaaaabbbabbbbaabaaabbababbababababbbaaabbbabbbbaababbbbabaaaababababaabababababaabbbbbaabbabbbbbbbaababbaabbaaaabbaaaabbbaaabaaababaaaabbbaaabaaababbabaaabaaaabbabaababbaaabaabbabbabbbbbabbaaabaabbaaaaaabaaaaabaabababaabaabbaabaaababaaabaabbbaaababbababbabbabababaaabbabaabaababaabaaaabbababaababaabbaabababababbbbabbaaaabbabababbaabbbbabbaaaaababbbbbbbababbbbbbbaaaabababbababbabbababaaaaabababbabbbabaababbbaaabababbababaaabaaaabaaabbabababbbabaaaabbaabaaaaabbbaaaaaabaabbbaaaababaabbabbabaabbbbababbbbabaabaabbaaaaaaaabbaababaabbaaabbaababaabbabaaabbbaabbabbbbbaababbaabbabaaababaaaaabaabababbbaaabbbbbabbbbabbbabbaabaabaaababaabbabbbaabbbaaaaabaababbaaaabbabbbababaabaaaaaaabaababbaababbbaaabababaabaabaababaaaabaabababbbaabbaaabbabababbaaaaabbaaaababbbbbaaaabbababaabbabbaabaabbabbabbbbaabbbbbaaaaaaababababbbbabbbbaaababbabbbbabbbabbaabaabbabbbbbbbbbbabbbbbaababbabaaaaaababbbababababaaabbbabaaabaababbaabbaabababbaaabbbababaaabbbaaaabaabbaabbbbaaababbbabbabbaaaaaabbabbbaabaaababaaabbbbaaabbbbbbbbbaaabaaabbbaaaaabbababbaaabbabbbababbabaaabbaaaababababbaabaabbbabaaabaaaaabbabbabbaababbbabbaaababbabbbaaabbaaaaabbabbbababbbabaaaabaabbbababbaaaabaaababbbbbbbbbaaaaaabbabaaaabaaabaaaaabababababbbbababbaabbabababbbbabaabbababbaaabbbbababbaaaabaaaaabababababbbaaaabbbaabaabbbabbaaabbbbbabaabbababababbabaaabbbbbabbabababbbbbaaabbbabaabbababbaaabaabbaabaabbbaaaaabbbbbabbbaaabbbbaaaababaaaabbbabbbbaaabaaaaabbaabbbaaababaaaaababaaaaaababbbbbaaabbbbabbaabababbababaaabbbabaaaabbaaabbaabbbaaaaaaaababaababbababbaaabbbbbabbaaababababbbaabbbaaabbbbbbbabaabaabababbabaabaabaaabaaabbbbbbaabbbaaabbabbaaaaaababaaababbabbbabaabbbbabababbabaaabbaabbabbbababaabababbaaaabbbbbabbbababbbbaaaaabbbbbbaaaaaabaabbbbbaaabbbbbbabbbbaabbbbabbbbaabbaabbaabababbbbabaaaaaaaaaaabbbaaababaaaaaabbaaaaaabbbbbbababaaabaabababaababaabaababbbaaabaabbaaaabaabbbbbbbbaaaababbbabbabbaababbbbbabaabaaabbabbbbbbaaaaaaaabababaababbaabbabbbaaaaabbbabbaabbabbbbbabbbbabaaabaabbbbabaaaabbbababbbbaaaaaababbbabaababbabbaabbbaaabbbbabbbbbbbbabbaababaaaababbbabbbbababbbbabaababababbbaabbbbababababbabababaababbbabbaabbbbaaaaaaaabbaabbaaaabbaabbaaabaabbbaabbbbaabbabaabbbbaaaabaabaabbaabbbabaabbbbbbaabbaaababbaabababaababaabbbbbbabbbbbbaaabbbaaabbbbbbabbbbbbaabbabbbbabaabbbababbbbbbababbbabbabaaabbbaabbbabbaabbbabbabbaababbbbbaaabbaababaababbbbaaabbaaabaaaaabbaaabaabaaaaababaaaabaaaabbababbaaaabbbbbabbaaabbaabbbbbbbbaabaaaabababbaaabbbaaabbbbbbbabbbaabbbbbaaabbbbaabbaaababbabbbbabaabbbbabbbabbabaababaabbaaabbaabbababbabaababbbbabbbababbaaaabbabbbaaaababaababbaabbbabbbababbbaabbbaabaaabababbbaaabbbbbabaaaabaabbabababbbbbbbaaaaaaaabbaabaabbabbbabbbbbaaaaabbbbbbaaaaaababaaabbaabaabawbbbabbbabaaaabbaabbabbbbbbabbbaabababaabaabbaababbbbaaabaaaabbbbbaaabaaaabbaaaabbabaababbaabaaababbbbbaababbbababbaaabbabaaaaabaaaabbbbababbbbaabbbbbabbbbbbaabbaabaabbbabbbbbaabbabaaaabbaabbbbababbbbabbbabbbbabbaaaabaaabbbababbbbbbabaaabaaaabaabbbababbbaabbbbabbbaaaaabbbbbabababbaabbbbbaabbabababaabbabbbbabaabbbbbbbabababbbaabbaabbaabababbbbaabbbbbbaabababaaabbbaaaaaabbabbababbaaabbbabbbabbbababbbaaaabbbbabaaabbbbabbaabbbbaababbbbbbabaabbbaaaabbbbbaabbbbaaabbaaaabbbbababaabbaabbbabbaabbbbbbabbabbbbaaaabbaabbbaabbaaaabbbbbbbbaabbabbabbababbbbaaabbbaaabbabbbabbbbbbbbbbaababbabbabaaabbaaaababbaaaabaaaaabaaabababbbbaabbaababbabbabaaababbababbbaaabbabaaabaaaaaaaaaababaabaababaaaaaabbaaaabbabbaaaaabaaabaabbbaababaabbabbbbbbbbabbaabbabbbabbaababaabbabbbabaabbaaaabbbabbaabaaaabbbabbbbbbbbbaaaabaabbabaaabbaababbbaababababbbaaabbabbbbbbaabaababbabbaababbabbababbabaabbaaabbbaabbaaaaaababaaaabbbababaaabababbaaabaabaabbaabaaababbababbbabbaaabbbbaaaaabbabaabaaabaababbbaaaabbbbababbbaaabbaaabababbabbaaaaaabbbababbbaababababaabbababaaabababaaabaaabbbabbabbbbabbbaabaaaabbbbababbababaabbbbbbbaaaabbbbbabbbbabbbababaaaabbaabaaabaabaaabaaabbbaaabbbabaaaabbaaaaabbabababababbaabbbbaabaaabbbaaaabbbbbaabbbaabaabbaaaaaaabbbbbabbaabbaabbbaabaaabbaabaaababaaababbabbbaaaabaaabaababaabaaabaaaaabbabbbababbbbbbaabaaabaaaabbbbbaaaabbaaabaaabbbbbbbbbbbbbbbaababbbabbaaabbabaabaabbbaaabbbababaaabbbbaaabaabbbaabbbababbababaaaababbabbabbbbbbaaabbaaabaabbbabaabbbaababaaabbaabbbabbbaabbabaabbbabaaaabaaaaaaabbbabababaaaabbaaaabababbbbbababbaaaabaabaababbbaaabbababbaaaababaaaababbabbabbbabbababbaababbaabababaabbaaaabbabbaababaaabaaabbababbabaabbaababbbaaaaaaabbabbaaaaaaabbaaaaabbaabbaababbbbaaabaabaaabaaaabbaababbabaaaababbabbbaabababbaabbbaabaaaaababaaababbbababbbbaababbbbaaabaabbaaaaaabbbaaaaaaabbbbaaabaaabaababbabbbabbbabaaaabbbbbbbabbaaabaaaabbaabaabbbbbbabbabbaabbaababbaabbbabbaaaabaababaabbabaaababaabbaababaabaababaaabbababbbabbbaaaaaaabaabbababbbaaabaabbbaabaababbbabbbbbbabaababaaababaabbaabaaaabbbbbbbababbababbbbbabbaabaabaabaaaababbababaaababaabbaabbaaaabaaaabbbbaaabbbabaababaabbabbaabbbbabbabbaababababbbbabbaabaabbaabbbbabbaaaaabbaaababbaaababbbababbbbaabbbabbbaabaaabbbabbabbaabbaabbbaaaababbbaabbbababaaabaaaaababaaaabbbababaabbbbbaaabbbbbaabaabaaaaabaabaaaabbbbaabbabbbbbbabbabaababaaabbabbbbaabbbbbaaaabbaabbaaabababbbaaaabaabbbbaababbbaaaaabbababbbbaabaaababbbabbbaaaaabaabaaaababbaabaaababbbbbabaabbbbababaabbaabababaabaaaaaabaaabbbaaaaaabbbaaabbbbabbbabbabbabbabbaaabbaaaaabbababbaabbaaaaaaababbaababbbaaabaaabaaaaaabbaaabbaaabaaabbaaaaababbaabaabbaabababaaabbbabbabbabbabbababaabbabbbaababaabaababbbaababbbabbbbbaaabbaaaabbaabbbaababaaabbaaaaaaabbbabaaabbaaaaabbbbbababbaaabaaaababaababaaabbbbaabaabbbbbbaaaabaabbbbabababbbaabbbabaaaaabbbaaababbbaaaabaaaabaaaabbaaabababbbbbaabbabbbbabbaabbbaaababbaababaabaabbbabaabbabbbabbbaabaaabbabbbbbabbabaaaaababbbbaabbabbbbbabbabbabababababaaaaabbbaabaabbbbbbbabaaaaaababaabaaaabaabbbabaaaababbabababbbbabbababaaaaababbbbababaababaaabbabbbbabbabbbbbababaabbbaabaabbaabbabbbbbabaabaabaaaaaaaaaaabbbbbbabbbabaaababaaaabbbbaababababbabbaaaabababaaabaabaaabaabbaabaabaabbbbaaababababbabbaaaaaaaabaaabbabbaaabaababaaaaaaabbaababaabbbbbbbbbabaabababbbbbaabbabaaabbbbbababaabbaaabbbbbbaaabbbaabbbbbababbbaaabbaaaabbaabaaaaaaaaaaabbbbaaaaaabbababbbabababaababbabbbabbaaabbabbaabbabbaaabbabaabbbbabaabaabbabaaaaaabbaababbabaabbaabaaaaaabbaaabbbbbbabbaabbaabababaaabaabbabbabbaabaaaabbbbababaababbbababbbaaababaaaabbaaababbaaabbaabbabaaabbbabaaabaabbbbabbababbbbbbbabbbaaaaaaabbbaabaabbaaabbbbababaabaaabbabbabaaaaabbaaaaabbbbbabaabaabbaabbbbbabaaababbbbaabbbbbbbbababbabbbbbbbabbabaababbabaaaabbaaabbbbbababbbbaabbabababbabbabbbabbbaaababbbbbaaabbabbbbaaabbaabaaaabaaaaabbbbbaabbbababaabaaaaabaaabbbabaaaaababbaabbaaabbbabaaaababbbabaaabababbaabbbbabbbbbabaaaaabbbaaabababbabababaaaabbbabbaabaabbabbbabaaabbbbababbbbbaabbaaabbbabbaaababbbbabbbabbaaaaabbbaababbbbbbbbbbbbbbaabbbbaabbabababaaabbbbbbbbaaaaaabbbbabbbbabbabbbbbbbbbabaabbbbbaaaabbaaaaaaaaabbababaabaaabbbbaabbbbaaabbbaababbabababaaabbbbabbaaabbaabbbaaaaaabaabaaabaaabbaabbbabaaabbabbbbaaaaabababababbbbabaaaaaabbbabaabaaaabbbbbaabaababbbbaababbbbaaababbaababbbaaaaaaabbaaabaaabaaababbbabbbaaabbbbaabbbababbbbabbaaaaaaabbabbaabbaababbaaaababaaabbaabaaaabbbbbababababbbbaaaabbbaabbbbbbaababaaaaaaabbabbaaaaabaabbbbaababbaaaaabaaabaabbabbbaabaaaaaaabbabaabaaaaabbabbbaaabbbababbbbbabbabaabaabaabbaaabbbbbbabbaabbabaababbbbaaababaabbbabbbaaabbbbabbaabbbbaabbabababbabbbbaaabababbbababbabbbabbbababaaabbbabbaabbbaaabbaabbbabaabbbabaabbababbabbaabaabaabaabbbaaaabaabbbaabbbbaabaaababbaaabbaaabbabbaaabaababababbbabaaaabaaabaaabbbaaabbbababbbbbababaababbaaaaabbaaabbaaababbbbbabbbbabbabaaaaaabababaabaaaaabbbabaaaaababbbbaaaabbbaabaabbaabbbbbaabababbaaababbabaaaababbbabbabaaabbbaabbbaabaaaaabaabbaababaabbaaabaaaabbbaabbbbaabaaabbabaababaaabbaabbaaaabbbbbabaaabbbbaabbbbaabbbbaaabaaaabababbabbabbaaababaaababbabbabbaaababbbbabbabbabbaababaaababbbbbbbabbabababbaabaaabbbbbbaabababbabababbbaaabaaaaaabaaabbbaaababaabbaaabbaaaaaabaaaabaaaababbbbabaabaaabaabaaabababaaabbbbabbbbaabbaabbbbababbbabbaabbababbaabbbaaabaaaabaaabbaabaabababbaaaabbaabbabbbaaaaaabaababbabbaabaaaaaababbbbbaababbbaaabbaabaabbbabbbbbbbababbbabaaaabbbbabababbabbaabbaaababbbbaaababaaabbbbabbabbbbbaaababbaababbabbaabbbbabbbaaabbbbbabaaaabaabbbaaababbbaabbabaabbabbbaababbbbbbbbaabaaaabaaabbabbbbaabbabbababababaabbababaabaaaaababaabbbaabbbbaaaabbababaaabbabaabbabbbbbabbaaaaabaaabbabbbbbbbbbbbbababbbaabaaaaabaabbbaabbaababaabbabaabbabaabaaabbaabababaababbabbabbbabaabbabbabbaabaaabbaaabaabbbbabaaabababbbaaaaabbaaabbaabbabbbbababbbabbbabbabbbaaaabbbababbaababbbbbbbabbbbaababaaaabbabaababaaaabbbaaabbbabbbaaaaabbabaaaababbbbaaaaaaaaababababaaabaabbaaaaabbaabbaaaabbbbaabbaabaabbabbbbaaaaabbaabbbbaabababbaababbaaaabbbbaaaabbbbaabbbbabbbbbaababaaabbbaaabbbbabaaaabbabbabbbabaabbaaabaababbbababbbbaaabbbaabaabbaababaabbaaabbababaabbaabbbbbabbaabbbabaaaaaaaabbababbaabbbaaaabaaabbbabbabababababbbaabbaabbbabaababbaaaabbbbaabbabaababababaabbbbbabbbbababbbbbbabaabaabbaaaabaabbaaaaaabaabbbaaabaabaaabaaabbaaabbbabaaaaabbabaababbbababbbbabaaabbbaabbbbbbaabaaaaabbabbbbaaabbabaabbababbbbaabbbbaabbbbbbbaabbbabababbaaabaababbbaaaababbaaaabbbbabaabaabbaaababbbabaaaabbaababbabbabbaaaaaaaabaaababaaabaaaaaabaabaabbbbabbabaabaabaabaabbbbaaabbaabbaaaababbababaabbaaabaabbaabaaababbabbbbabababbbbaabaaaabbaabaababbabaabbaabbabbbbbabbbaaabbabbbabbaaabbaaabbbaaababaaaaaabbabaabbababbaaababaabbbaabababbababbabaaabbbaababbababaaababbabbabaabaaabaabbaaabaaabbbbbaaaaaabbaaabaabbaabbbaaabababbabaaaabbbabbaaaabaaaabbbabbbbbaabbaabbabbbaaabbabbbababaaababaaabbbabbaababababaabbbbaabbbaaaaaabbabbaaaabbabbbbaabbbabbbabaaaabaaabbabbbaababbbababababaabbbaaabbbbbabaabababaabbbbbabbbaabbaaaaaabbbbbbbaababaaaabababaaabababaaabaaaaaaaaaabaabbbaaaabbbaaabbabaaaabbbabaabbbabaaabbaaabaabaabaaababbabbbabbaabbbbbbaabbabbbbaaaaabbbabaabbbababaaaaaaabbabbabaaaabbaaaaabbabaabaabbaaaaaababbbabaaaaabbaabbbbbabbabaabbbbaabbaaabbbbbbababbaabbbabbaaabaaaababbabaabababaabaaabbabaaabaaabbaabaaaaaaabbbaabbaaababbaabaababbbaabaababbbbabbbbbbbabaabbabbbababbaabaaaabaabbaaabbabbabbbaaaabababbbabaabbabbbbaaabbaabbaabbbbababbbbbbbbbbbaabbabaaabaaabbababababaabbababaabbbabbaababbbbbabbaaabbbabbabababababababbbbbbbabbbaabbbbbbaaabbbbaabbbbbbababaaaaaabbaaabbbbaabaabaaaaabbbbaabababbbbaababaabbbabbbbaaabababbababbaaaabbaabaabbbaabbbbbababbaabbbbbaabbbaaabaabbbaaabaaabbaaabaaaabbabbabbaaaabaababbbababbbaababbabaabaabaaaaaaabaababaaabaabbaaabbababababbbbabbbaabbbaaaaabbaaabbabbaaababbbaabbaaabbaabaabaaaabaaabbababbbbbbaaabbbaabaaabbaaaabababbaabbbbbbabaaabbbbbaaabbbbabaaakbaaaabbbbbbbbbaababbbbbbabbabbbaaaaaaaaaabaaaaabbbbbbbaaabaaabaabaaabbbbababbabaaaaababbabbbbaaaababbabbbaaaaaaaaabbabaabbaabaaababbbbabaaabaaababbabaaaababaaaabbababbaabbabababbbaababababaaaaababbabbbbaababbaababaabaaaaaabbabbaabaaaababaabbbbbbbababaabaaabaaaaabbabbbbbbbbabbabababbbbabbbbbabbababbabaaabbabaaaaaaababbaaaabbbaaaaaaaaaababaaabbababaaabababbaaabbaababbbbbaabaaabbababbbaabbbaabbbaaaabbaaabbbbbaabbaaababbbbababbaaaababaaabbbabbaabababbbabbaabbbbbbbbbbbabaabababaabbaaababbaabaaabaababbbbbbbbbababbbaaaabbabbbaaaaabbaabbabaaabbbaaaaabbabaabbbaaaabaaaabbbbabababbbaababaababaabbababbaaaaaabaabaababbbbaabbbabbabaababababbbabaabbaaabbbbababbbaababaaabaaaaababbabaabaabbabaabbbaabaaaaabbababbbabbabbaabbbbaaababbbabbbbbababbababbbabababbbbabbabbabbabbababababbaaabaaaabababaaaababbbbbaabbbababbbabaabbabaabbbbbaabababbababbababaaabbaabbabbbaabababababaabbaabbbababbbbbbabbbbbaaabaaaaabaabbbaaabaabbbbabbabbabaaaababbbaaaaabababababbbaabaabbbaabbbababbbaabaaabbbaaabaaabaaaaaaabaabbbbbbbbbbaaababababbaaaababbbbaaaabbaaaaaaababbabbbaabbbbbabbbaabaaabbababbbaaababbbbbbbbbbbaaabbaabbaabaabbabbaaaaaaaaaaabbbaababaaaaabaabbbbabaabbbaabbabbbaabababbaaabaabbaaaaababbbabababbbaaabbbaabbbbbababaaaabaabbabbbabababbababbbbbbaaabbbabbabbbbbbaababbaabbbbbabbababbbaabbbbababaaababbbabbbbbaaaaaaabaaabbbbbbbaaaaabbabbababaabaabbabbbbbabbbbbaabaabbababbbaabbbabaaaabaaaabaaaabaaabbaabbbbbbabbaaaabaaabbabbbababaaababaaaababbbbabaabbababaababbbbaabaabaaaabbbaaaababaabaabaaaaaaaabbbaaaaaaaabababbbababbbbbbaaabaaabaabbaaaaabbaaabaabababaaaaabbbaaaabaabbaabaabababababbbaaaaabbababababaaabbaaabbbaaaaaaaabbabbbbbaaabaabaababaabababaabaabbaabbbaabbbbbaababaabbabababbaababbaabbababaaaaababaaaabaaabbabaabaaaabbabbabaabababaaaaaaababbbbbabbabababbbbbaababaaabaaabbbaababababbabaabababbbbaaababbbbbbbbbabbbabbbabbbbabbaaaaaaabbbbbababbabaabbbabaabbbbaaabbbaababbbbaabbbabbbbbabbaabaababaaabbbbbabaaaabaaabbbbaabaaaabaaabbabbabbababbabaabbabaaababaaaabbbababababbbabbabababaabbbbbaababaabbaababaabbbbbaaababababaabbabbbbaabababaaabaabbabbaabaaabaaaaaabaaababbabbbabababbabbbbbabaaaaabababaabbbbaabbbbaaabaaaaaabaaaabaabbbbbaababbbabbbaaabbbbbbabbbbbaabbbabbbbbaaaababaabaababbabaabbaaaabbbaabbbbbababbbbabbaabbbbbababbabbbbbaaabbabababbbaaaababaaaaaaaaaaaaaaabbababaaaaaabababaaabbbabbababaaaaabbabaabbbabbbaaaabbbbabaaabaabbbbaabaaabbbaabbababbabbaaaabaabbabaabaababaaabaaaaabaabbbbbbbaababaababbbbbbaaabbbbaaaabbbabbbbbababababaababbabaaaaaabbbaabaababbabaaababbaaaaaaababbbaabbbbabbabbbbaabbbbaaaabababbabbaabaaaaabbabbaababaaabbabbabbbabaabbbaabbabbbaaabaabbabbbabaabbababaaaaababbbabbbbababbbbbabbbbbbbbaabbaabaabbabbabbaabbbaaabbbbaabbbaaaababbabaaabbabbbababbaabbbababababbabaabaabbbbabbabbabababababbaabaabbbbaabbabbaaabaababbbbbbaabbabababbbaaabababbababaababbaabaaaabbaabbaaaaaaabaaaabababaaabababababaaaabbbbbbbabbbaaaaabaababaaabaabbaaabbaaaabbbaaaababaaaabaabbbaabbbaababbbbaabaabaabbbbababbbabbababbaaabbbaaaabaaaabaaabbaababbbabbbbaababbbaabbbbababaaaaabababbbbabbaaabbbaabbbbaabbbaababbababbaabbbaaabbaaaaaabaabbbbababbbaababbbbbbababbabbbaaaabaaabbabababaababaaabaabaabaaababbbbaaabaaaaaabbbabbbbabaabaababbbbbaabbbaaabbbbbbbababbaabaaababbaabaabbaaaabaabbababbbbabaabaabbbbbaabbbbbbbbbbbbbbabbabbbaaabbbaaabbabaabbaaabbbbaabbaabababaababababaababbaabbaaaaabaaaabaabbaababaaababbbbbaabaaabbbbabbbbabaaababbbbbaabaaaaabbaabaaaabbabbbbbabbbbbabbbbaabaaaabbabbbbbbbabaaabaaabbababbbaabbaaabbbaaababbabaaaabbabaaabbaabaabbbaabaababbbbabbabaabbabbabbbbaabaaabbbbbbbabbbabaabaaabaabbabaabbbabbbaabaaaababbbaabaaaabaababaaabaaaabbaaaababaaaaaaaaaaaababbbabbaabbabababbabbaabbabbbabaaaabbbabaabbabbbaaaaabbabbabbbaaabaaabbaaababaaabbababaaaaaabbaaaabbbaabbbbabbbbbbaaabababbbababbaaabaaababbabaaabaaaabababbaaaabbbabaaabbbbbbaaabaabbabbbbbabbabbbababaaaaababaaabaabbaabbababbaabababbabbbabaabbbbbaaabaabbbbbbabbabababaabbabbaaaabbabaabbbaaabbbbbbbabababbbaababbabaabbabbaaaaabbbabbaababbbabbabaaabaabbababababbbbbabbbbbbaabaaaaabaabaabaababbabbbabbbaaaaabaaabaaaaaabbbbaaaaaaababaaababbbbabbabbaababaaaabaabbbaaaabbababbbaaabbbabbbaabbbbbaabababbababbbababbabbaaababbabbbbbbbabaaaaabaaaaabbbaaaaabaabaababbababaaaaaaabaaaabaababbbbaaabaaaaaaaabbbbbbbbbbabbbbaaaaabaabbbbaababbababbabbbabaaabbbbbaaabbabababaabbaaababaabbaaabbbbbaababbaabaabbabaabababbaabbabbbbbbbabbabaaabbaabbbaaaababaabbbabbaabababbabbabbaabbaabbbbaabababbbbabababbbbabbababababbabababababbbaaaabaabbbbabababaabbabbbabbbabbabababbaabaabbbaaaabbaabaabaaabbabbbbbaabbabbbbaababbbaabbabbbabbbbabaabbbaaaabaabababbbbabaabababbbbaaabaaaabbbbaaaaaababbaabaabbabbaaaabaabaababbbbbaabbaaaababbbaabbabbbbbbbaaaaabaabbbababbaababababbaabababbaaabbababbbabaaabaaababaaabbabbbbbbaaaabbaabbaaaaabbbaababaabbbbababaabaabbbbbbaabaaabbababbbbabbbbbaabbbaaaabaaabbabbbababbaaabbaabaaaabbbbaabaaabaaaabaabbbaaaababbbabaabbbabaaabbbabababbbaababbbaaabbbbbbabaaaabbabaaaabaabaaabbbbbaaaabbbbbbbabaaabbbbaaababbaabbaabaaabbbaaabbbbbbaabbabbaaabbabbbaaabbbaabaababbbbaaaaaaabbababbaaaabbbabbabbaabaaaaaaabbaababaabaabbbbaaaaaaabbaaabababaabbbaabbaababbbaababbbabaaaabaaabaaaabbbbbbbbbbtaaabbbabbabbbbaaabbbababbabbbabbbabbbbaabbbbababbabbbbbbaaaaabbaabbaabbabbbbbbbbabaaaaaaaaabaabbaaabaabaaaabbbbabbaaababaabababbabababbaaabaaaaabbbaabaababbaabbbbabbaaaabbbbaaaababbaaaaabbbaabbbababaababbaabbbbbbbbbaabbbbbabbbbbabbaaaabaaabbabbaaaabbbabaaaaabbbbaabbbbaabbaaaaaabbbabaaababbbbbaaaaaaabaaabbbaabaaabbababaabaaaabbbababbbbbaaababbaabbaaaabbabaabbabaaaabbbbbabbabaaabaabababaabbabaababbaaaaaababbbaabbaaaaabaababbabbbbbaababbbabbbbabaabaabbbaabaaaaaababbbabbbaaabababaaababbaaaabaabaababbbbaabbababbabaabbabbbbabbabbabababbabaabbbbababaabbaaabaababbbabbabbbbaabbaabbabbabaabaaabbbaaaabbbaaabbababaaabbbabbabaaabababbbaaaaaaabbbbaaaabbaabbabbabbabababaababaabbabbbabaaabbbaabbaababaaabbbbaabaabaabbbabbbabaaaaaabaaaabbbbbaaaabaabbbaabaababbbaaaaabaaaaabbabababbaaabaabbabbababbaaabbbbbbababaaabbababbaaaaaaaabbbbbbabaaaabbabaabaababbaaabaaabaabbabbaaabbbbbbaababababaabbbababbbbbbbaaabbbbaabaabbbaaababbbbbbbbbababbbaabbbbabaaabbaaaaabbaabaabababaaabaaabaaabaaaaabbaaabaaaabbaaaaaaaabababaabaabbbbbbabbbbbaabaabababbbaabbbaabaabaabaaabbbbbbbbbabaabbbaaabbaaaabaaabbbaaaabbaababbaabababbbbaaabaaabbababbabbabbbaabbbaabbbbaabababaaaaabbbbaaaaaabbbbabbabaababaaababbbbbbbaaaabbababaaaaaabbbbbaabaababbabbaabbbbaabbbbbaaabbbaabbabbbbbbabbaaababbababbaaaabbabbababababaabaaaaaabbbbababaaababbbbbaabaabbbbbaababababaaabbabaabbabaaabbbaaaabaaaababbabbbababbbbaabbbbaabbaaababbbbabbaabbbbabaabbbbabbaaabaaaabababbbbaaababbbbbabbbbbbbbbabbaaabaabbababaabaaabbbbbbaabbbbaabbbbaabbbaabbbbbaabaaaabbbbbbaababaaaaaabbaaaaaabaaabbabaabbbbbbabaaabbbaabaaaaabaaabbbbabbabbbbbbaabbbbaababaaaaaaaaabaabaaabbababbabaabbbaabaabbabaabaabaababaabbaaaababaaababbaaaaabaabbbaababababbbabbaababbaabbabbaaabaabbbabbabaaabaaabbbbaaabbbabbaabbaababbbaaaaabbbaabbaabbbbabaaabaabbaabbaaaaabbbbabbaaaaaababababbbababaabbbaaabbbbabbbbaabaabbbbbbaabbabaabbaabbbbaaabbbbabaaaabababbabaaaaabbabbbbbbbabbbbabbaaaabaababaaaabababaaaaaabaabbbabbbbababbbaaabbbaaabbabbaabbbbabbbbaaaabaaaaaabaabbabbaababaaaaaabaaaaaaababbaababbbbabbaabaaaaaababaabaabbbabbabbabaaaabbbabababbbbbbbabbbabbbaabbaabbabbaaabaabbbbabaabaabaaabbabbbaaaaababaaaabbbaaaabaaababbaaaaaaaabbbaabbbaaabaabbabbbbabbbbabaaabbbaaabababaabbbbabbbaababbbbbabbaabbbbabbaabaaaabaaaabbaaaabaabaabbabbbbbabbbbbabaaaabbbabbbbbabbaabababaabaabbababbaaaaababbabaababaabaaaabbbaaabbbbaabbaaababaaaaabaaababbbbababbbbbbbabbabaabbbababababaabbbbbbbbababbaababaaabbaabbbbbbaaaabbaaaabbaabbaaaaaabbbbbaababbaaaabbaaaabbabbaaabababbaabaabbbaabbaaabbaabbbaabbabbabaaabbababbabaababbababbaaaabbbbbbababbbbaabbabaabaabbaaaaabbaaababaabbbbbbbbaabaaaaabaaaaaabbbbbabbbbabbabaabaaaaababbaaabaababbbbaaabaaaaababbabbbbaaababbbbbbbaaababbaabaaaaabaabbbbbbbbaaabaababaabbabbaabaabbaabbbbbbbaaaabbaabbabbaabaabbababbababbaababbaaaaaaabababbbbaaaaaabbabaaabbbbbbabbaaabbbabaaabaabbaababababaabbabbaabbabbbbaaaaabbaaababbbbbabbababababaabaabbbbbababbabababaaaabbbaaabbabababbbbbbbabbaaaaaabbabbbaababbabbababaaababaaaaaabbbabaabbababbaaaaabaaabaabbbbbbaaaababbaaababaaabaababbabbaaaaaabbaababbbaabbaabbaaaaabbabbabaabbaababaaabababbabbbbaaabbababbaaaabbbaababababbbbabbbabbbbbbbabbbaaaabaaaabbababbbbaababaaaaababaaabbabbababbbaaaabbaaaababbbaaababaabbabbaaabbabbababaabaabababaabaaaabbaabaababbbaaaaabbaaaabaaabbbbbaabbaabbbabaaabbbabbabbbaababaabbbaaaaabbaaaaabaabababbaaaabbabaabbbaabaaabababaabbbababbbbabbbbaabaaaabbabababbabababababaaaabbbbbaababbbbbaaaabbaabbbabaaabbbbbabbaabbabababaabaabbabbbaabaaababbabbabababaaaaabbbabbabbabbaabbaabbbbbbaaaaabaababbabababbabababbbaaaabaaaaababaaabaaabbbbbabbbbbababbbbabbbbaaabababbbababbaabbabbbbabaababaaaabbbbbbaaaabababaababbbbaaabbbbbaabaababaaababbbaabbaabaaaabbabaaabbabbaababaaaaabbababbababbabaabaabbbbbbabaaabbaaababbaaabababaabaaabaababbbabaaabbbbaabaabaabbbabbabbabbbbbbbabaabaaababbbbababaaaaababbabaaababbaaababbbabaabbabaaaabbaaabbabaaaaaabbabbbabbbbaaabbabababbaabbabbbabbaaabbbbabbaaabbbbbabbbaabbaaabbbbabbaaabbaaaabbbbabbbbababaabababaabbaabababbbaababbaababbabaaaaaaabbaaabaabbabbababbbabbbaabbabaaaaaaabbaabababaaabbbbabbbaaababbbabaabaababbabbbaabbbbaabbaaabbaabbbbabbbbabbbaababaabbbababbabbabbababababbabababbababbaaabbbababbbaaaaaaabbaaaabbbaabaaaabbbbabbabbbaabaaababbbbabbaabbaaababaabbbababbbaaaaaabbbabababbbabbabababbaabbbbaababbabbbabbaababbababaaabbbbababaaaabbbaabbaaaababbaaaaaaababbababbbaaaaaabbbaababaabaabbababababbbaaabbbbabbbaabbbaaaabaabbaaaabbaabaabababbbabaabaabbabbbaaaaabaaaabbbbbbbaaabbbbabbaaabbaaabbabbbaaaaabbaabababbbabaaabbbbbabbbbaaabaababaaaaabaabaababbbaabbbaabbabbabbabaaaabaaabbaabbbbbaabbaaaaaabbabaaabaababbbbabbbbababaaabbaaababaabaaababaabbaabbbbbaaababbbbbaabbbaabbabbaabaaaabbbbaaabaaabbbbbabaaabbabbbbababaaabaabaaabaaaabbbabaabbbaaababababbbaaabbbaabaababaabbbabaabbbabbabbabbbbabbababaaabbabbaabbbabaaaaabababbaabbaabbaabababababbabbbbbbbbbaaababaaabbabbabbaababbaaaaabbabbbbbbaaaabbbaabbbbabbbaabbaabaaaaabbbbaabababbaabbaaabbaabaaabbbaaaaabbbbbbbaaabaabaabaaaaabbbaaabbabbaaaaaabbbaaababbbbbbaaaabbbaaaabbbbababbbbaabbbabababbbbbaaaabbbababrababaabaaaaababaaababbbbabaabaabbbaabbbbbbabbababbbaaaabaaaababbaaabaababbbaaaaabbaaabbaabaaaabaaaaabbbabaaaaaaababaaaabababaabbbaaaaaabbaaababbbbbbaaaaaabaaaababbaaabaabababaaabbabbabbbaaabaaabbabbaabaabaababababbabbbabbaabbbbbababaabaaaabaaaabbbbabbbbabbabbabaaaaaaaaababaabbbabaabbabaaaabababbaabbbaaabbbababaababbbbbbbbbaabbbbabaaabbabaabaabaabbaababaabaaabaaababbbaaabaababbbbbabaaaaabaaabaabbaabbbbaabbbbaaaabbbabaabaabababbbbbbaababbaaaaababbabbabaabbaabbaabbaabbabbbaaaabbaabbaababababbbbaaaaababbababaaabbaaaabaaabbbbbbbbbababaabababbbabaabbbabababaaaaaabbbabbaababbbabaaaabbbbaaaabbabbbabbbabaaaaaaabaaaabaababbabbaaabaabaabbbabaaabbaabababbaaabbabbabbbbaaababbaabaaaaaabbbaaaabbaabaabaabbbbbaaaabbbbbabbaaabaaaaabaaabbabbbbbaaaabaabbbbbbbbbaababbaaabababaabbbabbabbaaabbbbbbabbbaaabbaabbabbababbbbabaaabbbabbbbababbbaaabaaaabaaaaabaaaababbaaabbbbbaaabaaabaababaaaabaabbbbaababbbababbbabaaaabaaabbbabbaaabaabbbbbaabbaababbbabbbaababbbbabbbbababbaabbbbababaaaabbbabbaabaabbbabbbbabbaabaaabaabaaabbabaaabbbbbaabbbabbabbbbaaaaabbabbaaaabbbababbababbbbbabaaaaabbbbabaababaaaaaababaaaaaaaababaabababbabbaaaaabaaaababbbababbbabbabababaababaaabbbabbbaabbbbbabbbbaabbaaabbbbabbaababbbbbbaababbaabbaaabbaabaabaaaabbbaabbaaaabaaabaaabbbbbaaaabbbabaabbbbababaabaaaababbaabbbbbbbbbbaabbbbabaaaabababbaaaaabbaabaababaabaababaabaabaabbabaaabaaaabababbbabbabbbbbaaabbabbbababaaaaaaabababbabbaaababbbbabaaabaabababbaababababbbabbbabbabbbbaababbbbaabbaaabababababaaaaabaabbbbaaabbbaaabaababbbbabbbabaabaababbabababbbbaabbaabbbaabbaababbbaabbbbbbbaaaaaabbbaaaaaaaabaaabbaaaaaabaaabbbabbabaaaaabbbbababbbbbaaababaabaaaaabaaaababababbababaabaabaabbbbbbbabbabaababbaabbbabbbaaaababaabbaaabaabbaaaaabbbbbabbbbaaaababaaabbaabaaaaaaaaaaaaaabbaaaababbabaababaabbaaaababbbbabaabababbbbababbaababbbaabbabaaaababbaaababbbabbbaaababbbbaaaabbabbaabaabbaabaaabbaabbbbbabbbbbbbaaaabbabaabbababbabbaabbbabaabbbababbababbababbaabbaaabbbabaabaabaaabbaaaaaabbbbabbbaaaaabbbbabbaaaabbaabbbbaaaabbbbabbbabaababbaabaabbbbbaabbbbbbbaaababaabbbbabaabaaaaaaaaabbbbbaaaabbbaababaabbbbbabbbbbbbabababaababbbaabaaababbababbabbbbaaaabbbaabaaaaabbbbaabababbbaabbaabbabababaabababbbabababababbabaaaaaaaaabaabababababaaabaaabbaabbaaabaaaaaaabbaabaabaabbbbaabbbabaaabbbbbbaaabaaaabbbaaabbbabaabaabaaaabaabbaabbbabaabbbbaabbbbababbbbbaaabbabbbaaabbbabbbababbbabbaababbbbbbabbabbbbbbaabbabbbabbbaaabbbabbbaabaababbaaaaabbabbaabbbbbbaababaababbabaaaaaababbabbbaabbbbabbabbbbbbbabababaaababbabbbabaaaaabbabbbabbbaaabbaabbbbaabaaaaabaaabaaabbaabbbaaaabbbaaabbabbbabaabbbbbaaaaaaaaaabbabbaabaabbbbbbbabbababbbbbababbababbbabaabbababaabbbabaaabbabbbbabbbbaaabaaababaabbababbaaabbabbbbabaabbabbbaaabbaaaaaabbaaaaaaaabababbbbaabbbaabaabaabaaabbaaabaabaababaaaaaabaaabbbbbbababbaabbbaaabbbbababbabbaaabbabaabaabaaabbbaabaaaaabbabaaabaabababaaaabaaaaabaabbbbaaaaabaabbbaaaaaabaaababbabaaaaabaaabbaaabbbbbbabababaabaababbabbabbbaaabbbbbabaaaaabbbaabbbbbbabaaaaabbbaabbaaabbaabbbaaababbbbbabbbabaaabaaabaaaaabbbabababababaabbbababbbbbaabbbbaabbaaaababbbaabaabbabbbababbbabaabbaabbbbababbaaabaaababbaabaabbbbbbbbaabaaaaabbbbaaaabbaaabaaaabbbbaabababbbbaaaabaaabbbbbabbbbbbbbaabbaaabbaabababbaabababababbbbbabbbabbbabbaaababbbbababbbababbbaaabbabbbaabaababbbabbbaaabababbabaabbbababaabaababbabababbbababbbaaaabababaabaabbbbabaabbbbabaababbaababbaabbbabbaaabbbabbbaabaaabbbabbbaabbabbbbabbaabbbbbaababaaaabaaababbbababaababbbbbaabbbababbbbbbababbaaababbaaabbbaabbaabbbbaabaabaabaaaaaaaaabbabbbbbbaabbabbbabbbbbabbbbababbababbaaaaabbbbabaaabbababaaaaaaabbbbbbaabbaaabbbabbbaabaabaabbbbaaaababababbbbbbabbaaaaaababaaabbaabbbbbbaaabaaaabaaabbaaaaabbababbbabbaaaaaabbabbbaaabbbaaabbbabbaabaabbbaabaababaabbabbbabbbaabbbbaaabbbbaaaababaaabbbaaabbaaaabaabaaabaaaaaaabaaababababaabbbbbbbababbabaaaaabbbbbabbabbabbaabbbbaababbbabaaababbaaaabbbababaabbababbaaaabaaababbbaaaabbbbbbabbbbabbbaabaaabbbaaaaaabaaabbbaababbababaabaabbababbaabbbabbaaabaaabbaabbaaaaabbbabbaabaaaaabbbaaabbbabbbbbbbabbbaaaabaaabbbbbaaaabbbaabbbaabbaaabbbababbabaaaababbbaabbbabbaabaabbbaaaabaabbababbabbaabbabbbaababaababaaaabbabababbabaaaaaabbaabaabaabaaabababaaaaaaabbbabbbbbaaaaaaabbbbbbbabbabbaaabbabbbbaaabbaabbbbbabaabbaabbbbbaababbbabaaabbabaabaaabbbaaabbbbbbaaaabaaabbbabaaaaababbbbaaababbbabbaaababbbbbbabbabbbbbaaabaababbbbbabbabbbabbabaaaaaabaabaaaaababbbaaababbbbabababbaaabaabbaaaaababbbbaaaaaababababaaabaabaaaababaaaaabbbabbbaabbbabbababbbbbbabbbbbaabaaaabbaaabaabbabaaababaababbababbaaaaaabbbbabbabababaababbbabbaaabbbaaaaaaaaabaaabbbbbbbababbababbbbaaababbaaaabbbabbbabbababaabbbababbbababbbbaabaaaaaaabbaabaababababaabbabababbaababbbaabbaabbbabababaabbabaaabbbaaaabbabbbaabbaaaabbbaabbaababbabbbbabababaabaababaabbbaaabbbaabbaaabbabaaabaaaabaaabbbabaaabbabaabababababbaaabaabaabbaaaabbbbbbaaabaababaaabaabbabaababbbbbbbaabababaabbaaabbababababbbbaaaaabbaabbababbbbbbbabbbbbaabaababbaaababbbbaabaabbaaaababbabbbbbbbbaaaaaabbbbbbabbbaabbaaabbbbababbabababaaabbbabbbbbaabababbabbbabbbbbbabbababaabbabbbbbbabbaaaabababbaaaaabaabababbbaaaabaaaabbbaababbbbaaababbabaaaaaabbabaabbbabbabababbabaaababaabaabbaaabbbaabbababbbbbbbaaaababbbbbbaababaabbbbbbbabbabaabababbaaaaaaabaaaaabbababbabbbbbababbbbbbbbabbabbbbabaaababaabaaabbbaabbaaaababbbababbabbbbbabbbaabaaabaaaaaabbbbbbabbbbbbabaabbbbbaaaabbaabbabbabaaaaaaaabbabaaaaaaaaaaabbbabbbbaaabbbabbbbbbaabbbaaaaaaaaaaaabbaabbaaababaaaabbabaabbaaabaabbbabaaaabbbbbbbaabbbaaabaaabaabbbaabbaaaabaaabaaabbbaaabaababbbbabaaababbabbbaababbaaababaababbaabbbbbbbaabbabbbababbbaabbbaaabbaabbaaaaabbaababbbbaaaaaabaabaabbbbbabaabaabbabababbbabbaababbaaababaababbaabbabaaaabaaabaababababaaaabbaababbbabbbabaabbbbbbababbababababaaabaabbbabbabbbbbababbaaabbabbaaabbaabbbabbabaababbaabaaabbbbbbbabbaababaabbababbaabaaabaaabaababbaaaaaabbbbbbbaaaabbaabaaaaababaabaaabbbbbabbbbaabababbaaabbbbababaaaabaabbbbabbbaaaabbbabaaabababaaaaaaaabaaababbaabaabbbaabbbabbbaaaaaabaaabbbbaabaaabaaaabaaaaaabbbbaabbabbbabbbabbbbababbabbbaaaaabbaaabbbbbabbababaabbbbbaaaaabbabbbabbaaabbabaabaaabbaaaabbbaabaababbababbababaabaaabaabbabaabbbbaabbaaabbbaaabbbabbabababaabbbbaaaaaabbababbabaabaaaaaababbababbabaabbabbbbbabbaaaaaaabbbbbabbbbababaabbaabbabbbbbaabbaabaabaabbabaabaaaaabbbbbbbaabbbababbbbbaaaaaaaaaaabbbbababbbbaabbaabbbbbabbabaabababbbbaabaabaabaabbbaaaaaabbabbaabbabaabaaaabbabbbabbaabaaaaabaababbbababbabbabbabbbbbaaaaabbabbabaabbbbaabbababaabbbbbbbbbbaaababbbbabbbbabbbbabaaaabbbabbbaaaabaaababbaaababababbaaaabbabbabbabaabbabaabbaaaabbbaabbbabbbbbbaaaaaabbaabaabaabaaaaaabbabbababaaabbaababbbbabaaaababbaaabbbbaaaaabbbbbbabaabaaabbbbaababababbaabaabaaababbbbbbbbaabbaaaabbbabaabbbaaaaabbbaabbbabbbaaabbaabaaabaaaabbbaaaabbabaaababbbbaabaaabaaaaaaababbbbabaaaabbbbabbbbabbaabaabbaabbabbaabbababaaabbbbaaaababbbbaabbababaabaaaaabbababbbaaaabaabbbabbabbbbbaaababbababbbaabbbbbbbbbbaabbbaaabbaaabaaaabaaaababbbaabaabbbbbbababababbabbabaaaaaababbbbbbabaabaaabbabbaababbbbbaaaaaabaaabaaaabaaaabbaaabbbabbaababbaabaabaaabbabbaaaaabbaaaaaabbabababbaabababbbbbbbabbbbbbabbaaaababbabbababbaabbbaaaabaabbbbabaaabbbaaaabbbbbbababbbbbababbbaabbaaaababaaababbbbaaaabbabbbbaaabbbabbbbabababbbbaababaaabbbababaaaabbabaaabbbbbbaabbbbabaababaabaabbbabbaaabbabaabbaabaaaaabbbabbaabaaaababbaaaabbbababaaabbabbbbbabababbbbababbbbbbabbaaaaabbababbbbaabbbbaabbbabaababababbaabbabbbaabbababaaabbabbbabbbbbbbaabaabbaababababbaabbbaababbaabbaaaaaabbbaabbbaaaababbabbababaababaabbbaababbaaabaaaaaabbaabbbbbbbabaababbbbaaabbabbabbbaaaaaabbabbaabaaababbaababbabbbabaabaabbaaabbabbbbaabaaabbbbbababaaabaabaaaabbabaabbabaabbabaabbabbbaabbaabbaabbbabbabaabbaaaaabbaabbbaabaabbabbbbabbaabaabbbbabaabaaabbababaaaaaaabaabbabaaaabbbaabaaabbbaababbabaaababbbaaaababbaaaabbabbababbabbbbbbbbbbbaababaaaaaabababbabbbaabaaabbabababbaaabbabbabbbaaabbaababbababaabbbaababbbaabaabaababbbbaabaaaaabbaabbbbbbbbbaabbabaabbabbbbaabbbbbabaaaabbbaabbaaaaabbbaabbbbabbaabbbbabbbbabababaabababaabbbbaaaabaabbbbbbaabbbabbabbbabbaaabbbabbaaababbaaababababaababaabbbaaabaaaabaaabaaabaabbbbbaaaaaaaaabbaaabbababbbbbbbbaababbbaaaaabababababbabababbabbababbabbaaabaabbaaabbaaaababbbaababbbaababbbbabbaaababbabbaaabbbaabaabbbbaababaabbbaabababbaaababbbbabbbbbabbaaaaaababaabaabaabbbbaaaaabaabaabaabaaabaaaabaabbabbaababaabbbabaabbbbabbbbbbababaaaaaabbbbabbabbbabaaaaababbabaaaabbabbbbaaabbbabbaabbbbbaabaaaabaaababbabaaabaabbbbbbbababbbabababaaabababbaaaababababbaaabbabbaabaaabbbabbbbababaababaabbabaabbabaabbbabbbbaaaabbaaaaaabbaabbababaabbaaabbbbbbabbabaaaaababbbbbbabaaabaabbbbbbaabbaaaaaaababbbbabbbbbbbbbaabababaaaabbabbaaabbabbbaabaaabbaaabbbbbbbabbbaabbbbaaaaaaaababbaaabbabaaababbabbababbabababbabaababbbabaaabaaaaababaabbbbaaabaaabaaabbaabbabaabababbabbbbbaaabbbbbaaaabbabababababbaaaaabbaaaaabbababbbbbbbbaaaaaabbaaabaaaaaabbababbabbbaaaaabbbbaababaabbbbaaabbbbbabbbbaabbbbbaaabaaaaabbbaaaaaaaaabbaababbbaaabaaaaabaabbbbbababaabaababbabbbbbababaabbbaababbabaabbabbbababbabbabbabababaabbbababbabaabaabaaaaaabaaaabbaabbabbabbaabaaababbababbaabbaaaaaababbbbbabaababaabbabbabbbbaabaabaabaaabbbaaaabbabbabbabaaabababbbabaabaabbbaabababbabbabababbbaabbaabbaabaabbbaabbaaabbabbabaaaaabaabbaabbbbabbbbaababbaababbababbbbaaabaaabababbbababaabbababbbaaabbbbbabbabbabaaabbbbabbbbababbababababbabbbbbbaaabbabbaaababaabbbbbbbabbaaabaaabaaabbabbaaaaabbbaaaaaabbbbbabbaaabbbbaabbaabbbaaaababaabbbbaaabaabaababababbabbbbabababbaabaaabaaabbbababababababbbbbbbaaabbabbbabbabbaaababababaaabbabababbaaaababbbabbabbbabbaaaaaaaabbbabbabaaaabaaabbaababbbabbabaaabbbaabbabbabbaabbbbababbbbaabbaaabaaabbbaabbaabaaaaaabbbbabaaaaabbbbbbbaaaabbabbaaaababaababaabbbabbaabaabaababbbbaababbabbaabaaaabbbbbaaabbaabbaabababbbabaaaaaababbabbabbabbabbbaaabbaabbbabaaaabbbbaaabbaabaaabbabababaabbbbabbbbaabaabbbaabaababbaaaabbbaaabbbbaaabababaabbabababbaabbabaaabbaabbababaabbbbaaababbabbabababbbbabbbabaaabababaaaaaaabaababbaaaababaabbabaabbbabaabababbaaaababbbaabababababbaabbbaaaabbaaaaaabababaaaabbbaabbbbbabaaaababbbaabaabaaaabaabbabaaaaaaaaaabbababbbbaabbbbbbaaabbbabaaabbbaababbabaabaaabaababaabbaaaaabbaabbbbbbaabaaaaaabaabbbbbababaaaaaabaaababaaaaaaabaaabbbbbabaaabbbabaabbabababbaabbaabaabbabbbbababbbbaabbaaabaabbaaababbabaaabababababaabbbbbabbbaaaaaabbabaabaabaabbbabbaaababbbbbbaabbbabbababbabaabbbbabbaaaabaabbababbbbabbbaaababbabaabbaaaaaaaaababaaaaaaabbbaababbbbbaababaaaaaabaabbbbbaaaaaabbbaaaaabbbbabbbaababbbaabaaaaaabbaabaabbaaaabaaaaabaabbbbabbbbbaabaaabbabbbaababbbaabbaaaabababababbbaabbabbbaaabaabbbaabbbababbaaaaaabbbbbbbbaabaabbabbbaaaabbababaabababbbabbaaaabaaabbaabbbbaabaaaaaabbaaababaabbbababbabbabaabaabaaaaabbabaabbaaabaaaababbaaaaaaaaabbbabbaaabbbbbaaabaabbbbbbbbbbaabbbbbaaaaaababbaaabaaaabbabbbbaaabababaaabbabbbbabaabababaabbabbbabbaabbabaaabaababbabaaaaabbababbaaaaababbbaaaabaabaabbbaabbabbababababbbaaaaabbaabbbbabbaaabbbabbabaabbababaabbabbaabbababbaaaaaabbabbaababbbbbbabbbabaababbababbbbaababbbababaaaabbbaaabbabbbbbaababaabbbabaaabbaababbbabababaaaabbabbbbbabbbabbbbaabbbbaaabbbbbababbabbabaaabbbaaaaabaaabababbabbabbaaababbabbbaaaababbababaaaabbbbbabbaaabaaaaaaaaaabaabbaabababaaababaaabbbaabbbaabbaabbaaabbbbbbbbababbbbababaaababbbaaaaabaabbaaabbaaaaabaaaaaabbbbbabbaabbbbaababbaaaaaaabbbbabaaabbabbbaabbbaaaaabaabababaaaaabaabbbbababaaababababbbbbabbaabaabaabaaaaaaabaabbbabbaaabaaaabababababbbabbbbaabababbbaabbbbbaaaababbababbababbaabbaabbbbbbbbabaaaabbbaabaabbababbbaabbabaabbaaaaaaabbbbbabbbbaaaaabbbaababaabbaaabaaabababbbaabbbabbbbbbbaabbbabbbabaaabbbbaabbbabababbaababbbbbabaaaabaabbbbbaabababaaaaabaabbaabbaaababbbaaababbabbabbbabbaaaaaabaaabbbababbababbbaababbaaababbabaabbaabababbabbbaaaabababaababaabbaabbbbbbaabbabbabbabbbababaabbbaabbbabaaaaaabbbbbabaababbabbababbaabbabaababababaaaababaabbaabaaababaabbbabaaabbabaabababbabbbbabbbaaabbaaabbbbaaaaaaabbabbabbbbbabaabbbbaaabbbbbbabbaabbababaabababababbabbaaaaaabaaaabbbbabaabababbbbabbbbbbababaabaaaababbbaaabbaabbaaababaabbabbbabbbbbbabaabbaabbaabaaaabaabaaaababbaaabbabbbabbabbaababbbbbababbbabaaabbabbbbbbbbbbabababbabbbbbbabbaabbbbababaaabbbbabbabbabaabbababbbbabbaaabbaaabbaabaaaabbbbbbabaaabbbababaababbbbbbaaaabaaababbaaabbbababaaaabaabbaaaaaaabbbbabababbaabbbbababbababbbaabaabbbaababaababaaaababbbababbbbbaaabbbaaaaababbbbabbbbaaaaababaabbababbbbbaaaabaaaabbabbabaaabbbbababaaabbabaaaabbaaababbaabbbbaaaababaaabbabbaaaabbaabaabbabbbbbbbababbabbababbbaabaababaabbabbabbbbbbbbbbbbbbababbaabbbaaaaaaaabbbbbbbbbabbbbbaabbaaaaabaaaababaabaabbaaabbbabbaaababaabbbabbbabbabbbaabbbbbaaaabbabbababbabaabaaabaabbbbbaaaaaabbbbabbaabbaababbaabbaaaababbbabaababbaaaabbaaaabaaaabaabbbabaaaabbbaaaaaabbababbaaaabaaabaaabaaaababbaaababababbabaaabbaabbabaababaaaabbbabbaaaababbabbbbababbaabbbbbbababbbabbbbaabbababbabaabbbabbbbbbaabbbbbbbaaabababbabbbbbabaaaabaaabbbbbbbbaabbbbbaaabaaabaaaaaabbaabbabaabbaaaabbaabbabaabbbaabbbabaaabbbaabaababaaabbbbbbbbababbabaabbbaabbaaaaaaabbbabbaababaaaabbaaaabaabbabbabbbbbaabababbbabbbbbaaabaaabbbaaabababababbabbabaabbababaaabaabbabbaaaaabaaabbabaaabaaaaaabaaabaaabbbbababaabaaaabaaabbabbababababbbbabbbabaaabbaabbbaaaaaabbabbbbbbabababbaaaaaabaaaaaababaaabbaabbbababbbabaabaabbbbabaaaababbabbbbaaaaabbaabaaaaababbaabaaabaabaabbabaaabbabaababbbbbabbababbaaabaabbbbaaabbaaabaaaaababbbaababbabbaabaaaaabaaababbbabbabbbabaabbaaaabaaaabbbabbabbabbaabababbbbbbbabbbbbbabbabbabaaaabbbabababbabbbaababbbabaaaaababbabbbaababbaabbbbbbaabbaaabaabbbababbbbbabbbabaaaabbaaababbaaabaaabbbabbbaabbabaaababababaaabbaaaabbababaaabbabbbabaaabaabbaabbbababbbabaaaaaabbaaabbbbbabbbabbbaaabbabbaaaababaaaabaababbababbaabaaabbbabaababbbaababbababaabaabaaaaaabbbbbbabababababbbaaaaabaabbbaababaaaaaabababbabbbabbbaababbbaabbabbabbababaabbbaaabbaabbaaaaabbbbaaaabaabbbaaaabaababbabbbbabbaabbbaaaababaabbaabbabaaaaabaabbbbbbabbbaaaababaabaababaabbbaaabbabbaababababaabaababaabbaabababaabbbaaabbabbabbabaabbababbbbbbababbaabbaaabaabbaaabaaaaababaabaaaaaababbabbbbbaaaaaabaaababbbaabbabaaabbbbbabaabbabbabbabababababaaabbaaaabbbbbbaaaaabbababaabaaabbaaabbaabbabbbbabababbbabbbbbbbbbbbaaabbbbbbaaabbabbabaaaaabaababbaaaababaabbbaabbaaaaaaabaabbabaabbbbbbaaabaabbaabbabaabbbbbbbbabbbbabbbbbbabbbabbaaabbabababbbaababaabbbbaababbbbabbbaabbabbabbbaaabbaaaabbbabbbabbabbbbababbaabbabbaaabbaabaaabbbbbaaabaaabbabbaaabaabaabbbaabbabbbaabbababaabaabbaabbababaaaabbaabbbababbabbbbaabaabbbbaabaabbbbbaabaaabbaabbbaabaabbaabaaabababaabbababaaaabaabaabaaabbbaabbaaaabababbaabbaaaaabaaababbbaaabbabbbaaaabaaaababaabbabbababbabbabbaabababbaaabbbabbbaaabbaabbaaababaaaaaaaabbbaabaabbbaaabababbbbabababbbbbababaabaaabbbbabbabbbbbabaaaaabbaaaababbabbbbabbaababbabbbaaabbbabbabbbbabbbabbbababbbbababbbaabbbbaaaabaabbbabbbbaaaaaabababaaababbbbbaababaabaabbbaabaaabbaabaababbbbbaabaaabbbbaaabbababababbbbbabbababaaaaaababbababbbabbbabaabbabbbbabbaabbaaabaabbaaaabaabbbbaaaaaabbabaaabaabbbabaababaaabbabbbbbbbbbbabbaababaaaaababaaabababababababababbabababbbaaabbbaaabbababbbaababababbbbbabbbbababaaaabaaaaaaabbbabaababbbbbabbaaabaababbabbabaabaababbbbabbabbbababaaabbbbabbaabaababbbbbbbbaaabaaaabbbbabaaabbabbababaaababaaaabbbbaabbbaaabbbbbbbbbaababbbbababaaababaaaabbbbaaabbabaabbaaababaabbabaaaabaaababababbababbbaaababaabbabaabbaaaabababaabaabaabbbabababaaaabbbababbbabaabaaabaaabaabaaabaaaaaaabbbaabbabaababbbaabbaaaaaabbaaaabbaaabbabbbabababaabbbabaaabbabaababbabbaabbbababbabbbaababbbababbabaaaaabababaaaabbbbaaaaaababaaabbababbabaaaaaaaaaabaabbaaabbabaabbabaaaabbaabbbbbbbbbaaaabbaaabaababababbbabbabababaabbaaaabbaabababbaaaaaaaabbbaabbaaaaababaaababbaababababbbaababbabaabbaababaabbaabbabbbbbaabbbababbabbabbaaaaaababbaaaaaabbabbbabaaaabbaaaaabbaaabaababbaabaabbababaaaaaabbaabaabbabbbbbbabbbaabbbbbbbbabbabbabbaaabbbabbaaaaabbbbaaaabaabbaabbaabaababaababaabbaabaaabaabbaaaabaabbbabbbaaaabbabaaaabababbaaaaabbbbbaabbabbbbabbababaabbaaaaababababaaaaaaababababbaababbbaabaaabbbaabbbaabababbbbababaaaaabaabababaabaaabaabbabaaabbbbbababababbabaababaaaabaabbabbabbaaaaaabbbabbbabbbaababbbbabbbbbbabbaaabaabaaaabaaaabbbbbabbbaaabbaaaababbaaaabbbbbaabbaababaabbabbabaaaabbaaabbaabbbaaabbbabbbaaabbbbbbaaabbbaabbabaabaabbabbaaaababaabbaababaaaaabababbbbaabbabbaaabbaaabaabbaabaabbbbaabaaabbbbbabbabbaaaaabbaaabaabbaaabaaaabbbbabbabbbbaaabaaaabaababbaaabbabbbababbbaaabbabaaabbabbabbbbaaaaaababbababbabbababbaabbbbbabbbababbbaababaaabbbbbababbbabbabaaaaaaabaaaaaaaaababbababbbabaabbaababbababbaaaababbbaaabaabbbabababaabbabbaaaababbbbaabbbaabbaabbbaaabaaabaaaabaabbaabbbabbaabaaabbbabbaababaaaaabbbababbabababbbbaabbbbabbbaabaabaabaabbabbabbabaaababaabababababbaaaaabbaabaaaaaaabaaabbbbbaababababaababbaaabbbaabbabaabaabbbabbbbabbbabaabbababbabaabaaaaabbaaaaaabaaaabaababababaabaababaababbabbbbbaabababbabbbbbbbababaababbaaaabababbabbbaaaaabaaababaaaabbbbbbaabbbaabbaabababaaabaababbaaaabbbbbabaabababbabbaababababbbbbaabbababbbabbbbababbabaaaabaabbbaaabbaaabbbabbaabaabbaababbaabaaababaabaaaaaabababaaababaabaaaaaabbbaababaabbbbbaaabbbbababbbaaababaabbbabaabbaaabaaaaaabbbaaabbabababbaabbabaabaaabbabaaabbaaabaaabbababbabbbbbaaaabbabbbbbbbabaaabbaaabbbaabbbbbabaabbbbbaaababbaababaaaaababbababbaaaababaabaabbaaabaabbbabbaabbbbbaababbbbbabbabbbbbabaaaabbbbbaabbbabbbaaabaaaabbbbbababbbaabaaaaaabbaabbbababbabbbaaaabbbaaaaabbbbbbbbbabaaaabbbbabaaababbbabbabbabbbbabbabbbabbbbaabbbababbbbbbbababaababaabbabbaaabbbbababaaaaababbbbbbbbbababbbaabaaaababaaaabbabbbbaaababaabbbaababbaaaaabbbaabababbabbaaaabbbbabbbbababbabbbbabaababaaabbaaabbabbabaaaabaabbbaaaabbbbabbbabbbbbbbabbbaabbabbbbaaaaabaaabbbbbabababbababbaaaaababbaabbbaabaabbaabaabbabbbbaaabbbabbaaaaabaababbbbbbbaaabaabbbabaabbaabaaabaaaabbaaabababababbababbababbabababbabbaabbbbaababaabbbbbbbbaaaabaabaaaaaaabbabababaababbbbbabaabaabbabbaaabaaabbaaaabbbabbbaaabbbabaaabaaaabaaababbaababaaabbababbbbbabaabbbaabbbbbbabbbbbabbaaaabbbaaaaabaaababbaaabaaabbabababbabbbaabbabaaaaaabbaaabababbaaaaaabaaabbbabaabbababbabaababbbbbabbababbaaabbabbbabbabababaaaabaaaaabaaabaabbbbbbababababbbbaaabbbaaabbbbbabbaaaaabaaaababababbaaababaabaaaabbabaabbbaabbaabbbababbbbabbabbbbaababababbbbabbbabaababbabaaabaaaaabbabaabbababaaaabbabbbaabbbaaaaabbaabababbabbbabbababaaabbbababbababbaaabbabbbbbabaaaabbbbababababbababaaabbbabbbaabbabaaababaabbbbbbaabbbabbaaaaaaababbbababbabbbbbabbbbbabbbabbabbaaabaabaabbbaaabaabababaaaabbbbabbbbababbababbbbaaaaaaababbbbbabbbabbababaaaaabaabbbaaabbbbbbabbbabbabbaabbbabbaabaabaabbbbababababbaaaaababaaabbbaaaaabbbaabaabbbbaabbabaababbaaaabbabbabaababbaabaabaabbbbabbaabbaaabbaababbbabbaaaababbaabaaabbabbbbbababbbabaabaaabbabbaabbbbaaabbabaabbbaabbabaabbabaabbaaaababababaabbaaaaaabababaaaabaabbaaaaababbbbabababbbbbbababbbaabaaaaababaabbabbabbbabbabbabaababaabaabbbbbababbabbbababbbbbbabbbaaabaaabbabaaabaaabababbbbbbaabaaaaaaababaabbaabbbbbaaaaaaaabaaaabaababaabbabbabaabbaaabbbbbbaaaaaaabbbaabaaaabababbbbbbaabaabbbabaabbbbabbaabbbaaabbbaababbaabbababaaaabbabbabaaaaabbaabaababbbababaabbaabbbaabbababbaaabaababbbaaaabbbabaaabaaaaabaaaaaaaababbbbabaaaaababaababaabaaabbbbaaaaaaabaabbabababbbbbbbabaabbbabbbbabbbaabbbbaabaabbaaabbaabbaabbbbbabbaababbaaaabbbaaaabbabaabaaabbbabaaaaababbababbaaaaabaabbbaabababbbaaabbaabbaaabbbbabbbbabbbbbaaaabaaabbabaaabbbababbaaabbbaaaaaaababaabbabbaabbbbbbabbbaaaaaabbaabaabbbbbabbaaaaabaabbbbbaababaababaabbabaaabaabbbabaabbbaabaabbbbbaabbbaabaaabbaaaaaabbbbaababbabbbabbaaaaaabbabbababbbabbabbaabaabbbbaabaabbababbabababaabbbbbaaabaababbaabaaaabbbbaabaabaabbaaababbbbbbbbaabaabbbbababaabbabbbaababbaabbabbabbababbababaabbbbaabbabbbababbaaabbabbabbababbbbabababbbbbaababaaababaabaaaaabaababbaabaabbababbbabbbbaaaaabaabaaaabbaabbbbbababaabbbaababaaababaabababbbaabaaaaaabbbbbabbabbababbababbbbbaaabbabaabbabababbbbabababbaabbbabbabbbaabbbbaaabaaabaababbabaabaaaabbaabbbaaaababaaabbbabbbabbabbbaaaabaaabbbbabbbaaaaaaaaabbaaabaaabbbabbaabaababbbbbbbbbaabaaabbbbabaaabaabbaaababaaaabbbbbbbabababaaabbabbbaaaabbbbbbabbbbbbaaaabbbbbabbabbbbaabaababbbbabbbabaabbabaabaabbbbabbbaabaaaabbaaabbbaaabaababababbbabbabbbbaaabbabaababbaaabababaababbababaaaabaabbbababbaaaabbbabbaabbbaaaaabaabbbaababbabaaabaaabbaaabbbbaabbabaaabbbbaabbbbbaaaababbaabaabbbbbabbbabaabaabaabbbbaabbaabaababbbbaaaaaabbaaababbbaabbaaababbbaaabaabbbaabaabaaaaaabbbabbbbbaabaaabbabaabbabbbaabbbabaaababbabbabaaababbbbbaaaaabbbababbabbbbabbababbbababbababbbabbababbababaabaaabaaaaabaabbababababaaaabbabbabbbbabbabbabbababbbbaaabaabaaaaabbbbabbbaaaaabbbabbbbbbaababaabbabbbbbbaabbabaaababaaaaabaabbbaababaaaaaabbbaaaabbbbaabbbbbababaabbabbbbabbaaaababbbaababbbaabbbbaaabaaabaabbaaabbaaabaaaabaaaaaabaababbbbbabababaaaaaaaaaaabbbaabbbabbaabaaabbbbabbaaaabaaabbaabbabaaaabaabbabbabaaabaaaabaaaababaaaaaabaababbabaabbaaabbbaabababbaaaabbaabbbbabbabaaabbabbaaabbababaaabbbaababaabbaababbbbbbbababaabbbbabababaaaaaabaaaaabaaaabaabaabbabbbbabbbbababbaabbbabbbbbabaaaaabbaaaabababbbbbaababbaabbbbaababaabaaabaababbaabbababaaaaaabaabbbabbabbbbbababbaabbaaabbaabababbababaabbbaabaabbbaabbbabbbbabbabbbaabbbbbabbbbabbabababbbbaaababbabbababbababaaaababaaabaabbaababbaabbabbbaaaaaaaaabaaaaabababaaabaaaaababaaaabbabbbababbbabaaabbabababbbbabbababbabbaaabbaaabbbababbabbbababaaabbaababbabbaabbbabbaabaaabbabaabbaaaababbaabbbaaaabbbabbababbaabbaabbbaababaababaababaabbabbbbabbbabbabaaabababaabbbbabbbabbbaabbaaabaaabbabaababaabaaaaaabaabaaaaaabbabbbaaaabbbbbaabaaabaabbabbbbbababbbabbaaabbbbbabbbaabaaaaabbbabbaababbaabbbbbaaaaaaababbabbbabbaabaabaabbbbaaaaabbbabbabbabbbbaaaabbbababbbabbabaabbbbaaaababababaabaaabbabbbbbbbbbabaaabaaabaabbbbabbabaabbabbbbbaaabbbabbabbabaaaaababbabaabbabbabbabaabaaaabbaabababbbbbbbababbabaaaaaabbbbaababbababbbbbbaaaababbbbabbbbabaabaabbbaaabbbbbbbaaaaaaabbbabbaaaaababbbbbababbaabbababbaababbbbbababaaaabbaaaaaaaabaabbbabababababaabbbbaabbabbabaabaabaaababaaabbabbababbbbaabbbbbaabbbabbbbbaabababbaabbbaaaaaaababaabaabbabaababbbbaabbaababbbbbbaababbabbbababaaababbabbbaaaaabbbbababababababaaaabbaabbaaaaaaabbaaaabababaaabaabaabababaaaabbbaaabbababbaabbbabbababbabbaaaaaabaababaababaaabbabbababababbbbbbabbbabaaaabbabbbbaabaaaaabbbaaababaabaaaabbbbbaaaaababbbaaaabbbbbaaaabaabaaababbaaabbbbaabbababbbababaaaaaaaaaaabbaabbbabbbabbabbbbabbbbabbbabaaaaaababbaabababbbabbaababaabaababbbaaaaabbbaaabbbbaaaabaaaaabbbaaabbbbbabaaababbbbbbbbbaaababbabbabbababaaabaaaababbbbbbaabaabaaabaabbabaabbabababbbabbabbbaaababbababbaabbaabbbbbaaababbaabbbbbabbaaabababaabaaaababbabaaabbbaaabbabbbabababbaababaaaabbbbabbbbababbaabbaabababaababaaabbaaabaabbaaaaaaabaaaabaabbbbaabaabababbbaabaabaabbbaaabbbaaaaabaaababbbabbaabbbabbbababaabbabbbaababbabbabbbaaabaabaaaabaabaaababaabbaaabaabaaaabaaabbbabbbbbabbababbbbbabababbabbaaaabaaabbaaaaababaabbbbabbbaaabbaaaabbaaababaababbbbbabbabbabbabaaabaaaabbababababbaaabbaabaaaabaabaaabbaabbaababbbbbabababbbaaabbabbbbbbbaaaaaaabbbbbbabbbabbbbaaabbbaababababababbaabaaabbaabaaabbaaabbaababaababbbbabbaaaaabbaabbaaaaaabbbbaaaaabaabababaaaabaababbbaabaaaabaaababbabababaababaabababbaaabbaababaabbaabbbbbbbabbabaabbabbbaabaabaaaaaabbabbbbaabaabaabbaabbbbabbbbaabaababbabbbaaaabaabbbbbbaaaabbaaaaabbbaabbbbbaaaaabbbabaabbbabababbaaabbabaaabbaaaaabaabaabbaaabbaaaababaabaabbbabababbbbaabababaaaaababbbaaaaaabbaaabbbaaaaabbbbabaaaaabababaababbbbaaaabaaaaabaaabaabbaaaabababbabaabaaaaaaabbaaabbaaaabbbaaabbababbbabbbbabbabbbbbbbbaababaabbbaababbbbbabababaaabbaababbbabbabaabbbbbbbaaabababbbbbaabbbaaaaaabbbaabababaaababaaababaabaabbabaaaabbbabbaaaaabaaaaaababaabbbbbababbabbbbbbaaaabbbabbbbaaababaaabaaabbbbbbbbbbbbbbbaabbbaabbaaabbbbaaabbbaabbabbaaabaabbbababbabbaaaaaabaabababaabbbbabbbbbbbbabababbabbbbaaaaaaaaabbaaabaaabaabababbaaaaabbaababbabbbbaababbbaaaabbabaaabbaabbbababababbbbababbbaabbaaabbbbabbbaaabaababaababaaaaabababbbbbaabbaaabababbabbbabbbababbabbaaaabbaaaaaaaaababbabbababbaabbaaaaabbabbbaabbbbaaaabaaabbaaabbaabaabbbbbaaaaaabaaaaaabbbaaaabbbbbabababbbababbaabbababbbaabaabbaababaaabaaaabbbabbabaaabbaaababaabbabbbaabbbbbaabbabaaaabbabaabaabbabbabaababbababbaaabbabbbbbbbabbbbbbbaabbbaaaabbbaaababaabbbaababababbbababaabaabbabaaababaabbaaaaaaababaabbbabababbabbabbababbaababaabbbabaaaabbabbbbabaabaabbaabbaaababbabaababbababaabaabaaaabbbaaaabbbbababbabbbbabbabbaaaaaababaaabbabbbaabbbbabababbbbabbaaaaaaabaabaaababaabbbbbbabbaaababbbaaaabaabbaabaaaaababaaabababababbaabbbbbbbababaaaaabbaabbbbababaaaabbbbabaaababababbbbaaabbaabaababaaaaabbabababaabababaabaaaabbaaabbbbbaabaaabaaaabaaabaaaaaaaaaaababbaababaabbbaaabaabababbabaabbbbababbaaaaababaaaabaabbabbababbbbbaaaaababbbbbbabababababaababababababbabbbaabaaaaaaaabbaaaaaabababaabbabaaaabbbaaaabaabbbaabbbbbbaaaabbbaaaabababbbaababbbbabbabbbaabaaaaabbbbabaaabaaaaababbbaaaabaaabbbbbabbbaaabbababbbbbbbbbababbbababbaabbbabbabbabaaabbaaabbbabbaabbabbbbbbababbbbbababbbbaaaabaabbaaaaaaabababbbaababaabbaaaaababbbabbbababaababbbbaaaaabbbbbbaaabaabbbabaaabbaaaabbbabaaabbbbababbbabbbbaaaabbbbbabababaabaaaabbbabbaaababaabbaabaaabaabbaaababbbaabbbbaaabaabbbaaabababbbababbaababbbbabaababaaabbabaababbbbbabaaaabbbbabaabbbabbbbbbababbababaaababaabbbabbabbbbbaaaabbabbbbbabaabbabababbbaabaaabbbbbaababbabaaabababbbbabababaabbbaababaaabaabababaabbbaaabaabbabbabbbbaabaaabaabaabbbbbaaabbbaaaabbababaabababbbaaaababbbbaabaaaabbaabbabbaababaaaaaabbababbbbabaaaaabaaaaaabaaaababbaabbbaabbbbbabbabaabbaabaaabbbaaababaabaabbbaababbaabbaabbbbbbbbbbbbbaaaabbbaaabbabaaaababaabaababababaaabbabbaaaaabbbabbaaaabbbbbabbaabaabbbabbbabbbabaaaabaaaaaababbbbbbbabbaabbabbababaabbabbaaaabbaabbbbabbbababaaababbbabbbbbbababbabaabbbaaaaabaaabaababbbabbabbbaaabbaababbaababaaabaabbbbbbbaaaaaabaaaaaaaabaabbbbbababaabbaaabbbbbbabbabaaabababbaabbaababbaaaabaaaabababaabbaaaabbabbabbabaaaaabbbbaaaababbbabbbaabaaabaaabbbaabbbbaaaabbbabaabbabababaababbbaabaababbaaababbaaabbabababbaaabaaababababaaabbaabbbaaabaababbaaaaaaaaabaabaabbbbbaaaabaabbbaaabaaabaaabbbbbababbaabaababbbabbbbbbaabaabaabbaaabbbababbaabbaaaabbbbabaabbabbababbaaabbaaabbaabbbabbbaaaabbaabbabbaababbbbabaaabbbabababaaaaababbaaaaaabbbbaaaabbabbbabbbaabaabbbbbbaababbbabaaaabaaabbaababaabaaabbbbabaaabbbaabaaabbabbaaaaabbbaaaaaabbabaababababaaabbbbabbabbabbaabbbaaaaabaaaabaaababbbbbbabbaaabbaaaaaaaabababbbbabbabaabbabbbbbbbbbbbaaaabbbbbbbbabaaababbababbababbbbaabbbabbabbbbbbbbbaababaaaabaaababbbababbbababbbabaababbabaabbabaababbbbaabbbbbbaababbbbaabbaaaaaabbaaaababbabababababbbbaaaabaabbaaaaaabaaabaaaaaabaababbbaaababbbaabbbbabbabbabaaaababaaababaaabbaababbaabbbbabbabaabbabbbabaabbaabaaababaaaabaaaaaaabbbbbaabaaabaaabababbbabaababababbbabbbbabbbabbbaaabbbbbaabbabaababbabbaababaabbaaabbababbababbbbbbaabbabaabbabbabaabbaabaabaaaababababaaaaabababaabababbaaabbbaaabbabbababaabbabbababbabbbbaabaabababbabaaaaabbbbbbaaababbaaababaaabbaabbaabbabbbbbaabbaaaabbbbaababbaabbbbbbaabaaabaaabbbabaaaaaabbbaaaaababbaaaabaabbbaaaabababbbabaaabbbbbaaaabbaaaabbabaababaaabbabbbbaabbbbbaaaabbababbabaaaabbaabaabaaababaaaaaaaaababbaabaabbabababaabbabaabaabaabbbababbaaaaaabbbabaaaaaabbbbaaaabbaaabbaaaabaaabbbbbaababaaaaaaaabbaaaaaabbbbaaabbabbaabbbabbaababbaabbbbaabaabaabbaabbaababaaaaabbaaaabaabaababbbabaaababbbbbabbbbabaaaaaaabbababbabbbababaaaaabbaabbbabbbababaabaaabbaabbaaabbbbababbaabbabbaaaaabbbaaabbaaabaabaababaaaaaabbbabbbaabbbbaaaaaabbaababbaabaabbababaabbbbaabaabbaaabbaabbbaaaabaaabababababbbabaabbbbbbabbabaabaaaabbababbbbababbbabbaaababbaaababaaabbbaaaaaaaaaabaabbbbabbbaabbbabaababaabbbbabbabaaaabbbabbaabbbbaaabbabbbbababbbbabaabaabaaababbaaaabaabbabbababbbabaababbbbaabababaaaabbbabbaaaaaaababaaabbabaaabbbabbbbbaaaaaabbbbbbbbaaababaaabbaaabbbbbabbbbbbbbabaaaaaaaabbbababbaabaaaaababbbbabaababbbbbabbaaaaabaabbbaaaaabaababbbbbaaaaaabbaaaababaabaaaaababbaabaaabbbaaaaababbaaabaababbabbaaabaabaaaabbbbaaaaaabbbbbbaaabababaaaabbbaabbbbbbaaababaababaaabababbabbabaabbbaabbbaaaaabbaaabbabaaabbabbbbbbbabbaabaaababbabbbbbbaabaabaabbaabbaabaaabbbaaaabbbbababbbabaaaaaabbbbababbbbbabbababaabaaabaabaaababbabaaaabbababbaababbaabbaabababaababbaaaabaaabaabbabbaaabbbaababaaaaababbbbabbbbbbbbbbabbbbaabbabababababaaaaabbabbabababbababbababaaabbaababaabababaaaaaabaabbbaabbaaabbbbabababaabbabbaabbabbbbaaaaabaababaabbbaaaabbbbbbabaabbbbaaaaaabbbaaaabbabbbaabbaaababaabbaabbababbaabbbbababaaaabbababababbaaabbbabababaababaabaaabaaaaabaabbabbaaabbaabaabaaababaaababaaaaabbaaaaababaaabbbaaaaababbbababaaaabbaabbbaaaaababaabbbbbbbbbabaaaaabaabaabbbaabaabaaababbbbaababbaaaaababbbbbbababaaabbbabbabaaabbaaabbaaaabbbabbbbbbbaaabbaabbbabbabbbbbababbabbabbabbbaaababaaaaabaabbbbbaaabbbaabbaaaaaabaabaaaaaaaabbaabaaabbabbbbbbbabbaababbaababbababbbabbbbbbaabbababaaaaaaabbbaaabaaaaabaababbaabaaabbbaaaaabbaaaaaabbbabaabbabbbbbabbabbbababbaabbbabbbbaaaabbaababbbbaabbababaaaabaabbaaaaabbbbaabaaaaaaabaabbababbaabbbbaabbbbabababbbabbabaababbaabbabbababaaaaabbabbabaababaabbbbbababbaabbaaabbaaabbbbaabaababaaabaaaaabaabbabbbbbbbababbaaaabaaaabababaaaabbbbbabbabbababbababbaababbabaaabbbbbbaaaaababababaabaabbbbababbabbbaaaabbabbaaababbbabbbbabaaabbbbbbaaabbaababaaabaaabaababbabababbabaaaababbaaaabababaaabbaababbabbaaababbbbabbababaabaabbaabbaabbbbbaaaaabbbaaabaaaabaaaabaababaabbabbbaaaaaaaaaaabaaaaaabaababbaabaaaabababbabaabbbbbababbaabbaababbaabbaaaababbaabaabbaabbaabbaaabbaabaabbabababbabababababaaaabaaaaabbaaabaabbabbaaaaaababbbaaaabaabaabbbabaaabbbaaaaababbbaaaababbaabbabaaabbbbaabaabaabaababaaaaaabaaabbabbbababbabaababaabababbbbaaaababaabaabaaababababaabbaaababbbababaabbababaaaaabbabbbaaaabbababaabbabaabbbbbaabababbaabbbaabbaabaabbaabbababaaababaabaabbabbbaabbaabbbbababaaaabbababbaaaaababbaabbabbaaabaabbbaaaabbaaaabbaabbabbabbaaaabbbababbaaaabbbbbabaabaabababababbbbaabbbbbbbbaaababaabbbaabaaabaabbbbbabbaaaaaaaabbbaabababbbbbbbbabbababaabaabbbbbabbabbabaaabbaaaabbaaaaaaababbbbbbbbaabbbbaaabbbbaababababaaaaabbabbaabbaaabbaabbabbbabababbabaaaaaababbabbabbabaaaaababaaabaaabbaaabababbaaabababbbbbaabbaaaabababbabbbbbbabbbbaabbbaaaaaaaabbbabaababbaabbaabaaabbbbbaabbbbbaabaaabababbbbaabbbaababbababbbaaaababbaaaaabbababababbabbbbbabbbabbbabaaaabaababbbabbababbbbabaaaabbabbbababaabaabaaaabbaaababaabbbbababbaabaaaabbbabbababaaabbaabaabaaaaaabababbabbbaaabbaababbbbabababbbaabbbaabbbaaabbabbbbabaaabbaaabaaaaaabaabbababbbbbababbabbbababbaaabbaaababaababbbbabbaabbbbaabaaabbbabaaabbbbbbbaaaabbbbaababababbabbbaaaaaaaabaabbbababaaabaabbaabaababbaaabababbaaabbbaaabababbbbaabaabbbbababaababbaababbbbbabbbbbbabbbabaaaababababaaaababaaabbababbbaaaabaaaabbbbabbaaabbababaabbaabbbbbababaaaabbbabbabaaabbbabbababababbabbabbaabaaaaaabbaabbbbaabbabaababaaabbaabababbaaaabbbaabaaabaaabaabbbabaaaaababbaaaaabbaabbabaabbabbbabaababbababbaaababbaabbbbababbaaababbbbaaaaaaabbbababaababaababaabbaaabaaaabaaabbbababaabbbaaabbbbbabbaababababaaababaaaaabbaabbaaabaabaaaabaabbbaaabbbaabbaaabbabaabbaababaababaabbbabaaaabbaaaaaababbaaaabbaaaabbaaaaaaaaaabbbaababaaabbbababaabababbababbabaababbaaabbbbabbabaaabaabaaaabbbbbaababbababbaaaaabaaaabbabbbbbabbababaaaabbbabbbbbbabaaaaababbaabbbaaabbabbbbaababbaabaabaaaabababababbabaabbabbaabaaaaaaabaabaaaaababbaaabababababbabaabbabbabaaaabbbabbababaaababababbbababaaaaabbabbbaaabbbbbaabaaabaaaaabbabaababaabaaabbaabbbabbabaaabbabbaaaabbbbbbbababaabbabbbbaaabaababbbbbababaaaaabbaaaaabaabaabbaaabaababbbaabbaaaabbbaaaaaabbbbabaaababbabaabbbabaabbabbaaaababbbbabaaaabaaabbbbaabbaaaaaabbabaaaaaabbababaaabaaababbbabaaaabbbaaaabbbbabbabbabbbabbaaaababababbbabbbbbbaababbbabbaabbbbabbabbababbbaabbaabbbbbaaababbbbbbababbabbabaabababaabbaabbbabbbbbaaaabaaabbbbaaabbbbabbaaabbabaabaaababbbbaaaabbabbbaababbbbababbaabaaababaaaaabababbabaaaaabaabaabababbaabababbaaaabbbabbabaababbaaaaabbabbaabbbabbabbbbaabbbaaaaabaababbbabbbbbabbabbabbaabbbbbabaabbaaaaabbabbabbbaababaaabbbbbbbbabaababbaaaaababaaabaabababbbabababbabaabbbaabbbbabbabaabbbbbaaabbbbaabbabbabaabababbbababbaabbbbaaabbabbaaababaabaaaaaabaaabaaabbbabbbaaababbaaabaaabaabaaabbbbbaabaaabbaaabbaaaabaabbaabbaababbbbabbaabbbbabbabbbabbbabbbbbbaabaaaaaabaaaabbbabaabbbaabbbaaabbaaaabababaabababbbbababbbbbbaaaabbbbbaaaabababbbbaabbbabbbbaaaababaaabbaababababaaabbbbaaaaabaaabaaababbaabbaabbaaaaaabaaabbabaaaabbbbbbabbbbaaaabbbbabbaaaababbaaabbbbbbbabbbabbabbbbbabbaabbbabbbabbbababbbbababaabbbaaabbaababbaaaabbabbbbaaaaabbabaaaaabaababbabaaabaaaaaababbbaabaabbbbbbbbbbbbaababbabaaaaabaaaaaabaabaaaaaaaababbaabbaabbbaabaabababbabaababbbbaaabbaabbabbaaabaababbabbbbaabaabbababaaababbabaabbbabbaaabbbaababaaaaaaabbbbbaababbbabbabbbbabbaaababbbbaaaaabaabbaaaabaababbbbaabbaaabbabaabaaaabbbaaabbbabbbbbaaabaaaaabbaabaaabbbabaaababbbbabaabbbbbaabbaabbabbabbbbaaabbababbbsaaabbbabbabaaaabbaababbbaabbabbaabaabababbbabababbbabaabbbaaaaabaaaaaaabbbabaaababbbbaaaabaabbbaabaaabbbaabababaaabbaabbabbaaabbbabbbbaabbabbaaabaababaabbaababaabbbbabaaaaaabbababbaabaaabbbaaabbabbaabbaabaaabbabaababbbaabbbaabaabbbabbaabbaabbaaabaabbaabbabbaabbbababbabbabbbbbaaaaabbaabbaabababaabbbbbbaaaabaaababbbbabbaaabbabbaaabbbbbabbababbbbbbaabbbbabbaaabababaaababbaabbbabaaaabbaaaabbaabbbbbaaabbbbaaaababbbbbababbaabaaababbabababbbaabbabaababaabbaabbaaabaabbbabbaaaabababbbbaaabbbbaaaaabbaaaabbabbbbbbaabaaababaaabbbbabaaaabababbbbbbababbaabbababbababaabaaaabbabaaabaaaabbabbabaaabbabbaababaaabbbbabababbabbbabbaabbaababbaaabbababbabababaaaaabaabbaaababbaaaaaabaabaaabaaabaabbbbbbaaabbaababbabaabaabbbababaabbabbbaabbbbbbabbbaaaaaabaababbbabaaaabaabaabbaabbbbbbbaaaabaaabbbbbaabbbbaabaaaaaabbaaabaabaabaaaabbbbbabaababbbbbabaaaabaabaaabaabbbaabbabbbaaaaabbbbababbaabbbaabbbaabaababbaaaabbbabbbbaaabbabbababaaaaabaaaabbbabbbbabaaabbbababbbbabbaaaaababaaaaababbaaaaababbabbabaaabbaabbabaaabbaabaaaaaaaabaaaabbabbbbaaaaabaaaababbabaaaabaababbaaabbbbababaaaaabbaabbaababbaaaabbbaabaaaabaabbababbbbabbbbaaabbaaaaaaabababaabaabaaabbbabaaaabbabaabbaabbaabbabaababbaaaabbbbaabbabbbbaabbbaaababaaaabbaaababbaabaaaaaabbbababbbbabbaaaaaaabaaababbbbbabaababaabbaaababaaaaabbababbbabbaaaaababbbbbaaababbabbababbbaaaaaaaabbbbaabababaaaabbbbaabaaaabbaabaabaabbbbbaaabbbaabaaaaabbbbbabaaaaabbabaabbaaaabbaaababbabababaaabbababbbbabbbaaababaaaaababbabbbbbabababaabbaabbaabbabbabaabbababbbbbabbbbbaabbbbaaabaaabbabbbabaababaaabaababababaaaabaabaabbaaaaaabbababaababbbbaaaababbaaaabbababbaaaababababbbbaaaabbbbaabaaabbbbaababbaabbbbbbbbbbaabbabbaaaabbbbbabaabaaaabbabaabbbbabbaaabaaababababbabaabaaaabbabbbbbbaaaabbaaaabbaaaabbaabbbabbbbaabaabbabbbbbabbaaabbaabababbaabaaaabbbaaaabaabbbbbaaabbbbbabbaaaabbabaaaaaaaaaaaabbbbabbbbbbaabbbbababaababaabbbbbabbaabbbbbabaaaaabbababbbbaaabaabbababaabaabaabbbbbaabaaaaabaaaaabbbbbbbbbbaaabaabaaabbbabaababaabbabaababaabaaabbbabbbbbbaabbabbbbbbbbabaaabbabbbabaabababbaaabaaabaabaaabaabaababbbabaaababbaaabbaabbaabaabbabaababaabaabababbabbabbaaaabaaabbaababbababbbbabbaaaabbbbbbabbbabbbabbbbaabbbaabbabaababaabbababbababaaaaabbbbaaabbbbbbababababababbbbabaababababaabbabaaabaabababaaabaaaaabbbaaaabbabaaaabaaaaaaaaaaaaabbaabbbbabaaaaaaaaaabbabbaaaabbaababaabbbababbbbbaabbbbaabaaabbbbabaaabbbbbabbbabaaababbabababbbbaabaababbaaabbbbabbaaaabaabbbbababaabaabbabababbbaaaaaabababbbaababbabbbaababbaababbbababaaababbbbabaaabbaaaabbaabbbbabbaaababaaabaaaaababbabbbbaabababaabababbbbabaaabbabbbaabaabbbbaabaaaaababbbababaabababbababbaaaabbaaabbbaababbaababbabbbbbbbaabbbbbbabbbbaabbbaaabbabaaaabababaabbababbbbbabababbaaabbabbbbabaaabbbaaaababbbbabbbbaaaabbaaaaabaabbaabaaabbabbabbaabaaaabbabaaababbaaaaabbabaaabaabaaabbabaabbbaaaabaabbbbaabababaaaabbababaaabaaaaabbbababbbaababbaabbabaaabbaaaabbabbbabbaaabbbaaababbbbababbaaaaaaababbaaaabbaaaaaaabaabbaababaaaabbabaabbabbaabaabbaaaabaabbabababaabbbabbababbbabbbaabaabbbbbbabbbaababbababbbaaaabbababbbbabbabbababaabaaabbbabbbbaaababbabaaabbbaababaaaabbbbbaabaabbbbbbaaaabbabbbabbbabbababbbabbbbaabaaaabaabbbabbbabbbaabaaaaabbabaababaabbbbabbbbbbabbababaabaabbaabaabbaabbbbabbbaabababbbaababaaabbaaaabaababbbabaaaabbaaabbaabaaabbaabbabbaabbbbbaaaabbababbababbabbbaaabbabababbabbababaabbabbbabbbaaabbbabaaaaaabaabbbaaabbaabbababababbaabaaaabaabbbaabbaaaaaababbbaabaaaaababaaaaaababaabbaaaaaaaababbbbbaabaabaaaaaaabaaabaabaababaabbbbababbaabbabbaabbaabbaaabababbbbbaabaaabbbabbbbabbbbbbbabbabaababaaaaabbaababaaaabbbbabaaababbbbbbaaaabbbbbaaabbbabbaababaaabababbabbabaabaababbabababbbaaabbaababbbbabaababbbaabbbabbababbaabbabbbbabaabaaaaababaabbbabaababbbaabaabbaaabbbaaaaaaaaabaabbbabbbabaabaaaaaaaaabaaabbaaabababbaabaaaababbabaaaaabbbbbbbabbaaaaabbabbababbbababbbbaaababbabaababaabbaaaabbabbabbbabbbabaabbaabbbaaaababbbaaaaaabbaaabbbbbbbbbbabbaabaaaabbaaabbaabbaabbbabaabaababbbabbbaabbaabbaababbbbbabaaabaababbaababbaababbaababababaaaabbaaaaaababbabaabbbbbbbabbbaababbababaaabaabbaaaaaabaabaabbbababaaabaaaabaaaaabaababababaaabaabbababbaabaabaababbaaaaabaaaabbbabbabbaabaabbbaaababbabaabaaaaaabababaabaaabbababbabbbaaabbabababababababbbaaaaabbbbabaaabbbbbaababababbbbbaababbaaabbbbabbbbabbaabaababbaaaababaabaabaaaabbbbaabbbababbabbbbaabaababbaaabaaabbbbbbbaaaaaababaaabbbabaaaabbabbabbbabaabbaaaabbaaaaabbaaabbbaabbaabbaaabbaababbbbababaaaabbaaaaabbbaaaabaababbbbabbbaabbaababbababbaabbbbbbbbbbbaaaababbbaaabbabbaabbaaabbbaabaabbabaababbaabbabaaaabaabbbabbbaabbaabaaaabaabbbaaabbbbababbabbbbbababaaaabbbabbbaabbbabaaababaaababaaaababbaaaabbabbbaaabaaaabbabbabababababbbbabaaaabbababbaaaaabbbbbaaabbbabbaabbaabbabaaaabbababbaabbbaabaaaabababbbbbaababbbbbbabaaabaabababbbbbbbaabaaabaaaabbbbabaabbbbbbaaabbbaaaabbbbbbbaaaabbaabbababbaabaaaaababaabaaaabaabaaaaaaaabaaaabbaabaabbabbbbabbbaababaaaabbbaabbbbbbabbbbbbabbbaaabbbbbbabaabababbbabbaaabbbbababbbabbabbaabbabbababbaabbabaaaaababbaabaaabaaabbababbbbaaaaaaabbbababbaabbaaabaaaabbbbbaaabbabbabaaaabaabbabaabbbbabaabbbababbabaaabbbaaabaaaaaabbabbbaabbaaababbaaaaaaaaabbbbabbbbbababaaaaabaabbbbbaaaabbaabbaaabbbbbbbababbbabbaaabaaaabbbbaaabbbbababbabbabaaabbabbbbababaaabaabbaababbababaabbbbbbaaaabbbbbbaabaaaaaaaabbaaabbabbbababaabaaababbbbbaabababaaaaababbabaaaaaaabbabbaaababbbbbabaaabbbaaaaabbbaabbbbabaabbabbabbabbaabbaaabbbbaabbbbabaaababbabbababbabbabbabaaababababbbabbbbbaaaaaababbababbbaababaabbbabbbabbaaabbabbababaabbbbabbababbbaaababbbaaaaaabaabbbbbbbbaaaabaabbbabaababbbbababbbaaabbbaabbbabbbababaabaaababbbabaaabbbabaabbbababaababaaabbbbbaabbbabbaabbabaaabbaaaaababababbbabbbbbbbaaababaabaaaabbababbabbbbabbabbbaaaabbaababbaabbabaababbaaabbababaabbbabbbabbbbaabaaaaabbaababaaaaaabbbabaaabbaaaabaabaaabbbbabbbaaaabaabaabaaaababbaabbbabbaaabbaaaabbabaaabbababababaabbaaaaaaabaabababbbbaabababbbbbbbbbaabbbbbbbababaaababbbaabaabaabaababaaaaaabbbbbabaabbaabaabbbbbbbbaabbabbbbbbbbabbaaaaabbbbbbaababaaabbbbaabaaababbbabaaababaabaababbbbabbaabababaabababaabbabbbbaabbbbaabaabaaabbaaabaaabaabbaaabbaabbaaabbabbabbbbbaabbaaabbbababbabbaabbabbbaabbaaabaabababbbbabaaabaababaabbaaaabbaaaaaabbabbaaababaabbbbbbabbbbbbbabbababbabbbbaaabaaaabbabbbaabbbbaaabbaaabbabbaaaabaabbbaaabbabbaabbaaabaaababababaababbbbabaaaaababbaaaaabaabbaabbababbbbbabaaabbabbabbbbbbbbbbbbababaaaabbaababbaaabaaabbabaaabbbbbbbbabaabbaababaaaaaabbbabaabbbaaaabaaaabaabababbaaababbbbaaaabaaaabbabaabbbbabbbbbaabbaababbbaabbaaaabbaababaaabbbaaaababaabbbabaaababbbbaaababbaababbabbbbabaaababaababbaabaabaabababaabaaaaaabbabbbbbaabbbbaabababaaabaabbabbbabbbabaaababaababbaabababaababbbaabaaabbaabaaabbbbabbabababbbbbababaabbbbaaababaabbababbaaaabaabaabaabaabaababbbabbabbabbbbbababbbababbbabaabbaaaabbabaabaababaaaabbbaabababaaaaabbaaababbbbaaaaaaabbbaaaaababbaabbabbaabbbbbbaabbbbbaaabbaaabbbbbabaaaaabbbbbbabaababbbbbababaabbbabbaabaabbbbbababbbaababaabbababbabbabaabbabababbbbabababaaababaaababababaaabaabbbaabaabaaaabbabbbababababbbabbbabbbaaababbbaaaaaababbbaaabaababbbbbabbbaabbbbbbabbbaaaaaababbbbbbbaaababaaabaabbbbbbabbbbbabbbbaaababaaaaaababbabbbaaaabababaabaabbbabbbaaabbbbbbaaababaaabbabbaabaabaabbabaabababaabbbabbaabbaababbbbbaabaaaabbaaabbaabaaaaabaabbbabbbbababaababababaabaabbabababbbaaabbbbaaababaaabaaaaabbbbbaaaababaabbbaaaabaaaaababbababbabbabababbbbabbaaababbbaabaababaaabbaaaabbbaabbaaabbbbbbaabbabaaabaabaabbabbbbabbbbaabababbbaaababaaabbaaabbbbaabaabababaaabaabbabbbbbaabaaabaabbaabaabbaaaabbabbbaaaabaabbababaabaaabbbbbbbbbbaaababbaabbbbaabaaaabaaaabbbababbbabbabbaaaaaabbbabaabaabbababbabbaabbabbbbbaaababbababababbaaabbbbbbbbabababbbabbbbbbbbbaabaabaaabbbabbbbaabbbabbabbbaaaaaaaabbabababbaaabaaabbaaababbabbbbbaaabaaaababbbaabaaaaaaabaaabbbbabbabbbababbaabbbbbbbbbaababaaabbabaababaaaabbaabbbababbaabbbaabaaaaaaaaabbbaabaabbbbaaaabbbababbbbbaabaabaaabbbabbaaabaabaaabaababbbbabbbbaabababaabababaaabaabbbbaaabaabbbbaaaaabbaaababbbbbabbaabaabbaabaaababbabaabaaababbbbbbaabbbabbabbbbaabbbabbbbbaabbbabbaababbaabbbbbbbbbbabaaabbbaaaabbbaaaabaaaabaaabaaaaaabaaabababbbbbbaabbaaabbabbbabaababbbaaaabbbbaaaaaaabbbabababbaabaabaabbababbaaaabababbabbbababbbaabbababbabaaaabbbaaaaabbbabbbbabaaaabaaaaaabababbabaabbbbbaaabbbbbbabbabaaaaababbbababaabbbaabaaaababaabbaabababbaaaaaabbbbbbaaaabaaabaabbaaaaaabbbbaabbabaabababbaaabbbaabaaabbaaaaababaaaabbbbaaababbbbaaabbabababbaabaabbbbbbbbababaabbabbbbaaababaabbbbabababaabbbbbaababbbaaaaaabbababbaaaabbbabababbababbaaaabaaababbbbabbbaabaaaaaaaabbabaabbabbabaaababbbaabbbbbbbaabaaaaaabbbaabbabbaabbaaaabbabbbbbbabbbbaaabaaabaabbbaaaababbabbbabbababbbbbababbbaabbbbaaabbaaaababbaabbaabbbbababbbbaabbabbabbabababbbabaaaaabababaabaaaabaabaaabbbbabbabaaababaabbaaaabaababbbaabbaabbabbaabbabbabababbabbaaaabaabbbabbaabbbbaaaabbbbaabababbbabababbabaababbbaabababaabbbbabaaabbabaaabaababbbbabaaabaabbbbaaaabbaabbabaaabaaaaaabbabbabbababaaabbaabbbabbbabaabbbaaababbabababaabaabbbbabbabbbbaaaababbabbaaaabbaababbbabaaaabbabbabbbbababaababaababbbabbaaaaaababbababbbbabaabbabbaaabbaabaabaababbaaaabaaaaaabaababbaabaaaaabababbbaaaabaabbbababbabaabbabbbabbbbaaabaabaaababaaababbbbbabbbabaababaababbbbabaabaaaabaaaabbaaabababbbabababbbaaaabababbaaabbaabaabbbbabbabaaaabaabababababbaaabbaaabbababbababbbbbbaaaabaaababbabababbabaaabaaaaaababbabaaaabbaaaaababbaababbbaaaababbbabaaababbaaaaaaaabbbbabaabbbabaaababbbaaabbbabbbaaaaaabbabbbaaababbbbbbaababaababbbaabbabbabbaaaaabbabaaaaaabaabababababaabbabbaaabaaaabaaaaaabababbabbbbbbaaaabababaabbaabbbbabbabaaaabbabaaaabbbabaaabbaaaaaababbaaabaaabbbbabaaaababaaabaaaaaaaabbabababaabaabbabaaaaaabbbaababaababbabbabbaabbaaaabaaaaaaabbbabbbabaabaabbbaaabababbbbaabbabbbabaaaaabbabbbbaaaabbaaabbbaaabbaababaabaaaababbabbabaabbabbbbbbaabbabbabaabaababbbbbbaabbbaaaaabbabbaaaabbaaaaaaaabaaaabbbaaaaabbabbbabaabbababaabaabbbabbbaabbbbabbaababbaababaabbaabaabbabbbbbbabbaaabaabababaabbbbaabbbbaababbabaabbabbbaabbababbbaabbbababaabaabbbbaaababababbbbabbabbabaaababbabaabbbbbaaabbbbbababaaabbaaaaabbbabaabbbababbababaaaaabbaabbaabbaaaabaabbabbaababaabbaabaabbbbabbbbaababbabbaaaaaabbabbbbaaabbbbbbaabbbbbbabaaabbaababbbbbaabbaaabbababaaabbaaaaabbbbaabbbbabbaabaababbaabababababbbbabaabbbabaaababbbbbbaaabbbababaaabaabbbabbaabbbbbbaabbabaaababababaabbbaabbbaababbaaaaaabbbbbaaabbaaaabbabbaaaabababbbbabbaabaababababaaabbbabaaababaabbbbbbbaabaabbabbbbabbaaaaabbbabaabbbaabbbaaaabbaaababbbabbaabbaabbabaabbabbabbbbbabababbaabbabbbbbbbbabaaaabababaabbbaaabbbbabaaababbabaababbabbaaaabbbbbabababaabbaaababbbabbbbabbabbaabbbaababbaabbbbabbaaaaabaabbbaaaaababbbababbaabbbbabbbababbbaaaabaaaaaabbbaaaaaabababaabaaabbaabbbbbababaababaaaaaaabbaaabbbaaaabbbaaabaaabaaabbbbaabaaabbabaabaabbbabbbabbabbabbbabababbababababbabbabaabbbbbbabbabbaaaababbabbbabaaaaabbbabaaaababaaaaaabaabaaabbbabaaaaabaabbbababbbaabbaabbaabaabbbbabbabbbaaabaabbbbabbbaabaabbbaabbbaaaabbbbabbbbbabbbbababaaababababbaabbbbaabbbbabbababaaaaabbbbbabbaabbaabaabaabbbbbabaabbaabaaabaabbabbaababaaabbbbbabbbaababbbabbbbbabbaaaaabaabaaaababbbabbbaabbabaabbbabaabbabbbaaaaaabaabbbbbaabbbbababbbbabaaabaababaaaaababbaaaaabbbaaabbaaabaabaaabbaaabbabbbaaabaababaaaababaababbaabbbbaabaaabaaababbbaaaabaaabbaabbbaabbbbbbaaaababaabaaabbabbbaaaabaabababbbabbbbababaabaabaababbababbbbaaaaabaaabbbbbbaabbbbabaabbbaabaaabaaababaaaabbbbaabaaababbaaababaaababaababbbaabaabaabbaaaabababbbaaaabaabbbabbaabaaaaaaaaaababaaababbbbbaaabaabbbbaababaababbbaabbaabbaaabbabaabbbabbaabbbbababaaabbababbaabbaaabaaabbaababbabbbbabaaaaaabbbbbabbbaaababaabbbababababaaaabbbabaaabaaaabbbaabbabbabbabbbabaabbbbbabaabaaabaabbbbabbbabbabbababbbaabbbbbbabaaaaaaabbbbabababaaabbababaaaababaaabaaaabbaaaabbbbbbbbabbabababbabaaaabaaaabbabaabaaabbbaaabbababaabababaababaabaaaaabbbbbbbbbabbabababaabaaaaaaaaaaabaabaabbabbabaabaaabbbbbaabbabbabaabbbaaaabbbbabbbbbbabbabaaababbbbaabbababbaaabaabbbabbbbbaaaababbbbaaaaababaabbbbabaaabbabaabbabaaaaabbbbabababbaababaabbbbbabbababbabbaaaabaabbbbbabbbaabaaaabbbbbbbbabbababbbbabaabbbbbaabaababbbbbbabababababbbabaabaabbaabbabbbabaaaabbabbbaabbbaaabbbabbabbabbbbaabbababaaaababbbbbbbbabbbbbabbbabbaabbababbabababbbbabbabbbaaababbabaaaabbbbbaabbaabaaababbbbbbbbababbabaabbbbbababbbbbbabaabbbababbabbbbabaabbaaaaababbaaabaaaaabaabbbbaabbbbababbaaaaaababaababaaabbbaabbabbaaababbaaaaababbbbaaababaaabbabaaabbbbbabaaababaaabbaabbababaaaabbbabbbaabaabababbabbaaaaaaaababbbabababbbbaaaabbabbababaaaababbaaaaaabbabbbbbbbbbbabababbbaabbbbaaaababababababbbaabbabbbaaabbaabbbbaaaaaaaaaaaabaaaabaabbbababbbbbaaababbababbabaaaaabaabbbbaabaabababaaabbbbabbbabbaaabababbbaabbbabaabbbaabbaaaaaabbaabbabbaaababbaababaaaabbabbbaabbaaababbabbbabbbaabbabbaaaaababababababaaaabbbaaabbabbbabaababbabaaaabbaaabaaababbbbbaaaaabaaabbbabbbbaabbabaababbaaababbbbbaabaaabbbbbbbbaaabaabbabaaaabaaaaaabbaaabaabbabababbbaaaaabababbbabbbabbbbbbababbbabbabbbaabbabaabbaaaababaaaabaaabbabbbbbabaaabaaabbaaaabbabbaaabbabbbabbabbbbabaaababbbbbabbbbbbbbbabaaaabbbbbbaabbaaaababaabababbbaaaaaabbbbbaaaaaaabbaaababababbaaaabbbaabaabaabbbaaababababbbbaaabaabbbbbbbbbaaabbbbbaaabaabaababbbabaabbbabbababbbbaaaaaaabaaabbbabbabbaaababaabbabaabbaabaaabbbbbbaabaaaaaababbabababbbbabbaabbbbaabbbabaabbaabbbababbaaabaabbbbbabbabbbbaabbbaaabbaabaaaaaabbababbbbaaabbbbabaaaaabaabbabbabaabbbbbababbababaaaaaabbaaabbbaaaabbaabbabaaaabbaabaabaaabaabbbbbbbbaaaabbaabaaaabaaaababaaabaaabaaabbaaaabbbbbababbbbababbaabbbbbababbbabbabaaabbbaaabababbbbaaaabbbaaaabbababaaabbabbabaaaaabbbaaaabbaabbbbbbababbabbabaabbabaaababbaabbabaaabbabbabaaabababbababbbbbaaaabbabaabbbbbbbbaabaaabbbbbaaababababbaabbabbbbabbbaaabbabaabbabbaababaabaaaaaaabbbaaaaabaaababaaababababbabbbbaaababaababbbabaaabaaaaaaababaabbbaaababaabababbbabbbabbaabbbababababaabbaabaabbaaabaaabbbbbbbbbbabbbababbaabaabbabbabbabaabbbabaaabbaabbabbbaaaabbaabbbabbbbabbbabaaabaabaabbaaaaababaabaababbbaabbabaababbaabbbaaaaabaabbbaabbbaabbbbbabbbbbbaababaaaaaaabbaaababbaaabbbbbbbaaababbbbabaabaaabbbaaabaabbaaabbaabaaababbababaabbaaaababbbbaaabbbaaabbbbabaabaaabbaabbaabbaaababbabaaabbbbabaabaabbaaabbbbabaabbaaaabbbaaaaabaababaabbbaaabbbaabbaababababbbabababbaaabaabbaaaaaaabbbaababbbaaaaaaabaabbaaaabbbababbbaaabbaabbbabaabbababbbbbaabababbbbbbabababaaabababaabbaaababaaaaaabaaaabbbabbbbbbbbbbbababbaabaaababaabbaabaabbbaaaababababbbbababbbbabaabbbababbbabbabbabababbabbaabbaabbbbabbabbababababaaaabbaaaaabbbaabbbbbbbbbabaababaaabbbabbbabbaabbaababbaaaaaaababaaaaaabbaaaabbaaabbbaaabbaababaaaabbaabbaaaabaabbbaaabaabababaaaaaaaaaabbbabbbababbaaaaaaaabaaaabaaabaaaaaaaaaabbbabababbabbbababbbbaabbababbbabbaababbbaaaabaaabbaabaaabbaaabbabaabbbbaabbbaaaaaabbbbbabbbababaaababaabbbbbabbbbbaaaaabbbbaabaaaabaabbabbbbbaabababbabbaabbbbaabaaaabbabbabaababbbbbbbbabaaabbaabaaaaaaabaaaaabbbabbbbaabaabbaababbbabbabbbbbbabbbbaaabababaabbbbaaaabbbbbbbabbaabbbbbaababaaabbaaabbbbababbabababbbaabbababaabbbaaaaabbbbbabbabbbbbbabaaaabbabbabaabaaaabbbbbbbabbbaabbababbababbbabbabbbaababbbabbbaabbaabaabaaabbbbaaaabbaabaaabbababbaabbbaabaaaaaabbbabbaabaabbaabbaababbbbaabbbbbbaaabaababbaaaaaabaaaaaabbbbbbbbaabaabbaaabbbbabbaaaaabbaaabbbaababbbaaaaabaabbbbabbaababaabaaabbbbbbbabbabaabaabaabaaababaaaababaabaabbaaabbbaabbbabbaaababaaabbbbabbbbaaabaabbababaabbaaaaaaaaabbabaabaabbbababababbbabaaabbaababbbbbbaabaaababbabaabbaabababbbbaabbaaabbbabbabaabababbababbaaabaabbbabaababbabbaabababbabbbabbbbabaaaaabaaaaaababababbaabbbaaaaaabaabbbaabbababbaaabaaaabaaaaaaabbaabbaababbabbbbbbbbbabbabaabbaabbbabababbabbaabbabaaabbabbbaabbbbbbaabbbababaabbbbbbabbabaabaaabbbbabaaaabbaaababbabbaaabbbbaabbbbbbbabbbbbaaaaaaabbabbbbaabbbaaabbbbbabbbabbabbbbaabababbaaaabbbbababbabaaabbaaaabbabaaaabaabbbaabbaabbaaabbaababbababaaababaaaaaabbabbbabbbbbababababbabbbbabababbbbaaaabbababbababbbbababbaaababbbababbbbbbababababaabaaaabbbaaabbbabaabbbbaaabbabbbabbbaaaaaaaaaababbbbbbbbbbbaabbaabbbbbbbabaaababaaabbbbabbabbababbbaabbabbbbabaaaaabbabaababaaaaaaabbbbabaabaaabababbbaabbbbabbaabaaabbbbbbbbbabababaabababbbabbabaaababaaaaabbbaabbbbbababaababababaaabbbbbbbaabbbbaaaabbbabbbbabbbabbaaabbabbbabbababbabbbabbbbbbabbaaaaabbbaabbababaaabbabbbabbbaababbbaabbabbbaaabaaababbababbbbbaabaaaabaaaaababbabbbabbbabaaaababaaaaaabbaaabbbababbaaaabbaaaabbbaaaaabaabbbaababaabbbaaaaaaabaaabbbbbbaaaabbaaaabaabaaaabbbbbbababbbaababaaababbabbabaaababbabababbbbbaabbaabbabbbababababaaaaabaabbabbbbababbbaababaaaaaaaaaababbbbababababbaaaabaaabaabaaaaabbabaabaabbbbababbabbbaaaababbbaaaabbbbbabaaabbbbaaabaabaaababbbbababbbaaababbaaaabaaaabaaaabaababbbbaabaaaaabbaabbbbbbbabbbaaaabbbbaababaaaabababaaaaaaaaaabbbabaaabbabababbbaaaaabbabababbabaaaaaaaaaaaaabbbababbaababaaabaabbabbabaaaabbbababbaabaaaaaabababaabbbabaababbbbaaaabbababaabaabbbbbaaabbabbbaaababaabbbbaabbaaabbbababbababbaaaaabbbababbaabbbbaaaabaababababaabbbbaabaaaabaaaaabbaababbbaabbaaaabbaaababbbaaaaaaabbbabaabaabababbbbabbaaabbaabaaabaabbbbbbaabbabbabaabbabaaaababbabbaabaabbbbaababbabaabaabbbbaababaabbaababaaaababaaabbababbabbbaaaababaabbaaabbaababababbaabbaaabbaaabaaabbbaaabaabaababbaababbbbbbaabababbbabbbbababaababaababbabbabbabaaaabbbaaabbaaaabbbaabbaaaabaaaabbbaabaaaabbbbbabbbaaaabbbbbaaababaabbababbbaaabbaaababbabbbbabbbbaabaabbabbbbaaaabbbabaabbabaaabaaabbbbbababababbbbbaabaababaaaaabbababbababaaaaabbaabaaaabaabbaaaababbbaabbaabbabbaabbabbbbbabaabaaaaaabaabbaaabbaabaaababbabababaabababbababaaaabbbaababbbaaaaabaabbbbbababbaaabaabbbbbbbabbbabbbabbbbbbbbbbaaababaababbabbbbbbbbbbbbabbaabaabaabbbaabbaaaaabbabaaabaabbbbabbaabaabbabbaabbbabbbaaaaababbabaaababbabbaabaababbaabbabababbbabaaaabbbbabaabbaaababbaaababaaaaabaaababbbaaaabbbbaabbaababbbabaabbbbaaaaabababbabbababaabbbbbabababaabbbbbabbaababbbbbabbbbbababaaabaabbababbabbbaabbbaaabbaabbbbbbbbaaabbaaabaabaabbababbabaaaaababababbbabbaababbaabbabbbaabaaababbaaababbaabbbabbbaabaaabbbbbbababaabbbaaababababaaabbbababbaaaaabaaaaaaaabbbbabbbababbbbbbbabbbbaaabbbbbbbbaabbaaaaaaabbaaabaabbababababaabaabaabaababaaabababbbabbbaaaabbaaabbbabbbbabbaaaaabbaabbbabaabbbbaaabaabaaabaabbaaaabbbaaaabbaabbabbbbbaaababbbbbaabbbababaababaabaababbbabbabbaabaabababaaabbbbbbbbbbbbabbabababaaaaabbaabbbbbbaaabbabbbababaabbbabbbbaabababbabbbbbbabbaaaabbabbbbbabababbaaababbbaaababaaabbabbbbababbbbbbbabbababaabbbaaababbbaaabbaaaaaaabbabbabbaabbabaaabbabbaaaabbbbbaaabbbababbbaaabbabbabbaababbbbbabbbababababbaabbabaaabbabbbbabbababaaaabaaabbbababaaabababbbababbaaaabaaaababbaaaabaaabbbabbaaabaaabbbabbbbbaabaabbaaababbbbbaaaaabbabbbbbababbaabaabbbbbaababbaababaabaabaabbaaaabaaabbaabbbaaabbaabbbabbaababaaaaababbbaaaababbbabbbbbbaabaaaabbaabaaababbbabbaaaaabbbbbaabaaaaabaaabbbbabbbbaaaaababbbbbbaaaaaababaaabbabbabbbbaaababbaabaababaaabbbaaabbabaabaabbbbabbbaabaaabaabaaaabbbbaaabbbaabbabaaababababbabbbbabababbbabaababaabaababbaaaabaabbabaaaaaabaaaabaaabbabbaaaababbaaaabbabbbabbaabaaabaaabbabaabbabbbabbbbabaaaabbbabbabbaabbbbabbbababaabababbbaabababbbaabbbabbababbaabaabaabbbaaaababaaaabbabaabaabbababbabbbabbabbaaaaababaabaababbaababbbaaabbbbbaabbbababbababbbbaaababaabaaaaabaaabaaabaaabbababaaababbbbaaabbaabbaaaaaabbbbbabbbaaababbbbbabbaabbaaaaabbbabbbababaaabababbaabaaabbabbaabbbabababbaabaabbbaabaabbaaaaaabaaabaabaabababaabbaaabbabbaabbabbbbabbbabaaababbaabaabaaababbbabaaabbbbabbbabbaabbabaaabababbbbaabbababaabbbbbbbabbaaaababaaabaabbabbaabbbbbaaaababbbabaabababbbbbaabaababbabbabbabbbbbbbbababaabbbababbabbbaaabaabbabbabbabbbbbabbbababbabaaabbabaabbbbbbbaaababaaabbaaabaabbabbbbaaabaaaababbbbabbabaabababaaaaabaaabaaabbabababaaaaabbbbbbbababbbbbbbbaaaaaababaabbbbaabbabaaaaabababaabbabbabaabbabbaaaabaabbbbaaababababaabaabbbbbabaaaaabbabbbbbbbabbaaaaabbabbbabbbaabbaaaabbbbaaaaaababbabbaababababbabaababbbabaaaaaaabbbbaabbbabababbbbbbabaaaaabbbbaababababbaabaabbabbaaabbaabaabbbabbbbabaaababbababbbbaaaaabbabaaaaabbababaaaababbbababbabbbabbabbbbbbbbbbbbbabbbbaaaabbbabbbbbabbbbaabaabbbaaabbbaabbbaabbbbbbaaabbababaabbabaaaaaabbabbaabbbbbbbaaaababbaaabbaaaabbababababaabaaababababbbbbbabaaabbaabbaabbbbaabbbbbbaababbbbbbbababaababbbabaaababaababbaaabbaaabaabbabbabaabbabbaabbaaabbabbbbbbbabaaaabaabbbbbbabaaabbbabbbbababaaabaabbbaabbbbbbbbbababbbbaaababaaabaaaababbbaabababbbaabbaaabaaaaabababababbabaabaaabbbabbbbababbaaaaaaabaababaabbbbabbaaabbbbaaaabbbbbababaaaaaaabbabbaabbbbbbabaababaabaabbbaabaaaaaaabbaaabbabbabbbaababbaabaabbbbaaabababbababbbaaabbbabbaaabaabaabaaaaabababbabbabaababababbbaabbabbaababbbabbaaaaaaaaaaabaabaababbbbbbbbaabbaaaabbbbbbababaaaaababbbbaababaaabbaaabbbbabbaababbbbbaabbabbabbbbbabaababaababaaaabbababbababbbbbabaabaabaaabbabaababbabbaaabbabaaaaabbbbbabbbbbbaabaaabbbaaaaabbbbbbbbaaabaabbaaaaabaaabaaaaaaaabaabbbabaaaaaaaabaabbbbbaababbaababababaaabbbababaaaabbabaaaaababbabbbbaaaabbbbabaababaabaaaaaabaaabaabaaabaaaaaaabaababababaababbaaabbababaabaababaabbabaaaabababaababaaaabbbabbbbabaaaaabaabbababbbbbaabbabbabaaabbaabbbbbbabbaabbaaaaabbbaaabaababbbbbbabbbabaaaaaabbaabbaabbaaabbbababbaabbaabaabababaabbabaabbbbaaaabaaaaaabbbabaabababaabaabbbaabbbabbababaababaaabbbuabababbbaaabbabbaabaabbbbbabbbaaaaaabaaabbbaabbababbbaabaaababababbbbbaaabbbbabbabaabababbbabaaaabbbbbaabbaabbaabbbabaabaabaaabbabbabbbabbbaaaabbabaaababaabbbabbbbabababaabbaabaaaaaabbbaaabbabbaaaabbaaabbaabbbbbabbbabbaaaaabbaaaabbbabbabaaababababbabaabbbabababbaabbababbaabbababaaaaaabaabbbbbabbbbbbbaabbaaabbbbaaaaabbbaaaabbbaaabbbbbbbbbababaaaaabbbaabbaabbbaaaababbaababaaabbbbbbaabbbabbbaabbbbbaabaabbabababbaaaababbabababaaaaaaababbbbaaaabbabaaaabbabaaaabbabbabbaabaabbaaaababbbbaababbaaabbaabbbabababbabbbabaaababbaabbbaabbaaabaabbbaabbbbbabaaaabaaabbbabbabaabaaaaabaabbbbbbbbbaabbabbabbabbabaabbbbbabbbabbaababbbabbaaaabbaabbabbbaabababbaabababaabaaabbaaaabbbbbaababbaababbbbaabaabbaabaabbbbaaabbabbaabaaabbabbbaababaabbabaaababaabbbabababbaaabbaabbbaaabbbbaabaabbbaababbbbbabbbabbabbaaaaaabaaabbbaaaabbabbbaabbbaababaaaabbababbbbbababbbabbabaaabbbbabbaaaaaaaaaaababaaabbabbbbbababbaabbaaabbabaabbabaaabbabaaababaababbaabababbababaabaabaaabbbbbaaaabbabaaaabbabbbbabbbbabbbbbbbaabbabaaaaaababbbbaababbabbababaabaaabababababaaaabbaaabbbabbbaabbbbababbabaaaababbbbbbbbabbbbbaaabbbbbaabaabaabaaabbbabbbabbbaabaabbbbaababbaabbbabaabaabbaabbaabbaabbaabbbbbbababababbbaabaabaabbbbaaaaaaaababababbabbaaaaaabbbbbaabbbaaababababababababbaaaabaabbbbbaaaabbaabbabbbbabaaabaabbbbbabbaaaabaaaabbbbabbabababaaabbbbbabbaabbbbaaaababaaabbbabbabaaaabbaabbbbabaabbaababbbaaaababaabbbabaaabaabbababaabbbabaabbbbaabaabaaabbbbaabababaabaabbaabbbabbabbbbbaaababbabbbbbbbbaabaabbbbabbbbabbaaabbbbbaaabbabbabbbbbbaaababaababaabbbbbaaaabaaaaaabaabaababababbbaaaabbabaaabaabbaaaabbbbbaaaaabababaababbbabbbababaabbababababbbaaaabaabbabaaaabbabbbbaaaaababbbbaababababaaaabbaabbaabbabababbbbabaaaabbaaaaaabaaabaabbaababbaaabbaaaaaaabbbbaaabbabababbbbaaabbabbbaabaaabababaaaabaabbaabaaaababbaaaabbbaaabbbbbbbaabbaaabbabbabaabaabaababbabbbbaaaaabaaabaabababbbbbbbaabbbbaaaaabbbaabaabbaabaabbbaaababbbbaaaabaaabbaaababaaaabaabbabababbbbbabbabbaaaabbabaaaabbabaaabbbbabbaaabbbbaabbbbbbbbaabaaababaabaaababbbbbbaabbbaabaabbaabaabbbbbaababbaabbbaaaaabbabbaaabbbbbbaaaabaaaabaaabbbbbbaabbbbababbabaaabaaabbababbaaabbbaabbabbababbbaabaaabbbbbbbbbbbbabaaabbbbaabaaabbbbabababbbaabbaabaaaaabbababbbbbaabbbbabbabaaaaabbaababbbbabababbbbbbaabaaaaabaabaabbbaabbababbbbaabbaaabaaaabababbabbabbabababbbbabaabaaaabbbaababaabbabbbbbabaabbbaaababbaaabbbabbaabaabbaaabbbaababaabaaabbaababbbabbbaaabbbababbbaaaababbbabbabaaaaabaabaaababbbbababbabbabbbbbbaaaaaaabaabbbababbabbabbabbbabbbabbaabbaabbabaabbbbbaaaabaaaabbbabbbbbbbbabaaabbbbbabbbbabaaabababaaaaabaabababbaaaaaaababaaaaaabbbabbaaaabbbaaaaabbabaaaaababbaabababbbabaabaaaaabaababbaabbabbbbabaabababaaaaaabbbaabbabababababbaaaabbababaaaaaababbaaababaaabbabbaaaaaabbaababaaaaababbbaababbabaabbbbaabbbabababaaabaaabaaabababbaaabbbababbbabaabababaabbaaababbabbaaaaaaaabbabbaabaaabbbaabbbbbbabababababbabbaaaaabbbbaaaaaaaaabbaabaabbaabbbbbbaaabaaaabbabababbababaabbaaabababbabbbbbababbbbaaabaabbbaabaabbbabbbababaababbbaabababbaabbabbbababbbbbaaababbbaaabbaabaaabababbaabbaaababbaaababababbaaaaabaaabbbbbbaaaabbbbbbbbabaaabbbbaabaabaaabbabababbbabaaabbbaabbabbababaaaaabbaababbaabbabbaaaabbaababbbbbbbababbbbbbabbaabaaaaabababbaaabbbaabbbaababaaababbbbabbbbabaaaabbbbbbaabbbbabbbbbbaaaababbabbabaabbbbaabbabaaaabaababaaaabaaabaaaabaaaaaabbbbaaaabaababaabbbbabbbabaabbbbbabbbabaabaabaabababaaabbabbbabaabbabbbabbbbbababababaabbbbbbbaababaabbbaabaaaaaababaaabababbaabbabababaaaaabbbaabababbabaaaaabaabbbabaababbaaaabbaaaaaaaaabaabbbbabababababbaaabbabbabaabaabbbaaaaaaabaaabaaabbbbbbabbbbabaabaabbbbbbbbbabbabbbbababaaaaababbaaaabbabaaababbbbbababbbbababbbabbbaaaabbbbababbbbbabaaaabababbbbabaaabbabbbaaabababaaaaabababbabbabaaabaabaababbabaaaabbbbbbabbbbaaaaaababbbbaaaaaaabbbbaaabbabbabaabbbbaabaaaaaababaaabbabbbbababbbabababbaaaabbbbbabaaaabbbbaababaabaabaababbaaaaababbbbbbbbaabaabbabbbbabbbabbbaabbbbaababbbbaabbaabbbbbbbbabaababaabaaabbaaaaaaaaaaabbbabbaaabaabbabbbbbbaabaaaababbbbabaababbbaaabbaaababbbbbbaaabbaaaaababbbbaaaabaaaaabbbbbabbaababbbabaabbabbbabbaaabaabababbabbbababbabababbbaaaaaaabbaabbaaaababaabbbbaaaaabbabbabaaaaabbbbaaabbbabaaaabaabaaaaaaababbabbbaaababbbbabababbbbbabaaabbbabbababaaaaabababbbbaabbbbbbbbbbaabaababaabbaabaaaabbbaabbabaaaabaababaaababaaabbbbaaababbabbbabbababaaabbabaabaaaababaaabaabaabbaabbbbbaaabaaaaaabaabababbabbbbaabbababbbaabbbabaababbaabbbbbbababaaaaaabbabbbbbaabbaaaaaaabbaaababbabbbabbaaababbbabbababbbababbaaabbbbbbbaabaababaaaaaaabbabbbabbaaababaaababbabbbababaaaaaaabbbbbbabbbbaababbabaabbaaaaabbabbabbaabbaababbaabaababaabaaabaaaaaaaabaaabaaaabbabbababbbaaaaababaabbbbabbaaababababbaababaaaabbaababbaaaabbbbbabbaaabaaabbbbabbbabbaaabaaabbaaaababaaaaababbabaaabbbbabbabbbabbabaaabbaababaabaaabaaabbaaaabbbbaaaabbbbbbaaaababaaaaaabbaaaabaabaaaaaaaabaaaaababbbbabaabaabaaabbbaaabbababaaaabababbabbbaaababaaabababaabababaabaaaaaabaaabababaaaaaabaabaabababaababaaabbabaababbbbabaababababaabaabbbbababaabaaaabbbabbbababbbaaabaaabababbabaababaaaabababbbbabaabaaaabababaabbbaabbbbabaaabaabaaabbabaabbbbbbbabbbaabbabababbbabbaabbbbbaabbabbbaaabababbbbbbabbbaabbbababbabbabaabaaaabaaaaabbbbbaabbabbaabbbbaaaaabaabbbababaaababbbbabaaaaabbbaaaabbaabaaababababbaaabbabbbaabbaaaaabababbabbbaabbbaaaabaabababbaabbabbbabaabbabaabaabbabbabbaaaaabbabbbabbaaaaababbabbaaaaabaaabbbbbababbbbabbbabbabbbbbbbbbbaabbbaabbbaababbbbbaaabaaabbbbbbabbbaabaabbbbbbabaabbbababbaababbabaaaaaababaaabbbbbbabbabbaaaababaaababbaabbbbabbbbbbbabbaaaaabbbbbabbbaabbaabbbabbaaaabbbabbaaabbbaababbbbbaaaaabaabbbaabbabbaababbaaaabababaaaabaabbababaaaabaaabababbabaabaabbbaaaaaaababaabbbabbaabaabaabbbabbaaabaaaabbbbbabbbabbbabaabbbbaabababbbabbabbababbababbaaaababbbbbbababbbbabaaaabbaabbbabaaaaabbbaababaabbabbbbabaaabaaaabaabbabaabaabaabbbbabaababbbbbbaaabbabbababbbaabbbabbababbababaaabbabaaaabbbaaababbaabbbbbbabaaaaababbaabbaabbbbabaaabaaaaaaababbbaababaaaaaabaaaaabbbaabbbbbbbaabbbbbbbabaabbaabbabbaabbaabbaababbaababbaababaabaabbababaabbbaaabbaaaaabbaaaaaabbbbaaabbbaaabaabbabaabaaaababaaabaabaabaabaaabbaababababbbababababababbbaaabababbaabbabbababaabbabbaaababbabaaabbababaababbbaababbababbbbbbabbabaabaaabbbbbabbababbaaabbaaaabaabbaaaababbababbabaaabababaaababaaabbbbbababbaaaababaaabaaabaabaaaaabbbaabbbabbbbababbbbbbabbabaabbbababaababaaabbabbaababbabaabbbbabababbabbbbbaababbabbaabaabaaaaaabaabbabababbaabaaaaaaaabbbabbaabaabaaabbabbaabbbbbaababbabbbaabbbabababbaaaababbbaabaaaabababaaabbbbabababbababbbbaababaaaaaaaabbbababbbabababaabbabbbbbababbbbbabbbbaaabaaaaaaabaabaabbaabbabbbbbbaaabbabbaaaabbaabbaaabbababaabbaabaaaaababaabaabaaababbabbbbbaababbaababbbbaabbbabaaababbbbabbabbaaababbbbbbabaababaaababbaaaabbbbabbbabbaaabaaababaabbabbababbbabbaaaabaabaaababbabababaabbbaabaaabaaaaaaaaabaaaabbababaabbbabbaaabababaabbbbbaabbbbbbbbaabbbbbbabbabbabbaabababbbbaaabaabbbabbaabbbbabbbbaaabbbabaabababaabbbbaabbabbabbaabaabbbaabaababababaaaaababbaabaaabbaaabbaabbabaaaaabbaabaababbbabaabaaaaaaabbbabaaaababbabbaaabbaaaaabbbaaaaaabbbbbbababaabbaaaaaabbabaaabaabaabaabbababbbaaabbbabaaabaabbabaababbababbbbaaabbbabbabbbbbbbbaaabbaabaaabbbaababbbbaabbabbbbbaaabbbbababbbbabaaababbbabbabaabbaaabaabaabbbbbbbaaabbbaabbbbaabbbabaaaaabababaabbabbabbaaaabaaaabbbbabaaababbbaabbabbaabbaaabaaaaaababbaaaaaaaabbbabbaaaaabbaaaaaaababaaabbauabbaabababaaabaabbaabbabaababbbbbabbbbbabbaaaaaaabaabaaabaabaabaabbaababbbbaaabbabaaaabbaaabbbbaaaababbbabaabbbaabbbbaabaabaabbbababaababbbbbaaabaabbabbababaaabaaabaaabbbaaababbabaaabbabbaaaababbabbaabbaabbbbbaaaabbaaabbabbabbbaaaaaabbaababbaabbbababababbabbabbbbaaabababbaabbbaabbaaabaaaaaababbabbbbaaaababaaaabaaabbbaabbbaabbababababbaaabbbabaaaabaaaaabaaabbabbbbbbaaabbbbbabbaabbbbbbbaabbaabbbbbbaabbaaabababbbbbbabbbaababbabbababaabaaaaaaababbaabbaaabaaaabaababbbbbbbaabaabbabbabababbbbabbbabbbbabaaabbbaabbbbaaabbbabaabbbbbabbababababbabbbbaabbababbaaaabbbaaababaabbbbaabbbaabbbaabbababbbabbababbaaabbbbbbbbbbaaabababaabbbabbbabbaaaaaaaabaaaababbababaaaaaaabaabbaaaaabbabbaaaabbbabbbaaaabbaabbbbbbaababbaababbbaaaabbaabbaaabaaabbaaaabbabaaaababbaababbaaabaababbbaabbababbabaababaaabaaaaaabaabbbbaaaabaabbbabaababaabbabbbaaabaaabbaaababaaabababbaabbaabaaaababbababbbaaaabaabbbbbbbbabbabbaaaabbaabaabbaabbbaabbbbbabbbbaaabaaaaabbaaaaababbaabababbbabaabaaaabaababaaaabaabababbabbaaabababaaaaaabaaaaabaabbabaaaaabbbabbbbabbbbaaaabwbbbbbbaaaabbbbabaabbbababbabaaabbaabaaabbbbabbbbaaabaabababbaaaaaababbaabbbbabaabbbbaababaaababbabaaaabbababaabbbabbbababbbabbabbaaabaabbbabaaaababaaaaaaaaabaabaaabaabaaaababbaabaaaaaabaababaababaabbaaababaabbbbbababbbbabaaaaaabbaaabaabbabbaaaababaabababbbbbaaaabbaababbbbbbbabbbbbaabaabbbbbaaabbbaaaabbbbaabbabbbbababbbaaaabbaababbaaaabaabaaaaaabbbabbabbbababbbbabbaaaababbbbabaaaaababbbaaaaaabbaabbaaaaaaaababbbbbbbbbbaababbbabbbabbabbbaabaaabaaaaaabbbaababbbbaababbaaabaaaaaaabbbabbbbbaabaababbbababaabaaababbbbbbbabaaaabbaababaabaaabababbabaaaabaabbaabbbaabbabaaaaabaabaaaaaababbaaaababbbbbbababbaaabababaabbabbbbaabbbbaaaabbbaaababbbaaaabbbbbbbbbbabbbababbabbabbbaabaabbbbaaaaaaaabbabbaabbababaaaaaabbbbabbbaabbbbabbbbbabaaaaabaabababbbbbababbabbababaaaaaababbaabbbaabbabbbbbabbaabbabbbaabaaaaaabbaaaaabbbaabaababbbbbabbabbbbbababbbabaaabbababbbbababaabbabbbaaabbabbaabbbbbbbabbbbbbabbbaaabaaaaaaabbabbbababaaabbbbbaabaabbaaabaaabbbbbbabbababaaabaaaaabaabababababaaabbaabbabbababbbbbbbbbbaabaaababababbabbabbabbbbbbbaabaaaabaaabababbababbbaababbbbaaabbbaaabbbaaabbbabaabaaaabbaabbbbaabababbbaabaaaaaaaabababbaabaaababbbabaabaaabbabbbbbabbabbbabbaaabbbbabaabbbbabbaaabbbbaaaaaabbaababaaaaabbbbbbbbbbbabaaabaabaaaaaaabbbbbbbbbbbbbbabaabbbabaaabaabbaaaababbbabaaababababababbbabaabbabbabababbbaaababbababaaaaaabaabbabbbbabababbbbabaabbaaaaaabaaaabbbbbbabbbbbbabbaabbbabbabbabbbaabbbaababbaabbaaababbbaabaabaababbaaabbaaaabababaaaaabbbbaaabbbbaabbbabaaaaaaaaabbabbbbbbbbaabbbaaababaaaaabbbbababbbbbabababbabbabababbababaabbbaabaababbabbbbbbbaababbbbabbbabbbabbbbabbbabbbabababaaaabababbaaababbaababbaababbbabbaaaabbbaaaaabaabaaababbaaabbaaabaaaaabbabaababbbbbbbbbaabaaabbbaaabbaaabbaabaaaababaabaabbbbbbaaabbabbbbabbbaaaaababbaaababbaaaabbaaabbbbababbaaabbbbbbbbbbbaabbbabbbaaabbbbbababbabbabaaaaaabbbbababaaaaabaaabaabbbbbbbaaaababbbbbaaaabbbbbabbaabaabbababaababaabaaabaaabaaaaaaaabaabbbaaaaababaabbaaabbababbbbaabbbabbbabaababaaabbaabaaaabababaaabaabaaabbababbbbbbaabbabbaabbbababaabbbaabaabaabbabbbbbbabbbaaaabbbbaaaaabbbaabbbbaaaababaaaaaaabbaabbbbbabbbaabbbbbaabbaabaaabbabababbbabaaaaabbababaabbabaaabbbababbaaabaabababaaabaababababbababaaabbbaabbaaabbbbabaaababbbabaaaaabaababaabbaabbaabbaabaabbbabbabbabbaababababbaabbaaaabbbbabbbbbaababababbbaaababbabbaaaaabababbbbbababaaabbababbbaabaaababaaaaaabaabbaaaababaabbabbaabaaaaabbbbbbababbaabbaabbbbbbababbaabaaabaabbababbbbbabababbaaabbbaabbaaaaababaababbbaaaabbbbbabbaaaabaabbaababbaaaabbbbaababaaabbbbababbabbaaaaabbaabaababbaababbabbaaaabbabbbabaabbbaaaabbbbabbbbbababbaabbabababbbaaabbababbbbbbababbabaabbbaabababbbaabbaaabbbaabaababbaabababbaabaababbbbaabbbbbbbabbabaabbbbabbbaabaabbbbbababbabbaabaaaabbbabbaaabbbabaaaaaabaabbabaabaaabbaabaabbabbbabaabbabaabbbabbbbbabbababbbaababaabbbbbbbabbabaaabbbbbaaaaaaaaaaabaabbbbababaaababaaaaabbaabbaaabbbabbabbaaaaabaabbbabaabbaaaababbbbbbbbbabaaabbaabbaaaaaabaabbaaababbaabaabaaaabbaaabbbaaaababbabbaabababbbbbababbbaababbbaaaabbbbaabbabaaababbbbbbbaabbababaabaabbaaaaabaaaaabbabbabaabbbababbbbbbbaababbaaaabaabbbababaabababbaaabbbabbaabaabaaaaaaaaabbabaabbaabbbbbaababbbabaaabababbaaaaaabaaabbabbabbbbbaaabababaaababababbbabababbaababbbbaaabaabbbbaabaabbaaaaabbbababbaabbbabaaaabbaaabbaabbabbaabbababbbabbbbbbbbbaaaabababbbaaababbababbbbababbbabbabababaabbbabaaaabbbbaaabbabaababbbaaaaaaabbaabaabbbababbabbbaaabbaababaaaaabbbbaababbbbaaabaabaabbbbaabbbaabaabbbaabaabbbaaabbbbbbbbaaabbbaaaaaabbaabaaabababbabbbbbabbabaaabaaaaabbbabbaaabbbaabaaaaabaababbaabaababbbbabbabaabbbaabababbabaababbaabbbbabbaabbbaabaaabaabbaaaabbbaaaababbbbbabbbbbaaabbaabbababaabbaaaaabbaabaababbbbbabbbababbaaaabbaaabbbbbabaababbaaaabababbaabaaaababaabbababbaababaaaabbbabaaabbababaaababababaabbbbaaabbbbabababbabbbababbaabbabaaabbbbbaababaaabbaaaabaaabbaabaaabbabaaabbbbaabaaababbbbaaaabbaabaababbbaaababbaaaaaaaababbaaaabaaaababbbababababbabbaabaabbaabbabbbbbbaaaaabbaaabbabaabbabbbbbbbbabbbaababaabaaabbbaaabbaaababbaabababbabbbaababaaaabbbbbbabbaaababbaaabbabbbaaaaababbbaaabbabbbbbbababbaabaabaabbabaaabaabbbabaabbbabaababbbbabbbabbababbbaabaaabbbbaabaaabababbbbabaaaaabbbbbbabbbbbaaabbbaabaabbbbabbaaaabababaabbaaaaababbaabbabbbabaaababbaabababaabbaaaabaaabbbaaaabaaababaabaabbbaabbbaaaaaaabbabbaabaabbababbbbbbaabbbaaaaababaabbbbbaaabaaababbbbbbaaaaabbaabbababbbbbbabaababbabbbaaaaabbbabaaabaaaababbbabbbaabbaabbaaabbaaabbaabbbbabbaaabbbabbabbaabbabababaabababaabbaababbababbabbbbabbabbaaaaabababaaaaabbbababaabbbbbaaaabaabbaabbaaaaaababaaababbbbbbbbbbaaaabbbbbbabbabaaababaaaabbbaaabbaabbbbaaabababababaabaaabbbaaabbaabbbabaababaabaabababbaaabbbbabaaabbabaaaaaababaabaabbbaabbaabbbbbaabbbbabbbabaabbaababbabbaaababbbaabaaaabababaaaaaaabaabbbbaaababbabbbababbbbbbabbabbabababbbbaabbabababaababaaababbbabababbbaabaaaaabbbaabbabbababbaabbabababababaaabbbbaaabaabaaabbabaaaaaabaaabaabbbabbbbaaabbbabbbaabbbabbaaaaaaababbbaaabaabbabaabababaabaaabaabbaaabaabaabbbbbaaaaaabbbbaabbabbabbbbababaabbabbbaabbaababbabaaaaabbababbbaababbabbaaababbaabaabbbabbbbbabbaababbaabbbaabaaabaaababaababbbbababbbaaabbbabaaabaabbbbaaaaabababbbbbaabbbaababbbaabaabaaabbbabbababbaabbbbabaababaabaaaaaaabbbaababaaabaaaabaaaaabbabababbabbaaaaaabaabbabbbbbaabaaaabaabaaabbaabbbabaaabaaaaabaaaaabaaaabbbababaaaabbbabbaaaaaabbbaababaabbbbabbbbbabbabbbbbbbaaababaabaaabbbbbabaaaababbbbaaabaaaabbaabbabbababbbaaaabbabaaaabbababaabbbbaaabbaaaaaabbbbbbabbbaaaabbaabaabbabababaabbbbbaaaaaabababbbbabbbbabaaababababaabbabaaaabaaaaabaabbbabbbabbabaaabbababbabbbabababbabbabbaaaabababbbabbbabaababbbbaaabbbaaabbbbaaaaabaabababbabaaaaaabbbabaaabbbbabababbbaaabaabbbababbbaaaaabaaaabbbbbaabbaaaabaabbaaababababbbbaaaaaababaabbaaabbabbbbaaaababbbbabbbbbabbbababbbabaaabbbabbabaaabbabaaabbabbaabbaabbbabbbaaaabababbbaabbabbbbbabbaababbbbababbaabaabbabababbbbaaaabaaaabbababababaabaaaabbabbbabbabbbaaababbabbbbbbaaabaabbabbbaaabbbaabaababaabbbbaabaaabbbabbbbababababbaaaabaaabbaaabaabbbabbaababbaaabaabaabbaaaabbbbbabbabaaabbbaabbaaaababbabbabaabbbbbabbaabaabbbbabaaabaaaaaaabbbbabbaaabbbbaaaabbabbaababaaabbbbaaaaaaaaaaabbbbbbbabbbabbaaaabbabbbbbbaaabaaaabbbaabbaaababbabaababbbaaabbbaaabaabbaaaaaabbaabbbaaaaaaaabaaababbbaaaabbabbbbabbbbbaababbabbbaabbaaaababbabaaabbaaaabbababbabababbbaababbbbaaababbbabaaababaabbbabaaabbbabaabbbaaabbaabbbabaaaababaaabaababaabaaaaabbbbabbaabbbbbbaabaabaabbbaababbaabaabbbbabbaaaabbaaaaaaabbabaaabaababaabbbbabababbbababbbbbabaaaaababbbababababbaabbbaababaaabaabaabbabbabbbababaaaaababaabbaaabbbaaaabbbaabbbbbaaaaaaabaaaaabaabbabbaabaabbbbbabaabbbbbbabbaaaabbbbabbbaaaabbaabbbbbbabbababbbbaababababaababaaaaabaaabbbaaabbaaababbbabbaabaabaaaabbbaabbbaaabbaaababbbabaabaabbbabaaabaabaaabaabababbbaabbbaabbbabbbabbbbbbbbbbaabbabababbabbabbbbabbababbbbbbaaaabbababaaabababbbbaaaaaaabababbbabbabababbbaaabaabbbbabaaababbabbbbabbaaaabbabbbababbbababaabbbababbaaaabbabbaaaabaababbbabaaababaaaabaabbaababbbaabaaabbbbbbbbabbbbbbbbaabbaabbbbabaaabbabbaabababaabaabbaabbbaabaaabaabbaabbbbaaaaabbababbbbbaaaaabbbbaabaaabbabaababaababbbbabbabaaaabbbabaababbababbabbbabbbbbbbbbbaabaaabbbaabaabbbbaaaabbbbbaaaaaaabbbababbbabbabbabbabbbaabbbabaaabbbbbababababaaaaaabaabaaaaaaabababbbbbbbbbabaabbaaabbbabaabbaaaaaaaaabbbabbababbaabbabbbaaaaaaaaabbaaababbaaaabbaabbaaaaaaababbbbbaaabbbaaabbbbaabbabbbaaababaaaaababaaaababbbbaabbababbbbbbaabbbaaabbaaaaabbaabbabbbaabbbbababbababaabaababbaababbbbbaabbaaaaaaaaaababbabbbaaaabaaabaaababaaabaabbbaaabbabababbbabaaaabbbababababbabaaabaaaaaabbbababbabbaababaaaaaabaaaaabaaabaababbbbabbbaaababbbaabababaabbbaabbabbabbbababbabbabaaabbbaabaaaabababaaababbaabababbabaababaaababaaabbaabbaaabbbbabbaabaaaabbbaabbabbbabbbaabaabbaaabaabbabbaabaaabbbbaaaaaabbaabbbbababbaaabbbbabbbabbbbbaabbbababbabaaaaabbbbaabbbababababababbbabaaaaabbbbbabaaaabbaababaabaaaaaabbaaaaabbabbababbabbbbabababbbbaabbbaabbbbaaababbaaaaaabbabbbbabbbbaabbbaabbaaababababbbababbaabababbbbbbbabbaababbbaababbbbaabbaaaaaaaabaabbbbababaabaabaaabaaaaaaabbbbbaaabababbabaaabaaaabbaaaaaaaabbaabbbaaababaaaabaaabaabbbbbaaaaabbbbaabbbababbbabbaaaaabbbaabababaaaabaaaabaababbababbabbaabaaaababbbaaabaabbababbbbbbbabbaaaaabaaaaabbbabbaaabbababababaaaaabbabbabbbbaabaaabbabababbbbbabababaabbababbaaaaaaabbbabbaaabaababababbabbaaabbabbbabbaaabbbbbbaabababbaaaaabbaabbbbbbbabbbaabbaabbbbbaabbaaaaaaababaabaabbaabbbaaaabbaaabbbbabbabaaaabaabaabaabbbababbbaabbabbaaaabaaabbbbbaaaabbabababaabbabaaababaabaabaaaaaaabbaaabaaaaabaabbbaaaaabbbbbbabababbaabbaaaaaabbaababbbabbbabaaababbabbbabbabbabaababbbbbabbbabbaababababbaaaaabbaaaabbabbbbbabababbbaabbabbbabaaabababbabbabbabbbabaaabbabbbbbbbbaaaaaaabbaaabaaaabbaaabbaabaaabbaaabbbababaabbbbbbbbbbbbaababaabaaabababaaabbbaaaaabababaaababaaabbbbaaaaabaabababaababbabaaabaabbaaaaabbaaaaabaaabababababbbaaaaaabababbbaaaaaabbbbbbbbaaabbabbabbabbaabbbaaabbbaabbaabbaabbbaaaabbabbbabaaabbbabbaababbbabaabaabaaaabbaabbabaaabaaaaabbbabbbbbbbbbabbbaabaabaabaaaabaababababbaabbbbbababaabbbabbbbabaaababababaaaaaabaabaabbbbbbaaaababaaaaabbaaaaaabbbbbabbaabaabbbaaaababaabbbbbaaaaaabbababbbabbaaabbbbabbbbabaaaaabaaababbabbaabbbaaabbbbaaaaabababaabaaaaaabbbabbaaabbababbabbbbaaaabbbaaaababababbaabbbbabaabaaaabbabbbbaaabaaaabbbaabbbbbabaabababbaaabbbabaabababaaaaaaabbbabaaaabbabbabbaaaabaabbabababbabbaaaaaabaabbbbbbaabaabbbbaaaababbaabbabbbbbaaaabbaabbbaabaabbaabbbbaabababbbbbaabbbabbabaaabaaaabbbbbaabbbabbbbbbabaabaaababbababaabbabbaabbbbaaaaaaabbababbbababaabaabbbaabbbaaaaabbabaaabbaababbaaabaabababaabbbbbbbaaabbaaabbabbbabbbaabbaaaaaaaabbaabbaaabaabbbbaaababaaabaaabbbaabbaabbaabbbbaaaaaaaaabaabababaaabbaabbbbbbabbabaaabbbbabaababbbbbabbbbbbbababbabbbbaaaabaabbbaaabaaabaabbabaaabbbaabababaaababababaaabaabbbbbbaabbabbbbbbbbaabbaaaaaaaababbaabbbbaaabaaaababaaabbabbbaabaabbbaaaabbaabbbabababaaaabaabbbbaaaaaabaaabbabaabbaabbaaabbbaabbbabbabbaabbaabaabaaabbbaaababbaababababababaaabbbbbbabaababbabbbbbbbaabbabbabbaaabbabaabbbbababbubabbbbbaabbaaaababaabbaabbaabbaabbbaabbaaabbbababbaabbbababbbaabaaababababaabbbbabababbaaabbbaaababababababaaabbbbaababaaaaabbbabbbaabbababbababbbbbbaabbaabbbabbbbbbbabbbababaabaabaabbababbbbbabaaabbaaaaaaabababbbabbaabbabababbbababaabaababaabaaabbaaaabaaaaabababbbbabbaabaabaaabbaabbbabbbabbaabbababbaabbaaabaaabaaabbaabbbabbbbabaaaabbbaaabbabbbbbbabbbabbaabababaaaabbbbaaaaababbaabaabbaaabbabbbabbabbaabbaaabaabbaaaaabbabababbaabbabbabbaabbbababbabaaaabbbabbbaabbaabbbaaaaaaabaaaaaabaaabaaaaabbaababbaabbaaaabbaabababaaabbaaabaaaaaaaabbbbbababaaabbaabbbbabbbabbbabbaababaaabbaabbbabaaabbbbaaabbababbbbbbbabbbaaaabbabbbbababbaabbaabbaabbbbbbaabbbbaabaabbbaaabbbbbbabaabbababaaaaabaaabaabaaaabbbbbbbabaaaababbaaaababbabaaaaabbabbbaaabbbbabaabaabbababaaabbbbababbbbbbbbabaabbbababbbaaababbbbbaabbababaaaabbabaaaaabaaaabaabbaaaaabbabbbabbabbbabbbbabaababaabbbbbaaaabbabaababbbbbaabbaaaaabababbaabaabbaabbbaaaabbbbbaaaaaaaaabbababbbbbaaaaabbbbabbaabbbbbbaaaabaaaaaaaabababbabbababbbbabbbbababaaaaabbabaaaaababbbbaabaaaabaaaaabbbabbbbaabaabbbaaabbaaabbbbbabbbbbabaababbaaaaaabbababbaaaaaaababbbbbbaaabbbbaaabbaabaaaabbbabbaaaaabbbaaaabbaabbbbabbbabbababaaaabbbababbabbaabaabaabaabaabaaababaabbbaabababaaabbaaabbbbabaabbbbbbbbbbabbbaabaaaabbbaaaaabbaaaabbbbaabbbaabbabbbbababababbaabaabbbbbbaaaaaabbaabbabaabbbaaaaababbababbaabababbbabbbababbabaaabaabbbababaabaaabbbbbaabbaaabbaabaabbbabaaabbaabaababbababbbbbbaaaaabaaaabbbbabbbaaaabaababbaaaaaabbabbaaabababababbbabaaaaabaabababbbpaabbaaabbaaaaaaaabbbaaabbbbaabaabaababaaaaaabaabbbababbbaaaaabaababaaabaaaaabaaaabbbbaaaabbabbaaabbaabaabbbbbbabbbbbbababaabbbaabbbaababbaabaaaaaabbaababababbbbabbbbbbabaaabaabbabaaaabbaabbaaabbbabbbbaaaaabaaaabbbaabbbaaabbabbbbaaaaabaaabaaaabaaaaaaabaabbabaabaabbabababbbbbbbabbaabaaabaabaaaaabbaabbabbaaaaaabbaaaaaababababaaaaabbaabaabbbabbabbaabaabbaaaaaababbabbaababbbabaaabaabbabaaabaaababbaabaaaaabaabbbaabaabaabbaaabbbbbabaabbbbabaaabbbbbbbabbabbabaabbababbbbbabababbbbbaababbbaababbaababaaaabbabaabbbaabbaaabababbababbaaabaabaaaaabbbbbababbaababbbabaaaabaaaaababbbbbabbbaabbabaaabbabaababaababbbbaababbbababaaabbaaababbaaababaabbabbababbaabbbaaaababbababbabbaabbbbbaaaaabbbbaabbbaabaabbaaabaabbbaaaaabbbbabbababaabbbbabbaababbbaababaabaabbbbabaaaabbabaaabbbbbababaaaaabaabbababaabaaabbbaaabbaabbabaabaaabbbabaaaaaabbaabbbbaaabaabababababaabbabbbababaabaababbbbbbbabbabbabaaaaabaabaaaabbabaabaabbbabababaaababbbbaaaaabaabbabbababaabaababaababbbaabbaaaaabaabbababbbaabaaabbaaaaabaaaabababbabbaaaaaaaabbbbbabaaaabababbbaaabaabaabbabbaaabbbbaaaababbbbbaaabaabaaaababbbbaaabaaabbbaababbaabbbabbbabbbbabbbabbaababbaabaabababbbababaaabbaabaaaabbbbaaabbabaababaabbaabbababbaaaaaaabaabbbbbaabbabbbabbbaabaabbbaaaaabbaaaabbbabbbabbabbbbabbbaabbababbaabbabbbaaabaaababaabbbbabbbabbabbbababbaabbaaabbaabbaaababaabbbabbbbbabbbabbaabaaaababbaaabaabbabbbabababbbbbbbabaaaabbbbabbbaaaaaababbaaabbbababaaaabababbabaabbababaabbbbabbaabaaaaaabbbbbbbababababbaaabbabbbbbabaaaababbbbbabaabbbaaaaabbbabbbabbbaaaaaabaabbababbabaabbbaaaabbabbbbbbababbbaaababbbbbbbbaaabaabaaabbabbaababbabbaabbbbbaabbaaaaababbbbbbbabaaabbaabbbbaaaabbaaabbabaaaaaabbaaabbbbbbbbbaabbbabaaaababaaabbaabbabaababbaabbbabbbabaababbbaaabaabababababbabbbabaaaaaaabbabaaabbbabaaabaaabbbababbaaaaaabbbbbababbaababababbaaaababaaaaaaabbbbbbaaaabbaaabbbbaabbaaaabaaaaababbaaabbaabababbabbababbbabaababbabaaaabbbbabbaaabaabbbbbaabbababbabbbabbabbbbabbbbbbabbabaababaabbbabaabbbaaaabbaabbaabbaababaaabbbabaaababbabaaabbabbbbabbababaaaaaabaababaabbabbaaababaabbbbaaababbaabbbaababbbaaabaaaabbabaaaabaabbabbababaaaaaababbbbaaaabababaabbbbabbabbbbaaaaabbbaaaaaaabbaabbbaabbbaaabaaaabbbbbbbaabbbbbbaabaaaabbbaabababbbabbbaabaaabbaaaababaaaaaaaabaabbabbaabaaabbaaabbbabaabaababbabbaaabbbbababaaaabaababaabbbababbbbbbaaaaabaaaaabbbaabbaabaababaaaaaaababbaabbbbbbbbbababbbaabbabbbbbbababaaabaaaaaaabbabaaabaabbbbabbbbabbabbabbbbbbbabbabbaaaababaabaabbbaabbbabbbbbaababbbbbbabbabababbabababaabaaabbabbbbaaaaaaabaaabaaaaaaaaaaaaaabaabaaaaaabbbbababbababbabbabbbababbaabbaabaaabbaaaabbbbbbbbabbaaaabbbaababbbbaabaaabbaaaabaaabbaaaabbbaabbbbbbabbaabbbbaabaabbbbababbbbbbbbbaabaaababaaabbbaabbbabbabaaabababbaabbbbaaaaaabaaaaaabbaabbbbbbabbbabababbaaaaaabaaabbbabaaaabaaababbaaabbaaabaaaabbbbabaababbbabbaaabaababababaaaaabbbbabbabaaabbbabbbabbaaabbababbbaaabbaabbaabbaaaababaaabbaaabaababaababaabbaaaaabbaaaabbbaabaababaabbaabbbbbbbaaaabbbbbaabbbbabbbbabbaaabaaabbbabbbabbaaaabbabbabbabaabbabbaaabbbbabaabbbbbbaaaabbbaabaaabbbabbbbbaaabbababababaaaaabbabbbababbaaababaabbbaaabbbbbbaaaaabbaaababaabaabaaaabbbbaabaaaabbaabbaabbabababaaabbbbbbaabbbaaaabaaabbaabbbbabbbbbabbbabaaaaaababbbbbaaababbbababbbbaabbaababaababaababbbaaabababaaaaababababbbbababbaaaaabbabaabbaababbbbbaabbaababaabbbbbbbaaaaabbabaabbabababbbbbabbaabaaabaaabbbababbabaabbaaaaaabaaaababbabbbbabbaaaababaababbbbbbabbbbbbaaaabbaaabbbbabbababababbaabbbbbbbaaaaabaabbbbbbbabaabaabaabbaaaaabbbbbaabbbababaaabaabbbbabbababababbbbbbbabbababbbaaaabbaabababbbaababbbaaaaaabbbbaababababbababbabbbababbbabaabaabbbaaaaabaaababbbbbaabbaabaaaabaaababbbabbbaaaaaaaabbaabbbaaabaababbabaaaaabbbaabbababaabaabbbbbaabbbbabbaaabbaabaaaaababbabbbbaaabaaaaabbababbaabbaaabbbabaaaabababaabbbbaababbaabbbbbbabaababaabbaababaabaaaabaaaaaaaababbababaabbbababbaaabbbababbbaababaabaaabaaabbabbbababbbbbbbaaabbaabaabaaabaababbbbabababababbbaabbabbababababbabaabbaaababbbbbabaaaaaababaabaabbbaaabbaaabbaababbaabbbabbbbaaababbbbbbabbabbbbabaaabbbbbbaaaaaaababbbaaabbbbbbaaabbbabaababababbaaabbbabbbababbbaabbbabbbbbababababbbbabbaaaabbbbbbabbbaaaabbaaaaaabaabaabbbababbaabbabbaabbbbaaabbabbbaaabbbabbbbbabaaaaabbaabbabbbabaabbabbbbababbbabbbbaaaababbbabbbbbabbabbabaabbbbbaababbaaabaababbaabbbbaabaaaaaaabaabbabbaabbbabbaaabababbababaababbabaaaabaaaaaabbabbbaaaaababbabaabbbabababbbbabaabaabbbabaaaabbaaaabbbabaabaaaababaaabbapbaaaaaaababaabbbbbabbbbaaaabbbaabbaabaaaabaabaabbbabaabbabababaababbbaababbabababababaabaaabbbabbbbbabaaabbbaaaabbaabbbabbbbbbaabbbabbbbbbbabaaabbabaaabaabbbbabaaaabbbaaabbbaabbbaabaaabbbbbbaaabaaaaabaabbaaaabbabaabbbbaabaaabbbaaababbbaaabbbaababbababbababbaabbbabbabbbbbbabbaaabbaaababbaaabbaaaabbbabbababaaababababbabaabbaaaaabababbaaabaabbbbaaaabaaabaabaaabaabaababaaabbabbbaaaaaaabbabbbabbaaabaabbabbaababbabbbabbbbbabbbaabaabbabbabaabbbbbbbabaaababbbabbbbabaabbabbbbbaaabababbbaabbbababababbabaaabbbbaabbaaaaaabbaaaaabaabaaabaababaababaaaaaaaabbabbbbabaabaabbaaaaabaabbbaaaababaabaaaabaabbbbbaaaaaaababbbbaabbbbbaaaaaabbbababababbaaabababbaabaaababaabbbbbaaabbabbabbbaaabbbabbabbabbbbbabaaaaaabbabbaabbbabbabaabbabaaaabbbaabbbabbbaaababbbaabaaaaabbaaabaababaabbbaaaaabbaaababbabaaabababbbbababbbabaaaababbbabaababaabbbaaabbbabbbbbaaabbabbabaaababaaaaaaaaaabaaababbbbbbbbbabbabbababbbbababbaaaababbbababaaabbabbbababbbbbbbbaababaabbababbabbababaabbaaababaaaaaaabbaaaaababbaabbbbbbbabaabaaaaabaaaaaaababbabbbaaabbbababaabaaaaababbbabbbbbbabaababbabbbaaaaaaababaaabbabbaaaababbbbbbaaaaababbbbabaabbbbbaabaababaaaaaabbaaabbaaababbbbaabbabababbaaabbbabbaaaaabbbbaaaaabababbabababbbbbaaabbaaaaabaabaabababbbaaaaaaaaababbbbbabbbaaaaabaababbaabababaababbbbbbbaaaabbbabaababbbabaaabbbbabbbbababbaaaaaaaababaababbbbabaabbbbabaaabbabbaaaabbababbbaaabbbbbabaabbaabbbbababaabbbbabbabaabbbaabbbbabaaaabbbbaaaabbbaaabbbaabbbbabbaaaabbabbaabaabbaaaaaabbbbbbabbbabbbbbbabaabaabbaaaaaaabbbabbaaaaaabbabbaabbaaababbbaaabbbabbbbbabbaaaaaaabbaaabbababaababababbaaabababbababbbaabbaaabbabbbbabbbbabaaabaaabaabbababaabaaaabaabababbbbbbbbaabbbaaababbaababbbbaabbbaaababaaabaabbaabbbabbbabbababbbbbabbbabababaabbabbababbabaabbaaaabbbbbaaabbbabababaababaabbbabaabababaabbbbbbababbaababaaaabbabbbabbababbaaaababbaaaaababbbaaaaaaaaababaabaaaaaabaabaaabbbbabbbaababbabbaaabbbabbaaaaababbabaabbbabbababbaabababbbababbabbaaaaaababbaabbbaaaababbababbabbbbaabaaaabbbbabaaaabaaabbbabbbbabbbbaaabaabbaaaaababaabbaaaaaaabbabbabbaabbaababbababbbaabaabababaabbaaabaaabbbbabbabaaaabbbabaaaabbabbaabaabbabbbaaabbaaabbabbbbaaaaaaabaababbaabbabaabaabbaaababbbbbbbaabaaaaaaabbabbaaabaaabbabbabbababaaabbaabbbbbbabbabbabbbbabbabaabbababbabaaaaabbbabbabaabbbbaabbaababaabaabababbaabaabaaaabbabbaabbaabaaababaaababbbbbbbbbbabbaaaaaaabaabbabbbabbaabaaaaabbabaaabbababaabbbababaaaababaaabbabbabbaaabbabababbbaaababbbaaaabbaaaabaaaababaabaaabbbbbbbbabaaabbaabaabbbaaabbbaaaaababaaabaaabababbbaababaaaabaaaababbbaaaaababbaaabbaaaaababaababaaaababbbbbaaaabbaababaaaabbbbbaabbbbaababababbbbbbbbaababbaaaabbabbbababbbbbbabbaaaababbbaaabbabaababbababbabbbabaabbabbabaabaabaabbbbabbbaaababaaabaaabaaaabaabbaababaaaaaabbbbabbbbbbaaabbaaabaabbaaaaabbaaabbbabababbabaabbbbaabbaabbabaaabbbaabaaaaabaabaabaaaabbabbbbbaaabbbaabbbbaaabaaabbababbabaabaaabbabbbabbabaabbababaabbbaaabbababaaaabaaabaaaababababaaaaaabaabbabbbbabababababbaaaabababaaabaabaabbbbbbaaaababaaaabbabbaaaaaaaaabbaabbaaabbabaabaabaababbaabbaaababaaaabaaabababaaaabaabbaabbbabaababaabbaababbaabbbbabbbbbabaabaaabaaaabaaaaaaabbabababaaaabaaaabbbbbbabababbabbababbbababababbbbbaabbbababbbbabbbabbaaaabaabbbbabababaaabbbaabbaaaaaaabbbaabbabaabaabaababbbaaaaaaabababbbbbabbbbabbbbaabbaabbbaaabaaaababbbaaabbabbaabbabaaaaaabbaabbaabbbbbbbaabbaabbababbbbaabbbabaaaabaaaaabbbbaaaaaabbaabbaaaababbabaabababbbabababaaaababaaabbaaaababbbbbaabbaabbabaaaababbbbbabbaaabaaaaabbbbaaababbaabbabaabaabbaaaabbabbbbbaaaabbbabbababbbbbababaabbbbabbabbabbbabbbababaababbaaabbbbbabbabbbaaaaabbbababbabaaaabbaaabbabbaaaabbaaaaaabbaaababbabbbaabaabbabaabaaabbbaababaaaaaababaabbbbbabababababababaabbbbbabbbbbbbabbaaabbaababaabababaaabbaabbaabbaabbbbaaaababbaabababbbbbbbbbbabbbabbabaabaabaabaaabababbbbabbaaaaaabaaabbbbbbbbababaaaabaaaaaabbaababbaabbbabaababbbabbbbbaaabaababbaabaaaababaabbaaaaabbbaabbbaabbaaabbabaababbbabbbbbabababaababaabbbaaaaaabaabaaaabbbababbbbbbbbaabbabaaabbbabbaaaabababbabbabaabaabbabbaabbaabbaaaabaaaaaabbabbaaaaabbbaabbabbbabbabbbabbbbabbabaabaaabbabbbabaabbbbabbbaababbababbbaabbababbaaabbbbbbaaaaabbbbbbbbbbaababbababaaababbbaabaaabbabbbbaaaaaaaabbbabbaabbabaabaabaaaabababbabaabbaaabbbaababbbbaabbbbbaababaaabbbaabaaaabbbbbabbabbaababbbbababbbbbaaababaaaaababbaaababbabbbaababbaaaabaaaaabaaaabbabbbbabababbbaabababaaabbbbababbabaabaaaabbaabbbbaabaabaaabbbaabbbbaabbabbabbabbbabaaaaabaaaabbbaaabbabbaabbabbbbabbaababbababbabaaabaabbbabbbaabaabaababbbbbbbababaaaaaabbabaabbaabbbbbabbabbbbabaaaaabaabaabbabaaabababaaabbbbbabbabbabbbababaabaabbaaabaaababababbaaaaaabaabaaabbbbaabbaabbbbbbbbbbbaabbbbaabbbbbabbababbaababbabaaaababaababbaaaabbaaabbabbbaabbbbaabbbaabbaaabababbaaabaaabbabbabababbbaaabbbbabaabaabbbaaabbbabaabbbaabbaabbabbaaaabaaaababbaabababababbabbaabbbabbbabaaaaabbaaabbaaaabbbaabbaaaabbaaaaaabbaabbababbbbbbbabbabaababaababbaabababaabaabbabaababababbbabbbbbabaaabababbbbbbbaaabbbabbabbaabababbbbaabbabbaababbbabbbaabbbbabaaaabababbaaaaabbbbababaaabbaaaaaabbbababbbbbbaabbbbabbbbbabbabaaabaababbbaaaaaabbbbaabaaaaabaababaaababbaaaaabbbbabbaaaaababbbbbbbababbbaabaaabaabaaaaabaabbabaaababbbabaabaaabbbababbbbabbaababbabbbbaaaaabbaababbbababbbbbbabbbaabbbaababaaababaaaaaaabbaabababbbbbbabbbabbabaabaaabbbbbbbbbabbaababbbbabbbababaabbbabaabababbaaabbaabaabbbbbbbbbabaabbbabbbaabbbaaaabbabaaababbaaabaaaabaaaabbbaabbabaabbbabbababbbaabaabaaabbaaaaababababbbbabbbbbbbabbbaababababaabbbababbbbbbbbbabbbaababbbbbbbbababbbababbbbabaaaaaababaaaaaaabaaabbbbbaaabaaabbbabbbabaabababbabababbaabaabaabbaabbbaababbabbaaabbabbaaabbbbbabababbbabbbbaaaaabbbabababbaaaaabaaababaabaaabaaababaabaabaabaaabbbaabbabbababbbabaaaaaaabababbbaaababaaabaabaababbbaaabbbbbbbbaabaabbbabbbaaabaaaaaabababaabaaabaababaabbababbbbabbbabbbababbaabbaaabaabbabbabbbabaaaaabbbbabbbbbbbbbaabaabbbaabaaaabaabababbaaaaaabbababbbbbbbaabbaabbabbbbabbbabababaabaaababaabbbbbbbaaababababbbabbaaaaaaaabaababaaabbbbbbbbabaabbaaabbbabaabbbbbbbbbabbaaabaababbbbaaaaaabbaaabbaababbaabaaabbababbbaabbbaaababbbbbbbbaababbabaababbabbbbaaabbbbaabbbabbaababbbababababbbabbbbabaaaaabaababbbabaabbababaabbbabbbaaabbaabbbabbbaabbaaabbbbbabbabbabbbbabbbbbabaabababbbbaaabbaaababaaaabbaaaaabaaabaaaaabababbabaabbbbabbababbbaabaaaababbbbbabaaabbbbaabababbaaaabbbaaababaabbabababbabbbaabbaabbbbbbbabbabbbaababaababaababbbbaabbabbaaabbbbbbabbbbbbabaababaabababaaabbbabbbbbbabbbababbbbbabbaaababbbbbbaaaabbabaabbbbbbbaaaababbabaabaaaaabaabaaaabbbbaaabbbbbaabbaaaaaabaaabaaaabaaababbbaaaaaabaaababbabbaabbbbaaababbbababbabbbbaabbaababaaabbbaabaabbbbbaaaaaaabbbbaaaaaabababaabbaababbabaabababaabaabbbaaaaaabbbbaaaabaaababababbbbbbaaaaaababbbabaaabbbaabbabbbaaaabaababbbbbbaaaaaaabaaababababbabbbaababbbabbabbbaaabbababbaabaabbbbbabbbbbbabbbabbbaabababaababababbaaaababbbaabbbbbaaaabababaaabaabbaabbaabbaaabbababaabbabbabbabababbbbbbabbbbaabaaaaaaababbbabbbaabbababbaabbbabbbaabbaaabaabababbabbabbbaabaaabbaabbbbaabbabaabaababaababaaaababbabaababaabaaababbabbbbbbbbaaabbababbabbabbabbabbaabbbbbbbabaabbbbabaaabaaabbbbbbbbababbaabaabaaabbbabbaabbbaaabaaabaabaababbababaaabbbbabbaaabbaabaaaabbbabbaaaaabbbbbaaaaabbbaababbabbaaabaabbaabbbbbaababbaababbabbbababbbabbbbbbaaaabbbaaabbabbabaabbbbbabbababaabbbabbabaabaababbbbbbaabaabbbabbaaaabababbabbababbbbbbbabbababbaabaabababbbbbaaabbbabbbababbbaaabaaabbbababaabbabbbbabaaaabbbbabaabbabbabaaababbaaabbaabbabbbbbbbbabbabaababbabbbbaabbbabbbbbbbabaabbaaabbbaaababaabababbbbaaaababaaaabaabaababbbaaaabbabaaaaaabbbababbbbaabbbbabbabbbabbaaabbbaabbabbbababbbaabbabaabbabababababbbaaaaaaaabbaabbbbbaabaaaabaaaaaabaabbaababbbbbaabbbabbbabaaaabbaabbaababbabbaaaabaabbabbbaabbaabaabbabbbaababbabbababbaaabbbbababbbabaabaaaabaabbabababaabaaabababbbabbabbbbbaaabbbbbabbbabbaaababbaaabbaaaaaabaababbabaaababababbbaabbbbaaabaaabaababaababbbbbaaabaaabbbbbbbabbbaabbbbbabaaaaaaaaaaaabbaababaaaaabbbabbaaabababaababbaabbbabbbbbbababaabbaaababbbaabaaaabbababbbbaabbaabaabbbbbbbababaaabbaaabaababbbaabababbaabbbbbbabaaaaaaaabbbbbabbabababbbbabbbaaaababbabaaaababbaabaaababaabbaabababbbaabbabaabbbbbbbaabbbbbbbbbaabbabbbaaabbbbbbababbbbaababaabaaabababaabbaaaaaababbaababbbbbbbabbbaaaaabababbbbaabbbabaababababbbabbababaabaabbaababbaabbbbabaabbabbaabbababbabaabaababbbabaaaaaaaabbaaaaaabaababbababaababbabbaababbbbbbaaaabbabaaaaabbababbaabaaabaaababbbaaaaabbababbbbbbbbabaaaaabaabbbaabbbbaaababababbbababaabbbabbabbbbbbabbbaabbbbbbaaabbaaaababaabaabbbbbbaaabbaabaaaaaaabaaaabbabababbbbaabbaaabbbbabbaaaaabbaabbbabbaaabbbaaaababbbbbaabbababaabaaaaabababbabbababbabbaaabaababbbbabbaaaaaabaaabababaababaabbbaabbbbbaaaaaabbaabaaababbbabbbbbababaabbabaabababaabbbbbbabaabaabaaaabaaaabbaabbaaabaaabbbabaabbabaaabbaabaaaaabbbaaaabaaaabaababbaaabaaaabbabaaabaababbbbbabbbbaababababbbabaababaaaabaabaababbababbbbaababaaabaabababaaababaabbaabbbaababaabbbabaabaababababbaaaaaaaaabaaaaabaababbaababaaabaabbbbababbbbaaaababababbbbbabbbbbbbbbabaabaabbabbabaaabaabbbaaaabbabbbbbaaaabbbbbaabbababababaabaabaaaabaaabbabbbaaaababaaaaabbbbbaaabbaabaabbaabaababbabbbbabbbaabbbbabaabbbabaaaaaabbbaabbbaabaababbbbabbaabbbabbbaabaababbbaabbabbbabaaababbabaaaabbabbbaaaabbbabaabbbbbbaabbbbbbaabaababaaaaaaaaaabaaababbaabbbaababbaaaaaaabbbbaabbababaabbbbabbbaaabbbabbaaabbbbbababaaabaaabbbbababaaabaaaabaaabbaaabbabbbaaaaabbababaabbaabaaabbbbabaabaaababaaababbbbaaabaabbbbaaaaaaabaabbbbbaabbaababbabbabbbabbaaabbabaaabaabaaababbbaababbaabaaabaababbbbbaabaaaaabaababababbaabbabbabbbbbbbbaabaaabaaaaababbabaaaabbabaaaabbbbbababaabaabbaaabbbaaababbbabbababaaabbaabaababbbbababaaabaaaaabbaababbbbabababaaabbbaaaaaabaabaabaabbbaabbaaabbabbababbaababbbaabbbbaabbbabbababaaabbbabbaaaabaabaaaabaababbaaaaabbabbbbaaabbbaaabbabaabaaababbbabbaabbbabababaaabbbabbbbababbbbbabbaabbbbbaabbbbaababbababbaaababbabbbaababbaababbaaabbbabbaaabbaabbbbbabaabaabaaaaaaababbbababbbabbbaabaaabaababbaaabbbaaaaabbbaaaababbbaabbbababaabbaabaabbbbabbabababbabbbabaabbaababbbbbabababaababaabbbaabbbbbaabbbbbbbabbbbaabbabbbbaabbbbbbbabbbababbbabaaaabbaabbaabaaaaababbbabbaabaababbbabaabaabaaaaabbabbaabaabbbabbbaaabaaababaababbbbaabbabbabababaababbbbbbbabbbaabaabbaaaababaabbbbbabbabaabababaaaabbabababbbaabaaaaaabbabababaababaababbaabaabaabbbaabaaabbaaaababbabbbbbbaaababaabaaabbbaaaaaaaaaabbbababbbabaaabaaaabaaaaaaaabbabbbbbbbbbabaaaabaaabbbaabbabbbaaabaaaabbaambbaaaababaaababbaabbaaabbbaabababbabaabaaaabaabababababaaabaabaabbabaabbaaaaaabbbbbbbabababaabbbbaabbbaaaaaaabbabbabaabbababaabbaababbbabbbbaaabaabbababbaaaabbaababababbbbbbabbbabaabbababbbaabaaaaababababaaaababaaaabaabaaaaabbbbbaababaaabbabaaaababbaababaaabababbbababaaababbbbabaabbaaabaabaabababbbabaaaaaaabaabaaabbbabababababbabaabababbaaaabbaabaabababbbababbabaaaaabaaaabbaaaababbbabaabbbbbababbabbaaaabababaabbabaaabaababbabbabbabbbabaaaabaabaaaaabbaabbabbaaaabbababbbbaaaabaaabababbbbbabbaabbbbbbababbaabaaaababbbaaabaabaaabaabbabaabbbaabbbbbbaaaaabaabaabbaababbaaaababbaaabbbabbabbaabbbaaabababbbabbbaaaaabbaaaaabbbbababbabbbbbbaabbbbbabbbbbbaaabaababaaaaaaaaababbaabaaabbbbaaaaababaaabbabbbaabaabaababbbbabaaabbbaabbaaaabababbabaabbbbabbbbbababaaaaababbabaabbababbbaabbaabbabaaabbbbbaabbabbabbbaaaaaaaaabbabbabbabababbbaabababaabaabbbbbbbbabbaaababbbaabaaababbaabbabaabbabbaababaababbbabababbbbaabbabbaabaaabbbabababbababbbaabaaabbbbababababbbabaaaaaabbbbbbbaabaaabbbaabaabaababbbabaababababbabbbabbabbaabbabaabaababbbbaaabbabbbaabaaabbbababbaababababbaababbbbaabbababaabbbbbaabbbbbabababbbaaababbabbbabbabbabaaabababaabababaaabbbbbabbbaabaaababaabbbbabababbabbbaaaabaabaaabbbabbabaabbaaabbbbaabbbabaaaaabbaabaaabaaaaaaaaabbabaabababbbbbababbaaaaaaaaaababaabaabbabbabbbabaabbbbabbaaabbbbbaaabbabaaaaabaababaaaaaabbbabbbaabababbbbaaababbbbaabbabbaabaabbabbbabaaaabaabaabbbbaaabbaabbaabbbbbbaabbbaababaaaaabaaabaababbbbbbaaabbbbbbabbaaaaabbaaabbbbaabbabbabbbbbaababbabaabbaabbbaabbbbbaabaaabbbaababaaabbaaabaababaababaaababaabaabbaabbbaababbbbbaabbaaaaaababaabaabbababaaaaabbabbbaaababbbbbababaaabbbbababbabaabaaaabbabbaababaaabbabaaaaaabbabaababbbaababaabbbaabbaabbaaaaaaaabbabababaaaababbabbababbaaaababbabbaaaaaaaaabbabaabbaababbbababaabbbbbbbbbbaabbbbbbbabbbabbbbaaabbbaabaabbabbbaabbabaabababaabababbbaaabbabbbbaabbaabbbbbbbbaaaababbaaababbaababbabbaaaabbbaaaaaabbbbbbababbababbbbbababbbbabaabbbbababbaabbaabbbbabaabaabbababaaaabaabbaabbbbabbbbbababbbbaaaabaaaababababaabaaaaaabaabaabbaabbbbaaabaaabbbaabaaabbbbbaabbbbbaaababaaabaaaaabbbaabaababbabababbaabbabbbaaabaaabbababbabbbabbabababbbbabaaaabbabbbabababbabbbbababaababbabbbaabaaaabbaaaaaababbbaaaabababaaaaaaabbaaabbabbbababababbbaaaabbbbbbbabbababaabbbbbaaabbaaaabaaabaaabaabaaababababbbbabbbababaabbbbaaaabababbbbbbaabbbabaabaabbaaaabbbaaaabaababaababaabaaaaaaabaaabbbabaababaaabaabbbbbbaaaabaaababaabbaaabbbbbabaabaaababbbbbabbbbaabababbbabaabaabbbabbbaabbaaaaabbbbaabbbbaabbabaabaaaababbaababbaabbabbbaabababaaaaabaabaabababaaabbababababababbbbbbaababaababbaaaabaabababbabbaaaababbbaaaaababbbabaaaababbaabbbbabbabaaaaaaabbbaababbabaaaabbabbbababbbaabaabbbabaaaaabbaaaabaabbaaababbaaaaaabbbbaabbbaaabbbabbaabbbbabbaababaaabbbabaababaabbabaaabbbbbabbbaabaabaabbbbaabaabaababbaaaaaaababbabbaababbaabbaabaabaabbbabababbabbbbbbaababbaababbbaabbabbbaabaaabaabbbbabaaaaababaabbbbbbbaabbbaaabaabbbbabbaaabbbbaababaabaabaaaaaaaababbbaabbaaabbaaabbabaababbbbbaabbbbaaabbabbbaaaabaabaaababbbaabbbbbbabbababbaababaababbaababababaaabaababaaabbbbbaabbabbbbbbabbbabbabbbababaaaabaaaabbbababbbbaaabaabababaaaaaaaabbaabbaaabbbaabbabbabaababaaabaabbbaaabbbaaabbabaaaaabbabbbbabaabaabbbbbbaababbaaabbbabaabaabbbaabbaaabbaaaabbbbbbbbabbbabbaabaaaaabbabbbbbaabbbaababaaabbbabbbabaababbaaaabababaabaabbaabaaabaaababaabbbabbaabbaaabbbaaabaaabbbbabbbbbaabbaaaabaabaabaaaabaaabbaaabbaababbababaaaabbbaaaabbabbababbbaabbaabaabaabbabaaababaabbaababbbaabaaaabbbabbbabbbaaaaaabbbbbbaabbabbbaabbbaaabbabbaaabaaaabbbaabbbbababaaabaababbbabaaabbbabaaabaabaabaababbaaaaabaabbbbbbabbaaabababaaaabbbbbbabaababbaababaaaabbababbaababaaababbbabaabaababbaabbaaaaabaababbbaaaabaababaaabbabaabbabbabbaaabbabbabaaaabbaaaaabbbaaaabaaaabbbabbbaabaaaaabababbbbbaabbaaaaababbbbbbbaabbbaabaabbaaaaaaaabaaaabbbabbbbbbabaabaabbaabbbbbababbbbaababbaaaabbaaaaaabbbaabbaabbbbabbbbbbbabaaabaabbbbbabbaaaabaaabbbbbbaabaaababaaaaaaaaabaaaaabbbaaaaabaaabbabaababbaabbbaaaabaaabbabbabaabbaaaaabbbbaaababaababbbbbabaaaaaaaabaaabbababbbbabaabaaaaabbaaaaababbbbabbaaababbbaabbbaaabbbababaabbbbaabaaabbaabbbbaaaaabbaaaaabaaabbabaabababbbaabbbaaabaabbaabbbabbababaabaabbababbbbaabbbbaabbaababbabaaababbbababbbaabbaaababaaaaabaaaaaabaaaabababaaaaababaabaabbabaabaaaaabbaaabaaaaabaaababaaababbbbaaaabbaaaabbbbbbaaabbbaabbbaaaabbabbaabbaaababbabbbaabaabbbababaabbaaabbbbaaababbababaabababbaaabaabbaaabaabaabaaaababaabbaaabaaababaaaaabaabaaababbbaabbbbabaaaabbbbbaaabbabbaaababaabaabbbbababbbaaabababbbabbabaabababbbbbabbbabbaabaaaabaabaaabbabbbabbbbbbabababaaaabbabbaabbbaaabababbaaaaaabaaabaababbaabaabbababaaabbbbbbaabbbbbbaaabbaabbabababbaabbabbaaaabbbaabbabaabaaaaabbaaaaaababaaabaababbaaabababbbabbbbbbababbbabbaabbaaaaaaaaabaabaabababbaaaaabbaaaabaaabbaabaaaabaaaabaabaababbabbaaaabbbaabbaaaaaaaaaabbbaabaabaaabbaaaabababbababbabbabbbbabaaaababbaaabbabbbbbbaaaababaabaaaabaaabaabbbaaaabbbaaaaaabbbbabababaaaaababbbbabbbbababaabaabbbabaaaabbabbbbbabaabbaababbbaaabbbaaabbaabbabaaaabaabaabaaaababaaaababbabbbbbaabbabbbaabbbbaababbaaaabbabaabaaaaababbabbbaabbbaabaababaabbabbbaaaababaabaaababbbabbbaabababbbabaabbabbbabababaababaababbbaaababbaabaaaaabbaabbbbabaaabaabaabbabbbbbabbbbaabbbaabbaababbbabbbbabbbbaabbaabaaaaaababaababbaabaabbbaaabbaabaaaababbbaaaabbbabababaabaaabbbbbbababaababbaaaaaabbabbaabbbbabaababbabababbbaaabbaabbabababbabbbbabaaaabbbaaaabaabbababbaabbaabbabbbabaabbaaabbabbabbabbbababbbaaaabbaaaabaabbaabaabbbbbbbabababbbbbabaaabbbabbbbbbbbbababbabaabbbababbbbbbabbbaabaabaaabbbbbbabaaababaaabababbbaaabababababbbbbabbbbaababbaaaaabaaaaababaabaaabaabaabaaababbbaaaaababbbbbaaabaaaaaaaaaaabbaaabbbbbbaaaabbaaaabaaabaaabbaaabbaabaaaabbaabaaababbbabbbaababbaabbbbbaaabbbabbbbbabbaabaaababaaabbaababbabbbbbaabbbbbbbbababbbaabbbbabababbabbaabbabaabbbabbbbabbaabbaababbbbaaaaaaababaaaaaaabbabaaaabbabbbbbbbbabaabbaabbabbababbaaaaabbbbbababaaabaaabbbbbbabababaabababaabababbbbbabaaaaaabbbbabababbabbbaaabaaabaaababaaaabaababbbaababbaaaaabaaaaababaabaababbbabaaabbabbbabababbaabbabaabaaaaabaaabbbaaabababbbaaaabaaabbbaaababbbbabababbbbbaaabbaaabaabaabbabbbbabbbbababbbababaabbabbbaaabbaabbbbbbabbbbbabbbaaaabbbabbbbbaabaabbbabbaaaaaabbaaabbaabbaabbabbabaaabbabbbbbaabababaabbbaaabbaaabbbbbbbbbbbaaaabaabbbbbbbabbbaabaabaabbbabbabbbbbbabbbaaaabaabbbaabbbabbbababbababbbabbabbbbbaaabaabbbaaabaabbbbaabbbababababbbaaabaaaababaaabbaabbabaabbbbbbbabbabbbabaaabbbabababbbabbaaabbaabbbbaababbabbabaabaabbaaabbabaabbaaababaabbabbaabbbbabaabababbabaaababaaaaaaabaababaaabbbbbbaabaaaaaaaabbabaaabbbbbabbbaaaabbaabbbbbbaaabbbaaaabbaaabbbaaabbbbabaababbbaabbbbbaaaaabbbabbabababbabaaabbabbabbbaababbaaaababbababaabbabbbaaaabbaaaaaaababbbbaabbbaabbabbaaabbaabbababbbaaaababbbaabbabbabbaaaabaabbaababbabaababbaaabbaaabababbabaaabaaaauaaabbbaabababbaaaabbbaababaababaaaaabbbbbaaaaabaaabbbababbbbbbababbbbbaabbaabaaabaabbabbabababbbabaaabbabbababbbbaaaabababaaabaaabababbaababaabbbaaababbbaabababbabbbabaaaaabaabbbbabaaaababaaabbbaabaaaaabababaababbbbbbabaaababaabbaaaaaaabababbabaabbaaaaaaabaaabbabaabaaaabbabbabbbbbabbababbaaaaaababaabbabaaaaabbbababbbaaabbbababbbbababbababbbbbbbabbbbabbaabbabbbaaaabbababbbaababaaaaaabbababbbaaaaaaabbbbbbabaaaabbbababaaabbababbbbaaabbabaabbbbbabaaaabababaaaaababbbbbaabbaaabaabababababbbbaaaaabbabbbbababaaababbaabaabbbbbbbbbabbbaabaabbaaabbbbabaabbaabaabbbbbbaaaababaababbabbbbaabaaabbabbbaababbbababbaabbbbbaabbbbbabbabbaaaaabbaaabbaaabbaaababaabbaabbbbababbbbbbaabbaaaabbbbbbabaabbbbbaabbbbbababbaabaababaabbabbaaaaabbaababbbbababbbabbaaabbaaaaaaabbbaababaabaabbaabbaabaabbaaabaaababbbbabaaaaaaabababaabbaabbaabaabaaabbbbabababbabbbabbbbbbbaaaaabbabbbabbbaababbbbbabbabbababbbabaabaabaaaaaaaaababbbbbbbbaabaabaabaabbabbabaabaabaaaabaaabbababbbbbababbabaababbbbbabbbbaaabaaaababbaabaabbabaaababbababbbabaababaaaaabaabbbbbbbabbbbaabaaabbbbabaabbaabbaaaabbbaaaabaaaabbaabbabaaabbababbabaaabbabbabaaabaaaaaaabbbaabbbababbbbabbabbbbabbbabaaaabababbbbbbbaaababbbaabaaababbabaaababbabaaababaaabababbbaabbbbabbbabbaaabbbaabababbbbabbaaaabbbbbabbbbaababbabbbababbbaaabbaabbababbbaababaababaabbbbaaaabaaaaababbaabaaabbbaabbabbaaaababbabbabaabbaabaaabbabaaaaabaabbbaaababbabbbbbaabbabbbabbbbabaaaaabbbbbbabbbabaaabbbabaaaaaaabbababbabaababbbabbbbaaabaabbaaabbbabbbbbabaabbbbaababbabbaabbababbababaaaabaabbabbbaababbbbbaaabbabaabaabbaabbaaabbaabaabaaabaaaaabbbaabaabbabbbbbabababbbbaaaaaabbbabbbbbabababbaaabbabbbabbaaabbbaaaaabbabbababbabbbbaaaababbbbaabbabbbaaabbabaaabaabaaaabbbaabbabaabbbbbabaabbbbbbbbaabbaababaabbabbbaabbabaaabbabbbaaaabbabbbbaaaabbabbbabababbbbbbbabaabbbbaaaabbbabbaabbbbaaaabaaaabaaaabbbbbabbaababbaaaaabbbababbabbaaabaaaaababbababbabbaabbaabbbbbabbabbbaabbbaabaabaabaaaaabaaaabbaabbabbaabaaaaaababbaaaaabbbabaaabbaabbbbbababbbbbbbbababbbababababaaabbbababaaababababaaaababaaaaaabbbbababaabbabaaaabaabbbbabbabbbabbbabbbbaabbababaaaaaabbaabababaaabbbbbbbbbbbbabbbabbabbaaaababaabbabbbaaaababaabbabbaaaaaaabbaababaaababababbbaabaabbbaabaaabbbbaabaababbabaaabaabbaababbbbbabbaababaabbbabaabaabbbbabaabbbaabbbabbbbaaaabbaaaaaababbbabababbaaaababaaababbbbbabbababbbbbbaaabbabbababbaaaaaabaabbbaabbbbabbaaaabaabaabbaaababbbaaaabbaababababaaabaaabbbbbbabaaaaabbababaaabaaaaabbbaaabbbabbbbbbababbbbbabaaaabababbbaaabbbbaaaaabbbaaaaababbabbabababbbbaababaabaaabaaaabbbbabaaaabaaabbbabbbbababbbbabaabbaaaababbbbbbabbaabbabaaaaaaaaababbbbabbaaaababbaaabbbbbbaabbbabbbbabbabaabaabbabaaaaabbbabbaaabaabbabbaaaaabaabbbaababbbabbbbbabaabbababbabbabbbaaaabaaaabbaabbbbabbbabababaababaaaabbbbaaababaabbabbbaaabbabbbaaaaaaabababbbaaababbbabaabbbaaaaaaaaabaaaaaabbbabbbabbbbabbbaaababababbbbbbabbbabaaaabaababaaaaaababbbbbbbbbbabbbabaaaaaaaababbabababbaabbababbaabbaabbabaaaaabbabaabbbabaaaabbbbababbabbbabbaabbababbbbaaaaabbbbbabbaabbbbaaababababbbaaaaaaabababaaaaaaabaaaabbabbbabbaaaabaabaaaaabbabaabaaaaabbaaabbbbbbbabababbbbababbaaaabaaaabbbabaababaabaabaaababbbaabbaaabbbaaababbbbbbabbaaaabababaaaaaaabaaaaaaababaaaaabaaaaaaabbbbaabaaabaababaabaabbababaaaaaaababbaababbababaabaabbbababbbaaabbbaabbbbabbbbbbbaababaaaaabbbbaaaaaaaabaaabbbbabaaaaababaaaabbaaabbabaaaabaaabaabaaaaabbabbbbbbbaabbbaaabbbbabaaabbbbababbaaaabbbbbabbaaabaaaaaaababaabbbbbbbabaaababaabaaabbbbaaababaabababbaababaabbabaabbaabaabbaabababbbbbbbaabbbbbbbbabbbbaaaaaabbabbbbabbabbbbabbbbabaaabaaababbbaaaabaabababaabaaabbbabaaaaabaaaabbbbababaaaabaabbaaaabaabbabababaabaaaaaaababbabbaaabbababbaaaaababbbaaaabaabbaabbabbbbaababbbaaabaaaaabbabaabbbbabbbaaabababbababaaabbabbaaabababbbbaaabbaaababbbaaaaaababbaabbbababbaababaababbbbbbabbaaaabababbbaabaabaababaaaaabbbabbbaaababbabbababbaabaabbbbabbaaaaaaabbbbbbbbaaabbbaaaaaaaaaaaaabbbbbabbaaaaabbaaabaaabbaaaabaaaabaaaabbaaaaaabaababbaaaaaaabaabbabbbbbababbbabbbaaaabbbabbaaaababaaaaabaaaaabaaaabbbbbbaabbaaabbabbabbbabbbbaaaabbaabbbbbabbaababbaabaaabbaababaabaaaabbabbbababbbbaabaabbbbbbabbabbbbababbabaaaaabbbbaabbabbbbaabaabaabababbaaaabbbbabbbbaabbaaababaabbbbabbabbbbbbbabaabbaaaababaabbbbabababaaabbaabbbaabababbabaabaabaaababaaabbbabbaabbaaaabababbbaaaabbbbbaabbabbbbbaaabbbbaabbaaabaabbbbababaabbabbaaabbbbabbaaabbaabbbabababaaabbbabbabbbbbabbabbaababbaaabaaababbbabbaabaabbabaabbaabaabbbbaaabaabababbbabbabaababababbaabaaabbbaabaabbaabaabaababbabaaaaaabaaaabbbababbbabbababbabbbabbbabbaaabaabaaaabbaabbbbabaaabbabaaabbabaabbbaabaaabbaababbbababbbbaabaabbbbababbbbaaaabbbbaabbaababbbbbbabbabaababbbaaababbbbbbaaaabaaababbaaaaaaabbbbbaabaaaabaaaaaabbbbabbbaabaaabababbbbabbaabaababbbbaaabbbbbbbbbaaabaaabbaabbbbaabbbbbaaaaaababbbabbbaabababababbaabababbababaabaaaaababaaabaaaabbabbbbbababaaaabaabbababbbaabbbbaaabaabbbaaabbbabaabbabaaaaaaaababbbbabbbbbaaaabbbbbbbaaaaaaaaabbaaababbbbbbabbaababaaabaaaabbaababaaabbabababbbbabbbaaaaaaaaaaaaaabaaaabaabababaaabbbbbbabbbabaaabbaaabaaaaaaabbabaababbbaabbbaaaabbbbbaabbabbbabbbbabababaabbbbababbababbaabaaaabbababaabaaaabaabbaabaaababbabaabaabbbbabbbaabaaabbbbaaabaaaaabaabbaaabbbbbbabbabbaaaaaaaabbbaaabababaababbbaaabbbabaabaabaabbaababbbbbbbbaaaaaababbbbbbababaaabbbaabaababbaaaaaabbabbabaaabbbbbabbabbbabbabaaaababaaaaabbaaaabbbabaaabaaabababbbbababaababababbabaababbabbabbbaaabaaaaaabaaaabbbbbbabbaabaaabaaaababaaaaaabaaaabaaaabbaabbbbabbaabaabbbbbabbbabbbbaabbabbbaabaabaabaabbbbbabababaabbabbaababaabaaaaabaabbbbbaaabbabaaababbaabbabbabaaaaabbbbbabbbabababbabaabbabaabaabbbbbbbbbaaabaabbbaaabaaaaabbbbbbabaabaabbaabbaabbabbabbbabbbababaabbbaaabbaaabbbaaaabbbbaabbbaababbabaabababbabaaaaaaaabbaaaaaabaaababbaabbababaaaaaaaaabbbaaabaabbbbbabaaaaabbbaaabaabbababbbabbbbbbbbbbbbaabbbbabbaaaaaabbbbabaabbabbbbbababbaabbaaaabbbbaabbbbaaababbbbaabbbabbbbbaabaaaabbababaababbabbbbaabbbbbaaabababbbaabababaaabbaabbabbbaaabaabbabbaaaaaaabbbbabababababbbbbaababbbaabbbbbbaaabababbaabbbaabaabbaabbbaabbbaabaaaababbbbababaaaaabbbababbaaaaaabbbabbbbababbababaaaaabbbbbbabaabbbaaaabbabbaaaabaabbabbaabbbababbbbbaaaabbbbabbbabbbbaabbbaabbaaabbabaabbaabbbabbbabbabababbbabbabaababaabbabababbbbbababbbaabbaababbbabbaabbbbabbbaaaaaabaaaaaabaaaabaabbaabbabaaabbbbbaabababababbaabbbbabaabbababbaaabbbbaabbbabbaabaabaabababbaaaaabaaababbababbbbaaaabbbbbbbbabaabaaabbbbbaaaaaababaabbbbaaaababaaababbbbbabababbbaaaaaaabababababaabbaaaaaabbbabbaabbbbabbaabbabababaabaababbaaabaababbabbaaabbabbbbbaababbbababaabbbabbbbbbbaabababbababaaaaabbabbaaababaabbaaaaabbabaabaaabbaabbaaaaababbbbbbbbaaabbaabbaabaaaabababbbbbbbbaabbaaaabaaabbbbbaaabbbbbbbaaaaaaaabbabababaabaaaaabbabbbbaabbabaababaaaaabbbaaaaabbbbabbbbbaabbabaaaabbbaaababbbababaabbaaaababaaabaaabaaabbbbaababaabbbaabbbaaaabbbbbbabbbaaaabbaaaaabbaababbbbbaabaaaabbabababbaaabbbababbaaaabaababaabaabbbbababbbbbbbbbabbabbabbabaabaaaaaaaabbbaaabbaaabaaaaababbabbbbbaabbbaabbbaababaaabbaabbbabbbaaaaabbbbabababbabbbbbabbaaabbabbbbbaaaabbbbbababaabaaabbaabaaabaaaaabbbbbbbbbaabaabaabababbbaabbbaabaaabaabbabbbabbaabababaabbaabbabbbabaabababaaaabaabbbaaabaababbaaabbbbaabbbbbaaabbbaaababaaabaaabbbabbbaaabbabbbbbbabbabbbbbaabaaaabababbbabaaaababbababaabbbaababababbbbbabbbbaaaaaaaaababababbaaababaaababbbaababbaaabbaaabaaaabbbbbbabbabbaabababaabaaaaabaababbaaaabbaabbabbbaabaabbaabaabbbaabaabbaaabbbababbaaaaaabbaaababaabaaababaabbbabbbaababbabbbabbaababbaaabaaabaabbbbabaaabbbababaabaaabbbabaaabaabaaabbabbabaaaabbbaaaababbaaabbabbababbbbababbbbbbbabbababbababbbbaaaaaaabbabbaabbaaaaabaabaabbbabbaabababbbababaaaabbabbbbabbbbbabbbaabaabbbbabbbbabbbaaabbabaabaabbbbaaaaaaaaaabababaaaabbbbbbbbaaabbaababbbbbbaaabaabaaaababbbababaabbbaaaaabbbbbaababbababbbabbabababaabbbbaaaaababaabbbbabbabaabbabbbbabbabbabaaabaabbbbbbaababbababbaaaabababaabbabbabbaaabbabbbbabbbbbababbabbbbbababaaaaabbaabaababbabababbbaabbbbaaabababbabaaabbbbbaabbbabbbbaaaabbababaabaaabbabbbaababbbbbabbbabbabaaaabaabaaababbbbaabaaababaabbbbbabbabbaaabababababbaaaaabbbbbbaaababbbbabaababbabbbbaaabbbababbababaaaaabbbaabbaabbababaaabbbbaaabbbababbaabbabbbabbbaabaababaaabaaabbababbbabbbaaaababaaabbbaaabaabbbbbaaabbaaababbbaaabababbabbabbabbaaaaaaabbbaaaabaaabaabbabaaabaababbbaaaabbaaabaabbaabaaabaabaabbbbbababbaaabbbaabbaaababaababababbbbbabbaaabbbaabaaaaaabbbababbbbbabbbaabbbbabababbabbbabbabbbaaababbaabbaabaaaaabbabbaabbbababbabaaaaababbabbbbbbaaaababaabbaaabbbabbbabbbbabbaabbbaaaaaaaabaaaaabbabbaababbabbbaaabaaaababbbaabaaabbbabaabbabbaaaaaabbbbbbaaaaaabbabbbbabbabbbaaabaababaaabbabbbabaaabbabaababaaaaabbbbbaabaabbaabbaaabbbbababbbbaaababbbbbababbaababaaaabaaababbbabbbaaabbbabaabaaaababbabbabaabaababaabbaaaaabbabbbabbbaabbabbbababbababbbababbaabbabbbbbbbbaabbabbbaaaabbbabaabaaaaaabbaabbabbaabaaaaaaabababbbbbbbaaaabaabbabbaaabbbbbabbbabababaababbbbaaababbababbbaaabababbabaabbaabbbaaabababaababaabaabbbaaaabababaaabbabbbabaaabababbbbbbbabbabaababaaaabababaabbaababbaaaabbbabbbbbababbaaabbaaabbbabbbabbabbbaaabbbaabaabaabbaaaabbbaabbbaabbaabbabaaabbaaaababbabbaabaabbaaabbabbbbbbbbabbabbbbbbbbaaaaabaaaabaaaabbbaabaaabaababababbaabbbbababbbbbaabaaabbbababbbbaababbbbbabababbaaaabbaaababbbabbabbbaabbaaaaabbabbababaaababbaaaaabaaabaaaabbaabbbbbaabbbbbbaaaabbbaaabbbbabbbabbaababbbaaababaababaaaaaaaababbbbaaababbbabaaaababbbaaaabababaabaaaaababbbbbbabbaaaaabbaaaababbaabbbaaaaaaaaaabbbababbbbaaabbbbabbbaabbaaabaaaaabbaaabbaaaaaabbaabaabbabbaabbbbabbaabaaabbabaaabbbbbbbbaababbabaabaabababbbabaababbbbababbaabbbbaaabababababbbaabbababaaaaaababbbababbbabaaababbbaaaaaaaabbbaaaaaaaabbabbabbbabbabaababbaaabaabbbbbaababbbabbaababaaaaaaabbaabbbbaaaababbbabbabbbababbbbababbbaaabbaabaaaabbaaabbbbbbbbaabbababbaabaaaabaaaabbbaabbabbbbaabbbaaabaaaabbbbabaaabaaababaaaaaabababbbababbbbbaaaaabbaababbabbabbababbababbbbbabaabaababbbbbbbbabaababbaaabbbabbabababbbaabaaabbbaababaabbbabbabbaaaababbbbbbabbbbaabbaaaaabaabbbbaabbbababbbbbabbabbaaaaaaabbabaaaaabaababaabbbbbbbbaaabbaabbbaabbbbbabaaababbbbaabababaaabaabaaabaababbbbbbbaabbbbabbbabbabaaaaaaaababaababaabbbbaaaabaabbaabbbaabababbbaaaaabbbbbbbbaaabbbbbabababaaabaabaabbababbabbabaaabbbbaaaababbabbabaaabbabbbbabbaaabbbbaaabaababaaaaabbbabaaabababaaaabbabbbaaabbaabbaaabbbbbbabbaaabaabbabbaabaabbbaabaabbabbbbbbababbbaaaaaaaabbbaaabbaabbabbaaababaababbaabbbbabbaaabaaabbbabbbabaabbaabbbaaababbbababbaabaabababaaaaaabaaabababbbaaaabaabbbbabbbbbbbabaaabbbbabbaababbbaabbbaabbbbaabbbabaaaabbabbbaaaabbabbabbaaaabbaaaaaabbaabbbabababaabbbaaaababaaaabbababbbbbbbbaabbabaaabbbaabbbbabaaabaaaaabbaaaabaabbbbbbababbaaababbbabbaabbbbbabbbbbaaabbaaabbabbbbbbaabababbbbbaabbabaaaaaaababaaaabaabbbabaaabbabaaaabbbbbaaabababbbaabaababbabbbaaaaaaaabaaabbbbbbababaaababbbaaabababbaabbbbbbaaaaaabbbaababbbbbabbabbbaaaaababbbaabbbababaababaababaaabaaaaaababaabbbaaabaabaabbbabaabbabaaaaababaaababaaabbababababaaabbabbaabaaaaabaaabbbbbababbaaabbbbaabaaababbaabaabbaaaabababababbbaabbbbbbabababaaaabbaababbaabbabaaaaabaaabbbabaaaaaaaaababaaaaaaabaaabbbbbbaaabaabbbaaaababaabaababaabbbbbaabbbabbbaaaababbaabbabababbbbbaaababaaaaaaabaababbaaabbbaaaaaaaaabbbababaaaabaaaabababaaababbbaababaaaaaaaabbaaaabaababaaaabbbbbbbaaaaabbbabbbbbaaaaaaaabaaaabbaaabbaababababbaaaabbaabbbbbaaaabbabbbbbabbbbbaaaaabbbbabbabaaabbbabaaabbbbbaabbbabbaababbababbabbbbabaababbababbaabbbaababbabbabaabaabbbbbbabbaabababaabaaabbbbbbbaaabbbaabaaaabbaaabaaabaababaaaababaabbabbaaaaaaaaabaaaabbbaabbabbaaaabbabaabaabbababbbbabababbabbbaabaabbaaaabbbbaaaababbabababbaaabaaaaabbbbbbbabbbbaaaaabaabbbbaababaababbbbbbaabbbabbabbbbbaaaababaabbabaabbabababaababbabababaaabbabbbabbabababbbbaaababababbbbbaababbaaaabbbaaaabababbabbababbaaabaabbaababbabbabbbbbabababbaabbaabbabbabbaaaaabaaabbbababaaaabbabbbbaaaaaabbbbabbbabbaaaaabbbabaaaabababbaababbababbbbabababababbbbbaaabbbbaaaabbbaabbaaabaabaaabababbbbaaabababbbbababbbabbbbbbbabaaababbaaababaabbbabbbbbbbbbbbbbbaababaaababaabbbbabbabbbabbbaabbabbbbbbbababaabaabaaabababaababbbabaabbabbbabbbabaabababbabababbaababbababbababaaabbababbbaaaaaabbbbaabaabbbbaabababaaabbbbabbbbaaabbbbaabaaabbbabaabbbaaabaababaababbbbababbbbababbbaaaaabaaaaaaaabaaabbbaabbaaabbbaabbababbaaaabbbbabaabaaaabbababaaabababaabaabaaabbbbaababbbbbabaaabbbbbabbbbbbbbabbbbaaabbbbaabaaaaaabaababbbbaabaabbbbababababbababbaabbaababbbaababaaaaaabbabbbbaababbbbabbbbbbbaabaabbbbbbbababbababbabbabbaaabbabbabaaaabaaaaababbaabbbaabaabbbaabbaabbbabbbaaabbaaabbabbbaabbabbabbbbaabbbbbaabbbababbabbbbbaabbaabbaabbbbabbababbabaaabbabaaaaaababbabbbbabaaaababbbbbbbbbbbababaaabbbabbbbabaabbbbababbbabaabababaabbbababaabaabbbaabbaaabbbaabaabaabbbbbabbbbbaaabbabbaabbabbbabbbaabbabbabbabbaabbabbaaaaabbabababbbbabababbbbaaababaaaabaaabbbababbaaabaabaaaababbabbbaaabbababbbbbbabbabbaabbaaabaaabbaababbbabbaaababaabbaaabaabbbbbbbaababbbbbabbbbbbabbbbbabbaaabaabbaaaaababbbabababaaaabbbbabababaababbbbaaabbbaabbaabaabbaaaaabbabbbbaaabaabbbbbbbbabbaaabbaaabbbaaababababbbabbaababbbaabaaababbbabaaaabbbbbbaabbbaaaabaaaaaababbbabbaaabbbabbbabbabaabaabaabbbabbbabbaaabaabababababbababbbabbbbaaabbbbaaaaabbbbaabbbbbbbbbabbbbbbbaababbbbabababaaabbababbbbaaabaaaaabbbbbbabbaaaababbbbbbaaabbaaabbababaabbabbaabaaaabbaabbabaabbaaabbaaabbaaaaaabbbabbbabbbbbbbabbbaabaaabbbbbbaababbaabaaabaaaabbababaababbbaaaaabbaaabbbabaabababbbabaaaaabbbabbabaaabababbaaabbbaaaabaaaaabaabbbababaaabbabbaabaaaabbaabaabbabaabbabbaaaabaabaaaababbbbabbabaabbbbbabbbaabaaaaababaabbaababbabbabbabaabababbaabbaababbbbbbbbaabaaaaaaababbabaaababbbabaabbbbbabbbbabbabbbaaababaabaaabaaabaaaababbabbbbbabaabbbabaabbbbabababbabaaaabaabaaababaabbaababaabbababbabbbbaabababbababbaaabaabaabaaaaaabbabbabbbbbabaabbababbaaaabbbbbaaaaaaaaabbbbabaabaabaaaababbabaaaaabbaabaaabaabaaaaaababababbabbaaababbabbaabbbaaaabbaaabbbaaabbbbabbbbaabbabaaabaabaaabababaaaabaaabbbabaabbbaabaabbabbaababbbababbbbbababaaaaabaabbaaabaabbbbbaabbbabbbbaabaabaabbbaababbaaabbbbbbbaabbbbbaabbbabaaababbbbaaabbbbabaaaabaabaabbaaabbbaabbaabbabbbabbbaabbbbabbbbbbaaabbbbbbaaabbbaabaaabbbbbababbaaabbbbbbaaababbbbbaaaabbbbabbababaabbabbabaaaabaaababbbabbabbbabababbbbbaaaaaaababababbbbbbaabababaabbbbaabaaaaaababbaabababbbaababbaaaaabaaaaabbaabbabbbbababbbabaaababbabbabaaaaaaaaaaaabaabbabbbbbbabaabbaabaaabbaaabaaaababbbaaaabaaaaabbaaabaababbbaaaabaaabbababbaaaabbbbabaaababbbbbbaabaaaaabbbbabaabaaaaaabbabbbbbaabaababaaabaababaaabbaabbbbaaabaaabbbabaaababbbbbaabbbabbaaabaaabaabbabababbabbbbbbaaaabbababbaaaaababbbaaaaababbabbbabaaababbbbbabababbbaabaaaabababaababbbbaabbaaaaabbaaaaababbbabbabaaabaabbabbaaaaaaabaabaaaabbabbaabbbbbbbbabaabbbbaababaaabbaaaaaababbaaababababbbbbaaabbabbbbbaaaaaaaabbbbabbbbaabaabbaaababaaaaaaabbbbbabaaabaaaabbbbbbaabaaabbaabbaabbabbaababaabaaabbbbaaabaabababaaababbbaababbabbbaaaaaabaabbbaaabbbaaabbbbbaaabbbabbaabaabbbbabababaababbabbbabbabbbaababbababbbaabaababaaababbbaaaabababbbbabbbaabbbbbbaabbbaaabbbaabbbababbbbbaabbbaabbabaaababbabbaaaabbaabbaaaaababaaaabbbaabbabbabaabbaaaaabaabbababbabaaaaababbbbbaabbbbbbbabbbbbabbabbaaaaabbaabbababbabbbaaaaaaababbababaabaabaaababababaabaababaaababbaabaaaababbaaaaaaaabbbaaaababaababbaaaabbbbabbabaaaabbbaaababaaababaabbabbabaaaaabbaabbaabaababbaaaaaabbabaabaaababaababbbaababaaabaaabababbaaaababbbbbbbbbabaabbbabaababbbaabbbabaaaabaaabbaaaaabbbbababaabbbaabbabbbbaaaabbabaabbbabbbabababbaaabbaaaaaabbbbbbabbbbababbbbabbbbaabaaaaaaabaaaaabbababbbbbabbbbbbaaababaabbabaabbabbbabaaaabbbabbbabaaaabaababaabaaabbbbaaabbaabbabbbbbaabaaaaababbaabbaaaaabababababaababbababaaabaaabbbaababbabbbbabbabaabaaaabbaabbbaabbbaaaaabbbbbaaabbaabbbbabbbbaabbaaababbbbbabbbaaabbbbbaabababbaaabababbaaaaabbabbbabbabbbbabbabbbaaababaaaabbabaaabbbabaabbababaaabbabbabaabaabbbbbbaabaababaaabaaababaabbbaaababaaabbaaaababbaaabbbbbbaaabbbaaabbaaabaaabbaabbbbbaaabbabbbbbbabbaaabaaaabbabbaaaaaabaaaaabbbaabaabbabbabbbabbabbababbbabababbbbaaababaaaabbbbbbabbbbaaaaabbaaabbbabbabaaabbbabababbabbaabbbbbaababaabbabaabbaabababbbabbbbaaabbaaabbabbbaababbbbbbbbabaaabababbabaaabbbabbaababaabbababbabbbaaaaababaabbbbaaaabbabbabbaaaaaabaaabbbaaaaaaabaabbbbaaabbabbaaaabaaaabbababbbbbababbbabaabbaaaababaabbaababbbbbbbbaababbababbaabbaababbbaababbaaaaabaaabbaaaabbabbbbbaabbaabaabbababbaaabbaabaaababbaaaaababaabbabaaaababaaabbabbabaabaaaabbabbababbbaabaaaabbbbaaabbbabaabaaaabaaaaaabbbbabaaaabaabaabbababbbaabbabbabbaababaaabbbabbaabbaabaabababaaabaabbbaabaabbabbabbbbbaabbaabbbbbbbbbaaabaabbabbbbaababbbabbaabbbbabbaaaababbbbabbababbbaababaaabaaabbbbaabaaabaaaabbbaaaaaababbbaabaaaaababbbbraaaaaaaabaaababaaaaaaaaababababaaaababbbaabaababbabbbabbabaaaaaaaabbaababababaabaaaabbbabbbaaabaaabaabbaaaabbbbbbabaaaababbbaabaabbaaababbaabbabbbbabbaabaaaaaabbbbbabbabbaabbabbbbbabbababbaabaababbaabaaabbbbaababbababbbbaabaabaaababaabababaaabbbabaabbabbabaabbbbbbaabbabbaaaabbaabababbbbbbbbbbaababbabbaabaaabaabaaabbbbbabbbabbaaaaaabaabbbaabbbbaabaaaabababbabaaabaaabaaaabbbbbabaaabbbbabbaabbaababbbabaaaaaabaaaaabbbbbbabaaaaaaabbaaabaabaaabaababbbabbbaaabbbabbbbaabababaaabaabbaaabbababbaabbaabbaabaababaababaaabaababbbaabbaaaabbabbaabbaaabbbbaaabaabbabbaaaabbabbaaabbbbabaaabbbbababbbabbabbbbaaaaabbbbabbabbbababbabababbbabaaabaaababaaaaabaabbaaaabaaabbaabbbabaaaabbabaaaabababbbabaaabbbaaaababbaabaabaaaaabbaababaaabbbaabaaabaaaabaabaabbaaabbaaabbaaaabaabbaabbaaaaabbababbbaaaababbabbaabaabbaaabbbbaabaaabbaabaaaaabababbbaaaaaaaaaaaabbbbbababbaaaabaaabbaaaabaaabaababbabbbbbbaabbabbbbabbabbaaabaabbabbbababaaaabbabababbaaaabbabaabbabbbaaabaaababaababbbbbbbbbaaababaaabaabbbbababababaabbbbaaabaabbaaabbabbbbaaabaaababbabbbaaaaaabaababbbaabbabaaabbababababababbbbbbbbabbbbabababbabbbbaabbaaabaaabbabbababbabaaabaaabbaabaaaabaaabbabaabbabababbbbaaabaabaabbaabbabababaabbbbabababbababaabaaabaabaaababbbaaaabbbabaaaabbababbbbbbabaabbaaabbbaaabaaaaabaabbbbbaababbbababbbbbaaabbabbbaaababbabaaabbbaaabbabababaababbaaaaaabaabaabababaabaabaaaabbaabbbbbbaabbaabaabbbaababaababbbbaabaababbaabaaabbbaaabbaaaababbbbbbbaaabaaabbbabbbbbbaaaaababbabaabbbbababaabbababbabbabbaaabbbabbababbbaaabbbaabaaabbaabaabbbabbaabbbabbaaaabbaaaabbabbabbbbabbaabbbaabbbbababbbaabbababbaabaaaaaaabbabababaaabbabbabbaababbabbaabbbbbbbbaababbbaaaaaababbabbbbbbbbabaaaaabbbbbaaabbabbbbaababaababaaabbabaababbaababbbbbaaaabbbbaaaababbbabbabbbabbbaababaaaaabbaababaababbbbaababbbabaaabbbbbbbbabbbaabbaaabbabbaaababaaaabbaaaaaabbaaaaaaaabaaaababbabbbbabbbabbaabbbbbbabbbaabaaabbababbababbbabaababababbbbaababbbabbbbbaaaabbbbababbbbabbbbabbababaaaaabbbaaabbabbaaaaaaaaaaaabababbaabababbbbabbbbbaaabbbabababbabaaaaabbaababbbbbababaabbaabaabbaaaabbaaaabbbbaababbbbbabbaaaaaabbababbbabbbbbbabbabaaabbaaaaababbaaaaaaaabbabbbbabbbaabaaaaaababaaabbaaaaaaabbabbbabbabbaababbbababbaaabaaaabaaaaaaabaaaabbbaabbaaabbbaabbabaaabaaababaaaabbbabbbbabbbbababaabaaabbbaaabbababbbbaaabbabbaababaaababababbbbbbababaabaaabbbbababababaabbabaababbaabbbabbbbabababbbbbaaabbababbabbaabbabbaabbabbabaabbbaaababaaaaaaaababbaabbbabaaababbaaaabbbbbbaabbaabbbbbaaababaabbbaabaababababbababaaabbbabaaaabbaaabbbaaaaaabbbbaaababaabbabbaaabaabaaababaaaabaabbabbbbbbaaabbbbbbaaaabbabbbbbbbbbbbbbababbbabaabbaaabbbbbbbaabababaabaabbabbaabbbabbbaaaababbbbaaababaaaaaaaabbbbabaababaabbbaaaaaaabbbababababbaaaaabbaaababbbbbaaabbaaaabbabaaabababaaaabaaabaabbbbbaababbaabbbabaaabaabbbbaaabbabababaabaabaabbbaabbbaabababaaabbbbbabaaabbaabbabbabbabbbabbbabbbabaabbbabbabbbaabbabbbbbabbbbbbbaabbabbaababababbabbaaaaabbbaaaabababbababababbbababaaaaababbbbbabbbbbaaabbaaabaabaabbabaaaaaaaaabbbaaababaabaabbababbbbaaaaabbbbbbbabaabbbbbbbbbbabaaaaaabbbbaaaababababaabaaabbbabaabaaaababaaabbabaabbbabbababaabbabaabbaaabbbbbbabaabbabaaaaaaaaabbbaababaabaabaaabbaabaabbbbbbbbbaababbaabbababababaaaababbaaaabbbabababaaabaaabaabbaabaabaabbaaabaaabbabaabbbabbabaaaaaaaababbbaabaaabbaabbabbbabaaaababaaaaaababbbaabbbbbaaabbbabaabaaaabbababbaaabbabbbbabbaaaaaabababaaabaababaaabbaaaaaabbbaaaabababbaababaabbbbaabababbaaaaabbaaaaabbbabaabaabbaabbbbabaaabbaabaababbbabaabaababbaaaaaaababaaabbaaabbaabbbbbbaababaabbbabaababbaabbaabbabbaaaaabbbabbaabbbbbabbaaabaabaaaabaabaaaababaaaaabbbbbbaabababbbabbbbabbaabaaabbbaaaabaaabbabaabbabbaabaababababbabbaababbbaabaababbabbabaaabaabbbaaaabbaabbbaabababbbbbaabbaabaabbaabbbabaabbbbbaabbbbbabbaabababaabbbabbabbaaaabbbaabbbbabaabaabbbbbabbbbbabbbbaababaabaabababbbbabaaaabbaababbabaaaababbbbbbaaaaababababbbbbbbbababbbabbabababababaababaaababbbbbbaabbbbaabaaaaaababaabaaaaabaaabbbbbbbabababaaabbbbaaaabbbbbaaabaabababbbbbaabaabaaababaabaabaaabaaaaaabaaabbaabaababbboabaaabbababbbabbbaabbaabaaabaaabababbaabbababaabaabbbabbaaabbabbaababbbbbababbbbbabbbbbbabbbbaababbaababaababbabbbbababbabbbaabbbbabaababbbaaababbbabaabbbaabaaababaaaabaabbbbaaabbbabbabababbbaaaaabaabaaaabbaabbababaabaaabbbabaaaaababababbaabbbbaabbbabaabaaaaabbbaaaaabbbbbaabbabbsaaaabababbaaaaabbababaaaaabbaabbabbbaabbbbaababbbababaaaabbbaaabbaabbbbbabbbbbabbabababababbabaaabaabbaaaaaabbababbbabaaabbabaababbbbbabbbbabbabaabababbbaaaabbbaaabaaaabbbbbbbaaaaaaaaaaaabbabaaabaabaaabaabbbabbabbbbbaaaaabbbaabaaaaabababaabaaababbbaabababbbbabaaabbabaaabbaaaaabbbabbbabbaabaabbaaaaaababbabbbbaaaaaabbbabbabbbbbbaaabbabaabaaaabaabbbaabbabbbaaaababaaaababaabaaababbbabbbbbbbaaaaabbbbaabbbbbabbabaaaababbbbbbbbababbaabbbbabbbababbabbabbbbbbabbbbaaabbbababbbbaaaaabbaabbbaabaaaaabbbbbbbbabbababbaaabbaaaaaaaabaababbbbabaabbbaaaaaabbaaaabababbaaaabbbaabbbaabbbbaabbabbbabbbabbabbaabaabbbbaabababbbbbaabaabbababbbbbababbbbbaabababbaabbbbbabbabbabbababbbbaabbbabaababbbabbaabaabbbbaabbbaaaaaaaabbaaabbbabbbaaabbabbbbaabaaababbbbbbbbbaabaaaabbbaabaaaabbbbaabaaababbbbaabbaabbbabbbabbababbabbbbababbabbbbaaabbbabbabbaaaababbabbaabbababbbaaaaabbaabaaabaaabababaabaaaaabaaaababbabbababbabbaaabaabaabbbbaaaabaabaababbaabaabababbbabaaaababbaababbbaaaabbabbaababbabbaaaaaaaaaabbaabababbbbbbbaababaabaabbabaabbbaaaaaabaaaabaababaabbbabaabababbbbbbaabbaabababbbabbaabaabbbabbabaabbaabbbbbbbaabbaabbbaabbaabbbabbabababbbbaaaabbbaaabaaaabaabaaaaabababbbabababababbabbaaaaaababbbaaabababaabababbaabbaababbaabbbbbabaababbaabaaaaabbabbaabbbaabaabbbbbbbbabbabbbaaabbabbaabaabbbbbabbbababaabaabbbbbabbababbaababaaaabbbbaaabbabaabbbabbbabbaaaabbbbaabbababbbbaabaababbbaababbabbabbaabbabbbaaaaaaaaaabbaaaaaabaabbaabaabaabbaababaabbabababababbbbbbaabaabbabaababbababaabbbaaaaabbabbaaaaaababbaaaabbabbbbbbbbaaaaaabbbbbaabaabbaaabaabaabaabbabbbbbababbaaaabbaabbbaaabbaabbbababbbbbbaaabbbbbaaababbbaaabbbbbbaabaabaababbbbbabaaaaaaabbababbababaaaaaaababbaaaabbbbbaaaaaabbbaaaaabbbbbabbaaabaabaabababaaaaaabbaabaaaabaabaabbbabbbabbaaaabaabbbaaaabaabbbbababbabbabbbaaaabaaabbaaabaabababababaaabbbaababaaabbababbbbabbaabbbbaaaababaabbababbbbabbabbaabababaabaababbaabbabbababbbbaababbabbbbabbbbaaabbbabbabbaabbaababaabbbaaaabbaaababbbabbaaabbbababbaaaabbaaabaabbaaaabbbaaabbbababbaaaabbabbaabbbbabbbabaaabbbabbbaaababbbabbaabbbabbabbabbbabaabbbaabababbbaaabaabaaaabaabbbaabbbaaaabaabbaaabaaababbabaababaababbaababbbabbbbbbbabaabbabaaaabbabaabbbabbbbabbbbbabaaabbbabaabaababaaabbabaabbaaaaabaabbbbababbbaabbbbabaabaaababbabbbababbabaaaababbbaaaaabbbababbabbbbbabaaababbbabbbbaaabbbaababbbbaabaabaababaabbbabbaaabbaaaabbaaaaaaabbbaabaababaabaabaaabbbaabababaaaaababbabbaaaaaaabaabaabaabbabbbbaaabbbabbaaabaabbbabbaaabbbbbababbabbabababaabaababbbaaabbbaaababbababaabababbabaaabbaaaaabbaaaabbabaabbbaabaabbbaaaaaabbbabbbabaaaaabaaaaaaaabbbbaaaaabaabbaaababbbbbbbbbababaaaabbbbabbaabaababaaabbabbaaaaaaabbababaaaabbaaaaabbababbaababbaabbabaabbaaaabaabbababaabababbbbbaababababbbbbabaaaababbbababbabababbbababbbbbaabbaabaaabaababaabbabbbbaababbaabbbbaaaababbaaabbbbbaaaaaaaaabbabbbbababaaaaaaaaabaaabaabbbbbaaaaabaabbabbaaaabbbabbbbabaabaabaabaaabaaabbabaababaabaababbbababbabaaabaabbbaabaaaaaaaabbaaaaaaaabaabdbbbababbbabaaaabbabaaaaaaabbbbbbabbbbaaabbababbbabaababbaaaabaabaaaaaaabbbaabbaaaabbabaabaabaabaababbbbabaaaaaaaabbbababaabaaaabaaaabbbaaabaaaabaaaaabaaabbbaabbbabbbaabbaabbaaaaabbbbbababaabaaabaabbaaaaaabbaabbbabbabababbbbabbbbbaababbaabbbababbaaaaabaababababaabbbbaaaaababbababbabaaabbabbaaabbbbbaaaaabbbbaabbbaaabaaabbaaaababbbbbbababbbaabbaaabbbbbabaabaaaababaabaabbaabbaaababbaabbbbbbbbbabbbbbaaabaaaaabbabbabaababbbaabaabababaaabbabbaabbabaabbbabbbababbabbbaabbbbbbaababbbaaaabbbbbbaaababaababbbaaaaabbbaabbaabaaabbbababbbbbaaaabaaabababbabaaaaaabbbbbabbabaabaaaabbbbbbbabbabbaabaabbaaaaabaabbbbabbabaabbaaaabababbaaabaaaaaabababbaaaaaabaaababbbaaabbaabbababaaaabaabbaaababbbbabababaabbbababbbabaabbabbbababbbbababaaaaaabaaaaabbbbaaaaababbbbabababbbaaababaababaabbaaaaaaaaabbabbaabbbbbababbaaaaabbbbbabbabaaabbbabbabbaaabababaababababaaababbaaababaaaabaabbbababaabbaabaabaaaabbaaabbabbbabaabaababbbbaaabbbabbbbbabbaaabbbabaaabaaabbababababbababbababbabbbabaaababaabbbaaabbabababbbabbaaabbbabaabbbabbaaaaabbbabbababbabbabbbaabbabbbbabbbababbbbabbaabbbbbaaaaabbaaaabaaabaaabbaabababbbaabaaaabbbbbbbbbaaabbaaaaaabaaabbabbaaabaabbbababbabbabaaabaababbaaaaaabbabbababbbbbabbbababababbabbabbbbaaabaabaaaabaabbbbbbaaabbaabbbaaaababbbaaabbbabbbbaaaaaabbbabbaabaaaaabbabbabbabbbaaaaaaababababbaaabbaabbababaaabababbbaaaaaabaababbaabbbbbbabbbbaaaaaaabaaaaaabbbaabaabaaaabaababbbbaaaaabbababaaaaabbbabaaabbbbaaaaaabbababbbbabbaaabbbbbaabababaaaabbaabbbabbabbababbabaabbbbbbaabaaaaabaabbbaabbbaaabaabbabaaabbbaaaababbbaababaaabaaaaaaabbabaaaababaababaaaaababaabaaaaaaaaaababbaabbbabbbbbaabbbaaaabbbbbbbbabaababbababbaaabababbabbbababaaaaabbaababaabbaabbaaaabaaabbabaaabbaababbbababbabaaabaabaaaabbababaaabbbaabbaabaabbaabbbbbbaabaaabababbaabbaabbaababaaaaaabbabbabbaabaaaabababbbaabaabaabbaaabbabbbaaaaabbabbbbbaaabaababbabbbbaababbaaababbaabaababaaaaabbaabaaaaaaabbbabbaababaabbababbbbaaabaaaabaabababaaaabaaababaabaaabaaaabbbaaaaaaabababbbaaaaabbbaabbaaaabbbaaabaababbababbbaaaaababbbbbbaaabaabbabaabaabbabbbaaaaabbabaaabbbbababbbbbbbbaaababbabbbaababababbbbbabaaaabaaaaaabbaabbbbabbbbbababbbbbaaabbbaabaabaaabbbbaaabaaabababbbbbbbbabbbbbaabbbabababbabbabababababbbaaabababbbababbabbbabaabbbabaabaaabbababbabababaabaababaaabbbabbaaabaaaabbbabbababbbbaaabbaababbbaabaababaabbaababbbabbbbbbaaaaaaaaaaababababbabbaabbabbabbbababbbbaabbabbababaaaabbababbbbbabbaaaababbbaabbbaabbaabbbaaabbbbbaaaabbbabbabaabaabbbaaaabbbaababbbaabaabbabaaaaababbbbaabbbbaaabaaabbabbaaabbabababbbabbabbbaabbabbbabbbaabbabbbaaaababbaaaaaabbbbbaaabaabbabbaaabababaabbaaabaaabbaabbbabaaabbaabbbabbababbbaabbbabaabbaabbabaaaababbbaababbaabbaaaabaaaababbbbbabaaaabaabaabbbbabbbbaabbabbbaabaababbababaaabbbbaaabbbbbbbababbbbbababaabbbabbabaaaaabbbbababbaababbbabbbaaabababbaaabaaababaabaaabbbaabababbabbbbbbaabbaaaaabbabaaaabbbbaaabbabbababbbbaaaaabbaaababaababababbaaabbbbaabbbabbbbabbabaababbabbbbbaaaabababbaabbbaaabbbabaabbabbbbaaabbaaaabbabbbbababbaaaabbbbbabbbaabababaaababbaaabbbaabbabbabaabaabbaaaabbbaababaabbbaabbbaabaaaabbabaaabbbabbbbbbabaaabbbbbbbbababbaabaaabababbaaaabbababbaaaaabbbbbaabaaabbbabbbaaabaaaaaaababbbbabbabbaabaabbbabbbbbaaabaababbabaaaaabababbaababaaabaabbabaaababbaaaabbababbbaaabaaaaabababbababaabababaaaaaaabaaaaabbbbbbbabbaabaaababbabbbabbaaababaaaaaabababbbbbaabababaabbbbababbaabbbbaaabbbbaabababbaababaaabbbaabbbbbababaababbaabaabbaaabaaaabbabaaaabbbabaaabbbbabaabbaabbaaabaababbbbbbaabaaabaaabbbaabaaaaababbabaaaaaababaaababaaabbabbbbabbabababaababaabbbbabbbbbababaaaabbbbbabbabbabbbaaaaaababbbabababbbbababbbbbaababbbabaaaabbaabbbbaaabbbbbabaaabaaaababaaabbaababbbaaabbbababbbabababaabaabaabbabbaaaabaaaababbabbabbbbbaabaabbaabaaaaababbaaaaabaaaaababaabbbaabaaabbaaaaabbababbaaaaabaabbbbbabababbabbaaababbbbbbbbbbbababababbaaababbaabaabaaaabaabbbbbbbabaababbbaaababbbaabaabbaababaabaaaabbbbabaababbbbaababbabbbbabbabbbbbabaabaaababababbbaababbaaaabbbbaabbabbbbaaabbbabbaaabbbabbabbabbbbaaabbbbbabbaaaaabaaabaaaabaaaabbaaabbabaabaabbbbababbabaabbbbabbbaaaaababbbbabaaaababbbbbabbabaaaababbabbbabababbaaaaaaabaabababbbbbaaaaabbaabaabaaaabbaababababbbaaaaabbbaaaababbabaaabbbbabaabbbababbbbaaaaababababbbbbabbaabbbaabaaabbabaababaaabbbbaaabababaaabbabbbabaaaabbbbababbbbbababbabaaabaabaabaabbbbbbaaaaababbabbabbbaabbaaababaaaabbbaaaabaaaaaaabbbbbaaababbaabbaaaaaababaababbbababbbabbbbaaaabbbaaaabbabaababaaaaabaaaaabaabbbbbbabaabbaaaabaaaabbbbbbbabbbbbbabaaabbaaababbbaabbbbbbbbaaabaaaaaabbbbaabbbbabbaabaabbaabbbaaabaababbbbabbabaabaabaaaaabbbaabaaabbaaaabbbaabbabaaabbbaaaabaabbbbbbbaaaabababbbabbababaabaaabbaaaaabbbbbabbbaaaaabbabaabbbbbabbababbbabbabaabbabbbbbbbabbaaaaabaabaabaabbabaababaaababaabaaaabbbbbbaabaabbabbaabbaabbaababbabbbbaabaabbbaaaaabbbbbbaabbbabbbabaabbababbbabbaababbaabaaabbbabbbabaaaababaabbaabaaabbabaabaaaabaaaaabaaabbbbbababbbbaabababbabaababababbbbaaabaaaabaaaababbbaaabbaaaabaaabaabbaaabbaabaabaabbabbbbbaaaabaababbaaaaabaaabbababbabbbaaaabbaaababababababbbbaaabbaababbbbaaababbbbaabbaaaaaaaabbbaaaaaaabaabbaaaababababbbbabbbabbabaaabaabaabbbabaabaaaaaabbbbabbbbbbabaaaaabbbaabaabaaababbaababababaaaabbbaaaaaaaaaabaaababaaabbbbbabbabbabbaaaabbbaaaabababbbbababbbbbbbbababbbbaabbbaabbbaaabbbabaaaabababbaabababbbbbabababbaababbbbbbaababbabbbbabaaaabbbbbaabbaababababbabbbaaababbbabaabbaaaabababbbbabbaabaaabbabbbaaabbabbbaaabbaabbbaabbbababbaabbbaaabbbabaabbbbabbbabbbbaabbaaaaaababaaabaaaababaabbabbaabbbaaaaaababaaabbaaaaabaabbbbaaaaaabababaaabbabbbaabbbaabbabbabaaabbbaabbbaabaababbbaaababababbbbbbabbabaaaabbabbaabaabbababbbaaabbbabaaababbbaababaabbaaababaaaabbaaaaaabbaaabaabababbabbbaaabbabababbabbbbbaabbabbbbbaaabaaaaaaababbabbabbbbbbbbaaaaaaaaababbaabbbabaaaabaaaababaaaabbaabbbabbaabaaabbbababaabbaabbbaaabbbabaabaababbbbaabbabbabbbabaabbbabbaaaabbbbbaababbaabaabbbbbbaabbbbbabbbbaaababbbbbbaabaaabbaabbaaabbbabaabaaabaabbabbbaabaaaabbbbabbbabbbabbbbbbbbabaaabbbabbaaaaabbbaaabababaabaaaaabbabaabaabaabbbabbbaaaaaabbbbbaabbabbabaaabbabbabbaababbaabbaaaababbbabbaabaabbaaabbbabaaababbabbabbababbbbabbbababbbaaababbbaaababaabbbaabbabbaaababbaaabbaabbbbabbabababbbaabaabababababbbabbababbaabbbababbbabbbabbababbbababbbaaababbbbabaaabbaabbbbaabbababbbaabbbbbabbbaaaabaaaaabbaababbbaaaaabaaaabbbbaabaaababbbaabaaaabbbaababbbaabbabbabaabaaabbbbbaabbaabbbabababaababaaaabaabbabbaabbbaabaabbababbabbabaaaabbababaabaababbabbabaababaabaababbaababbaabaabbaaaabababbabbbabbbbabbabbbabbbbbbbbbbbaabaaaaabbaaaabbbababbbbbaaaababbabbbabbaaaabaabababbabbaabbbaaaaabaaabababbabbababaababbbbaabbbbaababababbbbabbbbabbaaabbabbababaabbaaabaaabbbbabbabbabbabbabbbaabaaaaabbbbbbbaaaababbabbaaaaabbbbbabaabaaaaaaaabbbbabbbabbbaaaabbaaaabbbbbabbababbbbabaabaabbbababbabbbabbaaabbbbbabbaaabbaaaaaabbabbaababbbbbaababbbbaaaaabaabbbbababaaabbbbbabbbbaaaaaabbaababbbaaabbbbbaaaabaabaaaabbbaabbbabaaaaaaabbaababbabbaaabababbbababbaabaaabbbaaababbbbabaabbaabbbbaabaaaabbabaabbaaabaababbbabaabaaaaabaaabbbbbabaabaaaaaabaaabaababbbabbbaabbabaabaaaaaababbbbbbaababbbabbbabbbbabbbaaabbbbabbaaaaaaabaaaabababbabbbbababaaaaabbaaabbaaaabbbababbaabbaaabbabaabababbbbaabaaaaaaaababbbababbbbaababbabbbababaabaabbabababababbaabbabbbbbabbbabbaabaababaababaababbababbaabababaabaaababbaabbabbaaaabbaaabbbbbbbbbaaaaaaaababbabbbbbaaaabbaaababaaabaabababbabbabbaaabababbbbabaabbabaaababbbbabbababbaabaabbbbbbaababaaaaabaabbbaabbabbabbbbabaaaaababbabababbbaabababaabbbbbaaabaabbbaaaabbbaabbxaababaaaaaabbbbaaaaaaababbabbbbaaabbaaabbabbaabababbabaaaabaabbabbbaababbbbbaabbaabbabaabbabaaaabababbbabbabbaabbbbaabbbbababaabababbbaaabababbaaabaababbbbaaabbbbbabbbbbbaabbbaaaababbbabbabaaabbaabbbbbabaabbababaaabbabbaaabaaabbbbbbbababababbbabbabaaabaabbbabbabbababbbbabaaabbbbbababbbbababaabbbabaaabaaaabaaabaaabaabaaababbaabaabbbababababbabbaaabbabaabaaababaabbbbabbbababaaabbbabaabababaaabaaabbaaaababaababbaaaaabaaabbaabaaaababaabbbabaaabaabaabbabaaabababaaaabaaababbababbaabaaabbabaaabaaabababaabbababbabbabbabbabbababaabbaabbabaabaabaaaabbabaabaaabbbaaaabbaaabbbabbaabbabbbbbaaababababaaabbbbbabaaabbaabbaaaaaabababaaaaaaabbbbbaababbabbaaabaaaaaabbaaabbbbbabaabbbaabbbbbbaaaababbbaaaaabaababbaaaaabbbbabaaabbbbbbbabbababbabababbaabbbbbbbaabbaaababbabbbbabbababbaaaabbaabbbbababbaababaaaabbabbaaaababaabaababbbaaabaaabbbbababaaaaabaabbaaabbaababaaababbabbaabbbbbbbbbbbbbbbbaabaaababbbabaaaaaabaaaaaaabaabaaabbbabbbaaababbbaaaababaaaaaaabbbbbaaaabbabababbaabaabbabaaabbabbaabaabbaababaabbaaababaaaababbbbbabaabbbaabaababaaaaaaaaaabbaabbbbbabbbbbbbaabbabbaaaabababaabbaabbaaabababbabbbaabbbbbaaavabbbbaaababbaaaaabbabbbaabbbbbaabaabaaaaaaabaaaabaaabaabbbbaaabbbbaaababaabbbababaaabbabbbbabbabbbbaabbabbbabaaabababbbaabbbbbbabbbbaaaababbbababbabbbaabbababbababaabbbbaaabbabaabbaaaaabaababaaabbaabaabbbbaaaabbabaababbabbabbbbbbaaaaababbaababbaaabaaaaaabaaababbbbbabbbbbaabbbababbaababbaaaabaaaaaaabaaaaabaababbabbbbbbbbbabbabbabaabbbabaabababbaabababaaaababbbaaabbaaaabbbbabaaabaaaaabbabbaaaabaaaababbaababbbaababbabaabbbbababaabaabbabbabbbabbbbbbaaabbaabaababbaaaaabbaaabbababbbaaaababbaabaaababbbabbbbbaabaababbabaabbaababbbabbbbabaaaabbbbaababaaaabaababbababbaabaaabbabbbbbaaaaaaaaaaabbbabaababbbbbbbbabbbbabbaaabbbaaabbbbbaaabaabbbaaaaabbbaabaaaababababaabaaabbbbbabababaaaaabaabaaabaaabababbbbabbbbabbabbaabababbabaababbabbaabbabaabaabbbbbaabbbbaaabaaabbbaabbbababababaabbaaabbbaaabbaaabaaabbbaaaaaaabbbbbbbaaaabaabbbbaabbbaabbaabbabbabbaaabaaaaaabbababbaababbababbbabbbabababbbababababaaaaababaaabaabbababaababababbaaaaaaabbbbbbbaaababbabwbabbbbabbbbbbaabbaabbbbababbaabbababbbababaabbaaaabaaaaaabbaabbaaabaaaabbbbbaabbababbbbbabaabaababbaaaaaababaaabbaabbbababaabbbbbbbaaabbbaabbaabbabbababaaaaababbaaaaaabbbbaabbaaabbaaaaaabbabbbabaabbbaaabaaababaaaabaaaabababbabbababbbbabababbbbaaabbbbbaaaaabbbaaaabaaaabbaabbaabbabbbaabbababaabbbbbbbaababbaabbaaaaababaaaaabbabbabbbaaaababbaabaababaababbaaaaabababbaaabbbabbbabbabaaaaaaaababbaaabbaabbaaaabaabbbaabbabbbabaaabbaabbbbbbabababbbaaaabaaabaaaabababaaababbababbbbababbbaababbabbbbabbabaaabaababaabbbbabababbbbaabbbaabaabbbbbbaaabbbaaabbbababbbaabbaaaabbaaaaaaaabbbbbaaabaaabbabbabaaabbabbbaabababaabbaababaaaaabbabbaababaaabaababbbababaaaaaaaaaabbabbbaababbbbaabbaababbbbbaabbbaaaaaaabababbbaaaabaabbbabaabaabbbabbabaaabbaababbbbbbaaababaaaaaaabaabbbabaabaaababaaabbbabaaabbbababaaabbaabbbababaabbbaaabaabababaaaaaaabaaaabbbbaababbabbabbabaabaababbbbaaaaabaaabbaabbaaaaaaabbaabaaabaabbbaaaaaabbabbbbaabbabababaaaaabaabababaabaaabaababbabaaabababbbabbbbabbbbbaaabaaabbbababbaaabaabaaabbaabaaaabbaaabaaabaaabbbabbabbbbabbaababaaabbaaabbbaababbbbbbabbbbbbabaabaababababababbababbbababaaaabaaaababbbabbaabaababaababaaaaabaaaabbaaaaaaaaabaabaabbbababababbabbaaaaabababaaabbabbabbbaaaaaabbbaabbabaabaabbbbbabbbbabbababbabbabbabbbabbbaabbabbabaabbbbbbaaabaaaababbaabababbbbaabbbbaabbabbbabaaabababaabbbaaaababbbaababbabaabbbabbabbbaababaaabbaababbbbababaaabaaaabaaaaaaabbbaababaaabbbaaaabbbbaabbabaaabaabbaaabbbababaaaaababbbbbaaabaaabaababaabaabbbbbbabbbabbbaabbbabbaabbbbbbaaabaaaababbbbaaaabbaaaaaaaaaabbbbabbabbabaabaaaabbbbababaabbbbbbabaaaaabbabbabbbabbbaabbbbbbbaabbabbaaaaaabbbbaababbbbbbababbbbaaabbabbbbbaaaaaabbbaabbaaababababababbbbbaaababbabbbaabbbabaabaabaaabbbaababbbbaaaaaaaaabbabbabbabbabababbbbaaababaaaaabbbbbbbbaabbaababbbbaaababbabbbbbbbbaaabbaaaabbabbabbababbaaabbabbbabbbaaaabbbaaabbbbbbabbaaaaabbbaabbaaaaaaaaaaabaabbababaabaaababaabababababbbabbbbbaaaabbabbaaaaaabbbbabbabbbbbbaabbbaabbbabababbbabbbbbbabbaabaababbaababbbbaaaabaabbabbaabaabbaabbbaabbbbbbbabaabaaaabaabbaaaababbbabbbababbaaaababbabababbbbbaababbbbabbbabbbababababbbbbaaaabaaabbbaaabbabbbbaabbbbabbaabbaabaaaaaabababbabbbabbbbaaaabbaaabbbbbbbbaaaaaaabaaaabbaaaabbababaaaaaababaaaaaabbaaaaababbbabbbbababbbaaaabbabaaaaabbaaaabbbaaabaaababbbbabababababbbbaaabbabbbababbbbabbbbbbbbabbbbbaabbbabbbbaaabbbbbbbaaaaababbbbababaabbabbabbbabbbbbaabaabaabbaabbbbbbbaabbaaabbbaabbaabababababaaaaaaaaabbbaaaaabababbbbaaababbaaaababbbbbbabbbaaaaabaabbbaabbbabbabbabbbabbbbabbaabbabbbabbbabaaababaaaaaaaaaabbaabbbaaaaaabaaabbaabbababbaabaaabaabaaabbbaaaabaabaaaaaabbaaabbbbbbabbbaabaaaaababbaaaaababaaabbaabbabaaabaaababbabbbbbbaabbabaaaaabaaaaabaabbbabbbbbbbaabaabbbbbbabbaabbbabaababbbbabaabbbaaabbbaabbabaaaaaaaabbbabaaaaabaaabbbbbbbabaababaababbabaaaabbabbabbbaabaabbaababbbaabaaaaabbaaababaaaababababbabaaababbbbababaaaaabaaaaabababbbaabbbabbababbabbbbabaaaabaaaaabababbbaabbaaaababaaabaabaabbbbabbbabbabbabaaaaaabbaabaaaabaababaabbbbabaabaabbbabaabbabaabaaaaaaabaaababbbbababbbbabaababababaaabababbaaaabaabaabbabbbbbaababaabbaabbbbbaaabbbbbabbabbaaaaabbabaaaaababaaaabbbbbabbbbaaabaabbbbaaaabbbbbbbbbbababababaaabaabbbbbabaabbaaabababbabbbaaababababbabbbbbbaaaabbbbbabbbaaaabbbbabbbbaaabbaaaaaababbaabbbabaabbaabbbabaaaaaaabbbbaaabbabbabbbbbbbaabaaaabaaaabbbbbaabaaabbbaaaaaabbaabbbbabbbbbbabbbaabaabaabaabbaabbaaaaabbabbaaaabaabbbbabbbbbbbbabbabbbbbabababbbaaaaabaabababaaaaaabaabaabaabbbabbbababaaaabbbbbbaaabbaabbaabbbaaaabbbabbabaababbbaabbaaaaababbbbaaaabbababababaaabbababbabababbbaabaababaabbbbaaaaaabababbbaaabaaaabbaabababaabbabbaaaababbaaabaabbbaabaabbaabaababbbabaaababaaaaaaabaaabbbbabbababbbaabbbaaabababbbaaabaaabaabaabaaaaaababbbaaababaabbbabbbbbabbbbaabaaaabababbaabbaabaaaababaaaaaaaaababaabbbbbbaaaabbbbabaaababbabbabbbbbbabbbabababbbbbababaabaabbbbbbabbabbaaabbbababbabaaabaaaabbbbabbabaabbbaaababaaababaababaabaaaaabbbabbbbabababaaaaaababaabbaaaaababbbbabbbbabaaababbbbbbbbbabbaaabbbbbabbaaaabaabaaaaababbaaaabaabaabbbaaabbbbbbbbababaabbbaabbababaabaaaabababbbabbbbbbbbbbbabbabbbbabbbaabbabaababababababaaaabaaaabaaaababaaaabaabbaaaabbabbbbaabbaaaaabaaaabbbbbaabbaaaaabbbaabbbbbabbbbbaabbabbbabbaaaabaaaabbabbbabbbbbaaaabbabbabbabbabaabaabbbababbbaaaabbabbaababbbbbbbbbababbababaaababbbbbbaabbbabbabaabbabaaaabaaabbaabbbabbabaabaaaaabbababaabaaabbbbbaababbabbbaabababbaabbabbbababbbababaabbaaaababbbbaabababaabbaaabababbbbaaaababbabaaaabbabaaaabbaaabababaaaabbbbaabaabbbaaabbababbbbabababaaaaabaabbaaababaaababbbbbaaabbbaaabbaabaaaaaaababbabbaabbaabbbbbbaababbbbbbabbbabbbabbbbbaaaabbaababaabbbbaaaabaaaabbbbababbabbaabbaabbbbaaabaabbbbbbbbbbbbabbbbabaaabbaabbbabbabbaaaabaabbaabaababaaabbaaabaaabbaabababbbbbabaabbbbabaaabbabbaaabbbaabababaabbbbaabbabbbbbbaaabbbabbbbbbbaabbabbbbbabababbbabaaabaaaaabbabbbbabaabbabababbbbabbaabbbbbbabbababaaabbaaaaaabbaaaababababbabbaabbbbbbabaabababaaabbbabaabbabbbbababbaaabbaaabbaaaabaaabaabaaabbabaabbaabbaaaabbbbbabbababbbbbaaabababbaabbaabbabbababbabbbaaabbaaaaaaabbaaaaqabbaabbabbabababbbaaaaaabaababaaaabaaaabaaabaabbaaabaabbaabbbaababbbabbababbababbbbbabaaaabaaaababbbbbaabbaaabbbbaaabbaabaaabaaaabbaaabaaabaaabbbababbababbaaaabbaaaaababaabbbaaaabbabaabababaaaaababababaababaaabbababaabaaabbbaababaaabbabbbbbbaaabaabbabbbaababbaaababaababbbaabbbbabaaababbbabbabaaabaaaabbaaaaaaabbababbababbbaabaaababbaaabbabbbbbabaaaaaabaaaaaaaabbabbbbbbaaaaabbbabbbabababbaaabaaaabbbabaaabbbbbbaaabbaabbbaaaaabbaabbbaaaabaabbaaabaaaaabbbbbbaababbbabbbbaaabbaabbaabaaaaababaaaaabbabaabaabbaabbaabaaaaabbaaabbababbbbaaabaaababaabaabbabbabbaaaaaababbbaabaabbbabbbbbabbbaabbabbabbbbabaababbabaaabbbbabababbbaaaabbabababbbabaababbaabbabaabaabbaaaaaaabbabbbbbbbbaaaaabababaabaaabbbaabbbababbabbabbbbababbaababababaaababbbabbabaaaabbbbabbababbbabaabbababaababaababbaabaabbaabababaabbbbaaaaaabbbbaabbbabbbbabaaaaaababbabaaaaababaabbbbaaaaaaabbababbbabbbbaaabaabbbbabaaabbaabbabaaabbabbabbababaaabbaaababbbabaaaaaaabbbbbabbababbbbaaaaabababbaaaaaaabaabaabbbbbaaaaabaaaaaaaabbaabababbababaaaabbbabaaabbbbbbbababababaabbabababbbbbabbaabbaabaaabbbbbbaabaababbabaaaaabbabaaaaabaaabaaabaabbbabaabbabbaabaaaaabaabbaaaaabbbabbabaaabbbbbbbbababaaaabaabbabbaaabaabbbabbabaababaaaabababbabaaaaabbabbaaababbaaaabbbaaabbbbbbababbaababbbbbbaabababaabbbbaaaaaabaaabbbaaaababaabbbabbabbabbabbaabaaaaabbaabaababbababaaabbbbabababaabaaabbbbabaabababaaabaaaabbbabbaabbabbabababababbbbaaaaabbaaababaabaabbbbababaabbabbbabbabbabbabbabbbbbbababbaaaaabbaabaaaabaaaaababbaaaaaabbaaabbbbaabbabaaabababababbababbaababaabbaabaaabbaababbabbaabbabbaaacabbabbbbbbbbbaabbbaaaaabaaabababababaabbbabbaaabaaaabbbbabbabbbaaaaabaabbaabbbbbbbabaababaaaabbbbabbbaaababbabaababbbabaaaabbbaaabbaabaaabaaababbbaaabbaababaaaaabaabbbbbaaabaaaabbaaaaaabbbaabaabbbbaaabaaabbbbaabbaaabbaaabbababaaaabbaaabaaaabbbababababbaaababbabbbababbbaabbabaabaababbaaaabaababaaabbbbaabaaababbbbbbaaabaabaaabaaaabbabbaabaabaaabbaababaaabbbaabaaabbaababbababaabaabababbbbababbabbbabaabaabaaaaaaaabaaabaabbbbabaababbbbbababababbabbababbaabbbbaaabaaaababbbbabbabbbabbaabaaaaabaabaaababbabaababbbababbbbbaaaabaababaabababbbbbaaabaaabaababaaaabaaaabaabaabaaabaaabaaabaabbabbaabbbabbaabbbbabbbabbabaaaaabaaabaaaaaabbbabbaaaabaabaabbaaaaabbaaaaabaaaaaaaaaabaabbaabbbabbbbbbaaababbbaaabaaabbabaaabbabbaaaabbbaabbbbbbbabbaabbbbbbaababaabbabaaaaabbbaababaabbbabbaaaaaababaaaaababbbbbbaabbabababbbaaabbabbaaaabaabaaabbbbbaaaaaaabbbbbaaababbaaababababaabbbbaabbbaaaabaabbbbabaabbbbbbbbbbaabababaabaababbaaabbaabaabaabbaababbbbbbbaaababbababbbabaababbbaaabbbabaababbabbaabababababaaaaaabbabbbaabbbbaabbabbababbabbbaaabaabaabbabbabababababbabaabbaabaababaaabaaabbaabbbaaababaabbabbbbbaaaabbaabaaabbbbbbbabbbbbaabbabaababbbbbababbbaabbbbbbbababababaaaaababaaabbbabbbabbbababbbbaaabbaaaabbbbabaaaaaaaaabbaabbabaaaabaaabbababbaabaabababababaabbbbbaaabaabaabaaaabbaabaaaabaababbaaaababbbbabbaaaabbaaaabbbbbbabbbabbabaaaaaabaaabaabbbabbabbbbabbbbabbabaaaabbbbbabbaabbaabbbaaaabaaabbaababababbbabbababbaabaaabaabbbbaabbbbaaabaaaabbabbabbbaaaabbbabbaabbbbbaaaabbaabaabaaababbbbbaaaabbaabbbaaababbbabaaaabbbaabaaaaaaabaaaabaabbbbaabaabbaabbbaabbbbbaabaabbabababbbabaaababbabaababbaabbaaaababaaaaabbaabababbbbbbbaaabbbbbaaaaaababaaabaaabbbaababaabbbaabaabaaaabaaabbaaaabbabbaaaababaabbbbbbbbbabaabbaabbbbaabbbaaabbbababbbabbaababbaabaabbbbaababababbbaaababbbbaaaabbabbbbabaaaaabaabbbaababaaabbbbbaabbababaabbaabbbbbabbbbaaaaabbbaaaaaabbbaaabbabbbaabbaabbbbbabaabbabbbababbaababaabbababaaabbbbababaabaabababaaaaabbbbbaabbbabbabaaabaabaaaabbabbaaabbaaaaabaabaaabaaababaaaabbaabbbaaaaaaabbbabbbbbaaaabbabaaabaaaaaabaaabaabbbabbbbbbabbbbbbbabbbbbabaaaabbaabaabbabbaababbabbaaabaaaaabaaaaaabbbaababbbbabbbabbabababaaababbbababbbbbbbabbbbbaababbabbbbaabbabbbbabababbabbaaaababbabbbaaabbabbbabbbaaaaabbabaabaaaabbaaaabbbabbabaabbaababbababaaaababbbabaaabaaaababaabbbbbabbbbaabbbbabbababbbbbbabaaabbbbaabaabbabbbaabbaababaabbbabbabbaaaaaabbabaabbbabbbabbaaaababababbbbabbbbbbabbbbabbaaaabababbbaabaaabaababbbaabbbaaabbbbaabbbbbbbabaaababbbbbaabbaabaaaaaaabbbbabababbaaaaaaababbabababbaabbaabaaaaaaaaabbbabbabababbbbbbbbabbababaabbbbabbaaaaabbbabbbababbaababaabbbabababbaababbabbaabababbaabbbbbbbaabbbabbaaaabababaaabbaababaaaabbaabaaaaabaaaaaaabbbbbaaabbbbaaaaababaabbbbabababaabaaaabaaabbbbbbbaabbbababbaaabaabaaaabbbbbaabababaaaaabaaabaababbbbabaaabbbaaabbabbbaaababbaabaaaabaaaababaabbbaabbaabbabbbaaabababbbbabbaaababaaaabbabbabbbbbbababbbaaaaababbbbbbababbababbbaababbaaababaaabbabbabbbabbabbbaaaabbaaabaaaabbabaabbababaaaaaabaaabbbbabbaabbaabbbabaababbbbaabaabbbbbbabbabaaaaabaaaaaabaaaaaabbaaaabaaabababbbbbaaaaabbabaababaababbbaabbabbbbbaabbbbbbaaaaabaaabaaabbabababababbbbaabababbbbbaabbbaabbbabbbabaabbbaaaabaababababbaaaaaaaaababbbbababbabaababbabaaabbbaabaabaabbbaaaaaabbabbaababbaabbabaabaabbaababbbabbbbbabbaaabbaababbbabbaabababbbaabbabaaaababbbaaaabbbbababbababbabbbabbabbbbabaabaabaabbabababbabbaaabaababaaaaabbaabbabbbaaabbbabbaaababbabaabbaabbbaabababbbaaabababbabbabbbaabbabbbbaabaaaabbaaababaababbbbabbbaababaaabbbbbababbaaabbbabaabbbaabbbabaaaaabaabababbabbabaabbabaaabbbbbbbaaaabbbbbbbbababbbbabbabbabaabbbbabbaabbaaaabbbbbbbabaaaabbaaaaabbaaaaababbabbaaaaabbbaaabaabababbabaaabababaaaabbaaabbaaaabaabbabaaabbaabbaabaaaabbabbbaaaabababbaaaaaaababbbaaaaaaaabbaaabaaaabbbaaababbbaabbbabbaabababaababbabababbabbbbbaabaaaabbaaababaabababbbbababaaabbaaabbabbbbbaaaaabaabaaababbaaabaabbbbbababababbbaaababbbbbaaabaaaaabbaabaaabbbbbababaaabaababbaaabbbbababaaababbbaabaabbaababbbaabaaabbababbaaabbbabbaaaaaaaabbaaaaabbaabbaabaaaabaaaabbabbbbaabbaaababaaabbbbaabaabababbbbbbbbaaababbabbaabbabbabbbbbbabaabbbbbaabaaaaaabbbaaababaaabbabaababbbabbbabaaaaabbbabbbabbaaaaaabaaaabbbbababaabbbabbabaaabbbbaaababbbbababbababbbbabbabaababbbaaababbbababbabbbaabbbbabbaabbbbbabaabaabaababababaaaabbbbababbbbbbabaaaababaaaabbbababaaaaaaabbaaaaabbabababaaaababbbbaaaaaaaaabbbbaabbbababbaaabbabbabbabaabaaabbabbbaabbabbaaaaaaabaaabaababaaaabbbaabbbbbabbbbabaaabbaaaababbaaaaabaabbbbbbabbbbabababbaaaaaaaababaabaababaaabaaaabababaaabbaabaabbbbbabbbabaabbbbbabbbbaaaaabbbabaabaaabbabababbabaaaababaabbbaabaabaababaaabaaabaaaabaaabbbaabbbaababaaabbbbaaabaaaaaaaabbaaaaaaababababbbbaaaabbaabbbbbabbabaaabbbaabaaabaaabababbbbabababbaabbabaababaaaababaaaaabaaaabbbbbaaababababbaabaabaabababbabbbbababbbbbbbaaaabaababaaababbbbabaaaaaabababaabaabbaaaaaababaababbbaabbbbbaaababbaaaaaabababbbaabbaaabbaababbaabababbbabbaaaabbaabbbababaaababbaaaaababaaababaaabbaababbbbabbbabbababaaabbbbbabaaaababababbabbabaaaaabbabbbbbbabbaabbabaaabbbabaaaababaaaabbaababbababaaaaabababaaaaabaaabbaaabbbaabbbabbabaaaabbbbaaaabbbaabbbaaaabaaaaabbbabbabaaaaabaaabaabbbbaabbaabbbaababaabbaabbbaaababbabbbabbbaaababbbbbaabbbbbaaaaaaaabababbabababbbbbbbbbbababaababaaaabaaaaababbbbaaaabbbaaabbbbaabbabbbbaabababbaaabaaaaabbbbabbbbabbbabbbaaaababaabbbbaabbabaaabbbbaabbaabbbbabaababbabaabbabaabababaaaaaaaabbaabbbababababbbaaababbabbbaaaaaaaabbaaaaabbaababbbbbabbbbababbabbaaabbaaaabaabbbaabbaaabbbbaabbbabbbbbbbbabbababbaaaabaaabababababbbbbabbbabbababbabbbbabbbababababbaabbbabbbababbbbabaabababbabbababbaabbaaaaabbabbbabbbbababaaaaababbabbaaabaaabbabbbabbaabbbaabaaaaabaabaaaabbbabaaabbaabbababbabaababaaabbababbabaababaaabbbaabbaaaaabbbababaabbabaabbaabbbabbbaaaabbabbaaababbabaaabaaabbabbbbbaabbaaaaababaababababaaabaaabbababbabbaaababbbaabbbbbbbbaabaaababaaababbbaabbbbaaaabaabbbbbaaaaaaaabbaaabaabbbbaabaabababaabababaabbabbbbbaaabbabbaabbababbabbaaaabbababbbabaaabaaaaabbaabbaaabaabbababaaababbbbbbabbaabbbabaaaaabbbbaabbbbbabbaabbbabbabbbaabbbababbaababaaabbbbbbbbbabaaaabaaabaaabaabbbaababbaaabbbbababbbbbbaaababbaabbabbabbbabbabbabaaabbbabaaabbaaaaabbbabbbbbaaabbaabbaabbbbabbbbaabababaabbbaabbababbabbbbbaabaaaaabbabbbbabbaabaaabababbaababbbbabbabaaaaabaabbbbaabbbbaaabbaabbaaaaaaaaaabbbabbbababababbaabaaabaabaabbbbabbabaaaabbabababbbabaabababbbbabbbbabbbababaaaaaababbbbaaaaabaababaababbbaaaabbbbbaaaabaaaaabbababaabaababbaabbaabbaababbbabaaaaabaaabbbbbabbaababababbabbbaaabbaabbbaaaabbababbaababababbbabbbabbbbaabbbbbabaaaaaaaababbabbbbababbaaaabbbaaabbababbaaaaababbbbababbaaaaaabababbabbaabbbbaaaababbabbaaabaabbbbbbabbbbbbaaababaabbabbaaabbbbaaabbbaaaabaabbaababbaababaabababbabababbabbaabbaabbaabbaaabbabaaabbbabbaaabbbbaabaaaaabaaabbbbababaaabaaaabbbbbbaabbbbbabbaabbbaabbbabbbbbbbbbaaaaabbabaababbaaabbbbbbbabaabaabbaabaaabaabbabaababbbababaabaaababbbbbabbbbbaabbaaaaabaaaabaabbbaabbabaababbabaaabaaaaaabbbbbaaabbaaaaabbbbbaaaabbabbabbabbaaaabbbbabbbaaaabaabbbabaababbbbabaabbbbbaabbabaabaaababbabbbaabaabbaaabaabaaaabbaabaaaaabaababbabbaababbbbbababaabbbbbbabaabbbabaaabaaabbabaababbbabbaaaaaaabbbabaaaaabaabaabbbbababbabbbbabbabaaaabaaaaaabaabbabbbabbbaaaabaaaaababbaaabbaaaabbbbaabbbbbbbbbaababbabaaabbaabbbaaaaaaaabbbbaaabbbbaaabbabaabbabbaabbaabababbbbaabaaabbbabbbabaabaaabbabaaaababbaaaabbbbaaaaabbababaabbaabbabbbbbaaaaaaababababbabaabbabbaaabbbabaaabbababbbbabbaaabbbbabbabaabababbbabbaaabaabbaaaabaabaaaabaaaaaabbbbbbbaabababbaabbababaababaaabbabaaaabababbbbbaaabaabbbababbbbaabbaaabaaabaaabbaababaaaaabbbbabbbabbababbabbaabaabbabaabaaaabbaababaabaabbbbaaabbaaaababaaaabbaaabaaabaaabbaaababaaaabbaabbaaaaaaabaaabaabbbabbabbbababaabaabababaababbaababbbababbaabbbabbabaaaabbabbbabbaabaaaabbbababbaaaabaaaabaaabbabbaaaabababbbbbaabaaaabaaabbbbbabaaaabbbbaaabbaaaaabbbababbbbabbbabbaaaababbbaababbbbabbbbbbababbabbbaababaaababaaabbbbaabbabbabbaabbbabaaaaaaabaabbaaabbaaaaabaabbbabbaabaaaaabbaaaaaaaaabaaabaaaaababababababbbabbbbaaababbbabbbbabbaabbbabbbbbbbabaaababbaabbaabababbaaababaaabbbabaababbabaabaabbbaaabbaabbbabbaaaaaabbbaabbaaaabaabaaabababbaaaaabbbaabbabaabbbaaaaabbabbabaabaabababaabaabbababbbbaabaaaaabaaaaaabaaaabbbabbbaaaaabaaababaaaabaaaababbaabaaaaabbabbbbaaaaaababaabbabaabbbabbaaaabbbabaaaaabbaabbbbbaaaaaabbbabbaababbbbbabaaaaabaaabaaabbbaabbaabababaaabbbbaabaaabbbbbabbbbbabbbaababbaaaabaaaababaaaaababbbbaabaaabababbababaabbbabbabbabababbbbbaababbabbbbabbaaababbbbbbaabaabbaaabaabaaaabaaabaaababaabbabbbaabbbbbabbabbbabbaaabbbbaabaaabbababaababababbbabbbbabbbbbaabbbabbbbbaaaabbababababaaaababbaaabaaabaaaabbaaaaaaaaaaaabbbabbbbbbbabbbbbabaabbaaaabaaaaaaababbaaabaaaaabbabbabbaababaababaaaababaababbbbabbbbbabbbaaaaaaabbbaababaaaaabaaaaabababbbbaabaaabbabaababbbbababbbabaaabaabaaaaaabbbbbaaaaaaaaabababbabababbbbabbabbbababbbbaabbaabbbaabababbbbbbbababbbbbbaaaabaabaaaaaaaaaabaabababaaabbbabaabaabbbaabaabaaaaaaabbbbbaaaaaabbaaabaaabbbbaababbbabbaaaaababbbaabbaaababbabbbbaabbaaabbbaabbbbabbbbbabababbaabaaabbaabbaaaababbababbabbaaaaaabbaabbbaabbaabbbbbaabbabaaabbaabaaabbababbbbabbabbbbbbabbbbbaababbbabbabbbbbbbababaabbabbabbbabbbbabbbbabbbbbababbbbaabbbabaabbbbaaaabaabaaabaabbaaabbbababbbbabbabbbbbabbabaabbabbbaaabbbbaaabbbabaaaabbababaabaabaabbbbbaaaaabbbabbbbbabaabbbaabbabaabbaababbbbaaabaaaabaaabaabaaaabababbbababbbabaababaaabbbbbbabaaababaaaaaaaababbbabaabaababaaaababbbbaabababbaaabaaabbababbbbbbbaabababbbbaaabbaaababaababbbbaabbabaabbababaabbbabbaaabbaaabbbbbabbaaaabbbabbababbaaababbabababbbaabbababaaabaabbaaabababbaabbaabababaabbbabbabbbbbbaabaaaaabbbaabbbabbabbbbabbabbaaabbbabbbaababbbababaaaabbbabbaaabbaaababbababbaaaaaababaabbaababbabbbbbaabbbbababbbbbbbbbaaabbabaaabaaababbbbabababbabbbbbbababbabaaaaabaabbbbaaaaaabbababaaababaaaaabbbbbbbababbabaabababbbbaaabbababbababbbbbabaaababbaabbabbbaabbabaaabbbaaababaababaabbabbaaaababbabababbaabaabbbbbbabbababaabaaabababbabbbbaaaabbaaaaaaabbababbbabaabbbbaabbabbbabaabaaaaababaabaabababaaaabbbbaabbbaaaaabbabbbaababbbbababaabaabbababaaababaaaaabaababbbaaaaabbbbabaaaabbbbbbababbbabbbaabaabbbbbabbababababaaaabbabbababbaabbabbbabbbaaaaaaabababaabbbababbabbbbaabbbabbbbaabaaaaabbaaaaabababbabbbababbaabaabaabababbabbbbbbbbbbaabbbaabbbbaaabababbaaaababbaabaabbababbbbbbbabaabbbbbaabbbababbabaabbbbaaabbabaaabbabbbbaabaaaaabbaabbbbabaaaabababaaabbaaabaababbbbbabaabbabaaabbababaaaabbaabaabbbaabbaababbaaaaaaaaaaaaabaaabaaababababaaaaaaabbbaababbbbbabbbbaaabaaabaabbbaaaaaabbaabbababbbabbaaabbbbababbbaabbabbbbaaabaaababbbabbabaaabbabaaaabbbabbbababbabaabaabaababbbabbabaabbbbbbbbbaaaaaababbaaaaabababbabababbaaaaaaaababaaaababbbbabbabbbbaabbabbaabbaaaaabbbbbbbbaaaabaabbbabbabaaababbbbaaabbabbbababbaabbbaaabbaaabbbababaabbbaaabaabbababaaababaababaabaaaabbbbababbbabaaaabaabaabaaabbbaaababaaabbbbbbabaababbbbbbaaaabbaaaabbbaaabaaabababaaaabbaabbabababbaaaaabbabbabababaabaaaaabaaaabbaabbbbbbbaababbaaabbabaabbbbbaaabbbaabbbbabbababaabaabaaaababababbbaaabbabaaaaaaaaabbabbaaabbbbaabaaabaabbabaabaababababbaaaaababbabbaababbaaaababbbbbbaaaaabababbaabaabbababbbbbaaabbbbbaabbababbbaaaaabbababababbabaaaaaabaabbbbaaaaaaaaaabaaabbbbbbaabbaaaaaabbabbbbbaaababbbaaabbbbbbabaabaabbaababaaaaabaababbabbbbaababbaabaabbbaababbabaaabaaaaaaaabbabbbbaababbaabbbaaabbbabbbbaaababababbbaababbaabbabaaaaabbaaaaaabbabaaababbabbaaabbabaabbbbbabaabaaababbabaaababbabbabaaaaaaabbbabaaabaaaaabbbbaaaaabbaababbaabbaaabaaaabaaabababbbabbbbaaaabbabbaaaabbbbabaabaabbbabbaaaaabbaaabaaabaaaabbaabbaaaaabaabababbaababaaaabbbaaabbababaabaabbabbaaaaabbabbbbabaabbbaabaaabbabbabbbbbbababbabbaababaaabbaaabaaabbaabbbaabbbbaaababaaabbabaaabbaabbbaababbbaabbababbbbbbaabbbaabbabbaabbaabbabbaaaababaaaabaaaabbbaabbaaaabbabaaaaabaaaabbaababbbbaaaaaaaaabaababbbabbbabbabbbbaabbaaababaabbbbaaaabbbaabbaabbbbbbbaabbaaababbbaabbbabaaabbabbaaaabbbbbbbbbbbababbabbbabbbbaabaabbbababbbaaaabbbabaaabbaaaababbababbabbaabaaaaabbbbabaaababaabaabbbaabbaabaababbaabbbbbbbbbabbbaaaaaaaaabbabaabbbaabaababbbaabaaaabababbbaabaabaabbbbbbbaabaaaaababaaaaaabaababbbbabbbbbbbabaaaababbababaaaabaaaabbbbaaabbbbbbaaaabaaabbbbbabbaabbaaaababbababaabbaaaabaabbbabaabaabbbabaaaabbaaaababbaaabbabbabaabbbaaabbbbbaaabbbbaaabbabbabaabaabbbbbababaaabababbbaaaaaababbaaaabbbaabbabababbbabbbabaaabaabbaaabababaaabbabbaaabaaaabaaabbbbaabaaababaaabbbaaaaabaabbaaaabbbaabaaaaabbaaabbaaaabaababbbbbababaabbaaaabaaabbbbbbaabbaaaaaaabbaababbbabaaabababbabaaababbbbbabbaabbaabbabababbbbabbbbabaabbabababbbbaaabaababaabaabbbbababababbaabababbaaababaababbaababbabbaabbbbbaaaabababbabaabbabbaabbbababbaaabbaaabbbabbababbbbaabaaaababbbbabaaaabababbabbbaaabbbbbbbaaababbabababbaaaababbaaabbbaababbbaababaabaababbbabbabbbbbabaababaabaaababbababbabaaaaaabababbaaabaaaaabaabbabaababbabbababbbbaaabbaabbabaaaabaaaababaaaaaabbababbaabbbbabbbababaabbabbbaabaaabaabbabbbbbaababbbaaaabbabbaaaabbbaabbbaabbaaabbaaaabbbbababbbbabbabbbaabaaaabbbabbabbbbabbaabaaaabaabaabbaababbaabbaababbabbabaababbabbbaabbbbabababbbbbabbabaaaaaaaaabaabbbabbbabbaaaabbbababbabaaaaaaaaabaaaabbaabaabaaabbbbaabbaaaabbbabababbabaaaaaaaabaababbbaaaabbaabbabbbbabbababaaabaaabbbbaaaaabbabaababaaaaaaaaababbabaabbbabbabbaabbbaababaaaaaababaabbaaaababbababbbbbbbabbbabaabaaababbabaabbbaaabbaabaaaaaabbbaabaabaabbbbaabbabbbbaababbbbababbbaababaabbbbbbabbbbbabababbbbaaabbaabaaaabbbabaabbaabaaaaaaabbaabbaabbabaaabaababbbabbabaaabbaabbaaabbaaababbbbaabbabbabaababbbbbababbbaaabbbaabbabaaabbbabbababababbaabaabbbbaaaabaabbabbbbbabaabaaaaabaabbbbbaababbbabaaabbaabbbbaaaaaaabbbabbabbababbaaaabaabbaaaaabaaabbbbaaababbbbbaaabaabababbabaabbbaaabaababbaaaaabaabaaaaaaaaaabbbbbbbbabbbbbaaabbbaaabbaaabababaaabbaaabbaabaaabaababaabaaaabbaaaabbbbabbbbbbbbbaabbababaabbbabbababbaabababaabbbaaaabaaaaabbbbbbababaaaababbaaababbaaabaababbbaaabaabbbbbbbaabbbaabaaabbaabbbaabbabaabbabaabbbabbbababaabaaaabbbaabbbaabbbbabbaaaaabaaabbabaaaaaabbabaaaabbbaabbbaabbbabaabbbbaaaabaaababbbbaabbaabbaabbbbbbbbbaababaaaababbbbabbbaaabaabbbaaabbbbbaababbbabbbbaaabaabbaaaabaaaabbbabaaaaabaaaaaabbabaaababbabbabababababaaabbbabbabbbaaaabbaaababaababaaaabbbbbabbbbbabaaaabbabbaaaabbaabbaabbbaabaaaaabbbbaaaabaabbabaabbaaabababababaaabbbbbbbbbbabaabbabaaaabbaaaaaabbbabbaabaabbaaaaabbaaabbbabbabbaabbbbbabbaabbaabbabaaaababaabbbbaababbaabaaabbbbababbabbabbabbaaabbbaaaaaabbbbaaabaaabbbaabbbbbabbaaaaabbaaaababbabaabaaaaabaabababbabbbababbaaabbaabaabaabbabababaabbababaaabbbbbbbaababbaabababaabbbbababbaaabbbaabbabaabbbababbbbabaabbabbbbaaaaaaaaaaaaababbbbaabbbaaabbaaaabbbabbaababbbbababaabbabbbababbbbabaabbaaaaababaaaabaaaaaaaabbabbbbbbababbbaaaababbbbabaaaaaababbaaabbabbbababbaabbaababaabaabbbbabaabbbabbbaabababbabbbbbbaaababaaaaabbaaabbaaabbabaabbaaaabbbababaabbababbabaaaaaabaabbbbaabbbabbaaaaabaababbaaabbabbbabbabbbbaaaabbbbabaaaaabaaabbabaabbbaababbbabbaaaaabaabbbabbbaabbaabaaabaabbaabbbbaaaaabaaabbbbbbabbaaaaaabaaabbaababbbbbbabbabbbbaaaaabbaaababbaabaabaababbaabbaaaaabbbabbabbbbbaaaabababbaaabaaaabbbabbbbbabaabbbbabbbbabbbbbbbababbbbaaaaababababababbaaabbaaaabbbabbaaaabbbaaaaaabbabaabbabaabbbbaababbaabaababbabbbababbbabababaabbabbababbababaababbaaaabbbbabaabaabbaaaaabaabbbababaabbbabbbaaaaaababaabbaabbaaaaabbbbaaababbbabbbbbaaababbaaaaababababbabbaaabaabbabbaababbaaaaababaabbabaaaaaabbbbbabaabbababaabbbbabaaababbababbabaaabbaaababbbbbbaababaabaabbaabababbbaaaabaabbaaaabababbbaaaaaaaabbbbbabbbababaabbbaababababaabaabababababbabaabbbbbabaababaabbababababbbabaabbbbbaaaaabbababbaabaababbaaaaaaabbaabababababababbabbabaaabbaaabababaababababaaaaabaaababbbabaaababbabbbabbaaabaaabbbaaaaabbbbbaaabbaaabbbbaabbabbbbbbbbabbaaabbbbbbaaabaababbbbbabbaaababbabbbabbabbababaabbababaabbbaaabaabbbababaaabababaaaabaabaabbbbaaabbbabaabaaaabbbaaabbababaababaababaaaaabaaabaabbbababbbbaabaabbaaabaaabababbaabaabbbabaabababaabababaabbbbabbaaaabbabaabbabaabaabababbbaaabaabbabbbbbaaabababbbabaaaabbbabbbbbaaabaabbbababaabbabbababbbababaaabbaabbbaababbbbbbbababaabbaaabbaababbaaaaabaabaaabbabbabaaabaabaaaabbbaabaaaaaaaababbaabaabaabbabbabbaababaabbbbbabaaabbaabbbbbbababbaabbabbaaaabaaabaabbaabaaabbbbbaabaaaaaaaaaaaaababbaaaabaababaabaaaabaaaaaaabaabaabaababbaabaaabbaababbbbbabbbbabbbabbbabbaaabaaaaababbbbbbaaaababbbbbbbaaabbabbbbabbbaabaabbaabbabaaaabbabbbbbbbbabbbbabaaaabbbbbaabaaaabbbabbbaabbaabbaaababbbabaaabaababaaaaabbababbaaaaaaaaaabbbbbaaabbbaabaaabaababaaabaabbbbbababbaabaabaabbabbabbbbabbbbababababaaaababaaaabbbbbabbababbbabababaabaaaabaaabaabbbbaababbaaabbbaaabbbbababbbbabaaaaaaabbaabaabbabbbbbbbbabaaaaaaabbbbbbbababaabbbaaaaaabbbbaabbbabbbaaaaababbbababbabababbbbbbbaababababaabbaaabbabbbbbaaabbbabababbabaaaaabbabaabbabababaaababababaaaaabbabbaaabbabbabbbabaabbbbaaaaabababbbbbaaabaaababbaabbaaaabababbbbababbbbbabbbbbbaabbabbbbbbbaaaababbaabbaabaaabaabaabaababaabaaabbbbabbaaabaabbbaabbabbaabbaaaaaaaaaaababaabbababaabbbbaabaaaabbbbabbaabbababbbbaaaaaaabbabbaababaabaabaabbbbababaabaaaaabbbbaababbaababbbbbbaaaaababbaabbabbabbaaababbbbbaabaababaababbbaaabbaabaaaabaaaaababababababaababbbaaabbaaaababaaabaaaabaaaabbaaaabbabaaabbaaaaabbbbaabaaabbaaabbbbaababbbbaabaabaabababbbaaaabbabaabbbabaaaaaabbbbabaabbbaaababaababbbabaabbbaaababaababbbaabbabbaabababbaabbabbaababbaabbbaabaabaaabaabbbbbbbaabaabaabaaabbbaaaaaababbbbabbabbabbabaaabbaaababbababbabbaaaaababbabbbababbbbbabbbabbbbaabaaabbababbaaaabbaabaaabbbabaaabbbbbabbbabbbabaabaaaaabaabbbabaababaabbbaaabbabbbaaababbbbbabbbaaabbaabbbabaabbbbabbaabaababbbababaaabbaaaaabbabbaabaabbbabbaaababbbbbaabbbaabbabbaaabbaaabaaaabbaabbababbaaabbabbabbabbbbaababbbaaaabaaaababbbabbabababaabaabaabbababbbabbababbbaaaaaaaaaabbbaaababbbaaabaabaaabaababbaaabaaaabbaabbbbabaaababaaaabbbbbbaaababbbbbabaaaabbabbbaabbbababaabbbaaababbbbaaaabaaabbbbaabbabaabababbbabbababababbaaabbbabaaaabababbaaaabaabbbababbbabababbbbaaababaabaaaababbaabaaaabaaaaabaaabbbaabaaabaaabaababaabbbaaaaaabbababaaaaabbababbbababbabaabbaabbaaabbabaaaabbabbabbaaababaabbaaaaabbbbaaaababaabbababbabbbbabababbbbaaabbbabaabbabaabbaaabaababaaabbababbabaaaabaaababaaababbabbaaaaaaabaabbaaabbaabaaabbaabbbabbbbabaabaaabbbbaabbbbabbbbbaaaaabbabbbaaaabbaabbbabababbabbbbaabbaabbaabbabbbaababababbbbababaababbbabaaabbababbbabbabababaabaaabbabaaaabbbabbbabbaabaaabaababaabaabbbaaaabbbbbbbbaabbbabbababababbbabbaababaaabbaaabaaabaaaaabababaaaaaabbababaabbbabbbaaaaaaabbaabbabbabbbbbbbaabbabababbbbaaaabbbbabaabbbbbabaaaabbababababbbbbbabbbabbaaabbaaabababbbaaaabaaaaababaababaabaaaabbbbabbababababbababbbaabbabbabbaabababbbabbbaabbabbaabaaaabbaaaaaabbaaababababaaaaabbbaabbaabbaabbbabbbbaabbbbbbbaaababbbbbaababaaaaabbbbabbababbababbababbbbbbbabbbbbabbbbaaababbbabaabbbababababbaabbaababbbabbbbbbaaabbaabbbbbabbbbabbbaabbbbaaaaabaababbbbaaabbaaaabbabaabbbbaaaaabbababbabbaaaabaabababaaabbaabaababbbbabbbaaaabaababaaabaaaabbabbababaaaaaabbabaabaabababbabbabbbbabbaabababbababaaaabbbbaaabbaabaaaaaabbbaabaaaaaaaaabaabaaaabbbbbabaaabaaaaaaababaababaabbbabaaaaababbaaabaabababbbaabaabaababaabaaaabababbabaaabbabaaabbaabbaabbaaaaabbabbaaabbbaabbabaabbaababbabbabbaaabbabaabaabaaaabbbabbaababababaabababbabbbabbabaaaababbbaaabbbbabbababbaabbbabaaabbbbabababbbaabbabbabbabbaabbbbbbbabbbbbbabaaababbababababbbaabbabaababbbaababbaaabbbbbabaababbbababaabbbaabbbbbbbaaababbbbbababbbabbbabbabbaabbaaaaabbaababbaaaabbbaaaababbabbbbabbbababbbbbbbaababaaaaabbbaababaaababbabaabbbbababaaaabbaabbaaaabbbaaaabbaaaaabaaaabbababbabbabbbaaaaaaaaabbbbbaabaaabbaaabbbbaaabbababaaaaaabaaababbaaaaaabaabaabaabaababaababbbbaabbabbabbbaaabbbaaabbbaaabaabaaaaaabbaabaabbbbaaaaabaabbbaaaaaabbbabaaaaaababbababaababbbabbabaabbaaababbaababbaabbbbbaaabababbbaaabbbbbaabaaabbbbbaabaaabbbbbbbbbbabbbbbabbbaaabbbaaabaaaaaabbbbbbaaaaabbbabbbaaabbbbaabaabaaaabaabbbababaaabaaabbabbababaaabbbaaabbbababbbbbbbababaaabbbabababbabababbababaaaabababaabaabbaaabaabbaabbaabaabaaaabbaaabaaabbabbbaaaaaaaabbbbbaaaababababbababaaababbaaabbabaaaaaabaabababbbbbabbbbbabaaabbbaababbbbabbbbaaaabbaabbaaaabbaaaabbbbabbbabaaaaaaabbbaaabaaaabbaaaababbbbbbaaabaababbbbbbbbabaaaaababaabbbababbaaaabbbbababbabaababaabaaaabaabaabbaaaabbababbaaabbbbbbbaaabbaabbbbbabbbabbbababaabbabbaaabbbabbababbbabbaaabababbbabbabbbbaaabbababaaabaaabaaaabbbbbabababaaabaabaabbbbababaaabaaababababbabbaabbaaabbabbababbbbaaaaabaaaababbaaababbbbbabbbabbbbaabababaabbaaaaaaabbaaabbbbbaaaaaabbbabaaaaaababbaabbbaaabaaababbbabaabbbaababaababbababbbababaaaaababaaaabbbaababbaaababbaaabaaaabbabbbbbabababbbbbbabbabbbaaabbababbabbabbbbbbbbaaaaaaaababbbbbabbbbabbbbaababaaabaababbbbaaababbbbbabaabbbbaabaabaaaaabbaaaababbaabbbbbbabbbabaabbbbabaabababbabbabaabbaaabbbaaaaaaaaaababaababbbaabbbababaabbbbaabaaabbbaabbaabababaababbbaabbabaaaabababbababbabaabbabbaabbbabbaaabbababbbbaabbbaabbababbbbbabaabbbbabaaaaabbbaaabababbbbabaabbbbaabaababbbbabbbbbababbbababaabaabaabaaabbbbababbabbabaaababababaabaabbabbbaabbbabaaaabababbbabaaaabaabbbbbbababbbababaabbabbaabbbbabbbbabaabaaabbbababbabaaabbbabaabaabaabaaaababbabbbbbababaaabaababababbaabababaabaabbbbbaaababbabaaabaaaaaaaabbababababbaaaabaabbbabababbbaabaaabaaabaaabaaaaaaabaabbaababbaaaaaabaababbaabbbbabaabaabaaaaabbbaabbaaabaaaabbabbbaabaabbbaaabbabbaabbaabbbaabbbabbbbaaabababbaaabbaaabaaaabaabbabbababbbabbbababbaabaaaaabababbaabbbababaaabbbbaababbababbbabbabbbabababbbaaaabaaabbbabbbbbaaaaabaabbaabaaabbaaaabbaaabbaaabaabaaabaaabbabaaaabbaaabbbaabbbbbbabbbabaabaababbbabbbaabaabaabbbbbbabaabaabbabaabbaababbbbaabbbababbaaabbbbaabaabbbbaabaabbbbbaaabbaabbabbabbabbabbbbbbbabaaabbbabbabbbaaabbabaaaabbbabbaabbbbabbaaabbbbaabababbbabbbaabababbabbbabbbbbbaaababbbbabbbbabaaabababbaaabbaaaabaaababaabaabababaabababababaabbabbbaaabbababbaaaabaaaaaababaabaababbbbbbbabbbabaabbbaaabaabaabababbbbababbbabbaaaaababbabaabbbbaabbbaaaaabbbbbbbaabbaaaabbabbbbbabbabbbbbabbaabaaaabbbabbbbbaaababbbaaaaaababbaabbabbbaabbbbabaaabbbbaabbbabbacaabbbabbbabbbbbbbbabababaababaaaaaaaaabbaabbabbaabaabbabbabaaaaaaabbbbaaabaaabaaaabbbaaabaaaabbbbababbbaaaabaaabbbbbbaababbbbabaaaabbbbaabaabbabbaabbbaaabbbabbabaaabaabaabbababbaababbbabbabbbababaababbbbaababaaababbaabaaababbabbbbabaabbbbbbaaababbbbbbaaaaabbbabbbbabbbaaaaaabbaabaababbaaaaabbababbabaaaabbaaaaaabbbbaaabbabbbabbabbbaaabbbbaabaabbbaababbaaabaaaaabbbaaaaabaaaabababbaaabaaabababaaabaaabbaaaabbbabaabbabbabbbbabbbbababbbaaababbbbbbaabaaaabbababbbaaabaaabaababbaaaaabbabbbababbabaaaaaababbbbbbabbaabababbaaabaababbbbabbbbabbbababaabbaaabbbabbbbbaababaababababbabaabbbbaabbbbabbabbaabaabbabaaabbbaabaaabaaaaaabbbbbababaabababaaabbaaabababaaabbbabbbabaaaaabbbaaababaabbababaababbabaabbbbaaaaababbbaabbbbabbaabbaabbaabbbababaaaaabbabaabbbaabaabaaaaabaabbbbbbbbbbaaabbbbabbaaaaabaaabbaabaaaabbbaabbaaababbaabaabbbbbabbabaaabaaaabbaaabaabbbbaaabaabbbbbbaaabaaabbbbabbbabaaaabbabaabaabbbbbbaabaabbaaabbbbbbbabbabbbabaababbaabbbbbaaabababaaababbbbabbabbabbabbabbbbbbaabaabbbbabbaabbaababbabaaabbabbabaaabaabbaabbaaabababbaaabaaaaabababaabbbabbbbabaaabbbbbabababaaaabaaabababbbbaabbababababbaaabbbaabbaaabaabbaabaabbbaabbbabbababbababbbbaaabaaababbaabbbaaaaaaabbabbbbbbbabaaabbbbbbaabababbbbbbabbababbababbabbbbaaababbbbbaabbbabbbbbabbababbbbaababbababaaaabbabaaabbaababaabbaabbaababababbbbabaaabaaaaaabbaabaabbbababbabaabaaabaababbbabbaababababbbbabaababaaabbbaaabbbbbbabbaaababbabaabaaabbbbbbabbaababaaaababbaabaabaabbbbabbabaaaaabbabbbaaabbabaabbaababbbbaaabaaaababaaabbbaaaaabbaabbbababbaaabaaabbbaaabbaabaaababbaabbabbbaabbbbabaaabaaabbababbbbbbbbaabaabbbaabbabaaaaaabaabbbbbbbbbbbbbbbbbaabbaaabaaaaaaabbaabaaabaaabbababaaaabaabbabbababaaabaababaabaabbbaaabbababbbbbaabbbbbabbbaaabbbbbabbbaababbbaaaabaaababaaabbbbbbbbababbabbbaababbbabaaababaaaabaaaababaabbaababbaaabbabbaabaaabbbabaaaaabbbababbabbaabbbaabbabaabbabbbbbbaaaaabaabaaabbababaabaababbbaaaababbbbbbabbabbaababaaaabbaaababababbbababbbaabaabbaaababbaabbaabbbaaabbabbabaaaabababaaabababbabbbaaaabaabbbaaabbabaabbbaababaabababbaabbbbabbbaabbaaaabaabbaababaabbabbbaababbbbaaaaaabbbbbabababababbbbaabbbbbbbbaabbbababbabaabbbbbabbbabbbabbaaabaabbaabaabababaabbaabbababbbaaabbabbbbaabbbbabbbbaaabbbabbababbababbbabbbbaabbbbbbaabababbbabababbaabbabbbbbabbbaaaababbaaaaabaaabaabbbbbaaaabbbababaaabbaaaaaabbbababbababbbaabbaaabbaabababaaabbbbbbbabbaabaabaaabbbabbaaabaabaabbbbbababbababaabaaaaaaabaaabaaaaaaabbbabbbabbabbbabbaabbbbaaaabaabbbbaabaabbababaaaaaaaaaabbbaabbbaaabbbbbaaaaaaabaaaabbbbbbbbaabaabbbaaabbbbaabbaaababbababbaaabbbaabbbaabbbbabbabaabaabababaabbbbabbbaaaabbaaabbaaabbbbaaabbaaababbaabbaaaaabbabababbbaaaaabaaaaabaabaabbbbaaabbabbaabbaaabbbbabaaabababbbaababbbbbbbabaabbababbaabbaaaabbbabbbaaaabbbbbababbbaabbbbaaabaabaababababbbabbbabbbbabbbbbaabaaaabbbbbbbbaaaabaabbabbababbaaabbbabaabbabbaaaaaaaabaabbbbbbbabaabaabaaaabbbaabbabaabbbaaaaaabbaaaaabbbbbaaababbbbabbababbaaaababaabbaaaaabababbbaabbbbbbaababbaaaaaaabbaaabaabbaabaabbaabbabaaaabaabbabbbaabbbabababbaabbaababaabaabbaabbababbbbaaababaaabbbabbbababbbbaaaabbbbaabaabbbbbaaaabaabaabaabaabaaaabaaabaaaaabbbababbaaaaaaaaababbabbbbabaaaabbbaabbbbaaabaabbaabaababaaabaabbaaaabbabaaabbbabbababbbaababbaababababaaaabaaaaaabaababaababbababaaaaabaaaababaaabaabbabbaaabaaababbbbabbababaaabababababbababbbaaababababbabbabaaabaaabaaabaababbbaababbaaaaaabbbabbbbababbababbbbbbbaaaaaaabaabbaaabbbaabbbabbbababbbbabbaaabbbabaabbabbbaababbbabaabaabbbbbabbbbaaabaaaaaaaaaabaaabbbbbaaababbbbabbbabaaababbbbbbabbaaaaaabbbbaabaaaaabbabbabbbbbbbaabbabbbbbbababaabaabbabbabaabaaaaabaabaaaababaaabaababbaabbbabbbbbbabbaabaaabbabbbbbbbabbaaaababbabababbbbaaababbabbbabbbbaaababbbabaabbbabbaaaaaabaaabbabaabbaaaaaababbabaabbbbbaabbaabbbabbbbabbaababbbaaaabbabbaabbaabbbbbabbbaaaabbbabbbabbbbbaabaaabababbaabaaabaabbbbaabbbbbaaaababaabbabbabbbbaabbbaaaaabbbbaabaabaabbabaaabbbabbbbaababbabaaababbaaabbbbaaaaaabbbaabbabbbaaaababbaaaaaaaababaabaabbabaabaaaaaaaaaaaabaaabbaaabbbaaababbabbabbbbabaaaabaabaabababbbbaaaaabaabbaaaaabbbaabbbbaaabaababaaaabbbabaaaabbabbabbbaaaaabaababaabbbbbbaaaabababbaabbaaaabaaabbbaabbaaabaababaaaaabaaabaaaababbabbbbaabbbbaaabababaaaaaabaabaaabbbabaabbbbaabbbbaabbabbbbbababbbbaaababbbaaaabbbbabbabbaabbabaabbabaaaaabbbbbbbababababbbaabbabbaabbaababbbaaabaaaaababbbabaababbaaaabaabababbbababaaabaabbabbaaabbbababbbbbbabaabaababbbbbbaaabbaaaabbaabaaabbbababbababaabbbbbaaaabbabaabaaabaabbabaaababaabaabbabaaaaababbabaabbbbababaaabbbaaaabbbbbbbababbababbbbbbbbaabbaabbbaaabbaaabaabbabbaaabbbababbabbabaabbaabbbaabaabaababbbbabaaaaaaaabaaabbbabaaaababbbbabababbaaaabbbabaaabaaabaaaaaababaaaaaabbabaabbabbabbabbbaabbaabbabbbbabbbababbabaaabababaababbaaabbbbbababaabbabaabbaabbabaaaababbaabbbaabaaababababbbaabbaaaaabaababbbbabbaabbabbaaaaaaaaaaabbabaabbabbbaaaaaaaabababaaaabababaabbabbaaaaabbbbbbaaaababbababbababaabbabbbabbaabbaaaabbaaabaabbaabbaababaaaabbbbbbbaababbbbaaababaabaababbbbbbaaaaaaabaaaabbaaaaaaaabababbbabbbabaababaabbbbbbabbbabbabbbabbaaababaabbbaaaabaaabbabbbbbabaaaaaabbabbabbabaababababbbbbbaaaabbabaabaabaaaabbaaabbbabbbbaaaaaaaaaabbabbbababbbbbaababbaaabaaabbabbbbbaababaababaababaaaaabaaaaaababaabaababaaabbabaaaaaabbabbbbbababbbaaaaabaabbaababbaaaaabbbabaaabbabbaabaaabaaabbbaabaabbaaabaabbbaabbbaabbaabababbababaaaaaababbbbabbbbbbbababaabbabbbbabbbaaababaabbbabbbabbbbbbbbabaababaaabbbbbababbbaaabaabbaaabaaabaaaaaabababaabbbabbbbabbbbbbaabbbbababbbbbbbbabbaabbabbbbabbaaaaabaaabaabaaabbbabbbaabbbabbaabbbbaabababbbbbbbbabbabaaabababaaaaaaaabbbbbaaabbbbaabbaabbabaabbbbbaaabbabaabbbbaaaabbabaaaabababbbbbbaaaaabbbbaabbabaaaababbbaabaaaaaaabbaabbbabbabbababaabbabaabbaabbaababbabaabaaaaaaaababaabbaaaabaabbaabababaaaabaaaababaabbaabbbaabaabababbabbbbbbbbababbaaababaaabaababaababaababaaabbababbaaabaaaaabaabaabbbaabbbbbbbaabbbaabaabbbababababbaabbaaaaababbbbbbbbbbbabaababbbbbabbabaabaabbbabaaaababbaaabaabbabbbbaaaaabaaaaaaaaabaaabaababbaabbaaababaaaabbbabbbbaabbaaabbbbabababababbbbbaaabaaabbabbabaaaabbabbbaaabbaabababbabbbbbbababbabaabababbbbabaaabaabbababaabbabbabaaabaaabbaaabbababaabbbbbbbaaaabaaaaaabababbbbabbbbaaabbbaabaaabaabbaabbaaaaaabaaaabbbabbaaabbbabbaaaabaaaaaabbbbaaabbbabbbabaaaaababbbbbbaaababbbaababbbbbbbbbbbbabbbbbbbaabbbbaababbbbbbbaaaabbaabababbbabbbbbbbabbaabbabaabbaaaabbaabbaaabbbaaaabaaabbaabaabbbbbbaaaabbbbbabaaaabaabaaaabababbabaaaaaaaaabbaaababaabbbabaaaaabaabbabbbaababbaaaabbaababaabbbaabbbabababaaabbabaabababbaaabaaababbbbaabbbbbaabbbaaaaaabaaabbbbaabbbaaaaaabaaaabbababbbaaaabbbbbaaabaaabaabbbaaaabaaaabaaaababaaabbbaabbbaababbbbbbabababbbbbaaabbbbaaabbbbaabbabbbbabbabbaabaabaaabbbbbaabbbbaabbaaaaaaabaabaabaaaaabaabbababaabaaababaabbbbaabaabbabaabbababbbbaabaaabbaaabbabaabbaabbbbbaaababbbbbbaabaabaaaabbabaaaababbaabbaabaabaaabbbbbaaaaaaaabbaaababbabbababbabaaababbaabbabbbaabbabaaaabaaababbbbabaabaaaaababbbaaaaabaababaabbabbbabbbaaaabaababababaaabbabbabbaaaaababbbbbaaabbabbabbabaababaaabaaaabababbabbbbbababaabbababaaabaaaabababaabaaaaabbbbaaaabaaaababababbaaabbbbbaaabbaaaabbaaaabbbbaaababbbbbbaabbaababaaaaababbaaabababababbbbababbaabbbbabbababbbbbaaababbabbabaabbbababaabbbbbaabbabaababbaaababbbbbaabaabaaaabaaaaaaaababaaabaaabbaaabaaababbbaaabbbabaabaabbabaaabbbabaabbbabaabbbabbababbbaabbaababbabbaabaaabbbababaabababaababaabbaabaaabbbbbaaaaaaabbbaababbabbaaabbbbaabababbbbaaaababaaabbabaabaabaabbbbbababbabbababbaabaaabbabababaaababbbaababbbbaabbbabaababbaaaaabbababbaaabbbbbaababaababbabaabbbbaaaaabbaaaabaabaaaaaaaabaabbbabaaaabbbbaaabababbbbbaaabbbababbabaabbaaabaaabababababbabbbabbbaabbaaabbbababbbbbaaabbaaaaabbaaabbabbabbabababaaabababaaabaabbbaababbbababaabbbbaabaababaaaababbaaaaaababbabbbbbbaababaababbbaaaabababaababaaabaaabaaaabaabbbbaabbaaaabbbaaababbaababbbbaaaabaababaaaababaaaaaabbbbbbabbaabbaabbbbaabaabbbaaaaababababbbbabbabbabaaabbbabaaaaaabaaababbaaaabbabbabbaabaaabbabbaabbabaabbbbaababbabaaababaaaababbbbaaabbbbbbbbaaabaabbbaaaaaaaababbbbaabaababaabbbabbabbaaababaabbbbaabbbababbabbabbaaaabbaabaaabaaabbabaaaabbaabababbbaabbabaabbaaabbbbabbbbbaababbbaabbaabaabaaabbabbbababaabbbaaaababaaaaaabbaaababaaaaabbbaabbbbaaabbabbabbbbabaabbbababbbbbaaaaaaaabbaaaaaaaababaaababbababaabbbabaaaaaaaabaabbaaaabbaaaaaabbabbbabaabaaaaaabbaabbbbaaabbbbbabaababbaabaaaaaababbbbbaabababaabbabaaabaaabbbabaaaaaabbaaababbbabbaaabaaaababbbaaababaababbbbbbbabaabaaabaaaaabbaaaababaaabaaabbababbbabaabababaaaabaabababbaaababbaaaabbaaaaaabaababbbabbbbababbabbbabbbabaaabbbaaaababbbbabababaaababbbbbbaaabbbabbababaabaabbaabaaabababbaaaabaaabbababbbbabbbaababaabbbababababbbabaaabbabbaababbbbabbabababbabbbbaababaabbbaababaaabbaaabbbabababababaaabbbbabbbabbbabaaaabbabbabbabbaaaabbaaabbaaaabaababbbabbaaaabbbabbbbbbbabbbabbabaababbbaababbbaabbaaababbbbaababbbbbbbabbaaaaababbbbaaabbbbbaaabababaaabbbaaaaabaaaababaabababbbabababbbbaabbbaaabbbbbbaabbaaabbbbababbbbbbaaabbbbbbabbabbbbabababbabbaabbbababaababbbaabbaaaabbaaababbbaaabbabaaabbababbbabaabababbbaaabbbbababaaabbbaabbaaaaabaababbaaaabbbbabaabbabaaabbbabbbaabbaabaaabbbbaabbabbbbabbbbabbbbabbabaabaaabaaaaababbabbbbabbbabbababbbabababaabaabbbbabaaaaaabbabaaaababbbabaabaabbaaabaababbaabababaabaaabbbaaaaaaabaaaaaaabbaaabaababbabbbbaabbabababbbaaaaabbaaaaaaaaaabaaabbbabbabaaabaaabaabbaaaabbbaababababbbaabaaaaaabbababbabbaabbababbbbaaaabaababbabaabbabaabbaabbbabbababbbabaababaabaabbbbbaabbaaabbbaababaaabbbbbaaabbbbbabbbbaabaababbababababbaabbaabbbaaaabbabbbababbaabbaaabaaabbabaaabbaaabbbabbaaabaabbabbbbabbbabbababbaabbababbabaababbbabaaaaabaaaabbaababbbbabababbabaaababaababaaababbbbaaaabaaabbaaaaabbaaaaaabbbaababbbbaabaabaaaabbabbbbabbabbbbabaaababababaabbaabbaaabababaaaabbaaaabbbbabbababbabaaaaabbabaabbbaaabbbbaababbbbbabababbabaaaaabbaabaaabbababbabbabaaabbbbabaaababaabababbbbbaabbbabaaababaabbbaabaabaaaaababbaabbbaabbbbabbbaaabaaaaaabbabbabaaaabaaabaaaaabbbbaaaaabbaaaabbaaaababbaabaabbbbababbbbbbbabaabaaabbaaabbbbabbbaaabbbaaaaaaaabbaaabbabbbbabaaabbbaabaaaabaabbbbbbabaaaaaabbabbabaaabbbbaababbabbbbbabbbabbbbbbabaaaaabababbbababaaababbababbaaaabaaabbbbbbbabbbbbbabbbbbbbabaaaabaabbbaabbaabaababbabaabbaaabbbbbbabbaaababaaabbaabaabaaabbbbbbaabaaababbbaabaabbabbbbbbbbaaaaabbaabbaaaaaaaabbbaabaaaabbbababaaaababbabaabbaabaaaaababababbbababababababbbabaabbbbabbabbbabbbabbabaabbbbbaaabbbaabbaabaaaaaaabaaabbabbbbbabbaaaabaabbababbbbbaabbbbababbabbabbbbabababbbaabbbbaaaabbbbbabaaaaababaabbaaaabbabaabbbbbbbabababaaabbababbbaaaabaabaabbbbbbabbbbabaaababbbbabbabaabbbbabaaabbbaaaaabbaabbbbbbabbabbabaaaabaaaaabbbaaaaaaabaabbbbaabbabbabbbbabbaabbabbabbbbbaaaaababbbababbaabbbabababaabbbaaaaaaabbaabbabbbbaabaaabbaaabbaaabbababbaaaaaaabbaaaaaabaaaaaaaabbabbabaaaababbbaaabaaabbaaaabbbaababbaaaaabbbaaaababaaabbbbbbabbaabbaabbabbabbbabbaaaaaabbbbbbbaaabaabaabbbaaaabbbbbbbbaaaaaabaaaababaabbabbaababaabbbabbaabbaaaabaaababbaaaababbabbaabbbbabbbaaababbabbbbbbbaaaabababbbbaabbbaabbbabbbbbbababbbaabbaabbbaaabbbbbabbbabbbbbbababbaaaaabaaaaabbabababbbbaabaabaabbabbaababbaaabbaababbbbbabababbbaaaaaaabababbaaaababbabbabbbbbabbaabaabbabaaabbaaabbbbabaabbbbaaabbababababbbabaaaaaaabbaabbbbabbabaaaaabbaababaaaabaabbbabbbabaaaabbabbaaabbbabababaabbabaabaabbbbbbaaaababaaabbabababaaaabaabbabbaabbabababbbbbaabbbbaabbabbaabbbababaaabbabbaabbaaabaabaaaabbabbbbaabbaabbabaabbabbbaaaaabababaaaaaababbabbbaaabaaabaabbbaabbbbbabbbabbabbabbbababbabaaaaababbabaaabbabbbaaabababbbabaaaabbbbbbbbbabaaaaaaabaaaabbbabbabbbabaabbabababbabbaabababaabaabbaaababbaabaaaaaaaaababbabbaabbbbbaaaabbabaaaabbaaabaabbbaabbabbbaabaabbabaaaababaabbabbabbaabbaabbbbaababbbabbabaaaabaabbbbaaabbabbaaabbaabaabbbbaababbbbbbabaaababbbbabbbbaaaaaaabababbabaabaabaabaababbbbabaaabbaaababbaaabbababaaabbabbaabbabaabaabbaaababababaaaaabbabbbabaabbabaaaabbabbabaabaabbbbaababbaababbbaabbabbbbabbbbbaababbbaabbabbabababbabbbbaaaabbabbaaaaabaaaabaababaabbabbabaabbbbbbbbbbbbbababaaaaabbbbbaaababaaabababababbbaabaaaaaaabbaaabbbaabaabaaaabbabbbaaaababaaaabbababbabbababbbbabbbbaaaabbbaaaaaaabbbbbaaaabaaabbabbabaabbabbaaabbbaabbbbabababaababbbbaaaabbaaababbaaaabbababbabbaabbababbaabbbbbaabaabbabbababbbaaabaaaaababbbbabbbbbababbaabaaaaaabbbababbbbaabaaabbbbaaabbaabbbbbabbabbaaaaaaabbbbbbaaaaabaaabbbbaabbbbbabaabaabbbaabbaabaaabbbaaabbbbbbabbabbbababaaaabaaaabaabbababbbaabbbbbbaaabbababaaaaababbaaaaaabaabbaabaabaaaabbaaabaabaaabaabbbbabbbbababbabaabaabbabbbaabababababaabbbabbbaababbbbabaaabbbabbaaababbbbaabaabababbaaaabababbbaabaaabaabaabbbbbabbbabbabbaaaaaaabaababaabbbabaabbabbabbabababababbbbabaaaaababbbabababbbaabaabbbbabbbaaababbabbbaabaaaabaabaababbbabbababababbaaabaabaabaaaabbbaaaaaabbbabaabbaabbbbbabaaaaabbbbbaababaaaabbaabbbaabaabbaabbaabaaaabaaaabbbaabbbabbbbabaaaaabaaaabbbabaaabbbababbbababbbaabbbbaabaaaaaaaaaabbbbbbbabbbbaaabaaabbabbbaaaaaaabbbbbabbbbbbabababbbbbabbbbaababababababaaababbaabbaabbbaaabaabbaabbaaababbabababbabaaaaabbbbbbaabbabbabaabaaababbabbaabbbbbbbaabbbaaababbabbbbbbaaabaabbabaabaababbabaaaaaaaaabbbaababbaabbbbbbabaaababbabbbabbaaaababaaabaabaabbbaabbbabbaaaababbbbbbbaaabbbaababababbabbbababababbbababbbbabbaaabbababababbbaaabbaabbbbaabababaaabbbbbabbabbabbbbabbbabbabbaabababababbbaaaaababbbbaabbbaabbbbbbabbabbaabbbaabaaaaaaabaaaabaaaababbababbbbabaabaabaabbaaaabaaaaaaaababbaabbbababbbaabbabaaabaababaaabaaaaaabbbababbaaaabaaaaabbbbaababbbababbbaaaaaababbbbaaaaaabbaabbbbbabaabababaabaaabaabbbbabbabbbbaabbbbaaaaababaababaabaabbaaaabbbbbaaaabaaabbaabbbaaabbbbbbaababaabbababbabbbabaaababbabbababbabaaabbbaaaabbabbbbbbbbabbabbabaaaaaaaababbbaabaababaababbaaaaababbbabaaabbbbbaaaabaaaabaaaababaaaabbaaaaaaaabbabbaabbbabbbaabababbbbbaabbaaabbbbabbbbbbbabbabbbabbbbbbbbababbbabaaabababbbbbabbabbbabbabaaaababababababaaabbababbaaabbabababbbbabaabaabbbababbabaaaaaaaabaaaaabbbaaaaabaabbbbbbbbbbbabaaaaaabbbabbaababbabbabbbbaabbbbbbbabbbbaaabbaabbbbbabaaaababbbbbbaaaabbaaaabbbabaaaaaabbbaaaabbaaabaaabbababbaaaaabaababbaaababaabbaababababbbbabaabaaabbabbabbbabbaabbabbabbaabbabbbbbbbabbbaaaabaaaaaabbaabbaaabbaababbabaabbbabaabaababaaaaabbaabbababbbabababbbaabbababbabaabbbabaabababaabbbbabaaaaaabaabbbbabbaaaababaaaaaaabaaaabbabbabaabaabaababababbbbbaaaaababbabbbbabbbaaabbbabbbabbbbbbbbbbbbabaaabaaabbbbbaabababaaaaabbbaababbbababaaaabbabaaaabaaaabababbabbbaaaabaaaaaaabbbbbaaabbbaaaaaaabaaaaababbababbaabbbbaabbabbabbaababbababbbbbabbbabbaaabaabababbababaabaababbaababaaaaaaabbabbbbabababbaaabaabbbbabaabbabbabbbaaaabbaaaabbaaaabbaaababbbbbaabbabbaaabbbbbbaababbbbbbaabbbbbababababbbaabbbaabbbaabababaaaaaabaababbbbbabbabbbbaabaabbababbbaabaabbaabbbabbbabaabbbabbaabbababbababbababbaababbaabbbaabaaabbbbaabbbbaaabbbbaaaabbaabbbaaabbaaababababaabbbababbaaabbaaaaabaaaabaaaaaaabbbbaaaaabaabbbaababbaaabbbbbabbbaababbaababbabababbaabababbaabaabbbaaababbbababbaaaaaabbabaabaaabaababbaabaaabbbabbbababbbaaaabbbababbbaaabbaababbaaabaabaabbbbabaabbabbbbbaaaaabbabaabbaabbaaaabbaaabbaaaaabbabbbaaabbbbbbbaabababbababbbbbbbaaaabaababbbabababaaaabbbbbbabbabbaaaabaaabaababbabbababbbbaabbbaaabbbaaababbabbbabaaaaaaaaaaaababaabbbbabaaaaaabbbaaaabaabaababbaaaaaabbaabaabbaaaababbbbbbbababaaabbbbababbabbabaaaaaabbaaabbbaaabaaabbbbbbabbababbbbbbaaaabbababbbbbaabaabaaaabbbaaabbbaaaaabaabbaaaabbbabbabaabbbaabbbabbaaaabaaabbabbabaababbaabbbbbabaaaabbaabababaabababaaaabbbaaababaabbbaaabbabbababbabbaababaaaaabaaaaabaababbbbbaabbbabaaabaaabbabaaaaabbaaabaaaaaabbaaabbaaababbabababbbbbbabbaabbaaabbbbbaabaabaaaaabbbbabbbbabbabbaabaaabaaabaabbaabaaababbabbaaababababababaaababaaaaaaababbbaaababbbbbabababaaabaaababbbaabaaababaabaaababbaaabaabaaabbbbabbabbbabaabbabaaabbbbabbaabbabbbbbaabaaaabbaabbabbabbaabbaabbabababaaababbbabbbbaaaaaabaabaabbbbbbbabaabaabaabaaabbbbaaaababbbaaabbaabbaaabbbbabaabaaabababbbaaaabbabbbaabaaaabababaabaaaabaaabbaaabbaaabbabbaaaaababbbaaabbabaaabbabaabababbbabaababbbbbabbaaabbaababbbaaaaababaaaabbbabbaaabbbbaabaababaababbabaaaabbdbabbbabbbaabbbaabaabbaaaaaabbaababaaaaababaaabbbbaababbbaabbababbabbaaaaaabababbaabababaaaaaaaaaaabaaabaabbaabaabaababaabbbbbaaabbbabbabaabaaaaabaabbabbabaabbbaaaababaababbabbabbaaaababbaaabbbabbbabbaaaaabbbabaaabaaababbabbabaaaaababbbbbaabbbbababababababbbbbbababaabbbaabbbaabbababababbaababbabaaabbbaaaabbabbabbabbbaaaaabbbaababbaaabbbbaaabaabbaaaabaaabbabbbbbbbabbabbabaaaababbaabbbbaaaababaabaababaabbbbbbaabbabbabaabaaaabbabaabbaaabbaabbaaaababbaaaaaabbbaaabbabbbabababbbabbaabaaaaababbaabbbabbaaaabbabaababaaababbaabbaaaaaabaabaaabbbabaaaaaabbbbabbaaabbbbaabaaabaabaaababbababbabbabbbbababbabaabbabbbbabbbbabbabbbabbabbabbabaaabbbaaaaabababbaabaababaabbbaabbaabaabbbaabaabbbaaaabbbabbaaabbababbaaabbbbaaabbaababbbbbabaaabaabbababbbaabbbbbaababaaaaaababbaaaabbababbbabbbbbbaaaababbaaaabbbbbaaabbbabbbbabbabaaabaaabaaabbbaaababbabbabbaaaabbaaababababbabbbabaaabaaababbbbaaaaababbabaabbbababbabaaabaababbabbaabaaabababbaaabbbaaaaaaaaaaaababaaabaababaaabbbbabababbababbbbabbbbbbabbbabbabbbabaabaababbbbaaabbababbbbbaababababbabaabbbbabaabbabaabbababaaabaaababaabbbbaaaabaaabaababbababbbbbaababababbaaabbbbaababaaababbababaaabaabbaabbbbaabbabaabbaabbbaabaabaabbaaabbababaaabbbaabbbbbaabbbabaababbbabbaababaabaaaababaaaaabbabbbbaaababbaababaabbbbabbbaaaabaaabbaabababbabbbbaabaabbbbbbbbbbabbbbabbbaabbbbbababaabaababbbbaaabbbaaaababbbaabbabbaabbababaabbbaaabaabaabbbaabbbaaabbaaabbbbbaabbbabbbabbababbbbbabbaaaabaaabbbaaaaababbaaababaabababaabbbbaabbaaaaabababbabababaababaabbabbbaabbbbbbbbababbbaabbabaabbbababbbaabaabbbbbabbababbbbabbaabbabbaabbbbabbabbbbbbabbbbbbbbaabaaaaabbabababbbbbbabbbbbaaaaaaaaaabaababbabababbbaaabaaaaabaaabaabbbabbabbbaabaaaaaabbaaaabaaabaabbbbbaabbaabababababbbabaababbababababbbaaabbbabbababaaabaaaabbbbbbaaaabbabbabbbaaaabbbabbbababbbbaabaabbababaaabbbaabaaaabbbaabbaaaabbbaabbbababbaabbaaaabbbaabababbabaabaabbbbababbabaaababbbbabaaaaabaaaaabbaaabbaabaaaaaabaaaabbbabaabbbbaabbbbabaaaaabbbababbbabaaaabbbabbabaabbbbbbbbbbabababaaabaaabbbabbbaabbaababababaaababbbbabbabbaaabaabaaababbababaaabbbbababbabaaaaabbbaaaaaaaababbabbbbbabaabbbabbabbbaababbaaaaabaabaaaabaaababbbbaaabbbbbabbbbaabaaabbbbbaabababaaaabbbaaababbbbabababbabbabbaabaaabbaababababbbaaaabbabbaaabaaaaaaababbbbbbabaaabaabbabbabbbaabaaabbaabbbbbaabaaaaaaabbbabbaaabbaaaababaabaabaaaaaabbabaaabbaaabaabbaaaabbbabaababaabbaaaaababaaaabbbbbbbabbbaabbaababaaaababbaabbaabbbabbaaaababbbaabbabbaabbbbaababbbbbababaabbbbbaabababbbbaabababbbbbbaabaabababbbbaabbabbaaabbabaabbabaabbbbbbbbabbabbaabbaabaaaaaabbbabbbbbaaababbbbabbbbaabaabaabbabaaaaaababbbbbaabbaabababaaaabaabaaaababababbabaabbaaabbababaaabbabaabababbbbaabbababbabaaababbababbbbaaabababaabbbbbbbaabababbabbbaaaabababaababbaaabbaabbbaaabbbaabbabbbbaabbbababbaabababaaabababaababbabaababbabaaabbaabbbaaabbababbbbbbaaababbbaababbbbaaabbbbbaaabbaaaabaabbbbabaabaabbbaaaabaabbbbababaabbaaaaaaabbabbbbbbbbbaaabaababbabbaabbbaabbaaaabaaaabbbbabbbbbabaabbaaabbabaababaabbabaabbaabbbaabbbaababbabbaababbbbabbbbbaabbaaaaaabaabbbabbbababbaabbabaaabaaabaaabbabbaabaaaaabbbaabaaabbbbaaaaababababaababbaaaaababbbaaaababbbbbabbbabaaabbabaaaabbabbaaababababaaabbbbaabaabbbbababbbaabbbbbabbbaabbababaaabbabbabaabbababbaababbaaababababbbbbbbbbabaabaabaaaabbabbaaaabbbabbbabbaaabbabbaabbaabbaaaabaaababaabbaaabaabababbbabbbabbbaaababaaabaaabaabaabaaabbabbbababbbbaaaabbbababaabbabababaaaaaabbaabbaababbabbaababbbaabbabbbbabababbbbaabaabbaaababbbababbabbaaaaaababaabaaabbaaaaaababaaaabbbababaaaaabbabbaaaabbabbaaabbabaababaabaababaaaaaaabbbaaabaabaaaabbbabaaaabaabababbaabbabaabaaabbabaaaababaaaabbbaabbaaaabaabbabbbaabbbbbaabbbbaabbbbabbaabaabbaaababbababbabababbbbaaabbbbaabbababbbabaababbbaaabbbabbabbbbbaababaaaaaaaaabbbabbbabbbbbaaabbbbaaabaabaaababbbbabaabaabbaaabbbaababbaabababaaabaaaaaababbaaabaaabbaaaaabbaaaabbaabaaaaaaabbabbbaababbaaaaabbbbabaabaaabababaabbabbbabbaaaaaaaaaaabbaabbaaabaabbbbabbaabbbabbbbbaababaabbaaaabaabaaabbaabaaaaabaababbabbabbbbabababbbbbbabbbbbbabbbaaabbaabaabbbbabaabbbabaabababbabbabbabababaaabbabbbbbabbbabaabbababbaabaaaabbbabbababababbaabbbbaaaaaaabbaaaabbabababaaaaaaaaabbbababbabaaabaabbbbaabbbaaabbbbaaabaaaabbabbababbbabababaababbabaaababaaaaabaababbaabababaabaaababbbbbbbbaabaaaaaaaaaabbbaabbbabaaaaabbaababbaabbaaababbbababaaaaabaaaaabaabaabbaababaaabaabbaabbbaaaabaaabaaabbbabbabbbbbbbbbaaababaaabaabbaaaaabaaabbababbbbabaaaaaabababbbbbbbabbbbababbabababaaaaabaabbbbaabbbbabbaaabbbaaaabaaabaaaabaabbbbabbababbbbbbabbbbbbbabbbabaabbabbaabbababbbbbabaaaabbbbbbababbbabbbabbbbbbaabababaabbaaaaaaaaaaaaaaaabbabaabbbbaaaaaabbbabbbbaaaaaababbbbabbaaabababbbaabaabaabbaababbabbbaaaaaabbbaabaabbbaabbabbbbbbaabbbababaaabbbbabaaabbbbabaabbbbaaaaabbabbbbabbabbabaabbaabbaababbababbbbbaabbaabbaababbabbabbaaaabbabbabaaaabaaaaaabbbaaaaabbbabbababbbbbbbbbabbbbbaababaababaabbaaaaabbabaabbababbbbbaaabbaabbaaaaaaaabbbbaaaaaabbbaababbabaabbaaaabbaaaaaabbaabbabaabbbabaaaabababaaabbbbbaaaaaabbabbbbaaabaaabbaaabbabaaabaabbbbaaabababaaabbababaabaababbbaabaababbbbabbbbbbbbbbabbabbbbaabaaabaabbaabbababbabaabbabbbaabbaabbaabaaaaabbbbaaabbabbbaaabbaaabbbaabaabbaabbbaabaaabbaabbbbabbabbbbbbbbbbababbaabababbabbabbababaababbbaaaaaaababbbbbbbababbaabbaaaaababbbaabbabbbbaaabbbbabaabaaabaaaabbaababaabbaaabababaabbabaaaababaaabbababbaababbbbbaababbababbbbabbbbbbaaabbaabbbbaaabbababbbbbaabaaaaabbbaabbbbabbbaaabbbaaabbbbabbbbbaabbbaabaabbaababaaaabbabbbaabbabaaabaababaaababaaaabbbbbababbaaaababbaabbaaaabbbbbbbabbaaabbabbaaaabbabaabbabbaaabaabbabaaabaaaabbbaaabababbaabbabbbbbaabaabbaabababaaaababbbbbababaaabbbbaaaabbaaaabbbabbbabaabaaaabbababbaaababbaaabbbaabababbaabbaaaaaababbbaabbabbabbbabbbabaaabbaababaabaaabaaaabaaaaabaaaabbabababbbaabbbbbababaabaaabbababbabbbbaabaabbaaaababaabbbbabababbaabbbababbaabaabaaababbabbaaaaabbabaabbaaabbaabbaabbbaaabbbaababbabaaabbbbaabbbbbbaabaaabbaabbaaabbbabababbbabbabaababbabbbaaaabbbaaabaabaaabbbbaaabbbabbbbababaabbbaabbbaaaaaababbaabaaababbabababbbbbabbbbabbabbaabaaaabaabaababaaaaaabbaabababaaababbbbaababbabbbbabaabaabbaabbaababbabbbaaaababababbaaaabbababbaaababbbaaabbbbbbbabbbbaabaaababaababbabaabaabbaabaaabbababbbaabbbbaabbbaaaabbabaaaaabbaabaaaaabaabbaaaabbbaaaabbbabbaaababbababaaaababaabbabaabbbbaabbbbbbbbbbbababababbbbbbbbaabaaaaabbbbabbbabbaaabbbbbbabbbbbbabaabbbabababbaabaaabaaaabaaaaababaabbbaabbaababbaaaababbaabaabbbaababbbbbabababbabababababaabaaaabababbaabbabababbbaabbaaaaaaabbbabbaabbbababababbbbbaaaabaabbbabababbbaaaaaaaaaabaaaaabbbabbbbbbbaabaabaababbbbbbaaabbabbbababbbbbbbbaaabababaaaaabbaaabbbbabbaaaaabaaaaaabaaaabaaaabbabaabbbbabaabbbaabaaabbaaaaaababbbbabbbbbaabbbbbaaabababbbabbabbbabbbaaaaaabababaababaaabbabaabababbabbbbabbbabaaaabbbbbababaabbbbbbabbbabbabbbbbbbbaaabbbbaabbbabbbbbabbabbabaabbbbbbbabbbaabbbabbbababbbbababbaabbbbbbbbbbbbaaabaaababbbaabbabbbbbbaaaaaaabbabaaaabbbaabaaaabbbababbabbaabbabbaabbbbbbbbbbbaabaaabbbbbbbbaaaaababbabbbabbaababababbbaaaaabbabaaaaabaababbaabaabaaaaaaabaaabbbbbababaabbaaaaabbabababbabbabaabbaaabbaaaaababaaabaabbaaaababbaababbbbaabbbabababaababaaaabababbaababaaabbaabbbabbbbaaaababaabbbabbbabaabbabbbabbaabaabaabaaababaabaaabbaaabbaaaaabbaabaaaababaabaaabaaaababbbaabbababbabaaaabbbababaaaaabbbabbbbbbabaababbaabbbbbaaaaaababaababaaabbaaabbaabababbbabaabaabaabbbabbbaaaaabbbaaabaaaaabaaababbbbabbaaaaabbbbaaabababaabaabaabbabaaabbabaaaaabbbbbbbbbbbaababaababaaaabbabbbabbabbaabaaaabbaaaaabbbabbbbbbbabaabaabaabbabbbabababaaaaababbbabbabbbbbabbaabbbbbabbbabbbabababaababaabaabaabaaaabbaabbbaababbaaaaaaaabbbbbbaaaaabaababbbbabbbaabbababbbaaabaaaabbaaaabbbabbabaaabbbabbabababbabbbbabaaaabbaabbaababbbabbbbbabbbbaaabbbabababbaabaaabbbaabbbaabbaaabaaaabaababbbabbaabbbbaaabaabbbabbabaaaabaaaabaabaabbaabababaaabaaabababbaabababbbababbbaababbbaaabaabbaababbaababbaaabababbaaaaababaaababbbabbbbbabaabbbbaaabbaabaaaaaaabbaabaabaabbbabababbbbbbbbabbaababbbaabbaabaabbababaabbbaabaaaabbbaabaababbabaabababbbbbbabaabbaabbbabbbaabaabaabaabababaaaaaaaabbabbaaaabbbbbbbbabbbaaabaabababbbbbabaaabaabaabbabbbbababaaaabbaaabaaabbabbbbaaaabaaaaabaababaabaaabbababaaaaabbbbaabbabbabaabbabbbbaaababbbaaabbabbaabbabbabbabbaaaabbaabaabbbbbabababbbbaababababbbabaabaaabbbbabbaababbaaaaaabaabbaaabbaaabababaaabbababbabbababbaabaaababbaaaaaaabbababbbbabaaaaababbabbabbaaaabbaabbaaabaabbbaaabbbbaabbbbaababbbabbbaaaababbbabbaaabababbbbaaabbbbaaaaaaaabbbabbaaaaabbaaaabaabaaabbbabbaaababaabbaaaaabbaabaababbbbbaaabbbbbbaaaabbbbbbaabbbaabbbabaaabbbabbbbabbababbbabbbbababbaaabaaabbabbbbababababaabbababababaaabbbaaaaaaabbaaabbabaabbabbbbbaaabbbaaaaaabbbbabaaabbbbbbaaaabaaaabbababaaaabbbbababbabbaaaaabbaabaabaabaabbabbaabbbbbaabaaaabaabbabbabbbbaaaaabbbabbbaabababbbbababbaababbabbaaabbbbbbaaabbbaaaaaaabaaaaaabaabbbbaaaabaaaabbbabbbaababaaabbabaaaabbbbbaaaababbbaabababaabbbbbbababbaaaabbbbabbabbbbaabbbbaaabbbabbbaabbbaabaaabbbbaabaaaabaabbaababbabaabbbbaaabbabbaaaabababbbbbbbabaababaaaabaabaabaaaaabbabbabbababbbabababbbababbbbaaababbbabaabababaaaaabaabbbabbbbabbbbabbbaaabababbbbbabaabbabbbababababaabaabaaabaababbbbbaababaaabbaabbababaaabbbbabaabaaabbabaaaabaaabbaabbbbaaaabbbabbbabbaabbbbabaabbbbbbbaaababaabbababbaaaaabbabbbbbaaababbaaabbbabbbaabbbbbbbabbabbbbabaabaabaababbabababaabababbbaabbabbabbabbbbbbabaabbabbbabaaabaababaaabaaababaaaabaaaaabaabbabababaabbbabbababbababababbabaaabbbbbaabababaabaaaaabaababaaaaaabbbabababbaabbabababaaaaabbaabbbbaabaaaabaababbabbbabbbbbababaabbaaaaaabbbabbbaabababbaaaabbbbabbabbbbbbaababbaabbababaabbabbbbaaabbabaaaaababbbbaabbbaaabbbbbaaabaabbaaabbaabbaabbabaaabaabaaaababaababaaababaabbbbbbaabbbabbaaababbbabbbbabbbaaaaabaaababbabbbbbbaababababbabbbaaabaaaaabbaaabaabbabbbbbabbababbbaabaabbbbbabbaabaabbababbbbabaaababaaaaaabaaabbaaaabbbabbabbaaabaababbbababbbaaaabbabbabbbaabbabbaaababbbbbaababbaabbbbaaaaababaaababbbbbbabbbabbbbbaabaababbabbabbbabbaaabbbaaabbbbabbbbbabaabaaaababbbababaabbababbbaababbababaaaaaabbaabbaaabbbababaaababaabaaaababbbaabbabbbbaabbbabbbabaabbbbbbabaaaabaaabbbbbababaaaabbbabaaabbabaabbaaabbbbbaabbaaababaabbabababbbaaaaaaaaabbbaaaabbbbabaabbabbaaaabbabaababbaabbbabbabbaabbbabbaaabbabbaabbabaabaaabbaaabbaababbabbababbababbaaabbaabbaababbbbbababababbbbaabbbbbaaaabbaaaaabbabbabbaabaaaabbbbabaabbbbaaabbabbabbbbbabbbaaaaaaaaaaaaabbbaaaaabbaabbbaabbaaabbabaaabbbaaaaaabbaaaaabbbabbbabbaabbaabbaaaaabbababbabbaabaaaaabbaababbbbbabbaaabbabbaaabbbababbabaababbabababbabaabbbaaababbbbbbaaabbaaababaaabbbaaaababbabbbaaaabbbabbaaabbbbaaabbbaaaaaabaabbbabbbaaaaaaabaaaaabababbbbbaaaaabaaabaabbababaaabbabaabaaaaaaaaaaabbbabbbaaaabbbababaaaabbaababbbbabbbbabbbaabbbaabbbbbaaaaaaabaababbbaaabbaaaaaaabbbbabbaababaaabaaabbabaabaabbbaabbabbbaabbbabbaabbbabaaaababaabbaaaabbbabbbabbabbabbabbababbaabababaababaabaaabbbabbbaaabaaaababbbabbababaaaababbaabbbaaaabbabbaaababaabaaaaababaababababbbbaaababbabababbabbababbbaaabaababaabbaaabbaaaaabaabaaabbbbabaababbaaababbabbaabbabaaaaabbababababababaabaaaababaaabbbbbaaabbaababaaabbaababbababbbbbbbbbaabaaaabbbbabababaaababbbaabababbaabababbaababbbaaaaabababbabbabbaaaaabaaabbaaaaabbabbbabaaaababbabbaabaaababbbbbbababaaabbbbbaaaabbabababbbbababaaababaaaaaaaaaabbabbbbbbaaababbbaabbaabaaaaaaaabbbbbababababaabbaaabaabbaaabaabbababbaaabababbbbbbaaabbabbbbbbaaabaababbbbabaabaabbababbabbbbabbaabbbbbbabbababbbabaabbabaabbbabbbbaaaaaabaaaabbaababbabababaabbbabbaababaaabbbabbaabbbabbbbaabaababbbbbaaabbbbbbababbbaababbbbbaabbaaaaabababaaabbaabaabbaabbaabbabaabaababbbaabaababaaaababbabbaaaabbbabaabbababbabbbbabbbaaaabaabbbaababbbbbabbaababbabbaaabbaabaababbbabbbaaababbbbbbabbabaaaabaaabbabbbabbbaabbbaaaaabbbbaababaaabbaaaababbbaaabaaababababbbaabaabbbabbbaababbbbabbbaaabbbabababbaaaaabaabaaaaabaaaaabbbaaabaaabbaaabaabbabbbaaaaabbaaabbbbbabbababbbbabaaababaabbaaaaabaaaabbaababbaabbabababbbaaaaaaabbbaababbabbababaabaabababaaabaaaaabababaababbbabbbaaaabbbbbaabbabababbbbaabbbbabaaaabbbbaaabbaabbbbabbaaababbabbabaaaaaabbaabaaaaabbaabbbabbbaababbbababbaaaababababaaabaababbaabbbabbbbbbabbabbbbaabbbaaabbbbbaaaaabbabaaabababbbabbbaaaaababbbbbbbbbaaaaaaaaababaababaaababbbbbabaaaabbaabaaaabaaabbbbaabbbbaabaabbbbbbababababbabbbaabaabaaaababbbbaaabaabbbaabaabbbbbabaaabbaaaaabbabbabbabaabaaaabbbbaaabbaaaabbbaaabaaaaabbabaaababaabbaaabbbaabaabbbbababbbbbababaaaabaabbabaabbbaabaabaabaabbabbbbbbbbbababaabbbbbaaabaaabbbbbbbbbbaaaabbbbabbaaabbbabbaabaaabbbbabbabaababbaababbbbaaaaaaaabaaababbbbbabbabaaabaabbbbaabbaaaabaabbbbaabaabaababbbaabaaaaaaabbbbabababaaabbabbaaabbabbbabbabbbabbabbabaaaabaaabaaabaaabaabbbbaaababaababaabbaaabbbbbaaabbbbbbbbaaabbbabbabaaabbababbabaabaaabaaaaabaaabaaaaaabbababaabbbabaaaaababbabbabbbaaabbbbbaabaaaaababbbbabaaaababaabaaaabbbbababbbbbaaaababaaabbbaabbaaaaabababbabababbabbbabaabababbbbbaaabbaaaaabbababbbaabaabbbbaababbababbaabaaaabaaaabaaabbbaaababbbbabaaaabbaabaaabbabaababaaabbbabbaaaaabbbaaabaaababbabbbabbbabababbbbbababbabaaaaabbbbbabbabbabbbaabbbbbabbaaabaaabbabaaabbbaaaababbbbabaaababaabaaaabaabbaabababababbbababbbbabbbaabbaabbbbabbaababbbbaabaabababbbaabaaaabbbaaaaabaaabbaababbbabaaabbaabbbbaaabaabaabbaaaaabababababbbababbbbabbabbaabbababbababbbaaaaababaabaaaaabbaabbbbbbbbbaaaabababaabbaaaaaaaaaabbaabaabbabbaababaababababaabbbbababaababbaabbbbaaaabbabbbabababbbaaaaababbbbaabbaabaabbbbabababaaaabbaabbbbbabbbaaabaaaabababaabbbabaabbbababaabababbabaaaabbaabbaabaaaababbaaabaabaababaaaaabaabaaaaaaaabbbaaabaabbabbbbbaabbabbbbbaababaaaabaaaabbaabbabaaaababbbabababbbaabbbbbbbaaaababaaabbbabbbababbbabbabbabaabbabbabaaabaaaabbabababaaabbbbaaabaaabbbbabababbabababbbaaaabbaabbbbaabaaaabbaaabbbbaaabbbbaabaabbababbbabbbbabbabaabbabbbbbbababaabbaaababaaabbaaabbbaaaabbabbbababbbbaaabbaabaababbbaabbbabbabbbbbbbabaaabaaabaabbbaabaaabbababbabaaababbbbabbaaaabbabbbbababbaabbaaabbbaaaababbbbbaababaababbbbbbabaabbbaaaababaaabbaabbaabaabaaaabbbbbbaaaaaaabbbbbbababaaaaaaaaabababbaaabbbabbbbbabbaabaaaaababaabababaaabababbbaababaabbaaaaaaabaaabaaaababbabaababaaabbbaabbbbabbababbbabbbbbabaabbaabbabaaaabaaaabbabbbbbbbbabbbababbbbaaaaaaababaaaabbaabaaabaaabbbbbbbaabbaabbbbaaabbaabbaaabbbababbaabaaaaabaaabbaaaababababaababbabbabbbbbbbaaaababababbbbbbabaaaabbabbaabababaaaaaabbbbbbbabbbbbbabbbbbabbbaabababbbbabbabababaabbbbaabbaababbbaabababbabaaababbbaaababaaabbbbaaaabaabbaababbabbaaabbabbbbbabbababababbbbbbbbbbbaaabaaaaabbabbaababbaaaaaaaaaabaabbababaaaababbaabbbabbbbaabbbaaabbbabaaaaabbaabbbaabaaabbbbbbbababaabbbbabbbaaababaababbbbaaaaabbbabaabbbbbbbabababbbbbbbaaaabbaababaaaabaaaabaabaaaaabbabbaaabbbbaababaabbbabababaaabbaabbabbabbabbaaababbaababbbbbbbbaaaaabbbbbababbbabababbbbbaaaaaaaaabaabaaabaabbbabbbabbabaabbabbaaabababbbaabbbabbaabbbbaaaaabbbbaabbbbabababaaaabaabbbaababbabbabbaabbaabaabbabaaabaababbbabaaabbbbaaaabaaaaabbaaabaaabbbabbababaaaaaabbaabaabbbbbbbaabbbbbabaababbbaaabbbaabaabbbabbbaababaaabaababaabbbbababbabbbbaaabbababaaabbbabaaabaabbaaababaaababaaaabaaabaaaaaaabbaaabaabbbabaabbababbbaababababbabbbabbbabaaaaaabbaababbabbaabbbaaaabbbbbbaaabaabaaaaabbaabbbabababaabbabbabaabbabbbbabbaabaaabbabaabababababaaaabbaaabaaabaabbbbabbbbabaaaaaaaaabaaaabaaabaaaaabaabababaaabaabaabaabbabbbbaaaaabbbababaabbbaababaaabbaaaabaababbaaaaaaabbabbabaaabbbbabaaaabbabbbaabbabaaabbbabaaabababbaaabbbbbaaaabaaaaabbabaabbbaababbbababbbabbbabaaababaabbaabbaabbababababbbaaabaaababbaabbabababaaaaaaabbbaabaababbbbabbaaabbaaabaabaabbbbababaaabbaabbabaaaabababaaababbbababbaaabaababbbabbbbbbbbbbbaaabababaabbbababaaaaabaabbbaabbbaababaaaaaaaaabbaabbbbabbbabbbbbaaaabbaaabaaabbbaaabbaaabbbaaaabbabaaaabababaabaabbbbbabaababbbbbbabaaaababbaabaabbbaabbbbaaabaaabaabbbabababbbababbababaaabaabaabbbababaabaaabaaaabbababbabaabbbabbbaaaaaaaabaaababbbaaaaabaaabbbaaabbbaababaabaabaabbaababaabaabbaaaabaabbbbaaabbbabbaaaaabaabaabbbbaabbbbaaaaaaaaaaaaaaaababaaabbabaabbbbababbabbaabbbaabbbabbbaaaabbaabbaaabbbaabbabbabbbbbabbaabbaaabbbaaababbbababaaabbaaaaabbabaabaabbbabaaaaaababbababbaaabaaababbbabbbabbaaababbbaabaabbabbbabbabaabbaabbababaabbaababababbaaabbaabaabbaababbaaaaaaabbbabbabbabbbaaaaababbababbbbbbaabbaaaaababbaaaabbaababaabbaabaabbbbbbbbaaaaabaaabababbaabbbaaaababaabbabbabbbbbbabbbbbbabaabbabbabbaababababbabaaabbbbbabbaabaababaabbbbabbbbbaaabbbabaabaaabbaabbababbaaaabbbbaaabbbbabbababaabaababaaabbaaaabbaaaababaaaaaabbbbaaababbbbbbbbaaababababbababaaababaaaaabaabbbbaabbababaaaaaaaaaaabaababababbbaababababbbababaabbaaababbabbaaaababbabbaaabbbbbbaabbaababbbbaaabbbabaababbaababbbabbaaaaabbabaaababbaabbbaababbabbbbaabaabbbbbbabaaaabababbbaabababababbababbbbaabaaaabaabbabaababbaaaaaaababbbababbbaaaabaaabbbbaaabbbbbababababaabbaaabababbbbaaabbabaaabbbaaabababaabbaaaabaaabaaaabbababbbaabbaababbbbbaabaabaaabababbbabaaaaaaabbbbaaabbbbaabaaaaabababbabbbabbaabbbbaaaaaabaabbbbabbbaaaaaabaabbaaaaababbaabbabaabbbbbabaaaabbaaabaaabbabbbbbaabbaaabbbbaabbabbbaabaaabaaababaabbaababbbbabbaabbbaabbbbbaaababbaaabbabbaabbbbaabbababbbbaaabbabaabbbabbaabbbbbbabaabbaabaabbaaaaaabbabbbababbbabbaabbaaababbbabbbaabbbbabbabababbbbbabbbbbaabaaabaaabbbaabbbbabbbbaababbabababaaaabaaababbbabaabbbbaaaaabaabbaabbaaaaabaaaabbaabaabbaaaaababbbbbbbababbbbbbbbabbaabbbbabababbaaaaaabbbaaabbbaabaaaaaababbabaaaaababbbababaabbbaaaabbbaababaaaabababaaaabababbbaabbbbbbbabbaaabababaaaababbbaabbbaabbbbaaaabbbabababbbbabaaaabbbabbaaabbabbabbbbabaaabbaaaabbbababaabbabbaaaabbbbaabbbabbabbbabbbbabbbbabababbbbaaabbbabaabaabbbbaaaaaaaabaabaabaabbbbbabababbabbaaaabbbaabaaabaaaaabbbbbabbbaabaaabbbbabaababbbaaabaababbabbbababaaabbbbaabaabaabbbaababbbabbbabaabaabbaabbbaaaabbabbaaaabaaaaaaababaabbabbbbbbbaaabbbbbbaaaabbbbabbababaababbabbaaabbaaaaaaaaabababbababaaaaaaabbaababbabbbaabaaaaababaaababbbaabaaaaaabaaaaaaabbbbaabaabaabaaaabbaaababbaabbaaaabbbbaabaaabaabbbaaaabbbbaaabbbabbabbbaabaabbbaabbaaaabbbbbbbababbbaaabbaabbabbaaababbababaabaaaaaaabbbbbaabbbbabaaabbbbabaaabaabbbaababbbabbabbaaababbbabbaabbaababbabaabbaaaaabbbabababaabaaaabbabbabaaabbababbbaaabaaaabbaaabababbaaabaabbaabbabbbbbbabbbabbabbbbaababbabbaabaaababaabaabbabbbaaabbaababaababaabaabbbbabaaabaabbabaabaaaabbaababbbbbbbabbbabaabaabaaaaababababaaaabaaaabbabaababbbbbbabbbbaaaabaaabaababbaaaaaaabaaababaabbbabbbbbbbbbaababbbabaaababaabbaaaabbaabbbbaaabaaaaaaaabaabaaabaaaabbbbabbaaabbabbaabaaababbbabbbbaabbaaaabaaabaaabbaaabaabababbbaabbbbaabaabbabbabbaabbbbaabbaabbbbbbbbaaabbabaabbbbaababababbbbabaaabbbaaaabbbaababaababbaaaabbaabaaaabaabbababbbbbaaaabbbbaaaaaaabbbaabbabbbbaabaaabbbaaabaabbbaabbbbabbbabbababbabbbababbabbbaababbbbbbbabaabbaaabbbbabababaaaabaabbababbbbaabbabbbbbbaaabaabaaaaabbaabaaababaabbabbaaaabbbbbabbbabbaabaabbbabbbaabaababbbaabaabbabbaabbaabaabaaaabaaabbbbabbbabbabaabbbaaabbbaaababbbaaabaaaaabaaabbbbbababaaabaabbaaaabbabaaaaabbaaabaababaabbabaaabbabbbbabaabababbbaabbababababaabaaaabaaaaabbbbbababbbbbbababbbababaabbabbabbababaabbbaaabababababbbbbaabbababbbabaabbabaabaabbabbbbbbaabbaaababbbababaababbbbabaabaaaaaabbbbbbabababbabbbaaaaabaabaababbaabbaaaaaababbababaaaabbbababbbbbaaababbbabbbabaabbababaabbababbaaabbbbbabbbaaabbbaaaabbbbabaaaaaabbaababaababbaaabbbbbaababaaaaababaabaabbbbabbaaaabbbabaaaaaaaababbaabababaaaabaaaaaaabbaaaaabbbabbbbbbaaabbbbababbabbaabbaabbababbabbaababbbabbbbbbbaaaabbabbbabaaaabaabbaaaabaaaabaababaababbbaaaaabbabaabbbbbabbaaaaaabbbbbabbaaababaaabbaabaaababbaaaabbaaabbabbabbbabbabbaaabaabaabaaabbbabbaababbababababbabbbbaabaaabbabbbaabaababbbbbaabbabbbabbbabababaabababbabaaaaababaaaaababbaaaaaaabaaaaabbbbaaaaaaaabbbbbbabaaabbabbbabaabbaaaabbbabbabaabaaabbbbaabaaaababbbbbabbaaaabbbabbbabbababbbbaaaabaabbbbbbaabbbabbbbbbaababaaaaaababaababbbbbabbaabaababbaababaaaababaabaaaaaabbaaaaabaaaaababbbbbbbbabbbababbababaaaaabbaaaaaaaaabbbbbbbaabbaaaaabaaaabbaababbbaabbbaabbbbbbbbaabaaabbaaabababaaaaabbaaabbbabbbaaabaaaababababbbbbbabbaaabaabbabbaabbbabbbababaababaabbbbaabaaaaaaabababbaabaaaaabaababaaaaabbaaabbaaabbaabaaabaabbbaabbaabbbbbabaaaaaabbabbbbbbaababaaaaaaababbbabaaabbabbbabbbabbababaaaabaabaabbaaaaabbaaabaabbbababababaabaaaabaaabbaaaabbbbbbbaaaabbbabbbababbbaaaaaababbbbbababbaababaabaaaabaabaabbbabbabbbaaaaaaabbaabaaaabaabaaabbbabaaabbaaabbabaaabbabbbabbbaaababaaaaabababbababbabaaaabaaaaabaabaabbabababbaaaaaabababbaaaaaaaaabbbbbbaabbbbbbabaababbaabbbaababaababaaaabbbbabbbaabbbaaaaabaaabbabbabbbabaababaabbbaabaaaaaabababbbaabaaaabaabaabaababbaaabaabbabbbaabbbabaabbbaaaaaaaabbabbaababaaaabaabababbabbbaabbbbbabbaabbaaababbaaaaababaaabbabababbabbbabababaaaaabaabbbaabbbbaabbbaaaabaaaaabbaabbbbababbbbabbabbbabaaaaaabbaabbbbaababbbabbaaabbbbbabbaaaaaaaaaabbaaabbaaaababaababbaabbbababaaababbbaaabaaaaaaaabbaabbbabbbbabbabbabbbabbbbaabbaabababaabaabababbbbaabbabaabbbaaaabaaaabbbbaabbaaabbbabbbbbbbabbaaababababaabbabbabbbaaababbbababaaaabaaaaabababbaaabbbaabaaabaaaaabbabaababaabbbabaaaaabaabbbbbbaabababaaabbaabbaaaaababbaaabbbbabaababbaaaababababababaaabbaaababbbbaaababaabbaaabaaabbabbbbbababbbbbbbbbbabbaabbaababbbbabbbaaabbbaaabbbabbbbaaabbaaaababaaaabaabaababaabbababbaaabaaabaaababbabbabbabaabbabbaaabbaabaaabbbbbaabababbbabaaaabbbabaabbbbaabbbbaaaaababbabaaabaaaaaababaabaaabbabbbbaabbabbaaabbbbabaabbabbaababaabbaabbabbaabbbbbaabbbbaabaabaaabbbbbbbabbbababbaaababaaababababbbababbaaabbaaabaabaaabbaababbabbababaabbbbbbbbbbbbabaaaabbaaaabbbaaaababbbbabbaaababababaaaaabbaaaaababaaaabaaaaabbbabbaaaababbbaaabbbbaabaabaabbbaaaababbbbaabbbaabaaabbbabbabbaaaabbbabbbabbabababaaaaabaaabbaabaaabababaababbaabbbaaabbabaababbaaabbaaaabaababababaaabbbaaababbabbbbabbbbbaaaaaaabaaabaaaaaaaaabaabbbbababbaabbbabbbababbbbbaaaabbbaaabaaabaaabbbabbababbabaabbbbbbaaaabbabbabbaababababaababaaabbbbbbbbbbbaabaabbabbaaabbabaabaabaabbabbbabbbbabaaabbababaaaabbbaabbbbaaaabaabbbaabaaaabbbbabbabbababbbaabbbababbbbbbbbbbabaabbaabaabbbaaabababaaabbaababbbaabaaaabaabaabbaaabbbbaabbbbaabbbbabaaaabbabaabaababbabbaabaababaabaababbababaaabbbbbabababababaaaaaaaaababbbabaaaabbaaabbaaabbababbbabbabbabbaabbaababaababbbbbbababaabbbbabbaabbaabbaaabbaabbaabbbbabbbbbbaaabbbbbabbbbabbbbaabbabaababbbaaababbbbabbbbbbbbbbbabbababababbaabbabbaabbbabbababbbbabababbaabbbabbbaaaabaabbbbaabaababaabaaabbabbbbaabbabbaaabbbbbaabbbbbbbaabababbbbaabbaaabbbaaaaabbabaaaabbaaabbbaabaaaabbabababbbbbabaaabbabbababbbbbababbabababaabbbbababbbaabbabbbaabbaaababbbbbaababbaabbbbaaabaabbbabbbbbbaabbabaaababbaaaaaababbabbbbaabbbaaabaaabbaabbbbbababbbaaaaaaaabbbabbababbaaaaabbbaaabbbaabbbbbaabbabbbaaaabaababaabaabbaaaaaabababaaaaabababbbababbbaaabababbbabbabbbaababbabbabaabaababaabaaababbbabbaabbbababbbbabbababbbabaaabbaababbaaaaaabaabaaabbaabbbaaabbaabbbbbbaabbaaaababbabaaaaaababbabababbbbbbbaaabaaaaabaabaaaabbbbbbaaaaabbbbababaaababbbabababaababaabaabababbabababbbaaabaaabbbabbbbbbbbbbaabababbbbbaaabbbababbabbbbbaabbbbbaabbabbaaabaabbbbbabaabbaaabaabaabaabbbbbaaaaabaababbbbabaabbabaaaabaaaabbbaaababbbbabbaabbabbbbbabababbbabbaabaababbbaabbbbbababbbbaabbbbabaabaaabaabbbaaaaaabaabbbbbabaaabbaabbbbabbbabbabbbaaababbbabaabbbaaababaabaaabaababbbbbabbbbbbbbbabbaabbbbaabbbabbbabbababbababbbabbaaabaaabaaabbbabbbabaabaababbaababbbaaabaababaabbbbabbabbbaaabbabbbbabbbbbabbaaabaaabaabbbababbaabbbabbbbbaaabaabbaabbaaabbaababaabbbbbbbabbabaabbbbbabaabbbaaaaaaaaaaaaabbababbaaabbabbaaaabbabaabbabbbbabbaabaaabaabababaaabaabbabbbabaaaaabbababbbabbabbabbaaabaaaabbabbbabaaaaaababbbbabbaaabaababbbbbbaabaaabbbabbabbabaabbbbbabaababbabbabbabaabbaabaabaaabbbbbbbbaaaababbabbbabbbbbbbbbabbbbbbaaaaaaabaabaabaaabbbaabbbbbabaabaaabbabbabbaabbbabaaaaaabbaaaabababbabaaabbbabbababbaabaababababaaabaabbaabaaaababababababbababbabbbaaabaabbbbbabbabbaaaababbbabbaabbbabbabaababbbbabbabbaaaabbaaabbbbabbbaabaaabaaabbbaababbbbbbabbbaababbbbabaaaabbabaaaabbaaabbaaaaaaabaabbabaaabbbabbaabbabaaabbbabbaaababbbaaabbbbabaabababaabbbabbabbbababbbbabbababaaaabbbbaaaaaaaabaaababaabbaabbaabaaaabbbbbbbbbaaabbaabaabbbaaabaabaabbaabbaaaabbabaabaaabaabbbbabbbaaaaaaabbaabababaaaaabbbbaabababbbaaabaaaabaabbababbbbbaabbababababaababbabababbaabaaabbbaaabbbaaabaaaaaaaaaaaabbbbbaabaaaababbbabaabbbaaaabaabbbbbbabbabaaaaaaaaabbbbbbaabaabbbbaabbaaabbbbbbbabaaabababbbbaaabbaababbbbaabaababbabbbbbbbbbaabbbbbbaabbabbaaaaaaaabaabababaaabbbbbbbbbbabababbbabbabbababbbbaabbababbabababbbbabbbbababababaabaabbbbbbbbababbbabbbbaaaababbaababbbbabbbbbbbaabbabbbabbbbbababbbaaababaabbaaababbbaabaabbaaaabaabbbaabaabaababababaaaaaababaaabaaaabbbbababaaabaaaabbbbbabbabbaabbababbbaaabbababaaaabbaabbbaaaaabbbbaabbaaabaaaabbaaaaaaabaababbbaabababbababbaabbbaaabbbabbaabbabbbabbbaabaaaaaabbbaaabbabaaabbbabbabbabaaababbbababbabbaabbbbbaabaabbbbbbbbaaabbbbaabaabbbabaababbabbbbaaababbbbbabaaaaabaabaaabbbbbbbbbabbabbbaaaabbaabbaaaaabbabaabaabaaaabbbbabbaaaaabaaaabbbbbabaaabaaaabababaaaaaabaaaaabaabbbabbbbbabaaabbabbababaaaaababbbabbbbababbbaaababaabaaaabbbbabbbbbababbbbbbaaabbabaaababbbbbabbabbbbbabbbabaaabbabbbababaabbbbabaabababbabaaaababbaaababbaaaaababbbaaabbbbaababbaaaabbabababaaaaababbabbaaaaabaaaaaaaabbbbbbbabbbbbabbbaaaabbaaabaaaabbbaabababbbbbbabaaaababbaaabbbabaabbbbbaaaaababbaaabbbaaabbaabbaabbaabbbaabbaabaaaaababbaaaaaabaaabbababaaabbabababbbbababbbbbaaaabaaabababaaabbaabbababbbbabbabbaabbabbbabaabbbbbabbbaaaabbbbbbbabababbbbaabbbbbbaaabbaaaabbbaabbaaabbaabababbbbbaaababaabbabbabbabaabaaababbabbbaaaababbaabbabbbbbaabaaabbbbbaababaabaababaabbbaabaabababaabaaabababaababbaaaaaabaaabbbbbabbabbbaababaabbaaabbabbababaaabbabbbaabbaabbabbbbaaabbaabbbbbbaaabaabbaaabaaaabaaababbbbbbbbbabaaaaaaaababaaaabaabbbbaabbababbbababbaabaababbbbbaaabbaaabbbbbaaaabaabbbabbaaabbaaaababaabbabaabbbaaabbaaaabbaabaabbbbabbbaaabbaabaaabbabaabababbbbbbbababaabaaaababbaabbababbbbbbbbbaababbbbabbaabbbbaaaaaaaababbbabbbbabbbaababbbaaabababbaabbaabbbbbbbababbbbaaaabbaaaaaabaaaaaaaabaabbabbbabbbbbaabaaabaaababaabbabaababababbbabbbabbbbabbabbaabbaababaababbbaabbaabbabbababbabbbabbbbbbabaaabaabaababaaabbabbaabaaabaabbabbaabbbabaabbababaaababaabaabbbaaaaabbbbbbabaababaababbbbbbababbaabbbbababbaabababbbaabaaaabbabbaabababaaaabababababbababbbbabbaaaaabaabbababaaaababaabaaababbaaabbabbaaaabaabbaabaaabaabbbbbabaabbababaaabbabaabbbbbbbaabbaabbaabaaaabbbbbbbabbabbbbaaaaaaaaabaababaabaaabbbbaabbbaabaabaaababbaabbbabbaabaaaabbabbaabaabaaaaaaabbbbabbbbbbabbaabaaaaaaaabbaabababbbbbaababaabbbbbbaabaabbaabbbbabbbbbabaabbbbabbaababababbabbaaabbbbbabbbabbbbaaaabbaaaaaaabbbbaabaaaaaaabaaabaabaabaaabaaabbbbabbbaabaaaabbabbabbbbbbbaabbaabaaabbabbabaaabbbaaaabbabaaababbaaaaabbbbabbaabbaabbbbaabbbbbbaaabababaabababaaababaabbbabaaaaababababbababaaabbbbaaaaaabaaabaaabbbaabbaaaaabbaabbaabbaaabbaabbabaabbbbbaabbabbabaabaaaabbbbabbbabbabaababbbaabaabaaaababbabbabbbbabbbbbaabbbbbbbabbabbbababbaabbbbbaaababbabbaabbbabbbbababbaabaababbbabbabaaaabbabaaaabbaaaabbbbabbaaaabbbbabbbabbababaabbabaaaaabbaaaabbaababaaaaaaaabbababbabbaaabaabbbaabbbbbbbbabbaaaabababbabbaabbaaaabababbbabbaabbbaababbaaaaaaabbbbabbabaaaaabbbaabbbbabbbabbabaabaaaabbababbbbabbabbababaaaaaaaaaaaabbabbaabaabbbbaaababaabaaabaaaaabaabaaabaaabaaabaaaabbabbbbabaaababaaaaaaabaababbbbaaabbaabbaabbbbbbaaabababaabbbbbbbabaaaabbaababbabbaababbaabbaaabbbabbbbbabaabaaaaaaabaaabababbaabbabaabaabbabbaaabaababbbabaababaabaabaaaaaabbaababaabbbbabbbbbbbaaaabbbbabbbbbabbbaaababbaaaaaabbbbaabbababbabaababbabaaaaabbabbaabaaaaaaaaaaababbaaaabbaaaabbaaaaabaaabaaabbbaabbaabaaabaaababaababaaabbbaabaabbbbaabbbaaabaaabaabaaaababaabaaabbaabaabababaabbabababaaaaababaabaaabbbbabababbbbbaaabbbbabbbaaaaabababaababbabaaabbbaabbabaaabbabbababbababbaaaabaabaaabbabbabbbaabbbaaaaaaabbbbabaaaaababaabbbabababbabbaaaabbbbabbabaaaabbbababbbabbbababaaaababbabbaabaaaabbabaaaabbaaabababaababbbbbaaabaabaaaabaaabaaaaabbbbabababbbbbbbbbbbaabbaababbbbaabbabaababaaaaaabbbbbabbaabbbbbbaaaabababbabbbbbbbbabaabaaabbaababbbbbaaaaabaaaabaaaaaababbabbaabbbbaababbbbbbabbaabbabbbabbaabbbaaaaabbababbabbaaabbbbaabbbbbaaabbabbabaabbababbbbaabaaabaaabbabaaabbabbaabaaababbabbabaababbabbbabbabbbaaaaaaaaabbabbabbbbabbbaababbbaabaaabbbbbabaaaaaaabaaabbababbbabbbaababbbbabbbbbaabbaabbabaabbbaaaaaaaabbabababaaabbbaaaaabbbbaaabbbaabbbababbabbababbbbababaaababaaababaabbabbbababbbaabbaaaaaabbaabbbbbaabbaaabaabaaaaabbaabaaabbabaaabaaaabababbbbabaaaabbabaaabaabbbaaaabbbaababaabaabbbababbbaabababbaabbbbbbaabbbaababaaaaabbaabbaaabbaaababaaaabbaabbbaabbabaabaabaabbaabbaabbabaabaababaaaaababbaabaabbabbbbbbabbbbbbbababbbbbbbbababaababbbaaabaabbaabbbabaaaabaabaabbaaaaaaabaaabaabbbbabbaaaababbaaaabaababbbaaaaabbbabbaaabaabbabbabaabbaaaababaaaababbabbabbbaaabaabbbaaaabababaabbbaaaaaabaabbbbbbabbbaaaaaabbaaaabbababaabaaaaabaabbbabbabbaabbbbbabbbbaaaabbabaaabaaaababbabaaaabbbababaaababbbbbaababbbbabbbabaabaababaabababaabbbaabbabbbabbbbbaaabbaabbbbabaabbaaabababbabbaaaaaabbbbabbbaaaabbabbaabaaaababbbbbbbbabbbaaaabbbabbbbbabbaabbbababbabaaabbaabaaaaaabbabbbbaabbbaaaabaaabaababbaaabababaabbbabbbaabaaabaaabbaabaaaabababbaabaaababbabbbaaabaaaaaababbaaaabaaabbabbabbbbbaababababbbbabbabbaabaaaaaabaaabbabbabaaabbabbababababaabbaaaabbbababbbaaababbaabaabbbbabbabbababbbaabbbbbabbbabaabbbbaaaabbaabbbbaabaababbbabaaaaablbbaaaaabbbaabbaabbbbbabaaaaaaaaabbabaaabaaaaabbbaababaaabbbbaaabbabbabaabaaabbbbbbabbbbbbbbabbaababaababbaababbbbbbbbbabbabbabaabbbabbbbabbabbbaaaabaaaaabbbbaabaabaaaaaababbabaabbbbaaaaabbbbbaaababbbaabbabbabaabbaaaabbbbabbbaabaabaaaaaaaabaabaaabbbbbaabaaaaaaaaaabababaaaababbbaaaaababbaaaaabbababaababbababbabbaaaaababbbbabbbbabaabaabbaaabababbaaabbaaababaaababaaaabbabaaaabbabbbabababbbbbbbbaaababaaaaabaabaabaaabbabbababababaaaababbbbaabaaabbaaaabbbbbbbbbbbaaabbabbabaaabbbbbaababbaaaabbbbabbbbabbaabbbbbbabaaabbaabababbbabbbbaababbabbaaabaabbaaaababbbbbaabbbbabaabbbbabbbabbbababbbabbbbbaabababbbbaaabaabbbababbbabaababbbbabaabbbababbaabbaaababbbbbaababbabaaabaaaabbbaaabaabaaaabbabbbbbaabaabaabaaaaabbbaaabbbbaaaababbbaabbabaababbababbabababbabbbbbababaabbbbaaabaaaaaabbbbababbbabaaaaaabbbaabaabababbaaaaabbbaabbbbaaabaabaabaaaaabaabbbaabaababbaaaaaabbbbaabaaaaabaaabaaaabbabbabbabbaabaaaabbaabbabababbaabababbabaaabababaababababbbaaaaaabaabaabbbabbbaabaaabbabbaababbbbbbbbbabbaaaaabbaaaaaaabaabbaababbbbbbaaabbaabbbaabaaaaaaaaabbaabbbbabaaabbaabaabbbababaaabbbbaaaaaaababaabbababbbabaabbaaaabbbbbabbabaababbaababbabbbaabbabbbbabaaaaaaabaabbaabbaababbbababaaaabababbbbbbabbbbbbbabbbbaaaaabbbaaabbbbbbaabaaaabaabbabbaaaabaabaabaabbabaabbababaaabbbabaabbbbaababbababbbababbabababbabbbaabaaaabbabbbbbaaaaaabbbaabbaabbbbbbabaaabbabaabababaabbababbbbaabaaaaaaaabbabaabbbaaabbaabbaaababbbabbbbbbbabaabbaabaabbbaabbbbbaaaaaaabaabbbbbaabababababbbbbabaabbbbbbabaaabbbaaababbbbbabaabbbbabbbababbbaabbaabbbbbaabaaabbbaabaababaabbbbbbbbbabaaababbbbabbbbbbaabaaababbababbabbaabbbbbbbbbabbbbbabaaaaabaabaabbbaaabbbabbabaabbabbbbaaaaaabbbbaaabbababbabaaababaaaaaaaabaababbbbbbbbbbbaaababbbbbbabaaabaaabbbbbababbaaaababbbaaabbababbbbbaaabaaaaabbaabaaababbabbbabbabbaaabbabaabbabbaababaababaaababbaabbaaabaababbababbaaabbbababaabaababbbaabbbbababaaabbbbaabbbbbbbaaaababbaaabbbaaaababbbbbabaabaaaabaaaaabbbaaaaaabbbbabbabbaaabbabbbbbaabaaabbbabbabbaabbbababaabbaabbbaabaabaabbbabbabbabaaabababaaabaaaaaabbbabbabbabbaaaabbbbbabbbbababbabbaabbabbbbaaabaaabbbabbbaababaaaaabaaaabbabababbaaabababbaababbbbbbaabaaaaaaabbaabababbaaaaaababbbaabaabbaabaabbabbbbabaabbbbaaaabbbaababbaaabbaaabbbabbbbabbabaaabbbbababbbbbabbbbbaabababaaabbbbaaaaaabababbababaabbababbaababbaabbaabbbaabaababbaaabbbaabbbaabbabababaaabbabaabbbbbabbbbabbabaaabbbbbbbabbbaabaaababbaababbbbbbaaabaabbbbbaaabaabaaabaabbbabbaaabbaaabbaabbabaaaababbabbabababbaabababbaabbaaabaabbbabbaabbbaabababbbabbaabaaaabbbaaabaaabbbababaaabbaaaabaababbbabaabaaabbbaabaabaaaabbaaababbbbbbbbbabaaaaabaaabbabbbbabbabbbbababbaabbaaabbabbaabbababaaaaaababaabbaabaabbabbabaaaaabbabbaabbabaaaabbbbaababbabaabbbaaaabbbbaababaaabbaabbbbbababbaabbabababbaaababaabaababbabbababbaabbbbbbaabaaabbbbbbbaaaaaaabbbbbababaaabaaaaababbababbbbbbbbabaaababbbbbbabbaabababbbaabaabbbbababaabbaababbabbabaaaaaaaaaaaababbabbaabbabaaabbbaaabbbaaaabbbbababbabbaaababbbbbaaaabbaaababbbaabbbabaabbbaaaabbaaabbbabbaabaaaaabaaaaabaabbbabaabbbabaababaaababaaabbbbbaabbbbbbabbabbbabbabbbabaaababababbbababaabbbaabaabbaabaaaaaaabbaaaaabaaabbabbbaabbababaaabababbaabaababbabaaabbbbbbabbaaabbabbbaabbbababaababababbbbaabbaabaababaaaababaaaaaaabbabbbbabababababaabbbabaaabbbbaaababbabbbbababbbbbaabbaaaabaaabbbaaaaaabaabbabaabaaabbbabbbbbbbabbbbbabaaabaaabbabbababbbabbaaabaabbbaabaabaaaaaabbbbabaaaabaabbabbbbbbaabbbaabbabbbaabbabbaaabbababaababaaabbbabbbaaaabbaaabaaabbbbbabababbabbbbbabbabbaababbbaaabbaaaaaabbaabbbabaabbaabaaabaaababbaaabaaaaaabbbaaabbbaabbbaaabaaaabaababaabbaaabbbbbbbbabaaaabaaabbbaaaaaabbaaabbbabaaabaaaabaabaaabbbabbabbaabbbabababbbaaabbabbbabbababbaabbaabaaaaababbbbaabaababbaabbabbbabbaaabababaabbbbaabaabaabbabbbbbabbabaabbbbbbbaabbbbbbabbaaabbbabaaaaaaabbaabaaaaababbbaabbbaaaabbabbbabbbbaaaaabbbababbaabbababbababaabbbbbaaaabaabaabaaaaaaababaaaababaaabbbabbabbbbbaabababbabbbbabbbaaaababbbbbabbbabbaaaaaababbbbbbbbbbaabaaabaaaaabbaaaaababaaabbabaaabaabbbabbabbaaabbbbabbbabbbabababbaaabbbababaabbbabbbaababbbbbbabababbaaaababbabaabbbbbabababbbabbbbbabbbbabbbbbbabbababaaaaabbbbabbbabbaabaababbabbbaabababbabbbabbbaaaabbbaaaaabbabbababbababbabaabababbbbabaaabababbbaaababbaabaaabbbabbbbababbaaabbaabababaaaaaaaaabbbaabaaaaaaabbabaaaaabbabbababbabbabbbababbbaaababbbbabbbbaaabaaabaababbaabababbaabbaabaabaababbbbbaaabbabbbbbbababaababbbbbabaabbabaabaaabbbbaabaabbaabaaaabbaaabbaaabbaabaabaabababbbaaaabaababbbaaabaabababbbabbabaababbaabaaabbbaabbababaababbbbbaababbbabbbaababbaaabbbabbaabbababaaabbbbaababbbabaabaaaabbbababbabaaabbaaaaabbaabbbbabbabbabbbbaaaabaabbbaaabbbaabbbbababaabaabbbabaaabbbabbbbbabaaaababaaaabaabbababbbbabbabbaababaabaababbbaabbbbaaabaaaabaaaababbbabbaababbabbbabbaabaaaabbabbaabbbabbababbbbabaabbbaababbaaabaababbbababbbabaabaaabaabaabbbabaabbaabbababababababaabababababbbabababaaabbaaabababbaaabbaabaabbbbabaabaaabbaababaabbbabbaaabbbbabbabbaabaaaabaaabaaaaababbbaabaaaabaaaabbaaaabbaabaaababbaaabbaaaabbababbbaaaabababbbbaabbaaaaabbbbbabaaaaabaabbaabaabbaaabbaaaaaaaabbaabbaabbabbaaabbbaabbaaaaabaabbabaaaaaababbaabbbaaaababbaabaabbaaaababaababaabaababbaaabaaaabaabbaabababababababbbabaaabbbabbaabaaabbaaababaabbaabbbbaababbaaabaabbaabbbbbabbbbabaaabbaaabbaaabaabaaabaabaaaababaaaaaabaaabaabaabbbbbbaabaaabbbabbaaabbabaabbbbbabaabbabbbbaaaabaabbbaaabababbabbaaabbaabaabaababbaabbbaaaabbababaababbabbbbbaabbbbaaaaababbbbbaabaabaabbbbababbaababbbababbaababaabbbbbabaaaabbaaabbaababbbbbbaaabbaaabbaababababbaababbaaabbbabbabbbabbbbababbababaabababbbababaabaababbabbaaababbbabbbaaabaabbbabababbbbaaaababbabaabaaabbbbbbabbababbbabbabbbaababbbabbaabbabaabaaaabaabaaaaababbaabaabaabababbaaabbbbaabbbbbbaabaaabbbbbbaabababababbabbaaabababbabbabaaabbbbabbababaaabbaaabababbbaaababbbabbaaaaaabbbbaaaaaaaabbbaaaaaabbbabbabbaabbaabbabbbaaabbaabaabbbaababbabbaaaabaaaabbaababbbaababbbbababbbbaaabababababaaababbbbbabbbabbbbabbbabbababababbbababaaaaaaaaababababbabaaaaabbbaaabbaabbbbaaababaababbbaaabbabbaabaabaaaaabaaabbbababaabaabbaabaabaabaaaaabaaabbaababbaabababbababbbaaaaaabaabababbaabaabbaaabbabbbbaabbbbabbbaabbbbbbbbbbbbaabaababbabbabbbbbabbaaabaaaabaaaaaaaaabaabaaababbbabbabababbbbbababbbbaababababbababaaababbabbbaababbbbbbbbaababaaabaabbbbbaabaabbaaabbaaabaabaabaaaabbbaabbabbaabbaabaaaababbbaaababbabaabaabaababababbbbaababaabbaababbbabbabbbbabbbabbbbbabbabbabaaabaaaabbaaaaabababaabababaaaabaabaabaabaaaabbbabbaaaaabaaababaaaaaaabaabaaaaabaaababbbbbbbbabaaababababaaaabaaabbaaabbaaaaabababbaabbbbaaaababbabbabaabbaabbabbaaaaaaaabbbabbabaaabbaaaababbabaabababbbbaabbabaaabbabbbbbbaabbbababababbabbbbbaaaaaaaabbaabbaaaabbbababababbbbbbabbabbbbabbabbabaabaabbbaaabbabaababbbabaabbabbbabbbaababbbbbabbabababbbaabaabbabaabbaabaabbaabbaaabbbbbabbaaabbbbabbaabbabbbbbbbbabbbbbabbabaababababbaaabbaabbbaabbbabbbabbbbabbaaaaabaabbbbabaabbbbbbabbbbbbbbbbbbaababaaaaaabbbbabaaaabbababaaabbbaaaaabbbabababbabbaabbbababbaabbbabaaabbabaaaaabbaaaabbbaaabbbaaaabbbaabbaababaabaabaabaaaabbbbaaabaabaabaaababbababbababbbbbbbaaabaabaaaabbaabaabababaaabbbbbaababbbbbaabaaababaabbbaabbbabbbbababbbbbaaaaababaaabbabbaabaabaababbaaababbbbbaabaaababababbbabbaaaaabaaaabbbbabbbaaaabbbaabaabbaabaaaaaaabaaaabaaabaabababaababbbaaaaaaabbbbbbbbbbaabbbbabbabaaaababaabbbababbaabbabbbbbaaaaaabbaabaabaaabaababbbbbaabbabbababbbbaabaaaaababaabaaabaabbaababbbaabbbbbbabababbbbaaaabaabaaaabbabaaaabbbbaababbbabbaaaaabaabaabaaabbaababaabaabaabbabbaaababbaababbababaaaaabababbaabaabbbabaaabaaababababaaabbbabbababbbbbbaabbaaabbbababbbbbabbbbbaaababbabbaababaabaaabbabaabaaabaaaaaaabaabababaabaabbaaaabbbabbabbbbbbaabbbaaabbbaaaaaabbbaaabbaabaabbaabaaaaaababbbabaaaaababbbabababaabaaaababaabaabbaabbbbbbbbabaaaababbababaaabbaababaaaaaabaabaaabbabaaaabbbbaaabaaabbaaababaaabbabbabbaaaabaaaabaababbbbbabbaaababababbbbaabbabbbabbaaabbbaabbaaabbaaaabbaaaabaaaabbaaaaabbaaaababaaaaabbaaabbbaaabaabbbabbaaaaaababbabbbaabaaaaabbbbbbbabaabaabaabaabbaaaabaaaabbaabaaababaaaabbbaabababbbbababbbabaaabbbbbbbbbbbabaaaaabbbbbbabbabbabbaabababbbaaabbbbaaabaabaaaaabbbbbbabbbbbbaabbbaaaaaabbabaabaaaaabbbbbaaaaabaaabaaaaaaaabaaababbaaaabbbabbbaaabaaaaaabaaaaabaabaabbababaabaabaabaaababbaaaaabbbaababaaaaaabaabbabaababbaabbbbaaabbbaabaababaaabbbabbabaabbbaaaaababaaabbabbabbabbabbbababaaaaabbbabbaaaaabbbbbaaabbabbabbabaaaaabbaaabaabbabaabbaababaaaababaabbbbbbaaabbaabbbabaaabaabbaabbbbabbabbaabaabaaaabbbbabaabbaaaaaabbbaababbbabbaabbbbbabbbaaaabaaabaabbbbabaabababbbaababbbbbbabbbababaabaaabbabbbaabbaaabbaabbbababaaabaabaababbbabbbbbababbabbababbbabbabbaabaaaababbbabbaaaaaabaabbababbbaaabaabbbbbbbbbabbbbababababaabbaabbaaabbabaaaabaabaababbbbaaabbbaaaabaaabaaabaabbabaaaaaaaaabbbbababbaabbaabbaaabaabaabbabaabaaabaabaabaabbbaabaabaaaaabbaabaabbaaaaaabbabaaabbaaaaaabaaaaaabbbabbaaabaaabaabbababbbabaaaabababbbbbbbabbaaaabaabaabaababbaaabababbaabaaaabbbbaaabbaabbbbaaababbbbaabababbbaaaabbaaaababbbabaabbbaababaaaaabbbabaabaaaabaaabababababbbabaaaabbababaabaababbababbbababaaaaabaaaaabbabaabaaaababbbaaaabaaaaabaaabaababbbababbabaaaabbabbaaabbbbbbbbababaaabbababababaaaaabaaaaaaabbabbbbabbabbabbbbabaabaaabaaabaaabaaaabbabbabbabaaabbbabbaabbaababbababbaabababbabaaabaaababbbababbababbbabbaababaaabaaabababaaaaaabaaaaabbbbababaabababaabababbbabaaababbbabbbabaabbbbaaaaabbaaababbbaaaaaaaaaabaabbbaabbbbababaaaabbbabaabbbbbbabaabbababbbabbabaabaabaabaaabbabbabbbbaabbaabbbbbbababaababaabbabbbaabbaabaaabaabbbbabbababbabaaababbbababaababaabbbbbaabaabbabbaabaabababaaabababbababbbabaababaaabaaababbbbbbaaaababaabbabababbbbbaabababaabbabababbbabababbbabbaaabaaababaabbbaaababaabaabababbbaababbbbabaababbabaabbaaaabbbbaababbaabbbbaabaababaabaabaaaabbbabaaabbbabbbabaaabaaaaababbbabaaaabaaababbaabbbbaaabaabaaaababaaabaabbabbaabbbbabbbbabbbababaabbbaaababbabababaabbbabaaabbaababbabaaabbabbbabbababbbabbbbbaaabbaaabaabaaaaaabbbbababbbbbbabbaaaabbababbbababaaaabababaaabbabbabbbabaaababaababbabaaaaaabaaaaabaababbabaabbbbbbbbabaaabbaaaabbaaaaaaabbbaaababababaaaaabbabaabbbabbaaababaabbabbaaababaabaaaaabbbababbaaaababbbababbaaaaaabaabbbbabbaaabbaaaaaaaabbaabbbbbababbbababbbbbaabaabbabbaabbbabbaabbbaabaabbbbbaabaaaabaaabaabaabaaaaababaabaaaaabaabbaabbbabbbaabaabbabbaabbabbbbbabbaabbabbbbabaaaabaaaabaaabbbbbbbabaaaaababaaaaabbabbabaabbabbbaabbababbabbaaabaabbaaaaabbbabbaaaabbbbabaaabababaabbaabbabaabaababbabbaabaaabbabaabaaaabaaababbaabbbbabababababaaabaababbabbaaabbaabbbbaaabbabbbaaaaaabbbabaaabbbabbbbabbbabbaababaaabbbbbabbbabbbaabbabbbbabbaaaaaabbaabbbabaaabbbbbabababbabbbaaabbaaaaaabbaababaababbaabaaabbabaabbbbbbabbabaaababbabbaabbaaabbaabbabbbbbbbbababbabaaaabbaabbababbabbbaaababaaaabaabaaabaaabbbaaabbbaabbbbbabbbbabaaabaaaabbababbababbabbaaabaaabbbbbbbababbaabaabaaaaaabaabbaababbbbbaabbbababbbbabababbaababbaabbaabaabbbbabaabbabbaaaababbabbbaabaabaaabbabbbbbbbaaaabbbabaaaabbbbbbabbbbbaaabbabaababaaabbaabbbbbbbbbbbbbabbaababbbaaaabaaaaaaaaabbbbaababbbabbbbbaabbaaaabbaaabaaabbbbabbabbaaaababaabbaabbbbabbaaabbaabbaaaaaaabaabaaababaaaabbababbbbbbaababbabbbbbbaaaaaaabaaaaabbabbaabbbbbbaababaabbaaabbaabaaabababbbababababbbbbbabababaaabbaabbababbababbbaabbbbbbbabbaaaabbbbaaaaababbabaaaabbbabaababaabbbaababbbbaababbbbbbaaaaaaabaabbbbaabaaaaabbbabbabaaaabbbabaaaaaabbbaaaabbbaababbaababaabaaabbabaabbaaababbbaabaaabaaababaabbbbbabbababaaaaabbbbbabbabababbbaabaabbbbbaabaaabbaabaabaabbbaaabbaabaaaaaaaaabaaabbabbababbbbaababbaaaaabaafbbbaaaaabbbaaabababbaaababaabbbbbaababbbbabbabaabaabababababbabaaaabbaabbabbaaaabbabbbbbababbbaabaaaaabbbaabbbbbbbabaabbaabbbbbaaabaaabbabaababaabaaaaaabababbbabbbbaababaabbabaabaaaaaabababaababaaaabbbbaabbbbbaaaabbabbbaaaabaabbbababbabbaaaaababaaaabbaabaaabaabaabbababbbbbaababbbbbbbaabaaaaabaaabbbababaaaababaababaaababababaaabbbaabbbaabbbaaaaaabaaaabbaabbabbabbaabaabbbabaabbaaabbbbbaabbaaabaabbaabaabaaaaaabaaababaabbaaababbbbababbaaaaaaababbbbbbaabaaababbbabbbaabbaaaababbaaabbabbbbbbaabbabaaabbababbaabbaabaababaabbbaaaabbabbbbbabaabbbabbaabbbaaabbaabbaabbabaaababbaaabbaaaababbbabbbaabbbbbbaaabaabaabbaababbbaabaaababaaabaabbbaabbbaaababbaaabbbbabababbaabababaabaabbaabbabaaabbbaababbaababbbabbaabbaabbbbbbbbabbbaabbabaabbbaaabaaaaababbbaaaaababaaababaaaabbbbaaaaababbbaabbaabbbbbbaabbaaababbabbabaabaabbaabbabbbbaaaabaabbabbbaaaaababbbabbabbabbbaaaaaabbbbabaabbbbaaaabbbabaaabababbabbbabababbaabbbbabaaaaabbbbaaaabbbaabbaaaaabbbaababbbabbbabbbbbaabbbabbbababbaabbbbaababbbabbbaaaaababbbaabaabbbabbabaaaaaaababbabaabbbbbbbaabbbbbbaabbababaabbaabaabbabbabbaabbbbabbabbabababbbaababbabaabbbbbbaababbbabaaaaaabaaabbabbabbabbaaaababaabbbbbaabbabaabaabbbbbaabbbabababaabbbbbabbababbaaababbbaaaaabbbaaaaaabbbaaaabbaaaabbabbbbaabbaababaabaabbbaaaababbabababbababbabbbbabaababbababaaaabbbabbbbababaababbbaaaaabbababbaaabbbaaaaaabbabbaaaabbbbbabbaaaabbbaaabbabbbaabaaabaaaabbabbbbbabbabbabaabbaabaabbbbbbbabaaabaabaaaabbbbababababbbbbabbaaaabaaabbbbbabaaaaaabbbbbababbbaaababaaabaababbbbaaaaaaabbbbabbaaababbaabbbbabaababbaaaaababbabaaababaaaabababaabbbbbaaaaaaaabbaaaabbbbabbbaababaaabbabaabbbabbabbbbabaababbbbaabbabbbbabaaabaaabaaabbabaaabbbbbbabaabaabbabbabbbbabbbbbaaaaabbaaabaaabbbabaabbaabababbbaabaaabbbbbbaabaaabaabbbbabaaaaaaabbaaaaabaaababaabaaababbabbaabbbaaababbbabababbabaabbbababaabbbbabaabaaaaababababaabaabbaabbaaaabbabbaaababbaabbbaababaaaaabababaabaaabbaabaaabbbaabaaabaabaaabbaabbaaaabbbabbabbbabbaabbbaabbbabaabababbabbabbaabaaababbabbbaababaaaaaaabbaaabbbbbaabababbbbaababababababaabbabaabaabbbbbbababbaabbabaabbabbababbbbbabaaabbbbbabbaabbbabbabaaabaaaaaabbababbbbbabaaabaabaaabaabbabbaaaabbababbabababbbbabbbabbbbbabaabbabbaabaaaabbaabbbaaaabbababbbaaaabbbabbbaababbaabaaaaababbbbabbabbbbbaaaabababbaaabbbabbbaaaababbbaaababaabbaabbabbbbbaaabaabaaaaabbaabbbababaaabbaabaabbbbabaabababbbbbbabaabbbabbbaaaabbaabaabbbabababbaababbbbababbbbbabbaaaaababaabaabbaaabbabbaabbabababaabbabbbabaaabbbbbabbaaabaabaaababbbbababbabababbbaaabbaaaaaaababbbaaababbbbaabbbababbbbbababbaaababbbaaaababaaabaaabbbbaaaabbbbbbaaaabbaabaabbbaaabbabbbabbbbbabbbbbabbaaaaabaaaabbaabbbbbbbabaaaabaabbbbbbaaabababbbbabbabbbaababbaabbbaababaababababbababaaaabaabbbbbabbabaabaabbbbbbabbaababbaabaaabbbaabababbbbbbbabbaababbbbabbbaaabbbbbaaaaaababbabbbbaaaabaabbabbabbbbbabaabbababbababbabbbbabbbabbbbaaabababbabbbabbabaababbabbabbaabababaaabbabbbbaabbbbabaaabbaabbaaaaababbbbbbabbbbbababbaabbababababaabbbabbaaaabababbbbbaabbabbabaaaaaabbbbaaaabaaababbbbabbbbbabaaaababbbabbbbabbaabbbaaababbabbabaaaaabbabaaaababbaabbbabbaabbbbbabaaaababababaabbabaabbbabbbbbabaabbbbbaaababbbbbbaaaabbbbbbbaaabbaaaaabbbaaaabaabbbabaabbbbbbbbbbabababbaababbabaabbbaaaabbabbabbabaabbababaabababaaaaaaabaaaababbbabaaabbabbababbaaababaaabaabbaabbbaababaaabababbabbbaaaabbabaaabababbabbbabbbaabbababbaaabababbabababaaaaaaabaabbbbbaabbabbbabbabbaabbbabbabbbaabbaabaabaaaaaaaaaababababababbaabbbabbabaabaabaaabaaabbaaaababbbababaaaaabbabbbbbabaaaabbbababbbabaabbabbbbbaaaaaaabaabaabbaabaabbaaabbbbbbbbababbaabbbbbaaaabbbbaaaaabbabaabbabaaaaaabaaaaaababbaaaabbbaabbaabaaabababbabaaaaaabbbbbbaaabbababbabbbabaaaaaababbabbbabbbbbabaabbbbabbabbbababaaaabbabbbabaabbaabbaabbaaaaaabababbababbaaabbbbbabbabaabbbaababbbbbbbbbaabaabbabbaaabaaabaaabaaabaaababbaabaaababaaabbaabbbabaabbabbabbabbbabbbaaaaaababbabbababababbaaaaaaabbaaaaaabbabbaaaabbaaababbbaaababaabaabbabaabaabbaaabaaababaaabbbaabaabbbabbabbbabbabababaabbbabbaabaabbbbaabaaaaabaabbbaabababbaabbbabbbaaabaaaababaaabaaaaaaaaabbbbbbbaaabababbbabbaaabbbaabababaaabaaabbabbbbbaaaabaaabbaaabbbaabbbbbbbbbabbbaaabbabbbbbaababaaaababbbabaaabbaaaaabaabaabbbabbbabababaaaababbaaaaabababbabbaaaabbbaabbbabbbbbbbbbbabbabababbbaaaaabaaaabbababbbabbaabbbaabaababbbaaabbaabaabbbbbbbabbbaabbbabababbbbabbbabbbaaababbaabaaaabbabbaabbbbabbaaaabaaababaabaaabaabbbbaababababababaabababaababbaabaaabaaababababbbbbbbababaabbaaaaabbbabbababaaaababbbababbabababaaaaababaaabbaabbabbabbaaabbabbabaabbabbbbbaabaaababaabaababbbbbaabbabbbaaaaaaabbabaaabbaaababbaabbabababbabbbabbaaaaabbabbabbbababbbbaabaabbabbabbbababbbbabbaabaaaaabbbbabaaabaabaaabbabbaabbabbabaabababbabbbbbabbabbbaabbbabaaaabaaaabbbbabbaaababbbabbbababaaaaabaabbaaaaababbbababbaaabaaabbaaababbaaabbbaaaaaabbabaabaaaabbabbaabababaababaabaabababbabbabbbababbaabaaaabbbbaaaabbbbbabbaabaaaaabaabbbbabbbaaaabbbaabaababababbaabaabaaabbbbbbbabaaaaabaabaaabaabaababaaaabaaaaaaaabbaaaababbaaabbaaababbbbabbabbbabbabbbbabababbaaaababbaabaababbbbaaaababbabbbababaabbaaabbabaaabbbababaaaabaabaabbaabbbababaaaaabbbabaaabbaaaabbaababbaabbbaaaaababbabbbbbbbbaaaabbabbabbbbabaaaaabaabaabaaaababbbbbbaabbabbbaababbabbaabaaabbbbaaaaabbaaaaabaabbbbabaabaaababbabbbbbbaabbbbabaaabbbbaabaaabbaaaaaabaaabaaaabbbbabbbaabbabbbbbbbaabbbbbbbababbaabbbaaabaabbbbababababbabbaababbbbabbbbbabbababaaabbaabababbabbbaabababaabbababbabbaaaabbaabbaaaaababbbaaaaaaaaabaaabbabaabbbbabbaaaaaaaaabbaabbbbbbbababbaababbaabaabaabbabbaababbbaaaaabaabbaabaaaaaaaabbbaaabbbbbbaaaaaabaaabbbabbbaabbbaabaaabaabaaabaabbaaabaaaababaabababaababbabbbaabaaabbbbababbbbbabaabbbbbabbbabaaaaaabbabbaaabaaaabaaaabbabbbbaaaabbbaabbaabababbbaaaaabbabbaabbbbbabaaabbbbaaaabbaaaaaaabbbabaaaabaabbabbbbbbbbabaaabbbbaabaaabbabbaabbaaaaabbbaaaabbaabbabbabaaaabbbbabbbbbaababbbbabaaabbbbbbbbbbabbbabbababbbabaaabaaaaabbaabbaababaaabbbbbbaabbaabbabbbabbabbbabbbbabbbababababbababaabbbbabaabaaabaabbaaabaabbbaaababaabaababaaaaaaabbbabbbbaababababbababaabbaabaaaabaaababbaaabbaabbbbaaabababbbbaaaaaabbabbaaababaaabbaabbaaabaaaababbbabbaabaabbbbbbaaabbabbababaabbbbaabbabaaaabbbababbbabbabaaaaabaabaaaaabbabbabaababaaaaaabaabaabbaabaaababbbaaabaaaabaaabaaaaaabbbaaaaabbabaabaabaabaaabbabaabbbabaaaaabbbabbaabaaaabaabbabaabbbabaabaabaaaaaaabbaaabaaabaababbabaabaaabbababaaabbbbbaabaaabaabbabaabbaaaaaababbbaabbbbbaababbaabaaabbbbbabbababbbaaaababaaabaabbbaabbabaabaabbababaaaabaabaabbabbbaaaaabbabbbbaabbbbbbabbaaaabababbabbbbabbbbababaababbabbbbaabbabbbbabaaababbabbabbabbaabaaababaabbababaaaaaaaababbbbbabbbbaabaabbbaabbabbbbbabbaaaaaaabababbbabbbbabaabaaabbbbaabbbaabbaaaaabababbaaaaabbbbbababbbabaabbbabaabbaaaaabaabaabaabaaaaabaaaabaaabbbbababbaababbaaaabbbbaabaaabbabbaaaaaaaaababbaabbabaaaaababbbaaaaaaabbbbaaabbbbaaabababbbaabaababbbaabababbabbbbbababaabababbaabbababaabaaabbaabaaaabbabbabbaaaaabbabbbbaabbaaaabaaaaababbaabbabababbabbbabbbbaaaabbababbaaabbaaaababbaaaaaaaababbaabbbbbabbbbabaabaaaaababbabbabbbbbabbaabbababbbbaabbbaaaababaababbaababbaababaaaabbaabbbbabaaabaaababbbbaaaababbaabbbbaaabaaabbaaaaaabbabbaabbabbbaaaabaaababbabbabbaaabbaaaabaabaaabaabbaababbbbbbbaaabaabbabbbbabbaaabbbbaaababbbabaaabbbabbbbbabaaaabbaababbbabbaabbababaaababbaabaaaaabbababbbbabaabababaaaaabbabbabbaaabbbaaabbbababaaaaaaaaaabaaaaaaabababbbbbbbabbbbbaabaaabbaabbbabaabbbbaababbaaabaabbabbbbaaabaaaabbaabbaabbababaaaabbbbbaabaaaabababaabbbbbabbbbababababaabbbaaabaababaabaabbaabbbabaaaaaaaaabbababaaaaabbabbaaaaaaaababbabbababaabbabbbaaaabaaaaabbbaabbbaaabbbaabbbbbaababbababaaaabbaabbaabbbaaaaaaabbaaabaaaabbabaaabbbabaaabbabaaabbababbabbbaaababbaaaababbbbababbbaabbbaabababbbabbbbaabaaababbbbbbbbbbabbbbbabbabbbbaabbbbbbaababbabbbbaabbbbbaaabbbbaababbaabbbbaabbbbbbaaabbbabbaababbbbaaaababaabbbababaabababaaaabbbbabaabaaabbbabbbaaababbbbaaaaababbbababaaabbbbbbbbaaaaabaaaabbbbbababbbbabbbaabaababaaaaababbabaababbabaabaaaaaabbaaaabbaaabaaababaabaabbbabbbabaaaaaabaaabbabbaabaaabababaaaabbbabbabaaaaabbbabbaababaaabbbbbabbbaabbabbabbbbaababaabbbbabbbababaaabbaaabaababaabbaabbbbabababbbaaaababbbaaaaaaababaaaaaabbabaaabbaaaaaabaaabbbabbbaababaaaabbaaabaaaaabababaabaaabaaaaaaaaaabbabbabaaabbabbaababbaaaababbbbaaababbaaabbbbbbabbaaabbabbbbbaabbbababbbbaabbbbaaabbbbbbaabbbbaaabaababbbabaaaaaaaaaabbbabaaaaaaabbababaaabababaabaaaababbaabbbaabbbbabbabbaaabbabaabaaaabbbbbbabbbbbbbabaaababaabbabaaabbabbbbabbbbbaabbbaaaaabaabaababababbababbabbbaababbbabbaaabbaabaababbbbbbbbbababbaabbbaababaababaaabbaaabaaaaaabaabaabababababbaabbabbbaaabbabbabbabbbbbaaaabbbbaabbbbbbaabbbaaaababbbbbabaabaaabbbbaaabaaababbbabbbabaabbaabbbaabbabbbbbabbabaaabaaabbbbabababaaabbbabababbaaaaaaaabbbbabaaaaaaabaabaabbabababbabaabbbbbaabababbbbabaabbbaabbabbabaaaababababababbbabbababaababaababbabbaaaaaababbaabbabbbbabaababaabaabababbbbbbbabababbbabaabbaaabaababbabbaabbabbbbbaabbababaaabbbbbabbababaabbabaaaabbaabbbbaaaabbbabaaabaaaababbbabababbbbabbbbaaababbbbabbbaaabbbbaabbbabbbbbabbbaababaabbabbbbbaaaabbabbbbabbaababaaababbabbaababbaaabbabbbabbaabbaabaabbbaabbbaaaabababbbbbababbaabbababaabbaaababbaaababaabababbbabbbbbbabaabbaababbaaaabababbbabaaabbababbabbabbbaaabbbbababaababbbabbbaabbaaabbbababbbabbaaaabbababaaaaababaabaabbabaaabababaabbaabaabbbbaabaaaaaaababaabbbabababbabaaabbababbaabbbbbbbaabbaababbbbbaaabbababbbababbabaaaaabbbaabaaaabbababbabbbbabbabbbaaabbbaaaaaaaaaabbabbbaaababbbabbbaabbbababaabbaababbababbabaaaabaaabababbaabaaaabaabababbbbbbabaaabbabbbbbaabbabababaabbaabababbaaaabaababaaabbbbabbabababbbaabaaabbaaabbabbababbbabaabaababababbabbbaaaabaaabaabbbbbbaabbbaaaabbaaabbbbbaababaaaababababbbaaaaabaaaabbaabaababaaababbabaaabaabbbaabbbaaabbbbbbbabaababababbbaaabbbaaaaaabababababbaabaabbabbaaababbaababaabaabbaabaaabababbbbabbbababbabbbbbabbaabaaabaaaaaababababbbaaabaaaabbaabaababbbaabbabaaabbbbbaabbabbbbbabbaabaaabababbbbabbbaaabbbbaababaaabababababbabaaabaabbbaababbbbabbaabbbaaaaababbbbabbaabaabbbbbababaabaaaaaabbbbabbbaaaabbbbaabaaaaaaaaaaabaaabaabbabbbbbbabbbbbaabbbaabbbaaababbaaaabbabbbabbbbaaaaabbabaaababbbaababaabbaaabaababaabbbbbababbabbbabbabaaaaababbabaaaaaabbbabaabaababbbbbabbbbaaaaaaabaaaababaabbbabbabbbaaaabbbaaababbbbbabaaabaabbbbababaaabababbbaaabbbbbaabbbbaaabbabbaabbaaababbaabbaaaaabbbbbaaaaaaaaaaaaaaaabbaaabbaabaabbabababbabaaabbbababbbabaabaaabababbbbabaabaabaabaabbabbbabbbbbabaaaaabaabaabaaabaaabaabababbbbaaaabbaabbaaabaabbabaababbbbbbbaabaaabaabaabbbbaaabaabbaabbaaaababaaababbbbbabbbabaaaabaaabababaabababbaababababaaaaaaabaababbbbbaaababaaababaabaaaaaaaabbbabbbaababaabbbaabbabbabbababbaabaaaababbaababbbabbaabaabbbabbaababaabaaababbbbbaabbabbabaabababaaabbaabaababbabbbabaabbbabbbbbbaabbaaaaaaaaaababaaaaaaaaaabbabaaababbababaabaababaaabbbaaaabababbabbabbbabbaaaabbabbbbababbabaabbbbabbaabbaabaaabbababbbbaabbaaabababbbbabaaabaaaaaabbabaababbaabbbbbbaabbabababbbababaaabbbbbbabaaabbaabababbbababaaaaabbbabbbbbaaaabaababbbaaabaaaabbababbabbbbabaababbbbaaababaabaaaaabaaaabbaabbaaaaabbaabaabbaaababaabbaabbaaaaababbaabbbbaaabbaaabbaaaaaabaaabbbabbbababaabbaaaabbbbabbabbbbaaaaaabaabaaaabaabbaaaabababaaaabaabababaaaabbbbbaabaaababbbbbbaababbababbaaaabbabaaabbbaabbaaaaaaaaababababbaaaababbbabaaabaabaabbbbbabaaabbbbbbaaaaabbbaabaaabbabbabbbbababaababaabbaabababbabbabbbabaaababaababbabbbabababaaaaaaaabaaaababaabaaababbabaaaabbbbaaababaabababaaaaaabaababbbaaaaaabaaaaaabaabaaabbbababaabaaaaaaabaaaaaabbabbbbaabbababbbabbbaaabbbabbaaaaababababaabababababbbbaababaababbaaaabbbaabababbaaaabaaabbbabbbaabaabaaababbbbabababaabbbabbaaaaababbaabaaaababababbaaababbbaabaaaaababbbbaabbabbbbaaaaabbbabaabbabbaababaaaabbbbaaabaaabaaababaaaabbaaabbbbbabaabbaaaaabababbbaabbabbaabbbabbbaabaabaabbbaababaaababbbabaaababbabbbbaabbbbabbbabbbabababaaabbbbbbbbbabbbbaabaaaaaaabbbbbaababababbbbbabbaaaabaabaababbaaaababbbabbbaababbaaaabbaaabbabaaaaababbbbbbbabaaaaaaabaabbbbaababbabbaaaaababbabaabbbaaaabbaaabbbbabbbbbbaaaaabaaaaabaabaabbbbbaabababbabaaaaaababaabaaababbbbbbbbbaaaabaabbbbbaaaababbabababaaabbaaabbabbaaaabaaaabbbbbbababbbaabaababbaabbaabbbbaaaabaabaabbbbaabaababaaabbabbababbbbabbbbbbabaabbbbaaaabbbbbbbaabaaababbbaaabbaaaaabbbbabaaabaaaababbbabbbaaaabababaabaabaaaaabaabaaaaaaabbbabaabbbabaaabbabbbabababaabbaaabababaaabbaaababababaaabababaabababaababbaabbbaaaaabbabbabbbababaabbabbbbbaababaabababbaababbbabaaaababbaaabaabaababbabbaabbbababaabbbabaababbbaabbbbaabaabaaaaaabbbabbbbaabbbbbaaabbbbabbbbaabaabaabbababbbabbaabaabbbabbbbbaaaabbaaaabbbaabbbbabbabbababababbabbaaababbaabbbababbaabbbaabbbaabbabaabbbabababaabbbbaabaaaaaababbaabaabbaaabaaaaaabbbabaaabbbaaaabaaababaaaaababbbbbbbbbbbbbabaabbbaaababababbababababbbbbabbbbbaaaaaaaaaaababbbbabaaaaabbbbbaabbabaaaaaaaabbababaaaabaaaaaabbbabaaabaaabaabbaabbbbabbababaaababaaaaabbabaabbbbaababbabbbbaaabbbbabbbabbbbbbababaabaabbabbbbbababbabaaaababaaaabbaabbbbabaabbaababaababaabaaaabaabaaababbaaabaabbabaabbaaabbbbabaabbaaabbaabaababaaabaaabbbababbaaabbbbaaaaaababbbaabbbbbbabbbaabbbbaaaaaabbabaabbbaabaaaabaababaaaabaabbbababbababbaabababbabaaaaababbbbaaaabaaaabbaaaababaaabaaaaabbbabbbbabaabaaaabbabaabbaabbababbabbabaababbbaabababaaaaabbbaaabaabbbbbaaaababbbabbabbaabbaabababbbbaaabbbbabaaabbbbabbbaabbbbaababbbbaabbbbabababababbaaaaabbabaaabaaabaaabbabababbbbbaabaaabbaaaaabbbabaabaaabbaabbbbbabbbbaabbbaababaaabbaabbaabbbbabbbbbbabaaaabbaaaaaaabbaaaabababababbabbbbbaabbabbbbabbabaaababababaaaaaaaaabbbbaabaaababaabaaaababbbbbabbbbabbaabaababbbabbbbaabbbbbbaabbaaabbbaaababbbbbbbaaabababbaabbbbbbbaabaaaabbaaabababaabbababbaababbabbbbababbaababbaaabababbabbbaaaaabbbbabbabbbaabbbbabbbbbbabaabbbaabaabbababaabbbbbbbbbaabbbaababbabbbabababaabbbaabbbaaaaaaaaaaaaababbbaaaaababbbababbbaaaabbabbbbababbbabbbbaabaabbbbaaaaabaabaabaabababbbabababbbababababbbbbaaaaabaaaibabbabbbbaaabbaaabbbaaaababbaabaabaaabaabbaabbaaaaaaababbaaababbaaaaababbbbaabbaabbabbbabbaaaaabaabababbabbaaabababaaababaabbaabababbabaaabbababababbbbbbabaaaaababaaabbaabaaabbbaabbabbaaabbabbabababaaaaaabbbabaaabbbbaaaabbbbbbaaabbbaaabbbbabbaaabababbababbbaabbbbabaabbbbaaaabbaabbbabbbbbbaaaabbabaaabababbbbbaabbabbbbabbaaaabaababbbabbbbabaabbbababaaabbabbbbabbababbaaaababbabbbabbbaaabbbaabbbbbaabbabbbbbaaaaababaaaaaabaaabaabbbaaababbbaabaaaaabbbabaaabbbbabbaabababbabbaababaababbaaabbbbbababaaabbbabaaabbaaaabaaabbbbaabbaaaabababbaaabaabaabbbabababbbabbabbabaabbabbbbaaaaaaaabbaabbbbabbbbbaabbaaabbabaabbbbaaabbbbbbbaabaabaaaabaabaabbaaabaabaaaabbbabbabaaabaababbbabbabaababbabaaababbaabababaabbababbabaaababbbbbbbbbbabbaabaabbbabaaaaabbaabaaaaaababbabababbbbaaababaababaababaaabbabaaaaabbbbbabbbbbabbaaababaaababbababaaaabbabaabaaaabaababbababaaabbaaabaaaaaabbbaabbaabaabaaaababaaaaaababbbabaaabbabbaababbbabaababbbabbababbbbbabbbbaaaaabbabbaabbbabbbaabababbaabababbbabbbabbbbbbaaababaababbbbaaaaaabbbbbabbaaabaaaaaabababaabbbbbbbabaaabbaaababbbbabbaaabbbbbbabaabababbaaababbbaabbababbbbabaabaaababaaabaabaababbabbbaaababbbaabaabbbbabbbabbbbaabbbbbabbbbbaabaaaabbabbbaaababaababbbbbbbaaabbbabbaabbaababbaaababbababbbabbbabaaabaaabbbbaaabbbaaaabbbbaaabbabaaaaabaabbabaababaaabbbaaaabaabbaaabaaabaaabbbaabaaabbaabbbabaaabbaabbbaabbbabaaaabababbbbbabaaaabbabaabbbabbbaababbaaababababbaaabbabbabbbabbbabbaaaabbbaaaaabbabaaaaaababbbbabbabaabbbaabbaaabbbbbbababbbaaabbbaaabaaaabbbabaabbabababbabbbabbaabbaaaababbaabababbabababbaababababaabbbbabababaababbaaaabbbababbbbbbbabbaaaaabbabbbabbbbabbabbaaaabaabbbabbbabaaababababbabbaaabbaaababababbbbbbbabaaabbabaaabbbbabaaabaaababababaabbbaaaabbaabbbbbabbabaaaabaaababaaaabaabbabbababbbababbbbbbaabbbbbbaababbbaabbaaaaabaaaabbabaabaaabbbaaabbbbaababbaaabbbabbaaaabbbaaaabaaaaabbbaaababaabbbaabaaababaabaabaababbbbababbaaabbbbabbbababbbbbbbaaabbabbaabbaabbbaabbbbaababaaababbbababbbaaabaabaaaabaaaaaaaabbbbbaaababaabbbbbaabaabaaababbbaaaabbbbbaababbbaaaabbaaaaabbabaaaabaabaabbbbababbbbbbbaabbbabaaabaababbaabbaaaaaabaabbbbababaabaaaababbaaabbbbbabaabbbaaabaaababaaabbbbbabaabbaaaaaaabaaabbbbaaabbbbabbbbbaabaabaaabbababbaababbaaabbaaabbababbabaaabbbabbbaabbbbbaababbbbbabbbbbaabbbbbaabbaaaabaaaaaabbbbaabbbbbababbbabaababbaaababbbabbbabbbbaaabbbbbabbababaabaabbbbabaaaabbaaabababaabbaaaaaabbbbbbaaabbaabbabaabbaaaaabababaaabbbaaabbabbaabbbababaaaababbaabaabaababbbaaabbaaaababbbababbaaabaaabbaaaaabaabbaababaaabbbabaabaaabaaabbbaabaaababbbbabbaabbaaababaabbbbbababbbbbbbbbbbaabaaaabbbbabaabbabbaabbbbbabbabaabaaaaaaaababbbaaaabbababaabbaaababbbabaababbbbaaabaabbbbababbbbbaabababbaaaabaaabbbbbbabbabbaaabbaabbababbaabababaaabaabaaabbbbbaababaaabbbaabbbbbbbbbabaabbaabbaabaaababaabbaaaaabbbaaaabbabbbbabbbbaabbabaabababbbabaaabaaaaabbbbabababaabaaabbbbabbbbbbabaabababbbbaaabaaabababbababababbabaabaaaabaaaaabbbaaaaaaabbaaaabbbaababaabbbbbaabbbbabaabbabaabbaaabbaabbbbaaabbbaabbbabaabaaabbaaaabbaaaabaabaabbbbaaaaababbbaaaaaabbaabaaababaaabaaaaaabbbbaabbbaababaabbaabbaaaabbbbaabbabbbbaaabbbbbbbaabaaabaaaaaabbaaabbbaaaaaabbaaaabbbaaaaababbbbbaaaabaababbbbaaabbbbbbaaaabbbbabbaabbabbababbaabbbaababaabbabaaabbaabbaabaababaaababbababbbbaabbabaabaaabbaaaaaaababbbaaaaaabaaaaaaaababbbbbbaabbabbbbaaaaaabbaaabbaabaababababbbaababaabbbbbbbaabbbaaaaabbabbabbbaabbaabbabbbbbaaabbbbaabaabaaaaaaaaabababbabbbbbabaabbbbaababbbaabbbababaabbbbbbaabbabaaabbbbbaaabbaaaabbaabbbbbbbbbbbbababaaabbaabbaabbbabaabbababaaaabbaabaaababaabbabaaabbaabbaabaababaabaabaaaaaabaaaaabbabbaabaababaaaabbbabbaabbbaaababaababaaaababaabaabbaabbbbabbabaaaaaabbaaabaaabbaaababaababaabbbabbabbabbbbbbabbabbababbababbaaaaaaaaababbbabbbbbbaaababbbbabbabbbabaabbbbabbaaababbbbbaaababaaabbbbbbabbabbbabaabbaaabbbbbaabbbbbbbaabbbbababababaaaabbaaabbbaaaababaabbbaabbbaabaabbabaabbabaaabbababbabbabbaaabaabbaababaabaabaabaabbababaabaaaababbabaabaaabbaaabbabbbabbabbabababbabaaababbababbaabbbaababbaaaabbabaabaabababaabbaaababbabbbabbbaabbababbbbbbbabbabaabbabbbaaabbababbbabbaaabbbabbbbabbabaaababbbbbaaabbaabababaabaaaababbbbbababbabbaabbbaabaaabbabbaaabaaabbbaabbabbaaaaabbabbbabbabbbaaaaabbaaaaaaababaabbbbbabaababbbabbaaabbbabbaaabbaabbbababbababaaaaaabbbbabbaabaabbbaabbaaaaababababaabaabaababbaaabaabaabbbbaaaaabbaaabaabaabbaaabbbbaabababbabbbabbaaabbabbaaaabababbbabbaabbbabbaaaaaabaaababbbbaaaaaaabababbbbabbbbbbababbababbabbbabbbbaaaabaaaaaaaaaabbbaaaabaaabaababbbbbbaaababbbbaababaababbbaaaabbaabaaabaabaababaabababbbaaabbaaabbbbababaaabbbabbababaaaabaaaaaabbbabbabbaababaabbbbbbabaabbababbbabaabaaaaaabbbbbabbbaababbabaaaabbabababbbbbbbabbbabbaaaababbbbaaaaababaaabbaaabaabbbaabbbbaaaababaabababbbbaabababaaabaaaababaabbbbbaaaabbbaaabbabaaabaaabbbabaabbaaaababbaaababbbbaaabaabaaabaaabbaabaabbbabbbaababbabbbbbaabaabbbaabababbbaabbbaabbabaaaaabbaaababbbaaaabbabababbbbabbbbababbababaaaabbbabbabbbaababbbaababbaaaaaabababbaaaaaabbabaaabaaababababaababaaabbabaaabbbaabbaaabababbaaaabaabaaabbbabbabaaaaabaaabbbbbabbbbaaaabbbabbaaabababbaaabbbabaaabbabaabbbaaabaaaaabaabbaababaaaabababbaaaaaaabaaababbbababbbbabbabbbbabababbaabbabaaaabbabaabbbbbaaabaaabbbabaaaaaaaabaaaaaabaababababbabbabbabbbbaabbbaaaabaababbaabbbaaabbbbbbabaabaabbbbabbbabbbaaaaabbabbaabbbaaaaaabbbabbabbbbabbbbbabbaaabaaaaaaaaaaaaababaabbaabbbbbaaabbbbbaaababbbbabbaabababaaababababaabbbabaaaaaaabbbababbaaababbababbbbababbbbaaaaabaababbaabbabbbbaabbababbaabaabbababbbabbbabababbbbababaaabbbbbaaabbaabaababaaaabababaaababbbbabaabbbababaabbbababababaaabbbbbbabbaabbbabbaaaabbababbbbbabaaaabaababaababbababbaabaabbabaaaababbbabbbbbbbaaabaaabbbaaaaabbbbbbbbbabaaaabababaaabababbbaabbbabaaaabbbbaaaabbbbbbabbbaabaaaababbbababababbbbabaaaabbbbaabbbbbbbbbbabbaababbbbaababababaaabbabbaaaaaabaabaabbbbbaabababaaabbabbaababaaaabbabaabbaaabbabaabbabbaabbaabaabababaabaaababaaabbaabaaababbababababaabbaaaaaabaabbaaabbbababaaaaaabbbaaaaaaaaabbbaababaaabbabbbbbbbbabbbbbaaabababababbbbbaababbbbaaabaabbaaaaaabaabababbbaaaabababbbbaaaaaaaaaaaaaaabbbbbbbaaabaaabbbbababbbbabbaabaaaabbbbbaaaabaaaaabbbaababbbaabbbbaaaabbbbbabbabababaabaaabbbbaaabaaabbbaabbaaababbbbaaabbababbaaaaaabbaaaaabbaaabaabaaaaabaabababbaaaabaabbbbbaaabbabbbbbaaaaaababbabbaaabbbabbaaaabbbaabbaaaaaabbbbabbaaaabbabbabbbbabbbbbbbaababbabaabbabbbbaabbbabaababaaaaaaaabbaaaabaaaaabbaabbbaabababbbaabbabbbababbbababbaaabbbbbaaaaabaaaabbabbabbbbaabbbabbbbbbbbaababbaabbbabababbbaaabababbababaabbabbbaabbbababaaaabbbaabbaabbbbbaababaababaaabaaababbaabaabababbabbababababbabbbbaaaabaababbbbbababababababaababbaaababbbaabaaabaaabbbbbbabbbabbbbababbabbbabbaaabababaababbbabbaababaaabbabbaabaabababaabbaabaaabbbbaaaaaaaabaaaaaaaababbbbaabaababababbbababaaaaabaaaabbbbabaaabbabaaaabbaaaabbabbaaabababaaabbbbbbbaaaabbaabbbaaababbbabbbbabbbabbbbaabbaababaaabaaabbbabbbaabaaaaabbbaaababbbbbbbaaaaabbbbbbabbabbbaababbbbaababaaaabbbabaabbbabaaabbabbaaabbbaabababbbbaaababaabaabbbaabbbbaabbaaababbabbbabbbabaabbababbaaabbbaababaabaaaabababbabaaaaaabbbabaaabaabbbababaabaabbbbababaaabbbababbbbabbaabaaaabbaababbbaabaabbbaaaaababbbabaabbabaaabaabaaabaaabababbaaaaababbbababbbbbaaababbbbbbbbababaaababbaabababaabaabaabbbbbbababababaaabaaabaaabbbabaaaabbabbabbabababbbbabbbaababbabbbaabbbbabaaababaabaabbbabaabaaaaabbaaabababbababbaabbbbbbabbbbbbababaabbbbaabbbbabbbbaabbabbaaaababbbbbaaaaaabaabbbabbaababababaaaaababbabbabbbaaaaabbbaabababbabbaababbabbaabbbbbbbbbababbbbabbaababbaaabbbabaabbbabbabaabaaabbbabaabbbbaaaabbbabaabbaabbabaaaaabaaaaaabbababbabbbaaabbbababbababbbbaaabbaabaabbaabbaaaaabbaabbbaabaabaaabbaaabbaaabbaababbabbbbabbbabbbaaabbbbabaabaaababbababaabbaaaabbaabababbbabaaaaabbbaabbbbbbbababaabbabaababbbaaaabaabbaabababbaabbbaaaabaaabbabbaaabbababbbaabbbababbbabbababaabbabababbaaabaaababbabbbbaaabaaaaabaabbaaabaabaaababbabaabbabbabbaabbbaabbaaabbbbbabbabbbbaababbbbbaababbbbaabababbbbbbbbabbaababbbbbaabbbaaabbaababbaaabababababababaabbbbbabbabbbbaaababbaaaaaaaabbabbbababbabbabbaabaabbaaaaabaababbbbababababbabbabababaaaabababbabbabbbaaaaabbabbbaabbbbbabbbaababababbabbbbaaabbaaababbabbbaaabaababbbaabbbbbaabaaabaaaabbaaabaaaaaaabbbbbaaaabbbabaaabbaaaaabababaababbaaabaabbabaabbbaabbabbbbbaabbbabbaaabbabbbbbbaaaaabbaabaaaaaabbbabbaaabbbaaaaaabababbbbbbbabaaabbbaabbbababbabbbaabababbababaabbbabababbabbabbbababaaabbabababbaaaabababbababaabbbaaaaaabbbaabaaababbbbbbabaabbbbbbbbabbabbabbbabbbbbbbababababbbbabaabbabaabaaabbbbbaababbbababaaabbbabbabbbbbbbbbabbbabbabaaaababbbabbbbabbbbabbbbbabbabbbbabaaabbaabbabaaabbabaabbbabababaaabaabbbbaaaaaaabbbbaaabbaaabbbabbaaaaaaabaabaabbbababbaaaaababaaaabaabaaaabbbaaaaaabbbbaabababaaaaaaabaaabbbabaaabaaaababbbabbbbabbaabbaabaaabaaaaaabbaaaabbbaaaaaaabbbbbabbbbababbbaaaabbbbabbaaaaabaaaaabababaababbabbaabbbbabbbbbbbbabbbabaaaabbbbaaabaaaabbaaaaabbaabaabaababbaaaababbaaaaaabbabbabaaaabbbabaaabbaabaaaaabbabaabababaaabbbababbaaababbbbaabbabbbbbabbbabaabbbaaaaabbabaabaabaaabaaaaaaaabaaabaabbbaabbabbaabababbaaabaaabaaabbbaabbaaaabaaaaabbabaaababababbbbbababbaaaabaabaaabaabbbaaabaabbbbaaaabbabbbbaabaaaabbaaaabababaabbaabbbaaaaaaabaabbbababaabbabbababbabaababaabbababbaaabbabbabbababbbaababbbbababbabaaaaabaaababaaababbabaaaabbabbabaabbbaaabbbbabbbbbbaabbabbaabbabababbbbbbabbabaababbabaababaaabbababaabbababaabaaaaaababbbbaaabbabaabbbbbaaaabbabbaaaabbbababbaabbbaababaabbbaaaaaabaabbaaabbbbbabbbababaabbababaababbbbbbaaaaaaaaabbbbabaaaabbbbbbbbbbababbbababbbbaabbbbbaabaaabbbaaababbbbabbbbbababbabaaababababbbbbaaabbbbbaaabaabababbbabbbabaabbabaababbbbabbbaabbbaabababaababbaababbbbababaabaaaaabbaabbbbabbababbbababaaaaaaaaabbbaababbaaabaaaabaaabaabbaaaaaaaabbbbbabbaababbaaaaaabbaababaaaaaaabaabbaabbabbbbbbbbbaabbabbbabaaabbbaabaaabaaaaaabbaaabbaaaabbbbbabbabaaabbbbabaabaabaababbbbbabaabbbbabbbabaaaaabaababaabbabbbabbbbaababbbababaabbabbbbaabbaaababbaaabbaababbaabaaabaaaabbbabbababaabababaaaaaaaaababaabaabaababbbabababbaabbababbbbbbbaabbbbabbbabaaaabbbaabbabababbaaabbababbbbbaaabbbaabbaaaabbbbbbbbaaabaaabbabbbbbbaaaaabaaababbaabbbababababbbbbbabbbbbaabaababbabbaaababbbababbbabbabbaabaababababaabaabbaaaababbaaabaababbaabababbaabaabbaaaabaaaabaaaaababaababbabbabbbabbbaaabbabbabbababbabbbbbabbababbbbabbaabbaabbbabbabbbbbbbaabaabababbbbbaaaabaabaaabbabbbbbabbbbaaaabbaabbabbabaababaaababbabaaaaaabbabbaabaabaaaabaababbabbbabaabbabbaaaabaaababbbaaababbabbbabababaaaabbaaabbbaabbabaaababaaaaabaabbbabbbababbbaaabbabbababaaaabaaaaabaabaabaaaabbbbababbaabbbbbabbbababbababbababbbbaaaababbaabbbbaaaabaaabaababbabbaaabbbbbaaaababbbbabaaaabaabaabaabbabbbaabbbbabbbbabbabaabababbbbbababaababbaaababaaaabaababbbbababbabaaababbbbabbabbaabababbbabaaababbaaaaaababbaabbaabbbaababbbabbaaaababbbabbbabbababaababbbbbabbabababbabbaaabbaaaabaaabbabbbaaababbbbbaabaaaaaabaaaaabaaabbabbbabbbbbbbbaaaabaabbababaaabbbaababaaabaabaabababbbabbbababbbbabaaaaabbbabaababbbabbaabbaabbaabbbbabbbabaabbbbaaabaabbbbbbbbabbbbbbbbbaababaababbbbabbbbababaaabaaabbbaabbbbaabaabbbabbbaaaaaabaabbbabaaaaaabbbbaaababbababbaaaabababababbbabaaaaaaaaaaabaabbbbabbbaaababababbaabbbaababaabbbbaabbaabbbbabbbababbabaababbaabbabababbbabbbaaaaaabbbbbaababaabaabaababbbabbbbbbaabbabbbbbabbabbaaabaabbaababababaaabbabbbabbaabbaaababaaabbabaabaaabbaaaaabbaabababbaaaaaaaaabbbbaabbbabbabababaaaabbabaabaabaaaababbbbaabaaabaababbbbabbbbbaaaabaabaabbaaababababbbbaaabbabaabaababbbbaabbabbaaaabbabbabaabababbbbbabbabbaabbabbaaabbbbaaabbabbbaabaabbaabaaaaaabbaaabbabababaabbbbaaaababaaaabbbbbbaabababbaaabbaabbaaabbbbabbabbabababaababbabababaabbabbabbaaabbbbaaababaabbbbbabaaaabaabababbaaabbabaaaaaaaaaabbbababaabbbbabaaabbabbabbababaaaabaabbabbabbabbbbbaaabbbabbabaabbbbbababbaababbabbbaabbbbaaaabbaabababaaaaabababbbaaaaabbabababbabaaaaabbaaababbbbbbbbbbbbabaaabbaaaaaababbabbbaabaabbbbaaaaaabababaaaababaaaaabbbbbaababababaaaaababbbbbaabbbbaabbbabbbbabbbbaaabbbabbabababbbabbaaaabbaaaabbbbaababbbbbaabbbaaaaabbbabbaaabababaabababbbbaabbbbaaababaaabbbabbaaabaabaaaabaabaabbababaabbbbaaababbababbabbbabaabaabbbbababbbbbaabababaaaaabbabbbbabbaaabaaaaaabbaaabbbabbbaaaabaaaabababababbbaabbbbbabbbbaabbbabbaaabaaaabbbaabbbbababaaababababbabbaaaabaababaabbbaabbababbbaabababaabababaabaaabbbaaaabaabaaaaababaaaaaabbaabaaaaabbababbaaaabbbbbbbaaaaaaaaaabaaaaaaaababbababaaaabaabaabaabaaababbabbabaabbbbaababbbbbbaaaabbbbbbbbaabaabaaaaabaababbbaabababbaaaaaaaaaaabababbaaaaabbbbabbaaabbbbaaabbaababbbbbabaaaaaaabababaaabaaabaaaabaabaabababaaababbaaabbbbbabaaaaabbbabbabaaabaabbaaabbbbbaabaaababbaabbabaabbbbbbabaaabaabbbbbbabbbaaabaababbaaaaabaaabaababbbaaabbaaabbaaabaababbbabbaabaabbabbbababaaabbabbabbbbbbbbbbaabaaaaaaababbabbaaababbaaabbaabaababaabaabaaabbaaaaabaaabaaabbbbaaabaaabaabbbbbabababbbaabbabaabbaabaaabbaabbbaaaabaabaabbabbaababbbbbbbbbbabbaaaababaabaaababababbbbbbbabaabbababbaababaaaabbbaaaaaabbbaababababaaaaaabbbaabbbaabaabbaabbbbbababbbaabbbbbbaaababbbbabbbaaaababababaaababaabbabbabbababbbaabaabbaabbbaaaabbaabaaabaaaaabbaababaababbaaabbbbaabbbabbaabbbbbaaaabbbbabaabbabbabababaaaabbbbaabaabbabbabbababbbbbaabaabaaabbbaabbaabaabaaaabaababaaabbbbababababbabbaaaabbaaabbabaabaababbbaaaaaaaabbababaaabaabaabbbaababaaabbaaaaabbbbbaabaaabbbbbbabbabbbabbbabbaaabaaabbabaaaabbababbbbbbaabbabababbbbbbaaababbabbbbaaabaabbabbbbbbbbaabbaaaabbaabaabaabbbbbbbbbabbaaabbbaabbaababbababbbbaaabaaaabbbbbaababababbaabbabbbbabbbbabbaaabaaabbabbbabbbbaabaaaaaabaaabaaaabbbaaababbbabbbababaaababaaaaabaabbaabbbbbbbabababaabaabaabaaabbbbababaaaabbbbaaabbaaaaaabbabbaababbaabbabbabbbbababbbabaaabbbbbaaaaabaababbabaaaabbbaaaaababbbbbbaaaaababbbabbbabaabaabbbbbbbbabababbaaaaaaabbababaaaabbababbbaabaabbbabbaaabbbabbbabababaabababaabbaabbabbbabbbbbaaaababababbbabbaabbbbbaaaaaaabbaabbaabbaabaaaaaabbababbbaabbbaabababbababbbbbbbbabbaaaabbbabaaaaaaabababbbababababbbabaaabababaaaabaabaababaabbabbbbaaabbaaaabbaabbbbbababaabbbabaaaaabaababbbbaaababbaabbbaabbbabbbaababbbaaabaaabbbbbbbaaaaabbbaabbaaaaaaaaaabbbaaabababbbbaaaaabbbbababbabbababbbaabbbababbbbbbbabbbbbaabaabbbbabbbababbbbbaabbaaaaabaaaabaaaabbabbabababaabbababbaabababbbaaababbaabbbbabbbabaabbbbaabbbabbbbbbabbbabbbbbabaabaababbbabaaaabbbaabbaababbaabaabbaabbabbababbaaaabaaaabaaabaaaabaaaabaabaaaabbabababbbbaaaababbbbaababbabbbabaabbabbbbaabaabbababaababaabaabbaaababbbbabaaababbbbbabaaaaababaabbbabaaaabbaaabbabbbbaababaaaababbbbaaabababbbaabbbaabbaaaabaaabaabbaaabbbabaaaabaabaaabbaaaababababbaabbbabaabaabbbaaabbbababbbabbabbabaaaabaaabababbabbbbabaababaaaaaabaaabaabaaababbababababbabaabbbabaabbbaabbbababbbabbbaabbabbabbabaaaabbaaabaabbbbbaaabbbabbababbaaabbbbbabaabaaababababbbabbaaabbbaaababbbaabaaabbbaaaaaabbabbbbbbbbaaababbaabbaababbaababbabbbbbababbbbaaabbaaababaabaaabbbabaabbabbaabaababbaabbaababaabbbaaaaabaabbabaaaababbbbbaaaaabbbbabababababaaababaaababaaaabbbbabbbaabbbababaabbbbabbbababaaabbabbbabaaabaabbabbbbabbabbbaabbabbbabaaabaaabaaaababbbabbbaaabbbaaaababbbabbabababbaabbbabbaabbaababbabaababaaaaabbbbbbababbaabbbbbabbababbbbbbaaabbbababaaaaabbbaaaaaababbbaabbaabbaaaaaaabaabbbaabaaaabbbabaabbaaabbaaaabbbbaaaabaaaaabbaabbaaaabbbabbababaaabbabbababbbbbbaabbbabbabaaaaaaaabaaaabbbbbbabaaaaaabbbaaaaaaabaaabababababbaabaabbaaabaabababbabbaaaaababbabaabbaaaabaababbaaababaaaaaaaaaaaaabababaaabaaabbbbbaabaababaaaabaabbbabbaabbaabbaaabaaaaaabbbbbaaabbaaabbbaaabbaaabababbabababababaaabbabbaababaabbaaabbbbaaabbaaaaaaabaabaaabaaaaaabbbbaaaabababaabbaaaabbbaaabaaabaaabaaaaabaababbababbabaaaaababbabaaabbbaaabaaabbbbaaabaabbbbbbbabaabaaabaabbbababbbabaaaabbaaabbbabaaabbabaaabbaaaaabaabaaaaaabababaabbbbabbbbaabbbbbbbbabbabbabbabababbaaaabaaaabbbbababaabbbaaaaabbabbaaababbbaaaababbaaabbbaaaaaabaabbabbbababaabaabaaabaabbbbaabaabababbabbbabbbabbaaabaabbbaabbaaababaaabbaaabaabaabaababbaabaaabbbbbbabbabbbaabbabaabababbabbaaaabbaabbbbbaaabbabaabbabaabaabaabbaaaababbabbbaaaabaabbabbbbabaaaabbababbbbbabaaaaaaabaaabbbabbbababbbbaabbbbbabaaabaabbabbbaaaabaaaabbaabbabbabbaabbbbbabbbabaaaabbaaaaaaababbaabbabbababbaabaaaaaaaabbababbabbaaabaabababbbaababbabbbbbbbabbbaaababaabaaaabbabababaaaaabbaababaabaababbaabaaabbbaababbabbbbaaabaababbabbaaaabbaababbbbbbaabaabbabbaaaababaabbbbbaabbaaaaaaababbbbabbbaaaababbbabaabbabbbbaaabaabbaabbaaababbbbaaaaabbabbbabbababbaababaaabaaaabbbabababaaabbabbaaabaabbababbababaaaaabaabaababbbaababaaaaaabbababbaaaaaaabbabaaabbaaabbaabbabbabbababbaaabbabbbbbbababbbababbabbababbababaabaababbbabbbabbaaaabbaababaabbaaababbabbaabbbabbbaabbbbabbbbaaaabaabaaaaababbbbbabaaaaaaaaaabbbababababbbabbaaabbbbbaababbabbbabaababaaaaabbabbaabaaaaabaaabbbabbbbaaababbabaabaaaabaaababaaaabaaaabbaaabaaababaabbaaaaaabbabbbaabaababbaaaaaabbaababbabaaabbabbaabaabababbbbbbaabbaaabbbbbabbbaababaabbbaabababbbaabbbbaaaabababaaaababaaaaababaababbaaabbbbaabbbaabbbbabababaaabaabbbaabaabaabaaaaabbaabbaabaaaaababbaaaaaabbbaaabbbaaababaaaaabaaaaabbbbbaabbabaabababbbbababbbbaaaaabbbabaaaabaabaaabbbbbbabaababaabbbbbbbbbaaaaaaabbbaaabbabbbbbaaabaabbababaababbaabbaababaaabaaabbbababbbaaabbbabbabaabaaaabbabaaaabaabbabbbaaaaabaabaaabaaaaabaabaabbabbabbaaaaabbbbbbabbababaaaabbaabbbbbbbbaabaabaaabbbababababaaabbaaaabaaaabababababaaabaabbbbabbaabbaabbbbaaaaaabaaaabaaaabbabaabababbbabaaabbabbababbaaaabaaaabaaaaaaabbaaaabbbaaaaaaaabaaabbaaabaaaabbbabbbabbabbbbbabbaaabbbbbaaabaabbbabaabababaabaabbbabaabaabbabbbabaabbbaabaaaabbaaaababaaabbabbbaabbbaaaaabbaabaaabaabbbbabaabbabbbabaabbbbbbbabbaabababbbbaabaabababbababbabaaababbabaaaabbbabbabbbbbbbabbaaabbbbaaaaaabbaabbbaabbbbbbaaaaabaaaabaabbbaabaababbabbaaabaaaaaaaaabbabbbabbaaaabaabbbabaababaaaaaaabbaababaaabbbbababbbbbbababbbbbaabbabbbbabbabababaaabbaaaabbaababaaabaaaaaaaabbabbbbbbbbaaaababababaaababbaabaaabbbbbbabaabbbaaabbbabaaabbbababababababbabaaabbbababababbbabbbbbaaaababaababbbaabaaaababababbbbbbbaaabbaaabbabaabaabaaabaabaabbbabbabbaabbabababbabbbbaaababaaaaabaabbbbbbbaaabaabbbababaabbbbababaaaaabababbabababbbbbabbbbaaabbbbbabbbbaababbabbbbabbaaaabbbbbaabbabaabbbabababbaaaababbbbaaaaaabbabbabaabaaaabababbbaabbabbbbaaaabaabbabababbbabaabbbbbbbbaabbaabbabaabaaaabbbabbaaaaabaaabbbaaaabbbbbababaaabbbabaaaabbababbaaabbbaaabaaababbabbbabbaaaabaabaaabaaababbbbabbbbabaaaaaaaabbbbbabbaaabbabbabaaabbaaaabababbaabbabaabbbbabaabaabaaaaabbaabbbbabbabaabaaaabbabbbbbbbaabbbaaaaabaaaaaabaabaabbbbbbbaabaabbbbabbaababbbabbbabbaababbbababbababbababbbabbbababaabaaaabbabbbabbbbaabbaaabaabaaabaabaaaabbabbbaabbaabbabbbaaabaaababbabbabaaaababbabaababababaabaaababababaaaaaabbbbbbabbbaabbbaaaaaabbaaabbabbabbabbbabaaabaaababbaabbbaababbaabbaaabbaaabaabaaababaaaabaaaababbbaabbbaabaaaaaabbbaabaabbaabaaabbabaaaabaabbbbbbbaabbaaaaaababbbbaaabbbbbbbaabbabbaabaaaabaabaaabbbbabbbbaabbabbabbaaaabaaaaaaabbaabbbbbbabaabbbbbbbabbabbbbbaaabbaaabbaabbabaaabbaabbbbaaabaabbabbababbabbabbabbbaabbbbbbbbbabaababbbbbbbbaabaaaababbbbabaabaaababbabaaabaabbaaaababbbaabbaaabaaaabaaaaaabaabababaabbbbbbaaabababbbbaabbbababbaaaaabbabbbaabaabaabbaaabaaaabbbaabaabbabaabaababbbaaaaaaaabaaaababbabbbbbabbabaabbbaabbaaaaabaaababaaaaaabbaaaaaababaaabbabbaabbaaababbbbaaaabaabbbaaaaabaaaaabbbbababbaabbabbabaaaaaabbaabbabaaaaababbbbaabababbbbbabbbbabaababaaaaaabaaaaaaabbaabbbbbbbababbaabaaaaaababaabbababaabbbabbabbbaaaabbbbbaabaaabaaabbabbbbbbaaaabbabbbbabbbbababaaaabaaabbbaaababaabbbbabaabababaaabbaaabaaababaaaaabaaabbbabababbabbbaaaaabbbaaababaabbaaaaaaabaababbaabbbaabbbbbbabbbabbaaabbbbbababbaaabbbbbabbaaabbabaababaababaabaaaabbabbabbaaaabbaaaaabbaaaaaabbbbbbbaaaabbbaaabbaaaaaabaaaababbbababbabbabbabaaaaabaababbbbbaaabbaaaaabababbaaaabbbababbbabbbababaaaaabbbabaabbbbbabbaabaaabaabaaababbbababaaaabbabaaaabbabbabbbabbbaabaaabbbaaaabbabbaaabbbabaaaabbababbbabbaaabbaaaaabbbbababbabbbbaaabbbbaaaaabbabaaaababbbbaabbbbababbbaaaaaabbaabaabababbbabbabbaaaaaaaabaababaabbbaaababbaaabaaaaababbaaaabaabbabbbaababbbabbaabbaaabbbbabbaabbbaaabbaaabababbaaaabbaababbbaaabbbbaaaabbabbaaabbaaabbbaaabbaabbbbbbaaababababaaaaaabaaabbabaabbababbbaabaabbbaababbabbababbabbabbabbaaaaaaababaaaabaabbaaabaaabababaaaaaaaabaabababbbbabbaaabbaaababbaaaababaabbbbbbbababbababaabaaaaabbabbabbaaabbaababababbbabbbbaabaababbbabbbaabaaabbabbababababbbbaaaaaaabbbbabaababaabbbabaaabbabbaabaabaaaaaababbaabbbabaaaabbabaabaaabbbbbbbaabbbabaabbbabaabbabbabbaabbabaaaaaabbbaaaabaabbbaaaababbaaaabaabbabaaaabbabaaabbbbaaaabbaaaaabaabbabbbbabbbbababbababaabbbbabaaaabbabbabbbbbbaabbbbbaabaabaabbbaabbabbbbbbbbbaaaaabababbbbbaaaaaabaaabbabbaabbbabbbbbababbabbbbbaabaabaaabbbaaabbbababaaabbaaaaaaaabaaabbbbbabbbaabaaabbaabababaaababbaaaaaababababbababbbbbbbbaabbbabaabaabaaabaabbbabbabbbbabbbbbabbabaaaaaaababababbababbabaaabbabbbabaaabbbbaaaaaaaaabaaabaabbaabbaaaaabbbbbaabbaabaabbbbbbbbaaabbbbabbbbababaabaaabbaaaabaaabbaaabbabababaaaababaabababaabaaabbbaaababaaabbbbaaabaaaaaaaababbbaabbaabaabbbbbaabbbbaaaababaabbabbababbaaabaaaabbbabaabbbbaababaababbbaabbbabbbbbaabaabaaabaabbbaaababbbaabbaaababaabababaaaabaabbbababaaababbbaabbbbaababaabbabaabbbababaaabbbbabaababbabbabbbbbaabaabababbbabbabbaaaababbbabbaababaaaababaabbbabbbbbabbabaabababbaaaabaababaabaabaaaaababbabbababaaabbbaabbaababaabaabaaabbbabaabbabbbbbaababaabaababbabbbababaaaaabbaaaabbbaabbbbbbbabbabbbabbababbbaaababbaabaaabaaaaaabbbaaabaabababababbaaabbabaaababbaabbbabaabbbbaabbbbabababbbabaaabbbbbbbbaabaabbaabaabbabbbbaaaaabaabaabaababbaabbaabaaaabbabbababbabbbbaaabaaababaaaabbabbabaaaaaaabbaabaababbbaaabaabaababbbbbbabbaabaabaaabaaaababaaabbaabbbbbbbbabaaabbbaaaaaabaababbbaabbbbaabaabbaababaabbbaaababbabaabbaabbbbaabbababbaabbababbaaabaabbbabaaaaaababbbbabbaaaabaaaaabbababaabaabbbaaaababbbbababbababbabbaaababbbbabaaabbbabaaaabaaaababaababaaababbaabbabaabbbababbabbbbaaaaabbbbbbabababababbaabbababbaababbbabaaababaaabbbbababbbbbbabaaabaababaabbabaaaabbaabababbababbabbaaaaabbbbbaaaabbbaaabaababbaabbbaaaabaaabbaaaaaabaaabaaababbbbabaaaaaaabaaabbbabbabbaababaaaaaabbbaabbbaaabbbbaabaabaaabbbababaababaabbabbabbabaaaaaabaabbbaaabbbabaaaabbabaabababbbaabaaabaabbbbabbbbaababaaaaabbbbbbbbbabbbbaaaaababaabaaaaabaabbbaaaabbbaabbbbbbaaababaabbbaaaaaabbaaababbbbababababbbabaababbbababaabaabaaabbbbbbaabaaaabbbbaaaabaabbbbabababaabbaaababbbbbababbaaabbbbababbabbbbaabababababbbabaababbabbaabbbaaabbabababbaababbbabbbbbbaaabbaaaabbbbbbbaabaabaaaaaaababaabbaaabbabababbaaaaaaababbbbaaabaaaaababaaaaaabbbaaababaaaaaaabbaaaabaaaaaaabaabbaaababaaaabbabaababaaabbbaabaabbbbbaababbabbaaaabbbabaabbabaabbbabaaabbbabbbbabaababbaaaabbbabbaaaaabbabbabbbaabaaaabababbbaabababbbbabababaaaaabbbbbbbbbaabbbabbabaabbbabbbabbbaaaaaaaababbbbbaabbaaaaabaaabbbaaabaabaaabaabbabaaabaaaababbabaaaaaabbbaabbabaaaabbbbabbbbaaaaababbbaaaabbbabaabbabbaaababbbbaabaabaaaabbaaaabbbbbbaaabbabbbababbbbabaaaaabaabaabbabbabbbaaabaabbababaabaabbbaaabaaaaabababbbbbabaabbaabbababaaaabbaabbabaaababababbbbaaaabbaaaababbaaaababbaabbbbabbbaabababbabbaaaaaabbbabbabaaababbabbaaaaabbabaabaaaabbabaaabbbaaaabaaabbaababbaabbbaaababbbbabbbbaaaabaaabbaaabbbbabbababbaababbabbabaabbabbbaaabbaabbabaabbabbbbabaabbabbbbbabbbabbbaaaaaabababbaaaaabaabbbababaabbbbbaaabaabbbabaababbaabaaabaababbbabbbaababaabababbbbbaababaabaaabababbaababaababbaabbbaaaaabaabbbbbabaaaabaabbbbbbaaabbbbbbaaaaabbbaaababababbbbaababbaaaaabbaabbababaaaaaababbaabaabbabaaaaaaaaabbaaaabbbaaabaabbbabbbabaaabbbaaaaaaabbaaabbbbbbbaaaabbaaabbaaabaabbabbbaaaaabaababaaababaaaababaababbbbbbaabaabbbbbaababbaabaaabbaaabaaaaaabbbbbabbbbabbbbaaaabababbabbbbaabababababaabbbaaabbaaabbbababbaababbbabaababbbbabababbaabbabbabaaabbbbbbbabaaabaabbbbbabbaabaabbababaabababbbbbabaaaaaabaabababbbaabababababbaabbbaaabaabaaaaaaabababbaabababaaababbbbbbbabababbabbaaabbbababbbaaababababbaaabaaaababaababbaaaaabbbaabbbbaaaababaabbbaabaaaaabbaabababbaabaaaaaaabbabaababbbbbaaabaabbababaaaaaabbbabbbababbabbabbaaabbbbabbaaaababbbaaaaabaaaaabaaaaabbbabaaaabaaabaabbbbaaaaabaabbbbbbbbaababbaaabababababbbabbbbbbbbabbbaaaabbbbbabbbabaabbbabbbbbbaabaabaaaabaaababaababbbaaabbbbbaabbabbbbbabbaaaabbbababbbbababbaabbbaaabaaaaaaaabbbabbaaaababaaaababbbaaaaaabbbbaabababbbbaaaababbbabbbabbbbbbbabbbbbbaaaaabaaabaababbbabbaabbaababaabaababbaabbbbabaabababbbabaaabaabbababaababaaaaababaabbbbbbbababababaaabbaabaaaabbbbbaabaaabaaabbaaabbbabbabbbabaabaaaaabbbbabbbabbabbaabbbaaaaaaabaaabababbbaabbbbaabbabbbbbababbbaabbabaabbaaaaaaaaabababbbabbabaabbbbabbbaaabbbaaabbaabababbabbbbbabbbabaababbabbbbbaabbababaabbbaaabababbabaaaaaaabbbaabaababbaabbbaaabbababaabbbababaabaaabbbbbabbbbbbaabbbaabbbbabaabbbbbaaaabbabaaaabbbaaaabaabaaababbaaabbaabbaaaabbbaabbbaabbbaabaaabbaaabbbbbbbaaabbbaaaabaabbbabbbbaaababbbbbaabbabaaaabbbaabbaabbbbababaaabbbaaaaabbbaaabaaabbbbababbbbbaabbaaababbbbbbabaabbbbabbaabaababaaaababbaabbbababbbbbabaaabababbbaaaabaaabbbabbbaaabbbaabbaaabaaaabbbbbbaaababaaabbbbaaabbabbbabbbbabbababbaaabaaabbbbabbbbaabbbbaaaaaaababaaababbaaabbaababbbaabbbbbbabbabaaaabbbbbabbabaabbabbaababbabaababbabbbbaabbaabbbabaabbbaabbaababbabbbaaaaaaabaabaaababbbbabbbaaabbbbbabbbbabbbaaaaaabbbaabbbbabbbaabaabababbabababbabbbabbaabbabbaabbabbbbbbaaabaaaaabbaaababababbaaaaabaaabaaaabbbaaaaabbbabababbaabaababbbbababbbbbbbbbbbababaaaabbbbbaaaababaaaabaabbabbbbabbaaaaabbabbabababaabaaaabbbabaabaabaabaaabbbbbbaababababbbabbbbbbbabaabbbaabababbaaababbabbaaabaaaaabbbaaaaabbaaabbaabbaabbaaaabbaaabaaaabbbbbbbababbabaabbaaaaabaabaababbbabbaaabbabbaaaabaabbabbbbaaaaabbbabbbbbababbbaaabaabaaabbababaabbbaabaabaabbaabbbaabbbaaaabbbaabbaaaaaabbbabaabbbabbaabbabaaabaaabaaabaabaabaabaabaaaabababbaabaabaaabbbbbbabbaababababbbabbabbbbbbabbabbabbbaababbbaabaaabbbaabbaaaabbaabbaaaababaaabababbabbbaaaaaabbbaabbbbabbbbbaaaabaabbaaabaaabaaabbbaabbbabbbbbaabbbbbaabbaaaaaabbabbbabaaabbbbbbbbabbabaabababbababbababbbbbbbabaaabababbaababbaaababbaabbaaababbaaaaaabaaaabbbaabbbaabbaaabaaabaaabaabbbbaabbbaaabbbabbbaaaaaaabaabaaaabaaaaababbbbbbbbabbbabbabbbabbaababaabaabaabbbbababbbbabbaaaaaaabbaaabaabbabbbbbaaabababaaabaaaabbbbbbbbabbbaaabbbbbbabaaabaabbbbaabbbbabbabbaaaaabbbabaabaaaaaaabbaabbabaaabbbababaabbabababbbababababbbaaaaaaabaaaaaabbbbbbbbabababaabbabbabbaabababbabbbbbaabaabbabbbbbaabbbaababbababbaaaabbaabbabaaaaaaaaaabaabbaaabbbabbaaabaabbbabbabbbabbbbaaabbabbababbababbbaabababaabbabbaabbbbbbaaabbaaaaaabbbabbabaaabbbaaaaababbaaabbbabaaabbabbbaabaaaaaaaaaaaaabaaaabaabbbabbbaabaababaaabaaaabaaabbabaababbbbbaabaaaaaababaababababbaaabaababaabbaaaaaabababbbababaaaabaaababbaababbbababaababbaabbbababbaaaaababbabaabaaabbabaaabbaaabaababababbabbbbababbbbabbbabaaaaaaaaababaababbaabbaabababbbbbababbbbaaabaababaababbbbbabaababbbbbbbabbabbabbbbbaaaaababbaaabababbaaabbabbbaaabbaabbbbbbbaabbaaababbabbbbbbbababbaabbaaabbbbbbbbbaabaababbbbbbaaaabbbabaabbaabbbbbbaaabbbbaabababbbbbaabbbbbbabbaaabbbbbabbabbbaaababbaaababbaaaaababbbbbbabbabbaababbababbbbbaabababababbaaaabbbbaaaaaaabbbabbaabaaaaabbbabbbabaaababaaabbbaaaaaaabaabaaaababaaaabaaaaaabbbaaaaaaabbbabbbbbaabbaabaaababbaabbbaabaaabaabbaaaaabaaaaaaabaabaaabaabbbaaaabbbbaaaabbaabaaaabaaabababbbababbaaabaaaaabbaaaabbabbbaabaabbbbbbbaaaabbbbabaaabbbbbabbbbabaaababaaababababaabbbbbaaabbbabbabbbbbbbababbababbbbbbbbbabaabbbbbababbbabbaabbbaabbbababbaabbbabaabbaabaaabbbbaaabaaababbaaaaababbbabaaaabaabaaaaabbaaabbbaaaababbbabbbbabaababbbbbababbbabbaaaaaaabbbabbabbaaabbbaabbaaabaabbbbbaaabbbaabbababbaabaababbaaaaaababbaaabaaaabbaaaaabbabbabaaaaababbbabbbbaabaabbbbabbaabbbbabbbbbbaabbaaaabaaababbaabbbbbbaabaabbbababaababbaabbaaaaaabbabbbababaabbbaabbaababbabbbabbbbbaaaaababaabbbbbaabaaabaababbbbbabaababaaabbbaabbbbabbaaabbbabaaaaaabbabbbaababbabbaabbaabbaaabaaabaaaaabbabaababbbaaaaaaabbababaabbaaaaabababbbbabbbaabaaabbabbbabbababababbaabaaaababaabaabbababababaabaabaaabaabaabaaabbabbaabbbabaabaaabbabbbbabbababbaabbbbaabbababbbbabbabbbaaabaaaaaaabababbbabbaaaabbaabbbabaaaaabbabaabaabaabaaaaabbaababbaaaaabaabbbabaabbababaaaabbbabaabbabbbbababbbaaabaabaaaabaababaaaabbaaaabbbbababbbaabbbaababbbaababbaabbaaababaaabbaabbabbbbaababbabaabbbaaababbbbaabaabaaabbbbbbbaabaaabbbbbabbaabbabbbbbbbbbbbbaabaabaabaabbbbbbababbabbabbaaabbabaaabababaabbaaabaabbbbbaabaaababbabababbabaaabbbabbbaabaaaababababbababababbbbabbbaaaababbaabaabbbbbabaaaabaabaaabbbaabbbaabbabbbbabbaabababbabbbaaabbaaabaaaabbabbbbbbaabbbbaaababbabbbabababababaaaabbbabbababbbabaaaaaaaabaabaababaaaabaaabbbbbbbabbababaaababbbaabbbabbabababbbbabbaabbbbababbbbbaaabaabbabbabbaaaababbbbabbabbabbbabbaababbbaabbbbaaabbabbababbbabababbbaababbababbbbaaabbbaababaabaaabbbabababbbbaaabbbaaabababbbbbbababbbabbbababaabbababaaaaababbabbbaaaabababbabbbbbaababbaaabbbbbaababaabbbbabbbaababbbababaabaababababbabaaabababbaaaabaaaabbbabaabbaaabbabbbabaabbbbabbbbbbabbbbbbbbbbbbbabababbbbbbaabbaabbabbabbaaabbbabbaabbbaabbbbbabbaaabbaabbbbaababaababababbbbbababbbbaaaabbbabaababaabbaabbbaabaaaaaaaabbbabbbaaabbbbabbabbbabaabaabababaaaabaaaabbbaabbabbbbbbaaabbbababaaabaabaabbbaabbaababbabaaaabaaababbbbbaaaababbbbbbbbbaabbaaabaabbaaaabbbbbabbaaabaabaabbaaaabbaaaaaaaababaabbabbbaabbabbbabbbbababbaaabaaabbabaaaabbabababababbbbbababbabbaaabbbbbbbaabbbabbaaaabbbbbbbbbbbbbaabbabbbaabaabbbbbababbbaaabaaaaaababbabaaaaabbaabbbaabbbaabaaabaaabbaaaaaabaaaabbbabababbbbabbbbbaababbbaaabbbaabbbbabaaaabbbabbababbbaaaaaaaabaaaabbaabbbaaaaabaababbabbbbbbabbbbaaaaabbbbaabbbabaabbabbaabaaababbaaabbabbaabbabaabaabababbabbbbbbbbbbbbbbaabbaabbaaaabbbaaaababbaaababaaaaabbaabababaaabbbabbbbaaababbaababbbbbbbaababaabbabbbaaaabababbababbbbaaababbaababbbbbaaaababbbaaaabbbaaababbbaabbaaaaababbaaabaabbbaababbabbbaabbbaabbbbaabaabbabbabaababaaabbabaaababababaaababaabbaabbbabbaaabaababbabbbabbabaabbaaabaabbaaaaaabaabbaababaaaaaababbbbaaaaabbbbbabbbbbbabbabbabbabbbaaaababbbaaaababbaababaababbabaabbbabbaabaababbaaababbbbbababbbaaabbaabaaabbbbbabbbbbaaaaababaabbabaaaabbbaabababbaaaabababbabbbabbbabaaabaaababababbabaaaabbbabbaabbabaababaaabaabababbbbbbbaabbbaaaaabbaaaaabbbbbabbabbabbaabbbababbabaababbabaabaaaabbabaaabbbbbabbbabbbbabbaaabababaaabbbabbbabbbbabaaabbabbbababbbabbbbaaaababbababaababbaabbbbaaaaaaabbabbabababbaababaababbabbabbaaabbabbaabaaabbaabbaabbbababaaabbbbbbbbbaaaaaabbbaabbbbbabbbabbbababaaabbabbabaaabaaababbaabababbbbbbaabaabaaababbbbbbbababaaabaabbbabbbbbbbababbbbaabaaabbababaaababaaabaaaabaaabaabababbaaaaaabbbbbbabaabaabaaaabaaabaaaabababaabbabbbbbbbababbbaaaabbaaabbaaabbaaabaabaabbbbaababbbbbbbbbaaababbbbabaaaabbbbbaaabaaaaaabaaabaabaaaaaabbabaabbbababbabbbaaabbbbbaabbababbabaabaabababababbaaaabbaaabbbbaabbbabbababbbbbaaaabbaababaabaaaabbbaabbaabbabaabaaaaaaabbaabbbaababbaabaabbabbbaababbbaaaaaaaaaaaababbbbbbbababaaaabaabbabababbaabbabbaabbabbbbabbbabbbbbbbbabbbaaabbbabbbbbababaababbbabbabaababbabbbabbbbaaaababaababbaabbbaaabaaabaaaaaaabaaabbbabbbabbbbbbabababaaabbaaabbaaabbaaaaaabbbabbaabbbaababaaaabbababaabbbabbbaaababbabbbaaaababaabbabbbbaaabbababbbaaaababbbbaaabaaaabbabbabaababbbbbaaaabbbabaabaabbbbbaaaabbabbababbaabbaabbbababbaabbabbaabaabaababbbbabbbaabbaabababababbababababbaaabbbaabbbabbbabbabaaabaabbbaabbbabbbabbabbaabbbbabaaababaaabaabbbaaababbaaaaaaaabaabbababbabaaabbabbaabaaabbbaabbaabaabaaabbababaaaaabbaabaaaaaabbabaaabaaaaabaabaaababaabaaaaaaabbabaaabbbbbbabbbaaabbaaabbbbbaaaaabbabbbaaababbbabaababbbaabbbababbbabaaaabbababaaaababbbbabbbbabbabaababaababbbbaabbabbbbaaababaababaaaabbbaabaabbaabbababbabbbbbbaaabbbbbaaabbbbbaaabbaabbabbabbaaaabbabaababaabbbbaaaabbbbabbbaaabbbbbaaabbbbabbbaaabbabaababbabbbabababbbbbabbabbaaababaabbababbbaaabbabbaaaaaababbabaababaaabaaaaababbababbabbabaabbbbbaaabbabbaababaabaabaababbababbbabababbabbaabbbabaababbabaabbbabbbaabababaabababbbbbbabbaabaaababbbaabbbbaaaaaababbababbaabaaaaaabababbababbbbbbabaaabaaabababaabbabaaaaaaabaaababaababbabbaaabaaabbbabbabbbbbabaabbbbabbbaaabaaaaabababbabaabbbbbbabababbbbbbbbbbaababbbbaaabaaaabaabbaaabaababbabbabaaabbbabaaaaabbababbbaabbbbabaabbabababbbbaaaabaabbaabbbbbababbaabbbaaaabbaaaabbbbababaababbbbaabaaaababababbababbbaaabbaaabbbbabbaaababbababaabbababbaaabbbabbabaababbaaabaaaabbaaabaabaabbbbbaababaabbabaaaababbbbabbabbabaabbabaabbbbbaaaaabbbaabbaaaaabababbabbaabbbbbbabbbbabbabbbbaaaaaabaaaabbbbbabaaabababaaaabaaabbababbbbbbbaabbaabbbaabbababbbaaaabbbbbababbbabbbbbbbabaaaaabaabababaababaabbbbbbbabbbbabbaaaabbababaababbaabbbbbaaabbababbbababaabbbbbbaaabaabbbaaabababbabaaaabaaaababbabaaaaaabbbbbbaabaabaabbbbaaabaababaababbbabababbbbaaaaaaaabaabbaaaaaaaaaaaaabaabbaababbbabbaabbabbabaaaaabababaaabbaabbaaaabaaabababbbaabaabbbabbbaaaaaabbaaabababbbaababbbbbabbbababaaaaabbabaabbababaaaaababbabbabbabbabbbbbbabbbaabbababaabababaaaaabbaaababaaabbbbbbabbbabbbbbabbbbaabbbbbabbababbababaabbbbbbbbabbabaabbbaaabbbbababaabaaaabbbbaabbaaababaababbabaaaaaaabaabbaaabbabbabbbabbbbbabbbaabbbabaaaabbaabbabbaaaaabaabaaaaaabababaababbabbabaabababbabbaaabbabaaabbababbbaaaabaabababbabbabbabaaabbaabaabaabbbaabbaaabbaaabbaaabaabbbabaabaabbbbbaaaabbbabbabababbabbaaabaaaaabbbbabbaababbbababaabaaaaabaaabbbbbaabbaaabbaabababaababaabaaaababbbbbabbababbabbaaaaaaabaaaabbaaaaabbbbbbabaabbaabbbbbabbbaaabbaaabbbaabaabbabaaabbbabbabbbbabaabbbbabaaabbababaabaabbaabaaaababbbababaaaaabbbaababbbaabbababbababbbaabaabaabbabbaabbbabbabbbababaaaabbbaabbaabaabbbbbaaabaaabbaaabbbbbbaaababaabbabaababbbbbabaabbbababaabbaaaababbababbaabbababbabaaabbbabbaababbbaaaaababbaaabbbbaaabbabbababbbabbabbabbaababaaabaaababaaababbbbbbbabbbaaaabaabbbabbbabbbbbabababaababbabaabbaaaaabbbbabbabbabaabbabbbbaabbabbbbaaaaaaaaabaabaababbaaabbaabbbbbabaabaaabbababaaaaaabbaabbbbbaabbaabbaababaabbbaaaabaaabbbaababbbbbbaaabbbabbbbbbabaababbaaabbbaaabbaaaaaaaaabbaaaababaabaaaaabbaabaaabbbaabbabbbababbbababbabaaaabbaabaaabbabbbbbbabbbbbabbbbbbababbaabaaabaabbaaababbababaababaaababababaabbbbaaababaabbbbabbaaaaababbababbabbbababbabababaabaaababaaaabaabbababbbaaaabbbbaabbbaaabababbbaaaababbbbbbbbaaabbaaaabbbaaababaabbbaaababbaaabaaaababaabbbababbbaabbbababbaabaabbbbbaabaaabaaabaabbaaabbaaaabababbaaaaabbbaabbababbbbbaaabaabababbbaabbabbababbabbbaabaabbbabbabaabbaabbbbbbaaaaabbbbabbabbbbabaabbaabbbbbabbbbabbbabbaaaaaaaaaaaaabbbabbabaaabbbaabbaababaabbaabbbaabbbaaabbbaababbabaaabbbabaabaaabaabababbbaaabababbbbbabbababbbabbbabaaababababaabababababbaaababbbbbabbabbbaabaaaaaaabbbbbbbabbbabababaaaaababbbbaaabbbaabaabbaabbaabbaaaabaababaaaabbbbbbababbbaaaaababbabbbbababbaabbbbbbaababbbbbabbaaababababbaaaabbabaaaababbbabaaabaaababaaabbbbababaaaaaabbaabbbaaaaaabaabbbbabbababbabababaabbbbaaaabbbbabaaaabbababaaabbbbbbaaabbabbbabbaabaababbbbaabbababbbabaaabbababaaabaaababbabbaaabaabaaabaaabbaabaaabbbbbbaaababbbaababaaaabaababbbbbbbbabbbaababaabaaaabbbbababbaababaaabbbbaaaaabaaaaaaaaabbababbbabbbababaaaabbbbbbbbbbaaababbabaabbabbbabbbaaabbbabbbbbabaaaaabaaaabbbabbbaabbbaaaaabaaabbabaababbabaababaabaaabababbbbbbbabbababaababaaabaabbbaaaaaaabbabbaababaabababaabbbaabbbabaabaaababbbbbbbaaabaaaabababbaabbabbbaabbbbaabaaaaababaaabbbabbbaaabbbbabbabaabababaaabaaaaaabbbaaabbbbbaaabaababaaabababaaaababbaabaabbbbbbaaaaabbaaababaaabbbaaaaaaabaababbbbabaaabbaaabbaaaababaabbabbbbbabbabaababbaabaabbbbbbaaababaaaaabaaababbaaabbbabbabbbbababaabaaabbaabbbbababbabaabbaaaaabbabbbababbbbbbbaababaaabbbababbabaabbabbaaaabaabbbbbbaaaabaaaabbaabaaaaaabbbbbbbabaaaababaaaabbbbabaabaaaaabbbbabaabbabbababbbaababbaababbaaaabaabbbbbabbbaaaaaabbaabbabbababaabaabaabbabaabbbabbbbaaabaaabbbaaabaaaaabbbaaabaabbababaaabbbaaaaaaabbababaaaaaaabaaaabbbabbbbaababababbaabbbbbaaaaabbabbabbaaabaaababaabbbbabbbaababaabbbbaaaaaabbabaabaabbbaaabbbabbabbabbaabbaabaabbaabbbbabbaabaabaabbabbaaaabbaababbbbabbabbaababbbaaaabaaabbbabbababbaaaabaabababaababbbbbababbaabbabbbbbbbaaaaaaaaabbbbababbbbbbababbbbabaaabaabaaabaababababbabbaabbbabaaabbabbbababbbaaabbbababbabbabbbabaaabbbbbbbabbaabbabaabbbbaaabaabbbaaaaaabbbaabbbbbbaabaabbababbbaaabaabbbaaabbaabbbababbbbaaabbaaabbabaaabaabbabbaaabaababbababbabbbbbaaaaaaabbbaababbaaaababbaaabababbbabbbbbbbabaaabbbbaababaaaaabbabababbaaaaabbbaabbbbaaabbbaabbbbbabababaabaaaababbbaabbaabbbabbbaabbabbbaaaabaabaabbaaaabbaababbaaabbbbabbbbbbbaabbbbbaabababbabaabaaaaaabaabbaaaaababbaaaaabbaababbaabbabbbbaaabbbbabababbbbaaabbbbbbaaaabbaababaababbbababaababbababbaabaaaaabbbabbaabbababaabaaabbabbbbbaaabababbaaabaaaaabbaabbababbabbaaabbabbbaaabbbbbaaaabbbabbaabaaaaaaaabbbbaaabaabbbbbbbbbababbabbababbbbaabbaaabaaaaabaaaaaaaaabbbabbbbaaaabbabbbbaaaaabbbabbaaaaabbabbaabbbbbbaaaabbbabbaababbababbbaaaaababbbbabaaaabbaabbababbbbbaabbaababbabbababaaabbabaabbbabaaaabbabbbabbbaaabaababbabbbabbbaaaaabbababbaabaabababbbbbaaababbbbbbaaabbaaabababbbbbaaababbabbabababbbbbbaabbbabaaaabbaabbbbbbaabaabbbbbbbbbbbababbbbaaaabbbbaaaabaabababbaabbaaabbbaabbaabbbbababaabaababaaabaaabaaabaaaabbaaabbbbbabbabbbbbaaababaaaaaabbabbbaababaaaabbabbaaaaabaaababbabbabbbbabbaaabbabbbbababababbabbabbabbaababbbbbbbabaabbbaaabbbbbbbabbaaabbababbbbbbbaabbaabbaabababaabbbbbbabaabbaaabbbaaaaababbaababbaaaaabaabbaaaaaaaaaabaaabbabaaababaabbaabbaaabbbbbbabbabbbbaaaabbabbabaaabbbbbbbabaabaabaabbabbbabbbbbbabbbbbbabbbaaaabaabaaaaababaababbabbbaabbbbabbaababbbababbababbbabbaaabaabbababaabbaabbaaababbaabbabbbbbaaaaabbaabaaabbaabbabaaababaaabaaaaaabbbbaaabbbbabababbbbaaabbbbbabababaabbbaaaabaabbbaabaaaaaaaabbababbaabababbaaaabbababbbbaabababbbbabbbabababbababbbabbabbbaaababbbabbbbbaaaaabbaabaabaaabbabbaaaaabbbaaabbaaabbabbbababbbaabaaabaabbabaababbbaaaaaababbbabbbbbbbabbbabbbaaaaaaabbbbabababbbbabaaaaabaababbbbabaaabaabbabbabbbaabbbabaaabbaaaababaabbababaabababababbaabbbaaabbbaabbbababaaaaaabbaaabbbababaaaaaaaabbbababbababaaaaabaaaabbbbaaaaaababbaababababaabbabaabbababaabababbaabbaabababbbaaabbababaaabbaabaabaaaababbabaabbbbaaabbababbabbbabbabbaaababaaaabbbbabbbaabbbabaaababbaaaabbbbabbbabaaabbbabaabaaabaaaabbaaabbaabaaabbaaaabaababbbabababaabbaaaababbaababbaaaababbbabaaabbabbababbbaababbbbbbaabbabbabbbbbabbaabaaabababbaabbbbaabbaabaaaaaabaaaababababaabbbbabaaabaabababbbbbbababaaabbababbabaabaaabbbabbbabaabbabaaabaaabbbabbaaabbbaaaaaababbbbbbabbbbaabaaaabaaaabaabbabaaaabaaabbabaaaaaaabaaaababaabaaaabbabbaaabbbbbbbabbbbbbaabbbaaabbabbabaaaabababbaaabaabbabbbbabbbbbabbbbaaaabababaaabaabbaaaaabababbaaababbabbaabaaabbbbabaaaaaabaabbabbabaabaaabbbbbabbabbababbbabababbababaaaaabbbabaaaabaabaaabaaabbbbababbabbbabbbbabaababbbaaababaaabaaaabaaaabbabbabbbbbbbbabababbabbabbabbbbbaaaabbbaaabbbabbabbababbabbaabaabbbbababbbaabaaabababaaabbabaabbbbaaaabbabbaaababaaabbabaaabaaababababbaaabaaabbbabbbbaaabbababbabbbaaabbbbbaaabbaabbbababaabbbaaaabbbbabbaaababaaaaababaababbaaaabababbaaaaababbbbbbaaaaaaabbbbbabbbaaabaababbaaaaaababaabbbaababbbbaabbbaaabbbaaabaaaaabaaaabbabaabaabbbaababaabbbbaaaababbaaaabbbaabbbaababbaabbbbaababbabaababbabaaababbabbababbaabaaaababababbaaaaaabbabaababababbbbabaaaabbbabbbabbbabbbabaaabbabaabbabaabababbaaabaaaaabbababbabbbbbbaaabbaabbaabbbaabbbbaabaaaabbbabbbaabaabbaabaaabaabbbbbabaaaaabbbaaabbabaaabbabbaaaaaabbbbbabbbbbbaababbabaabaaabaaabbaabaababbabbbbbabaaabababbaabbaaaabaaabababbababaabaabbbbaabbabbbbaabbaaabbbbbaababaaabaabbabaabbbbbabaababaaaabbababbaababaabbbbbaabbabbaaaabbabbaaaabbbaaabbbabbbaaabaaaaabbbbabbbbbbabbbaaaaabbbaaaaababbbbbaababbabbababbbbaabbabbaaabbbaaaaaabbabbaabbbababbaabbbaabaabbbbaaaabbabbababbbaaababbbabaabababbbabaabaabaababaabaabababaababaabbbabbabbbbaaabababbabaaaabaaaabbbababaabbbabbbbaaabaabbbababbbaaababbabaabbbabababaaabaaaaaabbabbbbbbaabaaaaabbabbbbaaabbaabaabbbabbaabdbaaaaabbbabbbbbabbaabbababbbaaaaaabbaaabababbabbbbabaabbbaabbababbaabbabbbbbbaababaaabbabbabbaabbbaaabbbaabbbabaabbabababbaaaabaaababbbabbababbababaabbbaaaabbbabaabbbbabbbbaaababaaabbaaaababbbbbababababbabaaaaaaababbbbbbabbbabaabbaaababbbbbabbbabaabaabbbaababbbabaababbbbabbaaababbbaabbabbabbabbbaaaaabbababbaabbbbbbaaabbbbabaabaaaabbbabababbbabbaabbbaababaaaabbbababbbabaabaababbbaabbabbabbabaaabbbababbaabaabbbbbaaaabababbbbabbbbbaaabbaabbabaaabbaaaabbbbbbaababbaaaabababaabbabbbbbbabbbaabbbbbbabaabbaabbbabbabaabbaabbaaabbaababbabbbbabbaabbbbbbbbaabaaaaababaaaabbbbabababbbaaaababbbabbaababbbaaaabbaaaaaaabbbababbababbabaabaaabbbbbabbbbbaabbbbbabbbbbbbbbbaaaaabbaabbabaabbaaabbababbbbabbbaaabbbbbaabaaababaaabbabbbaabaaaabaabbaabbabbbabbbbaaaaabbbaabababbaaabbbabbababababaaaaabbbbbabbabbbbbabaabbbaabaaaabbbbbabbbaaabbabaaabaabababaaaabbbaabaaabbaababbaaababbaabababaababbbbaabbbababbabbbbabbaababaaaaaabbaabaabaabaaaaaabaababaababaaabbabbbbabaaabbbbbaaaabbaababaabbaaaabbbabbaaababaaaabbabbbbbbbbaabbbbabbbbaabaaabbabbbbbbaabbabbbabbbbabbbaaabbbaabaaaaabaaabbabbbaaababbbabbaaaaaaabbaaabaabaaabbabbbbbbbbaaaaabaababbbabbaabaaaababbbbababaabaababbaababbabbbaabaaabbbaabaaaaabbabbabbabaababababaaaaabaabaabaabbbaaabaabaabbbaabbbbbaabbbaaaabbbbaaabababbabaaabbbabaabbaaabbbaababbbbabbaaabbbbaaabaababbaabaaabbbaaaaabbbababbaaabbaabbabbbbbababbabbaaaababbabaabbbaababbbababbaaabbaabaaabbaabbbaabbaaabbabbbbababaaaababbabbabbaaaabbabaaabbaabaabbababbabaabbbaaaaaaababaaaabbaaaaabbaaabaabaabaabbaabaaabbaaaabbbbbaaaaaabaaaaaaaababbaaabbbabababbbabaaabbabbaabababbabbabbbaaababbabbaababaaabbaabaaabaabbbbaabaababaaabbbabbbaabbabbbbbabaaabaabaaabababaaababbbaabaaababbabbbaaaaabbabbaabbaaaaaaaaabaabbaababbbabbbbbaabbbabbaaabbbabbaabaabaaabbbbbaaabaababababaaaaaaabbabbbbbbaaabbbbbaaabaabbaaaaaaaaaababbbbbbaaabbabaabbababbaaaaabaabbabbabbbbaaaaaaaabbaababbaaaababbbaabbbabaabaaaabaabbbaaabbaaaaabbbbbaababbbbbaababbbbbabbbbaaaababbbabaaaabaaaaaabbaaaabbaababaaabaabaabbaaaaaaaaabaabaaabbabbababbbaabbbbaabbaababbaaabbbbaaabbbabbababbbaaabbbaaabbaabbbabaaaabbbbaababbabbabbaaaaaababaabbaabbbaaaaabaabaaabbbaababbbbaaaababbbbaabaababaabbbbabaaabbaaaaaababbbaabababbbbaaabbbbabbaaabbabbababbaabaabbbabaaababbaabababbbaaabbbaaaaabbbabaaabaabababbabbaababbabbbabbaaaabbbbbaabaabaabaaabaabbbbaaaabaaababbbbabbabaabbbbbbabbababababbbabbbbabbbbabaababbaabbbbbbbabbaaababaabbaabbbbbbaabbababaaaabbbabbbabbbabbabbababaaabaaaaaabbaabababaaaabababbabaabbbbbabbaabbbbababababbabbabbbbbaaabaabbbaabaaaaaabaabaabbbaaaaaaababaaabbbbaaabbaaaaaabaaabbaabaabbaabaabaaaababaabbabbaabaabbababbaabbbbaabababababaabaabbbbabbbbbbbaababbbaaaaabaaaaaaaabbbabbbaababbbaaabbbbabbaabbaaaaaaaabaaaabbbbbaabbbabaabaaabaabaaaaaaabbbbbabbabbbaaabaabbbabbabaaabaabbbabbbabbbaaabbaabaaabbbbababababbbbbaaabaabaaaaaabbbababbbbaaabababaabaaaaaaababbbabaababbaaababbbbaabbabaaabbbbbabaaabaaaaaaabbbabaabbbabababbbabaabaabaaaabbbbaabaabbabbbbabababbabaaaababbabbbaaabbaaabbabbaababaaaaaabbbbbaababaaabaababbaaaaaabbabbbaabbbbabbbabaabababaabbbbaabbaabababbbbaaaaaabbaabbbbbabbabbaaabaaabaaabaababbbbaaabbbaabbbababbaabbbbbbaaabaaabbbaabbabbbabaabaabbababbbabbbaababbaabaaabaaababbbbbabaabaaabbbababbbabaababaaabbbabababbababbbbaaabbababbbaabbbabbbbbbabbbabbbabaaabaabbbababababaaabbbaaabaaaabaabaaababbaaabbabbbbaaabbaabbbaaaababbaaaaabbabbbbaabbbbaabbbbbbbbbabbaabbbababaaaaababababaabbaaabababbaaaaabaabbaaaababaabbaababababbaabbbbaabababaabaabbaaababbbbabaaabbbbabbbabaabbaaaaabababbabbaaaaabbaaabbabaabbaaabbabaaaabbbbbaabaaaaaaabaabbbaaabababbbaaabbbbabbaaabbaaabbaabbbababbbaaabaaaaababbbbbbbabbbaaaaabababaaabbaabbaaaaaabbabbbaaaaababbababababbababbbbbaaababababbbaabaabbbaaaaababaaabbbbabaaabbabbbbbbababaaaababbbbaaaaaabbaabaaaaabbbbaabbbabbbbabaabbbbbabbabbaabbbbbbabbaaabbabaabbbbbbbabbaababbabbaababbbabbabababaabaaabbbaabaabbaaabbaabbbbbbbbabaabaaabaababbbbbaabbaaaababaabaaaabaabbaabaaaabbababbaabbbaabaabbaaaababaaaaabbaabbbabbbbabbbbababbbaaabaabbaabbaaaaaaaaaababbaabaaaaaabbabaaaaaaaabbabaaaaababaababbaababbabbbababbaaabbabaababababbaaaaaabaaabaabaababbbbbbbbaaabbaaabaaaaababaabbabaabbbababbaababaabbbababbbaabbaabaaaaabbbabbbbaabaaabbabbababbabbbbaaabbaaaaabbaaaaabbbaababbbbabbbabaabbaaabaabbabababababbaabaabbbabaabbababbaabaabaabbbbbaabbbabbaaabbabbaaabbaaaaabbababbbbbaabbaaaaabaabaaaabbaabbbabbbaababaabbbaabbabaaaaabaabbbbbbaabaaabbbbaaaababbbbababbbbbbbababbbaaaabaabbabaabbabbabbaabbaabaaaabbabbababbaabaaaabbabaaaaabbabbabaaaaaabaaaaabaabbababbbbabbbbabbbbaabbabbbaaabbabbabbbbababbaaaababbaaabbaabaabaababaabaabbabbbabbbbaaabaabbbbabbbabbaabbaabaaabbaaaababbaabbaabaabbbbbaaaaaaababbbbbbaabbabaabbaabbbaaabbbabbbababbbbabbbbaaaababbbbabbbbaaaaababbbbaaaabaaabbbaaaaaaaaabababbabbaaabbbbbbaababaabababababbaabbabaaabbbbbaaabbaaaaaaaababababbabbbbaabaaaaaaababbababbabbbabbaabababbbaaaabbbbabbabababbabaaababbbbbbabbbbbbbbabaaabbbaabbbbbaaaababbababaaabaaabbbabababbababbabbababaaaabaababbbbababaabbabbbababbabbaaaabbbaabbababbbabababababbbaabbbbabbbaaaaabaaaaaabababbbabaaaaaabaaaabaababbaaabaabbaaaabbabbabbaaabaabaabaaabababbbaaababbbbbaaabbabbabbbbaabbabbbabaabbaababbbababbababbaaabaaabbbaaaabbbbaabbababaabaaaabababbbabbbaabababbbabbabbaabaaabbbbbababaaaaabbbbaabaabbbabaabaababaabbbabbaabbabaabbabbbaaaaabaabbabaaababaaaabaaaabbbabbbbbabbbbabababaabbabbabbbbbabbaaaabbbbabaaaaabbbbbbabbbbabbaabaababbababbbbabbbbbbaabbaabbaabaaaabbbbbbbbabbababbabaabbabbabbabaaababbaaabababbaabaaaaaababaaaabbbbaababbaaaabaabbabbabbbaabbbabbbbababaabbbaaaaaaabbaaabaaaabbabbaabbabbbabbaabaaaaaabaaabbbbbaaaabaaaaabbbbabaaaaabaaaabaabbaabaaaababaabaaabbaaabbabbaaabababaaabbabbaabbbbbabbbaaaababbababbaabaaabaaabbabbabbbbbbabababaabbaabaaaababbababbabbbabbaabbbababbbaaaaaabbaabaaaaabaabaaaaababbabaaababaaababbaaabababbbabaaabbbbbbbabbabaaaaaabaabaaababaaabbababbaaaaaaabbabbbbabbbaaabbbaaaaabaaaabaabbabbaabbbaabbaaaaaaabbbabbabbbbaaabbbabaaaababababbbaaaaababbabaaabababaababababaabaaabbababaaaabaabaaaabaaaabaababaaabbbbbbbbbbbabaaabbbabaaabaabaaabbababbabbbbbabbbbaaaaaaabbbaabababbbbabbbbabababaabaaaaaabbbbababbaaaaaaaabbbabaabaababbbbabbaabbaaababbbbbbaaaaabaaaaaaaabbabaabaabbbabbaaaababbbbbaaabababaaaabbbababababbabbaabaaaabaababababaabbabbbaaaababbbaababbbaababbaabababbbababbabababaaababaabaaaaaabbaabbaaababbbaaabaaabaaabaaaaaaabaabaaaaaabaabaabaaaaabbbabbabbbbbaaaaaaabbabaabaaaaabbabbaaabbbbbbabbbaaaabababbaabababababaababbbaabbabbabaaabbaaabaabbbbaaaababbbbabababbabaaaaaabbbbaaabaaaabaabaabaaabbabbaaaaabaabaababbbaabbabababaababaabbbabababbbbbabababaabbbbaabbbbabbbabaaabaaaaabbabbabbbababaabbbaabbabbbabbbbbaaaababababbaababaabbabbaabaabbabaababaabbaababaabaaabbaaaabbaaabbabbaabbbbababbaabbbbbabababbbbaaabaabaaaabbbaabbbabaabaaabaabbbbbbbbaababaabbbbaabbbbbabbbababababaabaabbbbaabaaaaababbaabaaabbaaaaabbbbbababaabbaaaaaabaabbbabbabaabbbbbaaaaaabbbbaabbababbababbaaaaabbabaaaaabababbbaabbbabaaaabaaabbabababbbabbabaabababbbbbababaaaaaabbaabbbbbbbbaabaaaabbaabaaaababababbaaaaaababbaaaabbbbbbbaaabbaaabbbbabababbbbaabbbbabbaaaabaaaaaabbbbbabbbabaabbbaaaaabaaabaabaabbaabbbabbbbabaabbaaababaaabaabbbbbaabaaababaaaabaababaaaabbbaabababbaabaababbabbbbaaaabbaaabbabbbbaaaabbabbbbbaabbbaaabaaaabbaabbbababbbababababbbbababaabbabaabaaabbbabbababbbaaaaaabaaaaabbbbaaabbbabaabbbbaaaabaaababaabbaababbabaababbaaababababbaabaaaabaaaaaaabababbaaabbabbbbabbbabbbbbbababbababaabababbbaaaaabbaabaababaabaabbababaabbaaabbbababbbbbaabbabbaabaaabbababbbabbbabbbbaabaaabbaaaaababbbaaaaabbbaaaaabaabbababababaaabaqababbbbababaabaabbaabababbaababbbaaaabbabaaabaabbbbabababbababaaabaaabaaababaababbababbabbabababaaabbbbbabaababaaabaaababaabaabbbbababbaaabbaabababaabbaaaaaabbaaabbaaababbaababbbbabbabbbaabbabaaaaaababbaababbaaaabbbbaabbabababbaababbaaabaaabaaabbbbaabababbbbabbbbbaabbabbbabaababaaabbabbaababaaaabaaabaababbbbbbaaaaaabbbaaabababbabbabaaabbbbaabbbabbababaaaaaabaaabbbbbbbaabbbabbbbaaabbbbabababbabbbaabbaaaabbabbbbbbbaaabaabbbbbbbbabbaabbbaaaaabbabbbbbaaaaababaabaabbaaaaaabbbbbabaaabaabbbababbabababbbabaababbaaaaabbababababaaabbaaabbababbababbabaaaabbabaababbbbbbaabaaaabbbbaabbabbbabbabbabbbbbbbaaaaabbaabbaababbaaaabbaaaaabaabababababababaaaaabaabbaabbbbaaaaaabbababbbbabbaabaabbbbbabbbaaaaaababaabbbabbababababbbabbbbaaaabaaababbbbabbaaaabbbabaabaaababbabbbaaabbabbaaaaabaaaabbabaabbabbababaaaaaaaabaaabbbababbabbaabaabbbaabbaaaabbaababaabbbbababbbbbabbbaaabababbababbaababaaaabbabbbbbbabbaaaabbbbbaaaabbbaaabbbbbabaabaaaaaaaaabbabbaabbaaabaaabbbbbbaabaaaaaaaabbbbaaaaababbabaabaaababaaabbbbabbabbababbbaaabbbbbabaabaaabbaabbabaaabbabbbaaababaaaababababbbabaaabbaabbaabbbaaabaaabbaaaaabaaabbaabaaaabbbbbbabbbbaabbabbabbaaabaabbbbbbbbaabbbbababbbbaaaaaabbbbbbababbaabbbabbbbbbbbabababbbbaabbbaababbbaaabbbabababaabaabbbaaaababbaabbbabababababaabaaaabbbaabababaababbaabaabaaabbabbabbbabbabbabbbaabbababbaaabbaabaaabababbbbbbaaaababbbbaabbababaaaaabaaabaaabbabaabbbabbababbbbbababaabbaaabbbabbbbbbbbaaabbaababbbaaaaaabbababbabbabaabbaabbababbabbaabbaaaabaabaababbbaabbbababaaaabbababaabbbbbababbbaaababbabaaabbbbaaaabababaaabaaaaaabaabbabbbaabbaaababbababaabababaababbabbabbaaaababaaabbaaabaababbbbbbaabbababababbabaaabaaaaaaaabbaababbaabaababaabbbaaabbbbabbaaaabaababbaabbbbabababbababaabbabbbaabaaaaababbbbbababaabbbabbabbaaabbbaababbaababbbaaabaabbbabaaabbaabbabbababbbbbbbbabbaaaabaabababababbaaabbbbbbaabbbaabbaaaabaabababbaabbaabbbbbaabbababaaaaababbaaaabaaababbaababbabbaabbabbbabaaaaabbbabbaabbaaabbabaaaabaaaaabbaaabababaabbbabbbaababbaababbbabbbbaabaaabaabbababbaaabbbabbababaaabbbabaabbbaabbbaaababbbbbbbbaabaabbababbbabaaaaabbabaababbababbbbbbaaababaabbaabaabbbbbaaaabbbbbbbaabaabbaabbababaabbbabbbaaabbaaababbabbbbbbbaabbbbbabaababaaaaabaababaabbababaababaababaabaaabaabaabaaababaaabbabaaaabbbbaaaaabbbabbbaabbbaaabbabaabbbabbbabbaabbaabbbaababaaaababaaabbaaabbbabbbabbbaaaabaabbabaaabaabaababaabababbaaabbabbbaabbbaababbabaaabbbbbbbbabaaabbaabaabbbaabbbbaababaaabbbbaaaaabbbabaabbaabaaababbbbbbbaabababaababbabbbaaaaaaabaabbbbaabbbbaaaabaabababbbabaabbbabaabbbaabaabaababbbbabababaabbbbabbbbbabbabbbabbabbabbaaababbbbababababbababaaababbabaabbaabaaababaabbbabbbaaabbaaaaaaabaabbabbbaaabaabbaaaaabbbaabaabbabaabbbabbbaaaabbbabbbbbbaaaaababaabbbbbaabbabbbbabbbbbababbabbbaaaabbaaabbbababbaababbbbbaabaabaabbaaabbaabbbabbababababaaaabbbbbabaababbbbaaaaabaababbbaaaaaabbaabbbbbaabaaabbabaabbbbaaabbabaababaababaabaaaabaaabababbabaaaababbbbbaabbabbbaaaaaaaaaaaaabbbaaaabbabbbbbbaaaaaabbbaaababaaaaaabbbabaabaaaaabaaaaaaabaababbbbbaabaaaaaaabaaaaaabababbaaaabbababaabbbaabbbaabbbabaaaaabababbabaaabaaaabaababababaaaaaababbbabaababaaaabbbaabaaaabaaabbaabaaababbaabbbbabaaabaabbababbaaababbbbbababbaaaaaaaaabbbbbbbbaabbbaaabbaabbbbbabbaabaaaabbaabaababbbaabbabbaaababaabbbbababaaaabbbbbabababbbbbaababbbbabbaaaabbbabbbaaababbbabbabaabbabbbaabababbbaaabbbaabaababaaaabaabbbaaaaaaaababaabababbbabaabaaabbabbababaabbabbaababbbbabbaabbbbaaabbbaaaababaabbbbaabbbbbaabaabbabbbaabbbababaabaabbabaaaaabbbabbbaaabaaaaabaabaaabbabbbaaabaabbabaabbabaaaaaabbaabbaabaaaabababaabbbbabbbbaaabbaaabbbaabbbabbaabaaaaabbbbbaaaaaabbaaabbbabbbbbabbbaaaabaaaaaabbaabbbbbbbbbaaabbaabbbbbabaabbbabbaaaabbaabbbbbaabbababbabbababaaaabaabaababaaabbbaaabaabaaaabaababbbbaabbbbabbbbaabbbabaaabaabbbaabaabababbbbaaaabaaababbabbabbabbbababaababbbbbaabbbbabbababaabbbbabaaabaabbaabababbbabbbaabababbbababaaaaaaaaaababbbbaabbabbbababbaabbaababaaababbabaaaabaabbbaaaabaabbaaabbabaabbabbabababbbbababaaaaaaabaabbbaaababbbbbbbbabbaabbababbbbbabbbabaabbbaabbabbbbbaabababaabaababbbabaabaaabaaabbbbababaabbabbababbabbaabaababbbbbbabbbaaabaaaababbbaabbabbbbbaaaababbbababaaaaabaabbabbabbababbbaaaaabbaaaaabbabbababbababababbbbabaabbbbabbaabbbbabaabaaabbbaababababbaabbbbbbbbaaaabaaaabaaaabbbbaaaababbbbaaaaaabbaabbaababbbbabaaabbbbbaaaabbbaabbababbbabaaaabaabbabbbbbaabbbaabaabbaaabbbababbbaaababbabaaababbbaabbbabababaaaaaaabbabababaaababaabbabababaaaaaaabbaaaaabbababbbbbbababaaabbbbbbaabaaabaaabbaaabbaabaababaaabaababbbbaaabaabaaaababbaaaaabbbaabaaaaabbabbbbaaababbaaaaabaababaaabababbbbbaabbbababbbaaababaababbabababbbbbaabbbbbaaaaabaababbabbbaabbabbaabaabbababbbbaabbbbbbbababbbabbbbbbbbabababbbbabbbbaabaaaabbabbaabbbabbaabbbbbbaaaabbbbabbaabbabbbaaababaaaaabbbbababbaabbbabbbbabbbabbabaaaaabaaabbbababaaaaabababbabaababbabaaaabaaabaaabbabaaaaaaabbbbbaaaaabaabaababbbabaaabaababbbbaaababbbaabbababbaabbbaaabababbbbaaabaabaabbbbbbbbbaaabaaaabaaaaabaaaaaaabbbbabbbbaabbbbbaababbaabbaababbbabbababbabaabbababababaaabbbaababbabaaababbabbbbbabaaabbbaaabbbbbabbbbaabaaaaabbbaabbbabbbbbababbabbbbbbabbabbbbabbbaabaabaaabbbaababbbbabbbabaabaababbbaababaabbaaaaaabaaabbbabbbbbabbbbabbaabbabaabbaabaabbabbaaaaaabbbbaabbbaabbbbaabbaaaababaaabaabbaabbaaaaaaabaabbabaababaaaaaaaaabaaabaaabbbbaaabbaaaaaababbbbaabaabbaababbbababaabaabbbbbabbbbbaabababbaabbabaabbababbbabaaabbbabbaaaababababbbbabaaabbaabbbbaaaabaaaabbbaaababbbaaabaaaaabaabaababaabaaaababaabbbbbbabbbabbaaabbbbabbbbaabbaabbababbbbbaababbabbaaabaababaaaaaababaaaaabbbabbbbabbababaabbabbbbaabbabaaaaaabbaaaabbbabbabaaabaaaaaababbbaaabbabbabaabbbbababbaabbbaabbbaabbbaaababbaabbbaaaaaabbbbbbbbabbaabbbbbbaaababaaabbaaabbaabbabaabbbbabaaaaabbbabaaaaaababbbbabbbbabbbbbbaaabbabaabbaabbaaababbbbabbbbbbabbabbabbaabbabababaaabbbababaabbbbabaaaaabaaaababbabbbababababbbbbbbaaababababbaababaaabbbababbbbabbaabaababbbbbaabbaaabbabbabbbaaabababbbbbbbbabbbaaabaababaabbbabbbbaaabaaaaabbbaabbbbababbabbabababbbabababaabaabababaaabbbbaaabbabbbbabbbabbbabbabaabaababbaaaabbbbbbbbababaaaaaabaaabaaaaabaabbaaaaababbabaabaaaabbbaaaaabababbbabaaaabbbbabbababbaaabbabbabbbabbaaabaababbbbaaabaababbbbbaabbaabbaaaababbbbbabbbbaaaabaaaababbababbaaabbbaabbbabaabbaababababaaabaaaabbbbaabbabbaaaabbaababbbbbbaaaabbbbbaabbabbabbababbbaabbbaabbbaaaaaabababbaababbaabbbaaabbaabbbaaabbaabbabbaababbbaaaabbaaabbbaaaaaabbbabbbaabaaabbbaaababaaaabbabaabaabbbbbababaaaaaaababbabaabbaaaaabbababaabbbabaaaaaabbaaaababaaabbbbbbaaaababababbabbaaababbaaaabbbbbbbabbbabbaaabbabaaabbaabbabababbabaaabbaaabbaaababaabbbbbabbbaaabaaabaaaaababbabaaaaaaaabbabbaaaabbbabbabbabaaaabbbaababbbabaabbaaabbbbaaabbababaabaabbaabaaaaabaaababaabaaabaababaababababaaabbbababaabbababaabbbbbbbbababbaababbababbbbaaabaaaaababaaaabababbbbbabbababaabababbaabbbabaababbbaabaaaabbbabbabbbbababbaabaabbbbaabbbaabbaaaabbbbaaaabbaababaaabbbbaababbbbaabbbbaabbbbabaababbababbabbbbaabababaabaaaaabbbabbaababbbabbbbaaabbaabbabbabbabbabbbbbababaabbbbabaaabbabbbbbbabbbbbababbbbaabbbbbabbaabbbbbbabbaaabaaaabbbaaababbaabbbababbbbbbbaababbbbabababbbbbaaaaaaaababbababababbabaaabbabababaabaabbabbbaaababbaabababbabaabbabbaabbbbbbabaabbbbaabbaaabaababbabbbabbabbaabbaaabaabaabbbbbbbbabaaaaaabbabbaabababbaabbbababbbabbbbbababaabaabababaaabbbbbaaaababbaabbabbbaaaabaaabbbbbabababaaababbbbabbababababbbaaabaaaabaabbbbabaaaabbabbbbbababbaaabbbabaabbaaabaaaababaaaaaababbbababbbabbbbaaababaabbaabbaaabbbbaababbaabbaaaabbaaaabaabaaababbaaaabbbbbbbaaaababaaaaabbbbabbbaaaabaababaaabbbaabbbbbababbabbbbabbbabbbaabbabbbbbbbabbbbabbabbabaaaabbbbbaaaabbaaaabaaaababbabaaabaaabbbbbbaaabbaaaabbaaaaabbaabbabaaaaabbabbbaaabaabaababbbaababbaabbabaabaabbbbbaaabaaabbbaababaaaababbbaababbbbbaababbaaaababaaabaabbabbaaababbababaaaabbaabbbbabaaababaabaaabbaaabbbababbabbbaaaaababaaabbbaaababbaaabaabaabbabbabbbbbbbabbaabaabbaabbbaababbaabbbaabbababaabaabaabbbabbaabababbbabaabaaaabbaaaababbaaabbaaabaabaababaaabaaabaabbabababaababaaaabaabaabbbbbaaabbababbbbbbaaaabbbabbbbaaaabbbababbbabaaaababbbabaaaabbbabaaaababbbabbaaababbbaaabbabbabaaaabbaaaabaabbbaabbabbbbabbbaabbbabbbabaabbaababbbaaabbbaaaabababbbbbbbbbababbbbbabbaabaabbaabaabaaabbbaabababbaabaabaaabbbbabaabaaabbbbaaaababbbabbbbaabbabbbbababbbabbbbbbbaaabbababbaaaabbabaabbbbbbbaabbbaaabbabbbaaababbbaaaabaababbabbabbaaababbbbbabbabbaabababbbaaaabaabbbbabaabbbbababaaaababaabbbbbabbaababbaaabaabbabababbbbbabbabbbbaaabaabaaaabbbabaabaabbaabbbbbbabaaaabbbaabaabbaaaababbbaabbaaabaabbbabbababbabbbaaaaabbaaabbbbabbababbabababbbbaabaaabaabaaaabbabaabbbbababbbbabbabbbaaabaabbaababbbbaaaaabbabaabbbaabaaabbabaaabbbbabbbbbaabbbbabbbaabbaaabbaaaaaabaaabbabaabbabbbaabaaaababbabaaabbaababbbaabbabaabbabbbabbabaaabaabbbbaabbaaaaabbbbbabaaabaababababbbaaaabbaaabbaaaaaabbabbaababaaabbabbabaaaababaaabaaababaaabaabbbabbabaaaabbababbbbaaabbbbabaababbabbabbbbabaababbbaaaabaaaabbbbbbababbaaaabaaabbbbabbaabbabbabaaabbaaaabbbbbaabaabbababaaabababaabbbbbabbababababbbbbbaababbabbbbbaabbaabaaaaabbbbbaaaaaabbbbaaabbabaaaababbaababbababbaabbbaaabaaaaabaaaaabbabaaaabbaababaabbbbbbaabababbabbbaabaabbabbabababbaaabaaaabaabbaaaabbbaaabbaaabbaabababbbbbbbbaabbbbbabbbaaaaabaabbababaaaabbabbabaaabbbbbaabaabbbaabaaaabbbabbaaabaaaaaaababaabbbabababbbbbbaabaabbaaababbabababbbaabbabbbaabbabaabaaaaaaaababbbababbaaababbabaabbbbbabaababbabbbabaaababaaaaabbabbaaabaabaaaababaaabbaaabbaababbabbabaaaaababbaabbaaabaabbbbbabbaabaabababbbbaabababbaaabbbbbaabbbaaaabbbabbabbbbabaaaaaabababbbbabbbaabaabbbaaaaaaabbbbabaaaabbaabaabbbabbbbabbaabbaabaaabaaaabaaababaaabbaabbaabbabbbaaaaabbbaabababaaaabaabbbaabbabbbbaaaaabababaaaaaabbaaabaaabaabaaaabaabaabbaababaaaabbaababbbbabbbaababbbbbaaaaabbabbbaaaabaabababaabbabaaaabbbaabbbaaaaaaaaabaaabaabababbababbbabbbabbabaaaaaaaaabbbbabbbbabbbbbaaabbaabaaaabbbabbabbbababbabbabababbaaaabbbbbaaababbaabaaaaabaabababbabaabbbbabbbabaaabbbaabaabbaaabbababbbaababaabaaaaaabaaababbbaaabbabbaabaababaabababaabaaabbaabbaaaabbbbbabbbabbabbaabbbaaabbbabbbbbabaaabababbabaaaaaaabaaababbbaabbaaabbbbbbaaaabaababbbbaaababbaaabbabbabbbbbbaaabaaabbaabbbbabbabbbbbabaabaaaabbabbbabaaabbababaaaaabbabbabbbbbbabababababbbaaaaabbaabbababaabbbbbbabaabaaabaabaabbaabbaaabbbababbbbbbaaaabbbbabbabbbabbbabaabbbbabbbbbaaaabaababbaaabaabaaabbbabbbabaaabaaabbbabbaabbbbbaabbabaaababababbbbbbabbaabbbabaababbaaaabaaabaaababbabaaabaabbbbbaaaabbbbbabbbbabababbbbbabbaabaaaabbbaaaabbababaabbababaaaaaabbabbbabbaaabbbabaaaaababaaaaaaaaaabbbabbbbbabbaababbbbabaaababbbbbabababaaaaaaabbbaaaaaabbaaaaabababababbbbbbbbaaaabbaaaaabaabaababbaababbbabaaababaaaaabbbaaabbbabbaaabbbabababbbaaaaaabaabaabbbaaaaabbaababbbbabbaabaaabaabbbaaaaaabbbabbaaaaabbabababbabbaaabbabaabaabbabbabababaaabaaababbaaaabababbaaabaaabbbaaabbbbbababaaabbabaaabbaabaaabaabbaabbaabbbbbbbbbbbabbbabbbbaabbbaaababbbbbbaaaaaabbbabbbbbaaaabaaabaaabbabbabbbbbbaaabbbbbaaaaabbaaababaabaaabbbabbaaaabaabbaabbbabababbbabaaaaaaaaababbabbabbabbbbbaaaaaabbbbbaaababbaabbbaaaaaaaaaabbbababbabaababbababaaaabaaaaabaaaaaabbbbaabbbabbababaaaaabaaabaaabbaaaabaabaabbaabbabbabaabbbabbbabbaaabbabbbaaabbbabaabbaaaabbaabaabaaaaababaabaababbbaaaaaaaaaaaababbbbbbbbbaabbaaabbaaababaaabaabaabbbaabaabbaaababaabbbaabbbabaabbabaaaabbbbabbbbabababbabaaaabaabbaababbbabbbbbaaabbbbbbabbabbbbbbabaaaabbaababababaabaaaabaaabbbabababbbabbabbbababbabaabbaabaaabaaabbbabababaaaabaababaabbbbabbabbaaaabbbaaababbabaaabbabaababbbbbbabbabbabaabaabbbabbbaabaababaababbbbabababbbababbabbbabbabbabbbaababababbabbaaaabbbaaaaabbaaaabbbabbabbaaaababaabbabababababbaaabbbabbbabaabbabaabaaaaaaaaaaababbbabbabaaaabbbbaaabbaabbaaaaaabbbaaabababaaababaabaabaabbaabaabbabababababbaabbbaaaaaabababbaabbbabbbbbbaaababaabbbbbbabbbbbbaabbaaaaabaabbaabbbbaaabaaabaaaabbaaaababbbababbabbbbabbbaaabbaaabbaabbbbbaaabbbababaabaaaabbbaaabbbbbaabaaaabbaabbaaaabbaabaaaaababaabbbbaaabbbbbababbbbaababaabbbbbbbaababbbbbbabaabbbbbbaaaabababababaaabaaabbbabaaaabbbbbbabbaaaaaaabbbabaabbbaaababbbbaabbaabbabbaaaabaaabbbbababbbbabaaabababaaabbababaaabbababbaaabaabbbbaaaabbabaabaaaaabababaaaababaababbabbabaababbabbabbababbbaabaaababbabbbbaaabbababbbbbaabbaaabaaabbbbaaaaaabaabbbbaaababaaaabbbaabbabaaabbaabbbbababaababbbabaaaaababaabbbbaaaaababbbaaaaaaaabbbbaaaabbaabbaabbbbaaabaabaabaaaaaababbaaababbabbabaabbbbbbbbbabbbaabbabbbbbabbbbabaabaabbbbabbaaabbbbbaaaabbaaabbabbaabbbabbbabbabaaabababbbababaabaababbbbabbbbbbbbbbaabbabbbbbbaabbbaaaabaabababababbbbbbabbbbbbbaaabbbbaaaabbaaabbabbaaaaaabaabbaabbaabbbbabbbaabbbaabbbbabbbbabbababbbabababbbbabaaabaabbabbaaaabaaabaabaaabaabbababbaaabaabbaabbaaaabaaabbaaabababbabbaaaaababbabbbabbbabbababaaaabbaabbaabbbaaaababaaaabbabbbabaabababaababbababbaaabbaaabbaaaabaabbbbbbaaabbbbaabaabbaabbaaaabbbbaaaabbbaaabbbabbababbabbbbbbaabaabbabaabbaaabbbababbbbbbabbaaabbabbaaabaabbbbaabbabbbbabaababbbbaababbbbbababbaabbabaabbabbbabbabababaaaaababbaaaabaaaaabababbababbbbbaaaababaaabababbbabbbaaabbbbbabbbaabbbbbbbaabbabbbbbbaababbaaabbaaaabbaaaabbabbbabaabaabaababbaaabbabbabbaaabbaaabaaaabbabbbbbbbbaaababbababaaabbaabaabbbbbbabbaaaababbaabbababababaababaaaaabaaabaabbaaabababbaabababaaaaababaaabbbbabbababbababaaabbbabbbbaabbaabbabbabaaaaabababbabbbabbabbabaabbbababaabbbbbbaaaaaabababbaaabbbabbbaaabaabbbaababbbbabbbaabaabababaaaabbabbbababaaaababbaaaabaaaabbbaaaababbbaaaaababaabbbaaabbabababaaabbabababaaababaaaaabaabaabaababbaaababbbbbaaaabbbaaaababbbbbaaaaaaaabaabbaaabbbababbaababaaaababaaabbaaaaabaabbaaaabbbbbaaaabababbbaaaaabbaaaaaaaaabaabbabababaaabbbbaaaaabbbbbabbaaabbbaaaababbaabbbbaabbbababaaabbabaabbbbbbaaabbbbaaabaabbaaabbbabaaabbbbbaaababbababaaaaaaaababaababaabbaaabaabbabbabaababbabbabbabaaabbbbabaababbbbabbaaaaabaaaabbbbbaabbbaabbbaaabbabbaabbbaabbbaabbabaaaaaabaabaaaabbbaabbbbbbbaaaabbaaaaaaabaabaababbabbbbababbbbbbbbbaabaaaabbaaaaababbababbabababbabbbbbbbbbabbbbabbbbbbbbababaaaabbabaabaabaaaabbaaabbabbabaababbbbaababbbabbbabbaababbabbbbbbaaaabbaaabaabbaaaabaabbaaabaaaabbaabbabaaaaaabaaaabbbbaaababbaaababbbaaabbaabaababbaabbbaaaabbaabbbabaaaaabbbabaababababaabaaaabbbaaaabaabaaaabaaaaaaababbababbaababbaabbbbbaabbabaaababaabaabbaaabbbbaabbbababbaaabbabbbabaababbbaaaaababbaabbaaaaaababbababaaabaababaababaabbbbbababaabbaaabbaabababbbbbbaaabaaabaababbbbaabaabbabbbbaaabbbabbbbbaababaaaabbaaaabbaabbabaaabbbbbbabbbaaabbbbbaaaaaaaabbbabbabbbabaaaaaaabaaabaababbaaaaaabbbbbabbabababaababbabaababbbbabababaabbbbbaaaabbaaaaabbababbbbabbaabaabbbabbbaabaaabbababbaaabbabbbbabbaabbbaaaaaabbbbababbaabaaaabbabaabaaaaaabaaabbabbbaaaababaabaabbabaaabbbbaabbababaaaabbbbbaaabbabaabaabbbabbaabbaaaaabbbbabababbaabbaabbbbabbbbababbbaaabbabaabbabaabbbabbaabbbbbbbbbabaababababbaaababbbbaaabababbbbbaabbabaaaaabbaabbbabbbaaaabbabaaaaabbabaababababbbaaaaaaababaabbbaaabaaaabbaaabbbaabbbbbbabbaabbaabbbbbbbaaaabbababbbbbaabbabbabaabaaaabaababbabbaabbaaabaaababbaaababbbaabaaaaabbbbbabbabaaaabababbbbabaaabbababbbbaaabbaaaabaabaabbabbbabbaaaabaaabbbabaabaaababbbabbabbbbbabbabaaababbabbbababbabbbbbababaaaaaababaababbabbabbaabbbbabbabaabbbababbbbbbaabbaaaaaababababbbbbababbbaaaabbbbabaaabbbbbaabaababbbabbbaabaaaaababbaababaabababaaabbbaaabaaaaaaababaabababbaaabbabaabaaababababbaabbaaaaababaabbbbabbababbababbabaabaabbabbbbabbbaaabbbaababbbaababaabababbabbababaaaaaaabbbaaaabaaabaaabbbbbbbaabbabaaaaaabbbbbaabaaaaabbbabbbbbaabaaaaababbaaaaaabaabbbaaabaabbbabababbbabaaababbaababbabbbaabbababababaabbbabbabbbabbabbbbbbbaabaaabaaaaaaaabbaabaabbabbabaaabaaabaaaababbbababbbaabababababbbbabbbababababaabbabababbbaabbaababaababaabbaabbabaabbbbbbabbbaaaaabbbabbabbaabaabaaaaabbbbabaaabbabbaabaabbabababbbbbaabbabbabbababbaabbabbabbbaabaaabbbababbaabbbbabbbaabababbababbbabaaaabbabbbbabbaaabbbabaaaaaaabaabbaabababaaaaaabbbbbabbaabbaabababbbabbbbbababaaabbaabbabaaabaaaabaaabbaaabaababbbbaaabababaabbbabababbaaabbbababbbabaabbabaabbabbababbaabbabaaaaaabbbbbaabbaaabbabaabbbbbbbabbbbabaabaabbaaaaabaaabbbbbaaaaababbababbbabababaaaaabaaabbbababbbabbbbabbabbbbbabaaaabbababaaababababbbababaaaabbbbaabbaabbababbbbababbabbbababbbbbbaabaaaaaabbabaaaabaaabaaabbabbbbbbbbaabababaabbaaabababbbbbbbabbbbaabababbababbbabbababaaaababaaabbbbbbaabaaaabaaaaaaaabbbbaabaababaaabbbaababbabbababbabbbbaaaabbbababbbaabbabbbaabbbaabbaabaaababbbbabbbababaabaaabbbaaabbaabbaaaababbbbbbbababbabbabbaabbabaaaabaabbbbabaaabbbbbbaaaabbbabbbababbaababbbababbbababbbaabbabaaabbaabbbaabaabaaaabbbaabaaabaaababbbabababbaaabbbbbaaabaaaabaaaaaabbbbbbbaabaabaaaaabbbbababbbbabaaaababbabaaababaabbabbababbabaaaaaabaaaabaabbbbbbabaaabbbaabbbbbbbaaabaaabaaababbbabbaabbabbbbbaaaabbbaababaaabbaaabbbbbbbbabbabbbbaabbbabaabbbabbbbaaaaaaaaaababababbbbbbabbbabaabbbaabaaaaaaabaaabbbbabababababaabbbbbbbbaababababbaaaaaaabbbbaaabbbbabaabbaabbaaaaabbaaaabaabaabaaaabbabaabaaaabbbaaaaaabbbbaabbaaaabaabaaaabbaabbbaabbaabbabbaabaaaaababbaabaababaabbabbaabbbabaabbbabaabbbababaaaaabaabaaaabaabbaabbbbaabbbbbaaababbbaabbabbabababbabbbabbbabaabbbbabbbabababbaabbbaababbbbbbabaaaaaaabaaababaababbbabbbbbababaabbbbbabbbabaaaabbbbababbbbbababbbbabaaaabababaababaaabbbabbaaaabbbbbaaabbabbabbbaabababbbbaaaaaababaaabbabbbabbbbbaaaabbbbbbbababaabaabbabbabbaaabbaabbababaaababbbbbababbabbabbbabaabbbbbababbabbababbaabaaaababaaaababbbaaaabababaabaaababaaabbabbabbababbbbbbbabaaaaaaaabbbaabbaaaabbaabbbabababaaabaaaababaaababaaabbaaabbbabbaaabaaaaaaabaaaabbabaabaabbabaabbabbaabbbaaaabbbbaabaabbbaaabaaaaabaaaabababaaaabbbbbbaabaabaaaaaaaabaaabbbaaabbaabababaabaababbaaaaaaabbbaaabbabbbababbabbbbabbbbbbabbbbbabbaabbababbbbababababaaabbabbababbabbababbaaababaaabbbaaaaababbaaaaaabbbbaaabbbabbbababbbabababababaaaabbbbbbbaabbbaaababbabaaaababaabbaabaabaabbbababbbaababbabaabbabbabbbbbaababbbababbaabaababbabbabbbbbabbaaaabbabbababbbbbbbaabbbbaaaaaabbaabbaababbaaababbaabbabbabaaaaabbbaabbabaaaaabbaabbaabbaabaababbaabbbabbaabaaaaaabbbbbaabbbbaaaaaabbbbbbaaabbabbaabbabbababbbbbbaababaaabaaaaabbabbbaaabaabbabababaaabbbbbbaabaabbbbababaaaabaababbbaabababaaababbaaabaabbaaabbabaabbbabbbbbaaaabababbbbbbabaaaaabaabbbababbabaabbaabbabaaabaabaabbbabbabaaabbbbbabbaaaabbabababbbabbbabbaaaaabbabbababbbababbbaababbaabaaaaabbbbbbababbaaabbbbbaaabbbaabababababbbaabbaabbaaaaaaaaabaaabbbabbaaaaaaabbbbbbbbbabbbabbaabbaabbbbabaabbabbbbbaababababababaaabbbabbaabaaabaabbaabaabaabbaabbbabaaaaaababababbbbaabbabbabbbbbababaaaaababbaabbbbbabbaaabbbbabbbbaaaaabaaaabbbbbbaabababbaabbbaaabbbbaabbaaabababaaaaaabbabaabbbbaabbabbbbbaabbababbaabbabbaabaabaaaabaaaaaaabaaabbbbaaabbbbbbabbbbabbaaabbababbabbbbaabbbbaaaababaaaabbbbabaaaababaaabbbabaaaaababbaabbbabababbbaabbbbaabbabbaababaababbbbbabaaaaaaabbababbaabaaaabbaaabbaaaaabbaaababbbabaabbbabaabbbabababaaabababbaaaaaabbbabbbbbbbbbbbbbbababbbbbbabbababbbbbbbbbbabbbaabababbabbaabbbabababbaaaaabbababbaabaaabbbaababbbbbbbaabbabbbbbbabbaaaaabaabaaaababaababbbbabaaaabbaababbabaababbabbbbabaaaabbaabaaabbabaaababbbbaaaabbbbbbbbbabaaaabaabbbabbbbabaabaaabaaabaabbabbbbbbbbbaaababbbbbbbababbabaabbbbbabaabbabbbbbabbbbbbbabbaaaabbbbbbababaabbaabbbabbaabaababbababababbbababaabababaaabbbabbbbbbaabbbababbbaaaaaaabaaababbbbbaaaaabbaaabbababbaaabaaaaaabaaaaaabaaabbbabaabbbbaabababaabbabbaababaaaaaabaaaaaaabbbbbbaabbaaababaabaaaaaabbaaaaaaabaaaaabbaaababbababbaabbbaaaabbbaaaababbbaababbbaabababaabbaabaababbabbbbbabaaababababbbaabbaabaaaabbbaabaabbbbbabbaaabbbbaaaaaaabbbbaaaababbbabaaaabaabaabbababaabaaaaaaaabbbabaaabaaaabbbaaaaabababbababbbbabbbaababbabbbabbbbbaaaabaaaaaaaabaabbababbbbaababaaabaaabbabbaaaaabbaababbbabbbabababbbaaabababbaaababaaababbbbabaabbaabbaaaaabbbabaaaabbaabbbbabaaaaaaabbbbaaaaaaabababbaaaabaaaaabaabaabbbaabbababaabbbaababaabaaabbbbbbbbaababbbabbbbaabaaaaabaabbabaababbaaabbababbbbbbabaaabaabbaaaaabbabbaaabbbabbbabbaaabbbbabbaabbabbaaaaaabbbabbbababbbabbaaaaabbbaabaababaababbbbbaabaaababbbabbbaabbbbbbaabbbbaabbbaabababbbbabbbaaabababaaaabaaaaaaaabaaabbaaababbaaabbaabaabaaaabbabaaabaaabaabbaababbbababaaabbbbbabaababaaaaaaaaaabaabaaaaabbaabaabbaababaaaabbaabbabaabaabbbaabbbaabaabbaaabaabbbabbbabaaaabbbaaabbbbabbbaaaaaaaabbabaabbabaabaaaabbabbbabbbbaababbaaababbbaaabbaabbbbbbbbaabbbabaaababababbaaabaaabbbbabbbbaaaabababbbbbbaaaaaaaaaabbaabbaabaabbbbaaabbbababbbbabbaabaabbaababbaaaaabbbbaaabaaabbbabababbaabaabbbbaabbbbaabbaaabaaaabaaaaaababbbbbabbababbbbbbbbaababbaaaabbaabbbbbbababbbbabaabbabbaaaababbbabbbaabbbaababaaaaabaaaaaabbabaababaaaaabbbbabababbbbbbabbbabababaabaabbaaaaaabbbbbabaabbaaaaabaabaababbabababaaaabaaaaabaabbabbabbbaaababbaaaabaaaabbbabaabaaaaaaababbaabbbababbbabbabaabababbbaabbbbbbbbabbaaaaaaabbabababbaaabaaababbbbaaabaabababbbaabababbbaaabaabaaabbbaaaaaaaaabbbbbababababbbaabaabbbaaabbaaaaaaabaababbaaaaabababbababaaaabaaaabaababbbbbbbaabbbaabbbabaababbaabbbaaabababbbaaababaabbaaaaababbabbbaaaaabbaaabbababbbbbaabaaabbbbbbbbbaaabbaababababababaaabbabaabaaaabbaabbaaaaaabaabaabaaaabbbbbabbabbaaaabaababbbbaababaaaaaabababbabbabbbaabbbaabbaabbbbaaaaaababaabaabbaaaabbaabaabbbaaaaaabbbbbbbbbbbbbababbbbbbaabbaaabbbaaabbabbbbbbbbbbbbbaababbbbbbabbbaabbaabaaaaaababbbbbaaaaaaabaaaaaaaaabaabaababbbbbbabaababaabaaabaabbbbbaabaaaabbbbbababbbbbbbbaabbabbbbbbbaababbbbaaaaaaabaababbbaabbbaabbaabbaaababaababbaabbbbababbabbbabababaaaabbabbaabababaabbabbbbbaaababaaabbbaabbbbaaaabaaaaabbabbbaaabbabababbababbbaabbabbabbbaaabababbaabbbbabaabababababaababbaabbabbbaaabababbbababaabaabaabbaababbabaabbbaabbababbbaababbbbbaabbaaaabbaaaaaababbbbaabbaabbbbaaaaababbbbbabbaaaabbaabaabaabbbabbaabbabbabbaababaaabababbabaaaabbbbbabababbaaaaaaababaabbaaabbaaababbabbbaaaabbbbbbaabbbbaaaababbbbaaabbaaabbbaaababbbbbaabbaabbaabbaaabbabbababababababbabbabababbbbabbabbbabbabababababbabaabaaabaaabababbbaabaabbbbababaabbaaaaaaabbbbaaabbbabaababaaaabaaaabbababaaaaabbaaabaabaababbbabbbababaaaaabbaababbabbbbbabbabbbabbbabaaababbaabababbbbbbabababbabaaabbbabbabbaabbabbbbaabbbabbbabbaaababaaabaabaaabbbbbaabbabababaabbbabaaabaaabbbbbaaaaabbbbaabaaabaaabbbaabbbbaababaaabaabaabbabbbabaababbbbabbaabbbbabbbabbbbbabbbbbabbaaaababbaabbbaaaabbbababaabbaaababbaaaabbbbaaaababbabaaabaaaabbbbbbbbbbbbbbabbaaaabbaabaaaababbababbaaaabbaaabaababbaaababbbaabbabbbaaaabbaabbaaabbbbbaabbaabbaaabbaabbababbaaaabababaabbaabbaaaaabbaaaabbababaabbabaaabaabbaababaabbbbbbabbabbbbabbabbbbbbaabaaaaabbbaaabaaabaabababaabbaabbbbaaababbababbaaaabababbbaababaabbabaaaaababaaabbaaaaabaaabaabaaaabbbbbabaaaaaabbabbababbaaabbbabbbbbaaababbaaabbabbbbbaaabaaabaaaaaabaabaaaaabaaabaaaaaaabbababaabbababababbbababbbbaabababbababaaaabaababaaabaaabbaaaaaaabbbaabaaabbaabaabbbbbaabaabbabbabbbabbbbbaabbbaababbabbbababbbaaababbabbababbabaababbbbaaaabbabababaaabbbabaabbabaaabbbbbbbaaaabbabaabbbabbbabbababaabaabbaaaaaaaabbabbbbbbbabbabaababaaaaabbbabaabababbaababbbbaaabaaabbbbabaababaababaaababababbbbbaabbabbbabbaabaaabbbbababbbababbbabbbbbbabbaabbbaabbbbaaabbaaaabaaabaaaaababaaaabbaabaaabaaabaabbbabbabbaaaaaabbabbabbbababaaabbbbbbbbaaaaabaaabbabaaabbbaabbabaabaabaabaaaabbabbbbbabbaabababbabbabbabbaaabaabaaaaabbbaabbbaababaaaabababbaaaaaabababaabbababbabbbbaaaaaaabbbabbabaabbaaaaababababbbbaababbbbababaaaaaaaaabbbaabbbaaababaabaaabaabababababbaabbaabbbbaababbbbbbbbbbabbbbbbbabaabaaaaabbaababbaaababaaabbaabaaaabaabaaabbbbaaabaabababbbbaaaababaaaabbabaabaabababbaaabaabaaababaababbaabaabbabbaabbbabbaybabbbbaabababbabaababbbbbabbbbbabbbaabbbaaaabbbbabaabaaaabbaaaaaabaaaabbaaabbbaabaaaaaaaabbaabbaabbababbaabbbaabaaaabaababaaabbbbbaabbbabaabbbabbaaaabaabbbbaaabababaababaaabbabbbabbabbabbababbababbbbabbaabbabaabaabbbababbbbbabababababbbaaaaababbaabbbbaabbbbbababbbaaabaabbbaaaabbbaabaabbbbababbabbbaaabababaabbbaaabbaaabbaabababbabbbaabababababaaabaabbbaaaaabbbbbbaaaaabbbaaabababbaababaabbabbbabbaababbaaabababaaaaaaabbaaabaaaaabaababbbabaaaaaabbbabaaababbaaabbabbabbbaabbbbbbbaabbabbabbbbaabaaaababbbbbaabbbbaabbaaabbaaabbbabbaabaaaaabbaaaababbabaaababbabababbbababaaaabababbbaabbaaaaaabbbaabbbabaabaabbbabbbbabaabababaabbbabaaaabababbabbbaabbaababaaabbababbbabbaabbbbbbbaaaabbbabaabbaabaababaabaabbbbabbbbabbabaaabbaaababbbbbbbababaaabbbabbbbabaaabbaabaaabaaabbaaaaabbbbbbbaaabaaaabbabbaababbabaababaabababababbbaaaababbaaaababbbbaabababbababbababaaaababbaaaabaaaaaababbabbbbbabaaaabbabbbabaaabbababbbabbbbbabbabababbbababaaabababaaabbabaabaabaababbbbaababbabbbbaabababaaabababaaabbbbbbaabbbbabbaaaaaababaabababababaababaabbabbabbbabbbbbbbbaababbaaaaabbbaabbbbbaaaababbbaabaabaaaababaababababababbabbaabbabbabbabababaaabaaaabaaabaaaaabbabaabbaabbbbbbbabbababaaaaabaaabbaabbbaaaabababbbbabaabaaaaabbababbbbaaaaabbbaababaaabbabbaabbaabaaaaaabbabaaaaaaabaaabbbbbabbaabbbbaaabbbaabbbbaabbbbaabaaaaabbababababbbabbbaabbbaaabaababaaabaaaabaababababaaaabaabbbbbabbbabbabaaaabbaabbbabbaaaaaaababbbbbbbbabaabbabaabaabaabbbaabaaababbbaababbaaabbbbabbababaaaabbbbabaaaaaaababbaaaabbaabababbbbbababaabaaabbaababaaababbabaaaaabababaabbbbbbaababbabaabbaaabaaaaabbbaabaaabababbbaabbaaababbbaababbbabbaabbabaabbbabaaaabaaabbbbaabbabbabbabbbbaababbabbbababaaaaaababbbaabbbbbaababbaabababbbbbbbbbbaaababbbbaaabbbabbaabaababaaaaabaabbaababbbabbaabaababbbaaabaabbaaaaaabbaaabbbbaabaaaaaabaabaaabaabbabbaabababbabaabbbabaabbbabaabbabbbbabbbaaaaabbbbbabbaaaaabbbaababaabbababbabbbaabaaabaaabbaaabaaaaaaabbabaababaaabababbbaabaabababaabaababbbbbababbbaababbaaabbbbabaababababaaaabababbabbbabbaaabbabaaaaabbbbabababbabbabaaabbbaaababababaabababbabbabbbababaaaaabbabababababbabbabbabbbbaaabababaaaabbabbaabbaabbaabaababbabbaababbaaabbbbbbaaabaabbaabbbbbabbbaabbbabbbaaaaaaabbaabbbaaabababaaaaaaabababbbbabbbabbbbbbaabbababbbaaaaabaabaabbaaabbabaabaabaababbbabbbaabbbbaababbababbaabaaabbaabaaaaaabbabaabaababaaabaaababbbbabbbabaaabbbaaabbbbabaabbbaaabbababbbabaabaabbabbbababbbbbaaabbaaaababbbaaaabbaababbbpbabbaaaabaabbbaabaaabaabaababbbabbaabaabbabbbaabaaabaaababbaaaabbabaababaaaabaaaaaabbbaabbbabbbababaabaabbaaabaabaaaaaaabaabbbabbaabbbabbabaabaabbbabbababbbbbbbaaababbabaabbabaabbbbbabaabaabbabaaaaaaabbbbbabaaababbabaabababababbbaaabbbaabaabaaabbbbaaabbbbabbbbbbbbbbababbbbaababababbbbbbbaaabbbabaaabbabbaabbbbbaaabbbbaabaaaabaaabaabbabbaabbbbababaabaaabbbbaaababbabbbbbabaabbabaaaaaaaabbbabaababbaaaaabbabbaabaabbabbbaaaababbababbaaabbabaaabbaaaababbbabaaabbabbaaaababaabbabaabbabbabbbbabbaaabaabaabbbbabaabbbaabaaabbabaabbbbbaabbbaaababbbabaaaaabbbbaaabbaaaabbabaababbabbbabbaaabaaabababbabbbaabbbbbbaaaaabaabbaababbbbbbabbababbbbabbbbbaaabbaabbbbabbbbbaaababbbbbbabaaababbaaabbabaaaabaabbbabbabbbbbabbaaabaabbbbbbbbaaaabbabbabbbbabbbbbabbbbbaabababaababbbaababbbbaaaaababbaabbbbbaabaabbbbbaabaababaaaaaabaabaabbbabababaabbabbabbbabaabaaababbbabaaaaaabbbabaaaabbaaaababaaabbbbbabaaaaababaabababbaabbbbaabbabbaabaabbabababbbaaaabaaabbabbbbabbaabbbbaaabbbbbaaaaabbaabbaaaaaababaabbbabbbbabbbbbabbaaabbababbaaabaaaaababaaabbaaababbaabbbbabaabbbabbbbbaabbbabaabaabaaabbbabbbbbbaaaaabaabaabbaaaaabaaaaaabbaabbabbbbbbabbbbaababaaaaaabaabaaabaabbbbaabaaaaaaababbabbbbbbabbabaaabbbabaabaababbaaabaabbbbbaaabbababaababbbabbaabbaaaabaabbbabbbabbbbabbaabbabbaaaaabbaabbbabaaabbaabbbbbbaaaaaabbaabbaabbabbaaaabaabaabbababbabaabbbbbbababbaabaabbaababbbaabbaabaaaaabbaababaaabbabaaaabbabbbaabaaabbaabaabbaabaabbbbaaabbbaaaabbbabbbaaabaaabbbabbabbbbbbbaabaaaaaaababbbbaaaaabbabbabaabbabaaabbbbbaabbaaaaababbababaaabaababaabbaababbaaaababaabbabbbaabbbaababbaaaababbbaaabbbabbaaaabbbaaababababbbbbabbbabbbaaaabaabbbbbabbbbabababaabaaabbabbbabababbababbbabbababaabbbbbaaaaabbabababbbbababbaaaaababaabababbbaaaababbabaaaaaaabbbabbaaabaaabbabaaabbabbaaaaabaabbaabbbaaabaabababbbbaabbbbabbaabbabbaabababbaaaabbbbabaaababaabbbbabaabbbbbbaababaababaabaabaaababaabbbbbbabababbaabababaababbbabbaabaabaaabababaabaaaababbbaaabbabaababbaaaaabbabaaaabbaabbaaaaaabbbbbbababbbbbbbaaaabaabaabbaaabbbabbababaaaaabbbbbabbabbaaaaaaaaabaaabbaabaaaabbbaabbababbbaabbbbabbaaababbababaabbbbbbabaaaaabaaaaabbbababbbbabaaabbbabbbabaabbaabbbabbbaabaabbbbaabaabbbababaaababbabbabbabaaaabaabaaabbbbbabbbabaabbaaabbbbaabbaaaabbbbaaabbbabbbbabbaaabbababaaaaabaaabbbbbbababbbbabaabaaabbbabbaaaabaabbaaabababbaabbbaaaabaabbbabbbbbaaababbbbaaabaaaabababbabbbbaaabababbabbaabbbaaaabaabaaabbaaaaaaaaabbaabaaabbaabaaaabbbaabaabaaababaababaaaaabbababbbbaaabaaababaabbbbbbbaaabbbaabbbababbaabababaaabbaabaabababbabaabaabbbaaaaaaaaabbaababaaaababbabbabaaaababaabbaabbbbbbbbabaabbbabaabbbbaaaabbbbbbabababaabababbaaaaabbababbaaabaaaababababaabbbbaaaaabbbababbbabbbababbabaaabababaabaabaababbbbbbabaabbbbaabbbbabaabaabbabbbaabbbaabbbbbaabababbaabaababaabaababaaaaabbbbbbabbbabbabbaaaaaabababababaabbabbaabaaaabaaaabaababaabababaaabbbabbbaabaaaabbbabbbabbbbbaaabaaaabbbaabaabbbbabababbbaabaabbabbbbbbbaaababaaaabbababbbabbbbaababbbababbbaababaaabababbbbaqbbaababaaababaababbababbbbabababbaaabbbabbbbbaaaaababaabababaaabbabbbbabaababaabbabbbaaaaaabbaaabaabbbbaaaaaabaaaabbbaabbababaaabbbaaaaabbabbabaaabbbabbbaaabababbabbaabaaabbaaabbbbbbabaabaaabbababbababaababbbbaabbbaabaabbbababbaaabbaaababbbbbababaababbbaaaababbaabaaabbbbaababaaaaaabbbabbaabbabaaabbbbbaabbaaaaaabbabbbaaabbaaaabbaaabaaaabaabbabaaaaaaaaabbaabbbbaabababababbaabaabbabbbbabababaabbaaaabaababaabbabbbbbabbabaabbabaabaaabbaaabbbabbaabababbabbbababbbabbbaabaaaabbbabababaaaaaaaaabbbbbaabaabbaaabaaabbaabababbbaaabaabbaabababaabbbaababbbbaaaabaabaababbabbbbbbbbabbbbbbbbbbbbbaaabbbbaaabaabaabbaaabaababaaaabaabbaaaabaababbbbbabbabababbbbbbbbaabbbaabbbabbbbaabaaaabbababagbabbbbbbababbbabaaabaaabbabbbbbabaaababbaaaabaaabbaababbbbbaabaabbaabbaaababbbabbbabbaaabaabbabababaaaabbbababaaaabbbabbbaaabbbbabbbbbabbbabbabaabbbbaabbbbbaabaaabaabaaaaaaabbbaaabbbaabbabbaaaabbbbaaaabbaaabbabbabaabbbaaabababbbbbaabaaaabbbbbaaaaabbaaabaabbaaababababbbbbbbabbbabbababbbaabbbaaabbbbabbaaaabaabaaababbbaabbbbbbababbbabbabaabbbbaabbabbbaaaabbaabaabbabbabbbaabaabbabbaaabbbababaaabaaaaaaaaaaabbbababbababbbbaaaabbbabbbaabbbbaabbbbbabbbbababaabbbbabbabaabaaaababbbbbaaababaabbaabbbbbbaaaabbbabababbbbbaaaaaaaaabbababbbaaabbaabbbabbabbabbbbbbaabababbbabaaababbaaaaaabbbabaababaaababbbaaaaaabbbbabbababbbabbbbaaabbbbbbbbaaaabaaaabbbbbaabbbaabababbabbbbbababbaabbaabaaabbabbbbababbbbabbabaaabbabaaababbaaaaabaabbaabaabababbabbabaabaababbabbababbabbabaabbbababbababbbabbbbbbaaabbbaaaababbbbabbbaaababaabababababbbbaaaaabbbbbabaaaaabbaabbbaaabbbaabababaabbbaabbbaababaaabbbaaaabbbaabbaaabbbbbbabbbabbbabbabbabababababaaabaabababbabbbabaabbabaaababbaaaaabbabbabbbabbbbabaabaababaaababbabaaabbbbaaaaaaaabbabbbabaaabbabaaaaaababbaaaabaabaababaaaaabaaaabbbbaabbbaaaabbbaabbaaaaabbaaaaaababbbabbbaabaaabbbabbaabaabaabbbbbababbbbbbbbabbbaaabbbaaababaababababababbabbaabaaabbbbbbabaabbbaaabaabbabbaaaaaababababaabaabbaabbbabbabaaaabbaaaabbabaaaabbaaabbbaabbbabbbbbaaaaabbaaabbbaaaaabbabaabbbaababbbabbabbabbbabaaaaababbbbabababbbaabbabbbaabbaaaabaaaababaabbaabbababaaaaabbbbbbaabbaababbbbbaabbbbabbaaaaabbabababbaabbbabbbaaababaaaabbbabaaababababbbbababaaabbaabababbabbabbabaaabaababaaaabbaaaaaaaabbbbbbbbaaaaaaabbaababaaaabbaaabaaaaaaaaabaabbbbabbbbbbbaabbbaabaabbbabaabaabbabaabaabaababbaabbabaaaaababaaabaaabbaabbabbababbababbabbaaaaabbaaabaaaababbbbbaaabbbbbbaababbaaabbbabbaabbaaaaababbabbabaabbabbbaabbaaabbaababaababaabababbabaaabbbabbbbbaabbabaabbabbbaaabbbbaababbbbaabababbaababaaababbbababbababbbbbbbaaaabbaababababaaaaabaabbaabaabaaaabbbbaababbbbbbabaaababbaabaaaabbaabaaaabbbbabaababaaabbbbaabaabbbbabababbbaabaabbababbabbbaaaaaabbbabbbaaababaabbbbaaaaaababaaaabaabbbbabbaaabbbbabbbabaaaaabaabbbbbbaaaaabababaabaabaaabbbabbbabababbbababbababbabaabbbbaaabbaaabbbbbaaaababbbbabbbbbbabaabaaaaaaaaaaabbababaabbaababbbbbbaabbaaabbababababaababaabbabaabaabababbababbaaaaaabbbbaabaaabaabaababbbaabbbababaabaaabbbaabbaababaabbabaababaaaabbabaaaababbabbbaaaabaaaaabbbaabbbbbbabaaabaababbaabaaaabbbbaaaabaaaabbaaabaabbabbaaaaabbaaababbbaaaaaaaababbbbbbaaaabababbaaaabaabbbabbbbbaaabbbbabbaaabababbbbababaabbbbbbabbaabaaaabababbbabaaaabaaabbbbbbaabababbbbabbbbbabaaabbabbbbbabaababbbbabababbabbbaaababbbbbbbabbaaabbbbbabababababbabaaabbabaabbbaababbabbbaaabbbabbababbaaaabbbbbbaababbbbbabaababbabababaababaabbaabaaabaabababbababbaabaaababbbbbaaaabbbbbababaaaaaaabbabbbbbbbabbbaaaabbbbabaabbbaabbabbbabbbaaaabbbbbbaaaabbabbbbabbbaaaaaaabbbbabbaabaabaababbababbabbbbbaabbaababaabababbbaabbbbbaaaaabbabbabbabaaaaaaababaabbbbabbbababaaaabbaabbabbbaaaaabbaabaabbabaabbbabaaabbbabbababaaabbaaabaaaaaaaabaabbaabbbaaaabaaabbbbbabaaaabaaaababbbbbbabbbbababbaabbbbabbaabaaabaabbbbaaabaababbabbaaaaabbbbbbbaaaaabbbabbaaaaaababbbababbbabbaabbaababbaaabbbbaabbbbababbbaabaaaabbabbabbbaabaabbababaababbbabaaaaabbaabaabbabbababbbaabbaababbbababaaaabbabbabaababbaaabbaaaaabbaabbbabbbaabbabbbbababbabbbabaaabbaaaabaaaaaaabababbaaaaaaabaaabbaaaaabbababbbbabbaabaabaaaaabbbabbbbbabbabaaabbaaabbbbaaaaaaaaabbbabbaabbbbbbababbaaabaabbbbabbbbbabbbabababbbbabbaabbabababaababaaaabaabababbbbabababbaaaaaaabbabbaaabaabaabaabaaababbbabbabaaaaabbabababaabbaabbabbaaabaabbabbabaababbabaabbbbabbbaabbbbaababbbabbabbbabbbbaaaaaaabbaaaaaabbaabababababbbbaabbaabaabbbabbbbbbabaabbaaabbbbaabbbaaabababbbbbbababbaaaaaaababbabbabbabbbabbaabbaababaabaaabbabaaaabababbaababababbaabaaabbbbaaababbbbbaaabaaaababaaabaaaaaaabbabbbaababbabaabbbabbbbbaaabbabbbbaabbabaabbababbaabaaaaaaabaaaabbbabbbababbababaabaabaaaaaabbabbaaaaaaababbbbbbbabaabbbabbababbaaaabaabbbbbabbababbaaaabaaababaababaababbbaaabbabbbbabbabaabaabaaabaaabaaaaababaaaaaabbbabbbabaababaaaabbbbbbbbbbaaaaabbaaaaabbabbbbbbbbaaabbabababbbabbababbbaaaaabbaaabbaaaaabbabbabbbbaaababbabbbbabaabbbabbbbbbbbbbaaababbbaaaabbababbaabbbbaaaaabbbaaaaaabbbbbbbbaabbabbbabaabaaabbababababbabbbbababbbabaaabbbabaaabbabbbbbabaaabaabbabbbabbaabbaaabbaaaaaaabbbaaaabbbbabbbaabbbaaaababbaaaaaaababaaaabaaaabbabbaabbbbbabbababaaaaaaaaaabbbabbabaabbbabbabaaabaaabaaaabbbabbbbbbbaaaabbbaababbbbaabbbabbaababaaabbbabaaaabababbabbaababbabaaaabbbbababbabbbaabaaabbbaabbabaabbaaaaaabbababbbabaaabababaababaabaaaabbbbbabaaaabbaaabaaabbbabbaabbbabbaaaabbbaaaaaababbabbbaabbbbbbbbbbaaabaabaaababbbbbbbbababaaabbabbbbbabaaabbabaaaaaaababbbbbabaaaababaaaaaaaabbaaaabbbbabbbbaababbbabbabbbbbbabbabbaaaabbabbbbbbaaabaabaabbaaabbaabaaaaabaaaaabbabbabaaabababaababbababbbbbabbbabbbaabaabaabaabbbaabbababaabbaabababbababbbaabaabbabaababbaabbaabbaabbaaaaaabaabbbbbabbababbbabbaaaaabbaabbaaaabbbababbbabbaabbabbabbaaaaabaaababaaabbabbbbaaaaaaaabaaaaababbbbbaaabababaababababbaabbbbbaaabaaabaaaababbbbabbbbaabbbbbaaabaaabbaaababaabaaaabababbbbbaabbbbbbbabbabbbaababbaaaabbaababbabbbaababaabbaabaaabbaababbaaabbaabbbbaababababaababaaaabaabbabbbaaababbaabbbabbbbbbabbbabaabbabbbbabababbbbabaaaabbababbbabaababaaaabbbbbbaaabbbabababbbbbbaabaaabaaaababababaabbaaababbbababbaaabbbabbabaaabaaaaabbbbbbaaaabbaabbaabbbaabaabbbbababbabbababbaaaababaabababbaaaababaabaabbbabababbabaaaaaaaabbabbaabaabbbbaaaaababaabbaaaabaabbabbbbaaaabbbbbbaabaabbbababaabbbbabaaabbbbaaabbabaaaaabbabbbbaaaaabababababaabbbaaaaabbbbbaabaaaabbbabaabbbbbabbbabbaaabaaabaaabbbaabbababbbababaabaaaaabaababaabbaaabbabbaaabbabbbbbbbaaabbbbaabbababbbbbbaaabbbaaaabbbabbabaabbbaaabbabaabbbbbaaabaababaaabaaabbaabbbbaabbbaababababababbbababaabaabaabbbbabbaaaababbbaaabbaabbababaaaabaaaabbbbbaabababbbabbabaaaaaababbbaaabbaaabbbaabaabbbbabbbaabaaabababaabbaabababbabbabbbaabbabbbbbbaabababaaabbbaaaabbaabaababbbbbaabbbabaabbbabbbaaaababbabbbaababbbabaaabbabbbbbabaababaabaabababaaaaababbaabbbbbbaabbbaababbaaaabaabbaababbbbaaaaaabbabaabaabbaaaabbbabaabbabbaaaabbaaaaaabbababbaabbabbaaaaabbabbaabbaaabbaabbbbbabbaaabbbbabbaaaaabbbabbbabbabaaabbbabaababaabaaaaabbbbbbbababbaaabbababbaabaaaaaaabbaabababbbaabbbaabbbaaabbbbbaaababbbbbaabbbaaaaaabaaaabaabbabbabaabbaabbaababaabaababaaaaabbabaaababbbaabaaaaaaabbbbaabbbabaabbbabababbbbaabbababbbbbabbbbbabbaaababaaabaaabbaaabbbaaababbabbbababbbbbaabbbaabaababbabbaabbbaabbaabaabbbbabaabbaaabaabbaaabbbaaaabbbaababaabbbabaaaabbbabbbabbbabaabababababbbbbaabbaababbabbaabbbabbbaaaabaabbbbbabbabbaaabbaaabbababbbabaaaaababababababaaaaababbabbaabababbaaaabbbbbabbbbaaaaaabaabaabbabbaaaababbbabbbbbbabbaaaaabbbaaaababbbbbabbbbbaaabbbbababababaaabbaabbbbaabbababbaaaaaaabbaababbaaaabaabaabbbabbbbabbbabbbbaabbaaaabbabbaabbbbababbababaababaabaabaabbbabbbaaabaabaabbabbbaaababbbaabaabaaaaaaabbbabaaaaabbbbababbbbbaaaabaabbaabbbbbabbaabaabbbabbabbabbbaababbabbbabbabaabbababbbabbaabaaabbbbaabaabaaababbabaaabbaaabbababbbbbaaaaaabbbaaababababaaaababaaaababaabbaaabbbababbbababbbbbabbabbbabbabaaaaabbabbbabaabbbaaabaaabbabaaaaaababbbbabbabaababbbaababaabbabbbababbbaaabaaabbbbbaaabbbabbabaabaabbbababbbbabaabaabbbaabbabbbabaaaaaaabaabbaaabaaaabbbaaabababaabbbaaaaaaaabbbbbbababbaabababaabbbbabbabbabbabaabbabaabbbabaabaaabbbbbbababbabbbabbbbaaaaaabbbabaabaaabbabbbaaabbaabbabbbabbbbbaaabbabbabaabbabababbabaabaabbbababbbbababbabaaaabaababaabbbabaabbbbbaababababbbabbbbabaabbbbbabbaaabababaabbabbabaaaabbaabaabaabaaaaaababbbabaababbaabaababbbbbbabaabbabbbabbabbabbbbaaabaaaaaaabaaaaababbbbababababbbbababbababababbabbbaaaaababaabbababbbbaaabaaabbaaabaabbbaabbababbbbababbaaababaaaabbbaababbababbbbabbaaaaabaababbaaabbbabbabaaababbbbbbbababaabbabababaaaababaabbabbbabbabaaaabababaaaabaaaabbbbbaaabbabaaababbbbaaaabbaababaaababbaaaabbabbabbbabababaabbabaabbbbaaaaaababbbaabbbaabbaababbabbaaabbabababaaabbbaaabaaabaaaabbaaabbabaabbababbbababbbaabbaabaabbbbabaaaababaabbbaaaaaabbbbabbbbbbbbabaabbaaabbbabbabbababbbababbaabbaabaaaababbbabbbabbaabbbbabbbabbababbaabbaabbbaaaabaabbbababaaabbaabbabbbabbaaaabaaaabbbaabbbbbbbaaaabbbbbbbaababaabaabaabaabababbabbabbbbabaaaabbaababaaabbaaaaabaabbbaaaaaaaababbabbaaababbbbbabbaaababaabbaabaaaaaabbbbbbaabbbbabaabbabbbbbaabbabbbaaabaabaabaabbbababbaabbbbbbbaabbabbbabbabaaaaaabbaaaabbbaabbaabaaabaaaabbabbbbabbababababbaabbaaaaaaabbbbabbbbaaaaaababababaabbbbbababbaabbabbbabbbbaabaababbaaaaabbbbbaaababbbaaabbaabaaabbbaaaaaaabbaaababbabbabaaaababbbbbabbabbabbaabaaaaaabbbbababbaabaaababbbbbbbaabaabbbabbbbaabbabbbbbbaabaaaabbaaabababbbaababbababbabbbbababababababaabbabbabaabababaaaaabbbabbbbbaabbaaaabaabbbabbbbaaaabaabbaabbbaaabbabaabbababbbabbabbaabaaabbbbbabaabbabbbaabbbbbaabaabbbbaaabaaababaababbbabaabaaaaabbbbaaabaaaabaabbbabbabbaaaaabbbabbaaaaabbabbbbaaaaaabaaaaabaabbbbabbbabbaaabababbbbbaababababaabbabaaababbbbbaaaabbbbabbaabaabbbbbbbbbbbbaaabaaababbbbababaaababaabbbbbaabbabaabaaaababbaaaaabababbaabbbabaabbbbbabbaaabbaabbbaaababaaaababbabbbabbaabaaaaababaaabaaabbbbbabaaabbbbababbbabaabbaaababbbbabbaaabbababbbaabbbaababbbabaabaabbbaababababbabaaaaaabaaabbbbbabbbbbaaaaabaaababbaaaabbbaabbaaabbaabbbbaabaabbabaabbabbbabbbaaababbbbbbaaabaaaaaaabaabaaaaaabaaabaaababaaaabbbbaabaaabbaaaaabaabababbbbbababbaababbbababbabbbaaaababbababbbbbbaabbbababaaabaabbbaabaabbbbbabbbbaabbbababbaaaaaabaababbbabaabababaabaaaaababaaabbbbaaabaaaabaababaababaaababbaababbbbbaaababaaaaabababaabbababbababbbabababbaaaababaababbbaabbbabaaaaaabbbaaaaaaabaaaaabbbbabbaabaabaabaabbbaababbbababbbababaabbaaaababbaaaaaababaabbaaabaabbbaaababbbaaabaabbaaaaaaaabbbbbabbabaabaaabbbabaaaaaaaaaabaaaabbbbbbbbaaabbbbbababbaaaaaabbbbaaaabaaabbbabababaaababbabbbaaababaaaabbabaaabaabbababaaaaaabbabaabbbaabbbbababbbaababbaaababaabaabbbabbbaababbaaabaabbbaabaabaaaabaaaaaaaabbaabbaababbabaabbaabbaababbbaababbbbabbaaabaaabbababaaabaabbbbbbaaabbababababbabababaabbabbbbababbbbbbbaababbaaaababbabbaaaabaabbabaaabaababbbbaababbabbbabbaaabababbababbaabbbbabbabaabbabbbabaaaaaaaabaababbaabaaaaababbaabaabbabbbbbbaaaaaaabbaabbabbaaaaaabbababaabbabbbaabbbabaababbaabaaabbaabbbaaabaaaabbabbaababaababababbbbbaababaaabbbbabbabaaaabbbbaaabbabaaabbbbbbaaaaababbbababbaaaabbbbbbbabaabbaabbabbbbababbaaaaabbbaababbbbabbbababbaaabaaaaabbbbaaaabaabbbaaaaaabbabbaaabbaabbaabbabaabaababbabbaabbabbaabaaaabaaaabaaaaabaabababbaababbbbbabababbbbabbbababaaababbbaaaabbbbbbbabaabbbbaaabbbbbbbabbabbabaabbbbaaababbbbbbbbaabbbaabbaababaaabaabaabbabbaaababbaaabbbbbabbbabaabbbababbbbabbbaabbabbabaaabababbabaabbbaaaababaaabaabbaabbbbabaabbabbaaabaabbbaaaaabbaabaaaabbababbbbbaabaabbababbaaabaabaaabaaaaaaaaaabababaabaabababbabaaaabaaababbabaabaabbbabbaabaaabbaaaaaaababbabaaaabaabaaaaabaaabbaaaabbabbbabbabababbbbbabaabaabbbbaabbbbababbaabbaaabbbbaabaabbbabaabbaabababaaaabaababaaaabbaaaababbbaabaabbbabaabbababaabbbaaaabaabbabaabaaabaabaaabbabababbbababaaabbaababbbaaaabaabbbbabbbaababbabaaabaaabaaabbaabaabbbabababaabaaabbabbbabbabbabaabbababbbaaaababbbbaaabbbbaabbababbabbbbabaabbbabbabbaaababbaaabaabaaabbbabbbababaaaaaaaabaaaaabbabbbabbaabbabbbabbaabaabaabbbbbaabaaabbbbbbbaabaabbaaaababaaababbaaabaaaaababbabbaaaabbaabbbaabbbabbaaaaaabaaabbbbbaabaabbbaabbbaaabaaaaaaaabbbaabababbaaaaaabbaabaaabbabbaabbbbbabbaabaaaaabbbaaaaababbbaaabaabaabaaabbbaabbbaaabbaabbbbaaaabbbbaaaabaabaabaaababaaabaababaabbabbababbbabaaaabbbabbbabaabaabaababbbaaaaababaaabbbaabbbbbbbaaabbbbaaabbbbaababbbabaaaabbaaaaabbabbbbaaabbababbabbbaaaaabaabbaaaabbbabbaaaabaabbaaabbbabaabaaabababaababaaaaababaaaabbbbbaaaaaaaabbababbaaabaabababbbaaabaabbabaababaaabaaabababaabbabaabaaabaaababaababbbaaaaaaabaaabaabbbbbababaaabbaaaaababbbbabbabababababaabaaabaabaaabbbaabbaabaabbaabbabbabbababaaaaaabbbaabbbaaabbababaaaaabbbbaaabbabaaabbbbbbabbbabbaabbbaaabaabaabbabbaabbbaaabaaabbabbababbaababaababbbbbababbbaaabaaabbbbaaaabbaaaaaabbbaaaaabbbaabaaabbabbaaabbabbbbaabbbbbbbaabaaaabbaaaabbbabbabbbbaabababaabababbabaabbbbabbaaaaaaababbaabbabababaababbaabbbbaabaababbbbaababbbaababbaaaabbbaaaaaababbaaabbbaaaaaabbaabaaabbababbabaabaabbaaaaaabaaabaaaabbbaaabaabbbbbaaaabaaaaaaababaabbaabbaabaabbbabaabbaabaabaaaaaabbbabaabbabbbbaaabbbbbbabaabbaaabaaaaabbaabbabbaaabbabaaaaabbabbabbbbbabbbabbbbbabababbbaabababbbaaababbaaabbabbbabaabaaabaaabaaabaabbaababaaabbbabaaaabbbaabaaaaaaabbaabaabbbabbbbababbbaaabaaabbaaaabbaaaababbabbabbaaaabbabaabaaaaaabbabaaabbabbbbababbabaabbabaabbabbababbaabbaabbbaababbbbbbabbabaabbabaababbabbabaababbbbbbbbaabbbaabbaaabababbabbbaaaabaababaabbbabbaaabababaabbaabaaaabbaaabbbbaabbabbaaaaaabbabbaaabbbbaaababaaaaaabbaaabbaaababbabaababbbabaabbbabaabbabbbbaaabbbbbbbaabbaaaaaaaabaabbaaabababbbbbaabbbabbbaaabbbbbbbabbaabbbbbbbbbbbaabbbabbaaabbaaaabbabaaabaaabaaababbabbbabababbabbabaaababbbaababababaabbaaababbaaabbaabaaaaaabaaababaaaabaabbbbaaaaabaaaababaabbbbaaaabaabaaababbaabaabbaababaabbabbabaabaaaaabaaabababbabaaabbaaaabaababaaaaabbbababaaababbbbababbabbbbbbabbabaaaaaaaabaaabbbaabaaabbaaabbbbbabbbbbabbaaaaaabaaabaababbbbaabbbbbaaabbababaababbabbbbaaaaaabaabaabbbbabaaaaaabaabaabbbbbabbbbbabbabbabbbbbabbabbbabaabbababbbbbbbabababaaaaaaaabbaaaabaaaaaabbbbbaaabababbabaabbabbbabaaaabbabbbbabbbabaaaaabaababbababaabbababaaabbbababbbaaabbbabbbbbbbaaabbabababababbbabaabaaaabbabbabababaaaababaaaababbbbabbbaaaaabaaaaabbbaaaabaabaabababbabbbaaabaabbbbbaaabbaaabbbaabbaabbbbbbbbabbaaabbabaaaabbaababbaabbbbbbbaababababbbababaaaababbbbaabbbabababbabaababbbabaaababbbaaaabbaabbbaabbabbababaaababaaabbbaaabbbaaabaaabbbaaabbbbbabbaabbabbbabbaaabbbabbbbaaabababaabbbabbbaabaabbbaabbbabbaaabaaaabbbbabaabbbabbaabbabaaaabbbaabbbbabababababaaaaaaabbaaaabaaaabbbaaabbbbbbbbabbaabaaabbbbbbbabbbbaaababbabbaaaaaaaaaaabbbaabbabbbbaaaabbaaabbbbbaaaaaaaabbaaabbaaabbababaaaaaaaaaaaaaaaaaabaaababaaaaaaababababbbbababbbbbbabbbababbbaabbbbbabbabbaaababaaabaabaabbabbbabaabbaabbaaaabababaabaaabbabaabaababaabbbabbabbbaaabbaabbbbaabbbabaabbababaabaabaabbabbbbabbabbaaabbbaabaabbbabbbaabaaababaabbabbbbbbbbbbbbababbaabbbaababbaaaaabaabaaabbabbbbabbaabbaaaaaabbbbbaaababbbabaaabbaaaababaabaaabbabaababbbabbaaaaabbabbaaabbaaaababababaababbabaaaabaabbaababbaabaaabbaaaabaabbabbabaabbabbaaabbbbaabaabbbbabaaabaabbaaabababbbbabbbbaaaaabaababbababbaaaabaabaaababbbbbabaabaaababaaaaabababbabbababaaaabbbabbbabbabbbbaabbabbababbababaabbbaabbaaabbabbbabbbaaaabaaaaaaababaabbabbbabbbbabaaaabbbbabbbaabaababbaaabbaaaaabbbbbbbbbbbbbaababbbabbbbbbbbabbaababbaabbbabbaabbbabaaabaabababaaaabaaabaabbabaaabbabaaabbbbaabbaaaababababbbbbaaaabbbbaaaabbbbbaaabbabaabaabbbabbbaababaaabbbaababaaaabbababaabaaaaaaababbabbbababbaabaaaaabbbbaabbaaabaabaaaaaababaaabbbabaaabababaaabaabbbabbbbbabaabaaababbbabbabbabaabbaaabbaabaabbbabababaaabbbabbaaabbaababaabbaabaaabaaaababbbaaabababbaaaabbbabaaabbabbbabbbbaaaaaaabbbbbbabbaabbbabbbababaaabbbabbaaabbbbbbbbababababbbbbaabbaabbbbaaabbbaabbaaaaaaababaabbbbabbaaabaaaabbababbbabbbababbbabbabbbababbabbaaaabaabaababbababbbaaaaabaabaaabbbbbbbabbbbaaaabababbbabbbbaaaaaaabbbabbbaaaabbbbbaababbaaaabbaaababbaaaaaabbabbbabababbbbabbabbbababbaabaaaaaababbaaaaaaaaababaaaaaabaabaaaababababaabaaabaababbbaabbbaabaabbabaaaaaabbbbbaaaaaabaabbbababbbbabbbbbbbbbbabbaabbabaababbbbababbaababaaabbaaaaaaabbbabbaaabbaaabaabababbabbbbbbaababbabaaaabbbabababaaaaababaaaaabbbbaaaabbabbbbbbbaaaabbaaabbaaabbaaabbbaaababbaabaabbaababbabbaaaaaababaaababababbbaaabbabbbbbabbaabbbbbbabaaaabbbaaababbbaababbabbabbaabaaaababbbbababbbabbaaaababaabaabaaabbabaababaaabaaaabbaabbabbabaaaaabbbaababbbaaaabbbababbbbbaabbabbbabaaabbaababbbababaababababbaaabbbaaabbbbababaababbaabaabaaaababababaaaabaaaaabababbabbbaabaabbabaaaaabaaaaaabbbaaaaabbababbbababbabbabaabaabbabbabbaababaaaabbabbbabbbbbbabbbabaabaabbabaabaabbbbbabbabbbabaabbbbaababbaaabaaabbbbaaaabbabaabbababbbbabbaabaaababbabaaaaaaabbabbabababaabbbbbabababaabaaabbaabbabaabbbbaabaaabbbbbbbbbabaababbbbbababaababaababbbbabaaaaaaabaabbbbbbaabbabaaabbbbbbbabbaaaabbaabbbbaaabababbaaabaaabaaababbabaaabaaabbabbaabbabbbabbaaaaabaabbbbabaabaaabaaaaaaaabbbbaaaaabaabbaaabababababaaabbbaaabbabaabababbabbaaaaaaabaabbbaaabbaabbabaabbaabbbabbbabbbbbaaaabbbbabaabababbabaaaababbbbaaaabbbbaaaabaaababbababaaaaababaaaabaaababaaabbaaaabababaabbaabbabaabbbbbbbbabbbaababbabbaabbaabaaaaaabbaababbbabbbbbaaaabbabaaaabbaabbaabbbaabaabbbbabbababababbababaaabbabaabbbbbabbabbbbaababaaabbaaaaaaabbbabababbbbaaaaabbbbbbbbaabaaaabbbaabbbbbbaaababbbbaabbaaaaaaabaabababaabbaaaaabaaaaaaaabbabbbabaabaaababbaabbabbabbaaabbbabaabbbbabaaabbaaabaabbbababaaabbabaabbbbbaaaaabbabbabbbbaabaabbaaabaaabaabaabbbbaabbbbaabbbaabbaabbaaabbbbaabbabbbabbaaabaaabbbbbbaaabbaaaaaaaabbabbbbaabbabbbbaaaababaabbaaabaaaabbabaaaabaabaaaaababbaaaaabbababbbbbbaaabbababaabababbbabbbbbabbababaabaabbbbabaaabbbababbaaaabaababbabbabbaaaabaabbabbbbaaaaabbaabbababbbbbbaaabaababbaaaabbbbaaabaabaaabbbabaabbbbaaaabbbababbbabbaaaaaabaababbbbabbabbaaaaabababbbaaaabbabaaaaabababaaaabbaaaaaaaababaaaaabbbbbbaaababbabaaababaaaaaabaababaabbbabbaaabaabbaaabbaabbbbbbaaaabbbababbbabaaabbabaaabbbbbaababaaabbabaabbbaaaaaaaabbabaabbbaabaababaaaaaabbabaabbbbbaaabbbaababbabaabbabaaaabaabbabbbabbbbaabbaaabbabbbabaaabbaaaabababaaabbabaaaaaaaabaaababbbaaaabababbaaaaaababbbabbbbbabbaabbbabbaaabbbabaaaaaaaaaabbaabbabbbaaaaabababaababaabbbbaaaaaaaaabbbbbbabababbbabaaaaaabaaaaababaabaababbabaabbabaabbbbbababaaabbbaaaaabbbabaaaababbabaababababaabbaabaabbbbbbaabbababaababbababbabbaabaaabababbbbabababaabbaabaabaabbbaaabbaabbbbaaaabbbbaaaaaaababbbbaaabaaaabababaaaabaabbaabaabaabbaabababaaabbaabaabbbaaaabaababbabaabbbbbaaaabbbaabbabaaababbbbabababbbbabaabbbaababaababbbbaaabaaaaabaabababaabbaaaabbbaabaaabbaaababbabbbbbbbbabbaababbbabbbabaaaaababbbbabbabbaaaaaabbaaaaababbbababbaababaabbbaabbbaababbabaaaaabaabbbabbbbabbababaaabbbaabbbaabbabaabbbaabbabaaabaaabaabbbaaaabbbaaaaabaabbaababbabaaaaaaabaaabababaabababbaaabaaabababbabaaaababbbababaabbbabbaaaaababbbabbbababbbaabbaaaaaaaaaabaaaaaababbabaababbababaaabbaabababaaabaabaabaabbbbababbbbabaabbaaabaaabbbaabbabbbabbaaabababbbaaaaabaaababaaaaaabbbbabbabbbaabababaaaaaabaabbbaabbbaaabbababbaabbaaabbababaabaaaaaaaabbbababbbababaabbaabbbabbabaaaabaababbabbbbaaabaabababaaababaabbbaaabbbbabbbbaaaaabbbabbbbbabbbaaabaabaaabbbbbbbabbbbbababbbbbbbbaabaabbabbaaaababaabababaabbbbbbaaaabbbaabababbaabbabbaaaabbaabbbbabbabbaabbbbbaaaaabbbbbabbbabbaaabababbabbabbbbabbbbaababbaaaabababbbbaaabbbaaaababaabbbbaabbbaabbbbbabaaabbbababbbaabaabbabaaabbbbababbbbbbbabaabaaaabbbaaabababbabbaabbbbabbbbbbabaababbaaabaabaabababbaaababaabbbbbbbbbaaabaaaabaababaaaabbabbbbbbaabababbaababbabaababbbaaabbaaaabaaabbabbaabbababbabbbaaababaaaabbbaabaaabababbbbbbabababaabbbbabbbbabaaaaaabaababaaaababbabbabaaabbbbaabaaaaabbabbabbbabaaaababbaabaaabbabbaabbbbababbbbbbbbaabaaaabbaabbaabbaabbbaaaababbabbabbabbaabbbbaaaaaabbabbbbbabbaaaabbbabababbabbbabbbbaabaabaaabaaabbabaabaaabbbbabbbababaabbabbbaabbbbbaaabbbbabbbabbabababaaabaabbaabaaaababaabababaaaaaabbbababbabbbabbabbbbbaaababbabbbaaaaabbbbabaaaababbaaaaaabbbbbbbbabaaabbabaaaaaabbbbababbabbbbbbabbbbababbbaaabbabbbbaaabbbbbabaaabaabbaabaabaababaabaaaaabbaabbbabaaabbabababbbbbaabaabaaaababababaabbabbaaababaaabaabbbababbbabaaababbaaabbbbbbbbaababbaaabbbabaababbaaaaababbbaabbbabbbaaabaabbaababaabbbbbbabbbaabbbbababbbaaabaababbbbaabbaaaabbaabbabababbaaababbaabbbabaaaaaababbbaabaaaababbbbbabbbbbaababbbabaaabaaabaabbbbaaaaabaaaabbbbbaaabbbbaabbabbbabbbbaaabbbbaaabbaabbbabbaaabaabbbbbbababbabaabbaaabbabbabbaaaaabaaaaaabbabbaabaaaabbbbbbbbbbaabbaaaabaaabbabbabbbbbbaabbbabbbbbbbaababbbabbaabaaababbaaabaaabbbaaaaababbaaaabbabbaabbaaaaabaaabaaaabbaaabababbaabbbbbbbbbabbbaabbabaabbbabbbbabbaabbbbbabbbbaaababaabbabaabbbbbaabbbabbbaaaabbaaaabbabaabababbaaaaabbabbaaabaaaaabbaaaabaaabbbbaaaabaababbabbbabaaabaabaaabbabbbbaababaaaababbbababbbbbbaabababaabbaaabaabbbabbaababbbabbbaababbabbbbbbbabaababaabaaaaaaaaaaabbaaaabbaaaabaababbabbaabaaaababbabbbabbaabaabbbaababbbaaaaabababbaabaabbabaaabbbabaabaaabababaabbbbabbbaaababaaabbbaabbaabbaabaaaaaababbbabbabbbbababbbbababbaabaaabbabababbabaababbbbbbbabaaaabbbbbbaaabbabaababbbbaaaaabbabbabaaababaaaababaaabbaabaababbabbaabaaabaabbabbabaabbbbbbaaabbababababaaabaaaaabbbbabbaabaabbbbabbabaaabaaabbbaabbabbabaabbbbbaababbabbaaabbaababbaaaabbababbaabaaaabbababbbbaabaaaaaaaabbabbbbabaababaabbaabaabaaabbaababaababbbbbabbaabbbaabaaababababbbabbababbabbaaaabaaaaabbbabbababbaabaaaabbbbbbbabaabbabaabbaaabaaabaaaaabaaabababbababbbbabbbbabbbaabbbbbaaaaaaabbabaabaabbbbabaaaaabbbbaabbabbaaabaabbbabaabbbabaabababbaabaababbbababbbabaabbbbbbbabaabaabbbabbaaabababaabbaabbaaaaabaabaabbbabbbbbaaababbabaabaaabbbaabbbaaaaababbbaaabaaabbababaaabbaaaabbaabbbbaaabbbabaababbbbababaaaaabaabbaabaaaabbaaaaabbaaabbbaabaaababbaaaaabaaaabbaabababbbbbbbbaabbbbbabbaabbabaabaabbaabaababbbababaaaaabbbbbbabbaabbaababaababbabbbabbbbabbbbaabaabbbabbababaaaaabbbbaabbbbbbbbbabbaababaaaaaaaaaaababbbaabaaababbaaababbbbbaaaaabaabbababbbabbbaabbaaababbabaaaaaaabbbbbabbabbabbaabbaaaabababbbababbbbabbbaaaaaaabbabbbbaababbbabbababaabaaabbbbabaabaaabaaaaabababbbbabbaaabaaaababbbabbbbaabaaaaaabaabbaabbabaaaababaaabaaaabbbabbbbbbaaabbaabaababaaababbaaaababaaabaabbbaabaabbbababaabbbbabaaaababababbaaaaaaabbaaaaabaaabababbbaabbaabbaaabaaaaaabbabbabababaaabbbabaaaabbbbaaabbaabaabbbbbaabbbbbbbbabaabaabababaaababaabbbaabaaabbaabaaaabaabbbaaababbbabbabbbbaabaaaaaabbbbbbaaaaaaaaaaaabbbaabbababbaaabbbbabbababbbbbbabbabbbabbbaaaaaabbababaabaababbbbbbabbbaababbbabaabababbabababaaababbbbaabbaabaaaabbbabaabaaabaabbbabababbbaabaabbaabaabbbbabaaabbaabbaaabababbaabaabababbaaababbbbabbaababbaabaababbaabbaaaaabbbababbabababbbbababaabaaabbababababaabaaaaabbbbabaabaaaabaabbaaaabaababbaababbbbababbaabaabaaaabaabababbababaaaabbabbbabbbabaabbaaabaabababaabaaabbaabaaaaaaabbbbaaaabaaaababbabaabbbbbaaaaaabbbbaabababbbaababababaababbaabbabbabbbbbbaaabaabbbbaaabaaaabbbbababbbaabbbbbbbaaabaabbbabbaababaaaaababaababbaabaaababbbaaabaaaaabaaabaaabbaaababbbbbababbababbaaabaabaaabaaaaabbababbabbaabbbbbbbbbaaabaaabababaabbbabbaabbbbbaaaaababbbaaabbbaababababbabbabbbabbabbbbbbbbbaaaaaababaaaaababbababbaabbabbbbbaaaabababbbabaabbbaaababababaabbabababbabaabbbabbaaaabbbbbabaaaababbaaababbbbaaababbbaabaababaababbbbaabbbabbabaababbaabaabbbbaabaaaaaaaabbbabbabaabbbbababaabbaabbbaaaaaabbbbbbaabaaaabaabbbbaaaabbbbbabbbababbbbbaaabaaaaaabbbbbbaababbbbaaabbbbbabbabaaaabbbbaabaababbabbabbbbababaababbabbaabbabaabbabaaaaabbbbbaaaaabababbbaaababbaabbbbababbaabaabbbbabaabbbababbbbaababbaabbbabaaabaabaaaaaaaaaaaaaaaabaaababaaababaaaabbbabababbabababbbaabaababbbababaabbabbabbbababaabaabaabbaabababbbbabaababbbaabababbabbbaaaabaababaaababaababaababbbbaabbbbbbbbbbbbbabaabbaabbbbbabaaabaabaabaaabbabbbaababbbaabaaaababbaabbbbbaababbbabbaaaaabbbbbaaaaaabbbbbbbbbbbaaaaaabaabbaaaaabaaaaabaaaabaabbababbbaabbbabbbbaabababbaaabbbaabaabbabbbbababaaaaababbabbbbbbaaaabbbbabbabbbabaabaabbaaabbbabbbbbaaaababbababaaaaaaabbbaaaaaaababaaaabbabbbbababbbabbabbbabababbaabbabaaabbbbabbabbaabaaaaaabbabbabbbabaaabababbbbbbbaaaabaabaabbbaabaaaabbaaabaaabababaabaaaaabbbbaaabaabbaabbbbababbaabbbbaaaababababbabbbbabaabaaabbbbbaaababbabbababaabbbbabbbbaabaaaaaabaaaababbaaaababaaaababbbaabbaabbbbabbbabbaaabbaaabbbabbaabaaaaaaaaaaaaaabbaabbababaaabaabbbaabbbbaaabbbbbaabbabbbababaabaaabbbbabaaabbababaabaaabaaaabaaaaabaaaababaaabababbabaabaabababaaaabbaabbaaaabaabbaabaabaabbbaabaababbaaabbbaabbbbabaaababbaabbbbabbabbbabbbbabaaabababbbbbababbaabbbbaabaaabbbaabbaabbbbaaaaaabababababbaabaaababbaaabaaabbabbbbabaaabaaaabbaabaaaabbbababbaababbabbbbabbbaaaabbbbaabbaabaaabababbbbaabaabaaabbbabbaababababbababaaabaaaababaabbbbbabbbabbaaababbaaabaabbaabbbbabbaaaabbabaababbbbbaabbabaaaabbabbbabaaaababbbbbaabbbbaaaabbbbaabaabababaabbbbabbbbbbabbbababbbbbbbbbbbbbabbbbbaaabbbabaaabbbbbbbbaabbbaaaabbaabbbaaaaabaabbbbbbababbaabababbaaabbabbbababaabaaaabbaabaaaababbabababaabbbabbabababbbbbabbbabaabbbbabababbaaaaababbbbaabaaabaabaaabbababaaaabbbbbabbabbabbabababababbabaabbbabbaaabaaaaaaababaaabbabaaabbaaaabbabbaabaaaabaaaaaaaabbbbaabbbbbaaaaabbaaaaabaaaabbbabbabbbbabbabaababbababaabbaaabbbbaabaabbbabbaaaabbbbababbbabbbbbbbaabbbbababbbbbbababbabbbaabbbbbaabbbabbababbbaaabbbbaabababbbbabbbaaabbbbaabbaabaaaaababbbbbaaaabbabababaabababbbaaabbbbbbbbaabaaabaaaababbabbabbaabbbaaaaababbaabbbabbbbbababaabbaaababbabbbaaabbbabbbbbbaaabbaabbbbbbabaaaaaaaaaabbabaaaaabbababababaababaabbbabaabababababbbabbabbbabbbaabbbbabbabababaabbbbbbaaaaaaaaaabbaaaaaabbbabbaaaaabbabaabbbbabaaaababbaabbbbbabbaaabaabaaabbaaaaabbbbabbbbbababbabbaaaabbbbbaaabbabbababaabbbbababbbaaaababaaaabbbbabaaaaaaaaaaaababaabbaababbbbbbbaabaaabbaabbaabaabaabbbbbabbbbaaabbaabbbabbbababbaabbaabaaabbaaaaabaabbbbabbbbabbaabbbbbbabbbbbabababbabaabaaabaabbbabbbaabbbbbbaaabbaabaaaabaabbaaaaaaaabbabaabbbbaabbbbbbabbabbbbaabababbbbaaaabbaaaaaaaaaabbaabaaabbaabbabbbabaababaabbabbbbabbababbbaabbababbaababbbbabaaaababbabbbaabbbabaaaabaabaaabbabbaabbaabbbaababbbbbababbbbbabbbaaabbbbabbaabbbbbbabaababaaabababaabbababbabababababaaababababbababbabbbabbbaaabaaabbbbaaaabaabaaabbbaababbaabababaaaaababbabbbbabbaaabaababbbbbababbabaaaaaaaaaaababaaaabbaabaabaabbbaaaaabaaaabaababababaaaabaababababaabbbbbbbababaababbabaabbbbbabbbbaaaaababbbabaabbababaabbaaaaababaaabaabbbbbbabaabababaabbbbaaabaabbabbabaaaaaaabaaaabbabbbaabbbaaababbbaaabbbbaaabbbaabaaabbaababbbbaabbaaabababaaaabaaabbbabaabbbbaaabaaababbaaabbbbbabbabbaaababbaabbaaaaabaabbabaaababaabbabbaabbbaabaaabbbabaabbabbbbbaaabbaabaaaaabbababaaabbabbabbbababbbbbbbaabbababbaaaaabbabbbbbaaaabaababbbbbaabbbbbbaaabbbbbabbbbababaaabbaabbbabaabaabaaaaabaaaabbbabaaabaabbbbbbabbbbaaaabaabbbaaaabbaabbbbabaabbaabaabbbbaabaabbaababaabaaababbabbababaaaabbbbabaaaaaaaaaababbaaabaaaabababaaaabbbababaabbababbbbaabababaaaababaabbbaabaaaaabaabbabbaaaababbbaaaabbaaaaabbbaaabaaaaabbabbabbabaabbaabbaabbabaababbaaabbabbababbbbababaababaaabaabbabbaabaababbabbababaababaaaaaababbbbbabaabababaaababaaaabbaaaabbbabbbbbbbbabbbbbbaabaabaaabaaaaabaabbabaabaababaaaabbbaabbaaabbabbbbabbbabaabbaaaaaaaaaabaaabbaaaaaaabbbbabbababbbbaaababbbbbbaabbaaabbbaaaaabababbaabbabaaaaabaaaaaaabbbbbababbbabaabaabaaaabbbababaaaabbaababbabaababbaaabbbaaabbbaabaaaaaaabbabbabbabbabaabbaabbbabbaaaaaaaabbbabbbbbbbaaaabbbbabbbbabaaaaabaaabbbabbaabbababaaababaabbbbabbbabbaaaababbabaababbaabaabbabbabaabbaababbbabaabaaaabbaaabbbbbababbbaabbbaabbbbbbbaaabaaaaabbbbbbabbabaaababbbbbabababbababbbbababbbbaabaabababbbaaaabbbabbbbbbabaaaaababbbbababbbbbaababababaaabbbbbbbbbbaabaaabbabbbaaabababbaaaabbabbaabaaaabbbabaaababababababbabbbbabbaaabaabbaaaaaaaaababbbabbbbbbabaabbaaaababbaababaababbaaaaaababaaaabbbabaaabaaabbaaababbbaaabbbabaaaabbabbbbabbbabbbbaaabaabaaabbbabbaabaabbbbbbbbbabbbbaaabaaabbabbaabbbabbbabbbbababbbbbbbabbbaaaabbaabaabbabaabbaabbbabbbbbabaaabaaabbaabbabbaabbababaaaaaabababbaaabbbaabbbbbbaabaaaabbababbbbababbabbbbabaabbbbbbabaababaaaaaabaabbbbbbbbabbbbaaabbabbaaababbababaaaaabababaaababbbaabbbbbbbabbaaabbabbbaaababbbabaaabbaababaaaabbbaababaaaabaabaabaaabbbbbbabaabbaaabbbbabbbbababbbbbaaaaaababaabbaaabbbabababbbbbbabbbabbaaabaabbbabaabbaabaaaaaaaabbbaabbaababbbabbbabbbbabababaaabbaaaaaabaaabaabbbbbaababaaaaabbbbbbbabbbbbaaaababaaababbaaaaabbbababbaabbbaaaaaabbaabbaaabbbbbbbbbbababaababbbaaabaaaabbaababbaabababaaabaaabaabaababbabbabbaaaaaaabaaaaaabbbbababbbaaaaaabbabaaaabbbaabbababaaaaaaaabaaabbaaaaababaabaabaabbbbbbbaabababbbbabaabbbbbabaabbbaaababaaaaaabbbabaaababaababbbbbaabbbaaabbaabbbabaabbaabbbabaaabbaabaaaaaaababaabaaabaaaaaabbbbaababaabaabaaaaabbabbabaaabababbbabaaabbbbbaaaaabaabbbababbbbbaaaabbaaaabaabaabaabbbbaabaabbabaabbbabbbbabbabbbaaabbbababababbbbaaabbaabbbbbabaaaaabaabbaabbbababbbbabaaaaaaabbbbbbabbbbaaabbabababbaabbaabbaabababbbbabaaabaabbaaaaabbbbaaaabbababbbabaaabbababbabaabaabbabbbbabbaaabaaaababbababbbabbbabbaaabaabbbbbaabaabbaabaabaabbbaabbbbabaaaaaaaaabbbaaaabaaaaaaaababbbbbbbaabbaabaaabbabbabbbbbbbbabbbaabbbaaaabaabbabbababbbbbabbbabbabbabbbbbaaababaabbabbabaaababbabbababbbabababbaabbabbbabbaabbbaaaaababbbabbabaabbbbbbaaaaabbbabbaabaabbabaabababaababbabbaababbaabbabaabbbaabaababbaaaabbbabbbbabbbbbaaabababaabaaaaabaababaaaabbaabababaaabaabababbabaabbbbbbababbbbbabaababbaaaababbbbabbbbaaabaabbbaababaaabaaaababbaabbbbabbbbaabaababbbbaabaabaaaabaaabbbabababababbbbaabaabaaaabbbbaaaaaaabaabbbbabaababaabaaabbbabaabbababaabbaabaabbbabbababbabaaaabbaabbaaaaabbabbaababaababababbaabbaaaaaabbaabbbaabbbbbabaaaabbaabbbababbbaaaaabbbbbabbbaaaabbabbbbbaabaaabbaabbaaaaaababbbbaababababaaaababaababababaabbbabaaabbbaabbbaababaabbbabbbbbaaaababbaaaabaabbabaabaaaaabaaabbbbaababababbaabaabbbbbaababbabbbbaabaabbaabbaaabbaababbbabbabbaaaabbabbabaaaaabbabaaaaaabbabaaabbaaabbaabbaabbabbaabbbbabbabaaabbbbaaaabbabbbabbbbbbbbabbbaaabbbaabaaabaabbababaaabbbabaaaabbaaabbaabbbbbaaaaabbbbababbaababbabbbbbbabaabbababaaaaabbaababaabaaababaaabaabbbbaaaaabaaabbbabbbbaaaabbaaaababbbababaabaaabbaaabbaabababbbbabbabbaabbbbbbaaabbbabbabbbbbabbbbbaabaaaabbbaabaabbaababbbabbabababbabaabbababbabaababaabbaabbabababbaabbaaaabbbbbbbaaaaabbaabbbaaabbaabababbababababbbabaaababbbbbaababbbbabaabaaabbaaabaaabaaaaabaaaaabbabbaabbbabbbbabaaabbabbbbbaabbbabbaabaaaabbbbbbababbbababbbbbabbbbbaaababbaaaababbabaaaabbbaabaabbbabbbabbababbaabbabaabbbaabbabbaaabbbbbbaabbabbaaabbabbbaababababbbbbbabababaaababaabbbbbaaaaaaabbabbbabbaaababbaaabbbabbbbabbbaaaaabababababbaabbabbabaabbabbabbbbaabaabbaaaaaaaaaaabbbbbaaabbbaabaabaabaaabaabbaabbbabbbbabbaaaaaabbbbabaaaaabbaaaaabaabbbaabbbbbbabbbbbbbbaabbabaaaaaaabbabaababbbabbbaabababaaaabbabaaaaabbbbbbababababaabaabbabbababaaabbbbaaababaaaaabbaaaabaaabbabbbbababbaaabaaaaababbbbbaabbababbabbbbaabbbbabbabaaabbabaabbbbbaaaabbabaaaaabaabbbbabbabbbababbabbaabbbbbaabababbabababbbababaaaaabaabbbababbabbabbababbbbbabbababbaabaaabababaaabaaabbaaababbaaaabbabaaaaaaaaabbabbbbaababbaaabaaaaaaabaaabbabbbabbbbaaabaaaaaaabbaaabbbbaaabaaababaabbbaabaaaaaaababbaaababaaabbaabbbabaabbaabababbabbbabbabbaaabbaaaaabbbbbbababaabaaababbbbbbababbbaaabbbabbabbbaaaaabbbbaabbabbbbaababbbabbaababbabbbaababbaaaaaabaabbbbbabbabaababaaabbaababaabbbaaabaabbabbbbaababaababaabbbaabbbbbbabababaaabbbbaabaabbbabaaababababbbbbaaabbbbabbbbbbbbaababbbabaabbabaabbbabbaaabaabaabaabbbbbbabbaabaaaabbaabaaaaabaabababbabbbbbabababbaaaaabbbbbaabaaaaaaaaaaaaabbabababbbbbbbbabaaaaabaabbabaabbaaabbbabbabbabbabababbbbbaaabaabbaaabbabbbbbbababbaabbbababbbbbbabababbbabbabbbabbbbabbbaabbaabaabababbbababbbbbbbbbbbaabbabaaabbababbaaabaaabbbabbaabbbbabaabaaababbaabbabbbaabbabbbabababaababbaabbbaaababbabaabababbbbbabaaaabaaaabaabbbaaaaaababbbbabaaaaaaaaaaaaaabbbbbaaabbbbaabbaabaabababbaaaaabbbbbabaabaabbabbaabbbbabababababbabbaaaaaaaabbabbbaaaabbbabbbbbaabbbbbbaaaababbbaabababaabbababaaabaaaababbaaabbbbababababbbabbbaaaaabaabbaabbbbabbababbabbbbbabaababbbababbababbaaabbaabaaaaaaaababbaabababaabbaabbaabbaabbaaabbaabbaabbaaaabaaabaaaaababbaabbbbaaaaabbababbabbababaababaaaaaabbbabaabbaabbabbbababaaabaabbaabbbabbbaaababbbabbbaababbbbabbaababbababbabaaabbaabaabaaaaaabbbabbaabbabbaaabaabaabbbbaabaabaabaababaaaabaababbabababaabbbbbbaaabaabbbbbbabbbabaabbaaababbbaaabbaaaaabaaaababababaababaaaabbabbabbbaabbabbbbaaabaababbabbabbbaaaaaabaaaaaaabaaabbaababaabaaaabbabbbbbababbbbaababababaababaabbbaabaabaabbbababbabaaaabbbbabbaabbabaabbbbbbabbbbababbbbaabababbbbbababbbbababababbaabbaaaaaaabbbbbbbaaaaaabbbbabbabbbbaabbabbababbabaaaabbaaababaaabaabaabaababbbbbabaaababaabbbaaabbabaabaaaabbabbabbaaabbbbbbbbbbabbababbabaabbaabaaabbaaaabaaabaababbbbbbaaabbaabbbbbabbbaaaaaababbbaaababbaabbaabbaaaabababaaaaababbbabbbaababaaabbbabbaaabbbbaaaabbabaaabaaabbabbbbbbaaaaabaaaaabbaabaaaaabaabaababbbabaababaababbabaaabbabbaaaaaabaabaaabbabaabbbbaabbbaabbaaaababbbbbbbbaabbaabbaabbbbaabbbbaaabbabbbbbaabbbababaabababbaaababbbaabaaababababaabbaabaaababbbaaabbaaabbabbbaaaabbbabaaabbabbababbabaaababababbabaabbbbaabbbbbbabaabbaabbabaaabababababbbabbaabbbbaaaaabbaaaabbbbabbbbbaabaaaaaabbabaababaaabaabbaaaabbababbbaaabbaabaabababaabbbaaababaabbbbaabbaaaababaaabaaaabbaababbbaaabbbbbabbaabbabbabbbaabaabaaaaabaabbaaaaabababaabaabbabaababbabababbbbaabbbababaaabbbbbaaabbbbbbaaaabbbababbbbaaaabbbaaabbaaaaabaabbbaabbabbaabbabaaaababbbbbbbaabbaaaaaaabbbabaaaababaabaababbbabaaababbaabbbbaaaabaaaaabbabaaaababaaaaaaabbbbaaaabbaabaabbbbbbbaaabbbbababbbaaaaabaabbaabbaaaaabbabbaaabbaababbbaaabbbaaabbabbbbbbababbbbbbaaabbbaabbaaababbbabaabaabbaaaaaabbbabaabbbaababbbaabbbbaabbbbabbbabbaabaabbaaabbbababbbbbabaabaaaababbbaabaababbabbabaaaabbaaabbaaabbbbbaababbbabbbabaabababbaaaabaabbbaaaaabbbbbababababbbaaabaaabaaaabababbbbaabbababbabbabaababbabbbaaabbaaaaaaabbaabbaababaabaabbaabbabbbbaaabbabbabbababbbbbbbaababbaaabbabbaabaababbababbaaaaaaabbbbbaaabbbaaabbbbabbbabbababaaababbaabbbabbbaabbabbaabbaabbbbabbbbabbbabaaaababbaaabaaaaabbbabbbababbaaaaabbaabaabaabababbbbbbabaaabaaabbaabbbabbbbaaaabbbbbabababbabbbaaabbaabbabababbaabaaaaabbabbabbaabbabaabbaabbbbabababbbbbaaaaaaababaaaababbabaaabaabaabaabaaaaabaabbaaabaabbababaabbababbabbbabbbabbaabaabbaabaababaaababaabbbabaababaaaabbbabaabaabbaabaabbabbaabbaabaaaabbbbbaabababbaabbababbbbbababbbbbaabbbbbabbaabaaaaaaababbbabbaabaabbbabbbababbbabbbbaabaabaaaaabaaabbbabababaaabbbababbaaaaaaabbaabbabbbbaaabbaaabbbababbabaaaabababbbaaabbabaabbbabaababaaaaabbaababababbbabbaaabbbbbbbaaaabbbaabbbabbbbbbaaabbabaabbabbaaabaabbaaaaabaaabaababaabbbaababaabbababbbbbbbbaaaaaaabaabaabaabaaaabaabbabaaaaababaaaabababbabbbabbaabbaaabbbaabbbbabababbbbbabbaabbbbabbababbabaaabaabaabaabbaabbbaabbbbaaabaababbbaabaaaaaaabababbabbabbaaabbbbbabbbaabbabbbaaabbaababbaabbaaaabbbaaaababbbababbaaaabbbabaabbaabaabbbabaabaabaaabbbaabbbbbabbaaaaaaaaabaaabbabaabbbbaabaaabbabbaabbaabbbbbbabbbaaaabaabaababbaaabababbbbbabbbbaaabaababaaabaabbaaabbaaaaabbabbabaaababbbabbbbaaabaaababbbababaabaaabbaaabbabbaaaaaaaabbabbabbaaaaaabbababaaabbbbabbaaabbbbbaabbaabbabababbbaaabbaabababaaabbabbaaaaabbaabaaabbabababaabbabaaabbabaabbbabbbbbbaaaabbbbbaabbaabbbbbbabababbbabbaabbabbbbbbabaabbbbbbbbabbaabaaabbbabaaabaababbbbaaababbaaababaababaabaaabbabbaabbabaabbabbaabbbaaabbbbbbababbbabbaabbbababbbbabaabaabaaaaaabababbbbbaaaabaabababbaababaabbabaabaababbaababaabbbbaaaabaabbaaabbaababaaabaabababbbbbbabbbbbabbbaaabbababbaaaabbabbbbaabbabababbbababaaabbabaabaabbaababbbbbbbbaaabbbbaaaabaabbabbabaaabaaabbbbbbbbaabaaabbbabaaabbbbbaabbabaaaabbbbbaabbabbbbaaaaaabbabaababaabbabbbbbbbaaaaababbababbbaabbaaaaaabbabaaabbbbbbaaaaaaabbaabbbabaaaaabaaaaaabababaaaabbabbbbabbabaaaaaaababbbabbbabaabaaabbaaabbaabbbabbabababbabbbabaabbbabbabaaaaaabbbaabababbbbabbaaabbbababbabbababaabbabbaaaaaaaabbaaaabbaaababbaaaaababbababbbbbbbbabbbbbbbbaabbbbaababaaabbbbaaaababbbaabbababaabbbbabbbaabbbbababbaababaaaaababbbbbbaaaabbbbabbabaabaabbbbbaaaabbaabbbbbbababbabbbbaabbbbbababbabbbabaabbbbabaaabaaaaabbbbabaababaabbabaababaaabbaaaaaabbaabaaaaaabaabbbbababbaaaaaaabababbbaaaabbbbaabaabaabababaababbbabbaabaaaabaabbabbaaabbbbaaabbaabaaabaabaaaaabbbbabbbaaaabbbaaabbbbaaabbabbbababaabbabbbbabbbbaaaaaabbbaaabbbbaaaaabaaaaababbbabbbbaababbbbbbbbbaabaabbababbaaabbababaababbbbbabbbbbabaababaabbabababbabbbbabbababaaaaaabbbaaaaaaabbbabbabbbabaaaabbaababaabaabbbbabaabbabaabbbbababbbbabbaabababbaaabbaaabbbabaabbbbaabbababbbababbaaabbaabaaaabbbbbbbbbaaabbaababaaaabaabaaabbbbbabaaaabbbababaabaaabbbabbbabbbababbbaabaabbabbabaaabbbbabbaaabbabaabaababaabbabababaabbbbbbaaababbbaababbabbabaabbabaabaaabaaaababbbabaabbbbabbbababababaaaababaaabbaaabbabaaaaaabbbbbbaaaabaaababbbbaababbababbabababbbabaababaabaabaaababbbabbabbabababbabbababaabbabaaabbbaaaaabbbaaaaabbbabbbbaaababbbaabbaababbaabbbaabbbbabaaabbaaaaaaabbababbbaabbababbabbbbabbaabaaabbababbbaabbbbaaaabbabbbbbbaabbbbbabaababaaabbaaababbbabbbbabbbbbbaaabbabaaabbababbbaaabbbbaababbbbabbaabbbaaababbbbbbababbbaaababbabbbbbbaaaaaaabaaaababbaabbbaaaabababaaaaaababbabbbbbbaaaaaaabaabaaaabbaaabbbbaaabbbbabaabbbbbaabbbbabbbbababaaabbbababbababaabaababaaabaaababbbbbbbbaaaaaaaaababbbaaaabbbaaaaaaabbbbaabbababbbbaaaabbbaaaabbbabaaabbbabababbbababbaaabbbaaabbbaaabbabbbbbbbbbbbaaaabbaabaabbaaabaabababbbbabbabbabbabbabbbbabbabaaaabbabbbaabbaaabaabbaababbbabbbabbababbbaabababbabbbabbaaabbbbbbbabbaabaababababaaabababbbaaababaaabaaaabbbabbaabbbbaaaaaabbabaabaababbbabbababbbaaaaaaabbbbbbbaababaaaababaabbabaababbbbabbbbaaaabaaabbaababababbabbabbbbaababbbbaaabababaababbbababbbbaabaabbbaabbbbbabbaaabbbbbaaabababababbbbabababaaaaabbabbabbabbabaaabbbabbabaaabbababbababababbaaaabbaaaaaaabbaabbaababbabbbaaababbaabbababbbaaaaabababaaaaabbaabbaaababbabbaabababababaabaabaaabbbaabbbbbbaaabbbaabbbaababaaababababbbaabaaaaabbbaababaabaaaabaabaaaaaaaaaababbbabbaababbbaaaaababababaababaabbbabbabbabaabaaabaabbbabaabbaababaababbabbaaaaaabaabbbbbbbbbaabababbbaabbbbaaaabbabbbbaababbbabbbaaabbabbbbbbbbbabbbababbbaaaaaaabbbaaaabbbbbaabbaabaabaaaabbabbaabaabbabbbaaabbabbaaabbbbbaaabbbaabbaaaaababaaaaaabbbbaaabbabbbbaaaaaaaaaaaabbbbbaaaabbaabbaaababbbaaababaaaaabaabaaabbaababbaaaaabbabbbabaaaaabbbaaabaababbbabaaaabbbbaabaababbabbaaabbabbaaaabaaabaaababbababbabaababaaabbababaababbaaaaabbbaabababababaaabbbbbbbbbbabbababaabbbabaaababaaabababbabaabbaabaaababbabbaaababbbaabbaabbbabbbaaaabbaabbaababababbaabbabaaabaaabaaaaabbaaaabababbbbaababaaaabbbbbbbbababababbbaaaaaabbaabbaabbbbababbabbaababababbbbabaaababbaabbbababababaabaaaaaaaaaaabbaaabaaabbbabaaaaabaaabbabaaaabaaabaabababaaabaaabbabaabbbbabbbaaaaabbbaabaabaaabaaaaaabaaaabbaabbaabbabaaabbbaababbbaababababaabaaabaaabaababaaaabbbaaaababbbabbbbbabbaaaaabaaabbaaaaaabaababbbbbbabaaaabbabbaabbbaaabbaaaabbbbbbaaabababaaaaabaabbbabaaaaaaaaabaabbabbabbbabaabababbaabbbabaaaaabbbabbbbbbaabaaabaabbbbaaabbbabaababbabbaabababbaababbaaabbbbaabbaaaababbbbabbaabaaabbabbbababaaabbabbbabaaaaaabababaabaaaaaaaaabbaaababbbbaabbaaabaaabbabbababaabaaababbabbaaaaaabaaaaabbbabbbbaabaabbabababbbbbababbbbbbababbaababbabababaababbaaaaaabbbabbbbbaababaaaababaabaababaabbabaabaabbbbababaabaaaaaababbababbbabbaaabbbbbbababbabbabbbababaaaaaaabbaaabbababaabbbbaaabaaaabbabbabbabbababbabbbaaaaabaababaabbbbbbaaabaabbbbbbaaaaaaabbbbbaaabbbabbbaabaaabaababaaaaababbabbabaaabbbaaababaaaaabbabaaaabaabbbbbaabbbaababbabaabbbaabbbabbbaabbbbabbbaaabaabababbbaabbabbabaabbaabbaaaaaaaaaaaaaaaabbaabbbbabbabbbbbabababbabaaaabaabaababbabababbbaaaaabbabaaaaaaaaaaaabbabaaaabaabababbabaaabababbababbbabababababaabbabbaabaaaaaaabbaabbaaaaaabaababbabababbaababaabbaaaaabaaabbabbbbbabaabbabbaaaaabbbbababaabbaabbbabbbbbaabbbaabbbaababaaaabababbbbbaabbbbbbaaabbbbbbbbbaabaabbbabbbbabbabbaaaaabbbbbbabbbaaabbbaaabaababbabbbaababbababaaabbbaaababbbaaaaaabbbaaaabbbabbbbbababbaaabbabababababababbbababbabaaaababbabaaaaabbababaaaaababbbbbbbbaaabbaabaabbbaaabbaabababbbbaaabaaaaaaaabaaaabbaabbababaaaaabbbbbbbabbabababaabbabaaabaabaabababaababbaaaabababbababbaabaaabbabbabbaabababbababaaaaaaabbababaabbaabaaababbbaaaabbabbbbababaaaaaabbaaabbaaaaaaaababaabababaaabaabbbababbaabbbbaaaabaabbabbababbbabaaabbabbaaabbaaaaabaabbabbaaaaababbbbbbbbaababbabababbaaabbaaabaaabbababaaabababbbaabaaaaaabbababbbbbaabaaaabaabababbbabbaabaabbaabbaabaaabbbbaabaaaaaaabababaaaababbbaababbababbaabbaaabbaaababbaaababbabaaaabbbbaaabaaaabaabbabaaaabbababbaabaaaaabaaaabbbbbaabbbaababaaabbaaaabababbaaabbbaaabababababaaabaabbabbaababaaabbbbababaabbaaabababaaabbabaaabbbabbbbbbbbbbabababbbbaaaaabbbaabbabbbababbaaaaaabbaaabaabaaabbbbababbbabbaaaaaababbabbabbaaabaaaaaababbbabaaaabaaaaabbaaaaaababaababaaaabbabbabbaabaaaaabbbbbbbaabaabaaaabaaabbaabbbbbbabbbbbbaabaabaabaababaaabbbbababbabbbaabbbbbbbbabbababaabbbbaaababaaaaabbbbbabaaabbabbabbbabaaabbbbabaaabaaabbabbbabbbbbbababaaabbbbbbaaabbabbabbaaaaaababababbaabaabaabbaabaaaaaababbbaaaabbbaabbabbbabaaababbbaabbaabbaaabbbbbabaaaaaaaabbabaabbbbabaabaabbbabbbabbaababaabbbabbaaababababbaabbbbbbaaabbaaaaabbbabbabaabbbbaaabbabbabbbabaaaababbaabbaaaaaababbaaaaabbabbabbbagaaabaabababaabbbbaabbabbabbaabbbbbbbbbbaababaaababaabbaaaabaaabbbabaabbbaabbbbbabbbbabaaabbabbabaabbaaababbbbbbaaabaaabababbbbbaabbaabbbababababbbbaababbaaaabbabbaababbababbaaabbbaaabaaaabbabaabbbabaabbbaabaababaaaabbbbaaabababbaaaaaaaabbbaababbabbbababaaaabbaabbababbbabbbabbabbaabaabababaaaabaaabbbababaabbbabaabbabbbaabaaabbababbaaabaaaababbabbabaaaaaabbabbbabbabaabbbaaabbababbaabbbaaabbbbbbbaabaabbbaabbbbabbbaabbbbaaaabaaabbabaaabaaaabbbabbaaaaabbabbabaabaaaabababbaabababbbaabbbbbabbabbabbbaaabbbabaabaaaabbbbabbbaababaaabaabaabbabbaaabbaabbbbabaabbbbbbbabaaabbbaabaababbbabaaaaaaababbbbabaaaabbbbaabbbaabaababbabbaaaaaabbbaabbaaabababbbaaabbbbbaaaabaabaabbbaabbbaabbbabaaaabaabbbbbabbbaabaaaaabababbabbaabbbabbabbabbbbababbbbbbaaabbbbaaaaaabaabababababbbaabbaaaaabaabbbabbabaaaaaababbabaababbaaaaabaabbabababaabbaabbabbbaabaaabbbaabbbaaababababbaaabbbabaaaabbaabbaabbbbaabababaaaaaabbbabaabbbbbababbaaabbabaabaabaaabababbbaabbbbaaaababaabaaabbababbbbaabbbaababbaaabaabaababbbbababbabaabbaababbbbbaabbbbbbabaabbbaaaabbabbabbbbaabaabaabaabaabbababababbababaabababbbbaaabaabbbbabbbabbaabbaabbaababbaaabaaabaabbaaabbaaabaaaaaaaabbaabbbbbabbaaaaaabbababaabbbbbbbbaaaaaabababababababbbaabbaaaaaababaaaabaababbbabbbaaaaaaabaaabaabbababbabbbbbbbbababbbbbbabaabababbbbabbbbbabaaaabaaabbaababaabbabbbbabbbbabbabbbbbaaabababbbbababaaabababbbababbabbaaabaaaaababbbbababbabbaabbaaaaaabbbbbbaaaabbaabbabbbbbaaabaabaabbbabaababababbbabbabaabababaaaababbaabbaaaabbbbbbaaabbbbaababaaaaabbbaabaabbaaaabababbaaabaaaaabaaabaaabbbaaabbabaabaaaaaabaaabaabaabbabaabaaaababaaabbabababaabbaabbbbbbbbabaabababbaababbbbaabaababbbaabbbbaabaaabbbabbabaabbbabbabaaabbbbaababbabababbbabbabbbabaaababbbaaaaabbaabbbbaabbbbabaaaabbbbaaababaaaaaabbbaaabbbabbbabbaaababbbbaabbbaaabbbababaaaaabbbaaaaabbababbbaabaaabbaabababbbaabbaabbbbaaaabaaaabbabaabaaabbbaabbaaababaabababaabbbaaaabbaaaababbaabaabaababbbaaababbaabaaababaaaabbbbaabbaaabaabaaaaabbaaabaaabaaaabaaaababbabaabbbbaaabbbbbaababbaabababaabbabbaaaabababaaabababbbabbbbabaaaabbabbbaaababbbbbbabbabbbaaaabbbabbaaabaaababbbbaabaaaabaaaaabbbaabbbbabbbbbabbbbbabbbbaaabaabbbaabaaaabbaababbaaabbbbbabaaaaababbabbaaaaaabaaaabbbaaabbbaabbaaabbbbbbabbaabaababbbbabbbabbabbbababaaaabababbbaababaababaaaaabaabbbabaaaaabbbaaabbabbbaaaababababaababbababbabbaaaaaabbbababababaababaaaabbbbbbababbabbaaaaabaaabbbbaaabaabbaaabbaaaaaabaabbbbaaababbaabbaaabbbabaabaabbabaabbabbbaaabaababaabaaabbbbabbbbbaabaabaabaaaaaaababbaaaaaabbababaabbabbabababaaabbbbbaababbabaabbabbbbabaabbbabaababbbbaaabbbabbabbabababababbbbababaaabbbaaababaaabbbaabaabbaaabbaaaabbbbabbbbbabababbaabaabbaaaaaaaabaabbaabbbaaaabaabababbbaaaaabbbabaababaaabaabaaaabbbabaabbbaaaabbbababbbbabaaabbabaaaaababbbaabbababbbbbaaabbbbbbabaabbaabbababbbababbbbababbbbbbabbaaababbaaabbababaaaabaabaaaababbaaaabaaaababaabbaabaaababbbbbbababbaabbbbabbabbbababbbbbaababbabaaaabaababbababbababbbaabbaababbaaabaabababbababbbabbababbbbbaaabababababbaabbbababbbaaabbbaaaabaabaaaaaaabbbabbbaaabababaabaaaabbbbabbabaababbaaaaabbbabbaabbaaaaabbbbaaabaabbbabbaaabbabbaabbabaaaabbbabbaaabaabbbbabbabbabbaababbabbabaaabaabbaaababbabbaababbbbbbaaabababbaaaaabaaabbaaabbbbabaaabbbaaabbbbababbbaabaabaababbabbbaaabaababbabbaababaaabbbbbbaaaaababbaabbabbababbababaababbbaabaababbbbababbbbabbbbabaaaaababaabbaabaaaaaaabbabbbabbabbbabaaaabbabbbaaaabbabbbaabbbababaabbaaabbabbbbbaaababbbbbbbbabbabababbbbbbaababbaabbaabbbbbabbaaaabbaaaaababaabaabbababbabababbababbaaaabbabbbbaabbbbbaaabababbbabbbabaabbaabababbbabbbbaaabababaaaabbbabbaababbaababaabbbbbbbbbaabaabbabaababaaababbabbbbbababbbabbabbaabbbaabbbaabaabbabbbaaabbabbabbbabbbaaabbbbbabaaaabbabbbaaaaaababbabbaaabbbabbbababababbbaaaaabbaaabbaabbabbabaaaababbabbbababbbaabbaaaaaabbababbbaabbababbbababaaabababbbbbbaababbabbabaaaabaaaababbaababaaababbbbbaababbaaabbbababbaababbbbbbbaababaaaabaaabaaabaaabbabababbbbbaaaababaaaaabaaabaaaaaabaababbbabbaaabbbabaabaabbabbbbbaabbababbbbbbabbabbaababaabbbabababbaabbababbbbabaaababbbbbbbabaabababbababbabbaaaabbabbbbbabbababaabbbbaababbaabbaaaabaabaaaaaabbaabbbbaabbbbabababaaabbbaaabbaabaabbbbabbbbbbbabbbbaababbabaaaabbaaabbbaaaaabaabaabbbbbaaabbabbaaaaabbaaaabaaaaabababaaaabababbbbabaabaabbbabababbbbababaaabbbbaaaaababbababbbbbbaaabbabaaaababaaabaabaababbaabbbbbaaaaaababaaabbbbbbababaaabbaabbbabbababbbbabbbbbaabaaabbbbaabbjaabaabbbaaaaaaabababbababbbaaaaaaaaabbaabbaabbaabbbbbbaabbbbababbbbbaaaaabaaabababbabbaabbbababbabbabbbabaabbbabababbaabbbaabaaaabababbabbbbaabaaaaaaaaabaabaaabbbaaabbaaaaabbabaaabaabaaabbbabbbbabaaaaabababbabbaabababbbabbbabaaabaaaaaaaabaaabaaaabbabbaabaabbaabbbbbbbbaaaaaababaaabbaaabbaaabbbababbbabbababbbbaaaababababbbbaaaaaababaababababaabbbabaaaaabaabababbabbabaababbaaaabbabbaabbaaababbbbaababbbbaaaabbbbababaaaaaabbaabaaabbaabbaababbababbbabbbaaaababbbabbbaaaabbbaaababbbbabbbbababbabbbaabbabbbabbbababaaaaabbaaabaabbabaabbbbbbaabaaaabaaababaabaabbbbbbabaaabbbabbbbbabbabbbaaaabbbaabbaabbaaaababaaaaabbaaaabbbbbbabbbabbbaaaabbbabbaabbbbaababbbababbabbbbaabbbaabaaabbbbabbbabbaaaaaabaababbbbabbbababaabababbaaaaababaabaaaabbbbaabbbaaabbbbaaaaabbbabaaabaaabaaaabbbabaabbaabbbbbbaaaabaabbababbbababbabbabbabbbabaaababaababababbbbbaabaaababaaaabbabbbbbbbaabaabbbaaabbbabbaabbabbbbababbbabbabbabbaaaaabbbabbaaabbaabaaaaabbabbabbbabaaaabababaaaabaaaaabaaaaaaababaabbbbbbbabbbbbbaaabbbbbbbbbbaaabbabababbaabaaabaaababbaaaababbaaaabbabaaabababaabbbabaabaaabaaababbaabbaababaaaabbbbababaabaaaaaabaabbaaabbbababbaaaaabaaaabaaaaabbbbbaaabaaaabbabaaabbabaabbabaabaababbbaaaabbbbababbaaaaababaabbabbabaaaaabbbabaaaaabaaaababaabaaababbabbbbbbababbabaaaaababbaaaaaaaabbbbabbaabbaaaaabbaaabaabbaaaababbbaabbabaabbabababababbbabbbbaababbabaaaabbbaababbbbaaaabbaabaabaaaaaaaabbbbbbaaabbbbbbbbbbaaabaaaabaababbbbbbbbaaaabbbbaabbaaaabbabbabbbabbbabbbbbbababaababaabbababbbaaaabababbabbbaabbaabbabaaabbabbabbababababbabbbaababbbaabbbbaabaabaaaaabbbababaaaaaaabbbababbaabaababbababbabbababaabbababbaabbaabaaaabbabbbaabbababbabbaaaaaabaabbbaabbaaaaaaabbaabbaaaabbbababaababaabababbbababaaabbbabbbaabaabbbababaabbaababaaaaababaabbaabbaabaaaabbabaabbbabbbbabbbbbabbaababbbabababbaabababbbbabaabbbaaaabbabaabaabaabbabbbababaabbaabbbaaaaaabbbbbbaabbabbabbaaaaabaabbbaaabaaaaababaabbabbbabaaaaabbabbbbaabaababbabbabaaaabaaaababbaabbbbbabaaaaaabbbbbbbbbbabbaabaababbbbababbbbaaaaaaaaabbbbbbaabbabbbaabbbaaabaababbbbaababaabaabbbbabbabaaaaaabbbbabaaaababbaabbbabbbaaaaabababbbabbabbaaaaaaaabbabbbaabaaababbaabaabaaabbaababaaabbbaababbabbbbabbbbaaabbabbabbabbbabbbbbbbabbbababbabbabbbbbbbbbbaaabbbabaaabbaaaabbbbbaaabbbaabbbbbababbbbbbabbabbbabbaababaaabaaabbabbaaaabbbabbababaaabaabababbbbbbababbbbaaabbababaaaabbbaaaabbabbaababbaabbaabbaabaaababaabbabbbabbbababbbababaaaaaababaabbaabaaaabbbaababababbbabaaabbbbaabbabaaababbbaaaababaaabababbabbabaaaabbaabbbaabbbbabbbabbbaaabaabbabbaababaaaaabbabbabbaabaaaabbaaabbbaababaabbbababaaabbbabbbbababaababbaaabbbaaaaaaabbbaabbbaababbbababaaabbaaaaababaaababbbbbabbbaabbaabaababaaaaaabaabbbabbbbabbaaaaaaabaaaaababbabbbabbaabbaabbababaaaabbbbaabbaaaabaabbabbbbabababbabbbbaabbbabaaaaaaaabaabaaababaabbabbbabbaabaabbabaaabbbbaababaabbbabbaababbbaabbaaaaaaabababbaaabaaaababbbabbbbbbabbbaaaaabbabbabaabbbabbaaaabbababababbabbbabbbabababaaaabbaaaababbabbbbabaababbaabbbbaababaaababbbababbabbabaabaabaabbabbbbaabaaaaabaaabaabbbbabaaaababbbbaabbaabbaaaabbbbbaabbaaaabaaabbabbaabaaaabbaabaaaaaaabbaabbbababbabaaaababbbaaabbaabbaaaabbabbbaabbababbabbaaaabaaaabbaaabbbaababbbabbababbabbabbbaaaabbbaaaabbabbaababbbbbababababbababbbbbbbbbbbbbaaabbbbbabaaaaaababaaabbbbbabaabbaabbbabbabbaaabaabbbbbbaabaabbabbbaaaaabababaabaaaaabaaaabaaaaabbaababaaaabbaabbbbabbbabbabbbaaaaaababbbaaabbabbaabbbbbaaaaaabaaaababababbaababbbabaaabaabbabbbbaaabaaababaababaaaaabaabbbaaababbaababaababaabbaaabbaabaaaaabbaabaababbababbaaababbababaaaababaaaabbbbbbbbbbabababaabbababaaaabbbaabaaaabbbbabaabaaabaaaaaaaaababbaaababbbaaaabaabaaaabababbaabbbbbbbbbbbaaabbaabbbbaaaababaabbbaaababaaabbaabbbbabbababbaaabbabaaababbbbbbbbabbabbababbbbbaababbbabbbababbbababbabababababbbbababbbbabbbbaabbbaaabaabaaaaabaaaaaabbabbabaaaabbbaaabbbabbaaabbbbbbbbaababbbbbbaabbbbbbbaaaabbabbbbabaaabbbababbaabbbbbabbbbaabaabbbaabbbababbabaabbbabbbaabbbababbaababbabababbabbbabbaabababbbaabbaaababaaabbaaabbaaaabaabbabababaaaabaabaabababaababbaabaababbaaabaabababbbaabbbabbbabaaabbbbaabaababaabbabbbabbabbbbbbabababbbbaabbaaaabaaabbaabbbabbababbaabbbbbbbababbbaaaaabaabaaaabbbbbaabbabaaaaaabbabaabababbaabbababaaabaaabaaabbbabbaabbaabbaababababbaaaaababaaabbabbabbaaababbbbabbbbbabbaaabaababbbaabaaaabbbaaaaaaabbaaaabbbbabbbaaaaabaabaabababaababaabbbaabaabbabaababbaaababababaababababbbabbaabababaaabbbbaaabbbabaaaabbaaaabaabbbaabbababbbbaaabbabbaaaabbaabaaaaababababbabbbbbaabbababbaabbabbbbbabbbabbaabbbababbbabbbbabbabbabbbbabbbbaabbabaababaaaabaaabbbabbbbaabaabbbbaaabaaabaaaababbaabbbbababababbaabbababbbbaabbababaabaaababaababaaabaabbbbbaabbbaaababbaaababaaaaabbabaaaaaababaabbaabaaabbaaabaababbabbbbbbabaabaaababbbaababbbaabbbaaaabbaaaaaaabaaaaabaaabbaaabbaabbbaaabbbbabbaaababaaaababaaaababaabbaaabbbbabbaababaaabaabbababababaabbbbaabaababbababaaaaabbaabbabaaaabaaaababaaabbaaabaaaabbabbaabaaabbbabbabbbbbbbbbbbabaaaaabaababaabbbbabbbaaabaabbaaabaaaabababaabbaabbabbbaaaaabbbaababaabbbbabbbbbbabaaaabbaaabaabbbaababbaaaaaaabbabaabbaaabbaaabbbabbabbabbaaaaaabaaaabaaabbbabbabbabaaababbaabbabababbbabbaaababaabaaaabbbbabababaabaabaabbabbababaaabaaabaabbaabaaabbabbbbabbbbabbbabababbabbabbbbabbaabaaababaaabbabbbbabbababaaababbaabbbaababababbababbbababbbbababbbbaabaaabaabbbabbaaaaaabbabbbabbbaabbbaabbaabbbbaaaabaabaaabbaabbabaabbbbbaabbababaaabbbabaaababbbaaabbababaabaaaaaabbaabbbbaabbabbaabbaaaabaaababaabbabbbbabbbabbaaabaabbbaaaabbaabaaaaabaaabbbabbbaabbbbbabaabbaaabbbaabbaababbababaaaabaaaaabaaaaabbababaaabaabbaaabbaaabbbaaaabababbbabaaabaabaababaaaaaabaaaabbbaaabaaabbbababbbaababbbabaabbbbbababaaabaabababaabbababbabbbabbbaaabaaaabbabbbaabbababbabaababbbbbabbabbaaababaabbbbabaaabbbaababbaaabaaaababbbbabaabbaaababaaabaaabbbbbaabbbaabbaabababaaaabbaaabaaabaabbababbaaabbabbaaabbbabaaabbaaabaaaaabbaabbbaabbbabbabbababaaabaaaabbaabaabaababbbababbaabbbaabababbbabaabbaabbabbaaabaabbabaaaaaabbabaabaaabbbaaababaababbbbbabbbaaabbaabababbaababaabbababbbbaaaabbaabbababbabbaababaaaaaabbabbbbbabaabbbaaaabaabbaabaaaabbbaabaaaaababaababaababaabbbbbaabbabbbbababaaabbaabbbaabbbaabaaaabaabaaabbbbaabababbbaaabbbaaabbababaaababbabaaaaabbbabaaaaabbbbabaaababbbabbbaaababbbaabaaaabbababaababbaabbbbaabbababaababbbaaababbabbabaaabbabababaaaaaaaabaaababbbaaabbbabababbabaabbaaabbbbaabaaaaaabaaababbabababbaababbabbababaaabaabbaabaababbbbbbbaababaaaabbaaaaabaaaaabbbaababbaaaabaabbbbbbbabbbbbaabaaababbbbbbabaabbbbababababbaaaaaabaabababbaaaabaabbbbbbbbabaababaabaaaababbbaabbabbaabbbbabbbabababaaaababbabababaabbbbabbabbaabaabbaaabaaaaabbabaaababaaabbabbaaabaabaaaaabbaaabaabababbbabbbabababbababbaabaaaabaaaabbabaaaaaaababbbbbbaaaaabbabbbbaaabbbabbabbaaabababbbaaabbabbaabbbbaaaaabbaabaaaabbabbbbbabababbbabbaaaaabaababbaaabbbbaaaaababaaaaaababaaaaaababbbaaaabbabbabbbabaabbabaabbabaaabbbbbbbaaaaababbbababbababaabaaaaabbbabbaabaaababbbaaaabbaaabbabaababbaaaaabbaaaaabbbaaaaaabbaabababbbaaabaaaaabbbaabbbabaaabaaaabbbaabababbabaaabbbabbaaaabaabaabbbaaabababbbabbbbaabbbbbaabaabbbaaaabaabbbbbaabbababbababbbaaababaaabaaabbbbbbbaaabaaaabaabaabbabaaabababbabbbbaaabaaabaaabbbaababbaabaabaaabbaaaaabbaabbbaabbaaabaabbabbaabaaaabaaabbbaaaaaababaabbbbbbabaabbbbaababaaaaabaabbbabababaabbbababbbabbaababaabbbbaaaabbbaabbaababaabaababbaabbabbbababbbaababaabbababaabaaabbababaabababbbaabaabaabaabbbaaaabbababaaabbaabbbabbbbbabababbbaaaaabababaabbababbababbbbbbaaabbaaabaaababababbbabbbbbaabababbaabbabbbaabaaabbababababaabbaababbbaabbbbabbabbbbabbbbabbbaababbabaababaabbbaaaabbbbbbbabaaabaaaabababbabbbabaabbbbbbabbaaaaaabbabaabbbbaababbaaaaaabbabaaababaaabababbabaaabbababaabbbabbababbbbaaaabbbabaabaabbaaaababaabbbbaababbabbbaaaabbbbbbabaabaabaaaabbbabababbbbbabbababbbbbbabbbbabbbaabbbababbbaaaabbababaabbbbbabbbbbaaababbbbbbbbbabbabbbababbaabbaaaabaaaabbabbbbbabbbaababbbababaababbabbbbbbbbaaaaaaabbaabaababaaabbbabbabaaabbaaabaaaaaaaabaaababaaaabaaabaabbabababbbabbbbbbaaaabbbaabbabbbababaaabaababbbbbbaaabbbaabbabbaaabbbbbbbabaaaaabbaabbabaabbaaabababbbaabbbaaaabaabbbbaaabbbbbbaabaaaaababbaaaabbbaabbababbabbababbbbabaaababaababbbabbbbbbbbbabbaaabbbaabbababaabaaabababaaaaaabaabbbbbaabbabbbaaabbbbaabaabbaaabababababaabbaaaabbaaabbbbaaaaaabbbbabaaabaabbababababbaababbaabbaaababbbbaaababaabbbbbaaabaabbbbabbbbabaaaababaabbbabbbaabbbbbbbabaabaabaaabaabbbababbbabaababbaabbabaabbbbaaabbbbababbbaaabbabbbbbbbaaaababbbaabbabbaabaaabbabbaaabbabaaaaaaababaaababaaababaaaabbbbabaabaaabbaababbabaaaaabbbaabbbbabbaaaaabaababbaabbbaaaaababbababaabaabbbababbabbaababbbbbabbbbbbabbbabbaaaababababbabbbbaabbababaabaaabaaaabbbbaaabaaaaaaabbbaababaaaabbaaaababbababaaaababaabaaaababbabbababbabbaabaabbbabbbabbbbaabbaabbbaabbabbbbbabbbbbaaaaaababbaabaababaaabaabbbaabbabbabbaaaaabaaabaababbbbbaababaabaabbbababbbbbbaabbbababbbabaaabbabbbaabaabaaaabaaabaaabbbbbbaaaaabaaaababbabbbaabbaaaaaabbbbaaaabbaabbabbbbaaababbbbababaabaaababaabbabaabaaabbbbabbaaabaabbbabaabbaabaaabbbbbbaaaaabaabaaaabbbaabaaabbabbaabbabbaabbabaaaaabbbaabbbbaabbaabaababaaaabaabbbabbbbbbbabbbbaababbbabaaaabaabbbaabbbbabbaaabbabbbbbabbbabbabaabbaaaaaaabbbbbbbababbabbabbaabbaaabaabaaaaabaaaabbaaaababbbaababbbaabbabaabbbaabaabbbbbbabaaaabbbabbaabbaaabaaaabbabbabbbaaaabaabbbbbaababbbbaaabbabbbbabbbbbaaabaaaabbababaabbaaaabbbbaabaaabbabaababbabbababababbabaaabbaaaabbabbaaabbaabbaabbbababbbbabaaaaabbaaaaabaabbabbbaabaabaaaabbabbbbbbabaaaabbababaabbabbaaababaaabbbaaababaabbbbaabaaaaabaaaaaaabbbaabaabbbabbabbbbaaaabaaaaaaaaaababbabbbbababaabababaabaabbabbbabbabbabbabaaaabaaabbbbbbbbabbbabbbbbabbaaaaaababaaaaaaaabbbabbabaabbbbababbbabbababaabbaabaabaaaabbbbabbbabaaabaaaabbabbabbaababbbbabaabbbabbbaaaaaaabbbabaaaabbbbaaabbbaabaababbbbaabbbbabaabbaaaabaababaabaaaabbbbabbaaabbabaaabbabbbaaaabaababbbabbbbaaabbbbbbaabbbbababaaaaaaabbaaabbbabaabbbaabaababaabbaabbaabbaaabaaabbbbaaaaababbaabbbabaabaabbabbaaabaaababbabababbaaaaabbaaaabbbabaabbaababaaabbbaaabaaaaababbbbaaababbaaaaaaaaaaabbaaabbaaababbaaabbbaabbbbbbbbaaabaaaabaaaabbababaaabbaabbbabbaaabbababbbbaababbababbababbbaabababbaabbbabaaaaabaabbababaaabbaaabbbbababaaaaaabbbbbabbaaaabaabbbbbbbabbaabaabbbbababaaaaabbaabbbbabbbaabbaabbabbbbbbabbbbaabaabbbbaababbabaaaaababbbbabbbabaaabbbaabbabbbbaabaaabbaabaaaabbabaababbbbbbbabbaaaabbbbbabaababbaabaabbabbaaaaaaaabaababbabaaaaaaaabbbbaabaaaaaabaaaaabaabaaaaabbababaabababbaabbbaabaaabbbaaaabbabbabbbabbaabbabaaaaababbaaabaabaaaaaaababbbbaabaabbaaabaabbbaaababababaabbababbbaabbbbabaababaaaabababbababaaaabababbbaaabababbaaabbaabaaaabbaaaabbbaaaaabbbabbbaabbabbbbbaabaaaababaababbbbaababababbabbaabaaabababaabbaaaabaabaaaaaabaaaaababbbaababbbbaabaaabbabbbbababaabbbabbaabbbaabbbabbaabbaaaaabbaabbbabaabbbaaaabaabbbabaaabaabbaaababbaabbabbbbababbaaaaababbabaabbbbaabbbbbbabbaaaaaabbaabbbabaaababaaababbbbabbbbbbaaababbbbabababbbbbabaaabbabbaaaaabbaaababbabbaaabbbbaaabbaaabbbbbbaabbbaabaaaaaaaaabbbbbabbaaabaabbbbbbbabbbababbbbabbabaababbbbabaabbbabbbabaabbabaabbabbaabaababbabbbbabababaabbaababaabababbbaabaaababbbaaababaaaaaaaaababaabaaaabbbbaaaababbabaabbbbabbbbaaaaabaabaaabbabbaabbbbbabbbbbaaabababababbbbbabbabbabbbbabbbbbbbbabbbbbaaabbababbabbabaaaabaaabbbaababaababbbbbaaaabaaaaaaaabbaabbabaababaababaabaabbaaaaabbabaabbabbaaaaabbabbbbabaabbbabbabbaabbbababbabbaabbbababbaabbaabbbbaabbaabaaabaabbbbbabaaabbaaaaabbbabbaabbaababbbaabaabbbbabbbbbabbabbaaaabbbbaaabaaabaabbabbbaabbbabbbaabbaababbaababbbabbbbabbabbbaaababaabbabaabbbbbbababaaabababaabaaabbbbaabbbaaaaababbabaabbbbbaaababbabaabaaabaaababbabbbaabababbbaababaaababbabaabaaabaaaabaaaabbbbbabbbbaabbbaabababaababaabbbbbaaababaaaaababbaabbbbbbaabbbbaaabbbaaabbbaaaaaaaaabaaaaaabbabbbaaabbbbababbbbaaabbbbaaaabbaabbbbaaabaabbabbbbbbbabbabbbababbabbaabbaabbaabbbabaaaaabbabbaaaabbbabbbbaabbaabaabbbaaaaaababbabababbaaabaabbabbaababaaaaabbaabababbbababaabbbabbbaabbaabaabababbaabaaaabaabbbaabaaaaabbbbbbaaaaaaaaabaaaaaabbbaabbbabaabbabaababbababaabbbababaabbababaaabbbaaababaababbaaabbabbabbaabbabbabaabbaaabababbaabaaaaabbbbababaababbaaaababbbbbabaababbbbbabbbbabaaaaabbaaabababbaaaabbbaabaabbbbabababbabaabaabaaaabbbabaabbbbbbbbbabbabbaaaababbbababaabbbabaabaaaabbbbbbbbaabbababababbbaaaabaaabaaabbababaaaaabbbbbaaabbaaaaabbabababaabbbbbbaababbaabaabbbaaaabbbaabbaaaaababbbbabaaaabbabaabaabbaabbbbababaabbaabbbbbaaaabaababbbaabaaaaabababbaabbbbbbbbaaabababbabbbbbbabaabbbbbbbaaaaabaabaababbaabbaababbbbaababbababbbbbbabaabbbabbabbbbbbbaaababaababaaaabbbbabbbbabaabbabaabaaabbabbaaabbabaabaaaabbaabbabbabbabaabbaaaabbbaabbbbbbabbababbbbabbaabbbbaabbbbaabbbbbabaabababbbabbbbabaaabbabababbbabbbaaabbbbbabbaaaabaaababbaababbabbbbabbbaaaaabbbaabaaabababbbabbbaaaaaababbaaaabababbaaaaaaabaabbbbabbbbbbaaabbbbaabbbbbbbbbaabbbbbbababbaabbbbababbbabababaaaabaaaaaaaabbaaaaaabaababbabaabbbbbbaababababababbbbaaabbabbaaaababbabbbabbbabaaabbabbbbbabbbaabbababbbbbbaabbbbaaaaaabbaabaabaabaabaabbbbaaabbaabababaaaabbababbbaababaababaabbaaabaabaaabbbabababbaabbbaaaaabaaaabbbbabbaaaaaaabbbaaaabbbbbababaabababbbbbaabaababaaaabbabbabbbbaabaabaaabbaaabababaaabaaabbabbbbabbababaababaabbababaaababbbaababaaaaabaabaaabbababbbababaaaaabababbaaaababbababababbbabbbaabababaaabaaabaaabaabbaaababbbababaaaaabbabbbaabbabababbaaaababbbabbaabbabbaabbbbbabaabbabbabbaabbbaabbbaabbbbabbaaaabbbbabbbbbabbaaabbaaabaaabbabbbbbbbbaababaababababaababaabaabbabbbabbaaaaabaababbabbbaabbabbaabbbaaaabbbbbaaabaaabaabaabbabbaabbabbbababababaabbbbabbbbbbaabbababaaaabbaaabaaaaaaabbaaabbbbaababbbbbbaabbababbbbabaabbaababbaaaabbbabbbaaabbababaaababbaabbbbbbabbaaaabbbaabaabababbbbabbbababaabbbabaabbabababbababbbbabaabababaaaaabababaabbbabbbaaaaaabbabbaabbbabbaabaabaaaabaabbabaaabbaabbaababbaabbaaabbababbbaabaabbaaaaabbabaababbaabababbbabbbbbabbababbababbbbbbbbabaaabbbbbbaaaabbabbaababaaabbaabaaaaaabbbbbbbbbababaabbabaaaababbababbabaabbabbabaaabaabaaabbaabbaaaabaaabbaaaaabbaabaaaaaabbbbbaabaaabaabaababbbbaaaabbbaabaabaabaabaabbaabaaababaaaabbbaaaabbabaaabbaaaaabbbaabbbaabaababbaaaaababbbababababaaabbaababbaaabbbbabbbaababbaaabbbbabbaaaabaababaabbbaabbbbabaabbbbaabaaaaaaaababaaaaabbbabbabbbaabaaaaabbaababbbabbbaaabbaabbaababbabaaabbbbabbababbaaaaabbabbabaababbaaabbabbabbbaaabbabbaaabbbbabbbbbabaabbbabaabaaabbabbaaaabbbaabbbaaaaaaabbbabbbaaaabaababbaaabbabbbbbaaaabaaaabbbbaababaabbabbbbaaaaabbbbbabbbbabbbalabbaabaabbbbaaaaaabbbababababababaaabaaabababbabaaaaababbabbbaabaabaaabbabaabababaabaabbabaabaaababbbabaaaaababababbaaabbbabbabaabbbaaaabbabbbaababaababababaaaababbababbababaaaababaababaaabbbaababaabaabaaabbabbababaaaaaaaaabaaabbbababbaaaaabbbbbbbabaabbaaabbbbabbbbaaababbaabbabbaabaabbbaaabaaabbbababaabaaabbaabbaaaaaaabbabbababbbaababbbabababbabbbbabbbabbaabbbbaabbaaaabbababbabbaaababaaabbabbaaaaaaaababaabbabbbbabbbbabaaaabbaabababbbabababaaaaaaababbaabbbabbbaabbbaabaabababababbabaaabaabbaaabaabaaaaabbbbababbbababaababbbaabbababbaabbbabbaababbabbabbbabbbaaaabaaaabaaaaaaabaababababbbaabbabbbbababaabaababaaaababbaabbaabbbbbaaaaabbbbaababaaabbbbaabaaabbaaaaabbabaaaaabbbbabaabbabaabaabaaaaaabbbbbbbbbabbbbabbbbbabaababbbbabbabbabbbabaabbbbbbbaabbbbbaaabbbbabbbabaaabaabaababbbbbbbbaabbbbbbaaaaabbbabaabbbaabbbaabaabaabaabbbbababbbbbabbbbaabaabbabbaabbbaaabbaaabbaabaaabababaabbbababaaabbbbbbaaabbbabbabaababbaabaabaaababbaaaabbbaabbbaaabababbbbbbaabbaaaaababaaabaaabbababbbaabaabbabaaabbaabbbabaababbbbbbaaaababbaababaabbaaaababbaaabbbaababababbbaabaababbbbbabaabbaabbabbaaabbbaabbababaaababbaaaaaaabbabbbaabaaaabaaabbabbaabbaaabbbaaaabbbababaabbbabaabbabaaaababbbbbbaabaabbbababbaaabbaaabaabbaababaababbbabbaabaabaabababbbbaaabaababaaabaaaabbabaaabbbabbaaabbbbbababaabbabababbaabaabbabbaaaababbbbaabaaaaabbaaababbbbaaaaabaabbaaabaabbbaaabbbaababbbaabbbabaaaababbabbbabababbaabbabbbaaababbabaababaaaabaabbaaaababaaabaabbaababaaabbaaaaaabbabbbbaaaabbaabbbbbabbababbabababababbaabbabbaabbababbbbbbaaaabaabbbaaaabbababbabbaabbaaaababbababaaababbaababbbbaababaaaaaabbbbbaaababbbababaaabaabbabbaaababaabaabbababbaaaaaaaaababaabababbbaabaaaabaabaabbbaabaabbbbbaabbbbaabaabbbaaaabbbbbbaaabbababaaabbabbbabbbaaaaabbbbaabababbababbbbaabaaaabbbbbaababbababbaaabbbaaabaaababbbbaabbbbbbbbaaaabbbaaaaaaabaaaabbabaaaabaaaaabbbabaabaabbbbabaaaababbbbaaaaaaaaaabaaaaaaababababaabaabbaaabaabaabbabbabbbbaabbabaaababaabbaaaabbababaabbbabbaabaabbbababbabaaaaabababbabbbbaababbababaaabababaabbbbbaabaaabaabaabbbbabaaabbbaabbbaababaaaaaabbabbbabaaabbabaabaaaabbabbaabbaabbbabbbbabaaabaabbbabbbbaaaaaabbbbbbaaaabaababbabbabaaabbbabababbbbbabaaabbabaaaaaabbbbaababbaabaaabbaabbaaaaaaabbbbbabbbaaababbbbbabaabaabaaaabaaaabababaaababbaaaaabbaaaaaaabbaabaabbbbbbbbbbbaaaaaabaabbabbaabaaaabbaaaaabbbabaabbabbbbaaabaabababbbbabaabbabaaaaabaababbaabbaabbbabbabababaabaabaaabaabababaaabbaaaaabbbbbbaaaaaabbaababbbaaababbbaaaaabaaaababbbaabbbbbabbabbabbabbabbaaaababaababbaababbaaaaabbabbaababaaaabbbbaababaaabbbbaabaabbabbaabbababbabaaaabbabbbaaabbbbbaabbbaabaaabaabaabbbbaabbbbbaaaabaabaabaaaabbabbbaaabaabbbbbabaaaababbaaababbbabbbbabbaaabaaaaabbbbaaaaabbaabaabaabbabababaaababbabbbbaabbaabbbbbbbbaaaaabbabbbbbaaababbbbababbaaaaaaaababaabbbbbbaaabbbbbabbbaaabaaabaabbaabaaabbabbaabbbaabbbaaaababaababababbabaabbbaaababbababbabaabbbbaaaabbaabbbbbabaaabaababaababbaaabbbbaaaabaaabbaaaaabbaababbabaabaaaabaaabababaaabaabaabbabaaabaaaaaaaaaababbbbbbbbbabbabbabbaaaaaabaaabaaabbababaabaaaaaabababaaabaaaaabbaaaabababbaabbabbababaaaaaabaaabaabbaaababaaaaaaabbbababaaaaaaabaaabababababbbbaabababbaaabbaabbabbaaabbbbbbaaaabaabbbbbaaabbaaaababbbbabaabaabbbabaabaaabbababbbbbaababbaaabaaabbaabaabbabaaaabaabbbbababbaaaaabababbabbaababbaaaaabaaaababaabbbbbbbaabbaaabbbbbbbbbbbaaababbbabaabbbbbbababaaabbbababbbbbbabaabbaabaaabbababbbaabbaaaababbaaabaabbabbbaabbbbabbaaaabaabbbbabababaababbbabaaaabbaaabbbabaaaaaababbbaabbaabbbbbbabbbababbababaaabbbaaaabbbabbaababaababbabaababaabbbaabbaababaaaaabaaaababbbabbabaababbbabbaaaabbaabbabbaabaabbbbbbaababaabaaaabaabbbbbaabaaabbababbbbaabaaabaaaabbbabbbabbbaabbaaabbbbababbbabbbababbbaabbabbabbabaaabaabbabaabaabaaabaabbabbabaabaabbaabbbabaaaabbbaabababaabaabaaabbbaabbbaababbbabbbbbbaaaabaabababaabbbabbaabbaaaabbaabababbaababaaabbababbbabbabbbbaabbaaaaabbbbaabaabbaaabbabaaabbabbbbaababbaaabbbaaabaaabbabaaaaaaabaaabbbbbbabaabbaabbababbbbbabbbbabaabaaabbbaabaaabaabaabaaabbbbaaaaababbabbabaaaabaabbbbbabbaabbbbbbaaabbbbbabbaabbabbaaababbbaaabaaababaabababababaabaabbbabaabaaabaabababababbbbbabaabbbbaaaaababbbabbbabaabaaabaaaabbbaabbbbababbbbbbbababbaaaabaaaaababbbabbbabbbabbabaaabababaabbabababbabaabbbabbbbbbabbaaaaabbaaabbabbbabbbaaababaabaaabbaaabaaabbbbaabbbaabbbbbababbaaaababbabbbbabbababbaaaabbbbbbbabbbbabbaabaabaaaaababbbaaabababaabaabababaabbbabaaaabbbabaabaaababbabaaabbbbabbbbabbababababbaabbababaabaaaaaabbbbbabaabaabaabaabaaababbaaaaabaabaaabbbaaaaaabbbabbbbaababbbaabbabbaabbabaabbaaababbabaabaabaaaababbbbbababaaababaabababaabaabbaababbbbaababbbaaababbbaabbababbaababaabbaabbbbbbaaaaabbabbbbabababaabbabbbbbaabaabbabbabbbbaabaabbbabbbbbbababababbbbabbbaaaaabbabbaaababbaabbbabbaabbabbbbaabababbaaaaabaaabbbabbabbaabbaabbabbaababaababbabbbbbabaaaaaabaaababbbabaaaaabaaaabbaabbababbbabbbababbabaabaababbaabaaababbbaaababbbabbababaaaaabbbbababaabbabbbbbbaabbaabbaabbabababbaabbbbaaabbbabbaabbbaababbbbabbaabbabbabbbabbabaabbababbabbbababbaaaabbbbabababababaaaaabababaabaabbbaabbbababaabbbaaabbbbbabbbbabbbaaabbbbbbbbbabbaaabbbabaaaabbaabababaabbbbaabbbabaabaabaaabaabbbaabaabbbbaabaabbaababbabbbbbababbababbbbaabbbaabaaabbbabaabababaabbaaababbaabbbabaaabaaabaababbbabbbbababaabaaaabbbbbabaabbbaaabaabaabbbbbbbbbabbaababaaabababbbbaaaababaaabaabaababaaaabaabaaabbaaaabbbbaaaabaabbabaaabbaabaabbbaaabbbbbababbabaabaaaaababaabbaaaaaababaaabababbbabaaabaabaaaaaabaaababaaabbaaaaabaabbbaaababbaaaaaabbbbbaaaabababbbbbbabaaabbabbbbbbaabbbbbbbaababaababbbbaabbabbabaabbbbbaabbaabbbabbaabaaabbbbbbaabbaabbbbbbabaaabbabaaaabbaaaaaaabaababbabaabbaababbbababaabbbabbaaabbaababbbbaaaabbabaaabaaababbbaaababbbabbbaabbbbaaababbbabbbabbbaabaaabbaababaabaababaabababbbbaabbabbbbbaabaabbbbbaabbababbabbababbaaaaababaabaaaaaaaaabbaaabbbabababbbbbaaabababaababbbbaaabaabbbabaababbbaaabbaaabbaabbbababaaaabbbaaaababbbabbabbbbbaaabbbaaaaaaabbbbbaabbbaabbbbbaabaababbbaaaabaaabababbaabaabbaabaababbaaaaabaaaabababbbaaaaababbabbbbaaaaabbaababbababbabbabbbaabaaaabababbababbbbbabbabbabbbbbaaabaabbabbabaaabbbbbbbaabbaaabbabababbbabbbbbaabaabababbabbaabbaaabbaabaabaaaaaabababbbbbbbaabababaaaaaaaaaaaabaababbabbaaaabbabbabaaabbaabbaaaabbabababbaabbaaaabaababaaaabbabbabbbaabaaaababbbabbbaabaaaaabbababaababbabbababbbabaaaaabababbabbaababbaabbabababaabbabaaaaaabbabbabbabaabbabaabbaababaaaaaaaabbabbabbbbabbbaabaabbbabbaabbbabbaababaaabaaaaaabbaabbbbbabaaaabaabaaaabbbbaaaababbbbbbaaaabbaaaabaababaababbabbabaaaaaabababaaabbaababaabbbabbbbabbbbbbaaaabaaaabaaabbaabaabbbbbaabaaabbabababbbabbaaabbbbabababaaaaabbaababbbabbababaabbaaaabaabaaaaaabbbbaabbbbbaaaaababaaaaaabaabbabbbababaaaaabbaaabaaabbbabaaaabaaaaaaababbbbbbaaabbabbbbbbaaaaabbbbabbbbababbbbabaababbbaaaaaababbbbaabaaaabbaabbabbaabaababbbaabaabaababbababbbabbbabababbbabbaabaaabaabaababaaaaabbbaabbabbabaabaabbbbbabbababbbbabababababaaabaababbbaaaababaababbbbbbabbbbbbbbbabaabbabbaaabbbababababaabbbaaaabaaabbbbaaaaaaababaababaabbbababaabbababbbbaabaaabaaababaaaabbabaabbaabbaaabbaabbabbbabbbabaaababaabababbbaabaaaababbaaaabbaaaababaabaababbbabbbbabbabaaaabbabaabaababbbabbaaabababbaaaababbbabbabaaaaabbabaaaaaabaaaabbaabbabbabaabaaaabaabbaabbbaaaaabbbabaabbabbabbabbababbbaaaaabbabbababaaababaabbabbaabbbaaabbbabbbabaaabbbaaabbaabbabbaababbbbbaabaaabbbbbbbabbbbabbbbbbbaaaaabaaaaaaaabbbbbaabbaaababbabbabaabbabaaaabaababbaaaaabbbabbaabbbaaabaabbbaabaaabaaaaababbaaabaabbbaabaabbbaaabbababbbaaaabbbaaababbbaabaababbbabaabbaabbbabbaaabababbbabaaabbababbbbaaaabbbbbbbbabbabaaaababbbbbbbabaaababbaaaabbbbababbaabbabbaabaaaaaababaaaabbaabbbabbbbaababbabaabaaabbabaaabaabbbbaabaabbbabbaabaabaaaabaababaaaaabbbbbabbababbbbbbbbabbbabbbaaaaaaabbaabbababbabaabbbbbbabbabbbaaaabbbaabbbaabbbbbaababababbbbbbabbaaabbaaaaabbbabbbabbbaaaaaaaababaaaabbaaabababbaabbbbaabaabbbbabaaaabaabababbbbbbbaaabbaabbbbaabbbaaabbbbbaaaaabbaaaaaabbabaaabababbbababaabbbbbababaababaababbbbbbbababaaabaaaaabbabaabbbbaabbabbbabaababbaabbbaaababababbaaaabbbaaaabbbabbbabbbbbbabbbbabaaaabaabbabbbabaaabbabbbaabaabbaabbaaaabbbbbaaaabaaababbaababababaaabaabbbbaaaaabaaaabaaabbababababbbababaababbaabbbbabaaabbabbbaaababaababbaaabbbbabbaabaaabaaabaabaaabbaabbbabbababaabbabbabbbaaaabbbaaaaabaabbabbbbaaaababbaaaaaababaaaabbbbbaabaaaababbbababaababbbaabbbabaaaaaabbbabbbabbbbabbbaabaababbabbbbbabbbbbbbaababaaabaababbaababaaaaabaaabaaabaabbbbbbaabaabababbbabbbbabbbbababbabbbabbbbbabbbabaaaaabbabbbbaabaaabbbbbbbabaaaaaaabbbbbbabababbabaabaababbbbaaaaabaabbbbbaaaaabbaaabbaabbabbaabbaabaababbabbabaabaaaaaabbabaabbbbbbbbababbaabbbbabbabababbbbaaababbaaabaababaabbbbbaababbaabbaaaabbababbabbbbbbbbaaababbaaabbabbabbbbabbbbabbaaaaabbaabbaababababbaababaaabbbabaabbbbabbaabaaaababaaabbababbbbbbbaababbbaaabbaaaabaaaaabbaabbbaaabaabaabbaaaaaababababbababaababbabaabbaaabaaaaaabbbaabaaaaaaaaabbbbbbbaabbaabbbaaaabaabbbbbabbabbbabaabaabbbabaabaaaababaaabbbbaaabbbabbbbaabaaaaabbbbaabaabbaababaaabaabbbbbabbabbaaabaabbabbbabbaababbababbbaaababbbbababaabaabbabbbaaaaabaababaaaaaaabbbaabaabbababaabbaaabaabaabbabbbabaabaababaaabaaababbaabbbababbaabbbbabbbababababbbaabbbabbabbbabbaaaabbaaabbbaabbbaaaabababbaabababaabbbbaaaaaabbaabbbbaabbbaaaabaabbbbababbabbbabaabbabbbbbabbbaaababbaabaabbabbaabbbaabababaaabaaaabaabbbbaabababaabbbaabaabbbbbbbaaaabababaabbaaabbbabbabbabbabbbbabaababbaaabbaaaaaabaabbaaaabbabbabbbaabaaaaaabaabababbbbaababbaaaababbaabbabbabbbbbababbbaabababbaabbbababbaabbaabbbaababbbbbbbabbaaaabbbbaababbaaababbbaabbbbbaababaabaaababbbbbabbabbaaababbbabbbbbabbbabbbababbbbaaabaaabbbabaababbbabbbbbababbbbabbaabbabaaaabbbabaabbaabaaababaaaabbbaaaaaaaababbbabbababbabbaababbbbbababbabaaaaaaaaaaaaaabaababaababbaabbbbabaaaaaaabaabbbaaaaabbbbbbaabbbaaaaababbaababbaaaaabbabaaabaabbbaaabaaaaabbbaabbbbabababaaabbaaabaabaaabbabbabaabbaaabbaaaabbaaabbaababaababbbbaabbaabbaaaaaaaaaaaaaaababbabbaaababbbbbbbbbbaaaabbbbbbaababbaaaaaabbabbabbabbbabbbabbaabbbbbbaabbabaababbabbbababbbababaabbbabaaabbbbaabbbabaaabbbbbbabbaabaabaaaabbababbaabbbaabaaabbbabbbbabaaaaabbaaabbaababbabaaabbbbaaaababababbbaaabaabbbbabbaabbbbabaabaaaaababaaababababbbbabbabbaaaaabbbabababbbabbbbaaaaaababbabaabbbbabbabbabbabaabaaaaaaababbababbabbabbbaababaabbbbbbbbbbaaaabababbbabaabaaaaabbbbbbbbbaaaaaaaabaabbaaabaaababaaaaaaabbbbabbabaaaabbbbaababbaabaabaabbbbabaabbaaaabaaaabbbbbabaabaabbaabbbabaabbbbaaaabaababaaabbaabbbabbaabbabbbbbbbbaaaaabababbababaaaaaaabaaababaaabbbabbaabbaaaabbabaabbabbabbbbbaaaaabbbaaaabbbbbbaababbaabaabbbbbbbbbabbaabbaabbabaaabbaababaababbbbbaabaaabbbababbbbaababbbabbababbbbabbaaabababbbbbaaaaaaabaabbbbbabbabbaabaaabbabbabbabbbbbabbbabababbbbbabbabaaaaaaabaabbaabbbbbbaabababbaaabbbaabbbbbbbbbaabbabaabaaabbaaaabbbbaabbbbababaababbbbbbaaabbbaabbaaababbbabbabaaabaaaaababbbabaaababbbabbabbabbbaabababaabaabbbbbbabbaabaabbbabbabaaabbaaaabbbbbaabbaaaaabbaaaababbbabaaaabbbabababbbababaabaaaaaaababaaababbbbbaabbabbaababaabbbaaaaabbbbaabbabbbbbbabaaabababaaaabababbabababbbabaabbabbaaabbaaaabbbabbbaaaabbabababbbabbbaaaabbbbbababbbaabaababbabbbaaaaaaaabbabbbbbabababbaaaaaaabaabbbbabaabbaaaabbbaabbabbabbbaababbaaababaaaabbabbabbbababbaabbaabbbbbbbabaabbbbaababbabbbbabaaabbbbabbbbbaababbababbabaaababababbaabbbaaaabaaabbbbaabbaababaababbaaaabbababbabaabaaabbaabaaaabababaaaabbaabaabbaabbaabaaababaabaaabaaaabbbaaabaaabbbaabbbbaaabaaabbbbaabaaaabbbbaaaaaabaaababaababababbbbbabbbaaaabbaaaaababbbbbaabbabaaaaabbaaabaabbbbbaaaaabbabbaaaaaabbbbaabbbbbbbaaaaabbaaabababaabababaaabaabaabbbabbbabababababbbabbbabababaaabaaabbbabbaabbbabbaaaabbbaaababbbbbabaabbbaaaaababababaababaabbaabbbaaabbbbbabbbbbbbbbbbbbbabaabbaabbbbaabbbbbbbaabbaabbabababaaabbabbaaabbbbbbababbbbaaaabbababaaaaaaaaabbbabbbbaaaaaabbbbbaaabbaaaaaaababaaaaabababaaaabbaabbaabbabaabbbaaababbaaabbbababaabaaabbbaaaabababaabbbbababaabaaaabaabbbbbbbaaababbbabababbbbbabbaaabaaabbbabbaabbabbbbbbababaabbbbbbbbbaabbbaaabbbabbbaabaaaaaaabbbabbaabaaaabbabaaababbbaabbbaaaababababbbbbbaabbaabbbaabbabbaabbaaabaababaaaabaabbbaaaaaabbaabaababbabbabaabbbbabaaaaaabbaaabaaaabbbbaaaabbbbbaababaaaaababbabababbabababbbbbaaabbbabaabbabbbababababaababaaaabaabbbaababbbbbbabbaaabababaaabbababbaababaabbabbbbabaaabaabaababbbaabbbabbabbabaaabbaabbbbabbaaabaaaababbbbaabaaabbaababaabababbababbbbabaaaaaabaaabbababababaaaabbaabbbbbbaabaababbbbbababaaababbbaaaaabbbbbaababaabbbbababbbbabbabbbaabbabbaaaaabaabbabaaabbababbbabaaaaaaabababababbbbaabaaaabbbbabbabbaabbababaaaaaaabaaaaaabaaabbabaabbabbbbabbbabaaabbbaabbabaaaabaabaaaaabaabaabbbabbbaaaaabbbabaaaaaabaababaaabbabbbbaaabbbababbabbbababababaaaaabbababaaababbbaabbbbaaabaaababbaababbbaaaaaabbbaaaaabbbaaaabbbbbaabbbbbaabaabbbabbbabbbababaaaaaaabbabaaababbbbbbaababbbabbaaaaaabaababbbbbbbbaabaaaaaabaaaaaaabbbaaaabbaabaaaababbabbaaaaaaabbaaabbbbabaabbbaabaaaabbbbababaababbbbabbaaabbbaaabaaaabbabaabababbaababbbaaabbbbabbabbbaabbbaaaabbbaaabbbaabbabbbbaaabbbbbaaababababbbabbaababbababaababaaaaababaaaaabaabbaabaaababbabaababbabbaaaababaaaaababaabbabbbabababbbababababbabbaaabbabaaaabaabbabbaaaaaaababbabbaaaaaaababaaabaaaababbbabbababbaabbbbbbaabbbbbbbbbaababbbababbbabaabbaaabababbbababaaaabababbaababbaaaaabbaaaabaaaaabbbaabaaaaabaabbbaaaaaabaaaabbaabbaabbbbbbbabbaabaaaabbbbbbbbabbbbbabaabbababbbabbaabbbaababbaababbaaababaabaaabababaabbbbaaaaababbbbabaaaabaaabbbabbbbabaaaababbaaabaaabbbbaabbbaaabbbbaaaabbbabbbabbbaabaababbbababbaabaaaaabbabbbaababaababaabbbaaabababaabbaaaaaaabbaaaabaaabababbbaabaabaabbbbababbbbabaababbabbbbaaabbbaaababbaabababaabbaaababbababaaabbaaabbabaaaabaabaaaaabaabaaaaaabbbbababaaaabbbaabaabaaaabbaaababaaabbabbbabaaabbbbabaaabaabaababababababbaabaaaabaabbaaaabbbbabaabababaabaabbaabbbbbbbbaabbabbaabababaabbaaaabbbbaababbabbbbabaabbbbbabbbbabaaaaabbabbbaabbaaaaaabbabbaabbbbaabbabbbabaabbabbbbbababbbababaabbaababbbbbaabbbbbbbaabbbbaabaabbbabbabbbaabaaaaaabbbbbbbabbaabbabbbbaababaaaaaaabaababaababaaabababbabaabbaabaababbbaababaabaaaabbabbaaabbaabaababbbaabbabbbabbabbbaaaabbbaaababaabaaabaaaaaaabaababababababbbaababaaaaaaabaaababaabbbbaabbabaabaababbabababbaabbbababaabbabbbbbabbbaabbbabbaaabbababbaaaaabbbbbaaababbaababbbbbaabaaabbaaaabbabbbbbbbabbbabbbaaababbbbbbbbaaaabbbaabbaababaaababbbbbbabbbabaabababaababaaababaaaabaabbaababaabbbaaaaabaabbbabbbabbbabababaaabaabbaabbaabbaabaabbabababbabaaabaaaaabbabaabaabaaaabbabbbaaaabbbbaabbbbabbbaaaaabaaabbaabbaaaaabaaaabbababbbabaaabbaabbabbababbbaaaaaaaaababaaaababaaabaabababbbbabbaabbbbbbbbbaaababbbabbbaabbabbaabbabbbbbbbbbbbbbabaaabababaabaababaaabaaabbbabaaabbbabbbbaabbbaabababbaaaabbaaaaabbabbbbaaabbabbbbabbabababbbaabaaabbbbbabbbbbaaababaaaabbbbbaaabbababbbabbbbbbbabbbabaaaaabbbabbaabaabbbbbbabbbabbaaababbaaaababbbaabbbbabbbbbabbbbaababbbbbabbbabbbaababbabbbabaaaabbabaaabaaabaabbabaabbbaaaabbabababaabbabaaaababaabaaabbbbbaabbabbbaaabaaabbaabbbbaaabbbabbbbbabbbabbabaaaabaabbaaababbababaabaabaaabaaaabbabbbbbbbabbabababbbababbbbbaaababbbaabbaaabaaababbbbabaabababbbbbaabaabbbbbbbababbababbaabbbbaabbbabbbbababbbbbabaabbbaaaaaaaabaaaabababaaabbaaabaabbbbbabaababaaabbaabbaabbbaabbbbaaaaaaaaaaaabbabbbaabbbbabababbbbbbabaaaaaaaaaaabaabbbaabaaaabbabaaababbaabbaaaabaabbaababbabbaababbbbbaaabbbaaaaaaaaabbbaaaabbbbababbbabbaaaabbaaaaabbaaaabaabaabbbbaababababababbaabaabbbbabbbbbaabaabbbababbababbbbabbbabbaabaabbabaabbbabaaababaababaababaabbbbaaabaabbbaabbbababbababbbabaaaaabbbbababbaabbbbbbbaabaaabaaabbbbabaabaabbaaababbaababaaabaaabaaaabbbaaabaaabbbabbabbaabbbbaabaabbbbaaaabaabbbbaaaaabababaaaabbbaaaaaabbbbbababbbbbababaaabbabaaaaaababbaaaababbaaaabbbbabaabbbaabaabbbbbabaaabbaabbbbaabbabbbbabaaabbbabbabbbaaaabababbabaaababbbbbbbaabbbabbbaabbbabbaaaaabbbbbaabbaabbabaaaaabbbabbbaaaabbbaababbbaabaabbbaaaaabbbbbbabbbbbbbbabaaaaabababbaabbbabbbababbbbabaaababbbbababbaabaaaaaabababbaabaabaabaabbaaabbaabababababbbbbabbaaaabbaaababbabbaaabaabbaabbaabbbbaaabbbaaaabbaabaaabbbbaaaaababbaabaabaababaaabaabbaaababbbbbbbaabbbaababbbbabbaabbabbaaabbbbbbabbbbaaaabaaababbbbaabaabababaaaaabbbaabbabbaabbbbbbbbaabbaaabbaaaaababbbaabbabaabbabbbaaaabababaabbbbbbbabbbaaabaaaabbaaababbaaabbbaaaaabbbabbababaabbabbabbaabbabbbbabbaaaaaabbbabbabaabbaababababbababbbbbabaabaabbabbaababaaabaabbababbaabbbabbbaabaaababbabaaabaabbabaabaaaabbaaabbbbbbbbabbabbbbabaabbbbbaaaaaabaaabababbaaaabaababbaaabbbbabbaabbbabbbabbaabaaaaabbababaaabbbbababaababaabaababaabbbababbbabaabaaaabbbaabbbbabaabbbaababbbbbaaabaabbbbbbbabaaaaaaaabbaaabbbabbbbabbabbabbbaaabbbbbbbbbaaaaaaababbbbbaaaabbbbaabbbaababbabababaaabaaabbaaabbbaaabbbbbaaababaabbbaababbaabbbaaaaababbabbbbbaabbaaaababbbbbabbbbbbbbbabaaaabaabbaaababbaaaaabbbaaabbbbbaaabaaaabbbaabaabaaaaaaabaaaaaaaaaaaabbbaaabbbaabababbbbaaaabaabbbabbbabbaaabbbabaaababbaaaaaaaabaababaaaababbababaaaababbbabbabbabaaaaaabababbabababaabaaabababbabaaabbaaaaaaaabaaabbaabababbbababbbbabaaababbbbabaaaaaaababbabbabababbbbabababaabbbabbabbbbbbabbabbaabaaabaabaaaaababbbbaaaaababbbbbbabbaaabaaaaaaaabaababbabababaaababbbbbbbabbbbaaabbaaaabbaaaabababbabbbbbbaaabbbbbbaabbaabbaabababbbbbbaababbbbbaaababaaabaabbbbbbbabbbababaabaabbbaabbaaabbabbaabbbabbababbabbbabaaaaaabbbbbbbbaaababaaababbbabbaaaabbbaabbabaaaabbaabbbaaaaaaabbaaabbbaababbabaabbabaabaabbbaabbaabbbbbbbbabaababaaaaabbbabaaaababbaaabbababbbaabbabbbbbbabaabbaabbbbbbbbaabaabbbaababbababbbbabbaaaaabbaabbbbabbabaaaababbbbbbbbbbabbbbbbbabbabababbbbabbbbaaaabbabbbababbaabababbaabbabaaaaabbbbbbaabaaaabbaaabaaaaabaabbabbbbbbabbbaabbbabbbabaabbbbaabaaababbaaabababbbababbaaabbaabbabbbbabbaabbbbbbbbbbbbabbababbbbbabbabbbabbbaabababbbaaabababababbbabaaaaaaaabbbbbbaaaabaabbaaaaaabbbabbbaaaaabbbaaaaaabababbbabbbbabbbbbbababaaabababaababbbbabbbbaabbababbaaababbbaabbabbbabbabbbbbaabbababbaabaaaaaababaabbbabbbbaaabbbbbaaabbabbaaabaaaaabaaaabbbabbbaaababbbabbbaaaabababaababababaaabbaabbbabbaabaabbaabbbababbbaabaabbababaaaababaaaabbbabbabbababbaababbbabbaabbaabbabbbaababaabaabaabaabbbaabbaaaababbbabbbaaabbaabaaaaabbbbbaabababaaaababaababbabaabbbaaaaabbbabaaaabbbabababbbabbbaabbbbbbbbabbbabbaaabbaaaaabbababbbabbabaaabbaaaaabaabbbbabababbbbaaaababaabbbaaaababbbabbaabbbbbababaaaabbbaaababaabbbabbbabaaaaaabaabaabbbbabaaabbabaabbaaaaaaaabaaabbbbaabaaaabbaaababbaabbaabaaaaaaabbbbbbbababbaabbbaaaaaaaababaaaabaababbbabbaaabbabaaaababbbaaaaabbbaaabbabbbbaababbbaababaaaabbbaaabaaabbaaababaabaabbbbaaaaabbaaabababbabbabbaaabbababbaaababababbaaabababbaaabbbaababbaaaaababbbaaaabbaaabbbbbabaaabaaaabbababaabaabbabbababbaabbabbaabaabaabbaaaaabbbabbabaabbababaaaaaaaabaaaaabbbaaabaaabbaabbabaaaabaaaababbbaaaaabaaaaaaaabbababbbbbbabaabbbbabbaabbaaabbababaabbabbbababbbbabaaabababbaaababbbababbaabaaaabbabbbbabaabbbbbbabbaababbabbaabbbabbaabbaabbbbbbbaabbbaaaaabbabbabaabbabbbaaaaabbaababbabaaababbbabbbaaaabbaaababbbaaaaaabbaaabbababbabbbabaaabaaaabbbbabbbabaaaabbabbabaabbbbaabbaabbbbbabbabbaabaabaaabbbbbbabbbbbbbbabbbbbbaaaabbabaabbabaaaabaabbbaaaabaabbbbbabaaabbabbabbababbaaaaaabaabaaaababbbbbabaaaabbbabaababbabbbaabaaaaaabbbbabbabbaaabababababbbabbabaaabbbabbaaaabaaaaaaabaaabbbaaabaabbabaaaaaabbbbaaabbbbbaabbbaabbaaabbaababbaabbbabbbaaaabbabbbaabbaababbbbbbbababababaaababbbaaabaabaabbaaaaaaabbabbaabbaabbababbabbabababbabaabababbbababbbababbaaabbabaaabababbabababbbaaaababbaaaabbaaabbaaabbbababaabaaaabbbaabbabbbaaaaababbbaaabaaaaababbbaaabaabaabbaabbabbaabbababbaababaabaababbabbbabbabbaaaaabbabababbaabababbbbabbabaabaaabaababbaaaaabbabaaabbababaaabbbaababbbbbbaaabaabaabaaaaabbaabaaaabaabaabaababbbabbaabaaabaaabbaaabbaabababbababaaabbbbaababaaabbbaaabbaabaaaaababababababbbbaabbabbbbaaabbabaaaaaabaabbbbbbababbbaaaabbbbababaababbaaabbaabaabaaaababbbababbbabaababababbabaaabbbbabbaabbbaabaaabaabaaabaabaababbaaababbabbbbabaababbbabaabbbabbbabbbaababbabbabaabaabbaabaaabaaaababbabbbbaaaabbaaaaababababaabbbaabbaabbaabbabaaabbababbabbbbbbabababbbbbbbbabbaabaaaaabaabaabbabbbabaaaaaaababaabbabbbababbaaaaabbabbabbbbbaabbaabaababbbaabaaaabbbabaaabbaababbbbbaababbbabaaaabbaaaaabaaaabbabbbbabbababaaaaabaabbabababababbbbbbabaababbbaabbbabbbaabaaaaabbbbaaaaaaaabaaaaaaaaabababbaabbbabbaaabaababaababbabbbbbbababbaaaabbabbbbbababbbaabababbbabaabababbbaaabbaaaaabbbbbbaababaaaaabbbbabaaaaaaaabaabbaabbbabbbabaabaabaababbaababbbabbbbaabbbaaaaabaaabbbbbbaabaabbaaaaabaaababaabaabaaabaaabbabbaaabbbbaabbabbabbababaaabaabababbaaaabaaababbabbbaaababbbbbababbbbbbbbaababaaababaabbaabbbaaaaaaaaaabababbbabbabbbbbabbaabbbbbbbabbbbaababbaabaaabaabaaaaaabbbbbbaabaabbbbabbabbbaabaaaaaaabaabbbabaaaabbaabaabbaabbbbbbbbbbabbbaaabaabaaaabaaabababbaabaaabaaaaabbbbbabbbbababbaaabbabbaababaaabbbbaabbabbabaaabaabbababababbbaabbabababbaaabbaabaaaaabaabbaaaabbbabbbabaabbbaabbabbbbabbabbaabaaabbaaaaaabaaabbabaaabaaaaabbaabbabbaabbbaabbbbbabbaabbabaabbabaaaabbbabaaaaababbaaaabbbbabbaababaabbabbaabaabbaaabbbaabbaaaabbaabbaababaabbabbabbbbaaabaaaaaababaaaabababababaabaabbbabbaabbabaabbbabbaaaabbabbabababaabbbbbabaaaababbbabbababbbbbbabbaabababaaabbabaaaabaabbabbbbbbaaabbabbbaabbbaaaaaaaaabaababaaababbaabbbaabbabbbababaaababbabbaabbabbaabbabbbaaabbbbabaababbbbaabbaabbaabbbaabbbbabbbababbbabababbaaababaababbabbaababababaababaaabababbbbaabbabaaabaaaabbabbbbaaaabbbbabaabbbbbabaaaaaabbaabbabbbaaababbaabaabbaaaaabbbbbabaabaabaabbbaababaaabaabbbaabaaaaabbbbbbababababaabbaabaabababbabbbbababbbabaabaaaabaabbaabbbbaaaaabaaaaabababaabaabbbaaabbbaaaababbbaaaabababbbbabaaaaaabbaabbababbaabbbabaabbabbaababbbbbabbabbaaabbabbaababaaaabbabaababaababaaaaabbabbababbaaaababbbbbbabaabaababbbbaaabbaaaaabbbbabaaaabbbababbbbbaabbaaaaababaaaabaaabbbbbaaabbbaaababbabbbbbaabbbababababbbabbababbaaabaaaaabaaabaabababaaaabbbaaaaaaaaababaaabababbaabbbaaaaabbbabbbbabaaabbaaaababaaabbbaaabbabbabbbbbbbbbbaaabaaaaabaababbbbbabababaababbababbaaaaabbbbaababbababaaaabbbbbbbbabaababbaabbbaabbaabbbbbaababbbbbbaaaabbabaabbabbabbaababaabbaabaaaaababbabbbbbabbababaaababbbabbabbabbbabababaaaaaaaaababbbbbabbbaababbbbbbbbaabaabababaabaababaaabaaaababbbbabbaaabaabbbbbbbbabbbaabbbbababbaabaaaabbabaabaaaabaababbaabbabbbbbabaabaabbababbbbbbababaaabaaaabbbbbaababaabaaabaaabababbaaabaaaabbbbaaaabbbbbbbbbabaabaabbaabaaabbaabababaaaaaabaaabbbbabaababbaaaabbaaabbabbbbabbbbbaabbaaabbbbabaaaaaababaaaababbaaababbaababaaaabaababbaabaababaaaaaaaabababaabbabaaabbaaaaaabbababaabbbbbaabbbbaaababababaaaaaabbbbbabbbbabbaaaaaaabbabbbbabababbababbaabbbabbbabababbbbaabababbabbbbababaaaababbaaaaaaaababbbbbaaabaaaabaabbabaabaaaaaaaaaabbbaabbbaaaabaaabaabbbbababbaabbababababbabbbbbbbbbaabbbabababbbaabbbabbbbbababbbbaababaaabbbbaabababbbabaaabbbbaaaaaabbbbbabbabaabababbbaabaabbaababbaababbbbababbaaaaabaaaabaaabbabbaabbbbbbbababbaaabbaaaaaaaababaaabaaabbbabbabbabbaabaabbbabbaaaabbbaaaaaababbbabaabbabababbababbabbaaaabbabbbaabbbbbabbbbbaaabbbbbababaabbbababaaaababbaaaaabbababbabababbabaabbbaabbaabaabaaaababbabaaabbaabbbbbbabbaabbbaaaabbaababababaaabaaaaabaabbbaabbbaabaaabbbbbbbaaaaababaabaabbbbbaaaabbabbabaaaabbaabbbbbaabbabaabaabbbbaaaaaaabababbaababbbaabbaabbabbaabaaabaaaaabbaaaabbabbaaaaabbabbabbaaabaaaababaabbaaaaaabbbbbbbabababaabbbbbabaabaabababbbbbaaaaaaaaabbbabbaaabbbabaababaaababbaaaabbbababbaaabaabbbabaabbbbabbaaaaababbbbbbaaaaabbabbaabbaabbbbabbabaaaabababbaaabaabbbaabbbbbababbbbabbbbbbaababaaabbabbbaabaaababbaaababaaababaaababbaabbbabbaaababbbaabaabaaaabaabaabaaaabaaaabbaaabbbaaabbbaabaabbbabbaaabbababaabbbbbabbbababbbaabbbabaababbbbbabbbbabbaaaaabbbabaaaabaabbbbababbbbbaabababaaaaabbaabbaaabbaaaabaabaaaabbbaabbabbabbabbbaaabaaaabbaabbabaaaababbabaabbabbabbbaaaababbbbaababbbababbabbababbbabbaabbbabbbababbbabbabbbbbbabbbbbaaaabbabbaaabaabbbaaaabaaabaabbaaabbbbbaaabbabbabbbbbbababbaabbbbbbbaaabbbaaabbabbbaabbbabbaabaaaaaabbaaabaaaaaaabbbbbbbbaaababbbbabbaaabaaaabbaaaababaaaaaaabbabbbababaabbbabaaaabbaaaaabbbbabbabbababaaaabbaaaaaaabbabbabaaabaabbabababbbabaaaabbbabbabaaaaabaaabaaabbaabbabbbbaaaaaabbabaaaaabaaabbabbabaabbabaaaabaaaababaabababbaabbbaabbbbabbbbbbabbabaabbaaababbbabaabbbaaabbabaabaaaabaabbbaaabbbbbbaabaaaabababbbbababbabababbbbabaabbbbababbbaaaaaaaaabbabbababababbabaabaaabaabbabbaabbaaabaaaaabbabbabaabababaabababbbaabbabaaabbbbaaaabbaaaaabaababbabbaaababbabaaabababababbbaabaabaaaaaabbabaabaabbbbaabbabaaaabaabababaaaaabbaaabbabbaaaaabbaaaaababbbbbbabbbbbbbbababbabbbabbbbaaabaababaabbbabbbbbababbababbabaabbaaaabbbbbaabbabbbbaaaaabbbbbbbbbababbaabbaaabbaaabbabaaababbbabaabbbabbbababbabbaaaaaabbbbbaabbbababbaaaaaaabaababaaaaaababaaabbbbabaabaabbaaabaaaaaaabaaaaabbabbaaababbbbbaabaaabbbababbbabaaaabbaabaaaaaaabaaaaabbabaabbbaabbbaabababbbbbbbbbbbbbbabbabaababaaabaabaaaabaabbaaababbaabbaabaaabbababbabbbabbaaababbbaababbaababababbaababaaabbbababbbbbababbbbbaaabbbabbabbbaabbaaabbabaaaaaaabaabbabaaaaabbaabbbaaaabbbbbbbabbbbabaaabbababababaaabbaaaabbbabaabaaaaaaaabbabaabababbbbaaabababaaabaabbbaabbaabbbbbaaaababbbbbbbbaabaaaabbabbbabbabbbbbbbbbabaaabaaabbbbbbbaabababaabbbbbabbababbbaaabaababaaaaaaaaabaabbabaabbaaabbbbbabaabaababbbbabbbbbbbabbbbababaaabaabbaabbaabbaabbbaabbbabaaababbababaaabaabbaabaabaaabaababbabbabababbaaaaaaaabbbabbaababaababbabababbbaabbbaababbbbabaaabbbababaabbbbbbbbbaabaaabaabbabbbbbbbbaaabbaabbbbaabbaababaaaabbabbabbbaabaaaaaabbaabababbaabbbaabbbabbaabbbbbbbaaabaabbabababbaaaabbbababbaaabbbbbbbbbbbbaababbaaaabbaabaaaaabaabababbabaabaabbbabbbabbaaaaaabbbaababaaabaabbbbaaaabbaaaabababaaababbbaabaaabbbaabababaabbaaabaabbabbababbaaaabaabaaaaaaabbbbabbaabbbbaaababbabbbabbaaaaabaabbaaaabbabababaaaabaaaabbaabbbaaaabbbbbbbbbabaabaaaabbbbaaabaabababaaabbbbbbbbbaabaaaaaabbaaaababbbbbabaabaabbababbbaaaabbbabbaabbbbbbbbaabbaaaababbbabbabaabbbaabbbabaaaabbbabbabbbabbaaabbbaaabaabaaabbaaaabaaabaaabbaaaabbbbaaaaabbbaabbaababbbabaabababaaaaabbaaabaaaaaaaaabbbbaaaabaaaaabaaaaaaaabbababbbbbbbbbaabababaabbbbbaaaaabaabbbaababbbaaabaaaaabbbbabbbbabbbababaaabbbabaaaabbbaaaaabaaabbaabbbbbbaaaabaaaaababbababaaaabbbaaaaabbbbabbbaababbbabbbbbbbaaabbaaabbaaabbabbbbabbaabbbbaababbbabaaababbbbbbaabaabbbaababbaaabababbbaabaaababaabaabbabbaabaabbbaababaaaabbabbaaaaabaaaaabbaaaabaaabaabaabbbbaabaabbaaaabbaabbaaabbababbbabaaaabbaaaabaabbbbbbabbaaaaabaaababaaabbaabbbabbbabaabaaabaaabbabbababbbbbabaaabbaababbabaaaaaabbbbabbbbbbabaabaaaabbabbabbaabbbbabbbaaaaabbabbababbaaaababbaaabbbbaaaaaabbababbabbbbabbaabbbaabbbbaabbaabaabbbaabaabaabbabaaabaababaabbaaaaaabbbbbbabbbaabbaaaabbaaabaababababbbaabbaabaaabaaabbabbbbaabbbabbabbaaabbbbbaaaaaaaaaabbbbabbbbabbaaaaaabbaabbbbaaaaabaabababbbaaaabaaabbbaaabaabaaabaababbabaaabababbbbbaabababaabaaabaaababbaaaabbbaababbabaaabaaababaabbbaababaabbbabaaabaaaaabababbbaaababbbbabbbbbbbaabaabbabbbaaaaabbbaabaaabbbbabaaaababaabbbbbbaaaaabbbaaabbbbbbaabaaabbbababbbbbababbbabbababbbaabbbaaaaabbaaaaabbbbbbbbbaaababbbbbababaaaaababbbbabababbbabaaabbbbaababaaababbabababaaaabbbaabbaabbaaabbabbbaaaaabbaabbbbabababbbbbbaaaaaabbaabaabbbababbbaaaaabbabababbbbaaaabbaaaaabbabbabbabbaaabaaaaabbbabababaabbabaababaaabaababaaaabaabaaaababbbbaabbaaabbabbababaabaaabbaabbababaaabababbabaabbaaabaaaaaabbbaabbabbbbbabaaababbbbbbbabbabbaaabbabaaaabbbbaabbaaabaaaabbababaaabaaabbbababbbbbaabaabbbaaaaaabbabaaaaaaaabbaababaaabbbbbabaababaabaaaabbaaababbaababbaaaaabbaaaaaabbbabbabbbabaababbbabaabbbbabbabbaaaabbbbaaababaabaabbbabbbbaaaabbabababbaabaaabababbbbabbaababbbaabbababbbabbbbaaaaaaaaababbbababbbbaababaabbbaabbaababbabaaaabbbaabbababaabaaabaaababbaaaabbbaabbabbbabbabbaabaaababbaaabaabababababbabbaabbabbbaababbaaababaaabaaaabaaaabbbaaaababbbbbabbabaababaaabbbbaaababaaaaaabaaabbabbabaabbbbbbbbaababbabbbababaaabbbbaabbbaaaaabbabbbabaaaaaaaabaaaabaaabbabaaabaaaabbbbbbbaabbbabbaabbababbabbabbaaaabaabbaaabbaabaababbabbbababaabaaaabbabbbabaaabbbabbabbaabbabaaaabbbbbabaabbabaaaaabbaababaababbbbbbabaaaabbaaababbabaaaabbbabbbababaaabbabbbabbbbabbababababbababaaaaaabaabbbaabaaaaabababaaababbbaaaabaaaaaaabbbabbbbabbbabbbbbabbbabbaabbaaaaabbbbbbaababaaabababbabbabbbababbaabbbbabaabaaabbaabaaabaaaabaabbabaaababbbabaaaaaabababaabbaabbaaabbbaaaababbaabbbabbbaabbaaabbbbaaaaabaaabbaabbbbbababaabababbbaaaabbabaaabbababbaaabbabaaaaaaaabbaaaabbabbbbbbbabaaaaabaaaaabbabaaabbbbbbaaabbbbbabaabababbbbabbabbababaabbbbbaaaabbbabbabbbbabbbaaaaabbbbbaaaabbaabababbbbbbababaabaababaaaaabbababaaabbaaaaaabbabbbbbbaaababbbabaabbaabaaabbaaaaabbbaabbbababababaabababaababbaabbbbbabaaababbabbbaabaaabaabbbabbaababababaaababbbbbbbbabbbbaabaaaabababaababaabaabbaaabbbbbabaabbabaababababbbaaabbbabbbabbabbabbabaaaaaabaaaaabbabbaaaaababaababbbabaabaaabaabaabbaaabbbbababaabbaabaabaaabbaabaaaaaaabbaabbaaababbabbaaabbabaaababaabbbaabbbbabaabbaabbbbbaabbabaaabaaaababbababbbbaaaababaaabbabbbbabaaabbaabababbaabbbabbbaabbabaabaabbbabbaabbbbbaaabaabbaaaaabaaaabbbaabababbaaaabbbabbabaababbaabbaabbabbaaabaababbaababbabbabbbabaaaabaaabbbbaaababaaabbaaabaaaaabbaabaaabbbabbaabbbababaaabbbbbbaaaaaababbabaabbbaaaaabaabaabbbabaababbabaabaabbbbbaabbaaabbaaabbaababbaababbbbbabbabbabbbaaaaabbaabbaaaabaababbbbaabbabbababaaaaaabbbaabbbabaaababaabbbaaabbaabaabbbaaaabbaabbabbababaababbbbbbbababaaabaaabbbbaaabaaabbaaaaabbbbaaababbabbbaaaabaabbbababbabbababbbababaabbaababbaaabbabbaaababbaaaabbaaaaaabbbaababbabaabbabaaabbbbaaaaaabaabbaabbbaaaabababaaaababaabaaabaabaababbaaabaaaaabbaaabbbbaaaaabbbbbaabbaababbaaaaababaabaabaaaaabbbababaabbbbbbbabbabbbbaaababaaaabaabababaabbaaaabbabbbbaabbaaabbbbbaaaababbbbbbbaababababbbabbaaabaabaababbaaaaababbaabbaaaabbbbabbbababaaabaababababbabbbbbaaaaabababaaabbbbbabaaabbabaabaabbaaabaaabaababbaaaabbabaaabbaabbbbbbbabbaabaabbbbaabababaabbbabbababbbababaaaabaaabbbabbbabababbaaaaaaaabaaabbabbbbbbaabbbbaaabbbbbaabbaababaaaaaababbbbbbaaaaababaaaababbbbbaababbbababbbaaaababaabbaaababbbbbbaaabbababaababbbbaabaabaabbbaaaabbbabbbbbabbbaababbababbbaabbbabbabbabababbababbbaaaabaaaaaabaabaaaabaaababbabbabaabbaabbbbaabbbbaababbaaabaababaababababbbbbaaaabbbababaaabbbbbabbaababbaabaabbaabbaaababbbbababbbabbaababbaaaaaaaaaaaaabbaabbabbaaabaabbbaabbbbabbabbaaabbabaaaabbbbbbabbbbabbbbbaababbbbbbbbbaababaaabbaaaabbabaaaabbaababbbababbababaaabbabbbaaababaaababbbaabbaaaaaaabbbbabababbbbbababaaababbbaaababbbbaabbbbbbbbaaaabbababababbbaababbbbbaaababbaabababbabbbaabbabbbaaabbbabaaaabbbbaabbaaaaaababbbabbaaabaaabbabbbaabbbbabbbababbaabbbabbbbaaaaababbabbbaabbbabbbaaaabbbbaaaabaaabbabaabbabbbabbbbbabababbbbbabbaabbabbbbbabbaaababbbbbaabaababbaabbaabbababbabbbbaaaababaaaabbaababbabbabbbbbaabaaabaaaaaaabaaabbbbbbbaabaabbaaaaaaabababaabbababbbbbbbabaaababaaaaabbaaabbbaababbabbabbbbaaabbbbbbbbaaaababababaabbbaaabbaaabbbabbabaaaaabbaaaabbabbaababbaaaaababbaaaababbaabbbbbaabbbbbbbbaaaababaabbbbabaabbbabbbbbbbabbbbbbbabbabbbbbaababbabaaaabbababbbbbaaaaaabbaababababaaabaababbabbbaaaaabbabbbbbabbbabababbaababbabababbbabbabbbabbababbbababbbbbabbabaaababbaaaaabaaabaaabbabbaaaabbbbbbabbaabaabbbaabaabaaaababababaaaabaaabaaabbbaabbabbbbbaaaabbbbbaaabbbabbbbabbbaaaaaabbbbbbbbaabbabababbbbbababaabaaaaaabbaaaabbbbabbbababbabbbaaababbbabbbabbbbaaabababbabbbaababbbabaabaababbbabbbbaaabbbbbaabaaabbbbbaabaabbabaababbabbbabababbaaaabbabbbbaabbabbbababbaaababbabaaaaaaaaabbabbabbbababaabbabbababaabbbbbbbbbabbbaabbaabbaababababababbaabaabbbabaaabbaabaabbababbaabbbaababaabbabaabaaaaaaabbabaaaabbbbaaaabaaabababaaababbabbbaaabbabbabbabababbababbabbaaaabaaabababababbababbbbbaaabbaabaaaababababaabbabbaabaabbbbbaabbbababaaababbaaabbbbbaaaabaababaaaaababbabbbbbabbabaaababbbbbbbbabaaaabaabbaaaabababaababbbbbbaabbbbabbbabbaabaaabaabaabaabbaabbababbaaabbbaaaaaaababaabbabaababbababbbaaabbaababababaaaaaaaababbbbbbbbbababbaaababbbbbbbabbbbaababaabbaaabbbabbbbaaabaababaabbaababbabbaabbbabbbbbbabaaaabbabbabaabbbaabaaabaaaabaabbaaabbbabbbababbbbaaabbaabbbaaaabbaabbaaaaabaaaabaaaaabbbbabaaabbbbbabbbabaabbbbbaabababaababbbabbbabababbaaabbaabaabbabbbbabaaabbbbaababbbbabaaaabbbbabaabbbababbababaaaabaabaabbabaababbabbbaaabbabbbbbbababaaabbbbaabbbbababaaababababbaaabbabbbaaabbaaabbabababaabbbbababbbbbbbbabaabbaabbbababbbbabaabbaaaaabbababbbaaabbbaaaaaababbaaabaabaaaaababaaaabbabbabbbabbbabbabbababbbaaaabababbabaababbbabbaabbbbbbbaabbbababbabaaaaabaaaabaaaabbbaabbbaaaaabbabbabaabbabbabababbaaaabbababaabbabaabbbabbaaabaabbabbababbbbaaaaabababbaaabbaaabbbbbabbaabbaaaaababbaabbababbbabbabbbbaaaabbbabbaaaaabbaaabbbbbaaabbabaaabbbabbbaabbbaaabababaaabaabbaaaabaabaaababbbabbabbbbbbabbaaababbbbaababbabbabbbaabbaabbbbabbaaaaaabbbbabbabbaaaabbaabaabbaabaaaaababbbababbaaabbaabbaaabbabbabbaabbbbababbbbbbabbbbbabbaabbabbabbbaaaaabbbbbaaababbabbaaabbbaabbbabbbbabbbbbaabbaabbaaabababbbabbbaabbbbbbabbbaaaaaabbbaaabbbaaaababbbbaabbbbbbbababbbabaabaababaabbaababbabbaaabbaaaaaabbbababbaaababbbbabababaaabbaaaaaabbbbabbbaababaabbbbabbabaaababaababaabbaababbaaabaaaaaaaaabbbbababbbbbaaaabaaababbbaaaabbbabaabbbbaabaaaaaaababbabbbabaaabbbbaaababababaabababbaababbaaababbababbbaaaabbbbabaaaabbabaabbababaaaabbbbbabaaaabababbaababbaabaabbbbbbaaaaaabbbaaabbbbabbababbabaabbbbababbaabababbbbbaababbbaaabaabbbbabaaabbaababbababbbaaababaaababbabbaabbababaabbaaabbbbaabbbbaaabaabaaabaaaaaaaaabbabaababbbbaaaababaabababbbbaaaabbbbababbbabababbaaababbbbabbbbabbbabbaabbbbababbbaaaaaabbabbbbbabbbbbabaabaaaaabbbaabbbababababbbaababbaaabaaaabbbbabaaaabbababbbbbaaababbbbbbaaabaabbaabbabbaaababbababaabaaabababaabbbbaaaababaababbbbaabaababbbbbabbbbababbabbbbaabbbaababaaaababbaaabbbbbbaaabbbabbabababaabbbaaaabbbaaaabbbaaabbbabbbbaabaababbbabbabbbbbbbbbbbababbaaaabaabbbbbbaabaabbaabbabbabbabbabababbbabababbbbaababbaabbbabbabbaaabaabbbbabaababaabbaaaababaabaaabbbbababababbabbbbabbabbabaaabbbabaabaabbabbababbabbbabbbbbbbbbaaaaaabbaaababbbaaaababaabaaaaaaabaabbbbabbbaaaababbbaaaabaaaaabaabbababababaabaaabaabbaabbaabbaaabbabbaabbbbaaabbbabbbbaaaaababaaabbaabbbbbbbbbababbbbbbabbbbbaabaaabbabbbbabbababbbabbaaabbbabababaaabbbaabaabbabaababaabbabbaaaababaaabbabbabbaabbaaaaaaababaabbbababaaababbbaabbabbbbbbaabbbabaabbbaababbabbabbaabaaababaabbbbaabbaaabbbabbbbbbabbaabbaaabbaaaabbbaaaabaaaabbabbbbbbabbbbabaababbbbaabbababbabbaaaabababaaabbbaaaaababbaaabaabbaabaaaaabaaabaababbbbaaabbaababaabaaabaabbbbbbbaabbbbbaabaaabbaaababbbabbbbbaaaabbaabaabbaaabbaababaaaababbaaabaabaaababaababaaaabbbaabaaabbbbbbbbbbbabaabbaabaabbbbaaaaaabaabbbbbabbbabaabaaabaaabbbaabaaaabaabbabbbbabaababbabbbaabbbaaaaaaaababaaaabababbabaabbaaaaaabbabaaaaabbbaabbaabaababababbbabbbbbaaabbbbabbbabbaabaaaaabaaaabababbabbbaabbabaabbabbabbbbaababbabaaaabbabbaaaaabbabaabaabaababbbbabbabaababaababaaabaaabaabaabbaaabbbbababbaaababbbabbbabaabbbabaabbbbbbaaabbbabababbabbbbbbabbbbbabbbabaabbbbbbaabbbbaaabbbbbabbaaaaaaabaabaaaaabbbbabbaaaaababababaaaaaaababaababaaaaaaaabbbbbaababbbbabbaabbabbbaabbbaabaaaabbaababbaaaababbabbbbbabaabaabbbbaaaababbbababaabbaabbaaaaaaabbbbbbbbbbaaabbabaaaaababbbbabbbabbbbbbaabaaaabaabbaababbabaabbbbabaababbbbbbaaabbaaaaababbbbbabbbbbbaababaaaaaaabbaaaaaaaaaaaaaaabbaaabaabbabababbabbabbbbbbabaababaaaabbbbaaabaaaabbbbbabbbaaababaabaaabaabbbabaaaaabaabaabbabbbaabaaababbbaabbababbbbbbabbaaabbaabaabaabaabbabbbaabaabbabaababaaababaabbabababbbaabbbabbbbbbabbabaaaaababbabbabaaaabaaaabaabaaabaaabaabbbaaaabaabbbaaabbaaababaabbbbaabaaaabbaaaabbbbbaabbaaaaabbabbbbbbbbababbbbbaaababbbbbaabababbbbbbbbaaaababababbaaaaabbbabaabaaabaababbaabaabbaabaabaabbbbaaababaaaaaabaabbbbbbaaaabbbaabbabbbbabababbabbbbabaaaababaabaababbbaabbbaaaaabaabbbbbbaabbaaababababbbbabaabaabaaaabbaaaaabbabafabbaaaabaabbaabbababaabbbbbaaababbabaaaaabaaabbbaabaaabbbaababbbbabbabababaaaabbbbbaabbaababaaaaaaaabaabaababaabababbabaaababbabbaabaaabbaabbababbabaaabbbababaabbbbabaababbbaaaabbbaaababbabababbabbabaaaaabbabbbbababababbababaaaababbbaabbabbabaaabbaabaabbbbbbaaaababbaabbbabbabbbabbbbaababaaababaabbbbabbaaaaabbabbbabaaaaabbaaabbbbaaabaaabbabbaaabbbbabaababbbaababbbabbbbbabaababbbbabababbbaaabababbabbbaaababbbaaaaabaaaabbaaaabababbabaaabbbaaaaabbaababbababbbabaabaababababbaaabbbabbbbbaaabbaabbaababbabbababbaaaabbabbabaaabaabaababbbaabbababbbbaaabbbbbaaaabaababbabbabbbbbbbbbaabaaaababbbabbbbabbaabbaabbbbaabbbabbbbababbbabababaabbaabaabaabbbbbbbbaaaaabbbbaabbbbaaaaaaababbbbaabaabababaaaaabaaaaaabaaaababbabbaabaabbbbbbabaaaabababbbbabbaaaabbbabbbabaabbabbabaabaabbababababaabababbaaababbabbbbbbbabaabbbaaaaababbabaabbbababbbbaaaaaabbaaabbbababaaaaababaabbbaabaabbbbabaaaaaaaababbbaaabaababbaabaaababaabaaabbabbbbaaabbbbaaaaabbabbaaaaabbabaabbbbbabaaaaabaaabbbaaababababbaaabaaaabaaaabbaabbabbbababbbbaabbaaaaabbbbaababaaabaaaaaaabaabaabaaaabbbbbbbbaaabbabbababbbabaaaabbababaabaabaaababbbaabaabbabbbbbaabaaababaabbbbbababbabaaababaabbbaabbaabbabbaaababbaaaabbbaaaaaaabababbabbbabbabbbaabbabaabbabababaaaaaababbaaabbbbabbbbabaaaaaabaaabaaaababaabbbbbaaabababbabbbbabaababbbabbababbabbbbababaababbbaaaaaaaabbbbababbbbaaaabbabaaaaababbbbabbbaababbbaabaaaaabbabaabbbaaabbbbabaabbaaaaabbbbbabaaabbbaaaaababaabbaabaaabbabaabababbbaabaabaabaaaabaabaabbababbbbabbbabbbababbababbbaabbaabaabbbabbabbbbbababababaaaabbbabbaaababaabaabbbaabbaaaabbaaabaabaaaaabbaabbaabbababbbaaaaabaaaabbbbbbbaabbbbbaaaaaabbbbaabbbbabaaabbbbabaabaababaabbbaabbaaabaaababbbaaababaaababaabbabbaabbbbbabbbbbbabababaabaabbabbbaabbbbaabbaabaabaaaaaabbbbabbababbbbbbbaaaabaaaaaababaaaaaaabbabbaaabaabbababaaabaaabbaabaabaabbabbbbbbbbbaabaabbabbabbbabbbbbbabbababbaaabbbbaaabababbabaabaaabbbaaaaabaabbbbbbbbaaabaababbbbbbbaaaababbababbabbbabbaabbaaaaaabbbbabbbbbabbbabaababaaaabaaabbbbaaabaabbbbabbabaaababbabbbabaabaababbaabbbabaaaaababaabbaababaababbbbbabbbaabbabaabaaabbbbbabbbbbabaaaabaaabaabbbaabbbbaaaabbbbaabaaabbaaaabbaababbbababbbabbaaaabaabbbabbbabbaaabaaaaaabababbabbbbabababbbbabbbbaaaaaabbaaabbbbaaaaabbabbaaaababbaaaabaabbaaaabbbaaaaababbabbababbabaaaabbaabbbbaaaabbbbababbbbbbbaabbaabaaabbbbababbaabbabaaaaabaaaaabbabaaaaaaababaaaaabaaabbbbbbbbababbababbbababababbbaaabbbaaaaaaaabbbbbaabbbbbbbaabbbaabbbbaabaaaaaaabbaabaaabbbaaabababbbbababbaaababbbabbabbbabaaabbbaabababababbabbbaaabbaabbbaabbaaabbbbbbabbaabbbabbabbbabbabaabbaababbbbaabbabbbabbabbaabbbbaabbbaabaaaababaabaabaaaabbbaabaabaaabbabbabababbbabbaaabbbbbbaaabbaaaaaaabbbaaaababbbbababbabbbbabaaabbaaaaababaabbbaababbababaabaaabaabaabaaaaabaabbbbbabaaabbaaababababbaaabaababbaababbabaabbbaaababbbabaabbaabbaabbaabbbbaababaababbabbababbbabaabbbaabbababbabaababbbabbbbbaaabaaaaababbbbbbaababaaaabaaabbabaabbaaaaabaabaaaaababbbaaaaaabaaaabbbaaabbabaabababbbaabababaaabbbabbabbaababbbabbbaaaabaaaaaaabaaaaabbbabbababbbabbbaabaaabbabbababbaabbabaabaabaaaaabbababbaaaaabbbbbabbbabbabaaaabbbabbaaababaabbbbaabbbbbbbbabaaaabbaababbabbaabaabaabbabbaabaabbababaabaabbbbbaabbbbbbaabbbabababaaaaabaaaaaaaabaaabababaaaaaabbbbbbabbaaaaaaabaabbaaaabbbbbbbaaabbabaaaaaabbbabbabaababaabaaabbbbaaaabbbbaaaababbaaaaababbbababbaaaaabaaaabbaaabaabaaabbbbbbbaabbbabbabbbbabaabaabbabbbbababaabbaaaabbabbbaabbababaaaaaaababbaaabbabaabaaabbbabbbaaabbaaaaababbabbaaaaabbabbbaabbaabbaabbabbbbbaabbabbaaabaaabbababbaababbbbbbbaaaaaabaabbbbbbbbabbababbbabaaaabababaabaabaabaababbababbabbbaaabaaababaaabaabbabbaaabbbaaaaabbbbaabbbbbbbbababbbbbaabaaabbabbaaaabbbbbaaaaaaabaaaabbbaaabaaabbababbbbbbbaabbbaababbaabbbbabaaabbaaabbbabbababbaaabbaabbbaabbbbaabbaababaaabbbabaaababbaaaaabaaaaabbbaaaabbbbbbaaaababaababbbabbabbababbbbaabbaabaaababaabbabbbaabbabababbbabbbabbbbbaabbbabbbbbbbaaaabbbabbbbbbbaabbaabbaabaabbaaabaabbaabbaabbababababbaababbbababaaaabaaabbaaabaabbbbaaaaabaaababbbbabbaabaaabbaaabbaababbbbaabaaabbbbaabbaaaaaaaaabbbbabaabbabbabbbaabbabaaababbbbaabbabaababaabaaabbaaabbbaaaababbbbabbaaaaaabababaabbbaabbaaaababaabababbababaabbbaaababbbbbababbbaabbbababbbabbbabbabbbbaabaabbaabbababbaabbbabaaaaaabbaaabbababbaabbbbaaabbbbaaaabbbaabaabbaabaaabbaaabaaaaababbaabaaaabbabbabaababaaababbbbbabaabbbbbaababbaabbbabbababbbaababaabababaababbbabaabaabbbabaaaababababaaaaabaaabbbbbabbaabbbbabbabbbbabbabbbbbabbbbabaaaaabbaabbbababbbbbbbabaaaaaaaabababbbbbababbbabbaabaaabbababbbabaabaaaaabbaabaaabbabbbaabaaaabbaaaabbabbaabaaababaababaabaababaaaabbababaababbaabbbabaaaabbaabaaabbbabbbbbababaabaabaabbabbbabbbbaabbabaaaababaababaaabaaaabaabbaaaaaaabaaabbbaabaaabbbaaaaabbbaabbbaaaabbbbbbbabaabaabaaababbbbababbbbabbbabbaaabaaaaabababbaaaaaaabbabbabbaabaabbbbbabbbbaaaaababaaaabbbaaaabababbaaaabaabaabaabbbabaabbaababbbbbbbaaabbaababbaabaaaabaaababbbaabbbbbbaaabbaaaabaaaababaabbbaaaabbaaabbaabbababbaaaaaaabbabbbabbaabaabbbbbbabbbbaaabababbababbabababbbaabbbbbbaabbabbaaaaaaabbbaabbbbaaabbaabbbabbaababbbababaaaabaabaabaababbaaabaaaabbabbbbaabbbbabbbaabbbbabbabaababbbabbbbbaababababababbaaababbaaabbaaaabbaabbbabaaaabaaaabbbaabaabbababaabbbaaabbabbaaabbaaaaabbabaaabbbaababbbbabbaababbbbabbaabbbaabbabbbabbbbbbbaabbbbbaabbabababbbbaababbaaaabaabbaabbbabbaabaaabbbbbbaababbababbbaaababbabbaaaaaaabaaabbbaaaabaababbaaabaabaabaaababaabbaaabaabbbbbabbababbaabaabaaaaaabaabaaababaabbaaabbbbbaaabaaabbbbbbabbbbabaaaaaabaabbabaababaabbaaabaaabaaaaaabaaaaababaabbbbbabbabbaaaabbbaaabaaabbaaabbbabaaaabbbaaaaaaabaaaaaabaaaaaaaabaabaababbabaabaabaababaaaabbaaabaababbbbbbbabbbbabaaabbaabbabbaaaaaaabbbabbabbbaaabaaaabbbabbabbbaaababaaaabababbbbaababbbbbababbbbbabbbbbabbaabababaabaaabbaabababbbbbaabbaabbaaababbabbaababaabbbbbbabbaaabaaaaababbaabaabaabaababaaabaaaaababbbabababbaabaabbaaabaaabbbbbaabbbaabbababbaaabbbbababaaabbbbabbbababaaabaabbbbabbaaabababbaaaabbabbbaabababbbbbaaabbbabababababbbbbaaababbababbbbabaabbbabababbabbaaabbaaaababbababaaabbbbbaaababbbaaabaababbabababaaabaabbaaabababaabaaaaaaaaabaababbabbbbbbaabbbabbbbbaaaaabaabbaaabbbbbbbbbbbaaabaaabababbbbaabbabababbaababaaaaababbaaaabaabbaabaabbabbabbaaaaabaabbbababbabbabababbbaaaababbaaaaaaaaaaaababbaaaabaabbbbabbabbabbabbaaabbbaabababbbaaaabaabbbbbbabbbabbaaaaabaaaaabbbaaabaaaababaabbabbaaabaaabaaaabbbbbbaabaaababbbababaaaabbabbbabaaabbabaabababaaabbbabbaaaababbaaaabbbabaabaabbaaaabaaaaababaaabbabbbbbaabbaaaababbaabbabaabaaaaaabbbbabaaabbbbaaaabbaabaaaababaaabbabaaaabbabbbbabababbaababbabaaaabbbabbaaabbbbbaabbabbbabbbabaababaabbaaabababbaabbbaaaaaabbaaababbaabbbbbababbbbbaaaabaabbbbbabbabaaaaaabbbbabbaabbabbbabbaababbaaaaabbabbbbabbbbbaaabaabbbabbabbbbbbabbbabaaababbbbbbabbabaaababbaabbaaaabababbaababbaabaaabaabbbaaaaabbabbbbaabbabbaabaaaabbbbaaabbbabbaabababbaabbabaababbbbbaaaabaaabbbabbaabaabbabbaaababbbabababaaaababaaababaaabbbabababbabaababbbaaabaaaabababaabbbbbababaaaabbbbabaaaabababbbaaabbaababaaabaaabaaabbbbabababababbbbaabaabaaaabbbbbbaabbaababbabaaabaababbbaaabbbaabbbbbbbababaaabaabbbbaababbaabaababaaabbabbababbbbbbaaaabbaabaaabbabaabaaaaabbbabaaaaaaaaababaababbaabbabbabbbbbbbaaaaabaaaaabbbaaabbbbbabbbaaaaaaabbbabaaaaaaaababbbaababbaaaabbbaabbababbbbbabaabbaabbbabbbbbabaabaaaababaabaaaababaaabbbaaabaabbabbbaabaababaaababbbbbabbbabaaaaabbbbbbbabbbaaaabaaabaabbbbabbabbbbbbaaaaaabaaabbbaaaabbbaaaaaabbabaaaaababaaabaaaaaaaabaaaabbabbabbbbbaabbbbaaaaababbbababaabbaabababbbaaabbabbabbaaaaaaaaabaabbababbaaabbabbabbbbbbaaabbaaaabaaaaaaabbabbaababbbbabbbabaababbbbbbabbbbbbabaabaaaabbbaabbbaaababbbaaababbbababbaabbbbbaaabbbbbababbbbaaabaabbaabaaababbbbbbbabbaabbbabbbbbbbaabaabbbaaaaaaabaaabababaaabaababaaababbababbbbabbbaabaaabaabbabbbbaaaabbaabaaabbbaabbaabaaabbaaaaaabbbbbabbbbabbabababaaabbbabbbaabbabaababaaaaabababaabbbbaaaabbaaababbabbaaabbababaabaaaaabbabbaabbabbabbabbbbbabaabbbbbaababbbbbbbaabbaabbaababbababbbabbabbbabaaaaaaabababbababbbabaaaaaabaabbabaaaabbaaabababbbaaaabaaaaabaabaabbababbababbbaabaababbbabaaaabaabaabbbabaaaabaaabbaabaaababababbabbbbabaaaabababbababaaaabbbaabbababaaaaabbbaaaaabbabbabbbbababbbbbaaabbbbababbbbababbaaababaabababbbaabbababaabaaaabaaabababaaaababbaaabbaaaabbababbbabbabaaabababaaabbaabbabbbbaaaabbbaabbbbbabbaabbabbbabababaaabaabbbbaaabbaabbabbaaaaabababaaaaababbbbbabaaaabbbbabbaabbbbabababaaabbbbbbaaaabbabaaaabbbaaaabababbbaababbaaababaabbbbbababbbbabaabaaababbabbaaababbaaaaaababaabbabbaaaaaaaaababbbaaaabaaaabaaabbaaababbaabbaaabaabbbbbbbabbbbbbabaababbaaabbbaabbaabaabaaaabbbababbaaaabbbabbbaaaabaaabaaaabaaabaaabbabbbbbbaabbabbabbaaaabbbabbbaaababbbbaabbbaaaabaabaaabababaaaababababbaaabbbababaababbabbbbbabaabbbabbababaaaaabaaaabbaabbbbabbbbbaabbabaabbaaabbbbbbaaaabaaaaaabbabaaaaabaabbabbbbbababbaababaaabbabbababaaababababbababbbbaaabaaaabbbbbbbaabaabbababababababaaaababbbbaaaabbbabaaabbbaaabbbabaabbbaaabbbaabaaababaababbbababbbaabbbabababaaabbbabbbbaaabbabbbabaaaabbabbaaabbabbbaababababbbabaababbababbbabaaabbbaaabbababbaababaaabaaaabbbbabababaaabaaaababbbaabababbbbaaaabaabbbbababaaabbbaababbbabaabaababaabbbababaabbabbaaaaabbbabbbabbbaababbaabbbbabaaabbabababbbbbaabbaaaabbbbbbbbbabbabbbaaabbabaaababbabbbabaabaaaaabbbbaaababaabbbaaaaabbbbbbabaabaaabbabbaaaabbbbbababaabbbbabaaaabababbbbbbbabbabbbabbbababbababbbaaabaaaaabbabbbbbbabaabaabbaaababbbaabaabbabaaaaabaabbabaabaabbbaababbbbaababbbabaaaababaabababbbaabbbbabaabbaaabbabbbababbbaaabbabaaabbbbaabbabbbbbbabbababababaaaabbbbbaabaaaaabbbbabaaaaaababbbbabbbaababaabababaababbbbbababbbababbbaabaabbabaabbaabaabbaabbabbabbbbbbabaabaaabaabbaaabbbbaabbbbbabbaaaabbabbbbabbbbaababbbabaaababbbbaabbbbbaaaababbbbaaaabaabbbaabbaaabababbaabbababbabaababbaaabaabababbbbbaabbbbbbbbbbabaabbbbbbbaabaaabaaaababaabaaababababbaaaabbbaaabababaabbaabbbbbaaababbbabbbbabbbabaabaabababaabaaaaaaaabbaabababaabbaaabaaababbbaaaaabababaaabbbabbaabbabaabaababbbbbaaababaaabababaaaabaaabbabbbbbaabaabbabbaaaaaaababbbbbababbabababaaaaabbaaabbbbaaababbbbbbbaaaaabbabaabbabaabbabbababaaaaabbbaabbaaabbbbbaaaabbabaabaaaaabbaaabbbaabaabaabaabbabbaaaabbbbbbbbaaaaaabbbabaabaabbababbaaaababaaabaaaaabbbabbbabaaabbbbbaabbaabbbaaababbbaabaaaaaaabaabaaabaababaabaaaabbbababaaabaaaabbbaabbababbbbaaabaabbbaabbaababaaaaaababababbbabaababaaaaaabaaababaababbbbaababaaabaabbaaaaabababaabbbbaaaaabbbbbababbabbaabbabbbaabbaabbbbbaabababbababaabbbbaaabaaabbabbbbaabababbbaabbabbabbbbaaaaababaaaaaabaabbbbaaababaabaaabaaaabaabbbabbababaabbaabbabaaaaaaabaaaaabbaababbbaabaaabbbabbaaabbaababbbabbbaabbbaabbbaabbabbabaaabbbabbbabbbbaaaabbbbaababababbaaaabbaabbababbbbabaaabbabaababbaabbababaabababbaabaabaaabaaabbaabbbaaaaaabababaaaababababaaabbaaaaababbaabbbaaaabbbbbbababaaaaaaabbbbababaabbbabbbbbabbbbbaaaabaaabbaabbbbbababaabababbaaabbaabbabbaabbaaaaaabbaabbbabbabbabbaabbbbaaabbbbaabbabbaaabbbbbbababbabbbbbbaabaaabaabbbaabbbaaabbabaabbaabababbaaaaaababbbaababbbbbbbaaabbbabbabaababbaabaaabbaabbaaabbbabaababbbabbbabaabaaabababbaababaaabbaabaabababbbaaababaabbaabbbabbabbbbababaababbaabbbaaababbbaabbabbababaabbaaaaabbaabbaababbaaaaabaaaaaaabaabababababababbbabbabbbababbbaaaabaabbbabbaabaabaaabbbbbbbbbaaabbbaabbaaaaaabbbabaaaaaaaaabbaabbbabaaababbababababbbbbbabaabababaaaabaaabbbbabbabbbabaaabababaaabbbabaaabaabaabbbbabaabbbaabaaabaaaabbaaabbabbbbbbbbbbaabbbbbabbbbabbaaaababababaaaabaaabababbaaabbabbbaebabbbbaabbbbbbabbbaabaabbaabaaaababbbaaaabababbbababbaaabaabbbabbbbaaababaabbaabbbbabababbaaabaabbababbabbababbbaaaabbbaaabbabaaababaaabaabbaaaaabbbbbbababaaaaaaaaaaaabaababbabaabaabaabbbbbbbaaaaabaabbbbbaabbababbaaaaabbaaababbbabbbbabaaaabbaaaaaabbababbbbbababbbaaaababbbabaaabbbbbabaabbaabaaabababbabaaaabaabaaaaaaabbbbbaabbabaabababaaabbabbbabaaabbbbabbbbaaaaababaaaabbbbabbabbbaabbaabbbbbbabbaaabaabaaaabbbaabaaaabbabababbbbaabaaabaabbababababababbbbbaaabbabbbbababbbbabbabaaaabbbaababaababbaabbbbabaaabbabaaabbbabbaaaabbaabbbaabbabaabaaabbbaababbbbbabbabaaabaaaabbabaababababbaaabbaabbaabbaababaabaabbaabbabbabbbaaabbabbaaabbaaaaaaabbbbaaabbaaaaaabbbaababbbbaaaabbbbaabaaabaaaabaaaaaabbbabbbabaaaaaaabababbbaaaaaabbbbbaabbaabbaaabbbaaaabbbaaabbaabbaababbbbbaabaaabbbabbbaaabbabaaaaaabaaaabaaabbbaaaababbbaaaababaabbababbbbaabbbaaabbbbbaaaabaaaabaabaabbbaaaaaaaabbbbabaabbababbabaaaaabbaaaabbaabaababaabaabbbabaaaababaabbbaaaabaabbaabbbbaaaabbaaaaaaaaababbbaabbaabbbbaaaabaaabbbbaababaaabababbbbbbaaaaababbabbbbabbbbbaaaabbbbbbbaabbbabaaaababbabbaabbaababbbaabababaabbbaabbbbbaabbababbbbbbaaabbabbbabbababaaababaaabbababbbbababbbaaaaabbbbbaabbabbbbabaabbbbbaababaaababbbbaabaaaaaabaabbbbaabaaabaaabaabaaaabaabaabaababaaaabaabaaaaaabaaabaabaaababbbbabaabaababaaaaabbbabaabaaabbbbbabbabbbabaaaaabbabaaaabbbbabaaabbbaaaaabaabbbbbababbaababbaaaaabababaababababbaaaaaabbbbbabbbbbabbaaabbbbaaaabbaaaabbbabaabbbababbbabbbaabbbbaabbabbabbaaabbaabbbababbabbaaabbbbbabaabbabbbabbabaabbaabbabbabaaaabaabaabaabaabbaabbaaaabbaabababbababbbabbbaaabbabbbbababbbbaaabbbababbabbbabbaaabbababbabbaaaababbbaaaabbaabbbbbbaabbaaabbbaaaabbbbbaaaaabbabbabaabaaaaabbabbababaabaabbbaaababaabbaaaabababbbaaaabbbaabaaabbabbbababaaabbbbabbbabbbabaaaaabbbabbaaaababaaaaababbbbaaabbbbbabaaababbaaaaaabbbbabbabbbbbabbabababbbbbaaaaabaaabaaaabbbaaababaababbaababaaabababbbaaabbaabaaaabaaabbabbbababbbbabbbaaabbaaababbabababaaaabbbbbababbabaaaabbbaabbbbabaabbbaaaaabbaaababaaaaaaaaaaaabababbbbbbabaabaaaabbbaabbabbabababbbabaaabbabbbbbbaabbabbaaabbabaaaaaabbbbabaabbbaaaaaabaaabbbaabbabbbabbabbaaabbbbbbababbabbabbbbbaabbabbbbababbaabababbabbbbbbbaaabababbbababbbbaabbabaabbaaabbbaababaabbaaaaabbaaabaababbbabbbababababababaaaaaabbbbaaabbbbbababaaaaabbbbbaababbabbbabbbabbaaababaaaabbaaabaaaaabbbabbaabababbbbbbbbbaaabbbababbbbabaabbbbbabbbbabaaabbbaabbaaabaaabbabababbbbbbbbabbbbaaabbbabbbaaaaabbaababaababbabbbbbbbaababbabbbaaaaaaaabaaaaaaaaabababbbaaaabbabaaabaaabbbababaaaabaabbaaabababbabbbbbaabababbaaabbaabababaaaaaaabaaaaabaababababaaaaababaaabababbabbabaaaaaaaabaaabaaabababbbaabbbbaabaabaabababaabaaabaaababaababaabaaabaababbabaabaaaaabaaaabbbbbababaababaabbbbababaaabaabaaabbaaababbaababaaaaababbbababbababbbbaabbbaaabbbaaaaaabaabbbbaaaaabbabbbabaabaaabababbbabbabbbbbbaaaaabbbbbabbaabbbbbaabbaabaaaabbaaaabbabbbabaaabbaababbbaaaababbbabaabbabaabbaababbababbbabbbaaabbbabbabbbaababaababbbbbaaabbabababbaabbbaaaabbaaabbbaaaaaaabbaaabaabbaabaaabaaabaaaaaaaaabbabbaabaabbbbbabaaaabaaabababbbbbabbabbaaababbbababaabbbbbbbbbbbbaabaababbaababbabbbbbabaabbabbaaabbbabbabbbababbbbaabbbbababbaaaabbabbbaaabbaabbabbbaababaababbbabbaabbabbaabbabbabbbbabababababbaaaaabbaaababaabbaaabbbbbaaaababbbbbababbbbaaabbbabababbabbaaabbaaaaaaaaabbabbbabaababbbbbbaaabaaabababbaabbaabaabaaaaaababaaababababbbbabbbbbbabaababbbbbabaaabaababbabbbabbaabbaababbbbaaaababaaaabbbaabbaaabaaabbaababaabbbabaabbbabaabbabaaabaabbaababbaabababbbaaabbbabababbbbababbaabbbbabbabaaaaabaaaaabbabaaaaaaababbaaaaabbbaabbaaaaaabbaaaabaaabbaaabaaaabbbaabaabbbbbbaaabbababbbabbabbaaaaaabababbbabbabbbbbbbabaabbabbbbbabbabaaababaaababaaababaaabaaaabbaabbaabbbbabbbaababbbabbbbabaababbbabbbaabaabbbbbaabbabaaababaaaabbaabbbaaaaabbbbaaabbababaaabbbaaabbbabaaaabbbbbabaaaababbaaababbaaaabbbbbabbbaaaabbbbabaabbaabbaabbaababbabbbbbbabbabbbbabababbaababbbababbaabbbaababaabbbaaaaabababbaaaaaabbbbaaaaaaabbababbbbaaaabbbbbabbaabbabaabaabbabbbbbbbababbbbabbbbaaababababbababbbbabbbaaabbbaabbbaaaaabbaaabbbbbaaaaababaabaaaabbaaaaaaaabaabbbaaaaabbbbbbbbbbaabaaabaaaaabbbbaaabbaaababaaabbabaabbaaaaabbababbaabbaaabaaaababababaababaababbbabbbaaabbbbbababbbabaabbababbaababababbaaababbabaaabaaabababbaabbbababaabaabbbaabaabbaaaabaaabbababbbabaabbaaabaaaaaaaabababababbabaabbbaababbbabaaaaabbbabbbababbbbbaaabbbaaaaabbbaabbbabbabaabaabbbabbbaaaaabbaaabaaaaabbbabbbaabbbbaabbbaaababababbbaabaabaaaababbbababaabaaabbabbaaaababbabbbbbbaabbaababbabaaaaaababbbaaaabaabbaaabaabbbbabaaabbabbaabaaabbbbbabbaabbbbbabbaaaaaabbbbabbbbbbabaaabababbababaabbbbbabbabaabaaabbbbbabbbbabbabbbaabbbbaabaaaaabaabbbabaabaababbaabbbabbbbbabbaababaababbabbaabaaababaaabbbbbbbbaaaaaababbbabbbababbababbbabbababbbbabbbabaababaabaabbaaaabaaaaabaaabababaaabbaaaaaabbbabaabaabbaaabbabbbabbbbbabbabbaabaaabaaababbabaabaaaaaabbbabaaaaabbbbabaaaaababbaaabbabbbbbbaaaabaabaabababbbbbababbbbabbbaaabbabababbaabbbbaaabbabbbbaaabbbaabaaaabbabaaabababbbbabbbabaaaaaabaabbabbbabbaabbbaabbabbbbaaaaababaaabaabbbaabaabbbababaaababbbbbbabbbabbababbaabbaaabaabaaaabbbabbaaaabbaaaaabbbbbaabbbabbbbbbbabbaabbaabaaababbbabaaabbabaaabaabaaabbababaaaaaaabbaaabbababaaabababaaabaabaaaaaababbabbababbbababbbabbabbababababbbaaabaababbaabbbaabbbbbaabababaaabaabbbaaabbaaabaababbabaaabbbbbaaaaaaabbabaaaaabaabbaabbbbaabaabaabbaaabbababaabaabbabbbaabaababbbabbbaabbaabbaaaabbbbabbbaaabaabbbbbbbbaabaaabbabaaabbbaabaabaaabbbaabaaaabbabaaabaabbbbbabbbabbaaaaaaabaababbbaabaaababababbabababababaababbabaaabababaababaaaaaabbbbaaaabbbbbbaaabaabbbbbbbaabbababbbababaaabbbbbaaabbbababbabbaabbaaaaaaaababaabababaaaaaaaababbbabbbabbaababaaaaabaaaaaaaaabbbbbaababaaaabbaababbbbaaababaaabbbbbbabbaabbbbaaaabbaabaaabbaaabbbbbbbbabaabaaaabbbabaabbbbbaaaaabbbababbbabbaabbaaaabaaabababbaabbababaabaaabbbaaaaaababbbbaabbbbbabbaababbababbabbbabaaabaabbbbbbbbaababababbabbbbabbaaabbbababbbabbaaabbaabbaaabbbababaaaababaabbbababaabbbaabbaabbaaabaabaabaaabbabbbaaabaabbababaabaaabbaabbbabbbabbbabbbabbaabaabbbaabbaaaabbabbabbbaabbbabbaaababbaaaabaaabaaababbaaaabbbbabababaabbaabbaabaababbabbbbabababbbababbaaabaaabaaaaaaabaabaabaabaabbaaabbaabbbaaabbababbabbbaabaabaabaaabbababaabbaabaabbababbabababbabbaaabaabbababaaabbbbaaabbaabababbbbbbbaabbbbabababaabaabbbabbbbabbbbbaabaaabbaabbbbaaaaabbbababbbaaaaabaaaabbabaaabbbbbaaaabaaaaaabaaabbbabbbbabbbbbabaabbbabbabbbaabaabaabbaaabbbbbabaaaabbbaaaabbabaabaabbbabaabbbabbaabbaabbaabaaaaabaabbaaaaaabbbbbabbbbbababbabbaaaaabbbaabbaaabbbbbaaabbbabbbabababbabaabbbbbabaaaabaaabaaaaabbbbbababaabbbbabaabbbaaaabbaabbbbbbbaabbabbabbaabaaaabbbbabaababaabbbaababaabababaaababbbabbbbabbaaaaaabaaabbbbabbbaaaabbabaaabbbaaabbbaabbbbbababbbabaabbaaaabbaaabbbbababbaaaabbbaabbbbbabbabbababbbabaaaabbabbbabbbbabbbbabbbbaaababbbaaaabbbabaabbaabaabaabaabaaaaababaaabaaaabbbbbaaaaabbaababaaabbbaabbbbaaaabbabababbaabaababbbbaabbaaaabababbaabbaaabaaabbaaabaaababbaaabbababbaabbbbbaaabbaaaabbabaaabaabbbaaababaaababbabbaabababaabbaaaababbaabbbbbaabbabababbbaaaabbabbaababaaabababbababaabbaababbaaabbabaaabbaabaabaabaababbaaababababaaabaabbaababbabaaaabbbbbaaabbaaabaabbbababbbbabbaaaabbbbbbababbabbbbaababbbaaabbaabababbababaabbabbbbaababbaabbbbbabaaabaababbbbbbababababbbaaaabaababbababbabaaaaabbbaaabababaaabbaaabbabbabaaabbabbbaaaabaabbbabbbbbbbbbbbbbaababaaabbababaaabbabbaabbaaababbbbabbabababaabbbbaabbbababbbabbbabbbbaaaabbbaaabbbbbaaabbabbbbaaabbababbaabbabbbaaabbbaabbababababaaaaaaabaaabbbabaaaabbbaabbbabbaabbababbbbabaaaababbbbbbbaababbaabbbabbbbababbaababbbbbaaabbbaaabbaabbaaababababbbbaaaaaabaabaaabaaaababbaabbbababaabaabaababbabbabaabbbabaaabaaabaaaaabaabbabaaaabbaabababbaaabababaabbaaaaaaababbabaaaabbbbabbabbabaaabaababababbaabbaaaaabbbbbabaabaaababaabbaaaaabaabbabaaabaaabbbbababbaaaabbabbaabaababbbbbbbaaabbabbbabbbaababbabbbbbbbbbbababbbbbaaabbbabababaabababbabbbaabbabbababbbbbaabbbabbbabaababbbbbabbaaaaaabbaababaabbaaaaaaabababbbbbbabaababaaabbabaabaaaaabbabbbbbbbaabbbabaabaabaababaababbbabaabaababbaabbbabababbaabbabaaabbbbbbaababbbbbaabbaaaaaaababbabbbbaabbbaabbbaaaaaabbaababaaabaaabaaabbbbabaabaabaabbbbbaabbbababaaaabbbaababababaabaaababbabbbbaabbbbaaabababaaaaaababaabbbbbaabaaabaaaaaabbabbabaaaabaabbabababbbaabaaaaabaaabaabbbbbbbabbbababaabaaaabbbaababbbbbabaababbabbaabbbbbababbbaaabbbbbbaababbaaaaabaaaabaaabbaaabbbbbbbaaaabbaaabaaaababaaaababbaabbbabbaabbbbaabbbbabaabbaaaaaabbaabbbabbbaabbaabbabbbabbbbbbbbabbbbabbabbbaaaababaabbbabaaaaabbbbbabbaaaabbaaaabbaababaaabbabaaaaabbbabbbaabbbbbbabaabbababbaaabbabababbabbabbbabaabbababbbabbaaabbbabbbbbbaabbbbbbbabbaaabbabaaabababababbbababbababaaaababaabbabbababaababaabaabbabbbababaabbaaaabbaaaabbaaaaabaaaaababaaabaababbabbbaabbaaaababbbabbabbabaabbaabaabbbaabbaabbbbbaaaabaaababaababbbaaabbbaabbbabbabbbbaaaababaaaabaababbbbbaaaabaabababbbabaaabbabbbbabaaabbaabbbbbaaabababbababbbbbbbababaaababbbaababbaaabbaabbaaaabbbbbbbabaaababbbbbbaaabaaaaaabbaaabababaaaabaabaabbbbabbbaaaabbabbaaaabbbababbabbabaaaaabababaaaaabbabaaabbbbabbabbabaaabaaaaababbbbaababbabaababbaaaababaaabaaaabaaaaabaabaaabaabaaaaaaaabaaabbaabbababbabbaabaaaabbaabaaabbababaaabbabbaaaaabbaaaaabbabababaababababbbaabbaaaaabbbabbbbabbbabaababaabaaabbaaaaabbbababaababaaaaaabababbaaaababbabbababababbabbaaaaabaabaabaabbbbbabbabbbabaabaabkabbaaabbabbaaaaabbababababaaaaaaabbbaaaabbaaabbabbbaababbabbabbabbabbaaaabaaaaabbaababbababbaabbaaabbbaaababbbbbaabaaaababbbbabbbbbbbbbbbbbbabbbaabaaabababaabbbbbaaabaabbbaababbabbaaabbbbabbbbababbbbbabbbbababaabaabaababaabaabbabbbbaabaaaaababaababaabbaaaabaaaabababaababbbbaaababbbbabaabaabbaaaabbbabababaabbaabbababbabbaabbaabbabbbbabbbbbaaabbaabaaabbabbbabbaaabbaabbabaababbaabaabaaabaababbaabbabaabbabaaaaaaaababbbbabaaabaaababaaabbbababaababbbbaaabaaaababbbababaaabaabbbaaaabaaaabbabbaabbabaaaaaabbabbbbaabbabbaaaababbbbababbabbbabababbbbaaabaaaababaabaabbbaaabaaabbaababbbababbabbbbaababbabaabbbaabbababbbbaabbbababbaabbbbbaaaaaabaabababbababbbabbbbbaaabababbaabaaabaabbbbbbbbbbbaaabbbababbabbaaababaababaaababaabbaababaaaababbbaabababbbabbaaaabaabaaaabbaabbaaaaabababbbbabaabbbbbabbbbababbbaaaaabbbaaaaabbaabababbbaaaaabbbbbbbbaaaabbbbbbaababaaabbabbaaababaaabaabaababaababaaaaabbbaabbbabababaababaabaabbaaabbbbbababbabbaabbaaaabaababbabbbbbaabaaaaaaabaabbbbbbabbbbabbabbbbabbaaaaaaabbaabaabaaababbbabbaabbbbbaaabababaaaaabaabaaaababababbabaaababababaaaaaabaabbaabbbbaaabbaabbbbbbbababbbabaaabbababaababbabbbbabbbababaabbabaababbbbbbbbbbabbbaabababaabbbbbbaabaabbbbbaaabaaababaaaaabbbaaaaabbababaabbbbbabbbaaaababbbbbaabaabbaaaabbbaaabbbbabbaababbbbbaababaaababbbaabbaaaaaababbabbabbbbaababaaabaaabaababbaabbbaaaaaabbbabbbabaaabababaaabaaaaabbaaabaabababbababaaabbabbaaabbaaababaababaababbaaaabaaabababbbbabaabababaabaababbabbbbabababaaaaaaabbabbbabbbaaabbabbaaabaaabbaaabaabaababbbbabbabababbabbaababaaabaabaababaaabbaabbabbbabbbabbbbabaaaabbabbbbbaaabbbaaaaaababbbbbabbabbbbbbbaaabaababbbabaaaaababbbbabaabbbbbbbbbbbabababaaaabbabbbaaabbbbbbaaaaaaaabbaabbababbaabbaabaaaabbbabbbbabaaabbaababbababababbbaaaaababaaaabbbaabaabaaaabbaabbbababbababbababaabbababbaabbabbaabbbbbabbbabaaaabababbbabbbaabbbbaabbabbbaabaaaaabaabbbaaabbabbbbbbbaabbaaaaaaaabaabaaaaabbabbbbaaabbabbbbbbaaaaabbbaaabbbbbabaabaaaaababaaabbbbabbbaababbbbaabaabaabbbaababbbbabaabbbabbbaaabbaabbbbbaaabbabbbbabbbaaaabbbbabbbaaaababbbabbabbabaababaabbbabbabbaaabbaabbbbbbabaabbbaabbbbbbbabbbbbabbaabbabbbbbabaaabababaabbaabbabbababbbbbbabababaaabbbbbbbbbababaaabbaaaaaaabaabbaaabaababaaaaaaaababbaaaaaababaaaabababbaabbbbbbbaaaaabaaabaaaaabbbbabbbbabaabbbabbbbbabaaaaabababababaaabaabaabaabaababbaaabbaaaababbaaaabbbbbbbaaaabbbababaaabbaabbaababbbbaabbaabbabbabbabaaaaabbabbbbbaaabbaaaaaaabbbbbababaaaaabbaaabbbbaaaabbbabbbabaabaabaaababaabbbaabbaaaaaabaaabbbababaababbabbbbabaabbabaaaabbbabaaaabbababaaabbabaaaabaabbabbbaabbabaababbbbbbbbbbbabaabaaaabaaabbaaababbbbaaabababbbababaaaaabbbbababbaaabbaababbbbbabbaaabababbbbaaaaabbabbbabbbbabaaaabbabbaaababababaabaaaabbaaabbbaabaaababbabaabbbaababaaaaabbbbbbabaaaabbababbbabababaaabbbbaababaabbabbabbaaaabbabbaaaaaabaaaaabbaaaaaababbbabbababbbabaabbbbabbababaaababbbbaaabbbbbaabbababbbabbaabaabbabaabaabbbababaabbbabbbaaabbaabbbbabbbabbabbbbaaabbabbbbbbaaabbabbbbabbbbabbbabbabbbbbaaabbababababbababaabababaabaababaabaaababababbbabbabbaaaaaaabaaaaabbaaaabababbbabababbababbabbaabbbbaaaabaaaaaaababaababbbabbbbbaabbaaaaababbbabaabbbaaabaaabbbbabbbabbaaabbbbaabbbaabaababbbabbababbaabaaabbaaaabbbbababbaaaabbabbaaaaaababbbaaabaaabaabbbbaabbabbbaabababaabbbabaaabbbabaaaaabaaabbabbbaaaabbbabbbbabaabababbaabbaabbbabbaaaabaaabbaabaaabababbbbabbaababbbaaaabaabbbbbbbbaabbaaabbbabaaaabbbbbaaababbbbaaaabbbaaabbbbabbbbabbabbabbaaaabbaaaaabaaabbabaabbbbaaabaaabbaabaaababbabaaaabbbaaabbaaaaaaabbbaabaaaababbabbaaabaababbababbaaabaaaabaaabbaabbabaaabbaaabbbabbababbbaaabaaabaabaaaaaabbabbbabbbabaabbaaaaabbbbabaababbbbbabaabbaabbabbabbbbaaabaabbbaaaabababbaaaaabaaabaabaaababbaaabaaaabbbaaaaabaabaaababbbbaaaababbaabbaaaabaaaabbbbbbbbaabababbabbbaabaaaabaaabbbaaabababaababbbaabaaaaaaabaababbaaaabababbaabaabbabbaaaaaaabbababbbbbbbbabbbbbbbabbabbbbaaabbbabbabababbaaabbabaaaaababbbabaabbabbbabbaabbbaaabbbbababbaabaababaabbbbabaabbbbbabbabbabbbaaaaaaaaabbbaaabababbbabaabbbabababbabbbaaaabababaaaaaaaaabababaaababbabaabbaababaaaabaabbaabaaaabbaaaaabbaabaaababaaaaabaaabbbbbabbabababbbbbabbbbbbbaaaabbabaabaaabbbbbbaabbaaaaaaabaabaabbaabbbabbabbaababaaababbaaabbbaaabbaaaabaababababaaaabaabbaabaaababbabbabbbbbbbbaabbbbbabbabbbbbaababbbabbbbaabaabbbbaaaabaaaabababbbaaaabaaabbaabbaabbaabbaaaabaabbbaaabbabbaababbbbaaabbaabbabaabbaabbaabaabbaaabababbbaaabaaaaaaabbbbaaabbbbabaababbbbbaaabbbabbbbbbbbaabaababbaabbbaaababbbaaabbbbbbbababbaaababbbaaabaaababbbbbabbbbbabbaabaaababaaaabbabaabababbaabbbbbabbaabbbbabaabbababbbabbbbbababbbabbbabbbaaaaabbbaabbabaaabaababbbaabaabbbaaabbabbaaaabbbabbbaababaaaabaaaaaababbaabaabaabbbbabaaaabbbbbbabbbbbbaaaaaaaaabaabaabbaaaaabaaabbaabaabbbbbaaabbababaabbabbbababbababbbbaaabbbabaaaabaabababbababaabaabababaababbbbbbabbbbabaaabbabaabbbbaaabbabaabaaabababaabababbaaabbbbabbbaaabaabbaaabbbbbbbbagbaababaabaaabbaaaaaabaaaabbaaabaabbaabbabbbabaaabbaabbbaabbaabbbaaabbabaabbbaaabababaaaaabbaabaabaaabababbababaabbbabaaabbbbbbbabaababbaabbbbababbabaababbaabbbaaaabaabaabbbbaaababbbbbbbaabbbbabaaabbbaababaaabbbbabbbbaabbbaabaaabbbabbbbabbbaaabbaabbabbbaaaabbaabaaaabaabbbabbabbbbaaababaababababbbaaabbabbbaaababbbbabbbbabbabbbabbaabbaaabbabbbbbbaaababbaabbabbababaabbaabbbabaaaaababaababaababbbaaaaaabaaaaaaabaaabbbaabbabbbabbbaaabbbbabbbbbbaabbaabaaaabaabbaabbbbbbbabbbaabbaabababaaabbbbbbbaaaabbbbbbbabbaabbbaabbaabbbaabbbaababbbabaabbbbbbbbbabbbababababbbaaaababbaaaabbbbababababaaabbaababbaaaababaababbaabbababbabaaabbbbabbaababaaabbbaabbbbbbabbaaabaaaabaaaaaabaaaaaabaaaaabbbbabbaaabbbbaaaababbbaabbbbababbbaabababaaabbbbaababaaabbabababbbbababbaabbbbabbbaaabbbbaabaabababaabbbaabbbbabaaaaabaaabaabbabaabbaabbaaababbaaaababbabaaaabbbbbabbbaabababbbbaaaabaaabbabababaababbabababbaaabbbbbaaabbababaaaaabaaabaaaabbaaaabaabbbbabaaabaaabaaabaaaabaabbaaaaaaaaabbaabbabbaabaaabbbaababbbabbaabababbabbabbbbaabaabbbaabbaababbaababaaabbbabbbbaaabbababbabaabbbaaaaaabaababbbbabaaaabbabbabbabaaaaaabaaaaabababbaaaabaabbabbaababababbabbaaaabaabbaabaabbbabbbabaabaaabbaaaaaaabaaabaabaaaaaaababaababaaaabaaaabbabaaaaabaabaaaabaaabbbaaaaaaaaaaababbaaaaaabbabbbbabbaabbaaabbbaaabaababbbabbbbaaaababaaaaaaaaabababbaabababbaaabbbbbababaaaabbabaaaaabaaaabbbaaabbaabaaabababbaaababbbbabbbbaabbabbbbbbbaabbbaabababbbabbaaabaabbbbbabbbabbababaaaaaaabbbababbbbbabaabbbbabbbababaaaababbababbbaabaabbabaaaabbabaabbabbabaabbaaabababbbbbabbbbbbaaaabababaaabaabaabbaaaaaabbababababbabbbbbabbabbaababbbabbaaaaababbbaabbbbbaaaaabbaababbaabababaaaaabaabababaababaaaaabbbabbabbabaababaaaaabaabbbabbaabbaabaaabbbabbabbbbbbaaabbbbabaabaabbabaabaaaaabaaaaaabaaabaaaaabbbbbbabbababbbaababaaabaabaaababaaaaabbbbbbbbaabaaaaabbbabaaaababbbabaababbbaaaaabbbaaabbbbbbababbabbabbbaababababaaabbaaaaabababbabaaaaaabbabababbbbaabbbaabbaaaaaaaaaaaaababbaabbababbbababbaaabbbabbbbaaabaaaababababbaaaabbbabbaabbababbbaaaababbaaabbbbbaababaaaabaaaaaabbbbabbbbabbbabbaaaaaaaabbaaaabbbbababaaabaaabababaaabaabbbbabbabbaaabbbbaaaaabaaabbbbbaabababbabaababbbabbabbbbaabbbabbbaababaababaaabaaabaabaabaabaaabbbabbbbbbbaaabaabbbbaabbbbbbbbababababaaaabaaaaaaaaabaababbbaabbbabababababbbababbbbbbaabbbabbabbabbababbbaaaaababaabbbbaaabbaabbabbabbbaaaaaaabaaaaaaaaaababbababababbbaabbabbbbbababaababaababaaaaabababaabbaabbbbabaaaabbabbaaaaabbaabaaaabbbabbbbbabbbbabbbababaabababaabaabbbabbbbbaaaaabababaabbabaaabbabbaaaabbabbbbbaaabbaababbbaabaaaabbbaabbaabababbbbbbbbaaaabbbabbbabaabbbbbbaaababbbaaaaaabaababaaabbbbbbbaabbaaaabbbbbabbabbbabbbbaabbbbbabbaaaaaabaaaabbabbbbabaaabaaabaabbabaabbbaaababbaabbbabbababbbaaaaaabbbabbbabababbbbababbaababbbbbabaababbaaaabbbaaabababbbbabbbbaaaaaaabbaaaabaabbaabaababbbbababbabbbbaabbbaabbaabbbbaabbbaaabbbbabbbaabbaabaaaabbabbbbabbaaaabbbabbabababbaabbaaaabaabaaaabaabbaabbabbbababbbabbbabaaababbababaabbbabaabbbababaaabaaabbaabaaabbaaaaabbaabbbbbbabababbbabaaabaaabbaabbaabbaaabbaabababababbbaaababaaababbbababaaabababaaaababbaabbaaaaabbbaabbbaaabbabaabbaabbababaaabaaababaaaabababbbbbbababbabaabbbabaabaaabbbaaababababaaaababbbaabbbbbaabbabbbbaaaaabbbabbbabbabbabbbbbabaabaaabbbaabbabbbabaaaaaaaabaabababababaababbaabaabbbbbbbabbababbbaaabaabbababbbaabaabbbaaaaaabaaaabbbaabbaabbbbaababaaaabbababbbabaaababbbbaaaaabbbbabbaaaaabbabbababbaaaaabbaaabbaaaabababaaabbbbbaaaaabbabbbaaaabbbaabaaababbaababaabaabbbababbaaaababbaaaaaabbbababaaaabaaaabbbbbababbbbbbbbbaabababaababaaabaabbbbaabbabababbaabababbabaaabbaaaabbaaabaaaabaabaaaabaaabaaabababbaabbbabaabbaabbaabababbbababbbbababaaaaabbbbababbbaabbbbbbabaaaaaaaaaababbbbbaaabaaabaaaaabaaaaaaabbbaabbbbbbabbbaabbaaababababbabaabbababbaaababbbaaabababbabbbabbaaaabbaaaabaabbbabaabbaaaaabaabbbbbbbbabaabbbababbbabaaabaaabaabbabaaaaababbbbbbbbababbbaaaaaababbabbaabaaaaaaaabbbbbbaaabbabbabaaababaabaabaabbabbababbbbbbaabbaaabaabababaababaababbaabaaaabaabbbabaabaaabaabbbaabbabbbbaababbabbababbaabbbabbabaaaababbbbbaababbbbaabababaaaabaabbbbabababababbaaaabbbaaabbaabbabbababbabaababbbbbabbabaabaaabababbbbbbabaaaaabaaaaaaaabaaaaaabaaaabababbbaaaabbaaaabbbaaaabbbaaaabbabbbaababaabaaabbaaabbbaaaaababbbaaababbabbbaaabaaabaabbaaababaaaaabbbbabaababaaabbbababaabbabbababaababbaaabaabababbbbbbbbababbababbbbbbbbababaabababbaabbbababbaaaabaababbbabbabbbbbaaabaaaaaaaababaabbaabaaabbbbaabbbabbabbbbbaaaaaaaaababbabaaabaabbabbbabbaabaabaaaaaaaaaabaaaaabaaabaababababbabbbbbbbbaabbbbbbaabaabaaabbbbbaaaaababaaabaaabaaabbbbabbbbbbbabaaaabbbbbbbabaabbababbaabbaababababbbbaaababaabbbaabaabbabbabbaaaaabababaabbabbabbbbbaaabbbbabbabaabbbaabbaabbbabaaaaababbababbaababbbabbabbbaabaabbbabaabbabbbbbaaaabaabbabbaabbbbbaaaaaaabaaabbbabbaaaaaabaaaabbabbaaaaaaabbbbabbbbbababbbbabbbbbabababbbaabbabbbababbbaabbaabbaaaaaababababbaabaaaabbaabbababbbaabaabbbaabaabbbaaababbbbabbabbbbbabaabaabbbababbbbbbbbababbbbabababaabaabbabaababbbbbaabaaabbbaabbabbbbababaabbaaaababababbaabaababbbbbababbaaabababbbaaabbbaaababbabbabbaababaabaaababbbbaabbbabaaabaaaaababaaaaaaaabbbabbbabbabbbaababbbbaabbabababbbbabaaabbbbbbaaaabbbabaaabbaaaababaababaabababbaaabababbababbbbaaababaaababababbaabbbabaaaaaaaaabbbbabaaababaabbbabaabbbaabbabbaabababababaabbabbabbbababbaaabbaaababbbbabaaaabaabaababababbaabbbbbbbabbaababaaabbbbbaaaaaabaaaaabbbaabbbbaaabaaaaabbbbaabbbbabbaabaaabaababbaaaaabbbbaabbbabaabaabbaaabaaaababbbbbbbbbbabbbaaabbabbaabbabbbbabbaabbbbabbababbaaaaaaaabbbabaabbaabaaaabbbaaaaabbabaaaaaabababbaaabaaabbabbabbaaababaaabaaaaaabbbabbbababaabbbbbbbbaabbbbbbbbabbbabbaabbaabbbaabbaaabaaabaabbbababbabaabbabaaaabbaabaabbbbbbabbaabaabaabbbaababaabaaaaababbaaabbbaabbabababbaabaaabbbbbbbababbbbbabbbabababbbaabababababbbbaaabbaabaaaabababbabbabbbababbbbbbaabbbaaabbababaabbbabbabbaabaaabbbabbaababbababbabababaaabbbbbbabbbabbaabbababbababbbaaabbabababbabbababbaaaabaabaaaaabbaaabababaaabbbbabbabbbababaaabaaabbabbaababbbbabaaaabbaabbabaabbaababaabaabbabaabbbbbabbaaabababbabaaaababaabaaabaabaabbbaaaabbbabbaabbbbaabbbbabbbbaaaaabbaaaabbbabaabaaaaaaabbbbaabbbbababbaabbbaaaabbabbaababbbbbbaabaaaaaababbaabbbababaaaabbbabbababababbaabaababbbaaabaababaabaabbaabbbbbbaabbbbbbaaabaaabbbbbaabbbaaabbababababbabaaabaabaabaabaabbabbbaaabaabbbaabbbbabababbbababbbbaaaabaaabbaaabbbbaaaaaaaaaaaaabbaabbbabbbbbbabbabaaaaaabaababbaaaaaababbbbaaabababbbaabbbaaaabbbbabbaaabaaababaabaaabababababaabababbbbaaaaaaababbbbabbbaaaaaababbabbabaaabbbbbabaaaababbaaaababaabbbabababababaaabaabaabaaabbabbabbbabbbabbbbbabaaaabaaaabaabbbbbbabbbaaabbaaabaabababbbbabaaabababbaabbaaabbbbbaaaaaabaaabbaabaaabaabbaabaaabaaaaabaabbbbabbabbaaabbaaaabbaaaabababbabababbbbbbaaabaabbbbbbabbbaaaaaabbbaaaaaabababbbbbabbbbbbaababbbbbaaaaabbabaaaaaaaabbaaaabbaabaabbbbabababaaaaabababaaabbaababaabbbbaababbaaaaaabaabbabaabbbbbbabaaabaabbabaaabbababbaabbbbbabbaaabaabaaaababbbabaaabbbaaababbbbabaabbaaabaaaabbbbbbbabababaaabbabbbaabaabbabbaabbbaabbaabbabababaabaabbaababbbbbbabbbbababaaabaabaaababbbabbabbbbbbbababababaabaabbbbbabbbabbbbababbaabbbaaaababbbbbbababbbababbbbbabbaabaababbaababbbbaaaababaabaabbbabbabaaaaaaababbbabaaababaaaabaabbbbbbaaabaaaaaaabaababbabaaabaababaabbabababbbbababbbbbbababaababaaabaabaaababbbbbbbbaababbbbbbaaaaaabbbaaababaabbbbbbaaababaaaabaabbbaabaaabbbabbbababbbabaabaaabaabbbbababbbbbbaabaabaaabaabaabababaaaabbabbbaababbababbbaabbbbbbbabaababbbbababbaaaabbbaaaaababbaabaaaababbaabbaabbbbabbaaaabbabaabaaaaababbaaaaabbbaaababbbaaaabaaabbbaaabaabbbbbbbbabaaaababbabbabbaaaaabaaaaababbaabaaaaaaaabbbababbbaabaaaabbbbbabaabbbaababbbaaaaabbbbaabbaaaaaaaabbabababbbaaabaabbaaaababbaaaaaabbbabbbbbaabbaaaabbaaaaaabaaaaabbbbbababbbaabababbbbbbaaabbbaaabbbabababbbbabaababaaabbabbbaabaabababbbaaaaaabbaaaabaabbbababbbabaababbbaabaabaabbaaaaababaababbbbbbaaaabaaaaaaabaaaabbabbaababbbbbbbbbbabbaabbaaaabababbabbabbbbbbaabaaabaaabbaaaaaababbbabbaaabaabbababbbaaaaaabbbbbabbbbaaabababbabaaaaaabbabaaaabbbbaabbaaaaaabbbbbaabbbabbaaaaabbabbbbabbbaabaaaabbbaaaaaababbbbabaaabbbabbbbaaaaabbbbbaabbaabbbaabbbabaabbbbabbbbaabaababbbbaaaaaabbaababaaababababbababbaababaaabbaabbabaabbabababbabababaaaabaaabbabbaaaaababbaabbabbbbbabaaaaababababbabbbbbbaaabbbabbbbaaaababbbabababaabbaaabbbbbababbaaabaaaabbbbbaaabbabbbbbbabbabbbabaabbaaabbbabaabaabaabbabbbaabbaaabbabbbbabbabbbbbbabbabaaaababbbbababaababaabbababaaaaababaaabbbbbaabbaaaabbbaaabbabbbbbbabbaaabaaababbbaabaaaaabaaaaababaabbabababbaaaaabaabbaabbabbbbbbabaaaaabaaabaaaaabaaaaaaabaababaababbabababaaaabbbbbabbbabbbbbbaaababbbbabbbbababaabaabaabbbabbabaaaaaabbaabaabbababababbbbbbbaabbbbaabababbbbbaabbbaaaababaaaaabaabbbbbabbabbabaabbaaaabbabbbbbaabbababaaaabbabaaabaabababbbbbbbbabbbbbbaabaaaabbbabbaababbbaaaaabababaaabababaabbbabaaaaabbbabbbaaaababaabbbabababbaabbaaababbbbbbbbbabbaaaabbbaabaabbaaaabbbbbbbbaabbaabbbaabbbaaabbaaabbaaaaababaabbabaaababbabbaabaabbaabbabababbabaaabaaabbbbaaaabaaaaabbaaaaaabbbaabbbbaabaabababbbaaabbbabbaaaaabbabbaabbbabbbbaaaaaaabbbabbaabbbabaabbabbbabbbabbabaabbbbbbbaaabbbbabbbbabbaaabaaabaaabbbababaaababababaababbaaaabbbbababbbbbaaabbbababbaaaaabaaababbbbaababaaabbaabbbabbaaababbbabaaabaaaaabaabbabbbaababababbbaabaaaaababaaabbababaabbabababbaaabbabbbabbbaaaabbabbbabbaabbaaabaaaaaababaaaabaababbaababbbbbbababbbabaaaaabababaabbaabbbbaababbbbbbbbabbbaabbabbbabababbaabababbbaababaaaaaaaaaababbabaaabbababababaabbababbbbbaaaaaabaabbbbbbbabbbbaaaaaababbbbbabababbabbbbabaaaabbaaababaabaaaabaaabbaaaaaababababaaaaabaaaababbabbbbabaabaaababababbbbababbbbbbbbaaababaabbabbabbaabbaabababbbbbabbaaaababbabbbbbaabbbbbaaabaaabaabbbbbaababbbbbbabbbbbaababbbbbaaabaababbbaabaaaababaababaababbaabbbaaabbaaabaabaaaababbaaabaaaaaaababbaabbbbaaaabaaabbbbbbaabaabaabbaabbabbbbaababbaaaaabbaabbababbbbaaabbaaabaababbbbbaaababbbaabbabaaaababbaaabbabaababaabbbbaaaaaabbabbbaaabaaaabababbaabbabaababbbabbbbabaabbbaaababbbbaabaabababbbabbabaaaaaabaaabbabbaaaaabbbbaaababbbaabbaabbbaaabbbbababaaabbbbbabbbbabbbbbbbbaabbbaababaababaabbababaabaaaabaaaabbbbbabbabbaabaaabaaabaaabaaabaaabbbbbbabaabbabbabbbaaabbbabbaaabaabbbbabaaaabbababababbabaaaaaabbbabbbbababaaaaaaaaaaabbaabaababababaababaaabaaaababbaaaaaaaabaaaaaabaaaaababbbbaabbbbabbabaabaaaababaaaabbababbababbbabbabbbaaabaaaaabbaaabbabaabaababababababbaaabbaabbabaabbabbabababaaaabbaaabbaabbbbabbaabaaaabbabbbabbabababbbbaaabbaababaaababbbaaabbbaaabababaabbbbabbbbbbbbabbabbaabbababbaabbbbabaaabaabbbbbbaabbabbaaaaabbbabaaababbabbababaababaaabaabbabbababbabaabbbbaabbbbaababaaaaabaaabbabaaabbaabaaaabbaaaaabbabbaabaaaabbaababaabaaababbabbbabbaaaabaabaabbbbbabbbaabbaabbabbabaaababababaababbabbbabaabbbbaabaabbbaababaaabaaabaabaababbaaabaaabaaaababbbbaabaaabbabaaaabbaabbaabbbbbabaaababaabbabaabaaaaaaabaabaabbabaababaaaaaaaabbbbbabbabbabaaaabaababbababbbaabbaababbbbbaaaaabaabaaabbbaaaaaaabbbaaabababaabbabababaaaabaaababbbabaababaabaababaaaabaabbbbbabbabababbaaaaaabbabbaabbbababaabbbaaabaaaababaaaaaabbaaaabaaaabbbbbaaabababbbabbbaaabbaaababababbbababaababbbbaabaabbabbabbaababbbaaabaaaabaabbabbbbabbbbbbbbaaaabbaaabbaabaabaabababaabbbbbbbbbbabbbaaabbaabaabbabbbabaabaabaababbbbbabaaaaaaaaaaabababababaaababaaaababbbaaaabbaaaabbaaabbabbabaabaababbabaaabbabaaabbbabaababaabbbaaaaabbbbbaabaababbaabbabbbabaabaaabaababbabbabbbababaabbabbaaabbababaaabaaababbbaabaabbbaaababaaabbbbabbbaaaaabbbbaaaabaaabbbbbbababaababbabaaaaabbaaabbaababaabbbbaaaaaaabaaaaaaabbaabbabbaabaabbbaabbbaababaabbaaabababaababaaabbaaaaababbbbbbbaabbabaaabbbaaaababaabbaabbabbaabbabaababbaaabbabbbbbabaaaaaaabaaaaabaaaababababaabbbbababbaabbabababbbabbabbbbbbbababbbbababbaabaaaabaabbbbbbabbaaaaaabaaaabaababbbabababaabbbbbbbaaaaaabbbaababaaaaababaabbbbbbbbbaabbabbabbbbabbabbabbaaababbbabaabaaabaababbbbabbbabbbbbbaaaabaabbbbbaaababbababbbbaababbbaaabaaabbbbaabbbbabaabbabababaaabbbaabbaabbbbaabbaaababbbbaabaabbbbaababaaaaaabaaabaabaaabababaabbbababbabbabbabbaaabbabaabaabbbbbbbbbabaababaaabbaabbbbbbbbaababaabbbbbbbbbabbbbaaabbbabbababbbabaabaaaaabbaaaaabbbabbbaaaaabbababbaabbabbabbaababbbbbbbbbabbbbbbaabbaababbbaaaaaaabbbbbaabaaaaaabaaaabbaaabaababbbaaaaaaabbabbaaaaabbaaaabaababbbbbabbabbabaabaababbbbbbbbababaaaababbbabbabaabbbabbaaababaaaaaaaabbbbaabbabbbbbabababbbbbababaabbabababaabbabaabbbbbabababbbabbaaabaabbbabbababbababaaaaaabababaaabbbaababbabbbbaabbbaaaaabbaaaabbabaaabaaaabaabbaabbbaabbbbbbbbbbbbaabaababbababbbaababbabaabababbbaaaabaaabbbbbbaaaabbaabbbaabbbaabaaabbbbaaaaababaababbaaababbbbbbbbaabbabbabbbabbaaabaaaabbbabbabbabbabbababbabaaaababbababaababbbabbababbbbabbbbabbbbbbabbbbbbabbaaaabaabbbbabaaababbaabbbaabaaabbaaaabaaaaaababbbbbaaaaabaaaabaabbbbaaabaabbabaaabbbbbabbbabaabbbbabbaabbbaaaaaababaaaaabbabbaabbababaaabbaaabbaaaaaaabbbababaabbabaaaaaaaabbabaaaabbabbbabaabbabaabbabbbbbabbbabbaababbaababbababbbaabbaabbbabbaaabbaabbaaabaaaababbababbbbbabbbbbbbaabaaababbabbbbaabbaaaabaabbaaabbbaaabbabbabababbbabbbbbaabbebabbaabbababbababaabaabaabbabbabbbbbabbbaabaaaabbbbbabbbbbbaabaaaaaababbbbbbaabbababbabbaaaaabbbaaabbbbaabbbaaababbbaabbaaaabaaaabaabbbbbabbaaabbbabbabbaaabbbbbaabbbbaaababbbbbabaabbaabbaaaaaaaaaaaabbaababbaaababbabaabbaabbaaabbaaaaaaabbabbabbbabbbbbbabbbbaaaaaabbaaaaaababbbbbaabaabaaaaabaaaabaaabaaabbbbaababaabbbbbaabaabbaaaababaabaaabbabaaaababbbabaabaabbbaaabbaabbabababbbbabbbbaaabaababaaaabbaabbbbbbbbabbbaaaabbaabaabbaabbabbbabaababababbbbbbababbbaaabababaabbabbbaaabaabbbbaaaaabaaabaaaababbbaaabababaabaabaabaaaaaaabbabbbbaaabaaabbbbaaababababbbbbbabaabaabaaabbbaaabaaaabbbbaabaaaaaabbabbaaaaaaaabbaabaaabaaaabbbbbabbbaabbbaaaaaaabbabbbaabbbabaababababbabbbbaaababbaaaabaabaaabaabbbbbbabbbabaababbaababaaabaaabaabaaabbaabaabbaaaaaaaaabbbbaabbbbbbabbaabbaabbbaaaaabaaabaaaabaabbbabaababbbbbbabbbabaaaabaabaaababbbaabbabbbbabaabaaabbbbbaabbbaabaaaabaabaabaaabbbbbbbbbbabbaabaabbbaabbabbaaaaaaababbaaaaaabaaabbabbabbbaabababaaaabbaaabbababaaaaaabaabaaaaaabaabbbaaabbbaabaabbbaaabbaaabbaabbaaabaaabbabbbaabbabbbabbbaaaaaaaabbbbabbbbbbabbbaabbbbbaabbabbaabbbbabbbbbabbbaaaaaabaabaabaaababbaaaaaaaaababababaaabbbaabaaaaaabbbbbabbabbbbbbbaabaaaabbbababbaabbbabbaaabbbabbaaabaaaababbaaabbbabbabbaabaaaaaabbaabbbbaaaabbbbaababbbbaaabbbbaaabbaabbabbbaaaababbabbbbaaaababaabbbaaababbbbababaabbabbbbbabaaaaaaaabbabbaababbbbababaabbbaabbbbaaabaaaaababbaaaabbbaabbbbbbbbbabbaaaaabaabbaaaababbbaaaabbbbabaaaaabababaaaabaaabaaabbbbaaabaabbbabaabbbbaaaaabbbaabbaaaaaababbbaababaabbbbaaaaababbaaaaabbbababbaaabbabbbabbbaaabbbbabbbbababbabbbabaabbaaaabbaaabbbabbaabbbabbaabaaabaabbbabbababbabbbbabbaaabbbabbaabbaaabababbbaaaabababaaaaaaabaabaabbbbabbbbaaabbaabbbaabbbabbaabbaaabbbabaabbabaababbbaaabaaaaababbbaabaabaaaaaaaabaaaaabbbbbabbaabaabaabaaaaabaaababbabbaabbbbaabbabbbabbbbabbaaaababababbabbaaabaaaababaabbaaabbabbbaabbbbababbbbbaabbbabbabaaaabbaabbbaabaabaabaaababbababbabbaabbaabbbbbaaabababababbabbbbbbaabaaabbabaaabababbbaabbabbbabbaabbbababaaaaaaaaabbabaababbaaaaaabaabbbabbbaaaababbbbabbabbbaaabaaaaabababbbababaabbabaabaabbaabaaabbbaabbbaababbabbaaababaababaabaaaabbabbbabbbbbaababbaaaababbbbabbbbbababaabbbabbabbaabbaaabbaabaaababbbababaaabbabababbbbaaabaaaabbaabaabbbabbbaabbbbbbaabbbbbbbbbaaaaaabaaaaabbabaaaaababbaaaaabbaabbbaabaaaaaabbbaaababbabaabaabaabbbaabbabbababbbbababaaaaabbbbaaaabababbbbbabbbaaaaabbabbaabbaaabbbbaababbaaabaaabaaaaaaabaaaaabababbbaaabaaaabaabbabbbbabbbabaabbaaabaaaabbbbbaaababbbbababbbbbaabbaabaaaaaaaaaaaaabbbabaaabbbbaaaaabbbaaaaabbbbbaabbbbbaabbaabbaabbaaabbaaabbbabaaababbbaabaaaaabbabaaabbbbabaabaabaabaaaaaabbabbaaaaabaaaabbaaababaaabaaaaabaabbababbabaaababaabbaababbbbaabbabbbbabaaabbaabbbabaaabbabbaaaaabbababbabbbbabbbaababaaababbbbaaabbbbabaabaaaabbaaabbbaaabbbaaababbbabbababaaabbababbbabbaaabaababbaababbaabbbbbabbbbbaaaaaabbaabbbababaaaabbaaabababababbbaaabbaababaaabbbababbbbabaabbabbabbabaaabaabbbabaabbbbaabbbaabbbbbabbaaaaabbabaabbbaabaaaababaaaabaaaaaaaabaaabbbbabbaabbabaababaaabaabaabbababbabaabaabaabbabaabaabababbabaaabaababbbbabbaabaabaaaaaabbababaabaaaabbbbabbbababaaaaabbbaabaaaaaababbaaabbaabbbbaabbaabbbbbaabbbabbaabababaababaaabbbbbabcabababbbaaabbbaabaaababbbaabbbaaabaaaaaabbabaababababaababababbaabbabababbabaaaabbababbbabaaaaaabaababbbababbbbaabbabaaabaabbbbaaabbaaaababbababaaababbbaaaababbbaaabbababaaababbaabbbaaabbabaabbbabababbaabbbbbababaaababbbaababbbbbaabbbabaaabaaabbabbaabbaaaabaabbbbababababbababababaabaaaaaaaaababbaaaabbbabababbbabaabbbbbaabababbaabbababbabbbbbabaababaabababaaaaababaabbbbbbabbababaabbbbaabbabaabbbabbaabababaababababababbbabbbbabaaabaabababaaaabbaaaaababaaaaababbbabaaababaabbaaababaaabaaabbbaabbababbbabbabaabbaaabbbbababbaaaabaaaaaaabaabaaazbbaabbaabaaaaabbbbbbabaaababbaababbaabbbaabbbbaabaaaabbbbaaabbbaaabaabbabbbaaaabbabbabbbaabaaababbaaaabbabaabbbabbbabbaaaaabbabbaabbaaaaaaabababbabaaaabbbbbabbbaababbabbbbbbabbabbbaabbbaaababaaaabbbbbbbbbbabbbabaaaaaabbbababbabaaaabbbbbaabbaabbbbaabbbabbbbbaaababbaaaabbaaabaaabbbababbbbababbbaaaababaaabbbbabbbbaabaabbaabbababbabaaabababbaaaabaaaaabbaaaabbabaabaabbbbbbabaaabbbbaabaabbabbabaabbbaaabbabababbbabbbabababbbbabbbbaaaaaaabababbbbaababbbaaabaabbbababbbabaaabbbabababaabbbabbbabbbbababababbbababaaaaaabbbbbaabbbaaababbaaaaaaabaaababbaabbbaabbbbbabaaabbababbbabaaabaabbabbaaabbbbabbaabaababaabaabbababababbababbbaaaaaabbabbbaaaaabbaaaaabababbbbbaabaabababbbbaababbbbaaaaaaaababaabbaabaaabaababababaaaabbaaaaaaaababaaabababbababbbbbabaababbaabbabbbababbaabbababbbabababbaabbababababbbababbaaabababaabbaabbbaababbabababaaabaababbababbaaaabaaabbbababbbbbbbbaababbbbababbababbaaaabbbbbaabbabaaaaabababbbabbbabaabaaabaaababbaaaabaaaaaaababaaabbaaaaabbbaababaababaabababbaaabaaabbaabbabaabababaababaaaabbbabbbaaaabbbaababbbaababbaabaababbaabaababbbbaabaabbbabbbabaaabbabaaabaaaaaaababbbbbaaabbabaabaaaaaababbbababbbaabbbaabbbaaaaaaaababbababbaabbaaaaababaaaabaaabaaabaaaaabbabbbbbbabbabbbbbaabaabbbaaabbbaabaabbababbbbbababaabaaaabbabaaaaababbaaababbaabaabbaabbbaaabaabaabbaaaabbbabbaaabbbabbbbaaaababaaaababaaabaabaabbababbbabbabbbbaaabaabbabbaaabbaaaaabbabaaababbbbbaababaabbabbabaaabbbbaaabaabbabaabababaaabbaaabaabaabbabbbababaaabbbaabbbabbabaabbbbbabaaabbabbabaabbabbaaaabbbaaaabbabaabaabbbbabbaababbaabbbaabaabaaaaabbaaaaabaaabbbabbbbbaabaabbabaababbbbbabbbbbbbabbabbaaabaaaabbaaaabaaababaabababaaaababaabbbabbbaabbbabbaaaabaabbbabbabababbbabbaabaaababaabaababbabbbaababbabaaaaababbaabbababbabbaaaaabaabaabbabaaaabbaaabbaabbaaabababaabaababbaaabbbaabbbaabbbaaabbababbabbbabaaabaaaababbbbababaaaaaaaaaabaababbbababbbbbaabbaabaababbbbbabbbbbaaaaabbbaabbbabaaaabbaaaaaaabbbbaaabaaaaabbbbbbaaaabbaaabaaabbbbbbbbbbaabbbabbaaaaabaabbbbbababbbaaaabaaaabaabbabbaaabbbbabbbabbbbbababbbbbbbabbabbbaabaababbabbababbabaaaabbaabbababaaabababaabaaabbaabbbbaaabbabbbbabaaaabbbbbaaabbbbababaabaabbbbbbabbbaaaaabababbbaabbabbabbababbbabbbbabbaaabbababaaaaababbbbbabaabbbabaaabaaababbbabbaabbababaaababbbababbbbbbbababaaaaababbbabbbaaabaabbbbbbbbbabababaaabaabbbaaabbabbaaabaababbbababbababbbbaabaaabababaabbbbaaaabbbbbababaababbbbbbbababbbbaaaaabababaaaaaabaaaababbbbbaaababaababaabbbbaaaabbaaaaaabbbbabaaabaababaabaaabaabbabaaabbaabbaaabababbbbbabbbabaaaabaaaabababbabaaaabbbbaaabbbbabaabbbabbabbbaabababbbaaababbbbbaababababbbbabababaaaaaaaabbaaaaabaabbabaaabbbaaabbbbbabbbabbabaabaabbbbbbbaaaaabbbbaaaabbabbaabbabbbabbaabbbabaabbaaaabaabaaaababbbbbababbabbaababbbbaaaabbabababbaabbbaabaabbbbaabaaabbbababbaabaaaabbaababaaabaaabaaabbaaaabbbaaabbbabbabaabbaababaabbabbbbaabababbabbabaabbababababaaaaaabbaaaabbabaaaaabaaaababbbbabaabbbaabaaabbbaaababbbbabbabbbaabbbaabbbababaaabaaaaabbbbabbbbbaaabbbabaaaaaaaaabaababbaaabaaababbabbbbbbabaabaabbbababbaaabaaaabbbbbbbabaaaabaaaaababababbabaabababbbbaabbbbbbaaaababbaabbbaaaabaaaababaaabbabababbababbabbaaababababbababbbabaabbbabbbaabaaababbbaababbababaaaaabaababbaaaaaaabbbbbbababbaaabaaaaabbbbbabaaabaabaababaabbbaabbbababbbaabababbaaaaaabbbbbabaaaaaaabaabbabbaaabaabbbabbababaabbaabbbabbabbabbbaaaabbbbabbbbbaaabbaabbbababababababbbbabbabbbbaaaabbaababbbaaaaababbabbabaaaaaabaaaaabbbaababbabbbaaaaabaaabbbabbbaaabbbbabbababbababaababbbabaaaaabbbabbabbabbaaabbbbaababbabababbababaabbabbbbaababbabaaaababaaabaaabaabbaaabbabbbbaabbabbbabbaaabbabbablbababaabbbababbbaaabbababbbbbabbababbbaabbabaaabbbbbaabaaabbaabbbababbbabbabbabbbaabbbaababbbaaabbbabbabbbaaaaaabbbabbaababaabbbaaaabbbaaababbaaabbaaaaababbaababbbbababaabaabaabaabbabbbbaabbaaaabbbabaabbbbaaababbababababbaaabbbbaabbbbaabbbababaaababaaaabbabbbaababababaabaabbabbaababaabbbaababaabbaabbbaaabbbbabaabbbaabbaabbabaaabbaaaabababababbbbabbabaaaabababbbabaabaaabaaababbbaabaabbbababbaaabbbbbbaabaaaaabaaaaaaaabbaababbbbbbaabbababaababbaababbbbbaabaabbbbaabbbaaabbaaaabaabaababbaabbababbbbbaabbbabaabbababaaabbabbaaaaabaaaaababbabaabaababaabaababaabbabbaabbbaabbbabbabababaaabbabaababaaabbabbbaabbbaababbababbaabbbaababaaaaaaababababaabaaababbbaabbabbaaaaababbabbabbabaaaaabaaabbabbbabbbbaaaabbabbaabbbbbbaaabaababbbbbaaabbbbaabbbaaababbaaabaaababababbabbbaaabbaababaabbbbbaaabbbababbbabbbbbaaabbaaabaaabaaaaabaababaabbbbbabbaabbaabbaabaaabbababbbbbaaaaabbbbbaaabbbbbaabaaabaabbbbbbaabbbbabbababbaaaaabbbbbbbbbbbaabbbaabbaabbaabbabbbaaaaabbbbabaaaaaabbbaaaaaababbaabababaaabbbabbbaaaabbbbabaaaaaabbbaababaababbbaabaaabbabaaabbaabaabbaaabbababbaabbbbbabbbaaaabbaaaaaabaaaabbbabbbabaabbbaabababbbaaaabbaaabbababaaaabaabaabaaaaaaaaaaaabbbabaaaabbaaabbbbaabaabbbbbaaaaaababbaaaababbbabaaabbabbbbabaabbbaaabaaabbbbbbaaabbaabbababaaabaaabbabaabbaabababaaabbbbaabbbbbbbbbabbbbbbabaabbbabbbbbbbaaaababbbbbbbababbaabaaabaaaabbbabbaaabababbaabaaaabbaaaabbabaaababaabaaabbbbbbabaabbbbaabbabaaaabaabaabbaabbbbaabbbaababbbbabbbbbabababaaaabaababbbbbbaaabbbaaaabbbbaaabbbbbbbaabbaaabbabbabbbababbaaababbababbababababbaababaaabbbbabbababbbaaaabaaabbaaabaabbabababaaaabababbaabbbbbaababbaaaababaabababaabbbbbabaaabaababababbabbbaabbaabbbbbaabaaabbaaaabaabbbaaaaaabbbaaabbbabaaababbbbbbaabbabaabbbababaababbaabaaaaaaabbbbabbaabaaaaaaaaaaaaabbbaaabbbbbbabbbaabbbabbbabbbaabbbbabababaabbbbaabbabaabbbbabaabaabbaabbaaabaaaaabbaabbbbbaaaabbabaababbbabbbaabbababbaababaabbbaababbbbbbbaaaababababbbbbbbabbbaabbbabbbabaababbabbbbaabababaaabbaaabaabaababbbbbabbbbaababaaaaabbababaabbbaaababbaabbababbabaabaababaabbaabbbbabbbabbaabbbbaabaabbabbbbababaaaababbababbaaabaaabbbbabaabbabaabbaaababbaababbababbaaabbabaaaaabbabababbabababbabbbabaabaaabaaaaaaabbaaabbbbabbabbbaabbbaababbaaaabbababbbbaaaaaabbaabababbababbbbabbbbabbabbbaaababaaaaabbbabbaabababbbbaaabbababaaaababbaabababaaabaabaababbbabaaabbaaaabaabbaaaabaabbabbbbbbaabbaaaababaaaaaababbbbbbbaaaabbbbaabaaaabbaaabbabbabbaaaaaaabbababbaababbbbababbbbabaaabbbbabaabbbbaabbbaabbbaabaaababbaabbbababbbbbbabaababbabbbabbbabababbaabaabaaaababbbaabbabaabbbaabaaaaaaababbaaaaabaaabbbbabbbbbabbabaabaabaaabbbababbbabbbbaaaaaabbbabbbabbabbbabaaababababbbbaabbbabbbabbbaaaaabbabababbaaaaabbababbbabbaaaaaabababbbabbbbbaaaaabaaaabbabbbaabbaaabbabaabbbaaabababbbabababaaabbbbbbbbbbaaabbbbbbaabaabbbabbababbaabababbbbabbbaabbabbaabbbababbbbbaabababbaaaabaabbaaaaabbabbababaaaabaaaabaaabbbaabbabbaabbaaaabbbaaaabbaabbbbbaaaabaaabbaabbababbbbabaabbbabbbaaaaaaaababbabbababbbaaabaabbababaaabbbbbbbbbabbbbbaaabbbbbaabaababbbaababaabaabbbbaaabbbbbbaabaabaabbbbbbabbaababaabaabababaaabaabbbaabbbababbbbbbbbbbaababbbaaababaababbaaababaaabbbaaabbbbbbbbbbbababababbaaababbabbaabbaaabaabaaababbaaabaaaalbabbabbabbababaabbabbaababbabaaabbabbaaabbabaaaaababbbababaaaababbaaabaabbaaabbababbabbbbbbbbaababaabbabbabaabbbbaabababbbbabbaaabaaabbababbaabaabaaaabbabbbabaaaaababaaabababababbbbaabaababbbabbabbbabaabaaaabbababaaaaaabbbbbbbaaabbabbaabaabbababbabaaabaaaababbbbabbabaaaabaabbbaaabaaaaababbbbbbaaaaababaabbbbbaaaabaabaabbbbbbbbbbbbbbaaabababbbababbbabaabbaabbababaaaabbbaaabaaababaaaaaabbbabaababababbabaaaabbabaabbbabababbabbaabbbaaabaabaaabbbbababbbbabbbbbaaabaaaaaaabaaababbabbaabaabbaabbbabbaabaaaabbaabbaabbabbaabbababababbaaaaaababbbbaaabaaaabbabababbaaabababaaaabbbbbbbbababbabbbabaabaaabbbbbbbbabababbabbbbababbbabbbaababbabbbbbbabaaaabbbbbabbbabbbbbaabaaabaabbaaaabbabbabababababaabbaabbaabaaabbbbaaabababaabbbaabaaaabbaabbaaaabbabbbabbaaaabbbabbbbabbabbaabbabbbaaaababbbbbbbabbbababaabababbabbabbaabaaaaabbaaaababbaaabaaaabaaaabaaaaabbbaabaaabbbbaaaaabaaaabababbaabaaabbbbbabbababaaaabababbabbbbbabbbaabbbabbbbabaabbaabbaabbbaaababbbaaaababaaabbbaaaaaabbabaabbbabaabaabbbaaaaaaabbaabbaabaababbbaababbbbabbbaabaaaabaabaaabbaababbbbbaaabbaaabaaaaaabbaabaaabbbbaabababbbaabbaaaabaaaaabbabbababbabbaabbbbaabbabaaabbaabaaaaabbabbbbabaabbbabbaabbbabbbbbaabaaaaababbaabbbabbbbbaaaababbbabababaabaababaaaabaaaaabababababbbababaabbbaabbaabbbabaaaaaababaabbaaabbbbaaaaabaaababbababbababbbbbbabbabbaaaabbbabaaaabbabbabbbaaaabaabbabaaabbbbbbbbbbaabaaaaabaaabaabababbabbaaabaaabaaabbbaababbbbbbaaaabbaaaabbaabbababbaabbbabaaaaababaabababaabaaabbaabaaabbabbabbaaabbabababbaaaabaabaaaaaaabbababaaaababbbbbaabababaaaabaabaabaaabaaababaabbbabbbaabaaababbaaaaababababaabaaaaababaaaabbabababbbbbaabbabaabbaabaaaababbbaaaaaabbbbbababaabbabbaabbbbbaabbbbabbbbaaabaabbabaabbbbbbbbabbbabaabbabaabaaaabbaaababbabbbaaaabbabababbbbbaabababbaabbaaabbbabbbbbabaaabbabbbaaabaabbababbbabbbbaababbabbababbabbabaababaabbaabbbbbaaababbbbbbbbaaaaabbabababbaaaabbabbabbbabaaabbbaababbababbbabbbaababaabbbababbabababaabbbabbbabbbbaabbbaaabaaaabaabbaaababbbababbabaaaaaababbaaabbbbaabbbababbababbbaaabbbbaababbbaabaaaabaababaaabbabbbbaabbabbaaababaaabbabbaabaaabaaaaababbabbabbbaababaabbaaabbabbababbaaaaabaabaabaaaaaabababaabababababbaabbababbaababaababababaabbbaaaaaaababbabbaababbbaaabababaaabaabbbaabaaaabababbbaaaababbaabababababbabbbbabababbbabbaabaaaabaaabbbbaaaaaababbbaabaababbababaabaaaaabbabaababbaababbbabbabbabbbabaabbbabaaabaababaabbababbbbaabbaaaaabbabbbaabbaabbbaabbbaabaabbbaabbbbabaaabaabaaabbbaabbbaaaaaaababaabaaababababbbaabaaaaaaaababbababababbaababaabbaaababbbbbbaaaaababbbaabbaabbaaabbabbbaabaaabbabaaaabaabbbbababbbabaabababaaaabbbbbaabaaabbbbaababbabbbaaaaabbbabbabbaaaaabaaabbaababbaababbbaabbabbaaaaabbbababbababaababbabbaaaabbbaabbbababbabbaabbabababbababababbabbbaabaaaabbabaaaaaaabbaaabbaabbaabbbaaaababaaabbbbbabbabaaababbbaababaaabbbaabaabbaababbababbbbbbaaaabbbaaaaaababbbbbbbbaaababbbbbaabababbaabbabababbabbababbabaaabbbbbaabaaabbabbaaababaabbaaaabbbbabaababbaabababaaabaaaaaabaaabbabbaaaaaabaaababbbaababaabbbabbbaabaabbbaababaabbbabaabaabaabbbbbbaaaaabbaabaabaaabababbbbaaababaaaaaababababaababbabbababbbbabaaaaaabaaaaabbbbabbaaabababbbbaaabbabbaababbaababaabaabbaaabaababababaabbbabababbaabbababaabbaabaabbababbabbabbbbaaabbbabbbaaababbaaabbbbbbbababbbbaaaabbabbbabaaabbbabbbbaaabbabbabbbbbaaaaaaaabaaababbababaabbabbabbaabaababbbabbaaababbaaaabbbaaaaababbbbaaabaaaabbaaabaaabaaaababbbabbabaaaabaababbbaababaaabaaabaaabaabbaaabbabbabababbbbbababbabaabbbbabaabaabaaaabaaaabbaabbaababbbaabaaaababbbaababbabbbbbabbabaababbaaaababbabbaababbabbbabaababbbaabbabaabbaaabbbbaabaaaaabbababbaaaabbabbabbbabbbabbaabbabbabbaaaaaabbaaaabbbbaaababaaaababbbbbbbabbbababbaabaabaababbbbbaaababbbbaabaaaaababbabbabbababaabaabbbbbabbabbbbbabbaaaabbbbaabaaaabababbbbaaaabbbaaababbbaababbbabbabaabbabaabaaaaabbbaaaaabbaabaabaaabbaaabaababbabbaabaaabbbabaaaaaabbababaaabbbabaabababaabaababbbbabababaaaaabbaaaabbababababbbbaaabbabbabbabbaaabaaababaabbaabaababaabbbaababbaabbabaabbaabababaaabababbbbaaaaababbababaaababbbaabbbbbaaabbbbbbaaabaaabaaabbaaaaaabaabbabbbbaabbbabbaaabbbabbaabbbbbaaaababbabbbaabbbaaaabaaabbbaaabaaaaaabaababbbababbbbaabbbabaaabbababaaababaaabaaabaaabbbbbbbbaaaabbbbaabbabaabbabbabbababbbaabbbaaaabaaabbbbbaabbaaabaabaaaabaaaaaaabaabbabbaaabaaaaabababaaaabbbbabbbbaaaababbbaabaabaaaabaabbaaababaaabaaaabbabbabaabbabbababaabbbaababaaabaabbbbbabaaabbbbababbbaabbbaabababaaabababbaabbbbbabaaaabaaabbaaabbbbabbbbabbbbbaabaabaabaaabbaabaaababbbbabbabbababbaaaaaabbabbbbbbaaaaaabbaabbbabbaabaaaaaaabaaabaabaababbababbbabaabaaabbbbbabaaababbbaaabababababababbbbbbaababbbbaababbbbababbbbaaaaaaababbabbbababbbaaabaaabbbbbabbbaabababbabaabbabababbababaaaabbabbbbabaaabababbaabaaaaabaaaaaabbabaaaaabaabbaabbbabbaabbaaabaaaabbbbaaabaabaababbbababaabbbabbbbbbbbbbbbbbbbbababaabbabbaaaaabbabbababaaaaaabaaabbbbabbabaabaaaaaaabbbababbbbbbabbabaaabbbaaabbabbabbababbababaabbaabbbaabaaaaabbabbaaaabbbaaabbaabbaaaaaabbaaababaabaaaabbbaabbabbbabababbbbaaabaabaabbaabbbabbbaabbbaaaaababbbabbabbbabaabbbaaaaaaaababaaaaaaaaabbabbbabbbabaaabaaaabaaabaaabbbbabbbbabbbabbbabbbbbabbaaaaaabbabababbbbbababaaabaabaaaabaaabbaabbaaabbabababbbbababbaaaababaaaababaabaabbabbbbbaaababbabbababbabbaaaaabbaaaabbbaabbbaaaaabbaaabbaaabbaaabbaabbabbababbbaabaabaaabbaabbababaababbabbbabaababababbaaabbbaaababbbbbaabbbabbbbabbbabbaaaabbabababbabbbaaaaaababaaababaababbbbbbababaababaabaaabbababababbbaaabbbbbabbbaababbabaaabbaaabbaaabbababbabaababababbababbaaabbabbaaaaababbaababaababbabbabbbbaaabbabaabbaabaaaabbaababbaaaababaaaabbbbbbaaaaabbbbbabbababbbbbbbbbabbbbbbbbabaabbaabbbbaaabaabbbbaaabbabbabbbbabbbbbbaaabaaabaabbbbabbbbbabababababbabaabbbbbbaabaabaabbbaaaabaababbbbbbabababababbaaaaabbbbbaaaaaaabbabaababbbaabbbbabbbabbbbbbaaaaaabbaaabbabaabbaabbbaaaaabbaaaaaaababbabbabbaaaaaabaaabaabababaaabbbbabaaaaabbabbbbaabbbabbbaaaabbbbbbbaaabbbabbbbbaabbaababbababbabbbabbaaabbbbbbaaabbaaabbbaabaaaabaabaaaabbbaabbabbbbabbabbbbbbbabbaabbabbaabaabbaaabbabaaabbbbbaababaaaabaabbbbaaaabbababaabaaabbbaabbabaaabaaaabababaaababbbbababbaaaaabbaaaaaaabbbbbbaabbaababbbaabbababaabbbbbabbaababbaabbbbbbbaaabaabaaabbabbbbbaaabbbbabbaaabbababbabbaababbbabbbabaaabaabaabaabbbbaaabaabababaaaabbbbbaaabbabbababbababbaaabbbbbbbbabbaaabaabaabababaabbbbbbabbbabaabbbaabbbbababbaaabbaababbbbabbaaabbbaabbababbababbababbaabaaaabbaaaabaabbaaaaabababbaaabaaaaaabababbbaabaaaaaaaaaabbbbbaaaaabbababaabbabababaababbaaababbababaaaaaabbabbaabbabaabaabaaabbbbabaaabbbaabbabbaaaabbbbbbbaababababbaaabaaabbabbabaabaabbbabaabababbbbbbbbabbbabbbbbaabbabbabaabbabbbaaababaaababaaabbabbbbbaabababbbbbbbbabaaaaaabbbbbbbbaaaabaabaabbababbbaaabbbabbabaaabbabbbbbaaabbbbababaaaabbabaabaabbabbbbabbaabbbabbbaabaaaabbabaaabbabbaaabbaabbaaaabaabaaabaabbbbabababbabaaababababababbaaaabbbaaababbbabaaaabbabbabbbbaabbabaabbbbbaabbabbaaababaaaaabaababaabbbababbaaaababbbabbaababaaaabbaabbaaababaabababaabbababbabaabbbaabbbaababaaaaabaababbbbbaabbaaabbbaabaaabbbbbbababbbabaaaaabababaabbabaabaaabbaabaabaaabbaaabbaababaaababbababaabbaababababaaabaababaaaabbbbbbbaaababbabaabbaabbbabaabbaababbabbbbbbbabbbbaabaaababbabbbaaabbbabaaaaabbbaaaaabaabaaabbbabbbbbaabaabbaabbbbabaababaaabaabaaabaabbabbbabbaababaaababbabbababbbbbaaaaabbbaaaaababbaabbbabbabbbaabbaabbaabaaababaaabaaabababbabbabbaaaaabbababbabbbbbbabbbaaaaaaabbbbaaabbbabbaaaaaaaaaaabbbbaababbbbabababbaaaaaaaaaabbaaaabaaaaabaabbbaabababaaaaabaaaabbabbbabaaaabbbaaabaabbaaabbaaaabaabaabaababbaabaabbbaabbbabaabababababbbababaababaaaabaaababaaaaaaaabbaabbababbbbbbbbbbbaaababbaabbaaabaabbbababaabbaabbaaaaabaabbaabbabbabaaabbaabababaababbabaabbaaabaababbbabbaaaaaaaabbbaaaaababaaaaabbaaabbbbaaabbaabbaaaaaaabaabbabbbbabbbababababaabbaaabaaaabbbabbaaababaababababbbbabaabbaaababbabbbaababbbabbaabaabaabaabbbaaaabaaaaabbbbbaaaaabbaabbbaaababbbaaaabaaaaaaaaabbbbaaaaabbaaaabaaabaabbabaaababbbabbbaabababbbbbbaaabbaabaabaaaabbaaabbbbabbababbabaabbaabbbbabbbbbaaabaaabbabbbabbabbbababbabaaaabbababbaaaaababbabbaababbababbaabbababbaababaababaabbbaaaaabababbbabaaababaabbbbbaaaaaababaaababaaaabbaaaababaabbbbbabaaaabbbbabbabbaabbbabaabbbaabbbabaabaaaabaababaabbabbbababaabbaabbaababababbaabaaaaabaabbabaaabababaabbbaabbaabbbabbaabbbaaabaabbababbaaababbbabaabbabaaabababbbbbbababaabbbbaaaaabbbabbbabaaabaaaabaabbabbaaababbbaaaaaababababbaababaaaaaababaabaabaabbaaaaabbbaaabaabbbbbbaabbbbaaabaabbbbaababababababaaabbbaaaaabbbbbaaaabbabbbbaaaaaabbabbabbbabaaababbbaabbaabbaabbbabbbbabababaaaabaabbaabbbaabababbababbbbbbbabbbbbbbababaabbaabaaabababaaabbbaaaaabbbaabbabaaaaabbbbabbabbbbabaaabbbaabbbaabbaaaababaaabbbabbbabbbabbabaaaabaabbbbbbbbaaaaaabbaabbababaaabaabbbbaaababaaaaaaaabaabababbaabaaaaabbbbbbbbabbbbbabaaaababaaabaaabaababbabbbbabbbbbaaaabaabaaaaababaaabbbaaaabaabaabaaaababbaabbbaaabaaabaaabbbbabbbabaababaaaaabbabaababbaabbabbbababaaaabaaabaabbbaaaaabbaababaabaaabababababababbabbaababbbaaabaabbaabbabbbbaababaaaaababbabbbbbabbbaabbaabaabbabbbbababbbabbabbbaaaababbabbaabbbababaabbbbbbabbbbaaabbbabbbaabaaabaabbbaaababaaaaabbbaabbbbbbababbabbbabbabaaaabababbbbbbbaaabbabaaaabbbabbaabbbaaabababbabaaaaaaaaabbaabbaaabbaaaabbabaabbbbbabbbaaaabaabababbaabbaabaaabbabaaaaabbbbabaaaabaaaababaabaaaaaababbabbabaaabbbbabbbbaaabababbaaababaaaaabbbabaaabababababaaaababbaababababaabaaaaaaaabbabaaaaababaaaaababbabbaabaaabbbaaabbababbabbbaaababbaababababbababbabaabbbababbaaaabaabaaabaaababbbabbaabbbaabbaaaabbbaabababbaaaaababaabababbaaaaabbbbbabaabaabaabbbbabbbbbabaaaabbbbaaabbbbbbaaababaabbaabbabaabaababbabbaabababbbbabbbaababbabbabbabaaababbbaaaababbbbbbbabbbbbbabbbbabaababaabaabbbbabbaaaabbbaabaabaabbbaababaaaabaaaabbbbbbaabaabaabbababaaabbaababbbabbaababbbaabaaaababaababbabaaabbbaaaabbaaaabbbbbaabaababaabbaabbaaabababbaaababababbaaababbaaaabaaabaaabbabbbaaabbaaabababaaababbbaabaaaababaaabababbaabbabaabbaabbbbbbaabbbaaaaabbaaabbababaaabbabbaabbabaaabbaaaabbbbbbbabaaabaaabababaaaabbbbbbaababaabaabaabaabababbaaaaabbabbbbaababbababaaabbaabaaaabababbbabbaaaabbbabbbbabaaabaaabaabaababbaabbababbaabaaababbbababbbababbbaaaaaabbbbbabbbbbbbabbabaaaaaaaaaabaababbbaaaaabbbabaababaaabaababbaaaaabababbbbababaabbabaaaabaabaaaabbaabbbbaabbaaababbabaabaabaabbaaabaabbbbaababbabaabbaaabbbbabaabaabbababbbababaabbbabbbabbbaabbbaaaabaaaaaaaababbabbbaabbbabbbaabaaaaababaaabbaabbbabaaabbabbababbabaaaaaaaabbbaabbabaabbabbababaaaabaaaabaaaababbabaabbbbbabaababbabbaababbaaabaabbabbbbaabaabbaaaaaabbbabbbabbbbbbaaaaaaaabbaaababbbaababbbabaabaabbababbaabbaaabbababbaabbaaaaaabaaaaaabbbabaababbababbbbbbbbaaaaabaabbababaabbbabbaabbbaaaabaabbbaabaabbbbaababaaaaababbbbaabbbbaabbbbbabaaaaabaaabbbabbbbbbbaababbabaaaababbbabaaabababbabbbbabbabbaaabababbabbbbabaaaabbabbbababbabbaaabbbbabbabababbabbbbabaaaaabbbabababbbabaabaaaaaaabbbbbaabbaabbbaaabbbababababaabaabbbbaaaaabbaabaabababaaabbabbaabbbbbabaaabaabaaabbbabbabaaababbbbaaabaabababbaaaabababbaabbbaaaababbaaabaaaabaaaaaaaabbaabbaaaaaaabbaabaababababbabaabbaaabbbbabaaabbbbbbaababbabaaaaabbbbabbabbbbbbaaabbabaaaaabbbbbabaabbabbbabbbaaabababbabaaaababababbbaabaaabbaaaabbbabbaabbbbbbbbbbbaababaaaaaabbbbabbbbbaaababbbaaabaaabababbbabbabbbaaaaabbbbabaaaababbbaaababaababbabaabbbbababbbabbaabaabbaabaabababaaabbbbaaaababbaaaabbabaabbaaabaaaaabaaabaaabaababbaabbbbbabbbbaabbababaababaababaabbabaaabaaaabaaabbbbbabbbabbbbaabiabbabaabbababaabaaaabaababbabbaaababbbaabbabbaabbabbbababbababbabaaaabbbbbbbbabbbaabbbbaaabaaabaababaaaabbbaaabababaaababbaabbbbbaabbaaabaabbabaabbaabbbbbabbbababaabbabaaaabaaababbbbbbbbaabbaaaaabbbabbbaaaaabbbabbaaabbababaaabaaaabababbaaababbbaababbaabbaabbbabbabbabbababaaababbbabbababbbbaabbbbbbbbababaabbbabbabaaababbaaabbbbabbaaaabbababbaabbaabbbbaabbabbabbbaaabbbabbbbbaabbaabbaaabaaaabaabaababaaabaabaabbabaabbaaabababbbbbbabbbbaaaaababbaaaaaaaabaabaababbabaabaaababaaabbbbbbbaaabaabbbbababbbbabbbbaababaabbaaababbabbbabaabaabbbabbabaaababababbabbbbaaaaaabaaaaaaabbabaaaaabaababaaaaabbabbbabbbababbbabaaabbaabbbaababaabbabbbaababbbababaababababbbbbabbabbabaababaaaabbaaaabaababaaabbbbbbabbaabaabaaabababbbabbbababaaaababbabaabbababbaaaaababaabababbaaaabbbaabbbaaaabbabbbbabbaabaaaabbaaabbbbbaaabbabbaaabaababaaabaababbbbabbbbbbabbaabbbabaaabbbabaababbaabaabaabbaabbababaaabbbbbbabababaaabbabbbbbaabbbabbbaabbbbababababbbaabbbaaaabaabbabbabababbabbabababaabbabaaaaaaabbbbbbaaaaabbbbabbaaaaaaaaaabbaaaaabbabaabbabbbaaaaabababababbbbbabaabbabbbaabababaaaaaaaabbbbabaababbbaaabbabbbbbbbabbbaabbabbbaaababbbbababbabaaabababaabababbbbbbbbbabbbabbaaaaaaaaaabbaaaaaababbbaaabbbbbbabbbaaaabaabbababbbbbaaaababbbabaabaabbaabbaaaaabbbbbbbbbbaaaababaaababaaaabbbbbbabaaaaabbbbbbabbbaabaabaaabbaabaaabbabbbaabbabaabababaaabbaabaabbbbaaababbbbaaaababaaaaabbabbbabbbaababbbababbbbaababaababbaaabbbabbaaaabaababbbaabbbabbabbabbabbbabaabbbbbabbaaaabaabbbaabbaabababbabbbabababaabbbbbbabbaaabbbaabbabbbbbbbbaabbababaabaabbbabaabbbbbabbbbbbabaabbbbbabaababbbbbabbbbaabbabbbbbabaabaaaaaabbbababaaabbbbaabbabbbabbbbabbbbaaaaabbaaaaaabbaaabbbaaaaabbaabbbabaabababababbabbabbaabaabaababaaabbbabbabbabbabbbabbbbaaabbaaaaaabbaabbbbbabbabbaabbbbbbbaabbabaabaabbabbababbabaaababaababaaabbbbbbbbbabababababbabbbbbaaaaabbbabbbabaabbababababbbbaabaabaaabbbabababbaaabaabbaabaaaababaabbbbbabababbbabababaabbbbabaababbbaabaababaabbaaabaaabbababbbbbbabbbaababbbaaabbaaababaabaaababbbbbbbbbaabbbababbaaabbabbaababbbbabbbbbbabaababbbbbbabbaaaabaabaaabaaaaabaababbbbbbaabbababbbbaaababbbbbababaaababbbbbaaabababbbaaabaabaaabbaaaaaaaabaabababbaababbabbbabbbabbaaaabaaabbaaababaaabbbbbbaaababaaaabbbaabbbabbbaaaabbbbbbabababbaaaaabbbababbaaabbbaaaaabaabaaaabbbaabaabaaabbbaaaabaababaababababbaababbaababbbbaaabbabbabbbbaabaabbababbaaabaaaabbbbaaaabababbaaaabbbbbaaaabbabbaabbbbbbababaaaaabbabbabaaaaabbbabbaaababbabaabbbaabbbbababaaabbabbbbaaabaabbabbababbaababbabbabbbaaaabbabbaaaaabaabbaaababaaabbaaababaabababbabbbbaabababbaaabaaaaaaabbabbbaaaabbabbabbbabaabbbabbbbbaabaaaababbabbbaabababaabaaaaaaaabbbabababbabaababbbabbabbbbbbbabaaabbaaaababbaaaaaaababbabbaaabaaabaaaabababaabababbbaaabbaaabababaaababbbabbaabaaababbaaabbaaaaabbabaabbaaabbabbbaabbaabbaabaabbaabbababaababaaabbabbbbbaaaabbaaabbaababaababbaaaabbbbabbabbaaabbaaabaababaaabaabaabbaaaabbabaababbbaabbbbbabbaabaabaababbabbaabababbbbbaababbbbaaaaababaaababbbaabaaaabbabbbaaababbababbbbbaaaabbbaaabbbbabbabbbbbababbbbababaaabaaabbaaaababaaaaaaabbbbbabaabbaababbbabbbbaaaaaabbaabbbbbabbaaaababbbabbbbbaaaaababbaaababbabbbbbbabbababaaabbbbabbbabbabaaaababbaaabaaabaaabbaaababbaababbaaaabbaaabbabbbabaaaaabbbbabbbbabbaabbbbbbbaaabbbbaababaabaabbbbbbbbbabaabbabababaaaabaaababbbabbbabaaaabababaaabbaabbbbabbbbaaabaabbbaabaaababaaababbbbaaabbbbbbabbbabababaaabaaaabbabbaabababbbaabbaabaaaaaaabbbabaabbaabaaaaaabaabbbabaaababbbbbaabbababbbaabbbababaabbbbababbbbabababbabbabaababaaabbbabbaabbbabbabaabbabbbabbaababbbababbaabbabbaabaaabbaabbabbaaabbabbaabbbbaaaaababbabbbbaabbbabbabaaababbbbabaabbaaaabbaaaaaaaaababaabbaaaaaaabbababbbbbababaababaababaaabbaaaababaabaabbbbabaabbbaaaaaaaaabbbbabbbabbbbaaabbbabbaaabbbbbaabbababababababbaabaaaabbababbbabaaaaaabaaabbbabaabaaababbbaaaabaaaaaaabbbbaabbbaababbabbbbaaabaaaaabababaaaabababbaabbabaaaababbaabaabbabbbbbabaaaaaaaaabaabbabbabbaabbaaaaaababbbbbabbaaaaabaaaabbaabbaaaaabbbbbabbabbaabbabaaaabbabbabbabaaabaaaabbababaababbbbababaaaaabbbbabbbbaaabbbaabaababbbabbabbbbbabbaabbabaaaaaababaaaababbbbbbabababbbbaabbbbbbbbbabbaaaabbbabbaaabaaaabbbbabaaaabaaaababbababbbbabbbbbaaabbaabaabbababbbbbbbbbbababbabaaaaabbbbaaaabbaabaaabbaabbbaabbbaaabaaaabbbbbbaaaabaaabababbaabbbbabbbaaababbbbbabbaaaaaaababbabbbabaaaaaaabbababbbabbbabbaaabbabaabaababbaaaaabbbbababaabbbbbaaaabbaababbabbaaabbbbabbababbababaabbabaabbbbbbabaaabbabaaaabbbbababaabbaaaabaaababaabbbaababaaabbbbbbbaabaabaaaabbaaabbababbbbaaaabaabbbbaabbbbaabaabbabbbabaabbabaaaabaaabbbabbababbbbbabababbbabbbababbbbaabaaabbaaababbbabbbaaabbabaaabaababbabaaabbaabbbbbaabbbbbabaabbabbbbbbaaaaaaaaababaaabbbbbaaabbabbbaaaaabaababaabbabbbbbbababbbaaabbabbbbbaabbbaaababaabbabbabbabbbabaababbabaabbbababababaabaaaabbaaaaabaaabbaaaaaaaaaabbababbbabbaaabbbaabbaaaaaabaababbbababbaaabababbabbbabbbabbaaababaababbbbbbbbbabbabbabbaaaabbbbaaaabbaababbbaabbbaaaabbabbbaabaababbbabbbaaaaabaabbbabaabbbabbbbbaaabbbaabaababbbbaaaabbbbbbabaabbbbbaabbbabaabbbbaaabaaaabbbabaabbbbaabbbaaaabbaaaaababbbaabaabbaaabbbbbabbaabbabaaaabbbaaababbbbabaabbababbaaababaaaaabbaabbabbbaaaabbbabaaabbbaaabaabaaaabbbbbaaabaabaabaaabaabbaabbaabbbbaabbbbbaababbaabbabaabaabbababbbabbbbbbabababaaabbabaaaaaabaaaabbaababaaaaaabbbababbbbabbababbbabaabaabbaabababbaababbbbaaaaabaaabbabbbbaaabbbababababababbbabaabbaaabbaaabaaabbaabbbabbbbabaaababbbaaabaaaabbbbabbaabaaababbbbabaaabaabbababbbaabbbabbbbabaababbbbbaabbaabbaaabbaaaaaabbaabbbabbbababbabbbaaabaababababababbababbbabbbbabbabbaabaaaabaabbbbaaaabbaaabababaaabbbbaaaaabbbaaabbbabbabaabbabaaabaaaabbbabaaaababaabbaaaabbbbaaaabaaabbabbabbabaababaaabababbaabbaaaaaabbabbbabaabbbbabaaaabbaabbabaaaabbbaabbbbbababbabaabaababbabababbbaaaaaaaaabbaaaaabbbbbbbabaabaabaabaaababbabbbbabababaaaabbbbaabbabbbaaaabbbbaaaaabbaaaabaaaababaabbbbbaabababbabababaabaaaaabbababbaabbbaabbbabbbaabaabbbbaaabaaabaabbaabaabbbaaaabbbabbaabaaabbababababaabaaaaaaababaaabababbbababbabbbbbbaabbaababbabaaabaabbbbaaaabababbbaabbbabbbbabbabaabbabababbbbabaabaabbbbabbbaaabbbbbaabbbbbbabaabbbbbababbbbaaabbabbbbbabaaababaabbbbaabbabbbabbbabbbbaababbabababaabaabbaabbbbbaababaabbaaabbababbababbbbbaaaabababaaaaabbaaababbbabbabbababbabbbbababbbaaababbabababbaaabbbaaaabbabababbbabbbaaaaabbbaabbaaababbababbaababaababbbbaabaabbabbbaaaabbaabbbaaaaabbaaabbbabbbbbaabaabbbaaabaababbaaabbaaabbabbabbaaaaaaaaabbaabaaaaaaaabaabbabbaabaababbbaabaabbaaaaabbabbabbbbbbbabaabbbbaaabaababbbbabbaaabbbaaabbbabaaabbbbbaaaaaabbaabbbabaaabbabaaaaaaaaabaaaabbbaaaaaabbaabbbbabbbabbbaaabaaabbbaababbaababbabbbbbabbbbbaabbabbaabababbbabbbbbaabbbbbababbbbaabaaababababbabaabaabaabbababbaaaabbbbaaabbaaababaabaabbbbbbbbabbbaaabbaaabbaababbaaabbaaabaabbbbbbaababaabbaaabaabbaaaababaaababbbaaaaabbbabaaaababbababaaaabaababaaabbbaabbabababaaababbbabbabbababbbabbabbabaabbaabaabbaaaabbbabaaaababbbbbbbaabbabbaabbabaaabbaabbbbbbbbbbbabbabbbababbbaaaabaabbbabbbaaabbbaababbabbabbabbabbabaababbaaaabaabbabbabbabaaaabaaaabaaaaaabbbbaaaabbaabbababbabbbabbbbaabaabaababbbbaaaaabbaaababbbbbaaabbabbaaaabbaababbaabbabaaaaaabbbbbaababbaabbabbbbbabbbaaabbabbbabaaababbabaabbbbbababaabababbbaaababaaabbabaabbaabbbaaaabaaabaababaabaaaaaabbaaaababbaababababbabbaabaabbbbbbbaabbbabaaabaabbaabaaabaaaabaabbabbaaaaabaaababaabaaabbbbbbabaaababaaaaaabababbbbaababbbabaaababbbbbbabbabbbababaaababbabbaaaaababaaaabbbbbbaabaabbbababaaaaaaaabababaababaabbbbbabaabbbaabbaaabbbababbaaaabaabbbabaabaabbabbabbbababbbaaaaaaabbbbbbaaaaabbabaabbbaaaaabbbbbaaaaaabaabaabaabaaaabbbbaaabababaabbbaabbabaabaabbabaababbbaaaabbabababababaababbaaaaabbbaabaabbbaaaaabbbababbbbabbbbabbbabababbbabaaabbaaabaabbabbaabaaaaaaabbaabbababaababbaabbbaaaabbbbababaabbaaabbabbabaabbabbaaaaabbabbaabbbbbbbbaaababbbaaabababbbbbbaabaababbabaaabbababbbbbbabbabababbbababaaaabaaaaababaabbbbabbabbbaabbbabbaaaaaabbababbaaababaaaaaabbabaabbaaaaaabbbaabbabbbaaababaabbababaabaababbaaabbabbbababbabaaabaaaabbabbbababaaaaaaabbbaaababaabbbbaabaabbbbabaaabbbbbbaaabaabbaaabbabbbbbaaaaabababbbaaaaaaaaababbbbbaaabbaabaabababaababaabbabbbaabaabbbaaabbabaabbbbbabaaabaabaabaaabbbaabaaaabaabaabbbbbbaabababbbaaababaabaaaaabbaabbbbababbbbbbabbabbbaaabbbabbaaabaaaabbbaaaababbaaabbbabbbaabaabbbabbabbaabaaaaabbababbbabaaababaaabaabbabbaabbbaabbbbbababaaaaabbabbabbabaaabbbbbaabaabbabaaaaabbaaabbbabaaaaaaaabbbbababbbbabbabbbbbbabababbbaaaababbbababbbaaabbaaababaabaaaabaabbabbabbbbbbaabbbaaaaaaabbaaaabaaabbabbaabbaaaabaaaaaaabbbbaaaaababbbbbbaaaabaaabaaababaabbbbabbaaaaaabbbabaabbabbababbababababbbabbbbbbabaaabbbbabbbababbbabaabbbbbaaaaabbbbabbbabbaabababaabaababbbbabbbbbbbaabbabaabaaaaabaabbababbbbaabbabaaababbbbbabbabbbbabaaabbabbbababaaaaabbaaaabaaabbbaaaaaaababbaaaaaabbaaaaaaaaaabababbaaaaababaabbababbbababbaaabaabbbaaabbaabaaaababaabbabbbaaabbbaaabbbbbaaaaaabbabaababbbaabbbaabbabaaaaabababaabaaababbbaaababbabbaaaaabaabbbaaabbaabababaaaaaabaaabbaaaaababbbbbaaababbbaaaabaaaaabababbbabaabaaabbbabbbbabaaababbbbabbaaaabaaaabbaaaabbaababbaabaabaaabaabaaaababaaaabbbabbbaaaaabbababbaababababbbabaaabbaaaaababaabaababababbabbababbbaaaaabbbbabbaabbabababaaaabbbbbaabbabbaaabbababababbbaaaabbbabbbaaaabbbbbabbabbbbbbaabaabaaabbabbbaabbbaaabbbabbaaaabbbabbbbabbbaaaaabbabbbabababbbbbaababaaabbababbaaaabbbaaaaabbababaabbbbaaabbabababaaabbbaabbbbbababbbbaaaabaababaabbabbababbaaabaaabaaabbbbabbbaabababaabaaabaaaabbbbbaababaabbaaabbaaaabbaababababaabaabbbbbbaabbabbbbabaaabababaaaabbaaabaabaaaaaabaabbaaaabababababaaaababbbbbaababbbbaabbbabaaabaaabaaaaaabaaabbabbaabbbbbbaaaababaaabbbbbbabbaaabbaaaabaabbbababaaabbabbbaabaababaabaaabbababaabbaababbbbababaabaaabbababaababaaabbbababbaaabababaaaabbbabbaababaaabababbaaabbaabababbabbbaaabaabaabbbabbbaabbaabbaaabaaaababbaaaabbabbaaabbaabbbbaabbbbbbbbabababbabaaaaaababbbaaabababaabbaabbbbaaababaabbbbbbaaababbbbbbababbaabbbaaabbaaababaababbabaaabbbababbbabaaabaaabababaaaaaabbbbabbbaaaaaaaaaababbbabbbbbabaaaababbabbaaabbabaabaabababbaabbbabbbbabbabaaabaaabaababbabbbbaaaababbbaabbbbaaaabbaabbbaaababbaaaabaabbbaaaabbbbbabbbbabaaabbbbbabbabaaaaaabaaaaabaaaabaaaabbabbbaababbabaabaaaababaaabbabbbababbbababaababbbabaaaabbbabaaaaabaaaabaaaabbbbbbbaabaaabaaaaaabaababbababaababaabbabbaabbabbaaabaaabaababbaabaaabbbabaababababbbbbaabbbabbababaaabaabaabababbaababbabbabaababaababaaabbababaabaabbbabbbabaaaaaababababbabaaabbaabbbbbabbabbabbbbaabbbabaaaabaaaaabababababbaababaaaababbbbabaaababaaababbbabaaababaabbababbaabbbbababbbabbbbababbabaabbabaabbabaaaaabaababbbabbaaabbabaaabbbbabaaabbabbbaaaabababbaabaaaaaaabbaabbbaaaabaaabaaaabaaabbabbbbabbbabbaaabaabbbabbaaabaaaabbaabaaaaabaaababaaabababbbabaaabbaaaabbbabbbaaaabaabbbaaabaabbbabbbbbabbbababbaaaaaabbaababbbbbbaaabbbbbbaaabbaabbbabbaabababbabaaaabaaabbbbabbabbaaaabbabaababbbabbbaaaaaabaabbabbabaaabababbbbabbaaaaaabbbaaaababbaabababbabbabababbbbaabbbabbbbbaaabbbbabbbbbababababbbabbabbbbaababbbbbbabaaabbbbbababbbabaabaaaaaaabababbbaaababbabaabaabaaabbbbbbaaabbaaabbbbbbaaaabbaabbabbaaaaabbabbbaabbbaaaaaaaababababaaabaaaaabababababbbbabaabbababbabaaaabbaabaabbaababbbaaabbbbaabbbabaaabbbaaaaaaaaaabbabaaaabbabaabbabbaaabbbbbaaaabbaaabababaabbaaaabbbbbbbaaaabbbbbbaabbbbbbabbaabaabbbaabbbabbbbbbabbaaabaaaabbaabbbbbaaabbaabbbbbaabbabaaabaaaaababaababbbbabbaabbababaaababbbabbaabbaabbababbbbbbbbbaabaaaaaabaabbabbabbabbbaaababbabbbabaaaababbbabaaabbabaaaabbaaabbabbabaaaaabbbbaaaaaaaaaabaaabaabababbbabbababaaababaaabbabbbababaabbbbaabababbbbbaaaaaaaaabbaabbbbbbbbbbaaaabababbaaabbbbaabbbabaabaaaabaabbabaaabaabbabbbbaabbaaaabbbababbaaabbabbbabaaababbabbabbbabababbabbaabbabaaaaabbabbaaaaabbbaaaabababbaaaabaabbhbbaababbabbabaabbabababaaaaaabbaabaababbbbbbbabaaabaaabababbaaababbaabbbbabbaabaaabaababababbbbabaaabbabaaabbbabaaaaabbaabbabaabbbabbbabaabbbbaaaaaabbabbbbaaabbabbaabbbabbbaababbaabbabbabaabaaaaabaaabbababbabbaabbabaabbbbabaababaabbabbaaabaabbaabababbabaabbaabbbbbabbbbaaabbaaaaabbaabbabbaaabbaaabaabababababaababbaababaabbabbbabaaabbbababbabbbabbababababbabaabaaaaababaabaaaabbbbaaabaabbbaaabaababaaaabbbaaaaaaaaaaabababbbaabbbbbbbbbbabbabababbbbaabbaaaaabaaabbbaaababaabababbababaaaaababbbbabbbbabaabbbabbbbabaabbbbabbababbaabbbaabaabbaabaaabababbbbaababbabbbbabbabaabbaaaabababbaababbabbbbbabbbabaaabbaaabaaabaaabaaaabababaabaababababaaaababbbaaaabbbbbbabbbaababaababbbabbababaababbbabbbabbbbaababbbaaabaaabaaaabbaaaabbbbbaaaaaabbababbbbbbbabbaababaaaaabaababbaabaaababbbbbbbbbbabbaabaaababbaaaabbbbbababbbabbaaabbbbabbbabbaabaaaabbbbbababbabaaaababbababaaabbbabbbababaaaabaabaaabbabbabbbbabaaabbaabbbbaaaabbbbbbbabbaaababbbbbbbbbabbbbbaabbbaabaabaabbababaabbababbbabbbbabbbaaaaaaaaaabaaaaabaabababababbabaabbabbbabbabbabaababababbaaaaaaabababbaaaaaabbaabaababbbbbabbabaaabbabaaabbaabaaaaabbbbbbabaaaabbbaaaaaaabbaabaababaaabbaaaabaabbbabbbaaaabbbbbaabbbbbababbbabbabbabbaabbabbabbabbaabbaabbaababbbabbbbaaaabbababbabbabaabababaaaaabbbbbabbbaaabbababaabaaaaaaababbabaaaabaaabbababbaaababbaaababaabbbbabaaababaabababbaabababbaabbbbbaabbbbbaabbbaabaabbbaabababbbaabaabaabaaaaaaaababbaababaaabaaaaaaabababaaaaaaaaabbbabbabababbbaabababbabbbbbbaaabbbbbbbabbabaaaaabaabbbbbabbaabbbbaabbababbbbbaabbaaabaaaabbbbbbbabaaaaaabaabababaabbabbaabaabbababababaabaabbaaaabababbaaabaabbbaaababbaabaabaabbaababaaaaaaaabbbbababbbbbbabbabbabbbaabaabbaaababaaabaaaaababbaabbaaabbbababbababaabbababaabaababbaababaabbaabaaababababbbabbbaaababbbbbbaaaababaabbaabbbbbbbbabbbaabaabbbbabaaabbaabbbaabbbababbbabbabbbaabbabbabaaaabbbabaabbabaababbababbbaaaabababbbaaabbaabbbbbaaabbaabbaaaaaaabaaabbbaaaabbaaabbababbaabaabababbbbbbaababaaaabaaabbbaaaabbbaabbbabaababbbbbabbbaaababbbbbaaaabbaabaabbaaabbabaabbabaabaaabaaabaaabbabaaaaabaabbabbbbbabaabbaaabbbbbaabbabbabaabbbaababbbbbbababbabbabaababbbbaababbabaabaaababbabbbaabbabaaababbabaabbbaabababbabaaabbbbabaababbbaaabaabbababbabbbabbbbbabbbbababbaaabbababaababaabaaaaaaabbbabbbaabaaabaabaaaaaaabababaaaababaaabbbbaaaabbaaabbaabaababababbaaabababbbbabbbbbaaababbaababaaaabaabaaaaaabaaaaabbababababbbaababaaaaabaaababbaabbbbbbbabaaaabbaaabbaabbbbbaabbaaababbbbaabbaaaabaaababbabaabbbaabbaaaabbabaaabbabbbbabbbabbaabaaaabbbabaaabbbbbbabaaaaababbababbaabaaaabaabbaaabbbaaabbbbababaabababbbbabbbaababbabbbbbababbbaabbaaabbaabbabaabababbabbbabababbbaaaabbaaabbaababaaabbaababababaaabaabbababbbabbbbabbabbabbabbbaabaabbabaabababbbbababaabbaaaaaababaaaaababbaabababbbabababbbbbbbbbbaaabbbbbaaabaaaaabbaaaaaaabaaaaaaaabaaaabbbbbbbabbbabaaabbaabaabbaabbbabbbbbbaabbaababaabbaaaabbbbaabbaabbbbbaaaababaababbabbbaaaabababbbabaabbaaaaabbbbbaabaabaababbabaabbbaabbbaaababbbbabababababbbbabaababaaabbaaaaababaaaabbababbbababbbbbbbaababbababbbabbabbbaaaaabbababbaababbbbbabababbbbababaabbbbbabbaaabbbababbaababaabbbabaaaabababababbabbaaabbabaaaaaabbbaabaaabbbababbbaabbbbabbababaaabaaaabbaaabbaabaaaabababababaababababbaaabbbbaaaaabbababbabbbbaaabaaaaaaabbbaaaaababbaaababbabbbbbaaabbaabbbbabbbaaabaaabbaaabababbaaabaabbaaabbbbaaababbbbbaaabbbbababaaabbbbaabbbabbbbabbaaabaaabaabaabaaabaabbbaababbabbbaaaabababaabbbbaaababbaaabbabbbbaabaaaabbaababbaabbbaaabababbbabbbaaabaabababaaaabababbaaabbabbbabbbaaaaababbaaabbbbbabbaaabbaabaababbbababaabbaaaaaababbbbaaaaaabbbbbaaaaaaabaabbaababaaabbabbabbbbabbaaabaabaabbaabbbaaabbbbabaaaaabbaaabababbaaababaaababaaaabbbbbbbaaabbabaabaababaaabaabbabababbbaabaaaabbaabbabbbbababbbbaaabaabbabbaabababbaaaaabaabbaaababaabbabaabaabbababaaaabaaabbbababbabaabaaaabbabbbbbababbaaabaabbaabbaabbaababbbaabbbbabbabbbabababbaababaaabbaaabbbaabbbbababaabaababaaaaabaaaabbaabababbbaababbababaabbaaababbbbbbbababbaaaabbbaabbaababbbaaabaaaaabbaabbabbaaaababaaabababbbbbbbabbbbabbbaaabaabbbaababbababaaaabbabaabbbaabaaaabbaaaaabbababaabababaaaaaabaabbaaabbbbbbabbabaaabaaabaaabbbbabbbbabaaaaaabbababbaabbbbabbbabaaababaaaabbbaaaabbbaaaaabbababaabbbaabbbabbabaabbaaabbbaabbbbaabbbbabbaaaaaabbbabbbbbbbabaabbaaaaaabbbaabbbbbbbaaababbbbababaaaaabbbbbbbbbbabaabbaababaaaabaaabbaaaaaaaabbabbabbbababbabbabbabbaaabbabbbbabbbabbbbbaaabbaaabbaabbabaaababaaaabbaabbbababbbabbbabbaaaabbbbabbabaaabaaababbababbbaaabbaabbbabbbbbbbbbabaabaabbbbbbbbabbaababbababbabababbbbbbbabaaabbabbbabaaaababaaaaaabaabbababbbaabababbaabaaabbaaabbaaaaabbabababaaaaaaabbbbbbbbaaabaaabaaabbaaaaaabaababaabaabbbbbabbabaabaaaaaabbbaaaabbabaabbbabaaababababababaaababaabaaabbbababaabbabbbbabbbaabaabbbaaaabaabaaababbbbbaababbbabbbabaaabaabbaabbaabbbabbaabbaaabbabbabbbababbbbaabaabbababbbaaaabaaabaaaaaaababaabaababaaaaaaaaaaabaaaaabbabbabaaaaabbbbbabbbbabbaabbbabbabaabaabaabbbbbbababaaabaaaabbabbabaaabaaaaababbbababbbbaababaabbabbbbbbaabbbbbbbbbaaabbabababbaaaaabaabaaabbababaaabaaabbababbababababbbbaabababbabaabaaaaaaabababbabbbbaaabbbaabaabbaabababaaaaaaabbabbabbbbabaaababaabaabbbbbbbaaabaaaaaabaaabbaaaaabaaabbbbbaabaaabaaabbbbbbbbaababaaaabbaaaaaabbbbabaabaaabbabaaabbabababbabbbbbabbaaaaaaaaaaabaaabbbbbbaaabbaaabbaaaaabbaabbaaabbabbabbaaaaaaaababbababaabbabaabbaababbbbaabaabaabaaabbbbbbbabbbababbabbbbaababbabbbabaaabbaabbaabaabbbaabbbbbbbaabbabbababababaababbbabababaaaaaabbbaaabbaaabbbbaabbbaaaaabaabbaabbababbbaaabbbbbbaabababbbabbaaaaaabababbaabbbbabaaaababaabbbbabbaabaabbbbbbabaabbaabaaabbaaaaabaaaaababbbbbaaaaabaaaabbbabbaabbabaababaaaaaabbaabaabbabbababbabbbabaabaaabbbaabbabbbbabaaababaaaaabbabbabaabbbbbabbbaaabaabbabaaaabaaabbaaababbbbabbbababbbbaabbbabaabbabaaabaabababbabbbbaaaabbbaaaababaabbababbbbabbbaabbaabaaabbbbaaababaaabababaaaabbbaabbaabaabbbbababaabbaababbaaaaaaabbaabaaaababbaabaaaaaaaabbababbaaaabababaabbababaaaabbaaabbaabbaaabbabababbabababbbbbbbbbabbbaaaaaaabbbbaaabaaabababbabbaaaaabbbbababaaabbabbbaabbbbabbbbaababbbaabbbbbaaabbbaabbbaababbbababaaabaaababbaababbaabbbbaabbbbbaabaabbbabbbbbbbbbaababaaaababbabbaaaabaabbaaabbaabbbbaaaaaabbaabababbaaabbbaabababbbabaaaabbaabaabbbababbaaaabbababbbababaaabbabbbbbbbbbabbbaaaaabaabbbaaaabbbbaaababaaabaababbbaabbabaabbbbbbbbabbaabbbaaabbabababaabbbbaabbabaabbabbbaababbababbbbbababababbabbbbbbbbaabaabbbaaabaababaababbbbaaabaaabbaababbabbabbbabaabbabbaaaaaaabbbaabbabbbbbbabbbbbbaabbaabaabbbbaabbabaabaabbaabaaababbbbababaabbbaaabababbabbbabbbabaaaababbbababbabaabbbaabbabbbaaabbbabaaabbaabaaabbababbaaabbbabababbabbbbbbbbbbaaaaaaaabbbbbbbaaabaabaaabaaaaaaabaaabaabbbbababbaaaabaabbabbbbbbbaaababbbbbbbbabaaaaabbaaaabbaabababbbbababaaaaabaabaaabaabbbbababbaaabbaabbbabaabaabbabaababbababaaabbbaabbaabbabbabbabababbaabbabaaabbabbaaabbaababaababbbbbbbaabbaaaabbaaaaabbbbbbbaabbbaaaaaaaababababbaabbabbbababbbbbbbbbabaaaaaababbabaabaababbabbabaaabbabbaaabbaabbbaaaabbbbbaabaaaabaaabaaaaabbaabbabbaaaabbbaaabbaaababbaaaaaababbabababaaaaaababaabababbbaaabaaaaababaaaaababaabaaaaaaaababbababbaaaabaaababaabbbabababababbaababbbbaaaaabababbaaaabbabbbaabbbaaaaababaabbababbabaababbabbaaabbabbaababbabbaabababbaabaaaaaaabbaaaabbabbbaaababbbaaabbaabbaabaabaabaabaabaabaabaabaaabaabbaababaaabababaabbbaabbbbbabaabbbbbababbabaaabbbababbbababbbabaababaaababaabbaaaaaaabaababbbbbaababbbbabaabbaababaaabaaaabbbbbaaaaaabbaabbbabbaaabbaaabaabbaababbbaaaaaabaaabbbabbbbaaaaabbbabbbabaabaaaabbaabbaaababbbbbbbaababbabbbabbaabaaaaabaaabaababaababbababbbbaabbbaaaababaaaabbaabaaabaaaaababaabbaabbbbaaaaaabbbbbaaaabaaaabbabbaaabaaabbbabbbbbbaaababaaabbbabbbbbaababaaaaababbbbaaababbabbababaaabaabaaabbabaaabaaababbbbaaababbabbbababbabaaaabbabbbababaabaaaababbabaabbbbbbbbbbababaabbbaaaabbbaababbaaabbbbaaaaababbbaaaaaaaaababbbbababbaabbabaaababaabbbaaaabababbaaababbbbbbababaaabbbaababbabaaababaababbbbbabaabbabaaabaaaaaaabaabbbbbbbabbabababbaaaaaabaaaabbbaabbbabbbabbaaaabaabbbbbbbbbbbbababbbbaaabababaaaaaabaabbaababbaaaaaaabbabbabbbbababbababbaababbbbabaabbbbbbbaabbbbbaabaaabaabbbaabaaaaaaababaababaaaaabbbbabbbbbabaaabbbbaaaabbbbbbababbbbbbabbbaabbabaaaaababbbbaabaaabbaabbabaabbbaabbaabbabababbbaaabaabbbbabababababaababaabaaaaaaaaaabaabaababaaababaaaaaabbaabaabaaaaaaabbabbabbaabbbabbbbbaaaabaaaaababaaabbbaabbbabbabbbbbabbbabaabbbbbababbbbabbaaabaaaaabbbbbabaaaaabaaabaabaaaaabbababbbbaaabbababaabbabbbabaabbbababaaababbaabababbababbabbbabbbbbabbbabaabbbabbababbbbbabbbbababaabababbbaabbbbbaabaaabbabbbaaaaaaaababbaabaaababbabbbabbabbbabaaabbaabaabbaabbbaaabbaabaabbbaabababaabbbaaaaabaabbbaaaabaabaabbaabaabaaabbabaaababbbbababbaabaabbbbbaabbbabbbabaabbbbbabaabbbbaabbbbaabaaababbbbabbavabaabaaabbbaaababbbababbabaababaaaabbababbaabaababbaabaaaabbbbaabbaababaababaaababaaababbabaaaabbaabbbaababaabbaabbbbbbbabbbbbbbaaabababbabbaaabbabbaaaabaaaabbbbbaabaabbabbbababaabbaabaaaaaabbabbbabbababaabaabbbabbbababbbaababaabbaababbbbabaaabbaaaaaaaabaaabbabaaaabbaaaaaaabbabbbbbbabaaaaaaaaaabaabbabbbbbbaaabbabbabbaaabaaaababbaabaabbaaabbbbbababbabababbbabbabababbaaabababaabbbababaaabbababbbbaabaabbaababbbbaabbaabbbbaabbbababaaaabbaabaabbbbbabbababbbbbaaababbbbaabbabaabbbaabbbabbaaabbaabbabbabbaabbaabbbbbbbaaabbbbbaabbabababbabbabbababababaaabaabaaaaabbababaaabaaaaaabaaaabaaaabbaaaabbaaabaababbaaaaaabbabababababbbbbbabbaabbaaabbaaaabbaababbaabbbabaabaaaabbabbbaababaababbaaaabbaaaaabaaabbbabababbaaaaaababaababbaabaaababaaabbbababbaaabaababaaabbbbabbaabaabbabababaaaaaaaaaaaabbbaaaabbbbbabaaaaaaabaaaaaaaabaabbabbaaabaabaabaabbabbababbbaabaaaababbaaabaaabaabbbbaaaabbbaabaabaabbbbbaaaaabbbabaaaaabaabababaabaabbaaabbbbbbaabbbaaabbabababaabaaabbbabbabbababbaabbbabbaaababbabaabbabbbbbbaaaaaaaaaababababbbbbabaabbbaabbbbbbbaaaaabbabbaabbabbbbbaabaabbbabbababaababaabbbababaabababbbaabaaabbaaaabbaababbaaaababaaaababbabbaaabaaabaabaabbbbbbbaaaabbbbbbaabaaabbbbaababaaabababbbaababbbbbbbabbaaaaaaaababbbaabbbabbaaabbbaaabaaaaaaaabbbbbbaaababbbbabababaabbabbabaabbaabaaaabaababbbaabbaabbbaaabbabaaababbabaaaaaabbaabaabbabbbbbbbaaabbbbbbabbbbbbabaaabbbbbbbbbbabaaabaabbaabaababbbbaabaaaaaaababaaaabaabbabbbabbaabaabaabbabaababbbababbbabababbbaaabbabbabbbabbabbbbbbbbbabbbbbbabaaabbbbaabbaaaaabaaababababbaaabaababaaababbaaaaabbaaabaabbababbaababbabaaaaaaaababaaaaabbaaabaaabbaaabaaabbaabbbaabbabbbabaaabbaaababaaabaaaaaaababaabbbabbbaabaaabbbbbabaabababaaabaabbaaabbaabbbaaaaaabaabbbabbbabbbaaaaabbbbaaabbbabbbabaaabbabbbaabbbaaabbbaabbbaaabaaaaaaabbaaaaabbabbbbbbabbabbbabaaabaabaabbbbbbbbbbbbbbabbaababbababbabaaabbabbaabbabaaaaaaababbaabaaabaaaaaabaaabaababbaaababbabbbbaabaaabbabaabaaabaaaaabbabbabbbabbaaabbbbaaaaaaaaaabbbbabbaaabababbbabbbbbbbababaabaabaabbbabaaabaababaabbaabaabababbbbbaaabbaababaabbaabbbabbbabbbbaabbbbabbaaaabbababbbbbaaaabbbaaaabaaaaaaabbbbbabbabbabaababbababaabababbaabbbbbbbbaaaaabbaaabbbaabaabbbabbbabaaaaabaaabababbbbabaabbaaaabababbabaabbbbbbbabaabbabbbabaabaaaaaaabaaaabaaaabbabaaaabbbbbbbbbabbbaaaaabababbbaaabababbbaababbaaaabbbaabbababaabbbabbabbabbbabbaabbbabbabaaaaabbaababababaaaabbabbbabaaaaababbbababababbbbaababbabbbaaaabaaabbaaabbbbaaaaabaabbbaaabaabababbbbbabbbbabaaabababaababbbabaabababbbbabababbabbaaaabbbbaaabbaaabbbbbbaaaabaabbbbabaaaabbaababaaaabababbaabbabaabbbaabbaaabaababaababbbabbaababbbabbbbbbbaaaabaaabaabbaaaaababababbbabbaabbbbabbbbaaabababbbabbaabbaaabababaabbbabbbaaabbaabbaaaaaaabbaabbbababaabaabaabbabaaabbbbaabbabaabbaaabaaabbbaabbaaaabaaaaaaaaabaaababbaaaaabababbbaababbbbbbabbbbbaabaaaabaabaabaaaabbabbaabbbabbbbaaaaabaabbbbbabbbbbabaabbababaabbbbbbaaaabbbbbababbaabbabbbbbbabbaaabbaaaababbbaaaaaaaabbaaaaabaabaabbbbbaaabbbabbbbbbaababaabbabbbbaababbaabaaabaaaabbabbbaaaabbabaaabaaabbbaabaaabbbbbabbbbabababaabbbbbbbbbabababbabbababbbbbbbaabaaababbabaaabbabaabbbbabbaabaaabbbbaaaabababbbbabaabaabbbbbbbbababbababababaaabaaabbbaababaabbaabaabaaaabbabbaaabbaaaaaaaabaaaaaaaaaabaaabaaababbbabababbbaaaabaaaabbabbaabbaaabaabbbbabaabbbaaaababbbbaabaaabbbababaababaabbaababababbaaabaaaaabaabaababbaaaaaababbaabaabaabaaababbbabaabbbabbaababbaabbbabaaaababaaabbbaaaababaaaaaaaabaaabaaabaaaaababbbaaabbbaaaabbbbbbababaabbbbabbabbaabaaaabbbbaaaaaaabaabbbabbbaaaabaabbbaaaabbaaababbaababbbbaaabbbabaabbaabaabaaabbbabaabbaabbaabbabbbaaaabbabbbbbabaabbabbbababbbbaaababbaababaaaaaabbaaaaaaabbbbbabbabaaaabaabaaaababaabbbbabbbaaaababbbbabbaaabbbbabbbbabbabaabbbbaaaabbabaabaaaaabbababbbabaaaabbbaabaabbaaababbbababaaabaabbabbbbaababbbbbaaababbabababbabbaabbbbbbbbbbbbaaaaabbaabbbaabbbbaabbbaaaabbabbaabababbababaabbbbabbabaaaaabaaabbaaaabbbabaabababbabbbbabbabaabbaaaaaaaabaababaabbaaababbbaabbabbbbbbbaabbabaabbbaaaabaaaaababbabbabbabbabbabbabbbbbaaaaaabaabbababbbaaaaaaabbaabaababbbbbbabaaaaaaabaabababbbbbabbbabbaaabaabbbbbabbbbaabbabaabaaaaaaaaababbaaabbbbbbaabaabaabaaaababbabbbbaaaaaabaabaaaaabaabbaabbbaabbabbbabbaababbbbbbbbaaabbababaababbabbaaaabbbabbbbaaabaabaaabbababbbaabbabbaababbbaabbbabbabbaabababbbabbbabbbabaaabbabaabbaaabaabaabbbabbbbbabaabbbbbbabbaababbaabababaaaaaaabbaabbabbbabaabbabaaabbbbbaaaaaaaabaabaaaaabbaabbbbbbabbbbabaaabaaabbabbbbaabaabbbabbbbabbaabbbabbbabbbbaabaabbbabbbabbbabaababbbababaaaababbaabbababbaabbbaaaaabbbaabaaaaabababababaabababbbabbbbbaabbabaabababbaaabaabbabaabaabababbbaabbbbbaaaaaabaaaabbababbbbbbababbbbbaabaabbbaaaaaaaabbbababbbbbabbaabaaabaaaaabbbbabbaaaaaabaaabbbbaabaaababbbbaabbabbabbabbaabababbbabbaabbaabbbbaaababbbabbbaababaaabababaabaaaabaaabbaababbbaaababbababbbabbaaabbaaaabbababbbbbababbaababbaaabbabaaaaaabaaabbaaababbbabaaabaabaaaabbabbabbaabaabbababbbaabbbabaababaaaaabababbabaaabbababaabaabbbaaaababbbaabbbbababaabbbababaabbbaaaabaababbaabbabbbbaaaabbbaabaabaabbabaaaabaaabaabaababaaaaabbbababaababbbbbaabbabaaaaabbbababaababbababbbaaabbbbbbaabbabaabbbaaaaabbbaabbbaaabbaaabbbbbbabababaababbabaabbabaaababbabbabbaaabbbaaaabbabbaaaaaaababbbabaaaabbbabbabababaabaabbbabaaababbaaabbaaabbbaabaaaaabaaabaabbaabaaabbaabbbaabaababbaaaabaabbaaabaaabbbbbaaaaabbbababaaaaaabbbbbbbbaababaaabbbbaabaababbaaabaabbaabababbbbbbbbabbabbaaaaabbaabbaabaababaaaaababbbaaaaabbabbaaabaababbaaaababbabbbbaababbaaaaaaabbabbbabbbaaaaabababbbbbabaaabbbbbabaaaabbbbabaaabbaabaabbbaaaababbabababaaabbababbbbbbbbababbbaaaaaaabbababbbbabaaaabbababbbaaabaaaabaabbabbbaaabbbabbbbabaababbabbbabbbbbbbaaabbbbbaabaaabababbaabbbabbbbababaaaaabbaaaababbbabbbbbbbbbabbbaaaabbbbababbababbabbabbabbaaabbaaabaabbbbbbbabababbaabbabbbabbaabbbaababbaaaaaabbbbbbaabaabbaabaababaabbbbaabbabaaababbbbbbbabbaaaaaaaaaabbbbbbbababbbbbbabbaaabbabaabaaaabbaabbbababbbbbbbbabbbababbababaabbbbaaababbaaaaabababbbbbbbbbbbbbbaabaabaabaababbbabaaabbbaabbbbaaabbbbabaaaaabbababbabbaababbabbabaaabbbbbbbaaabbabababaabbababbaababbaabbaaaaabababbababbaabbbbbabbbbaabbababbbaababbbbbaabaaabaaabbbbabbabbbbbaaaaaabaabbabbaabbbaababaababaaabbaaabaaabbaaabaabbbbbabbbababaaabbbabbababbaaabababbaaabaaabbbbaabbaaabbabbabaabbabaaabbabbaaabbbabbaabaabbbbaabbaaaabaaaaabbabaabaabbaaabbabababababbbaaabbbbaabbaabaaabaabbaaaaaabababbbbbbababaabbbbaabababaaababaababbaaaaabaababbbbbabaaaaaaababaaabaaababaabaaabbabbabbbbabbaabbabbbabaabbbabbababbbabaabbababbaabaabbaaabaabbbbaabababbbbaabbbababbbbabaaaababbbbaabaaaabbbaaabaababbabbbabaaababaaaababaabaabababaabbbabbbabaababbbaabaaaaaaaabbaaabbbbabbbaabbababaaabbaababaabbbabababaaaaaabbbaaaabaabbaaaabbbbaaaababbbbaaaabbababaabababbbbbaaabaababbbbabababaaaaaabbabbbababaabbbababbbababaababbbbbaabaababbbbbabbbbabaababbaaabbaababaabaaaabbbabbbaaaabaabaaabbabbaaababbabaaabaabbabbaaabaaaabbbbbabababababaaabaabbbbaabbbabbaabbaaababbaabbbaaaababaabbbaababbbaabbaabaabbbabbababaaabababbbbaaabaababaaaabbbabbbaaaaaaaabababbbbababaabbbbbbbbabbbbbbabbaaaabbabaaabbaaabbaabbabaaababbaabbbabbbbbbabbbabbaaabaababaaoaaaaaaababaaaaabbbabaaaabbbabaaabababbaabbbaaababaabbbaaaabaaaabbbbbbbaaababaaaaaaabaaabbbbbbbbabababbbabbbabbbabbbaaaaaabbabbbbbbaaaaabaaababbbbaaabbaabbbabbaaaaaababbaabaaaaaabbbbaaabbbaabbababbaaababbabbbbbaaaabbababaabbaaabbabbbaaababababbbaaabbbbbbbabbaaabbbababbabbaabbbbbaabbbbababbababbabbbbbbbbaaaaababbbabbbbbabbabaaaabbbabbbbabbaabaaabaaabbabbaaabaababaaaababababbabaabaaaaaaaabaaaaaaaabbbabaabababaaabaabbabaababbbbabbbaaaabaaabaababbabbaabbaaabbabbaaabaabbababbabaabbabababaabaabbbbbbabbbbabaabaaaaabbbababbaabaabbaaaaaaaaabaabbbbbabbabbabaaabaaaabbaaaaabbbabbbbaabbbbabbabababbaabbaabaabbbbbbbbaabaabbabbaaaaaaabbbbbaaaababbabbbaaaaaaababbabbbbbbbaabbabbaababaabbaabbaaabbaaababbaabbbaaabbbbabbabaaaabaaabaabaabababbabbbbbaaabaaabbabbabaabababbaabbabbbbaabaababbabbbaabbbbbbaaaaabababbbabaabbbbbbaabbaaabababaaabaaabaabaabbbababbbaaababaabaaaaababaaabaabbaaaabbaaababaaaabbaaaabbaaaabaaaabaaabaababbbbaabababbbababbaaaabaaaaaabaabaaabbaaabbbbababbbabbbabbabbbbbaaaabbbabbabababbaaabababbbaabbbbaabaababaabbabaaabaaaabbbbabbbbbbaabbbaaabaabbabaabbabbaabbbbaabbbabbbbbabbaaabaabbaaaabbbbbaaababbbaaabbbababbaaabbabbbaaaabababbaaababbabaaabaaaabaaabaaabbbaaaaaaaaabbbaaababbbbababaaaabbabaaabaabbbaaabbbaabaaabbbaabbbbaaababaabaaabbabaaabbbababbbababbbbabbbbbbbaabababaaaabbbaaababbbbabaaabababbaaaababaaaabaabbaaabbaaaaababbabaabbabbbbbbbaaaaabbbaabbabbbbbbabaaaaaaaababbbbbbabbabaaabaabababaabbbaaababaabbbbbbbbabaaabababbbabbaaabbbbabababbbabababbaaaaaabaabbaaabbbabbbbbabbbaaabbababbaaababbbbaaabaaababbbbabaabaaaaabbbbbaababbabbbaaabbaabbabbbabaaabababababbbabababbbaababbaaaabababbabbabbabbbbabaaabaaaabaabbbabbabbbaaaaabaababababbabbabbbbabbaababbaababbaababbbabbaaabaabbbbbaaabaabaabababbababaabaababbaababaabbbaabaabaabbbabbaababababbabbbbaabababbaabbaaaaabbabbbbaababbbbabbbabbbabbaaababbbababbababbbbaaaabaababbaababbbabababbabaabbaababaaabababbaabbbbbbbaaaababbaaabaaaabbbaaabaaabbaabbbbbbbbbaabbbbabaaaaaabaabbbabaaaabbbbbabbababababbbbaaaabbabbbbababbbabbbbbbaaaabbaaaaabababaaabaaaaababbbaaabaabbbabbbbabbbbaaaaabaabbbabbaaabbaaabbaaaaabbaabbabbaabbbabbbababaaaaabbabaaabbbbaaababbaabbaababaaaaaabbabbbbabbbbbabbabbabababababbabbbbabbaaaabbaabbaaababaaabbbaaabaaabbbaababbaabaabbbaaaaaaabbabbabbabaaabbabaabbabaababaaaabaabaaaaaaabaababaaaaaaabbbbbabbbabababaababbbaaabbbbbbabaaaababbbbbbbaaaabababababbaabbbabbababbbbabbaababbaabababbbbabbbaaababaaabbbbaabbaabbaaabbabbababbbababbababbbaababaaababbababaaabbbbbabababaaaabaaaaabbbbbabbaabababaaaabaaaabbabbaabbababababbbababbbbaabaaabbabbaaabbbbbbbbabbbbbbbbaaabbababaabaababaaabbbabbaaaaaabaaabbbbaabbbbaaaabbabbbbabbbaaaaabaabaabbbbabbaabbabbbbabbbaaababaaabaababababbbbabbbababbaabbbbabaaabbaabbababbaabbbbbabbbbaabbbaabbaabbbababbaaabbaaabaabbbabbbbabbaaababbbbbbabaaabababaababbbaabaaaaaabbbbbbaabbbaabaaaaaaabaabababbbaaaabbaabbaaaabaaaaaabbabbbabaaaaaababbabbbbbabbaabaabaaabbabaaaabbbbaabababbbbababbaaaabababaaabbaabbaabababbaabaaaabbaabaabbbabbbbaaaababbbbaabaaabbaaaabbbaaaababbbaababbaabaaaaaabbabbbbabababaabaabaaababbbbbabbaaabbaabbaaaabbaaabbbabbababbaababbbbbbabbbbbabaaabbbaababbaaaabaaababababaaababbbbabbbabaababaaabbababbbababbabbbbabababbbaaaaabaaaaababaaabbbababaabbabaabbbabaaabaabaaaabaaaababaabaabbabbbbabaaabbbbbbbaabababbaabbbabbaaababbbaaabbbabaaaabababbaaaabbabababbaaaabbbbbbbaaaabaaaaaabbabaabbbbaabbbabbababbaabbabbbbababbababbababababbabaabaaabaababaabaabbabaabbabbbabbaaaaababbaabaababbbbbbbaabbaabbbaaabaaaabaabaabbbbaaaabbabaaaaaaaaaabbaaabbaaabaababbabbbaabaabbaabbbaababaaaaaababbaaabaaabbbbababbbbbbabbaaaaababbbababaaabaabbbaabaabaabaaabbabbbababaabaaababbaaabaabaabbaaababbaabbbaabbabaaababbaabababaababaaaaabaabbaaaaababaaabaaabaaabaaabbbababaaabaaabaabaababbbabbabaabbaaaaaaaabbbabbbbaabaabbbbaabbbabaabaaaabbbbababbbaabbaaabbaaaaaaabbbababaaababaaabbbababaaaaababbabaaaabbbabbbaaabbaabaabbbbbabaabbbaabbababbbbabbaabbaabbabbbbaaabaaaababbbababbbabaabbbbbabbbbbabbababbbabbaaaabbbbaaabbabaaaaaabbbbbbbaabbbbabaababaaabbababbabbbbaaabbabaabbabbaaabbaababaaabababbbbbbbabbaaaabbabbaababbbaaaaababaaabaababbababbbbabbbababbababbaaaaaabbbbaaaababbaaaaabbaabbaabaabbabaabbbaabaabaabbbaaaabbabbbbaaaabbbbbbaaaaaaabaaaabaaaabbbbbaabbbbaaabababbababbabababaabbabbaaaabaabbaaabaaabaabbabbaaababbbabbabbbbaaaabaaabaabbabbaaabaaabbbbabbaaaaabaaaaabbaaaaaabaabaabbabaaabbbbabbbbabbaaaabaabbbaaaaaaababaabaababbaabaabbaaabbbaabababbbbbaabbaaaaaaabaaaabbabbabbbbaaaaaaabaabbaababbbaabbbbbbbaaabbabbaaaababbaaaabaaabaaababbaaaabaaabbaaaabbaaabbababbaaaaabbbabbaaaabbbbbbbbbbbaaaaabbabaabaabbbbbbbbaabababbaabbbabbbbbaabbbbbaabaaabbabaaaaaaabbbabaaaaabbaaabaaaabaaaababbbbbabaaabbaababbaabbaaaabbabbaaabaabbabbbbbaaaaababbabbbbaaaababaabbaabbaabbbbabbaaabaaababbaabbabbaababbbaabbbbbbbbbaaaabaabbaabaaaaababababbbaaababbaabbbabbbaaababaabababbaaaaabababbbbaaababbbabaabababbbbbababbaaaabbaababaabaabbbbbbabbbbbbaaabbaaaabbbabbbbbababbaaaababbababaabbaababbbabbaaaabbbbbababbbbaabaaaabababababbbbaabaabbabbbbaaaabababbabaabababaabbaaaaaabaaaaaaaaabbabababbaabbababaaaaabbabbabbaaaaaabbabbaabbaabbaabaababbaaabaaabaaabbabaabbabbbbbbaabbbbaaaaabaaabbbababbbbbbbbbabaaaababaabaaabbabbbbbbabaabaaaaaaababaaabbaabbaaabbaaabaabbbaabbaababaabbabbbbaabaaaababbbabbabbbabbbbaabbbbaaaaaabaaaaaaababbabbbbbaabaaaabbaabaaabbbbaabaaabbabaaabbbabbabbbababbabaaabaaaaabaaabbbabbbababbbabbbbbbbaababbbaabbbbbbabbabbabbaaaaabbababaabbaaabababbaaabababbbbaaabababaabababababaabababbbaaaabbbabbbababbaabaaabaabbbbababbaaabbbbabaaabbbababaaaabaabaaaabbbaaaaaababbbaaababaaaaaabbaaaabaabababbbbbbaabbbabaaaabbbbabbbaaabbaaabaaabbbabaabbbaaabbbbbbabaabbbbbabbbbbbbaababaaaaaababbbaaabbbbbbabbaaabbababaaaabaaaababbbabbabaaabbbaaaabbabaababaaaaaaaaaaababaabbbabbbabbbbabbbabbbbbaaabbabbabbaabaaaaabbaabbabbbbbaaaabbbbaabaaaaaabaaabaabbbaababbaaaabbbbbbbabababbaabababaaabbbbbbbabbbbbaaaaaabaaaababbaaabbbaaabbabaaabbabbaabaababaaabaabaabaabbaabbabbabaabbbbbabbaaaabaabaabbaabbbabbaaabbababaabbabaaaabaaabaaaabaaaaaaabbaabbaaababbaabbbbaabaabbbbababbbbaaabbbaaaabbaaaabbaaabbbbaabbabaabbaabbaaabaabbaabababbbaaaabaaaaaaabaaaaabaaaabbbababaabbabaabbbbaababbbbaabbabbaabaabbbbabbbbaaaaabbababbbbaabaaabababaabbaabbaaaaabaaaaaaabbbbbababaaabaabbaaababaaaabbbbbabbabbaabaaababbabbaaababbabbbbbbbbabbbabababbabababaababababaaabbbbbababaaaaaabbbbbaaababbabababbbababaaabbbbbbaabaabaabbbabaabbaabaabaaaaaabbababbbabababbbbbbaabbbaaababbbaabbbaabbbabaaabbabbbaabaabbaababbaaaababbabbabbaabbbbbbaabaabaabbbbabbbbaaabbbbabbabababaaabaabaababaababbbbababbbbaabbaabbbababababbbbaaaabbababbabaababbbbbbaaaaabbababbbbbbbbbbbbbbaabbbaababbabaabbaabaabbbaaabaaaabbababbbbabbabababbbaaaabaabbababaabbbbbabbbbbbbaabbaabaabbaaaabbaabaabbaabababaababbababbbabbbabbbabaabbaaabbbaaabbbabbaaabbaababaabaababbabaaabbaababaaabaaaabaaabaaabaabbaabaaaabbbaabbaababababbaaaaaaaaaaaabbbbabaaabbaababbaaababaaabbabaabbbbabbaaaaababbaababbbaabaababaaabbababbbbabaaaaaabbabbabaababbbaaaaababaababbabababbbaababbbabaaabaaabbbbababbbbabbbbabbbbbbababbaaabbaaaaaaaabaaaaababbabaaaabababaaabbbabababbbbabbabaabbbaaabbabbabaaaabbababbabaabbbaabbaaaabbbaabbbaabbbbbbabaababaaaaaababaaaabbbbbbabbbbababbbaabaababbaabbbaababaabaabaaabbbabbabaaabbbaababaabbaaaabbaabaabbbbababaabbbbaababbababaabbabbbbbbababbbaaaabaabbabaababbbababbbaaabaabbabbaaaaaaabbababbaabbabaabababbbaabbaabbbbbaaaaaaaaaaaaabbbabbabaaaaaabababbaaaaabbaabbaabbbbbbbbaaababababaabbbababaaaabbbabbbbbbaabbbbabbaababbabbaaabaaaababaababababababbabbbbbabbbaabbababbbbabbbababbabbaaaabaaababbbbbbbaababbaaaaaabbaaabbbaaaababbbabbaaabaaabaabbaababaaaaababbabbbbabbbaaabbabbabbabbbaabaaabbaababbaaaabbbabbbaabbaaaaaabbbbbaaabbbaaabaaaaabbaaaabbbbbaababababbbababbabbabbababbbbbaaaabaaaaabababbabaabaabbbaaaabbbaaababaababbaaaabbbaaaabbabbabbababaaabbbaaaababbaaaabbaaabaaaaabbbaaaaaabbaaaababaababaabbbaabbbabbaababaabbaabbaabaaaabababaabbabbaaaabbbabbbbaabaabaabbaaabababababaaabbbbaaabbabbaababbabaabbbababaabaabababaabbaaaababaabaabaaaabbbaabbaaabbbbbababaaabbaababbaaababbaaaabaaabaaaaaababbaabbbaaaababababababbbbbbabbbbbbababbaaababababbabbaaaaaaabbbaaaaaabaaabbbbabababbbaaaabbaaaaaaabaabbbbabaaaaaabaabaabaaabbababaaaabbabbaaabaaaabbbbabababbaababbabbbabbbaabbbbbaaaaaabaabaabbabbabaabababbaabaabbbbbaaaaababaababbbabaabababbbbbabbbaaaaabaaabbbaabbaaaababbaabbbbbbbbbababbababbbbbbabbbbaaaababbaabaaaaaaababaaaabbbabbbbababaabbbbaaabbbaaaaabbbbbaaaaaabaaabaababbbaababaabbbabbabbabbbabbaabaaaabaaabbbaaabbbbaabbbaabbabbbaaaaaabaaabbbbabbbbaaababbbaaabbbbbaaabaaaaabbaaaaabbbaabaaababaabbabbabaaaabaaabbbbbbbbabababbbaabbbabbbabbbbaaababbbababbbbbabbbabbbbabbaaababbbbbabbabbbabbababaaabaaabbbbbaabaaaabbbabaababaabbaaaaaabababaaaabbabbbabaaaaaababbbbbaabbbbbbbaaaababaaaaaaabbbbabaabbbaaaabaababbaabababbbbbbaaabbbbabbbabaaabbbabaabbaaaaaaaabbabbabbaaabaabaabbbaaaaabbbbbbabbabaabaaaaabaaaaabaabbababaaabaaaaabaaaaaaababbaabbaababbbaabbababbababaababbaaaabbabababaabaabbbbbbaaabaababbbaabaabaaaababbbaabbbabbababbbbaabaababbaababbabbabbbaabbbbbabbaaabbbabbaaaaaaaababaabaaaaababbbabbabababbaaaabaaabbbaabbaaaaababaabaabaababbbbbaaaabbaabababbbabaaaabaabababbbbaaaabbbababaaabbaabbaabaababababababaabaabbbaabbabbbabaaaaabbbaaabaabababaababbababbababaabbbaaabbaabbbaaabaabaaabaaabbbbaaaaabaaabaaabaaaaabbbbbaaabaabbaaabaaaababbaababaaabbaaababbbbbaaaabbababaaaabbbbabbbabbbbbabbaaabaababbaaaaababbabaaaaaaabbbbaabababaaabbaaabbababaaaaabbbbabbabbbaaabbabbababbbbbabaabbaaabbbbaaaabaababbbbbaabaaabaaabbaaabaaaaabbababaaabbbbbabaaabbbbbbbbaaaaabbaabbbbbbbaabaaaaaaababaaaaababbbbbbbbaaabbbabbaabbaaabaaaaaaabbabaaabbbbaaaaabbbbabbabbbbbabbababbaabababbbbaabaaaababbabbbbaabaaabbaababbaabaaabbaababaaaaaaabbaaababbaabaabbabababbbaabaaaabbaaabababbbbaabbbaaaaaaaabbaabaabbaaabababbaabbaaaabaababbbaabaabbbaabbbbbbbaabbbbabaaababababbbbaaabbabaabaaaabaabbababaabababbbaaaabbbaaababbaababbaabbaaabbbaaaaaaabaababbaaabbabaabaaaabbabaaabbabaaabbbbbbbabbabaabbbbabababbabaaaaaabaaaababaabbbabaabbabbababbbabaabbaabbabbbabaaaaaababbbbbbaaaababaaabbabbbababaaaabaaababbbbbbbbbbbbbbbabaaabbabbbbbabaabbbbaabaabbbbbbbabbaabbbbababbbbabaababbabbbbabbaabaababaaabbaabbabaabbabbabaaaaababaaaaaabbabbbaabbaaababbbbbbbbabbbabbaabbaaaaabbabbbbbbaabbaaabbaaababbbbbabbbabbabbbababbaaaaaabbaaabbaabaaabbbabaababababababbbaabbababbaabbbabbababbaabbbbabbaaaabbbabbbaaaaaabaaaaabaabaabbaaaaaaaabaaaabbbabbbabbaabbbbabaabaaabbaababaaaaaabbaabaaaaaababbbbaaababbaabababbaabbbbaaaababaabbbaabbbabaabbaababbabaabbbbaaabbabbbbbbaababaaaabbbaababbaabbabbabbabbababaaaaaaaaabbbbbaaaababbaaaaabababaaaabbabaabaaaababbaabbbabbababababaabbababababbbbbaababbbbabaaaaabbbabaaaaababaaaaabaababbabaaabbbbaaaabaaaaabaabbbbbaababaabbbbaaabbbabbabaabbaabbbbbbabbaabbbbbbababbbaaababbaabbaabaabbbbabaaaabbaabbbabaaaabbbbbbbaabbbababbaaabbbaabbbabbbababbabaaabbbbabbbbbabaaabbabbaaaabbabbbbbbababaabbbbaaabbbaabbabababaabbbabaaabbaababbaabaaabbabbbabbabbbabbaaabbbabbbbaababaaaaabbabbababaaababbaabbbbbabaabbbbaaabaaababaabaaabbbbaabbabbaababaaaaabbaaababbbbabbabaababbabaaabaabbbbabbabaaaabbbbbbbaabbaaaaababbbbaaaaaabbabaaababbbababaaaaaaaaababbaaaabababbababbbbbababbabaaaaaaaaaaaabbbaaaaabababbbbbbabaabbbaaaaabbbababbabbaababbaaaaaaabababbabbaabbbabbbbbbabaabbaabbaaaaabaababaaaaaaabbaaaabbaaabbabaaaaaabaababbbbbaababbaaababbababbbbabbbabbbbbbabaaabbbaabbbababbbabbbababaabbbbbabbbababbbbbabbabbbabaababaaaaaababbbabbabbaabbababbbabababbabaaaaabbbbbabbbaaababbbbbabbbbbaaaaabbabaaaaaabbbbbbbbababaaaaababbaaabbbbbbababaaabbaabbaaabaababaabbbabaaabbaaaaabaaaabbaabbababaaaaabbbbbaaaaaaabbbbabbbaabababaaabaaabaabbaaaaaabbaababaaaaaabaabbbabbabbababbabbbabbbbbabaaabaaabaabaaaaabaabbabbbaaabbbbaabbaabbbabbabbbabbbbaaabaabbabbbbabaabaaaabbabbbbaaaabbaabbababbaaabbbbbabbbbabbbabababaaabbaaabaaabbababbbbaabaabaaabbaaaaabaabbabbbabbbbbabbbaababaaabaababbaabaaabaaabbbbaabbaaaabaabaaaaabbaababaaabaaaabbabbbbbaabbaababaaaaaabbbabbbabbbabbbaaabbaaababababbbbabaabbbbbababbbbaabbaaaababababbbabbbaaaabbaabbbbabbbbbaaabbaaababaabaaaaaabbbababbbabbababbabaabbbbabaaabbaaabababbabbaababababaaabababbbaabaabbaaabaaaaaababbaaaabbaabababbaaababaababbbababaabbaababaabbabbaabbbbaaaabbbbbbabaaababbabbbbabbbbaaabbbabbbbabbbaabbabaaaaabbbababbaabaaaaabbabbaaaaaaababaabaaaaaababbbbbbbabbbabaabaabaabbaababbbabbabbababbbbabaabaaaabbababbbbabaababbbabbbabbabaaaaabaaababbbababbbbbbabbaaabbbbbbbaabababbaaaaabbbbbaaabaabbabaaabbaabaaaaabaababaabbbbaababaaaaababaabbbaababababbabbaaabbbaaababaaaaaaaaaabbbabbbaabaababaabbaabbabaaaaaaababaaaaaabbaaabababbbbbbbabaababbbaabbabaababbabbbaaabbbaaaaabbbabaaaabaabbbaaabaaaabababbbaababbaaaaaaaabaaabaababbaababbabbbabbabbaababbabaabbaabbbaaabaaaaabababaabaaabaaaabaaaabaaabbbaaaaabaaabababbbaaaaabaaaaaabbbabbbaaabbaababaaabbabbbaaaabbaabbbabbbbababaaabbbbabbbbbaabaabbaaabbbbaaababaaaabbbababbabbabaaaabbabbbbaaabbaaababbaaaabaabbbabbabbbbbbbaaaaaaabbabbbabbbbabbabbbaabbbbbababaabaabbbbababbabababbabbbbabaababbbaaaaababababbaabbaaabbbbabbaabbbabbbabbaaaabbbaaaababbbbabbbbaaaabbaaaababaababababaaaaabbbbbabbabbaabaabbbbbbaaaabbbabbabbbbabbbbbbabbaababaabbbbbaabbabaabbabbbabbbaaabbbaabaaabbbabaababababbbbabaababbababaaaaabaababbbbbabbabbbbbbaabbabbbbbabbbbabaaaaaabbbbabbbbbbababbaaabaabbabbbbbaaabaaaaaaaaabbbabbaaaabbbabaaaaabaabbabaaaabaabbbbabbaaaaaabbaabbbbaaaabbababbabbbbbaaaabaabbbbaabababaabbaababbbabbbbbbbaaaabbabbbbbbbbabaabbabbabbababbbaabbaabababaabbbbabaaaabbaaaaabbaabbbabbaaaaaabbaaaabaabaaaaaababaaabbbabaaabbbaaaaaaabbaaabaaabababaaaaaabbbbaaaaabababbababbabababbbabaabbbababbaabaaabaaaaababaaaaabbbabaabbaaabbabbabbaabaababbababbaaabaaabbbabababbbaaabaababbbbbbaaaabbaaaabbbbbbbaababbbbababaababbbbabaababbbbabbbbababbaabbabbaaaaabaabaaabaabbaaabaaaabbbaabaabbbaababaaaaabbbbabbbbabaabbaabaabbbaaaabbbbaabbbbaaabbaaaaabbbaabbbbabaaaababaabbabbbbbbbaaaaabbabaaaaabbbabababaabbabbabbaaaaabbbabaaaaaabbbbbbaababaaabbaaababababaabaabbbaaabbababbaaabbabbbabaabbabaaaaaaaaabaaababbbbaabbababaababbbaaaaababaaabaababaaaababbabbaababbabaabbababbabbabbbabababababaabbabbababaabaabbbaaaabaaabbbabbabbaabbbbbabbbbaaaababaababbbabbbaaaabbaabababaabbbbabababababbbbbbbbaaabbabbaabaaabaaabbaabbbbbaaaaabbababbbbbaaaaaabbbbbababbbabaabbbbaabaababaabaaaabbbabbabbbbaabaaaabaababaabaaabaabaabbbabbaababbaabaaaabbbbbababbaabaabbaabbaabbaabaabaabaabaaaababbaabbbababaaababaabbabaaababbaaabaabbbaabaabbabbbabababaabbaabbbaabbbbbaabaabbbabbabbbbbabaaababbaabbaabbabaababbbbabbbaaaabaabaaaabaaababbbbaabbbaababaaaabbbbbaaabababaababababbaabaaababbaabbababbbbabbbabbbaababaaabababbaaabaabaaabbabbaabbbaaabaabbbabbbabbbbabaaabaabababaaabaabbaababbbbbbbabbabbaaaaabababaabaabaabbababbbbbbaaabbbbbababbbaaaaabbabaabaaaabababbbabbabaaababaaabbaaabbbbbaabbabbabababbbbbaabbbbbbaabbbbaabbbabbabbbababbaabbbaaabbbbbabbababaababbbababbaabaabbbbbbabbabbabbbbabaabbabaabbbbababbaabababbbbaaaabaaaabbbbbbbabaabbaaabaaaababbaabbabbbabbababbbbbabbaaaabbbababbaabaaabbbaababbbbaabbbabbababbbababbbabbabbabababbabbaababaabbaaaabababbbabbaabaabbbbaaaabaaabbbabababaaabaaaaabbbabbbbaabaaabbbbbabbbaaaaaabbbbabaaaaaabaabbbbaabaabbbbbaaaababbbbabbbaaaabbaabbababbbbbbbbbbbbabaaaaabaabaabaabbabababaabaabbbbbbabbaabbbbaabbabbaabbababbbbaaaaabbbbbaabbbabaabaababbbbbbabbaaaaabaababaababbaaabbbabbabaaaaabbaaabaabaabbbababbabaaaababbaaaabbbabbaaaabbbabaaabbababbaaaaabaabababbaaaababbaabababaabaabaaabaababbabaaaabbbbbabbbababbbbbabbbabbbbbaaabbabaaaaaaababababbbbbbaaabbbbaaaaaaaaabbbbbbbaaabbaaabaabaabbbaaababbbbbbababbbabaabbaaaaababbaabbabbbabbaababbaaababbabbaaaabbaababaaababaaaaaaabbababbbbababbbbbbbbaaabbabbbbbbbbbaababbaaaabbbbaaaabbbaaaababbababbabaaaababbabbbaaababbbbbbabaaaaaabaaaaababaaabaaaaababaaaabbaaabbababbaabaaaaababaabbaabbababbbbaabaabababaaabbbabaaaabaabaabaababaaabbaabbaaabbaaaaabababaabbbbbabbbabbbaabaaaabbaabaabbbbbbbaaabbbbbaaaabbaabaaaaaaaabbbbaabaabbabbbabaaabbaaaabbababbaaaabababbabbabaabbbbabbaaabbabbbbabaaabaababbbabbbbbbabbbabababbaaabaabababbaaabbbaabbbbababaabababbbbababbaabbaaabbbaaabaabbabbabababababaaaaababaaaaaaaaabaabbbbbbbbbbabbabababaaaaabaababaaaabbbaabbaabbabbbaabaabbbbbabaabaabbbbabbbaabbabbbbbbaabbabbaababbbbaabaaaabbaabbaabbaabbbbbaababbaabbabbaaaaaaaabbbbaaabaaababbbaaabaaabaaabaabbababaaabaaaabtaaabaaababbababaaabaabbabbabbabbaabbabbbabbaabbabaabbbaabbbaaaaaaabbbbbbbaaabbabbabbaabaaaaaaabbabbaaababbbaaaaabaababbbabaabbbbaabbbabbbaabbabbbbaabbbbbaaaaababbbbaaabababababbabbaaaabbababbbabaabbaaabbbbbaaaabbaaabbbaabbaaababbaaaaabbabbbbbbbbaaaaabbaaaaaaaaababbbbaaabbbabbabaaaababbaaaabbaaaabbbbbbbabbabaabbbabbbabaababbaaaaaaaabbabaabaaabbabbbbbbaabbbbaabaababbabbabababbabbbbbabbbababbaaabababbbbbbbaabbaabbaaabaaabbbaaaabaabaabbaaabbaabbaaabaaaaabbabaababbabaababaaaaaaaababaaabbbbbaabaabbabbaabaabaaaababbababababbbbabbababaabbabbbbbabbaabbbaaaaabaababaabbabbaabbabaabbbbaababbbaaaaaabababbababbbbbbbabaababaabbbbaabbbaabaabbababbabbbbbbaaaaaaaababbabbbaaaaabbbaaabbabbabbaabbbaabbabbababbabababaabbbbaaaabbaaabbbbabbbaaabbbbababaaabaaaaabbbbababaaaabbbabbbbaabaabaaabbabaabababaabbbbaaaaababbababaaaaabaaaaaabbbbaaaabbbabbabbaabbbababaaaabaaaaabaaabbbbabbbaaababbbbbbaabbababbbbbbbbbaababaaababaabbbaaabaaaaaaabbbabaaabbababbbbbabbaaabbaabaaababaabbabaabbababbabbababbbbabbbbbabbabbaaabababbbbbbaabbbabbbabbbbabbabbababbbbaabababbbabbaabbbbababaaaabbaabbbbbabbbabbababbaabaababbbaaabababbaabbbbbababbbabbaaaabbaaaabbbbaabbbabbbbbbaaabbaaaababbbbaabaaaaabbbabbaaaaaaaabbbabbaabbaabbaabbababaaaabbabbababababbbaaaabaaabaaaaabbbbbbbaaabaaaaabbababbbbbbbabbbabbbaababbbbabbaabbabaaabbaabababbaabbabbababbbbabbabaabaabaaabaaabababababaabbaaabbabaaaabbbabbbaaaabababaabaabbaabaaabbbbbabbaababbabaaaaabbbbbbabbbababbbbbbbabaabaabbaaaababaabbabbbbbbbabaabbbbabbabaabbbaaaaabbabaabbbbbbbaabbaabaabbbaabbaababbaabbbbbabbaabaaabaaaababababbbaaaaaaaaabaababbbbabababababbaabbaaabbaaaababbbabaaabbbbbaaaaaaabaabbbbbaababbbabbaaabbbababaaabaaababbbaabbaabbbaababaababbbbabbbaaaabaababbbabbabbbaabbabababaaaabbabbbbaabbaaabbaaababbaaaaaabaaaabbaababbbbbbbaabbbabaaaaabbbaabbbbbbbbaaaabbabbababbbbaabbaabbbabbabbabbabaaabbaaabaaaaaababaaaaaaabaaaaaabbaaaabbbbaabbbbababbbbbbaabbababbaaabbabbababababbaaababaaaaababaaabbabaaaabbaaabaaaabaabaabababbaaabbbbabaaaabaabbababbaaaabbababbaaaaaaabbbaabaaabaabbaabbabbbbbbbaabababaababaabaabbbaabbabaabbabbababbbbabbaaabaabbaabaabbbbbbaababbababbaaaabbbbbaabbbaabaabababababbbbbaaabbaaababbbbbbbbaaaaaababbabbbbbabaaabbabaabbbbbabaabaaababababbababbabbaabaabaaabbababbaabaabaabbbbbbaaaaaaababaaababaabaababbaabbaaaaabbbabbbababaaabbabbbabaababbbabbaabaaabbbaaaaaaaaaabbbbbabbaabbbbbaabbaaabbabaaaaabbbbaabababaabababbaabbbbababbaabbabbaaaaaababaababbabbbbbbaabbbababbbabbabbbabaabbaaabbbbbbbbbbaabaaaabbbababbaabbbaaaaabababaabaaabbbaaabbaabaaabbabababbaaababababaabbababaaababbbaaaaabaaaaaabbbbabaaaababaaabbbaabaaababbaabbbbbaabbbbbaaabbabaaaabaabbbabbaaaaabbabbababbaabbbaabbbaabababbbbabbabaaaabbbaaababababbbbbbabaabbaabbaaaabaababaaabaababbabbbbabbbaaaabaaabbabababbaababbbbabbabaaabaabbbbababbbbbaabaaabbabbbbbbbbaabaabaaaabbbbbbabbbabaabaababaabbbaaabbbbbabbbabaaaaaabbaaabbbaaaaaaaababbaaababbbaaaaaaaaaabaabaabbabbabbbbabbbbaaaabbbbabaabbaabababbaaaababbbaaabbbbbaaaaaababbaaabbbbbbbaabbbaaabaaaabbabaabbaaaaabababbabbaabbabbababbababbaabaaabababbabaaaabaaaaabbbbaaabaaaabbabbbbbbabaaaabbbaabaababbbababbbbaababbbbaabbaabababbaabaabbbbbaababaaababbaaaaaabbaaabbaaaabbbbbababbaaabbbabbabbababaababbbbbaaaabbababbabaaaaaaababbaaaaaababbaaabbabbaabbaaabbabbbbababaabaaabaabbbbbbbbbaaabababaabbabbabbbbabaaababbaabaabbbbaababaababbaabbaababbbbaabaaabababbbbbaabbaaabbbabbbbaabaabbabababbbabbabababaabbbbaaaaabbabababaabbbbaaabaaaabbaabaaaabbbbaaabbbaabaaabbbbabbaabbbababbbbbabbababaaaabbabbabaabaababbabbaaabaababbaabbabbaaaabbbababaaaabaabbbbababababaabbaabbaabbaabbaabaabbbbabaabbbabbbaababbbbaaaaaabaabbbababbbaababbbbbaababbbaaaaabbbbbbaaabbbbbaababababababbababaababaabbaaabbbaabbbbabaaabaababababababaabbbabaaaaabababbbbaabaabbaabaaabbbbbbabaabaaaaabababbbbabaabababaaaabababbbabaabbbbbbbbabbbbabbaaaababbabaaaaababaababaaabbaabbabaaaaaabababaabaaaabaababaabaabbbbbbbbababbabaaabaaababaababaabbabbbaabaaaabbbabaaaabbbbbabaaabbbbaaaababbbabbbbabbaaabaaababbaabbababaabaaababaaaabbababaaabababbaaababbbabbababaaabaababaababbababaaaaaaaabbbabababbbaabbbaaaabaaababbaabbbaabbaaababaabababbbabbbaaabababbabaaaaaabbbabbaaabbbbaabbbbbabaababbabbbabaaabbbabaabbbbbaabaabbbaabaaaaababaaabaaaaaaabababbbaaabaaaabaaaabbabaaaabbbaababbaabbaaaabbbbaaabaaaabbbbbaaabaaaabbabbbbbaabbbaabbbaaababbbaabbbabbabbbabaaaabababaabaaabbbaabababbbbabbbbaabbbbabbbabaabbbaabbbbabbbabaaabbbaaaaaababaaabbabbabbbbbabbabbbaababbbabaaababbbaabbaaaaaaaaabbbaaaaaaabbbabbaaababbbbababbbabbbababbabaabaaaaaaabbabbbbaaaabbbabbabbabbaabbbbbaabbaabbaaaabbbabaabbbbbaabbbbbaaaaabbabbbababaabbbbbbbabbabbbabbaaababbababbaabbabaabaababbaaaabababaabaababaabaabababbabaababbbaaabaabbbabaabbabbaabaababaaabbbabbabaaabaabbaaaaabbababbaaaabbaaabaabaaaaabbbbabbbababaabbbbaabbabbbaaabbaaaaaabbabaaaaabbbbbabbbbaaabbaaaabaaaaaaabbbbaabbbaabbbbabaabaaaaaabbaabbbbabbbaabaabbabaaabbaabaabbaabbabbbbaabbbaabbbbaabbabbbabbbbbababbababbbbbbbaaabaababbbbaaaababbbaaaaabbbabaaaaababababbabaaabaabbaaabbabaabbbabbbbbabbabaabbaaaaabababbbabbbbbababbaaabbaabbabbaaaabbabaaabbbabbababbabaaaababaaabbbbababbbabaabbbbaaaaaaaaabbbaabbbaaabbbaababbaaabbabaaaabaabaaabbaabbaaaaaabbabbaabaaaabaabbaabaabbbaabbbabaaabbbbbaaaaaababbbbabaabaaabbbbbaabbbaaaabbbbbbaaaaaabbbbabaabababbaaaabbbaaaababaaaababbbaaaabbbbbaaaabbabbaabbaaaabbbbabbbaaababaababaaabbbbababaaaabbbababababbaaaaabababaabbbbaaaabbbbbbaaabaabbbbabbbbaababbaaaaaabababbaabbbbbbbbbbbaaaaabaababbaaaaababababbaaabbabbaabbbaababababbabaaaaabbbbbbabbbaaabaabababbaaaabbbbaaaabbaabbbaabbbabaabbabaaaababbaaabababbbaababababbbbaabbbabaabbbababbbaaaabbbaaabaaaababbbbbbabbbaabbbababbaabbbbbbbbabbaaaabaaaabbbababbbaaaaaaaaaabbaaaabbbbabaaababbbaaaababbabbabaabaaaabbaaabbbbbbabbababbbaabbabbabbbbabaaaabaaababbabbabbbabaaabbaaaaaaaaaabaabbbbbbaababaaaaaaababaaabbbbbabaabbabaabaabbaabbabbbbaaabbbbbabbbaabbbbbaaabbaaabbaabababbbabaabbabbabbaababbbbbaaaaababbbbbbaaaaaabbbaaabbabababaaabbbabaaaabbaaabbbababaaaababbaababbbbbbaaabbbbbbbaabbbbabaaaaaabaaabaabbbaababababaaaaaaaababbaabbababbbbbaaaabbaaaaabbbabbabbbbbbbbabbaababaaaabaaababaababaababbbbbabbaabbabbbbbabaabaaabbbabbbabaaabbbbbbbaabaaabbaaabababaababbbbbaabaaabbbbababbbbaabbaabbaabbbaababaaababbabaaaaabbabbbbaabababbaababaabababababbbbabaabbbabbbaaaabbabbaaaabbbbabbbbabbabaabbaaababbaaaabbbbbbbbabaaaabbabbaabaabbaaabbbabbaaabbaabaaaabbabbbbaababbabbaabaaaabababbabbbaaaabbabbbbbbaabbaabababababaaaaabbabaaababbbbbaabbbbbbaaaaabbbaaaabbbbbaaabaaababbabaababababaabaabaaaababbbaaababaabaabaaabbbabaabbbbbbabbbaababbbabbabbbbbbbababababbabaababaabaaabbbabaabaaabbbbbaabbabbbbababbbbaaabaaaabbaaaabbbaaaabbaaaaaaabbbaaaabababbaabbaabbabbaaabaababbababbaabbaaabbbbbabbbbbbbbababbbbaabaaababbabbaabbbbbbbaaababbbbbbbbbbbbbbaaaabaabbbbaabbbbbbbaaaaaaabbaabaaabababaaabbbbabbbabaaabbababbabaaabababbbbbabbbaaabababababbbababbaabbabbaaaaabbaabbbbbbaaabbbbaaabaaaabbababbbbabbbabbabababbabbaababaabaabaabbabbbabbaabbaaaababaaabaababbbbbaabbaabaaaaaaaabbbababbababaabaabababababbabaabbbaabababbbababaabbbbbbaaabaababababaabaabaabbaaaaabbbbbaaabaababbbbbbaaaaaabbaabbaaaabaaaaaabbbbbbaaaabbbbbbbaaabaaaaabbabbabbaabaaaaababbaabbababbabbbaaaaabaaababaabbaaabbbaabbaaabbabbbaaaababbbaabbbabbaaabbbaabbbbbbaaabaabbbbbaababbabbbbabbbbabaaabbabbbabbaaaaababbabaabbaaabaabbaaabaabbaaabbaaabbbbabaaabbbaaabaabbbababbbbbbbaaabaaabaababbbaaaaaababbaabbaababaaabaabbbaaababaabaaaaabbaabbababbabbbbababbbaabaaabbaabbbbbabaabbbabbbabbababaaaaababaababbaabbaabbaaabaaabbbbbabaaaaababbaabbaaabbbababaaaaaaabaabbababbbabbbaaaabbabbbbbababaababbbaaababbaaaabbbbabbabababbababbaabaaabaababababbbbbbbbaaaabaabbbbabaabaaabbbbbaabaabaabbbaabbabaabbbbaaabbbabaaabbabbbabbaabbbbababbaabbaabbabababaaaabaabaabbbbabbbabbbbabbbbbbaabbaabbaaabbaabbaabbaabbbbabbabbbbbbabaababbaaaabbbbaaaabbaabaabbabababaabbaabaabbbababbbaababbbaaabaaaabbbbabaababababaaaaababbabbababababbbaababaabaabaababababbababbbabbbbababbbbabaaaabaaabbbbabbbbabaaabaaaababbbbaaabbbabbaababbaaabaaaabbbbbbaaabaabbaaaaaaabaabaaabbabbaabbabbaabbabbaabaabbabaaabaababaabbabbbbabaaaaabbbbbbbbbbbabbbbbaaabbbaababaabbabbbbbbbbaabbbaaabbbbaaaaababbbaaabbabaabbaaaabbbbbabbabaababaabbabbbaaabaaaaababaabbbaababbaaaaaababbbbbaaababbbbaababaabbaababaabaabbaaaababaabbbbbbaababbabbbaabaaabaaaaabaaabaaaabbbaabaabaabbbbaabaabaaabbaaaababbabaaabbbbaaaabbabbbbababaaaabaaababbbbbaabbbaaabbaabbbbaabbbababbbaabbaababaababbbbbabbbaabbaaabaababaaaabaaabaabbababbabbabaaaaaaaabaaaabaabbbbbababbbbbbabbbabaaabbaabbbabbbababbbaaaabaabbbabbaabaaaabababaabaaaababbaaababaaababbbbabbababbbbbaaabababbabbabbabaabaaaababbbbbbabbaaaaababbbababbaababababaaabbaaaabbaabbaaabbaabaabbbabbababbbbaabaaababbbbbaabbabbbbaaabaaaaababaabababbbabbaabbababbabababababaaaaaaaabbbababbabbabbaababaaabbbbabbabaabababbbabbaaabbaabababaaabaabbbaaaabaabaaaabaabaaabbbbaabbbbbbabaababbbbbbabbabaabbbababbaabbbaaabbababbabababbaaaababbbaabbaaaaababbabbababbbaaaabaaabbbbbaabababbbbbbbbaaabaabaababbaaababbbbbbababbbbbbabaaababbaaaaaabbabaabbbbabaabbbaaabbbaabbaababbababbbaabaabbabaabababaaabbabbbaaabbabbbaaaabbaaaabbaaababaaabbbbbbabaabaaabbaaabbabaaababbabbbabababbbaabaaabbbabbbbbbaabbbbaaabababbbaabbababaaaaabbabbbaabbbbabbaaabbaabbbbabbbabbabbabbaaaaababbbbbababbbabaaabaaabbbabbbbaabaaaaaaababaaaabaaababbaabbaabbbbabbbbbaaabababaabbaaaabbabaabaabbbabbabaaaaabaaabbabaabbbbbbaabbaaaabaababaaaaaababaabababbbaaabbaaaaaaaabbbabbbbbbabbbabbaaaaaabaaabaabbbabbbbabaababbbabababaaababababaabbbaabbbabababaaabbabbbbabaabbbaabbabbabaaaaabbbababaaabaaabaaaaaaababbbbaaaaabbaabbabbbbbbbbaaabababaabbbbbabbaaaababbabaabbabbaaaabbaabbbbbaabbbbaaabbababababaaaabbbababbbaaabbabaabbbabaaabaababbaababbaaababaabababbbaabbbbaaabbabbbabbbbbbabaaaaabaaababbbbababbbbaabaaaabaabbaabaaabbbabaaabaababbabbbbbaaaaaaabababbabbbbbbbabbaaaaaabbbaaabbaabbbabbbaaaaaababbaabaababaaaabbbaaababbbabaaabbaabaaaaaaabaaaaaabbabbabaaaabaaabbbbaabbbaabaaabaabaabbbbaababbbaabbbaaaaaababbbaaaabbabaabaaabaabaabbabbbabbabbaaaabbaaabaaababbaaaabbaaaaaabbbbbaaaaaabbbaabaaababbbaaaaabbbaaabbbbbabbaababababbbaabbbaabbaabbbaaabbaaabbaaabbaababaaabbbbbbbbbaababbbbbabbabbbabbbbababaabbaabbabaababaabbbbabbaabbabbbbabbbbaabbababbaaabbabbbbabbbbbabbaabbbaaabaaabbababaabaaabbbabbbbaaabbaababbabaaaabbaabababaaaabbaabbbabbbaabbbaaaabaabababaababaabbbbabbbbbbaaaaabaaaabbbbaabbbbbaaaaabbbabbbbbbababbbbaaaaaabaaaabbbbbabaaaabbaabbabbabaaaaababaaaaabbbaaaabbbbabbbabbbbabaaaabbbbbbbaabbabaaaababbbabaaaaabaabbbbaabbbbbabbbbaaabaabbbababaaabbaaabaabaabbaabbabbbbbabbbbaabaabbbaabaababaaaabaaaaaaababaaaaaabbbabbababbaaaaababbbbbbabaaabbaaabbababbbbabbaaabbaabbbabaabbabbbbbaabbbbabbabbaabbabbbabaababbbabbbbabbabbababbbabbbabbbabbbbbaaaaaaaabaaaabbbbbaaaababaaaabbbbaababbaaaabbbbbbbaabbabbbbbaaaaabbbbabaabbbabbabaaaaabbabbabbbbbbaabbaaaabbaabaaabaaaaabaabbbabbbbbabaabaaaaaaaabaabbbabbbbaaaabababaabbabbbbbbabbaabaabaabbabbaaabaaababababbbbbbbbbbbbabbbaabaabaabbaaaaabbaababaaaaaaaaaabaababaabbbabaaabbbbbaaaaabbbaaabaaabbababbaabbbaaababbabaaaaaaaabbbbabbbbbbbbbbbbbababaaabbaabbbbbbabbbbbbbaaaaabbbaabaaababbababbaabbaabbabbbbbbbabaabbaababbabaabababbabaaabbbbaaabbababababaabbabbbabbbabaabababbbbbababaaabbabbbbaaabababbbbbbbabaabaabbbaaaababbbaaaababaaabaababaaabbbbaaabbbbabaabbbababbbbabbbaabbbababaabbbaabaabaaabbaaabaaaababbabbbbbbaabaabbaabbbabbaaaaabaabaabbabaabbbbaabaabbababaaaabaaaaaaabaabbbbbbbaaaabbaabbabbaaababaabbaabbbabaaabaabbababaaabbbbabaabaabaabbaaabbbbbbbaabbbbbbbaaaaaaabbaaabaaaabbaaaabbbbbabaaabbbababbabbbaabbbabbbbbaabaaaabbaabbabaaaabaaabaabaaabbbbabbbbabaaabbbaaabbaabbabaabbbbbbabaaababaabbabababaaaaabaabbabababaabbaabababbaaaaaaaaabbabbbbbabaababbaabaababbabbbaaaababababbbaaabbbaabbaaabbbaabaabbaababaaababbababbbaaabaaaaabbabaaaabbababbbabbbbbabaaaaabaabbbbaaabbabbababbabbbaabbbabaabbabaaaabbabbbbabaaaabbbababaabbaabaaababaabbbaabbbbabbaaaaaaababaaaaaaaaabaabaabaabbaabaaaaabbbabaaaaaaaaaabbaabaaaababaaababbbaabaabbabbbbbaabbabbaaaaaabbabababbabaaaabaabbbbaabaaababababaaaababbababbbbbaabbabbbbaababbaaabaaabaabbabbaaabaaabbababbaababbbbabbaabbbabbbababababaaababababbbaaabbbaaababbaababababbaabbbbaaabaabbbabbaabaabbbababbbbabaabbaabbbaabaabbaaabbabbaaaaaabaaaabbaaaaaababbabbbbaaaababbaabbaabbbaabbbabbaabbbabbababaaabaababbbaabbabbbababaabbabaaababbabbabbabbabbbaabbabbbabbaababaababaaabbbbabbaaababaaabaaaaaabaaabbabaabbbbbbbbabbaabbbbbaabaaaaababbbbbbaabbbaaaababbabaaabaabbaaaabaabbbaaaabaabbbbaaababbabaaabbbabbbaaababbbbaabaaaababaaabbaaabababbaabababbaaababaaaaaababbabaaaaabababaabbbbbbababaaabbaabbababbbbbbbaaabbbabaaaabbbbabbbbaabbaababbbbbabbabbaaaabbbbaabaaababaabbaababaaabbbabababaababbababbabaababbbaababbbababbbaabbaabaabababbbbaaabbabaaaabbbbbaababaaaaabbaababaabaabbbaaaaaaabaaabbbbaabbbbabbabbaaaaabbbbbbbabaabaaabaabababaaaabaabbabbbaaaaababbabaaaaaaaabbbaabaabbbabbaabbabaabababbbbabbbbaaaabaabbababaaaaaaaaaabbbbaabaaaaaabaaaabbaaaaabbaabaabaabbbbbbbbbbabbbabbbabbbbbbbaaaabaaaabbabbabaabbbbbaaaaaababaabbabababaaaabaaaababaabbbaabaabbabbbabbbbbabaaaaabbababbbbbbbaabababababbbababbbbabbabaaaababaaaababaabbbabbbabbaabbbabbbaaaaaababaaabbbbababaaaaabaabbbbaaaabbaababbbababaaababaabaaabbbbabaababbbabaaaaaabaabaaaaabaaabbabbbabbaaabbababbbaabaabbaabababbababbabbabaabbaabababbbabababbaaaabbaabbababbbabaabaaababbbbabaaaabbbaaabaaababbbbababbaaabababbabbaabbbaaaabbbbbbaabbbaabbaaaaaaaabbaaabbbbbbbabababbaaaaaabbaaabbbbbbbabbbbaabaabaabbaabbaaaabbbbaabaaaabbaabbababbbabaabbaaabbaabbbaabbbababaababbabbabbbbaabbbbbbbbbaaababbbabbabaabbabbbbbabbbaaaabaaababbbabbbbaabbabaaabbaaabbbbaaaababaabaaabbbabaababbbaabaaabbaaabbaaaaaabbbbaaabbbaaababbabaabaabbabaaabaabbaaababaabbbbbababababaabbbbaaababbbbbaaaaabbbabaabbbbbaaababbabbbabaaaabaaabaaabaabaabababbaabaaaaabbaabbbbbaabbaabbaaaababbaaaaaaaaaababbbbaabbbbbbbbaabbaaababbabbababaaabaabaababaaaaabaabaaababaaaabbbbbabbbbabaabbbabaabaaabaaaaaaaababbbaabaaabbbbbbbbaaaabbabaababaabaabaababbbbbbaabababbabbbaabbbbbabaaaabbbabbaaabbababbbabbaaabaaaaaababbabbbbabbbbabbbababbbabbaaabbbbbbaababbaaabaaabaababbbabbabaaaaababaaabaaabaabbbabaaaabbaaaaabbabbabaabbbbbaabbaabbabbbbabbbbabbaaaabaababbabaaaabaaabbaabbbabbbaabbaaaaabbababaaabbbbbbaaaabbabbaabbbbaaaabbbaaaabaabbbabbbabbabbaabbabaaabbaabbaababbbababababaababbbbabbbaaabaabbaaaaaababaaabaabbbaaabbabbbbaaaabaaaabaabbbbbaaaabbaaaabbbabbabbbaaaaaababbbbaaabbabaaabaabbabbbbabbabbababaabbababaabaababbaaaaabbaaaabbabaababbbbaaabaababbaabbababaaabbabaaabaabaabbabbbabbbbbabbbababbabbbbbababbaabaabababbaaababbabbbabbabbaaabbabbaaabbbaabaabbbababababaabaabaaaabaabbabaabbababaaababaababaaababbbaabaabaabbbabaaaaaaaaababaaabbbbbaabbabbabbaaaaaaabbbbbbbabaabbbbbaaabaaaabaaabaaababbbababaababbaaaababaabbaabbaababbaabbbbbaaaab