acccccccacccbbacbccbcaaacbcbcacbacababbacbbaacbcabbccacaccccbabcbcabaaccabcacccbbcaccbbaccbbcabcccbbbabcbbcccbcacabaabaccbaaabaabcbbacbaabbcacbaaaaccacaaacbabcbcbbbbcacababacbbbbabbbabaabacbabcbbbbbcabacbcccbcbacacaabbcbbcccbbabaaccbcbbabcbbbbbaacabbbbabbbcaaaabacabbabaacaaaabbbaacbccabbababcabaacbcaacababbabbcacbcaabbbbabcabbbcbcabcaccbcccbbcbabccbabcaaaabbbccacbcbbababcabbaccaababcbcbbccacccbcabccbcabcccaabcbbaaabaabbabaacaacccabbaaabcaabbbaaacbacacababcbbcbaaabaabbcaaacabbacbbaaaccacabbabacbbccbbbaaaaabbaccabcacccaacacbabcbabaabbcaaaacacaccbccaaaaaacbabcbaabcbbcccbabacaabcaaaaaabbabbbcbcaaabbbabbabacacbbbababbccbcbaaabcccbccbabbbaacbbbacbcaabcababaacbcbccbbbbaaacbbabccababbaabccccabaaabcaccaccaaacbbaccbaccbbacacbccccbaaccbcbabbbaaabaacabbccbcacbcccbcbaacacacababaaaababacbbcaaaccbabcbbbccccaacbccccabacaccbcacbaabacaaabbbbcbaccacbbbbbbabbbbcabbbacbbcacabbabacbbcbaccababbcccbbabbbccccaccccbbacacbaaabbccabcababacbbbbcbaabbacbcbabbaaacbbabcabbaabcabbccbbabbbacbbabbcbcccabcaacaacbcbbbbbacbcbcbcccaaccbaacaaacbbcccaaaaccacbbaaccbcbccabcabacacbbaccacabaaaabaaaacbcacbacaaaaaaaaabcabacacbbcaaaacbbabbccbcccacbbbaabcbbacaccabcaaaabbaacacacaabaacccbcabacabacbbccaacacaaabbaccbabbccabacbaacabbaccacaacccabaaaabacbabbacccccbccbabcbcbacaaabcabbababbabacbabbcbaccccbcbbababcbccaacaccaccaaaaacabccccbcbabbcbcaccaabccbaccbcabbccccbaccccaaacbaccabcaabbabababbbaaccabbccacbcaababaaccbaaabaccbccbabbbabccccbbcbbacbaccbbcacbcbcbbbbaccccabacacbbcaccbcaacbcccbbcaaabbabbcabcccabbbacacccccbccaaacacbccbbccacbaabbbbbcaabcaacabbccbabbbcacabbbcccbcaaabaabbbccaccbccbccbbbcabaaaabcccbbaaaaacabcbcacbbacbcabcccabacbbccabbbaabacbaabbaacabbaababaaacabccbacacccaacbcbbbbbcccbbbacabbaccaccccbbaaccbcbbbcbbacccbbbcbbbcabcbbccabaacbaaaaccbaacccabbcbcabbbbbbaccacccbbaacbcbacccbcbccccaacbabbbaabbbbabcbccccbcaccabcabbacabcbbabaacbbaabbccbccbbcbccabbcccbbccbcccacacbcaccbacabacacbbabcaaabbbbababbaacaacccabbccacbbabcccabbcccaabcabccccbcaaacbbabcbcbbacaabaaabababaccbaccaccabbccbbbbacabcababacbbacabcaaabbbcacaaaccbcbaababbbbbcbbaacbbcbabbbbabbbcacbbcbbcbccabccaaacccaacaabbaccbbaccacbcccabcccbbabbcbbcacacabbbbccaacbabcbbbcabbaabaacabcaabbcbcbcccccccbbabaaccaabccccbbbaccabbcabcbbaabcbbcbbbabcabcbcababacacbacbaccbccbaaaaaccbbacbbcccbcaacbbcbcbacbcccaaaabbbcbbaccacccacbbacbccbcbacaaacbcabbcaabcabcacbaaccbcacabacacaaacaccbbacccabcbaaacaabcaacbbabccbcaccabccabccccbcbbaacaacbabcaccaacccabbbabbabbabbaccbcbbbaccabbcaaaabaaccbcbababbbccbaccacbacbbcacabacabbabababbbbcccacbccaacbccbbabbcbbabcacbabbcacacbbbbabccacbcbaccacaaabbcbcacbabaabccaccbcbbacbbbbcbccbbbcabbacaaabcbccbaccbacaababbbcabbcbabcbacccccbbacbabbcabbcbaaabbcbbacabaaaabccabbbccababacbbbabbababacbcaabccaccbcaabcbbccacbcbcbbcccbabaccbcbccaacccabcbcccaaaaaaacabaaaabbbbbababbbabccabcbabcaaaabcbcccabaaaaacbbabaaabbccacabacbaccccbbbabaaccaaacacbcaacbababccaaabcabcaaabcccbbcbccbabaacbaccaaaaabcbacaacbccaccbcccaaacccbbaaabacabbbccbaaaaabbaabacbbababbaabcbcbaaaccccbcaaaabbacbacaacbcabbacabbbbabbbbbbcaaccbabbbacbcbccbacbbccbcacaacabbababcbbbcbaacacacabcacbcaacbabacbaabcbcbbabbaabbaccbccbbcaabbbacbabbacabacbcababbaaaaaabababaaacaaababaaacccacbbabccaccbcccabbbacbcbbbbbacaccbaacccacbabcabaacaaabacbbacbcaccaccacccccabaaccbbbabcaabccabcccbbacaccaacccbbababcabbbbaabaacbcbbbbbaaccbcaaacacacbbabbbbcccabacbbacaacacbabbaabbaabbcbcbcaaccacccababcbaabcbbbcabcacbcbacbbbbcabccacbaccccccabaacbcaacccbabbbbabbabbacacbabaabbcaabbabccaaacbaabbbacaacbcbcbcbaaaccaccaabcaccbcbabaaacbacbacaaaaacbbaccaaacabaabaaacbaaaaccbaaaabccccabbcaacacbbcccbcabaccaaaacbbacbaccbbcacccbcbccccababcaacabcbacbbaabccaababcbbababcccaccaaabcbabbaccbbcbcbccbcbcbcbcaacabccbccbabbbabcaccbabcabbbcbabbcbcaabbbcbacaabcbaaccabcacbcbcabbbbcacacbcaabbcccccacaaccbabccabbacaacccabaccbaacaaaaabcccacaabbbaabcbbacaaabcbacaaccbbcabbbbcacaacaababbabbaabaaacbabcabbbabccaabaabbcabccaccababababcacabbcbbccaaacaabaabaaacabcbacbbbcabacabbcbabaabcbbbcccbaaaaacacccbbccbabaccbbbaccabacbcbcbbacbcbbcaacaaaacabbabcccccccccacbacacacbaccbcbaabbbbacbbccaacacbccbcacabbccbcbaabababbaccaaacbcbacbacccacacbbbcbcbcbbcbacbbccabcabbaccabcaaaabcbabcacbbbbcaacbcabaccbcbacbcbbbbcbababbabaccacaacaaccaccaaacaacbcbbcacbccbcaccccaacbccbcbbababcabaaaccbbbaabbcbcbbabaaaccbabcbccbbcbcbacbcbababcbacabcbaccacaabbabbbaacbbaacbbabccbabcccaababacaccabbacbacbababbbccbbaababaaabaaacbccbcbaccbaaaaaaaccabaaaccbaaccabbbbbabbbcbabaaccbacbacccaacbbabcccccbcabccbabbbcaaacaccacccabccccbcbacbbbcbbaaabbacbccaaabbbbababcaacbaabbbaccabaaabcccccacaaccccbccbaccacbaabbccacaabcccabbccbcaaabbbaabcbcbbaccccbabbbcbcaacaacbcbcaaabccacacaacaacacbcabcbbcaaccabbabbbbcabcbbabbcbcaaababbaababcacbaacccbbaaaaaaaccaccaacbccccccbcbabbabacacaabaabbbaabcacbcacabbabbbbbccbbaaaacabcacbbbaabaaaabacbcabbbaacbbcbaacaaabbabacababcaaacaabcccacacacabaacccaccabcabccbcbbaabcabaababbbccabcccbabcabaacbbcbccbbabccbcbbbbacabbbcbbacabcccaabccbbbbbcaaccabaacacbacaaabbbcacccbbabbaacbcacaccbcbcababcccbcacbcbcbbcaaaabaaccabaaacacbbbbbabbaacacccacbaababcbcacaaabacababbbabaacacaaacacbcabacabcacaccbcbaaaacbabbcbcabbacbbcbaabcbbcabcbaccacaababccabccbacbccbcaaaabababaabaaacbabacbccbababaaccaababbbcababbbcbaababbcabbbcacbbbccacccacbbbcbacaccaaabcabcbbcccccbbbbabbbcabbbacbbccbabcbaccccbacbaaaccacabbaacaabcbacbbbacbbbbaabcbbcbcbacbbcbccbbbbaacaaabcccbbcacbcacabcaccabbaaacbbcbbbbccaaccbaaccbbcccacaaaaacccccbaaacbabacbcaaaabaccbcaacbaccacbcbbbbbaccbbabbccabcccbbbcacacbbbaababbcbccabbabbababaabcabcacabacbbaccacbacabcaaacabbcbabababbccbbcaaaccaccbcabaabcbcaacbbaaacaccaaacbbbcaaccbabababacacaacaaabccbcbcaaaaaaaacbcacaabaccbcaabcccabbacbbbcccbbbcbcbccaabbacbbbbbbbbaaaabbaabcbcccbbababbcabccbcabcabcccbabaaccbcbbbabababcbbbbccbbbcbccbabbaabababaaababcbbabbabaccabbbaccabbaabccacaacbacbaabaacccaaacaaacbbbcbbccbacacabaccabaaaabcaababbccabacbcbbbaaaaabcbbaabbccbbbacaaabaaacbcaabcaccabbbcacacbbbabacbabbccbcbbcccabacbabbcbaccbaabbbccaccbcbabbabaaaabbccbbbcccbabbbcbaababccbbbbbbaacaccacbbabbcccbbccccccacbabaaccabbaaacbacbbbbcbbaccabccbaacabbbcaacccacacaabcaccccaabaaabccbccbabbcbbcacacaaccabbcababbcbacbbbbbbbcbaccabbaacbcaaacbccbccabbcccaacbabaccbacacbbbcabaccabbbcbcaaaacccbcbbacccacbccbaabcbbcbbcccacacacaabccbacbcbbcbbabccabbbcacbbcbacabbaababcbccbabaccbccacbcbcbcaaccaaabbabccbccbcabcabcaacaabbccbcbbbbaabaccacbbabcaabcaaaacbacbcbccbbcaccbcacccaacacbbcabcccaacabcbacaaaaccbbbaabaaaaacbbbcaccccabacbcbcababbcbcacabacbbacbbcbcaabccbaabcbabaacaaccccaacabbccbcbcccbccabacababbaaacbcacacbbaabcbbccaacbacabcccbbabccccabacaccbbbaabcacbccbccabaabaccbabbbbaacaccbabbcbcbaabacacacbaacbbabaabbcaacccaacccabbbaccabcaabbaaaaaccbcbaacabbabaccbccbbbcbabbcaacbcacccbcbccbbcbccbbbabcbaaaaabacaaaacbbaacbacbaacccccaaacaaccabcbaabaccabaabaaaabccaababbcbbcacacbbcacaaaccaabbcccccbaaabacacaaabaaaaacccaccbbaacacbbcbbcababcbcbcacbaabcbacaacaaacbccbbcaababbcccabbcaccaacabcccababbcabbbbbbcbbcbccaabcbbabccacabcbbbbaabcaccbbaaacaaababbcaaabbbccbbbaaccccabcacbcbbcbaacaccaaacacacbaabcaabbccbacabbcababcaacaabcbbcaaabcccabcbbaccbababbbacaaaacaabcccaacbbcbccabbbbcbcaabcbbabccbabccacbbcbabaabbabcaababbaabaabcaacabcbcbacaaccbabbcbccccacacbbaaccaaabcbaabaccaacbcbcccccbaaacbccbbbcabcacbabaccbbacaaaabbbaabacaaabbbaaaacabcbabbccbaaaaaacbbaabcbacabbaabbccccbbcccccaaacbcbbaaacbaabaaccacacacaaababbcaabbcbaacabcaaacccbbcaccbcbbaabbaabbbbaabcbbbcaacacbcbcbaaccacaaaccabcaabcbcbbbabbcaccbbaaaabacbacacccaccaccaacbcbbbcbacacaaacbaabbbcbbaccaabacbaabaacccaccbccbabcbcbacaaaaacccbabababcbaacbcbbbbbcbbaaaaccbabaccccabacaabccbababbbacbbbbcbaabbcbcbccbcbbccababcbcaabbbcbaaacabbcabbbbcbbacabcbccbbbcbbabbacbcacbcabcabbbbccaacaaccabbaabacaaaabbbbbcbccababcbababaaaacbaabbbaabacccbabcacacbbaaabacbcabbabbacbaaabbaabccabbccababbcccccabaabccabcbbaababaaabbbccbbbccaccbbcbcbbccaabaccbbbbbaabbcaaabcacacacbbcbcabababccabcbbbacbaaabaacbbaaaabcbbcbcbcbacbbacbaabbcacaaccbaccbcbbaacaccbbcccaaacabbabbbbbcabaaabcbbcaabbabbcbaccbabbabbcbaabcbbaccaacbbbaacbabaaccbcbaccbabccbcabbbbbcabcbaabacbbbbcbcacbccaabbcbcccaabbbbcacaacacabbbcccaabbbabbccabbacbaaaccccabbbcccbaccacacaaaacacbbaabbbbbcacacbccaabaabbcccbacbbaabcaabaacbcaaaaccccbbbacbaaaccaacaaccbbcbbbcbacbcccbbabbbbcabbcaccccaabcbacacbbabaaacbabacbcbcbcbcbacaaaccbbacbcaabababcababbacbcbccbaaacbabacbcbbbacacccacccababcbabaaaaaabbababaaacacccaabbaccccccbcbbcacbaaaccaccaacbaaababcccbbcbabacbbccabcccbbbcbbcbabcabaaaacccbbcbbcbaaccabbcbbababcbcccaaaccbaabbcbcacaccbacabbbbcbaabbbbcbbabbababbcaaaccbcabccbaabccbcccabcaabbaaccccbacabbcccababcbacbacabcaaaaaaabaacaababacaccbbabbbabccccaacababcacbabcbaaccbcbcaacbcaccccabaaaabbbbbcbcbcbcaaaabccbbbabaccaaabcacabbbabbaababbbcccbbbcbbabcbaabcabaabcbbbcacbabccaabccacacabccabbcbcbacbaaaacccbacbbcabcbabacabbabaacbbccbbbbcacaaaccacabcabbabbcbbaacaccababcbcaaacbcbbacaccacaacabbbaacbabbcbbaabaccacacaaaacbaaabbaaaaabbaabaababaacabbcabbbbcbabbbcacacbccbabbccbacbabaaacaccbacaccbaabcbacbbbacacbaaccbabaccacabaccccbcbbaacbcaacbcbabccbbccacaabbcbbaabacbcaacababaaccccbbaaacaaabcbbacbcbabbacbaaabbacbabcbbbccabacccacabbbacbaaccaacbbcababbccaababcbaaababcccaaaabcabbbcabcabbbbbbbbcabbbbcbcaabccccaabaabaabbbbabcbbbacaccabaacaabaabcacabaacbacabacabacaababcbacaccccaccbcabcbaabcacbaabacccabcabbaccbcbbbcaabbacbacaabccacacabaaabbacbabbbcbcacacbcaacabacbaacaaccbbbcbabbabbbbaabaaaacacaacbccbcbbcbbccaaaabaaaacabcbbaabbaabcccaabcabcacbbbcababcabaacaacbcabcbababccacabcacabbcbcabbbacaaacabaabbbabbacabbaccacbccacccaabbcacaaaabccbbbaabcacbcbabcaaacabcbbaacbacabcbaaaaabacccbbbacaacbccbbbbacbcccacacbcbabcabbacbabbaaabbcacacaccbbcacbcacabaacbcbaaaacccbcbabcccabcbbbbaacaabacbbbccaccbabbbcacbbcccbaaacbabcccbbcaabbaaacbbcbbabbaaacabacbcbcbcaccabbbacacacabccbaacccbabcbccaacbcccaababaaacaaaccaaaaccabccbbbcaccbcbbaacaabcbcacbbababaabbbbaababaaacbaacaccbcabcaccbccabbcababcaaaacccacaccaaaaacacccabbbabaaabcbbccbaccbabcccbbbcabcabaccbcbbcabbaacabcbacacaaaacbabcbcaabcbbccacccbbacbbaaccabbccbabcbbbcccbaaacabaaaabbacbabbabbcacaabcbbcbaccbbbbabacccbbccbabababbabccbaacabcbcaacbaababbcbcaabcbbaaacbaabbcbbcccccbbbccacaccbcabbcaaaccccbbacabccbaacacabbabccbbaacababaacbcacaccbbccbaaaabbcaaaaabaabacccbabcababccbcccacbcbbaacabccbabcbabbccbabcaccabbbccbacbaaccacbcacbabcccccbaacacbbccabcbcbacbcaacbaababacccababaabbaacbaaabacabcbbcbaaaaabcacbbbbcbcaccaccbcacbcccbcccbccaccbbcbcaaabbacbbbbacbbabcccabaaabccacababccabcbbbbcabaaababcccbacbacbbcabaababbacbbbaaccbcbbabaaaccbcbabacbabbabaacbbbacbbcbaaaaabcbaacccbbcacbabbbabaabbaaacaabbbbbbbabbbbbbaaacbbacbacbbcbabbbccaaabcaacbababbcabbcacaaccacabcbcbbbbbcaaaaabacbcaababbcaabbabbcbabcabaababcaaabbacbacacccaabbabccabaccbaababbcaaacbbbccaaabcaccbcbacabcabcaacbabbbcbcabbbcbacbaaabcccbacbcaaccbabbabccacbbaaaacaababccabacacccccbbcbabbcaabccacacabbcbcacbcbbcaacbcacbccabbbcaabcccaacccccacbbabbaaaaaabacbcbbaabaacabaaaaccaabcaabcbaacccccbbccccabccbccabcacccbcaccbaccbccbabbabbbcaabbabcbccaabcbccccccbacababbbaaacbbabccccbbaaabaacababcabaacacabcbababbbbaaacabbaccbaccbbbbcbcccabcabbcbbcbbbaaccbacaababcbcabcbaaacbbcccbcaaacbcaaaccaacaaaaabcaaacaabaccaabccacccaabbacbaaacabaacbbaaccbbccbacbaabacbaacabacbababbbcccbbbcbbaaaacaccaccbbcabbabcccbbacbbbbabbacababccabcacacaacccbacacaabbbccabcbcacbccbbcabacabcabbcacaaaaaabaaacbccccaabbccccbbbbcbabbaaccabccccbacabccabcbcacabcabbbabcacbabccacccbbbacabaabbabbbaccccbacccabcabacbcbbacaaabcbcaaaacbaabccbcbccbbcacabcccbcccacaacababbacbcacccacaacaccaccbbaabccbababbbccbccacbbcbbbcbbcbacbaaaaaacbabbbbaaacacbbcccbcbcabccaccaccccabbcccabaaacbbbccaabbbaacbbabccbabbbbcbabcabcbcaaccbbaabaacbbaabcacbbaacbbaabbcccaabcbbabbbcccabaccacbacbacbacbcaccabcaabbbbcacccbbacacaaabaccbcbbaabcbaaacaabccbabaacbcaaacaaacbcabacbcccacbababbbbcbbacacccaaabccaaaaaaaaccbcabbcaaabccacabbabbbccaabccbbcacccacaaaababbabbacccbacabbcccbbcabbcaabaccbcacacbbbcaacbababacccccabcaaabbccbacbcacacaaccaabacbacbaabbaacbcaccaacacbcacbccccbababbaaaaabccbbcabacbbbbcbbacbccabbacaacbaacabbccacacaaaaccbabbcaaabaacbcbacbbccaacbcaaaccbabcbcabaabacbccaabbbbcbbcabbcacbaabbccacbbcbacaacbbcbaccbcabbcababaaabcbabcbbbcccbbcababbbcccbacbaabcaccacbcbbbbaabcccbcbcabcbcbbbbacccccbacbbaaccbcabcbcbccaacbccaacacaacbabccaccbcbccccbcbbaaabcacccbbaaccbaaaacacbcbabcbacbbcacacaccacbbcbccaacbbccacacbbccbcaabbcacacaaaccaaccacbbcaaaaccaabaabbaacaababccbbaccacbbcacccacbbababcbbaaabacbacbccbcbabccbcaaaaaaacaacbabbbccccaabcbbcbcaaabbcababaabbbbbbaccbcbbacabbaacbbabacababacbbbbaacccabacaaabaaaaccbbacccbbabaabbcbabccabacbcabbccacbbbcbabacbbbcbbcccccaacbcccacccacccabaacbacaccbaaacbacacbacacbaaaacacbcbbaccbbcacbbabcbabbbcababcaabccbcabbacbbccabcabcccaabcbcbababcbabbbbccbcababacccaabaaccacbcbcbbbabcbbcbcbbacbbbbbbaaaccbcaacacbcaacaabcbbabbabccbbaccbaacbbbabbccbaaccacabbcaabcbbbcaccbbbcbccabcbcabcacacbcbcbbcbbabccbabbbcabbaaacaababbbbbcbbccabaaaaabbccbccbaabbaccbcccaabacacbcaacccbbccbbbccccccaacababacbcbcacaccccbabcbabcaaccaacaacccbbbbaacabcacaaccbbccabbbbbbcabaacbacbbcccbaccbcbcbbbbcabbbcacbabcaabcbaaaacacacabcacbcccbcccccccbbbaabaacaaaabcacbaaabbacacaccaabcbcbcbbccabbacaacbaaacbaaabbabacacbababcbabcaacaaabccbbccccbaacbbbcaabacbbaaabcbccacbccbcaabbaaacbcabcbabcabaabaccbababcbbacabbcacabaccccbccbaacbabcbbacaabbabbccbacabcbbbccaaaccbacababaccaccaabcbaacbcaaccbbcccbcacaabaccbbbcaacbcbbbbccbaaccbbacbbaaccaaccbaccaabacbacbbaabcaaccbaaaaccababcabcabacaabcbbcababbcacabaacbccacbbbacccccabcbaabbacbabbbcaaccccbcaaaacbbaacbabccabccbabacabbcbcaabbccbabcababbbbabcaaaaabccaacbbcbabbcbaaacababaaccaabaaaacbcbbcaccbcabccabacbcccabaaabcbababccaccaacbababccbbccaacbbaabbcaabccccabcbabcccacbbaaccacbcccbccaaabcbcbcaabbcccabbcbaaacbbbccacbaccbccbcbcaaccbccbabbbbbcbcbcaabacabcabaacbaaaabcacbbaabacbccccabcbcbbabbcccacccccabaaaabcbacbbabbcbbcbbcbaccaccaccacbabbbbcbabccabccccccaccaaabcbbabbcabcbbbaaaaaaababacacacabacbcaacbcabcccaacaccbabcbccabcccaabbcacbacbbbcbaaaaabcbabbbccbcacbcaabacccbbcbccacccacbccccabacbbacbbcaccbbbacbcccaccbabaaaabcbbababccabcbcbaacabaacabaaaabcacbbccbacccbbcacabcababcbbcaabcabcbcbbbccccbbababcbccbacccacbbccbbcbacbabbcaacacbccbcabababbcaacbaaabacbcbababbbccabbbaacbabbbbcacbbbbbcaaacccbcbaabbcbcbbbaabcacababbbccccccababcbccbbcbacccbbbbacabbcabbaabbbbbbaccbcbcabbcbcbabaaacacabbbcacbcbccbcacaaabbaccaaababaccbbaaaaacbbccaaaaccccbbaccaaaabbbbcccbcccccbccaabbbaaaccbcbcaaaaabbbabaccbbbbbabbacaacccbcacaccbcbbacaccbccaacaccaaabccacbcaccbccaabaaabaaabbbcaacaaaaaaabbababcbbbabcccbbacbaabbabbbcabccbccbaababbccabccacaccbabcbbaacaacbbccaabbcbccbbccccccbabbccbcacbcccbbbabcabbbabccbcccbaababacbcbcaccaccabcbcbccbacbcabbaaacbaaaacaababbacbccacccbacbccbaccacaccbbcbccaccaaccbbcacbcaacbbcabcbabccabacaaaacabccaaacaacbcabababcbcabbbcabbaccccacaacbbbbaccbcabaabbbbbccaccbacacccacabbbcaacbabacccacbaaacbbbccccacacababaabcbacaaaabcababccbaacabaacccccccbbbbbacaaaabaaaababcbccbabaabccababbacbcaccaacbaaaaacbcbbcabbbcbbbcbcbaabbaaaccbbccabbbbbbaaccbcabaccaacbbacbcabbcbaaaaacabccccaaaaaacccacabaaaaccbcaccbaaacaaabcbcabbbccbccbccccbcbacccbbabacabaabaccbcbbaaccaacbabbbcbcacabaacabbacacbaacacaccacbaabccbbabcbbccbbcccccbabccabcbbcbaccbcbcaabbabbabcabcccbacbccaccacacccccaabbcacbacbabaaccbbaccbccccbaccbcccbcacacacbcbabbacabaacccbbccbcaabcababbcbacbbacababaaacbacccaacbcabcccaacabaacabbbabacabbbbccbaaabbcaaacabbacbabccccbccabbcccccbcbbbbcacbccbccbccabaacbbabbccbbabbbaacabacbaccacacccccacbcbcabacccbcabbbcbacacacaccbaabacacbbcaaaacbbcaacacaccbcbababcbabcbabbbaaaabcbbaccbbabbbcbbcccaaccacaabbabacacbcbcaaccbbbcbbbaaccaccaabcacbbbcacaabbacbababaacbbbbccbbccbbbbabbcccbbbbbbcaabbbbcaacaaaabbbabbacbbccaaacbccbbacbabbaccbbbccacbcccabacaccbccacabbcbacbccccbcccbaaabbcbbbbbbacbbbabbaaccacbbcacacaaccbababcaabaabcbaccacbbcaaaaabcbcbbbbbaabbaabccbcaccbaaacccbaccccbcaaabaacacccbabcbccbcaacabbacabcbbbacbcccbcabacbbcabbcbcbcbcbcabbcaacccaabcbacbcaaaabbacbabbbcaccabcbaababcccccbacbabcbcbacacccccacccaccbbccabcccabccaabcbcbcaacbabcaabbcccccbcbccacaccbbcbbbacbabacbcbccbbcbbcccacbcbacbccbbaababbabbaaacabbbcbcaacbcacbcbaaaaacccabbccaabbbacbcbcbbcbbaacabacacacbcbbabaaccbabcbbcbccbcaccaabbacbccabcbcbaabcccaccaccbabacbabccacbabacccacbabcaaacacbcaacaaabaabbcbbbcaacbcbbabcccaccbbbbabcaaaccbacbacbaccbccbcbacbbcbcaabcbcabbcaaaaacabcaaccccabbabcacabcbaccaccaccbcbbabcabcbbbaaaaacbccbacaaaaacabacbaacabbcaccbbbbbaabcaaccccccaaaaacccaccaabbbbcccccccbcbbbbbbabbcbccbabcbaccababacbacabaaaabaaaacaacbbabcabccabaacbcbaccbccbaccbccbbcaccaaacacbccabbababcacabacbacabaccabbacababcccbbacccaabbacbacccaccbbbabccccbbaaccbacabbbaaaabbccbabcbcbbbbaacacaababaabbabcabaaaccbacaabaacabbaabbcacabaccbaccccacaabaaaaabaccacbbbbacbbabaabbbacacacbccbaaabbbbcaccbacbbabaccccbabbccbaccbccbaaaabcbababcbacaccbbcabbcaaacbbbabcaaaacabcbbbbaabcbaaaacaabaababbcabacaabcbbcccabcaacbbbcbcabacacacacbacbcaaaacbababaacbbabcbccacbbabbcccbcaaccccbcabbccbbbbaaccacabcccbbbcbcbbaabbacbacabaaaccccbbcbbcbcccacacbbbabbcacbbbcccaccbcbbbbccccabbccbcccbbaccaaaccccaacbcaccbaaabbaaacbbbaacbbbabcbcabacbaacbccbbabcbbaccbcaaacabcaabbcbbbaacaacacabcbcaacaacabbaaacbaababaababbcbbbaaaaabaabbcabbbaacbccbbcaccbbbcbccaabcabcccaacbbcaacabbccabcacccaaaacbaabcbbaaccbbcbbacabbcaccbcabacbccaaacbaabcccccacbcbabaababcccacaabcabcabbcbacabbccaaccbaaacbacccacbcabbaccabbbaccbbbccbaabbccbaccbbcbcbcacbcaacbababcccabcaccbabbcbcccccbcbccacbcacaaacbcaccabcabcbcbabcabaccbabaaacacbbbbcbabcababbbcacbcbabbbbacabcbcbbcbcbbbcaabacbccacbcccccaacbabbcbbcaabcabccccccabbbacaccbcabccbbbabbcbbbbcbabbbcabbaabcbbbbbacaacbbccbacbabbbcbbbcabbcbbbbaabbaabacbccabbaaaaabaaabbabbcbcacaacaacabcbbbbcbcabcabcbcaccabcaacbacbcbabbbccbcbabbccabcaaccbbcaacaabaacacbbbcaccbaaaacbacacaabccbabcabbcbbabcbbcbbbacbbaabccbabcacccbbbbbaaacbabcbcaaaabacbcabbabbcaabaccbcabcabbbaccacaaacbacacbabcaacccbbacabbbcaaccabaaacbbacbaabbbcacccccacbacbbbbaabbabacaccacaccbacccbcaaaccbbabcabbcbabbbbcbcaccacabbaacbaaccbbbcaabaaababcacacbbcaabbccaaaccbacacbcacabbacabaaccabaacaccbababbbccaabbccccbabbbaaabccccbccacaaacbcbaccbccbbccbcccbbacccbbacbbbccccbbcababcaccbccacccabbbcbbbaacacbbccaabacccaabacccaacaacbcbcaabbcaabccacccbcbbcbacbabacbabbabbbbabaccbbabbcccbbcccccbaacbcccbcabbaaabacacabaabbaaaccbaccaabccbbabcabbbaaacbcbcaaccbbbaccbaaabccabcccabcaaacaaacacbccbbbcbaacabaabcccbcbccbacaaccccaccbbcacaaaabcccccbbcbabcbcabbcaabaaaabbbccacaccccacbbcabcbcabbacbbaabccababacccabcaabbababaacbaacbcbcacaaaccbcaacbcbbbccccaccbccabbbcbbbbbaccacbcacaccaabcccbacbccaacabccacacababaababcbccabaabbcbaccbacbacabbccbaabbbbababaaccacbabccabcbbacaaaacaaabaaacacccbaababcbbbcbbabaacbccabbabaaabacccabbabbcbbcccccbaacaaaacbaabbcacacbccabaabbcccbcabbcbcacbbbcccbbcbacbacccababcbbbbcbcccabcacacacccbacaccbbbacbacbccabcbbcbbbcaacccaccbaccccbbaabababcbabcbacbaaaabbbacaccccacccbababbcbbaaacaabbacbbbacbbcbccaccaaaabbcabbabaabcabaaaacbabbacbcbbcacaacbbccbaccbaaaacbcaaabccbabababbaccbacccbbbbcaacbcacacbccaccabcabcaacaabbaccbaaabbacaaacbbabcbbcabacbaaaacbacbcbacaaaabbcaababcbcbaccbccaaccbbacaacaaccaccacbabcacccaaababbbcabaabacccbaaaccacaccaabbabccabaabbacaaccaacccbbbbcacabcacaaccbacacbbbabaacacccacacccabaaccbccccaaacccaccbbababaaabbccccaabccccaccabaabbbababaccaabccccaaabcaaccabcbbcabcbccccbbaaacaacbcacabaccccbccacbbabcbbbcabcabccccbbbbcccacaaabbcbacaacbabbcbbbcbbcbbcbcccabcabcbbcbbabcbbaabbcbcaabaccbbbaabccabbbcababcbbaabbbabcbbbaaacccaacbaacacbabcaabaaaaccacabcacaccaaabacacccbcbababcccaccaaaacbaccbabbbccbcbaababcbcbaabcbcbacbcbcbbbbaccbacabcbcaabaccaabcbabcbcbbaaaaababcbccacbbcabaabbacaacabbaccacbbaabbbcbbaaaacbabcaaccbbcccabacbbbaabbcbbabbbaabbbbabcbcbccbaaabbabacccbabbcbbbccbbabbbacaaaacbccabcbaaabaaacacbaabbbbabbcbbcbbcacabbbabacababbcabbccaacbabcabbaabbbcbbacaabcaaccbaabccaccbabaacaaabcbcbabbcccaccccbaacccbcacbabbbbcacabbabacbbbaaccacaacbacacbbaccbacbbbcbbbabcaccbabbabcbbcaccccaaabcabaababbcaababcababacabbabcbbababaaaccaabccbabbacbabbcbcbacabbcaaacaaaccccbacacacbaccbabacbabacbacaacabcbaabaabcbcccbcaabbbcbabaccaccacaababcccbbabbaaaabaccacaaccacbbcabbaabccbaaccabcaababacbcabcbccbaacbbcbbbcabacaaabcacaabccbacbcabbacbbbacacbbabccaccbcbabcbbcbbcccacabbbbbbbcaccbaaacacaaabbabccbbcababcbbbababaaccaaaabaaacabcbcacccabbacbbabcccacabaabababcccbbccaccbcaacbaaacbbbcaacbcbbccbbaaabcbbcbcccabccaaccabbcabaaabbaacaabcacbcbbcaacaacaaaabaaabbccaccbbccbbbcaaaacaabacbcabaaabacccccaacbcccbcbbcbaaaccacbcbcaaababbaaabcabaabbacbcbbaaaccbabcaaabacababcccbbbcbccaacbbcbcababbcaaabbccbabcaabcababcbbbccbaccbbcabaabcaaabbbaabacccacbaabcabbabccaabcabbbababcaaaaacaacaabccbbabbacabcabacacaacbbccbbacbbcbacbabbaacbacabcbbaaaacbabaacacabccacbaaabbacccbacabccbcaaaaabbabcaccbbacaabaacabbbcaabacccabaabacacbcbbcccccbaccbbabbababaaacabbaaaababccbbababacaacbabcaaacacaacabbbcbbcaccbabacbcacaababbcbbaababbacbcababccbbbbcbbababbbabccacbbaababcaabbbcccbcbaacbcbbbabcbacbccaaabbccacbbcbbbabccbbbbbacabacaabbcacabbaabaccbbcaabbccbbaabaacbbccccbbbabacbbaacbbccbbabccbcaccbcaacbaabbbbbabcbbcaccabcccbbbbaabcabcbccbcacabbbbacaabacaaabbbcaacbcaacbccbabcbacbabcbababbbbbbbbacccbcbbbaacacabbcacbacbcbabbbcbcbcccbbbbbccacaacaabaccccbcacbaaaccaacbccbbbacaccaaccccbcabcaaccabcacccbbabcbacacaabcbcbabbbbbabcbccbabcbbbcbbabbaaccbbcbccabccacabbbccbccbcccacaaccabccacacccbbbcacbbaacbccababbabcacbbbabacabccbaaacbbbbbbacabbaaabbcacaccbbbbcaacaabcaacabbcbbacabccaaaabbcccacccabbacabbaccbbcabbbcbcacbbaaaaaacabbbcaacbbcbcbaabbccaabaaabbbcbbcccbcabcababcacbcacaccbcabacabcaacaabaaabcaacaaacabaaacbabbcaaaacbcbcccaaaaacccabaccaaccbbcbbbcacccbaaccbaccbbcccccaabcabaabcbaaabcaabbbccbacbaaabbbbacaabbbbabbacaacabcaaaccacabbcccbbcacaaabbaaabccccbcbacccabbcabaacbcbaaabcccbcbcbccacacabaaccbccbaccaccabcbcbbccaccaacababbaaaacacaaccccaaacbababacacbbccccccabbcbabaabbbbabcabbacaacbbaccabaababaacbaacccaccababaacccacabaccaccbaaabccaaccbbcaabacacbbcaccbcbccbcabaacabaacbbabbcaabacbbabaccccccbcabbabcacaaaabcaaababcaaaacbbbcaaccaccabcbcacccbcabcbaabaabcccbbabbabaacbcbbabaaabcaacbaabbaacaaacabcbbaaabacacaacaaabcaaccaaacbccabbaccababbbbcbabccabccbbccaacacbcbbcacbacbaabcccccabccacbbacbacaaccbacbccaacbcbacccbbcbacaccbccaccbaccccbcbbabbcbcbcbbbbaaccabcccbcacbcbaccacccabcbbaabcbbbcbcbacabaaabcccaabaabbaccaaccbcaacbcacaaacbaaabacbcacaaacbbccccbbabbacbcbbbbcbcbbcccbbbacbabbbccabbccbcabbbbbabacacbbccabaabcccaaabcbbbcabbbccbccbaaaabbabcbaaccbcbcbabcbccccaabcccbabbccabcacabcbccacccacaabacccabcccaccbcbbcbccacbcaaabbcabcbcbbbbcabaaabaabbcabcccabcabacbbacacabcbaacbcbacaacbacbacccccbcbabcbabaabaabaccabcacababbbaccbbcabbacabacbaabacaacbaccabcccaaccaccbbabaacabbccccacbaacbbcabcccbabaccbacbbbbcbaacbcabbabbaccbccbbbabacaabbbccaaccaabcbbababcbccbcaacabbcaaccaacbcaacaccbaccaacccabbabbcacabccbcbbbcaaabaccaaabaccaabbbbacaacccbccbccbabaccbacbcccbaaacbbbcaabcabaacccacaccbabbcbabcbabcbcaccabbacbbacbabaacbbbbaaaaaaacaccbbccbabacbbbcbabccabccabbcbababababbbacbcccbabacacbbaaccbccbbbcababbccbbcaabababbabccabbcbcbccbacabaabcaabababbaabaaaacabcabbcaabacacbabcabbbbacbbbccaaabaccabccbcbcacbacbbbbaccbcbaabcccabacbbcbacaabaccbbcacaabccbcaabaacbccabaacbabcabbaccacbcabbcbcbcacaaabbbbbacabaccbaccbbbbcabcabcabbbcacbacbabaaacaabacbcabacccaccbbcacaabbcbccbbbcaaaaccacababbccbcaabaacccbbabcabcbaccbbcacaacbbbcaacaccbabccccaabaaaabcaaccbbcacaabaaacbcbbaacbcbcccccaabaaaabbabbbcacabcabcbbccaacbabcbaccacbccbbbacacbacacbcabccabaaaccabccbaabccaababaaabbccccbaaaaaaacacaaaabaaaccccaaaacbbbacccbccbcaaabcabbacbbaccbccacbbcbbcbcaacaacacacbbbcabacbaacacaaacaaaaccbcacbabbcccbcbbbbaaccbaaaabbacccabaaabccabcbabaaacaaacbbbbbcbbaccaabcbcbcabbabbabaabbcbacabbbbbbbcacacacaacbcacacabbcbccabcbcbabbcaabbcaacbbaabaaabbaaccbccabababbbcabcabbcbbcbcbbbacacbcaabbbcaacabaabbcbbabaabccacbccbcbacbbaccbbcaabcccabacbaccacccbbbabbbacabbccbbcabbcbbbbbcbaabacbcaaccbcabacbaccbcabbaabccccabacbbcaccabcbacbabbcbcabbbbabcbabccccabbabacbaccccabbabbbcaacccccbbbabbbacbbacaacacbccbcbbcbbcbacbaacaabcaabccacabaabbbcacbbabccbcabaabbabacacccbbcccbccbcaaaccbbaccabcbcbaaacaaabbcacabacccbbabbaccaabcacbbaaabcbababacaccbacbccaccbacccaabaccabaccacccbbccbcabaabcaaabbcbbbcbbcccbaaabaaaacababcaacabaccbcaacabbccacaabcaacbabaaacbcbbbbaacacacaabbbabcbbcbbacabcbbbccbcaaccaaacacbcbbcbcbccccbcabaccbccbbbbbcbabbcbbcbcccbabcaaccbacacbaacbacbaccaacacacaaccbbbbbbbbacaabccbcbaabaccbabccaabbcaacaacacccccbcccccacaaabacacccacaaacacacaabcbaacaabaacbbcbcaababbbabbccbcbbabbaabcababcabbaaaaaababbcaccbaabcbaaacbcaaabcacbccaabacccabcaaccabcacacaaaacbcccabcababacbaabbcbaacabbcbabbcbcabccbbbaaabbbcaacccacbbbbcbaacaaacabcabbaaaabaccccabaaabccabcaabccaaaacbbbcacbaabcbbbbcbaaaccabbabccaccacacacacbcabcacbacbcaaabccccbbcaaccaaaacacacbabccababaabcacaaabcacccaacacabaaacbacaaaacaacccbcacbbcbacbcbcaaacbaaaabbcacbbabbccbaaaabbcabbcbcbbacaabbcabcbccababacbcbbcaabbabbabbacaabcccbbbcbacaccbbbbababaaccaaaaaaaccababacababbababbabbcabaaaaabbaaccaacaacbcbcbacabcabbacacaabbacbabaabcbaacabacaaacbababaabbcbcaaccaacaabaccbbacaaaabaacccbabacbcabcbccbaccbaaacaaccababbacbccbbbbacbbbaaacbcbbbcbcabcaabbabbcaacbccbaccccabbccbacacaacbcbbccbcbcccbccbbacacbabababaccbaabcbbbaccbccbbababccbbaaaacaaaccccaccbbcccaccaacaccbbcbbabacaabcbabcbbcaaaabcaaabbcbcacbaccbbaabbccbaacbabaccaabbbbacaaabaccbaacccccbccbbaaccabaaaacbcbabbcbacacaccccbcaccacaaababbbababaccbbccbcbccacacaabcacabcbbccccaacacabcbbbcbaaacbbcaccbbcbbcbcaaabbbbabcaacbbccabbbaacabbbabbababccacccaaaabacbbaccbbcbabbaabcbaaaacbcabaccbbbccaacbcacacaacbaacabaaccbcbaccbaaabccabcbbcccaaacaccaaabbcaaaacaacaabcbcbaaabbacbbcabcbacbbccbbbacaccccaccacbbcabccbbaccccccabaaaacaacbbbabcaccccbbcccaaaabccacbabababccbccbbababacabcbcacabcaabcbbcacabaabcacacbccbbabacaccbababcbcbaabcbaccbccacccccbacccbccbbaaccaacaaccbaabbabcbbbabaabcccbbaccbcbcaccacaacabcbccaccbababccbcabbbabcbbbbaacabbabbcbcabbaccabcacaabccbaabbaacacabcbabbaababbbccbbccaaacabbbacbabcabbabaabcacbbbaaacbbababbbacbaacaaabacbacbcccacabaccaabcaaaacaabcaccacaacaabbcccbcccbbaabaccccaccbaacbabcaabccacabbccccacccbbcbabbaabbaabbcbbacaccacbbacacacccbcaaaaccaacbcabcbccbcbaacbaccaacabcabcbbbaabbbabaabacabaaacbbbbcabbacbbacaabcaaaabcbcccacbbbbcbbbcaaccbbacbccbbbcbabcbbbbcabaabaacccbcccccbacbbbaabacbbbabacbabaacbbcabbbcccbcccbbabbaabaacccabcababaabcbaaabbccbbaabbcaaabacbbaccabcaaaaccabaaabbaccabbaacbbabcbbababcbbbcbaaccbccbcabbaabaabaacbcbacbacbbccbcbaacbaaaabcaccabbbbbbbcaaccaabbbcbabbaabacaacccbbabcccabcacbcabaacbacacaacbbaacccacacbababacbbccbcbabbbabaabcaabccccbaaaaacbabcbbbccaacccabacacbaabbccbccccccccbcbaaacbbaaaaaabbabaccbbbaacbbcabaababbabbbaaabbccbbcbabbaabaaaabcaaaccabbaabcbaccbcbcbaccaaaaccbacccacabbbacacbaabbcaaacccacaccaaaaaabacccbbaabbcbbccaababbcaaaaaacbbbacabbcabccbccbabaabbcaaaaabcbcbacaaccbcbacaabaaabaabccccabaaabbacabcbbbbcccacacacccababacccbaaaacaaaabaaaacbbbbabaabaaacaccbbaccabbacbaabacabbacabbcacccbcbcccbabaaabacaaaaabbaabbcbccabccbabbbbbcbacbcbacbabcbcacabcaacabbcaacaacaccacbbaabbccbbbcccababacbaaabbaabcbaabaaccabacacbbcbbabcacccacbbbbaccacabaacacaccbbbaaacbbcaabcbcaaabbcbabbaabbbbbcacbcbbabacaabacaabacabcbaaaabbccabbbcaacccccbbbaabcbcacacbbbcbcbbbbcccccacaccbacabcbbcababccaccbccbbbbabaacaccabacaababcbacbcbbaaabababcbcccabacbcabacaccccaababacbbbabbaccaabccccccaabcabcbbbbccaabbabaabcaaacbcbaacacbaaaabacccaabaccbcbcccabcbbcacbacbccacabcbaabccacbcabbcbcbaaaabcbaaaacaaaaacbabcbaccacaacccccbbccbacccaabcabacccbcabcabcacbacabaacbabcacccbaaaccbbbcaaccabccbaabbcabcababacaabccaccccaccbbaccccbcacacababbcacacccbccaccbaacbccbbccacaabaacbabcbcaacbacacbcaaaabaacccbcbcbccbcacabcaacccbbacbcccaacbccacccaccbbcabbbaacbccbbcbccaaabacccaabacacaccacbccccaabaaaabbbbabcbbbaacaabbaaacabbcacaacaacaaaaabbbaabbbbcbbbbbcbbabcaccabcbcbcccacccbcbbcaaacbaaaabcbbaacbabbcccccabacbcccbaababbcbbcaaaaabccabcccbcaabcbaaaccaacaacaacabcbcbbbacabcbacbbccbccbbccbbbabcacbcbbcbccabababbbaccbacbcbbaabaabcccbbccacbbacabbabacaabbcbcacaccbbbaabcabcbbbbcbbaaacbcabccacaaaacacbaaccccaaabcbaaabcbbcccaacbbcccaccbcbacbbbabcaccbbababbbcccbbaaabaabbcabbabccabcaaacaaccbbccacbaaaabcbbccaabaabccaccaababbaccbaabbcbbbcccbcccbaaccbaccccabccabbbbacbabbaaaabacabbabacbacbabccbccbabcaaaacabbbcbcbabbabaaacccbbbabccbacabbcbbcaabaacbaaababccbcaaacabccbacacbcabbacccccabbaaababbbcbabaaaababaacccacacccbccbcbbacabbbcacbaccbabccbcbcbbbabbbbbbacbbcacacaaabbacbbbccabbcacccbbbbaccbbacaabbbaabbacccbaabacaaaabbcaaccbcacbabababbabacbaababcbbbbabaaabbacbcaccaabbbacabccaccaabaaacbcbabbcbacabbcbcabaaabababcccacccccccabacbababaccbacaccccbbbaaaccacaabcabaabbcbaccccacbbccbbbabcbabbaabacbaccbcaaacbcbabcabacbacccbbcaacabbcccaabbcabbbbbacccbacaababbbbbcbcbaaacabbaaccabcabbcaabaacacbaababbcacaaabbaccccbcacababcaaaaacbbacacacacacaacbcbcbbcbcababbbbbaacababbcbabcacbaccbbaacababccbbcbaaacaaaaccaaaccacbaacccbbcbccbbbaaabcbbaabccbbbbcbbcbcaaaaabbbcbcbaaccabcaaaacbaaaccacaccbaababbacaacbaaaccbaabcbcbccbbbaacacbabbccabcbccbaccacbabccabcabccccbaabbcbbaabcccbaaaacbcacaccbaaaabcccaacaccabaaccacabbbacacacabcbcbccbbccaabaaacbbcbccbbabacaabccacbbcacaaccbcccbaaacbbaabacababacbbababacabaaaabcbccacacbcbacccabccaacbbacbcccbccbcaabbaabbbbbcbabccaabcbcabccbacaabbcbbbcbcbcabbbaccccaaacccccacbcaccccabababcabbbabbbcbabcbbbaacccacacbabcaaccabcbabccaccabcaababcbaacacbbcacbcbaaaaccbcbcbcbaccabbabaacacabbcbbcbaaabbbbcabcabbabcabbcbaacbaccccbaaabacbaabaccacaaccbabcccabbbbbbacabbbacaaaabbcbcaaccaccabaabaabbacbaabbaaabbccacccaacbaacabaababacacaaaabcbcbabcbcababbcaaaabcabacabcbacbcaacbbbbccaabaaacaacacabbabcccbcbbbbcacbabbcccacbabcbabcabcbbaabccbacbbbccaaaaaacacabccbabaacbcbaababaabaaacbacccabababbacbbaaabcbabcccacaccacacbababcccbbaaccccbbbacbaaccbcbccaaaabaaacaccbccbababccbcbccbababbccbacbaccabcccaacbcabbbcbccacacbccbbcccacbabcabaccabbabacbcbabbabaabbbbbcbbbaccabaaabcccabcaabbccbbbababcababbaccbbaccabbcaaaababcaacbcbbbbbbabacababbccabacabbaaabbbabaacaabaaaaaaabcccbbbccaaabccaccababbbbcbabaaccaabbcbaabaccaacabbbcbacbabccbbaababcacaaccbcbcccccbccbacccacbbacbccbacccaaaccacccccbcbababcaccbcbbabcaaababbcbcbbcbccbabababbccacbbaccccabbbbaaccaaacbcaaaaaabaaccacbcacabcabbbbabcbaaabbcbcabbbcbcccabbbbaaccbcaacbbacccaccccacccaabaccbaacbacaaaaaabbaacaacbaaacabcbccaccbaacbaacbcabcccacbaacababccbbacababacaabbcccacabcacaccbbbaabaaccbcbcbbcabcaabbaabaaaaaaabaabaabbccbbccbbcbabaabbbbcbccccaacabaaabcabacbbbcabaababbacbaacaccccbaccaabbaacbbccbbbccbbacbacbcabbabccabbbbbbaaabaaabaabacbcaaabbbccbbaababbcbacbbcbbbacaccbacbbcbcbccaabcccabbbcababcbbacabbbacbcccaaccaacaacaccbbcaccacabcbbcbccbcbababcbbbabcbbcaacbccccabbbaaabcacacbbbccbbccbccbcbbbaabaaaccabbcccacbbcbaacaacacccbbbcccbaacbaaaabbbaacbabbacbbccccbaaaababcaaacaabbbcbccacacaaacbccbbabaacccbcbacacbbabacabccaabacbcbcbabaababbabacaaacccbbbbaaaacbabacabacbaccbacaaccaaabcbbabcabccbcbcabccccbcbccbcbaacaaacaaaabaccaccccccbcaaaaacbaccbcaccaabacacbbcbcccbbccbacabcacacbaacacacaaababaccccbbabccbacaccbbbbcacacbacbbccbccbabaccababccacbacaabaacaababbabcabccabbabbccccbaabaaabbaccbbaacaabcbacacaccbbabccbaaabbcabbbcabccbbcabbaccbcacbcbccbcabbabbbbbbbbcabaababccacacccccaacbcbbacaacaaacbbaccabcbacaababaaaabbbacabcaacbbaaaabcccccbcacbabacabcaccbacaccaabcccabbbacabcbbcbbaacbcccbacbbbbcacccccabccbbbcaccbbcbcbacbcbbcaabbbbbcbabcccbbbcbcabcbcaacbbaaaccbaaaaccbbababcccacacbbcbaaccacccbacbabbbbabaaaabcbacbbbcbccbbbccbcbbcbbcaabcbacaaabacbccbcbcbccbaacabaacbcababaaabcabbaaacabcacabbbaabcabcbccccbbbbcbbbabababbbcbcbccbcccaaaabcaaaaaaabaaccbbaabcabbbcbcbcbbcaaacbbaccacbcbcaacbcabccaccccbcabbababbbbcbcccababaababbaabcaccaacbabcaaaccccacbccbbaacaacbbaabcaabbccabbaabcbbccbccabcaacaaaabcbcbcbccccababcbbabcacccccbcbcaabcbbcbbcabccccacbbcccbbbcabbbcabbbcbbaacbbccbaaabccbaccabbbbbcabacccbaaacaaaabbababbaababbbabaccbbbbacbbabbbbbccaabaaaacccccbbbaaaaabbbbbbbbbacabbcaccacbababaccaccabbacccbcbbbbccbbaaacbabbaccbbccbaacbaabcccbaaacbbcacaaabccbcccbcabbcacbcbbbabbacbcbabccabcaabccbcbaacbcccbbbccacaabacaccbbcabbacbbbacacaabcaaaabcacbabcaacaaabcaabcccbabbbbbbbccbccbbacccaaabaaabbbacccabbbacaabbbaaacbaccbcaabcbaaababcabacaacaacbaabbbaabbbbccbbcabacbabcbcbbcbabccbcccbabcaabbaaccbbbabacaccccccbbcaabbacaaaaaacbbcbbcacbcbcbabcaaaaabaabccbcaccababcbcbbbbacccacabccbbcbbaacbabacbccccacbcabcbacaccbcccbcbbcbacabbbbccabbaacbbbabbbbbacbbbbcabbbbabccaaccabbbccccbaabcaaacccbcbaabcacabcbcbaabacccbcaabbaaabccbbacbacbacaaaccacbcccbaaabccacbcbbcbbacbbacccbccbbcacabcccbaaacacababcabaabbcccaccbababcabaaabbbbbbabcbcaabbaaccccabcccacabaaaaabcabaccabaaaabcaaabccbbabaababcbbbbaacacbacccaaccacacabcccaaaccbcabcbcabcbccacbacaaccbbaaabbcabaaaabbccbbaabbcaacaaabccbcabcabbcaacbaabcbbcbccbcabcacbcbccccbbcbcacbbcaabacabbbaacabaaacabccacbbcbcbacbabbbcccababccccbaccacccbccbabbcccbabaaaacccbaaabbccccaabaacbcbbacabbbabacaabbacbaabcbabbbcbbbbacaacabbbabbccbccbbccbabcabbcbacabaabcacaacaabacaababbccabaababbcaacaaabaccaacbcbbacaabccaacbabbbacbcababcbccaccaaabcaacaaaccccaabaaabcaacabbbcaccaaacbcabacccbbabccabbbcabacbbbccbcacaccccabccbbbbbbbccccabccaccbccaaacabaacbaaccabaacbcccccccbbbbcbaccbcbccabbaababbcabbbabccbacbbbbaacaabcbbbbacbccacbbcbccccaabbcabbaccaaaacaccbbcaccacacaabccbcabcaccbcbaaabccbcbcaaaccaaccbbccbcbbcbaabcbbcabcabcbbbccaabbacbbabcabcbaccaacbcbabaccbbaccbaccacbbbcacbcaababcccaababaaaaccaaaacbcaabbabcacbaaacbbbbaababcccbbaabcbcabacabbabaabaccaaccaccaaacccabacbbcbbcbacbbcbaabcbbbabacbabacbcacccaabacbcaccbbcabbbabbbcacbcabababbabbcacaabcbacbbacccbbbbabcbbcabcbabccccbbacbcbacaaacbccbbcbbbaaaaaacbcacccbacbbbcabcaacbcabccaaabccaabbabccbaccbaacbbacbabcaacababccabccabcbbcbabacccabbbacccccaabcacabbcabcbccacabbbababccacccbbccbacbcacbbcccabacbbbabbaabbacacaabacbccacabaaacbabccaccbaccaaababbcbabbcbcccaabcaabbbccbcabbccaabbacbccacabbaccbbccabbacaaaacaaaaabcbcbccaaabaaccababacaaaabcabccbbacaabbcacbcacbabacbababcbacabbcaaacacccccacbaabcbabbcaccbabcaacbbbabcacabacaaabbbccbabbcaaaabccbbbcacaacccaccbbcabcbbaacbacacababbcbbabbbcbbabccacccccbcccaaaabbcbbbbcaccaabaabccacaabcabbaaaabbccccbaccccccbcacbaacbcacaaabcaaccacaabbcbcaaabacabbbacbabcacaccaaacabaaababbaaccbbaaaabbbccbaabbcabacaabbbcbbaaccbacababcbabacccccbabaaccabcbaacaacccacbcbccbcbbccaccaccbacbcacabbaaaacbcabaaacccbaaccccbcabbacbcccccbbcaaccccbcbbccbaaacbacaccbbabccccacbccaacbabccbacbabbaabaabbccaccbcbacbcbabaacabcbabbcbcbcbaccbacccbaaacbaccbcbaacbaccabaacbcbaabbaacaccabbbbcbccbbabbbcabacbcbbabcaabbcbbabbbcabbaacaacacabbcbbbbabacabcacbaacabacbbacbaacbabcbcbcbaabbcaacbaccabcbbabbbbbacabbbcbcbbacaaaacbcabccbaaaacabccbcaacacbaacbabacbabbbcacccbcbaaccbbbcbcbbabccaccaaabacbccaabbbcacbcbbbbacbbbabccbbbabcbccbccccacbabcbccbbbbaccccccabbacbbbacbaaaacaacaacbcabaabaccbbaaaccacbccbbcbcaaacbcbbabbbbccbbccaaccbbccbcaccbabacabbbcbcbcaacababcababbbabbbcabacaabbaccaabbcaaaaacbabbbaaacacbabacaaaababcacabcaaaabcccaacccccaccabaaaabaabacabcaabcbbccaccccccccaacbabccbaacbabbcabcacaacbbbccccabacabaababcaaccccaacbcabcabbbcacbccbcbaaccaacbbcbbcbccabbccaabacbacbbcbaaaacaaccaaacbaaabbacabcabacbbacaccccbabbbaabababbccbcacbaacbaacaccbbbacbcbacbbbbccccaabcbcbbcacbaaabbccbcaababbabacccccccbcbbbacaacaccbaaaccbbaacabcacccbcabaacbccacbbbbabccbbccbabbbcacacccababccbbbabbcbaacabaacbccaccbaaccacacbcacababacabcaababcbbcbabbababbbcccaaacabacacbabaacccaccbabbcccaacbccaacabcabaabcbbaaccaabccbcbbbbcbbbcbcccacbccabcbabacbcbacbcacbcabcbabcbbcbbcbaccabccacccacbaacbcbcabbababbccbaccbcbbaabcbababcbabcacbbaaaaccabccaabaccccbaacaabaccabcbccabbcccabcacabcbabbcbcbccaaabbabbabbbccbccababbcbbaaabaaaabbaacbacaaabaccabbcbbcbabccacbaaabcbbaaaccbabaaacabbccacbacbbbaaabbabaacbbbabacaacaacbcacabcbcaccaaabccbbacbaccbccacbbbcabaaacccacacabcccbccccbbabbbaccccbcacbcabcacaccabcaabbcacccbabcacacccabcbbcaaaacbbacbaaabccccbbbcaabbbbcaabccccacacaacbbcababcbababcacabccccacabaabbabbbbacbaccbcaabcaaccbbaaacabbabcacababbbaabacabbaabccbbbaaccbcabcaacbbcaccabcaaabbaccaacbabccacbcbbcaacabbabaaacabcbbabbccccbccacccbccacbcbabbaabcccbcaabbbcbbcabbcbcabaaabcbbbaccabacbbbbabcbbcbcaabccabbcababaabccbaaaabaacbbbacbccbaacbabcabccbacaaabbaabbabcacccbacaacacbbcabbacaacbcbcacbbacbbbccbbbaabbaccbaabacaaaabbbbcbcacacccccccbccaacccbbabbbcbaccbbcabbbcbbaccacbaacbbacaaccabcbcaccacbbccccabaaabbbacbbacbbbccababbbacbcabaccaccacabbbaccaacaabbcbbbabccacbcabcbcbcbbaaccabbababacccacabbbbbccbcaabcacbcaabaabccbbcacabaccabccaccaabababbcbbcabbbcaacccbbabbcabacaabccaacbccbaaabccbbcbcbbaacbabbbacbcbbccbcbabbcaaaaabbcacccccbbbcbbacabcccbaacacbabbaabcccbaaccabbbcbcaccbccaaabaabbaacabaabbcaaabbcbbaacabaabacbbbcabacbccbcbbcacacbbacbcccabbcacbbaabaacabcaabbbacbaabcccbabcabbccaccaabcacbacbbabbbaccaaaaccacbaccbbabcbccbacaccacaccccbcbbbabaccaccbcaccbbacbccaccababbbaacbabcaaaabccbbccabacacaccaabccacaaabaaaabcbacabaabbccbabbbabbbbcbbabaccacacbbcabaaaccacaaccaaaabbccbcaccababbcccbabbacbbccccccacabbcaaaaccbccbbbbccaabbabacaccbbbaaaabbcaaccbcaaccabbaabbaaccaabbaaccabbbbbcabbacccbcacabbabaaccbacaccccbbcbcbbcacbcabbaccabcbbaacbbabbababcabbcacbaacaababbaacbcbcbcbbaacaacacabbcacbccacccacaabacbaacaaccaaaaabcacabcbccbcbbcbbaccaaccbbaabcaacaabbababbcbabaaccaababcbcaacbacbbcaaccaaaccaaccacbcabbbaaababcbabbaaccbaaabbbaabbbaacccaaaaaacccccaccabbaabacbbbbacccaacbcaabccbbbaaaaabbabacccacbcacabcccccbcaaccaabcbccbccaaabcaacaabacaccbababccaabaabbcaacbbaacabbcacbcaababaabbacccbcabacccbcacbaaccacbbaaabbbcbccbacbccccabbabbcabcbcacacbcaacabcbbcabbacaabcaacabaccacabcacbccbabbbcbcbcabaacabacabcbccabbccacbabcbcabcbabbcbbaccbcbabcbbaccbabcbababaabccbccacacaccbcccbcbacaabaacabacaaacbcbcccbbbbaaacabcbaaacaabccccbacaaabbcbabbbacccbaababbacbbbaccbbbbbbbccaaabaabaccbaabcbcccaaccbcbcccccbbcbbbcabacbcaaabcbbabaabacabbbccbabaaabbbacaacbcccabbbccaaccbbbccaababcccbbccaaabcbabccabbacbcbcbbacacccabccccabbbccccaabcabbbbcacabbcaaabcbaccbbcbcbbcbcccbbbcccbcaccbcacabbbabcbcaaabcbccaabaaccccbabaabccbaaaccbccbccbccbcabbccbabcbacacbbbaccabbaccaaabccccbbaacbcacacabaaaacbcccacbcbccacbabcccbcabbaacbbaccbaacacacccbaaaabbcbbaacbaaccbbccbabbbbbbbbacbbbacbcbcbacbcabbcaaacacbcccaabacccbcbabcbaccaaabbabccacbaacaaccacaccacccccabcaacccccacabacbbcaccabcbbabbabcaacccabbacaacbcbabacabaaaaacbcaccbcaacaacaaabaaabbababbbbbccabaabacacabcabacabcaabcacbaacbabbbcabcaaaccaccbaabcbcbbccabcaaacbaabccacaabcabcaacbaacbaabbabcacaabcbcacaacbbabcbacabcbcccabbbcacbabcbcccbabbaacacbacccbabaaaaacbabccbbacbbbacbcbacbcaabbbabaababcabcccababcbacccacbccaacaabbaaaccacacbccbacccabbcbbbcbccbaabbbccacbbbbabcbcbacbbabbaabcabbabcacbbbacaabcaacccacabbacaabcabbbacbbacacccbabcbabcaacaaccbcabbaacbacbccaaaccbcbbabaccaccbababbcaaabacaaacaccbcbcbcaaabbabaaccbbbabaaccaacbbaabacccbbccbcabbabccbbccbcbccccabcabacabcbacababbccbaacccabcacbcbbbcabbaaccbaccbaabcaaabacccabaaaaaabbabcacbacacabaacacaaacacabbbcbcbbbacaaccbaaacaccbcbcacbbcabaabccaaabbbbacbcbacbbbcbaacbabcaccbbabcbccacbacacbcababbccacbbabaababccacbccbaaccbaaaccbaababccaacccabbbbbaaacbbaaccbaaaccaccbcbabacccaccbbbacbcaccccbcbbaccacacbcaaaababbcaacbbbcbcaabbcbccacbccccbbbabbcacabacbbcabaacacacbbbcbbcccbabcbcabccabacccaaacbaaccbbaacbbacacbbccaabaccacbbbaacabaacbcabacbbbcbcabcabbbcccbcbcaabacabbbcbaabbababcbbcbabaabaccacbababababcabacabbbbacbbbacbbcabcaccbabacacbcacacbcbbcbcbabcbabaccbaccaabbbcbaccbcaaaccabccacccbacbcaaaababacababcaaaabcccccbccbcaabaaaacbbcbcabcaaacccacbbbbbbbbcaaaabbbabcacbacacabcbbcabaaaacbccbaaaabaaaaacccacbccbbcbcacababbaacccaaccaaacccbcccbaacbbbabaacaaabccacabbabbbabbacbaccbbcabccccabbabacaabcabbccacbcbbabbaabcbaabacaabaaabbcbbbcaccbbabbbbabccbcbaabaabbccbbabcbbcccabcbbabacbccabbcabaaaaaaccabacbcbcabbcbbbcabccaaaacbababcacacbacbbcababababacabcaacacbbcacabcaccbbacbbbbccbababbaaaaccbaacababbaacbacbcccbaaaacaabbccabaccbcbcbccbaaabaabcabbbaacacabbbcbacababbbabcbbcbacaccbacabccbcbaacaabbbcccbaababcabbcbcaabbbbaaaacacbaabacacbbbaccbcbbcaabbaaccbabbcccabacaabccacabcabaabbaaccbacbbcababbbbbabaacaaaccabcbbabbaabccaaabbcccbaabbcbbcccacbbcabbbacaabbcccbabccaacababbcbabcccccabcabbccbcbabcbbbaacabbaabcccbbaabccbabccbbacaacccbaaccabbbacbbcaccbbababcbbbbacbacaaccbacbaccaaacbbcabcaaccaccbccbaaaaabbaaacbcbbcccbccbbbccaaaaaabcbcbbccbbcacbbabcbcbcaababacaccacbaccabacbaacbacaabbbaabcbcaaaaabbccccacacabbcacbaaaccabaaacccacccbcccaaaabbabbaaacccaabcaaccbcaacbacacaacccbbbbabaaacaacbcbcbbbbaabbcccbbacbababbabccaacbbacbbcaacaaacabacbbcbcbabbbaabbbcbacccbbbbabbabbaccbababcaaabcbbbcccbbcbcacbbccbccbaacaccaccabaabcabcbbaacaaaccccccbabccbbcbbbbbccaabbbaaacacbcbcaaaaaabaacabcabaaabbbcbaccabaabbaccacabbbbaacbcbbcaacbbbcababbcbbaaccccaccbaaaaacbabaccbcbccabacabbcbbcaacaccaccbaccaaacbcacccaaccbaacacbabcbaabbbcabbccaabbbabcbccabbccbbaaabcbcccacacaaaacbaccacabacbbbccbcbabccaabbabccbcabbcbcbbcbbbbcacccbccccabacccbcbbbaaacacaaccbabbccaacccbccababcccaacabccbacbaabcccbccbaaccbabaccacccaabbbbbaabbbbcbaaccaabbbcaaaaacaaabcbcbbabbbacabcaabaabaaaccacbccbabaaabaabaabbacabaacbaccbbccaabccbcacbcacaabbcaabccbcccbcbacccbbabcbbabacccbcaabaabcacccaccbbabcabccaabbbbcaabbbbcbccbcacbcbaabbbabbcccccbbbaaccabbbcaccaacbbaabaaabbbbbcbccaabcccbbabbbccccbbcabaabbcbbbccabacbccbabbabbcbabababbbacacabbabcccbccbaacabaabaccbababcacacbcbcabbccbbabcacbcabaaabbbacbbbbaaababcbcaacbaaabaabbbcabcaabbacbcacbcabacaabbbccbaaaccabbacbcccccbbacccaacacaabcabcacabbcabbbcccabccbabbcccaabcabacbacaaabbcbcababbcacaacbbaabababbbaabaababcccaabaccabbcbcbcaaaccccaccccbcbabbbaacbbbbbbaabbabbaccbacbbcabccaaccbcccbabcbababcaacbbbcabbabcbbabcacbcababababbbbbacbbbbccbaccabcacbcabaccbcabaabbbaccabacbaacbbbbaaabbcbcbbacbbcbcbabaccbbbccccaaaaaabcbbabacaaacabcacacaaacaabcccaaacaacaacaabbacccbbcbaccaaccacaaaaccacbccbbccbccaaacacbcacacccbaacaabacabaccacbcacbabacacbcacaabcbaccbccaabcbcbcbbbccbaabcbcbcccbccababaabccaabbaacaccbcbabcaabbbcbaacccbbacabaaabcbccccbacbacacbbaacaaacabaaaaccababbabbcccbcbbacacaabbcbbcabbcbbcbbbcabcaacbcbbbcacbcbcbbaabbcbaccaccbabcaabaabaabccacbbcbcacbbcabbababbbacbbccacbcbbbcbacbbbcbbcbcbcacbbccbcbacaaabbcbbcabbbccbccabbcabcccaabbbacacbbccabccbaaccbbbaacbcccbccaacabbbcaacccbaacaacbbaccacbbbbacabcbaaababbabcbaaccaabbaccbccabbcabccbbacbcccacacbaaaacbbccaabaaacacaabbabcccbabacaaaaccbcbcabcbbcbcbaaacbccccaaacbacbcccbaaaabaccbacbccaccbcbcaababcbabbcaaacaacccbbaaabcbbaaccccacabbccabbbbaccacbabcacaccacbabbcbabbabcccbacccbabccaababaccbccbacbabcbabaaccccabcacabbbbaaaaaaacccaababcaacacaacbcbabbbbabccaaaaacabccbacbaccbccbbccacbbcababcabcbbcababcbbcccbbcccbcccabccaaaaaabbacacbbabbabccacaabcccccbcbcacaacaaccccbabbabcaccabccabbbbbbcbcbaccacabccbcbabcbaaacbcabacabacaccaacabacbacbbbbbbbcbcabcccbabbacbabcabcaaaaacbcccbbcbcacaaaabbbaacaaaaaabaabababcacbbccccbacaacabcbbbcabcbbcabacbbccaccbabababaacbcbbaabbbababbbccacacacabbcaabbbcbcbabbcaabbcbbbbbbcbccacbcbcabaccbcbcbacaaabaabbaccbcabbbcabcbbcaccbbbbaaaccbabacccbaaabcbcccbcbccaacacbccccbcbcccbcacccabcbaabaccacbbcacaaabbacbcabcbcbcabcbcbacbaacbabbbbcbcabbaccaabbaccacbbaccbbaabcacabacbbbacbcbbcaacbccbbcccccaacbaaaabbabaababccccccbaacabbabbcbababbbbcccbbbccaabccbbcbbacbcbaccaabacabcbcbbcbccbaabbcbcbbbbacbacbabaacabaccbccbabcbcbacbbbcabcaaaaabbabaaaacacbbacacabbcabbaabaacbbbccbabacbbcaaababbcbbacaacbaacabcccbabcccaacccbbcccbbbaaaabaabababccaaacccaaaabacaabacabbbcbbcacbbcababbcbcccccbacbcabaabbcabcacbaabcbabccbbcbacbbabbbaacccbbbccaabbcaacbcbbbbcabbaaabacabcbcbbbbbbbbccaaaaacbbcccabaacaaacaaaccaaabccbbbcbacccabaababbabbcccbaacaacaabbabbaacbcacccbaccbbbaccbaaacaaccababbbcabaaccabcccacaaaccaccbaabababaabcbcababbbbbbabcaabccbccccbacbcacaacbcbaababbabccacaccbccabcaccccaababccacaabaccbbbccbbaabbcaacaacccccbcbcccccccbcabcbaacccabcacccaacabacacccacbabcaabccbaaaaccaccacbabaccaabaabbcccbbbbbacbabcbccaccbbaacbbabcacacbcccbcccaccabcaabbbbbbcbcbbabababccccbacccacbacbcaaacaabacbcacaabbaacbcaaccbcaabcbaccaabcaccccbbaabbcccbaccacbacaacbacabcbbcaaacabacbaabcbacbabacacccbcccbccbcccaacbabbbbbacacbccbcaabcbbcbbcbaabbbcbbbacbcacccbaccccccbaaccaccacacbbcaacaacbacacccccccaabbbcacacbbbccacabccacaabaaccacccbabbbbbccbcbbbbbbabbacabbcabbaabbbccbacbaaacbbbbabaaabaaaccccacaabaccabbabbacbacaaaaccccccacabcaaacbbcbccaacbbcbbcaacacbccbccaabccacbcbbcacbcbbbbbcccbcbacabbbcccabcaabbccbaccbaaaccbaccabacccabaaaccaacbacabbbcbbbaacaaacbccaacbbbcbaacccabbaaabbabcababababbbaacbaaaabaacabbbbccabbaacbcbbaaacaabccbccbbcccacbabbbcccbbaacbbcbabcaaabccabaaabaabaabcabccbccabbbaabababbbabbbbbacbabbbbcabbacbaccabbbbbbacbaaacaaacbbccbccbcacabbabbbaacaccccaacabbbacacaccbccbcaabbaccbccbbbcbbcacbbacbacccbaabbaaccbcccacccccccacccbbacbccbcaaacbcbcacbacababbacbbaacbcabbccacaccccbabcbcabaaccabcacccbbcaccbbaccbbcabcccbbbabcbbcccbcacabaabaccbaaabaabcbbacbaabbcacbaaaaccacaaacbabcbcbbbbcacababacbbbbabbbabaabacbabcbbbbbcabacbcccbcbacacaabbcbbcccbbabaaccbcbbabcbbbbbaacabbbbabbbcaaaabacabbabaacaaaabbbaacbccabbababcabaacbcaacababbabbcacbcaabbbbabcabbbcbcabcaccbcccbbcbabccbabcaaaabbbccacbcbbababcabbaccaababcbcbbccacccbcabccbcabcccaabcbbaaabaabbabaacaacccabbaaabcaabbbaaacbacacababcbbcbaaabaabbcaaacabbacbbaaaccacabbabacbbccbbbaaaaabbaccabcacccaacacbabcbabaabbcaaaacacaccbccaaaaaacbabcbaabcbbcccbabacaabcaaaaaabbabbbcbcaaabbbabbabacacbbbababbccbcbaaabcccbccbabbbaacbbbacbcaabcababaacbcbccbbbbaaacbbabccababbaabccccabaaabcaccaccaaacbbaccbaccbbacacbccccbaaccbcbabbbaaabaacabbccbcacbcccbcbaacacacababaaaababacbbcaaaccbabcbbbccccaacbccccabacaccbcacbaabacaaabbbbcbaccacbbbbbbabbbbcabbbacbbcacabbabacbbcbaccababbcccbbabbbccccaccccbbacacbaaabbccabcababacbbbbcbaabbacbcbabbaaacbbabcabbaabcabbccbbabbbacbbabbcbcccabcaacaacbcbbbbbacbcbcbcccaaccbaacaaacbbcccaaaaccacbbaaccbcbccabcabacacbbaccacabaaaabaaaacbcacbacaaaaaaaaabcabacacbbcaaaacbbabbccbcccacbbbaabcbbacaccabcaaaabbaacacacaabaacccbcabacabacbbccaacacaaabbaccbabbccabacbaacabbaccacaacccabaaaabacbabbacccccbccbabcbcbacaaabcabbababbabacbabbcbaccccbcbbababcbccaacaccaccaaaaacabccccbcbabbcbcaccaabccbaccbcabbccccbaccccaaacbaccabcaabbabababbbaaccabbccacbcaababaaccbaaabaccbccbabbbabccccbbcbbacbaccbbcacbcbcbbbbaccccabacacbbcaccbcaacbcccbbcaaabbabbcabcccabbbacacccccbccaaacacbccbbccacbaabbbbbcaabcaacabbccbabbbcacabbbcccbcaaabaabbbccaccbccbccbbbcabaaaabcccbbaaaaacabcbcacbbacbcabcccabacbcabaaaaabbccccaccaabacabbacbaccccbbccccbacbabbbbcccacbcababaccbacbcccacccbbacacbcbbabababccbcacbbaabcabacbabaccccacbcacbccccbbacabccacbbcaaabcabcacbcccbcabcacbaabcaacccaaaaacabbcabcacaccabbcbcbabccbbbcbbcaacbcaccabbbcbbbbcacaaabbbcaaabaacbcbbaacacbbbcbcabacccabbaababccbbbbaccbcbbbbcaacbcaccbcabbabcccabbbaabaccaabbcaaaaccaaccbccacaacccaabcbcaacbccacaaaabbccbccccccccbcccaccbacacababcaccbcbcababccbbbccbbbbbabcabbccccbaababcabaccbaababccbaabacaacaabbcbbcaabacbaaccaabcbabbcbcbbccbcbabaabcaabaabbccccbabacbcabcbabbcbbaacbacbbaaacabbbacccabbbaacabbbaabbbcbaaaabcacacbcbbaabcccbcbcacbaabbabacabacbaacabcaacaabcbbcbbccbbcabaabccaacccababbaccbaaaaabcaccbabaaacbcacacaaabaaabcabbaacacbccbaabaccacbbabaaababcabccaababcabccaabcbababbccbabbacaacacbacaacbaababcabcaacccbaacbccbccabccbbcaaccccccabcbacbacabcaccbabacbbbccccbcccacaacbbbbabcccbaacbbcbcbbbabcacbcbcabcbcbbbccaaaabccbacababacbacccabccababbbbabaabcbbacabcaaacabbcccccbbcbcabaaacbabbabbacbbcacbbcccaaaaccabbacbbcccaabbbccabcacacbacaaacccccaacaabbbaccaacbbaaacbbbcbaccabacaccccaaaacabcbbbcbcbcaabacbbbcacaaccbbbcbbabbccababcababbabaaacaabaacabbcbcaacacabaabacaababbaccbaacbcaabcabbaabccbbbabbcababaaaaabbaaccbbccacabbacbabcbbaaaabcbcabcbacbbbcbacbabbccabacacaabcabcbcbaacbbabacbaccbcbcbaaaacbabbacbaccbbacccabababbbaabcacacbaccbbccaacccbbacbaabbaabbbabbacbcbbbcbaabcbbacbcbcbbbbccbbcccccbbabcbabcbcabbabbccbbcacbcbbccacaccaabcbccabbaabbacccababcaaacccccbcbcbacacaabcaacacbcacbbacbccbbccaccacacbccaacbacabbbabacabaccbbcbcccccbabaabcaacccabaaccccccaacaabbbaccacaacacabcabbbaccabccbabaaacacccaaabbabbcbbabbcccaccbbbccabacbcbcacaaababaccabcbbaabbbccbbcaaaabaaacacbacabcaabcaaaacbccbabccbbbaccbacccbcabacccacacbabbbbcccbcbaaabcccababcacaababbbcbbaaaacaacbcacacacaccaababababaaccccccabcabacbbcaaccacbaaccbacccabccaccaabbaabbbaaccbaacaacbbaaaaccbccaabcaaacbcaacabacaaabbcbaccabbbcabbbaabaacabbbabaacbabcbcaacbacbccabccbbbacaccbbaccbcbaaaacbacbccabccbabacaacacacacacaacccaccabbacaacaacaabbbbcbccaccbbbaccbaaaaacbabcaacbcbababbbcbbcbaabbcaacbcbcbcacabccacbacbbbabcbaacacabbbabcaccccccacbaabaacacaacabaaacbabcbbbacababcaacbccbbabbaaaacccaccaacaabbaaaacbacabacaaabbbcccaabacaacbabbbbcaabaaacbacbcbcacbbaccccaccabacccaaabbbbaabbbccbacbacabbcacccaaabaacbbbbcbaabcccbccabbcccababbcaaccaaabacbbccabacbbaababcbacbcacbbabbccabbabbaaabcbbaaaabaaacacbaaacaaaabacbacbabbcbbbabacacbccabbbcbcccaccbacbcbcbaabcbbcbcaaabcabbbabaaaabcabcbccacbabbcbacaabbabcabcccbabccbabcaacacabaacbacbbabaaacbcaaaccacbccaaaaccbbcbbbaacaabbcaacabaacaccacbbacaabbcabcabcbccccbabbcbcbaccccaccacccabcabcbcccbaccbacabcabccbcabbcbbbaccccaacacabccbccbcabbcccacabacccabbccabccbcbbabaccccacbabbcabacbbababcacbcabbaaabbbcaabbacbccacbcaaacaaacacabbcbbcacaaacccccbbbaabccbbaacbcbbbccacbcbcbacccccabcccabcbaccaabbbbaaabbabccbbbcbbaccaaacacccbacacaaacbacacbbccbbbbbabaaaacaacaabaaacbbbabcbbbccccaaaacccbcaabbababbbccabbcbcabbacccccabababcbbaaabbaabbcabcbababababcbabccaabcababacbcaaacbabaababcacbbbbcccbacaacacccabcbbaccabbbabaacbaaacccbbabbbabcccbbcaaccacaabbcbacacbaccbaaaaaacbcaabcbabababccabccbcccacbaaacabaccbccaccacabbacabbcbabbacbacbbaccbcaccbccbccbaacacbbbbabbcbccbaabacaabcbabbbbbbbacbaaaccbaaaabbcababbbbaabbcacaacaabaacbabcbcbaaaccccabaaaacbaacbbcccaabccbbbbabbcacccbacbcbaaaabbaccccacbacccacbccbbbaaaacccaacbacaacbcccabacacbcaababbbabbbabcccacbcbbaaacbcabbbacbbcbbbcababcbbcccaccccabbcaaccccbcbababbccbabaaccbbbbbcaacbcbabcbbbabcaabccbbbcabcabaacacbacbbaabbcccacbbbabbcabcaaaabccaaaabbcabaaababbcbbcabacacabcacbaaabcacccbbcbabcaacbcccbaaccbcccbbccbbbacbbbabcaccbaccbcaaccaabbccaaacccaaccbabcacbaabaabbaacabccbcbbccaaabbbccacabcacbcbbaacbcaaaaaabbbaabbacabbababbbaccccccacacacccccaababbaaacacccababacbcabacbbcbbcaaaacbbbaabcbaabbabcbaccbcbbccbaaacabbabccabbcbbccbccaaccbaccbabcbcbbcaacccbbabbcbbabbaccccaabacbccabbbcccbbabcacbbbbcbbcabbcababaabbbccccaaaacacbbbbabaabbbccbcabcccbaaaaccbccbccacbbaaabacbaaabcbbaccabbccabcbccababcccabbaabaaaccabbbbcbcbabbabbbbbaaaccabcaaaaacabbccabbccaccbcabaabacaaacabbabbcabbaaabbabaccbabaaacbabcbacbbacbaaaccbccbacababbcaabccbcabbbaaccbcacccacbaaaccbaaccbcabbababbbbbaabcacaccacbbaaaaabcbbcaaabcacbbccabbbbcabbbbbbccbbcccabaababbaaabbbaaccabccbacbcacccccbacacabcbaaaacaccccaaacbacbcabcababaabcbaccabaaaccbbacababccbaaccbcccbbbcaacaccbbabbbbabacaaaacccabbcaabaaccabacbcbacaaaabccabcbbbacbaabcbcacabacaababccbabcbacccaccaacbccacacbacacbbcaacbcbcacbccbbcaaaacbcaccbbccccbaccbbcbabbacbabccbbcbcbaabcccbbbcaaacabacaccaaacaacabcabaabcacababababbbcabacaabbcbbbabaccccccaacaaaaaacaaabaacbbacacbcbcbcbaccbabccaaaaaccbccbbaccbbbccbaccbcaabbbabaaacbccccbccbbbcabaabaaaccbbcabccaccbcbaacacbccccbaccacccbacbbcaacccaacccaaaababcbbbacccbbaabaaababaaacbbbbbcbcbbbccacaccccccabcbaabaabbccabaaabaabbbccbcacbbbaccccabbbaabbbccabcaacaaacabcccabbcbcbcaacbbcaccababbcbaacbccaabbcacaccacaaacbcccbcabccccabbaaabaacbcaccbbbcacccbabcacccabbbacbacacbccbcccbacaaabcbabaccbabcccbaabbbbcabacbcccbacbacacbbbbbabbaccabaccbacbbccbacbaaacacabbbabbcabccbabacbacaaaaaabbaccbaaaaccbcabcccbcbabbabccabaaaaabbaaacabccacbbccbbacacaacccccccaacaacaabacaccacbacaabbccccbccbcbaabcbbcabcbbcbaaabaaabbacbbaaaabacccbaacaacbaaaccbbcbcbcaaaaaaabbaaabccacbcccbcaacabaabbaccbbaabaaaacabbbbabccbbbcabbaaacbbcaabbacbbbabbbbbbcccbbbacbcbbccccbcccacbacabaaabaaabccbcbbbbbcaccabcbccaabbbccabacacccabacbcaaaacbabccbcaaccabcbaabbaabcbcacacbababcbabacaaaababbbbcaaabbcccbbcabbcabbbcabcabbbacccbacabccccbbaaccbbccbaccbbacbcacaabcbcbcbcccbaabaacabacbcbacbabaccbbcbbbbbaaaabcacccbabcbbbabbcbabaabcabaacaaabbccbacbabcccabcbcbabcaaabaacbabbcbaabbbababbcccacbbbaaabacbcacabbbabaaabbcabcacbcaabccbbcbaaaaccbccbcaacacbbaabbbbabcbcaaabbcacccccbbcaaababbccaabacabbacacbccccacbbacabaaabcaabaccbcabaccbacbacbbabbccccaabcccbbbaabcabbababbabcabcacbcbcacababcbbccbcbcbcaccababbbaabcccacccabbcbaababcacccccaaccabaabbbabbcacbabacbcabbbacaabccababcbcabbcaccaaaaababcacabcabcabaccbccaabcccaaccabcbbabbbabaccbaacabcaacbcaabbbcbaacaaababcccbbabbcbcacacaabaaaabaacccbaabbcaabcacacbaabbabccaacacaacbacbabcbaccbbacccbbcacbbaabcacabaccbcbcccbbcbbbcbccacabaaaacaabaabcbacaacabccbacccbacbabbacbacaacccccabcaabccababcbbacbaaaaacacbaccabacacccbabcbcaccaaaaacbaacaaccaccacaaccbbaccaacbcabcbccabbaccaabacaabbcbaccaccaacabacbbccaccacaaccaccbcaccbcbcaaaccbccbbbbccaabbccccbbabbaccabcbabaaaaabbbaacaacbbccabcaaccabcabacbbcbcbccbacacbbccabacbcbacbbbcaccaabcccabaaabaaabababccbcbbbbbccaccbccbaabbbbcaaacccaacacabbacaacaaaccbbbccbcccacaaababacbcccbacacbccabcbccacabbabacacaaabbacaaccbacccbbcbbbcccabbbccaacbaccccbaabbcabcabcbbabbccaaacccabccacacaabaaaabbbaacbbacccbccabcabbabaccbbbccacbacbbabbbabaacbcccababccabbcbbbbcbabbcbccbcacbcbbaabaccccbcbbbccabbaabccbaacbcabcabbabcbcaacbccbaccbbaabcabcabbbbacbcacbacabcabbcbbaaabacaaccaacababbacccabbcbbcbbaaaaacaacbaacacbbbbccccaacbccabaacaaabcabaaccccaabacccccbabaaaabbbacbbbaaacbacbcabbccccccacbccbcabbbaccacbcaabaaaaaacbcbbabccbbcacacbcbcbacabbaccacbaabaaabcbcccbacbcbabababbcbacaaabbaabbaabbaccbcbcbccbcbcbaccaccbbccababacbbcbabbbbbbccbccabccacbcbcccabbbbcabbcacbbaacaaabccbbaabbbbcccacaabcccccccaccaaccaccacccbcbaaacbacbcbabccbcbacabbaccbbcaacaaccacbbcaccacbaabacbbbbccbccbbcaaabbaccacabcccabcaaaacabbbccabaacbcacaabbaaaccccbbbcbabbbccccaabcbaaacbccaccccacabbaaacabbbcbbbbaaacbaacaaaccaacbbcababcbbacccaccbbcabbbababbaabcbababcaabcaacbabbacccabacabbbbcccabaaccccbaccccaaacbbbaaaacccbabccabbccbbaababcbcccacbbaabbcbbcccbcccaabbaacbacbcabcaacbbccaaabbbbaabcbcbacacabbcaabcabbcccbcabcccbacccbccabacbaabacbcaaaabcbaaaacacbccaaaacbbccabababcabcbcabaaccbcbabbccccccababaababbbabbcbccccbccbaccaaaacababcbbbacbbbacbcccbbaabcaacbcbaaaaaabaaccabbccccabaabbcbacbaacbbacabccaabacabcabcccabacacaacbaacacbabcabbbbbbacbabacbbcaabaabacbaaacabaacaaaaacaccbcbcbcacbabcbcacbbccaabaacccaaaaabcabcbbbbacaccbccabacaaaacbcbcbcccbcccbaccbaccbbbbabbacababcccabcabcbbbcaaabaabccbbbccbcabaabbabbbbcbcbacaacacabbcbaccbbbaacbbbbcbaccbbcaacbcbacabcacaacbcccbccacbccbbcbbbcccabcbbbcaaaacbbbabccbaaccabbabbbbaaacbacbcabbbabaacaaabcabbcabbbcbcbbbbbccbbcaacbcaabcbaccbaaaacabbabbaabbbcacabbbabccaacaaabbbccbaababbbabababacabbabccbbcacaabbacaacbaababcacbaccbabccabbccccbcaaaaabacbcaccacccbbabbacbbbcaabcaccbacccbabbacacbabcbbbccacbccbabccbacaaabaccbacbacaaccaabcaaccacaabaacbbcbbbbacbbbaaacbbcbbbbcbccbaaccaaccaabacbaabccbacbccbccaacbbbbbbabababbacccbbabaabbaacbbcacacaabcbcbabbaabbccbbbcabcccabcbbccbacaaabbbbbaccbaaccbcaacabccbbaaaaaaabbabaaababbaabbcbbaabbcbaabbbbbccaaaacbaaaaaccacabccbbaacabbccbccacabcbccacabaabaacbbacbabcbaaacbbcacaaacacbaaabaacbcaccacbbcaabbaaccbccbcaabbaaabacbbcbccbaaaacacccbbaccacacbccacbbabbbabbabacbacbaaccbaaaabbcabacbacccbabbcaccabbbbcabccabcccbabbaabacbbbccbccacaacbacabcaacbabcacacbaabbacbbcbbccbaabaacabbcbbcbacbabbccbccacaccacacaccbbabcbabcbbcccaaaabbbbaabbbbbaaabaacacacbaaaaabcacbcaacbcbcccbbbcbcbacbccaabbbccbacabaabbbabbbaacabcbbaacaabcbcabbccacbbccbaacbaaccbbbaacabccabbbabcabbaaccaabcbcaacbccacccbcbbcaacbbbcbbcaacbbaacbbababbbbaaaccccbcbcbcabcbcbcacaababcbaccaabacbcacccabcbcaacaacbcbcbaccccaccaacccccccbcabcacbabbccacacbbcccbccbbbbbbccabcacababcbbacbaacacbbcccaaccacbbcbabbbacbcacbaababbcabcbcaabacabccbbbccbbbcaaabbbbbcccaacabaaaccbbabbabbaccbaabcccbbbcaabacbaaabcbcbbcacccccbabbaacbbccbcbccacaabbcacbcacaabbabbcbcbbaabbbcaaaacbccbbcccbcbcbcabbccabcacbcaacbaacccabaccaaccbcbaaaabcacbcbcbccccacbaabcbbbabacbacaccabbbcbaccabcabcaabcaacbbcabaaaaaabacacababccaabccbcacbbabbbacaaaabaaaaabcabacbccacbccbbccccaabcbacaacccbabbacbbacabccacacabbccbbbcccccccacbbbbbbacacaabcababcbaccccabbacaacbcbaabcaacbabbbcbcbaabaacaacbccacabccbaacbcabbabbbbccaacbcababcaccacbbcaacaacaacbaabbbcbcccabcaacbbaaccbaccbaacaababcccabbbaacacbabbccbbbaabbccacbaacbabacabcccaacababbaccbbabcbbccaaccaaaccccaacbabaabccabccabbcbaccccbcaacbaccbcccccacbbbbbccbbccaacaccbbcabaccbaaccabbcbccbabcacbccbbabccccbacbaccccaaacaabcccbbcbabaccbccbacccabbabccbbcaacaaaaccabcccbaccabbaaacbbbbcbaaccababcabcacccbaccbaaacbaabaabbbbcbbbcacaaacccaaacccbcbaacccacbababcbbaaabcbabbbababcbbbacccccabacabbcacbbacbaaccababcbbcacbcbccabbbccccbbbcabababbccbbabccaccbbacacbcccabbccaabbcccabccaaaaccbaabababbbbcbaababbbccbacbbaacababcbbaacacaabababcacabccbbaccccccacbabbabbbbcabcaacacbcabaccacbbccccbcaccaaacbccbbbccacabbbcabaabccacbabaaabcaacbccaabbabcbaabccbacbaababcacbcaabaabbbbbbcaccbcabbabbbbcbaabbbccbcbccbbabbaaabbccabbbbcaabbcacacabcacbbaaccbacababccaacbaacbbcbcaacbcbaacabaaabacacccbaabcccabbcbcbbbaaaccacaaabbcbbabccaabbaccaaacbabababbcbbcbcacbaccbbbbabbbbcaaaaccabccbababbaaacbbbbbabbaaccbaacacbabcababacaccccbbabbbbcbbabacbbcbbbbaacbaaabccaaacabbcbbaaaabaabbbbcababbabbbbbccbcbbccbbbbcbbabbccccbaaabaccbbbcaaabcabbbbacaccacccabaabbbbbbccacbccacbabbcbbcacbbacbaaccccbaccbcbcccacbabbbbacbbccbbcccacacaacbacbaaaccbbbabcbabcbbacacabababbcccababccbbbabbaaacaccacccbbaaccbcbaabbaaaccaaabbccccaabbaaccacbbacacccbcabcbccabacbbcabccacccbbaacbbcacbacabbaabbbcbcaabcbcaccccccaaaacbbaacbcbbcabcacbbccbccbabbaaccbbabaabaacbbaababcaaaacabcccacaacbaccabbcaacabaaaccaacabcacbcaccaaccbaaccbbbbccbcacacbcacbcabbabcabccabacaaabbbbccaccbcaaaabbbcbbbacbaaabccbaaabbccaaacbbccaaacbbccbbcbcabcaabcbaccaccbbccccccbcbacbbcbbcacbaaacabbcbbbcbbcacbacbcaabcbbabaaaabbcbcbbbabacaabbabbacaabbbaaaaabcacbbaacabcbcccbccabccacccccbacaccbccbabbacababbabaccaaabbaabccaabccccbcabbccacbbbaabbcccbabbccbacabcacabbcccabaaaacbabcabcbaaaccacaccbcacbbbacccaacbcabbbaccbbccbbcabbbabbbbcacbabbcaabbbcbccbbbacacaacccccbcaabbaababcacbbbbbbaccbbbaacbbacaaacabccbabbcccbabcbcbccaaccbbaaaabcbbcccbcbbbcbccabbacacbaaaaacaaacabcbbbcacccabccbabcbbbcbcbbaaaaacbaccabccbaaaabccccbabaaacacccccbcbccabacbcabcaabbcaababbaaccbcbaaccbbaacabacccbcbcccabbaacbaacccaabbbcccbbbaccaaccccbbbcbcabacbbaaabbccababcacabaabbbcacabbbbbcbbbccaacbccccbbcaacbbcaaabcccaccbcababaaabacbbcacaaacabcbcbbbbcbaaccbcbccabaaccbbbbbcabcacabcbaacbcbcabaccccbbbcacabaabbbbcaacbbcaaacacbcbbcaacaaabbaacbbacbbabababcabbccaccbbacabbcaaacaccccabbbbbccbcbaaccbabcabaabccbaabccaaacaacacbabcaaaacbcbbacbbaaaabacbccccabccbaccaacbcccaccbaacccccbbabbaabccbbccbaaaabcbbaabcbbabaacacbcabccbcaaccabbbbbbabbbbccbbccbbccacbbaabaccbaacacabaaaaaaaabcacaacbbbcbacacabcababcaaacaacaccaacaabcbcccaacacaccaccbccbabcbcaabcccbabacccacbbbcccccbccccbabccbccabbbcbaaacaabbaacbaacaccabbccabbbcabbaaaccaccbcacbacaabbcbaaacaabbbcaabcabacbcbbcabcaaaccccbabccacbcccbabbbaacbbabbbbbabccaccabaaaaaccbacbabcbaccbbcccbacabbbcbcbbcaaccacaabbaabcbaacbaaacaaaacbbbacbabcaacaacccacacccabcccaabccccaaaaabaccaaabaacaccaacabbbbccbcbbaaabaccbacacbabcbccbbbcabbcbbccbcbaabbabcccbabcccaabacbcccaacccaaaccbbcaccbbbcabacabacacccbbccbcaaaabbaabbbaabcbababacaaaabacabccacaaababbccccccbcabbacaacaacabaacabccbccbaccbabcbaacabbcaabbbbaabaccbcbcaacabbbcbcbaababbccbbcbbaccccbbbbbaccccacacbcaaaabbcbbcccbaabaacabbcabbabbccccabcbcbccbbcbcbabcaaabbbcaacabacccbbbcabaabacacaaabbcbaabcbabccabbbbabbcccccaaacbcbcbaacabcacabccbacbaaabacabcbcbcbbbcaabbacaccbbbccccaacbbbcbccbcbbabbbbccbbbcccabbbcabccbccbabbacbcabccaacaaacbbbbabcaaaaabaacaccaaccbabacbaccaccbacacbbbbaacaccaccccababcacacacabcacabacaaacacabccabccacbcabccacbbacbccbcbaabbcccccbbccccbccabbabcbbabcababbaccbbabbbabacbbbaabcbaabaaacccaaabcacbacbacccaacbbaccacbbabcccacacbbaabcaaaccbbbaabcbbabbbabaabcccaaabbcaaaabccbabcccbcbabcbbabcabccccaacaaccabacabbbbabcabcacacaacaccbcabacbaaccbcaccccacccacabccbacbbbabbbabbbcbcabcccbcaabbccbbaaaacbabccbacaabbbacbaacbbaaabcacabbabcbbbbacbcbbacacacbcbccccbcacabbacabbaaaabbbacbabaabcbbbacbcabbbaaacbbacbcabcababbaabcbbbbcbbaaaccccaccbccaababaabaabaccbabcbbcacaacaacbabbbaabcaaacccaabcbcabbabbcbaccacacbabcccccbcccaacabbbbbacbcacbabcccaabacabcccbbcbbacbbcababaaaabcbcbaabbababbbabcbcbccabaacccacbcbbabaacccacbbabbcbbcaaaabcaaaaabcabbacacabcbaacbbabccbbccbbacbbcccabcababbcabbabacbabbccacbcbcbcabaaaabbabccaacabbacbccccbccbcbabcccbaacbccabcaaaacbccbacacbbbabbbabaabacccababbcbcabcbcaccacbbacaccacaaacccaabcaabacbccaabacccacbcbccaabcbacabaabacacabbbcababbbcbcababccbcaababaabbacaaabacbabbbcabaaabaacaabbbabacbabcbcaccbccbaabcccabacccbbbabbacbbcbcbccaabcbaccabbbcbbabbbaaaabcabcaaaacacbcaacccbbbabcaacaabcabbbbbcaaabcccaabbabaacbcbcccbbbabbcacabccbcaaaabcabbbabbccbbbaaaabaacbbbcbbccbcaccccacbababcbccbbbaacccbcbacbbcabbabbcbaccbcbcacaaaabcbbabaacbbcbababbabcaaaaabacaaaaababcbacccbccaacacbcbccabbacbaacbcbabbcbaaaacabbbabababccbbaabcabcbcaaccccaabcabaacbcaacbbbbbbababbabcacaabbcaaaabcaacbacabcbcacbcccababbacabccabaabcbccaabcbbcbacacbcababcaaccacaccabcbaccbaacbccacacabaacaabcaaccbacccbccbbacbbccaaccbcbababacaaaacaaabbbacbccbbabcbaacbbbbbcababcccbacccbbbabaacabccaccbbcbababcbbaccccbaaccbcbbaaccbaaacabcbbaccaabcccbbabbbabaabcabaaaaaabcccabcaabacababcbbbabcccccccabbccaabcbacacbabbbccccbcbccbbbaccbcbbbcaacabcabacaacaaacbcccabcbcaccbcacabbbbcaacacaacaccbbbbaacccaacbbccbabbaabacbaacacaacbbaaababacacbccbacccbababcabaccbcacaacabccbbcbbccacbaabbabbcbacbbcbacabbcbaacbbbcbbcccbaccacacabbcbbbbaabaccbbcbcaaabaaaccbcbbccbbacbbaabbccbccbabcbbccbabaabcaccaccabaacabcbbbcaaacaaabcaaaccaaaaabccbaabcccbbcaaccaaacbccbbabcbabcbbababbabcbabacbbabcbbbbccccbabbacaacaaaaacacaaccbabcbbbbbabbaaaaacacaaabccaaacabbacabbabbccbbaabcabbabcccaaabbacccbbbcacbaacabcbcbbbcbacccbcaacbbbcbcccbbcbbbbbbbcabbacbbcbcacccbcbacabccabcbacacbcbacccbcaaabbbbcbccbbbbabcaacbcbaccbabbcaaaaaacbcacbcbbcaaababbcbcccbcacabcacacaccbcaabbbccbbcccaabbabbcbbbabaaccbcabbacbcbaaaabcccbcbbbcbbacabbcabbacccacbababcccacccbabbcaababcbbcccbbbbabbabbbaccacaacccbababaaacacbbacbcabacbabbaacccccacbabaaabcacbabbabacaabbcaccccabacacaaacbbacbcbabababcccabbbccaaccabcacabcbcacbbbaaacbaccaaaabcbcaaaacbacbbbcabbaaaaacacacccabbcbcccccbbcaaaabaaababaaccaccabaaccbacacbabaccaaabbaaaaabbbcbaaabcaccaababcabcabcbacbaccbabacbabbacbabccaacccacababbaaacbaacbbbbacccbabbccaaacbcaacabccbababbbaabbccbbacbaccabccbcccbbcbcaccabbcaaccccbbbccacbaacbbabcabbccacbbbcabbbbaccacbacccccabbcabbaababccbbbcababaabaacbcbacaaabbaacaaccabbaccccccbcbcabbcabbbccabbbacbbaaabbaacaccbccbcacacaccbbbcbcbbbbabaacaabbcccababcaaccccbbacabaacabbbacbccbcbaacbccbacbaccbacabbbcacbbccbabbbaabbccaaabaabacabbccbccbbbccaabcbbcbcbbababbbccbbcbabcbabbccbccabacacaccbbccccaacbbbbbaaccbbabcabaccabbcaaccababcbbabaacbbcacbbabaababbaccaaaccbbcbccccbbacaaaabbcccbacabccccacccbcbcbbabccacacccbaaacaccacbaaccbcccbcacbccbcbabaaccbbcbacaacbbccababacaababbccbbbacbbabcccabbccacabcaacabcbbbababbaaabbcbbbaacbcabcbcacbbcbbccacbaaccbbbacbacabcabcaaccabaccaaacbbabccacabbaccbbacccaaaacbcabbcbabbabacbcbbacbaacccabbcaacaacbbbacbabccbbbccaccaaccacaabbbbcacacbbbbccaacbbcbbccacaaaaacccbccabbcbaaabaaccbbacabcaabbbcabacccbccbbabaabacbcccabaababccaabbbcccbaaaaababbcaaaacaabacabcbbbacababcbbccaababbabaacacbcbaacccbbbabbcbbcbbcabacccbcccbacacbcbccacbccaaaacbcabcbcacabbbaccaacbaaccbbcccbacabacacccbbabbacbcccabccacbaaabcbbbcabccaccbcbccbbaccbbcaabaaababacaabaccabaabccbabbcacaabbaabbabbcbabcababbcaabbcacacbaaabaababaaccabbcaccacabacacbcbaabcccbbabcbabcbbcccaacbbaaabcbbacaaaabcbbabbbcbaccaabcccabbabbaacbbbaaaaaaabccccacbaacabbcaccbcbaabacabbcbbaacabbccbbaccbabbbcccaccaabccacbaaccbcacaaabbbbccbcbbcaabacaacaababcbbccbacaabbcbcbbbaabbcaaacacacbcaaaacabcabbbbbbbbbacbbababbcbabbcacbbcabacbacbbbacabccccbcbcbcabbcacacbcaaaacabbaaacbcabaabcacccbcbbabacabbaccccccaabaccabbbabccaacbaabcaccccabbbaaabbbaabacaaabaabaccccbabccbcaccaababcbabbbaccbccbacbaaabcaaabccaabcacccbbaaccbbacccbcbcaabccababccbbaabbbbabaacccbacbbaaaaccbbcbbbbaacbccacbacabcbbbabbbabaccacacaaaabcacccacbbaabbcacbcabbaacaaccbaacccbcccaabaaaaabcbcbbcababcbcabbcabbcbcaacbcbbaccccbbbaccabcabaccabababbbacaaabccabcbccbcccababbcacbbbcaccaaaaaccabbbabcaccccabcbcaccbcbbcaabbbcaaacbacbabaabababcbaccccbacbccaaacabcccabcacccbcbbcacbbbacbaabbbccbaacaaaccabcaabaccaabaaabcbacaabaacbaccaccbabaabbaccbcbaabcbbccaacacabaccccabbabacbcabacbababbcaabccbacaaabababbbbbccabccbccbcaaaccbcbcaaaacabacbabcccbbbcbabcbacacacbbabbcbbaacbbbacbbbbbcacaacbacbccacacbaacabbbcbbccbcababcccbbbbacbbaaccccabacacbababbcbcabcaaabcaacbbbbbcaabaabccbbabacabcbbabacccbbccaaaccbcccbbccbcbcabcaabcabacbbabcaabaabcacccabbabccacbaabbabccbcccacbbabcabbacbbccbabccccbaaaabcaabacabaacacacbcacabacbbcbcbbcbbbbbbbbbcbbbaaaabbababacbccabbacaabaccbaaccbccbcccbaabccbaaccaaabaaacbcaaabcabbaabaacbacaccbcbccaaabaccccbabaacccabacccaccbcccbbacbaccabbabcabaaccbbbbbcabbccbbbbbcabbbbaaabbbbbcbacccaaccabcabcbabaaacacbaccbaccbccbbabaacbaabacbababbbcbbacccabcacbabaacaabcaacacacbacbabcaaccbaaabbbcbbbabcbcccbcacccacbacbbabacaacbccaaaabaaaabbbaabbcacaccbbacbcbcbbaaacaccaabcbaaacbbacccbcbacccbbcacbbbcacacbacbcabcbbaacbbcbaccabccacccbabbbbaabacccaccacacbacaabcccbaaaaacabbbbcccbaaaaccccbcabbcbabbbccbbbbcaccccacaabcaaccaacccbbbccaabbbbbccccbbcbcbcaabcbbcbcbabbabaacbaaccacbcbccbacccaababbbbcaacccacccbacacabbacbabcbaacbcacbccaacbaccabbabbacbcaaccbbbaacacbbcaababbbcbaaaccaacabcabcaaacbcbabcabbbaaaccabbbbcaaabcaccbcccbcbaaaabaabccabbbccbcaaccacbbaccbaacaaacbbbbbbaacaacbaaacabbbbbacaaccccabbcbbacabaacaabaabcbbaacabbbacbbacaaaccbbcabbaaaccbbcaabbbbcccaccbbabaccacccaacbcbcaaaccaaaabbabbbccccbbccccbcaccbcbcbbccbcaccabaacabbcbbbabbcbbccacacbbaacaccabbcacbccbcabcabacbcbbacbcbcccaccbcbcabbabcccaaccabcbababcaaacbabacccaaaabbaacacaaccacabbcbcababaccabbccbbbbacbbaaacababcbbccccbbabbaabacaacccabaabacacbbaabcbbbcbaccaaccabaabcbcccccaaabcaacaabccbbcbcaabcbccaaababccbbacabaacccabaccbbbbbbcabcaccacabaaaaccacacacacaaabaacabcbcaacbcbababcacabcacbbabbbbcbcccacbcaccaabbababbacabbccbabbcccabcacbccbbccaabacacabacbaaccaabaacbbaacbbcaabccbbcacacbcaabbcccaacacbbaabaacacccabbbbaaaacaaabbaacaaabbcbccccacbbababaabcaccabaacababbcacbaababcabcaccccaaacbabbcbbcaacbccccbbacabbaababcbbaabbaacaaaccbaacacbbcaccaacbccccbacabbbaacacaacbabbaacabbbcbbbbbcacbbaccbbbbbcbaababccabbaaabbaabbccabbacccbcaabbccbcbaabcabbcccbbcbabbbaabccabccbcabbbcccabcbabbcacbcbcbbaaaacbaccbcababcccbbcbaaacabcccbcbabacccbbaaaacbcabbccbacbcbcbcbbbcacccccacccabbcccbbcbabcbbcaccbcbbacbcaacaccabbccccbcbcabcacacacbccccbccaabcaccbcaccaabacbccbbccbabcaccbbcacacabacacaaaacaaaaaabaabaacbcabbabaaaaaabbabbabbabaaccccabcccbabcabbacacababacabcabbbcbcabcbbaacaaaccbaccaccaaccbbaabbcaacbcabccaaacbbacbcaacaaabcaaabccaaababacacaccaacbaaacaababaabcbcabcccaacbbacaacaaccbaaccbaacabbabcbbcbbccabbaabcacbcbcccabcbbabbbaacbbbbabcaacaacacccaabccacaaaccccbcabbbcbaabaaccbbbaabababaaabbbcbcacccbcaccccacaacbcacbaabaccbcccbcbacbcabbaababcabbcababaaccbcbbcacbbbaccbacaacbbccbaacacbcacbacbbaccbbcbbbbcabbabbcbabacbbbbabacccbaccccccabbcaccacbaacacbbabbaaaaacbcbbacbaaacacccbcaaababcacabccbacbbaabbbbaabacaaaccacbbabccbcabababbaacacbaaacbcbcbcbbbccaabbaaaaaacabbcbbccaabbbccaabbbbbabaccbcaaacbabcacbacbacbccaaaabcbbccbaabcacbcbbacabccbbabacbcaaaccbcbbbbcabbaaaaaabaaaabbccbcbaabcccccbbbcbacbccacaccabbaaacaaccbabacccaaccccbbacaaccbbbcbacabccbbcbaacccbcbcabacccbcbabbcbabbabcacccacabacccbaabaacabbabacccabcaacacabacbcabacaaabbabacbcaacababacacccbaccbbccacabbbbacbcaabbbcbacbcbbcaaaacbbbcbaccbaacabbcabcaaacacbcbcbcbbccabacbccccbbbcbccbcabcabcbaacbcbabacbcabaccbabbaaaaccacbbabbbbccbabccacbbaabbaaccacabcbabbabbaccbbcbabbabbbacacaabcbbbbcabcaaccababccbcbcbbbcaaabaccacbabcaaacbbbabbbabbacccbacccccccbacccbabbababbacccacbacaccbcbabacaccaacbbccaaabbcbcaabacaccaccbcacccbbbabbabaccbccbcabbbcaabbcbaaabbaaabccbacccacbaacbbcbbacbcaccbabbacacbababcbcabbaccacbbccbbabbbacaabcbbbacccaabccacacaacaacaacbcabaabaaacbcbbbbacaaacccacacccccbaacbccbaaccbbbcabcbaccaabbacaacbaacbabbcabaaabccaaaabccccaaaababbcabababcbcacaacacccbbabbcbabcacbbabcbacacaccbaccaccbaaaacacbbbcccbaabccbbbcabababaaccacababaacbbcacbacbbccaaccbcbccacacccccbccbbaaacbaacbccaacccacaccbacabcbbbcabbbbbbaccbbcacbabbbbbcaacccacbcbccaacabacaabbbabbcacacacbaaaabccaccacaaacaacccaaccaaccbbaabcbacaaaabcbacbcccbbccacbcacccababbaacccbcaabbcabbaabccbccbaacabacccbbacabbcbbaacbcbbcabcacababbcaabbaacaacbcbccabaaaaccbacaccbbabcacbbcbcaccbcabcacababbbaccaaabaabcccacabbcbccccbcaacabcbcacaccbcaaaccbbbcbaaabaabbcabbbbabaacccbccbbcbcbabccbbbabcbacababcabccbacacacabbcbcbaabcaccacacaccaaababbcbaccbbccbbccabbbaccbccabaaabbbccbbaaabcbbbbccbbacbbbbbbccaaabcbacacabbabcbacabcbaabbaccacbcbcbaabcbbccaaabacacbbaabaaaaabcabbaccabcaabbabbbbbbbbbabcacabacbbbaaaabccbbcbcaaaccacbcabcbacbbccbcbbcbcacbcbcacaaabbacbbaaabaacaacccacaabbaccbbbcaaabccaabbcbabacaaaacbcacbbbccaaacbcaccbcbcbbccaacabbabbcbaaaacbbacaacbcbbaaacaaccccabaabbaacacabbbccacabaabccacccaacbcabcbbbcbaccbcbaaaaccaaabaaaaaababcabbcccaccbacabbccbacacbbaccccbabcbcacaaacacbbcbbaababbacaabacccccccaaaccacbccababacbbabbabbaabaccbabcaaababbbccabacaccabbabcbbabbacacacabccccccaacacaccbbbccbbabbbcabaabbabacaabcccacbcaabbcbabaccbaaaaccaacacaccaccccbbaccbbaacbacabbbcbcabacccbaababbcbacaaccaaacccccbbcabbaabcbcacacbaccbbacaacabacbbaccabbabbacbccabaaccccbccccbccbabbbaabbbbbbbcbaaaabcbcbcccccabbbbcacbbaabccabbbaacaabcbcbcbabcbbaaaaacccccacbcbaacbacbbaaaaabbaabccbccbbaaacbccccaabbbccacbbcaccbacbbccacaaaabbaabbabbbbbbacaababbcbbaacbcaccabccabbbabacaacabacbabbacbbbbbbcbabbacaaabcbaacbacacbbbaacaabccaacbbbbccaacccbbaacabbabcbbbacbccbbcbaabbbabccccbbcbbbcaacccaacbcbcbbbaaaaaabbaaccbaabaabacacacccaccaaacbcbcabacccacabccaacbccccbacaaaabccaababaccccacbbcbabbbcbcabbacbcccacabababbbacaccccbcabbccbaabaaabbaccbbcaccaaabbccaaacbacaccbaaabcabbcccccccaabbccbabbcbbcacabbcbaacaccabacababbbaaaaabccbbcababcccccbccccaaccbcccabababcbacbcbbaaaaacacbbbabbaaaaaabbbbcaacbaaacaccbabbcbacaaacccabcacccaabbbcaabcabacacababaaaaabaaccacbbcbcbcbbbcccbabbaabaaacacccbaacacaaaacacabbbbcbabbcabbcbbacaaccababaccbcbccbacaabbcacaccbccbacaaacacacbcbaaaaaaccacabcbaacabccbbabcaccbccbcbaababaaabcccacacaccbbccccbbacccccabacbabbbcaaabacbcbbbbacbcbcbbbccaccbbaaaccbaaaccccccccababbbacbcaccbcbaacaabbacaacaaaabbacaacacabcbabcbcacabbbaaaccacccbbacbcbbcacaabccbaccbaccabaabbbbcabaccaaacccbcaacaaabcabababcccbbcccbbcacacbacbaacaacbbccccaacbabababcabcaaccbcbbbccbbccaabaabccbacabbaacbabcabbcabbcbacbacccabbcbccacabbbcccaaaabccbcbbcbbcabaabacaccabcaabacccbaabcbbbacccbcabaacccacaaccabcbbbbcccbbaaaabcbcaaccccbaaacacabbbcbbabbcabbbbbcbcaacbababbaccaabaacbacababababcacabcbaccacccbcbcbbbbcccbccaacbababcbccacabaaaabcacbbcccbbbabccbbcbabccaaacbcbcbbaacbaaccaccaaccbcbabaaabaabbbbcaaaaaabcaccabbaacaaaccccbacbbbaabaabacacabcaabbcaababbcbcabaabcaaacbabaaaababbabbcccbaccacbcbccbbcaccbcacaccccbacaaccbbbaabcbcaabbccbaacccbcbbbaaaabccacbbaacbccbaacaacabaaaacaabbaccaaccbabccacaaccaccbcccaabbaaccccccbccacbaaabbcccabcaacccabbacbacbbbabbaccbcaaacacbcacaacccbababaacaaaccccabcabacbabaabbbacaaaabaaccccaabcbcbaccbcaacbcbcccbccbcbccaaabcaaaacacbbcbbaaacccccbabbbccbbaccbcacaacaccbccbcaabbcabbababcaabccbbaabcaaccabbccaabbccabccbbbcbccacbacacbbbabaabcccbbbcacbbaccacaccbbcabaaacabcbbccbcaaaabbcabcbbacacbaaabcbbcbbacbcbbbcbbaaccaaabbaaccabbabbcccacbabcbaccacaccbccabccbbccbcbcbccbbbbbbaaccaabcaaaacbbbbbbbaaaaaababcaaaabccacbbaaaaccbbcaabbabccacabbcacccabcccbaaabccacaabbccbabbabbbaabbcbcabcbabcccabcbccbaaaabcbcbbbcabbaaabcccababbcbaccaaabacaacaccbaacbaabaccbbccbbcbccaccabacabaaabbacaabccbaccabcaaabcbccbaaaaccabaacabbcbbccbbcbcabbcccaccbcaabacbbcaaabcaacaababbbcbaabbabaabacacbbbbccbabcabbbaaabbcabcacacaccbccbccbcbccccbabbbbaaaccccbabbbcbabcbbacabbbcbbcbabccaaabbccbbbabbcbcbabbccbbbcababbacacaabbbcaaaabaabcbbaabaabbacbbacbcababcbbabbccabbacbacbcbaccaccaaaaaacabbbaaacbacbacaccaababbbbacbcacbccaacbbcbaccabbbaacbbcccaabcaaabbcbccbacaaaabccaabccabbbccaccacabacaaaccaccaaaabbaabbcbbcbccacbbcabcaaabcbbacccbabbbaabaaabcbbcccbccaacbccccacabaacacacbcbbaaabbccbaaaccacababbcbccbbaaaabcbacacbacacbbbcacbabcacaccababccbccbbcccacccabbbccbbbaccababccccbabaabcbcacaabaaaacabcccaccccaababbbbcccbbabcaaaaabbaaacccbbcbaccbbabccbbbbbcbcaacbacbabccccabcbcbacabbcacbbcbaabacacbbaacabcacaabacbccacbaccbbbcbbbcaccacaabaaaaaccacbcccccabcaaccbccbcbcbabacaababbacabbbbbbcabcccbbabacabcbbcbcabbacacabcbccbcbcaacbbaabcbaaabcaaabcccabbcacbcbaccacaabcabbbbaccbabcacabcabaccbbcaacccbabbaaccccccbacaaccaacabacabaaccccbabacbaacabbbbaacabccbaaabccacbacbbbccacccccbbabbcabcbccccbacabcabcbabbabcaacccabccabbccabaaabcacbbcaabaccabccbbcbbbaacbbbaacbabccabbbbbabacbcabbbaccabcbbababbababcaabbababaacbbbbabbabbabcabbccbcacbbbabbbcbaacaaaaccccacbbabacccbbcccbcccabcbbaabbbcbbbaacccbcccbcbabcbcaccbccabaaacaaccaccbbacacbcccbccbabacaccbbcabcaabcabaacbacbbcccbbacaaccaccaaabcbaabbbcbbbbaabacabcabacaaaabcbbcacbaabbccaaacbacbcbcccbabbccababcaacaacacbcbabacacccabaaaaacbacaabbaccaaaccacaccbccaccbababacabbccbcbacbaaacccbbacccbbbbcccabbbaabacababcccbbabbbbbaaacaabcabbbcbbccabbcacabbccbabccbaacbabbaaccacccabcbbccbacbbcaabbcccccbaabaacaccacbaabbbacbbcbcacaacbacabcacaacccccbaaccbbcabaaccbaabacaaabaaaabacaabaacccbacbacaaaacbacaccbccaaaacaccbbbcababbbbabbaccbcccacabcccaccccbbbaccbbabbccaccbaaabacbbbaacccbcbcaacaabccccccccaabacbbacaabcbbbaaacbccccabcbaccbbacacabcaccbabcbbbbbaabbcaabaaabacaccababaccbbabbbaccbbbaaccbacbaccbccbcbaaccacabaaabbbcbaabcacababcccbabcbabccccccbcabbbbbcbbcabbabaacccbacbcacacacbcaacccbcccbacaaaabacbcabbacbbbabacabacccbbcccaccaacbacbcbcbabbbcaabbcbabbabcbaaacccaacacababbcbaabbabbbaabacbaababccbcbbcbbcccbacacbbaaaccabcabbcabbbcbcababccbcaaaaacccbaccbbaccbcbbabbaaababacbbcacbabbaaabbbcbcacbcaabbcaaaaabaaaaaabbbbcbcbccbbbacbbacabaccbbcbaaacbbccccccaabcbbcacaabcbccbbcaaccaabbcbcbcaabccaaacbcabbbbabcbbacacbbcbbccababbcacbbabcacaccabbbaacbacbcbababaaaaacbcbcbbcacabccbbabacbacabbabacacaaacccbcaabbbacabbcacbcbcacaabcccacabbcbbacaaaaaabccccbcccaabccabccbbbccccbbcccaabbacbcccbaccbbcbaabacbabcbaacbaacbcacbbbacabbabcbbaabbaabbaacbccbcbbbbbbbaacbcaabccbbababaabbcbccaabbbaccbbaaabcbbaabcacaababbcaccaaabbbabcabcbbbbbbcbbccacabcaacbcccaacbcccbbbbbbcaaabbbcaaaaaccbccccabbbbccabbbbabbcacbbbccaabaacacacbbcbaaccbccacbccbcabccbcabbcaacbcabacccaaaabccbaccabbbaabcbbcbbabaaaabccbabcbcbccabbcacccacbaccabccacbcbbcabaacacccabbcccaccacaccbabaaacabcbbbcbaaaacbabbbcaacbaacaccbbabcaacabbbbcbabbbabcacbcbbcbacaccabcbbacacbbbcbabcbcccaaaacccbcaacbabcacaabcccacacacbaaccacaccbaaabbacbbccbcbbcbbbbbcbaaabababccbaacacbbbbcbaaaaaacbbaaccaccbbbcabaaccabcacccaaacaabcaccaacacbacacccaabcaaccbbabcccaacbabccbcbaacaaaccacccababcccbbbccccbbccbbcabbbaccbbaaaaacbabccaacbbacbcbbbcbbacbbccacabccbbcbacabbcbccbcbaabcaaccbcacbaccacbbabcabacaabbabaccabccbacaabaaabacbcbcaacacabcbbabaabaacbcacaaabbcbabbacccaabcaaccacbcbabbbaacbcabacbccaaccacccbaccbcbcbbcbbbaacbccbcccacbacabccbbabcbabbcaacacabcbacbcabbaccbacaacbabbaacbacabacabcaabccbabaaabaacababaacccbcbbbacacabcaabcbaabccabcabaaabcbaabbbcbabcbcacbaabacabababacbabbbccbbaabaacccbbacbbcaacacaabbaababcbbccaccbaaccaabccabcbbaaacaabbccbaccabcbbbbbcbccaaccbcbabccccbcabcaccccbacaccabbabaacaccabacccacbbbaabbacbabaccaacbaaaacababccccabcbacabbcccbcacabcbbabbcbacbacccbacababccbbbcbbbcbbcbcbcacabbcbcbbbcbaacbbaaabccccbcabbcaaacaabbbbabbbbaaacccbccbcbbcaaaabaacccaacacbabcbaccaababacbbbacbbbacbcaccbabacbaacbcaaacbbacbabbacccabbabababccbcbcbcaacacacaaaaacccccbbbcbbabcbbcaaaccabacbaccccacbbccacacbccabbacaabcbcaacbbabcbcbbbcbaabcbcbaccabbcbaacccbabcaabbbccbcccbbbabbcaaaacabcacbbccbabbbbcbbababbbcabcacaabbbacaaabcbbbbcaacabbaccaabbccaabacaabaabbccaaacbbbbcacbbbbbbbcabacbbccbbabccaaababccaabbcababbacacbbbcaabaccbbbbacabababbbacaabcacabcccccbbbbbbcbccaaabccbaabbaaacaaabcbcccababbabccccbccccacabcbbabbccbcabbcbaaccccababbabacccccacbabaabbcabbbcacbbcccaaacacbacabcccbcbccbaabcaababaabaccaaabcabcbcbccaabbbacacbcaaabbcacacccabbccaababccbcaaacbcbcbbcbbcaacaacabbaaacccabbabbbacababccabaabcccacbbcbcbbcabcacccbbacbacaabbbabaacaccacbccacccbcccaacabaaaccaabaabacbbbcacabbccaaaacabbccbcbbaabaabccbabccabccbaacbbaababcababaaaacaccbcababbcccbaabcaabaccbcaacaabccaccacabbbabbcaabbcaccabbccaaacbccbcbbbccaacbccabaaababbbccaaccbaaabbcccbabcbaaccbbcbaaccbaccbcabcbabbccabccbabaaaccacbabacabcccbacbccabccccbaaccbaccbcaaccabacccaaccabbcbcccaaaabbbbcbcaaccbccbccabcbbcbbacacaccabcabaabaababbcbcaccccbbaaacbccbaacabbbabcbcabbcaaabaaaaabbacbbcabcabbccbcacbcacbababaacaccbbbcbbacaccbababcbaacaaccbabbbabaabccccbbbcaabbaaacccaaaaabcaaabaccccccaccccaacabbcabaacabbbcabbcaccaccbacaaccabccbacaacaaaaaaccacacbccbccccbaacbcccacacccabacbbbcbbaabccaaaabbbcbbbcbbcaaabbcbbbcabbaaaabbcbbaccabccabccabcbbabbbccacccbcabaabaacaccacbabccaacbacaaccaaccbacbaacbacbccbbbacbbcabcbabbcbccbbccaacbcabbbbaaaabababbcaabcabbbcaaacaabbaaaacaabcbacccbaccccaacbabaccabbaabccbcacbbabbbccbabcaccccbccbbabbbbcacbbcabbbaacaacccaacaaacacabbbbacaabbaaccaccbabccbcaabcaaacaaccbabbccbbbaaabcbacacbbbaaccbcacccbacabbababcbcabcaacbcbccbacabaccbcccbcaaabaaabbababbaaaccabcbccacbbacbaaaacbccaacacacacbcbbccabaacaaaabbcccabcabababaacccabbccccacbbacaabaacaacccaaabbabccbbabacbcabaaaacccbcabccacaacbbaaacbbccacccbbcbabaacbabaacbccbaacbaaaaaacaabbbaaaacbbcccaaababaccacbcbbcbbbcbacbcabacbccaaaacbbcaabbaaabcaabcbaacabaaaabccbccbcbacbaacacbaacbaaacccccbababaaabbabccaababcaabcccaacbcbacbabbbbcabbccabaaacbcacaaaabcccabccbaabcbbcccbaaabaacbbbaaaccbbcbcabaababbcaacabcabbbccaaacabcbabaabcababbaccbcabaccabcbaccacbacbacabccbabbabbacccbbcabbbabbaababacabcccaccbaaababcbbbcacbabbacbbbbbabbbaacbbacbbabcccaaababbbbccbcababbccbcaaabcaccbcbabaccababbbcacaaaaaacbabcaaccabccacaabccaabbcaaacababbbbabababbbaccbcaacbcccbbcaaccbacaccbbcabbacbcabbbabacacaacacbccbacccccbaabcaccbcaabacbcccbbcbbbacbbccbaaaaacbccacbaabccbabbaaabbabcccabccaaccbacacbcacacbcbcccabcbabbbbacbcaaabbbbaabbccbbbbcabbaccbcbcbcbcbabcaccaccacccabbcbbacabbbbcacccacccabbccaaaababbcaabbbbbbcbabccacccabcabcabbbbabbcabcbbcbcbcbbaabcbacbcbbbaaabaacccccccacbcbbbbccbcbaababcabacabaacacccaccbbcacbccbbcabaaaaacbcccabcbbabbbccbccbbcbcbbcbcbbccbcaabcaccacacbbcacccabccbcabcaccbbccccccaacacabbbbcbcbcabcccabaabaaacaaacbcabccccbbaccaacababcbabcbbbabaaacbbbcacbbaccccccccaccabcacaaacbabbbccaaaaacabcaccabcbbccabbcacbbcccaabaccababcacabaccacbccbcaaababbbbbbcabbaaccbacaacbcccaacaacacbaacbcabcabcbbccababbcbcbbabcccbbbbacbbcababbbbbbcbcaabcaacaacccacaabccabcaaacccababcccbcbbaaccabbababbacabaabbabcbccbabbcabbcabbabbbacbccaccaccabcbccbbbbabbcaabbabccbaacbbacbbabacbacccacccbcbcccbbcabcbccaaabaaacbcbcbbbacccabaccbcbacaabbaabccbccbabcbccabcaaacaaacacbbcaaabccaaacabbaacbcaabacaaccabcbbabbacaababbcabccbcbaaababccccabcaabbcaabcbaababcbcacccbbcbcabacaccacbacbcaccacbacacabcaaaacaabcbbcabbccaccacbabcbcaaaabbacbaccaabbbaaabbbcbcbccabacaaaacbcbbcaacbcbbcbabcbbcacbcabbcaacaccccaabbcbccbccbccccabbbbacaacbcccbbbabaaabaacabccbaacabcabbcabaabcccbacbcacbaababbacabacccbaabbbaccaacaaaacbbcaaccacabbbabbcbccbcabacbacababcbabcbacbabbacacbbabbbccbabcabaacacbaabcaababcabcaacbcacacccbaabbbcaacbbcabaabcbcacccccbbbacbbacabbbcbbbbbaaaaaccbabacbcaacaaaaabcccccacbcbccbcccabbbccbcaacbcacaccbaccaaccaccaaaabaacccbbbbacacbbbbababcaccbcbaaaaaaabccacccbccabababcacccbcbaacabccbbbacabbbbabcaabccbcbacbbbbbccaccaabcacacabbcbabbbaabbcccaaacacbacbaacaccbaabbaaccccaabbaabbcbbbabcaaccbbcbbbcaabbababbccabbbabbabcababbbbbabbaacccacaacbcbbccacbaacbbcccaacabccabcccaccabcbabcaacccbaccbccbabcabbcbbbbcaabaaaabbccbaaccbbcccacbbbaaaaaaccabbbabcccaabcacbbbbcbabccaabcbacbccbaccbbbbacaacbbabccacccacbabbcabbbcbbbbcbacbbaaccccccacabbbbcababaccbabcaaccbccbacbbaacccbcbcabaccbcacbcbbaacccbbbacacbcbbaacaaabacbaaaacbbabacacbbbcbacccccabccccabaabbbccabaacabaababaabcccbbaaabbbbcccbccbacbccaaacaccccbbaccaacbbaabcabcabbcaaabaacccacaccbbabababbbcabaccabcabbcbcaaaabaababbabaaccbcbccbbbbbabcaaccaccccaabbcaabcaccbcccccbabbbcbccbcccbbaababcbcaccabaabccccbcbcacbcbcabbcbacaabbbcabaaaaabbcbcbbccbaabbbbbcabacacbbaaabcccccbabcabccaabcbacbacbcaccbabcbcacaccbbbcaccbcabbbaacbbacbbbabcbccabaababababcbaabbababbaabbaccbabcbbabbaaacbbcccbcbccbbabcccbbcccbbcbbabbcacbcbababaaaccaacacaaacbcccbcacbabcbaabbcbacabbabbacbcaccaaccccbcbbbbacbbaabbabbbabacbbbabbbbbbcababcbbcaabcbcbccbaacccbcababababbaabbaabaaabcbbacabcbcbbcccaabbcbbacacaabccbbacacbbbcbcaaacbaabccaaccbcbccabbcbccacbcbccbaccbabccacabcbbcaabcaaccababbbabbabcccbaacaaabbccaaccbbaacabcacbcbcccbacccaccccaaacccabbcbbacbbabcccbbacccacaccbccbcbcacbababccccbbbbabbbbaaccbcababacbaabbcaabcaababcbbcbbbbaaaacaabccbaacccacbabbcbbcaacacbcaabbacabccabbcbcbaacaaaccbaccccccbbcaaacabaaabcabbccaabaccabcaccacaaacccbbacbacbbacccabaaabbabbccaaabcacbcccccbccbbaacabaaabbbaacaaabaaaaccabaaaccabcbabcbbbabcabbaabaaccccaccbaaaacacaaccabbcbcabbbbaaccbcabaaccaccbcbbcbbcccbabcbbabaaccabcbbaaccaaccabbbaacaabbcabcbacbbbcbbbabaccabcbbcabbcaacabccbcacbccacbcbabacbbbbcbabbbbbcabaccbcbcbcbacbcbbaaacacaccaccacccaabbbbcbcbbbbcbbccaaabaccacccbacbbacacbaabaacbbaacabacbacbbabcbcaaabcccbaabbccabbbbbbcbaaccacccaaaaaacacbaaaccabbbaaaacbbbabbabbaabccabacbcabbacacbacbaaabaaaccacccbaaccacaccabacaacaacbabccbccbbabcaaabacabcbcabbcbaaaacaccabcaabbacaaacacacbccbacccbbbaaccbccbbbaccccaababccaccbaacabcbaaacbacbbacccccacbaaaccbcbcccbaaccaaaabcbbcaabbcccacaaacbbccaaacbcababbaababbabcbcabcbccbccbbaabbccbaaccacabacbacaccababaacabcccbabcbbccbbccaabbcbccacccabbbaaabbcbacbacbaaaccbcaccccbaaaabcbcbabbbcbabbccbaaabcbabacaabaabaabcccbaaccbaacbaaabccbacbcccaaacccabacccaccabbacbabbcbbaccaccbacbaaccaaccccbcbcbacbbccabbbcccaaabcccbbccabbccabcabccabaaaaabbbccbaacbbaccbcabcaabccccbaabccccccacccacccaabcaccbbaaccabacabcabaaccababaabccabababccababbccabbabbbccaabcbbcbcccaacaccbbcabcacabaababbbaaacbbcbaccabbbbaaaaabaaabacccbccccacbcaaacbbaababbaababccbccbcaaacacabbcababccbababaaaabbbaccbabaaacacbcccccbcbcaccbaaacacacbbcabbccaabaaabcbaabacacaaaabccbbcacabbcbabaaacacccbbcabbaaaaaccccbcbcbccabcaaabbbbbcaccbcbccbaabbbcbbccaaabbabbaababacbacbacbcbcbcbbbcacaabaccaccabbbacacbccabbcbbbbabbaacaccabbaccbabacbabbaabacbacbcacababaabacbacabaaacccbcbaacbbabcaacbbaacbbcbcabcbbabbcaaccbbbcaaaacacbacaabbabcbaacbaccabbacbcabcabcccbcbbbcbbacbacabbcabcbcccababaacccacaacacbaccbccccaabccacbbabccbbabbbbaccacacacbbabccbaaabaacabaaaaabaaabbbccbcccccbccaaacbabcabaabcbaabbabbcaaaaababaaaccbabbabaabbbbabaabaccaacbcccababacababbbababbcacbaccccbcccaabccbcabccbbcabbbcabbcbbbbabcbcbcbbcaacaaaccccccabcaccbcbbacbaabaabacacaabbbabcbabbcbbbbbacaccabbbcabacbccccacbaacbcccbcbabccaacccaacccbacacaaaabcccacbbbcabbaabacbcbaababbbbbaaaaccbabbbbbacbbbbbbacccaacaabbcbbccbaaacbcccbcabcababccbaaacaacbaaacaccbcbccacacbcbcaabaacbbaccbbcbcacabaaccbbbcacabbabbcccaaabaaaaabbbabbabbbbcccbccbbbcbbbcbabcbbabcccacbabacbaabaacbcacaccaacbccccbcaaabaabbcaabacbbbaabaacbbaccccaabcabcacbbcabccbcbbaccbacbccbbbbcbbbccbcbbabcababcabcbacccabcabbbcbaacbaacaccabbccbabbaabcabcbacbcacabcabbaacbaaacbaabbcaccabacababaaacabbbabacccccacaacaabcababaabbcbccccaaaaabbacabccbcacbbbaabcbaaabbbcbbaaacbabccbacaacacaabbacabbbbacabaccababcccbbbacbbaccbbbcccbbcbbaacbcbcacbbbaacbbbabccaaacbcbcbaababaacabcabbaaabccccabbbbacbacbacacbacaacbbbcbcbacabcaccbbcaabccbabbbabccccbabababcbaccbbcabbcbcabcbacbacacccaabaaaaacabcccabbbbcbccccbcbabacaabcaacbaccbbccabbbabccaacbbccaabbbcbaaabbacccbaabccabbbccbbbcaccabcccbcbccbcaaabbcbbcbacacbbbbcccbbaababcccabaaaacaacbaacbaabcacaacbcbbcccbcbcabccbacbabaccabcbccaaabacabaccbbcbcabaabbcabcccaccccacaabbbabbbabcaabababbcbbcbababbaccabcaccbbbacbbaaabaabcbacaacacabccaccccaccbcaacbcaabaccbbcccbbbccbcacbabbbcaabcbcaaaaabbbaabacbaaaacaaacbaccbcabaaabaabccbbcbacabcabbbbbcaaacaabcbacbacbbbbbbcbbacaccbabcacbacccacacbaacbaabcacbbcbcbcababbaaaaacbacbbcaacbcabaccacbcaaaacccbbccaabbcbcbcbbccabbcccccacabacababbcaccaaabccbbbaaaaaccaccaabbcabbbcacbcbbabbaacababacabbcbbaababbacacaacbbbaacbabccacbabaacabbaacacbbbcccabcaabaabcbccbaacababcccbcacccaccabcbacccababcbcbcbbcccbaaacacbbbbbcbcbcaacbbacacbbabaccbaacaccabccccaaccabbababcabcbaaabcbacbaccbcacabbbacbbbcacbaccacacbaccaaaccbbaaabcaabccccabbcaaccbcbbbacacbbbbbbcbcccbabbbabcaaabbabbaabaaccbcbaaaaaaaaabbcabbabcbccbbbcbcacccbaababcbbaccaacaacbbaacaaaacabbaacccaacbcccccaabcaabacccbbcacacbcbbcbbbaccccccbcbcccabcccaabcaaccbbcaaabaabbcababbabbbaabacbbcbbacbacaacccaaabbcbbbacacbccbcacbbccaaaabaaaccbabbcaaaaabbacacacbcbabaaaabbababbcabcabbcbbbbacabaaabccccaaaacaacbccabbbabacbcacaacbccabbcaaaabccbbaacccbaacbccbbacacbbacababaabcbbbbaccbcccaccaabbccbabccacbcaabaaabbbaacaaacbcaaaabccabbcbabaccacbcacababaccbcccacabcaaccabaaabcacacbccbabbcabbccacaccaabcaacbccaacaabcabaacccbaccccbbcbcbbccaaaccbababbccbcacbcccabccbabccbabaabcaaacbbcbabccbccacbbcbbccbbcaabbbbcbbacaacabccccbacababcabcbbabcaabbbcbcacaabcbabbbacbbbccbccaccabaacababbaccbbaabbcbbbabaaccaababcbccacacccbaabacbbcbcaacacbaacaccbcabbccbcbaaaaccabaabcabcababacabbbbbbacaaaccccccaaabaabcaccaacccbbbacaaaabbcbccbcccabbcccbacbcbacaccaabaacccbaabaaacaabbacabbabcbababaaaaabccccbaabbababbcabcacbaabccbccaabaabaaacabbcacbcbccbaabcacbcccbcaabcbabaccbaaaccbacaacaabbcbcbccacbacbbbacbacbbabacacbbbccbbbccbbaccbacacccbcbaabbcccbbcabbbcbaaaaaccaababaabccbabccaaaccacbccabccbbcbcaaccbcbbcacaacbcaaabcbabbabbacaccaaaaaccbbaaaccbbcbbcccaabacacbaabcaabaccbcbbcacabcacbbaaacbabcabbaaabababccbabacbbccbaabcbcaaaabacaacbaaccbcaaabbcbccabbbaabbcbcaacabbabbcbcbabbcbccacbaabbbaccaccbbbcabcabbcbccbacaacbbcaccacbaaccaabbbbaccabccbaabbbacabbaabbccaccbbbcbbbcbaabbacabcbabbbbacaaababcaabcbbaccaababccbcbaacbbbbbbbbbaabaccccbaabacacbbcbcbbccabcccaacbaabccbbbcacbbaaccbcbbbccbabaacccbaccbccbbbbbcacbbacbbbbaacbbabacccbacaabbacccabbcbcbbacabbabcabbccabaacaacacabccacbccbcacbcabacccbabbcbbbaccbcbaaabcbcacbcbaaccbccccaabcbbccccbcacbabaaaaaccbcaabaabcbababaabcaaacbcccccabbcbccabbabcabccaccaaacccaabcccbccabaaacccacacbaabaaccbcbbbabcacbcaaabaccababbacabababacaaaacaccbaabcacabccbbbbacabbbbccaacaaabcaaccbacbbbacabbbbcbbbacbbacabaaacbccaabaaccccbbccbcbbccababccbcbbbaccacbbbbaacbcababcccbaacbccaacaacacbacabccbccccbbaaacaccbbccbabbacacaabcbccbcbaacbabcbbabaaabaccaccbbbacaccbcababacccaacaccbcaaaaaccaacacbcababcccabbbaabccbaabbccbbbbabccaaabcabaaacaabbcbbbcbcbabcbbbbbcabaaaababbabccaabcccabbacbbcbababaccaccaabbcacbacbaaccabacbcbabcbcabaaaaacaabaabaabcccabcaacacaabaabcccacacccacbacbbbcbcccababcbaccbbbbabbcbbacbacaaccabcccccbccbabaaaaaaabababbcabaababacbabbbcaaabcacacbacbaabbcbbcbbcabaaaaaaabbaacacbcacacccbabbcaaabcacabcbaacacabbacaccccccaaacabbbaabacaabacbbaccabacacaabacaabacbcaaaccbbaaaccabcccbaabbcbcbaabcbcbccbcaacacbcbabbbbbbbbaaacaaacbabbcbacbcaabbccaacacbbcbbcabbacccacbaaabababcacccbacabbcababacabcbaaaaaacccbbcccbaabcbaaabccccaaccacbcbcccbbcaabbababaabbbababbaacbaccbacbabaaacbbaacabaccabccbaccaacaccacabacbbcaabaaabbbbbbacabbcabccbaccacaccbabbcabcbabbaacbbbcbbaccacccacbaabbcaaabaacacbbaabaaaccccccacbaabbbbbacccaaaaaababacacbcabbbbacaacbabaabaabcaacabaabcccbabbbbcbaabbcccacbccbbcbccacaccbccbbbbbbcabcbbacacacbcacaccaaacbbcbcbbbbccbbbbbcacccbbabacbccbacaccbccabcbabaaabaacacaababcbaaacaaabbcaabbaacbcacbaacbccaccacbbbacbabccbcbaaaaabaabbbcbbbcbaaacccabaacacbaaaaaaccbbaacbbbbaabaacacabcaaaaaccaacbcacacbbbabcccaacbaaaaacbaaaaabccabbaabbbbbabacaccbcbbaabaaaaccacbbabbccbbabcccabccccabccbccabbcabaccbcbbacbcbaaccaabbaaccabcbacbccccacabbbaacababaaaabbbcbcaccaabccbbbabcabaacccacababaabcacabcbaabbcbababacccacbbabbbbaaaccabbbabcbbcbabcababaabbabcbabcccaabccaaaaaaacbbbbbaccbcbbbbacbabcacbbacbbaccacbcbcabbbcacccbbaabcbabcabccaabbccbbccabcbaccbbbcccbccbabcbbabcaababcbabcccbcbbbbbcbacbaabcabbccaccccacccbcacabcaaabbbcabccbaacaacbbbcacbaacccccbbacacbccccbcabcbabaaaabcabcbacccbbacbcccccabaacbbccbbbacaaaaabcbacbabbccbaccacacaccbcabcabccbbbbaccbaacaabbaacbbbcbaabccbbbbaaccacaaaacbaaccbccabbbbcaacccbaabacabcbaabcbccabcaacaaacaaccaacbabcaaacaacbcaccbabbabaababccabcbacbaaccccaacaaaabcacccbaaccbcabbacaacbbbbcabcabbccaabcaaaccbccbcbcbaacaacaacccccccaccabcabacaccaaacbbbabbaacaaaccaacccbbbaaacacbaaaaacbcbaccbabcaaabbbbabcbcbcbcaaccbbcbcbcbcaaabbaaaccaacabacccbabacccaaacbcacabbcbbbbaaacabaacabaabaaaccacbbbacaaabbabcccbacaaacaaaabcbacaabcacccbaacacaccbaaaacbababcabbaaacbabbabbbaabbbcabccacbabbbcccabbaccbcaacaacaabbcbcbccaaacabacaccbabcabccbaaabcaabaaaccaacbcccababacbbccbababbbbcbbabbabccacabaccacbaaccbcacaccacaaabaacbaabcbbccabccbbccccccabbabbaaaacababbcaaaababaaacbbacccabbacaacbaaacacabbabccacbcbabbcccbaacaaabccbbabacabbaaaacccbaacbabcacaaaababcbaabaacbabaabbbcaaabaccccabbacaaaaacacabbcccacbccbbaacbbbbbbbcbcaccacaabbcacbcabccbcacabbccaaabbbbbcbccbacaabaaccbbaabcacbabaabaacbaaaccbaacabcbbccaabbaaaabccacbbabbaaaaacbcbaaacabbabccccbabbcbcbcaabaccabacacbbcacbbccabbaaacabbabccccacbcabcbaaaccbccbaabcacaabbbaaacbabccbacaacbbcaacccaacbccbacbcccacbccacaccaaacabcbcabcbbbcbabaacaabbccaacbcbbbabbcbacbbbbccaaacbcaccacbcbcbbabbaacaaacaccacbcccccacbbbccacccccabacaabbbacbacaaccaaabcabbbaabbbaabacaacabbcbaccbcaaaacabcacbacbacbcacbcaabbaaabcabccacacabaccaacccccabbcaabbbcbbbbacacacbccacbbcacaaabaacacabababccabcbbcaacccbcabcacacacbbcaaaabacbcccbbaacabaabaacbbbaaccabbaabbbbacbacabcabbcaabcaabcababcacbaaacbaaacccacbbcbaaaabbbcaabaabacbabcacabccababcabacbabbbbccacabcaabbbabcbccacaccbbabcaaacacbcbbcacaccabbbababaabaabababcbcbabcbabbbabcacbbbcbbcaaaabcacbccbbacbbbaccbbccbaabcabcabbcabbbcbcbcabbabbcabcbbbccccaaababcaacbaaccbbbbabbccccbccbaabaacaabbccbacbacbbccbbccbbcacccccbaaabbbccbaccbaccabccabbabbaaacabbbccacacacbacbbabcacbbbabcbbcbcbccbbbbccbcacbcabbcabbbbbaccaccaacbaaaacaccabcbbcaababcbaccabcbbaabcbbbabccbbacbabbccabbbacbbbaabacbacbaacaacbbcabaccaccacabbabaacbcccbabbaaacbabbbcbabbccacbbcccabacbcbbccabaaccaabbabbacccbacaacabcccbcbbabbabbaacbcbaccacbcbbbbcaaccabcaacaaaacbbbcccbaccaacbabcbababaacabacccbccbbbabbbaaccbbbccbbccabaaabaaaabcbcabababbbaccbcbaabaccaccaacccabaccbbcbcaaacabbbcbacaabaabcaaabcababcbcabbcbacabbacbbcabababacbbcabbbccaaabaabaaccacbbccbcbbabcccbcbacabbabccbccbbcbacabcabbccbcabbbcbbcababbbbcaacabcbbcbaaaaabcbcaaccacaabaccacbbcabbbccbcccababbcbcbbccacccccbcbbbbacbabbcacbbcbaccccbccabacbcbcaabbaaccaabcacbccaaacabcbcacabbcbbcaccbababcbbcacacacbbaccaacbacacabaccabcacbaabacaccacabcbabccaacabaacaaaacbbcabababbbcaacccabbacaaccbbaabbacbcabbacaaacaacacabcabbacaaabcaccacacabcccbbbcabbcaabacbcbbccbbaabbcabacaabcbcbbaacaccaacbccabbbbabcbccaccbbbbacbcbaacbaabacbbaababcbbcaacbcaacaacbbacaaababbbbbaacbbcbaacaaaaaabbcccaaacacaacbccaccbaacbabcacacbbbacbbcaaacaacaaaaaaaaaabbacbcbbcbbaabbbcabcaaacccaccccbcaaabcbcacaabccbcbbcaaacbabbcaaabbaaaccabcaabaacbcacbabcaacacaaaaccbbabccbbbabaabbaacbbacbbccbbbbcacababbacaacbbcbbbaacaabbcbabaccbccccaccabcabcbacbaababbacccbcbbabcaacbbcbcbcabaaacbbcbcbcbcacbaacabbbccbbcabacaabbccccbaabaabbabaccbbbabbabacbccabccacbabcaaccacbabcbcbaabccccaaacbabacacbcabbbbaaabbabcbacbcbcabbbaacaacacbbaccbaaaacbbcaccabcabbbbacacbaaacbbabcaaaaabbcaaabcaccaacacaaabcaacabcabcacacacccacccacccbbcccbbcbbaacabbabbbcbccaabcaacacbcccbaaabacccabbaabacaabacabbbbbbccabbaabaaaccbacbbccaaaaacbbbacbbcaaaaaccccccbaccbcccabccaabcabcbcbcacccabbbacaacacbbccbcbaccaabcabbccbcaaacaabaacaaabbbaabbbbaabaabbcbbcbcccbbccabaacaabbbcbcbbacbcabbaacccacbcaabbbccbababbabcaaabaccacaabccabaacbaccbaabaaaaacbabbcbabccbbbaabbbaaaaccccbaabccbcacbbacbbcbccaaabbbbcacbacccbacbbacacabbacaaaaccccbbbcbbcaacbcbbbbbcccaaaacbacabbcbcccbccbccbbaabbbcaaabaabaccbbabcababaacccabbaccccbbababbcccbaacbaaabaabacbacbacacccbccaacbbbcbbccbacbcbbcbcacaaaacabacccbbbccaccaabcabcaaaabbcbababcacaccaabacbbbacbcccaaabcbaabcababcaaccacbbaabbcacccaccacbcbabaaccccbbbacbbccacbccbaccbccccabcacbabaaaaacbbabcaccbbccccaabbccbacbcbaacaaccbbccbbbbabcbbabaaabbaacaabccaccbbacacbacabbabaabaccaabbbcbacaabbbcbaacacbaaaabacbabbbccacbbbababccbcaabcbccccaabcbccbacbaabaaacbbacbbcbacbcbbabbcacbcacbbacabbabcbbcccbccabacbccabcbcababbcabbcbbacbbcacacbbccbcabbbabaaacaccbbabcaabcbbbbbacbaaccabcbacbcbcbababaaacbacbbccbcccbaccacbbbbacabbabccbbcabccccbcbbacbcbbabbcaacbcbcabbcbcbcbabaacbccaacacbabcbbccababcbacbabacabcbcbbbcbaaacacbcbcbbbbaaaaccbccbccbcbaababbbccaccbbcccccacbabacaabcacabcabccbaabbbbcaacbaacabccbcccccacbbccacaccaacccabcaaabcabbcbacabcabbbacccacbcbacaaaacbacbbcbaccbccbcccccbccbabbacbbbcbcbcbcabacccbccccabaaaacabbaabaccaabbbbbacabcbababcccaacccccacabbbaaababbcbbccabbcabbcbacaabacbbcacbacaabbbccbbcccaccababcbcabcbaabccaacaacbacbababbabaacaacbbcabcbcabccbbcabacacbbcbbcbbacbaaccccabcbaccbbccbbabcaabcacbaaaacbccabbcabcbcabcababacbbbabbababbcacccbaabacbbacacaabbacaccbbabcbabacacbaaaaabccccacbabbcccbacbccccacabacbbcbacabcbcabbcbcbbcabaaccbabbcbcbcabbbaabbbcacccabaaacaccbccabbcbaaababacabbcbabbcaccacbccaabbbcbcccbacccbbcacabaacccbabcaacbcbccbcaaccacbcccbaaabcbccccbccccaababbcbacbcbbabacacbbbbbbbabbccabbccbccbcacccbcaaaacacaabbccccbbcabccbaccabcbabbcccccbbcaaababbbaabccccccaaabbcaccbabcbbccbcbbcacaaabbbbccbcacaaaaabbbccccabccacbacbbbaccaabbbbbaaaaacabaaccbbbbcabcbcacbaacbbbbaabcacbaaabacbcbaacbbbbccabbbaaabbaccabbabaccabbccbcaabcbbacbabbbbaababccacaaaaacccbbaaababbaacacacabbbbcacbabcaabacbcabaabcacbbbacacacacbbabbcabaacbaaacbbacbccbbbbccbbcacccbbbcbbcbbaabbaccccaccccbccbbaaccbccaccacacacabbbaaabcaabacbbbcabbacbabbccacbcaaacbaabccabacacababcabbcacbcaccbaacccbaaacbbbccccbbaababccbacbbbbbcacbabccaabccbcacaccabaabbaabcaaccccbcaacbaabbbcbcabaacbbbaabbabcabccbcbcbcababbaabbbaacccacbbbcbcbaabccaaccbbaacaaacbbaaacabcbbccbbabccccababccbbbacaacbacaacacacaabbcbbbaaacaacccbccbacabcabbbacbbabcccbcaaccbcbbcacbbabcaccbcabcbabaabababbabbcbacbcbbabcccbccabaccbbbbacaaaababccbabbcbaccabacbccccabacbbabbbcaabcaccccabababbbabacacaaaaaabcabbacabcabccbaaaacaabbabaacabccacbaabbaacbcbacacbcacabcabbaaabbbcccbabbcbbcbbaaaaabaccaabccccaaaccabcbbcbccbaabaabbcabbbacabccaababcbacabaaacacbccabbababacaaaccbcabcabbbbbcaccacbbbbacbaacaabccbbacbabababcabcbbacacabbabbbbbabccbbcabacccbbbbcacbbbcaabcacacbbaacbbcbcbccbbbcbaabbcacabbcacabcccbccbbcbabaabbbcbcbacbbabcabcbaaccccccccacbabbccabbbabcabccbbcbabaabaccabaaabbaccbbcacbabbcbacbcaaccbcbaacbbaacaacbcacabbbabbcbacabcbbcbcaaaabcaccaaccccbbbbabcaaaabcbccacaccbabaabcabbbabcbaaaaccbcacbbbacbabbccbccacacaabcaabbccccaabcbaabaaaacbbbccaccabcccbccbbaabababaccabbbaccaaabbbbbabcacababaccbccbcbcaccaccbacbbbaacccaaacbaacbabbccbbcacccbabcacbabcaaaaccaaacabacccbacbaaccccccbaaacacabcbbaacccabacccabacabcbbbbcabbcbbcabbbbacbcabcbccabcaacbccbbbaccbcaccaabbacbbcccbaccbaacbabaabbacbacbaaaaccccbbcababbbababbabacbcbcabbcbacbcabcacaaaacabccbccbbcbbcacbcccbcbcaabacbbbbcbcaacacbacbbccbbaabaaaacbbabaaabbccbccbacabbcacacbbabacaaccbccababbabcccaacbacbaccbabbcbbababccabacaacbabbcccacacabbbcbbcbccbcbbbccaabbacaccaabbbcabccbaacbaccbcccaabbaccacacacbbacabaacbaaabcbbacccacbabbcaabaccbcccbbccbbcaacabcbbaaaaaaacaabccacccbbcaabacbabccaaabcbbbbbbbacbababacaacbccbaccacaccaabababbcbcacbcbbbbabababcbcccbbbbbabbcccacbaacacaacbcaacaaacabbacaaabcbbaaabbabcbabacccbbbabcacaacbcbcabbcbcbacabbccbaaccabbaababcccababbccacacbcbcccabacaacbccaabbacacbacbaaacabcbbcaabbbcbaacbccaccbcbbcaaaacacaabccbbbabcaacbbabbacacacabbaabcacbcbcccaaabacbbbabcbcccabacaabbbaccbbbcbaabccbbaabaaabccabcbababaababbacaaabacabababcbccaabcbccccabbbbbababaabcbaaabccbacabcaacacccaccccacabacaababababbacacbcbbaaaabacbbcacaccbbcbbacabbcbcbaabcbbaabcbacabacaaccbbabccbacccabacbbccbacbcbaaaaabccbbacbccbcbcbccbbccacbacbabaaaaabababaabcbbcbaaccacbcbbccccccaabccbbbccaaaacaacbcaabacabccaacaacbaccbaaaabccbccaaabacaacaaaacccbcabbabbbbbbbccbcacccbbbcbaaccbaccbbccbcbbbabbbbababcbabaaccbcbbccbbcbbabcabababcababacabcaccaccacbcaaabcbbbbccbccaabaabaaabbbbaabacbcabacbbaabbabccabbacacaaabbacabbabbcacabccbaabacbaababaababcccccbacbccbcbaccbcbaaacacabacaabacaacccabacbaaccaaaabaccccbbbcaacbabcaabcbabbbababcacccbacaaababbacbaaaccabacabacbcbbabbcbbbbabacbbbcabcbbabbccaabaaccaabbcbacaacacaabbbbbbaacacbbcbbbabacabbbaabbbbbbcaccabcccaabbaaabcaabaabbbcbbcabcaababccaabccbccaacabcaaccaacababcbaabbccaabccbaaabbacccbcaabacbbacabbcacbcaabbaaaacabaccbbabcababcbcbccbabcbbbaabaaacabcccbacbbcaabcbcaccbbaacccccccaccaabcccbcabbccbcacccbccccbcaabbbabbababcbabbcabbcbabcbbbaaabacaacabaccbacbccacacbabbcbaacacabbcccccccccbbabbbcccbccbacbccacabbabaaccbcccacabccaacabbbaaacabccacbbbcbbccbabaacaccababcacbacbaaacbaababacacbcaaaccabccbabacccbaaaaaccbbcacbcccccbcbbbacaaccbcbacaaabcbccaaabaaaacbbccbcabaabababacaaaabcbcabbccbcbabccbabbabbcaaaaacabcabcaabcaaaaaaabaabaaaacacabacabcccccbcbabbbcbbcbcbaaacabbabcacbbbccacbccccabcaacabcbccbacaacaabaccabcaccccbcacabaaabbaababacbcbcabacbbccbbaaacabacaaacabbccbcbcbbababbabccbcbaabcababbcbbbbaabbabbbbcaabacccbcbcacabbcbcbaaaacbcacacbbcaccccbaabcbcaccabbcbabaaabcacbbbaabcaaaccbbcabcacaabcaacccccbabbbabcbbbbacbbbcaabbcaacbcaaabcaccbacabccacccacbbcbccaaacaccccaccabbacbbbaaaabaaaaacbbbcbacaccbbcaaacabaccbaaabbaabbbccbcabacaabbcaaaaaabaacababcbaabaccacaacbcccaacaaaabbcbbbcbbabaaabbcbacbcbabbbabacbcbcccabccbbccabccabcaaabcabcacbbbbbbcabbaaaccaaacabccaacccacaccbcabbbbaaacabbabacccbcacbacabcacbbbbbcaaabaabcababbcbaccbbbbacacacbcbaaaacabacacbcccbcbbcccbbabcaacaaabcabcaccccbbcacbcbabcacbccaabcacccabcbabcbbacaaaabccbccccbbbacbcbbbaabbbcccababaacccacacbbababbbcabcbbcccaccaabcbacaacbccaccacaaacacabcbcabacbbaaaaabccbaabcbbbabaacbccbacccabaaacacbaacacbabacbcbacabcabccbbaacabbbbaacacaacacbbaacacaabbbaaaacbaacbbaacaaacaacababbaabbbaacaaacccaacaabbcaacabacbbbaccaaaccaabbbabcbcbabbbbabbbccabbabacabcbabcccacaaaaaaaabcbbbbcbcacacacbaacccccbacccbbbccaacbaaacbbacbcbaabaccbacbbbbbaacbabbcbccbabbcabaaaababbcabcbbcaabbcbbcccbabaababcbacabbacbcabbabbaabcccabacacabaabbcbbccacabbbabccbaaaabbbbbcaccaabbacbabbbcbacbcacacccccaaacbbabcaacbbcbcbabacabacabcabccccacaacbbabcbcabbcbccbaacaacacbbcacabbacbccbcabccacaaaccaabcbbcabbcbbbcacccaacbccacacccbaabccaacccccbbaccbcbbcaaabbaacccaccaabcccacbacaabacbbabcabaccabacccbccbbacacabcacbbacbbccaccbabbbbabaaaaacabacbcabcbaaaababcabbcbbcbbcaababcabcccbbaabbcccbcbcacabaacaccccbcacaccaabaacbbcabcccacbbabbbbccbaccabcabaaaaabcababbabccbabcaccccbacccbacbbbbcaccbbaaabbaccbacaaccacacbacbbbbccbbbbaacaabacccbaccabbccbaccaccbbaccbcbcbacacbccbbbbacbcabbcbbbbbbacaababacbbbbcbcabbaaacbbcbbcaacacabcaabaaabbaacbcbcbacacbcbabbbbaacbcbbaabaaabacbbcaaccabbcabbbcaabaabccccbbbcbbbbcacaaabacaaaacbaacbbbcaacabcacbcbbcccabbaabaccbabbcbcacccbbacbacaccbabcccbabaaacaccbbcbbacbbccccbcabcabacbbbccabccbcabbbbbbbcbbbccbbabbbcbbababaacaacbbbcbbbbaccbcbbcbbbacbbbbaacacbccbaabbbcbcabbabaaababaabccabaaaabbbbcaabccbacbbcacbbbcccbbbabcccbcbaccbbbcacabcbaabbcccabcabcbaaacabcaaaabbccaacacabcccabccaaaccaabcbabbcbbbabcacccababbbaaabbcacabcbaaaccbacccbbccbcacbcbcabacbccccbaaccaaaabccccbcaacbcaccbbacacbacabacaccacaacbabcccabacbbcaabcacaaabcbcaacbbababcccacccbbcababccbaabbaacccaabbaabccabbbababbcbaabcacabcbabcccabababaaabacbbbbabbabbcaaabbabbcacbabaacacbcbccaaacccaacbbcccaaababbbacaaacccaaaabacabbbaaaacbacbaabbacaaabbcaabcabaccacaaabcbbbccaaabcccccabcccaababaacbabaccbcbbcbccbccbcbccbacccbcabcbabcaaaaaabbabbcabbcbcbabacbcbacabacbcaaccaccacabbabcbbcccbccbcacbbacabcbbbbccccbcabbccabbbbbccccbcbcccbcbbcbacccbabcccaababbcacbbacbcaccabbcacabccbbcbbbbabbbabaacaaccbabaaacababacaabcbaaccaccbcccacabcaaacbabbcbbaaacacbacbbbabaabccccaabbbaaacaabbcbcbccabaababacabcbabcabcbbbcacbbcbbcbaabccccaaabbcababcccbaacacccbbaabaaabcbacabbcbabababbaccbaabcacababbaccccccbbcccbbccccbcabaabcabbabcccccaaababbacabcccaabaabbbbbacbbaccaabbcaababccabbcbacbbbcbbcacabbbacccbaccccaabbacbbbbcbbccaccacaaaacacacccabbbbccabbbbaaacccacbbbbccaabcbbccbaacabaccaabcabbbacbbbbbbbbcccbabcacbabbacccccccacccbbacbccbcaaacbcbcacbacababbacbbaacbcabbccacaccccbabcbcabaaccabcacccbbcaccbbaccbbcabcccbbbabcbbcccbcacabaabaccbaaabaabcbbacbaabbcacbaaaaccacaaacbabcbcbbbbcacababacbbbbabbbabaabacbabcbbbbbcabacbcccbcbacacaabbcbbcccbbabaaccbcbbabcbbbbbaacabbbbabbbcaaaabacabbabaacaaaabbbaacbccabbababcabaacbcaacababbabbcacbcaabbbbabcabbbcbcabcaccbcccbbcbabccbabcaaaabbbccacbcbbababcabbaccaababcbcbbccacccbcabccbcabcccaabcbbaaabaabbabaacaacccabbaaabcaabbbaaacbacacababcbbcbaaabaabbcaaacabbacbbaaaccacabbabacbbccbbbaaaaabbaccabcacccaacacbabcbabaabbcaaaacacaccbccaaaaaacbabcbaabcbbcccbabacaabcaaaaaabbabbbcbcaaabbbabbabacacbbbababbccbcbaaabcccbccbabbbaacbbbacbcaabcababaacbcbccbbbbaaacbbabccababbaabccccabaaabcaccaccaaacbbaccbaccbbacacbccccbaaccbcbabbbaaabaacabbccbcacbcccbcbaacacacababaaaababacbbcaaaccbabcbbbccccaacbccccabacaccbcacbaabacaaabbbbcbaccacbbbbbbabbbbcabbbacbbcacabbabacbbcbaccababbcccbbabbbccccaccccbbacacbaaabbccabcababacbbbbcbaabbacbcbabbaaacbbabcabbaabcabbccbbabbbacbbabbcbcccabcaacaacbcbbbbbacbcbcbcccaaccbaacaaacbbcccaaaaccacbbaaccbcbccabcabacacbbaccacabaaaabaaaacbcacbacaaaaaaaaabcabacacbbcaaaacbbabbccbcccacbbbaabcbbacaccabcaaaabbaacacacaabaacccbcabacabacbbccaacacaaabbaccbabbccabacbaacabbaccacaacccabaaaabacbabbacccccbccbabcbcbacaaabcabbababbabacbabbcbaccccbcbbababcbccaacaccaccaaaaacabccccbcbabbcbcaccaabccbaccbcabbccccbaccccaaacbaccabcaabbabababbbaaccabbccacbcaababaaccbaaabaccbccbabbbabccccbbcbbacbaccbbcacbcbcbbbbaccccabacacbbcaccbcaacbcccbbcaaabbabbcabcccabbbacacccccbccaaacacbccbbccacbaabbbbbcaabcaacabbccbabbbcacabbbcccbcaaabaabbbccaccbccbccbbbcabaaaabcccbbaaaaacabcbcacbbacbcabcccaba