Identifier
Mp00085:
Standard tableaux
—Schützenberger involution⟶
Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
[[1]] => [[1]] =>
[[1,2]] => [[1,2]] => 0
[[1],[2]] => [[1],[2]] => 1
[[1,2,3]] => [[1,2,3]] => 00
[[1,3],[2]] => [[1,2],[3]] => 01
[[1,2],[3]] => [[1,3],[2]] => 10
[[1],[2],[3]] => [[1],[2],[3]] => 11
[[1,2,3,4]] => [[1,2,3,4]] => 000
[[1,3,4],[2]] => [[1,2,3],[4]] => 001
[[1,2,4],[3]] => [[1,2,4],[3]] => 010
[[1,2,3],[4]] => [[1,3,4],[2]] => 100
[[1,3],[2,4]] => [[1,3],[2,4]] => 101
[[1,2],[3,4]] => [[1,2],[3,4]] => 010
[[1,4],[2],[3]] => [[1,2],[3],[4]] => 011
[[1,3],[2],[4]] => [[1,3],[2],[4]] => 101
[[1,2],[3],[4]] => [[1,4],[2],[3]] => 110
[[1],[2],[3],[4]] => [[1],[2],[3],[4]] => 111
[[1,2,3,4,5]] => [[1,2,3,4,5]] => 0000
[[1,3,4,5],[2]] => [[1,2,3,4],[5]] => 0001
[[1,2,4,5],[3]] => [[1,2,3,5],[4]] => 0010
[[1,2,3,5],[4]] => [[1,2,4,5],[3]] => 0100
[[1,2,3,4],[5]] => [[1,3,4,5],[2]] => 1000
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => 0101
[[1,2,5],[3,4]] => [[1,2,3],[4,5]] => 0010
[[1,3,4],[2,5]] => [[1,3,4],[2,5]] => 1001
[[1,2,4],[3,5]] => [[1,3,5],[2,4]] => 1010
[[1,2,3],[4,5]] => [[1,2,5],[3,4]] => 0100
[[1,4,5],[2],[3]] => [[1,2,3],[4],[5]] => 0011
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => 0101
[[1,2,5],[3],[4]] => [[1,2,5],[3],[4]] => 0110
[[1,3,4],[2],[5]] => [[1,3,4],[2],[5]] => 1001
[[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => 1010
[[1,2,3],[4],[5]] => [[1,4,5],[2],[3]] => 1100
[[1,4],[2,5],[3]] => [[1,3],[2,4],[5]] => 1011
[[1,3],[2,5],[4]] => [[1,2],[3,4],[5]] => 0101
[[1,2],[3,5],[4]] => [[1,2],[3,5],[4]] => 0110
[[1,3],[2,4],[5]] => [[1,4],[2,5],[3]] => 1101
[[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => 1010
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => 0111
[[1,4],[2],[3],[5]] => [[1,3],[2],[4],[5]] => 1011
[[1,3],[2],[4],[5]] => [[1,4],[2],[3],[5]] => 1101
[[1,2],[3],[4],[5]] => [[1,5],[2],[3],[4]] => 1110
[[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => 1111
[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => 00000
[[1,3,4,5,6],[2]] => [[1,2,3,4,5],[6]] => 00001
[[1,2,4,5,6],[3]] => [[1,2,3,4,6],[5]] => 00010
[[1,2,3,5,6],[4]] => [[1,2,3,5,6],[4]] => 00100
[[1,2,3,4,6],[5]] => [[1,2,4,5,6],[3]] => 01000
[[1,2,3,4,5],[6]] => [[1,3,4,5,6],[2]] => 10000
[[1,3,5,6],[2,4]] => [[1,2,3,5],[4,6]] => 00101
[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]] => 00010
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => 01001
[[1,2,4,6],[3,5]] => [[1,2,4,6],[3,5]] => 01010
[[1,2,3,6],[4,5]] => [[1,2,3,6],[4,5]] => 00100
[[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]] => 10001
[[1,2,4,5],[3,6]] => [[1,3,4,6],[2,5]] => 10010
[[1,2,3,5],[4,6]] => [[1,3,5,6],[2,4]] => 10100
[[1,2,3,4],[5,6]] => [[1,2,5,6],[3,4]] => 01000
[[1,4,5,6],[2],[3]] => [[1,2,3,4],[5],[6]] => 00011
[[1,3,5,6],[2],[4]] => [[1,2,3,5],[4],[6]] => 00101
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => 00110
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => 01001
[[1,2,4,6],[3],[5]] => [[1,2,4,6],[3],[5]] => 01010
[[1,2,3,6],[4],[5]] => [[1,2,5,6],[3],[4]] => 01100
[[1,3,4,5],[2],[6]] => [[1,3,4,5],[2],[6]] => 10001
[[1,2,4,5],[3],[6]] => [[1,3,4,6],[2],[5]] => 10010
[[1,2,3,5],[4],[6]] => [[1,3,5,6],[2],[4]] => 10100
[[1,2,3,4],[5],[6]] => [[1,4,5,6],[2],[3]] => 11000
[[1,3,5],[2,4,6]] => [[1,3,5],[2,4,6]] => 10101
[[1,2,5],[3,4,6]] => [[1,3,4],[2,5,6]] => 10010
[[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]] => 01001
[[1,2,4],[3,5,6]] => [[1,2,4],[3,5,6]] => 01010
[[1,2,3],[4,5,6]] => [[1,2,3],[4,5,6]] => 00100
[[1,4,6],[2,5],[3]] => [[1,2,4],[3,5],[6]] => 01011
[[1,3,6],[2,5],[4]] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,6],[3,5],[4]] => [[1,2,3],[4,6],[5]] => 00110
[[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]] => 01101
[[1,2,6],[3,4],[5]] => [[1,2,4],[3,6],[5]] => 01010
[[1,4,5],[2,6],[3]] => [[1,3,4],[2,5],[6]] => 10011
[[1,3,5],[2,6],[4]] => [[1,3,5],[2,4],[6]] => 10101
[[1,2,5],[3,6],[4]] => [[1,3,6],[2,4],[5]] => 10110
[[1,3,4],[2,6],[5]] => [[1,2,5],[3,4],[6]] => 01001
[[1,2,4],[3,6],[5]] => [[1,2,6],[3,4],[5]] => 01010
[[1,2,3],[4,6],[5]] => [[1,2,6],[3,5],[4]] => 01100
[[1,3,5],[2,4],[6]] => [[1,3,5],[2,6],[4]] => 10101
[[1,2,5],[3,4],[6]] => [[1,3,4],[2,6],[5]] => 10010
[[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]] => 11001
[[1,2,4],[3,5],[6]] => [[1,4,6],[2,5],[3]] => 11010
[[1,2,3],[4,5],[6]] => [[1,3,6],[2,5],[4]] => 10100
[[1,5,6],[2],[3],[4]] => [[1,2,3],[4],[5],[6]] => 00111
[[1,4,6],[2],[3],[5]] => [[1,2,4],[3],[5],[6]] => 01011
[[1,3,6],[2],[4],[5]] => [[1,2,5],[3],[4],[6]] => 01101
[[1,2,6],[3],[4],[5]] => [[1,2,6],[3],[4],[5]] => 01110
[[1,4,5],[2],[3],[6]] => [[1,3,4],[2],[5],[6]] => 10011
[[1,3,5],[2],[4],[6]] => [[1,3,5],[2],[4],[6]] => 10101
[[1,2,5],[3],[4],[6]] => [[1,3,6],[2],[4],[5]] => 10110
[[1,3,4],[2],[5],[6]] => [[1,4,5],[2],[3],[6]] => 11001
[[1,2,4],[3],[5],[6]] => [[1,4,6],[2],[3],[5]] => 11010
[[1,2,3],[4],[5],[6]] => [[1,5,6],[2],[3],[4]] => 11100
[[1,4],[2,5],[3,6]] => [[1,4],[2,5],[3,6]] => 11011
[[1,3],[2,5],[4,6]] => [[1,3],[2,5],[4,6]] => 10101
>>> Load all 2275 entries. <<<
[[1,2],[3,5],[4,6]] => [[1,3],[2,4],[5,6]] => 10110
[[1,3],[2,4],[5,6]] => [[1,2],[3,5],[4,6]] => 01101
[[1,2],[3,4],[5,6]] => [[1,2],[3,4],[5,6]] => 01010
[[1,5],[2,6],[3],[4]] => [[1,3],[2,4],[5],[6]] => 10111
[[1,4],[2,6],[3],[5]] => [[1,2],[3,4],[5],[6]] => 01011
[[1,3],[2,6],[4],[5]] => [[1,2],[3,5],[4],[6]] => 01101
[[1,2],[3,6],[4],[5]] => [[1,2],[3,6],[4],[5]] => 01110
[[1,4],[2,5],[3],[6]] => [[1,4],[2,5],[3],[6]] => 11011
[[1,3],[2,5],[4],[6]] => [[1,3],[2,5],[4],[6]] => 10101
[[1,2],[3,5],[4],[6]] => [[1,3],[2,6],[4],[5]] => 10110
[[1,3],[2,4],[5],[6]] => [[1,5],[2,6],[3],[4]] => 11101
[[1,2],[3,4],[5],[6]] => [[1,4],[2,6],[3],[5]] => 11010
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => 01111
[[1,5],[2],[3],[4],[6]] => [[1,3],[2],[4],[5],[6]] => 10111
[[1,4],[2],[3],[5],[6]] => [[1,4],[2],[3],[5],[6]] => 11011
[[1,3],[2],[4],[5],[6]] => [[1,5],[2],[3],[4],[6]] => 11101
[[1,2],[3],[4],[5],[6]] => [[1,6],[2],[3],[4],[5]] => 11110
[[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => 11111
[[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => 000000
[[1,3,4,5,6,7],[2]] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,4,5,6,7],[3]] => [[1,2,3,4,5,7],[6]] => 000010
[[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => 000100
[[1,2,3,4,6,7],[5]] => [[1,2,3,5,6,7],[4]] => 001000
[[1,2,3,4,5,7],[6]] => [[1,2,4,5,6,7],[3]] => 010000
[[1,2,3,4,5,6],[7]] => [[1,3,4,5,6,7],[2]] => 100000
[[1,3,5,6,7],[2,4]] => [[1,2,3,4,6],[5,7]] => 000101
[[1,2,5,6,7],[3,4]] => [[1,2,3,4,5],[6,7]] => 000010
[[1,3,4,6,7],[2,5]] => [[1,2,3,5,6],[4,7]] => 001001
[[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => 001010
[[1,2,3,6,7],[4,5]] => [[1,2,3,4,7],[5,6]] => 000100
[[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => 010001
[[1,2,4,5,7],[3,6]] => [[1,2,4,5,7],[3,6]] => 010010
[[1,2,3,5,7],[4,6]] => [[1,2,4,6,7],[3,5]] => 010100
[[1,2,3,4,7],[5,6]] => [[1,2,3,6,7],[4,5]] => 001000
[[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]] => 100001
[[1,2,4,5,6],[3,7]] => [[1,3,4,5,7],[2,6]] => 100010
[[1,2,3,5,6],[4,7]] => [[1,3,4,6,7],[2,5]] => 100100
[[1,2,3,4,6],[5,7]] => [[1,3,5,6,7],[2,4]] => 101000
[[1,2,3,4,5],[6,7]] => [[1,2,5,6,7],[3,4]] => 010000
[[1,4,5,6,7],[2],[3]] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,5,6,7],[2],[4]] => [[1,2,3,4,6],[5],[7]] => 000101
[[1,2,5,6,7],[3],[4]] => [[1,2,3,4,7],[5],[6]] => 000110
[[1,3,4,6,7],[2],[5]] => [[1,2,3,5,6],[4],[7]] => 001001
[[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => 001010
[[1,2,3,6,7],[4],[5]] => [[1,2,3,6,7],[4],[5]] => 001100
[[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => 010001
[[1,2,4,5,7],[3],[6]] => [[1,2,4,5,7],[3],[6]] => 010010
[[1,2,3,5,7],[4],[6]] => [[1,2,4,6,7],[3],[5]] => 010100
[[1,2,3,4,7],[5],[6]] => [[1,2,5,6,7],[3],[4]] => 011000
[[1,3,4,5,6],[2],[7]] => [[1,3,4,5,6],[2],[7]] => 100001
[[1,2,4,5,6],[3],[7]] => [[1,3,4,5,7],[2],[6]] => 100010
[[1,2,3,5,6],[4],[7]] => [[1,3,4,6,7],[2],[5]] => 100100
[[1,2,3,4,6],[5],[7]] => [[1,3,5,6,7],[2],[4]] => 101000
[[1,2,3,4,5],[6],[7]] => [[1,4,5,6,7],[2],[3]] => 110000
[[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => 010101
[[1,2,5,7],[3,4,6]] => [[1,2,4,5],[3,6,7]] => 010010
[[1,3,4,7],[2,5,6]] => [[1,2,3,6],[4,5,7]] => 001001
[[1,2,4,7],[3,5,6]] => [[1,2,3,5],[4,6,7]] => 001010
[[1,2,3,7],[4,5,6]] => [[1,2,3,4],[5,6,7]] => 000100
[[1,3,5,6],[2,4,7]] => [[1,3,4,6],[2,5,7]] => 100101
[[1,2,5,6],[3,4,7]] => [[1,3,4,5],[2,6,7]] => 100010
[[1,3,4,6],[2,5,7]] => [[1,3,5,6],[2,4,7]] => 101001
[[1,2,4,6],[3,5,7]] => [[1,3,5,7],[2,4,6]] => 101010
[[1,2,3,6],[4,5,7]] => [[1,3,4,7],[2,5,6]] => 100100
[[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]] => 010001
[[1,2,4,5],[3,6,7]] => [[1,2,5,7],[3,4,6]] => 010010
[[1,2,3,5],[4,6,7]] => [[1,2,4,7],[3,5,6]] => 010100
[[1,2,3,4],[5,6,7]] => [[1,2,3,7],[4,5,6]] => 001000
[[1,4,6,7],[2,5],[3]] => [[1,2,3,5],[4,6],[7]] => 001011
[[1,3,6,7],[2,5],[4]] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,6,7],[3,5],[4]] => [[1,2,3,4],[5,7],[6]] => 000110
[[1,3,6,7],[2,4],[5]] => [[1,2,3,6],[4,7],[5]] => 001101
[[1,2,6,7],[3,4],[5]] => [[1,2,3,5],[4,7],[6]] => 001010
[[1,4,5,7],[2,6],[3]] => [[1,2,4,5],[3,6],[7]] => 010011
[[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,5],[7]] => 010101
[[1,2,5,7],[3,6],[4]] => [[1,2,4,7],[3,5],[6]] => 010110
[[1,3,4,7],[2,6],[5]] => [[1,2,3,6],[4,5],[7]] => 001001
[[1,2,4,7],[3,6],[5]] => [[1,2,3,7],[4,5],[6]] => 001010
[[1,2,3,7],[4,6],[5]] => [[1,2,3,7],[4,6],[5]] => 001100
[[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,7],[5]] => 010101
[[1,2,5,7],[3,4],[6]] => [[1,2,4,5],[3,7],[6]] => 010010
[[1,3,4,7],[2,5],[6]] => [[1,2,5,6],[3,7],[4]] => 011001
[[1,2,4,7],[3,5],[6]] => [[1,2,5,7],[3,6],[4]] => 011010
[[1,2,3,7],[4,5],[6]] => [[1,2,4,7],[3,6],[5]] => 010100
[[1,4,5,6],[2,7],[3]] => [[1,3,4,5],[2,6],[7]] => 100011
[[1,3,5,6],[2,7],[4]] => [[1,3,4,6],[2,5],[7]] => 100101
[[1,2,5,6],[3,7],[4]] => [[1,3,4,7],[2,5],[6]] => 100110
[[1,3,4,6],[2,7],[5]] => [[1,3,5,6],[2,4],[7]] => 101001
[[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,4],[6]] => 101010
[[1,2,3,6],[4,7],[5]] => [[1,3,6,7],[2,4],[5]] => 101100
[[1,3,4,5],[2,7],[6]] => [[1,2,5,6],[3,4],[7]] => 010001
[[1,2,4,5],[3,7],[6]] => [[1,2,5,7],[3,4],[6]] => 010010
[[1,2,3,5],[4,7],[6]] => [[1,2,6,7],[3,4],[5]] => 010100
[[1,2,3,4],[5,7],[6]] => [[1,2,6,7],[3,5],[4]] => 011000
[[1,3,5,6],[2,4],[7]] => [[1,3,4,6],[2,7],[5]] => 100101
[[1,2,5,6],[3,4],[7]] => [[1,3,4,5],[2,7],[6]] => 100010
[[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]] => 101001
[[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,6],[4]] => 101010
[[1,2,3,6],[4,5],[7]] => [[1,3,4,7],[2,6],[5]] => 100100
[[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]] => 110001
[[1,2,4,5],[3,6],[7]] => [[1,4,5,7],[2,6],[3]] => 110010
[[1,2,3,5],[4,6],[7]] => [[1,4,6,7],[2,5],[3]] => 110100
[[1,2,3,4],[5,6],[7]] => [[1,3,6,7],[2,5],[4]] => 101000
[[1,5,6,7],[2],[3],[4]] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,4,6,7],[2],[3],[5]] => [[1,2,3,5],[4],[6],[7]] => 001011
[[1,3,6,7],[2],[4],[5]] => [[1,2,3,6],[4],[5],[7]] => 001101
[[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => 001110
[[1,4,5,7],[2],[3],[6]] => [[1,2,4,5],[3],[6],[7]] => 010011
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => 010101
[[1,2,5,7],[3],[4],[6]] => [[1,2,4,7],[3],[5],[6]] => 010110
[[1,3,4,7],[2],[5],[6]] => [[1,2,5,6],[3],[4],[7]] => 011001
[[1,2,4,7],[3],[5],[6]] => [[1,2,5,7],[3],[4],[6]] => 011010
[[1,2,3,7],[4],[5],[6]] => [[1,2,6,7],[3],[4],[5]] => 011100
[[1,4,5,6],[2],[3],[7]] => [[1,3,4,5],[2],[6],[7]] => 100011
[[1,3,5,6],[2],[4],[7]] => [[1,3,4,6],[2],[5],[7]] => 100101
[[1,2,5,6],[3],[4],[7]] => [[1,3,4,7],[2],[5],[6]] => 100110
[[1,3,4,6],[2],[5],[7]] => [[1,3,5,6],[2],[4],[7]] => 101001
[[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => 101010
[[1,2,3,6],[4],[5],[7]] => [[1,3,6,7],[2],[4],[5]] => 101100
[[1,3,4,5],[2],[6],[7]] => [[1,4,5,6],[2],[3],[7]] => 110001
[[1,2,4,5],[3],[6],[7]] => [[1,4,5,7],[2],[3],[6]] => 110010
[[1,2,3,5],[4],[6],[7]] => [[1,4,6,7],[2],[3],[5]] => 110100
[[1,2,3,4],[5],[6],[7]] => [[1,5,6,7],[2],[3],[4]] => 111000
[[1,4,6],[2,5,7],[3]] => [[1,3,5],[2,4,6],[7]] => 101011
[[1,3,6],[2,5,7],[4]] => [[1,3,4],[2,5,6],[7]] => 100101
[[1,2,6],[3,5,7],[4]] => [[1,3,4],[2,5,7],[6]] => 100110
[[1,3,6],[2,4,7],[5]] => [[1,3,6],[2,4,7],[5]] => 101101
[[1,2,6],[3,4,7],[5]] => [[1,3,5],[2,4,7],[6]] => 101010
[[1,4,5],[2,6,7],[3]] => [[1,2,5],[3,4,6],[7]] => 010011
[[1,3,5],[2,6,7],[4]] => [[1,2,4],[3,5,6],[7]] => 010101
[[1,2,5],[3,6,7],[4]] => [[1,2,4],[3,5,7],[6]] => 010110
[[1,3,4],[2,6,7],[5]] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,4],[3,6,7],[5]] => [[1,2,3],[4,5,7],[6]] => 001010
[[1,2,3],[4,6,7],[5]] => [[1,2,3],[4,6,7],[5]] => 001100
[[1,3,5],[2,4,7],[6]] => [[1,2,6],[3,4,7],[5]] => 010101
[[1,2,5],[3,4,7],[6]] => [[1,2,5],[3,4,7],[6]] => 010010
[[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5,7],[4]] => 011001
[[1,2,4],[3,5,7],[6]] => [[1,2,5],[3,6,7],[4]] => 011010
[[1,2,3],[4,5,7],[6]] => [[1,2,4],[3,6,7],[5]] => 010100
[[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]] => 110101
[[1,2,5],[3,4,6],[7]] => [[1,4,5],[2,6,7],[3]] => 110010
[[1,3,4],[2,5,6],[7]] => [[1,3,6],[2,5,7],[4]] => 101001
[[1,2,4],[3,5,6],[7]] => [[1,3,5],[2,6,7],[4]] => 101010
[[1,2,3],[4,5,6],[7]] => [[1,3,4],[2,6,7],[5]] => 100100
[[1,4,7],[2,5],[3,6]] => [[1,2,5],[3,6],[4,7]] => 011011
[[1,3,7],[2,5],[4,6]] => [[1,2,4],[3,6],[5,7]] => 010101
[[1,2,7],[3,5],[4,6]] => [[1,2,4],[3,5],[6,7]] => 010110
[[1,3,7],[2,4],[5,6]] => [[1,2,3],[4,6],[5,7]] => 001101
[[1,2,7],[3,4],[5,6]] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,4,6],[2,5],[3,7]] => [[1,3,5],[2,6],[4,7]] => 101011
[[1,3,6],[2,5],[4,7]] => [[1,3,4],[2,6],[5,7]] => 100101
[[1,2,6],[3,5],[4,7]] => [[1,3,4],[2,5],[6,7]] => 100110
[[1,3,6],[2,4],[5,7]] => [[1,3,6],[2,4],[5,7]] => 101101
[[1,2,6],[3,4],[5,7]] => [[1,3,5],[2,4],[6,7]] => 101010
[[1,4,5],[2,6],[3,7]] => [[1,4,5],[2,6],[3,7]] => 110011
[[1,3,5],[2,6],[4,7]] => [[1,4,6],[2,5],[3,7]] => 110101
[[1,2,5],[3,6],[4,7]] => [[1,4,7],[2,5],[3,6]] => 110110
[[1,3,4],[2,6],[5,7]] => [[1,3,6],[2,5],[4,7]] => 101001
[[1,2,4],[3,6],[5,7]] => [[1,3,7],[2,5],[4,6]] => 101010
[[1,2,3],[4,6],[5,7]] => [[1,3,7],[2,4],[5,6]] => 101100
[[1,3,5],[2,4],[6,7]] => [[1,2,6],[3,4],[5,7]] => 010101
[[1,2,5],[3,4],[6,7]] => [[1,2,5],[3,4],[6,7]] => 010010
[[1,3,4],[2,5],[6,7]] => [[1,2,6],[3,5],[4,7]] => 011001
[[1,2,4],[3,5],[6,7]] => [[1,2,7],[3,5],[4,6]] => 011010
[[1,2,3],[4,5],[6,7]] => [[1,2,7],[3,4],[5,6]] => 010100
[[1,5,7],[2,6],[3],[4]] => [[1,2,4],[3,5],[6],[7]] => 010111
[[1,4,7],[2,6],[3],[5]] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,7],[2,6],[4],[5]] => [[1,2,3],[4,6],[5],[7]] => 001101
[[1,2,7],[3,6],[4],[5]] => [[1,2,3],[4,7],[5],[6]] => 001110
[[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => 011011
[[1,3,7],[2,5],[4],[6]] => [[1,2,4],[3,6],[5],[7]] => 010101
[[1,2,7],[3,5],[4],[6]] => [[1,2,4],[3,7],[5],[6]] => 010110
[[1,3,7],[2,4],[5],[6]] => [[1,2,6],[3,7],[4],[5]] => 011101
[[1,2,7],[3,4],[5],[6]] => [[1,2,5],[3,7],[4],[6]] => 011010
[[1,5,6],[2,7],[3],[4]] => [[1,3,4],[2,5],[6],[7]] => 100111
[[1,4,6],[2,7],[3],[5]] => [[1,3,5],[2,4],[6],[7]] => 101011
[[1,3,6],[2,7],[4],[5]] => [[1,3,6],[2,4],[5],[7]] => 101101
[[1,2,6],[3,7],[4],[5]] => [[1,3,7],[2,4],[5],[6]] => 101110
[[1,4,5],[2,7],[3],[6]] => [[1,2,5],[3,4],[6],[7]] => 010011
[[1,3,5],[2,7],[4],[6]] => [[1,2,6],[3,4],[5],[7]] => 010101
[[1,2,5],[3,7],[4],[6]] => [[1,2,7],[3,4],[5],[6]] => 010110
[[1,3,4],[2,7],[5],[6]] => [[1,2,6],[3,5],[4],[7]] => 011001
[[1,2,4],[3,7],[5],[6]] => [[1,2,7],[3,5],[4],[6]] => 011010
[[1,2,3],[4,7],[5],[6]] => [[1,2,7],[3,6],[4],[5]] => 011100
[[1,4,6],[2,5],[3],[7]] => [[1,3,5],[2,6],[4],[7]] => 101011
[[1,3,6],[2,5],[4],[7]] => [[1,3,4],[2,6],[5],[7]] => 100101
[[1,2,6],[3,5],[4],[7]] => [[1,3,4],[2,7],[5],[6]] => 100110
[[1,3,6],[2,4],[5],[7]] => [[1,3,6],[2,7],[4],[5]] => 101101
[[1,2,6],[3,4],[5],[7]] => [[1,3,5],[2,7],[4],[6]] => 101010
[[1,4,5],[2,6],[3],[7]] => [[1,4,5],[2,6],[3],[7]] => 110011
[[1,3,5],[2,6],[4],[7]] => [[1,4,6],[2,5],[3],[7]] => 110101
[[1,2,5],[3,6],[4],[7]] => [[1,4,7],[2,5],[3],[6]] => 110110
[[1,3,4],[2,6],[5],[7]] => [[1,3,6],[2,5],[4],[7]] => 101001
[[1,2,4],[3,6],[5],[7]] => [[1,3,7],[2,5],[4],[6]] => 101010
[[1,2,3],[4,6],[5],[7]] => [[1,3,7],[2,6],[4],[5]] => 101100
[[1,3,5],[2,4],[6],[7]] => [[1,4,6],[2,7],[3],[5]] => 110101
[[1,2,5],[3,4],[6],[7]] => [[1,4,5],[2,7],[3],[6]] => 110010
[[1,3,4],[2,5],[6],[7]] => [[1,5,6],[2,7],[3],[4]] => 111001
[[1,2,4],[3,5],[6],[7]] => [[1,5,7],[2,6],[3],[4]] => 111010
[[1,2,3],[4,5],[6],[7]] => [[1,4,7],[2,6],[3],[5]] => 110100
[[1,6,7],[2],[3],[4],[5]] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,5,7],[2],[3],[4],[6]] => [[1,2,4],[3],[5],[6],[7]] => 010111
[[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => 011011
[[1,3,7],[2],[4],[5],[6]] => [[1,2,6],[3],[4],[5],[7]] => 011101
[[1,2,7],[3],[4],[5],[6]] => [[1,2,7],[3],[4],[5],[6]] => 011110
[[1,5,6],[2],[3],[4],[7]] => [[1,3,4],[2],[5],[6],[7]] => 100111
[[1,4,6],[2],[3],[5],[7]] => [[1,3,5],[2],[4],[6],[7]] => 101011
[[1,3,6],[2],[4],[5],[7]] => [[1,3,6],[2],[4],[5],[7]] => 101101
[[1,2,6],[3],[4],[5],[7]] => [[1,3,7],[2],[4],[5],[6]] => 101110
[[1,4,5],[2],[3],[6],[7]] => [[1,4,5],[2],[3],[6],[7]] => 110011
[[1,3,5],[2],[4],[6],[7]] => [[1,4,6],[2],[3],[5],[7]] => 110101
[[1,2,5],[3],[4],[6],[7]] => [[1,4,7],[2],[3],[5],[6]] => 110110
[[1,3,4],[2],[5],[6],[7]] => [[1,5,6],[2],[3],[4],[7]] => 111001
[[1,2,4],[3],[5],[6],[7]] => [[1,5,7],[2],[3],[4],[6]] => 111010
[[1,2,3],[4],[5],[6],[7]] => [[1,6,7],[2],[3],[4],[5]] => 111100
[[1,5],[2,6],[3,7],[4]] => [[1,4],[2,5],[3,6],[7]] => 110111
[[1,4],[2,6],[3,7],[5]] => [[1,3],[2,5],[4,6],[7]] => 101011
[[1,3],[2,6],[4,7],[5]] => [[1,3],[2,4],[5,6],[7]] => 101101
[[1,2],[3,6],[4,7],[5]] => [[1,3],[2,4],[5,7],[6]] => 101110
[[1,4],[2,5],[3,7],[6]] => [[1,2],[3,5],[4,6],[7]] => 011011
[[1,3],[2,5],[4,7],[6]] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,5],[4,7],[6]] => [[1,2],[3,4],[5,7],[6]] => 010110
[[1,3],[2,4],[5,7],[6]] => [[1,2],[3,6],[4,7],[5]] => 011101
[[1,2],[3,4],[5,7],[6]] => [[1,2],[3,5],[4,7],[6]] => 011010
[[1,4],[2,5],[3,6],[7]] => [[1,5],[2,6],[3,7],[4]] => 111011
[[1,3],[2,5],[4,6],[7]] => [[1,4],[2,6],[3,7],[5]] => 110101
[[1,2],[3,5],[4,6],[7]] => [[1,4],[2,5],[3,7],[6]] => 110110
[[1,3],[2,4],[5,6],[7]] => [[1,3],[2,6],[4,7],[5]] => 101101
[[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => 101010
[[1,6],[2,7],[3],[4],[5]] => [[1,3],[2,4],[5],[6],[7]] => 101111
[[1,5],[2,7],[3],[4],[6]] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,4],[2,7],[3],[5],[6]] => [[1,2],[3,5],[4],[6],[7]] => 011011
[[1,3],[2,7],[4],[5],[6]] => [[1,2],[3,6],[4],[5],[7]] => 011101
[[1,2],[3,7],[4],[5],[6]] => [[1,2],[3,7],[4],[5],[6]] => 011110
[[1,5],[2,6],[3],[4],[7]] => [[1,4],[2,5],[3],[6],[7]] => 110111
[[1,4],[2,6],[3],[5],[7]] => [[1,3],[2,5],[4],[6],[7]] => 101011
[[1,3],[2,6],[4],[5],[7]] => [[1,3],[2,6],[4],[5],[7]] => 101101
[[1,2],[3,6],[4],[5],[7]] => [[1,3],[2,7],[4],[5],[6]] => 101110
[[1,4],[2,5],[3],[6],[7]] => [[1,5],[2,6],[3],[4],[7]] => 111011
[[1,3],[2,5],[4],[6],[7]] => [[1,4],[2,6],[3],[5],[7]] => 110101
[[1,2],[3,5],[4],[6],[7]] => [[1,4],[2,7],[3],[5],[6]] => 110110
[[1,3],[2,4],[5],[6],[7]] => [[1,6],[2,7],[3],[4],[5]] => 111101
[[1,2],[3,4],[5],[6],[7]] => [[1,5],[2,7],[3],[4],[6]] => 111010
[[1,7],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,6],[2],[3],[4],[5],[7]] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[[1,5],[2],[3],[4],[6],[7]] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[[1,4],[2],[3],[5],[6],[7]] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[[1,3],[2],[4],[5],[6],[7]] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[[1,2],[3],[4],[5],[6],[7]] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => 111111
[[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => 0000000
[[1,3,4,5,6,7,8],[2]] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,4,5,6,7,8],[3]] => [[1,2,3,4,5,6,8],[7]] => 0000010
[[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,5,7,8],[6]] => 0000100
[[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,6,7,8],[5]] => 0001000
[[1,2,3,4,5,7,8],[6]] => [[1,2,3,5,6,7,8],[4]] => 0010000
[[1,2,3,4,5,6,8],[7]] => [[1,2,4,5,6,7,8],[3]] => 0100000
[[1,2,3,4,5,6,7],[8]] => [[1,3,4,5,6,7,8],[2]] => 1000000
[[1,3,5,6,7,8],[2,4]] => [[1,2,3,4,5,7],[6,8]] => 0000101
[[1,2,5,6,7,8],[3,4]] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,3,4,6,7,8],[2,5]] => [[1,2,3,4,6,7],[5,8]] => 0001001
[[1,2,4,6,7,8],[3,5]] => [[1,2,3,4,6,8],[5,7]] => 0001010
[[1,2,3,6,7,8],[4,5]] => [[1,2,3,4,5,8],[6,7]] => 0000100
[[1,3,4,5,7,8],[2,6]] => [[1,2,3,5,6,7],[4,8]] => 0010001
[[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => 0010010
[[1,2,3,5,7,8],[4,6]] => [[1,2,3,5,7,8],[4,6]] => 0010100
[[1,2,3,4,7,8],[5,6]] => [[1,2,3,4,7,8],[5,6]] => 0001000
[[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => 0100001
[[1,2,4,5,6,8],[3,7]] => [[1,2,4,5,6,8],[3,7]] => 0100010
[[1,2,3,5,6,8],[4,7]] => [[1,2,4,5,7,8],[3,6]] => 0100100
[[1,2,3,4,6,8],[5,7]] => [[1,2,4,6,7,8],[3,5]] => 0101000
[[1,2,3,4,5,8],[6,7]] => [[1,2,3,6,7,8],[4,5]] => 0010000
[[1,3,4,5,6,7],[2,8]] => [[1,3,4,5,6,7],[2,8]] => 1000001
[[1,2,4,5,6,7],[3,8]] => [[1,3,4,5,6,8],[2,7]] => 1000010
[[1,2,3,5,6,7],[4,8]] => [[1,3,4,5,7,8],[2,6]] => 1000100
[[1,2,3,4,6,7],[5,8]] => [[1,3,4,6,7,8],[2,5]] => 1001000
[[1,2,3,4,5,7],[6,8]] => [[1,3,5,6,7,8],[2,4]] => 1010000
[[1,2,3,4,5,6],[7,8]] => [[1,2,5,6,7,8],[3,4]] => 0100000
[[1,4,5,6,7,8],[2],[3]] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,5,6,7,8],[2],[4]] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[[1,2,5,6,7,8],[3],[4]] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[[1,3,4,6,7,8],[2],[5]] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[[1,2,4,6,7,8],[3],[5]] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[[1,3,4,5,7,8],[2],[6]] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[[1,2,3,5,7,8],[4],[6]] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[[1,2,3,4,7,8],[5],[6]] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[[1,2,4,5,6,8],[3],[7]] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[[1,2,3,5,6,8],[4],[7]] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[[1,2,3,4,6,8],[5],[7]] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[[1,2,3,4,5,8],[6],[7]] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[[1,3,4,5,6,7],[2],[8]] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[[1,2,4,5,6,7],[3],[8]] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[[1,2,3,5,6,7],[4],[8]] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[[1,2,3,4,6,7],[5],[8]] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[[1,2,3,4,5,7],[6],[8]] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[[1,2,3,4,5,6],[7],[8]] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[[1,3,5,7,8],[2,4,6]] => [[1,2,3,5,7],[4,6,8]] => 0010101
[[1,2,5,7,8],[3,4,6]] => [[1,2,3,5,6],[4,7,8]] => 0010010
[[1,3,4,7,8],[2,5,6]] => [[1,2,3,4,7],[5,6,8]] => 0001001
[[1,2,4,7,8],[3,5,6]] => [[1,2,3,4,6],[5,7,8]] => 0001010
[[1,2,3,7,8],[4,5,6]] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,5,6,8],[2,4,7]] => [[1,2,4,5,7],[3,6,8]] => 0100101
[[1,2,5,6,8],[3,4,7]] => [[1,2,4,5,6],[3,7,8]] => 0100010
[[1,3,4,6,8],[2,5,7]] => [[1,2,4,6,7],[3,5,8]] => 0101001
[[1,2,4,6,8],[3,5,7]] => [[1,2,4,6,8],[3,5,7]] => 0101010
[[1,2,3,6,8],[4,5,7]] => [[1,2,4,5,8],[3,6,7]] => 0100100
[[1,3,4,5,8],[2,6,7]] => [[1,2,3,6,7],[4,5,8]] => 0010001
[[1,2,4,5,8],[3,6,7]] => [[1,2,3,6,8],[4,5,7]] => 0010010
[[1,2,3,5,8],[4,6,7]] => [[1,2,3,5,8],[4,6,7]] => 0010100
[[1,2,3,4,8],[5,6,7]] => [[1,2,3,4,8],[5,6,7]] => 0001000
[[1,3,5,6,7],[2,4,8]] => [[1,3,4,5,7],[2,6,8]] => 1000101
[[1,2,5,6,7],[3,4,8]] => [[1,3,4,5,6],[2,7,8]] => 1000010
[[1,3,4,6,7],[2,5,8]] => [[1,3,4,6,7],[2,5,8]] => 1001001
[[1,2,4,6,7],[3,5,8]] => [[1,3,4,6,8],[2,5,7]] => 1001010
[[1,2,3,6,7],[4,5,8]] => [[1,3,4,5,8],[2,6,7]] => 1000100
[[1,3,4,5,7],[2,6,8]] => [[1,3,5,6,7],[2,4,8]] => 1010001
[[1,2,4,5,7],[3,6,8]] => [[1,3,5,6,8],[2,4,7]] => 1010010
[[1,2,3,5,7],[4,6,8]] => [[1,3,5,7,8],[2,4,6]] => 1010100
[[1,2,3,4,7],[5,6,8]] => [[1,3,4,7,8],[2,5,6]] => 1001000
[[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]] => 0100001
[[1,2,4,5,6],[3,7,8]] => [[1,2,5,6,8],[3,4,7]] => 0100010
[[1,2,3,5,6],[4,7,8]] => [[1,2,5,7,8],[3,4,6]] => 0100100
[[1,2,3,4,6],[5,7,8]] => [[1,2,4,7,8],[3,5,6]] => 0101000
[[1,2,3,4,5],[6,7,8]] => [[1,2,3,7,8],[4,5,6]] => 0010000
[[1,4,6,7,8],[2,5],[3]] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[[1,3,6,7,8],[2,5],[4]] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,6,7,8],[3,5],[4]] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[[1,3,6,7,8],[2,4],[5]] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[[1,2,6,7,8],[3,4],[5]] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[[1,4,5,7,8],[2,6],[3]] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[[1,3,5,7,8],[2,6],[4]] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[[1,2,5,7,8],[3,6],[4]] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[[1,3,4,7,8],[2,6],[5]] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[[1,2,4,7,8],[3,6],[5]] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[[1,3,5,7,8],[2,4],[6]] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[[1,2,5,7,8],[3,4],[6]] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[[1,3,4,7,8],[2,5],[6]] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[[1,2,4,7,8],[3,5],[6]] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[[1,2,3,7,8],[4,5],[6]] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[[1,4,5,6,8],[2,7],[3]] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[[1,3,5,6,8],[2,7],[4]] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[[1,2,5,6,8],[3,7],[4]] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[[1,3,4,6,8],[2,7],[5]] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[[1,2,4,6,8],[3,7],[5]] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[[1,2,3,6,8],[4,7],[5]] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[[1,3,4,5,8],[2,7],[6]] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[[1,2,4,5,8],[3,7],[6]] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[[1,2,3,5,8],[4,7],[6]] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[[1,2,3,4,8],[5,7],[6]] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[[1,3,5,6,8],[2,4],[7]] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[[1,2,5,6,8],[3,4],[7]] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[[1,3,4,6,8],[2,5],[7]] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[[1,2,4,6,8],[3,5],[7]] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[[1,2,3,6,8],[4,5],[7]] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[[1,3,4,5,8],[2,6],[7]] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[[1,2,4,5,8],[3,6],[7]] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[[1,2,3,5,8],[4,6],[7]] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[[1,2,3,4,8],[5,6],[7]] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[[1,4,5,6,7],[2,8],[3]] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[[1,3,5,6,7],[2,8],[4]] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[[1,2,5,6,7],[3,8],[4]] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[[1,3,4,6,7],[2,8],[5]] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[[1,2,4,6,7],[3,8],[5]] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[[1,2,3,6,7],[4,8],[5]] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[[1,3,4,5,7],[2,8],[6]] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[[1,2,4,5,7],[3,8],[6]] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[[1,2,3,5,7],[4,8],[6]] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[[1,2,3,4,7],[5,8],[6]] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[[1,3,4,5,6],[2,8],[7]] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[[1,2,4,5,6],[3,8],[7]] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[[1,2,3,5,6],[4,8],[7]] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[[1,2,3,4,6],[5,8],[7]] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[[1,2,3,4,5],[6,8],[7]] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[[1,3,5,6,7],[2,4],[8]] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[[1,2,5,6,7],[3,4],[8]] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[[1,3,4,6,7],[2,5],[8]] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[[1,2,4,6,7],[3,5],[8]] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[[1,2,3,6,7],[4,5],[8]] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[[1,3,4,5,7],[2,6],[8]] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[[1,2,3,5,7],[4,6],[8]] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[[1,2,3,4,7],[5,6],[8]] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[[1,2,4,5,6],[3,7],[8]] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[[1,2,3,5,6],[4,7],[8]] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[[1,2,3,4,6],[5,7],[8]] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[[1,2,3,4,5],[6,7],[8]] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[[1,5,6,7,8],[2],[3],[4]] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,4,6,7,8],[2],[3],[5]] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[[1,3,6,7,8],[2],[4],[5]] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[[1,4,5,7,8],[2],[3],[6]] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[[1,3,5,7,8],[2],[4],[6]] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[[1,3,4,7,8],[2],[5],[6]] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[[1,4,5,6,8],[2],[3],[7]] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[[1,2,5,6,8],[3],[4],[7]] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[[1,2,4,6,8],[3],[5],[7]] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[[1,2,3,6,8],[4],[5],[7]] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[[1,3,4,5,8],[2],[6],[7]] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[[1,2,4,5,8],[3],[6],[7]] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[[1,2,3,5,8],[4],[6],[7]] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[[1,2,3,4,8],[5],[6],[7]] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[[1,4,5,6,7],[2],[3],[8]] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[[1,3,5,6,7],[2],[4],[8]] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[[1,2,5,6,7],[3],[4],[8]] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[[1,3,4,6,7],[2],[5],[8]] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[[1,2,4,6,7],[3],[5],[8]] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[[1,2,3,6,7],[4],[5],[8]] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[[1,3,4,5,7],[2],[6],[8]] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[[1,2,4,5,7],[3],[6],[8]] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[[1,2,3,5,7],[4],[6],[8]] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[[1,2,3,4,7],[5],[6],[8]] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[[1,3,4,5,6],[2],[7],[8]] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[[1,2,4,5,6],[3],[7],[8]] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[[1,2,3,5,6],[4],[7],[8]] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[[1,2,3,4,6],[5],[7],[8]] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[[1,2,3,4,5],[6],[7],[8]] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[[1,3,5,7],[2,4,6,8]] => [[1,3,5,7],[2,4,6,8]] => 1010101
[[1,2,5,7],[3,4,6,8]] => [[1,3,5,6],[2,4,7,8]] => 1010010
[[1,3,4,7],[2,5,6,8]] => [[1,3,4,7],[2,5,6,8]] => 1001001
[[1,2,4,7],[3,5,6,8]] => [[1,3,4,6],[2,5,7,8]] => 1001010
[[1,2,3,7],[4,5,6,8]] => [[1,3,4,5],[2,6,7,8]] => 1000100
[[1,3,5,6],[2,4,7,8]] => [[1,2,5,7],[3,4,6,8]] => 0100101
[[1,2,5,6],[3,4,7,8]] => [[1,2,5,6],[3,4,7,8]] => 0100010
[[1,3,4,6],[2,5,7,8]] => [[1,2,4,7],[3,5,6,8]] => 0101001
[[1,2,4,6],[3,5,7,8]] => [[1,2,4,6],[3,5,7,8]] => 0101010
[[1,2,3,6],[4,5,7,8]] => [[1,2,4,5],[3,6,7,8]] => 0100100
[[1,3,4,5],[2,6,7,8]] => [[1,2,3,7],[4,5,6,8]] => 0010001
[[1,2,4,5],[3,6,7,8]] => [[1,2,3,6],[4,5,7,8]] => 0010010
[[1,2,3,5],[4,6,7,8]] => [[1,2,3,5],[4,6,7,8]] => 0010100
[[1,2,3,4],[5,6,7,8]] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,4,6,8],[2,5,7],[3]] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[[1,3,6,8],[2,5,7],[4]] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[[1,2,6,8],[3,5,7],[4]] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[[1,2,6,8],[3,4,7],[5]] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[[1,4,5,8],[2,6,7],[3]] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[[1,3,5,8],[2,6,7],[4]] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[[1,2,5,8],[3,6,7],[4]] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[[1,3,4,8],[2,6,7],[5]] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,8],[3,6,7],[5]] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[[1,2,3,8],[4,6,7],[5]] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[[1,3,5,8],[2,4,7],[6]] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[[1,2,5,8],[3,4,7],[6]] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[[1,3,4,8],[2,5,7],[6]] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[[1,2,4,8],[3,5,7],[6]] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[[1,2,3,8],[4,5,7],[6]] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[[1,3,5,8],[2,4,6],[7]] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[[1,2,5,8],[3,4,6],[7]] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[[1,3,4,8],[2,5,6],[7]] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[[1,2,4,8],[3,5,6],[7]] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[[1,2,3,8],[4,5,6],[7]] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[[1,4,6,7],[2,5,8],[3]] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[[1,3,6,7],[2,5,8],[4]] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[[1,2,6,7],[3,5,8],[4]] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[[1,3,6,7],[2,4,8],[5]] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[[1,2,6,7],[3,4,8],[5]] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[[1,4,5,7],[2,6,8],[3]] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[[1,3,5,7],[2,6,8],[4]] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[[1,2,5,7],[3,6,8],[4]] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[[1,3,4,7],[2,6,8],[5]] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[[1,2,4,7],[3,6,8],[5]] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[[1,3,5,7],[2,4,8],[6]] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[[1,2,5,7],[3,4,8],[6]] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[[1,3,4,7],[2,5,8],[6]] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[[1,2,4,7],[3,5,8],[6]] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[[1,2,3,7],[4,5,8],[6]] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[[1,4,5,6],[2,7,8],[3]] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[[1,3,5,6],[2,7,8],[4]] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[[1,2,5,6],[3,7,8],[4]] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[[1,3,4,6],[2,7,8],[5]] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[[1,2,4,6],[3,7,8],[5]] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[[1,2,3,6],[4,7,8],[5]] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[[1,3,4,5],[2,7,8],[6]] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[[1,2,4,5],[3,7,8],[6]] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[[1,2,3,5],[4,7,8],[6]] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[[1,2,3,4],[5,7,8],[6]] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[[1,3,5,6],[2,4,8],[7]] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[[1,2,5,6],[3,4,8],[7]] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[[1,3,4,6],[2,5,8],[7]] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[[1,2,4,6],[3,5,8],[7]] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[[1,2,3,6],[4,5,8],[7]] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[[1,3,4,5],[2,6,8],[7]] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[[1,2,4,5],[3,6,8],[7]] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[[1,2,3,5],[4,6,8],[7]] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[[1,2,3,4],[5,6,8],[7]] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[[1,3,5,7],[2,4,6],[8]] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[[1,2,5,7],[3,4,6],[8]] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[[1,3,4,7],[2,5,6],[8]] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[[1,2,4,7],[3,5,6],[8]] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[[1,2,3,7],[4,5,6],[8]] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[[1,3,5,6],[2,4,7],[8]] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[[1,2,5,6],[3,4,7],[8]] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[[1,3,4,6],[2,5,7],[8]] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[[1,2,4,6],[3,5,7],[8]] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[[1,2,3,6],[4,5,7],[8]] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[[1,3,4,5],[2,6,7],[8]] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[[1,2,4,5],[3,6,7],[8]] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[[1,2,3,5],[4,6,7],[8]] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[[1,2,3,4],[5,6,7],[8]] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[[1,4,7,8],[2,5],[3,6]] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[[1,3,7,8],[2,5],[4,6]] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[[1,2,7,8],[3,5],[4,6]] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[[1,3,7,8],[2,4],[5,6]] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[[1,2,7,8],[3,4],[5,6]] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,6,8],[2,5],[3,7]] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[[1,3,6,8],[2,5],[4,7]] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[[1,2,6,8],[3,5],[4,7]] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[[1,3,6,8],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[[1,2,6,8],[3,4],[5,7]] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[[1,3,5,8],[2,6],[4,7]] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[[1,2,5,8],[3,6],[4,7]] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[[1,3,4,8],[2,6],[5,7]] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[[1,2,4,8],[3,6],[5,7]] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[[1,2,3,8],[4,6],[5,7]] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[[1,3,5,8],[2,4],[6,7]] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[[1,2,5,8],[3,4],[6,7]] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[[1,3,4,8],[2,5],[6,7]] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[[1,2,4,8],[3,5],[6,7]] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[[1,2,3,8],[4,5],[6,7]] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[[1,4,6,7],[2,5],[3,8]] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[[1,3,6,7],[2,5],[4,8]] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[[1,2,6,7],[3,5],[4,8]] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[[1,3,6,7],[2,4],[5,8]] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[[1,2,6,7],[3,4],[5,8]] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[[1,4,5,7],[2,6],[3,8]] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[[1,3,5,7],[2,6],[4,8]] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[[1,2,5,7],[3,6],[4,8]] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[[1,3,4,7],[2,6],[5,8]] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[[1,2,4,7],[3,6],[5,8]] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[[1,2,3,7],[4,6],[5,8]] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[[1,3,5,7],[2,4],[6,8]] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[[1,2,5,7],[3,4],[6,8]] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[[1,3,4,7],[2,5],[6,8]] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[[1,2,4,7],[3,5],[6,8]] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[[1,2,3,7],[4,5],[6,8]] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[[1,4,5,6],[2,7],[3,8]] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[[1,3,5,6],[2,7],[4,8]] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[[1,2,5,6],[3,7],[4,8]] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[[1,3,4,6],[2,7],[5,8]] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[[1,2,4,6],[3,7],[5,8]] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[[1,2,3,6],[4,7],[5,8]] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[[1,3,4,5],[2,7],[6,8]] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[[1,2,4,5],[3,7],[6,8]] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[[1,2,3,5],[4,7],[6,8]] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[[1,2,3,4],[5,7],[6,8]] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[[1,3,5,6],[2,4],[7,8]] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[[1,2,5,6],[3,4],[7,8]] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[[1,3,4,6],[2,5],[7,8]] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[[1,2,4,6],[3,5],[7,8]] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[[1,2,3,6],[4,5],[7,8]] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[[1,3,4,5],[2,6],[7,8]] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[[1,2,4,5],[3,6],[7,8]] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[[1,2,3,5],[4,6],[7,8]] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[[1,2,3,4],[5,6],[7,8]] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[[1,5,7,8],[2,6],[3],[4]] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[[1,4,7,8],[2,6],[3],[5]] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,7,8],[2,6],[4],[5]] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[[1,2,7,8],[3,6],[4],[5]] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[[1,4,7,8],[2,5],[3],[6]] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[[1,3,7,8],[2,5],[4],[6]] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[[1,2,7,8],[3,5],[4],[6]] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[[1,3,7,8],[2,4],[5],[6]] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[[1,2,7,8],[3,4],[5],[6]] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[[1,5,6,8],[2,7],[3],[4]] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[[1,4,6,8],[2,7],[3],[5]] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[[1,2,6,8],[3,7],[4],[5]] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[[1,4,5,8],[2,7],[3],[6]] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[[1,3,5,8],[2,7],[4],[6]] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[[1,2,5,8],[3,7],[4],[6]] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[[1,3,4,8],[2,7],[5],[6]] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[[1,2,4,8],[3,7],[5],[6]] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[[1,2,3,8],[4,7],[5],[6]] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[[1,4,6,8],[2,5],[3],[7]] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[[1,3,6,8],[2,5],[4],[7]] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[[1,2,6,8],[3,5],[4],[7]] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[[1,2,6,8],[3,4],[5],[7]] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[[1,3,5,8],[2,6],[4],[7]] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[[1,2,5,8],[3,6],[4],[7]] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[[1,3,4,8],[2,6],[5],[7]] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[[1,2,4,8],[3,6],[5],[7]] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[[1,2,3,8],[4,6],[5],[7]] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[[1,3,5,8],[2,4],[6],[7]] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[[1,2,5,8],[3,4],[6],[7]] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[[1,3,4,8],[2,5],[6],[7]] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[[1,2,4,8],[3,5],[6],[7]] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[[1,2,3,8],[4,5],[6],[7]] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[[1,5,6,7],[2,8],[3],[4]] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[[1,4,6,7],[2,8],[3],[5]] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[[1,3,6,7],[2,8],[4],[5]] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[[1,2,6,7],[3,8],[4],[5]] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[[1,4,5,7],[2,8],[3],[6]] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[[1,3,5,7],[2,8],[4],[6]] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[[1,2,5,7],[3,8],[4],[6]] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[[1,3,4,7],[2,8],[5],[6]] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[[1,2,4,7],[3,8],[5],[6]] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[[1,2,3,7],[4,8],[5],[6]] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[[1,4,5,6],[2,8],[3],[7]] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[[1,3,5,6],[2,8],[4],[7]] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[[1,2,5,6],[3,8],[4],[7]] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[[1,2,4,6],[3,8],[5],[7]] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[[1,2,3,6],[4,8],[5],[7]] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[[1,2,4,5],[3,8],[6],[7]] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[[1,2,3,5],[4,8],[6],[7]] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[[1,2,3,4],[5,8],[6],[7]] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[[1,4,6,7],[2,5],[3],[8]] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[[1,3,6,7],[2,5],[4],[8]] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[[1,2,6,7],[3,5],[4],[8]] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[[1,3,6,7],[2,4],[5],[8]] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[[1,2,6,7],[3,4],[5],[8]] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[[1,4,5,7],[2,6],[3],[8]] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[[1,3,5,7],[2,6],[4],[8]] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[[1,2,5,7],[3,6],[4],[8]] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[[1,3,4,7],[2,6],[5],[8]] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[[1,2,4,7],[3,6],[5],[8]] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[[1,2,3,7],[4,6],[5],[8]] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[[1,3,5,7],[2,4],[6],[8]] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[[1,2,5,7],[3,4],[6],[8]] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[[1,3,4,7],[2,5],[6],[8]] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[[1,2,4,7],[3,5],[6],[8]] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[[1,2,3,7],[4,5],[6],[8]] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[[1,4,5,6],[2,7],[3],[8]] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[[1,3,5,6],[2,7],[4],[8]] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[[1,2,5,6],[3,7],[4],[8]] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[[1,3,4,6],[2,7],[5],[8]] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[[1,2,4,6],[3,7],[5],[8]] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[[1,2,3,6],[4,7],[5],[8]] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[[1,3,4,5],[2,7],[6],[8]] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[[1,2,4,5],[3,7],[6],[8]] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[[1,2,3,5],[4,7],[6],[8]] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[[1,2,3,4],[5,7],[6],[8]] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[[1,3,5,6],[2,4],[7],[8]] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[[1,2,5,6],[3,4],[7],[8]] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[[1,3,4,6],[2,5],[7],[8]] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[[1,2,4,6],[3,5],[7],[8]] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[[1,2,3,6],[4,5],[7],[8]] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[[1,3,4,5],[2,6],[7],[8]] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[[1,2,4,5],[3,6],[7],[8]] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[[1,2,3,5],[4,6],[7],[8]] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[[1,2,3,4],[5,6],[7],[8]] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[[1,6,7,8],[2],[3],[4],[5]] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,5,7,8],[2],[3],[4],[6]] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[[1,4,7,8],[2],[3],[5],[6]] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[[1,3,7,8],[2],[4],[5],[6]] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[[1,2,7,8],[3],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[[1,4,6,8],[2],[3],[5],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[[1,2,6,8],[3],[4],[5],[7]] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[[1,4,5,8],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[[1,2,5,8],[3],[4],[6],[7]] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[[1,3,4,8],[2],[5],[6],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[[1,2,4,8],[3],[5],[6],[7]] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[[1,2,3,8],[4],[5],[6],[7]] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[[1,5,6,7],[2],[3],[4],[8]] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[[1,4,6,7],[2],[3],[5],[8]] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[[1,3,6,7],[2],[4],[5],[8]] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[[1,2,6,7],[3],[4],[5],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[[1,4,5,7],[2],[3],[6],[8]] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[[1,3,5,7],[2],[4],[6],[8]] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[[1,2,5,7],[3],[4],[6],[8]] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[[1,3,4,7],[2],[5],[6],[8]] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[[1,2,4,7],[3],[5],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[[1,2,3,7],[4],[5],[6],[8]] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[[1,4,5,6],[2],[3],[7],[8]] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[[1,3,5,6],[2],[4],[7],[8]] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[[1,2,5,6],[3],[4],[7],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[[1,3,4,6],[2],[5],[7],[8]] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[[1,2,4,6],[3],[5],[7],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[[1,2,3,6],[4],[5],[7],[8]] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[[1,3,4,5],[2],[6],[7],[8]] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[[1,2,4,5],[3],[6],[7],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[[1,2,3,5],[4],[6],[7],[8]] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[[1,2,3,4],[5],[6],[7],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[[1,4,7],[2,5,8],[3,6]] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[[1,3,7],[2,5,8],[4,6]] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[[1,2,7],[3,5,8],[4,6]] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[[1,3,7],[2,4,8],[5,6]] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[[1,2,7],[3,4,8],[5,6]] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[[1,4,6],[2,5,8],[3,7]] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[[1,3,6],[2,5,8],[4,7]] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[[1,2,6],[3,5,8],[4,7]] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[[1,3,6],[2,4,8],[5,7]] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[[1,2,6],[3,4,8],[5,7]] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[[1,4,5],[2,6,8],[3,7]] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[[1,3,5],[2,6,8],[4,7]] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[[1,2,5],[3,6,8],[4,7]] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[[1,3,4],[2,6,8],[5,7]] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[[1,2,4],[3,6,8],[5,7]] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[[1,2,3],[4,6,8],[5,7]] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[[1,3,5],[2,4,8],[6,7]] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[[1,2,5],[3,4,8],[6,7]] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,5,8],[6,7]] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[[1,2,4],[3,5,8],[6,7]] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[[1,2,3],[4,5,8],[6,7]] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[[1,4,6],[2,5,7],[3,8]] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[[1,3,6],[2,5,7],[4,8]] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[[1,2,6],[3,5,7],[4,8]] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[[1,3,6],[2,4,7],[5,8]] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[[1,2,6],[3,4,7],[5,8]] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[[1,4,5],[2,6,7],[3,8]] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[[1,3,5],[2,6,7],[4,8]] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[[1,2,5],[3,6,7],[4,8]] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[[1,3,4],[2,6,7],[5,8]] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[[1,2,4],[3,6,7],[5,8]] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[[1,2,3],[4,6,7],[5,8]] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[[1,3,5],[2,4,7],[6,8]] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[[1,2,5],[3,4,7],[6,8]] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[[1,3,4],[2,5,7],[6,8]] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[[1,2,4],[3,5,7],[6,8]] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[[1,2,3],[4,5,7],[6,8]] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[[1,3,5],[2,4,6],[7,8]] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[[1,2,5],[3,4,6],[7,8]] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[[1,3,4],[2,5,6],[7,8]] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[[1,2,4],[3,5,6],[7,8]] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[[1,2,3],[4,5,6],[7,8]] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[[1,5,7],[2,6,8],[3],[4]] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[[1,4,7],[2,6,8],[3],[5]] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[[1,3,7],[2,6,8],[4],[5]] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[[1,2,7],[3,6,8],[4],[5]] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[[1,4,7],[2,5,8],[3],[6]] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[[1,3,7],[2,5,8],[4],[6]] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[[1,2,7],[3,5,8],[4],[6]] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[[1,3,7],[2,4,8],[5],[6]] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[[1,2,7],[3,4,8],[5],[6]] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[[1,5,6],[2,7,8],[3],[4]] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[[1,4,6],[2,7,8],[3],[5]] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[[1,3,6],[2,7,8],[4],[5]] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[[1,2,6],[3,7,8],[4],[5]] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[[1,4,5],[2,7,8],[3],[6]] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,7,8],[4],[6]] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[[1,2,5],[3,7,8],[4],[6]] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[[1,3,4],[2,7,8],[5],[6]] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[[1,2,4],[3,7,8],[5],[6]] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[[1,2,3],[4,7,8],[5],[6]] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[[1,4,6],[2,5,8],[3],[7]] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[[1,3,6],[2,5,8],[4],[7]] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[[1,2,6],[3,5,8],[4],[7]] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[[1,3,6],[2,4,8],[5],[7]] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[[1,2,6],[3,4,8],[5],[7]] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[[1,4,5],[2,6,8],[3],[7]] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[[1,3,5],[2,6,8],[4],[7]] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[[1,2,5],[3,6,8],[4],[7]] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[[1,3,4],[2,6,8],[5],[7]] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[[1,2,4],[3,6,8],[5],[7]] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[[1,2,3],[4,6,8],[5],[7]] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[[1,3,5],[2,4,8],[6],[7]] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[[1,2,5],[3,4,8],[6],[7]] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[[1,3,4],[2,5,8],[6],[7]] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[[1,2,4],[3,5,8],[6],[7]] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[[1,2,3],[4,5,8],[6],[7]] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[[1,4,6],[2,5,7],[3],[8]] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[[1,3,6],[2,5,7],[4],[8]] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[[1,2,6],[3,5,7],[4],[8]] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[[1,3,6],[2,4,7],[5],[8]] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[[1,2,6],[3,4,7],[5],[8]] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[[1,4,5],[2,6,7],[3],[8]] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[[1,3,5],[2,6,7],[4],[8]] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[[1,2,5],[3,6,7],[4],[8]] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[[1,3,4],[2,6,7],[5],[8]] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[[1,2,4],[3,6,7],[5],[8]] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[[1,2,3],[4,6,7],[5],[8]] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[[1,3,5],[2,4,7],[6],[8]] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[[1,2,5],[3,4,7],[6],[8]] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[[1,3,4],[2,5,7],[6],[8]] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[[1,2,4],[3,5,7],[6],[8]] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[[1,2,3],[4,5,7],[6],[8]] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[[1,3,5],[2,4,6],[7],[8]] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[[1,2,5],[3,4,6],[7],[8]] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[[1,3,4],[2,5,6],[7],[8]] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[[1,2,4],[3,5,6],[7],[8]] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[[1,2,3],[4,5,6],[7],[8]] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[[1,5,8],[2,6],[3,7],[4]] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[[1,4,8],[2,6],[3,7],[5]] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[[1,3,8],[2,6],[4,7],[5]] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[[1,2,8],[3,6],[4,7],[5]] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[[1,4,8],[2,5],[3,7],[6]] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[[1,3,8],[2,5],[4,7],[6]] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,5],[4,7],[6]] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[[1,3,8],[2,4],[5,7],[6]] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[[1,2,8],[3,4],[5,7],[6]] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[[1,4,8],[2,5],[3,6],[7]] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[[1,3,8],[2,5],[4,6],[7]] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[[1,2,8],[3,5],[4,6],[7]] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[[1,3,8],[2,4],[5,6],[7]] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[[1,2,8],[3,4],[5,6],[7]] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[[1,5,7],[2,6],[3,8],[4]] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[[1,4,7],[2,6],[3,8],[5]] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[[1,3,7],[2,6],[4,8],[5]] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[[1,2,7],[3,6],[4,8],[5]] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[[1,4,7],[2,5],[3,8],[6]] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[[1,3,7],[2,5],[4,8],[6]] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[[1,2,7],[3,5],[4,8],[6]] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[[1,3,7],[2,4],[5,8],[6]] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[[1,2,7],[3,4],[5,8],[6]] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[[1,5,6],[2,7],[3,8],[4]] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[[1,4,6],[2,7],[3,8],[5]] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[[1,3,6],[2,7],[4,8],[5]] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[[1,2,6],[3,7],[4,8],[5]] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[[1,4,5],[2,7],[3,8],[6]] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[[1,3,5],[2,7],[4,8],[6]] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[[1,2,5],[3,7],[4,8],[6]] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[[1,3,4],[2,7],[5,8],[6]] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[[1,2,4],[3,7],[5,8],[6]] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[[1,2,3],[4,7],[5,8],[6]] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[[1,4,6],[2,5],[3,8],[7]] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[[1,3,6],[2,5],[4,8],[7]] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[[1,2,6],[3,5],[4,8],[7]] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[[1,3,6],[2,4],[5,8],[7]] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[[1,2,6],[3,4],[5,8],[7]] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[[1,4,5],[2,6],[3,8],[7]] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[[1,3,5],[2,6],[4,8],[7]] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[[1,2,5],[3,6],[4,8],[7]] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[[1,3,4],[2,6],[5,8],[7]] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[[1,2,4],[3,6],[5,8],[7]] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[[1,2,3],[4,6],[5,8],[7]] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[[1,3,5],[2,4],[6,8],[7]] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[[1,2,5],[3,4],[6,8],[7]] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[[1,3,4],[2,5],[6,8],[7]] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[[1,2,4],[3,5],[6,8],[7]] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[[1,2,3],[4,5],[6,8],[7]] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[[1,4,7],[2,5],[3,6],[8]] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[[1,3,7],[2,5],[4,6],[8]] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[[1,2,7],[3,5],[4,6],[8]] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[[1,3,7],[2,4],[5,6],[8]] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[[1,2,7],[3,4],[5,6],[8]] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[[1,4,6],[2,5],[3,7],[8]] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[[1,3,6],[2,5],[4,7],[8]] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[[1,2,6],[3,5],[4,7],[8]] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[[1,3,6],[2,4],[5,7],[8]] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[[1,2,6],[3,4],[5,7],[8]] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[[1,4,5],[2,6],[3,7],[8]] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[[1,3,5],[2,6],[4,7],[8]] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[[1,2,5],[3,6],[4,7],[8]] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[[1,3,4],[2,6],[5,7],[8]] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[[1,2,4],[3,6],[5,7],[8]] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[[1,2,3],[4,6],[5,7],[8]] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[[1,3,5],[2,4],[6,7],[8]] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[[1,2,5],[3,4],[6,7],[8]] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[[1,3,4],[2,5],[6,7],[8]] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[[1,2,4],[3,5],[6,7],[8]] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[[1,2,3],[4,5],[6,7],[8]] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[[1,6,8],[2,7],[3],[4],[5]] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,8],[2,7],[3],[5],[6]] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[[1,2,8],[3,7],[4],[5],[6]] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[[1,5,8],[2,6],[3],[4],[7]] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[[1,4,8],[2,6],[3],[5],[7]] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[[1,3,8],[2,6],[4],[5],[7]] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[[1,2,8],[3,6],[4],[5],[7]] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[[1,2,8],[3,5],[4],[6],[7]] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[[1,2,8],[3,4],[5],[6],[7]] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[[1,6,7],[2,8],[3],[4],[5]] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[[1,5,7],[2,8],[3],[4],[6]] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[[1,4,7],[2,8],[3],[5],[6]] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[[1,3,7],[2,8],[4],[5],[6]] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[[1,2,7],[3,8],[4],[5],[6]] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[[1,5,6],[2,8],[3],[4],[7]] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[[1,4,6],[2,8],[3],[5],[7]] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[[1,3,6],[2,8],[4],[5],[7]] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[[1,2,6],[3,8],[4],[5],[7]] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[[1,4,5],[2,8],[3],[6],[7]] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[[1,3,5],[2,8],[4],[6],[7]] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[[1,2,5],[3,8],[4],[6],[7]] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[[1,3,4],[2,8],[5],[6],[7]] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[[1,2,4],[3,8],[5],[6],[7]] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[[1,2,3],[4,8],[5],[6],[7]] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[[1,5,7],[2,6],[3],[4],[8]] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[[1,4,7],[2,6],[3],[5],[8]] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[[1,3,7],[2,6],[4],[5],[8]] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[[1,2,7],[3,6],[4],[5],[8]] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[[1,4,7],[2,5],[3],[6],[8]] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[[1,3,7],[2,5],[4],[6],[8]] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[[1,2,7],[3,5],[4],[6],[8]] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[[1,3,7],[2,4],[5],[6],[8]] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[[1,2,7],[3,4],[5],[6],[8]] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[[1,5,6],[2,7],[3],[4],[8]] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[[1,4,6],[2,7],[3],[5],[8]] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[[1,3,6],[2,7],[4],[5],[8]] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[[1,2,6],[3,7],[4],[5],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[[1,4,5],[2,7],[3],[6],[8]] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[[1,3,5],[2,7],[4],[6],[8]] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[[1,2,5],[3,7],[4],[6],[8]] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[[1,3,4],[2,7],[5],[6],[8]] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[[1,2,4],[3,7],[5],[6],[8]] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[[1,2,3],[4,7],[5],[6],[8]] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[[1,4,6],[2,5],[3],[7],[8]] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[[1,3,6],[2,5],[4],[7],[8]] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[[1,2,6],[3,5],[4],[7],[8]] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[[1,3,6],[2,4],[5],[7],[8]] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[[1,2,6],[3,4],[5],[7],[8]] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[[1,4,5],[2,6],[3],[7],[8]] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[[1,3,5],[2,6],[4],[7],[8]] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[[1,2,5],[3,6],[4],[7],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[[1,3,4],[2,6],[5],[7],[8]] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[[1,2,4],[3,6],[5],[7],[8]] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[[1,2,3],[4,6],[5],[7],[8]] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[[1,3,5],[2,4],[6],[7],[8]] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[[1,2,5],[3,4],[6],[7],[8]] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[[1,3,4],[2,5],[6],[7],[8]] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[[1,2,4],[3,5],[6],[7],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[[1,2,3],[4,5],[6],[7],[8]] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[[1,6,7],[2],[3],[4],[5],[8]] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[[1,5,7],[2],[3],[4],[6],[8]] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[[1,4,7],[2],[3],[5],[6],[8]] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[[1,3,7],[2],[4],[5],[6],[8]] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[[1,2,7],[3],[4],[5],[6],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[[1,5,6],[2],[3],[4],[7],[8]] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[[1,4,6],[2],[3],[5],[7],[8]] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[[1,3,6],[2],[4],[5],[7],[8]] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[[1,2,6],[3],[4],[5],[7],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[[1,4,5],[2],[3],[6],[7],[8]] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[[1,3,5],[2],[4],[6],[7],[8]] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[[1,2,5],[3],[4],[6],[7],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[[1,3,4],[2],[5],[6],[7],[8]] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[[1,2,4],[3],[5],[6],[7],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[[1,5],[2,6],[3,7],[4,8]] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[[1,4],[2,6],[3,7],[5,8]] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[[1,3],[2,6],[4,7],[5,8]] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[[1,2],[3,6],[4,7],[5,8]] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[[1,4],[2,5],[3,7],[6,8]] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[[1,3],[2,5],[4,7],[6,8]] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[[1,2],[3,5],[4,7],[6,8]] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[[1,3],[2,4],[5,7],[6,8]] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[[1,2],[3,4],[5,7],[6,8]] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[[1,4],[2,5],[3,6],[7,8]] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[[1,3],[2,5],[4,6],[7,8]] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[[1,2],[3,5],[4,6],[7,8]] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[[1,3],[2,4],[5,6],[7,8]] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[[1,2],[3,4],[5,6],[7,8]] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,6],[2,7],[3,8],[4],[5]] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[[1,5],[2,7],[3,8],[4],[6]] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[[1,4],[2,7],[3,8],[5],[6]] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[[1,3],[2,7],[4,8],[5],[6]] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[[1,2],[3,7],[4,8],[5],[6]] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[[1,4],[2,6],[3,8],[5],[7]] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,6],[4,8],[5],[7]] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[[1,2],[3,6],[4,8],[5],[7]] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[[1,3],[2,5],[4,8],[6],[7]] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[[1,2],[3,5],[4,8],[6],[7]] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[[1,3],[2,4],[5,8],[6],[7]] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[[1,2],[3,4],[5,8],[6],[7]] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[[1,5],[2,6],[3,7],[4],[8]] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[[1,4],[2,6],[3,7],[5],[8]] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[[1,3],[2,6],[4,7],[5],[8]] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[[1,2],[3,6],[4,7],[5],[8]] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[[1,4],[2,5],[3,7],[6],[8]] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[[1,3],[2,5],[4,7],[6],[8]] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[[1,2],[3,5],[4,7],[6],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[[1,3],[2,4],[5,7],[6],[8]] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[[1,2],[3,4],[5,7],[6],[8]] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[[1,4],[2,5],[3,6],[7],[8]] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[[1,3],[2,5],[4,6],[7],[8]] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[[1,2],[3,5],[4,6],[7],[8]] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[[1,3],[2,4],[5,6],[7],[8]] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[[1,2],[3,4],[5,6],[7],[8]] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,5],[2,8],[3],[4],[6],[7]] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[[1,2],[3,8],[4],[5],[6],[7]] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[[1,5],[2,7],[3],[4],[6],[8]] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[[1,4],[2,7],[3],[5],[6],[8]] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[[1,3],[2,7],[4],[5],[6],[8]] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[[1,2],[3,7],[4],[5],[6],[8]] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[[1,5],[2,6],[3],[4],[7],[8]] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[[1,4],[2,6],[3],[5],[7],[8]] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[[1,3],[2,6],[4],[5],[7],[8]] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[[1,2],[3,6],[4],[5],[7],[8]] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[[1,4],[2,5],[3],[6],[7],[8]] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[[1,3],[2,5],[4],[6],[7],[8]] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[[1,2],[3,5],[4],[6],[7],[8]] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[[1,3],[2,4],[5],[6],[7],[8]] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[[1,2],[3,4],[5],[6],[7],[8]] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[[1,6],[2],[3],[4],[5],[7],[8]] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[[1,4],[2],[3],[5],[6],[7],[8]] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111
[[1,3,5,7,9],[2,4,6,8,10]] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[[1,3,5,7,8],[2,4,6,9,10]] => [[1,2,5,7,9],[3,4,6,8,10]] => 010010101
[[1,3,5,6,9],[2,4,7,8,10]] => [[1,3,4,7,9],[2,5,6,8,10]] => 100100101
[[1,3,5,6,8],[2,4,7,9,10]] => [[1,2,4,7,9],[3,5,6,8,10]] => 010100101
[[1,3,5,6,7],[2,4,8,9,10]] => [[1,2,3,7,9],[4,5,6,8,10]] => 001000101
[[1,3,4,7,9],[2,5,6,8,10]] => [[1,3,5,6,9],[2,4,7,8,10]] => 101001001
[[1,3,4,7,8],[2,5,6,9,10]] => [[1,2,5,6,9],[3,4,7,8,10]] => 010001001
[[1,3,4,6,9],[2,5,7,8,10]] => [[1,3,4,6,9],[2,5,7,8,10]] => 100101001
[[1,3,4,6,8],[2,5,7,9,10]] => [[1,2,4,6,9],[3,5,7,8,10]] => 010101001
[[1,3,4,6,7],[2,5,8,9,10]] => [[1,2,3,6,9],[4,5,7,8,10]] => 001001001
[[1,3,4,5,9],[2,6,7,8,10]] => [[1,3,4,5,9],[2,6,7,8,10]] => 100010001
[[1,3,4,5,8],[2,6,7,9,10]] => [[1,2,4,5,9],[3,6,7,8,10]] => 010010001
[[1,3,4,5,7],[2,6,8,9,10]] => [[1,2,3,5,9],[4,6,7,8,10]] => 001010001
[[1,3,4,5,6],[2,7,8,9,10]] => [[1,2,3,4,9],[5,6,7,8,10]] => 000100001
[[1,2,5,7,9],[3,4,6,8,10]] => [[1,3,5,7,8],[2,4,6,9,10]] => 101010010
[[1,2,5,7,8],[3,4,6,9,10]] => [[1,2,5,7,8],[3,4,6,9,10]] => 010010010
[[1,2,5,6,9],[3,4,7,8,10]] => [[1,3,4,7,8],[2,5,6,9,10]] => 100100010
[[1,2,5,6,8],[3,4,7,9,10]] => [[1,2,4,7,8],[3,5,6,9,10]] => 010100010
[[1,2,5,6,7],[3,4,8,9,10]] => [[1,2,3,7,8],[4,5,6,9,10]] => 001000010
[[1,2,4,7,9],[3,5,6,8,10]] => [[1,3,5,6,8],[2,4,7,9,10]] => 101001010
[[1,2,4,7,8],[3,5,6,9,10]] => [[1,2,5,6,8],[3,4,7,9,10]] => 010001010
[[1,2,4,6,9],[3,5,7,8,10]] => [[1,3,4,6,8],[2,5,7,9,10]] => 100101010
[[1,2,4,6,8],[3,5,7,9,10]] => [[1,2,4,6,8],[3,5,7,9,10]] => 010101010
[[1,2,4,6,7],[3,5,8,9,10]] => [[1,2,3,6,8],[4,5,7,9,10]] => 001001010
[[1,2,4,5,9],[3,6,7,8,10]] => [[1,3,4,5,8],[2,6,7,9,10]] => 100010010
[[1,2,4,5,8],[3,6,7,9,10]] => [[1,2,4,5,8],[3,6,7,9,10]] => 010010010
[[1,2,4,5,7],[3,6,8,9,10]] => [[1,2,3,5,8],[4,6,7,9,10]] => 001010010
[[1,2,4,5,6],[3,7,8,9,10]] => [[1,2,3,4,8],[5,6,7,9,10]] => 000100010
[[1,2,3,7,9],[4,5,6,8,10]] => [[1,3,5,6,7],[2,4,8,9,10]] => 101000100
[[1,2,3,7,8],[4,5,6,9,10]] => [[1,2,5,6,7],[3,4,8,9,10]] => 010000100
[[1,2,3,6,9],[4,5,7,8,10]] => [[1,3,4,6,7],[2,5,8,9,10]] => 100100100
[[1,2,3,6,8],[4,5,7,9,10]] => [[1,2,4,6,7],[3,5,8,9,10]] => 010100100
[[1,2,3,6,7],[4,5,8,9,10]] => [[1,2,3,6,7],[4,5,8,9,10]] => 001000100
[[1,2,3,5,9],[4,6,7,8,10]] => [[1,3,4,5,7],[2,6,8,9,10]] => 100010100
[[1,2,3,5,8],[4,6,7,9,10]] => [[1,2,4,5,7],[3,6,8,9,10]] => 010010100
[[1,2,3,5,7],[4,6,8,9,10]] => [[1,2,3,5,7],[4,6,8,9,10]] => 001010100
[[1,2,3,5,6],[4,7,8,9,10]] => [[1,2,3,4,7],[5,6,8,9,10]] => 000100100
[[1,2,3,4,9],[5,6,7,8,10]] => [[1,3,4,5,6],[2,7,8,9,10]] => 100001000
[[1,2,3,4,8],[5,6,7,9,10]] => [[1,2,4,5,6],[3,7,8,9,10]] => 010001000
[[1,2,3,4,7],[5,6,8,9,10]] => [[1,2,3,5,6],[4,7,8,9,10]] => 001001000
[[1,2,3,4,6],[5,7,8,9,10]] => [[1,2,3,4,6],[5,7,8,9,10]] => 000101000
[[1,2,3,4,5],[6,7,8,9,10]] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 10101010101
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => 01001010101
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => 10010010101
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => 01010010101
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => 00100010101
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => 10100100101
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => 01000100101
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => 10010100101
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => 01010100101
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => 00100100101
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => 10001000101
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => 01001000101
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => 00101000101
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => 00010000101
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => 10101001001
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => 01001001001
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => 10010001001
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => 01010001001
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => 00100001001
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => 10100101001
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => 01000101001
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => 10010101001
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => 01010101001
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => 00100101001
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => 10001001001
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => 01001001001
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => 00101001001
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => 00010001001
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => 10100010001
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => 01000010001
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => 10010010001
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => 01010010001
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => 00100010001
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => 10001010001
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => 01001010001
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => 00101010001
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => 00010010001
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => 10000100001
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => 01000100001
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => 00100100001
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => 00010100001
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => 00001000001
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => 10101010010
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => 01001010010
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => 10010010010
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => 01010010010
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => 00100010010
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => 10100100010
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => 01000100010
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => 10010100010
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => 01010100010
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => 00100100010
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => 10001000010
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => 01001000010
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => 00101000010
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => 00010000010
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => 10101001010
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => 01001001010
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => 10010001010
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => 01010001010
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => 00100001010
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => 10100101010
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => 01000101010
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => 10010101010
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => 01010101010
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => 00100101010
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => 10001001010
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => 01001001010
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => 00101001010
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => 00010001010
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => 10100010010
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => 01000010010
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => 10010010010
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => 01010010010
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => 00100010010
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => 10001010010
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => 01001010010
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => 00101010010
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => 00010010010
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => 10000100010
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => 01000100010
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => 00100100010
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => 00010100010
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => 00001000010
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => 10101000100
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => 01001000100
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => 10010000100
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => 01010000100
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => 00100000100
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => 10100100100
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => 01000100100
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => 10010100100
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => 01010100100
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => 00100100100
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => 10001000100
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => 01001000100
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => 00101000100
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => 00010000100
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => 10100010100
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => 01000010100
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => 10010010100
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => 01010010100
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => 00100010100
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => 10001010100
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => 01001010100
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => 00101010100
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => 00010010100
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => 10000100100
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => 01000100100
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => 00100100100
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => 00010100100
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => 00001000100
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => 10100001000
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => 01000001000
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => 10010001000
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => 01010001000
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => 00100001000
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => 10001001000
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => 01001001000
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => 00101001000
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => 00010001000
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => 10000101000
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => 01000101000
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => 00100101000
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => 00010101000
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => 00001001000
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => 10000010000
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => 01000010000
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => 00100010000
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => 00010010000
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => 00001010000
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => 00000000
[[1,2,3,4,5,6,7,8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[[1,2,3,4,5,6,7],[8,9]] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[[1,2,3,4,5,6,7],[8],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[[1,2,3,4,5,6],[7,8,9]] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[[1,2,3,4,5,6],[7,8],[9]] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[[1,2,3,4,5,6],[7],[8],[9]] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[[1,2,3,4,5],[6,7,8,9]] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[[1,2,3,4,5],[6,7,8],[9]] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[[1,2,3,4,5],[6,7],[8,9]] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000
[[1,2,3,4,5],[6,7],[8],[9]] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[[1,2,3,4,5],[6],[7],[8],[9]] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[[1,2,3,4],[5,6,7,8],[9]] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[[1,2,3,4],[5,6,7],[8,9]] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000
[[1,2,3,4],[5,6,7],[8],[9]] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000
[[1,2,3,4],[5,6],[7,8],[9]] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000
[[1,2,3,4],[5,6],[7],[8],[9]] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[[1,2,3],[4,5,6],[7,8,9]] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100
[[1,2,3],[4,5,6],[7,8],[9]] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100
[[1,2,3],[4,5,6],[7],[8],[9]] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100
[[1,2,3],[4,5],[6,7],[8,9]] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100
[[1,2,3],[4,5],[6,7],[8],[9]] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100
[[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111
[[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000
[[1,2,3,4,5,6,7,8,9],[10]] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[[1,2,3,4,5,6,7,8],[9,10]] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[[1,2,3,4,5,6,7,8],[9],[10]] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[[1,2,3,4,5,6,7],[8,9,10]] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[[1,2,3,4,5,6,7],[8,9],[10]] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[[1,2,3,4,5,6,7],[8],[9],[10]] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000
[[1,2,3,4,5,6],[7,8,9,10]] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[[1,2,3,4,5,6],[7,8,9],[10]] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000
[[1,2,3,4,5,6],[7,8],[9,10]] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000
[[1,2,3,4,5,6],[7,8],[9],[10]] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[[1,2,3,4,5],[6,7,8,9],[10]] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[[1,2,3,4,5],[6,7,8],[9,10]] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000
[[1,2,3,4,5],[6,7,8],[9],[10]] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000
[[1,2,3,4,5],[6,7],[8,9],[10]] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[[1,2,3,4],[5,6,7,8],[9,10]] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[[1,2,3,4],[5,6,7,8],[9],[10]] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[[1,2,3,4],[5,6,7],[8,9,10]] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000
[[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000
[[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[[1,2,3],[4,5,6],[7,8,9],[10]] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100
[[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111
[[1,2,3,4,5,6,7,8,9,10,11,12]] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 00000000000
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => 11111111111
[[1,3,4,5,6,7,8,9],[2]] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[[1,2,5,6,7,8,9],[3,4]] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,4,5,6,7,8,9],[2],[3]] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[[1,2,3,7,8,9],[4,5,6]] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,3,6,7,8,9],[2,5],[4]] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,5,6,7,8,9],[2],[3],[4]] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[[1,2,3,4,9],[5,6,7,8]] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[[1,3,4,8,9],[2,6,7],[5]] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,7,8,9],[3,4],[5,6]] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,4,7,8,9],[2,6],[3],[5]] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,6,7,8,9],[2],[3],[4],[5]] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[[1,3,4,5],[2,7,8,9],[6]] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[[1,2,5,9],[3,4,8],[6,7]] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[[1,4,5,9],[2,7,8],[3],[6]] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[[1,3,8,9],[2,5],[4,7],[6]] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,5,8,9],[2,7],[3],[4],[6]] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,7,8,9],[2],[3],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[[1,3,6],[2,5,9],[4,8],[7]] => [[1,2,3],[4,5,6],[7,8],[9]] => 00100101
[[1,5,6],[2,8,9],[3],[4],[7]] => [[1,2,3],[4,5,6],[7],[8],[9]] => 00100111
[[1,2,9],[3,4],[5,6],[7,8]] => [[1,2,3],[4,5],[6,7],[8,9]] => 00101010
[[1,4,9],[2,6],[3,8],[5],[7]] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[[1,6,9],[2,8],[3],[4],[5],[7]] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[[1,3],[2,5],[4,7],[6,9],[8]] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[[1,5],[2,7],[3,9],[4],[6],[8]] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 01010111
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[[1,3,4,5,6,7,8,9,10],[2]] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,5,6,7,8,9,10],[3,4]] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,4,5,6,7,8,9,10],[2],[3]] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[[1,2,3,7,8,9,10],[4,5,6]] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,3,6,7,8,9,10],[2,5],[4]] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,5,6,7,8,9,10],[2],[3],[4]] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[[1,2,3,4,9,10],[5,6,7,8]] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[[1,3,4,8,9,10],[2,6,7],[5]] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,7,8,9,10],[3,4],[5,6]] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,4,7,8,9,10],[2,6],[3],[5]] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[[1,3,4,5,10],[2,7,8,9],[6]] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,5,9,10],[3,4,8],[6,7]] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,4,5,9,10],[2,7,8],[3],[6]] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[[1,3,8,9,10],[2,5],[4,7],[6]] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[[1,2,5,6],[3,4,9,10],[7,8]] => [[1,2,3,4],[5,6,7,8],[9,10]] => 000100010
[[1,4,5,6],[2,8,9,10],[3],[7]] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011
[[1,2,3,10],[4,5,6],[7,8,9]] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[[1,3,6,10],[2,5,9],[4,8],[7]] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[[1,2,9,10],[3,4],[5,6],[7,8]] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[[1,3,4],[2,6,7],[5,9,10],[8]] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001
[[1,2,7],[3,4,10],[5,6],[8,9]] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 001001011
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 010101011
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 010101111
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[[1,7],[2,8],[3,9],[4],[5],[6]] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111
[[1,7,9],[2,8],[3],[4],[5],[6]] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[[1,6],[2,7],[3,8],[4,9],[5]] => [[1,5],[2,6],[3,7],[4,8],[9]] => 11101111
[[1,6,9],[2,7],[3,8],[4],[5]] => [[1,2,5],[3,6],[4,7],[8],[9]] => 01101111
[[1,6,8],[2,7,9],[3],[4],[5]] => [[1,3,5],[2,4,6],[7],[8],[9]] => 10101111
[[1,6,8,9],[2,7],[3],[4],[5]] => [[1,2,3,5],[4,6],[7],[8],[9]] => 00101111
[[1,5,9],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5,9]] => 01110111
[[1,5,8],[2,6,9],[3,7],[4]] => [[1,3,6],[2,4,7],[5,8],[9]] => 10110111
[[1,5,8,9],[2,6],[3,7],[4]] => [[1,2,3,6],[4,7],[5,8],[9]] => 00110111
[[1,5,7,9],[2,6,8],[3],[4]] => [[1,2,4,6],[3,5,7],[8],[9]] => 01010111
[[1,5,7,8,9],[2,6],[3],[4]] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[[1,4,7],[2,5,8],[3,6,9]] => [[1,4,7],[2,5,8],[3,6,9]] => 11011011
[[1,4,7,9],[2,5,8],[3,6]] => [[1,2,4,7],[3,5,8],[6,9]] => 01011011
[[1,4,7,8,9],[2,5],[3,6]] => [[1,2,3,4,7],[5,8],[6,9]] => 00011011
[[1,4,6,8],[2,5,7,9],[3]] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[[1,4,6,8,9],[2,5,7],[3]] => [[1,2,3,5,7],[4,6,8],[9]] => 00101011
[[1,4,6,7,8,9],[2,5],[3]] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[[1,3,5,7,9],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[[1,3,5,7,8,9],[2,4,6]] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[[1,3,5,6,7,8,9],[2,4]] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[[1,8],[2,9],[3,10],[4],[5],[6],[7]] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[[1,8,10],[2,9],[3],[4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111
[[1,7],[2,8],[3,9],[4,10],[5],[6]] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 111011111
[[1,7,10],[2,8],[3,9],[4],[5],[6]] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => 011011111
[[1,7,9],[2,8,10],[3],[4],[5],[6]] => [[1,3,5],[2,4,6],[7],[8],[9],[10]] => 101011111
[[1,7,9,10],[2,8],[3],[4],[5],[6]] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => 001011111
[[1,6],[2,7],[3,8],[4,9],[5,10]] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[[1,6,10],[2,7],[3,8],[4,9],[5]] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111
[[1,6,9],[2,7,10],[3,8],[4],[5]] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => 101101111
[[1,6,9,10],[2,7],[3,8],[4],[5]] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => 001101111
[[1,6,8,10],[2,7,9],[3],[4],[5]] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[[1,6,8,9,10],[2,7],[3],[4],[5]] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => 000101111
[[1,5,9],[2,6,10],[3,7],[4,8]] => [[1,3,7],[2,4,8],[5,9],[6,10]] => 101110111
[[1,5,9,10],[2,6],[3,7],[4,8]] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 001110111
[[1,5,8],[2,6,9],[3,7,10],[4]] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 110110111
[[1,5,8,10],[2,6,9],[3,7],[4]] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[[1,5,8,9,10],[2,6],[3,7],[4]] => [[1,2,3,4,7],[5,8],[6,9],[10]] => 000110111
[[1,5,7,9],[2,6,8,10],[3],[4]] => [[1,3,5,7],[2,4,6,8],[9],[10]] => 101010111
[[1,5,7,9,10],[2,6,8],[3],[4]] => [[1,2,3,5,7],[4,6,8],[9],[10]] => 001010111
[[1,5,7,8,9,10],[2,6],[3],[4]] => [[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111
[[1,4,7,10],[2,5,8],[3,6,9]] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[[1,4,7,9],[2,5,8,10],[3,6]] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[[1,4,7,9,10],[2,5,8],[3,6]] => [[1,2,3,5,8],[4,6,9],[7,10]] => 001011011
[[1,4,7,8,9,10],[2,5],[3,6]] => [[1,2,3,4,5,8],[6,9],[7,10]] => 000011011
[[1,4,6,8,10],[2,5,7,9],[3]] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[[1,4,6,8,9,10],[2,5,7],[3]] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[[1,4,6,7,8,9,10],[2,5],[3]] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[[1,3,5,7,9,10],[2,4,6,8]] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[[1,3,5,7,8,9,10],[2,4,6]] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[[1,3,5,6,7,8,9,10],[2,4]] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[[1,4],[2,5],[3,6],[7],[8],[9]] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 11111011
[[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 11111010
[[1,5],[2,6],[3,7],[4,8],[9]] => [[1,6],[2,7],[3,8],[4,9],[5]] => 11110111
[[1,2,5],[3,6],[4,7],[8],[9]] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[[1,3,5],[2,4,6],[7],[8],[9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => 11110101
[[1,2,3,5],[4,6],[7],[8],[9]] => [[1,6,8,9],[2,7],[3],[4],[5]] => 11110100
[[1,2,6],[3,7],[4,8],[5,9]] => [[1,5,9],[2,6],[3,7],[4,8]] => 11101110
[[1,3,6],[2,4,7],[5,8],[9]] => [[1,5,8],[2,6,9],[3,7],[4]] => 11101101
[[1,2,3,6],[4,7],[5,8],[9]] => [[1,5,8,9],[2,6],[3,7],[4]] => 11101100
[[1,2,4,6],[3,5,7],[8],[9]] => [[1,5,7,9],[2,6,8],[3],[4]] => 11101010
[[1,2,3,4,6],[5,7],[8],[9]] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[[1,2,4,7],[3,5,8],[6,9]] => [[1,4,7,9],[2,5,8],[3,6]] => 11011010
[[1,2,3,4,7],[5,8],[6,9]] => [[1,4,7,8,9],[2,5],[3,6]] => 11011000
[[1,3,5,7],[2,4,6,8],[9]] => [[1,4,6,8],[2,5,7,9],[3]] => 11010101
[[1,2,3,5,7],[4,6,8],[9]] => [[1,4,6,8,9],[2,5,7],[3]] => 11010100
[[1,2,3,4,5,7],[6,8],[9]] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[[1,2,4,6,8],[3,5,7,9]] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[[1,2,3,4,6,8],[5,7,9]] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[[1,2,3,4,5,6,8],[7,9]] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[[1,4],[2,5],[3,6],[7],[8],[9],[10]] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 111111011
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 111111010
[[1,5],[2,6],[3,7],[4,8],[9],[10]] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 111110111
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 111110110
[[1,3,5],[2,4,6],[7],[8],[9],[10]] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 111110101
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 111110100
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 111101110
[[1,3,6],[2,4,7],[5,8],[9],[10]] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 111101101
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 111101100
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 111101010
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[[1,3,7],[2,4,8],[5,9],[6,10]] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 111011101
[[1,2,3,7],[4,8],[5,9],[6,10]] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 111011100
[[1,4,7],[2,5,8],[3,6,9],[10]] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 111011011
[[1,2,4,7],[3,5,8],[6,9],[10]] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[[1,2,3,4,7],[5,8],[6,9],[10]] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[[1,3,5,7],[2,4,6,8],[9],[10]] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[[1,2,3,5,7],[4,6,8],[9],[10]] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[[1,2,3,4,5,7],[6,8],[9],[10]] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 111010000
[[1,2,5,8],[3,6,9],[4,7,10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => 110110110
[[1,3,5,8],[2,4,6,9],[7,10]] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[[1,2,3,5,8],[4,6,9],[7,10]] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[[1,2,3,4,5,8],[6,9],[7,10]] => [[1,4,7,8,9,10],[2,5],[3,6]] => 110110000
[[1,2,4,6,8],[3,5,7,9],[10]] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[[1,2,3,4,6,8],[5,7,9],[10]] => [[1,4,6,8,9,10],[2,5,7],[3]] => 110101000
[[1,2,3,4,5,6,8],[7,9],[10]] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[[1,2,3,5,7,9],[4,6,8,10]] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[[1,2,3,4,5,7,9],[6,8,10]] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[[1,2,3,4,5,6,7,9],[8,10]] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[[1,2],[3,4],[5,6],[7,9],[8,10]] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => 101101010
[[1,2],[3,4],[5,7],[6,8],[9,10]] => [[1,2],[3,5],[4,6],[7,8],[9,10]] => 011011010
[[1,2],[3,4],[5,7],[6,9],[8,10]] => [[1,3],[2,5],[4,6],[7,8],[9,10]] => 101011010
[[1,2],[3,4],[5,8],[6,9],[7,10]] => [[1,4],[2,5],[3,6],[7,8],[9,10]] => 110111010
[[1,2],[3,5],[4,6],[7,8],[9,10]] => [[1,2],[3,4],[5,7],[6,8],[9,10]] => 010110110
[[1,2],[3,5],[4,6],[7,9],[8,10]] => [[1,3],[2,4],[5,7],[6,8],[9,10]] => 101110110
[[1,2],[3,5],[4,7],[6,8],[9,10]] => [[1,2],[3,5],[4,7],[6,8],[9,10]] => 011010110
[[1,2],[3,5],[4,7],[6,9],[8,10]] => [[1,3],[2,5],[4,7],[6,8],[9,10]] => 101010110
[[1,2],[3,5],[4,8],[6,9],[7,10]] => [[1,4],[2,5],[3,7],[6,8],[9,10]] => 110110110
[[1,2],[3,6],[4,7],[5,8],[9,10]] => [[1,2],[3,6],[4,7],[5,8],[9,10]] => 011101110
[[1,2],[3,6],[4,7],[5,9],[8,10]] => [[1,3],[2,6],[4,7],[5,8],[9,10]] => 101101110
[[1,2],[3,6],[4,8],[5,9],[7,10]] => [[1,4],[2,6],[3,7],[5,8],[9,10]] => 110101110
[[1,2],[3,7],[4,8],[5,9],[6,10]] => [[1,5],[2,6],[3,7],[4,8],[9,10]] => 111011110
[[1,3],[2,4],[5,6],[7,8],[9,10]] => [[1,2],[3,4],[5,6],[7,9],[8,10]] => 010101101
[[1,3],[2,4],[5,6],[7,9],[8,10]] => [[1,3],[2,4],[5,6],[7,9],[8,10]] => 101101101
[[1,3],[2,4],[5,7],[6,8],[9,10]] => [[1,2],[3,5],[4,6],[7,9],[8,10]] => 011011101
[[1,3],[2,4],[5,7],[6,9],[8,10]] => [[1,3],[2,5],[4,6],[7,9],[8,10]] => 101011101
[[1,3],[2,4],[5,8],[6,9],[7,10]] => [[1,4],[2,5],[3,6],[7,9],[8,10]] => 110111101
[[1,3],[2,5],[4,6],[7,8],[9,10]] => [[1,2],[3,4],[5,7],[6,9],[8,10]] => 010110101
[[1,3],[2,5],[4,6],[7,9],[8,10]] => [[1,3],[2,4],[5,7],[6,9],[8,10]] => 101110101
[[1,3],[2,5],[4,7],[6,8],[9,10]] => [[1,2],[3,5],[4,7],[6,9],[8,10]] => 011010101
[[1,3],[2,5],[4,7],[6,9],[8,10]] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => 101010101
[[1,3],[2,5],[4,8],[6,9],[7,10]] => [[1,4],[2,5],[3,7],[6,9],[8,10]] => 110110101
[[1,3],[2,6],[4,7],[5,8],[9,10]] => [[1,2],[3,6],[4,7],[5,9],[8,10]] => 011101101
[[1,3],[2,6],[4,7],[5,9],[8,10]] => [[1,3],[2,6],[4,7],[5,9],[8,10]] => 101101101
[[1,3],[2,6],[4,8],[5,9],[7,10]] => [[1,4],[2,6],[3,7],[5,9],[8,10]] => 110101101
[[1,3],[2,7],[4,8],[5,9],[6,10]] => [[1,5],[2,6],[3,7],[4,9],[8,10]] => 111011101
[[1,4],[2,5],[3,6],[7,8],[9,10]] => [[1,2],[3,4],[5,8],[6,9],[7,10]] => 010111011
[[1,4],[2,5],[3,6],[7,9],[8,10]] => [[1,3],[2,4],[5,8],[6,9],[7,10]] => 101111011
[[1,4],[2,5],[3,7],[6,8],[9,10]] => [[1,2],[3,5],[4,8],[6,9],[7,10]] => 011011011
[[1,4],[2,5],[3,7],[6,9],[8,10]] => [[1,3],[2,5],[4,8],[6,9],[7,10]] => 101011011
[[1,4],[2,5],[3,8],[6,9],[7,10]] => [[1,4],[2,5],[3,8],[6,9],[7,10]] => 110111011
[[1,4],[2,6],[3,7],[5,8],[9,10]] => [[1,2],[3,6],[4,8],[5,9],[7,10]] => 011101011
[[1,4],[2,6],[3,7],[5,9],[8,10]] => [[1,3],[2,6],[4,8],[5,9],[7,10]] => 101101011
[[1,4],[2,6],[3,8],[5,9],[7,10]] => [[1,4],[2,6],[3,8],[5,9],[7,10]] => 110101011
[[1,4],[2,7],[3,8],[5,9],[6,10]] => [[1,5],[2,6],[3,8],[4,9],[7,10]] => 111011011
[[1,5],[2,6],[3,7],[4,8],[9,10]] => [[1,2],[3,7],[4,8],[5,9],[6,10]] => 011110111
[[1,5],[2,6],[3,7],[4,9],[8,10]] => [[1,3],[2,7],[4,8],[5,9],[6,10]] => 101110111
[[1,5],[2,6],[3,8],[4,9],[7,10]] => [[1,4],[2,7],[3,8],[5,9],[6,10]] => 110110111
[[1,5],[2,7],[3,8],[4,9],[6,10]] => [[1,5],[2,7],[3,8],[4,9],[6,10]] => 111010111
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] => [[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => 10110101010
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] => [[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] => 01101101010
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] => [[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] => 10101101010
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] => [[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] => 11011101010
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] => [[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] => 01011011010
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] => [[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] => 10111011010
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] => [[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] => 01101011010
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] => [[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] => 10101011010
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] => [[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] => 11011011010
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] => [[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] => 01110111010
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] => [[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] => 10110111010
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] => [[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => 11010111010
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] => [[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] => 11101111010
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] => [[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] => 01010110110
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] => [[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] => 10110110110
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => [[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => 01101110110
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] => [[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] => 10101110110
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] => [[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] => 11011110110
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] => [[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] => 01011010110
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] => [[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] => 10111010110
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] => [[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] => 01101010110
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] => [[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] => 10101010110
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] => [[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => 11011010110
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] => [[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] => 01110110110
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] => [[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] => 10110110110
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] => [[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] => 11010110110
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] => [[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] => 11101110110
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] => [[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] => 01011101110
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] => [[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] => 10111101110
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] => [[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] => 01101101110
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] => [[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] => 10101101110
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => [[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => 11011101110
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] => [[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] => 01110101110
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] => [[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] => 10110101110
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] => [[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] => 11010101110
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] => [[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] => 11101101110
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => [[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => 01111011110
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] => [[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] => 10111011110
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] => [[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => 11011011110
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] => [[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] => 11101011110
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => [[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => 11110111110
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => [[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] => 01010101101
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] => [[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] => 10110101101
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] => [[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] => 01101101101
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] => [[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] => 10101101101
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] => [[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] => 11011101101
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] => [[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] => 01011011101
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] => [[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] => 10111011101
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] => [[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] => 01101011101
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] => [[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] => 10101011101
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] => [[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] => 11011011101
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] => [[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] => 01110111101
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] => [[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] => 10110111101
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] => [[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] => 11010111101
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] => [[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] => 11101111101
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] => [[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] => 01010110101
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] => [[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] => 10110110101
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] => [[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] => 01101110101
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] => [[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] => 10101110101
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] => [[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] => 11011110101
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] => [[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] => 01011010101
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] => [[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] => 10111010101
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] => [[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] => 01101010101
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => 10101010101
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] => [[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] => 11011010101
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] => [[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] => 01110110101
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] => [[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] => 10110110101
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] => [[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] => 11010110101
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] => [[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] => 11101110101
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] => [[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] => 01011101101
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] => [[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] => 10111101101
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] => [[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] => 01101101101
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] => [[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] => 10101101101
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] => [[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] => 11011101101
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] => [[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] => 01110101101
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] => [[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] => 10110101101
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] => [[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] => 11010101101
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] => [[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] => 11101101101
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] => [[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] => 01111011101
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] => [[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] => 10111011101
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] => [[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] => 11011011101
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] => [[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] => 11101011101
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] => [[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] => 11110111101
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] => [[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] => 01010111011
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] => [[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] => 10110111011
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] => [[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] => 01101111011
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] => [[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] => 10101111011
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => [[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => 11011111011
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] => [[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] => 01011011011
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] => [[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] => 10111011011
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => [[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] => 01101011011
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] => [[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] => 10101011011
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] => [[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] => 11011011011
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => [[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => 01110111011
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] => [[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] => 10110111011
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => [[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => 11010111011
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] => [[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] => 11101111011
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => [[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] => 01011101011
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] => [[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] => 10111101011
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] => [[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] => 01101101011
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] => [[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] => 10101101011
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => [[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => 11011101011
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] => [[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] => 01110101011
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] => [[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] => 10110101011
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] => [[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] => 11010101011
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] => [[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] => 11101101011
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => [[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] => 01111011011
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] => [[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] => 10111011011
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] => [[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] => 11011011011
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] => [[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] => 11101011011
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => [[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => 11110111011
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] => [[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] => 01011110111
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] => [[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] => 10111110111
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] => [[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] => 01101110111
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] => [[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] => 10101110111
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] => [[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] => 11011110111
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] => [[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] => 01110110111
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] => [[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] => 10110110111
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] => [[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] => 11010110111
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] => [[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] => 11101110111
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] => [[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] => 01111010111
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] => [[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] => 10111010111
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] => [[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] => 11011010111
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] => [[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] => 11101010111
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] => [[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] => 11110110111
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => [[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => 01111101111
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] => [[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] => 10111101111
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => [[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => 11011101111
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] => [[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] => 11101101111
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => [[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => 11110101111
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[[1,2,3,4,5,6,7,9],[8]] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[[1,2,3,4,5,6,9],[7,8]] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[[1,2,3,4,9],[5,6],[7,8]] => [[1,2,3,8,9],[4,5],[6,7]] => 00101000
[[1,2,3,4,9],[5,6],[7],[8]] => [[1,2,5,8,9],[3,7],[4],[6]] => 01101000
[[1,2,3,9],[4,5,6],[7,8]] => [[1,2,3,6],[4,5,9],[7,8]] => 00100100
[[1,2,3,9],[4],[5],[6],[7],[8]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 01111100
[[1,2,9],[3,4],[5,6],[7],[8]] => [[1,2,5],[3,7],[4,9],[6],[8]] => 01101010
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[[1,2,3,4,5,6,7,8,10],[9]] => [[1,2,4,5,6,7,8,9,10],[3]] => 010000000
[[1,2,3,4,5,6,7,10],[8,9]] => [[1,2,3,6,7,8,9,10],[4,5]] => 001000000
[[1,2,3,4,5,6,10],[7,8,9]] => [[1,2,3,4,8,9,10],[5,6,7]] => 000100000
[[1,2,3,4,5,6,10],[7,8],[9]] => [[1,2,4,7,8,9,10],[3,6],[5]] => 010100000
[[1,2,3,4,5,10],[6,7],[8,9]] => [[1,2,3,8,9,10],[4,5],[6,7]] => 001010000
[[1,2,3,4,10],[5,6,7],[8,9]] => [[1,2,3,6,10],[4,5,9],[7,8]] => 001001000
[[1,2,3,4,10],[5,6],[7],[8],[9]] => [[1,2,6,9,10],[3,8],[4],[5],[7]] => 011101000
[[1,2,3,10],[4],[5],[6],[7],[8],[9]] => [[1,2,9,10],[3],[4],[5],[6],[7],[8]] => 011111100
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[] => [] =>
[[1,2,4,5,6,7,8,9],[3]] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[[1,3,5,6,7,8,9],[2],[4]] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[[1,4,6,7,8,9],[2],[3],[5]] => [[1,2,3,4,5,7],[6],[8],[9]] => 00001011
[[1,2,5,7,9],[3,6,8],[4]] => [[1,2,4,6,9],[3,5,7],[8]] => 01010110
[[1,5,7,8,9],[2],[3],[4],[6]] => [[1,2,3,4,6],[5],[7],[8],[9]] => 00010111
[[1,6,8,9],[2],[3],[4],[5],[7]] => [[1,2,3,5],[4],[6],[7],[8],[9]] => 00101111
[[1,4,7],[2,8,9],[3],[5],[6]] => [[1,2,4],[3,5,7],[6],[8],[9]] => 01011011
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[[1,4],[2,6],[3,8],[5],[7],[9]] => [[1,3],[2,5],[4,7],[6],[8],[9]] => 10101011
[[1,6],[2,8],[3],[4],[5],[7],[9]] => [[1,3],[2,5],[4],[6],[7],[8],[9]] => 10101111
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[[1,2,4,5,6,7,8,9,10],[3]] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[[1,3,5,6,7,8,9,10],[2],[4]] => [[1,2,3,4,5,6,7,9],[8],[10]] => 000000101
[[1,4,6,7,8,9,10],[2],[3],[5]] => [[1,2,3,4,5,6,8],[7],[9],[10]] => 000001011
[[1,2,5,7,9,10],[3,6,8],[4]] => [[1,2,3,5,7,10],[4,6,8],[9]] => 001010110
[[1,5,7,8,9,10],[2],[3],[4],[6]] => [[1,2,3,4,5,7],[6],[8],[9],[10]] => 000010111
[[1,6,8,9,10],[2],[3],[4],[5],[7]] => [[1,2,3,4,6],[5],[7],[8],[9],[10]] => 000101111
[[1,5,8,10],[2,6],[3,7],[4,9]] => [[1,2,4,7],[3,8],[5,9],[6,10]] => 010110111
[[1,7,9,10],[2],[3],[4],[5],[6],[8]] => [[1,2,3,5],[4],[6],[7],[8],[9],[10]] => 001011111
[[1,5,8],[2,9,10],[3],[4],[6],[7]] => [[1,2,4],[3,5,7],[6],[8],[9],[10]] => 010110111
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [[1,2,4],[3],[5],[6],[7],[8],[9],[10]] => 010111111
[[1,3],[2,5],[4,7],[6,9],[8],[10]] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[[1,5],[2,7],[3,9],[4],[6],[8],[10]] => [[1,3],[2,5],[4,7],[6],[8],[9],[10]] => 101010111
[[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => [[1,3],[2,5],[4],[6],[7],[8],[9],[10]] => 101011111
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[[1,3,4,5,6,7,8],[2,9]] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[[1,3,4,5,6,7,8],[2],[9]] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[[1,3,4,5,6,7],[2,9],[8]] => [[1,2,5,6,7,8],[3,4],[9]] => 01000001
[[1,3,4,5,6,7],[2],[8],[9]] => [[1,4,5,6,7,8],[2],[3],[9]] => 11000001
[[1,3,4,5,6],[2,8,9],[7]] => [[1,2,3,7,8],[4,5,6],[9]] => 00100001
[[1,3,4,5,6],[2,8],[7],[9]] => [[1,3,6,7,8],[2,5],[4],[9]] => 10100001
[[1,3,4,5,6],[2],[7],[8],[9]] => [[1,5,6,7,8],[2],[3],[4],[9]] => 11100001
[[1,3,4,5],[2,7,8],[6,9]] => [[1,3,4,8],[2,6,7],[5,9]] => 10010001
[[1,3,4,5],[2,7,8],[6],[9]] => [[1,3,4,8],[2,6,7],[5],[9]] => 10010001
[[1,3,4,5],[2,7],[6,9],[8]] => [[1,2,7,8],[3,4],[5,6],[9]] => 01010001
[[1,3,4,5],[2,7],[6],[8],[9]] => [[1,4,7,8],[2,6],[3],[5],[9]] => 11010001
[[1,3,4,5],[2],[6],[7],[8],[9]] => [[1,6,7,8],[2],[3],[4],[5],[9]] => 11110001
[[1,3,4],[2,6,7],[5,8,9]] => [[1,2,5],[3,4,8],[6,7,9]] => 01001001
[[1,3,4],[2,6,7],[5,9],[8]] => [[1,2,5],[3,4,8],[6,7],[9]] => 01001001
[[1,3,4],[2,6,7],[5],[8],[9]] => [[1,4,5],[2,7,8],[3],[6],[9]] => 11001001
[[1,3,4],[2,6],[5,8],[7],[9]] => [[1,3,8],[2,5],[4,7],[6],[9]] => 10101001
[[1,3,4],[2,6],[5],[7],[8],[9]] => [[1,5,8],[2,7],[3],[4],[6],[9]] => 11101001
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001
[[1,3],[2,5],[4,7],[6],[8],[9]] => [[1,4],[2,6],[3,8],[5],[7],[9]] => 11010101
[[1,3],[2,5],[4],[6],[7],[8],[9]] => [[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[[1,3,4,5,6,7,8,9],[2,10]] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[[1,3,4,5,6,7,8,9],[2],[10]] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[[1,3,4,5,6,7,8],[2,10],[9]] => [[1,2,5,6,7,8,9],[3,4],[10]] => 010000001
[[1,3,4,5,6,7,8],[2],[9],[10]] => [[1,4,5,6,7,8,9],[2],[3],[10]] => 110000001
[[1,3,4,5,6,7],[2,9,10],[8]] => [[1,2,3,7,8,9],[4,5,6],[10]] => 001000001
[[1,3,4,5,6,7],[2,9],[8],[10]] => [[1,3,6,7,8,9],[2,5],[4],[10]] => 101000001
[[1,3,4,5,6,7],[2],[8],[9],[10]] => [[1,5,6,7,8,9],[2],[3],[4],[10]] => 111000001
[[1,3,4,5,6],[2,8,9,10],[7]] => [[1,2,3,4,9],[5,6,7,8],[10]] => 000100001
[[1,3,4,5,6],[2,8,9],[7],[10]] => [[1,3,4,8,9],[2,6,7],[5],[10]] => 100100001
[[1,3,4,5,6],[2,8],[7,10],[9]] => [[1,2,7,8,9],[3,4],[5,6],[10]] => 010100001
[[1,3,4,5,6],[2,8],[7],[9],[10]] => [[1,4,7,8,9],[2,6],[3],[5],[10]] => 110100001
[[1,3,4,5,6],[2],[7],[8],[9],[10]] => [[1,6,7,8,9],[2],[3],[4],[5],[10]] => 111100001
[[1,3,4,5],[2,7,8,9],[6],[10]] => [[1,3,4,5],[2,7,8,9],[6],[10]] => 100010001
[[1,3,4,5],[2,7,8],[6,10],[9]] => [[1,2,5,9],[3,4,8],[6,7],[10]] => 010010001
[[1,3,4,5],[2,7,8],[6],[9],[10]] => [[1,4,5,9],[2,7,8],[3],[6],[10]] => 110010001
[[1,3,4,5],[2,7],[6,9],[8],[10]] => [[1,3,8,9],[2,5],[4,7],[6],[10]] => 101010001
[[1,3,4,5],[2,7],[6],[8],[9],[10]] => [[1,5,8,9],[2,7],[3],[4],[6],[10]] => 111010001
[[1,3,4,5],[2],[6],[7],[8],[9],[10]] => [[1,7,8,9],[2],[3],[4],[5],[6],[10]] => 111110001
[[1,3,4],[2,6,7],[5,9],[8],[10]] => [[1,3,6],[2,5,9],[4,8],[7],[10]] => 101001001
[[1,3,4],[2,6,7],[5],[8],[9],[10]] => [[1,5,6],[2,8,9],[3],[4],[7],[10]] => 111001001
[[1,3,4],[2,6],[5,8],[7,10],[9]] => [[1,2,9],[3,4],[5,6],[7,8],[10]] => 010101001
[[1,3,4],[2,6],[5,8],[7],[9],[10]] => [[1,4,9],[2,6],[3,8],[5],[7],[10]] => 110101001
[[1,3,4],[2,6],[5],[7],[8],[9],[10]] => [[1,6,9],[2,8],[3],[4],[5],[7],[10]] => 111101001
[[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => [[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => 111111001
[[1,3],[2,5],[4,7],[6],[8],[9],[10]] => [[1,5],[2,7],[3,9],[4],[6],[8],[10]] => 111010101
[[1,3],[2,5],[4],[6],[7],[8],[9],[10]] => [[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => 111110101
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => 111111101
[[1,2,4,6,8,10],[3,5,7,9]] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[[1,2,4,6,8,9,10],[3,5,7]] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[[1,2,4,6,7,8,10],[3,5,9]] => [[1,2,4,5,6,8,10],[3,7,9]] => 010001010
[[1,2,4,6,7,9,10],[3,5,8]] => [[1,2,3,5,6,8,10],[4,7,9]] => 001001010
[[1,2,4,6,7,8,9,10],[3,5]] => [[1,2,3,4,5,6,8,10],[7,9]] => 000001010
[[1,2,4,5,6,8,10],[3,7,9]] => [[1,2,4,6,7,8,10],[3,5,9]] => 010100010
[[1,2,4,5,6,9,10],[3,7,8]] => [[1,2,3,4,7,8,10],[5,6,9]] => 000100010
[[1,2,4,5,7,8,10],[3,6,9]] => [[1,2,4,5,7,8,10],[3,6,9]] => 010010010
[[1,2,4,5,7,9,10],[3,6,8]] => [[1,2,3,5,7,8,10],[4,6,9]] => 001010010
[[1,2,4,5,7,8,9,10],[3,6]] => [[1,2,3,4,5,7,8,10],[6,9]] => 000010010
[[1,2,4,5,6,7,8,10],[3,9]] => [[1,2,4,5,6,7,8,10],[3,9]] => 010000010
[[1,2,4,5,6,7,9,10],[3,8]] => [[1,2,3,5,6,7,8,10],[4,9]] => 001000010
[[1,2,4,5,6,8,9,10],[3,7]] => [[1,2,3,4,6,7,8,10],[5,9]] => 000100010
[[1,2,3,4,6,8,10],[5,7,9]] => [[1,2,4,6,8,9,10],[3,5,7]] => 010101000
[[1,2,3,4,6,9,10],[5,7,8]] => [[1,2,3,4,6,9,10],[5,7,8]] => 000101000
[[1,2,3,4,7,8,10],[5,6,9]] => [[1,2,4,5,6,9,10],[3,7,8]] => 010001000
[[1,2,3,4,7,9,10],[5,6,8]] => [[1,2,3,5,6,9,10],[4,7,8]] => 001001000
[[1,2,3,4,7,8,9,10],[5,6]] => [[1,2,3,4,5,6,9,10],[7,8]] => 000001000
[[1,2,3,5,6,8,10],[4,7,9]] => [[1,2,4,6,7,9,10],[3,5,8]] => 010100100
[[1,2,3,5,6,9,10],[4,7,8]] => [[1,2,3,4,7,9,10],[5,6,8]] => 000100100
[[1,2,3,5,7,8,10],[4,6,9]] => [[1,2,4,5,7,9,10],[3,6,8]] => 010010100
[[1,2,3,5,7,9,10],[4,6,8]] => [[1,2,3,5,7,9,10],[4,6,8]] => 001010100
[[1,2,3,5,7,8,9,10],[4,6]] => [[1,2,3,4,5,7,9,10],[6,8]] => 000010100
[[1,2,3,5,6,7,8,10],[4,9]] => [[1,2,4,5,6,7,9,10],[3,8]] => 010000100
[[1,2,3,5,6,7,9,10],[4,8]] => [[1,2,3,5,6,7,9,10],[4,8]] => 001000100
[[1,2,3,5,6,8,9,10],[4,7]] => [[1,2,3,4,6,7,9,10],[5,8]] => 000100100
[[1,2,3,5,6,7,8,9,10],[4]] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[[1,2,3,4,5,6,8,10],[7,9]] => [[1,2,4,6,7,8,9,10],[3,5]] => 010100000
[[1,2,3,4,5,6,9,10],[7,8]] => [[1,2,3,4,7,8,9,10],[5,6]] => 000100000
[[1,2,3,4,5,7,8,10],[6,9]] => [[1,2,4,5,7,8,9,10],[3,6]] => 010010000
[[1,2,3,4,5,7,9,10],[6,8]] => [[1,2,3,5,7,8,9,10],[4,6]] => 001010000
[[1,2,3,4,5,8,9,10],[6,7]] => [[1,2,3,4,5,8,9,10],[6,7]] => 000010000
[[1,2,3,4,6,7,8,10],[5,9]] => [[1,2,4,5,6,8,9,10],[3,7]] => 010001000
[[1,2,3,4,6,7,9,10],[5,8]] => [[1,2,3,5,6,8,9,10],[4,7]] => 001001000
[[1,2,3,4,6,8,9,10],[5,7]] => [[1,2,3,4,6,8,9,10],[5,7]] => 000101000
[[1,2,3,4,6,7,8,9,10],[5]] => [[1,2,3,4,5,6,8,9,10],[7]] => 000001000
[[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,5,6,7,8,9,10],[4]] => 001000000
[[1,2,3,4,5,6,8,9,10],[7]] => [[1,2,3,4,6,7,8,9,10],[5]] => 000100000
[[1,2,3,4,5,7,8,9,10],[6]] => [[1,2,3,4,5,7,8,9,10],[6]] => 000010000
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => 01010101010
[[1,2,4,6,8,10,11,12],[3,5,7,9]] => [[1,2,3,4,6,8,10,12],[5,7,9,11]] => 00010101010
[[1,2,4,6,8,9,10,12],[3,5,7,11]] => [[1,2,4,5,6,8,10,12],[3,7,9,11]] => 01000101010
[[1,2,4,6,8,9,11,12],[3,5,7,10]] => [[1,2,3,5,6,8,10,12],[4,7,9,11]] => 00100101010
[[1,2,4,6,8,9,10,11,12],[3,5,7]] => [[1,2,3,4,5,6,8,10,12],[7,9,11]] => 00000101010
[[1,2,4,6,7,8,10,12],[3,5,9,11]] => [[1,2,4,6,7,8,10,12],[3,5,9,11]] => 01010001010
[[1,2,4,6,7,8,11,12],[3,5,9,10]] => [[1,2,3,4,7,8,10,12],[5,6,9,11]] => 00010001010
[[1,2,4,6,7,9,10,12],[3,5,8,11]] => [[1,2,4,5,7,8,10,12],[3,6,9,11]] => 01001001010
[[1,2,4,6,7,9,11,12],[3,5,8,10]] => [[1,2,3,5,7,8,10,12],[4,6,9,11]] => 00101001010
[[1,2,4,6,7,9,10,11,12],[3,5,8]] => [[1,2,3,4,5,7,8,10,12],[6,9,11]] => 00001001010
[[1,2,4,6,7,8,9,10,12],[3,5,11]] => [[1,2,4,5,6,7,8,10,12],[3,9,11]] => 01000001010
[[1,2,4,6,7,8,9,11,12],[3,5,10]] => [[1,2,3,5,6,7,8,10,12],[4,9,11]] => 00100001010
[[1,2,4,6,7,8,10,11,12],[3,5,9]] => [[1,2,3,4,6,7,8,10,12],[5,9,11]] => 00010001010
[[1,2,4,6,7,8,9,10,11,12],[3,5]] => [[1,2,3,4,5,6,7,8,10,12],[9,11]] => 00000001010
[[1,2,4,5,6,8,10,12],[3,7,9,11]] => [[1,2,4,6,8,9,10,12],[3,5,7,11]] => 01010100010
[[1,2,4,5,6,8,11,12],[3,7,9,10]] => [[1,2,3,4,6,9,10,12],[5,7,8,11]] => 00010100010
[[1,2,4,5,6,9,10,12],[3,7,8,11]] => [[1,2,4,5,6,9,10,12],[3,7,8,11]] => 01000100010
[[1,2,4,5,6,9,11,12],[3,7,8,10]] => [[1,2,3,5,6,9,10,12],[4,7,8,11]] => 00100100010
[[1,2,4,5,6,9,10,11,12],[3,7,8]] => [[1,2,3,4,5,6,9,10,12],[7,8,11]] => 00000100010
[[1,2,4,5,7,8,10,12],[3,6,9,11]] => [[1,2,4,6,7,9,10,12],[3,5,8,11]] => 01010010010
[[1,2,4,5,7,8,11,12],[3,6,9,10]] => [[1,2,3,4,7,9,10,12],[5,6,8,11]] => 00010010010
[[1,2,4,5,7,9,10,12],[3,6,8,11]] => [[1,2,4,5,7,9,10,12],[3,6,8,11]] => 01001010010
[[1,2,4,5,7,9,11,12],[3,6,8,10]] => [[1,2,3,5,7,9,10,12],[4,6,8,11]] => 00101010010
[[1,2,4,5,7,9,10,11,12],[3,6,8]] => [[1,2,3,4,5,7,9,10,12],[6,8,11]] => 00001010010
[[1,2,4,5,7,8,9,10,12],[3,6,11]] => [[1,2,4,5,6,7,9,10,12],[3,8,11]] => 01000010010
[[1,2,4,5,7,8,9,11,12],[3,6,10]] => [[1,2,3,5,6,7,9,10,12],[4,8,11]] => 00100010010
[[1,2,4,5,7,8,10,11,12],[3,6,9]] => [[1,2,3,4,6,7,9,10,12],[5,8,11]] => 00010010010
[[1,2,4,5,7,8,9,10,11,12],[3,6]] => [[1,2,3,4,5,6,7,9,10,12],[8,11]] => 00000010010
[[1,2,4,5,6,7,8,10,12],[3,9,11]] => [[1,2,4,6,7,8,9,10,12],[3,5,11]] => 01010000010
[[1,2,4,5,6,7,8,11,12],[3,9,10]] => [[1,2,3,4,7,8,9,10,12],[5,6,11]] => 00010000010
[[1,2,4,5,6,7,9,10,12],[3,8,11]] => [[1,2,4,5,7,8,9,10,12],[3,6,11]] => 01001000010
[[1,2,4,5,6,7,9,11,12],[3,8,10]] => [[1,2,3,5,7,8,9,10,12],[4,6,11]] => 00101000010
[[1,2,4,5,6,7,10,11,12],[3,8,9]] => [[1,2,3,4,5,8,9,10,12],[6,7,11]] => 00001000010
[[1,2,4,5,6,8,9,10,12],[3,7,11]] => [[1,2,4,5,6,8,9,10,12],[3,7,11]] => 01000100010
[[1,2,4,5,6,8,9,11,12],[3,7,10]] => [[1,2,3,5,6,8,9,10,12],[4,7,11]] => 00100100010
[[1,2,4,5,6,8,10,11,12],[3,7,9]] => [[1,2,3,4,6,8,9,10,12],[5,7,11]] => 00010100010
[[1,2,4,5,6,8,9,10,11,12],[3,7]] => [[1,2,3,4,5,6,8,9,10,12],[7,11]] => 00000100010
[[1,2,4,5,6,7,8,9,10,12],[3,11]] => [[1,2,4,5,6,7,8,9,10,12],[3,11]] => 01000000010
[[1,2,4,5,6,7,8,9,11,12],[3,10]] => [[1,2,3,5,6,7,8,9,10,12],[4,11]] => 00100000010
[[1,2,4,5,6,7,8,10,11,12],[3,9]] => [[1,2,3,4,6,7,8,9,10,12],[5,11]] => 00010000010
[[1,2,4,5,6,7,9,10,11,12],[3,8]] => [[1,2,3,4,5,7,8,9,10,12],[6,11]] => 00001000010
[[1,2,4,5,6,7,8,9,10,11,12],[3]] => [[1,2,3,4,5,6,7,8,9,10,12],[11]] => 00000000010
[[1,2,3,4,6,8,10,12],[5,7,9,11]] => [[1,2,4,6,8,10,11,12],[3,5,7,9]] => 01010101000
[[1,2,3,4,6,8,11,12],[5,7,9,10]] => [[1,2,3,4,6,8,11,12],[5,7,9,10]] => 00010101000
[[1,2,3,4,6,9,10,12],[5,7,8,11]] => [[1,2,4,5,6,8,11,12],[3,7,9,10]] => 01000101000
[[1,2,3,4,6,9,11,12],[5,7,8,10]] => [[1,2,3,5,6,8,11,12],[4,7,9,10]] => 00100101000
[[1,2,3,4,6,9,10,11,12],[5,7,8]] => [[1,2,3,4,5,6,8,11,12],[7,9,10]] => 00000101000
[[1,2,3,4,7,8,10,12],[5,6,9,11]] => [[1,2,4,6,7,8,11,12],[3,5,9,10]] => 01010001000
[[1,2,3,4,7,8,11,12],[5,6,9,10]] => [[1,2,3,4,7,8,11,12],[5,6,9,10]] => 00010001000
[[1,2,3,4,7,9,10,12],[5,6,8,11]] => [[1,2,4,5,7,8,11,12],[3,6,9,10]] => 01001001000
[[1,2,3,4,7,9,11,12],[5,6,8,10]] => [[1,2,3,5,7,8,11,12],[4,6,9,10]] => 00101001000
[[1,2,3,4,7,9,10,11,12],[5,6,8]] => [[1,2,3,4,5,7,8,11,12],[6,9,10]] => 00001001000
[[1,2,3,4,7,8,9,10,12],[5,6,11]] => [[1,2,4,5,6,7,8,11,12],[3,9,10]] => 01000001000
[[1,2,3,4,7,8,9,11,12],[5,6,10]] => [[1,2,3,5,6,7,8,11,12],[4,9,10]] => 00100001000
[[1,2,3,4,7,8,10,11,12],[5,6,9]] => [[1,2,3,4,6,7,8,11,12],[5,9,10]] => 00010001000
[[1,2,3,4,7,8,9,10,11,12],[5,6]] => [[1,2,3,4,5,6,7,8,11,12],[9,10]] => 00000001000
[[1,2,3,5,6,8,10,12],[4,7,9,11]] => [[1,2,4,6,8,9,11,12],[3,5,7,10]] => 01010100100
[[1,2,3,5,6,8,11,12],[4,7,9,10]] => [[1,2,3,4,6,9,11,12],[5,7,8,10]] => 00010100100
[[1,2,3,5,6,9,10,12],[4,7,8,11]] => [[1,2,4,5,6,9,11,12],[3,7,8,10]] => 01000100100
[[1,2,3,5,6,9,11,12],[4,7,8,10]] => [[1,2,3,5,6,9,11,12],[4,7,8,10]] => 00100100100
[[1,2,3,5,6,9,10,11,12],[4,7,8]] => [[1,2,3,4,5,6,9,11,12],[7,8,10]] => 00000100100
[[1,2,3,5,7,8,10,12],[4,6,9,11]] => [[1,2,4,6,7,9,11,12],[3,5,8,10]] => 01010010100
[[1,2,3,5,7,8,11,12],[4,6,9,10]] => [[1,2,3,4,7,9,11,12],[5,6,8,10]] => 00010010100
[[1,2,3,5,7,9,10,12],[4,6,8,11]] => [[1,2,4,5,7,9,11,12],[3,6,8,10]] => 01001010100
[[1,2,3,5,7,9,11,12],[4,6,8,10]] => [[1,2,3,5,7,9,11,12],[4,6,8,10]] => 00101010100
[[1,2,3,5,7,9,10,11,12],[4,6,8]] => [[1,2,3,4,5,7,9,11,12],[6,8,10]] => 00001010100
[[1,2,3,5,7,8,9,10,12],[4,6,11]] => [[1,2,4,5,6,7,9,11,12],[3,8,10]] => 01000010100
[[1,2,3,5,7,8,9,11,12],[4,6,10]] => [[1,2,3,5,6,7,9,11,12],[4,8,10]] => 00100010100
[[1,2,3,5,7,8,10,11,12],[4,6,9]] => [[1,2,3,4,6,7,9,11,12],[5,8,10]] => 00010010100
[[1,2,3,5,7,8,9,10,11,12],[4,6]] => [[1,2,3,4,5,6,7,9,11,12],[8,10]] => 00000010100
[[1,2,3,5,6,7,8,10,12],[4,9,11]] => [[1,2,4,6,7,8,9,11,12],[3,5,10]] => 01010000100
[[1,2,3,5,6,7,8,11,12],[4,9,10]] => [[1,2,3,4,7,8,9,11,12],[5,6,10]] => 00010000100
[[1,2,3,5,6,7,9,10,12],[4,8,11]] => [[1,2,4,5,7,8,9,11,12],[3,6,10]] => 01001000100
[[1,2,3,5,6,7,9,11,12],[4,8,10]] => [[1,2,3,5,7,8,9,11,12],[4,6,10]] => 00101000100
[[1,2,3,5,6,7,10,11,12],[4,8,9]] => [[1,2,3,4,5,8,9,11,12],[6,7,10]] => 00001000100
[[1,2,3,5,6,8,9,10,12],[4,7,11]] => [[1,2,4,5,6,8,9,11,12],[3,7,10]] => 01000100100
[[1,2,3,5,6,8,9,11,12],[4,7,10]] => [[1,2,3,5,6,8,9,11,12],[4,7,10]] => 00100100100
[[1,2,3,5,6,8,10,11,12],[4,7,9]] => [[1,2,3,4,6,8,9,11,12],[5,7,10]] => 00010100100
[[1,2,3,5,6,8,9,10,11,12],[4,7]] => [[1,2,3,4,5,6,8,9,11,12],[7,10]] => 00000100100
[[1,2,3,5,6,7,8,9,10,12],[4,11]] => [[1,2,4,5,6,7,8,9,11,12],[3,10]] => 01000000100
[[1,2,3,5,6,7,8,9,11,12],[4,10]] => [[1,2,3,5,6,7,8,9,11,12],[4,10]] => 00100000100
[[1,2,3,5,6,7,8,10,11,12],[4,9]] => [[1,2,3,4,6,7,8,9,11,12],[5,10]] => 00010000100
[[1,2,3,5,6,7,9,10,11,12],[4,8]] => [[1,2,3,4,5,7,8,9,11,12],[6,10]] => 00001000100
[[1,2,3,5,6,7,8,9,10,11,12],[4]] => [[1,2,3,4,5,6,7,8,9,11,12],[10]] => 00000000100
[[1,2,3,4,5,6,8,10,12],[7,9,11]] => [[1,2,4,6,8,9,10,11,12],[3,5,7]] => 01010100000
[[1,2,3,4,5,6,8,11,12],[7,9,10]] => [[1,2,3,4,6,9,10,11,12],[5,7,8]] => 00010100000
[[1,2,3,4,5,6,9,10,12],[7,8,11]] => [[1,2,4,5,6,9,10,11,12],[3,7,8]] => 01000100000
[[1,2,3,4,5,6,9,11,12],[7,8,10]] => [[1,2,3,5,6,9,10,11,12],[4,7,8]] => 00100100000
[[1,2,3,4,5,6,10,11,12],[7,8,9]] => [[1,2,3,4,5,6,10,11,12],[7,8,9]] => 00000100000
[[1,2,3,4,5,7,8,10,12],[6,9,11]] => [[1,2,4,6,7,9,10,11,12],[3,5,8]] => 01010010000
[[1,2,3,4,5,7,8,11,12],[6,9,10]] => [[1,2,3,4,7,9,10,11,12],[5,6,8]] => 00010010000
[[1,2,3,4,5,7,9,10,12],[6,8,11]] => [[1,2,4,5,7,9,10,11,12],[3,6,8]] => 01001010000
[[1,2,3,4,5,7,9,11,12],[6,8,10]] => [[1,2,3,5,7,9,10,11,12],[4,6,8]] => 00101010000
[[1,2,3,4,5,7,10,11,12],[6,8,9]] => [[1,2,3,4,5,7,10,11,12],[6,8,9]] => 00001010000
[[1,2,3,4,5,8,9,10,12],[6,7,11]] => [[1,2,4,5,6,7,10,11,12],[3,8,9]] => 01000010000
[[1,2,3,4,5,8,9,11,12],[6,7,10]] => [[1,2,3,5,6,7,10,11,12],[4,8,9]] => 00100010000
[[1,2,3,4,5,8,10,11,12],[6,7,9]] => [[1,2,3,4,6,7,10,11,12],[5,8,9]] => 00010010000
[[1,2,3,4,5,8,9,10,11,12],[6,7]] => [[1,2,3,4,5,6,7,10,11,12],[8,9]] => 00000010000
[[1,2,3,4,6,7,8,10,12],[5,9,11]] => [[1,2,4,6,7,8,10,11,12],[3,5,9]] => 01010001000
[[1,2,3,4,6,7,8,11,12],[5,9,10]] => [[1,2,3,4,7,8,10,11,12],[5,6,9]] => 00010001000
[[1,2,3,4,6,7,9,10,12],[5,8,11]] => [[1,2,4,5,7,8,10,11,12],[3,6,9]] => 01001001000
[[1,2,3,4,6,7,9,11,12],[5,8,10]] => [[1,2,3,5,7,8,10,11,12],[4,6,9]] => 00101001000
[[1,2,3,4,6,7,10,11,12],[5,8,9]] => [[1,2,3,4,5,8,10,11,12],[6,7,9]] => 00001001000
[[1,2,3,4,6,8,9,10,12],[5,7,11]] => [[1,2,4,5,6,8,10,11,12],[3,7,9]] => 01000101000
[[1,2,3,4,6,8,9,11,12],[5,7,10]] => [[1,2,3,5,6,8,10,11,12],[4,7,9]] => 00100101000
[[1,2,3,4,6,8,10,11,12],[5,7,9]] => [[1,2,3,4,6,8,10,11,12],[5,7,9]] => 00010101000
[[1,2,3,4,6,8,9,10,11,12],[5,7]] => [[1,2,3,4,5,6,8,10,11,12],[7,9]] => 00000101000
[[1,2,3,4,6,7,8,9,10,12],[5,11]] => [[1,2,4,5,6,7,8,10,11,12],[3,9]] => 01000001000
[[1,2,3,4,6,7,8,9,11,12],[5,10]] => [[1,2,3,5,6,7,8,10,11,12],[4,9]] => 00100001000
[[1,2,3,4,6,7,8,10,11,12],[5,9]] => [[1,2,3,4,6,7,8,10,11,12],[5,9]] => 00010001000
[[1,2,3,4,6,7,9,10,11,12],[5,8]] => [[1,2,3,4,5,7,8,10,11,12],[6,9]] => 00001001000
[[1,2,3,4,6,7,8,9,10,11,12],[5]] => [[1,2,3,4,5,6,7,8,10,11,12],[9]] => 00000001000
[[1,2,3,4,5,6,7,8,10,12],[9,11]] => [[1,2,4,6,7,8,9,10,11,12],[3,5]] => 01010000000
[[1,2,3,4,5,6,7,8,11,12],[9,10]] => [[1,2,3,4,7,8,9,10,11,12],[5,6]] => 00010000000
[[1,2,3,4,5,6,7,9,10,12],[8,11]] => [[1,2,4,5,7,8,9,10,11,12],[3,6]] => 01001000000
[[1,2,3,4,5,6,7,9,11,12],[8,10]] => [[1,2,3,5,7,8,9,10,11,12],[4,6]] => 00101000000
[[1,2,3,4,5,6,7,10,11,12],[8,9]] => [[1,2,3,4,5,8,9,10,11,12],[6,7]] => 00001000000
[[1,2,3,4,5,6,8,9,10,12],[7,11]] => [[1,2,4,5,6,8,9,10,11,12],[3,7]] => 01000100000
[[1,2,3,4,5,6,8,9,11,12],[7,10]] => [[1,2,3,5,6,8,9,10,11,12],[4,7]] => 00100100000
[[1,2,3,4,5,6,8,10,11,12],[7,9]] => [[1,2,3,4,6,8,9,10,11,12],[5,7]] => 00010100000
[[1,2,3,4,5,6,9,10,11,12],[7,8]] => [[1,2,3,4,5,6,9,10,11,12],[7,8]] => 00000100000
[[1,2,3,4,5,7,8,9,10,12],[6,11]] => [[1,2,4,5,6,7,9,10,11,12],[3,8]] => 01000010000
[[1,2,3,4,5,7,8,9,11,12],[6,10]] => [[1,2,3,5,6,7,9,10,11,12],[4,8]] => 00100010000
[[1,2,3,4,5,7,8,10,11,12],[6,9]] => [[1,2,3,4,6,7,9,10,11,12],[5,8]] => 00010010000
[[1,2,3,4,5,7,9,10,11,12],[6,8]] => [[1,2,3,4,5,7,9,10,11,12],[6,8]] => 00001010000
[[1,2,3,4,5,7,8,9,10,11,12],[6]] => [[1,2,3,4,5,6,7,9,10,11,12],[8]] => 00000010000
[[1,2,3,4,5,6,7,8,9,10,12],[11]] => [[1,2,4,5,6,7,8,9,10,11,12],[3]] => 01000000000
[[1,2,3,4,5,6,7,8,9,11,12],[10]] => [[1,2,3,5,6,7,8,9,10,11,12],[4]] => 00100000000
[[1,2,3,4,5,6,7,8,10,11,12],[9]] => [[1,2,3,4,6,7,8,9,10,11,12],[5]] => 00010000000
[[1,2,3,4,5,6,7,9,10,11,12],[8]] => [[1,2,3,4,5,7,8,9,10,11,12],[6]] => 00001000000
[[1,2,3,4,5,6,8,9,10,11,12],[7]] => [[1,2,3,4,5,6,8,9,10,11,12],[7]] => 00000100000
[[1,4,5,6,7,8],[2],[3],[9]] => [[1,3,4,5,6,7],[2],[8],[9]] => 10000011
[[1,5,6,7,8],[2],[3],[4],[9]] => [[1,3,4,5,6],[2],[7],[8],[9]] => 10000111
[[1,6,7,8],[2],[3],[4],[5],[9]] => [[1,3,4,5],[2],[6],[7],[8],[9]] => 10001111
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111
[[1,4,5,6,7,8,9],[2],[3],[10]] => [[1,3,4,5,6,7,8],[2],[9],[10]] => 100000011
[[1,5,6,7,8,9],[2],[3],[4],[10]] => [[1,3,4,5,6,7],[2],[8],[9],[10]] => 100000111
[[1,6,7,8,9],[2],[3],[4],[5],[10]] => [[1,3,4,5,6],[2],[7],[8],[9],[10]] => 100001111
[[1,2,5,9],[3,4,8],[6,7],[10]] => [[1,3,4,5],[2,7,8],[6,10],[9]] => 100010010
[[1,7,8,9],[2],[3],[4],[5],[6],[10]] => [[1,3,4,5],[2],[6],[7],[8],[9],[10]] => 100011111
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => 100111111
[[1,2,5,6,7,8,9],[3],[4]] => [[1,2,3,4,5,6,9],[7],[8]] => 00000110
[[1,2,6,7,8,9],[3],[4],[5]] => [[1,2,3,4,5,9],[6],[7],[8]] => 00001110
[[1,2,7,8,9],[3],[4],[5],[6]] => [[1,2,3,4,9],[5],[6],[7],[8]] => 00011110
[[1,2,5,6],[3,8,9],[4],[7]] => [[1,2,3,9],[4,5,6],[7],[8]] => 00100110
[[1,2,8,9],[3],[4],[5],[6],[7]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => 00111110
[[1,2],[3,8],[4],[5],[6],[7],[9]] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[[1,2,5,6,7,8,9,10],[3],[4]] => [[1,2,3,4,5,6,7,10],[8],[9]] => 000000110
[[1,2,6,7,8,9,10],[3],[4],[5]] => [[1,2,3,4,5,6,10],[7],[8],[9]] => 000001110
[[1,2,7,8,9,10],[3],[4],[5],[6]] => [[1,2,3,4,5,10],[6],[7],[8],[9]] => 000011110
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [[1,2,3,4,10],[5],[6],[7],[8],[9]] => 000111110
[[1,2,4,7],[3,6,10],[5,9],[8]] => [[1,2,3,10],[4,5,6],[7,8],[9]] => 001001010
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [[1,2,3,10],[4],[5],[6],[7],[8],[9]] => 001111110
[[1,2,5],[3,7,8],[4,10],[6],[9]] => [[1,2,5],[3,4,10],[6,7],[8],[9]] => 010010110
[[1,2,4],[3,6],[5,8],[7,10],[9]] => [[1,2,10],[3,4],[5,6],[7,8],[9]] => 010101010
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => 101111110
[[1,2,5,6,7,8],[3],[4],[9]] => [[1,3,4,5,6,9],[2],[7],[8]] => 10000110
[[1,2,7,8],[3],[4],[5],[6],[9]] => [[1,3,4,9],[2],[5],[6],[7],[8]] => 10011110
[[1,2,3,4,9,10],[5,6],[7,8]] => [[1,2,3,4,9,10],[5,6],[7,8]] => 000101000
[[1,3],[2,5],[4,9],[6],[7],[8],[10]] => [[1,3],[2,7],[4,9],[5],[6],[8],[10]] => 101110101
[[1,3],[2,5],[4,8],[6],[7],[9],[10]] => [[1,4],[2,7],[3,9],[5],[6],[8],[10]] => 110110101
[[1,3],[2,7],[4,9],[5],[6],[8],[10]] => [[1,3],[2,5],[4,9],[6],[7],[8],[10]] => 101011101
[[1,3],[2,7],[4,8],[5],[6],[9],[10]] => [[1,5],[2,6],[3,9],[4],[7],[8],[10]] => 111011101
[[1,3],[2,6],[4,9],[5],[7],[8],[10]] => [[1,3],[2,6],[4,9],[5],[7],[8],[10]] => 101101101
[[1,3],[2,6],[4,8],[5],[7],[9],[10]] => [[1,4],[2,6],[3,9],[5],[7],[8],[10]] => 110101101
[[1,3],[2,6],[4],[5],[7],[8],[9],[10]] => [[1,6],[2,9],[3],[4],[5],[7],[8],[10]] => 111101101
[[1,3],[2,9],[4],[5],[6],[7],[8],[10]] => [[1,3],[2,9],[4],[5],[6],[7],[8],[10]] => 101111101
[[1,3],[2,8],[4],[5],[6],[7],[9],[10]] => [[1,4],[2,9],[3],[5],[6],[7],[8],[10]] => 110111101
[[1,3],[2,7],[4],[5],[6],[8],[9],[10]] => [[1,5],[2,9],[3],[4],[6],[7],[8],[10]] => 111011101
[[1,5],[2,7],[3,8],[4],[6],[9],[10]] => [[1,5],[2,7],[3,8],[4],[6],[9],[10]] => 111010111
[[1,5],[2,6],[3,9],[4],[7],[8],[10]] => [[1,3],[2,7],[4,8],[5],[6],[9],[10]] => 101110111
[[1,5],[2,6],[3,8],[4],[7],[9],[10]] => [[1,4],[2,7],[3,8],[5],[6],[9],[10]] => 110110111
[[1,5],[2,6],[3],[4],[7],[8],[9],[10]] => [[1,7],[2,8],[3],[4],[5],[6],[9],[10]] => 111110111
[[1,4],[2,7],[3,9],[5],[6],[8],[10]] => [[1,3],[2,5],[4,8],[6],[7],[9],[10]] => 101011011
[[1,4],[2,7],[3,8],[5],[6],[9],[10]] => [[1,5],[2,6],[3,8],[4],[7],[9],[10]] => 111011011
[[1,4],[2,6],[3,9],[5],[7],[8],[10]] => [[1,3],[2,6],[4,8],[5],[7],[9],[10]] => 101101011
[[1,4],[2,6],[3,8],[5],[7],[9],[10]] => [[1,4],[2,6],[3,8],[5],[7],[9],[10]] => 110101011
[[1,4],[2,6],[3],[5],[7],[8],[9],[10]] => [[1,6],[2,8],[3],[4],[5],[7],[9],[10]] => 111101011
[[1,4],[2,9],[3],[5],[6],[7],[8],[10]] => [[1,3],[2,8],[4],[5],[6],[7],[9],[10]] => 101111011
[[1,4],[2,8],[3],[5],[6],[7],[9],[10]] => [[1,4],[2,8],[3],[5],[6],[7],[9],[10]] => 110111011
[[1,4],[2,7],[3],[5],[6],[8],[9],[10]] => [[1,5],[2,8],[3],[4],[6],[7],[9],[10]] => 111011011
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => 111111011
[[1,7],[2,8],[3],[4],[5],[6],[9],[10]] => [[1,5],[2,6],[3],[4],[7],[8],[9],[10]] => 111011111
[[1,6],[2,9],[3],[4],[5],[7],[8],[10]] => [[1,3],[2,6],[4],[5],[7],[8],[9],[10]] => 101101111
[[1,6],[2,8],[3],[4],[5],[7],[9],[10]] => [[1,4],[2,6],[3],[5],[7],[8],[9],[10]] => 110101111
[[1,6],[2,7],[3],[4],[5],[8],[9],[10]] => [[1,6],[2,7],[3],[4],[5],[8],[9],[10]] => 111101111
[[1,5],[2,9],[3],[4],[6],[7],[8],[10]] => [[1,3],[2,7],[4],[5],[6],[8],[9],[10]] => 101110111
[[1,5],[2,8],[3],[4],[6],[7],[9],[10]] => [[1,4],[2,7],[3],[5],[6],[8],[9],[10]] => 110110111
[[1,5],[2,7],[3],[4],[6],[8],[9],[10]] => [[1,5],[2,7],[3],[4],[6],[8],[9],[10]] => 111010111
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => 111110111
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => 110111111
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => 111101111
[[1,3],[2,5],[4,7],[6,9],[8,11],[10],[12]] => [[1,3],[2,5],[4,7],[6,9],[8,11],[10],[12]] => 10101010101
[[1,3],[2,5],[4,7],[6,9],[8],[10],[11],[12]] => [[1,5],[2,7],[3,9],[4,11],[6],[8],[10],[12]] => 11101010101
[[1,3],[2,5],[4,7],[6,11],[8],[9],[10],[12]] => [[1,3],[2,7],[4,9],[5,11],[6],[8],[10],[12]] => 10111010101
[[1,3],[2,5],[4,7],[6,10],[8],[9],[11],[12]] => [[1,4],[2,7],[3,9],[5,11],[6],[8],[10],[12]] => 11011010101
[[1,3],[2,5],[4,7],[6],[8],[9],[10],[11],[12]] => [[1,7],[2,9],[3,11],[4],[5],[6],[8],[10],[12]] => 11111010101
[[1,3],[2,5],[4,9],[6,11],[7],[8],[10],[12]] => [[1,3],[2,5],[4,9],[6,11],[7],[8],[10],[12]] => 10101110101
[[1,3],[2,5],[4,9],[6,10],[7],[8],[11],[12]] => [[1,5],[2,6],[3,9],[4,11],[7],[8],[10],[12]] => 11101110101
[[1,3],[2,5],[4,8],[6,11],[7],[9],[10],[12]] => [[1,3],[2,6],[4,9],[5,11],[7],[8],[10],[12]] => 10110110101
[[1,3],[2,5],[4,8],[6,10],[7],[9],[11],[12]] => [[1,4],[2,6],[3,9],[5,11],[7],[8],[10],[12]] => 11010110101
[[1,3],[2,5],[4,8],[6],[7],[9],[10],[11],[12]] => [[1,6],[2,9],[3,11],[4],[5],[7],[8],[10],[12]] => 11110110101
[[1,3],[2,5],[4,11],[6],[7],[8],[9],[10],[12]] => [[1,3],[2,9],[4,11],[5],[6],[7],[8],[10],[12]] => 10111110101
[[1,3],[2,5],[4,10],[6],[7],[8],[9],[11],[12]] => [[1,4],[2,9],[3,11],[5],[6],[7],[8],[10],[12]] => 11011110101
[[1,3],[2,5],[4,9],[6],[7],[8],[10],[11],[12]] => [[1,5],[2,9],[3,11],[4],[6],[7],[8],[10],[12]] => 11101110101
[[1,3],[2,5],[4],[6],[7],[8],[9],[10],[11],[12]] => [[1,9],[2,11],[3],[4],[5],[6],[7],[8],[10],[12]] => 11111110101
[[1,3],[2,7],[4,9],[5,11],[6],[8],[10],[12]] => [[1,3],[2,5],[4,7],[6,11],[8],[9],[10],[12]] => 10101011101
[[1,3],[2,7],[4,9],[5,10],[6],[8],[11],[12]] => [[1,5],[2,7],[3,8],[4,11],[6],[9],[10],[12]] => 11101011101
[[1,3],[2,7],[4,8],[5,11],[6],[9],[10],[12]] => [[1,3],[2,7],[4,8],[5,11],[6],[9],[10],[12]] => 10111011101
[[1,3],[2,7],[4,8],[5,10],[6],[9],[11],[12]] => [[1,4],[2,7],[3,8],[5,11],[6],[9],[10],[12]] => 11011011101
[[1,3],[2,7],[4,8],[5],[6],[9],[10],[11],[12]] => [[1,7],[2,8],[3,11],[4],[5],[6],[9],[10],[12]] => 11111011101
[[1,3],[2,6],[4,9],[5,11],[7],[8],[10],[12]] => [[1,3],[2,5],[4,8],[6,11],[7],[9],[10],[12]] => 10101101101
[[1,3],[2,6],[4,9],[5,10],[7],[8],[11],[12]] => [[1,5],[2,6],[3,8],[4,11],[7],[9],[10],[12]] => 11101101101
[[1,3],[2,6],[4,8],[5,11],[7],[9],[10],[12]] => [[1,3],[2,6],[4,8],[5,11],[7],[9],[10],[12]] => 10110101101
[[1,3],[2,6],[4,8],[5,10],[7],[9],[11],[12]] => [[1,4],[2,6],[3,8],[5,11],[7],[9],[10],[12]] => 11010101101
[[1,3],[2,6],[4,8],[5],[7],[9],[10],[11],[12]] => [[1,6],[2,8],[3,11],[4],[5],[7],[9],[10],[12]] => 11110101101
[[1,3],[2,6],[4,11],[5],[7],[8],[9],[10],[12]] => [[1,3],[2,8],[4,11],[5],[6],[7],[9],[10],[12]] => 10111101101
[[1,3],[2,6],[4,10],[5],[7],[8],[9],[11],[12]] => [[1,4],[2,8],[3,11],[5],[6],[7],[9],[10],[12]] => 11011101101
[[1,3],[2,6],[4,9],[5],[7],[8],[10],[11],[12]] => [[1,5],[2,8],[3,11],[4],[6],[7],[9],[10],[12]] => 11101101101
[[1,3],[2,6],[4],[5],[7],[8],[9],[10],[11],[12]] => [[1,8],[2,11],[3],[4],[5],[6],[7],[9],[10],[12]] => 11111101101
[[1,3],[2,9],[4,11],[5],[6],[7],[8],[10],[12]] => [[1,3],[2,5],[4,11],[6],[7],[8],[9],[10],[12]] => 10101111101
[[1,3],[2,9],[4,10],[5],[6],[7],[8],[11],[12]] => [[1,5],[2,6],[3,11],[4],[7],[8],[9],[10],[12]] => 11101111101
[[1,3],[2,8],[4,11],[5],[6],[7],[9],[10],[12]] => [[1,3],[2,6],[4,11],[5],[7],[8],[9],[10],[12]] => 10110111101
[[1,3],[2,8],[4,10],[5],[6],[7],[9],[11],[12]] => [[1,4],[2,6],[3,11],[5],[7],[8],[9],[10],[12]] => 11010111101
[[1,3],[2,8],[4,9],[5],[6],[7],[10],[11],[12]] => [[1,6],[2,7],[3,11],[4],[5],[8],[9],[10],[12]] => 11110111101
[[1,3],[2,7],[4,11],[5],[6],[8],[9],[10],[12]] => [[1,3],[2,7],[4,11],[5],[6],[8],[9],[10],[12]] => 10111011101
[[1,3],[2,7],[4,10],[5],[6],[8],[9],[11],[12]] => [[1,4],[2,7],[3,11],[5],[6],[8],[9],[10],[12]] => 11011011101
[[1,3],[2,7],[4,9],[5],[6],[8],[10],[11],[12]] => [[1,5],[2,7],[3,11],[4],[6],[8],[9],[10],[12]] => 11101011101
[[1,3],[2,7],[4],[5],[6],[8],[9],[10],[11],[12]] => [[1,7],[2,11],[3],[4],[5],[6],[8],[9],[10],[12]] => 11111011101
[[1,3],[2,11],[4],[5],[6],[7],[8],[9],[10],[12]] => [[1,3],[2,11],[4],[5],[6],[7],[8],[9],[10],[12]] => 10111111101
[[1,3],[2,10],[4],[5],[6],[7],[8],[9],[11],[12]] => [[1,4],[2,11],[3],[5],[6],[7],[8],[9],[10],[12]] => 11011111101
[[1,3],[2,9],[4],[5],[6],[7],[8],[10],[11],[12]] => [[1,5],[2,11],[3],[4],[6],[7],[8],[9],[10],[12]] => 11101111101
[[1,3],[2,8],[4],[5],[6],[7],[9],[10],[11],[12]] => [[1,6],[2,11],[3],[4],[5],[7],[8],[9],[10],[12]] => 11110111101
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]] => 11111111101
[[1,5],[2,7],[3,9],[4,11],[6],[8],[10],[12]] => [[1,3],[2,5],[4,7],[6,9],[8],[10],[11],[12]] => 10101010111
[[1,5],[2,7],[3,9],[4,10],[6],[8],[11],[12]] => [[1,5],[2,7],[3,9],[4,10],[6],[8],[11],[12]] => 11101010111
[[1,5],[2,7],[3,8],[4,11],[6],[9],[10],[12]] => [[1,3],[2,7],[4,9],[5,10],[6],[8],[11],[12]] => 10111010111
[[1,5],[2,7],[3,8],[4,10],[6],[9],[11],[12]] => [[1,4],[2,7],[3,9],[5,10],[6],[8],[11],[12]] => 11011010111
[[1,5],[2,7],[3,8],[4],[6],[9],[10],[11],[12]] => [[1,7],[2,9],[3,10],[4],[5],[6],[8],[11],[12]] => 11111010111
[[1,5],[2,6],[3,9],[4,11],[7],[8],[10],[12]] => [[1,3],[2,5],[4,9],[6,10],[7],[8],[11],[12]] => 10101110111
[[1,5],[2,6],[3,9],[4,10],[7],[8],[11],[12]] => [[1,5],[2,6],[3,9],[4,10],[7],[8],[11],[12]] => 11101110111
[[1,5],[2,6],[3,8],[4,11],[7],[9],[10],[12]] => [[1,3],[2,6],[4,9],[5,10],[7],[8],[11],[12]] => 10110110111
[[1,5],[2,6],[3,8],[4,10],[7],[9],[11],[12]] => [[1,4],[2,6],[3,9],[5,10],[7],[8],[11],[12]] => 11010110111
[[1,5],[2,6],[3,8],[4],[7],[9],[10],[11],[12]] => [[1,6],[2,9],[3,10],[4],[5],[7],[8],[11],[12]] => 11110110111
[[1,5],[2,6],[3,11],[4],[7],[8],[9],[10],[12]] => [[1,3],[2,9],[4,10],[5],[6],[7],[8],[11],[12]] => 10111110111
[[1,5],[2,6],[3,10],[4],[7],[8],[9],[11],[12]] => [[1,4],[2,9],[3,10],[5],[6],[7],[8],[11],[12]] => 11011110111
[[1,5],[2,6],[3,9],[4],[7],[8],[10],[11],[12]] => [[1,5],[2,9],[3,10],[4],[6],[7],[8],[11],[12]] => 11101110111
[[1,5],[2,6],[3],[4],[7],[8],[9],[10],[11],[12]] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8],[11],[12]] => 11111110111
[[1,4],[2,7],[3,9],[5,11],[6],[8],[10],[12]] => [[1,3],[2,5],[4,7],[6,10],[8],[9],[11],[12]] => 10101011011
[[1,4],[2,7],[3,9],[5,10],[6],[8],[11],[12]] => [[1,5],[2,7],[3,8],[4,10],[6],[9],[11],[12]] => 11101011011
[[1,4],[2,7],[3,8],[5,11],[6],[9],[10],[12]] => [[1,3],[2,7],[4,8],[5,10],[6],[9],[11],[12]] => 10111011011
[[1,4],[2,7],[3,8],[5,10],[6],[9],[11],[12]] => [[1,4],[2,7],[3,8],[5,10],[6],[9],[11],[12]] => 11011011011
[[1,4],[2,7],[3,8],[5],[6],[9],[10],[11],[12]] => [[1,7],[2,8],[3,10],[4],[5],[6],[9],[11],[12]] => 11111011011
[[1,4],[2,6],[3,9],[5,11],[7],[8],[10],[12]] => [[1,3],[2,5],[4,8],[6,10],[7],[9],[11],[12]] => 10101101011
[[1,4],[2,6],[3,9],[5,10],[7],[8],[11],[12]] => [[1,5],[2,6],[3,8],[4,10],[7],[9],[11],[12]] => 11101101011
[[1,4],[2,6],[3,8],[5,11],[7],[9],[10],[12]] => [[1,3],[2,6],[4,8],[5,10],[7],[9],[11],[12]] => 10110101011
[[1,4],[2,6],[3,8],[5,10],[7],[9],[11],[12]] => [[1,4],[2,6],[3,8],[5,10],[7],[9],[11],[12]] => 11010101011
[[1,4],[2,6],[3,8],[5],[7],[9],[10],[11],[12]] => [[1,6],[2,8],[3,10],[4],[5],[7],[9],[11],[12]] => 11110101011
[[1,4],[2,6],[3,11],[5],[7],[8],[9],[10],[12]] => [[1,3],[2,8],[4,10],[5],[6],[7],[9],[11],[12]] => 10111101011
[[1,4],[2,6],[3,10],[5],[7],[8],[9],[11],[12]] => [[1,4],[2,8],[3,10],[5],[6],[7],[9],[11],[12]] => 11011101011
[[1,4],[2,6],[3,9],[5],[7],[8],[10],[11],[12]] => [[1,5],[2,8],[3,10],[4],[6],[7],[9],[11],[12]] => 11101101011
[[1,4],[2,6],[3],[5],[7],[8],[9],[10],[11],[12]] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9],[11],[12]] => 11111101011
[[1,4],[2,9],[3,11],[5],[6],[7],[8],[10],[12]] => [[1,3],[2,5],[4,10],[6],[7],[8],[9],[11],[12]] => 10101111011
[[1,4],[2,9],[3,10],[5],[6],[7],[8],[11],[12]] => [[1,5],[2,6],[3,10],[4],[7],[8],[9],[11],[12]] => 11101111011
[[1,4],[2,8],[3,11],[5],[6],[7],[9],[10],[12]] => [[1,3],[2,6],[4,10],[5],[7],[8],[9],[11],[12]] => 10110111011
[[1,4],[2,8],[3,10],[5],[6],[7],[9],[11],[12]] => [[1,4],[2,6],[3,10],[5],[7],[8],[9],[11],[12]] => 11010111011
[[1,4],[2,8],[3,9],[5],[6],[7],[10],[11],[12]] => [[1,6],[2,7],[3,10],[4],[5],[8],[9],[11],[12]] => 11110111011
[[1,4],[2,7],[3,11],[5],[6],[8],[9],[10],[12]] => [[1,3],[2,7],[4,10],[5],[6],[8],[9],[11],[12]] => 10111011011
[[1,4],[2,7],[3,10],[5],[6],[8],[9],[11],[12]] => [[1,4],[2,7],[3,10],[5],[6],[8],[9],[11],[12]] => 11011011011
[[1,4],[2,7],[3,9],[5],[6],[8],[10],[11],[12]] => [[1,5],[2,7],[3,10],[4],[6],[8],[9],[11],[12]] => 11101011011
[[1,4],[2,7],[3],[5],[6],[8],[9],[10],[11],[12]] => [[1,7],[2,10],[3],[4],[5],[6],[8],[9],[11],[12]] => 11111011011
[[1,4],[2,11],[3],[5],[6],[7],[8],[9],[10],[12]] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9],[11],[12]] => 10111111011
[[1,4],[2,10],[3],[5],[6],[7],[8],[9],[11],[12]] => [[1,4],[2,10],[3],[5],[6],[7],[8],[9],[11],[12]] => 11011111011
[[1,4],[2,9],[3],[5],[6],[7],[8],[10],[11],[12]] => [[1,5],[2,10],[3],[4],[6],[7],[8],[9],[11],[12]] => 11101111011
[[1,4],[2,8],[3],[5],[6],[7],[9],[10],[11],[12]] => [[1,6],[2,10],[3],[4],[5],[7],[8],[9],[11],[12]] => 11110111011
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10],[11],[12]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9],[11],[12]] => 11111111011
[[1,7],[2,9],[3,11],[4],[5],[6],[8],[10],[12]] => [[1,3],[2,5],[4,7],[6],[8],[9],[10],[11],[12]] => 10101011111
[[1,7],[2,9],[3,10],[4],[5],[6],[8],[11],[12]] => [[1,5],[2,7],[3,8],[4],[6],[9],[10],[11],[12]] => 11101011111
[[1,7],[2,8],[3,11],[4],[5],[6],[9],[10],[12]] => [[1,3],[2,7],[4,8],[5],[6],[9],[10],[11],[12]] => 10111011111
[[1,7],[2,8],[3,10],[4],[5],[6],[9],[11],[12]] => [[1,4],[2,7],[3,8],[5],[6],[9],[10],[11],[12]] => 11011011111
[[1,7],[2,8],[3,9],[4],[5],[6],[10],[11],[12]] => [[1,7],[2,8],[3,9],[4],[5],[6],[10],[11],[12]] => 11111011111
[[1,6],[2,9],[3,11],[4],[5],[7],[8],[10],[12]] => [[1,3],[2,5],[4,8],[6],[7],[9],[10],[11],[12]] => 10101101111
[[1,6],[2,9],[3,10],[4],[5],[7],[8],[11],[12]] => [[1,5],[2,6],[3,8],[4],[7],[9],[10],[11],[12]] => 11101101111
[[1,6],[2,8],[3,11],[4],[5],[7],[9],[10],[12]] => [[1,3],[2,6],[4,8],[5],[7],[9],[10],[11],[12]] => 10110101111
[[1,6],[2,8],[3,10],[4],[5],[7],[9],[11],[12]] => [[1,4],[2,6],[3,8],[5],[7],[9],[10],[11],[12]] => 11010101111
[[1,6],[2,8],[3,9],[4],[5],[7],[10],[11],[12]] => [[1,6],[2,8],[3,9],[4],[5],[7],[10],[11],[12]] => 11110101111
[[1,6],[2,7],[3,11],[4],[5],[8],[9],[10],[12]] => [[1,3],[2,8],[4,9],[5],[6],[7],[10],[11],[12]] => 10111101111
[[1,6],[2,7],[3,10],[4],[5],[8],[9],[11],[12]] => [[1,4],[2,8],[3,9],[5],[6],[7],[10],[11],[12]] => 11011101111
[[1,6],[2,7],[3,9],[4],[5],[8],[10],[11],[12]] => [[1,5],[2,8],[3,9],[4],[6],[7],[10],[11],[12]] => 11101101111
[[1,6],[2,7],[3],[4],[5],[8],[9],[10],[11],[12]] => [[1,8],[2,9],[3],[4],[5],[6],[7],[10],[11],[12]] => 11111101111
[[1,5],[2,9],[3,11],[4],[6],[7],[8],[10],[12]] => [[1,3],[2,5],[4,9],[6],[7],[8],[10],[11],[12]] => 10101110111
[[1,5],[2,9],[3,10],[4],[6],[7],[8],[11],[12]] => [[1,5],[2,6],[3,9],[4],[7],[8],[10],[11],[12]] => 11101110111
[[1,5],[2,8],[3,11],[4],[6],[7],[9],[10],[12]] => [[1,3],[2,6],[4,9],[5],[7],[8],[10],[11],[12]] => 10110110111
[[1,5],[2,8],[3,10],[4],[6],[7],[9],[11],[12]] => [[1,4],[2,6],[3,9],[5],[7],[8],[10],[11],[12]] => 11010110111
[[1,5],[2,8],[3,9],[4],[6],[7],[10],[11],[12]] => [[1,6],[2,7],[3,9],[4],[5],[8],[10],[11],[12]] => 11110110111
[[1,5],[2,7],[3,11],[4],[6],[8],[9],[10],[12]] => [[1,3],[2,7],[4,9],[5],[6],[8],[10],[11],[12]] => 10111010111
[[1,5],[2,7],[3,10],[4],[6],[8],[9],[11],[12]] => [[1,4],[2,7],[3,9],[5],[6],[8],[10],[11],[12]] => 11011010111
[[1,5],[2,7],[3,9],[4],[6],[8],[10],[11],[12]] => [[1,5],[2,7],[3,9],[4],[6],[8],[10],[11],[12]] => 11101010111
[[1,5],[2,7],[3],[4],[6],[8],[9],[10],[11],[12]] => [[1,7],[2,9],[3],[4],[5],[6],[8],[10],[11],[12]] => 11111010111
[[1,5],[2,11],[3],[4],[6],[7],[8],[9],[10],[12]] => [[1,3],[2,9],[4],[5],[6],[7],[8],[10],[11],[12]] => 10111110111
[[1,5],[2,10],[3],[4],[6],[7],[8],[9],[11],[12]] => [[1,4],[2,9],[3],[5],[6],[7],[8],[10],[11],[12]] => 11011110111
[[1,5],[2,9],[3],[4],[6],[7],[8],[10],[11],[12]] => [[1,5],[2,9],[3],[4],[6],[7],[8],[10],[11],[12]] => 11101110111
[[1,5],[2,8],[3],[4],[6],[7],[9],[10],[11],[12]] => [[1,6],[2,9],[3],[4],[5],[7],[8],[10],[11],[12]] => 11110110111
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10],[11],[12]] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10],[11],[12]] => 11111110111
[[1,9],[2,11],[3],[4],[5],[6],[7],[8],[10],[12]] => [[1,3],[2,5],[4],[6],[7],[8],[9],[10],[11],[12]] => 10101111111
[[1,9],[2,10],[3],[4],[5],[6],[7],[8],[11],[12]] => [[1,5],[2,6],[3],[4],[7],[8],[9],[10],[11],[12]] => 11101111111
[[1,8],[2,11],[3],[4],[5],[6],[7],[9],[10],[12]] => [[1,3],[2,6],[4],[5],[7],[8],[9],[10],[11],[12]] => 10110111111
[[1,8],[2,10],[3],[4],[5],[6],[7],[9],[11],[12]] => [[1,4],[2,6],[3],[5],[7],[8],[9],[10],[11],[12]] => 11010111111
[[1,8],[2,9],[3],[4],[5],[6],[7],[10],[11],[12]] => [[1,6],[2,7],[3],[4],[5],[8],[9],[10],[11],[12]] => 11110111111
[[1,7],[2,11],[3],[4],[5],[6],[8],[9],[10],[12]] => [[1,3],[2,7],[4],[5],[6],[8],[9],[10],[11],[12]] => 10111011111
[[1,7],[2,10],[3],[4],[5],[6],[8],[9],[11],[12]] => [[1,4],[2,7],[3],[5],[6],[8],[9],[10],[11],[12]] => 11011011111
[[1,7],[2,9],[3],[4],[5],[6],[8],[10],[11],[12]] => [[1,5],[2,7],[3],[4],[6],[8],[9],[10],[11],[12]] => 11101011111
[[1,7],[2,8],[3],[4],[5],[6],[9],[10],[11],[12]] => [[1,7],[2,8],[3],[4],[5],[6],[9],[10],[11],[12]] => 11111011111
[[1,6],[2,11],[3],[4],[5],[7],[8],[9],[10],[12]] => [[1,3],[2,8],[4],[5],[6],[7],[9],[10],[11],[12]] => 10111101111
[[1,6],[2,10],[3],[4],[5],[7],[8],[9],[11],[12]] => [[1,4],[2,8],[3],[5],[6],[7],[9],[10],[11],[12]] => 11011101111
[[1,6],[2,9],[3],[4],[5],[7],[8],[10],[11],[12]] => [[1,5],[2,8],[3],[4],[6],[7],[9],[10],[11],[12]] => 11101101111
[[1,6],[2,8],[3],[4],[5],[7],[9],[10],[11],[12]] => [[1,6],[2,8],[3],[4],[5],[7],[9],[10],[11],[12]] => 11110101111
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10],[11],[12]] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10],[11],[12]] => 11111101111
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => 10111111111
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9],[11],[12]] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10],[11],[12]] => 11011111111
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10],[11],[12]] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10],[11],[12]] => 11101111111
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10],[11],[12]] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10],[11],[12]] => 11110111111
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10],[11],[12]] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10],[11],[12]] => 11111011111
[[1,2,4],[3],[5],[6],[7],[8],[9]] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010
[[1,2,3,5],[4],[6],[7],[8],[9]] => [[1,6,8,9],[2],[3],[4],[5],[7]] => 11110100
[[1,2,3,4,6],[5],[7],[8],[9]] => [[1,5,7,8,9],[2],[3],[4],[6]] => 11101000
[[1,2,3,4,5,7],[6],[8],[9]] => [[1,4,6,7,8,9],[2],[3],[5]] => 11010000
[[1,2,3,5,6],[4,8],[7,9]] => [[1,3,6,8,9],[2,5],[4,7]] => 10100100
[[1,2,3,4,5,6,8],[7],[9]] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[[1,2,3,5,7,9],[4,6,8]] => [[1,2,4,6,8,9],[3,5,7]] => 01010100
[[1,2,3,4,5,7,9],[6,8]] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[[1,2,4],[3],[5],[6],[7],[8],[9],[10]] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => 111111010
[[1,2,3,5],[4],[6],[7],[8],[9],[10]] => [[1,7,9,10],[2],[3],[4],[5],[6],[8]] => 111110100
[[1,2,3,4,6],[5],[7],[8],[9],[10]] => [[1,6,8,9,10],[2],[3],[4],[5],[7]] => 111101000
[[1,2,3,4,5,7],[6],[8],[9],[10]] => [[1,5,7,8,9,10],[2],[3],[4],[6]] => 111010000
[[1,2,3,4],[5,6,7,9],[8],[10]] => [[1,3,5,6],[2,8,9,10],[4],[7]] => 101001000
[[1,2,3,4,5,6,8],[7],[9],[10]] => [[1,4,6,7,8,9,10],[2],[3],[5]] => 110100000
[[1,2,3,4,6,7],[5,9],[8,10]] => [[1,3,6,8,9,10],[2,5],[4,7]] => 101001000
[[1,2,3,4,5,6,7,9],[8],[10]] => [[1,3,5,6,7,8,9,10],[2],[4]] => 101000000
[[1,2,8],[3,9],[4],[5],[6],[7]] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[[1,2,7],[3,8],[4,9],[5],[6]] => [[1,4,9],[2,5],[3,6],[7],[8]] => 11011110
[[1,2,7,9],[3,8],[4],[5],[6]] => [[1,2,4,9],[3,5],[6],[7],[8]] => 01011110
[[1,2,6,9],[3,7],[4,8],[5]] => [[1,2,5,9],[3,6],[4,7],[8]] => 01101110
[[1,2,6,8],[3,7,9],[4],[5]] => [[1,3,5,9],[2,4,6],[7],[8]] => 10101110
[[1,2,6,8,9],[3,7],[4],[5]] => [[1,2,3,5,9],[4,6],[7],[8]] => 00101110
[[1,2,5,8],[3,6,9],[4,7]] => [[1,3,6,9],[2,4,7],[5,8]] => 10110110
[[1,2,5,8,9],[3,6],[4,7]] => [[1,2,3,6,9],[4,7],[5,8]] => 00110110
[[1,2,5,7,8,9],[3,6],[4]] => [[1,2,3,4,6,9],[5,7],[8]] => 00010110
[[1,2,4,6,8,9],[3,5,7]] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[[1,2,4,6,7,8,9],[3,5]] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [[1,3,10],[2,4],[5],[6],[7],[8],[9]] => 101111110
[[1,2,8],[3,9],[4,10],[5],[6],[7]] => [[1,4,10],[2,5],[3,6],[7],[8],[9]] => 110111110
[[1,2,8,10],[3,9],[4],[5],[6],[7]] => [[1,2,4,10],[3,5],[6],[7],[8],[9]] => 010111110
[[1,2,7],[3,8],[4,9],[5,10],[6]] => [[1,5,10],[2,6],[3,7],[4,8],[9]] => 111011110
[[1,2,7,10],[3,8],[4,9],[5],[6]] => [[1,2,5,10],[3,6],[4,7],[8],[9]] => 011011110
[[1,2,7,9],[3,8,10],[4],[5],[6]] => [[1,3,5,10],[2,4,6],[7],[8],[9]] => 101011110
[[1,2,7,9,10],[3,8],[4],[5],[6]] => [[1,2,3,5,10],[4,6],[7],[8],[9]] => 001011110
[[1,2,6,10],[3,7],[4,8],[5,9]] => [[1,2,6,10],[3,7],[4,8],[5,9]] => 011101110
[[1,2,6,9],[3,7,10],[4,8],[5]] => [[1,3,6,10],[2,4,7],[5,8],[9]] => 101101110
[[1,2,6,9,10],[3,7],[4,8],[5]] => [[1,2,3,6,10],[4,7],[5,8],[9]] => 001101110
[[1,2,6,8,10],[3,7,9],[4],[5]] => [[1,2,4,6,10],[3,5,7],[8],[9]] => 010101110
[[1,2,6,8,9,10],[3,7],[4],[5]] => [[1,2,3,4,6,10],[5,7],[8],[9]] => 000101110
[[1,2,5,8,10],[3,6,9],[4,7]] => [[1,2,4,7,10],[3,5,8],[6,9]] => 010110110
[[1,2,5,8,9,10],[3,6],[4,7]] => [[1,2,3,4,7,10],[5,8],[6,9]] => 000110110
[[1,2,5,7,9],[3,6,8,10],[4]] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[[1,2,5,7,8,9,10],[3,6],[4]] => [[1,2,3,4,5,7,10],[6,8],[9]] => 000010110
[[1,2,4,6],[3,8],[5,9],[7,10]] => [[1,4,8,10],[2,6],[3,7],[5,9]] => 110101010
[[1,2,4,7],[3,8],[5,9],[6,10]] => [[1,5,8,10],[2,6],[3,7],[4,9]] => 111011010
[[1,2,6,7],[3,8],[4,9],[5,10]] => [[1,5,6,10],[2,7],[3,8],[4,9]] => 111001110
[[1,2,7,12],[3,8],[4,9],[5,10],[6,11]] => [[1,2,7,12],[3,8],[4,9],[5,10],[6,11]] => 01111011110
[[1,5,7],[2,6,8],[3],[4],[9]] => [[1,4,6],[2,5,7],[3],[8],[9]] => 11010111
[[1,3,4,9],[2],[5],[6],[7],[8]] => [[1,2,7,8],[3],[4],[5],[6],[9]] => 01111001
[[1,3,4,5,6,9],[2],[7],[8]] => [[1,2,5,6,7,8],[3],[4],[9]] => 01100001
[[1,7],[2,8],[3,9],[4],[5],[6],[10]] => [[1,5],[2,6],[3,7],[4],[8],[9],[10]] => 111011111
[[1,5,7],[2,6,8],[3],[4],[9],[10]] => [[1,5,7],[2,6,8],[3],[4],[9],[10]] => 111010111
[[1,3,6],[2,5,8],[4,7,9]] => [[1,3,6],[2,5,8],[4,7,9]] => 10100101
[[1,3,6,8,9],[2,5],[4,7]] => [[1,2,3,5,6],[4,8],[7,9]] => 00100101
[[1,4,8,10],[2,6],[3,7],[5,9]] => [[1,2,4,6],[3,8],[5,9],[7,10]] => 010101011
[[1,3,6,8,9,10],[2,5],[4,7]] => [[1,2,3,4,6,7],[5,9],[8,10]] => 000100101
[[1,3,5,7,9],[2,6,8,10],[4]] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[[1,6,8],[2,7],[3],[4],[5],[9]] => [[1,3,5],[2,6],[4],[7],[8],[9]] => 10101111
[[1,5,8],[2,6],[3,7],[4],[9]] => [[1,3,6],[2,7],[4,8],[5],[9]] => 10110111
[[1,5,7,8],[2,6],[3],[4],[9]] => [[1,3,4,6],[2,7],[5],[8],[9]] => 10010111
[[1,4,7],[2,5,8],[3,6],[9]] => [[1,4,7],[2,5,8],[3,9],[6]] => 11011011
[[1,4,7,8],[2,5],[3,6],[9]] => [[1,3,4,7],[2,8],[5,9],[6]] => 10011011
[[1,4,6,8],[2,5,7],[3],[9]] => [[1,3,5,7],[2,6,8],[4],[9]] => 10101011
[[1,4,6,7,8],[2,5],[3],[9]] => [[1,3,4,5,7],[2,8],[6],[9]] => 10001011
[[1,3,5,7,8],[2,4,6],[9]] => [[1,3,4,6,8],[2,7,9],[5]] => 10010101
[[1,3,5,6,7,8],[2,4],[9]] => [[1,3,4,5,6,8],[2,9],[7]] => 10000101
[[1,2,4,5,6,7,8],[3,9]] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[[1,7,9],[2,8],[3],[4],[5],[6],[10]] => [[1,3,5],[2,6],[4],[7],[8],[9],[10]] => 101011111
[[1,6,9],[2,7],[3,8],[4],[5],[10]] => [[1,3,6],[2,7],[4,8],[5],[9],[10]] => 101101111
[[1,6,8,9],[2,7],[3],[4],[5],[10]] => [[1,3,4,6],[2,7],[5],[8],[9],[10]] => 100101111
[[1,5,9],[2,6],[3,7],[4,8],[10]] => [[1,3,7],[2,8],[4,9],[5,10],[6]] => 101110111
[[1,5,8],[2,6,9],[3,7],[4],[10]] => [[1,4,7],[2,5,8],[3,9],[6],[10]] => 110110111
[[1,5,8,9],[2,6],[3,7],[4],[10]] => [[1,3,4,7],[2,8],[5,9],[6],[10]] => 100110111
[[1,5,7,9],[2,6,8],[3],[4],[10]] => [[1,3,5,7],[2,6,8],[4],[9],[10]] => 101010111
[[1,5,7,8,9],[2,6],[3],[4],[10]] => [[1,3,4,5,7],[2,8],[6],[9],[10]] => 100010111
[[1,4,7,9],[2,5,8],[3,6],[10]] => [[1,3,5,8],[2,6,9],[4,10],[7]] => 101011011
[[1,4,7,8,9],[2,5],[3,6],[10]] => [[1,3,4,5,8],[2,9],[6,10],[7]] => 100011011
[[1,4,6,8,9],[2,5,7],[3],[10]] => [[1,3,4,6,8],[2,7,9],[5],[10]] => 100101011
[[1,4,6,7,8,9],[2,5],[3],[10]] => [[1,3,4,5,6,8],[2,9],[7],[10]] => 100001011
[[1,3,5,7,9],[2,4,6,8],[10]] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[[1,3,5,7,8,9],[2,4,6],[10]] => [[1,3,4,5,7,9],[2,8,10],[6]] => 100010101
[[1,3,5,6,7,8,9],[2,4],[10]] => [[1,3,4,5,6,7,9],[2,10],[8]] => 100000101
[[1,2,4,6,8,9],[3,5,7,10]] => [[1,3,4,6,8,10],[2,5,7,9]] => 100101010
[[1,2,4,5,6,7,8,9],[3,10]] => [[1,3,4,5,6,7,8,10],[2,9]] => 100000010
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[[1,2,5],[3,6,8],[4,7,9]] => [[1,3,6],[2,4,7],[5,8,9]] => 10110110
[[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[[1,2,4,7,11],[3,5,8,12],[6,9,13],[10,14],[15]] => [[1,6,10,13,15],[2,7,11,14],[3,8,12],[4,9],[5]] => 11110111011010
[[1,5,6,10],[2,7],[3,8],[4,9]] => [[1,2,6,7],[3,8],[4,9],[5,10]] => 011100111
[[1,3,4,6,8],[2,7,9],[5]] => [[1,3,5,7,8],[2,4,6],[9]] => 10101001
[[1,3,4,7],[2,8],[5,9],[6],[10]] => [[1,5,8,9],[2,6],[3,7],[4],[10]] => 111011001
[[1,3,4,6,8,10],[2,5,7,9]] => [[1,2,4,6,8,9],[3,5,7,10]] => 010101001
[[1,3,4,5,6,8,10],[2,7,9]] => [[1,2,4,6,7,8,9],[3,5,10]] => 010100001
[[1,3,4,5,6,7,8,10],[2,9]] => [[1,2,4,5,6,7,8,9],[3,10]] => 010000001
[[1,2,4,6,9],[3,5,7,8]] => [[1,2,3,5,7],[4,6,8,9]] => 00101010
[[1,2,3,4,5,8,9],[6,7]] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[[1,2,9],[3],[4],[5],[6],[7],[8],[10]] => [[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => 101111110
[[1,2,3,4,6,7,9],[5,8,10]] => [[1,3,5,6,8,9,10],[2,4,7]] => 101001000
[[1,2,3,4,5,6,8,9],[7,10]] => [[1,3,4,6,7,8,9,10],[2,5]] => 100100000
[[1,2,3,4,7,9],[5,6],[8]] => [[1,2,4,5,8,9],[3,7],[6]] => 01001000
[[1,2,3,4,7,10],[5,6],[8],[9]] => [[1,2,5,6,9,10],[3,8],[4],[7]] => 011001000
[[1,2,4],[3,5,7],[6,8,9]] => [[1,2,4],[3,5,7],[6,8,9]] => 01011010
[[1,2,4],[3,5,7],[6],[8],[9]] => [[1,4,7],[2,8,9],[3],[5],[6]] => 11011010
[[1,2,3,5],[4,6,7,9],[8],[10]] => [[1,3,5,7],[2,8,9,10],[4],[6]] => 101010100
[[1,2,4],[3,5,7],[6],[8],[9],[10]] => [[1,5,8],[2,9,10],[3],[4],[6],[7]] => 111011010
[[1,5,6],[2,8],[3],[4],[7],[9]] => [[1,3,6],[2,5],[4],[7],[8],[9]] => 10100111
[[1,6],[2,7],[3],[4],[5],[8],[9]] => [[1,5],[2,6],[3],[4],[7],[8],[9]] => 11101111
[[1,3,4],[2,6,7],[5,8,9],[10]] => [[1,3,6],[2,5,9],[4,8,10],[7]] => 101001001
[[1,6,7],[2,9],[3],[4],[5],[8],[10]] => [[1,3,6],[2,5],[4],[7],[8],[9],[10]] => 101001111
[[1,3,4,6,8],[2,5,7,9]] => [[1,3,5,7,8],[2,4,6,9]] => 10101001
[[1,3,5,6],[2,4,8,9],[7],[10]] => [[1,3,4,9],[2,6,7,10],[5],[8]] => 100100101
[[1,2,5,6,7],[3,8],[4,9]] => [[1,4,5,6,9],[2,7],[3,8]] => 11000110
[[1,2,5,6,7,8],[3,9],[4,10]] => [[1,4,5,6,7,10],[2,8],[3,9]] => 110000110
[[1,3,5,7],[2,8,9,10],[4],[6]] => [[1,2,3,5],[4,6,7,9],[8],[10]] => 001010101
[[1,3,5,6],[2,8,9,10],[4],[7]] => [[1,2,3,4],[5,6,7,9],[8],[10]] => 000100101
[[1,3,4,5],[2,8,9,10],[6],[7]] => [[1,2,3,4],[5,7,8,9],[6],[10]] => 000110001
[[1,3,4,5,6],[2,8,9,10,11],[7],[12]] => [[1,3,4,5,6],[2,8,9,10,11],[7],[12]] => 10000100001
[[1,2,3,4],[5,7,8,9],[6],[10]] => [[1,3,4,5],[2,8,9,10],[6],[7]] => 100011000
[[1,2,3,7],[4,5,6],[8,9],[10]] => [[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100
[[1,2,3,7],[4,6,10],[5,9],[8]] => [[1,2,3,10],[4,5,6],[7,9],[8]] => 001001100
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
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