Processing math: 100%

Identifier
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
[1] => [[1]] =>
[1,2] => [[1,2]] => 0
[2,1] => [[1],[2]] => 1
[1,2,3] => [[1,2,3]] => 00
[1,3,2] => [[1,2],[3]] => 01
[2,1,3] => [[1,3],[2]] => 10
[2,3,1] => [[1,2],[3]] => 01
[3,1,2] => [[1,3],[2]] => 10
[3,2,1] => [[1],[2],[3]] => 11
[1,2,3,4] => [[1,2,3,4]] => 000
[1,2,4,3] => [[1,2,3],[4]] => 001
[1,3,2,4] => [[1,2,4],[3]] => 010
[1,3,4,2] => [[1,2,3],[4]] => 001
[1,4,2,3] => [[1,2,4],[3]] => 010
[1,4,3,2] => [[1,2],[3],[4]] => 011
[2,1,3,4] => [[1,3,4],[2]] => 100
[2,1,4,3] => [[1,3],[2,4]] => 101
[2,3,1,4] => [[1,2,4],[3]] => 010
[2,3,4,1] => [[1,2,3],[4]] => 001
[2,4,1,3] => [[1,2],[3,4]] => 010
[2,4,3,1] => [[1,2],[3],[4]] => 011
[3,1,2,4] => [[1,3,4],[2]] => 100
[3,1,4,2] => [[1,3],[2,4]] => 101
[3,2,1,4] => [[1,4],[2],[3]] => 110
[3,2,4,1] => [[1,3],[2],[4]] => 101
[3,4,1,2] => [[1,2],[3,4]] => 010
[3,4,2,1] => [[1,2],[3],[4]] => 011
[4,1,2,3] => [[1,3,4],[2]] => 100
[4,1,3,2] => [[1,3],[2],[4]] => 101
[4,2,1,3] => [[1,4],[2],[3]] => 110
[4,2,3,1] => [[1,3],[2],[4]] => 101
[4,3,1,2] => [[1,4],[2],[3]] => 110
[4,3,2,1] => [[1],[2],[3],[4]] => 111
[1,2,3,4,5] => [[1,2,3,4,5]] => 0000
[1,2,3,5,4] => [[1,2,3,4],[5]] => 0001
[1,2,4,3,5] => [[1,2,3,5],[4]] => 0010
[1,2,4,5,3] => [[1,2,3,4],[5]] => 0001
[1,2,5,3,4] => [[1,2,3,5],[4]] => 0010
[1,2,5,4,3] => [[1,2,3],[4],[5]] => 0011
[1,3,2,4,5] => [[1,2,4,5],[3]] => 0100
[1,3,2,5,4] => [[1,2,4],[3,5]] => 0101
[1,3,4,2,5] => [[1,2,3,5],[4]] => 0010
[1,3,4,5,2] => [[1,2,3,4],[5]] => 0001
[1,3,5,2,4] => [[1,2,3],[4,5]] => 0010
[1,3,5,4,2] => [[1,2,3],[4],[5]] => 0011
[1,4,2,3,5] => [[1,2,4,5],[3]] => 0100
[1,4,2,5,3] => [[1,2,4],[3,5]] => 0101
[1,4,3,2,5] => [[1,2,5],[3],[4]] => 0110
[1,4,3,5,2] => [[1,2,4],[3],[5]] => 0101
[1,4,5,2,3] => [[1,2,3],[4,5]] => 0010
[1,4,5,3,2] => [[1,2,3],[4],[5]] => 0011
[1,5,2,3,4] => [[1,2,4,5],[3]] => 0100
[1,5,2,4,3] => [[1,2,4],[3],[5]] => 0101
[1,5,3,2,4] => [[1,2,5],[3],[4]] => 0110
[1,5,3,4,2] => [[1,2,4],[3],[5]] => 0101
[1,5,4,2,3] => [[1,2,5],[3],[4]] => 0110
[1,5,4,3,2] => [[1,2],[3],[4],[5]] => 0111
[2,1,3,4,5] => [[1,3,4,5],[2]] => 1000
[2,1,3,5,4] => [[1,3,4],[2,5]] => 1001
[2,1,4,3,5] => [[1,3,5],[2,4]] => 1010
[2,1,4,5,3] => [[1,3,4],[2,5]] => 1001
[2,1,5,3,4] => [[1,3,5],[2,4]] => 1010
[2,1,5,4,3] => [[1,3],[2,4],[5]] => 1011
[2,3,1,4,5] => [[1,2,4,5],[3]] => 0100
[2,3,1,5,4] => [[1,2,4],[3,5]] => 0101
[2,3,4,1,5] => [[1,2,3,5],[4]] => 0010
[2,3,4,5,1] => [[1,2,3,4],[5]] => 0001
[2,3,5,1,4] => [[1,2,3],[4,5]] => 0010
[2,3,5,4,1] => [[1,2,3],[4],[5]] => 0011
[2,4,1,3,5] => [[1,2,5],[3,4]] => 0100
[2,4,1,5,3] => [[1,2,4],[3,5]] => 0101
[2,4,3,1,5] => [[1,2,5],[3],[4]] => 0110
[2,4,3,5,1] => [[1,2,4],[3],[5]] => 0101
[2,4,5,1,3] => [[1,2,3],[4,5]] => 0010
[2,4,5,3,1] => [[1,2,3],[4],[5]] => 0011
[2,5,1,3,4] => [[1,2,5],[3,4]] => 0100
[2,5,1,4,3] => [[1,2],[3,4],[5]] => 0101
[2,5,3,1,4] => [[1,2,5],[3],[4]] => 0110
[2,5,3,4,1] => [[1,2,4],[3],[5]] => 0101
[2,5,4,1,3] => [[1,2],[3,5],[4]] => 0110
[2,5,4,3,1] => [[1,2],[3],[4],[5]] => 0111
[3,1,2,4,5] => [[1,3,4,5],[2]] => 1000
[3,1,2,5,4] => [[1,3,4],[2,5]] => 1001
[3,1,4,2,5] => [[1,3,5],[2,4]] => 1010
[3,1,4,5,2] => [[1,3,4],[2,5]] => 1001
[3,1,5,2,4] => [[1,3,5],[2,4]] => 1010
[3,1,5,4,2] => [[1,3],[2,4],[5]] => 1011
[3,2,1,4,5] => [[1,4,5],[2],[3]] => 1100
[3,2,1,5,4] => [[1,4],[2,5],[3]] => 1101
[3,2,4,1,5] => [[1,3,5],[2],[4]] => 1010
[3,2,4,5,1] => [[1,3,4],[2],[5]] => 1001
[3,2,5,1,4] => [[1,3],[2,5],[4]] => 1010
[3,2,5,4,1] => [[1,3],[2,4],[5]] => 1011
[3,4,1,2,5] => [[1,2,5],[3,4]] => 0100
[3,4,1,5,2] => [[1,2,4],[3,5]] => 0101
[3,4,2,1,5] => [[1,2,5],[3],[4]] => 0110
[3,4,2,5,1] => [[1,2,4],[3],[5]] => 0101
[3,4,5,1,2] => [[1,2,3],[4,5]] => 0010
[3,4,5,2,1] => [[1,2,3],[4],[5]] => 0011
[3,5,1,2,4] => [[1,2,5],[3,4]] => 0100
[3,5,1,4,2] => [[1,2],[3,4],[5]] => 0101
>>> Load all 34050 entries. <<<
[3,5,2,1,4] => [[1,2],[3,5],[4]] => 0110
[3,5,2,4,1] => [[1,2],[3,4],[5]] => 0101
[3,5,4,1,2] => [[1,2],[3,5],[4]] => 0110
[3,5,4,2,1] => [[1,2],[3],[4],[5]] => 0111
[4,1,2,3,5] => [[1,3,4,5],[2]] => 1000
[4,1,2,5,3] => [[1,3,4],[2,5]] => 1001
[4,1,3,2,5] => [[1,3,5],[2],[4]] => 1010
[4,1,3,5,2] => [[1,3,4],[2],[5]] => 1001
[4,1,5,2,3] => [[1,3,5],[2,4]] => 1010
[4,1,5,3,2] => [[1,3],[2,4],[5]] => 1011
[4,2,1,3,5] => [[1,4,5],[2],[3]] => 1100
[4,2,1,5,3] => [[1,4],[2,5],[3]] => 1101
[4,2,3,1,5] => [[1,3,5],[2],[4]] => 1010
[4,2,3,5,1] => [[1,3,4],[2],[5]] => 1001
[4,2,5,1,3] => [[1,3],[2,5],[4]] => 1010
[4,2,5,3,1] => [[1,3],[2,4],[5]] => 1011
[4,3,1,2,5] => [[1,4,5],[2],[3]] => 1100
[4,3,1,5,2] => [[1,4],[2,5],[3]] => 1101
[4,3,2,1,5] => [[1,5],[2],[3],[4]] => 1110
[4,3,2,5,1] => [[1,4],[2],[3],[5]] => 1101
[4,3,5,1,2] => [[1,3],[2,5],[4]] => 1010
[4,3,5,2,1] => [[1,3],[2],[4],[5]] => 1011
[4,5,1,2,3] => [[1,2,5],[3,4]] => 0100
[4,5,1,3,2] => [[1,2],[3,4],[5]] => 0101
[4,5,2,1,3] => [[1,2],[3,5],[4]] => 0110
[4,5,2,3,1] => [[1,2],[3,4],[5]] => 0101
[4,5,3,1,2] => [[1,2],[3,5],[4]] => 0110
[4,5,3,2,1] => [[1,2],[3],[4],[5]] => 0111
[5,1,2,3,4] => [[1,3,4,5],[2]] => 1000
[5,1,2,4,3] => [[1,3,4],[2],[5]] => 1001
[5,1,3,2,4] => [[1,3,5],[2],[4]] => 1010
[5,1,3,4,2] => [[1,3,4],[2],[5]] => 1001
[5,1,4,2,3] => [[1,3,5],[2],[4]] => 1010
[5,1,4,3,2] => [[1,3],[2],[4],[5]] => 1011
[5,2,1,3,4] => [[1,4,5],[2],[3]] => 1100
[5,2,1,4,3] => [[1,4],[2,5],[3]] => 1101
[5,2,3,1,4] => [[1,3,5],[2],[4]] => 1010
[5,2,3,4,1] => [[1,3,4],[2],[5]] => 1001
[5,2,4,1,3] => [[1,3],[2,5],[4]] => 1010
[5,2,4,3,1] => [[1,3],[2],[4],[5]] => 1011
[5,3,1,2,4] => [[1,4,5],[2],[3]] => 1100
[5,3,1,4,2] => [[1,4],[2,5],[3]] => 1101
[5,3,2,1,4] => [[1,5],[2],[3],[4]] => 1110
[5,3,2,4,1] => [[1,4],[2],[3],[5]] => 1101
[5,3,4,1,2] => [[1,3],[2,5],[4]] => 1010
[5,3,4,2,1] => [[1,3],[2],[4],[5]] => 1011
[5,4,1,2,3] => [[1,4,5],[2],[3]] => 1100
[5,4,1,3,2] => [[1,4],[2],[3],[5]] => 1101
[5,4,2,1,3] => [[1,5],[2],[3],[4]] => 1110
[5,4,2,3,1] => [[1,4],[2],[3],[5]] => 1101
[5,4,3,1,2] => [[1,5],[2],[3],[4]] => 1110
[5,4,3,2,1] => [[1],[2],[3],[4],[5]] => 1111
[1,2,3,4,5,6] => [[1,2,3,4,5,6]] => 00000
[1,2,3,4,6,5] => [[1,2,3,4,5],[6]] => 00001
[1,2,3,5,4,6] => [[1,2,3,4,6],[5]] => 00010
[1,2,3,5,6,4] => [[1,2,3,4,5],[6]] => 00001
[1,2,3,6,4,5] => [[1,2,3,4,6],[5]] => 00010
[1,2,3,6,5,4] => [[1,2,3,4],[5],[6]] => 00011
[1,2,4,3,5,6] => [[1,2,3,5,6],[4]] => 00100
[1,2,4,3,6,5] => [[1,2,3,5],[4,6]] => 00101
[1,2,4,5,3,6] => [[1,2,3,4,6],[5]] => 00010
[1,2,4,5,6,3] => [[1,2,3,4,5],[6]] => 00001
[1,2,4,6,3,5] => [[1,2,3,4],[5,6]] => 00010
[1,2,4,6,5,3] => [[1,2,3,4],[5],[6]] => 00011
[1,2,5,3,4,6] => [[1,2,3,5,6],[4]] => 00100
[1,2,5,3,6,4] => [[1,2,3,5],[4,6]] => 00101
[1,2,5,4,3,6] => [[1,2,3,6],[4],[5]] => 00110
[1,2,5,4,6,3] => [[1,2,3,5],[4],[6]] => 00101
[1,2,5,6,3,4] => [[1,2,3,4],[5,6]] => 00010
[1,2,5,6,4,3] => [[1,2,3,4],[5],[6]] => 00011
[1,2,6,3,4,5] => [[1,2,3,5,6],[4]] => 00100
[1,2,6,3,5,4] => [[1,2,3,5],[4],[6]] => 00101
[1,2,6,4,3,5] => [[1,2,3,6],[4],[5]] => 00110
[1,2,6,4,5,3] => [[1,2,3,5],[4],[6]] => 00101
[1,2,6,5,3,4] => [[1,2,3,6],[4],[5]] => 00110
[1,2,6,5,4,3] => [[1,2,3],[4],[5],[6]] => 00111
[1,3,2,4,5,6] => [[1,2,4,5,6],[3]] => 01000
[1,3,2,4,6,5] => [[1,2,4,5],[3,6]] => 01001
[1,3,2,5,4,6] => [[1,2,4,6],[3,5]] => 01010
[1,3,2,5,6,4] => [[1,2,4,5],[3,6]] => 01001
[1,3,2,6,4,5] => [[1,2,4,6],[3,5]] => 01010
[1,3,2,6,5,4] => [[1,2,4],[3,5],[6]] => 01011
[1,3,4,2,5,6] => [[1,2,3,5,6],[4]] => 00100
[1,3,4,2,6,5] => [[1,2,3,5],[4,6]] => 00101
[1,3,4,5,2,6] => [[1,2,3,4,6],[5]] => 00010
[1,3,4,5,6,2] => [[1,2,3,4,5],[6]] => 00001
[1,3,4,6,2,5] => [[1,2,3,4],[5,6]] => 00010
[1,3,4,6,5,2] => [[1,2,3,4],[5],[6]] => 00011
[1,3,5,2,4,6] => [[1,2,3,6],[4,5]] => 00100
[1,3,5,2,6,4] => [[1,2,3,5],[4,6]] => 00101
[1,3,5,4,2,6] => [[1,2,3,6],[4],[5]] => 00110
[1,3,5,4,6,2] => [[1,2,3,5],[4],[6]] => 00101
[1,3,5,6,2,4] => [[1,2,3,4],[5,6]] => 00010
[1,3,5,6,4,2] => [[1,2,3,4],[5],[6]] => 00011
[1,3,6,2,4,5] => [[1,2,3,6],[4,5]] => 00100
[1,3,6,2,5,4] => [[1,2,3],[4,5],[6]] => 00101
[1,3,6,4,2,5] => [[1,2,3,6],[4],[5]] => 00110
[1,3,6,4,5,2] => [[1,2,3,5],[4],[6]] => 00101
[1,3,6,5,2,4] => [[1,2,3],[4,6],[5]] => 00110
[1,3,6,5,4,2] => [[1,2,3],[4],[5],[6]] => 00111
[1,4,2,3,5,6] => [[1,2,4,5,6],[3]] => 01000
[1,4,2,3,6,5] => [[1,2,4,5],[3,6]] => 01001
[1,4,2,5,3,6] => [[1,2,4,6],[3,5]] => 01010
[1,4,2,5,6,3] => [[1,2,4,5],[3,6]] => 01001
[1,4,2,6,3,5] => [[1,2,4,6],[3,5]] => 01010
[1,4,2,6,5,3] => [[1,2,4],[3,5],[6]] => 01011
[1,4,3,2,5,6] => [[1,2,5,6],[3],[4]] => 01100
[1,4,3,2,6,5] => [[1,2,5],[3,6],[4]] => 01101
[1,4,3,5,2,6] => [[1,2,4,6],[3],[5]] => 01010
[1,4,3,5,6,2] => [[1,2,4,5],[3],[6]] => 01001
[1,4,3,6,2,5] => [[1,2,4],[3,6],[5]] => 01010
[1,4,3,6,5,2] => [[1,2,4],[3,5],[6]] => 01011
[1,4,5,2,3,6] => [[1,2,3,6],[4,5]] => 00100
[1,4,5,2,6,3] => [[1,2,3,5],[4,6]] => 00101
[1,4,5,3,2,6] => [[1,2,3,6],[4],[5]] => 00110
[1,4,5,3,6,2] => [[1,2,3,5],[4],[6]] => 00101
[1,4,5,6,2,3] => [[1,2,3,4],[5,6]] => 00010
[1,4,5,6,3,2] => [[1,2,3,4],[5],[6]] => 00011
[1,4,6,2,3,5] => [[1,2,3,6],[4,5]] => 00100
[1,4,6,2,5,3] => [[1,2,3],[4,5],[6]] => 00101
[1,4,6,3,2,5] => [[1,2,3],[4,6],[5]] => 00110
[1,4,6,3,5,2] => [[1,2,3],[4,5],[6]] => 00101
[1,4,6,5,2,3] => [[1,2,3],[4,6],[5]] => 00110
[1,4,6,5,3,2] => [[1,2,3],[4],[5],[6]] => 00111
[1,5,2,3,4,6] => [[1,2,4,5,6],[3]] => 01000
[1,5,2,3,6,4] => [[1,2,4,5],[3,6]] => 01001
[1,5,2,4,3,6] => [[1,2,4,6],[3],[5]] => 01010
[1,5,2,4,6,3] => [[1,2,4,5],[3],[6]] => 01001
[1,5,2,6,3,4] => [[1,2,4,6],[3,5]] => 01010
[1,5,2,6,4,3] => [[1,2,4],[3,5],[6]] => 01011
[1,5,3,2,4,6] => [[1,2,5,6],[3],[4]] => 01100
[1,5,3,2,6,4] => [[1,2,5],[3,6],[4]] => 01101
[1,5,3,4,2,6] => [[1,2,4,6],[3],[5]] => 01010
[1,5,3,4,6,2] => [[1,2,4,5],[3],[6]] => 01001
[1,5,3,6,2,4] => [[1,2,4],[3,6],[5]] => 01010
[1,5,3,6,4,2] => [[1,2,4],[3,5],[6]] => 01011
[1,5,4,2,3,6] => [[1,2,5,6],[3],[4]] => 01100
[1,5,4,2,6,3] => [[1,2,5],[3,6],[4]] => 01101
[1,5,4,3,2,6] => [[1,2,6],[3],[4],[5]] => 01110
[1,5,4,3,6,2] => [[1,2,5],[3],[4],[6]] => 01101
[1,5,4,6,2,3] => [[1,2,4],[3,6],[5]] => 01010
[1,5,4,6,3,2] => [[1,2,4],[3],[5],[6]] => 01011
[1,5,6,2,3,4] => [[1,2,3,6],[4,5]] => 00100
[1,5,6,2,4,3] => [[1,2,3],[4,5],[6]] => 00101
[1,5,6,3,2,4] => [[1,2,3],[4,6],[5]] => 00110
[1,5,6,3,4,2] => [[1,2,3],[4,5],[6]] => 00101
[1,5,6,4,2,3] => [[1,2,3],[4,6],[5]] => 00110
[1,5,6,4,3,2] => [[1,2,3],[4],[5],[6]] => 00111
[1,6,2,3,4,5] => [[1,2,4,5,6],[3]] => 01000
[1,6,2,3,5,4] => [[1,2,4,5],[3],[6]] => 01001
[1,6,2,4,3,5] => [[1,2,4,6],[3],[5]] => 01010
[1,6,2,4,5,3] => [[1,2,4,5],[3],[6]] => 01001
[1,6,2,5,3,4] => [[1,2,4,6],[3],[5]] => 01010
[1,6,2,5,4,3] => [[1,2,4],[3],[5],[6]] => 01011
[1,6,3,2,4,5] => [[1,2,5,6],[3],[4]] => 01100
[1,6,3,2,5,4] => [[1,2,5],[3,6],[4]] => 01101
[1,6,3,4,2,5] => [[1,2,4,6],[3],[5]] => 01010
[1,6,3,4,5,2] => [[1,2,4,5],[3],[6]] => 01001
[1,6,3,5,2,4] => [[1,2,4],[3,6],[5]] => 01010
[1,6,3,5,4,2] => [[1,2,4],[3],[5],[6]] => 01011
[1,6,4,2,3,5] => [[1,2,5,6],[3],[4]] => 01100
[1,6,4,2,5,3] => [[1,2,5],[3,6],[4]] => 01101
[1,6,4,3,2,5] => [[1,2,6],[3],[4],[5]] => 01110
[1,6,4,3,5,2] => [[1,2,5],[3],[4],[6]] => 01101
[1,6,4,5,2,3] => [[1,2,4],[3,6],[5]] => 01010
[1,6,4,5,3,2] => [[1,2,4],[3],[5],[6]] => 01011
[1,6,5,2,3,4] => [[1,2,5,6],[3],[4]] => 01100
[1,6,5,2,4,3] => [[1,2,5],[3],[4],[6]] => 01101
[1,6,5,3,2,4] => [[1,2,6],[3],[4],[5]] => 01110
[1,6,5,3,4,2] => [[1,2,5],[3],[4],[6]] => 01101
[1,6,5,4,2,3] => [[1,2,6],[3],[4],[5]] => 01110
[1,6,5,4,3,2] => [[1,2],[3],[4],[5],[6]] => 01111
[2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 10000
[2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => 10001
[2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 10010
[2,1,3,5,6,4] => [[1,3,4,5],[2,6]] => 10001
[2,1,3,6,4,5] => [[1,3,4,6],[2,5]] => 10010
[2,1,3,6,5,4] => [[1,3,4],[2,5],[6]] => 10011
[2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 10100
[2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 10101
[2,1,4,5,3,6] => [[1,3,4,6],[2,5]] => 10010
[2,1,4,5,6,3] => [[1,3,4,5],[2,6]] => 10001
[2,1,4,6,3,5] => [[1,3,4],[2,5,6]] => 10010
[2,1,4,6,5,3] => [[1,3,4],[2,5],[6]] => 10011
[2,1,5,3,4,6] => [[1,3,5,6],[2,4]] => 10100
[2,1,5,3,6,4] => [[1,3,5],[2,4,6]] => 10101
[2,1,5,4,3,6] => [[1,3,6],[2,4],[5]] => 10110
[2,1,5,4,6,3] => [[1,3,5],[2,4],[6]] => 10101
[2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => 10010
[2,1,5,6,4,3] => [[1,3,4],[2,5],[6]] => 10011
[2,1,6,3,4,5] => [[1,3,5,6],[2,4]] => 10100
[2,1,6,3,5,4] => [[1,3,5],[2,4],[6]] => 10101
[2,1,6,4,3,5] => [[1,3,6],[2,4],[5]] => 10110
[2,1,6,4,5,3] => [[1,3,5],[2,4],[6]] => 10101
[2,1,6,5,3,4] => [[1,3,6],[2,4],[5]] => 10110
[2,1,6,5,4,3] => [[1,3],[2,4],[5],[6]] => 10111
[2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => 01000
[2,3,1,4,6,5] => [[1,2,4,5],[3,6]] => 01001
[2,3,1,5,4,6] => [[1,2,4,6],[3,5]] => 01010
[2,3,1,5,6,4] => [[1,2,4,5],[3,6]] => 01001
[2,3,1,6,4,5] => [[1,2,4,6],[3,5]] => 01010
[2,3,1,6,5,4] => [[1,2,4],[3,5],[6]] => 01011
[2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => 00100
[2,3,4,1,6,5] => [[1,2,3,5],[4,6]] => 00101
[2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => 00010
[2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => 00001
[2,3,4,6,1,5] => [[1,2,3,4],[5,6]] => 00010
[2,3,4,6,5,1] => [[1,2,3,4],[5],[6]] => 00011
[2,3,5,1,4,6] => [[1,2,3,6],[4,5]] => 00100
[2,3,5,1,6,4] => [[1,2,3,5],[4,6]] => 00101
[2,3,5,4,1,6] => [[1,2,3,6],[4],[5]] => 00110
[2,3,5,4,6,1] => [[1,2,3,5],[4],[6]] => 00101
[2,3,5,6,1,4] => [[1,2,3,4],[5,6]] => 00010
[2,3,5,6,4,1] => [[1,2,3,4],[5],[6]] => 00011
[2,3,6,1,4,5] => [[1,2,3,6],[4,5]] => 00100
[2,3,6,1,5,4] => [[1,2,3],[4,5],[6]] => 00101
[2,3,6,4,1,5] => [[1,2,3,6],[4],[5]] => 00110
[2,3,6,4,5,1] => [[1,2,3,5],[4],[6]] => 00101
[2,3,6,5,1,4] => [[1,2,3],[4,6],[5]] => 00110
[2,3,6,5,4,1] => [[1,2,3],[4],[5],[6]] => 00111
[2,4,1,3,5,6] => [[1,2,5,6],[3,4]] => 01000
[2,4,1,3,6,5] => [[1,2,5],[3,4,6]] => 01001
[2,4,1,5,3,6] => [[1,2,4,6],[3,5]] => 01010
[2,4,1,5,6,3] => [[1,2,4,5],[3,6]] => 01001
[2,4,1,6,3,5] => [[1,2,4],[3,5,6]] => 01010
[2,4,1,6,5,3] => [[1,2,4],[3,5],[6]] => 01011
[2,4,3,1,5,6] => [[1,2,5,6],[3],[4]] => 01100
[2,4,3,1,6,5] => [[1,2,5],[3,6],[4]] => 01101
[2,4,3,5,1,6] => [[1,2,4,6],[3],[5]] => 01010
[2,4,3,5,6,1] => [[1,2,4,5],[3],[6]] => 01001
[2,4,3,6,1,5] => [[1,2,4],[3,6],[5]] => 01010
[2,4,3,6,5,1] => [[1,2,4],[3,5],[6]] => 01011
[2,4,5,1,3,6] => [[1,2,3,6],[4,5]] => 00100
[2,4,5,1,6,3] => [[1,2,3,5],[4,6]] => 00101
[2,4,5,3,1,6] => [[1,2,3,6],[4],[5]] => 00110
[2,4,5,3,6,1] => [[1,2,3,5],[4],[6]] => 00101
[2,4,5,6,1,3] => [[1,2,3,4],[5,6]] => 00010
[2,4,5,6,3,1] => [[1,2,3,4],[5],[6]] => 00011
[2,4,6,1,3,5] => [[1,2,3],[4,5,6]] => 00100
[2,4,6,1,5,3] => [[1,2,3],[4,5],[6]] => 00101
[2,4,6,3,1,5] => [[1,2,3],[4,6],[5]] => 00110
[2,4,6,3,5,1] => [[1,2,3],[4,5],[6]] => 00101
[2,4,6,5,1,3] => [[1,2,3],[4,6],[5]] => 00110
[2,4,6,5,3,1] => [[1,2,3],[4],[5],[6]] => 00111
[2,5,1,3,4,6] => [[1,2,5,6],[3,4]] => 01000
[2,5,1,3,6,4] => [[1,2,5],[3,4,6]] => 01001
[2,5,1,4,3,6] => [[1,2,6],[3,4],[5]] => 01010
[2,5,1,4,6,3] => [[1,2,5],[3,4],[6]] => 01001
[2,5,1,6,3,4] => [[1,2,4],[3,5,6]] => 01010
[2,5,1,6,4,3] => [[1,2,4],[3,5],[6]] => 01011
[2,5,3,1,4,6] => [[1,2,5,6],[3],[4]] => 01100
[2,5,3,1,6,4] => [[1,2,5],[3,6],[4]] => 01101
[2,5,3,4,1,6] => [[1,2,4,6],[3],[5]] => 01010
[2,5,3,4,6,1] => [[1,2,4,5],[3],[6]] => 01001
[2,5,3,6,1,4] => [[1,2,4],[3,6],[5]] => 01010
[2,5,3,6,4,1] => [[1,2,4],[3,5],[6]] => 01011
[2,5,4,1,3,6] => [[1,2,6],[3,5],[4]] => 01100
[2,5,4,1,6,3] => [[1,2,5],[3,6],[4]] => 01101
[2,5,4,3,1,6] => [[1,2,6],[3],[4],[5]] => 01110
[2,5,4,3,6,1] => [[1,2,5],[3],[4],[6]] => 01101
[2,5,4,6,1,3] => [[1,2,4],[3,6],[5]] => 01010
[2,5,4,6,3,1] => [[1,2,4],[3],[5],[6]] => 01011
[2,5,6,1,3,4] => [[1,2,3],[4,5,6]] => 00100
[2,5,6,1,4,3] => [[1,2,3],[4,5],[6]] => 00101
[2,5,6,3,1,4] => [[1,2,3],[4,6],[5]] => 00110
[2,5,6,3,4,1] => [[1,2,3],[4,5],[6]] => 00101
[2,5,6,4,1,3] => [[1,2,3],[4,6],[5]] => 00110
[2,5,6,4,3,1] => [[1,2,3],[4],[5],[6]] => 00111
[2,6,1,3,4,5] => [[1,2,5,6],[3,4]] => 01000
[2,6,1,3,5,4] => [[1,2,5],[3,4],[6]] => 01001
[2,6,1,4,3,5] => [[1,2,6],[3,4],[5]] => 01010
[2,6,1,4,5,3] => [[1,2,5],[3,4],[6]] => 01001
[2,6,1,5,3,4] => [[1,2,6],[3,4],[5]] => 01010
[2,6,1,5,4,3] => [[1,2],[3,4],[5],[6]] => 01011
[2,6,3,1,4,5] => [[1,2,5,6],[3],[4]] => 01100
[2,6,3,1,5,4] => [[1,2,5],[3,6],[4]] => 01101
[2,6,3,4,1,5] => [[1,2,4,6],[3],[5]] => 01010
[2,6,3,4,5,1] => [[1,2,4,5],[3],[6]] => 01001
[2,6,3,5,1,4] => [[1,2,4],[3,6],[5]] => 01010
[2,6,3,5,4,1] => [[1,2,4],[3],[5],[6]] => 01011
[2,6,4,1,3,5] => [[1,2,6],[3,5],[4]] => 01100
[2,6,4,1,5,3] => [[1,2,5],[3,6],[4]] => 01101
[2,6,4,3,1,5] => [[1,2,6],[3],[4],[5]] => 01110
[2,6,4,3,5,1] => [[1,2,5],[3],[4],[6]] => 01101
[2,6,4,5,1,3] => [[1,2,4],[3,6],[5]] => 01010
[2,6,4,5,3,1] => [[1,2,4],[3],[5],[6]] => 01011
[2,6,5,1,3,4] => [[1,2,6],[3,5],[4]] => 01100
[2,6,5,1,4,3] => [[1,2],[3,5],[4],[6]] => 01101
[2,6,5,3,1,4] => [[1,2,6],[3],[4],[5]] => 01110
[2,6,5,3,4,1] => [[1,2,5],[3],[4],[6]] => 01101
[2,6,5,4,1,3] => [[1,2],[3,6],[4],[5]] => 01110
[2,6,5,4,3,1] => [[1,2],[3],[4],[5],[6]] => 01111
[3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => 10000
[3,1,2,4,6,5] => [[1,3,4,5],[2,6]] => 10001
[3,1,2,5,4,6] => [[1,3,4,6],[2,5]] => 10010
[3,1,2,5,6,4] => [[1,3,4,5],[2,6]] => 10001
[3,1,2,6,4,5] => [[1,3,4,6],[2,5]] => 10010
[3,1,2,6,5,4] => [[1,3,4],[2,5],[6]] => 10011
[3,1,4,2,5,6] => [[1,3,5,6],[2,4]] => 10100
[3,1,4,2,6,5] => [[1,3,5],[2,4,6]] => 10101
[3,1,4,5,2,6] => [[1,3,4,6],[2,5]] => 10010
[3,1,4,5,6,2] => [[1,3,4,5],[2,6]] => 10001
[3,1,4,6,2,5] => [[1,3,4],[2,5,6]] => 10010
[3,1,4,6,5,2] => [[1,3,4],[2,5],[6]] => 10011
[3,1,5,2,4,6] => [[1,3,5,6],[2,4]] => 10100
[3,1,5,2,6,4] => [[1,3,5],[2,4,6]] => 10101
[3,1,5,4,2,6] => [[1,3,6],[2,4],[5]] => 10110
[3,1,5,4,6,2] => [[1,3,5],[2,4],[6]] => 10101
[3,1,5,6,2,4] => [[1,3,4],[2,5,6]] => 10010
[3,1,5,6,4,2] => [[1,3,4],[2,5],[6]] => 10011
[3,1,6,2,4,5] => [[1,3,5,6],[2,4]] => 10100
[3,1,6,2,5,4] => [[1,3,5],[2,4],[6]] => 10101
[3,1,6,4,2,5] => [[1,3,6],[2,4],[5]] => 10110
[3,1,6,4,5,2] => [[1,3,5],[2,4],[6]] => 10101
[3,1,6,5,2,4] => [[1,3,6],[2,4],[5]] => 10110
[3,1,6,5,4,2] => [[1,3],[2,4],[5],[6]] => 10111
[3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => 11000
[3,2,1,4,6,5] => [[1,4,5],[2,6],[3]] => 11001
[3,2,1,5,4,6] => [[1,4,6],[2,5],[3]] => 11010
[3,2,1,5,6,4] => [[1,4,5],[2,6],[3]] => 11001
[3,2,1,6,4,5] => [[1,4,6],[2,5],[3]] => 11010
[3,2,1,6,5,4] => [[1,4],[2,5],[3,6]] => 11011
[3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => 10100
[3,2,4,1,6,5] => [[1,3,5],[2,6],[4]] => 10101
[3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => 10010
[3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => 10001
[3,2,4,6,1,5] => [[1,3,4],[2,6],[5]] => 10010
[3,2,4,6,5,1] => [[1,3,4],[2,5],[6]] => 10011
[3,2,5,1,4,6] => [[1,3,6],[2,5],[4]] => 10100
[3,2,5,1,6,4] => [[1,3,5],[2,6],[4]] => 10101
[3,2,5,4,1,6] => [[1,3,6],[2,4],[5]] => 10110
[3,2,5,4,6,1] => [[1,3,5],[2,4],[6]] => 10101
[3,2,5,6,1,4] => [[1,3,4],[2,6],[5]] => 10010
[3,2,5,6,4,1] => [[1,3,4],[2,5],[6]] => 10011
[3,2,6,1,4,5] => [[1,3,6],[2,5],[4]] => 10100
[3,2,6,1,5,4] => [[1,3],[2,5],[4,6]] => 10101
[3,2,6,4,1,5] => [[1,3,6],[2,4],[5]] => 10110
[3,2,6,4,5,1] => [[1,3,5],[2,4],[6]] => 10101
[3,2,6,5,1,4] => [[1,3],[2,4],[5,6]] => 10110
[3,2,6,5,4,1] => [[1,3],[2,4],[5],[6]] => 10111
[3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => 01000
[3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => 01001
[3,4,1,5,2,6] => [[1,2,4,6],[3,5]] => 01010
[3,4,1,5,6,2] => [[1,2,4,5],[3,6]] => 01001
[3,4,1,6,2,5] => [[1,2,4],[3,5,6]] => 01010
[3,4,1,6,5,2] => [[1,2,4],[3,5],[6]] => 01011
[3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => 01100
[3,4,2,1,6,5] => [[1,2,5],[3,6],[4]] => 01101
[3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => 01010
[3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => 01001
[3,4,2,6,1,5] => [[1,2,4],[3,6],[5]] => 01010
[3,4,2,6,5,1] => [[1,2,4],[3,5],[6]] => 01011
[3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => 00100
[3,4,5,1,6,2] => [[1,2,3,5],[4,6]] => 00101
[3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => 00110
[3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => 00101
[3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => 00010
[3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => 00011
[3,4,6,1,2,5] => [[1,2,3],[4,5,6]] => 00100
[3,4,6,1,5,2] => [[1,2,3],[4,5],[6]] => 00101
[3,4,6,2,1,5] => [[1,2,3],[4,6],[5]] => 00110
[3,4,6,2,5,1] => [[1,2,3],[4,5],[6]] => 00101
[3,4,6,5,1,2] => [[1,2,3],[4,6],[5]] => 00110
[3,4,6,5,2,1] => [[1,2,3],[4],[5],[6]] => 00111
[3,5,1,2,4,6] => [[1,2,5,6],[3,4]] => 01000
[3,5,1,2,6,4] => [[1,2,5],[3,4,6]] => 01001
[3,5,1,4,2,6] => [[1,2,6],[3,4],[5]] => 01010
[3,5,1,4,6,2] => [[1,2,5],[3,4],[6]] => 01001
[3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => 01010
[3,5,1,6,4,2] => [[1,2,4],[3,5],[6]] => 01011
[3,5,2,1,4,6] => [[1,2,6],[3,5],[4]] => 01100
[3,5,2,1,6,4] => [[1,2,5],[3,6],[4]] => 01101
[3,5,2,4,1,6] => [[1,2,6],[3,4],[5]] => 01010
[3,5,2,4,6,1] => [[1,2,5],[3,4],[6]] => 01001
[3,5,2,6,1,4] => [[1,2,4],[3,6],[5]] => 01010
[3,5,2,6,4,1] => [[1,2,4],[3,5],[6]] => 01011
[3,5,4,1,2,6] => [[1,2,6],[3,5],[4]] => 01100
[3,5,4,1,6,2] => [[1,2,5],[3,6],[4]] => 01101
[3,5,4,2,1,6] => [[1,2,6],[3],[4],[5]] => 01110
[3,5,4,2,6,1] => [[1,2,5],[3],[4],[6]] => 01101
[3,5,4,6,1,2] => [[1,2,4],[3,6],[5]] => 01010
[3,5,4,6,2,1] => [[1,2,4],[3],[5],[6]] => 01011
[3,5,6,1,2,4] => [[1,2,3],[4,5,6]] => 00100
[3,5,6,1,4,2] => [[1,2,3],[4,5],[6]] => 00101
[3,5,6,2,1,4] => [[1,2,3],[4,6],[5]] => 00110
[3,5,6,2,4,1] => [[1,2,3],[4,5],[6]] => 00101
[3,5,6,4,1,2] => [[1,2,3],[4,6],[5]] => 00110
[3,5,6,4,2,1] => [[1,2,3],[4],[5],[6]] => 00111
[3,6,1,2,4,5] => [[1,2,5,6],[3,4]] => 01000
[3,6,1,2,5,4] => [[1,2,5],[3,4],[6]] => 01001
[3,6,1,4,2,5] => [[1,2,6],[3,4],[5]] => 01010
[3,6,1,4,5,2] => [[1,2,5],[3,4],[6]] => 01001
[3,6,1,5,2,4] => [[1,2,6],[3,4],[5]] => 01010
[3,6,1,5,4,2] => [[1,2],[3,4],[5],[6]] => 01011
[3,6,2,1,4,5] => [[1,2,6],[3,5],[4]] => 01100
[3,6,2,1,5,4] => [[1,2],[3,5],[4,6]] => 01101
[3,6,2,4,1,5] => [[1,2,6],[3,4],[5]] => 01010
[3,6,2,4,5,1] => [[1,2,5],[3,4],[6]] => 01001
[3,6,2,5,1,4] => [[1,2],[3,4],[5,6]] => 01010
[3,6,2,5,4,1] => [[1,2],[3,4],[5],[6]] => 01011
[3,6,4,1,2,5] => [[1,2,6],[3,5],[4]] => 01100
[3,6,4,1,5,2] => [[1,2,5],[3,6],[4]] => 01101
[3,6,4,2,1,5] => [[1,2,6],[3],[4],[5]] => 01110
[3,6,4,2,5,1] => [[1,2,5],[3],[4],[6]] => 01101
[3,6,4,5,1,2] => [[1,2,4],[3,6],[5]] => 01010
[3,6,4,5,2,1] => [[1,2,4],[3],[5],[6]] => 01011
[3,6,5,1,2,4] => [[1,2,6],[3,5],[4]] => 01100
[3,6,5,1,4,2] => [[1,2],[3,5],[4],[6]] => 01101
[3,6,5,2,1,4] => [[1,2],[3,6],[4],[5]] => 01110
[3,6,5,2,4,1] => [[1,2],[3,5],[4],[6]] => 01101
[3,6,5,4,1,2] => [[1,2],[3,6],[4],[5]] => 01110
[3,6,5,4,2,1] => [[1,2],[3],[4],[5],[6]] => 01111
[4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => 10000
[4,1,2,3,6,5] => [[1,3,4,5],[2,6]] => 10001
[4,1,2,5,3,6] => [[1,3,4,6],[2,5]] => 10010
[4,1,2,5,6,3] => [[1,3,4,5],[2,6]] => 10001
[4,1,2,6,3,5] => [[1,3,4,6],[2,5]] => 10010
[4,1,2,6,5,3] => [[1,3,4],[2,5],[6]] => 10011
[4,1,3,2,5,6] => [[1,3,5,6],[2],[4]] => 10100
[4,1,3,2,6,5] => [[1,3,5],[2,6],[4]] => 10101
[4,1,3,5,2,6] => [[1,3,4,6],[2],[5]] => 10010
[4,1,3,5,6,2] => [[1,3,4,5],[2],[6]] => 10001
[4,1,3,6,2,5] => [[1,3,4],[2,6],[5]] => 10010
[4,1,3,6,5,2] => [[1,3,4],[2,5],[6]] => 10011
[4,1,5,2,3,6] => [[1,3,5,6],[2,4]] => 10100
[4,1,5,2,6,3] => [[1,3,5],[2,4,6]] => 10101
[4,1,5,3,2,6] => [[1,3,6],[2,4],[5]] => 10110
[4,1,5,3,6,2] => [[1,3,5],[2,4],[6]] => 10101
[4,1,5,6,2,3] => [[1,3,4],[2,5,6]] => 10010
[4,1,5,6,3,2] => [[1,3,4],[2,5],[6]] => 10011
[4,1,6,2,3,5] => [[1,3,5,6],[2,4]] => 10100
[4,1,6,2,5,3] => [[1,3,5],[2,4],[6]] => 10101
[4,1,6,3,2,5] => [[1,3,6],[2,4],[5]] => 10110
[4,1,6,3,5,2] => [[1,3,5],[2,4],[6]] => 10101
[4,1,6,5,2,3] => [[1,3,6],[2,4],[5]] => 10110
[4,1,6,5,3,2] => [[1,3],[2,4],[5],[6]] => 10111
[4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => 11000
[4,2,1,3,6,5] => [[1,4,5],[2,6],[3]] => 11001
[4,2,1,5,3,6] => [[1,4,6],[2,5],[3]] => 11010
[4,2,1,5,6,3] => [[1,4,5],[2,6],[3]] => 11001
[4,2,1,6,3,5] => [[1,4,6],[2,5],[3]] => 11010
[4,2,1,6,5,3] => [[1,4],[2,5],[3,6]] => 11011
[4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => 10100
[4,2,3,1,6,5] => [[1,3,5],[2,6],[4]] => 10101
[4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => 10010
[4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => 10001
[4,2,3,6,1,5] => [[1,3,4],[2,6],[5]] => 10010
[4,2,3,6,5,1] => [[1,3,4],[2,5],[6]] => 10011
[4,2,5,1,3,6] => [[1,3,6],[2,5],[4]] => 10100
[4,2,5,1,6,3] => [[1,3,5],[2,6],[4]] => 10101
[4,2,5,3,1,6] => [[1,3,6],[2,4],[5]] => 10110
[4,2,5,3,6,1] => [[1,3,5],[2,4],[6]] => 10101
[4,2,5,6,1,3] => [[1,3,4],[2,6],[5]] => 10010
[4,2,5,6,3,1] => [[1,3,4],[2,5],[6]] => 10011
[4,2,6,1,3,5] => [[1,3,6],[2,5],[4]] => 10100
[4,2,6,1,5,3] => [[1,3],[2,5],[4,6]] => 10101
[4,2,6,3,1,5] => [[1,3,6],[2,4],[5]] => 10110
[4,2,6,3,5,1] => [[1,3,5],[2,4],[6]] => 10101
[4,2,6,5,1,3] => [[1,3],[2,4],[5,6]] => 10110
[4,2,6,5,3,1] => [[1,3],[2,4],[5],[6]] => 10111
[4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => 11000
[4,3,1,2,6,5] => [[1,4,5],[2,6],[3]] => 11001
[4,3,1,5,2,6] => [[1,4,6],[2,5],[3]] => 11010
[4,3,1,5,6,2] => [[1,4,5],[2,6],[3]] => 11001
[4,3,1,6,2,5] => [[1,4,6],[2,5],[3]] => 11010
[4,3,1,6,5,2] => [[1,4],[2,5],[3,6]] => 11011
[4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => 11100
[4,3,2,1,6,5] => [[1,5],[2,6],[3],[4]] => 11101
[4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => 11010
[4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => 11001
[4,3,2,6,1,5] => [[1,4],[2,6],[3],[5]] => 11010
[4,3,2,6,5,1] => [[1,4],[2,5],[3],[6]] => 11011
[4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => 10100
[4,3,5,1,6,2] => [[1,3,5],[2,6],[4]] => 10101
[4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => 10110
[4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => 10101
[4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => 10010
[4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => 10011
[4,3,6,1,2,5] => [[1,3,6],[2,5],[4]] => 10100
[4,3,6,1,5,2] => [[1,3],[2,5],[4,6]] => 10101
[4,3,6,2,1,5] => [[1,3],[2,6],[4],[5]] => 10110
[4,3,6,2,5,1] => [[1,3],[2,5],[4],[6]] => 10101
[4,3,6,5,1,2] => [[1,3],[2,4],[5,6]] => 10110
[4,3,6,5,2,1] => [[1,3],[2,4],[5],[6]] => 10111
[4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => 01000
[4,5,1,2,6,3] => [[1,2,5],[3,4,6]] => 01001
[4,5,1,3,2,6] => [[1,2,6],[3,4],[5]] => 01010
[4,5,1,3,6,2] => [[1,2,5],[3,4],[6]] => 01001
[4,5,1,6,2,3] => [[1,2,4],[3,5,6]] => 01010
[4,5,1,6,3,2] => [[1,2,4],[3,5],[6]] => 01011
[4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => 01100
[4,5,2,1,6,3] => [[1,2,5],[3,6],[4]] => 01101
[4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => 01010
[4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => 01001
[4,5,2,6,1,3] => [[1,2,4],[3,6],[5]] => 01010
[4,5,2,6,3,1] => [[1,2,4],[3,5],[6]] => 01011
[4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => 01100
[4,5,3,1,6,2] => [[1,2,5],[3,6],[4]] => 01101
[4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => 01110
[4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => 01101
[4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => 01010
[4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => 01011
[4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 00100
[4,5,6,1,3,2] => [[1,2,3],[4,5],[6]] => 00101
[4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => 00110
[4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => 00101
[4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => 00110
[4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => 00111
[4,6,1,2,3,5] => [[1,2,5,6],[3,4]] => 01000
[4,6,1,2,5,3] => [[1,2,5],[3,4],[6]] => 01001
[4,6,1,3,2,5] => [[1,2,6],[3,4],[5]] => 01010
[4,6,1,3,5,2] => [[1,2,5],[3,4],[6]] => 01001
[4,6,1,5,2,3] => [[1,2,6],[3,4],[5]] => 01010
[4,6,1,5,3,2] => [[1,2],[3,4],[5],[6]] => 01011
[4,6,2,1,3,5] => [[1,2,6],[3,5],[4]] => 01100
[4,6,2,1,5,3] => [[1,2],[3,5],[4,6]] => 01101
[4,6,2,3,1,5] => [[1,2,6],[3,4],[5]] => 01010
[4,6,2,3,5,1] => [[1,2,5],[3,4],[6]] => 01001
[4,6,2,5,1,3] => [[1,2],[3,4],[5,6]] => 01010
[4,6,2,5,3,1] => [[1,2],[3,4],[5],[6]] => 01011
[4,6,3,1,2,5] => [[1,2,6],[3,5],[4]] => 01100
[4,6,3,1,5,2] => [[1,2],[3,5],[4,6]] => 01101
[4,6,3,2,1,5] => [[1,2],[3,6],[4],[5]] => 01110
[4,6,3,2,5,1] => [[1,2],[3,5],[4],[6]] => 01101
[4,6,3,5,1,2] => [[1,2],[3,4],[5,6]] => 01010
[4,6,3,5,2,1] => [[1,2],[3,4],[5],[6]] => 01011
[4,6,5,1,2,3] => [[1,2,6],[3,5],[4]] => 01100
[4,6,5,1,3,2] => [[1,2],[3,5],[4],[6]] => 01101
[4,6,5,2,1,3] => [[1,2],[3,6],[4],[5]] => 01110
[4,6,5,2,3,1] => [[1,2],[3,5],[4],[6]] => 01101
[4,6,5,3,1,2] => [[1,2],[3,6],[4],[5]] => 01110
[4,6,5,3,2,1] => [[1,2],[3],[4],[5],[6]] => 01111
[5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => 10000
[5,1,2,3,6,4] => [[1,3,4,5],[2,6]] => 10001
[5,1,2,4,3,6] => [[1,3,4,6],[2],[5]] => 10010
[5,1,2,4,6,3] => [[1,3,4,5],[2],[6]] => 10001
[5,1,2,6,3,4] => [[1,3,4,6],[2,5]] => 10010
[5,1,2,6,4,3] => [[1,3,4],[2,5],[6]] => 10011
[5,1,3,2,4,6] => [[1,3,5,6],[2],[4]] => 10100
[5,1,3,2,6,4] => [[1,3,5],[2,6],[4]] => 10101
[5,1,3,4,2,6] => [[1,3,4,6],[2],[5]] => 10010
[5,1,3,4,6,2] => [[1,3,4,5],[2],[6]] => 10001
[5,1,3,6,2,4] => [[1,3,4],[2,6],[5]] => 10010
[5,1,3,6,4,2] => [[1,3,4],[2,5],[6]] => 10011
[5,1,4,2,3,6] => [[1,3,5,6],[2],[4]] => 10100
[5,1,4,2,6,3] => [[1,3,5],[2,6],[4]] => 10101
[5,1,4,3,2,6] => [[1,3,6],[2],[4],[5]] => 10110
[5,1,4,3,6,2] => [[1,3,5],[2],[4],[6]] => 10101
[5,1,4,6,2,3] => [[1,3,4],[2,6],[5]] => 10010
[5,1,4,6,3,2] => [[1,3,4],[2],[5],[6]] => 10011
[5,1,6,2,3,4] => [[1,3,5,6],[2,4]] => 10100
[5,1,6,2,4,3] => [[1,3,5],[2,4],[6]] => 10101
[5,1,6,3,2,4] => [[1,3,6],[2,4],[5]] => 10110
[5,1,6,3,4,2] => [[1,3,5],[2,4],[6]] => 10101
[5,1,6,4,2,3] => [[1,3,6],[2,4],[5]] => 10110
[5,1,6,4,3,2] => [[1,3],[2,4],[5],[6]] => 10111
[5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => 11000
[5,2,1,3,6,4] => [[1,4,5],[2,6],[3]] => 11001
[5,2,1,4,3,6] => [[1,4,6],[2,5],[3]] => 11010
[5,2,1,4,6,3] => [[1,4,5],[2,6],[3]] => 11001
[5,2,1,6,3,4] => [[1,4,6],[2,5],[3]] => 11010
[5,2,1,6,4,3] => [[1,4],[2,5],[3,6]] => 11011
[5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => 10100
[5,2,3,1,6,4] => [[1,3,5],[2,6],[4]] => 10101
[5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => 10010
[5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => 10001
[5,2,3,6,1,4] => [[1,3,4],[2,6],[5]] => 10010
[5,2,3,6,4,1] => [[1,3,4],[2,5],[6]] => 10011
[5,2,4,1,3,6] => [[1,3,6],[2,5],[4]] => 10100
[5,2,4,1,6,3] => [[1,3,5],[2,6],[4]] => 10101
[5,2,4,3,1,6] => [[1,3,6],[2],[4],[5]] => 10110
[5,2,4,3,6,1] => [[1,3,5],[2],[4],[6]] => 10101
[5,2,4,6,1,3] => [[1,3,4],[2,6],[5]] => 10010
[5,2,4,6,3,1] => [[1,3,4],[2],[5],[6]] => 10011
[5,2,6,1,3,4] => [[1,3,6],[2,5],[4]] => 10100
[5,2,6,1,4,3] => [[1,3],[2,5],[4,6]] => 10101
[5,2,6,3,1,4] => [[1,3,6],[2,4],[5]] => 10110
[5,2,6,3,4,1] => [[1,3,5],[2,4],[6]] => 10101
[5,2,6,4,1,3] => [[1,3],[2,4],[5,6]] => 10110
[5,2,6,4,3,1] => [[1,3],[2,4],[5],[6]] => 10111
[5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => 11000
[5,3,1,2,6,4] => [[1,4,5],[2,6],[3]] => 11001
[5,3,1,4,2,6] => [[1,4,6],[2,5],[3]] => 11010
[5,3,1,4,6,2] => [[1,4,5],[2,6],[3]] => 11001
[5,3,1,6,2,4] => [[1,4,6],[2,5],[3]] => 11010
[5,3,1,6,4,2] => [[1,4],[2,5],[3,6]] => 11011
[5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => 11100
[5,3,2,1,6,4] => [[1,5],[2,6],[3],[4]] => 11101
[5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => 11010
[5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => 11001
[5,3,2,6,1,4] => [[1,4],[2,6],[3],[5]] => 11010
[5,3,2,6,4,1] => [[1,4],[2,5],[3],[6]] => 11011
[5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => 10100
[5,3,4,1,6,2] => [[1,3,5],[2,6],[4]] => 10101
[5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => 10110
[5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => 10101
[5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => 10010
[5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => 10011
[5,3,6,1,2,4] => [[1,3,6],[2,5],[4]] => 10100
[5,3,6,1,4,2] => [[1,3],[2,5],[4,6]] => 10101
[5,3,6,2,1,4] => [[1,3],[2,6],[4],[5]] => 10110
[5,3,6,2,4,1] => [[1,3],[2,5],[4],[6]] => 10101
[5,3,6,4,1,2] => [[1,3],[2,4],[5,6]] => 10110
[5,3,6,4,2,1] => [[1,3],[2,4],[5],[6]] => 10111
[5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => 11000
[5,4,1,2,6,3] => [[1,4,5],[2,6],[3]] => 11001
[5,4,1,3,2,6] => [[1,4,6],[2],[3],[5]] => 11010
[5,4,1,3,6,2] => [[1,4,5],[2],[3],[6]] => 11001
[5,4,1,6,2,3] => [[1,4,6],[2,5],[3]] => 11010
[5,4,1,6,3,2] => [[1,4],[2,5],[3],[6]] => 11011
[5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => 11100
[5,4,2,1,6,3] => [[1,5],[2,6],[3],[4]] => 11101
[5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => 11010
[5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => 11001
[5,4,2,6,1,3] => [[1,4],[2,6],[3],[5]] => 11010
[5,4,2,6,3,1] => [[1,4],[2,5],[3],[6]] => 11011
[5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => 11100
[5,4,3,1,6,2] => [[1,5],[2,6],[3],[4]] => 11101
[5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => 11110
[5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => 11101
[5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => 11010
[5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => 11011
[5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => 10100
[5,4,6,1,3,2] => [[1,3],[2,5],[4],[6]] => 10101
[5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => 10110
[5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => 10101
[5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => 10110
[5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => 10111
[5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => 01000
[5,6,1,2,4,3] => [[1,2,5],[3,4],[6]] => 01001
[5,6,1,3,2,4] => [[1,2,6],[3,4],[5]] => 01010
[5,6,1,3,4,2] => [[1,2,5],[3,4],[6]] => 01001
[5,6,1,4,2,3] => [[1,2,6],[3,4],[5]] => 01010
[5,6,1,4,3,2] => [[1,2],[3,4],[5],[6]] => 01011
[5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => 01100
[5,6,2,1,4,3] => [[1,2],[3,5],[4,6]] => 01101
[5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => 01010
[5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => 01001
[5,6,2,4,1,3] => [[1,2],[3,4],[5,6]] => 01010
[5,6,2,4,3,1] => [[1,2],[3,4],[5],[6]] => 01011
[5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => 01100
[5,6,3,1,4,2] => [[1,2],[3,5],[4,6]] => 01101
[5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => 01110
[5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => 01101
[5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => 01010
[5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => 01011
[5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => 01100
[5,6,4,1,3,2] => [[1,2],[3,5],[4],[6]] => 01101
[5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => 01110
[5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => 01101
[5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => 01110
[5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => 01111
[6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => 10000
[6,1,2,3,5,4] => [[1,3,4,5],[2],[6]] => 10001
[6,1,2,4,3,5] => [[1,3,4,6],[2],[5]] => 10010
[6,1,2,4,5,3] => [[1,3,4,5],[2],[6]] => 10001
[6,1,2,5,3,4] => [[1,3,4,6],[2],[5]] => 10010
[6,1,2,5,4,3] => [[1,3,4],[2],[5],[6]] => 10011
[6,1,3,2,4,5] => [[1,3,5,6],[2],[4]] => 10100
[6,1,3,2,5,4] => [[1,3,5],[2,6],[4]] => 10101
[6,1,3,4,2,5] => [[1,3,4,6],[2],[5]] => 10010
[6,1,3,4,5,2] => [[1,3,4,5],[2],[6]] => 10001
[6,1,3,5,2,4] => [[1,3,4],[2,6],[5]] => 10010
[6,1,3,5,4,2] => [[1,3,4],[2],[5],[6]] => 10011
[6,1,4,2,3,5] => [[1,3,5,6],[2],[4]] => 10100
[6,1,4,2,5,3] => [[1,3,5],[2,6],[4]] => 10101
[6,1,4,3,2,5] => [[1,3,6],[2],[4],[5]] => 10110
[6,1,4,3,5,2] => [[1,3,5],[2],[4],[6]] => 10101
[6,1,4,5,2,3] => [[1,3,4],[2,6],[5]] => 10010
[6,1,4,5,3,2] => [[1,3,4],[2],[5],[6]] => 10011
[6,1,5,2,3,4] => [[1,3,5,6],[2],[4]] => 10100
[6,1,5,2,4,3] => [[1,3,5],[2],[4],[6]] => 10101
[6,1,5,3,2,4] => [[1,3,6],[2],[4],[5]] => 10110
[6,1,5,3,4,2] => [[1,3,5],[2],[4],[6]] => 10101
[6,1,5,4,2,3] => [[1,3,6],[2],[4],[5]] => 10110
[6,1,5,4,3,2] => [[1,3],[2],[4],[5],[6]] => 10111
[6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => 11000
[6,2,1,3,5,4] => [[1,4,5],[2,6],[3]] => 11001
[6,2,1,4,3,5] => [[1,4,6],[2,5],[3]] => 11010
[6,2,1,4,5,3] => [[1,4,5],[2,6],[3]] => 11001
[6,2,1,5,3,4] => [[1,4,6],[2,5],[3]] => 11010
[6,2,1,5,4,3] => [[1,4],[2,5],[3],[6]] => 11011
[6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => 10100
[6,2,3,1,5,4] => [[1,3,5],[2,6],[4]] => 10101
[6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => 10010
[6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => 10001
[6,2,3,5,1,4] => [[1,3,4],[2,6],[5]] => 10010
[6,2,3,5,4,1] => [[1,3,4],[2],[5],[6]] => 10011
[6,2,4,1,3,5] => [[1,3,6],[2,5],[4]] => 10100
[6,2,4,1,5,3] => [[1,3,5],[2,6],[4]] => 10101
[6,2,4,3,1,5] => [[1,3,6],[2],[4],[5]] => 10110
[6,2,4,3,5,1] => [[1,3,5],[2],[4],[6]] => 10101
[6,2,4,5,1,3] => [[1,3,4],[2,6],[5]] => 10010
[6,2,4,5,3,1] => [[1,3,4],[2],[5],[6]] => 10011
[6,2,5,1,3,4] => [[1,3,6],[2,5],[4]] => 10100
[6,2,5,1,4,3] => [[1,3],[2,5],[4],[6]] => 10101
[6,2,5,3,1,4] => [[1,3,6],[2],[4],[5]] => 10110
[6,2,5,3,4,1] => [[1,3,5],[2],[4],[6]] => 10101
[6,2,5,4,1,3] => [[1,3],[2,6],[4],[5]] => 10110
[6,2,5,4,3,1] => [[1,3],[2],[4],[5],[6]] => 10111
[6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => 11000
[6,3,1,2,5,4] => [[1,4,5],[2,6],[3]] => 11001
[6,3,1,4,2,5] => [[1,4,6],[2,5],[3]] => 11010
[6,3,1,4,5,2] => [[1,4,5],[2,6],[3]] => 11001
[6,3,1,5,2,4] => [[1,4,6],[2,5],[3]] => 11010
[6,3,1,5,4,2] => [[1,4],[2,5],[3],[6]] => 11011
[6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => 11100
[6,3,2,1,5,4] => [[1,5],[2,6],[3],[4]] => 11101
[6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => 11010
[6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => 11001
[6,3,2,5,1,4] => [[1,4],[2,6],[3],[5]] => 11010
[6,3,2,5,4,1] => [[1,4],[2,5],[3],[6]] => 11011
[6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => 10100
[6,3,4,1,5,2] => [[1,3,5],[2,6],[4]] => 10101
[6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => 10110
[6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => 10101
[6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => 10010
[6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => 10011
[6,3,5,1,2,4] => [[1,3,6],[2,5],[4]] => 10100
[6,3,5,1,4,2] => [[1,3],[2,5],[4],[6]] => 10101
[6,3,5,2,1,4] => [[1,3],[2,6],[4],[5]] => 10110
[6,3,5,2,4,1] => [[1,3],[2,5],[4],[6]] => 10101
[6,3,5,4,1,2] => [[1,3],[2,6],[4],[5]] => 10110
[6,3,5,4,2,1] => [[1,3],[2],[4],[5],[6]] => 10111
[6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => 11000
[6,4,1,2,5,3] => [[1,4,5],[2,6],[3]] => 11001
[6,4,1,3,2,5] => [[1,4,6],[2],[3],[5]] => 11010
[6,4,1,3,5,2] => [[1,4,5],[2],[3],[6]] => 11001
[6,4,1,5,2,3] => [[1,4,6],[2,5],[3]] => 11010
[6,4,1,5,3,2] => [[1,4],[2,5],[3],[6]] => 11011
[6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => 11100
[6,4,2,1,5,3] => [[1,5],[2,6],[3],[4]] => 11101
[6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => 11010
[6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => 11001
[6,4,2,5,1,3] => [[1,4],[2,6],[3],[5]] => 11010
[6,4,2,5,3,1] => [[1,4],[2,5],[3],[6]] => 11011
[6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => 11100
[6,4,3,1,5,2] => [[1,5],[2,6],[3],[4]] => 11101
[6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => 11110
[6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => 11101
[6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => 11010
[6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => 11011
[6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => 10100
[6,4,5,1,3,2] => [[1,3],[2,5],[4],[6]] => 10101
[6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => 10110
[6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => 10101
[6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => 10110
[6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => 10111
[6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => 11000
[6,5,1,2,4,3] => [[1,4,5],[2],[3],[6]] => 11001
[6,5,1,3,2,4] => [[1,4,6],[2],[3],[5]] => 11010
[6,5,1,3,4,2] => [[1,4,5],[2],[3],[6]] => 11001
[6,5,1,4,2,3] => [[1,4,6],[2],[3],[5]] => 11010
[6,5,1,4,3,2] => [[1,4],[2],[3],[5],[6]] => 11011
[6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => 11100
[6,5,2,1,4,3] => [[1,5],[2,6],[3],[4]] => 11101
[6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => 11010
[6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => 11001
[6,5,2,4,1,3] => [[1,4],[2,6],[3],[5]] => 11010
[6,5,2,4,3,1] => [[1,4],[2],[3],[5],[6]] => 11011
[6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => 11100
[6,5,3,1,4,2] => [[1,5],[2,6],[3],[4]] => 11101
[6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => 11110
[6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => 11101
[6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => 11010
[6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => 11011
[6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => 11100
[6,5,4,1,3,2] => [[1,5],[2],[3],[4],[6]] => 11101
[6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => 11110
[6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => 11101
[6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => 11110
[6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => 11111
[1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => 000000
[1,2,3,4,5,7,6] => [[1,2,3,4,5,6],[7]] => 000001
[1,2,3,4,6,5,7] => [[1,2,3,4,5,7],[6]] => 000010
[1,2,3,4,6,7,5] => [[1,2,3,4,5,6],[7]] => 000001
[1,2,3,4,7,5,6] => [[1,2,3,4,5,7],[6]] => 000010
[1,2,3,4,7,6,5] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,3,5,4,6,7] => [[1,2,3,4,6,7],[5]] => 000100
[1,2,3,5,4,7,6] => [[1,2,3,4,6],[5,7]] => 000101
[1,2,3,5,6,4,7] => [[1,2,3,4,5,7],[6]] => 000010
[1,2,3,5,6,7,4] => [[1,2,3,4,5,6],[7]] => 000001
[1,2,3,5,7,4,6] => [[1,2,3,4,5],[6,7]] => 000010
[1,2,3,5,7,6,4] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,3,6,4,5,7] => [[1,2,3,4,6,7],[5]] => 000100
[1,2,3,6,4,7,5] => [[1,2,3,4,6],[5,7]] => 000101
[1,2,3,6,5,4,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,3,6,5,7,4] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,3,6,7,4,5] => [[1,2,3,4,5],[6,7]] => 000010
[1,2,3,6,7,5,4] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,3,7,4,5,6] => [[1,2,3,4,6,7],[5]] => 000100
[1,2,3,7,4,6,5] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,3,7,5,4,6] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,3,7,5,6,4] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,3,7,6,4,5] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,3,7,6,5,4] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,2,4,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 001000
[1,2,4,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 001001
[1,2,4,3,6,5,7] => [[1,2,3,5,7],[4,6]] => 001010
[1,2,4,3,6,7,5] => [[1,2,3,5,6],[4,7]] => 001001
[1,2,4,3,7,5,6] => [[1,2,3,5,7],[4,6]] => 001010
[1,2,4,3,7,6,5] => [[1,2,3,5],[4,6],[7]] => 001011
[1,2,4,5,3,6,7] => [[1,2,3,4,6,7],[5]] => 000100
[1,2,4,5,3,7,6] => [[1,2,3,4,6],[5,7]] => 000101
[1,2,4,5,6,3,7] => [[1,2,3,4,5,7],[6]] => 000010
[1,2,4,5,6,7,3] => [[1,2,3,4,5,6],[7]] => 000001
[1,2,4,5,7,3,6] => [[1,2,3,4,5],[6,7]] => 000010
[1,2,4,5,7,6,3] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,4,6,3,5,7] => [[1,2,3,4,7],[5,6]] => 000100
[1,2,4,6,3,7,5] => [[1,2,3,4,6],[5,7]] => 000101
[1,2,4,6,5,3,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,4,6,5,7,3] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,4,6,7,3,5] => [[1,2,3,4,5],[6,7]] => 000010
[1,2,4,6,7,5,3] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,4,7,3,5,6] => [[1,2,3,4,7],[5,6]] => 000100
[1,2,4,7,3,6,5] => [[1,2,3,4],[5,6],[7]] => 000101
[1,2,4,7,5,3,6] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,4,7,5,6,3] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,4,7,6,3,5] => [[1,2,3,4],[5,7],[6]] => 000110
[1,2,4,7,6,5,3] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,2,5,3,4,6,7] => [[1,2,3,5,6,7],[4]] => 001000
[1,2,5,3,4,7,6] => [[1,2,3,5,6],[4,7]] => 001001
[1,2,5,3,6,4,7] => [[1,2,3,5,7],[4,6]] => 001010
[1,2,5,3,6,7,4] => [[1,2,3,5,6],[4,7]] => 001001
[1,2,5,3,7,4,6] => [[1,2,3,5,7],[4,6]] => 001010
[1,2,5,3,7,6,4] => [[1,2,3,5],[4,6],[7]] => 001011
[1,2,5,4,3,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,5,4,3,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[1,2,5,4,6,3,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,5,4,6,7,3] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,5,4,7,3,6] => [[1,2,3,5],[4,7],[6]] => 001010
[1,2,5,4,7,6,3] => [[1,2,3,5],[4,6],[7]] => 001011
[1,2,5,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 000100
[1,2,5,6,3,7,4] => [[1,2,3,4,6],[5,7]] => 000101
[1,2,5,6,4,3,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,2,5,6,4,7,3] => [[1,2,3,4,6],[5],[7]] => 000101
[1,2,5,6,7,3,4] => [[1,2,3,4,5],[6,7]] => 000010
[1,2,5,6,7,4,3] => [[1,2,3,4,5],[6],[7]] => 000011
[1,2,5,7,3,4,6] => [[1,2,3,4,7],[5,6]] => 000100
[1,2,5,7,3,6,4] => [[1,2,3,4],[5,6],[7]] => 000101
[1,2,5,7,4,3,6] => [[1,2,3,4],[5,7],[6]] => 000110
[1,2,5,7,4,6,3] => [[1,2,3,4],[5,6],[7]] => 000101
[1,2,5,7,6,3,4] => [[1,2,3,4],[5,7],[6]] => 000110
[1,2,5,7,6,4,3] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,2,6,3,4,5,7] => [[1,2,3,5,6,7],[4]] => 001000
[1,2,6,3,4,7,5] => [[1,2,3,5,6],[4,7]] => 001001
[1,2,6,3,5,4,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,6,3,5,7,4] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,6,3,7,4,5] => [[1,2,3,5,7],[4,6]] => 001010
[1,2,6,3,7,5,4] => [[1,2,3,5],[4,6],[7]] => 001011
[1,2,6,4,3,5,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,6,4,3,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[1,2,6,4,5,3,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,6,4,5,7,3] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,6,4,7,3,5] => [[1,2,3,5],[4,7],[6]] => 001010
[1,2,6,4,7,5,3] => [[1,2,3,5],[4,6],[7]] => 001011
[1,2,6,5,3,4,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,6,5,3,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[1,2,6,5,4,3,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,2,6,5,4,7,3] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,2,6,5,7,3,4] => [[1,2,3,5],[4,7],[6]] => 001010
[1,2,6,5,7,4,3] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,2,6,7,3,4,5] => [[1,2,3,4,7],[5,6]] => 000100
[1,2,6,7,3,5,4] => [[1,2,3,4],[5,6],[7]] => 000101
[1,2,6,7,4,3,5] => [[1,2,3,4],[5,7],[6]] => 000110
[1,2,6,7,4,5,3] => [[1,2,3,4],[5,6],[7]] => 000101
[1,2,6,7,5,3,4] => [[1,2,3,4],[5,7],[6]] => 000110
[1,2,6,7,5,4,3] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,2,7,3,4,5,6] => [[1,2,3,5,6,7],[4]] => 001000
[1,2,7,3,4,6,5] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,7,3,5,4,6] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,7,3,5,6,4] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,7,3,6,4,5] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,7,3,6,5,4] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,2,7,4,3,5,6] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,7,4,3,6,5] => [[1,2,3,6],[4,7],[5]] => 001101
[1,2,7,4,5,3,6] => [[1,2,3,5,7],[4],[6]] => 001010
[1,2,7,4,5,6,3] => [[1,2,3,5,6],[4],[7]] => 001001
[1,2,7,4,6,3,5] => [[1,2,3,5],[4,7],[6]] => 001010
[1,2,7,4,6,5,3] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,2,7,5,3,4,6] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,7,5,3,6,4] => [[1,2,3,6],[4,7],[5]] => 001101
[1,2,7,5,4,3,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,2,7,5,4,6,3] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,2,7,5,6,3,4] => [[1,2,3,5],[4,7],[6]] => 001010
[1,2,7,5,6,4,3] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,2,7,6,3,4,5] => [[1,2,3,6,7],[4],[5]] => 001100
[1,2,7,6,3,5,4] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,2,7,6,4,3,5] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,2,7,6,4,5,3] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,2,7,6,5,3,4] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,2,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7]] => 001111
[1,3,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 010000
[1,3,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 010001
[1,3,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 010010
[1,3,2,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 010001
[1,3,2,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 010010
[1,3,2,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 010011
[1,3,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 010100
[1,3,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 010101
[1,3,2,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 010010
[1,3,2,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 010001
[1,3,2,5,7,4,6] => [[1,2,4,5],[3,6,7]] => 010010
[1,3,2,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => 010011
[1,3,2,6,4,5,7] => [[1,2,4,6,7],[3,5]] => 010100
[1,3,2,6,4,7,5] => [[1,2,4,6],[3,5,7]] => 010101
[1,3,2,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 010110
[1,3,2,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 010101
[1,3,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 010010
[1,3,2,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => 010011
[1,3,2,7,4,5,6] => [[1,2,4,6,7],[3,5]] => 010100
[1,3,2,7,4,6,5] => [[1,2,4,6],[3,5],[7]] => 010101
[1,3,2,7,5,4,6] => [[1,2,4,7],[3,5],[6]] => 010110
[1,3,2,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => 010101
[1,3,2,7,6,4,5] => [[1,2,4,7],[3,5],[6]] => 010110
[1,3,2,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,3,4,2,5,6,7] => [[1,2,3,5,6,7],[4]] => 001000
[1,3,4,2,5,7,6] => [[1,2,3,5,6],[4,7]] => 001001
[1,3,4,2,6,5,7] => [[1,2,3,5,7],[4,6]] => 001010
[1,3,4,2,6,7,5] => [[1,2,3,5,6],[4,7]] => 001001
[1,3,4,2,7,5,6] => [[1,2,3,5,7],[4,6]] => 001010
[1,3,4,2,7,6,5] => [[1,2,3,5],[4,6],[7]] => 001011
[1,3,4,5,2,6,7] => [[1,2,3,4,6,7],[5]] => 000100
[1,3,4,5,2,7,6] => [[1,2,3,4,6],[5,7]] => 000101
[1,3,4,5,6,2,7] => [[1,2,3,4,5,7],[6]] => 000010
[1,3,4,5,6,7,2] => [[1,2,3,4,5,6],[7]] => 000001
[1,3,4,5,7,2,6] => [[1,2,3,4,5],[6,7]] => 000010
[1,3,4,5,7,6,2] => [[1,2,3,4,5],[6],[7]] => 000011
[1,3,4,6,2,5,7] => [[1,2,3,4,7],[5,6]] => 000100
[1,3,4,6,2,7,5] => [[1,2,3,4,6],[5,7]] => 000101
[1,3,4,6,5,2,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,3,4,6,5,7,2] => [[1,2,3,4,6],[5],[7]] => 000101
[1,3,4,6,7,2,5] => [[1,2,3,4,5],[6,7]] => 000010
[1,3,4,6,7,5,2] => [[1,2,3,4,5],[6],[7]] => 000011
[1,3,4,7,2,5,6] => [[1,2,3,4,7],[5,6]] => 000100
[1,3,4,7,2,6,5] => [[1,2,3,4],[5,6],[7]] => 000101
[1,3,4,7,5,2,6] => [[1,2,3,4,7],[5],[6]] => 000110
[1,3,4,7,5,6,2] => [[1,2,3,4,6],[5],[7]] => 000101
[1,3,4,7,6,2,5] => [[1,2,3,4],[5,7],[6]] => 000110
[1,3,4,7,6,5,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,3,5,2,4,6,7] => [[1,2,3,6,7],[4,5]] => 001000
[1,3,5,2,4,7,6] => [[1,2,3,6],[4,5,7]] => 001001
[1,3,5,2,6,4,7] => [[1,2,3,5,7],[4,6]] => 001010
[1,3,5,2,6,7,4] => [[1,2,3,5,6],[4,7]] => 001001
[1,3,5,2,7,4,6] => [[1,2,3,5],[4,6,7]] => 001010
[1,3,5,2,7,6,4] => [[1,2,3,5],[4,6],[7]] => 001011
[1,3,5,4,2,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,3,5,4,2,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[1,3,5,4,6,2,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,3,5,4,6,7,2] => [[1,2,3,5,6],[4],[7]] => 001001
[1,3,5,4,7,2,6] => [[1,2,3,5],[4,7],[6]] => 001010
[1,3,5,4,7,6,2] => [[1,2,3,5],[4,6],[7]] => 001011
[1,3,5,6,2,4,7] => [[1,2,3,4,7],[5,6]] => 000100
[1,3,5,6,2,7,4] => [[1,2,3,4,6],[5,7]] => 000101
[1,3,5,6,4,2,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,3,5,6,4,7,2] => [[1,2,3,4,6],[5],[7]] => 000101
[1,3,5,6,7,2,4] => [[1,2,3,4,5],[6,7]] => 000010
[1,3,5,6,7,4,2] => [[1,2,3,4,5],[6],[7]] => 000011
[1,3,5,7,2,4,6] => [[1,2,3,4],[5,6,7]] => 000100
[1,3,5,7,2,6,4] => [[1,2,3,4],[5,6],[7]] => 000101
[1,3,5,7,4,2,6] => [[1,2,3,4],[5,7],[6]] => 000110
[1,3,5,7,4,6,2] => [[1,2,3,4],[5,6],[7]] => 000101
[1,3,5,7,6,2,4] => [[1,2,3,4],[5,7],[6]] => 000110
[1,3,5,7,6,4,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,3,6,2,4,5,7] => [[1,2,3,6,7],[4,5]] => 001000
[1,3,6,2,4,7,5] => [[1,2,3,6],[4,5,7]] => 001001
[1,3,6,2,5,4,7] => [[1,2,3,7],[4,5],[6]] => 001010
[1,3,6,2,5,7,4] => [[1,2,3,6],[4,5],[7]] => 001001
[1,3,6,2,7,4,5] => [[1,2,3,5],[4,6,7]] => 001010
[1,3,6,2,7,5,4] => [[1,2,3,5],[4,6],[7]] => 001011
[1,3,6,4,2,5,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,3,6,4,2,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[1,3,6,4,5,2,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,3,6,4,5,7,2] => [[1,2,3,5,6],[4],[7]] => 001001
[1,3,6,4,7,2,5] => [[1,2,3,5],[4,7],[6]] => 001010
[1,3,6,4,7,5,2] => [[1,2,3,5],[4,6],[7]] => 001011
[1,3,6,5,2,4,7] => [[1,2,3,7],[4,6],[5]] => 001100
[1,3,6,5,2,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[1,3,6,5,4,2,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,3,6,5,4,7,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,3,6,5,7,2,4] => [[1,2,3,5],[4,7],[6]] => 001010
[1,3,6,5,7,4,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,3,6,7,2,4,5] => [[1,2,3,4],[5,6,7]] => 000100
[1,3,6,7,2,5,4] => [[1,2,3,4],[5,6],[7]] => 000101
[1,3,6,7,4,2,5] => [[1,2,3,4],[5,7],[6]] => 000110
[1,3,6,7,4,5,2] => [[1,2,3,4],[5,6],[7]] => 000101
[1,3,6,7,5,2,4] => [[1,2,3,4],[5,7],[6]] => 000110
[1,3,6,7,5,4,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,3,7,2,4,5,6] => [[1,2,3,6,7],[4,5]] => 001000
[1,3,7,2,4,6,5] => [[1,2,3,6],[4,5],[7]] => 001001
[1,3,7,2,5,4,6] => [[1,2,3,7],[4,5],[6]] => 001010
[1,3,7,2,5,6,4] => [[1,2,3,6],[4,5],[7]] => 001001
[1,3,7,2,6,4,5] => [[1,2,3,7],[4,5],[6]] => 001010
[1,3,7,2,6,5,4] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,3,7,4,2,5,6] => [[1,2,3,6,7],[4],[5]] => 001100
[1,3,7,4,2,6,5] => [[1,2,3,6],[4,7],[5]] => 001101
[1,3,7,4,5,2,6] => [[1,2,3,5,7],[4],[6]] => 001010
[1,3,7,4,5,6,2] => [[1,2,3,5,6],[4],[7]] => 001001
[1,3,7,4,6,2,5] => [[1,2,3,5],[4,7],[6]] => 001010
[1,3,7,4,6,5,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,3,7,5,2,4,6] => [[1,2,3,7],[4,6],[5]] => 001100
[1,3,7,5,2,6,4] => [[1,2,3,6],[4,7],[5]] => 001101
[1,3,7,5,4,2,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,3,7,5,4,6,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,3,7,5,6,2,4] => [[1,2,3,5],[4,7],[6]] => 001010
[1,3,7,5,6,4,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,3,7,6,2,4,5] => [[1,2,3,7],[4,6],[5]] => 001100
[1,3,7,6,2,5,4] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,3,7,6,4,2,5] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,3,7,6,4,5,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,3,7,6,5,2,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,3,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7]] => 001111
[1,4,2,3,5,6,7] => [[1,2,4,5,6,7],[3]] => 010000
[1,4,2,3,5,7,6] => [[1,2,4,5,6],[3,7]] => 010001
[1,4,2,3,6,5,7] => [[1,2,4,5,7],[3,6]] => 010010
[1,4,2,3,6,7,5] => [[1,2,4,5,6],[3,7]] => 010001
[1,4,2,3,7,5,6] => [[1,2,4,5,7],[3,6]] => 010010
[1,4,2,3,7,6,5] => [[1,2,4,5],[3,6],[7]] => 010011
[1,4,2,5,3,6,7] => [[1,2,4,6,7],[3,5]] => 010100
[1,4,2,5,3,7,6] => [[1,2,4,6],[3,5,7]] => 010101
[1,4,2,5,6,3,7] => [[1,2,4,5,7],[3,6]] => 010010
[1,4,2,5,6,7,3] => [[1,2,4,5,6],[3,7]] => 010001
[1,4,2,5,7,3,6] => [[1,2,4,5],[3,6,7]] => 010010
[1,4,2,5,7,6,3] => [[1,2,4,5],[3,6],[7]] => 010011
[1,4,2,6,3,5,7] => [[1,2,4,6,7],[3,5]] => 010100
[1,4,2,6,3,7,5] => [[1,2,4,6],[3,5,7]] => 010101
[1,4,2,6,5,3,7] => [[1,2,4,7],[3,5],[6]] => 010110
[1,4,2,6,5,7,3] => [[1,2,4,6],[3,5],[7]] => 010101
[1,4,2,6,7,3,5] => [[1,2,4,5],[3,6,7]] => 010010
[1,4,2,6,7,5,3] => [[1,2,4,5],[3,6],[7]] => 010011
[1,4,2,7,3,5,6] => [[1,2,4,6,7],[3,5]] => 010100
[1,4,2,7,3,6,5] => [[1,2,4,6],[3,5],[7]] => 010101
[1,4,2,7,5,3,6] => [[1,2,4,7],[3,5],[6]] => 010110
[1,4,2,7,5,6,3] => [[1,2,4,6],[3,5],[7]] => 010101
[1,4,2,7,6,3,5] => [[1,2,4,7],[3,5],[6]] => 010110
[1,4,2,7,6,5,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,4,3,2,5,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,4,3,2,5,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[1,4,3,2,6,5,7] => [[1,2,5,7],[3,6],[4]] => 011010
[1,4,3,2,6,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[1,4,3,2,7,5,6] => [[1,2,5,7],[3,6],[4]] => 011010
[1,4,3,2,7,6,5] => [[1,2,5],[3,6],[4,7]] => 011011
[1,4,3,5,2,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,4,3,5,2,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[1,4,3,5,6,2,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,4,3,5,6,7,2] => [[1,2,4,5,6],[3],[7]] => 010001
[1,4,3,5,7,2,6] => [[1,2,4,5],[3,7],[6]] => 010010
[1,4,3,5,7,6,2] => [[1,2,4,5],[3,6],[7]] => 010011
[1,4,3,6,2,5,7] => [[1,2,4,7],[3,6],[5]] => 010100
[1,4,3,6,2,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[1,4,3,6,5,2,7] => [[1,2,4,7],[3,5],[6]] => 010110
[1,4,3,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => 010101
[1,4,3,6,7,2,5] => [[1,2,4,5],[3,7],[6]] => 010010
[1,4,3,6,7,5,2] => [[1,2,4,5],[3,6],[7]] => 010011
[1,4,3,7,2,5,6] => [[1,2,4,7],[3,6],[5]] => 010100
[1,4,3,7,2,6,5] => [[1,2,4],[3,6],[5,7]] => 010101
[1,4,3,7,5,2,6] => [[1,2,4,7],[3,5],[6]] => 010110
[1,4,3,7,5,6,2] => [[1,2,4,6],[3,5],[7]] => 010101
[1,4,3,7,6,2,5] => [[1,2,4],[3,5],[6,7]] => 010110
[1,4,3,7,6,5,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,4,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 001000
[1,4,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => 001001
[1,4,5,2,6,3,7] => [[1,2,3,5,7],[4,6]] => 001010
[1,4,5,2,6,7,3] => [[1,2,3,5,6],[4,7]] => 001001
[1,4,5,2,7,3,6] => [[1,2,3,5],[4,6,7]] => 001010
[1,4,5,2,7,6,3] => [[1,2,3,5],[4,6],[7]] => 001011
[1,4,5,3,2,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[1,4,5,3,2,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[1,4,5,3,6,2,7] => [[1,2,3,5,7],[4],[6]] => 001010
[1,4,5,3,6,7,2] => [[1,2,3,5,6],[4],[7]] => 001001
[1,4,5,3,7,2,6] => [[1,2,3,5],[4,7],[6]] => 001010
[1,4,5,3,7,6,2] => [[1,2,3,5],[4,6],[7]] => 001011
[1,4,5,6,2,3,7] => [[1,2,3,4,7],[5,6]] => 000100
[1,4,5,6,2,7,3] => [[1,2,3,4,6],[5,7]] => 000101
[1,4,5,6,3,2,7] => [[1,2,3,4,7],[5],[6]] => 000110
[1,4,5,6,3,7,2] => [[1,2,3,4,6],[5],[7]] => 000101
[1,4,5,6,7,2,3] => [[1,2,3,4,5],[6,7]] => 000010
[1,4,5,6,7,3,2] => [[1,2,3,4,5],[6],[7]] => 000011
[1,4,5,7,2,3,6] => [[1,2,3,4],[5,6,7]] => 000100
[1,4,5,7,2,6,3] => [[1,2,3,4],[5,6],[7]] => 000101
[1,4,5,7,3,2,6] => [[1,2,3,4],[5,7],[6]] => 000110
[1,4,5,7,3,6,2] => [[1,2,3,4],[5,6],[7]] => 000101
[1,4,5,7,6,2,3] => [[1,2,3,4],[5,7],[6]] => 000110
[1,4,5,7,6,3,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,4,6,2,3,5,7] => [[1,2,3,6,7],[4,5]] => 001000
[1,4,6,2,3,7,5] => [[1,2,3,6],[4,5,7]] => 001001
[1,4,6,2,5,3,7] => [[1,2,3,7],[4,5],[6]] => 001010
[1,4,6,2,5,7,3] => [[1,2,3,6],[4,5],[7]] => 001001
[1,4,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => 001010
[1,4,6,2,7,5,3] => [[1,2,3,5],[4,6],[7]] => 001011
[1,4,6,3,2,5,7] => [[1,2,3,7],[4,6],[5]] => 001100
[1,4,6,3,2,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[1,4,6,3,5,2,7] => [[1,2,3,7],[4,5],[6]] => 001010
[1,4,6,3,5,7,2] => [[1,2,3,6],[4,5],[7]] => 001001
[1,4,6,3,7,2,5] => [[1,2,3,5],[4,7],[6]] => 001010
[1,4,6,3,7,5,2] => [[1,2,3,5],[4,6],[7]] => 001011
[1,4,6,5,2,3,7] => [[1,2,3,7],[4,6],[5]] => 001100
[1,4,6,5,2,7,3] => [[1,2,3,6],[4,7],[5]] => 001101
[1,4,6,5,3,2,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,4,6,5,3,7,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,4,6,5,7,2,3] => [[1,2,3,5],[4,7],[6]] => 001010
[1,4,6,5,7,3,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,4,6,7,2,3,5] => [[1,2,3,4],[5,6,7]] => 000100
[1,4,6,7,2,5,3] => [[1,2,3,4],[5,6],[7]] => 000101
[1,4,6,7,3,2,5] => [[1,2,3,4],[5,7],[6]] => 000110
[1,4,6,7,3,5,2] => [[1,2,3,4],[5,6],[7]] => 000101
[1,4,6,7,5,2,3] => [[1,2,3,4],[5,7],[6]] => 000110
[1,4,6,7,5,3,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,4,7,2,3,5,6] => [[1,2,3,6,7],[4,5]] => 001000
[1,4,7,2,3,6,5] => [[1,2,3,6],[4,5],[7]] => 001001
[1,4,7,2,5,3,6] => [[1,2,3,7],[4,5],[6]] => 001010
[1,4,7,2,5,6,3] => [[1,2,3,6],[4,5],[7]] => 001001
[1,4,7,2,6,3,5] => [[1,2,3,7],[4,5],[6]] => 001010
[1,4,7,2,6,5,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,4,7,3,2,5,6] => [[1,2,3,7],[4,6],[5]] => 001100
[1,4,7,3,2,6,5] => [[1,2,3],[4,6],[5,7]] => 001101
[1,4,7,3,5,2,6] => [[1,2,3,7],[4,5],[6]] => 001010
[1,4,7,3,5,6,2] => [[1,2,3,6],[4,5],[7]] => 001001
[1,4,7,3,6,2,5] => [[1,2,3],[4,5],[6,7]] => 001010
[1,4,7,3,6,5,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,4,7,5,2,3,6] => [[1,2,3,7],[4,6],[5]] => 001100
[1,4,7,5,2,6,3] => [[1,2,3,6],[4,7],[5]] => 001101
[1,4,7,5,3,2,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,4,7,5,3,6,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,4,7,5,6,2,3] => [[1,2,3,5],[4,7],[6]] => 001010
[1,4,7,5,6,3,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,4,7,6,2,3,5] => [[1,2,3,7],[4,6],[5]] => 001100
[1,4,7,6,2,5,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,4,7,6,3,2,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,4,7,6,3,5,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,4,7,6,5,2,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,4,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7]] => 001111
[1,5,2,3,4,6,7] => [[1,2,4,5,6,7],[3]] => 010000
[1,5,2,3,4,7,6] => [[1,2,4,5,6],[3,7]] => 010001
[1,5,2,3,6,4,7] => [[1,2,4,5,7],[3,6]] => 010010
[1,5,2,3,6,7,4] => [[1,2,4,5,6],[3,7]] => 010001
[1,5,2,3,7,4,6] => [[1,2,4,5,7],[3,6]] => 010010
[1,5,2,3,7,6,4] => [[1,2,4,5],[3,6],[7]] => 010011
[1,5,2,4,3,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,5,2,4,3,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[1,5,2,4,6,3,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,5,2,4,6,7,3] => [[1,2,4,5,6],[3],[7]] => 010001
[1,5,2,4,7,3,6] => [[1,2,4,5],[3,7],[6]] => 010010
[1,5,2,4,7,6,3] => [[1,2,4,5],[3,6],[7]] => 010011
[1,5,2,6,3,4,7] => [[1,2,4,6,7],[3,5]] => 010100
[1,5,2,6,3,7,4] => [[1,2,4,6],[3,5,7]] => 010101
[1,5,2,6,4,3,7] => [[1,2,4,7],[3,5],[6]] => 010110
[1,5,2,6,4,7,3] => [[1,2,4,6],[3,5],[7]] => 010101
[1,5,2,6,7,3,4] => [[1,2,4,5],[3,6,7]] => 010010
[1,5,2,6,7,4,3] => [[1,2,4,5],[3,6],[7]] => 010011
[1,5,2,7,3,4,6] => [[1,2,4,6,7],[3,5]] => 010100
[1,5,2,7,3,6,4] => [[1,2,4,6],[3,5],[7]] => 010101
[1,5,2,7,4,3,6] => [[1,2,4,7],[3,5],[6]] => 010110
[1,5,2,7,4,6,3] => [[1,2,4,6],[3,5],[7]] => 010101
[1,5,2,7,6,3,4] => [[1,2,4,7],[3,5],[6]] => 010110
[1,5,2,7,6,4,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,5,3,2,4,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,5,3,2,4,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[1,5,3,2,6,4,7] => [[1,2,5,7],[3,6],[4]] => 011010
[1,5,3,2,6,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[1,5,3,2,7,4,6] => [[1,2,5,7],[3,6],[4]] => 011010
[1,5,3,2,7,6,4] => [[1,2,5],[3,6],[4,7]] => 011011
[1,5,3,4,2,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,5,3,4,2,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[1,5,3,4,6,2,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,5,3,4,6,7,2] => [[1,2,4,5,6],[3],[7]] => 010001
[1,5,3,4,7,2,6] => [[1,2,4,5],[3,7],[6]] => 010010
[1,5,3,4,7,6,2] => [[1,2,4,5],[3,6],[7]] => 010011
[1,5,3,6,2,4,7] => [[1,2,4,7],[3,6],[5]] => 010100
[1,5,3,6,2,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[1,5,3,6,4,2,7] => [[1,2,4,7],[3,5],[6]] => 010110
[1,5,3,6,4,7,2] => [[1,2,4,6],[3,5],[7]] => 010101
[1,5,3,6,7,2,4] => [[1,2,4,5],[3,7],[6]] => 010010
[1,5,3,6,7,4,2] => [[1,2,4,5],[3,6],[7]] => 010011
[1,5,3,7,2,4,6] => [[1,2,4,7],[3,6],[5]] => 010100
[1,5,3,7,2,6,4] => [[1,2,4],[3,6],[5,7]] => 010101
[1,5,3,7,4,2,6] => [[1,2,4,7],[3,5],[6]] => 010110
[1,5,3,7,4,6,2] => [[1,2,4,6],[3,5],[7]] => 010101
[1,5,3,7,6,2,4] => [[1,2,4],[3,5],[6,7]] => 010110
[1,5,3,7,6,4,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,5,4,2,3,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,5,4,2,3,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[1,5,4,2,6,3,7] => [[1,2,5,7],[3,6],[4]] => 011010
[1,5,4,2,6,7,3] => [[1,2,5,6],[3,7],[4]] => 011001
[1,5,4,2,7,3,6] => [[1,2,5,7],[3,6],[4]] => 011010
[1,5,4,2,7,6,3] => [[1,2,5],[3,6],[4,7]] => 011011
[1,5,4,3,2,6,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,5,4,3,2,7,6] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,5,4,3,6,2,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,5,4,3,6,7,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,5,4,3,7,2,6] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,5,4,3,7,6,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,5,4,6,2,3,7] => [[1,2,4,7],[3,6],[5]] => 010100
[1,5,4,6,2,7,3] => [[1,2,4,6],[3,7],[5]] => 010101
[1,5,4,6,3,2,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,5,4,6,3,7,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,5,4,6,7,2,3] => [[1,2,4,5],[3,7],[6]] => 010010
[1,5,4,6,7,3,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,5,4,7,2,3,6] => [[1,2,4,7],[3,6],[5]] => 010100
[1,5,4,7,2,6,3] => [[1,2,4],[3,6],[5,7]] => 010101
[1,5,4,7,3,2,6] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,5,4,7,3,6,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,5,4,7,6,2,3] => [[1,2,4],[3,5],[6,7]] => 010110
[1,5,4,7,6,3,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,5,6,2,3,4,7] => [[1,2,3,6,7],[4,5]] => 001000
[1,5,6,2,3,7,4] => [[1,2,3,6],[4,5,7]] => 001001
[1,5,6,2,4,3,7] => [[1,2,3,7],[4,5],[6]] => 001010
[1,5,6,2,4,7,3] => [[1,2,3,6],[4,5],[7]] => 001001
[1,5,6,2,7,3,4] => [[1,2,3,5],[4,6,7]] => 001010
[1,5,6,2,7,4,3] => [[1,2,3,5],[4,6],[7]] => 001011
[1,5,6,3,2,4,7] => [[1,2,3,7],[4,6],[5]] => 001100
[1,5,6,3,2,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[1,5,6,3,4,2,7] => [[1,2,3,7],[4,5],[6]] => 001010
[1,5,6,3,4,7,2] => [[1,2,3,6],[4,5],[7]] => 001001
[1,5,6,3,7,2,4] => [[1,2,3,5],[4,7],[6]] => 001010
[1,5,6,3,7,4,2] => [[1,2,3,5],[4,6],[7]] => 001011
[1,5,6,4,2,3,7] => [[1,2,3,7],[4,6],[5]] => 001100
[1,5,6,4,2,7,3] => [[1,2,3,6],[4,7],[5]] => 001101
[1,5,6,4,3,2,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[1,5,6,4,3,7,2] => [[1,2,3,6],[4],[5],[7]] => 001101
[1,5,6,4,7,2,3] => [[1,2,3,5],[4,7],[6]] => 001010
[1,5,6,4,7,3,2] => [[1,2,3,5],[4],[6],[7]] => 001011
[1,5,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 000100
[1,5,6,7,2,4,3] => [[1,2,3,4],[5,6],[7]] => 000101
[1,5,6,7,3,2,4] => [[1,2,3,4],[5,7],[6]] => 000110
[1,5,6,7,3,4,2] => [[1,2,3,4],[5,6],[7]] => 000101
[1,5,6,7,4,2,3] => [[1,2,3,4],[5,7],[6]] => 000110
[1,5,6,7,4,3,2] => [[1,2,3,4],[5],[6],[7]] => 000111
[1,5,7,2,3,4,6] => [[1,2,3,6,7],[4,5]] => 001000
[1,5,7,2,3,6,4] => [[1,2,3,6],[4,5],[7]] => 001001
[1,5,7,2,4,3,6] => [[1,2,3,7],[4,5],[6]] => 001010
[1,5,7,2,4,6,3] => [[1,2,3,6],[4,5],[7]] => 001001
[1,5,7,2,6,3,4] => [[1,2,3,7],[4,5],[6]] => 001010
[1,5,7,2,6,4,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,5,7,3,2,4,6] => [[1,2,3,7],[4,6],[5]] => 001100
[1,5,7,3,2,6,4] => [[1,2,3],[4,6],[5,7]] => 001101
[1,5,7,3,4,2,6] => [[1,2,3,7],[4,5],[6]] => 001010
[1,5,7,3,4,6,2] => [[1,2,3,6],[4,5],[7]] => 001001
[1,5,7,3,6,2,4] => [[1,2,3],[4,5],[6,7]] => 001010
[1,5,7,3,6,4,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,5,7,4,2,3,6] => [[1,2,3,7],[4,6],[5]] => 001100
[1,5,7,4,2,6,3] => [[1,2,3],[4,6],[5,7]] => 001101
[1,5,7,4,3,2,6] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,5,7,4,3,6,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,5,7,4,6,2,3] => [[1,2,3],[4,5],[6,7]] => 001010
[1,5,7,4,6,3,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,5,7,6,2,3,4] => [[1,2,3,7],[4,6],[5]] => 001100
[1,5,7,6,2,4,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,5,7,6,3,2,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,5,7,6,3,4,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,5,7,6,4,2,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,5,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => 001111
[1,6,2,3,4,5,7] => [[1,2,4,5,6,7],[3]] => 010000
[1,6,2,3,4,7,5] => [[1,2,4,5,6],[3,7]] => 010001
[1,6,2,3,5,4,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,6,2,3,5,7,4] => [[1,2,4,5,6],[3],[7]] => 010001
[1,6,2,3,7,4,5] => [[1,2,4,5,7],[3,6]] => 010010
[1,6,2,3,7,5,4] => [[1,2,4,5],[3,6],[7]] => 010011
[1,6,2,4,3,5,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,6,2,4,3,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[1,6,2,4,5,3,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,6,2,4,5,7,3] => [[1,2,4,5,6],[3],[7]] => 010001
[1,6,2,4,7,3,5] => [[1,2,4,5],[3,7],[6]] => 010010
[1,6,2,4,7,5,3] => [[1,2,4,5],[3,6],[7]] => 010011
[1,6,2,5,3,4,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,6,2,5,3,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[1,6,2,5,4,3,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,6,2,5,4,7,3] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,6,2,5,7,3,4] => [[1,2,4,5],[3,7],[6]] => 010010
[1,6,2,5,7,4,3] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,6,2,7,3,4,5] => [[1,2,4,6,7],[3,5]] => 010100
[1,6,2,7,3,5,4] => [[1,2,4,6],[3,5],[7]] => 010101
[1,6,2,7,4,3,5] => [[1,2,4,7],[3,5],[6]] => 010110
[1,6,2,7,4,5,3] => [[1,2,4,6],[3,5],[7]] => 010101
[1,6,2,7,5,3,4] => [[1,2,4,7],[3,5],[6]] => 010110
[1,6,2,7,5,4,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,6,3,2,4,5,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,6,3,2,4,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[1,6,3,2,5,4,7] => [[1,2,5,7],[3,6],[4]] => 011010
[1,6,3,2,5,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[1,6,3,2,7,4,5] => [[1,2,5,7],[3,6],[4]] => 011010
[1,6,3,2,7,5,4] => [[1,2,5],[3,6],[4,7]] => 011011
[1,6,3,4,2,5,7] => [[1,2,4,6,7],[3],[5]] => 010100
[1,6,3,4,2,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[1,6,3,4,5,2,7] => [[1,2,4,5,7],[3],[6]] => 010010
[1,6,3,4,5,7,2] => [[1,2,4,5,6],[3],[7]] => 010001
[1,6,3,4,7,2,5] => [[1,2,4,5],[3,7],[6]] => 010010
[1,6,3,4,7,5,2] => [[1,2,4,5],[3,6],[7]] => 010011
[1,6,3,5,2,4,7] => [[1,2,4,7],[3,6],[5]] => 010100
[1,6,3,5,2,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[1,6,3,5,4,2,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,6,3,5,4,7,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,6,3,5,7,2,4] => [[1,2,4,5],[3,7],[6]] => 010010
[1,6,3,5,7,4,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,6,3,7,2,4,5] => [[1,2,4,7],[3,6],[5]] => 010100
[1,6,3,7,2,5,4] => [[1,2,4],[3,6],[5,7]] => 010101
[1,6,3,7,4,2,5] => [[1,2,4,7],[3,5],[6]] => 010110
[1,6,3,7,4,5,2] => [[1,2,4,6],[3,5],[7]] => 010101
[1,6,3,7,5,2,4] => [[1,2,4],[3,5],[6,7]] => 010110
[1,6,3,7,5,4,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,6,4,2,3,5,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,6,4,2,3,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[1,6,4,2,5,3,7] => [[1,2,5,7],[3,6],[4]] => 011010
[1,6,4,2,5,7,3] => [[1,2,5,6],[3,7],[4]] => 011001
[1,6,4,2,7,3,5] => [[1,2,5,7],[3,6],[4]] => 011010
[1,6,4,2,7,5,3] => [[1,2,5],[3,6],[4,7]] => 011011
[1,6,4,3,2,5,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,6,4,3,2,7,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,6,4,3,5,2,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,6,4,3,5,7,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,6,4,3,7,2,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,6,4,3,7,5,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,6,4,5,2,3,7] => [[1,2,4,7],[3,6],[5]] => 010100
[1,6,4,5,2,7,3] => [[1,2,4,6],[3,7],[5]] => 010101
[1,6,4,5,3,2,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,6,4,5,3,7,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,6,4,5,7,2,3] => [[1,2,4,5],[3,7],[6]] => 010010
[1,6,4,5,7,3,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,6,4,7,2,3,5] => [[1,2,4,7],[3,6],[5]] => 010100
[1,6,4,7,2,5,3] => [[1,2,4],[3,6],[5,7]] => 010101
[1,6,4,7,3,2,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,6,4,7,3,5,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,6,4,7,5,2,3] => [[1,2,4],[3,5],[6,7]] => 010110
[1,6,4,7,5,3,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[1,6,5,2,3,4,7] => [[1,2,5,6,7],[3],[4]] => 011000
[1,6,5,2,3,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[1,6,5,2,4,3,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,6,5,2,4,7,3] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,6,5,2,7,3,4] => [[1,2,5,7],[3,6],[4]] => 011010
[1,6,5,2,7,4,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,6,5,3,2,4,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,6,5,3,2,7,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,6,5,3,4,2,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,6,5,3,4,7,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,6,5,3,7,2,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,6,5,3,7,4,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,6,5,4,2,3,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,6,5,4,2,7,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,6,5,4,3,2,7] => [[1,2,7],[3],[4],[5],[6]] => 011110
[1,6,5,4,3,7,2] => [[1,2,6],[3],[4],[5],[7]] => 011101
[1,6,5,4,7,2,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,6,5,4,7,3,2] => [[1,2,5],[3],[4],[6],[7]] => 011011
[1,6,5,7,2,3,4] => [[1,2,4,7],[3,6],[5]] => 010100
[1,6,5,7,2,4,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,6,5,7,3,2,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,6,5,7,3,4,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,6,5,7,4,2,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,6,5,7,4,3,2] => [[1,2,4],[3],[5],[6],[7]] => 010111
[1,6,7,2,3,4,5] => [[1,2,3,6,7],[4,5]] => 001000
[1,6,7,2,3,5,4] => [[1,2,3,6],[4,5],[7]] => 001001
[1,6,7,2,4,3,5] => [[1,2,3,7],[4,5],[6]] => 001010
[1,6,7,2,4,5,3] => [[1,2,3,6],[4,5],[7]] => 001001
[1,6,7,2,5,3,4] => [[1,2,3,7],[4,5],[6]] => 001010
[1,6,7,2,5,4,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,6,7,3,2,4,5] => [[1,2,3,7],[4,6],[5]] => 001100
[1,6,7,3,2,5,4] => [[1,2,3],[4,6],[5,7]] => 001101
[1,6,7,3,4,2,5] => [[1,2,3,7],[4,5],[6]] => 001010
[1,6,7,3,4,5,2] => [[1,2,3,6],[4,5],[7]] => 001001
[1,6,7,3,5,2,4] => [[1,2,3],[4,5],[6,7]] => 001010
[1,6,7,3,5,4,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,6,7,4,2,3,5] => [[1,2,3,7],[4,6],[5]] => 001100
[1,6,7,4,2,5,3] => [[1,2,3],[4,6],[5,7]] => 001101
[1,6,7,4,3,2,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,6,7,4,3,5,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,6,7,4,5,2,3] => [[1,2,3],[4,5],[6,7]] => 001010
[1,6,7,4,5,3,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[1,6,7,5,2,3,4] => [[1,2,3,7],[4,6],[5]] => 001100
[1,6,7,5,2,4,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,6,7,5,3,2,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,6,7,5,3,4,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[1,6,7,5,4,2,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[1,6,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7]] => 001111
[1,7,2,3,4,5,6] => [[1,2,4,5,6,7],[3]] => 010000
[1,7,2,3,4,6,5] => [[1,2,4,5,6],[3],[7]] => 010001
[1,7,2,3,5,4,6] => [[1,2,4,5,7],[3],[6]] => 010010
[1,7,2,3,5,6,4] => [[1,2,4,5,6],[3],[7]] => 010001
[1,7,2,3,6,4,5] => [[1,2,4,5,7],[3],[6]] => 010010
[1,7,2,3,6,5,4] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,2,4,3,5,6] => [[1,2,4,6,7],[3],[5]] => 010100
[1,7,2,4,3,6,5] => [[1,2,4,6],[3,7],[5]] => 010101
[1,7,2,4,5,3,6] => [[1,2,4,5,7],[3],[6]] => 010010
[1,7,2,4,5,6,3] => [[1,2,4,5,6],[3],[7]] => 010001
[1,7,2,4,6,3,5] => [[1,2,4,5],[3,7],[6]] => 010010
[1,7,2,4,6,5,3] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,2,5,3,4,6] => [[1,2,4,6,7],[3],[5]] => 010100
[1,7,2,5,3,6,4] => [[1,2,4,6],[3,7],[5]] => 010101
[1,7,2,5,4,3,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,2,5,4,6,3] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,2,5,6,3,4] => [[1,2,4,5],[3,7],[6]] => 010010
[1,7,2,5,6,4,3] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,2,6,3,4,5] => [[1,2,4,6,7],[3],[5]] => 010100
[1,7,2,6,3,5,4] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,2,6,4,3,5] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,2,6,4,5,3] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,2,6,5,3,4] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,2,6,5,4,3] => [[1,2,4],[3],[5],[6],[7]] => 010111
[1,7,3,2,4,5,6] => [[1,2,5,6,7],[3],[4]] => 011000
[1,7,3,2,4,6,5] => [[1,2,5,6],[3,7],[4]] => 011001
[1,7,3,2,5,4,6] => [[1,2,5,7],[3,6],[4]] => 011010
[1,7,3,2,5,6,4] => [[1,2,5,6],[3,7],[4]] => 011001
[1,7,3,2,6,4,5] => [[1,2,5,7],[3,6],[4]] => 011010
[1,7,3,2,6,5,4] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,7,3,4,2,5,6] => [[1,2,4,6,7],[3],[5]] => 010100
[1,7,3,4,2,6,5] => [[1,2,4,6],[3,7],[5]] => 010101
[1,7,3,4,5,2,6] => [[1,2,4,5,7],[3],[6]] => 010010
[1,7,3,4,5,6,2] => [[1,2,4,5,6],[3],[7]] => 010001
[1,7,3,4,6,2,5] => [[1,2,4,5],[3,7],[6]] => 010010
[1,7,3,4,6,5,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,3,5,2,4,6] => [[1,2,4,7],[3,6],[5]] => 010100
[1,7,3,5,2,6,4] => [[1,2,4,6],[3,7],[5]] => 010101
[1,7,3,5,4,2,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,3,5,4,6,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,3,5,6,2,4] => [[1,2,4,5],[3,7],[6]] => 010010
[1,7,3,5,6,4,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,3,6,2,4,5] => [[1,2,4,7],[3,6],[5]] => 010100
[1,7,3,6,2,5,4] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,7,3,6,4,2,5] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,3,6,4,5,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,3,6,5,2,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,7,3,6,5,4,2] => [[1,2,4],[3],[5],[6],[7]] => 010111
[1,7,4,2,3,5,6] => [[1,2,5,6,7],[3],[4]] => 011000
[1,7,4,2,3,6,5] => [[1,2,5,6],[3,7],[4]] => 011001
[1,7,4,2,5,3,6] => [[1,2,5,7],[3,6],[4]] => 011010
[1,7,4,2,5,6,3] => [[1,2,5,6],[3,7],[4]] => 011001
[1,7,4,2,6,3,5] => [[1,2,5,7],[3,6],[4]] => 011010
[1,7,4,2,6,5,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,7,4,3,2,5,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,4,3,2,6,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,7,4,3,5,2,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,4,3,5,6,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,4,3,6,2,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,7,4,3,6,5,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,7,4,5,2,3,6] => [[1,2,4,7],[3,6],[5]] => 010100
[1,7,4,5,2,6,3] => [[1,2,4,6],[3,7],[5]] => 010101
[1,7,4,5,3,2,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[1,7,4,5,3,6,2] => [[1,2,4,6],[3],[5],[7]] => 010101
[1,7,4,5,6,2,3] => [[1,2,4,5],[3,7],[6]] => 010010
[1,7,4,5,6,3,2] => [[1,2,4,5],[3],[6],[7]] => 010011
[1,7,4,6,2,3,5] => [[1,2,4,7],[3,6],[5]] => 010100
[1,7,4,6,2,5,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,7,4,6,3,2,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,7,4,6,3,5,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,7,4,6,5,2,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,7,4,6,5,3,2] => [[1,2,4],[3],[5],[6],[7]] => 010111
[1,7,5,2,3,4,6] => [[1,2,5,6,7],[3],[4]] => 011000
[1,7,5,2,3,6,4] => [[1,2,5,6],[3,7],[4]] => 011001
[1,7,5,2,4,3,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,5,2,4,6,3] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,5,2,6,3,4] => [[1,2,5,7],[3,6],[4]] => 011010
[1,7,5,2,6,4,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,7,5,3,2,4,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,5,3,2,6,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,7,5,3,4,2,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,5,3,4,6,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,5,3,6,2,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,7,5,3,6,4,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[1,7,5,4,2,3,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,5,4,2,6,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,7,5,4,3,2,6] => [[1,2,7],[3],[4],[5],[6]] => 011110
[1,7,5,4,3,6,2] => [[1,2,6],[3],[4],[5],[7]] => 011101
[1,7,5,4,6,2,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,7,5,4,6,3,2] => [[1,2,5],[3],[4],[6],[7]] => 011011
[1,7,5,6,2,3,4] => [[1,2,4,7],[3,6],[5]] => 010100
[1,7,5,6,2,4,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,7,5,6,3,2,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,7,5,6,3,4,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[1,7,5,6,4,2,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[1,7,5,6,4,3,2] => [[1,2,4],[3],[5],[6],[7]] => 010111
[1,7,6,2,3,4,5] => [[1,2,5,6,7],[3],[4]] => 011000
[1,7,6,2,3,5,4] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,6,2,4,3,5] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,6,2,4,5,3] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,6,2,5,3,4] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,6,2,5,4,3] => [[1,2,5],[3],[4],[6],[7]] => 011011
[1,7,6,3,2,4,5] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,6,3,2,5,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,7,6,3,4,2,5] => [[1,2,5,7],[3],[4],[6]] => 011010
[1,7,6,3,4,5,2] => [[1,2,5,6],[3],[4],[7]] => 011001
[1,7,6,3,5,2,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,7,6,3,5,4,2] => [[1,2,5],[3],[4],[6],[7]] => 011011
[1,7,6,4,2,3,5] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,6,4,2,5,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[1,7,6,4,3,2,5] => [[1,2,7],[3],[4],[5],[6]] => 011110
[1,7,6,4,3,5,2] => [[1,2,6],[3],[4],[5],[7]] => 011101
[1,7,6,4,5,2,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[1,7,6,4,5,3,2] => [[1,2,5],[3],[4],[6],[7]] => 011011
[1,7,6,5,2,3,4] => [[1,2,6,7],[3],[4],[5]] => 011100
[1,7,6,5,2,4,3] => [[1,2,6],[3],[4],[5],[7]] => 011101
[1,7,6,5,3,2,4] => [[1,2,7],[3],[4],[5],[6]] => 011110
[1,7,6,5,3,4,2] => [[1,2,6],[3],[4],[5],[7]] => 011101
[1,7,6,5,4,2,3] => [[1,2,7],[3],[4],[5],[6]] => 011110
[1,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 100000
[2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 100001
[2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 100010
[2,1,3,4,6,7,5] => [[1,3,4,5,6],[2,7]] => 100001
[2,1,3,4,7,5,6] => [[1,3,4,5,7],[2,6]] => 100010
[2,1,3,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 100100
[2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 100101
[2,1,3,5,6,4,7] => [[1,3,4,5,7],[2,6]] => 100010
[2,1,3,5,6,7,4] => [[1,3,4,5,6],[2,7]] => 100001
[2,1,3,5,7,4,6] => [[1,3,4,5],[2,6,7]] => 100010
[2,1,3,5,7,6,4] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,3,6,4,5,7] => [[1,3,4,6,7],[2,5]] => 100100
[2,1,3,6,4,7,5] => [[1,3,4,6],[2,5,7]] => 100101
[2,1,3,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,3,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 100010
[2,1,3,6,7,5,4] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,3,7,4,5,6] => [[1,3,4,6,7],[2,5]] => 100100
[2,1,3,7,4,6,5] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,3,7,5,4,6] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,3,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,3,7,6,4,5] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,3,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => 100111
[2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 101000
[2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 101001
[2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 101010
[2,1,4,3,6,7,5] => [[1,3,5,6],[2,4,7]] => 101001
[2,1,4,3,7,5,6] => [[1,3,5,7],[2,4,6]] => 101010
[2,1,4,3,7,6,5] => [[1,3,5],[2,4,6],[7]] => 101011
[2,1,4,5,3,6,7] => [[1,3,4,6,7],[2,5]] => 100100
[2,1,4,5,3,7,6] => [[1,3,4,6],[2,5,7]] => 100101
[2,1,4,5,6,3,7] => [[1,3,4,5,7],[2,6]] => 100010
[2,1,4,5,6,7,3] => [[1,3,4,5,6],[2,7]] => 100001
[2,1,4,5,7,3,6] => [[1,3,4,5],[2,6,7]] => 100010
[2,1,4,5,7,6,3] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,4,6,3,5,7] => [[1,3,4,7],[2,5,6]] => 100100
[2,1,4,6,3,7,5] => [[1,3,4,6],[2,5,7]] => 100101
[2,1,4,6,5,3,7] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,4,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,4,6,7,3,5] => [[1,3,4,5],[2,6,7]] => 100010
[2,1,4,6,7,5,3] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,4,7,3,5,6] => [[1,3,4,7],[2,5,6]] => 100100
[2,1,4,7,3,6,5] => [[1,3,4],[2,5,6],[7]] => 100101
[2,1,4,7,5,3,6] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,4,7,5,6,3] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,4,7,6,3,5] => [[1,3,4],[2,5,7],[6]] => 100110
[2,1,4,7,6,5,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[2,1,5,3,4,6,7] => [[1,3,5,6,7],[2,4]] => 101000
[2,1,5,3,4,7,6] => [[1,3,5,6],[2,4,7]] => 101001
[2,1,5,3,6,4,7] => [[1,3,5,7],[2,4,6]] => 101010
[2,1,5,3,6,7,4] => [[1,3,5,6],[2,4,7]] => 101001
[2,1,5,3,7,4,6] => [[1,3,5,7],[2,4,6]] => 101010
[2,1,5,3,7,6,4] => [[1,3,5],[2,4,6],[7]] => 101011
[2,1,5,4,3,6,7] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,5,4,3,7,6] => [[1,3,6],[2,4,7],[5]] => 101101
[2,1,5,4,6,3,7] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,5,4,6,7,3] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,5,4,7,3,6] => [[1,3,5],[2,4,7],[6]] => 101010
[2,1,5,4,7,6,3] => [[1,3,5],[2,4,6],[7]] => 101011
[2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => 100100
[2,1,5,6,3,7,4] => [[1,3,4,6],[2,5,7]] => 100101
[2,1,5,6,4,3,7] => [[1,3,4,7],[2,5],[6]] => 100110
[2,1,5,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => 100101
[2,1,5,6,7,3,4] => [[1,3,4,5],[2,6,7]] => 100010
[2,1,5,6,7,4,3] => [[1,3,4,5],[2,6],[7]] => 100011
[2,1,5,7,3,4,6] => [[1,3,4,7],[2,5,6]] => 100100
[2,1,5,7,3,6,4] => [[1,3,4],[2,5,6],[7]] => 100101
[2,1,5,7,4,3,6] => [[1,3,4],[2,5,7],[6]] => 100110
[2,1,5,7,4,6,3] => [[1,3,4],[2,5,6],[7]] => 100101
[2,1,5,7,6,3,4] => [[1,3,4],[2,5,7],[6]] => 100110
[2,1,5,7,6,4,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[2,1,6,3,4,5,7] => [[1,3,5,6,7],[2,4]] => 101000
[2,1,6,3,4,7,5] => [[1,3,5,6],[2,4,7]] => 101001
[2,1,6,3,5,4,7] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,6,3,5,7,4] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,6,3,7,4,5] => [[1,3,5,7],[2,4,6]] => 101010
[2,1,6,3,7,5,4] => [[1,3,5],[2,4,6],[7]] => 101011
[2,1,6,4,3,5,7] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,6,4,3,7,5] => [[1,3,6],[2,4,7],[5]] => 101101
[2,1,6,4,5,3,7] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,6,4,5,7,3] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,6,4,7,3,5] => [[1,3,5],[2,4,7],[6]] => 101010
[2,1,6,4,7,5,3] => [[1,3,5],[2,4,6],[7]] => 101011
[2,1,6,5,3,4,7] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,6,5,3,7,4] => [[1,3,6],[2,4,7],[5]] => 101101
[2,1,6,5,4,3,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[2,1,6,5,4,7,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[2,1,6,5,7,3,4] => [[1,3,5],[2,4,7],[6]] => 101010
[2,1,6,5,7,4,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[2,1,6,7,3,4,5] => [[1,3,4,7],[2,5,6]] => 100100
[2,1,6,7,3,5,4] => [[1,3,4],[2,5,6],[7]] => 100101
[2,1,6,7,4,3,5] => [[1,3,4],[2,5,7],[6]] => 100110
[2,1,6,7,4,5,3] => [[1,3,4],[2,5,6],[7]] => 100101
[2,1,6,7,5,3,4] => [[1,3,4],[2,5,7],[6]] => 100110
[2,1,6,7,5,4,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[2,1,7,3,4,5,6] => [[1,3,5,6,7],[2,4]] => 101000
[2,1,7,3,4,6,5] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,7,3,5,4,6] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,7,3,5,6,4] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,7,3,6,4,5] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,7,3,6,5,4] => [[1,3,5],[2,4],[6],[7]] => 101011
[2,1,7,4,3,5,6] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,7,4,3,6,5] => [[1,3,6],[2,4,7],[5]] => 101101
[2,1,7,4,5,3,6] => [[1,3,5,7],[2,4],[6]] => 101010
[2,1,7,4,5,6,3] => [[1,3,5,6],[2,4],[7]] => 101001
[2,1,7,4,6,3,5] => [[1,3,5],[2,4,7],[6]] => 101010
[2,1,7,4,6,5,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[2,1,7,5,3,4,6] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,7,5,3,6,4] => [[1,3,6],[2,4,7],[5]] => 101101
[2,1,7,5,4,3,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[2,1,7,5,4,6,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[2,1,7,5,6,3,4] => [[1,3,5],[2,4,7],[6]] => 101010
[2,1,7,5,6,4,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[2,1,7,6,3,4,5] => [[1,3,6,7],[2,4],[5]] => 101100
[2,1,7,6,3,5,4] => [[1,3,6],[2,4],[5],[7]] => 101101
[2,1,7,6,4,3,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[2,1,7,6,4,5,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[2,1,7,6,5,3,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[2,1,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7]] => 101111
[2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 010000
[2,3,1,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 010001
[2,3,1,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 010010
[2,3,1,4,6,7,5] => [[1,2,4,5,6],[3,7]] => 010001
[2,3,1,4,7,5,6] => [[1,2,4,5,7],[3,6]] => 010010
[2,3,1,4,7,6,5] => [[1,2,4,5],[3,6],[7]] => 010011
[2,3,1,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 010100
[2,3,1,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 010101
[2,3,1,5,6,4,7] => [[1,2,4,5,7],[3,6]] => 010010
[2,3,1,5,6,7,4] => [[1,2,4,5,6],[3,7]] => 010001
[2,3,1,5,7,4,6] => [[1,2,4,5],[3,6,7]] => 010010
[2,3,1,5,7,6,4] => [[1,2,4,5],[3,6],[7]] => 010011
[2,3,1,6,4,5,7] => [[1,2,4,6,7],[3,5]] => 010100
[2,3,1,6,4,7,5] => [[1,2,4,6],[3,5,7]] => 010101
[2,3,1,6,5,4,7] => [[1,2,4,7],[3,5],[6]] => 010110
[2,3,1,6,5,7,4] => [[1,2,4,6],[3,5],[7]] => 010101
[2,3,1,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 010010
[2,3,1,6,7,5,4] => [[1,2,4,5],[3,6],[7]] => 010011
[2,3,1,7,4,5,6] => [[1,2,4,6,7],[3,5]] => 010100
[2,3,1,7,4,6,5] => [[1,2,4,6],[3,5],[7]] => 010101
[2,3,1,7,5,4,6] => [[1,2,4,7],[3,5],[6]] => 010110
[2,3,1,7,5,6,4] => [[1,2,4,6],[3,5],[7]] => 010101
[2,3,1,7,6,4,5] => [[1,2,4,7],[3,5],[6]] => 010110
[2,3,1,7,6,5,4] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => 001000
[2,3,4,1,5,7,6] => [[1,2,3,5,6],[4,7]] => 001001
[2,3,4,1,6,5,7] => [[1,2,3,5,7],[4,6]] => 001010
[2,3,4,1,6,7,5] => [[1,2,3,5,6],[4,7]] => 001001
[2,3,4,1,7,5,6] => [[1,2,3,5,7],[4,6]] => 001010
[2,3,4,1,7,6,5] => [[1,2,3,5],[4,6],[7]] => 001011
[2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => 000100
[2,3,4,5,1,7,6] => [[1,2,3,4,6],[5,7]] => 000101
[2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => 000010
[2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => 000001
[2,3,4,5,7,1,6] => [[1,2,3,4,5],[6,7]] => 000010
[2,3,4,5,7,6,1] => [[1,2,3,4,5],[6],[7]] => 000011
[2,3,4,6,1,5,7] => [[1,2,3,4,7],[5,6]] => 000100
[2,3,4,6,1,7,5] => [[1,2,3,4,6],[5,7]] => 000101
[2,3,4,6,5,1,7] => [[1,2,3,4,7],[5],[6]] => 000110
[2,3,4,6,5,7,1] => [[1,2,3,4,6],[5],[7]] => 000101
[2,3,4,6,7,1,5] => [[1,2,3,4,5],[6,7]] => 000010
[2,3,4,6,7,5,1] => [[1,2,3,4,5],[6],[7]] => 000011
[2,3,4,7,1,5,6] => [[1,2,3,4,7],[5,6]] => 000100
[2,3,4,7,1,6,5] => [[1,2,3,4],[5,6],[7]] => 000101
[2,3,4,7,5,1,6] => [[1,2,3,4,7],[5],[6]] => 000110
[2,3,4,7,5,6,1] => [[1,2,3,4,6],[5],[7]] => 000101
[2,3,4,7,6,1,5] => [[1,2,3,4],[5,7],[6]] => 000110
[2,3,4,7,6,5,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,3,5,1,4,6,7] => [[1,2,3,6,7],[4,5]] => 001000
[2,3,5,1,4,7,6] => [[1,2,3,6],[4,5,7]] => 001001
[2,3,5,1,6,4,7] => [[1,2,3,5,7],[4,6]] => 001010
[2,3,5,1,6,7,4] => [[1,2,3,5,6],[4,7]] => 001001
[2,3,5,1,7,4,6] => [[1,2,3,5],[4,6,7]] => 001010
[2,3,5,1,7,6,4] => [[1,2,3,5],[4,6],[7]] => 001011
[2,3,5,4,1,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[2,3,5,4,1,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[2,3,5,4,6,1,7] => [[1,2,3,5,7],[4],[6]] => 001010
[2,3,5,4,6,7,1] => [[1,2,3,5,6],[4],[7]] => 001001
[2,3,5,4,7,1,6] => [[1,2,3,5],[4,7],[6]] => 001010
[2,3,5,4,7,6,1] => [[1,2,3,5],[4,6],[7]] => 001011
[2,3,5,6,1,4,7] => [[1,2,3,4,7],[5,6]] => 000100
[2,3,5,6,1,7,4] => [[1,2,3,4,6],[5,7]] => 000101
[2,3,5,6,4,1,7] => [[1,2,3,4,7],[5],[6]] => 000110
[2,3,5,6,4,7,1] => [[1,2,3,4,6],[5],[7]] => 000101
[2,3,5,6,7,1,4] => [[1,2,3,4,5],[6,7]] => 000010
[2,3,5,6,7,4,1] => [[1,2,3,4,5],[6],[7]] => 000011
[2,3,5,7,1,4,6] => [[1,2,3,4],[5,6,7]] => 000100
[2,3,5,7,1,6,4] => [[1,2,3,4],[5,6],[7]] => 000101
[2,3,5,7,4,1,6] => [[1,2,3,4],[5,7],[6]] => 000110
[2,3,5,7,4,6,1] => [[1,2,3,4],[5,6],[7]] => 000101
[2,3,5,7,6,1,4] => [[1,2,3,4],[5,7],[6]] => 000110
[2,3,5,7,6,4,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,3,6,1,4,5,7] => [[1,2,3,6,7],[4,5]] => 001000
[2,3,6,1,4,7,5] => [[1,2,3,6],[4,5,7]] => 001001
[2,3,6,1,5,4,7] => [[1,2,3,7],[4,5],[6]] => 001010
[2,3,6,1,5,7,4] => [[1,2,3,6],[4,5],[7]] => 001001
[2,3,6,1,7,4,5] => [[1,2,3,5],[4,6,7]] => 001010
[2,3,6,1,7,5,4] => [[1,2,3,5],[4,6],[7]] => 001011
[2,3,6,4,1,5,7] => [[1,2,3,6,7],[4],[5]] => 001100
[2,3,6,4,1,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[2,3,6,4,5,1,7] => [[1,2,3,5,7],[4],[6]] => 001010
[2,3,6,4,5,7,1] => [[1,2,3,5,6],[4],[7]] => 001001
[2,3,6,4,7,1,5] => [[1,2,3,5],[4,7],[6]] => 001010
[2,3,6,4,7,5,1] => [[1,2,3,5],[4,6],[7]] => 001011
[2,3,6,5,1,4,7] => [[1,2,3,7],[4,6],[5]] => 001100
[2,3,6,5,1,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[2,3,6,5,4,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,3,6,5,4,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,3,6,5,7,1,4] => [[1,2,3,5],[4,7],[6]] => 001010
[2,3,6,5,7,4,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,3,6,7,1,4,5] => [[1,2,3,4],[5,6,7]] => 000100
[2,3,6,7,1,5,4] => [[1,2,3,4],[5,6],[7]] => 000101
[2,3,6,7,4,1,5] => [[1,2,3,4],[5,7],[6]] => 000110
[2,3,6,7,4,5,1] => [[1,2,3,4],[5,6],[7]] => 000101
[2,3,6,7,5,1,4] => [[1,2,3,4],[5,7],[6]] => 000110
[2,3,6,7,5,4,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,3,7,1,4,5,6] => [[1,2,3,6,7],[4,5]] => 001000
[2,3,7,1,4,6,5] => [[1,2,3,6],[4,5],[7]] => 001001
[2,3,7,1,5,4,6] => [[1,2,3,7],[4,5],[6]] => 001010
[2,3,7,1,5,6,4] => [[1,2,3,6],[4,5],[7]] => 001001
[2,3,7,1,6,4,5] => [[1,2,3,7],[4,5],[6]] => 001010
[2,3,7,1,6,5,4] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,3,7,4,1,5,6] => [[1,2,3,6,7],[4],[5]] => 001100
[2,3,7,4,1,6,5] => [[1,2,3,6],[4,7],[5]] => 001101
[2,3,7,4,5,1,6] => [[1,2,3,5,7],[4],[6]] => 001010
[2,3,7,4,5,6,1] => [[1,2,3,5,6],[4],[7]] => 001001
[2,3,7,4,6,1,5] => [[1,2,3,5],[4,7],[6]] => 001010
[2,3,7,4,6,5,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,3,7,5,1,4,6] => [[1,2,3,7],[4,6],[5]] => 001100
[2,3,7,5,1,6,4] => [[1,2,3,6],[4,7],[5]] => 001101
[2,3,7,5,4,1,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,3,7,5,4,6,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,3,7,5,6,1,4] => [[1,2,3,5],[4,7],[6]] => 001010
[2,3,7,5,6,4,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,3,7,6,1,4,5] => [[1,2,3,7],[4,6],[5]] => 001100
[2,3,7,6,1,5,4] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,3,7,6,4,1,5] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,3,7,6,4,5,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,3,7,6,5,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,3,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[2,4,1,3,5,6,7] => [[1,2,5,6,7],[3,4]] => 010000
[2,4,1,3,5,7,6] => [[1,2,5,6],[3,4,7]] => 010001
[2,4,1,3,6,5,7] => [[1,2,5,7],[3,4,6]] => 010010
[2,4,1,3,6,7,5] => [[1,2,5,6],[3,4,7]] => 010001
[2,4,1,3,7,5,6] => [[1,2,5,7],[3,4,6]] => 010010
[2,4,1,3,7,6,5] => [[1,2,5],[3,4,6],[7]] => 010011
[2,4,1,5,3,6,7] => [[1,2,4,6,7],[3,5]] => 010100
[2,4,1,5,3,7,6] => [[1,2,4,6],[3,5,7]] => 010101
[2,4,1,5,6,3,7] => [[1,2,4,5,7],[3,6]] => 010010
[2,4,1,5,6,7,3] => [[1,2,4,5,6],[3,7]] => 010001
[2,4,1,5,7,3,6] => [[1,2,4,5],[3,6,7]] => 010010
[2,4,1,5,7,6,3] => [[1,2,4,5],[3,6],[7]] => 010011
[2,4,1,6,3,5,7] => [[1,2,4,7],[3,5,6]] => 010100
[2,4,1,6,3,7,5] => [[1,2,4,6],[3,5,7]] => 010101
[2,4,1,6,5,3,7] => [[1,2,4,7],[3,5],[6]] => 010110
[2,4,1,6,5,7,3] => [[1,2,4,6],[3,5],[7]] => 010101
[2,4,1,6,7,3,5] => [[1,2,4,5],[3,6,7]] => 010010
[2,4,1,6,7,5,3] => [[1,2,4,5],[3,6],[7]] => 010011
[2,4,1,7,3,5,6] => [[1,2,4,7],[3,5,6]] => 010100
[2,4,1,7,3,6,5] => [[1,2,4],[3,5,6],[7]] => 010101
[2,4,1,7,5,3,6] => [[1,2,4,7],[3,5],[6]] => 010110
[2,4,1,7,5,6,3] => [[1,2,4,6],[3,5],[7]] => 010101
[2,4,1,7,6,3,5] => [[1,2,4],[3,5,7],[6]] => 010110
[2,4,1,7,6,5,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,4,3,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[2,4,3,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[2,4,3,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => 011010
[2,4,3,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[2,4,3,1,7,5,6] => [[1,2,5,7],[3,6],[4]] => 011010
[2,4,3,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => 011011
[2,4,3,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[2,4,3,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[2,4,3,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 010010
[2,4,3,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 010001
[2,4,3,5,7,1,6] => [[1,2,4,5],[3,7],[6]] => 010010
[2,4,3,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => 010011
[2,4,3,6,1,5,7] => [[1,2,4,7],[3,6],[5]] => 010100
[2,4,3,6,1,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[2,4,3,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => 010110
[2,4,3,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 010101
[2,4,3,6,7,1,5] => [[1,2,4,5],[3,7],[6]] => 010010
[2,4,3,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => 010011
[2,4,3,7,1,5,6] => [[1,2,4,7],[3,6],[5]] => 010100
[2,4,3,7,1,6,5] => [[1,2,4],[3,6],[5,7]] => 010101
[2,4,3,7,5,1,6] => [[1,2,4,7],[3,5],[6]] => 010110
[2,4,3,7,5,6,1] => [[1,2,4,6],[3,5],[7]] => 010101
[2,4,3,7,6,1,5] => [[1,2,4],[3,5],[6,7]] => 010110
[2,4,3,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,4,5,1,3,6,7] => [[1,2,3,6,7],[4,5]] => 001000
[2,4,5,1,3,7,6] => [[1,2,3,6],[4,5,7]] => 001001
[2,4,5,1,6,3,7] => [[1,2,3,5,7],[4,6]] => 001010
[2,4,5,1,6,7,3] => [[1,2,3,5,6],[4,7]] => 001001
[2,4,5,1,7,3,6] => [[1,2,3,5],[4,6,7]] => 001010
[2,4,5,1,7,6,3] => [[1,2,3,5],[4,6],[7]] => 001011
[2,4,5,3,1,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[2,4,5,3,1,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[2,4,5,3,6,1,7] => [[1,2,3,5,7],[4],[6]] => 001010
[2,4,5,3,6,7,1] => [[1,2,3,5,6],[4],[7]] => 001001
[2,4,5,3,7,1,6] => [[1,2,3,5],[4,7],[6]] => 001010
[2,4,5,3,7,6,1] => [[1,2,3,5],[4,6],[7]] => 001011
[2,4,5,6,1,3,7] => [[1,2,3,4,7],[5,6]] => 000100
[2,4,5,6,1,7,3] => [[1,2,3,4,6],[5,7]] => 000101
[2,4,5,6,3,1,7] => [[1,2,3,4,7],[5],[6]] => 000110
[2,4,5,6,3,7,1] => [[1,2,3,4,6],[5],[7]] => 000101
[2,4,5,6,7,1,3] => [[1,2,3,4,5],[6,7]] => 000010
[2,4,5,6,7,3,1] => [[1,2,3,4,5],[6],[7]] => 000011
[2,4,5,7,1,3,6] => [[1,2,3,4],[5,6,7]] => 000100
[2,4,5,7,1,6,3] => [[1,2,3,4],[5,6],[7]] => 000101
[2,4,5,7,3,1,6] => [[1,2,3,4],[5,7],[6]] => 000110
[2,4,5,7,3,6,1] => [[1,2,3,4],[5,6],[7]] => 000101
[2,4,5,7,6,1,3] => [[1,2,3,4],[5,7],[6]] => 000110
[2,4,5,7,6,3,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,4,6,1,3,5,7] => [[1,2,3,7],[4,5,6]] => 001000
[2,4,6,1,3,7,5] => [[1,2,3,6],[4,5,7]] => 001001
[2,4,6,1,5,3,7] => [[1,2,3,7],[4,5],[6]] => 001010
[2,4,6,1,5,7,3] => [[1,2,3,6],[4,5],[7]] => 001001
[2,4,6,1,7,3,5] => [[1,2,3,5],[4,6,7]] => 001010
[2,4,6,1,7,5,3] => [[1,2,3,5],[4,6],[7]] => 001011
[2,4,6,3,1,5,7] => [[1,2,3,7],[4,6],[5]] => 001100
[2,4,6,3,1,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[2,4,6,3,5,1,7] => [[1,2,3,7],[4,5],[6]] => 001010
[2,4,6,3,5,7,1] => [[1,2,3,6],[4,5],[7]] => 001001
[2,4,6,3,7,1,5] => [[1,2,3,5],[4,7],[6]] => 001010
[2,4,6,3,7,5,1] => [[1,2,3,5],[4,6],[7]] => 001011
[2,4,6,5,1,3,7] => [[1,2,3,7],[4,6],[5]] => 001100
[2,4,6,5,1,7,3] => [[1,2,3,6],[4,7],[5]] => 001101
[2,4,6,5,3,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,4,6,5,3,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,4,6,5,7,1,3] => [[1,2,3,5],[4,7],[6]] => 001010
[2,4,6,5,7,3,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,4,6,7,1,3,5] => [[1,2,3,4],[5,6,7]] => 000100
[2,4,6,7,1,5,3] => [[1,2,3,4],[5,6],[7]] => 000101
[2,4,6,7,3,1,5] => [[1,2,3,4],[5,7],[6]] => 000110
[2,4,6,7,3,5,1] => [[1,2,3,4],[5,6],[7]] => 000101
[2,4,6,7,5,1,3] => [[1,2,3,4],[5,7],[6]] => 000110
[2,4,6,7,5,3,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,4,7,1,3,5,6] => [[1,2,3,7],[4,5,6]] => 001000
[2,4,7,1,3,6,5] => [[1,2,3],[4,5,6],[7]] => 001001
[2,4,7,1,5,3,6] => [[1,2,3,7],[4,5],[6]] => 001010
[2,4,7,1,5,6,3] => [[1,2,3,6],[4,5],[7]] => 001001
[2,4,7,1,6,3,5] => [[1,2,3],[4,5,7],[6]] => 001010
[2,4,7,1,6,5,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,4,7,3,1,5,6] => [[1,2,3,7],[4,6],[5]] => 001100
[2,4,7,3,1,6,5] => [[1,2,3],[4,6],[5,7]] => 001101
[2,4,7,3,5,1,6] => [[1,2,3,7],[4,5],[6]] => 001010
[2,4,7,3,5,6,1] => [[1,2,3,6],[4,5],[7]] => 001001
[2,4,7,3,6,1,5] => [[1,2,3],[4,5],[6,7]] => 001010
[2,4,7,3,6,5,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,4,7,5,1,3,6] => [[1,2,3,7],[4,6],[5]] => 001100
[2,4,7,5,1,6,3] => [[1,2,3,6],[4,7],[5]] => 001101
[2,4,7,5,3,1,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,4,7,5,3,6,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,4,7,5,6,1,3] => [[1,2,3,5],[4,7],[6]] => 001010
[2,4,7,5,6,3,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,4,7,6,1,3,5] => [[1,2,3],[4,6,7],[5]] => 001100
[2,4,7,6,1,5,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,4,7,6,3,1,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,4,7,6,3,5,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,4,7,6,5,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,4,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[2,5,1,3,4,6,7] => [[1,2,5,6,7],[3,4]] => 010000
[2,5,1,3,4,7,6] => [[1,2,5,6],[3,4,7]] => 010001
[2,5,1,3,6,4,7] => [[1,2,5,7],[3,4,6]] => 010010
[2,5,1,3,6,7,4] => [[1,2,5,6],[3,4,7]] => 010001
[2,5,1,3,7,4,6] => [[1,2,5,7],[3,4,6]] => 010010
[2,5,1,3,7,6,4] => [[1,2,5],[3,4,6],[7]] => 010011
[2,5,1,4,3,6,7] => [[1,2,6,7],[3,4],[5]] => 010100
[2,5,1,4,3,7,6] => [[1,2,6],[3,4,7],[5]] => 010101
[2,5,1,4,6,3,7] => [[1,2,5,7],[3,4],[6]] => 010010
[2,5,1,4,6,7,3] => [[1,2,5,6],[3,4],[7]] => 010001
[2,5,1,4,7,3,6] => [[1,2,5],[3,4,7],[6]] => 010010
[2,5,1,4,7,6,3] => [[1,2,5],[3,4,6],[7]] => 010011
[2,5,1,6,3,4,7] => [[1,2,4,7],[3,5,6]] => 010100
[2,5,1,6,3,7,4] => [[1,2,4,6],[3,5,7]] => 010101
[2,5,1,6,4,3,7] => [[1,2,4,7],[3,5],[6]] => 010110
[2,5,1,6,4,7,3] => [[1,2,4,6],[3,5],[7]] => 010101
[2,5,1,6,7,3,4] => [[1,2,4,5],[3,6,7]] => 010010
[2,5,1,6,7,4,3] => [[1,2,4,5],[3,6],[7]] => 010011
[2,5,1,7,3,4,6] => [[1,2,4,7],[3,5,6]] => 010100
[2,5,1,7,3,6,4] => [[1,2,4],[3,5,6],[7]] => 010101
[2,5,1,7,4,3,6] => [[1,2,4],[3,5,7],[6]] => 010110
[2,5,1,7,4,6,3] => [[1,2,4],[3,5,6],[7]] => 010101
[2,5,1,7,6,3,4] => [[1,2,4],[3,5,7],[6]] => 010110
[2,5,1,7,6,4,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,5,3,1,4,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[2,5,3,1,4,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[2,5,3,1,6,4,7] => [[1,2,5,7],[3,6],[4]] => 011010
[2,5,3,1,6,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[2,5,3,1,7,4,6] => [[1,2,5,7],[3,6],[4]] => 011010
[2,5,3,1,7,6,4] => [[1,2,5],[3,6],[4,7]] => 011011
[2,5,3,4,1,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[2,5,3,4,1,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[2,5,3,4,6,1,7] => [[1,2,4,5,7],[3],[6]] => 010010
[2,5,3,4,6,7,1] => [[1,2,4,5,6],[3],[7]] => 010001
[2,5,3,4,7,1,6] => [[1,2,4,5],[3,7],[6]] => 010010
[2,5,3,4,7,6,1] => [[1,2,4,5],[3,6],[7]] => 010011
[2,5,3,6,1,4,7] => [[1,2,4,7],[3,6],[5]] => 010100
[2,5,3,6,1,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[2,5,3,6,4,1,7] => [[1,2,4,7],[3,5],[6]] => 010110
[2,5,3,6,4,7,1] => [[1,2,4,6],[3,5],[7]] => 010101
[2,5,3,6,7,1,4] => [[1,2,4,5],[3,7],[6]] => 010010
[2,5,3,6,7,4,1] => [[1,2,4,5],[3,6],[7]] => 010011
[2,5,3,7,1,4,6] => [[1,2,4,7],[3,6],[5]] => 010100
[2,5,3,7,1,6,4] => [[1,2,4],[3,6],[5,7]] => 010101
[2,5,3,7,4,1,6] => [[1,2,4,7],[3,5],[6]] => 010110
[2,5,3,7,4,6,1] => [[1,2,4,6],[3,5],[7]] => 010101
[2,5,3,7,6,1,4] => [[1,2,4],[3,5],[6,7]] => 010110
[2,5,3,7,6,4,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,5,4,1,3,6,7] => [[1,2,6,7],[3,5],[4]] => 011000
[2,5,4,1,3,7,6] => [[1,2,6],[3,5,7],[4]] => 011001
[2,5,4,1,6,3,7] => [[1,2,5,7],[3,6],[4]] => 011010
[2,5,4,1,6,7,3] => [[1,2,5,6],[3,7],[4]] => 011001
[2,5,4,1,7,3,6] => [[1,2,5],[3,6,7],[4]] => 011010
[2,5,4,1,7,6,3] => [[1,2,5],[3,6],[4,7]] => 011011
[2,5,4,3,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,5,4,3,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,5,4,3,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,5,4,3,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,5,4,3,7,1,6] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,5,4,3,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,5,4,6,1,3,7] => [[1,2,4,7],[3,6],[5]] => 010100
[2,5,4,6,1,7,3] => [[1,2,4,6],[3,7],[5]] => 010101
[2,5,4,6,3,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,5,4,6,3,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,5,4,6,7,1,3] => [[1,2,4,5],[3,7],[6]] => 010010
[2,5,4,6,7,3,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,5,4,7,1,3,6] => [[1,2,4],[3,6,7],[5]] => 010100
[2,5,4,7,1,6,3] => [[1,2,4],[3,6],[5,7]] => 010101
[2,5,4,7,3,1,6] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,5,4,7,3,6,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,5,4,7,6,1,3] => [[1,2,4],[3,5],[6,7]] => 010110
[2,5,4,7,6,3,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,5,6,1,3,4,7] => [[1,2,3,7],[4,5,6]] => 001000
[2,5,6,1,3,7,4] => [[1,2,3,6],[4,5,7]] => 001001
[2,5,6,1,4,3,7] => [[1,2,3,7],[4,5],[6]] => 001010
[2,5,6,1,4,7,3] => [[1,2,3,6],[4,5],[7]] => 001001
[2,5,6,1,7,3,4] => [[1,2,3,5],[4,6,7]] => 001010
[2,5,6,1,7,4,3] => [[1,2,3,5],[4,6],[7]] => 001011
[2,5,6,3,1,4,7] => [[1,2,3,7],[4,6],[5]] => 001100
[2,5,6,3,1,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[2,5,6,3,4,1,7] => [[1,2,3,7],[4,5],[6]] => 001010
[2,5,6,3,4,7,1] => [[1,2,3,6],[4,5],[7]] => 001001
[2,5,6,3,7,1,4] => [[1,2,3,5],[4,7],[6]] => 001010
[2,5,6,3,7,4,1] => [[1,2,3,5],[4,6],[7]] => 001011
[2,5,6,4,1,3,7] => [[1,2,3,7],[4,6],[5]] => 001100
[2,5,6,4,1,7,3] => [[1,2,3,6],[4,7],[5]] => 001101
[2,5,6,4,3,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[2,5,6,4,3,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[2,5,6,4,7,1,3] => [[1,2,3,5],[4,7],[6]] => 001010
[2,5,6,4,7,3,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[2,5,6,7,1,3,4] => [[1,2,3,4],[5,6,7]] => 000100
[2,5,6,7,1,4,3] => [[1,2,3,4],[5,6],[7]] => 000101
[2,5,6,7,3,1,4] => [[1,2,3,4],[5,7],[6]] => 000110
[2,5,6,7,3,4,1] => [[1,2,3,4],[5,6],[7]] => 000101
[2,5,6,7,4,1,3] => [[1,2,3,4],[5,7],[6]] => 000110
[2,5,6,7,4,3,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[2,5,7,1,3,4,6] => [[1,2,3,7],[4,5,6]] => 001000
[2,5,7,1,3,6,4] => [[1,2,3],[4,5,6],[7]] => 001001
[2,5,7,1,4,3,6] => [[1,2,3],[4,5,7],[6]] => 001010
[2,5,7,1,4,6,3] => [[1,2,3],[4,5,6],[7]] => 001001
[2,5,7,1,6,3,4] => [[1,2,3],[4,5,7],[6]] => 001010
[2,5,7,1,6,4,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,5,7,3,1,4,6] => [[1,2,3,7],[4,6],[5]] => 001100
[2,5,7,3,1,6,4] => [[1,2,3],[4,6],[5,7]] => 001101
[2,5,7,3,4,1,6] => [[1,2,3,7],[4,5],[6]] => 001010
[2,5,7,3,4,6,1] => [[1,2,3,6],[4,5],[7]] => 001001
[2,5,7,3,6,1,4] => [[1,2,3],[4,5],[6,7]] => 001010
[2,5,7,3,6,4,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,5,7,4,1,3,6] => [[1,2,3],[4,6,7],[5]] => 001100
[2,5,7,4,1,6,3] => [[1,2,3],[4,6],[5,7]] => 001101
[2,5,7,4,3,1,6] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,5,7,4,3,6,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,5,7,4,6,1,3] => [[1,2,3],[4,5],[6,7]] => 001010
[2,5,7,4,6,3,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,5,7,6,1,3,4] => [[1,2,3],[4,6,7],[5]] => 001100
[2,5,7,6,1,4,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,5,7,6,3,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,5,7,6,3,4,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,5,7,6,4,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,5,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[2,6,1,3,4,5,7] => [[1,2,5,6,7],[3,4]] => 010000
[2,6,1,3,4,7,5] => [[1,2,5,6],[3,4,7]] => 010001
[2,6,1,3,5,4,7] => [[1,2,5,7],[3,4],[6]] => 010010
[2,6,1,3,5,7,4] => [[1,2,5,6],[3,4],[7]] => 010001
[2,6,1,3,7,4,5] => [[1,2,5,7],[3,4,6]] => 010010
[2,6,1,3,7,5,4] => [[1,2,5],[3,4,6],[7]] => 010011
[2,6,1,4,3,5,7] => [[1,2,6,7],[3,4],[5]] => 010100
[2,6,1,4,3,7,5] => [[1,2,6],[3,4,7],[5]] => 010101
[2,6,1,4,5,3,7] => [[1,2,5,7],[3,4],[6]] => 010010
[2,6,1,4,5,7,3] => [[1,2,5,6],[3,4],[7]] => 010001
[2,6,1,4,7,3,5] => [[1,2,5],[3,4,7],[6]] => 010010
[2,6,1,4,7,5,3] => [[1,2,5],[3,4,6],[7]] => 010011
[2,6,1,5,3,4,7] => [[1,2,6,7],[3,4],[5]] => 010100
[2,6,1,5,3,7,4] => [[1,2,6],[3,4,7],[5]] => 010101
[2,6,1,5,4,3,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[2,6,1,5,4,7,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[2,6,1,5,7,3,4] => [[1,2,5],[3,4,7],[6]] => 010010
[2,6,1,5,7,4,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[2,6,1,7,3,4,5] => [[1,2,4,7],[3,5,6]] => 010100
[2,6,1,7,3,5,4] => [[1,2,4],[3,5,6],[7]] => 010101
[2,6,1,7,4,3,5] => [[1,2,4],[3,5,7],[6]] => 010110
[2,6,1,7,4,5,3] => [[1,2,4],[3,5,6],[7]] => 010101
[2,6,1,7,5,3,4] => [[1,2,4],[3,5,7],[6]] => 010110
[2,6,1,7,5,4,3] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,6,3,1,4,5,7] => [[1,2,5,6,7],[3],[4]] => 011000
[2,6,3,1,4,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[2,6,3,1,5,4,7] => [[1,2,5,7],[3,6],[4]] => 011010
[2,6,3,1,5,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[2,6,3,1,7,4,5] => [[1,2,5,7],[3,6],[4]] => 011010
[2,6,3,1,7,5,4] => [[1,2,5],[3,6],[4,7]] => 011011
[2,6,3,4,1,5,7] => [[1,2,4,6,7],[3],[5]] => 010100
[2,6,3,4,1,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[2,6,3,4,5,1,7] => [[1,2,4,5,7],[3],[6]] => 010010
[2,6,3,4,5,7,1] => [[1,2,4,5,6],[3],[7]] => 010001
[2,6,3,4,7,1,5] => [[1,2,4,5],[3,7],[6]] => 010010
[2,6,3,4,7,5,1] => [[1,2,4,5],[3,6],[7]] => 010011
[2,6,3,5,1,4,7] => [[1,2,4,7],[3,6],[5]] => 010100
[2,6,3,5,1,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[2,6,3,5,4,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,6,3,5,4,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,6,3,5,7,1,4] => [[1,2,4,5],[3,7],[6]] => 010010
[2,6,3,5,7,4,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,6,3,7,1,4,5] => [[1,2,4,7],[3,6],[5]] => 010100
[2,6,3,7,1,5,4] => [[1,2,4],[3,6],[5,7]] => 010101
[2,6,3,7,4,1,5] => [[1,2,4,7],[3,5],[6]] => 010110
[2,6,3,7,4,5,1] => [[1,2,4,6],[3,5],[7]] => 010101
[2,6,3,7,5,1,4] => [[1,2,4],[3,5],[6,7]] => 010110
[2,6,3,7,5,4,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,6,4,1,3,5,7] => [[1,2,6,7],[3,5],[4]] => 011000
[2,6,4,1,3,7,5] => [[1,2,6],[3,5,7],[4]] => 011001
[2,6,4,1,5,3,7] => [[1,2,5,7],[3,6],[4]] => 011010
[2,6,4,1,5,7,3] => [[1,2,5,6],[3,7],[4]] => 011001
[2,6,4,1,7,3,5] => [[1,2,5],[3,6,7],[4]] => 011010
[2,6,4,1,7,5,3] => [[1,2,5],[3,6],[4,7]] => 011011
[2,6,4,3,1,5,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,6,4,3,1,7,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,6,4,3,5,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,6,4,3,5,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,6,4,3,7,1,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,6,4,3,7,5,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,6,4,5,1,3,7] => [[1,2,4,7],[3,6],[5]] => 010100
[2,6,4,5,1,7,3] => [[1,2,4,6],[3,7],[5]] => 010101
[2,6,4,5,3,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,6,4,5,3,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,6,4,5,7,1,3] => [[1,2,4,5],[3,7],[6]] => 010010
[2,6,4,5,7,3,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,6,4,7,1,3,5] => [[1,2,4],[3,6,7],[5]] => 010100
[2,6,4,7,1,5,3] => [[1,2,4],[3,6],[5,7]] => 010101
[2,6,4,7,3,1,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,6,4,7,3,5,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,6,4,7,5,1,3] => [[1,2,4],[3,5],[6,7]] => 010110
[2,6,4,7,5,3,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[2,6,5,1,3,4,7] => [[1,2,6,7],[3,5],[4]] => 011000
[2,6,5,1,3,7,4] => [[1,2,6],[3,5,7],[4]] => 011001
[2,6,5,1,4,3,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[2,6,5,1,4,7,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[2,6,5,1,7,3,4] => [[1,2,5],[3,6,7],[4]] => 011010
[2,6,5,1,7,4,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,6,5,3,1,4,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,6,5,3,1,7,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,6,5,3,4,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,6,5,3,4,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,6,5,3,7,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,6,5,3,7,4,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,6,5,4,1,3,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[2,6,5,4,1,7,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,6,5,4,3,1,7] => [[1,2,7],[3],[4],[5],[6]] => 011110
[2,6,5,4,3,7,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[2,6,5,4,7,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,6,5,4,7,3,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[2,6,5,7,1,3,4] => [[1,2,4],[3,6,7],[5]] => 010100
[2,6,5,7,1,4,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,6,5,7,3,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,6,5,7,3,4,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,6,5,7,4,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,6,5,7,4,3,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[2,6,7,1,3,4,5] => [[1,2,3,7],[4,5,6]] => 001000
[2,6,7,1,3,5,4] => [[1,2,3],[4,5,6],[7]] => 001001
[2,6,7,1,4,3,5] => [[1,2,3],[4,5,7],[6]] => 001010
[2,6,7,1,4,5,3] => [[1,2,3],[4,5,6],[7]] => 001001
[2,6,7,1,5,3,4] => [[1,2,3],[4,5,7],[6]] => 001010
[2,6,7,1,5,4,3] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,6,7,3,1,4,5] => [[1,2,3,7],[4,6],[5]] => 001100
[2,6,7,3,1,5,4] => [[1,2,3],[4,6],[5,7]] => 001101
[2,6,7,3,4,1,5] => [[1,2,3,7],[4,5],[6]] => 001010
[2,6,7,3,4,5,1] => [[1,2,3,6],[4,5],[7]] => 001001
[2,6,7,3,5,1,4] => [[1,2,3],[4,5],[6,7]] => 001010
[2,6,7,3,5,4,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,6,7,4,1,3,5] => [[1,2,3],[4,6,7],[5]] => 001100
[2,6,7,4,1,5,3] => [[1,2,3],[4,6],[5,7]] => 001101
[2,6,7,4,3,1,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,6,7,4,3,5,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,6,7,4,5,1,3] => [[1,2,3],[4,5],[6,7]] => 001010
[2,6,7,4,5,3,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[2,6,7,5,1,3,4] => [[1,2,3],[4,6,7],[5]] => 001100
[2,6,7,5,1,4,3] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,6,7,5,3,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,6,7,5,3,4,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[2,6,7,5,4,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[2,6,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[2,7,1,3,4,5,6] => [[1,2,5,6,7],[3,4]] => 010000
[2,7,1,3,4,6,5] => [[1,2,5,6],[3,4],[7]] => 010001
[2,7,1,3,5,4,6] => [[1,2,5,7],[3,4],[6]] => 010010
[2,7,1,3,5,6,4] => [[1,2,5,6],[3,4],[7]] => 010001
[2,7,1,3,6,4,5] => [[1,2,5,7],[3,4],[6]] => 010010
[2,7,1,3,6,5,4] => [[1,2,5],[3,4],[6],[7]] => 010011
[2,7,1,4,3,5,6] => [[1,2,6,7],[3,4],[5]] => 010100
[2,7,1,4,3,6,5] => [[1,2,6],[3,4,7],[5]] => 010101
[2,7,1,4,5,3,6] => [[1,2,5,7],[3,4],[6]] => 010010
[2,7,1,4,5,6,3] => [[1,2,5,6],[3,4],[7]] => 010001
[2,7,1,4,6,3,5] => [[1,2,5],[3,4,7],[6]] => 010010
[2,7,1,4,6,5,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[2,7,1,5,3,4,6] => [[1,2,6,7],[3,4],[5]] => 010100
[2,7,1,5,3,6,4] => [[1,2,6],[3,4,7],[5]] => 010101
[2,7,1,5,4,3,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[2,7,1,5,4,6,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[2,7,1,5,6,3,4] => [[1,2,5],[3,4,7],[6]] => 010010
[2,7,1,5,6,4,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[2,7,1,6,3,4,5] => [[1,2,6,7],[3,4],[5]] => 010100
[2,7,1,6,3,5,4] => [[1,2,6],[3,4],[5],[7]] => 010101
[2,7,1,6,4,3,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[2,7,1,6,4,5,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[2,7,1,6,5,3,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[2,7,1,6,5,4,3] => [[1,2],[3,4],[5],[6],[7]] => 010111
[2,7,3,1,4,5,6] => [[1,2,5,6,7],[3],[4]] => 011000
[2,7,3,1,4,6,5] => [[1,2,5,6],[3,7],[4]] => 011001
[2,7,3,1,5,4,6] => [[1,2,5,7],[3,6],[4]] => 011010
[2,7,3,1,5,6,4] => [[1,2,5,6],[3,7],[4]] => 011001
[2,7,3,1,6,4,5] => [[1,2,5,7],[3,6],[4]] => 011010
[2,7,3,1,6,5,4] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,7,3,4,1,5,6] => [[1,2,4,6,7],[3],[5]] => 010100
[2,7,3,4,1,6,5] => [[1,2,4,6],[3,7],[5]] => 010101
[2,7,3,4,5,1,6] => [[1,2,4,5,7],[3],[6]] => 010010
[2,7,3,4,5,6,1] => [[1,2,4,5,6],[3],[7]] => 010001
[2,7,3,4,6,1,5] => [[1,2,4,5],[3,7],[6]] => 010010
[2,7,3,4,6,5,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,7,3,5,1,4,6] => [[1,2,4,7],[3,6],[5]] => 010100
[2,7,3,5,1,6,4] => [[1,2,4,6],[3,7],[5]] => 010101
[2,7,3,5,4,1,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,7,3,5,4,6,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,7,3,5,6,1,4] => [[1,2,4,5],[3,7],[6]] => 010010
[2,7,3,5,6,4,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,7,3,6,1,4,5] => [[1,2,4,7],[3,6],[5]] => 010100
[2,7,3,6,1,5,4] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,7,3,6,4,1,5] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,7,3,6,4,5,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,7,3,6,5,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,7,3,6,5,4,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[2,7,4,1,3,5,6] => [[1,2,6,7],[3,5],[4]] => 011000
[2,7,4,1,3,6,5] => [[1,2,6],[3,5,7],[4]] => 011001
[2,7,4,1,5,3,6] => [[1,2,5,7],[3,6],[4]] => 011010
[2,7,4,1,5,6,3] => [[1,2,5,6],[3,7],[4]] => 011001
[2,7,4,1,6,3,5] => [[1,2,5],[3,6,7],[4]] => 011010
[2,7,4,1,6,5,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,7,4,3,1,5,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,7,4,3,1,6,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,7,4,3,5,1,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,7,4,3,5,6,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,7,4,3,6,1,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,7,4,3,6,5,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,7,4,5,1,3,6] => [[1,2,4,7],[3,6],[5]] => 010100
[2,7,4,5,1,6,3] => [[1,2,4,6],[3,7],[5]] => 010101
[2,7,4,5,3,1,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[2,7,4,5,3,6,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[2,7,4,5,6,1,3] => [[1,2,4,5],[3,7],[6]] => 010010
[2,7,4,5,6,3,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[2,7,4,6,1,3,5] => [[1,2,4],[3,6,7],[5]] => 010100
[2,7,4,6,1,5,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,7,4,6,3,1,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,7,4,6,3,5,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,7,4,6,5,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,7,4,6,5,3,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[2,7,5,1,3,4,6] => [[1,2,6,7],[3,5],[4]] => 011000
[2,7,5,1,3,6,4] => [[1,2,6],[3,5,7],[4]] => 011001
[2,7,5,1,4,3,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[2,7,5,1,4,6,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[2,7,5,1,6,3,4] => [[1,2,5],[3,6,7],[4]] => 011010
[2,7,5,1,6,4,3] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,7,5,3,1,4,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,7,5,3,1,6,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,7,5,3,4,1,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,7,5,3,4,6,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,7,5,3,6,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,7,5,3,6,4,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[2,7,5,4,1,3,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[2,7,5,4,1,6,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,7,5,4,3,1,6] => [[1,2,7],[3],[4],[5],[6]] => 011110
[2,7,5,4,3,6,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[2,7,5,4,6,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,7,5,4,6,3,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[2,7,5,6,1,3,4] => [[1,2,4],[3,6,7],[5]] => 010100
[2,7,5,6,1,4,3] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,7,5,6,3,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,7,5,6,3,4,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[2,7,5,6,4,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[2,7,5,6,4,3,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[2,7,6,1,3,4,5] => [[1,2,6,7],[3,5],[4]] => 011000
[2,7,6,1,3,5,4] => [[1,2,6],[3,5],[4],[7]] => 011001
[2,7,6,1,4,3,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[2,7,6,1,4,5,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[2,7,6,1,5,3,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[2,7,6,1,5,4,3] => [[1,2],[3,5],[4],[6],[7]] => 011011
[2,7,6,3,1,4,5] => [[1,2,6,7],[3],[4],[5]] => 011100
[2,7,6,3,1,5,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,7,6,3,4,1,5] => [[1,2,5,7],[3],[4],[6]] => 011010
[2,7,6,3,4,5,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[2,7,6,3,5,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,7,6,3,5,4,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[2,7,6,4,1,3,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[2,7,6,4,1,5,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[2,7,6,4,3,1,5] => [[1,2,7],[3],[4],[5],[6]] => 011110
[2,7,6,4,3,5,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[2,7,6,4,5,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[2,7,6,4,5,3,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[2,7,6,5,1,3,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[2,7,6,5,1,4,3] => [[1,2],[3,6],[4],[5],[7]] => 011101
[2,7,6,5,3,1,4] => [[1,2,7],[3],[4],[5],[6]] => 011110
[2,7,6,5,3,4,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[2,7,6,5,4,1,3] => [[1,2],[3,7],[4],[5],[6]] => 011110
[2,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 100000
[3,1,2,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 100001
[3,1,2,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 100010
[3,1,2,4,6,7,5] => [[1,3,4,5,6],[2,7]] => 100001
[3,1,2,4,7,5,6] => [[1,3,4,5,7],[2,6]] => 100010
[3,1,2,4,7,6,5] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,2,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 100100
[3,1,2,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 100101
[3,1,2,5,6,4,7] => [[1,3,4,5,7],[2,6]] => 100010
[3,1,2,5,6,7,4] => [[1,3,4,5,6],[2,7]] => 100001
[3,1,2,5,7,4,6] => [[1,3,4,5],[2,6,7]] => 100010
[3,1,2,5,7,6,4] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,2,6,4,5,7] => [[1,3,4,6,7],[2,5]] => 100100
[3,1,2,6,4,7,5] => [[1,3,4,6],[2,5,7]] => 100101
[3,1,2,6,5,4,7] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,2,6,5,7,4] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,2,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 100010
[3,1,2,6,7,5,4] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,2,7,4,5,6] => [[1,3,4,6,7],[2,5]] => 100100
[3,1,2,7,4,6,5] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,2,7,5,4,6] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,2,7,5,6,4] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,2,7,6,4,5] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,2,7,6,5,4] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,1,4,2,5,6,7] => [[1,3,5,6,7],[2,4]] => 101000
[3,1,4,2,5,7,6] => [[1,3,5,6],[2,4,7]] => 101001
[3,1,4,2,6,5,7] => [[1,3,5,7],[2,4,6]] => 101010
[3,1,4,2,6,7,5] => [[1,3,5,6],[2,4,7]] => 101001
[3,1,4,2,7,5,6] => [[1,3,5,7],[2,4,6]] => 101010
[3,1,4,2,7,6,5] => [[1,3,5],[2,4,6],[7]] => 101011
[3,1,4,5,2,6,7] => [[1,3,4,6,7],[2,5]] => 100100
[3,1,4,5,2,7,6] => [[1,3,4,6],[2,5,7]] => 100101
[3,1,4,5,6,2,7] => [[1,3,4,5,7],[2,6]] => 100010
[3,1,4,5,6,7,2] => [[1,3,4,5,6],[2,7]] => 100001
[3,1,4,5,7,2,6] => [[1,3,4,5],[2,6,7]] => 100010
[3,1,4,5,7,6,2] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,4,6,2,5,7] => [[1,3,4,7],[2,5,6]] => 100100
[3,1,4,6,2,7,5] => [[1,3,4,6],[2,5,7]] => 100101
[3,1,4,6,5,2,7] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,4,6,5,7,2] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,4,6,7,2,5] => [[1,3,4,5],[2,6,7]] => 100010
[3,1,4,6,7,5,2] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,4,7,2,5,6] => [[1,3,4,7],[2,5,6]] => 100100
[3,1,4,7,2,6,5] => [[1,3,4],[2,5,6],[7]] => 100101
[3,1,4,7,5,2,6] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,4,7,5,6,2] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,4,7,6,2,5] => [[1,3,4],[2,5,7],[6]] => 100110
[3,1,4,7,6,5,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,1,5,2,4,6,7] => [[1,3,5,6,7],[2,4]] => 101000
[3,1,5,2,4,7,6] => [[1,3,5,6],[2,4,7]] => 101001
[3,1,5,2,6,4,7] => [[1,3,5,7],[2,4,6]] => 101010
[3,1,5,2,6,7,4] => [[1,3,5,6],[2,4,7]] => 101001
[3,1,5,2,7,4,6] => [[1,3,5,7],[2,4,6]] => 101010
[3,1,5,2,7,6,4] => [[1,3,5],[2,4,6],[7]] => 101011
[3,1,5,4,2,6,7] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,5,4,2,7,6] => [[1,3,6],[2,4,7],[5]] => 101101
[3,1,5,4,6,2,7] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,5,4,6,7,2] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,5,4,7,2,6] => [[1,3,5],[2,4,7],[6]] => 101010
[3,1,5,4,7,6,2] => [[1,3,5],[2,4,6],[7]] => 101011
[3,1,5,6,2,4,7] => [[1,3,4,7],[2,5,6]] => 100100
[3,1,5,6,2,7,4] => [[1,3,4,6],[2,5,7]] => 100101
[3,1,5,6,4,2,7] => [[1,3,4,7],[2,5],[6]] => 100110
[3,1,5,6,4,7,2] => [[1,3,4,6],[2,5],[7]] => 100101
[3,1,5,6,7,2,4] => [[1,3,4,5],[2,6,7]] => 100010
[3,1,5,6,7,4,2] => [[1,3,4,5],[2,6],[7]] => 100011
[3,1,5,7,2,4,6] => [[1,3,4,7],[2,5,6]] => 100100
[3,1,5,7,2,6,4] => [[1,3,4],[2,5,6],[7]] => 100101
[3,1,5,7,4,2,6] => [[1,3,4],[2,5,7],[6]] => 100110
[3,1,5,7,4,6,2] => [[1,3,4],[2,5,6],[7]] => 100101
[3,1,5,7,6,2,4] => [[1,3,4],[2,5,7],[6]] => 100110
[3,1,5,7,6,4,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,1,6,2,4,5,7] => [[1,3,5,6,7],[2,4]] => 101000
[3,1,6,2,4,7,5] => [[1,3,5,6],[2,4,7]] => 101001
[3,1,6,2,5,4,7] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,6,2,5,7,4] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,6,2,7,4,5] => [[1,3,5,7],[2,4,6]] => 101010
[3,1,6,2,7,5,4] => [[1,3,5],[2,4,6],[7]] => 101011
[3,1,6,4,2,5,7] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,6,4,2,7,5] => [[1,3,6],[2,4,7],[5]] => 101101
[3,1,6,4,5,2,7] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,6,4,5,7,2] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,6,4,7,2,5] => [[1,3,5],[2,4,7],[6]] => 101010
[3,1,6,4,7,5,2] => [[1,3,5],[2,4,6],[7]] => 101011
[3,1,6,5,2,4,7] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,6,5,2,7,4] => [[1,3,6],[2,4,7],[5]] => 101101
[3,1,6,5,4,2,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,1,6,5,4,7,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,1,6,5,7,2,4] => [[1,3,5],[2,4,7],[6]] => 101010
[3,1,6,5,7,4,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,1,6,7,2,4,5] => [[1,3,4,7],[2,5,6]] => 100100
[3,1,6,7,2,5,4] => [[1,3,4],[2,5,6],[7]] => 100101
[3,1,6,7,4,2,5] => [[1,3,4],[2,5,7],[6]] => 100110
[3,1,6,7,4,5,2] => [[1,3,4],[2,5,6],[7]] => 100101
[3,1,6,7,5,2,4] => [[1,3,4],[2,5,7],[6]] => 100110
[3,1,6,7,5,4,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,1,7,2,4,5,6] => [[1,3,5,6,7],[2,4]] => 101000
[3,1,7,2,4,6,5] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,7,2,5,4,6] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,7,2,5,6,4] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,7,2,6,4,5] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,7,2,6,5,4] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,1,7,4,2,5,6] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,7,4,2,6,5] => [[1,3,6],[2,4,7],[5]] => 101101
[3,1,7,4,5,2,6] => [[1,3,5,7],[2,4],[6]] => 101010
[3,1,7,4,5,6,2] => [[1,3,5,6],[2,4],[7]] => 101001
[3,1,7,4,6,2,5] => [[1,3,5],[2,4,7],[6]] => 101010
[3,1,7,4,6,5,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,1,7,5,2,4,6] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,7,5,2,6,4] => [[1,3,6],[2,4,7],[5]] => 101101
[3,1,7,5,4,2,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,1,7,5,4,6,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,1,7,5,6,2,4] => [[1,3,5],[2,4,7],[6]] => 101010
[3,1,7,5,6,4,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,1,7,6,2,4,5] => [[1,3,6,7],[2,4],[5]] => 101100
[3,1,7,6,2,5,4] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,1,7,6,4,2,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,1,7,6,4,5,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,1,7,6,5,2,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,1,7,6,5,4,2] => [[1,3],[2,4],[5],[6],[7]] => 101111
[3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[3,2,1,4,5,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[3,2,1,4,6,5,7] => [[1,4,5,7],[2,6],[3]] => 110010
[3,2,1,4,6,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[3,2,1,4,7,5,6] => [[1,4,5,7],[2,6],[3]] => 110010
[3,2,1,4,7,6,5] => [[1,4,5],[2,6],[3,7]] => 110011
[3,2,1,5,4,6,7] => [[1,4,6,7],[2,5],[3]] => 110100
[3,2,1,5,4,7,6] => [[1,4,6],[2,5,7],[3]] => 110101
[3,2,1,5,6,4,7] => [[1,4,5,7],[2,6],[3]] => 110010
[3,2,1,5,6,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[3,2,1,5,7,4,6] => [[1,4,5],[2,6,7],[3]] => 110010
[3,2,1,5,7,6,4] => [[1,4,5],[2,6],[3,7]] => 110011
[3,2,1,6,4,5,7] => [[1,4,6,7],[2,5],[3]] => 110100
[3,2,1,6,4,7,5] => [[1,4,6],[2,5,7],[3]] => 110101
[3,2,1,6,5,4,7] => [[1,4,7],[2,5],[3,6]] => 110110
[3,2,1,6,5,7,4] => [[1,4,6],[2,5],[3,7]] => 110101
[3,2,1,6,7,4,5] => [[1,4,5],[2,6,7],[3]] => 110010
[3,2,1,6,7,5,4] => [[1,4,5],[2,6],[3,7]] => 110011
[3,2,1,7,4,5,6] => [[1,4,6,7],[2,5],[3]] => 110100
[3,2,1,7,4,6,5] => [[1,4,6],[2,5],[3,7]] => 110101
[3,2,1,7,5,4,6] => [[1,4,7],[2,5],[3,6]] => 110110
[3,2,1,7,5,6,4] => [[1,4,6],[2,5],[3,7]] => 110101
[3,2,1,7,6,4,5] => [[1,4,7],[2,5],[3,6]] => 110110
[3,2,1,7,6,5,4] => [[1,4],[2,5],[3,6],[7]] => 110111
[3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[3,2,4,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[3,2,4,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 101010
[3,2,4,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[3,2,4,1,7,5,6] => [[1,3,5,7],[2,6],[4]] => 101010
[3,2,4,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 101011
[3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[3,2,4,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 100010
[3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 100001
[3,2,4,5,7,1,6] => [[1,3,4,5],[2,7],[6]] => 100010
[3,2,4,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => 100011
[3,2,4,6,1,5,7] => [[1,3,4,7],[2,6],[5]] => 100100
[3,2,4,6,1,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[3,2,4,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => 100110
[3,2,4,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => 100101
[3,2,4,6,7,1,5] => [[1,3,4,5],[2,7],[6]] => 100010
[3,2,4,6,7,5,1] => [[1,3,4,5],[2,6],[7]] => 100011
[3,2,4,7,1,5,6] => [[1,3,4,7],[2,6],[5]] => 100100
[3,2,4,7,1,6,5] => [[1,3,4],[2,6],[5,7]] => 100101
[3,2,4,7,5,1,6] => [[1,3,4,7],[2,5],[6]] => 100110
[3,2,4,7,5,6,1] => [[1,3,4,6],[2,5],[7]] => 100101
[3,2,4,7,6,1,5] => [[1,3,4],[2,5],[6,7]] => 100110
[3,2,4,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,2,5,1,4,6,7] => [[1,3,6,7],[2,5],[4]] => 101000
[3,2,5,1,4,7,6] => [[1,3,6],[2,5,7],[4]] => 101001
[3,2,5,1,6,4,7] => [[1,3,5,7],[2,6],[4]] => 101010
[3,2,5,1,6,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[3,2,5,1,7,4,6] => [[1,3,5],[2,6,7],[4]] => 101010
[3,2,5,1,7,6,4] => [[1,3,5],[2,6],[4,7]] => 101011
[3,2,5,4,1,6,7] => [[1,3,6,7],[2,4],[5]] => 101100
[3,2,5,4,1,7,6] => [[1,3,6],[2,4,7],[5]] => 101101
[3,2,5,4,6,1,7] => [[1,3,5,7],[2,4],[6]] => 101010
[3,2,5,4,6,7,1] => [[1,3,5,6],[2,4],[7]] => 101001
[3,2,5,4,7,1,6] => [[1,3,5],[2,4,7],[6]] => 101010
[3,2,5,4,7,6,1] => [[1,3,5],[2,4,6],[7]] => 101011
[3,2,5,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 100100
[3,2,5,6,1,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[3,2,5,6,4,1,7] => [[1,3,4,7],[2,5],[6]] => 100110
[3,2,5,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => 100101
[3,2,5,6,7,1,4] => [[1,3,4,5],[2,7],[6]] => 100010
[3,2,5,6,7,4,1] => [[1,3,4,5],[2,6],[7]] => 100011
[3,2,5,7,1,4,6] => [[1,3,4],[2,6,7],[5]] => 100100
[3,2,5,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 100101
[3,2,5,7,4,1,6] => [[1,3,4],[2,5,7],[6]] => 100110
[3,2,5,7,4,6,1] => [[1,3,4],[2,5,6],[7]] => 100101
[3,2,5,7,6,1,4] => [[1,3,4],[2,5],[6,7]] => 100110
[3,2,5,7,6,4,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,2,6,1,4,5,7] => [[1,3,6,7],[2,5],[4]] => 101000
[3,2,6,1,4,7,5] => [[1,3,6],[2,5,7],[4]] => 101001
[3,2,6,1,5,4,7] => [[1,3,7],[2,5],[4,6]] => 101010
[3,2,6,1,5,7,4] => [[1,3,6],[2,5],[4,7]] => 101001
[3,2,6,1,7,4,5] => [[1,3,5],[2,6,7],[4]] => 101010
[3,2,6,1,7,5,4] => [[1,3,5],[2,6],[4,7]] => 101011
[3,2,6,4,1,5,7] => [[1,3,6,7],[2,4],[5]] => 101100
[3,2,6,4,1,7,5] => [[1,3,6],[2,4,7],[5]] => 101101
[3,2,6,4,5,1,7] => [[1,3,5,7],[2,4],[6]] => 101010
[3,2,6,4,5,7,1] => [[1,3,5,6],[2,4],[7]] => 101001
[3,2,6,4,7,1,5] => [[1,3,5],[2,4,7],[6]] => 101010
[3,2,6,4,7,5,1] => [[1,3,5],[2,4,6],[7]] => 101011
[3,2,6,5,1,4,7] => [[1,3,7],[2,4],[5,6]] => 101100
[3,2,6,5,1,7,4] => [[1,3,6],[2,4],[5,7]] => 101101
[3,2,6,5,4,1,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,2,6,5,4,7,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,2,6,5,7,1,4] => [[1,3,5],[2,4],[6,7]] => 101010
[3,2,6,5,7,4,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,2,6,7,1,4,5] => [[1,3,4],[2,6,7],[5]] => 100100
[3,2,6,7,1,5,4] => [[1,3,4],[2,6],[5,7]] => 100101
[3,2,6,7,4,1,5] => [[1,3,4],[2,5,7],[6]] => 100110
[3,2,6,7,4,5,1] => [[1,3,4],[2,5,6],[7]] => 100101
[3,2,6,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 100110
[3,2,6,7,5,4,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[3,2,7,1,4,5,6] => [[1,3,6,7],[2,5],[4]] => 101000
[3,2,7,1,4,6,5] => [[1,3,6],[2,5],[4,7]] => 101001
[3,2,7,1,5,4,6] => [[1,3,7],[2,5],[4,6]] => 101010
[3,2,7,1,5,6,4] => [[1,3,6],[2,5],[4,7]] => 101001
[3,2,7,1,6,4,5] => [[1,3,7],[2,5],[4,6]] => 101010
[3,2,7,1,6,5,4] => [[1,3],[2,5],[4,6],[7]] => 101011
[3,2,7,4,1,5,6] => [[1,3,6,7],[2,4],[5]] => 101100
[3,2,7,4,1,6,5] => [[1,3,6],[2,4],[5,7]] => 101101
[3,2,7,4,5,1,6] => [[1,3,5,7],[2,4],[6]] => 101010
[3,2,7,4,5,6,1] => [[1,3,5,6],[2,4],[7]] => 101001
[3,2,7,4,6,1,5] => [[1,3,5],[2,4],[6,7]] => 101010
[3,2,7,4,6,5,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,2,7,5,1,4,6] => [[1,3,7],[2,4],[5,6]] => 101100
[3,2,7,5,1,6,4] => [[1,3,6],[2,4],[5,7]] => 101101
[3,2,7,5,4,1,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,2,7,5,4,6,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,2,7,5,6,1,4] => [[1,3,5],[2,4],[6,7]] => 101010
[3,2,7,5,6,4,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[3,2,7,6,1,4,5] => [[1,3,7],[2,4],[5,6]] => 101100
[3,2,7,6,1,5,4] => [[1,3],[2,4],[5,6],[7]] => 101101
[3,2,7,6,4,1,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[3,2,7,6,4,5,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[3,2,7,6,5,1,4] => [[1,3],[2,4],[5,7],[6]] => 101110
[3,2,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 010000
[3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => 010001
[3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => 010010
[3,4,1,2,6,7,5] => [[1,2,5,6],[3,4,7]] => 010001
[3,4,1,2,7,5,6] => [[1,2,5,7],[3,4,6]] => 010010
[3,4,1,2,7,6,5] => [[1,2,5],[3,4,6],[7]] => 010011
[3,4,1,5,2,6,7] => [[1,2,4,6,7],[3,5]] => 010100
[3,4,1,5,2,7,6] => [[1,2,4,6],[3,5,7]] => 010101
[3,4,1,5,6,2,7] => [[1,2,4,5,7],[3,6]] => 010010
[3,4,1,5,6,7,2] => [[1,2,4,5,6],[3,7]] => 010001
[3,4,1,5,7,2,6] => [[1,2,4,5],[3,6,7]] => 010010
[3,4,1,5,7,6,2] => [[1,2,4,5],[3,6],[7]] => 010011
[3,4,1,6,2,5,7] => [[1,2,4,7],[3,5,6]] => 010100
[3,4,1,6,2,7,5] => [[1,2,4,6],[3,5,7]] => 010101
[3,4,1,6,5,2,7] => [[1,2,4,7],[3,5],[6]] => 010110
[3,4,1,6,5,7,2] => [[1,2,4,6],[3,5],[7]] => 010101
[3,4,1,6,7,2,5] => [[1,2,4,5],[3,6,7]] => 010010
[3,4,1,6,7,5,2] => [[1,2,4,5],[3,6],[7]] => 010011
[3,4,1,7,2,5,6] => [[1,2,4,7],[3,5,6]] => 010100
[3,4,1,7,2,6,5] => [[1,2,4],[3,5,6],[7]] => 010101
[3,4,1,7,5,2,6] => [[1,2,4,7],[3,5],[6]] => 010110
[3,4,1,7,5,6,2] => [[1,2,4,6],[3,5],[7]] => 010101
[3,4,1,7,6,2,5] => [[1,2,4],[3,5,7],[6]] => 010110
[3,4,1,7,6,5,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => 011000
[3,4,2,1,5,7,6] => [[1,2,5,6],[3,7],[4]] => 011001
[3,4,2,1,6,5,7] => [[1,2,5,7],[3,6],[4]] => 011010
[3,4,2,1,6,7,5] => [[1,2,5,6],[3,7],[4]] => 011001
[3,4,2,1,7,5,6] => [[1,2,5,7],[3,6],[4]] => 011010
[3,4,2,1,7,6,5] => [[1,2,5],[3,6],[4,7]] => 011011
[3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => 010100
[3,4,2,5,1,7,6] => [[1,2,4,6],[3,7],[5]] => 010101
[3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => 010010
[3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => 010001
[3,4,2,5,7,1,6] => [[1,2,4,5],[3,7],[6]] => 010010
[3,4,2,5,7,6,1] => [[1,2,4,5],[3,6],[7]] => 010011
[3,4,2,6,1,5,7] => [[1,2,4,7],[3,6],[5]] => 010100
[3,4,2,6,1,7,5] => [[1,2,4,6],[3,7],[5]] => 010101
[3,4,2,6,5,1,7] => [[1,2,4,7],[3,5],[6]] => 010110
[3,4,2,6,5,7,1] => [[1,2,4,6],[3,5],[7]] => 010101
[3,4,2,6,7,1,5] => [[1,2,4,5],[3,7],[6]] => 010010
[3,4,2,6,7,5,1] => [[1,2,4,5],[3,6],[7]] => 010011
[3,4,2,7,1,5,6] => [[1,2,4,7],[3,6],[5]] => 010100
[3,4,2,7,1,6,5] => [[1,2,4],[3,6],[5,7]] => 010101
[3,4,2,7,5,1,6] => [[1,2,4,7],[3,5],[6]] => 010110
[3,4,2,7,5,6,1] => [[1,2,4,6],[3,5],[7]] => 010101
[3,4,2,7,6,1,5] => [[1,2,4],[3,5],[6,7]] => 010110
[3,4,2,7,6,5,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => 001000
[3,4,5,1,2,7,6] => [[1,2,3,6],[4,5,7]] => 001001
[3,4,5,1,6,2,7] => [[1,2,3,5,7],[4,6]] => 001010
[3,4,5,1,6,7,2] => [[1,2,3,5,6],[4,7]] => 001001
[3,4,5,1,7,2,6] => [[1,2,3,5],[4,6,7]] => 001010
[3,4,5,1,7,6,2] => [[1,2,3,5],[4,6],[7]] => 001011
[3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => 001100
[3,4,5,2,1,7,6] => [[1,2,3,6],[4,7],[5]] => 001101
[3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => 001010
[3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => 001001
[3,4,5,2,7,1,6] => [[1,2,3,5],[4,7],[6]] => 001010
[3,4,5,2,7,6,1] => [[1,2,3,5],[4,6],[7]] => 001011
[3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => 000100
[3,4,5,6,1,7,2] => [[1,2,3,4,6],[5,7]] => 000101
[3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => 000110
[3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => 000101
[3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => 000010
[3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => 000011
[3,4,5,7,1,2,6] => [[1,2,3,4],[5,6,7]] => 000100
[3,4,5,7,1,6,2] => [[1,2,3,4],[5,6],[7]] => 000101
[3,4,5,7,2,1,6] => [[1,2,3,4],[5,7],[6]] => 000110
[3,4,5,7,2,6,1] => [[1,2,3,4],[5,6],[7]] => 000101
[3,4,5,7,6,1,2] => [[1,2,3,4],[5,7],[6]] => 000110
[3,4,5,7,6,2,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[3,4,6,1,2,5,7] => [[1,2,3,7],[4,5,6]] => 001000
[3,4,6,1,2,7,5] => [[1,2,3,6],[4,5,7]] => 001001
[3,4,6,1,5,2,7] => [[1,2,3,7],[4,5],[6]] => 001010
[3,4,6,1,5,7,2] => [[1,2,3,6],[4,5],[7]] => 001001
[3,4,6,1,7,2,5] => [[1,2,3,5],[4,6,7]] => 001010
[3,4,6,1,7,5,2] => [[1,2,3,5],[4,6],[7]] => 001011
[3,4,6,2,1,5,7] => [[1,2,3,7],[4,6],[5]] => 001100
[3,4,6,2,1,7,5] => [[1,2,3,6],[4,7],[5]] => 001101
[3,4,6,2,5,1,7] => [[1,2,3,7],[4,5],[6]] => 001010
[3,4,6,2,5,7,1] => [[1,2,3,6],[4,5],[7]] => 001001
[3,4,6,2,7,1,5] => [[1,2,3,5],[4,7],[6]] => 001010
[3,4,6,2,7,5,1] => [[1,2,3,5],[4,6],[7]] => 001011
[3,4,6,5,1,2,7] => [[1,2,3,7],[4,6],[5]] => 001100
[3,4,6,5,1,7,2] => [[1,2,3,6],[4,7],[5]] => 001101
[3,4,6,5,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[3,4,6,5,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[3,4,6,5,7,1,2] => [[1,2,3,5],[4,7],[6]] => 001010
[3,4,6,5,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[3,4,6,7,1,2,5] => [[1,2,3,4],[5,6,7]] => 000100
[3,4,6,7,1,5,2] => [[1,2,3,4],[5,6],[7]] => 000101
[3,4,6,7,2,1,5] => [[1,2,3,4],[5,7],[6]] => 000110
[3,4,6,7,2,5,1] => [[1,2,3,4],[5,6],[7]] => 000101
[3,4,6,7,5,1,2] => [[1,2,3,4],[5,7],[6]] => 000110
[3,4,6,7,5,2,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[3,4,7,1,2,5,6] => [[1,2,3,7],[4,5,6]] => 001000
[3,4,7,1,2,6,5] => [[1,2,3],[4,5,6],[7]] => 001001
[3,4,7,1,5,2,6] => [[1,2,3,7],[4,5],[6]] => 001010
[3,4,7,1,5,6,2] => [[1,2,3,6],[4,5],[7]] => 001001
[3,4,7,1,6,2,5] => [[1,2,3],[4,5,7],[6]] => 001010
[3,4,7,1,6,5,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,4,7,2,1,5,6] => [[1,2,3,7],[4,6],[5]] => 001100
[3,4,7,2,1,6,5] => [[1,2,3],[4,6],[5,7]] => 001101
[3,4,7,2,5,1,6] => [[1,2,3,7],[4,5],[6]] => 001010
[3,4,7,2,5,6,1] => [[1,2,3,6],[4,5],[7]] => 001001
[3,4,7,2,6,1,5] => [[1,2,3],[4,5],[6,7]] => 001010
[3,4,7,2,6,5,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,4,7,5,1,2,6] => [[1,2,3,7],[4,6],[5]] => 001100
[3,4,7,5,1,6,2] => [[1,2,3,6],[4,7],[5]] => 001101
[3,4,7,5,2,1,6] => [[1,2,3,7],[4],[5],[6]] => 001110
[3,4,7,5,2,6,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[3,4,7,5,6,1,2] => [[1,2,3,5],[4,7],[6]] => 001010
[3,4,7,5,6,2,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[3,4,7,6,1,2,5] => [[1,2,3],[4,6,7],[5]] => 001100
[3,4,7,6,1,5,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,4,7,6,2,1,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,4,7,6,2,5,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,4,7,6,5,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,4,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[3,5,1,2,4,6,7] => [[1,2,5,6,7],[3,4]] => 010000
[3,5,1,2,4,7,6] => [[1,2,5,6],[3,4,7]] => 010001
[3,5,1,2,6,4,7] => [[1,2,5,7],[3,4,6]] => 010010
[3,5,1,2,6,7,4] => [[1,2,5,6],[3,4,7]] => 010001
[3,5,1,2,7,4,6] => [[1,2,5,7],[3,4,6]] => 010010
[3,5,1,2,7,6,4] => [[1,2,5],[3,4,6],[7]] => 010011
[3,5,1,4,2,6,7] => [[1,2,6,7],[3,4],[5]] => 010100
[3,5,1,4,2,7,6] => [[1,2,6],[3,4,7],[5]] => 010101
[3,5,1,4,6,2,7] => [[1,2,5,7],[3,4],[6]] => 010010
[3,5,1,4,6,7,2] => [[1,2,5,6],[3,4],[7]] => 010001
[3,5,1,4,7,2,6] => [[1,2,5],[3,4,7],[6]] => 010010
[3,5,1,4,7,6,2] => [[1,2,5],[3,4,6],[7]] => 010011
[3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => 010100
[3,5,1,6,2,7,4] => [[1,2,4,6],[3,5,7]] => 010101
[3,5,1,6,4,2,7] => [[1,2,4,7],[3,5],[6]] => 010110
[3,5,1,6,4,7,2] => [[1,2,4,6],[3,5],[7]] => 010101
[3,5,1,6,7,2,4] => [[1,2,4,5],[3,6,7]] => 010010
[3,5,1,6,7,4,2] => [[1,2,4,5],[3,6],[7]] => 010011
[3,5,1,7,2,4,6] => [[1,2,4,7],[3,5,6]] => 010100
[3,5,1,7,2,6,4] => [[1,2,4],[3,5,6],[7]] => 010101
[3,5,1,7,4,2,6] => [[1,2,4],[3,5,7],[6]] => 010110
[3,5,1,7,4,6,2] => [[1,2,4],[3,5,6],[7]] => 010101
[3,5,1,7,6,2,4] => [[1,2,4],[3,5,7],[6]] => 010110
[3,5,1,7,6,4,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,5,2,1,4,6,7] => [[1,2,6,7],[3,5],[4]] => 011000
[3,5,2,1,4,7,6] => [[1,2,6],[3,5,7],[4]] => 011001
[3,5,2,1,6,4,7] => [[1,2,5,7],[3,6],[4]] => 011010
[3,5,2,1,6,7,4] => [[1,2,5,6],[3,7],[4]] => 011001
[3,5,2,1,7,4,6] => [[1,2,5],[3,6,7],[4]] => 011010
[3,5,2,1,7,6,4] => [[1,2,5],[3,6],[4,7]] => 011011
[3,5,2,4,1,6,7] => [[1,2,6,7],[3,4],[5]] => 010100
[3,5,2,4,1,7,6] => [[1,2,6],[3,4,7],[5]] => 010101
[3,5,2,4,6,1,7] => [[1,2,5,7],[3,4],[6]] => 010010
[3,5,2,4,6,7,1] => [[1,2,5,6],[3,4],[7]] => 010001
[3,5,2,4,7,1,6] => [[1,2,5],[3,4,7],[6]] => 010010
[3,5,2,4,7,6,1] => [[1,2,5],[3,4,6],[7]] => 010011
[3,5,2,6,1,4,7] => [[1,2,4,7],[3,6],[5]] => 010100
[3,5,2,6,1,7,4] => [[1,2,4,6],[3,7],[5]] => 010101
[3,5,2,6,4,1,7] => [[1,2,4,7],[3,5],[6]] => 010110
[3,5,2,6,4,7,1] => [[1,2,4,6],[3,5],[7]] => 010101
[3,5,2,6,7,1,4] => [[1,2,4,5],[3,7],[6]] => 010010
[3,5,2,6,7,4,1] => [[1,2,4,5],[3,6],[7]] => 010011
[3,5,2,7,1,4,6] => [[1,2,4],[3,6,7],[5]] => 010100
[3,5,2,7,1,6,4] => [[1,2,4],[3,6],[5,7]] => 010101
[3,5,2,7,4,1,6] => [[1,2,4],[3,5,7],[6]] => 010110
[3,5,2,7,4,6,1] => [[1,2,4],[3,5,6],[7]] => 010101
[3,5,2,7,6,1,4] => [[1,2,4],[3,5],[6,7]] => 010110
[3,5,2,7,6,4,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,5,4,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => 011000
[3,5,4,1,2,7,6] => [[1,2,6],[3,5,7],[4]] => 011001
[3,5,4,1,6,2,7] => [[1,2,5,7],[3,6],[4]] => 011010
[3,5,4,1,6,7,2] => [[1,2,5,6],[3,7],[4]] => 011001
[3,5,4,1,7,2,6] => [[1,2,5],[3,6,7],[4]] => 011010
[3,5,4,1,7,6,2] => [[1,2,5],[3,6],[4,7]] => 011011
[3,5,4,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[3,5,4,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,5,4,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[3,5,4,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[3,5,4,2,7,1,6] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,5,4,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,5,4,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => 010100
[3,5,4,6,1,7,2] => [[1,2,4,6],[3,7],[5]] => 010101
[3,5,4,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[3,5,4,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[3,5,4,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => 010010
[3,5,4,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[3,5,4,7,1,2,6] => [[1,2,4],[3,6,7],[5]] => 010100
[3,5,4,7,1,6,2] => [[1,2,4],[3,6],[5,7]] => 010101
[3,5,4,7,2,1,6] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,5,4,7,2,6,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,5,4,7,6,1,2] => [[1,2,4],[3,5],[6,7]] => 010110
[3,5,4,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,5,6,1,2,4,7] => [[1,2,3,7],[4,5,6]] => 001000
[3,5,6,1,2,7,4] => [[1,2,3,6],[4,5,7]] => 001001
[3,5,6,1,4,2,7] => [[1,2,3,7],[4,5],[6]] => 001010
[3,5,6,1,4,7,2] => [[1,2,3,6],[4,5],[7]] => 001001
[3,5,6,1,7,2,4] => [[1,2,3,5],[4,6,7]] => 001010
[3,5,6,1,7,4,2] => [[1,2,3,5],[4,6],[7]] => 001011
[3,5,6,2,1,4,7] => [[1,2,3,7],[4,6],[5]] => 001100
[3,5,6,2,1,7,4] => [[1,2,3,6],[4,7],[5]] => 001101
[3,5,6,2,4,1,7] => [[1,2,3,7],[4,5],[6]] => 001010
[3,5,6,2,4,7,1] => [[1,2,3,6],[4,5],[7]] => 001001
[3,5,6,2,7,1,4] => [[1,2,3,5],[4,7],[6]] => 001010
[3,5,6,2,7,4,1] => [[1,2,3,5],[4,6],[7]] => 001011
[3,5,6,4,1,2,7] => [[1,2,3,7],[4,6],[5]] => 001100
[3,5,6,4,1,7,2] => [[1,2,3,6],[4,7],[5]] => 001101
[3,5,6,4,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[3,5,6,4,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[3,5,6,4,7,1,2] => [[1,2,3,5],[4,7],[6]] => 001010
[3,5,6,4,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[3,5,6,7,1,2,4] => [[1,2,3,4],[5,6,7]] => 000100
[3,5,6,7,1,4,2] => [[1,2,3,4],[5,6],[7]] => 000101
[3,5,6,7,2,1,4] => [[1,2,3,4],[5,7],[6]] => 000110
[3,5,6,7,2,4,1] => [[1,2,3,4],[5,6],[7]] => 000101
[3,5,6,7,4,1,2] => [[1,2,3,4],[5,7],[6]] => 000110
[3,5,6,7,4,2,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[3,5,7,1,2,4,6] => [[1,2,3,7],[4,5,6]] => 001000
[3,5,7,1,2,6,4] => [[1,2,3],[4,5,6],[7]] => 001001
[3,5,7,1,4,2,6] => [[1,2,3],[4,5,7],[6]] => 001010
[3,5,7,1,4,6,2] => [[1,2,3],[4,5,6],[7]] => 001001
[3,5,7,1,6,2,4] => [[1,2,3],[4,5,7],[6]] => 001010
[3,5,7,1,6,4,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,5,7,2,1,4,6] => [[1,2,3],[4,6,7],[5]] => 001100
[3,5,7,2,1,6,4] => [[1,2,3],[4,6],[5,7]] => 001101
[3,5,7,2,4,1,6] => [[1,2,3],[4,5,7],[6]] => 001010
[3,5,7,2,4,6,1] => [[1,2,3],[4,5,6],[7]] => 001001
[3,5,7,2,6,1,4] => [[1,2,3],[4,5],[6,7]] => 001010
[3,5,7,2,6,4,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,5,7,4,1,2,6] => [[1,2,3],[4,6,7],[5]] => 001100
[3,5,7,4,1,6,2] => [[1,2,3],[4,6],[5,7]] => 001101
[3,5,7,4,2,1,6] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,5,7,4,2,6,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,5,7,4,6,1,2] => [[1,2,3],[4,5],[6,7]] => 001010
[3,5,7,4,6,2,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,5,7,6,1,2,4] => [[1,2,3],[4,6,7],[5]] => 001100
[3,5,7,6,1,4,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,5,7,6,2,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,5,7,6,2,4,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,5,7,6,4,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,5,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[3,6,1,2,4,5,7] => [[1,2,5,6,7],[3,4]] => 010000
[3,6,1,2,4,7,5] => [[1,2,5,6],[3,4,7]] => 010001
[3,6,1,2,5,4,7] => [[1,2,5,7],[3,4],[6]] => 010010
[3,6,1,2,5,7,4] => [[1,2,5,6],[3,4],[7]] => 010001
[3,6,1,2,7,4,5] => [[1,2,5,7],[3,4,6]] => 010010
[3,6,1,2,7,5,4] => [[1,2,5],[3,4,6],[7]] => 010011
[3,6,1,4,2,5,7] => [[1,2,6,7],[3,4],[5]] => 010100
[3,6,1,4,2,7,5] => [[1,2,6],[3,4,7],[5]] => 010101
[3,6,1,4,5,2,7] => [[1,2,5,7],[3,4],[6]] => 010010
[3,6,1,4,5,7,2] => [[1,2,5,6],[3,4],[7]] => 010001
[3,6,1,4,7,2,5] => [[1,2,5],[3,4,7],[6]] => 010010
[3,6,1,4,7,5,2] => [[1,2,5],[3,4,6],[7]] => 010011
[3,6,1,5,2,4,7] => [[1,2,6,7],[3,4],[5]] => 010100
[3,6,1,5,2,7,4] => [[1,2,6],[3,4,7],[5]] => 010101
[3,6,1,5,4,2,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,6,1,5,4,7,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,6,1,5,7,2,4] => [[1,2,5],[3,4,7],[6]] => 010010
[3,6,1,5,7,4,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,6,1,7,2,4,5] => [[1,2,4,7],[3,5,6]] => 010100
[3,6,1,7,2,5,4] => [[1,2,4],[3,5,6],[7]] => 010101
[3,6,1,7,4,2,5] => [[1,2,4],[3,5,7],[6]] => 010110
[3,6,1,7,4,5,2] => [[1,2,4],[3,5,6],[7]] => 010101
[3,6,1,7,5,2,4] => [[1,2,4],[3,5,7],[6]] => 010110
[3,6,1,7,5,4,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,6,2,1,4,5,7] => [[1,2,6,7],[3,5],[4]] => 011000
[3,6,2,1,4,7,5] => [[1,2,6],[3,5,7],[4]] => 011001
[3,6,2,1,5,4,7] => [[1,2,7],[3,5],[4,6]] => 011010
[3,6,2,1,5,7,4] => [[1,2,6],[3,5],[4,7]] => 011001
[3,6,2,1,7,4,5] => [[1,2,5],[3,6,7],[4]] => 011010
[3,6,2,1,7,5,4] => [[1,2,5],[3,6],[4,7]] => 011011
[3,6,2,4,1,5,7] => [[1,2,6,7],[3,4],[5]] => 010100
[3,6,2,4,1,7,5] => [[1,2,6],[3,4,7],[5]] => 010101
[3,6,2,4,5,1,7] => [[1,2,5,7],[3,4],[6]] => 010010
[3,6,2,4,5,7,1] => [[1,2,5,6],[3,4],[7]] => 010001
[3,6,2,4,7,1,5] => [[1,2,5],[3,4,7],[6]] => 010010
[3,6,2,4,7,5,1] => [[1,2,5],[3,4,6],[7]] => 010011
[3,6,2,5,1,4,7] => [[1,2,7],[3,4],[5,6]] => 010100
[3,6,2,5,1,7,4] => [[1,2,6],[3,4],[5,7]] => 010101
[3,6,2,5,4,1,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,6,2,5,4,7,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,6,2,5,7,1,4] => [[1,2,5],[3,4],[6,7]] => 010010
[3,6,2,5,7,4,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,6,2,7,1,4,5] => [[1,2,4],[3,6,7],[5]] => 010100
[3,6,2,7,1,5,4] => [[1,2,4],[3,6],[5,7]] => 010101
[3,6,2,7,4,1,5] => [[1,2,4],[3,5,7],[6]] => 010110
[3,6,2,7,4,5,1] => [[1,2,4],[3,5,6],[7]] => 010101
[3,6,2,7,5,1,4] => [[1,2,4],[3,5],[6,7]] => 010110
[3,6,2,7,5,4,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,6,4,1,2,5,7] => [[1,2,6,7],[3,5],[4]] => 011000
[3,6,4,1,2,7,5] => [[1,2,6],[3,5,7],[4]] => 011001
[3,6,4,1,5,2,7] => [[1,2,5,7],[3,6],[4]] => 011010
[3,6,4,1,5,7,2] => [[1,2,5,6],[3,7],[4]] => 011001
[3,6,4,1,7,2,5] => [[1,2,5],[3,6,7],[4]] => 011010
[3,6,4,1,7,5,2] => [[1,2,5],[3,6],[4,7]] => 011011
[3,6,4,2,1,5,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[3,6,4,2,1,7,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,6,4,2,5,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[3,6,4,2,5,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[3,6,4,2,7,1,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,6,4,2,7,5,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,6,4,5,1,2,7] => [[1,2,4,7],[3,6],[5]] => 010100
[3,6,4,5,1,7,2] => [[1,2,4,6],[3,7],[5]] => 010101
[3,6,4,5,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[3,6,4,5,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[3,6,4,5,7,1,2] => [[1,2,4,5],[3,7],[6]] => 010010
[3,6,4,5,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[3,6,4,7,1,2,5] => [[1,2,4],[3,6,7],[5]] => 010100
[3,6,4,7,1,5,2] => [[1,2,4],[3,6],[5,7]] => 010101
[3,6,4,7,2,1,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,6,4,7,2,5,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,6,4,7,5,1,2] => [[1,2,4],[3,5],[6,7]] => 010110
[3,6,4,7,5,2,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[3,6,5,1,2,4,7] => [[1,2,6,7],[3,5],[4]] => 011000
[3,6,5,1,2,7,4] => [[1,2,6],[3,5,7],[4]] => 011001
[3,6,5,1,4,2,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,6,5,1,4,7,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,6,5,1,7,2,4] => [[1,2,5],[3,6,7],[4]] => 011010
[3,6,5,1,7,4,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,6,5,2,1,4,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,6,5,2,1,7,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,6,5,2,4,1,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,6,5,2,4,7,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,6,5,2,7,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,6,5,2,7,4,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,6,5,4,1,2,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,6,5,4,1,7,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,6,5,4,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 011110
[3,6,5,4,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[3,6,5,4,7,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,6,5,4,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[3,6,5,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 010100
[3,6,5,7,1,4,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,6,5,7,2,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,6,5,7,2,4,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,6,5,7,4,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,6,5,7,4,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[3,6,7,1,2,4,5] => [[1,2,3,7],[4,5,6]] => 001000
[3,6,7,1,2,5,4] => [[1,2,3],[4,5,6],[7]] => 001001
[3,6,7,1,4,2,5] => [[1,2,3],[4,5,7],[6]] => 001010
[3,6,7,1,4,5,2] => [[1,2,3],[4,5,6],[7]] => 001001
[3,6,7,1,5,2,4] => [[1,2,3],[4,5,7],[6]] => 001010
[3,6,7,1,5,4,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,6,7,2,1,4,5] => [[1,2,3],[4,6,7],[5]] => 001100
[3,6,7,2,1,5,4] => [[1,2,3],[4,6],[5,7]] => 001101
[3,6,7,2,4,1,5] => [[1,2,3],[4,5,7],[6]] => 001010
[3,6,7,2,4,5,1] => [[1,2,3],[4,5,6],[7]] => 001001
[3,6,7,2,5,1,4] => [[1,2,3],[4,5],[6,7]] => 001010
[3,6,7,2,5,4,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,6,7,4,1,2,5] => [[1,2,3],[4,6,7],[5]] => 001100
[3,6,7,4,1,5,2] => [[1,2,3],[4,6],[5,7]] => 001101
[3,6,7,4,2,1,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,6,7,4,2,5,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,6,7,4,5,1,2] => [[1,2,3],[4,5],[6,7]] => 001010
[3,6,7,4,5,2,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[3,6,7,5,1,2,4] => [[1,2,3],[4,6,7],[5]] => 001100
[3,6,7,5,1,4,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,6,7,5,2,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,6,7,5,2,4,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[3,6,7,5,4,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[3,6,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[3,7,1,2,4,5,6] => [[1,2,5,6,7],[3,4]] => 010000
[3,7,1,2,4,6,5] => [[1,2,5,6],[3,4],[7]] => 010001
[3,7,1,2,5,4,6] => [[1,2,5,7],[3,4],[6]] => 010010
[3,7,1,2,5,6,4] => [[1,2,5,6],[3,4],[7]] => 010001
[3,7,1,2,6,4,5] => [[1,2,5,7],[3,4],[6]] => 010010
[3,7,1,2,6,5,4] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,7,1,4,2,5,6] => [[1,2,6,7],[3,4],[5]] => 010100
[3,7,1,4,2,6,5] => [[1,2,6],[3,4,7],[5]] => 010101
[3,7,1,4,5,2,6] => [[1,2,5,7],[3,4],[6]] => 010010
[3,7,1,4,5,6,2] => [[1,2,5,6],[3,4],[7]] => 010001
[3,7,1,4,6,2,5] => [[1,2,5],[3,4,7],[6]] => 010010
[3,7,1,4,6,5,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,7,1,5,2,4,6] => [[1,2,6,7],[3,4],[5]] => 010100
[3,7,1,5,2,6,4] => [[1,2,6],[3,4,7],[5]] => 010101
[3,7,1,5,4,2,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,7,1,5,4,6,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,7,1,5,6,2,4] => [[1,2,5],[3,4,7],[6]] => 010010
[3,7,1,5,6,4,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,7,1,6,2,4,5] => [[1,2,6,7],[3,4],[5]] => 010100
[3,7,1,6,2,5,4] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,7,1,6,4,2,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,7,1,6,4,5,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,7,1,6,5,2,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,7,1,6,5,4,2] => [[1,2],[3,4],[5],[6],[7]] => 010111
[3,7,2,1,4,5,6] => [[1,2,6,7],[3,5],[4]] => 011000
[3,7,2,1,4,6,5] => [[1,2,6],[3,5],[4,7]] => 011001
[3,7,2,1,5,4,6] => [[1,2,7],[3,5],[4,6]] => 011010
[3,7,2,1,5,6,4] => [[1,2,6],[3,5],[4,7]] => 011001
[3,7,2,1,6,4,5] => [[1,2,7],[3,5],[4,6]] => 011010
[3,7,2,1,6,5,4] => [[1,2],[3,5],[4,6],[7]] => 011011
[3,7,2,4,1,5,6] => [[1,2,6,7],[3,4],[5]] => 010100
[3,7,2,4,1,6,5] => [[1,2,6],[3,4],[5,7]] => 010101
[3,7,2,4,5,1,6] => [[1,2,5,7],[3,4],[6]] => 010010
[3,7,2,4,5,6,1] => [[1,2,5,6],[3,4],[7]] => 010001
[3,7,2,4,6,1,5] => [[1,2,5],[3,4],[6,7]] => 010010
[3,7,2,4,6,5,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,7,2,5,1,4,6] => [[1,2,7],[3,4],[5,6]] => 010100
[3,7,2,5,1,6,4] => [[1,2,6],[3,4],[5,7]] => 010101
[3,7,2,5,4,1,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,7,2,5,4,6,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,7,2,5,6,1,4] => [[1,2,5],[3,4],[6,7]] => 010010
[3,7,2,5,6,4,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[3,7,2,6,1,4,5] => [[1,2,7],[3,4],[5,6]] => 010100
[3,7,2,6,1,5,4] => [[1,2],[3,4],[5,6],[7]] => 010101
[3,7,2,6,4,1,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[3,7,2,6,4,5,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[3,7,2,6,5,1,4] => [[1,2],[3,4],[5,7],[6]] => 010110
[3,7,2,6,5,4,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[3,7,4,1,2,5,6] => [[1,2,6,7],[3,5],[4]] => 011000
[3,7,4,1,2,6,5] => [[1,2,6],[3,5,7],[4]] => 011001
[3,7,4,1,5,2,6] => [[1,2,5,7],[3,6],[4]] => 011010
[3,7,4,1,5,6,2] => [[1,2,5,6],[3,7],[4]] => 011001
[3,7,4,1,6,2,5] => [[1,2,5],[3,6,7],[4]] => 011010
[3,7,4,1,6,5,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,7,4,2,1,5,6] => [[1,2,6,7],[3],[4],[5]] => 011100
[3,7,4,2,1,6,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,7,4,2,5,1,6] => [[1,2,5,7],[3],[4],[6]] => 011010
[3,7,4,2,5,6,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[3,7,4,2,6,1,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,7,4,2,6,5,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,7,4,5,1,2,6] => [[1,2,4,7],[3,6],[5]] => 010100
[3,7,4,5,1,6,2] => [[1,2,4,6],[3,7],[5]] => 010101
[3,7,4,5,2,1,6] => [[1,2,4,7],[3],[5],[6]] => 010110
[3,7,4,5,2,6,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[3,7,4,5,6,1,2] => [[1,2,4,5],[3,7],[6]] => 010010
[3,7,4,5,6,2,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[3,7,4,6,1,2,5] => [[1,2,4],[3,6,7],[5]] => 010100
[3,7,4,6,1,5,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,7,4,6,2,1,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,7,4,6,2,5,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,7,4,6,5,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,7,4,6,5,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[3,7,5,1,2,4,6] => [[1,2,6,7],[3,5],[4]] => 011000
[3,7,5,1,2,6,4] => [[1,2,6],[3,5,7],[4]] => 011001
[3,7,5,1,4,2,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,7,5,1,4,6,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,7,5,1,6,2,4] => [[1,2,5],[3,6,7],[4]] => 011010
[3,7,5,1,6,4,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,7,5,2,1,4,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,7,5,2,1,6,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,7,5,2,4,1,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,7,5,2,4,6,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,7,5,2,6,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,7,5,2,6,4,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[3,7,5,4,1,2,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,7,5,4,1,6,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,7,5,4,2,1,6] => [[1,2,7],[3],[4],[5],[6]] => 011110
[3,7,5,4,2,6,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[3,7,5,4,6,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,7,5,4,6,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[3,7,5,6,1,2,4] => [[1,2,4],[3,6,7],[5]] => 010100
[3,7,5,6,1,4,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,7,5,6,2,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,7,5,6,2,4,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[3,7,5,6,4,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[3,7,5,6,4,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[3,7,6,1,2,4,5] => [[1,2,6,7],[3,5],[4]] => 011000
[3,7,6,1,2,5,4] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,7,6,1,4,2,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,7,6,1,4,5,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,7,6,1,5,2,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,7,6,1,5,4,2] => [[1,2],[3,5],[4],[6],[7]] => 011011
[3,7,6,2,1,4,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,7,6,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 011101
[3,7,6,2,4,1,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[3,7,6,2,4,5,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[3,7,6,2,5,1,4] => [[1,2],[3,5],[4,7],[6]] => 011010
[3,7,6,2,5,4,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[3,7,6,4,1,2,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,7,6,4,1,5,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[3,7,6,4,2,1,5] => [[1,2,7],[3],[4],[5],[6]] => 011110
[3,7,6,4,2,5,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[3,7,6,4,5,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[3,7,6,4,5,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[3,7,6,5,1,2,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[3,7,6,5,1,4,2] => [[1,2],[3,6],[4],[5],[7]] => 011101
[3,7,6,5,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 011110
[3,7,6,5,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[3,7,6,5,4,1,2] => [[1,2],[3,7],[4],[5],[6]] => 011110
[3,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => 100000
[4,1,2,3,5,7,6] => [[1,3,4,5,6],[2,7]] => 100001
[4,1,2,3,6,5,7] => [[1,3,4,5,7],[2,6]] => 100010
[4,1,2,3,6,7,5] => [[1,3,4,5,6],[2,7]] => 100001
[4,1,2,3,7,5,6] => [[1,3,4,5,7],[2,6]] => 100010
[4,1,2,3,7,6,5] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,2,5,3,6,7] => [[1,3,4,6,7],[2,5]] => 100100
[4,1,2,5,3,7,6] => [[1,3,4,6],[2,5,7]] => 100101
[4,1,2,5,6,3,7] => [[1,3,4,5,7],[2,6]] => 100010
[4,1,2,5,6,7,3] => [[1,3,4,5,6],[2,7]] => 100001
[4,1,2,5,7,3,6] => [[1,3,4,5],[2,6,7]] => 100010
[4,1,2,5,7,6,3] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,2,6,3,5,7] => [[1,3,4,6,7],[2,5]] => 100100
[4,1,2,6,3,7,5] => [[1,3,4,6],[2,5,7]] => 100101
[4,1,2,6,5,3,7] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,2,6,5,7,3] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,2,6,7,3,5] => [[1,3,4,5],[2,6,7]] => 100010
[4,1,2,6,7,5,3] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,2,7,3,5,6] => [[1,3,4,6,7],[2,5]] => 100100
[4,1,2,7,3,6,5] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,2,7,5,3,6] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,2,7,5,6,3] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,2,7,6,3,5] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,2,7,6,5,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,1,3,2,5,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[4,1,3,2,5,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[4,1,3,2,6,5,7] => [[1,3,5,7],[2,6],[4]] => 101010
[4,1,3,2,6,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[4,1,3,2,7,5,6] => [[1,3,5,7],[2,6],[4]] => 101010
[4,1,3,2,7,6,5] => [[1,3,5],[2,6],[4,7]] => 101011
[4,1,3,5,2,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[4,1,3,5,2,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[4,1,3,5,6,2,7] => [[1,3,4,5,7],[2],[6]] => 100010
[4,1,3,5,6,7,2] => [[1,3,4,5,6],[2],[7]] => 100001
[4,1,3,5,7,2,6] => [[1,3,4,5],[2,7],[6]] => 100010
[4,1,3,5,7,6,2] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,3,6,2,5,7] => [[1,3,4,7],[2,6],[5]] => 100100
[4,1,3,6,2,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[4,1,3,6,5,2,7] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,3,6,5,7,2] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,3,6,7,2,5] => [[1,3,4,5],[2,7],[6]] => 100010
[4,1,3,6,7,5,2] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,3,7,2,5,6] => [[1,3,4,7],[2,6],[5]] => 100100
[4,1,3,7,2,6,5] => [[1,3,4],[2,6],[5,7]] => 100101
[4,1,3,7,5,2,6] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,3,7,5,6,2] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,3,7,6,2,5] => [[1,3,4],[2,5],[6,7]] => 100110
[4,1,3,7,6,5,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,1,5,2,3,6,7] => [[1,3,5,6,7],[2,4]] => 101000
[4,1,5,2,3,7,6] => [[1,3,5,6],[2,4,7]] => 101001
[4,1,5,2,6,3,7] => [[1,3,5,7],[2,4,6]] => 101010
[4,1,5,2,6,7,3] => [[1,3,5,6],[2,4,7]] => 101001
[4,1,5,2,7,3,6] => [[1,3,5,7],[2,4,6]] => 101010
[4,1,5,2,7,6,3] => [[1,3,5],[2,4,6],[7]] => 101011
[4,1,5,3,2,6,7] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,5,3,2,7,6] => [[1,3,6],[2,4,7],[5]] => 101101
[4,1,5,3,6,2,7] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,5,3,6,7,2] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,5,3,7,2,6] => [[1,3,5],[2,4,7],[6]] => 101010
[4,1,5,3,7,6,2] => [[1,3,5],[2,4,6],[7]] => 101011
[4,1,5,6,2,3,7] => [[1,3,4,7],[2,5,6]] => 100100
[4,1,5,6,2,7,3] => [[1,3,4,6],[2,5,7]] => 100101
[4,1,5,6,3,2,7] => [[1,3,4,7],[2,5],[6]] => 100110
[4,1,5,6,3,7,2] => [[1,3,4,6],[2,5],[7]] => 100101
[4,1,5,6,7,2,3] => [[1,3,4,5],[2,6,7]] => 100010
[4,1,5,6,7,3,2] => [[1,3,4,5],[2,6],[7]] => 100011
[4,1,5,7,2,3,6] => [[1,3,4,7],[2,5,6]] => 100100
[4,1,5,7,2,6,3] => [[1,3,4],[2,5,6],[7]] => 100101
[4,1,5,7,3,2,6] => [[1,3,4],[2,5,7],[6]] => 100110
[4,1,5,7,3,6,2] => [[1,3,4],[2,5,6],[7]] => 100101
[4,1,5,7,6,2,3] => [[1,3,4],[2,5,7],[6]] => 100110
[4,1,5,7,6,3,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,1,6,2,3,5,7] => [[1,3,5,6,7],[2,4]] => 101000
[4,1,6,2,3,7,5] => [[1,3,5,6],[2,4,7]] => 101001
[4,1,6,2,5,3,7] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,6,2,5,7,3] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,6,2,7,3,5] => [[1,3,5,7],[2,4,6]] => 101010
[4,1,6,2,7,5,3] => [[1,3,5],[2,4,6],[7]] => 101011
[4,1,6,3,2,5,7] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,6,3,2,7,5] => [[1,3,6],[2,4,7],[5]] => 101101
[4,1,6,3,5,2,7] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,6,3,5,7,2] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,6,3,7,2,5] => [[1,3,5],[2,4,7],[6]] => 101010
[4,1,6,3,7,5,2] => [[1,3,5],[2,4,6],[7]] => 101011
[4,1,6,5,2,3,7] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,6,5,2,7,3] => [[1,3,6],[2,4,7],[5]] => 101101
[4,1,6,5,3,2,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,1,6,5,3,7,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,1,6,5,7,2,3] => [[1,3,5],[2,4,7],[6]] => 101010
[4,1,6,5,7,3,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,1,6,7,2,3,5] => [[1,3,4,7],[2,5,6]] => 100100
[4,1,6,7,2,5,3] => [[1,3,4],[2,5,6],[7]] => 100101
[4,1,6,7,3,2,5] => [[1,3,4],[2,5,7],[6]] => 100110
[4,1,6,7,3,5,2] => [[1,3,4],[2,5,6],[7]] => 100101
[4,1,6,7,5,2,3] => [[1,3,4],[2,5,7],[6]] => 100110
[4,1,6,7,5,3,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,1,7,2,3,5,6] => [[1,3,5,6,7],[2,4]] => 101000
[4,1,7,2,3,6,5] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,7,2,5,3,6] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,7,2,5,6,3] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,7,2,6,3,5] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,7,2,6,5,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,1,7,3,2,5,6] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,7,3,2,6,5] => [[1,3,6],[2,4],[5,7]] => 101101
[4,1,7,3,5,2,6] => [[1,3,5,7],[2,4],[6]] => 101010
[4,1,7,3,5,6,2] => [[1,3,5,6],[2,4],[7]] => 101001
[4,1,7,3,6,2,5] => [[1,3,5],[2,4],[6,7]] => 101010
[4,1,7,3,6,5,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,1,7,5,2,3,6] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,7,5,2,6,3] => [[1,3,6],[2,4,7],[5]] => 101101
[4,1,7,5,3,2,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,1,7,5,3,6,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,1,7,5,6,2,3] => [[1,3,5],[2,4,7],[6]] => 101010
[4,1,7,5,6,3,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,1,7,6,2,3,5] => [[1,3,6,7],[2,4],[5]] => 101100
[4,1,7,6,2,5,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,1,7,6,3,2,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,1,7,6,3,5,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,1,7,6,5,2,3] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,1,7,6,5,3,2] => [[1,3],[2,4],[5],[6],[7]] => 101111
[4,2,1,3,5,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[4,2,1,3,5,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[4,2,1,3,6,5,7] => [[1,4,5,7],[2,6],[3]] => 110010
[4,2,1,3,6,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[4,2,1,3,7,5,6] => [[1,4,5,7],[2,6],[3]] => 110010
[4,2,1,3,7,6,5] => [[1,4,5],[2,6],[3,7]] => 110011
[4,2,1,5,3,6,7] => [[1,4,6,7],[2,5],[3]] => 110100
[4,2,1,5,3,7,6] => [[1,4,6],[2,5,7],[3]] => 110101
[4,2,1,5,6,3,7] => [[1,4,5,7],[2,6],[3]] => 110010
[4,2,1,5,6,7,3] => [[1,4,5,6],[2,7],[3]] => 110001
[4,2,1,5,7,3,6] => [[1,4,5],[2,6,7],[3]] => 110010
[4,2,1,5,7,6,3] => [[1,4,5],[2,6],[3,7]] => 110011
[4,2,1,6,3,5,7] => [[1,4,6,7],[2,5],[3]] => 110100
[4,2,1,6,3,7,5] => [[1,4,6],[2,5,7],[3]] => 110101
[4,2,1,6,5,3,7] => [[1,4,7],[2,5],[3,6]] => 110110
[4,2,1,6,5,7,3] => [[1,4,6],[2,5],[3,7]] => 110101
[4,2,1,6,7,3,5] => [[1,4,5],[2,6,7],[3]] => 110010
[4,2,1,6,7,5,3] => [[1,4,5],[2,6],[3,7]] => 110011
[4,2,1,7,3,5,6] => [[1,4,6,7],[2,5],[3]] => 110100
[4,2,1,7,3,6,5] => [[1,4,6],[2,5],[3,7]] => 110101
[4,2,1,7,5,3,6] => [[1,4,7],[2,5],[3,6]] => 110110
[4,2,1,7,5,6,3] => [[1,4,6],[2,5],[3,7]] => 110101
[4,2,1,7,6,3,5] => [[1,4,7],[2,5],[3,6]] => 110110
[4,2,1,7,6,5,3] => [[1,4],[2,5],[3,6],[7]] => 110111
[4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[4,2,3,1,5,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[4,2,3,1,6,5,7] => [[1,3,5,7],[2,6],[4]] => 101010
[4,2,3,1,6,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[4,2,3,1,7,5,6] => [[1,3,5,7],[2,6],[4]] => 101010
[4,2,3,1,7,6,5] => [[1,3,5],[2,6],[4,7]] => 101011
[4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[4,2,3,5,1,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => 100010
[4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => 100001
[4,2,3,5,7,1,6] => [[1,3,4,5],[2,7],[6]] => 100010
[4,2,3,5,7,6,1] => [[1,3,4,5],[2,6],[7]] => 100011
[4,2,3,6,1,5,7] => [[1,3,4,7],[2,6],[5]] => 100100
[4,2,3,6,1,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[4,2,3,6,5,1,7] => [[1,3,4,7],[2,5],[6]] => 100110
[4,2,3,6,5,7,1] => [[1,3,4,6],[2,5],[7]] => 100101
[4,2,3,6,7,1,5] => [[1,3,4,5],[2,7],[6]] => 100010
[4,2,3,6,7,5,1] => [[1,3,4,5],[2,6],[7]] => 100011
[4,2,3,7,1,5,6] => [[1,3,4,7],[2,6],[5]] => 100100
[4,2,3,7,1,6,5] => [[1,3,4],[2,6],[5,7]] => 100101
[4,2,3,7,5,1,6] => [[1,3,4,7],[2,5],[6]] => 100110
[4,2,3,7,5,6,1] => [[1,3,4,6],[2,5],[7]] => 100101
[4,2,3,7,6,1,5] => [[1,3,4],[2,5],[6,7]] => 100110
[4,2,3,7,6,5,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,2,5,1,3,6,7] => [[1,3,6,7],[2,5],[4]] => 101000
[4,2,5,1,3,7,6] => [[1,3,6],[2,5,7],[4]] => 101001
[4,2,5,1,6,3,7] => [[1,3,5,7],[2,6],[4]] => 101010
[4,2,5,1,6,7,3] => [[1,3,5,6],[2,7],[4]] => 101001
[4,2,5,1,7,3,6] => [[1,3,5],[2,6,7],[4]] => 101010
[4,2,5,1,7,6,3] => [[1,3,5],[2,6],[4,7]] => 101011
[4,2,5,3,1,6,7] => [[1,3,6,7],[2,4],[5]] => 101100
[4,2,5,3,1,7,6] => [[1,3,6],[2,4,7],[5]] => 101101
[4,2,5,3,6,1,7] => [[1,3,5,7],[2,4],[6]] => 101010
[4,2,5,3,6,7,1] => [[1,3,5,6],[2,4],[7]] => 101001
[4,2,5,3,7,1,6] => [[1,3,5],[2,4,7],[6]] => 101010
[4,2,5,3,7,6,1] => [[1,3,5],[2,4,6],[7]] => 101011
[4,2,5,6,1,3,7] => [[1,3,4,7],[2,6],[5]] => 100100
[4,2,5,6,1,7,3] => [[1,3,4,6],[2,7],[5]] => 100101
[4,2,5,6,3,1,7] => [[1,3,4,7],[2,5],[6]] => 100110
[4,2,5,6,3,7,1] => [[1,3,4,6],[2,5],[7]] => 100101
[4,2,5,6,7,1,3] => [[1,3,4,5],[2,7],[6]] => 100010
[4,2,5,6,7,3,1] => [[1,3,4,5],[2,6],[7]] => 100011
[4,2,5,7,1,3,6] => [[1,3,4],[2,6,7],[5]] => 100100
[4,2,5,7,1,6,3] => [[1,3,4],[2,6],[5,7]] => 100101
[4,2,5,7,3,1,6] => [[1,3,4],[2,5,7],[6]] => 100110
[4,2,5,7,3,6,1] => [[1,3,4],[2,5,6],[7]] => 100101
[4,2,5,7,6,1,3] => [[1,3,4],[2,5],[6,7]] => 100110
[4,2,5,7,6,3,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,2,6,1,3,5,7] => [[1,3,6,7],[2,5],[4]] => 101000
[4,2,6,1,3,7,5] => [[1,3,6],[2,5,7],[4]] => 101001
[4,2,6,1,5,3,7] => [[1,3,7],[2,5],[4,6]] => 101010
[4,2,6,1,5,7,3] => [[1,3,6],[2,5],[4,7]] => 101001
[4,2,6,1,7,3,5] => [[1,3,5],[2,6,7],[4]] => 101010
[4,2,6,1,7,5,3] => [[1,3,5],[2,6],[4,7]] => 101011
[4,2,6,3,1,5,7] => [[1,3,6,7],[2,4],[5]] => 101100
[4,2,6,3,1,7,5] => [[1,3,6],[2,4,7],[5]] => 101101
[4,2,6,3,5,1,7] => [[1,3,5,7],[2,4],[6]] => 101010
[4,2,6,3,5,7,1] => [[1,3,5,6],[2,4],[7]] => 101001
[4,2,6,3,7,1,5] => [[1,3,5],[2,4,7],[6]] => 101010
[4,2,6,3,7,5,1] => [[1,3,5],[2,4,6],[7]] => 101011
[4,2,6,5,1,3,7] => [[1,3,7],[2,4],[5,6]] => 101100
[4,2,6,5,1,7,3] => [[1,3,6],[2,4],[5,7]] => 101101
[4,2,6,5,3,1,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,2,6,5,3,7,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,2,6,5,7,1,3] => [[1,3,5],[2,4],[6,7]] => 101010
[4,2,6,5,7,3,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,2,6,7,1,3,5] => [[1,3,4],[2,6,7],[5]] => 100100
[4,2,6,7,1,5,3] => [[1,3,4],[2,6],[5,7]] => 100101
[4,2,6,7,3,1,5] => [[1,3,4],[2,5,7],[6]] => 100110
[4,2,6,7,3,5,1] => [[1,3,4],[2,5,6],[7]] => 100101
[4,2,6,7,5,1,3] => [[1,3,4],[2,5],[6,7]] => 100110
[4,2,6,7,5,3,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,2,7,1,3,5,6] => [[1,3,6,7],[2,5],[4]] => 101000
[4,2,7,1,3,6,5] => [[1,3,6],[2,5],[4,7]] => 101001
[4,2,7,1,5,3,6] => [[1,3,7],[2,5],[4,6]] => 101010
[4,2,7,1,5,6,3] => [[1,3,6],[2,5],[4,7]] => 101001
[4,2,7,1,6,3,5] => [[1,3,7],[2,5],[4,6]] => 101010
[4,2,7,1,6,5,3] => [[1,3],[2,5],[4,6],[7]] => 101011
[4,2,7,3,1,5,6] => [[1,3,6,7],[2,4],[5]] => 101100
[4,2,7,3,1,6,5] => [[1,3,6],[2,4],[5,7]] => 101101
[4,2,7,3,5,1,6] => [[1,3,5,7],[2,4],[6]] => 101010
[4,2,7,3,5,6,1] => [[1,3,5,6],[2,4],[7]] => 101001
[4,2,7,3,6,1,5] => [[1,3,5],[2,4],[6,7]] => 101010
[4,2,7,3,6,5,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,2,7,5,1,3,6] => [[1,3,7],[2,4],[5,6]] => 101100
[4,2,7,5,1,6,3] => [[1,3,6],[2,4],[5,7]] => 101101
[4,2,7,5,3,1,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,2,7,5,3,6,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,2,7,5,6,1,3] => [[1,3,5],[2,4],[6,7]] => 101010
[4,2,7,5,6,3,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,2,7,6,1,3,5] => [[1,3,7],[2,4],[5,6]] => 101100
[4,2,7,6,1,5,3] => [[1,3],[2,4],[5,6],[7]] => 101101
[4,2,7,6,3,1,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,2,7,6,3,5,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,2,7,6,5,1,3] => [[1,3],[2,4],[5,7],[6]] => 101110
[4,2,7,6,5,3,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[4,3,1,2,5,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[4,3,1,2,5,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[4,3,1,2,6,5,7] => [[1,4,5,7],[2,6],[3]] => 110010
[4,3,1,2,6,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[4,3,1,2,7,5,6] => [[1,4,5,7],[2,6],[3]] => 110010
[4,3,1,2,7,6,5] => [[1,4,5],[2,6],[3,7]] => 110011
[4,3,1,5,2,6,7] => [[1,4,6,7],[2,5],[3]] => 110100
[4,3,1,5,2,7,6] => [[1,4,6],[2,5,7],[3]] => 110101
[4,3,1,5,6,2,7] => [[1,4,5,7],[2,6],[3]] => 110010
[4,3,1,5,6,7,2] => [[1,4,5,6],[2,7],[3]] => 110001
[4,3,1,5,7,2,6] => [[1,4,5],[2,6,7],[3]] => 110010
[4,3,1,5,7,6,2] => [[1,4,5],[2,6],[3,7]] => 110011
[4,3,1,6,2,5,7] => [[1,4,6,7],[2,5],[3]] => 110100
[4,3,1,6,2,7,5] => [[1,4,6],[2,5,7],[3]] => 110101
[4,3,1,6,5,2,7] => [[1,4,7],[2,5],[3,6]] => 110110
[4,3,1,6,5,7,2] => [[1,4,6],[2,5],[3,7]] => 110101
[4,3,1,6,7,2,5] => [[1,4,5],[2,6,7],[3]] => 110010
[4,3,1,6,7,5,2] => [[1,4,5],[2,6],[3,7]] => 110011
[4,3,1,7,2,5,6] => [[1,4,6,7],[2,5],[3]] => 110100
[4,3,1,7,2,6,5] => [[1,4,6],[2,5],[3,7]] => 110101
[4,3,1,7,5,2,6] => [[1,4,7],[2,5],[3,6]] => 110110
[4,3,1,7,5,6,2] => [[1,4,6],[2,5],[3,7]] => 110101
[4,3,1,7,6,2,5] => [[1,4,7],[2,5],[3,6]] => 110110
[4,3,1,7,6,5,2] => [[1,4],[2,5],[3,6],[7]] => 110111
[4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[4,3,2,1,5,7,6] => [[1,5,6],[2,7],[3],[4]] => 111001
[4,3,2,1,6,5,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[4,3,2,1,6,7,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[4,3,2,1,7,5,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[4,3,2,1,7,6,5] => [[1,5],[2,6],[3,7],[4]] => 111011
[4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[4,3,2,5,1,7,6] => [[1,4,6],[2,7],[3],[5]] => 110101
[4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[4,3,2,5,7,1,6] => [[1,4,5],[2,7],[3],[6]] => 110010
[4,3,2,5,7,6,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[4,3,2,6,1,5,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[4,3,2,6,1,7,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[4,3,2,6,5,1,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[4,3,2,6,5,7,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[4,3,2,6,7,1,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[4,3,2,6,7,5,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[4,3,2,7,1,5,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[4,3,2,7,1,6,5] => [[1,4],[2,6],[3,7],[5]] => 110101
[4,3,2,7,5,1,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[4,3,2,7,5,6,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[4,3,2,7,6,1,5] => [[1,4],[2,5],[3,7],[6]] => 110110
[4,3,2,7,6,5,1] => [[1,4],[2,5],[3,6],[7]] => 110111
[4,3,5,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => 101000
[4,3,5,1,2,7,6] => [[1,3,6],[2,5,7],[4]] => 101001
[4,3,5,1,6,2,7] => [[1,3,5,7],[2,6],[4]] => 101010
[4,3,5,1,6,7,2] => [[1,3,5,6],[2,7],[4]] => 101001
[4,3,5,1,7,2,6] => [[1,3,5],[2,6,7],[4]] => 101010
[4,3,5,1,7,6,2] => [[1,3,5],[2,6],[4,7]] => 101011
[4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[4,3,5,2,1,7,6] => [[1,3,6],[2,7],[4],[5]] => 101101
[4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[4,3,5,2,7,1,6] => [[1,3,5],[2,7],[4],[6]] => 101010
[4,3,5,2,7,6,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[4,3,5,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 100100
[4,3,5,6,1,7,2] => [[1,3,4,6],[2,7],[5]] => 100101
[4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[4,3,5,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 100010
[4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[4,3,5,7,1,2,6] => [[1,3,4],[2,6,7],[5]] => 100100
[4,3,5,7,1,6,2] => [[1,3,4],[2,6],[5,7]] => 100101
[4,3,5,7,2,1,6] => [[1,3,4],[2,7],[5],[6]] => 100110
[4,3,5,7,2,6,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[4,3,5,7,6,1,2] => [[1,3,4],[2,5],[6,7]] => 100110
[4,3,5,7,6,2,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,3,6,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => 101000
[4,3,6,1,2,7,5] => [[1,3,6],[2,5,7],[4]] => 101001
[4,3,6,1,5,2,7] => [[1,3,7],[2,5],[4,6]] => 101010
[4,3,6,1,5,7,2] => [[1,3,6],[2,5],[4,7]] => 101001
[4,3,6,1,7,2,5] => [[1,3,5],[2,6,7],[4]] => 101010
[4,3,6,1,7,5,2] => [[1,3,5],[2,6],[4,7]] => 101011
[4,3,6,2,1,5,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[4,3,6,2,1,7,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[4,3,6,2,5,1,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[4,3,6,2,5,7,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[4,3,6,2,7,1,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[4,3,6,2,7,5,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[4,3,6,5,1,2,7] => [[1,3,7],[2,4],[5,6]] => 101100
[4,3,6,5,1,7,2] => [[1,3,6],[2,4],[5,7]] => 101101
[4,3,6,5,2,1,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,3,6,5,2,7,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,3,6,5,7,1,2] => [[1,3,5],[2,4],[6,7]] => 101010
[4,3,6,5,7,2,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,3,6,7,1,2,5] => [[1,3,4],[2,6,7],[5]] => 100100
[4,3,6,7,1,5,2] => [[1,3,4],[2,6],[5,7]] => 100101
[4,3,6,7,2,1,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[4,3,6,7,2,5,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[4,3,6,7,5,1,2] => [[1,3,4],[2,5],[6,7]] => 100110
[4,3,6,7,5,2,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[4,3,7,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => 101000
[4,3,7,1,2,6,5] => [[1,3,6],[2,5],[4,7]] => 101001
[4,3,7,1,5,2,6] => [[1,3,7],[2,5],[4,6]] => 101010
[4,3,7,1,5,6,2] => [[1,3,6],[2,5],[4,7]] => 101001
[4,3,7,1,6,2,5] => [[1,3,7],[2,5],[4,6]] => 101010
[4,3,7,1,6,5,2] => [[1,3],[2,5],[4,6],[7]] => 101011
[4,3,7,2,1,5,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[4,3,7,2,1,6,5] => [[1,3],[2,6],[4,7],[5]] => 101101
[4,3,7,2,5,1,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[4,3,7,2,5,6,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[4,3,7,2,6,1,5] => [[1,3],[2,5],[4,7],[6]] => 101010
[4,3,7,2,6,5,1] => [[1,3],[2,5],[4,6],[7]] => 101011
[4,3,7,5,1,2,6] => [[1,3,7],[2,4],[5,6]] => 101100
[4,3,7,5,1,6,2] => [[1,3,6],[2,4],[5,7]] => 101101
[4,3,7,5,2,1,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[4,3,7,5,2,6,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[4,3,7,5,6,1,2] => [[1,3,5],[2,4],[6,7]] => 101010
[4,3,7,5,6,2,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[4,3,7,6,1,2,5] => [[1,3,7],[2,4],[5,6]] => 101100
[4,3,7,6,1,5,2] => [[1,3],[2,4],[5,6],[7]] => 101101
[4,3,7,6,2,1,5] => [[1,3],[2,4],[5,7],[6]] => 101110
[4,3,7,6,2,5,1] => [[1,3],[2,4],[5,6],[7]] => 101101
[4,3,7,6,5,1,2] => [[1,3],[2,4],[5,7],[6]] => 101110
[4,3,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => 010000
[4,5,1,2,3,7,6] => [[1,2,5,6],[3,4,7]] => 010001
[4,5,1,2,6,3,7] => [[1,2,5,7],[3,4,6]] => 010010
[4,5,1,2,6,7,3] => [[1,2,5,6],[3,4,7]] => 010001
[4,5,1,2,7,3,6] => [[1,2,5,7],[3,4,6]] => 010010
[4,5,1,2,7,6,3] => [[1,2,5],[3,4,6],[7]] => 010011
[4,5,1,3,2,6,7] => [[1,2,6,7],[3,4],[5]] => 010100
[4,5,1,3,2,7,6] => [[1,2,6],[3,4,7],[5]] => 010101
[4,5,1,3,6,2,7] => [[1,2,5,7],[3,4],[6]] => 010010
[4,5,1,3,6,7,2] => [[1,2,5,6],[3,4],[7]] => 010001
[4,5,1,3,7,2,6] => [[1,2,5],[3,4,7],[6]] => 010010
[4,5,1,3,7,6,2] => [[1,2,5],[3,4,6],[7]] => 010011
[4,5,1,6,2,3,7] => [[1,2,4,7],[3,5,6]] => 010100
[4,5,1,6,2,7,3] => [[1,2,4,6],[3,5,7]] => 010101
[4,5,1,6,3,2,7] => [[1,2,4,7],[3,5],[6]] => 010110
[4,5,1,6,3,7,2] => [[1,2,4,6],[3,5],[7]] => 010101
[4,5,1,6,7,2,3] => [[1,2,4,5],[3,6,7]] => 010010
[4,5,1,6,7,3,2] => [[1,2,4,5],[3,6],[7]] => 010011
[4,5,1,7,2,3,6] => [[1,2,4,7],[3,5,6]] => 010100
[4,5,1,7,2,6,3] => [[1,2,4],[3,5,6],[7]] => 010101
[4,5,1,7,3,2,6] => [[1,2,4],[3,5,7],[6]] => 010110
[4,5,1,7,3,6,2] => [[1,2,4],[3,5,6],[7]] => 010101
[4,5,1,7,6,2,3] => [[1,2,4],[3,5,7],[6]] => 010110
[4,5,1,7,6,3,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,5,2,1,3,6,7] => [[1,2,6,7],[3,5],[4]] => 011000
[4,5,2,1,3,7,6] => [[1,2,6],[3,5,7],[4]] => 011001
[4,5,2,1,6,3,7] => [[1,2,5,7],[3,6],[4]] => 011010
[4,5,2,1,6,7,3] => [[1,2,5,6],[3,7],[4]] => 011001
[4,5,2,1,7,3,6] => [[1,2,5],[3,6,7],[4]] => 011010
[4,5,2,1,7,6,3] => [[1,2,5],[3,6],[4,7]] => 011011
[4,5,2,3,1,6,7] => [[1,2,6,7],[3,4],[5]] => 010100
[4,5,2,3,1,7,6] => [[1,2,6],[3,4,7],[5]] => 010101
[4,5,2,3,6,1,7] => [[1,2,5,7],[3,4],[6]] => 010010
[4,5,2,3,6,7,1] => [[1,2,5,6],[3,4],[7]] => 010001
[4,5,2,3,7,1,6] => [[1,2,5],[3,4,7],[6]] => 010010
[4,5,2,3,7,6,1] => [[1,2,5],[3,4,6],[7]] => 010011
[4,5,2,6,1,3,7] => [[1,2,4,7],[3,6],[5]] => 010100
[4,5,2,6,1,7,3] => [[1,2,4,6],[3,7],[5]] => 010101
[4,5,2,6,3,1,7] => [[1,2,4,7],[3,5],[6]] => 010110
[4,5,2,6,3,7,1] => [[1,2,4,6],[3,5],[7]] => 010101
[4,5,2,6,7,1,3] => [[1,2,4,5],[3,7],[6]] => 010010
[4,5,2,6,7,3,1] => [[1,2,4,5],[3,6],[7]] => 010011
[4,5,2,7,1,3,6] => [[1,2,4],[3,6,7],[5]] => 010100
[4,5,2,7,1,6,3] => [[1,2,4],[3,6],[5,7]] => 010101
[4,5,2,7,3,1,6] => [[1,2,4],[3,5,7],[6]] => 010110
[4,5,2,7,3,6,1] => [[1,2,4],[3,5,6],[7]] => 010101
[4,5,2,7,6,1,3] => [[1,2,4],[3,5],[6,7]] => 010110
[4,5,2,7,6,3,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => 011000
[4,5,3,1,2,7,6] => [[1,2,6],[3,5,7],[4]] => 011001
[4,5,3,1,6,2,7] => [[1,2,5,7],[3,6],[4]] => 011010
[4,5,3,1,6,7,2] => [[1,2,5,6],[3,7],[4]] => 011001
[4,5,3,1,7,2,6] => [[1,2,5],[3,6,7],[4]] => 011010
[4,5,3,1,7,6,2] => [[1,2,5],[3,6],[4,7]] => 011011
[4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => 011100
[4,5,3,2,1,7,6] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => 011010
[4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => 011001
[4,5,3,2,7,1,6] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,5,3,2,7,6,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,5,3,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => 010100
[4,5,3,6,1,7,2] => [[1,2,4,6],[3,7],[5]] => 010101
[4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => 010110
[4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => 010101
[4,5,3,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => 010010
[4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => 010011
[4,5,3,7,1,2,6] => [[1,2,4],[3,6,7],[5]] => 010100
[4,5,3,7,1,6,2] => [[1,2,4],[3,6],[5,7]] => 010101
[4,5,3,7,2,1,6] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,5,3,7,2,6,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,5,3,7,6,1,2] => [[1,2,4],[3,5],[6,7]] => 010110
[4,5,3,7,6,2,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => 001000
[4,5,6,1,2,7,3] => [[1,2,3,6],[4,5,7]] => 001001
[4,5,6,1,3,2,7] => [[1,2,3,7],[4,5],[6]] => 001010
[4,5,6,1,3,7,2] => [[1,2,3,6],[4,5],[7]] => 001001
[4,5,6,1,7,2,3] => [[1,2,3,5],[4,6,7]] => 001010
[4,5,6,1,7,3,2] => [[1,2,3,5],[4,6],[7]] => 001011
[4,5,6,2,1,3,7] => [[1,2,3,7],[4,6],[5]] => 001100
[4,5,6,2,1,7,3] => [[1,2,3,6],[4,7],[5]] => 001101
[4,5,6,2,3,1,7] => [[1,2,3,7],[4,5],[6]] => 001010
[4,5,6,2,3,7,1] => [[1,2,3,6],[4,5],[7]] => 001001
[4,5,6,2,7,1,3] => [[1,2,3,5],[4,7],[6]] => 001010
[4,5,6,2,7,3,1] => [[1,2,3,5],[4,6],[7]] => 001011
[4,5,6,3,1,2,7] => [[1,2,3,7],[4,6],[5]] => 001100
[4,5,6,3,1,7,2] => [[1,2,3,6],[4,7],[5]] => 001101
[4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => 001110
[4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => 001101
[4,5,6,3,7,1,2] => [[1,2,3,5],[4,7],[6]] => 001010
[4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => 001011
[4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => 000100
[4,5,6,7,1,3,2] => [[1,2,3,4],[5,6],[7]] => 000101
[4,5,6,7,2,1,3] => [[1,2,3,4],[5,7],[6]] => 000110
[4,5,6,7,2,3,1] => [[1,2,3,4],[5,6],[7]] => 000101
[4,5,6,7,3,1,2] => [[1,2,3,4],[5,7],[6]] => 000110
[4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[4,5,7,1,2,3,6] => [[1,2,3,7],[4,5,6]] => 001000
[4,5,7,1,2,6,3] => [[1,2,3],[4,5,6],[7]] => 001001
[4,5,7,1,3,2,6] => [[1,2,3],[4,5,7],[6]] => 001010
[4,5,7,1,3,6,2] => [[1,2,3],[4,5,6],[7]] => 001001
[4,5,7,1,6,2,3] => [[1,2,3],[4,5,7],[6]] => 001010
[4,5,7,1,6,3,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,5,7,2,1,3,6] => [[1,2,3],[4,6,7],[5]] => 001100
[4,5,7,2,1,6,3] => [[1,2,3],[4,6],[5,7]] => 001101
[4,5,7,2,3,1,6] => [[1,2,3],[4,5,7],[6]] => 001010
[4,5,7,2,3,6,1] => [[1,2,3],[4,5,6],[7]] => 001001
[4,5,7,2,6,1,3] => [[1,2,3],[4,5],[6,7]] => 001010
[4,5,7,2,6,3,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,5,7,3,1,2,6] => [[1,2,3],[4,6,7],[5]] => 001100
[4,5,7,3,1,6,2] => [[1,2,3],[4,6],[5,7]] => 001101
[4,5,7,3,2,1,6] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,5,7,3,2,6,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,5,7,3,6,1,2] => [[1,2,3],[4,5],[6,7]] => 001010
[4,5,7,3,6,2,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,5,7,6,1,2,3] => [[1,2,3],[4,6,7],[5]] => 001100
[4,5,7,6,1,3,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,5,7,6,2,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,5,7,6,2,3,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,5,7,6,3,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,5,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[4,6,1,2,3,5,7] => [[1,2,5,6,7],[3,4]] => 010000
[4,6,1,2,3,7,5] => [[1,2,5,6],[3,4,7]] => 010001
[4,6,1,2,5,3,7] => [[1,2,5,7],[3,4],[6]] => 010010
[4,6,1,2,5,7,3] => [[1,2,5,6],[3,4],[7]] => 010001
[4,6,1,2,7,3,5] => [[1,2,5,7],[3,4,6]] => 010010
[4,6,1,2,7,5,3] => [[1,2,5],[3,4,6],[7]] => 010011
[4,6,1,3,2,5,7] => [[1,2,6,7],[3,4],[5]] => 010100
[4,6,1,3,2,7,5] => [[1,2,6],[3,4,7],[5]] => 010101
[4,6,1,3,5,2,7] => [[1,2,5,7],[3,4],[6]] => 010010
[4,6,1,3,5,7,2] => [[1,2,5,6],[3,4],[7]] => 010001
[4,6,1,3,7,2,5] => [[1,2,5],[3,4,7],[6]] => 010010
[4,6,1,3,7,5,2] => [[1,2,5],[3,4,6],[7]] => 010011
[4,6,1,5,2,3,7] => [[1,2,6,7],[3,4],[5]] => 010100
[4,6,1,5,2,7,3] => [[1,2,6],[3,4,7],[5]] => 010101
[4,6,1,5,3,2,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,6,1,5,3,7,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,6,1,5,7,2,3] => [[1,2,5],[3,4,7],[6]] => 010010
[4,6,1,5,7,3,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,6,1,7,2,3,5] => [[1,2,4,7],[3,5,6]] => 010100
[4,6,1,7,2,5,3] => [[1,2,4],[3,5,6],[7]] => 010101
[4,6,1,7,3,2,5] => [[1,2,4],[3,5,7],[6]] => 010110
[4,6,1,7,3,5,2] => [[1,2,4],[3,5,6],[7]] => 010101
[4,6,1,7,5,2,3] => [[1,2,4],[3,5,7],[6]] => 010110
[4,6,1,7,5,3,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,6,2,1,3,5,7] => [[1,2,6,7],[3,5],[4]] => 011000
[4,6,2,1,3,7,5] => [[1,2,6],[3,5,7],[4]] => 011001
[4,6,2,1,5,3,7] => [[1,2,7],[3,5],[4,6]] => 011010
[4,6,2,1,5,7,3] => [[1,2,6],[3,5],[4,7]] => 011001
[4,6,2,1,7,3,5] => [[1,2,5],[3,6,7],[4]] => 011010
[4,6,2,1,7,5,3] => [[1,2,5],[3,6],[4,7]] => 011011
[4,6,2,3,1,5,7] => [[1,2,6,7],[3,4],[5]] => 010100
[4,6,2,3,1,7,5] => [[1,2,6],[3,4,7],[5]] => 010101
[4,6,2,3,5,1,7] => [[1,2,5,7],[3,4],[6]] => 010010
[4,6,2,3,5,7,1] => [[1,2,5,6],[3,4],[7]] => 010001
[4,6,2,3,7,1,5] => [[1,2,5],[3,4,7],[6]] => 010010
[4,6,2,3,7,5,1] => [[1,2,5],[3,4,6],[7]] => 010011
[4,6,2,5,1,3,7] => [[1,2,7],[3,4],[5,6]] => 010100
[4,6,2,5,1,7,3] => [[1,2,6],[3,4],[5,7]] => 010101
[4,6,2,5,3,1,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,6,2,5,3,7,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,6,2,5,7,1,3] => [[1,2,5],[3,4],[6,7]] => 010010
[4,6,2,5,7,3,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,6,2,7,1,3,5] => [[1,2,4],[3,6,7],[5]] => 010100
[4,6,2,7,1,5,3] => [[1,2,4],[3,6],[5,7]] => 010101
[4,6,2,7,3,1,5] => [[1,2,4],[3,5,7],[6]] => 010110
[4,6,2,7,3,5,1] => [[1,2,4],[3,5,6],[7]] => 010101
[4,6,2,7,5,1,3] => [[1,2,4],[3,5],[6,7]] => 010110
[4,6,2,7,5,3,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,6,3,1,2,5,7] => [[1,2,6,7],[3,5],[4]] => 011000
[4,6,3,1,2,7,5] => [[1,2,6],[3,5,7],[4]] => 011001
[4,6,3,1,5,2,7] => [[1,2,7],[3,5],[4,6]] => 011010
[4,6,3,1,5,7,2] => [[1,2,6],[3,5],[4,7]] => 011001
[4,6,3,1,7,2,5] => [[1,2,5],[3,6,7],[4]] => 011010
[4,6,3,1,7,5,2] => [[1,2,5],[3,6],[4,7]] => 011011
[4,6,3,2,1,5,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,6,3,2,1,7,5] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,6,3,2,5,1,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,6,3,2,5,7,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,6,3,2,7,1,5] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,6,3,2,7,5,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,6,3,5,1,2,7] => [[1,2,7],[3,4],[5,6]] => 010100
[4,6,3,5,1,7,2] => [[1,2,6],[3,4],[5,7]] => 010101
[4,6,3,5,2,1,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,6,3,5,2,7,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,6,3,5,7,1,2] => [[1,2,5],[3,4],[6,7]] => 010010
[4,6,3,5,7,2,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,6,3,7,1,2,5] => [[1,2,4],[3,6,7],[5]] => 010100
[4,6,3,7,1,5,2] => [[1,2,4],[3,6],[5,7]] => 010101
[4,6,3,7,2,1,5] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,6,3,7,2,5,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,6,3,7,5,1,2] => [[1,2,4],[3,5],[6,7]] => 010110
[4,6,3,7,5,2,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[4,6,5,1,2,3,7] => [[1,2,6,7],[3,5],[4]] => 011000
[4,6,5,1,2,7,3] => [[1,2,6],[3,5,7],[4]] => 011001
[4,6,5,1,3,2,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,6,5,1,3,7,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,6,5,1,7,2,3] => [[1,2,5],[3,6,7],[4]] => 011010
[4,6,5,1,7,3,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,6,5,2,1,3,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,6,5,2,1,7,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,6,5,2,3,1,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,6,5,2,3,7,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,6,5,2,7,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,6,5,2,7,3,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,6,5,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,6,5,3,1,7,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,6,5,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 011110
[4,6,5,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[4,6,5,3,7,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,6,5,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[4,6,5,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => 010100
[4,6,5,7,1,3,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,6,5,7,2,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,6,5,7,2,3,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,6,5,7,3,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,6,5,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[4,6,7,1,2,3,5] => [[1,2,3,7],[4,5,6]] => 001000
[4,6,7,1,2,5,3] => [[1,2,3],[4,5,6],[7]] => 001001
[4,6,7,1,3,2,5] => [[1,2,3],[4,5,7],[6]] => 001010
[4,6,7,1,3,5,2] => [[1,2,3],[4,5,6],[7]] => 001001
[4,6,7,1,5,2,3] => [[1,2,3],[4,5,7],[6]] => 001010
[4,6,7,1,5,3,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,6,7,2,1,3,5] => [[1,2,3],[4,6,7],[5]] => 001100
[4,6,7,2,1,5,3] => [[1,2,3],[4,6],[5,7]] => 001101
[4,6,7,2,3,1,5] => [[1,2,3],[4,5,7],[6]] => 001010
[4,6,7,2,3,5,1] => [[1,2,3],[4,5,6],[7]] => 001001
[4,6,7,2,5,1,3] => [[1,2,3],[4,5],[6,7]] => 001010
[4,6,7,2,5,3,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,6,7,3,1,2,5] => [[1,2,3],[4,6,7],[5]] => 001100
[4,6,7,3,1,5,2] => [[1,2,3],[4,6],[5,7]] => 001101
[4,6,7,3,2,1,5] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,6,7,3,2,5,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,6,7,3,5,1,2] => [[1,2,3],[4,5],[6,7]] => 001010
[4,6,7,3,5,2,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[4,6,7,5,1,2,3] => [[1,2,3],[4,6,7],[5]] => 001100
[4,6,7,5,1,3,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,6,7,5,2,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,6,7,5,2,3,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[4,6,7,5,3,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[4,6,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[4,7,1,2,3,5,6] => [[1,2,5,6,7],[3,4]] => 010000
[4,7,1,2,3,6,5] => [[1,2,5,6],[3,4],[7]] => 010001
[4,7,1,2,5,3,6] => [[1,2,5,7],[3,4],[6]] => 010010
[4,7,1,2,5,6,3] => [[1,2,5,6],[3,4],[7]] => 010001
[4,7,1,2,6,3,5] => [[1,2,5,7],[3,4],[6]] => 010010
[4,7,1,2,6,5,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,1,3,2,5,6] => [[1,2,6,7],[3,4],[5]] => 010100
[4,7,1,3,2,6,5] => [[1,2,6],[3,4],[5,7]] => 010101
[4,7,1,3,5,2,6] => [[1,2,5,7],[3,4],[6]] => 010010
[4,7,1,3,5,6,2] => [[1,2,5,6],[3,4],[7]] => 010001
[4,7,1,3,6,2,5] => [[1,2,5],[3,4],[6,7]] => 010010
[4,7,1,3,6,5,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,1,5,2,3,6] => [[1,2,6,7],[3,4],[5]] => 010100
[4,7,1,5,2,6,3] => [[1,2,6],[3,4,7],[5]] => 010101
[4,7,1,5,3,2,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,1,5,3,6,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,1,5,6,2,3] => [[1,2,5],[3,4,7],[6]] => 010010
[4,7,1,5,6,3,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,1,6,2,3,5] => [[1,2,6,7],[3,4],[5]] => 010100
[4,7,1,6,2,5,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,1,6,3,2,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,1,6,3,5,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,1,6,5,2,3] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,1,6,5,3,2] => [[1,2],[3,4],[5],[6],[7]] => 010111
[4,7,2,1,3,5,6] => [[1,2,6,7],[3,5],[4]] => 011000
[4,7,2,1,3,6,5] => [[1,2,6],[3,5],[4,7]] => 011001
[4,7,2,1,5,3,6] => [[1,2,7],[3,5],[4,6]] => 011010
[4,7,2,1,5,6,3] => [[1,2,6],[3,5],[4,7]] => 011001
[4,7,2,1,6,3,5] => [[1,2,7],[3,5],[4,6]] => 011010
[4,7,2,1,6,5,3] => [[1,2],[3,5],[4,6],[7]] => 011011
[4,7,2,3,1,5,6] => [[1,2,6,7],[3,4],[5]] => 010100
[4,7,2,3,1,6,5] => [[1,2,6],[3,4],[5,7]] => 010101
[4,7,2,3,5,1,6] => [[1,2,5,7],[3,4],[6]] => 010010
[4,7,2,3,5,6,1] => [[1,2,5,6],[3,4],[7]] => 010001
[4,7,2,3,6,1,5] => [[1,2,5],[3,4],[6,7]] => 010010
[4,7,2,3,6,5,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,2,5,1,3,6] => [[1,2,7],[3,4],[5,6]] => 010100
[4,7,2,5,1,6,3] => [[1,2,6],[3,4],[5,7]] => 010101
[4,7,2,5,3,1,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,2,5,3,6,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,2,5,6,1,3] => [[1,2,5],[3,4],[6,7]] => 010010
[4,7,2,5,6,3,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,2,6,1,3,5] => [[1,2,7],[3,4],[5,6]] => 010100
[4,7,2,6,1,5,3] => [[1,2],[3,4],[5,6],[7]] => 010101
[4,7,2,6,3,1,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,2,6,3,5,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,2,6,5,1,3] => [[1,2],[3,4],[5,7],[6]] => 010110
[4,7,2,6,5,3,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[4,7,3,1,2,5,6] => [[1,2,6,7],[3,5],[4]] => 011000
[4,7,3,1,2,6,5] => [[1,2,6],[3,5],[4,7]] => 011001
[4,7,3,1,5,2,6] => [[1,2,7],[3,5],[4,6]] => 011010
[4,7,3,1,5,6,2] => [[1,2,6],[3,5],[4,7]] => 011001
[4,7,3,1,6,2,5] => [[1,2,7],[3,5],[4,6]] => 011010
[4,7,3,1,6,5,2] => [[1,2],[3,5],[4,6],[7]] => 011011
[4,7,3,2,1,5,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,3,2,1,6,5] => [[1,2],[3,6],[4,7],[5]] => 011101
[4,7,3,2,5,1,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,3,2,5,6,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,3,2,6,1,5] => [[1,2],[3,5],[4,7],[6]] => 011010
[4,7,3,2,6,5,1] => [[1,2],[3,5],[4,6],[7]] => 011011
[4,7,3,5,1,2,6] => [[1,2,7],[3,4],[5,6]] => 010100
[4,7,3,5,1,6,2] => [[1,2,6],[3,4],[5,7]] => 010101
[4,7,3,5,2,1,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[4,7,3,5,2,6,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[4,7,3,5,6,1,2] => [[1,2,5],[3,4],[6,7]] => 010010
[4,7,3,5,6,2,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[4,7,3,6,1,2,5] => [[1,2,7],[3,4],[5,6]] => 010100
[4,7,3,6,1,5,2] => [[1,2],[3,4],[5,6],[7]] => 010101
[4,7,3,6,2,1,5] => [[1,2],[3,4],[5,7],[6]] => 010110
[4,7,3,6,2,5,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[4,7,3,6,5,1,2] => [[1,2],[3,4],[5,7],[6]] => 010110
[4,7,3,6,5,2,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[4,7,5,1,2,3,6] => [[1,2,6,7],[3,5],[4]] => 011000
[4,7,5,1,2,6,3] => [[1,2,6],[3,5,7],[4]] => 011001
[4,7,5,1,3,2,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,5,1,3,6,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,5,1,6,2,3] => [[1,2,5],[3,6,7],[4]] => 011010
[4,7,5,1,6,3,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,7,5,2,1,3,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,5,2,1,6,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,7,5,2,3,1,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,5,2,3,6,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,5,2,6,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,7,5,2,6,3,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[4,7,5,3,1,2,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,5,3,1,6,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[4,7,5,3,2,1,6] => [[1,2,7],[3],[4],[5],[6]] => 011110
[4,7,5,3,2,6,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[4,7,5,3,6,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[4,7,5,3,6,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[4,7,5,6,1,2,3] => [[1,2,4],[3,6,7],[5]] => 010100
[4,7,5,6,1,3,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,7,5,6,2,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,7,5,6,2,3,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[4,7,5,6,3,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[4,7,5,6,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[4,7,6,1,2,3,5] => [[1,2,6,7],[3,5],[4]] => 011000
[4,7,6,1,2,5,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,6,1,3,2,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,6,1,3,5,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,6,1,5,2,3] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,6,1,5,3,2] => [[1,2],[3,5],[4],[6],[7]] => 011011
[4,7,6,2,1,3,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,6,2,1,5,3] => [[1,2],[3,6],[4,7],[5]] => 011101
[4,7,6,2,3,1,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[4,7,6,2,3,5,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[4,7,6,2,5,1,3] => [[1,2],[3,5],[4,7],[6]] => 011010
[4,7,6,2,5,3,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[4,7,6,3,1,2,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,6,3,1,5,2] => [[1,2],[3,6],[4,7],[5]] => 011101
[4,7,6,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => 011110
[4,7,6,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[4,7,6,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => 011010
[4,7,6,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[4,7,6,5,1,2,3] => [[1,2,7],[3,6],[4],[5]] => 011100
[4,7,6,5,1,3,2] => [[1,2],[3,6],[4],[5],[7]] => 011101
[4,7,6,5,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => 011110
[4,7,6,5,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[4,7,6,5,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 011110
[4,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => 100000
[5,1,2,3,4,7,6] => [[1,3,4,5,6],[2,7]] => 100001
[5,1,2,3,6,4,7] => [[1,3,4,5,7],[2,6]] => 100010
[5,1,2,3,6,7,4] => [[1,3,4,5,6],[2,7]] => 100001
[5,1,2,3,7,4,6] => [[1,3,4,5,7],[2,6]] => 100010
[5,1,2,3,7,6,4] => [[1,3,4,5],[2,6],[7]] => 100011
[5,1,2,4,3,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[5,1,2,4,3,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[5,1,2,4,6,3,7] => [[1,3,4,5,7],[2],[6]] => 100010
[5,1,2,4,6,7,3] => [[1,3,4,5,6],[2],[7]] => 100001
[5,1,2,4,7,3,6] => [[1,3,4,5],[2,7],[6]] => 100010
[5,1,2,4,7,6,3] => [[1,3,4,5],[2,6],[7]] => 100011
[5,1,2,6,3,4,7] => [[1,3,4,6,7],[2,5]] => 100100
[5,1,2,6,3,7,4] => [[1,3,4,6],[2,5,7]] => 100101
[5,1,2,6,4,3,7] => [[1,3,4,7],[2,5],[6]] => 100110
[5,1,2,6,4,7,3] => [[1,3,4,6],[2,5],[7]] => 100101
[5,1,2,6,7,3,4] => [[1,3,4,5],[2,6,7]] => 100010
[5,1,2,6,7,4,3] => [[1,3,4,5],[2,6],[7]] => 100011
[5,1,2,7,3,4,6] => [[1,3,4,6,7],[2,5]] => 100100
[5,1,2,7,3,6,4] => [[1,3,4,6],[2,5],[7]] => 100101
[5,1,2,7,4,3,6] => [[1,3,4,7],[2,5],[6]] => 100110
[5,1,2,7,4,6,3] => [[1,3,4,6],[2,5],[7]] => 100101
[5,1,2,7,6,3,4] => [[1,3,4,7],[2,5],[6]] => 100110
[5,1,2,7,6,4,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,1,3,2,4,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[5,1,3,2,4,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[5,1,3,2,6,4,7] => [[1,3,5,7],[2,6],[4]] => 101010
[5,1,3,2,6,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[5,1,3,2,7,4,6] => [[1,3,5,7],[2,6],[4]] => 101010
[5,1,3,2,7,6,4] => [[1,3,5],[2,6],[4,7]] => 101011
[5,1,3,4,2,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[5,1,3,4,2,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[5,1,3,4,6,2,7] => [[1,3,4,5,7],[2],[6]] => 100010
[5,1,3,4,6,7,2] => [[1,3,4,5,6],[2],[7]] => 100001
[5,1,3,4,7,2,6] => [[1,3,4,5],[2,7],[6]] => 100010
[5,1,3,4,7,6,2] => [[1,3,4,5],[2,6],[7]] => 100011
[5,1,3,6,2,4,7] => [[1,3,4,7],[2,6],[5]] => 100100
[5,1,3,6,2,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[5,1,3,6,4,2,7] => [[1,3,4,7],[2,5],[6]] => 100110
[5,1,3,6,4,7,2] => [[1,3,4,6],[2,5],[7]] => 100101
[5,1,3,6,7,2,4] => [[1,3,4,5],[2,7],[6]] => 100010
[5,1,3,6,7,4,2] => [[1,3,4,5],[2,6],[7]] => 100011
[5,1,3,7,2,4,6] => [[1,3,4,7],[2,6],[5]] => 100100
[5,1,3,7,2,6,4] => [[1,3,4],[2,6],[5,7]] => 100101
[5,1,3,7,4,2,6] => [[1,3,4,7],[2,5],[6]] => 100110
[5,1,3,7,4,6,2] => [[1,3,4,6],[2,5],[7]] => 100101
[5,1,3,7,6,2,4] => [[1,3,4],[2,5],[6,7]] => 100110
[5,1,3,7,6,4,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,1,4,2,3,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[5,1,4,2,3,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[5,1,4,2,6,3,7] => [[1,3,5,7],[2,6],[4]] => 101010
[5,1,4,2,6,7,3] => [[1,3,5,6],[2,7],[4]] => 101001
[5,1,4,2,7,3,6] => [[1,3,5,7],[2,6],[4]] => 101010
[5,1,4,2,7,6,3] => [[1,3,5],[2,6],[4,7]] => 101011
[5,1,4,3,2,6,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[5,1,4,3,2,7,6] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,1,4,3,6,2,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[5,1,4,3,6,7,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[5,1,4,3,7,2,6] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,1,4,3,7,6,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,1,4,6,2,3,7] => [[1,3,4,7],[2,6],[5]] => 100100
[5,1,4,6,2,7,3] => [[1,3,4,6],[2,7],[5]] => 100101
[5,1,4,6,3,2,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[5,1,4,6,3,7,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[5,1,4,6,7,2,3] => [[1,3,4,5],[2,7],[6]] => 100010
[5,1,4,6,7,3,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[5,1,4,7,2,3,6] => [[1,3,4,7],[2,6],[5]] => 100100
[5,1,4,7,2,6,3] => [[1,3,4],[2,6],[5,7]] => 100101
[5,1,4,7,3,2,6] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,1,4,7,3,6,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,1,4,7,6,2,3] => [[1,3,4],[2,5],[6,7]] => 100110
[5,1,4,7,6,3,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,1,6,2,3,4,7] => [[1,3,5,6,7],[2,4]] => 101000
[5,1,6,2,3,7,4] => [[1,3,5,6],[2,4,7]] => 101001
[5,1,6,2,4,3,7] => [[1,3,5,7],[2,4],[6]] => 101010
[5,1,6,2,4,7,3] => [[1,3,5,6],[2,4],[7]] => 101001
[5,1,6,2,7,3,4] => [[1,3,5,7],[2,4,6]] => 101010
[5,1,6,2,7,4,3] => [[1,3,5],[2,4,6],[7]] => 101011
[5,1,6,3,2,4,7] => [[1,3,6,7],[2,4],[5]] => 101100
[5,1,6,3,2,7,4] => [[1,3,6],[2,4,7],[5]] => 101101
[5,1,6,3,4,2,7] => [[1,3,5,7],[2,4],[6]] => 101010
[5,1,6,3,4,7,2] => [[1,3,5,6],[2,4],[7]] => 101001
[5,1,6,3,7,2,4] => [[1,3,5],[2,4,7],[6]] => 101010
[5,1,6,3,7,4,2] => [[1,3,5],[2,4,6],[7]] => 101011
[5,1,6,4,2,3,7] => [[1,3,6,7],[2,4],[5]] => 101100
[5,1,6,4,2,7,3] => [[1,3,6],[2,4,7],[5]] => 101101
[5,1,6,4,3,2,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,1,6,4,3,7,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,1,6,4,7,2,3] => [[1,3,5],[2,4,7],[6]] => 101010
[5,1,6,4,7,3,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,1,6,7,2,3,4] => [[1,3,4,7],[2,5,6]] => 100100
[5,1,6,7,2,4,3] => [[1,3,4],[2,5,6],[7]] => 100101
[5,1,6,7,3,2,4] => [[1,3,4],[2,5,7],[6]] => 100110
[5,1,6,7,3,4,2] => [[1,3,4],[2,5,6],[7]] => 100101
[5,1,6,7,4,2,3] => [[1,3,4],[2,5,7],[6]] => 100110
[5,1,6,7,4,3,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,1,7,2,3,4,6] => [[1,3,5,6,7],[2,4]] => 101000
[5,1,7,2,3,6,4] => [[1,3,5,6],[2,4],[7]] => 101001
[5,1,7,2,4,3,6] => [[1,3,5,7],[2,4],[6]] => 101010
[5,1,7,2,4,6,3] => [[1,3,5,6],[2,4],[7]] => 101001
[5,1,7,2,6,3,4] => [[1,3,5,7],[2,4],[6]] => 101010
[5,1,7,2,6,4,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,1,7,3,2,4,6] => [[1,3,6,7],[2,4],[5]] => 101100
[5,1,7,3,2,6,4] => [[1,3,6],[2,4],[5,7]] => 101101
[5,1,7,3,4,2,6] => [[1,3,5,7],[2,4],[6]] => 101010
[5,1,7,3,4,6,2] => [[1,3,5,6],[2,4],[7]] => 101001
[5,1,7,3,6,2,4] => [[1,3,5],[2,4],[6,7]] => 101010
[5,1,7,3,6,4,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,1,7,4,2,3,6] => [[1,3,6,7],[2,4],[5]] => 101100
[5,1,7,4,2,6,3] => [[1,3,6],[2,4],[5,7]] => 101101
[5,1,7,4,3,2,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,1,7,4,3,6,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,1,7,4,6,2,3] => [[1,3,5],[2,4],[6,7]] => 101010
[5,1,7,4,6,3,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,1,7,6,2,3,4] => [[1,3,6,7],[2,4],[5]] => 101100
[5,1,7,6,2,4,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,1,7,6,3,2,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,1,7,6,3,4,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,1,7,6,4,2,3] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,1,7,6,4,3,2] => [[1,3],[2,4],[5],[6],[7]] => 101111
[5,2,1,3,4,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[5,2,1,3,4,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[5,2,1,3,6,4,7] => [[1,4,5,7],[2,6],[3]] => 110010
[5,2,1,3,6,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[5,2,1,3,7,4,6] => [[1,4,5,7],[2,6],[3]] => 110010
[5,2,1,3,7,6,4] => [[1,4,5],[2,6],[3,7]] => 110011
[5,2,1,4,3,6,7] => [[1,4,6,7],[2,5],[3]] => 110100
[5,2,1,4,3,7,6] => [[1,4,6],[2,5,7],[3]] => 110101
[5,2,1,4,6,3,7] => [[1,4,5,7],[2,6],[3]] => 110010
[5,2,1,4,6,7,3] => [[1,4,5,6],[2,7],[3]] => 110001
[5,2,1,4,7,3,6] => [[1,4,5],[2,6,7],[3]] => 110010
[5,2,1,4,7,6,3] => [[1,4,5],[2,6],[3,7]] => 110011
[5,2,1,6,3,4,7] => [[1,4,6,7],[2,5],[3]] => 110100
[5,2,1,6,3,7,4] => [[1,4,6],[2,5,7],[3]] => 110101
[5,2,1,6,4,3,7] => [[1,4,7],[2,5],[3,6]] => 110110
[5,2,1,6,4,7,3] => [[1,4,6],[2,5],[3,7]] => 110101
[5,2,1,6,7,3,4] => [[1,4,5],[2,6,7],[3]] => 110010
[5,2,1,6,7,4,3] => [[1,4,5],[2,6],[3,7]] => 110011
[5,2,1,7,3,4,6] => [[1,4,6,7],[2,5],[3]] => 110100
[5,2,1,7,3,6,4] => [[1,4,6],[2,5],[3,7]] => 110101
[5,2,1,7,4,3,6] => [[1,4,7],[2,5],[3,6]] => 110110
[5,2,1,7,4,6,3] => [[1,4,6],[2,5],[3,7]] => 110101
[5,2,1,7,6,3,4] => [[1,4,7],[2,5],[3,6]] => 110110
[5,2,1,7,6,4,3] => [[1,4],[2,5],[3,6],[7]] => 110111
[5,2,3,1,4,6,7] => [[1,3,5,6,7],[2],[4]] => 101000
[5,2,3,1,4,7,6] => [[1,3,5,6],[2,7],[4]] => 101001
[5,2,3,1,6,4,7] => [[1,3,5,7],[2,6],[4]] => 101010
[5,2,3,1,6,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[5,2,3,1,7,4,6] => [[1,3,5,7],[2,6],[4]] => 101010
[5,2,3,1,7,6,4] => [[1,3,5],[2,6],[4,7]] => 101011
[5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => 100100
[5,2,3,4,1,7,6] => [[1,3,4,6],[2,7],[5]] => 100101
[5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => 100010
[5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => 100001
[5,2,3,4,7,1,6] => [[1,3,4,5],[2,7],[6]] => 100010
[5,2,3,4,7,6,1] => [[1,3,4,5],[2,6],[7]] => 100011
[5,2,3,6,1,4,7] => [[1,3,4,7],[2,6],[5]] => 100100
[5,2,3,6,1,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[5,2,3,6,4,1,7] => [[1,3,4,7],[2,5],[6]] => 100110
[5,2,3,6,4,7,1] => [[1,3,4,6],[2,5],[7]] => 100101
[5,2,3,6,7,1,4] => [[1,3,4,5],[2,7],[6]] => 100010
[5,2,3,6,7,4,1] => [[1,3,4,5],[2,6],[7]] => 100011
[5,2,3,7,1,4,6] => [[1,3,4,7],[2,6],[5]] => 100100
[5,2,3,7,1,6,4] => [[1,3,4],[2,6],[5,7]] => 100101
[5,2,3,7,4,1,6] => [[1,3,4,7],[2,5],[6]] => 100110
[5,2,3,7,4,6,1] => [[1,3,4,6],[2,5],[7]] => 100101
[5,2,3,7,6,1,4] => [[1,3,4],[2,5],[6,7]] => 100110
[5,2,3,7,6,4,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,2,4,1,3,6,7] => [[1,3,6,7],[2,5],[4]] => 101000
[5,2,4,1,3,7,6] => [[1,3,6],[2,5,7],[4]] => 101001
[5,2,4,1,6,3,7] => [[1,3,5,7],[2,6],[4]] => 101010
[5,2,4,1,6,7,3] => [[1,3,5,6],[2,7],[4]] => 101001
[5,2,4,1,7,3,6] => [[1,3,5],[2,6,7],[4]] => 101010
[5,2,4,1,7,6,3] => [[1,3,5],[2,6],[4,7]] => 101011
[5,2,4,3,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[5,2,4,3,1,7,6] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,2,4,3,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[5,2,4,3,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[5,2,4,3,7,1,6] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,2,4,3,7,6,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,2,4,6,1,3,7] => [[1,3,4,7],[2,6],[5]] => 100100
[5,2,4,6,1,7,3] => [[1,3,4,6],[2,7],[5]] => 100101
[5,2,4,6,3,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[5,2,4,6,3,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[5,2,4,6,7,1,3] => [[1,3,4,5],[2,7],[6]] => 100010
[5,2,4,6,7,3,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[5,2,4,7,1,3,6] => [[1,3,4],[2,6,7],[5]] => 100100
[5,2,4,7,1,6,3] => [[1,3,4],[2,6],[5,7]] => 100101
[5,2,4,7,3,1,6] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,2,4,7,3,6,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,2,4,7,6,1,3] => [[1,3,4],[2,5],[6,7]] => 100110
[5,2,4,7,6,3,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,2,6,1,3,4,7] => [[1,3,6,7],[2,5],[4]] => 101000
[5,2,6,1,3,7,4] => [[1,3,6],[2,5,7],[4]] => 101001
[5,2,6,1,4,3,7] => [[1,3,7],[2,5],[4,6]] => 101010
[5,2,6,1,4,7,3] => [[1,3,6],[2,5],[4,7]] => 101001
[5,2,6,1,7,3,4] => [[1,3,5],[2,6,7],[4]] => 101010
[5,2,6,1,7,4,3] => [[1,3,5],[2,6],[4,7]] => 101011
[5,2,6,3,1,4,7] => [[1,3,6,7],[2,4],[5]] => 101100
[5,2,6,3,1,7,4] => [[1,3,6],[2,4,7],[5]] => 101101
[5,2,6,3,4,1,7] => [[1,3,5,7],[2,4],[6]] => 101010
[5,2,6,3,4,7,1] => [[1,3,5,6],[2,4],[7]] => 101001
[5,2,6,3,7,1,4] => [[1,3,5],[2,4,7],[6]] => 101010
[5,2,6,3,7,4,1] => [[1,3,5],[2,4,6],[7]] => 101011
[5,2,6,4,1,3,7] => [[1,3,7],[2,4],[5,6]] => 101100
[5,2,6,4,1,7,3] => [[1,3,6],[2,4],[5,7]] => 101101
[5,2,6,4,3,1,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,2,6,4,3,7,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,2,6,4,7,1,3] => [[1,3,5],[2,4],[6,7]] => 101010
[5,2,6,4,7,3,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 100100
[5,2,6,7,1,4,3] => [[1,3,4],[2,6],[5,7]] => 100101
[5,2,6,7,3,1,4] => [[1,3,4],[2,5,7],[6]] => 100110
[5,2,6,7,3,4,1] => [[1,3,4],[2,5,6],[7]] => 100101
[5,2,6,7,4,1,3] => [[1,3,4],[2,5],[6,7]] => 100110
[5,2,6,7,4,3,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,2,7,1,3,4,6] => [[1,3,6,7],[2,5],[4]] => 101000
[5,2,7,1,3,6,4] => [[1,3,6],[2,5],[4,7]] => 101001
[5,2,7,1,4,3,6] => [[1,3,7],[2,5],[4,6]] => 101010
[5,2,7,1,4,6,3] => [[1,3,6],[2,5],[4,7]] => 101001
[5,2,7,1,6,3,4] => [[1,3,7],[2,5],[4,6]] => 101010
[5,2,7,1,6,4,3] => [[1,3],[2,5],[4,6],[7]] => 101011
[5,2,7,3,1,4,6] => [[1,3,6,7],[2,4],[5]] => 101100
[5,2,7,3,1,6,4] => [[1,3,6],[2,4],[5,7]] => 101101
[5,2,7,3,4,1,6] => [[1,3,5,7],[2,4],[6]] => 101010
[5,2,7,3,4,6,1] => [[1,3,5,6],[2,4],[7]] => 101001
[5,2,7,3,6,1,4] => [[1,3,5],[2,4],[6,7]] => 101010
[5,2,7,3,6,4,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,2,7,4,1,3,6] => [[1,3,7],[2,4],[5,6]] => 101100
[5,2,7,4,1,6,3] => [[1,3,6],[2,4],[5,7]] => 101101
[5,2,7,4,3,1,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,2,7,4,3,6,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,2,7,4,6,1,3] => [[1,3,5],[2,4],[6,7]] => 101010
[5,2,7,4,6,3,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,2,7,6,1,3,4] => [[1,3,7],[2,4],[5,6]] => 101100
[5,2,7,6,1,4,3] => [[1,3],[2,4],[5,6],[7]] => 101101
[5,2,7,6,3,1,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,2,7,6,3,4,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,2,7,6,4,1,3] => [[1,3],[2,4],[5,7],[6]] => 101110
[5,2,7,6,4,3,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[5,3,1,2,4,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[5,3,1,2,4,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[5,3,1,2,6,4,7] => [[1,4,5,7],[2,6],[3]] => 110010
[5,3,1,2,6,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[5,3,1,2,7,4,6] => [[1,4,5,7],[2,6],[3]] => 110010
[5,3,1,2,7,6,4] => [[1,4,5],[2,6],[3,7]] => 110011
[5,3,1,4,2,6,7] => [[1,4,6,7],[2,5],[3]] => 110100
[5,3,1,4,2,7,6] => [[1,4,6],[2,5,7],[3]] => 110101
[5,3,1,4,6,2,7] => [[1,4,5,7],[2,6],[3]] => 110010
[5,3,1,4,6,7,2] => [[1,4,5,6],[2,7],[3]] => 110001
[5,3,1,4,7,2,6] => [[1,4,5],[2,6,7],[3]] => 110010
[5,3,1,4,7,6,2] => [[1,4,5],[2,6],[3,7]] => 110011
[5,3,1,6,2,4,7] => [[1,4,6,7],[2,5],[3]] => 110100
[5,3,1,6,2,7,4] => [[1,4,6],[2,5,7],[3]] => 110101
[5,3,1,6,4,2,7] => [[1,4,7],[2,5],[3,6]] => 110110
[5,3,1,6,4,7,2] => [[1,4,6],[2,5],[3,7]] => 110101
[5,3,1,6,7,2,4] => [[1,4,5],[2,6,7],[3]] => 110010
[5,3,1,6,7,4,2] => [[1,4,5],[2,6],[3,7]] => 110011
[5,3,1,7,2,4,6] => [[1,4,6,7],[2,5],[3]] => 110100
[5,3,1,7,2,6,4] => [[1,4,6],[2,5],[3,7]] => 110101
[5,3,1,7,4,2,6] => [[1,4,7],[2,5],[3,6]] => 110110
[5,3,1,7,4,6,2] => [[1,4,6],[2,5],[3,7]] => 110101
[5,3,1,7,6,2,4] => [[1,4,7],[2,5],[3,6]] => 110110
[5,3,1,7,6,4,2] => [[1,4],[2,5],[3,6],[7]] => 110111
[5,3,2,1,4,6,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[5,3,2,1,4,7,6] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,3,2,1,6,4,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,3,2,1,6,7,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,3,2,1,7,4,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,3,2,1,7,6,4] => [[1,5],[2,6],[3,7],[4]] => 111011
[5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[5,3,2,4,1,7,6] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[5,3,2,4,7,1,6] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,3,2,4,7,6,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,3,2,6,1,4,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,3,2,6,1,7,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,3,2,6,4,1,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,3,2,6,4,7,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,3,2,6,7,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,3,2,6,7,4,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,3,2,7,1,4,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,3,2,7,1,6,4] => [[1,4],[2,6],[3,7],[5]] => 110101
[5,3,2,7,4,1,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,3,2,7,4,6,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,3,2,7,6,1,4] => [[1,4],[2,5],[3,7],[6]] => 110110
[5,3,2,7,6,4,1] => [[1,4],[2,5],[3,6],[7]] => 110111
[5,3,4,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => 101000
[5,3,4,1,2,7,6] => [[1,3,6],[2,5,7],[4]] => 101001
[5,3,4,1,6,2,7] => [[1,3,5,7],[2,6],[4]] => 101010
[5,3,4,1,6,7,2] => [[1,3,5,6],[2,7],[4]] => 101001
[5,3,4,1,7,2,6] => [[1,3,5],[2,6,7],[4]] => 101010
[5,3,4,1,7,6,2] => [[1,3,5],[2,6],[4,7]] => 101011
[5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[5,3,4,2,1,7,6] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[5,3,4,2,7,1,6] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,3,4,2,7,6,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,3,4,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => 100100
[5,3,4,6,1,7,2] => [[1,3,4,6],[2,7],[5]] => 100101
[5,3,4,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[5,3,4,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[5,3,4,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => 100010
[5,3,4,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[5,3,4,7,1,2,6] => [[1,3,4],[2,6,7],[5]] => 100100
[5,3,4,7,1,6,2] => [[1,3,4],[2,6],[5,7]] => 100101
[5,3,4,7,2,1,6] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,3,4,7,2,6,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,3,4,7,6,1,2] => [[1,3,4],[2,5],[6,7]] => 100110
[5,3,4,7,6,2,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,3,6,1,2,4,7] => [[1,3,6,7],[2,5],[4]] => 101000
[5,3,6,1,2,7,4] => [[1,3,6],[2,5,7],[4]] => 101001
[5,3,6,1,4,2,7] => [[1,3,7],[2,5],[4,6]] => 101010
[5,3,6,1,4,7,2] => [[1,3,6],[2,5],[4,7]] => 101001
[5,3,6,1,7,2,4] => [[1,3,5],[2,6,7],[4]] => 101010
[5,3,6,1,7,4,2] => [[1,3,5],[2,6],[4,7]] => 101011
[5,3,6,2,1,4,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,3,6,2,1,7,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,3,6,2,4,1,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,3,6,2,4,7,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,3,6,2,7,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,3,6,2,7,4,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,3,6,4,1,2,7] => [[1,3,7],[2,4],[5,6]] => 101100
[5,3,6,4,1,7,2] => [[1,3,6],[2,4],[5,7]] => 101101
[5,3,6,4,2,1,7] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,3,6,4,2,7,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,3,6,4,7,1,2] => [[1,3,5],[2,4],[6,7]] => 101010
[5,3,6,4,7,2,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,3,6,7,1,2,4] => [[1,3,4],[2,6,7],[5]] => 100100
[5,3,6,7,1,4,2] => [[1,3,4],[2,6],[5,7]] => 100101
[5,3,6,7,2,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,3,6,7,2,4,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,3,6,7,4,1,2] => [[1,3,4],[2,5],[6,7]] => 100110
[5,3,6,7,4,2,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[5,3,7,1,2,4,6] => [[1,3,6,7],[2,5],[4]] => 101000
[5,3,7,1,2,6,4] => [[1,3,6],[2,5],[4,7]] => 101001
[5,3,7,1,4,2,6] => [[1,3,7],[2,5],[4,6]] => 101010
[5,3,7,1,4,6,2] => [[1,3,6],[2,5],[4,7]] => 101001
[5,3,7,1,6,2,4] => [[1,3,7],[2,5],[4,6]] => 101010
[5,3,7,1,6,4,2] => [[1,3],[2,5],[4,6],[7]] => 101011
[5,3,7,2,1,4,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,3,7,2,1,6,4] => [[1,3],[2,6],[4,7],[5]] => 101101
[5,3,7,2,4,1,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,3,7,2,4,6,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,3,7,2,6,1,4] => [[1,3],[2,5],[4,7],[6]] => 101010
[5,3,7,2,6,4,1] => [[1,3],[2,5],[4,6],[7]] => 101011
[5,3,7,4,1,2,6] => [[1,3,7],[2,4],[5,6]] => 101100
[5,3,7,4,1,6,2] => [[1,3,6],[2,4],[5,7]] => 101101
[5,3,7,4,2,1,6] => [[1,3,7],[2,4],[5],[6]] => 101110
[5,3,7,4,2,6,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[5,3,7,4,6,1,2] => [[1,3,5],[2,4],[6,7]] => 101010
[5,3,7,4,6,2,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[5,3,7,6,1,2,4] => [[1,3,7],[2,4],[5,6]] => 101100
[5,3,7,6,1,4,2] => [[1,3],[2,4],[5,6],[7]] => 101101
[5,3,7,6,2,1,4] => [[1,3],[2,4],[5,7],[6]] => 101110
[5,3,7,6,2,4,1] => [[1,3],[2,4],[5,6],[7]] => 101101
[5,3,7,6,4,1,2] => [[1,3],[2,4],[5,7],[6]] => 101110
[5,3,7,6,4,2,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[5,4,1,2,3,6,7] => [[1,4,5,6,7],[2],[3]] => 110000
[5,4,1,2,3,7,6] => [[1,4,5,6],[2,7],[3]] => 110001
[5,4,1,2,6,3,7] => [[1,4,5,7],[2,6],[3]] => 110010
[5,4,1,2,6,7,3] => [[1,4,5,6],[2,7],[3]] => 110001
[5,4,1,2,7,3,6] => [[1,4,5,7],[2,6],[3]] => 110010
[5,4,1,2,7,6,3] => [[1,4,5],[2,6],[3,7]] => 110011
[5,4,1,3,2,6,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[5,4,1,3,2,7,6] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,4,1,3,6,2,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[5,4,1,3,6,7,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[5,4,1,3,7,2,6] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,4,1,3,7,6,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,4,1,6,2,3,7] => [[1,4,6,7],[2,5],[3]] => 110100
[5,4,1,6,2,7,3] => [[1,4,6],[2,5,7],[3]] => 110101
[5,4,1,6,3,2,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,4,1,6,3,7,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,4,1,6,7,2,3] => [[1,4,5],[2,6,7],[3]] => 110010
[5,4,1,6,7,3,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,4,1,7,2,3,6] => [[1,4,6,7],[2,5],[3]] => 110100
[5,4,1,7,2,6,3] => [[1,4,6],[2,5],[3,7]] => 110101
[5,4,1,7,3,2,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,4,1,7,3,6,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,4,1,7,6,2,3] => [[1,4,7],[2,5],[3,6]] => 110110
[5,4,1,7,6,3,2] => [[1,4],[2,5],[3,6],[7]] => 110111
[5,4,2,1,3,6,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[5,4,2,1,3,7,6] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,4,2,1,6,3,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,4,2,1,6,7,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,4,2,1,7,3,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,4,2,1,7,6,3] => [[1,5],[2,6],[3,7],[4]] => 111011
[5,4,2,3,1,6,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[5,4,2,3,1,7,6] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,4,2,3,6,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[5,4,2,3,6,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[5,4,2,3,7,1,6] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,4,2,3,7,6,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,4,2,6,1,3,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,4,2,6,1,7,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,4,2,6,3,1,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,4,2,6,3,7,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,4,2,6,7,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,4,2,6,7,3,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[5,4,2,7,1,3,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,4,2,7,1,6,3] => [[1,4],[2,6],[3,7],[5]] => 110101
[5,4,2,7,3,1,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[5,4,2,7,3,6,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[5,4,2,7,6,1,3] => [[1,4],[2,5],[3,7],[6]] => 110110
[5,4,2,7,6,3,1] => [[1,4],[2,5],[3,6],[7]] => 110111
[5,4,3,1,2,6,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[5,4,3,1,2,7,6] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,4,3,1,6,2,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,4,3,1,6,7,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[5,4,3,1,7,2,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[5,4,3,1,7,6,2] => [[1,5],[2,6],[3,7],[4]] => 111011
[5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => 111100
[5,4,3,2,1,7,6] => [[1,6],[2,7],[3],[4],[5]] => 111101
[5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => 111010
[5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[5,4,3,2,7,1,6] => [[1,5],[2,7],[3],[4],[6]] => 111010
[5,4,3,2,7,6,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[5,4,3,6,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,4,3,6,1,7,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 110110
[5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[5,4,3,6,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[5,4,3,7,1,2,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[5,4,3,7,1,6,2] => [[1,4],[2,6],[3,7],[5]] => 110101
[5,4,3,7,2,1,6] => [[1,4],[2,7],[3],[5],[6]] => 110110
[5,4,3,7,2,6,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[5,4,3,7,6,1,2] => [[1,4],[2,5],[3,7],[6]] => 110110
[5,4,3,7,6,2,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[5,4,6,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => 101000
[5,4,6,1,2,7,3] => [[1,3,6],[2,5,7],[4]] => 101001
[5,4,6,1,3,2,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,4,6,1,3,7,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,4,6,1,7,2,3] => [[1,3,5],[2,6,7],[4]] => 101010
[5,4,6,1,7,3,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,4,6,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,4,6,2,1,7,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,4,6,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,4,6,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,4,6,2,7,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,4,6,2,7,3,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[5,4,6,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,4,6,3,1,7,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 101110
[5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[5,4,6,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[5,4,6,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 100100
[5,4,6,7,1,3,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,4,6,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,4,6,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[5,4,6,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[5,4,7,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => 101000
[5,4,7,1,2,6,3] => [[1,3,6],[2,5],[4,7]] => 101001
[5,4,7,1,3,2,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,4,7,1,3,6,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,4,7,1,6,2,3] => [[1,3,7],[2,5],[4,6]] => 101010
[5,4,7,1,6,3,2] => [[1,3],[2,5],[4,6],[7]] => 101011
[5,4,7,2,1,3,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,4,7,2,1,6,3] => [[1,3],[2,6],[4,7],[5]] => 101101
[5,4,7,2,3,1,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[5,4,7,2,3,6,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[5,4,7,2,6,1,3] => [[1,3],[2,5],[4,7],[6]] => 101010
[5,4,7,2,6,3,1] => [[1,3],[2,5],[4,6],[7]] => 101011
[5,4,7,3,1,2,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[5,4,7,3,1,6,2] => [[1,3],[2,6],[4,7],[5]] => 101101
[5,4,7,3,2,1,6] => [[1,3],[2,7],[4],[5],[6]] => 101110
[5,4,7,3,2,6,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[5,4,7,3,6,1,2] => [[1,3],[2,5],[4,7],[6]] => 101010
[5,4,7,3,6,2,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[5,4,7,6,1,2,3] => [[1,3,7],[2,4],[5,6]] => 101100
[5,4,7,6,1,3,2] => [[1,3],[2,4],[5,6],[7]] => 101101
[5,4,7,6,2,1,3] => [[1,3],[2,4],[5,7],[6]] => 101110
[5,4,7,6,2,3,1] => [[1,3],[2,4],[5,6],[7]] => 101101
[5,4,7,6,3,1,2] => [[1,3],[2,4],[5,7],[6]] => 101110
[5,4,7,6,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => 010000
[5,6,1,2,3,7,4] => [[1,2,5,6],[3,4,7]] => 010001
[5,6,1,2,4,3,7] => [[1,2,5,7],[3,4],[6]] => 010010
[5,6,1,2,4,7,3] => [[1,2,5,6],[3,4],[7]] => 010001
[5,6,1,2,7,3,4] => [[1,2,5,7],[3,4,6]] => 010010
[5,6,1,2,7,4,3] => [[1,2,5],[3,4,6],[7]] => 010011
[5,6,1,3,2,4,7] => [[1,2,6,7],[3,4],[5]] => 010100
[5,6,1,3,2,7,4] => [[1,2,6],[3,4,7],[5]] => 010101
[5,6,1,3,4,2,7] => [[1,2,5,7],[3,4],[6]] => 010010
[5,6,1,3,4,7,2] => [[1,2,5,6],[3,4],[7]] => 010001
[5,6,1,3,7,2,4] => [[1,2,5],[3,4,7],[6]] => 010010
[5,6,1,3,7,4,2] => [[1,2,5],[3,4,6],[7]] => 010011
[5,6,1,4,2,3,7] => [[1,2,6,7],[3,4],[5]] => 010100
[5,6,1,4,2,7,3] => [[1,2,6],[3,4,7],[5]] => 010101
[5,6,1,4,3,2,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,6,1,4,3,7,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,6,1,4,7,2,3] => [[1,2,5],[3,4,7],[6]] => 010010
[5,6,1,4,7,3,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,6,1,7,2,3,4] => [[1,2,4,7],[3,5,6]] => 010100
[5,6,1,7,2,4,3] => [[1,2,4],[3,5,6],[7]] => 010101
[5,6,1,7,3,2,4] => [[1,2,4],[3,5,7],[6]] => 010110
[5,6,1,7,3,4,2] => [[1,2,4],[3,5,6],[7]] => 010101
[5,6,1,7,4,2,3] => [[1,2,4],[3,5,7],[6]] => 010110
[5,6,1,7,4,3,2] => [[1,2,4],[3,5],[6],[7]] => 010111
[5,6,2,1,3,4,7] => [[1,2,6,7],[3,5],[4]] => 011000
[5,6,2,1,3,7,4] => [[1,2,6],[3,5,7],[4]] => 011001
[5,6,2,1,4,3,7] => [[1,2,7],[3,5],[4,6]] => 011010
[5,6,2,1,4,7,3] => [[1,2,6],[3,5],[4,7]] => 011001
[5,6,2,1,7,3,4] => [[1,2,5],[3,6,7],[4]] => 011010
[5,6,2,1,7,4,3] => [[1,2,5],[3,6],[4,7]] => 011011
[5,6,2,3,1,4,7] => [[1,2,6,7],[3,4],[5]] => 010100
[5,6,2,3,1,7,4] => [[1,2,6],[3,4,7],[5]] => 010101
[5,6,2,3,4,1,7] => [[1,2,5,7],[3,4],[6]] => 010010
[5,6,2,3,4,7,1] => [[1,2,5,6],[3,4],[7]] => 010001
[5,6,2,3,7,1,4] => [[1,2,5],[3,4,7],[6]] => 010010
[5,6,2,3,7,4,1] => [[1,2,5],[3,4,6],[7]] => 010011
[5,6,2,4,1,3,7] => [[1,2,7],[3,4],[5,6]] => 010100
[5,6,2,4,1,7,3] => [[1,2,6],[3,4],[5,7]] => 010101
[5,6,2,4,3,1,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,6,2,4,3,7,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,6,2,4,7,1,3] => [[1,2,5],[3,4],[6,7]] => 010010
[5,6,2,4,7,3,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,6,2,7,1,3,4] => [[1,2,4],[3,6,7],[5]] => 010100
[5,6,2,7,1,4,3] => [[1,2,4],[3,6],[5,7]] => 010101
[5,6,2,7,3,1,4] => [[1,2,4],[3,5,7],[6]] => 010110
[5,6,2,7,3,4,1] => [[1,2,4],[3,5,6],[7]] => 010101
[5,6,2,7,4,1,3] => [[1,2,4],[3,5],[6,7]] => 010110
[5,6,2,7,4,3,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[5,6,3,1,2,4,7] => [[1,2,6,7],[3,5],[4]] => 011000
[5,6,3,1,2,7,4] => [[1,2,6],[3,5,7],[4]] => 011001
[5,6,3,1,4,2,7] => [[1,2,7],[3,5],[4,6]] => 011010
[5,6,3,1,4,7,2] => [[1,2,6],[3,5],[4,7]] => 011001
[5,6,3,1,7,2,4] => [[1,2,5],[3,6,7],[4]] => 011010
[5,6,3,1,7,4,2] => [[1,2,5],[3,6],[4,7]] => 011011
[5,6,3,2,1,4,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,6,3,2,1,7,4] => [[1,2,6],[3,7],[4],[5]] => 011101
[5,6,3,2,4,1,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,6,3,2,4,7,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,6,3,2,7,1,4] => [[1,2,5],[3,7],[4],[6]] => 011010
[5,6,3,2,7,4,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => 010100
[5,6,3,4,1,7,2] => [[1,2,6],[3,4],[5,7]] => 010101
[5,6,3,4,2,1,7] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,6,3,4,2,7,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,6,3,4,7,1,2] => [[1,2,5],[3,4],[6,7]] => 010010
[5,6,3,4,7,2,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,6,3,7,1,2,4] => [[1,2,4],[3,6,7],[5]] => 010100
[5,6,3,7,1,4,2] => [[1,2,4],[3,6],[5,7]] => 010101
[5,6,3,7,2,1,4] => [[1,2,4],[3,7],[5],[6]] => 010110
[5,6,3,7,2,4,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[5,6,3,7,4,1,2] => [[1,2,4],[3,5],[6,7]] => 010110
[5,6,3,7,4,2,1] => [[1,2,4],[3,5],[6],[7]] => 010111
[5,6,4,1,2,3,7] => [[1,2,6,7],[3,5],[4]] => 011000
[5,6,4,1,2,7,3] => [[1,2,6],[3,5,7],[4]] => 011001
[5,6,4,1,3,2,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,6,4,1,3,7,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,6,4,1,7,2,3] => [[1,2,5],[3,6,7],[4]] => 011010
[5,6,4,1,7,3,2] => [[1,2,5],[3,6],[4],[7]] => 011011
[5,6,4,2,1,3,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,6,4,2,1,7,3] => [[1,2,6],[3,7],[4],[5]] => 011101
[5,6,4,2,3,1,7] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,6,4,2,3,7,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,6,4,2,7,1,3] => [[1,2,5],[3,7],[4],[6]] => 011010
[5,6,4,2,7,3,1] => [[1,2,5],[3,6],[4],[7]] => 011011
[5,6,4,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,6,4,3,1,7,2] => [[1,2,6],[3,7],[4],[5]] => 011101
[5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => 011110
[5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => 011101
[5,6,4,3,7,1,2] => [[1,2,5],[3,7],[4],[6]] => 011010
[5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => 011011
[5,6,4,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => 010100
[5,6,4,7,1,3,2] => [[1,2,4],[3,6],[5],[7]] => 010101
[5,6,4,7,2,1,3] => [[1,2,4],[3,7],[5],[6]] => 010110
[5,6,4,7,2,3,1] => [[1,2,4],[3,6],[5],[7]] => 010101
[5,6,4,7,3,1,2] => [[1,2,4],[3,7],[5],[6]] => 010110
[5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => 010111
[5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => 001000
[5,6,7,1,2,4,3] => [[1,2,3],[4,5,6],[7]] => 001001
[5,6,7,1,3,2,4] => [[1,2,3],[4,5,7],[6]] => 001010
[5,6,7,1,3,4,2] => [[1,2,3],[4,5,6],[7]] => 001001
[5,6,7,1,4,2,3] => [[1,2,3],[4,5,7],[6]] => 001010
[5,6,7,1,4,3,2] => [[1,2,3],[4,5],[6],[7]] => 001011
[5,6,7,2,1,3,4] => [[1,2,3],[4,6,7],[5]] => 001100
[5,6,7,2,1,4,3] => [[1,2,3],[4,6],[5,7]] => 001101
[5,6,7,2,3,1,4] => [[1,2,3],[4,5,7],[6]] => 001010
[5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7]] => 001001
[5,6,7,2,4,1,3] => [[1,2,3],[4,5],[6,7]] => 001010
[5,6,7,2,4,3,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[5,6,7,3,1,2,4] => [[1,2,3],[4,6,7],[5]] => 001100
[5,6,7,3,1,4,2] => [[1,2,3],[4,6],[5,7]] => 001101
[5,6,7,3,2,1,4] => [[1,2,3],[4,7],[5],[6]] => 001110
[5,6,7,3,2,4,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[5,6,7,3,4,1,2] => [[1,2,3],[4,5],[6,7]] => 001010
[5,6,7,3,4,2,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => 001100
[5,6,7,4,1,3,2] => [[1,2,3],[4,6],[5],[7]] => 001101
[5,6,7,4,2,1,3] => [[1,2,3],[4,7],[5],[6]] => 001110
[5,6,7,4,2,3,1] => [[1,2,3],[4,6],[5],[7]] => 001101
[5,6,7,4,3,1,2] => [[1,2,3],[4,7],[5],[6]] => 001110
[5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[5,7,1,2,3,4,6] => [[1,2,5,6,7],[3,4]] => 010000
[5,7,1,2,3,6,4] => [[1,2,5,6],[3,4],[7]] => 010001
[5,7,1,2,4,3,6] => [[1,2,5,7],[3,4],[6]] => 010010
[5,7,1,2,4,6,3] => [[1,2,5,6],[3,4],[7]] => 010001
[5,7,1,2,6,3,4] => [[1,2,5,7],[3,4],[6]] => 010010
[5,7,1,2,6,4,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,1,3,2,4,6] => [[1,2,6,7],[3,4],[5]] => 010100
[5,7,1,3,2,6,4] => [[1,2,6],[3,4],[5,7]] => 010101
[5,7,1,3,4,2,6] => [[1,2,5,7],[3,4],[6]] => 010010
[5,7,1,3,4,6,2] => [[1,2,5,6],[3,4],[7]] => 010001
[5,7,1,3,6,2,4] => [[1,2,5],[3,4],[6,7]] => 010010
[5,7,1,3,6,4,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,1,4,2,3,6] => [[1,2,6,7],[3,4],[5]] => 010100
[5,7,1,4,2,6,3] => [[1,2,6],[3,4],[5,7]] => 010101
[5,7,1,4,3,2,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,1,4,3,6,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,1,4,6,2,3] => [[1,2,5],[3,4],[6,7]] => 010010
[5,7,1,4,6,3,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,1,6,2,3,4] => [[1,2,6,7],[3,4],[5]] => 010100
[5,7,1,6,2,4,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,1,6,3,2,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,1,6,3,4,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,1,6,4,2,3] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,1,6,4,3,2] => [[1,2],[3,4],[5],[6],[7]] => 010111
[5,7,2,1,3,4,6] => [[1,2,6,7],[3,5],[4]] => 011000
[5,7,2,1,3,6,4] => [[1,2,6],[3,5],[4,7]] => 011001
[5,7,2,1,4,3,6] => [[1,2,7],[3,5],[4,6]] => 011010
[5,7,2,1,4,6,3] => [[1,2,6],[3,5],[4,7]] => 011001
[5,7,2,1,6,3,4] => [[1,2,7],[3,5],[4,6]] => 011010
[5,7,2,1,6,4,3] => [[1,2],[3,5],[4,6],[7]] => 011011
[5,7,2,3,1,4,6] => [[1,2,6,7],[3,4],[5]] => 010100
[5,7,2,3,1,6,4] => [[1,2,6],[3,4],[5,7]] => 010101
[5,7,2,3,4,1,6] => [[1,2,5,7],[3,4],[6]] => 010010
[5,7,2,3,4,6,1] => [[1,2,5,6],[3,4],[7]] => 010001
[5,7,2,3,6,1,4] => [[1,2,5],[3,4],[6,7]] => 010010
[5,7,2,3,6,4,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,2,4,1,3,6] => [[1,2,7],[3,4],[5,6]] => 010100
[5,7,2,4,1,6,3] => [[1,2,6],[3,4],[5,7]] => 010101
[5,7,2,4,3,1,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,2,4,3,6,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,2,4,6,1,3] => [[1,2,5],[3,4],[6,7]] => 010010
[5,7,2,4,6,3,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,2,6,1,3,4] => [[1,2,7],[3,4],[5,6]] => 010100
[5,7,2,6,1,4,3] => [[1,2],[3,4],[5,6],[7]] => 010101
[5,7,2,6,3,1,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,2,6,3,4,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,2,6,4,1,3] => [[1,2],[3,4],[5,7],[6]] => 010110
[5,7,2,6,4,3,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[5,7,3,1,2,4,6] => [[1,2,6,7],[3,5],[4]] => 011000
[5,7,3,1,2,6,4] => [[1,2,6],[3,5],[4,7]] => 011001
[5,7,3,1,4,2,6] => [[1,2,7],[3,5],[4,6]] => 011010
[5,7,3,1,4,6,2] => [[1,2,6],[3,5],[4,7]] => 011001
[5,7,3,1,6,2,4] => [[1,2,7],[3,5],[4,6]] => 011010
[5,7,3,1,6,4,2] => [[1,2],[3,5],[4,6],[7]] => 011011
[5,7,3,2,1,4,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,3,2,1,6,4] => [[1,2],[3,6],[4,7],[5]] => 011101
[5,7,3,2,4,1,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,3,2,4,6,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,3,2,6,1,4] => [[1,2],[3,5],[4,7],[6]] => 011010
[5,7,3,2,6,4,1] => [[1,2],[3,5],[4,6],[7]] => 011011
[5,7,3,4,1,2,6] => [[1,2,7],[3,4],[5,6]] => 010100
[5,7,3,4,1,6,2] => [[1,2,6],[3,4],[5,7]] => 010101
[5,7,3,4,2,1,6] => [[1,2,7],[3,4],[5],[6]] => 010110
[5,7,3,4,2,6,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[5,7,3,4,6,1,2] => [[1,2,5],[3,4],[6,7]] => 010010
[5,7,3,4,6,2,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[5,7,3,6,1,2,4] => [[1,2,7],[3,4],[5,6]] => 010100
[5,7,3,6,1,4,2] => [[1,2],[3,4],[5,6],[7]] => 010101
[5,7,3,6,2,1,4] => [[1,2],[3,4],[5,7],[6]] => 010110
[5,7,3,6,2,4,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[5,7,3,6,4,1,2] => [[1,2],[3,4],[5,7],[6]] => 010110
[5,7,3,6,4,2,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[5,7,4,1,2,3,6] => [[1,2,6,7],[3,5],[4]] => 011000
[5,7,4,1,2,6,3] => [[1,2,6],[3,5],[4,7]] => 011001
[5,7,4,1,3,2,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,4,1,3,6,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,4,1,6,2,3] => [[1,2,7],[3,5],[4,6]] => 011010
[5,7,4,1,6,3,2] => [[1,2],[3,5],[4,6],[7]] => 011011
[5,7,4,2,1,3,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,4,2,1,6,3] => [[1,2],[3,6],[4,7],[5]] => 011101
[5,7,4,2,3,1,6] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,4,2,3,6,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,4,2,6,1,3] => [[1,2],[3,5],[4,7],[6]] => 011010
[5,7,4,2,6,3,1] => [[1,2],[3,5],[4,6],[7]] => 011011
[5,7,4,3,1,2,6] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,4,3,1,6,2] => [[1,2],[3,6],[4,7],[5]] => 011101
[5,7,4,3,2,1,6] => [[1,2],[3,7],[4],[5],[6]] => 011110
[5,7,4,3,2,6,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[5,7,4,3,6,1,2] => [[1,2],[3,5],[4,7],[6]] => 011010
[5,7,4,3,6,2,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[5,7,4,6,1,2,3] => [[1,2,7],[3,4],[5,6]] => 010100
[5,7,4,6,1,3,2] => [[1,2],[3,4],[5,6],[7]] => 010101
[5,7,4,6,2,1,3] => [[1,2],[3,4],[5,7],[6]] => 010110
[5,7,4,6,2,3,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[5,7,4,6,3,1,2] => [[1,2],[3,4],[5,7],[6]] => 010110
[5,7,4,6,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[5,7,6,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => 011000
[5,7,6,1,2,4,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,6,1,3,2,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,6,1,3,4,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,6,1,4,2,3] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,6,1,4,3,2] => [[1,2],[3,5],[4],[6],[7]] => 011011
[5,7,6,2,1,3,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,6,2,1,4,3] => [[1,2],[3,6],[4,7],[5]] => 011101
[5,7,6,2,3,1,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[5,7,6,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[5,7,6,2,4,1,3] => [[1,2],[3,5],[4,7],[6]] => 011010
[5,7,6,2,4,3,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[5,7,6,3,1,2,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,6,3,1,4,2] => [[1,2],[3,6],[4,7],[5]] => 011101
[5,7,6,3,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 011110
[5,7,6,3,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[5,7,6,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => 011010
[5,7,6,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[5,7,6,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => 011100
[5,7,6,4,1,3,2] => [[1,2],[3,6],[4],[5],[7]] => 011101
[5,7,6,4,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => 011110
[5,7,6,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[5,7,6,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 011110
[5,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => 100000
[6,1,2,3,4,7,5] => [[1,3,4,5,6],[2,7]] => 100001
[6,1,2,3,5,4,7] => [[1,3,4,5,7],[2],[6]] => 100010
[6,1,2,3,5,7,4] => [[1,3,4,5,6],[2],[7]] => 100001
[6,1,2,3,7,4,5] => [[1,3,4,5,7],[2,6]] => 100010
[6,1,2,3,7,5,4] => [[1,3,4,5],[2,6],[7]] => 100011
[6,1,2,4,3,5,7] => [[1,3,4,6,7],[2],[5]] => 100100
[6,1,2,4,3,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[6,1,2,4,5,3,7] => [[1,3,4,5,7],[2],[6]] => 100010
[6,1,2,4,5,7,3] => [[1,3,4,5,6],[2],[7]] => 100001
[6,1,2,4,7,3,5] => [[1,3,4,5],[2,7],[6]] => 100010
[6,1,2,4,7,5,3] => [[1,3,4,5],[2,6],[7]] => 100011
[6,1,2,5,3,4,7] => [[1,3,4,6,7],[2],[5]] => 100100
[6,1,2,5,3,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[6,1,2,5,4,3,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,1,2,5,4,7,3] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,1,2,5,7,3,4] => [[1,3,4,5],[2,7],[6]] => 100010
[6,1,2,5,7,4,3] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,1,2,7,3,4,5] => [[1,3,4,6,7],[2,5]] => 100100
[6,1,2,7,3,5,4] => [[1,3,4,6],[2,5],[7]] => 100101
[6,1,2,7,4,3,5] => [[1,3,4,7],[2,5],[6]] => 100110
[6,1,2,7,4,5,3] => [[1,3,4,6],[2,5],[7]] => 100101
[6,1,2,7,5,3,4] => [[1,3,4,7],[2,5],[6]] => 100110
[6,1,2,7,5,4,3] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,1,3,2,4,5,7] => [[1,3,5,6,7],[2],[4]] => 101000
[6,1,3,2,4,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[6,1,3,2,5,4,7] => [[1,3,5,7],[2,6],[4]] => 101010
[6,1,3,2,5,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[6,1,3,2,7,4,5] => [[1,3,5,7],[2,6],[4]] => 101010
[6,1,3,2,7,5,4] => [[1,3,5],[2,6],[4,7]] => 101011
[6,1,3,4,2,5,7] => [[1,3,4,6,7],[2],[5]] => 100100
[6,1,3,4,2,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[6,1,3,4,5,2,7] => [[1,3,4,5,7],[2],[6]] => 100010
[6,1,3,4,5,7,2] => [[1,3,4,5,6],[2],[7]] => 100001
[6,1,3,4,7,2,5] => [[1,3,4,5],[2,7],[6]] => 100010
[6,1,3,4,7,5,2] => [[1,3,4,5],[2,6],[7]] => 100011
[6,1,3,5,2,4,7] => [[1,3,4,7],[2,6],[5]] => 100100
[6,1,3,5,2,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[6,1,3,5,4,2,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,1,3,5,4,7,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,1,3,5,7,2,4] => [[1,3,4,5],[2,7],[6]] => 100010
[6,1,3,5,7,4,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,1,3,7,2,4,5] => [[1,3,4,7],[2,6],[5]] => 100100
[6,1,3,7,2,5,4] => [[1,3,4],[2,6],[5,7]] => 100101
[6,1,3,7,4,2,5] => [[1,3,4,7],[2,5],[6]] => 100110
[6,1,3,7,4,5,2] => [[1,3,4,6],[2,5],[7]] => 100101
[6,1,3,7,5,2,4] => [[1,3,4],[2,5],[6,7]] => 100110
[6,1,3,7,5,4,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,1,4,2,3,5,7] => [[1,3,5,6,7],[2],[4]] => 101000
[6,1,4,2,3,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[6,1,4,2,5,3,7] => [[1,3,5,7],[2,6],[4]] => 101010
[6,1,4,2,5,7,3] => [[1,3,5,6],[2,7],[4]] => 101001
[6,1,4,2,7,3,5] => [[1,3,5,7],[2,6],[4]] => 101010
[6,1,4,2,7,5,3] => [[1,3,5],[2,6],[4,7]] => 101011
[6,1,4,3,2,5,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,1,4,3,2,7,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,1,4,3,5,2,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,1,4,3,5,7,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,1,4,3,7,2,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,1,4,3,7,5,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,1,4,5,2,3,7] => [[1,3,4,7],[2,6],[5]] => 100100
[6,1,4,5,2,7,3] => [[1,3,4,6],[2,7],[5]] => 100101
[6,1,4,5,3,2,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,1,4,5,3,7,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,1,4,5,7,2,3] => [[1,3,4,5],[2,7],[6]] => 100010
[6,1,4,5,7,3,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,1,4,7,2,3,5] => [[1,3,4,7],[2,6],[5]] => 100100
[6,1,4,7,2,5,3] => [[1,3,4],[2,6],[5,7]] => 100101
[6,1,4,7,3,2,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,1,4,7,3,5,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,1,4,7,5,2,3] => [[1,3,4],[2,5],[6,7]] => 100110
[6,1,4,7,5,3,2] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,1,5,2,3,4,7] => [[1,3,5,6,7],[2],[4]] => 101000
[6,1,5,2,3,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[6,1,5,2,4,3,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,1,5,2,4,7,3] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,1,5,2,7,3,4] => [[1,3,5,7],[2,6],[4]] => 101010
[6,1,5,2,7,4,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,1,5,3,2,4,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,1,5,3,2,7,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,1,5,3,4,2,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,1,5,3,4,7,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,1,5,3,7,2,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,1,5,3,7,4,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,1,5,4,2,3,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,1,5,4,2,7,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,1,5,4,3,2,7] => [[1,3,7],[2],[4],[5],[6]] => 101110
[6,1,5,4,3,7,2] => [[1,3,6],[2],[4],[5],[7]] => 101101
[6,1,5,4,7,2,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,1,5,4,7,3,2] => [[1,3,5],[2],[4],[6],[7]] => 101011
[6,1,5,7,2,3,4] => [[1,3,4,7],[2,6],[5]] => 100100
[6,1,5,7,2,4,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,1,5,7,3,2,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,1,5,7,3,4,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,1,5,7,4,2,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,1,5,7,4,3,2] => [[1,3,4],[2],[5],[6],[7]] => 100111
[6,1,7,2,3,4,5] => [[1,3,5,6,7],[2,4]] => 101000
[6,1,7,2,3,5,4] => [[1,3,5,6],[2,4],[7]] => 101001
[6,1,7,2,4,3,5] => [[1,3,5,7],[2,4],[6]] => 101010
[6,1,7,2,4,5,3] => [[1,3,5,6],[2,4],[7]] => 101001
[6,1,7,2,5,3,4] => [[1,3,5,7],[2,4],[6]] => 101010
[6,1,7,2,5,4,3] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,1,7,3,2,4,5] => [[1,3,6,7],[2,4],[5]] => 101100
[6,1,7,3,2,5,4] => [[1,3,6],[2,4],[5,7]] => 101101
[6,1,7,3,4,2,5] => [[1,3,5,7],[2,4],[6]] => 101010
[6,1,7,3,4,5,2] => [[1,3,5,6],[2,4],[7]] => 101001
[6,1,7,3,5,2,4] => [[1,3,5],[2,4],[6,7]] => 101010
[6,1,7,3,5,4,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,1,7,4,2,3,5] => [[1,3,6,7],[2,4],[5]] => 101100
[6,1,7,4,2,5,3] => [[1,3,6],[2,4],[5,7]] => 101101
[6,1,7,4,3,2,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,1,7,4,3,5,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,1,7,4,5,2,3] => [[1,3,5],[2,4],[6,7]] => 101010
[6,1,7,4,5,3,2] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,1,7,5,2,3,4] => [[1,3,6,7],[2,4],[5]] => 101100
[6,1,7,5,2,4,3] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,1,7,5,3,2,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,1,7,5,3,4,2] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,1,7,5,4,2,3] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,1,7,5,4,3,2] => [[1,3],[2,4],[5],[6],[7]] => 101111
[6,2,1,3,4,5,7] => [[1,4,5,6,7],[2],[3]] => 110000
[6,2,1,3,4,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[6,2,1,3,5,4,7] => [[1,4,5,7],[2,6],[3]] => 110010
[6,2,1,3,5,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[6,2,1,3,7,4,5] => [[1,4,5,7],[2,6],[3]] => 110010
[6,2,1,3,7,5,4] => [[1,4,5],[2,6],[3,7]] => 110011
[6,2,1,4,3,5,7] => [[1,4,6,7],[2,5],[3]] => 110100
[6,2,1,4,3,7,5] => [[1,4,6],[2,5,7],[3]] => 110101
[6,2,1,4,5,3,7] => [[1,4,5,7],[2,6],[3]] => 110010
[6,2,1,4,5,7,3] => [[1,4,5,6],[2,7],[3]] => 110001
[6,2,1,4,7,3,5] => [[1,4,5],[2,6,7],[3]] => 110010
[6,2,1,4,7,5,3] => [[1,4,5],[2,6],[3,7]] => 110011
[6,2,1,5,3,4,7] => [[1,4,6,7],[2,5],[3]] => 110100
[6,2,1,5,3,7,4] => [[1,4,6],[2,5,7],[3]] => 110101
[6,2,1,5,4,3,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,2,1,5,4,7,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,2,1,5,7,3,4] => [[1,4,5],[2,6,7],[3]] => 110010
[6,2,1,5,7,4,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,2,1,7,3,4,5] => [[1,4,6,7],[2,5],[3]] => 110100
[6,2,1,7,3,5,4] => [[1,4,6],[2,5],[3,7]] => 110101
[6,2,1,7,4,3,5] => [[1,4,7],[2,5],[3,6]] => 110110
[6,2,1,7,4,5,3] => [[1,4,6],[2,5],[3,7]] => 110101
[6,2,1,7,5,3,4] => [[1,4,7],[2,5],[3,6]] => 110110
[6,2,1,7,5,4,3] => [[1,4],[2,5],[3,6],[7]] => 110111
[6,2,3,1,4,5,7] => [[1,3,5,6,7],[2],[4]] => 101000
[6,2,3,1,4,7,5] => [[1,3,5,6],[2,7],[4]] => 101001
[6,2,3,1,5,4,7] => [[1,3,5,7],[2,6],[4]] => 101010
[6,2,3,1,5,7,4] => [[1,3,5,6],[2,7],[4]] => 101001
[6,2,3,1,7,4,5] => [[1,3,5,7],[2,6],[4]] => 101010
[6,2,3,1,7,5,4] => [[1,3,5],[2,6],[4,7]] => 101011
[6,2,3,4,1,5,7] => [[1,3,4,6,7],[2],[5]] => 100100
[6,2,3,4,1,7,5] => [[1,3,4,6],[2,7],[5]] => 100101
[6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => 100010
[6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => 100001
[6,2,3,4,7,1,5] => [[1,3,4,5],[2,7],[6]] => 100010
[6,2,3,4,7,5,1] => [[1,3,4,5],[2,6],[7]] => 100011
[6,2,3,5,1,4,7] => [[1,3,4,7],[2,6],[5]] => 100100
[6,2,3,5,1,7,4] => [[1,3,4,6],[2,7],[5]] => 100101
[6,2,3,5,4,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,2,3,5,4,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,2,3,5,7,1,4] => [[1,3,4,5],[2,7],[6]] => 100010
[6,2,3,5,7,4,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,2,3,7,1,4,5] => [[1,3,4,7],[2,6],[5]] => 100100
[6,2,3,7,1,5,4] => [[1,3,4],[2,6],[5,7]] => 100101
[6,2,3,7,4,1,5] => [[1,3,4,7],[2,5],[6]] => 100110
[6,2,3,7,4,5,1] => [[1,3,4,6],[2,5],[7]] => 100101
[6,2,3,7,5,1,4] => [[1,3,4],[2,5],[6,7]] => 100110
[6,2,3,7,5,4,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,2,4,1,3,5,7] => [[1,3,6,7],[2,5],[4]] => 101000
[6,2,4,1,3,7,5] => [[1,3,6],[2,5,7],[4]] => 101001
[6,2,4,1,5,3,7] => [[1,3,5,7],[2,6],[4]] => 101010
[6,2,4,1,5,7,3] => [[1,3,5,6],[2,7],[4]] => 101001
[6,2,4,1,7,3,5] => [[1,3,5],[2,6,7],[4]] => 101010
[6,2,4,1,7,5,3] => [[1,3,5],[2,6],[4,7]] => 101011
[6,2,4,3,1,5,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,2,4,3,1,7,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,2,4,3,5,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,2,4,3,5,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,2,4,3,7,1,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,2,4,3,7,5,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,2,4,5,1,3,7] => [[1,3,4,7],[2,6],[5]] => 100100
[6,2,4,5,1,7,3] => [[1,3,4,6],[2,7],[5]] => 100101
[6,2,4,5,3,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,2,4,5,3,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,2,4,5,7,1,3] => [[1,3,4,5],[2,7],[6]] => 100010
[6,2,4,5,7,3,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,2,4,7,1,3,5] => [[1,3,4],[2,6,7],[5]] => 100100
[6,2,4,7,1,5,3] => [[1,3,4],[2,6],[5,7]] => 100101
[6,2,4,7,3,1,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,2,4,7,3,5,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,2,4,7,5,1,3] => [[1,3,4],[2,5],[6,7]] => 100110
[6,2,4,7,5,3,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,2,5,1,3,4,7] => [[1,3,6,7],[2,5],[4]] => 101000
[6,2,5,1,3,7,4] => [[1,3,6],[2,5,7],[4]] => 101001
[6,2,5,1,4,3,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,2,5,1,4,7,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,2,5,1,7,3,4] => [[1,3,5],[2,6,7],[4]] => 101010
[6,2,5,1,7,4,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,2,5,3,1,4,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,2,5,3,1,7,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,2,5,3,4,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,2,5,3,4,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,2,5,3,7,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,2,5,3,7,4,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,2,5,4,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,2,5,4,1,7,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,2,5,4,3,1,7] => [[1,3,7],[2],[4],[5],[6]] => 101110
[6,2,5,4,3,7,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[6,2,5,4,7,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,2,5,4,7,3,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[6,2,5,7,1,3,4] => [[1,3,4],[2,6,7],[5]] => 100100
[6,2,5,7,1,4,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,2,5,7,3,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,2,5,7,3,4,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,2,5,7,4,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,2,5,7,4,3,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[6,2,7,1,3,4,5] => [[1,3,6,7],[2,5],[4]] => 101000
[6,2,7,1,3,5,4] => [[1,3,6],[2,5],[4,7]] => 101001
[6,2,7,1,4,3,5] => [[1,3,7],[2,5],[4,6]] => 101010
[6,2,7,1,4,5,3] => [[1,3,6],[2,5],[4,7]] => 101001
[6,2,7,1,5,3,4] => [[1,3,7],[2,5],[4,6]] => 101010
[6,2,7,1,5,4,3] => [[1,3],[2,5],[4,6],[7]] => 101011
[6,2,7,3,1,4,5] => [[1,3,6,7],[2,4],[5]] => 101100
[6,2,7,3,1,5,4] => [[1,3,6],[2,4],[5,7]] => 101101
[6,2,7,3,4,1,5] => [[1,3,5,7],[2,4],[6]] => 101010
[6,2,7,3,4,5,1] => [[1,3,5,6],[2,4],[7]] => 101001
[6,2,7,3,5,1,4] => [[1,3,5],[2,4],[6,7]] => 101010
[6,2,7,3,5,4,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,2,7,4,1,3,5] => [[1,3,7],[2,4],[5,6]] => 101100
[6,2,7,4,1,5,3] => [[1,3,6],[2,4],[5,7]] => 101101
[6,2,7,4,3,1,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,2,7,4,3,5,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,2,7,4,5,1,3] => [[1,3,5],[2,4],[6,7]] => 101010
[6,2,7,4,5,3,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,2,7,5,1,3,4] => [[1,3,7],[2,4],[5,6]] => 101100
[6,2,7,5,1,4,3] => [[1,3],[2,4],[5,6],[7]] => 101101
[6,2,7,5,3,1,4] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,2,7,5,3,4,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,2,7,5,4,1,3] => [[1,3],[2,4],[5,7],[6]] => 101110
[6,2,7,5,4,3,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[6,3,1,2,4,5,7] => [[1,4,5,6,7],[2],[3]] => 110000
[6,3,1,2,4,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[6,3,1,2,5,4,7] => [[1,4,5,7],[2,6],[3]] => 110010
[6,3,1,2,5,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[6,3,1,2,7,4,5] => [[1,4,5,7],[2,6],[3]] => 110010
[6,3,1,2,7,5,4] => [[1,4,5],[2,6],[3,7]] => 110011
[6,3,1,4,2,5,7] => [[1,4,6,7],[2,5],[3]] => 110100
[6,3,1,4,2,7,5] => [[1,4,6],[2,5,7],[3]] => 110101
[6,3,1,4,5,2,7] => [[1,4,5,7],[2,6],[3]] => 110010
[6,3,1,4,5,7,2] => [[1,4,5,6],[2,7],[3]] => 110001
[6,3,1,4,7,2,5] => [[1,4,5],[2,6,7],[3]] => 110010
[6,3,1,4,7,5,2] => [[1,4,5],[2,6],[3,7]] => 110011
[6,3,1,5,2,4,7] => [[1,4,6,7],[2,5],[3]] => 110100
[6,3,1,5,2,7,4] => [[1,4,6],[2,5,7],[3]] => 110101
[6,3,1,5,4,2,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,3,1,5,4,7,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,3,1,5,7,2,4] => [[1,4,5],[2,6,7],[3]] => 110010
[6,3,1,5,7,4,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,3,1,7,2,4,5] => [[1,4,6,7],[2,5],[3]] => 110100
[6,3,1,7,2,5,4] => [[1,4,6],[2,5],[3,7]] => 110101
[6,3,1,7,4,2,5] => [[1,4,7],[2,5],[3,6]] => 110110
[6,3,1,7,4,5,2] => [[1,4,6],[2,5],[3,7]] => 110101
[6,3,1,7,5,2,4] => [[1,4,7],[2,5],[3,6]] => 110110
[6,3,1,7,5,4,2] => [[1,4],[2,5],[3,6],[7]] => 110111
[6,3,2,1,4,5,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,3,2,1,4,7,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,3,2,1,5,4,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,3,2,1,5,7,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,3,2,1,7,4,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,3,2,1,7,5,4] => [[1,5],[2,6],[3,7],[4]] => 111011
[6,3,2,4,1,5,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,3,2,4,1,7,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,3,2,4,7,1,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,3,2,4,7,5,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,3,2,5,1,4,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,3,2,5,1,7,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,3,2,5,4,1,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,3,2,5,4,7,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,3,2,5,7,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,3,2,5,7,4,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,3,2,7,1,4,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,3,2,7,1,5,4] => [[1,4],[2,6],[3,7],[5]] => 110101
[6,3,2,7,4,1,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,3,2,7,4,5,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,3,2,7,5,1,4] => [[1,4],[2,5],[3,7],[6]] => 110110
[6,3,2,7,5,4,1] => [[1,4],[2,5],[3,6],[7]] => 110111
[6,3,4,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => 101000
[6,3,4,1,2,7,5] => [[1,3,6],[2,5,7],[4]] => 101001
[6,3,4,1,5,2,7] => [[1,3,5,7],[2,6],[4]] => 101010
[6,3,4,1,5,7,2] => [[1,3,5,6],[2,7],[4]] => 101001
[6,3,4,1,7,2,5] => [[1,3,5],[2,6,7],[4]] => 101010
[6,3,4,1,7,5,2] => [[1,3,5],[2,6],[4,7]] => 101011
[6,3,4,2,1,5,7] => [[1,3,6,7],[2],[4],[5]] => 101100
[6,3,4,2,1,7,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]] => 101010
[6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[6,3,4,2,7,1,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,3,4,2,7,5,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,3,4,5,1,2,7] => [[1,3,4,7],[2,6],[5]] => 100100
[6,3,4,5,1,7,2] => [[1,3,4,6],[2,7],[5]] => 100101
[6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]] => 100110
[6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[6,3,4,5,7,1,2] => [[1,3,4,5],[2,7],[6]] => 100010
[6,3,4,5,7,2,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[6,3,4,7,1,2,5] => [[1,3,4],[2,6,7],[5]] => 100100
[6,3,4,7,1,5,2] => [[1,3,4],[2,6],[5,7]] => 100101
[6,3,4,7,2,1,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,3,4,7,2,5,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,3,4,7,5,1,2] => [[1,3,4],[2,5],[6,7]] => 100110
[6,3,4,7,5,2,1] => [[1,3,4],[2,5],[6],[7]] => 100111
[6,3,5,1,2,4,7] => [[1,3,6,7],[2,5],[4]] => 101000
[6,3,5,1,2,7,4] => [[1,3,6],[2,5,7],[4]] => 101001
[6,3,5,1,4,2,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,3,5,1,4,7,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,3,5,1,7,2,4] => [[1,3,5],[2,6,7],[4]] => 101010
[6,3,5,1,7,4,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,3,5,2,1,4,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,3,5,2,1,7,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,3,5,2,4,1,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,3,5,2,4,7,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,3,5,2,7,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,3,5,2,7,4,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,3,5,4,1,2,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,3,5,4,1,7,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,3,5,4,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 101110
[6,3,5,4,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[6,3,5,4,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,3,5,4,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[6,3,5,7,1,2,4] => [[1,3,4],[2,6,7],[5]] => 100100
[6,3,5,7,1,4,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,3,5,7,2,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,3,5,7,2,4,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,3,5,7,4,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,3,5,7,4,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[6,3,7,1,2,4,5] => [[1,3,6,7],[2,5],[4]] => 101000
[6,3,7,1,2,5,4] => [[1,3,6],[2,5],[4,7]] => 101001
[6,3,7,1,4,2,5] => [[1,3,7],[2,5],[4,6]] => 101010
[6,3,7,1,4,5,2] => [[1,3,6],[2,5],[4,7]] => 101001
[6,3,7,1,5,2,4] => [[1,3,7],[2,5],[4,6]] => 101010
[6,3,7,1,5,4,2] => [[1,3],[2,5],[4,6],[7]] => 101011
[6,3,7,2,1,4,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,3,7,2,1,5,4] => [[1,3],[2,6],[4,7],[5]] => 101101
[6,3,7,2,4,1,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,3,7,2,4,5,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,3,7,2,5,1,4] => [[1,3],[2,5],[4,7],[6]] => 101010
[6,3,7,2,5,4,1] => [[1,3],[2,5],[4,6],[7]] => 101011
[6,3,7,4,1,2,5] => [[1,3,7],[2,4],[5,6]] => 101100
[6,3,7,4,1,5,2] => [[1,3,6],[2,4],[5,7]] => 101101
[6,3,7,4,2,1,5] => [[1,3,7],[2,4],[5],[6]] => 101110
[6,3,7,4,2,5,1] => [[1,3,6],[2,4],[5],[7]] => 101101
[6,3,7,4,5,1,2] => [[1,3,5],[2,4],[6,7]] => 101010
[6,3,7,4,5,2,1] => [[1,3,5],[2,4],[6],[7]] => 101011
[6,3,7,5,1,2,4] => [[1,3,7],[2,4],[5,6]] => 101100
[6,3,7,5,1,4,2] => [[1,3],[2,4],[5,6],[7]] => 101101
[6,3,7,5,2,1,4] => [[1,3],[2,4],[5,7],[6]] => 101110
[6,3,7,5,2,4,1] => [[1,3],[2,4],[5,6],[7]] => 101101
[6,3,7,5,4,1,2] => [[1,3],[2,4],[5,7],[6]] => 101110
[6,3,7,5,4,2,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[6,4,1,2,3,5,7] => [[1,4,5,6,7],[2],[3]] => 110000
[6,4,1,2,3,7,5] => [[1,4,5,6],[2,7],[3]] => 110001
[6,4,1,2,5,3,7] => [[1,4,5,7],[2,6],[3]] => 110010
[6,4,1,2,5,7,3] => [[1,4,5,6],[2,7],[3]] => 110001
[6,4,1,2,7,3,5] => [[1,4,5,7],[2,6],[3]] => 110010
[6,4,1,2,7,5,3] => [[1,4,5],[2,6],[3,7]] => 110011
[6,4,1,3,2,5,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,4,1,3,2,7,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,4,1,3,5,2,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,4,1,3,5,7,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,4,1,3,7,2,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,4,1,3,7,5,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,4,1,5,2,3,7] => [[1,4,6,7],[2,5],[3]] => 110100
[6,4,1,5,2,7,3] => [[1,4,6],[2,5,7],[3]] => 110101
[6,4,1,5,3,2,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,4,1,5,3,7,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,4,1,5,7,2,3] => [[1,4,5],[2,6,7],[3]] => 110010
[6,4,1,5,7,3,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,4,1,7,2,3,5] => [[1,4,6,7],[2,5],[3]] => 110100
[6,4,1,7,2,5,3] => [[1,4,6],[2,5],[3,7]] => 110101
[6,4,1,7,3,2,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,4,1,7,3,5,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,4,1,7,5,2,3] => [[1,4,7],[2,5],[3,6]] => 110110
[6,4,1,7,5,3,2] => [[1,4],[2,5],[3,6],[7]] => 110111
[6,4,2,1,3,5,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,4,2,1,3,7,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,4,2,1,5,3,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,4,2,1,5,7,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,4,2,1,7,3,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,4,2,1,7,5,3] => [[1,5],[2,6],[3,7],[4]] => 111011
[6,4,2,3,1,5,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,4,2,3,1,7,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,4,2,3,5,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,4,2,3,5,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,4,2,3,7,1,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,4,2,3,7,5,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,4,2,5,1,3,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,4,2,5,1,7,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,4,2,5,3,1,7] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,4,2,5,3,7,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,4,2,5,7,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,4,2,5,7,3,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,4,2,7,1,3,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,4,2,7,1,5,3] => [[1,4],[2,6],[3,7],[5]] => 110101
[6,4,2,7,3,1,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,4,2,7,3,5,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,4,2,7,5,1,3] => [[1,4],[2,5],[3,7],[6]] => 110110
[6,4,2,7,5,3,1] => [[1,4],[2,5],[3,6],[7]] => 110111
[6,4,3,1,2,5,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,4,3,1,2,7,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,4,3,1,5,2,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,4,3,1,5,7,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,4,3,1,7,2,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,4,3,1,7,5,2] => [[1,5],[2,6],[3,7],[4]] => 111011
[6,4,3,2,1,5,7] => [[1,6,7],[2],[3],[4],[5]] => 111100
[6,4,3,2,1,7,5] => [[1,6],[2,7],[3],[4],[5]] => 111101
[6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => 111010
[6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[6,4,3,2,7,1,5] => [[1,5],[2,7],[3],[4],[6]] => 111010
[6,4,3,2,7,5,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[6,4,3,5,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,4,3,5,1,7,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 110110
[6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[6,4,3,5,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,4,3,5,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[6,4,3,7,1,2,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,4,3,7,1,5,2] => [[1,4],[2,6],[3,7],[5]] => 110101
[6,4,3,7,2,1,5] => [[1,4],[2,7],[3],[5],[6]] => 110110
[6,4,3,7,2,5,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[6,4,3,7,5,1,2] => [[1,4],[2,5],[3,7],[6]] => 110110
[6,4,3,7,5,2,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[6,4,5,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => 101000
[6,4,5,1,2,7,3] => [[1,3,6],[2,5,7],[4]] => 101001
[6,4,5,1,3,2,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,4,5,1,3,7,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,4,5,1,7,2,3] => [[1,3,5],[2,6,7],[4]] => 101010
[6,4,5,1,7,3,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,4,5,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,4,5,2,1,7,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,4,5,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,4,5,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,4,5,2,7,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,4,5,2,7,3,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[6,4,5,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,4,5,3,1,7,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[6,4,5,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => 101110
[6,4,5,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[6,4,5,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[6,4,5,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[6,4,5,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => 100100
[6,4,5,7,1,3,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,4,5,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,4,5,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[6,4,5,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[6,4,5,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[6,4,7,1,2,3,5] => [[1,3,6,7],[2,5],[4]] => 101000
[6,4,7,1,2,5,3] => [[1,3,6],[2,5],[4,7]] => 101001
[6,4,7,1,3,2,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,4,7,1,3,5,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,4,7,1,5,2,3] => [[1,3,7],[2,5],[4,6]] => 101010
[6,4,7,1,5,3,2] => [[1,3],[2,5],[4,6],[7]] => 101011
[6,4,7,2,1,3,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,4,7,2,1,5,3] => [[1,3],[2,6],[4,7],[5]] => 101101
[6,4,7,2,3,1,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,4,7,2,3,5,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,4,7,2,5,1,3] => [[1,3],[2,5],[4,7],[6]] => 101010
[6,4,7,2,5,3,1] => [[1,3],[2,5],[4,6],[7]] => 101011
[6,4,7,3,1,2,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,4,7,3,1,5,2] => [[1,3],[2,6],[4,7],[5]] => 101101
[6,4,7,3,2,1,5] => [[1,3],[2,7],[4],[5],[6]] => 101110
[6,4,7,3,2,5,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[6,4,7,3,5,1,2] => [[1,3],[2,5],[4,7],[6]] => 101010
[6,4,7,3,5,2,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[6,4,7,5,1,2,3] => [[1,3,7],[2,4],[5,6]] => 101100
[6,4,7,5,1,3,2] => [[1,3],[2,4],[5,6],[7]] => 101101
[6,4,7,5,2,1,3] => [[1,3],[2,4],[5,7],[6]] => 101110
[6,4,7,5,2,3,1] => [[1,3],[2,4],[5,6],[7]] => 101101
[6,4,7,5,3,1,2] => [[1,3],[2,4],[5,7],[6]] => 101110
[6,4,7,5,3,2,1] => [[1,3],[2,4],[5],[6],[7]] => 101111
[6,5,1,2,3,4,7] => [[1,4,5,6,7],[2],[3]] => 110000
[6,5,1,2,3,7,4] => [[1,4,5,6],[2,7],[3]] => 110001
[6,5,1,2,4,3,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,5,1,2,4,7,3] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,5,1,2,7,3,4] => [[1,4,5,7],[2,6],[3]] => 110010
[6,5,1,2,7,4,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,5,1,3,2,4,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,5,1,3,2,7,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,5,1,3,4,2,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,5,1,3,4,7,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,5,1,3,7,2,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,5,1,3,7,4,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,5,1,4,2,3,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,5,1,4,2,7,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,5,1,4,3,2,7] => [[1,4,7],[2],[3],[5],[6]] => 110110
[6,5,1,4,3,7,2] => [[1,4,6],[2],[3],[5],[7]] => 110101
[6,5,1,4,7,2,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,5,1,4,7,3,2] => [[1,4,5],[2],[3],[6],[7]] => 110011
[6,5,1,7,2,3,4] => [[1,4,6,7],[2,5],[3]] => 110100
[6,5,1,7,2,4,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,5,1,7,3,2,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,5,1,7,3,4,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,5,1,7,4,2,3] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,5,1,7,4,3,2] => [[1,4],[2,5],[3],[6],[7]] => 110111
[6,5,2,1,3,4,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,5,2,1,3,7,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,5,2,1,4,3,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,5,2,1,4,7,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,5,2,1,7,3,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,5,2,1,7,4,3] => [[1,5],[2,6],[3,7],[4]] => 111011
[6,5,2,3,1,4,7] => [[1,4,6,7],[2],[3],[5]] => 110100
[6,5,2,3,1,7,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,5,2,3,4,1,7] => [[1,4,5,7],[2],[3],[6]] => 110010
[6,5,2,3,4,7,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[6,5,2,3,7,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,5,2,3,7,4,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[6,5,2,4,1,3,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,5,2,4,1,7,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,5,2,4,3,1,7] => [[1,4,7],[2],[3],[5],[6]] => 110110
[6,5,2,4,3,7,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[6,5,2,4,7,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,5,2,4,7,3,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[6,5,2,7,1,3,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,5,2,7,1,4,3] => [[1,4],[2,6],[3,7],[5]] => 110101
[6,5,2,7,3,1,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[6,5,2,7,3,4,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[6,5,2,7,4,1,3] => [[1,4],[2,5],[3,7],[6]] => 110110
[6,5,2,7,4,3,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[6,5,3,1,2,4,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,5,3,1,2,7,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,5,3,1,4,2,7] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,5,3,1,4,7,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,5,3,1,7,2,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,5,3,1,7,4,2] => [[1,5],[2,6],[3,7],[4]] => 111011
[6,5,3,2,1,4,7] => [[1,6,7],[2],[3],[4],[5]] => 111100
[6,5,3,2,1,7,4] => [[1,6],[2,7],[3],[4],[5]] => 111101
[6,5,3,2,4,1,7] => [[1,5,7],[2],[3],[4],[6]] => 111010
[6,5,3,2,4,7,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[6,5,3,2,7,1,4] => [[1,5],[2,7],[3],[4],[6]] => 111010
[6,5,3,2,7,4,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[6,5,3,4,1,2,7] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,5,3,4,1,7,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => 110110
[6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[6,5,3,4,7,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[6,5,3,4,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[6,5,3,7,1,2,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,5,3,7,1,4,2] => [[1,4],[2,6],[3,7],[5]] => 110101
[6,5,3,7,2,1,4] => [[1,4],[2,7],[3],[5],[6]] => 110110
[6,5,3,7,2,4,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[6,5,3,7,4,1,2] => [[1,4],[2,5],[3,7],[6]] => 110110
[6,5,3,7,4,2,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[6,5,4,1,2,3,7] => [[1,5,6,7],[2],[3],[4]] => 111000
[6,5,4,1,2,7,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[6,5,4,1,3,2,7] => [[1,5,7],[2],[3],[4],[6]] => 111010
[6,5,4,1,3,7,2] => [[1,5,6],[2],[3],[4],[7]] => 111001
[6,5,4,1,7,2,3] => [[1,5,7],[2,6],[3],[4]] => 111010
[6,5,4,1,7,3,2] => [[1,5],[2,6],[3],[4],[7]] => 111011
[6,5,4,2,1,3,7] => [[1,6,7],[2],[3],[4],[5]] => 111100
[6,5,4,2,1,7,3] => [[1,6],[2,7],[3],[4],[5]] => 111101
[6,5,4,2,3,1,7] => [[1,5,7],[2],[3],[4],[6]] => 111010
[6,5,4,2,3,7,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[6,5,4,2,7,1,3] => [[1,5],[2,7],[3],[4],[6]] => 111010
[6,5,4,2,7,3,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[6,5,4,3,1,2,7] => [[1,6,7],[2],[3],[4],[5]] => 111100
[6,5,4,3,1,7,2] => [[1,6],[2,7],[3],[4],[5]] => 111101
[6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[6,5,4,3,7,1,2] => [[1,5],[2,7],[3],[4],[6]] => 111010
[6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[6,5,4,7,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 110100
[6,5,4,7,1,3,2] => [[1,4],[2,6],[3],[5],[7]] => 110101
[6,5,4,7,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 110110
[6,5,4,7,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[6,5,4,7,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 110110
[6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[6,5,7,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 101000
[6,5,7,1,2,4,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,5,7,1,3,2,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,5,7,1,3,4,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,5,7,1,4,2,3] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,5,7,1,4,3,2] => [[1,3],[2,5],[4],[6],[7]] => 101011
[6,5,7,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,5,7,2,1,4,3] => [[1,3],[2,6],[4,7],[5]] => 101101
[6,5,7,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[6,5,7,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[6,5,7,2,4,1,3] => [[1,3],[2,5],[4,7],[6]] => 101010
[6,5,7,2,4,3,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[6,5,7,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,5,7,3,1,4,2] => [[1,3],[2,6],[4,7],[5]] => 101101
[6,5,7,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => 101110
[6,5,7,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[6,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => 101010
[6,5,7,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[6,5,7,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 101100
[6,5,7,4,1,3,2] => [[1,3],[2,6],[4],[5],[7]] => 101101
[6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 101110
[6,5,7,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[6,5,7,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 101110
[6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => 010000
[6,7,1,2,3,5,4] => [[1,2,5,6],[3,4],[7]] => 010001
[6,7,1,2,4,3,5] => [[1,2,5,7],[3,4],[6]] => 010010
[6,7,1,2,4,5,3] => [[1,2,5,6],[3,4],[7]] => 010001
[6,7,1,2,5,3,4] => [[1,2,5,7],[3,4],[6]] => 010010
[6,7,1,2,5,4,3] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,1,3,2,4,5] => [[1,2,6,7],[3,4],[5]] => 010100
[6,7,1,3,2,5,4] => [[1,2,6],[3,4],[5,7]] => 010101
[6,7,1,3,4,2,5] => [[1,2,5,7],[3,4],[6]] => 010010
[6,7,1,3,4,5,2] => [[1,2,5,6],[3,4],[7]] => 010001
[6,7,1,3,5,2,4] => [[1,2,5],[3,4],[6,7]] => 010010
[6,7,1,3,5,4,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,1,4,2,3,5] => [[1,2,6,7],[3,4],[5]] => 010100
[6,7,1,4,2,5,3] => [[1,2,6],[3,4],[5,7]] => 010101
[6,7,1,4,3,2,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,1,4,3,5,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,1,4,5,2,3] => [[1,2,5],[3,4],[6,7]] => 010010
[6,7,1,4,5,3,2] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,1,5,2,3,4] => [[1,2,6,7],[3,4],[5]] => 010100
[6,7,1,5,2,4,3] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,1,5,3,2,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,1,5,3,4,2] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,1,5,4,2,3] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,1,5,4,3,2] => [[1,2],[3,4],[5],[6],[7]] => 010111
[6,7,2,1,3,4,5] => [[1,2,6,7],[3,5],[4]] => 011000
[6,7,2,1,3,5,4] => [[1,2,6],[3,5],[4,7]] => 011001
[6,7,2,1,4,3,5] => [[1,2,7],[3,5],[4,6]] => 011010
[6,7,2,1,4,5,3] => [[1,2,6],[3,5],[4,7]] => 011001
[6,7,2,1,5,3,4] => [[1,2,7],[3,5],[4,6]] => 011010
[6,7,2,1,5,4,3] => [[1,2],[3,5],[4,6],[7]] => 011011
[6,7,2,3,1,4,5] => [[1,2,6,7],[3,4],[5]] => 010100
[6,7,2,3,1,5,4] => [[1,2,6],[3,4],[5,7]] => 010101
[6,7,2,3,4,1,5] => [[1,2,5,7],[3,4],[6]] => 010010
[6,7,2,3,4,5,1] => [[1,2,5,6],[3,4],[7]] => 010001
[6,7,2,3,5,1,4] => [[1,2,5],[3,4],[6,7]] => 010010
[6,7,2,3,5,4,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,2,4,1,3,5] => [[1,2,7],[3,4],[5,6]] => 010100
[6,7,2,4,1,5,3] => [[1,2,6],[3,4],[5,7]] => 010101
[6,7,2,4,3,1,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,2,4,3,5,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,2,4,5,1,3] => [[1,2,5],[3,4],[6,7]] => 010010
[6,7,2,4,5,3,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,2,5,1,3,4] => [[1,2,7],[3,4],[5,6]] => 010100
[6,7,2,5,1,4,3] => [[1,2],[3,4],[5,6],[7]] => 010101
[6,7,2,5,3,1,4] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,2,5,3,4,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,2,5,4,1,3] => [[1,2],[3,4],[5,7],[6]] => 010110
[6,7,2,5,4,3,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[6,7,3,1,2,4,5] => [[1,2,6,7],[3,5],[4]] => 011000
[6,7,3,1,2,5,4] => [[1,2,6],[3,5],[4,7]] => 011001
[6,7,3,1,4,2,5] => [[1,2,7],[3,5],[4,6]] => 011010
[6,7,3,1,4,5,2] => [[1,2,6],[3,5],[4,7]] => 011001
[6,7,3,1,5,2,4] => [[1,2,7],[3,5],[4,6]] => 011010
[6,7,3,1,5,4,2] => [[1,2],[3,5],[4,6],[7]] => 011011
[6,7,3,2,1,4,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,3,2,1,5,4] => [[1,2],[3,6],[4,7],[5]] => 011101
[6,7,3,2,4,1,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,3,2,4,5,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,3,2,5,1,4] => [[1,2],[3,5],[4,7],[6]] => 011010
[6,7,3,2,5,4,1] => [[1,2],[3,5],[4,6],[7]] => 011011
[6,7,3,4,1,2,5] => [[1,2,7],[3,4],[5,6]] => 010100
[6,7,3,4,1,5,2] => [[1,2,6],[3,4],[5,7]] => 010101
[6,7,3,4,2,1,5] => [[1,2,7],[3,4],[5],[6]] => 010110
[6,7,3,4,2,5,1] => [[1,2,6],[3,4],[5],[7]] => 010101
[6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => 010010
[6,7,3,4,5,2,1] => [[1,2,5],[3,4],[6],[7]] => 010011
[6,7,3,5,1,2,4] => [[1,2,7],[3,4],[5,6]] => 010100
[6,7,3,5,1,4,2] => [[1,2],[3,4],[5,6],[7]] => 010101
[6,7,3,5,2,1,4] => [[1,2],[3,4],[5,7],[6]] => 010110
[6,7,3,5,2,4,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[6,7,3,5,4,1,2] => [[1,2],[3,4],[5,7],[6]] => 010110
[6,7,3,5,4,2,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[6,7,4,1,2,3,5] => [[1,2,6,7],[3,5],[4]] => 011000
[6,7,4,1,2,5,3] => [[1,2,6],[3,5],[4,7]] => 011001
[6,7,4,1,3,2,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,4,1,3,5,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,4,1,5,2,3] => [[1,2,7],[3,5],[4,6]] => 011010
[6,7,4,1,5,3,2] => [[1,2],[3,5],[4,6],[7]] => 011011
[6,7,4,2,1,3,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,4,2,1,5,3] => [[1,2],[3,6],[4,7],[5]] => 011101
[6,7,4,2,3,1,5] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,4,2,3,5,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,4,2,5,1,3] => [[1,2],[3,5],[4,7],[6]] => 011010
[6,7,4,2,5,3,1] => [[1,2],[3,5],[4,6],[7]] => 011011
[6,7,4,3,1,2,5] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,4,3,1,5,2] => [[1,2],[3,6],[4,7],[5]] => 011101
[6,7,4,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => 011110
[6,7,4,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[6,7,4,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => 011010
[6,7,4,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[6,7,4,5,1,2,3] => [[1,2,7],[3,4],[5,6]] => 010100
[6,7,4,5,1,3,2] => [[1,2],[3,4],[5,6],[7]] => 010101
[6,7,4,5,2,1,3] => [[1,2],[3,4],[5,7],[6]] => 010110
[6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[6,7,4,5,3,1,2] => [[1,2],[3,4],[5,7],[6]] => 010110
[6,7,4,5,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[6,7,5,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => 011000
[6,7,5,1,2,4,3] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,5,1,3,2,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,5,1,3,4,2] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,5,1,4,2,3] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,5,1,4,3,2] => [[1,2],[3,5],[4],[6],[7]] => 011011
[6,7,5,2,1,3,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,5,2,1,4,3] => [[1,2],[3,6],[4,7],[5]] => 011101
[6,7,5,2,3,1,4] => [[1,2,7],[3,5],[4],[6]] => 011010
[6,7,5,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => 011001
[6,7,5,2,4,1,3] => [[1,2],[3,5],[4,7],[6]] => 011010
[6,7,5,2,4,3,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[6,7,5,3,1,2,4] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,5,3,1,4,2] => [[1,2],[3,6],[4,7],[5]] => 011101
[6,7,5,3,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => 011110
[6,7,5,3,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[6,7,5,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => 011010
[6,7,5,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => 011011
[6,7,5,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => 011100
[6,7,5,4,1,3,2] => [[1,2],[3,6],[4],[5],[7]] => 011101
[6,7,5,4,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => 011110
[6,7,5,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => 011101
[6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => 011110
[6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => 100000
[7,1,2,3,4,6,5] => [[1,3,4,5,6],[2],[7]] => 100001
[7,1,2,3,5,4,6] => [[1,3,4,5,7],[2],[6]] => 100010
[7,1,2,3,5,6,4] => [[1,3,4,5,6],[2],[7]] => 100001
[7,1,2,3,6,4,5] => [[1,3,4,5,7],[2],[6]] => 100010
[7,1,2,3,6,5,4] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,2,4,3,5,6] => [[1,3,4,6,7],[2],[5]] => 100100
[7,1,2,4,3,6,5] => [[1,3,4,6],[2,7],[5]] => 100101
[7,1,2,4,5,3,6] => [[1,3,4,5,7],[2],[6]] => 100010
[7,1,2,4,5,6,3] => [[1,3,4,5,6],[2],[7]] => 100001
[7,1,2,4,6,3,5] => [[1,3,4,5],[2,7],[6]] => 100010
[7,1,2,4,6,5,3] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,2,5,3,4,6] => [[1,3,4,6,7],[2],[5]] => 100100
[7,1,2,5,3,6,4] => [[1,3,4,6],[2,7],[5]] => 100101
[7,1,2,5,4,3,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,2,5,4,6,3] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,2,5,6,3,4] => [[1,3,4,5],[2,7],[6]] => 100010
[7,1,2,5,6,4,3] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,2,6,3,4,5] => [[1,3,4,6,7],[2],[5]] => 100100
[7,1,2,6,3,5,4] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,2,6,4,3,5] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,2,6,4,5,3] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,2,6,5,3,4] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,2,6,5,4,3] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,1,3,2,4,5,6] => [[1,3,5,6,7],[2],[4]] => 101000
[7,1,3,2,4,6,5] => [[1,3,5,6],[2,7],[4]] => 101001
[7,1,3,2,5,4,6] => [[1,3,5,7],[2,6],[4]] => 101010
[7,1,3,2,5,6,4] => [[1,3,5,6],[2,7],[4]] => 101001
[7,1,3,2,6,4,5] => [[1,3,5,7],[2,6],[4]] => 101010
[7,1,3,2,6,5,4] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,1,3,4,2,5,6] => [[1,3,4,6,7],[2],[5]] => 100100
[7,1,3,4,2,6,5] => [[1,3,4,6],[2,7],[5]] => 100101
[7,1,3,4,5,2,6] => [[1,3,4,5,7],[2],[6]] => 100010
[7,1,3,4,5,6,2] => [[1,3,4,5,6],[2],[7]] => 100001
[7,1,3,4,6,2,5] => [[1,3,4,5],[2,7],[6]] => 100010
[7,1,3,4,6,5,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,3,5,2,4,6] => [[1,3,4,7],[2,6],[5]] => 100100
[7,1,3,5,2,6,4] => [[1,3,4,6],[2,7],[5]] => 100101
[7,1,3,5,4,2,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,3,5,4,6,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,3,5,6,2,4] => [[1,3,4,5],[2,7],[6]] => 100010
[7,1,3,5,6,4,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,3,6,2,4,5] => [[1,3,4,7],[2,6],[5]] => 100100
[7,1,3,6,2,5,4] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,1,3,6,4,2,5] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,3,6,4,5,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,3,6,5,2,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,1,3,6,5,4,2] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,1,4,2,3,5,6] => [[1,3,5,6,7],[2],[4]] => 101000
[7,1,4,2,3,6,5] => [[1,3,5,6],[2,7],[4]] => 101001
[7,1,4,2,5,3,6] => [[1,3,5,7],[2,6],[4]] => 101010
[7,1,4,2,5,6,3] => [[1,3,5,6],[2,7],[4]] => 101001
[7,1,4,2,6,3,5] => [[1,3,5,7],[2,6],[4]] => 101010
[7,1,4,2,6,5,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,1,4,3,2,5,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,4,3,2,6,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,1,4,3,5,2,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,4,3,5,6,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,4,3,6,2,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,1,4,3,6,5,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,1,4,5,2,3,6] => [[1,3,4,7],[2,6],[5]] => 100100
[7,1,4,5,2,6,3] => [[1,3,4,6],[2,7],[5]] => 100101
[7,1,4,5,3,2,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,1,4,5,3,6,2] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,1,4,5,6,2,3] => [[1,3,4,5],[2,7],[6]] => 100010
[7,1,4,5,6,3,2] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,1,4,6,2,3,5] => [[1,3,4,7],[2,6],[5]] => 100100
[7,1,4,6,2,5,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,1,4,6,3,2,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,1,4,6,3,5,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,1,4,6,5,2,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,1,4,6,5,3,2] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,1,5,2,3,4,6] => [[1,3,5,6,7],[2],[4]] => 101000
[7,1,5,2,3,6,4] => [[1,3,5,6],[2,7],[4]] => 101001
[7,1,5,2,4,3,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,5,2,4,6,3] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,5,2,6,3,4] => [[1,3,5,7],[2,6],[4]] => 101010
[7,1,5,2,6,4,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,1,5,3,2,4,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,5,3,2,6,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,1,5,3,4,2,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,5,3,4,6,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,5,3,6,2,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,1,5,3,6,4,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,1,5,4,2,3,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,5,4,2,6,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,1,5,4,3,2,6] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,1,5,4,3,6,2] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,1,5,4,6,2,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,1,5,4,6,3,2] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,1,5,6,2,3,4] => [[1,3,4,7],[2,6],[5]] => 100100
[7,1,5,6,2,4,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,1,5,6,3,2,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,1,5,6,3,4,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,1,5,6,4,2,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,1,5,6,4,3,2] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,1,6,2,3,4,5] => [[1,3,5,6,7],[2],[4]] => 101000
[7,1,6,2,3,5,4] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,6,2,4,3,5] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,6,2,4,5,3] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,6,2,5,3,4] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,6,2,5,4,3] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,1,6,3,2,4,5] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,6,3,2,5,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,1,6,3,4,2,5] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,1,6,3,4,5,2] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,1,6,3,5,2,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,1,6,3,5,4,2] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,1,6,4,2,3,5] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,6,4,2,5,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,1,6,4,3,2,5] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,1,6,4,3,5,2] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,1,6,4,5,2,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,1,6,4,5,3,2] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,1,6,5,2,3,4] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,1,6,5,2,4,3] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,1,6,5,3,2,4] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,1,6,5,3,4,2] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,1,6,5,4,2,3] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,1,6,5,4,3,2] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[7,2,1,3,4,5,6] => [[1,4,5,6,7],[2],[3]] => 110000
[7,2,1,3,4,6,5] => [[1,4,5,6],[2,7],[3]] => 110001
[7,2,1,3,5,4,6] => [[1,4,5,7],[2,6],[3]] => 110010
[7,2,1,3,5,6,4] => [[1,4,5,6],[2,7],[3]] => 110001
[7,2,1,3,6,4,5] => [[1,4,5,7],[2,6],[3]] => 110010
[7,2,1,3,6,5,4] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,2,1,4,3,5,6] => [[1,4,6,7],[2,5],[3]] => 110100
[7,2,1,4,3,6,5] => [[1,4,6],[2,5,7],[3]] => 110101
[7,2,1,4,5,3,6] => [[1,4,5,7],[2,6],[3]] => 110010
[7,2,1,4,5,6,3] => [[1,4,5,6],[2,7],[3]] => 110001
[7,2,1,4,6,3,5] => [[1,4,5],[2,6,7],[3]] => 110010
[7,2,1,4,6,5,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,2,1,5,3,4,6] => [[1,4,6,7],[2,5],[3]] => 110100
[7,2,1,5,3,6,4] => [[1,4,6],[2,5,7],[3]] => 110101
[7,2,1,5,4,3,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,2,1,5,4,6,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,2,1,5,6,3,4] => [[1,4,5],[2,6,7],[3]] => 110010
[7,2,1,5,6,4,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,2,1,6,3,4,5] => [[1,4,6,7],[2,5],[3]] => 110100
[7,2,1,6,3,5,4] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,2,1,6,4,3,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,2,1,6,4,5,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,2,1,6,5,3,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,2,1,6,5,4,3] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,2,3,1,4,5,6] => [[1,3,5,6,7],[2],[4]] => 101000
[7,2,3,1,4,6,5] => [[1,3,5,6],[2,7],[4]] => 101001
[7,2,3,1,5,4,6] => [[1,3,5,7],[2,6],[4]] => 101010
[7,2,3,1,5,6,4] => [[1,3,5,6],[2,7],[4]] => 101001
[7,2,3,1,6,4,5] => [[1,3,5,7],[2,6],[4]] => 101010
[7,2,3,1,6,5,4] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,2,3,4,1,5,6] => [[1,3,4,6,7],[2],[5]] => 100100
[7,2,3,4,1,6,5] => [[1,3,4,6],[2,7],[5]] => 100101
[7,2,3,4,5,1,6] => [[1,3,4,5,7],[2],[6]] => 100010
[7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => 100001
[7,2,3,4,6,1,5] => [[1,3,4,5],[2,7],[6]] => 100010
[7,2,3,4,6,5,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,2,3,5,1,4,6] => [[1,3,4,7],[2,6],[5]] => 100100
[7,2,3,5,1,6,4] => [[1,3,4,6],[2,7],[5]] => 100101
[7,2,3,5,4,1,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,2,3,5,4,6,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,2,3,5,6,1,4] => [[1,3,4,5],[2,7],[6]] => 100010
[7,2,3,5,6,4,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,2,3,6,1,4,5] => [[1,3,4,7],[2,6],[5]] => 100100
[7,2,3,6,1,5,4] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,2,3,6,4,1,5] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,2,3,6,4,5,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,2,3,6,5,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,2,3,6,5,4,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,2,4,1,3,5,6] => [[1,3,6,7],[2,5],[4]] => 101000
[7,2,4,1,3,6,5] => [[1,3,6],[2,5,7],[4]] => 101001
[7,2,4,1,5,3,6] => [[1,3,5,7],[2,6],[4]] => 101010
[7,2,4,1,5,6,3] => [[1,3,5,6],[2,7],[4]] => 101001
[7,2,4,1,6,3,5] => [[1,3,5],[2,6,7],[4]] => 101010
[7,2,4,1,6,5,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,2,4,3,1,5,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,2,4,3,1,6,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,2,4,3,5,1,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,2,4,3,5,6,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,2,4,3,6,1,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,2,4,3,6,5,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,2,4,5,1,3,6] => [[1,3,4,7],[2,6],[5]] => 100100
[7,2,4,5,1,6,3] => [[1,3,4,6],[2,7],[5]] => 100101
[7,2,4,5,3,1,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,2,4,5,3,6,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,2,4,5,6,1,3] => [[1,3,4,5],[2,7],[6]] => 100010
[7,2,4,5,6,3,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,2,4,6,1,3,5] => [[1,3,4],[2,6,7],[5]] => 100100
[7,2,4,6,1,5,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,2,4,6,3,1,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,2,4,6,3,5,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,2,4,6,5,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,2,4,6,5,3,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,2,5,1,3,4,6] => [[1,3,6,7],[2,5],[4]] => 101000
[7,2,5,1,3,6,4] => [[1,3,6],[2,5,7],[4]] => 101001
[7,2,5,1,4,3,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,2,5,1,4,6,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,2,5,1,6,3,4] => [[1,3,5],[2,6,7],[4]] => 101010
[7,2,5,1,6,4,3] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,2,5,3,1,4,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,2,5,3,1,6,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,2,5,3,4,1,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,2,5,3,4,6,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,2,5,3,6,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,2,5,3,6,4,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,2,5,4,1,3,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,2,5,4,1,6,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,2,5,4,3,1,6] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,2,5,4,3,6,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,2,5,4,6,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,2,5,4,6,3,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,2,5,6,1,3,4] => [[1,3,4],[2,6,7],[5]] => 100100
[7,2,5,6,1,4,3] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,2,5,6,3,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,2,5,6,3,4,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,2,5,6,4,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,2,5,6,4,3,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,2,6,1,3,4,5] => [[1,3,6,7],[2,5],[4]] => 101000
[7,2,6,1,3,5,4] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,2,6,1,4,3,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,2,6,1,4,5,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,2,6,1,5,3,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,2,6,1,5,4,3] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,2,6,3,1,4,5] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,2,6,3,1,5,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,2,6,3,4,1,5] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,2,6,3,4,5,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,2,6,3,5,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,2,6,3,5,4,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,2,6,4,1,3,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,2,6,4,1,5,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,2,6,4,3,1,5] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,2,6,4,3,5,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,2,6,4,5,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,2,6,4,5,3,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,2,6,5,1,3,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,2,6,5,1,4,3] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,2,6,5,3,1,4] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,2,6,5,3,4,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,2,6,5,4,1,3] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,2,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[7,3,1,2,4,5,6] => [[1,4,5,6,7],[2],[3]] => 110000
[7,3,1,2,4,6,5] => [[1,4,5,6],[2,7],[3]] => 110001
[7,3,1,2,5,4,6] => [[1,4,5,7],[2,6],[3]] => 110010
[7,3,1,2,5,6,4] => [[1,4,5,6],[2,7],[3]] => 110001
[7,3,1,2,6,4,5] => [[1,4,5,7],[2,6],[3]] => 110010
[7,3,1,2,6,5,4] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,3,1,4,2,5,6] => [[1,4,6,7],[2,5],[3]] => 110100
[7,3,1,4,2,6,5] => [[1,4,6],[2,5,7],[3]] => 110101
[7,3,1,4,5,2,6] => [[1,4,5,7],[2,6],[3]] => 110010
[7,3,1,4,5,6,2] => [[1,4,5,6],[2,7],[3]] => 110001
[7,3,1,4,6,2,5] => [[1,4,5],[2,6,7],[3]] => 110010
[7,3,1,4,6,5,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,3,1,5,2,4,6] => [[1,4,6,7],[2,5],[3]] => 110100
[7,3,1,5,2,6,4] => [[1,4,6],[2,5,7],[3]] => 110101
[7,3,1,5,4,2,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,3,1,5,4,6,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,3,1,5,6,2,4] => [[1,4,5],[2,6,7],[3]] => 110010
[7,3,1,5,6,4,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,3,1,6,2,4,5] => [[1,4,6,7],[2,5],[3]] => 110100
[7,3,1,6,2,5,4] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,3,1,6,4,2,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,3,1,6,4,5,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,3,1,6,5,2,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,3,1,6,5,4,2] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,3,2,1,4,5,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,3,2,1,4,6,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,3,2,1,5,4,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,3,2,1,5,6,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,3,2,1,6,4,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,3,2,1,6,5,4] => [[1,5],[2,6],[3,7],[4]] => 111011
[7,3,2,4,1,5,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,3,2,4,1,6,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,3,2,4,5,1,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,3,2,4,6,1,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,3,2,4,6,5,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,3,2,5,1,4,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,3,2,5,1,6,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,3,2,5,4,1,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,3,2,5,4,6,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,3,2,5,6,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,3,2,5,6,4,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,3,2,6,1,4,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,3,2,6,1,5,4] => [[1,4],[2,6],[3,7],[5]] => 110101
[7,3,2,6,4,1,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,3,2,6,4,5,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,3,2,6,5,1,4] => [[1,4],[2,5],[3,7],[6]] => 110110
[7,3,2,6,5,4,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,3,4,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => 101000
[7,3,4,1,2,6,5] => [[1,3,6],[2,5,7],[4]] => 101001
[7,3,4,1,5,2,6] => [[1,3,5,7],[2,6],[4]] => 101010
[7,3,4,1,5,6,2] => [[1,3,5,6],[2,7],[4]] => 101001
[7,3,4,1,6,2,5] => [[1,3,5],[2,6,7],[4]] => 101010
[7,3,4,1,6,5,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,3,4,2,1,5,6] => [[1,3,6,7],[2],[4],[5]] => 101100
[7,3,4,2,1,6,5] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,3,4,2,5,1,6] => [[1,3,5,7],[2],[4],[6]] => 101010
[7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]] => 101001
[7,3,4,2,6,1,5] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,3,4,2,6,5,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,3,4,5,1,2,6] => [[1,3,4,7],[2,6],[5]] => 100100
[7,3,4,5,1,6,2] => [[1,3,4,6],[2,7],[5]] => 100101
[7,3,4,5,2,1,6] => [[1,3,4,7],[2],[5],[6]] => 100110
[7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]] => 100101
[7,3,4,5,6,1,2] => [[1,3,4,5],[2,7],[6]] => 100010
[7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => 100011
[7,3,4,6,1,2,5] => [[1,3,4],[2,6,7],[5]] => 100100
[7,3,4,6,1,5,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,3,4,6,2,1,5] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,3,4,6,2,5,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,3,4,6,5,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,3,4,6,5,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,3,5,1,2,4,6] => [[1,3,6,7],[2,5],[4]] => 101000
[7,3,5,1,2,6,4] => [[1,3,6],[2,5,7],[4]] => 101001
[7,3,5,1,4,2,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,3,5,1,4,6,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,3,5,1,6,2,4] => [[1,3,5],[2,6,7],[4]] => 101010
[7,3,5,1,6,4,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,3,5,2,1,4,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,3,5,2,1,6,4] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,3,5,2,4,1,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,3,5,2,4,6,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,3,5,2,6,1,4] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,3,5,2,6,4,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,3,5,4,1,2,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,3,5,4,1,6,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,3,5,4,2,1,6] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,3,5,4,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,3,5,4,6,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,3,5,4,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,3,5,6,1,2,4] => [[1,3,4],[2,6,7],[5]] => 100100
[7,3,5,6,1,4,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,3,5,6,2,1,4] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,3,5,6,2,4,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,3,5,6,4,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,3,5,6,4,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,3,6,1,2,4,5] => [[1,3,6,7],[2,5],[4]] => 101000
[7,3,6,1,2,5,4] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,3,6,1,4,2,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,3,6,1,4,5,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,3,6,1,5,2,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,3,6,1,5,4,2] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,3,6,2,1,4,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,3,6,2,1,5,4] => [[1,3],[2,6],[4,7],[5]] => 101101
[7,3,6,2,4,1,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,3,6,2,4,5,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,3,6,2,5,1,4] => [[1,3],[2,5],[4,7],[6]] => 101010
[7,3,6,2,5,4,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,3,6,4,1,2,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,3,6,4,1,5,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,3,6,4,2,1,5] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,3,6,4,2,5,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,3,6,4,5,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,3,6,4,5,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,3,6,5,1,2,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,3,6,5,1,4,2] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,3,6,5,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,3,6,5,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,3,6,5,4,1,2] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,3,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[7,4,1,2,3,5,6] => [[1,4,5,6,7],[2],[3]] => 110000
[7,4,1,2,3,6,5] => [[1,4,5,6],[2,7],[3]] => 110001
[7,4,1,2,5,3,6] => [[1,4,5,7],[2,6],[3]] => 110010
[7,4,1,2,5,6,3] => [[1,4,5,6],[2,7],[3]] => 110001
[7,4,1,2,6,3,5] => [[1,4,5,7],[2,6],[3]] => 110010
[7,4,1,2,6,5,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,4,1,3,2,5,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,4,1,3,2,6,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,4,1,3,5,2,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,4,1,3,5,6,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,4,1,3,6,2,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,4,1,3,6,5,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,4,1,5,2,3,6] => [[1,4,6,7],[2,5],[3]] => 110100
[7,4,1,5,2,6,3] => [[1,4,6],[2,5,7],[3]] => 110101
[7,4,1,5,3,2,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,4,1,5,3,6,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,4,1,5,6,2,3] => [[1,4,5],[2,6,7],[3]] => 110010
[7,4,1,5,6,3,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,4,1,6,2,3,5] => [[1,4,6,7],[2,5],[3]] => 110100
[7,4,1,6,2,5,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,4,1,6,3,2,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,4,1,6,3,5,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,4,1,6,5,2,3] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,4,1,6,5,3,2] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,4,2,1,3,5,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,4,2,1,3,6,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,4,2,1,5,3,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,4,2,1,5,6,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,4,2,1,6,3,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,4,2,1,6,5,3] => [[1,5],[2,6],[3,7],[4]] => 111011
[7,4,2,3,1,5,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,4,2,3,1,6,5] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,4,2,3,5,1,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,4,2,3,5,6,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,4,2,3,6,1,5] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,4,2,3,6,5,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,4,2,5,1,3,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,4,2,5,1,6,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,4,2,5,3,1,6] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,4,2,5,3,6,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,4,2,5,6,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,4,2,5,6,3,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,4,2,6,1,3,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,4,2,6,1,5,3] => [[1,4],[2,6],[3,7],[5]] => 110101
[7,4,2,6,3,1,5] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,4,2,6,3,5,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,4,2,6,5,1,3] => [[1,4],[2,5],[3,7],[6]] => 110110
[7,4,2,6,5,3,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,4,3,1,2,5,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,4,3,1,2,6,5] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,4,3,1,5,2,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,4,3,1,5,6,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,4,3,1,6,2,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,4,3,1,6,5,2] => [[1,5],[2,6],[3,7],[4]] => 111011
[7,4,3,2,1,5,6] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,4,3,2,1,6,5] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,4,3,2,5,1,6] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,4,3,2,6,1,5] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,4,3,2,6,5,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,4,3,5,1,2,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,4,3,5,1,6,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,4,3,5,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,4,3,5,6,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,4,3,6,1,2,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,4,3,6,1,5,2] => [[1,4],[2,6],[3,7],[5]] => 110101
[7,4,3,6,2,1,5] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,4,3,6,2,5,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,4,3,6,5,1,2] => [[1,4],[2,5],[3,7],[6]] => 110110
[7,4,3,6,5,2,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,4,5,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => 101000
[7,4,5,1,2,6,3] => [[1,3,6],[2,5,7],[4]] => 101001
[7,4,5,1,3,2,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,4,5,1,3,6,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,4,5,1,6,2,3] => [[1,3,5],[2,6,7],[4]] => 101010
[7,4,5,1,6,3,2] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,4,5,2,1,3,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,4,5,2,1,6,3] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,4,5,2,3,1,6] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,4,5,2,3,6,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,4,5,2,6,1,3] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,4,5,2,6,3,1] => [[1,3,5],[2,6],[4],[7]] => 101011
[7,4,5,3,1,2,6] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,4,5,3,1,6,2] => [[1,3,6],[2,7],[4],[5]] => 101101
[7,4,5,3,2,1,6] => [[1,3,7],[2],[4],[5],[6]] => 101110
[7,4,5,3,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => 101101
[7,4,5,3,6,1,2] => [[1,3,5],[2,7],[4],[6]] => 101010
[7,4,5,3,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => 101011
[7,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5]] => 100100
[7,4,5,6,1,3,2] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,4,5,6,2,1,3] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,4,5,6,2,3,1] => [[1,3,4],[2,6],[5],[7]] => 100101
[7,4,5,6,3,1,2] => [[1,3,4],[2,7],[5],[6]] => 100110
[7,4,5,6,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => 100111
[7,4,6,1,2,3,5] => [[1,3,6,7],[2,5],[4]] => 101000
[7,4,6,1,2,5,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,4,6,1,3,2,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,4,6,1,3,5,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,4,6,1,5,2,3] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,4,6,1,5,3,2] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,4,6,2,1,3,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,4,6,2,1,5,3] => [[1,3],[2,6],[4,7],[5]] => 101101
[7,4,6,2,3,1,5] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,4,6,2,3,5,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,4,6,2,5,1,3] => [[1,3],[2,5],[4,7],[6]] => 101010
[7,4,6,2,5,3,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,4,6,3,1,2,5] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,4,6,3,1,5,2] => [[1,3],[2,6],[4,7],[5]] => 101101
[7,4,6,3,2,1,5] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,4,6,3,2,5,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,4,6,3,5,1,2] => [[1,3],[2,5],[4,7],[6]] => 101010
[7,4,6,3,5,2,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,4,6,5,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,4,6,5,1,3,2] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,4,6,5,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,4,6,5,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,4,6,5,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,4,6,5,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[7,5,1,2,3,4,6] => [[1,4,5,6,7],[2],[3]] => 110000
[7,5,1,2,3,6,4] => [[1,4,5,6],[2,7],[3]] => 110001
[7,5,1,2,4,3,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,5,1,2,4,6,3] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,5,1,2,6,3,4] => [[1,4,5,7],[2,6],[3]] => 110010
[7,5,1,2,6,4,3] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,5,1,3,2,4,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,5,1,3,2,6,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,5,1,3,4,2,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,5,1,3,4,6,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,5,1,3,6,2,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,5,1,3,6,4,2] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,5,1,4,2,3,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,5,1,4,2,6,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,5,1,4,3,2,6] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,5,1,4,3,6,2] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,5,1,4,6,2,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,5,1,4,6,3,2] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,5,1,6,2,3,4] => [[1,4,6,7],[2,5],[3]] => 110100
[7,5,1,6,2,4,3] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,5,1,6,3,2,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,5,1,6,3,4,2] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,5,1,6,4,2,3] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,5,1,6,4,3,2] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,5,2,1,3,4,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,5,2,1,3,6,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,5,2,1,4,3,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,5,2,1,4,6,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,5,2,1,6,3,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,5,2,1,6,4,3] => [[1,5],[2,6],[3,7],[4]] => 111011
[7,5,2,3,1,4,6] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,5,2,3,1,6,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,5,2,3,4,1,6] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,5,2,3,4,6,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,5,2,3,6,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,5,2,3,6,4,1] => [[1,4,5],[2,6],[3],[7]] => 110011
[7,5,2,4,1,3,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,5,2,4,1,6,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,5,2,4,3,1,6] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,5,2,4,3,6,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,5,2,4,6,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,5,2,4,6,3,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,5,2,6,1,3,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,5,2,6,1,4,3] => [[1,4],[2,6],[3,7],[5]] => 110101
[7,5,2,6,3,1,4] => [[1,4,7],[2,5],[3],[6]] => 110110
[7,5,2,6,3,4,1] => [[1,4,6],[2,5],[3],[7]] => 110101
[7,5,2,6,4,1,3] => [[1,4],[2,5],[3,7],[6]] => 110110
[7,5,2,6,4,3,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,5,3,1,2,4,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,5,3,1,2,6,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,5,3,1,4,2,6] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,5,3,1,4,6,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,5,3,1,6,2,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,5,3,1,6,4,2] => [[1,5],[2,6],[3,7],[4]] => 111011
[7,5,3,2,1,4,6] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,5,3,2,1,6,4] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,5,3,2,4,1,6] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,5,3,2,4,6,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,5,3,2,6,1,4] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,5,3,2,6,4,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,5,3,4,1,2,6] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,5,3,4,1,6,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,5,3,4,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,5,3,4,6,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,5,3,6,1,2,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,5,3,6,1,4,2] => [[1,4],[2,6],[3,7],[5]] => 110101
[7,5,3,6,2,1,4] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,5,3,6,2,4,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,5,3,6,4,1,2] => [[1,4],[2,5],[3,7],[6]] => 110110
[7,5,3,6,4,2,1] => [[1,4],[2,5],[3],[6],[7]] => 110111
[7,5,4,1,2,3,6] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,5,4,1,2,6,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,5,4,1,3,2,6] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,5,4,1,3,6,2] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,5,4,1,6,2,3] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,5,4,1,6,3,2] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,5,4,2,1,3,6] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,5,4,2,1,6,3] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,5,4,2,3,1,6] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,5,4,2,3,6,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,5,4,2,6,1,3] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,5,4,2,6,3,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,5,4,3,1,2,6] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,5,4,3,1,6,2] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,5,4,3,2,1,6] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[7,5,4,3,6,1,2] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[7,5,4,6,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,5,4,6,1,3,2] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,5,4,6,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,5,4,6,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,5,4,6,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,5,4,6,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[7,5,6,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => 101000
[7,5,6,1,2,4,3] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,5,6,1,3,2,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,5,6,1,3,4,2] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,5,6,1,4,2,3] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,5,6,1,4,3,2] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,5,6,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,5,6,2,1,4,3] => [[1,3],[2,6],[4,7],[5]] => 101101
[7,5,6,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => 101010
[7,5,6,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => 101001
[7,5,6,2,4,1,3] => [[1,3],[2,5],[4,7],[6]] => 101010
[7,5,6,2,4,3,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,5,6,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,5,6,3,1,4,2] => [[1,3],[2,6],[4,7],[5]] => 101101
[7,5,6,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,5,6,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => 101010
[7,5,6,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => 101011
[7,5,6,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => 101100
[7,5,6,4,1,3,2] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,5,6,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,5,6,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => 101101
[7,5,6,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => 101110
[7,5,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => 101111
[7,6,1,2,3,4,5] => [[1,4,5,6,7],[2],[3]] => 110000
[7,6,1,2,3,5,4] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,6,1,2,4,3,5] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,6,1,2,4,5,3] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,6,1,2,5,3,4] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,6,1,2,5,4,3] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,1,3,2,4,5] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,6,1,3,2,5,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,6,1,3,4,2,5] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,6,1,3,4,5,2] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,6,1,3,5,2,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,6,1,3,5,4,2] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,1,4,2,3,5] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,6,1,4,2,5,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,6,1,4,3,2,5] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,1,4,3,5,2] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,1,4,5,2,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,6,1,4,5,3,2] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,1,5,2,3,4] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,6,1,5,2,4,3] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,1,5,3,2,4] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,1,5,3,4,2] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,1,5,4,2,3] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,1,5,4,3,2] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[7,6,2,1,3,4,5] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,6,2,1,3,5,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,6,2,1,4,3,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,6,2,1,4,5,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,6,2,1,5,3,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,6,2,1,5,4,3] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,6,2,3,1,4,5] => [[1,4,6,7],[2],[3],[5]] => 110100
[7,6,2,3,1,5,4] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,6,2,3,4,1,5] => [[1,4,5,7],[2],[3],[6]] => 110010
[7,6,2,3,4,5,1] => [[1,4,5,6],[2],[3],[7]] => 110001
[7,6,2,3,5,1,4] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,6,2,3,5,4,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,2,4,1,3,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,6,2,4,1,5,3] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,6,2,4,3,1,5] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,2,4,3,5,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,2,4,5,1,3] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,6,2,4,5,3,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,2,5,1,3,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,6,2,5,1,4,3] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,6,2,5,3,1,4] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,2,5,3,4,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,2,5,4,1,3] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,6,2,5,4,3,1] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[7,6,3,1,2,4,5] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,6,3,1,2,5,4] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,6,3,1,4,2,5] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,6,3,1,4,5,2] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,6,3,1,5,2,4] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,6,3,1,5,4,2] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,6,3,2,1,4,5] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,3,2,1,5,4] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,6,3,2,4,1,5] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,3,2,4,5,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,3,2,5,1,4] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,6,3,2,5,4,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,6,3,4,1,2,5] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,6,3,4,1,5,2] => [[1,4,6],[2,7],[3],[5]] => 110101
[7,6,3,4,2,1,5] => [[1,4,7],[2],[3],[5],[6]] => 110110
[7,6,3,4,2,5,1] => [[1,4,6],[2],[3],[5],[7]] => 110101
[7,6,3,4,5,1,2] => [[1,4,5],[2,7],[3],[6]] => 110010
[7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => 110011
[7,6,3,5,1,2,4] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,6,3,5,1,4,2] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,6,3,5,2,1,4] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,6,3,5,2,4,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,6,3,5,4,1,2] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,6,3,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[7,6,4,1,2,3,5] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,6,4,1,2,5,3] => [[1,5,6],[2,7],[3],[4]] => 111001
[7,6,4,1,3,2,5] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,4,1,3,5,2] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,4,1,5,2,3] => [[1,5,7],[2,6],[3],[4]] => 111010
[7,6,4,1,5,3,2] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,6,4,2,1,3,5] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,4,2,1,5,3] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,6,4,2,3,1,5] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,4,2,3,5,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,4,2,5,1,3] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,6,4,2,5,3,1] => [[1,5],[2,6],[3],[4],[7]] => 111011
[7,6,4,3,1,2,5] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,4,3,1,5,2] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,6,4,3,2,1,5] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[7,6,4,3,2,5,1] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[7,6,4,3,5,1,2] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[7,6,4,5,1,2,3] => [[1,4,7],[2,6],[3],[5]] => 110100
[7,6,4,5,1,3,2] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,6,4,5,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,6,4,5,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => 110101
[7,6,4,5,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => 110110
[7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => 110111
[7,6,5,1,2,3,4] => [[1,5,6,7],[2],[3],[4]] => 111000
[7,6,5,1,2,4,3] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,5,1,3,2,4] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,5,1,3,4,2] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,5,1,4,2,3] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,5,1,4,3,2] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[7,6,5,2,1,3,4] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,5,2,1,4,3] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,6,5,2,3,1,4] => [[1,5,7],[2],[3],[4],[6]] => 111010
[7,6,5,2,3,4,1] => [[1,5,6],[2],[3],[4],[7]] => 111001
[7,6,5,2,4,1,3] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,6,5,2,4,3,1] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[7,6,5,3,1,2,4] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,5,3,1,4,2] => [[1,6],[2,7],[3],[4],[5]] => 111101
[7,6,5,3,2,1,4] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[7,6,5,3,2,4,1] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[7,6,5,3,4,1,2] => [[1,5],[2,7],[3],[4],[6]] => 111010
[7,6,5,3,4,2,1] => [[1,5],[2],[3],[4],[6],[7]] => 111011
[7,6,5,4,1,2,3] => [[1,6,7],[2],[3],[4],[5]] => 111100
[7,6,5,4,1,3,2] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[7,6,5,4,2,1,3] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[7,6,5,4,2,3,1] => [[1,6],[2],[3],[4],[5],[7]] => 111101
[7,6,5,4,3,1,2] => [[1,7],[2],[3],[4],[5],[6]] => 111110
[7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111
[8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111
[7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[8,6,7,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[8,7,5,6,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[7,8,5,6,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[8,6,5,7,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[8,5,6,7,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[6,7,5,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[7,5,6,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[6,5,7,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[7,8,6,4,5,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[8,6,7,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[7,6,8,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,7,5,4,6,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[8,6,5,4,7,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[8,5,6,4,7,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,6,4,5,7,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[8,4,5,6,7,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[6,7,5,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[7,5,6,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[6,5,7,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[5,6,7,4,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[7,6,4,5,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[6,7,4,5,8,3,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[7,5,4,6,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[7,4,5,6,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[6,5,4,7,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[5,6,4,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[6,4,5,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[5,4,6,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[8,7,6,5,3,4,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[7,8,6,5,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[8,6,7,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[7,6,8,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[8,7,5,6,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[7,8,5,6,3,4,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[8,5,6,7,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,6,5,8,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[6,7,5,8,3,4,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[6,5,7,8,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[5,6,7,8,3,4,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[8,7,6,4,3,5,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[7,8,6,4,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[8,6,7,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[7,6,8,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[6,7,8,4,3,5,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[8,7,6,3,4,5,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,8,6,3,4,5,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,6,7,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[7,6,8,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[6,7,8,3,4,5,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[7,8,5,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[8,7,4,5,3,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[8,7,5,3,4,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,8,5,3,4,6,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[7,8,3,4,5,6,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,6,5,4,3,7,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[8,6,4,3,5,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,5,4,3,6,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,5,3,4,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[8,4,3,5,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[6,7,5,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[7,5,6,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[6,5,7,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[5,6,7,4,3,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[6,7,4,5,3,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,5,4,6,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[7,4,5,6,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[6,5,4,7,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[6,4,5,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[5,4,6,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[4,5,6,7,3,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[7,6,5,3,4,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,6,4,3,5,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,6,3,4,5,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[7,5,4,3,6,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,5,3,4,6,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[7,3,4,5,6,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[6,5,4,3,7,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[6,5,3,4,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[6,3,4,5,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[5,4,3,6,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[5,3,4,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[4,3,5,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[8,7,6,5,4,2,3,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[7,8,6,5,4,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[8,6,7,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[7,6,8,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,7,5,6,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,6,5,7,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,5,6,7,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,6,5,8,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[6,7,5,8,4,2,3,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[7,5,6,8,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[5,6,7,8,4,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,7,6,4,5,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,6,8,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,7,5,4,6,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,7,4,5,6,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[7,8,4,5,6,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[8,6,5,4,7,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,5,6,4,7,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,6,4,5,7,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,4,5,6,7,2,3,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,6,5,4,8,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[7,5,6,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[6,5,7,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[6,7,4,5,8,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,5,6,7,8,2,3,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[8,7,6,5,3,2,4,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[7,8,6,5,3,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[8,6,7,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[7,6,8,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[6,7,8,5,3,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[8,7,5,6,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,6,5,7,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,5,6,7,3,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,6,5,8,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[6,7,5,8,3,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,6,7,8,3,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,7,6,5,2,3,4,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,6,7,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[7,6,8,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,7,8,5,2,3,4,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,7,5,6,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,8,5,6,2,3,4,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[8,6,5,7,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,5,6,7,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[7,6,5,8,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,7,5,8,2,3,4,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[6,5,7,8,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[5,6,7,8,2,3,4,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[8,7,6,4,3,2,5,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[7,8,6,4,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[8,6,7,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[7,6,8,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[6,7,8,4,3,2,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[8,7,6,3,4,2,5,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,8,6,3,4,2,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,6,7,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,6,8,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,7,8,3,4,2,5,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[7,6,8,4,2,3,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,7,8,4,2,3,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,7,6,3,2,4,5,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[7,8,6,3,2,4,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[8,6,7,3,2,4,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,7,8,3,2,4,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,7,6,2,3,4,5,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,8,6,2,3,4,5,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,6,7,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,6,8,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,7,8,2,3,4,5,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[8,7,5,4,3,2,6,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[7,8,5,4,3,2,6,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[8,7,5,3,4,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,8,5,3,4,2,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,7,4,3,5,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,7,5,3,2,4,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,7,4,3,2,5,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[7,8,4,3,2,5,6,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,8,3,4,2,5,6,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,8,4,2,3,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,8,3,2,4,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,7,2,3,4,5,6,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,8,2,3,4,5,6,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[8,5,6,4,3,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,6,4,5,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[8,5,4,6,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[8,6,5,3,4,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,5,6,3,4,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[8,5,4,3,6,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,4,5,3,6,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,4,3,5,6,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[8,3,4,5,6,2,7,1] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[8,6,5,4,2,3,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,6,5,3,2,4,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,6,4,3,2,5,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,6,4,2,3,5,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,6,2,3,4,5,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,4,5,3,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,3,4,5,2,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[8,5,4,2,3,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,4,5,2,3,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,3,4,2,5,6,7,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,4,2,3,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[6,7,5,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[7,5,6,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[6,5,7,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[5,6,7,4,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[7,6,4,5,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[6,7,4,5,3,2,8,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[7,4,5,6,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[6,5,4,7,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[6,4,5,7,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[4,5,6,7,3,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[7,6,5,3,4,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,5,6,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,5,7,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,6,4,3,5,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,6,3,4,5,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,5,4,3,6,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,4,5,3,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[7,5,3,4,6,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,3,4,5,6,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[6,5,4,3,7,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[6,4,5,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[4,5,6,3,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[6,5,3,4,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[5,6,3,4,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,4,3,5,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[6,3,4,5,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[5,4,3,6,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[4,5,3,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[4,3,5,6,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[3,4,5,6,7,2,8,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[7,6,5,4,2,3,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[6,7,5,4,2,3,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,5,6,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,5,7,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,6,7,4,2,3,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[7,6,4,5,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,7,4,5,2,3,8,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[7,5,4,6,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,4,5,6,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,5,4,7,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[5,6,4,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,4,6,7,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[4,5,6,7,2,3,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[7,6,5,3,2,4,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[6,7,5,3,2,4,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[6,5,7,3,2,4,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[7,6,5,2,3,4,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,5,6,2,3,4,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,6,7,2,3,4,8,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,7,4,3,2,5,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,6,4,2,3,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,6,3,2,4,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[6,7,3,2,4,5,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,6,2,3,4,5,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[6,7,2,3,4,5,8,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,5,4,3,2,6,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[7,4,3,5,2,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[7,5,4,2,3,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,4,5,2,3,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,5,3,2,4,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,5,2,3,4,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,4,3,2,5,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,3,2,4,5,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[5,4,6,3,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[4,5,6,3,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[6,5,3,4,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[6,3,4,5,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[5,4,3,6,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[3,4,5,6,2,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[6,5,4,2,3,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[5,6,4,2,3,7,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[6,4,5,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,4,6,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,5,6,2,3,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[6,5,3,2,4,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[6,5,2,3,4,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[6,2,3,4,5,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[4,5,3,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[5,3,4,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[4,3,5,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[5,4,2,3,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[4,5,2,3,6,7,8,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[5,3,2,4,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[5,2,3,4,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[8,7,6,5,4,3,1,2] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,6,7,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[7,6,8,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[6,7,8,5,4,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,7,5,6,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[7,8,5,6,4,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[8,6,5,7,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[7,6,5,8,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[6,7,5,8,4,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,5,6,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[6,5,7,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,6,7,8,4,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[8,7,6,4,5,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[8,6,7,4,5,3,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[6,7,8,4,5,3,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[8,7,5,4,6,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[8,5,6,4,7,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,6,4,5,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,5,4,6,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,6,5,4,8,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[7,5,6,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,5,7,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,6,4,5,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[6,7,4,5,8,3,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,5,4,7,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[5,6,4,7,8,3,1,2] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[5,4,6,7,8,3,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,5,6,7,8,3,1,2] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[8,7,6,5,3,4,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[7,8,6,5,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[7,6,8,5,3,4,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[6,7,8,5,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[8,7,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[8,6,5,7,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,5,6,7,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,6,5,8,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[6,7,5,8,3,4,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[7,5,6,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[6,5,7,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[6,7,8,4,3,5,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[8,7,6,3,4,5,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,6,7,3,4,5,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[7,8,5,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[8,7,4,5,3,6,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,8,4,5,3,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,5,3,4,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,7,4,3,5,6,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,8,4,3,5,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,7,3,4,5,6,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,6,5,4,3,7,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,5,4,6,3,7,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,5,4,3,6,7,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,5,3,4,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,4,3,5,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,3,4,5,6,7,1,2] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,6,5,4,3,8,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[7,5,6,4,3,8,1,2] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,6,7,4,3,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[6,7,4,5,3,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,5,4,6,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[6,5,4,7,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,6,4,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,5,6,7,3,8,1,2] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[7,6,5,3,4,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,4,3,5,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,3,4,5,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,5,4,3,6,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,4,5,3,6,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,5,3,4,6,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,3,4,5,6,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,5,4,3,7,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[5,6,4,3,7,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,4,6,3,7,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,5,6,3,7,8,1,2] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[5,6,3,4,7,8,1,2] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,4,3,5,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,3,4,5,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,4,3,6,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,5,3,6,7,8,1,2] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[5,3,4,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,3,5,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[8,7,6,5,4,2,1,3] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[7,8,6,5,4,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,6,7,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[7,6,8,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[6,7,8,5,4,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,7,5,6,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[7,8,5,6,4,2,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[7,6,5,8,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[6,7,5,8,4,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,5,6,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[6,5,7,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,6,7,8,4,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[8,7,6,4,5,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[8,4,5,6,7,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,6,5,4,8,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[6,7,5,4,8,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,5,7,4,8,2,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[5,6,7,4,8,2,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,6,4,5,8,2,1,3] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,4,5,6,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,4,6,7,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,5,6,7,8,2,1,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[8,7,6,5,4,1,2,3] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,6,5,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,6,8,5,4,1,2,3] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[7,8,5,6,4,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[8,6,5,7,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,5,6,7,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,6,5,8,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,7,5,8,4,1,2,3] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[7,5,6,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,5,7,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,6,7,8,4,1,2,3] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[8,7,6,4,5,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,6,7,4,5,1,2,3] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[8,7,5,4,6,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,8,5,4,6,1,2,3] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,7,4,5,6,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,8,4,5,6,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[8,6,5,4,7,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,5,6,4,7,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,6,4,5,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,5,4,6,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,4,5,6,7,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,6,5,4,8,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,7,5,4,8,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,5,7,4,8,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[5,6,7,4,8,1,2,3] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[6,7,4,5,8,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[7,5,4,6,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,5,4,7,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,6,4,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,4,6,7,8,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,5,6,7,8,1,2,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[8,7,6,5,3,2,1,4] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[7,8,6,5,3,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,6,7,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[7,6,8,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[6,7,8,5,3,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,7,5,6,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[7,8,5,6,3,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[8,6,5,7,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[8,5,6,7,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,6,5,8,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[6,7,5,8,3,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,5,6,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[6,5,7,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,6,7,8,3,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[8,7,6,5,2,3,1,4] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,8,6,5,2,3,1,4] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[8,6,7,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,6,8,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,7,8,5,2,3,1,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,7,5,6,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,8,5,6,2,3,1,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[8,6,5,7,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,5,6,7,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[7,6,5,8,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,7,5,8,2,3,1,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[7,5,6,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[6,5,7,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,6,7,8,2,3,1,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[8,7,6,5,3,1,2,4] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,6,5,3,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,6,7,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,6,8,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,7,5,6,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,8,5,6,3,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,6,5,8,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,7,5,8,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[7,5,6,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,5,7,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,6,7,8,3,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[8,7,6,5,2,1,3,4] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,6,5,2,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,6,8,5,2,1,3,4] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,7,8,5,2,1,3,4] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,7,5,6,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,8,5,6,2,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[8,6,5,7,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,5,6,7,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,6,5,8,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,7,5,8,2,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[7,5,6,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,5,7,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,6,7,8,2,1,3,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[8,7,6,5,1,2,3,4] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,6,5,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,6,7,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,6,8,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,7,8,5,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[8,7,5,6,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,8,5,6,1,2,3,4] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[8,6,5,7,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,5,6,7,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,6,5,8,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,7,5,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[7,5,6,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,5,7,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[8,7,6,4,3,2,1,5] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[7,8,6,4,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,6,7,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[7,6,8,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[6,7,8,4,3,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,7,6,3,4,2,1,5] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[7,8,6,3,4,2,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,7,8,3,4,2,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[8,7,6,4,2,3,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,6,8,4,2,3,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,7,8,4,2,3,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,7,6,3,2,4,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,6,7,3,2,4,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,7,8,3,2,4,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,7,6,2,3,4,1,5] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,6,7,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,6,8,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,7,8,2,3,4,1,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[8,7,6,4,3,1,2,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[6,7,8,4,3,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,7,6,3,4,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,8,6,3,4,1,2,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,6,7,3,4,1,2,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,7,8,3,4,1,2,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[8,7,6,4,2,1,3,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,6,4,2,1,3,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,6,7,4,2,1,3,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,7,8,4,2,1,3,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,7,6,4,1,2,3,5] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,6,4,1,2,3,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[7,6,8,4,1,2,3,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,7,8,4,1,2,3,5] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[8,7,6,3,2,1,4,5] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,6,3,2,1,4,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,6,7,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,6,8,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,7,8,3,2,1,4,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,7,6,2,3,1,4,5] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,8,6,2,3,1,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[8,6,7,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,6,8,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,7,8,2,3,1,4,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[8,7,6,3,1,2,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,6,3,1,2,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,6,7,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,6,8,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,7,8,3,1,2,4,5] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[8,7,6,2,1,3,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,6,2,1,3,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,6,7,2,1,3,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,7,8,2,1,3,4,5] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[8,7,6,1,2,3,4,5] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,8,6,1,2,3,4,5] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,6,7,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,6,8,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,7,8,1,2,3,4,5] => [[1,2,3,7,8],[4,5,6]] => 0010000
[8,7,5,4,3,2,1,6] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[7,8,5,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,7,4,5,3,2,1,6] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[7,8,4,5,3,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[8,7,5,3,4,2,1,6] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,7,3,4,5,2,1,6] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[7,8,3,4,5,2,1,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,7,4,5,2,3,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,8,4,5,2,3,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[8,7,5,3,2,4,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,8,5,2,3,4,1,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[8,7,4,3,2,5,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,8,4,3,2,5,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[8,7,3,4,2,5,1,6] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,8,3,4,2,5,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,7,2,3,4,5,1,6] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[7,8,2,3,4,5,1,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,7,5,4,3,1,2,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,5,4,3,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,5,3,4,1,2,6] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,3,4,5,1,2,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,8,3,4,5,1,2,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[7,8,5,4,2,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,5,4,1,2,3,6] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,5,4,1,2,3,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,4,5,1,2,3,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,8,4,5,1,2,3,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[8,7,5,3,2,1,4,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,5,3,2,1,4,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,5,3,1,2,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,5,3,1,2,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,5,2,1,3,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,5,2,1,3,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,5,1,2,3,4,6] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,8,5,1,2,3,4,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,7,4,3,2,1,5,6] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,8,4,3,2,1,5,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,3,4,2,1,5,6] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[7,8,3,4,2,1,5,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,8,4,2,3,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[8,7,3,2,4,1,5,6] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,8,3,2,4,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[8,7,2,3,4,1,5,6] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,8,2,3,4,1,5,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[7,8,4,3,1,2,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,3,4,1,2,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,8,3,4,1,2,5,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[8,7,4,2,1,3,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,4,2,1,3,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,4,1,2,3,5,6] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,8,4,1,2,3,5,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,7,3,2,1,4,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,8,3,2,1,4,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,7,2,3,1,4,5,6] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[7,8,2,3,1,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[7,8,3,1,2,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,7,2,1,3,4,5,6] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,8,2,1,3,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,7,1,2,3,4,5,6] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => 0100000
[8,6,5,4,3,2,1,7] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[8,5,6,4,3,2,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,6,4,5,3,2,1,7] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[8,4,5,6,3,2,1,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,6,5,3,4,2,1,7] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,5,6,3,4,2,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,4,5,3,6,2,1,7] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,4,3,5,6,2,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,3,4,5,6,2,1,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,6,5,4,2,3,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,5,6,4,2,3,1,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,4,5,6,2,3,1,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,6,5,3,2,4,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,6,5,2,3,4,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,5,6,2,3,4,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,6,4,2,3,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,6,3,2,4,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,5,4,3,2,6,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,4,3,5,2,6,1,7] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,5,4,2,3,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,4,5,2,3,6,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,5,3,2,4,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,5,2,3,4,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,3,4,2,5,6,1,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,3,2,4,5,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,2,3,4,5,6,1,7] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,6,5,4,3,1,2,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[8,6,4,5,3,1,2,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,6,5,3,4,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,5,6,3,4,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,6,3,4,5,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,5,4,3,6,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,4,5,3,6,1,2,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,5,3,4,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,4,3,5,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,3,4,5,6,1,2,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,6,5,4,2,1,3,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[8,5,6,4,2,1,3,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,4,5,6,2,1,3,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,6,5,4,1,2,3,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,5,6,4,1,2,3,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,6,4,5,1,2,3,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,4,5,6,1,2,3,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,6,5,3,2,1,4,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[8,5,6,3,2,1,4,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,6,5,2,3,1,4,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,5,6,2,3,1,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,5,6,3,1,2,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,6,5,2,1,3,4,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,5,6,2,1,3,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,6,5,1,2,3,4,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,5,6,1,2,3,4,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,6,4,3,2,1,5,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[8,6,3,4,2,1,5,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,6,4,2,3,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,6,3,2,4,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,6,2,3,4,1,5,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[8,6,4,3,1,2,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,6,3,4,1,2,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,6,4,2,1,3,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,6,4,1,2,3,5,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,6,3,2,1,4,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,6,1,2,3,4,5,7] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[8,5,4,3,2,1,6,7] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[8,4,5,3,2,1,6,7] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[8,4,3,5,2,1,6,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,3,4,5,2,1,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[8,4,5,2,3,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,5,2,3,4,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[8,4,2,3,5,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[8,2,3,4,5,1,6,7] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[8,5,3,4,1,2,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,3,4,5,1,2,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[8,5,4,2,1,3,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,5,4,1,2,3,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,4,5,1,2,3,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,5,3,2,1,4,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,5,3,1,2,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,5,2,1,3,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,5,1,2,3,4,6,7] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[8,4,3,2,1,5,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[8,3,4,2,1,5,6,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[8,4,2,3,1,5,6,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[8,2,3,4,1,5,6,7] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[8,3,4,1,2,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,4,2,1,3,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,4,1,2,3,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[8,3,2,1,4,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[8,2,3,1,4,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,3,1,2,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[8,2,1,3,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => 1000000
[7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110
[6,7,5,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[7,5,6,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[6,5,7,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[5,6,7,4,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[7,6,4,5,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[6,7,4,5,3,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,5,4,6,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[7,4,5,6,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[6,5,4,7,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[5,6,4,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[5,4,6,7,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[4,5,6,7,3,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[7,6,5,3,4,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[6,7,5,3,4,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[7,5,6,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[6,5,7,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,6,7,3,4,2,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[6,7,4,3,5,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[7,5,4,3,6,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[7,3,4,5,6,2,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[6,5,4,3,7,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[5,6,4,3,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[5,4,6,3,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[5,4,3,6,7,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[3,4,5,6,7,2,1,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[7,6,5,4,2,3,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[6,7,5,4,2,3,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[7,5,6,4,2,3,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[5,6,7,4,2,3,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,6,4,5,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,7,4,5,2,3,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,5,4,6,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,5,4,7,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,6,4,7,2,3,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[5,4,6,7,2,3,1,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[4,5,6,7,2,3,1,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[7,6,5,3,2,4,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[6,5,7,3,2,4,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[5,6,7,3,2,4,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,6,5,2,3,4,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[6,7,5,2,3,4,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[7,5,6,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,5,7,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,6,7,2,3,4,1,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[7,6,4,3,2,5,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[6,7,4,3,2,5,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[6,7,3,4,2,5,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,6,4,2,3,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[6,7,4,2,3,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[7,6,3,2,4,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[6,7,3,2,4,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[7,6,2,3,4,5,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[6,7,2,3,4,5,1,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,4,5,3,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,4,3,5,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,4,5,2,3,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,5,3,2,4,6,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[7,4,2,3,5,6,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[5,6,4,3,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[5,4,6,3,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[5,6,3,4,2,7,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,3,4,5,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[5,4,3,6,2,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[5,3,4,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[3,4,5,6,2,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[5,4,6,2,3,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,5,3,2,4,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[6,4,2,3,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[6,3,2,4,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[3,4,5,2,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[5,4,2,3,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[4,5,2,3,6,7,1,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,2,3,4,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[3,4,2,5,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[4,2,3,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[7,6,5,4,3,1,2,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[6,7,5,4,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,5,6,4,3,1,2,8] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,6,4,5,3,1,2,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,4,6,7,3,1,2,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[4,5,6,7,3,1,2,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[7,6,5,3,4,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[6,5,4,3,7,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,4,5,3,7,1,2,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[5,6,3,4,7,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[6,3,4,5,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[4,3,5,6,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,4,5,6,7,1,2,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[7,6,5,4,2,1,3,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[6,5,7,4,2,1,3,8] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,6,4,5,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,5,4,6,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,4,6,7,2,1,3,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[4,5,6,7,2,1,3,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[7,6,5,4,1,2,3,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[7,4,5,6,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,4,6,7,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,5,6,7,1,2,3,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[7,6,5,3,2,1,4,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,6,5,2,3,1,4,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[6,7,5,2,3,1,4,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,5,6,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,5,7,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,6,7,2,3,1,4,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[7,6,5,2,1,3,4,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[6,7,5,2,1,3,4,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[7,5,6,2,1,3,4,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,6,7,2,1,3,4,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[7,6,5,1,2,3,4,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[6,7,5,1,2,3,4,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[7,5,6,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,5,7,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,6,7,1,2,3,4,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[7,6,4,3,2,1,5,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[6,7,4,3,2,1,5,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,6,3,4,2,1,5,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[6,7,3,4,2,1,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,6,4,2,3,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,6,3,2,4,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[6,7,3,2,4,1,5,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,6,2,3,4,1,5,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[6,7,2,3,4,1,5,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[7,6,4,3,1,2,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[6,7,3,4,1,2,5,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[7,6,4,2,1,3,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,6,3,2,1,4,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[6,7,3,2,1,4,5,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[7,6,2,3,1,4,5,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,7,2,3,1,4,5,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,7,3,1,2,4,5,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[7,6,1,2,3,4,5,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[7,5,4,3,2,1,6,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[7,4,5,3,2,1,6,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[7,4,3,5,2,1,6,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[7,3,4,5,2,1,6,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[7,5,4,2,3,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,5,3,2,4,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,5,2,3,4,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,4,2,3,5,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,2,3,4,5,1,6,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[7,5,4,3,1,2,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,4,5,2,1,3,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,4,5,1,2,3,6,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,5,3,2,1,4,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,5,2,3,1,4,6,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[7,5,3,1,2,4,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,5,1,2,3,4,6,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[7,4,3,2,1,5,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[7,2,3,4,1,5,6,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[7,4,3,1,2,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,3,4,1,2,5,6,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,4,1,2,3,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[7,3,2,1,4,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[7,2,3,1,4,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[7,3,1,2,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[7,2,1,3,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100
[5,6,4,3,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[5,4,6,3,2,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[4,5,6,3,2,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[5,6,3,4,2,1,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[5,4,3,6,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[3,4,5,6,2,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[5,4,6,2,3,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,6,3,2,4,1,7,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[6,5,2,3,4,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,6,2,3,4,1,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[4,5,3,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[4,3,5,2,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[3,4,5,2,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[5,3,2,4,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,2,3,4,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[3,4,2,5,6,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[4,2,3,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[6,5,4,3,1,2,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[6,4,5,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,4,6,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,6,3,4,1,2,7,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,4,3,6,1,2,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[4,3,5,6,1,2,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,4,5,6,1,2,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[6,5,4,2,1,3,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[5,6,4,2,1,3,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,4,5,2,1,3,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[4,5,6,2,1,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[6,5,4,1,2,3,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[6,5,3,2,1,4,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[5,6,3,2,1,4,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,6,2,1,3,4,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[6,4,3,2,1,5,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[6,3,4,2,1,5,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[6,4,3,1,2,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[6,4,2,1,3,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[6,4,1,2,3,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[6,2,3,1,4,5,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[6,3,1,2,4,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000
[4,5,3,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[5,3,4,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[4,3,5,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[3,4,5,2,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[5,4,2,3,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[4,5,2,3,1,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 0001000
[5,4,3,1,2,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[5,3,4,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[4,3,5,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[3,4,5,1,2,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[5,4,2,1,3,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[4,5,2,1,3,6,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[5,4,1,2,3,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[4,5,1,2,3,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[5,3,2,1,4,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[5,2,3,1,4,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[5,3,1,2,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[5,2,1,3,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => 1110000
[3,4,2,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[4,3,1,2,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[4,2,1,3,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => 1100000
[2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1000000
[1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => 0000000
[6,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[5,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[5,7,8,6,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[6,5,8,7,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[5,6,8,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[5,7,6,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[4,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[4,7,8,6,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[4,6,8,7,5,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[4,7,6,8,5,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[4,6,7,8,5,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[5,4,7,8,6,3,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,5,8,7,6,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[4,5,7,8,6,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[5,6,4,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[4,6,5,8,7,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[4,5,6,8,7,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[5,7,6,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[4,7,6,5,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[4,6,7,5,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[5,4,7,6,8,3,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,5,7,6,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[4,6,5,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[3,7,8,6,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[3,6,8,7,5,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[3,7,6,8,5,4,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[3,5,8,7,6,4,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[3,5,7,8,6,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[3,5,6,8,7,4,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[3,7,6,5,8,4,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[3,5,7,6,8,4,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[3,5,6,7,8,4,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[4,3,8,7,6,5,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[4,3,7,8,6,5,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,3,6,7,8,5,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,4,8,7,6,5,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[3,4,6,7,8,5,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[5,4,3,8,7,6,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[5,4,3,7,8,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[3,5,4,7,8,6,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,5,8,7,6,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[3,4,5,7,8,6,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[6,5,4,3,8,7,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[5,6,4,3,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,5,6,3,8,7,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,6,5,4,8,7,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,3,6,5,8,7,2,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[5,4,3,6,8,7,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[4,5,3,6,8,7,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,5,6,8,7,2,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[5,7,6,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[4,7,6,5,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[5,4,7,6,3,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,7,6,5,4,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[3,5,7,6,4,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[3,5,6,7,4,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[4,3,7,6,5,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,4,7,6,5,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[3,4,6,7,5,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[4,5,3,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,5,4,7,6,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[4,3,5,7,6,8,2,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,4,5,7,6,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[3,6,5,4,7,8,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[3,5,6,4,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[4,3,6,5,7,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,4,6,5,7,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[3,5,4,6,7,8,2,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[2,7,8,6,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,6,8,7,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,7,6,8,5,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[2,6,7,8,5,4,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[2,5,8,7,6,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,6,7,5,8,4,3,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[2,5,6,7,8,4,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,4,8,7,6,5,3,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,4,7,8,6,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[2,4,6,8,7,5,3,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[2,4,6,7,8,5,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,5,4,8,7,6,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[2,5,4,7,8,6,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,4,5,7,8,6,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,6,5,4,8,7,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,5,6,4,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,4,6,5,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,4,5,6,8,7,3,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,7,6,5,4,8,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[2,5,6,7,4,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,4,7,6,5,8,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[2,4,6,7,5,8,3,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,5,4,7,6,8,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,6,5,4,7,8,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[2,5,6,4,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,4,6,5,7,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,5,4,6,7,8,3,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,4,5,6,7,8,3,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[3,2,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[3,2,7,8,6,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[3,2,6,8,7,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[3,2,5,7,8,6,4,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,2,5,7,6,8,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,2,5,6,7,8,4,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,3,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[2,3,6,7,8,5,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,5,7,8,6,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,6,5,8,7,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,3,5,6,8,7,4,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,7,6,5,8,4,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[2,3,5,7,6,8,4,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,3,5,6,7,8,4,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[4,3,2,8,7,6,5,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[4,3,2,7,8,6,5,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,4,2,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,4,2,7,8,6,5,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,4,3,8,7,6,5,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[2,4,3,6,8,7,5,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,4,3,6,7,8,5,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,2,4,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,3,4,8,7,6,5,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[2,3,4,7,8,6,5,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,4,6,8,7,5,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,4,7,6,8,5,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,3,4,6,7,8,5,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[5,4,3,2,8,7,6,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[5,4,3,2,7,8,6,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[3,5,4,2,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,4,5,2,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,5,4,3,8,7,6,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[2,5,4,3,7,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,4,5,3,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,2,5,4,7,8,6,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,3,5,4,8,7,6,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,3,5,4,7,8,6,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,3,2,5,8,7,6,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,3,2,5,7,8,6,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,4,2,5,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,2,5,7,8,6,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,2,4,5,7,8,6,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,3,4,5,8,7,6,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[2,3,4,5,7,8,6,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[6,5,4,3,2,8,7,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[4,6,5,3,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[5,4,6,3,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[4,5,6,3,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,6,5,4,2,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[3,5,6,4,2,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,3,6,5,2,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,4,3,6,2,8,7,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[4,5,3,6,2,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,4,5,6,2,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[2,6,5,4,3,8,7,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,4,6,5,3,8,7,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[2,4,5,6,3,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,2,6,5,4,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,3,5,6,4,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,3,2,6,5,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,4,3,6,5,8,7,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,2,4,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,3,4,6,5,8,7,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[5,4,3,2,6,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[2,5,4,3,6,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,4,5,3,6,8,7,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,2,5,4,6,8,7,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,3,2,5,6,8,7,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,4,2,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,4,3,5,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,2,4,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,3,4,5,6,8,7,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[5,7,6,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[4,7,6,5,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[4,6,7,5,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[4,6,5,7,3,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[3,5,7,6,4,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[3,5,6,7,4,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[4,3,7,6,5,2,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,3,6,7,5,2,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,4,7,6,5,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[3,4,6,7,5,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[5,4,3,7,6,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[3,5,4,7,6,2,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,4,5,7,6,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[4,6,5,3,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[3,6,5,4,7,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[3,5,6,4,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[4,3,6,5,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,4,6,5,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[3,5,4,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,7,6,5,4,3,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[2,6,5,7,4,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,5,6,7,4,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,4,6,7,5,3,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,5,4,7,6,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,4,6,5,7,3,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[2,5,4,6,7,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,4,5,6,7,3,8,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[3,2,7,6,5,4,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[3,2,6,7,5,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,2,5,7,6,4,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,2,6,5,7,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,5,6,7,4,8,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,3,7,6,5,4,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[2,3,5,7,6,4,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,3,5,6,7,4,8,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[4,3,2,7,6,5,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[4,3,2,6,7,5,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,4,2,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,4,2,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,4,3,7,6,5,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,4,3,6,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[3,2,4,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,3,4,7,6,5,8,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,3,4,6,7,5,8,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[5,4,3,2,7,6,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[3,5,4,2,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,3,5,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,4,5,2,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,5,4,3,7,6,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,2,5,4,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,3,5,4,7,6,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,3,2,5,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,4,2,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,4,3,5,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[3,2,4,5,7,6,8,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,3,4,5,7,6,8,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[3,6,5,4,2,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[3,5,6,4,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[3,4,6,5,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[3,5,4,6,2,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,6,5,4,3,7,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[2,5,6,4,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,4,6,5,3,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,4,5,6,3,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[3,2,5,6,4,7,8,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[2,3,6,5,4,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,3,5,6,4,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[4,3,2,6,5,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,4,2,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,3,6,5,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,3,4,6,5,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[3,5,4,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,5,4,3,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,4,5,3,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[3,2,5,4,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,3,5,4,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[2,4,3,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[1,7,8,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,6,8,7,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,7,6,8,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[1,6,7,8,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,5,8,7,6,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,6,5,8,7,4,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,7,6,5,8,4,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[1,6,7,5,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,5,7,6,8,4,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,6,5,7,8,4,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[1,5,6,7,8,4,3,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,4,8,7,6,5,3,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,4,7,8,6,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,4,6,8,7,5,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,4,6,7,8,5,3,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,5,4,7,8,6,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,4,5,8,7,6,3,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,4,6,5,8,7,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,7,6,5,4,8,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,4,7,6,5,8,3,2] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,4,6,7,5,8,3,2] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,6,5,4,7,8,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,5,6,4,7,8,3,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,5,4,6,7,8,3,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,4,5,6,7,8,3,2] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,3,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,3,7,8,6,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,3,6,8,7,5,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,3,6,7,8,5,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,3,5,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,3,5,7,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,3,5,6,8,7,4,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,3,6,7,5,8,4,2] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,3,6,5,7,8,4,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,3,5,6,7,8,4,2] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,4,3,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,4,3,7,8,6,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,4,3,6,8,7,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,4,3,7,6,8,5,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,4,3,6,7,8,5,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,4,8,7,6,5,2] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,3,4,7,6,8,5,2] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,3,4,6,7,8,5,2] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,5,4,3,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,4,5,3,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,4,5,3,7,8,6,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,3,5,4,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,4,3,5,8,7,6,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,4,3,5,7,8,6,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,4,5,8,7,6,2] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,3,4,5,7,8,6,2] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,6,5,4,3,8,7,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,5,6,4,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,4,6,5,3,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,4,5,6,3,8,7,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,3,6,5,4,8,7,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,4,3,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,5,4,3,6,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,4,5,3,6,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,3,4,5,6,8,7,2] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,7,6,5,4,3,8,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[1,6,7,5,4,3,8,2] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[1,6,5,7,4,3,8,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,5,6,7,4,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,4,6,7,5,3,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,5,6,4,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,4,6,5,7,3,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,5,4,6,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,4,5,6,7,3,8,2] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,3,6,5,7,4,8,2] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,3,5,6,7,4,8,2] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,3,4,7,6,5,8,2] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,3,4,6,7,5,8,2] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,3,5,4,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,3,4,5,7,6,8,2] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,5,4,6,3,7,8,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,4,3,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,3,4,6,5,7,8,2] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,5,4,3,6,7,8,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,4,5,3,6,7,8,2] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,4,3,5,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,3,4,5,6,7,8,2] => [[1,2,3,4,5,6,7],[8]] => 0000001
[2,1,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[2,1,7,8,6,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,6,8,7,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,7,6,8,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[2,1,6,7,8,5,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,5,8,7,6,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,5,7,8,6,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,6,5,8,7,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,1,5,6,8,7,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,7,6,5,8,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,1,6,7,5,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,5,7,6,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,6,5,7,8,4,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,5,6,7,8,4,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,4,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,4,7,8,6,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,4,6,8,7,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,4,6,7,8,5,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,5,4,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,1,5,4,7,8,6,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,4,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,4,5,7,8,6,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,6,5,4,8,7,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,1,5,6,4,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,4,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,5,4,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,4,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,7,6,5,4,8,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[2,1,6,7,5,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,5,7,6,4,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,6,5,7,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,5,6,7,4,8,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,4,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,4,6,7,5,8,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,5,4,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,5,6,4,7,8,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[2,1,5,4,6,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,4,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,2,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[1,2,7,8,6,5,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,2,7,6,8,5,4,3] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,2,6,7,8,5,4,3] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,5,8,7,6,4,3] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,2,6,5,8,7,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,5,6,8,7,4,3] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,7,6,5,8,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,2,5,7,6,8,4,3] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,6,5,7,8,4,3] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,2,5,6,7,8,4,3] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,4,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,2,4,7,8,6,5,3] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,4,6,8,7,5,3] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,4,6,7,8,5,3] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,5,4,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,4,5,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,4,5,7,8,6,3] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,6,5,4,8,7,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,5,4,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,2,4,5,6,8,7,3] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,7,6,5,4,8,3] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[1,2,5,7,6,4,8,3] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,5,6,7,4,8,3] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,4,7,6,5,8,3] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,5,4,7,6,8,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,2,6,5,4,7,8,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,2,5,6,4,7,8,3] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,5,4,6,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,2,4,5,6,7,8,3] => [[1,2,3,4,5,6,7],[8]] => 0000001
[3,2,1,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[3,2,1,7,8,6,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,2,1,6,8,7,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,2,1,7,6,8,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,2,1,6,7,8,5,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,5,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,2,1,5,7,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,6,5,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[3,2,1,5,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,7,6,5,8,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,2,1,6,7,5,8,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,2,1,5,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,2,1,6,5,7,8,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,1,5,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,3,1,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[2,3,1,7,8,6,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,3,1,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,3,1,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,3,1,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,3,1,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,3,1,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,3,1,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,3,1,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,3,1,5,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,3,1,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,3,2,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,3,2,6,8,7,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,3,2,7,6,8,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,2,6,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,2,5,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,3,2,5,7,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,2,6,5,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,3,2,5,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,2,7,6,5,8,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,3,2,6,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,3,2,6,5,7,8,4] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,3,2,5,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => 0100001
[2,1,3,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,3,7,8,6,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,3,6,8,7,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,3,6,7,8,5,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,3,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,3,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,2,3,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[1,2,3,7,8,6,5,4] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,3,6,8,7,5,4] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,3,7,6,8,5,4] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,3,6,7,8,5,4] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,5,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,3,5,7,8,6,4] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,6,5,8,7,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,3,5,6,8,7,4] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,7,6,5,8,4] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,3,6,7,5,8,4] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,3,5,7,6,8,4] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,3,6,5,7,8,4] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,3,5,6,7,8,4] => [[1,2,3,4,5,6,7],[8]] => 0000001
[4,3,2,1,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[4,3,2,1,7,8,6,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[4,3,2,1,6,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[4,3,2,1,7,6,8,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[4,3,2,1,6,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[3,4,2,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[3,4,2,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,4,2,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,4,2,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[3,4,2,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,4,3,1,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[2,4,3,1,7,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,4,3,1,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,4,3,1,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[2,4,3,1,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[3,2,4,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[3,2,4,1,7,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,2,4,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,2,4,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,2,4,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,3,4,1,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,3,4,1,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,3,4,1,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,3,4,1,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,3,4,1,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,4,3,2,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,4,3,2,6,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,4,3,2,7,6,8,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,4,3,2,6,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,3,4,2,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,3,4,2,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,3,4,2,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,3,4,2,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,3,4,2,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 0010001
[2,1,4,3,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,1,4,3,7,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,4,3,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,4,3,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,4,3,6,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[1,2,4,3,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,4,3,7,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,2,4,3,6,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,2,4,3,7,6,8,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,2,4,3,6,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 0010001
[3,2,1,4,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,2,1,4,7,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,4,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,4,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,2,1,4,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,3,1,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,3,1,4,7,8,6,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,3,1,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,3,1,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,3,2,4,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,3,2,4,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,2,4,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,3,2,4,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 0100001
[2,1,3,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,1,3,4,7,8,6,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,3,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,3,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,2,3,4,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[1,2,3,4,7,8,6,5] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,4,6,8,7,5] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,4,7,6,8,5] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,3,4,6,7,8,5] => [[1,2,3,4,5,6,7],[8]] => 0000001
[5,4,3,2,1,8,7,6] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[5,4,3,2,1,7,8,6] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[4,5,3,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,5,4,2,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,5,4,2,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,3,5,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[3,4,5,2,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[2,5,4,3,1,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,5,4,3,1,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,4,5,3,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[2,4,5,3,1,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,2,5,4,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[3,2,5,4,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,3,5,4,1,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,3,2,5,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[4,3,2,5,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[3,4,2,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,4,2,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[2,4,3,5,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,4,3,5,1,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[3,2,4,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[2,3,4,5,1,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[2,3,4,5,1,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,5,4,3,2,8,7,6] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,5,4,3,2,7,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,4,5,3,2,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,4,5,3,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,3,5,4,2,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,3,4,5,2,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,3,4,5,2,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 0001001
[2,1,5,4,3,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[2,1,4,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[1,2,5,4,3,8,7,6] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,2,5,4,3,7,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,4,5,3,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,4,5,3,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,3,2,5,4,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,3,2,5,4,7,8,6] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,1,3,5,4,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,3,5,4,7,8,6] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,2,3,5,4,8,7,6] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,3,5,4,7,8,6] => [[1,2,3,4,6,7],[5,8]] => 0001001
[4,3,2,1,5,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[4,3,2,1,5,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[2,4,3,1,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,2,4,1,5,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,2,4,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,3,4,1,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,3,4,1,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,4,3,2,5,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,4,3,2,5,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,3,4,2,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 0010001
[2,1,4,3,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,4,3,5,7,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[1,2,4,3,5,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,2,4,3,5,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 0010001
[3,2,1,4,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,2,1,4,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,3,1,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,3,2,4,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,3,2,4,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 0100001
[2,1,3,4,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,3,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,2,3,4,5,8,7,6] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[1,2,3,4,5,7,8,6] => [[1,2,3,4,5,6,7],[8]] => 0000001
[6,5,4,3,2,1,8,7] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[5,6,4,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[4,6,5,3,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,4,6,3,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,5,6,3,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[3,6,5,4,2,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[3,5,6,4,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,3,6,5,2,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[3,4,6,5,2,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,4,3,6,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[4,5,3,6,2,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,3,5,6,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,4,5,6,2,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,6,5,4,3,1,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[2,5,6,4,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,4,6,5,3,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[3,2,6,5,4,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[3,2,5,6,4,1,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,3,6,5,4,1,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,3,5,6,4,1,8,7] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[4,3,2,6,5,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[3,4,2,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,4,3,6,5,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[5,4,3,2,6,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,5,3,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,5,4,2,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,3,5,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[3,4,5,2,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,5,4,3,6,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,4,5,3,6,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[3,2,5,4,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,3,2,5,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[3,4,2,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[2,4,3,5,6,1,8,7] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[2,3,4,5,6,1,8,7] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,6,5,4,3,2,8,7] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,5,6,4,3,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,5,4,6,3,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,3,6,5,4,2,8,7] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,3,4,5,6,2,8,7] => [[1,2,3,4,5,7],[6,8]] => 0000101
[2,1,6,5,4,3,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,1,5,6,4,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,1,4,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,1,5,4,6,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,4,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,2,4,5,6,3,8,7] => [[1,2,3,4,5,7],[6,8]] => 0000101
[3,2,1,6,5,4,8,7] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[2,3,1,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,3,2,6,5,4,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,3,2,5,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,1,3,5,6,4,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,2,3,6,5,4,8,7] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,2,3,5,6,4,8,7] => [[1,2,3,4,5,7],[6,8]] => 0000101
[4,3,2,1,6,5,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[3,4,2,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,4,3,1,6,5,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,2,4,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[2,3,4,1,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,3,4,2,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 1010101
[1,2,4,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,3,1,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,3,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,2,3,4,6,5,8,7] => [[1,2,3,4,5,7],[6,8]] => 0000101
[5,4,3,2,1,6,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[4,5,3,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,5,4,2,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,3,5,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[3,4,5,2,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,5,4,3,1,6,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,4,5,3,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,2,5,4,1,6,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,3,5,4,1,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,4,3,5,1,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[2,3,4,5,1,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,4,5,3,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,3,5,4,2,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,1,4,5,3,6,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,2,5,4,3,6,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,1,3,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,2,3,5,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 0001001
[4,3,2,1,5,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[3,2,4,1,5,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,3,4,1,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,4,3,2,5,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,3,4,2,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 0010001
[2,1,4,3,5,6,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[1,2,4,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 0010001
[3,2,1,4,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,3,1,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,3,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 0100001
[2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,2,3,4,5,6,8,7] => [[1,2,3,4,5,6,7],[8]] => 0000001
[5,7,6,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[4,7,6,5,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[4,6,7,5,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[5,4,7,6,3,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,5,7,6,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[4,6,5,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[3,5,7,6,4,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[3,5,6,7,4,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[4,3,7,6,5,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,4,7,6,5,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[5,4,3,7,6,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,5,3,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[3,5,4,7,6,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,3,5,7,6,2,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,6,5,4,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[3,5,6,4,7,2,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[4,3,6,5,7,2,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,7,6,5,4,3,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[2,6,7,5,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,5,7,6,4,3,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,5,6,7,4,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,4,6,7,5,3,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,5,4,7,6,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,5,6,4,7,3,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[2,5,4,6,7,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[2,4,5,6,7,3,1,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[3,2,7,6,5,4,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,2,6,7,5,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,2,5,7,6,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,2,6,5,7,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,2,5,6,7,4,1,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[2,3,7,6,5,4,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,3,6,7,5,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,3,5,7,6,4,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,3,6,5,7,4,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[2,3,5,6,7,4,1,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[4,3,2,6,7,5,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,4,2,7,6,5,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[3,4,2,6,7,5,1,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[3,2,4,6,7,5,1,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[2,3,4,7,6,5,1,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,3,4,6,7,5,1,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[5,4,3,2,7,6,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[4,5,3,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,5,4,2,7,6,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[4,3,5,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,4,5,2,7,6,1,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[3,2,5,4,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[4,3,2,5,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,4,2,5,7,6,1,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[2,3,4,5,7,6,1,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[3,6,5,4,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[3,5,6,4,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[3,4,6,5,2,7,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[3,5,4,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[2,5,4,6,3,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[3,2,6,5,4,7,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[2,3,5,6,4,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[4,3,2,6,5,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[3,4,2,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,4,3,6,5,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,3,4,6,5,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[3,5,4,2,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[2,5,4,3,6,7,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[2,3,5,4,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,7,6,5,4,3,2,8] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[1,6,7,5,4,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,6,5,7,4,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[1,5,6,7,4,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,4,7,6,5,3,2,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,4,6,7,5,3,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,5,6,4,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,4,6,5,7,3,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,5,4,6,7,3,2,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,4,5,6,7,3,2,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,3,6,7,5,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,3,5,7,6,4,2,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,3,6,5,7,4,2,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,3,5,6,7,4,2,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,3,4,6,7,5,2,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,3,5,4,7,6,2,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,4,3,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,3,4,5,7,6,2,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,5,4,6,3,7,2,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,3,6,5,4,7,2,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[1,3,5,6,4,7,2,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,4,3,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,4,3,6,7,2,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,4,5,3,6,7,2,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,3,4,5,6,7,2,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[2,1,7,6,5,4,3,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,1,6,7,5,4,3,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,1,5,6,7,4,3,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[2,1,4,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,2,7,6,5,4,3,8] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,2,6,7,5,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,2,5,7,6,4,3,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,2,5,6,7,4,3,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,4,6,7,5,3,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,5,6,4,7,3,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,2,5,4,6,7,3,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,2,4,5,6,7,3,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[3,2,1,7,6,5,4,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,2,1,5,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,3,1,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[2,3,1,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,3,1,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,3,2,7,6,5,4,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,3,2,6,7,5,4,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,3,2,5,7,6,4,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,3,2,6,5,7,4,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,3,2,5,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[2,1,3,6,7,5,4,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[1,2,3,7,6,5,4,8] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,2,3,6,7,5,4,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,3,5,7,6,4,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,3,6,5,7,4,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,2,3,5,6,7,4,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[4,3,2,1,7,6,5,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,3,2,1,6,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,2,4,1,7,6,5,8] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,2,4,1,6,7,5,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[2,3,4,1,7,6,5,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[2,3,4,1,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,4,3,2,7,6,5,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,4,3,2,6,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,3,4,2,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,4,3,6,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[3,2,1,4,7,6,5,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,3,1,4,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,3,2,4,7,6,5,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,2,3,4,7,6,5,8] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,3,4,6,7,5,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[5,4,3,2,1,7,6,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[4,5,3,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,5,4,2,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,4,5,2,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[2,5,4,3,1,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,4,5,3,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[3,2,5,4,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,3,5,4,1,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[3,4,2,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,4,3,5,1,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,3,4,5,1,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,5,4,3,2,7,6,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,4,5,3,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,3,5,4,2,7,6,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,4,3,5,2,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,3,4,5,2,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[2,1,5,4,3,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[1,2,4,5,3,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[3,2,1,5,4,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[2,3,1,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,3,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,2,3,5,4,7,6,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[4,3,2,1,5,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,2,4,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[2,3,4,1,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,4,3,2,5,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,3,4,2,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,4,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[2,3,1,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,3,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,2,3,4,5,7,6,8] => [[1,2,3,4,5,6,8],[7]] => 0000010
[3,6,5,4,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[4,3,6,5,2,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,4,6,5,3,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[2,4,5,6,3,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[2,3,6,5,4,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[2,3,5,6,4,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[4,3,2,6,5,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[2,4,3,6,5,1,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[2,3,4,6,5,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[3,5,4,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[2,3,5,4,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,6,5,4,3,2,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,5,6,4,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,4,6,5,3,2,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,5,4,6,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,4,5,6,3,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,3,5,6,4,2,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,4,3,6,5,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,5,4,3,6,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[1,4,5,3,6,2,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,4,3,5,6,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,3,4,5,6,2,7,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[2,1,5,6,4,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[2,1,4,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[1,2,6,5,4,3,7,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,2,5,6,4,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,2,4,6,5,3,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,2,4,5,6,3,7,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[3,2,1,6,5,4,7,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[3,2,1,5,6,4,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[2,3,1,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[2,3,1,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,3,2,6,5,4,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,3,2,5,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,3,6,5,4,7,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,2,3,5,6,4,7,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[4,3,2,1,6,5,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,4,3,1,6,5,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[3,2,4,1,6,5,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,3,4,1,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[2,1,4,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[1,2,4,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,3,2,4,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[2,1,3,4,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,2,3,4,6,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[3,5,4,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[2,5,4,3,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[2,4,5,3,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[3,2,5,4,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,3,5,4,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[2,4,3,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,5,4,3,2,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,4,5,3,2,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,3,4,5,2,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 0001000
[2,1,5,4,3,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,1,4,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,2,5,4,3,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[3,2,1,5,4,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[2,3,1,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,3,2,5,4,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,2,3,5,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 0001000
[2,4,3,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,4,3,2,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,3,4,2,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[2,1,4,3,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[1,2,4,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[1,3,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[1,2,3,4,8,6,7,5] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,3,5,8,6,7,4] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,3,7,5,6,4,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,2,3,7,5,6,8,4] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,3,8,5,6,7,4] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,3,8,5,7,6,4] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,3,8,6,5,7,4] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,3,8,6,7,5,4] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,4,5,8,6,7,3] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,2,4,7,5,6,8,3] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,4,8,5,6,7,3] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,4,8,6,5,7,3] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,5,4,8,6,7,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,2,6,4,5,3,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,2,6,4,5,7,8,3] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,2,7,4,5,6,8,3] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,2,8,4,5,6,7,3] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,2,8,4,6,7,5,3] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,2,8,4,7,6,5,3] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,2,7,5,4,6,3,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[1,2,7,5,4,6,8,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,2,8,5,4,6,7,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,2,8,5,4,7,6,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,8,5,6,4,7,3] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,2,8,5,6,7,4,3] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,2,8,6,5,4,7,3] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[1,2,8,6,5,7,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,2,8,7,5,6,4,3] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,3,2,4,8,6,7,5] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,3,2,7,5,6,8,4] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,3,2,8,5,7,6,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,2,8,6,5,7,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,3,2,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,4,2,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,3,4,5,8,6,7,2] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[1,3,4,8,5,6,7,2] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,3,6,4,5,2,8,7] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,3,6,4,5,7,2,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,3,6,4,5,7,8,2] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,3,6,4,5,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,3,7,4,5,6,2,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,3,7,4,5,6,8,2] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,3,8,4,5,6,7,2] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,3,8,4,6,5,7,2] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,3,8,5,4,6,7,2] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,3,8,5,4,7,6,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,3,8,5,6,7,4,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,3,8,5,7,6,4,2] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,3,8,6,5,7,4,2] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,3,8,7,5,6,4,2] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,4,3,5,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,4,3,8,5,6,7,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,4,3,8,5,7,6,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,4,3,8,6,5,7,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,4,3,8,6,7,5,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,5,3,4,2,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,5,3,4,2,7,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,5,3,4,2,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,5,3,4,6,2,8,7] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,5,3,4,6,7,2,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,5,3,4,6,7,8,2] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,5,3,4,8,6,7,2] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,6,3,4,5,2,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,6,3,4,5,8,7,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,7,3,4,5,6,2,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,7,3,4,5,6,8,2] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,8,3,4,5,6,7,2] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,8,3,4,6,7,5,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,6,3,5,4,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,6,3,5,4,8,7,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,7,3,5,4,6,2,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,8,3,5,4,6,7,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,8,3,5,6,4,7,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,8,3,5,6,7,4,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,8,3,5,7,6,4,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[1,7,3,6,5,4,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[1,7,3,6,5,4,8,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,8,3,6,5,4,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,8,3,7,5,6,4,2] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[1,8,3,7,6,5,4,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[1,6,4,3,5,2,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[1,6,4,3,5,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,8,4,3,5,6,7,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,8,4,3,5,7,6,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,7,4,3,6,5,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,8,4,3,6,5,7,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,8,4,3,6,7,5,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,6,4,5,3,2,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,6,4,5,3,2,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,6,4,5,3,8,7,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,7,4,5,3,6,8,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,8,4,5,3,6,7,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,7,4,5,6,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,8,4,5,6,3,7,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,8,4,5,6,7,3,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,7,4,6,5,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[1,8,4,6,5,3,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,8,4,6,5,7,3,2] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[1,8,4,7,6,5,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[1,7,5,4,3,6,2,8] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,7,5,4,3,6,8,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,8,5,4,3,6,7,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,8,5,4,6,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[1,8,5,4,6,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,8,5,4,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,7,6,4,5,3,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,8,6,4,5,3,7,2] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[1,8,6,4,5,7,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,8,7,4,5,6,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,8,7,4,6,5,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[1,8,6,5,4,3,7,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[1,8,6,5,4,7,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,8,7,5,4,6,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,8,7,5,6,4,3,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[2,1,3,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,3,5,8,6,7,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,3,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[2,1,3,8,5,7,6,4] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,3,8,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,3,8,6,7,5,4] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,4,3,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,4,5,8,6,7,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,1,4,8,5,6,7,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[2,1,4,8,5,7,6,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,4,8,6,5,7,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,4,8,6,7,5,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,1,5,4,8,6,7,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,4,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,6,4,5,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,6,4,5,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,8,4,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,8,4,5,7,6,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,7,4,6,5,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,8,4,6,5,7,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,8,4,6,7,5,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,8,4,7,6,5,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[2,1,8,5,4,6,7,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[2,1,8,5,4,7,6,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,1,7,5,6,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,8,5,6,4,7,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,8,5,6,7,4,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,8,5,7,6,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[2,1,8,6,5,4,7,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[2,1,8,6,5,7,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,1,8,7,5,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,3,1,7,5,6,4,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,3,1,8,5,6,7,4] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,3,1,8,6,7,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,3,4,1,8,6,7,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,3,4,5,8,6,7,1] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[2,3,4,7,5,6,1,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[2,3,4,7,5,6,8,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[2,3,4,8,5,6,7,1] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[2,3,4,8,5,7,6,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,3,4,8,6,5,7,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,3,4,8,6,7,5,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,3,5,4,8,6,7,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,3,6,4,5,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[2,3,6,4,5,1,8,7] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,3,6,4,5,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[2,3,6,4,5,8,7,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,3,7,4,5,6,8,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[2,3,8,4,5,6,7,1] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[2,3,7,4,6,5,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[2,3,8,4,6,7,5,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,3,7,5,4,6,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[2,3,7,5,4,6,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,3,8,5,4,6,7,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,3,7,5,6,4,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[2,3,7,5,6,4,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[2,3,8,5,6,4,7,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[2,3,8,5,6,7,4,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,3,8,5,7,6,4,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[2,3,8,6,5,4,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[2,4,3,5,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,4,3,7,5,6,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,3,8,5,6,7,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,3,8,5,7,6,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,4,3,8,6,5,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,5,3,4,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[2,5,3,4,1,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,5,3,4,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[2,5,3,4,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[2,5,3,4,6,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,5,3,4,7,6,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,5,3,4,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,5,3,4,8,7,6,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,6,3,4,5,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[2,6,3,4,5,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[2,6,3,4,5,8,7,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,7,3,4,5,6,1,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[2,8,3,4,5,6,7,1] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[2,8,3,4,5,7,6,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,6,3,5,4,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,6,3,5,4,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,6,3,5,4,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[2,7,3,5,4,6,8,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,8,3,5,4,7,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[2,7,3,5,6,4,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,8,3,5,6,7,4,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,8,3,5,7,6,4,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[2,7,3,6,5,4,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[2,8,3,7,5,6,4,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[2,8,3,7,6,5,4,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[2,5,4,3,8,6,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,6,4,3,5,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,6,4,3,5,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,6,4,3,5,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,7,4,3,5,6,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,8,4,3,5,6,7,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,8,4,3,5,7,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,7,4,3,6,5,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,8,4,3,6,5,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,8,4,3,6,7,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,8,4,3,7,6,5,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,6,4,5,3,1,7,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[2,6,4,5,3,7,8,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,8,4,5,3,6,7,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,7,4,5,6,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[2,7,4,5,6,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,8,4,5,6,3,7,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,8,4,5,6,7,3,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,7,4,6,5,3,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[2,7,4,6,5,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,8,4,6,5,3,7,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,8,4,7,6,5,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[2,7,5,4,3,6,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[2,8,5,4,3,6,7,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[2,8,5,4,3,7,6,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,7,5,4,6,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[2,8,5,4,6,7,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[2,8,5,4,7,6,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,7,6,4,5,3,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[2,8,7,4,5,6,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[2,8,7,4,6,5,3,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[2,8,7,5,4,6,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[2,8,7,5,6,4,3,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[3,2,1,4,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,2,1,5,8,6,7,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,2,1,7,5,6,8,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,1,8,5,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,1,8,5,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,2,1,8,6,5,7,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,2,1,8,6,7,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,2,4,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,2,4,5,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[3,2,4,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,2,4,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,2,4,8,6,7,5,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,2,5,4,8,6,7,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,2,6,4,5,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,2,7,4,5,6,1,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,2,8,4,5,6,7,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[3,2,7,4,6,5,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,2,7,4,6,5,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,8,4,6,5,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,7,5,4,6,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[3,2,8,5,4,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[3,2,8,5,4,7,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[3,2,7,5,6,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,2,7,5,6,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,8,5,6,4,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,8,5,7,6,4,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[3,2,8,6,5,7,4,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,2,8,7,5,6,4,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[4,2,3,1,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[4,2,3,1,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,2,3,1,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,3,1,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,2,3,1,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[4,2,3,1,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,2,3,1,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,2,3,1,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,2,3,5,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,2,3,5,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,2,3,5,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,2,3,5,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[4,2,3,5,6,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,2,3,5,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[4,2,3,6,5,8,7,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,2,3,7,5,6,1,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[4,2,3,7,5,6,8,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[4,2,3,8,5,6,7,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[4,2,3,8,5,7,6,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,2,3,7,6,5,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,2,3,8,7,6,5,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[5,2,3,4,1,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,2,3,4,1,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,2,3,4,1,8,7,6] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[5,2,3,4,6,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[5,2,3,4,7,6,1,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,2,3,4,8,6,7,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,2,3,4,8,7,6,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,2,3,4,5,1,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[6,2,3,4,5,8,7,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[8,2,3,4,5,7,6,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,2,3,4,6,5,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[6,2,3,5,4,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[6,2,3,5,4,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[6,2,3,5,4,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[6,2,3,5,4,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[7,2,3,5,4,6,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,2,3,5,4,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[7,2,3,5,6,4,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,2,3,5,6,7,4,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,2,3,5,7,6,4,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,2,3,6,5,4,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,2,3,6,5,4,7,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[8,2,3,7,5,6,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[5,2,4,3,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[5,2,4,3,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[5,2,4,3,1,7,6,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[5,2,4,3,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,2,4,3,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[5,2,4,3,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,2,4,3,6,7,1,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[5,2,4,3,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,2,4,3,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,2,4,3,8,7,6,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,2,4,3,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,2,4,3,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,4,3,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,4,3,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,4,3,6,7,5,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[6,2,4,5,3,1,7,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[7,2,4,5,3,6,1,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[7,2,4,5,3,6,8,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[8,2,4,5,3,7,6,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,2,4,5,6,7,3,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,2,4,5,7,6,3,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,2,4,6,5,3,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[7,2,4,6,5,3,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[8,2,4,7,5,6,3,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,2,4,7,6,5,3,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[6,2,5,4,3,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[6,2,5,4,3,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,2,5,4,3,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[6,2,5,4,3,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[7,2,5,4,3,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,2,5,4,3,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,2,5,4,3,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,2,5,4,6,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,2,5,4,7,6,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,2,6,4,5,3,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[7,2,6,4,5,3,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,2,6,4,5,3,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,2,6,4,5,7,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,2,7,4,5,6,3,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,2,7,4,6,5,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[7,2,6,5,4,3,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,2,6,5,4,3,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,2,6,5,4,7,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,2,7,5,4,6,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,2,7,5,6,4,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,2,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[4,3,2,1,8,6,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[4,3,2,7,5,6,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,3,2,8,5,6,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,3,2,8,5,7,6,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,3,2,8,6,7,5,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,3,2,4,1,6,8,7] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[5,3,2,4,1,7,6,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,3,2,4,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,3,2,4,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,3,2,4,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,3,2,4,6,7,5,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,3,2,5,4,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,3,2,5,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[6,3,2,5,4,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,3,2,5,4,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[6,3,2,5,4,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,3,2,5,4,6,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,3,2,5,4,7,6,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,3,2,5,6,4,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,3,2,5,6,4,7,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,3,2,5,6,7,4,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,3,2,5,7,6,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,3,2,6,5,7,4,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,3,2,7,5,6,4,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,3,2,7,6,5,4,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[5,3,4,2,1,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[5,3,4,2,1,7,8,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[5,3,4,2,1,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,3,4,2,6,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,3,4,2,7,6,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,3,4,2,7,6,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,3,4,2,8,6,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,3,4,2,5,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,3,4,2,6,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,3,4,2,6,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,3,4,2,6,5,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,3,4,5,2,1,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[6,3,4,5,2,8,7,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,3,4,5,2,7,6,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,3,4,5,7,6,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,3,4,6,5,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,3,4,7,6,5,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[6,3,5,4,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,3,5,4,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[6,3,5,4,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[6,3,5,4,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,3,5,4,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,3,5,4,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,3,5,4,2,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,3,5,4,6,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[7,3,5,4,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,3,5,4,6,7,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,3,5,4,7,6,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,3,6,4,5,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[7,3,6,4,5,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,3,6,4,5,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,3,7,4,5,6,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,3,7,4,6,5,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[7,3,6,5,4,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[7,3,6,5,4,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,3,6,5,4,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,3,6,5,4,7,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,3,7,5,4,6,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,3,7,5,6,4,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,3,7,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[5,4,3,2,8,6,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[6,4,3,2,5,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,4,3,2,5,8,7,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[7,4,3,2,6,5,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,4,3,2,6,7,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,4,3,2,7,6,5,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[6,4,3,5,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,4,3,5,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,4,3,5,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,4,3,6,5,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,4,3,6,5,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[8,4,3,7,5,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,4,3,7,6,5,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[6,5,3,4,2,1,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,5,3,4,2,7,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,5,3,4,7,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,7,3,4,6,5,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[7,6,3,5,4,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[7,6,3,5,4,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[8,6,3,5,4,7,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[8,7,3,5,4,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[8,7,3,5,6,4,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[8,7,3,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[8,5,4,3,2,7,6,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,5,4,3,7,6,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,4,3,6,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,4,6,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[2,4,1,3,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 0100101
[2,1,4,6,3,5,8,7] => [[1,3,4,7],[2,5,6,8]] => 1001001
[2,4,1,6,3,5,8,7] => [[1,2,4,7],[3,5,6,8]] => 0101001
[2,4,6,1,3,5,8,7] => [[1,2,3,7],[4,5,6,8]] => 0010001
[2,1,4,3,6,8,5,7] => [[1,3,5,6],[2,4,7,8]] => 1010010
[2,4,1,3,6,8,5,7] => [[1,2,5,6],[3,4,7,8]] => 0100010
[2,1,4,6,3,8,5,7] => [[1,3,4,6],[2,5,7,8]] => 1001010
[2,4,1,6,3,8,5,7] => [[1,2,4,6],[3,5,7,8]] => 0101010
[2,4,6,1,3,8,5,7] => [[1,2,3,6],[4,5,7,8]] => 0010010
[2,1,4,6,8,3,5,7] => [[1,3,4,5],[2,6,7,8]] => 1000100
[2,4,1,6,8,3,5,7] => [[1,2,4,5],[3,6,7,8]] => 0100100
[2,4,6,1,8,3,5,7] => [[1,2,3,5],[4,6,7,8]] => 0010100
[2,4,6,8,1,3,5,7] => [[1,2,3,4],[5,6,7,8]] => 0001000
[2,4,1,3,6,5,7,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,4,6,3,5,7,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,4,1,6,3,5,7,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,4,6,1,3,5,7,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,1,4,6,3,7,5,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[2,4,1,6,3,7,5,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,4,6,1,3,7,5,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,4,6,7,1,3,5,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[2,4,1,3,6,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,1,4,6,3,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 1001001
[2,4,1,6,3,7,8,5] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,1,4,6,7,3,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[2,4,1,6,7,3,8,5] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,4,6,1,7,3,8,5] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,4,6,7,1,3,8,5] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,1,4,6,7,8,3,5] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,4,1,6,7,8,3,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,4,6,7,8,1,3,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,4,3,7,5,8,6] => [[1,3,5,7],[2,4,6,8]] => 1010101
[2,4,1,3,7,5,8,6] => [[1,2,5,7],[3,4,6,8]] => 0100101
[2,1,4,7,3,5,8,6] => [[1,3,4,7],[2,5,6,8]] => 1001001
[2,4,1,7,3,5,8,6] => [[1,2,4,7],[3,5,6,8]] => 0101001
[2,4,7,1,3,5,8,6] => [[1,2,3,7],[4,5,6,8]] => 0010001
[2,1,4,3,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 1010010
[2,4,1,3,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => 0100010
[2,4,1,7,3,8,5,6] => [[1,2,4,6],[3,5,7,8]] => 0101010
[2,1,4,7,8,3,5,6] => [[1,3,4,5],[2,6,7,8]] => 1000100
[2,4,1,7,8,3,5,6] => [[1,2,4,5],[3,6,7,8]] => 0100100
[2,4,7,1,8,3,5,6] => [[1,2,3,5],[4,6,7,8]] => 0010100
[2,4,7,8,1,3,5,6] => [[1,2,3,4],[5,6,7,8]] => 0001000
[2,4,1,5,3,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,4,5,1,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,4,5,1,7,3,6,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[2,4,1,3,5,7,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,4,1,5,3,7,8,6] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,4,5,1,3,7,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[2,1,4,5,7,3,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[2,4,1,5,7,3,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,4,5,1,7,3,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,1,4,5,7,8,3,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,4,5,1,7,8,3,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,4,5,7,1,8,3,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,4,5,7,8,1,3,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,4,3,8,5,6,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[2,4,1,3,8,5,6,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,4,8,3,5,6,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,4,1,8,3,5,6,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,4,8,1,3,5,6,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,1,4,3,5,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[2,4,1,5,3,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,1,4,5,8,3,6,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[2,4,1,5,8,3,6,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[2,4,5,1,8,3,6,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[2,4,1,5,3,6,8,7] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,4,1,5,6,3,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,4,5,1,6,3,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,4,5,6,1,3,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,1,4,5,6,8,3,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,4,1,5,6,8,3,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,4,5,1,6,8,3,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,4,5,6,1,8,3,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,4,5,6,8,1,3,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,4,1,3,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[2,4,1,5,3,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[2,4,5,1,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[2,4,1,5,6,3,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[2,4,5,1,6,3,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[2,4,5,6,1,3,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[2,4,1,5,6,7,3,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[2,4,5,6,1,7,3,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[2,4,5,6,7,1,3,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[2,4,1,5,6,7,8,3] => [[1,2,4,5,6,7],[3,8]] => 0100001
[2,4,5,1,6,7,8,3] => [[1,2,3,5,6,7],[4,8]] => 0010001
[2,4,5,6,1,7,8,3] => [[1,2,3,4,6,7],[5,8]] => 0001001
[2,4,5,6,7,1,8,3] => [[1,2,3,4,5,7],[6,8]] => 0000101
[2,4,5,6,7,8,1,3] => [[1,2,3,4,5,6],[7,8]] => 0000010
[2,1,5,3,6,4,8,7] => [[1,3,5,7],[2,4,6,8]] => 1010101
[2,5,1,3,6,4,8,7] => [[1,2,5,7],[3,4,6,8]] => 0100101
[2,1,5,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 1001001
[2,5,1,6,3,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 0101001
[2,5,6,1,3,4,8,7] => [[1,2,3,7],[4,5,6,8]] => 0010001
[2,1,5,3,6,8,4,7] => [[1,3,5,6],[2,4,7,8]] => 1010010
[2,5,1,3,6,8,4,7] => [[1,2,5,6],[3,4,7,8]] => 0100010
[2,5,6,1,3,8,4,7] => [[1,2,3,6],[4,5,7,8]] => 0010010
[2,1,5,6,8,3,4,7] => [[1,3,4,5],[2,6,7,8]] => 1000100
[2,5,1,6,8,3,4,7] => [[1,2,4,5],[3,6,7,8]] => 0100100
[2,5,6,8,1,3,4,7] => [[1,2,3,4],[5,6,7,8]] => 0001000
[2,5,1,3,6,4,7,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,5,6,3,4,7,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,5,1,6,3,4,7,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,1,5,3,6,7,4,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[2,1,5,6,3,7,4,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[2,5,1,6,3,7,4,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,5,6,1,3,7,4,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,1,5,6,7,3,4,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[2,5,1,6,7,3,4,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[2,5,6,1,7,3,4,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[2,1,5,3,6,7,8,4] => [[1,3,5,6,7],[2,4,8]] => 1010001
[2,5,1,3,6,7,8,4] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,1,5,6,3,7,8,4] => [[1,3,4,6,7],[2,5,8]] => 1001001
[2,5,1,6,3,7,8,4] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,5,6,1,3,7,8,4] => [[1,2,3,6,7],[4,5,8]] => 0010001
[2,1,5,6,7,3,8,4] => [[1,3,4,5,7],[2,6,8]] => 1000101
[2,5,1,6,7,3,8,4] => [[1,2,4,5,7],[3,6,8]] => 0100101
[2,5,6,7,1,3,8,4] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,1,5,6,7,8,3,4] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,5,1,6,7,8,3,4] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,5,6,1,7,8,3,4] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,5,6,7,1,8,3,4] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,5,6,7,8,1,3,4] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,5,3,7,4,8,6] => [[1,3,5,7],[2,4,6,8]] => 1010101
[2,5,1,3,7,4,8,6] => [[1,2,5,7],[3,4,6,8]] => 0100101
[2,1,5,7,3,4,8,6] => [[1,3,4,7],[2,5,6,8]] => 1001001
[2,5,1,7,3,4,8,6] => [[1,2,4,7],[3,5,6,8]] => 0101001
[2,5,7,1,3,4,8,6] => [[1,2,3,7],[4,5,6,8]] => 0010001
[2,1,5,3,7,8,4,6] => [[1,3,5,6],[2,4,7,8]] => 1010010
[2,5,1,3,7,8,4,6] => [[1,2,5,6],[3,4,7,8]] => 0100010
[2,1,5,7,3,8,4,6] => [[1,3,4,6],[2,5,7,8]] => 1001010
[2,1,5,7,8,3,4,6] => [[1,3,4,5],[2,6,7,8]] => 1000100
[2,5,1,7,8,3,4,6] => [[1,2,4,5],[3,6,7,8]] => 0100100
[2,5,7,1,8,3,4,6] => [[1,2,3,5],[4,6,7,8]] => 0010100
[2,5,7,8,1,3,4,6] => [[1,2,3,4],[5,6,7,8]] => 0001000
[2,5,1,3,7,4,6,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,5,7,3,4,6,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,3,5,1,4,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,3,5,7,1,4,6,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[2,3,5,1,7,4,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,3,5,7,1,4,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,3,1,5,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,3,5,7,1,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,3,5,7,8,1,4,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,5,3,8,4,6,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[2,5,1,3,8,4,6,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,5,8,3,4,6,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,5,1,8,3,4,6,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,5,8,1,3,4,6,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,3,5,1,4,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,1,3,5,8,4,6,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[2,3,5,1,8,4,6,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[2,3,5,8,1,4,6,7] => [[1,2,3,4,8],[5,6,7]] => 0001000
[2,1,5,3,4,6,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[2,3,5,1,6,4,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,3,5,6,1,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,1,3,5,6,8,4,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,3,1,5,6,8,4,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,3,5,1,6,8,4,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,3,5,6,1,8,4,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,3,5,6,8,1,4,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,5,3,4,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[2,5,1,3,4,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[2,3,5,1,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[2,3,5,1,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[2,3,5,6,1,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[2,3,5,6,7,1,4,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[2,3,5,1,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => 0010001
[2,3,5,6,1,7,8,4] => [[1,2,3,4,6,7],[5,8]] => 0001001
[2,3,5,6,7,1,8,4] => [[1,2,3,4,5,7],[6,8]] => 0000101
[2,3,5,6,7,8,1,4] => [[1,2,3,4,5,6],[7,8]] => 0000010
[2,1,6,3,7,4,8,5] => [[1,3,5,7],[2,4,6,8]] => 1010101
[2,6,1,3,7,4,8,5] => [[1,2,5,7],[3,4,6,8]] => 0100101
[2,1,6,7,3,4,8,5] => [[1,3,4,7],[2,5,6,8]] => 1001001
[2,6,1,7,3,4,8,5] => [[1,2,4,7],[3,5,6,8]] => 0101001
[2,6,7,1,3,4,8,5] => [[1,2,3,7],[4,5,6,8]] => 0010001
[2,1,6,3,7,8,4,5] => [[1,3,5,6],[2,4,7,8]] => 1010010
[2,6,1,3,7,8,4,5] => [[1,2,5,6],[3,4,7,8]] => 0100010
[2,6,1,7,3,8,4,5] => [[1,2,4,6],[3,5,7,8]] => 0101010
[2,6,7,1,3,8,4,5] => [[1,2,3,6],[4,5,7,8]] => 0010010
[2,1,6,7,8,3,4,5] => [[1,3,4,5],[2,6,7,8]] => 1000100
[2,6,1,7,8,3,4,5] => [[1,2,4,5],[3,6,7,8]] => 0100100
[2,6,7,1,8,3,4,5] => [[1,2,3,5],[4,6,7,8]] => 0010100
[2,6,7,8,1,3,4,5] => [[1,2,3,4],[5,6,7,8]] => 0001000
[2,1,6,3,7,4,5,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[2,6,1,7,3,4,5,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,6,7,1,3,4,5,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,6,1,3,4,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[2,3,1,6,4,7,5,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,3,6,1,4,7,5,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,1,6,3,4,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[2,6,1,3,4,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,3,6,1,4,7,8,5] => [[1,2,3,6,7],[4,5,8]] => 0010001
[2,1,3,6,7,4,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[2,1,3,6,7,8,4,5] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,3,1,6,7,8,4,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,3,6,1,7,8,4,5] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,3,6,7,1,8,4,5] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,3,6,7,8,1,4,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,6,3,8,4,5,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[2,6,1,3,8,4,5,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,6,8,3,4,5,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,6,1,8,3,4,5,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,6,8,1,3,4,5,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,1,6,3,4,8,5,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[2,6,1,3,4,8,5,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[2,3,1,6,4,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,3,6,1,4,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,3,1,6,8,4,5,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[2,3,6,1,8,4,5,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[2,1,6,3,4,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[2,6,1,3,4,5,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,1,3,6,4,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[2,3,6,1,4,5,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[2,3,4,1,6,8,5,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,3,4,6,1,8,5,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,3,4,6,8,1,5,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,6,1,3,4,5,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[2,1,3,6,4,5,7,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[2,3,1,6,4,5,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[2,3,6,1,4,5,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[2,3,4,6,1,5,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[2,3,4,6,1,7,5,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[2,3,4,6,7,1,5,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[2,3,4,6,1,7,8,5] => [[1,2,3,4,6,7],[5,8]] => 0001001
[2,3,4,6,7,8,1,5] => [[1,2,3,4,5,6],[7,8]] => 0000010
[2,1,7,3,8,4,5,6] => [[1,3,5,7,8],[2,4,6]] => 1010100
[2,7,1,3,8,4,5,6] => [[1,2,5,7,8],[3,4,6]] => 0100100
[2,1,7,8,3,4,5,6] => [[1,3,4,7,8],[2,5,6]] => 1001000
[2,7,1,8,3,4,5,6] => [[1,2,4,7,8],[3,5,6]] => 0101000
[2,7,8,1,3,4,5,6] => [[1,2,3,7,8],[4,5,6]] => 0010000
[2,1,7,3,4,8,5,6] => [[1,3,5,6,8],[2,4,7]] => 1010010
[2,1,3,7,4,8,5,6] => [[1,3,4,6,8],[2,5,7]] => 1001010
[2,3,1,7,4,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 0101010
[2,3,7,1,4,8,5,6] => [[1,2,3,6,8],[4,5,7]] => 0010010
[2,1,3,7,8,4,5,6] => [[1,3,4,5,8],[2,6,7]] => 1000100
[2,3,1,7,8,4,5,6] => [[1,2,4,5,8],[3,6,7]] => 0100100
[2,3,7,8,1,4,5,6] => [[1,2,3,4,8],[5,6,7]] => 0001000
[2,1,7,3,4,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[2,7,1,3,4,5,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[2,3,1,7,4,5,8,6] => [[1,2,4,6,7],[3,5,8]] => 0101001
[2,3,7,1,4,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[2,1,3,4,7,5,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[2,3,4,1,7,5,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[2,3,4,7,1,5,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[2,1,3,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[2,3,1,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[2,3,4,1,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[2,3,4,7,1,8,5,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[2,3,4,7,8,1,5,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[2,1,7,3,4,5,6,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[2,7,1,3,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[2,3,7,1,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[2,1,3,4,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[2,3,1,4,7,5,6,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[2,3,4,1,7,5,6,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[2,3,4,7,1,5,6,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[2,3,4,5,7,1,6,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[2,3,4,5,7,1,8,6] => [[1,2,3,4,5,7],[6,8]] => 0000101
[2,3,4,5,7,8,1,6] => [[1,2,3,4,5,6],[7,8]] => 0000010
[2,1,8,3,4,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 1010000
[2,8,1,3,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 0100000
[2,1,3,8,4,5,6,7] => [[1,3,4,6,7,8],[2,5]] => 1001000
[2,3,1,8,4,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 0101000
[2,3,8,1,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 0010000
[2,1,3,4,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => 1000100
[2,3,1,4,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => 0100100
[2,3,4,1,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 0010100
[2,3,4,8,1,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 0001000
[2,1,3,4,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 1000010
[2,3,1,4,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 0100010
[2,3,4,1,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 0010010
[2,3,4,5,1,8,6,7] => [[1,2,3,4,6,8],[5,7]] => 0001010
[2,3,4,5,8,1,6,7] => [[1,2,3,4,5,8],[6,7]] => 0000100
[2,3,4,5,6,8,1,7] => [[1,2,3,4,5,6],[7,8]] => 0000010
[3,1,4,2,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 1010101
[3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 0100101
[3,1,4,6,2,5,8,7] => [[1,3,4,7],[2,5,6,8]] => 1001001
[3,4,1,6,2,5,8,7] => [[1,2,4,7],[3,5,6,8]] => 0101001
[3,4,6,1,2,5,8,7] => [[1,2,3,7],[4,5,6,8]] => 0010001
[3,1,4,2,6,8,5,7] => [[1,3,5,6],[2,4,7,8]] => 1010010
[3,4,1,2,6,8,5,7] => [[1,2,5,6],[3,4,7,8]] => 0100010
[3,1,4,6,2,8,5,7] => [[1,3,4,6],[2,5,7,8]] => 1001010
[3,4,1,6,2,8,5,7] => [[1,2,4,6],[3,5,7,8]] => 0101010
[3,1,4,6,8,2,5,7] => [[1,3,4,5],[2,6,7,8]] => 1000100
[3,4,1,6,8,2,5,7] => [[1,2,4,5],[3,6,7,8]] => 0100100
[3,4,6,8,1,2,5,7] => [[1,2,3,4],[5,6,7,8]] => 0001000
[3,1,4,2,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,4,1,2,6,5,7,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,4,2,6,7,5,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,4,1,2,6,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,4,1,6,2,7,5,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[3,4,6,1,2,7,5,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,4,1,6,7,2,5,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[3,4,6,7,1,2,5,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,1,4,2,6,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,4,1,2,6,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,4,6,2,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 1001001
[3,4,1,6,2,7,8,5] => [[1,2,4,6,7],[3,5,8]] => 0101001
[3,4,6,1,2,7,8,5] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,4,6,7,2,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[3,4,1,6,7,2,8,5] => [[1,2,4,5,7],[3,6,8]] => 0100101
[3,4,6,1,7,2,8,5] => [[1,2,3,5,7],[4,6,8]] => 0010101
[3,4,6,7,1,2,8,5] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,4,6,7,8,2,5] => [[1,3,4,5,6],[2,7,8]] => 1000010
[3,4,1,6,7,8,2,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[3,4,6,1,7,8,2,5] => [[1,2,3,5,6],[4,7,8]] => 0010010
[3,4,6,7,1,8,2,5] => [[1,2,3,4,6],[5,7,8]] => 0001010
[3,4,6,7,8,1,2,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,4,2,7,5,8,6] => [[1,3,5,7],[2,4,6,8]] => 1010101
[3,4,1,2,7,5,8,6] => [[1,2,5,7],[3,4,6,8]] => 0100101
[3,1,4,7,2,5,8,6] => [[1,3,4,7],[2,5,6,8]] => 1001001
[3,4,7,1,2,5,8,6] => [[1,2,3,7],[4,5,6,8]] => 0010001
[3,1,4,2,7,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 1010010
[3,4,1,2,7,8,5,6] => [[1,2,5,6],[3,4,7,8]] => 0100010
[3,4,7,1,8,2,5,6] => [[1,2,3,5],[4,6,7,8]] => 0010100
[3,4,7,8,1,2,5,6] => [[1,2,3,4],[5,6,7,8]] => 0001000
[3,1,4,2,7,5,6,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,4,1,2,7,5,6,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,4,1,2,5,7,6,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,1,4,5,2,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[3,4,1,5,2,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[3,4,1,5,7,2,6,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[3,4,5,7,1,2,6,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,1,4,2,5,7,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,4,1,2,5,7,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,4,5,2,7,8,6] => [[1,3,4,6,7],[2,5,8]] => 1001001
[3,4,5,1,2,7,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,4,5,7,2,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[3,4,1,5,7,2,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[3,4,5,7,1,2,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,4,5,7,8,2,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[3,4,1,5,7,8,2,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[3,4,5,1,7,8,2,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[3,4,5,7,1,8,2,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[3,4,5,7,8,1,2,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,4,2,8,5,6,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,4,1,2,8,5,6,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,4,8,2,5,6,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,4,1,8,2,5,6,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,4,8,1,2,5,6,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,1,4,2,5,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,4,1,2,5,8,6,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,4,1,5,2,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[3,4,5,1,2,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,1,4,5,8,2,6,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[3,4,1,5,8,2,6,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[3,4,5,8,1,2,6,7] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,4,1,2,5,6,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,4,5,1,2,6,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,4,5,6,2,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[3,4,1,5,6,2,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[3,4,5,1,6,2,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[3,4,5,6,1,2,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,4,5,6,8,2,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[3,4,1,5,6,8,2,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[3,4,5,6,1,8,2,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[3,4,5,6,8,1,2,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,4,2,5,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[3,1,4,5,2,6,7,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[3,4,1,5,2,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[3,4,1,5,6,2,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[3,4,5,1,6,2,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[3,1,4,5,6,7,2,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[3,4,1,5,6,7,2,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[3,4,5,1,6,7,2,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[3,4,5,6,1,7,2,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[3,1,4,5,6,7,8,2] => [[1,3,4,5,6,7],[2,8]] => 1000001
[3,4,1,5,6,7,8,2] => [[1,2,4,5,6,7],[3,8]] => 0100001
[3,4,5,1,6,7,8,2] => [[1,2,3,5,6,7],[4,8]] => 0010001
[3,4,5,6,1,7,8,2] => [[1,2,3,4,6,7],[5,8]] => 0001001
[3,4,5,6,7,1,8,2] => [[1,2,3,4,5,7],[6,8]] => 0000101
[3,1,5,2,6,4,8,7] => [[1,3,5,7],[2,4,6,8]] => 1010101
[3,5,1,2,6,4,8,7] => [[1,2,5,7],[3,4,6,8]] => 0100101
[3,1,5,6,2,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 1001001
[3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 0101001
[3,5,6,1,2,4,8,7] => [[1,2,3,7],[4,5,6,8]] => 0010001
[3,1,5,2,6,8,4,7] => [[1,3,5,6],[2,4,7,8]] => 1010010
[3,5,1,2,6,8,4,7] => [[1,2,5,6],[3,4,7,8]] => 0100010
[3,1,5,6,2,8,4,7] => [[1,3,4,6],[2,5,7,8]] => 1001010
[3,5,6,1,2,8,4,7] => [[1,2,3,6],[4,5,7,8]] => 0010010
[3,1,5,6,8,2,4,7] => [[1,3,4,5],[2,6,7,8]] => 1000100
[3,5,1,6,8,2,4,7] => [[1,2,4,5],[3,6,7,8]] => 0100100
[3,5,6,1,8,2,4,7] => [[1,2,3,5],[4,6,7,8]] => 0010100
[3,5,6,8,1,2,4,7] => [[1,2,3,4],[5,6,7,8]] => 0001000
[3,1,5,6,2,4,7,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,5,1,6,2,4,7,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,5,6,1,2,4,7,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,5,1,2,6,7,4,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,5,1,6,2,7,4,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[3,5,6,1,2,7,4,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,5,1,6,7,2,4,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[3,5,6,1,7,2,4,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[3,5,6,7,1,2,4,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,1,5,2,6,7,8,4] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,5,1,2,6,7,8,4] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,5,6,2,7,8,4] => [[1,3,4,6,7],[2,5,8]] => 1001001
[3,5,1,6,2,7,8,4] => [[1,2,4,6,7],[3,5,8]] => 0101001
[3,5,6,1,2,7,8,4] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,5,6,7,2,8,4] => [[1,3,4,5,7],[2,6,8]] => 1000101
[3,5,1,6,7,2,8,4] => [[1,2,4,5,7],[3,6,8]] => 0100101
[3,5,6,1,7,2,8,4] => [[1,2,3,5,7],[4,6,8]] => 0010101
[3,5,6,7,1,2,8,4] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,5,6,7,8,2,4] => [[1,3,4,5,6],[2,7,8]] => 1000010
[3,5,1,6,7,8,2,4] => [[1,2,4,5,6],[3,7,8]] => 0100010
[3,5,6,1,7,8,2,4] => [[1,2,3,5,6],[4,7,8]] => 0010010
[3,5,6,7,1,8,2,4] => [[1,2,3,4,6],[5,7,8]] => 0001010
[3,5,6,7,8,1,2,4] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,5,2,7,4,8,6] => [[1,3,5,7],[2,4,6,8]] => 1010101
[3,5,1,2,7,4,8,6] => [[1,2,5,7],[3,4,6,8]] => 0100101
[3,1,5,7,2,4,8,6] => [[1,3,4,7],[2,5,6,8]] => 1001001
[3,5,1,7,2,4,8,6] => [[1,2,4,7],[3,5,6,8]] => 0101001
[3,5,7,1,2,4,8,6] => [[1,2,3,7],[4,5,6,8]] => 0010001
[3,1,5,2,7,8,4,6] => [[1,3,5,6],[2,4,7,8]] => 1010010
[3,5,1,2,7,8,4,6] => [[1,2,5,6],[3,4,7,8]] => 0100010
[3,1,5,7,2,8,4,6] => [[1,3,4,6],[2,5,7,8]] => 1001010
[3,5,1,7,2,8,4,6] => [[1,2,4,6],[3,5,7,8]] => 0101010
[3,1,5,7,8,2,4,6] => [[1,3,4,5],[2,6,7,8]] => 1000100
[3,5,1,7,8,2,4,6] => [[1,2,4,5],[3,6,7,8]] => 0100100
[3,5,7,8,1,2,4,6] => [[1,2,3,4],[5,6,7,8]] => 0001000
[3,1,5,2,7,4,6,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,5,1,2,7,4,6,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,5,7,2,4,6,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,5,1,7,2,4,6,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,5,7,1,2,4,6,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,1,5,2,4,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,5,1,2,4,7,6,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,1,2,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,3,5,2,4,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,1,2,5,7,4,6,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,3,2,5,7,4,6,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,3,5,2,7,4,6,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,3,5,7,2,4,6,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,5,1,2,4,7,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,2,5,7,4,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,3,5,2,7,4,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,3,5,7,2,4,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[1,3,2,5,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,3,5,2,7,8,4,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,3,5,7,2,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,3,5,7,8,2,4,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,5,2,8,4,6,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,5,1,2,8,4,6,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,5,8,2,4,6,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,5,1,8,2,4,6,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,1,5,2,4,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,5,1,2,4,8,6,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[1,3,2,5,4,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,3,5,2,4,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,1,2,5,8,4,6,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,3,2,5,8,4,6,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,3,5,2,8,4,6,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,3,5,8,2,4,6,7] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,5,1,2,4,6,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,2,5,4,6,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,3,5,2,4,6,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[1,3,5,6,2,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,2,5,6,8,4,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,3,5,2,6,8,4,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,3,5,6,2,8,4,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,3,5,6,8,2,4,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,5,1,2,4,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[1,3,5,2,4,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[1,3,5,6,2,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[3,1,2,5,6,7,4,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,3,5,2,6,7,4,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,3,5,6,2,7,4,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,3,5,6,7,2,4,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[3,1,2,5,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,3,5,6,2,7,8,4] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,3,5,6,7,2,8,4] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,3,5,6,7,8,2,4] => [[1,2,3,4,5,6],[7,8]] => 0000010
[3,1,6,2,7,4,8,5] => [[1,3,5,7],[2,4,6,8]] => 1010101
[3,6,1,2,7,4,8,5] => [[1,2,5,7],[3,4,6,8]] => 0100101
[3,6,1,7,2,4,8,5] => [[1,2,4,7],[3,5,6,8]] => 0101001
[3,6,7,1,2,4,8,5] => [[1,2,3,7],[4,5,6,8]] => 0010001
[3,6,1,2,7,8,4,5] => [[1,2,5,6],[3,4,7,8]] => 0100010
[3,1,6,7,2,8,4,5] => [[1,3,4,6],[2,5,7,8]] => 1001010
[3,6,1,7,2,8,4,5] => [[1,2,4,6],[3,5,7,8]] => 0101010
[3,6,7,1,2,8,4,5] => [[1,2,3,6],[4,5,7,8]] => 0010010
[3,6,1,7,8,2,4,5] => [[1,2,4,5],[3,6,7,8]] => 0100100
[3,6,7,8,1,2,4,5] => [[1,2,3,4],[5,6,7,8]] => 0001000
[3,1,6,2,7,4,5,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,1,6,7,2,4,5,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,6,7,1,2,4,5,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,1,6,2,4,7,5,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,6,1,2,4,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,1,2,6,4,7,5,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,3,2,6,4,7,5,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,3,6,2,4,7,5,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[1,3,2,6,7,4,5,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,3,6,2,7,4,5,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[3,1,6,2,4,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,6,1,2,4,7,8,5] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,2,6,4,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,3,6,2,4,7,8,5] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,2,6,7,4,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,3,2,6,7,4,8,5] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,3,6,2,7,4,8,5] => [[1,2,3,5,7],[4,6,8]] => 0010101
[3,1,2,6,7,8,4,5] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,3,2,6,7,8,4,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,3,6,2,7,8,4,5] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,3,6,7,8,2,4,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,6,2,8,4,5,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,6,1,2,8,4,5,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,6,8,2,4,5,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,6,1,8,2,4,5,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,6,8,1,2,4,5,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,1,6,2,4,8,5,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[3,6,1,2,4,8,5,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[1,3,2,6,4,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,3,6,2,4,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,1,2,6,8,4,5,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,3,2,6,8,4,5,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[3,1,6,2,4,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,6,1,2,4,5,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[3,1,2,6,4,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,3,6,2,4,5,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,2,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,3,4,6,2,5,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[3,1,2,4,6,8,5,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,3,2,4,6,8,5,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,3,4,6,8,2,5,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,6,2,4,5,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[3,6,1,2,4,5,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[1,3,2,6,4,5,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,3,6,2,4,5,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[1,3,4,6,2,5,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[3,1,2,4,6,7,5,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,3,4,6,2,7,5,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,3,4,6,7,2,5,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[3,1,2,4,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,3,4,6,7,2,8,5] => [[1,2,3,4,5,7],[6,8]] => 0000101
[3,1,7,2,8,4,5,6] => [[1,3,5,7,8],[2,4,6]] => 1010100
[3,7,1,2,8,4,5,6] => [[1,2,5,7,8],[3,4,6]] => 0100100
[3,1,7,8,2,4,5,6] => [[1,3,4,7,8],[2,5,6]] => 1001000
[3,7,1,8,2,4,5,6] => [[1,2,4,7,8],[3,5,6]] => 0101000
[3,7,8,1,2,4,5,6] => [[1,2,3,7,8],[4,5,6]] => 0010000
[3,7,1,2,4,8,5,6] => [[1,2,5,6,8],[3,4,7]] => 0100010
[3,1,2,7,4,8,5,6] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,3,2,7,4,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,3,7,2,4,8,5,6] => [[1,2,3,6,8],[4,5,7]] => 0010010
[3,1,2,7,8,4,5,6] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,3,7,2,8,4,5,6] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,3,7,8,2,4,5,6] => [[1,2,3,4,8],[5,6,7]] => 0001000
[3,1,7,2,4,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[3,7,1,2,4,5,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[1,3,7,2,4,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[3,1,2,4,7,5,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,3,2,4,7,5,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,3,4,2,7,5,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[3,1,2,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,3,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,3,4,2,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,3,4,7,8,2,5,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[3,1,7,2,4,5,6,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[3,7,1,2,4,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[3,1,2,7,4,5,6,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,3,2,7,4,5,6,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,3,7,2,4,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[3,1,2,4,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,3,4,7,2,5,6,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[3,1,2,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,3,4,5,7,2,6,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[3,1,2,4,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,3,4,5,7,8,2,6] => [[1,2,3,4,5,6],[7,8]] => 0000010
[3,1,8,2,4,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 1010000
[3,8,1,2,4,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 0100000
[3,1,2,8,4,5,6,7] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,3,2,8,4,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,3,8,2,4,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 0010000
[3,1,2,4,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,3,2,4,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,3,4,2,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,3,4,8,2,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 0001000
[3,1,2,4,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,3,2,4,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,3,4,2,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,3,4,5,2,8,6,7] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,3,4,5,8,2,6,7] => [[1,2,3,4,5,8],[6,7]] => 0000100
[3,1,2,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,3,4,5,6,8,2,7] => [[1,2,3,4,5,6],[7,8]] => 0000010
[4,1,5,2,6,3,8,7] => [[1,3,5,7],[2,4,6,8]] => 1010101
[4,5,1,2,6,3,8,7] => [[1,2,5,7],[3,4,6,8]] => 0100101
[4,1,5,6,2,3,8,7] => [[1,3,4,7],[2,5,6,8]] => 1001001
[4,5,1,6,2,3,8,7] => [[1,2,4,7],[3,5,6,8]] => 0101001
[4,5,6,1,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 0010001
[4,1,5,2,6,8,3,7] => [[1,3,5,6],[2,4,7,8]] => 1010010
[4,5,1,2,6,8,3,7] => [[1,2,5,6],[3,4,7,8]] => 0100010
[4,1,5,6,2,8,3,7] => [[1,3,4,6],[2,5,7,8]] => 1001010
[4,5,1,6,2,8,3,7] => [[1,2,4,6],[3,5,7,8]] => 0101010
[4,5,6,1,2,8,3,7] => [[1,2,3,6],[4,5,7,8]] => 0010010
[4,1,5,6,8,2,3,7] => [[1,3,4,5],[2,6,7,8]] => 1000100
[4,5,1,6,8,2,3,7] => [[1,2,4,5],[3,6,7,8]] => 0100100
[4,5,6,1,8,2,3,7] => [[1,2,3,5],[4,6,7,8]] => 0010100
[4,5,6,8,1,2,3,7] => [[1,2,3,4],[5,6,7,8]] => 0001000
[4,1,5,2,6,3,7,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,1,5,6,2,3,7,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[4,5,1,6,2,3,7,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[4,5,1,2,6,7,3,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[4,5,1,6,2,7,3,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[4,5,6,1,2,7,3,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[4,1,5,6,7,2,3,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[4,5,1,6,7,2,3,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[4,5,6,1,7,2,3,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[4,1,5,2,6,7,8,3] => [[1,3,5,6,7],[2,4,8]] => 1010001
[4,5,1,2,6,7,8,3] => [[1,2,5,6,7],[3,4,8]] => 0100001
[4,5,1,6,2,7,8,3] => [[1,2,4,6,7],[3,5,8]] => 0101001
[4,5,6,1,2,7,8,3] => [[1,2,3,6,7],[4,5,8]] => 0010001
[4,1,5,6,7,2,8,3] => [[1,3,4,5,7],[2,6,8]] => 1000101
[4,5,1,6,7,2,8,3] => [[1,2,4,5,7],[3,6,8]] => 0100101
[4,5,6,1,7,2,8,3] => [[1,2,3,5,7],[4,6,8]] => 0010101
[4,5,6,7,1,2,8,3] => [[1,2,3,4,7],[5,6,8]] => 0001001
[4,1,5,6,7,8,2,3] => [[1,3,4,5,6],[2,7,8]] => 1000010
[4,5,1,6,7,8,2,3] => [[1,2,4,5,6],[3,7,8]] => 0100010
[4,5,6,1,7,8,2,3] => [[1,2,3,5,6],[4,7,8]] => 0010010
[4,5,6,7,1,8,2,3] => [[1,2,3,4,6],[5,7,8]] => 0001010
[4,1,5,2,7,3,8,6] => [[1,3,5,7],[2,4,6,8]] => 1010101
[4,5,1,7,2,3,8,6] => [[1,2,4,7],[3,5,6,8]] => 0101001
[4,1,5,2,7,8,3,6] => [[1,3,5,6],[2,4,7,8]] => 1010010
[4,5,1,2,7,8,3,6] => [[1,2,5,6],[3,4,7,8]] => 0100010
[4,1,5,7,2,8,3,6] => [[1,3,4,6],[2,5,7,8]] => 1001010
[4,5,1,7,2,8,3,6] => [[1,2,4,6],[3,5,7,8]] => 0101010
[4,5,7,1,2,8,3,6] => [[1,2,3,6],[4,5,7,8]] => 0010010
[4,5,1,7,8,2,3,6] => [[1,2,4,5],[3,6,7,8]] => 0100100
[4,5,7,8,1,2,3,6] => [[1,2,3,4],[5,6,7,8]] => 0001000
[4,1,5,2,7,3,6,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,5,1,2,7,3,6,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[4,1,5,2,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[4,5,1,2,3,7,6,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[4,1,2,5,3,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,4,2,5,3,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,4,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 0010010
[4,1,2,5,7,3,6,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,4,2,5,7,3,6,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,4,5,2,7,3,6,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,4,5,7,2,3,6,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[4,1,5,2,3,7,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[4,1,2,5,3,7,8,6] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,4,5,2,3,7,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[4,1,2,5,7,3,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,4,2,5,7,3,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,4,5,2,7,3,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,4,5,7,2,3,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[4,1,2,5,7,8,3,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,4,2,5,7,8,3,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,4,5,2,7,8,3,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,4,5,7,8,2,3,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[4,1,5,2,8,3,6,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,5,1,2,8,3,6,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[4,5,1,8,2,3,6,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[4,5,8,1,2,3,6,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[4,1,5,2,3,8,6,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[4,5,1,2,3,8,6,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[4,1,2,5,3,8,6,7] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,4,2,5,3,8,6,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,4,5,2,3,8,6,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[4,1,2,5,8,3,6,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,4,2,5,8,3,6,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,4,5,2,8,3,6,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,4,2,5,3,6,8,7] => [[1,2,4,6,7],[3,5,8]] => 0101001
[4,1,2,5,6,3,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,4,5,2,6,3,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[4,1,2,5,6,8,3,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,4,2,5,6,8,3,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,4,5,2,6,8,3,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,4,5,6,8,2,3,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[4,1,5,2,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[4,1,2,5,3,6,7,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,4,2,5,3,6,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,4,5,2,3,6,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[4,1,2,5,6,3,7,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,4,5,2,6,3,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,4,5,6,2,3,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[4,1,2,5,6,7,3,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,4,2,5,6,7,3,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,4,5,2,6,7,3,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,4,5,6,2,7,3,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,4,5,6,7,2,3,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[4,1,2,5,6,7,8,3] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,4,2,5,6,7,8,3] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,4,5,2,6,7,8,3] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,4,5,6,2,7,8,3] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,4,5,6,7,2,8,3] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,4,5,6,7,8,2,3] => [[1,2,3,4,5,6],[7,8]] => 0000010
[4,1,6,2,7,3,8,5] => [[1,3,5,7],[2,4,6,8]] => 1010101
[4,1,6,7,2,3,8,5] => [[1,3,4,7],[2,5,6,8]] => 1001001
[4,6,7,1,2,3,8,5] => [[1,2,3,7],[4,5,6,8]] => 0010001
[4,6,1,2,7,8,3,5] => [[1,2,5,6],[3,4,7,8]] => 0100010
[4,6,1,7,2,8,3,5] => [[1,2,4,6],[3,5,7,8]] => 0101010
[4,6,7,1,2,8,3,5] => [[1,2,3,6],[4,5,7,8]] => 0010010
[4,1,6,7,8,2,3,5] => [[1,3,4,5],[2,6,7,8]] => 1000100
[4,6,1,7,8,2,3,5] => [[1,2,4,5],[3,6,7,8]] => 0100100
[4,6,7,1,8,2,3,5] => [[1,2,3,5],[4,6,7,8]] => 0010100
[4,6,7,8,1,2,3,5] => [[1,2,3,4],[5,6,7,8]] => 0001000
[4,1,6,2,7,3,5,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,6,1,2,7,3,5,8] => [[1,2,5,7,8],[3,4,6]] => 0100100
[4,1,6,7,2,3,5,8] => [[1,3,4,7,8],[2,5,6]] => 1001000
[4,6,1,7,2,3,5,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[4,6,7,1,2,3,5,8] => [[1,2,3,7,8],[4,5,6]] => 0010000
[4,1,6,2,3,7,5,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[4,6,1,2,3,7,5,8] => [[1,2,5,6,8],[3,4,7]] => 0100010
[4,1,2,6,3,7,5,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,4,2,6,3,7,5,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[4,1,2,6,7,3,5,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,4,2,6,7,3,5,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,4,6,2,7,3,5,8] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,4,6,7,2,3,5,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[4,1,6,2,3,7,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[4,1,2,6,3,7,8,5] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,4,6,2,3,7,8,5] => [[1,2,3,6,7],[4,5,8]] => 0010001
[4,1,2,6,7,3,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,4,6,2,7,3,8,5] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,4,2,6,7,8,3,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,4,6,2,7,8,3,5] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,4,6,7,2,8,3,5] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,4,6,7,8,2,3,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[4,1,6,2,8,3,5,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,6,1,2,8,3,5,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[4,1,6,8,2,3,5,7] => [[1,3,4,7,8],[2,5,6]] => 1001000
[4,6,1,8,2,3,5,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[4,6,8,1,2,3,5,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[4,1,6,2,3,8,5,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[4,6,1,2,3,8,5,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[4,1,2,6,3,8,5,7] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,4,2,6,3,8,5,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,4,6,2,3,8,5,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[1,4,2,6,8,3,5,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,4,6,2,8,3,5,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,4,6,8,2,3,5,7] => [[1,2,3,4,8],[5,6,7]] => 0001000
[4,1,6,2,3,5,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[4,6,1,2,3,5,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[4,1,2,6,3,5,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,4,2,6,3,5,8,7] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,4,6,2,3,5,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[4,1,2,3,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,4,2,3,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,2,4,6,3,5,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[4,1,2,3,6,8,5,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,2,4,3,6,8,5,7] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,2,4,6,8,3,5,7] => [[1,2,3,4,5],[6,7,8]] => 0000100
[4,1,6,2,3,5,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[4,6,1,2,3,5,7,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[1,4,2,6,3,5,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,4,6,2,3,5,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[4,1,2,3,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,4,2,3,6,5,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,4,6,3,5,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[4,1,2,3,6,7,5,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,4,2,3,6,7,5,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[4,1,2,3,6,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,4,2,3,6,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,4,6,7,8,3,5] => [[1,2,3,4,5,6],[7,8]] => 0000010
[4,1,7,2,8,3,5,6] => [[1,3,5,7,8],[2,4,6]] => 1010100
[4,7,1,2,8,3,5,6] => [[1,2,5,7,8],[3,4,6]] => 0100100
[4,1,7,8,2,3,5,6] => [[1,3,4,7,8],[2,5,6]] => 1001000
[4,7,1,8,2,3,5,6] => [[1,2,4,7,8],[3,5,6]] => 0101000
[4,7,8,1,2,3,5,6] => [[1,2,3,7,8],[4,5,6]] => 0010000
[4,1,7,2,3,8,5,6] => [[1,3,5,6,8],[2,4,7]] => 1010010
[4,7,1,2,3,8,5,6] => [[1,2,5,6,8],[3,4,7]] => 0100010
[1,4,2,7,3,8,5,6] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,4,7,2,3,8,5,6] => [[1,2,3,6,8],[4,5,7]] => 0010010
[4,1,2,7,8,3,5,6] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,4,2,7,8,3,5,6] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,4,7,2,8,3,5,6] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,4,7,8,2,3,5,6] => [[1,2,3,4,8],[5,6,7]] => 0001000
[4,1,7,2,3,5,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[4,7,1,2,3,5,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[4,1,2,7,3,5,8,6] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,4,2,7,3,5,8,6] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,4,7,2,3,5,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[4,1,2,3,7,5,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,4,2,3,7,5,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,2,4,3,7,5,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,2,4,7,3,5,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[4,1,2,3,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,4,2,3,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,2,4,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,2,4,7,3,8,5,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,2,4,7,8,3,5,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[4,1,7,2,3,5,6,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[4,7,1,2,3,5,6,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[4,1,2,7,3,5,6,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,4,2,7,3,5,6,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,4,7,2,3,5,6,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[4,1,2,3,7,5,6,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,4,2,3,7,5,6,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,4,3,7,5,6,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,4,7,3,5,6,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[4,1,2,3,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,4,2,3,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,4,5,7,3,6,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[4,1,2,3,5,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,4,2,3,5,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,4,5,7,3,8,6] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,2,4,5,7,8,3,6] => [[1,2,3,4,5,6],[7,8]] => 0000010
[4,1,8,2,3,5,6,7] => [[1,3,5,6,7,8],[2,4]] => 1010000
[4,8,1,2,3,5,6,7] => [[1,2,5,6,7,8],[3,4]] => 0100000
[4,1,2,8,3,5,6,7] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,4,2,8,3,5,6,7] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,4,8,2,3,5,6,7] => [[1,2,3,6,7,8],[4,5]] => 0010000
[4,1,2,3,8,5,6,7] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,4,2,3,8,5,6,7] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,4,3,8,5,6,7] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,4,8,3,5,6,7] => [[1,2,3,4,7,8],[5,6]] => 0001000
[4,1,2,3,5,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,4,2,3,5,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,4,3,5,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,4,5,3,8,6,7] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,2,4,5,8,3,6,7] => [[1,2,3,4,5,8],[6,7]] => 0000100
[4,1,2,3,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,4,2,3,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,4,5,6,8,3,7] => [[1,2,3,4,5,6],[7,8]] => 0000010
[1,4,2,3,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[5,1,6,2,7,3,8,4] => [[1,3,5,7],[2,4,6,8]] => 1010101
[5,6,1,2,7,3,8,4] => [[1,2,5,7],[3,4,6,8]] => 0100101
[5,1,6,7,2,3,8,4] => [[1,3,4,7],[2,5,6,8]] => 1001001
[5,6,1,7,2,3,8,4] => [[1,2,4,7],[3,5,6,8]] => 0101001
[5,6,7,1,2,3,8,4] => [[1,2,3,7],[4,5,6,8]] => 0010001
[5,6,1,2,7,8,3,4] => [[1,2,5,6],[3,4,7,8]] => 0100010
[5,1,6,7,2,8,3,4] => [[1,3,4,6],[2,5,7,8]] => 1001010
[5,6,7,1,2,8,3,4] => [[1,2,3,6],[4,5,7,8]] => 0010010
[5,1,6,7,8,2,3,4] => [[1,3,4,5],[2,6,7,8]] => 1000100
[5,6,1,7,8,2,3,4] => [[1,2,4,5],[3,6,7,8]] => 0100100
[5,6,7,1,8,2,3,4] => [[1,2,3,5],[4,6,7,8]] => 0010100
[5,1,6,2,7,3,4,8] => [[1,3,5,7,8],[2,4,6]] => 1010100
[5,6,1,7,2,3,4,8] => [[1,2,4,7,8],[3,5,6]] => 0101000
[5,1,6,2,3,7,4,8] => [[1,3,5,6,8],[2,4,7]] => 1010010
[5,1,2,6,3,7,4,8] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,5,2,6,3,7,4,8] => [[1,2,4,6,8],[3,5,7]] => 0101010
[5,1,2,6,7,3,4,8] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,5,2,6,7,3,4,8] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,5,6,7,2,3,4,8] => [[1,2,3,4,8],[5,6,7]] => 0001000
[5,1,6,2,3,7,8,4] => [[1,3,5,6,7],[2,4,8]] => 1010001
[5,6,1,2,3,7,8,4] => [[1,2,5,6,7],[3,4,8]] => 0100001
[5,1,2,6,3,7,8,4] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,5,2,6,3,7,8,4] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,5,6,2,3,7,8,4] => [[1,2,3,6,7],[4,5,8]] => 0010001
[5,1,2,6,7,3,8,4] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,5,6,7,2,3,8,4] => [[1,2,3,4,7],[5,6,8]] => 0001001
[5,1,2,6,7,8,3,4] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,5,2,6,7,8,3,4] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,5,6,2,7,8,3,4] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,5,6,7,2,8,3,4] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,5,6,7,8,2,3,4] => [[1,2,3,4,5],[6,7,8]] => 0000100
[5,1,6,2,8,3,4,7] => [[1,3,5,7,8],[2,4,6]] => 1010100
[5,6,1,2,8,3,4,7] => [[1,2,5,7,8],[3,4,6]] => 0100100
[5,6,1,8,2,3,4,7] => [[1,2,4,7,8],[3,5,6]] => 0101000
[5,6,8,1,2,3,4,7] => [[1,2,3,7,8],[4,5,6]] => 0010000
[5,1,6,2,3,8,4,7] => [[1,3,5,6,8],[2,4,7]] => 1010010
[5,6,1,2,3,8,4,7] => [[1,2,5,6,8],[3,4,7]] => 0100010
[5,1,2,6,3,8,4,7] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,5,2,6,3,8,4,7] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,5,6,2,3,8,4,7] => [[1,2,3,6,8],[4,5,7]] => 0010010
[5,1,2,6,8,3,4,7] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,5,2,6,8,3,4,7] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,5,6,2,8,3,4,7] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,5,6,8,2,3,4,7] => [[1,2,3,4,8],[5,6,7]] => 0001000
[5,1,6,2,3,4,8,7] => [[1,3,5,6,7],[2,4,8]] => 1010001
[5,6,1,2,3,4,8,7] => [[1,2,5,6,7],[3,4,8]] => 0100001
[5,1,2,6,3,4,8,7] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,5,2,6,3,4,8,7] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,5,6,2,3,4,8,7] => [[1,2,3,6,7],[4,5,8]] => 0010001
[1,5,2,3,6,4,8,7] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,2,5,3,6,4,8,7] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,2,5,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 0001001
[5,1,2,3,6,8,4,7] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,5,2,3,6,8,4,7] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,2,5,6,3,8,4,7] => [[1,2,3,4,6],[5,7,8]] => 0001010
[5,1,6,2,3,4,7,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[5,1,2,6,3,4,7,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,5,2,6,3,4,7,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,5,6,2,3,4,7,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[5,1,2,3,6,4,7,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,5,2,3,6,4,7,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,5,3,6,4,7,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,5,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[5,1,2,3,6,7,4,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,5,2,3,6,7,4,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,5,3,6,7,4,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,5,6,3,7,4,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[5,1,2,3,6,7,8,4] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,5,2,3,6,7,8,4] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,5,3,6,7,8,4] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,5,6,3,7,8,4] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,2,5,6,7,3,8,4] => [[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
[5,1,7,2,8,3,4,6] => [[1,3,5,7,8],[2,4,6]] => 1010100
[5,7,1,2,8,3,4,6] => [[1,2,5,7,8],[3,4,6]] => 0100100
[5,1,7,8,2,3,4,6] => [[1,3,4,7,8],[2,5,6]] => 1001000
[5,7,1,8,2,3,4,6] => [[1,2,4,7,8],[3,5,6]] => 0101000
[5,7,8,1,2,3,4,6] => [[1,2,3,7,8],[4,5,6]] => 0010000
[5,1,7,2,3,8,4,6] => [[1,3,5,6,8],[2,4,7]] => 1010010
[5,7,1,2,3,8,4,6] => [[1,2,5,6,8],[3,4,7]] => 0100010
[5,1,2,7,3,8,4,6] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,5,2,7,3,8,4,6] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,5,7,2,3,8,4,6] => [[1,2,3,6,8],[4,5,7]] => 0010010
[5,1,2,7,8,3,4,6] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,5,2,7,8,3,4,6] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,5,7,2,8,3,4,6] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,5,7,8,2,3,4,6] => [[1,2,3,4,8],[5,6,7]] => 0001000
[5,1,7,2,3,4,8,6] => [[1,3,5,6,7],[2,4,8]] => 1010001
[5,7,1,2,3,4,8,6] => [[1,2,5,6,7],[3,4,8]] => 0100001
[5,1,2,7,3,4,8,6] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,5,2,7,3,4,8,6] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,5,7,2,3,4,8,6] => [[1,2,3,6,7],[4,5,8]] => 0010001
[5,1,2,3,7,4,8,6] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,5,2,3,7,4,8,6] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,2,5,3,7,4,8,6] => [[1,2,3,5,7],[4,6,8]] => 0010101
[1,2,5,7,3,4,8,6] => [[1,2,3,4,7],[5,6,8]] => 0001001
[5,1,2,3,7,8,4,6] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,5,2,3,7,8,4,6] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,2,5,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,2,5,7,8,3,4,6] => [[1,2,3,4,5],[6,7,8]] => 0000100
[5,1,7,2,3,4,6,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[5,7,1,2,3,4,6,8] => [[1,2,5,6,7,8],[3,4]] => 0100000
[5,1,2,7,3,4,6,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,5,2,7,3,4,6,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,5,2,3,7,4,6,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,5,3,7,4,6,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,5,7,3,4,6,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[1,5,2,3,4,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,5,3,4,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,3,5,7,4,6,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[5,1,2,3,4,7,8,6] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,5,2,3,4,7,8,6] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,5,3,4,7,8,6] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,3,5,7,4,8,6] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,2,3,5,7,8,4,6] => [[1,2,3,4,5,6],[7,8]] => 0000010
[5,1,8,2,3,4,6,7] => [[1,3,5,6,7,8],[2,4]] => 1010000
[5,8,1,2,3,4,6,7] => [[1,2,5,6,7,8],[3,4]] => 0100000
[5,1,2,8,3,4,6,7] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,5,2,8,3,4,6,7] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,5,8,2,3,4,6,7] => [[1,2,3,6,7,8],[4,5]] => 0010000
[5,1,2,3,8,4,6,7] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,5,2,3,8,4,6,7] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,5,3,8,4,6,7] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,5,8,3,4,6,7] => [[1,2,3,4,7,8],[5,6]] => 0001000
[5,1,2,3,4,8,6,7] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,5,2,3,4,8,6,7] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,5,3,4,8,6,7] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,3,5,4,8,6,7] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,2,3,5,8,4,6,7] => [[1,2,3,4,5,8],[6,7]] => 0000100
[5,1,2,3,4,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,5,2,3,4,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,5,3,4,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,3,5,6,8,4,7] => [[1,2,3,4,5,6],[7,8]] => 0000010
[1,5,2,3,4,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[1,2,5,3,4,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[6,1,7,2,8,3,4,5] => [[1,3,5,7,8],[2,4,6]] => 1010100
[6,7,1,2,8,3,4,5] => [[1,2,5,7,8],[3,4,6]] => 0100100
[6,1,7,8,2,3,4,5] => [[1,3,4,7,8],[2,5,6]] => 1001000
[6,7,1,8,2,3,4,5] => [[1,2,4,7,8],[3,5,6]] => 0101000
[6,1,7,2,3,8,4,5] => [[1,3,5,6,8],[2,4,7]] => 1010010
[6,7,1,2,3,8,4,5] => [[1,2,5,6,8],[3,4,7]] => 0100010
[6,1,2,7,3,8,4,5] => [[1,3,4,6,8],[2,5,7]] => 1001010
[1,6,2,7,3,8,4,5] => [[1,2,4,6,8],[3,5,7]] => 0101010
[1,6,7,2,3,8,4,5] => [[1,2,3,6,8],[4,5,7]] => 0010010
[6,1,2,7,8,3,4,5] => [[1,3,4,5,8],[2,6,7]] => 1000100
[1,6,2,7,8,3,4,5] => [[1,2,4,5,8],[3,6,7]] => 0100100
[1,6,7,2,8,3,4,5] => [[1,2,3,5,8],[4,6,7]] => 0010100
[1,6,7,8,2,3,4,5] => [[1,2,3,4,8],[5,6,7]] => 0001000
[6,1,7,2,3,4,8,5] => [[1,3,5,6,7],[2,4,8]] => 1010001
[6,7,1,2,3,4,8,5] => [[1,2,5,6,7],[3,4,8]] => 0100001
[6,1,2,7,3,4,8,5] => [[1,3,4,6,7],[2,5,8]] => 1001001
[1,6,2,7,3,4,8,5] => [[1,2,4,6,7],[3,5,8]] => 0101001
[1,6,7,2,3,4,8,5] => [[1,2,3,6,7],[4,5,8]] => 0010001
[6,1,2,3,7,4,8,5] => [[1,3,4,5,7],[2,6,8]] => 1000101
[1,6,2,3,7,4,8,5] => [[1,2,4,5,7],[3,6,8]] => 0100101
[1,2,6,3,7,4,8,5] => [[1,2,3,5,7],[4,6,8]] => 0010101
[6,1,2,3,7,8,4,5] => [[1,3,4,5,6],[2,7,8]] => 1000010
[1,6,2,3,7,8,4,5] => [[1,2,4,5,6],[3,7,8]] => 0100010
[1,2,6,3,7,8,4,5] => [[1,2,3,5,6],[4,7,8]] => 0010010
[1,2,6,7,3,8,4,5] => [[1,2,3,4,6],[5,7,8]] => 0001010
[1,2,6,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 0000100
[6,1,7,2,3,4,5,8] => [[1,3,5,6,7,8],[2,4]] => 1010000
[6,1,2,7,3,4,5,8] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,6,2,7,3,4,5,8] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,6,7,2,3,4,5,8] => [[1,2,3,6,7,8],[4,5]] => 0010000
[6,1,2,3,7,4,5,8] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,6,2,3,7,4,5,8] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,6,3,7,4,5,8] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,6,7,3,4,5,8] => [[1,2,3,4,7,8],[5,6]] => 0001000
[6,1,2,3,4,7,5,8] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,6,2,3,4,7,5,8] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,6,3,4,7,5,8] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,3,6,4,7,5,8] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,2,3,6,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 0000100
[6,1,2,3,4,7,8,5] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,6,2,3,4,7,8,5] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,6,3,4,7,8,5] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,3,6,4,7,8,5] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,2,3,6,7,4,8,5] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,2,3,6,7,8,4,5] => [[1,2,3,4,5,6],[7,8]] => 0000010
[6,1,8,2,3,4,5,7] => [[1,3,5,6,7,8],[2,4]] => 1010000
[6,8,1,2,3,4,5,7] => [[1,2,5,6,7,8],[3,4]] => 0100000
[6,1,2,8,3,4,5,7] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,6,2,8,3,4,5,7] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,6,8,2,3,4,5,7] => [[1,2,3,6,7,8],[4,5]] => 0010000
[6,1,2,3,8,4,5,7] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,6,2,3,8,4,5,7] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,6,3,8,4,5,7] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,6,8,3,4,5,7] => [[1,2,3,4,7,8],[5,6]] => 0001000
[6,1,2,3,4,8,5,7] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,6,2,3,4,8,5,7] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,6,3,4,8,5,7] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,3,6,4,8,5,7] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,2,3,6,8,4,5,7] => [[1,2,3,4,5,8],[6,7]] => 0000100
[6,1,2,3,4,5,8,7] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,6,2,3,4,5,8,7] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,6,3,4,5,8,7] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,3,6,4,5,8,7] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,2,3,4,6,8,5,7] => [[1,2,3,4,5,6],[7,8]] => 0000010
[1,6,2,3,4,5,7,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[1,2,6,3,4,5,7,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[1,2,3,6,4,5,7,8] => [[1,2,3,4,6,7,8],[5]] => 0001000
[7,1,8,2,3,4,5,6] => [[1,3,5,6,7,8],[2,4]] => 1010000
[7,1,2,8,3,4,5,6] => [[1,3,4,6,7,8],[2,5]] => 1001000
[1,7,2,8,3,4,5,6] => [[1,2,4,6,7,8],[3,5]] => 0101000
[1,7,8,2,3,4,5,6] => [[1,2,3,6,7,8],[4,5]] => 0010000
[7,1,2,3,8,4,5,6] => [[1,3,4,5,7,8],[2,6]] => 1000100
[1,7,2,3,8,4,5,6] => [[1,2,4,5,7,8],[3,6]] => 0100100
[1,2,7,3,8,4,5,6] => [[1,2,3,5,7,8],[4,6]] => 0010100
[1,2,7,8,3,4,5,6] => [[1,2,3,4,7,8],[5,6]] => 0001000
[7,1,2,3,4,8,5,6] => [[1,3,4,5,6,8],[2,7]] => 1000010
[1,7,2,3,4,8,5,6] => [[1,2,4,5,6,8],[3,7]] => 0100010
[1,2,7,3,4,8,5,6] => [[1,2,3,5,6,8],[4,7]] => 0010010
[1,2,3,7,4,8,5,6] => [[1,2,3,4,6,8],[5,7]] => 0001010
[1,2,3,7,8,4,5,6] => [[1,2,3,4,5,8],[6,7]] => 0000100
[7,1,2,3,4,5,8,6] => [[1,3,4,5,6,7],[2,8]] => 1000001
[1,7,2,3,4,5,8,6] => [[1,2,4,5,6,7],[3,8]] => 0100001
[1,2,7,3,4,5,8,6] => [[1,2,3,5,6,7],[4,8]] => 0010001
[1,2,3,7,4,5,8,6] => [[1,2,3,4,6,7],[5,8]] => 0001001
[1,2,3,4,7,5,8,6] => [[1,2,3,4,5,7],[6,8]] => 0000101
[1,2,3,4,7,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 0000010
[1,7,2,3,4,5,6,8] => [[1,2,4,5,6,7,8],[3]] => 0100000
[1,2,7,3,4,5,6,8] => [[1,2,3,5,6,7,8],[4]] => 0010000
[1,2,3,7,4,5,6,8] => [[1,2,3,4,6,7,8],[5]] => 0001000
[1,2,3,4,7,5,6,8] => [[1,2,3,4,5,7,8],[6]] => 0000100
[1,8,2,3,4,5,6,7] => [[1,2,4,5,6,7,8],[3]] => 0100000
[1,2,8,3,4,5,6,7] => [[1,2,3,5,6,7,8],[4]] => 0010000
[1,2,3,8,4,5,6,7] => [[1,2,3,4,6,7,8],[5]] => 0001000
[1,2,3,4,8,5,6,7] => [[1,2,3,4,5,7,8],[6]] => 0000100
[1,2,3,4,5,8,6,7] => [[1,2,3,4,5,6,8],[7]] => 0000010
[5,3,2,6,1,4,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,3,2,5,4,8,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,4,5,2,3,7,6,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,4,5,2,3,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,4,5,2,3,1,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,4,6,2,1,3,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[3,6,1,5,4,2,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,6,5,1,3,2,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[5,6,4,3,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,5,4,3,2,8,1,6] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,6,4,3,7,2,5,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[7,6,4,3,8,2,1,5] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[6,7,4,3,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[5,7,4,3,1,8,2,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[4,7,5,1,3,8,2,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[3,7,1,5,4,8,2,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,1,7,5,4,8,3,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[3,8,1,5,4,7,6,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,8,5,1,3,7,6,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,8,4,3,1,7,6,2] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[6,8,4,3,7,1,5,2] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[7,8,4,3,6,5,1,2] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[6,8,5,7,3,1,4,2] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[5,8,6,7,1,3,4,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[4,8,6,1,7,3,5,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[3,8,1,6,7,4,5,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,1,8,6,7,4,5,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,7,6,8,4,3,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,7,1,6,8,4,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[4,7,6,1,8,3,2,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[5,7,6,8,1,3,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,4,7,2,1,8,3,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,4,7,2,8,1,3,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,4,6,2,8,3,1,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,4,6,2,7,3,5,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,3,2,6,7,4,5,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[7,3,2,6,8,4,1,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[6,3,2,7,8,1,4,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,3,2,7,1,8,4,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[4,3,2,1,7,8,5,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[3,4,1,2,8,7,6,5] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[5,3,2,8,1,7,6,4] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[6,3,2,8,7,1,5,4] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[7,3,2,8,6,5,1,4] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[8,4,7,2,6,5,3,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[7,4,8,2,6,5,1,3] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,4,8,2,7,1,5,3] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[5,4,8,2,1,7,6,3] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[4,5,8,1,2,7,6,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,5,1,8,2,7,6,4] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[2,1,5,8,3,7,6,4] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[2,1,6,8,7,3,5,4] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,6,1,8,7,2,5,4] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[4,6,8,1,7,2,5,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,6,8,7,1,2,4,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[6,5,8,7,2,1,4,3] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[7,5,8,6,2,4,1,3] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[8,5,7,6,2,4,3,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[5,7,8,6,1,4,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,7,8,1,6,5,2,3] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[3,7,1,8,6,5,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[2,1,7,8,6,5,3,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,8,1,7,6,5,4,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[4,8,7,1,6,5,3,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[5,8,7,6,1,4,3,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[6,8,7,5,4,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[3,4,1,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => 010010101
[4,3,2,1,6,5,8,7,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[6,5,4,3,2,1,8,7,10,9] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 111110101
[8,9,5,6,3,4,10,1,2,7] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[4,3,2,1,8,7,6,5,10,9] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 111011101
[8,7,6,5,4,3,2,1,10,9] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[9,7,6,5,4,3,2,10,1,8] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010
[10,8,9,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[7,3,2,8,9,10,1,4,5,6] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[8,5,4,3,2,9,10,1,6,7] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[2,1,4,3,6,5,10,9,8,7] => [[1,3,5,7],[2,4,6,8],[9],[10]] => 101010111
[2,1,6,5,4,3,10,9,8,7] => [[1,3,7],[2,4,8],[5,9],[6,10]] => 101110111
[6,5,4,3,2,1,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 111110111
[9,7,5,10,3,8,2,6,1,4] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010
[2,1,4,3,10,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9],[10]] => 101011111
[4,3,2,1,10,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 111011111
[2,1,10,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[9,10,8,7,6,5,4,3,1,2] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111
[4,2,5,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,2,4,1,3,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[3,2,6,1,4,5,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[4,2,6,1,3,5,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,3,6,1,2,4,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,2,4,1,3,5,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,3,5,1,2,4,7,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,3,7,1,2,4,6,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,4,7,1,2,3,6,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,2,7,1,3,4,5,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,3,7,1,2,4,5,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,4,7,1,2,3,5,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,3,5,1,2,4,6,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,3,6,1,2,4,5,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,4,6,1,2,3,5,8] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[3,2,8,1,4,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[4,2,8,1,3,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[5,4,8,1,2,3,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,2,8,1,3,4,5,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,3,8,1,2,4,5,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,4,8,1,2,3,5,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[6,5,8,1,2,3,4,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,2,8,1,3,4,5,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,3,8,1,2,4,5,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,4,8,1,2,3,5,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[7,5,8,1,2,3,4,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,2,4,1,3,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,3,5,1,2,4,6,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,3,6,1,2,4,5,7] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,3,7,1,2,4,5,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,4,7,1,2,3,5,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[8,5,7,1,2,3,4,6] => [[1,3,6,7,8],[2,5],[4]] => 1010000
[3,2,5,7,1,4,6,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,2,5,7,1,3,6,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,2,4,7,1,3,6,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,2,6,7,1,3,5,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,2,6,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,2,5,7,1,3,4,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,3,5,7,1,2,4,8] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[3,2,5,8,1,4,6,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,2,5,8,1,3,6,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,3,5,8,1,2,6,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,2,4,8,1,3,6,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[3,2,6,8,1,4,5,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,2,6,8,1,3,5,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,2,6,8,1,3,4,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,2,4,8,1,3,5,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,3,4,8,1,2,5,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,2,5,8,1,3,4,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,3,5,8,1,2,4,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,4,5,8,1,2,3,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[3,2,7,8,1,4,5,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,3,7,8,1,2,5,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,3,7,8,1,2,4,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[5,4,7,8,1,2,3,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,2,7,8,1,3,4,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,3,7,8,1,2,4,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[6,4,7,8,1,2,3,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,2,4,8,1,3,5,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,3,4,8,1,2,5,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,3,5,8,1,2,4,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,4,5,8,1,2,3,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[7,4,6,8,1,2,3,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,3,4,6,1,2,5,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,3,5,6,1,2,4,7] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,2,4,7,1,3,5,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,2,5,7,1,3,4,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,3,5,7,1,2,4,6] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,2,6,7,1,3,4,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[8,4,6,7,1,2,3,5] => [[1,3,4,8],[2,6,7],[5]] => 1001000
[4,6,2,5,1,3,7,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,6,3,5,1,2,7,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[3,7,2,5,1,4,6,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,7,3,5,1,2,6,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,7,2,4,1,3,6,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[3,7,2,6,1,4,5,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,7,3,6,1,2,5,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,7,2,6,1,3,4,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[6,7,2,5,1,3,4,8] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,8,2,5,1,3,6,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,2,4,1,3,6,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,3,4,1,2,6,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[3,8,2,6,1,4,5,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,3,6,1,2,4,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,4,6,1,2,3,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[6,8,3,5,1,2,4,7] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[3,8,2,7,1,4,5,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,8,2,7,1,3,5,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,8,3,7,1,2,5,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,2,7,1,3,4,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[5,8,3,7,1,2,4,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[6,8,2,7,1,3,4,5] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[6,8,3,7,1,2,4,5] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[6,8,5,7,1,2,3,4] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[7,8,2,4,1,3,5,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[7,8,2,5,1,3,4,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[7,8,3,5,1,2,4,6] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[7,8,4,6,1,2,3,5] => [[1,2,7,8],[3,4],[5,6]] => 0101000
[4,3,2,6,1,5,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[5,3,2,6,1,4,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,3,2,5,1,4,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,5,2,4,1,3,7,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[4,3,2,7,1,5,6,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[5,3,2,7,1,4,6,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[5,4,3,7,1,2,6,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,3,2,7,1,4,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,4,2,7,1,3,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,4,3,7,1,2,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,5,2,7,1,3,4,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,5,3,7,1,2,4,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,3,2,5,1,4,6,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,4,2,5,1,3,6,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,3,2,6,1,4,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,4,2,6,1,3,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,4,3,6,1,2,5,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,5,2,6,1,3,4,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,5,3,6,1,2,4,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,6,3,5,1,2,4,8] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[4,3,2,8,1,5,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[5,3,2,8,1,4,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[5,4,3,8,1,2,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,3,2,8,1,4,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,4,2,8,1,3,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,4,3,8,1,2,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,5,2,8,1,3,4,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[6,5,3,8,1,2,4,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,3,2,8,1,4,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,4,2,8,1,3,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,4,3,8,1,2,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,5,3,8,1,2,4,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,5,4,8,1,2,3,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[7,6,2,8,1,3,4,5] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,3,2,5,1,4,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,4,2,5,1,3,6,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,3,2,6,1,4,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,4,2,6,1,3,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,5,3,6,1,2,4,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,6,2,4,1,3,5,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,6,2,5,1,3,4,7] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,3,2,7,1,4,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,4,2,7,1,3,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,4,3,7,1,2,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,5,2,7,1,3,4,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,5,3,7,1,2,4,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,6,3,7,1,2,4,5] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,2,4,1,3,5,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,2,5,1,3,4,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,3,5,1,2,4,6] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,2,6,1,3,4,5] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,3,6,1,2,4,5] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[8,7,4,6,1,2,3,5] => [[1,4,7,8],[2,6],[3],[5]] => 1101000
[4,6,3,5,8,1,2,7] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,6,2,4,8,1,3,7] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[4,7,2,5,8,1,3,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[4,7,3,5,8,1,2,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,7,2,4,8,1,3,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,7,3,4,8,1,2,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[4,7,3,6,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,7,2,6,8,1,3,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,7,4,6,8,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[6,7,3,4,8,1,2,5] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[6,7,3,5,8,1,2,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[3,8,2,5,7,1,4,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[4,8,3,5,7,1,2,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,8,2,4,7,1,3,6] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[3,8,2,6,7,1,4,5] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,8,2,6,7,1,3,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[5,8,3,6,7,1,2,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[6,8,2,5,7,1,3,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[6,8,4,5,7,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[7,8,2,4,6,1,3,5] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[7,8,2,5,6,1,3,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[7,8,3,5,6,1,2,4] => [[1,2,5],[3,4,8],[6,7]] => 0100100
[4,3,2,6,8,1,5,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,3,2,6,8,1,4,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,4,2,6,8,1,3,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,4,3,6,8,1,2,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,3,2,5,8,1,4,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,4,3,5,8,1,2,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,5,2,4,8,1,3,7] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[4,3,2,7,8,1,5,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,3,2,7,8,1,4,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,4,2,7,8,1,3,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[5,4,3,7,8,1,2,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,4,2,7,8,1,3,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,4,3,7,8,1,2,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[6,5,2,7,8,1,3,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,4,2,5,8,1,3,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,4,3,5,8,1,2,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,5,2,6,8,1,3,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,5,3,6,8,1,2,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,6,2,4,8,1,3,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[7,6,3,5,8,1,2,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,3,2,5,7,1,4,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,4,2,5,7,1,3,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,5,2,4,7,1,3,6] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,3,2,6,7,1,4,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,5,2,6,7,1,3,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,5,3,6,7,1,2,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,6,2,4,7,1,3,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,7,2,4,6,1,3,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,7,3,4,6,1,2,5] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[8,7,2,5,6,1,3,4] => [[1,4,5],[2,7,8],[3],[6]] => 1100100
[4,3,7,2,6,1,5,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,3,7,2,6,1,4,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,7,2,6,1,3,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,3,7,2,5,1,4,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,4,7,2,5,1,3,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,4,7,3,5,1,2,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,3,6,2,5,1,4,8] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[4,3,8,2,6,1,5,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,3,8,2,6,1,4,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,8,2,6,1,3,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,8,3,6,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,4,8,2,5,1,3,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,4,8,3,5,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,5,8,2,4,1,3,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,5,8,3,4,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[4,3,8,2,7,1,5,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,3,8,2,7,1,4,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,8,2,7,1,3,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,8,3,7,1,2,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,3,8,2,7,1,4,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[6,4,8,2,7,1,3,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,3,8,2,5,1,4,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,4,8,3,5,1,2,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,5,8,2,4,1,3,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,5,8,2,6,1,3,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,5,8,4,6,1,2,3] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,6,8,2,5,1,3,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[7,6,8,3,5,1,2,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,3,6,2,5,1,4,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,5,6,2,4,1,3,7] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,3,7,2,5,1,4,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,4,7,3,5,1,2,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,5,7,2,4,1,3,6] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,3,7,2,6,1,4,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,4,7,2,6,1,3,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,4,7,3,6,1,2,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,5,7,2,6,1,3,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,6,7,2,4,1,3,5] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,6,7,2,5,1,3,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[8,6,7,3,5,1,2,4] => [[1,3,8],[2,5],[4,7],[6]] => 1010100
[5,4,3,2,7,1,6,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,4,3,2,7,1,5,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,5,3,2,7,1,4,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,5,4,2,7,1,3,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,5,3,2,6,1,4,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,5,4,2,6,1,3,8] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[5,4,3,2,8,1,6,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,5,3,2,8,1,4,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,5,4,2,8,1,3,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[6,5,4,3,8,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,5,3,2,8,1,4,6] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,5,4,2,8,1,3,6] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,6,3,2,8,1,4,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,6,4,3,8,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[7,6,5,2,8,1,3,4] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,5,3,2,6,1,4,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,5,4,2,6,1,3,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,6,5,2,4,1,3,7] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,5,3,2,7,1,4,6] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,6,3,2,7,1,4,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,6,4,3,7,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,3,2,6,1,4,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,4,2,6,1,3,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,4,3,6,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,5,2,6,1,3,4] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,6,2,4,1,3,5] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,6,2,5,1,3,4] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[8,7,6,3,5,1,2,4] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100
[4,8,3,7,2,6,1,5] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[5,8,3,7,2,6,1,4] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[5,8,4,7,2,6,1,3] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[5,8,4,7,3,6,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[6,8,3,7,2,5,1,4] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[6,8,4,7,2,5,1,3] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[6,8,4,7,3,5,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[6,8,5,7,2,4,1,3] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[6,8,5,7,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[7,8,3,6,2,5,1,4] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[7,8,4,6,2,5,1,3] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[7,8,4,6,3,5,1,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[7,8,5,6,2,4,1,3] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[5,4,3,8,2,7,1,6] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[6,4,3,8,2,7,1,5] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[6,5,3,8,2,7,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[6,5,4,8,3,7,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,4,3,8,2,6,1,5] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,5,3,8,2,6,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,5,4,8,2,6,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,6,3,8,2,5,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,6,4,8,2,5,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[7,6,5,8,2,4,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,4,3,7,2,6,1,5] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,5,3,7,2,6,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,5,4,7,2,6,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,5,4,7,3,6,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,6,3,7,2,5,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,6,4,7,2,5,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,6,4,7,3,5,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,6,5,7,2,4,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,7,3,6,2,5,1,4] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,7,4,6,2,5,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,7,4,6,3,5,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[8,7,5,6,2,4,1,3] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010
[6,5,4,3,2,8,1,7] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[7,6,5,4,2,8,1,3] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,5,4,3,2,7,1,6] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,6,5,3,2,7,1,4] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,4,3,2,6,1,5] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,5,3,2,6,1,4] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,5,4,2,6,1,3] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,6,3,2,5,1,4] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,6,4,2,5,1,3] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,7,6,5,2,4,1,3] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010
[8,1,2,3,4,7,5,6] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,1,2,3,6,4,5,7] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[8,1,2,3,7,4,5,6] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[7,1,2,3,6,4,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[5,1,2,3,8,7,4,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[8,1,2,3,6,7,4,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,1,2,8,3,7,5,6] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[8,1,2,5,3,4,6,7] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[7,1,2,5,3,4,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[8,1,2,6,3,4,5,7] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[7,1,2,6,3,4,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[6,1,2,5,3,8,4,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,2,5,3,7,4,6] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,2,6,3,7,4,5] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[6,1,2,5,3,7,8,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,1,2,8,6,3,5,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,1,2,8,7,3,5,6] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,1,2,7,6,3,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[8,1,2,5,6,3,4,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,1,2,5,7,3,4,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,1,2,7,6,3,4,5] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[7,1,2,5,6,3,8,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[4,1,2,5,8,7,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,1,2,8,6,7,3,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,1,2,5,6,7,3,4] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[3,1,8,2,4,7,5,6] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,1,8,2,6,4,5,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,1,8,2,7,4,5,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,1,7,2,6,4,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,5,2,8,7,4,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,1,8,2,6,7,4,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,1,4,2,3,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[7,1,4,2,3,5,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[6,1,4,2,3,8,5,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,1,4,2,3,7,5,6] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[6,1,4,2,3,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,1,5,2,3,4,6,7] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[7,1,5,2,3,4,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,1,7,2,3,4,5,6] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[6,1,5,2,3,8,4,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,1,5,2,3,7,4,6] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[6,1,8,2,3,7,4,5] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,1,5,2,3,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,1,4,2,8,3,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[5,1,4,2,7,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,4,2,6,3,5,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[8,1,4,2,7,3,5,6] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,4,2,6,3,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,5,2,6,3,4,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[8,1,5,2,7,3,4,6] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,8,2,6,3,4,5] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[7,1,5,2,6,3,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,4,2,6,8,3,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,1,4,2,8,7,3,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[8,1,4,2,6,7,3,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,1,5,2,6,7,3,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,1,4,2,6,7,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[3,1,4,8,2,7,5,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[3,1,8,5,2,4,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,1,7,5,2,4,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,1,8,6,2,4,5,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,1,7,6,2,4,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,1,6,5,2,8,4,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,1,8,5,2,7,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,1,8,6,2,7,4,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,1,6,5,2,7,8,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[8,1,4,5,2,3,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[7,1,4,5,2,3,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,1,4,6,2,3,5,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[7,1,4,8,2,3,5,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[7,1,4,6,2,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,1,6,5,2,3,4,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[7,1,8,5,2,3,4,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,1,8,6,2,3,4,5] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,1,6,5,2,3,8,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[6,1,4,5,2,8,3,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,1,4,5,2,7,3,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,1,4,6,2,7,3,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,1,6,5,2,7,3,4] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,1,4,5,2,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[3,1,4,8,6,2,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,1,4,8,7,2,5,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,1,4,7,6,2,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,1,8,5,6,2,4,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,1,8,5,7,2,4,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,1,8,7,6,2,4,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,1,7,5,6,2,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,1,4,5,6,2,3,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,1,4,5,7,2,3,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,1,4,7,6,2,3,5] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,7,5,6,2,3,4] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,1,4,5,6,2,8,3] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[3,1,4,5,8,7,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,1,4,8,6,7,2,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[3,1,8,5,6,7,2,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,1,4,5,6,7,2,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[2,8,1,3,4,7,5,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[2,8,1,3,6,4,5,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[2,8,1,3,7,4,5,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[2,7,1,3,6,4,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,5,1,3,8,7,4,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,8,1,3,6,7,4,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[2,4,1,8,3,7,5,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,8,1,5,3,4,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[2,7,1,5,3,4,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,8,1,6,3,4,5,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[2,7,1,6,3,4,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,6,1,5,3,8,4,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,8,1,5,3,7,4,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,6,1,5,3,7,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,4,1,8,6,3,5,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,4,1,8,7,3,5,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,4,1,7,6,3,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,8,1,5,6,3,4,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,8,1,5,7,3,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,8,1,7,6,3,4,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[2,7,1,5,6,3,8,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,4,1,5,8,7,3,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,4,1,8,6,7,3,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,8,1,5,6,7,3,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[7,3,1,2,4,5,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,3,1,2,4,8,5,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[8,3,1,2,4,7,5,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[6,3,1,2,4,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,3,1,2,8,4,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,3,1,2,7,4,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,3,1,2,6,4,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[8,3,1,2,7,4,5,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,3,1,2,6,4,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[5,3,1,2,6,8,4,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,3,1,2,8,7,4,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[8,3,1,2,6,7,4,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,3,1,2,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,4,1,2,3,5,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,4,1,2,3,8,5,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[8,4,1,2,3,7,5,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[6,4,1,2,3,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,6,1,2,3,4,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,8,1,2,3,7,4,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,6,1,2,3,7,4,5] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[5,4,1,2,8,3,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,4,1,2,7,3,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,4,1,2,6,3,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[8,4,1,2,7,3,5,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,4,1,2,6,3,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[5,8,1,2,6,3,4,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[5,8,1,2,7,3,4,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[8,7,1,2,6,3,4,5] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,7,1,2,6,3,8,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[5,4,1,2,6,8,3,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,4,1,2,8,7,3,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[8,4,1,2,6,7,3,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,8,1,2,6,7,3,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,4,1,2,6,7,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[4,3,1,8,2,5,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,3,1,7,2,5,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[4,3,1,6,2,8,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,3,1,8,2,7,5,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[4,3,1,6,2,7,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[8,3,1,5,2,4,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,3,1,5,2,4,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[8,3,1,6,2,4,5,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,3,1,8,2,4,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,3,1,6,2,4,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,3,1,5,2,8,4,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,3,1,5,2,7,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,3,1,6,2,7,4,5] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,3,1,5,2,7,8,4] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[8,4,1,5,2,3,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,4,1,5,2,3,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[8,4,1,6,2,3,5,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,4,1,8,2,3,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,4,1,6,2,3,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,8,1,5,2,3,4,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[8,7,1,5,2,3,4,6] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[8,7,1,6,2,3,4,5] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,7,1,5,2,3,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[6,4,1,5,2,8,3,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,4,1,5,2,7,3,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,4,1,6,2,7,3,5] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,8,1,5,2,7,3,4] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,4,1,5,2,7,8,3] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[4,3,1,5,8,2,6,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,3,1,5,7,2,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[4,3,1,8,6,2,5,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[4,3,1,8,7,2,5,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[4,3,1,7,6,2,8,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[8,3,1,5,6,2,4,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[8,3,1,5,7,2,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[8,3,1,7,6,2,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,1,5,6,2,8,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,4,1,5,6,2,3,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[8,4,1,5,7,2,3,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[8,4,1,7,6,2,3,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,8,1,5,6,2,3,4] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[7,4,1,5,6,2,8,3] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[4,3,1,5,6,8,2,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,3,1,5,8,7,2,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[4,3,1,8,6,7,2,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[8,3,1,5,6,7,2,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,4,1,5,6,7,2,3] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,3,1,5,6,7,8,2] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,3,8,1,4,7,5,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[2,3,8,1,6,4,5,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,3,8,1,7,4,5,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,3,7,1,6,4,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,3,5,1,8,7,4,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,3,8,1,6,7,4,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,8,4,1,3,5,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[2,7,4,1,3,5,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,6,4,1,3,8,5,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,8,4,1,3,7,5,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,6,4,1,3,7,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,8,5,1,3,4,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[2,7,5,1,3,4,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,8,7,1,3,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[2,6,5,1,3,8,4,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,8,5,1,3,7,4,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,6,8,1,3,7,4,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,6,5,1,3,7,8,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,5,4,1,8,3,6,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,5,4,1,7,3,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,8,4,1,6,3,5,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,8,4,1,7,3,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,7,4,1,6,3,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,8,5,1,6,3,4,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,8,5,1,7,3,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,7,8,1,6,3,4,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,7,5,1,6,3,8,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,5,4,1,6,8,3,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,5,4,1,8,7,3,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[2,8,4,1,6,7,3,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,8,5,1,6,7,3,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,5,4,1,6,7,8,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[7,3,4,1,2,5,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,4,1,2,8,5,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,3,4,1,2,7,5,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,3,4,1,2,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,3,5,1,2,4,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,7,1,2,4,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,5,1,2,8,4,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,3,5,1,2,7,4,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,3,8,1,2,7,4,5] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,3,5,1,2,7,8,4] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,5,4,1,2,3,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,8,4,1,2,3,5,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[6,7,4,1,2,3,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,8,5,1,2,3,4,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[6,7,5,1,2,3,8,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,5,4,1,2,8,3,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,5,4,1,2,7,3,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,8,4,1,2,7,3,5] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,8,5,1,2,7,3,4] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,5,4,1,2,7,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,3,4,1,8,2,6,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[5,3,4,1,7,2,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,3,4,1,6,2,5,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,3,4,1,7,2,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,3,4,1,6,2,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,3,5,1,6,2,4,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,3,5,1,7,2,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,3,8,1,6,2,4,5] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[7,3,5,1,6,2,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,5,4,1,6,2,3,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,5,4,1,7,2,3,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,8,4,1,6,2,3,5] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,8,5,1,6,2,3,4] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,5,4,1,6,2,8,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[5,3,4,1,6,8,2,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,3,4,1,8,7,2,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[8,3,4,1,6,7,2,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,3,5,1,6,7,2,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,5,4,1,6,7,2,3] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[5,3,4,1,6,7,8,2] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,3,4,8,1,7,5,6] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,3,8,5,1,4,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,3,7,5,1,4,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,3,8,6,1,4,5,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,3,7,6,1,4,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,3,6,5,1,8,4,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,3,8,5,1,7,4,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,3,8,6,1,7,4,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,3,6,5,1,7,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,8,4,5,1,3,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,7,4,5,1,3,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[2,8,4,6,1,3,5,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[2,7,4,8,1,3,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[2,7,4,6,1,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[2,8,6,5,1,3,4,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,7,8,5,1,3,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,7,8,6,1,3,4,5] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,7,6,5,1,3,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[2,6,4,5,1,8,3,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,8,4,5,1,7,3,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,8,4,6,1,7,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,8,6,5,1,7,3,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,6,4,5,1,7,8,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[7,3,4,5,1,2,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,3,4,6,1,2,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,3,6,5,1,2,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,3,8,5,1,2,4,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[7,3,8,6,1,2,4,5] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[7,3,6,5,1,2,8,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,6,4,5,1,2,8,3] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,3,4,5,1,8,2,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,3,4,5,1,7,2,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,3,4,6,1,7,2,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,3,6,5,1,7,2,4] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,6,4,5,1,7,2,3] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,3,4,5,1,7,8,2] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[2,3,4,8,6,1,5,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[2,3,4,8,7,1,5,6] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[2,3,4,7,6,1,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,3,8,5,6,1,4,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[2,3,8,5,7,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,3,8,7,6,1,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,3,7,5,6,1,8,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,8,4,5,6,1,3,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,8,4,5,7,1,3,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,8,4,7,6,1,3,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[2,8,7,5,6,1,3,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,7,4,5,6,1,8,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[8,3,4,5,7,1,2,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,3,4,7,6,1,2,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,3,7,5,6,1,2,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,3,4,5,6,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[2,3,4,5,8,7,1,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[2,3,4,8,6,7,1,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,3,8,5,6,7,1,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[2,8,4,5,6,7,1,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[9,1,2,3,4,5,6,7,8] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[8,1,2,3,4,5,6,9,7] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[7,1,2,3,4,5,9,6,8] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[7,1,2,3,4,5,8,9,6] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[8,1,2,3,4,7,5,9,6] => [[1,3,4,5,6,8],[2,9],[7]] => 10000101
[6,1,2,3,4,7,9,5,8] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[9,1,2,3,4,7,8,5,6] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[6,1,2,3,4,7,8,9,5] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[5,1,2,3,6,7,8,9,4] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[4,1,2,5,6,7,9,3,8] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[9,1,2,5,6,7,8,3,4] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[4,1,2,5,6,7,8,9,3] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[3,1,9,2,4,5,6,7,8] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[3,1,5,2,7,4,9,6,8] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[9,1,8,2,3,4,5,6,7] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[8,1,4,5,6,7,2,9,3] => [[1,3,4,5,6,8],[2,9],[7]] => 10000101
[3,1,4,5,6,7,9,2,8] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[9,1,4,5,6,7,8,2,3] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[3,1,4,5,6,7,8,9,2] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[2,9,1,3,4,5,6,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[2,8,1,3,4,5,6,9,7] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[2,7,1,3,4,5,8,9,6] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[2,5,1,3,6,7,8,9,4] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[2,4,1,6,3,8,5,9,7] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,4,1,5,6,7,9,3,8] => [[1,2,4,5,6,7],[3,8,9]] => 01000010
[2,4,1,5,6,7,8,9,3] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[9,3,1,2,4,5,6,7,8] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[8,3,1,2,4,5,6,9,7] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[6,3,1,2,4,7,8,9,5] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[5,3,1,2,6,7,8,9,4] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[9,4,1,2,3,5,6,7,8] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[7,4,1,2,3,5,8,9,6] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[6,4,1,2,3,7,8,9,5] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[5,9,1,2,3,4,6,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[5,8,1,2,3,4,6,9,7] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[5,7,1,2,3,4,8,9,6] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[9,6,1,2,3,4,5,7,8] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[8,6,1,2,3,4,5,9,7] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[9,7,1,2,3,4,5,6,8] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[8,9,1,2,3,4,5,6,7] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[8,7,1,2,3,4,5,9,6] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[7,6,1,2,3,4,8,9,5] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[5,6,1,2,3,7,8,9,4] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[5,4,1,2,6,7,8,9,3] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[4,3,1,9,2,5,6,7,8] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[9,3,1,8,2,4,5,6,7] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[9,4,1,5,2,3,6,7,8] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[9,4,1,8,2,3,5,6,7] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[9,7,1,6,2,3,4,5,8] => [[1,4,6,7,8,9],[2],[3],[5]] => 11010000
[8,7,1,9,2,3,4,5,6] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[9,4,1,6,2,8,3,5,7] => [[1,4,6,8,9],[2,5,7],[3]] => 11010100
[9,8,1,6,2,7,3,4,5] => [[1,4,6,8,9],[2,7],[3],[5]] => 11010100
[4,3,1,5,6,7,8,9,2] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[2,3,9,1,4,5,6,7,8] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[2,6,9,1,3,4,5,7,8] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[2,6,7,1,3,4,8,9,5] => [[1,2,3,7,8],[4,5,6,9]] => 00100001
[2,9,4,1,6,3,8,5,7] => [[1,2,5,7],[3,6,8,9],[4]] => 01101010
[9,3,4,1,2,5,6,7,8] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[9,3,7,1,2,4,5,6,8] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[9,3,8,1,2,4,5,6,7] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[9,5,4,1,2,3,6,7,8] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[8,5,4,1,2,3,6,9,7] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[9,7,4,1,2,3,5,6,8] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[9,8,4,1,2,3,5,6,7] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[8,7,5,1,2,3,4,9,6] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[6,7,9,1,2,3,4,5,8] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[9,7,8,1,2,3,4,5,6] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[6,7,8,1,2,3,4,9,5] => [[1,2,3,7,8],[4,5,6,9]] => 00100001
[9,8,5,1,7,2,3,4,6] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[9,5,4,1,8,7,2,3,6] => [[1,5,8,9],[2,6],[3,7],[4]] => 11101100
[2,3,4,9,1,5,6,7,8] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[2,3,7,9,1,4,5,6,8] => [[1,2,3,4,8,9],[5,6,7]] => 00010000
[2,9,4,5,1,3,6,7,8] => [[1,2,4,7,8,9],[3,6],[5]] => 01010000
[2,7,8,9,1,3,4,5,6] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[9,3,4,8,1,2,5,6,7] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[7,3,8,9,1,2,4,5,6] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[9,8,4,5,1,2,3,6,7] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[9,8,6,5,1,2,3,4,7] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[8,3,6,5,1,7,2,9,4] => [[1,3,6,8],[2,7,9],[4],[5]] => 10110101
[8,6,4,5,1,7,2,9,3] => [[1,4,6,8],[2,7,9],[3],[5]] => 11010101
[2,3,4,5,9,1,8,6,7] => [[1,2,3,4,5,9],[6,7],[8]] => 00001010
[9,7,4,5,6,1,2,3,8] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000
[8,9,4,5,6,1,2,3,7] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000
[2,3,4,5,6,9,1,7,8] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[2,3,4,5,6,8,1,9,7] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[2,3,4,9,6,7,1,5,8] => [[1,2,3,4,6,9],[5,8],[7]] => 00010100
[2,9,8,5,6,7,1,3,4] => [[1,2,5,6],[3,8,9],[4],[7]] => 01100100
[9,3,4,5,6,8,1,2,7] => [[1,3,4,5,6],[2,8,9],[7]] => 10000100
[9,8,4,5,6,7,1,2,3] => [[1,4,5,6],[2,8,9],[3],[7]] => 11000100
[8,3,4,5,6,7,1,9,2] => [[1,3,4,5,6,8],[2,9],[7]] => 10000101
[2,3,4,5,6,7,9,1,8] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,4,5,6,9,8,1,7] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[2,3,4,5,9,7,8,1,6] => [[1,2,3,4,5,7],[6,9],[8]] => 00001010
[2,9,4,5,6,7,8,1,3] => [[1,2,4,5,6,7],[3,9],[8]] => 01000010
[9,3,4,5,6,7,8,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[2,3,4,5,6,7,8,9,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[] => [] =>
[3,5,2,6,1,4,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,5,2,6,4,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,5,2,7,4,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,5,2,7,4,8,6,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[4,5,7,2,3,8,6,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,5,7,2,3,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,5,6,2,3,1,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,5,6,2,1,3,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[3,5,1,6,4,2,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[4,5,6,1,3,2,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,5,6,3,1,2,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,5,7,3,2,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,5,7,3,2,8,6,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,6,7,3,8,2,5,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,6,7,3,8,2,1,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[4,6,7,3,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,5,7,3,1,8,2,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,5,7,1,3,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,5,1,7,4,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,1,5,7,4,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,1,5,7,4,8,6,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,5,1,7,4,8,6,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[4,5,7,1,3,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,5,7,3,1,8,6,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,6,7,3,8,1,5,2] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,6,7,3,8,5,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[4,6,7,3,8,5,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,6,7,8,3,1,4,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,6,7,8,1,3,4,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,6,7,1,8,3,5,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,6,1,7,8,4,5,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,1,6,7,8,4,5,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,1,6,7,8,4,3,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,6,1,7,8,4,2,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,6,7,1,8,3,2,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,6,7,8,1,3,2,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,5,7,2,1,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,6,7,2,8,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,6,7,2,8,3,1,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,6,7,2,8,3,5,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,6,2,7,8,4,5,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[3,6,2,7,8,4,1,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,6,2,7,8,1,4,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[3,5,2,7,1,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,4,2,1,7,8,5,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,4,1,2,7,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,5,2,7,1,8,6,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,6,2,7,8,1,5,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[3,6,2,7,8,5,1,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[3,6,2,7,8,5,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,6,7,2,8,5,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[4,6,7,2,8,5,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[4,6,7,2,8,1,5,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,5,7,2,1,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,5,7,1,2,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,5,1,7,2,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,1,5,7,3,8,6,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,6,7,8,3,5,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,6,1,7,8,2,5,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[4,6,7,1,8,2,5,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,6,7,8,1,2,4,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[5,6,7,8,2,1,4,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,6,7,8,2,4,1,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[5,6,7,8,2,4,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,6,7,8,1,4,2,3] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,6,7,1,8,5,2,3] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,6,1,7,8,5,2,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,1,6,7,8,5,3,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,6,1,7,8,5,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,6,7,1,8,5,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,6,7,8,1,4,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,6,7,8,4,1,3,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,4,2,1,6,5,8,7,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]] => 011010101
[3,5,2,7,4,8,6,1,10,9] => [[1,2,4,6,9],[3,5,7,10],[8]] => 010101101
[3,5,2,7,4,9,6,10,8,1] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[4,6,8,3,9,5,10,7,2,1] => [[1,2,3,5,7],[4,6,8],[9],[10]] => 001010111
[5,7,8,9,4,10,6,3,2,1] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => 000101111
[6,7,8,9,10,1,4,5,3,2] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[6,7,8,9,10,1,4,5,2,3] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[6,7,8,9,10,4,3,2,1,5] => [[1,2,3,4,5],[6,10],[7],[8],[9]] => 000011110
[6,7,8,9,10,1,3,4,5,2] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[6,7,8,9,10,1,5,4,3,2] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[6,7,8,9,10,5,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[6,5,8,7,3,4,1,2] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[3,6,7,4,5,8,1,2] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[2,6,7,4,5,1,8,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,6,7,4,5,2,3,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[1,5,4,7,6,2,3,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[2,5,4,7,6,1,8,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,5,4,7,6,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,5,3,7,8,6,1,2] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[5,4,3,8,7,6,1,2] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[6,4,8,3,7,5,1,2] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,3,8,4,5,7,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,3,4,8,6,7,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,3,5,6,8,7,1,2] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[3,2,5,6,1,8,7,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,2,5,6,8,1,7,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,2,4,8,6,1,7,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[6,2,8,4,5,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,8,2,4,5,1,6,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,1,4,5,2,3,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[6,1,8,4,5,2,3,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,1,4,8,6,2,3,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,1,3,2,8,6,5,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[5,1,3,8,2,6,4,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[6,1,8,3,2,5,4,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,8,1,3,2,5,4,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,2,3,1,5,6,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,2,8,3,1,5,7,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[5,2,3,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[6,3,8,2,1,7,5,4] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[7,8,3,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[7,8,4,2,6,1,5,3] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[5,4,2,8,7,1,6,3] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[4,5,2,7,8,1,6,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[2,5,3,7,1,6,8,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,5,3,7,2,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,6,7,3,2,5,4,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,6,7,3,1,5,8,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,6,7,2,1,8,5,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[7,8,5,6,2,1,4,3] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[6,5,8,7,1,2,3,4] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,4,1,8,7,2,3,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,4,8,1,7,2,3,5] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[7,8,3,1,2,6,4,5] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,3,1,8,2,7,4,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[4,3,1,2,8,7,5,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,2,1,3,8,5,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[5,2,1,8,3,4,7,6] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[6,2,8,1,3,4,7,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[7,8,2,1,3,4,6,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,3,1,2,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[5,3,1,6,2,4,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,3,1,5,2,4,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,3,1,5,2,8,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,4,5,1,2,7,3,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,4,5,1,2,8,3,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,4,5,1,2,3,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[5,4,6,1,2,3,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[2,1,6,5,3,4,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,6,1,5,2,4,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,6,5,1,2,3,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,6,4,1,2,3,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,5,4,1,2,3,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,5,4,1,2,8,3,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,6,4,1,7,2,3,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,6,4,1,8,2,3,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,7,4,1,8,2,3,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[5,7,4,1,2,8,3,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,7,5,1,2,8,3,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,7,1,5,2,8,4,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,1,7,5,3,8,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,1,8,5,3,7,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,8,1,5,2,7,4,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,8,5,1,2,7,3,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,8,4,1,2,7,3,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,8,4,1,7,2,3,5] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[8,7,4,1,6,2,3,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,8,6,7,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,8,6,1,7,2,3,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,8,1,6,7,2,4,5] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,1,8,6,7,3,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,1,7,6,8,3,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,7,1,6,8,2,4,5] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,7,6,1,8,2,3,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[5,7,6,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[5,4,7,1,2,8,3,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,4,7,1,8,2,3,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,4,6,1,8,2,3,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,4,6,1,7,2,3,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,3,1,6,7,2,4,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,3,1,6,8,2,4,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,3,1,7,8,2,4,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,3,1,7,2,8,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,3,1,2,7,8,5,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,1,4,3,8,7,5,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,4,1,2,8,7,5,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[6,3,1,8,7,2,4,5] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,3,1,8,6,2,4,5] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[8,4,7,1,6,2,3,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,4,8,1,6,2,3,5] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,4,8,1,2,7,3,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[4,5,8,1,2,7,3,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,5,1,8,2,7,4,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,1,5,8,3,7,4,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,1,6,8,7,3,4,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,6,1,8,7,2,4,5] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,6,8,1,7,2,3,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[5,6,8,7,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[7,5,8,6,1,2,3,4] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[8,5,7,6,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,7,8,6,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,7,8,1,6,2,3,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,7,1,8,6,2,4,5] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,1,7,8,6,3,4,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[2,1,8,7,6,3,4,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,8,1,7,6,2,4,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,8,7,1,6,2,3,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,8,7,6,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,8,7,5,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,4,7,3,8,5,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[6,4,7,3,5,8,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,4,7,2,5,1,8,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,4,2,7,6,1,3,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,4,2,7,6,1,8,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,4,3,7,6,8,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,4,3,7,8,6,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,4,8,3,5,7,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,4,3,8,6,7,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,4,3,6,8,7,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[5,4,2,6,7,1,8,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,4,2,6,7,1,3,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,3,2,6,1,7,4,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,3,2,6,1,7,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[5,3,2,6,1,8,7,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,4,2,6,8,1,7,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,4,2,8,6,1,7,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[6,4,8,2,5,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,8,4,2,5,1,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,8,4,2,5,1,3,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,4,2,8,6,1,3,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,3,2,6,1,8,4,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[4,3,2,1,6,8,5,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,3,2,1,8,6,5,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[5,3,2,8,1,6,4,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,3,8,2,1,5,4,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,8,3,2,1,5,4,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,3,2,1,5,6,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,3,8,2,1,5,7,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,3,2,8,1,6,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[5,4,2,7,8,1,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,3,2,7,1,8,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,3,2,7,1,6,8,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[5,3,2,7,1,6,4,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,3,7,2,1,5,4,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,3,7,2,1,5,8,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[6,3,7,2,1,8,5,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[6,4,7,2,8,1,5,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,5,7,8,2,1,4,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,5,8,7,2,1,3,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,3,7,2,1,8,4,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,3,7,2,1,4,8,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,3,7,2,1,4,5,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,3,2,7,1,4,8,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[5,4,2,8,7,1,3,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,8,4,2,6,1,3,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,8,3,2,1,6,4,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,3,8,2,1,7,4,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[5,3,2,8,1,7,4,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,3,2,1,8,7,5,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,3,2,1,7,5,8,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[4,3,2,1,7,5,6,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,3,2,1,8,5,7,6] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,3,2,8,1,4,7,6] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,3,8,2,1,4,7,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,8,3,2,1,4,6,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,3,8,2,1,4,5,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[4,3,2,1,8,5,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,3,2,1,5,8,6,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,8,5,6,1,2,4,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[7,8,4,1,6,2,5,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[7,8,1,4,6,2,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[6,1,8,4,7,2,5,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[1,6,8,4,7,2,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,6,8,3,2,7,5,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,1,8,3,2,7,5,4] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,8,1,3,2,6,5,4] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,8,3,1,2,6,5,4] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,8,3,4,6,5,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,2,4,6,1,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[7,8,2,3,1,6,5,4] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,8,2,1,3,6,5,4] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,8,1,2,3,6,5,4] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[6,1,8,2,3,7,5,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[1,6,8,2,3,7,5,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,5,2,8,3,7,6,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[5,1,2,8,3,7,6,4] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,2,1,8,3,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,2,8,1,3,7,5,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,2,8,3,1,7,5,4] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,2,8,4,7,1,5,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,3,8,4,7,5,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[3,6,8,4,7,5,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,6,8,4,7,1,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,6,8,3,1,7,5,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[2,6,8,1,3,7,5,4] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,5,1,8,3,7,6,4] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[1,2,5,8,3,7,6,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,1,3,8,7,6,5] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,5,3,8,1,7,6,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,5,4,8,7,1,6,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,5,4,8,7,6,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,3,4,8,7,6,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,2,4,8,7,1,6,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,2,3,8,1,7,6,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,2,1,3,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,1,2,3,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[1,4,2,3,8,7,6,5] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,1,3,2,8,7,6,5] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,3,1,2,8,7,6,5] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,3,8,1,2,7,5,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,3,1,8,2,7,6,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,1,3,8,2,7,6,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[1,5,3,8,2,7,6,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,5,4,8,7,2,6,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,1,4,8,7,2,6,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,4,1,8,7,2,6,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[6,4,8,1,7,2,5,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,5,8,7,1,2,4,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,6,8,7,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,6,8,7,2,1,4,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,5,1,8,7,2,6,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[4,1,5,8,7,2,6,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[1,4,5,8,7,2,6,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,3,5,8,2,7,6,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,1,5,8,2,7,6,4] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,6,8,1,2,7,5,4] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,6,8,2,1,7,5,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,6,8,2,7,1,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[4,6,8,3,7,5,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,5,3,8,7,6,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,5,2,8,7,1,6,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,5,2,8,1,7,6,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[3,1,4,2,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[3,1,2,4,8,7,6,5] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,2,5,8,1,7,6,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,2,5,8,7,1,6,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[4,3,5,8,7,6,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,4,5,8,7,6,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,4,5,8,7,1,6,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,3,5,8,1,7,6,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,1,3,2,6,5,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,3,2,6,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,1,3,2,5,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,1,3,2,5,4,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,3,2,5,4,7,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,4,2,5,3,7,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,1,4,2,5,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,1,4,2,5,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,4,2,6,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[2,1,6,3,5,4,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,6,2,5,4,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,6,2,5,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[6,2,5,1,4,3,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,2,6,1,4,3,8,7] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,2,7,1,4,3,8,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,2,8,1,4,3,7,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[6,2,8,1,4,3,7,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[6,2,7,1,4,3,8,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[7,2,6,1,4,3,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,2,5,1,4,3,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[4,1,7,2,5,3,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,7,2,5,4,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,7,3,5,4,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,8,3,5,4,7,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,8,2,5,4,7,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,8,2,5,3,7,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,2,5,1,4,3,7,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,2,6,1,4,3,7,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,1,4,3,8,2,6,5] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,1,4,3,7,2,6,5] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,1,5,3,7,2,6,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,1,5,3,8,2,6,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,2,6,1,5,3,7,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,1,8,2,6,3,7,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,8,2,6,3,7,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,8,2,6,4,7,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,8,3,6,4,7,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,7,3,6,4,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,7,2,6,3,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,1,7,2,6,3,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[7,2,6,1,5,3,8,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,2,7,1,5,3,8,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[6,2,8,1,5,3,7,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[8,1,5,2,6,3,7,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,1,5,2,7,3,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,1,4,2,7,3,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,4,2,6,3,7,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,1,3,2,6,4,7,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,1,3,2,6,4,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,1,3,2,7,4,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,3,2,7,4,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,1,3,2,7,5,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[2,1,4,3,8,5,7,6] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,4,2,8,5,7,6] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,3,2,8,5,7,6] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,1,3,2,8,4,7,6] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[6,1,3,2,8,4,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,4,7,1,3,2,6,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,4,8,1,3,2,6,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,3,8,1,4,2,6,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[8,3,7,1,4,2,6,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,1,4,2,8,3,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,1,4,2,8,3,7,6] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,1,5,2,8,3,7,6] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,5,2,8,4,7,6] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,5,3,8,4,7,6] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,3,8,4,7,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,6,2,8,4,7,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,6,2,8,3,7,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,1,6,2,8,3,7,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[6,1,5,2,8,3,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,3,7,1,5,2,6,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,3,8,1,5,2,6,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[6,2,7,3,8,1,5,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,2,8,3,7,1,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,3,7,2,6,1,5,4] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[5,1,8,3,7,2,6,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[4,1,8,3,7,2,6,5] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[3,1,8,4,7,2,6,5] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,8,4,7,3,6,5] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,7,4,8,3,6,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[3,1,7,4,8,2,6,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[4,1,7,3,8,2,6,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[5,1,7,3,8,2,6,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[7,3,8,2,6,1,5,4] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[8,2,6,3,7,1,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,2,6,3,8,1,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[3,4,2,6,8,1,5,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,3,6,2,8,1,4,7] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[5,3,6,2,4,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,7,3,8,2,4,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,7,3,8,2,4,6,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[7,4,2,5,8,3,6,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[7,4,2,5,8,3,1,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[4,5,2,6,3,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[4,5,2,1,6,8,3,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,3,1,6,8,2,4,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,6,2,8,1,3,4,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,5,6,1,4,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,1,5,6,3,8,2,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,5,1,6,3,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[4,5,6,3,2,8,1,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[7,4,5,3,8,2,1,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,4,5,3,8,2,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[6,7,4,8,3,2,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,7,4,8,3,2,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,7,4,1,8,3,2,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[7,4,5,3,1,8,2,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[4,7,1,5,8,3,2,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[5,3,7,8,1,4,2,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[7,5,8,2,4,6,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[7,3,5,8,1,4,6,2] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,5,1,7,8,3,6,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[7,4,1,5,8,3,6,2] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[6,7,4,3,8,1,5,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,7,4,8,3,1,5,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[6,7,4,8,3,5,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,6,7,3,8,4,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,6,7,3,1,8,4,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[5,6,1,7,3,8,4,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[5,1,6,7,3,8,4,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[6,4,7,1,8,3,5,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[6,7,8,3,1,4,5,2] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[6,7,2,8,4,5,1,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,7,2,8,4,1,3,5] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[6,1,7,4,8,3,2,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,1,6,7,3,2,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,6,1,7,3,2,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[5,6,7,3,2,1,8,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,6,7,3,2,8,4,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[5,6,2,7,3,8,4,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[5,6,2,7,3,1,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[5,6,2,1,7,3,8,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[6,1,7,4,2,8,3,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[6,7,2,1,8,3,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,5,8,2,1,3,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,7,3,1,8,2,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[4,7,1,5,2,8,3,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[7,4,2,5,1,8,3,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,7,4,2,1,8,3,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,7,4,2,8,3,1,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[6,7,4,2,8,3,5,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[3,6,7,2,8,4,5,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,6,7,2,8,4,1,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,6,7,2,1,8,4,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,7,3,8,2,1,4,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,4,7,8,2,1,5,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,7,8,1,4,6,2,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[3,4,7,8,2,6,1,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[5,7,3,8,2,6,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,6,7,2,8,5,1,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,6,7,8,5,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,6,7,8,5,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,4,7,8,2,5,3,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,4,7,8,2,1,5,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,1,5,7,8,2,6,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,3,7,8,1,6,2,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[6,7,2,8,5,1,3,4] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[6,4,1,7,8,2,5,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,1,6,2,7,8,4,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,6,2,1,7,8,4,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[5,6,2,7,1,8,4,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[5,6,2,7,8,4,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[5,6,7,2,8,4,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,6,7,2,1,8,4,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[5,6,1,7,2,8,4,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[5,1,6,7,2,8,4,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[6,4,7,1,8,2,5,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,6,7,1,8,5,2,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[6,7,8,5,2,4,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,7,8,3,5,1,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[4,6,7,8,1,5,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,1,6,7,8,4,3,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,6,1,7,8,4,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[5,6,7,1,8,4,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[8,6,1,3,4,2,5,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[8,3,2,5,1,6,4,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,5,3,6,2,4,1,7] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,3,2,7,4,1,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,5,3,8,2,4,6,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,2,4,5,8,3,6,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[2,4,5,3,7,1,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[8,2,4,5,6,3,1,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,2,4,5,6,1,3,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,1,2,4,5,6,3,7] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,2,5,1,3,6,4,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,5,6,2,1,4,3,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,5,3,6,4,1,2,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,4,1,5,6,3,2,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,1,4,5,6,3,2,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[4,5,3,7,2,1,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[7,4,5,8,3,2,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[4,3,6,7,2,8,5,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[4,3,6,7,2,8,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[1,4,3,6,7,2,8,5] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[4,5,3,7,1,8,2,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[4,1,5,3,7,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,3,4,7,1,2,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,5,8,2,1,4,6,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,5,3,8,4,1,6,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,4,5,8,3,6,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[4,3,6,7,8,1,5,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[1,6,4,7,8,3,5,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[6,4,7,8,3,5,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[3,5,6,7,8,4,1,2] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,1,5,6,7,8,4,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,6,1,7,8,3,5,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[3,6,7,1,4,8,5,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[6,2,4,1,7,8,5,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[2,6,7,1,4,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,3,6,7,8,1,2,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,5,3,6,7,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,5,6,7,8,2,1,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,5,6,7,8,2,4,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,2,7,1,3,8,4,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,3,1,7,8,2,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,5,2,7,8,1,3,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,2,6,7,8,3,1,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,2,6,7,8,3,5,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,6,2,7,4,8,5,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,6,2,7,4,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,2,1,6,4,7,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,7,4,2,1,5,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,7,3,4,2,5,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[4,7,2,1,3,5,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[7,8,4,2,1,3,6,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[7,8,1,3,4,2,6,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,3,4,2,1,6,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,3,2,7,1,8,5,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[3,6,2,7,1,8,5,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[6,7,3,8,2,5,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[6,4,7,8,5,2,3,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[2,6,4,7,8,1,5,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,6,2,7,8,1,5,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[7,4,5,8,6,2,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[7,4,1,5,8,6,2,3] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[7,5,3,8,6,1,2,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,5,8,2,1,6,3,4] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,2,7,1,3,8,5,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,3,1,7,8,2,5,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,6,1,7,8,5,2,3] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[5,1,2,6,7,8,4,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[5,2,6,7,8,4,1,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,2,6,7,8,4,3,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,5,6,7,8,4,1,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,5,2,6,7,8,4,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,6,4,7,8,5,2,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[2,6,7,1,3,8,5,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[6,7,8,2,1,5,4,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,7,3,8,5,1,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,4,7,8,5,3,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,5,2,3,7,6,1,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[6,4,3,7,2,5,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,4,3,6,5,1,2,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[1,5,6,3,4,8,7,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,6,2,7,3,5,1,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,2,6,7,4,5,1,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,7,2,6,5,3,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,7,6,2,4,3,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,7,5,4,8,3,6,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[8,7,5,4,1,3,2,6] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[6,8,5,4,2,1,3,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[5,8,6,2,4,1,3,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,8,2,6,5,1,3,7] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[3,2,8,6,5,1,4,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,1,2,6,5,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[5,1,6,2,4,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[6,1,5,4,2,8,7,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,1,5,4,8,2,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,1,5,4,7,6,2,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[1,8,6,7,4,5,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,1,6,7,4,5,2,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,1,6,8,4,2,5,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,1,7,8,2,4,5,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,1,7,2,8,4,6,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,2,7,8,5,6,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,2,1,7,8,5,6,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[3,2,8,7,1,5,4,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,8,2,7,1,5,3,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,7,2,1,4,3,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,8,7,1,2,4,3,5] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[7,8,6,1,4,2,3,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[8,7,6,1,4,3,2,5] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[1,7,6,8,4,3,5,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,6,7,8,3,4,5,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[8,6,7,1,3,4,2,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,6,8,1,3,2,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,7,8,2,1,3,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,7,2,8,1,3,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,2,6,8,4,1,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,6,2,8,3,1,5,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[5,6,8,2,3,1,4,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,5,8,3,2,1,4,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,5,8,3,1,2,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,5,7,3,1,4,2,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[1,5,7,3,8,4,6,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,4,3,7,8,5,6,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,4,3,7,1,5,2,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,4,3,8,2,1,5,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[4,5,2,3,8,1,6,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,2,5,4,8,1,6,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,5,2,3,1,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[6,4,3,1,2,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,4,3,1,8,2,6,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,4,3,1,7,6,2,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[1,5,8,3,7,6,4,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[8,5,1,3,7,6,2,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,5,1,3,8,2,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[6,5,1,3,2,8,7,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,6,1,2,3,8,7,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,6,2,1,3,8,7,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,2,6,1,4,8,7,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[3,2,7,1,8,4,6,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,7,2,1,8,3,6,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,7,1,2,8,3,6,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,1,8,2,3,5,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[7,6,1,8,3,2,5,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,6,1,7,3,5,2,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[1,6,8,7,3,5,4,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[1,7,8,6,5,3,4,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[8,7,1,6,5,3,2,4] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[7,8,1,6,5,2,3,4] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,8,1,7,2,5,3,4] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,8,1,2,7,6,3,4] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,8,2,1,7,6,3,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[3,2,8,1,7,6,4,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,1,2,8,7,6,5,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[5,1,8,2,7,6,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[6,1,8,7,2,5,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[7,1,8,6,5,2,4,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,1,7,6,5,4,2,3] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[3,1,2,6,5,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,1,6,2,4,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[3,1,5,2,4,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,5,1,2,3,8,7,6] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,6,1,2,3,8,7,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[1,6,5,3,4,8,7,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,1,5,2,4,8,7,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[6,5,1,2,3,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[6,4,1,2,3,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,4,1,2,3,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,4,1,2,7,3,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[6,4,1,7,2,3,5,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[6,4,1,8,2,3,5,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,4,1,2,8,3,6,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,5,1,2,8,3,6,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,1,5,2,8,4,6,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,7,5,3,8,4,6,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,8,5,3,7,4,6,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[8,1,5,2,7,4,6,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,5,1,2,7,3,6,4] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,4,1,2,7,3,6,5] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,4,1,7,2,3,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,4,1,6,2,3,5,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,6,1,7,2,3,5,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,1,6,7,2,4,5,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,8,6,7,3,4,5,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,7,6,8,3,4,5,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[7,1,6,8,2,4,5,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,6,1,8,2,3,5,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,7,1,2,8,3,6,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,1,7,2,8,4,6,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,2,7,8,5,6,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[1,4,3,8,7,5,6,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,1,2,8,7,5,6,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,1,2,8,7,5,6,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,1,8,2,7,4,6,5] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,1,8,7,2,4,5,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,1,7,6,2,4,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,7,1,6,2,3,5,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,8,1,6,2,3,5,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,8,1,7,2,3,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,8,1,2,7,3,6,5] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,8,1,2,7,3,6,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,1,8,2,7,4,6,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[1,5,8,3,7,4,6,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,6,8,7,3,4,5,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[6,1,8,7,2,4,5,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,8,1,7,2,3,5,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,8,7,1,2,3,4,5] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[5,8,7,1,2,3,4,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[5,8,6,1,2,3,4,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[5,7,6,1,2,3,4,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[7,8,1,6,2,3,5,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,1,8,6,2,4,5,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[1,7,8,6,3,4,5,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,8,7,6,3,4,5,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[8,1,7,6,2,4,5,3] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,7,1,6,2,3,5,4] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[3,2,5,1,6,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,2,5,4,7,1,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,2,5,3,7,6,8,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,2,5,3,7,1,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,2,5,3,6,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,2,5,1,6,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,1,5,4,6,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,5,3,6,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,3,5,1,6,2,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,3,5,2,7,1,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[4,3,6,2,7,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,3,6,2,7,1,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[4,3,6,1,7,2,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,3,5,1,7,2,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,1,5,4,7,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,5,4,7,3,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,5,4,7,6,8,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,5,3,7,6,8,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,3,5,1,7,6,8,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,3,6,1,7,5,8,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,3,6,5,7,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,3,6,4,7,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,3,6,4,7,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,3,6,1,7,4,8,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,1,6,3,7,4,8,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,6,3,7,5,8,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,6,4,7,5,8,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,4,7,5,8,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,4,7,3,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,6,4,7,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,6,3,7,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,1,6,3,7,2,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,3,6,1,7,2,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,3,6,2,7,1,8,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,3,6,2,7,4,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,2,6,3,7,4,8,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,2,6,3,7,1,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,2,6,1,7,3,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,5,1,7,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,6,1,7,3,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,6,3,7,1,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,2,6,3,7,5,8,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,2,6,4,7,5,8,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,2,6,4,7,1,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,2,6,1,7,4,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,2,5,1,7,4,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,2,4,1,7,5,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,1,4,2,7,6,8,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,2,5,1,7,6,8,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,2,6,1,7,5,8,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,2,6,5,7,1,8,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,2,6,5,7,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,2,6,5,7,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,2,6,1,7,5,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,2,5,1,7,6,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,1,5,2,7,6,8,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,5,2,7,6,8,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,5,3,7,6,8,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,3,7,5,8,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,6,2,7,5,8,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,6,2,7,5,8,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,1,6,2,7,4,8,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,2,6,1,7,4,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,2,6,4,7,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,2,6,4,7,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,4,6,2,7,3,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,4,6,2,7,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,4,6,1,7,2,8,3] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,6,4,7,2,8,3] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,6,5,7,2,8,3] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,6,5,7,2,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,6,5,7,3,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,6,5,7,4,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,1,6,5,7,3,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,1,6,4,7,3,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,4,6,1,7,3,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,4,6,3,7,1,8,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,3,5,2,1,6,4,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,6,3,5,2,4,1,7] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[3,7,5,2,4,1,8,6] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[8,3,7,5,2,4,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,2,4,5,7,3,6,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[2,4,5,7,3,1,8,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[8,2,4,6,5,3,1,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,2,5,4,6,1,3,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,6,3,5,1,4,2,7] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,6,1,4,5,3,2,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,1,5,6,4,3,2,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[5,7,4,3,2,1,8,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[8,5,7,4,3,2,6,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[4,6,8,3,2,7,5,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,7,6,3,2,8,1,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,4,6,7,3,2,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[5,4,7,3,1,8,2,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[1,7,4,5,3,2,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[3,7,5,1,4,2,8,6] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[5,7,4,2,1,3,8,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[8,5,7,4,2,1,6,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,3,7,5,1,4,6,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,4,1,7,5,3,6,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[4,6,3,8,7,1,5,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,7,4,8,6,3,5,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[8,4,7,6,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[3,6,5,8,7,4,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,1,5,8,6,7,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,8,1,6,7,3,5,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[3,6,4,1,8,7,5,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[8,2,6,1,4,7,5,3] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[2,7,6,8,1,4,3,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,7,1,6,4,8,2,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,7,3,5,6,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,3,6,7,5,8,2,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,7,6,5,8,2,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,6,8,5,7,2,4,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,3,5,7,6,8,1,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,1,6,5,7,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,2,7,6,8,3,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[4,2,6,8,7,3,5,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,8,2,4,6,7,5,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,7,2,6,4,8,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,2,6,1,4,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[5,3,7,2,1,8,4,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[4,7,3,2,1,5,8,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[8,7,6,1,3,4,2,5] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,5,7,3,2,1,6,4] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,3,6,7,2,1,5,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[3,7,8,6,2,1,5,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[8,7,6,3,5,2,4,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[2,7,4,8,1,6,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,6,8,2,1,7,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,4,1,5,7,2,6,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,5,3,7,1,6,2,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,5,7,2,1,3,6,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,2,6,7,1,3,5,4] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,3,6,1,7,5,2,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,6,1,8,7,2,5,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[8,1,2,5,6,7,4,3] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,2,6,5,7,4,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[2,1,7,8,5,6,4,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[8,2,5,7,6,4,3,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[2,7,6,8,5,4,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,7,2,5,8,6,4,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,7,4,8,2,6,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[3,7,8,1,6,5,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[2,7,8,6,1,3,5,4] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,7,6,3,5,1,4,2] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,4,7,6,5,1,3,2] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,7,1,5,6,4,3,2] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[8,1,6,7,5,4,3,2] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[6,5,3,1,2,4,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[4,6,3,5,1,2,8,7] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[8,5,3,7,2,1,4,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,8,1,4,5,7,3,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,7,2,4,5,1,3,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,6,2,4,5,1,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,6,1,4,5,3,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,1,2,4,5,3,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[5,6,3,2,1,4,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,4,3,6,1,2,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,3,1,4,5,2,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[3,1,6,4,5,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,3,7,4,5,1,2,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[5,8,7,4,2,6,3,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[2,8,7,4,1,6,3,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[8,1,7,4,2,6,3,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[3,7,8,4,5,1,2,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[2,1,8,7,5,3,4,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,1,6,8,5,7,3,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,6,3,8,1,7,2,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[7,6,1,4,5,8,3,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[3,7,6,4,5,8,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[8,5,7,4,1,6,3,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[5,1,8,4,7,6,2,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[2,5,8,4,7,6,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,4,8,3,5,6,7,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,1,8,3,5,6,7,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[3,8,4,2,5,6,7,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[8,4,1,3,5,6,7,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,5,8,4,3,6,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[6,5,3,8,4,1,7,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,1,5,8,4,6,7,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,1,4,8,3,6,7,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[6,4,3,8,2,1,7,5] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[7,3,8,4,2,6,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,3,1,2,5,6,7,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[3,1,8,2,5,6,7,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,3,8,1,5,6,7,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,3,8,2,5,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,8,2,3,5,6,7,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,8,2,1,5,6,7,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[2,8,1,3,5,6,7,4] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[8,1,2,3,5,6,7,4] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[7,8,2,4,3,6,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,3,2,4,1,7,5] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,1,8,3,4,6,7,5] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,7,8,5,4,3,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,7,3,8,1,4,2,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[7,1,8,4,5,3,2,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,7,8,4,5,3,1,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,7,1,4,3,6,2,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[3,8,7,4,2,6,1,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[5,7,8,4,3,6,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,6,3,8,4,2,7,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[4,8,3,6,2,1,7,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,6,3,1,4,2,7,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,5,3,8,2,4,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,4,3,1,8,5,7,6] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,1,3,2,6,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,5,3,6,2,8,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,6,3,5,1,2,7,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[5,8,3,2,6,1,7,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,5,3,8,6,2,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,5,8,4,7,6,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,8,2,4,7,6,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[8,7,5,4,1,6,2,3] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[2,7,6,4,5,8,1,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,1,6,4,5,8,2,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,7,3,6,1,8,2,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[2,1,7,6,5,8,3,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,1,8,5,3,6,7,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[6,8,3,5,2,1,7,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,5,4,2,6,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[8,1,4,2,5,6,7,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,8,4,1,5,6,7,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,8,1,2,5,6,7,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,4,8,1,5,6,7,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,4,2,8,5,6,7,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,1,8,5,6,7,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[4,1,2,8,5,6,7,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[8,4,2,1,5,6,7,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,5,2,4,8,6,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,5,3,2,8,1,7,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[2,1,5,3,8,6,7,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[6,4,3,5,8,1,7,2] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,3,5,4,8,6,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,3,4,1,5,6,7,2] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,3,1,8,5,6,7,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,1,4,8,5,6,7,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,5,3,7,2,8,4,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,3,7,4,5,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,7,2,4,5,8,3,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,1,7,4,8,6,3,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,5,7,4,8,6,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,6,3,7,1,8,4,2] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,8,7,4,5,2,1,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[3,7,5,4,8,6,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[5,7,1,4,8,6,2,3] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,6,3,1,8,2,7,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[4,6,3,5,8,2,7,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,6,3,8,1,2,7,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,7,8,4,1,6,2,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[3,2,5,1,6,8,4,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[3,6,2,5,4,8,1,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,5,2,4,7,1,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,5,8,2,4,7,6,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[4,2,5,8,3,7,6,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,2,6,5,3,8,1,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[5,4,2,1,6,8,3,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[6,3,5,1,4,8,2,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,6,1,5,3,8,2,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,1,6,4,3,8,2,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[5,4,3,2,7,1,8,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[5,4,3,8,2,7,6,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[4,3,6,2,8,7,5,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,3,7,6,2,1,8,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,4,3,1,7,2,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,5,4,3,1,8,2,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[1,4,7,5,8,3,2,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,1,3,5,8,4,2,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,2,5,8,4,1,3,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,8,5,7,4,6,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,5,8,7,1,4,6,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[1,4,5,8,7,3,6,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,5,4,8,7,3,6,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,4,3,8,1,7,5,2] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[4,3,7,1,8,6,5,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,8,3,7,6,5,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[5,3,8,7,6,4,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[7,5,3,1,8,6,4,2] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[1,8,6,5,3,7,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,5,8,6,3,7,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,6,1,8,7,3,5,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[6,8,7,3,1,4,5,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,2,8,7,4,5,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,6,2,8,4,1,3,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,3,1,6,8,4,2,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[1,7,6,4,8,3,2,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,7,1,6,3,2,8,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,1,7,5,3,2,8,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[7,6,5,3,2,1,8,4] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[6,5,3,2,8,7,4,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[5,2,6,3,8,7,4,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[5,2,7,6,3,1,8,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[6,5,2,1,7,3,8,4] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[5,2,7,4,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,7,2,6,3,1,8,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[2,4,8,6,3,7,5,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,8,6,2,4,7,5,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,3,6,2,4,1,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[3,6,7,2,1,4,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,3,7,8,2,1,5,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,3,7,1,4,6,2,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[3,8,2,5,7,1,6,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[8,3,6,2,7,1,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,8,3,6,2,1,5,4] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[8,7,3,6,2,5,4,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[4,7,8,2,1,6,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,2,6,8,1,7,5,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,4,8,2,7,1,6,3] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[4,8,1,5,7,2,6,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[5,8,3,7,1,6,2,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,7,2,6,1,3,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,6,2,7,5,1,3,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[3,6,8,1,7,5,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[5,1,6,8,2,7,4,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,5,2,8,1,7,4,3] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[5,2,7,1,8,6,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[5,8,2,7,6,4,3,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[6,2,8,7,5,4,3,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[7,6,2,1,8,5,4,3] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[6,1,7,2,8,5,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[7,5,1,8,2,6,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,7,1,8,6,2,5,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[7,8,3,1,6,5,2,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,7,4,6,1,5,3,2] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[8,5,7,1,6,4,3,2] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[6,8,1,7,5,4,3,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[7,1,8,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[5,4,2,3,7,6,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,4,2,7,3,5,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,4,2,6,3,5,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,2,6,3,1,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,2,7,6,4,5,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,7,2,6,3,5,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,7,6,2,3,4,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[1,6,5,2,3,8,4,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,5,2,8,3,4,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,8,5,2,3,1,4,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,8,6,2,3,1,4,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,8,2,6,3,1,5,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,2,8,6,4,1,5,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,2,1,6,4,8,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[7,1,5,2,8,3,4,6] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[1,8,5,2,7,3,4,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,8,6,7,2,3,4,5] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[8,1,6,7,2,3,4,5] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[7,1,6,8,2,3,4,5] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,2,1,7,8,4,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,2,8,7,1,4,5,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,8,7,2,1,3,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[1,7,6,8,2,3,4,5] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[6,5,8,2,3,1,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,5,7,2,1,3,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,4,2,8,3,1,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,4,2,3,8,1,6,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,2,5,4,1,8,6,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,5,2,3,1,8,6,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,4,2,3,1,8,6,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,4,2,1,3,8,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,4,2,1,8,3,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,4,2,1,7,3,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,4,2,8,7,3,5,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,5,8,2,7,3,4,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[8,5,1,2,7,3,4,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,5,1,2,8,3,4,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[6,5,1,2,3,8,4,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[4,6,2,1,3,8,5,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,2,6,1,4,8,5,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[3,2,7,1,8,4,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,7,2,1,8,3,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,6,1,8,2,3,4,5] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,6,1,7,2,3,4,5] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,6,8,7,2,3,4,5] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,7,8,6,2,3,4,5] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[7,8,1,6,2,3,4,5] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,8,1,7,2,3,4,5] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,8,2,1,7,3,5,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,2,8,1,7,4,5,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,2,1,8,7,4,5,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,1,8,2,7,3,4,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[6,1,8,7,2,3,4,5] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,1,7,6,2,3,4,5] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[1,8,7,6,2,3,4,5] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[6,3,5,1,2,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[4,3,5,6,1,2,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,3,7,5,2,1,4,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,3,7,5,1,8,4,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,5,2,7,1,8,3,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,5,2,7,4,1,3,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[2,6,1,5,4,3,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,4,3,5,1,2,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[5,3,1,4,6,2,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[3,1,4,6,5,2,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,7,4,6,2,8,3,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[8,1,4,7,2,6,3,5] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[3,4,7,8,5,2,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,1,8,5,7,3,4,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[8,6,3,5,1,7,4,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[5,8,2,4,6,7,3,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,4,8,6,5,7,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[7,5,4,8,1,6,3,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[5,1,4,6,8,2,7,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[2,5,4,6,7,1,8,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[2,4,6,3,7,5,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,1,6,3,8,5,7,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,7,4,2,8,6,5,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[7,4,1,3,5,8,6,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,5,8,4,1,7,3,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[8,5,3,7,4,1,6,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,1,4,8,3,7,6,5] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[7,4,3,8,2,1,6,5] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[6,3,7,4,1,8,2,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[8,3,1,2,5,7,6,4] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,1,8,2,7,6,5,4] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[2,3,8,1,6,7,5,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,3,7,2,6,8,5,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,7,2,3,8,5,6,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,8,2,1,7,5,6,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[2,8,1,3,6,5,7,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,7,8,5,4,3,1,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,7,1,6,3,4,2,5] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[3,8,6,7,2,4,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,3,8,7,4,2,6,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,3,8,7,2,1,6,5] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[8,3,6,1,4,2,7,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,3,5,8,2,4,1,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[2,3,4,1,8,5,7,6] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,1,3,2,6,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,3,5,6,2,7,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,3,6,1,8,7,2,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,6,2,8,7,4,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[7,8,5,6,1,4,2,3] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,8,6,5,4,7,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,1,6,4,5,7,2,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,8,3,6,1,7,2,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[2,1,8,6,5,7,3,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,1,7,5,3,6,8,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[6,7,3,5,2,1,8,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,1,4,2,5,6,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,7,4,1,6,5,8,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,6,1,2,8,7,3,5] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,4,1,5,8,7,6,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,1,2,5,8,6,7,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,4,2,1,5,8,7,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,5,2,4,6,1,7,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,5,3,2,6,8,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[2,1,5,3,6,8,7,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[7,3,5,4,6,1,8,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,3,4,1,5,7,8,2] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,3,1,5,7,6,8,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,1,4,5,6,8,7,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,5,2,6,3,1,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[6,5,2,1,4,3,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,5,2,7,4,8,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,5,2,7,4,1,6,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,3,7,5,2,1,6,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,3,7,5,2,8,4,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,1,6,5,4,2,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[5,6,3,2,4,1,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[3,6,2,4,1,5,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,6,1,3,5,4,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,7,2,3,4,8,5,1] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[8,7,2,3,4,1,6,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,1,7,3,8,4,6,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,5,7,3,8,6,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[7,6,1,3,5,8,4,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[3,6,7,4,1,8,5,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[5,6,3,7,4,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,1,6,7,4,8,5,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,8,7,4,3,6,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[5,8,3,7,4,2,6,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[3,8,7,4,1,2,6,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,8,1,3,5,2,6,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,8,7,3,2,6,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[2,8,6,3,1,5,7,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[8,1,6,3,2,5,4,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,8,4,1,6,3,7,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,8,1,2,7,6,3,5] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,8,4,2,5,7,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,8,3,5,2,7,4,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[2,1,5,3,8,7,6,4] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[6,5,3,2,8,7,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[7,5,2,4,8,1,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,4,2,8,5,7,6,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,4,1,8,7,6,5,3] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[8,4,2,1,7,5,3,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,3,1,8,6,7,5,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,1,4,8,6,5,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[7,1,6,5,4,8,2,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[3,7,5,6,8,4,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[5,7,1,6,8,2,4,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[8,6,2,5,1,7,4,3] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[5,6,2,1,8,7,3,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[4,6,2,5,8,3,7,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[7,5,2,6,3,8,1,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,1,2,3,6,8,7,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,4,3,1,8,5,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[7,5,2,8,3,4,6,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,6,2,8,4,3,1,7] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,7,2,8,1,5,3,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[8,7,2,1,4,5,6,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[3,6,8,7,1,5,4,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,7,8,6,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[7,1,8,5,4,3,6,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[2,7,8,4,5,3,6,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,7,3,8,1,4,6,2] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[2,1,7,8,5,4,6,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[2,1,5,8,4,6,3,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,5,3,8,4,1,2,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,5,8,4,3,6,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[2,4,8,3,5,6,1,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[4,1,8,3,6,5,2,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,4,8,1,7,2,5,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[8,4,1,3,7,2,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,1,8,2,4,7,6,5] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,3,8,1,4,6,7,5] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,3,8,2,5,1,7,6] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,3,8,4,2,5,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[7,4,3,8,2,5,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,1,4,8,3,5,7,6] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[6,8,2,4,3,5,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,8,2,3,5,1,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,8,2,1,4,6,5,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[2,8,1,3,4,5,7,6] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[2,8,4,1,6,5,3,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,8,4,1,6,5,7,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,8,7,6,1,4,3,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,8,5,6,7,4,3,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[7,5,8,6,1,4,2,3] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,5,7,6,1,4,2,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[3,5,7,2,4,1,6,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[7,5,8,2,4,1,6,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[2,8,5,3,4,7,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,8,5,3,4,1,7,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,8,5,3,4,1,6,7] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[2,8,7,6,1,4,5,3] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[2,8,5,3,6,1,7,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,8,5,6,7,4,1,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,8,5,3,4,7,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,8,5,3,4,6,1,7] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[2,8,5,3,4,6,7,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[3,5,7,2,4,6,1,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,5,2,7,3,1,4,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,5,2,8,3,1,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[6,5,2,8,3,1,4,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,5,8,2,4,6,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[7,5,8,6,1,4,3,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[6,5,8,2,1,3,7,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[3,5,6,2,1,8,7,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[3,5,7,6,1,4,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,5,7,2,4,1,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,5,7,2,4,6,8,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,5,2,7,3,1,8,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[4,5,2,6,3,1,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[4,1,2,3,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,5,2,7,3,4,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,1,6,7,4,3,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[5,1,2,6,4,8,7,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[5,1,2,8,6,4,7,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[5,1,6,8,7,3,4,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,5,2,8,3,7,4,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,1,2,3,8,7,5,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,1,2,3,8,6,5,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,1,2,3,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[4,1,2,3,7,6,5,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,1,2,3,8,5,7,6] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[7,1,6,8,4,3,5,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[6,1,2,8,4,5,7,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,6,8,2,3,1,7,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[6,5,8,2,4,3,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[6,5,8,2,4,3,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,5,2,8,3,4,1,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,5,2,8,3,7,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,5,2,7,3,4,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,1,6,7,4,3,2,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,1,6,8,7,3,2,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,1,6,8,4,3,2,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,7,8,6,3,4,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,1,8,3,6,5,7,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,1,8,3,6,2,7,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,1,4,8,6,2,7,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,1,4,8,6,5,2,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[7,1,6,5,8,3,2,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[4,1,6,7,8,3,2,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,1,6,5,7,3,2,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,5,2,6,3,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[4,5,2,7,3,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,5,6,2,4,8,7,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,5,6,2,4,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,7,5,6,8,4,1,2] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[3,6,5,2,8,1,7,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,1,2,5,8,4,7,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,1,6,5,8,3,4,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,5,2,6,3,8,4,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,1,2,3,5,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,1,2,3,7,8,6,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,5,2,7,3,8,6,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[4,1,6,7,8,3,5,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[4,1,2,6,8,5,7,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[4,1,2,5,6,8,7,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,5,2,6,3,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,8,5,6,1,4,3,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[7,8,4,2,1,5,3,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,2,1,6,5,3,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,4,1,2,5,7,3,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[2,4,8,1,5,7,3,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,3,8,1,7,2,5,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,3,1,4,7,2,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,8,3,4,5,1,6,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,3,5,4,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,8,4,1,2,3,6,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[7,8,3,6,5,4,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[7,8,2,1,5,3,4,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,8,2,6,4,1,3,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,8,2,5,6,4,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,1,6,5,4,3,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[6,2,1,7,5,4,3,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[2,1,8,7,5,4,3,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,3,8,2,6,4,7,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,3,7,1,6,4,8,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,3,6,2,7,4,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,1,2,5,8,7,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,3,1,8,4,2,7,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,4,2,1,5,3,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,4,3,7,5,8,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[4,3,8,7,5,6,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[2,4,7,1,5,3,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,3,7,6,4,2,8,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,1,7,5,6,8,4,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,7,2,8,6,4,1,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[3,8,1,7,6,4,5,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[1,8,5,7,3,6,4,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,7,5,8,3,6,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,5,6,8,2,4,7,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,6,8,5,3,1,4,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,6,1,4,7,3,5,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,6,7,3,8,4,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,2,8,1,4,7,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[4,6,7,5,2,1,3,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,5,6,7,2,8,1,3] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,5,7,6,1,8,3,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,5,8,6,2,7,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,6,5,8,3,2,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,6,5,7,1,2,8,3] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,7,5,6,3,1,8,2] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[5,1,6,3,4,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,7,1,4,2,3,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,7,6,4,3,8,1,2] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[6,3,4,5,8,7,1,2] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[6,2,4,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[6,2,3,5,4,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,1,3,4,5,8,7,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[5,1,4,2,7,6,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[1,6,2,4,7,8,3,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[5,7,2,4,1,6,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,1,4,2,8,5,3,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[6,7,5,8,1,4,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,7,6,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[5,8,7,6,2,3,1,4] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[4,1,7,2,6,5,3,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,8,2,1,5,6,3,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[4,2,7,8,1,6,3,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[2,1,8,7,6,5,3,4] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,1,4,7,8,2,6,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,1,7,4,5,6,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,2,7,1,6,3,8,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,3,7,5,6,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[4,8,6,3,5,7,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,8,1,2,5,3,7,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,8,6,5,2,4,1,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,8,5,6,1,4,7,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,3,7,8,2,1,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[5,2,8,7,1,6,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[1,6,8,7,5,2,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,6,7,8,5,1,4,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,7,6,8,5,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[3,7,8,5,1,2,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,7,1,6,4,2,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,1,8,6,2,3,5,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,7,8,6,3,5,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,8,7,6,5,4,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[2,1,7,6,5,3,4,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,8,1,6,4,5,3,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[2,8,7,5,1,4,3,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,8,6,7,5,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[2,7,8,6,5,4,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,4,2,7,1,3,8,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,4,2,5,1,3,8,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,5,3,6,1,7,2,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[7,3,6,2,4,8,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,3,7,1,2,5,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[3,6,2,7,1,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[5,3,6,7,1,2,8,4] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[6,3,7,4,1,2,8,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,7,1,5,2,3,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,7,5,1,2,4,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[7,6,4,2,3,8,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,6,4,2,3,7,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[4,7,6,3,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[5,7,4,2,3,8,1,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[3,7,6,1,4,8,2,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[6,4,7,5,2,8,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,4,8,5,2,6,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[5,8,2,6,3,7,1,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,8,6,2,4,7,1,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,8,6,2,7,1,3,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,6,5,8,1,3,4,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[2,5,7,4,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,4,6,7,2,8,1,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[3,5,7,1,4,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[5,3,7,2,4,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,4,7,3,8,1,2,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,4,6,3,8,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,4,6,3,7,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,4,1,6,7,2,3,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,4,1,6,8,2,3,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,5,3,7,1,8,2,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,5,1,2,7,8,3,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,3,6,4,7,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,3,7,4,8,5,1,2] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,7,1,5,8,6,2,3] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[7,5,1,2,8,6,3,4] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[7,6,1,8,5,2,3,4] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,6,1,7,5,2,3,4] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,7,2,8,1,6,3,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,3,7,8,5,1,2,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,6,8,2,7,1,4,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[2,4,8,7,1,3,5,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,3,8,7,1,2,5,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,3,8,7,1,2,4,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[8,3,7,6,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,4,7,6,1,2,3,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[3,5,8,7,1,2,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,5,8,7,1,3,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[6,8,4,7,5,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[5,8,7,1,6,2,3,4] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[2,8,7,6,1,3,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,8,7,6,1,2,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,8,7,6,1,2,3,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,6,3,1,4,2,8,7] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[7,5,3,8,2,1,6,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[3,8,7,4,5,1,6,2] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,1,7,8,5,3,6,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[5,7,3,8,1,2,6,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[8,7,1,4,5,3,2,6] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[2,7,8,4,1,6,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[7,1,8,4,2,6,5,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,5,1,4,8,6,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[6,5,3,1,8,4,7,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,6,3,1,2,5,7,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,7,1,4,2,6,5,3] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[2,3,4,5,6,7,8,1,9] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[2,3,4,5,6,8,9,1,7] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,4,5,7,8,9,1,6] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,4,6,7,8,9,1,5] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,5,6,7,8,9,1,4] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,4,5,6,7,8,9,1,3] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[3,4,5,6,7,8,9,1,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,4,5,6,7,8,9,10,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[2,3,4,5,6,7,8,9,1,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[2,3,4,5,6,7,8,10,1,9] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,3,4,5,6,1,9,7,8] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[2,3,4,5,6,7,9,10,1,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,3,4,5,6,8,9,10,1,7] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,3,4,5,7,8,9,10,1,6] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,3,1,6,7,8,9,4,5] => [[1,2,4,5,6,7],[3,8,9]] => 01000010
[2,3,4,6,7,8,9,10,1,5] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,1,5,6,7,8,9,3,4] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[2,3,5,6,7,8,9,10,1,4] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[1,4,5,6,7,8,9,2,3] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,4,5,6,7,8,9,10,1,3] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[3,4,5,6,7,8,9,10,1,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[3,6,4,5,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[5,3,2,7,4,6,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,5,3,6,2,4,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,3,2,5,1,8,4,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,5,3,6,2,7,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,2,6,3,4,7,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,2,6,3,4,5,8,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[6,2,7,3,4,5,8,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,2,5,7,3,6,8,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,4,7,6,2,3,8,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,7,3,5,2,4,8,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,7,6,2,4,5,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,7,6,3,4,5,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[6,5,3,1,2,8,4,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,6,5,2,3,7,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,5,2,1,7,3,4,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,5,2,1,8,3,4,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,6,3,2,8,4,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[5,6,2,3,1,8,4,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,4,8,6,2,7,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,8,3,5,2,7,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,5,2,3,6,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,8,2,1,7,3,4,5] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[1,8,6,3,7,2,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,8,2,7,3,4,5,6] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[2,8,1,7,3,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,8,6,1,7,2,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[4,8,1,5,7,2,3,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,2,8,3,7,1,5,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[8,1,2,7,3,4,5,6] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[3,6,2,7,1,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[6,3,7,1,2,8,4,5] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,2,6,1,8,3,4,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,3,1,5,8,2,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,2,1,5,8,4,6,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,4,1,3,6,8,2,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,5,3,4,6,8,2,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[4,3,5,1,6,8,2,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,4,6,3,8,7,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,6,4,5,8,7,1,2] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[6,5,3,4,8,7,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[5,3,2,8,7,1,4,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,3,1,8,7,2,4,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[8,5,3,7,6,1,2,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,1,8,3,7,2,4,5] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[6,3,8,1,7,2,4,5] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[7,6,8,2,3,5,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[3,7,8,2,4,6,1,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,7,3,8,2,5,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,4,7,8,2,6,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[4,2,5,8,7,1,3,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,3,8,7,1,4,5,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[7,2,8,6,1,3,4,5] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[2,1,8,7,3,4,5,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,2,7,6,1,3,4,5] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[1,2,8,7,3,4,5,6] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,3,8,7,2,4,5,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,7,8,3,6,2,4,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[4,1,5,8,7,2,3,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,4,8,7,6,1,2,3] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,8,3,7,5,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,8,6,2,5,1,3,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,1,6,7,3,2,5,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,1,6,7,3,2,4,5] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,5,3,7,2,4,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,1,5,3,6,2,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,5,1,3,6,2,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,5,8,3,6,2,4,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,4,8,3,2,6,5,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[7,4,1,3,2,6,5,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,1,4,3,2,6,5,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,1,4,3,2,7,5,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,1,4,3,2,7,6,5] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,1,5,4,6,7,2,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[8,1,5,3,6,2,7,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,4,3,2,6,7,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,1,4,3,2,5,7,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,1,4,3,2,5,6,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[7,4,1,3,2,5,6,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[7,4,8,3,2,5,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,4,3,8,2,5,7,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,4,3,1,2,5,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,4,1,3,2,5,8,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,4,1,3,2,6,8,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,5,1,3,6,2,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,5,1,4,6,8,2,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,5,8,3,6,2,1,4] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[7,4,8,3,2,6,1,5] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[7,4,8,3,2,5,1,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,4,3,8,2,5,1,7] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,4,3,7,2,5,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[5,4,3,2,8,6,1,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,4,3,2,8,7,1,6] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[6,5,3,8,7,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[6,5,4,8,7,1,2,3] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,5,4,1,7,8,2,3] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[6,5,3,1,7,2,8,4] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,4,3,1,2,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,4,3,2,1,8,6,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[6,5,3,1,8,2,7,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,5,4,1,8,7,2,3] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,1,4,8,6,2,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,4,1,3,2,8,6,5] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,4,1,3,2,8,5,6] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,4,3,1,2,8,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,4,3,1,2,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,4,3,8,2,7,5,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[6,5,3,8,7,2,4,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,5,3,1,7,2,4,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,5,3,1,8,2,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,5,1,3,8,2,4,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,6,1,8,3,2,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,6,1,8,4,5,2,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,6,8,1,4,5,2,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[7,6,8,1,3,2,5,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,5,3,7,8,2,4,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,4,3,7,2,8,5,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,4,3,7,2,1,5,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,4,8,3,2,1,5,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,4,8,3,2,1,6,5] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[7,5,8,3,1,2,6,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,5,8,4,1,6,2,3] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,5,4,8,1,7,2,3] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,5,3,8,1,2,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[5,4,3,2,8,1,7,6] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[6,4,3,7,2,1,8,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,5,3,7,1,2,8,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,5,4,7,1,8,2,3] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,5,3,7,8,2,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[6,4,3,7,2,8,1,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,4,3,2,7,8,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[5,4,3,2,6,8,1,7] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[5,6,2,1,3,4,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,3,7,8,2,1,4,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,6,1,2,5,8,3,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[2,1,7,8,4,3,5,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,8,1,2,5,4,6,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,4,1,3,7,6,2,5] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,5,2,1,8,7,4,3] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[4,7,2,8,1,3,6,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[7,3,8,6,1,2,5,4] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,4,7,1,8,2,6,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,8,2,4,3,5,6,7] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,7,2,4,3,5,6,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,6,2,4,3,5,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,5,2,4,3,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,6,2,5,3,4,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,7,2,5,3,4,6,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,8,2,5,3,4,6,7] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,8,2,6,3,4,5,7] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,7,2,6,3,4,5,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,8,2,7,3,5,4,6] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,7,2,8,3,5,4,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,6,2,8,3,5,4,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,2,8,3,6,4,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,2,8,3,6,5,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,3,2,8,4,6,5,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,2,3,8,4,6,5,7] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,2,3,7,4,6,5,8] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,3,2,7,4,6,5,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,2,7,3,6,5,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,2,7,3,6,4,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,6,2,7,3,5,4,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,7,2,6,3,5,4,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,8,2,6,3,5,4,7] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,8,2,5,3,6,4,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,2,5,3,6,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,6,2,5,3,7,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,5,2,4,3,7,6,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,6,2,4,3,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,2,4,3,6,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,8,2,4,3,6,5,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,8,2,3,4,6,5,7] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,7,2,3,4,6,5,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,8,2,3,4,7,5,6] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,8,2,4,3,7,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,2,4,3,8,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,6,2,4,3,8,5,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,5,2,4,3,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,6,2,5,3,8,4,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,2,5,3,8,4,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,8,2,5,3,7,4,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,8,2,6,3,7,4,5] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,2,6,3,8,4,5] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,2,3,8,4,7,5,6] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,3,2,8,4,7,5,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,2,8,3,7,5,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,2,8,3,7,4,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,6,2,8,3,7,4,5] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,7,2,8,3,6,4,5] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,8,2,7,3,6,4,5] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[4,6,3,7,2,5,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,6,3,7,5,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,6,3,8,5,1,7,2] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[4,6,3,8,5,1,2,7] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[5,6,8,3,4,1,2,7] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[5,6,8,3,4,1,7,2] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,6,2,7,5,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,6,7,2,4,3,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,6,8,4,3,1,7,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,8,4,3,1,2,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,7,8,4,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[5,7,8,4,1,6,3,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,8,4,1,3,6,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[5,6,8,4,2,1,7,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,8,2,4,1,7,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,6,2,8,5,1,7,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[3,2,6,8,5,1,7,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[3,2,6,8,5,1,4,7] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[4,6,2,8,5,1,3,7] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[5,6,8,2,4,1,3,7] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[5,6,8,4,2,1,3,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,7,8,4,1,3,2,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,7,8,4,1,2,6,3] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,7,8,4,1,2,3,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[6,7,8,1,5,2,3,4] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,7,8,1,5,2,4,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[6,7,8,1,5,3,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,7,8,1,3,5,2,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[5,7,8,2,1,6,3,4] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,7,2,8,1,6,3,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,2,7,8,1,6,4,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[3,2,7,8,1,6,5,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,7,2,8,1,6,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,7,8,2,1,6,4,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,7,8,1,3,5,4,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,7,8,1,5,3,4,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[6,7,8,1,5,4,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[6,7,8,1,5,4,2,3] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,7,8,1,4,5,2,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,7,8,1,4,5,3,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,7,8,1,4,3,5,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[6,7,8,1,3,4,5,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,7,8,2,1,4,6,3] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,7,2,8,1,5,6,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,2,7,8,1,5,6,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[3,2,6,8,4,1,7,5] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[4,6,2,8,3,1,7,5] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[5,6,8,3,2,1,7,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,7,8,3,1,4,6,2] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,7,8,3,1,6,4,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,8,3,1,6,2,4] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,7,3,8,1,6,2,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[4,7,3,8,1,6,5,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,7,3,8,1,5,6,2] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[4,6,3,8,2,1,7,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,5,3,2,8,1,7,6] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,5,2,3,8,1,7,6] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[3,2,5,4,8,1,7,6] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[4,5,3,2,8,1,6,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,6,3,8,2,1,5,7] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,7,3,8,1,5,2,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[4,7,3,8,1,2,6,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[4,7,3,8,1,2,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[5,7,8,3,1,2,4,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[5,7,8,3,1,2,6,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,7,8,3,1,4,2,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[5,6,8,3,2,1,4,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,2,7,8,1,5,4,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,7,8,2,1,4,3,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,7,8,1,3,4,2,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,7,8,1,4,3,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,7,8,1,4,2,5,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[6,7,8,1,4,2,3,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,7,8,1,2,5,3,4] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,7,8,1,2,5,4,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,7,8,1,2,4,5,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,7,8,1,3,2,5,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[5,7,8,2,1,3,6,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[3,2,7,8,1,4,6,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[6,7,8,1,3,2,4,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,7,8,1,2,4,3,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,7,8,1,2,3,5,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[7,2,8,5,1,6,4,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[1,3,7,5,2,6,4,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,3,7,5,4,2,6,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[7,2,8,5,4,1,6,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[2,8,5,4,3,1,7,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[2,8,4,5,6,1,7,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[2,8,6,5,7,3,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,8,4,5,3,7,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,4,3,5,6,1,7] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[7,2,8,4,5,6,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[1,6,3,7,5,2,4,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[6,2,3,8,5,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[6,3,2,8,5,1,4,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,4,8,2,5,6,3,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[7,4,8,5,2,1,3,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,4,8,5,1,3,7,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,3,7,5,2,1,8,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[4,3,7,5,1,2,8,6] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,3,7,1,5,6,8,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[3,6,1,7,5,2,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,4,1,2,7,6,8,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,4,2,1,7,5,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,6,5,7,1,4,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,5,2,7,4,1,8,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[3,5,2,6,4,8,7,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[5,3,1,8,6,4,7,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[5,6,1,8,7,2,4,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[6,3,5,8,2,7,4,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,5,8,4,2,3,7,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,2,5,8,3,7,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[1,6,5,7,3,4,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,5,2,7,4,6,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[5,2,1,8,7,6,3,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[7,1,3,8,4,6,2,5] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[2,3,4,8,6,1,7,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,3,4,8,6,5,1,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,7,3,5,8,6,1,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[3,2,4,7,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[1,5,4,6,2,7,3,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[5,2,4,7,1,8,3,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[5,3,6,4,1,8,7,2] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[5,3,6,1,4,8,2,7] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[7,3,5,6,8,4,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[6,3,5,1,8,2,7,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[2,6,1,5,8,4,7,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,7,6,5,8,3,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[5,7,1,6,3,8,4,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[3,2,4,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[3,1,4,2,7,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,1,4,7,2,8,6,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,6,4,7,8,2,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,1,4,6,8,5,7,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[6,3,4,5,7,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[2,5,4,6,1,7,8,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[7,2,1,4,3,6,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[7,3,4,1,2,6,5,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,4,3,2,1,6,5,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,6,3,2,5,4,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[6,7,3,2,5,4,8,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,8,3,2,5,4,7,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,8,4,5,2,3,7,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[7,3,5,1,6,2,4,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,2,1,5,6,3,4,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,2,1,6,5,4,3,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,3,6,1,5,4,2,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[7,4,6,5,1,3,2,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[1,8,5,4,3,2,7,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,8,6,4,3,7,2,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[6,5,7,4,3,1,8,2] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,4,7,5,1,3,8,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,3,7,1,5,4,8,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,2,1,7,5,4,8,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,2,1,8,5,4,7,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[2,5,8,4,3,1,7,6] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,6,8,4,3,7,1,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[2,7,8,4,3,6,5,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,8,7,4,3,6,5,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,8,7,5,6,3,4,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,7,8,5,6,3,4,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,6,8,5,7,3,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,5,8,6,7,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,4,8,6,1,7,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[3,2,1,8,6,7,4,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[5,3,7,1,6,8,4,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,4,7,6,1,8,3,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,5,7,6,8,1,3,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,6,7,5,8,3,1,2] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,8,6,5,7,3,2,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[1,8,5,6,7,2,3,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,6,5,7,8,2,1,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[5,4,6,7,1,8,2,3] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[5,3,6,1,7,8,2,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,2,1,6,7,8,3,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,2,1,5,7,3,8,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,3,5,1,7,2,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,4,5,7,1,2,8,3] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[6,5,4,7,2,1,8,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[5,6,4,7,2,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,4,6,2,7,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,8,3,2,6,7,4,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,7,3,2,6,8,4,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[5,6,3,2,7,8,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,5,3,2,7,1,8,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,4,3,2,1,7,8,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,2,1,4,3,7,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[4,6,3,2,8,7,1,5] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,7,3,2,8,6,5,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,8,3,2,7,6,5,4] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,8,4,7,2,6,5,3] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,6,4,8,2,7,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,4,5,8,1,2,7,6] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,3,5,1,8,2,7,6] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,2,1,5,8,3,7,6] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,2,1,6,8,7,3,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[3,4,6,8,1,7,2,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,5,6,8,7,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,6,5,8,7,2,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,8,5,7,6,2,4,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,8,6,7,5,4,2,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[3,6,7,8,5,4,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,5,7,8,6,1,4,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,4,7,8,1,6,5,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,2,1,7,8,6,5,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[2,3,8,1,7,6,5,4] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,4,8,7,1,6,5,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[2,1,4,3,6,5,8,7,10,9,12,11] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 10101010101
[6,5,4,3,2,1,12,11,10,9,8,7] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[12,11,10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => 11111111111
[7,4,6,1,8,3,5,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,3,5,1,7,4,6,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,3,4,1,7,5,6,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,8,3,1,7,5,6,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[4,6,2,1,7,5,8,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,4,6,2,7,5,8,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,7,5,2,6,8,4,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,5,2,1,6,8,4,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,8,4,3,1,7,5,2] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[3,6,8,4,1,7,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,6,7,5,1,8,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[7,5,6,1,8,3,4,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[3,4,6,5,7,1,8,2] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[4,7,5,6,1,8,3,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,7,5,1,8,4,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[6,8,4,1,7,5,3,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,7,5,3,1,8,4,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[8,4,2,1,6,7,5,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[1,8,4,2,6,7,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,5,3,2,7,6,8,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[5,3,2,1,7,6,8,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[2,5,3,1,7,6,8,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[2,8,4,1,6,7,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,7,5,1,6,8,4,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,4,6,1,7,5,8,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,7,1,6,5,8,2,3] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,8,2,6,5,7,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,6,1,2,7,5,8,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[7,5,1,2,6,8,4,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,4,1,2,6,7,5,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,3,1,2,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[1,2,5,3,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,3,1,2,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[3,5,1,2,7,6,8,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,1,5,8,2,3,4] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,7,6,1,5,8,3,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[2,3,5,1,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[7,6,1,5,8,3,2,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[3,6,7,1,5,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,1,6,5,8,2,4,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,5,1,6,8,4,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,4,1,6,7,5,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,2,3,1,7,6,8,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,5,2,1,7,6,8,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,3,5,2,7,6,8,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,7,6,2,5,8,3,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,6,2,1,5,8,3,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,3,1,5,7,6,2,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[6,2,4,1,7,5,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[6,2,5,1,7,4,8,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,1,6,4,8,2,5,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,2,6,4,7,1,5,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,1,5,2,7,4,8,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,6,2,5,8,3,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,3,5,7,6,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[1,8,3,5,7,6,2,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,5,2,3,7,6,8,4] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[5,2,1,3,7,6,8,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,5,2,6,8,4,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,4,2,6,7,5,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,1,4,2,7,5,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,2,6,5,7,1,4,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[3,6,8,2,5,7,1,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[8,3,2,5,7,6,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[5,1,3,2,7,6,8,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,1,3,2,7,6,8,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,2,1,3,7,6,8,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[1,4,2,3,7,6,8,5] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,4,1,3,7,6,8,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,5,1,3,7,6,8,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,8,3,5,7,6,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[6,8,2,3,5,7,1,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,7,1,3,5,8,2,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,3,5,7,6,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,1,2,3,7,6,8,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[3,1,2,4,7,6,8,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[10,8,9,5,6,7,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,8,9,4,5,6,1,2,3,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,7,8,5,6,9,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,7,8,4,5,9,1,2,3,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,6,7,4,5,8,1,2,3,9] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,7,8,3,4,9,1,2,5,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[10,6,7,3,4,8,1,2,5,9] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,8,10,5,6,7,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,8,10,4,5,6,1,2,3,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,7,10,5,6,8,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,7,10,4,5,8,1,2,3,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,4,5,7,1,2,3,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,7,10,3,4,8,1,2,5,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,3,4,7,1,2,5,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,7,9,5,6,10,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,7,9,4,5,10,1,2,3,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,4,5,10,1,2,3,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,6,8,4,5,9,1,2,3,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,7,9,3,4,10,1,2,5,6] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,3,4,10,1,2,5,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,6,8,3,4,9,1,2,5,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,5,7,8,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,4,7,8,1,2,3,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,5,10,4,6,7,1,2,3,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,3,7,8,1,2,4,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,5,10,3,6,7,1,2,4,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,5,7,10,1,2,3,4] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,4,7,10,1,2,3,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,5,9,4,6,10,1,2,3,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,5,8,4,6,9,1,2,3,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,3,7,10,1,2,4,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,5,9,3,6,10,1,2,4,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,5,8,3,6,9,1,2,4,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,4,9,3,5,10,1,2,6,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,4,8,3,5,9,1,2,6,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,6,10,2,7,8,1,3,4,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[9,5,10,2,6,7,1,3,4,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,6,9,2,7,10,1,3,4,5] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,5,9,2,6,10,1,3,4,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,5,8,2,6,9,1,3,4,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,4,9,2,5,10,1,3,6,7] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[7,4,8,2,5,9,1,3,6,10] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[8,1,2,4,3,6,5,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,3,5,6,2,7,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[8,1,3,4,2,6,7,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[8,1,3,2,4,5,7,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,7,8,3,4,5,6,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[2,6,3,8,4,5,7,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[6,3,2,1,4,5,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,3,1,4,2,6,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,4,1,5,6,8,2,3] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,7,8,5,6,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[3,7,8,5,6,2,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,7,8,4,2,6,1,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,7,8,2,4,5,1,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,6,2,8,4,5,1,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,3,6,7,4,5,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,5,2,4,8,6,1,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,5,4,2,8,7,1,6] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,6,5,8,7,1,2,3] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[6,4,5,1,7,8,2,3] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[7,4,1,2,3,8,5,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[6,2,4,1,3,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[2,6,4,8,3,7,5,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,6,5,8,7,3,4,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,2,5,1,7,3,4,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,5,2,1,8,3,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,5,6,7,8,3,4,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,4,6,7,3,8,5,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,2,6,7,3,1,5,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,7,8,2,3,1,5,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,7,8,3,2,1,6,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,4,8,1,7,2,3] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[5,6,3,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[4,2,5,3,7,1,6,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,3,6,7,2,1,8,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,4,6,7,2,8,1,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,4,5,2,7,8,1,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[3,4,2,5,6,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[5,2,7,8,6,4,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,1,2,7,8,6,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[4,7,1,8,6,5,2,3] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,7,1,2,8,6,5,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[4,6,8,1,2,7,5,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,8,7,1,5,3,2,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,8,7,3,5,1,2,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,8,1,6,3,5,2,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,1,3,6,5,2,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,3,6,5,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[4,7,2,8,6,1,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,7,3,4,8,6,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,2,7,1,8,6,5,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[7,8,2,3,6,5,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[8,5,7,1,6,2,3,4] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,5,7,1,2,6,3,4] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,8,2,7,1,3,5,4] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[6,8,7,2,5,3,1,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,2,4,8,7,1,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[1,6,8,3,7,4,5,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,6,8,3,4,7,5,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,2,4,8,1,7,5,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,8,7,2,3,5,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,8,2,1,7,3,5,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,5,7,2,1,6,3,4] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,5,7,1,2,3,6,4] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,7,6,2,1,4,3,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,7,2,3,1,6,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,8,4,2,7,1,6,3] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[1,8,7,5,3,4,6,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,8,7,3,5,4,6,2] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[8,2,5,4,7,1,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,5,2,7,3,1,6,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,7,6,2,4,3,1,5] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,7,6,1,2,4,3,5] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,7,6,1,4,2,3,5] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,7,6,4,1,3,2,5] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[5,8,4,7,2,1,6,3] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[1,8,7,5,4,3,6,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[1,6,8,4,3,7,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,8,7,3,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[6,8,1,7,3,2,5,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,5,7,3,1,6,2,4] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,5,7,1,3,2,6,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,5,7,3,1,2,6,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,8,4,7,1,2,6,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,8,4,1,7,2,6,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,8,4,7,1,6,2,3] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[8,1,2,6,5,7,4,3] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,2,5,6,7,4,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,8,5,7,1,6,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,5,7,1,2,6,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[4,8,5,1,7,2,6,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[8,5,3,1,7,2,6,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,5,3,7,1,2,6,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,8,1,3,7,2,5,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,6,2,8,1,7,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,6,4,8,3,7,5,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,8,7,4,5,3,6,2] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[4,8,5,7,2,1,6,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[8,5,3,7,2,1,6,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,7,6,3,1,4,2,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,7,6,1,3,2,4,5] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,5,3,2,7,1,6,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[4,8,5,2,7,1,6,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[1,8,7,4,3,5,6,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,8,7,3,4,5,6,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[8,2,4,5,7,1,6,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,5,2,3,7,1,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[6,3,1,5,4,2,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,3,1,5,2,7,6,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,5,4,2,1,7,3,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,4,2,1,7,6,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[6,5,4,2,1,3,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,5,4,2,3,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,3,2,5,1,4,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,5,4,3,1,2,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,5,4,1,3,2,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,5,4,1,2,7,6,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,7,4,1,6,3,2,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,7,4,1,6,3,5,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,7,4,1,6,5,3,2] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,5,4,1,3,7,6,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,5,4,3,1,7,6,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,3,2,5,1,7,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[2,1,8,5,3,7,6,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,3,2,5,1,7,4,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,5,4,3,1,7,2,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,4,1,3,7,2,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,4,1,6,5,2,3] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,7,4,1,6,2,5,3] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,7,6,5,2,1,4,3] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[8,7,4,3,6,2,1,5] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[8,3,2,7,6,4,1,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[2,1,8,7,6,4,3,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,1,8,7,6,4,5,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,3,2,7,6,4,5,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[8,7,4,3,6,2,5,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,7,6,5,2,4,3,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[8,5,4,2,3,7,6,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,7,4,2,6,5,3,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,4,2,6,3,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,7,4,2,6,3,1,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,3,1,7,6,4,2,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,3,1,7,6,4,5,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[8,3,1,7,6,5,4,2] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[8,3,1,5,4,7,6,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,3,1,5,4,7,2,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,3,1,7,6,5,2,4] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,3,1,7,6,2,5,4] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[8,7,4,2,6,1,5,3] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[8,7,4,2,6,5,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[8,5,4,2,3,7,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,3,2,5,4,7,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[2,1,8,5,4,7,3,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[8,3,2,7,6,5,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,7,4,3,6,5,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[8,7,6,5,3,1,4,2] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[8,7,6,5,1,3,2,4] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,7,6,5,1,3,4,2] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[8,7,6,5,1,4,3,2] => [[1,6],[2],[3],[4],[5],[7],[8]] => 1111011
[8,7,6,5,4,1,3,2] => [[1,7],[2],[3],[4],[5],[6],[8]] => 1111101
[8,7,4,3,6,1,5,2] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[8,3,2,7,6,1,5,4] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[2,1,8,7,6,3,5,4] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,3,2,7,6,1,4,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,7,6,5,1,4,2,3] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[8,7,6,5,1,2,4,3] => [[1,6,7],[2],[3],[4],[5],[8]] => 1111001
[7,3,5,1,8,4,6,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,3,4,1,8,5,6,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,5,6,2,1,8,7,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,6,5,2,7,4,3,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,4,3,1,8,6,5,2] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[7,6,5,1,8,4,3,2] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[7,6,4,1,8,5,3,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[6,4,2,1,8,7,5,3] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[1,6,4,2,7,5,3,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,5,3,2,7,6,4,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[5,3,2,1,8,7,6,4] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[2,5,3,1,7,8,6,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,6,4,1,7,8,5,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,6,5,1,7,8,4,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,5,7,1,6,8,2,3] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[6,5,1,2,8,4,3,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,4,1,2,8,5,3,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,3,1,2,8,6,4,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,3,1,2,8,6,5,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[6,1,2,5,8,3,4,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,1,3,4,8,2,5,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,1,5,6,8,2,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[2,6,1,5,7,8,3,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[7,4,1,6,8,5,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,2,3,1,8,6,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,5,2,1,6,8,7,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,6,2,5,7,3,4,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[6,2,1,5,8,7,3,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[7,3,1,5,8,6,2,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[6,2,4,1,8,5,7,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[6,2,5,1,8,4,7,3] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,3,1,4,8,6,2,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[6,2,1,4,8,7,3,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[1,6,2,4,7,3,5,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[5,2,1,3,8,7,4,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[7,4,1,3,8,5,2,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[7,5,1,3,8,4,2,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,6,7,1,4,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,6,1,4,8,3,2,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[4,2,1,3,8,7,5,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,6,1,4,7,8,3,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[7,1,4,6,8,2,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,1,3,5,8,2,4,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,1,2,4,8,3,5,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[5,2,3,1,6,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,4,5,2,3,1,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,6,7,3,5,2,4,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,3,5,2,4,1,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,3,5,2,4,1,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,2,4,1,6,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,1,6,3,5,2,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[6,3,4,1,5,2,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,2,6,3,4,1,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,2,7,3,4,1,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,2,8,6,7,3,4,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[6,2,8,5,7,3,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,2,7,3,4,1,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[7,3,4,1,5,2,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,1,7,3,5,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,7,4,5,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,7,4,5,3,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,8,6,7,4,5,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,1,8,6,7,3,5,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[8,6,7,3,4,1,5,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,5,7,3,4,1,6,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,5,6,2,7,3,4,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,4,7,3,5,1,6,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,1,8,4,7,3,6,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[4,1,8,5,7,3,6,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[3,1,8,5,7,4,6,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,8,5,7,4,6,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,7,4,6,3,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,7,4,6,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[4,1,7,3,6,2,8,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,1,7,3,6,2,8,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,2,7,3,5,1,8,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,2,8,4,7,3,5,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,4,7,3,6,2,5,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,3,6,2,5,1,8,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,2,5,1,7,3,8,4] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,2,4,1,7,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[6,2,4,1,7,3,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,5,7,3,6,2,4,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,5,7,4,6,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,4,6,2,3,1,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,2,3,1,7,4,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,2,3,1,7,4,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,3,1,7,5,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[3,1,4,2,8,6,7,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[6,2,3,1,8,5,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,5,6,2,3,1,7,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,4,8,5,6,2,3,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,3,8,5,6,2,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,5,6,2,4,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,2,4,1,8,6,7,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,1,5,2,8,6,7,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,5,2,8,6,7,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,1,6,3,8,5,7,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,6,2,8,5,7,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,6,2,8,5,7,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,1,6,2,8,4,7,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[8,4,6,2,5,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,3,8,4,6,2,5,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,2,7,3,8,4,5,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[8,4,5,1,6,2,7,3] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[5,1,8,4,6,2,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,1,8,5,6,2,7,3] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,8,5,6,2,7,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,8,5,6,3,7,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[2,1,7,4,8,5,6,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[3,1,7,4,8,5,6,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,7,3,8,5,6,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[7,3,8,4,5,1,6,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,4,5,1,7,3,6,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,3,6,2,8,4,5,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,8,5,6,1,3,4,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[7,8,1,3,6,2,5,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[1,3,8,4,7,2,5,6] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[3,6,1,4,7,2,5,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,6,1,2,5,7,3,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,4,8,2,5,7,3,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,8,2,4,5,6,1,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[7,8,1,5,4,6,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,8,2,1,6,3,4,5] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,8,3,5,6,4,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,1,4,2,3,6,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,8,5,1,4,2,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,8,4,5,3,1,6,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[1,5,8,4,3,2,7,6] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,1,4,3,2,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[2,6,4,8,3,7,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,4,6,8,3,7,5,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,8,5,3,1,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[2,5,8,1,4,7,6,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,5,8,4,7,6,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[1,6,2,4,7,3,8,5] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[5,6,2,1,4,7,8,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,6,2,5,3,1,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,7,5,1,3,6,8,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,5,3,6,2,4,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,7,3,6,1,4,8,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,3,6,7,2,1,8,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[6,1,7,5,2,4,8,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,3,1,2,4,5,8,7] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[1,4,7,2,5,3,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,6,7,8,3,5,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,6,1,8,4,2,5,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[1,6,7,5,8,2,4,3] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,5,6,7,8,1,4,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,6,5,7,8,2,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[5,2,7,6,1,4,3,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,5,7,6,8,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,7,5,6,8,4,1,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,1,6,8,4,5,3,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,7,1,8,5,3,4,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[3,7,6,8,5,4,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,3,8,5,6,7,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[4,2,8,1,6,3,7,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,1,8,5,4,6,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[3,2,8,4,5,6,1,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,4,2,8,6,1,7,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,4,7,1,5,2,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[4,3,7,8,1,2,6,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[1,7,3,8,5,2,6,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[4,1,8,3,6,2,5,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,7,8,6,3,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[5,7,8,6,1,3,4,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[7,6,5,8,1,3,4,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[1,6,4,3,8,2,5,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[7,1,3,4,8,2,6,5] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,6,5,4,1,2,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,4,5,1,7,8,6,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,6,3,4,5,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,6,4,1,8,3,7,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[7,3,6,4,8,5,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,2,1,4,8,3,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,1,6,5,3,8,4,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,2,5,6,3,8,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,5,2,7,1,8,4,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,6,2,7,3,1,4,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[5,6,7,4,2,8,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,7,6,4,1,8,3,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[6,7,1,5,2,8,3,4] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[1,7,5,2,4,8,3,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,1,5,2,8,3,4,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[6,7,5,3,8,4,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[1,6,5,4,2,3,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[7,1,5,3,4,2,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,6,1,5,3,2,8,4] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,5,6,4,1,2,8,3] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,7,5,4,3,1,8,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[7,5,2,4,3,1,6,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[7,4,6,1,2,5,3,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,1,4,2,5,3,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[6,8,1,4,2,5,7,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[1,6,4,2,5,7,3,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,6,3,7,5,4,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[6,8,1,3,7,5,4,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[7,1,3,5,6,4,2,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[7,3,1,6,4,5,2,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,4,2,6,5,1,3,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,4,6,3,1,5,2,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,2,4,1,5,3,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,2,3,5,4,1,6,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[6,8,1,2,3,4,7,5] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[1,5,7,2,3,8,6,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[5,1,8,2,3,6,7,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,8,2,3,7,6,4,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,2,8,1,3,7,4,5] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,8,2,3,5,4,7,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,8,2,4,1,5,7,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,8,3,1,2,4,7,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[2,6,4,1,5,7,3,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[2,6,3,5,7,1,4,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,5,1,7,8,3,6,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,5,3,6,8,4,7,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,1,4,7,8,5,6,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,4,7,6,8,5,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,5,3,7,6,1,8,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,5,7,8,1,4,6,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,5,7,4,1,6,2,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,3,4,1,8,6,7,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,2,8,4,6,1,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,2,1,8,6,3,7,4] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[4,2,8,6,5,3,7,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,2,8,5,7,6,3,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[1,4,2,7,5,8,6,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[4,1,8,6,7,5,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[5,3,8,7,6,2,4,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,8,4,7,6,2,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[5,8,7,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[6,4,8,3,1,7,2,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,4,2,8,7,1,3,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,3,8,7,2,5,1,4] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[5,8,3,7,1,6,4,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,1,3,8,6,7,2,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[1,5,3,7,8,6,2,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,5,7,6,4,2,8,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,8,7,4,1,6,2,3] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,4,8,1,2,7,3,5] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,8,5,1,2,3,7,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[6,8,5,2,4,3,7,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[6,8,5,3,1,2,7,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[4,5,1,2,7,6,3,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[4,5,1,2,6,8,7,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,5,6,1,8,4,7,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,5,7,1,2,8,6,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,6,2,7,5,1,4,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[4,2,6,1,7,3,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,6,3,1,2,7,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,5,3,1,7,6,2,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[4,2,5,7,1,6,3,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[3,5,2,7,8,1,6,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[3,1,4,7,5,6,2,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[3,4,6,5,8,7,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,1,4,5,8,6,7,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[3,4,6,8,5,2,7,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,5,6,2,8,4,7,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[4,2,5,6,1,8,7,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,5,3,1,6,8,7,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,1,7,5,8,6,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,2,7,5,3,8,6,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,1,2,7,3,8,6,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[6,4,1,7,5,2,3,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,1,3,7,5,2,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[3,1,2,6,8,5,4,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,7,1,2,5,4,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[1,3,7,2,4,8,6,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,4,1,7,8,6,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,7,5,1,8,6,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[2,7,4,1,5,8,6,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,3,7,1,5,8,6,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[5,2,8,1,3,7,4,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[2,1,6,8,3,4,7,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,6,8,3,1,5,7,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[2,8,6,4,1,5,7,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,6,4,8,5,1,7,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[6,3,7,4,5,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[2,6,3,7,5,8,1,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[5,2,1,7,8,3,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,7,2,3,6,8,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[5,2,7,3,6,8,1,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,7,4,6,2,8,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,7,3,4,6,1,8,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,3,8,4,6,1,7,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,5,2,4,1,6,7,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,2,3,5,1,6,7,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,2,8,3,6,7,1,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[2,4,8,1,7,3,5,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[8,4,1,3,6,2,5,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[4,8,3,1,7,2,5,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,2,8,4,7,1,6,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,8,4,7,3,1,6,2] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[4,6,8,3,1,7,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,3,8,2,7,1,5,4] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[6,3,1,8,2,4,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,3,8,1,2,6,4,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[5,7,4,1,6,2,3,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[8,5,4,1,2,6,3,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[5,1,8,4,2,7,3,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,6,2,8,5,3,7,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[6,8,5,3,1,7,4,2] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[8,4,5,1,2,6,3,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,6,3,7,1,2,4,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[1,6,3,7,2,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[6,3,2,7,8,5,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[4,5,7,8,3,1,6,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,7,2,5,8,1,6,3] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[8,1,3,4,6,2,5,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,8,2,4,6,7,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,5,6,8,2,7,1,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,4,5,6,8,1,7,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,8,3,5,6,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,6,2,3,7,8,1,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,8,7,3,4,1,2,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,7,3,4,1,2,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,4,7,1,5,3,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[6,8,4,7,2,5,3,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,4,8,7,2,6,3,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[5,4,8,7,1,6,3,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[5,3,8,7,6,1,2,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,3,8,7,6,1,2,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,8,3,7,5,1,2,6] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[8,3,4,6,5,1,2,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,8,4,7,5,1,2,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,4,8,7,6,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,5,8,7,6,1,2,4] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,5,8,7,6,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,5,8,7,1,6,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,5,8,7,2,6,3,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,5,8,2,7,6,4,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,5,8,1,7,6,4,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,5,8,1,7,6,4,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,5,8,7,1,6,3,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,4,8,7,1,6,3,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,8,4,7,1,5,3,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[8,2,4,6,1,5,3,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,1,4,6,2,5,3,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[1,8,4,7,2,5,3,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,4,8,7,2,6,3,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,5,8,7,2,6,3,4] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,5,8,2,7,6,4,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,5,8,3,7,6,4,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[1,4,2,8,7,6,5,3] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,3,8,2,7,6,4,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,8,3,2,7,5,4,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[8,1,3,2,6,5,4,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[8,2,3,1,6,5,4,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[2,8,3,1,7,5,4,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,3,8,1,7,6,4,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[3,4,1,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[4,3,1,8,7,6,5,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[4,2,1,8,7,6,5,3] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[3,8,2,1,7,5,4,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,3,2,1,6,5,4,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,4,2,6,1,5,3,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,2,8,7,1,6,3,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,2,8,7,1,6,3,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,2,8,1,7,6,4,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[5,3,8,1,7,6,4,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[5,3,8,2,7,6,4,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[6,8,3,2,7,5,4,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,8,3,1,7,5,4,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,8,2,1,7,5,4,3] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,8,2,7,1,5,3,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,7,2,1,4,3,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[8,5,6,1,2,4,3,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,8,7,1,2,4,3,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[6,8,1,2,7,5,4,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,8,2,3,7,5,4,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[5,2,8,3,7,6,4,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[5,1,8,3,7,6,4,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[5,1,8,7,2,6,3,4] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,1,8,7,2,6,3,5] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,8,1,7,2,5,3,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,4,1,6,2,5,3,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,3,1,2,6,5,4,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,8,1,2,7,5,4,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,1,8,2,7,6,4,5] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,1,2,8,7,6,5,4] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,1,3,8,7,6,5,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[3,1,4,8,7,6,5,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,1,8,3,7,6,4,5] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,8,1,3,7,5,4,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,2,1,3,6,5,4,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,1,2,3,6,5,4,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[1,8,2,3,7,5,4,6] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,2,8,3,7,6,4,5] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,4,3,6,8,2,5,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[3,1,6,2,5,8,4,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,5,1,8,2,4,7,6] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[1,4,5,2,8,3,7,6] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,4,2,6,5,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,5,4,2,6,8,3,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,1,6,5,8,2,4,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[1,6,4,2,5,8,3,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[1,5,2,6,4,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,2,6,5,4,8,3,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,2,5,4,7,3,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[4,1,2,6,3,8,7,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[7,1,5,4,2,8,3,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,4,7,5,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[7,1,3,5,2,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[7,2,5,1,8,3,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[1,4,5,2,8,7,3,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,6,4,2,8,3,7,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,4,2,8,3,7,6,5] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,2,5,3,8,7,6,4] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,8,6,5,3,7,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,5,2,8,6,3,7,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,6,4,2,8,7,3,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[6,2,1,8,7,3,4,5] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,6,2,1,8,3,4,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,3,1,6,2,8,4,5] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[1,7,6,4,2,8,3,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,7,5,2,6,3,8,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,6,2,7,5,3,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,2,7,6,5,3,8,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,2,6,5,3,8,7,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,5,2,6,3,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,5,2,7,6,3,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,6,5,2,7,3,8,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,5,7,4,2,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,1,2,8,6,3,7,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,1,8,6,2,4,7,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,3,7,1,8,2,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,3,1,6,2,4,7,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,1,8,3,2,4,6,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[1,8,7,3,2,4,6,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,4,2,8,7,3,6,5] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,7,4,2,8,3,6,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[8,1,5,4,2,7,3,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,4,8,5,2,7,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[8,5,3,1,7,2,4,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,6,2,1,7,3,4,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,8,6,4,2,7,3,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,8,5,2,6,3,7,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,5,2,7,3,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,2,8,5,3,7,6,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,6,3,8,7,5,4] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,7,6,3,8,5,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,6,2,7,3,8,5,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,7,2,8,5,3,6,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,7,4,2,8,6,3,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[7,1,8,3,2,6,4,5] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,2,1,8,6,3,4,5] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[1,8,7,3,2,6,4,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,4,2,8,7,6,3,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,2,8,7,5,3,6,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,2,8,6,3,7,5,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,7,3,8,6,5,4] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[4,1,7,3,6,5,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,1,8,7,6,2,4,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,1,7,6,3,4,5,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[5,7,8,6,2,4,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,7,1,6,2,4,3,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,4,1,5,2,7,3,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,1,4,5,3,7,6,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[6,1,4,5,3,8,7,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[6,1,4,5,3,7,8,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[5,1,7,8,6,2,4,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,1,4,8,3,5,7,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,1,8,6,3,4,5,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[7,1,4,5,3,8,6,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,1,4,5,3,6,8,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[8,1,4,5,3,6,7,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[7,4,1,5,2,6,3,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,3,5,7,2,1,4,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,3,5,8,2,1,7,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,3,5,7,2,1,8,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,4,5,7,3,6,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[6,4,5,8,3,7,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[5,8,7,6,2,4,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[5,4,8,6,3,1,7,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,4,1,8,2,3,7,6] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,8,1,6,2,4,3,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,4,1,5,2,6,3,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,3,5,8,2,1,4,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,3,4,1,8,6,5,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[8,3,5,6,2,1,4,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[2,3,8,5,1,4,7,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,3,8,6,1,5,7,4] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,8,6,7,1,3,5,4] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[8,3,5,7,2,1,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[2,3,8,5,6,1,7,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[7,4,5,6,3,1,8,2] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,4,5,6,3,1,7,2] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,3,5,6,2,8,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,3,5,8,2,1,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[7,3,5,6,2,1,4,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[2,7,6,5,1,3,4,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,7,6,8,1,3,5,4] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[2,7,6,5,8,3,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[8,7,5,6,1,4,2,3] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,6,4,1,8,5,7,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[2,6,1,3,8,5,7,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,7,1,3,6,5,8,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,7,6,8,4,3,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[2,7,6,1,8,3,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,7,6,1,4,3,5,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,3,5,1,2,8,4,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,4,1,5,2,3,7,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,8,1,6,3,4,2,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,4,1,8,3,2,7,5] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,3,8,6,4,1,7,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,8,6,7,4,3,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[8,3,5,7,2,4,1,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[2,3,4,1,8,7,5,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[2,8,6,1,7,3,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,3,8,1,6,4,7,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,3,8,1,4,5,7,6] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[2,8,6,1,4,3,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,2,3,4,5,6,7,9,8] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[1,2,3,4,5,6,7,8,10,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[9,1,2,3,4,5,6,7,10,8] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[1,8,2,3,4,5,6,9,7] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[7,1,2,3,4,5,6,9,8] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[2,1,9,3,4,5,6,7,8] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[2,8,1,3,4,5,6,7,9] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[2,10,1,3,4,5,6,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[8,4,3,6,5,1,7,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,5,6,3,4,1,7,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,6,5,4,3,1,7,2] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[1,7,6,5,4,2,3,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,8,6,5,2,7,3,4] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[8,7,5,4,1,6,3,2] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[7,8,5,4,1,3,6,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[6,8,5,4,2,1,7,3] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,8,6,2,4,1,7,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,8,2,6,5,1,7,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[3,2,8,6,5,1,7,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,2,1,7,6,4,5,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[4,1,3,7,6,2,5,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[5,1,7,3,6,2,4,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[6,1,7,5,3,2,4,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,1,6,5,2,4,3,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,1,6,5,2,3,7,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,2,7,6,3,4,5,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,2,8,3,7,4,5,6] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[8,1,7,2,6,3,5,4] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[7,1,8,2,6,4,3,5] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[6,1,8,2,4,7,3,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,1,8,3,2,7,4,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[4,1,3,8,2,7,5,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[3,2,1,8,4,7,5,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,2,8,7,1,6,5,4] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[4,8,2,7,1,6,5,3] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,8,7,2,1,6,4,3] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,8,7,1,3,5,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[7,8,6,1,5,3,4,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,7,6,1,5,4,3,2] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[1,8,7,2,6,5,3,4] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,7,8,2,5,6,3,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[8,6,7,1,4,5,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[7,6,8,1,4,3,5,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,5,8,3,2,1,7,4] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[7,5,8,3,1,4,6,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,5,7,3,1,6,4,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[1,6,8,4,2,7,3,5] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,5,4,8,2,7,3,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[8,4,3,7,1,6,5,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,4,3,8,1,5,6,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,4,3,1,5,2,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,4,3,1,2,6,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,4,3,1,2,5,7,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,5,4,2,3,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[8,5,1,4,2,3,7,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,5,1,4,2,6,3,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,5,1,4,3,2,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[5,6,1,3,4,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,6,2,1,5,3,7,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,2,6,1,5,4,7,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,2,7,1,4,6,5,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[4,7,2,1,3,6,5,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,7,1,3,2,6,4,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,1,2,4,5,3,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[7,6,1,2,5,4,3,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,6,1,2,5,3,7,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[1,7,2,3,6,4,5,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[8,7,1,2,3,6,5,4] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[7,8,1,2,3,5,6,4] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[6,8,1,2,4,3,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,8,1,3,2,4,7,6] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,8,2,1,3,5,7,6] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,2,8,1,4,5,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,1,3,2,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[5,1,2,4,3,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[6,1,2,3,5,4,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[7,1,2,3,4,6,5,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,1,2,3,4,5,7,6] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[6,7,3,8,5,1,2,4] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[6,7,4,5,1,8,3,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,4,7,6,8,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[5,3,7,8,6,1,2,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,8,4,5,7,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[3,4,8,6,7,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,5,6,7,1,8,3,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,5,6,2,7,4,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,5,6,1,7,8,4,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,5,6,1,8,7,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,5,6,8,1,7,3,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[8,2,4,5,1,6,3,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[1,4,8,6,2,3,7,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,5,6,8,2,3,7,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,5,6,2,8,4,7,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,5,6,3,4,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,4,2,6,8,5,7,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,1,3,2,5,4,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[8,2,3,1,5,6,4,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[2,8,3,1,5,7,4,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,4,1,6,8,7,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,1,6,7,8,5,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,3,1,7,6,8,5,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,2,7,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,3,7,2,6,4,8,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,7,3,1,5,8,4,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,7,2,1,8,5,4,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,7,2,8,1,5,3,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,7,8,2,1,4,3,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,7,1,2,8,4,5,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,1,3,4,8,5,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,2,7,3,4,6,8,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,1,7,3,4,8,6,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,1,7,8,2,3,6,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[4,1,8,7,2,3,6,5] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[3,8,1,2,7,4,5,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,1,3,7,5,8,6,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,1,4,5,7,8,6,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,1,8,3,4,7,6,5] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[8,2,1,3,4,6,5,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,8,2,3,4,5,7,6] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,2,8,3,4,6,7,5] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[4,2,1,6,5,8,7,3] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[5,2,6,1,4,8,7,3] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[5,2,6,4,1,8,7,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[5,2,7,4,8,1,6,3] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[5,2,7,4,8,6,1,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,7,2,3,8,6,1,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,7,2,3,8,1,6,4] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[5,6,2,3,1,8,7,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,6,2,1,3,8,7,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,1,6,4,2,8,7,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[5,6,1,3,2,8,7,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,6,3,1,2,8,7,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,6,3,2,1,8,7,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[5,7,3,2,8,1,6,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[5,7,3,2,8,6,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,7,3,8,2,1,5,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[6,7,3,8,1,2,5,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[5,7,3,1,8,2,6,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,7,1,3,8,2,6,4] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[5,1,7,4,8,2,6,3] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[1,5,7,4,8,3,6,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,5,7,4,8,6,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,1,7,4,8,6,2,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,7,1,3,8,6,2,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,7,3,1,8,6,2,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[6,7,3,8,1,5,2,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,7,3,8,5,2,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[6,7,8,3,1,4,2,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,7,1,8,3,5,2,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,1,7,8,4,5,2,3] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[1,6,7,8,4,5,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,6,7,8,4,3,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,1,7,8,4,2,5,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[6,7,1,8,3,2,5,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[5,7,2,1,8,3,6,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[6,7,2,8,1,3,5,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,7,2,8,3,1,5,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[6,7,2,8,3,5,1,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,2,7,8,4,5,1,3] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[6,2,7,8,4,1,5,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[6,2,7,8,1,4,5,3] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[5,2,7,1,8,4,6,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,2,1,7,8,5,6,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,1,2,7,8,6,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,2,7,8,1,5,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,2,7,8,5,1,4,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,2,7,8,5,4,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,7,2,8,5,3,1,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,7,2,1,8,6,3,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[5,7,1,2,8,6,3,4] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[5,1,7,2,8,6,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,5,7,3,8,6,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,6,7,8,3,5,4,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[6,1,7,8,2,5,4,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,7,1,8,2,5,3,4] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[6,7,8,2,4,1,3,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[6,7,8,2,4,3,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,7,1,8,5,2,3,4] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[6,1,7,8,5,2,4,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[1,6,7,8,5,3,4,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,1,7,8,5,4,2,3] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,7,1,8,5,3,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[6,7,8,4,1,3,2,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,3,8,5,2,7,4,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,5,2,8,4,7,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[6,3,4,5,8,7,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,6,1,4,8,7,3,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,6,4,8,5,7,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[5,1,4,8,6,3,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,4,7,1,8,6,5,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[6,3,8,4,2,7,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,6,8,7,1,4,2,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,3,7,1,6,8,2,4] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[4,3,8,5,6,7,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,6,1,2,7,8,5,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,6,4,2,8,7,5,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,3,7,5,2,8,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,5,2,7,4,8,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,7,1,4,8,3,2,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[7,8,3,5,1,4,6,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,8,1,4,6,7,2,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,5,8,4,3,7,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[6,3,7,4,2,8,5,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,7,1,6,2,4,5,3] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[3,8,6,7,1,4,5,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,3,8,7,4,1,2,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,3,8,7,1,5,6,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[8,3,6,1,2,5,7,4] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,6,1,8,7,3,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,4,2,7,3,6,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,5,3,6,4,2,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[6,4,1,5,3,8,2,7] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,2,6,3,4,7,5,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,2,6,3,5,4,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[6,2,7,4,3,5,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[3,7,6,4,5,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[2,7,6,5,3,4,8,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[6,5,4,3,1,8,2,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,6,5,4,2,7,3,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,5,4,1,7,2,6,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,4,1,8,3,2,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[1,6,5,2,8,3,4,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,6,5,3,4,8,2,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,4,6,3,1,8,2,7] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,5,8,4,2,7,3,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[5,8,2,6,4,7,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,8,5,3,2,6,4,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,8,3,1,7,2,5,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,8,6,3,7,5,2,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[8,7,5,2,6,4,3,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,1,6,2,5,4,3] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[7,8,1,6,3,2,5,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,8,1,7,3,5,6,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,8,1,3,7,2,6,5] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,2,8,5,7,3,6,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,1,7,6,8,3,2,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[6,7,3,1,8,4,2,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[1,7,3,8,4,5,2,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,7,2,8,5,3,4,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[7,6,1,8,4,3,2,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,6,1,7,4,2,5,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,1,2,7,3,4,6,5] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[7,1,2,8,3,5,4,6] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[8,2,6,1,7,3,5,4] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[4,2,1,5,8,3,6,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,4,3,1,6,8,2,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,7,5,6,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[6,5,4,8,2,7,3,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[6,5,1,8,7,4,2,3] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,6,4,7,5,3,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[5,1,8,3,7,6,2,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,4,8,1,7,2,6,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[3,6,8,2,4,7,5,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[5,7,3,8,2,6,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,7,2,8,6,3,5,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[2,3,8,7,4,5,6,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[7,2,8,6,4,3,5,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[2,1,8,7,5,6,3,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[8,2,7,6,3,5,4,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,1,7,6,5,2,4,3] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[7,1,8,6,5,3,2,4] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,2,8,7,6,3,4,5] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,3,8,7,4,6,2,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,1,6,8,7,4,2,3] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,8,7,2,5,4,3,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[3,8,7,6,4,5,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[2,8,7,6,5,3,4,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[1,8,7,6,5,4,2,3] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[5,8,6,7,3,4,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,8,6,7,3,5,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,8,6,7,4,5,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,8,6,7,4,5,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,8,6,7,4,5,2,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,8,5,7,4,6,2,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,8,5,7,4,6,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,8,5,7,3,6,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[7,8,3,6,4,5,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,3,7,4,5,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,3,7,4,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[3,7,4,8,5,6,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,7,3,8,5,6,1,2] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,7,2,8,5,6,1,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,7,1,8,5,6,2,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,7,1,8,5,6,2,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,7,2,8,5,6,1,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[2,7,3,8,5,6,1,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,7,4,8,5,6,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[5,8,2,7,4,6,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,2,7,4,5,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,2,6,4,5,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,1,6,4,5,2,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,1,7,4,5,2,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,1,7,4,6,2,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[1,7,4,8,5,6,2,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,7,3,8,5,6,2,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,8,5,6,1,7,3,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,8,5,6,2,7,3,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,7,3,8,4,6,2,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,8,1,7,3,6,2,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,1,7,3,6,2,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,1,7,3,5,2,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,2,6,3,5,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,2,7,3,5,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,2,7,3,6,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,8,2,7,3,6,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[2,7,3,8,4,6,1,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[3,7,2,8,4,6,1,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,7,1,8,4,6,2,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[1,8,4,7,3,6,2,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,8,4,7,3,6,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,8,4,7,2,6,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,8,5,7,2,6,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,8,5,7,2,6,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,8,5,7,3,6,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,8,5,7,3,6,2,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,8,6,7,3,5,2,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,8,6,7,3,5,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,8,6,7,2,5,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,8,6,7,2,5,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,8,6,7,2,4,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[6,8,5,7,1,4,2,3] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,6,7,1,4,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,6,7,1,5,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,8,6,7,1,5,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[1,5,2,8,6,7,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,5,1,8,6,7,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,6,1,8,5,7,3,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[1,6,2,8,5,7,3,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[3,8,5,7,1,6,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,8,4,7,1,5,2,3] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,4,6,1,5,2,3] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,3,6,1,5,2,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,3,7,1,5,2,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[4,8,3,7,1,6,2,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[3,8,4,7,1,6,2,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[1,6,2,8,4,7,3,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,6,1,8,4,7,3,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,7,2,6,1,8,4,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[3,7,1,6,2,8,4,5] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,8,1,6,2,7,3,5] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,8,1,6,2,7,3,4] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[7,8,1,5,2,6,3,4] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,2,5,1,6,3,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[6,8,2,5,1,7,3,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,2,6,1,7,3,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,8,2,6,1,7,3,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[1,7,3,6,2,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,7,3,6,1,8,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9]] => 00000000
[1,2,3,4,5,6,8,9,7] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,2,3,4,5,7,8,9,6] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,2,3,4,6,7,8,9,5] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,2,3,5,6,7,8,9,4] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,2,4,5,6,7,8,9,3] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,3,4,5,6,7,8,9,2] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[1,2,3,4,5,6,7,8,9,10] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000
[1,2,3,4,5,6,9,8,7] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,4,5,6,7,9,10,8] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[1,2,3,4,5,8,7,9,6] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[1,2,3,4,5,6,8,9,10,7] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[1,2,3,4,5,7,8,9,10,6] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[1,2,3,4,6,7,8,9,10,5] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[1,2,3,5,6,7,8,9,10,4] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[1,2,4,5,6,7,8,9,10,3] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[3,2,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[1,3,4,5,6,7,8,9,10,2] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[6,7,4,8,3,5,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[6,7,4,5,2,8,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,7,4,6,2,3,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,7,4,6,3,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,7,4,8,3,6,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[6,8,4,5,3,7,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,4,6,3,7,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,6,4,8,3,7,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,6,3,7,2,4,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[5,6,3,7,2,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,6,3,8,2,7,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,6,4,8,2,7,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,8,4,6,2,7,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,4,5,2,7,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,4,5,2,6,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,4,5,2,3,1,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,4,6,2,3,1,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,6,4,8,2,3,1,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,6,3,8,2,4,1,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,6,3,4,2,8,1,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,6,3,5,2,7,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,6,3,5,2,8,1,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,6,3,8,2,5,1,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,3,6,2,5,1,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,3,6,2,4,1,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,3,5,2,4,1,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,3,5,2,4,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,3,5,2,6,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,3,6,2,7,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,8,3,6,2,7,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,6,3,8,2,7,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,6,3,7,2,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,7,3,6,2,5,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[4,7,3,6,2,8,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,7,3,8,2,6,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,7,4,8,2,6,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,7,3,6,2,8,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,7,3,6,2,4,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,7,3,5,2,4,1,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,7,3,5,2,8,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,7,4,8,2,5,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[6,7,5,8,2,4,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[6,8,5,7,2,3,1,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,7,4,8,2,3,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,7,3,8,2,4,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,7,3,4,2,8,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,7,3,4,2,6,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,7,3,4,2,8,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,7,4,8,2,3,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,8,4,7,2,3,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,4,7,2,3,1,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,4,6,2,3,1,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,3,6,2,4,1,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,3,7,2,4,1,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,3,7,2,4,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[4,8,3,7,2,5,1,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[4,7,3,8,2,5,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,7,3,5,2,8,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,7,3,5,2,6,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,3,7,2,6,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,5,3,7,2,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,5,3,8,2,7,1,6] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,8,3,5,2,7,1,6] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,3,4,2,7,1,6] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,3,4,2,7,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,3,4,2,6,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,3,4,2,5,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,8,3,4,2,6,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,8,3,5,2,6,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,3,8,2,6,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,5,3,6,2,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,7,5,2,1,8,3,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[4,8,5,2,1,7,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,6,5,2,1,3,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,6,4,2,3,1,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,4,5,3,1,2,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[5,4,6,1,3,2,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[4,6,8,1,7,3,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,8,1,6,3,5,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[7,4,8,1,6,5,3,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[5,4,8,1,3,7,6,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[8,4,5,3,1,7,6,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,4,7,1,3,8,2,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,4,8,1,7,5,2,3] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,6,8,7,2,1,3,4] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,5,7,6,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[8,4,6,3,7,2,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,3,2,8,7,4,1,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[2,1,6,8,7,4,3,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,1,7,8,6,4,5,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[7,3,2,8,6,4,5,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,6,8,5,2,4,3,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[5,7,8,6,2,3,1,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,8,7,6,3,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[6,8,7,5,3,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[5,8,4,2,3,7,6,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,8,4,2,6,5,3,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[4,8,7,2,6,3,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[4,8,6,2,7,3,1,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[3,6,1,8,7,4,2,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[3,7,1,8,6,4,5,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,8,1,6,7,5,2,4] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[3,7,1,6,8,2,5,4] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,7,6,2,8,1,3,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,7,4,2,8,1,5,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,8,4,2,7,5,1,3] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[2,1,8,6,7,5,3,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[8,3,2,6,7,5,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,6,4,3,7,5,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[5,8,6,7,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[6,7,5,8,1,3,4,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[7,6,5,8,1,4,3,2] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[8,6,5,7,4,1,3,2] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[7,6,4,3,8,1,5,2] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,3,2,6,8,1,5,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[2,1,7,6,8,3,5,4] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[7,5,6,8,1,4,2,3] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[6,5,7,8,1,2,4,3] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,1,3,7,4,6,5,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[5,2,8,7,4,6,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,6,2,5,4,7,3,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[6,2,7,5,4,8,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[8,1,3,5,4,7,6,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[6,1,5,4,3,8,7,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,1,8,3,4,5,7,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[7,1,5,3,4,8,6,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,1,4,3,5,6,8,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,1,3,4,5,6,7,2] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[1,7,2,4,5,6,3,8] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[6,3,2,7,5,1,8,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,4,7,2,5,6,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,5,8,2,4,7,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,5,2,1,4,3,7,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,5,2,8,4,1,3,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,6,2,1,4,8,3,7] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[3,6,1,8,5,2,4,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[1,2,6,3,5,4,7,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[3,4,1,2,8,6,5,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[4,3,1,2,6,8,5,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,8,1,6,3,2,4,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,3,8,5,2,1,4,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[8,3,1,5,2,4,7,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,8,2,6,1,5,7,4] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,8,6,7,2,1,5,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[8,5,6,4,2,1,7,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[7,2,5,8,3,1,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[1,7,5,6,3,2,4,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[6,1,2,3,8,5,7,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[7,1,2,3,6,5,8,4] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[7,2,1,3,8,6,4,5] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[1,5,7,3,2,4,6,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[5,2,7,3,1,8,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[5,8,2,4,1,3,7,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[8,7,2,6,3,4,1,5] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[4,8,1,6,3,2,7,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[3,1,8,6,4,2,7,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[8,1,6,7,4,3,2,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,5,8,7,2,4,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,2,1,3,7,8,5,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,4,1,3,8,7,5,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,5,8,3,1,7,4,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[8,6,1,3,7,2,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[2,8,1,3,6,4,7,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,8,2,3,4,1,5,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[5,1,8,3,2,4,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111
[8,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[8,7,9,6,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[8,7,6,5,4,3,2,9,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[8,7,6,5,4,3,2,1,9] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[9,10,8,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[7,8,9,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[9,8,10,7,6,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[8,6,7,9,5,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111
[9,8,7,10,6,5,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => 110111111
[9,8,7,6,10,5,4,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[9,8,7,6,5,10,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => 111101111
[9,8,7,6,5,4,10,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => 111110111
[8,7,6,5,4,2,3,9,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001
[9,8,7,6,5,4,3,10,2,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => 111111011
[8,7,6,5,4,3,1,2,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[9,8,7,6,5,4,3,2,10,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => 111111101
[9,8,7,6,5,4,3,2,1,10] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[1,4,2,7,8,6,3,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,6,2,4,8,5,3,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,6,2,4,7,5,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,7,3,8,5,2,4,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,7,3,2,8,6,4,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[4,2,5,7,8,6,1,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[7,2,3,1,8,5,6,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,2,5,1,7,3,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,2,1,8,3,4,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[6,2,8,3,5,1,7,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,2,4,8,5,7,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[1,3,6,4,8,5,7,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,3,6,4,7,5,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[6,2,4,7,5,8,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[6,2,1,3,7,8,4,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[7,8,2,1,4,3,5,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,6,4,2,3,1,8,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[5,7,2,3,1,6,8,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,5,4,2,6,8,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[1,7,5,3,4,6,8,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[8,2,5,4,6,7,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,2,6,3,1,8,7,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[8,2,6,4,3,1,7,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,2,7,4,1,3,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[1,2,8,4,3,5,6,7] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,7,4,2,3,5,6,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[6,8,4,1,3,2,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,8,7,4,3,2,5,6] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,6,3,8,2,4,7,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[5,3,8,1,2,7,4,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[5,1,8,3,2,6,4,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[5,7,3,1,2,6,4,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[1,7,5,4,2,6,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,5,8,2,4,6,3,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,5,8,4,2,7,3,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,4,6,2,8,3,7,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,3,1,6,7,2,4,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,3,6,1,2,8,4,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[1,6,3,2,7,8,4,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[1,7,4,5,3,8,6,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,3,4,1,2,5,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,1,4,2,7,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[1,8,3,2,4,5,6,7] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[8,6,3,2,4,1,7,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,5,3,2,6,7,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[4,5,2,6,8,1,7,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,2,5,6,7,8,1,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,2,3,6,7,1,8,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[6,2,3,4,1,7,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[7,2,3,1,4,5,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,6,1,4,3,2,5,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,3,1,6,5,2,4,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,7,5,1,8,2,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[4,1,5,2,8,7,3,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[8,1,2,4,6,5,3,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,1,2,5,4,6,3,7] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,2,6,5,1,3,4,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,3,1,6,2,5,4,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,1,2,6,4,5,3,7] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,1,2,5,6,4,3,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,1,2,6,5,4,3,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[1,7,5,4,2,8,3,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[5,1,4,8,2,7,3,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[1,4,6,8,2,7,3,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,4,7,6,2,8,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,1,4,7,2,8,3,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[1,7,4,5,2,8,3,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,7,5,1,2,8,4,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,7,2,8,1,3,4,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[5,2,8,7,1,3,4,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,1,5,8,2,7,3,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[1,4,6,2,8,7,3,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,4,2,8,6,7,3,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,1,2,6,4,8,7,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,7,6,3,4,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,1,2,7,4,6,8,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,4,7,2,6,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,2,3,6,8,5,7,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,1,4,2,7,8,3,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,4,2,7,6,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,4,2,6,8,7,3,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,1,2,8,4,6,7,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,1,2,7,6,4,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,3,7,1,8,2,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[1,7,4,3,2,5,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,8,7,2,1,3,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[1,8,7,3,4,2,5,6] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[3,1,7,8,2,6,4,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[1,4,2,7,8,3,6,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,2,8,1,3,4,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[2,1,8,6,3,4,7,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[1,4,2,6,8,3,7,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,2,3,7,8,5,6,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,3,7,5,8,6,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,4,2,7,3,8,6,5] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,1,7,2,8,6,4,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,1,7,8,3,4,6,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[1,2,3,8,7,5,6,4] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[10,1,2,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[9,1,10,2,3,4,5,6,7,8] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[10,9,1,2,3,4,5,6,7,8] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[8,1,2,3,4,5,6,9,10,7] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[2,9,10,1,3,4,5,6,7,8] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[4,7,8,5,6,2,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,7,8,4,2,6,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,7,8,4,2,5,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[8,6,3,7,2,1,5,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[7,6,3,8,2,1,5,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[6,7,8,3,2,1,5,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,7,8,3,2,1,6,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,7,8,4,3,5,6,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,7,8,4,2,5,1,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,7,8,3,2,1,5,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,7,8,3,2,1,4,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[7,6,3,8,2,1,4,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,6,3,7,2,1,4,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,6,3,8,2,1,4,7] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,6,4,8,2,5,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,6,4,8,3,5,7,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,6,4,7,3,5,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,6,4,7,2,5,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,6,3,7,2,1,5,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[5,6,3,7,2,1,4,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,4,3,2,1,6,5,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[6,4,3,2,1,7,5,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[4,5,3,2,7,1,6,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,5,4,2,8,6,1,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[6,4,3,2,1,8,5,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,4,3,2,1,8,5,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,4,3,2,1,7,5,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,4,3,2,1,7,6,5] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[7,4,3,2,1,8,6,5] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[6,4,3,2,1,8,7,5] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[5,6,3,8,2,1,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[7,5,3,2,8,1,6,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[8,5,4,2,7,6,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[7,5,4,2,8,6,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[6,5,4,2,8,7,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[4,6,5,8,7,2,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,6,5,7,8,3,4,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[6,5,4,2,7,8,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,5,4,2,6,7,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,5,3,2,6,1,7,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,5,3,2,6,1,8,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[5,6,3,7,2,1,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,6,3,7,2,1,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[3,6,4,7,2,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,6,4,7,3,8,5,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,5,4,2,7,8,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[4,5,3,2,7,1,8,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[7,4,3,2,1,6,8,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,4,3,2,1,6,7,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,4,3,2,1,5,7,6] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,4,3,2,1,5,8,6] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,4,3,2,1,5,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[3,5,4,2,6,8,1,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,5,3,7,2,6,4,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[8,5,7,4,2,6,3,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[6,8,3,7,5,1,4,2] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[5,7,3,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,2,6,4,8,5,1,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,5,2,4,1,7,6,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,2,5,8,3,1,6,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,1,5,4,2,8,6,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,1,5,8,3,2,6,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,3,8,5,2,1,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,7,3,5,2,1,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,3,2,7,5,1,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[4,3,6,2,5,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,6,3,2,5,1,7,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,3,1,5,7,2,6,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,3,6,1,5,2,7,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,6,3,1,5,2,7,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,3,6,4,1,2,7,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,3,6,1,7,2,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,2,4,1,3,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[3,6,4,1,2,7,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,6,3,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[5,6,2,7,1,3,4,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,5,2,7,3,1,6,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,6,2,1,7,3,5,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,2,6,1,4,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[3,5,2,7,4,6,1,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,7,2,4,8,5,1,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[7,3,1,4,6,8,2,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[3,2,6,1,5,7,4,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,3,2,1,5,7,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,4,2,1,5,3,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,2,6,1,5,3,7,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,2,1,7,5,3,6,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,4,1,5,6,2,3,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,3,1,5,2,6,4,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,3,5,1,2,7,4,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,2,6,4,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,6,5,1,2,7,4,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[6,5,2,1,4,7,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,5,3,1,4,7,2,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[2,3,1,8,5,4,7,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,4,1,5,8,3,7,6] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,4,1,5,3,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,4,5,1,2,8,7,6] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,4,5,1,8,2,7,6] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,4,5,8,2,1,7,6] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,4,5,2,8,1,7,6] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[3,4,6,2,1,7,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,4,6,2,1,7,5,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[3,5,6,2,7,1,4,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[3,5,6,2,7,1,8,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[3,5,6,2,7,8,1,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,8,4,6,3,7,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,4,6,8,2,7,5,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,4,6,2,8,7,5,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,5,6,2,7,8,4,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,5,6,2,7,4,1,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[4,5,6,7,2,8,3,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,5,6,8,7,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,5,8,6,7,3,4,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,5,8,6,7,3,1,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,5,6,8,7,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,5,6,7,2,1,8,3] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,3,1,8,6,7,4,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,8,3,2,6,7,5,4] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,5,1,6,7,8,4,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,5,1,6,7,4,8,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,5,1,6,7,4,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[3,5,6,1,7,4,2,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[3,5,6,1,7,4,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,4,6,8,1,7,5,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,8,6,1,7,5,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,5,6,8,7,1,4,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,5,6,7,8,1,3,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,5,6,7,1,3,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[4,5,6,7,1,3,2,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[4,5,6,7,3,1,8,2] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,5,6,8,7,4,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,5,8,6,7,4,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,8,5,6,7,4,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[2,5,8,6,7,4,3,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[8,2,5,3,7,1,6,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,2,4,3,7,1,6,5] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[5,8,2,4,3,7,1,6] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,2,5,6,1,8,3,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[4,2,5,6,1,7,3,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[6,1,5,7,3,2,4,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,1,5,8,3,2,4,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,8,2,4,7,1,5,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[3,6,8,2,4,7,1,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[4,3,5,6,7,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[3,7,1,5,6,8,2,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,7,1,5,8,2,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[8,3,2,4,6,1,5,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,3,2,4,6,1,5,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,2,5,1,7,4,6,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[3,2,5,1,8,4,6,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[3,2,5,1,7,8,4,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[7,8,3,2,4,6,1,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,1,5,7,8,3,2,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,2,5,6,1,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,7,6,1,8,3,4,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,8,6,1,7,3,4,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[6,1,5,8,7,3,2,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[8,7,3,2,4,6,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[3,2,5,1,8,7,4,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[3,2,5,1,6,4,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[3,2,4,1,8,7,5,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,2,5,1,6,8,7,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,8,6,5,1,7,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[3,7,6,5,1,8,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[6,5,1,7,8,4,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[3,2,5,1,6,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[3,2,4,1,8,5,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[3,2,4,1,7,5,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[3,2,4,1,6,8,5,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[3,2,4,1,8,5,7,6] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,3,2,4,7,6,1,5] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[3,2,5,1,8,4,7,6] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,2,5,1,6,7,4,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[6,5,1,7,4,2,3,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,5,1,8,4,2,3,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,4,2,3,7,5,1,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,2,6,1,8,3,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[5,2,6,1,8,3,7,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[8,4,6,1,7,3,5,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,2,6,1,8,4,7,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[7,4,2,3,8,5,1,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,5,1,6,4,2,3,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,5,1,6,4,2,3,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,2,5,1,7,6,4,8] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,2,5,1,8,6,4,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,3,2,4,8,6,1,5] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,6,1,5,7,3,2,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[4,2,6,1,8,5,7,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[8,5,6,1,7,3,4,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[3,6,8,5,1,7,4,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,5,1,6,7,4,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[3,2,5,1,8,6,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,2,4,1,8,6,5,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,2,4,1,5,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[3,2,5,1,7,8,6,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,8,5,1,6,4,2,3] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[3,8,5,1,7,6,4,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[3,7,5,1,8,6,4,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[8,7,5,1,6,4,2,3] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[3,2,5,1,8,7,6,4] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,5,7,3,1,8,4,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[4,6,3,7,1,8,5,2] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[4,6,3,7,5,1,8,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[4,2,6,1,7,5,3,8] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[2,5,7,4,1,6,3,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,5,7,4,1,6,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[5,4,7,3,6,1,8,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,4,7,8,3,1,6,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,3,7,5,1,8,6,2] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[6,4,3,8,5,1,7,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,8,4,3,6,1,7,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,4,8,3,6,1,7,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,4,3,6,7,1,8,2] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[2,5,4,6,1,7,3,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,2,5,8,1,6,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[2,5,4,6,8,1,7,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[5,2,8,4,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,6,2,1,8,5,7,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[2,4,1,7,5,8,6,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,4,1,7,5,3,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,6,4,1,8,5,3,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[5,4,8,2,1,6,3,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[2,5,8,4,1,6,3,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[3,2,5,6,1,8,4,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[4,8,3,2,6,1,5,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[3,5,2,8,1,6,4,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,2,1,6,8,5,4,7] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[3,2,7,1,5,4,8,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,2,7,1,5,8,6,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[3,8,2,5,1,6,7,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,8,3,2,6,7,1,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,3,8,2,6,7,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[4,3,2,6,7,8,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,3,2,6,7,1,5,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[4,3,7,2,6,8,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[4,3,7,8,2,6,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[2,5,7,4,8,1,6,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[3,2,5,7,8,1,6,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,2,5,7,1,6,8,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[3,2,5,7,1,6,4,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[6,3,2,7,1,5,4,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,3,2,7,1,5,8,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,3,2,7,8,1,5,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[4,2,6,1,7,8,5,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[6,5,2,1,7,8,4,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[2,1,7,5,3,8,6,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[6,2,1,8,5,3,7,4] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,3,2,7,1,4,8,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,3,2,1,4,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,3,2,1,4,7,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,5,2,1,7,4,6,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,5,2,1,7,8,4,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,8,4,2,1,7,3,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[4,6,2,1,8,3,7,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[2,4,1,7,3,8,6,5] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,2,7,1,4,8,6,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[3,5,8,2,1,7,4,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,8,3,7,2,1,5,6] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[4,3,7,2,8,1,5,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,3,7,2,1,5,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[4,8,3,2,7,1,5,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[3,5,2,8,1,7,4,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,3,2,8,1,4,7,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[3,2,1,4,7,5,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[5,3,2,1,8,4,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,8,3,2,1,5,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,3,8,2,1,5,6,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[1,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[1,10,9,8,7,6,5,4,3,2] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[6,2,3,1,5,4,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,4,5,2,3,1,7,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,6,7,2,5,3,4,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,2,5,3,4,1,7,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,2,5,3,4,1,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,1,5,2,4,3,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,4,5,1,3,2,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,1,5,3,4,2,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,3,5,1,4,2,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,3,5,2,4,1,7,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,3,7,5,6,2,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,3,7,2,4,1,6,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,3,5,1,4,2,7,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,1,5,3,4,2,7,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,4,5,1,3,2,7,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[2,1,8,4,5,3,7,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,6,7,4,5,1,3,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,6,7,1,5,3,4,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,6,7,3,5,1,4,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,3,7,5,6,1,4,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,5,7,3,6,1,4,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,3,7,4,6,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,3,7,4,6,1,5,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,3,7,1,6,4,5,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,7,3,6,4,5,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,1,7,5,6,3,4,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,7,5,6,1,3,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[2,1,8,4,7,5,6,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,1,7,3,4,2,6,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,7,3,6,2,5,4] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,3,7,1,6,2,5,4] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,3,7,2,6,4,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,2,7,3,6,4,5,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,2,7,3,6,1,5,4] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,2,7,1,6,3,5,4] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,7,2,4,3,6,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,3,2,7,4,6,5] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[2,1,8,3,7,4,6,5] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,1,5,2,4,3,7,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,2,7,1,4,3,6,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,2,7,3,4,1,6,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,2,7,5,6,3,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,7,5,6,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,7,2,3,1,6,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,2,3,1,7,4,6,5] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,3,1,5,4,7,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,2,3,1,8,5,7,6] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,1,3,2,8,6,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,6,7,2,3,1,5,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,2,3,1,7,5,6,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,5,7,2,6,3,4,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,5,7,2,6,1,4,3] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,2,7,5,6,1,4,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,6,7,2,5,1,4,3] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,6,7,1,5,2,4,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,6,7,1,3,2,5,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[2,1,8,6,7,3,5,4] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,8,3,7,5,6,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,1,3,2,7,5,6,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,1,7,5,6,2,4,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,1,7,2,6,4,5,3] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[8,2,7,1,6,4,5,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,2,7,4,6,1,5,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,2,7,4,6,3,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,7,2,6,3,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,4,7,2,6,1,5,3] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,4,7,1,6,2,5,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,7,4,6,2,5,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,5,7,1,6,2,4,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[2,1,8,5,7,3,6,4] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[8,5,7,4,6,1,3,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,5,7,1,6,3,4,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,7,4,6,3,5,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,7,1,6,3,5,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,4,7,3,6,1,5,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[2,4,8,3,6,1,7,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[6,5,8,1,3,2,7,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,5,8,6,3,2,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[6,5,8,7,3,1,2,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[1,5,8,7,3,6,2,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[1,7,2,8,4,6,5,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[6,7,2,8,4,1,5,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[3,6,2,8,4,5,7,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,6,1,8,4,5,7,3] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,8,4,6,1,5,7,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,3,1,8,4,5,7,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,1,6,8,4,5,7,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,3,6,8,4,5,7,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[6,3,7,8,4,1,5,2] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[1,3,7,8,4,6,5,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,5,7,8,2,4,6,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[5,1,7,8,2,4,6,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[3,6,7,8,4,2,5,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[7,6,1,8,4,2,5,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,6,8,7,3,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,8,3,7,1,6,5,4] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,2,8,7,3,6,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,2,1,8,4,6,5,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,2,7,8,4,6,5,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,2,7,8,1,4,6,3] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[1,2,7,8,5,4,6,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,2,1,3,8,5,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,2,5,8,3,4,6,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,2,8,5,4,3,1,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,8,3,5,4,1,6,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[2,8,4,5,3,1,6,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[6,4,8,5,2,3,1,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,3,5,8,2,4,6,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,3,1,2,8,5,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[3,4,2,1,8,5,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,7,6,8,4,3,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,7,1,8,3,4,6,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,7,5,8,1,4,6,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[1,7,5,8,3,4,6,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,6,8,5,4,3,2,7] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[4,6,8,5,1,3,2,7] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,6,8,1,4,3,2,7] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[7,5,8,6,3,4,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[2,4,8,3,6,5,1,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,8,4,1,5,6,3,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[4,1,8,3,5,6,2,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[5,6,8,4,1,3,2,7] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,6,8,1,5,3,2,7] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[1,6,8,4,5,3,2,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,7,3,8,5,4,6,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,7,1,8,5,4,6,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[2,7,3,8,4,6,5,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[7,1,3,8,4,6,5,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,7,8,4,3,6,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[2,8,7,4,1,6,5,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,8,5,4,3,1,6,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[6,5,8,4,2,3,1,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[4,1,3,2,8,5,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[1,4,3,2,8,5,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[7,3,2,8,5,4,6,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[6,4,8,2,5,3,1,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[2,8,4,3,5,1,6,7] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[2,8,3,4,5,1,6,7] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[6,2,8,4,5,3,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,2,3,8,5,4,6,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,2,3,1,8,5,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[3,2,1,4,8,5,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,1,3,2,4,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[2,8,1,5,3,4,7,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,2,8,4,5,3,7,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,4,2,8,5,3,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,8,4,2,5,3,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[8,1,5,3,2,4,6,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[3,8,1,5,2,4,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,5,1,4,8,2,6,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[1,5,2,8,4,3,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,2,8,5,4,3,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,2,5,4,3,8,6,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,4,8,5,3,7,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,2,7,4,8,5,3,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,5,2,7,8,4,3,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[5,1,2,7,4,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,3,5,1,4,7,2,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[2,8,1,5,4,7,3,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,2,8,5,7,4,3,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,2,4,8,7,5,3,6] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,8,1,4,3,7,6,5] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[6,1,2,8,7,4,3,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,4,1,2,8,7,3,5] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[3,6,4,8,1,7,2,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[7,6,1,4,2,8,3,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,1,6,2,8,4,3,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,6,7,2,8,4,3,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[6,7,1,4,2,8,3,5] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[6,3,7,1,4,8,2,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[3,7,8,1,5,2,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[7,1,2,8,5,3,4,6] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[1,7,2,8,4,5,3,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,2,7,8,5,3,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[6,1,2,8,4,3,7,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[6,4,1,2,8,3,7,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,6,1,3,2,4,8,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,7,1,3,2,4,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,2,7,3,5,8,4,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,2,7,5,8,3,4,6] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[5,8,1,3,7,2,4,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,2,5,8,7,3,4,6] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,2,5,8,3,7,4,6] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,8,1,7,3,5,4,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,6,1,3,2,4,7,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,2,8,1,7,3,6,5] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[2,8,1,7,4,3,6,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[7,1,2,8,4,3,6,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[1,2,8,4,7,5,3,6] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,2,8,7,4,5,3,6] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[2,8,1,7,5,3,4,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[8,3,7,1,5,2,4,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[3,8,6,1,4,7,2,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[8,6,1,4,2,7,3,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,1,6,2,7,4,3,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,1,2,8,6,4,3,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[7,4,1,2,8,6,3,5] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[3,7,4,8,1,6,2,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,4,8,7,1,6,2,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,2,8,1,7,6,3,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[2,8,1,7,6,4,3,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,8,3,4,1,5,2,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,3,4,1,6,2,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[6,8,3,4,1,7,2,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[6,7,3,4,1,8,2,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,7,3,4,1,8,2,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,3,4,1,7,2,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,3,4,1,6,2,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,8,3,4,1,5,2,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,3,4,1,5,2,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,7,3,4,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,6,2,8,3,4,1,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,6,2,7,3,4,1,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,6,2,8,3,5,1,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,7,3,5,1,6,2,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[4,8,3,5,1,6,2,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[4,8,3,5,1,7,2,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,7,3,5,1,8,2,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,6,2,3,1,7,4,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,6,2,4,1,8,3,7] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,6,2,4,1,7,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[4,6,2,5,1,7,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[4,6,2,5,1,8,3,7] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,5,1,8,3,7,2,6] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,5,1,7,3,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[4,6,2,7,3,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,6,2,7,3,8,1,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,6,2,7,4,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[5,6,3,8,4,7,1,2] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[5,6,2,8,4,7,1,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[5,6,2,8,3,7,1,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,6,2,8,3,7,1,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,5,1,7,3,6,2,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,5,1,8,3,6,2,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[9,2,1,3,4,5,6,7,8] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[10,2,1,3,4,5,6,7,8,9] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[9,2,3,1,4,5,6,7,8] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[4,2,3,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[3,2,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[6,5,3,2,1,4,8,7] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[4,6,3,5,2,1,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[8,7,3,5,2,4,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,8,2,4,5,7,3,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,7,2,4,5,3,1,6] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[3,6,1,4,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[8,3,7,4,5,2,1,6] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[6,3,8,4,5,7,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[5,8,7,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[2,8,7,4,3,6,1,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,1,7,4,3,6,2,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,7,3,5,1,4,2,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,1,6,8,5,7,4,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,8,3,5,1,7,4,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,1,8,4,7,6,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[2,5,8,4,7,6,3,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,3,8,1,5,6,7,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,8,1,3,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[5,8,7,4,1,6,3,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[5,8,3,6,1,4,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,8,3,6,1,2,7,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[3,8,7,4,1,6,2,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,8,1,2,5,6,7,4] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[8,7,1,4,2,6,3,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,6,3,1,2,4,7,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,1,7,4,5,2,3,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,8,7,4,5,1,3,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[8,7,2,4,1,6,3,5] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[5,8,3,6,2,4,7,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[8,6,3,2,1,4,7,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,7,3,5,2,1,4,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,8,3,6,2,1,7,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,8,7,4,2,6,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[2,6,8,4,5,7,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[6,1,8,4,5,7,2,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,8,3,5,1,7,2,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[2,1,5,8,3,6,7,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,8,3,6,1,2,7,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[4,1,8,2,5,6,7,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,4,8,1,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,8,2,1,5,6,7,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,4,8,2,5,6,7,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[5,8,1,4,7,6,2,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[5,8,3,1,6,2,7,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,5,3,8,6,1,7,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,4,1,8,5,6,7,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,6,8,10,1,3,5,7,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,4,6,9,10,1,3,5,7,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,4,7,8,10,1,3,5,6,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,4,7,9,10,1,3,5,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,4,8,9,10,1,3,5,6,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,5,6,8,10,1,3,4,7,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,5,6,9,10,1,3,4,7,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,5,7,8,10,1,3,4,6,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,5,7,9,10,1,3,4,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,5,8,9,10,1,3,4,6,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,6,7,8,10,1,3,4,5,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,6,7,9,10,1,3,4,5,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,6,8,9,10,1,3,4,5,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,7,8,9,10,1,3,4,5,6] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,4,6,8,10,1,2,5,7,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,4,6,9,10,1,2,5,7,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,4,7,8,10,1,2,5,6,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,4,7,9,10,1,2,5,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,4,8,9,10,1,2,5,6,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,5,6,8,10,1,2,4,7,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,5,6,9,10,1,2,4,7,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,5,7,8,10,1,2,4,6,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,5,7,9,10,1,2,4,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,5,8,9,10,1,2,4,6,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,6,7,8,10,1,2,4,5,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,6,7,9,10,1,2,4,5,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,6,8,9,10,1,2,4,5,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[3,7,8,9,10,1,2,4,5,6] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,5,6,8,10,1,2,3,7,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,5,6,9,10,1,2,3,7,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,5,7,8,10,1,2,3,6,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,5,7,9,10,1,2,3,6,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,5,8,9,10,1,2,3,6,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,6,7,8,10,1,2,3,5,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,6,7,9,10,1,2,3,5,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,6,8,9,10,1,2,3,5,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[4,7,8,9,10,1,2,3,5,6] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[5,6,7,8,10,1,2,3,4,9] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[5,6,7,9,10,1,2,3,4,8] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[5,6,8,9,10,1,2,3,4,7] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[5,7,8,9,10,1,2,3,4,6] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[2,4,6,8,10,12,1,3,5,7,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,6,8,11,12,1,3,5,7,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,6,9,10,12,1,3,5,7,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,6,9,11,12,1,3,5,7,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,6,10,11,12,1,3,5,7,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,7,8,10,12,1,3,5,6,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,7,8,11,12,1,3,5,6,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,7,9,10,12,1,3,5,6,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,7,9,11,12,1,3,5,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,7,10,11,12,1,3,5,6,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,8,9,10,12,1,3,5,6,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,8,9,11,12,1,3,5,6,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,8,10,11,12,1,3,5,6,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,4,9,10,11,12,1,3,5,6,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,6,8,10,12,1,3,4,7,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,6,8,11,12,1,3,4,7,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,6,9,10,12,1,3,4,7,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,6,9,11,12,1,3,4,7,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,6,10,11,12,1,3,4,7,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,7,8,10,12,1,3,4,6,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,7,8,11,12,1,3,4,6,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,7,9,10,12,1,3,4,6,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,7,9,11,12,1,3,4,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,7,10,11,12,1,3,4,6,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,8,9,10,12,1,3,4,6,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,8,9,11,12,1,3,4,6,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,8,10,11,12,1,3,4,6,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,5,9,10,11,12,1,3,4,6,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,7,8,10,12,1,3,4,5,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,7,8,11,12,1,3,4,5,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,7,9,10,12,1,3,4,5,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,7,9,11,12,1,3,4,5,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,7,10,11,12,1,3,4,5,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,8,9,10,12,1,3,4,5,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,8,9,11,12,1,3,4,5,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,8,10,11,12,1,3,4,5,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,6,9,10,11,12,1,3,4,5,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,7,8,9,10,12,1,3,4,5,6,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,7,8,9,11,12,1,3,4,5,6,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,7,8,10,11,12,1,3,4,5,6,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,7,9,10,11,12,1,3,4,5,6,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[2,8,9,10,11,12,1,3,4,5,6,7] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,6,8,10,12,1,2,5,7,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,6,8,11,12,1,2,5,7,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,6,9,10,12,1,2,5,7,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,6,9,11,12,1,2,5,7,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,6,10,11,12,1,2,5,7,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,7,8,10,12,1,2,5,6,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,7,8,11,12,1,2,5,6,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,7,9,10,12,1,2,5,6,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,7,9,11,12,1,2,5,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,7,10,11,12,1,2,5,6,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,8,9,10,12,1,2,5,6,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,8,9,11,12,1,2,5,6,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,8,10,11,12,1,2,5,6,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,4,9,10,11,12,1,2,5,6,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,6,8,10,12,1,2,4,7,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,6,8,11,12,1,2,4,7,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,6,9,10,12,1,2,4,7,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,6,9,11,12,1,2,4,7,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,6,10,11,12,1,2,4,7,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,7,8,10,12,1,2,4,6,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,7,8,11,12,1,2,4,6,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,7,9,10,12,1,2,4,6,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,7,9,11,12,1,2,4,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,7,10,11,12,1,2,4,6,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,8,9,10,12,1,2,4,6,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,8,9,11,12,1,2,4,6,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,8,10,11,12,1,2,4,6,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,5,9,10,11,12,1,2,4,6,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,7,8,10,12,1,2,4,5,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,7,8,11,12,1,2,4,5,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,7,9,10,12,1,2,4,5,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,7,9,11,12,1,2,4,5,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,7,10,11,12,1,2,4,5,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,8,9,10,12,1,2,4,5,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,8,9,11,12,1,2,4,5,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,8,10,11,12,1,2,4,5,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,6,9,10,11,12,1,2,4,5,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,7,8,9,10,12,1,2,4,5,6,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,7,8,9,11,12,1,2,4,5,6,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,7,8,10,11,12,1,2,4,5,6,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,7,9,10,11,12,1,2,4,5,6,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[3,8,9,10,11,12,1,2,4,5,6,7] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,6,8,10,12,1,2,3,7,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,6,8,11,12,1,2,3,7,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,6,9,10,12,1,2,3,7,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,6,9,11,12,1,2,3,7,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,6,10,11,12,1,2,3,7,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,8,10,12,1,2,3,6,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,8,11,12,1,2,3,6,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,9,10,12,1,2,3,6,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,9,11,12,1,2,3,6,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,10,11,12,1,2,3,6,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,8,9,10,12,1,2,3,6,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,8,9,11,12,1,2,3,6,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,8,10,11,12,1,2,3,6,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,9,10,11,12,1,2,3,6,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,7,8,10,12,1,2,3,5,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,7,8,11,12,1,2,3,5,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,7,9,10,12,1,2,3,5,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,7,9,11,12,1,2,3,5,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,7,10,11,12,1,2,3,5,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,8,9,10,12,1,2,3,5,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,8,9,11,12,1,2,3,5,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,8,10,11,12,1,2,3,5,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,6,9,10,11,12,1,2,3,5,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,7,8,9,10,12,1,2,3,5,6,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,7,8,9,11,12,1,2,3,5,6,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,7,8,10,11,12,1,2,3,5,6,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,7,9,10,11,12,1,2,3,5,6,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,8,9,10,11,12,1,2,3,5,6,7] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,7,8,10,12,1,2,3,4,9,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,7,8,11,12,1,2,3,4,9,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,7,9,10,12,1,2,3,4,8,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,7,9,11,12,1,2,3,4,8,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,7,10,11,12,1,2,3,4,8,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,8,9,10,12,1,2,3,4,7,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,8,9,11,12,1,2,3,4,7,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,8,10,11,12,1,2,3,4,7,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,6,9,10,11,12,1,2,3,4,7,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,7,8,9,10,12,1,2,3,4,6,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,7,8,9,11,12,1,2,3,4,6,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,7,8,10,11,12,1,2,3,4,6,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,7,9,10,11,12,1,2,3,4,6,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[5,8,9,10,11,12,1,2,3,4,6,7] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[6,7,8,9,10,12,1,2,3,4,5,11] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[6,7,8,9,11,12,1,2,3,4,5,10] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[6,7,8,10,11,12,1,2,3,4,5,9] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[6,7,9,10,11,12,1,2,3,4,5,8] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[6,8,9,10,11,12,1,2,3,4,5,7] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[7,8,9,10,11,12,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[4,5,7,6,2,3,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,5,7,2,6,4,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,5,7,3,6,4,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,5,7,3,6,8,4,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[8,4,3,7,6,1,5,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,7,2,3,5,4,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,2,7,3,6,4,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,3,4,7,6,1,5,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,2,4,7,1,6,5,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[3,1,4,7,6,8,5,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,1,3,7,6,8,5,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,1,7,3,6,8,4,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,7,1,3,5,8,4,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,8,7,3,6,1,4,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[4,8,3,7,6,1,5,2] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[3,8,4,7,6,1,5,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,8,4,7,1,6,5,3] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,1,4,7,2,6,5,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,1,3,2,7,6,5,4] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[2,8,3,1,7,6,5,4] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[3,8,2,1,7,6,5,4] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,7,1,2,8,5,4,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,2,3,1,7,6,5,4] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,3,2,1,7,6,5,4] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[3,4,1,7,6,8,5,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,4,2,7,8,6,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,4,2,7,1,6,5,3] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[8,5,7,2,1,6,4,3] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[1,5,7,2,8,6,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,5,7,1,8,6,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,5,7,1,6,8,4,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,7,4,5,8,1,3,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[5,4,7,6,8,1,3,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[2,5,7,8,1,6,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,5,7,8,2,6,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[8,5,7,1,2,6,4,3] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,4,1,7,2,6,5,3] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[1,4,8,7,2,6,5,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,4,8,7,6,1,5,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[4,3,8,7,6,1,5,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,3,7,8,6,1,4,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,7,2,8,1,5,4,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,2,7,8,1,6,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,2,8,7,1,6,5,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[3,2,8,1,7,6,5,4] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[1,3,8,2,7,6,5,4] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[8,3,1,2,7,6,5,4] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,2,1,3,7,6,5,4] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[1,2,8,3,7,6,5,4] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[2,1,8,3,7,6,5,4] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,1,8,7,2,6,5,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[5,1,7,8,2,6,4,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,7,1,8,2,5,4,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,8,7,1,2,6,4,3] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[4,8,1,7,2,6,5,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[3,8,1,2,7,6,5,4] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[2,8,1,3,7,6,5,4] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[1,8,2,3,7,6,5,4] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[8,1,2,3,7,6,5,4] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[3,1,4,5,6,7,8,9,10,2] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[10,1,4,5,6,7,8,9,2,3] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[9,1,4,5,6,7,8,2,10,3] => [[1,3,4,5,6,7,9],[2,10],[8]] => 100000101
[6,7,1,8,4,5,2,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,7,1,5,8,2,6,4] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[2,7,1,5,8,3,6,4] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[2,6,5,1,8,3,7,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,6,5,1,8,2,7,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[4,6,5,1,8,7,2,3] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[5,6,4,1,8,7,2,3] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[8,1,4,5,7,6,2,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,4,5,1,8,7,2,3] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,4,6,1,8,7,2,3] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,5,6,1,8,7,2,3] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,6,1,8,2,7,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,5,6,1,8,3,7,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,4,6,1,3,8,7,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,4,6,1,2,8,7,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,3,6,1,2,8,7,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[5,3,6,1,8,2,7,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[7,3,1,5,8,2,6,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[8,1,3,5,7,2,6,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,1,2,5,7,3,6,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,2,1,5,8,3,6,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[6,2,5,1,8,3,7,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,2,6,1,3,8,7,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[2,3,6,1,4,8,7,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,2,5,3,1,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[6,2,4,1,3,8,7,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[7,2,1,4,3,8,6,5] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[8,1,2,4,3,7,6,5] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,1,3,4,2,7,6,5] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,3,1,4,2,8,6,5] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[6,3,4,1,2,8,7,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[4,6,3,1,2,8,7,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,6,4,1,2,8,7,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[2,6,4,1,3,8,7,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[2,7,1,4,3,8,6,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[3,7,1,4,2,8,6,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[4,7,1,3,2,8,6,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[8,1,6,7,2,3,5,4] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[4,7,1,2,3,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,7,1,2,4,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,7,1,3,4,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,6,3,1,4,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,6,2,1,4,8,7,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,6,2,1,8,3,7,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[6,5,2,1,8,3,7,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,1,5,2,7,3,6,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,1,4,2,3,7,6,5] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,4,1,2,3,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[6,4,2,1,3,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[5,4,2,3,1,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[3,5,2,4,1,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[6,3,2,1,4,8,7,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,3,1,2,4,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[8,1,3,2,4,7,6,5] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,1,2,3,4,7,6,5] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,2,1,3,4,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[6,2,3,1,4,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[2,4,3,6,1,5,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[2,4,3,6,5,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,4,6,3,5,8,7,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,4,6,3,5,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,4,6,1,5,3,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,2,6,5,3,1,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[4,2,6,5,1,8,7,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,2,6,5,8,1,7,3] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[4,2,6,5,8,1,3,7] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,2,6,5,8,3,1,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[2,4,6,1,5,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,4,1,6,5,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,1,4,6,5,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,4,1,6,5,8,7,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,4,6,1,5,8,7,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,2,6,5,8,3,7,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,6,4,3,8,7,5,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,2,6,8,5,3,7,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[2,4,6,8,1,5,7,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,4,6,1,8,5,7,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,4,1,6,8,5,7,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,1,4,6,8,5,7,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,1,4,6,8,5,3,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[2,4,1,6,8,5,3,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,4,6,1,8,5,3,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,4,6,8,1,5,3,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,2,6,8,5,1,3,7] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,4,6,8,3,5,7,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,4,6,8,3,5,1,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[2,4,6,8,3,1,5,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,4,6,3,1,8,5,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,4,6,3,8,1,5,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,4,6,3,8,5,1,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,4,6,3,8,5,7,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,4,3,6,8,5,7,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,4,3,6,8,5,1,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,4,3,6,8,1,5,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,4,3,1,6,8,5,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,4,1,3,6,8,7,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,4,3,6,1,8,7,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,4,3,6,8,1,7,5] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,6,5,2,8,7,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[2,4,6,3,8,1,7,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[2,1,4,6,8,3,7,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,4,1,6,8,3,7,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,4,6,1,8,3,7,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,4,6,8,1,3,7,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,4,6,8,3,1,7,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,6,2,8,5,7,1,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,2,4,8,7,1,3,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,4,2,8,7,5,3,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[2,6,4,8,1,7,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,6,4,1,8,7,5,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[2,6,1,4,8,7,5,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,1,6,4,8,7,5,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,6,1,4,8,7,3,5] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[6,4,2,8,7,5,1,3] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[1,6,4,7,3,8,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,3,7,4,5,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[5,2,4,7,3,6,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,7,6,3,4,8,2,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,1,6,3,7,2,4,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,1,6,3,8,2,4,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,2,7,4,8,3,5,6] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[6,1,7,3,4,8,2,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,1,7,4,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,1,4,7,3,8,2,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[4,3,1,7,5,8,2,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[2,8,6,3,7,1,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[6,8,1,3,7,2,4,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[5,8,2,1,7,3,4,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,7,2,1,8,3,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,7,1,3,8,2,4,5] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,1,2,4,8,3,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[4,3,6,1,5,8,2,7] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,6,1,4,5,8,3,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[6,5,1,3,4,8,2,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,6,2,4,8,3,5,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,5,1,3,7,2,4,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,5,3,2,8,4,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,4,2,1,5,8,3,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[2,5,3,4,1,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[4,3,5,2,1,8,6,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,6,4,8,7,1,3,5] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[1,6,4,8,7,2,3,5] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[2,7,8,3,6,1,4,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[4,3,2,8,7,1,5,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,2,4,8,7,1,3,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,2,8,3,7,1,4,5] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,1,4,8,7,2,3,6] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,8,2,5,1,3,7,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[4,7,2,5,1,3,8,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[3,7,2,1,5,4,8,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[3,8,2,1,5,4,7,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[8,3,2,1,5,4,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,3,2,1,6,4,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,4,2,5,1,6,3,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,3,2,1,5,6,4,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,3,2,1,4,6,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,8,2,1,4,5,7,6] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,7,2,1,4,5,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[3,2,7,1,4,6,8,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[3,2,8,1,4,6,7,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[3,2,8,1,4,7,6,5] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[3,8,2,1,4,7,5,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,8,2,1,5,7,4,6] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[4,8,2,5,1,7,3,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,7,2,5,1,8,3,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[3,7,2,1,5,8,4,6] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[3,7,2,1,4,8,5,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,2,1,7,5,8,6,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[3,2,7,1,6,8,4,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[4,2,7,6,1,8,3,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,3,7,6,8,1,2,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,3,8,6,7,1,2,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,2,8,6,1,7,3,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[3,2,8,1,6,7,4,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[3,2,1,8,7,5,6,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,8,2,1,7,4,5,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,2,8,1,7,4,6,5] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[3,2,8,1,6,4,7,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,2,7,1,6,4,8,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,2,7,6,1,3,8,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,2,8,6,1,3,7,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,2,8,7,1,3,6,5] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,7,8,3,4,1,2,6] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[4,2,7,8,1,3,6,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[4,2,6,8,1,3,7,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[4,2,6,7,1,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[3,2,6,1,8,4,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,7,2,1,8,4,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,7,2,1,8,5,4,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[4,7,3,8,5,1,2,6] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[4,3,7,8,6,1,2,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,2,7,1,8,6,4,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[3,2,1,6,8,5,7,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[3,2,6,1,8,7,4,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,2,6,8,1,7,3,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,3,6,8,7,1,2,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[4,2,6,7,1,8,3,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,2,6,1,7,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[3,4,6,8,7,5,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,3,6,4,8,7,1,2] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[1,4,6,2,7,8,5,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,1,8,5,4,2,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[1,2,7,5,4,8,6,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,3,7,5,4,8,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,3,8,5,4,6,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,8,7,5,4,6,1,2] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,3,6,7,8,5,1,2] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[4,5,6,3,8,7,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,6,8,5,4,7,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,8,3,5,4,7,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,6,3,5,4,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[1,6,2,5,4,8,7,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,1,2,5,8,3,6,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[1,8,2,5,7,3,6,4] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[6,2,1,5,4,8,7,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,1,6,2,8,7,5,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[7,8,1,2,4,6,5,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,8,3,1,4,2,6,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,3,6,1,8,2,7,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[2,3,8,5,4,1,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[4,8,1,5,2,3,7,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,5,1,6,4,3,2,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[5,8,1,6,4,3,2,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[6,1,5,7,4,3,2,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[1,5,8,6,4,3,2,7] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[3,4,6,1,5,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,8,4,1,5,3,2,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,8,5,1,6,3,2,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[2,6,1,5,7,3,8,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[1,6,8,7,4,3,2,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,8,1,7,4,3,2,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,6,1,7,4,3,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,1,7,6,4,3,2,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,1,7,8,4,3,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,1,8,6,4,3,2,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,8,7,6,4,3,2,5] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[2,1,7,5,6,3,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[3,1,6,7,5,8,2,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[7,8,1,6,5,3,2,4] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,8,2,1,4,5,6,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[2,8,1,5,4,6,7,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,2,1,5,4,6,8,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[1,2,8,5,6,3,7,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[6,1,2,5,7,3,8,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[4,2,1,5,6,3,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[4,3,6,1,5,7,2,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[5,1,6,3,7,8,2,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,3,6,8,5,7,2,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,4,6,3,7,1,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,3,6,4,8,7,2,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[4,1,6,7,3,8,2,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[5,4,6,1,3,7,2,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,4,1,5,2,3,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,1,7,5,2,3,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[1,2,4,5,8,3,7,6] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[7,2,3,5,4,1,8,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[2,8,3,5,4,1,7,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,2,6,3,8,1,7,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[7,8,2,3,4,1,6,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,1,4,6,3,2,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[3,1,6,4,7,8,2,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,8,5,7,4,3,2,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,1,5,8,4,3,2,6] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,1,8,7,4,3,2,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,5,1,8,4,3,2,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,5,7,1,4,3,2,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[7,5,8,1,4,3,2,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,8,7,1,4,3,2,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,5,7,8,4,3,2,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,4,7,5,1,3,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[7,8,4,6,1,3,2,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,5,4,1,3,2,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,5,6,4,1,8,2,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,6,4,5,1,3,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[1,6,5,8,4,3,2,7] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,8,5,1,4,3,2,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[7,6,5,1,4,3,2,8] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[1,2,3,4,5,6,9,7,8] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[1,2,3,4,5,8,6,9,7] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[1,4,2,5,6,7,8,9,3] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[9,8,1,2,3,4,5,6,7] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[7,8,9,1,2,3,4,5,6] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[9,8,7,1,2,3,4,5,6] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[6,7,8,9,1,2,3,4,5] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[9,6,7,8,1,2,3,4,5] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[8,9,6,7,1,2,3,4,5] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000
[9,8,6,7,1,2,3,4,5] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[9,8,7,6,1,2,3,4,5] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[9,5,6,7,8,1,2,3,4] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[8,9,5,6,7,1,2,3,4] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000
[9,8,5,6,7,1,2,3,4] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000
[9,7,8,5,6,1,2,3,4] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000
[9,8,7,5,6,1,2,3,4] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[9,8,7,6,5,1,2,3,4] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[7,8,9,4,5,6,1,2,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100
[9,7,8,4,5,6,1,2,3] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100
[9,8,7,4,5,6,1,2,3] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100
[8,9,6,7,4,5,1,2,3] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100
[9,8,6,7,4,5,1,2,3] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100
[9,8,7,6,4,5,1,2,3] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100
[9,8,7,6,5,4,1,2,3] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[9,7,8,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[9,8,7,5,6,3,4,1,2] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010
[9,8,7,6,5,3,4,1,2] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[9,8,7,6,5,4,3,1,2] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[9,10,1,2,3,4,5,6,7,8] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[8,9,10,1,2,3,4,5,6,7] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[10,8,9,1,2,3,4,5,6,7] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[10,9,8,1,2,3,4,5,6,7] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000
[7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[10,7,8,9,1,2,3,4,5,6] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000
[9,10,7,8,1,2,3,4,5,6] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000
[10,9,7,8,1,2,3,4,5,6] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000
[10,9,8,7,1,2,3,4,5,6] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[10,6,7,8,9,1,2,3,4,5] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[9,10,6,7,8,1,2,3,4,5] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000
[10,9,6,7,8,1,2,3,4,5] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000
[10,8,9,6,7,1,2,3,4,5] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000
[10,9,8,6,7,1,2,3,4,5] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[10,9,8,7,6,1,2,3,4,5] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[9,10,5,6,7,8,1,2,3,4] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[10,9,5,6,7,8,1,2,3,4] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[8,9,10,5,6,7,1,2,3,4] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000
[10,9,8,5,6,7,1,2,3,4] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000
[9,10,7,8,5,6,1,2,3,4] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000
[10,9,7,8,5,6,1,2,3,4] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000
[10,9,8,7,5,6,1,2,3,4] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000
[10,9,8,7,6,5,1,2,3,4] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[10,7,8,9,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100
[9,10,7,8,4,5,6,1,2,3] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[10,9,7,8,4,5,6,1,2,3] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100
[10,9,8,7,4,5,6,1,2,3] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[10,8,9,6,7,4,5,1,2,3] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100
[10,9,8,6,7,4,5,1,2,3] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100
[10,9,8,7,6,4,5,1,2,3] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100
[10,9,8,7,6,5,4,1,2,3] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010
[10,9,7,8,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010
[10,9,8,7,5,6,3,4,1,2] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010
[10,9,8,7,6,5,3,4,1,2] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010
[10,9,8,7,6,5,4,3,1,2] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[3,4,6,2,7,1,5,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[3,6,2,5,4,1,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,2,7,5,4,1,6,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,3,6,2,8,1,5,7] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,1,2,5,4,7,8,3] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[6,2,4,5,1,3,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[4,2,8,5,1,3,7,6] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,3,6,8,1,7,2,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,3,6,4,1,7,2,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,2,1,5,8,3,7,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[1,6,7,4,8,3,5,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,4,6,3,7,5,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,6,7,2,5,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[2,4,6,1,7,5,3,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[2,7,5,4,1,6,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[7,5,4,6,2,8,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[1,7,5,4,3,8,6,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,4,6,3,5,8,7,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,5,8,4,3,6,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[5,4,6,2,7,8,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,5,4,1,6,7,3,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[5,6,3,2,7,1,4,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,6,3,2,7,1,8,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[8,5,6,3,2,7,1,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,4,6,2,8,1,7,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[2,4,1,7,8,5,3,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,5,4,1,6,3,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[5,6,3,2,1,8,4,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,5,2,1,6,4,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,8,4,3,2,1,5,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[5,3,8,2,1,6,4,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[3,7,5,8,2,1,4,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[7,3,2,8,5,1,6,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,4,6,3,2,1,7,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,6,4,3,2,1,7,5] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[7,6,4,3,2,1,8,5] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[7,8,4,3,2,1,6,5] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,4,7,2,1,8,6,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,5,8,3,2,6,1,4] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[5,7,3,2,1,6,8,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,7,3,2,1,6,4,8] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,3,7,2,5,1,8,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,7,8,3,5,2,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[6,2,5,7,8,4,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[2,1,5,7,8,6,3,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,6,7,2,8,1,4,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[6,3,7,2,8,1,4,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[3,2,6,1,7,4,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[3,5,2,1,4,7,6,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[7,3,5,2,1,8,4,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[2,5,4,1,3,7,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,5,8,4,1,3,7,6] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[2,4,1,7,8,3,6,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[3,7,2,8,6,1,4,5] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,6,8,2,1,7,4,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[5,3,8,2,1,4,7,6] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[4,8,7,3,2,1,5,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,7,3,2,1,5,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,4,7,3,2,1,5,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,3,5,2,1,4,7,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,3,2,8,6,1,4,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[3,5,2,1,4,6,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[7,8,6,5,4,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,8,9,7,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[8,9,7,6,5,4,3,2,1,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[6,8,7,5,4,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,8,7,9,6,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[1,7,9,8,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[1,9,10,8,7,6,5,4,3,2] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[7,8,3,5,4,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[8,6,3,7,5,2,4,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[5,4,1,6,3,2,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[5,4,1,6,2,3,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,7,1,6,2,8,3,4] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,7,1,6,2,8,4,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[2,7,6,5,1,8,3,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,7,6,5,1,8,4,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,3,6,5,1,4,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,3,6,4,1,5,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,3,6,1,5,4,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,7,6,1,4,8,5,3] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,7,6,1,4,8,3,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,3,5,1,8,4,2,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[7,3,5,1,8,6,4,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[2,7,6,1,5,8,4,3] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[2,7,6,4,1,8,5,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,1,7,6,3,8,5,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,1,7,6,3,8,4,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[5,7,3,6,2,8,4,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[2,7,6,4,1,8,3,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[7,3,5,1,8,6,2,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,3,5,1,8,2,4,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[2,3,4,8,7,6,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,3,4,8,5,7,1,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[7,3,5,4,8,1,2,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,4,3,5,8,7,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[2,1,4,5,8,7,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,4,3,5,8,7,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,3,5,4,8,1,6,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[2,3,4,8,7,5,6,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,3,4,8,7,5,1,6] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,7,6,5,4,8,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[7,3,5,6,8,4,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,3,5,6,8,1,4,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,3,5,6,8,1,2,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,4,1,5,8,7,2,3] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[6,4,1,5,8,7,3,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,4,1,5,8,3,7,2] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,7,1,6,3,8,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,4,1,5,8,3,2,7] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[7,4,1,5,8,2,3,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,4,1,5,8,2,6,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[6,3,5,7,8,2,1,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,3,5,7,8,2,4,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[2,7,6,4,5,8,3,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[5,7,3,6,1,8,4,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[2,1,4,5,8,6,3,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[7,3,5,4,8,6,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[2,3,4,8,5,6,1,7] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[2,3,4,8,7,1,6,5] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,3,4,8,1,7,6,5] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,3,4,8,1,6,7,5] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,3,4,8,5,1,7,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[6,3,5,4,8,2,7,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,4,3,5,8,2,1,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[2,1,4,5,8,3,7,6] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[7,4,3,5,8,2,6,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,3,5,4,8,2,1,7] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[2,3,4,8,5,1,6,7] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[2,3,4,8,1,6,5,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,3,4,8,1,5,7,6] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[7,8,2,6,1,5,3,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,1,6,2,5,3,4] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,6,7,2,5,3,4] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,8,5,7,2,6,3,4] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[5,8,1,7,2,6,3,4] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,8,2,7,1,6,3,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,8,6,7,1,5,3,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,8,5,7,1,6,3,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,8,1,7,5,6,3,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,8,2,7,5,6,3,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,2,7,4,6,3,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,1,7,4,6,3,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,8,4,7,1,6,3,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,2,7,1,6,3,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[4,8,1,7,2,6,3,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,4,7,2,6,3,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,8,1,7,5,6,2,3] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,8,4,7,5,6,2,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,3,7,5,6,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,8,1,7,5,6,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,8,1,7,4,6,2,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,8,3,7,4,6,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,3,7,2,6,4,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,8,1,7,2,6,4,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[3,8,2,7,1,6,4,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[3,8,2,7,4,6,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[3,8,2,7,5,6,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,8,2,7,5,6,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,8,3,7,5,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[3,8,4,7,5,6,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,4,7,5,6,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,3,7,5,6,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,3,7,4,6,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,3,7,1,6,4,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,8,1,7,3,6,4,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,5,2,8,6,4,1,3] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[7,5,1,8,6,2,3,4] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,4,8,6,1,5,2,3] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,1,8,4,5,2,6,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,8,1,7,4,2,5,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[1,6,7,4,2,8,5,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,6,7,3,8,5,2,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[7,1,8,3,5,6,2,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[7,3,8,6,2,5,1,4] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[7,4,2,8,6,1,3,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,3,1,8,4,2,5,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,2,8,4,1,5,3,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,2,8,3,5,1,6,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,2,8,3,4,6,1,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[1,5,7,8,2,6,3,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[6,2,3,8,5,7,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,2,4,8,5,3,1,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,3,1,4,8,5,2,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,6,3,7,8,5,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,6,3,7,8,4,5,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,4,7,3,5,6,8,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[2,4,7,3,6,8,5,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,5,3,7,8,1,6,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[3,1,5,4,7,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,3,1,4,8,2,6,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,2,4,8,6,1,3,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[5,2,3,8,4,6,7,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[4,8,2,3,6,1,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[4,8,2,3,5,7,1,6] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[1,4,7,8,3,6,2,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[4,8,1,3,6,7,2,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[5,3,8,2,4,7,1,6] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,4,3,8,1,2,7,6] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,4,2,8,1,3,7,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,3,8,2,5,1,7,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,3,8,1,4,7,2,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[5,8,1,3,6,2,7,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[1,5,7,4,2,6,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[5,8,1,4,2,6,3,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,8,4,1,2,7,6,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,5,1,2,8,7,3,4] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[6,5,3,1,4,2,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[5,3,1,6,4,2,7,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,2,6,4,1,7,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[4,6,1,7,5,2,8,3] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[4,5,1,7,2,6,3,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,5,6,1,2,8,7,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,5,7,1,8,6,2,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,6,2,7,5,1,8,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[4,2,5,7,1,8,6,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,4,7,2,8,6,1,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,4,5,8,2,7,1,6] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,4,6,2,8,1,5,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,5,2,6,8,1,7,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,2,5,6,1,3,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[4,3,1,2,5,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,3,6,8,4,7,2,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,7,2,5,4,8,6,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[8,4,2,5,7,3,6,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[3,1,6,5,4,8,2,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,1,6,5,8,3,2,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,1,6,8,4,3,2,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[8,5,4,7,6,3,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[2,7,1,5,4,3,8,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[8,2,1,5,4,3,7,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,4,1,5,7,3,2,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,4,6,1,7,3,2,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,3,6,1,4,7,2,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[2,7,6,1,4,3,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,7,8,5,1,3,2,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,7,8,2,4,3,5,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,7,6,2,8,3,5,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[8,3,6,2,4,7,5,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[3,7,6,2,4,8,5,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,7,3,8,4,6,2,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,7,3,5,8,6,2,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,7,2,1,4,3,6,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,7,3,1,4,6,2,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,7,6,3,2,5,4,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,7,3,5,1,6,2,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,7,2,5,1,3,6,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,4,6,5,7,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[3,7,6,5,1,8,2,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[8,1,2,3,4,5,6,7,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[1,9,2,3,4,5,6,7,8] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[9,1,2,3,4,5,6,7,8,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[7,8,1,2,3,4,5,6,9] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[1,8,9,2,3,4,5,6,7] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[1,10,2,3,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9,10],[3]] => 010000000
[8,9,1,2,3,4,5,6,7,10] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[7,1,8,2,3,4,5,6,9] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[6,8,1,2,3,4,5,7,9] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[1,8,2,9,3,4,5,6,7] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[1,7,9,2,3,4,5,6,8] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[1,9,10,2,3,4,5,6,7,8] => [[1,2,3,6,7,8,9,10],[4,5]] => 001000000
[3,6,4,8,7,5,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,6,4,3,8,7,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[1,6,2,4,7,8,5,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,6,2,4,8,1,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,4,7,2,8,1,6,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,4,7,2,5,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[7,3,8,4,5,6,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[3,5,6,4,8,7,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[4,6,8,5,3,7,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,8,5,3,4,7,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[1,6,5,4,2,8,7,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,8,5,2,7,3,6,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,2,7,5,1,8,6,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[7,8,1,4,2,6,5,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[1,3,6,4,8,2,5,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[4,1,7,5,3,2,6,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,5,1,3,4,2,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[4,8,5,3,1,7,2,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[7,4,5,3,2,8,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,8,3,6,1,4,2,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,5,8,6,4,1,3,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,4,6,2,5,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,6,2,5,8,1,7,4] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[1,6,8,7,4,2,3,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[6,1,7,8,2,4,3,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[7,1,8,6,3,4,2,5] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[7,2,1,4,5,6,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[1,2,8,3,6,5,7,4] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[6,1,3,2,7,5,8,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[1,6,3,8,5,7,2,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,6,4,1,7,5,8,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[7,6,5,8,1,4,2,3] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,8,6,7,3,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,6,4,3,7,2,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,6,3,4,8,7,1,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,1,3,4,5,2,8,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[1,8,3,5,4,2,7,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,1,6,3,8,2,7,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[7,8,2,4,6,3,1,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[3,2,6,4,7,8,1,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,8,5,7,4,3,1,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,2,5,8,3,4,1,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[5,3,8,7,1,2,6,4] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,5,3,8,2,1,7,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[7,5,8,4,1,2,3,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,8,7,4,1,3,2,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,5,7,8,4,1,2,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,4,7,5,3,8,2,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,4,6,7,3,1,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,8,4,6,3,1,2,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[2,6,4,5,3,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,6,5,8,4,2,1,7] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,6,8,4,2,3,1,7] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,8,5,4,3,1,2,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,1,4,2,8,5,7,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,8,6,5,3,2,7,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[8,6,5,1,2,4,7,3] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[6,7,5,8,2,1,4,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,7,5,8,2,6,4,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,3,8,5,7,6,2,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[6,3,8,5,7,1,2,4] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[8,3,1,5,6,2,7,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,8,5,2,1,4,7,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,8,2,5,6,1,7,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[2,8,1,5,6,3,7,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[8,1,2,5,6,3,7,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[1,8,2,5,7,6,3,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[5,1,8,6,2,7,3,4] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,5,8,6,1,7,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[8,6,1,5,7,2,3,4] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,8,6,5,7,1,2,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[7,6,5,8,1,2,4,3] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[5,1,7,6,8,4,2,3] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,1,3,7,8,6,2,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[7,2,5,8,1,6,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,2,8,5,7,6,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,2,1,5,7,6,3,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,2,8,6,1,7,3,4] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,2,8,6,5,7,3,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,2,1,3,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[8,2,5,6,3,7,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,2,6,5,4,1,8,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,1,3,5,4,7,8,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[6,1,5,3,4,7,8,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[7,5,6,2,4,1,8,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,5,2,6,3,7,1,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,3,1,2,6,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[8,1,6,5,7,3,2,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[3,5,8,6,2,7,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,8,1,6,3,7,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,8,5,6,3,7,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,7,6,5,4,2,8,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,7,6,1,4,2,8,3] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,1,4,2,6,5,8,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,1,7,3,5,6,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,7,4,1,5,6,8,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[5,7,6,4,1,2,8,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,7,6,1,5,2,8,3] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[1,7,6,4,5,2,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,8,3,6,5,7,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,8,1,6,5,7,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[8,1,3,5,7,6,2,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,8,5,4,1,6,2,3] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,1,5,4,3,7,8,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[7,5,6,4,2,1,8,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,3,2,6,5,7,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,4,6,2,5,1,8,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,1,4,3,5,7,8,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[6,1,3,4,5,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[7,2,6,4,5,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,2,3,6,5,7,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,4,7,3,6,8,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[3,4,7,8,5,6,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,4,7,2,5,1,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,4,7,2,5,8,3,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,6,2,4,7,1,5,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[6,8,3,4,5,7,1,2] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[4,3,6,7,5,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[6,3,7,5,8,4,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,3,8,6,4,5,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,2,7,6,5,1,4,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[1,2,7,6,5,8,3,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,8,2,6,1,5,3,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,3,8,6,4,1,5,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[4,3,6,2,5,1,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,8,3,2,5,1,4,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,8,1,2,5,6,3,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[4,1,6,2,5,7,3,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,1,2,5,8,7,3,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[2,1,8,6,4,7,3,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[7,1,3,6,8,4,2,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[1,8,3,6,7,4,5,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[7,1,5,8,3,6,2,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[5,1,8,7,2,3,6,4] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,1,5,7,4,2,8,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,1,6,4,7,2,5,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,4,7,5,1,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[6,5,7,1,4,2,3,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,6,8,1,3,2,4,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,8,5,1,3,4,2,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[2,8,3,4,5,1,7,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[6,2,4,3,1,5,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[4,2,8,3,1,7,5,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,3,7,4,8,2,5,6] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[5,3,7,4,1,6,2,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[2,4,7,3,6,1,8,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[5,8,7,6,3,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,5,6,8,1,4,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,4,7,1,6,5,3,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,2,7,8,5,4,3,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[6,3,1,2,8,4,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[4,2,1,3,6,5,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[2,8,1,4,5,6,3,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[7,2,1,5,4,6,3,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[4,2,6,1,8,5,3,7] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[7,8,2,1,4,5,3,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[7,8,4,1,5,3,6,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[3,4,6,1,5,8,7,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[7,5,1,6,4,3,8,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[5,8,1,6,3,4,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,5,1,8,2,7,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,8,1,7,5,2,3,4] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,6,1,8,5,3,2,4] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[5,6,1,7,4,8,2,3] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,6,1,5,7,4,2,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,5,6,1,7,4,8,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,1,7,5,6,4,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,1,7,6,4,8,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,1,7,8,5,3,4,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[7,1,8,6,5,4,2,3] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,6,5,7,3,4,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,6,4,7,5,8,2,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[8,5,3,6,2,7,4,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[1,3,7,4,6,8,2,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[4,7,5,6,3,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,7,6,5,4,8,2,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,1,6,5,7,2,4,3] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[1,2,7,6,8,3,4,5] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[6,1,7,5,3,8,2,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,1,7,5,6,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,4,1,7,6,8,2,3] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[4,8,5,6,2,7,3,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,8,6,4,2,7,5,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[7,8,5,2,4,6,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[2,8,6,3,7,4,5,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,8,1,6,2,4,5,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,8,1,4,7,2,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[3,8,4,1,7,2,6,5] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,4,7,1,8,3,2,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[3,7,4,1,8,5,2,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[6,7,1,4,8,3,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[2,7,1,8,4,5,3,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[6,1,2,8,4,3,5,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[6,5,1,4,3,8,2,7] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[1,6,2,5,8,3,4,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,5,1,3,7,2,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,4,2,1,7,3,6,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,4,2,1,8,5,3,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[1,5,4,2,8,3,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,4,3,1,5,8,2,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[3,7,6,8,4,5,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,7,6,8,5,3,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,7,6,8,5,4,2,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,4,8,6,7,5,2,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,4,8,6,7,3,5,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[7,3,8,5,4,6,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,4,8,5,6,7,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[6,3,5,8,4,7,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[5,4,3,8,6,7,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[5,4,2,8,7,3,6,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[6,2,5,8,7,3,4,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,2,8,5,7,4,6,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[1,3,8,7,5,6,2,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,1,8,7,4,6,3,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[3,1,8,5,7,6,2,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[6,1,5,8,7,4,2,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,4,1,8,7,6,2,3] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,8,6,7,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[4,8,7,5,6,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[4,2,1,6,3,5,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,2,1,4,3,5,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,2,1,4,3,8,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,2,1,4,3,6,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,2,4,1,3,8,5,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,2,4,1,3,5,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[2,1,6,4,3,5,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,6,1,4,3,5,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,6,4,1,3,5,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,6,2,1,3,5,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,4,2,1,3,5,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,4,2,1,3,6,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,4,2,1,6,3,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,4,2,1,8,3,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,6,1,4,3,8,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,1,6,4,3,8,5,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,1,8,4,3,6,5,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,8,1,4,3,6,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,8,4,1,3,6,5,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,8,2,1,3,6,5,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,8,2,1,4,3,5,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[8,6,2,1,4,3,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,8,1,4,6,3,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,6,1,4,8,3,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,6,4,1,8,3,5,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,6,4,8,1,3,5,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,6,2,8,1,3,5,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,2,6,1,8,3,5,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,2,4,1,8,3,5,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,2,1,6,8,3,5,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,2,1,6,3,8,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,2,1,3,6,8,5,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,1,4,3,8,6,5,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,4,1,3,8,6,5,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[4,2,1,3,8,6,5,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,2,1,8,3,6,5,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[4,2,1,8,6,3,5,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[8,2,1,6,4,3,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,2,6,1,4,3,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,2,8,1,3,6,5,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[2,4,8,1,3,6,5,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,4,1,8,3,6,5,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,1,4,8,3,6,5,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,1,4,8,6,3,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[2,4,8,1,6,3,5,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,4,8,6,1,3,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,2,8,6,1,3,5,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[8,4,6,2,1,3,5,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[4,6,8,2,1,3,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,6,8,4,1,3,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,6,8,1,4,3,5,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,6,1,8,4,3,5,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,1,6,8,4,3,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[2,1,8,6,4,3,5,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,8,6,4,1,3,5,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,8,6,2,1,3,5,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,8,4,2,1,3,5,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,2,6,1,5,4,8,7] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,2,4,3,8,1,7,6] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,2,4,1,5,3,8,7] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,3,6,1,5,2,8,7] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,3,5,2,8,1,7,6] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[4,3,7,2,6,5,8,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[4,3,8,2,6,1,7,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,3,8,1,7,2,6,5] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[4,3,8,1,5,2,7,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,1,8,3,4,2,7,6] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[5,4,8,1,3,2,7,6] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[2,1,5,4,8,3,7,6] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[5,1,7,6,8,3,4,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,3,7,6,8,1,5,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[4,3,7,1,8,5,6,2] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,3,6,5,8,1,7,2] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,3,5,4,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[6,3,5,4,8,1,7,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,1,6,3,8,4,5,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,4,6,5,8,1,3,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[2,1,8,4,6,3,7,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,4,6,1,3,2,7,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,1,6,3,4,2,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,6,3,7,2,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,3,5,1,7,2,6,4] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,3,5,2,6,1,7,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,3,5,2,6,4,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,6,3,5,1,7,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,2,7,1,5,3,6,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,2,4,1,5,3,7,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,2,4,1,7,3,6,5] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,2,4,3,6,1,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[3,2,8,4,6,1,7,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,2,8,1,5,4,7,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,2,7,6,8,1,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[3,2,7,1,8,5,6,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,2,6,5,8,1,7,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,5,7,2,4,3,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,5,8,2,4,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,2,4,1,8,5,6,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[7,6,8,2,4,1,5,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,6,8,1,5,2,4,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[2,1,7,3,8,5,6,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[7,1,3,2,8,5,6,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[7,1,8,5,6,2,4,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,1,8,2,6,4,5,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,2,8,1,5,4,6,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,2,7,4,5,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,4,7,2,6,3,8,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,4,8,2,6,1,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,5,8,1,7,2,4,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[2,1,6,5,8,3,7,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,5,7,4,8,1,3,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[6,5,7,1,8,3,4,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[6,1,7,4,8,3,5,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,4,7,1,8,3,6,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,4,6,3,8,1,7,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[2,8,3,1,5,4,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,5,3,4,7,1,8,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[2,4,8,3,5,7,6,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,2,5,3,1,8,6,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,2,1,8,5,3,6,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,4,1,3,8,2,6,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,1,4,8,3,2,6,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[1,5,8,4,3,2,6,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,8,5,4,3,2,6,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,7,4,3,8,5,2,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,5,7,3,8,4,2,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,1,4,7,8,3,2,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,8,1,5,7,3,6,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[8,1,5,3,7,4,6,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,8,4,7,6,5,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[1,6,8,5,3,7,4,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,8,1,7,4,3,5,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[6,4,8,1,7,3,5,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,4,8,7,1,5,2,3] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,6,4,1,3,8,2,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[1,7,5,6,3,2,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,2,1,7,8,5,3,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[2,7,4,6,3,1,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,6,8,4,3,7,5,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,2,4,8,3,7,5,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,2,6,3,4,1,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[2,6,7,3,1,4,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,7,1,8,3,5,4,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,1,7,3,5,8,4,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,7,1,3,6,2,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,2,1,7,3,5,6,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,8,2,6,3,1,5,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,7,2,6,3,5,4,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[1,2,8,7,4,5,6,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[8,3,7,1,5,6,2,4] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[8,6,1,2,7,5,3,4] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,1,6,2,7,4,5,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,8,5,2,6,7,4,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,2,1,8,6,7,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[2,8,5,7,6,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[1,7,8,5,2,6,4,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[7,8,1,6,4,2,5,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,6,1,5,3,2,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[7,3,8,6,1,5,2,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,7,6,1,5,3,4,2] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,7,1,6,4,5,3,2] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[8,1,7,5,6,4,3,2] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[1,8,6,7,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[6,3,5,2,1,4,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,3,5,7,2,8,4,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,5,2,7,4,3,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,5,3,6,1,2,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,5,1,4,6,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[8,3,4,5,7,2,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,7,4,6,3,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[2,8,4,6,3,7,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,1,4,7,3,6,2,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,3,4,7,5,1,2,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,5,1,4,7,3,2,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,5,3,7,1,4,2,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[2,1,8,5,7,4,3,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[6,5,3,7,1,8,4,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,5,1,4,7,8,3,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[6,3,4,7,5,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,1,4,6,8,3,7,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,7,1,3,5,8,6,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,8,3,7,1,2,6,5] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,8,6,4,1,7,2,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,8,1,2,5,7,6,4] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[2,8,7,5,4,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,2,6,4,1,3,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[3,8,6,7,4,2,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,7,6,8,4,2,3,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,3,7,8,2,4,6,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,3,6,2,1,4,7,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[5,3,7,6,2,1,8,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,3,6,2,8,7,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,7,8,6,4,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,6,7,5,4,8,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[6,1,7,4,5,8,2,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,7,3,5,1,8,2,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[2,1,6,7,5,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,1,5,7,3,6,8,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,7,3,6,1,2,8,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[4,1,7,2,5,6,8,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,4,7,1,6,5,8,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,6,2,1,8,7,5,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[3,4,6,2,7,8,5,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,6,1,2,5,8,7,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,6,1,4,8,2,7,3] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[5,6,3,1,8,7,2,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,5,6,4,7,1,8,2] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[3,4,6,1,5,7,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,4,1,5,7,6,8,2] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[3,8,2,7,1,6,5,4] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[3,8,2,7,6,1,5,4] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[3,8,2,7,6,5,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[3,8,2,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[4,8,7,2,6,5,3,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[4,8,7,2,6,5,1,3] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[4,8,7,2,6,1,5,3] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[4,8,7,2,1,6,5,3] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[4,8,7,3,1,6,5,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[4,8,7,3,2,1,6,5] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[4,8,7,3,2,6,1,5] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[4,8,7,3,2,6,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[4,8,7,3,6,2,5,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[4,8,7,3,6,2,1,5] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[4,8,7,3,6,1,5,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[4,8,7,3,6,5,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[4,8,7,3,6,5,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[5,8,7,6,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[5,8,7,6,3,1,4,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,8,7,6,3,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[5,8,7,6,2,4,3,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[5,8,7,6,2,1,4,3] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,8,7,6,4,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[5,8,7,6,4,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[5,8,7,6,4,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[5,8,7,6,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[7,3,5,2,6,4,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,1,5,6,4,3,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,4,6,7,3,8,2,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,4,5,7,1,3,8,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,3,5,1,7,4,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,2,1,5,7,4,8,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,2,1,5,7,4,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[2,4,6,7,3,8,1,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,4,6,7,3,8,5,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,5,6,7,8,3,4,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,5,6,7,8,3,1,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,2,1,6,7,8,4,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,2,1,6,7,8,4,3] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,3,6,1,7,8,4,2] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,4,6,7,1,8,3,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[1,5,6,7,8,3,2,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[6,4,5,7,2,1,8,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[5,4,6,7,2,8,3,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[6,3,4,2,1,7,8,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,3,6,2,7,8,5,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[3,4,6,7,2,8,5,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,2,1,5,7,3,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[1,5,6,7,8,2,4,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,5,6,7,8,4,2,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,4,6,7,1,8,5,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,3,6,1,7,8,5,2] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[2,4,1,6,3,7,5,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,4,1,5,3,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,3,1,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[1,3,2,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,4,1,3,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => 010010101
[2,4,1,6,3,5,8,7,10,9] => [[1,2,4,7,9],[3,5,6,8,10]] => 010100101
[2,4,1,6,3,8,5,7,10,9] => [[1,2,4,6,9],[3,5,7,8,10]] => 010101001
[2,4,1,6,3,8,5,10,7,9] => [[1,2,4,6,8],[3,5,7,9,10]] => 010101010
[2,4,1,6,3,7,5,8,9] => [[1,2,4,6,8,9],[3,5,7]] => 01010100
[2,4,1,6,3,8,5,9,7,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[2,4,1,5,3,8,6,9,7] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,4,1,6,3,7,5,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[2,3,1,6,4,7,5,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,4,1,5,3,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[1,4,2,5,3,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,3,1,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[1,3,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[7,1,2,3,4,5,6,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[1,4,3,6,2,5,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,4,3,7,2,5,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,4,3,7,6,8,2,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,4,3,7,5,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,4,3,7,2,6,5,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,5,3,7,4,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,3,2,6,5,8,4,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,5,4,8,2,6,3,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,5,4,8,3,7,2,6] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,2,3,6,5,8,4,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,8,2,4,5,7,1,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,7,8,4,5,2,6,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[7,8,1,4,5,3,6,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,8,7,4,1,6,5,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[4,8,3,6,1,5,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,8,3,1,6,4,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,8,1,4,7,6,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[7,5,1,8,6,2,4,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,4,1,8,2,6,3,5] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[7,1,8,4,2,6,3,5] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,6,3,8,5,2,4,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[6,1,3,8,5,2,4,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[7,1,8,3,6,2,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,3,1,8,4,2,6,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[7,2,8,4,1,6,5,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,2,8,3,6,5,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,2,8,3,6,1,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,1,8,2,3,6,5,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,1,2,8,3,5,4,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[1,5,2,3,8,4,7,6] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[5,1,2,3,8,4,7,6] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,2,3,8,1,4,7,6] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[6,2,8,1,3,5,4,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,2,4,1,8,7,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,3,1,4,2,8,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[3,1,6,4,2,8,5,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,6,3,8,7,1,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[2,6,3,8,5,1,4,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[2,5,1,8,3,4,7,6] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,5,1,3,8,4,7,6] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,2,5,3,8,4,7,6] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,2,4,8,3,7,6,5] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,8,1,3,7,6,5] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,4,8,3,7,1,6,5] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,4,8,3,7,6,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,5,3,8,1,7,4,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,5,4,1,3,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,1,5,4,8,2,7,6] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[5,3,1,4,8,2,7,6] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,2,3,8,4,7,1,6] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,8,2,3,7,6,1,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,8,2,3,7,1,6,5] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,8,1,2,3,7,6,5] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[1,4,8,2,3,7,6,5] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,4,8,3,7,2,6,5] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[6,3,8,1,5,2,4,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,3,8,1,2,4,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[5,1,3,8,2,4,7,6] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[1,5,3,8,2,4,7,6] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,5,4,8,2,7,6,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,1,4,8,2,7,6,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,4,8,1,2,7,6,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,5,1,2,8,7,4,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[5,3,1,6,4,2,8,7] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[5,1,6,2,8,7,4,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,1,5,8,2,7,6,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,1,2,5,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[1,4,2,5,8,7,6,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,3,5,2,8,7,4,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,1,2,8,7,4,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,6,2,8,7,5,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,2,6,1,8,7,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,3,1,5,8,2,7,6] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[3,5,2,8,7,1,4,6] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,4,8,7,2,6,1,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,4,8,7,1,2,6,5] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[3,4,8,1,7,2,6,5] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[1,3,4,8,7,2,6,5] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,3,4,8,2,7,6,5] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,4,8,1,2,7,6,5] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,4,8,2,7,1,6,5] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,4,8,2,7,6,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,2,5,8,1,7,6,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,3,1,2,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[3,1,4,2,5,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,3,5,1,8,7,6,4] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[7,8,2,1,5,3,6,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,4,1,2,7,3,5,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[2,3,7,5,4,1,8,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,3,1,5,4,2,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,8,1,5,4,2,6,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,3,5,4,1,6,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,2,5,4,1,3,6] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,8,2,5,4,6,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,2,1,5,4,7,3,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,3,6,1,4,7,8,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[5,3,6,2,4,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,4,2,1,7,3,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[4,3,7,5,8,6,1,2] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,2,7,1,8,3,6,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,2,6,7,4,8,1,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[3,1,6,7,4,8,5,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[1,7,6,5,3,8,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,7,6,5,3,8,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,7,6,5,2,4,8,3] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[2,7,6,5,3,1,4,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[2,7,1,4,8,3,5,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,7,6,4,8,5,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,7,6,3,8,4,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,1,6,2,4,8,3,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,7,6,5,2,1,3,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,7,6,5,2,8,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,7,6,5,1,8,3,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,7,6,5,2,8,3,4] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,7,6,5,3,2,8,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[4,7,6,5,1,2,8,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,7,6,5,3,1,8,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[6,1,3,5,4,8,7,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[5,2,6,3,4,1,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,1,6,2,4,7,8,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,2,6,3,4,8,7,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,7,2,4,8,3,6,5] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[6,1,4,2,8,3,5,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[4,1,8,2,6,3,5,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,7,2,1,5,3,6,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[4,7,1,6,2,3,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,7,2,6,8,3,5,4] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,2,6,7,4,8,5,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,1,6,7,4,2,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,2,8,5,4,6,1,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,7,6,3,5,8,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,7,1,2,5,3,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,7,6,5,2,4,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,7,6,5,1,4,8,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,7,6,5,2,1,8,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,7,6,5,8,2,4,3] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[3,7,6,5,8,1,4,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[3,7,6,5,1,2,4,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,1,6,8,4,2,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,7,6,8,3,5,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,7,6,5,1,4,3,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,7,6,5,8,1,3,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,7,6,5,8,4,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,3,2,1,7,4,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[4,2,1,7,3,5,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,3,1,5,4,2,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,4,1,5,2,7,6,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,2,5,1,3,7,6,4] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[4,3,7,2,1,5,8,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[4,7,2,5,3,1,8,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[2,7,5,4,1,3,8,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,5,4,3,2,1,8,6] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[6,5,2,1,8,4,3,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[5,7,4,3,2,8,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,7,6,2,4,8,3,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,7,3,6,4,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[6,2,7,5,3,8,1,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[7,1,8,5,3,6,4,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[5,8,3,2,7,1,6,4] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[8,7,3,1,6,5,4,2] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,2,6,1,5,4,3] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[1,8,5,7,4,3,6,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,8,5,7,2,4,6,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,8,6,1,7,2,5,4] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[7,2,8,5,6,1,4,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,3,7,5,8,2,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[3,7,2,6,8,4,1,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[3,6,5,8,1,4,2,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,6,5,8,4,1,3,7] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[6,5,4,8,3,2,1,7] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[6,3,5,1,8,4,2,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,4,1,5,7,3,6,2] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,4,1,6,8,2,3,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,3,7,4,8,5,2,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,7,2,5,8,6,3,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,3,1,8,4,7,5,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,5,3,8,7,4,1,2] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[5,4,8,1,7,6,2,3] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,2,8,1,7,3,6,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,4,7,8,1,5,3,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,5,8,7,1,3,6,4] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[5,3,8,7,2,1,6,4] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[8,3,7,6,1,5,4,2] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[8,2,7,6,5,1,4,3] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[4,3,8,7,6,2,1,5] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[2,4,8,7,6,1,3,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,5,8,7,2,6,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,7,3,8,6,5,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[7,5,8,6,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[5,8,7,3,6,4,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[4,8,7,6,2,5,3,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[3,8,7,6,5,1,4,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[2,8,7,6,5,4,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[3,4,1,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[3,2,1,4,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[4,5,6,1,2,3,7,8,9] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[4,2,5,1,3,6,7,8,9] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[4,3,2,1,5,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[5,6,7,8,1,2,3,4,9] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[5,2,6,7,1,3,4,8,9] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[5,6,3,4,1,2,7,8,9] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000
[5,3,2,6,1,4,7,8,9] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[5,4,3,2,1,6,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[6,2,7,8,9,1,3,4,5] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[6,7,3,4,8,1,2,5,9] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000
[6,3,2,7,8,1,4,5,9] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000
[6,4,7,2,5,1,3,8,9] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000
[6,4,3,2,7,1,5,8,9] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[6,5,4,3,2,1,7,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[7,4,8,2,5,9,1,3,6] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100
[7,4,3,2,8,9,1,5,6] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100
[7,8,5,6,3,4,1,2,9] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100
[7,5,3,8,2,6,1,4,9] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100
[7,5,4,3,2,8,1,6,9] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100
[7,6,5,4,3,2,1,8,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[8,6,9,4,7,2,5,1,3] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[8,6,4,3,9,2,7,1,5] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010
[8,6,5,4,3,2,9,1,7] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[3,4,1,2,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[3,2,1,4,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[4,5,6,1,2,3,7,8,9,10] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[4,2,5,1,3,6,7,8,9,10] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[4,3,2,1,5,6,7,8,9,10] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000
[5,6,7,8,1,2,3,4,9,10] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[5,2,6,7,1,3,4,8,9,10] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000
[5,6,3,4,1,2,7,8,9,10] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000
[5,3,2,6,1,4,7,8,9,10] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000
[5,4,3,2,1,6,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[6,2,7,8,9,1,3,4,5,10] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[6,7,3,4,8,1,2,5,9,10] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000
[6,3,2,7,8,1,4,5,9,10] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000
[6,4,7,2,5,1,3,8,9,10] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000
[6,4,3,2,7,1,5,8,9,10] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[6,5,4,3,2,1,7,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[7,8,3,4,9,10,1,2,5,6] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[7,8,9,4,5,6,1,2,3,10] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000
[7,4,3,2,8,9,1,5,6,10] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000
[7,8,5,6,3,4,1,2,9,10] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000
[7,5,3,8,2,6,1,4,9,10] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000
[7,5,4,3,2,8,1,6,9,10] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000
[7,6,5,4,3,2,1,8,9,10] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[8,5,9,10,2,6,7,1,3,4] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100
[8,5,3,9,2,6,10,1,4,7] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100
[8,6,9,4,7,2,5,1,3,10] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100
[8,6,4,3,9,2,7,1,5,10] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100
[8,6,5,4,3,2,9,1,7,10] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100
[8,7,6,5,4,3,2,1,9,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,7,5,4,3,10,2,8,1,6] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010
[3,6,5,1,2,4,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[3,7,5,8,2,4,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,8,5,7,2,4,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,1,7,8,4,3,2,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,1,2,6,4,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,1,2,5,4,3,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[5,1,2,4,6,3,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[4,1,2,6,5,3,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,1,5,7,8,3,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,1,5,8,7,3,2,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[4,7,1,8,3,6,2,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,1,7,8,5,2,3,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,1,7,4,8,2,3,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[7,5,3,8,1,4,2,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[2,1,5,8,7,3,4,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,1,8,4,7,2,3,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[4,1,8,7,5,2,3,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,7,1,6,3,2,8,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,1,2,3,7,5,8,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[7,1,2,3,8,6,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[7,1,2,3,5,8,6,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[6,8,1,4,3,7,2,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[8,7,3,2,4,1,6,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[2,1,7,3,4,8,6,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[7,8,3,2,4,1,6,5] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,7,1,4,3,8,2,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[8,1,2,3,5,7,6,4] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,1,2,3,6,7,5,4] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,1,2,3,6,8,5,4] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,1,2,3,8,5,6,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[8,1,2,3,7,5,6,4] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[8,1,2,3,6,5,7,4] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[7,1,8,5,4,3,2,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[7,8,2,6,3,4,1,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,8,2,7,3,4,1,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,7,2,8,3,4,1,5] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,8,7,1,4,2,6,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[3,7,8,1,4,2,6,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[3,6,8,1,4,2,7,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[3,5,7,8,2,4,1,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,6,7,1,4,2,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[7,6,2,8,3,1,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,6,2,7,3,1,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,1,7,5,4,3,2,6] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,1,7,4,5,3,2,6] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[5,8,3,7,1,4,2,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,1,7,3,4,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[6,7,3,2,4,1,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[8,7,2,4,3,6,1,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,1,2,3,5,6,8,4] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[6,1,2,3,8,7,4,5] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,1,2,3,7,8,6,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[5,1,2,3,8,7,6,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,1,2,3,8,6,7,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,1,2,3,5,8,7,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[8,6,2,4,3,1,7,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,6,3,2,4,8,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[2,1,6,3,4,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[8,6,3,2,4,7,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,2,4,3,1,8,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,1,2,3,5,7,8,4] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[5,1,2,3,6,8,7,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[7,8,1,2,6,3,5,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,4,8,2,7,3,5,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,2,8,5,4,7,3,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,3,8,5,4,2,7,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,3,6,8,4,7,1,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[1,3,6,8,4,7,5,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,8,1,7,3,6,5] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[3,4,8,5,7,6,1,2] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,2,6,8,4,5,7,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[7,5,1,2,4,3,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,4,6,1,5,2,3,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,1,4,2,6,3,5,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[6,8,1,4,7,2,3,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,6,4,2,8,3,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,6,3,8,5,4,2,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[6,8,1,7,3,5,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,1,3,6,5,4,2,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[7,3,1,6,5,4,2,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,2,1,4,6,3,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,2,3,6,5,1,4,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,1,2,3,6,5,4,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[6,8,1,2,7,3,5,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,6,2,3,8,5,4,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,5,8,2,7,6,3,4] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,1,8,2,7,6,3,4] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,8,2,7,6,3,4,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[6,2,8,1,7,3,5,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,8,2,1,7,4,3,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[3,6,4,1,2,8,5,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,1,6,3,8,5,4,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,5,1,8,7,6,3,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[2,5,3,8,7,4,6,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,2,5,3,8,7,4,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[2,4,8,7,6,5,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,5,3,8,7,1,6,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[2,5,8,4,1,7,6,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,5,8,7,1,4,2,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,3,8,4,1,7,6,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,2,8,7,6,3,5,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,2,8,7,6,5,3,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[4,1,8,7,6,5,3,2] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[4,3,8,7,6,5,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,3,1,8,7,2,5,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[5,8,3,7,6,1,4,2] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[5,1,3,8,7,6,2,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[1,5,3,8,7,6,2,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,5,8,4,7,2,6,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[5,1,8,4,7,2,6,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,8,7,4,6,1,2,3] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,5,1,2,4,7,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,6,3,1,2,4,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,6,2,4,3,1,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[5,6,1,2,4,3,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,5,8,1,7,2,3,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,5,8,1,7,2,6,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[1,3,2,5,8,7,4,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,5,1,8,7,4,6,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,5,1,8,7,2,6,4] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[4,3,6,1,2,8,5,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[4,5,8,3,1,7,2,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,5,2,8,7,1,3,6] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,2,5,8,7,1,6,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,4,8,7,6,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[3,1,4,8,7,6,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,4,8,7,6,5,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,3,4,8,7,6,2,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,4,8,7,6,2,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,2,5,8,7,4,6,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[4,5,8,3,1,7,6,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[2,1,3,5,8,7,4,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,2,7,5,8,6,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[7,1,4,8,2,6,5,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,8,1,3,7,5,2,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[3,7,8,1,2,6,5,4] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[1,3,7,8,2,6,5,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,3,7,8,1,6,5,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,7,8,1,3,6,5,4] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[8,1,2,6,7,3,5,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,1,2,6,7,5,3,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[8,2,5,7,1,3,6,4] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[2,8,1,6,7,3,5,4] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,6,8,3,7,1,5,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,8,6,4,7,1,5,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,8,3,4,1,7,5,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,8,3,7,4,1,5,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,6,8,3,7,5,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,8,1,6,7,5,3,4] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[8,2,5,7,1,6,3,4] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[8,4,7,2,3,6,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,5,7,4,2,6,1,3] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,3,5,7,4,1,6,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,5,2,4,7,1,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,2,3,5,7,1,6,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,2,4,7,3,6,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,2,7,1,4,6,3,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[8,7,1,2,4,6,3,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,7,1,4,6,2,3,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,4,7,1,3,6,2,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[1,6,8,3,7,2,5,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[8,3,5,7,1,2,6,4] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[5,8,7,1,3,6,2,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,5,4,7,1,6,2,3] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,5,4,7,1,2,6,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,5,1,4,7,2,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[1,4,6,8,2,7,5,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,6,5,8,2,7,4,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[8,5,6,3,1,7,4,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,6,2,8,1,7,4,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,8,4,5,7,2,6,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[5,8,7,3,6,1,2,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,3,5,7,1,6,2,4] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[1,6,8,3,7,5,2,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[6,3,8,2,7,5,1,4] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,8,4,2,7,1,5,3] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[8,6,4,7,3,1,5,2] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,4,5,7,3,1,6,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,4,2,5,7,1,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,3,4,7,2,6,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,7,1,3,4,6,2,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,3,7,2,4,6,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[2,8,4,5,7,1,6,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,7,3,4,5,1,6,2] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,7,4,5,2,6,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,8,7,2,3,6,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,7,2,3,4,6,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,7,2,3,6,1,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,3,2,8,5,4,7,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[4,2,8,5,3,7,1,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[5,2,1,8,4,3,7,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,2,8,4,3,7,5,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,2,8,4,3,1,6,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,3,4,8,2,1,6,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,3,4,8,2,7,5,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,3,4,1,8,2,7,6] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[8,1,4,5,2,3,7,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,1,5,4,3,2,7,6] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[3,5,4,2,8,1,7,6] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,5,3,2,8,7,1,6] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,4,3,2,8,7,5,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[6,5,3,2,1,7,8,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[5,6,3,2,7,8,4,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,1,6,3,2,7,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,6,4,2,7,8,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,1,6,4,3,7,2,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,1,7,4,3,6,5,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[2,7,4,1,3,6,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,7,4,2,6,1,5,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,1,7,3,2,6,5,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[5,7,3,2,6,4,8,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,7,3,2,5,4,1,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,6,3,2,1,5,4,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[4,7,5,6,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,1,7,5,6,2,4,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,7,5,6,1,3,4,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[2,6,5,7,1,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,6,5,7,2,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,6,4,7,2,8,3,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,5,4,1,7,2,8,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,5,4,6,2,1,8,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,4,5,7,1,8,2,3] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[5,4,6,1,7,8,2,3] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,1,5,6,7,2,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[2,1,4,6,8,7,3,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,4,6,8,7,1,2,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,3,1,6,8,7,2,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,3,6,8,7,2,4,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,3,5,1,8,7,2,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[7,3,5,8,6,2,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[7,2,8,5,6,3,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,2,8,5,1,7,3,4] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,2,1,8,6,7,3,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[1,3,2,8,6,7,4,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,3,8,6,7,1,4,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[8,1,3,2,6,7,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[2,3,8,7,1,6,5,4] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,2,8,7,6,1,5,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,2,8,7,6,4,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[7,2,1,8,6,5,4,3] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,3,6,1,8,5,4,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,3,7,8,5,4,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[5,3,7,8,6,4,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,3,1,7,8,6,5,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,4,7,8,6,1,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,1,5,7,6,2,4,3] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,5,7,6,8,1,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,5,7,6,8,3,1,2] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[5,4,1,7,6,8,3,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,4,7,5,8,3,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[7,4,6,5,1,8,3,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,5,6,4,3,1,8,2] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[6,5,1,7,4,3,8,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[4,6,7,5,3,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,6,7,5,1,4,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[8,1,6,7,5,4,2,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,1,7,6,5,4,3,2] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[2,7,6,1,5,4,3,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[3,7,6,5,1,4,2,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[4,7,6,5,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,6,4,3,1,5,7,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,6,4,1,5,2,7,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,6,5,1,3,2,7,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,6,3,1,7,2,4,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,7,3,1,5,2,4,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,3,1,7,2,4,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,7,1,2,4,5,3,6] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,6,1,2,4,7,3,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,5,1,2,6,7,3,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,5,1,6,4,2,7,3] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,5,1,3,6,4,7,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,6,1,5,3,4,7,2] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,6,1,5,2,4,7,3] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,6,1,2,5,7,3,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,6,1,2,7,4,3,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,7,1,2,5,4,3,6] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[5,1,4,2,3,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[5,1,4,2,7,3,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,5,8,2,6,3,4] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[5,7,8,1,2,4,6,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,7,8,1,3,4,6,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,8,1,7,3,4,6,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[8,1,5,7,2,4,6,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,4,1,2,7,6,3,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,4,2,3,8,7,5,6] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,4,2,7,6,3,5,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[6,1,2,8,7,5,3,4] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,1,2,4,8,7,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,1,8,4,6,7,5,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,1,7,6,4,8,5,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[7,1,2,4,6,8,5,3] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,1,2,6,8,5,3,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,1,2,7,8,5,3,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,1,2,7,4,8,5,3] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,1,6,4,7,8,5,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,7,1,3,8,4,6,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,7,1,8,4,2,6,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[7,1,5,3,2,8,6,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,1,4,5,2,8,6,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,7,3,1,5,8,6,2] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[4,8,7,3,1,5,6,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[8,1,7,4,5,2,6,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,7,5,3,2,6,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,3,7,1,2,6,4,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[3,1,2,8,4,7,5,6] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[3,1,2,8,6,4,5,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,1,7,2,6,4,5,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,4,2,3,8,6,5,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,4,2,3,8,5,7,6] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[5,8,1,7,2,4,6,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,8,1,3,4,7,6,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,1,8,6,4,7,5,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,1,2,6,7,4,5,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,1,2,8,7,3,5,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[1,2,3,5,8,4,7,6] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,3,5,8,6,4,7] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[7,1,2,8,3,6,5,4] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[7,1,2,8,6,4,5,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,1,7,8,4,6,5,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,1,8,7,6,4,5,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,1,2,7,4,6,5,3] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,1,2,7,3,6,5,4] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[1,2,3,5,8,7,4,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,3,6,8,5,4,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[7,8,5,6,3,1,4,2] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[7,5,6,3,1,4,2,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,5,8,3,1,4,2,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,8,5,3,1,4,2,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,5,3,1,6,2,4] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,5,3,1,6,4,2] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[7,8,5,3,6,1,4,2] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[7,8,5,3,6,4,1,2] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[7,5,8,3,4,1,6,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,5,6,3,4,1,8,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,5,6,3,1,2,8,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,5,3,6,1,2,8,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,5,3,1,4,2,6,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,5,3,1,6,4,8,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,3,6,4,1,8,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,5,3,6,4,8,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,5,3,8,4,6,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,5,3,8,1,4,6,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,5,3,1,8,4,6,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,3,1,8,2,6,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,3,1,6,4,2,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,3,1,8,4,2,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,3,1,8,6,2,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,3,8,1,6,4,2] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[7,5,3,8,6,1,4,2] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[7,5,3,8,6,4,1,2] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[7,5,8,3,6,4,1,2] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[7,5,8,3,6,1,4,2] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[7,5,8,3,1,6,4,2] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[7,5,3,6,1,4,2,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,5,3,8,4,1,2,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,5,8,6,3,1,2,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[7,5,8,6,3,1,4,2] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[7,5,8,6,3,4,1,2] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[7,5,6,8,3,1,4,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[7,5,6,3,8,1,2,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,5,3,4,1,8,2,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[7,5,6,3,1,8,2,4] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,5,6,3,1,8,4,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,5,6,3,8,1,4,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,5,6,3,8,4,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,5,3,6,1,8,4,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,5,3,1,6,8,2,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[7,5,3,1,2,8,4,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,5,3,1,2,8,6,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,5,3,1,4,8,6,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,5,3,4,8,1,6,2] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,5,3,4,1,6,8,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,5,3,1,4,6,8,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[3,6,2,5,4,1,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[3,5,2,8,4,7,6,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,4,7,3,2,8,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[5,4,8,3,2,7,6,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[6,4,5,3,2,1,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[5,3,2,6,4,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[4,5,8,3,2,7,6,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,7,6,3,8,5,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,8,6,3,7,5,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,8,5,3,2,7,6,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[5,8,4,3,2,7,6,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[5,3,2,8,4,7,6,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[2,1,5,8,4,7,6,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,3,2,7,4,8,6,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[5,7,4,3,2,8,6,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[4,7,5,3,2,8,6,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[4,7,8,3,6,5,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,6,8,3,7,5,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[7,6,4,3,8,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[7,3,2,6,8,5,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[2,1,8,6,7,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[8,3,2,6,7,5,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,6,4,3,7,5,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,5,7,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[8,4,5,3,2,7,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,4,7,3,6,5,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,4,6,3,7,5,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,4,6,3,8,5,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[3,7,2,6,8,5,4,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,8,2,6,7,5,4,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,8,2,5,4,7,6,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[3,7,2,8,6,5,4,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,6,2,8,7,5,4,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,4,7,3,8,5,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,4,8,3,7,5,2,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,4,8,3,6,5,2,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,4,5,3,2,8,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,5,4,3,2,8,6,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[7,3,2,5,4,8,6,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,1,7,5,4,8,6,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[7,3,2,8,6,5,4,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,8,4,3,6,5,2,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,8,5,7,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[6,8,4,3,7,5,2,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,3,2,8,7,5,4,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[6,3,2,7,8,5,4,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,7,4,3,8,5,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,3,1,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[2,3,1,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 010000000
[2,4,3,1,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 01100000
[2,3,4,1,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 001000000
[2,3,4,5,1,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => 000100000
[2,3,4,5,6,1,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 000010000
[2,3,4,5,6,7,1,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => 000001000
[2,3,4,5,6,8,7,1,9] => [[1,2,3,4,5,6,9],[7],[8]] => 00000110
[2,3,4,5,6,7,8,1,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[2,3,4,5,6,7,9,8,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[4,6,8,3,5,7,1,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,8,1,2,4,5,7,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,5,8,2,4,7,1,6] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[8,3,5,2,4,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,2,5,7,3,6,1,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,5,2,8,3,1,6,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,2,5,8,3,7,1,6] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[2,1,6,8,4,7,3,5] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[1,2,5,8,3,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[5,3,6,8,4,7,1,2] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[1,6,5,8,2,4,7,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,1,2,6,8,5,7,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[1,4,3,8,2,6,7,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[5,4,8,3,2,1,6,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[5,4,3,7,2,6,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[4,3,6,2,7,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,6,3,2,1,8,5,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[4,1,7,3,2,5,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,3,1,7,8,2,6,5] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[3,5,1,2,7,8,6,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[7,5,1,4,8,2,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,4,7,3,8,6,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,8,4,7,6,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[5,8,7,1,4,2,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[8,3,5,1,2,7,6,4] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[4,8,3,1,7,2,6,5] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,8,4,3,5,2,7,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,6,3,1,5,2,8,7] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,7,3,6,5,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,3,7,6,4,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,6,3,4,2,8,7,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,8,3,6,2,7,5,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,6,8,7,4,2,5,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[6,4,8,7,5,3,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[7,6,4,3,8,5,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[1,7,6,2,8,4,5,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,1,3,2,6,8,5,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[1,5,3,2,7,4,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[6,3,2,1,8,5,4,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,5,3,2,7,4,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,2,6,3,7,4,1,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,8,5,3,1,6,4,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,1,7,3,8,5,4,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[1,6,2,3,7,8,5,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,6,7,2,8,4,5,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,7,1,8,2,4,6,3] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[5,1,2,7,8,3,6,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,4,1,7,8,6,3,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,2,1,7,3,8,5,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,2,8,4,3,1,5,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,3,2,1,8,4,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,8,3,2,5,6,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[7,1,8,2,4,5,6,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[8,7,6,1,2,4,5,3] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,3,7,6,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[3,2,8,7,5,1,4,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[8,3,6,5,2,1,4,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[7,6,3,5,2,4,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,4,6,2,5,3,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,2,4,1,6,5,3,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,2,8,1,7,5,3,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,2,4,1,7,6,3,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,7,1,5,6,2,4,3] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,5,7,3,6,4,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[6,8,3,7,5,4,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[8,1,6,7,5,2,4,3] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,1,2,6,4,3,7,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[2,8,1,7,5,4,3,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[2,5,1,8,6,4,3,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,7,2,6,4,3,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[6,2,7,5,4,3,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,1,8,6,5,4,3,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,2,7,5,4,3,8,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,7,2,4,3,8,6,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,7,2,8,3,6,5,4] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,7,8,6,5,2,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[7,3,8,6,5,4,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[1,8,7,6,5,2,4,3] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[8,1,7,3,2,6,5,4] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[5,1,4,3,2,8,7,6] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,6,5,3,2,1,7,4] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[8,6,3,2,1,7,4,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,6,5,4,1,7,2,3] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,6,5,1,7,3,2,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,6,1,7,4,3,2,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,6,3,2,7,5,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,4,3,7,2,5,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[7,4,8,3,1,6,2,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,1,5,8,3,2,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[5,7,4,1,8,2,6,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,7,4,3,1,8,6,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,8,7,2,5,4,6,3] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[1,8,5,3,7,2,6,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,3,1,8,7,5,2,6] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[1,4,8,6,3,5,2,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,4,6,3,5,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[1,3,5,6,8,4,2,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,5,4,8,7,1,2,6] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,1,4,6,8,7,2,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,6,3,8,7,2,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,6,2,4,8,7,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,4,1,6,7,5,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,1,6,4,8,5,2,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,3,6,8,5,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[1,3,7,2,6,8,4,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,6,5,2,8,1,4,7] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[3,6,5,7,2,4,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,2,6,3,8,1,5,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,2,6,7,3,5,1,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[3,6,2,4,7,5,1,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,6,2,4,1,8,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[7,3,8,2,1,6,4,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,3,5,2,1,8,6,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,7,6,4,3,1,5,2] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[8,7,6,4,1,5,2,3] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[3,8,7,2,1,4,6,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,8,2,7,1,5,4,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[3,6,8,2,1,5,4,7] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[2,4,8,1,6,5,3,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[4,2,8,1,5,7,3,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[8,5,7,6,1,4,2,3] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,6,1,7,3,5,4,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,6,1,7,5,4,2,3] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,6,2,8,7,3,5,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,8,2,4,6,7,3,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,8,5,4,7,1,3,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,1,5,8,6,4,3,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[7,2,5,6,4,3,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[1,2,5,7,8,4,3,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,7,4,8,6,3,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,2,7,8,3,6,5,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[7,1,8,6,3,5,4,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,8,7,6,3,5,2,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,8,7,4,6,3,2,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[7,1,5,8,3,4,6,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,1,6,4,2,3,5,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[8,6,2,4,7,3,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,6,2,4,5,7,3,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[2,7,1,4,5,8,3,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[7,1,6,4,5,2,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,1,4,5,6,8,2,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,1,4,6,5,8,3,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[7,1,2,3,8,5,4,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[7,1,5,4,3,8,2,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,1,3,4,2,6,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[7,1,5,4,6,2,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,1,5,6,4,3,8,2] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[7,1,6,5,4,3,2,8] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,6,2,5,4,3,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[2,5,1,7,4,3,6,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,5,1,4,7,8,6,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,5,1,4,8,6,2,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,6,2,4,7,8,1,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,6,2,4,8,7,1,3] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[6,3,8,2,4,7,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,5,8,7,2,3,1,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[6,5,7,8,2,4,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[6,3,4,2,8,5,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,4,7,2,5,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,6,8,1,3,5,2,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[4,3,8,1,2,7,5,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[3,6,4,1,7,2,5,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,8,3,1,5,6,4,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[3,8,7,1,5,4,2,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[4,3,1,7,6,8,2,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[3,4,1,7,5,6,8,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[3,4,1,5,7,6,2,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[3,7,4,1,6,2,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[8,4,7,2,5,3,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[4,7,8,1,2,3,6,5] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,8,6,1,5,3,7,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,6,5,1,3,8,2,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,5,1,3,4,8,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,2,6,4,1,3,8,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,7,5,2,1,3,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[8,4,5,3,7,2,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[4,7,5,2,8,1,6,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[2,6,4,3,1,5,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[7,3,8,4,1,5,2,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,2,3,4,1,6,5,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[4,2,8,3,6,1,5,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[6,8,5,7,2,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[4,8,5,2,7,1,3,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,3,5,2,1,7,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,8,5,3,1,4,2,7] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[3,6,5,4,2,8,1,7] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,6,4,7,2,5,3,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,6,4,8,2,5,3,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,6,5,8,2,4,3,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,6,8,2,4,3,7,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,6,2,4,3,7,8,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,5,6,2,4,7,3,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,5,6,2,4,7,8,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,5,8,2,4,7,3,6] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[1,5,7,2,4,8,3,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,6,5,7,2,4,3,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,6,7,2,4,3,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,5,6,7,2,4,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,5,8,2,4,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,5,7,2,4,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,5,7,8,3,2,4,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,5,8,3,2,4,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,5,6,2,4,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,7,6,2,8,3,4,5] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,7,3,4,2,8,6,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,6,2,4,3,8,7,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,5,6,2,4,8,7,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,5,8,7,3,2,4,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,4,2,3,5,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,5,2,3,4,8,7,6] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,6,5,2,3,8,7,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,7,4,2,8,6,5,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,7,6,5,2,8,4,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,6,7,5,2,3,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,7,5,2,8,4,3,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,7,5,6,2,8,3,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,5,7,6,2,4,8,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,5,8,3,2,4,7,6] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,6,5,2,3,7,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,6,5,2,3,7,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,6,8,4,2,3,7,5] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,7,4,6,2,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,7,3,5,2,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,6,8,5,2,3,7,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,6,4,2,3,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,6,4,2,3,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,5,8,6,2,4,7,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,5,7,3,2,4,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,7,3,4,2,8,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,7,4,2,8,5,3,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,6,7,4,2,3,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,6,4,2,3,8,5,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,6,4,2,8,5,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,7,5,2,8,6,4,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,6,4,2,3,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[7,3,5,6,1,4,8,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[3,7,5,6,1,4,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[8,2,4,1,6,7,5,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,6,1,4,2,7,5,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[3,6,1,4,2,8,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[1,6,7,4,3,5,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[6,7,1,4,3,5,8,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,6,1,4,3,5,8,2] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[3,5,4,1,6,7,8,2] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,7,1,6,3,5,8,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,1,4,7,6,5,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[6,1,7,4,3,5,8,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[7,1,6,4,3,5,8,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[1,7,6,4,3,5,8,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[8,1,6,4,2,7,5,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,4,1,3,7,2,5,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[4,7,1,3,8,2,5,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[7,4,1,3,8,2,5,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,3,6,4,2,8,5,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[4,7,3,1,2,8,5,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,7,8,1,2,6,5,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,8,1,4,2,7,5,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[1,8,6,4,2,7,5,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,8,1,3,7,2,5,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[8,7,1,3,6,2,5,4] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,8,5,7,3,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[1,8,4,3,7,2,5,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,8,3,4,7,6,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[3,7,8,4,6,2,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,7,4,6,8,2,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,4,3,7,8,6,1,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,4,7,3,8,2,5,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,7,6,8,3,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[2,5,3,4,8,6,1,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[3,7,5,4,8,2,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[7,1,3,4,2,8,5,6] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[6,1,4,3,8,2,5,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[4,1,7,3,8,2,5,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[8,1,4,3,7,2,5,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,2,3,4,7,6,1,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,2,3,7,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,2,3,4,8,6,1,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[2,7,5,6,3,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,7,2,6,3,8,1,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,7,2,6,8,4,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,2,5,6,8,4,1,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,2,3,8,5,6,1,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[5,2,3,8,7,6,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[8,2,3,7,5,6,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,1,8,3,7,2,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[1,7,8,4,2,6,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,7,1,8,2,5,6,3] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,7,4,8,5,2,1,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,4,3,8,5,6,1,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,8,3,6,2,5,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,5,8,6,3,2,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,5,8,7,3,2,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[8,5,7,6,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[2,5,3,8,7,6,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,7,5,8,6,2,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,7,8,6,5,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,8,7,3,6,2,5,4] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[6,8,7,5,3,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[5,7,6,8,3,4,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,7,6,8,4,5,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,5,4,7,6,8,2,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,7,4,6,5,8,2,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,7,4,6,5,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,5,4,8,6,7,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[3,8,4,6,5,7,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,6,4,7,5,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,6,2,7,5,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,6,4,8,5,7,2,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,8,4,6,5,7,2,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,5,4,8,6,7,2,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[7,8,1,5,4,6,2,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,1,5,2,4,3,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,2,6,5,7,3,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,7,2,8,5,6,3,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,7,2,6,5,8,3,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,5,2,7,6,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,7,6,8,2,5,3,4] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,7,6,8,4,5,2,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[5,7,6,8,1,4,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[7,8,5,6,1,3,2,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,6,7,1,3,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[1,3,2,7,6,8,4,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,7,6,8,2,4,3,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[7,8,1,3,2,6,4,5] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,1,6,2,4,3,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,6,7,2,4,3,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[7,8,1,4,2,6,3,5] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,1,4,2,5,3,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,2,1,4,3,6,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[7,8,1,2,4,3,5,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,3,6,5,8,7,1,2] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[3,4,6,5,7,8,1,2] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[3,4,1,5,6,7,8,9,2] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[3,4,5,6,7,8,1,9,2] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[3,1,2,5,6,7,8,9,4] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[3,4,1,5,6,7,8,9,10,2] => [[1,2,4,5,6,7,8,9],[3,10]] => 010000001
[3,4,1,2,6,7,8,9,5] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[3,4,5,6,7,8,1,2,9] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[3,4,5,6,7,8,9,1,10,2] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[1,6,2,3,8,7,4,5] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,7,4,3,2,8,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,4,7,6,2,5,8,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,2,6,5,3,7,4,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,6,5,3,7,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,3,7,5,2,6,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,3,7,4,2,6,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,6,4,3,7,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,6,4,3,7,5,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,4,7,3,2,5,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,4,3,2,5,8,6,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,5,3,2,4,8,6,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,5,3,2,8,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,5,3,2,4,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[7,6,5,4,3,1,8,2] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[6,8,5,4,3,2,1,7] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,7,6,5,4,3,1,9,2] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[7,9,6,5,4,3,2,1,8] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[9,8,7,6,5,4,3,1,10,2] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,1,5,4,3,8,6,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[3,6,5,4,8,1,7,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,8,1,4,3,2,7,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,8,5,4,3,7,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,9,6,5,4,3,2,8,7] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[8,10,7,6,5,4,3,2,1,9] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[7,6,1,4,3,8,5,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[4,6,5,8,3,1,7,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[6,8,5,1,3,2,7,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[1,8,2,4,3,7,6,5] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,8,5,4,7,2,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,9,6,5,4,3,8,1,7] => [[1,2,7],[3,9],[4],[5],[6],[8]] => 01111010
[1,10,7,6,5,4,3,2,9,8] => [[1,2,9],[3,10],[4],[5],[6],[7],[8]] => 011111101
[1,3,6,5,4,9,8,7,2] => [[1,2,3,6],[4,7],[5,8],[9]] => 00110111
[7,6,5,1,3,8,4,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[1,6,3,4,8,7,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,4,5,8,3,7,6,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[6,8,5,4,1,2,7,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[1,8,5,2,3,7,6,4] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,8,2,4,3,7,1,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[1,8,3,4,7,2,6,5] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[7,5,8,4,3,2,1,6] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[4,8,5,7,3,2,1,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[2,10,7,6,5,4,3,9,1,8] => [[1,2,8],[3,10],[4],[5],[6],[7],[9]] => 011111010
[5,1,7,6,8,4,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[8,4,7,5,2,6,1,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,4,6,8,2,1,7,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,4,6,5,2,1,7,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,8,7,5,6,1,3,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,7,5,1,8,4,3,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[5,1,8,7,4,2,3,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,8,6,7,4,3,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[3,6,5,2,4,1,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[5,2,3,6,4,1,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,1,4,5,3,2,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,8,7,1,4,6,5,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[5,7,1,2,4,3,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,3,7,6,8,2,5,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,3,6,8,1,7,2,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[3,2,6,8,5,7,1,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[6,3,7,2,4,8,5,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,4,8,6,5,2,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[7,1,8,2,5,4,3,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,5,3,7,4,1,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,6,4,7,5,1,8,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[8,4,7,6,2,3,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,4,7,1,2,5,6,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,2,8,7,3,5,6,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[8,1,7,4,2,5,6,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,4,3,8,2,5,6,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,4,1,5,8,2,7,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[2,5,8,7,3,6,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[2,1,5,8,7,4,6,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[8,3,5,6,7,4,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,4,3,2,8,5,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[4,2,7,1,8,5,6,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,1,7,2,8,5,6,3] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,4,8,7,3,5,6,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,7,8,3,1,5,6,2] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[3,4,7,2,8,5,6,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,7,1,4,8,5,6,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[7,2,3,4,8,5,6,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,1,8,5,2,7,4,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[2,1,7,4,5,8,6,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,8,3,6,7,5,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[8,2,1,6,4,7,5,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,8,2,6,4,1,5,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,6,3,5,8,7,1,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,6,2,1,5,8,4,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[4,5,2,7,6,1,8,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[5,1,6,8,4,7,2,3] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[3,6,8,7,5,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[7,4,8,6,5,2,3,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[8,1,6,4,7,3,2,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,6,4,1,2,3,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[2,6,4,8,5,3,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[7,3,5,8,4,2,1,6] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,2,5,8,4,1,7,6] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[8,4,7,1,5,2,3,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,8,7,5,6,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,1,4,8,7,3,5,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,2,8,4,3,5,6,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,7,8,1,3,5,6,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[8,7,3,4,1,5,6,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,8,2,7,3,5,6,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,1,8,7,2,5,6,4] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[3,8,1,7,2,5,6,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[8,2,3,7,1,5,6,4] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,4,8,7,1,3,2,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,8,4,6,7,3,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,3,8,2,7,6,1,5] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,8,4,2,1,3,7,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[7,8,2,4,3,5,6,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[2,8,3,7,1,5,6,4] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[8,1,2,7,3,5,6,4] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[6,4,1,3,2,8,5,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,3,8,6,2,1,4,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,6,5,2,8,3,1,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,3,7,5,1,8,2,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[6,8,5,2,7,4,3,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[7,2,5,4,3,8,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[3,6,8,1,4,5,2,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,8,1,2,4,5,3,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,1,6,2,4,5,3,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[3,8,6,1,2,5,4,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,1,6,2,3,4,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,1,6,5,8,2,3,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,3,8,6,2,5,1,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,3,6,1,4,5,2,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[2,3,6,8,4,5,1,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,7,5,4,3,8,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[6,3,8,7,4,2,5,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[5,8,4,3,7,6,1,2] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[8,7,4,3,1,6,2,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[1,7,4,3,8,6,2,5] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[7,1,5,3,4,8,2,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,8,6,1,7,4,5,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,8,6,5,7,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[4,7,6,8,2,1,5,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[6,1,8,7,4,3,5,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,5,4,3,1,6,7,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[1,5,8,6,3,4,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,5,8,6,3,4,7,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,1,3,8,5,6,7,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,5,8,4,3,1,7,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[4,6,5,2,8,1,7,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[7,2,8,1,3,6,4,5] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[1,8,5,2,3,6,7,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,8,3,2,5,6,7,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,8,3,1,5,6,7,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,8,3,2,5,6,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,2,3,1,5,6,7,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,1,8,3,5,6,7,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,4,8,2,3,6,7,5] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,1,2,7,8,6,4,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[7,5,1,8,2,4,3,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[3,5,8,1,2,4,7,6] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,5,8,1,2,3,7,6] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,2,7,1,8,6,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[3,8,4,1,2,6,7,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,4,8,2,3,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,8,3,6,7,4,1,2] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[2,3,1,6,8,4,7,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,4,3,7,1,8,5,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,4,7,3,2,8,5,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,7,1,4,3,8,5,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,4,1,8,6,3,7,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[8,4,1,3,6,2,7,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[6,8,5,1,7,2,3,4] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,3,6,5,8,2,1,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,6,3,5,8,2,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[4,5,8,7,3,6,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,5,2,8,6,1,7,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[8,2,5,6,1,4,7,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,6,5,4,1,2,7,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[2,6,1,8,3,7,5,4] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,7,1,6,2,8,5,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[6,1,5,3,8,7,2,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[2,8,6,3,7,1,5,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[7,6,1,5,8,2,3,4] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,6,8,5,1,2,7,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[6,5,2,4,8,1,7,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,1,4,8,2,6,7,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,8,2,5,1,6,7,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[3,4,8,5,2,6,7,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[4,2,1,8,5,6,7,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[1,5,4,8,2,6,7,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[7,2,1,5,8,6,3,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[2,8,4,5,1,6,7,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[5,4,8,3,7,6,1,2] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[3,1,5,8,6,2,7,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,3,4,8,5,1,7,2] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[5,3,4,8,1,6,7,2] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[7,6,1,2,8,3,5,4] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,5,8,4,1,2,6,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,5,8,4,6,1,3,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[6,5,4,8,7,1,3,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,5,4,8,1,2,7,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,5,1,6,2,3,8,4] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,5,1,6,8,2,4,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[6,5,4,1,8,2,7,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,5,4,7,1,2,8,3] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,5,4,7,8,1,3,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,5,3,7,1,4,2,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,5,3,1,8,4,2,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,1,4,8,3,2,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,1,6,4,7,3,5,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,5,1,4,8,3,6,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,5,3,7,1,4,8,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,4,3,1,5,8,7,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,4,1,5,3,8,6,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,1,5,4,3,7,6,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,1,5,4,3,7,2,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,4,1,5,3,8,2,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[7,4,1,5,3,2,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,1,5,4,3,2,6,7] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[8,1,6,4,2,5,3,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,5,3,1,2,7,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,5,3,8,1,4,2,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,6,8,1,4,3,2,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,1,7,2,5,4,3,6] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,1,7,2,5,4,6,3] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[7,6,1,2,5,4,8,3] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[6,5,3,8,1,4,7,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,5,3,1,2,7,8,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,5,1,4,2,6,8,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,1,6,4,2,5,7,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,4,1,5,3,2,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[6,4,3,1,5,2,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,4,3,1,5,7,2,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,4,1,5,3,6,2,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,1,5,4,3,6,2,7] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,1,5,4,3,6,7,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[7,4,1,5,3,6,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[6,4,3,1,5,7,8,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,7,3,8,4,5,1,2] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,7,4,5,1,8,2,3] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,7,5,6,2,3,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,7,5,6,1,8,2,3] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[4,7,5,6,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,7,5,8,4,6,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,5,3,8,6,7,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,8,3,6,5,7,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,6,4,7,1,8,2,3] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[5,6,1,7,3,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,6,1,8,2,7,3,4] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,6,1,8,4,7,2,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,8,1,6,5,7,2,3] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,5,1,8,6,7,2,3] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[7,8,4,5,1,6,2,3] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[4,8,2,3,1,6,5,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,6,2,8,1,4,3,7] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[5,6,3,4,1,8,2,7] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[3,6,4,5,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[3,6,4,5,1,8,2,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,6,4,8,1,5,3,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,8,3,6,1,5,4,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,8,3,4,1,6,5,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[7,8,2,5,3,4,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,8,1,5,3,6,2,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[1,5,3,8,6,7,2,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,8,3,6,2,7,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,6,4,8,2,7,3,5] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,6,4,7,3,5,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,7,3,6,4,5,1,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,7,3,6,4,8,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,7,2,8,4,6,3,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,7,5,8,4,6,2,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[1,7,5,8,2,6,3,4] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,7,5,6,3,8,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,7,5,6,3,4,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[6,7,2,5,3,4,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,7,1,5,3,8,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,7,5,8,1,4,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,8,6,7,2,3,1,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,7,2,3,1,8,4,5] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[6,7,2,8,1,4,3,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,4,2,7,5,6,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[3,4,1,7,5,8,2,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,7,5,8,1,4,3,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,3,1,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,3,1,8,4,7,5,6] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[7,8,2,3,1,6,4,5] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,2,6,1,4,3,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[2,8,6,7,1,4,3,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,8,1,4,3,7,5,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,7,2,5,4,6,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,2,7,3,6,1,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,5,1,8,2,7,3,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,4,1,8,2,7,5,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,4,1,8,6,7,2,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,4,2,5,1,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,4,2,8,1,6,5,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,8,2,5,1,6,4,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[4,5,2,8,1,6,3,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[4,5,3,6,1,8,2,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[8,6,7,1,4,2,5,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[8,6,3,7,5,1,2,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,6,1,8,3,5,2,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,6,2,8,3,5,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,6,2,3,8,5,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,6,2,7,3,1,5,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,7,2,5,1,6,3,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,4,2,1,7,6,3,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,5,7,2,1,4,3,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[5,8,7,3,1,4,2,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,8,7,3,1,4,6,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[8,5,7,2,1,4,6,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,4,2,1,3,7,6,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,4,3,1,7,2,6,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,5,1,3,2,7,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,2,8,6,4,1,3,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[8,4,7,5,1,6,2,3] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,4,7,5,1,2,3,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,7,3,5,1,2,6,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,3,2,6,5,1,4,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,8,6,3,5,1,2,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,8,7,3,1,5,2,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[8,4,7,2,1,5,3,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,3,2,7,1,5,4,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,7,3,1,4,2,6,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,7,3,1,2,6,4,5] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,7,3,1,2,4,6,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,3,2,1,4,7,6,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,3,2,1,7,4,6,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,3,2,7,1,5,6,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,4,7,2,1,5,6,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,7,2,1,6,3,4,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[3,6,5,4,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[3,8,5,6,7,4,1,2] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,7,5,8,6,2,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,5,7,8,6,3,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,8,5,7,6,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,6,3,2,1,5,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[6,2,1,5,3,4,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,8,1,3,7,6,4,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[4,7,2,3,6,1,8,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[3,7,4,2,8,1,5,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,2,6,8,5,7,3,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,4,2,7,3,8,5,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,1,6,7,5,3,4,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[2,1,5,8,7,6,3,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,1,4,7,6,3,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,4,7,8,5,3,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,1,3,7,6,2,8,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[8,5,1,6,3,2,7,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[6,3,7,1,5,2,8,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,2,6,8,4,7,5,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[8,4,6,1,3,2,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,2,8,6,7,3,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[7,4,3,8,2,1,5,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[4,7,5,8,1,6,3,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[6,4,3,2,7,8,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[4,2,5,1,6,7,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,4,8,5,7,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,7,1,4,6,8,5,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,8,2,5,6,1,4,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[2,4,3,8,7,5,6,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,6,7,3,5,1,8,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[7,6,8,4,2,5,3,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[8,5,7,1,6,3,2,4] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[6,5,7,2,8,4,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[3,4,8,6,5,2,1,7] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,7,6,1,4,5,8,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[6,5,8,2,1,7,3,4] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,4,3,5,1,6,8,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,1,6,3,5,8,7,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[6,2,5,8,4,3,7,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,6,7,1,5,4,3,2] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[2,1,6,5,8,4,7,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,1,6,8,5,4,3,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[4,1,8,5,6,2,3,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,6,4,8,7,3,5,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,2,8,4,3,5,1,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,8,2,7,6,1,3,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[3,1,8,2,7,5,4,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,8,1,2,6,7,4,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,8,4,3,2,7,1,6] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[7,4,8,6,3,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,8,4,7,2,1,3,6] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[2,1,8,4,3,7,5,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[6,3,8,2,4,5,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,8,4,2,3,6,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,2,4,3,1,6,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[2,8,3,1,6,4,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[8,2,1,3,4,7,5,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,4,8,2,6,3,5,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,2,7,3,5,4,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,2,3,8,4,5,7,6] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,2,8,3,4,5,7,6] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[1,3,8,2,6,4,5,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,5,7,2,3,6,4,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,7,2,3,5,4,8,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,3,8,2,4,5,7,6] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,2,3,8,4,6,7,5] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[1,8,2,3,5,4,6,7] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,7,8,2,3,6,4,5] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,6,7,8,2,3,5,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,7,8,2,5,3,6,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,7,8,2,4,5,3,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,2,8,3,6,4,5,7] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,8,2,3,6,4,5,7] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,2,8,3,5,4,6,7] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,2,7,8,3,6,4,5] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,5,2,7,8,3,6,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,3,2,8,4,6,7,5] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,8,2,3,4,6,7,5] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,7,8,2,4,3,6,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[6,7,3,1,5,2,8,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,8,3,1,5,2,7,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,7,4,5,1,2,8,3] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[7,3,6,1,5,2,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,7,5,4,1,2,8,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,8,6,4,1,7,2,3] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[5,7,6,4,1,8,2,3] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,4,7,5,1,2,8,3] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[6,2,1,7,5,3,8,4] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,3,8,1,5,2,7,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,6,8,4,1,7,2,3] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,6,8,5,7,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[4,5,8,6,7,1,2,3] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,4,8,6,1,7,2,3] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[5,3,8,1,6,7,2,4] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[5,2,1,7,6,8,3,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[5,4,7,6,1,8,2,3] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,8,6,5,7,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[4,7,5,6,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,6,5,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,7,4,6,1,8,2,3] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,4,6,1,7,2,3] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,3,1,6,7,2,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,7,3,1,6,8,2,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,6,3,1,7,8,2,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,8,3,1,7,6,2,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,7,4,8,1,6,2,3] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[5,4,6,8,1,7,2,3] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,8,6,7,5,1,2,3] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,2,1,7,8,6,3,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,3,8,1,7,6,2,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,4,8,7,1,6,2,3] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,6,8,7,5,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,7,8,6,5,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,8,7,6,5,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[2,5,4,7,3,6,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,4,6,3,7,5,1,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[4,2,7,3,6,5,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,2,6,3,1,5,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,5,3,1,6,4,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,5,3,7,6,4,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,6,5,3,7,4,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[4,2,7,6,3,5,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[2,7,5,3,6,4,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,6,3,7,5,4,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,7,5,2,3,8,4,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[2,1,3,7,5,4,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,3,1,8,6,5,4,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,5,3,1,8,6,4,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[4,2,8,3,1,6,5,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[8,3,2,6,4,1,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,6,8,2,1,4,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[1,5,2,8,3,4,7,6] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,2,6,3,8,7,4,5] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,2,8,3,6,4,7,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,2,7,6,3,4,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,1,3,8,7,5,4,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[1,2,3,8,6,4,7,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,2,3,7,4,8,6,5] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,7,6,3,8,4,5] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,3,6,4,8,7,5] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,3,7,6,4,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,6,3,1,8,5,4,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,1,3,8,5,4,7,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[7,1,8,4,2,3,5,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,1,8,4,3,5,7,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,2,6,3,1,8,5,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[5,4,2,8,3,1,6,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,5,8,2,4,1,6,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,5,4,8,3,1,6,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[4,2,1,8,3,5,7,6] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[1,8,7,4,2,3,5,6] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,5,2,8,7,3,4,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,2,7,3,6,4,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,2,8,6,3,7,4,5] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,7,3,8,6,4,5] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,2,3,8,4,7,6,5] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,7,3,4,8,6,5] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,2,6,3,8,4,7,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,5,2,3,8,7,4,6] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[4,2,1,8,3,7,5,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[8,3,2,1,7,4,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,8,4,2,7,3,5,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,2,8,6,3,4,7,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,7,3,8,4,6,5] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,2,3,8,7,4,6,5] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,2,3,8,7,6,4,5] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[2,5,3,8,1,6,4,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,6,4,7,1,5,3,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,6,5,7,1,4,3,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,8,5,7,1,2,6,4] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[3,8,5,7,2,6,4,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,4,8,6,2,5,7,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,4,8,6,1,2,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[2,5,7,1,4,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,4,8,1,5,7,6,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,4,3,8,1,6,5,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,8,1,7,5,6,4,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[2,3,8,1,6,5,7,4] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,4,8,1,3,5,7,6] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,5,7,6,1,2,4,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,5,7,6,2,4,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,8,6,7,2,3,5,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[4,8,6,7,1,2,3,5] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,8,6,7,1,3,5,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[3,4,8,6,1,5,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,8,5,7,1,6,4,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,2,8,5,6,1,7,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,8,5,7,2,1,6,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[3,4,8,6,2,1,5,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[3,5,7,6,2,1,4,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,8,6,7,2,1,3,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,8,6,7,3,5,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,6,7,3,4,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,6,7,2,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,8,6,7,2,1,4,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,8,6,7,2,1,5,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,3,1,7,5,2,8,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[4,3,2,8,5,1,7,6] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[4,3,8,5,1,6,7,2] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,8,6,7,1,5,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,6,7,1,4,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,6,7,2,3,4,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,8,6,7,2,4,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,8,6,7,1,2,4,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[4,2,3,8,5,1,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,2,8,5,1,7,6,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,4,2,8,5,6,1,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[3,2,4,8,6,1,5,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[3,2,5,7,6,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,8,6,7,1,3,2,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,6,7,1,2,5,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[4,8,6,7,2,5,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[4,3,8,5,2,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,3,8,5,1,2,6,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,2,6,7,5,1,3,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[3,8,5,7,1,4,2,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,8,4,7,1,5,2,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,5,2,8,4,6,1,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,5,1,7,4,6,2,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,8,4,7,2,5,1,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,1,3,8,5,2,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,1,2,6,7,5,3,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,2,6,7,5,3,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,8,6,7,3,2,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[4,8,6,7,3,1,2,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,1,5,7,6,2,4,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,4,1,7,5,6,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[4,1,7,5,2,8,6,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,1,6,7,5,2,3,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,8,6,7,2,3,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,8,6,7,3,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,8,6,7,4,2,3,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,8,6,7,4,1,2,3] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,8,6,7,4,1,3,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,8,6,7,3,1,4,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,8,6,7,3,1,5,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,1,6,7,5,3,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,1,7,5,3,2,8,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[4,2,8,5,3,1,7,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[4,2,1,6,7,5,3,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,8,6,7,3,2,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,8,6,7,4,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,8,6,7,4,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,3,5,8,1,4,2,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[3,8,7,6,1,4,2,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,1,8,3,6,7,2,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[1,4,7,8,5,6,2,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,4,7,1,5,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,6,1,4,7,8,5,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[1,6,8,4,7,5,2,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[6,8,1,3,5,7,2,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[7,6,1,4,3,8,2,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[3,8,1,6,5,4,2,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,1,3,7,5,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,1,7,3,8,4,2,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[7,1,8,6,3,5,2,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,1,7,6,5,8,4,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[8,2,7,6,5,3,4,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,4,2,6,7,5,3,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[4,8,1,6,7,5,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[7,4,1,6,8,2,5,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[1,3,8,6,2,7,5,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,1,3,2,7,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,8,6,2,5,3,4,7] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[4,7,2,6,8,1,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[8,7,3,6,4,5,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[5,7,8,6,2,1,4,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,7,4,1,6,8,3,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,7,2,4,5,1,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[1,8,6,4,5,2,3,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,8,4,6,5,1,3,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,4,1,7,5,2,6,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[7,5,8,6,1,2,4,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,6,8,7,3,1,4,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,5,4,3,6,8,1,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,8,5,4,6,2,1,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[4,8,2,1,3,7,5,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,4,1,2,7,5,8,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,1,8,3,6,7,5,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[8,3,7,4,5,2,6,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[4,3,7,8,5,1,6,2] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[5,4,8,2,7,6,1,3] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[1,2,7,3,6,5,8,4] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[2,8,7,6,3,4,1,5] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[5,8,2,6,3,4,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,1,7,5,8,6,2,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,1,7,8,4,3,6,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[8,2,7,5,4,3,6,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[6,3,8,1,4,7,5,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[3,8,4,5,6,1,2,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,4,3,5,7,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[6,5,8,7,1,3,4,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,6,7,2,4,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,5,2,7,4,3,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,8,5,6,4,3,1,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[1,8,6,5,4,3,2,7] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[6,1,5,2,8,4,7,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,6,1,8,5,7,2,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,7,1,2,8,5,6,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,4,7,2,8,5,6,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,7,3,5,8,6,2,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,3,5,8,6,1,2,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,6,8,1,5,7,2,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[3,4,6,5,8,1,7,2] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[6,8,1,5,7,2,3,4] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[7,1,2,5,8,6,3,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[1,7,2,5,8,6,3,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,7,6,8,2,3,5,4] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[7,6,8,1,2,3,5,4] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[2,7,1,5,8,6,3,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[2,4,7,1,8,5,6,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[4,7,5,8,3,1,6,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,7,2,1,8,5,6,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[7,6,8,2,1,3,5,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[1,2,7,6,8,3,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,7,6,8,2,1,5,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[7,4,2,1,6,8,5,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,7,4,1,8,5,3,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,7,4,3,1,8,5,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,7,4,1,6,8,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,3,7,6,8,1,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[7,4,2,6,8,5,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,3,2,5,8,6,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[3,1,7,6,8,2,5,4] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[3,7,6,8,1,2,5,4] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[1,3,7,6,8,2,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,7,4,2,6,8,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,4,1,2,6,8,5,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,1,4,2,8,5,6,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[7,1,8,2,5,4,6,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,3,8,4,6,1,5,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,2,8,1,6,4,5,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,1,6,8,5,4,2,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,1,2,6,8,5,4,3] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[1,7,2,6,8,5,4,3] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[1,7,6,8,3,2,5,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[7,6,8,3,1,2,5,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,1,5,8,6,3,2,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[7,2,5,8,6,3,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,6,7,1,8,5,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[7,2,6,8,5,4,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,6,8,2,3,1,5,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[2,7,6,8,3,1,5,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[2,7,1,6,8,5,4,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,7,3,1,8,5,4,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,7,1,8,5,4,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[7,2,1,6,8,5,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,6,8,3,2,1,5,4] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[4,7,8,5,6,1,3,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[4,6,5,8,7,1,3,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,6,4,8,1,2,7,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[8,1,5,6,7,2,4,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,4,5,1,8,2,7,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[5,4,6,7,1,2,8,3] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[4,3,6,7,2,1,5,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[5,3,6,7,1,4,2,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[8,1,4,6,7,3,2,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[8,1,3,6,7,4,5,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,2,1,6,8,4,5,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,2,6,7,1,4,8,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,2,6,7,3,1,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,2,4,1,5,8,7,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,2,1,5,4,8,6,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,1,4,5,3,7,2,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,3,1,5,4,8,2,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,3,4,1,5,8,2,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,3,4,2,1,8,6,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,3,5,2,7,1,6,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[5,6,3,8,1,4,2,7] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[8,1,7,2,4,5,6,3] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[7,6,1,2,4,5,8,3] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[4,7,8,2,3,1,6,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[5,6,2,8,1,4,7,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,5,2,1,3,7,8,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,5,1,3,2,6,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,1,6,3,2,5,7,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,4,1,3,5,2,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,4,2,3,1,6,8,7] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,3,1,4,5,6,2,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[8,1,4,3,5,6,2,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[6,2,3,1,5,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[7,8,4,2,1,6,5,3] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[7,8,4,2,1,5,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,2,3,4,8,7,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[6,2,3,4,7,8,1,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,8,3,4,6,2,1,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,3,6,4,2,1,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,8,3,5,6,2,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,2,3,8,7,5,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,2,3,7,8,5,1,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,2,6,3,8,1,7,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,3,2,5,8,7,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,3,2,8,4,7,1,5] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,4,3,8,7,5,1,2] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[6,4,3,7,8,5,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,2,4,1,7,3,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,3,2,7,4,8,1,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,3,2,5,7,8,1,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[5,7,2,3,6,1,8,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,8,2,3,6,1,7,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[4,7,5,8,3,2,1,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,5,6,8,3,2,1,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,6,8,5,3,2,1,7] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[5,6,1,4,2,3,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[5,6,8,4,3,7,1,2] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,6,1,4,2,3,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,2,8,3,4,1,7,6] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,5,8,6,3,2,1,7] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[4,6,5,8,3,2,1,7] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,7,5,6,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[6,2,3,4,5,8,1,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,1,4,3,6,2,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,1,4,3,7,2,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,1,4,3,8,2,7,6] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[5,6,2,4,1,7,8,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,6,2,4,1,8,7,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,7,2,4,1,8,6,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[6,1,4,2,8,7,5,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,1,4,2,7,8,5,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,8,2,4,1,7,6,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,2,7,4,1,6,8,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[5,4,1,3,7,2,6,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,1,4,3,6,2,7,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[5,8,6,4,3,7,1,2] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[5,8,1,4,2,3,7,6] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,1,6,3,4,2,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,8,6,5,3,2,1,7] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[4,8,5,6,3,2,1,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[5,4,7,8,3,2,1,6] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,4,8,7,3,2,1,6] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[4,6,8,7,3,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[4,6,7,8,3,2,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,7,6,8,3,2,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,7,8,5,3,2,1,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[5,7,1,3,4,2,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[5,1,8,4,2,3,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,1,7,4,2,3,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,8,1,3,4,2,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,8,7,5,3,2,1,6] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[4,7,8,6,3,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[4,8,7,6,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[4,8,2,6,3,7,5,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,3,8,1,6,2,5,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,3,8,7,2,5,1,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,8,4,3,7,1,6,2] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[6,8,1,2,4,3,5,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[5,8,7,1,3,4,2,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,8,7,6,3,1,2,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,3,8,2,7,5,6,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[1,4,3,8,2,6,5,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[4,3,2,8,1,6,5,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,1,3,8,2,6,5,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,1,8,3,7,5,6,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,7,8,1,5,4,2,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[7,3,8,1,5,4,6,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[3,4,8,1,6,2,5,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,4,2,1,8,6,5,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[3,6,7,8,4,1,2,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,1,7,8,5,3,2,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,7,6,8,4,2,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[3,7,8,2,6,4,5,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,2,3,8,1,6,5,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,3,1,8,2,6,5,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[2,6,8,4,7,3,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[7,3,6,8,4,2,1,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,6,2,8,3,5,4,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[3,2,4,8,1,6,5,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[2,4,8,3,6,1,5,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,4,1,8,5,2,6,3] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[1,3,2,4,8,6,5,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[3,1,2,4,8,6,5,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[3,1,4,8,2,6,5,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[3,7,4,8,5,1,2,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[6,7,2,8,3,5,4,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[2,1,3,4,8,6,5,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[1,2,3,4,8,6,5,7] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[4,8,3,6,2,1,5,7] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[3,5,8,2,6,1,4,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,6,5,8,2,4,1,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,3,8,7,2,4,6,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,8,4,5,7,3,6,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,4,5,7,3,8,1,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,2,4,5,8,3,1,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,8,1,2,5,6,3,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,1,3,5,2,6,4,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[5,2,1,6,3,8,4,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,2,5,1,8,4,3,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[3,6,1,5,8,4,2,7] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[6,1,4,5,8,3,2,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,6,4,8,1,3,2,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,5,4,3,8,2,1,7] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[5,4,3,7,2,8,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,8,4,3,7,2,6,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[4,6,8,3,7,2,5,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[7,4,6,3,2,8,1,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[1,4,3,6,2,7,8,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,5,4,3,7,2,8,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,7,8,5,3,1,2,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,7,3,4,1,2,8,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[8,5,4,7,6,2,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,5,7,4,3,6,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[4,3,8,1,6,7,5,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,7,8,3,6,1,5,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[5,3,8,6,7,4,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,3,8,6,4,7,5,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[8,6,2,7,4,1,5,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,6,2,1,4,3,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,6,1,3,4,2,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[1,5,7,3,2,6,8,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,6,7,3,2,5,8,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,2,6,8,5,7,4,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,8,2,3,6,7,4,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,5,2,3,1,6,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[1,6,4,7,2,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,1,7,5,2,8,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,5,7,4,1,8,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,2,6,1,7,8,3,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[4,2,7,6,3,8,1,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[6,4,8,7,2,3,5,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,2,6,8,7,4,5,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,2,7,4,1,6,8,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,3,2,1,7,8,4,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[3,7,1,8,4,2,5,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,2,1,3,7,5,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,1,3,7,4,2,6,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,4,3,7,6,2,1,5] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,3,5,2,7,6,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,6,2,8,7,1,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[7,3,2,8,1,6,5,4] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[3,8,7,2,6,5,4,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[4,2,7,8,6,1,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,8,2,4,7,1,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[5,2,1,8,7,3,6,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,2,1,6,3,7,5,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[6,8,3,1,7,5,2,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,8,1,6,7,2,4,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,2,8,1,5,7,4,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,7,8,2,6,1,4,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[8,7,2,5,6,4,3,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[8,6,7,5,2,4,3,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[7,2,6,8,1,5,4,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[1,2,7,8,5,6,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[7,4,8,1,6,2,5,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[3,7,1,8,2,6,5,4] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[2,1,7,3,8,6,5,4] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[8,2,1,7,6,5,4,3] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[8,1,4,7,6,5,3,2] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[8,6,7,5,1,4,3,2] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[7,8,6,5,4,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[5,8,4,3,2,1,6,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,4,7,3,2,1,8,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[5,4,7,3,2,1,6,8] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,5,3,7,2,1,4,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,8,3,6,2,1,4,7] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[6,3,7,8,2,1,4,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,3,7,6,2,1,4,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,8,7,6,2,1,4,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[5,8,4,2,6,1,3,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,8,7,2,5,1,3,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,8,3,2,6,1,4,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,8,3,2,5,1,7,6] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,3,7,2,5,1,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[3,8,7,2,5,1,4,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,4,2,7,5,1,3,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,3,2,7,5,1,4,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,3,2,6,7,1,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,8,2,6,5,1,4,7] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[6,2,7,8,5,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[5,2,7,6,8,1,3,4] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,2,7,6,5,1,3,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,8,7,6,5,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,5,4,3,1,7,8,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,4,7,3,1,5,8,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,4,7,3,1,8,6,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[6,4,3,7,1,5,8,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[5,4,3,6,1,8,7,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,3,7,8,1,4,5,2] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[5,3,7,6,1,4,8,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[4,3,7,6,1,5,8,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,8,7,6,1,4,5,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[6,5,4,2,1,7,3,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[6,4,7,2,1,5,3,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[4,8,7,2,1,5,3,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,8,3,2,1,4,7,6] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[4,8,3,2,1,5,7,6] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,3,7,2,1,4,8,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[3,8,7,2,1,4,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,5,2,7,1,4,3,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[5,8,2,6,1,4,3,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,4,2,7,1,5,3,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[5,4,2,6,1,8,3,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[4,3,2,6,1,5,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,2,7,8,1,4,3,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,2,7,6,1,5,3,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,2,7,6,1,4,5,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[6,5,4,1,8,7,3,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[5,8,4,1,6,7,3,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,4,7,1,5,8,3,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,4,7,1,6,8,3,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,8,7,1,5,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[5,4,3,1,6,8,7,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[4,8,3,1,5,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,8,7,1,5,4,6,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[5,8,2,1,6,4,3,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,3,2,1,5,4,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[5,3,2,1,6,4,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[3,8,2,1,5,4,6,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[6,2,7,1,5,4,3,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,2,7,1,6,4,3,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,2,7,1,5,6,3,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[3,2,7,1,5,4,6,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[2,8,7,1,5,4,3,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,5,1,7,8,4,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[5,8,1,6,7,4,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,4,1,7,5,8,3,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,4,1,6,7,8,3,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,8,1,6,5,7,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,3,1,7,5,4,8,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[5,3,1,6,7,4,8,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,3,1,6,5,7,8,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,8,1,6,5,4,7,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[5,2,1,6,7,4,3,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,2,1,6,5,7,3,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[2,8,1,6,5,4,3,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[6,1,7,8,5,4,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,1,7,6,5,8,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,1,7,6,5,4,8,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,5,8,1,2,6,3,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[1,4,5,7,2,6,3,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,7,3,5,6,2,4,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,1,3,5,7,2,4,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[3,6,8,1,7,2,4,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,4,5,6,8,1,7,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,5,8,2,6,7,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[8,2,3,5,6,7,1,4] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[1,7,2,3,5,4,6,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[8,1,2,3,5,4,6,7] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[2,7,8,1,3,5,4,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,7,8,3,5,6,1,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[2,4,5,7,8,1,6,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,5,8,1,7,6,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,5,8,7,2,1,6,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[8,7,3,5,6,2,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,7,2,1,3,5,4,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,6,8,7,2,1,5,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[8,6,4,1,7,5,3,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[7,6,4,3,1,8,5,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[2,3,6,7,8,1,5,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,6,8,1,2,5,4,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[1,3,6,7,2,5,4,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[7,4,1,8,5,2,3,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[7,1,4,2,8,3,6,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[7,1,8,2,5,3,6,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,1,7,5,4,2,3,6] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[1,7,2,6,5,4,3,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[1,7,6,3,2,5,4,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[8,6,3,1,2,5,4,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,1,7,6,3,2,4,5] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[8,2,5,7,6,3,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,6,8,1,7,5,4,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[8,2,6,7,5,4,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[2,7,8,6,3,1,5,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,7,8,1,6,5,4,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[7,3,1,8,6,5,4,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[8,7,2,1,6,5,4,3] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,7,6,3,2,1,5,4] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[2,1,8,6,3,7,4,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[8,6,1,5,2,7,4,3] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,5,1,7,4,2,6,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,1,7,5,4,3,8,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,1,7,8,3,6,5,4] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[2,1,4,8,5,7,3,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,5,3,1,6,2,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,4,1,5,2,3,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[8,3,7,5,2,6,1,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,3,7,4,6,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,8,3,7,6,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[4,2,6,3,8,5,1,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,8,2,1,7,6,4,3] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[8,3,2,4,1,7,5,6] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,2,8,1,4,6,5,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,8,1,4,5,3,2,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,2,6,1,4,7,3,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[8,3,5,6,1,7,4,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[6,3,5,4,1,2,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[8,7,3,6,5,1,4,2] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[2,7,4,3,6,1,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,4,7,2,8,1,5,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,2,3,5,8,1,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,8,4,7,1,6,5,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,2,4,6,1,5,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,3,4,5,7,6,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[3,2,4,5,6,8,1,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,6,8,1,4,2,7,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[1,5,7,8,4,6,2,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[1,3,5,7,8,6,2,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,5,7,8,6,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,5,1,6,8,2,7,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[3,1,5,6,8,2,7,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,3,5,6,8,1,7,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,6,4,8,2,1,7,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[5,1,6,3,8,4,7,2] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,5,1,6,8,3,7,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,1,2,6,8,3,7,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,7,1,8,6,2,3,4] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[1,5,2,7,8,6,3,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,6,7,5,2,8,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[6,1,7,5,2,8,3,4] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,6,7,5,1,8,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,7,2,8,6,1,3,4] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,5,7,8,6,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,1,7,8,6,3,4,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[5,1,3,7,8,6,4,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,2,7,8,4,6,1,3] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[3,2,5,7,8,6,1,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[6,2,7,5,1,8,3,4] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,2,6,7,5,8,3,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,2,7,5,4,1,8,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,7,5,2,4,1,8,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,7,2,5,3,8,1,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,7,4,5,2,1,8,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,1,7,8,6,4,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[2,5,7,8,6,3,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,1,7,8,6,3,2,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,3,7,5,1,8,2,4] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,6,7,5,3,8,2,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,6,7,5,4,2,8,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,7,5,1,4,2,8,3] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[5,7,8,6,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,1,7,2,6,5,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,4,7,1,5,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[6,7,4,1,5,2,8,3] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[1,6,7,4,5,2,8,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,6,3,7,5,8,2,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[6,3,1,7,5,8,2,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[2,5,3,7,8,6,1,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[6,7,5,4,2,1,8,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[6,3,2,7,5,8,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,7,4,2,5,1,8,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,2,7,4,5,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,2,3,7,5,8,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[7,5,1,6,3,8,2,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[2,7,6,1,3,8,5,4] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,3,5,1,8,2,6,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[7,3,5,1,8,2,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[3,7,5,1,8,6,2,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[2,6,7,4,1,8,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,1,6,7,3,8,5,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,6,5,1,8,4,7,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[3,6,5,1,8,4,2,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[3,7,5,4,8,1,6,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,6,1,5,8,7,3,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[7,5,1,6,2,8,4,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,3,4,7,8,1,6,5] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[6,8,5,4,3,2,7,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[7,9,6,5,4,3,2,8,1] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => 01111101
[8,9,6,5,4,3,2,1,7] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[6,8,5,4,3,7,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[5,8,4,3,2,1,7,6] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[6,5,4,3,1,8,7,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,7,6,5,4,3,9,1,2] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[8,7,5,4,3,1,6,2] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[9,7,6,5,4,3,1,8,2] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[8,3,4,6,2,1,5,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,5,6,2,1,8,4,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[3,5,2,6,8,4,1,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[7,5,3,2,8,4,1,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[7,5,3,2,8,4,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[2,4,5,7,3,8,6,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,2,5,6,8,3,1,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,2,8,1,5,6,3,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[2,5,6,1,8,4,3,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,3,6,8,1,4,2,7] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,5,6,8,1,3,2,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,4,5,6,8,3,2,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[4,5,6,3,8,2,1,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[4,5,3,7,2,8,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,4,7,3,2,8,5,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,1,4,7,3,2,8,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[1,7,8,4,5,3,2,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,1,7,3,8,4,2,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,5,1,7,4,3,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,5,7,4,1,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[5,3,7,1,4,8,6,2] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,4,3,1,7,8,5,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,4,1,7,3,8,5,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[5,6,3,7,8,4,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[5,1,6,3,7,8,4,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,6,1,3,7,8,4,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,6,1,7,8,3,4,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,6,3,7,4,8,5,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[6,7,2,4,1,8,5,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[6,7,2,1,4,3,8,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,4,7,3,1,2,8,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[5,6,3,1,2,7,8,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,6,1,3,2,7,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,6,3,2,1,7,8,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,5,6,3,7,8,4,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,5,6,3,1,7,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,6,4,7,3,1,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,3,7,2,8,4,5,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[6,3,7,2,8,4,1,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[6,3,2,7,1,8,4,5] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[7,5,3,2,1,8,4,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,3,8,4,2,1,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,7,2,1,3,8,6,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[1,3,7,8,6,4,2,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[7,3,8,4,6,2,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,7,3,8,2,1,6,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[6,3,7,8,5,2,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,6,2,7,8,5,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,6,2,1,7,8,5,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[7,4,5,8,1,2,6,3] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[2,5,1,7,3,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[6,7,2,1,3,8,5,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,1,6,7,8,2,4,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[6,3,7,1,8,5,2,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,2,1,7,3,8,5,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[6,2,7,1,8,5,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,3,1,7,8,5,4,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,1,3,6,8,2,5,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,2,3,6,8,1,5,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[5,3,2,1,8,4,7,6] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[3,6,5,8,2,1,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,5,2,1,3,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,2,6,4,5,8,1,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,4,6,5,8,1,3,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,6,2,4,5,8,3,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[5,3,2,1,6,8,4,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[6,2,4,5,8,1,3,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,3,4,6,5,8,2,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,6,3,4,5,8,2,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,4,1,8,5,2,7,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,8,4,1,7,6,3,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[8,1,4,2,7,3,6,5] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,5,3,2,8,7,4,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[8,2,1,7,5,3,4,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[1,7,6,4,5,8,3,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[5,8,7,4,1,2,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,8,7,4,6,2,1,3] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[3,4,2,5,8,6,7,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[4,1,3,5,6,8,7,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[2,4,8,6,7,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,3,6,2,8,1,7,5] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[3,7,4,8,2,1,6,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[2,3,5,8,6,7,1,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,2,5,6,8,7,1,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[2,1,8,5,6,7,3,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,2,8,3,5,6,7,4] => [[1,2,3,5,6,7],[4],[8]] => 0010001
[4,2,3,7,1,8,6,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,2,6,4,8,1,7,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[8,2,1,6,7,3,4,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[2,7,8,5,4,1,3,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[1,7,5,3,8,4,2,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[4,7,5,3,1,2,8,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,2,4,8,5,3,1,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[4,8,3,1,2,7,6,5] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[3,5,2,7,4,1,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[8,4,2,3,7,1,5,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[2,8,4,7,1,3,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[8,2,4,6,7,1,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,8,2,3,6,7,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,5,2,7,6,1,8,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,6,3,2,5,8,7,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[5,8,3,2,1,6,7,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,8,7,3,4,6,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[5,8,2,7,4,1,6,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,1,4,2,8,7,6,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,7,6,5,8,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,3,7,1,6,2,8,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,2,6,8,7,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,3,2,1,8,5,7,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[2,7,5,4,1,8,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,2,5,6,8,7,1,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[1,8,4,2,5,6,7,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[3,8,4,1,5,6,7,2] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,2,8,5,6,7,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,2,4,7,1,8,6,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[5,3,4,7,1,8,6,2] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[8,6,4,1,3,2,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,1,3,6,5,2,4,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,4,3,6,5,2,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,6,5,2,1,8,7,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[8,3,2,4,6,5,1,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,4,2,1,6,5,3,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,4,1,2,6,5,3,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,6,4,2,1,5,3,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,3,6,4,1,5,2,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,2,6,3,4,5,1,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[1,3,4,8,5,7,2,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[5,8,4,7,6,2,3,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[1,3,4,7,5,8,2,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,3,5,2,4,8,7,6] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,6,5,1,3,8,7,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[4,7,1,6,5,8,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[5,4,8,7,6,3,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[2,8,5,1,4,7,6,3] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[4,3,1,5,8,6,7,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,1,3,5,8,6,7,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,5,3,8,4,7,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,4,2,1,6,8,7,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,8,4,3,2,7,1,5] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[3,4,7,8,2,1,6,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,1,3,2,8,6,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,3,1,2,8,6,7,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[5,2,3,1,6,8,7,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,3,2,1,8,6,7,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,2,1,3,6,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[2,4,7,3,8,1,6,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[6,3,8,2,7,4,1,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,2,1,3,6,4,7,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[3,5,1,7,8,4,2,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,7,4,5,8,3,1,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,8,4,3,7,2,6,5] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,4,8,7,2,1,6,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,4,7,8,3,6,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[6,4,3,8,7,2,1,5] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[6,3,8,7,4,1,2,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,5,7,2,4,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[8,4,7,2,3,1,5,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,4,7,1,3,2,5,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,4,7,2,1,3,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,6,4,2,1,3,7,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,6,4,1,3,2,7,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,6,4,2,3,1,7,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[3,5,7,2,6,1,8,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[6,1,3,8,5,7,2,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,8,3,2,6,7,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,8,5,3,6,2,7,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[2,8,1,5,4,7,6,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[1,5,8,7,4,6,2,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[2,1,7,6,4,5,8,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[1,7,2,4,6,5,8,3] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[3,5,1,7,6,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,8,2,6,1,3,7,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,3,5,8,7,2,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[2,5,7,8,4,1,6,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,2,8,1,5,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,1,5,2,6,8,7,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[3,4,5,1,6,8,7,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,2,8,5,1,6,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,1,8,5,2,6,7,3] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,7,1,8,5,4,6,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[5,8,6,2,1,3,7,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[8,2,4,1,5,6,7,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,6,3,5,8,1,7,2] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[1,7,8,3,5,4,6,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,4,5,1,8,6,7,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,8,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,4,5,7,8,2,6,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,4,6,2,8,5,1,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,4,6,8,1,5,2,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,4,7,2,1,8,6,5] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[3,4,8,2,1,5,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[3,5,2,7,8,4,6,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[3,5,6,2,8,4,1,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,6,8,4,1,2,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,5,7,2,4,8,6,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,5,7,2,8,4,6,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,5,7,8,4,1,6,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,6,2,1,8,5,4,7] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,6,7,2,8,5,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,6,8,2,4,5,1,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,7,2,1,4,8,6,5] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,7,2,8,4,5,6,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,8,2,1,4,5,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,1,5,6,7,8,3,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,1,5,7,3,8,6,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,1,6,3,7,8,5,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,1,6,3,8,5,2,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[4,1,6,7,3,8,5,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,1,6,8,3,5,2,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,1,7,3,2,8,6,5] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,1,8,3,2,5,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,5,2,6,8,1,3,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,5,7,3,8,1,6,2] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,5,8,3,2,1,6,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,6,2,7,8,5,1,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[4,6,7,3,2,8,5,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,7,2,8,3,5,6,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[4,7,8,3,2,5,6,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[4,8,2,3,1,5,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[5,1,2,6,8,4,3,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,1,6,3,8,4,2,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,1,6,7,4,8,2,3] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[5,6,2,3,8,4,1,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[5,6,2,7,8,4,1,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[5,6,8,3,4,2,1,7] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[5,7,2,3,4,8,6,1] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,7,8,3,4,2,6,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,8,2,3,4,1,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[6,1,2,3,7,8,5,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[6,1,2,3,8,5,4,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[6,1,2,7,8,5,4,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,1,7,3,8,5,4,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[6,1,7,8,4,5,3,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,1,8,3,4,5,2,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,7,2,3,8,5,4,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,7,2,8,4,5,3,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[7,1,2,3,4,8,6,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[7,1,2,8,4,5,6,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[7,1,8,3,4,5,6,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[6,4,1,8,2,3,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,8,1,2,4,3,7,6] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[1,3,5,7,2,6,4,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[3,5,8,6,1,2,4,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,1,6,8,2,4,7,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[3,6,2,8,1,5,7,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[2,6,1,3,8,4,7,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,7,5,2,3,4,6,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[2,7,5,1,3,8,4,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[8,2,5,7,4,6,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,2,1,3,7,6,4,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,2,5,1,3,7,4,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,2,7,5,3,1,6,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,2,6,5,4,7,1,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,6,5,2,4,8,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,8,2,5,3,1,6,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,1,8,6,3,2,4,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,8,1,5,3,2,4,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[1,6,7,5,3,2,4,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[6,5,1,2,4,8,3,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,8,1,6,4,2,3,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[8,4,1,2,5,6,3,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,7,3,6,5,2,4,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,1,3,7,2,6,4,5] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[7,3,2,6,5,1,8,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,8,4,2,5,6,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,2,7,4,5,6,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[8,2,3,6,5,1,7,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[6,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[5,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[4,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[3,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[2,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[8,10,9,7,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[6,9,7,8,5,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[7,10,9,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[4,8,6,5,7,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[6,10,9,8,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[3,8,7,5,4,6,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[4,8,5,6,7,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[5,10,9,8,7,6,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[2,8,7,6,4,3,5,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[3,8,7,4,5,6,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[4,10,9,8,7,6,5,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[1,8,7,6,5,3,2,4] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[2,8,7,6,3,4,5,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[3,10,9,8,7,6,5,4,2,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[1,8,7,6,5,2,3,4] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,9,8,7,6,5,4,2,3] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[2,10,9,8,7,6,5,4,3,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[7,2,8,6,5,4,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[7,2,8,5,4,6,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,3,2,8,5,1,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[6,8,5,4,3,1,7,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,8,6,4,1,3,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,6,1,8,5,2,7,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[3,4,1,2,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,8,3,5,4,1,7,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,2,5,8,3,6,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,6,3,8,5,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[7,2,6,4,8,3,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[4,2,3,1,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,2,8,4,1,7,6,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,8,3,4,5,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[1,6,3,2,5,8,4,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[8,3,2,1,5,4,7,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[6,3,7,1,5,8,4,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[2,5,1,8,4,3,7,6] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[6,2,5,4,8,1,3,7] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,3,1,6,5,8,2,7] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[1,3,5,4,6,8,2,7] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[6,1,3,4,5,8,2,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[8,3,4,1,5,2,7,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,5,4,2,6,8,3,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,2,6,4,1,7,3,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,3,8,4,5,2,1,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,2,5,1,8,4,3,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[1,7,3,2,5,4,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[8,7,2,1,5,3,4,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[3,6,1,5,8,7,4,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,3,6,4,5,1,7,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,4,6,8,1,2,7,3] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[6,4,7,2,3,5,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,8,4,1,3,5,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,4,7,8,6,2,5,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,1,3,5,7,8,6,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[6,5,1,8,4,7,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[5,3,1,8,4,7,6,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[8,2,7,4,6,1,3,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,7,3,2,8,1,6,5] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,3,1,4,7,2,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,7,3,6,1,5,2,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,4,3,6,8,2,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[2,4,7,3,8,5,6,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,8,6,1,5,7,3,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,8,2,5,4,3,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[1,8,3,4,2,7,6,5] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[8,5,3,7,4,2,6,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[5,7,3,2,4,1,8,6] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[2,8,3,4,7,1,5,6] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[4,1,3,6,7,8,2,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[1,7,6,3,2,5,8,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,8,1,5,6,2,7,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[8,2,5,6,1,7,4,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,1,5,2,8,6,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,5,4,8,7,2,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[1,8,6,4,5,2,7,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,8,5,3,6,2,7,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,6,2,1,7,5,8,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[2,5,4,1,8,7,6,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,7,2,6,5,8,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,1,4,2,7,3,5] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,3,4,7,1,8,2,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,4,7,8,2,5,6,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,8,2,4,5,6,7,3] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[5,2,4,1,6,8,7,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,2,5,7,6,1,8,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,3,5,6,1,8,7,2] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[5,3,4,1,7,6,8,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,1,4,6,5,7,8,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,4,7,3,5,6,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,3,2,7,5,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,4,2,5,8,3,7,6] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[4,1,2,6,8,5,3,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,5,2,4,8,7,6,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,2,6,4,8,7,5,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,2,7,4,8,6,5,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,3,2,7,5,8,4,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,3,2,8,5,7,4,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,5,2,4,8,7,3,6] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,2,6,4,8,7,3,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,2,7,8,5,6,3,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[1,3,8,2,6,7,4,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,6,7,8,2,5,3,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,5,7,8,2,3,6,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,5,2,7,8,4,6,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,3,6,2,4,8,7,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,6,7,3,4,8,5,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,5,3,7,4,8,6,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,8,4,1,5,3,7,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,3,8,4,2,7,6,5] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,7,4,8,3,6,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,2,6,4,8,3,7,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,5,2,4,8,3,7,6] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,8,3,5,2,7,4,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,3,8,6,2,7,4,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,2,6,8,5,3,7,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,2,7,8,6,3,5,4] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,6,7,8,5,2,3,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,5,7,8,6,2,3,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,4,7,6,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,3,8,7,4,1,6,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,2,6,8,7,5,3,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,2,7,8,6,5,3,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,2,6,7,3,4,8,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,2,4,7,6,3,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[5,6,2,1,7,8,3,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,6,2,1,4,8,7,3] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[2,6,1,4,5,8,7,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,4,2,7,6,3,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[2,3,7,6,4,5,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,6,1,7,5,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,6,1,7,4,8,5,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[5,1,2,7,8,4,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[2,6,1,7,4,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,6,4,1,7,8,2,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,4,6,1,3,8,7,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[3,6,4,1,5,8,7,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,6,1,5,4,8,7,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[2,6,1,4,7,8,5,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,1,2,4,8,6,7,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,1,2,4,8,7,3,6] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,1,2,4,8,7,6,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[1,2,3,8,5,4,7,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[4,3,1,2,8,5,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[2,1,5,3,8,6,4,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[1,2,3,8,5,6,4,7] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[1,2,3,8,6,4,5,7] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,2,3,8,6,5,4,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,2,3,8,5,4,6,7] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[2,6,1,5,4,8,3,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,1,2,4,8,6,3,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,1,2,4,8,3,7,6] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,6,3,1,4,8,2,7] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[2,5,4,3,1,8,6,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[5,4,6,3,1,8,7,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[3,6,4,5,1,8,7,2] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,6,5,4,1,8,7,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[5,2,6,1,7,8,4,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,1,6,2,8,7,3,4] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,1,3,7,8,6,4,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[2,1,3,7,8,5,6,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,2,4,1,7,8,6,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[4,3,1,2,8,6,7,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[5,1,4,2,8,6,7,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[2,1,3,6,8,5,7,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[1,2,3,8,6,7,4,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,2,3,8,7,5,4,6] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,2,3,8,7,4,5,6] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,2,3,8,5,7,4,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,1,3,6,8,7,4,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,4,1,2,8,7,6,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,1,6,2,8,7,5,4] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,2,3,4,5,6,7,10,8,9] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[1,2,3,4,5,9,7,6,8] => [[1,2,3,4,5,6,9],[7],[8]] => 00000110
[1,2,3,4,5,6,10,7,8,9] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[1,2,3,4,5,10,6,7,8,9] => [[1,2,3,4,5,6,8,9,10],[7]] => 000001000
[1,2,3,4,10,5,6,7,8,9] => [[1,2,3,4,5,7,8,9,10],[6]] => 000010000
[1,8,3,4,2,5,6,7] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,2,3,10,4,5,6,7,8,9] => [[1,2,3,4,6,7,8,9,10],[5]] => 000100000
[1,8,4,3,2,5,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,9,3,2,4,5,6,7,8] => [[1,2,5,6,7,8,9],[3],[4]] => 01100000
[1,2,10,3,4,5,6,7,8,9] => [[1,2,3,5,6,7,8,9,10],[4]] => 001000000
[8,4,7,6,5,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => 1011111
[8,4,7,5,6,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,5,7,4,6,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,7,6,3,5,4,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[8,6,7,3,5,4,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,5,7,3,6,4,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,1,7,4,6,5,3,2] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,1,7,3,6,5,4,2] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,2,7,3,6,5,4,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,3,7,2,6,5,4,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,5,7,2,6,4,3,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,6,7,2,5,4,3,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,7,6,2,5,4,3,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => 1110111
[8,4,7,1,6,5,3,2] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,3,7,1,6,5,4,2] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,2,7,1,6,5,4,3] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[8,1,7,2,6,5,4,3] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,7,6,2,5,3,4,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,1,7,6,5,3,4,2] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,3,7,6,5,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,4,7,6,5,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,5,7,6,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,6,7,5,4,1,3,2] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,5,7,6,4,1,3,2] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,3,7,6,5,1,4,2] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[8,7,6,4,5,1,3,2] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,7,6,2,5,1,4,3] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,7,6,1,5,2,4,3] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[6,8,1,3,2,5,4,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,8,1,4,2,5,3,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,3,6,1,4,2,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,2,5,3,6,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,8,2,5,1,4,3,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,8,1,4,3,6,2,5] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,1,4,3,7,2,6] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,2,5,1,4,3,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,2,5,3,7,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,8,2,5,4,7,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[2,5,4,7,6,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,5,3,7,6,8,1,4] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,5,1,4,3,7,6,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,6,1,4,3,7,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,6,5,8,1,4,3,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[2,6,1,5,3,7,4,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,6,3,7,4,8,1,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,6,4,7,5,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[5,8,3,6,4,7,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,8,2,6,4,7,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,8,2,6,3,7,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,8,1,5,3,7,2,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,8,1,5,2,6,3,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,8,3,7,1,5,2,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,3,7,1,4,2,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,8,1,3,2,6,4,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,8,4,7,1,3,2,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,4,7,1,3,2,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,8,5,7,1,3,2,4] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,7,6,8,2,4,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,7,6,8,1,3,2,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,7,5,8,1,3,2,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,7,1,3,2,6,5,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[3,7,1,4,2,6,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,7,5,8,1,4,2,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,7,6,8,1,4,2,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,7,6,8,2,5,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,7,6,8,2,5,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,7,5,8,3,6,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,7,5,8,2,6,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,7,5,8,2,6,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,7,4,8,2,6,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[3,7,4,8,1,5,2,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,7,1,5,2,6,4,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,7,2,6,1,5,4,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[3,7,2,6,5,8,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[4,7,3,6,5,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[3,6,5,8,4,7,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,6,5,8,4,7,1,3] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,6,5,8,3,7,1,4] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[2,6,3,7,1,5,4,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[7,6,4,2,8,5,3,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[7,6,4,3,8,2,5,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[7,6,4,8,5,2,3,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,8,4,3,7,2,1,5] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[6,7,4,3,5,1,8,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,7,3,5,4,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,8,3,7,5,2,4,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[7,6,8,3,5,2,4,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,6,3,5,8,2,4,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[7,6,3,5,2,4,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,6,4,2,5,1,8,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,6,2,8,4,1,5,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,6,3,8,2,4,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,6,3,4,8,2,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,8,3,7,4,5,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,7,3,5,8,4,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[5,7,8,3,6,2,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,8,3,6,7,2,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,3,4,8,7,2,5,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,3,8,4,7,2,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,2,8,4,1,7,5,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,2,7,4,1,5,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,3,4,7,5,8,2,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,3,5,7,8,4,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[5,7,3,6,8,2,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[5,6,8,3,7,2,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,6,7,3,4,1,8,2] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,6,7,8,3,5,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,6,8,3,5,7,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[4,7,3,5,6,8,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,7,3,5,8,2,6,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[5,3,4,7,8,2,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,3,8,2,4,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,3,4,8,2,6,1,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[4,8,3,6,2,5,7,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,8,3,5,7,2,6,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,8,3,5,6,7,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,7,8,3,5,6,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[4,7,8,3,6,2,5,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[4,8,3,6,7,2,5,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,8,3,7,2,5,6,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,3,4,8,2,7,6,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,3,8,2,4,1,7,6] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,2,8,4,1,7,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[6,4,2,5,1,8,7,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,4,3,5,8,2,1,7] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[6,3,5,8,7,2,4,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,8,3,7,2,6,4,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,7,3,4,8,2,1,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[5,8,4,2,3,1,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,8,4,2,3,1,7,6] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,4,5,3,8,2,1,7] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,4,8,5,3,7,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,4,3,8,5,7,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[6,4,2,8,5,3,1,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,4,2,7,3,1,8,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[6,4,3,7,8,5,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[6,4,5,3,7,1,8,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,7,4,2,3,1,6,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,6,3,7,1,8,2,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[5,6,3,4,7,1,8,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,6,3,4,8,2,1,7] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[6,3,5,7,4,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[6,3,5,4,7,8,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[6,4,3,5,7,1,8,2] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[6,4,2,5,1,7,3,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,3,7,2,4,1,6,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,3,4,7,2,6,1,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[4,7,3,6,2,5,8,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,7,3,6,8,2,5,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,6,7,3,5,8,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,5,7,8,3,6,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,5,8,3,6,7,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,5,8,3,7,2,6,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[5,3,4,6,8,2,1,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,3,6,8,2,1,4,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,3,6,7,1,8,2,4] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[5,3,4,6,7,1,8,2] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[4,6,3,5,7,8,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,5,7,3,6,8,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,5,6,8,3,7,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,7,4,8,6,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,2,6,5,1,8,7,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[3,5,6,7,2,8,4,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[7,6,9,8,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[6,5,4,9,8,7,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111
[6,8,5,9,7,4,3,2,1] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[6,7,8,9,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[5,4,3,2,9,8,7,6,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => 11101111
[5,8,4,3,9,7,6,2,1] => [[1,2,5],[3,6],[4,7],[8],[9]] => 01101111
[5,4,7,6,9,8,3,2,1] => [[1,3,5],[2,4,6],[7],[8],[9]] => 10101111
[5,7,8,4,9,6,3,2,1] => [[1,2,3,5],[4,6],[7],[8],[9]] => 00101111
[5,6,7,8,9,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[4,8,3,2,1,9,7,6,5] => [[1,2,6],[3,7],[4,8],[5,9]] => 01110111
[4,3,7,6,2,9,8,5,1] => [[1,3,6],[2,4,7],[5,8],[9]] => 10110111
[4,7,8,3,2,9,6,5,1] => [[1,2,3,6],[4,7],[5,8],[9]] => 00110111
[4,6,3,8,5,9,7,2,1] => [[1,2,4,6],[3,5,7],[8],[9]] => 01010111
[4,6,7,8,3,9,5,2,1] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[4,5,6,7,8,9,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[3,2,1,6,5,4,9,8,7] => [[1,4,7],[2,5,8],[3,6,9]] => 11011011
[3,6,2,8,5,1,9,7,4] => [[1,2,4,7],[3,5,8],[6,9]] => 01011011
[3,6,7,8,2,1,9,5,4] => [[1,2,3,4,7],[5,8],[6,9]] => 00011011
[3,2,5,4,7,6,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[3,5,7,2,8,4,9,6,1] => [[1,2,3,5,7],[4,6,8],[9]] => 00101011
[3,5,6,7,8,2,9,4,1] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[3,4,5,6,7,8,9,2,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[2,4,6,7,1,8,3,9,5] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[2,4,5,6,7,8,1,9,3] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[8,7,10,9,6,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[8,9,10,7,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[7,6,5,10,9,8,4,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[7,9,6,10,8,5,4,3,2,1] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111
[7,8,9,10,6,5,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[6,5,4,3,10,9,8,7,2,1] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 111011111
[6,9,5,4,10,8,7,3,2,1] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => 011011111
[6,5,8,7,10,9,4,3,2,1] => [[1,3,5],[2,4,6],[7],[8],[9],[10]] => 101011111
[6,8,9,5,10,7,4,3,2,1] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => 001011111
[5,4,3,2,1,10,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[5,9,4,3,2,10,8,7,6,1] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111
[5,4,8,7,3,10,9,6,2,1] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => 101101111
[5,8,9,4,3,10,7,6,2,1] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => 001101111
[5,7,4,9,6,10,8,3,2,1] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[5,6,7,8,9,10,4,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[4,3,8,7,2,1,10,9,6,5] => [[1,3,7],[2,4,8],[5,9],[6,10]] => 101110111
[4,8,9,3,2,1,10,7,6,5] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 001110111
[4,3,2,7,6,5,10,9,8,1] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 110110111
[4,7,3,9,6,2,10,8,5,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,7,8,9,3,2,10,6,5,1] => [[1,2,3,4,7],[5,8],[6,9],[10]] => 000110111
[4,3,6,5,8,7,10,9,2,1] => [[1,3,5,7],[2,4,6,8],[9],[10]] => 101010111
[4,6,7,8,9,3,10,5,2,1] => [[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111
[4,5,6,7,8,9,10,3,2,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[3,6,2,1,9,5,4,10,8,7] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[3,2,6,5,8,7,1,10,9,4] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[3,6,8,2,9,5,1,10,7,4] => [[1,2,3,5,8],[4,6,9],[7,10]] => 001011011
[3,6,7,8,9,2,1,10,5,4] => [[1,2,3,4,5,8],[6,9],[7,10]] => 000011011
[3,5,7,8,2,9,4,10,6,1] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[3,5,6,7,8,9,2,10,4,1] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[3,4,5,6,7,8,9,10,2,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[2,4,6,1,8,3,9,5,10,7] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[2,4,6,7,8,1,9,3,10,5] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[2,4,5,6,7,8,9,1,10,3] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[1,6,2,5,3,4,8,7] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,3,8,2,4,6,5,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,7,2,3,6,4,8,5] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,6,8,2,5,3,7,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,8,2,5,3,4,7,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,8,2,3,6,4,7,5] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,3,5,2,8,4,7,6] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,2,7,3,5,4,6,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[1,8,2,7,3,4,6,5] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,5,8,2,3,7,4,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,6,8,2,3,5,4,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[5,3,6,1,2,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,1,5,8,4,2,3,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,5,7,4,2,3,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,1,4,5,8,2,3,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,4,1,6,2,8,3,5] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,4,1,7,2,6,3,5] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,1,4,7,5,2,3,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,5,4,7,2,3,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,1,7,5,8,3,4,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[7,1,5,4,8,2,3,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,1,4,8,5,2,3,6] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[6,4,1,7,2,3,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,8,3,1,2,4,6,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[8,7,1,6,4,2,3,5] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,6,1,7,4,2,3,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,6,1,8,4,2,3,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,8,1,2,4,6,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[8,3,7,1,2,4,6,5] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,3,6,1,2,4,7,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,3,7,5,1,2,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,3,6,1,2,4,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,7,1,8,4,2,3,5] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[6,8,1,7,4,2,3,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,1,8,5,4,2,3,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,1,8,4,5,2,3,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[2,1,7,8,5,3,4,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,6,3,1,2,4,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,1,2,3,8,7,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,8,1,4,2,3,7,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,8,3,1,2,7,4,5] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,7,3,1,2,8,4,5] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[6,7,1,4,2,3,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,3,6,8,5,7,1,2] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[6,1,2,5,4,8,3,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,2,1,5,8,3,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[1,3,6,8,7,4,2,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,2,8,5,7,3,4,6] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[2,6,1,5,8,3,4,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,7,1,6,8,4,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[4,8,1,2,5,7,3,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[8,4,6,2,5,7,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,3,6,4,7,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[3,8,1,4,7,2,5,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[1,7,8,4,6,2,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,7,4,8,5,1,6,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,7,1,6,5,4,8,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[2,7,3,1,5,8,4,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,7,4,6,8,1,3,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,7,5,8,6,4,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[8,2,6,7,5,4,3,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[3,8,7,1,6,4,5,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,6,8,2,7,4,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[1,5,2,8,7,4,6,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,4,2,7,8,1,6,5] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,1,3,7,5,6,8,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,3,8,1,7,4,2,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,5,8,7,1,4,2,3] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,1,7,3,8,5,2,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,6,1,4,5,8,2,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[1,6,7,4,5,3,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[6,1,7,3,5,4,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,3,1,2,5,8,4,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[1,4,7,2,8,5,3,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,6,8,7,2,4,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,8,5,7,1,2,4,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[2,8,4,1,7,5,6,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[8,2,4,3,7,5,6,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,8,2,1,5,7,3,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[7,2,8,4,1,6,3,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,2,4,8,6,5,3,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[7,1,5,6,8,4,3,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[2,7,8,1,4,6,3,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[4,8,2,5,7,1,6,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,1,6,8,5,3,7,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[5,2,6,4,8,3,1,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[6,7,1,3,4,5,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[1,7,3,2,4,8,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,3,6,5,2,8,4,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[7,1,6,5,3,4,8,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[6,3,4,2,8,7,5,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,3,8,7,5,2,6,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[6,8,7,4,2,3,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,6,4,5,2,8,7,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[8,6,1,3,5,4,2,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[5,3,8,6,1,2,4,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[2,5,6,3,4,8,7,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,5,3,6,8,7,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,8,7,3,5,2,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,8,7,2,6,4,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[6,3,5,4,8,7,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[4,3,8,6,1,5,2,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,7,6,2,5,3,8,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[7,5,2,6,8,1,4,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,5,2,7,1,4,3,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[1,8,5,3,6,2,4,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,1,7,2,4,3,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[1,5,3,4,8,6,2,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[5,4,1,3,8,6,2,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,1,8,6,3,4,2,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,5,2,8,3,7,6,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[8,2,3,7,6,4,5,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[5,8,2,4,7,6,3,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,8,2,5,3,4,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,2,5,6,4,8,1,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[1,6,7,4,8,2,3,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[7,1,3,5,8,2,6,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[8,2,1,3,5,6,7,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,3,1,4,7,5,8,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,1,3,8,2,6,7,5] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[2,8,3,6,7,5,4,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,1,7,2,8,5,4,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,6,1,4,7,2,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[1,5,8,4,7,2,3,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,1,3,6,2,8,4,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[6,2,7,4,5,8,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[2,1,8,4,5,7,3,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,8,5,7,3,2,4,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[2,1,8,5,4,3,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,7,4,1,5,3,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[7,4,8,6,2,3,1,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,7,1,4,6,3,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,7,5,6,8,1,3,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[7,1,3,2,8,5,4,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[2,8,5,4,1,3,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,1,7,4,2,3,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,8,6,5,1,4,2,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[1,3,4,8,6,5,2,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[4,1,8,6,5,3,2,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,8,5,2,7,3,6,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[7,2,8,5,3,6,4,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[5,2,8,4,3,7,6,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[8,4,7,5,2,3,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[7,5,2,8,4,6,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,7,4,3,6,2,8,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[6,7,5,1,2,8,3,4] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,2,6,8,3,4,7,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[7,6,2,4,5,8,3,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[3,6,8,4,7,2,5,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[7,6,3,8,4,2,5,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[2,6,3,8,4,7,5,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[7,2,3,6,5,8,4,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[6,2,7,5,8,3,1,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[2,8,3,6,4,5,7,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,1,5,6,8,3,7,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,8,1,2,6,4,7,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,6,8,3,2,7,4,5] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[6,5,7,2,8,4,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,5,1,2,8,4,6,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[5,4,8,3,6,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[5,8,2,7,4,3,6,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[6,4,5,8,2,7,3,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,7,3,6,4,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[1,5,6,4,8,2,7,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[3,1,5,6,4,8,7,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,5,1,6,4,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[3,6,1,4,2,7,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,2,6,4,3,8,5,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,6,3,5,8,7,4] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,3,5,1,8,4,7,6] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,3,6,1,8,5,4,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,1,7,5,4,8,6,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[1,2,7,6,4,8,5,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,2,7,3,6,8,5,4] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,3,6,1,8,5,7,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,2,5,8,4,7,3,6] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[1,3,6,8,5,2,7,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,2,6,8,5,4,3,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,3,5,8,2,4,7,6] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,4,6,8,3,2,5,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,3,7,5,6,8,2,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,2,6,7,3,8,5,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,2,5,7,3,8,6,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,1,5,7,6,8,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,5,4,6,8,2,7,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,3,6,5,8,7,1,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,2,7,5,6,8,4,3] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[3,1,6,7,5,8,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,6,2,7,5,8,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,5,7,4,8,2,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,4,7,6,8,3,5,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,4,6,8,3,5,7,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,3,5,8,2,7,4,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,2,5,8,4,7,6,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,2,5,8,7,4,3,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,3,5,8,7,2,4,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[5,7,1,2,8,6,4,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,4,5,7,2,8,1,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,3,4,7,2,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[3,2,7,4,6,8,1,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,3,6,2,7,1,4,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,6,3,4,7,1,5,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,7,3,4,5,8,1,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,7,4,5,6,8,1,2] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,5,7,3,6,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[4,7,6,2,3,8,1,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,3,5,2,4,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[7,6,2,4,5,8,1,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,5,2,3,4,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[5,3,1,2,8,4,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,5,2,3,7,1,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,2,1,7,3,4,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[5,2,1,8,3,4,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[6,3,2,8,4,5,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,3,1,2,8,4,6,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,4,1,3,8,5,7,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,2,3,1,8,4,7,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[8,3,5,2,7,1,4,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,6,2,4,7,1,5,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,5,2,3,6,1,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,2,1,7,3,4,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,6,3,7,2,4,5,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,1,6,2,3,4,5,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,2,7,3,4,5,6,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,1,6,2,3,4,5,7] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,1,7,3,4,5,6,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,6,1,7,2,4,5,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,1,5,7,2,3,6,4] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,7,5,8,2,3,6,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[7,2,1,8,3,4,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,3,8,2,4,5,6,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,2,8,3,4,5,6,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,7,8,3,4,5,6,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,4,5,8,3,6,7,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,5,7,1,8,3,6,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[6,2,7,1,8,4,5,3] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,7,1,3,8,5,6,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,6,2,8,4,5,7,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[4,1,3,6,8,2,7,5] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,3,4,6,8,2,7,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,6,3,8,7,1,2,5] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[6,4,5,8,7,1,2,3] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[5,3,4,8,7,1,2,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,2,8,7,1,4,6,5] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,1,8,7,2,4,6,5] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,3,7,6,1,2,4,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[1,8,3,7,2,4,5,6] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[3,8,1,7,2,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,8,2,3,5,1,4,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[4,7,8,2,6,1,3,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[6,2,8,7,1,4,5,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,8,7,1,4,5,6,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,8,6,1,3,4,5,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[2,7,6,1,3,4,5,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,7,6,2,3,4,5,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,8,6,2,3,4,5,7] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[2,8,7,3,4,5,6,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[3,8,7,2,4,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,8,3,6,2,4,5,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[1,5,8,7,2,3,6,4] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[8,7,6,1,3,4,5,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[3,6,2,4,7,1,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,4,7,2,5,1,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,1,6,4,8,5,3,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[4,1,8,5,3,2,7,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[3,6,2,5,7,1,4,8] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,2,8,3,7,5,4,6] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[6,1,3,2,8,5,4,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[5,6,1,2,8,4,3,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[1,6,3,8,7,4,2,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,3,8,1,2,6,7,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[3,4,5,6,10,9,8,7,1,2] => [[1,2,3,4,5],[6,10],[7],[8],[9]] => 000011110
[9,10,7,8,5,6,1,2,4,3] => [[1,2,9],[3,4],[5,6],[7,8],[10]] => 010101001
[1,8,10,6,9,4,7,2,5,3] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[1,2,7,10,5,9,3,8,6,4] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[1,2,3,6,10,4,9,8,7,5] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[1,2,3,4,5,10,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[11,12,9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010
[3,1,2,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[2,4,1,3,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[2,3,5,1,4,6,7,8,9] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[2,3,4,6,1,5,7,8,9] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[2,3,4,5,6,8,1,7,9] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[3,6,8,7,1,2,5,4] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[6,5,7,2,4,8,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[3,4,1,6,5,8,7,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,5,1,2,4,8,7,6] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,7,5,2,1,4,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,8,5,2,7,4,1,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[5,2,8,4,7,3,1,6] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,2,7,4,1,3,6,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,3,5,1,2,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[3,1,4,6,2,8,7,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[1,4,6,5,2,8,7,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[3,4,5,6,1,8,7,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,4,5,8,7,2,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,4,7,2,6,3,5,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[8,4,7,5,2,1,6,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,1,4,7,2,3,6,5] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,8,5,7,3,4,6,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,3,5,1,7,4,2,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,1,4,8,7,3,2,5] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,4,8,5,7,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[5,4,8,1,6,3,2,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[1,4,8,6,3,7,2,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,4,7,6,3,8,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[4,6,3,7,5,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,1,3,5,8,6,2,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,7,4,3,8,1,2,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[1,4,8,3,7,6,5,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,3,8,2,1,6,5,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[3,8,4,2,7,1,5,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,1,2,5,7,6,4,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[1,8,2,7,6,5,4,3] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[3,8,1,6,7,5,4,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,7,2,6,8,5,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,2,3,8,5,6,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[8,2,1,7,5,6,4,3] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,1,3,6,5,7,4,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,2,4,3,6,1,5,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,7,8,5,4,3,6,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[1,8,4,5,3,2,6,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[7,8,5,4,3,1,6,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[7,1,6,3,4,2,5,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[6,8,7,1,4,2,5,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[3,6,1,4,2,7,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,4,1,8,5,7,6,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,6,5,1,2,8,4,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,8,5,6,7,2,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,1,7,6,2,4,3,5] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,5,6,1,4,2,3,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,6,5,4,7,1,3,2] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[1,6,4,5,7,2,3,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,3,6,1,7,2,4,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[1,8,6,5,7,3,4,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[1,7,5,3,6,8,4,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,4,1,6,5,8,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[4,1,5,8,7,6,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[1,2,5,8,6,7,3,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,2,1,5,8,7,3,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,2,4,6,1,7,3,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[1,5,3,6,8,7,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,5,4,6,1,8,2,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,1,5,7,6,8,2,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[1,4,5,6,8,7,2,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,4,6,3,7,2,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,7,3,6,5,2,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,6,2,5,4,1,7,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[3,7,2,6,5,4,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,6,2,5,4,3,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[4,7,5,2,6,3,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,2,6,4,7,5,1,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,2,3,7,5,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[1,3,4,7,6,2,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,8,3,6,1,7,5,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[8,7,2,5,1,6,4,3] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[3,8,2,6,5,1,7,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,2,5,4,1,6,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,8,5,2,6,1,7,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,5,1,3,7,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,1,3,7,5,2,8,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[7,1,3,6,2,8,5,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,1,3,6,2,7,5,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[1,2,4,7,3,8,6,5] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[7,1,8,2,6,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[3,1,8,6,2,7,5,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,1,7,8,2,6,5,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,6,1,8,2,7,4,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,2,7,8,1,6,5,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,2,8,6,1,7,5,4] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,2,8,1,6,5,4,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[1,8,7,2,6,5,4,3] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[2,8,7,1,6,5,4,3] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[3,8,7,1,6,5,4,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[4,8,7,5,1,6,3,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[6,7,8,5,1,4,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,6,3,8,4,1,7,2] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[7,3,8,5,4,1,6,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,4,8,6,5,1,7,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[8,3,7,5,1,6,4,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[1,4,8,6,2,7,5,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[8,4,6,7,1,5,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[5,6,4,7,8,1,3,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,4,6,5,1,2,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[7,3,5,1,2,8,6,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[1,4,6,2,3,8,7,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,3,2,7,4,8,6,5] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[7,2,1,6,3,8,5,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,3,1,7,6,4,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[4,5,2,1,7,3,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[5,6,7,1,2,8,4,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,7,5,1,2,8,6,3] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[3,7,1,6,2,8,5,4] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[7,6,1,2,8,5,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[2,7,1,3,8,6,5,4] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,6,1,2,7,5,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[1,7,2,3,8,6,5,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,7,1,2,6,5,4,3] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[7,8,1,2,6,5,4,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,8,1,6,2,7,5,4] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,8,5,1,2,7,6,3] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,6,8,1,2,7,4,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,1,3,7,4,8,6,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,2,7,3,6,8,1,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,3,6,4,2,8,1,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,1,5,3,8,2,7,6] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[5,2,6,4,7,3,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,6,3,4,7,5,1,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[2,6,3,5,4,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,7,4,3,5,8,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,3,6,4,2,8,1,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,6,4,5,2,8,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,4,3,1,8,2,7,6] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,5,4,2,7,3,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,4,1,7,2,6,3,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[5,4,1,8,3,2,6,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,5,2,8,3,4,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,4,2,1,8,3,6,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,5,3,4,8,2,7,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,1,5,3,8,2,7,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[4,6,3,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,8,4,2,7,3,1,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,2,6,4,7,3,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,6,2,5,7,4,1,3] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,5,3,2,6,4,1,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,3,1,7,2,5,4,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,5,2,6,4,3,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,1,6,2,5,4,3,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,1,7,3,5,6,4,2] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,6,1,7,4,5,2,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[8,1,3,7,2,6,5,4] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[1,7,6,8,3,2,4,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[7,1,5,8,4,2,6,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[7,3,8,4,5,2,6,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,2,8,5,3,4,6,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,1,8,4,3,2,5,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,1,7,4,2,5,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,2,7,3,4,6,5,8] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,7,8,4,3,5,6,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,6,2,8,3,5,7,4] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,6,1,7,3,5,4,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,1,5,8,4,2,6,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,3,1,6,8,2,7,5] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,7,4,8,3,2,1,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,4,8,2,7,3,1,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,2,8,7,3,4,1,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,4,7,5,3,2,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,8,3,7,6,2,4,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[5,8,3,2,6,4,1,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,8,2,4,7,5,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,3,8,2,6,4,1,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,6,8,2,7,3,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[2,6,8,7,3,4,1,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,2,8,6,3,5,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,8,1,7,2,5,4,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[3,8,7,4,5,6,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,8,6,4,3,5,1,7] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[2,7,6,3,5,4,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,7,6,5,2,4,3,8] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,8,6,5,3,2,4,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[3,8,7,4,6,2,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[5,8,3,7,6,2,4,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[7,1,8,6,5,2,3,4] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[8,4,7,5,3,2,1,6] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,7,2,5,4,3,1,6] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[6,8,3,2,5,4,7,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,5,7,8,4,3,6,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,3,8,1,5,4,7,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,2,1,8,5,4,7,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[2,6,5,7,4,1,3,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[2,5,6,8,4,3,7,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,5,4,7,1,8,6,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[5,2,1,8,7,6,4,3] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[4,8,6,7,5,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,5,4,8,2,1,7,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[5,8,4,7,2,6,3,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,8,3,2,7,6,4,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[5,2,1,4,3,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[3,5,7,4,2,6,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,2,1,6,5,3,7,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[4,2,1,5,7,6,3,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[3,5,4,7,1,6,2,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,4,5,8,6,7,1,2] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,3,5,1,6,8,7,2] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[4,3,2,1,7,6,5,9,8,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,3,2,1,6,5,4,9,8,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,9,6,5,8,7,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,3,2,1,9,5,4,8,7,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[9,3,2,1,8,5,4,7,6,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,5,2,1,9,4,3,8,7,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[9,5,2,1,8,4,3,7,6,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,7,6,5,10,8,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,3,2,1,6,5,4,10,8,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,8,6,5,10,7,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,3,2,1,8,5,4,10,7,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[8,3,2,1,7,5,4,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,5,2,1,8,4,3,10,7,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[8,5,2,1,7,4,3,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,10,6,5,9,7,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,3,2,1,10,5,4,9,7,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,3,2,1,10,5,4,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,3,2,1,9,5,4,8,6,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[6,5,2,1,10,4,3,9,7,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,5,2,1,10,4,3,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,5,2,1,9,4,3,8,6,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,8,7,5,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,3,2,1,8,7,4,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[8,3,2,1,7,6,4,10,5,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,4,2,1,8,7,3,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[8,4,2,1,7,6,3,10,5,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[4,3,2,1,10,7,5,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,3,2,1,10,7,4,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,3,2,1,10,6,4,9,5,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,3,2,1,9,6,4,8,5,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,4,2,1,10,7,3,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,4,2,1,10,6,3,9,5,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,4,2,1,9,6,3,8,5,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,6,2,1,10,5,3,9,4,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,6,2,1,9,5,3,8,4,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,4,3,1,8,7,2,10,6,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[8,4,3,1,7,6,2,10,5,9] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[5,4,3,1,10,7,2,9,6,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,4,3,1,10,6,2,9,5,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,4,3,1,9,6,2,8,5,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[7,6,3,1,10,5,2,9,4,8] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,6,3,1,9,5,2,8,4,7] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[10,3,1,5,2,7,4,9,6,8] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[10,9,4,1,6,2,8,3,5,7] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[10,9,8,5,1,7,2,3,4,6] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[2,4,6,8,1,3,5,7,9] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[8,7,6,5,4,3,2,10,1,9] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010
[6,5,4,10,3,9,2,8,1,7] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010
[6,5,4,3,2,8,10,1,7,9] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[4,8,3,7,2,6,10,1,5,9] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[4,3,2,6,8,10,1,5,7,9] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[2,1,7,3,8,4,6,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,1,8,2,7,3,6,5] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,1,7,2,8,3,6,5] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[7,1,3,2,8,4,6,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[7,1,8,2,4,3,6,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,1,7,2,5,3,6,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,1,5,2,8,3,6,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,1,7,2,8,3,6,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,1,8,2,7,3,6,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,1,8,2,4,3,7,6] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,1,6,2,4,3,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,1,8,2,4,3,7,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[6,1,8,2,5,3,7,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,1,6,2,5,3,7,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,6,2,7,3,5,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,1,8,2,7,3,5,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,1,7,2,8,3,5,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[6,1,7,2,5,3,8,4] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[6,1,7,2,4,3,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,1,6,2,4,3,8,7] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[7,1,5,2,4,3,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,1,6,2,4,3,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,1,6,2,5,3,8,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,1,6,2,8,3,5,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,1,8,2,6,3,5,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[1,8,2,7,5,4,6,3] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[1,8,2,7,4,3,5,6] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,8,6,4,7,2,3,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,8,4,2,6,3,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[7,4,8,1,5,2,3,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,1,7,2,6,3,5,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,1,7,4,3,6,2,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[7,5,8,3,2,4,1,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[1,8,5,4,3,6,2,7] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,8,5,4,3,7,2,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,8,5,4,7,2,6,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[1,8,4,2,5,3,7,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,8,5,4,2,6,7,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[7,4,8,2,1,3,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[4,1,7,3,2,5,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,5,4,8,2,3,6,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[3,1,7,2,6,8,4,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,1,7,4,2,6,8,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,1,6,3,2,5,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,3,1,6,2,5,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[6,5,4,3,7,1,8,2] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,5,1,7,3,8,2,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,3,2,8,5,7,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,5,4,3,8,2,7,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[6,5,4,3,8,7,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[7,6,3,8,5,4,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[5,4,8,2,1,7,3,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,4,2,8,5,1,3,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,6,4,8,5,1,2,3] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,2,8,6,3,1,4,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,2,8,6,1,5,3,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,1,7,8,3,6,4,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,4,1,7,8,2,3,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,2,1,6,7,3,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[4,3,1,5,2,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,4,2,7,3,8,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,1,5,3,2,8,6,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,1,6,2,8,7,4,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,3,1,7,8,5,2,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[6,5,4,1,7,8,3,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,4,3,1,6,7,2,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,5,4,2,7,8,3,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,4,2,6,3,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,3,1,5,2,6,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,4,2,1,6,7,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,4,3,1,6,7,8,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,3,8,1,2,5,7,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[3,6,7,1,2,5,8,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[7,8,3,1,2,5,6,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[7,8,1,3,2,4,6,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,8,2,1,3,5,4,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,2,3,7,1,8,6,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[2,5,3,6,1,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,6,7,3,1,8,4,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,6,7,1,3,5,4,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,2,8,3,1,7,4,5] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[3,2,5,7,1,8,4,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[4,3,1,2,7,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,1,2,7,3,6,4,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[5,1,4,7,8,2,3,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[5,3,4,7,8,6,1,2] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[3,5,4,6,8,7,1,2] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,5,4,6,8,2,3,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[1,6,7,3,2,4,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,5,3,6,2,7,8,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[5,1,3,7,2,6,8,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[5,2,4,7,8,1,6,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[4,2,5,7,6,1,8,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,5,2,8,6,1,7,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[5,3,1,8,2,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[6,1,8,3,2,4,7,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,3,5,7,6,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,1,5,7,6,2,3,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,5,1,8,6,2,3,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[5,2,1,8,3,6,4,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,4,2,1,8,7,5,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[7,6,5,4,2,1,8,3] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[7,6,5,4,8,1,3,2] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,7,6,5,4,2,1,9,3] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[7,6,5,8,2,1,4,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,7,6,5,3,2,1,9,4] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[8,7,6,4,3,2,1,9,5] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[8,7,5,4,3,2,1,9,6] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[8,5,4,3,2,1,7,6] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[8,6,5,4,3,2,1,9,7] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[7,6,5,4,3,2,1,9,8] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[7,6,5,4,1,8,3,2] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,7,6,5,4,9,1,3,2] => [[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101
[9,8,7,6,5,4,2,1,10,3] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,6,5,2,8,1,4,3] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[9,8,7,6,5,3,2,1,10,4] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,6,5,8,4,1,3,2] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[9,8,7,6,4,3,2,1,10,5] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,6,8,5,2,1,4,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,7,9,4,3,2,1,6,5] => [[1,3],[2,8],[4,9],[5],[6],[7]] => 10111101
[9,8,7,5,4,3,2,1,10,6] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,8,6,3,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[8,9,5,4,3,2,1,7,6] => [[1,2],[3,8],[4,9],[5],[6],[7]] => 01111101
[9,8,6,5,4,3,2,1,10,7] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[8,7,4,3,2,1,6,5] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[9,6,5,4,3,2,1,8,7] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[9,7,6,5,4,3,2,1,10,8] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[7,8,4,5,9,2,3,6,10,1] => [[1,2,5,9],[3,4,8],[6,7],[10]] => 010010001
[7,8,2,4,5,1,3,6] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[4,6,7,2,5,1,3,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,8,1,3,2,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[7,8,4,1,5,2,3,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,6,7,2,1,4,5,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[5,2,3,6,1,4,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[2,5,3,6,1,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,6,7,3,1,4,5,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[4,6,7,1,5,2,3,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,6,7,3,5,8,1,2] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[6,4,7,1,5,2,3,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,2,7,3,1,4,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,2,5,6,1,4,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,5,2,6,1,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[5,1,4,6,7,2,3,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,5,4,6,7,8,1,2] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,5,4,6,7,2,3,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,6,7,3,2,4,5,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,5,3,6,2,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[5,1,3,6,2,4,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[5,2,4,6,7,1,3,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[2,5,4,6,7,1,3,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,6,7,4,5,1,3,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[6,2,7,4,5,1,3,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[4,2,5,6,7,1,3,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[4,5,2,6,7,1,3,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[5,3,1,6,2,4,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[6,1,7,3,2,4,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[6,1,7,4,5,2,3,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[6,3,7,4,5,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,4,1,6,7,2,3,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,2,1,6,3,4,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,3,2,5,4,1,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,5,4,2,1,6,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[7,3,5,2,4,1,6,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,6,5,2,1,4,3,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[1,3,6,7,5,2,8,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,3,4,1,6,2,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,3,4,1,6,5,2,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,3,4,1,5,6,2,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[7,3,2,5,1,6,4,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,6,5,4,1,3,2,8] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[7,3,4,1,5,2,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[1,3,6,7,2,5,8,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,7,4,6,2,8,5,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[4,3,1,7,2,6,8,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,6,1,4,7,3,8,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,3,2,1,7,4,8,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[1,3,4,5,8,7,2,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[6,3,4,5,8,1,7,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[2,4,5,1,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,1,2,5,6,8,7,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,3,2,5,6,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[3,7,5,4,6,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,1,4,6,5,8,2,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,3,4,5,8,6,1,7] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[2,3,4,5,8,1,7,6] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,1,4,6,5,8,7,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,7,5,4,6,8,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[5,6,1,4,7,2,8,3] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,3,1,7,5,6,8,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[4,3,1,7,6,5,8,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,1,4,6,7,8,5,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[1,4,5,2,6,8,7,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,7,5,2,6,8,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,7,5,2,6,8,4,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,6,1,2,7,4,8,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,3,5,2,4,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,3,2,1,4,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,3,1,4,2,7,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,3,1,2,4,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,1,5,2,6,8,4,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,1,5,2,6,8,3,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,7,4,6,5,8,3,2] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[2,7,4,6,1,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,7,4,6,1,8,5,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[2,3,6,7,1,5,8,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,3,6,7,5,1,8,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[4,3,2,6,7,1,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,3,2,5,6,8,1,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,1,5,4,6,8,2,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,7,4,6,5,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[7,3,4,5,8,6,1,2] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[7,3,4,5,8,1,6,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[7,3,4,5,8,1,2,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,3,4,5,8,6,2,7] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,3,4,5,8,2,7,6] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[6,3,4,5,8,2,1,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,3,4,5,8,2,7,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,3,4,5,8,6,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,7,4,6,5,8,3,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[7,1,5,4,6,8,3,2] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[7,3,2,5,6,8,4,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,7,4,6,1,8,3,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,3,4,5,8,1,2,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,3,4,5,8,2,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,3,4,5,8,2,6,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,8,6,1,7,5,2,3] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,7,8,2,6,1,5,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[7,6,4,2,8,3,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,6,4,2,7,5,3,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[8,4,7,3,6,5,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[8,4,6,1,7,5,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,4,7,1,8,3,2,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[7,4,8,3,6,1,5,2] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[6,12,5,11,4,10,3,9,2,8,1,7] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010
[6,2,1,7,3,5,4,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[2,1,8,6,3,5,4,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[2,1,7,3,5,8,6,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,7,3,1,5,4,6,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,6,3,1,4,8,5,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[4,2,1,8,3,6,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[2,1,8,6,3,5,7,4] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,2,1,7,3,5,8,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[2,7,3,1,4,8,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[3,2,1,6,4,5,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[3,2,1,5,7,8,4,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,1,7,3,6,8,4,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,7,3,1,5,6,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,4,7,5,1,6,8,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[4,3,7,5,6,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,3,6,8,5,1,7,2] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[2,6,1,8,3,5,7,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,1,6,8,3,7,4,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,1,8,3,5,7,4,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,2,1,5,6,8,4,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[3,2,1,5,7,4,6,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[2,1,7,3,6,4,5,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[2,1,6,3,5,8,4,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,2,4,1,7,5,6,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,8,4,7,5,1,6,2] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,4,3,6,1,7,5,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[8,2,1,7,3,5,4,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[2,6,1,8,3,5,4,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,7,3,1,5,6,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[2,4,7,5,1,6,3,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[8,2,4,1,7,5,3,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,8,6,3,1,7,4,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,4,7,1,8,5,3,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,4,8,5,1,6,3,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[6,2,1,7,3,4,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,2,1,7,8,3,5,4] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[2,7,1,8,3,5,6,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,1,8,3,6,4,5,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,2,1,6,7,4,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,2,1,7,4,5,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[3,2,1,6,8,4,5,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[2,1,8,3,7,4,5,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[2,1,8,3,6,7,4,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,4,8,5,1,6,7,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[4,3,8,5,6,1,7,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,2,1,8,4,5,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,6,8,3,7,2,4,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,8,1,5,7,2,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[1,2,6,8,4,7,3,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[6,1,5,8,2,4,7,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,2,4,8,3,6,7,5] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[4,1,2,7,8,3,6,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,5,7,4,8,6,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,3,8,4,7,6,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,7,1,2,5,4,6,3] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[5,8,1,2,3,7,6,4] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[1,2,8,4,3,5,7,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,5,3,7,6,4,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[6,1,2,8,7,4,5,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[7,1,6,2,8,4,5,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,2,6,3,8,5,4,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,2,8,5,3,6,4,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,7,3,8,5,4,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[4,1,2,7,8,6,3,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,6,2,8,4,3,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,6,4,2,7,3,5,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,8,6,3,2,4,5,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,7,3,2,8,4,5,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[3,1,7,8,6,2,4,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[1,8,7,2,4,5,6,3] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,8,7,3,5,6,2,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,3,2,8,7,4,5,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,8,3,2,6,4,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,7,6,3,2,4,5,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,2,8,4,3,7,5,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[8,5,1,7,2,4,6,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,3,8,7,4,6,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,8,6,4,7,5,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,1,8,2,7,4,5,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[1,2,5,3,8,6,4,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,2,7,5,3,6,4,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,6,3,7,5,4,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,2,3,7,5,4,8,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,7,4,8,6,5,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,8,2,7,6,4,5,3] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,9,8,7,6,5,4,1,3] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[2,8,7,6,5,1,4,3] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[7,1,6,3,2,5,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,7,6,3,1,5,8,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,8,4,3,6,5,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,8,4,6,5,3,2,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[7,4,2,1,6,5,3,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,6,1,4,3,5,2,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,4,1,3,5,2,6,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,3,1,2,4,6,5,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,8,6,3,4,5,2,7] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,6,7,4,2,5,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[3,6,2,1,4,8,5,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,1,7,2,4,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[3,4,7,1,5,2,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,6,7,4,1,5,8,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,3,2,7,1,5,8,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[3,1,2,8,6,5,4,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,4,8,6,1,2,3,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,6,8,7,4,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,8,2,7,4,3,6,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,5,8,2,3,7,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,4,8,5,3,1,7,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,7,8,6,1,3,2,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,4,8,1,6,3,7,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,1,2,8,6,4,7,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,3,2,6,4,8,1,7] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,1,6,3,5,8,2,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,4,5,3,8,6,1,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,8,5,3,2,7,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,8,4,5,2,6,7,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[4,1,2,7,6,5,8,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,4,1,6,7,8,5,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,8,4,3,6,2,7,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,6,7,3,2,8,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,5,7,3,6,8,4,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,3,2,1,4,8,6,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[5,3,1,4,2,8,6,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[7,6,1,3,8,5,4,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[3,4,7,8,1,2,6,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,6,7,8,1,4,5,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,6,2,8,1,5,4,7] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[2,3,6,8,5,1,4,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,1,6,4,8,2,5,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[7,3,2,6,8,5,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,3,5,8,4,6,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,5,2,8,4,1,6,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[7,4,5,8,2,1,3,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[1,8,5,2,4,6,3,7] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,4,2,3,5,7,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[6,4,2,8,3,5,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,3,4,8,2,5,7,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,5,4,8,3,6,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[2,7,4,8,5,3,6,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[7,1,5,4,8,3,6,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,3,2,5,8,4,6,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,4,6,3,7,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,4,6,3,8,5,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[2,5,6,8,3,4,1,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[8,4,6,2,7,5,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,5,6,7,2,4,3,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,5,6,8,4,3,1,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,5,7,8,4,1,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[6,5,7,8,4,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,5,6,8,2,4,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,4,6,2,8,5,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[4,3,2,6,8,5,1,7] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[3,5,6,8,2,4,1,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,5,6,8,4,2,1,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,6,7,8,1,4,5,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,6,7,8,1,4,2,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,5,7,8,2,1,4,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,6,7,8,1,4,3,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[6,5,7,8,3,1,4,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[2,5,7,8,3,1,4,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,4,7,3,8,1,5,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[6,4,7,3,8,1,5,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,4,7,3,8,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,4,6,3,8,2,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,3,2,5,4,8,1,7] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,4,5,2,3,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,4,5,3,2,8,1,7] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,4,6,3,8,2,1,7] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[5,4,7,3,8,1,6,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[2,5,7,8,3,1,6,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,5,7,8,3,1,2,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,5,6,8,2,3,1,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[5,4,6,2,8,3,1,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[5,3,2,6,8,4,1,7] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,4,7,2,8,1,3,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,5,7,8,2,1,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,6,7,8,1,3,2,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,6,7,8,1,3,5,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,6,7,8,1,3,5,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,6,7,8,1,5,3,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,6,7,8,1,5,2,3] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,6,7,8,1,2,5,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,5,7,8,2,1,6,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,4,7,2,8,1,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[5,3,2,7,8,1,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[4,3,2,7,8,1,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,5,7,8,2,1,6,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,6,7,8,1,2,5,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,6,7,8,1,5,2,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[3,6,7,8,1,5,4,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,6,7,8,1,5,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,4,5,6,7,8,9,1,2,10] => [[1,2,3,4,5,6,7,10],[8,9]] => 000000100
[2,4,5,6,7,8,1,3,9] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[1,4,5,6,7,8,2,9,3] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[1,4,5,6,7,8,9,10,2,3] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[4,2,7,1,5,3,8,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,2,8,6,1,5,3,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,2,6,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[2,7,1,3,5,4,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,7,2,1,5,8,6,3] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[7,2,1,3,5,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[2,3,6,4,7,1,5,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,3,4,8,2,7,5,6] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[3,1,4,8,2,6,7,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[8,3,1,6,2,5,7,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,8,6,2,1,5,7,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[4,8,3,6,5,1,7,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,4,7,3,5,1,8,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,4,7,5,1,8,2,3] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[3,6,1,7,5,8,2,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[7,3,5,1,6,8,2,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[4,7,3,5,6,1,8,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[3,4,6,8,5,1,7,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,6,8,2,1,5,7,3] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[6,8,2,1,3,5,7,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[1,8,2,3,5,7,4,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,7,3,6,1,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,6,1,3,5,8,4,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[7,3,2,5,6,1,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[4,7,5,2,6,1,3,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,6,2,8,1,5,3,7] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[8,4,1,2,7,5,3,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,5,6,2,7,1,3,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[8,5,1,2,6,3,4,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[1,6,2,7,4,8,3,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[6,2,1,7,8,5,3,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[6,7,3,8,4,1,5,2] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[2,7,8,4,1,5,6,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[2,7,1,8,5,6,3,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[8,2,5,1,6,7,3,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,2,4,5,1,6,7,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[3,8,4,5,6,1,7,2] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[4,5,8,3,6,7,1,2] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[4,5,8,3,7,6,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,2,8,3,7,1,6,5] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,2,3,4,8,1,6,5] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[7,2,3,4,8,1,5,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,6,3,4,8,5,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,6,3,5,8,4,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,6,3,8,4,5,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,2,3,8,5,1,4,6] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[7,2,3,8,5,1,6,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[2,6,4,8,1,5,7,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[7,2,3,8,4,1,5,6] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[7,2,3,5,8,1,4,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,8,2,3,6,1,4,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[7,8,2,3,6,1,5,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,2,6,3,7,1,5,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[7,2,3,5,8,1,6,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[7,2,3,8,4,1,6,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[2,6,4,8,1,3,7,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,6,4,8,1,7,5,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[7,6,5,1,2,3,8,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,6,5,1,4,2,8,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[2,6,4,5,1,8,7,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,5,6,4,1,2,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[7,8,5,4,1,2,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,5,6,4,1,2,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[7,6,5,1,4,2,3,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,6,5,1,2,4,3,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[7,6,5,1,2,4,8,3] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,6,5,1,3,2,8,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,6,5,1,3,2,4,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,6,5,1,3,4,2,8] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[7,2,3,4,5,1,8,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[2,6,4,3,1,5,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,6,4,3,1,8,5,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,6,4,3,1,8,7,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,5,8,4,1,2,7,6] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[3,5,8,4,1,2,6,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,5,8,4,1,6,2,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[4,2,8,3,6,1,7,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,5,8,4,1,6,7,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[2,5,8,4,1,7,3,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[3,6,4,2,1,7,8,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,6,4,2,1,7,5,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,5,6,4,1,8,7,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[2,6,4,5,1,3,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[7,6,5,1,4,3,8,2] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[7,6,5,1,2,8,4,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[7,6,5,1,2,8,3,4] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,6,5,1,8,2,4,3] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,6,5,1,8,2,3,4] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,6,5,1,8,3,2,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[7,6,5,1,4,8,2,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[3,6,4,5,1,7,2,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,5,6,4,1,7,8,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[7,8,5,4,1,6,3,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[2,5,6,4,1,7,3,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[3,6,4,5,1,7,8,2] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[7,6,5,1,4,8,3,2] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,6,5,1,8,3,4,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,6,5,1,8,4,2,3] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[4,1,7,6,2,8,5,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[7,8,6,2,1,3,5,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,7,6,1,2,8,4,5] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,6,5,3,1,4,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,6,1,5,3,2,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[3,6,1,4,2,5,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,6,4,5,7,8,1,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[8,7,1,6,5,2,4,3] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[7,2,5,6,8,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,1,3,4,2,8,7,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[2,4,5,6,1,8,7,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[8,4,1,6,5,7,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[2,8,3,4,7,5,1,6] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[6,8,2,7,4,3,5,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[4,7,8,5,1,6,3,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,2,6,4,7,3,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[4,8,6,1,7,3,2,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[8,7,3,2,1,5,4,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[3,8,5,1,7,2,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,8,7,1,3,2,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[2,5,1,8,7,4,6,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,7,1,8,4,5,6,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[6,2,3,8,4,7,5,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[8,6,4,3,1,7,2,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,3,7,4,6,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,1,3,8,6,4,5,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,3,5,8,6,7,4,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[7,4,2,1,8,6,5,3] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[4,6,7,2,5,8,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[7,6,2,5,3,8,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[6,2,1,3,4,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[6,5,4,2,8,3,1,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,4,3,1,8,7,2,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,1,4,3,8,5,2,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,7,6,2,8,1,5,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,4,5,1,7,8,3,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,2,3,1,7,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[3,4,2,1,8,6,7,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[2,7,6,8,1,5,3,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,4,5,8,3,1,2,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,1,3,2,5,6,7,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[3,6,8,1,5,2,4,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,2,8,7,4,5,1,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,3,8,5,7,4,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[7,4,6,8,5,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,1,4,8,7,5,3,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,1,6,8,3,7,5,4] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,6,8,2,4,1,5,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,2,8,1,7,5,4,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[2,6,5,4,8,1,3,7] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,5,3,4,8,1,7,2] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,4,3,2,5,1,7,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,2,8,1,5,3,6,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,1,8,2,6,4,3,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,4,8,6,2,1,3,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,6,2,8,3,7,5,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[2,1,5,8,3,6,4,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,8,5,3,6,7,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,8,5,6,4,1,3,2] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[5,8,4,1,6,3,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[4,8,1,3,5,7,6,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,8,1,4,5,6,2,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[9,7,5,8,3,6,1,4,2] => [[1,4],[2,6],[3,8],[5,9],[7]] => 11010101
[7,9,5,8,3,6,1,4,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[7,6,8,3,5,1,4,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,9,5,7,3,6,1,4,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[8,9,6,7,3,5,1,4,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[8,9,6,7,4,5,1,3,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[8,9,6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[9,10,7,8,5,6,3,1,4,2] => [[1,2],[3,4],[5,6],[7,9],[8,10]] => 010101101
[9,10,7,8,5,3,6,1,4,2] => [[1,2],[3,4],[5,7],[6,9],[8,10]] => 010110101
[9,10,7,5,8,3,6,1,4,2] => [[1,2],[3,5],[4,7],[6,9],[8,10]] => 011010101
[9,7,10,5,8,3,6,1,4,2] => [[1,3],[2,5],[4,7],[6,9],[8,10]] => 101010101
[7,8,6,3,5,1,4,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[5,3,8,7,6,1,4,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[9,8,5,7,3,6,1,4,2] => [[1,4],[2,6],[3,8],[5],[7],[9]] => 11010101
[10,7,9,5,8,3,6,1,4,2] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[7,9,6,8,3,5,1,4,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[10,8,9,5,7,3,6,1,4,2] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[6,5,8,4,7,1,3,2] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,9,5,7,4,6,1,3,2] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[10,8,9,6,7,3,5,1,4,2] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[8,9,6,7,3,5,2,4,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[10,8,9,6,7,4,5,1,3,2] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[6,7,4,2,5,3,1,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,6,4,8,3,1,5,2] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[7,4,8,5,6,1,3,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,4,2,5,6,3,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,2,7,5,6,3,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,4,7,5,6,2,1,8] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[4,7,3,5,6,2,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,7,2,5,6,4,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[7,8,3,5,6,1,4,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[1,6,8,5,2,7,4,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,2,8,5,1,7,4,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,7,4,8,2,1,5,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[3,2,7,8,6,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,8,4,1,2,3,7,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,1,8,5,6,3,2,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[1,8,2,5,6,4,3,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[6,1,8,5,3,7,4,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,8,1,5,2,7,6,4] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[8,2,1,5,3,7,6,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[1,5,2,4,6,7,8,3] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[4,1,5,3,6,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[8,1,6,5,3,7,2,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,1,4,6,3,2,8,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,2,6,4,1,7,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[7,6,4,3,1,2,8,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,6,3,5,1,7,2,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[4,5,3,1,6,7,8,2] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[3,5,2,1,6,7,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[5,2,3,1,6,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[1,5,3,2,6,7,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[8,4,6,5,1,7,2,3] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,5,4,6,1,2,8,3] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[3,2,5,6,1,7,8,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[3,2,8,7,6,1,4,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,8,4,7,2,1,3,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[3,8,7,5,6,1,2,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[8,2,7,5,6,1,3,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,8,6,5,1,7,3,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,7,4,6,2,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[7,6,4,2,1,5,8,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[5,7,4,6,1,3,8,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[8,6,4,7,3,1,2,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,2,4,3,7,1,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[3,5,4,2,7,1,8,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[8,6,4,1,3,5,2,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[6,7,4,1,5,3,8,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[7,5,4,1,2,6,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,7,4,2,3,6,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,8,2,5,3,7,6,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,8,1,5,4,7,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[8,2,1,5,6,4,3,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,8,1,5,6,4,2,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[6,8,4,1,2,5,3,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,2,8,1,6,5,4,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[3,2,6,1,5,7,8,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[7,6,4,1,5,2,8,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,6,1,5,4,7,2,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[3,5,1,4,6,7,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[5,2,1,4,6,7,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,4,1,3,6,7,8,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,4,1,5,3,7,2,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[7,5,4,1,3,2,8,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[3,2,5,1,4,7,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,1,4,3,5,2,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,3,5,4,7,2,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,1,3,4,6,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[3,1,8,2,5,7,4,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,3,2,6,1,4,7,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[2,8,1,6,4,3,7,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[2,6,1,3,8,7,5,4] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,5,7,1,3,8,6,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,6,8,1,5,7,4,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,7,1,5,8,4,6,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,7,1,6,4,8,3,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,7,1,6,5,3,8,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[2,8,1,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[8,3,2,7,1,6,5,4] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[4,1,8,7,3,2,6,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[4,1,7,2,8,6,5,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[3,7,1,8,6,5,4,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,7,6,1,4,2,5,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,7,5,1,4,6,8,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,6,8,5,1,4,7,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[7,3,5,8,2,1,4,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,3,6,2,1,4,5,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,3,6,2,1,5,4,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[7,4,2,8,1,6,5,3] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[8,7,5,3,2,1,6,4] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[7,5,2,6,3,1,4,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,4,6,2,1,8,3,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,8,4,5,2,1,7,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,6,8,5,1,7,3,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,7,5,1,3,8,6,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[4,7,6,1,5,3,2,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,1,7,6,3,8,2,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[5,1,7,6,4,2,8,3] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[5,1,8,7,6,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[8,5,2,1,7,6,4,3] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[8,5,2,1,6,3,7,4] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[5,1,8,6,3,2,7,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[3,6,1,7,4,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[4,1,8,6,3,7,2,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[8,4,2,5,7,3,1,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[3,4,6,8,5,7,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[5,4,8,2,7,3,6,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,4,8,7,3,6,1,2] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[8,5,4,7,3,6,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[6,4,3,8,7,1,2,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,3,7,2,4,8,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,6,8,4,2,7,3,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,4,2,8,1,3,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,5,2,7,1,3,8,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,6,5,4,2,1,7,3] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[6,4,7,3,1,8,2,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[5,7,4,3,8,6,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[7,5,8,4,6,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[7,6,4,8,3,5,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[7,6,5,3,8,2,4,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[6,5,4,3,2,1,9,8,7] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 11111011
[6,5,4,3,2,1,8,7,9] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 11111010
[5,4,3,2,1,9,8,7,6] => [[1,6],[2,7],[3,8],[4,9],[5]] => 11110111
[5,4,3,2,1,8,7,6,9] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[5,4,3,2,1,7,6,9,8] => [[1,6,8],[2,7,9],[3],[4],[5]] => 11110101
[5,4,3,2,1,7,6,8,9] => [[1,6,8,9],[2,7],[3],[4],[5]] => 11110100
[4,3,2,1,8,7,6,5,9] => [[1,5,9],[2,6],[3,7],[4,8]] => 11101110
[4,3,2,1,7,6,5,9,8] => [[1,5,8],[2,6,9],[3,7],[4]] => 11101101
[4,3,2,1,7,6,5,8,9] => [[1,5,8,9],[2,6],[3,7],[4]] => 11101100
[4,3,2,1,6,5,8,7,9] => [[1,5,7,9],[2,6,8],[3],[4]] => 11101010
[4,3,2,1,6,5,7,8,9] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[3,2,1,6,5,4,8,7,9] => [[1,4,7,9],[2,5,8],[3,6]] => 11011010
[3,2,1,6,5,4,7,8,9] => [[1,4,7,8,9],[2,5],[3,6]] => 11011000
[3,2,1,5,4,7,6,9,8] => [[1,4,6,8],[2,5,7,9],[3]] => 11010101
[3,2,1,5,4,7,6,8,9] => [[1,4,6,8,9],[2,5,7],[3]] => 11010100
[3,2,1,5,4,6,7,8,9] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[2,1,4,3,6,5,7,8,9] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[2,1,4,3,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[7,6,5,4,3,2,1,10,9,8] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 111111011
[7,6,5,4,3,2,1,9,8,10] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 111111010
[6,5,4,3,2,1,9,8,7,10] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 111110110
[6,5,4,3,2,1,8,7,9,10] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 111110100
[5,4,3,2,1,9,8,7,6,10] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 111101110
[5,4,3,2,1,8,7,6,10,9] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 111101101
[5,4,3,2,1,8,7,6,9,10] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 111101100
[5,4,3,2,1,7,6,9,8,10] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 111101010
[5,4,3,2,1,7,6,8,9,10] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[4,3,2,1,8,7,6,5,9,10] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 111011100
[4,3,2,1,7,6,5,10,9,8] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 111011011
[4,3,2,1,7,6,5,8,9,10] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[4,3,2,1,6,5,8,7,9,10] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[4,3,2,1,6,5,7,8,9,10] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 111010000
[3,2,1,6,5,4,9,8,7,10] => [[1,4,7,10],[2,5,8],[3,6,9]] => 110110110
[3,2,1,6,5,4,8,7,10,9] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[3,2,1,6,5,4,8,7,9,10] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[3,2,1,6,5,4,7,8,9,10] => [[1,4,7,8,9,10],[2,5],[3,6]] => 110110000
[3,2,1,5,4,7,6,9,8,10] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[3,2,1,5,4,7,6,8,9,10] => [[1,4,6,8,9,10],[2,5,7],[3]] => 110101000
[3,2,1,5,4,6,7,8,9,10] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[2,1,4,3,6,5,8,7,9,10] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[2,1,4,3,6,5,7,8,9,10] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[2,1,4,3,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[5,6,3,7,4,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,6,3,8,5,1,4,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,4,8,1,3,2,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,4,8,6,3,1,5,2] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[4,2,7,6,5,3,1,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,7,2,4,6,5,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,1,3,4,5,2,6,7] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[1,6,8,4,2,5,3,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[6,2,8,4,1,5,7,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,7,4,8,5,1,2,3] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,2,7,8,5,1,6,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[3,2,8,1,5,4,6,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,1,4,8,5,3,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[1,4,8,5,2,6,7,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[6,1,8,4,3,7,2,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,7,1,4,2,5,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,2,1,4,3,5,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,1,5,3,6,8,2,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[6,1,8,5,3,2,7,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,1,4,6,3,8,5,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[3,2,6,4,1,8,7,5] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[7,6,4,3,1,8,2,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[3,5,2,1,8,7,6,4] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[1,5,3,2,8,6,4,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[5,4,2,1,7,8,6,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,2,7,6,5,1,3,4] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,6,2,7,1,4,5,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[1,7,3,6,2,8,5,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,6,3,2,1,8,5,4] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,6,3,7,4,1,2,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,2,3,4,7,1,8,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[8,6,3,1,4,5,7,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,7,3,1,5,4,2,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,8,3,1,2,4,7,6] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[8,1,3,2,4,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,4,1,7,2,3,6,5] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,2,1,6,5,4,7,3] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[3,8,1,5,6,4,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,8,4,1,2,5,7,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,2,8,1,6,5,7,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,6,4,1,5,2,3,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,6,1,5,4,7,3,2] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[3,5,1,4,6,7,2,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,2,1,4,7,6,3,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,5,8,2,1,3,7,6] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,8,2,3,1,4,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,2,1,3,5,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,4,1,3,6,2,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,5,4,1,3,6,2,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[3,2,5,1,4,6,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,1,4,3,5,6,7,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[7,1,3,5,4,6,2,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[5,1,3,4,6,2,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[4,1,3,2,5,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[3,1,4,2,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[3,1,5,2,6,4,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[3,1,4,2,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[4,1,5,2,6,3,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[3,1,6,2,7,4,8,5,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[3,1,5,2,7,4,9,6,8,10] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[3,1,2,5,4,7,6,9,8,10] => [[1,3,4,6,8,10],[2,5,7,9]] => 100101010
[4,6,7,3,1,5,2,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[6,8,1,3,5,2,7,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[6,8,3,1,4,5,7,2] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[7,5,1,8,2,3,6,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,3,8,4,2,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,1,8,3,5,7,2,6] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[4,5,7,2,3,6,8,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,6,3,4,7,5,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[4,5,2,7,1,6,8,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[3,4,1,6,5,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[7,3,1,4,8,5,6,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,4,2,8,7,1,5,3] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[7,2,4,8,1,5,3,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,6,3,1,7,8,5,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[5,3,1,6,7,8,4,2] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,1,6,2,7,8,5,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,1,3,4,8,7,5,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,5,6,7,8,9,1,2,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[4,5,6,7,8,9,2,3,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[5,6,7,8,9,1,2,3,4] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[6,7,8,9,2,3,4,5,1] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[8,9,6,7,5,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[4,5,6,7,8,9,10,1,2,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[4,5,6,7,8,9,10,2,3,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[5,6,7,8,9,10,1,2,3,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[5,6,7,8,9,10,3,4,1,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[7,8,9,10,3,4,5,6,1,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 000100010
[7,8,9,10,5,6,3,4,1,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[8,9,10,5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001
[4,8,3,7,6,5,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[6,3,8,7,5,4,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[5,3,8,7,6,4,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[2,8,7,6,1,5,4,3] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[5,2,8,7,6,1,4,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[6,2,8,7,5,1,4,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[7,8,2,6,5,1,4,3] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[6,1,8,7,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[3,1,8,7,6,5,4,2] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[7,8,2,6,1,5,4,3] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[6,2,8,7,1,5,4,3] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[4,2,8,1,7,6,5,3] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[4,8,2,7,6,1,5,3] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[3,8,7,2,1,6,5,4] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,5,8,7,1,4,3,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[4,8,1,7,6,5,3,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[5,4,1,8,7,6,3,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[6,4,8,1,7,5,3,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,8,4,1,6,5,3,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[7,8,3,1,6,5,4,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,3,8,1,7,5,4,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[5,3,1,8,7,6,4,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,8,2,1,6,5,4,3] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,5,3,1,8,7,4,2] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[6,4,3,1,8,7,5,2] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[5,4,3,1,8,7,6,2] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[7,5,2,1,8,6,4,3] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[5,4,2,1,8,7,6,3] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[7,3,2,1,8,6,5,4] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[6,3,2,1,8,7,5,4] => [[1,5],[2,6],[3,7],[4,8]] => 1110111
[9,7,5,3,1,10,8,6,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,7,5,3,1,10,9,6,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,6,5,3,1,10,8,7,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,6,5,3,1,10,9,7,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,6,5,3,1,10,9,8,4,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,7,4,3,1,10,8,6,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,7,4,3,1,10,9,6,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,6,4,3,1,10,8,7,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,6,4,3,1,10,9,7,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,6,4,3,1,10,9,8,5,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,5,4,3,1,10,8,7,6,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,5,4,3,1,10,9,7,6,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,5,4,3,1,10,9,8,6,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[6,5,4,3,1,10,9,8,7,2] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,7,5,2,1,10,8,6,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,7,5,2,1,10,9,6,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,6,5,2,1,10,8,7,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,6,5,2,1,10,9,7,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,6,5,2,1,10,9,8,4,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,7,4,2,1,10,8,6,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,7,4,2,1,10,9,6,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,6,4,2,1,10,8,7,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,6,4,2,1,10,9,7,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,6,4,2,1,10,9,8,5,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,5,4,2,1,10,8,7,6,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,5,4,2,1,10,9,7,6,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,5,4,2,1,10,9,8,6,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[6,5,4,2,1,10,9,8,7,3] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,7,3,2,1,10,8,6,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,7,3,2,1,10,9,6,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,6,3,2,1,10,8,7,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,6,3,2,1,10,9,7,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,6,3,2,1,10,9,8,5,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,5,3,2,1,10,8,7,6,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,5,3,2,1,10,9,7,6,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,5,3,2,1,10,9,8,6,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[6,5,3,2,1,10,9,8,7,4] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[9,4,3,2,1,10,8,7,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[8,4,3,2,1,10,9,7,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[7,4,3,2,1,10,9,8,6,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[6,4,3,2,1,10,9,8,7,5] => [[1,6],[2,7],[3,8],[4,9],[5,10]] => 111101111
[11,9,7,5,3,1,12,10,8,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,7,5,3,1,12,11,8,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,7,5,3,1,12,10,9,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,7,5,3,1,12,11,9,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,7,5,3,1,12,11,10,6,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,6,5,3,1,12,10,8,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,6,5,3,1,12,11,8,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,6,5,3,1,12,10,9,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,6,5,3,1,12,11,9,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,6,5,3,1,12,11,10,7,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,6,5,3,1,12,10,9,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,6,5,3,1,12,11,9,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,6,5,3,1,12,11,10,8,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,6,5,3,1,12,11,10,9,4,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,7,4,3,1,12,10,8,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,7,4,3,1,12,11,8,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,7,4,3,1,12,10,9,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,7,4,3,1,12,11,9,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,7,4,3,1,12,11,10,6,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,6,4,3,1,12,10,8,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,6,4,3,1,12,11,8,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,6,4,3,1,12,10,9,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,6,4,3,1,12,11,9,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,6,4,3,1,12,11,10,7,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,6,4,3,1,12,10,9,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,6,4,3,1,12,11,9,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,6,4,3,1,12,11,10,8,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,6,4,3,1,12,11,10,9,5,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,5,4,3,1,12,10,8,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,5,4,3,1,12,11,8,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,5,4,3,1,12,10,9,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,5,4,3,1,12,11,9,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,5,4,3,1,12,11,10,7,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,5,4,3,1,12,10,9,8,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,5,4,3,1,12,11,9,8,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,5,4,3,1,12,11,10,8,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,5,4,3,1,12,11,10,9,6,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,6,5,4,3,1,12,10,9,8,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,6,5,4,3,1,12,11,9,8,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,6,5,4,3,1,12,11,10,8,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,6,5,4,3,1,12,11,10,9,7,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[7,6,5,4,3,1,12,11,10,9,8,2] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,7,5,2,1,12,10,8,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,7,5,2,1,12,11,8,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,7,5,2,1,12,10,9,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,7,5,2,1,12,11,9,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,7,5,2,1,12,11,10,6,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,6,5,2,1,12,10,8,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,6,5,2,1,12,11,8,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,6,5,2,1,12,10,9,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,6,5,2,1,12,11,9,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,6,5,2,1,12,11,10,7,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,6,5,2,1,12,10,9,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,6,5,2,1,12,11,9,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,6,5,2,1,12,11,10,8,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,6,5,2,1,12,11,10,9,4,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,7,4,2,1,12,10,8,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,7,4,2,1,12,11,8,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,7,4,2,1,12,10,9,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,7,4,2,1,12,11,9,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,7,4,2,1,12,11,10,6,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,6,4,2,1,12,10,8,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,6,4,2,1,12,11,8,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,6,4,2,1,12,10,9,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,6,4,2,1,12,11,9,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,6,4,2,1,12,11,10,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,6,4,2,1,12,10,9,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,6,4,2,1,12,11,9,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,6,4,2,1,12,11,10,8,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,6,4,2,1,12,11,10,9,5,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,5,4,2,1,12,10,8,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,5,4,2,1,12,11,8,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,5,4,2,1,12,10,9,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,5,4,2,1,12,11,9,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,5,4,2,1,12,11,10,7,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,5,4,2,1,12,10,9,8,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,5,4,2,1,12,11,9,8,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,5,4,2,1,12,11,10,8,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,5,4,2,1,12,11,10,9,6,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,6,5,4,2,1,12,10,9,8,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,6,5,4,2,1,12,11,9,8,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,6,5,4,2,1,12,11,10,8,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,6,5,4,2,1,12,11,10,9,7,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[7,6,5,4,2,1,12,11,10,9,8,3] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,7,3,2,1,12,10,8,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,7,3,2,1,12,11,8,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,7,3,2,1,12,10,9,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,7,3,2,1,12,11,9,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,7,3,2,1,12,11,10,6,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,6,3,2,1,12,10,8,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,6,3,2,1,12,11,8,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,6,3,2,1,12,10,9,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,6,3,2,1,12,11,9,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,6,3,2,1,12,11,10,7,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,6,3,2,1,12,10,9,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,6,3,2,1,12,11,9,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,6,3,2,1,12,11,10,8,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,6,3,2,1,12,11,10,9,5,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,5,3,2,1,12,10,8,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,5,3,2,1,12,11,8,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,5,3,2,1,12,10,9,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,5,3,2,1,12,11,9,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,5,3,2,1,12,11,10,7,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,5,3,2,1,12,10,9,8,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,5,3,2,1,12,11,9,8,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,5,3,2,1,12,11,10,8,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,5,3,2,1,12,11,10,9,6,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,6,5,3,2,1,12,10,9,8,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,6,5,3,2,1,12,11,9,8,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,6,5,3,2,1,12,11,10,8,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,6,5,3,2,1,12,11,10,9,7,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[7,6,5,3,2,1,12,11,10,9,8,4] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,9,4,3,2,1,12,10,8,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,9,4,3,2,1,12,11,8,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,8,4,3,2,1,12,10,9,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,8,4,3,2,1,12,11,9,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,8,4,3,2,1,12,11,10,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,7,4,3,2,1,12,10,9,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,7,4,3,2,1,12,11,9,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,7,4,3,2,1,12,11,10,8,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,7,4,3,2,1,12,11,10,9,6,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,6,4,3,2,1,12,10,9,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,6,4,3,2,1,12,11,9,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,6,4,3,2,1,12,11,10,8,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,6,4,3,2,1,12,11,10,9,7,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[7,6,4,3,2,1,12,11,10,9,8,5] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[11,5,4,3,2,1,12,10,9,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[10,5,4,3,2,1,12,11,9,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[9,5,4,3,2,1,12,11,10,8,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[8,5,4,3,2,1,12,11,10,9,7,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[7,5,4,3,2,1,12,11,10,9,8,6] => [[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => 11111011111
[6,1,4,2,3,5,8,7] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,6,1,4,2,3,5,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,8,1,4,2,3,5,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[8,1,4,2,3,6,5,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[4,1,8,2,3,6,5,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[8,2,3,6,1,4,5,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,2,3,8,1,4,5,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[4,6,2,3,8,1,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,8,2,3,6,1,5,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[8,2,3,6,4,1,5,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[8,4,3,6,2,1,5,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,2,3,8,4,1,5,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[8,4,2,3,6,1,5,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[6,4,2,3,8,1,5,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[2,6,4,3,8,1,5,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,8,4,3,6,1,5,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,6,3,8,4,1,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[6,3,8,4,2,1,5,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,6,3,8,1,4,5,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,8,3,6,1,4,5,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[8,3,6,4,2,1,5,7] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[2,8,3,6,4,1,5,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[8,3,6,2,4,1,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,3,6,2,1,4,5,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,2,1,3,8,4,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[8,2,1,3,6,4,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[6,3,8,2,4,1,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,2,4,3,8,1,5,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,6,4,7,8,5,1,2] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,6,4,2,7,5,8,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[3,6,4,2,7,1,5,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,4,7,2,5,6,8,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[6,4,8,5,3,7,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,6,5,4,2,7,8,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,2,5,3,6,1,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[7,1,5,3,6,2,8,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[1,6,5,2,4,8,7,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,4,6,2,8,5,7,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[7,8,1,4,2,5,6,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[3,4,8,5,2,1,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[4,8,5,3,1,6,2,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[6,1,3,5,8,2,7,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[6,1,8,7,4,2,3,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[1,2,8,5,7,3,6,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,3,6,8,7,5,2,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,8,2,5,4,7,6,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,1,2,4,5,8,6,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[1,2,7,3,5,8,6,4] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[6,1,3,2,5,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,6,2,1,7,5,3,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,6,3,7,8,5,2,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[4,6,2,3,7,8,1,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[4,6,3,7,1,2,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,2,1,3,5,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,3,2,4,5,1,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[3,8,2,5,4,1,7,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[7,8,4,2,6,3,1,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[4,2,6,3,8,7,1,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,8,2,7,4,3,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,3,8,5,1,7,2,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,3,6,8,1,2,7,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[6,4,3,5,2,8,1,7] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[6,5,3,8,4,2,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,1,7,2,8,3,9,4,10,5] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[6,1,7,8,9,10,2,3,4,5] => [[1,3,4,5,6],[2,7,8,9,10]] => 100001000
[7,1,8,2,9,3,10,4,11,5,12,6] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => 10101010101
[1,8,6,7,5,3,4,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,5,8,7,2,6,4,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,4,8,6,2,3,7,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,7,6,1,3,5,4,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[6,4,1,8,2,5,7,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[2,8,6,1,3,5,4,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,1,3,6,5,8,7,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,6,3,5,8,7,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,4,1,3,8,5,7,6] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,4,1,3,5,8,7,6] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,6,1,3,5,8,7,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,6,1,3,5,8,7,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[6,1,4,3,5,8,7,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[6,4,1,3,5,8,7,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,2,1,3,5,8,7,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,2,1,3,6,5,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[4,2,1,6,3,5,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[6,2,1,8,3,5,7,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[6,2,1,3,8,5,7,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,1,4,3,8,5,7,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,6,4,3,8,5,7,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[8,1,4,3,6,5,7,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,4,1,3,6,5,7,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,2,1,3,6,5,7,4] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,2,1,6,3,5,7,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,2,1,4,3,5,7,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,2,1,4,3,5,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,2,4,1,3,5,7,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,2,6,1,3,5,7,4] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,4,6,1,3,5,7,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,4,1,6,3,5,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,1,4,6,3,5,7,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,8,4,6,3,5,7,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,6,4,8,3,5,7,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,4,1,8,3,5,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[6,4,8,1,3,5,7,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,2,8,1,3,5,7,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,2,8,1,3,5,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[2,6,8,1,3,5,7,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,6,8,1,3,5,7,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,6,1,8,3,5,7,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[4,1,6,8,3,5,7,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[1,4,6,3,8,5,7,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[4,6,1,3,8,5,7,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,4,1,8,3,5,7,6] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,1,6,8,3,5,7,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[4,1,3,6,8,5,7,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[1,4,3,6,8,5,7,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[4,1,3,8,6,5,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,8,3,6,5,7,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,6,4,3,5,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,6,1,4,3,5,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[2,8,1,4,3,5,7,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,8,1,6,3,5,7,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,8,1,3,6,5,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,4,8,3,6,5,7,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,4,8,6,3,5,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,1,8,6,3,5,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,8,1,6,3,5,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,8,6,1,3,5,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,8,6,1,3,5,7,4] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,8,4,1,3,5,7,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,6,4,1,3,5,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,6,2,1,3,5,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[6,8,1,4,3,5,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,1,8,4,3,5,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[1,6,8,4,3,5,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,8,6,4,3,5,7,2] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[8,1,6,4,3,5,7,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,6,1,4,3,5,7,2] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,6,4,1,3,5,7,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,6,2,1,3,5,7,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,4,2,1,3,5,7,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,8,6,5,2,1,4,3] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,7,4,1,8,6,3,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,6,4,2,8,3,7,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,6,4,2,7,3,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[5,7,1,4,6,3,2,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[5,8,1,4,6,3,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,6,7,4,5,8,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,5,7,4,6,8,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,8,4,1,7,2,5,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,4,6,1,7,8,3,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[5,6,4,1,8,7,3,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[3,5,8,4,6,7,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,6,8,4,5,7,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,7,8,4,5,6,2,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,8,1,4,5,3,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,7,1,4,5,3,2,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,7,1,5,4,6,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[3,8,1,5,4,6,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,7,1,5,4,6,8,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,7,1,4,5,3,8,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,7,1,4,6,3,8,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,6,4,2,7,3,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,4,7,2,8,3,1,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[5,4,7,2,8,3,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,6,4,2,8,3,1,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[5,8,1,4,6,3,2,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,8,1,5,4,6,2,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[3,6,1,5,4,2,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,6,1,5,4,8,2,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,8,3,1,4,2,5,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[7,3,8,1,4,2,5,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,7,3,1,4,2,8,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[3,6,1,5,4,7,8,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,4,1,2,7,6,5,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,4,1,2,6,8,7,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[6,8,3,1,4,7,2,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[6,4,7,2,8,5,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,8,1,4,7,3,2,6] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,8,1,4,5,3,2,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,8,1,5,4,7,2,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,6,1,5,4,8,7,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[3,6,1,5,4,7,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,7,3,1,4,2,5,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[6,8,3,1,4,2,7,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[7,8,3,1,4,6,2,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[7,8,4,2,6,5,1,3] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[6,5,8,7,3,4,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[7,8,3,1,4,6,5,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,7,3,1,4,5,2,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,7,1,5,4,2,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,8,1,5,4,2,7,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[5,8,1,4,7,3,6,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[6,8,4,2,7,5,3,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,4,7,2,8,5,3,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,3,7,1,4,8,5,2] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,8,3,1,4,7,5,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[3,7,1,5,4,8,6,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[3,4,1,2,8,5,7,6] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,4,1,2,5,8,7,6] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,7,1,5,4,2,8,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,7,3,1,4,5,8,2] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[7,3,8,1,4,5,2,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,3,8,1,4,5,6,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[6,8,3,1,4,5,2,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,8,1,5,4,2,6,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[9,8,7,6,5,4,2,1,3] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[9,8,7,6,5,3,2,1,4] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[8,7,6,3,5,2,1,4] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[9,8,7,6,4,3,2,1,5] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[8,7,4,6,3,2,1,5] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[9,8,7,5,4,3,2,1,6] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[8,5,7,4,3,2,1,6] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[9,8,6,5,4,3,2,1,7] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[9,7,6,5,4,3,2,1,8] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110
[9,8,7,6,5,4,1,3,2] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[10,9,8,7,6,5,4,2,1,3] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[9,8,7,6,5,2,4,1,3] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[10,9,8,7,6,5,3,2,1,4] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[10,9,8,7,6,4,3,2,1,5] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[8,7,6,2,5,4,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[10,9,8,7,5,4,3,2,1,6] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[8,5,4,7,3,2,1,6] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[8,7,3,6,5,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[10,9,8,6,5,4,3,2,1,7] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[6,5,8,4,3,2,1,7] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[8,4,7,6,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[9,6,8,5,4,3,2,1,7] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[10,9,7,6,5,4,3,2,1,8] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[5,8,7,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[10,8,7,6,5,4,3,2,1,9] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110
[5,8,6,2,3,4,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,5,2,7,3,1,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[4,8,2,6,3,5,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,1,7,2,5,8,6,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[1,6,2,5,8,4,3,7] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[7,3,1,6,8,5,2,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,2,7,1,8,6,3,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,5,2,8,1,7,3,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[2,8,3,5,1,7,4,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[5,4,3,8,7,1,6,2] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[8,5,4,3,7,2,6,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,3,7,4,2,6,5,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[2,8,6,5,1,7,4,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[6,3,2,8,4,1,7,5] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,8,3,4,1,7,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[5,4,2,8,3,1,7,6] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,8,4,3,1,7,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,8,5,3,1,7,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,8,6,4,1,7,5,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,8,7,5,1,6,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[8,3,7,5,2,6,4,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,4,7,6,2,5,3,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[4,8,7,6,1,5,3,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[7,4,8,6,2,1,5,3] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[7,3,8,5,2,1,6,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,3,8,4,2,1,6,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,5,4,3,8,2,1,6] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[3,7,8,4,1,2,6,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[3,7,8,5,1,2,6,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,7,8,6,1,2,5,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,7,4,6,3,5,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[5,7,8,6,1,2,4,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[6,4,7,8,3,1,2,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,3,4,8,2,1,5,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,6,4,8,3,2,1,5] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[7,5,8,6,2,1,4,3] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[6,5,8,7,3,1,4,2] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[2,4,8,3,1,5,7,6] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[6,3,2,4,8,1,5,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[2,3,8,4,1,6,7,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[2,3,8,5,1,6,7,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[6,4,8,7,3,1,5,2] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[8,6,4,7,3,2,5,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,3,4,7,2,5,6,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[3,4,8,7,1,5,6,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,4,8,6,1,5,7,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,5,8,6,1,4,7,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[8,3,5,7,2,4,6,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,4,6,7,2,3,5,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,6,8,7,1,3,5,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[2,6,8,5,1,3,7,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[2,6,8,4,1,3,7,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[2,5,8,3,1,4,7,6] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[5,6,8,7,1,3,4,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[7,4,6,8,2,1,3,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,3,5,4,1,8,6,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[2,3,6,4,8,1,5,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,8,4,6,3,5,2,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[5,4,8,6,2,1,3,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,3,6,8,1,5,4,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[2,5,6,1,4,7,8,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[2,5,6,1,4,7,3,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[7,3,5,1,6,8,4,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[2,7,6,1,8,5,4,3] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,7,6,8,1,4,5,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[1,8,7,6,3,2,5,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,8,7,6,3,2,4,5] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[5,7,8,6,2,3,4,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[2,7,6,1,8,5,3,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[6,3,5,1,7,2,4,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[2,3,4,7,6,1,5,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[7,3,5,8,4,1,2,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[1,8,4,5,2,7,3,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,8,4,5,2,7,6,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,3,5,8,4,1,6,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[2,7,6,4,8,5,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[7,3,5,4,6,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,3,5,4,7,1,8,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,3,5,4,7,1,2,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,4,1,5,6,8,7,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,7,1,6,8,5,2,4] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[2,3,1,8,6,4,7,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,8,4,3,6,2,5,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,3,1,8,6,4,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[3,7,1,6,8,5,4,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,3,5,4,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[7,3,5,4,6,8,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[2,7,6,4,8,5,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,8,4,5,2,6,3,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[6,4,8,5,3,1,2,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[7,3,5,8,4,6,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,3,4,6,5,8,1,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,3,4,7,5,1,8,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,3,4,7,5,1,6,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[2,3,4,7,1,6,5,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,3,4,7,1,6,8,5] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,3,4,6,1,8,7,5] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[6,3,5,8,4,2,7,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,4,8,5,3,2,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,8,4,5,2,3,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[7,4,8,5,3,2,6,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[6,3,5,8,4,2,1,7] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[5,2,4,6,8,3,7,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[1,5,7,4,6,3,2,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,2,8,4,6,3,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,8,5,4,6,7,2,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[6,8,3,4,5,7,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[2,5,7,4,6,3,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,4,1,7,8,3,2,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,4,2,7,8,3,6,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,1,4,6,8,3,2,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[5,1,8,4,6,3,2,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[8,1,6,4,5,3,2,7] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,1,3,5,4,6,2,7] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,1,6,2,4,3,5,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,7,1,2,4,3,5,6] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[1,7,6,2,4,3,5,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[8,7,3,2,4,6,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,2,6,3,4,5,7,1] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[1,7,6,3,4,5,2,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,7,2,5,4,3,6,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[8,7,2,4,5,3,6,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[5,8,2,4,7,3,6,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[6,8,3,2,4,7,5,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[8,7,1,3,4,5,2,6] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,1,6,3,4,5,2,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,1,2,5,4,3,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[3,4,8,7,5,2,6,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[3,2,8,6,1,5,4,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,6,1,2,4,3,5,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[8,7,3,6,4,2,5,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[3,8,7,2,5,4,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,7,2,4,5,6,3,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[5,3,6,2,4,8,7,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[3,5,2,8,6,1,4,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,7,2,5,1,4,8,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[5,1,8,6,2,3,4,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,5,4,1,8,6,3,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[3,7,6,1,8,2,5,4] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[7,6,3,1,8,2,4,5] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,2,3,6,1,4,7,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[1,8,2,6,3,4,7,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[8,1,3,6,4,7,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,1,3,6,4,8,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,2,1,3,5,7,4,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,2,6,3,1,4,7,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,5,4,1,3,8,2,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[2,7,5,8,3,4,1,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[7,3,8,5,4,1,2,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[7,2,3,6,1,4,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[1,3,7,2,5,8,4,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,7,2,3,5,8,4,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[7,4,8,1,3,6,2,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,1,2,3,5,7,4,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,1,2,3,5,8,4,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[8,6,1,4,7,3,2,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[2,6,3,7,1,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[2,6,3,8,1,4,7,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[7,5,4,8,1,3,2,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,5,4,7,1,3,2,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,3,1,8,5,4,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[8,6,5,1,3,4,2,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,5,1,7,6,3,4,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[3,4,7,6,1,8,5,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,5,2,6,7,1,8,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[3,2,8,4,7,5,1,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[8,4,7,5,1,3,2,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[3,8,1,6,5,2,7,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,1,2,8,3,4,7,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,8,3,1,7,2,4,5] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,7,2,5,6,1,8,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[6,8,4,2,5,1,7,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,7,5,3,8,4,1,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[8,3,1,4,7,2,6,5] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,3,2,1,5,7,4,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[2,8,3,6,4,7,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[7,3,6,4,8,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,3,6,4,7,1,2,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[1,2,8,3,5,7,4,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,8,3,2,5,7,4,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[6,5,1,7,4,2,8,3] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,3,6,4,8,2,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[4,6,1,7,3,5,2,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,6,1,7,3,4,2,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[6,1,7,3,4,2,8,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[7,3,8,1,6,5,2,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,3,7,1,6,5,2,4] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,1,7,4,2,8,6,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[2,8,1,7,6,5,3,4] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,2,8,6,5,1,7,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,4,2,8,5,1,7,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,6,4,7,1,5,2,3] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,6,4,8,1,5,2,3] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[5,1,6,4,2,3,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,2,3,8,7,5,1,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,8,7,1,6,5,2,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[2,4,3,8,1,6,7,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[2,4,3,7,1,6,8,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[4,2,3,7,8,5,1,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,1,6,4,2,3,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[6,4,7,8,1,5,2,3] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[8,7,4,6,1,5,2,3] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,5,7,8,1,4,2,3] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[4,7,8,6,1,5,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[3,2,4,7,8,1,5,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[3,2,4,8,7,1,5,6] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,8,7,6,1,5,2,3] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,8,7,6,1,4,2,3] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[8,6,5,7,1,4,2,3] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,1,6,7,4,2,3,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[6,7,4,8,1,5,2,3] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[8,4,7,6,1,5,2,3] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,3,2,4,7,1,5,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,3,2,4,8,1,5,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[2,5,3,7,1,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[8,4,6,7,1,5,2,3] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[7,4,6,8,1,5,2,3] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,1,6,8,4,2,3,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,2,3,7,5,1,6,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,7,5,8,1,6,2,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[2,4,3,7,1,6,5,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,4,7,1,5,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,2,4,7,6,1,5,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,7,6,8,1,5,2,3] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[8,5,6,7,1,4,2,3] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[8,6,7,5,1,4,2,3] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,6,8,5,1,4,2,3] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,8,7,5,1,4,2,3] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,6,8,7,1,4,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,6,8,7,1,5,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,4,6,7,1,5,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,2,4,6,1,5,7,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,7,8,5,1,4,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[7,8,6,5,1,4,2,3] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,1,7,5,4,2,8,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,1,8,5,4,6,3,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,1,8,5,2,3,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,4,1,3,6,7,2,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,4,1,2,6,3,7,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,2,7,1,5,3,4,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[3,2,7,1,5,8,4,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[6,3,7,1,5,4,2,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,3,8,1,5,4,2,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,1,5,3,8,4,2,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,5,1,3,6,8,2,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,6,8,1,5,4,2,7] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,8,3,1,5,4,2,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,6,3,1,5,4,2,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[3,6,2,1,5,8,4,7] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[8,6,2,1,5,3,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,8,2,1,7,5,3,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[2,3,8,1,5,7,4,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,1,3,2,8,6,4,5] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,1,6,2,8,3,4,5] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[4,7,1,2,6,3,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,7,8,1,5,3,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,7,2,1,5,3,4,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[4,7,2,1,8,5,3,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[8,7,2,1,4,5,3,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,7,5,6,1,4,3,2] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[5,7,8,6,1,4,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[2,7,4,1,6,5,3,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,7,1,4,5,6,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,1,6,4,5,8,3,2] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[3,5,1,4,7,6,8,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,6,4,1,7,5,3,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[5,6,8,7,1,4,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[6,8,5,7,1,4,3,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[8,6,5,7,1,4,3,2] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[8,5,7,6,1,4,3,2] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[6,5,7,8,1,4,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,2,3,1,5,6,4,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[4,2,8,1,6,5,3,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,2,4,1,8,5,3,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[8,3,1,4,5,6,7,2] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,3,1,4,8,6,7,2] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,5,1,6,3,4,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,1,5,8,4,3,6,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[5,8,1,6,4,3,7,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[5,3,1,8,4,6,7,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[8,3,1,5,4,6,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,2,6,1,4,5,3,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,2,8,1,4,5,3,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,2,6,1,5,3,4,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[2,8,6,1,5,3,4,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,2,1,5,6,3,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[7,1,2,5,8,3,4,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,1,4,5,6,8,3,2] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,5,6,7,1,4,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,6,8,5,1,4,3,2] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[6,8,7,5,1,4,3,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[2,6,7,1,4,5,3,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,5,1,7,4,6,8,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[7,1,5,6,4,8,3,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[7,1,6,5,4,8,3,2] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[2,7,6,1,4,5,3,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,7,6,8,1,4,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[7,8,6,5,1,4,3,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[4,3,1,6,5,8,7,2] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[5,3,1,2,4,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,3,6,2,1,8,7,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,3,7,2,1,4,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,3,7,2,8,4,1,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[7,2,4,5,8,3,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,2,4,5,1,3,6,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,2,4,5,1,8,7,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,1,4,5,2,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[1,6,4,5,2,8,7,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,7,4,5,1,2,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[3,7,4,5,8,2,1,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,7,4,2,6,3,5,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[8,7,4,5,2,1,6,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,3,7,1,8,4,2,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,7,4,1,6,3,2,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[1,7,4,8,6,3,2,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,7,4,8,6,3,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,8,3,5,6,7,1,2] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[1,8,3,5,6,7,2,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[4,8,1,5,6,7,2,3] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[4,1,3,5,6,7,2,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[5,8,4,3,6,1,2,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,3,8,4,1,7,2,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,5,8,4,6,7,3,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,4,8,3,6,7,5,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,3,8,2,1,7,5,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[3,8,4,2,6,1,5,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,8,2,5,6,7,4,3] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[3,8,1,5,6,7,4,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,8,2,5,6,7,1,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,2,1,5,6,7,4,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,1,3,5,6,7,4,2] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[7,1,4,3,6,2,5,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,8,4,3,6,2,1,5] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[4,3,1,8,5,7,6,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,3,1,6,8,7,5,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,3,1,8,2,7,4,5] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[6,3,5,8,2,7,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,5,4,8,6,2,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[7,1,4,8,6,2,3,5] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[7,5,4,1,6,2,3,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,6,4,5,8,1,3,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[1,6,4,5,8,2,3,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[7,3,6,1,8,2,4,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[1,7,6,5,8,3,4,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[1,8,5,3,6,7,4,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[8,3,5,2,1,7,4,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,4,1,5,6,7,3,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,4,2,5,6,7,1,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,1,8,5,6,7,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[1,2,8,5,6,7,3,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[4,2,1,5,6,7,3,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,5,3,8,6,7,4,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,4,5,8,6,7,3,2] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[4,3,5,8,1,7,2,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[3,5,4,8,6,1,2,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,4,8,5,6,7,2,3] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[3,4,8,5,6,7,1,2] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[2,7,1,5,6,3,4,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,7,1,4,3,6,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,3,7,2,5,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[2,6,3,1,4,5,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[3,7,1,4,2,6,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,7,1,5,6,2,8,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,7,1,5,6,8,2,3] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[8,5,2,6,7,3,1,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,4,2,6,3,7,1,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,4,2,3,5,7,1,6] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,7,3,2,5,6,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,3,4,6,2,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,3,7,4,2,8,1,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[6,4,7,2,3,8,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,5,7,2,8,3,1,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[5,3,7,2,4,8,6,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[2,6,5,1,8,3,4,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[8,7,6,1,4,5,2,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,6,1,3,2,5,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,7,2,4,3,1,6,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,7,4,5,1,6,2,3] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,5,6,4,1,7,2,3] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,5,6,3,1,2,7,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[8,4,6,2,3,1,7,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,3,5,4,2,1,7,6] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[5,7,3,4,2,1,8,6] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,7,4,2,3,1,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,7,5,3,1,2,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[6,7,5,4,1,8,2,3] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[10,3,1,2,4,5,6,7,8,9] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[10,4,1,2,3,5,6,7,8,9] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[5,10,1,2,3,4,6,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[10,6,1,2,3,4,5,7,8,9] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[10,7,1,2,3,4,5,6,8,9] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[8,10,1,2,3,4,5,6,7,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[2,3,10,1,4,5,6,7,8,9] => [[1,2,3,6,7,8,9,10],[4,5]] => 001000000
[4,3,1,10,2,5,6,7,8,9] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[8,9,1,2,3,4,5,6,10,7] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[7,3,5,4,1,8,6,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[2,6,5,7,3,1,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,3,2,4,7,5,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,2,1,6,3,7,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,2,1,6,3,7,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[4,2,1,3,7,8,6,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,8,1,7,4,3,2,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,2,1,8,3,5,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,2,1,6,3,8,7,5] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,3,4,2,6,8,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,6,7,5,2,4,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,6,7,5,2,4,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,2,1,7,3,6,5,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,7,6,8,4,2,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,8,1,7,4,2,6,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[3,7,8,6,2,4,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[4,2,1,3,5,8,6,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[4,2,1,8,3,7,6,5] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[2,6,1,5,4,7,8,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,6,3,5,8,7,1,2] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[3,5,6,1,4,8,7,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,7,5,1,8,3,4,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[4,7,5,2,1,3,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,5,6,2,4,1,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,5,6,1,4,8,3,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[6,7,8,4,1,5,3,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[7,1,6,8,4,5,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,4,6,5,2,8,1,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,1,5,6,4,2,3,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[5,7,4,6,8,1,3,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[5,7,8,1,4,6,3,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[8,1,5,7,4,6,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[1,8,4,6,7,5,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[6,1,8,4,7,5,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,5,8,6,1,7,3,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,8,5,1,6,7,3,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[8,1,4,5,6,7,3,2] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[5,6,7,1,4,2,3,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[8,4,2,6,1,5,7,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[4,8,5,2,1,6,7,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,1,8,4,2,6,3,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,8,4,6,2,5,3,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[6,1,5,2,3,4,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,3,1,4,6,2,5,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,1,8,2,5,6,4,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,5,1,8,2,6,4,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,5,1,2,8,4,7,6] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,3,5,8,6,1,7,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[8,2,4,3,6,7,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,2,8,5,7,1,6,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[3,6,2,8,5,1,7,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[6,2,1,8,4,7,5,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[2,8,7,1,4,6,5,3] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,2,7,1,5,4,6,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,2,5,3,6,8,1,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,3,1,5,6,2,4,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,7,5,1,6,2,4,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,7,3,6,5,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,7,2,4,1,6,5,3] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[1,8,7,2,3,6,5,4] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,7,8,2,6,4,3,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,7,3,8,2,6,4,5] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,2,7,3,6,4,5,8] => [[1,2,3,5,7,8],[4],[6]] => 0010100
[7,1,5,8,3,2,4,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[1,6,2,8,4,3,7,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,3,8,7,2,4,6,5] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,8,3,7,2,5,4,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[8,1,4,7,3,2,5,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[4,7,8,1,3,2,5,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[7,1,4,2,3,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[8,2,1,4,7,3,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[2,1,3,8,4,6,7,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,2,3,4,8,5,7,6] => [[1,2,3,4,5,7],[6],[8]] => 0000101
[2,4,7,5,6,8,3,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[2,4,8,7,5,6,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[2,5,3,8,4,7,6,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,8,5,7,3,6,4,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,1,8,5,2,7,6,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,8,6,3,4,5,7,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,5,7,3,4,8,6,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[8,3,7,6,1,4,5,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[3,1,7,8,2,5,6,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[7,3,8,5,1,6,4,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,5,1,2,3,4,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[4,8,1,5,2,7,3,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,1,2,5,3,8,7,6] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,3,6,8,7,5,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,4,1,8,2,7,6,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,4,8,1,2,5,3,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,7,3,1,4,8,5,2] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,4,1,6,8,2,7,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,4,7,1,2,8,6,3] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,7,4,1,2,8,3,5] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[6,5,1,2,3,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,5,1,2,3,4,8,7] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,7,4,1,2,5,3,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[2,4,6,3,5,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,4,6,3,7,2,5,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[8,6,2,5,3,1,7,4] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,2,3,4,5,1,7,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[1,8,3,4,2,7,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,8,3,4,1,6,7,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[8,7,2,3,1,6,5,4] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[3,8,2,4,6,1,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,2,4,3,1,6,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,5,8,2,3,1,7,6] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[5,1,4,3,7,2,6,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[6,1,3,5,7,2,4,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[2,1,4,7,5,3,6,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[7,1,3,6,2,5,4,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,1,3,6,2,4,7,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[2,1,8,3,7,5,4,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,1,8,2,5,6,3,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,1,5,8,2,7,3,4] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,5,2,8,1,6,7,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[6,2,5,8,1,4,7,3] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[3,2,8,5,1,6,7,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[8,2,7,1,4,6,5,3] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[1,3,8,2,5,7,4,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,8,7,1,6,4,5,3] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,8,7,1,5,6,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,4,8,5,6,1,7,2] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[8,3,7,4,1,6,5,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[1,4,8,6,2,7,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[8,4,5,7,1,6,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[3,5,6,8,4,1,7,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[6,2,3,1,5,4,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,2,3,1,4,6,5,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,2,3,1,4,5,7,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,5,1,3,2,4,7,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,5,1,3,2,6,4,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[2,6,1,4,5,3,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,6,4,1,5,2,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[4,5,6,1,3,2,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[4,5,7,1,2,6,3,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,7,4,1,2,6,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[6,7,1,4,2,5,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[2,7,1,3,5,6,4,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,6,1,2,4,3,7,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[2,8,1,3,4,6,7,5] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,8,1,2,5,3,6,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[3,8,4,1,2,5,7,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[1,2,6,7,5,3,8,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,7,5,3,2,8,4,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,6,7,5,3,8,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,6,5,7,2,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[1,3,8,2,6,5,7,4] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,2,5,7,6,3,4,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,3,4,8,2,5,7,6] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,5,7,6,2,3,4,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,5,3,8,2,6,4,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,4,8,3,2,5,7,6] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,4,8,3,5,7,6,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,2,4,8,3,5,7,6] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,3,8,4,2,6,7,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,4,8,2,3,5,7,6] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[6,5,7,3,8,2,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[4,2,6,7,5,8,3,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,7,5,2,1,8,4,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,4,8,7,5,2,1,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,7,5,2,8,4,6,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,6,8,3,1,7,2,4] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,1,4,8,3,2,7,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[3,4,7,1,8,6,2,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,4,6,8,2,1,5,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,8,2,5,6,1,4,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[3,5,2,8,6,4,1,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,2,5,7,3,8,6,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[7,4,2,5,3,8,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[3,1,2,8,5,6,4,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[5,2,1,6,8,3,4,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,2,6,8,4,1,3,7] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[1,5,6,8,3,4,2,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,5,8,1,6,3,2,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[4,5,1,6,8,3,2,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,5,7,3,8,2,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[6,4,3,7,8,2,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,4,3,1,7,8,2,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,5,3,1,7,8,2,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[7,1,3,5,4,8,2,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,5,2,8,1,4,3,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[5,7,3,8,4,6,1,2] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[1,4,5,7,3,8,6,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,6,3,7,8,5,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[5,3,6,7,8,4,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[1,5,3,6,7,8,4,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,6,1,7,3,8,5,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[6,3,7,1,8,4,5,2] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[6,7,2,4,8,1,5,3] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[2,6,1,4,7,3,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,2,5,6,7,8,1,4] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,2,3,6,7,8,4,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[6,7,1,3,2,8,4,5] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[6,2,7,1,3,4,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[5,2,1,7,3,8,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,4,2,7,1,8,3,5] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[4,2,6,3,7,8,1,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,2,6,3,7,8,5,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[6,7,3,8,2,4,5,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[3,6,2,7,4,1,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[6,7,3,2,1,4,8,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,1,8,3,4,2,5,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[7,2,4,1,8,3,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,2,4,8,6,1,3,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[7,3,4,8,6,2,1,5] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,5,7,2,1,8,6,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[6,7,8,3,2,5,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,3,7,8,2,5,4,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,6,7,4,8,5,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[6,2,4,7,1,8,5,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,6,2,7,1,8,5,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,7,4,8,5,2,6,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,3,7,8,5,2,6,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[2,5,7,8,1,6,3,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[6,3,7,1,8,2,5,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[1,6,4,7,8,2,5,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[2,5,6,1,7,8,4,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[5,6,1,2,7,8,4,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[6,7,2,1,8,5,3,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[6,7,2,8,5,4,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,6,7,4,8,5,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,8,2,4,6,3,5,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,5,7,4,3,6,2,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,8,4,5,3,6,2,7] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,8,5,3,4,7,2,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,8,2,4,6,3,7,5] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,8,2,5,4,6,7,3] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[3,6,2,7,1,4,5,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[1,4,7,5,2,6,8,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[4,6,5,3,7,1,8,2] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,2,3,8,6,7,1,5] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,2,4,8,1,3,7,6] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[6,2,5,4,8,3,7,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[6,4,3,5,8,2,7,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[5,2,3,4,8,1,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,5,2,4,7,1,6,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,3,4,8,1,6,2,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,5,3,7,1,6,2,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[7,6,3,8,5,1,2,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,2,6,7,3,8,1,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[1,5,7,4,2,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,3,7,2,8,6,4,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,4,3,7,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,5,3,6,8,2,7,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,3,6,5,7,8,1,2] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[4,2,3,5,6,8,1,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,2,6,7,3,8,5,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,2,5,6,8,1,7,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[6,4,5,2,3,8,7,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[6,4,2,5,3,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,6,4,7,5,2,3,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[8,6,2,7,4,5,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[4,6,2,5,3,8,7,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,6,5,2,3,8,7,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,8,2,7,4,5,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,8,7,2,4,5,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[2,6,4,5,8,7,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,6,4,8,7,5,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[8,2,4,6,7,5,3,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[4,2,6,8,7,5,3,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,2,6,5,8,7,3,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,2,3,6,8,7,5,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,4,8,7,2,5,3,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[6,4,8,7,5,2,3,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[4,6,5,8,7,2,3,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[8,2,6,4,7,5,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[4,6,8,2,7,5,3,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,6,5,8,2,7,3,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,1,8,6,4,7,5,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[6,8,7,4,2,5,3,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[9,2,4,6,8,1,3,5,7] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[9,4,6,8,1,2,3,5,7] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[9,6,8,1,2,3,4,5,7] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[3,5,7,9,1,2,4,6,8] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[5,7,9,1,2,3,4,6,8] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[7,9,1,2,3,4,5,6,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[10,9,8,7,6,5,2,4,1,3] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010
[10,9,4,8,3,7,2,6,1,5] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010
[10,9,8,7,2,4,6,1,3,5] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[6,10,5,9,2,4,8,1,3,7] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[10,9,2,4,6,8,1,3,5,7] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[10,3,5,7,9,1,2,4,6,8] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[10,5,7,9,1,2,3,4,6,8] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000
[10,7,9,1,2,3,4,5,6,8] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[4,2,5,6,3,8,1,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,2,5,7,4,8,3,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,5,2,1,4,7,6,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,7,3,2,5,8,4,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[3,2,6,4,8,1,5,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,3,6,4,7,8,5,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[7,5,1,8,3,4,6,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,7,8,2,6,3,4,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[7,1,6,3,5,8,4,2] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[6,3,1,7,8,4,5,2] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,3,6,7,4,1,8,2] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[7,3,1,2,5,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[1,6,3,5,2,4,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,4,8,2,7,5,1,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[6,3,2,8,5,7,4,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,8,4,7,2,5,6,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,4,8,1,5,3,7,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,4,8,1,6,2,7,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,8,4,6,7,3,5,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,1,6,3,4,5,7,2] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[7,6,5,4,1,2,8,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[5,7,6,8,3,4,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,8,1,6,5,7,4,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[4,6,8,2,5,3,7,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,2,3,7,6,1,8,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[8,1,2,4,6,7,3,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,2,3,7,4,8,6,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[5,2,6,8,4,3,1,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,8,1,5,4,3,6,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[7,2,4,8,5,3,6,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,7,5,1,8,4,6,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[2,7,8,5,4,6,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,7,4,3,8,6,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,8,1,6,3,5,2,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,3,1,7,4,2,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,1,8,2,4,5,7,6] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[8,1,3,7,6,2,4,5] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[2,3,6,8,7,1,4,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,3,2,8,5,7,1,6] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[3,6,4,2,8,5,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,7,3,2,5,1,8,6] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[3,2,4,7,5,8,6,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,2,3,8,6,5,1,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,4,3,5,1,8,6,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,2,8,1,4,6,5,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[4,7,8,3,1,2,6,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,7,8,2,1,3,6,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,1,6,8,2,3,7,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[4,5,1,2,8,3,7,6] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[4,6,2,8,1,3,7,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,6,2,8,4,7,1,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[3,2,6,8,4,7,1,5] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[4,2,6,8,3,1,7,5] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[4,2,5,1,8,3,7,6] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,1,2,5,8,3,7,6] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,2,4,1,3,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[4,2,5,3,8,1,7,6] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[3,2,5,4,8,7,1,6] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,1,4,2,3,8,7,6] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,4,1,3,2,8,7,6] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[5,4,3,1,2,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[3,5,1,4,8,7,2,6] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[2,5,6,8,7,3,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,4,5,1,8,7,2,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,3,6,8,2,1,7,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[2,4,6,8,3,7,5,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,4,5,2,8,7,1,6] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,3,1,4,2,8,7,6] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[5,3,2,1,4,8,7,6] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[4,3,2,5,8,1,7,6] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,2,4,5,8,7,1,6] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,2,1,3,4,8,7,6] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,1,2,3,4,8,7,6] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[8,6,2,5,4,1,3,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,5,7,4,2,8,3,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,7,5,3,8,2,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[8,2,1,6,3,4,5,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,3,5,6,2,4,1,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,6,2,1,3,5,4,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,1,2,3,4,6,5,7] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[6,2,3,7,8,4,5,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[7,5,8,2,6,3,4,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,3,1,6,5,8,4,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[1,5,6,7,3,4,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[6,7,8,2,1,4,5,3] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[8,4,7,6,2,1,3,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[5,3,8,4,7,2,6,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,1,3,7,6,4,2,5] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[5,3,1,7,8,6,2,4] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[3,5,8,2,7,1,6,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[6,2,8,5,3,1,7,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,2,6,4,7,1,3,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[3,4,2,8,5,1,7,6] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,8,6,5,2,1,7,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[8,3,7,4,2,5,6,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[4,8,5,7,2,1,3,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,4,1,8,2,6,7,5] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[8,4,6,3,7,1,5,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,8,3,4,1,5,7,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,1,7,6,2,8,4,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[6,8,2,5,7,4,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[2,8,5,6,7,1,3,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,5,7,6,3,1,8,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,2,8,3,1,5,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,5,7,3,8,4,6,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[4,2,7,1,8,5,3,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,2,1,8,7,5,6,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,3,6,7,1,5,4,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[1,3,7,5,8,6,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,7,8,4,3,1,6,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,7,4,5,8,3,6,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,5,7,1,4,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[7,2,8,5,1,4,6,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[1,6,5,3,8,4,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[5,7,4,8,3,6,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[4,8,6,1,3,5,2,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[1,8,3,2,4,7,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[8,4,3,2,5,7,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[3,6,4,8,2,5,7,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[4,3,7,2,5,8,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[3,2,4,7,8,5,6,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,6,4,3,8,5,1,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,8,2,1,6,4,5,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[8,2,1,3,4,5,7,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[4,6,8,3,2,1,5,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,2,6,8,5,4,1,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,3,8,2,5,4,1,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,2,5,3,8,7,6,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,8,2,6,5,3,1,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[2,6,8,5,4,1,3,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,1,8,6,5,4,2,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[5,4,8,7,3,2,6,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[6,4,8,3,7,2,5,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[4,7,3,6,2,1,8,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,4,3,7,1,8,2,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[7,3,8,5,1,4,2,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,4,8,7,6,2,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[3,8,1,5,7,4,6,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,8,5,7,3,1,6,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,5,4,8,3,7,6,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,8,3,6,7,1,5,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,7,8,3,1,6,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,7,5,3,6,4,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[4,6,1,3,8,7,5,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,8,2,1,7,4,5,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[3,7,1,6,4,2,8,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[3,1,2,7,5,6,8,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,6,1,2,7,5,8,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,7,6,2,5,8,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,6,2,5,8,7,4,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,5,2,3,6,7,4,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,7,2,6,3,8,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,3,2,4,8,7,5,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,7,2,4,6,1,8,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,3,7,2,8,1,4,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,3,2,8,7,5,1,4] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[7,3,8,2,6,5,1,4] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,4,8,7,2,5,1,3] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[2,5,4,8,1,7,6,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,2,8,1,7,6,3,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,2,1,3,8,7,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,6,1,8,7,5,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,6,1,2,8,7,4,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[7,5,2,8,1,6,4,3] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[2,7,6,8,1,5,4,3] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[7,8,5,1,6,2,4,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[7,4,8,6,1,2,5,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[7,2,1,8,3,6,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,8,7,1,6,4,3,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[7,6,5,4,3,2,9,8,1] => [[1,7],[2,8],[3],[4],[5],[6],[9]] => 11111011
[10,7,6,5,4,3,2,1,9,8] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[9,6,5,4,3,2,8,1,7] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[9,7,5,4,3,2,1,8,6] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[8,5,4,3,7,2,1,6] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[6,5,4,8,3,2,7,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[7,6,5,4,3,9,2,8,1] => [[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101
[7,6,4,3,2,8,5,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,6,5,4,3,2,9,7,1] => [[1,7],[2,8],[3],[4],[5],[6],[9]] => 11111011
[8,7,6,5,4,3,2,10,9,1] => [[1,8],[2,9],[3],[4],[5],[6],[7],[10]] => 111111011
[7,3,1,4,8,2,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,4,1,2,5,8,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,7,4,2,5,1,3,8] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,7,2,4,6,8,1,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[4,7,5,1,6,2,8,3] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[5,7,4,6,3,1,8,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,5,1,4,3,2,8,6] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,6,4,2,3,7,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[6,4,7,1,3,8,5,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[5,4,2,7,3,1,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[4,5,1,2,7,6,8,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,4,6,8,3,1,2,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,4,8,1,3,7,2,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[4,6,1,3,8,5,2,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[1,3,8,4,5,7,2,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[2,6,7,4,5,3,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,6,8,4,3,5,1,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,3,7,4,2,8,5,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[4,6,1,3,7,2,5,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[7,5,8,6,2,1,3,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,8,1,3,6,5,4,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,8,7,3,5,4,1,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[3,4,2,6,8,7,1,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,4,2,3,6,1,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,4,2,3,6,5,7,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,3,8,4,1,2,6,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[6,8,3,2,7,1,5,4] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[2,8,5,6,3,7,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[7,4,2,5,8,1,6,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[2,7,8,3,4,5,1,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[3,7,1,2,4,6,5,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[7,5,6,8,2,1,4,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[3,1,6,5,2,7,4,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,8,6,5,3,4,1,7] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,7,2,3,5,6,8,4] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[3,7,4,2,1,5,6,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[3,4,6,2,8,5,7,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[4,2,1,7,5,8,3,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[4,7,2,6,5,1,3,8] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[3,7,4,1,2,5,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,7,1,6,5,2,8,3] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,7,3,6,5,1,8,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,3,7,1,6,8,5,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,2,1,7,5,6,8,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,4,8,6,7,1,5] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,2,6,8,7,3,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,4,6,1,8,5,2,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,1,6,7,5,8,2,3] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,3,6,7,5,1,2,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,3,7,1,6,8,2,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[4,3,7,5,6,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,1,7,3,6,5,2,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,8,7,4,5,3,1,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[2,8,7,4,3,5,1,6] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[3,8,1,4,2,6,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,1,7,3,6,2,5,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,8,7,6,1,2,4,3] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,8,7,6,2,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,1,7,2,6,8,5,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,2,7,3,6,1,8,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,2,7,3,6,5,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,8,2,4,5,6,7,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,8,2,4,1,6,7,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[3,8,5,6,2,4,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,8,6,5,3,7,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[3,8,6,5,1,4,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,8,2,1,4,6,7,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,8,2,5,4,6,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,2,7,5,6,3,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,2,7,5,6,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,2,6,7,5,3,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,2,6,1,4,5,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[2,8,7,3,4,5,1,6] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[3,8,1,2,4,6,5,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,8,7,6,1,3,4,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,8,7,6,2,3,4,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[4,1,7,5,6,2,3,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,8,1,5,2,6,4,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,8,7,5,3,4,1,6] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[2,8,7,5,4,3,1,6] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[4,1,7,5,6,3,2,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,8,7,6,1,3,2,4] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,8,7,6,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[5,4,2,3,7,6,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,4,3,5,2,8,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,4,3,7,5,1,6,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,4,7,2,5,1,6,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,4,6,2,3,5,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,1,7,2,4,6,8,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,5,7,1,2,6,8,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,4,1,7,3,6,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,6,4,7,5,2,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,4,7,6,2,5,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,7,5,6,1,3,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,7,6,4,3,1,8,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,7,6,3,1,4,8,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[7,5,2,3,4,8,1,6] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,7,5,3,4,1,6,2] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,7,1,3,8,4,2,5] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[7,6,1,3,4,8,5,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,6,5,2,7,8,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,2,8,6,7,1,4,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,8,3,6,5,2,1,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[1,8,6,5,4,2,3,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,8,7,2,3,5,4,6] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,7,2,5,3,4,6] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[3,6,8,5,1,2,4,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,7,5,1,8,2,6,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[7,1,2,8,3,5,6,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,1,7,8,2,5,3,4] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,7,5,2,8,1,4,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[7,1,4,5,8,6,2,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,7,6,4,2,8,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[7,5,6,1,2,8,4,3] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[4,1,3,7,8,6,2,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,1,4,3,6,8,7,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,5,7,6,8,2,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[5,7,6,8,4,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,1,6,8,4,2,7,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[7,4,8,2,3,6,5,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,6,8,4,7,3,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[6,4,7,8,5,2,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,6,4,8,5,1,2,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,7,4,8,1,2,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[7,4,3,8,2,6,5,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,6,8,3,2,5,4,1] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[8,7,1,3,5,4,6,2] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,1,8,3,4,2,6,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,6,8,3,1,4,5,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[3,1,4,8,2,5,7,6] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[4,8,5,2,1,3,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,8,2,6,3,1,4,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,8,2,3,7,4,1,5] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[7,8,2,3,4,6,5,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,1,7,2,4,5,3,6] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,1,3,6,2,5,4,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[7,2,1,6,3,5,4,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[2,7,1,6,3,5,4,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[2,7,1,5,4,3,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,2,1,5,4,3,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,1,3,5,4,2,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[8,1,5,3,4,2,6,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,1,5,6,2,3,7,4] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,1,4,5,3,2,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[8,1,4,3,5,2,6,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[7,2,1,4,5,3,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[2,7,1,4,5,3,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[2,6,3,1,5,4,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,3,2,1,5,4,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,3,1,4,5,2,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,3,1,5,4,2,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,1,6,2,5,4,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[3,7,1,6,2,5,4,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[3,7,1,4,5,2,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,6,2,1,5,4,7,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[2,3,6,1,5,4,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[3,5,2,4,1,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,3,4,1,5,2,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[6,2,4,1,5,3,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,6,4,1,5,3,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,6,5,1,3,7,4,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[6,2,5,1,3,7,4,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,5,2,1,3,7,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,6,1,2,4,5,3,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[6,7,1,2,8,3,5,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,1,2,5,4,3,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[5,6,2,1,3,7,4,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,2,6,1,3,7,4,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[2,4,6,1,5,3,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[4,7,1,3,5,2,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,7,1,5,3,2,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[5,7,1,4,2,6,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,7,1,6,2,3,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,6,3,1,2,7,4,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,2,5,3,1,6,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,3,6,1,2,7,4,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[3,4,6,1,5,2,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[6,5,1,8,7,3,4,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,2,7,5,4,1,3,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,8,5,2,3,4,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[8,5,6,2,7,1,4,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,5,1,2,7,8,4,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,7,6,1,5,3,8,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[5,7,6,4,1,3,8,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,6,2,4,5,3,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[6,1,7,5,3,8,4,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,6,7,5,3,1,4,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,5,2,7,1,6,4,3] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,6,1,5,3,8,4,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[5,6,2,4,7,8,1,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,4,6,1,7,8,5,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[3,4,8,6,7,1,5,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,8,5,6,7,2,3,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[5,8,6,4,1,2,7,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,8,6,1,7,2,4,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,8,7,3,2,6,4,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[5,8,1,7,2,6,4,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[8,1,5,7,2,6,4,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,1,7,2,5,6,3,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,8,7,2,5,1,3,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,8,7,2,1,6,3,4] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[4,8,1,5,2,6,7,3] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,7,8,5,1,6,2,4] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,5,2,7,8,1,4,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,1,2,8,5,6,3,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[8,7,2,1,5,6,3,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,6,7,1,5,2,3,4] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,1,7,8,5,2,3,4] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,5,6,2,1,8,4,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,7,5,2,1,6,4,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[7,1,3,5,8,6,2,4] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,1,3,4,6,8,7,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,5,3,6,8,2,7,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[5,6,3,4,8,1,7,2] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[4,6,7,8,5,1,3,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,4,3,1,2,6,7,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,5,1,6,3,4,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,1,8,6,3,4,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,6,8,1,5,3,7,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[6,4,5,8,3,2,7,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,6,4,8,7,1,5,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,5,8,1,3,4,7,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,6,8,3,1,2,7,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[6,1,8,3,5,2,7,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,6,8,3,5,2,1,4] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[8,6,1,3,5,2,7,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,7,1,3,5,6,2,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,7,8,3,5,1,2,4] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[3,4,8,1,2,6,7,5] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,8,2,4,3,6,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,8,2,3,1,6,7,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,8,2,3,5,1,7,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,2,3,5,6,1,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,6,5,1,4,3,7,2] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[2,6,5,4,1,3,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,1,7,6,3,8,2,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,8,2,5,7,6,3,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,4,6,5,1,8,2,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,6,5,3,4,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,6,1,5,2,3,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[6,2,3,5,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[2,6,7,5,1,8,4,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[8,6,1,2,5,3,4,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[6,2,5,1,8,3,4,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,6,5,2,8,3,4,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[2,6,3,5,1,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,4,7,6,5,8,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,1,4,8,7,6,3,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,4,6,8,5,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[8,1,3,5,7,4,6,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,2,8,7,5,1,6,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[4,8,5,1,6,7,2,3] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,8,5,1,6,7,2,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[7,8,6,1,3,5,2,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,6,7,2,8,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,5,1,8,6,7,4,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,5,1,8,6,7,4,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[5,2,3,8,6,7,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[8,3,5,4,6,7,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,1,3,8,6,7,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,2,5,8,6,7,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,2,1,5,3,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[5,6,3,2,8,1,4,7] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[8,1,6,3,5,2,7,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,7,6,2,5,3,1,4] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[4,7,6,8,3,2,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,7,5,8,1,3,4,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[7,6,2,8,5,1,4,3] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[8,1,3,7,5,2,6,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,4,8,7,5,1,6,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,3,8,1,4,2,5,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,3,8,5,7,4,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,4,6,8,5,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[2,1,4,8,7,5,6,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[7,1,5,8,2,6,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,6,8,2,4,1,7,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,5,8,2,6,7,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,2,8,1,6,7,3,4] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,5,8,4,6,7,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,8,3,4,6,7,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,4,3,2,6,7,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[4,2,8,1,6,7,3,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,4,8,1,6,7,3,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[5,1,8,2,6,7,3,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,4,8,7,2,1,5,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,8,5,3,6,4,2,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[2,8,5,7,4,1,3,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,8,4,1,6,7,2,3] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[3,8,1,4,6,7,2,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[8,2,3,4,6,7,1,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,2,7,3,8,4,1,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[7,4,3,2,8,5,1,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,3,2,8,4,6,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,2,6,5,3,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,4,2,5,3,1,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,3,6,2,5,4,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,4,8,3,2,6,1,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[3,5,8,2,4,6,1,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,4,7,8,2,3,1,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,8,3,6,4,2,1,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,8,6,2,5,3,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,6,4,3,2,8,7,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,5,3,2,8,4,7,6] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[5,7,4,3,1,2,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,8,7,3,5,1,4,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[7,3,8,6,4,1,2,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,1,2,7,3,8,5,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[2,1,7,4,3,8,6,5] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[6,1,4,3,8,2,7,5] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[5,1,3,2,8,7,4,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[1,8,4,2,7,6,5,3] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,8,3,7,2,6,5,4] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,1,4,8,3,7,2,6] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[2,1,6,8,5,4,7,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,1,5,7,8,2,4,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,3,1,6,7,2,5,4] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[7,4,8,6,1,3,2,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,7,6,1,2,5,3,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[3,7,6,1,5,2,4,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,5,4,8,3,2,7,6] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[7,3,6,1,2,5,4,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,4,7,1,3,2,6,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,7,4,8,2,1,3,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,6,8,2,5,1,3,7] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[7,4,6,2,1,5,3,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[1,2,6,3,8,5,7,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[1,5,2,6,8,4,7,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,7,2,3,8,1,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[6,4,7,5,8,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[7,4,8,5,1,6,3,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[5,8,3,6,1,7,4,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[8,6,4,2,1,7,5,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[7,4,2,1,5,8,6,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,6,4,1,8,5,2,3] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[1,6,4,8,7,5,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,3,1,2,8,4,7,5] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,5,1,3,2,8,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[4,7,1,2,5,8,6,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[6,8,4,1,2,7,5,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,5,8,1,2,6,4,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[7,4,8,1,6,3,5,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,8,2,1,7,3,6,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[3,6,1,8,2,4,7,5] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[1,3,8,7,6,2,5,4] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[5,4,1,8,7,3,2,6] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,5,1,8,7,2,4,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,6,1,8,3,7,2,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,7,1,2,8,6,3,5] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[5,8,4,1,7,6,2,3] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,6,8,1,5,4,2,3] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,6,1,7,5,4,3,2] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[7,1,5,8,6,4,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[5,1,8,7,3,6,4,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[4,1,8,7,6,2,5,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[3,1,8,7,6,5,2,4] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[1,6,4,5,2,3,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,7,4,5,2,3,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,7,3,5,2,4,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,6,3,5,2,4,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,6,3,4,2,5,7,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,7,3,4,2,5,6,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,8,6,7,3,4,2,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,8,5,7,3,4,2,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,7,3,4,2,6,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,5,2,8,4,7,3,6] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,4,2,8,5,7,3,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,7,3,5,2,6,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,8,4,7,3,5,2,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,7,3,6,2,5,4,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,7,3,6,2,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,7,4,6,2,3,5,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,8,5,6,2,3,4,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,8,5,6,2,4,3,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,3,2,8,5,6,4,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,2,8,5,6,3,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,2,8,4,6,3,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,6,2,8,4,5,3,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[8,1,2,4,5,3,6,7] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[3,4,7,8,5,6,9,10,1,2] => [[1,2,3,4,7,8],[5,6],[9,10]] => 000100010
[1,8,9,6,7,4,5,2,3,10] => [[1,2,3,10],[4,5],[6,7],[8,9]] => 001010100
[1,6,7,8,9,4,5,2,3,10] => [[1,2,3,4,5,10],[6,7],[8,9]] => 000010100
[1,4,5,6,7,8,9,2,3,10] => [[1,2,3,4,5,6,7,10],[8,9]] => 000000100
[1,8,9,6,7,2,3,4,5,10] => [[1,2,3,8,9,10],[4,5],[6,7]] => 001010000
[1,6,7,8,9,2,3,4,5,10] => [[1,2,3,4,5,10],[6,7,8,9]] => 000010000
[1,2,7,8,5,6,3,4,9,10] => [[1,2,3,4,9,10],[5,6],[7,8]] => 000101000
[1,2,5,6,7,8,3,4,9,10] => [[1,2,3,4,5,6,9,10],[7,8]] => 000001000
[1,8,9,2,3,4,5,6,7,10] => [[1,2,3,6,7,8,9,10],[4,5]] => 001000000
[1,2,7,8,3,4,5,6,9,10] => [[1,2,3,4,7,8,9,10],[5,6]] => 000100000
[1,2,3,6,7,4,5,8,9,10] => [[1,2,3,4,5,8,9,10],[6,7]] => 000010000
[9,10,11,12,7,8,5,6,3,4,1,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[9,10,11,12,5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 00010001010
[7,8,9,10,11,12,3,4,5,6,1,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 00000100010
[11,12,9,10,5,6,7,8,1,2,3,4] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[11,12,7,8,9,10,1,2,3,4,5,6] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 01000100000
[1,2,5,6,7,8,9,10,3,4,11,12] => [[1,2,3,4,5,6,7,8,11,12],[9,10]] => 00000001000
[1,2,3,6,7,8,9,4,5,10,11,12] => [[1,2,3,4,5,6,7,10,11,12],[8,9]] => 00000010000
[1,2,9,10,3,4,5,6,7,8,11,12] => [[1,2,3,4,7,8,9,10,11,12],[5,6]] => 00010000000
[1,2,3,8,9,4,5,6,7,10,11,12] => [[1,2,3,4,5,8,9,10,11,12],[6,7]] => 00001000000
[1,2,3,4,7,8,5,6,9,10,11,12] => [[1,2,3,4,5,6,9,10,11,12],[7,8]] => 00000100000
[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
[8,6,4,7,2,1,3,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[1,6,4,7,2,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,4,7,3,5,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[8,4,6,2,3,5,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,4,8,2,3,6,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,4,8,5,2,3,1,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,8,6,2,4,5,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,8,6,2,3,5,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[1,7,5,3,4,8,2,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,7,6,4,8,2,3,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,8,7,4,1,2,3,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,8,5,3,4,1,2,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,3,7,2,1,4,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[8,5,1,6,3,7,2,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,1,3,7,4,8,2,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,1,7,3,5,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[7,1,6,4,8,2,3,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,8,5,7,2,3,4,6] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[6,1,5,8,2,3,4,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[5,1,7,3,8,2,4,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[6,1,5,7,8,2,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,4,8,6,1,2,3,5] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,8,7,5,1,2,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,7,6,1,2,4,5,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,7,6,1,2,3,5,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,6,5,8,2,3,4,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[6,5,8,4,1,2,3,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,5,7,4,1,2,3,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[1,5,7,4,8,2,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[7,6,4,8,2,1,3,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,6,2,3,8,1,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,4,8,5,1,6,2,3] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[8,6,2,3,1,7,4,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,6,4,1,2,7,3,5] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[1,7,2,8,6,3,4,5] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[7,6,1,3,8,2,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,5,8,1,3,6,2,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,4,1,8,2,3,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,4,8,7,2,3,5,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,5,8,7,2,3,4,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[6,5,1,8,2,3,4,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[5,7,1,3,8,2,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[7,6,8,1,5,2,3,4] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,1,5,8,6,2,3,4] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[6,1,8,2,7,3,4,5] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,1,8,7,2,3,5,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,1,8,7,2,3,4,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[1,8,7,6,4,5,3,2] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,8,7,3,6,5,4,2] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[7,1,5,8,3,4,2,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[7,1,4,3,2,5,6,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[6,4,2,3,8,5,7,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,4,2,7,5,8,3,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[2,4,1,7,5,8,3,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[7,1,4,6,5,2,3,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,1,4,6,5,8,2,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,1,4,6,3,8,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,1,4,3,2,5,8,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,1,4,6,5,2,8,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,1,4,6,5,3,8,2] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[7,1,4,6,5,3,2,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[6,4,2,7,5,3,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,4,7,2,6,8,5,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,4,7,1,6,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,4,7,1,6,8,5,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,4,1,7,5,3,6,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[3,4,1,7,8,6,2,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[6,4,2,3,8,5,1,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,4,2,7,5,8,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,4,2,7,5,3,1,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,4,7,2,6,8,1,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[5,4,7,3,6,8,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[3,4,7,2,6,5,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[4,8,3,2,5,6,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,8,7,3,5,1,2,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,8,7,1,3,5,2,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,8,3,1,2,6,5,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,4,7,1,6,2,5,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,4,7,1,6,2,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,4,7,2,6,5,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,8,3,1,2,6,7,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[5,8,1,6,3,4,2,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,8,5,1,3,7,2,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,8,5,1,3,4,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,8,3,4,2,6,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,4,7,3,6,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[5,4,7,2,6,1,8,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,4,3,7,5,1,2,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,4,3,7,5,1,8,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[6,2,4,3,1,5,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[3,8,7,4,1,5,2,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,4,7,3,6,1,5,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[5,8,3,2,1,6,4,7] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,8,7,4,3,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[5,4,7,3,6,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[7,3,8,2,1,6,5,4] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[7,4,3,8,5,2,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,5,2,8,4,3,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,3,2,8,6,5,1,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[4,3,8,7,5,1,6,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,2,5,8,6,1,4,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[8,4,3,7,5,2,6,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[4,3,7,8,5,1,2,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[5,3,7,8,4,1,2,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,2,5,8,3,1,4,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,2,4,8,3,1,5,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[5,2,3,8,4,1,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[5,3,8,7,4,1,6,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,3,2,8,6,4,1,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[7,5,3,8,4,2,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,7,5,3,6,2,4,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[8,6,5,3,7,2,4,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[7,5,4,3,8,2,6,1] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[6,4,5,3,8,2,7,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,4,6,3,8,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,5,6,3,8,2,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,5,6,3,7,2,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,4,6,3,5,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,4,6,3,5,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,4,7,3,5,2,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,5,7,3,4,2,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,5,8,4,3,2,6,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[6,5,8,4,3,2,7,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[6,5,8,3,4,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,5,8,3,4,2,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,5,8,4,6,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,4,8,3,6,2,5,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[7,4,8,3,5,2,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,4,8,3,5,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,4,7,3,5,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[5,4,8,3,7,2,6,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[6,5,8,3,7,2,4,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[6,5,8,4,7,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[6,5,8,4,7,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[6,4,7,3,8,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[5,4,7,3,8,2,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[5,4,6,3,8,2,7,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[5,3,6,2,4,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,3,6,1,4,8,7,2] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[5,3,7,2,4,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,3,1,5,6,8,7,2] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,2,1,5,8,6,3,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,2,1,5,8,6,7,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,2,1,5,8,7,6,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,3,1,5,7,8,6,2] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,3,1,7,5,8,6,2] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[6,7,3,1,4,8,2,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,3,7,1,4,8,2,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[4,3,1,5,7,8,2,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[3,2,1,8,5,4,6,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[3,2,1,8,5,7,4,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[3,2,1,8,7,5,4,6] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,2,7,1,8,4,3,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,7,2,1,8,4,3,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[6,7,2,1,8,4,5,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,2,1,8,5,6,4,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,2,1,8,6,5,4,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[4,3,1,6,7,8,5,2] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,2,1,6,8,7,5,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,2,1,6,8,5,7,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,2,1,6,8,5,3,7] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,2,6,1,8,4,3,7] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,2,6,1,8,7,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[5,2,6,1,8,7,3,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,2,6,1,8,3,4,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,2,1,6,8,3,7,5] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,3,1,6,7,8,2,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,7,3,1,5,8,2,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[4,2,1,7,8,6,3,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[3,2,1,8,7,6,4,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,2,1,8,6,4,7,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[3,2,1,8,6,4,5,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[3,2,1,8,4,6,5,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,2,1,8,4,6,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,1,8,4,7,6,5] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,2,1,8,7,4,6,5] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[4,2,1,7,8,3,6,5] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,2,7,1,8,3,6,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[6,7,2,1,8,3,5,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,2,7,1,8,3,4,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,2,1,7,8,3,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,2,1,8,4,5,7,6] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[7,5,2,8,6,3,4,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,4,8,6,2,5,3,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[7,3,8,6,2,4,5,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[7,4,3,1,8,2,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,4,2,8,5,6,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,3,8,5,2,4,6,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[7,3,8,4,5,6,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,3,8,2,4,5,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,3,8,2,5,7,4,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,4,3,8,1,5,2,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,3,7,8,2,4,1,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,6,7,3,8,2,4,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,4,7,2,6,8,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,3,8,2,4,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,3,8,2,4,7,5,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,7,4,2,6,8,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,4,8,2,7,5,1,3] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,5,3,1,4,2,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,7,4,2,6,1,3,8] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,6,4,2,3,8,1,7] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[5,6,3,7,8,2,4,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[5,6,3,8,2,4,7,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[6,3,7,2,4,5,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,3,7,2,5,8,4,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,3,6,8,2,4,7,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[5,4,6,2,3,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,3,6,7,8,2,4,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,6,4,2,1,5,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,5,8,6,4,2,1,7] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[5,8,6,3,4,2,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,6,3,4,2,1,8,7] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,3,4,2,1,5,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[5,6,4,2,1,3,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[2,5,4,1,7,8,6,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[2,7,8,5,4,1,6,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,8,5,4,1,6,3,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,6,3,8,5,4,1,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,8,6,3,5,4,1,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[5,8,6,4,2,1,3,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,2,1,5,7,8,6,3] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[2,7,8,6,3,5,4,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,3,8,5,7,6,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[7,6,2,1,8,4,3,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[2,1,8,5,6,4,3,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,2,1,8,5,6,3,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[8,4,2,1,5,6,3,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[2,5,6,3,8,4,1,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[6,3,4,2,1,8,5,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[3,7,8,5,6,4,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,8,5,6,4,2,1,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[3,6,4,2,1,8,5,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,8,6,4,2,1,5,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[3,7,8,6,4,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[8,5,3,7,6,2,4,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[7,6,2,4,1,8,5,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[8,5,4,1,7,6,2,3] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,6,2,3,8,5,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[2,1,7,8,6,4,3,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,1,6,4,3,7,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[6,4,2,1,3,7,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,3,7,8,4,2,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,8,4,2,1,6,3,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,7,6,2,3,8,4,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,6,1,8,4,3,7,5] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[2,6,1,7,5,8,4,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[8,4,2,3,7,5,6,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,5,7,6,2,1,4,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[4,8,5,7,6,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[4,7,6,2,1,3,8,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,5,6,1,8,4,2,3] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[2,7,5,8,4,3,6,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,8,4,3,6,1,7,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[6,4,7,8,3,2,1,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,6,5,4,3,2,8,1,9] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010
[6,9,8,5,4,3,2,1,7] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[8,7,9,6,5,4,3,2,1,10] => [[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => 101111110
[6,4,3,7,5,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,5,3,2,8,4,1,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[6,5,2,7,8,4,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,6,5,4,2,8,9,1,3] => [[1,6,7],[2,9],[3],[4],[5],[8]] => 11110010
[7,6,5,4,3,1,8,9,2] => [[1,7,8],[2,9],[3],[4],[5],[6]] => 11111001
[7,10,9,6,5,4,3,2,1,8] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[6,5,8,7,4,3,2,1,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[5,9,8,7,4,3,2,1,6] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[6,4,3,2,5,8,1,7] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,4,3,9,5,2,1,8] => [[1,5,9],[2,6],[3],[4],[7],[8]] => 11101110
[6,3,7,2,5,4,1,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,6,5,4,2,1,8,3,9] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 11111010
[6,3,2,7,5,4,1,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,7,6,5,4,2,9,10,1,3] => [[1,7,8],[2,10],[3],[4],[5],[6],[9]] => 111110010
[8,7,6,5,4,3,1,10,9,2] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 111111011
[8,4,2,6,3,1,7,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[1,5,3,7,4,2,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,6,7,3,4,2,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[8,6,5,2,3,1,7,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[1,7,6,3,4,2,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,8,6,3,2,5,7,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[8,7,5,2,1,4,6,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,8,5,2,1,4,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,8,5,2,3,1,7,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,8,6,2,3,1,7,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[4,8,2,6,3,1,7,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[3,2,8,6,4,1,7,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[3,2,1,7,5,4,8,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[4,1,3,7,5,2,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,1,7,3,4,2,8,6] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[7,1,6,3,2,5,8,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,2,7,4,3,6,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[6,1,8,2,4,5,7,3] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,1,8,3,2,6,7,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[3,2,8,7,1,5,6,4] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[4,8,2,7,1,5,6,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,8,7,2,1,4,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,8,7,1,3,4,5,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,8,6,1,3,4,5,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[1,7,8,2,4,5,6,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[8,6,7,1,3,4,5,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,6,8,1,3,4,5,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,5,8,2,3,1,7,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[1,6,8,3,2,5,7,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,5,3,8,2,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[8,4,2,7,1,5,6,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,4,2,8,1,5,6,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,4,2,8,3,1,7,5] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,4,2,3,8,1,7,6] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[4,5,2,3,1,6,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,4,2,1,3,6,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,4,2,1,3,6,7,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,5,3,2,4,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[8,5,1,3,2,6,7,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[5,6,1,3,4,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,6,2,1,5,3,8,7] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,7,2,1,3,6,8,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[5,7,1,3,2,6,8,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,7,1,2,4,5,8,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[8,6,1,2,4,5,7,3] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[1,8,2,3,5,6,7,4] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[8,7,1,2,4,5,6,3] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,8,1,2,4,5,6,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[5,8,1,3,2,6,7,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,8,2,1,3,6,7,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,1,3,2,5,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,1,2,4,3,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,4,8,1,2,3,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[1,4,7,6,3,2,5,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,8,3,2,7,6,1,5] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[4,3,8,2,7,1,6,5] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[4,3,2,8,1,7,6,5] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[4,1,8,7,3,2,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,7,8,1,2,5,3,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,3,6,7,4,1,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,6,3,4,7,8,1,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,1,7,8,4,2,5,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,7,8,2,6,4,1,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[3,7,2,4,8,6,1,5] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[1,3,6,4,7,2,5,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[4,7,1,5,8,2,3,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[8,7,5,2,6,3,4,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,6,5,2,7,3,4,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,4,8,5,6,3,2,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[3,4,6,7,8,5,1,2] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,6,4,7,5,8,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,1,7,5,4,2,6,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,3,8,5,4,7,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,6,2,5,4,7,8,3] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,8,2,5,6,3,7,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,2,6,4,8,5,7,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[7,8,3,1,4,2,5,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[4,8,1,5,2,3,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[7,4,1,5,2,3,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[5,6,1,8,4,3,2,7] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,1,8,6,4,3,2,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[5,1,6,3,8,7,2,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[6,1,2,5,8,3,7,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[6,1,8,7,4,3,2,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[7,1,2,5,4,8,6,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[1,2,7,5,8,3,6,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,1,6,3,7,5,2,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[1,3,6,7,8,5,2,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,6,4,7,8,5,3] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,1,6,3,7,8,2,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,1,6,4,8,2,7,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[7,8,4,1,6,3,2,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[4,1,6,3,8,7,2,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[7,5,1,8,4,3,2,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,5,1,7,4,3,2,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,1,8,5,2,3,7,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,1,6,8,3,7,2,5] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,4,6,1,3,8,2,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,5,8,1,4,3,2,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[1,3,5,7,4,6,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,3,5,4,7,2,6,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,3,5,4,7,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,3,5,4,7,2,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,3,5,7,4,8,2,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,3,5,7,4,8,6,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,3,5,7,8,4,2,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,6,3,2,7,4,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,5,1,6,2,8,7,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,3,7,2,5,4,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,3,7,5,2,4,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,5,7,4,3,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,5,3,7,4,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,2,6,7,8,1,5,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,5,2,7,8,4,1,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,5,7,4,8,3,2,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,5,2,6,8,4,7,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,5,7,4,3,8,6,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,5,7,2,4,8,6,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,6,3,7,2,8,5,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,4,7,3,8,6,2,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,1,6,8,2,4,3,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[5,3,7,8,2,4,1,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[8,5,3,7,2,4,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,2,4,7,3,1,5,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[2,4,7,8,3,1,5,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[6,3,1,5,8,2,4,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,5,3,4,2,8,1,7] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,2,4,3,8,1,6,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,2,4,8,1,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,2,4,6,8,1,5,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,1,5,7,3,2,4,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,4,6,7,2,3,1,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[4,6,7,8,2,3,1,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[7,4,6,8,2,3,1,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[7,2,4,8,3,1,5,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[5,3,8,7,2,4,1,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,4,8,7,3,1,5,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,6,8,7,2,3,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,7,4,6,2,3,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,6,8,7,2,3,1,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,4,8,7,2,3,1,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,1,7,4,2,8,6,5] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[3,2,8,4,1,7,6,5] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,6,4,8,2,3,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[5,7,6,8,2,3,1,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,7,6,8,2,3,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[8,6,4,7,2,3,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,2,3,7,4,1,6,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[2,3,7,8,4,1,6,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,7,4,8,2,5,1,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,3,7,4,1,6,8,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[8,1,6,4,2,3,7,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,7,8,6,2,3,1,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,4,7,3,1,5,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,3,1,7,4,2,8,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[8,5,7,6,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,5,8,6,2,3,1,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,1,6,4,2,3,8,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[3,1,7,6,4,2,8,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[4,8,7,6,2,3,1,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[6,8,7,5,2,3,1,4] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[4,3,6,1,5,8,7,2] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[4,3,6,5,1,8,7,2] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,6,3,5,1,8,7,2] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[4,6,3,1,5,8,7,2] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[4,1,6,5,3,8,7,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,6,1,5,3,8,7,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[2,6,5,3,1,8,7,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,6,5,1,8,7,3,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[2,6,5,8,1,7,3,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[2,6,5,8,1,3,7,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[2,6,5,8,3,1,7,4] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[2,6,5,3,8,1,7,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,6,1,5,8,3,7,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,1,6,5,8,3,7,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[1,4,6,5,8,3,7,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,1,6,5,8,7,3,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,6,5,3,8,7,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,4,3,8,7,1,5,2] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[6,4,8,3,7,1,5,2] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[2,6,8,5,3,7,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,6,8,1,5,7,3,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[4,6,1,8,5,7,3,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,1,6,8,5,7,3,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[1,4,6,8,5,7,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,4,6,8,5,3,7,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,6,1,8,5,3,7,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[2,6,8,5,3,1,7,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,6,8,5,1,7,3,4] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,6,8,3,5,1,7,2] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,6,8,3,1,5,7,2] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,6,3,1,8,5,7,2] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[4,6,3,8,1,5,7,2] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[4,6,3,8,5,7,1,2] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,3,6,8,1,5,7,2] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[4,3,6,1,8,5,7,2] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[4,3,1,6,8,5,7,2] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[4,1,3,6,8,7,5,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[4,3,6,1,8,7,5,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,3,6,8,1,7,5,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,5,2,8,7,3,1,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,5,2,8,7,1,3,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,2,5,8,7,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,2,5,8,7,3,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,6,3,8,1,7,5,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,6,3,1,8,7,5,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,1,6,3,8,7,5,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,4,6,3,8,7,5,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[4,1,6,8,3,7,5,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,6,1,8,3,7,5,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,6,8,1,3,7,5,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,2,8,5,7,3,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,2,8,5,7,1,3,4] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[2,4,8,7,1,5,3,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,2,8,7,5,3,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,4,1,8,7,5,3,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[6,1,4,8,7,5,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[1,6,4,8,7,3,5,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,4,1,8,7,3,5,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[4,2,8,7,5,1,3,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,4,8,7,3,5,1,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[2,3,4,5,6,8,9,7,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[2,3,4,5,7,8,9,6,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[2,4,5,6,7,8,9,3,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[2,3,4,7,8,5,6,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,3,7,1,4,8,6,5] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,6,1,3,7,8,5,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,3,4,5,6,7,10,1,8,9] => [[1,2,3,4,5,6,7,10],[8,9]] => 000000100
[1,5,3,2,6,4,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,5,3,2,6,7,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,3,2,8,5,4,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,3,2,7,5,4,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[6,5,2,4,3,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[6,4,2,5,3,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,4,7,6,2,3,1,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,6,4,8,2,1,5,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,6,2,8,5,3,4,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[4,6,2,3,7,5,1,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[4,7,2,3,6,5,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,7,2,3,5,6,1,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,3,2,7,4,6,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,3,2,6,4,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[4,6,2,3,5,7,1,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[3,5,2,1,6,8,4,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[1,5,2,6,8,4,3,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,5,7,2,8,4,3,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,2,1,8,6,4,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[3,6,8,4,2,1,5,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,3,2,6,1,8,5,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[1,5,8,2,7,4,3,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,7,2,3,4,8,6,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[6,8,2,3,4,1,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[4,1,8,2,3,5,7,6] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,3,1,8,4,5,7,6] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,3,2,1,4,5,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,8,1,4,3,5,2,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,1,2,3,4,6,8,5] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[6,1,2,3,4,8,7,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[1,8,2,3,4,7,6,5] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[8,1,2,3,4,6,7,5] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[2,8,1,3,5,4,7,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[8,7,1,4,3,5,2,6] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,3,2,1,4,5,7,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[3,8,2,1,5,6,4,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,8,2,1,6,5,4,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[1,7,8,3,5,4,2,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[7,4,1,8,3,5,2,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,1,7,3,5,2,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[3,8,4,6,2,1,5,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,4,2,5,3,1,6,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,5,2,4,3,1,6,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,3,2,5,4,1,6,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[4,3,2,5,1,8,6,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[3,5,2,4,1,8,6,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,4,7,8,1,5,3,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,8,7,3,5,4,2,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[5,1,8,2,7,4,3,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,1,7,2,8,4,3,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,1,2,8,5,3,4,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[6,3,2,1,8,4,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,3,2,8,4,5,1,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[2,7,8,4,3,5,1,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,1,8,3,5,4,2,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,8,2,3,4,6,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,7,1,3,4,8,2,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[6,8,1,3,4,7,2,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[1,7,2,3,4,6,8,5] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,6,2,3,4,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[7,6,2,3,4,1,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,6,2,3,4,1,7,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,1,7,3,5,4,2,6] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,3,2,7,4,5,1,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,7,2,3,4,1,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[7,6,2,3,4,8,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,6,2,3,4,7,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,3,4,8,7,5,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,8,7,3,5,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,8,7,5,3,6,1,2] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[5,8,7,3,4,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,8,4,2,1,6,7,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,8,4,1,2,6,7,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[5,3,7,2,6,1,8,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,2,8,1,6,3,7,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,8,2,1,4,7,6,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,8,2,5,1,7,6,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,8,4,1,2,6,5,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,8,1,5,2,7,6,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[5,8,1,2,4,7,6,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,2,8,3,6,7,1,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[3,8,7,6,2,4,1,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,8,7,6,4,1,3,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,8,2,6,5,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[1,8,7,6,4,2,3,5] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[2,8,7,6,3,1,4,5] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,8,7,6,2,4,3,5] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,8,7,6,3,4,2,5] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[2,8,1,4,5,6,7,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[2,1,7,3,6,5,8,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,1,7,2,6,5,8,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,2,7,1,6,5,8,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,1,2,8,5,7,3,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[6,2,1,8,5,7,3,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,3,1,8,5,7,2,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,4,2,1,7,5,8,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,1,3,8,5,2,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[2,3,7,1,6,8,5,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,3,7,2,6,8,5,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[7,8,2,6,5,3,1,4] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[3,2,6,7,5,8,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[1,2,7,5,6,3,8,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,8,7,6,4,3,1,5] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[3,8,7,6,1,2,5,4] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,8,7,6,2,1,5,4] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[4,8,7,6,2,1,3,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,8,7,6,1,3,2,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,8,7,6,4,1,2,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,8,3,6,5,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[2,3,7,5,6,8,1,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[3,8,7,6,4,2,1,5] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[5,1,4,6,8,2,3,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,7,6,3,5,4,8,2] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[4,3,7,2,6,5,1,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[3,4,6,1,5,7,2,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,6,8,5,7,3,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,4,1,5,8,6,3,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[4,6,1,2,5,8,3,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,6,7,2,1,4,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[7,8,6,5,1,2,4,3] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[1,3,6,5,7,8,2,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[7,4,8,5,3,1,6,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,8,5,2,4,1,7,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,3,1,6,8,5,7,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[7,3,2,5,1,4,8,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,1,4,2,3,6,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[1,5,8,3,4,6,7,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[8,3,1,2,4,7,6,5] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[2,3,8,1,6,5,4,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,1,4,7,2,5,3,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[3,5,2,4,1,7,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,4,7,8,6,2,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,4,8,6,2,7,1,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,8,2,1,6,7,3,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,7,2,8,6,4,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,1,2,7,5,3,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[7,3,2,8,6,4,1,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[2,7,8,4,6,3,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[1,4,5,7,2,6,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[7,3,5,2,6,1,8,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,5,2,3,6,1,7,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,1,6,3,5,7,2,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,8,6,4,3,7,1,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,3,2,6,4,7,1,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[2,3,8,7,6,5,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,2,8,7,3,6,5,4] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[4,2,8,7,3,6,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[4,5,8,7,1,2,6,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[1,5,8,7,3,2,6,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,5,8,7,3,2,1,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,6,8,1,7,5,4,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,6,8,4,7,2,1,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,5,8,3,7,6,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,2,8,4,7,6,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,5,8,3,7,2,6,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,5,8,4,7,2,1,6] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,6,8,2,3,7,1,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[1,6,8,4,2,7,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,5,8,4,2,7,6,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,5,8,2,3,7,6,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,1,8,4,3,7,6,5] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,5,8,4,3,7,1,6] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,6,8,4,1,2,7,3] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,6,8,1,3,2,7,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[1,6,8,4,3,2,7,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,8,4,3,2,1,7] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[7,1,2,8,6,5,4,3] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[7,1,4,8,6,2,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,3,1,8,6,2,5,4] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,2,4,8,3,6,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,1,4,8,3,2,6,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[7,4,5,8,3,2,1,6] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[1,6,2,8,7,5,4,3] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,6,4,8,7,2,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,6,4,8,7,2,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,2,5,8,7,6,1,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,2,4,8,7,6,1,5] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,1,5,8,7,2,6,4] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,1,4,8,7,2,6,5] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[1,6,4,8,2,7,5,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,4,5,8,2,7,6,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,5,8,3,7,1,6] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[4,6,5,8,1,2,7,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[1,6,4,8,3,2,7,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,4,5,8,3,2,7,6] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[7,6,1,4,8,2,5,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,6,1,3,8,2,5,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,6,3,4,8,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,2,5,1,8,6,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[7,2,5,3,8,6,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,2,1,4,8,6,5,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,2,1,3,8,6,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,2,3,4,8,6,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[7,3,5,4,8,2,1,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[2,6,5,1,8,7,4,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[2,3,5,4,8,7,1,6] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,6,5,4,8,2,7,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[1,6,5,3,8,2,7,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[1,6,3,4,8,2,7,5] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,3,5,4,8,2,7,6] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[3,6,5,4,8,2,1,7] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[7,6,5,2,3,8,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,1,4,2,8,5,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,6,1,2,3,8,5,4] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,6,2,4,3,8,1,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,1,5,4,2,8,6,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,1,5,2,3,8,6,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,1,2,4,3,8,6,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[2,6,5,4,3,8,1,7] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[7,6,1,4,3,2,8,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,1,5,4,3,2,8,6] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[3,4,2,6,7,8,1,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,1,4,2,6,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[8,3,4,2,6,1,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[2,6,7,3,5,4,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,7,8,3,5,4,1,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,6,8,3,5,4,1,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[4,7,1,2,8,5,3,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[4,8,1,2,7,5,3,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,1,6,3,7,5,4,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,7,1,3,6,8,4,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[6,7,3,2,8,1,4,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[7,3,4,2,6,1,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,4,1,2,8,5,3,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[8,7,4,2,1,5,3,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,4,1,2,6,5,3,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[7,4,3,1,5,6,8,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,7,4,1,5,8,3,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,7,5,1,6,8,3,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,5,3,1,7,6,8,2] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,6,1,2,7,5,3,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,7,1,3,6,5,4,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,1,8,2,6,5,3,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,6,1,2,8,5,3,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[8,4,3,1,5,6,7,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[4,5,3,1,8,6,7,2] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,8,5,6,3,1,7,2] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[5,1,3,4,8,6,7,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,4,3,8,1,6,7,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,5,3,4,1,6,7,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,4,8,2,1,5,3,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,7,3,2,5,1,4,8] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,3,2,5,1,4,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,7,1,4,6,8,3,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,1,3,4,7,6,8,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[6,1,4,2,7,5,3,8] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[5,4,3,7,1,6,8,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,7,5,4,1,8,3,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[7,6,4,2,1,5,3,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,2,7,6,5,4,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[7,2,8,6,5,4,3,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[8,1,9,7,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[2,10,9,8,7,6,5,4,1,3] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[9,2,8,7,6,5,4,1,3] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[3,9,8,7,6,5,4,1,2] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[8,7,2,6,5,4,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[3,2,8,7,6,5,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[4,8,7,6,5,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[7,8,6,1,5,4,3,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[8,9,1,7,6,5,4,3,2] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[7,3,8,6,5,4,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[8,2,9,7,6,5,4,3,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[9,1,10,8,7,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[4,8,5,7,6,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[3,8,7,4,6,5,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[2,8,7,6,3,5,4,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[8,5,6,1,3,2,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,6,1,5,3,2,4,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[7,8,1,5,3,2,4,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[8,1,7,5,3,2,4,6] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[8,6,1,4,5,2,3,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,6,3,1,5,2,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,4,6,1,5,2,3,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,6,2,1,5,4,3,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,5,2,6,1,4,3,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,5,2,1,7,4,3,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,8,2,1,5,4,3,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,8,3,1,5,2,4,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[8,2,7,5,1,3,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,4,1,7,5,2,3,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,2,7,1,5,4,3,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,2,6,1,7,4,3,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,1,7,4,3,2,6,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,1,5,7,3,2,6,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[5,7,8,1,3,2,6,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[8,2,6,1,5,7,3,4] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,8,1,6,7,2,3,4] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,7,6,1,8,2,3,4] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,7,2,5,1,8,3,4] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[7,5,1,6,8,2,3,4] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,5,7,1,8,2,3,4] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,7,3,8,1,2,4,5] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[7,5,4,1,8,2,3,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,6,1,4,8,2,3,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,1,6,4,7,2,3,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,5,8,1,3,2,4,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,8,4,1,3,2,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[8,3,7,4,1,2,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,5,1,7,3,2,4,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,8,1,7,3,2,4,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,1,8,4,3,6,2,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,3,1,8,6,4,2,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,3,1,7,4,6,2,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,4,5,1,7,2,3,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[5,6,8,1,7,2,3,4] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,5,8,1,2,7,3,4] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,3,1,8,5,6,2,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,2,7,8,3,1,5,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[5,8,1,7,3,2,6,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,4,1,7,3,2,6,5] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,3,4,7,1,2,6,5] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,2,7,4,1,3,6,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,4,8,2,1,3,6,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,4,3,8,1,2,6,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,2,3,6,7,1,5,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,8,5,2,3,6,4,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,8,5,2,3,4,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,5,2,6,8,1,4,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[3,5,2,4,6,8,1,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[2,4,5,7,3,6,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,4,5,3,6,8,1,7] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[5,2,4,6,8,1,3,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[5,1,3,4,6,8,2,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,3,5,2,6,8,1,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,3,5,7,2,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[4,3,5,7,2,6,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[4,6,3,7,2,5,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[4,6,3,1,7,8,2,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,3,5,1,7,8,2,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,7,1,3,4,8,2,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,7,1,3,4,6,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[4,5,7,1,3,6,8,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,3,6,7,1,5,8,2] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,6,3,5,1,7,8,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,6,3,5,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,5,6,4,1,7,8,2] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,1,5,6,7,4,8,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,1,6,7,3,4,8,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[6,4,7,1,3,5,8,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[1,6,7,3,4,5,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[2,6,7,4,5,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[2,6,7,4,8,1,3,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,3,6,1,2,7,8,4] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[3,5,2,6,1,7,8,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[3,5,2,6,7,4,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[5,2,3,6,7,4,8,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,2,3,6,1,7,8,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,2,6,1,3,7,8,4] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[4,2,6,7,3,5,8,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[6,3,7,2,4,5,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[3,5,7,2,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,7,2,4,8,1,5,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[7,2,4,6,8,1,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[7,1,3,4,6,8,2,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[3,7,2,4,6,8,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,5,7,2,6,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[6,3,7,2,5,8,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,3,5,7,2,8,1,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,3,5,7,2,4,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,2,4,5,7,3,8,1] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[6,2,4,5,1,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,7,1,2,5,6,8,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[2,6,7,5,8,1,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,6,7,1,2,5,8,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,6,2,4,7,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,4,2,6,7,3,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[5,4,2,6,1,7,8,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[1,5,4,6,2,7,8,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[5,6,4,1,2,7,8,3] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,4,5,1,2,7,8,3] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,5,1,7,8,2,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[6,5,7,2,8,1,3,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,5,7,1,3,4,8,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,6,4,7,1,3,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,4,6,3,1,7,8,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,5,3,2,4,8,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,4,5,2,6,1,3,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,5,4,2,1,6,3,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,3,4,1,6,2,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,4,5,3,1,6,2,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[7,5,4,2,1,8,3,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,5,4,2,1,6,8,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,4,5,3,1,6,8,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,4,3,5,6,1,8,2] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,6,3,7,4,1,8,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[5,6,7,3,1,4,8,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[6,7,3,4,1,5,8,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,7,4,2,1,5,8,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,6,7,3,1,8,2,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,6,3,7,8,1,2,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,6,3,7,2,4,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,6,7,2,3,8,1,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,4,5,2,8,1,3,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,7,3,2,4,8,1,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,6,4,2,1,3,8,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,6,3,4,1,2,8,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,6,3,2,4,1,8,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,7,3,2,5,1,8,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,5,3,2,7,8,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[6,5,3,2,7,4,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[6,4,5,2,7,3,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,4,5,2,7,8,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,4,5,2,6,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[7,4,5,6,1,2,8,3] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,5,6,2,1,3,8,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,7,3,5,1,2,8,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[5,6,7,4,1,2,8,3] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[5,6,7,2,4,1,8,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[5,6,4,2,7,8,1,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,5,7,2,1,8,3,4] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,5,7,2,1,4,8,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,4,6,7,3,1,8,2] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,7,8,5,6,1,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,7,8,5,6,3,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,7,5,8,6,3,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,7,5,8,6,1,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,7,3,8,6,4,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,5,7,8,6,3,4,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,5,7,8,3,6,4,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,3,7,8,1,6,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,8,1,5,6,3,4,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[7,1,8,5,6,3,4,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,1,5,8,6,3,4,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,1,7,8,3,6,4,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,1,7,8,5,6,4,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[1,3,7,8,5,6,4,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,1,7,5,8,6,4,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[5,1,7,3,8,6,4,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[7,1,5,3,8,6,4,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[7,1,5,8,3,6,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,3,5,8,1,6,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,3,7,1,8,6,4,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[3,5,7,1,8,6,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,7,5,3,8,6,4,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,7,3,1,8,6,4,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,7,3,8,6,1,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,7,5,8,1,6,4,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,7,5,8,3,6,4,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,7,8,5,3,6,4,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,8,6,3,1,4,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[7,5,8,6,1,3,4,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,7,8,1,6,3,4,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[3,7,8,1,5,6,4,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[1,7,8,3,5,6,4,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,7,3,8,5,6,4,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,7,1,8,5,6,4,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,7,1,8,3,6,4,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,7,1,8,6,3,4,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[7,5,1,8,6,3,4,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,5,8,1,6,3,4,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,8,5,1,6,3,4,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[7,5,8,1,3,6,4,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[7,5,1,8,3,6,4,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[7,5,1,3,8,6,4,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[5,7,1,3,8,6,4,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,7,1,5,8,6,4,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[1,7,3,5,8,6,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,5,3,7,8,6,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,5,1,7,8,6,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[5,3,1,7,8,6,4,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,3,1,5,8,6,4,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,3,1,8,5,6,4,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[7,8,3,1,5,6,4,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,1,8,3,5,6,4,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[7,1,3,8,5,6,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[7,1,3,5,8,6,4,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,1,5,7,8,6,4,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,7,3,4,8,6,1,2] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,7,3,4,8,1,6,2] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[5,7,3,4,1,8,6,2] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,7,3,1,4,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,7,3,1,4,8,6,2] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[5,3,7,4,1,2,6,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,3,7,1,4,2,6,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,3,7,1,4,2,8,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[3,7,5,1,2,8,6,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[7,8,3,5,1,2,6,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[7,3,5,8,1,2,6,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[3,7,5,1,2,6,8,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,1,4,3,5,2,8,7] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[2,5,7,3,8,4,1,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,4,7,8,6,1,3,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,5,6,2,8,3,1,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,7,2,5,8,3,1,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[6,2,4,5,1,3,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[5,1,4,6,3,2,8,7] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,5,6,2,4,1,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,8,6,7,5,4,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,2,7,8,3,4,1,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,5,3,4,8,1,7,6] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[8,7,1,2,5,3,4,6] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,1,8,2,3,4,7,6] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,4,7,6,2,8,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,7,8,1,5,4,6,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[7,1,3,4,6,8,5,2] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,3,6,5,7,1,4,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[5,8,7,1,4,6,2,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,7,6,1,8,3,5,2] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,7,2,6,3,8,5,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[2,1,8,4,6,7,3,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,7,8,6,3,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,8,1,5,6,7,2,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[6,7,2,4,8,5,3,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,8,3,6,7,5,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,2,1,7,6,3,5,4] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[3,2,4,5,8,1,7,6] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[7,4,6,3,2,1,8,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,7,3,2,1,8,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[6,4,7,5,2,3,8,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,4,8,1,7,3,2,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,8,7,2,3,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,2,3,1,8,7,5,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,6,8,1,3,5,2,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,7,5,2,3,1,8,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[4,7,2,6,5,1,8,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,4,2,1,8,5,7,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,2,1,5,6,8,4,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,7,2,6,4,1,5,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,7,8,2,5,3,1,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[2,1,7,3,6,8,5,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,5,7,8,4,6,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,5,7,8,3,6,1,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[6,4,1,5,7,2,8,3] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[7,4,8,1,2,5,6,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,2,7,8,6,3,5,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,1,7,4,3,2,8,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[6,8,3,4,2,1,7,5] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,2,6,1,5,7,8,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[2,4,6,7,3,5,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[6,5,8,3,7,4,1,2] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[7,1,4,8,3,5,6,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,8,7,5,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[4,8,6,3,1,5,7,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,4,8,2,5,7,6,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,5,7,4,8,6,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,6,3,7,5,1,8,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,6,4,8,7,5,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[6,3,7,2,8,5,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,6,2,5,8,7,1,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,2,8,4,7,6,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,2,4,8,6,5,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,2,4,8,7,5,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[2,4,5,8,7,6,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,2,7,3,8,1,6,5] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[2,5,1,4,7,3,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,1,3,8,7,2,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,1,5,6,2,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,1,5,2,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,1,5,3,2,8,7,6] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[7,2,3,5,1,8,6,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,4,5,1,8,7,6,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,4,5,2,8,7,6,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,6,4,2,8,7,5,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[7,4,2,5,1,8,6,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[4,6,2,7,5,1,8,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,5,3,6,2,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,5,8,3,2,7,6,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,5,8,2,1,7,6,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,6,2,5,1,4,8,7] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[2,4,8,7,1,3,6,5] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[1,3,8,2,4,7,6,5] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,3,1,7,2,8,5,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,5,1,2,8,6,4,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[1,5,2,3,8,7,6,4] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,5,1,2,8,7,6,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,4,1,2,8,7,5,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[5,2,8,1,3,7,6,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,7,5,6,8,3,1,2] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,6,4,7,5,3,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[7,5,2,6,4,1,3,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[1,6,3,7,5,8,4,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,7,4,5,8,6,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[7,2,6,3,4,1,5,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,3,7,4,6,5,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,8,4,7,5,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[4,8,7,5,6,3,1,2] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,8,7,6,4,5,1,2] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,6,5,2,8,3,7,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[8,6,5,2,1,4,3,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[2,7,6,3,1,4,5,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[6,8,5,3,2,1,4,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[2,7,6,4,5,1,3,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,7,2,6,4,1,3,8] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[6,1,3,7,5,8,4,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,1,7,3,6,8,5,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[8,1,6,4,3,7,5,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[2,1,7,4,8,6,3,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[1,8,6,3,7,5,4,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,8,2,7,3,6,5,4] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[2,1,3,8,4,7,5,6] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[8,1,2,7,4,3,6,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[5,3,1,6,8,4,7,2] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[6,2,8,7,1,4,3,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,7,2,1,5,4,3,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,2,3,1,4,6,5,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[2,4,8,3,1,5,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[3,4,2,7,1,5,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[4,7,3,8,2,1,5,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,2,7,3,1,4,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,3,7,2,1,5,4,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[1,3,7,2,8,4,6,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,4,2,5,8,6,7,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[6,5,3,8,2,1,4,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[2,6,4,5,7,1,3,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[5,4,6,2,7,1,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,6,3,1,8,4,5,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,6,2,1,8,5,3,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[1,7,5,8,6,4,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,5,1,2,8,3,7,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[8,6,1,4,3,7,5,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,8,4,1,3,7,5,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,5,7,1,3,8,4,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[5,8,3,1,7,4,6,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,3,1,7,5,4,6,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[1,3,8,7,4,6,5,2] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[1,2,8,7,6,3,5,4] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[8,2,1,7,6,4,3,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[2,3,1,8,7,4,5,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[2,4,1,8,5,7,3,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,8,2,1,7,6,3,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,2,7,1,8,5,3,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[8,7,1,6,5,4,3,2] => [[1,4],[2],[3],[5],[6],[7],[8]] => 1101111
[7,1,8,3,6,5,4,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,1,8,7,5,6,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[8,1,2,3,4,5,9,6,7] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[8,1,2,9,3,4,5,6,7] => [[1,3,4,6,7,8,9],[2,5]] => 10010000
[8,1,9,2,3,4,5,6,7] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[9,1,2,3,4,5,6,10,7,8] => [[1,3,4,5,6,7,8,10],[2,9]] => 100000010
[3,5,8,7,2,6,4,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,8,2,7,1,6,4,3] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[2,1,6,4,5,8,3,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,6,3,7,5,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[4,6,3,8,5,2,1,7] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,6,3,7,5,2,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,5,7,8,2,6,1,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[7,2,3,4,6,8,5,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[4,8,3,7,5,1,6,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,2,3,4,8,7,1,6] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[5,2,3,4,6,8,1,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,2,8,5,7,6,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[3,7,6,4,5,1,8,2] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,8,3,7,5,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[8,7,3,6,5,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[4,2,7,5,8,6,3,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[5,8,1,7,3,6,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[5,2,7,8,4,6,3,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,2,8,3,7,6,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,2,7,3,1,6,4,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,2,3,4,8,5,1,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[6,2,3,4,1,8,5,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[7,2,3,4,1,8,6,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[7,2,3,4,1,5,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[1,2,3,4,8,7,5,6] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,8,5,3,4,6,7] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,8,4,2,3,5,6,7] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[8,6,7,4,1,5,3,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[4,8,6,7,5,1,3,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[7,1,8,4,6,5,2,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,7,1,5,4,6,2,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,5,7,1,4,6,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[6,4,8,5,1,7,3,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,8,5,7,1,6,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,4,7,1,5,6,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,7,1,4,5,6,3,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[8,7,4,5,6,1,3,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,7,5,1,4,6,2,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,2,5,1,4,6,3] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[4,8,7,2,5,1,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[1,6,4,8,5,2,7,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[8,7,1,4,2,5,6,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,7,5,1,2,4,6,3] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[7,1,8,5,6,2,3,4] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[3,8,7,1,2,5,6,4] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,5,8,7,1,2,6,4] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[2,3,8,5,7,1,6,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,8,7,1,5,6,2,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[3,5,8,7,1,6,2,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[2,3,8,6,7,5,1,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,2,8,6,7,5,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,1,8,6,2,7,5,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,7,4,1,2,6,5,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[1,3,8,6,7,5,2,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[5,7,1,8,2,6,3,4] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,8,7,1,5,6,3,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[8,7,1,5,2,4,6,3] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[7,1,8,2,4,6,5,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[1,6,2,8,4,7,5,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,8,5,7,2,6,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,8,3,7,2,5,6,4] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,8,7,1,3,5,6,4] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,7,1,8,2,3,6,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[7,1,8,2,3,5,6,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[8,6,3,7,4,1,5,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[4,2,8,6,7,5,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,4,2,7,5,6,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[4,8,3,6,1,7,5,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[8,3,4,7,5,1,6,2] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,3,7,4,5,1,6,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,7,4,2,5,6,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,5,1,6,2,3,4] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,7,2,4,1,5,6,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,8,6,1,7,2,5,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,7,1,8,2,6,5,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,2,8,6,7,1,5,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,7,4,1,2,5,6,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,2,7,1,6,3,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,2,7,1,3,6,4,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[2,8,3,6,7,1,5,4] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,7,2,1,3,5,6,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,8,7,2,3,6,4,5] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,7,2,6,3,4,5] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[8,2,7,3,6,1,4,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,8,7,3,6,2,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,8,2,7,6,3,4,5] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[8,2,7,4,1,5,6,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,2,1,7,5,6,3,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,7,3,1,5,6,2,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[2,8,7,3,5,6,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,3,1,6,7,5,2,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,5,2,1,6,7,4,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[1,5,2,8,6,7,4,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,2,8,6,7,5,3,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,8,3,6,7,5,2,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,2,3,6,7,5,1,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[8,3,7,2,5,6,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,1,3,7,5,6,2,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,4,1,2,7,5,6,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,1,4,2,6,7,5,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[1,2,8,6,7,3,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[8,1,2,7,3,6,4,5] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,1,7,3,6,2,4,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,1,7,2,6,3,4,5] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,1,7,2,3,6,4,5] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,1,3,7,2,5,6,4] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,8,3,6,7,2,5,4] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,7,8,2,3,6,5,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[8,3,7,1,2,5,6,4] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,7,1,2,3,6,4,5] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[2,8,5,7,4,6,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[3,1,8,5,7,4,2,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[8,3,5,7,4,2,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,3,6,2,4,5,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[2,8,6,4,3,5,7,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[2,6,8,3,5,4,7,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,7,5,8,4,6,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,4,2,7,6,1,3,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,8,1,7,6,3,2,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,1,7,6,2,3,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,7,1,8,6,2,5,4] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,1,7,6,4,5,2,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[3,1,7,5,8,4,2,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,1,6,8,7,5,2,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,3,8,7,5,2,4,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[7,3,5,8,4,2,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,3,6,4,2,8,5,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,8,3,6,2,5,4,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[7,4,8,2,1,6,3,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,7,4,6,3,2,5,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[7,8,5,2,1,4,3,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,5,2,3,1,4,8,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,4,6,2,3,8,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,4,2,5,8,3,7,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[4,6,5,8,1,3,2,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,7,1,5,3,8,2,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,7,8,1,3,6,2,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[5,7,1,3,4,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,7,1,4,2,3,6,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[5,8,1,3,2,4,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,8,6,1,3,2,7,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[8,4,6,2,1,3,7,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[5,4,8,7,2,3,6,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,4,8,7,3,1,2,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,8,3,7,2,5,4,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,4,6,8,2,3,7,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[5,7,4,2,8,3,6,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[6,4,7,2,1,8,3,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[6,5,3,4,1,2,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,8,5,4,1,3,2,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[6,4,3,7,1,5,2,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[9,8,7,6,5,2,3,1,4] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010
[7,4,2,6,1,5,3,8] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,4,2,5,6,1,3,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[6,4,2,8,1,5,7,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,3,7,8,2,5,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,3,5,6,4,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[7,4,3,1,5,6,2,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,4,5,2,6,1,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[5,3,7,2,8,6,4,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[5,3,8,2,6,7,4,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,3,8,2,5,4,7,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,4,8,2,1,5,7,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[6,4,3,1,8,2,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,3,7,8,2,6,4,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,7,8,5,6,3,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,3,7,6,8,2,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,7,8,4,6,2,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,8,4,3,6,7,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,8,6,4,7,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,3,8,6,2,7,4,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,7,5,8,6,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[4,8,6,7,5,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[6,3,8,7,2,4,1,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,3,8,7,2,6,4,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[5,3,8,6,7,2,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,3,7,8,6,2,4,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,7,6,4,8,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,8,4,6,7,2,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,4,2,8,1,7,3,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,5,2,4,3,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[5,4,6,2,8,7,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,6,3,8,7,2,4,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,7,4,3,1,8,2,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[5,7,4,3,6,8,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,7,3,8,6,2,4,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,5,8,6,7,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[4,6,8,5,7,3,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,6,8,3,7,2,4,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[5,4,6,8,2,7,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[5,7,8,2,6,4,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,6,8,5,7,1,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,7,4,8,6,2,3,5] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,6,2,5,7,8,1,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[5,2,7,4,6,8,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,3,6,7,1,8,4,2] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,2,5,6,7,1,8,3] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[8,1,3,6,7,2,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,1,4,2,7,5,3,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,1,3,8,2,7,4,5] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[1,7,5,2,8,6,3,4] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[3,6,4,8,1,5,7,2] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,5,8,4,2,6,3,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[3,5,7,4,1,6,8,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,5,7,1,2,6,4,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[4,5,1,8,2,3,7,6] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[4,7,1,8,2,6,3,5] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[7,5,1,2,3,8,6,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[5,2,6,1,3,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,8,4,5,1,3,2,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,7,1,3,2,5,4,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,1,4,3,5,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,8,2,3,1,5,4,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,8,2,4,3,5,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,8,2,4,1,5,3,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[1,4,2,6,5,7,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[5,6,1,4,2,7,3,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[6,7,2,4,1,5,3,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,2,4,3,5,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,7,2,3,1,5,4,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,3,5,4,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[2,4,1,6,5,7,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,2,6,4,7,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,5,1,6,4,7,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[3,6,5,7,4,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,6,2,4,3,7,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,2,6,1,7,3,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[4,5,1,6,3,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[4,5,3,6,1,7,2,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[5,6,3,4,1,7,2,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,6,1,4,3,7,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,6,1,3,2,7,4,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[5,6,4,7,1,3,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[6,7,4,5,1,3,2,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,7,5,8,1,3,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,5,1,3,2,7,6,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,6,5,7,1,3,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[4,6,1,3,2,7,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[1,4,3,6,2,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,4,1,6,5,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[4,5,2,3,1,7,6,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,5,3,7,6,8,1,2] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,6,5,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,6,5,7,2,3,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,5,4,6,1,7,2,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,5,1,6,4,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,3,6,4,7,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,3,6,2,7,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,5,2,6,1,7,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,5,2,6,4,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[3,4,2,6,1,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[4,6,2,3,1,7,5,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,4,3,6,1,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,5,3,6,4,7,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,5,3,6,1,7,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,6,2,7,5,4,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,6,1,7,3,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,2,6,7,4,3,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,5,2,7,6,4,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,5,7,2,8,3,6,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,5,7,3,1,8,4,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,1,5,6,8,4,3,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,3,7,2,8,5,4,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,6,2,7,1,8,3,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[1,5,4,3,6,8,2,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,6,4,5,7,8,3,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,1,5,6,8,4,7,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,1,5,6,8,7,3,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,6,5,2,7,8,4,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,2,4,7,5,8,3,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[1,5,7,8,4,2,6,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,7,4,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,4,6,8,5,7,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,2,5,7,3,1,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,5,6,2,8,7,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,5,6,8,1,7,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,5,6,1,8,7,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[4,5,6,3,1,8,7,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,3,6,2,1,7,5,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,6,3,2,1,7,5,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[4,6,3,1,7,5,2,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[4,5,3,7,6,1,8,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[4,5,1,7,3,8,6,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,5,7,1,4,3,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,3,5,7,6,1,8,2] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,3,6,1,7,5,2,8] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[4,3,2,6,1,7,5,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,3,2,1,6,4,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,3,1,6,2,7,4,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,1,6,3,2,7,4,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,6,1,4,7,5,3,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,6,1,7,4,2,5,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,6,1,7,5,3,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,1,6,3,7,4,2,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,3,6,4,2,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,3,2,6,4,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,2,1,6,3,7,4,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,2,6,3,1,7,4,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,2,6,3,1,7,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,6,2,1,7,4,5,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,6,2,7,4,1,5,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[3,5,7,2,8,6,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,4,7,1,3,6,5,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,6,1,3,7,5,4,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,6,1,7,5,2,4,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[5,1,6,2,7,4,3,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,2,6,4,3,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,2,1,6,4,3,7,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,4,2,1,6,3,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,4,2,6,3,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,4,1,6,2,7,3,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,1,6,4,2,7,3,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,6,1,7,5,4,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,6,1,5,4,3,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,1,6,2,5,4,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,1,6,4,3,2,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,4,1,6,3,2,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,4,3,1,6,2,7,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,3,1,6,5,4,8,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[7,2,8,1,5,4,3,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,2,7,6,5,8,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[3,8,2,6,5,4,1,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[3,2,8,7,6,5,4,1,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[7,3,2,1,5,4,6,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,2,8,6,1,4,3,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,2,7,6,8,4,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[3,8,7,2,5,4,1,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[3,9,2,7,6,5,4,1,8] => [[1,2,9],[3,4],[5],[6],[7],[8]] => 01011110
[3,2,9,8,7,6,5,4,1,10] => [[1,3,10],[2,4],[5],[6],[7],[8],[9]] => 101111110
[8,3,2,1,6,5,4,7,9] => [[1,5,8,9],[2,6],[3,7],[4]] => 11101100
[7,5,1,6,8,4,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,4,2,1,5,6,3,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,2,8,6,5,1,3,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[5,3,2,6,7,4,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,3,7,2,5,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[3,10,2,8,7,6,5,4,1,9] => [[1,2,10],[3,4],[5],[6],[7],[8],[9]] => 010111110
[6,7,1,4,3,2,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,4,2,6,7,1,5,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[3,7,1,6,5,2,4,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,5,6,2,4,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[3,5,8,7,2,4,6,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[1,7,8,2,5,4,3,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,7,2,5,4,3,6,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[2,5,6,4,7,1,3,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[4,7,1,6,3,5,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,3,8,7,2,6,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,4,5,3,7,8,2,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,4,8,2,7,6,3,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[4,7,3,5,1,8,6,2] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[8,7,3,6,1,5,4,2] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[2,5,8,7,4,6,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,4,2,1,7,8,3,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,7,8,3,5,2,1,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,6,2,1,8,3,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[1,4,6,7,3,5,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[8,3,6,2,1,7,5,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,3,7,6,4,2,1,5] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[2,3,1,8,4,7,6,5] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,7,4,8,6,5,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[8,6,5,1,4,7,3,2] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,5,4,1,7,3,6,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[6,3,7,2,8,5,4,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[1,6,3,8,2,7,5,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,7,5,3,8,2,6,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,2,7,4,1,8,5,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[8,6,3,2,7,5,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[2,7,5,1,3,8,6,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[1,7,6,4,3,8,2,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[3,7,2,4,8,6,5,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,4,2,8,7,6,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,1,4,3,2,7,8,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[3,7,8,5,2,4,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[3,7,6,2,4,1,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[1,6,8,2,5,7,4,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,7,2,5,8,4,3,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[5,2,7,8,4,3,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,3,1,7,8,4,2,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[2,7,6,4,1,3,8,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,1,7,6,3,2,8,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[8,4,2,7,6,3,1,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,3,1,7,5,2,8,4] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,2,7,5,3,1,8,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[1,5,8,2,7,4,6,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,7,2,8,4,6,3,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,7,3,1,8,4,6,2] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[8,4,7,3,1,6,5,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[2,6,8,5,7,4,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[6,5,2,1,7,4,8,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,7,4,6,2,1,8,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,6,4,8,3,7,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[6,7,1,8,3,4,2,5] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[7,8,3,5,1,4,2,6] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,6,2,7,1,8,3,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[6,7,2,4,3,8,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,4,3,8,6,7,1,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[1,8,2,7,4,5,3,6] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[2,5,4,8,3,6,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,3,1,8,5,6,4,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[3,8,5,6,4,7,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,7,3,6,4,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[5,7,2,3,1,6,4,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,7,2,4,3,6,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,6,2,7,1,5,3,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[4,7,1,6,2,5,3,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,7,1,5,3,6,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,6,3,5,1,7,2,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[6,7,3,5,1,4,2,8] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[5,6,3,7,1,4,2,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[5,7,1,6,3,4,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,5,6,3,4,2,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,8,5,6,4,7,2,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,7,1,6,4,8,2,3] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,6,5,8,1,7,2,3] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,7,1,4,2,8,5,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,5,1,4,2,8,6,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[4,6,5,8,3,7,1,2] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,6,5,8,2,3,1,7] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,4,2,6,5,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,5,4,6,2,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,3,5,4,7,2,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,4,2,7,1,8,5,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[4,7,2,3,1,8,5,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,4,3,8,1,7,5,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,5,3,8,4,7,1,6] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,6,3,8,1,7,4,5] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,7,1,8,3,6,4,5] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,5,1,8,7,6,2,3] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,5,7,8,2,6,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,2,6,8,3,7,4,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,1,6,8,7,4,5,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,1,4,8,7,2,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,1,8,4,7,3,5,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,8,3,5,7,1,4,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,6,7,8,2,5,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[7,4,5,2,8,6,3,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,8,2,5,3,7,4,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,3,8,4,2,7,5,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,4,7,5,8,6,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,7,5,3,8,6,4,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,6,2,8,3,7,4,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[1,5,8,2,7,3,6,4] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[6,7,4,8,1,5,3,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,7,4,8,6,2,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,8,5,3,7,2,4,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[6,8,5,2,3,7,4,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,5,3,8,2,6,4,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,5,2,3,8,6,4,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,7,3,4,8,5,2,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,6,4,7,8,5,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[7,4,2,5,8,6,3,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,4,5,8,1,6,3,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[6,3,4,7,8,5,2,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,1,2,7,4,5,8,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[2,5,8,3,4,1,6,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[5,6,2,7,4,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,6,7,3,2,5,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,6,7,3,8,5,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,6,1,8,4,5,3,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[2,5,7,8,4,3,6,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,6,8,4,5,7,1,2] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[1,6,8,4,7,2,3,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[1,4,5,7,8,2,6,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,4,5,7,8,6,1,2] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,4,5,7,6,8,1,2] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,6,7,4,8,5,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,4,5,6,8,7,1,2] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,4,5,8,7,2,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,2,5,8,3,6,4,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,4,5,8,6,2,3,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[7,8,1,4,6,2,3,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,6,7,4,8,2,5,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,4,5,6,8,2,7,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,4,5,8,6,2,7,3] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,2,5,8,3,4,7,6] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,6,7,2,3,5,8,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[7,8,1,2,3,5,4,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,6,7,2,3,5,4,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,4,5,7,6,2,3,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,2,5,7,3,6,4,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,2,5,7,3,6,8,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,6,8,2,3,5,7,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,6,8,4,5,2,3,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[1,6,8,4,5,2,7,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,6,8,2,3,4,7,5] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,6,8,2,3,7,4,5] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,4,5,7,6,2,8,3] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,8,1,4,5,2,6,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[7,8,1,2,3,4,6,5] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,8,1,2,3,6,4,5] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,6,7,2,3,8,5,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,2,5,6,3,8,7,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,2,1,6,5,3,8,7] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,8,2,1,4,3,7,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[8,6,2,4,3,1,5,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[4,6,5,2,8,3,7,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[2,6,4,5,8,3,7,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,4,2,6,3,5,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[4,2,6,3,5,8,7,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[6,2,4,3,8,5,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,4,3,6,5,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,2,1,8,4,3,7,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[6,4,8,5,2,1,7,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[4,6,8,7,5,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,6,8,7,4,5,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,2,8,6,5,7,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,2,6,4,5,1,3,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,8,5,3,1,4,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[2,7,4,8,3,5,1,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,7,4,8,3,5,6,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[7,2,8,4,3,5,1,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[8,4,2,1,5,3,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,5,1,4,2,3,6,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[8,4,1,5,3,2,6,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,7,3,8,4,2,5,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[6,7,3,8,4,2,1,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[7,1,8,4,3,5,2,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[1,7,8,4,3,5,2,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,1,4,8,3,5,2,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[7,4,8,1,5,6,2,3] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[7,1,8,4,3,5,6,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,7,3,1,8,4,5,2] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[6,7,3,8,4,5,2,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[6,7,1,4,8,3,5,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,7,4,1,3,8,2,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[1,6,7,8,4,3,2,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[7,2,1,8,4,5,3,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[6,2,7,1,8,4,3,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,2,7,8,4,3,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,2,7,8,4,3,5,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[2,6,7,4,8,3,5,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,6,7,4,8,3,1,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,8,1,3,6,2,4,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,2,7,8,6,3,4,5] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[2,6,7,1,8,5,3,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,6,7,8,5,3,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,6,7,8,5,3,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,2,7,8,4,5,3,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[7,2,1,8,4,5,6,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[1,7,2,8,4,5,6,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[3,7,8,1,5,6,2,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,3,7,8,1,5,2,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[6,7,1,2,8,5,3,4] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[1,6,7,8,4,2,5,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,1,2,7,6,5,8,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[6,1,2,4,7,3,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[1,7,5,3,6,4,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,1,2,6,7,4,8,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[4,1,5,7,3,2,6,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,6,1,7,3,2,5,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,6,1,8,3,2,5,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,7,1,8,3,5,2,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,1,7,8,6,2,3,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[1,6,5,7,8,3,4,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,6,5,8,7,3,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,1,8,7,6,2,3,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,8,1,7,3,5,2,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,8,1,6,3,2,5,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,7,1,6,3,2,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,1,2,3,7,5,4,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[6,8,1,5,3,7,2,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[8,7,5,2,4,1,6,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[1,5,7,3,4,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[1,5,8,3,4,7,6,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[7,8,5,2,4,1,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,1,2,3,5,6,4,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,1,2,3,5,6,4,7] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[8,1,2,3,5,4,7,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,1,8,4,6,3,2,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,8,2,4,3,1,5,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,7,2,4,3,1,5,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,8,1,2,4,5,7,6] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,7,1,8,6,4,2,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[1,6,4,3,7,5,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,1,2,6,7,5,8,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[3,8,1,7,6,4,2,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,6,2,4,3,1,5,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,7,2,4,3,5,1,6] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,1,7,4,6,3,2,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,1,7,6,5,3,2,4] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[1,5,7,3,4,6,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[8,7,2,5,3,6,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,1,2,3,5,4,8,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[6,1,2,3,5,8,4,7] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,1,2,3,5,7,4,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[5,1,2,3,7,6,4,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,1,2,3,8,6,4,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[1,5,6,3,4,7,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[8,6,5,2,4,7,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,2,5,3,1,8,4] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,4,5,2,3,8,6,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[8,2,3,7,4,5,1,6] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,4,7,3,2,5,1,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[5,4,6,3,1,2,8,7] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[4,6,2,3,1,5,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,2,3,4,5,8,6,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[8,2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,3,4,6,8,5,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,7,3,2,8,6,1,5] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[3,7,4,5,1,8,6,2] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[3,8,2,6,7,4,5,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,8,1,5,6,7,3,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,8,2,4,6,7,1,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,8,1,3,4,2,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,8,2,4,3,1,7,6] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,1,7,6,8,5,3,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,7,6,1,8,5,2,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,7,2,3,8,5,1,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[7,1,3,6,4,8,5,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,6,1,4,8,5,2,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,2,3,7,8,5,4,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,2,3,8,4,5,1,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[7,2,3,6,8,4,1,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[8,2,3,5,7,1,4,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,4,8,3,5,1,7,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[5,4,8,3,6,7,1,2] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[3,5,1,8,4,6,7,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,6,1,8,4,5,2,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,6,8,3,5,2,7,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,7,8,3,2,4,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,8,2,3,5,6,1,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[6,8,2,3,1,4,5,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[5,2,7,4,8,3,1,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,7,8,2,1,4,6,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[3,7,5,2,8,4,1,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[6,3,2,4,1,8,7,5] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,2,3,4,8,5,1,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,7,3,1,4,2,6,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,7,4,1,8,2,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,3,7,4,8,1,2,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[8,3,7,4,2,6,1,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[3,7,4,1,5,6,2,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,8,3,2,4,5,7,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[8,4,1,6,3,7,5,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[8,7,4,2,1,6,3,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,3,5,2,7,4,1,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[1,5,3,8,7,6,4,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[7,2,4,8,1,3,6,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[1,2,8,7,5,6,3,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,1,8,6,7,5,2,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[1,4,8,6,5,7,2,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,6,5,4,8,2,3,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,1,6,8,3,4,2,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,2,5,1,7,4,3,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,2,1,8,7,4,3,6] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,2,6,3,8,1,4,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[5,2,8,3,4,6,1,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,2,8,4,3,1,7,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,2,8,1,3,6,5,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[7,3,8,1,4,6,2,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[1,7,8,5,4,6,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[1,5,8,4,6,3,7,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,3,8,4,1,2,7,6] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[5,8,4,3,6,2,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,8,3,6,5,2,7,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,8,2,4,7,6,5,3] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,8,1,4,6,7,5,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,8,2,5,1,7,6,4] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[4,3,8,2,5,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,2,4,3,5,1,7,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,2,1,4,6,5,7,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,1,3,4,5,7,6,2] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[6,1,5,2,4,7,8,3] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[4,1,8,5,2,7,6,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,1,8,2,3,7,5,6] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[5,3,8,7,2,1,4,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,7,3,5,1,4,8,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[6,4,7,5,8,2,3,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,7,8,4,2,6,3,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,4,1,6,8,3,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[5,8,4,6,1,7,3,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,6,1,4,7,8,3,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,3,6,7,4,8,2,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,4,8,6,2,7,3,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,4,8,5,6,2,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,6,3,8,4,7,2,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,6,3,8,2,7,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,3,7,2,8,6,5,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,7,3,8,5,2,4,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,2,7,5,1,4,8,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,5,7,8,4,6,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,3,7,8,4,6,2,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[2,5,8,4,3,7,6,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,7,4,8,6,2,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,6,4,8,7,2,5,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,5,4,8,2,7,6,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,5,7,3,8,6,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,5,6,8,4,7,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[6,3,1,8,7,5,4,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[5,4,8,1,7,6,3,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[8,5,4,1,7,6,3,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[1,8,2,5,6,3,4,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[7,2,8,4,5,1,3,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[1,3,7,5,6,2,4,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,6,7,4,3,5,2,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,8,5,2,3,7,4,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,8,2,5,3,6,7,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[2,6,8,4,3,5,7,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[7,5,8,3,2,1,6,4] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[7,2,8,4,1,5,6,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[7,5,8,1,2,6,3,4] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[1,6,7,4,3,2,8,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,5,2,6,4,7,8,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,5,4,6,2,3,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[6,2,5,7,1,4,8,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,5,4,3,8,1,7,2] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,3,6,8,5,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[2,7,8,3,6,5,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,7,8,5,4,6,3,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[2,6,5,8,3,4,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,6,5,7,3,4,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[6,2,5,7,4,1,3,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,2,5,8,4,1,3,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,7,8,4,6,1,3,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[6,1,2,8,3,7,4,5] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[6,1,2,8,5,4,7,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[6,2,5,7,8,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,5,4,2,6,7,3,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[2,6,5,7,3,8,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,6,2,7,5,8,4,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,3,2,7,8,5,6,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,6,2,4,8,7,3,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[6,5,2,1,8,7,3,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[2,6,5,3,7,8,4,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,2,5,3,8,4,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,5,2,3,8,7,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[5,4,1,2,3,8,6,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[5,1,4,2,3,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[1,5,4,2,6,3,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[5,1,6,3,8,2,7,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[9,8,7,6,5,4,3,1,2,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[8,7,6,5,4,2,1,3,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[1,9,8,7,6,5,3,2,4] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,8,7,6,2,5,4,3] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,10,9,8,7,6,5,4,2,3] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[2,1,9,8,7,6,5,4,3] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[1,2,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[3,2,1,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111
[1,3,2,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[1,2,3,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[4,3,2,1,9,8,7,6,5] => [[1,5],[2,6],[3,7],[4,8],[9]] => 11101111
[1,4,3,2,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9]] => 01101111
[2,1,4,3,9,8,7,6,5] => [[1,3,5],[2,4,6],[7],[8],[9]] => 10101111
[1,2,4,3,9,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8],[9]] => 00101111
[1,2,3,4,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,5,4,3,2,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9]] => 01110111
[2,1,5,4,3,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9]] => 10110111
[1,2,5,4,3,9,8,7,6] => [[1,2,3,6],[4,7],[5,8],[9]] => 00110111
[1,3,2,5,4,9,8,7,6] => [[1,2,4,6],[3,5,7],[8],[9]] => 01010111
[1,2,3,5,4,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[1,2,3,4,5,9,8,7,6] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,3,2,6,5,4,9,8,7] => [[1,2,4,7],[3,5,8],[6,9]] => 01011011
[1,2,3,6,5,4,9,8,7] => [[1,2,3,4,7],[5,8],[6,9]] => 00011011
[2,1,4,3,6,5,9,8,7] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[1,2,4,3,6,5,9,8,7] => [[1,2,3,5,7],[4,6,8],[9]] => 00101011
[1,2,3,4,6,5,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[1,2,3,5,4,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,2,3,4,5,7,6,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[1,2,10,9,8,7,6,5,4,3] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[3,2,1,10,9,8,7,6,5,4] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[1,3,2,10,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111
[1,2,3,10,9,8,7,6,5,4] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[1,4,3,2,10,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => 011011111
[1,2,4,3,10,9,8,7,6,5] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => 001011111
[1,2,3,4,10,9,8,7,6,5] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,5,4,3,2,10,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111
[2,1,5,4,3,10,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => 101101111
[1,2,5,4,3,10,9,8,7,6] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => 001101111
[1,3,2,5,4,10,9,8,7,6] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[1,2,3,5,4,10,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => 000101111
[1,2,6,5,4,3,10,9,8,7] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 001110111
[3,2,1,6,5,4,10,9,8,7] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 110110111
[1,3,2,6,5,4,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,2,3,6,5,4,10,9,8,7] => [[1,2,3,4,7],[5,8],[6,9],[10]] => 000110111
[1,2,4,3,6,5,10,9,8,7] => [[1,2,3,5,7],[4,6,8],[9],[10]] => 001010111
[1,2,3,4,6,5,10,9,8,7] => [[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111
[1,2,3,4,5,6,10,9,8,7] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,4,3,2,7,6,5,10,9,8] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[2,1,4,3,7,6,5,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[1,2,4,3,7,6,5,10,9,8] => [[1,2,3,5,8],[4,6,9],[7,10]] => 001011011
[1,2,3,4,7,6,5,10,9,8] => [[1,2,3,4,5,8],[6,9],[7,10]] => 000011011
[1,3,2,5,4,7,6,10,9,8] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,2,3,5,4,7,6,10,9,8] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[1,2,3,4,5,7,6,10,9,8] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[1,2,3,4,5,6,7,10,9,8] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,4,3,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[1,2,3,4,6,5,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,2,3,4,5,6,8,7,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[5,2,7,4,1,6,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[4,7,3,1,5,6,2,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,8,3,4,1,6,7,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[1,7,8,4,5,6,2,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[1,5,8,4,2,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,6,3,8,5,2,7,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[6,2,3,7,5,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[1,7,3,4,8,6,2,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[8,7,3,2,1,6,5,4] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,7,6,3,1,5,2,4] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,1,7,2,3,4,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[9,8,7,6,5,2,1,4,3] => [[1,8],[2,9],[3],[4],[5],[6],[7]] => 11111101
[9,8,7,3,2,1,6,5,4] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 11111011
[9,8,7,6,3,1,5,2,4] => [[1,7,9],[2,8],[3],[4],[5],[6]] => 11111010
[9,4,3,2,1,8,7,6,5] => [[1,6],[2,7],[3,8],[4,9],[5]] => 11110111
[9,8,4,3,1,7,6,2,5] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[9,8,7,2,1,4,3,6,5] => [[1,6,8],[2,7,9],[3],[4],[5]] => 11110101
[9,8,7,4,1,6,2,3,5] => [[1,6,8,9],[2,7],[3],[4],[5]] => 11110100
[5,4,3,1,9,8,7,2,6] => [[1,5,9],[2,6],[3,7],[4,8]] => 11101110
[9,5,2,1,8,4,3,7,6] => [[1,5,8],[2,6,9],[3,7],[4]] => 11101101
[9,8,3,1,5,2,7,4,6] => [[1,5,7,9],[2,6,8],[3],[4]] => 11101010
[6,3,1,9,5,2,8,4,7] => [[1,4,7,9],[2,5,8],[3,6]] => 11011010
[6,5,1,9,8,2,3,4,7] => [[1,4,7,8,9],[2,5],[3,6]] => 11011000
[9,2,1,4,3,6,5,8,7] => [[1,4,6,8],[2,5,7,9],[3]] => 11010101
[9,6,1,8,2,3,4,5,7] => [[1,4,6,7,8,9],[2,5],[3]] => 11010000
[5,1,7,2,9,3,4,6,8] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[7,1,9,2,3,4,5,6,8] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[10,9,8,7,6,5,2,1,4,3] => [[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => 111111101
[10,9,8,7,3,2,1,6,5,4] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 111111011
[10,9,8,7,6,3,1,5,2,4] => [[1,8,10],[2,9],[3],[4],[5],[6],[7]] => 111111010
[10,9,4,3,2,1,8,7,6,5] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 111110111
[10,9,8,4,3,1,7,6,2,5] => [[1,7,10],[2,8],[3,9],[4],[5],[6]] => 111110110
[10,9,8,7,2,1,4,3,6,5] => [[1,7,9],[2,8,10],[3],[4],[5],[6]] => 111110101
[10,9,8,7,4,1,6,2,3,5] => [[1,7,9,10],[2,8],[3],[4],[5],[6]] => 111110100
[10,5,4,3,1,9,8,7,2,6] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 111101110
[10,9,5,2,1,8,4,3,7,6] => [[1,6,9],[2,7,10],[3,8],[4],[5]] => 111101101
[10,9,5,4,1,8,7,2,3,6] => [[1,6,9,10],[2,7],[3,8],[4],[5]] => 111101100
[10,9,8,3,1,5,2,7,4,6] => [[1,6,8,10],[2,7,9],[3],[4],[5]] => 111101010
[6,5,2,1,10,9,4,3,8,7] => [[1,5,9],[2,6,10],[3,7],[4,8]] => 111011101
[6,5,4,1,10,9,8,2,3,7] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 111011100
[10,3,2,1,6,5,4,9,8,7] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 111011011
[10,6,5,1,9,8,2,3,4,7] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[10,9,2,1,4,3,6,5,8,7] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[10,9,6,1,8,2,3,4,5,7] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 111010000
[4,3,1,7,6,2,10,9,5,8] => [[1,4,7,10],[2,5,8],[3,6,9]] => 110110110
[7,2,1,10,4,3,6,5,9,8] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[7,4,1,10,6,2,9,3,5,8] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[7,6,1,10,9,2,3,4,5,8] => [[1,4,7,8,9,10],[2,5],[3,6]] => 110110000
[10,5,1,7,2,9,3,4,6,8] => [[1,4,6,8,9,10],[2,5,7],[3]] => 110101000
[10,7,1,9,2,3,4,5,6,8] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[4,1,6,2,8,3,10,5,7,9] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[6,1,8,2,10,3,4,5,7,9] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[8,1,10,2,3,4,5,6,7,9] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[2,4,8,5,3,7,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,4,1,8,5,3,7,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,4,8,6,3,1,7,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[3,4,6,8,2,1,7,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,4,1,5,8,2,7,6] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,1,4,5,3,2,7,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,4,1,5,2,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,4,6,2,1,8,7,5] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[3,5,6,2,1,7,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,4,6,2,7,8,1,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[8,1,4,6,3,7,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,1,4,6,3,7,5,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[3,5,6,2,1,7,4,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[8,1,5,6,7,3,4,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,1,5,6,7,3,2,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[3,4,1,6,8,7,2,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,5,6,1,8,7,2,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,1,3,8,6,7,4,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,1,3,2,6,7,5,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[2,3,8,6,7,1,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,4,1,8,6,7,5,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[2,5,8,6,1,7,4,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,5,6,1,8,7,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,4,1,6,8,7,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,4,6,8,7,1,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,1,4,6,2,7,5,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[3,5,1,6,7,8,4,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,5,6,1,7,8,3,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,5,6,1,7,3,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,5,1,6,7,4,8,2] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[8,1,5,6,7,4,2,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[8,1,5,6,7,4,3,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[3,5,1,6,7,4,2,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[4,5,6,1,7,3,2,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[6,5,8,7,4,3,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,4,2,7,8,5,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,1,4,8,7,5,2,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[1,6,4,8,7,5,2,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,8,6,2,4,7,3,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,1,6,2,4,7,3,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,6,2,1,4,8,3,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[6,4,1,7,8,5,2,3] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[7,6,1,2,4,8,3,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,6,1,3,4,8,2,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,1,6,3,4,7,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[1,8,6,3,4,7,2,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,7,2,5,4,8,3,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[7,1,2,5,4,8,3,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[2,7,1,5,4,8,3,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,8,6,3,4,7,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,8,6,1,4,7,3,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,2,1,5,4,8,3,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[1,2,7,5,4,8,3,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,2,7,5,4,8,1,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,5,8,4,7,3,1,6] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,3,7,5,4,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[6,8,3,2,4,7,1,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,7,2,5,4,8,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,1,7,5,4,8,2,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,3,7,5,4,8,2,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,5,8,4,7,3,2,6] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,1,8,4,7,3,2,6] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,8,2,4,7,3,1,6] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,8,4,3,7,5,1,2] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[8,7,5,6,2,1,4,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,5,2,4,7,3,1,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,1,5,4,7,3,2,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[1,8,5,4,7,3,2,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[1,7,3,5,4,8,2,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,6,3,1,4,7,2,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,6,4,2,7,5,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[8,6,4,1,7,2,5,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,3,7,4,6,8,2,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,1,3,2,7,8,5,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,4,3,2,7,8,5,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,4,3,1,7,8,5,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,7,3,5,4,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,5,4,7,3,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,7,3,4,6,8,2,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,2,5,4,7,3,1,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,2,3,5,4,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[3,2,1,4,7,8,5,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,1,7,6,4,3,5,2] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[8,6,4,5,2,7,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,1,8,6,4,3,5,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[7,4,2,5,1,6,3,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,3,6,5,2,1,4,8] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,3,6,5,2,1,7,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[7,3,6,5,2,1,8,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[7,5,8,6,4,2,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[5,4,2,8,1,3,7,6] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[5,8,2,6,4,1,3,7] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[6,4,2,5,1,8,3,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,3,5,2,1,4,7,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[2,5,8,6,3,1,4,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,3,5,8,1,4,7,6] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,3,6,8,1,5,7,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[6,3,8,5,2,7,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,3,7,5,2,1,4,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,5,7,6,3,1,4,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,8,7,6,3,1,5,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[2,5,8,7,6,3,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[2,4,8,1,6,5,7,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,8,7,3,6,1,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[7,3,5,2,1,4,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,4,2,5,1,3,7,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[2,3,6,8,1,4,7,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,7,8,6,3,1,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,3,8,5,2,1,4,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,3,6,1,8,4,7,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,8,6,3,1,4,5,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[8,3,5,2,1,4,6,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[2,4,8,1,3,7,5,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,5,8,1,7,3,6,4] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[2,8,1,5,7,3,6,4] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[3,8,6,1,4,7,5,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,6,8,1,5,7,3,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[2,7,1,5,8,3,4,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,7,5,8,1,2,6,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[7,3,6,1,2,8,4,5] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,4,8,1,6,5,2,3] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,4,5,8,6,1,2,3] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,8,4,5,1,7,2,3] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,1,8,7,6,2,3,4] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,6,1,8,7,5,2,3] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,5,1,8,7,2,3,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[3,4,8,7,1,2,5,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[6,4,8,7,1,2,5,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[5,6,8,3,7,1,4,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[6,5,1,2,7,3,8,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,5,1,8,2,7,3,4] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[6,5,1,8,7,2,3,4] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,5,1,7,2,8,3,4] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,5,1,7,2,3,8,4] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,6,8,7,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[6,8,5,7,4,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,3,8,1,5,2,4,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,1,7,5,3,6,2,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[1,8,4,2,3,6,7,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,5,8,3,4,6,7,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,1,7,2,3,6,8,5] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,6,2,1,5,7,8,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,5,2,3,1,7,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,2,6,7,4,1,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,6,2,7,1,4,8,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[6,2,3,8,1,7,4,5] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[2,6,8,3,4,7,1,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[4,6,2,7,5,1,3,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[2,6,3,1,8,4,5,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,4,3,7,8,1,5,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,3,2,7,4,8,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[5,1,2,7,6,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,6,3,1,8,7,4,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[3,5,6,4,7,8,1,2] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[5,3,6,4,2,8,7,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,4,2,3,7,8,6,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,1,8,2,5,7,3,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,1,8,4,7,2,5,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[6,2,3,8,4,1,7,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[2,6,4,1,5,3,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,2,7,6,4,1,8,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,5,4,1,7,6,8,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[6,2,1,4,7,8,3,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,6,5,1,7,8,3,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,7,5,2,1,6,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[4,2,3,7,8,1,6,5] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,8,3,1,7,2,4,6] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[6,8,3,1,5,2,4,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,1,7,4,2,6,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,8,3,2,5,1,7,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[6,8,4,3,1,5,7,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[6,8,4,2,1,5,7,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,1,7,3,2,4,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,2,1,8,3,6,7,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[4,3,8,1,6,2,7,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,2,1,8,5,7,3,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,3,2,1,7,4,5,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,4,2,1,7,5,3,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,5,2,1,8,6,3,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[5,3,2,7,6,1,4,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[5,3,2,8,6,1,4,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,3,2,8,7,1,4,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,2,8,1,7,3,5,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,3,8,7,2,1,5,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,1,5,8,4,7,3,6] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[4,3,1,6,2,7,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,4,1,7,2,8,6,3] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[6,5,3,1,7,8,4,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,4,2,1,7,8,5,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[5,3,2,1,6,7,8,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,6,1,4,5,7,2,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[5,2,8,3,7,4,6,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,2,8,5,4,7,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,8,6,3,7,4,2,5] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,8,6,5,7,2,3,4] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,2,8,4,3,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,4,2,7,3,6,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,4,2,8,3,6,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,5,3,8,4,7,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[5,2,8,4,3,7,1,6] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,2,8,3,7,4,1,5] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,4,2,7,3,1,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[6,4,3,7,1,2,8,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[6,4,3,8,1,2,7,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,6,3,8,4,2,1,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,2,8,5,1,6,3,4] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[7,2,8,4,3,1,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,5,3,8,4,2,6,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[6,4,2,7,3,1,5,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,6,4,8,2,3,5,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,6,8,1,2,5,3,4] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,3,1,7,8,4,6,2] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[5,3,2,7,8,4,6,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,4,1,6,3,8,7,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[6,5,1,7,8,2,3,4] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,3,1,7,8,4,2,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,4,1,7,3,8,2,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,3,2,7,8,4,1,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[6,1,5,4,3,2,8,7] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,7,6,1,3,5,2,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,1,6,5,7,3,4,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,4,1,5,7,6,2,3] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[7,8,6,2,5,3,1,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,1,3,5,2,8,4,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[8,1,3,7,4,2,5,6] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[4,3,8,7,5,2,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,7,1,8,5,3,4,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[2,7,6,4,8,3,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[6,5,2,7,1,4,8,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,4,6,1,3,2,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,5,2,1,3,8,4,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,4,7,6,3,1,5,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[7,4,1,5,6,3,8,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,4,7,5,6,1,8,2] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,4,7,5,6,3,8,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[5,4,1,7,6,2,8,3] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[3,5,6,7,1,4,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,7,6,1,3,4,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[5,7,2,1,6,3,8,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,7,2,5,6,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,6,2,5,7,1,4,3] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[2,7,4,5,3,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[6,8,7,1,3,2,5,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,8,6,5,7,1,4,3] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[5,8,4,3,2,6,7,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[1,8,5,6,2,4,7,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[8,1,5,6,2,4,7,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,4,8,1,3,2,7,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[1,4,5,2,8,6,7,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,3,1,7,8,6,4,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,5,7,6,2,8,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,5,6,1,2,8,7,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[5,4,1,2,8,6,7,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[8,4,5,2,1,6,7,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[3,1,2,6,8,4,7,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,1,3,2,7,8,4,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,5,4,2,7,8,3,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,6,7,8,3,1,5,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[7,6,2,8,4,3,1,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[5,2,8,6,3,4,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,6,8,4,3,2,7,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[5,3,8,1,7,2,4,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,6,7,8,4,2,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[6,5,1,8,4,3,7,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[6,3,8,4,2,1,7,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[2,5,8,3,1,6,7,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,5,8,1,2,6,7,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,2,8,1,5,6,7,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[1,5,8,3,2,6,7,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[1,3,8,6,2,4,7,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[3,2,7,8,4,6,1,5] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,1,8,3,4,6,7,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,8,7,2,1,6,3,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[2,8,1,6,3,4,7,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[8,3,4,2,1,6,5,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,4,7,2,5,8,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,4,5,2,6,3,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[2,4,5,8,3,6,1,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[3,5,8,1,2,6,4,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[8,6,1,3,5,2,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,5,1,2,6,4,3,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,8,6,1,3,4,2,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,4,6,1,3,2,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[7,3,4,5,2,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,7,4,3,6,1,8,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,6,4,3,7,8,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,4,1,8,3,2,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,2,1,7,8,4,5,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[7,6,3,1,5,4,8,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[2,4,6,5,1,7,8,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,4,7,5,6,8,2,3] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,4,7,6,5,8,2,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,7,5,2,4,6,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,6,1,7,4,2,8,3] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,7,4,8,1,2,6,5] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,3,5,7,8,1,4,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,6,5,7,1,8,4,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,4,7,8,2,1,3,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,7,3,8,4,1,2,5] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[2,7,8,3,4,6,1,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[7,5,8,4,1,3,2,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[4,7,5,8,3,1,2,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,6,7,4,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,7,3,1,6,8,4,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[2,7,3,1,8,6,4,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,8,4,3,1,5,7,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,8,1,2,3,5,7,6] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,6,8,1,2,4,3,5] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,6,8,5,1,3,2,4] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[2,8,5,4,6,1,7,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[8,4,5,2,7,6,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,7,6,4,1,2,5,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,7,1,3,5,2,8,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,7,2,3,6,8,1,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,5,3,2,7,6,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[3,4,6,7,5,8,1,2] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,4,5,7,6,1,8,2] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,6,4,5,7,8,3,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[3,8,5,1,6,2,7,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[2,5,1,3,6,8,7,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,4,6,1,3,7,8,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,3,5,7,1,4,8,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,3,4,6,8,1,5,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,7,8,4,1,5,6,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[8,7,5,4,2,1,6,3] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[6,7,2,5,1,8,4,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[3,6,1,2,5,8,4,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[1,4,5,8,2,3,7,6] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,2,6,4,5,8,3,7] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,5,2,4,6,8,3,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,6,1,5,8,2,4,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,6,5,1,4,8,3,7] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[5,2,6,1,4,8,3,7] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,5,1,8,4,7,3,6] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[2,7,1,4,3,6,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,3,7,5,8,2,4,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[8,2,1,5,7,3,4,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[2,5,4,8,1,3,7,6] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[2,4,1,3,8,6,7,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[8,4,3,7,1,2,6,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[1,7,3,5,8,2,6,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,8,4,2,6,7,3,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,1,6,8,7,2,4,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,2,1,6,8,3,4,5] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[3,1,7,6,8,2,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,1,7,2,6,8,3,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,1,7,2,3,6,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[7,2,1,6,3,5,8,4] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[2,6,1,7,3,5,8,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[7,1,2,5,3,6,8,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,4,1,2,7,8,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,1,3,2,4,6,7,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[7,3,1,2,4,6,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[1,8,3,4,7,2,5,6] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[3,5,8,1,2,7,4,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,6,8,1,2,4,7,5] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,1,3,8,7,2,6,5] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[1,3,7,4,8,2,6,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,4,6,8,2,3,7,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,5,8,1,7,2,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,6,8,1,7,3,4,5] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,1,5,8,2,3,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[1,8,3,2,7,5,6,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,1,7,2,8,5,6,4] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[2,6,7,3,8,1,5,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[8,4,1,7,3,6,2,5] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[3,7,2,8,6,1,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,2,3,8,7,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,1,7,8,4,2,6,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[5,1,8,7,4,2,6,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[4,7,2,8,3,6,5,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,1,7,8,5,3,6,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[5,1,7,4,8,3,6,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,1,8,7,5,3,6,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,8,2,7,3,6,5,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[4,7,2,6,3,5,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,8,2,4,3,7,5,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,7,2,4,3,8,5,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[6,8,2,7,3,5,4,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[3,8,7,2,4,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,7,8,2,4,1,5,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,6,8,2,4,5,7,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,6,7,2,4,5,8,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,5,1,4,2,3,8,7] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,6,1,7,2,5,4,3] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,7,6,1,2,3,5,4] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[5,4,3,1,6,2,8,7] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,3,4,7,1,6,2,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[6,3,4,1,8,5,2,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,8,5,2,7,1,6,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[2,8,6,7,5,3,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,1,8,7,3,6,4,5] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[3,6,5,8,2,4,7,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,2,1,8,7,3,4,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,5,2,7,4,3,8,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[4,6,5,2,7,3,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[6,2,7,1,8,3,5,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[2,7,5,4,8,3,6,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[8,7,5,1,2,6,4,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,4,3,2,7,1,6,5] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,1,6,2,3,8,5,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,8,1,3,2,7,5,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[3,8,1,4,7,5,2,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[6,3,8,7,4,5,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,1,4,8,5,2,3,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[8,5,7,4,6,2,1,3] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[4,6,7,8,2,3,5,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[8,7,4,6,2,1,5,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[7,6,1,3,5,2,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,8,3,2,4,6,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[8,2,6,5,3,1,7,4] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,8,7,6,5,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[2,1,8,6,4,3,7,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,1,7,6,5,3,8,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,7,6,1,3,5,8,4] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,2,5,4,6,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[4,7,6,1,2,5,8,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,4,1,7,6,8,5,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,4,1,7,8,5,6,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[7,5,4,3,1,8,6,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,5,6,2,7,3,1,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,4,2,5,6,1,7,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[6,3,5,4,1,7,8,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,1,3,6,7,5,8,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[1,7,2,4,5,8,3,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,7,4,5,8,3,2,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,6,4,7,8,3,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,2,6,4,7,8,3,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[6,1,4,7,8,3,5,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,6,4,7,8,1,5,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,3,6,7,1,8,2,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,6,4,7,8,1,2,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,7,2,1,5,3,8,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[1,3,6,4,7,2,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[3,6,4,7,2,8,5,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[5,1,3,4,2,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,4,2,1,3,7,8,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,6,7,3,8,2,5,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[6,1,4,7,8,5,2,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[6,3,2,1,7,8,5,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,6,5,1,3,2,4,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[6,4,7,8,3,2,5,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,8,4,7,1,2,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[8,6,1,2,5,4,3,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[4,8,6,1,5,3,2,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,8,6,4,1,3,2,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[8,3,6,4,5,2,1,7] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[6,8,5,7,4,2,3,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[2,3,8,7,1,6,4,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,3,7,8,1,6,2,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[3,5,8,7,4,1,2,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[7,3,8,4,1,2,5,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,8,1,2,7,3,5,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[6,8,1,2,7,4,5,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,6,8,4,1,3,7,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,5,4,7,1,6,3,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[2,5,8,7,3,6,4,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[2,4,8,7,5,6,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,7,4,8,5,6,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[6,4,8,7,5,1,2,3] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,8,5,2,4,6,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,7,1,8,4,6,2,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,3,8,7,2,1,4,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,3,7,8,5,6,1,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,7,6,8,5,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[2,6,7,8,5,1,3,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,4,7,8,1,6,3,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[5,4,7,8,2,6,3,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,8,3,4,1,5,7,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[6,8,3,4,1,2,7,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,8,7,1,5,2,3,4] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,8,3,2,7,6,1,4] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[2,5,3,1,8,6,7,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,5,3,2,8,6,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,5,8,6,1,4,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,8,5,6,1,4,7,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[4,8,6,1,5,2,7,3] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[5,8,2,3,7,6,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,6,8,5,3,2,7,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[2,6,4,8,5,1,7,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[7,6,4,8,5,2,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[3,4,8,6,5,2,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[3,4,8,7,5,6,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[7,5,3,2,8,6,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[2,5,1,3,8,6,7,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[4,5,1,2,8,6,7,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,4,8,1,3,6,7,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,3,5,4,1,6,7,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,3,4,8,5,6,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[6,1,5,7,2,4,8,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,4,5,1,2,3,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,4,3,1,2,8,5,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,4,7,6,2,1,5,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,4,6,5,7,1,3,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,2,1,4,5,8,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[7,4,1,6,3,5,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,5,7,6,4,1,8,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,7,5,2,1,3,8,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,7,2,3,6,4,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,6,2,3,7,1,4,5] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,7,2,4,8,3,6,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[1,7,2,4,8,6,3,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,6,1,5,4,8,3,2] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[4,7,3,2,1,8,5,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,1,7,2,5,8,4,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,8,7,6,1,2,5,3] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,8,6,1,3,2,5,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[2,8,6,7,4,1,3,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,8,6,4,2,3,1,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,8,3,1,6,5,4,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,8,1,2,5,7,4,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[6,8,5,4,2,7,3,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,8,3,1,2,4,5,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,6,8,7,3,1,5,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[6,5,3,7,8,4,1,2] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[4,1,3,8,7,5,6,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[6,2,7,4,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[8,4,5,2,1,6,3,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,3,2,6,8,1,7,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,1,5,6,3,8,2,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,1,2,4,7,8,3,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[3,5,4,2,8,1,6,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,1,3,8,4,2,7,6] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[6,2,8,7,3,5,4,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[7,1,8,4,3,6,5,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,6,8,7,4,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,6,8,1,7,3,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[3,1,6,8,7,4,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,4,6,8,2,1,5,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,5,8,4,3,1,2,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[2,5,8,3,6,7,4,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[8,5,1,3,7,4,6,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[1,5,8,3,7,4,2,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[3,8,2,7,1,5,6,4] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,8,2,3,6,4,1,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[6,8,2,3,4,7,5,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,5,1,8,4,2,6,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[3,6,8,5,2,7,4,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[2,1,6,5,4,8,3,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,1,7,8,4,6,5,3] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[2,1,7,4,3,5,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,5,7,8,4,6,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[7,5,2,8,4,6,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[7,8,2,4,3,1,5,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,6,3,8,1,5,4,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[8,4,3,1,7,5,2,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,3,1,4,6,8,5,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,3,8,7,1,6,5,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[5,2,4,3,6,8,1,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,8,6,5,4,1,2,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,7,5,6,3,8,2,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[4,2,7,5,8,3,6,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,8,2,7,3,4,6,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,7,2,4,5,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,3,2,1,4,8,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,2,3,1,4,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,2,1,3,6,4,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[7,1,8,3,5,4,6,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,1,2,4,8,5,6,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[7,2,1,3,4,5,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[8,7,3,5,4,2,1,6] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[8,4,6,5,3,2,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[5,1,6,4,3,2,8,7] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[8,3,7,1,4,6,5,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[2,8,3,6,4,7,5,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,2,1,7,5,8,3,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,3,8,7,5,2,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,7,2,1,5,8,4,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[9,1,8,7,6,5,4,3,2] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[7,6,8,1,5,4,3,2] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[7,1,9,8,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[6,1,9,8,7,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[5,4,8,7,6,1,3,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,1,9,8,7,6,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[4,1,9,8,7,6,5,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[3,1,9,8,7,6,5,4,2] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[10,1,9,8,7,6,5,4,3,2] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[7,6,1,8,5,4,3,2] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[8,7,9,1,6,5,4,3,2] => [[1,3],[2,5],[4],[6],[7],[8],[9]] => 10101111
[8,1,10,9,7,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[6,5,8,1,7,4,3,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,1,10,9,8,6,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[6,1,10,9,8,7,5,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[6,5,8,7,4,1,3,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,1,10,9,8,7,6,4,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[4,3,9,8,7,6,5,1,2] => [[1,3],[2,4],[5,9],[6],[7],[8]] => 10111110
[4,1,10,9,8,7,6,5,3,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[3,2,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[3,1,10,9,8,7,6,5,4,2] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[1,6,4,8,3,2,5,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,8,3,5,6,2,4,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,4,8,5,6,2,3,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,2,8,5,3,7,4,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[6,1,4,8,2,3,5,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[8,7,2,5,6,1,4,3] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[1,8,2,5,4,7,3,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,7,4,1,2,3,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[1,7,4,2,5,3,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[6,7,4,2,1,3,8,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[6,4,3,8,5,7,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[7,4,3,6,2,1,5,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,2,5,3,4,1,6,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,3,7,4,5,6,1,2] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,7,4,3,1,5,6,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[6,8,4,2,3,1,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,7,5,2,4,1,6,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,1,3,2,8,4,5,6] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,1,7,4,8,3,5,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[5,2,8,6,1,3,4,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[2,8,3,1,4,5,6,7] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[7,4,8,2,3,1,5,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,2,7,3,1,5,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,3,7,2,1,4,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,5,2,4,7,1,3,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[6,5,7,4,1,8,2,3] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,6,4,5,1,8,2,3] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[8,6,4,1,3,7,2,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[6,4,3,1,8,2,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,4,1,2,8,3,5,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[4,8,1,3,5,7,2,6] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[7,8,4,1,3,6,2,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,5,8,1,3,7,2,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,3,6,1,8,2,4,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,7,3,1,8,2,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[8,3,1,7,2,4,5,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[2,8,1,4,7,3,5,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,1,8,5,4,7,6,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,1,5,8,3,7,6,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,1,5,3,8,7,6,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,5,1,8,2,7,6,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,8,5,3,1,7,6,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,5,2,8,1,7,6,3] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,5,2,1,8,7,6,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,6,2,7,8,1,4,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[4,6,2,8,7,1,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,8,6,3,7,1,5,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,8,6,3,7,5,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,6,8,2,7,5,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,6,2,8,7,5,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,6,2,7,4,1,8,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[5,6,7,2,3,1,8,4] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,6,7,2,8,3,1,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,6,7,2,1,8,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,6,7,2,1,3,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[5,6,1,7,8,2,4,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,6,1,7,2,4,8,3] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[5,1,6,7,8,3,4,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[4,1,6,8,7,3,5,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,1,8,6,7,5,4,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,1,6,8,7,5,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[5,1,6,7,4,8,3,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,6,1,7,8,4,2,3] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,6,8,1,7,5,2,3] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,8,6,1,7,5,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[5,6,7,1,8,3,2,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[5,6,7,1,3,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[5,6,7,1,3,2,8,4] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,6,7,3,1,2,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[5,6,7,3,8,1,2,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,6,8,7,4,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[5,6,7,3,8,2,1,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,4,6,2,3,5,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[1,4,8,6,3,2,5,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,4,1,6,3,8,5,2] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,6,3,1,5,8,4,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[6,4,2,5,7,3,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,2,5,7,6,3,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[7,4,5,6,1,8,3,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[4,1,5,8,6,3,2,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,2,7,6,1,8,5,4] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,7,5,1,6,8,2,3] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[8,6,5,1,2,7,4,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[3,2,5,1,4,8,7,6] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[8,5,4,1,3,2,7,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[1,4,2,3,6,8,7,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[5,4,8,3,7,1,6,2] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[4,7,1,8,2,5,3,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[6,4,1,8,5,3,7,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,4,6,1,3,5,2,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[3,2,5,4,7,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,2,4,3,7,8,1,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[8,1,6,7,2,5,3,4] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[3,1,7,6,5,8,2,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,2,7,5,6,8,3,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[6,1,4,7,2,8,3,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,2,1,7,6,8,4,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[3,2,8,6,4,7,1,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[7,8,4,6,3,2,1,5] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[1,8,6,5,3,7,2,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,2,5,3,6,7,1,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,8,5,2,7,6,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,7,5,3,1,8,6,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,5,3,6,8,1,7,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[3,5,2,6,1,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,6,3,5,7,2,8,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,5,4,6,7,8,2,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[8,4,6,5,7,2,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[7,4,5,2,6,8,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,4,2,6,8,7,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,5,1,4,3,2,8,7] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[3,6,4,5,2,1,8,7] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[7,5,4,2,3,8,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,8,1,3,5,6,2,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[1,7,8,3,5,6,2,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[3,1,7,8,5,2,6,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[1,3,7,5,8,2,6,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[3,1,7,5,8,2,6,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[3,5,7,1,8,4,6,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,5,7,8,1,4,6,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[5,3,7,8,4,6,1,2] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,3,7,1,8,4,6,2] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[5,1,3,7,8,4,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,6,2,1,4,5,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,6,2,5,1,3,8,7] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,4,2,5,1,3,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,6,1,7,3,2,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[2,5,8,1,7,3,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[6,8,2,7,3,1,4,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,8,2,3,7,1,4,5] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[8,6,2,7,4,5,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[5,2,8,1,7,3,4,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,2,3,8,1,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[5,2,8,3,7,1,4,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,2,8,4,6,1,3,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[2,1,5,8,4,3,6,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,8,3,2,7,1,4,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,1,3,8,2,5,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,5,8,2,7,1,4,6] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[4,5,8,2,6,1,3,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[2,6,8,3,7,1,4,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[5,1,8,3,7,2,4,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,1,8,4,6,2,3,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,8,4,1,6,2,3,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[4,5,8,1,6,2,3,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[5,4,8,1,6,2,3,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,8,5,1,6,2,3,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[2,1,5,4,8,3,6,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,4,3,8,1,5,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[3,1,8,4,2,5,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,8,4,2,1,5,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[2,3,8,4,1,5,6,7] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[3,4,2,8,1,5,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[3,8,5,2,7,1,4,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[4,8,5,2,6,1,3,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,1,4,8,5,3,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,2,8,4,1,5,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[2,8,4,3,1,5,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[4,1,7,5,6,2,8,3] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[5,7,4,3,8,1,6,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[5,7,4,3,8,2,6,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[3,8,4,2,6,7,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,8,4,1,6,7,5,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,1,7,5,2,8,4,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,6,4,3,2,8,1,7] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[2,6,7,5,3,8,4,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,7,4,8,2,5,3,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,1,6,7,5,3,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,8,4,2,1,6,7,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,7,4,3,8,2,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,7,4,8,1,2,5,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,7,5,8,1,2,4,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[6,7,4,8,3,1,2,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,4,8,1,2,5,7,6] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,1,3,4,8,2,5,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[6,2,3,4,8,1,5,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,4,8,2,1,5,7,6] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[6,7,5,8,2,4,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[6,7,5,8,3,1,4,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[3,4,8,1,5,7,6,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,5,7,6,1,4,8,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[6,7,4,8,2,3,5,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[6,7,4,8,1,3,5,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[2,6,7,5,1,3,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,3,1,4,8,2,5,7] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,7,4,8,1,3,2,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[6,7,5,8,4,1,3,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,7,4,8,2,1,3,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[6,7,4,8,1,2,3,5] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[1,5,6,3,4,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,4,3,6,5,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[8,1,3,4,7,2,6,5] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[5,1,7,3,4,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[6,7,8,2,3,5,4,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[5,8,6,2,3,7,4,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,8,3,4,7,5,6,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,8,3,4,7,6,2,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,7,2,3,6,5,4,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[3,8,1,7,5,2,6,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,8,1,6,7,2,5,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,1,3,8,4,6,5,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[8,2,1,7,4,3,6,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[1,3,2,8,5,4,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[8,3,1,5,7,2,6,4] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,4,5,1,7,2,6,3] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[1,5,6,8,7,4,2,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[8,4,5,7,6,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[1,4,8,5,7,6,2,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,4,8,5,7,3,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,3,8,6,5,7,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,7,2,8,5,3,4,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[5,2,7,8,6,3,4,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[4,2,8,6,7,3,5,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[3,2,8,7,5,4,6,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[3,1,8,7,5,6,2,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,1,8,6,7,5,2,3] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,1,7,8,6,4,2,3] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,7,1,8,5,4,2,3] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[7,8,3,2,6,1,4,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[3,4,8,2,6,1,7,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[7,8,4,1,5,6,3,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,8,1,4,5,6,3,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,8,1,2,6,3,4,5] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[7,8,5,1,4,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[7,8,4,5,1,6,3,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,3,8,4,1,6,7,2] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,2,4,8,1,5,3,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[3,4,8,5,1,6,7,2] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,5,8,1,4,6,7,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[1,4,8,2,6,3,7,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,3,8,1,4,6,7,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,2,6,8,1,5,3,7] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[7,4,2,8,1,5,3,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,1,7,5,8,4,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[6,2,1,8,4,5,3,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[1,2,7,8,5,3,4,6] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[6,3,7,8,5,4,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,1,5,7,8,4,3,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[1,7,5,6,8,4,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,1,8,4,5,6,7,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,4,8,6,5,3,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,4,1,8,6,5,3,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,2,1,8,6,5,3,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,2,7,8,5,1,4,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,3,7,8,5,1,4,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,7,3,8,5,1,4,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,6,2,8,5,1,4,7] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[4,1,2,8,7,5,3,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[1,4,2,8,7,5,3,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,3,6,8,5,4,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,2,1,8,5,3,4,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[1,2,6,8,4,5,3,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[7,1,6,5,8,4,3,2] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[6,5,7,1,8,4,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[5,7,6,1,8,4,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[6,7,1,5,8,4,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,7,3,8,5,4,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[7,1,2,8,4,5,3,6] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[7,6,1,5,8,4,3,2] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[7,5,6,1,8,4,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,7,9,10,5,6,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7,10],[9]] => 100101010
[8,6,9,4,7,3,5,10,1,2] => [[1,3,8],[2,5],[4,7],[6,10],[9]] => 101010010
[7,1,6,5,3,2,4,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[1,8,7,5,3,2,4,6] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[1,8,7,4,2,5,3,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[8,7,4,2,5,3,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,1,6,4,2,5,3,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,6,5,4,7,1,3,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[7,1,5,3,6,4,2,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,3,7,1,6,4,2,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[5,3,6,4,2,7,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[1,5,3,8,7,4,2,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,4,2,8,6,3,5,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[5,3,6,1,8,7,4,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,1,5,3,8,7,4,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[2,8,7,5,4,6,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[2,3,1,8,7,5,4,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,3,8,7,4,2,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[7,4,2,1,8,6,3,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,6,3,5,7,4,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[1,8,6,3,5,7,4,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[6,3,8,5,2,1,7,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,6,3,7,4,2,1,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[2,8,6,4,7,5,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,1,8,6,3,7,4,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[6,3,7,4,1,8,5,2] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[8,5,2,6,3,7,4,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[6,1,8,7,4,2,5,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,6,3,7,4,2,5,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[1,8,6,3,2,4,7,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[8,6,3,2,4,7,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[7,5,1,8,6,3,2,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,1,8,7,5,3,2,4] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,3,2,8,7,6,1,5] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[2,4,5,1,3,8,7,6] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[7,5,8,6,3,2,4,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[1,7,5,8,6,3,2,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,7,4,2,5,8,6,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[8,6,3,1,7,4,2,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,7,4,2,5,3,1,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,3,1,8,7,4,2,6] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[4,1,8,7,5,3,2,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,8,6,4,1,3,7,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,1,8,6,3,2,7,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[7,4,2,8,6,3,1,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,3,1,8,5,2,7,4] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[8,5,2,6,3,1,7,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,4,8,5,2,6,3,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[1,8,5,2,7,4,6,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[8,5,2,7,4,6,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[7,4,6,3,1,8,5,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[6,3,1,7,4,8,5,2] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[8,6,3,1,5,7,4,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[4,1,7,5,8,6,3,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,3,1,7,5,8,6,4] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[7,4,8,5,2,1,6,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,5,2,1,7,4,6,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[1,7,4,6,3,8,5,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[4,1,8,5,7,3,2,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[2,1,5,7,8,4,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,1,7,4,8,3,2,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[4,7,2,8,3,6,1,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,6,2,7,3,1,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,3,2,7,6,5,10,9,8,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,4,3,6,5,2,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,4,3,7,6,2,10,9,8,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,5,4,7,6,3,10,9,8,2] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,4,3,8,7,2,10,9,6,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[1,5,4,8,7,3,10,9,6,2] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,3,1,6,5,4,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,3,1,7,6,5,10,9,8,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,4,1,6,5,3,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,4,1,7,6,3,10,9,8,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,7,6,4,10,9,8,3] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,4,1,8,7,3,10,9,6,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,8,7,4,10,9,6,3] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,4,2,6,5,1,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,4,2,7,6,1,10,9,8,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,7,6,1,10,9,8,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,5,3,7,6,2,10,9,8,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,4,2,8,7,1,10,9,6,5] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,8,7,1,10,9,6,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,5,3,8,7,2,10,9,6,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,6,4,3,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,7,4,3,10,9,8,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,6,1,7,5,4,10,9,8,3] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,8,4,3,10,9,7,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,6,1,8,5,4,10,9,7,3] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,6,4,1,10,9,8,7] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,7,4,1,10,9,8,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,6,2,7,5,1,10,9,8,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,6,3,7,5,2,10,9,8,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,8,4,1,10,9,7,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,6,2,8,5,1,10,9,7,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,6,3,8,5,2,10,9,7,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,7,2,8,6,1,10,9,5,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,7,3,8,6,2,10,9,5,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,5,1,9,4,3,10,8,7,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[2,6,1,9,5,4,10,8,7,3] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,5,2,9,4,1,10,8,7,6] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,6,2,9,5,1,10,8,7,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,6,3,9,5,2,10,8,7,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[3,7,2,9,6,1,10,8,5,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[6,2,8,4,1,7,3,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[6,3,4,8,1,7,2,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[1,8,5,4,2,3,7,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,5,4,8,1,2,7,6] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[5,6,3,8,7,1,2,4] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[2,6,8,4,1,7,3,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[1,8,7,4,2,6,3,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[6,3,5,8,7,1,2,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[5,2,8,6,7,1,3,4] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[6,2,8,7,5,1,3,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[1,8,5,7,6,2,3,4] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,6,7,8,5,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,8,6,7,5,2,3,4] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[5,7,6,4,8,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,3,8,7,5,1,2,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,8,7,4,1,3,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,4,8,7,1,3,2,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,8,6,1,3,2,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,4,2,7,6,8,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[2,8,7,1,4,5,3,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,2,1,8,7,3,5,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,1,6,3,2,8,7,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,6,1,8,7,3,2,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[8,7,2,3,5,4,1,6] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[5,3,1,4,8,7,2,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[4,3,5,2,8,7,1,6] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,4,2,8,6,1,5,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,7,6,8,1,5,2,4] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[8,1,4,2,3,6,7,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[3,7,2,1,8,6,4,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[2,8,6,1,7,3,5,4] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[1,7,6,3,5,8,2,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,7,5,1,6,8,2,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,6,5,8,1,4,7,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[8,1,5,6,4,7,2,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[3,6,7,4,1,8,2,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,7,4,6,8,2,5,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[7,5,8,2,6,3,1,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[2,7,1,6,5,4,8,3] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[7,3,2,6,1,8,5,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,4,7,2,3,1,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,3,1,8,4,6,2,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,8,1,6,7,4,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[2,7,4,3,6,8,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,8,4,6,1,5,3,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[8,4,1,6,3,2,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[4,7,3,8,5,2,1,6] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[3,1,7,4,8,5,2,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[7,4,1,6,3,2,8,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[3,8,6,2,7,4,1,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[7,3,1,4,5,2,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,1,4,8,5,3,2,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,1,2,4,6,7,5,3] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[8,1,3,6,7,5,4,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,5,2,3,8,6,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,6,2,4,1,3,7,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[4,7,5,1,8,6,3,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,7,3,2,8,5,6,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[8,4,5,7,6,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,5,8,4,2,3,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[3,8,4,6,1,7,5,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,7,4,6,5,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[4,2,7,6,1,5,8,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[8,3,1,4,5,7,6,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,5,1,6,8,4,7,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[6,1,5,7,3,8,4,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[5,8,4,7,3,2,6,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[7,2,6,5,8,4,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,3,2,5,1,6,7,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[2,6,8,3,7,4,1,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,1,5,6,4,7,3,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[2,5,8,1,6,4,7,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[7,4,1,8,3,2,6,5] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,3,7,4,2,1,6,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[5,2,6,8,3,1,7,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[3,6,5,8,4,1,7,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[7,3,6,1,8,4,5,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,2,7,3,4,6,5,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[7,3,8,2,5,6,4,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,7,3,1,6,4,8,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,1,3,2,4,8,7,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[8,7,4,2,3,6,1,5] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,1,5,4,2,3,6] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[3,7,1,5,2,8,6,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[8,7,2,5,4,1,3,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,7,2,5,3,1,4,6] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[5,2,8,7,1,4,3,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,1,8,6,2,4,3,5] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[8,1,6,2,7,5,3,4] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,1,6,2,8,5,3,4] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,3,4,1,7,2,8,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[7,2,4,3,5,1,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,1,7,2,3,8,6,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[8,2,3,5,1,7,6,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,6,3,1,4,8,2,5] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[6,1,8,2,7,5,3,4] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,2,8,1,6,5,3,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,2,6,4,3,8,1,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,1,7,4,3,8,2,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[5,3,1,7,4,8,2,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[7,4,8,2,1,5,3,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,2,4,1,6,3,7,5] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,2,7,5,1,6,4,3] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,1,7,3,2,8,5,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[4,7,2,1,6,3,8,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,2,1,5,3,8,4,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,3,1,6,2,8,4,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,1,5,2,8,4,3,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,4,3,8,1,5,2,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,4,8,1,5,3,2,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,1,5,3,2,8,4,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,3,2,8,4,1,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,4,2,8,5,1,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,1,6,3,4,2,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,5,1,3,7,4,2,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,8,6,1,5,2,7,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[8,6,1,3,7,5,2,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[4,8,5,6,1,7,3,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,7,1,3,8,5,2,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[3,6,7,1,5,2,8,4] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[7,1,3,8,4,2,6,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[5,6,2,7,1,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[5,6,2,8,1,3,7,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,1,8,3,7,5,2,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,4,2,1,5,8,3,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[7,4,1,5,8,3,2,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[7,3,2,6,4,8,1,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,4,2,7,3,8,1,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[5,1,8,3,7,4,2,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,4,8,3,1,5,2,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[5,2,1,7,4,8,3,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,1,8,4,5,2,7,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,1,6,4,5,2,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[3,5,2,7,1,6,8,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[4,5,7,3,1,6,8,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,5,7,2,8,6,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,5,1,7,2,6,8,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[4,5,7,2,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[4,6,7,2,1,5,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,6,7,1,3,8,5,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,6,1,5,7,8,4,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,6,7,1,5,8,3,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[6,1,3,7,4,8,5,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,2,1,7,4,8,5,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,1,5,2,7,6,3,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,5,1,3,7,6,4,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,5,1,4,3,8,6,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,7,2,1,5,8,6,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[6,2,7,1,4,8,5,3] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[3,7,4,2,1,8,5,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[7,2,5,3,1,8,6,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[7,5,1,4,2,8,6,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,5,4,1,3,8,6,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,3,2,1,7,6,4,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,3,2,8,1,5,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,4,3,2,8,1,6,5] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,6,2,4,8,3,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[7,3,6,4,8,1,5,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[2,7,5,3,8,1,4,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,8,5,3,6,4,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[8,6,2,3,7,5,4,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,6,3,2,7,5,4,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[8,3,2,7,1,6,4,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,2,6,1,5,4,3,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,5,7,4,3,6,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[8,5,7,2,4,6,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,4,6,7,1,3,2,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[2,8,5,6,1,4,3,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[7,2,6,8,4,1,5,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[7,6,4,8,3,2,5,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[6,5,8,1,4,2,7,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,5,8,4,1,3,7,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,4,8,3,2,1,7,6] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[4,3,7,2,1,6,5,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[2,5,8,1,4,3,7,6] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[3,6,8,2,1,5,7,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[5,7,4,8,1,3,6,2] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,7,1,4,8,2,6,3] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[2,7,4,1,8,3,6,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,5,1,8,4,2,7,6] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[4,1,5,7,3,6,2,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,2,5,8,3,1,7,6] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[6,1,2,7,8,3,5,4] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,3,1,8,6,4,2,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,1,8,4,7,5,2,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,2,8,7,3,5,1,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,8,1,7,6,2,3,5] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[6,8,1,4,7,5,2,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,3,8,1,6,4,2,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[4,7,8,1,5,3,2,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[7,1,8,6,2,5,3,4] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[5,8,7,1,3,6,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,8,7,2,1,6,4,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[2,8,7,1,6,3,5,4] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,7,6,1,5,4,2,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[4,8,7,6,1,3,5,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,8,7,2,6,1,4,3] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[6,8,1,7,5,2,4,3] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[7,3,8,6,5,1,2,4] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[5,7,8,4,3,1,2,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,8,6,4,3,2,1,7] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[8,7,3,6,4,2,1,5] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[6,1,4,2,5,3,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[1,3,7,5,4,2,8,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,1,3,5,4,2,7,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[6,1,2,5,4,7,3,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[5,1,6,3,4,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,2,6,3,4,7,1,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,4,7,5,8,6,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,4,7,1,5,3,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,3,6,7,4,8,1,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,3,6,7,4,8,5,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[2,7,6,5,3,1,8,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,2,6,1,4,7,8,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,7,6,5,2,1,8,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,3,6,2,4,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,7,4,2,1,3,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,3,1,5,4,7,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,3,6,1,4,2,7,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[1,7,4,2,6,3,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[5,7,4,1,2,3,6,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[6,4,1,2,5,3,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[4,7,6,3,8,5,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[3,7,6,5,2,8,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[3,7,6,5,1,2,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,7,2,6,1,3,8,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[2,7,1,6,8,3,5,4] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[2,7,6,5,8,1,4,3] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[9,1,2,3,4,5,6,8,7] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[10,1,2,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[9,1,2,3,4,5,7,8,6] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[2,3,4,5,6,9,7,8,1] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[2,3,4,5,6,7,8,10,9,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[9,2,1,8,7,6,5,4,3] => [[1,4],[2,5],[3],[6],[7],[8],[9]] => 11011111
[3,2,10,9,8,7,6,5,4,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[3,9,2,8,7,6,5,4,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[4,2,9,8,7,6,5,3,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[5,2,8,7,6,4,3,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[8,2,7,6,1,5,4,3] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[9,2,8,1,7,6,5,4,3] => [[1,3],[2,5],[4],[6],[7],[8],[9]] => 10101111
[8,4,1,7,6,5,3,2] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[9,3,1,8,7,6,5,4,2] => [[1,4],[2,5],[3],[6],[7],[8],[9]] => 11011111
[10,2,1,9,8,7,6,5,4,3] => [[1,4],[2,5],[3],[6],[7],[8],[9],[10]] => 110111111
[4,5,6,2,3,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,5,3,2,7,8,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,5,7,3,8,4,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,8,7,2,4,3,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,2,7,4,5,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[6,8,1,5,2,4,3,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,3,4,6,1,5,2,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[2,3,4,7,5,8,1,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,3,4,7,8,2,5,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[5,3,7,4,8,6,1,2] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[8,3,6,4,1,7,2,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[1,3,7,4,8,6,2,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,7,8,5,4,1,2,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,4,3,1,7,8,2,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[5,7,6,2,8,4,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,1,7,5,8,3,4,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[7,5,6,4,1,3,8,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[1,5,6,8,4,7,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,1,3,7,6,5,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,4,1,7,5,8,6,2] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[8,5,7,4,3,1,6,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[6,8,5,1,7,2,4,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,2,4,1,3,7,6,5] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,8,3,6,2,1,4,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[8,1,7,4,2,3,6,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,8,7,2,3,5,6,4] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,8,3,1,6,7,5,4] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[8,2,3,1,5,7,6,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[3,8,4,1,2,7,6,5] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,4,7,2,3,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,3,2,1,8,4,7,5] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[2,3,7,4,1,8,5,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[6,4,1,3,2,7,8,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[2,7,8,5,1,3,6,4] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[8,2,5,6,7,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[2,8,5,4,7,6,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,7,1,5,8,2,4,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,8,7,6,2,3,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[7,8,1,5,3,2,6,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,5,7,3,8,2,1,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,1,4,7,2,5,6,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,3,4,6,1,5,8,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,3,4,5,7,1,6,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,2,6,8,3,1,5,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,7,6,2,4,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[2,3,6,5,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,3,5,8,6,1,4,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[4,2,3,8,6,1,5,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[6,4,1,2,8,3,5,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[1,2,3,7,4,6,8,5] => [[1,2,3,4,6,7],[5],[8]] => 0001001
[3,2,7,1,4,5,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[2,1,5,3,8,7,4,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,8,3,2,4,1,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,2,7,1,8,3,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,1,8,2,7,3,5,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,2,7,5,3,8,4,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[3,2,7,1,4,8,5,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[1,2,3,7,6,8,4,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,2,3,6,8,7,4,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,3,7,8,4,6,5] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,3,6,8,4,7,5] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,3,7,8,6,4,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[6,2,8,3,7,5,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,2,8,3,7,5,6,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,3,4,8,6,5,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,3,4,8,7,2,6,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[4,3,5,8,7,2,6,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[4,6,3,8,5,7,2,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[7,5,3,8,6,2,4,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[2,6,8,3,7,4,5,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,8,4,3,7,5,6,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,5,8,3,7,4,6,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[7,4,3,8,6,2,5,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[3,5,4,8,7,2,6,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,5,3,8,6,7,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,6,7,8,4,5,2,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,6,8,5,4,7,3,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[1,8,5,6,4,7,3,2] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[2,5,8,6,4,7,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[7,4,6,5,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[6,3,7,8,4,5,2,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,3,7,8,5,6,2,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,2,8,6,4,7,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[4,2,8,6,5,7,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,2,8,6,7,4,5,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[2,3,8,7,5,4,6,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[1,8,2,7,4,5,6,3] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[7,2,8,6,3,4,5,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,2,8,4,5,7,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[5,2,8,4,6,7,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,2,8,5,6,7,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,3,6,8,5,7,2,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[3,4,6,8,7,2,5,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[7,3,5,8,6,2,4,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[1,8,3,5,7,4,6,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,7,8,4,5,6,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,7,5,8,4,6,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,7,4,6,8,3,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,6,5,8,4,7,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,6,8,4,5,7,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,2,7,1,3,8,5,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[4,2,5,1,3,8,6,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,3,6,1,7,2,4,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[3,7,1,2,5,8,6,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,7,4,1,2,8,5,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[7,5,1,3,4,8,6,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,5,1,2,4,8,6,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,4,2,3,7,1,5,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,6,3,8,1,2,5,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,4,2,3,8,1,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[4,7,5,2,8,1,3,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[8,2,6,3,7,1,4,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,6,1,2,7,4,5,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[8,4,7,1,2,3,6,5] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,5,7,1,2,4,6,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,5,7,1,3,4,6,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,6,2,7,1,3,5,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[3,8,5,6,1,2,4,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,7,5,8,1,2,4,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[7,6,4,8,1,3,5,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,5,8,1,2,4,7,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[3,6,8,1,2,5,7,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,7,2,4,8,1,6,5] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[4,6,3,8,1,2,5,7] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,6,3,7,1,2,5,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,1,7,8,2,3,6,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,1,2,8,6,3,4,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[5,3,8,1,6,2,4,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,1,8,5,2,3,4,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[6,1,7,5,2,3,4,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[6,8,1,3,7,4,5,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[7,2,8,1,6,3,4,5] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,7,8,2,5,1,3,6] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[6,8,2,7,1,4,5,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,8,7,1,3,5,6,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,8,7,1,2,4,6,5] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,8,7,1,2,3,6,5] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,8,7,1,2,4,6,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,8,7,1,3,4,6,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,1,8,6,2,3,5,4] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,8,6,4,1,2,3,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[7,8,4,1,2,5,3,6] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[7,8,1,2,6,5,3,4] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[1,4,8,2,7,5,3,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[6,1,3,4,7,2,5,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,8,2,1,6,3,5,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,1,2,7,5,4,3,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[1,2,8,7,5,4,3,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[5,1,7,3,6,4,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,2,1,5,7,4,3,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,2,3,7,4,1,5,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,4,8,7,5,6,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,3,8,7,4,1,5,6] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[2,7,3,8,6,4,1,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,8,3,7,6,4,5,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[5,2,7,1,4,6,8,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,6,7,5,2,1,8,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,3,1,4,5,7,8,2] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,3,1,4,6,2,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,1,2,4,7,6,8,3] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,7,4,1,2,6,3,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[4,8,1,2,6,7,3,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[4,1,7,8,2,6,3,5] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[1,2,8,7,6,5,3,4] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[3,1,2,4,6,8,7,5] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[3,1,8,4,5,7,6,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,2,8,5,4,7,1,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,2,8,1,5,3,7,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,3,8,5,7,6,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,8,2,1,6,3,7,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[3,8,6,5,2,7,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[3,8,5,6,1,7,4,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,5,7,8,1,2,6,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,7,8,5,2,1,6,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[3,7,2,8,4,1,6,5] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[2,8,1,7,4,6,5,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[2,8,7,5,1,6,4,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,8,6,7,5,1,4,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,1,3,4,6,7,2,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[1,3,4,8,7,5,2,6] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[8,2,4,1,7,3,5,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[8,6,1,4,2,3,7,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[3,6,1,4,2,8,7,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[1,6,8,4,3,7,2,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,1,4,7,8,5,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,1,7,4,3,8,2,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,8,7,4,3,6,2,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[7,4,1,3,8,2,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[4,8,2,3,1,5,7,6] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,8,6,2,1,3,7,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[2,7,4,1,8,3,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[1,7,8,4,2,3,6,5] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,7,1,3,8,2,6,5] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[8,7,1,3,4,2,6,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[1,7,4,3,6,2,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,8,6,4,5,2,1,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[3,8,4,6,5,2,1,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[2,4,3,7,5,8,1,6] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[1,4,7,3,6,2,8,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,8,3,4,2,6,7,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[6,4,1,3,7,2,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,1,4,3,6,2,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[4,2,3,8,5,7,1,6] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[2,8,5,7,3,4,1,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[5,8,2,6,4,3,1,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,2,5,8,4,3,1,6] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[4,2,3,5,8,7,1,6] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[8,2,3,5,4,7,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,1,8,3,4,2,7,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[1,8,6,4,2,3,7,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[3,8,4,5,6,2,1,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[2,4,3,5,7,8,1,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,8,6,5,4,2,1,7] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[6,3,1,4,2,8,7,5] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,3,8,1,2,6,4,5] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,1,4,5,3,2,6,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[1,8,4,2,6,5,3,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[5,1,4,8,6,3,2,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,3,1,8,4,7,2,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[4,3,8,1,5,7,2,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[6,3,1,2,5,7,4,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[7,1,4,2,6,5,3,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,8,4,1,6,5,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,3,6,4,5,8,2,1] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,7,2,4,5,1,6,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,1,5,4,8,6,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[2,1,8,7,5,3,6,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[5,8,3,7,4,1,6,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[5,7,1,4,8,6,3,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,5,7,4,8,6,2,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,3,7,4,8,6,2,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[7,5,8,4,1,6,3,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[2,7,8,4,5,1,6,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[5,7,3,8,4,1,6,2] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[5,6,3,8,1,4,7,2] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,7,8,4,1,6,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,7,3,1,5,4,2,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[3,6,2,1,5,4,8,7] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[5,4,2,6,1,3,8,7] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[3,2,6,5,1,4,8,7] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[2,5,8,1,7,4,3,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,8,2,7,4,3,1,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[6,8,2,3,7,5,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,6,2,5,4,8,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[2,6,5,1,8,4,3,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,2,7,3,1,8,5,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,2,3,7,1,5,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[5,2,7,3,8,6,1,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[2,1,5,8,4,3,7,6] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[5,8,4,2,6,7,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,2,4,8,1,5,7,6] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[2,4,8,3,1,7,5,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[4,8,3,2,1,7,6,5] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[4,1,3,7,2,6,8,5] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[3,4,8,2,1,6,5,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[6,8,3,7,2,1,5,4] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[3,5,8,1,7,2,6,4] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,1,7,4,6,8,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[7,6,4,8,1,5,3,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[5,3,7,1,8,2,6,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[2,7,6,3,8,1,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,1,7,6,4,8,3,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[2,1,5,4,8,7,3,6] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,4,8,7,2,6,1,3] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[2,4,3,8,7,1,5,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,4,1,8,6,2,7,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,8,5,4,2,1,7,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[4,8,6,5,2,7,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[3,2,8,7,5,4,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,8,6,5,4,3,1,7] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[5,4,2,6,3,1,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,3,6,5,2,8,4,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,6,2,3,4,8,5,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,7,5,3,1,4,2,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,1,5,3,8,4,6,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,7,6,4,2,8,5,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,1,8,7,4,3,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,8,7,4,2,1,5,6] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[8,5,2,6,1,7,3,4] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[5,4,2,6,8,3,7,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[6,5,2,8,1,4,3,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[2,7,8,4,5,1,3,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,4,8,1,5,2,7,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,8,1,2,5,3,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[8,1,2,4,3,5,6,7] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[5,8,7,4,6,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[4,8,7,6,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[3,8,7,6,5,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[7,9,6,8,5,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[5,8,4,7,6,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[6,9,8,5,7,4,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8],[9]] => 01101111
[6,8,5,4,7,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[3,8,7,6,2,5,4,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[4,8,7,6,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[3,9,8,7,6,5,2,4,1] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => 01111101
[3,8,7,6,5,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[8,6,9,4,7,3,5,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[8,6,9,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[8,7,9,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[9,7,10,8,5,6,3,4,1,2] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => 101101010
[9,7,10,5,8,6,3,4,1,2] => [[1,3],[2,5],[4,6],[7,8],[9,10]] => 101011010
[9,7,10,5,8,3,6,4,1,2] => [[1,3],[2,5],[4,7],[6,8],[9,10]] => 101010110
[7,5,8,4,6,3,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[8,6,9,4,7,3,5,2,1] => [[1,3],[2,5],[4,7],[6],[8],[9]] => 10101011
[9,7,10,5,8,3,6,2,4,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[8,6,9,5,7,2,4,1,3] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[9,7,10,5,8,4,6,2,3,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[7,6,8,2,5,1,4,3] => [[1,3],[2,5],[4,7],[6],[8]] => 1010101
[8,7,9,4,6,3,5,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[9,7,10,6,8,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[9,6,8,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010
[9,8,10,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[3,5,2,4,7,6,1,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[3,5,4,7,2,6,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,5,4,7,6,1,2,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,5,4,7,6,1,8,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,5,7,4,6,1,8,2] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[3,5,7,4,6,1,2,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,5,7,4,6,2,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[3,2,5,7,4,6,1,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[3,5,2,7,6,4,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[3,5,7,2,6,4,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,3,7,6,2,4,1,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,3,7,6,1,2,8,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[5,3,7,6,1,4,2,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,3,7,6,4,1,2,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,5,7,2,6,1,4,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,5,2,7,6,1,4,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[5,3,7,6,4,1,8,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,7,5,4,1,8,2,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,7,5,4,1,8,6,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,7,5,1,4,8,6,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[3,7,5,1,4,8,2,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[3,5,7,1,2,6,8,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,5,7,2,1,6,8,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,5,2,7,1,6,4,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,5,7,2,1,6,4,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,3,7,1,6,2,4,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,5,7,1,4,6,8,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,5,7,1,4,6,2,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,5,7,1,4,2,6,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,5,7,2,1,4,6,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,5,2,7,1,4,6,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,2,5,7,4,1,6,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,5,2,7,4,1,6,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[3,5,7,4,2,1,6,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[3,5,7,4,1,2,6,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,5,4,7,1,6,8,2] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[3,5,4,7,1,2,6,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,5,4,7,2,1,6,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,5,4,2,7,1,6,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,2,5,4,7,1,6,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,5,4,7,2,1,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[3,5,4,7,1,2,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[5,7,6,3,1,8,4,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[5,7,6,3,1,8,2,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,5,7,4,1,2,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[3,5,7,4,2,1,8,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[3,2,5,7,4,1,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,2,5,7,1,4,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[3,5,2,7,1,4,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,5,7,2,1,4,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[3,5,7,1,4,2,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,7,5,2,1,8,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,7,2,5,1,8,6,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[3,2,7,5,1,8,6,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[3,2,7,5,1,8,4,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[3,7,2,5,1,8,4,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[3,7,5,2,1,8,4,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,1,7,5,8,4,6,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[1,3,4,5,6,7,9,2,8] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[2,3,4,5,6,7,1,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[2,1,4,5,6,7,8,9,3] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[3,1,4,5,6,7,8,2,9] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[5,8,3,4,1,7,6,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,8,7,2,4,1,6,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[3,8,6,4,1,7,5,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,3,5,6,8,1,7,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,7,6,4,1,8,5,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[3,7,4,1,8,6,5,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[3,8,4,1,7,6,5,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[3,2,7,6,1,5,4,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[3,2,8,7,6,1,5,4] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,7,8,2,4,1,6,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,2,5,8,1,6,7,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,2,5,8,1,7,3,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,8,2,4,1,6,3,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[8,4,2,6,5,1,3,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[3,2,6,8,1,5,4,7] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[8,3,2,5,6,1,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,2,8,6,7,1,5,4] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[3,2,6,8,7,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,2,6,7,1,5,4,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[8,7,3,2,5,6,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,2,8,1,5,3,6,4] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[8,4,2,7,5,1,3,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,4,2,8,5,1,3,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,2,4,1,8,3,6,5] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[3,2,8,5,7,1,4,6] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[2,6,5,7,1,8,3,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,5,1,8,7,4,3,6] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[8,1,4,6,3,5,2,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,3,5,4,1,6,2,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,6,3,4,1,5,2,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,4,7,6,8,2,3,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[4,1,8,2,3,7,6,5] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,1,8,5,3,4,7,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[5,2,4,6,8,7,3,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[1,6,8,3,4,5,7,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[5,7,4,8,6,1,3,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,4,2,6,7,8,1,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,4,2,7,3,5,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,4,1,8,3,5,6,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[6,5,4,8,7,3,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,7,4,2,1,3,6,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,7,1,3,2,5,6,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,8,2,3,1,7,5,4] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,4,3,2,6,8,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[2,7,4,3,8,5,6,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[8,3,7,2,1,5,6,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,7,8,2,4,3,1,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[8,4,7,3,2,6,1,5] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,3,1,6,7,4,2,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[3,2,5,7,4,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,2,7,3,4,1,5,6] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[7,1,6,3,5,8,2,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,8,5,6,7,1,4,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,5,2,7,8,6,4,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,6,8,5,1,4,7,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[1,4,2,8,6,5,7,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,5,1,6,8,7,2,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[5,7,6,2,1,3,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[2,5,8,7,4,1,6,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,1,7,5,2,6,8,3] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[7,6,2,4,5,1,8,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,3,4,2,5,8,6,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,7,4,2,5,1,6,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[8,1,4,5,2,6,7,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,2,4,8,6,7,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[8,5,6,2,1,3,7,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[4,2,1,5,6,7,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[3,4,6,5,1,7,8,2] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[7,3,5,2,4,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,3,7,2,4,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[3,7,5,2,4,6,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,7,3,2,4,6,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[1,5,3,2,4,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,5,3,2,7,4,6,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[5,7,3,2,1,4,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,7,3,2,4,1,6,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,7,2,5,4,1,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[5,1,3,2,4,7,6,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[5,1,3,2,7,4,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,3,2,5,4,6,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[1,7,3,2,5,4,6,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[7,1,3,5,2,4,6,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[5,1,3,7,2,4,6,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,2,7,5,1,4,6,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,7,5,1,2,4,6,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[5,7,3,1,2,4,6,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,5,3,7,2,4,6,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[5,3,2,7,4,1,6,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,3,2,4,7,1,6,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,3,2,1,4,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[5,3,2,1,7,4,6,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,3,2,7,5,4,6,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,3,7,2,5,4,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[7,3,1,2,5,4,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,3,1,2,7,4,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,3,1,2,4,7,6,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[3,2,5,1,4,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,3,1,5,2,4,6,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,3,7,5,2,4,6,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[7,5,1,3,2,4,6,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[5,7,1,3,2,4,6,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,7,1,5,2,4,6,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,7,1,2,5,4,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,7,2,1,5,4,6,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,2,1,7,5,4,6,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[3,1,2,7,5,4,6,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,1,7,2,5,4,6,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,1,7,5,2,4,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,1,5,3,2,4,6,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[1,7,5,3,2,4,6,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,2,3,4,5,7,9,6,8] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[1,2,3,4,6,9,5,7,8] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[1,2,4,9,3,5,6,7,8] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[1,3,9,2,4,5,6,7,8] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[1,9,2,8,7,6,5,4,3] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[3,9,8,7,6,5,2,1,4] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[1,8,7,4,2,6,5,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,8,5,1,7,6,4,3] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[6,8,5,1,2,7,4,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[2,10,1,9,8,7,6,5,4,3] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[3,10,9,8,7,6,5,2,1,4] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[1,9,8,7,6,3,2,5,4] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[4,9,8,7,6,3,2,1,5] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[2,8,1,4,7,6,5,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[1,8,7,4,3,2,6,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,7,2,9,8,6,5,4,3] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[1,8,5,4,2,7,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[9,2,1,10,8,7,6,5,4,3] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[8,5,6,3,7,4,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,5,6,2,7,4,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,7,6,3,4,1,5,2] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[1,7,2,3,6,8,5,4] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[3,5,6,4,8,2,7,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,5,1,4,8,2,7,6] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[1,7,5,4,8,2,6,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,7,5,1,6,4,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,7,5,4,8,1,3,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,7,5,4,8,6,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[1,7,5,4,8,6,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,5,1,4,8,7,3,6] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[3,6,4,2,8,7,1,5] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[3,5,2,4,8,1,6,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,5,6,4,8,1,2,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,5,6,4,8,7,2,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,6,4,1,8,7,2,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,6,4,5,8,7,2,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,6,4,3,8,5,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,1,3,4,5,8,2,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,6,1,4,5,3,8,2] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,6,1,3,5,4,8,2] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,1,3,2,5,8,4,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,6,4,2,8,5,3,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[7,6,5,8,2,4,3,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[7,6,5,8,3,1,4,2] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[2,6,4,3,8,1,7,5] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[2,6,4,3,8,5,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,2,3,1,5,8,6,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,1,5,6,3,8,4,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,3,6,5,1,4,8,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[7,2,6,5,3,8,1,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[7,2,3,1,4,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,2,3,5,4,8,6,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[2,6,4,5,8,1,7,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,5,6,4,8,3,7,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,5,6,4,8,3,1,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,5,6,1,4,7,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[7,6,1,3,4,5,8,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[7,1,3,2,4,8,5,6] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[7,6,1,5,3,4,8,2] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[7,6,1,5,4,3,8,2] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[1,6,4,5,8,3,2,7] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[7,6,5,8,1,3,2,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[3,4,6,8,7,2,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,5,6,8,2,1,7,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,2,1,5,3,7,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[4,2,5,6,3,1,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,5,6,8,1,7,2,4] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,1,5,6,3,2,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,5,3,1,7,2,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,1,3,5,2,7,8,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[2,5,4,7,3,8,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,5,7,1,8,4,2,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,1,5,3,2,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,5,3,7,1,2,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,3,6,1,2,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,1,3,2,4,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[3,6,1,7,4,5,2,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,1,3,4,2,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[5,3,1,4,2,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,5,2,3,7,1,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,2,6,1,3,7,5,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[4,6,2,1,3,7,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[3,6,2,1,7,4,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,1,4,7,6,5,2,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[3,6,2,7,1,5,8,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[4,6,2,7,1,3,5,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,5,7,1,8,2,6,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,1,4,2,3,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[3,6,1,7,2,5,8,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,6,5,3,4,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[3,6,1,7,5,4,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,1,4,3,2,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[5,4,1,3,2,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,2,4,5,1,8,3,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[2,1,4,8,6,3,7,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,4,8,2,5,3,7,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[8,6,2,4,7,5,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[4,6,8,2,3,5,7,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,6,8,1,4,5,7,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[8,4,2,6,7,3,1,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[7,6,4,5,1,3,8,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[1,6,7,5,3,4,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[7,6,2,3,8,4,1,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,6,7,5,8,2,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[6,2,5,8,3,4,7,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,2,3,8,7,4,1,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,4,7,3,5,8,6,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,5,3,7,1,8,4,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[5,2,8,3,1,4,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,8,2,3,6,5,7,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,8,1,3,6,4,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[5,8,1,4,3,6,2,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,8,4,1,3,7,6,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,4,5,3,8,1,7,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[4,6,5,3,7,1,2,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,5,1,3,6,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,2,6,5,1,7,3,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[4,3,5,7,2,1,6,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,4,7,6,8,1,2,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,4,6,2,5,8,7,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,5,2,4,6,1,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,2,5,1,6,8,3,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,8,2,3,6,5,7,4] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[4,2,8,3,5,7,1,6] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[4,3,8,6,5,7,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,3,7,2,6,5,8,4] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,3,6,4,2,5,8,7] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,5,4,7,3,6,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,2,3,8,4,1,7,6] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[7,5,3,4,8,2,1,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,2,8,3,4,1,5,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[7,4,3,8,5,2,6,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[4,6,2,7,3,1,5,8] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[7,6,3,8,2,4,5,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,2,8,5,1,3,4,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[1,5,3,7,6,8,4,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,6,3,7,8,2,4,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[1,4,3,7,8,5,2,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,2,6,5,7,8,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,2,6,7,5,8,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[3,2,4,7,8,5,1,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,2,6,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[5,1,8,3,6,4,7,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,8,5,6,1,7,2,4] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,4,8,1,7,6,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,6,8,5,1,3,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,7,4,8,5,1,3,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,4,8,3,1,7,5,2] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[3,6,5,8,7,1,4,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,7,4,8,2,6,3,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,6,4,8,2,7,3,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[6,5,3,8,2,7,4,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[6,4,8,1,3,7,5,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[7,6,3,1,4,2,5,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[1,5,4,3,7,8,2,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,8,4,2,5,3,1,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[4,2,7,8,5,3,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[4,2,5,3,1,7,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,2,8,7,6,3,1,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,2,7,6,3,1,5,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,3,1,7,5,2,4,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,3,1,8,7,5,2,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,6,3,1,7,5,2,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,2,7,6,3,1,8,5] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[7,6,3,1,8,4,2,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,6,4,2,1,8,3,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[1,8,2,7,6,4,3,5] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[8,3,5,7,6,4,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[8,4,2,5,7,6,3,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,5,2,4,8,6,3,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,7,5,2,4,6,3,1] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[7,5,2,4,6,3,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[5,2,8,6,3,7,4,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,4,7,5,2,6,3,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,3,6,4,7,5,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[1,8,2,7,5,3,6,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[7,5,2,1,8,3,6,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,2,6,3,1,8,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[5,2,7,4,1,8,6,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[5,2,8,7,4,1,6,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,7,4,1,5,2,6,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,4,1,5,2,8,6,3] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,6,3,1,4,2,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,5,2,8,6,3,1,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,7,5,2,6,3,1,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[7,5,2,1,3,6,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,7,5,2,1,3,6,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,5,2,1,3,8,6,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[1,3,7,6,5,8,2,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[8,6,4,7,5,2,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[6,4,8,7,5,2,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,4,7,5,2,1,3,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,3,1,4,7,5,2,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[6,3,1,4,8,7,5,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[8,6,3,1,4,7,5,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,5,7,6,3,1,4,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[1,8,2,5,7,6,4,3] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[1,8,2,6,4,7,5,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,5,2,1,6,4,8,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,3,8,7,4,1,5,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,3,7,4,1,5,2,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,4,1,6,3,5,2,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,4,1,8,6,3,5,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,4,6,3,1,7,5,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[6,4,7,5,2,1,8,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[1,6,4,7,5,3,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[8,6,3,5,2,7,4,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,3,5,2,8,7,4,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,3,5,2,7,4,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,4,7,3,5,2,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[5,7,4,2,6,3,1,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[4,2,6,3,5,7,1,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[2,4,5,8,1,6,7,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[6,1,3,7,4,2,5,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,2,6,8,1,5,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[8,2,6,1,5,4,7,3] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,6,2,7,1,5,4,3] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,6,8,3,1,5,4,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[6,3,7,2,8,1,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,5,2,8,6,1,4,3] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[2,7,3,8,1,5,6,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,6,8,5,2,4,3,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,5,7,2,8,1,6,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[8,4,6,5,3,1,7,2] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,5,3,1,7,2,6,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,8,1,2,4,3,6,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[8,4,1,6,2,3,7,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,1,3,4,2,8,5,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,4,3,5,7,6,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[5,2,4,1,3,7,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[1,7,4,3,6,8,2,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,7,1,3,6,5,4,2] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[1,8,5,7,4,2,6,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,7,5,3,8,2,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[8,1,5,4,7,2,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,3,5,8,7,4,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[1,4,8,7,3,5,6,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[8,1,7,6,3,5,4,2] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[3,6,8,5,7,4,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,7,6,8,5,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[3,8,7,5,6,4,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[2,8,7,6,4,5,3,1] => [[1,2,6],[3],[4],[5],[7],[8]] => 0111011
[1,8,7,6,5,3,4,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[4,6,7,2,5,3,1,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,4,7,8,1,6,5,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[4,2,6,8,7,1,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,1,8,4,2,7,6,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[2,7,3,8,1,6,5,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,6,8,4,1,7,5,3] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[4,6,7,1,2,8,5,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,6,1,8,2,7,5,4] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,7,4,1,2,8,6,3] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[6,3,7,1,2,8,5,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[1,7,8,5,4,3,2,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,2,6,7,8,4,3,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[8,1,4,6,7,3,5,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,7,1,3,6,8,2,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[3,7,6,4,8,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[3,7,5,4,2,1,8,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,3,6,7,4,2,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,6,4,8,2,7,5,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[8,1,6,7,5,3,2,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,7,2,4,6,5,3,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[1,7,8,2,6,4,5,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[8,7,2,5,4,6,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,7,3,2,1,5,6,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[3,7,8,2,1,6,5,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,7,6,1,4,5,3,2] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[4,8,1,2,3,7,5,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,8,2,3,6,5,4,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[3,5,8,4,7,2,6,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,8,5,4,6,2,3,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,8,5,4,6,1,2,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,8,5,1,6,4,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,8,5,4,6,1,3,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,8,5,4,6,3,1,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,8,5,4,6,3,2,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[2,5,8,4,7,3,6,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,6,4,2,7,8,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,5,4,1,6,2,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[4,5,8,1,7,6,2,3] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[3,5,8,4,7,1,6,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,5,8,4,7,3,6,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,6,4,1,7,8,5,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,6,4,8,7,5,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,6,4,3,7,8,5,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,1,3,4,8,6,5,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[7,6,1,3,8,4,2,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,6,4,2,7,8,3,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,6,4,3,7,1,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,6,4,1,7,8,3,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[7,2,3,4,8,6,5,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[7,2,3,1,8,6,4,5] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,2,3,4,1,6,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[1,2,4,3,8,5,7,6] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[7,3,8,6,1,4,2,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,2,8,6,3,4,1,5] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[7,2,3,1,5,6,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[7,2,3,8,1,6,5,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,2,3,8,5,6,4,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[2,6,4,8,7,1,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,5,8,4,7,6,2,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,5,8,1,6,7,2,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,6,1,3,5,8,2,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,1,3,2,5,6,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[7,1,3,8,2,6,5,4] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,6,1,8,5,4,2,3] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[3,2,6,5,8,4,7,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,3,7,1,6,5,8,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,2,6,4,8,3,7,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,3,7,5,8,2,6,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,3,7,4,8,2,6,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,3,7,4,8,1,6,2] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[4,3,7,1,5,2,8,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,4,8,2,6,3,7,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,4,8,1,6,3,7,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[4,1,7,5,2,3,6,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,1,7,8,6,3,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,8,3,2,1,4,7,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[7,2,4,1,6,5,8,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,5,8,4,3,1,6,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[6,8,2,4,1,3,7,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[2,8,4,7,6,3,5,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,1,2,7,5,8,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,2,7,3,8,5,6,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,5,2,6,8,3,7,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[4,8,3,2,5,7,6,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,8,5,3,4,7,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[6,8,4,1,5,3,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,3,4,7,6,2,5,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[1,8,3,5,2,6,7,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[6,8,3,5,1,4,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[6,8,5,4,2,3,7,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,8,2,4,3,7,6,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[8,1,3,4,2,6,5,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,3,2,5,6,4,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,1,2,4,5,3,7,6] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[10,1,3,2,5,4,7,6,9,8] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[10,1,2,3,4,6,7,8,9,5] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[6,5,3,8,4,2,7,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[7,4,5,1,6,2,8,3] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[4,7,3,5,6,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,7,8,4,1,3,5,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[3,1,6,8,4,7,5,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[8,3,6,1,5,7,4,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[3,2,7,5,8,6,1,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[2,5,4,7,8,1,6,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[2,4,6,7,8,1,5,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,4,6,8,1,7,5,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[7,4,3,8,6,2,1,5] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[2,4,7,8,3,5,6,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,2,7,6,1,8,4,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[3,2,6,8,1,7,4,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,3,6,2,1,8,5,7] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[4,6,2,3,7,5,8,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,8,4,2,3,6,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,4,5,3,2,1,7,6] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[5,8,3,4,2,1,7,6] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,8,4,2,3,7,5,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[6,4,8,3,2,7,1,5] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[5,8,3,7,2,1,6,4] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[2,5,6,4,7,1,8,3] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[6,4,7,3,8,2,1,5] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,7,4,3,2,1,8,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[8,4,3,7,2,1,5,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[1,2,6,5,8,7,3,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,5,2,8,4,6,7,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,5,2,7,4,6,8,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[5,1,2,7,3,6,8,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,1,2,8,3,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,6,3,4,8,7,2,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,5,3,4,8,7,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[4,1,2,8,3,6,7,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[4,1,2,7,3,6,8,5] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[7,5,3,8,4,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,5,3,7,4,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[5,8,1,2,3,4,7,6] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[7,1,2,8,3,6,4,5] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[6,1,8,2,3,5,7,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[6,1,7,2,3,5,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,6,8,2,4,5,7,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,3,8,7,5,6,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,8,2,7,4,6,5,3] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[7,1,6,2,3,5,8,4] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,1,6,2,3,5,7,4] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,1,7,2,3,5,6,4] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[5,8,3,7,4,6,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,8,7,3,4,5,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[1,8,7,2,4,5,3,6] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[8,7,1,2,3,4,6,5] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,6,1,2,3,4,7,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[8,1,6,2,3,5,4,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[1,7,6,2,4,5,3,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,7,4,6,3,5,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[1,8,3,5,7,2,6,4] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,3,4,6,8,5,7,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,3,5,7,4,8,6,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[2,4,6,3,7,8,5,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[2,5,7,1,8,6,3,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,6,7,1,8,4,5,3] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,8,3,1,4,2,6,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,8,4,2,6,7,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,4,1,8,5,6,3,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,6,2,7,8,5,3,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,5,2,6,7,8,4,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,5,1,6,7,3,8,2] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,8,4,1,7,5,3,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[8,5,3,1,7,4,2,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,2,8,7,1,5,3,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,2,6,8,1,7,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[5,7,3,2,6,8,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,4,7,3,1,6,2,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,7,1,2,3,5,8,4] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,1,6,7,8,4,2,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[3,1,4,8,5,6,2,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[8,3,1,4,5,7,2,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[1,6,7,8,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[6,7,8,9,1,2,3,4,5,10] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[6,7,8,1,2,3,4,5,9] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[1,7,8,9,2,3,4,5,6] => [[1,2,3,4,8,9],[5,6,7]] => 00010000
[1,7,8,9,10,2,3,4,5,6] => [[1,2,3,4,5,10],[6,7,8,9]] => 000010000
[5,6,7,8,9,1,2,3,4,10] => [[1,2,3,4,5,10],[6,7,8,9]] => 000010000
[4,6,7,8,1,2,3,5,9] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[1,6,7,8,2,9,3,4,5] => [[1,2,3,4,6],[5,7,8,9]] => 00010100
[1,5,7,8,9,2,3,4,6] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[1,6,7,8,9,10,2,3,4,5] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[8,6,2,3,5,1,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[8,2,4,5,7,3,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[2,6,3,8,7,5,4,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[8,2,3,7,5,4,1,6] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,2,6,3,5,4,1,7] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,6,1,5,2,4,3,7] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,6,2,4,1,5,3,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,4,1,6,5,3,2,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,3,6,1,5,4,2,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,3,2,6,5,4,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,3,2,5,7,4,1,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,3,1,7,5,4,2,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,2,7,4,1,5,3,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,1,3,8,7,5,4,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[3,6,1,8,7,5,4,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,8,1,5,7,6,4,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,5,2,8,7,6,4,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,4,8,2,7,6,5,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,4,8,7,1,6,5,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[8,1,3,5,7,6,4,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[4,1,8,5,7,6,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[8,2,7,1,4,5,6,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,1,7,3,4,6,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[8,3,1,7,2,6,5,4] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[3,8,2,4,7,6,5,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[2,8,3,7,4,6,5,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[8,2,3,7,1,6,5,4] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,2,7,1,3,6,5,4] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,1,7,2,6,4,3,5] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,1,7,5,2,4,3,6] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,2,3,7,4,6,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[2,4,8,5,7,6,3,1] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[8,2,4,3,7,6,1,5] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,2,7,3,5,1,4,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,2,7,4,3,1,5,6] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[8,2,7,3,1,5,6,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,2,1,5,7,6,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[6,2,1,8,7,5,4,3] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[6,1,8,2,7,5,4,3] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[8,1,7,3,5,2,6,4] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,1,5,2,7,6,4,3] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,1,7,2,4,6,5,3] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,2,4,1,7,6,5,3] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[4,2,8,3,7,6,5,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[4,8,2,1,7,6,5,3] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[5,1,8,7,2,6,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[5,8,1,3,7,6,2,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[8,2,5,4,1,7,6,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,1,4,8,7,6,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[8,1,4,3,7,6,5,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[4,8,1,3,7,6,5,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[4,3,8,1,7,6,5,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[5,8,6,3,2,1,7,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,7,6,3,2,4,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[6,5,7,2,4,3,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,7,1,3,2,8,6,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,8,1,3,2,7,4,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[8,5,1,3,2,4,6,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[7,5,8,2,1,4,3,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[6,7,1,2,5,4,8,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,8,1,2,5,7,4,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,1,6,4,2,3,5,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[1,5,4,8,2,3,7,6] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,7,8,2,3,5,6,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[7,5,8,2,3,1,4,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,4,1,2,6,8,3,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,2,8,1,5,7,3,4] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[7,3,5,4,2,1,8,6] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[7,3,2,8,5,6,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[1,7,4,3,6,8,5,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,7,6,5,2,3,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[4,7,6,5,1,3,8,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[6,7,4,2,1,8,5,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,7,6,3,2,8,4,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[6,5,8,1,7,3,4,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,5,8,2,3,7,4,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,1,2,8,5,3,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[3,5,8,2,6,1,7,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[3,7,6,1,5,2,8,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[1,7,6,2,5,8,4,3] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[1,7,6,5,8,4,2,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,7,6,2,8,4,5,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,3,6,8,5,1,2,7] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,7,1,5,8,4,3,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[2,7,6,1,8,4,3,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[7,1,2,6,3,5,4,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[7,2,6,3,4,5,1,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[6,7,8,4,2,5,3,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[6,1,2,5,7,8,4,3] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[4,1,2,7,8,5,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,7,3,1,2,6,8,5] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,7,6,1,5,8,2,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[3,8,5,6,4,2,7,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[3,2,6,4,7,8,5,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,2,7,5,8,3,1,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[4,2,7,1,3,8,6,5] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[5,2,1,4,7,8,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,6,2,7,3,4,8,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[6,1,3,8,5,4,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,7,6,8,5,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[2,7,6,8,5,3,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,5,8,6,4,2,3,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,5,8,6,4,1,7,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,6,2,3,5,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,7,2,3,1,6,8,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[6,7,3,1,5,4,8,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[7,4,6,2,8,3,5,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,3,5,1,4,8,2,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[3,4,6,5,1,2,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[7,5,4,3,8,6,2,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[4,3,8,2,6,7,5,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,3,8,2,5,7,1,6] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[5,1,8,6,4,7,2,3] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[6,7,2,3,1,5,8,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,5,2,3,8,1,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,5,2,3,8,4,1,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,5,1,7,6,3,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[8,1,7,5,2,3,4,6] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[8,6,3,1,4,2,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,5,1,6,2,8,7,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[4,8,3,6,1,7,2,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[6,2,7,8,3,4,5,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[9,2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[4,2,3,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[1,2,4,6,8,9,7,5,3] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,2,4,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 001000000
[1,2,4,6,8,10,9,7,5,3] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,2,4,6,8,5,7,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,1,7,5,8,6,3,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,7,3,8,6,5,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,8,7,4,6,5,1,2] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[7,3,8,4,6,5,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,4,3,6,5,8,1,2] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[4,5,8,7,2,6,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,8,6,7,5,1,4,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[4,2,7,6,5,8,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[4,6,7,8,5,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,5,3,8,2,7,6,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[3,8,5,4,1,7,6,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[6,4,7,2,5,8,3,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[6,3,8,7,5,1,4,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,3,6,4,1,2,8,7] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[6,8,4,3,5,7,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,2,4,8,7,6,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,2,5,1,7,8,3,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[2,5,4,1,3,8,6,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[1,4,5,3,8,2,6,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[5,1,8,2,4,3,6,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,5,4,8,2,3,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[4,8,3,1,6,7,2,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[3,4,8,2,6,5,7,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,6,2,4,8,7,1,5] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[4,7,3,2,6,8,1,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[7,3,4,6,8,1,2,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[3,6,7,2,5,8,1,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[1,5,6,8,3,7,2,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[6,1,5,8,3,4,7,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[5,6,8,1,3,4,7,2] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,8,5,6,3,4,7,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,8,1,3,5,4,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,1,6,3,5,4,7,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[7,1,2,5,8,4,6,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,2,4,8,1,7,3,5] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[3,1,7,8,5,4,6,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[1,6,2,7,4,8,5,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[2,7,1,8,4,3,5,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[6,7,1,8,3,2,4,5] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[2,7,6,3,5,8,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,7,5,6,8,1,3,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,7,2,8,1,3,4,5] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[5,1,6,8,7,2,3,4] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[1,5,7,6,8,2,3,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[7,4,6,8,5,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,8,6,7,5,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,7,5,8,6,3,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[1,6,8,3,2,5,4,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,6,8,1,5,4,7,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[1,5,4,7,6,2,8,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,3,7,6,5,1,8,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,1,5,8,3,2,7,4] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[3,1,2,4,8,5,7,6] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,5,8,4,6,3,1,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[7,1,5,4,8,3,2,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,4,1,7,5,3,2,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[2,7,6,4,8,1,5,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[7,2,5,4,8,1,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[1,7,2,5,3,8,6,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[7,2,3,8,6,1,5,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,3,2,5,8,1,6,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,3,8,4,1,2,6,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[2,4,8,3,7,1,5,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[5,2,8,4,1,6,3,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,6,5,2,1,8,4,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[2,7,5,1,8,3,6,4] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,1,8,7,4,3,6,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[3,8,7,2,4,6,1,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,7,1,3,2,4,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,2,7,6,3,5,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[8,4,7,6,3,5,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,1,7,4,2,3,5,6] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[6,5,1,3,8,7,4,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,7,8,3,2,5,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,1,8,5,3,7,2,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[5,1,6,8,3,7,4,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[8,6,5,1,7,4,3,2] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[7,6,4,1,3,5,8,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,2,3,7,1,4,5,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[2,8,3,7,1,4,5,6] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[5,6,2,7,4,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[8,6,2,7,4,1,3,5] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[3,7,8,5,2,1,4,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[6,8,4,7,3,1,5,2] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[4,8,6,5,1,2,7,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,8,6,5,1,2,3,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,4,5,1,7,6,8,2] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[3,8,7,6,5,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,4,6,7,1,2,5,3] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[5,7,2,6,1,8,4,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[5,7,2,6,1,3,8,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[5,8,2,6,1,4,7,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,8,7,5,6,1,4,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[6,8,4,7,2,1,5,3] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[7,4,6,5,1,3,8,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[1,7,3,4,5,2,8,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[4,8,2,1,3,5,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,7,2,5,4,3,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,6,7,3,4,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,1,5,7,4,3,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,1,8,7,5,6,2,3] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,5,8,7,4,3,6,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,4,1,3,8,7,5,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[2,1,7,4,6,8,3,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,7,2,4,6,8,3,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[8,6,4,2,7,3,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,4,6,1,2,3,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[1,8,6,2,7,3,5,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,7,8,6,2,3,5,4] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,1,8,3,5,7,6,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,5,8,1,7,6,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[2,8,1,3,6,7,5,4] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,2,4,8,6,1,5,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[2,4,1,5,6,7,8,9,10,3] => [[1,2,4,5,6,7,8,9],[3,10]] => 010000001
[2,3,4,5,6,7,9,1,10,8] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[4,1,2,5,6,7,8,9,10,3] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[8,2,1,3,4,5,6,7,9] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[9,2,1,3,4,5,6,7,8,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[8,3,1,2,4,5,6,7,9] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[8,2,3,1,4,5,6,7,9] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[5,8,4,3,1,6,7,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[8,7,2,4,6,10,1,3,5,9] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[2,10,7,9,4,6,8,1,3,5] => [[1,2,4,7],[3,6,10],[5,9],[8]] => 010100100
[6,5,2,4,8,10,1,3,7,9] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[2,8,5,7,4,6,10,1,3,9] => [[1,2,4,7],[3,6,10],[5,9],[8]] => 010100100
[8,7,6,5,2,4,10,1,3,9] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100
[4,10,3,9,2,6,8,1,5,7] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100
[3,6,10,2,5,9,4,8,1,7] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[3,5,7,10,2,4,6,9,8,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011
[10,9,8,7,3,6,2,5,4,1] => [[1,6],[2,8],[3],[4],[5],[7],[9],[10]] => 111101011
[5,10,4,9,3,8,2,7,6,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 010101011
[4,6,10,3,5,9,8,7,2,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111
[10,9,4,8,3,7,6,5,2,1] => [[1,4],[2,6],[3],[5],[7],[8],[9],[10]] => 110101111
[5,10,4,9,8,7,6,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[12,11,2,4,6,8,10,1,3,5,7,9] => [[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => 11000010000
[10,9,2,4,6,8,12,1,3,5,7,11] => [[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => 11000010000
[8,7,2,4,6,10,12,1,3,5,9,11] => [[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => 11000010000
[8,12,7,11,2,4,6,10,1,3,5,9] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[6,5,2,4,8,10,12,1,3,7,9,11] => [[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => 11000010000
[6,12,5,11,2,4,8,10,1,3,7,9] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[6,10,5,9,2,4,8,12,1,3,7,11] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[12,11,6,10,5,9,2,4,8,1,3,7] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[8,7,6,12,5,11,2,4,10,1,3,9] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[8,7,6,12,5,11,10,9,2,4,1,3] => [[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => 11010111010
[4,3,2,6,8,10,12,1,5,7,9,11] => [[1,4,5,6,7],[2,9,10,11,12],[3],[8]] => 11000010000
[4,12,3,11,2,6,8,10,1,5,7,9] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[4,10,3,9,2,6,8,12,1,5,7,11] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[12,11,4,10,3,9,2,6,8,1,5,7] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[4,8,3,7,2,6,10,12,1,5,9,11] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000
[10,9,4,8,3,7,2,6,12,1,5,11] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[3,5,8,12,2,4,7,11,6,10,1,9] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 00010001010
[12,11,10,9,8,7,3,6,2,5,4,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9],[11],[12]] => 11111101011
[6,5,4,12,3,11,2,8,10,1,7,9] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[6,5,4,10,3,9,2,8,12,1,7,11] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 11010100100
[12,11,5,10,4,9,3,8,2,7,6,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9],[11],[12]] => 11010101011
[4,7,12,3,6,11,5,10,2,9,8,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 00100101011
[12,11,10,9,4,8,3,7,6,5,2,1] => [[1,6],[2,8],[3],[4],[5],[7],[9],[10],[11],[12]] => 11110101111
[12,11,5,10,4,9,8,7,6,3,2,1] => [[1,4],[2,6],[3],[5],[7],[8],[9],[10],[11],[12]] => 11010111111
[6,3,7,2,5,4,8,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,4,7,3,2,6,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,7,2,6,3,4,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,7,5,4,6,2,8,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[6,8,3,2,1,7,4,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[4,8,1,7,5,3,2,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,4,3,7,2,8,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[3,6,5,7,2,8,4,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[4,6,5,3,8,2,1,7] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,6,5,8,7,3,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[6,3,8,4,1,7,2,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[7,2,8,1,6,4,3,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,2,6,4,3,5,1,7] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[5,4,2,8,6,3,7,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[2,8,7,5,3,1,4,6] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[2,5,6,3,1,4,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[2,4,7,8,5,3,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[6,5,3,2,4,1,8,7] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[6,5,8,7,3,2,4,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[2,1,4,7,8,5,3,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[8,5,6,7,3,1,4,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,7,5,3,2,6,4,1] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[8,5,3,1,4,6,7,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,5,1,6,4,3,7,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[6,1,4,3,7,8,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,1,2,7,5,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,7,3,1,4,6,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,8,3,1,6,5,7,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,8,5,6,7,1,2,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,5,8,1,4,6,7,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,1,8,7,5,4,6,3] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[7,8,3,4,1,6,5,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[8,7,3,4,2,6,5,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,4,5,2,3,7,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,7,2,8,6,3,1,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,7,5,2,3,8,1,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[6,4,7,5,2,8,3,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,5,1,3,6,4,8,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,5,2,3,7,8,4,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,2,6,3,1,5,8,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,6,3,8,7,5,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,8,4,1,5,7,6,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,8,4,2,5,7,6,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,8,5,4,1,7,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[2,5,8,3,7,1,6,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,8,5,2,4,7,6,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,4,6,2,8,7,5,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[7,8,2,4,1,6,5,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[2,4,6,1,8,7,5,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,8,4,5,1,7,6,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,5,8,2,7,6,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[2,1,6,8,7,5,3,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[1,8,2,4,5,7,6,3] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,2,8,3,5,7,6,4] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,3,8,2,5,7,6,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,3,8,1,5,7,6,4] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[2,6,1,8,7,5,3,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[1,6,2,8,7,5,3,4] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,6,3,8,7,5,2,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,6,3,8,7,5,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,2,8,1,5,7,6,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[3,1,8,2,5,7,6,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,8,1,4,5,7,6,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,8,2,1,4,6,5,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[2,3,6,8,7,5,1,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,1,6,8,7,2,5,4] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,8,4,5,1,6,2,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[6,1,4,5,7,2,3,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,1,4,7,6,3,2,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,3,1,6,4,7,2,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[5,3,8,6,2,7,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,3,6,1,5,7,2,4] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[8,4,6,3,1,2,5,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[6,8,1,4,5,2,3,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,5,8,4,6,2,3,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[2,1,6,5,3,8,4,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[5,6,8,1,4,2,3,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[5,7,4,8,1,2,3,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[8,2,1,5,3,7,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,7,8,1,2,6,3,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[8,7,1,5,6,2,3,4] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,6,5,8,7,2,3,4] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,7,1,6,2,4,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,1,2,7,6,8,3,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,1,7,2,5,8,3,4] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[1,7,6,5,8,2,3,4] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,6,8,5,7,2,3,4] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,5,1,2,6,8,3,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,1,5,2,7,8,3,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,6,3,8,7,2,4,5] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,7,3,2,4,6,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[8,3,1,4,2,5,7,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,1,2,7,8,4,6,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,1,2,6,8,7,3,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,8,6,2,5,7,3,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,7,8,1,2,6,3,4] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[8,1,5,7,6,2,3,4] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,1,6,8,5,2,3,4] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,7,1,2,8,4,6,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[8,3,1,2,7,6,4,5] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,5,8,7,6,2,3,4] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,8,6,1,5,2,3,4] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,10,3,4,5,6,7,8,9,2] => [[1,2,4,5,6,7,8,9],[3],[10]] => 010000001
[7,8,6,3,1,5,2,4] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,1,3,4,5,2,6] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,7,4,8,2,5,3,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,8,6,1,4,2,7,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,1,8,2,4,6,3,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[7,6,8,4,1,5,3,2] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[7,3,2,8,1,5,4,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[3,5,4,1,7,2,6,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,4,7,3,2,5,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,6,5,3,8,4,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[6,4,5,7,8,1,3,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[3,7,4,1,6,8,5,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,1,2,7,6,8,5,4] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,3,2,8,4,5,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,1,8,3,5,4,2,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,8,5,2,4,6,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[1,6,4,8,3,5,2,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,5,4,8,6,3,7,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,8,2,5,3,7,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,8,4,5,2,6,7,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[4,1,8,6,5,3,7,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[5,7,8,4,6,3,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,3,2,8,6,4,7,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[6,8,1,2,7,4,3,5] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[5,8,7,3,6,2,4,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[7,5,2,3,4,8,6,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,3,5,4,2,8,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[5,6,1,3,2,4,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[2,5,1,3,7,8,6,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,3,7,2,1,8,6,5] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[4,6,7,2,1,3,5,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,6,2,3,1,5,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,6,4,2,5,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[3,1,6,4,7,5,2,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,6,2,7,5,4,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,4,7,5,3,6,1,8] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[2,5,7,3,4,1,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,3,5,8,6,4,7,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[2,4,7,3,8,6,5,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,4,2,7,5,8,6,1] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[3,1,5,4,7,8,6,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,5,7,2,3,1,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,7,8,1,4,6,5,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,5,8,7,4,1,3,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[2,6,4,7,5,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[6,2,4,7,1,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,3,5,1,4,2,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,4,7,1,3,2,8,6] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,1,4,7,5,3,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[8,7,4,3,1,5,6,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,7,1,4,3,5,6,2] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[6,1,8,4,7,3,2,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,7,3,6,1,2,8,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[5,2,1,7,4,3,8,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[4,7,6,2,3,1,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,6,8,2,5,3,4,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[2,3,6,1,8,7,5,4] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,6,8,7,5,3,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,4,1,7,5,2,8,3] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[5,7,8,2,3,6,1,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[4,8,7,1,2,5,6,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[2,8,7,4,1,5,6,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[8,6,2,1,5,7,4,3] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[3,8,6,7,5,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,1,3,7,5,8,2,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,7,3,1,8,5,6,2] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[2,6,7,5,3,4,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,6,4,5,7,3,8,1] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[6,1,4,5,8,3,7,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,1,8,5,3,4,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,1,5,6,8,3,7,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[6,4,1,8,7,2,5,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,1,2,3,4,5,6,7,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[1,7,2,3,4,5,6,9,8] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[6,9,1,2,3,4,5,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[1,3,8,5,2,7,4,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,3,8,6,7,2,4,5] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,8,3,7,6,1,4,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[4,2,7,8,6,1,3,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[1,3,8,7,6,2,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,4,6,8,5,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[5,2,6,7,8,1,3,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,5,6,8,1,2,7,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,5,8,6,1,2,7,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,2,6,8,7,1,3,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[1,4,6,8,7,2,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,5,3,8,1,7,2,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,5,8,4,1,7,2,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[1,6,5,7,8,2,3,4] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,5,4,8,1,3,7,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,6,4,8,5,1,3,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,3,7,5,2,4,8,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[8,1,2,7,4,5,3,6] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[2,5,7,4,6,1,3,8] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[6,1,7,4,5,3,8,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,2,7,3,1,5,4,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,6,4,8,3,1,7,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[8,1,3,7,5,6,4,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[1,2,5,3,8,6,7,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,1,6,5,7,8,2,3] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[6,1,3,7,4,2,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,7,2,4,1,3,8,5] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[7,3,8,4,2,6,5,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[8,5,3,4,2,7,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[1,3,8,2,5,6,7,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,8,6,7,2,5,4,3] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[7,6,8,3,5,4,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => 1010111
[1,6,7,3,8,5,4,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[8,7,2,4,6,1,5,3] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[7,8,6,5,2,4,3,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[3,6,7,5,2,8,4,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[5,4,6,7,8,1,3,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[5,3,6,7,8,1,4,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,3,7,6,8,4,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,5,3,2,8,6,4,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[5,4,8,6,7,2,3,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,4,8,6,3,1,2,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[4,5,7,3,6,2,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,5,6,3,8,2,7,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,4,8,7,2,1,3,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[2,5,4,7,8,1,3,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,3,6,4,8,2,7,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,3,7,4,6,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,2,6,3,7,4,5,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,2,4,7,3,5,6,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,2,6,5,7,3,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[4,5,6,2,7,3,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[5,4,6,2,8,3,7,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,4,6,1,7,2,5,3] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,2,1,6,3,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[4,5,6,3,7,1,8,2] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[6,3,2,8,5,4,1,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[4,3,1,5,2,8,6,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[8,5,4,1,3,2,6,7] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[3,8,4,1,5,2,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[2,5,4,3,8,1,6,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,5,7,4,3,1,6,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[5,3,4,2,7,1,6,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,7,5,4,1,2,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,3,5,1,2,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[4,1,6,3,5,2,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,2,1,8,6,3,7,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[3,1,7,2,5,6,4,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,7,5,4,2,1,6,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[3,7,2,4,1,6,5,8] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[7,3,2,1,6,4,5,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,8,6,1,7,4,3,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[2,5,4,6,1,3,7,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,5,6,4,1,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[8,5,2,6,1,3,7,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,1,5,6,3,2,4,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,1,2,5,4,6,3,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[2,4,1,6,5,3,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[4,1,2,7,5,6,3,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[7,1,2,6,5,4,3,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,2,1,5,6,3,7,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[2,8,5,1,6,4,7,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[6,1,4,5,3,2,7,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[3,1,6,5,4,2,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,1,4,6,5,2,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[2,1,8,6,3,7,5,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,8,3,1,7,6,4,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[7,6,3,2,8,5,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[5,6,3,8,7,4,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,2,6,8,7,4,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,3,8,5,4,1,2,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,3,8,4,5,1,2,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,2,3,1,4,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[5,4,1,3,2,8,6,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[5,1,3,4,2,8,6,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[5,2,1,4,3,8,6,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,2,7,3,8,5,1,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[4,7,3,2,8,5,1,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,3,7,2,8,5,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,3,1,2,4,8,6,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[5,4,3,1,2,8,6,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[5,3,4,1,2,8,6,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,2,3,4,1,8,6,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[5,1,7,3,4,6,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,8,7,4,3,1,6,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[6,8,1,3,4,5,7,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,1,7,8,2,5,4,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,2,3,7,4,1,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,3,7,4,1,2,5,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[7,2,6,8,4,3,1,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,7,2,8,6,5,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,6,7,5,1,2,4,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[7,4,5,1,8,2,3,6] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,2,3,1,8,4,5,6] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,1,4,8,3,7,5,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,8,1,6,7,3,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[1,2,7,8,4,3,6,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,8,1,3,5,6,2,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,3,7,8,4,2,6,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[6,3,7,8,2,4,5,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,5,2,4,3,1,7,6] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,5,4,2,3,1,8,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[3,5,4,6,7,1,8,2] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,4,2,6,5,8,7,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,3,2,6,4,8,7,5] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,4,2,5,3,8,7,6] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,5,2,6,4,8,7,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,6,2,5,3,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,5,1,4,3,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[1,7,3,5,4,8,6,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,8,2,6,3,7,5,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,8,3,6,4,7,5,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,7,2,6,4,8,5,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,7,2,6,3,8,5,4] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,5,2,7,4,8,6,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,4,2,8,5,7,6,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[4,8,1,3,2,6,5,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[1,5,3,8,4,7,6,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,8,4,7,3,6,5,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,6,3,8,1,5,4,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[8,3,1,4,2,6,5,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[4,8,7,3,5,2,1,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,8,7,3,5,2,4,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[8,3,5,1,2,6,4,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,6,3,1,5,4,2,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,6,4,1,5,3,2,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,6,5,4,1,3,2,7] => [[1,6,8],[2],[3],[4],[5],[7]] => 1111010
[5,3,8,7,4,6,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,3,8,7,4,6,1,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[8,3,5,7,4,1,2,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[4,8,5,3,1,2,7,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[6,8,7,3,1,5,4,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,8,5,4,1,3,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[2,5,8,7,4,6,3,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,8,7,6,5,1,3,2] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[3,8,7,5,1,6,2,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,3,8,7,5,6,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,8,7,1,3,6,4,5] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[8,5,4,7,2,1,3,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,8,7,3,5,2,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[3,5,8,6,4,2,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[6,8,4,1,5,2,7,3] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[6,8,2,1,7,5,3,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,8,4,6,1,2,7,3] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[2,4,8,6,5,1,7,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,8,7,6,5,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[4,8,7,5,1,6,2,3] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[4,5,2,1,8,6,7,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,5,8,3,1,6,7,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[5,7,2,8,4,6,1,3] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,7,3,2,4,8,5,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,2,8,6,4,5,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,7,2,6,5,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[5,2,7,8,4,1,3,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,7,8,6,4,1,3,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[7,6,3,5,2,8,4,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,2,7,4,8,5,3,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[8,6,5,1,7,2,4,3] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[6,8,5,1,7,3,2,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[1,6,8,3,7,4,2,5] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,1,6,3,4,8,2,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,5,2,6,4,8,1,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,5,2,4,8,1,7,6] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[6,3,8,2,4,1,7,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,6,3,8,7,5,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,3,8,7,5,4,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[6,8,4,2,1,7,5,3] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[5,2,6,4,3,8,1,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[6,5,3,1,4,8,2,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[3,1,7,8,6,4,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,8,1,7,6,2,5,4] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[8,1,7,6,4,2,5,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[7,2,6,3,8,5,4,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,3,8,6,4,1,5,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[1,7,5,8,2,4,3,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[6,1,5,2,4,8,3,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[1,5,6,3,8,2,4,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[8,7,1,3,6,5,2,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[2,6,7,4,3,8,5,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[5,2,4,7,3,8,6,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[1,5,8,7,2,4,6,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,4,8,7,3,6,5,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[8,3,7,2,5,1,6,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[3,7,2,8,1,5,4,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,2,6,1,5,8,4,7] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[7,2,1,5,8,4,3,6] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[7,2,8,1,4,3,6,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[1,7,8,3,2,6,5,4] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,7,4,8,3,2,6,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,7,5,4,8,3,2,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,1,5,4,3,8,2,7] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[1,7,4,5,6,8,2,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,3,4,5,6,7,9,8,2] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[2,3,4,5,6,7,9,8,1,10] => [[1,2,3,4,5,6,7,10],[8],[9]] => 000000110
[1,8,4,5,6,7,9,2,3] => [[1,2,4,5,6,7],[3,9],[8]] => 01000010
[1,3,4,5,6,8,7,9,2] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[1,3,4,5,6,7,8,10,9,2] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,6,4,2,3,5,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,8,7,2,3,4,5,6] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,5,8,6,2,3,4,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,6,5,7,2,3,4,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,7,5,6,2,3,4,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,3,2,7,6,4,5,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,2,3,7,6,4,5,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,5,4,2,3,7,6,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,5,4,2,3,8,6,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,3,2,8,6,4,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,7,5,8,2,3,4,6] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,8,7,5,2,3,4,6] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[2,1,5,8,6,3,7,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,5,8,4,6,1,7,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[2,5,3,8,6,1,7,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,6,3,5,8,1,7,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[6,3,2,5,8,1,7,4] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,3,2,8,6,1,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,8,4,6,1,3,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,3,8,6,1,4,7,2] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,6,5,4,8,1,7,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[8,3,5,7,2,6,4,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,4,6,8,5,3,7,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,4,8,1,7,6,5,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,3,8,1,5,7,6,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[3,8,4,1,5,7,6,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,3,6,8,5,2,7,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[8,5,4,7,2,6,3,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[3,6,8,5,4,2,7,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,6,4,8,5,2,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,6,4,1,8,2,7,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,6,4,1,5,2,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,8,6,5,1,3,7,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[2,8,3,5,6,7,1,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[5,6,2,4,7,1,8,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[2,7,5,4,6,1,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,3,7,4,6,1,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,6,7,4,1,3,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,5,7,4,1,3,8,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[2,4,6,3,5,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,1,6,3,5,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[3,6,4,2,5,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[2,3,6,1,5,7,8,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[4,3,6,2,5,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,6,1,2,5,7,8,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[2,6,4,1,5,7,8,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,4,1,6,5,7,8,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,5,4,2,6,1,8,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,7,3,1,8,6,5,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,6,4,2,7,1,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,2,7,5,3,1,8,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[5,3,6,4,8,2,1,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[7,3,2,5,4,1,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,3,2,5,1,8,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[4,6,3,8,7,2,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,7,6,3,8,2,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[4,7,3,8,6,2,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,7,3,2,6,1,8,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,7,3,2,6,4,1,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[2,7,5,3,1,8,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[7,5,2,8,4,3,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,3,2,4,1,8,6,5] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[8,4,3,2,7,5,1,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[4,3,7,5,8,2,1,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[8,4,5,3,7,2,1,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[4,3,5,2,8,6,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,2,3,4,5,9,7,8,6] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[1,2,3,4,5,6,10,8,9,7] => [[1,2,3,4,5,6,7,9],[8],[10]] => 000000101
[1,2,8,6,4,5,7,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,8,5,3,4,6,7,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,9,4,3,5,6,7,8,2] => [[1,2,5,6,7,8],[3],[4],[9]] => 01100001
[9,3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3],[9]] => 11000001
[10,2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[3,5,6,7,8,9,4,2,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[7,8,4,1,6,3,5,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,7,5,6,1,3,4,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[1,2,3,6,4,7,5,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,2,3,4,6,8,5,7,9] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[1,2,3,4,7,5,8,6,9] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[1,2,3,4,7,5,8,6,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,2,5,6,3,7,4,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,2,3,6,4,7,5,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[3,2,6,4,1,8,5,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[2,8,6,5,3,1,4,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[5,4,8,6,2,3,1,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[4,8,7,5,2,3,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,2,4,7,6,8,3,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,4,2,8,7,5,1,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[8,5,7,6,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[6,4,1,8,7,3,2,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[1,8,5,4,2,7,3,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,7,6,1,5,8,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,6,5,8,2,7,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[8,3,2,7,4,6,5,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[7,5,8,4,1,3,6,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[7,1,6,2,3,8,4,5] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[6,4,7,1,3,2,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,1,3,8,7,2,6,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[8,7,1,6,2,5,3,4] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[3,8,5,2,4,7,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,1,5,2,4,8,3,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,8,5,1,4,7,2,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,2,5,4,1,3,8,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,5,8,1,6,3,2,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[2,3,1,9,4,5,6,7,8] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[4,9,1,2,3,5,6,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[3,9,1,2,4,5,6,7,8] => [[1,2,5,6,7,8,9],[3,4]] => 01000000
[7,10,1,2,3,4,5,6,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[6,10,1,2,3,4,5,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[4,10,1,2,3,5,6,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[3,10,1,2,4,5,6,7,8,9] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000
[1,8,2,3,4,5,6,7,9] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[7,4,6,1,3,2,5,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[1,4,5,8,6,3,2,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[8,4,5,7,2,6,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[4,5,2,6,7,3,1,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[8,1,7,5,3,6,2,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,2,8,3,6,1,4,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,2,6,3,1,7,8,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,3,5,1,6,7,8,2] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,7,6,1,2,3,8,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[3,6,7,5,1,2,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,7,6,8,5,2,4,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,7,6,8,1,2,4,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,6,3,7,1,4,8,2] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[5,3,2,1,8,6,4,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[10,9,8,7,5,6,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => 111101111
[1,8,7,6,5,4,3,2,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,9,8,7,6,5,4,3,2,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[2,1,8,7,6,5,4,3,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[2,8,9,7,6,5,4,3,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[7,8,6,1,4,5,2,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,5,8,3,7,2,1,4] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[7,8,5,3,6,2,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[7,8,5,3,6,2,4,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[7,8,4,3,2,6,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[1,8,4,3,2,6,7,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,4,3,8,2,1,7,6] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[6,4,8,3,2,1,7,5] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[1,8,4,3,2,7,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,8,6,7,3,2,4,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[7,8,6,1,3,2,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,8,4,3,2,7,5,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[5,4,3,8,2,1,6,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[1,8,4,3,2,5,7,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,4,3,8,2,6,7,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[4,5,1,2,6,7,8,9,3] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[6,4,2,3,5,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,2,3,6,1,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[5,2,3,8,6,4,7,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[5,2,3,7,4,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,6,3,2,5,4,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,2,3,4,5,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,2,8,1,5,3,4,6] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,8,6,4,7,2,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,1,8,6,4,5,7,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,8,2,5,7,3,1,6] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[5,8,2,3,4,7,1,6] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[6,3,4,7,8,2,1,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[3,8,5,1,4,7,6,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[4,8,5,1,3,6,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,6,8,5,2,7,3,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,7,8,5,2,6,4,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[3,8,6,2,7,4,5,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[8,5,4,7,1,3,6,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,3,6,2,8,1,5,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,1,5,2,3,7,6,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[6,4,2,3,7,8,5,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,4,2,3,6,7,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,5,8,3,7,2,1,6] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,7,2,8,4,5,1,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,5,1,8,4,6,2,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,2,1,5,6,8,3,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,1,2,6,5,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,1,8,3,2,6,7,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,2,7,5,8,1,3,6] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,6,2,7,8,3,1,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,6,1,3,8,2,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,3,6,2,1,8,7,5] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[3,7,4,5,1,6,2,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,6,4,5,8,2,1,7] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[6,1,4,5,2,8,7,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[7,2,4,5,1,6,3,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[7,5,4,1,6,3,2,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[1,5,4,8,6,3,2,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,5,4,8,6,3,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[1,8,7,5,3,6,4,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[8,3,7,4,1,6,2,5] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,5,4,1,6,3,2,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[1,7,4,2,6,5,3,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[8,2,1,5,6,7,3,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,3,1,8,4,7,2,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[7,1,4,8,6,3,2,5] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,1,8,5,6,7,2,3] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,7,4,8,6,2,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[5,3,6,8,2,7,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[6,3,7,4,8,2,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,3,6,1,4,7,2,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[4,3,6,8,2,7,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[5,3,7,4,8,2,1,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[5,3,8,4,1,6,2,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[5,3,8,1,4,7,2,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[5,8,4,1,6,3,2,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[7,3,8,4,1,6,2,5] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,5,8,3,6,7,4,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,8,2,5,6,7,3,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[7,8,4,1,6,5,2,3] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,3,8,1,5,7,2,4] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[8,3,1,2,5,7,4,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,1,4,2,6,5,3,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,8,1,2,3,4,5,9,6] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[2,8,9,1,3,4,5,6,7] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[2,8,9,10,1,3,4,5,6,7] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[7,1,8,2,9,3,4,5,6] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[6,1,7,2,8,3,9,4,5] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[5,1,6,2,7,3,8,4,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[8,1,9,2,10,3,4,5,6,7] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[7,1,8,2,3,9,4,5,6] => [[1,3,5,6,8,9],[2,4,7]] => 10100100
[7,1,8,2,9,3,10,4,5,6] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[6,1,7,2,8,3,4,9,5] => [[1,3,5,7,8],[2,4,6,9]] => 10101001
[5,1,6,2,7,3,9,4,8] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[5,1,6,2,7,3,8,4,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[4,1,5,2,7,3,8,6,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[4,1,5,2,6,3,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 101010101
[5,1,3,7,4,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[5,1,3,4,7,8,2,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[2,5,8,7,4,3,6,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[5,1,7,8,3,4,2,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[2,5,4,8,3,7,6,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,6,8,2,3,4,1,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,3,5,7,4,6,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,7,4,5,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[3,7,8,1,4,5,2,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[5,8,2,1,6,3,4,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[4,8,1,3,7,5,2,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,4,7,8,5,3,6,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[5,3,1,4,7,2,8,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[2,4,7,5,8,3,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,3,5,8,2,1,7,6] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,8,5,3,7,1,2,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[4,8,5,7,3,1,2,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,8,7,5,1,3,2,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,7,8,4,1,5,2,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,8,5,7,2,4,3,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,8,5,4,2,3,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,3,6,8,5,4,2,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,6,3,8,2,7,4,5] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,8,2,3,6,7,5,4] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,3,6,8,2,7,5,4] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,6,5,4,3,8,2,7] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[1,8,3,4,5,6,2,7] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,8,3,6,2,4,5,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,4,5,8,3,6,2,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,2,7,8,4,5,3,6] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[7,2,8,5,6,3,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,6,3,8,5,4,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[6,2,8,7,5,4,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,2,8,4,3,7,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[5,2,8,4,3,1,7,6] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[1,2,5,4,8,3,7,6] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,4,3,6,8,7,2,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[3,2,5,7,6,8,1,4] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,3,2,6,8,4,7,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[3,1,8,6,4,7,2,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[3,1,6,8,5,4,2,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,3,2,8,7,6,4,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[5,3,8,2,7,6,1,4] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,5,4,8,3,7,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[4,8,5,1,3,7,2,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,3,8,7,2,6,5,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[2,7,5,1,8,4,6,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[7,8,5,2,1,6,4,3] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[7,6,4,8,1,2,5,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,5,4,8,3,2,6,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[3,8,5,6,2,7,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,4,5,8,7,3,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,4,5,8,6,7,1,3] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,3,1,5,6,2,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[4,1,5,8,6,7,2,3] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,3,7,6,1,2,8,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[4,7,5,6,1,2,8,3] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,3,7,5,6,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,5,1,8,6,7,3,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,4,5,8,6,7,2,1] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[2,1,5,8,6,7,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,4,5,8,7,1,2,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,7,1,5,6,2,8,3] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,6,4,7,1,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[5,3,8,6,4,7,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,4,1,5,7,8,3,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[3,6,4,7,2,1,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[3,8,4,6,1,7,2,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,8,5,6,4,7,2,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[3,8,4,5,6,7,2,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[3,8,6,5,2,7,4,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[3,8,7,5,2,1,4,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[3,8,6,5,1,7,2,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,4,1,7,3,2,8,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[5,1,4,6,7,2,8,3] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[6,5,4,7,1,3,8,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[2,1,6,5,3,7,8,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[6,1,4,7,2,3,8,5] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[2,1,3,4,5,6,8,9,7] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[2,1,3,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[2,1,3,4,5,6,7,9,10,8] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[2,3,1,4,5,6,8,9,7] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[1,3,2,4,5,6,8,9,7] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[2,3,1,4,5,6,7,9,8] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[1,3,2,4,5,6,7,9,8] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[2,1,3,4,5,6,7,8,10,9] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[1,6,2,5,4,8,3,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[4,1,2,7,5,8,3,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,1,3,5,8,2,4,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[5,6,4,3,1,8,2,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,2,3,5,8,1,4,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,7,2,3,8,4,5,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,2,1,3,8,4,5] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,7,4,1,8,3,2,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,1,7,5,8,3,6,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[6,7,1,3,8,4,5,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,6,7,4,3,8,5,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,1,7,4,2,8,5,3] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[2,1,6,7,4,3,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,7,3,2,1,8,4,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,5,7,3,1,4,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,7,3,2,8,4,5,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[1,2,6,7,4,3,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[2,7,1,8,4,6,3,5] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[2,7,5,8,1,6,3,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,7,1,8,4,5,3,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[8,3,7,6,1,2,5,4] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,7,3,4,6,2,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,2,5,7,1,4,6,3] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[8,2,4,7,1,5,6,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,2,3,4,7,1,5,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,7,3,5,6,2,4,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,7,4,6,5,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,4,6,7,5,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,4,6,7,5,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,3,5,7,6,1,4,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,7,3,6,2,1,5,4] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,7,3,4,6,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,7,4,6,5,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[8,6,5,2,7,4,3,1] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[8,4,3,7,6,5,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,5,6,7,4,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,5,7,6,4,1,2,3] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,4,2,7,5,1,6,3] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,3,4,2,7,5,6,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,4,7,6,5,1,2,3] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,3,5,2,7,4,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,5,2,6,7,4,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,5,3,7,6,4,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,6,2,5,7,3,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,6,2,4,7,3,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,5,2,3,7,4,1,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,5,3,2,7,6,4,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[8,6,1,5,4,3,2,7] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[2,4,5,8,3,1,6,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[2,7,4,6,1,5,8,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,4,3,8,5,1,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[7,8,3,2,5,4,6,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,5,6,7,3,8,2,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,6,5,4,8,3,2,7] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[1,7,3,5,8,4,6,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[7,2,1,6,4,8,5,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,5,8,3,2,4,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[3,8,7,2,4,6,5,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[1,3,7,6,4,8,5,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,1,8,7,6,4,2,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,1,8,7,5,4,2,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,1,7,6,5,4,2,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,7,1,6,5,3,2,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,8,1,6,5,3,2,7] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[8,4,1,7,6,3,2,5] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[5,4,1,8,6,3,2,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,4,1,7,6,3,2,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,4,1,8,5,3,2,7] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[8,4,1,7,5,3,2,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,4,1,6,5,3,2,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[7,5,6,1,4,3,2,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,5,6,1,4,3,2,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,5,7,1,4,3,2,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,7,6,1,4,3,2,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,8,6,1,4,3,2,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,7,5,1,4,3,2,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[8,7,5,1,4,3,2,6] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,6,5,1,4,3,2,7] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,6,1,7,2,5,3,4] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[1,8,6,3,4,2,5,7] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[3,1,6,4,5,8,2,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[7,6,3,8,4,5,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,2,7,6,1,4,3,5] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[5,2,7,8,1,4,3,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,6,3,8,4,1,2,7] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[8,2,7,6,1,4,5,3] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,2,3,4,7,1,6,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[5,2,3,7,1,6,8,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[8,7,5,3,1,6,4,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[1,4,7,8,5,2,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[5,8,3,7,6,4,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[6,5,1,7,2,4,8,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,6,7,1,4,2,5,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,7,5,8,2,1,3,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[8,1,2,7,5,4,3,6] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[6,5,1,8,3,7,2,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[1,8,7,5,3,2,6,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[7,8,1,5,4,2,3,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,4,6,8,1,5,7,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[6,8,1,7,5,4,2,3] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[7,6,3,1,2,8,5,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[6,3,5,7,1,4,2,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[1,7,5,2,6,4,8,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,1,3,6,8,2,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,2,5,7,8,4,6,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,1,2,7,5,4,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,7,4,1,3,2,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[1,7,2,8,4,3,5,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,6,3,5,7,8,2,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[8,6,1,7,5,2,4,3] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[7,6,4,1,8,3,2,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,4,1,6,5,2,7,3] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[1,5,3,4,7,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[4,2,1,5,7,8,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,4,1,6,7,8,2,3] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[5,1,4,6,7,8,2,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,1,5,3,7,8,2,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,1,4,6,5,2,7,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,1,5,4,6,3,2,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,2,1,6,7,5,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[1,2,4,7,6,3,8,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[6,7,4,1,8,5,2,3] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[8,6,4,1,5,7,3,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,2,4,3,7,1,6,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[6,1,5,4,8,3,2,7] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[1,2,8,7,4,3,6,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[3,2,1,7,5,8,4,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[1,3,6,4,7,8,2,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[4,5,1,3,7,8,2,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,2,3,1,7,8,4,6] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,6,4,3,7,8,2,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,6,4,3,1,5,2,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,5,4,6,1,3,2,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,4,6,5,1,2,7,3] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[1,5,6,3,7,8,2,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[7,1,2,3,4,5,8,9,10,6] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[6,7,1,2,3,4,8,9,5] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[6,1,2,3,4,7,8,9,10,5] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[5,1,2,3,6,7,8,9,10,4] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[1,5,2,4,3,8,7,6] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[8,6,5,7,2,1,4,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[1,6,3,8,4,5,7,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,5,4,2,6,3,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[9,7,6,5,4,3,1,2,8] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[2,3,8,4,7,5,6,1] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[3,7,2,8,6,4,5,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[6,3,7,5,8,2,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[4,3,7,8,6,2,5,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,8,1,7,5,2,4,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[2,4,7,8,6,1,5,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,4,8,5,1,7,3,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,8,3,5,1,6,4,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[8,2,4,6,3,7,5,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[4,5,3,8,2,1,7,6] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,5,6,7,8,9,2,1,3] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[1,4,6,2,7,5,3,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[8,2,1,4,5,6,7,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,3,1,2,5,6,4,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[7,8,2,1,5,4,6,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,4,8,5,2,6,3,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[5,2,3,7,8,1,6,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[1,2,8,4,3,6,7,5] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,7,5,3,4,6,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,7,3,2,6,8,4,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[7,2,1,3,6,8,4,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,7,8,1,6,5,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,5,8,6,1,4,2,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,8,4,2,7,6,3,5] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,3,8,1,6,5,4,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,3,8,2,6,5,4,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,1,3,8,6,5,4,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[8,1,3,7,6,5,4,2] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[2,4,1,8,7,3,6,5] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[7,3,8,6,1,5,4,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[3,5,1,7,8,2,6,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,4,7,8,2,1,6,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[6,3,8,7,1,5,4,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[8,6,4,7,1,5,3,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[3,4,6,2,1,8,5,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,5,7,2,1,6,3,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,6,4,8,3,2,1,7] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[5,7,4,8,2,1,6,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,7,5,8,2,1,6,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[5,7,4,2,6,3,8,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,7,4,1,6,2,8,3] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[8,5,6,1,7,3,2,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,5,1,6,7,8,3,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[4,5,2,6,1,3,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[8,4,6,7,2,5,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,1,4,6,8,3,5,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,7,1,2,4,8,5,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[1,6,3,4,7,8,5,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,3,6,4,7,5,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[7,8,1,3,4,5,6,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[1,8,2,6,7,3,4,5] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[4,7,3,2,8,1,5,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[7,1,2,6,3,8,5,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,1,2,6,3,7,5,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,1,2,7,6,3,5,4] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[4,8,7,3,1,6,2,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[4,7,8,3,1,6,2,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[7,4,3,1,6,2,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[7,4,3,1,8,6,2,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[3,7,6,2,4,8,1,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,3,7,2,8,6,1,5] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[6,1,2,7,4,3,8,5] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[5,1,2,6,3,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[5,1,2,7,3,8,6,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[6,1,2,7,3,5,8,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[7,5,3,2,1,8,6,4] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[4,2,1,5,3,6,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,6,4,3,2,1,9,7,5] => [[1,7],[2,8],[3,9],[4],[5],[6]] => 11111011
[7,5,3,1,8,6,4,2,9] => [[1,5,9],[2,6],[3,7],[4,8]] => 11101110
[7,4,1,8,5,2,9,6,3] => [[1,4,7],[2,5,8],[3,6,9]] => 11011011
[5,3,1,6,4,2,7,8,9] => [[1,4,7,8,9],[2,5],[3,6]] => 11011000
[4,1,5,2,6,3,7,8,9] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[3,1,4,2,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[9,7,5,4,3,2,1,10,8,6] => [[1,8],[2,9],[3,10],[4],[5],[6],[7]] => 111111011
[7,5,3,1,8,6,4,2,9,10] => [[1,5,9,10],[2,6],[3,7],[4,8]] => 111011100
[7,4,1,8,5,2,9,6,3,10] => [[1,4,7,10],[2,5,8],[3,6,9]] => 110110110
[5,3,1,6,4,2,7,8,9,10] => [[1,4,7,8,9,10],[2,5],[3,6]] => 110110000
[5,1,6,2,7,3,8,4,9,10] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[4,1,5,2,6,3,7,8,9,10] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[3,1,4,2,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[6,2,5,4,1,8,7,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[4,6,3,2,1,8,7,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[6,5,3,2,1,8,7,4] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,4,3,2,7,6,1,5] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[1,5,8,4,7,6,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,2,7,4,8,6,1,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[7,4,3,2,8,6,1,5] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[6,8,3,7,5,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[5,7,8,4,3,2,1,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,4,3,8,5,2,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,2,5,4,7,6,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,2,5,4,8,6,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[4,5,3,2,8,6,1,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[3,2,5,4,8,6,1,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,2,8,6,5,4,1,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[8,4,3,6,5,2,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,4,3,7,5,2,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[3,2,7,8,5,4,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,8,7,4,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[3,6,1,4,8,7,2,5] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[5,8,1,3,7,2,6,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,7,5,1,8,2,6,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[6,3,2,1,8,7,4,5] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,2,3,1,8,7,4,5] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,2,5,1,8,3,6,4] => [[1,3,5],[2,6,7],[4,8]] => 1010101
[7,2,1,5,8,4,6,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[4,2,8,1,7,5,6,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,3,1,5,2,8,6,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,1,6,4,2,8,5,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[3,7,4,1,5,8,6,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[5,8,6,1,2,7,4,3] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,8,1,4,3,7,5,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,7,1,4,3,8,5,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,7,1,5,3,8,6,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[6,8,1,2,4,7,5,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[7,1,6,4,8,3,5,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[8,6,4,1,3,7,5,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,5,3,6,1,7,4,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[7,2,1,4,5,8,6,3] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[8,5,6,1,2,7,4,3] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[8,6,2,5,4,7,3,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[8,5,7,3,2,4,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,5,2,1,4,3,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,8,4,1,3,6,7,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[8,1,2,4,5,6,7,3] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[6,1,4,3,2,7,8,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,8,3,6,7,2,4,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[1,2,8,3,7,4,6,5] => [[1,2,3,5,7],[4],[6],[8]] => 0010101
[1,9,2,3,4,5,6,7,8,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 010000000
[1,7,2,3,4,5,6,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[8,2,6,5,4,3,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,2,7,6,4,5,3,1] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,7,3,5,4,2,6,1] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[4,6,7,2,1,8,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[3,7,1,8,2,5,4,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[4,5,8,6,1,3,7,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,5,8,6,2,7,3,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,6,7,1,5,3,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,6,7,2,1,8,5,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,2,5,6,7,8,3,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[4,1,3,5,6,7,8,2] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[3,7,8,4,5,1,6,2] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,6,8,3,2,7,1,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,6,8,2,3,7,1,5] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[3,8,1,7,4,5,2,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,5,8,3,7,1,2,6] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[3,7,8,4,6,2,5,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[3,6,1,5,7,8,2,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,8,2,5,4,7,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,8,6,2,5,1,7,4] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,5,8,6,2,1,7,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,5,8,6,1,2,7,3] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,6,8,5,2,7,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,7,8,5,2,6,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,7,8,5,4,1,6,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,6,8,5,3,1,7,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[7,8,2,3,5,4,1,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,6,5,2,7,8,1,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,6,5,2,3,4,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,6,5,1,7,3,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,7,3,1,2,4,8,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,3,2,5,1,7,4,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,1,2,4,8,5,3,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[6,3,1,7,2,5,8,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,6,5,8,1,7,2,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[1,2,3,4,5,6,7,9,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[5,2,7,3,4,6,1,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[1,3,5,8,6,4,7,2] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[1,3,5,8,6,7,2,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,1,7,4,8,5,3,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[5,7,4,1,3,6,8,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,4,3,1,6,5,8,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,8,1,4,6,5,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[7,8,6,1,4,5,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[6,2,7,3,8,5,4,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,2,7,5,3,4,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[7,2,8,3,6,4,5,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,2,7,8,3,1,4,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[1,7,8,2,5,3,4,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,2,8,7,3,4,6,5] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[8,2,7,4,5,1,6,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[3,8,1,5,7,2,6,4] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[7,5,4,8,6,1,2,3] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,1,8,6,4,5,2,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,7,5,1,4,3,6,2] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[6,8,4,3,1,7,2,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[8,4,1,3,7,5,6,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[4,8,1,3,7,5,6,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,1,6,8,5,3,4,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,5,1,3,8,6,7,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[1,2,6,8,5,3,4,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[5,6,8,7,3,1,2,4] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[6,7,5,3,8,1,2,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,8,5,7,3,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[5,1,4,2,6,8,7,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[6,3,2,4,7,1,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[1,5,8,6,2,4,3,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[5,1,8,6,2,4,3,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[5,8,6,3,7,1,2,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[5,7,6,3,8,1,2,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[6,8,7,5,3,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[1,2,5,3,6,8,7,4] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[6,8,7,2,1,5,3,4] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,3,6,1,4,8,2,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[7,8,1,6,5,3,4,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[8,7,3,2,1,4,6,5] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,3,5,1,7,4,2,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[3,5,6,8,4,2,7,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[5,8,2,6,4,3,7,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[2,8,6,3,4,1,7,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,7,2,3,5,8,6,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,8,3,7,5,1,6,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,4,8,7,2,1,5,3] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[1,8,2,3,7,5,6,4] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,8,4,3,6,7,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[7,3,2,5,6,1,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[1,6,7,8,2,4,3,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,1,2,8,5,3,7,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[3,8,4,2,5,1,7,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,8,5,6,4,3,2,7] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[2,8,3,5,6,4,1,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[7,6,8,3,2,5,1,4] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[2,7,1,4,5,3,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[1,5,2,7,4,3,6,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[5,1,3,8,4,6,2,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[6,5,8,7,1,3,2,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,7,3,5,1,6,8,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[5,7,6,8,2,1,4,3] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,3,6,5,2,7,4,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,6,5,3,4,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,7,2,5,6,8,3,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,7,2,4,8,3,5,6] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,6,2,4,5,3,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,3,2,8,4,5,7,6] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,6,8,2,4,3,5,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,7,2,5,3,4,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,2,8,3,6,7,4,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,7,2,5,3,4,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[10,3,4,5,6,7,8,9,1,2] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[9,3,4,5,6,7,8,1,10,2] => [[1,3,4,5,6,7,9],[2,10],[8]] => 100000101
[4,3,1,5,6,7,8,9,10,2] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[3,1,4,5,6,7,8,10,2,9] => [[1,3,4,5,6,7,8],[2,9,10]] => 100000010
[7,1,5,6,2,3,8,4] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[8,2,1,4,6,7,3,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[7,2,6,1,3,4,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[4,1,3,7,2,5,8,6] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[6,2,7,5,1,3,8,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[1,7,5,6,2,3,8,4] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,7,6,1,2,4,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[8,6,1,3,5,7,2,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,7,4,3,8,2,5,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[6,1,5,3,4,8,2,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,6,7,5,2,8,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[7,8,4,1,5,6,2,3] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,8,1,3,6,7,2,4] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[2,8,4,3,7,1,5,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,8,4,6,7,1,2,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,3,8,4,7,1,2,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[1,2,5,4,8,3,6,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[7,1,3,8,2,4,5,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[8,1,3,7,2,4,5,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,5,4,7,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[8,3,1,4,7,2,5,6] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[1,6,4,7,8,2,3,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,2,3,6,7,8,1,4] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,2,7,3,8,5,1,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[1,3,7,8,5,6,2,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[8,2,6,7,5,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,1,7,4,6,2,3,5] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,5,8,4,7,1,3,6] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[4,5,8,7,1,2,3,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,1,8,5,7,2,3,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[1,8,7,4,6,2,3,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[2,6,5,4,1,8,3,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,2,5,1,4,8,3,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,5,4,1,3,8,2,7] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[6,3,5,4,2,8,1,7] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[1,3,8,7,4,2,6,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[8,7,4,3,1,5,2,6] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,2,5,1,4,6,7,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[3,8,4,5,1,6,7,2] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[8,5,4,1,3,6,7,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,3,1,7,5,6,4,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,4,7,6,5,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[8,1,4,5,7,6,3,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[2,4,1,8,5,7,6,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[8,2,1,4,7,6,3,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,3,1,7,4,2,6,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,2,7,3,1,6,5,4] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[1,8,4,2,3,7,6,5] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,1,2,8,7,4,6,5] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[8,5,1,2,4,3,7,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[2,8,3,7,4,1,6,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,4,5,7,6,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[2,3,1,8,7,6,4,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,2,8,7,3,1,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[1,3,4,8,7,2,5,6] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[8,1,3,4,6,7,2,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[3,4,8,2,6,7,1,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[3,6,8,2,5,1,7,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[3,8,2,5,7,4,6,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[8,4,2,1,7,5,6,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,2,7,5,6,4,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[6,2,8,5,4,1,7,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,8,5,4,1,7,2,3] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[2,8,1,5,7,6,3,4] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[3,1,8,2,7,5,6,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,5,7,1,6,4,2,3] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[2,8,4,7,3,6,5,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,4,7,2,1,6,5,3] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[1,8,4,7,6,5,2,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[3,5,8,1,7,4,6,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[8,4,7,1,3,6,5,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,2,3,4,5,6,9,1,7] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[9,2,3,4,5,6,7,10,1,8] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[2,3,4,7,6,8,1,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,8,1,2,5,6,4,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,5,2,1,4,6,7,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[4,8,1,6,5,2,7,3] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,2,6,3,8,5,7,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[4,5,2,6,7,1,8,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[8,3,5,4,2,7,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[2,8,6,4,7,3,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,1,8,6,5,2,7,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[8,3,1,5,2,6,7,4] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,8,2,4,1,5,7,6] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,8,3,2,4,1,7,6] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,2,6,8,4,3,5,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[6,5,3,2,4,8,1,7] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[5,2,4,6,1,3,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,2,3,4,6,8,1,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[8,3,4,6,7,5,1,2] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,8,3,4,7,5,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[5,8,6,1,3,4,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,8,1,5,7,6,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[3,7,4,6,8,2,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[4,7,1,6,8,3,2,5] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[4,5,2,8,1,7,3,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[3,7,5,2,8,6,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,8,5,2,6,7,1,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,4,8,6,1,2,7,3] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[8,4,6,5,2,7,3,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,1,6,4,7,5,2,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,2,7,6,4,8,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,6,2,3,5,1,7,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,2,5,7,4,1,3,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,2,4,5,6,8,1,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[7,1,3,5,6,2,8,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,1,5,8,4,6,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[6,3,8,4,7,1,5,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,1,4,3,2,8,5,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[5,3,6,1,4,2,8,7] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[5,7,2,1,4,3,8,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[7,1,8,3,5,2,4,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[7,2,4,8,1,5,6,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[7,1,8,4,2,5,6,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,4,2,5,8,1,7,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[2,1,7,5,8,3,6,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[7,3,8,5,6,2,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[2,7,4,8,1,5,6,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[7,4,8,3,1,5,6,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[6,1,5,8,3,7,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,6,3,5,8,7,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,6,5,3,7,2,1,4] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[4,8,5,3,7,2,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[7,4,8,6,5,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[7,4,8,5,6,3,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,8,4,1,3,5,6,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,8,3,4,1,5,6,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,3,1,8,2,5,6,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[7,2,3,8,1,5,6,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[6,4,8,7,3,2,1,5] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[2,7,4,8,6,3,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[6,4,8,2,3,1,7,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,2,1,8,3,5,6,4] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[5,1,6,3,8,2,4,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,6,5,1,4,8,7,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,3,6,2,8,4,1,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[7,5,4,8,1,6,2,3] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,3,5,8,7,1,2,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[3,5,6,8,1,4,2,7] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,3,5,8,2,1,6,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,4,7,2,3,1,5,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,8,1,5,4,2,7,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,8,6,3,1,4,2,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,6,3,5,1,2,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,2,8,5,4,6,3,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,1,8,4,7,2,3,5] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[5,6,4,3,7,1,8,2] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[6,5,3,7,2,4,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[5,6,2,8,4,3,7,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[7,1,3,6,5,8,4,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[5,7,4,3,6,8,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[4,6,2,7,8,3,5,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,1,2,4,6,7,8,3] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[4,6,3,5,2,8,7,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[5,6,3,4,8,2,7,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[5,2,6,4,1,7,8,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[5,8,4,6,3,2,7,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[5,4,3,8,6,2,7,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[5,7,8,2,4,3,6,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[5,6,2,4,8,3,7,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,4,7,8,2,3,5,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[3,7,5,2,4,8,1,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,7,5,2,3,8,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,4,7,3,2,5,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,7,3,2,8,4,6,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,3,7,2,8,4,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[4,3,7,2,5,8,6,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[4,7,3,2,5,8,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[4,7,3,2,6,8,5,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,5,3,2,6,4,8,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,5,2,6,7,3,4,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,4,2,6,3,7,5,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,4,6,2,3,8,5,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,5,6,2,8,3,4,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,7,6,2,8,3,4,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,7,6,2,3,8,5,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[7,6,3,2,5,8,1,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[7,6,4,2,5,8,3,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[6,3,8,5,4,7,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,3,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[1,4,2,3,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 01000000
[1,3,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 010000000
[2,4,6,3,8,7,5,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,4,3,6,8,7,1,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[2,4,6,3,8,7,1,5] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,4,6,5,8,7,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,4,6,8,5,7,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,4,6,8,5,7,1,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,4,6,8,3,7,1,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,4,6,8,1,7,3,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[2,4,6,5,8,3,7,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,4,6,5,8,1,7,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[2,4,6,8,5,1,7,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[2,4,6,8,7,3,5,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,4,6,8,7,1,5,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,4,6,8,7,1,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,4,6,8,5,1,3,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,4,6,5,1,8,3,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,4,6,5,3,8,1,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,4,6,5,8,3,1,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,4,6,8,5,3,1,7] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,4,6,8,7,3,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,4,6,8,7,5,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,8,7,5,2,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,1,4,7,5,8,2,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[1,8,6,5,3,2,7,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,6,3,5,8,2,4,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,6,1,7,8,5,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[6,1,2,7,8,4,5,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[6,1,3,2,7,8,5,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,6,3,1,7,4,8,2] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[4,8,3,7,1,6,5,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[8,7,2,6,5,1,4,3] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[5,8,3,2,1,7,6,4] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[5,4,3,8,1,7,6,2] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[6,5,3,8,7,1,4,2] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[4,3,8,2,7,6,5,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[4,8,2,7,6,5,3,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[7,8,2,6,5,4,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[3,8,7,6,2,5,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[4,8,3,7,2,1,6,5] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[8,6,3,1,7,5,4,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[8,6,3,7,1,5,4,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[4,8,3,7,6,2,5,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[5,8,2,7,6,4,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[8,4,2,1,7,6,5,3] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[1,6,4,2,5,3,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,8,6,2,7,3,4,5] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,6,3,2,4,5,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,5,2,6,4,3,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,5,2,4,6,3,7,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,8,6,2,3,7,4,5] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,5,2,8,6,3,4,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,3,6,8,2,7,4,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,4,3,8,2,5,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[1,7,2,3,8,5,4,6] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,3,8,4,2,5,6,7] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,6,2,8,5,4,3,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,7,2,3,8,6,4,5] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,5,3,8,2,7,4,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,4,8,2,5,6,3,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,5,7,3,2,8,4,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,2,7,3,6,8,4,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,7,2,3,6,8,4,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,4,8,3,2,5,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,7,2,5,8,3,4,6] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,2,3,4,5,6,7,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[3,2,9,4,5,6,7,8,1] => [[1,3,5,6,7,8],[2,4],[9]] => 10100001
[9,2,3,4,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[6,2,3,5,8,1,7,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[5,2,4,8,1,6,7,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[3,2,10,4,5,6,7,8,9,1] => [[1,3,5,6,7,8,9],[2,4],[10]] => 101000001
[2,10,3,4,5,6,7,8,9,1] => [[1,2,4,5,6,7,8,9],[3],[10]] => 010000001
[2,3,5,6,7,1,8,4,9] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[2,6,4,5,7,3,1,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[2,5,6,3,4,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,3,7,5,6,8,4,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[1,3,6,7,4,5,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,3,4,6,7,8,2,9,5] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[1,5,6,3,4,2,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,5,3,6,4,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,5,3,7,4,6,2,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,5,7,3,6,4,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,5,7,4,1,3,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,7,3,1,8,5,2,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[4,6,3,5,8,2,1,7] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[7,4,5,2,1,8,6,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[4,7,5,2,1,8,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[8,5,3,6,2,1,7,4] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[4,5,7,3,1,2,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,5,1,8,3,2,7,6] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[5,7,4,6,3,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[3,6,1,2,4,8,7,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,5,3,8,4,1,7,6] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[7,5,2,3,1,8,6,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,3,1,2,4,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[4,7,5,2,3,6,1,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[3,6,8,4,5,1,2,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[5,2,3,7,6,4,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,2,7,3,5,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,2,6,5,3,4,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[8,2,6,5,4,1,3,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[6,2,8,4,5,1,3,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[2,3,1,7,8,5,6,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[7,2,8,5,1,4,3,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,6,7,1,4,2,3,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,8,7,1,4,3,2,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[6,8,2,5,3,1,4,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,7,8,5,1,4,2,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[4,8,7,3,1,2,5,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,8,6,2,3,1,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,8,5,4,2,1,6,7] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[4,5,3,8,2,1,6,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,7,4,1,8,2,6,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,8,4,1,7,6,2,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[3,7,2,1,8,4,6,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[8,7,1,6,5,2,3,4] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,5,1,2,7,6,3,4] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[3,8,2,1,7,6,4,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[3,5,7,8,2,4,6,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[7,8,2,5,4,3,6,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[4,5,3,7,8,2,6,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,5,4,7,3,6,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,7,3,6,8,4,5,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[4,6,8,2,7,3,5,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,7,6,3,5,1,8,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,8,3,6,1,5,4,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[2,5,7,8,4,6,1,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[3,7,5,6,2,1,4,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[6,2,1,7,4,5,3,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[1,2,6,4,7,5,3,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[7,5,6,3,8,4,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,5,4,2,1,6,7,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[2,6,8,4,7,5,1,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[6,7,5,1,4,8,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[7,4,1,6,5,3,8,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[5,8,2,7,3,6,4,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[1,6,5,7,3,8,4,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,5,6,8,4,2,7,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[7,5,4,1,8,2,6,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,4,1,8,2,7,5,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[7,8,5,3,2,6,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[8,2,5,1,7,6,4,3] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,7,4,3,8,2,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[3,4,2,7,8,6,1,5] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,8,6,1,4,3,2,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[2,4,7,8,6,1,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,7,8,6,5,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[4,5,2,7,8,6,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[4,6,2,5,3,1,7,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,1,5,6,3,2,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[2,6,7,5,4,1,3,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[4,1,6,7,5,3,2,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,7,4,3,1,5,2,8] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[1,7,5,6,4,3,2,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[7,6,5,3,1,8,4,2] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[7,8,6,4,3,1,5,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[4,1,7,8,6,5,3,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,5,7,3,8,6,1,2] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[6,8,5,3,7,2,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[4,7,1,5,8,2,6,3] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[2,7,5,8,3,6,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[7,4,8,2,6,5,3,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,5,4,8,2,6,3,1] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[4,3,8,1,6,5,2,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[2,3,6,5,7,8,1,4] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[8,3,4,1,2,6,7,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[7,3,4,8,5,2,1,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[7,3,8,4,1,5,6,2] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[7,2,4,5,1,8,3,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[7,3,1,2,8,5,6,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,8,2,3,5,7,6,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,5,2,3,8,6,7,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,7,4,8,5,3,2,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[4,3,5,6,1,7,8,2] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[3,5,2,6,4,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[4,1,2,8,5,7,6,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,1,5,6,4,7,8,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,1,4,6,7,5,8,2] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[2,6,4,5,8,1,3,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,4,1,3,5,8,2,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[3,4,1,7,2,6,8,5] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[2,4,7,5,8,1,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,7,6,2,1,5,8,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[4,2,6,1,3,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,5,4,2,7,6,3,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[2,8,4,6,7,1,3,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[5,8,2,1,4,6,7,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[8,4,6,1,2,5,7,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[3,7,8,4,2,6,5,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,6,2,8,7,1,3,4] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[7,1,3,8,4,5,6,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[7,8,1,4,3,5,6,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,6,7,2,8,1,5,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[2,6,7,1,3,5,8,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,6,7,1,8,2,5,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[3,4,1,8,7,2,6,5] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,1,5,7,2,8,6,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,8,1,3,2,7,6,5] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[4,1,8,3,2,7,6,5] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[3,8,2,4,7,1,6,5] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[3,2,4,8,7,1,6,5] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[3,2,5,7,1,8,6,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,2,8,3,1,7,6,5] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[4,8,2,1,3,7,6,5] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,2,8,1,3,7,6,5] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[2,3,4,6,8,7,1,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[5,6,4,7,1,2,8,3] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,6,7,5,8,2,3,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,5,7,1,6,8,3,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,2,7,6,8,1,4,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[4,5,1,7,6,8,2,3] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[6,7,2,8,3,1,4,5] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[7,6,3,1,2,8,4,5] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,2,7,8,4,1,3,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[7,8,5,2,4,1,3,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,6,2,3,1,8,4,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[4,2,5,1,3,7,8,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[3,4,1,7,8,5,2,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,1,3,7,8,5,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,3,1,8,5,2,7,6] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[7,6,3,5,8,4,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[4,5,1,3,2,7,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,1,3,2,4,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,3,5,6,1,7,2,4] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[4,5,8,1,2,6,7,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,3,6,7,8,2,1,4] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[1,3,4,8,6,2,7,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,2,4,1,3,8,5,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,4,5,2,6,1,7,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[4,6,8,2,3,7,5,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[4,5,7,2,3,6,1,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,7,3,4,1,5,6,8] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[6,7,2,3,4,8,1,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,5,2,4,6,7,8,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[4,2,6,3,5,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,3,4,5,6,1,8,7,9] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[2,3,1,5,4,6,7,8,9] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[1,4,8,5,6,2,7,3] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[2,8,7,4,5,1,6,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,3,8,5,2,6,7,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[7,2,8,4,5,1,6,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,6,2,4,1,5,7,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[1,6,4,3,2,7,8,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[8,5,3,2,1,6,7,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[1,7,5,2,3,6,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[7,1,5,2,3,6,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,1,2,5,3,6,7,4] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[8,4,1,6,3,7,2,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[6,7,5,3,8,2,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,2,6,8,3,7,1,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[4,2,5,8,6,7,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,8,6,3,4,1,7,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[3,7,2,4,1,8,6,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[2,4,7,8,5,1,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,5,3,8,4,1,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[3,1,7,4,5,6,2,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[2,4,8,3,5,7,1,6] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[8,1,7,2,4,3,5,6] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[1,3,8,2,4,7,5,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,3,7,2,4,6,5,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,7,3,2,4,6,5,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,8,3,7,4,2,5,6] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[8,7,3,1,4,2,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,8,4,3,5,7,1,6] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,2,8,7,4,1,5,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[3,2,1,7,4,6,5,8] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[3,2,6,5,1,7,8,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[5,3,2,6,7,1,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[3,2,8,6,7,4,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[8,4,6,2,7,3,1,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,3,8,6,7,2,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,3,6,2,8,7,1,5] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,8,4,7,6,5,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,8,4,2,6,3,5,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[3,2,7,8,6,4,5,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,2,7,5,6,8,4,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[5,7,8,6,3,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,5,4,2,1,7,8,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[5,4,2,1,7,6,3,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[4,1,6,5,2,7,8,3] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[5,4,1,6,7,2,8,3] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,8,5,3,1,7,2,4] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,2,6,3,8,7,1,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[8,6,1,7,3,4,2,5] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[1,8,3,6,7,4,2,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,6,3,5,2,7,8,4] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,5,7,3,2,6,4,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,1,3,7,2,6,4,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[8,1,6,7,2,4,3,5] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[6,1,4,8,2,7,3,5] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[6,2,4,8,3,7,1,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,7,2,6,3,5,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,1,7,6,5,2,3,4] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[7,1,5,6,8,2,4,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,7,1,5,2,4,8,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,6,1,5,2,4,3,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,1,6,3,5,4,2,8] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[1,6,7,3,5,4,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,7,3,5,6,8,4,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,7,8,3,6,4,5,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,8,7,6,4,5,2,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,2,7,4,6,5,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[2,8,5,7,6,4,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,4,5,1,6,8,3,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,1,7,5,6,8,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[5,6,7,4,3,1,8,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[6,7,8,5,3,1,4,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[1,4,6,2,5,3,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,3,2,5,4,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,6,8,2,5,4,7,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,5,4,2,6,3,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,2,6,4,3,5,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,6,8,2,7,5,4,3] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[1,7,4,3,2,6,8,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,5,4,7,2,6,8,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,3,7,6,2,8,5,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,7,6,2,8,4,3,5] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,5,2,8,4,3,7,6] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,2,8,4,3,6,5,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,2,8,5,6,3,4,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,7,3,5,2,8,6,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,6,7,2,5,8,4,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,5,8,3,2,7,4,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,4,5,8,2,6,3,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,7,6,4,8,2,5,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[1,4,8,6,5,2,7,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,3,8,2,6,5,4,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,7,6,3,8,2,4,5] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,5,2,7,6,4,8,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,2,4,3,8,7,5,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,4,3,8,7,2,5,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,3,8,6,2,4,5,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,3,8,5,4,2,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,7,2,4,8,6,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,6,5,3,2,8,7,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[1,3,2,8,7,5,4,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,2,8,6,5,4,3,7] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[8,1,3,4,6,5,2,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[8,3,1,4,6,5,2,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,8,3,1,2,6,4,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[4,8,1,7,5,2,3,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,8,1,7,5,2,6,3] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[8,5,1,4,2,6,3,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,4,1,3,5,6,2,7] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[8,5,3,2,1,6,4,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,1,5,4,2,6,3,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,5,2,4,1,6,3,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[4,8,7,1,5,2,6,3] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[4,8,7,1,5,2,3,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,6,8,4,1,3,2,5] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,6,8,4,1,3,5,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[3,8,7,5,4,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,8,2,7,5,1,3,6] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,6,8,4,1,5,2,3] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,7,6,1,5,2,3,4] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[7,1,4,8,6,3,5,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[8,1,6,5,3,4,7,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[8,6,2,5,3,4,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,6,5,1,3,4,7,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[8,7,5,1,3,6,2,4] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,7,1,5,3,6,2,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,6,1,3,5,4,7,2] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[7,1,4,8,3,6,5,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,8,5,2,4,3,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[7,3,8,2,5,4,6,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[8,4,2,5,3,7,6,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,8,1,5,3,7,6,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[7,4,8,2,6,3,5,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[7,4,8,2,6,3,1,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,7,3,1,6,4,2,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,7,3,1,6,4,5,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,7,3,1,4,6,5,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,4,3,2,7,5,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[6,4,1,7,8,5,3,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,6,3,4,1,8,5,2] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[8,7,3,1,6,2,5,4] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,8,6,4,2,5,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[7,8,2,4,6,5,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[8,1,7,3,5,6,2,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[8,7,5,2,4,6,1,3] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[8,1,7,5,4,6,2,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,7,3,2,6,1,5,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[5,3,1,7,6,4,2,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[1,8,6,4,2,9,7,5,3] => [[1,2,6],[3,7],[4,8],[5,9]] => 01110111
[9,7,5,3,1,8,6,4,2,10] => [[1,6,10],[2,7],[3,8],[4,9],[5]] => 111101110
[8,6,4,2,1,7,5,3,9] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[8,7,5,3,1,6,4,2,9] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[7,5,3,2,1,6,4,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,6,5,3,1,4,2,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[1,8,6,4,3,2,7,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,9,7,5,3,2,8,6,4] => [[1,2,7],[3,8],[4,9],[5],[6]] => 01111011
[1,8,7,6,4,2,5,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,9,8,6,4,2,7,5,3] => [[1,2,7],[3,8],[4,9],[5],[6]] => 01111011
[1,10,8,6,4,2,9,7,5,3] => [[1,2,7],[3,8],[4,9],[5,10],[6]] => 011110111
[8,4,6,7,5,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[1,4,8,6,7,5,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[7,6,2,5,8,4,3,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[1,7,3,6,8,5,4,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[8,6,2,5,7,4,3,1] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[7,1,3,6,8,5,4,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[1,8,3,6,7,5,4,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[8,1,7,6,4,5,3,2] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[7,1,8,6,4,5,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,6,2,7,4,5,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,8,2,6,4,3,5,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,7,2,6,4,3,5,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,7,2,5,4,6,3,8] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[6,5,7,2,8,3,4,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[6,2,7,5,8,1,4,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,7,2,5,8,1,4,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[6,5,7,3,8,1,4,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,3,7,4,8,2,5,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[6,3,7,4,8,1,5,2] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[6,7,5,1,4,3,8,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[7,8,5,1,4,3,6,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[7,2,1,5,3,8,6,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[5,8,2,7,6,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[5,1,8,7,3,4,2,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[8,2,3,6,7,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,2,3,1,5,8,6,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,6,5,4,3,2,1,7,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[3,1,2,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[9,7,6,5,4,3,2,1,8,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[2,4,8,7,5,3,1,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,6,8,7,5,3,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[2,6,5,1,4,3,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,5,1,2,4,3,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[4,6,5,3,1,2,8,7] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,8,7,5,3,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[4,6,8,7,5,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,8,7,5,3,1,4,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[8,7,5,6,3,1,4,2] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[8,7,3,4,6,5,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[2,1,4,8,7,3,6,5] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[4,8,7,3,1,2,6,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[8,7,3,4,1,2,6,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,7,3,1,6,5,2,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,7,3,2,6,5,1,4] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[2,8,7,3,4,6,5,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[2,8,7,3,6,5,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,8,7,1,6,5,3,4] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[8,7,1,2,6,5,3,4] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,7,1,2,4,3,6,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[2,1,8,7,3,4,6,5] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[8,7,5,1,2,4,3,6] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[2,8,7,1,4,3,6,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[2,8,7,3,4,1,6,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,8,7,5,6,3,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,4,8,7,3,1,6,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[2,8,7,3,1,4,6,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,4,3,1,8,7,5,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[4,3,1,2,6,8,7,5] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[2,8,7,5,6,3,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,8,7,5,3,1,6,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[2,8,7,5,3,6,4,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,8,7,5,6,1,4,3] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,6,8,7,5,1,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,8,7,5,1,2,4,3] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[8,7,5,6,1,2,4,3] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,7,1,2,4,6,5,3] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[2,4,8,7,3,6,5,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[8,7,2,4,3,6,5,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[4,8,7,1,2,6,5,3] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,7,5,3,1,2,6,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,7,5,3,6,4,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[8,7,1,4,3,6,5,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,7,3,4,1,6,5,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[10,3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => 110000001
[9,4,3,2,5,6,7,8,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => 11100001
[7,1,2,3,5,4,6,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[8,1,2,3,4,7,6,5,9] => [[1,3,4,5,6,9],[2],[7],[8]] => 10000110
[7,1,2,6,4,5,3,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[7,1,2,4,3,5,6,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[1,10,2,3,4,5,6,7,9,8] => [[1,2,4,5,6,7,8,9],[3],[10]] => 010000001
[4,7,3,6,5,1,2,8] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[7,5,4,2,8,3,1,6] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,3,6,1,5,2,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[3,1,6,8,5,7,2,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,7,2,1,8,4,6,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[7,2,8,6,4,3,1,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,3,8,7,4,2,1,5] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[7,6,3,2,8,4,1,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,6,1,3,2,4,5,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[5,8,3,7,4,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,1,7,3,5,8,6,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[8,4,7,3,5,2,1,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,4,8,1,3,2,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,5,8,2,1,3,6,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[8,1,3,5,2,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[1,8,3,5,7,2,4,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[8,1,4,2,7,6,3,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,3,4,5,6,7,8,2,9] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[1,3,4,5,6,7,8,10,2,9] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[2,1,4,5,6,7,9,3,8] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[2,1,4,5,6,7,8,3,9] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[1,3,4,5,6,7,8,9,2,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[1,5,7,3,6,8,2,4] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[8,4,6,2,5,7,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[1,3,4,7,6,8,2,5] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[8,1,3,6,7,4,2,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[1,2,4,7,8,5,3,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,1,4,7,6,8,2,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,1,3,7,6,8,2,5] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[5,1,7,3,6,8,2,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,7,8,2,4,5,1,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[5,8,6,2,4,7,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,8,2,6,5,7,1,4] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[2,8,3,6,7,4,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,7,2,5,6,3,1,4] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,7,1,6,4,3,2,5] => [[1,4,8],[2],[3],[5],[6],[7]] => 1101110
[1,8,2,7,5,4,3,6] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[3,8,1,7,5,4,2,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,8,6,1,7,3,2,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[6,7,1,2,8,4,3,5] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,1,3,8,6,5,4,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,2,1,7,5,4,3,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,3,2,8,6,5,4,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[3,4,1,7,6,8,2,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,5,7,1,8,4,3,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,7,1,6,8,2,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[4,5,7,6,1,8,2,3] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[5,4,7,6,8,3,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,5,7,8,6,3,2,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[8,4,6,7,5,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,3,7,5,6,2,1,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[1,4,8,6,7,3,2,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,4,8,6,7,3,1,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[5,2,7,8,6,3,1,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,3,8,7,5,4,1,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,3,8,7,5,4,2,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[8,2,7,6,4,3,1,5] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[8,1,7,6,4,3,2,5] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[4,1,8,6,7,3,2,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[4,8,7,5,6,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[1,3,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[1,5,8,4,3,7,6,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[8,1,7,2,5,6,4,3] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[8,1,3,5,2,7,6,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[2,7,1,5,4,8,6,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[8,6,2,4,3,7,5,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[2,4,1,6,7,5,8,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[8,1,4,5,6,3,7,2] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[8,1,4,5,6,2,7,3] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[8,1,4,7,6,2,5,3] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[2,5,1,7,8,6,4,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,5,6,2,8,7,4,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[2,4,5,1,7,6,3,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[7,3,1,5,6,4,2,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,3,2,5,6,7,1,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,4,5,3,7,6,2,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[3,4,5,6,2,8,1,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[3,7,4,2,8,5,1,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,3,4,1,6,8,2,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[2,6,3,1,4,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[7,2,1,6,3,4,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,3,4,1,6,5,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,7,4,2,5,8,6,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,3,5,1,4,8,7,6] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[2,7,1,3,6,8,5,4] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[2,7,1,3,8,4,6,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,8,7,1,6,2,5,4] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,8,7,1,4,5,2,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[3,7,4,2,1,8,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,8,5,7,2,6,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[8,4,5,7,3,2,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,3,7,2,4,1,5,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,6,7,2,1,4,3,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,3,7,5,1,2,6,4] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[7,3,4,6,2,1,5,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[3,7,4,6,1,5,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,4,7,6,1,2,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,5,8,7,6,1,3,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[8,7,3,5,6,1,4,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,5,2,7,6,1,3,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,4,2,5,1,6,7,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,5,3,1,6,4,7,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[8,7,3,1,4,5,6,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,5,3,7,1,6,4,2] => [[1,4],[2,6],[3,7],[5],[8]] => 1101011
[7,6,3,8,1,4,2,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,4,8,2,6,1,5,3] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[6,4,7,3,1,5,2,8] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,5,3,1,6,4,2,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,7,5,1,2,6,3,4] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,6,4,1,2,7,5,3] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[8,7,4,1,2,5,3,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[6,5,3,7,4,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,6,3,8,4,2,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[4,7,2,5,3,6,1,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,3,4,5,2,6,7] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,8,6,4,2,5,3,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[8,2,6,4,1,5,7,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,8,3,4,6,1,5,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[4,8,7,5,3,1,6,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[6,1,4,8,3,2,5,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[4,1,8,5,3,2,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[8,1,6,4,2,7,3,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[3,1,7,4,2,5,8,6] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[1,2,7,4,3,5,6,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[6,1,8,5,2,4,3,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,8,2,5,1,4,7,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,5,2,1,6,8,7,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[7,2,8,6,5,1,4,3] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[7,4,8,6,1,5,3,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[8,7,2,6,1,4,5,3] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[1,7,8,6,2,4,3,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[7,6,3,1,2,5,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[8,5,3,1,2,4,7,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,2,1,6,5,3,4,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,8,1,5,6,2,4,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[6,8,4,1,5,2,3,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[3,2,8,1,6,4,5,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,2,1,3,7,6,4,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,4,1,2,8,3,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[5,8,4,1,2,3,7,6] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[7,1,2,5,3,4,6,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[1,6,7,3,2,8,4,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,8,6,3,2,7,4,5] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,4,6,2,8,5,3,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,5,6,2,8,4,3,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,2,5,7,4,6,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,5,8,6,1,7,2,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,3,7,1,8,6,4,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,6,1,7,8,5,3,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,8,3,1,6,5,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[1,6,8,5,4,2,7,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[6,5,8,4,2,1,7,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[1,7,8,6,5,4,2,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,8,7,4,5,1,3,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[3,6,4,2,5,1,8,7] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,1,5,8,6,4,7,3] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,2,8,5,6,3,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,7,2,3,4,6,8,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[1,8,7,3,2,5,6,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,7,1,2,3,8,6,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[7,8,6,2,4,1,5,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,2,8,4,6,1,5,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,4,6,2,8,1,5,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,1,5,8,2,3,6,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[7,6,4,8,2,1,5,3] => [[1,4],[2,7],[3,8],[5],[6]] => 1101101
[6,1,8,4,2,3,5,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,3,6,2,1,8,5,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[1,8,6,4,2,5,7,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,6,2,1,8,4,7,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[2,8,1,6,5,7,3,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,1,6,4,3,8,7,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,4,6,8,1,3,7,2] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[3,7,1,6,4,5,8,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[3,5,2,1,4,6,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,3,8,7,5,4,6,2] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[1,2,3,4,5,7,9,8,6] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,4,6,7,9,8,5] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,4,6,8,9,7,5] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,4,6,9,8,7,5] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,2,3,5,6,7,9,8,4] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,5,6,8,9,7,4] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,5,6,9,8,7,4] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,2,3,5,7,9,8,6,4] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,2,3,5,9,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,2,4,5,7,8,9,6,3] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,4,5,7,9,8,6,3] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,2,4,5,9,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,2,4,6,9,8,7,5,3] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,2,4,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[1,3,5,7,9,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,3,5,9,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[1,2,3,4,5,6,8,10,9,7] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,4,5,7,8,10,9,6] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,4,5,7,9,10,8,6] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,4,5,7,10,9,8,6] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,4,6,7,8,10,9,5] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,4,6,7,9,10,8,5] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,4,6,7,10,9,8,5] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,4,6,8,10,9,7,5] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,4,6,10,9,8,7,5] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,2,3,5,6,7,9,10,8,4] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,5,6,7,10,9,8,4] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,5,6,8,9,10,7,4] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,2,3,5,6,8,10,9,7,4] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,5,6,10,9,8,7,4] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,2,3,5,7,9,10,8,6,4] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,3,5,7,10,9,8,6,4] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,2,3,5,10,9,8,7,6,4] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,2,4,5,7,8,10,9,6,3] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,4,5,7,9,10,8,6,3] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,2,4,5,7,10,9,8,6,3] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,2,4,5,10,9,8,7,6,3] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,2,4,6,10,9,8,7,5,3] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,2,4,10,9,8,7,6,5,3] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[1,3,5,7,9,10,8,6,4,2] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,3,5,7,10,9,8,6,4,2] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,3,5,10,9,8,7,6,4,2] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[1,3,10,9,8,7,6,5,4,2] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[6,7,3,4,8,5,1,2] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[7,4,1,8,2,5,6,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,1,7,2,5,6,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[4,1,5,7,3,2,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,4,1,7,2,8,5,3] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,3,1,6,2,8,5,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,8,2,5,3,1,6,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[5,1,3,4,8,2,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[6,1,4,5,7,8,2,3] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,3,4,7,1,8,5,2] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[7,1,3,4,5,6,8,2] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[8,5,2,7,6,3,1,4] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,8,3,5,6,2,7,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[8,3,2,5,6,1,7,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[4,2,5,1,6,8,7,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,4,2,7,8,6,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,8,7,2,1,3,4,5] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,7,6,8,5,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,7,8,5,2,6,3,4] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[7,6,1,2,5,3,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,6,2,4,8,1,5,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[1,5,7,3,8,6,2,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[6,7,5,1,8,2,3,4] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,6,1,2,4,3,8,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[6,7,2,1,5,3,8,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,3,2,8,7,1,6,5] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[4,8,3,1,7,6,5,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[5,3,8,7,1,6,4,2] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[5,8,7,3,1,6,4,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[5,3,8,2,1,7,6,4] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[3,8,7,2,6,5,1,4] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[7,4,1,8,6,5,3,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[5,4,2,8,1,7,6,3] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[5,8,4,2,1,7,6,3] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[5,8,4,7,1,6,3,2] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,4,8,3,1,7,6,2] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[8,5,6,1,4,7,2,3] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[6,7,4,1,2,5,8,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[1,6,7,4,2,5,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[3,6,7,5,8,1,2,4] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,6,7,5,8,3,2,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,8,6,5,7,4,1,2] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,2,1,6,8,4,7,3] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[6,5,8,7,4,2,3,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[6,8,5,7,4,2,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[4,7,5,3,6,1,2,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[4,7,5,3,1,6,2,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,7,5,3,6,4,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,7,5,3,8,1,6,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[4,7,5,3,6,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[2,7,5,6,3,8,4,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[8,7,5,3,1,4,6,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[2,7,5,3,1,4,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[5,7,6,2,8,3,1,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[5,1,6,3,2,4,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[5,7,6,1,8,3,2,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[3,8,7,2,1,5,4,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,1,7,2,8,4,3,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,7,6,2,8,5,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,1,7,3,8,5,2,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[7,1,8,3,2,5,4,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[2,7,8,3,1,5,4,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,8,6,2,7,4,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[2,4,6,7,8,5,1,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[2,4,6,7,8,3,1,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[4,7,6,2,8,5,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,8,7,3,2,4,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[4,6,5,8,7,3,1,2] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[8,3,1,7,2,6,4,5] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[4,5,1,2,8,7,3,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[5,6,1,2,8,3,7,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,8,7,1,6,2,4,3] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,4,5,1,7,6,2,3] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[6,3,1,4,8,2,7,5] => [[1,4,5],[2,6,7],[3,8]] => 1100101
[8,5,6,1,7,2,4,3] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,5,6,1,3,8,4,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[5,7,6,1,3,8,4,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,7,1,4,2,8,5,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[1,5,7,8,4,2,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,3,6,4,2,5,7,8] => [[1,2,3,6,7,8],[4],[5]] => 0011000
[1,4,5,7,8,3,6,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,5,7,8,3,6,2,4] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[1,5,7,8,2,4,3,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[6,8,4,7,3,2,1,5] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[6,8,5,4,2,7,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[1,8,4,6,3,2,7,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,4,8,5,3,2,1,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[3,5,6,1,4,2,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,3,8,4,2,7,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[7,1,3,2,4,6,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[2,6,5,7,8,3,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,1,8,2,6,7,5,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,6,7,8,2,1,4,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,5,7,1,6,3,4,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,2,8,3,6,5,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[6,3,8,7,2,4,5,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[7,6,1,8,2,4,5,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[2,5,6,3,4,8,1,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[5,2,4,7,8,6,1,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[7,2,1,3,4,8,5,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[2,4,5,7,1,8,6,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[8,1,6,2,3,4,7,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[6,1,4,2,5,7,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[6,5,1,2,3,7,8,9,4] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[1,8,3,4,5,2,7,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,8,3,6,4,7,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,4,7,2,5,6,3,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[7,3,5,8,2,6,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[3,4,8,6,7,2,1,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,4,8,2,5,1,7,6] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,7,2,5,8,4,3,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,4,6,7,8,3,5,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,1,5,3,6,8,7,2] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,8,7,4,6,2,3,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[1,6,8,3,5,2,7,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[7,2,1,8,6,4,5,3] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[2,4,7,8,5,6,1,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,6,3,8,5,1,7,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,8,5,4,1,3,7,6] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,4,6,3,1,7,2,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,3,6,5,1,8,2,7] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[1,5,6,8,7,3,2,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,4,8,3,6,5,2,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,3,8,6,4,7,2,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,2,8,6,4,3,7,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,1,7,6,8,3,2,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[1,8,4,7,6,2,3,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[7,2,3,8,4,5,6,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,8,4,3,7,2,1,6] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[6,1,2,8,7,3,4,5] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,5,1,7,6,2,8,3] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[6,5,1,8,7,4,3,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,5,1,8,6,4,3,2] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[8,5,1,7,6,4,3,2] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[8,5,3,7,6,1,4,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[3,8,7,6,1,5,4,2] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[9,7,1,2,3,4,5,6,10,8] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[8,3,7,5,4,1,6,2] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,5,3,1,8,7,2,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,4,8,1,5,2,6,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[8,6,5,7,1,3,2,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[1,5,8,6,2,7,4,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,1,8,5,7,2,6,4] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[6,8,5,3,4,2,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[8,5,2,6,4,3,1,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,5,2,6,1,4,7,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[2,7,5,8,1,4,6,3] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[3,2,6,7,1,8,5,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,4,6,7,8,2,1,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,2,6,7,8,4,1,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,2,7,4,8,5,1,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[6,7,1,3,8,5,4,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[6,7,1,8,5,2,4,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[1,6,7,4,8,3,2,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,4,6,7,8,3,2,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[10,3,4,5,6,7,9,1,2,8] => [[1,3,4,5,6,7],[2,9,10],[8]] => 100000100
[8,7,2,1,5,4,6,3] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[2,7,4,8,6,5,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[7,6,5,2,4,1,8,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,6,4,3,1,5,8,2] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,1,8,7,2,3,5,4] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[8,6,1,2,7,3,4,5] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[3,6,8,2,7,1,5,4] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[2,8,6,1,4,5,7,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[6,8,7,2,5,4,1,3] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[3,5,7,9,1,2,4,6,8,10] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000
[4,1,2,3,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[5,1,2,3,4,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[8,1,2,3,4,5,6,7,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[7,1,2,3,4,5,6,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[6,1,2,3,4,5,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000
[3,2,6,4,8,7,5,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[4,7,2,8,6,5,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,7,1,8,6,5,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[2,7,4,8,3,6,1,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[4,7,3,8,6,1,5,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,3,6,8,7,2,5,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[4,3,8,2,5,7,6,1] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,1,2,6,8,7,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,1,6,4,8,7,2,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,1,6,8,7,5,2,3] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,8,1,4,5,7,2,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,8,1,4,2,5,7,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,1,8,3,5,2,7,6] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,8,1,2,5,4,7,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[4,2,3,6,8,7,1,5] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[4,2,8,3,5,1,7,6] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,2,8,3,5,7,6,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,8,2,4,5,7,6,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,8,2,5,1,4,7,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[4,2,8,5,7,1,3,6] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[3,8,1,5,2,4,7,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,5,6,4,1,3,2,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[7,8,6,4,1,3,2,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[7,1,4,2,5,6,3,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[7,3,2,1,4,6,5,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,6,1,4,3,2,5,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[7,4,1,3,5,6,2,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[2,7,1,3,5,6,8,4] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[3,6,2,1,5,8,7,4] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[2,3,6,1,5,8,7,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,4,7,1,5,6,8,2] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,6,7,4,1,2,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,3,2,7,1,6,8,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[7,3,2,8,1,6,4,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,4,8,1,5,6,3,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[2,6,8,1,5,3,7,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[6,8,2,1,5,3,7,4] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,8,2,5,3,6,7,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,5,8,2,3,6,7,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,4,8,5,3,6,7,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[5,3,2,6,4,8,7,1] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,4,5,3,8,6,7,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,3,5,2,8,6,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,8,5,3,2,6,7,1] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[3,5,4,2,8,6,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,1,2,7,5,6,8,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,6,7,4,2,8,3,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[2,5,7,4,6,8,3,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[7,5,2,4,3,8,6,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,8,1,2,5,4,7,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[6,4,1,8,5,2,7,3] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[2,6,1,8,5,4,7,3] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[7,1,2,8,5,6,4,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,3,2,6,8,5,7,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[3,7,6,4,8,5,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[3,1,6,8,5,4,7,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[2,3,5,8,4,6,7,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,5,2,8,4,6,7,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,4,5,8,2,6,7,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[5,4,2,8,3,6,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,3,4,8,2,6,7,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[2,5,4,8,3,6,7,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[6,3,2,5,8,4,7,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[6,1,8,3,5,4,7,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[5,4,8,3,2,6,7,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[5,8,2,3,4,6,7,1] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[6,2,1,7,8,5,4,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,4,6,8,3,2,5,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,4,5,2,7,1,6,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[7,5,6,1,2,3,8,4] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[1,5,7,6,3,2,8,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[8,4,6,7,3,2,5,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,4,6,2,3,1,5,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,5,2,1,4,3,8,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[3,1,7,8,5,4,2,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[3,4,5,2,1,8,6,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[7,6,4,8,3,1,2,5] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,4,8,5,6,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[6,2,8,5,1,3,4,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,2,7,8,6,1,4,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[6,8,2,5,1,3,7,4] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,7,4,2,1,5,3,8] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,7,4,1,3,6,2,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,2,7,5,1,8,3,6] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[4,1,6,5,3,8,2,7] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,5,4,6,3,8,2,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,6,4,7,3,2,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[4,7,1,8,6,3,5,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[5,4,8,1,7,3,6,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[4,3,8,6,2,1,7,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[8,3,6,2,4,1,7,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,8,3,2,4,6,5,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[7,2,8,5,3,1,6,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[2,5,4,8,7,3,6,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,4,2,8,7,3,1,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,6,8,1,7,4,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[7,8,6,3,1,4,5,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[3,8,6,1,7,5,2,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[2,7,5,4,8,3,1,6] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,8,7,5,2,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,6,2,8,5,1,3,4] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[1,5,7,6,2,8,4,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,6,5,2,7,8,4,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,7,8,5,6,2,3,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[6,7,8,4,2,1,5,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,7,8,1,2,5,6,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[8,6,4,1,2,5,7,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[6,1,4,7,2,5,8,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[6,7,8,3,5,4,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,6,3,2,7,4,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,6,4,3,7,5,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,2,3,6,1,8,4,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,4,6,5,7,1,2,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[7,6,2,3,5,4,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[8,5,2,4,3,6,1,7] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,5,7,2,4,1,6,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,4,8,2,1,5,6,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[2,3,6,7,8,5,1,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[8,3,7,1,6,4,2,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,2,1,7,6,5,3,4] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[6,5,1,2,8,3,4,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[5,6,8,1,3,7,2,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[1,6,8,5,3,2,4,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[5,8,1,6,7,4,2,3] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[7,2,8,4,6,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[6,2,7,4,3,8,1,5] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,7,8,4,6,2,3,5] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,1,8,4,6,2,3,5] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[8,1,6,5,4,7,2,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[4,1,6,8,7,3,2,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,1,4,6,7,3,8,2] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[7,1,3,4,6,2,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[3,4,1,6,2,5,8,7,10,9] => [[1,2,4,7,9],[3,5,6,8,10]] => 010100101
[8,7,1,4,6,3,2,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[1,4,7,5,8,6,3,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[6,1,8,3,4,7,2,5] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[1,8,6,3,5,2,7,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,7,1,6,8,3,5,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[3,6,5,2,8,4,1,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[7,1,8,4,2,5,3,6] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[1,4,8,7,5,2,6,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,5,6,4,2,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[5,8,7,4,2,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[1,8,7,3,2,5,4,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,2,5,4,8,7,3,6] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,2,4,8,6,3,5,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,5,2,4,7,3,8,6] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[8,6,3,5,7,4,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,5,3,2,1,4,7,6] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[1,2,7,6,8,4,3,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,6,3,2,5,7,8,4] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,7,3,4,2,6,8,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,6,3,5,8,4,2,7] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,5,6,3,2,8,4,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,2,5,8,4,6,3,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,5,3,2,7,8,4,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,1,8,6,2,3,7,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[7,5,8,6,2,3,4,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[1,7,6,4,3,8,5,2] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,8,5,7,6,3,2,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,4,7,3,6,8,5,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,6,3,5,7,8,4,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,5,6,3,2,7,8,4] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,2,7,6,8,4,5,3] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,8,4,7,5,3,2,6] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[6,8,5,2,1,7,4,3] => [[1,2],[3,6],[4,7],[5,8]] => 0111011
[1,2,6,8,4,3,7,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,3,7,2,6,4,1,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,6,2,5,3,4,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,6,2,4,5,3,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[7,6,2,4,3,5,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[7,6,2,3,5,4,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,4,2,7,1,6,3,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,7,6,1,5,3,2,4] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,7,6,1,4,3,5,2] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[8,7,6,1,3,5,4,2] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,7,6,1,5,4,2,3] => [[1,5,8],[2],[3],[4],[6],[7]] => 1110110
[8,6,2,7,1,5,3,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[5,3,7,2,8,1,6,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[8,3,5,4,2,1,6,7] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[7,8,4,3,1,5,2,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[8,7,6,1,2,5,3,4] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[8,7,6,1,2,5,4,3] => [[1,5,6],[2],[3],[4],[7],[8]] => 1110011
[8,7,6,1,4,2,5,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,7,5,8,6,1,3,2] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,5,7,3,8,4,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,7,5,4,1,2,6,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,6,7,1,5,3,2,4] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,7,1,3,4,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[7,3,5,6,4,8,1,2] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[1,5,3,7,8,4,6,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,5,7,3,8,2,6,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,3,7,5,8,6,2,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,7,5,8,4,1,2,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[5,3,7,6,8,1,2,4] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[3,1,2,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[3,1,2,5,7,8,6,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[3,7,1,2,8,5,6,4] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,3,1,7,4,6,8,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[2,4,7,3,5,6,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[5,7,6,4,2,3,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,8,2,4,6,1,3,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[6,1,4,8,5,2,7,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[3,4,5,8,1,6,7,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[5,6,8,4,7,3,1,2] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,1,6,8,5,2,7,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[2,3,8,1,5,6,4,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[5,4,8,1,2,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,1,8,2,3,6,7,5] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[5,2,3,8,1,7,4,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[1,5,3,8,2,4,6,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[8,6,2,7,5,1,4,3] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[2,7,1,8,6,3,5,4] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[5,7,6,1,3,2,8,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[3,5,4,6,1,7,8,2] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[8,1,5,4,6,3,7,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[2,7,1,5,6,4,3,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,4,2,5,6,3,7,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[5,4,7,2,8,6,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,5,6,4,1,7,2,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[2,5,6,1,7,4,3,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[2,7,1,8,6,5,4,3] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[3,7,6,1,8,5,4,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[8,6,4,2,1,3,5,7,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[8,6,2,1,4,3,5,7,9] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[8,4,2,1,6,3,5,7,9] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[6,4,2,1,8,3,5,7,9] => [[1,5,7,8,9],[2,6],[3],[4]] => 11101000
[8,6,4,2,9,1,3,5,7] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[9,6,4,2,7,1,3,5,8] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[9,7,4,2,5,1,3,6,8] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[9,7,5,2,3,1,4,6,8] => [[1,5,7,8,9],[2],[3],[4],[6]] => 11101000
[9,7,5,3,1,2,4,6,8] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[10,8,6,4,2,1,3,5,7,9] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[10,8,6,2,1,4,3,5,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[8,2,1,4,3,6,5,7,9] => [[1,4,6,8,9],[2,5,7],[3]] => 11010100
[10,8,4,2,1,6,3,5,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[10,6,4,2,1,8,3,5,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[8,6,4,2,1,10,3,5,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[6,4,2,7,1,3,5,8,9] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[8,6,4,2,9,1,3,5,7,10] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[6,2,8,3,1,4,5,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[9,6,4,2,7,1,3,5,8,10] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[2,7,8,3,1,4,5,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[9,7,4,2,5,1,3,6,8,10] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000
[9,7,4,5,1,2,3,6,8] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[9,7,5,2,3,1,4,6,8,10] => [[1,5,7,8,9,10],[2],[3],[4],[6]] => 111010000
[9,7,5,3,1,2,4,6,8,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[1,5,3,2,8,6,7,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,8,5,3,2,6,7,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,5,6,7,3,2,8,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,7,5,2,3,4,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,7,5,2,4,8,6,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[1,6,7,8,3,2,4,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,4,8,6,2,3,5,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,8,4,5,6,7,2,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,2,8,6,3,5,7,4] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[1,2,7,8,4,3,5,6] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,8,6,7,4,2,3,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,6,7,8,4,2,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[1,6,7,8,3,4,2,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[1,7,4,2,3,8,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,8,4,2,3,5,6] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,7,3,5,6,2,8,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,7,8,3,4,2,5,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,2,3,7,8,5,4,6] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,7,4,6,3,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,7,8,4,5,2,3,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[1,7,8,3,4,5,2,6] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,2,8,4,5,6,3,7] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[1,8,4,5,6,2,3,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[5,8,2,7,3,4,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,8,7,2,3,4,1,5] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[3,8,7,5,2,6,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,8,7,3,2,5,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[5,3,8,1,6,7,4,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,8,2,1,3,7,6,4] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[5,1,8,3,6,7,4,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[3,1,8,4,6,2,7,5] => [[1,3,5,7],[2,4,8],[6]] => 1010101
[8,4,1,6,5,2,3,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[1,8,7,6,4,3,5,2] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[6,1,8,7,5,3,4,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[6,8,7,3,2,4,1,5] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[2,3,7,5,6,8,4,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[3,2,4,7,5,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,8,7,6,4,5,1,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,8,7,6,3,1,5,2] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[3,5,2,4,7,6,8,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,3,2,6,4,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,3,2,6,7,4,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[5,3,2,7,6,4,8,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,3,5,2,8,4,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[3,5,2,7,4,6,8,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,2,5,7,4,6,8,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[3,2,7,5,4,8,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[3,7,5,2,4,8,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,3,7,5,4,8,6,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,4,7,6,8,2,5,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,2,8,4,1,3,6,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,8,5,2,1,4,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[7,6,4,1,8,2,5,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,5,4,2,1,6,3,8] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,1,6,7,3,4,2,5] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,2,1,6,7,4,3,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,2,8,6,3,7,1,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[7,6,8,1,2,5,4,3] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[2,1,3,4,8,5,7,6] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[1,2,3,4,5,9,6,8,7] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[1,2,3,9,4,5,6,10,7,8] => [[1,2,3,4,6,7,8,10],[5,9]] => 000100010
[1,2,3,4,5,6,9,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[5,7,1,2,6,8,3,4] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[1,5,2,3,6,8,7,4] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[3,4,1,2,5,6,8,9,7] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[3,5,7,4,1,8,2,6] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[8,6,4,7,5,1,2,3] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,6,4,1,2,5,3,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[2,8,4,3,1,6,5,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,8,4,6,1,5,2,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[8,3,5,6,1,4,7,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,8,7,3,5,4,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[3,1,2,8,5,7,4,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,1,2,3,4,6,9,5,7] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[8,1,2,4,6,9,3,5,7] => [[1,3,4,5,6],[2,8,9],[7]] => 10000100
[9,1,2,3,4,5,7,10,6,8] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[7,3,1,2,5,8,4,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,3,5,7,2,1,4,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,1,3,8,5,7,4,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[9,1,2,3,5,7,10,4,6,8] => [[1,3,4,5,6,7],[2,9,10],[8]] => 100000100
[9,1,3,5,7,10,2,4,6,8] => [[1,3,4,5,6],[2,8,9,10],[7]] => 100001000
[7,3,1,2,8,4,5,6] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[2,1,4,7,6,3,5,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,2,4,5,3,8,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,4,2,5,6,7,3,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,4,1,6,3,7,8,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,5,1,3,6,7,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[5,1,7,6,3,4,8,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,1,7,5,4,8,2,3] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[3,7,2,1,6,8,4,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[1,5,8,2,4,7,6,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,8,1,6,4,7,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[3,8,6,5,7,2,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[6,8,1,4,7,3,5,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[1,6,8,2,7,4,5,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,7,2,1,8,4,3,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[5,7,1,6,8,3,2,4] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[5,6,2,1,8,3,4,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,4,1,7,3,8,2,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,2,5,6,7,1,4,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,2,4,6,8,3,1,5] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[6,2,4,7,8,1,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[6,1,4,3,2,8,5,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[2,7,4,8,6,1,5,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[2,4,8,6,5,7,3,1] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[3,7,8,6,4,2,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,2,8,4,7,5,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,4,7,2,6,8,5,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[4,2,8,5,1,6,3,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,5,8,1,4,2,3,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[2,3,8,4,1,6,5,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[4,5,7,3,1,6,2,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[5,1,8,7,4,6,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,4,8,7,5,1,3,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[3,5,7,6,1,8,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,5,7,6,2,8,4,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,5,3,2,8,7,6,4] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,1,4,3,8,7,5,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,3,1,8,7,4,2,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,3,6,2,8,7,4,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,3,5,2,1,8,7,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[2,8,4,1,3,7,6,5] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,2,3,8,7,5,4,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[4,1,3,5,8,7,6,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,4,7,5,8,1,2,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[2,7,8,3,4,1,5,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,8,6,7,5,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[7,2,6,8,1,4,3,5] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,3,6,2,8,4,7,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[8,1,6,3,7,4,5,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[2,4,3,7,1,8,6,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[2,6,5,7,3,8,4,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,8,2,7,4,1,5,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,1,7,8,5,3,2,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,6,5,4,7,1,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,8,3,4,6,1,7,2] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[6,1,7,4,2,5,8,3] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,8,7,1,5,4,2,3] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[4,8,3,1,5,7,6,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[5,3,8,2,7,1,6,4] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[8,3,4,5,2,7,1,6] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,1,5,2,6,3,4,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[3,7,1,5,2,6,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[6,7,1,8,3,4,5,2] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,7,1,6,8,4,5,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[3,8,5,2,6,7,1,4] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[3,6,5,2,7,1,4,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,7,1,6,5,2,8,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[8,3,5,2,7,1,6,4] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[3,8,6,4,7,1,5,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,7,1,4,8,6,5,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[3,7,1,4,5,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,3,7,6,5,8,1,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,3,5,6,7,8,9,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[6,7,8,5,4,3,2,1,9] => [[1,2,3,9],[4],[5],[6],[7],[8]] => 00111110
[6,5,7,8,4,3,2,1,9] => [[1,3,4,9],[2],[5],[6],[7],[8]] => 10011110
[7,8,9,5,4,3,2,1,6] => [[1,2,3],[4,9],[5],[6],[7],[8]] => 00111110
[7,8,9,6,5,4,3,2,1,10] => [[1,2,3,10],[4],[5],[6],[7],[8],[9]] => 001111110
[6,7,8,9,4,3,2,1,5] => [[1,2,3,4],[5,9],[6],[7],[8]] => 00011110
[6,5,4,3,2,7,8,9,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => 11110001
[3,5,7,6,8,2,1,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[4,2,5,3,7,6,1,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,2,4,3,7,5,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,3,6,4,7,5,2,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[8,2,5,3,6,4,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,5,3,6,4,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,2,5,3,7,4,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,2,6,3,7,5,1,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,2,7,3,6,4,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,3,6,2,5,4,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[6,3,8,2,5,4,1,7] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,3,1,4,6,5,2,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,3,7,2,5,4,1,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,2,8,3,6,4,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,2,8,4,6,5,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[1,4,7,3,6,5,2,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,2,5,4,1,6,3,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,2,6,4,1,5,3,7] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,4,8,3,7,5,2,6] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[6,2,1,4,8,5,3,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,2,1,4,8,6,3,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[3,2,1,5,8,6,4,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[4,2,8,3,7,5,1,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,2,8,3,7,4,1,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[8,3,7,2,6,4,1,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[7,3,1,4,8,5,2,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[1,3,7,4,8,5,2,6] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[8,2,6,3,7,4,1,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,6,3,8,4,1,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,2,7,3,8,4,1,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[3,2,7,4,8,5,1,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,2,6,3,8,4,1,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,2,5,3,8,4,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,5,3,8,4,1,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[8,2,5,3,7,4,1,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,3,6,4,8,5,2,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,3,5,4,8,6,2,7] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[8,2,4,3,7,5,1,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,2,4,3,8,5,1,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[6,2,4,3,8,5,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,2,4,3,8,6,1,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[4,2,5,3,8,6,1,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[4,2,5,3,1,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[6,2,4,3,1,7,5,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[7,2,4,3,1,6,5,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,5,1,3,6,4,2,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[8,4,1,3,6,5,2,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[1,5,2,4,7,6,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[7,2,5,3,1,6,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,2,5,3,1,7,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,2,6,3,1,7,5,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,2,6,4,1,7,5,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,2,7,4,1,6,5,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[4,2,7,3,1,6,5,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[5,2,7,3,1,6,4,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,2,7,3,1,5,4,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,2,6,3,1,5,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,5,2,4,8,6,3,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[8,4,1,3,7,5,2,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,2,1,5,3,7,4,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[3,2,1,6,4,7,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[3,2,8,5,1,6,4,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[6,2,8,4,1,5,3,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[8,3,7,4,1,5,2,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[7,1,3,2,5,6,4,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[6,3,5,2,4,8,1,7] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[1,5,2,8,7,4,3,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,7,2,8,1,4,3,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[4,8,3,1,5,2,7,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[7,1,5,3,2,6,8,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,7,6,5,3,2,1,4,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[8,7,6,4,3,2,1,5,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[8,7,5,4,3,2,1,6,9] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[8,7,6,5,4,1,2,3,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[9,8,7,6,5,4,2,1,3,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[8,7,6,5,2,3,1,4,9] => [[1,6,8,9],[2],[3],[4],[5],[7]] => 11110100
[9,8,7,6,5,3,2,1,4,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,8,7,6,4,3,2,1,5,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,8,7,5,4,3,2,1,6,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,8,6,5,4,3,2,1,7,10] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[6,7,5,4,3,2,1,8,9] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 01111100
[8,6,2,3,1,5,7,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[1,4,2,7,3,6,8,5] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[3,2,1,7,8,5,4,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[7,3,4,2,1,5,8,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,7,6,3,2,4,8,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[2,1,6,4,7,8,5,3] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[1,6,3,2,4,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,2,3,7,5,8,4,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[1,8,5,3,2,4,7,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,7,8,1,5,6,2,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[3,6,7,1,8,4,2,5] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,3,7,6,2,4,5,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,7,3,8,4,5,6,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,1,4,3,8,5,6,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,6,2,7,8,3,4,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[7,4,1,8,5,6,2,3] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[7,2,5,8,1,6,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[6,4,8,1,5,7,2,3] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,7,4,1,3,6,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,2,1,4,7,5,8,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,8,7,9,5,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[2,6,1,5,4,7,3,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[2,3,6,8,4,1,7,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,7,2,8,6,3,5,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[8,4,2,3,7,1,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,2,4,8,7,3,1,6] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[3,2,4,6,7,8,1,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[5,2,6,8,1,3,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[4,8,1,6,3,7,5,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[7,1,5,2,6,4,3,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[8,3,5,2,6,1,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,8,5,6,2,7,4,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[4,2,7,6,1,8,5,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[7,2,4,8,6,3,5,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,3,2,1,8,5,4,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,3,2,1,6,4,8,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[3,6,5,2,1,8,4,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[6,7,2,4,3,5,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,3,8,2,1,5,7,6] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[4,3,2,8,1,6,7,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[4,5,8,3,2,7,1,6] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[6,8,5,2,7,3,4,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,4,7,8,2,3,6,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,3,8,2,1,6,7,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[9,1,3,4,5,6,7,8,2] => [[1,3,4,5,6,7,8],[2],[9]] => 10000001
[3,5,7,4,6,2,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[5,3,7,6,2,4,8,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[4,6,7,2,5,3,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[6,4,7,8,3,1,5,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,4,7,3,1,5,6,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[5,8,1,7,6,4,2,3] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,6,7,1,8,3,4,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[7,1,8,6,2,5,4,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[8,5,1,7,6,4,2,3] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,5,8,2,6,4,7,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,5,7,4,6,8,3,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,4,7,5,6,8,3,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[5,6,7,4,8,1,3,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[8,1,2,6,4,5,7,3] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[4,8,1,7,2,5,6,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[2,6,7,1,5,4,8,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,2,7,6,5,8,1,4] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,7,3,4,5,8,2,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[7,1,8,4,5,6,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[10,1,3,4,5,6,7,8,9,2] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[1,8,3,4,5,6,9,2,7] => [[1,2,4,5,6,7],[3,9],[8]] => 01000010
[1,2,7,4,5,8,3,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,2,3,4,5,6,7,8,9,12,10,11] => [[1,2,3,4,5,6,7,8,9,10,12],[11]] => 00000000010
[6,7,3,2,5,8,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,1,8,4,5,3,7,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,6,2,5,1,8,7,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[5,1,4,6,2,8,7,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[7,3,5,2,1,6,8,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,5,1,2,6,3,7,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[1,5,8,7,4,6,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,7,2,1,3,6,8,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,7,2,6,8,1,5,4] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[7,4,8,6,5,1,3,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[2,7,6,8,5,1,4,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,6,4,5,7,3,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,5,4,7,8,6,2,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,3,1,6,8,2,5,4] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[7,1,6,8,5,2,4,3] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,5,8,7,6,4,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,5,7,8,6,2,4,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,6,2,1,4,7,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[6,8,2,7,5,4,3,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[5,8,1,7,6,4,3,2] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[10,1,5,2,3,4,6,7,8,9] => [[1,3,5,6,7,8,9,10],[2],[4]] => 101000000
[7,6,1,2,3,4,10,9,5,8] => [[1,4,5,6,7,10],[2,8],[3,9]] => 110000110
[5,9,1,2,3,4,6,7,10,8] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[10,8,4,9,1,2,3,5,6,7] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000
[3,1,5,2,10,4,6,7,8,9] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[4,1,2,10,3,5,6,7,8,9] => [[1,3,4,6,7,8,9,10],[2,5]] => 100100000
[4,1,5,6,7,8,9,2,3] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[2,3,4,5,8,9,1,6,7] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[8,6,3,2,1,5,4,7] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,5,3,2,4,1,7,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,5,2,4,3,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,5,1,4,6,3,2,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,5,1,6,3,4,2,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,3,6,1,5,2,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,4,3,5,2,1,7,6] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,4,3,2,8,7,1,5] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[8,5,1,4,3,7,2,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,5,4,2,1,3,7,6] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[4,7,3,6,1,8,5,2] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,6,2,4,1,5,8,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,1,6,3,7,4,2,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,3,8,2,6,7,1,4] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,2,5,1,7,6,3,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,2,4,6,3,7,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,2,6,4,3,5,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[7,3,6,2,4,5,8,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,3,7,2,1,4,6,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,6,4,1,3,2,8,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,3,8,2,1,5,6,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[6,2,5,7,4,3,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[6,2,5,4,8,7,1,3] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,2,4,8,5,1,6,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,2,7,6,8,5,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,1,6,2,8,5,4,3] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,1,6,3,8,5,2,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[7,2,6,8,1,3,5,4] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[7,2,8,5,1,3,6,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[7,1,8,5,3,2,6,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,1,8,2,5,6,4,3] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,1,5,8,7,2,4,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,1,5,7,4,8,3,2] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[6,1,5,7,8,3,4,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,6,7,3,1,8,5,2] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[4,2,6,3,1,8,7,5] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[6,1,4,2,5,8,7,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[1,5,3,8,4,6,2,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[7,2,3,5,8,4,1,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[7,6,4,2,8,5,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[1,7,6,4,8,5,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[8,7,4,2,1,5,6,3] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[8,2,3,5,1,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[8,7,4,1,3,2,6,5] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,1,4,8,3,6,2,5] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[4,1,8,5,7,6,2,3] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,7,5,8,4,2,1,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,1,5,8,3,4,2,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[6,7,5,1,3,2,4,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,2,6,1,7,3,4,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[4,2,6,8,3,7,1,5] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[6,8,5,1,4,2,3,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,8,4,5,1,3,6,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[1,7,8,5,3,4,6,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,5,8,3,6,4,7,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[6,3,8,1,4,2,7,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,8,1,5,6,3,7,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,8,2,6,5,3,7,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[3,8,1,7,2,6,5,4] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,3,8,1,2,6,5,4] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[8,1,4,2,3,5,7,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[8,1,2,4,6,5,7,3] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[5,1,8,3,7,4,6,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,3,7,1,5,4,6,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,4,7,1,5,3,6,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,2,5,3,4,6,1,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[7,6,4,2,5,3,1,8] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[5,8,4,3,6,2,7,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[1,7,2,6,3,4,8,5] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[7,5,1,6,3,2,4,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,1,2,6,3,4,5,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[7,3,1,4,6,2,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,1,6,5,4,2,3,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[5,8,4,3,1,7,2,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[3,6,8,5,2,4,7,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[5,7,8,4,3,2,6,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[1,3,8,4,7,2,6,5] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[6,7,1,3,2,8,5,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[1,5,3,2,6,8,4,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,7,6,5,8,2,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[5,7,4,2,8,6,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,4,3,7,8,2,6,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[3,8,5,7,6,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,3,6,8,7,2,5,4] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[5,8,7,1,4,2,3,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[2,6,3,7,1,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[7,6,8,4,3,1,5,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[1,7,6,5,3,2,4,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[2,7,6,5,4,1,3,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,2,3,5,8,4,1,7] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,7,6,1,5,8,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[9,8,7,6,5,4,2,3,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[2,3,9,8,7,6,5,4,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[9,1,3,2,4,5,6,7,8] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[6,8,7,1,5,4,3,2] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[8,7,4,6,5,1,3,2] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[9,10,1,8,7,6,5,4,3,2] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[2,4,3,6,5,8,7,1,9] => [[1,2,4,6,9],[3,5,7],[8]] => 01010110
[3,2,5,4,7,6,9,8,1,10] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[2,4,3,6,5,8,7,10,9,1] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[7,2,6,1,5,8,3,4] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,7,3,8,6,2,5,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[4,7,3,6,8,2,1,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[5,4,7,3,8,2,1,6] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,7,2,4,6,3,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[4,3,5,7,2,6,1,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[1,7,2,8,5,4,3,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,4,8,3,6,2,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[6,8,2,5,7,1,4,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[3,8,6,2,7,5,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,8,4,2,7,3,6,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[8,2,7,3,4,5,1,6] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,1,5,2,4,6,3,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[8,6,1,3,4,5,7,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[8,5,1,2,4,6,7,3] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[2,6,8,7,3,4,5,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,7,8,5,6,4,2,3] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[8,3,1,2,4,6,7,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[3,1,7,5,8,2,4,6] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[8,1,3,2,4,6,5,7] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[8,1,5,6,4,2,3,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,6,5,4,3,2,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[2,6,8,1,5,4,3,7] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[3,5,8,2,1,4,7,6] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[4,2,8,5,3,7,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,2,7,5,3,8,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[6,4,5,1,8,3,2,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[5,4,7,8,3,1,2,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[4,5,8,1,3,7,2,6] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[1,5,3,6,8,7,2,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[7,6,2,8,1,4,3,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,7,2,6,8,3,5,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,3,2,8,7,4,5,1] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[7,4,3,8,5,6,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[3,1,5,8,7,6,2,4] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[8,2,1,6,5,7,3,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[3,1,8,6,5,7,2,4] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[1,2,7,6,4,5,8,3] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[7,2,6,5,1,8,3,4] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[4,2,8,5,6,3,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,7,3,2,5,1,6,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,2,5,3,8,7,1,6] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[7,2,5,3,8,4,6,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,7,3,2,5,4,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,5,6,1,8,3,2,4] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,5,6,2,7,3,1,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[3,5,1,4,6,8,2,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[8,5,7,4,2,1,3,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[4,6,2,7,5,8,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[7,8,1,4,2,3,5,6] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,5,2,4,8,7,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,5,2,4,1,3,7,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[5,1,2,4,3,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[8,6,2,7,5,3,1,4] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[4,3,8,1,5,2,6,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,1,3,6,7,2,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,4,8,6,5,1,2,3] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,7,8,6,5,1,2,4] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[8,4,5,7,2,6,3,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[4,5,8,2,7,3,1,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[6,5,8,2,7,3,1,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,4,8,2,7,3,1,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,8,1,3,6,4,2,5] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,5,7,8,3,2,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,7,3,4,2,6,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,7,4,2,3,6,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,4,7,3,2,8,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[6,8,3,2,4,5,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,3,4,6,1,2,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[6,4,3,8,5,1,2,7] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[6,4,8,2,3,5,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,4,6,8,2,3,1,7] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[5,6,8,4,1,2,3,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[6,4,8,5,1,2,3,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[7,4,8,3,1,2,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,7,8,2,3,1,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[5,4,7,8,2,1,3,6] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[5,8,6,3,1,2,4,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[6,8,5,2,1,3,4,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,6,1,3,2,4,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,3,8,1,2,5,7,6] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,6,3,2,8,5,7,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,3,7,2,1,8,6,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,4,8,3,7,2,1,6] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[3,6,8,5,2,1,7,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[6,1,5,4,7,2,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[5,4,8,3,2,7,1,6] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[5,4,3,7,8,2,1,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[3,4,5,6,7,8,2,9,1] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[3,4,5,6,7,8,9,2,10,1] => [[1,2,3,4,5,6,7,9],[8],[10]] => 000000101
[1,4,5,6,7,8,3,9,2] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[3,4,5,6,7,2,1,9,8] => [[1,2,3,4,5,8],[6,9],[7]] => 00001101
[2,4,5,6,7,8,3,1,9] => [[1,2,3,4,5,6,9],[7],[8]] => 00000110
[2,4,5,6,7,8,9,10,3,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[1,4,8,6,3,2,7,5] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,1,8,6,2,5,7,3] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,7,2,5,3,8,4,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[6,3,4,8,1,2,7,5] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[2,6,3,1,5,8,7,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[7,1,3,2,6,5,8,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,3,5,8,4,7,2,6] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,3,8,7,5,1,6,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,1,3,5,6,2,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[6,4,8,7,3,5,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[8,2,3,5,6,1,4,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,8,2,7,6,4,1,5] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,3,8,6,2,7,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,3,4,5,1,6,7,2] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[7,8,1,3,5,4,6,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,5,7,6,4,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,3,7,8,5,4,6,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,3,2,7,8,5,4,6] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,5,7,6,8,3,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[6,5,8,4,3,7,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[6,7,3,1,5,2,4,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,2,4,1,8,3,6,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[2,1,7,4,3,8,5,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[7,2,3,8,5,4,1,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[4,1,5,7,6,3,8,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,2,1,6,4,8,5,10,7,9] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[3,2,1,10,7,4,9,5,6,8] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[5,4,2,3,1,8,6,10,7,9] => [[1,4,6,8,10],[2,7,9],[3],[5]] => 110101010
[1,4,2,6,3,8,5,10,7,9] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[1,10,5,2,7,3,9,4,6,8] => [[1,2,5,7,9,10],[3,6,8],[4]] => 011010100
[1,10,9,6,2,8,3,4,5,7] => [[1,2,6,8,9,10],[3,7],[4],[5]] => 011101000
[1,10,9,8,7,2,3,4,5,6] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => 011110000
[3,2,1,12,7,4,9,5,11,6,8,10] => [[1,4,7,9,11,12],[2,5,8,10],[3,6]] => 11011010100
[1,4,2,6,3,8,5,10,7,12,9,11] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => 01010101010
[1,4,8,2,3,6,5,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,4,6,7,3,5,2,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,4,8,2,6,7,5,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[1,7,3,2,4,5,6,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,7,3,2,4,5,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,6,4,3,2,5,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[4,2,6,5,3,1,7,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,2,1,6,8,7,4,3] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[1,3,5,8,6,2,7,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,7,8,5,4,2,6,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[8,3,2,7,5,6,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[1,3,8,5,7,4,2,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,2,3,7,5,4,6,8] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[1,4,2,8,6,3,5,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[2,8,6,3,5,7,4,1] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[6,1,8,2,5,3,4,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,5,4,2,3,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[6,1,5,2,3,4,8,7] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[3,1,2,4,8,6,7,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[3,1,2,5,8,7,4,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,5,2,1,8,4,7,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,6,2,4,3,8,1,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,7,5,2,8,1,4,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[5,1,4,7,3,2,8,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[4,1,5,8,6,2,3,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,4,8,6,3,7,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,5,2,3,1,8,7,4] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,4,7,5,3,8,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[5,7,4,8,3,1,6,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,3,5,1,8,7,2,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[2,5,3,6,1,8,4,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[2,5,6,8,3,1,7,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[7,1,4,5,3,6,2,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[1,7,2,4,5,3,6,8] => [[1,2,4,5,7,8],[3],[6]] => 0100100
[1,7,4,5,3,2,6,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[1,6,4,7,3,5,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,5,6,4,8,2,1,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,6,4,7,5,2,3,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,5,2,6,7,4,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[8,5,6,1,4,3,7,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[2,5,4,7,8,3,1,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[6,4,5,8,2,3,1,7] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[8,6,1,3,2,5,7,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,5,8,1,4,6,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[4,2,6,7,8,1,5,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,4,6,7,8,1,5,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[4,7,3,8,5,1,6,2] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[4,3,2,7,5,8,1,6] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,8,5,3,2,6,1,7] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[2,8,4,5,3,6,1,7] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[8,1,5,3,2,4,7,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,8,4,1,3,6,5,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[8,6,1,3,2,7,4,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,3,8,2,4,1,6,5] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[6,2,3,7,8,1,5,4] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[6,3,7,8,1,5,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,6,3,7,8,1,5,4] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[7,5,8,1,6,4,2,3] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[8,1,4,3,7,5,6,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,4,8,5,3,2,6,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[8,2,7,6,4,1,5,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[2,7,4,3,8,5,1,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[6,8,2,7,3,1,5,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,2,6,3,4,1,7,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,1,2,8,5,3,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,1,5,8,3,6,7,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[7,5,2,8,1,6,3,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[4,8,5,7,1,3,2,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[3,4,7,2,1,5,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,8,2,7,1,3,6,5] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[8,2,1,7,4,6,3,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,2,5,8,3,6,7,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,1,6,8,3,2,7,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[4,1,5,6,8,2,7,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[4,5,2,8,7,3,1,6] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,8,5,3,1,6,7,2] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[6,2,3,1,7,8,5,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[5,2,3,6,8,4,7,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[6,2,1,7,8,4,3,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,2,1,3,8,4,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[5,2,7,8,4,1,6,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[6,2,7,8,3,5,4,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[5,2,8,6,4,1,7,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,1,2,8,4,3,7,6] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[6,7,8,3,2,5,4,1] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[5,7,2,6,4,8,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,2,3,4,7,8,5,1] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[7,2,1,8,4,3,5,6] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[6,2,1,3,7,5,8,4] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,8,7,3,4,5,1,2] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,2,3,7,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[1,7,6,4,2,3,5,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,3,2,5,8,6,4,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[6,1,4,7,2,8,5,3] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[1,6,7,2,4,8,5,3] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[5,7,2,4,3,6,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,7,3,4,6,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,8,3,6,1,7,4,5] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[4,3,1,8,5,2,6,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[1,8,4,5,6,2,7,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[7,3,8,2,1,4,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,2,5,3,1,7,4,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,3,5,8,1,7,4,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,5,4,8,6,1,7,2] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[7,5,2,3,8,4,6,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[2,7,5,1,4,8,3,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[5,7,6,1,2,8,3,4] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[7,4,6,5,1,8,2,3] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,1,3,2,6,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[4,3,5,2,8,1,6,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,7,3,8,2,4,6,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[2,7,4,8,5,3,1,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[6,1,3,8,4,2,7,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[5,4,1,8,6,2,7,3] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[5,4,6,8,1,3,2,7] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[3,6,1,5,8,4,7,2] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,4,8,3,5,7,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[3,5,8,2,4,1,7,6] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[7,2,8,4,1,3,6,5] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[5,8,1,2,4,3,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[8,4,3,5,7,2,6,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[4,1,5,2,3,8,7,6] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[6,3,5,8,2,4,7,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[2,8,7,1,4,6,3,5] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[1,8,5,3,7,4,2,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[7,5,6,2,8,4,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[5,7,6,2,8,1,4,3] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[6,3,8,1,2,5,4,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,6,4,8,5,3,2,1] => [[1,4],[2,5],[3],[6],[7],[8]] => 1101111
[8,6,9,7,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => 10111111
[3,2,5,4,7,6,1,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[3,2,5,4,9,8,7,6,1,10] => [[1,3,5,10],[2,4,6],[7],[8],[9]] => 101011110
[3,2,5,4,1,8,7,10,9,6] => [[1,3,6,8],[2,4,7,9],[5,10]] => 101101011
[3,2,5,4,1,10,9,8,7,6] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => 101101111
[5,4,3,2,9,8,7,6,1,10] => [[1,5,10],[2,6],[3,7],[4,8],[9]] => 111011110
[1,4,3,6,5,8,7,10,9,2] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,4,3,6,5,10,9,8,7,2] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[1,4,3,10,9,8,7,6,5,2] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111
[1,6,5,4,3,10,9,8,7,2] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111
[3,2,5,4,7,6,1,12,11,10,9,8] => [[1,3,5,8],[2,4,6,9],[7,10],[11],[12]] => 10101101111
[3,2,1,8,7,6,5,12,11,10,9,4] => [[1,4,8],[2,5,9],[3,6,10],[7,11],[12]] => 11011101111
[1,4,3,6,5,8,7,12,11,10,9,2] => [[1,2,4,6,8],[3,5,7,9],[10],[11],[12]] => 01010101111
[1,4,3,8,7,6,5,12,11,10,9,2] => [[1,2,4,8],[3,5,9],[6,10],[7,11],[12]] => 01011101111
[1,5,7,2,4,3,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,5,3,2,4,7,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,7,2,4,6,5,3,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,4,7,2,6,5,3,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,2,6,8,7,4,3,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,2,7,4,3,5,8,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,6,2,8,7,4,3,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,7,4,2,3,5,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,8,5,2,3,6,4,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,4,8,5,2,3,6] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,4,7,5,2,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,6,3,7,4,2,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,8,5,2,7,4,3,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,4,8,7,5,3,2,6] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[1,2,5,8,6,3,7,4] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,2,4,7,5,8,6,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[1,5,8,7,6,2,4,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[1,3,5,8,7,6,2,4] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[1,5,2,4,3,6,8,7] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,6,8,7,5,3,2,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,2,5,7,4,3,8,6] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[1,5,3,2,6,8,7,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,4,2,6,8,7,5,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,5,8,6,3,2,7,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,8,5,2,6,3,4,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,7,4,6,3,2,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,6,3,2,8,5,4,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,3,8,6,4,2,5,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,5,7,4,2,3,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,3,7,5,4,2,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[7,5,2,6,3,4,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,8,2,7,5,4,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,4,8,6,7,1,2,3] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[2,7,3,6,8,5,4,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,7,2,8,1,6,4,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[8,5,2,4,6,7,3,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[2,5,8,7,1,4,3,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[3,4,6,5,8,2,7,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,2,4,1,6,7,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[4,2,7,1,6,8,3,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[5,2,8,6,4,7,1,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[6,1,3,4,7,2,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[8,4,7,2,5,3,1,6] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,3,4,5,2,1,7,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,6,1,4,7,3,5,2] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[5,3,6,7,2,8,4,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[5,3,6,7,2,4,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,6,1,4,7,5,2,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[1,5,8,2,6,7,4,3] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[7,1,3,6,5,2,8,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[8,2,1,4,5,7,6,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[1,4,7,5,2,3,8,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[6,1,7,5,4,2,8,3] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[2,7,3,6,5,1,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,6,5,1,3,7,4,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,7,6,2,4,8,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,7,5,6,4,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[7,6,8,1,3,5,4,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[2,8,4,6,1,7,5,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[2,8,6,4,7,3,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[8,7,1,4,6,5,3,2] => [[1,4,5],[2],[3],[6],[7],[8]] => 1100111
[3,5,8,6,7,1,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,2,4,6,8,5,3,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,1,5,8,6,2,4,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[2,5,4,6,8,1,3,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,5,2,4,7,8,1,3] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,2,5,8,6,4,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,2,8,3,4,7,6,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,4,3,8,7,1,6,5] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,5,8,7,4,2,6,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[6,8,7,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[5,3,4,8,6,2,7,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,4,5,8,6,2,7,1] => [[1,2,3,4,7],[5],[6],[8]] => 0001101
[5,4,2,3,6,1,8,7] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[5,1,7,4,3,6,8,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,3,7,6,8,2,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[8,1,4,7,2,3,5,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,1,8,5,2,7,3,4] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[8,7,2,6,3,1,4,5] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,7,1,6,4,5,2,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[5,4,1,3,7,2,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,3,4,7,6,2,1,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[3,1,8,7,5,2,4,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[6,5,8,7,2,4,3,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[4,3,6,5,8,2,1,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[7,6,3,2,8,5,4,1] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[4,3,7,1,8,5,2,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[3,2,8,5,6,7,1,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[8,3,2,1,4,7,5,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[4,7,3,1,8,5,2,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[3,7,8,2,5,6,1,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[7,5,1,4,2,3,6,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[7,8,6,1,2,4,5,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[1,5,3,4,7,8,6,2] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[5,1,2,4,7,8,6,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[5,1,7,8,6,2,3,4] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[8,5,1,6,7,2,3,4] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[7,5,1,2,4,6,8,3] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[6,1,5,2,7,3,4,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,2,6,4,5,8,3] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[1,7,3,6,4,5,8,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,8,3,6,4,5,7,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[8,1,6,2,7,3,4,5] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[7,1,6,2,5,3,4,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,1,6,2,5,3,4,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,1,7,2,5,3,4,6] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[8,1,2,7,4,5,6,3] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[1,8,3,7,4,5,6,2] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[8,1,6,7,5,2,3,4] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,3,1,2,6,4,5,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[3,1,2,8,5,6,7,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[6,3,1,2,7,4,5,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[6,1,7,4,2,3,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[1,7,3,4,6,8,5,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[1,7,3,8,4,5,6,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,1,8,2,5,3,4,6] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[6,1,7,2,5,3,4,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,1,7,2,6,3,4,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,1,8,2,6,3,4,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,6,3,7,4,5,8,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,4,7,3,5,1,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[2,4,8,6,3,5,1,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[2,3,7,5,4,1,6,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[3,4,6,2,1,5,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[3,4,7,2,1,6,5,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,6,8,3,5,1,4,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[2,3,6,1,5,8,4,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,3,7,1,6,5,8,4] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,4,7,1,3,6,8,5] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,4,7,8,1,3,2,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[2,5,7,1,4,6,3,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,4,7,1,6,3,5,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,3,7,1,6,5,4,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[2,5,7,1,4,3,6,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[2,5,7,3,1,4,6,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[3,4,7,2,1,6,8,5] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,6,3,7,1,5,2,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[5,7,3,2,8,1,4,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,6,5,7,1,8,4,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,6,8,5,4,1,7,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,4,7,8,1,3,6,2] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[2,5,7,1,4,6,8,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[2,4,7,1,6,3,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,4,7,1,6,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,2,3,4,5,6,1,9,8] => [[1,3,4,5,6,8],[2,9],[7]] => 10000101
[2,1,9,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4],[9]] => 10100001
[8,6,5,1,2,4,3,7] => [[1,5,6,8],[2],[3],[4],[7]] => 1110010
[7,6,1,4,2,3,5,8] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,5,1,4,8,3,2,7] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,7,5,1,4,2,3,6] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[8,4,1,2,5,3,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[8,6,1,4,2,5,3,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,7,1,4,3,2,6,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[2,8,3,7,4,5,6,1] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[8,7,5,2,4,3,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[4,2,5,7,3,1,6,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[8,2,4,5,3,1,6,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[8,4,5,1,3,2,6,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,3,7,5,2,1,6,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[1,6,7,4,3,2,5,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,4,5,7,3,2,6,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[3,5,1,4,7,2,6,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,5,1,4,7,8,3,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[4,3,7,1,5,2,6,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[3,5,1,6,4,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[6,4,3,1,7,2,5,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[6,2,7,4,3,1,5,8] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[2,6,4,1,7,3,5,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,3,2,7,4,5,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,2,4,1,3,6,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[6,3,2,5,7,1,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,2,6,5,7,1,4,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[1,7,3,2,5,6,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[2,1,7,3,5,6,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,1,6,3,5,7,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,6,3,2,5,7,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,4,6,5,2,7,3,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[5,6,2,1,4,3,7,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[2,5,1,6,4,3,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[2,5,4,1,6,3,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[4,6,1,5,2,7,3,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[1,6,5,3,7,2,4,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,2,5,3,4,8,7,6] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[5,2,7,6,1,8,4,3] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[5,8,2,6,1,7,4,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[1,5,8,3,6,2,7,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,2,6,4,7,3,8,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,2,7,8,3,5,6,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,7,4,5,8,1,6,3] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[2,6,1,8,5,4,3,7] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,8,6,2,3,4,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,5,8,6,2,1,3,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[6,4,7,5,8,2,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,3,7,4,2,5,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[7,5,6,2,4,3,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[4,6,2,5,7,3,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[4,2,8,5,3,6,1,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[8,1,7,4,5,6,2,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,1,7,8,4,5,6,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[8,2,1,4,3,7,6,5] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[7,6,5,3,1,2,8,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[5,4,1,6,2,8,3,7] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[6,2,3,1,7,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[3,1,8,6,7,2,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,2,5,1,8,6,7,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[4,5,3,7,1,6,8,2] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[4,2,8,5,3,6,7,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[2,8,6,3,5,4,7,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[3,5,2,8,6,4,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[7,3,5,1,6,4,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,1,4,7,2,6,8,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[1,8,2,5,6,4,7,3] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,7,1,4,8,5,6,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[2,8,4,6,1,3,7,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[8,4,6,2,5,3,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,3,7,6,2,1,5,4] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[8,5,2,7,6,1,4,3] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[5,8,2,7,6,1,4,3] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[8,3,7,6,2,5,1,4] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[7,3,8,6,5,1,4,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[9,8,7,6,1,2,3,4,5,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[2,6,3,7,5,4,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[5,4,7,1,3,8,6,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[2,8,5,1,4,7,3,6] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[7,2,6,5,8,4,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[5,8,2,3,4,6,1,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[6,1,3,4,2,5,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[1,5,6,3,2,4,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[6,3,5,2,4,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[7,8,3,5,2,4,6,1] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[2,4,5,7,3,6,1,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,5,3,1,6,4,7,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,5,1,3,4,2,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,7,4,3,2,6,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[6,8,7,4,3,5,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[2,6,7,8,4,3,5,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,7,8,4,5,3,6,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[7,1,8,5,3,4,6,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,7,4,2,1,6,3,8] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[5,1,4,7,3,6,2,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[7,4,8,6,3,5,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[4,7,6,3,5,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,6,5,8,7,4,2,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[6,1,3,8,7,5,2,4] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[7,6,2,1,8,3,5,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,1,3,6,8,2,5,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[1,7,5,6,8,2,4,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,6,7,5,8,2,4,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,7,4,5,2,8,6,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[7,5,4,2,1,8,6,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[3,6,7,4,2,8,5,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,6,3,2,7,8,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,6,1,3,4,2,5,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[7,8,2,6,4,5,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,2,5,4,6,1,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,1,2,4,5,6,3,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[7,3,2,1,5,6,4,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,6,2,1,7,5,4,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,6,7,3,1,5,4,8] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,1,6,4,7,5,3,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[7,2,8,5,6,4,3,1] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[7,6,8,5,4,1,3,2] => [[1,3],[2,7],[4],[5],[6],[8]] => 1011101
[7,1,8,4,6,5,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[7,8,6,3,1,5,4,2] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[7,6,1,4,5,3,2,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[7,1,5,6,4,3,2,8] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[4,1,3,8,6,2,7,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[5,6,3,2,8,1,7,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[8,2,6,3,1,5,7,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,2,5,6,7,4,3,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[8,2,5,3,4,7,6,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,5,3,2,4,1,8,6] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[7,1,2,3,6,8,4,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[6,7,2,8,3,4,5,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,1,8,4,6,5,7,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,1,2,3,8,4,7,5] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[8,1,6,7,4,2,3,5] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,1,6,4,5,2,3,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,6,4,1,2,3,7,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,6,1,4,2,5,7,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,6,4,2,5,3,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,6,4,1,5,7,2,3] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,6,1,4,7,2,5,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[8,6,4,1,5,2,3,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,6,7,1,4,5,2,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[3,4,7,5,8,2,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[8,7,1,4,6,5,2,3] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,3,7,6,4,5,1,2] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,3,8,6,4,1,7,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[10,8,1,9,2,3,4,5,6,7] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[8,7,1,2,3,4,5,9,10,6] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[6,1,2,3,4,5,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[5,1,2,3,4,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[4,1,2,3,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 10000000
[7,4,5,1,2,8,6,3] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,4,7,1,8,5,2,3] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[5,7,4,2,3,8,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[3,8,2,5,1,7,4,6] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[5,8,4,2,3,7,1,6] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[4,8,5,2,1,7,3,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[8,5,7,6,1,2,4,3] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,8,7,5,2,4,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[5,7,6,8,4,1,3,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[7,3,1,6,8,5,4,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[5,3,1,7,4,8,6,2] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,3,1,8,6,4,5,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,6,4,1,7,3,2,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[4,6,8,3,7,1,2,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[3,5,2,8,4,7,1,6] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[6,4,8,3,7,2,1,5] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[3,6,2,8,7,4,1,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[6,8,4,2,7,3,1,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[9,8,2,3,4,5,6,7,1] => [[1,4,5,6,7,8],[2],[3],[9]] => 11000001
[8,9,2,3,4,5,6,7,1] => [[1,2,5,6,7,8],[3,4],[9]] => 01000001
[5,6,7,9,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[5,6,7,8,9,1,4,3,2] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[10,9,2,3,4,5,6,7,8,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => 110000001
[3,4,7,8,5,1,2,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,7,3,2,5,6,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,2,7,6,4,5,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[1,7,3,6,8,4,2,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,3,6,5,1,8,7,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[8,3,1,2,6,4,7,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[1,7,8,2,4,3,5,6] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[3,6,4,7,1,2,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[5,7,4,8,1,3,2,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,3,7,8,1,5,2,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[8,5,4,2,6,1,7,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[3,2,6,8,7,4,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[2,3,7,5,1,8,6,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[6,3,1,2,8,7,4,5] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,2,1,3,8,7,6,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[7,2,1,5,3,8,4,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[1,5,8,2,4,3,6,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[4,3,6,8,1,5,2,7] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,4,6,8,3,1,7,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[3,6,8,4,5,1,7,2] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[8,6,1,7,2,4,3,5] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,3,1,2,8,6,4,5] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,3,7,6,1,8,5,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,2,7,8,6,4,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[6,2,8,3,1,4,7,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[3,1,2,8,7,4,5,6] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[2,1,3,8,7,4,6,5] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,1,3,8,7,4,5,6] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[1,6,8,3,2,4,7,5] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[8,5,1,7,2,4,3,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,1,7,3,2,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,3,1,6,2,7,5,4] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[1,3,2,8,7,6,4,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[2,1,3,8,7,6,4,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[2,4,3,1,6,5,8,7,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]] => 011010101
[1,6,3,7,2,5,4,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[1,7,2,4,6,3,5,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[5,6,2,8,4,1,3,7] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[3,5,8,4,2,1,6,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,5,8,3,1,4,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,8,1,3,5,7,4,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[5,4,7,8,3,2,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,6,8,2,5,1,4,7] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[3,6,8,7,2,5,4,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,4,6,5,8,2,1,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,4,6,7,8,3,5,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,4,2,5,7,6,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,4,2,6,8,5,3,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,2,6,8,3,5,4,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,6,8,3,5,4,2,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,5,3,2,4,6,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,5,8,7,6,3,2,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,5,7,6,3,2,4,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,6,3,2,4,7,5,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,6,3,2,4,8,7,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,2,7,6,4,3,5,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,8,7,5,2,4,6,3] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,7,5,2,4,6,3,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,7,4,2,5,3,6,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,8,4,7,5,2,6,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,7,5,2,3,6,4,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,7,5,2,6,3,4,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,6,3,7,4,2,5,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,6,3,2,7,5,4,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,4,7,5,2,6,3,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,3,6,4,8,7,5,2] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[1,3,7,6,4,2,5,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,3,2,4,8,5,7,6] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,3,8,7,5,2,4,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,4,6,3,2,7,5,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,4,6,3,2,8,7,5] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,5,7,6,4,2,3,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,6,3,2,8,4,7,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,6,3,5,2,7,4,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[1,6,3,5,2,8,7,4] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,8,3,7,5,2,4,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[6,4,7,1,5,3,8,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,3,8,2,6,4,7,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[4,3,8,2,6,5,7,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,7,1,4,8,2,3,6] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[6,5,7,1,4,3,8,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[5,7,6,1,2,4,8,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,8,3,5,7,6,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[1,3,4,2,8,5,7,6] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[5,7,6,2,4,8,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[6,7,5,2,3,8,4,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[6,7,5,3,8,4,2,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[3,2,1,4,8,5,7,6] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[7,3,1,4,2,6,5,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[7,4,1,6,2,5,3,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,4,1,8,2,6,3,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[5,3,1,8,2,6,4,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[4,7,1,5,2,6,3,8] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[6,5,1,4,2,7,3,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[1,8,7,3,4,5,2,6] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,7,4,5,2,3,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,2,6,8,7,3,4,5] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,3,7,8,4,5,6,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[8,4,2,3,1,6,5,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,4,5,2,8,1,7,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[4,8,6,2,3,1,7,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,4,2,1,8,5,3,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,4,2,3,5,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[2,8,6,4,5,1,7,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[8,2,4,6,7,1,5,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[2,6,3,1,7,4,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[6,5,1,8,3,2,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[1,4,3,7,2,8,6,5] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,8,7,4,5,3,2,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[2,8,3,1,4,5,7,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[8,3,2,1,5,6,7,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,7,4,6,3,8,2,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,6,4,1,3,8,2,7] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,5,3,1,8,7,6,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[6,3,4,2,7,8,5,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,7,4,5,1,6,3,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[6,2,7,8,1,3,5,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[5,1,8,4,3,7,2,6] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[7,2,8,1,4,5,6,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[1,4,8,2,5,6,7,3] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[8,1,6,7,2,5,4,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,5,2,3,6,8,4,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[8,1,4,6,5,3,2,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,1,4,7,6,5,2,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,1,2,7,6,5,4,3] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[4,5,8,1,6,7,2,3] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,7,2,5,8,4,6,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[6,7,8,4,1,5,2,3] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,2,8,3,5,1,4,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[6,2,7,4,5,3,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[6,8,2,5,3,4,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,8,7,5,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[7,4,5,6,1,8,2,3] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[6,1,8,7,4,5,2,3] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[4,8,7,1,6,3,2,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[4,8,2,7,5,3,6,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[1,3,2,6,8,7,4,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,3,8,2,5,4,6,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,2,5,8,7,3,4] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,6,8,7,2,3,5,4] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,6,8,7,2,5,3,4] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,5,2,4,8,3,6,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,2,4,5,8,6,3,7] => [[1,2,3,4,5,8],[6],[7]] => 0000110
[1,2,8,3,5,4,7,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,3,8,2,5,4,7,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,6,7,5,2,4,8,3] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[1,5,6,4,7,2,3,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,7,4,2,5,8,3,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[1,6,4,3,7,5,2,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,6,5,4,7,2,3,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,7,3,2,6,4,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,5,8,2,3,6,7,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,3,2,6,8,5,4,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[1,6,3,2,7,4,5,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,7,8,5,4,2,3,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,8,4,2,3,6,5,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,4,2,7,5,3,8,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,5,7,6,2,4,3,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,8,4,7,3,2,6,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[1,3,8,4,2,6,5,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,7,4,2,6,5,8,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,6,5,8,3,7,4,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[1,7,4,8,3,2,5,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,4,8,3,2,7,5,6] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,8,3,6,4,5,2,7] => [[1,2,4,6,8],[3],[5],[7]] => 0101010
[1,6,4,7,3,2,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,2,3,7,4,5,6,1] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[8,5,7,2,3,6,4,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[7,5,2,1,6,8,3,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[7,6,1,5,4,8,2,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,6,3,2,1,8,4,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[2,8,7,3,4,6,1,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[6,5,1,3,7,2,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,1,7,3,4,5,2,6] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[7,1,8,3,4,5,2,6] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,8,7,3,4,2,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[3,8,7,1,2,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,8,5,3,4,6,2,7] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[7,1,6,5,4,3,8,2] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[7,1,3,6,4,5,8,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[7,1,5,3,6,4,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[6,1,5,3,7,8,2,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,8,7,1,2,6,3,4] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[6,8,2,3,4,7,1,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[5,1,7,3,8,6,2,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[6,1,3,2,4,7,8,5] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[6,2,1,3,4,7,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[3,4,5,6,8,1,9,2,7] => [[1,2,3,4,5,7],[6,8,9]] => 00001010
[3,4,5,6,8,9,1,2,7] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[3,4,5,6,8,1,2,7,9] => [[1,2,3,4,5,9],[6,7,8]] => 00001000
[2,3,4,5,6,8,9,1,10,7] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[2,3,1,5,6,7,8,9,4] => [[1,2,4,5,6,7,8],[3,9]] => 01000001
[3,2,5,8,7,4,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[4,2,5,8,7,3,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[8,3,4,1,6,5,2,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,4,8,5,7,2,1,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[3,6,4,8,5,7,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[5,8,4,7,3,6,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[4,2,8,7,3,1,6,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[6,5,8,2,1,7,4,3] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[6,1,4,3,8,7,2,5] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[5,1,3,2,6,8,7,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[6,1,3,8,7,2,4,5] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[1,2,8,4,5,7,3,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[4,2,1,8,7,6,3,5] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[3,2,5,8,7,1,4,6] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[5,6,3,8,7,2,1,4] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,5,8,4,7,1,6,3] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,6,2,4,8,5,7,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[3,1,6,5,8,7,2,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,8,5,3,6,7,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,8,5,3,4,7,6,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,7,1,3,6,4,5,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[8,1,7,3,5,4,6,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[1,8,6,3,2,5,4,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,2,4,8,5,7,1,6] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[8,1,2,4,7,5,6,3] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[6,4,5,8,3,1,7,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,6,2,1,5,7,3,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,6,2,8,5,3,7,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[8,7,2,4,1,5,3,6] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,5,3,4,8,6,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[2,8,3,1,4,6,7,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,3,6,5,1,2,7,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[5,8,3,7,6,4,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[1,3,8,7,6,5,2,4] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[4,8,7,2,6,3,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,8,7,2,6,3,5,4] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[8,7,2,1,4,3,5,6] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[2,8,7,1,6,3,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,2,8,7,6,5,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[1,2,5,7,4,8,6,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[6,2,1,8,7,5,3,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,3,8,7,4,5,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[2,8,3,4,1,5,6,7] => [[1,2,4,6,7,8],[3],[5]] => 0101000
[1,3,7,5,4,8,6,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[4,5,6,3,1,8,2,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,5,6,3,8,4,2,7] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,6,5,3,8,4,1,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[5,7,3,8,4,2,6,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[5,3,6,2,8,4,1,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[2,3,6,5,4,8,1,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,7,5,4,8,2,6,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[5,3,7,1,2,8,4,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,3,8,7,2,5,4,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[9,7,8,5,4,3,2,1,6] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[6,8,4,1,7,5,2,3] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,1,4,6,7,5,2,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[2,6,8,1,4,7,5,3] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[6,4,8,1,2,7,5,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,2,8,1,6,7,5,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[8,1,2,6,4,7,5,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,4,1,6,2,7,5,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[4,8,1,2,6,7,5,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[4,8,2,1,6,7,5,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[8,2,4,6,1,7,5,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[2,1,4,5,6,7,8,9,10,3] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[2,3,4,1,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[4,3,5,6,7,8,9,10,1,2] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[2,3,4,5,6,1,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[6,3,4,5,7,8,9,10,1,2] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[2,3,4,5,6,7,8,1,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[8,3,4,5,6,7,9,10,1,2] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[5,4,7,6,3,1,2,8] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,6,4,8,1,5,2,7] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[3,6,8,4,1,5,2,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[8,7,1,4,2,3,5,6] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[3,8,6,4,1,5,2,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[8,2,6,5,7,1,3,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,6,1,3,2,8,7,5] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[7,1,4,8,2,3,6,5] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,5,3,6,7,1,8,2] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,4,7,8,3,5,2,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,6,1,3,5,2,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,5,1,4,8,3,7,6] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[6,1,2,5,4,8,7,3] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,4,1,7,3,5,6,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,4,1,2,5,7,3,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[2,4,5,6,8,3,1,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[3,4,5,8,6,2,1,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[4,5,1,8,6,3,7,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,3,4,5,6,8,9,2,7] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[8,3,7,2,1,6,5,4] => [[1,3],[2,6],[4,7],[5],[8]] => 1011011
[8,4,7,6,2,5,1,3] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,4,7,3,6,2,1,5] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[3,8,7,5,6,4,1,2] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,8,7,5,6,2,1,4] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[3,8,7,5,6,2,4,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,8,7,5,6,4,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[4,5,2,3,6,7,8,9,1] => [[1,2,5,6,7,8],[3,4],[9]] => 01000001
[4,3,2,5,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]] => 11000001
[5,6,7,2,3,4,8,9,1] => [[1,2,3,7,8],[4,5,6],[9]] => 00100001
[5,3,6,2,4,7,8,9,1] => [[1,3,6,7,8],[2,5],[4],[9]] => 10100001
[5,4,3,2,6,7,8,9,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => 11100001
[6,3,7,8,2,4,5,9,1] => [[1,3,4,8],[2,6,7],[5],[9]] => 10010001
[6,7,4,5,2,3,8,9,1] => [[1,2,7,8],[3,4],[5,6],[9]] => 01010001
[6,4,3,7,2,5,8,9,1] => [[1,4,7,8],[2,6],[3],[5],[9]] => 11010001
[7,8,4,5,9,2,3,6,1] => [[1,2,5],[3,4,8],[6,7],[9]] => 01001001
[7,4,3,8,9,2,5,6,1] => [[1,4,5],[2,7,8],[3],[6],[9]] => 11001001
[7,5,8,3,6,2,4,9,1] => [[1,3,8],[2,5],[4,7],[6],[9]] => 10101001
[7,5,4,3,8,2,6,9,1] => [[1,5,8],[2,7],[3],[4],[6],[9]] => 11101001
[7,6,5,4,3,2,8,9,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001
[8,6,4,9,3,7,2,5,1] => [[1,4],[2,6],[3,8],[5],[7],[9]] => 11010101
[8,6,5,4,3,9,2,7,1] => [[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101
[4,5,2,3,6,7,8,9,10,1] => [[1,2,5,6,7,8,9],[3,4],[10]] => 010000001
[4,3,2,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => 110000001
[5,6,7,2,3,4,8,9,10,1] => [[1,2,3,7,8,9],[4,5,6],[10]] => 001000001
[5,3,6,2,4,7,8,9,10,1] => [[1,3,6,7,8,9],[2,5],[4],[10]] => 101000001
[5,4,3,2,6,7,8,9,10,1] => [[1,5,6,7,8,9],[2],[3],[4],[10]] => 111000001
[6,7,8,9,2,3,4,5,10,1] => [[1,2,3,4,9],[5,6,7,8],[10]] => 000100001
[6,3,7,8,2,4,5,9,10,1] => [[1,3,4,8,9],[2,6,7],[5],[10]] => 100100001
[6,7,4,5,2,3,8,9,10,1] => [[1,2,7,8,9],[3,4],[5,6],[10]] => 010100001
[6,4,3,7,2,5,8,9,10,1] => [[1,4,7,8,9],[2,6],[3],[5],[10]] => 110100001
[6,5,4,3,2,7,8,9,10,1] => [[1,6,7,8,9],[2],[3],[4],[5],[10]] => 111100001
[7,8,9,10,1,3,4,5,6,2] => [[1,2,3,4,9],[5,6,7,8],[10]] => 000100001
[7,3,8,9,10,2,4,5,6,1] => [[1,3,4,5],[2,7,8,9],[6],[10]] => 100010001
[7,4,3,8,9,2,5,6,10,1] => [[1,4,5,9],[2,7,8],[3],[6],[10]] => 110010001
[7,5,8,3,6,2,4,9,10,1] => [[1,3,8,9],[2,5],[4,7],[6],[10]] => 101010001
[7,5,4,3,8,2,6,9,10,1] => [[1,5,8,9],[2,7],[3],[4],[6],[10]] => 111010001
[7,6,5,4,3,2,8,9,10,1] => [[1,7,8,9],[2],[3],[4],[5],[6],[10]] => 111110001
[8,5,9,3,6,10,2,4,7,1] => [[1,3,6],[2,5,9],[4,8],[7],[10]] => 101001001
[8,5,4,3,9,10,2,6,7,1] => [[1,5,6],[2,8,9],[3],[4],[7],[10]] => 111001001
[8,9,6,7,4,5,2,3,10,1] => [[1,2,9],[3,4],[5,6],[7,8],[10]] => 010101001
[8,6,4,9,3,7,2,5,10,1] => [[1,4,9],[2,6],[3,8],[5],[7],[10]] => 110101001
[8,6,5,4,3,9,2,7,10,1] => [[1,6,9],[2,8],[3],[4],[5],[7],[10]] => 111101001
[8,7,6,5,4,3,2,9,10,1] => [[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => 111111001
[9,7,5,4,10,3,8,2,6,1] => [[1,5],[2,7],[3,9],[4],[6],[8],[10]] => 111010101
[9,7,6,5,4,3,10,2,8,1] => [[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => 111110101
[1,5,6,3,8,2,7,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[2,6,3,8,4,7,1,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,6,3,5,7,8,1,4] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,5,6,3,7,2,8,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,7,5,3,6,2,8,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,5,7,3,4,2,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,5,8,3,4,2,7,6] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[1,4,5,3,7,2,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,4,5,3,8,2,7,6] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[6,5,1,4,2,7,8,3] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,5,1,4,2,8,7,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[1,7,5,4,2,8,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[5,1,6,8,3,7,2,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[3,1,7,6,2,4,5,10,9,8] => [[1,3,6,7,8],[2,4,9],[5,10]] => 101100011
[9,4,1,6,2,8,3,5,7,10] => [[1,4,6,8,9,10],[2,5,7],[3]] => 110101000
[9,8,5,1,7,2,3,4,6,10] => [[1,5,7,8,9,10],[2,6],[3],[4]] => 111010000
[5,4,7,1,8,6,3,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[2,4,1,5,3,6,7,8,9] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[1,4,8,2,6,5,3,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[8,5,1,3,6,2,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[7,5,1,8,3,4,2,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,2,8,1,7,4,3,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[1,2,5,6,8,7,3,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,5,6,8,2,7,4,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,6,7,3,4,1,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,6,5,7,8,2,4,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[1,5,6,7,2,8,4,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,7,6,1,8,2,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[1,3,7,2,6,4,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,5,8,6,7,3,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,6,5,8,7,2,4,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[1,5,7,6,2,8,3,4] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,2,5,8,6,7,4,3] => [[1,2,3,4,6],[5],[7],[8]] => 0001011
[1,2,6,5,7,3,8,4] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,7,5,8,6,4,2,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,6,5,8,1,2,7,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[5,4,7,8,1,6,3,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[2,5,6,8,1,3,7,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[5,3,6,8,1,2,7,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[4,6,5,8,3,2,7,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[4,5,6,8,2,3,7,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,5,8,7,1,6,4,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,7,5,8,3,6,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[7,3,6,8,5,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,3,6,7,5,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,4,5,7,3,6,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,4,7,8,5,6,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,6,8,7,5,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,4,7,8,5,1,3,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,8,4,6,5,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[6,8,4,7,5,1,3,2] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[4,5,6,7,8,3,9,1,2] => [[1,2,3,4,5,7],[6,9],[8]] => 00001010
[6,5,7,8,9,1,2,3,4] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[7,6,1,2,3,5,4,8] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[2,8,7,5,1,6,3,4] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[8,7,6,4,2,1,5,3] => [[1,7],[2,8],[3],[4],[5],[6]] => 1111101
[3,8,7,5,2,6,4,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[3,8,7,5,1,2,6,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,8,3,7,1,4,6,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,8,7,4,2,6,5,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[5,8,3,2,4,7,6,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[5,3,8,2,4,6,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[4,5,8,3,2,6,1,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[5,8,2,1,4,6,3,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[4,1,5,8,3,6,2,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[4,5,8,3,6,1,2,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[3,2,7,1,8,5,4,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,7,8,5,2,3,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[6,2,7,8,1,5,3,4] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[2,7,1,3,8,5,4,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,6,7,8,4,1,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,6,7,8,4,3,1,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[7,1,2,3,4,5,8,6,9] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[4,1,2,5,3,6,7,8,9] => [[1,3,4,6,7,8,9],[2,5]] => 10010000
[7,1,2,6,3,8,4,5] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[8,1,2,6,5,3,7,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,4,1,8,2,5,3,6] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[7,4,8,3,1,2,6,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,4,5,3,1,6,7,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,2,3,1,6,7,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,2,1,7,4,3,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,2,6,8,4,1,3,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,2,5,1,6,8,3,4] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[6,2,1,7,4,8,3,5] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[1,7,4,3,2,5,6,8] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,7,4,3,6,2,5,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[3,7,5,8,2,4,6,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,2,1,6,3,4,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,1,3,4,6,2,8,7] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[3,8,4,5,7,2,6,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,8,4,7,5,6,2,1] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[4,2,8,6,3,7,5,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[4,1,7,6,3,8,5,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[7,4,1,8,5,3,6,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[3,5,6,8,4,7,1,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[5,4,1,8,6,7,2,3] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[6,2,8,4,5,3,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,5,2,1,8,7,3,6] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[4,7,3,8,2,6,5,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,7,3,1,8,6,2,5] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[6,2,1,3,7,4,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[6,3,7,1,2,5,8,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[5,1,4,7,8,2,6,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[7,2,5,8,1,3,6,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[8,3,6,7,2,4,5,1] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[3,8,7,5,2,1,6,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[3,8,5,6,2,7,4,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,6,5,8,4,2,7,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,8,3,2,5,7,4,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,1,5,6,8,7,3,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[8,4,2,3,6,7,5,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,1,2,4,5,7,8,3] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[4,5,1,3,7,6,8,2] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,5,4,8,6,2,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,6,2,4,5,8,7,1] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[8,1,3,7,4,5,6,2] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[8,1,5,3,6,4,7,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[2,6,4,8,3,1,5,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[2,6,4,1,5,8,7,3] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,6,4,5,2,8,1,7] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,1,5,4,7,3,6,2] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,6,5,4,1,8,2,3] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[8,1,5,4,7,6,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[2,5,1,4,6,7,3,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[3,6,4,1,5,7,8,2] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[7,6,5,2,8,4,1,3] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[3,1,6,5,2,8,7,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[1,7,2,4,3,5,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[3,8,1,7,4,2,6,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[8,1,7,4,3,5,6,2] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[6,8,2,4,5,3,7,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[4,8,5,3,6,1,7,2] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,8,3,1,4,7,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[8,6,3,2,7,4,1,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[2,7,3,1,8,4,5,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,2,8,3,5,6,4,7] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[3,5,7,4,8,1,6,2] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[2,8,1,3,5,4,6,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[1,5,2,8,6,4,3,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,4,8,6,3,1,2,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,6,8,4,1,2,5,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,7,8,5,2,1,3,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[6,1,5,2,8,7,3,4] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[8,1,3,5,7,4,2,6] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[3,1,8,5,4,7,2,6] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[3,1,6,4,8,5,2,7] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[5,1,3,4,2,6,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[3,2,6,4,1,5,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[5,4,2,1,8,3,6,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[4,2,5,1,8,7,3,6] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[6,8,2,7,1,4,3,5] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[1,8,4,7,3,2,5,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,6,3,1,5,7,2,4] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[5,8,3,1,4,7,6,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[1,2,5,4,7,8,3,6] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[1,8,3,2,6,4,7,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,7,1,2,5,3,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[6,8,4,1,3,7,2,5] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,2,6,1,7,8,5,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,6,4,1,8,3,5,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[5,4,1,6,7,3,2,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[7,4,1,6,5,8,2,3] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,5,4,1,6,7,3,2] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[5,2,1,6,4,7,8,3] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[1,6,2,3,5,7,8,4] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,3,4,8,5,2,6,7] => [[1,2,3,4,7,8],[5],[6]] => 0001100
[8,2,4,6,1,7,3,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[1,5,7,2,3,6,8,4] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[7,3,1,4,2,5,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,2,5,7,8,4,1,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,3,5,1,6,2,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[8,6,3,5,4,1,2,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,3,2,6,1,5,4,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,5,1,7,4,6,2,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[4,8,1,7,6,3,5,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[8,5,1,7,4,3,6,2] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[8,5,7,6,2,1,3,4] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[5,4,8,3,1,7,2,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[5,1,4,8,3,2,7,6] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,8,1,7,6,5,2,3] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[4,3,8,7,2,6,1,5] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[3,8,7,2,6,4,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[8,2,5,7,4,3,6,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[3,8,7,4,6,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[8,7,6,3,5,4,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => 1110110
[2,8,4,7,6,1,5,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,5,4,8,3,1,7,6] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[5,4,8,2,1,3,7,6] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[3,8,7,2,6,1,5,4] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[1,8,4,7,6,3,5,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,8,3,7,6,5,2,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,4,3,8,7,2,6,5] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[7,1,5,4,6,2,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,4,1,3,6,2,5,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,4,3,1,7,6,2,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[2,6,8,3,1,7,4,5] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,5,4,8,1,7,3,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[7,5,2,4,8,3,6,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[7,8,2,6,3,5,4,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,2,6,5,8,3,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[5,6,3,1,4,2,7,8] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[2,6,5,3,4,8,7,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[2,6,1,5,3,4,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,4,7,8,5,1,6,2] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,6,2,4,7,8,5,1] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[5,3,6,4,8,7,2,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,5,4,8,6,2,7,3] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[4,5,2,7,6,3,8,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[7,6,2,5,3,8,4,1] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[8,4,6,1,3,7,2,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,8,5,1,2,3,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,6,2,4,5,1,3,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[4,5,1,3,8,6,2,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[7,4,2,3,6,8,5,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[2,1,6,7,4,8,3,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[7,8,1,3,6,4,5,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[7,2,6,8,4,5,3,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,3,6,8,5,1,4,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,5,8,1,6,2,4,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[5,7,8,1,6,3,2,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[7,2,6,8,5,1,4,3] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[7,5,2,4,8,3,1,6] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[7,8,3,1,6,2,5,4] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,7,8,4,3,1,5,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[7,8,3,6,4,1,5,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[7,3,8,1,6,4,5,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[1,7,5,8,2,4,6,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[7,5,2,8,1,4,6,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[3,7,8,2,6,5,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,7,8,2,1,6,4,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[7,8,1,6,3,5,4,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,7,8,2,5,4,3,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[6,7,8,3,1,5,4,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[7,8,1,6,2,5,4,3] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[5,6,1,4,3,8,2,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[5,1,6,8,3,4,7,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[7,1,6,8,5,4,3,2] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[5,6,8,1,2,3,7,4] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,8,1,2,7,6,5,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[4,6,1,2,8,5,7,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[6,4,7,3,5,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,7,8,4,2,1,3,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[3,1,6,2,5,7,8,4] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,6,4,5,2,7,3,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[6,2,1,4,5,3,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[1,2,3,4,5,8,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[1,2,3,4,7,9,5,8,6] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[1,2,4,6,8,3,7,5] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,5,9,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6],[9]] => 00010001
[1,3,5,8,2,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,9,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4],[9]] => 01000001
[6,1,3,7,2,8,5,4] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[6,4,5,8,3,7,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,1,4,3,6,7,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,6,8,4,3,1,7,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[8,1,5,2,6,4,3,7] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[1,6,7,4,2,8,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[1,7,8,4,3,6,2,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[1,4,7,2,3,6,8,5] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,1,2,6,7,8,5,4] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[3,8,1,6,4,2,7,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[1,6,3,4,7,8,2,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[3,1,5,7,6,2,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,3,1,4,2,7,8,5] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[2,4,3,7,6,1,8,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[3,1,7,6,5,2,8,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[1,4,7,6,8,3,2,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,2,1,5,6,3,8,4] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[4,3,1,8,6,2,7,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[3,1,5,2,8,7,6,4] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[1,2,8,4,3,7,6,5] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[2,6,1,8,7,4,3,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[7,5,1,8,3,2,6,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[4,7,6,3,1,8,2,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[5,3,1,8,6,2,4,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[5,1,8,6,3,2,4,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[1,5,4,2,8,6,3,7] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,4,2,8,5,3,7,6] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[8,3,1,6,4,2,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[1,7,4,8,3,5,2,6] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[7,3,2,4,8,5,1,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,7,8,1,4,2,6,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[2,6,3,8,1,7,5,4] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,5,1,8,6,3,7,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,8,6,4,1,7,3,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[1,8,4,2,7,5,3,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[6,5,1,7,2,8,4,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[2,8,1,7,5,3,6,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[1,2,8,7,6,4,3,5] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[4,1,7,8,6,3,5,2] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[1,6,5,7,8,4,2,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,1,8,7,6,3,5,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[4,8,2,6,3,5,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[4,3,5,7,1,6,2,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,1,8,5,3,6,2,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,4,2,5,3,1,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,1,5,8,2,7,4,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[6,4,1,5,3,2,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,2,1,5,4,3,7,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[3,1,8,5,4,6,2,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,1,8,4,5,3,2,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,5,2,7,1,6,3,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[4,3,5,7,1,6,8,2] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,1,8,5,3,6,7,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,3,8,4,5,1,7,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[3,1,6,8,5,7,4,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[2,6,1,8,5,7,4,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[6,3,8,4,5,2,1,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[6,5,8,7,2,3,4,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[6,3,8,4,5,2,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[2,1,6,8,5,3,7,4] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[3,2,6,8,5,4,7,1] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[4,1,8,5,2,6,3,7] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,1,6,8,5,2,4,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[6,5,8,7,4,1,2,3] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[6,5,8,7,4,2,1,3] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[6,5,8,7,2,4,1,3] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[6,2,8,4,5,7,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,1,8,4,5,7,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[1,9,2,10,3,4,5,6,7,8] => [[1,2,4,6,7,8,9,10],[3,5]] => 010100000
[4,2,7,3,5,8,6,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[3,6,2,4,8,5,7,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,5,1,8,4,7,6,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[3,6,1,8,5,4,7,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[2,4,8,3,7,6,5,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,6,8,2,5,7,4,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,6,8,5,4,3,7,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,6,8,2,5,4,7,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,6,8,3,2,5,7,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[4,6,2,8,3,5,7,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,6,1,8,5,7,4,2] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,2,6,8,4,1,7,3] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[4,6,3,8,7,2,5,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,5,8,2,7,4,6,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[2,6,8,5,7,4,3,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,4,8,7,6,3,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[7,5,1,6,3,2,8,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[2,7,6,3,4,1,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,7,6,3,1,2,8,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,8,2,1,7,5,6,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,3,8,5,7,2,4,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[1,5,4,8,6,2,3,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[8,2,1,7,5,3,6,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,2,1,6,7,3,5,4] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[6,2,8,1,7,5,3,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[3,5,1,8,7,6,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[1,3,4,2,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[3,4,5,1,6,2,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[3,1,2,4,6,5,8,7,9] => [[1,3,4,5,7,9],[2,6,8]] => 10001010
[1,3,4,2,6,5,8,7,10,9] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[4,7,8,3,5,6,1,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[2,1,3,4,5,6,9,7,8] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[1,2,3,4,5,7,8,6,9] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[2,1,3,4,5,6,7,10,8,9] => [[1,3,4,5,6,7,8,10],[2,9]] => 100000010
[3,2,5,6,8,4,7,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[8,4,5,2,6,3,7,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[2,5,6,4,8,3,7,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,2,5,7,3,8,1,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,7,3,1,6,8,2,5] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[4,2,7,6,8,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[1,7,4,6,8,3,2,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,7,2,5,6,3,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[5,4,1,3,7,8,2,6] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,1,5,8,3,7,2,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[7,2,1,6,8,3,5,4] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,6,4,1,8,3,2,7] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[2,3,7,8,5,1,6,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,2,6,7,4,3,5,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[5,8,6,3,4,1,2,7] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[3,10,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4],[10]] => 010000001
[6,2,3,1,8,5,4,7] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[5,1,2,6,4,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[8,6,2,3,7,5,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,7,9,1,2,3,4,5,6] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[4,5,2,8,6,1,3,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[3,4,8,2,5,6,1,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[6,8,2,7,5,3,1,4] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[6,3,2,5,8,4,1,7] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,6,7,2,8,4,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,8,3,6,4,1,7,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,3,8,5,2,7,1,6] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[2,8,4,5,1,6,3,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,2,5,8,4,7,1,6] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[2,5,8,1,3,4,7,6] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,5,1,8,7,4,2,6] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[4,6,1,3,8,2,7,5] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[8,6,1,2,3,5,7,4] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[5,1,7,8,3,2,4,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,1,7,6,2,8,5,4] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[5,3,6,7,4,2,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[5,4,2,8,6,7,3,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,1,4,2,8,7,3,5] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[3,7,2,6,8,4,5,1] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[4,6,5,2,7,8,3,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,4,6,2,7,8,3,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[5,1,8,6,4,2,7,3] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[6,2,1,8,5,7,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,4,6,2,3,1,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[6,5,7,8,1,3,4,2] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[2,1,7,6,8,4,5,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[6,4,7,2,8,3,1,5] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[6,3,2,7,8,4,5,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[4,7,3,1,5,2,8,6] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,7,6,3,1,5,8,2] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[2,7,3,1,8,5,4,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,8,3,1,7,4,5,6] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[7,6,8,9,1,2,3,4,5] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[5,4,6,7,8,9,1,2,3] => [[1,3,4,5,6],[2,8,9],[7]] => 10000100
[1,8,2,7,3,5,6,4] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[1,7,4,8,6,5,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,6,3,5,7,4,8,2] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[1,5,4,7,2,8,3,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[3,8,5,2,6,1,7,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,7,4,8,5,2,6,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[8,1,2,6,5,3,4,7] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[3,7,4,2,5,6,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[6,8,7,1,3,4,2,5] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[3,4,2,8,6,7,5,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,7,8,6,1,4,2,5] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[3,6,1,5,2,7,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[8,1,2,6,3,5,7,4] => [[1,3,4,6,7],[2],[5],[8]] => 1001001
[6,2,8,4,7,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[3,7,8,4,2,5,6,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,4,2,8,5,1,6,7] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,4,3,2,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 01100000
[6,8,2,7,5,4,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[1,8,4,3,7,6,2,5] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,3,8,7,1,2,6,5] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[1,8,4,5,7,6,2,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,3,8,5,7,1,6,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,3,4,8,7,2,1,5] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[5,3,8,4,7,1,6,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[5,2,8,7,1,4,6,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[3,2,8,7,1,6,4,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,7,8,3,1,6,4,5] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,7,8,5,1,4,6,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[3,5,8,7,4,1,6,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[7,4,6,8,3,5,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[2,7,8,1,3,6,4,5] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[2,7,8,1,5,4,6,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[2,7,8,1,4,5,6,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[3,6,7,8,2,4,1,5] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[4,5,7,8,6,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[5,4,6,8,7,3,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,5,8,6,7,1,3,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,7,6,8,2,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[3,7,6,8,2,4,1,5] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[5,4,7,8,6,3,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[4,5,7,8,2,6,1,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[4,5,6,8,7,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[6,1,5,3,8,4,7,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,8,6,2,5,4,7,3] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[3,8,4,1,7,5,2,6] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[6,2,7,4,8,3,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[2,8,5,1,4,3,7,6] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[6,8,2,7,5,1,4,3] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[8,3,4,5,6,1,7,2] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[5,3,6,4,7,2,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,2,6,5,7,3,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,4,6,2,7,3,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[3,2,6,5,8,4,1,7] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,2,6,5,8,7,1,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,2,6,5,8,7,1,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,2,6,4,8,7,1,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,4,7,6,8,2,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,4,7,5,8,3,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,2,7,5,8,6,1,3] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[3,2,7,5,8,4,1,6] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[4,3,7,2,8,5,1,6] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,3,6,2,8,5,1,7] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[4,3,7,6,8,5,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,3,7,6,8,2,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,3,7,2,8,6,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[3,2,6,4,8,7,1,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[4,2,7,3,8,6,1,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[5,2,7,6,8,3,1,4] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,2,7,6,8,4,1,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[3,2,7,6,8,5,1,4] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[6,2,7,5,8,4,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,8,1,7,3,2,5,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,7,4,8,2,1,5,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,7,8,2,5,4,6,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,7,5,8,3,2,6,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[6,7,1,3,2,5,8,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[8,7,6,4,1,5,3,2] => [[1,6],[2,7],[3],[4],[5],[8]] => 1111011
[3,8,5,2,6,4,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,2,5,3,4,8,1,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,2,5,3,7,8,6,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,3,6,2,4,1,8,7] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[7,8,6,2,3,5,4,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[5,8,2,6,3,7,4,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[4,8,2,3,7,5,6,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[7,5,6,2,3,8,4,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[2,7,5,6,4,3,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,8,4,3,7,5,6,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,8,5,7,6,4,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[7,8,6,3,5,4,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[2,7,6,3,8,5,4,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[7,4,2,5,6,3,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,2,7,5,3,8,4,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,4,8,3,7,5,6,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,8,3,7,5,6,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[6,2,5,8,3,7,4,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[4,7,3,8,2,5,6,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[8,2,5,6,3,7,4,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[4,5,3,7,1,2,6,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[8,5,6,4,1,3,2,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[6,7,2,8,4,3,1,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[6,7,3,2,8,4,1,5] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[4,7,8,3,1,5,2,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,5,8,1,3,2,6,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[4,7,8,1,6,3,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,1,3,8,6,5,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[5,7,2,8,3,4,6,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,7,2,8,5,6,4,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[3,1,5,8,6,4,7,2] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,3,8,6,4,5,7,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,5,6,1,8,7,3,4] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,6,2,8,4,7,5,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[8,5,6,3,1,4,2,7] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[5,7,8,3,4,6,2,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,5,1,8,6,4,2,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,5,3,8,6,4,2,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[5,1,3,8,6,4,2,7] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[1,5,8,3,6,4,2,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[7,5,8,3,6,4,2,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[1,5,8,6,3,4,2,7] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[3,7,5,8,2,6,4,1] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,7,8,1,4,6,2,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[1,3,7,8,4,2,6,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[6,1,2,5,3,4,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[1,4,6,5,7,2,3,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[8,1,6,7,3,5,4,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[4,2,5,1,3,7,6,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[1,3,2,6,8,4,7,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,1,7,5,4,2,6,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[1,2,6,4,7,3,5,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,6,4,3,7,2,5,8] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,7,8,3,2,6,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[2,3,4,5,6,9,8,7,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[2,3,4,5,8,7,9,6,1] => [[1,2,3,4,5,7],[6],[8],[9]] => 00001011
[2,3,4,5,6,7,10,9,8,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[2,3,4,5,8,9,7,6,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[2,3,4,5,6,9,8,10,7,1] => [[1,2,3,4,5,6,8],[7],[9],[10]] => 000001011
[8,4,5,1,3,7,6,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[8,6,4,3,7,1,5,2] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,3,1,8,6,5,2,4] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[2,7,3,1,4,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[3,1,6,5,7,8,4,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,3,1,5,8,7,6,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,7,1,3,2,5,6,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[1,7,2,5,6,8,4,3] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[4,7,6,8,3,1,5,2] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[3,5,4,7,1,8,6,2] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[7,1,5,4,2,3,6,8] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[7,1,3,6,4,5,2,8] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[6,1,3,8,4,5,2,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[2,1,8,7,3,6,5,4] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[5,8,6,3,1,2,7,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,8,2,7,1,3,6,4] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[2,6,5,4,1,3,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,1,5,7,6,3,2,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[4,5,1,7,6,3,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,4,2,1,8,7,3,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[6,2,1,5,4,3,8,7] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[1,4,2,6,7,8,5,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,4,2,5,6,8,7,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[2,5,3,6,7,8,4,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,8,6,2,4,3,5,7] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[3,2,4,5,7,8,1,6] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[2,3,4,7,5,8,6,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[6,5,2,8,7,4,3,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,8,5,4,2,1,6,3] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[7,5,2,8,6,4,3,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[7,8,3,2,6,5,4,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[8,2,6,3,7,5,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,6,7,2,5,3,1,4] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[1,6,2,7,8,4,5,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,6,2,7,5,4,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[1,6,8,2,7,5,3,4] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[7,6,3,2,8,1,5,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[5,1,7,4,3,8,6,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,6,3,7,2,4,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[1,7,8,6,4,2,3,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,2,8,6,4,1,3,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[1,5,3,7,4,2,6,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,7,6,4,3,2,8,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,7,6,3,4,2,5,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[1,2,7,4,3,8,6,5] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,5,4,2,3,8,7,6] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[1,5,3,2,4,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => 0110000
[1,5,4,2,3,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,2,7,6,3,5,8,4] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[8,1,3,2,6,5,7,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,2,7,5,6,1,8,4] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,4,5,1,6,3,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,5,6,1,4,3,8,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,4,3,5,2,7,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[10,5,9,4,8,3,7,2,6,1] => [[1,3],[2,5],[4,7],[6,9],[8],[10]] => 101010101
[3,4,1,5,2,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[1,4,2,5,3,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[8,3,6,5,4,1,2,7] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[1,7,5,8,4,6,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[6,5,7,1,2,8,3,4] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[7,1,4,2,3,8,6,5] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[8,1,2,5,3,7,6,4] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,6,5,2,4,1,7,3] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[3,6,5,2,4,1,7,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[6,8,5,2,4,3,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[3,4,2,8,6,7,1,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,6,7,2,5,1,8,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[3,6,2,5,1,7,8,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[3,4,2,7,8,1,5,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[7,1,4,2,5,8,6,3] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[7,8,5,1,2,4,3,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,1,4,3,6,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[7,2,3,8,6,4,1,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,2,3,8,7,4,1,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,7,6,3,1,2,4,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,2,6,8,1,3,5,7,9] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000
[4,6,2,7,8,1,3,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,2,3,7,1,4,5,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[4,2,5,7,9,1,3,6,8] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000
[2,3,5,7,9,1,4,6,8] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[4,2,6,8,10,1,3,5,7,9] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[6,4,2,8,1,3,5,7,9] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000
[4,6,7,8,2,1,3,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[4,8,2,5,9,1,3,6,7] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000
[4,2,5,7,9,1,3,6,8,10] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[1,4,5,7,9,2,3,6,8] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[2,3,5,7,9,1,4,6,8,10] => [[1,2,3,4,5,10],[6,7,8,9]] => 000010000
[8,6,3,2,1,7,5,4] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[8,6,4,9,7,5,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111
[8,6,4,2,9,7,5,3,1] => [[1,5],[2,6],[3,7],[4,8],[9]] => 11101111
[6,2,7,3,8,4,9,5,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,5,6,7,8,2,9,3,1] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[4,5,6,7,1,8,2,9,3] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[9,7,10,8,6,5,4,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => 101111111
[9,7,5,10,8,6,4,3,2,1] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[8,5,2,9,6,3,10,7,4,1] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 110110111
[7,3,8,4,9,5,1,10,6,2] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[6,1,3,4,2,5,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,1,3,6,2,4,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[1,5,7,6,8,2,4,3] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,7,1,3,8,4,2,6] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,6,1,4,3,7,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[1,6,2,4,3,5,8,7] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[5,3,7,6,1,8,4,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[1,5,6,3,7,8,4,2] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[1,5,7,6,3,8,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[7,3,5,6,1,8,4,2] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,3,6,1,5,8,4,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[1,6,3,7,8,5,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,7,8,6,3,5,4,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,7,5,6,1,8,4,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[5,6,2,8,4,7,3,1] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[7,3,5,4,1,2,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,8,5,1,3,2,4,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[7,5,1,3,8,6,2,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[7,1,3,8,2,5,4,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[3,1,5,4,7,2,6,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[5,7,6,1,3,8,2,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[5,7,6,3,8,1,4,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[5,1,3,7,6,2,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[1,6,3,7,2,4,5,8] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[5,3,2,4,8,1,7,6] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[6,8,5,3,2,7,1,4] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[8,3,7,2,6,5,1,4] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[4,6,2,7,1,3,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,5,1,4,7,2,8,6] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[5,1,4,8,7,3,2,6] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,1,3,4,2,7,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[6,5,2,3,7,8,1,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,5,3,8,4,2,7,6] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[5,4,2,1,8,3,7,6] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[3,1,7,4,2,6,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[7,4,8,2,3,5,1,6] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,4,1,3,2,6,7,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,1,7,3,2,5,6,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,6,5,2,7,3,1,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[3,1,6,8,4,2,7,5] => [[1,3,4],[2,5,7],[6,8]] => 1001101
[2,3,4,5,6,7,10,8,9,1] => [[1,2,3,4,5,6,7,9],[8],[10]] => 000000101
[2,9,4,3,5,6,7,8,1] => [[1,2,5,6,7,8],[3],[4],[9]] => 01100001
[2,3,4,5,9,7,8,6,1] => [[1,2,3,4,5,7],[6],[8],[9]] => 00001011
[5,6,2,3,7,4,1,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[6,2,4,7,3,5,1,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[1,4,8,5,3,6,7,2] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[2,5,6,3,1,8,4,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[4,5,1,2,7,8,6,3] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,8,5,1,2,6,7,3] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,6,7,5,1,2,8,3] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[7,2,8,1,4,5,3,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,1,4,7,3,8,2,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[7,1,6,3,4,8,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,8,4,6,3,1,5,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,2,6,3,5,1,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,7,4,1,5,8,2,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,8,4,1,7,2,5,6] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[6,7,5,1,3,8,2,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[8,5,1,3,6,7,2,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,8,6,2,4,1,3,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,2,4,1,3,6,7,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,1,3,6,2,5,7,4] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,5,6,3,8,4,7,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,6,1,3,7,2,8,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[5,6,1,8,2,3,7,4] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[5,6,1,2,8,4,7,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,7,8,1,6,4,2,5] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[1,7,8,6,3,4,2,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,7,3,8,6,4,2,5] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,7,1,8,6,4,2,3] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[7,8,1,5,6,4,2,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[7,1,8,5,6,4,2,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,1,5,8,6,4,2,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[8,1,3,5,6,4,2,7] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[1,3,8,5,6,4,2,7] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,3,5,8,6,4,2,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[1,5,7,8,6,4,2,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,1,4,3,6,5,9,8,10,7] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[2,1,4,3,7,6,9,8,10,5] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[2,1,5,4,7,6,9,8,10,3] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[3,2,4,1,6,5,8,7,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[3,2,5,4,7,6,9,8,10,1] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[1,8,2,6,5,3,4,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[8,6,1,5,2,3,4,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[8,5,1,6,2,3,4,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[7,6,1,2,3,8,4,5] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[2,7,8,4,1,3,5,6] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[6,8,1,2,3,7,4,5] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[8,1,3,5,6,7,2,4] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[8,1,2,5,3,4,7,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[5,2,7,3,4,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[2,7,5,4,1,3,6,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,7,4,6,5,1,8,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,8,7,5,2,1,4,3] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[2,8,6,3,5,1,4,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[1,2,8,6,4,5,3,7] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[1,5,8,7,6,3,4,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[1,6,4,8,5,7,3,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,6,8,5,2,7,3,4] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[2,1,8,3,4,5,6,7,9] => [[1,3,5,6,7,8,9],[2,4]] => 10100000
[3,1,6,4,2,5,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[5,4,2,3,6,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[8,2,6,3,5,7,1,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[3,1,7,8,6,2,5,4] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[2,8,1,6,5,3,7,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[2,1,5,7,6,3,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,3,5,1,7,8,6,2] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[1,8,5,2,3,4,7,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[1,5,8,2,3,4,7,6] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[1,2,7,8,4,5,6,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,2,3,4,5,6,9,7,10,8] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[2,3,4,5,6,9,10,1,7,8] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[4,3,8,7,6,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,4,8,2,7,6,3,1] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[2,3,6,1,7,5,8,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[4,6,5,2,1,7,8,3] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,6,1,7,5,8,3,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[4,1,5,7,6,8,3,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,5,6,2,1,4,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[4,3,6,5,1,7,8,2] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,6,5,3,1,7,8,2] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,2,3,4,5,7,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => 000001000
[1,2,3,5,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => 000100000
[1,2,3,5,4,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[5,8,1,4,2,3,6,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,5,8,2,3,1,6,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,5,4,8,1,7,2,6] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[5,3,6,8,1,4,7,2] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[3,5,1,8,6,4,7,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,7,2,8,3,1,6,5] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[1,2,5,6,8,3,7,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,3,8,4,6,2,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,4,8,1,5,2,6,3] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[8,3,2,1,6,5,7,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[4,1,5,6,8,7,2,3] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,2,5,6,8,4,7,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,5,6,8,4,7,2,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[5,6,8,1,2,4,7,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,8,1,4,5,7,2,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[4,3,5,1,8,6,7,2] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[1,3,5,6,8,4,7,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[5,6,8,2,3,4,7,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,5,1,2,4,8,7,3] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,8,7,2,1,3,6,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,1,7,2,8,6,3,4] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[6,1,5,3,4,8,7,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[5,8,6,3,2,1,4,7] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[8,7,1,6,3,5,4,2] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[3,2,1,7,8,6,4,5] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[8,6,7,1,2,5,3,4] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[1,5,6,4,2,8,7,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[7,5,1,4,8,2,3,6] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[3,2,8,1,7,5,6,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[8,4,3,1,7,5,6,2] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[6,1,7,8,4,2,3,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,4,3,1,8,5,2,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,8,1,6,3,4,5,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[6,8,1,7,3,4,2,5] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,5,6,7,8,9,2,3,4] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[1,8,9,10,2,3,4,5,6,7] => [[1,2,3,4,8,9,10],[5,6,7]] => 000100000
[1,5,2,6,7,8,9,3,4] => [[1,2,4,5,6,7],[3,8,9]] => 01000010
[1,5,6,7,8,9,10,2,3,4] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[3,4,2,1,5,6,7,8,9] => [[1,2,5,6,7,8,9],[3],[4]] => 01100000
[4,3,1,2,5,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[3,4,2,1,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3],[4]] => 011000000
[5,3,1,2,4,6,7,8,9] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000
[4,3,5,1,2,6,7,8,9] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[4,3,1,2,5,6,7,8,9,10] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000
[4,6,5,3,8,2,7,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[4,5,6,3,8,1,7,2] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[7,8,3,5,2,1,6,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,3,7,5,2,4,1,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[6,2,4,5,7,3,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[7,8,1,5,6,4,3,2] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[6,3,7,5,1,4,2,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[1,3,8,2,4,6,7,5] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[6,1,7,3,4,2,5,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,1,7,2,5,8,6,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,8,7,6,3,5,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[2,8,7,1,5,6,4,3] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,5,6,2,8,1,7,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,1,5,7,3,8,2,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[7,1,6,8,2,5,3,4] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[1,6,5,7,4,2,3,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[7,2,8,4,5,6,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[5,4,3,1,2,6,7,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[6,5,4,3,1,2,7,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[8,5,4,3,9,1,2,6,7] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[6,5,4,3,1,2,7,8,9,10] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000
[7,6,5,4,3,1,2,8,9,10] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[9,6,5,4,3,10,1,2,7,8] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000
[6,8,7,3,2,4,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,8,6,1,4,5,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[7,5,8,6,4,1,3,2] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[2,7,6,3,8,5,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[2,3,1,8,4,6,5,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,3,1,7,6,8,4,5] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[2,3,1,8,4,6,7,5] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[4,2,3,5,1,8,6,7] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[2,3,4,5,9,7,1,8,6] => [[1,2,3,4,5,8],[6,9],[7]] => 00001101
[2,3,4,5,6,7,10,9,1,8] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[2,3,4,5,6,10,8,9,1,7] => [[1,2,3,4,5,6,8],[7,10],[9]] => 000001010
[2,3,4,5,6,10,8,1,9,7] => [[1,2,3,4,5,6,9],[7,10],[8]] => 000001101
[2,3,4,5,6,10,1,7,8,9] => [[1,2,3,4,5,6,9,10],[7,8]] => 000001000
[2,3,4,5,10,7,8,1,6,9] => [[1,2,3,4,5,7,10],[6,9],[8]] => 000010100
[2,3,4,5,10,1,6,7,8,9] => [[1,2,3,4,5,8,9,10],[6,7]] => 000010000
[2,3,4,10,1,5,6,7,8,9] => [[1,2,3,4,7,8,9,10],[5,6]] => 000100000
[2,10,4,1,6,3,8,5,9,7] => [[1,2,5,7,9],[3,6,8,10],[4]] => 011010101
[5,8,7,2,6,4,1,3] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[6,8,5,1,7,4,3,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[6,8,5,2,7,4,1,3] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[7,3,8,6,5,2,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[7,5,8,1,6,4,3,2] => [[1,3],[2,5],[4,6],[7],[8]] => 1010111
[7,5,8,2,6,4,1,3] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,3,2,8,1,7,5,4] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[2,1,3,4,5,6,8,7,9] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[2,3,4,5,6,8,7,9,1] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[2,6,8,7,1,3,5,4] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[5,3,8,7,6,2,1,4] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[3,7,6,1,4,5,2,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,1,6,2,7,5,3,8] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[7,6,2,5,3,1,4,8] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[4,3,1,7,6,2,5,8] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[4,5,3,1,2,8,6,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[2,4,5,3,1,8,6,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[5,7,6,2,3,1,4,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,1,3,7,5,2,6,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,1,6,3,2,7,5,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[7,5,4,1,3,2,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => 1110100
[2,4,8,5,6,3,1,7] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[2,5,7,4,1,3,6,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[5,7,4,1,3,2,6,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[2,6,8,4,5,3,1,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[5,2,3,7,4,1,6,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,5,1,6,3,2,7,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[5,1,6,3,2,4,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,2,5,1,6,3,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[5,1,6,2,4,3,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,3,4,8,7,6,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[8,3,1,6,7,5,4,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,4,6,5,7,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[1,8,2,6,7,4,5,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,5,7,2,4,3,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,5,3,6,4,7,2,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,2,5,3,6,7,4,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[1,2,8,3,4,7,6,5] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[6,8,5,2,7,1,3,4] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[7,6,4,5,2,1,8,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,2,4,7,6,3,1,5] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[7,3,8,5,4,2,1,6] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[6,3,4,7,2,8,5,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[8,1,7,3,6,4,2,5] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[7,1,8,5,3,4,2,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,8,4,3,1,5,2,7] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[1,4,5,8,3,2,6,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,5,2,4,7,8,6,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[5,2,7,4,3,8,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,7,3,4,8,5,6,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[2,7,6,8,3,5,4,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,7,4,5,3,8,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[6,2,3,7,4,5,8,1] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,6,3,2,7,5,8,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[7,3,5,2,6,8,1,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,4,2,7,1,5,8,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[2,5,3,6,4,7,8,1] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[4,2,5,3,6,7,8,1] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[1,6,5,2,4,7,3,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[1,8,7,2,4,6,3,5] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,8,7,2,5,4,3,6] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,5,4,2,7,3,6,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[1,5,4,2,8,7,3,6] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[1,6,8,3,5,2,4,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[1,7,6,2,3,5,8,4] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,2,8,3,6,5,4,7] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[1,3,8,6,5,2,4,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,4,7,3,2,8,6,5] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,8,6,5,2,4,7,3] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[1,6,8,4,3,2,5,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,7,5,3,2,6,4,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,2,6,5,3,8,4,7] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[1,7,3,2,8,4,6,5] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,6,5,2,8,4,7,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,8,3,7,2,4,6,5] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,4,2,8,7,6,1,3] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[8,6,3,2,5,7,4,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[7,3,2,1,6,5,8,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[7,3,2,6,1,5,8,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[6,8,5,2,7,1,4,3] => [[1,2],[3,5],[4,7],[6,8]] => 0110101
[6,8,2,5,1,7,4,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[6,8,5,7,2,1,4,3] => [[1,2],[3,4],[5,7],[6,8]] => 0101101
[6,5,8,2,7,4,1,3] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[6,2,1,7,5,8,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[1,6,4,8,5,3,7,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,2,6,7,8,1,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[4,6,5,1,3,7,8,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[5,1,7,2,6,4,8,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,1,7,6,5,8,2,3] => [[1,3,6],[2,4,8],[5],[7]] => 1011010
[4,2,3,6,7,8,1,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[4,7,2,1,6,5,8,3] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[2,4,3,6,7,8,1,5] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[6,8,5,2,7,3,1,4] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,5,1,3,7,8,2,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,2,1,4,3,5,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,1,2,4,3,7,8,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[8,1,5,4,2,3,6,7] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[7,1,2,4,6,3,8,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,1,2,6,5,3,8,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,5,6,1,2,4,8,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,1,4,5,2,3,6,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,1,4,8,7,2,3,5] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[6,1,8,5,7,2,3,4] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[1,6,7,5,8,3,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[6,1,7,5,8,2,3,4] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[6,1,4,7,8,2,3,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,1,2,3,7,5,4,6] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[5,8,6,1,2,4,7,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[1,6,8,7,5,3,4,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,1,8,7,5,2,3,4] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[8,3,1,2,4,6,5,7] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[8,3,1,2,4,5,7,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,3,1,2,4,7,5,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[6,7,1,4,2,3,5,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,1,7,4,8,2,3,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[6,7,8,5,1,2,4,3] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[8,6,5,4,3,2,7,9,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001
[7,6,5,4,3,8,9,1,2] => [[1,6,7],[2,9],[3],[4],[5],[8]] => 11110010
[9,6,5,4,3,2,7,1,8] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010
[8,7,6,5,4,3,2,9,1,10] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => 111111010
[3,1,5,6,7,8,9,2,4] => [[1,3,4,5,6,7],[2,8,9]] => 10000010
[2,1,3,5,6,7,8,9,4] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[4,3,8,5,6,2,7,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,3,8,6,7,2,5,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,6,8,1,5,3,4,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,4,6,1,5,3,8,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,3,8,1,7,2,5,4] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,1,5,4,8,2,7,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[6,2,5,4,7,1,8,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[8,3,6,7,5,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[2,7,1,8,5,6,4,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[4,6,8,2,3,5,1,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[6,8,2,1,3,5,4,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,5,1,6,4,8,2,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,5,8,6,2,1,4,7] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,4,8,5,6,1,3,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[4,8,2,5,6,1,3,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[5,3,8,4,2,7,6,1] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[2,8,5,3,1,4,7,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,7,8,4,6,3,2,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[8,7,2,4,6,3,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,7,3,2,1,6,4,5] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[7,8,3,4,6,5,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[8,7,3,6,5,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[3,1,2,8,6,5,7,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[3,8,2,7,5,4,6,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[8,7,1,4,5,3,6,2] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[2,8,7,4,6,3,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,8,7,4,6,3,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[8,3,4,1,2,5,7,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,4,1,3,2,5,7,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[7,3,8,6,2,1,4,5] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[7,2,8,4,6,5,1,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[5,8,6,4,7,2,3,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[4,7,2,6,5,8,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[3,6,8,5,7,4,2,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[6,7,5,2,4,8,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,1,2,7,5,6,3,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,2,7,3,4,6,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,7,5,4,8,1,3,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[8,3,5,6,4,7,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[8,5,6,2,4,3,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,5,8,1,3,4,2,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[6,8,4,5,1,3,2,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[6,4,8,7,5,3,2,1] => [[1,3],[2,4],[5],[6],[7],[8]] => 1011111
[6,7,1,4,3,2,8,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[7,2,5,1,4,8,3,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[5,8,1,3,4,2,7,6] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[1,5,6,3,2,8,7,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[1,3,7,6,8,4,2,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[1,6,7,3,2,8,5,4] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[3,2,7,6,8,4,5,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[1,3,8,5,2,7,6,4] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,4,1,5,2,8,7,3] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[7,6,5,3,1,8,2,4] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[2,5,1,4,7,3,6,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[3,1,6,5,7,2,4,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[2,6,1,5,7,4,8,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,5,7,1,6,3,8,4] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[2,6,1,5,7,4,3,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,1,6,5,2,4,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[3,6,5,1,4,2,7,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,6,5,1,7,2,4,8] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[3,6,5,2,1,4,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,4,3,6,1,7,2,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[4,5,2,7,6,1,3,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[4,6,5,3,1,2,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[5,4,1,6,3,7,2,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[5,4,2,6,3,7,8,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[3,6,5,7,1,4,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,6,5,1,4,7,2,8] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,3,6,5,7,1,2,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[4,2,6,5,1,3,7,8] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,1,6,5,3,7,8,2] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[4,2,5,7,6,1,3,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[3,4,7,6,1,2,5,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,2,5,7,6,3,8,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[4,1,6,5,2,7,3,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[3,6,5,7,2,1,4,8] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[3,5,7,6,2,4,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[5,4,2,6,3,7,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[4,6,5,2,7,3,1,8] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[4,6,5,2,1,7,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,5,8,2,1,4,6,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[3,5,8,2,4,6,7,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[5,3,8,2,1,4,6,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[5,3,1,8,2,4,6,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[5,1,3,8,2,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[1,5,8,4,2,3,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[5,8,2,1,4,3,6,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[5,8,2,4,1,6,7,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,8,2,4,6,3,1,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[5,8,2,4,3,6,1,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[5,8,1,4,6,2,3,7] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,5,8,4,6,7,2,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[5,1,8,4,6,7,2,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[5,8,2,4,6,3,7,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,8,4,6,7,2,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[3,8,4,6,7,2,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[8,4,3,6,7,2,5,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,4,3,6,7,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[8,6,2,4,5,3,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[1,8,6,4,5,7,2,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[8,6,2,4,5,3,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[1,8,6,4,2,3,5,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[3,8,1,6,2,4,5,7] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[3,8,6,2,1,4,5,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,8,6,2,4,1,5,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,8,6,2,4,5,7,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,3,6,2,4,5,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,1,3,6,2,4,5,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[8,3,6,7,2,1,4,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[3,8,6,7,2,1,4,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[8,2,6,4,5,1,7,3] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[1,8,4,6,7,5,2,3] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,4,6,2,3,7,5,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[8,4,7,2,1,3,6,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[2,7,1,6,3,5,8,4] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[8,4,2,1,5,3,7,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[8,2,1,4,7,3,6,5] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[1,6,2,5,8,4,7,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,1,5,8,7,3,6,4] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[3,2,1,6,7,4,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[4,3,1,7,8,5,2,6] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,6,8,2,4,3,7,1] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[2,8,5,3,6,4,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,2,8,6,4,7,3,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,3,2,7,8,6,4,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,2,7,8,3,5,6,1] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,8,3,7,1,4,6,5] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,8,7,1,5,3,6,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,3,5,6,4,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[3,8,4,2,7,6,5,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,8,3,2,7,5,6,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[3,2,4,8,7,5,6,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[2,6,8,1,5,3,4,7] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[3,2,5,6,8,1,4,7] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[3,8,1,6,4,5,2,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,1,3,6,5,4,2,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[7,4,3,6,2,1,8,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[1,2,4,8,6,3,7,5] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,2,1,5,3,4,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,7,2,3,1,4,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,1,5,2,4,6,8,3] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[8,4,2,7,3,5,6,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[1,8,6,4,7,5,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[7,4,1,5,8,6,3,2] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[4,5,8,7,3,1,2,6] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[1,3,8,7,6,4,2,5] => [[1,2,3,8],[4],[5],[6],[7]] => 0011110
[2,8,5,1,7,4,6,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[1,8,6,4,7,5,2,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[2,7,4,6,3,8,5,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,2,8,6,4,7,5,3] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,4,5,6,7,9,1,2,8] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[3,4,5,7,8,9,1,2,6] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[3,5,6,7,8,9,1,2,4] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[3,4,5,6,8,9,10,1,2,7] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[3,5,6,7,8,9,10,1,2,4] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[3,4,5,6,7,8,1,2,9,10] => [[1,2,3,4,5,6,9,10],[7,8]] => 000001000
[3,4,5,6,9,1,2,7,8] => [[1,2,3,4,5,9],[6,7,8]] => 00001000
[3,4,5,6,1,2,7,8,9] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[5,1,6,7,8,9,2,3,4] => [[1,3,4,5,6],[2,7,8,9]] => 10000100
[4,1,8,6,3,7,5,2] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[8,4,3,1,6,2,5,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,5,4,3,8,1,6,2] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[5,3,1,6,2,8,7,4] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[3,5,4,1,7,8,2,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[6,4,2,1,5,7,3,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,1,5,8,7,2,4,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,2,5,7,8,4,6,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[5,3,7,4,2,6,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,3,7,4,2,6,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[5,3,8,4,2,1,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,2,8,4,3,1,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,1,8,4,3,2,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[5,2,7,4,3,6,1,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[5,2,7,4,3,6,8,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[5,3,7,4,1,6,8,2] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[3,1,5,7,8,4,6,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[3,1,5,7,8,4,2,6] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,2,7,4,1,3,8,6] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[6,2,3,7,4,8,5,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[6,2,3,7,4,8,1,5] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,2,3,7,4,5,1,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[6,1,3,7,4,5,8,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,2,8,6,4,3,5,7] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[6,1,3,7,4,5,2,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[1,8,6,3,5,4,2,7] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[2,6,1,8,5,3,4,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,5,7,8,1,6,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[2,5,7,8,4,6,3,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,8,2,7,5,3,4,6] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[2,5,4,1,8,6,7,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[7,3,5,1,4,8,6,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,1,3,2,4,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[3,8,7,1,4,2,5,6] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,1,7,8,2,4,3,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[8,5,4,6,1,7,3,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[5,3,2,1,4,6,8,7] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,3,2,4,8,1,6,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[5,3,2,4,7,1,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,4,5,3,7,1,2,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[4,8,1,7,3,5,6,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[5,3,2,4,6,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,6,8,3,7,1,5,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[1,7,6,4,2,5,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[7,6,4,2,8,3,1,5] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,5,2,4,3,7,1,6] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,5,1,4,3,7,6,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[7,5,4,1,3,6,8,2] => [[1,5,6,7],[2],[3],[4],[8]] => 1110001
[3,6,7,2,5,1,8,4] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[2,6,5,7,1,4,8,3] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,5,1,7,8,4,6,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,5,2,4,6,8,7,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[8,1,2,4,7,6,5,3] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[3,4,1,8,6,7,5,2] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[4,3,8,5,1,7,6,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[6,1,3,2,8,5,7,4] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[3,1,2,4,5,6,7,9,8] => [[1,3,4,5,6,7,8],[2,9]] => 10000001
[8,5,3,2,4,7,1,6] => [[1,5,6],[2,8],[3],[4],[7]] => 1110010
[6,7,4,2,5,8,3,1] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[8,5,4,2,6,3,1,7] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,5,2,1,6,4,3,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[8,4,6,5,1,3,2,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[1,3,8,4,7,5,2,6] => [[1,2,3,5,8],[4],[6],[7]] => 0010110
[5,3,7,1,4,6,8,2] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[5,7,2,6,1,4,8,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[3,8,5,7,6,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[8,4,7,5,2,1,3,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[3,8,6,4,7,2,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[5,2,7,4,6,8,3,1] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[4,8,6,3,7,2,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,8,3,1,7,6,4,5] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,5,6,4,8,1,7,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[5,7,2,1,6,8,3,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[4,7,8,5,1,6,2,3] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[4,5,2,1,6,7,8,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,5,6,3,1,7,8,2] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[3,5,6,7,4,1,8,2] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,5,1,4,2,8,7,6] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[3,5,1,4,2,6,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,5,1,4,2,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[1,3,8,4,6,2,5,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,8,4,2,3,7,5,6] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,4,8,3,2,7,6,5] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,3,7,6,5,2,4,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,2,8,6,7,5,4,3] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[1,7,5,4,3,2,6,8] => [[1,2,7,8],[3],[4],[5],[6]] => 0111100
[8,9,10,5,6,7,1,3,4,2] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001
[8,9,10,5,6,3,4,7,1,2] => [[1,2,3],[4,5,8],[6,7],[9,10]] => 001010010
[8,9,5,6,10,1,3,4,7,2] => [[1,2,5,9],[3,4,8],[6,7],[10]] => 010010001
[8,9,10,5,6,7,1,3,2,4] => [[1,2,3],[4,5,6],[7,8,10],[9]] => 001001010
[8,9,5,6,10,1,3,7,2,4] => [[1,2,5],[3,4,8],[6,7,10],[9]] => 010010010
[8,9,10,1,5,6,3,2,4,7] => [[1,2,3,10],[4,5,6],[7,9],[8]] => 001001100
[8,5,9,10,3,6,7,1,2,4] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100
[3,8,5,7,4,6,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[7,6,3,2,5,1,8,4] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,2,5,7,8,6,3,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,7,2,4,5,1,8,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[5,2,7,8,3,6,1,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[8,5,1,2,3,7,4,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[5,2,8,3,1,4,7,6] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[8,7,2,5,1,4,3,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,4,1,3,2,7,6,5] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[8,3,5,1,2,4,7,6] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,6,5,1,7,4,2,3] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[8,7,4,5,1,2,6,3] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[3,8,6,2,7,1,5,4] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,8,4,2,1,7,6,5] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[8,3,1,7,5,6,2,4] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,4,1,7,5,2,6,3] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,4,2,7,5,3,1,6] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,4,3,7,5,1,2,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,5,7,6,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[8,4,7,6,5,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => 1011110
[8,3,1,4,7,6,2,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[8,3,5,7,6,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[1,4,6,8,2,5,7,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[3,6,2,4,8,1,7,5] => [[1,2,5],[3,4,7],[6,8]] => 0100101
[7,3,8,2,4,6,1,5] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[1,5,2,6,8,3,7,4] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[4,5,3,1,8,2,6,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,2,8,4,1,3,5,6] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[6,1,7,3,2,8,4,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[6,2,1,7,3,8,4,5] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,8,2,1,3,4,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,2,5,1,8,3,6,7] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[7,4,2,8,3,1,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,4,2,8,3,5,1,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[6,7,8,5,2,1,4,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[1,6,2,7,8,4,3,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[7,3,4,1,8,6,2,5] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[4,7,6,3,5,8,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,7,6,5,2,4,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[1,4,7,8,6,2,5,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,6,7,8,3,2,5,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,3,2,7,8,4,6,5] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[5,7,1,4,6,2,8,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[6,3,1,4,7,8,2,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[9,1,7,8,6,5,4,3,2] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111
[4,5,7,1,8,6,2,3] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[4,3,8,6,5,2,7,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[2,3,8,6,5,1,7,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,4,7,3,1,2,6,8] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[3,1,2,6,5,7,8,4] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[7,3,2,6,1,4,8,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[3,2,5,6,8,4,1,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[7,2,6,8,5,4,3,1] => [[1,3,4],[2],[5],[6],[7],[8]] => 1001111
[3,7,5,6,2,4,1,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,3,4,5,6,7,2,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[3,4,5,6,7,1,9,2,8] => [[1,2,3,4,5,7],[6,8,9]] => 00001010
[3,2,4,1,6,5,8,7,9] => [[1,3,5,7,9],[2,6,8],[4]] => 10101010
[4,2,5,1,6,3,8,7,9] => [[1,3,5,7,9],[2,6,8],[4]] => 10101010
[4,2,6,1,7,3,8,5,9] => [[1,3,5,7,9],[2,6,8],[4]] => 10101010
[4,2,6,1,8,3,9,5,7] => [[1,3,5,7],[2,6,8,9],[4]] => 10101010
[4,2,5,1,6,3,8,7,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,2,6,1,7,3,8,5,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,2,6,1,8,3,9,5,10,7] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,2,5,1,3,6,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[5,3,4,2,7,1,8,6] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[6,5,2,1,3,8,4,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[2,4,3,5,6,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[6,3,2,4,8,5,1,7] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,3,1,2,7,8,4,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[8,4,7,1,2,5,3,6] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[7,4,6,1,8,5,2,3] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[8,5,6,7,2,1,4,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[2,5,6,3,8,4,7,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[1,7,6,2,8,3,5,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,1,3,8,5,2,7,6] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[1,8,5,4,7,2,3,6] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[8,2,5,6,4,3,1,7] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[2,4,3,8,6,5,1,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[3,1,4,5,8,6,2,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[1,8,3,2,5,4,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[5,1,7,3,2,8,4,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[5,7,8,1,3,2,4,6] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[8,2,4,1,6,7,3,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,7,3,6,2,4,1,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[1,7,4,8,3,6,2,5] => [[1,2,4],[3,6],[5,8],[7]] => 0101010
[7,8,6,1,3,5,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[1,7,5,8,4,3,2,6] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[6,3,1,2,7,8,5,4] => [[1,4,5,6],[2,7],[3,8]] => 1100011
[8,2,7,5,3,4,1,6] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[6,3,1,2,8,7,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[8,4,7,2,6,3,1,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[7,6,3,4,2,1,8,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,4,6,2,3,7,1,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[3,4,5,8,1,7,2,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[6,3,4,2,7,8,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[5,6,3,7,8,2,1,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,6,3,4,7,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[4,3,8,6,7,5,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,5,6,2,7,8,3,1] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,5,6,2,7,1,8,3] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[4,5,6,2,1,7,8,3] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[4,5,6,2,1,7,3,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[6,8,7,2,3,1,4,5] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,5,1,6,7,3,2,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[2,5,1,8,3,7,4,6] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,7,2,1,3,8,4,6] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[7,1,5,4,2,6,3,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[7,6,5,4,3,1,2,9,8] => [[1,7,8],[2,9],[3],[4],[5],[6]] => 11111001
[8,7,6,5,4,3,1,2,10,9] => [[1,8,9],[2,10],[3],[4],[5],[6],[7]] => 111111001
[7,6,5,4,2,1,3,9,8] => [[1,7,8],[2,9],[3],[4],[5],[6]] => 11111001
[7,6,5,4,1,3,2,9,8] => [[1,6,8],[2,9],[3],[4],[5],[7]] => 11110101
[9,8,7,6,5,3,2,4,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[10,9,8,7,6,5,4,2,3,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => 111111101
[2,7,4,5,6,8,1,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,3,4,6,8,1,7,5] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[8,3,4,5,6,7,9,2,1] => [[1,3,4,5,6,7],[2],[8],[9]] => 10000011
[2,3,4,5,7,9,1,8,6] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[2,3,4,6,7,1,9,5,8] => [[1,2,3,4,5,7],[6,8,9]] => 00001010
[2,3,5,8,1,6,7,4] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,4,7,5,6,8,1,3] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[3,4,1,5,6,7,9,2,8] => [[1,2,4,5,6,7],[3,8,9]] => 01000010
[3,2,4,5,6,7,9,1,8] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[9,3,4,5,6,7,8,10,1,2] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[2,3,4,5,6,8,10,1,9,7] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[2,3,4,7,6,9,8,5,1] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[2,3,4,5,7,8,1,10,6,9] => [[1,2,3,4,5,6,8],[7,9,10]] => 000001010
[7,3,4,6,2,8,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[4,7,6,5,2,8,3,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[2,5,4,8,6,7,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[7,5,4,1,6,8,2,3] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[3,5,1,4,6,7,9,8,2] => [[1,2,5,6,7],[3,4,8],[9]] => 01000011
[3,4,1,5,6,7,8,10,2,9] => [[1,2,4,5,6,7,8],[3,9,10]] => 010000010
[4,2,3,5,6,7,9,1,8] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[8,5,2,1,7,6,3,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[2,7,3,6,4,1,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[7,2,1,8,5,6,4,3] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[3,6,5,1,4,8,2,7] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[6,3,5,4,8,1,2,7] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[2,5,1,4,6,3,8,7] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[3,1,5,6,4,2,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[8,5,6,4,3,1,7,2] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[8,3,5,6,7,1,2,4] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[2,1,4,7,3,6,8,5] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[5,3,7,6,4,8,2,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,7,6,4,2,8,1,5] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,6,1,4,3,7,2,5] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,4,7,5,1,6,3,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[2,1,5,3,7,8,6,4] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[5,1,4,7,6,8,2,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[8,4,1,3,7,6,5,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,3,4,1,6,7,5,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,1,4,2,6,5,7,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,8,1,4,3,2,6,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[5,6,4,3,8,2,7,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[1,6,4,3,8,2,7,5] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[7,8,1,4,3,2,5,6] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[7,1,8,4,5,3,6,2] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,3,1,8,6,5,7,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[4,3,2,7,5,1,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[5,2,3,7,4,1,8,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,1,7,4,3,6,8,5] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[7,1,2,4,5,6,8,3] => [[1,3,4,5,6,7],[2],[8]] => 1000001
[2,8,7,1,4,5,6,3] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[8,7,1,3,4,5,6,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[5,8,3,1,4,6,7,2] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[1,7,2,5,4,6,8,3] => [[1,2,4,6,7],[3],[5],[8]] => 0101001
[2,5,3,8,1,6,7,4] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,6,4,2,5,7,8,3] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[6,5,3,4,1,7,8,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[5,6,3,4,1,7,8,2] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[2,5,3,1,4,7,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[6,8,2,3,1,5,7,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[4,3,1,5,2,7,8,6] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[5,2,3,1,4,7,8,6] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[7,2,1,3,5,6,8,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,2,4,7,8,6,3,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,4,8,7,2,3,1,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[8,1,4,5,3,6,2,7] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[8,3,5,1,4,6,2,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[5,8,2,1,7,4,3,6] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[6,5,7,2,1,8,4,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[1,5,4,7,3,8,6,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[7,4,1,3,8,5,6,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,6,8,4,1,7,2,5] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[2,1,8,4,7,6,3,5] => [[1,3,5],[2,4,8],[6],[7]] => 1010110
[2,7,5,6,8,4,3,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,5,2,4,7,8,6,1] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[7,5,6,3,8,2,1,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[1,6,2,7,4,5,8,3] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[7,4,2,6,1,5,8,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,4,1,6,2,5,7,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[7,3,4,5,1,6,8,2] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[1,4,2,6,3,7,5,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[1,3,2,6,4,7,5,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[2,1,6,3,7,4,8,5,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[8,4,2,7,6,1,5,3] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[8,4,7,1,2,6,5,3] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,4,7,6,1,2,5,3] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,7,6,2,1,5,3,4] => [[1,6,8],[2,7],[3],[4],[5]] => 1111010
[5,7,8,1,6,2,4,3] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[6,8,7,4,2,5,1,3] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[6,8,4,5,7,2,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[6,5,4,3,2,7,1,8,9] => [[1,6,8,9],[2],[3],[4],[5],[7]] => 11110100
[5,4,3,2,6,1,7,8,9] => [[1,5,7,8,9],[2],[3],[4],[6]] => 11101000
[4,3,2,5,1,6,7,8,9] => [[1,4,6,7,8,9],[2],[3],[5]] => 11010000
[3,2,4,1,5,6,7,8,9] => [[1,3,5,6,7,8,9],[2],[4]] => 10100000
[3,1,6,5,4,7,2,8] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[4,1,2,6,5,3,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[4,6,1,3,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,2,6,3,5,1,7,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,6,1,2,5,3,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[5,8,4,7,1,3,6,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[6,8,3,1,5,4,7,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,1,3,6,7,4,2,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,2,8,6,7,1,3,5] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[6,1,2,4,7,3,5,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[1,2,4,3,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[1,3,5,7,2,9,4,6,8] => [[1,2,3,4,6],[5,7,8,9]] => 00010100
[5,6,1,4,8,3,2,7] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[3,6,4,1,7,2,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,2,5,1,6,4,7,8,9] => [[1,3,5,7,8,9],[2,6],[4]] => 10101000
[3,6,4,1,7,2,8,5,9] => [[1,2,5,7,9],[3,6,8],[4]] => 01101010
[4,3,2,6,1,7,5,8,9] => [[1,4,6,8,9],[2,7],[3],[5]] => 11010100
[5,4,3,2,7,1,8,6,9] => [[1,5,7,9],[2,8],[3],[4],[6]] => 11101010
[6,5,4,3,2,8,1,9,7] => [[1,6,8],[2,9],[3],[4],[5],[7]] => 11110101
[2,4,1,5,3,6,7,8,9,10] => [[1,2,4,6,7,8,9,10],[3,5]] => 010100000
[3,2,5,1,6,4,7,8,9,10] => [[1,3,5,7,8,9,10],[2,6],[4]] => 101010000
[3,6,4,1,7,2,8,5,9,10] => [[1,2,5,7,9,10],[3,6,8],[4]] => 011010100
[4,3,2,6,1,7,5,8,9,10] => [[1,4,6,8,9,10],[2,7],[3],[5]] => 110101000
[3,4,7,1,8,2,9,5,10,6] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[5,4,3,2,7,1,8,6,9,10] => [[1,5,7,9,10],[2,8],[3],[4],[6]] => 111010100
[6,5,4,3,2,8,1,9,7,10] => [[1,6,8,10],[2,9],[3],[4],[5],[7]] => 111101010
[7,6,5,4,3,2,9,1,10,8] => [[1,7,9],[2,10],[3],[4],[5],[6],[8]] => 111110101
[5,2,6,3,7,8,4,1] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[2,4,1,3,7,8,6,5] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[2,6,1,5,7,8,4,3] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,1,6,4,7,8,2,3] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[8,4,6,3,7,5,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[4,7,6,8,2,3,5,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[5,7,4,8,1,2,6,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[3,6,7,5,8,1,4,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,7,5,6,8,2,4,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,7,1,6,8,4,5,3] => [[1,2,5],[3,4,7],[6],[8]] => 0100101
[1,5,4,7,2,6,3,8] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[2,4,5,8,3,1,7,6] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[1,4,7,5,8,3,6,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,6,8,7,3,5,1,4] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,7,8,6,2,5,1,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[4,8,7,3,5,6,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[1,7,6,3,5,4,2,8] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[4,3,8,1,6,5,7,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[1,3,6,2,5,8,7,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[5,8,7,1,4,6,3,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[6,2,5,1,3,4,8,7] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[2,6,5,1,3,4,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,6,5,1,2,7,3,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,6,4,1,2,7,3,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[8,1,5,6,2,4,3,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[6,4,5,1,2,7,3,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[5,4,6,1,3,2,7,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,7,1,4,3,2,6,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[2,6,4,1,3,7,5,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[7,8,5,3,2,1,6,4] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[1,2,6,7,8,4,5,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[6,1,4,8,2,7,5,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,2,3,1,8,4,6,5] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[5,4,1,7,3,2,8,6] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,3,4,5,1,8,6,2] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[1,5,6,7,4,8,2,3] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[6,3,2,5,7,4,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[4,5,2,7,6,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,5,2,1,7,6,3,8] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,6,7,8,3,1,4,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[6,3,2,5,1,7,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,6,3,7,8,2,1,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[5,6,7,1,8,4,2,3] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[1,7,3,2,8,6,5,4] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[3,7,1,2,8,6,5,4] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,7,8,1,6,5,3,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[8,1,5,7,3,4,6,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[5,8,2,7,6,3,1,4] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[2,8,4,7,6,3,1,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,8,2,4,7,6,3,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[4,5,8,7,1,6,2,3] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[1,8,2,4,6,7,5,3] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,5,1,8,4,7,6,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[3,4,2,8,1,7,6,5] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,4,5,8,1,7,6,3] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,1,8,2,6,7,5,4] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[2,6,8,1,4,3,7,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[1,6,5,2,8,7,3,4] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,6,1,5,8,7,3,4] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[8,1,7,3,5,2,4,6] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,1,3,2,7,6,4,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,3,4,8,6,2,5,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,5,8,1,6,2,3,4] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,8,4,5,3,1,7,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[6,7,5,3,2,8,4,1] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[6,2,5,3,8,1,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,6,1,3,5,2,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[6,2,4,5,3,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,1,5,4,7,2,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[6,8,5,4,7,1,3,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[1,6,8,4,2,5,7,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[7,5,8,1,3,4,2,6] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[1,4,2,8,3,5,7,6] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,3,5,4,8,7,2,6] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[1,6,2,4,8,3,7,5] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,7,8,5,4,2,6,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[1,5,2,8,6,4,7,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,6,5,2,7,4,8,3] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,1,6,7,4,2,8,3] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[1,5,4,2,8,6,7,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,8,5,4,6,2,7,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,7,5,4,6,2,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,8,4,1,6,2,7,3] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[4,8,1,3,7,6,2,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,5,3,1,2,8,7,6] => [[1,2,6],[3,5,7],[4,8]] => 0110011
[6,4,2,3,1,8,7,5] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,5,2,1,3,8,7,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,6,1,8,2,5,3,4] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,4,2,3,7,6,1,5] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[5,7,8,1,2,4,3,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[1,7,6,8,3,5,4,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[5,7,6,4,2,1,3,8] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[6,5,7,4,1,3,2,8] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[4,6,1,8,3,5,2,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[7,1,6,8,2,5,4,3] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[4,7,1,8,3,2,5,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,8,3,6,1,5,2,7] => [[1,2,8],[3,4],[5,6],[7]] => 0101010
[1,7,8,6,4,5,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,2,8,6,4,5,1,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[8,4,3,6,2,5,1,7] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[1,6,8,7,4,3,5,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,1,2,6,8,7,5,4] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[5,7,4,2,1,8,6,3] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[8,6,5,7,2,4,3,1] => [[1,4],[2,6],[3],[5],[7],[8]] => 1101011
[7,4,6,1,8,5,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[7,4,6,3,8,1,5,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,4,8,1,6,3,2,5] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,4,8,3,6,2,1,5] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[6,4,8,2,3,5,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[4,6,8,2,5,7,1,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,4,8,2,5,7,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[6,2,4,5,8,3,7,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[6,8,2,4,7,3,5,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[8,4,6,2,7,1,3,5] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[6,8,4,2,7,1,3,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[6,8,2,4,1,7,3,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[7,5,1,6,2,4,8,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,2,5,7,1,6,8,3] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[4,5,2,3,8,7,1,6] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[2,5,4,7,6,1,3,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[5,2,3,7,6,1,4,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,2,3,7,6,1,5,8] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[4,2,7,3,5,1,6,8] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[5,6,2,3,8,4,7,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[5,6,2,3,1,7,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[5,7,2,3,4,1,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[6,2,7,3,5,1,4,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[7,2,6,3,5,1,4,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[6,5,2,3,1,7,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,5,2,3,8,4,7,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,5,2,1,4,6,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,5,2,3,1,6,4,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,6,2,3,1,5,4,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,2,6,3,1,7,4,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,6,3,4,2,7,5,8] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[8,5,2,7,3,4,6,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[1,7,2,4,5,6,8,3] => [[1,2,4,5,6,7],[3],[8]] => 0100001
[1,8,3,2,5,6,4,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[7,2,8,1,4,6,3,5] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[2,7,8,1,5,6,3,4] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[6,8,2,3,1,5,4,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,8,2,3,1,6,4,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,7,2,1,4,6,8,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[4,2,7,1,5,6,8,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[4,2,3,8,1,7,5,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,2,1,5,3,7,6,8] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[5,1,3,8,4,6,7,2] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[5,1,3,2,6,7,8,4] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,1,3,4,2,7,6,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[6,1,3,4,2,7,5,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[7,2,1,3,5,8,4,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,8,7,2,3,4,5,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[1,9,8,10,7,6,5,4,3,2] => [[1,2,4],[3],[5],[6],[7],[8],[9],[10]] => 010111111
[2,8,7,9,6,5,4,3,1] => [[1,2,4],[3],[5],[6],[7],[8],[9]] => 01011111
[3,7,2,8,1,4,5,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[5,2,3,7,4,6,1,8] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[2,5,3,7,4,6,1,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[2,6,7,3,4,5,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[6,2,7,3,4,5,1,8] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,8,4,5,2,1,6,7] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[2,7,6,3,4,5,1,8] => [[1,2,5,6,8],[3],[4],[7]] => 0110010
[2,8,7,5,1,3,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[3,1,2,9,4,5,6,7,8] => [[1,3,4,6,7,8,9],[2,5]] => 10010000
[6,1,2,3,4,5,9,7,8] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[2,1,10,3,4,5,6,7,8,9] => [[1,3,5,6,7,8,9,10],[2,4]] => 101000000
[3,1,2,10,4,5,6,7,8,9] => [[1,3,4,6,7,8,9,10],[2,5]] => 100100000
[6,7,1,2,3,4,5,9,8] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[7,1,2,3,4,5,6,10,8,9] => [[1,3,4,5,6,7,8,10],[2,9]] => 100000010
[4,5,7,2,8,3,6,1] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[9,7,5,3,1,8,6,4,2] => [[1,6],[2,7],[3,8],[4,9],[5]] => 11110111
[8,5,2,9,6,3,7,4,1] => [[1,4,7],[2,5,8],[3,6],[9]] => 11011011
[9,5,1,6,2,7,3,8,4] => [[1,4,6,8],[2,5,7,9],[3]] => 11010101
[8,4,7,3,6,2,9,5,1] => [[1,3,7],[2,5],[4,8],[6],[9]] => 10101011
[7,2,8,3,9,4,5,6,1] => [[1,3,5,7,8],[2,4,6],[9]] => 10101001
[4,5,6,9,3,8,2,7,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[10,8,6,4,2,9,7,5,3,1] => [[1,6],[2,7],[3,8],[4,9],[5],[10]] => 111101111
[10,7,4,1,8,5,2,9,6,3] => [[1,5,8],[2,6,9],[3,7,10],[4]] => 111011011
[9,6,3,8,5,2,10,7,4,1] => [[1,4,7],[2,5,8],[3,9],[6],[10]] => 110110111
[10,6,2,7,3,8,4,9,5,1] => [[1,4,6,8],[2,5,7,9],[3],[10]] => 110101011
[8,4,7,3,10,6,2,9,5,1] => [[1,3,5],[2,6,8],[4,9],[7],[10]] => 101011011
[10,4,5,6,7,1,8,2,9,3] => [[1,3,4,5,7,9],[2,8,10],[6]] => 100010101
[8,2,9,3,10,4,5,6,7,1] => [[1,3,5,7,8,9],[2,4,6],[10]] => 101010001
[5,2,1,3,6,7,8,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[7,5,2,6,1,8,4,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[6,1,5,2,7,8,4,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[7,5,6,8,4,1,3,2] => [[1,3,4],[2,7],[5],[6],[8]] => 1001101
[8,3,7,5,1,4,2,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,1,5,7,3,6,2,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[8,3,2,6,4,5,1,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,5,3,7,4,1,2,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[8,5,6,2,7,1,3,4] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[8,4,7,2,6,5,1,3] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[8,5,7,3,2,6,1,4] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,1,2,3,6,4,7,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,6,2,3,5,8,1,4] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[4,5,3,7,8,1,6,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[3,4,2,8,1,6,7,5] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[8,3,4,1,5,7,6,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,3,7,5,1,6,2,8] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[5,2,6,1,4,3,7,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,3,7,4,2,8,6,1] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[7,2,5,8,6,1,4,3] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[5,3,1,4,6,7,8,2] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[4,6,2,1,3,7,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,5,4,1,3,6,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,2,5,6,7,8,9,1,3] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[3,1,6,7,8,4,5,2] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[7,4,5,6,2,1,8,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[4,2,5,6,7,8,9,10,1,3] => [[1,3,4,5,6,7,8],[2,10],[9]] => 100000010
[3,7,5,6,2,1,8,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,7,6,3,8,4,5,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[6,4,1,2,7,8,3,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[6,4,1,3,5,2,7,8] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,1,8,3,4,6,2,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[4,5,8,2,3,7,1,6] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[7,3,4,8,2,5,1,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[4,7,2,5,1,6,8,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[7,2,8,1,5,6,4,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[5,6,4,2,1,8,3,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[2,4,3,5,8,1,6,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,6,5,3,8,1,4,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[6,1,2,4,3,5,7,8] => [[1,3,4,6,7,8],[2],[5]] => 1001000
[6,5,8,2,7,3,4,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[1,7,6,8,4,3,2,5] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[1,7,6,5,3,8,2,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[6,1,2,4,3,5,8,7] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,6,1,3,7,8,5,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[8,4,1,5,2,6,7,3] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[1,5,6,3,8,7,2,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[5,3,2,6,8,7,1,4] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[6,3,5,2,7,1,4,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,5,2,6,7,1,4,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[5,3,8,7,1,4,2,6] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[6,4,5,3,1,8,7,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[8,5,1,2,3,6,7,4] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[2,8,6,1,5,4,7,3] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,3,2,6,1,5,7,4] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[3,8,6,4,7,1,2,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[1,8,7,5,4,3,2,6] => [[1,2,8],[3],[4],[5],[6],[7]] => 0111110
[8,6,4,7,1,3,2,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[3,1,4,7,6,2,5,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,3,4,1,6,2,7,8] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,7,1,4,6,3,5,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[7,3,1,6,5,2,4,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,1,5,2,4,6,3,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[6,1,4,5,2,7,3,8] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[6,1,5,8,2,7,4,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,1,2,3,6,4,5,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[2,8,4,6,5,1,7,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[7,4,1,3,6,5,2,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,7,2,8,1,3,6,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[6,5,1,4,7,3,2,8] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[2,7,8,4,1,3,6,5] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[2,4,6,5,7,8,1,3] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[2,4,6,7,5,8,1,3] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,4,6,3,7,8,1,5] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[2,4,5,6,8,7,1,3] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[2,4,5,6,8,3,7,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,4,5,6,3,8,1,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,3,4,6,8,5,1,7] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[5,2,8,3,4,1,6,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[3,6,4,1,2,7,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,1,7,3,8,6,2,5] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[8,4,1,2,5,3,7,6] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[1,5,2,7,6,8,4,3] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[4,7,6,8,3,1,2,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[4,8,2,7,6,5,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[7,4,2,8,6,5,1,3] => [[1,4],[2,5],[3,6],[7,8]] => 1101110
[8,6,5,2,7,1,4,3] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[6,5,8,2,7,1,4,3] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[7,5,8,2,1,6,4,3] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[3,2,1,6,5,8,4,7] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[2,6,4,8,5,7,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[6,3,1,4,5,8,2,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[3,4,8,5,2,1,7,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,8,7,1,3,2,6,5] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,8,7,4,6,1,3,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[3,4,1,8,7,6,2,5] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[1,3,5,6,8,7,2,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[2,8,7,5,4,1,6,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[8,1,5,7,4,2,6,3] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[5,8,7,3,4,1,6,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,6,1,3,2,8,5,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[2,6,5,8,3,1,4,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[6,7,8,2,4,5,3,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[3,2,8,4,5,7,1,6] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,1,8,2,4,5,3,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[8,3,6,4,2,7,1,5] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[1,3,8,4,7,6,2,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[8,3,7,5,4,1,2,6] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[2,6,4,7,8,5,1,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[5,4,3,7,6,1,8,2] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[8,6,3,7,1,4,2,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[3,1,2,8,7,6,4,5] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,5,4,1,2,3,7,6] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[8,3,2,1,6,4,7,5] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[2,3,8,4,1,7,5,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[4,6,1,3,2,7,8,5] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[6,7,2,5,8,4,1,3] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,1,7,8,2,5,6,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[3,4,6,7,1,5,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,4,5,7,8,1,6,2] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,8,7,4,3,5,2,6] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[2,4,5,8,1,3,7,6] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[6,3,1,5,8,4,2,7] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[2,8,3,5,6,1,4,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,3,6,4,2,7,5,8] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[2,3,7,5,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[3,2,8,5,6,1,4,7] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[7,2,5,8,1,4,6,3] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,7,5,8,1,2,6,3] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[4,7,5,8,1,2,3,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[3,4,7,5,2,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,3,2,5,7,8,1,6] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[2,4,7,5,8,3,1,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,5,4,7,3,8,1,6] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[3,7,8,4,2,1,6,5] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,6,7,9,1,2,3,4,8] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[4,5,6,7,9,1,2,3,8] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[7,8,10,1,2,3,4,5,6,9] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[4,5,6,7,8,10,1,2,3,9] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[8,5,4,7,6,3,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[1,5,4,8,7,6,2,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[3,2,4,5,8,1,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[3,6,8,4,2,7,1,5] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[3,6,5,1,7,2,8,4] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[7,4,1,6,2,8,5,3] => [[1,4,6],[2,5,7],[3],[8]] => 1101011
[1,3,6,8,2,4,7,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,6,7,4,3,8,2,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[7,3,1,6,5,2,8,4] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,5,4,1,6,2,7,3] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[4,7,2,8,5,1,6,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[7,8,6,2,1,5,4,3] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[2,1,3,8,7,5,6,4] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[8,1,7,3,6,5,2,4] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[1,6,4,7,3,8,5,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,2,3,4,5,6,8,10,7,9] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[3,4,5,6,7,8,2,1,9] => [[1,2,3,4,5,6,9],[7],[8]] => 00000110
[4,5,6,7,8,1,2,3,9] => [[1,2,3,4,5,9],[6,7,8]] => 00001000
[4,8,1,6,3,7,2,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[8,5,4,1,6,3,7,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[1,7,6,2,4,8,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,7,3,2,4,8,6,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[2,8,4,6,3,5,1,7] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[2,7,8,3,6,4,5,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,8,1,4,6,5,2,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,7,5,4,1,8,3,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[4,6,1,8,5,3,2,7] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[3,8,5,2,1,6,4,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[5,1,4,8,2,6,3,7] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[4,5,8,1,3,7,6,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[8,6,7,1,4,3,2,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[1,4,7,8,6,3,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[8,5,2,6,3,4,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,3,6,1,2,7,4,5] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[3,8,6,1,2,5,7,4] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,7,6,2,1,8,5,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,3,7,6,1,8,5,2] => [[1,3,6],[2,4],[5,7],[8]] => 1011011
[8,6,3,2,7,1,5,4] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[6,8,1,5,4,7,2,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[6,7,2,5,4,8,1,3] => [[1,2,6],[3,4],[5,8],[7]] => 0101010
[7,6,2,4,8,5,1,3] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[4,6,8,7,3,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[4,7,5,2,6,3,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[3,5,6,2,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[8,9,10,4,5,6,2,3,1,7] => [[1,2,3,10],[4,5,6],[7,8],[9]] => 001001010
[8,4,5,9,10,2,3,6,1,7] => [[1,3,4,5],[2,7,8,10],[6],[9]] => 100010010
[8,4,5,9,2,3,6,10,1,7] => [[1,3,4,8],[2,6,7,10],[5],[9]] => 100100010
[8,9,10,4,5,6,2,1,3,7] => [[1,2,3,10],[4,5,6],[7,9],[8]] => 001001100
[8,4,5,9,10,2,1,3,6,7] => [[1,3,4,5],[2,8,9,10],[6],[7]] => 100011000
[8,4,5,9,2,10,1,3,6,7] => [[1,3,4,6],[2,8,9,10],[5],[7]] => 100101000
[8,4,5,9,2,1,3,6,10,7] => [[1,3,4,9],[2,7,8,10],[5],[6]] => 100110001
[8,4,9,2,5,6,10,1,3,7] => [[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100
[8,4,2,5,9,10,1,3,6,7] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000
[8,4,2,5,9,1,3,6,10,7] => [[1,4,5,9],[2,7,8,10],[3],[6]] => 110010001
[4,8,9,2,5,6,10,1,3,7] => [[1,2,3,7],[4,5,6,10],[8,9]] => 001000100
[4,8,2,5,9,10,1,3,6,7] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[6,1,8,2,4,3,5,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[1,6,8,2,5,3,4,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[5,4,8,7,1,2,6,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,5,6,4,3,8,1,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[8,7,3,5,1,4,6,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,6,3,5,2,1,4,7] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[8,7,3,5,2,4,6,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,4,2,7,6,5,1,3] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[4,6,3,8,5,2,7,1] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[4,1,3,8,5,6,2,7] => [[1,3,4,6,8],[2,5],[7]] => 1001010
[5,2,8,3,1,6,7,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[1,7,8,6,3,2,5,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[3,2,8,1,5,7,4,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[3,4,6,7,2,1,5,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[2,6,7,1,4,3,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[3,2,7,4,8,5,6,1] => [[1,3,5,7],[2,4,6],[8]] => 1010101
[5,8,2,7,4,6,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[4,5,2,8,3,7,1,6] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[7,8,5,1,6,4,3,2] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[8,7,5,1,6,4,3,2] => [[1,5],[2,6],[3],[4],[7],[8]] => 1110111
[4,5,8,3,1,2,7,6] => [[1,2,3],[4,6,7],[5,8]] => 0011001
[1,4,6,3,7,5,2,8] => [[1,2,3,5,8],[4,6],[7]] => 0010110
[1,3,8,7,4,5,6,2] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[7,3,1,8,4,5,6,2] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[3,2,8,7,4,5,6,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[6,2,4,3,7,5,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,8,2,1,5,7,6,4] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[1,3,2,8,7,4,6,5] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[7,5,2,8,3,1,6,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[4,6,3,7,8,1,2,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,2,5,4,1,7,8,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,1,5,6,3,8,7,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[8,5,1,6,3,2,4,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[6,8,7,4,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => 0111101
[8,1,5,4,6,7,3,2] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[2,8,5,1,3,7,6,4] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,6,4,1,8,2,7,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[6,4,5,1,3,8,7,2] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[6,1,3,5,4,8,2,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[1,3,8,7,2,5,6,4] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,5,4,1,8,3,7,6] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,1,4,8,3,7,6,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[8,4,1,2,7,6,5,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[4,8,3,2,7,6,5,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[1,8,7,3,4,6,5,2] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[8,7,5,3,1,2,4,6,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[7,5,3,1,2,4,6,9,8] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[6,3,1,2,4,8,7,5,9] => [[1,4,5,6,9],[2,7],[3,8]] => 11000110
[8,7,5,3,1,2,4,6,10,9] => [[1,6,7,8,9],[2,10],[3],[4],[5]] => 111100001
[8,5,3,1,2,4,6,9,7] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[10,9,7,5,3,1,2,4,6,8] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000
[5,3,1,2,4,6,8,7] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[8,5,7,3,1,2,4,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[7,5,3,1,2,4,6,8,9] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[3,1,2,8,7,5,4,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[5,3,1,2,4,9,7,6,8] => [[1,4,5,6,9],[2,7],[3,8]] => 11000110
[1,4,3,8,5,7,2,6] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[6,7,1,5,2,8,4,3] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[1,5,3,7,6,4,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[4,8,1,3,6,2,7,5] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[2,7,3,4,8,6,5,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,8,2,4,7,3,6,5] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,7,1,6,5,8,3,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[6,2,3,8,1,5,7,4] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[2,5,7,4,8,3,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[8,5,6,2,4,7,1,3] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,1,5,7,3,6,4,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[3,8,6,2,7,5,4,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[4,8,1,6,2,5,3,7] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[1,8,4,2,5,7,3,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[5,8,3,1,2,4,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,4,8,5,2,3,6,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,4,8,5,2,3,7,6] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,5,8,7,2,4,3,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,5,4,2,8,3,7,6] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,2,8,7,3,5,4,6] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[8,7,1,3,2,5,4,6] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[6,7,4,2,8,1,3,5] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[4,1,6,8,7,2,3,5] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,7,5,6,2,8,3,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[8,4,3,6,7,5,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[6,7,5,2,8,4,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[6,8,4,3,2,7,5,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,1,7,3,5,8,2,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[1,3,7,6,4,8,2,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,6,4,8,7,3,1,5] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[2,1,8,7,3,5,4,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,1,8,5,7,4,3,2] => [[1,3,5],[2,4],[6],[7],[8]] => 1010111
[8,5,1,4,7,6,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,1,3,7,2,4,6,5] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[5,3,1,6,4,8,2,7] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[2,5,6,7,1,4,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[4,7,5,3,2,8,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,7,5,2,8,6,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,8,1,2,7,4,3,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[6,3,1,8,2,4,5,7] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[4,6,3,7,8,1,5,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[6,3,1,8,4,5,2,7] => [[1,4,6,8],[2,5],[3,7]] => 1101010
[7,6,2,4,8,3,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[6,5,8,1,4,3,7,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,1,4,2,7,5,6,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[1,7,2,8,3,9,4,10,5,6] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[7,1,2,8,3,9,4,10,5,6] => [[1,3,4,6,8,10],[2,5,7,9]] => 100101010
[7,1,8,2,9,3,4,10,5,6] => [[1,3,5,7,8,10],[2,4,6,9]] => 101010010
[1,8,2,9,3,10,4,11,5,12,6,7] => [[1,2,4,6,8,10,12],[3,5,7,9,11]] => 01010101010
[8,6,3,5,2,1,7,4] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[6,8,3,1,2,5,4,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[5,8,6,4,7,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[2,5,1,8,7,3,4,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[1,7,6,5,4,3,2,9,8] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[6,8,4,3,5,1,7,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[1,4,7,3,6,8,2,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[3,7,1,4,6,8,2,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[2,4,7,3,6,8,1,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[8,5,7,6,1,3,2,4] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[2,7,5,6,1,8,4,3] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[1,2,6,7,4,5,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[6,5,2,8,7,1,4,3] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[7,2,3,6,8,1,4,5] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[2,6,1,3,8,5,4,7] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[6,4,1,8,3,2,5,7] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[5,8,1,4,2,7,3,6] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[2,3,1,6,8,7,4,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[6,4,8,2,1,7,3,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[2,3,1,8,7,5,6,4] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[1,5,6,7,2,4,3,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,8,6,4,1,5,3,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[6,7,4,5,1,3,8,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[1,6,5,3,8,2,4,7] => [[1,2,5,8],[3,7],[4],[6]] => 0110100
[5,6,1,2,4,8,3,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[8,7,4,5,1,3,2,6] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[8,5,1,2,7,4,3,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[4,1,8,7,2,5,3,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[3,2,4,6,1,8,7,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,6,7,4,1,2,5,8] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[1,4,7,5,8,2,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,6,8,4,7,3,2,5] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[3,6,7,5,4,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,5,7,2,6,3,8,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[2,1,5,7,4,6,8,3] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,3,5,7,8,1,6,4] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,5,7,4,2,3,6,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,4,7,5,3,6,8,1] => [[1,2,3,6,7],[4],[5],[8]] => 0011001
[8,1,7,2,4,6,3,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[1,2,4,7,8,6,3,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,3,6,2,5,8,4,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,5,3,6,8,2,4,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[4,8,1,2,6,3,7,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[5,8,1,2,6,3,7,4] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[1,6,2,3,7,5,8,4] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[4,1,2,6,5,7,8,3] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,8,4,2,7,3,6,5] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[1,7,5,2,3,8,6,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[8,1,4,7,3,5,2,6] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[8,4,3,6,1,7,2,5] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[2,6,1,8,3,7,4,5] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[8,4,2,1,3,7,5,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[2,5,1,7,6,8,3,4] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[5,3,1,8,2,4,7,6] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[1,2,6,3,7,5,8,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[5,1,8,3,2,4,7,6] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[3,1,5,4,6,7,8,2] => [[1,3,5,6,7],[2,4],[8]] => 1010001
[2,8,5,7,3,1,4,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[2,6,8,7,3,1,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,4,2,1,3,8,5,6] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[7,2,1,3,8,5,4,6] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[2,1,7,3,8,6,4,5] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[1,7,5,3,2,4,8,6] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,4,2,7,6,5,8,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,4,1,6,5,7,8,2] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[2,8,7,3,4,1,5,6] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[5,7,6,2,3,8,1,4] => [[1,2,6],[3,5,8],[4],[7]] => 0110010
[4,5,7,6,2,8,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[3,1,8,7,5,2,6,4] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[4,5,6,8,7,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[2,8,3,1,5,4,7,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,8,4,1,5,2,7,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,8,6,2,4,3,7,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[4,8,3,1,6,2,7,5] => [[1,2,7],[3,5,8],[4,6]] => 0110101
[2,8,3,1,6,4,7,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[6,2,7,1,5,8,4,3] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[1,7,8,9,6,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[1,6,7,8,9,5,4,3,2] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[1,5,6,7,8,9,4,3,2] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[1,4,5,6,7,8,9,3,2] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,8,9,10,7,6,5,4,3,2] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[1,7,8,9,10,6,5,4,3,2] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[1,6,7,8,9,10,5,4,3,2] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[1,5,6,7,8,9,10,4,3,2] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[1,4,5,6,7,8,9,10,3,2] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[4,8,5,1,3,2,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,4,3,1,2,7,6,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[4,1,6,5,2,3,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[7,1,5,2,3,6,4,8] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[4,1,6,3,7,2,5,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,6,1,2,8,3,7,5] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[4,1,3,6,7,2,5,8] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[2,6,5,1,3,4,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[2,6,7,4,3,1,5,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[2,6,3,1,7,4,5,8] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[6,5,3,7,2,4,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[2,3,6,7,1,5,4,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[2,7,5,8,1,3,6,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[5,1,6,7,3,2,4,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[5,6,1,4,7,2,3,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[1,2,5,7,8,6,3,4] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[1,2,6,7,4,5,3,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,2,7,8,4,6,3,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[8,6,5,2,1,7,4,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[4,3,8,6,7,1,5,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[8,3,2,4,7,1,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[7,3,2,8,6,1,5,4] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[7,5,8,2,6,1,4,3] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[7,4,1,2,6,5,8,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[5,2,7,4,6,1,8,3] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[7,4,1,2,3,6,8,5] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[5,4,8,6,3,2,1,7] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[8,4,6,7,3,1,5,2] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,1,3,6,8,5,2,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,3,5,7,1,2,8,4] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[1,8,5,3,2,4,6,7] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[1,6,7,3,4,2,5,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,8,3,4,2,5,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,8,7,5,3,4,2,6] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[1,7,8,5,3,4,2,6] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[1,7,6,8,4,2,3,5] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,7,8,6,4,3,2,5] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[9,8,7,6,5,2,1,3,4] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[7,2,8,9,10,1,3,4,5,6] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[9,7,8,6,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[5,1,7,8,4,2,3,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[3,8,2,1,6,7,5,4] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[2,8,3,1,7,5,6,4] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[9,7,5,3,10,2,4,6,8,1] => [[1,5,8,9],[2,7],[3],[4],[6],[10]] => 111010001
[10,5,6,7,8,4,3,2,1,9] => [[1,3,4,5,10],[2],[6],[7],[8],[9]] => 100011110
[7,5,8,9,10,4,6,3,2,1] => [[1,3,4,5],[2,7],[6],[8],[9],[10]] => 100010111
[2,10,4,5,6,7,9,1,3,8] => [[1,2,4,5,6,7],[3,9,10],[8]] => 010000100
[2,7,4,1,5,8,3,6] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,1,6,4,7,8,3,5] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[5,7,8,3,4,2,1,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,5,3,8,2,6,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,6,4,7,8,5,3,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[7,8,4,5,6,1,3,2] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[2,5,1,8,4,6,7,3] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[6,5,8,3,4,2,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[8,2,7,6,3,4,5,1] => [[1,3,6,7],[2],[4],[5],[8]] => 1011001
[6,8,7,3,2,1,4,5] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[3,4,8,2,7,1,5,6] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[7,2,6,1,4,8,3,5] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[7,8,1,2,4,6,3,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[7,2,8,3,4,5,1,6] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[6,1,8,3,4,2,5,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[7,5,1,2,4,3,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,6,8,1,4,2,3,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[2,4,3,7,8,5,6,1] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[2,1,7,6,3,4,5,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[6,1,5,3,8,2,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[2,3,6,8,5,1,7,4] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[3,2,4,8,6,1,7,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[2,1,3,8,4,5,7,6] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[3,1,2,8,5,4,7,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,1,3,7,8,4,6,5] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[2,1,3,8,4,7,6,5] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,1,2,8,4,5,7,6] => [[1,3,4,6,7],[2,5],[8]] => 1001001
[1,2,8,7,5,4,6,3] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[4,6,7,2,3,8,1,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,2,6,5,7,8,1,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[2,1,8,7,4,6,5,3] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[6,1,5,8,4,7,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[1,4,6,8,5,7,2,3] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[2,8,5,1,6,4,3,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[2,4,7,1,8,3,6,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[6,1,5,4,2,3,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[6,4,5,1,2,8,3,7] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,4,1,5,7,6,3,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,1,6,3,5,2,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[4,6,2,5,3,8,1,7] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[4,6,5,2,1,8,3,7] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[5,8,4,3,6,7,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[6,8,2,1,5,3,4,7] => [[1,2,7,8],[3,5],[4,6]] => 0110100
[2,5,3,8,6,7,4,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,2,6,5,1,8,4,7] => [[1,3,6],[2,4,8],[5,7]] => 1011010
[7,4,5,8,1,6,2,3] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[4,5,8,1,6,7,3,2] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,1,8,4,6,7,3,2] => [[1,3,5,6],[2,4],[7],[8]] => 1010011
[6,5,3,8,1,7,2,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,3,7,1,6,2,4,5] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[8,1,4,6,5,7,2,3] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[8,1,7,5,6,4,2,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[8,6,1,5,3,7,2,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[7,2,3,6,8,1,5,4] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[2,6,3,7,8,1,4,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[6,3,8,7,2,1,5,4] => [[1,3],[2,4],[5,7],[6,8]] => 1011101
[7,2,5,6,3,4,8,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[7,2,8,6,3,1,5,4] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[7,2,4,5,8,6,3,1] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[6,3,8,4,7,2,5,1] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[7,2,3,6,8,5,4,1] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,2,8,5,4,1,3,6] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[7,4,5,2,8,1,6,3] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,5,4,2,8,1,6,3] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[7,6,3,2,8,4,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,2,3,6,8,4,5,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,2,5,4,8,3,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,2,8,3,6,1,4,5] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[7,4,5,2,8,3,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[5,1,3,2,4,6,8,7] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[6,5,3,4,1,8,2,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[6,4,5,3,8,1,2,7] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[7,2,4,6,3,8,5,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[2,8,3,7,6,1,5,4] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,4,2,6,8,7,3,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[3,7,2,5,8,6,4,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[4,6,5,3,8,1,7,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[2,4,8,7,6,1,5,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[3,2,8,7,4,6,5,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[8,2,6,5,1,4,3,7] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[4,8,5,2,7,6,3,1] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[2,8,6,5,7,1,3,4] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[3,8,4,7,2,1,6,5] => [[1,2,4],[3,7],[5,8],[6]] => 0101101
[4,8,5,1,7,6,3,2] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[5,8,1,7,6,2,3,4] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[3,4,6,2,5,7,1,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,7,5,2,6,8,3,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[7,4,8,3,6,5,1,2] => [[1,3],[2,5],[4,6],[7,8]] => 1010110
[1,5,4,3,8,7,2,6] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[1,5,8,2,6,4,3,7] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[10,9,8,6,4,2,1,3,5,7] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[10,8,7,6,4,2,1,3,5,9] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[10,9,8,7,6,4,2,1,3,5] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,8,6,5,4,2,1,3,7,9] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[10,9,8,6,5,4,2,1,3,7] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,8,7,6,5,4,2,1,3,9] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,7,9,6,5,4,2,1,8,3] => [[1,3],[2,9],[4,10],[5],[6],[7],[8]] => 101111101
[10,8,6,4,3,2,1,5,7,9] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000
[10,9,8,6,4,3,2,1,5,7] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,8,7,6,4,3,2,1,5,9] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,7,9,6,4,3,2,1,8,5] => [[1,3],[2,9],[4,10],[5],[6],[7],[8]] => 101111101
[10,9,8,7,6,3,5,2,4,1] => [[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => 111110101
[10,8,6,5,4,3,2,1,7,9] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[10,9,8,5,7,4,3,2,6,1] => [[1,5],[2,9],[3],[4],[6],[7],[8],[10]] => 111011101
[10,9,8,4,7,6,3,5,2,1] => [[1,5],[2,8],[3],[4],[6],[7],[9],[10]] => 111011011
[10,7,9,6,5,4,3,2,8,1] => [[1,3],[2,9],[4],[5],[6],[7],[8],[10]] => 101111101
[10,6,9,8,5,4,3,7,2,1] => [[1,3],[2,8],[4],[5],[6],[7],[9],[10]] => 101111011
[10,5,9,8,7,4,6,3,2,1] => [[1,3],[2,7],[4],[5],[6],[8],[9],[10]] => 101110111
[12,11,10,9,8,7,6,3,5,2,4,1] => [[1,9],[2,11],[3],[4],[5],[6],[7],[8],[10],[12]] => 11111110101
[12,11,10,9,8,5,7,4,3,2,6,1] => [[1,7],[2,11],[3],[4],[5],[6],[8],[9],[10],[12]] => 11111011101
[12,11,10,9,8,4,7,6,3,5,2,1] => [[1,7],[2,10],[3],[4],[5],[6],[8],[9],[11],[12]] => 11111011011
[12,11,10,7,9,6,5,4,3,2,8,1] => [[1,5],[2,11],[3],[4],[6],[7],[8],[9],[10],[12]] => 11101111101
[12,11,10,6,9,8,5,4,3,7,2,1] => [[1,5],[2,10],[3],[4],[6],[7],[8],[9],[11],[12]] => 11101111011
[12,11,10,5,9,8,7,4,6,3,2,1] => [[1,5],[2,9],[3],[4],[6],[7],[8],[10],[11],[12]] => 11101110111
[12,9,11,8,7,6,5,4,3,2,10,1] => [[1,3],[2,11],[4],[5],[6],[7],[8],[9],[10],[12]] => 10111111101
[12,8,11,10,7,6,5,4,3,9,2,1] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9],[11],[12]] => 10111111011
[12,7,11,10,9,6,5,4,8,3,2,1] => [[1,3],[2,9],[4],[5],[6],[7],[8],[10],[11],[12]] => 10111110111
[12,6,11,10,9,8,5,7,4,3,2,1] => [[1,3],[2,8],[4],[5],[6],[7],[9],[10],[11],[12]] => 10111101111
[3,5,6,2,4,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => 0010001
[3,5,6,7,2,4,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,5,7,6,8,2,4,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,5,7,2,6,8,4,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[3,5,2,7,6,8,4,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,5,7,4,2,6,8,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,5,4,7,2,6,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,4,5,7,2,6,8,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[3,4,5,7,2,8,6,1] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,5,4,7,8,2,6,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,5,4,7,2,8,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,2,5,7,4,8,6,1] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,5,7,4,2,8,6,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[3,5,7,8,4,2,6,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[2,3,5,7,8,4,6,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,5,2,7,8,6,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,5,7,8,2,6,4,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[3,5,7,8,6,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[3,2,5,6,7,8,9,1,4] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[4,2,5,6,7,3,8,1] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[8,6,1,4,3,5,2,7] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[6,1,8,4,3,5,2,7] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[5,1,6,4,8,2,3,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[8,1,4,2,5,3,6,7] => [[1,3,5,7,8],[2,6],[4]] => 1010100
[2,8,4,1,5,3,6,7] => [[1,2,5,7,8],[3,6],[4]] => 0110100
[8,4,1,3,5,2,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[4,1,8,3,5,2,6,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[8,3,1,2,5,4,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[3,1,8,2,5,4,6,7] => [[1,3,5,7,8],[2,4],[6]] => 1010100
[4,2,5,1,8,7,6,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[5,2,4,8,1,7,6,3] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[7,3,2,4,6,8,1,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,4,8,6,7,2,5,3] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,4,5,7,3,8,2,6] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,6,8,1,2,5,3,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[3,5,6,8,2,1,4,7] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[8,2,5,4,1,3,7,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[2,4,5,8,6,3,1,7] => [[1,2,3,4,8],[5],[6],[7]] => 0001110
[5,4,8,2,3,1,7,6] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,7,5,8,2,3,1,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,6,7,5,1,8,3,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[1,7,3,6,5,8,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,3,4,2,6,7,1,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,5,3,8,6,2,1,4] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[7,3,1,8,2,6,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,6,7,5,2,8,3,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[5,8,7,2,4,3,1,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,1,2,8,6,7,3,4] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[2,5,7,8,6,1,4,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[7,2,6,8,4,5,1,3] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[5,1,7,6,8,2,3,4] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[1,7,6,2,4,3,8,5] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[7,1,6,2,4,5,3,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[5,7,1,6,2,3,4,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[6,2,5,8,3,4,1,7] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[5,6,8,7,1,3,2,4] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[1,5,3,4,8,2,6,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,1,3,6,5,8,4,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[5,1,2,8,6,3,7,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[6,1,5,7,8,4,2,3] => [[1,3,4,5],[2,8],[6],[7]] => 1000110
[4,6,1,5,7,2,8,3] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[2,5,8,4,6,3,7,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,3,7,1,2,6,8,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[8,1,6,5,2,7,4,3] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,8,1,5,2,7,4,3] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[4,5,8,2,3,7,6,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[1,7,3,2,4,8,6,5] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[4,3,1,8,2,6,7,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[4,8,1,3,2,5,7,6] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[1,7,5,3,8,6,2,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[2,5,3,8,1,4,7,6] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[4,2,5,8,1,3,7,6] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[8,1,2,4,3,5,7,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[2,4,3,8,1,5,7,6] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[3,1,7,4,8,6,5,2] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[6,4,5,3,2,8,7,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[2,7,3,8,5,1,6,4] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[8,7,3,2,5,6,4,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[3,1,8,2,6,5,4,7] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[7,6,2,8,1,4,5,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[2,3,8,4,1,5,7,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[8,4,2,3,1,5,7,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,2,3,4,1,5,7,6] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[7,1,6,2,4,8,3,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[2,7,8,1,4,3,6,5] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[6,5,8,1,3,2,4,7] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[2,1,8,5,3,4,6,7] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,4,1,3,2,5,6,7] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[8,6,1,2,3,5,4,7] => [[1,4,5,6,8],[2],[3],[7]] => 1100010
[7,8,1,5,2,4,6,3] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[2,8,6,3,1,5,4,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[5,7,2,8,4,1,6,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[2,5,6,3,8,1,4,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[7,4,5,6,8,1,3,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[7,6,8,1,4,5,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[7,5,1,8,4,6,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[1,7,8,5,6,4,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[2,8,1,7,4,5,3,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[7,3,6,2,5,4,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[1,6,2,3,5,8,4,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,8,5,6,4,3,7,2] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[2,6,8,4,5,1,7,3] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,6,5,7,8,1,3,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,5,8,6,4,7,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,3,2,1,7,8,4,6] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[8,4,1,3,6,7,2,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[1,6,5,3,8,4,7,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,6,2,3,5,1,4,8] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[6,2,5,3,4,8,1,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,2,5,3,4,8,7,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[2,6,5,3,4,8,1,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,3,4,8,1,7,2,6] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[5,1,3,4,8,7,2,6] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[1,5,3,4,8,7,2,6] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[5,1,3,8,4,7,6,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,3,8,1,4,7,6,2] => [[1,3,6],[2,5],[4,7],[8]] => 1010011
[4,3,5,8,1,7,6,2] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,6,5,4,8,1,2,7] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[3,6,5,4,8,2,7,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[3,5,2,4,8,7,6,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[2,5,3,6,8,4,1,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[4,6,2,5,1,7,8,3] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[2,3,1,7,4,8,6,5] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[1,8,3,6,4,2,7,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,1,7,4,8,5,3,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[8,1,7,3,2,5,4,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[7,8,5,2,6,4,3,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[8,1,2,5,7,4,6,3] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[8,2,5,3,6,1,4,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[6,8,7,4,1,5,2,3] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[8,6,4,7,5,1,3,2] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[6,1,2,4,7,8,3,5] => [[1,3,4,5,6],[2,8],[7]] => 1000010
[2,4,6,5,7,1,8,3] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[3,2,8,9,10,1,4,5,6,7] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[3,5,2,1,7,8,6,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[4,2,7,8,6,5,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[1,2,7,8,6,4,5,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,8,1,2,6,5,3,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[7,1,6,3,2,4,8,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[6,4,8,1,2,3,7,5] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[7,4,1,3,6,8,5,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,2,5,1,6,4,3,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[5,2,7,1,4,6,3,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[6,3,8,5,7,1,4,2] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[2,4,3,8,5,7,1,6] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[2,8,3,1,4,6,5,7] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[4,5,7,6,1,3,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,7,1,6,5,8,2,4] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[7,4,3,6,8,2,1,5] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[3,8,5,4,7,6,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[1,4,6,8,7,3,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,6,5,1,3,8,7,2] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,4,6,2,1,8,7,3] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[3,2,8,5,1,4,6,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[3,5,4,1,2,8,6,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[5,3,8,1,4,2,6,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[5,3,8,1,4,2,7,6] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[1,4,7,5,8,6,2,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[8,5,7,6,3,4,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[7,5,2,6,1,4,8,3] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[2,4,5,1,8,3,7,6] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[7,2,8,5,3,4,1,6] => [[1,3,6,8],[2,4],[5],[7]] => 1011010
[6,4,5,3,1,7,8,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,3,5,6,4,1,8,2] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[2,3,4,7,8,9,1,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[2,3,6,7,8,9,1,4,5] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[2,5,6,7,8,9,1,3,4] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[2,3,4,5,8,9,10,1,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[2,3,4,7,8,9,10,1,5,6] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[2,1,6,7,8,9,3,4,5] => [[1,3,4,5,6],[2,7,8,9]] => 10000100
[2,3,6,7,8,9,10,1,4,5] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[2,5,6,7,8,9,10,1,3,4] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[2,5,6,3,4,1,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[4,6,2,1,5,8,3,7] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[4,6,7,2,3,8,5,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[4,5,3,7,8,1,2,6] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[2,3,5,8,1,6,4,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,7,4,5,8,3,6,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[2,8,5,6,3,1,4,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[4,8,2,6,1,5,7,3] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[2,3,7,8,1,5,4,6] => [[1,2,3,4],[5,6,8],[7]] => 0001010
[5,2,6,7,8,3,1,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[5,6,2,7,8,3,1,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,3,7,5,8,4,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,7,8,5,1,4,6,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[2,5,6,7,1,8,4,3] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[6,4,7,8,1,2,5,3] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[7,5,8,1,2,3,6,4] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[1,2,8,7,4,6,5,3] => [[1,2,3,6],[4],[5],[7],[8]] => 0011011
[5,1,4,8,7,3,6,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[4,3,1,8,7,5,6,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[4,3,2,7,6,1,5,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[7,2,6,5,3,1,4,8] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[1,3,7,6,2,4,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,3,8,2,7,4,6,5] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[8,2,7,1,6,4,3,5] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[4,3,2,8,1,7,5,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,5,4,1,6,3,8,2] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[1,6,5,3,2,4,8,7] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[1,7,3,5,2,4,8,6] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[4,3,7,2,5,1,6,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[5,1,4,3,2,6,8,7] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,2,1,3,5,4,6,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[8,3,7,5,4,2,6,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[1,6,8,7,5,2,3,4] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,3,6,2,5,4,8,7] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,2,7,3,8,4,9,5,10,6] => [[1,2,3,5,7,9],[4,6,8,10]] => 001010101
[4,5,7,6,3,1,8,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[4,6,7,5,1,3,8,2] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[3,6,5,1,4,7,8,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[4,6,7,3,1,5,8,2] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[5,4,1,8,7,3,6,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[6,2,4,7,5,3,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[6,2,5,1,8,7,3,4] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[3,2,6,1,5,8,7,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[4,2,3,6,7,5,1,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[6,2,3,5,7,4,1,8] => [[1,3,4,5,8],[2],[6],[7]] => 1000110
[1,6,3,8,4,7,2,5] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[8,1,5,2,4,7,3,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[7,5,8,1,4,2,3,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[4,1,2,3,6,5,8,7,9] => [[1,3,4,5,7,9],[2,6,8]] => 10001010
[1,3,4,8,5,6,2,7] => [[1,2,3,4,6,8],[5],[7]] => 0001010
[3,2,7,1,8,6,5,4] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,2,4,1,5,7,8,3] => [[1,3,5,6,7],[2,8],[4]] => 1010001
[5,8,4,1,3,6,7,2] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[6,7,2,3,8,1,4,5] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,2,8,1,7,4,6,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[2,5,4,7,3,1,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,6,3,1,2,5,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[7,4,6,8,3,1,2,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,5,4,7,3,1,2,6] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[7,3,2,1,5,4,8,6] => [[1,5,7],[2,6,8],[3],[4]] => 1110101
[2,5,6,4,8,1,3,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[5,4,1,6,2,3,7,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,3,6,5,2,4,7,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[5,4,1,2,7,6,3,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,8,7,3,1,2,4,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,7,8,1,4,5,3,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[4,1,2,8,7,3,6,5] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[6,1,2,4,3,8,7,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[3,7,8,1,2,4,6,5] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[7,3,4,1,2,6,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,4,3,1,2,6,5,7] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[3,8,2,7,4,5,1,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[8,6,2,3,5,4,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[8,2,6,1,3,5,4,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,4,3,7,2,5,6,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,3,1,7,4,5,2,6] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,2,4,5,1,7,3,6] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[6,8,2,4,5,1,7,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[4,3,8,1,7,5,6,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[8,4,3,7,1,5,6,2] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,3,4,7,2,6,5,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,1,3,7,6,4,5,2] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[8,3,7,1,4,5,6,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,7,3,6,1,2,5,4] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,3,7,6,2,4,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[8,7,2,3,6,1,5,4] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[8,2,7,1,3,4,6,5] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,1,8,4,2,3,7,6] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[8,2,4,7,3,1,6,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[8,2,7,6,3,1,4,5] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[6,8,1,4,7,3,2,5] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[8,5,7,2,6,3,1,4] => [[1,3,8],[2,5],[4],[6],[7]] => 1010110
[5,8,2,7,3,1,6,4] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[8,1,2,6,7,5,4,3] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[8,4,1,7,5,6,2,3] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[8,2,4,7,6,5,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,2,7,6,4,5,1,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,4,7,2,3,6,5,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,2,4,7,3,6,5,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,1,7,6,4,5,2,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,1,2,7,6,4,5,3] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[8,1,4,7,3,6,5,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[2,3,1,9,8,7,6,5,4] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[3,4,2,1,9,8,7,6,5] => [[1,2,5],[3,6],[4,7],[8],[9]] => 01101111
[4,5,3,2,1,9,8,7,6] => [[1,2,6],[3,7],[4,8],[5,9]] => 01110111
[5,6,4,3,2,1,9,8,7] => [[1,2,7],[3,8],[4,9],[5],[6]] => 01111011
[6,7,5,4,3,2,1,9,8] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[2,8,1,5,3,7,6,4] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[1,8,2,4,7,5,6,3] => [[1,2,4,5,7],[3],[6],[8]] => 0100101
[2,3,8,4,7,1,6,5] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,8,2,3,5,6,4,7] => [[1,2,4,5,6,8],[3],[7]] => 0100010
[1,4,7,6,2,3,5,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[1,7,6,2,3,8,4,5] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[1,8,2,3,7,6,4,5] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,7,3,8,6,2,5,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[5,8,2,3,7,4,1,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,2,8,3,7,6,1,5] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,3,5,6,4,8,2,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[4,6,1,8,2,7,5,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[3,4,8,5,6,1,2,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,7,6,2,5,4,8,3] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[5,6,1,7,4,3,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[3,7,2,1,5,6,8,4] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[3,1,5,6,4,2,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[8,1,6,4,3,5,2,7] => [[1,3,6,8],[2],[4],[5],[7]] => 1011010
[2,1,6,5,3,8,7,4] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[3,7,5,6,4,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[6,1,4,3,7,5,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[3,8,6,4,5,2,7,1] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[4,5,8,6,2,3,7,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,6,8,5,3,7,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,5,7,2,8,6,3,1] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[3,7,4,5,1,6,8,2] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[4,6,8,1,2,5,7,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[4,6,8,5,1,3,7,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[3,7,4,5,2,8,6,1] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[3,7,8,4,6,1,5,2] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[4,5,7,2,1,6,8,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[4,5,1,6,8,3,7,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[8,3,5,4,6,1,2,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,4,5,6,1,7,2,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,7,4,5,2,6,8,3] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[3,4,5,6,7,1,8,2,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,4,2,6,5,3,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,1,5,8,4,6,2,7] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[8,2,6,3,4,1,5,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[4,6,5,8,2,1,3,7] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[1,4,8,3,5,6,2,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,8,7,4,2,3,6,5] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,3,1,8,5,7,2,6] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[7,3,2,4,8,1,6,5] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,7,2,4,5,8,1,6] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[3,2,7,4,6,1,8,5] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[8,3,2,4,6,1,7,5] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,3,2,4,5,7,1,6] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[7,4,6,2,1,3,8,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[3,6,7,2,4,1,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,4,8,7,6,2,3,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,2,3,8,7,1,6,4] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[7,5,2,4,1,3,8,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[7,2,6,8,5,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[8,2,3,4,1,6,7,5] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[7,4,3,8,1,6,5,2] => [[1,4],[2,6],[3,7],[5,8]] => 1101011
[6,5,1,4,3,8,7,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[4,7,6,2,5,8,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[6,3,2,4,5,8,1,7] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[2,6,4,5,8,3,1,7] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[3,7,4,8,6,2,5,1] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[7,3,5,2,8,1,4,6] => [[1,3,5],[2,7,8],[4],[6]] => 1010100
[1,5,8,7,4,2,3,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[1,7,2,4,5,8,6,3] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[1,4,6,8,7,2,5,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[1,6,2,7,5,3,4,8] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,3,7,2,6,4,5,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,7,3,2,8,5,6,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[1,6,5,2,4,8,3,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,7,3,8,4,2,5,6] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,6,2,4,7,5,8,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,6,2,7,4,3,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,5,8,2,3,6,4,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[6,8,9,1,2,3,4,5,7] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[5,8,9,1,2,3,4,6,7] => [[1,2,3,7,8,9],[4,5,6]] => 00100000
[2,5,3,6,7,1,4,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[6,4,1,5,7,2,3,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,4,1,5,7,3,8,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[1,2,7,3,8,5,6,4] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[7,4,1,6,3,8,2,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[1,5,7,4,3,8,6,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[2,7,3,1,4,5,8,6] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,3,4,5,1,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[2,3,4,1,6,5,8,7,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[2,3,4,5,6,7,1,9,8,10] => [[1,2,3,4,5,6,8,10],[7,9]] => 000001010
[2,3,4,5,1,8,6,9,7] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[2,3,4,1,7,5,8,6,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[2,3,4,5,1,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[6,5,8,3,2,7,1,4] => [[1,3],[2,6],[4,8],[5],[7]] => 1011010
[8,4,3,1,7,6,5,2] => [[1,5],[2,6],[3,7],[4],[8]] => 1110111
[1,2,6,7,5,3,4,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[3,4,5,6,7,9,1,8,2] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,4,5,6,8,2,7,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[3,4,5,6,7,8,10,1,9,2] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[3,4,5,6,7,9,2,8,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,4,5,6,7,1,9,8,2] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[7,2,1,4,5,6,3,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,5,6,7,3,4,2,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[4,6,8,5,2,1,7,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[1,6,7,8,2,4,5,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[5,7,8,3,2,4,6,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[5,7,8,2,3,1,6,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,5,2,7,8,6,1,3] => [[1,2,4,5],[3,6],[7,8]] => 0100110
[1,3,5,8,7,2,6,4] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[6,4,1,8,5,7,3,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,1,3,8,7,5,2,6] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,5,1,6,7,2,4,3] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[3,6,7,2,1,5,8,4] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[2,5,6,1,3,8,7,4] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[7,2,5,6,1,3,8,4] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[6,4,1,2,5,8,3,7] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[4,7,3,5,2,6,8,1] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[2,3,5,4,7,1,8,6] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[6,8,4,1,5,7,3,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[8,1,6,2,3,7,5,4] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[2,8,3,6,4,1,7,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,5,3,4,8,2,1,7] => [[1,4,5],[2,8],[3],[6],[7]] => 1100110
[5,4,8,7,3,6,2,1] => [[1,3],[2,4],[5,6],[7],[8]] => 1011011
[3,4,5,1,2,6,7,8,9] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[5,2,7,6,8,3,4,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[8,4,5,2,7,3,6,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[6,3,7,4,5,2,8,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,3,4,2,8,5,6,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[4,3,6,5,8,2,7,1] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[8,2,7,4,5,3,6,1] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[7,2,8,4,5,3,6,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[6,3,8,2,7,4,5,1] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[3,2,8,4,7,5,6,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[8,3,6,2,7,4,5,1] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[4,2,3,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[1,7,8,4,3,6,5,2] => [[1,2,3],[4,6],[5,7],[8]] => 0011011
[1,7,8,3,6,5,4,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[5,8,1,7,2,4,3,6] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[2,5,7,3,8,1,4,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[8,3,5,2,1,6,7,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[2,6,4,7,1,8,5,3] => [[1,2,4,6],[3,7],[5,8]] => 0101011
[1,6,5,7,3,8,2,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[1,8,5,3,7,6,2,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,4,2,3,8,7,5,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[6,1,4,2,7,8,3,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[6,5,1,3,7,8,4,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,7,4,2,3,8,5,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,8,7,3,2,4,6,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,1,3,2,6,8,4,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,7,1,4,6,8,2,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[2,4,1,7,5,6,3,8] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[1,4,3,7,6,2,8,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[1,6,2,5,7,3,8,4] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,4,3,8,2,5,7,6] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[1,5,7,3,6,4,2,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,6,7,2,4,8,3,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[3,7,2,8,4,1,5,6] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[5,3,4,1,7,8,6,2] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[4,7,6,5,8,2,3,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[1,2,6,8,4,3,5,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[7,2,6,3,1,8,4,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[5,8,4,1,3,7,2,6] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[3,4,2,1,6,8,5,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[8,1,3,5,6,4,7,2] => [[1,3,4,5,7],[2],[6],[8]] => 1000101
[3,4,7,1,5,6,2,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[4,8,2,6,5,3,7,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[4,8,7,2,5,6,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[5,8,6,4,7,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => 0110111
[8,5,2,3,1,6,7,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[2,8,6,3,5,1,7,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[8,3,2,6,4,1,7,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[8,4,1,5,3,6,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,3,5,1,4,6,7,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[8,5,1,3,4,6,7,2] => [[1,4,5,6,7],[2],[3],[8]] => 1100001
[3,8,6,2,5,4,7,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[3,8,4,6,5,2,7,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[8,1,7,4,2,5,3,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,3,2,5,1,4,7,6] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[8,4,5,1,2,6,7,3] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,1,5,3,2,6,7,4] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[8,1,5,2,4,6,7,3] => [[1,3,5,6,7],[2],[4],[8]] => 1010001
[5,2,6,4,1,3,8,7] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[8,6,4,7,1,3,5,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[2,1,8,5,4,3,7,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[6,4,8,5,3,2,7,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[9,10,6,7,4,5,2,3,1,8] => [[1,2,10],[3,4],[5,6],[7,8],[9]] => 010101010
[8,5,4,6,2,7,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[6,8,5,4,7,2,3,1] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[2,5,7,3,4,8,1,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[5,2,4,7,8,1,3,6] => [[1,3,4,5],[2,7,8],[6]] => 1000100
[8,5,9,3,6,1,2,4,7] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000
[9,7,5,4,1,3,8,2,6] => [[1,6,7],[2,9],[3],[4],[5],[8]] => 11110010
[8,9,4,5,10,1,2,3,6,7] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000
[8,4,3,9,10,1,2,5,6,7] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000
[9,6,10,1,3,7,8,2,4,5] => [[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100
[9,10,6,7,4,5,1,2,3,8] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000
[9,6,4,10,3,7,1,2,5,8] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000
[10,1,8,9,6,7,4,5,2,3] => [[1,3,4],[2,6],[5,8],[7,10],[9]] => 100101010
[10,8,6,5,4,1,3,9,2,7] => [[1,7,8],[2,10],[3],[4],[5],[6],[9]] => 111110010
[10,8,7,6,5,4,3,1,2,9] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[4,8,5,6,1,2,7,3] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[2,5,6,8,7,1,4,3] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,6,8,1,5,2,7,3] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[8,2,3,6,4,1,7,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[2,3,7,5,8,6,1,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[3,8,5,1,2,4,7,6] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[1,3,6,4,8,2,7,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,2,3,4,6,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 000010000
[1,2,3,4,5,6,8,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[1,7,6,2,8,5,3,4] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,5,8,6,4,7,2,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,6,2,8,1,7,3,4] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[6,8,4,5,1,3,7,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[5,2,3,8,1,4,6,7] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[1,6,8,3,2,4,5,7] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[9,6,5,4,3,2,1,7,8] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[10,7,6,5,4,3,2,1,8,9] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100
[9,8,5,4,3,2,1,6,7] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[8,6,5,2,4,3,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => 1110101
[6,2,5,3,7,4,8,1] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,5,4,2,6,3,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,5,3,2,6,4,7,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[7,4,6,5,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,3,6,5,8,2,4,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,3,6,4,8,2,5,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,3,5,4,8,2,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[7,3,6,8,4,5,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[1,6,5,7,4,2,8,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,2,7,4,8,5,6,3] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,6,7,4,8,5,1,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,5,8,6,4,3,7,1] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[6,4,2,5,7,1,8,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[9,1,2,3,4,5,8,7,6] => [[1,3,4,5,6,7],[2],[8],[9]] => 10000011
[8,1,4,7,3,5,6,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[8,3,7,2,4,5,6,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[10,1,2,3,4,5,6,9,8,7] => [[1,3,4,5,6,7,8],[2],[9],[10]] => 100000011
[9,1,2,3,4,7,8,6,5] => [[1,3,4,5,6,7],[2],[8],[9]] => 10000011
[9,1,2,3,6,8,5,7,4] => [[1,3,4,5,6],[2,8],[7],[9]] => 10000101
[8,1,4,5,7,3,6,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[9,3,8,2,4,5,6,7,1] => [[1,3,6,7,8],[2,5],[4],[9]] => 10100001
[5,6,3,4,2,8,7,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[2,5,7,4,6,8,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[2,5,6,4,1,3,8,7] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,6,1,3,5,7,2,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[3,2,7,5,8,1,6,4] => [[1,3,5],[2,4,7],[6,8]] => 1010101
[4,3,6,8,5,2,1,7] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[4,5,3,2,1,8,6,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,6,5,8,1,7,4,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,1,6,8,5,2,3,7] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[4,5,2,8,6,7,1,3] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[4,5,2,8,6,7,3,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[3,5,8,6,2,4,7,1] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[2,5,1,6,4,8,3,7] => [[1,2,4,6],[3,5,8],[7]] => 0101010
[3,2,4,5,8,6,1,7] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,5,2,1,3,8,6,7] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[4,2,3,6,8,5,1,7] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[4,5,1,3,2,8,6,7] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,4,5,8,6,1,7,2] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[3,4,5,8,6,1,2,7] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[6,4,1,3,7,8,2,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,3,1,2,5,4,8,7] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,2,6,4,1,3,7,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[1,5,8,2,4,3,7,6] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,3,7,8,2,6,5,1] => [[1,3,4],[2,6],[5,7],[8]] => 1001011
[3,8,5,1,2,6,7,4] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,4,7,8,3,6,5,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[5,4,7,8,3,6,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[6,8,1,3,2,5,7,4] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[1,4,8,5,7,2,3,6] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,8,7,3,2,4,5,6] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[8,6,2,7,3,4,1,5] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[8,6,2,7,3,4,5,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,6,3,2,8,7,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,1,6,7,8,3,2,4] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[1,5,6,3,7,2,4,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,5,6,7,4,2,3,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[5,1,6,7,3,4,2,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[8,6,1,7,3,4,5,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[6,8,5,1,7,4,2,3] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,4,2,3,5,7,6,1] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,8,5,2,3,1,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[5,4,8,3,1,2,6,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,4,7,3,2,5,6,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[6,8,5,1,7,3,4,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,2,7,3,8,1,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[8,4,2,6,7,1,5,3] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[1,7,8,3,6,5,2,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[4,6,7,5,1,8,2,3] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[3,5,2,6,8,7,4,1] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[7,3,6,8,4,1,2,5] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[6,4,2,3,7,5,8,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,3,7,5,1,2,8,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[7,2,5,4,8,6,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,2,3,8,7,4,5,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[7,1,2,8,4,6,5,3] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[3,5,8,1,2,7,6,4] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[1,4,3,6,8,5,2,7] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[7,6,2,8,5,3,4,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[6,8,3,5,4,7,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[8,2,7,6,4,1,3,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[8,3,7,5,1,6,2,4] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,5,7,1,4,2,6,3] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,7,1,5,6,3,2,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[4,5,7,1,6,3,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[4,6,5,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,6,7,2,5,8,4,1] => [[1,2,3,6],[4,5],[7],[8]] => 0010011
[5,3,6,7,4,8,1,2] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[4,2,7,8,3,6,5,1] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[4,2,7,8,5,6,1,3] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[5,4,3,7,8,1,6,2] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,5,7,8,4,2,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,6,7,3,2,8,1,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,6,5,3,7,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,6,2,4,7,8,3,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[5,6,3,2,8,4,7,1] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[5,6,2,8,3,4,7,1] => [[1,2,4,7],[3,5,6],[8]] => 0101001
[3,7,4,8,1,6,5,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[5,2,4,8,6,7,3,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,2,6,4,8,7,3,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,4,7,8,6,5,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,4,5,6,8,9,1,7,2] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,4,6,7,8,9,1,5,2] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,5,6,7,8,9,1,4,2] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[4,5,6,7,8,9,1,3,2] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,4,5,6,7,9,10,1,8,2] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[3,4,5,7,8,9,10,1,6,2] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[5,2,6,7,8,1,4,3] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[3,4,6,7,8,9,10,1,5,2] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[4,5,6,7,8,9,10,1,3,2] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[4,8,2,7,5,3,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[1,2,4,6,5,8,3,7] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[5,4,2,3,1,7,8,6] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[3,5,8,1,7,4,2,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[5,8,6,1,7,2,3,4] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[5,1,4,3,8,2,6,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[8,4,7,5,6,2,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => 1010110
[3,8,6,7,5,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[8,2,5,4,7,3,6,1] => [[1,3,5],[2,7],[4],[6],[8]] => 1010101
[4,2,8,7,3,6,5,1] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[3,7,8,6,1,4,5,2] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[4,6,7,8,2,1,5,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,7,6,3,8,1,5,2] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,8,1,4,6,2,5,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[2,4,5,3,8,7,1,6] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[4,7,5,6,2,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[8,7,5,1,6,3,2,4] => [[1,5,8],[2,6],[3],[4],[7]] => 1110110
[7,8,6,2,3,5,1,4] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[2,8,4,6,7,3,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[4,1,6,7,8,2,5,3] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[8,6,3,4,1,2,7,5] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[2,5,8,4,6,1,3,7] => [[1,2,3,8],[4,5],[6,7]] => 0010100
[4,7,8,6,5,1,3,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,8,4,7,3,5,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[7,4,5,8,3,6,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,4,7,3,5,6,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[3,6,4,2,8,1,7,5] => [[1,2,5],[3,7],[4,8],[6]] => 0110101
[3,8,6,2,1,7,4,5] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,1,8,2,4,6,5,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[8,1,7,6,2,5,4,3] => [[1,3,6],[2],[4],[5],[7],[8]] => 1011011
[8,5,4,3,7,6,1,2] => [[1,5],[2,6],[3,8],[4],[7]] => 1110110
[4,8,1,3,6,7,5,2] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[3,5,8,6,1,7,4,2] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[8,1,4,7,5,2,6,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[1,4,8,6,7,3,5,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,1,6,7,8,5,3,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,7,8,6,4,1,5,2] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[5,4,2,3,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]] => 11000001
[6,5,4,2,3,7,8,9,1] => [[1,5,6,7,8],[2],[3],[4],[9]] => 11100001
[7,6,5,4,2,3,8,9,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => 11110001
[4,6,1,5,7,2,3,8] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,8,5,3,2,7,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[5,4,8,1,3,7,2,6] => [[1,3,6],[2,5],[4,8],[7]] => 1010010
[8,4,5,3,1,7,2,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[7,4,5,3,1,8,6,2] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[5,6,8,7,2,4,3,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[5,7,8,6,4,2,3,1] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[6,8,7,5,1,3,2,4] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[3,8,2,6,7,5,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,7,6,3,8,2,5,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[6,7,4,1,8,2,5,3] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[5,7,6,8,3,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[7,6,4,2,8,1,5,3] => [[1,5],[2,7],[3,8],[4],[6]] => 1110101
[6,3,4,8,7,1,2,5] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[2,7,4,8,1,6,3,5] => [[1,2,4],[3,6,8],[5,7]] => 0101010
[5,3,1,6,7,8,2,4] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[3,4,7,8,6,1,2,5] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[2,1,4,7,8,6,3,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[2,4,5,8,1,6,3,7] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[3,4,6,8,2,5,7,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[1,8,5,6,4,2,3,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,8,7,6,2,4,5,3] => [[1,2,6,7],[3],[4],[5],[8]] => 0111001
[6,4,8,5,7,3,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[1,6,4,7,2,5,8,3] => [[1,2,4,7],[3,6],[5,8]] => 0101001
[2,7,5,1,8,6,3,4] => [[1,2,5],[3,6,8],[4,7]] => 0110110
[4,7,1,6,5,3,8,2] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[1,7,5,6,4,8,2,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,4,8,5,7,3,1,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[8,3,1,4,6,2,7,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[7,2,6,4,5,8,1,3] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,6,7,8,9,1,2,3,5] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[5,7,8,9,1,2,3,4,6] => [[1,2,3,4,9],[5,6,7,8]] => 00010000
[2,7,1,5,3,8,6,4] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[3,5,7,2,8,4,1,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[2,4,3,8,5,1,7,6] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[7,3,2,1,4,8,6,5] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[2,8,3,4,1,7,6,5] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[4,7,6,8,2,5,3,1] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,6,7,1,4,5,8,3] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[8,7,2,6,1,5,3,4] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[7,1,3,8,2,6,4,5] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[6,2,5,3,4,7,1,8] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[2,7,3,4,1,5,8,6] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[2,5,8,1,6,7,3,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[6,2,8,3,4,5,1,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[3,6,4,1,2,5,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[3,5,4,1,6,2,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,5,7,2,8,3,1,6] => [[1,2,3,5],[4,6,8],[7]] => 0010110
[3,5,1,7,6,2,8,4] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[8,3,6,2,7,5,4,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,4,2,6,5,3,7,1] => [[1,4,7],[2,5],[3],[6],[8]] => 1101101
[5,4,2,7,1,8,6,3] => [[1,4,6],[2,7],[3,8],[5]] => 1101011
[4,1,7,6,5,3,2,8] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[2,3,6,7,1,8,5,4] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[3,6,1,2,7,8,5,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[4,5,1,8,7,6,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[8,4,5,2,7,6,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[4,1,3,6,7,5,2,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[3,1,4,5,7,6,2,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,5,1,3,6,8,7,2] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,8,5,1,2,4,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[8,5,1,2,4,3,6,7] => [[1,4,5,7,8],[2],[3],[6]] => 1100100
[5,8,4,1,2,3,6,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[3,5,8,1,4,2,7,6] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[2,8,5,7,1,4,3,6] => [[1,2,4],[3,6,8],[5],[7]] => 0101010
[4,8,7,5,1,2,3,6] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,1,2,4,6,3,7,5] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[7,6,1,4,2,3,8,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[6,1,2,7,8,4,3,5] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[7,8,1,2,5,3,4,6] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[1,8,4,7,5,2,3,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,4,7,2,1,6,3,5] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[4,5,8,2,1,6,7,3] => [[1,2,3,7],[4,6],[5,8]] => 0011001
[7,4,2,5,3,6,1,8] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[3,1,6,7,5,2,4,8] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[8,4,2,5,3,6,7,1] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[4,8,1,5,3,6,7,2] => [[1,2,6,7],[3,4],[5],[8]] => 0101001
[4,1,7,5,2,6,3,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[7,1,5,3,6,8,2,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,5,2,6,1,8,3,7] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[5,1,8,6,7,3,4,2] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[5,4,8,2,1,3,6,7] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[1,4,8,3,2,6,5,7] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[1,3,8,4,2,7,5,6] => [[1,2,3,6,8],[4,7],[5]] => 0011010
[7,2,8,3,1,4,5,6] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[8,1,3,2,7,5,4,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[2,3,4,7,8,9,6,5,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[2,3,6,7,8,9,5,4,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[2,5,6,7,8,9,4,3,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[2,3,4,5,6,1,9,8,7] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[2,3,4,5,1,9,8,7,6] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[2,3,4,5,6,9,10,8,7,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[2,3,4,5,8,9,10,7,6,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[2,3,4,7,8,9,10,6,5,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[2,3,6,7,8,9,10,5,4,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[2,5,6,7,8,9,10,4,3,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[9,10,2,4,6,8,1,3,5,7] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[7,8,2,4,6,10,1,3,5,9] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[9,7,10,2,4,6,8,1,3,5] => [[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100
[5,6,2,4,8,10,1,3,7,9] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000
[5,6,9,10,2,4,8,1,3,7] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[7,5,8,2,4,6,10,1,3,9] => [[1,3,6,7],[2,5,10],[4,9],[8]] => 101000100
[8,9,6,10,5,7,2,4,1,3] => [[1,2,4],[3,6],[5,8],[7,10],[9]] => 010101010
[3,4,2,6,8,10,1,5,7,9] => [[1,2,4,5,6],[3,8,9,10],[7]] => 010001000
[3,4,9,10,2,6,8,1,5,7] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[9,3,4,7,10,2,6,8,1,5] => [[1,3,4,5],[2,7,8],[6,10],[9]] => 100010010
[8,9,10,3,4,7,2,6,1,5] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[5,3,6,2,4,8,10,1,7,9] => [[1,3,6,7],[2,5,9,10],[4],[8]] => 101000100
[5,3,6,9,10,2,4,8,1,7] => [[1,3,4,5],[2,7,8],[6,10],[9]] => 100010010
[4,5,6,3,9,10,2,8,1,7] => [[1,2,3,5,6],[4,8],[7,10],[9]] => 001001010
[4,8,5,9,10,3,7,2,6,1] => [[1,2,4,5],[3,7],[6,9],[8],[10]] => 010010101
[7,8,9,5,10,4,6,3,2,1] => [[1,2,3,5],[4,7],[6],[8],[9],[10]] => 001010111
[3,10,11,12,4,7,9,2,6,8,1,5] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 00010010010
[5,3,6,2,4,8,10,12,1,7,9,11] => [[1,3,6,7,8],[2,5,10,11,12],[4],[9]] => 10100001000
[5,10,11,12,3,6,9,2,4,8,1,7] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 00010010010
[7,6,1,8,2,5,4,3] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[8,4,1,6,7,3,5,2] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[5,8,4,2,1,6,3,7] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,6,4,1,2,5,3,8] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[5,4,2,8,1,6,3,7] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[8,7,2,6,4,5,3,1] => [[1,4,6],[2],[3],[5],[7],[8]] => 1101011
[7,2,8,4,3,6,1,5] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[1,7,5,4,8,6,2,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[4,8,6,3,5,2,1,7] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[5,8,6,3,2,7,1,4] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[5,7,6,3,2,4,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[5,7,3,2,8,6,4,1] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,5,1,6,8,2,7,3] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[1,2,4,5,6,8,10,9,3,7] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[1,2,3,5,7,8,10,6,9,4] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[1,2,4,5,7,8,10,3,9,6] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[1,2,4,6,7,5,10,8,3,9] => [[1,2,3,4,5,7,10],[6,8],[9]] => 000010110
[1,3,4,6,7,2,10,8,5,9] => [[1,2,3,4,5,7,10],[6,8],[9]] => 000010110
[1,2,3,5,6,9,8,10,7,4] => [[1,2,3,4,5,6,8],[7],[9],[10]] => 000001011
[1,2,4,5,6,9,8,10,3,7] => [[1,2,3,4,5,6,8],[7,10],[9]] => 000001010
[1,2,3,5,7,9,6,10,8,4] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[1,2,4,5,7,9,3,10,8,6] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[1,3,4,6,8,2,9,5,10,7] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,2,3,6,5,9,7,10,8,4] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[1,2,4,6,3,9,7,10,8,5] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[1,3,2,6,4,9,7,10,8,5] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,6,3,7,2,4,8,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[8,9,7,6,5,4,3,1,2] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[8,7,9,6,5,4,3,1,2] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[9,7,8,6,5,4,3,1,2] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[4,3,1,6,7,2,5,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[6,3,1,5,7,2,4,8] => [[1,4,5,8],[2,6,7],[3]] => 1100100
[5,2,1,4,8,6,7,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[4,5,2,1,3,7,6,8] => [[1,2,6,8],[3,5,7],[4]] => 0110010
[8,2,7,4,1,6,5,3] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[3,2,8,4,1,6,5,7] => [[1,3,6,8],[2,4],[5,7]] => 1011010
[7,1,8,4,2,3,6,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[2,7,6,4,5,1,8,3] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[3,6,8,1,5,7,4,2] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,8,3,1,6,7,4,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,5,6,8,2,1,7,3] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[4,5,6,8,1,3,7,2] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,5,8,3,2,1,7,6] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,5,1,3,2,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => 0101000
[4,7,3,2,1,6,5,8] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[4,7,8,3,5,1,6,2] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[4,7,1,3,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[4,8,3,2,1,6,7,5] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,2,8,1,4,6,7,3] => [[1,3,6,7],[2,5],[4,8]] => 1010001
[5,6,3,7,8,1,4,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[5,7,1,4,3,6,2,8] => [[1,2,6,8],[3,4],[5],[7]] => 0101010
[6,2,3,7,1,5,4,8] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[6,2,8,1,5,4,7,3] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[6,1,3,4,5,2,7,8] => [[1,3,4,5,7,8],[2],[6]] => 1000100
[7,1,3,4,5,6,2,8] => [[1,3,4,5,6,8],[2],[7]] => 1000010
[7,2,5,1,3,6,4,8] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[6,5,2,7,8,4,3,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,5,3,6,4,2,1,8] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[1,3,6,7,5,2,4,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[1,5,2,6,8,7,3,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[3,2,1,5,6,7,8,9,4] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[4,3,2,1,6,7,8,9,5] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[5,4,3,2,1,7,8,9,6] => [[1,6,7,8],[2,9],[3],[4],[5]] => 11110001
[4,3,2,8,9,1,5,6,7] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000
[6,5,4,3,2,1,8,9,7] => [[1,7,8],[2,9],[3],[4],[5],[6]] => 11111001
[6,9,4,7,2,5,1,3,8] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100
[6,4,3,9,2,7,1,5,8] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100
[6,5,4,3,2,9,1,7,8] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100
[5,6,1,2,3,7,8,9,10,4] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[2,5,1,3,6,7,8,9,10,4] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[3,2,1,5,6,7,8,9,10,4] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[6,7,8,1,2,3,4,9,10,5] => [[1,2,3,7,8,9],[4,5,6,10]] => 001000001
[2,6,7,1,3,4,8,9,10,5] => [[1,2,3,7,8,9],[4,5,6,10]] => 001000001
[4,3,2,1,6,7,8,9,10,5] => [[1,5,6,7,8,9],[2,10],[3],[4]] => 111000001
[2,7,8,9,1,3,4,5,10,6] => [[1,2,3,4,9],[5,6,7,8,10]] => 000100001
[5,4,3,2,1,7,8,9,10,6] => [[1,6,7,8,9],[2,10],[3],[4],[5]] => 111100001
[8,3,4,9,10,1,2,5,6,7] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000
[4,3,2,8,9,1,5,6,10,7] => [[1,4,5,9],[2,7,8,10],[3],[6]] => 110010001
[6,5,4,3,2,1,8,9,10,7] => [[1,7,8,9],[2,10],[3],[4],[5],[6]] => 111110001
[5,9,10,2,6,7,1,3,4,8] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000
[9,5,6,3,4,10,1,2,7,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[5,3,9,2,6,10,1,4,7,8] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000
[5,4,3,2,9,10,1,6,7,8] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000
[7,6,5,4,3,2,1,9,10,8] => [[1,8,9],[2,10],[3],[4],[5],[6],[7]] => 111111001
[10,7,8,5,6,3,4,1,2,9] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100
[7,5,10,3,8,2,6,1,4,9] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100
[7,5,4,3,10,2,8,1,6,9] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100
[7,6,5,4,3,2,10,1,8,9] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100
[5,3,4,7,2,1,6,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[4,8,5,7,1,2,3,6] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,2,3,7,6,1,8,5] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,2,6,3,1,5,7,8] => [[1,3,6,7,8],[2,4],[5]] => 1011000
[4,6,3,2,5,8,7,1] => [[1,2,6],[3,5,7],[4],[8]] => 0110011
[5,8,4,3,2,6,1,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[1,5,7,4,8,6,2,3] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[6,1,5,7,3,8,2,4] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[1,2,7,8,6,4,3,5] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[3,5,1,7,8,6,2,4] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[5,2,4,1,7,6,8,3] => [[1,3,5,7],[2,6],[4,8]] => 1010101
[2,1,3,4,5,7,8,9,10,6] => [[1,3,4,5,6,7,8,9],[2,10]] => 100000001
[1,3,2,5,4,7,6,9,10,8] => [[1,2,4,6,8,9],[3,5,7,10]] => 010101001
[1,3,2,5,4,6,8,9,10,7] => [[1,2,4,6,7,8,9],[3,5,10]] => 010100001
[1,3,2,4,5,7,8,9,10,6] => [[1,2,4,5,6,7,8,9],[3,10]] => 010000001
[1,2,4,5,6,3,8,7,10,9] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,2,3,5,6,7,8,4,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 000000101
[9,3,4,5,6,7,8,2,1] => [[1,3,4,5,6,7],[2],[8],[9]] => 10000011
[2,3,4,5,6,10,8,9,7,1] => [[1,2,3,4,5,6,8],[7],[9],[10]] => 000001011
[10,3,4,5,6,7,8,9,2,1] => [[1,3,4,5,6,7,8],[2],[9],[10]] => 100000011
[5,4,3,8,1,7,2,6] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[7,3,1,5,6,8,4,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[2,9,1,3,4,5,6,7,10,8] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[9,3,1,2,4,5,6,7,10,8] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[7,2,3,1,6,8,4,5] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[5,7,8,1,6,2,3,4] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[1,6,4,2,7,3,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,4,2,5,8,6,3,7] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[4,8,2,1,5,7,3,6] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,2,7,1,6,3,4,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[4,8,2,5,1,6,3,7] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[5,8,1,2,4,6,3,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[5,1,7,3,6,4,2,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[3,2,7,5,6,1,4,8] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[3,2,7,1,6,4,5,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[6,3,1,7,5,4,2,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[6,2,8,7,3,4,5,1] => [[1,3,6,7],[2,4],[5],[8]] => 1011001
[9,3,4,5,6,7,2,1,8] => [[1,3,4,5,6,9],[2],[7],[8]] => 10000110
[7,3,4,8,5,6,2,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[7,3,6,8,4,5,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[10,3,4,5,6,7,8,2,1,9] => [[1,3,4,5,6,7,10],[2],[8],[9]] => 100000110
[5,6,2,8,3,1,7,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[1,4,7,5,6,2,8,3] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[1,7,4,8,3,5,6,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[5,3,1,4,8,6,2,7] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[5,2,4,8,3,1,6,7] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,4,5,1,8,6,2,3] => [[1,3,5],[2,6,8],[4,7]] => 1010110
[8,1,5,7,6,3,2,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[1,8,6,7,5,3,2,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,4,8,3,1,6,5,2] => [[1,3],[2,6],[4,7],[5,8]] => 1011011
[8,1,5,3,7,6,2,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[6,4,8,7,3,5,1,2] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[6,1,4,2,3,5,7,8] => [[1,3,5,6,7,8],[2],[4]] => 1010000
[7,1,4,3,8,6,5,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[6,1,5,7,2,8,3,4] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[1,8,2,6,7,4,3,5] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[1,6,2,7,3,8,4,9,5] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[1,8,5,2,9,6,3,10,7,4] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[7,2,4,1,8,5,3,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[7,3,2,1,4,6,8,5] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[4,7,2,6,1,8,3,5] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[7,5,3,2,1,6,8,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[6,8,1,3,4,2,5,7] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,6,1,4,7,8,2,5] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[2,5,7,1,3,6,4,8] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[1,4,7,2,5,3,6,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[4,5,3,1,2,6,8,7] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,5,1,3,8,2,6,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,1,5,3,2,7,6,8] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[7,3,5,1,4,2,6,8] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,2,1,7,4,3,8,5] => [[1,4,7],[2,5,8],[3,6]] => 1101101
[2,4,3,6,7,1,5,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[7,3,5,2,1,6,4,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[4,6,5,2,1,3,7,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[2,5,6,1,4,3,7,8] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[6,1,5,3,7,2,4,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[3,6,5,4,1,7,2,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[10,9,3,8,7,6,5,4,2,1] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => 110111111
[10,9,8,6,5,4,7,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => 111110111
[6,8,7,5,4,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => 0111110
[1,6,8,7,3,2,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[8,7,5,4,6,1,3,2] => [[1,5],[2,7],[3],[4],[6],[8]] => 1110101
[1,7,8,2,4,6,3,5] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[7,5,4,8,1,3,6,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[5,6,1,8,4,3,7,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[1,8,2,6,7,5,4,3] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[2,7,5,1,6,8,3,4] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[8,5,4,2,7,3,6,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[3,8,6,1,2,4,5,7] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[1,8,5,3,2,7,4,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,8,4,7,2,3,5,6] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[3,2,8,1,7,5,4,6] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,1,5,6,2,3,4,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[6,5,1,7,2,3,4,8] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[1,6,8,2,7,3,4,5] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[1,6,8,7,3,4,2,5] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[4,1,3,6,7,8,5,2] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[7,4,1,5,6,8,3,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[4,1,2,6,7,8,5,3] => [[1,3,4,5,6],[2,7],[8]] => 1000011
[3,4,5,8,9,1,2,6,7] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[3,4,7,8,9,1,2,5,6] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[3,6,7,8,9,1,2,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[3,4,5,6,7,10,1,2,8,9] => [[1,2,3,4,5,6,10],[7,8,9]] => 000001000
[3,4,5,6,9,10,1,2,7,8] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[3,4,5,8,9,10,1,2,6,7] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[1,3,7,8,9,2,4,5,6] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[3,4,7,8,9,10,1,2,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[2,6,7,8,9,1,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[3,6,7,8,9,10,1,2,4,5] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[6,3,7,1,8,2,4,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[2,1,4,3,6,5,10,7,9,8] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[2,1,4,3,10,5,6,8,9,7] => [[1,3,5,7,8,9],[2,4,6],[10]] => 101010001
[2,1,10,3,4,5,7,8,9,6] => [[1,3,5,6,7,8,9],[2,4],[10]] => 101000001
[4,1,3,2,6,5,8,7,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[8,6,3,1,4,2,7,5,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[6,1,2,4,5,3,8,7,10,9] => [[1,3,4,5,7,9],[2,8,10],[6]] => 100010101
[8,1,2,3,5,6,7,4,10,9] => [[1,3,4,5,6,7,9],[2,10],[8]] => 100000101
[8,6,3,1,4,2,7,5,10,9,12,11] => [[1,5,7,9,11],[2,6,8,10,12],[3],[4]] => 11101010101
[12,7,3,1,11,5,2,8,4,10,6,9] => [[1,5,8,10,12],[2,6,9,11],[3,7],[4]] => 11101101010
[1,5,4,7,8,3,6,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[5,1,4,7,8,3,6,2] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[4,8,1,5,6,2,3,7] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[5,6,4,1,7,3,8,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[4,3,7,8,2,5,1,6] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[3,7,8,5,4,2,1,6] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[1,7,4,5,6,8,3,2] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[7,2,4,5,6,8,3,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[2,7,4,5,6,8,3,1] => [[1,2,4,5,6],[3],[7],[8]] => 0100011
[2,4,7,8,3,1,6,5] => [[1,2,3,4],[5,7],[6,8]] => 0001101
[5,4,3,6,8,1,7,2] => [[1,4,5],[2,7],[3,8],[6]] => 1100101
[3,7,4,5,8,1,6,2] => [[1,2,4,5],[3,7],[6,8]] => 0100101
[1,4,3,5,6,8,2,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[1,4,6,5,8,2,7,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[4,6,1,7,3,2,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[1,7,3,6,4,2,8,5] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[4,7,3,5,1,2,8,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[1,6,4,2,3,5,8,7] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[4,8,3,5,2,1,6,7] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[10,9,7,6,5,4,3,8,2,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => 111111011
[1,6,8,4,7,5,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[4,7,1,6,8,2,3,5] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[4,6,5,8,2,3,7,1] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[7,1,8,2,4,5,3,6] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[5,7,8,2,3,4,1,6] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[5,2,3,8,7,1,4,6] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[8,7,1,3,2,6,4,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[2,7,6,4,8,3,1,5] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[2,6,3,7,5,8,4,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[7,5,1,2,3,8,4,6] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[3,2,4,1,5,6,7,8,9,10] => [[1,3,5,6,7,8,9,10],[2],[4]] => 101000000
[8,6,2,1,3,7,4,5] => [[1,5,6,8],[2,7],[3],[4]] => 1110010
[4,2,3,6,8,5,7,1] => [[1,3,4,5],[2,6,7],[8]] => 1000101
[4,7,3,2,6,5,1,8] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[4,3,7,8,2,1,6,5] => [[1,3,4],[2,7],[5,8],[6]] => 1001101
[4,8,7,2,1,5,6,3] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[7,3,8,2,5,1,6,4] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[4,5,3,8,6,1,2,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[6,3,5,8,4,1,2,7] => [[1,3,4],[2,7,8],[5],[6]] => 1001100
[7,3,8,4,5,1,2,6] => [[1,3,5,8],[2,4],[6,7]] => 1010100
[4,8,7,5,1,2,6,3] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[7,8,4,6,1,3,5,2] => [[1,2,7],[3,4],[5,6],[8]] => 0101001
[4,8,7,5,1,3,6,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[4,5,3,6,8,1,2,7] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[7,8,6,2,1,4,3,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[7,8,6,3,1,2,5,4] => [[1,2,7],[3,6],[4,8],[5]] => 0111001
[5,2,8,4,7,1,3,6] => [[1,3,5],[2,4,8],[6,7]] => 1010100
[7,3,1,2,8,6,5,4] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[8,7,1,3,2,4,5,6] => [[1,4,6,7,8],[2],[3],[5]] => 1101000
[6,8,2,1,4,5,3,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[2,1,4,3,6,5,10,7,8,9] => [[1,3,5,7,9,10],[2,4,6,8]] => 101010100
[2,1,4,3,10,5,6,7,8,9] => [[1,3,5,7,8,9,10],[2,4,6]] => 101010000
[6,5,2,1,4,3,8,7,10,9] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[6,5,2,1,4,3,10,7,8,9] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[10,9,2,1,4,5,6,7,8,3] => [[1,5,6,7,8,9],[2,10],[3],[4]] => 111000001
[6,5,2,1,4,3,8,7,10,9,12,11] => [[1,5,7,9,11],[2,6,8,10,12],[3],[4]] => 11101010101
[1,5,4,8,7,3,2,6] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,3,1,2,6,5,7,8] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[7,5,8,1,2,4,6,3] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[6,1,5,2,8,7,4,3] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,6,3,5,7,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[1,4,7,2,6,5,8,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[1,5,7,2,6,4,8,3] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[7,2,4,6,1,8,3,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[1,2,7,8,3,5,4,6] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[1,7,6,2,8,5,4,3] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,2,7,8,3,4,6,5] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[1,7,6,8,3,4,2,5] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[3,4,1,7,8,6,5,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[2,4,8,6,5,7,1,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[5,1,3,4,8,2,7,6] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[8,7,3,6,1,4,2,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,5,1,8,3,4,7,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[8,2,1,5,6,4,7,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,5,6,1,3,4,8,2] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[5,7,2,4,6,1,8,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[2,1,5,6,3,8,7,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[3,2,7,5,8,6,4,1] => [[1,3,5],[2,4,6],[7],[8]] => 1010111
[2,4,5,3,8,1,7,6] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[7,2,5,4,3,8,6,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,5,3,1,2,6,7,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[7,2,5,1,3,6,8,4] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[8,4,7,3,1,2,6,5] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[1,8,7,3,5,2,6,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,4,8,3,6,5,7,1] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,1,8,2,6,5,7,4] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[4,6,7,8,5,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[4,7,2,1,8,6,5,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[5,6,2,8,4,1,7,3] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[5,7,2,4,8,6,1,3] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[6,7,2,4,8,5,1,3] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[6,7,3,2,8,5,1,4] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[7,2,3,1,8,6,5,4] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[7,2,8,3,5,6,1,4] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[7,2,3,8,4,6,1,5] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[1,7,3,4,8,5,2,6] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,7,3,8,5,4,2,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,2,8,4,5,3,1,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[2,8,6,4,3,1,7,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,7,3,4,8,2,5,6] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,5,8,3,4,6,2,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,3,8,4,2,5,7,6] => [[1,2,3,6,7],[4,8],[5]] => 0011001
[1,4,7,6,2,3,8,5] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,8,4,6,7,2,3,5] => [[1,2,4,5],[3,7,8],[6]] => 0100100
[1,4,2,3,7,8,6,5] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[5,7,1,6,4,8,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[1,2,9,7,5,3,10,8,6,4] => [[1,2,3,7],[4,8],[5,9],[6,10]] => 001110111
[7,4,5,8,1,3,6,2] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[1,4,3,6,2,5,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[1,3,6,5,8,2,4,7] => [[1,2,3,5],[4,7,8],[6]] => 0010100
[1,4,6,3,2,8,5,7] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[6,8,4,1,5,7,2,3] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[5,2,6,7,4,1,8,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[8,5,6,4,1,7,3,2] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,8,3,1,6,4,5,2] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[5,8,2,6,3,1,7,4] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[4,5,8,1,6,3,7,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[8,1,4,6,2,5,7,3] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[4,5,8,1,6,2,7,3] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[5,2,6,8,1,4,3,7] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[6,7,3,8,2,1,4,5] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[2,4,1,5,6,7,8,10,3,9] => [[1,2,4,5,6,7,8],[3,9,10]] => 010000010
[2,7,3,5,4,1,8,6] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,6,3,7,4,1,8,5] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[2,1,4,8,5,3,7,6] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[2,7,3,8,4,1,6,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,6,3,1,5,4,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,5,8,3,4,7,2,6] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[5,3,8,1,4,6,2,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[4,5,8,1,3,6,2,7] => [[1,2,3,8],[4,5,6],[7]] => 0010010
[7,4,6,5,2,8,3,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[4,1,3,8,5,7,6,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[4,1,3,7,2,8,6,5] => [[1,3,4,6],[2,7],[5,8]] => 1001011
[4,6,3,1,7,2,8,5] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[7,2,6,3,1,8,5,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[4,8,7,2,5,3,1,6] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,6,3,2,8,7,4,5] => [[1,2,5,8],[3,6],[4,7]] => 0110110
[2,8,1,7,5,4,6,3] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[6,8,3,1,5,7,2,4] => [[1,2,6],[3,5,8],[4,7]] => 0110010
[8,7,3,1,2,5,6,4] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[1,3,5,7,2,8,4,9,6] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,3,5,6,2,7,4,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,3,4,5,2,7,6,9,8] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[3,5,7,1,2,4,6,9,8] => [[1,2,3,7,8],[4,5,6,9]] => 00100001
[3,5,7,8,1,9,2,4,6] => [[1,2,3,4,6],[5,7,8,9]] => 00010100
[1,3,5,7,2,9,4,10,6,8] => [[1,2,3,4,6,8],[5,7,9,10]] => 000101010
[3,5,6,7,1,8,2,9,4] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,3,5,7,2,8,4,9,6,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[1,3,5,6,2,7,4,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[1,3,4,5,2,7,6,9,8,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[5,4,3,6,1,7,8,2] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[3,2,7,8,5,6,1,4] => [[1,3,4],[2,5,6],[7,8]] => 1001010
[4,8,3,2,1,7,5,6] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[1,9,8,7,6,4,3,2,5] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,9,8,7,5,4,3,2,6] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,9,8,6,5,4,3,2,7] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,9,7,6,5,4,3,2,8] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[1,9,8,7,6,5,2,3,4] => [[1,2,8,9],[3],[4],[5],[6],[7]] => 01111100
[1,10,9,8,7,6,5,3,2,4] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[1,10,9,8,7,6,4,3,2,5] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[1,10,9,8,7,5,4,3,2,6] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[1,10,9,8,6,5,4,3,2,7] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[1,8,4,5,6,3,2,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,10,9,7,6,5,4,3,2,8] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[1,7,8,6,5,4,3,2,9] => [[1,2,3,9],[4],[5],[6],[7],[8]] => 00111110
[1,10,8,7,6,5,4,3,2,9] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[8,5,1,7,4,6,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[1,3,7,8,4,6,2,5] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[4,8,7,3,6,1,2,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,8,4,3,7,1,2,6] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[5,6,4,8,7,2,1,3] => [[1,2,4],[3,5],[6,8],[7]] => 0101110
[4,8,3,7,6,1,2,5] => [[1,2,8],[3,4],[5,7],[6]] => 0101100
[2,8,4,7,1,3,6,5] => [[1,2,4],[3,6,7],[5],[8]] => 0101001
[6,7,8,9,2,3,4,1,5] => [[1,2,3,4],[5,6,7,9],[8]] => 00010010
[7,8,9,10,2,3,4,5,1,6] => [[1,2,3,4,10],[5,6,7,8],[9]] => 000100010
[4,5,6,7,8,1,9,2,3] => [[1,2,3,4,5,7],[6,8,9]] => 00001010
[4,5,6,7,8,9,10,2,1,3] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[6,8,3,4,5,2,1,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[3,7,1,4,5,6,2,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[3,6,1,4,5,2,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[3,8,2,4,5,1,7,6] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[3,7,2,1,5,6,4,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[3,6,8,1,5,4,7,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[1,7,4,6,3,5,2,8] => [[1,2,4,8],[3,6],[5],[7]] => 0101010
[1,3,6,5,7,2,4,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,7,2,5,6,4,3,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,6,8,5,4,3,7,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[2,5,7,8,4,3,1,6] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[6,8,5,3,2,4,1,7] => [[1,2,8],[3,6],[4],[5],[7]] => 0111010
[1,6,8,5,3,2,7,4] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,6,1,8,7,5,3,2] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[1,3,7,6,8,5,2,4] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[4,1,7,8,6,5,2,3] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[5,4,3,7,6,1,2,8] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,7,6,1,2,3,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,5,2,6,7,8,1,3] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[2,8,7,6,5,4,3,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[3,7,6,5,4,2,1,9,8] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[4,6,5,3,2,1,9,8,7] => [[1,2,7],[3,8],[4,9],[5],[6]] => 01111011
[1,7,6,2,3,8,5,4] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[4,5,1,3,7,6,2,8] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[7,2,3,8,6,4,5,1] => [[1,3,4,7],[2,5],[6],[8]] => 1001101
[1,5,4,3,8,6,2,7] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[1,3,7,5,8,4,6,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,8,1,2,7,6,4,3] => [[1,2,5],[3,4],[6],[7],[8]] => 0100111
[1,6,7,4,5,3,2,8] => [[1,2,3,8],[4,5],[6],[7]] => 0010110
[1,4,2,6,7,5,3,8] => [[1,2,4,5,8],[3,6],[7]] => 0100110
[1,8,2,4,6,5,3,7] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[7,2,1,6,4,3,8,5] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[1,4,8,7,2,3,6,5] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,1,3,6,5,8,2,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[4,3,7,1,5,8,2,6] => [[1,3,6],[2,5,8],[4,7]] => 1010010
[1,8,6,5,2,7,4,3] => [[1,2,6],[3,7],[4],[5],[8]] => 0111011
[1,8,6,2,7,4,3,5] => [[1,2,5,8],[3,6],[4],[7]] => 0110110
[6,4,1,8,3,7,5,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,5,8,7,3,6,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[3,5,4,1,7,8,6,2] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[6,8,7,2,1,5,4,3] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[8,1,6,3,7,5,4,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,5,1,3,7,6,4,2] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,3,6,5,4,2,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => 1011110
[6,1,3,5,7,2,8,4] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[2,8,1,5,6,4,3,7] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[1,6,7,5,8,4,2,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[7,4,1,6,5,2,8,3] => [[1,4,7],[2,5,8],[3],[6]] => 1101101
[7,4,2,8,6,5,3,1] => [[1,4],[2,5],[3,6],[7],[8]] => 1101111
[6,8,4,7,3,2,5,1] => [[1,2],[3,4],[5,7],[6],[8]] => 0101101
[5,8,7,3,2,1,6,4] => [[1,2],[3,7],[4,8],[5],[6]] => 0111101
[5,8,7,2,6,4,3,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[6,8,7,3,5,1,4,2] => [[1,2],[3,5],[4,7],[6],[8]] => 0110101
[7,2,5,6,8,3,4,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[1,6,5,7,8,3,2,4] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[8,6,7,2,3,5,4,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[5,4,8,6,7,3,1,2] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[4,2,7,3,1,6,8,5] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[7,3,6,4,2,1,8,5] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,8,5,2,7,3,1,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[6,4,3,1,8,5,2,7] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,4,3,1,5,8,6,2] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,4,8,6,5,3,1,2] => [[1,3],[2,4],[5,8],[6],[7]] => 1011110
[4,8,5,2,6,7,3,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[7,3,2,1,8,5,6,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[5,6,7,8,1,9,2,3,4] => [[1,2,3,4,6],[5,7,8,9]] => 00010100
[1,5,7,2,4,3,8,6] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[1,2,7,5,8,4,3,6] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[5,1,3,8,2,7,4,6] => [[1,3,4,8],[2,6],[5,7]] => 1001010
[5,7,1,3,2,8,4,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[7,1,6,3,2,8,4,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,1,7,2,3,6,5,4] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[7,1,2,6,4,3,8,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[1,4,7,8,3,2,5,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[8,7,1,3,2,4,6,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,1,6,3,2,4,7,5] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[1,8,2,7,6,3,5,4] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[8,1,6,3,2,7,4,5] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,2,1,7,6,3,4,5] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[8,7,2,4,3,1,5,6] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[6,1,3,2,5,4,8,7,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[8,1,3,2,5,4,7,6,10,9] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,7,6,2,3,1,5,8] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[4,7,6,1,3,2,8,5] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,2,6,5,4,3,1,9,8] => [[1,3,8],[2,9],[4],[5],[6],[7]] => 10111101
[2,8,1,3,5,6,4,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[2,6,3,4,7,8,5,1] => [[1,2,4,5,6],[3,7],[8]] => 0100011
[7,6,3,1,8,5,2,4] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[7,2,1,3,6,8,5,4] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[7,6,3,8,1,5,2,4] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[1,6,4,7,8,5,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[7,2,5,8,6,1,3,4] => [[1,3,4],[2,5,8],[6,7]] => 1001100
[4,1,3,6,2,5,8,7] => [[1,3,4,7],[2,6,8],[5]] => 1001001
[7,1,4,6,3,2,5,8] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[7,4,5,8,6,2,3,1] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,7,2,3,8,4,1,5] => [[1,2,5,8],[3,4,6],[7]] => 0100110
[2,7,8,1,5,4,3,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[1,5,2,6,8,7,4,3] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[1,2,3,4,5,6,8,9,7,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[1,8,3,7,5,2,6,4] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[8,1,3,6,5,2,7,4] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,1,3,8,5,2,6,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,7,1,5,2,6,8,3] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[7,4,1,5,2,6,8,3] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[3,1,6,7,5,2,8,4] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[8,6,2,4,5,1,7,3] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,6,7,5,2,1,4,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[7,1,4,5,2,6,8,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[4,1,6,2,3,8,7,5] => [[1,3,5,6],[2,4,7],[8]] => 1010011
[4,1,7,6,5,2,8,3] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[8,4,1,5,6,2,7,3] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[8,4,5,3,6,1,7,2] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[2,8,4,7,3,5,6,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,5,4,8,3,2,6,7] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[1,5,7,6,3,8,2,4] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,6,3,1,7,8,4,5] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[2,1,7,8,3,5,4,6] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[1,5,8,6,7,4,2,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[8,7,1,3,5,2,6,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[3,7,8,2,5,4,1,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,7,6,5,8,1,3,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[4,7,8,6,2,1,5,3] => [[1,2,3],[4,7],[5,8],[6]] => 0011101
[4,8,6,3,2,1,7,5] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[5,1,4,7,6,8,3,2] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[5,6,4,7,1,8,3,2] => [[1,2,4,6],[3,7],[5],[8]] => 0101011
[5,3,7,4,6,1,8,2] => [[1,3,5,7],[2,4],[6,8]] => 1010101
[4,1,5,7,8,6,3,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[3,6,7,1,5,4,8,2] => [[1,2,3,7],[4,5],[6],[8]] => 0010101
[3,6,4,7,5,8,2,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[9,1,2,3,4,8,6,5,7] => [[1,3,4,5,6,9],[2],[7],[8]] => 10000110
[10,1,2,3,4,5,9,7,6,8] => [[1,3,4,5,6,7,10],[2],[8],[9]] => 100000110
[4,1,9,2,3,5,6,8,7] => [[1,3,5,6,7,8],[2,4],[9]] => 10100001
[3,8,1,2,4,5,6,9,7] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[8,2,1,3,4,5,6,9,7] => [[1,4,5,6,7,8],[2,9],[3]] => 11000001
[9,1,2,3,8,5,4,7,6] => [[1,3,4,5,8],[2,9],[6],[7]] => 10001101
[9,8,2,1,4,5,6,7,3] => [[1,5,6,7,8],[2,9],[3],[4]] => 11100001
[8,1,7,3,2,4,5,6] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[3,9,1,2,4,5,6,7,10,8] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[10,2,1,3,4,5,6,7,9,8] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[6,4,7,1,5,2,8,3] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[1,6,5,2,8,7,4,3] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[2,3,4,5,7,8,1,9,6] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[1,2,3,4,5,7,8,6,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[2,3,4,5,7,9,1,6,8] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[1,2,3,4,5,7,8,9,6,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 000000010
[2,1,4,5,3,6,7,8,9] => [[1,3,4,6,7,8,9],[2,5]] => 10010000
[1,3,2,5,4,6,7,8,9] => [[1,2,4,6,7,8,9],[3,5]] => 01010000
[4,1,7,2,5,8,3,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,2,5,8,6,1,7,4] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,5,1,7,2,8,6,3] => [[1,2,4,6],[3,5,7],[8]] => 0101011
[6,4,7,2,5,3,1,8] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[7,1,4,3,6,8,2,5] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[4,1,6,2,8,3,5,7,9] => [[1,3,5,7,8,9],[2,4,6]] => 10101000
[4,1,6,2,8,3,9,5,7] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[4,1,6,2,7,3,8,5,9] => [[1,3,5,7,9],[2,4,6,8]] => 10101010
[4,8,7,3,5,1,6,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,3,8,7,1,6,2,4] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[5,2,6,7,4,3,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,5,1,6,4,3,2,7] => [[1,4,8],[2,5],[3],[6],[7]] => 1101110
[8,6,3,5,2,7,1,4] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[8,4,6,2,1,5,7,3] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,5,2,1,6,4,7,3] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[1,7,2,8,5,4,6,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[6,7,1,4,8,5,3,2] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[7,3,2,8,5,1,4,6] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[4,1,7,3,2,8,5,6] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[8,3,5,2,4,7,1,6] => [[1,3,6],[2,5,8],[4],[7]] => 1010010
[4,3,7,8,6,1,5,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[1,2,6,3,7,8,5,4] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[6,1,3,7,8,5,4,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,6,4,7,5,3,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[4,5,1,8,6,2,7,3] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[5,6,1,8,7,2,3,4] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[4,5,1,6,8,7,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[3,9,2,4,5,6,7,8,1] => [[1,2,5,6,7,8],[3,4],[9]] => 01000001
[3,8,6,1,5,2,4,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[3,2,8,1,5,6,4,7] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[5,8,7,3,2,1,4,6] => [[1,2,8],[3,7],[4],[5],[6]] => 0111100
[3,4,7,6,8,2,1,5] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,8,1,3,7,5,6,4] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,8,7,2,5,6,4,3] => [[1,2,5,6],[3],[4],[7],[8]] => 0110011
[3,4,7,1,5,8,2,6] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[1,3,5,2,4,6,7,8,9] => [[1,2,3,6,7,8,9],[4,5]] => 00100000
[4,1,2,3,5,6,8,7,9] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[1,2,4,7,3,5,6,8,9] => [[1,2,3,4,7,8,9],[5,6]] => 00010000
[1,4,7,5,2,3,6,8] => [[1,2,3,7,8],[4,6],[5]] => 0011000
[2,5,7,6,8,3,4,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[3,1,6,7,2,8,5,4] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[1,5,3,6,8,4,7,2] => [[1,2,4,5],[3,6,7],[8]] => 0100101
[6,5,1,3,8,4,7,2] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[1,7,4,8,5,3,2,6] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[7,3,1,6,8,4,5,2] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[8,5,1,4,6,7,3,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[3,4,7,5,6,8,2,1] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[3,4,7,8,5,2,6,1] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[4,8,1,7,5,6,3,2] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[1,8,7,5,2,6,3,4] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,7,6,3,4,5,8,2] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,8,7,4,5,6,2,3] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[1,8,7,3,6,4,2,5] => [[1,2,5,8],[3],[4],[6],[7]] => 0110110
[1,4,7,5,8,2,6,3] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,4,7,2,3,6,5,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,7,2,5,6,3,4,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[1,2,6,5,8,3,4,7] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[1,5,8,2,6,3,4,7] => [[1,2,3,7,8],[4,5],[6]] => 0010100
[6,8,3,2,7,5,1,4] => [[1,2],[3,5],[4,6],[7,8]] => 0110110
[7,3,6,8,1,2,5,4] => [[1,3,4],[2,6,7],[5],[8]] => 1001001
[4,1,5,7,2,6,3,8] => [[1,3,4,8],[2,5,6],[7]] => 1001010
[5,7,2,1,3,6,4,8] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,7,9,1,2,3,4,5,10,8] => [[1,2,3,7,8,9],[4,5,6,10]] => 001000001
[8,7,1,10,2,3,4,5,6,9] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[3,5,6,7,2,4,1,8] => [[1,2,3,4,8],[5,6],[7]] => 0001010
[6,4,7,5,2,3,1,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[1,5,6,4,8,3,2,7] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,1,5,6,4,8,3,7] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[5,1,4,7,8,6,2,3] => [[1,3,4,5],[2,6],[7,8]] => 1000110
[1,6,7,2,8,5,4,3] => [[1,2,3,5],[4,6],[7],[8]] => 0010111
[5,3,2,1,7,8,6,4] => [[1,5,6],[2,7],[3,8],[4]] => 1110011
[7,4,3,8,6,1,5,2] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[4,3,7,1,5,8,6,2] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[8,2,4,5,3,1,7,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[1,4,3,2,7,5,8,6] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[1,5,2,8,6,3,10,9,7,4] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[4,1,5,2,8,6,3,10,9,7] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[1,7,5,2,8,6,3,10,9,4] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[4,1,7,5,2,8,3,10,9,6] => [[1,3,6,8],[2,4,7,9],[5,10]] => 101101011
[6,4,1,7,5,2,8,3,10,9] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[3,4,1,7,2,8,5,10,9,6] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[3,6,4,1,7,2,8,5,10,9] => [[1,2,5,7,9],[3,6,8,10],[4]] => 011010101
[1,5,2,9,8,6,3,10,7,4] => [[1,2,4,8],[3,5,9],[6,10],[7]] => 010111011
[1,7,5,2,9,6,3,10,8,4] => [[1,2,5,8],[3,6,9],[4,7,10]] => 011011011
[4,1,7,5,2,9,3,10,8,6] => [[1,3,6,8],[2,4,7,9],[5,10]] => 101101011
[3,4,1,7,2,9,5,10,8,6] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,8,7,5,2,9,6,3,10,4] => [[1,2,6,9],[3,7,10],[4,8],[5]] => 011101101
[6,4,1,8,5,2,9,3,10,7] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[7,6,4,1,8,5,2,9,3,10] => [[1,5,8,10],[2,6,9],[3,7],[4]] => 111011010
[3,6,4,1,8,2,9,5,10,7] => [[1,2,5,7,9],[3,6,8,10],[4]] => 011010101
[3,7,6,4,1,8,2,9,5,10] => [[1,2,6,8,10],[3,7,9],[4],[5]] => 011101010
[5,4,1,9,6,2,7,3,10,8] => [[1,4,7,9],[2,5,8,10],[3,6]] => 110110101
[9,5,3,1,6,2,7,4,10,8] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[6,4,1,8,2,9,7,3,10,5] => [[1,4,6,9],[2,5,7,10],[3,8]] => 110101101
[8,5,4,1,6,2,9,3,10,7] => [[1,5,7,9],[2,6,8,10],[3],[4]] => 111010101
[5,7,4,1,8,6,2,9,3,10] => [[1,2,5,8,10],[3,6,9],[4,7]] => 011011010
[3,6,1,8,2,9,7,4,10,5] => [[1,2,4,6,9],[3,5,7,10],[8]] => 010101101
[7,4,3,5,1,8,2,9,6,10] => [[1,4,6,8,10],[2,7,9],[3],[5]] => 110101010
[8,2,5,1,6,3,9,4,10,7] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,8,7,2,6,1,3,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[4,5,8,2,1,7,3,6] => [[1,2,3],[4,6,8],[5,7]] => 0011010
[6,8,4,1,7,3,2,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,6,4,3,2,1,7,8,9] => [[1,2,7,8,9],[3],[4],[5],[6]] => 01111000
[5,6,4,3,2,1,7,8,9,10] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => 011110000
[4,5,3,2,1,6,7,8,9] => [[1,2,6,7,8,9],[3],[4],[5]] => 01110000
[6,7,5,4,3,2,1,8,9,10] => [[1,2,8,9,10],[3],[4],[5],[6],[7]] => 011111000
[7,5,4,3,1,2,6,8,9] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[6,5,4,3,7,1,2,8,9] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000
[6,7,9,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[7,6,8,9,5,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111
[7,8,10,9,6,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[6,7,5,9,8,4,3,2,1] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[5,7,9,8,6,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[8,7,9,10,6,5,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => 100111111
[6,3,1,8,2,7,5,4] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[4,1,7,8,3,2,5,6] => [[1,3,4,8],[2,5,7],[6]] => 1001100
[7,6,2,8,4,5,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[5,8,2,1,3,6,4,7] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[8,5,1,7,3,4,6,2] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[5,7,6,3,4,1,8,2] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[7,8,9,10,1,5,6,3,4,2] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[1,8,3,5,2,6,4,7] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[3,4,6,1,8,5,7,2] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[2,3,8,7,4,5,1,6] => [[1,2,3,6,8],[4],[5],[7]] => 0011010
[1,8,3,5,7,4,2,6] => [[1,2,4,5],[3,8],[6],[7]] => 0100110
[2,5,8,4,6,7,1,3] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[9,8,6,1,2,3,4,5,7] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000
[9,8,7,5,1,2,3,4,6] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000
[9,8,7,6,4,1,2,3,5] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[9,8,7,6,5,3,1,2,4] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[7,1,2,6,4,3,5,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[7,1,2,6,5,3,4,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[4,7,8,6,2,3,5,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[7,1,2,4,8,6,5,3] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
[2,7,5,6,4,8,1,3] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[2,8,3,6,5,7,1,4] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[9,3,8,7,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[9,2,8,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => 10111111
[10,9,8,5,7,6,4,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[10,9,8,4,7,6,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[10,9,4,8,7,6,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => 110111111
[10,3,9,8,7,6,5,4,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[10,2,9,8,7,6,5,4,3,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[7,4,3,1,6,5,2,8] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[3,5,1,2,6,8,7,4] => [[1,2,5,6],[3,4,7],[8]] => 0100011
[3,1,2,4,8,7,5,6] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[5,4,1,2,3,7,8,6] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[1,6,7,2,5,8,3,4] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[7,8,5,6,2,4,3,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[5,3,8,6,2,4,1,7] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[2,7,4,6,3,8,1,5] => [[1,2,4,6],[3,8],[5],[7]] => 0101010
[5,4,7,8,6,2,1,3] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[2,7,4,8,3,1,5,6] => [[1,2,4,8],[3,7],[5],[6]] => 0101100
[8,2,1,3,7,4,6,5] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,5,8,2,3,4,7,1] => [[1,3,6,7],[2,5],[4],[8]] => 1010001
[7,8,2,3,6,4,5,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,1,2,7,5,3,4,6] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[4,2,8,1,3,7,5,6] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[7,5,1,8,2,3,4,6] => [[1,4,6,7,8],[2,5],[3]] => 1101000
[8,2,4,1,3,7,5,6] => [[1,3,6,8],[2,5,7],[4]] => 1010010
[8,1,6,2,3,7,4,5] => [[1,3,5,6,8],[2,7],[4]] => 1010010
[7,1,8,2,3,6,4,5] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[4,2,6,7,5,1,8,3] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,7,2,5,3,8,1,6] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[3,5,7,4,2,8,1,6] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,4,7,6,3,8,1,5] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,6,8,5,1,2,3,7] => [[1,2,3,8],[4,6,7],[5]] => 0011000
[4,6,5,7,1,2,3,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[4,6,5,7,1,3,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,4,7,6,1,8,2,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[8,5,2,1,6,3,4,7] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[7,1,8,5,3,2,4,6] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[10,8,5,2,1,6,3,4,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[9,5,2,1,10,6,3,4,7,8] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[10,7,2,1,8,5,3,4,6,9] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[10,6,2,1,7,3,8,4,5,9] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[9,2,1,10,6,3,7,4,5,8] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[7,2,1,8,3,9,4,10,5,6] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[10,8,6,3,1,4,2,5,7,9] => [[1,6,8,9,10],[2,7],[3],[4],[5]] => 111101000
[10,7,3,1,8,4,2,5,6,9] => [[1,5,8,9,10],[2,6],[3,7],[4]] => 111011000
[8,3,1,9,4,2,10,5,6,7] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[10,8,4,1,5,2,6,3,7,9] => [[1,5,7,9,10],[2,6,8],[3],[4]] => 111010100
[9,4,1,10,5,2,6,3,7,8] => [[1,4,7,9,10],[2,5,8],[3,6]] => 110110100
[10,5,1,6,2,7,3,8,4,9] => [[1,4,6,8,10],[2,5,7,9],[3]] => 110101010
[7,1,8,2,9,3,10,5,4,6] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[11,2,1,12,7,3,8,4,9,5,6,10] => [[1,4,7,9,11,12],[2,5,8,10],[3,6]] => 11011010100
[9,3,1,10,4,2,11,5,12,6,7,8] => [[1,4,7,9,11,12],[2,5,8,10],[3,6]] => 11011010100
[11,5,1,12,6,2,7,3,8,4,9,10] => [[1,4,7,9,11,12],[2,5,8,10],[3,6]] => 11011010100
[8,2,7,5,4,1,6,3] => [[1,3,7],[2,8],[4],[5],[6]] => 1011101
[4,2,8,5,7,1,6,3] => [[1,3,5],[2,4],[6,7],[8]] => 1010101
[6,8,7,4,5,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => 0110111
[5,2,6,7,4,8,3,1] => [[1,3,4,6],[2,5],[7],[8]] => 1001011
[6,5,8,1,7,3,2,4] => [[1,3,8],[2,5],[4,6],[7]] => 1010110
[6,4,8,1,5,2,3,7] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[7,2,4,1,6,3,5,8] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[2,6,1,5,3,4,8,7] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[3,8,7,5,4,2,6,1] => [[1,2,7],[3],[4],[5],[6],[8]] => 0111101
[5,7,8,2,3,6,4,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[2,8,7,3,1,4,5,6] => [[1,2,6,7,8],[3],[4],[5]] => 0111000
[5,6,1,2,4,7,8,3] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[10,2,3,1,4,5,6,7,8,9] => [[1,3,5,6,7,8,9,10],[2],[4]] => 101000000
[10,9,8,6,5,7,4,3,2,1] => [[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => 111101111
[3,8,6,7,5,4,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => 0101111
[7,8,5,1,4,6,2,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,2,7,5,4,6,1,3] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[8,4,7,6,3,1,2,5] => [[1,3,8],[2,7],[4],[5],[6]] => 1011100
[4,6,7,1,3,2,8,5] => [[1,2,3,7],[4,5,8],[6]] => 0010101
[6,4,7,5,3,2,8,1] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,4,6,3,1,5,7,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,3,1,4,5,6,8,2] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,7,3,4,2,1,8,5] => [[1,2,7],[3,4,8],[5],[6]] => 0101101
[6,4,8,3,1,5,7,2] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[7,4,2,3,5,1,8,6] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[3,1,6,5,2,4,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[2,5,3,8,6,4,1,7] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,8,4,1,3,2,7,6] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,3,4,7,6,1,8,2] => [[1,3,4,7],[2,5],[6,8]] => 1001101
[4,5,2,1,6,3,8,7] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[4,5,2,1,6,7,3,8] => [[1,2,5,6,8],[3,7],[4]] => 0110010
[5,3,8,6,2,4,7,1] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,5,1,6,4,3,8,7] => [[1,2,4,7],[3,5,8],[6]] => 0101101
[3,6,2,8,5,7,1,4] => [[1,2,4],[3,5,6],[7,8]] => 0101010
[4,6,8,1,5,7,2,3] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[4,1,2,5,7,6,3,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[4,6,5,8,1,7,3,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[2,1,3,6,4,8,7,5] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,8,1,2,7,5,6,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,6,4,3,8,7,5,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[4,5,1,6,8,7,2,3] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[2,5,1,8,6,4,7,3] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[2,5,8,7,3,1,4,6] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[9,8,7,4,3,2,1,5,6] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[9,8,7,6,3,2,1,4,5] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100
[3,8,7,2,6,1,4,5] => [[1,2,8],[3,5],[4,7],[6]] => 0110100
[8,4,5,1,6,7,2,3] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[8,4,7,3,1,5,2,6] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[2,5,1,8,3,6,4,7] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[5,8,4,7,3,2,1,6] => [[1,2],[3,4],[5,8],[6],[7]] => 0101110
[4,3,8,6,1,2,5,7] => [[1,3,7,8],[2,4],[5,6]] => 1011000
[4,8,6,5,7,1,3,2] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[7,2,3,5,6,8,4,1] => [[1,3,4,5,6],[2],[7],[8]] => 1000011
[5,8,1,3,4,7,2,6] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,3,4,2,7,6,1,5] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[8,7,5,6,4,1,3,2] => [[1,4],[2,7],[3],[5],[6],[8]] => 1101101
[8,7,4,2,3,6,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[8,4,2,3,7,6,5,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,2,4,5,3,1,6,8] => [[1,3,4,7,8],[2],[5],[6]] => 1001100
[7,6,3,1,4,5,8,2] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[5,4,1,7,8,6,2,3] => [[1,4,5],[2,6,8],[3,7]] => 1100110
[5,3,4,7,8,1,6,2] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[4,3,7,6,5,1,8,2] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[5,1,4,8,2,3,7,6] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[3,2,8,5,4,1,6,7] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[7,8,9,1,3,4,5,6,2] => [[1,2,3,7,8],[4,5,6],[9]] => 00100001
[6,1,2,9,3,4,5,7,8] => [[1,3,4,6,7,8,9],[2,5]] => 10010000
[3,1,2,4,5,6,9,7,8] => [[1,3,4,5,6,7,9],[2,8]] => 10000010
[1,2,8,3,4,6,5,7] => [[1,2,3,5,6,8],[4],[7]] => 0010010
[8,1,2,7,3,5,4,6] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[5,7,1,2,6,3,4,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[1,2,7,5,6,3,4,8] => [[1,2,3,5,8],[4,7],[6]] => 0010100
[5,1,4,7,2,3,6,8] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[4,8,1,2,3,6,5,7] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[1,2,3,5,6,7,8,4,9] => [[1,2,3,4,5,6,7,9],[8]] => 00000010
[2,1,5,3,6,7,4,8,9] => [[1,3,5,6,8,9],[2,4,7]] => 10100100
[3,5,2,1,6,4,7,8,9] => [[1,2,5,7,8,9],[3,6],[4]] => 01101000
[1,3,4,6,7,2,8,5,9] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[4,6,3,2,1,7,5,8,9] => [[1,2,6,8,9],[3,7],[4],[5]] => 01110100
[1,3,5,7,8,6,4,2,9] => [[1,2,3,4,5,9],[6],[7],[8]] => 00001110
[3,5,7,2,1,8,6,4,9] => [[1,2,3,6,9],[4,7],[5,8]] => 00110110
[5,7,4,3,2,1,8,6,9] => [[1,2,7,9],[3,8],[4],[5],[6]] => 01111010
[2,4,6,8,1,9,7,5,3] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[4,6,8,3,2,1,9,7,5] => [[1,2,3,7],[4,8],[5,9],[6]] => 00111011
[6,8,5,4,3,2,1,9,7] => [[1,2,8],[3,9],[4],[5],[6],[7]] => 01111101
[1,3,4,2,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 001000000
[1,2,4,5,6,3,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 000010000
[1,2,3,5,6,7,8,4,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 000000100
[2,1,5,3,6,7,4,8,9,10] => [[1,3,5,6,8,9,10],[2,4,7]] => 101001000
[3,5,2,1,6,4,7,8,9,10] => [[1,2,5,7,8,9,10],[3,6],[4]] => 011010000
[1,3,4,6,7,2,8,5,9,10] => [[1,2,3,4,5,7,9,10],[6,8]] => 000010100
[4,6,3,2,1,7,5,8,9,10] => [[1,2,6,8,9,10],[3,7],[4],[5]] => 011101000
[1,2,4,5,7,8,9,6,3,10] => [[1,2,3,4,5,6,7,10],[8],[9]] => 000000110
[5,7,4,3,2,1,8,6,9,10] => [[1,2,7,9,10],[3,8],[4],[5],[6]] => 011110100
[1,3,5,6,8,9,4,2,10,7] => [[1,2,3,4,5,6,9],[7,10],[8]] => 000001101
[2,4,6,8,1,9,7,5,3,10] => [[1,2,3,4,6,10],[5,7],[8],[9]] => 000101110
[6,8,5,4,3,2,1,9,7,10] => [[1,2,8,10],[3,9],[4],[5],[6],[7]] => 011111010
[3,5,7,9,2,1,10,8,6,4] => [[1,2,3,4,7],[5,8],[6,9],[10]] => 000110111
[7,9,6,5,4,3,2,1,10,8] => [[1,2,9],[3,10],[4],[5],[6],[7],[8]] => 011111101
[6,2,3,8,7,1,4,5] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[8,2,3,6,4,7,5,1] => [[1,3,4,6],[2,7],[5],[8]] => 1001011
[7,2,3,6,4,8,1,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[5,4,1,6,2,7,8,3] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,1,3,5,4,2,8,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,6,8,2,4,5,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[4,2,8,6,5,1,3,7] => [[1,3,8],[2,4],[5,7],[6]] => 1011100
[3,8,5,4,7,1,2,6] => [[1,2,5],[3,7,8],[4],[6]] => 0110100
[1,4,8,3,6,2,7,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[6,3,2,4,8,7,1,5] => [[1,4,5],[2,6],[3,8],[7]] => 1100110
[8,3,2,7,4,1,5,6] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[7,3,2,6,5,8,1,4] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[3,6,2,5,7,4,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[2,7,1,5,8,6,4,3] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[7,2,4,1,6,8,5,3] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[6,4,7,2,3,8,5,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[6,1,8,5,7,4,2,3] => [[1,3,5],[2,4],[6,8],[7]] => 1010110
[7,1,4,3,6,5,8,2] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[7,1,5,6,3,4,8,2] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[6,1,8,5,4,7,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[7,6,1,5,4,2,8,3] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[5,1,6,8,7,2,4,3] => [[1,3,4],[2,5,7],[6],[8]] => 1001101
[4,6,7,5,3,1,8,2] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,3,2,6,8,7,4,1] => [[1,4,5],[2,6],[3,7],[8]] => 1100111
[5,4,6,2,8,7,3,1] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[4,5,8,6,7,2,3,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[4,5,7,6,1,2,8,3] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[4,6,5,7,2,1,8,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[2,3,4,10,6,9,8,7,5,1] => [[1,2,3,4,6],[5],[7],[8],[9],[10]] => 000101111
[2,5,4,9,6,10,8,7,3,1] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[2,3,5,7,10,8,9,6,4,1] => [[1,2,3,4,5,7],[6],[8],[9],[10]] => 000010111
[2,4,6,7,8,9,10,5,3,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[3,5,6,8,9,7,10,4,2,1] => [[1,2,3,4,5,7],[6],[8],[9],[10]] => 000010111
[3,5,6,7,8,9,4,2,1,10] => [[1,2,3,4,5,6,10],[7],[8],[9]] => 000001110
[7,4,8,6,3,5,1,2] => [[1,3],[2,4],[5,6],[7,8]] => 1011010
[7,2,4,3,6,1,8,5] => [[1,3,5,7],[2,8],[4],[6]] => 1010101
[2,3,4,7,8,6,1,5] => [[1,2,3,4,5],[6,8],[7]] => 0000110
[6,3,7,1,4,2,8,5] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,6,3,5,1,8,2,7] => [[1,2,6],[3,4,8],[5,7]] => 0101010
[8,5,7,6,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[3,5,6,7,8,9,2,4,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[3,4,6,7,8,2,5,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,4,6,7,8,9,1,3,5] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[2,5,6,7,3,8,1,4] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[2,5,6,7,8,9,3,1,4] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[5,8,4,6,2,1,7,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[1,6,8,3,4,2,7,5] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,1,7,6,2,8,3,5] => [[1,3,6,8],[2,4,7],[5]] => 1011010
[4,1,8,2,7,5,3,6] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[4,1,7,2,8,5,3,6] => [[1,3,5,8],[2,4,6],[7]] => 1010110
[2,5,6,3,7,4,8,1] => [[1,2,3,5,7],[4,6],[8]] => 0010101
[2,6,5,3,8,4,7,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[2,6,5,3,7,4,8,1] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[7,1,6,3,5,4,8,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[5,7,3,2,8,4,1,6] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[2,8,6,1,7,5,3,4] => [[1,2,5],[3,6,8],[4],[7]] => 0110110
[8,1,5,2,7,4,3,6] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[7,1,4,2,8,5,3,6] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[2,6,8,1,7,5,3,4] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[1,4,6,5,3,8,2,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[2,4,5,8,7,1,3,6] => [[1,2,3,4],[5,7,8],[6]] => 0001100
[3,1,6,8,7,5,4,2] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[3,1,8,7,5,6,4,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[5,1,8,7,6,3,4,2] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[8,2,7,5,3,6,4,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[8,7,2,3,1,5,6,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[2,8,5,7,6,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[1,8,7,2,6,4,5,3] => [[1,2,5,7],[3],[4],[6],[8]] => 0110101
[8,7,2,1,6,4,5,3] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[1,8,4,7,6,2,5,3] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[8,7,1,6,4,3,5,2] => [[1,4,7],[2],[3],[5],[6],[8]] => 1101101
[8,4,1,7,3,6,5,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[4,5,6,7,8,9,1,10,2,3] => [[1,2,3,4,5,6,8],[7,9,10]] => 000001010
[2,5,6,7,8,1,9,3,4] => [[1,2,3,4,5,7],[6,8,9]] => 00001010
[1,3,6,7,8,9,2,4,5] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[4,5,1,8,7,3,6,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[3,8,5,2,6,7,4,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[3,6,4,7,5,2,1,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,7,4,1,2,6,8,3] => [[1,2,6,7],[3,5],[4,8]] => 0110001
[2,8,6,7,5,3,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => 0101110
[7,4,5,2,6,3,1,8] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[8,6,3,4,5,1,7,2] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[8,6,3,5,4,1,7,2] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[8,7,4,5,1,3,6,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[8,6,2,5,3,1,4,7] => [[1,4,7,8],[2],[3],[5],[6]] => 1101100
[8,4,7,3,1,2,5,6] => [[1,3,7,8],[2,6],[4],[5]] => 1011000
[8,7,3,5,1,6,4,2] => [[1,4,6],[2,7],[3],[5],[8]] => 1101011
[4,8,3,2,6,1,7,5] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[4,3,7,6,1,5,2,8] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[7,5,4,3,6,1,8,2] => [[1,5,7],[2,8],[3],[4],[6]] => 1110101
[4,6,8,5,3,1,2,7] => [[1,2,3],[4,7,8],[5],[6]] => 0011100
[5,6,8,4,3,7,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[7,5,8,4,2,1,6,3] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[1,4,8,7,6,2,5,3] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[7,2,4,1,5,3,8,6] => [[1,3,5,7],[2,6,8],[4]] => 1010101
[8,5,3,4,1,7,2,6] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[2,8,5,4,3,6,1,7] => [[1,2,6,8],[3],[4],[5],[7]] => 0111010
[8,6,5,3,1,2,7,4] => [[1,6,7],[2,8],[3],[4],[5]] => 1111001
[7,4,6,5,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => 1011101
[5,6,7,2,3,8,4,1] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[8,4,2,6,5,7,3,1] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[1,7,4,2,8,5,6,3] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[3,2,1,7,4,6,8,5] => [[1,4,6,7],[2,5],[3,8]] => 1101001
[6,2,5,7,1,4,3,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[4,8,5,3,1,2,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[8,5,2,4,6,1,3,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,5,3,4,7,2,6,8] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[8,4,6,1,5,7,3,2] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[6,4,7,2,1,3,8,5] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[6,7,3,1,2,4,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[3,1,8,7,6,2,5,4] => [[1,3,7],[2,4],[5],[6],[8]] => 1011101
[1,3,8,6,7,2,5,4] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[5,2,3,6,1,8,4,7] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,2,6,4,7,1,5,8] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[3,6,2,5,7,8,4,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[2,7,4,6,8,3,5,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,7,6,8,1,5,4,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[1,5,7,6,8,4,2,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,7,4,6,8,5,3,1] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[3,7,6,8,5,1,4,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[7,1,3,8,6,2,4,5] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[2,7,1,8,6,5,3,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[2,3,4,5,7,8,6,9,1] => [[1,2,3,4,5,6,8],[7],[9]] => 00000101
[2,3,4,5,7,9,8,6,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[8,1,5,2,6,4,7,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[5,3,4,7,6,2,1,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[4,1,8,5,7,2,6,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[4,1,8,2,7,5,6,3] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[7,6,8,2,4,3,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[7,4,5,3,8,1,6,2] => [[1,3,5],[2,7],[4,8],[6]] => 1010101
[7,3,6,1,4,2,8,5] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,7,2,6,4,5,1,3] => [[1,4,6],[2,8],[3],[5],[7]] => 1101010
[1,2,3,4,7,9,5,6,8] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[1,2,3,4,6,7,9,5,8] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[1,2,3,4,7,8,5,9,6] => [[1,2,3,4,5,6,8],[7,9]] => 00000101
[7,1,4,6,8,5,3,2] => [[1,3,4,5],[2],[6],[7],[8]] => 1000111
[7,2,5,1,6,4,8,3] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[2,7,1,5,6,4,8,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[1,5,7,8,4,6,3,2] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[1,4,8,5,7,6,3,2] => [[1,2,3,5],[4],[6],[7],[8]] => 0010111
[2,8,1,5,6,4,7,3] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,7,2,8,1,5,6,4] => [[1,2,4],[3,6,7],[5,8]] => 0101001
[7,3,2,5,1,6,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[8,7,2,1,3,6,5,4] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[7,3,2,8,1,4,6,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[3,6,2,1,8,4,7,5] => [[1,2,5],[3,6,7],[4,8]] => 0110101
[3,5,1,7,6,4,8,2] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[8,7,4,2,1,6,5,3] => [[1,6],[2,7],[3,8],[4],[5]] => 1111011
[5,4,7,6,2,1,8,3] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,5,2,8,7,1,6,4] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[3,7,6,5,4,1,8,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[4,6,5,3,1,8,7,2] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[4,5,2,6,7,3,8,1] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[9,3,10,1,2,4,5,6,7,8] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[10,3,1,9,2,4,5,6,7,8] => [[1,4,6,7,8,9,10],[2,5],[3]] => 110100000
[8,6,7,4,3,1,5,2] => [[1,3],[2,7],[4,8],[5],[6]] => 1011101
[4,7,1,8,5,3,2,6] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[8,6,7,1,4,3,5,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[8,6,7,2,1,3,5,4] => [[1,3,7],[2,6],[4,8],[5]] => 1011001
[8,5,6,1,7,4,2,3] => [[1,3,5],[2,6,8],[4],[7]] => 1010110
[6,4,1,2,5,7,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[6,1,5,4,2,7,3,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[6,4,2,3,1,7,5,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[3,4,6,1,8,2,7,5] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[5,3,1,4,7,6,2,8] => [[1,4,5,8],[2,6],[3,7]] => 1100110
[6,4,5,2,7,1,3,8] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[7,4,3,5,1,6,2,8] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,5,3,6,2,1,4,8] => [[1,4,8],[2,7],[3],[5],[6]] => 1101100
[6,4,3,7,1,8,2,5] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[3,1,2,7,6,4,5,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[5,1,2,7,6,3,4,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[5,6,1,7,2,4,3,8] => [[1,2,4,8],[3,5,6],[7]] => 0101010
[3,5,6,8,1,2,7,4] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[2,6,5,7,1,3,4,8] => [[1,2,4,8],[3,6,7],[5]] => 0101000
[2,3,7,1,5,6,4,8] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[2,6,5,3,4,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => 0110100
[2,6,1,3,5,4,7,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,6,1,5,2,8,7,3] => [[1,2,6],[3,4,7],[5,8]] => 0101011
[6,1,5,4,2,7,8,3] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[4,6,1,5,2,7,8,3] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[2,8,6,5,1,3,7,4] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[5,1,8,6,2,7,4,3] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[3,6,8,2,7,5,1,4] => [[1,2,3],[4,5],[6,8],[7]] => 0010110
[5,6,4,1,7,2,8,3] => [[1,2,5,7],[3,6,8],[4]] => 0110101
[3,8,6,1,5,7,4,2] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[8,1,6,3,4,2,5,7] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[7,4,2,3,1,6,8,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[9,8,10,7,6,5,4,3,1,2] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => 101111110
[8,7,9,6,5,4,2,1,3] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[8,9,7,6,5,4,2,1,3] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[8,9,7,6,5,4,2,3,1] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => 01111101
[1,6,4,5,7,3,2,8] => [[1,2,4,5,8],[3],[6],[7]] => 0100110
[1,6,4,5,7,2,8,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[1,7,5,6,4,8,3,2] => [[1,2,4,6],[3],[5],[7],[8]] => 0101011
[1,5,6,7,3,2,4,8] => [[1,2,3,4,8],[5,7],[6]] => 0001100
[8,2,4,3,1,7,5,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,2,1,4,3,7,5,6] => [[1,4,6,8],[2,5,7],[3]] => 1101010
[7,6,8,2,1,5,3,4] => [[1,3,8],[2,6],[4,7],[5]] => 1011010
[8,6,2,5,1,3,7,4] => [[1,4,7],[2,6,8],[3],[5]] => 1101001
[5,7,2,6,4,1,8,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[4,5,6,1,3,8,2,7] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[6,3,5,7,4,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[7,6,4,8,5,3,1,2] => [[1,4],[2,5],[3,8],[6],[7]] => 1101110
[8,2,1,6,4,7,3,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[1,3,8,6,5,2,7,4] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[2,7,3,8,5,6,4,1] => [[1,2,4,6],[3,5],[7],[8]] => 0101011
[1,2,8,5,7,4,6,3] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,6,8,5,4,7,2,3] => [[1,2,3],[4,6],[5,8],[7]] => 0011010
[5,7,1,8,3,2,6,4] => [[1,2,4],[3,5,7],[6,8]] => 0101101
[8,2,5,4,3,7,1,6] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,8,4,3,7,6,2,1] => [[1,2],[3,5],[4,6],[7],[8]] => 0110111
[8,1,5,3,4,7,2,6] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,1,8,7,4,5,3,2] => [[1,3,6],[2,4],[5],[7],[8]] => 1011011
[1,5,8,6,4,3,7,2] => [[1,2,3,7],[4],[5],[6],[8]] => 0011101
[5,8,6,4,2,1,7,3] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[2,6,1,8,4,7,5,3] => [[1,2,4],[3,5,6],[7],[8]] => 0101011
[5,3,8,6,1,2,7,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[5,8,1,4,6,2,7,3] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[3,7,6,2,1,4,8,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[4,6,2,3,7,1,8,5] => [[1,2,5,7],[3,4,8],[6]] => 0100101
[6,8,7,5,1,3,4,2] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[6,4,3,2,7,8,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[2,7,6,1,5,3,8,4] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[7,8,6,4,2,5,3,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[6,4,5,8,7,1,3,2] => [[1,3,4],[2,5],[6,7],[8]] => 1001101
[6,4,1,7,8,3,2,5] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[2,3,4,5,9,6,8,7,1] => [[1,2,3,4,5,7],[6],[8],[9]] => 00001011
[6,2,3,4,5,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => 100000001
[2,6,3,4,5,7,8,9,10,1] => [[1,2,4,5,6,7,8,9],[3],[10]] => 010000001
[6,4,3,8,7,2,5,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[5,4,7,2,1,3,8,6] => [[1,3,7],[2,6,8],[4],[5]] => 1011001
[2,6,4,5,7,1,8,3] => [[1,2,4,5,7],[3,8],[6]] => 0100101
[3,7,4,6,1,5,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[3,4,6,5,2,8,1,7] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[4,6,7,5,8,2,1,3] => [[1,2,3,5],[4,8],[6],[7]] => 0010110
[2,5,7,6,4,1,8,3] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[5,1,4,6,2,7,8,3] => [[1,3,4,6,7],[2,8],[5]] => 1001001
[1,2,5,3,7,8,6,4] => [[1,2,3,5,6],[4,7],[8]] => 0010011
[4,8,3,5,1,2,7,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,1,3,7,2,8,4,5] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[3,8,5,4,1,7,2,6] => [[1,2,6],[3,7,8],[4],[5]] => 0111010
[3,1,5,8,2,6,7,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[2,8,5,3,1,7,4,6] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[6,5,2,3,7,1,8,4] => [[1,4,5,7],[2,8],[3],[6]] => 1100101
[7,2,1,6,4,8,3,5] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[2,1,3,7,5,8,4,6] => [[1,3,4,6],[2,5,8],[7]] => 1001010
[6,2,4,5,7,1,8,3] => [[1,3,4,5,7],[2,8],[6]] => 1000101
[2,3,8,7,1,4,6,5] => [[1,2,3,7],[4,6],[5],[8]] => 0011001
[4,2,7,5,6,8,1,3] => [[1,3,5,6],[2,4],[7,8]] => 1010010
[6,8,2,5,4,7,3,1] => [[1,2,6],[3,4],[5],[7],[8]] => 0101011
[7,2,3,4,5,6,9,1,8] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[3,2,9,1,4,5,6,7,8] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000
[5,3,2,7,6,1,8,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[5,6,4,2,8,7,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,7,4,2,6,1,8,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[5,4,7,1,6,2,8,3] => [[1,3,7],[2,5,8],[4,6]] => 1010101
[4,5,8,7,6,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,4,7,1,2,3,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[4,5,6,8,2,9,3,10,7,1] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[10,4,5,6,9,3,8,2,7,1] => [[1,3,4,5],[2,7],[6,9],[8],[10]] => 100010101
[4,5,10,6,9,3,8,2,7,1] => [[1,2,3,5],[4,7],[6,9],[8],[10]] => 001010101
[10,6,9,5,4,3,8,2,7,1] => [[1,3],[2,7],[4,9],[5],[6],[8],[10]] => 101110101
[4,5,6,8,2,10,7,1,9,3] => [[1,2,3,4,6],[5,7,9],[8,10]] => 000101101
[4,5,9,3,10,7,1,8,2,6] => [[1,2,3,5],[4,6,8],[7,9,10]] => 001011010
[1,8,7,2,3,4,6,5] => [[1,2,5,6,7],[3],[4],[8]] => 0110001
[1,8,3,7,6,2,5,4] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[1,3,8,2,5,6,4,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[1,3,2,7,4,6,8,5] => [[1,2,4,6,7],[3,5],[8]] => 0101001
[1,3,8,4,6,2,7,5] => [[1,2,3,5,7],[4,8],[6]] => 0010101
[8,2,3,6,7,4,5,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[5,6,4,2,1,7,3,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[2,5,7,6,3,8,4,1] => [[1,2,3,6],[4,7],[5],[8]] => 0011011
[6,4,7,1,2,5,3,8] => [[1,3,6,8],[2,5],[4,7]] => 1010010
[1,2,7,5,8,6,3,4] => [[1,2,3,5],[4,6],[7,8]] => 0010110
[2,1,9,8,7,6,5,3,4] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[2,1,9,8,7,6,4,3,5] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[2,1,10,9,8,7,6,5,3,4] => [[1,3,10],[2,4],[5],[6],[7],[8],[9]] => 101111110
[7,4,5,1,6,8,2,3] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[1,7,8,4,2,6,3,5] => [[1,2,3,8],[4,6],[5,7]] => 0011010
[6,3,2,5,7,4,1,8] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[6,2,1,5,3,7,8,4] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[6,2,5,1,3,8,7,4] => [[1,3,6],[2,5,7],[4,8]] => 1010011
[6,2,8,5,1,3,7,4] => [[1,3,7],[2,4,8],[5,6]] => 1011001
[10,7,2,6,1,3,8,4,9,5] => [[1,4,7,9],[2,6,8,10],[3],[5]] => 110100101
[9,4,10,8,3,7,2,6,1,5] => [[1,3],[2,4],[5,6],[7,8],[9,10]] => 101101010
[12,8,2,7,1,3,9,4,10,5,11,6] => [[1,4,7,9,11],[2,6,8,10,12],[3],[5]] => 11010010101
[11,5,12,10,4,9,3,8,2,7,1,6] => [[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => 10110101010
[4,1,7,8,3,6,5,2] => [[1,3,4],[2,5,6],[7],[8]] => 1001011
[6,4,2,1,7,3,5,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[5,8,4,2,1,3,6,7] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[4,5,3,6,7,8,9,1,2] => [[1,2,4,5,6,7],[3,9],[8]] => 01000010
[5,3,4,6,7,8,9,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => 10000010
[1,7,5,8,4,3,6,2] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[5,8,1,6,4,7,2,3] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[2,4,7,5,1,8,6,3] => [[1,2,3,6],[4,7],[5,8]] => 0011011
[2,3,7,1,8,5,6,4] => [[1,2,3,5],[4,6,7],[8]] => 0010101
[6,5,1,2,7,4,8,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[3,6,5,7,8,2,4,1] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,6,5,1,8,7,4,2] => [[1,2,5],[3,6],[4,7],[8]] => 0110111
[7,8,1,2,5,4,3,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[2,8,4,3,5,1,7,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,2,4,7,6,8,1,3] => [[1,3,4,6],[2,5],[7,8]] => 1001010
[3,1,5,7,4,8,6,2] => [[1,3,4,6],[2,5,7],[8]] => 1001011
[4,1,7,6,8,2,5,3] => [[1,3,5],[2,4,7],[6],[8]] => 1010101
[7,2,6,4,1,5,3,8] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[1,2,6,5,8,3,7,4] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[7,3,5,6,1,4,2,8] => [[1,3,4,8],[2,6],[5],[7]] => 1001010
[5,8,3,1,6,7,4,2] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[4,5,8,1,7,3,6,2] => [[1,2,3],[4,5,7],[6],[8]] => 0010101
[4,7,1,6,8,5,2,3] => [[1,2,5],[3,4,8],[6],[7]] => 0100110
[5,8,7,1,6,4,2,3] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[1,7,3,8,2,5,4,6] => [[1,2,4,8],[3,6],[5,7]] => 0101010
[8,4,1,3,6,7,5,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,3,1,8,6,7,4,2] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[6,2,7,1,4,3,5,8] => [[1,3,7,8],[2,5],[4,6]] => 1010100
[9,5,4,3,2,1,6,7,8] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[10,3,4,1,2,5,6,7,8,9] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[8,3,2,6,5,1,7,4] => [[1,4,7],[2,5],[3,8],[6]] => 1101101
[2,6,8,4,7,1,3,5] => [[1,2,3],[4,5,8],[6,7]] => 0010100
[7,8,6,3,2,5,4,1] => [[1,2],[3,6],[4,7],[5],[8]] => 0111011
[1,6,4,8,2,3,5,7] => [[1,2,4,7,8],[3,6],[5]] => 0101000
[2,8,5,6,4,1,7,3] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[1,4,7,3,5,8,6,2] => [[1,2,3,6],[4,5,7],[8]] => 0010011
[3,7,8,2,5,1,6,4] => [[1,2,3],[4,5,7],[6,8]] => 0010101
[8,6,1,4,3,2,7,5] => [[1,4,7],[2,8],[3],[5],[6]] => 1101101
[7,3,8,2,4,1,5,6] => [[1,3,7,8],[2,5],[4],[6]] => 1010100
[6,3,7,8,1,2,5,4] => [[1,3,4],[2,6,7],[5,8]] => 1001001
[7,6,1,5,2,3,8,4] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[5,1,8,6,7,2,3,4] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[5,7,1,6,8,2,3,4] => [[1,2,5,8],[3,4,7],[6]] => 0100100
[6,8,4,2,1,7,3,5] => [[1,2,8],[3,6],[4,7],[5]] => 0111010
[6,3,2,8,1,7,4,5] => [[1,4,8],[2,6],[3,7],[5]] => 1101010
[6,4,1,3,7,8,5,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[6,8,5,4,3,7,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => 0111010
[5,7,4,8,3,1,2,6] => [[1,2,4],[3,7,8],[5],[6]] => 0101100
[6,1,2,4,8,3,7,5] => [[1,3,4,5],[2,7],[6,8]] => 1000101
[2,5,6,8,1,4,7,3] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[7,4,1,6,5,2,3,8] => [[1,4,7,8],[2,5],[3],[6]] => 1101100
[4,1,6,5,2,3,8,7] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[4,5,1,7,8,6,2,3] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[8,5,7,3,4,6,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[6,8,7,4,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[6,8,7,5,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => 0111011
[5,8,6,2,4,7,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[4,8,6,2,5,7,3,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[1,6,4,7,5,3,2,8] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[1,6,5,3,2,7,4,8] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[1,6,8,7,4,5,3,2] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[1,4,7,5,3,2,6,8] => [[1,2,3,7,8],[4],[5],[6]] => 0011100
[1,7,5,4,3,2,8,6] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[1,4,7,5,3,2,8,6] => [[1,2,3,7],[4,8],[5],[6]] => 0011101
[1,7,4,6,8,5,3,2] => [[1,2,4,5],[3],[6],[7],[8]] => 0100111
[6,8,7,2,3,5,4,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[5,7,6,1,8,2,4,3] => [[1,2,5],[3,6,7],[4],[8]] => 0110101
[4,8,6,5,7,2,3,1] => [[1,2,5],[3,7],[4],[6],[8]] => 0110101
[2,7,8,5,1,4,3,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,5,6,2,4,7,3,1] => [[1,3,6],[2,5],[4],[7],[8]] => 1010011
[8,1,3,6,4,5,2,7] => [[1,3,4,6,8],[2],[5],[7]] => 1001010
[1,2,3,7,4,8,5,9,6] => [[1,2,3,4,6,8],[5,7,9]] => 00010101
[1,2,3,4,7,5,9,8,6] => [[1,2,3,4,5,7],[6,8],[9]] => 00001011
[1,2,6,3,7,4,9,8,5] => [[1,2,3,5,7],[4,6,8],[9]] => 00101011
[1,2,3,8,6,4,9,7,5] => [[1,2,3,4,7],[5,8],[6,9]] => 00011011
[1,2,3,6,4,9,8,7,5] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[5,1,6,2,7,3,9,8,4] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[1,5,2,8,6,3,9,7,4] => [[1,2,4,7],[3,5,8],[6,9]] => 01011011
[1,5,2,6,3,9,8,7,4] => [[1,2,4,6],[3,5,7],[8],[9]] => 01010111
[1,2,7,5,3,9,8,6,4] => [[1,2,3,6],[4,7],[5,8],[9]] => 00110111
[1,2,5,3,9,8,7,6,4] => [[1,2,3,5],[4,6],[7],[8],[9]] => 00101111
[4,1,7,5,2,9,8,6,3] => [[1,3,6],[2,4,7],[5,8],[9]] => 10110111
[4,1,5,2,9,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8],[9]] => 10101111
[1,6,4,2,9,8,7,5,3] => [[1,2,5],[3,6],[4,7],[8],[9]] => 01101111
[1,4,2,9,8,7,6,5,3] => [[1,2,4],[3,5],[6],[7],[8],[9]] => 01011111
[7,5,3,1,9,8,6,4,2] => [[1,5],[2,6],[3,7],[4,8],[9]] => 11101111
[5,3,1,9,8,7,6,4,2] => [[1,4],[2,5],[3,6],[7],[8],[9]] => 11011111
[1,2,3,4,8,5,9,6,10,7] => [[1,2,3,4,5,7,9],[6,8,10]] => 000010101
[1,2,3,4,5,8,6,10,9,7] => [[1,2,3,4,5,6,8],[7,9],[10]] => 000001011
[1,2,3,7,4,8,5,10,9,6] => [[1,2,3,4,6,8],[5,7,9],[10]] => 000101011
[1,2,3,4,9,7,5,10,8,6] => [[1,2,3,4,5,8],[6,9],[7,10]] => 000011011
[1,2,3,4,7,5,10,9,8,6] => [[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111
[1,6,2,7,3,8,4,10,9,5] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,2,6,3,9,7,4,10,8,5] => [[1,2,3,5,8],[4,6,9],[7,10]] => 001011011
[1,2,6,3,7,4,10,9,8,5] => [[1,2,3,5,7],[4,6,8],[9],[10]] => 001010111
[1,2,3,8,6,4,10,9,7,5] => [[1,2,3,4,7],[5,8],[6,9],[10]] => 000110111
[1,2,3,6,4,10,9,8,7,5] => [[1,2,3,4,6],[5,7],[8],[9],[10]] => 000101111
[5,1,6,2,9,7,3,10,8,4] => [[1,3,5,8],[2,4,6,9],[7,10]] => 101011011
[5,1,6,2,7,3,10,9,8,4] => [[1,3,5,7],[2,4,6,8],[9],[10]] => 101010111
[1,5,2,6,3,10,9,8,7,4] => [[1,2,4,6],[3,5,7],[8],[9],[10]] => 010101111
[1,2,7,5,3,10,9,8,6,4] => [[1,2,3,6],[4,7],[5,8],[9],[10]] => 001101111
[1,2,5,3,10,9,8,7,6,4] => [[1,2,3,5],[4,6],[7],[8],[9],[10]] => 001011111
[7,4,1,8,5,2,10,9,6,3] => [[1,4,7],[2,5,8],[3,6,9],[10]] => 110110111
[4,1,9,7,5,2,10,8,6,3] => [[1,3,7],[2,4,8],[5,9],[6,10]] => 101110111
[4,1,7,5,2,10,9,8,6,3] => [[1,3,6],[2,4,7],[5,8],[9],[10]] => 101101111
[4,1,5,2,10,9,8,7,6,3] => [[1,3,5],[2,4,6],[7],[8],[9],[10]] => 101011111
[1,8,6,4,2,10,9,7,5,3] => [[1,2,6],[3,7],[4,8],[5,9],[10]] => 011101111
[1,6,4,2,10,9,8,7,5,3] => [[1,2,5],[3,6],[4,7],[8],[9],[10]] => 011011111
[1,4,2,10,9,8,7,6,5,3] => [[1,2,4],[3,5],[6],[7],[8],[9],[10]] => 010111111
[7,5,3,1,10,9,8,6,4,2] => [[1,5],[2,6],[3,7],[4,8],[9],[10]] => 111011111
[5,3,1,10,9,8,7,6,4,2] => [[1,4],[2,5],[3,6],[7],[8],[9],[10]] => 110111111
[4,3,1,6,2,5,8,7] => [[1,4,6,7],[2,5,8],[3]] => 1101001
[7,5,2,1,8,4,3,6] => [[1,5,8],[2,6],[3,7],[4]] => 1110110
[5,3,1,4,7,8,2,6] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[7,1,2,4,8,3,5,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[8,6,1,3,5,7,4,2] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[7,1,5,8,2,3,4,6] => [[1,3,4,7,8],[2,6],[5]] => 1001000
[3,6,8,5,1,4,2,7] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[5,2,4,1,6,8,3,7] => [[1,3,5,6],[2,7,8],[4]] => 1010010
[2,5,3,4,6,8,1,7] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[4,7,1,2,5,6,3,8] => [[1,2,5,6,8],[3,4],[7]] => 0100010
[6,7,3,1,8,2,4,5] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[7,3,1,4,6,2,8,5] => [[1,4,5,7],[2,6,8],[3]] => 1100101
[7,4,1,2,5,6,3,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[5,4,1,3,6,8,7,2] => [[1,4,5,6],[2,7],[3],[8]] => 1100011
[5,7,4,8,1,6,3,2] => [[1,2,4],[3,6],[5,7],[8]] => 0101011
[4,3,1,2,5,7,6,8] => [[1,4,5,6,8],[2,7],[3]] => 1100010
[1,2,3,4,5,8,9,7,6] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[1,2,3,4,8,9,6,7,5] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[1,2,4,7,8,5,6,3] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[1,2,8,9,4,5,6,7,3] => [[1,2,3,4,7,8],[5,6],[9]] => 00010001
[8,3,6,5,7,4,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,2,6,5,7,4,3,1] => [[1,3,5],[2],[4],[6],[7],[8]] => 1010111
[8,4,7,1,5,2,6,3] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[8,2,6,3,7,5,4,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,2,5,3,7,6,4,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[8,5,7,1,4,3,6,2] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[5,3,1,8,4,2,6,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[2,1,6,5,8,7,3,4] => [[1,3,5],[2,4,6],[7,8]] => 1010110
[6,1,5,4,7,3,8,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[3,1,8,4,2,7,6,5] => [[1,3,6],[2,4,7],[5],[8]] => 1011011
[2,8,7,4,1,3,6,5] => [[1,2,7],[3,6,8],[4],[5]] => 0111001
[8,2,3,1,7,6,4,5] => [[1,3,5,8],[2,6],[4],[7]] => 1010110
[8,7,2,3,1,6,4,5] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[7,2,5,8,3,1,4,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[6,8,2,3,1,7,4,5] => [[1,2,6,8],[3,4],[5,7]] => 0101010
[8,2,5,7,3,1,4,6] => [[1,3,4,8],[2,7],[5],[6]] => 1001100
[8,2,7,3,1,4,5,6] => [[1,3,6,7,8],[2],[4],[5]] => 1011000
[5,3,2,8,7,1,6,4] => [[1,4],[2,5],[3,7],[6,8]] => 1101101
[8,6,7,4,1,3,5,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[4,1,3,6,5,2,8,7] => [[1,3,4,7],[2,5,8],[6]] => 1001101
[4,6,3,2,5,1,8,7] => [[1,2,7],[3,5,8],[4],[6]] => 0110101
[4,8,3,2,6,5,7,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[4,8,3,6,5,2,7,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[8,1,6,2,5,4,7,3] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[2,4,3,8,6,1,7,5] => [[1,2,4,7],[3,5],[6,8]] => 0101101
[2,6,3,8,5,4,7,1] => [[1,2,4,7],[3,5],[6],[8]] => 0101101
[6,1,3,2,5,8,7,4] => [[1,3,5,6],[2,7],[4,8]] => 1010011
[6,8,4,2,5,3,7,1] => [[1,2,7],[3,5],[4,6],[8]] => 0110101
[6,8,4,3,5,2,7,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,1,4,6,5,3,7,2] => [[1,3,4,7],[2],[5],[6],[8]] => 1001101
[3,5,4,6,1,2,8,7] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[3,1,5,2,9,6,7,8,4] => [[1,3,5,7,8],[2,4,6],[9]] => 10101001
[1,2,4,5,7,9,6,3,8] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[7,3,5,6,1,8,2,4] => [[1,3,4,6],[2,7,8],[5]] => 1001010
[5,7,6,3,4,2,8,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[4,6,7,2,3,5,8,1] => [[1,2,3,7],[4,5,6],[8]] => 0010001
[6,5,4,8,7,2,3,1] => [[1,4],[2,5],[3,7],[6],[8]] => 1101101
[7,2,8,3,9,4,10,5,1,6] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[7,2,8,3,9,4,10,1,5,6] => [[1,3,5,7,10],[2,4,6,9],[8]] => 101010100
[4,8,7,6,5,3,2,1,9] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => 01111110
[5,9,8,7,6,4,3,2,1,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => 011111110
[5,7,4,3,6,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[10,9,8,6,1,7,5,4,3,2] => [[1,6],[2,7],[3],[4],[5],[8],[9],[10]] => 111101111
[1,8,2,9,4,3,5,6,7] => [[1,2,4,7,8,9],[3,5],[6]] => 01011000
[1,5,2,9,3,10,4,6,7,8] => [[1,2,4,6,8,9,10],[3,5,7]] => 010101000
[1,8,5,6,2,3,7,4] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[1,8,3,9,4,2,5,6,7] => [[1,2,4,7,8,9],[3,5],[6]] => 01011000
[2,1,3,4,5,9,6,10,7,8] => [[1,3,4,5,6,8,10],[2,7,9]] => 100001010
[8,5,6,1,3,2,7,4] => [[1,3,7],[2,5,8],[4],[6]] => 1010101
[5,3,7,8,2,6,1,4] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[4,5,8,3,6,1,7,2] => [[1,2,3,7],[4,5],[6,8]] => 0010101
[4,5,8,7,2,3,1,6] => [[1,2,3],[4,6,8],[5],[7]] => 0011010
[8,2,6,4,3,7,5,1] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[6,3,1,8,7,4,5,2] => [[1,4,7],[2,5],[3,6],[8]] => 1101101
[8,6,3,2,7,4,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[1,3,6,8,7,4,5,2] => [[1,2,3,4],[5,7],[6],[8]] => 0001101
[5,7,1,3,6,2,4,8] => [[1,2,5,8],[3,4],[6,7]] => 0100100
[4,7,5,2,3,6,8,1] => [[1,2,6,7],[3,5],[4],[8]] => 0110001
[3,6,4,1,2,5,7,8] => [[1,2,6,7,8],[3,5],[4]] => 0110000
[4,7,1,3,2,5,8,6] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[4,7,1,3,2,6,8,5] => [[1,2,6,7],[3,4],[5,8]] => 0101001
[5,7,1,3,6,2,8,4] => [[1,2,5,7],[3,4],[6,8]] => 0100101
[6,8,2,5,7,3,1,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,8,5,2,3,6,1,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[5,8,6,3,4,7,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => 0110011
[3,7,5,4,2,8,1,6] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[4,6,5,1,7,8,2,3] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[4,7,1,3,2,8,5,6] => [[1,2,6,8],[3,4,7],[5]] => 0101010
[3,6,5,1,8,2,4,7] => [[1,2,5,8],[3,6,7],[4]] => 0110100
[5,8,7,3,4,2,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[8,5,2,3,7,4,6,1] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[6,3,1,5,4,8,2,7] => [[1,4,6],[2,5,8],[3],[7]] => 1101010
[4,7,6,3,5,2,8,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[1,7,5,3,4,8,6,2] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,8,2,3,4,7,6,1] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[8,7,3,2,6,4,5,1] => [[1,5,7],[2,6],[3],[4],[8]] => 1110101
[8,3,1,4,7,5,2,6] => [[1,4,5,8],[2,6],[3],[7]] => 1100110
[5,3,1,6,4,8,7,2] => [[1,4,6],[2,5,7],[3,8]] => 1101011
[3,4,8,5,7,2,6,1] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[8,5,1,2,7,6,4,3] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[10,7,8,1,2,3,4,5,6,9] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000
[6,7,10,1,2,3,4,5,8,9] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000
[3,7,8,5,6,2,4,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[7,4,3,6,2,5,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[4,3,8,7,1,6,2,5] => [[1,3,8],[2,4],[5,6],[7]] => 1011010
[1,5,3,8,4,7,2,6] => [[1,2,4,6],[3,5],[7,8]] => 0101010
[8,2,3,1,6,5,7,4] => [[1,3,5,7],[2,6],[4],[8]] => 1010101
[8,4,2,7,1,3,6,5] => [[1,4,7],[2,6],[3,8],[5]] => 1101001
[8,4,2,3,1,6,7,5] => [[1,4,6,7],[2,8],[3],[5]] => 1101001
[4,7,2,3,6,5,8,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[3,8,2,6,4,7,1,5] => [[1,2,6],[3,4,8],[5],[7]] => 0101010
[1,7,5,8,6,2,4,3] => [[1,2,4],[3,5],[6,7],[8]] => 0101101
[6,5,1,7,4,8,3,2] => [[1,4,6],[2,5],[3],[7],[8]] => 1101011
[10,9,8,6,7,5,4,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[7,6,3,5,1,4,8,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[6,5,4,1,7,2,3,8] => [[1,5,7,8],[2,6],[3],[4]] => 1110100
[8,3,6,1,7,4,5,2] => [[1,3,5],[2,6,7],[4],[8]] => 1010101
[7,1,2,6,4,8,3,5] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[3,5,1,8,6,2,4,7] => [[1,2,4,8],[3,5,7],[6]] => 0101100
[9,8,7,6,4,3,2,5,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[8,5,6,7,4,3,2,1,9] => [[1,3,4,9],[2],[5],[6],[7],[8]] => 10011110
[10,9,7,6,8,5,4,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[10,8,7,6,9,5,4,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => 111011111
[8,9,7,6,4,3,2,1,5] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[7,6,5,3,2,1,4,8,9] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000
[9,8,7,6,4,3,5,1,2] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010
[9,8,7,6,4,3,2,5,1,10] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => 111111010
[9,8,7,6,4,5,2,3,1] => [[1,6],[2,8],[3],[4],[5],[7],[9]] => 11110101
[1,8,7,5,4,6,2,3] => [[1,2,6],[3,8],[4],[5],[7]] => 0111010
[8,1,6,7,4,5,3,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[8,1,6,4,7,5,3,2] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[6,4,8,1,5,3,7,2] => [[1,3,7],[2,5],[4,6],[8]] => 1010101
[1,6,4,3,5,8,2,7] => [[1,2,5,6],[3,8],[4],[7]] => 0110010
[5,1,4,3,7,8,6,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[5,7,1,8,6,3,2,4] => [[1,2,4],[3,5,8],[6],[7]] => 0101110
[5,7,6,3,4,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => 0110110
[4,1,3,7,6,5,2,8] => [[1,3,4,8],[2,5],[6],[7]] => 1001110
[8,7,6,5,4,2,3,1,9] => [[1,7,9],[2],[3],[4],[5],[6],[8]] => 11111010
[4,3,6,1,2,7,8,5] => [[1,3,6,7],[2,5,8],[4]] => 1010001
[5,8,3,6,7,2,4,1] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[8,1,6,2,5,7,4,3] => [[1,3,5,6],[2],[4],[7],[8]] => 1010011
[2,7,1,5,3,6,8,4] => [[1,2,6,7],[3,4,8],[5]] => 0101001
[6,8,7,3,4,2,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[1,8,6,2,4,7,5,3] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[5,7,3,6,4,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => 0101110
[5,7,3,6,4,1,8,2] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[3,7,5,6,4,1,8,2] => [[1,2,4,7],[3,8],[5],[6]] => 0101101
[6,8,1,2,3,4,5,9,7] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[2,8,5,7,3,4,6,1] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[2,6,4,1,5,3,7,8,9] => [[1,2,5,7,8,9],[3,6],[4]] => 01101000
[4,5,2,6,3,1,7,8,9] => [[1,2,4,7,8,9],[3,5],[6]] => 01011000
[2,8,4,1,6,3,7,5,9] => [[1,2,5,7,9],[3,6,8],[4]] => 01101010
[3,5,9,7,1,8,2,6,4] => [[1,2,3,6],[4,7,8],[5],[9]] => 00110101
[5,7,8,3,9,4,1,6,2] => [[1,2,3,5],[4,6,8],[7,9]] => 00101101
[7,8,2,3,4,5,9,6,1] => [[1,2,5,6,7],[3,4,8],[9]] => 01000011
[2,4,3,1,5,6,7,8,9,10] => [[1,2,5,6,7,8,9,10],[3],[4]] => 011000000
[2,6,4,1,5,3,7,8,9,10] => [[1,2,5,7,8,9,10],[3,6],[4]] => 011010000
[4,5,2,6,3,1,7,8,9,10] => [[1,2,4,7,8,9,10],[3,5],[6]] => 010110000
[2,8,4,1,6,3,7,5,9,10] => [[1,2,5,7,9,10],[3,6,8],[4]] => 011010100
[2,7,4,9,6,3,10,8,5,1] => [[1,2,4,7],[3,5,8],[6,9],[10]] => 010110111
[8,9,2,3,4,5,6,10,7,1] => [[1,2,5,6,7,8],[3,4,9],[10]] => 010000011
[2,1,3,8,5,4,6,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[5,3,6,8,2,4,1,7] => [[1,3,4],[2,6,8],[5],[7]] => 1001010
[1,7,8,6,3,2,4,5] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,1,2,5,3,8,4,6] => [[1,3,4,6,8],[2,7],[5]] => 1001010
[3,7,4,2,5,1,8,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,8,3,4,5,7,2,6] => [[1,2,4,5,6],[3,8],[7]] => 0100010
[4,5,7,6,2,1,3,8] => [[1,2,3,8],[4,7],[5],[6]] => 0011100
[7,8,2,6,5,4,3,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[5,3,7,8,4,2,1,6] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,3,6,8,1,5,4,2] => [[1,3,4],[2,6],[5],[7],[8]] => 1001011
[7,5,8,2,4,3,6,1] => [[1,3,7],[2,5],[4],[6],[8]] => 1010101
[6,5,8,2,3,4,1,7] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[8,1,5,3,4,6,2,7] => [[1,3,5,6,8],[2],[4],[7]] => 1010010
[5,8,7,2,4,3,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[1,7,2,4,8,5,6,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[5,8,2,3,7,4,6,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[7,8,2,3,5,4,6,1] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,4,1,3,2,6,5,7] => [[1,4,6,8],[2,7],[3],[5]] => 1101010
[8,7,2,3,5,4,6,1] => [[1,4,5,7],[2],[3],[6],[8]] => 1100101
[1,7,6,8,4,5,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[2,7,3,1,8,5,6,4] => [[1,2,5,7],[3,6],[4,8]] => 0110101
[3,8,5,2,1,6,7,4] => [[1,2,6,7],[3,8],[4],[5]] => 0111001
[4,8,7,1,2,5,3,6] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[8,7,2,6,1,4,3,5] => [[1,4,8],[2,6],[3],[5],[7]] => 1101010
[6,1,7,3,8,2,4,5] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[7,1,8,6,4,2,3,5] => [[1,3,7,8],[2,4],[5],[6]] => 1011100
[4,1,3,5,8,2,6,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[1,8,5,7,4,6,3,2] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[1,4,7,6,8,3,5,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[1,7,2,8,6,5,3,4] => [[1,2,4,8],[3,5],[6],[7]] => 0101110
[5,7,1,6,4,2,3,8] => [[1,2,7,8],[3,4],[5],[6]] => 0101100
[4,8,2,7,5,1,6,3] => [[1,2,7],[3,4],[5,8],[6]] => 0101101
[2,8,4,6,7,1,5,3] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[3,8,5,1,4,2,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[1,7,6,2,5,3,8,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[1,7,5,2,4,3,8,6] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[2,8,5,1,4,3,6,7] => [[1,2,7,8],[3,5],[4],[6]] => 0110100
[9,7,6,5,4,3,2,8,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9]] => 11111101
[3,1,2,5,7,6,8,4] => [[1,3,4,5,7],[2,6],[8]] => 1000101
[5,1,7,3,2,6,8,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[4,7,2,3,5,1,6,8] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[4,8,2,3,7,5,1,6] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[8,7,2,4,3,5,6,1] => [[1,4,6,7],[2],[3],[5],[8]] => 1101001
[8,6,2,4,3,5,1,7] => [[1,4,6,8],[2],[3],[5],[7]] => 1101010
[8,1,2,4,7,3,5,6] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[7,6,2,8,4,5,1,3] => [[1,4,6],[2,5],[3,8],[7]] => 1101010
[6,8,1,5,7,3,2,4] => [[1,2,5],[3,4],[6,8],[7]] => 0100110
[4,1,7,5,6,8,2,3] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,7,6,2,1,4,5,8] => [[1,2,7,8],[3,6],[4],[5]] => 0111000
[1,6,8,7,2,5,4,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[1,4,8,7,6,3,5,2] => [[1,2,3],[4,7],[5],[6],[8]] => 0011101
[4,6,7,5,2,3,1,8] => [[1,2,3,8],[4,6],[5],[7]] => 0011010
[6,2,5,3,1,8,7,4] => [[1,3,6],[2,7],[4,8],[5]] => 1011011
[6,2,5,3,8,7,1,4] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[6,4,5,3,8,7,1,2] => [[1,3,5],[2,6],[4,8],[7]] => 1010110
[1,6,4,5,8,7,3,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,4,7,5,2,3,1,6] => [[1,3,8],[2,6],[4],[5],[7]] => 1011010
[8,2,7,4,5,3,1,6] => [[1,3,5,8],[2],[4],[6],[7]] => 1010110
[8,2,4,7,5,3,1,6] => [[1,3,4,8],[2],[5],[6],[7]] => 1001110
[8,2,6,7,5,3,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[8,4,6,7,5,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => 1001110
[6,4,5,8,7,3,1,2] => [[1,3,4],[2,5],[6,8],[7]] => 1001110
[6,2,8,7,5,3,1,4] => [[1,3,8],[2,4],[5],[6],[7]] => 1011110
[4,6,5,3,8,7,1,2] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[6,7,2,4,5,3,1,8] => [[1,2,5,8],[3,4],[6],[7]] => 0100110
[6,8,7,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[2,8,4,7,5,3,1,6] => [[1,2,4,8],[3],[5],[6],[7]] => 0101110
[5,8,7,4,6,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => 0110110
[6,5,8,4,7,2,1,3] => [[1,3],[2,5],[4,8],[6],[7]] => 1010110
[4,8,6,2,5,7,1,3] => [[1,2,6],[3,5],[4,8],[7]] => 0110010
[8,1,6,2,5,7,3,4] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,8,1,2,4,7,3,5] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[8,1,5,3,2,7,4,6] => [[1,3,6,8],[2,7],[4],[5]] => 1011010
[8,3,7,6,2,5,4,1] => [[1,3],[2,6],[4],[5],[7],[8]] => 1011011
[5,3,1,2,6,7,8,9,10,4] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[1,2,3,4,7,8,5,6,9] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[1,2,3,4,6,5,8,7,9] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[1,2,3,4,8,9,5,6,7] => [[1,2,3,4,5,6,9],[7,8]] => 00000100
[4,6,1,3,5,8,2,7] => [[1,2,5,6],[3,4,8],[7]] => 0100010
[4,5,1,3,8,7,2,6] => [[1,2,5],[3,4,6],[7,8]] => 0100110
[6,2,7,1,8,3,4,5] => [[1,3,5,8],[2,6,7],[4]] => 1010100
[6,4,5,8,1,7,2,3] => [[1,3,4],[2,6,8],[5,7]] => 1001010
[6,2,8,5,1,4,7,3] => [[1,3,7],[2,4],[5,6],[8]] => 1011001
[2,4,7,6,1,8,3,5] => [[1,2,3,6],[4,7,8],[5]] => 0011010
[2,6,7,8,9,10,1,3,4,5] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[9,7,5,3,8,6,4,2,1] => [[1,5],[2,6],[3,7],[4],[8],[9]] => 11101111
[10,8,9,7,6,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => 101111111
[7,4,5,8,6,3,2,1] => [[1,3,4],[2,5],[6],[7],[8]] => 1001111
[8,6,9,7,4,3,2,1,5] => [[1,3],[2,4],[5,9],[6],[7],[8]] => 10111110
[8,6,4,9,7,5,2,1,3] => [[1,4],[2,5],[3,6],[7,9],[8]] => 11011110
[10,8,6,4,9,7,5,3,2,1] => [[1,5],[2,6],[3,7],[4],[8],[9],[10]] => 111011111
[10,8,6,4,2,1,9,7,5,3] => [[1,7],[2,8],[3,9],[4,10],[5],[6]] => 111110111
[9,6,7,8,5,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => 10011111
[10,8,9,6,5,4,3,2,1,7] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => 101111110
[9,7,10,8,5,4,3,2,1,6] => [[1,3],[2,4],[5,10],[6],[7],[8],[9]] => 101111110
[8,6,3,2,1,9,7,4,5] => [[1,6,9],[2,7],[3,8],[4],[5]] => 11110110
[8,6,9,7,3,2,1,4,5] => [[1,3,9],[2,4],[5,8],[6],[7]] => 10111100
[9,7,5,10,8,6,3,2,1,4] => [[1,4],[2,5],[3,6],[7,10],[8],[9]] => 110111110
[2,5,1,6,3,7,4,8,9] => [[1,2,4,6,8,9],[3,5,7]] => 01010100
[2,6,1,7,3,8,4,9,5] => [[1,2,4,6,8],[3,5,7,9]] => 01010101
[3,4,6,1,7,2,8,5,9] => [[1,2,3,5,7,9],[4,6,8]] => 00101010
[3,2,6,1,7,4,8,5,9] => [[1,3,5,7,9],[2,6,8],[4]] => 10101010
[4,2,5,7,1,8,3,9,6] => [[1,3,4,6,8],[2,7,9],[5]] => 10010101
[2,5,1,6,3,7,4,8,9,10] => [[1,2,4,6,8,9,10],[3,5,7]] => 010101000
[3,4,5,1,6,2,7,8,9,10] => [[1,2,3,5,7,8,9,10],[4,6]] => 001010000
[2,6,1,7,3,8,4,9,5,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 010101010
[3,4,6,1,7,2,8,5,9,10] => [[1,2,3,5,7,9,10],[4,6,8]] => 001010100
[3,2,6,1,7,4,8,5,9,10] => [[1,3,5,7,9,10],[2,6,8],[4]] => 101010100
[3,2,7,1,8,4,9,5,10,6] => [[1,3,5,7,9],[2,6,8,10],[4]] => 101010101
[4,5,6,7,1,8,2,9,3,10] => [[1,2,3,4,6,8,10],[5,7,9]] => 000101010
[5,2,6,7,8,1,9,3,10,4] => [[1,3,4,5,7,9],[2,8,10],[6]] => 100010101
[9,8,7,6,5,2,3,4,1] => [[1,7,8],[2],[3],[4],[5],[6],[9]] => 11111001
[4,5,6,7,1,9,2,3,8] => [[1,2,3,4,6],[5,7,8,9]] => 00010100
[3,5,6,7,9,1,2,4,8] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[4,1,6,7,8,9,2,3,5] => [[1,3,4,5,6],[2,7,8,9]] => 10000100
[5,1,6,7,8,9,10,2,3,4] => [[1,3,4,5,6,7],[2,8,9,10]] => 100000100
[7,4,1,3,6,8,2,5] => [[1,4,5,6],[2,8],[3],[7]] => 1100010
[6,8,1,2,7,3,4,5] => [[1,2,5,7,8],[3,4],[6]] => 0100100
[1,6,2,8,7,3,4,5] => [[1,2,4,7,8],[3,5],[6]] => 0101100
[1,6,8,5,7,4,3,2] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[3,8,1,2,4,7,6,5] => [[1,2,5,6],[3,4],[7],[8]] => 0100011
[1,4,5,7,3,6,8,2] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[2,3,8,1,4,6,5,7] => [[1,2,3,6,8],[4,5],[7]] => 0010010
[3,6,2,4,7,5,8,1] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,1,8,4,6,2,5,7] => [[1,3,5,8],[2,4,7],[6]] => 1010100
[4,2,7,3,5,8,1,6] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[3,1,8,4,5,6,2,7] => [[1,3,5,6,8],[2,4],[7]] => 1010010
[4,2,7,8,6,3,1,5] => [[1,3,4],[2,5,8],[6],[7]] => 1001110
[7,1,4,2,8,6,3,5] => [[1,3,5,8],[2,6],[4,7]] => 1010110
[2,3,7,4,8,1,6,5] => [[1,2,3,5],[4,7],[6,8]] => 0010101
[1,6,3,5,8,7,4,2] => [[1,2,4,5],[3,6],[7],[8]] => 0100111
[8,4,6,3,5,1,7,2] => [[1,3,7],[2,5],[4,8],[6]] => 1010101
[7,3,2,6,8,4,5,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[2,4,5,7,1,6,8,3] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[8,4,2,6,7,3,5,1] => [[1,4,5],[2,6,7],[3],[8]] => 1100101
[4,1,5,7,8,6,2,3] => [[1,3,4,5],[2,6,8],[7]] => 1000110
[6,1,4,8,2,3,7,5] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[7,6,2,3,5,8,4,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[2,8,5,7,6,3,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => 0101101
[2,5,7,8,6,4,1,3] => [[1,2,3,4],[5,8],[6],[7]] => 0001110
[7,4,1,6,2,5,8,3] => [[1,4,6,7],[2,5],[3],[8]] => 1101001
[2,3,1,5,6,8,9,4,7] => [[1,2,4,5,6,7],[3,8,9]] => 01000010
[5,6,2,4,8,7,3,1] => [[1,2,5],[3,4,6],[7],[8]] => 0100111
[8,5,6,2,3,7,4,1] => [[1,3,6],[2,5,7],[4],[8]] => 1010011
[7,8,1,4,5,6,2,3] => [[1,2,5,6],[3,4],[7,8]] => 0100010
[5,6,7,8,9,1,3,4,2] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[6,7,8,9,1,3,4,5,2] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[6,7,8,9,1,4,5,2,3] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[6,7,8,9,1,4,5,3,2] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[6,7,8,9,1,5,4,3,2] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[7,8,9,1,5,6,3,4,2] => [[1,2,3],[4,5,6],[7,8],[9]] => 00100101
[7,8,9,1,5,6,4,3,2] => [[1,2,3],[4,5,6],[7],[8],[9]] => 00100111
[7,8,9,1,6,5,4,3,2] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[9,1,7,8,5,6,3,4,2] => [[1,3,4],[2,6],[5,8],[7],[9]] => 10010101
[9,1,7,8,5,6,4,3,2] => [[1,3,4],[2,6],[5],[7],[8],[9]] => 10010111
[5,6,7,8,9,10,1,3,4,2] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[5,6,7,8,9,10,1,4,3,2] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[7,8,9,10,1,4,5,6,2,3] => [[1,2,3,4],[5,6,7,8],[9,10]] => 000100010
[7,8,9,10,1,4,5,6,3,2] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011
[7,8,9,10,1,5,6,4,3,2] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[7,8,9,10,1,6,5,4,3,2] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[8,9,10,1,6,7,4,5,2,3] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[8,9,10,1,6,7,4,5,3,2] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 001001011
[8,9,10,1,6,7,5,4,3,2] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111
[8,9,10,1,7,6,5,4,3,2] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[10,1,8,9,6,7,4,5,3,2] => [[1,3,4],[2,6],[5,8],[7],[9],[10]] => 100101011
[10,1,8,9,6,7,5,4,3,2] => [[1,3,4],[2,6],[5],[7],[8],[9],[10]] => 100101111
[10,1,8,9,7,6,5,4,3,2] => [[1,3,4],[2],[5],[6],[7],[8],[9],[10]] => 100111111
[2,6,1,4,7,5,8,3] => [[1,2,5,7],[3,4,6],[8]] => 0100101
[3,1,5,7,2,6,8,4] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[3,1,7,5,2,6,8,4] => [[1,3,6,7],[2,4,8],[5]] => 1011001
[3,2,7,5,1,6,8,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[5,2,7,3,1,6,8,4] => [[1,3,6,7],[2,4],[5,8]] => 1011001
[6,7,2,1,3,4,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[4,6,3,1,2,7,8,5] => [[1,2,6,7],[3,5,8],[4]] => 0110001
[2,3,4,5,7,9,6,8,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[2,3,5,6,8,4,7,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[2,3,5,9,4,6,7,8,1] => [[1,2,3,4,7,8],[5,6],[9]] => 00010001
[2,4,5,8,3,6,7,1] => [[1,2,3,4,7],[5,6],[8]] => 0001001
[5,9,8,7,6,4,3,1,2] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => 01111110
[5,4,8,7,6,3,2,1,9] => [[1,3,9],[2,4],[5],[6],[7],[8]] => 10111110
[4,5,8,7,6,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => 0011110
[6,5,9,8,7,4,3,1,2] => [[1,3],[2,4],[5,9],[6],[7],[8]] => 10111110
[8,7,4,6,5,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => 1101110
[9,5,8,7,6,4,3,1,2] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => 10111110
[6,10,9,8,7,5,4,3,1,2] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[8,1,4,3,6,2,5,7] => [[1,3,5,8],[2,7],[4],[6]] => 1010100
[1,6,3,7,8,4,2,5] => [[1,2,4,5],[3,6,8],[7]] => 0100110
[7,4,2,8,5,6,3,1] => [[1,4,6],[2,5],[3,7],[8]] => 1101011
[5,2,1,3,8,4,6,7] => [[1,4,5,7,8],[2,6],[3]] => 1100100
[1,4,3,5,8,2,6,7] => [[1,2,4,5,8],[3,7],[6]] => 0100100
[2,1,3,8,6,4,5,7] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[1,3,6,4,5,8,2,7] => [[1,2,3,5,6],[4,8],[7]] => 0010010
[6,1,4,3,5,8,2,7] => [[1,3,5,6],[2,8],[4],[7]] => 1010010
[6,5,1,3,8,2,4,7] => [[1,4,5,8],[2,7],[3],[6]] => 1100100
[1,4,3,8,6,2,5,7] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[4,1,3,8,6,2,5,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[7,1,5,4,6,3,8,2] => [[1,3,5,7],[2],[4],[6],[8]] => 1010101
[6,4,7,8,3,5,1,2] => [[1,3,4],[2,6],[5,8],[7]] => 1001010
[3,5,6,7,1,8,4,2] => [[1,2,3,4,6],[5,7],[8]] => 0001011
[4,5,8,1,7,3,2,6] => [[1,2,3],[4,5,8],[6],[7]] => 0010110
[4,6,7,1,3,8,2,5] => [[1,2,3,6],[4,5,8],[7]] => 0010010
[2,6,3,1,4,7,8,5] => [[1,2,5,6,7],[3,8],[4]] => 0110001
[2,7,3,4,1,8,5,6] => [[1,2,4,6,8],[3,7],[5]] => 0101010
[2,3,1,5,6,7,8,9,10,4] => [[1,2,4,5,6,7,8,9],[3,10]] => 010000001
[8,6,4,5,1,3,7,2] => [[1,4,7],[2,6],[3],[5],[8]] => 1101001
[7,4,8,5,3,6,1,2] => [[1,3,6],[2,4],[5,8],[7]] => 1011010
[8,4,6,5,1,3,7,2] => [[1,3,7],[2,6],[4],[5],[8]] => 1011001
[4,5,3,8,7,1,2,6] => [[1,2,4],[3,5,8],[6,7]] => 0101100
[8,5,4,7,6,1,2,3] => [[1,4,8],[2,5],[3,7],[6]] => 1101100
[2,3,7,8,1,4,6,5] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[8,2,3,5,4,1,7,6] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[7,1,3,8,2,4,6,5] => [[1,3,4,7],[2,6],[5,8]] => 1001001
[7,2,3,6,4,1,8,5] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[6,5,2,4,1,8,3,7] => [[1,4,6],[2,7,8],[3],[5]] => 1101010
[5,7,2,4,1,3,8,6] => [[1,2,7],[3,4,8],[5,6]] => 0101001
[6,2,5,4,1,8,3,7] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[4,2,5,3,7,6,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,2,6,3,7,5,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,2,6,3,8,5,9,7,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,2,6,3,5,8,1,7] => [[1,3,5,6],[2,4,8],[7]] => 1010010
[4,2,5,3,7,6,9,8,1,10] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[5,2,6,3,7,4,9,8,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,2,6,3,7,5,9,8,1,10] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[4,2,7,3,8,5,9,6,1] => [[1,3,5,7],[2,4,6,8],[9]] => 10101011
[4,2,6,3,8,5,9,7,1,10] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[4,2,6,3,8,5,10,7,1,9] => [[1,3,5,7,10],[2,4,6,8],[9]] => 101010110
[4,2,6,3,8,5,7,9,1] => [[1,3,5,7,8],[2,4,6],[9]] => 10101001
[4,2,6,3,8,5,10,7,9,1] => [[1,3,5,7,9],[2,4,6,8],[10]] => 101010101
[7,4,2,6,8,5,3,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[8,5,2,4,6,3,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => 1100110
[7,4,1,2,8,5,6,3] => [[1,4,5,7],[2,6],[3,8]] => 1100101
[6,4,1,8,5,2,3,7] => [[1,4,7,8],[2,5],[3,6]] => 1101100
[8,4,1,6,3,5,2,7] => [[1,4,6,8],[2,5],[3],[7]] => 1101010
[7,3,4,1,6,8,5,2] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[8,6,2,3,5,7,4,1] => [[1,4,5,6],[2],[3],[7],[8]] => 1100011
[8,6,2,5,7,3,4,1] => [[1,4,5],[2,7],[3],[6],[8]] => 1100101
[6,3,4,8,5,1,2,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[8,5,1,2,7,4,6,3] => [[1,4,5,7],[2,6],[3],[8]] => 1100101
[7,2,6,8,3,4,5,1] => [[1,3,4,7],[2,6],[5],[8]] => 1001001
[1,6,7,5,4,8,2,3] => [[1,2,3,6],[4,8],[5],[7]] => 0011010
[1,8,5,4,2,6,3,7] => [[1,2,6,8],[3,7],[4],[5]] => 0111010
[3,4,5,8,2,9,1,7,6] => [[1,2,3,4,6],[5,8],[7,9]] => 00010101
[5,2,6,7,8,9,1,4,3] => [[1,3,4,5,6],[2,8],[7,9]] => 10000101
[3,4,5,6,9,2,10,1,8,7] => [[1,2,3,4,5,7],[6,9],[8,10]] => 000010101
[3,4,7,8,5,9,1,2,6] => [[1,2,3,4,6],[5,8,9],[7]] => 00010100
[3,6,7,4,8,9,1,5,2] => [[1,2,3,5,6],[4,8],[7,9]] => 00100101
[3,7,2,4,8,9,1,5,6] => [[1,2,5,6],[3,4,8,9],[7]] => 01000100
[6,2,3,7,8,9,1,5,4] => [[1,3,4,5,6],[2,8],[7,9]] => 10000101
[5,2,6,7,8,9,10,1,3,4] => [[1,3,4,5,6,7],[2,9,10],[8]] => 100000100
[8,9,7,6,5,4,1,3,2] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => 01111101
[9,10,8,7,6,5,4,1,3,2] => [[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => 011111101
[10,8,7,6,5,4,3,2,9,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => 111111101
[5,8,6,1,2,4,3,7] => [[1,2,6,8],[3,5],[4],[7]] => 0110010
[4,1,5,7,3,6,8,2] => [[1,3,4,7],[2,5,6],[8]] => 1001001
[1,4,5,7,6,8,2,3] => [[1,2,3,4,6],[5,8],[7]] => 0001010
[5,7,2,1,6,8,4,3] => [[1,2,6],[3,5],[4,7],[8]] => 0110011
[2,6,3,1,7,8,5,4] => [[1,2,5,6],[3,7],[4,8]] => 0110011
[6,2,5,7,4,1,8,3] => [[1,3,4,7],[2,8],[5],[6]] => 1001101
[3,6,1,8,7,4,5,2] => [[1,2,4],[3,5,7],[6],[8]] => 0101101
[6,8,4,5,1,3,7,9,2] => [[1,2,7,8],[3,4],[5,6],[9]] => 01010001
[4,7,1,3,5,6,8,2] => [[1,2,5,6,7],[3,4],[8]] => 0100001
[4,3,5,7,8,2,6,1] => [[1,3,4,5],[2,7],[6],[8]] => 1000101
[5,3,2,7,6,4,1,8] => [[1,4,8],[2,5],[3,6],[7]] => 1101110
[5,3,7,4,6,2,1,8] => [[1,3,5,8],[2,4],[6],[7]] => 1010110
[5,7,3,2,1,8,6,4] => [[1,2,6],[3,7],[4,8],[5]] => 0111011
[5,7,6,3,2,1,8,4] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[3,2,7,5,4,1,8,6] => [[1,3,7],[2,4,8],[5],[6]] => 1011101
[1,7,3,5,4,2,6,8] => [[1,2,4,7,8],[3],[5],[6]] => 0101100
[5,3,7,4,1,8,6,2] => [[1,3,6],[2,4,7],[5,8]] => 1011011
[7,3,5,4,1,6,8,2] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,5,1,6,8,3,2,4] => [[1,4,5],[2,6,8],[3],[7]] => 1100110
[5,3,1,7,6,8,2,4] => [[1,4,6],[2,5,8],[3,7]] => 1101010
[7,1,5,3,2,4,8,6] => [[1,3,6,7],[2,8],[4],[5]] => 1011001
[7,1,5,2,4,3,6,8] => [[1,3,5,7,8],[2],[4],[6]] => 1010100
[5,6,7,8,9,3,2,1,4] => [[1,2,3,4,5],[6,9],[7],[8]] => 00001110
[7,8,9,3,4,5,1,2,6] => [[1,2,3,9],[4,5,6],[7,8]] => 00100100
[7,8,9,3,4,5,2,1,6] => [[1,2,3,9],[4,5,6],[7],[8]] => 00100110
[8,9,5,6,3,4,1,2,7] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100
[8,9,5,6,3,4,2,1,7] => [[1,2,9],[3,4],[5,6],[7],[8]] => 01010110
[8,9,5,6,4,3,2,1,7] => [[1,2,9],[3,4],[5],[6],[7],[8]] => 01011110
[5,6,7,8,9,10,3,2,1,4] => [[1,2,3,4,5,6],[7,10],[8],[9]] => 000001110
[7,8,9,10,5,4,3,2,1,6] => [[1,2,3,4],[5,10],[6],[7],[8],[9]] => 000111110
[8,9,10,4,5,6,1,2,3,7] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000
[8,9,10,4,5,6,3,2,1,7] => [[1,2,3,10],[4,5,6],[7],[8],[9]] => 001001110
[8,9,10,6,5,4,3,2,1,7] => [[1,2,3],[4,10],[5],[6],[7],[8],[9]] => 001111110
[9,10,6,7,4,5,3,2,1,8] => [[1,2,10],[3,4],[5,6],[7],[8],[9]] => 010101110
[9,10,6,7,5,4,3,2,1,8] => [[1,2,10],[3,4],[5],[6],[7],[8],[9]] => 010111110
[9,10,7,6,5,4,3,2,1,8] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => 011111110
[10,7,8,6,5,4,3,2,1,9] => [[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => 101111110
[1,8,3,6,2,4,7,5] => [[1,2,4,7],[3,6,8],[5]] => 0101001
[1,8,7,5,6,4,2,3] => [[1,2,5],[3,8],[4],[6],[7]] => 0110110
[6,8,2,1,5,4,3,7] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[8,6,1,2,3,4,5,9,10,7] => [[1,4,5,6,7,8,9],[2,10],[3]] => 110000001
[5,7,1,2,3,4,8,9,10,6] => [[1,2,5,6,7,8,9],[3,4,10]] => 010000001
[6,3,2,1,5,8,4,7] => [[1,5,6],[2,7,8],[3],[4]] => 1110010
[4,3,5,6,2,8,1,7] => [[1,3,4,6],[2,8],[5],[7]] => 1001010
[6,3,5,2,7,8,4,1] => [[1,3,5,6],[2,7],[4],[8]] => 1010011
[4,5,3,1,6,8,2,7] => [[1,2,5,6],[3,7,8],[4]] => 0110010
[3,4,6,7,5,1,8,2] => [[1,2,3,4,7],[5,8],[6]] => 0001101
[7,4,1,2,5,6,8,3] => [[1,4,5,6,7],[2,8],[3]] => 1100001
[4,8,2,6,7,1,5,3] => [[1,2,5],[3,4],[6,7],[8]] => 0100101
[6,5,8,3,7,1,4,2] => [[1,3],[2,5],[4,7],[6,8]] => 1010101
[2,3,4,5,6,10,1,9,7,8] => [[1,2,3,4,5,6,10],[7,8],[9]] => 000001010
[1,5,2,4,7,6,8,3] => [[1,2,4,5,7],[3,6],[8]] => 0100101
[1,2,5,4,7,6,9,8,3] => [[1,2,3,5,7],[4,6,8],[9]] => 00101011
[1,4,2,6,5,8,7,10,9,3] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,5,2,6,4,8,7,10,9,3] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,5,2,7,4,8,6,10,9,3] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[1,5,2,7,4,9,6,10,8,3] => [[1,2,4,6,8],[3,5,7,9],[10]] => 010101011
[2,5,4,7,1,8,3,6] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[8,1,2,4,6,3,5,7] => [[1,3,4,5,8],[2,7],[6]] => 1000100
[4,5,6,7,9,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[5,4,6,7,8,9,3,2,1] => [[1,3,4,5,6],[2],[7],[8],[9]] => 10000111
[5,6,7,8,10,9,4,3,2,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[6,5,7,8,9,4,3,2,1] => [[1,3,4,5],[2],[6],[7],[8],[9]] => 10001111
[6,5,7,8,9,10,4,3,2,1] => [[1,3,4,5,6],[2],[7],[8],[9],[10]] => 100001111
[4,5,6,7,8,10,9,3,2,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[4,5,6,7,3,9,8,2,1] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[3,5,6,7,9,8,4,2,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[5,4,6,7,8,9,10,3,2,1] => [[1,3,4,5,6,7],[2],[8],[9],[10]] => 100000111
[3,4,5,6,8,9,7,1,2] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[3,4,5,7,8,9,6,1,2] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[3,5,6,7,8,9,4,1,2] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[4,5,6,7,8,9,3,1,2] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[3,4,5,6,7,9,10,8,1,2] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[3,4,5,8,1,9,7,6,2] => [[1,2,3,4,6],[5,7],[8],[9]] => 00010111
[3,4,5,6,8,9,10,7,1,2] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[3,4,6,7,8,9,10,5,1,2] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[3,5,6,7,8,9,10,4,1,2] => [[1,2,3,4,5,6,7],[8,10],[9]] => 000000110
[1,5,6,7,8,9,3,2,4] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[3,4,5,8,9,6,7,1,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[3,4,5,6,9,1,10,8,7,2] => [[1,2,3,4,5,7],[6,8],[9],[10]] => 000010111
[3,4,5,9,1,6,7,8,2] => [[1,2,3,4,7,8],[5,6],[9]] => 00010001
[3,7,8,4,5,6,1,2] => [[1,2,3,6],[4,5],[7,8]] => 0010010
[1,2,6,7,8,9,4,3,5] => [[1,2,3,4,5,6],[7,9],[8]] => 00000110
[1,3,8,6,7,4,5,2] => [[1,2,3,5],[4,7],[6],[8]] => 0010101
[2,6,5,3,7,1,8,4] => [[1,2,5,7],[3,8],[4],[6]] => 0110101
[5,7,1,3,6,4,8,2] => [[1,2,5,7],[3,4],[6],[8]] => 0100101
[8,2,5,4,1,7,3,6] => [[1,3,6],[2,7,8],[4],[5]] => 1011010
[8,1,7,6,4,2,3,5] => [[1,3,7,8],[2],[4],[5],[6]] => 1011100
[1,8,6,3,7,4,5,2] => [[1,2,5,7],[3,6],[4],[8]] => 0110101
[5,7,3,4,2,8,6,1] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[5,8,3,4,2,7,6,1] => [[1,2,6],[3,4],[5,7],[8]] => 0101011
[7,6,4,2,3,8,5,1] => [[1,5,6],[2,7],[3],[4],[8]] => 1110011
[3,5,6,8,2,4,7,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[4,8,7,3,2,5,6,1] => [[1,2,7],[3,6],[4],[5],[8]] => 0111001
[3,7,4,2,6,8,5,1] => [[1,2,5,6],[3,7],[4],[8]] => 0110011
[6,4,8,7,3,2,5,1] => [[1,3],[2,4],[5,7],[6],[8]] => 1011101
[5,6,2,8,7,4,3,1] => [[1,2,4],[3,5],[6],[7],[8]] => 0101111
[6,2,8,3,7,4,5,1] => [[1,3,5,7],[2,4],[6],[8]] => 1010101
[3,7,5,6,4,2,8,1] => [[1,2,4,7],[3],[5],[6],[8]] => 0101101
[5,2,3,8,6,1,4,7] => [[1,3,4,8],[2,5],[6,7]] => 1001100
[1,4,3,8,5,6,2,7] => [[1,2,4,6,8],[3,5],[7]] => 0101010
[7,8,2,6,4,3,5,1] => [[1,2,7],[3,4],[5],[6],[8]] => 0101101
[4,5,8,7,2,3,6,1] => [[1,2,3],[4,6,7],[5],[8]] => 0011001
[7,8,6,1,4,2,5,3] => [[1,2,7],[3,5],[4,8],[6]] => 0110101
[10,5,4,1,2,3,6,7,8,9] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000
[8,3,6,5,2,7,1,4] => [[1,3,6],[2,8],[4],[5],[7]] => 1011010
[5,1,3,6,4,2,7,8] => [[1,3,4,7,8],[2,5],[6]] => 1001100
[6,1,2,4,7,5,3,8] => [[1,3,4,5,8],[2,6],[7]] => 1000110
[8,3,1,4,6,7,2,5] => [[1,4,5,6],[2,7,8],[3]] => 1100010
[7,8,5,1,2,6,3,4] => [[1,2,6,8],[3,5],[4,7]] => 0110010
[6,4,5,1,8,7,3,2] => [[1,3,5],[2,6],[4,7],[8]] => 1010111
[8,6,2,1,7,3,5,4] => [[1,5,7],[2,6],[3,8],[4]] => 1110101
[9,3,4,5,6,8,7,2,1] => [[1,3,4,5,6],[2],[7],[8],[9]] => 10000111
[10,3,4,5,6,7,9,8,2,1] => [[1,3,4,5,6,7],[2],[8],[9],[10]] => 100000111
[9,3,4,5,6,2,8,7,1] => [[1,3,4,5,7],[2,8],[6],[9]] => 10001011
[9,2,4,5,6,8,7,3,1] => [[1,3,4,5,6],[2],[7],[8],[9]] => 10000111
[7,8,6,1,4,3,5,2] => [[1,2,7],[3,5],[4],[6],[8]] => 0110101
[4,3,6,2,5,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => 1010010
[1,6,5,7,3,4,8,2] => [[1,2,4,7],[3,6],[5],[8]] => 0101001
[1,2,3,4,8,5,9,6,7] => [[1,2,3,4,5,7,9],[6,8]] => 00001010
[1,2,3,4,5,8,6,9,7,10] => [[1,2,3,4,5,6,8,10],[7,9]] => 000001010
[1,2,3,4,5,9,6,10,7,8] => [[1,2,3,4,5,6,8,10],[7,9]] => 000001010
[8,2,6,5,1,7,4,3] => [[1,3,6],[2,7],[4],[5],[8]] => 1011011
[7,6,4,1,2,5,8,3] => [[1,5,6,7],[2,8],[3],[4]] => 1110001
[2,6,5,4,8,7,1,3] => [[1,2,5],[3,6],[4,8],[7]] => 0110110
[5,6,7,1,3,2,4,8] => [[1,2,3,8],[4,5,7],[6]] => 0010100
[7,1,8,4,3,2,6,5] => [[1,3,7],[2,4],[5,8],[6]] => 1011101
[3,7,1,2,4,5,6,9,8] => [[1,2,5,6,7,8],[3,4,9]] => 01000001
[1,8,5,2,7,6,4,3] => [[1,2,5],[3,6],[4],[7],[8]] => 0110111
[1,7,6,8,2,5,4,3] => [[1,2,4],[3,6],[5],[7],[8]] => 0101011
[1,7,8,6,2,5,4,3] => [[1,2,3],[4,6],[5],[7],[8]] => 0011011
[4,6,5,7,1,8,2,3] => [[1,2,4,6],[3,7,8],[5]] => 0101010
[7,5,3,6,8,4,2,1] => [[1,4,5],[2,6],[3],[7],[8]] => 1100111
[7,2,5,6,4,8,3,1] => [[1,3,4,6],[2],[5],[7],[8]] => 1001011
[7,4,6,2,8,5,3,1] => [[1,3,5],[2,6],[4],[7],[8]] => 1010111
[10,8,7,6,5,4,3,9,2,1] => [[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => 111111011
[10,9,7,6,5,4,8,3,2,1] => [[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => 111110111
[1,6,3,4,2,5,8,7] => [[1,2,4,6,7],[3,8],[5]] => 0101001
[1,5,7,6,2,3,8,4] => [[1,2,3,7],[4,6,8],[5]] => 0011001
[1,4,3,7,6,2,5,8] => [[1,2,4,8],[3,5],[6,7]] => 0101100
[1,3,7,4,6,8,5,2] => [[1,2,3,5,6],[4],[7],[8]] => 0010011
[3,7,4,6,8,1,5,2] => [[1,2,4,5],[3,7],[6],[8]] => 0100101
[4,8,3,1,7,6,2,5] => [[1,2,8],[3,5],[4,6],[7]] => 0110110
[5,6,1,4,3,8,7,2] => [[1,2,6],[3,4,7],[5],[8]] => 0101011
[5,8,6,4,3,1,7,2] => [[1,2,7],[3,8],[4],[5],[6]] => 0111101
[4,1,3,7,8,6,5,2] => [[1,3,4,5],[2,6],[7],[8]] => 1000111
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.