Identifier
Mp00081:
Standard tableaux
—reading word permutation⟶
Permutations
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00109: Permutations —descent word⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Images
[[1]] => [1] => =>
[[1,2]] => [1,2] => 0 => 0
[[1],[2]] => [2,1] => 1 => 1
[[1,2,3]] => [1,2,3] => 00 => 00
[[1,3],[2]] => [2,1,3] => 10 => 01
[[1,2],[3]] => [3,1,2] => 10 => 01
[[1],[2],[3]] => [3,2,1] => 11 => 11
[[1,2,3,4]] => [1,2,3,4] => 000 => 000
[[1,3,4],[2]] => [2,1,3,4] => 100 => 001
[[1,2,4],[3]] => [3,1,2,4] => 100 => 001
[[1,2,3],[4]] => [4,1,2,3] => 100 => 001
[[1,3],[2,4]] => [2,4,1,3] => 010 => 010
[[1,2],[3,4]] => [3,4,1,2] => 010 => 010
[[1,4],[2],[3]] => [3,2,1,4] => 110 => 011
[[1,3],[2],[4]] => [4,2,1,3] => 110 => 011
[[1,2],[3],[4]] => [4,3,1,2] => 110 => 011
[[1],[2],[3],[4]] => [4,3,2,1] => 111 => 111
[[1,2,3,4,5]] => [1,2,3,4,5] => 0000 => 0000
[[1,3,4,5],[2]] => [2,1,3,4,5] => 1000 => 0001
[[1,2,4,5],[3]] => [3,1,2,4,5] => 1000 => 0001
[[1,2,3,5],[4]] => [4,1,2,3,5] => 1000 => 0001
[[1,2,3,4],[5]] => [5,1,2,3,4] => 1000 => 0001
[[1,3,5],[2,4]] => [2,4,1,3,5] => 0100 => 0010
[[1,2,5],[3,4]] => [3,4,1,2,5] => 0100 => 0010
[[1,3,4],[2,5]] => [2,5,1,3,4] => 0100 => 0010
[[1,2,4],[3,5]] => [3,5,1,2,4] => 0100 => 0010
[[1,2,3],[4,5]] => [4,5,1,2,3] => 0100 => 0010
[[1,4,5],[2],[3]] => [3,2,1,4,5] => 1100 => 0011
[[1,3,5],[2],[4]] => [4,2,1,3,5] => 1100 => 0011
[[1,2,5],[3],[4]] => [4,3,1,2,5] => 1100 => 0011
[[1,3,4],[2],[5]] => [5,2,1,3,4] => 1100 => 0011
[[1,2,4],[3],[5]] => [5,3,1,2,4] => 1100 => 0011
[[1,2,3],[4],[5]] => [5,4,1,2,3] => 1100 => 0011
[[1,4],[2,5],[3]] => [3,2,5,1,4] => 1010 => 0101
[[1,3],[2,5],[4]] => [4,2,5,1,3] => 1010 => 0101
[[1,2],[3,5],[4]] => [4,3,5,1,2] => 1010 => 0101
[[1,3],[2,4],[5]] => [5,2,4,1,3] => 1010 => 0101
[[1,2],[3,4],[5]] => [5,3,4,1,2] => 1010 => 0101
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => 1110 => 0111
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => 1110 => 0111
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => 1110 => 0111
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => 1110 => 0111
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 1111 => 1111
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 00000 => 00000
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 10000 => 00001
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 10000 => 00001
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 10000 => 00001
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 10000 => 00001
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 10000 => 00001
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 01000 => 00010
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 01000 => 00010
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 01000 => 00010
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 01000 => 00010
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 01000 => 00010
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 01000 => 00010
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 01000 => 00010
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 01000 => 00010
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 01000 => 00010
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 11000 => 00011
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 11000 => 00011
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 11000 => 00011
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 11000 => 00011
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 11000 => 00011
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 11000 => 00011
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 11000 => 00011
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 11000 => 00011
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 11000 => 00011
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 11000 => 00011
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 00100 => 00100
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 00100 => 00100
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 00100 => 00100
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 00100 => 00100
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 00100 => 00100
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 10100 => 00101
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 10100 => 00101
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 10100 => 00101
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 10100 => 00101
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 10100 => 00101
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 10100 => 00101
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 10100 => 00101
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 10100 => 00101
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 10100 => 00101
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 10100 => 00101
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 10100 => 00101
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 10100 => 00101
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 10100 => 00101
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 10100 => 00101
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 10100 => 00101
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 10100 => 00101
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 11100 => 00111
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 11100 => 00111
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 11100 => 00111
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 11100 => 00111
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 11100 => 00111
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 11100 => 00111
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 11100 => 00111
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 11100 => 00111
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 11100 => 00111
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 11100 => 00111
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 01010 => 01010
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 01010 => 01010
>>> Load all 1624 entries. <<<
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 01010 => 01010
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 01010 => 01010
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 01010 => 01010
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 11010 => 01011
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 11010 => 01011
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 11010 => 01011
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 11010 => 01011
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 11010 => 01011
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 11010 => 01011
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 11010 => 01011
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 11010 => 01011
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 11010 => 01011
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 11110 => 01111
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 11110 => 01111
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 11110 => 01111
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 11110 => 01111
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 11110 => 01111
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 11111 => 11111
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 000000 => 000000
[[1,3,4,5,6,7],[2]] => [2,1,3,4,5,6,7] => 100000 => 000001
[[1,2,4,5,6,7],[3]] => [3,1,2,4,5,6,7] => 100000 => 000001
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => 100000 => 000001
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => 100000 => 000001
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => 100000 => 000001
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => 100000 => 000001
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => 010000 => 000010
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => 010000 => 000010
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => 010000 => 000010
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => 010000 => 000010
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => 010000 => 000010
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => 010000 => 000010
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => 010000 => 000010
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => 010000 => 000010
[[1,2,3,4,7],[5,6]] => [5,6,1,2,3,4,7] => 010000 => 000010
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => 010000 => 000010
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => 010000 => 000010
[[1,2,3,5,6],[4,7]] => [4,7,1,2,3,5,6] => 010000 => 000010
[[1,2,3,4,6],[5,7]] => [5,7,1,2,3,4,6] => 010000 => 000010
[[1,2,3,4,5],[6,7]] => [6,7,1,2,3,4,5] => 010000 => 000010
[[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => 110000 => 000011
[[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => 110000 => 000011
[[1,2,5,6,7],[3],[4]] => [4,3,1,2,5,6,7] => 110000 => 000011
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => 110000 => 000011
[[1,2,4,6,7],[3],[5]] => [5,3,1,2,4,6,7] => 110000 => 000011
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => 110000 => 000011
[[1,3,4,5,7],[2],[6]] => [6,2,1,3,4,5,7] => 110000 => 000011
[[1,2,4,5,7],[3],[6]] => [6,3,1,2,4,5,7] => 110000 => 000011
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => 110000 => 000011
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => 110000 => 000011
[[1,3,4,5,6],[2],[7]] => [7,2,1,3,4,5,6] => 110000 => 000011
[[1,2,4,5,6],[3],[7]] => [7,3,1,2,4,5,6] => 110000 => 000011
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => 110000 => 000011
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => 110000 => 000011
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => 110000 => 000011
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => 001000 => 000100
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => 001000 => 000100
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => 001000 => 000100
[[1,2,4,7],[3,5,6]] => [3,5,6,1,2,4,7] => 001000 => 000100
[[1,2,3,7],[4,5,6]] => [4,5,6,1,2,3,7] => 001000 => 000100
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => 001000 => 000100
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => 001000 => 000100
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => 001000 => 000100
[[1,2,4,6],[3,5,7]] => [3,5,7,1,2,4,6] => 001000 => 000100
[[1,2,3,6],[4,5,7]] => [4,5,7,1,2,3,6] => 001000 => 000100
[[1,3,4,5],[2,6,7]] => [2,6,7,1,3,4,5] => 001000 => 000100
[[1,2,4,5],[3,6,7]] => [3,6,7,1,2,4,5] => 001000 => 000100
[[1,2,3,5],[4,6,7]] => [4,6,7,1,2,3,5] => 001000 => 000100
[[1,2,3,4],[5,6,7]] => [5,6,7,1,2,3,4] => 001000 => 000100
[[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => 101000 => 000101
[[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => 101000 => 000101
[[1,2,6,7],[3,5],[4]] => [4,3,5,1,2,6,7] => 101000 => 000101
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => 101000 => 000101
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => 101000 => 000101
[[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => 101000 => 000101
[[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => 101000 => 000101
[[1,2,5,7],[3,6],[4]] => [4,3,6,1,2,5,7] => 101000 => 000101
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => 101000 => 000101
[[1,2,4,7],[3,6],[5]] => [5,3,6,1,2,4,7] => 101000 => 000101
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => 101000 => 000101
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => 101000 => 000101
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => 101000 => 000101
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => 101000 => 000101
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => 101000 => 000101
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => 101000 => 000101
[[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => 101000 => 000101
[[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => 101000 => 000101
[[1,2,5,6],[3,7],[4]] => [4,3,7,1,2,5,6] => 101000 => 000101
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => 101000 => 000101
[[1,2,4,6],[3,7],[5]] => [5,3,7,1,2,4,6] => 101000 => 000101
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => 101000 => 000101
[[1,3,4,5],[2,7],[6]] => [6,2,7,1,3,4,5] => 101000 => 000101
[[1,2,4,5],[3,7],[6]] => [6,3,7,1,2,4,5] => 101000 => 000101
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => 101000 => 000101
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => 101000 => 000101
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => 101000 => 000101
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => 101000 => 000101
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => 101000 => 000101
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => 101000 => 000101
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => 101000 => 000101
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => 101000 => 000101
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => 101000 => 000101
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => 101000 => 000101
[[1,2,3,4],[5,6],[7]] => [7,5,6,1,2,3,4] => 101000 => 000101
[[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => 111000 => 000111
[[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => 111000 => 000111
[[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => 111000 => 000111
[[1,2,6,7],[3],[4],[5]] => [5,4,3,1,2,6,7] => 111000 => 000111
[[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => 111000 => 000111
[[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => 111000 => 000111
[[1,2,5,7],[3],[4],[6]] => [6,4,3,1,2,5,7] => 111000 => 000111
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => 111000 => 000111
[[1,2,4,7],[3],[5],[6]] => [6,5,3,1,2,4,7] => 111000 => 000111
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => 111000 => 000111
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => 111000 => 000111
[[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => 111000 => 000111
[[1,2,5,6],[3],[4],[7]] => [7,4,3,1,2,5,6] => 111000 => 000111
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => 111000 => 000111
[[1,2,4,6],[3],[5],[7]] => [7,5,3,1,2,4,6] => 111000 => 000111
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => 111000 => 000111
[[1,3,4,5],[2],[6],[7]] => [7,6,2,1,3,4,5] => 111000 => 000111
[[1,2,4,5],[3],[6],[7]] => [7,6,3,1,2,4,5] => 111000 => 000111
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => 111000 => 000111
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => 111000 => 000111
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => 100100 => 001001
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => 100100 => 001001
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => 100100 => 001001
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => 100100 => 001001
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => 100100 => 001001
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => 100100 => 001001
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => 100100 => 001001
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => 100100 => 001001
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => 100100 => 001001
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => 100100 => 001001
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => 100100 => 001001
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => 100100 => 001001
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => 100100 => 001001
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => 100100 => 001001
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => 100100 => 001001
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => 100100 => 001001
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => 100100 => 001001
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => 100100 => 001001
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => 100100 => 001001
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => 100100 => 001001
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => 100100 => 001001
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => 010100 => 001010
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => 010100 => 001010
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => 010100 => 001010
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => 010100 => 001010
[[1,2,7],[3,4],[5,6]] => [5,6,3,4,1,2,7] => 010100 => 001010
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => 010100 => 001010
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => 010100 => 001010
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => 010100 => 001010
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => 010100 => 001010
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => 010100 => 001010
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => 010100 => 001010
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => 010100 => 001010
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => 010100 => 001010
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => 010100 => 001010
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => 010100 => 001010
[[1,2,3],[4,6],[5,7]] => [5,7,4,6,1,2,3] => 010100 => 001010
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => 010100 => 001010
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => 010100 => 001010
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => 010100 => 001010
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => 010100 => 001010
[[1,2,3],[4,5],[6,7]] => [6,7,4,5,1,2,3] => 010100 => 001010
[[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => 110100 => 001011
[[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => 110100 => 001011
[[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => 110100 => 001011
[[1,2,7],[3,6],[4],[5]] => [5,4,3,6,1,2,7] => 110100 => 001011
[[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => 110100 => 001011
[[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => 110100 => 001011
[[1,2,7],[3,5],[4],[6]] => [6,4,3,5,1,2,7] => 110100 => 001011
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => 110100 => 001011
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => 110100 => 001011
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => 110100 => 001011
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => 110100 => 001011
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => 110100 => 001011
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => 110100 => 001011
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => 110100 => 001011
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => 110100 => 001011
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => 110100 => 001011
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => 110100 => 001011
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => 110100 => 001011
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => 110100 => 001011
[[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => 110100 => 001011
[[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => 110100 => 001011
[[1,2,6],[3,5],[4],[7]] => [7,4,3,5,1,2,6] => 110100 => 001011
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => 110100 => 001011
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => 110100 => 001011
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => 110100 => 001011
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => 110100 => 001011
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => 110100 => 001011
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => 110100 => 001011
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => 110100 => 001011
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => 110100 => 001011
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => 110100 => 001011
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => 110100 => 001011
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => 110100 => 001011
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => 110100 => 001011
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => 110100 => 001011
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => 111100 => 001111
[[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => 111100 => 001111
[[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => 111100 => 001111
[[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => 111100 => 001111
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => 111100 => 001111
[[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => 111100 => 001111
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => 111100 => 001111
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => 111100 => 001111
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => 111100 => 001111
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => 111100 => 001111
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => 111100 => 001111
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => 111100 => 001111
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => 111100 => 001111
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => 111100 => 001111
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => 111100 => 001111
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => 101010 => 010101
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => 101010 => 010101
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => 101010 => 010101
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => 101010 => 010101
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => 101010 => 010101
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => 101010 => 010101
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => 101010 => 010101
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => 101010 => 010101
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => 101010 => 010101
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => 101010 => 010101
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => 101010 => 010101
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => 101010 => 010101
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => 101010 => 010101
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => 101010 => 010101
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => 111010 => 010111
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => 111010 => 010111
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => 111010 => 010111
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => 111010 => 010111
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => 111010 => 010111
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => 111010 => 010111
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => 111010 => 010111
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => 111010 => 010111
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => 111010 => 010111
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => 111010 => 010111
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => 111010 => 010111
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => 111010 => 010111
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => 111010 => 010111
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => 111010 => 010111
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => 111110 => 011111
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => 111110 => 011111
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => 111110 => 011111
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => 111110 => 011111
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => 111110 => 011111
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => 111110 => 011111
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => 111111 => 111111
[[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => 0000000 => 0000000
[[1,3,4,5,6,7,8],[2]] => [2,1,3,4,5,6,7,8] => 1000000 => 0000001
[[1,2,4,5,6,7,8],[3]] => [3,1,2,4,5,6,7,8] => 1000000 => 0000001
[[1,2,3,5,6,7,8],[4]] => [4,1,2,3,5,6,7,8] => 1000000 => 0000001
[[1,2,3,4,6,7,8],[5]] => [5,1,2,3,4,6,7,8] => 1000000 => 0000001
[[1,2,3,4,5,7,8],[6]] => [6,1,2,3,4,5,7,8] => 1000000 => 0000001
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => 1000000 => 0000001
[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => 1000000 => 0000001
[[1,3,5,6,7,8],[2,4]] => [2,4,1,3,5,6,7,8] => 0100000 => 0000010
[[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => 0100000 => 0000010
[[1,3,4,6,7,8],[2,5]] => [2,5,1,3,4,6,7,8] => 0100000 => 0000010
[[1,2,4,6,7,8],[3,5]] => [3,5,1,2,4,6,7,8] => 0100000 => 0000010
[[1,2,3,6,7,8],[4,5]] => [4,5,1,2,3,6,7,8] => 0100000 => 0000010
[[1,3,4,5,7,8],[2,6]] => [2,6,1,3,4,5,7,8] => 0100000 => 0000010
[[1,2,4,5,7,8],[3,6]] => [3,6,1,2,4,5,7,8] => 0100000 => 0000010
[[1,2,3,5,7,8],[4,6]] => [4,6,1,2,3,5,7,8] => 0100000 => 0000010
[[1,3,4,5,6,8],[2,7]] => [2,7,1,3,4,5,6,8] => 0100000 => 0000010
[[1,2,4,5,6,8],[3,7]] => [3,7,1,2,4,5,6,8] => 0100000 => 0000010
[[1,2,3,5,6,8],[4,7]] => [4,7,1,2,3,5,6,8] => 0100000 => 0000010
[[1,2,3,4,6,8],[5,7]] => [5,7,1,2,3,4,6,8] => 0100000 => 0000010
[[1,2,3,4,5,8],[6,7]] => [6,7,1,2,3,4,5,8] => 0100000 => 0000010
[[1,3,4,5,6,7],[2,8]] => [2,8,1,3,4,5,6,7] => 0100000 => 0000010
[[1,2,4,5,6,7],[3,8]] => [3,8,1,2,4,5,6,7] => 0100000 => 0000010
[[1,2,3,5,6,7],[4,8]] => [4,8,1,2,3,5,6,7] => 0100000 => 0000010
[[1,2,3,4,6,7],[5,8]] => [5,8,1,2,3,4,6,7] => 0100000 => 0000010
[[1,2,3,4,5,7],[6,8]] => [6,8,1,2,3,4,5,7] => 0100000 => 0000010
[[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => 0100000 => 0000010
[[1,4,5,6,7,8],[2],[3]] => [3,2,1,4,5,6,7,8] => 1100000 => 0000011
[[1,3,5,6,7,8],[2],[4]] => [4,2,1,3,5,6,7,8] => 1100000 => 0000011
[[1,2,5,6,7,8],[3],[4]] => [4,3,1,2,5,6,7,8] => 1100000 => 0000011
[[1,3,4,6,7,8],[2],[5]] => [5,2,1,3,4,6,7,8] => 1100000 => 0000011
[[1,2,4,6,7,8],[3],[5]] => [5,3,1,2,4,6,7,8] => 1100000 => 0000011
[[1,2,3,6,7,8],[4],[5]] => [5,4,1,2,3,6,7,8] => 1100000 => 0000011
[[1,3,4,5,7,8],[2],[6]] => [6,2,1,3,4,5,7,8] => 1100000 => 0000011
[[1,2,4,5,7,8],[3],[6]] => [6,3,1,2,4,5,7,8] => 1100000 => 0000011
[[1,2,3,5,7,8],[4],[6]] => [6,4,1,2,3,5,7,8] => 1100000 => 0000011
[[1,3,4,5,6,8],[2],[7]] => [7,2,1,3,4,5,6,8] => 1100000 => 0000011
[[1,2,4,5,6,8],[3],[7]] => [7,3,1,2,4,5,6,8] => 1100000 => 0000011
[[1,2,3,5,6,8],[4],[7]] => [7,4,1,2,3,5,6,8] => 1100000 => 0000011
[[1,2,3,4,6,8],[5],[7]] => [7,5,1,2,3,4,6,8] => 1100000 => 0000011
[[1,2,3,4,5,8],[6],[7]] => [7,6,1,2,3,4,5,8] => 1100000 => 0000011
[[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => 1100000 => 0000011
[[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => 1100000 => 0000011
[[1,2,3,5,6,7],[4],[8]] => [8,4,1,2,3,5,6,7] => 1100000 => 0000011
[[1,2,3,4,6,7],[5],[8]] => [8,5,1,2,3,4,6,7] => 1100000 => 0000011
[[1,2,3,4,5,7],[6],[8]] => [8,6,1,2,3,4,5,7] => 1100000 => 0000011
[[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => 1100000 => 0000011
[[1,3,5,7,8],[2,4,6]] => [2,4,6,1,3,5,7,8] => 0010000 => 0000100
[[1,2,4,7,8],[3,5,6]] => [3,5,6,1,2,4,7,8] => 0010000 => 0000100
[[1,2,3,7,8],[4,5,6]] => [4,5,6,1,2,3,7,8] => 0010000 => 0000100
[[1,2,4,6,8],[3,5,7]] => [3,5,7,1,2,4,6,8] => 0010000 => 0000100
[[1,3,4,5,8],[2,6,7]] => [2,6,7,1,3,4,5,8] => 0010000 => 0000100
[[1,2,4,5,8],[3,6,7]] => [3,6,7,1,2,4,5,8] => 0010000 => 0000100
[[1,2,3,5,8],[4,6,7]] => [4,6,7,1,2,3,5,8] => 0010000 => 0000100
[[1,2,3,4,8],[5,6,7]] => [5,6,7,1,2,3,4,8] => 0010000 => 0000100
[[1,3,5,6,7],[2,4,8]] => [2,4,8,1,3,5,6,7] => 0010000 => 0000100
[[1,2,5,6,7],[3,4,8]] => [3,4,8,1,2,5,6,7] => 0010000 => 0000100
[[1,3,4,6,7],[2,5,8]] => [2,5,8,1,3,4,6,7] => 0010000 => 0000100
[[1,2,3,6,7],[4,5,8]] => [4,5,8,1,2,3,6,7] => 0010000 => 0000100
[[1,3,4,5,7],[2,6,8]] => [2,6,8,1,3,4,5,7] => 0010000 => 0000100
[[1,2,4,5,7],[3,6,8]] => [3,6,8,1,2,4,5,7] => 0010000 => 0000100
[[1,2,3,5,7],[4,6,8]] => [4,6,8,1,2,3,5,7] => 0010000 => 0000100
[[1,2,3,4,7],[5,6,8]] => [5,6,8,1,2,3,4,7] => 0010000 => 0000100
[[1,3,4,5,6],[2,7,8]] => [2,7,8,1,3,4,5,6] => 0010000 => 0000100
[[1,2,4,5,6],[3,7,8]] => [3,7,8,1,2,4,5,6] => 0010000 => 0000100
[[1,2,3,5,6],[4,7,8]] => [4,7,8,1,2,3,5,6] => 0010000 => 0000100
[[1,2,3,4,6],[5,7,8]] => [5,7,8,1,2,3,4,6] => 0010000 => 0000100
[[1,2,3,4,5],[6,7,8]] => [6,7,8,1,2,3,4,5] => 0010000 => 0000100
[[1,4,6,7,8],[2,5],[3]] => [3,2,5,1,4,6,7,8] => 1010000 => 0000101
[[1,3,6,7,8],[2,5],[4]] => [4,2,5,1,3,6,7,8] => 1010000 => 0000101
[[1,2,6,7,8],[3,5],[4]] => [4,3,5,1,2,6,7,8] => 1010000 => 0000101
[[1,3,6,7,8],[2,4],[5]] => [5,2,4,1,3,6,7,8] => 1010000 => 0000101
[[1,2,6,7,8],[3,4],[5]] => [5,3,4,1,2,6,7,8] => 1010000 => 0000101
[[1,4,5,7,8],[2,6],[3]] => [3,2,6,1,4,5,7,8] => 1010000 => 0000101
[[1,3,5,7,8],[2,6],[4]] => [4,2,6,1,3,5,7,8] => 1010000 => 0000101
[[1,2,4,7,8],[3,6],[5]] => [5,3,6,1,2,4,7,8] => 1010000 => 0000101
[[1,3,5,7,8],[2,4],[6]] => [6,2,4,1,3,5,7,8] => 1010000 => 0000101
[[1,2,4,7,8],[3,5],[6]] => [6,3,5,1,2,4,7,8] => 1010000 => 0000101
[[1,3,4,6,8],[2,7],[5]] => [5,2,7,1,3,4,6,8] => 1010000 => 0000101
[[1,2,4,6,8],[3,7],[5]] => [5,3,7,1,2,4,6,8] => 1010000 => 0000101
[[1,2,3,6,8],[4,7],[5]] => [5,4,7,1,2,3,6,8] => 1010000 => 0000101
[[1,3,4,5,8],[2,7],[6]] => [6,2,7,1,3,4,5,8] => 1010000 => 0000101
[[1,2,4,5,8],[3,7],[6]] => [6,3,7,1,2,4,5,8] => 1010000 => 0000101
[[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => 1010000 => 0000101
[[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => 1010000 => 0000101
[[1,2,5,6,8],[3,4],[7]] => [7,3,4,1,2,5,6,8] => 1010000 => 0000101
[[1,2,4,6,8],[3,5],[7]] => [7,3,5,1,2,4,6,8] => 1010000 => 0000101
[[1,2,3,6,8],[4,5],[7]] => [7,4,5,1,2,3,6,8] => 1010000 => 0000101
[[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => 1010000 => 0000101
[[1,2,3,5,8],[4,6],[7]] => [7,4,6,1,2,3,5,8] => 1010000 => 0000101
[[1,2,3,4,8],[5,6],[7]] => [7,5,6,1,2,3,4,8] => 1010000 => 0000101
[[1,4,5,6,7],[2,8],[3]] => [3,2,8,1,4,5,6,7] => 1010000 => 0000101
[[1,3,5,6,7],[2,8],[4]] => [4,2,8,1,3,5,6,7] => 1010000 => 0000101
[[1,3,4,6,7],[2,8],[5]] => [5,2,8,1,3,4,6,7] => 1010000 => 0000101
[[1,2,3,6,7],[4,8],[5]] => [5,4,8,1,2,3,6,7] => 1010000 => 0000101
[[1,3,4,5,7],[2,8],[6]] => [6,2,8,1,3,4,5,7] => 1010000 => 0000101
[[1,2,4,5,7],[3,8],[6]] => [6,3,8,1,2,4,5,7] => 1010000 => 0000101
[[1,2,3,5,7],[4,8],[6]] => [6,4,8,1,2,3,5,7] => 1010000 => 0000101
[[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => 1010000 => 0000101
[[1,3,4,5,6],[2,8],[7]] => [7,2,8,1,3,4,5,6] => 1010000 => 0000101
[[1,2,4,5,6],[3,8],[7]] => [7,3,8,1,2,4,5,6] => 1010000 => 0000101
[[1,2,3,5,6],[4,8],[7]] => [7,4,8,1,2,3,5,6] => 1010000 => 0000101
[[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => 1010000 => 0000101
[[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => 1010000 => 0000101
[[1,3,5,6,7],[2,4],[8]] => [8,2,4,1,3,5,6,7] => 1010000 => 0000101
[[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => 1010000 => 0000101
[[1,2,4,6,7],[3,5],[8]] => [8,3,5,1,2,4,6,7] => 1010000 => 0000101
[[1,2,3,6,7],[4,5],[8]] => [8,4,5,1,2,3,6,7] => 1010000 => 0000101
[[1,2,4,5,7],[3,6],[8]] => [8,3,6,1,2,4,5,7] => 1010000 => 0000101
[[1,2,3,4,7],[5,6],[8]] => [8,5,6,1,2,3,4,7] => 1010000 => 0000101
[[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => 1010000 => 0000101
[[1,2,3,5,6],[4,7],[8]] => [8,4,7,1,2,3,5,6] => 1010000 => 0000101
[[1,2,3,4,6],[5,7],[8]] => [8,5,7,1,2,3,4,6] => 1010000 => 0000101
[[1,2,3,4,5],[6,7],[8]] => [8,6,7,1,2,3,4,5] => 1010000 => 0000101
[[1,5,6,7,8],[2],[3],[4]] => [4,3,2,1,5,6,7,8] => 1110000 => 0000111
[[1,4,6,7,8],[2],[3],[5]] => [5,3,2,1,4,6,7,8] => 1110000 => 0000111
[[1,3,6,7,8],[2],[4],[5]] => [5,4,2,1,3,6,7,8] => 1110000 => 0000111
[[1,2,6,7,8],[3],[4],[5]] => [5,4,3,1,2,6,7,8] => 1110000 => 0000111
[[1,4,5,7,8],[2],[3],[6]] => [6,3,2,1,4,5,7,8] => 1110000 => 0000111
[[1,3,5,7,8],[2],[4],[6]] => [6,4,2,1,3,5,7,8] => 1110000 => 0000111
[[1,2,5,7,8],[3],[4],[6]] => [6,4,3,1,2,5,7,8] => 1110000 => 0000111
[[1,2,3,7,8],[4],[5],[6]] => [6,5,4,1,2,3,7,8] => 1110000 => 0000111
[[1,4,5,6,8],[2],[3],[7]] => [7,3,2,1,4,5,6,8] => 1110000 => 0000111
[[1,2,5,6,8],[3],[4],[7]] => [7,4,3,1,2,5,6,8] => 1110000 => 0000111
[[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => 1110000 => 0000111
[[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => 1110000 => 0000111
[[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => 1110000 => 0000111
[[1,3,5,6,7],[2],[4],[8]] => [8,4,2,1,3,5,6,7] => 1110000 => 0000111
[[1,3,4,6,7],[2],[5],[8]] => [8,5,2,1,3,4,6,7] => 1110000 => 0000111
[[1,2,4,6,7],[3],[5],[8]] => [8,5,3,1,2,4,6,7] => 1110000 => 0000111
[[1,2,3,6,7],[4],[5],[8]] => [8,5,4,1,2,3,6,7] => 1110000 => 0000111
[[1,2,3,5,7],[4],[6],[8]] => [8,6,4,1,2,3,5,7] => 1110000 => 0000111
[[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => 1110000 => 0000111
[[1,3,4,5,6],[2],[7],[8]] => [8,7,2,1,3,4,5,6] => 1110000 => 0000111
[[1,2,3,5,6],[4],[7],[8]] => [8,7,4,1,2,3,5,6] => 1110000 => 0000111
[[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => 1110000 => 0000111
[[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => 1110000 => 0000111
[[1,3,5,7],[2,4,6,8]] => [2,4,6,8,1,3,5,7] => 0001000 => 0001000
[[1,2,5,7],[3,4,6,8]] => [3,4,6,8,1,2,5,7] => 0001000 => 0001000
[[1,3,4,7],[2,5,6,8]] => [2,5,6,8,1,3,4,7] => 0001000 => 0001000
[[1,2,4,7],[3,5,6,8]] => [3,5,6,8,1,2,4,7] => 0001000 => 0001000
[[1,2,3,7],[4,5,6,8]] => [4,5,6,8,1,2,3,7] => 0001000 => 0001000
[[1,3,5,6],[2,4,7,8]] => [2,4,7,8,1,3,5,6] => 0001000 => 0001000
[[1,2,5,6],[3,4,7,8]] => [3,4,7,8,1,2,5,6] => 0001000 => 0001000
[[1,3,4,6],[2,5,7,8]] => [2,5,7,8,1,3,4,6] => 0001000 => 0001000
[[1,2,4,6],[3,5,7,8]] => [3,5,7,8,1,2,4,6] => 0001000 => 0001000
[[1,2,3,6],[4,5,7,8]] => [4,5,7,8,1,2,3,6] => 0001000 => 0001000
[[1,3,4,5],[2,6,7,8]] => [2,6,7,8,1,3,4,5] => 0001000 => 0001000
[[1,2,4,5],[3,6,7,8]] => [3,6,7,8,1,2,4,5] => 0001000 => 0001000
[[1,2,3,5],[4,6,7,8]] => [4,6,7,8,1,2,3,5] => 0001000 => 0001000
[[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => 0001000 => 0001000
[[1,4,6,8],[2,5,7],[3]] => [3,2,5,7,1,4,6,8] => 1001000 => 0001001
[[1,3,6,8],[2,5,7],[4]] => [4,2,5,7,1,3,6,8] => 1001000 => 0001001
[[1,2,6,8],[3,5,7],[4]] => [4,3,5,7,1,2,6,8] => 1001000 => 0001001
[[1,3,6,8],[2,4,7],[5]] => [5,2,4,7,1,3,6,8] => 1001000 => 0001001
[[1,2,6,8],[3,4,7],[5]] => [5,3,4,7,1,2,6,8] => 1001000 => 0001001
[[1,3,5,8],[2,6,7],[4]] => [4,2,6,7,1,3,5,8] => 1001000 => 0001001
[[1,3,4,8],[2,6,7],[5]] => [5,2,6,7,1,3,4,8] => 1001000 => 0001001
[[1,2,4,8],[3,6,7],[5]] => [5,3,6,7,1,2,4,8] => 1001000 => 0001001
[[1,2,3,8],[4,6,7],[5]] => [5,4,6,7,1,2,3,8] => 1001000 => 0001001
[[1,3,4,8],[2,5,7],[6]] => [6,2,5,7,1,3,4,8] => 1001000 => 0001001
[[1,2,4,8],[3,5,7],[6]] => [6,3,5,7,1,2,4,8] => 1001000 => 0001001
[[1,3,5,8],[2,4,6],[7]] => [7,2,4,6,1,3,5,8] => 1001000 => 0001001
[[1,2,5,8],[3,4,6],[7]] => [7,3,4,6,1,2,5,8] => 1001000 => 0001001
[[1,2,4,8],[3,5,6],[7]] => [7,3,5,6,1,2,4,8] => 1001000 => 0001001
[[1,2,3,8],[4,5,6],[7]] => [7,4,5,6,1,2,3,8] => 1001000 => 0001001
[[1,4,6,7],[2,5,8],[3]] => [3,2,5,8,1,4,6,7] => 1001000 => 0001001
[[1,3,6,7],[2,5,8],[4]] => [4,2,5,8,1,3,6,7] => 1001000 => 0001001
[[1,2,6,7],[3,5,8],[4]] => [4,3,5,8,1,2,6,7] => 1001000 => 0001001
[[1,3,6,7],[2,4,8],[5]] => [5,2,4,8,1,3,6,7] => 1001000 => 0001001
[[1,4,5,7],[2,6,8],[3]] => [3,2,6,8,1,4,5,7] => 1001000 => 0001001
[[1,3,5,7],[2,6,8],[4]] => [4,2,6,8,1,3,5,7] => 1001000 => 0001001
[[1,2,5,7],[3,6,8],[4]] => [4,3,6,8,1,2,5,7] => 1001000 => 0001001
[[1,3,4,7],[2,6,8],[5]] => [5,2,6,8,1,3,4,7] => 1001000 => 0001001
[[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => 1001000 => 0001001
[[1,2,5,7],[3,4,8],[6]] => [6,3,4,8,1,2,5,7] => 1001000 => 0001001
[[1,3,4,7],[2,5,8],[6]] => [6,2,5,8,1,3,4,7] => 1001000 => 0001001
[[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => 1001000 => 0001001
[[1,2,3,7],[4,5,8],[6]] => [6,4,5,8,1,2,3,7] => 1001000 => 0001001
[[1,4,5,6],[2,7,8],[3]] => [3,2,7,8,1,4,5,6] => 1001000 => 0001001
[[1,2,5,6],[3,7,8],[4]] => [4,3,7,8,1,2,5,6] => 1001000 => 0001001
[[1,2,4,6],[3,7,8],[5]] => [5,3,7,8,1,2,4,6] => 1001000 => 0001001
[[1,3,4,5],[2,7,8],[6]] => [6,2,7,8,1,3,4,5] => 1001000 => 0001001
[[1,2,4,5],[3,7,8],[6]] => [6,3,7,8,1,2,4,5] => 1001000 => 0001001
[[1,2,3,5],[4,7,8],[6]] => [6,4,7,8,1,2,3,5] => 1001000 => 0001001
[[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => 1001000 => 0001001
[[1,3,5,6],[2,4,8],[7]] => [7,2,4,8,1,3,5,6] => 1001000 => 0001001
[[1,2,5,6],[3,4,8],[7]] => [7,3,4,8,1,2,5,6] => 1001000 => 0001001
[[1,2,4,6],[3,5,8],[7]] => [7,3,5,8,1,2,4,6] => 1001000 => 0001001
[[1,2,3,6],[4,5,8],[7]] => [7,4,5,8,1,2,3,6] => 1001000 => 0001001
[[1,2,3,5],[4,6,8],[7]] => [7,4,6,8,1,2,3,5] => 1001000 => 0001001
[[1,2,3,4],[5,6,8],[7]] => [7,5,6,8,1,2,3,4] => 1001000 => 0001001
[[1,3,5,7],[2,4,6],[8]] => [8,2,4,6,1,3,5,7] => 1001000 => 0001001
[[1,2,5,7],[3,4,6],[8]] => [8,3,4,6,1,2,5,7] => 1001000 => 0001001
[[1,3,4,7],[2,5,6],[8]] => [8,2,5,6,1,3,4,7] => 1001000 => 0001001
[[1,2,4,7],[3,5,6],[8]] => [8,3,5,6,1,2,4,7] => 1001000 => 0001001
[[1,2,3,7],[4,5,6],[8]] => [8,4,5,6,1,2,3,7] => 1001000 => 0001001
[[1,3,5,6],[2,4,7],[8]] => [8,2,4,7,1,3,5,6] => 1001000 => 0001001
[[1,3,4,6],[2,5,7],[8]] => [8,2,5,7,1,3,4,6] => 1001000 => 0001001
[[1,2,4,6],[3,5,7],[8]] => [8,3,5,7,1,2,4,6] => 1001000 => 0001001
[[1,3,4,5],[2,6,7],[8]] => [8,2,6,7,1,3,4,5] => 1001000 => 0001001
[[1,2,3,5],[4,6,7],[8]] => [8,4,6,7,1,2,3,5] => 1001000 => 0001001
[[1,2,3,4],[5,6,7],[8]] => [8,5,6,7,1,2,3,4] => 1001000 => 0001001
[[1,4,7,8],[2,5],[3,6]] => [3,6,2,5,1,4,7,8] => 0101000 => 0001010
[[1,3,7,8],[2,5],[4,6]] => [4,6,2,5,1,3,7,8] => 0101000 => 0001010
[[1,2,7,8],[3,5],[4,6]] => [4,6,3,5,1,2,7,8] => 0101000 => 0001010
[[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => 0101000 => 0001010
[[1,4,6,8],[2,5],[3,7]] => [3,7,2,5,1,4,6,8] => 0101000 => 0001010
[[1,2,6,8],[3,5],[4,7]] => [4,7,3,5,1,2,6,8] => 0101000 => 0001010
[[1,3,6,8],[2,4],[5,7]] => [5,7,2,4,1,3,6,8] => 0101000 => 0001010
[[1,2,6,8],[3,4],[5,7]] => [5,7,3,4,1,2,6,8] => 0101000 => 0001010
[[1,4,5,8],[2,6],[3,7]] => [3,7,2,6,1,4,5,8] => 0101000 => 0001010
[[1,2,5,8],[3,6],[4,7]] => [4,7,3,6,1,2,5,8] => 0101000 => 0001010
[[1,3,4,8],[2,6],[5,7]] => [5,7,2,6,1,3,4,8] => 0101000 => 0001010
[[1,2,4,8],[3,6],[5,7]] => [5,7,3,6,1,2,4,8] => 0101000 => 0001010
[[1,2,5,8],[3,4],[6,7]] => [6,7,3,4,1,2,5,8] => 0101000 => 0001010
[[1,3,4,8],[2,5],[6,7]] => [6,7,2,5,1,3,4,8] => 0101000 => 0001010
[[1,3,6,7],[2,5],[4,8]] => [4,8,2,5,1,3,6,7] => 0101000 => 0001010
[[1,3,6,7],[2,4],[5,8]] => [5,8,2,4,1,3,6,7] => 0101000 => 0001010
[[1,2,6,7],[3,4],[5,8]] => [5,8,3,4,1,2,6,7] => 0101000 => 0001010
[[1,4,5,7],[2,6],[3,8]] => [3,8,2,6,1,4,5,7] => 0101000 => 0001010
[[1,3,5,7],[2,6],[4,8]] => [4,8,2,6,1,3,5,7] => 0101000 => 0001010
[[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => 0101000 => 0001010
[[1,2,3,7],[4,6],[5,8]] => [5,8,4,6,1,2,3,7] => 0101000 => 0001010
[[1,3,5,7],[2,4],[6,8]] => [6,8,2,4,1,3,5,7] => 0101000 => 0001010
[[1,2,5,7],[3,4],[6,8]] => [6,8,3,4,1,2,5,7] => 0101000 => 0001010
[[1,2,4,7],[3,5],[6,8]] => [6,8,3,5,1,2,4,7] => 0101000 => 0001010
[[1,2,3,7],[4,5],[6,8]] => [6,8,4,5,1,2,3,7] => 0101000 => 0001010
[[1,4,5,6],[2,7],[3,8]] => [3,8,2,7,1,4,5,6] => 0101000 => 0001010
[[1,3,5,6],[2,7],[4,8]] => [4,8,2,7,1,3,5,6] => 0101000 => 0001010
[[1,2,5,6],[3,7],[4,8]] => [4,8,3,7,1,2,5,6] => 0101000 => 0001010
[[1,3,4,6],[2,7],[5,8]] => [5,8,2,7,1,3,4,6] => 0101000 => 0001010
[[1,2,4,6],[3,7],[5,8]] => [5,8,3,7,1,2,4,6] => 0101000 => 0001010
[[1,2,3,6],[4,7],[5,8]] => [5,8,4,7,1,2,3,6] => 0101000 => 0001010
[[1,3,4,5],[2,7],[6,8]] => [6,8,2,7,1,3,4,5] => 0101000 => 0001010
[[1,2,4,5],[3,7],[6,8]] => [6,8,3,7,1,2,4,5] => 0101000 => 0001010
[[1,2,3,4],[5,7],[6,8]] => [6,8,5,7,1,2,3,4] => 0101000 => 0001010
[[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => 0101000 => 0001010
[[1,2,5,6],[3,4],[7,8]] => [7,8,3,4,1,2,5,6] => 0101000 => 0001010
[[1,3,4,6],[2,5],[7,8]] => [7,8,2,5,1,3,4,6] => 0101000 => 0001010
[[1,2,4,6],[3,5],[7,8]] => [7,8,3,5,1,2,4,6] => 0101000 => 0001010
[[1,2,3,6],[4,5],[7,8]] => [7,8,4,5,1,2,3,6] => 0101000 => 0001010
[[1,2,3,5],[4,6],[7,8]] => [7,8,4,6,1,2,3,5] => 0101000 => 0001010
[[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => 0101000 => 0001010
[[1,5,7,8],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8] => 1101000 => 0001011
[[1,4,7,8],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8] => 1101000 => 0001011
[[1,2,7,8],[3,6],[4],[5]] => [5,4,3,6,1,2,7,8] => 1101000 => 0001011
[[1,4,7,8],[2,5],[3],[6]] => [6,3,2,5,1,4,7,8] => 1101000 => 0001011
[[1,3,7,8],[2,5],[4],[6]] => [6,4,2,5,1,3,7,8] => 1101000 => 0001011
[[1,3,7,8],[2,4],[5],[6]] => [6,5,2,4,1,3,7,8] => 1101000 => 0001011
[[1,5,6,8],[2,7],[3],[4]] => [4,3,2,7,1,5,6,8] => 1101000 => 0001011
[[1,4,6,8],[2,7],[3],[5]] => [5,3,2,7,1,4,6,8] => 1101000 => 0001011
[[1,2,6,8],[3,7],[4],[5]] => [5,4,3,7,1,2,6,8] => 1101000 => 0001011
[[1,4,5,8],[2,7],[3],[6]] => [6,3,2,7,1,4,5,8] => 1101000 => 0001011
[[1,3,5,8],[2,7],[4],[6]] => [6,4,2,7,1,3,5,8] => 1101000 => 0001011
[[1,2,5,8],[3,7],[4],[6]] => [6,4,3,7,1,2,5,8] => 1101000 => 0001011
[[1,2,4,8],[3,7],[5],[6]] => [6,5,3,7,1,2,4,8] => 1101000 => 0001011
[[1,4,6,8],[2,5],[3],[7]] => [7,3,2,5,1,4,6,8] => 1101000 => 0001011
[[1,3,6,8],[2,5],[4],[7]] => [7,4,2,5,1,3,6,8] => 1101000 => 0001011
[[1,2,6,8],[3,4],[5],[7]] => [7,5,3,4,1,2,6,8] => 1101000 => 0001011
[[1,4,5,8],[2,6],[3],[7]] => [7,3,2,6,1,4,5,8] => 1101000 => 0001011
[[1,3,5,8],[2,6],[4],[7]] => [7,4,2,6,1,3,5,8] => 1101000 => 0001011
[[1,2,5,8],[3,6],[4],[7]] => [7,4,3,6,1,2,5,8] => 1101000 => 0001011
[[1,3,4,8],[2,6],[5],[7]] => [7,5,2,6,1,3,4,8] => 1101000 => 0001011
[[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => 1101000 => 0001011
[[1,2,3,8],[4,6],[5],[7]] => [7,5,4,6,1,2,3,8] => 1101000 => 0001011
[[1,2,4,8],[3,5],[6],[7]] => [7,6,3,5,1,2,4,8] => 1101000 => 0001011
[[1,2,3,8],[4,5],[6],[7]] => [7,6,4,5,1,2,3,8] => 1101000 => 0001011
[[1,5,6,7],[2,8],[3],[4]] => [4,3,2,8,1,5,6,7] => 1101000 => 0001011
[[1,4,6,7],[2,8],[3],[5]] => [5,3,2,8,1,4,6,7] => 1101000 => 0001011
[[1,2,6,7],[3,8],[4],[5]] => [5,4,3,8,1,2,6,7] => 1101000 => 0001011
[[1,4,5,7],[2,8],[3],[6]] => [6,3,2,8,1,4,5,7] => 1101000 => 0001011
[[1,3,5,7],[2,8],[4],[6]] => [6,4,2,8,1,3,5,7] => 1101000 => 0001011
[[1,2,5,7],[3,8],[4],[6]] => [6,4,3,8,1,2,5,7] => 1101000 => 0001011
[[1,3,4,7],[2,8],[5],[6]] => [6,5,2,8,1,3,4,7] => 1101000 => 0001011
[[1,2,4,7],[3,8],[5],[6]] => [6,5,3,8,1,2,4,7] => 1101000 => 0001011
[[1,2,3,7],[4,8],[5],[6]] => [6,5,4,8,1,2,3,7] => 1101000 => 0001011
[[1,4,5,6],[2,8],[3],[7]] => [7,3,2,8,1,4,5,6] => 1101000 => 0001011
[[1,3,5,6],[2,8],[4],[7]] => [7,4,2,8,1,3,5,6] => 1101000 => 0001011
[[1,2,5,6],[3,8],[4],[7]] => [7,4,3,8,1,2,5,6] => 1101000 => 0001011
[[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => 1101000 => 0001011
[[1,2,3,6],[4,8],[5],[7]] => [7,5,4,8,1,2,3,6] => 1101000 => 0001011
[[1,3,4,5],[2,8],[6],[7]] => [7,6,2,8,1,3,4,5] => 1101000 => 0001011
[[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => 1101000 => 0001011
[[1,4,6,7],[2,5],[3],[8]] => [8,3,2,5,1,4,6,7] => 1101000 => 0001011
[[1,3,6,7],[2,5],[4],[8]] => [8,4,2,5,1,3,6,7] => 1101000 => 0001011
[[1,2,6,7],[3,4],[5],[8]] => [8,5,3,4,1,2,6,7] => 1101000 => 0001011
[[1,4,5,7],[2,6],[3],[8]] => [8,3,2,6,1,4,5,7] => 1101000 => 0001011
[[1,3,5,7],[2,6],[4],[8]] => [8,4,2,6,1,3,5,7] => 1101000 => 0001011
[[1,2,4,7],[3,6],[5],[8]] => [8,5,3,6,1,2,4,7] => 1101000 => 0001011
[[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => 1101000 => 0001011
[[1,2,5,7],[3,4],[6],[8]] => [8,6,3,4,1,2,5,7] => 1101000 => 0001011
[[1,3,4,7],[2,5],[6],[8]] => [8,6,2,5,1,3,4,7] => 1101000 => 0001011
[[1,2,3,7],[4,5],[6],[8]] => [8,6,4,5,1,2,3,7] => 1101000 => 0001011
[[1,4,5,6],[2,7],[3],[8]] => [8,3,2,7,1,4,5,6] => 1101000 => 0001011
[[1,3,5,6],[2,7],[4],[8]] => [8,4,2,7,1,3,5,6] => 1101000 => 0001011
[[1,2,5,6],[3,7],[4],[8]] => [8,4,3,7,1,2,5,6] => 1101000 => 0001011
[[1,3,4,6],[2,7],[5],[8]] => [8,5,2,7,1,3,4,6] => 1101000 => 0001011
[[1,2,4,6],[3,7],[5],[8]] => [8,5,3,7,1,2,4,6] => 1101000 => 0001011
[[1,2,3,6],[4,7],[5],[8]] => [8,5,4,7,1,2,3,6] => 1101000 => 0001011
[[1,2,4,5],[3,7],[6],[8]] => [8,6,3,7,1,2,4,5] => 1101000 => 0001011
[[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => 1101000 => 0001011
[[1,3,5,6],[2,4],[7],[8]] => [8,7,2,4,1,3,5,6] => 1101000 => 0001011
[[1,2,5,6],[3,4],[7],[8]] => [8,7,3,4,1,2,5,6] => 1101000 => 0001011
[[1,3,4,6],[2,5],[7],[8]] => [8,7,2,5,1,3,4,6] => 1101000 => 0001011
[[1,2,4,6],[3,5],[7],[8]] => [8,7,3,5,1,2,4,6] => 1101000 => 0001011
[[1,2,3,6],[4,5],[7],[8]] => [8,7,4,5,1,2,3,6] => 1101000 => 0001011
[[1,3,4,5],[2,6],[7],[8]] => [8,7,2,6,1,3,4,5] => 1101000 => 0001011
[[1,2,4,5],[3,6],[7],[8]] => [8,7,3,6,1,2,4,5] => 1101000 => 0001011
[[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => 1101000 => 0001011
[[1,2,3,4],[5,6],[7],[8]] => [8,7,5,6,1,2,3,4] => 1101000 => 0001011
[[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => 1111000 => 0001111
[[1,5,7,8],[2],[3],[4],[6]] => [6,4,3,2,1,5,7,8] => 1111000 => 0001111
[[1,4,7,8],[2],[3],[5],[6]] => [6,5,3,2,1,4,7,8] => 1111000 => 0001111
[[1,3,7,8],[2],[4],[5],[6]] => [6,5,4,2,1,3,7,8] => 1111000 => 0001111
[[1,2,7,8],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8] => 1111000 => 0001111
[[1,5,6,8],[2],[3],[4],[7]] => [7,4,3,2,1,5,6,8] => 1111000 => 0001111
[[1,4,6,8],[2],[3],[5],[7]] => [7,5,3,2,1,4,6,8] => 1111000 => 0001111
[[1,2,6,8],[3],[4],[5],[7]] => [7,5,4,3,1,2,6,8] => 1111000 => 0001111
[[1,4,5,8],[2],[3],[6],[7]] => [7,6,3,2,1,4,5,8] => 1111000 => 0001111
[[1,3,5,8],[2],[4],[6],[7]] => [7,6,4,2,1,3,5,8] => 1111000 => 0001111
[[1,2,5,8],[3],[4],[6],[7]] => [7,6,4,3,1,2,5,8] => 1111000 => 0001111
[[1,3,4,8],[2],[5],[6],[7]] => [7,6,5,2,1,3,4,8] => 1111000 => 0001111
[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => 1111000 => 0001111
[[1,5,6,7],[2],[3],[4],[8]] => [8,4,3,2,1,5,6,7] => 1111000 => 0001111
[[1,4,6,7],[2],[3],[5],[8]] => [8,5,3,2,1,4,6,7] => 1111000 => 0001111
[[1,3,6,7],[2],[4],[5],[8]] => [8,5,4,2,1,3,6,7] => 1111000 => 0001111
[[1,3,5,7],[2],[4],[6],[8]] => [8,6,4,2,1,3,5,7] => 1111000 => 0001111
[[1,2,5,7],[3],[4],[6],[8]] => [8,6,4,3,1,2,5,7] => 1111000 => 0001111
[[1,3,4,7],[2],[5],[6],[8]] => [8,6,5,2,1,3,4,7] => 1111000 => 0001111
[[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => 1111000 => 0001111
[[1,4,5,6],[2],[3],[7],[8]] => [8,7,3,2,1,4,5,6] => 1111000 => 0001111
[[1,3,5,6],[2],[4],[7],[8]] => [8,7,4,2,1,3,5,6] => 1111000 => 0001111
[[1,3,4,6],[2],[5],[7],[8]] => [8,7,5,2,1,3,4,6] => 1111000 => 0001111
[[1,2,4,6],[3],[5],[7],[8]] => [8,7,5,3,1,2,4,6] => 1111000 => 0001111
[[1,2,3,6],[4],[5],[7],[8]] => [8,7,5,4,1,2,3,6] => 1111000 => 0001111
[[1,3,4,5],[2],[6],[7],[8]] => [8,7,6,2,1,3,4,5] => 1111000 => 0001111
[[1,2,4,5],[3],[6],[7],[8]] => [8,7,6,3,1,2,4,5] => 1111000 => 0001111
[[1,2,3,5],[4],[6],[7],[8]] => [8,7,6,4,1,2,3,5] => 1111000 => 0001111
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => 1111000 => 0001111
[[1,4,7],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7] => 0100100 => 0010010
[[1,2,7],[3,5,8],[4,6]] => [4,6,3,5,8,1,2,7] => 0100100 => 0010010
[[1,3,7],[2,4,8],[5,6]] => [5,6,2,4,8,1,3,7] => 0100100 => 0010010
[[1,3,6],[2,5,8],[4,7]] => [4,7,2,5,8,1,3,6] => 0100100 => 0010010
[[1,2,6],[3,5,8],[4,7]] => [4,7,3,5,8,1,2,6] => 0100100 => 0010010
[[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => 0100100 => 0010010
[[1,2,6],[3,4,8],[5,7]] => [5,7,3,4,8,1,2,6] => 0100100 => 0010010
[[1,4,5],[2,6,8],[3,7]] => [3,7,2,6,8,1,4,5] => 0100100 => 0010010
[[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => 0100100 => 0010010
[[1,3,4],[2,6,8],[5,7]] => [5,7,2,6,8,1,3,4] => 0100100 => 0010010
[[1,2,3],[4,6,8],[5,7]] => [5,7,4,6,8,1,2,3] => 0100100 => 0010010
[[1,2,5],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5] => 0100100 => 0010010
[[1,2,4],[3,5,8],[6,7]] => [6,7,3,5,8,1,2,4] => 0100100 => 0010010
[[1,2,3],[4,5,8],[6,7]] => [6,7,4,5,8,1,2,3] => 0100100 => 0010010
[[1,4,6],[2,5,7],[3,8]] => [3,8,2,5,7,1,4,6] => 0100100 => 0010010
[[1,3,6],[2,5,7],[4,8]] => [4,8,2,5,7,1,3,6] => 0100100 => 0010010
[[1,2,6],[3,5,7],[4,8]] => [4,8,3,5,7,1,2,6] => 0100100 => 0010010
[[1,3,6],[2,4,7],[5,8]] => [5,8,2,4,7,1,3,6] => 0100100 => 0010010
[[1,4,5],[2,6,7],[3,8]] => [3,8,2,6,7,1,4,5] => 0100100 => 0010010
[[1,2,5],[3,6,7],[4,8]] => [4,8,3,6,7,1,2,5] => 0100100 => 0010010
[[1,3,4],[2,6,7],[5,8]] => [5,8,2,6,7,1,3,4] => 0100100 => 0010010
[[1,2,4],[3,6,7],[5,8]] => [5,8,3,6,7,1,2,4] => 0100100 => 0010010
[[1,3,4],[2,5,7],[6,8]] => [6,8,2,5,7,1,3,4] => 0100100 => 0010010
[[1,2,4],[3,5,7],[6,8]] => [6,8,3,5,7,1,2,4] => 0100100 => 0010010
[[1,2,3],[4,5,7],[6,8]] => [6,8,4,5,7,1,2,3] => 0100100 => 0010010
[[1,3,5],[2,4,6],[7,8]] => [7,8,2,4,6,1,3,5] => 0100100 => 0010010
[[1,3,4],[2,5,6],[7,8]] => [7,8,2,5,6,1,3,4] => 0100100 => 0010010
[[1,2,4],[3,5,6],[7,8]] => [7,8,3,5,6,1,2,4] => 0100100 => 0010010
[[1,2,3],[4,5,6],[7,8]] => [7,8,4,5,6,1,2,3] => 0100100 => 0010010
[[1,5,7],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7] => 1100100 => 0010011
[[1,4,7],[2,6,8],[3],[5]] => [5,3,2,6,8,1,4,7] => 1100100 => 0010011
[[1,3,7],[2,6,8],[4],[5]] => [5,4,2,6,8,1,3,7] => 1100100 => 0010011
[[1,2,7],[3,6,8],[4],[5]] => [5,4,3,6,8,1,2,7] => 1100100 => 0010011
[[1,4,7],[2,5,8],[3],[6]] => [6,3,2,5,8,1,4,7] => 1100100 => 0010011
[[1,2,7],[3,5,8],[4],[6]] => [6,4,3,5,8,1,2,7] => 1100100 => 0010011
[[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => 1100100 => 0010011
[[1,5,6],[2,7,8],[3],[4]] => [4,3,2,7,8,1,5,6] => 1100100 => 0010011
[[1,4,6],[2,7,8],[3],[5]] => [5,3,2,7,8,1,4,6] => 1100100 => 0010011
[[1,3,6],[2,7,8],[4],[5]] => [5,4,2,7,8,1,3,6] => 1100100 => 0010011
[[1,2,6],[3,7,8],[4],[5]] => [5,4,3,7,8,1,2,6] => 1100100 => 0010011
[[1,4,5],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5] => 1100100 => 0010011
[[1,3,5],[2,7,8],[4],[6]] => [6,4,2,7,8,1,3,5] => 1100100 => 0010011
[[1,2,5],[3,7,8],[4],[6]] => [6,4,3,7,8,1,2,5] => 1100100 => 0010011
[[1,3,4],[2,7,8],[5],[6]] => [6,5,2,7,8,1,3,4] => 1100100 => 0010011
[[1,2,3],[4,7,8],[5],[6]] => [6,5,4,7,8,1,2,3] => 1100100 => 0010011
[[1,3,6],[2,5,8],[4],[7]] => [7,4,2,5,8,1,3,6] => 1100100 => 0010011
[[1,2,6],[3,5,8],[4],[7]] => [7,4,3,5,8,1,2,6] => 1100100 => 0010011
[[1,2,6],[3,4,8],[5],[7]] => [7,5,3,4,8,1,2,6] => 1100100 => 0010011
[[1,4,5],[2,6,8],[3],[7]] => [7,3,2,6,8,1,4,5] => 1100100 => 0010011
[[1,3,4],[2,6,8],[5],[7]] => [7,5,2,6,8,1,3,4] => 1100100 => 0010011
[[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => 1100100 => 0010011
[[1,2,3],[4,6,8],[5],[7]] => [7,5,4,6,8,1,2,3] => 1100100 => 0010011
[[1,3,5],[2,4,8],[6],[7]] => [7,6,2,4,8,1,3,5] => 1100100 => 0010011
[[1,2,4],[3,5,8],[6],[7]] => [7,6,3,5,8,1,2,4] => 1100100 => 0010011
[[1,2,3],[4,5,8],[6],[7]] => [7,6,4,5,8,1,2,3] => 1100100 => 0010011
[[1,4,6],[2,5,7],[3],[8]] => [8,3,2,5,7,1,4,6] => 1100100 => 0010011
[[1,3,6],[2,5,7],[4],[8]] => [8,4,2,5,7,1,3,6] => 1100100 => 0010011
[[1,3,6],[2,4,7],[5],[8]] => [8,5,2,4,7,1,3,6] => 1100100 => 0010011
[[1,4,5],[2,6,7],[3],[8]] => [8,3,2,6,7,1,4,5] => 1100100 => 0010011
[[1,3,5],[2,6,7],[4],[8]] => [8,4,2,6,7,1,3,5] => 1100100 => 0010011
[[1,3,4],[2,6,7],[5],[8]] => [8,5,2,6,7,1,3,4] => 1100100 => 0010011
[[1,2,4],[3,6,7],[5],[8]] => [8,5,3,6,7,1,2,4] => 1100100 => 0010011
[[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => 1100100 => 0010011
[[1,3,5],[2,4,7],[6],[8]] => [8,6,2,4,7,1,3,5] => 1100100 => 0010011
[[1,2,4],[3,5,7],[6],[8]] => [8,6,3,5,7,1,2,4] => 1100100 => 0010011
[[1,2,3],[4,5,7],[6],[8]] => [8,6,4,5,7,1,2,3] => 1100100 => 0010011
[[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => 1100100 => 0010011
[[1,2,5],[3,4,6],[7],[8]] => [8,7,3,4,6,1,2,5] => 1100100 => 0010011
[[1,3,4],[2,5,6],[7],[8]] => [8,7,2,5,6,1,3,4] => 1100100 => 0010011
[[1,2,4],[3,5,6],[7],[8]] => [8,7,3,5,6,1,2,4] => 1100100 => 0010011
[[1,2,3],[4,5,6],[7],[8]] => [8,7,4,5,6,1,2,3] => 1100100 => 0010011
[[1,5,8],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8] => 1010100 => 0010101
[[1,4,8],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4,8] => 1010100 => 0010101
[[1,3,8],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3,8] => 1010100 => 0010101
[[1,4,8],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4,8] => 1010100 => 0010101
[[1,3,8],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8] => 1010100 => 0010101
[[1,2,8],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2,8] => 1010100 => 0010101
[[1,4,8],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4,8] => 1010100 => 0010101
[[1,2,8],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2,8] => 1010100 => 0010101
[[1,5,7],[2,6],[3,8],[4]] => [4,3,8,2,6,1,5,7] => 1010100 => 0010101
[[1,4,7],[2,6],[3,8],[5]] => [5,3,8,2,6,1,4,7] => 1010100 => 0010101
[[1,3,7],[2,6],[4,8],[5]] => [5,4,8,2,6,1,3,7] => 1010100 => 0010101
[[1,2,7],[3,6],[4,8],[5]] => [5,4,8,3,6,1,2,7] => 1010100 => 0010101
[[1,3,7],[2,5],[4,8],[6]] => [6,4,8,2,5,1,3,7] => 1010100 => 0010101
[[1,2,7],[3,5],[4,8],[6]] => [6,4,8,3,5,1,2,7] => 1010100 => 0010101
[[1,3,7],[2,4],[5,8],[6]] => [6,5,8,2,4,1,3,7] => 1010100 => 0010101
[[1,2,7],[3,4],[5,8],[6]] => [6,5,8,3,4,1,2,7] => 1010100 => 0010101
[[1,5,6],[2,7],[3,8],[4]] => [4,3,8,2,7,1,5,6] => 1010100 => 0010101
[[1,4,6],[2,7],[3,8],[5]] => [5,3,8,2,7,1,4,6] => 1010100 => 0010101
[[1,3,6],[2,7],[4,8],[5]] => [5,4,8,2,7,1,3,6] => 1010100 => 0010101
[[1,2,6],[3,7],[4,8],[5]] => [5,4,8,3,7,1,2,6] => 1010100 => 0010101
[[1,4,5],[2,7],[3,8],[6]] => [6,3,8,2,7,1,4,5] => 1010100 => 0010101
[[1,3,5],[2,7],[4,8],[6]] => [6,4,8,2,7,1,3,5] => 1010100 => 0010101
[[1,2,5],[3,7],[4,8],[6]] => [6,4,8,3,7,1,2,5] => 1010100 => 0010101
[[1,4,6],[2,5],[3,8],[7]] => [7,3,8,2,5,1,4,6] => 1010100 => 0010101
[[1,2,6],[3,5],[4,8],[7]] => [7,4,8,3,5,1,2,6] => 1010100 => 0010101
[[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => 1010100 => 0010101
[[1,2,6],[3,4],[5,8],[7]] => [7,5,8,3,4,1,2,6] => 1010100 => 0010101
[[1,4,5],[2,6],[3,8],[7]] => [7,3,8,2,6,1,4,5] => 1010100 => 0010101
[[1,3,5],[2,6],[4,8],[7]] => [7,4,8,2,6,1,3,5] => 1010100 => 0010101
[[1,3,4],[2,6],[5,8],[7]] => [7,5,8,2,6,1,3,4] => 1010100 => 0010101
[[1,2,4],[3,6],[5,8],[7]] => [7,5,8,3,6,1,2,4] => 1010100 => 0010101
[[1,2,3],[4,6],[5,8],[7]] => [7,5,8,4,6,1,2,3] => 1010100 => 0010101
[[1,3,4],[2,5],[6,8],[7]] => [7,6,8,2,5,1,3,4] => 1010100 => 0010101
[[1,2,4],[3,5],[6,8],[7]] => [7,6,8,3,5,1,2,4] => 1010100 => 0010101
[[1,4,7],[2,5],[3,6],[8]] => [8,3,6,2,5,1,4,7] => 1010100 => 0010101
[[1,3,7],[2,4],[5,6],[8]] => [8,5,6,2,4,1,3,7] => 1010100 => 0010101
[[1,2,7],[3,4],[5,6],[8]] => [8,5,6,3,4,1,2,7] => 1010100 => 0010101
[[1,4,6],[2,5],[3,7],[8]] => [8,3,7,2,5,1,4,6] => 1010100 => 0010101
[[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => 1010100 => 0010101
[[1,4,5],[2,6],[3,7],[8]] => [8,3,7,2,6,1,4,5] => 1010100 => 0010101
[[1,3,5],[2,6],[4,7],[8]] => [8,4,7,2,6,1,3,5] => 1010100 => 0010101
[[1,2,5],[3,6],[4,7],[8]] => [8,4,7,3,6,1,2,5] => 1010100 => 0010101
[[1,3,4],[2,6],[5,7],[8]] => [8,5,7,2,6,1,3,4] => 1010100 => 0010101
[[1,3,5],[2,4],[6,7],[8]] => [8,6,7,2,4,1,3,5] => 1010100 => 0010101
[[1,2,5],[3,4],[6,7],[8]] => [8,6,7,3,4,1,2,5] => 1010100 => 0010101
[[1,3,4],[2,5],[6,7],[8]] => [8,6,7,2,5,1,3,4] => 1010100 => 0010101
[[1,2,4],[3,5],[6,7],[8]] => [8,6,7,3,5,1,2,4] => 1010100 => 0010101
[[1,2,3],[4,5],[6,7],[8]] => [8,6,7,4,5,1,2,3] => 1010100 => 0010101
[[1,6,8],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8] => 1110100 => 0010111
[[1,5,8],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8] => 1110100 => 0010111
[[1,4,8],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4,8] => 1110100 => 0010111
[[1,3,8],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3,8] => 1110100 => 0010111
[[1,2,8],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2,8] => 1110100 => 0010111
[[1,4,8],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4,8] => 1110100 => 0010111
[[1,3,8],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3,8] => 1110100 => 0010111
[[1,4,8],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4,8] => 1110100 => 0010111
[[1,2,8],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2,8] => 1110100 => 0010111
[[1,6,7],[2,8],[3],[4],[5]] => [5,4,3,2,8,1,6,7] => 1110100 => 0010111
[[1,4,7],[2,8],[3],[5],[6]] => [6,5,3,2,8,1,4,7] => 1110100 => 0010111
[[1,3,7],[2,8],[4],[5],[6]] => [6,5,4,2,8,1,3,7] => 1110100 => 0010111
[[1,2,7],[3,8],[4],[5],[6]] => [6,5,4,3,8,1,2,7] => 1110100 => 0010111
[[1,4,6],[2,8],[3],[5],[7]] => [7,5,3,2,8,1,4,6] => 1110100 => 0010111
[[1,3,6],[2,8],[4],[5],[7]] => [7,5,4,2,8,1,3,6] => 1110100 => 0010111
[[1,4,5],[2,8],[3],[6],[7]] => [7,6,3,2,8,1,4,5] => 1110100 => 0010111
[[1,2,5],[3,8],[4],[6],[7]] => [7,6,4,3,8,1,2,5] => 1110100 => 0010111
[[1,3,4],[2,8],[5],[6],[7]] => [7,6,5,2,8,1,3,4] => 1110100 => 0010111
[[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => 1110100 => 0010111
[[1,4,7],[2,6],[3],[5],[8]] => [8,5,3,2,6,1,4,7] => 1110100 => 0010111
[[1,3,7],[2,6],[4],[5],[8]] => [8,5,4,2,6,1,3,7] => 1110100 => 0010111
[[1,2,7],[3,6],[4],[5],[8]] => [8,5,4,3,6,1,2,7] => 1110100 => 0010111
[[1,3,7],[2,5],[4],[6],[8]] => [8,6,4,2,5,1,3,7] => 1110100 => 0010111
[[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => 1110100 => 0010111
[[1,2,7],[3,4],[5],[6],[8]] => [8,6,5,3,4,1,2,7] => 1110100 => 0010111
[[1,4,6],[2,7],[3],[5],[8]] => [8,5,3,2,7,1,4,6] => 1110100 => 0010111
[[1,4,5],[2,7],[3],[6],[8]] => [8,6,3,2,7,1,4,5] => 1110100 => 0010111
[[1,3,5],[2,7],[4],[6],[8]] => [8,6,4,2,7,1,3,5] => 1110100 => 0010111
[[1,2,5],[3,7],[4],[6],[8]] => [8,6,4,3,7,1,2,5] => 1110100 => 0010111
[[1,2,6],[3,4],[5],[7],[8]] => [8,7,5,3,4,1,2,6] => 1110100 => 0010111
[[1,4,5],[2,6],[3],[7],[8]] => [8,7,3,2,6,1,4,5] => 1110100 => 0010111
[[1,3,5],[2,6],[4],[7],[8]] => [8,7,4,2,6,1,3,5] => 1110100 => 0010111
[[1,2,5],[3,6],[4],[7],[8]] => [8,7,4,3,6,1,2,5] => 1110100 => 0010111
[[1,3,4],[2,6],[5],[7],[8]] => [8,7,5,2,6,1,3,4] => 1110100 => 0010111
[[1,2,3],[4,6],[5],[7],[8]] => [8,7,5,4,6,1,2,3] => 1110100 => 0010111
[[1,3,5],[2,4],[6],[7],[8]] => [8,7,6,2,4,1,3,5] => 1110100 => 0010111
[[1,2,5],[3,4],[6],[7],[8]] => [8,7,6,3,4,1,2,5] => 1110100 => 0010111
[[1,3,4],[2,5],[6],[7],[8]] => [8,7,6,2,5,1,3,4] => 1110100 => 0010111
[[1,2,4],[3,5],[6],[7],[8]] => [8,7,6,3,5,1,2,4] => 1110100 => 0010111
[[1,2,3],[4,5],[6],[7],[8]] => [8,7,6,4,5,1,2,3] => 1110100 => 0010111
[[1,7,8],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8] => 1111100 => 0011111
[[1,6,8],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6,8] => 1111100 => 0011111
[[1,5,8],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5,8] => 1111100 => 0011111
[[1,4,8],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4,8] => 1111100 => 0011111
[[1,3,8],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3,8] => 1111100 => 0011111
[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => 1111100 => 0011111
[[1,6,7],[2],[3],[4],[5],[8]] => [8,5,4,3,2,1,6,7] => 1111100 => 0011111
[[1,5,7],[2],[3],[4],[6],[8]] => [8,6,4,3,2,1,5,7] => 1111100 => 0011111
[[1,4,7],[2],[3],[5],[6],[8]] => [8,6,5,3,2,1,4,7] => 1111100 => 0011111
[[1,3,7],[2],[4],[5],[6],[8]] => [8,6,5,4,2,1,3,7] => 1111100 => 0011111
[[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => 1111100 => 0011111
[[1,5,6],[2],[3],[4],[7],[8]] => [8,7,4,3,2,1,5,6] => 1111100 => 0011111
[[1,4,6],[2],[3],[5],[7],[8]] => [8,7,5,3,2,1,4,6] => 1111100 => 0011111
[[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => 1111100 => 0011111
[[1,4,5],[2],[3],[6],[7],[8]] => [8,7,6,3,2,1,4,5] => 1111100 => 0011111
[[1,3,5],[2],[4],[6],[7],[8]] => [8,7,6,4,2,1,3,5] => 1111100 => 0011111
[[1,2,5],[3],[4],[6],[7],[8]] => [8,7,6,4,3,1,2,5] => 1111100 => 0011111
[[1,3,4],[2],[5],[6],[7],[8]] => [8,7,6,5,2,1,3,4] => 1111100 => 0011111
[[1,2,4],[3],[5],[6],[7],[8]] => [8,7,6,5,3,1,2,4] => 1111100 => 0011111
[[1,2,3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3] => 1111100 => 0011111
[[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => 0101010 => 0101010
[[1,4],[2,6],[3,7],[5,8]] => [5,8,3,7,2,6,1,4] => 0101010 => 0101010
[[1,3],[2,6],[4,7],[5,8]] => [5,8,4,7,2,6,1,3] => 0101010 => 0101010
[[1,2],[3,6],[4,7],[5,8]] => [5,8,4,7,3,6,1,2] => 0101010 => 0101010
[[1,4],[2,5],[3,7],[6,8]] => [6,8,3,7,2,5,1,4] => 0101010 => 0101010
[[1,3],[2,5],[4,7],[6,8]] => [6,8,4,7,2,5,1,3] => 0101010 => 0101010
[[1,2],[3,5],[4,7],[6,8]] => [6,8,4,7,3,5,1,2] => 0101010 => 0101010
[[1,3],[2,4],[5,7],[6,8]] => [6,8,5,7,2,4,1,3] => 0101010 => 0101010
[[1,2],[3,4],[5,7],[6,8]] => [6,8,5,7,3,4,1,2] => 0101010 => 0101010
[[1,4],[2,5],[3,6],[7,8]] => [7,8,3,6,2,5,1,4] => 0101010 => 0101010
[[1,3],[2,5],[4,6],[7,8]] => [7,8,4,6,2,5,1,3] => 0101010 => 0101010
[[1,2],[3,5],[4,6],[7,8]] => [7,8,4,6,3,5,1,2] => 0101010 => 0101010
[[1,3],[2,4],[5,6],[7,8]] => [7,8,5,6,2,4,1,3] => 0101010 => 0101010
[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => 0101010 => 0101010
[[1,6],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6] => 1101010 => 0101011
[[1,5],[2,7],[3,8],[4],[6]] => [6,4,3,8,2,7,1,5] => 1101010 => 0101011
[[1,4],[2,7],[3,8],[5],[6]] => [6,5,3,8,2,7,1,4] => 1101010 => 0101011
[[1,3],[2,7],[4,8],[5],[6]] => [6,5,4,8,2,7,1,3] => 1101010 => 0101011
[[1,2],[3,7],[4,8],[5],[6]] => [6,5,4,8,3,7,1,2] => 1101010 => 0101011
[[1,5],[2,6],[3,8],[4],[7]] => [7,4,3,8,2,6,1,5] => 1101010 => 0101011
[[1,4],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4] => 1101010 => 0101011
[[1,3],[2,6],[4,8],[5],[7]] => [7,5,4,8,2,6,1,3] => 1101010 => 0101011
[[1,4],[2,5],[3,8],[6],[7]] => [7,6,3,8,2,5,1,4] => 1101010 => 0101011
[[1,3],[2,5],[4,8],[6],[7]] => [7,6,4,8,2,5,1,3] => 1101010 => 0101011
[[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => 1101010 => 0101011
[[1,2],[3,4],[5,8],[6],[7]] => [7,6,5,8,3,4,1,2] => 1101010 => 0101011
[[1,5],[2,6],[3,7],[4],[8]] => [8,4,3,7,2,6,1,5] => 1101010 => 0101011
[[1,4],[2,6],[3,7],[5],[8]] => [8,5,3,7,2,6,1,4] => 1101010 => 0101011
[[1,3],[2,6],[4,7],[5],[8]] => [8,5,4,7,2,6,1,3] => 1101010 => 0101011
[[1,2],[3,6],[4,7],[5],[8]] => [8,5,4,7,3,6,1,2] => 1101010 => 0101011
[[1,4],[2,5],[3,7],[6],[8]] => [8,6,3,7,2,5,1,4] => 1101010 => 0101011
[[1,3],[2,5],[4,7],[6],[8]] => [8,6,4,7,2,5,1,3] => 1101010 => 0101011
[[1,3],[2,4],[5,7],[6],[8]] => [8,6,5,7,2,4,1,3] => 1101010 => 0101011
[[1,2],[3,4],[5,7],[6],[8]] => [8,6,5,7,3,4,1,2] => 1101010 => 0101011
[[1,4],[2,5],[3,6],[7],[8]] => [8,7,3,6,2,5,1,4] => 1101010 => 0101011
[[1,3],[2,5],[4,6],[7],[8]] => [8,7,4,6,2,5,1,3] => 1101010 => 0101011
[[1,2],[3,5],[4,6],[7],[8]] => [8,7,4,6,3,5,1,2] => 1101010 => 0101011
[[1,3],[2,4],[5,6],[7],[8]] => [8,7,5,6,2,4,1,3] => 1101010 => 0101011
[[1,2],[3,4],[5,6],[7],[8]] => [8,7,5,6,3,4,1,2] => 1101010 => 0101011
[[1,7],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7] => 1111010 => 0101111
[[1,6],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6] => 1111010 => 0101111
[[1,5],[2,8],[3],[4],[6],[7]] => [7,6,4,3,2,8,1,5] => 1111010 => 0101111
[[1,3],[2,8],[4],[5],[6],[7]] => [7,6,5,4,2,8,1,3] => 1111010 => 0101111
[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => 1111010 => 0101111
[[1,6],[2,7],[3],[4],[5],[8]] => [8,5,4,3,2,7,1,6] => 1111010 => 0101111
[[1,5],[2,7],[3],[4],[6],[8]] => [8,6,4,3,2,7,1,5] => 1111010 => 0101111
[[1,4],[2,7],[3],[5],[6],[8]] => [8,6,5,3,2,7,1,4] => 1111010 => 0101111
[[1,3],[2,7],[4],[5],[6],[8]] => [8,6,5,4,2,7,1,3] => 1111010 => 0101111
[[1,2],[3,7],[4],[5],[6],[8]] => [8,6,5,4,3,7,1,2] => 1111010 => 0101111
[[1,5],[2,6],[3],[4],[7],[8]] => [8,7,4,3,2,6,1,5] => 1111010 => 0101111
[[1,4],[2,6],[3],[5],[7],[8]] => [8,7,5,3,2,6,1,4] => 1111010 => 0101111
[[1,3],[2,6],[4],[5],[7],[8]] => [8,7,5,4,2,6,1,3] => 1111010 => 0101111
[[1,4],[2,5],[3],[6],[7],[8]] => [8,7,6,3,2,5,1,4] => 1111010 => 0101111
[[1,3],[2,5],[4],[6],[7],[8]] => [8,7,6,4,2,5,1,3] => 1111010 => 0101111
[[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => 1111010 => 0101111
[[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => 1111010 => 0101111
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => 1111110 => 0111111
[[1,7],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7] => 1111110 => 0111111
[[1,6],[2],[3],[4],[5],[7],[8]] => [8,7,5,4,3,2,1,6] => 1111110 => 0111111
[[1,5],[2],[3],[4],[6],[7],[8]] => [8,7,6,4,3,2,1,5] => 1111110 => 0111111
[[1,4],[2],[3],[5],[6],[7],[8]] => [8,7,6,5,3,2,1,4] => 1111110 => 0111111
[[1,3],[2],[4],[5],[6],[7],[8]] => [8,7,6,5,4,2,1,3] => 1111110 => 0111111
[[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => 1111110 => 0111111
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => 1111111 => 1111111
[[1,3,5,7,9],[2,4,6,8,10]] => [2,4,6,8,10,1,3,5,7,9] => 000010000 => 000010000
[[1,3,5,7,8],[2,4,6,9,10]] => [2,4,6,9,10,1,3,5,7,8] => 000010000 => 000010000
[[1,3,5,6,9],[2,4,7,8,10]] => [2,4,7,8,10,1,3,5,6,9] => 000010000 => 000010000
[[1,3,5,6,8],[2,4,7,9,10]] => [2,4,7,9,10,1,3,5,6,8] => 000010000 => 000010000
[[1,3,5,6,7],[2,4,8,9,10]] => [2,4,8,9,10,1,3,5,6,7] => 000010000 => 000010000
[[1,3,4,7,9],[2,5,6,8,10]] => [2,5,6,8,10,1,3,4,7,9] => 000010000 => 000010000
[[1,3,4,7,8],[2,5,6,9,10]] => [2,5,6,9,10,1,3,4,7,8] => 000010000 => 000010000
[[1,3,4,6,9],[2,5,7,8,10]] => [2,5,7,8,10,1,3,4,6,9] => 000010000 => 000010000
[[1,3,4,6,8],[2,5,7,9,10]] => [2,5,7,9,10,1,3,4,6,8] => 000010000 => 000010000
[[1,3,4,6,7],[2,5,8,9,10]] => [2,5,8,9,10,1,3,4,6,7] => 000010000 => 000010000
[[1,3,4,5,9],[2,6,7,8,10]] => [2,6,7,8,10,1,3,4,5,9] => 000010000 => 000010000
[[1,3,4,5,8],[2,6,7,9,10]] => [2,6,7,9,10,1,3,4,5,8] => 000010000 => 000010000
[[1,3,4,5,7],[2,6,8,9,10]] => [2,6,8,9,10,1,3,4,5,7] => 000010000 => 000010000
[[1,3,4,5,6],[2,7,8,9,10]] => [2,7,8,9,10,1,3,4,5,6] => 000010000 => 000010000
[[1,2,5,7,9],[3,4,6,8,10]] => [3,4,6,8,10,1,2,5,7,9] => 000010000 => 000010000
[[1,2,5,7,8],[3,4,6,9,10]] => [3,4,6,9,10,1,2,5,7,8] => 000010000 => 000010000
[[1,2,5,6,9],[3,4,7,8,10]] => [3,4,7,8,10,1,2,5,6,9] => 000010000 => 000010000
[[1,2,5,6,8],[3,4,7,9,10]] => [3,4,7,9,10,1,2,5,6,8] => 000010000 => 000010000
[[1,2,5,6,7],[3,4,8,9,10]] => [3,4,8,9,10,1,2,5,6,7] => 000010000 => 000010000
[[1,2,4,7,9],[3,5,6,8,10]] => [3,5,6,8,10,1,2,4,7,9] => 000010000 => 000010000
[[1,2,4,7,8],[3,5,6,9,10]] => [3,5,6,9,10,1,2,4,7,8] => 000010000 => 000010000
[[1,2,4,6,9],[3,5,7,8,10]] => [3,5,7,8,10,1,2,4,6,9] => 000010000 => 000010000
[[1,2,4,6,8],[3,5,7,9,10]] => [3,5,7,9,10,1,2,4,6,8] => 000010000 => 000010000
[[1,2,4,6,7],[3,5,8,9,10]] => [3,5,8,9,10,1,2,4,6,7] => 000010000 => 000010000
[[1,2,4,5,9],[3,6,7,8,10]] => [3,6,7,8,10,1,2,4,5,9] => 000010000 => 000010000
[[1,2,4,5,8],[3,6,7,9,10]] => [3,6,7,9,10,1,2,4,5,8] => 000010000 => 000010000
[[1,2,4,5,7],[3,6,8,9,10]] => [3,6,8,9,10,1,2,4,5,7] => 000010000 => 000010000
[[1,2,4,5,6],[3,7,8,9,10]] => [3,7,8,9,10,1,2,4,5,6] => 000010000 => 000010000
[[1,2,3,7,9],[4,5,6,8,10]] => [4,5,6,8,10,1,2,3,7,9] => 000010000 => 000010000
[[1,2,3,7,8],[4,5,6,9,10]] => [4,5,6,9,10,1,2,3,7,8] => 000010000 => 000010000
[[1,2,3,6,9],[4,5,7,8,10]] => [4,5,7,8,10,1,2,3,6,9] => 000010000 => 000010000
[[1,2,3,6,8],[4,5,7,9,10]] => [4,5,7,9,10,1,2,3,6,8] => 000010000 => 000010000
[[1,2,3,6,7],[4,5,8,9,10]] => [4,5,8,9,10,1,2,3,6,7] => 000010000 => 000010000
[[1,2,3,5,9],[4,6,7,8,10]] => [4,6,7,8,10,1,2,3,5,9] => 000010000 => 000010000
[[1,2,3,5,8],[4,6,7,9,10]] => [4,6,7,9,10,1,2,3,5,8] => 000010000 => 000010000
[[1,2,3,5,7],[4,6,8,9,10]] => [4,6,8,9,10,1,2,3,5,7] => 000010000 => 000010000
[[1,2,3,5,6],[4,7,8,9,10]] => [4,7,8,9,10,1,2,3,5,6] => 000010000 => 000010000
[[1,2,3,4,9],[5,6,7,8,10]] => [5,6,7,8,10,1,2,3,4,9] => 000010000 => 000010000
[[1,2,3,4,8],[5,6,7,9,10]] => [5,6,7,9,10,1,2,3,4,8] => 000010000 => 000010000
[[1,2,3,4,7],[5,6,8,9,10]] => [5,6,8,9,10,1,2,3,4,7] => 000010000 => 000010000
[[1,2,3,4,6],[5,7,8,9,10]] => [5,7,8,9,10,1,2,3,4,6] => 000010000 => 000010000
[[1,2,3,4,5],[6,7,8,9,10]] => [6,7,8,9,10,1,2,3,4,5] => 000010000 => 000010000
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [2,4,6,8,10,12,1,3,5,7,9,11] => 00000100000 => 00000100000
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,4,6,8,11,12,1,3,5,7,9,10] => 00000100000 => 00000100000
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [2,4,6,9,10,12,1,3,5,7,8,11] => 00000100000 => 00000100000
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [2,4,6,9,11,12,1,3,5,7,8,10] => 00000100000 => 00000100000
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [2,4,6,10,11,12,1,3,5,7,8,9] => 00000100000 => 00000100000
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [2,4,7,8,10,12,1,3,5,6,9,11] => 00000100000 => 00000100000
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [2,4,7,8,11,12,1,3,5,6,9,10] => 00000100000 => 00000100000
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [2,4,7,9,10,12,1,3,5,6,8,11] => 00000100000 => 00000100000
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,4,7,9,11,12,1,3,5,6,8,10] => 00000100000 => 00000100000
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [2,4,7,10,11,12,1,3,5,6,8,9] => 00000100000 => 00000100000
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [2,4,8,9,10,12,1,3,5,6,7,11] => 00000100000 => 00000100000
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [2,4,8,9,11,12,1,3,5,6,7,10] => 00000100000 => 00000100000
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [2,4,8,10,11,12,1,3,5,6,7,9] => 00000100000 => 00000100000
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [2,4,9,10,11,12,1,3,5,6,7,8] => 00000100000 => 00000100000
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [2,5,6,8,10,12,1,3,4,7,9,11] => 00000100000 => 00000100000
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [2,5,6,8,11,12,1,3,4,7,9,10] => 00000100000 => 00000100000
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [2,5,6,9,10,12,1,3,4,7,8,11] => 00000100000 => 00000100000
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [2,5,6,9,11,12,1,3,4,7,8,10] => 00000100000 => 00000100000
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [2,5,6,10,11,12,1,3,4,7,8,9] => 00000100000 => 00000100000
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [2,5,7,8,10,12,1,3,4,6,9,11] => 00000100000 => 00000100000
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [2,5,7,8,11,12,1,3,4,6,9,10] => 00000100000 => 00000100000
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [2,5,7,9,10,12,1,3,4,6,8,11] => 00000100000 => 00000100000
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,5,7,9,11,12,1,3,4,6,8,10] => 00000100000 => 00000100000
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [2,5,7,10,11,12,1,3,4,6,8,9] => 00000100000 => 00000100000
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [2,5,8,9,10,12,1,3,4,6,7,11] => 00000100000 => 00000100000
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [2,5,8,9,11,12,1,3,4,6,7,10] => 00000100000 => 00000100000
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [2,5,8,10,11,12,1,3,4,6,7,9] => 00000100000 => 00000100000
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [2,5,9,10,11,12,1,3,4,6,7,8] => 00000100000 => 00000100000
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [2,6,7,8,10,12,1,3,4,5,9,11] => 00000100000 => 00000100000
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [2,6,7,8,11,12,1,3,4,5,9,10] => 00000100000 => 00000100000
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [2,6,7,9,10,12,1,3,4,5,8,11] => 00000100000 => 00000100000
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [2,6,7,9,11,12,1,3,4,5,8,10] => 00000100000 => 00000100000
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [2,6,7,10,11,12,1,3,4,5,8,9] => 00000100000 => 00000100000
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [2,6,8,9,10,12,1,3,4,5,7,11] => 00000100000 => 00000100000
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [2,6,8,9,11,12,1,3,4,5,7,10] => 00000100000 => 00000100000
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [2,6,8,10,11,12,1,3,4,5,7,9] => 00000100000 => 00000100000
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [2,6,9,10,11,12,1,3,4,5,7,8] => 00000100000 => 00000100000
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [2,7,8,9,10,12,1,3,4,5,6,11] => 00000100000 => 00000100000
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [2,7,8,9,11,12,1,3,4,5,6,10] => 00000100000 => 00000100000
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [2,7,8,10,11,12,1,3,4,5,6,9] => 00000100000 => 00000100000
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [2,7,9,10,11,12,1,3,4,5,6,8] => 00000100000 => 00000100000
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [2,8,9,10,11,12,1,3,4,5,6,7] => 00000100000 => 00000100000
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [3,4,6,8,10,12,1,2,5,7,9,11] => 00000100000 => 00000100000
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [3,4,6,8,11,12,1,2,5,7,9,10] => 00000100000 => 00000100000
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [3,4,6,9,10,12,1,2,5,7,8,11] => 00000100000 => 00000100000
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [3,4,6,9,11,12,1,2,5,7,8,10] => 00000100000 => 00000100000
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [3,4,6,10,11,12,1,2,5,7,8,9] => 00000100000 => 00000100000
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [3,4,7,8,10,12,1,2,5,6,9,11] => 00000100000 => 00000100000
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [3,4,7,8,11,12,1,2,5,6,9,10] => 00000100000 => 00000100000
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [3,4,7,9,10,12,1,2,5,6,8,11] => 00000100000 => 00000100000
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [3,4,7,9,11,12,1,2,5,6,8,10] => 00000100000 => 00000100000
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [3,4,7,10,11,12,1,2,5,6,8,9] => 00000100000 => 00000100000
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [3,4,8,9,10,12,1,2,5,6,7,11] => 00000100000 => 00000100000
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [3,4,8,9,11,12,1,2,5,6,7,10] => 00000100000 => 00000100000
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [3,4,8,10,11,12,1,2,5,6,7,9] => 00000100000 => 00000100000
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [3,4,9,10,11,12,1,2,5,6,7,8] => 00000100000 => 00000100000
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [3,5,6,8,10,12,1,2,4,7,9,11] => 00000100000 => 00000100000
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [3,5,6,8,11,12,1,2,4,7,9,10] => 00000100000 => 00000100000
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [3,5,6,9,10,12,1,2,4,7,8,11] => 00000100000 => 00000100000
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [3,5,6,9,11,12,1,2,4,7,8,10] => 00000100000 => 00000100000
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [3,5,6,10,11,12,1,2,4,7,8,9] => 00000100000 => 00000100000
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [3,5,7,8,10,12,1,2,4,6,9,11] => 00000100000 => 00000100000
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [3,5,7,8,11,12,1,2,4,6,9,10] => 00000100000 => 00000100000
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [3,5,7,9,10,12,1,2,4,6,8,11] => 00000100000 => 00000100000
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,5,7,9,11,12,1,2,4,6,8,10] => 00000100000 => 00000100000
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [3,5,7,10,11,12,1,2,4,6,8,9] => 00000100000 => 00000100000
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [3,5,8,9,10,12,1,2,4,6,7,11] => 00000100000 => 00000100000
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [3,5,8,9,11,12,1,2,4,6,7,10] => 00000100000 => 00000100000
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [3,5,8,10,11,12,1,2,4,6,7,9] => 00000100000 => 00000100000
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [3,5,9,10,11,12,1,2,4,6,7,8] => 00000100000 => 00000100000
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [3,6,7,8,10,12,1,2,4,5,9,11] => 00000100000 => 00000100000
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [3,6,7,8,11,12,1,2,4,5,9,10] => 00000100000 => 00000100000
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [3,6,7,9,10,12,1,2,4,5,8,11] => 00000100000 => 00000100000
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [3,6,7,9,11,12,1,2,4,5,8,10] => 00000100000 => 00000100000
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [3,6,7,10,11,12,1,2,4,5,8,9] => 00000100000 => 00000100000
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [3,6,8,9,10,12,1,2,4,5,7,11] => 00000100000 => 00000100000
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [3,6,8,9,11,12,1,2,4,5,7,10] => 00000100000 => 00000100000
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [3,6,8,10,11,12,1,2,4,5,7,9] => 00000100000 => 00000100000
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [3,6,9,10,11,12,1,2,4,5,7,8] => 00000100000 => 00000100000
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [3,7,8,9,10,12,1,2,4,5,6,11] => 00000100000 => 00000100000
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [3,7,8,9,11,12,1,2,4,5,6,10] => 00000100000 => 00000100000
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [3,7,8,10,11,12,1,2,4,5,6,9] => 00000100000 => 00000100000
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [3,7,9,10,11,12,1,2,4,5,6,8] => 00000100000 => 00000100000
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [3,8,9,10,11,12,1,2,4,5,6,7] => 00000100000 => 00000100000
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [4,5,6,8,10,12,1,2,3,7,9,11] => 00000100000 => 00000100000
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [4,5,6,8,11,12,1,2,3,7,9,10] => 00000100000 => 00000100000
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [4,5,6,9,10,12,1,2,3,7,8,11] => 00000100000 => 00000100000
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [4,5,6,9,11,12,1,2,3,7,8,10] => 00000100000 => 00000100000
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [4,5,6,10,11,12,1,2,3,7,8,9] => 00000100000 => 00000100000
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [4,5,7,8,10,12,1,2,3,6,9,11] => 00000100000 => 00000100000
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [4,5,7,8,11,12,1,2,3,6,9,10] => 00000100000 => 00000100000
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [4,5,7,9,10,12,1,2,3,6,8,11] => 00000100000 => 00000100000
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [4,5,7,9,11,12,1,2,3,6,8,10] => 00000100000 => 00000100000
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [4,5,7,10,11,12,1,2,3,6,8,9] => 00000100000 => 00000100000
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [4,5,8,9,10,12,1,2,3,6,7,11] => 00000100000 => 00000100000
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [4,5,8,9,11,12,1,2,3,6,7,10] => 00000100000 => 00000100000
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [4,5,8,10,11,12,1,2,3,6,7,9] => 00000100000 => 00000100000
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [4,5,9,10,11,12,1,2,3,6,7,8] => 00000100000 => 00000100000
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [4,6,7,8,10,12,1,2,3,5,9,11] => 00000100000 => 00000100000
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [4,6,7,8,11,12,1,2,3,5,9,10] => 00000100000 => 00000100000
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [4,6,7,9,10,12,1,2,3,5,8,11] => 00000100000 => 00000100000
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [4,6,7,9,11,12,1,2,3,5,8,10] => 00000100000 => 00000100000
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [4,6,7,10,11,12,1,2,3,5,8,9] => 00000100000 => 00000100000
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [4,6,8,9,10,12,1,2,3,5,7,11] => 00000100000 => 00000100000
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [4,6,8,9,11,12,1,2,3,5,7,10] => 00000100000 => 00000100000
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [4,6,8,10,11,12,1,2,3,5,7,9] => 00000100000 => 00000100000
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [4,6,9,10,11,12,1,2,3,5,7,8] => 00000100000 => 00000100000
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [4,7,8,9,10,12,1,2,3,5,6,11] => 00000100000 => 00000100000
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [4,7,8,9,11,12,1,2,3,5,6,10] => 00000100000 => 00000100000
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [4,7,8,10,11,12,1,2,3,5,6,9] => 00000100000 => 00000100000
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [4,7,9,10,11,12,1,2,3,5,6,8] => 00000100000 => 00000100000
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [4,8,9,10,11,12,1,2,3,5,6,7] => 00000100000 => 00000100000
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [5,6,7,8,10,12,1,2,3,4,9,11] => 00000100000 => 00000100000
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [5,6,7,8,11,12,1,2,3,4,9,10] => 00000100000 => 00000100000
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [5,6,7,9,10,12,1,2,3,4,8,11] => 00000100000 => 00000100000
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [5,6,7,9,11,12,1,2,3,4,8,10] => 00000100000 => 00000100000
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [5,6,7,10,11,12,1,2,3,4,8,9] => 00000100000 => 00000100000
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [5,6,8,9,10,12,1,2,3,4,7,11] => 00000100000 => 00000100000
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [5,6,8,9,11,12,1,2,3,4,7,10] => 00000100000 => 00000100000
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [5,6,8,10,11,12,1,2,3,4,7,9] => 00000100000 => 00000100000
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [5,6,9,10,11,12,1,2,3,4,7,8] => 00000100000 => 00000100000
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [5,7,8,9,10,12,1,2,3,4,6,11] => 00000100000 => 00000100000
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [5,7,8,9,11,12,1,2,3,4,6,10] => 00000100000 => 00000100000
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [5,7,8,10,11,12,1,2,3,4,6,9] => 00000100000 => 00000100000
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [5,7,9,10,11,12,1,2,3,4,6,8] => 00000100000 => 00000100000
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [5,8,9,10,11,12,1,2,3,4,6,7] => 00000100000 => 00000100000
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [6,7,8,9,10,12,1,2,3,4,5,11] => 00000100000 => 00000100000
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,7,8,9,11,12,1,2,3,4,5,10] => 00000100000 => 00000100000
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,7,8,10,11,12,1,2,3,4,5,9] => 00000100000 => 00000100000
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,7,9,10,11,12,1,2,3,4,5,8] => 00000100000 => 00000100000
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,8,9,10,11,12,1,2,3,4,5,7] => 00000100000 => 00000100000
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [7,8,9,10,11,12,1,2,3,4,5,6] => 00000100000 => 00000100000
[[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => 00000000 => 00000000
[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => 10000000 => 00000001
[[1,2,3,4,5,6,7],[8,9]] => [8,9,1,2,3,4,5,6,7] => 01000000 => 00000010
[[1,2,3,4,5,6,7],[8],[9]] => [9,8,1,2,3,4,5,6,7] => 11000000 => 00000011
[[1,2,3,4,5,6],[7,8,9]] => [7,8,9,1,2,3,4,5,6] => 00100000 => 00000100
[[1,2,3,4,5,6],[7,8],[9]] => [9,7,8,1,2,3,4,5,6] => 10100000 => 00000101
[[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => 11100000 => 00000111
[[1,2,3,4,5],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5] => 00010000 => 00001000
[[1,2,3,4,5],[6,7,8],[9]] => [9,6,7,8,1,2,3,4,5] => 10010000 => 00001001
[[1,2,3,4,5],[6,7],[8,9]] => [8,9,6,7,1,2,3,4,5] => 01010000 => 00001010
[[1,2,3,4,5],[6,7],[8],[9]] => [9,8,6,7,1,2,3,4,5] => 11010000 => 00001011
[[1,2,3,4,5],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5] => 11110000 => 00001111
[[1,2,3,4],[5,6,7,8],[9]] => [9,5,6,7,8,1,2,3,4] => 10001000 => 00010001
[[1,2,3,4],[5,6,7],[8,9]] => [8,9,5,6,7,1,2,3,4] => 01001000 => 00010010
[[1,2,3,4],[5,6,7],[8],[9]] => [9,8,5,6,7,1,2,3,4] => 11001000 => 00010011
[[1,2,3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,1,2,3,4] => 10101000 => 00010101
[[1,2,3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,1,2,3,4] => 11101000 => 00010111
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => 11111000 => 00011111
[[1,2,3],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3] => 00100100 => 00100100
[[1,2,3],[4,5,6],[7,8],[9]] => [9,7,8,4,5,6,1,2,3] => 10100100 => 00100101
[[1,2,3],[4,5,6],[7],[8],[9]] => [9,8,7,4,5,6,1,2,3] => 11100100 => 00100111
[[1,2,3],[4,5],[6,7],[8,9]] => [8,9,6,7,4,5,1,2,3] => 01010100 => 00101010
[[1,2,3],[4,5],[6,7],[8],[9]] => [9,8,6,7,4,5,1,2,3] => 11010100 => 00101011
[[1,2,3],[4,5],[6],[7],[8],[9]] => [9,8,7,6,4,5,1,2,3] => 11110100 => 00101111
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,1,2,3] => 11111100 => 00111111
[[1,2],[3,4],[5,6],[7,8],[9]] => [9,7,8,5,6,3,4,1,2] => 10101010 => 01010101
[[1,2],[3,4],[5,6],[7],[8],[9]] => [9,8,7,5,6,3,4,1,2] => 11101010 => 01010111
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,4,1,2] => 11111010 => 01011111
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => 11111110 => 01111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => 11111111 => 11111111
[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => 000000000 => 000000000
[[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => 100000000 => 000000001
[[1,2,3,4,5,6,7,8],[9,10]] => [9,10,1,2,3,4,5,6,7,8] => 010000000 => 000000010
[[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => 110000000 => 000000011
[[1,2,3,4,5,6,7],[8,9,10]] => [8,9,10,1,2,3,4,5,6,7] => 001000000 => 000000100
[[1,2,3,4,5,6,7],[8,9],[10]] => [10,8,9,1,2,3,4,5,6,7] => 101000000 => 000000101
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10,9,8,1,2,3,4,5,6,7] => 111000000 => 000000111
[[1,2,3,4,5,6],[7,8,9,10]] => [7,8,9,10,1,2,3,4,5,6] => 000100000 => 000001000
[[1,2,3,4,5,6],[7,8,9],[10]] => [10,7,8,9,1,2,3,4,5,6] => 100100000 => 000001001
[[1,2,3,4,5,6],[7,8],[9,10]] => [9,10,7,8,1,2,3,4,5,6] => 010100000 => 000001010
[[1,2,3,4,5,6],[7,8],[9],[10]] => [10,9,7,8,1,2,3,4,5,6] => 110100000 => 000001011
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => 111100000 => 000001111
[[1,2,3,4,5],[6,7,8,9],[10]] => [10,6,7,8,9,1,2,3,4,5] => 100010000 => 000010001
[[1,2,3,4,5],[6,7,8],[9,10]] => [9,10,6,7,8,1,2,3,4,5] => 010010000 => 000010010
[[1,2,3,4,5],[6,7,8],[9],[10]] => [10,9,6,7,8,1,2,3,4,5] => 110010000 => 000010011
[[1,2,3,4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,1,2,3,4,5] => 101010000 => 000010101
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,1,2,3,4,5] => 111010000 => 000010111
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,1,2,3,4,5] => 111110000 => 000011111
[[1,2,3,4],[5,6,7,8],[9,10]] => [9,10,5,6,7,8,1,2,3,4] => 010001000 => 000100010
[[1,2,3,4],[5,6,7,8],[9],[10]] => [10,9,5,6,7,8,1,2,3,4] => 110001000 => 000100011
[[1,2,3,4],[5,6,7],[8,9,10]] => [8,9,10,5,6,7,1,2,3,4] => 001001000 => 000100100
[[1,2,3,4],[5,6,7],[8,9],[10]] => [10,8,9,5,6,7,1,2,3,4] => 101001000 => 000100101
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [10,9,8,5,6,7,1,2,3,4] => 111001000 => 000100111
[[1,2,3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,1,2,3,4] => 010101000 => 000101010
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,1,2,3,4] => 110101000 => 000101011
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,1,2,3,4] => 111101000 => 000101111
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => 111111000 => 000111111
[[1,2,3],[4,5,6],[7,8,9],[10]] => [10,7,8,9,4,5,6,1,2,3] => 100100100 => 001001001
[[1,2,3],[4,5,6],[7,8],[9,10]] => [9,10,7,8,4,5,6,1,2,3] => 010100100 => 001001010
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [10,9,7,8,4,5,6,1,2,3] => 110100100 => 001001011
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [10,9,8,7,4,5,6,1,2,3] => 111100100 => 001001111
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [10,8,9,6,7,4,5,1,2,3] => 101010100 => 001010101
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [10,9,8,6,7,4,5,1,2,3] => 111010100 => 001010111
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,5,1,2,3] => 111110100 => 001011111
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,1,2,3] => 111111100 => 001111111
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => 010101010 => 010101010
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [10,9,7,8,5,6,3,4,1,2] => 110101010 => 010101011
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [10,9,8,7,5,6,3,4,1,2] => 111101010 => 010101111
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,4,1,2] => 111111010 => 010111111
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => 111111110 => 011111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => 111111111 => 111111111
[[1,2,3,4,5,6,7,8,9,10,11,12]] => [1,2,3,4,5,6,7,8,9,10,11,12] => 00000000000 => 00000000000
[[1,2,3,4,5,6],[7,8,9,10],[11,12]] => [11,12,7,8,9,10,1,2,3,4,5,6] => 01000100000 => 00000100010
[[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => [11,12,9,10,5,6,7,8,1,2,3,4] => 01010001000 => 00010001010
[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,1,2,3,4] => 01010101000 => 00010101010
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,3,4,1,2] => 01010101010 => 01010101010
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,3,2,1] => 11111111111 => 11111111111
[[1,3,4,5,6,7,8,9],[2]] => [2,1,3,4,5,6,7,8,9] => 10000000 => 00000001
[[1,2,5,6,7,8,9],[3,4]] => [3,4,1,2,5,6,7,8,9] => 01000000 => 00000010
[[1,4,5,6,7,8,9],[2],[3]] => [3,2,1,4,5,6,7,8,9] => 11000000 => 00000011
[[1,2,3,7,8,9],[4,5,6]] => [4,5,6,1,2,3,7,8,9] => 00100000 => 00000100
[[1,3,6,7,8,9],[2,5],[4]] => [4,2,5,1,3,6,7,8,9] => 10100000 => 00000101
[[1,5,6,7,8,9],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9] => 11100000 => 00000111
[[1,2,3,4,9],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9] => 00010000 => 00001000
[[1,3,4,8,9],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9] => 10010000 => 00001001
[[1,2,7,8,9],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9] => 01010000 => 00001010
[[1,4,7,8,9],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9] => 11010000 => 00001011
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9] => 11110000 => 00001111
[[1,3,4,5],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5] => 10001000 => 00010001
[[1,2,5,9],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9] => 01001000 => 00010010
[[1,4,5,9],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9] => 11001000 => 00010011
[[1,3,8,9],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9] => 10101000 => 00010101
[[1,5,8,9],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8,9] => 11101000 => 00010111
[[1,7,8,9],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9] => 11111000 => 00011111
[[1,3,6],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6] => 10100100 => 00100101
[[1,5,6],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6] => 11100100 => 00100111
[[1,2,9],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9] => 01010100 => 00101010
[[1,4,9],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9] => 11010100 => 00101011
[[1,6,9],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6,9] => 11110100 => 00101111
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9] => 11111100 => 00111111
[[1,3],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3] => 10101010 => 01010101
[[1,5],[2,7],[3,9],[4],[6],[8]] => [8,6,4,3,9,2,7,1,5] => 11101010 => 01010111
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7] => 11111010 => 01011111
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => 11111110 => 01111111
[[1,3,4,5,6,7,8,9,10],[2]] => [2,1,3,4,5,6,7,8,9,10] => 100000000 => 000000001
[[1,2,5,6,7,8,9,10],[3,4]] => [3,4,1,2,5,6,7,8,9,10] => 010000000 => 000000010
[[1,4,5,6,7,8,9,10],[2],[3]] => [3,2,1,4,5,6,7,8,9,10] => 110000000 => 000000011
[[1,2,3,7,8,9,10],[4,5,6]] => [4,5,6,1,2,3,7,8,9,10] => 001000000 => 000000100
[[1,3,6,7,8,9,10],[2,5],[4]] => [4,2,5,1,3,6,7,8,9,10] => 101000000 => 000000101
[[1,5,6,7,8,9,10],[2],[3],[4]] => [4,3,2,1,5,6,7,8,9,10] => 111000000 => 000000111
[[1,2,3,4,9,10],[5,6,7,8]] => [5,6,7,8,1,2,3,4,9,10] => 000100000 => 000001000
[[1,3,4,8,9,10],[2,6,7],[5]] => [5,2,6,7,1,3,4,8,9,10] => 100100000 => 000001001
[[1,2,7,8,9,10],[3,4],[5,6]] => [5,6,3,4,1,2,7,8,9,10] => 010100000 => 000001010
[[1,4,7,8,9,10],[2,6],[3],[5]] => [5,3,2,6,1,4,7,8,9,10] => 110100000 => 000001011
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8,9,10] => 111100000 => 000001111
[[1,3,4,5,10],[2,7,8,9],[6]] => [6,2,7,8,9,1,3,4,5,10] => 100010000 => 000010001
[[1,2,5,9,10],[3,4,8],[6,7]] => [6,7,3,4,8,1,2,5,9,10] => 010010000 => 000010010
[[1,4,5,9,10],[2,7,8],[3],[6]] => [6,3,2,7,8,1,4,5,9,10] => 110010000 => 000010011
[[1,3,8,9,10],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3,8,9,10] => 101010000 => 000010101
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5,8,9,10] => 111010000 => 000010111
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7,8,9,10] => 111110000 => 000011111
[[1,2,5,6],[3,4,9,10],[7,8]] => [7,8,3,4,9,10,1,2,5,6] => 010001000 => 000100010
[[1,4,5,6],[2,8,9,10],[3],[7]] => [7,3,2,8,9,10,1,4,5,6] => 110001000 => 000100011
[[1,2,3,10],[4,5,6],[7,8,9]] => [7,8,9,4,5,6,1,2,3,10] => 001001000 => 000100100
[[1,3,6,10],[2,5,9],[4,8],[7]] => [7,4,8,2,5,9,1,3,6,10] => 101001000 => 000100101
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [7,4,3,2,8,9,1,5,6,10] => 111001000 => 000100111
[[1,2,9,10],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2,9,10] => 010101000 => 000101010
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [7,5,3,8,2,6,1,4,9,10] => 110101000 => 000101011
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [7,5,4,3,2,8,1,6,9,10] => 111101000 => 000101111
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8,9,10] => 111111000 => 000111111
[[1,3,4],[2,6,7],[5,9,10],[8]] => [8,5,9,10,2,6,7,1,3,4] => 100100100 => 001001001
[[1,2,7],[3,4,10],[5,6],[8,9]] => [8,9,5,6,3,4,10,1,2,7] => 010100100 => 001001010
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [8,5,3,9,2,6,10,1,4,7] => 110100100 => 001001011
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [8,5,4,3,2,9,10,1,6,7] => 111100100 => 001001111
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [8,6,9,4,7,2,5,1,3,10] => 101010100 => 001010101
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [8,6,4,3,9,2,7,1,5,10] => 111010100 => 001010111
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,9,1,7,10] => 111110100 => 001011111
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9,10] => 111111100 => 001111111
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [9,7,5,10,3,8,2,6,1,4] => 110101010 => 010101011
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [9,7,5,4,3,10,2,8,1,6] => 111101010 => 010101111
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,10,1,8] => 111111010 => 010111111
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => 111111110 => 011111111
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,9,1,8] => 11111010 => 01011111
[[1,7],[2,8],[3,9],[4],[5],[6]] => [6,5,4,3,9,2,8,1,7] => 11101010 => 01010111
[[1,7,9],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7,9] => 11110100 => 00101111
[[1,6],[2,7],[3,8],[4,9],[5]] => [5,4,9,3,8,2,7,1,6] => 10101010 => 01010101
[[1,6,9],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6,9] => 11010100 => 00101011
[[1,6,8],[2,7,9],[3],[4],[5]] => [5,4,3,2,7,9,1,6,8] => 11100100 => 00100111
[[1,6,8,9],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8,9] => 11101000 => 00010111
[[1,5,9],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5,9] => 01010100 => 00101010
[[1,5,8],[2,6,9],[3,7],[4]] => [4,3,7,2,6,9,1,5,8] => 10100100 => 00100101
[[1,5,8,9],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8,9] => 10101000 => 00010101
[[1,5,7,9],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7,9] => 11001000 => 00010011
[[1,5,7,8,9],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8,9] => 11010000 => 00001011
[[1,4,7],[2,5,8],[3,6,9]] => [3,6,9,2,5,8,1,4,7] => 00100100 => 00100100
[[1,4,7,9],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7,9] => 01001000 => 00010010
[[1,4,7,8,9],[2,5],[3,6]] => [3,6,2,5,1,4,7,8,9] => 01010000 => 00001010
[[1,4,6,8],[2,5,7,9],[3]] => [3,2,5,7,9,1,4,6,8] => 10001000 => 00010001
[[1,4,6,8,9],[2,5,7],[3]] => [3,2,5,7,1,4,6,8,9] => 10010000 => 00001001
[[1,4,6,7,8,9],[2,5],[3]] => [3,2,5,1,4,6,7,8,9] => 10100000 => 00000101
[[1,3,5,7,9],[2,4,6,8]] => [2,4,6,8,1,3,5,7,9] => 00010000 => 00001000
[[1,3,5,7,8,9],[2,4,6]] => [2,4,6,1,3,5,7,8,9] => 00100000 => 00000100
[[1,3,5,6,7,8,9],[2,4]] => [2,4,1,3,5,6,7,8,9] => 01000000 => 00000010
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,10,1,9] => 111111010 => 010111111
[[1,8],[2,9],[3,10],[4],[5],[6],[7]] => [7,6,5,4,3,10,2,9,1,8] => 111101010 => 010101111
[[1,8,10],[2,9],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,9,1,8,10] => 111110100 => 001011111
[[1,7],[2,8],[3,9],[4,10],[5],[6]] => [6,5,4,10,3,9,2,8,1,7] => 110101010 => 010101011
[[1,7,10],[2,8],[3,9],[4],[5],[6]] => [6,5,4,3,9,2,8,1,7,10] => 111010100 => 001010111
[[1,7,9],[2,8,10],[3],[4],[5],[6]] => [6,5,4,3,2,8,10,1,7,9] => 111100100 => 001001111
[[1,7,9,10],[2,8],[3],[4],[5],[6]] => [6,5,4,3,2,8,1,7,9,10] => 111101000 => 000101111
[[1,6],[2,7],[3,8],[4,9],[5,10]] => [5,10,4,9,3,8,2,7,1,6] => 010101010 => 010101010
[[1,6,10],[2,7],[3,8],[4,9],[5]] => [5,4,9,3,8,2,7,1,6,10] => 101010100 => 001010101
[[1,6,9],[2,7,10],[3,8],[4],[5]] => [5,4,3,8,2,7,10,1,6,9] => 110100100 => 001001011
[[1,6,9,10],[2,7],[3,8],[4],[5]] => [5,4,3,8,2,7,1,6,9,10] => 110101000 => 000101011
[[1,6,8,10],[2,7,9],[3],[4],[5]] => [5,4,3,2,7,9,1,6,8,10] => 111001000 => 000100111
[[1,6,8,9,10],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6,8,9,10] => 111010000 => 000010111
[[1,5,9],[2,6,10],[3,7],[4,8]] => [4,8,3,7,2,6,10,1,5,9] => 010100100 => 001001010
[[1,5,9,10],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5,9,10] => 010101000 => 000101010
[[1,5,8],[2,6,9],[3,7,10],[4]] => [4,3,7,10,2,6,9,1,5,8] => 100100100 => 001001001
[[1,5,8,10],[2,6,9],[3,7],[4]] => [4,3,7,2,6,9,1,5,8,10] => 101001000 => 000100101
[[1,5,8,9,10],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5,8,9,10] => 101010000 => 000010101
[[1,5,7,9],[2,6,8,10],[3],[4]] => [4,3,2,6,8,10,1,5,7,9] => 110001000 => 000100011
[[1,5,7,9,10],[2,6,8],[3],[4]] => [4,3,2,6,8,1,5,7,9,10] => 110010000 => 000010011
[[1,5,7,8,9,10],[2,6],[3],[4]] => [4,3,2,6,1,5,7,8,9,10] => 110100000 => 000001011
[[1,4,7,10],[2,5,8],[3,6,9]] => [3,6,9,2,5,8,1,4,7,10] => 001001000 => 000100100
[[1,4,7,9],[2,5,8,10],[3,6]] => [3,6,2,5,8,10,1,4,7,9] => 010001000 => 000100010
[[1,4,7,9,10],[2,5,8],[3,6]] => [3,6,2,5,8,1,4,7,9,10] => 010010000 => 000010010
[[1,4,7,8,9,10],[2,5],[3,6]] => [3,6,2,5,1,4,7,8,9,10] => 010100000 => 000001010
[[1,4,6,8,10],[2,5,7,9],[3]] => [3,2,5,7,9,1,4,6,8,10] => 100010000 => 000010001
[[1,4,6,8,9,10],[2,5,7],[3]] => [3,2,5,7,1,4,6,8,9,10] => 100100000 => 000001001
[[1,4,6,7,8,9,10],[2,5],[3]] => [3,2,5,1,4,6,7,8,9,10] => 101000000 => 000000101
[[1,3,5,7,9,10],[2,4,6,8]] => [2,4,6,8,1,3,5,7,9,10] => 000100000 => 000001000
[[1,3,5,7,8,9,10],[2,4,6]] => [2,4,6,1,3,5,7,8,9,10] => 001000000 => 000000100
[[1,3,5,6,7,8,9,10],[2,4]] => [2,4,1,3,5,6,7,8,9,10] => 010000000 => 000000010
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,4,1,3] => 11111010 => 01011111
[[1,4],[2,5],[3,6],[7],[8],[9]] => [9,8,7,3,6,2,5,1,4] => 11101010 => 01010111
[[1,2,4],[3,5],[6],[7],[8],[9]] => [9,8,7,6,3,5,1,2,4] => 11110100 => 00101111
[[1,5],[2,6],[3,7],[4,8],[9]] => [9,4,8,3,7,2,6,1,5] => 10101010 => 01010101
[[1,2,5],[3,6],[4,7],[8],[9]] => [9,8,4,7,3,6,1,2,5] => 11010100 => 00101011
[[1,3,5],[2,4,6],[7],[8],[9]] => [9,8,7,2,4,6,1,3,5] => 11100100 => 00100111
[[1,2,3,5],[4,6],[7],[8],[9]] => [9,8,7,4,6,1,2,3,5] => 11101000 => 00010111
[[1,2,6],[3,7],[4,8],[5,9]] => [5,9,4,8,3,7,1,2,6] => 01010100 => 00101010
[[1,3,6],[2,4,7],[5,8],[9]] => [9,5,8,2,4,7,1,3,6] => 10100100 => 00100101
[[1,2,3,6],[4,7],[5,8],[9]] => [9,5,8,4,7,1,2,3,6] => 10101000 => 00010101
[[1,2,4,6],[3,5,7],[8],[9]] => [9,8,3,5,7,1,2,4,6] => 11001000 => 00010011
[[1,2,3,4,6],[5,7],[8],[9]] => [9,8,5,7,1,2,3,4,6] => 11010000 => 00001011
[[1,2,4,7],[3,5,8],[6,9]] => [6,9,3,5,8,1,2,4,7] => 01001000 => 00010010
[[1,2,3,4,7],[5,8],[6,9]] => [6,9,5,8,1,2,3,4,7] => 01010000 => 00001010
[[1,3,5,7],[2,4,6,8],[9]] => [9,2,4,6,8,1,3,5,7] => 10001000 => 00010001
[[1,2,3,5,7],[4,6,8],[9]] => [9,4,6,8,1,2,3,5,7] => 10010000 => 00001001
[[1,2,3,4,5,7],[6,8],[9]] => [9,6,8,1,2,3,4,5,7] => 10100000 => 00000101
[[1,2,4,6,8],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8] => 00010000 => 00001000
[[1,2,3,4,6,8],[5,7,9]] => [5,7,9,1,2,3,4,6,8] => 00100000 => 00000100
[[1,2,3,4,5,6,8],[7,9]] => [7,9,1,2,3,4,5,6,8] => 01000000 => 00000010
[[1,3],[2,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,2,4,1,3] => 111111010 => 010111111
[[1,4],[2,5],[3,6],[7],[8],[9],[10]] => [10,9,8,7,3,6,2,5,1,4] => 111101010 => 010101111
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,3,5,1,2,4] => 111110100 => 001011111
[[1,5],[2,6],[3,7],[4,8],[9],[10]] => [10,9,4,8,3,7,2,6,1,5] => 110101010 => 010101011
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [10,9,8,4,7,3,6,1,2,5] => 111010100 => 001010111
[[1,3,5],[2,4,6],[7],[8],[9],[10]] => [10,9,8,7,2,4,6,1,3,5] => 111100100 => 001001111
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [10,9,8,7,4,6,1,2,3,5] => 111101000 => 000101111
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [10,5,9,4,8,3,7,1,2,6] => 101010100 => 001010101
[[1,3,6],[2,4,7],[5,8],[9],[10]] => [10,9,5,8,2,4,7,1,3,6] => 110100100 => 001001011
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [10,9,5,8,4,7,1,2,3,6] => 110101000 => 000101011
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [10,9,8,3,5,7,1,2,4,6] => 111001000 => 000100111
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [10,9,8,5,7,1,2,3,4,6] => 111010000 => 000010111
[[1,3,7],[2,4,8],[5,9],[6,10]] => [6,10,5,9,2,4,8,1,3,7] => 010100100 => 001001010
[[1,2,3,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,1,2,3,7] => 010101000 => 000101010
[[1,4,7],[2,5,8],[3,6,9],[10]] => [10,3,6,9,2,5,8,1,4,7] => 100100100 => 001001001
[[1,2,4,7],[3,5,8],[6,9],[10]] => [10,6,9,3,5,8,1,2,4,7] => 101001000 => 000100101
[[1,2,3,4,7],[5,8],[6,9],[10]] => [10,6,9,5,8,1,2,3,4,7] => 101010000 => 000010101
[[1,3,5,7],[2,4,6,8],[9],[10]] => [10,9,2,4,6,8,1,3,5,7] => 110001000 => 000100011
[[1,2,3,5,7],[4,6,8],[9],[10]] => [10,9,4,6,8,1,2,3,5,7] => 110010000 => 000010011
[[1,2,3,4,5,7],[6,8],[9],[10]] => [10,9,6,8,1,2,3,4,5,7] => 110100000 => 000001011
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,7,10,3,6,9,1,2,5,8] => 001001000 => 000100100
[[1,3,5,8],[2,4,6,9],[7,10]] => [7,10,2,4,6,9,1,3,5,8] => 010001000 => 000100010
[[1,2,3,5,8],[4,6,9],[7,10]] => [7,10,4,6,9,1,2,3,5,8] => 010010000 => 000010010
[[1,2,3,4,5,8],[6,9],[7,10]] => [7,10,6,9,1,2,3,4,5,8] => 010100000 => 000001010
[[1,2,4,6,8],[3,5,7,9],[10]] => [10,3,5,7,9,1,2,4,6,8] => 100010000 => 000010001
[[1,2,3,4,6,8],[5,7,9],[10]] => [10,5,7,9,1,2,3,4,6,8] => 100100000 => 000001001
[[1,2,3,4,5,6,8],[7,9],[10]] => [10,7,9,1,2,3,4,5,6,8] => 101000000 => 000000101
[[1,2,3,5,7,9],[4,6,8,10]] => [4,6,8,10,1,2,3,5,7,9] => 000100000 => 000001000
[[1,2,3,4,5,7,9],[6,8,10]] => [6,8,10,1,2,3,4,5,7,9] => 001000000 => 000000100
[[1,2,3,4,5,6,7,9],[8,10]] => [8,10,1,2,3,4,5,6,7,9] => 010000000 => 000000010
[[1,2],[3,4],[5,6],[7,9],[8,10]] => [8,10,7,9,5,6,3,4,1,2] => 010101010 => 010101010
[[1,2],[3,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,3,4,1,2] => 010101010 => 010101010
[[1,2],[3,4],[5,7],[6,9],[8,10]] => [8,10,6,9,5,7,3,4,1,2] => 010101010 => 010101010
[[1,2],[3,4],[5,8],[6,9],[7,10]] => [7,10,6,9,5,8,3,4,1,2] => 010101010 => 010101010
[[1,2],[3,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,3,5,1,2] => 010101010 => 010101010
[[1,2],[3,5],[4,6],[7,9],[8,10]] => [8,10,7,9,4,6,3,5,1,2] => 010101010 => 010101010
[[1,2],[3,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,3,5,1,2] => 010101010 => 010101010
[[1,2],[3,5],[4,7],[6,9],[8,10]] => [8,10,6,9,4,7,3,5,1,2] => 010101010 => 010101010
[[1,2],[3,5],[4,8],[6,9],[7,10]] => [7,10,6,9,4,8,3,5,1,2] => 010101010 => 010101010
[[1,2],[3,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,3,6,1,2] => 010101010 => 010101010
[[1,2],[3,6],[4,7],[5,9],[8,10]] => [8,10,5,9,4,7,3,6,1,2] => 010101010 => 010101010
[[1,2],[3,6],[4,8],[5,9],[7,10]] => [7,10,5,9,4,8,3,6,1,2] => 010101010 => 010101010
[[1,2],[3,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,3,7,1,2] => 010101010 => 010101010
[[1,3],[2,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,2,4,1,3] => 010101010 => 010101010
[[1,3],[2,4],[5,6],[7,9],[8,10]] => [8,10,7,9,5,6,2,4,1,3] => 010101010 => 010101010
[[1,3],[2,4],[5,7],[6,8],[9,10]] => [9,10,6,8,5,7,2,4,1,3] => 010101010 => 010101010
[[1,3],[2,4],[5,7],[6,9],[8,10]] => [8,10,6,9,5,7,2,4,1,3] => 010101010 => 010101010
[[1,3],[2,4],[5,8],[6,9],[7,10]] => [7,10,6,9,5,8,2,4,1,3] => 010101010 => 010101010
[[1,3],[2,5],[4,6],[7,8],[9,10]] => [9,10,7,8,4,6,2,5,1,3] => 010101010 => 010101010
[[1,3],[2,5],[4,6],[7,9],[8,10]] => [8,10,7,9,4,6,2,5,1,3] => 010101010 => 010101010
[[1,3],[2,5],[4,7],[6,8],[9,10]] => [9,10,6,8,4,7,2,5,1,3] => 010101010 => 010101010
[[1,3],[2,5],[4,7],[6,9],[8,10]] => [8,10,6,9,4,7,2,5,1,3] => 010101010 => 010101010
[[1,3],[2,5],[4,8],[6,9],[7,10]] => [7,10,6,9,4,8,2,5,1,3] => 010101010 => 010101010
[[1,3],[2,6],[4,7],[5,8],[9,10]] => [9,10,5,8,4,7,2,6,1,3] => 010101010 => 010101010
[[1,3],[2,6],[4,7],[5,9],[8,10]] => [8,10,5,9,4,7,2,6,1,3] => 010101010 => 010101010
[[1,3],[2,6],[4,8],[5,9],[7,10]] => [7,10,5,9,4,8,2,6,1,3] => 010101010 => 010101010
[[1,3],[2,7],[4,8],[5,9],[6,10]] => [6,10,5,9,4,8,2,7,1,3] => 010101010 => 010101010
[[1,4],[2,5],[3,6],[7,8],[9,10]] => [9,10,7,8,3,6,2,5,1,4] => 010101010 => 010101010
[[1,4],[2,5],[3,6],[7,9],[8,10]] => [8,10,7,9,3,6,2,5,1,4] => 010101010 => 010101010
[[1,4],[2,5],[3,7],[6,8],[9,10]] => [9,10,6,8,3,7,2,5,1,4] => 010101010 => 010101010
[[1,4],[2,5],[3,7],[6,9],[8,10]] => [8,10,6,9,3,7,2,5,1,4] => 010101010 => 010101010
[[1,4],[2,5],[3,8],[6,9],[7,10]] => [7,10,6,9,3,8,2,5,1,4] => 010101010 => 010101010
[[1,4],[2,6],[3,7],[5,8],[9,10]] => [9,10,5,8,3,7,2,6,1,4] => 010101010 => 010101010
[[1,4],[2,6],[3,7],[5,9],[8,10]] => [8,10,5,9,3,7,2,6,1,4] => 010101010 => 010101010
[[1,4],[2,6],[3,8],[5,9],[7,10]] => [7,10,5,9,3,8,2,6,1,4] => 010101010 => 010101010
[[1,4],[2,7],[3,8],[5,9],[6,10]] => [6,10,5,9,3,8,2,7,1,4] => 010101010 => 010101010
[[1,5],[2,6],[3,7],[4,8],[9,10]] => [9,10,4,8,3,7,2,6,1,5] => 010101010 => 010101010
[[1,5],[2,6],[3,7],[4,9],[8,10]] => [8,10,4,9,3,7,2,6,1,5] => 010101010 => 010101010
[[1,5],[2,6],[3,8],[4,9],[7,10]] => [7,10,4,9,3,8,2,6,1,5] => 010101010 => 010101010
[[1,5],[2,7],[3,8],[4,9],[6,10]] => [6,10,4,9,3,8,2,7,1,5] => 010101010 => 010101010
[[1,2],[3,4],[5,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,5,6,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,5,6,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,5,6,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,5,6,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,5,7,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,5,7,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,5,7,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,5,7,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,5,7,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,5,8,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,5,8,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,5,8,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,4],[5,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,5,9,3,4,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,4,6,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,4,6,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,4,6,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,4,6,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,4,6,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,4,7,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,4,7,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,4,7,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,4,7,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,4,7,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,4,8,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,4,8,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,4,8,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,5],[4,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,4,9,3,5,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,4,7,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,4,7,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,4,7,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,4,7,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,4,7,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,4,8,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,4,8,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,4,8,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,6],[4,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,4,9,3,6,1,2] => 01010101010 => 01010101010
[[1,2],[3,7],[4,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,4,8,3,7,1,2] => 01010101010 => 01010101010
[[1,2],[3,7],[4,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,4,8,3,7,1,2] => 01010101010 => 01010101010
[[1,2],[3,7],[4,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,4,8,3,7,1,2] => 01010101010 => 01010101010
[[1,2],[3,7],[4,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,4,9,3,7,1,2] => 01010101010 => 01010101010
[[1,2],[3,8],[4,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,4,9,3,8,1,2] => 01010101010 => 01010101010
[[1,3],[2,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,5,6,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,5,6,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,5,6,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,5,6,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,5,7,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,5,7,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,5,7,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,5,7,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,5,7,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,5,8,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,5,8,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,5,8,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,4],[5,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,5,9,2,4,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,4,6,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,4,6,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,4,6,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,4,6,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,4,6,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,4,7,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,4,7,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,4,7,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,4,7,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,4,7,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,4,8,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,4,8,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,4,8,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,5],[4,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,4,9,2,5,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,4,7,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,4,7,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,4,7,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,4,7,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,4,7,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,4,8,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,4,8,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,4,8,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,6],[4,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,4,9,2,6,1,3] => 01010101010 => 01010101010
[[1,3],[2,7],[4,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,4,8,2,7,1,3] => 01010101010 => 01010101010
[[1,3],[2,7],[4,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,4,8,2,7,1,3] => 01010101010 => 01010101010
[[1,3],[2,7],[4,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,4,8,2,7,1,3] => 01010101010 => 01010101010
[[1,3],[2,7],[4,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,4,9,2,7,1,3] => 01010101010 => 01010101010
[[1,3],[2,8],[4,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,4,9,2,8,1,3] => 01010101010 => 01010101010
[[1,4],[2,5],[3,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,3,6,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,6],[7,8],[9,11],[10,12]] => [10,12,9,11,7,8,3,6,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,6],[7,9],[8,10],[11,12]] => [11,12,8,10,7,9,3,6,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,6],[7,9],[8,11],[10,12]] => [10,12,8,11,7,9,3,6,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,6],[7,10],[8,11],[9,12]] => [9,12,8,11,7,10,3,6,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,7],[6,8],[9,10],[11,12]] => [11,12,9,10,6,8,3,7,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,7],[6,8],[9,11],[10,12]] => [10,12,9,11,6,8,3,7,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,7],[6,9],[8,10],[11,12]] => [11,12,8,10,6,9,3,7,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,7],[6,9],[8,11],[10,12]] => [10,12,8,11,6,9,3,7,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,7],[6,10],[8,11],[9,12]] => [9,12,8,11,6,10,3,7,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,8],[6,9],[7,10],[11,12]] => [11,12,7,10,6,9,3,8,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,8],[6,9],[7,11],[10,12]] => [10,12,7,11,6,9,3,8,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,8],[6,10],[7,11],[9,12]] => [9,12,7,11,6,10,3,8,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,5],[3,9],[6,10],[7,11],[8,12]] => [8,12,7,11,6,10,3,9,2,5,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,7],[5,8],[9,10],[11,12]] => [11,12,9,10,5,8,3,7,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,7],[5,8],[9,11],[10,12]] => [10,12,9,11,5,8,3,7,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,7],[5,9],[8,10],[11,12]] => [11,12,8,10,5,9,3,7,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,7],[5,9],[8,11],[10,12]] => [10,12,8,11,5,9,3,7,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,7],[5,10],[8,11],[9,12]] => [9,12,8,11,5,10,3,7,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,8],[5,9],[7,10],[11,12]] => [11,12,7,10,5,9,3,8,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,8],[5,9],[7,11],[10,12]] => [10,12,7,11,5,9,3,8,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,8],[5,10],[7,11],[9,12]] => [9,12,7,11,5,10,3,8,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,6],[3,9],[5,10],[7,11],[8,12]] => [8,12,7,11,5,10,3,9,2,6,1,4] => 01010101010 => 01010101010
[[1,4],[2,7],[3,8],[5,9],[6,10],[11,12]] => [11,12,6,10,5,9,3,8,2,7,1,4] => 01010101010 => 01010101010
[[1,4],[2,7],[3,8],[5,9],[6,11],[10,12]] => [10,12,6,11,5,9,3,8,2,7,1,4] => 01010101010 => 01010101010
[[1,4],[2,7],[3,8],[5,10],[6,11],[9,12]] => [9,12,6,11,5,10,3,8,2,7,1,4] => 01010101010 => 01010101010
[[1,4],[2,7],[3,9],[5,10],[6,11],[8,12]] => [8,12,6,11,5,10,3,9,2,7,1,4] => 01010101010 => 01010101010
[[1,4],[2,8],[3,9],[5,10],[6,11],[7,12]] => [7,12,6,11,5,10,3,9,2,8,1,4] => 01010101010 => 01010101010
[[1,5],[2,6],[3,7],[4,8],[9,10],[11,12]] => [11,12,9,10,4,8,3,7,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,7],[4,8],[9,11],[10,12]] => [10,12,9,11,4,8,3,7,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,7],[4,9],[8,10],[11,12]] => [11,12,8,10,4,9,3,7,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,7],[4,9],[8,11],[10,12]] => [10,12,8,11,4,9,3,7,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,7],[4,10],[8,11],[9,12]] => [9,12,8,11,4,10,3,7,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,8],[4,9],[7,10],[11,12]] => [11,12,7,10,4,9,3,8,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,8],[4,9],[7,11],[10,12]] => [10,12,7,11,4,9,3,8,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,8],[4,10],[7,11],[9,12]] => [9,12,7,11,4,10,3,8,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,6],[3,9],[4,10],[7,11],[8,12]] => [8,12,7,11,4,10,3,9,2,6,1,5] => 01010101010 => 01010101010
[[1,5],[2,7],[3,8],[4,9],[6,10],[11,12]] => [11,12,6,10,4,9,3,8,2,7,1,5] => 01010101010 => 01010101010
[[1,5],[2,7],[3,8],[4,9],[6,11],[10,12]] => [10,12,6,11,4,9,3,8,2,7,1,5] => 01010101010 => 01010101010
[[1,5],[2,7],[3,8],[4,10],[6,11],[9,12]] => [9,12,6,11,4,10,3,8,2,7,1,5] => 01010101010 => 01010101010
[[1,5],[2,7],[3,9],[4,10],[6,11],[8,12]] => [8,12,6,11,4,10,3,9,2,7,1,5] => 01010101010 => 01010101010
[[1,5],[2,8],[3,9],[4,10],[6,11],[7,12]] => [7,12,6,11,4,10,3,9,2,8,1,5] => 01010101010 => 01010101010
[[1,6],[2,7],[3,8],[4,9],[5,10],[11,12]] => [11,12,5,10,4,9,3,8,2,7,1,6] => 01010101010 => 01010101010
[[1,6],[2,7],[3,8],[4,9],[5,11],[10,12]] => [10,12,5,11,4,9,3,8,2,7,1,6] => 01010101010 => 01010101010
[[1,6],[2,7],[3,8],[4,10],[5,11],[9,12]] => [9,12,5,11,4,10,3,8,2,7,1,6] => 01010101010 => 01010101010
[[1,6],[2,7],[3,9],[4,10],[5,11],[8,12]] => [8,12,5,11,4,10,3,9,2,7,1,6] => 01010101010 => 01010101010
[[1,6],[2,8],[3,9],[4,10],[5,11],[7,12]] => [7,12,5,11,4,10,3,9,2,8,1,6] => 01010101010 => 01010101010
[[1,7],[2,8],[3,9],[4,10],[5,11],[6,12]] => [6,12,5,11,4,10,3,9,2,8,1,7] => 01010101010 => 01010101010
[[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => 10000000 => 00000001
[[1,2,3,4,5,6,9],[7,8]] => [7,8,1,2,3,4,5,6,9] => 01000000 => 00000010
[[1,2,3,4,5,9],[6,7,8]] => [6,7,8,1,2,3,4,5,9] => 00100000 => 00000100
[[1,2,3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,1,2,3,9] => 11111000 => 00011111
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => 11111100 => 00111111
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => 100000000 => 000000001
[[1,2,3,4,5,6,7,10],[8,9]] => [8,9,1,2,3,4,5,6,7,10] => 010000000 => 000000010
[[1,2,3,4,5,10],[6,7,8,9]] => [6,7,8,9,1,2,3,4,5,10] => 000100000 => 000001000
[[1,2,3,4,5,10],[6],[7],[8],[9]] => [9,8,7,6,1,2,3,4,5,10] => 111100000 => 000001111
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2,10] => 111111100 => 001111111
[[1,2,4,5,6,7,8,9],[3]] => [3,1,2,4,5,6,7,8,9] => 10000000 => 00000001
[[1,2,4,7,8,9],[3,5],[6]] => [6,3,5,1,2,4,7,8,9] => 10100000 => 00000101
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7,9] => 11111100 => 00111111
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => 11111110 => 01111111
[[1,2,4,5,6,7,8,9,10],[3]] => [3,1,2,4,5,6,7,8,9,10] => 100000000 => 000000001
[[1,2,4,7,8,9,10],[3,5],[6]] => [6,3,5,1,2,4,7,8,9,10] => 101000000 => 000000101
[[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8,10] => 111111100 => 001111111
[[1,3],[2,5],[4,7],[6,9],[8],[10]] => [10,8,6,9,4,7,2,5,1,3] => 110101010 => 010101011
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [10,8,7,6,5,4,3,2,1,9] => 111111110 => 011111111
[[1,3,4,5,6,7,8],[2,9]] => [2,9,1,3,4,5,6,7,8] => 01000000 => 00000010
[[1,3,4,5,6,7,8],[2],[9]] => [9,2,1,3,4,5,6,7,8] => 11000000 => 00000011
[[1,3,4,5,6,7],[2,8,9]] => [2,8,9,1,3,4,5,6,7] => 00100000 => 00000100
[[1,3,4,5,6],[2,7,8,9]] => [2,7,8,9,1,3,4,5,6] => 00010000 => 00001000
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [9,8,7,6,5,2,1,3,4] => 11111100 => 00111111
[[1,3],[2,5],[4,7],[6],[8],[9]] => [9,8,6,4,7,2,5,1,3] => 11101010 => 01010111
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3] => 11111110 => 01111111
[[1,3,4,5,6,7,8,9],[2,10]] => [2,10,1,3,4,5,6,7,8,9] => 010000000 => 000000010
[[1,3,4,5,6,7,8,9],[2],[10]] => [10,2,1,3,4,5,6,7,8,9] => 110000000 => 000000011
[[1,3,4,5,6,7,8],[2,9,10]] => [2,9,10,1,3,4,5,6,7,8] => 001000000 => 000000100
[[1,3,4,5,6,7],[2,8,9,10]] => [2,8,9,10,1,3,4,5,6,7] => 000100000 => 000001000
[[1,3,4,5,6],[2,8,9,10],[7]] => [7,2,8,9,10,1,3,4,5,6] => 100010000 => 000010001
[[1,3,4,5],[2,7,8],[6,10],[9]] => [9,6,10,2,7,8,1,3,4,5] => 101001000 => 000100101
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,2,1,3] => 111111110 => 011111111
[[1,2,4,6,8,10],[3,5,7,9]] => [3,5,7,9,1,2,4,6,8,10] => 000100000 => 000001000
[[1,2,3,5,6,7,8,9,10],[4]] => [4,1,2,3,5,6,7,8,9,10] => 100000000 => 000000001
[[1,2,3,4,6,7,8,9,10],[5]] => [5,1,2,3,4,6,7,8,9,10] => 100000000 => 000000001
[[1,2,3,4,5,6,7,9,10],[8]] => [8,1,2,3,4,5,6,7,9,10] => 100000000 => 000000001
[[1,2,3,4,5,6,8,9,10],[7]] => [7,1,2,3,4,5,6,8,9,10] => 100000000 => 000000001
[[1,2,3,4,5,7,8,9,10],[6]] => [6,1,2,3,4,5,7,8,9,10] => 100000000 => 000000001
[[1,2,4,5,6,7,8,9,10,11,12],[3]] => [3,1,2,4,5,6,7,8,9,10,11,12] => 10000000000 => 00000000001
[[1,2,5,6,7,8],[3,4],[9]] => [9,3,4,1,2,5,6,7,8] => 10100000 => 00000101
[[1,6,7,8],[2],[3],[4],[5],[9]] => [9,5,4,3,2,1,6,7,8] => 11111000 => 00011111
[[1,3,8],[2,5],[4,7],[6,9]] => [6,9,4,7,2,5,1,3,8] => 01010100 => 00101010
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,1,7,8] => 11111100 => 00111111
[[1,2,5,6,7,8,9],[3,4],[10]] => [10,3,4,1,2,5,6,7,8,9] => 101000000 => 000000101
[[1,2,5,9],[3,4,8],[6,7],[10]] => [10,6,7,3,4,8,1,2,5,9] => 101001000 => 000100101
[[1,2,9],[3,4],[5,6],[7,8],[10]] => [10,7,8,5,6,3,4,1,2,9] => 101010100 => 001010101
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [10,7,6,5,4,3,2,1,8,9] => 111111100 => 001111111
[[1,2,5,6,7,8,9],[3],[4]] => [4,3,1,2,5,6,7,8,9] => 11000000 => 00000011
[[1,2,6,7,8,9],[3],[4],[5]] => [5,4,3,1,2,6,7,8,9] => 11100000 => 00000111
[[1,2,7,8,9],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9] => 11110000 => 00001111
[[1,2,5,6,7,8,9,10],[3],[4]] => [4,3,1,2,5,6,7,8,9,10] => 110000000 => 000000011
[[1,2,7,8,9,10],[3],[4],[5],[6]] => [6,5,4,3,1,2,7,8,9,10] => 111100000 => 000001111
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8,9,10] => 111110000 => 000011111
[[1,2,4,7],[3,6,10],[5,9],[8]] => [8,5,9,3,6,10,1,2,4,7] => 101001000 => 000100101
[[1,2,6,7],[3,9],[4],[5],[8]] => [8,5,4,3,9,1,2,6,7] => 11101000 => 00010111
[[1,2,4,5,6,7,8,9],[3],[10]] => [10,3,1,2,4,5,6,7,8,9] => 110000000 => 000000011
[[1,2,7,8],[3,10],[4],[5],[6],[9]] => [9,6,5,4,3,10,1,2,7,8] => 111101000 => 000101111
[[1,7,11],[2,8,12],[3,9],[4,10],[5],[6]] => [6,5,4,10,3,9,2,8,12,1,7,11] => 11010100100 => 00100101011
[[1,5,9,11],[2,6,10,12],[3,7],[4,8]] => [4,8,3,7,2,6,10,12,1,5,9,11] => 01010001000 => 00010001010
[[1,4],[2],[3],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,3,2,1,4] => 111111110 => 011111111
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10]] => [10,9,8,7,6,4,3,2,1,5] => 111111110 => 011111111
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [10,9,7,6,5,4,3,2,1,8] => 111111110 => 011111111
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10]] => [10,9,8,6,5,4,3,2,1,7] => 111111110 => 011111111
[[1,6],[2],[3],[4],[5],[7],[8],[9],[10]] => [10,9,8,7,5,4,3,2,1,6] => 111111110 => 011111111
[[1,3],[2],[4],[5],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,5,4,2,1,3] => 11111111110 => 01111111111
[[1,5],[2],[3],[4],[6],[7],[8],[9],[10],[11],[12]] => [12,11,10,9,8,7,6,4,3,2,1,5] => 11111111110 => 01111111111
[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10],[12]] => [12,10,9,8,7,6,5,4,3,2,1,11] => 11111111110 => 01111111111
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10],[11],[12]] => [12,11,10,8,7,6,5,4,3,2,1,9] => 11111111110 => 01111111111
[[1,7],[2],[3],[4],[5],[6],[8],[9],[10],[11],[12]] => [12,11,10,9,8,6,5,4,3,2,1,7] => 11111111110 => 01111111111
[[1,2],[3,5],[4],[6],[7],[8],[9]] => [9,8,7,6,4,3,5,1,2] => 11111010 => 01011111
[[1,2,4],[3],[5],[6],[7],[8],[9]] => [9,8,7,6,5,3,1,2,4] => 11111100 => 00111111
[[1,2,3,5],[4],[6],[7],[8],[9]] => [9,8,7,6,4,1,2,3,5] => 11111000 => 00011111
[[1,2],[3,4],[5,6],[7,9],[8]] => [8,7,9,5,6,3,4,1,2] => 10101010 => 01010101
[[1,2,3,4,6],[5],[7],[8],[9]] => [9,8,7,5,1,2,3,4,6] => 11110000 => 00001111
[[1,2,3,4,5,7],[6],[8],[9]] => [9,8,6,1,2,3,4,5,7] => 11100000 => 00000111
[[1,2,3,4,5,6,8],[7],[9]] => [9,7,1,2,3,4,5,6,8] => 11000000 => 00000011
[[1,2,3,4,5,7,9],[6,8]] => [6,8,1,2,3,4,5,7,9] => 01000000 => 00000010
[[1,3,10],[2],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,2,1,3,10] => 111111100 => 001111111
[[1,5,8],[2,7],[3,9],[4],[6]] => [6,4,3,9,2,7,1,5,8] => 11010100 => 00101011
[[1,3,5,7,9],[2,6,8],[4]] => [4,2,6,8,1,3,5,7,9] => 10010000 => 00001001
[[1,6,9],[2,8],[3,10],[4],[5],[7]] => [7,5,4,3,10,2,8,1,6,9] => 111010100 => 001010111
[[1,3,5,7,9],[2,6,8,10],[4]] => [4,2,6,8,10,1,3,5,7,9] => 100010000 => 000010001
[[1,3,7],[2,4,8],[5,9],[6,10],[11],[12]] => [12,11,6,10,5,9,2,4,8,1,3,7] => 11010100100 => 00100101011
[[1,7],[2,8],[3],[4],[5],[6],[9]] => [9,6,5,4,3,2,8,1,7] => 11111010 => 01011111
[[1,2,4,5,6,7,8],[3,9]] => [3,9,1,2,4,5,6,7,8] => 01000000 => 00000010
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,9,1,2] => 11111010 => 01011111
[[1,2,3,4,5,6],[7,9],[8]] => [8,7,9,1,2,3,4,5,6] => 10100000 => 00000101
[[1,2,3,4,5,7],[6,8,9]] => [6,8,9,1,2,3,4,5,7] => 00100000 => 00000100
[[1,3,5,9],[2,4,6,10],[7,11],[8,12]] => [8,12,7,11,2,4,6,10,1,3,5,9] => 01010001000 => 00010001010
[[1,3,4,5,6,7,9],[2,8]] => [2,8,1,3,4,5,6,7,9] => 01000000 => 00000010
[[1,2,3,4,6],[5,7,8,9]] => [5,7,8,9,1,2,3,4,6] => 00010000 => 00001000
[[1,5,7,9,11],[2,6,8,10,12],[3],[4]] => [4,3,2,6,8,10,12,1,5,7,9,11] => 11000010000 => 00001000011
[[1,3,4,5,6,7,8,10],[2],[9]] => [9,2,1,3,4,5,6,7,8,10] => 110000000 => 000000011
[[1,3,6,7],[2,5,10],[4,9],[8]] => [8,4,9,2,5,10,1,3,6,7] => 101001000 => 000100101
[[1,3,6,7],[2,5,9,10],[4],[8]] => [8,4,2,5,9,10,1,3,6,7] => 110001000 => 000100011
[[1,3,4,5,6,7],[2,9,10,11,12],[8]] => [8,2,9,10,11,12,1,3,4,5,6,7] => 10000100000 => 00000100001
[[1,4,5,6,7,8],[2,9],[3]] => [3,2,9,1,4,5,6,7,8] => 10100000 => 00000101
[[1,2,5,6,7],[3,4,8],[9]] => [9,3,4,8,1,2,5,6,7] => 10010000 => 00001001
[[1,7,8],[2,9],[3],[4],[5],[6]] => [6,5,4,3,2,9,1,7,8] => 11110100 => 00101111
[[1,8,9],[2,10],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,10,1,8,9] => 111110100 => 001011111
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.