Identifier
Mp00083:
Standard tableaux
—shape⟶
Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
Images
[[1]] => [1] => [[1]] =>
[[1,2]] => [2] => [[1,2]] => 0
[[1],[2]] => [1,1] => [[1],[2]] => 1
[[1,2,3]] => [3] => [[1,2,3]] => 00
[[1,3],[2]] => [2,1] => [[1,2],[3]] => 01
[[1,2],[3]] => [2,1] => [[1,2],[3]] => 01
[[1],[2],[3]] => [1,1,1] => [[1],[2],[3]] => 11
[[1,2,3,4]] => [4] => [[1,2,3,4]] => 000
[[1,3,4],[2]] => [3,1] => [[1,2,3],[4]] => 001
[[1,2,4],[3]] => [3,1] => [[1,2,3],[4]] => 001
[[1,2,3],[4]] => [3,1] => [[1,2,3],[4]] => 001
[[1,3],[2,4]] => [2,2] => [[1,2],[3,4]] => 010
[[1,2],[3,4]] => [2,2] => [[1,2],[3,4]] => 010
[[1,4],[2],[3]] => [2,1,1] => [[1,2],[3],[4]] => 011
[[1,3],[2],[4]] => [2,1,1] => [[1,2],[3],[4]] => 011
[[1,2],[3],[4]] => [2,1,1] => [[1,2],[3],[4]] => 011
[[1],[2],[3],[4]] => [1,1,1,1] => [[1],[2],[3],[4]] => 111
[[1,2,3,4,5]] => [5] => [[1,2,3,4,5]] => 0000
[[1,3,4,5],[2]] => [4,1] => [[1,2,3,4],[5]] => 0001
[[1,2,4,5],[3]] => [4,1] => [[1,2,3,4],[5]] => 0001
[[1,2,3,5],[4]] => [4,1] => [[1,2,3,4],[5]] => 0001
[[1,2,3,4],[5]] => [4,1] => [[1,2,3,4],[5]] => 0001
[[1,3,5],[2,4]] => [3,2] => [[1,2,3],[4,5]] => 0010
[[1,2,5],[3,4]] => [3,2] => [[1,2,3],[4,5]] => 0010
[[1,3,4],[2,5]] => [3,2] => [[1,2,3],[4,5]] => 0010
[[1,2,4],[3,5]] => [3,2] => [[1,2,3],[4,5]] => 0010
[[1,2,3],[4,5]] => [3,2] => [[1,2,3],[4,5]] => 0010
[[1,4,5],[2],[3]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,3,5],[2],[4]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,2,5],[3],[4]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,3,4],[2],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,2,4],[3],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,2,3],[4],[5]] => [3,1,1] => [[1,2,3],[4],[5]] => 0011
[[1,4],[2,5],[3]] => [2,2,1] => [[1,2],[3,4],[5]] => 0101
[[1,3],[2,5],[4]] => [2,2,1] => [[1,2],[3,4],[5]] => 0101
[[1,2],[3,5],[4]] => [2,2,1] => [[1,2],[3,4],[5]] => 0101
[[1,3],[2,4],[5]] => [2,2,1] => [[1,2],[3,4],[5]] => 0101
[[1,2],[3,4],[5]] => [2,2,1] => [[1,2],[3,4],[5]] => 0101
[[1,5],[2],[3],[4]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0111
[[1,4],[2],[3],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0111
[[1,3],[2],[4],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0111
[[1,2],[3],[4],[5]] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 0111
[[1],[2],[3],[4],[5]] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111
[[1,2,3,4,5,6]] => [6] => [[1,2,3,4,5,6]] => 00000
[[1,3,4,5,6],[2]] => [5,1] => [[1,2,3,4,5],[6]] => 00001
[[1,2,4,5,6],[3]] => [5,1] => [[1,2,3,4,5],[6]] => 00001
[[1,2,3,5,6],[4]] => [5,1] => [[1,2,3,4,5],[6]] => 00001
[[1,2,3,4,6],[5]] => [5,1] => [[1,2,3,4,5],[6]] => 00001
[[1,2,3,4,5],[6]] => [5,1] => [[1,2,3,4,5],[6]] => 00001
[[1,3,5,6],[2,4]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,5,6],[3,4]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,3,4,6],[2,5]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,4,6],[3,5]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,3,6],[4,5]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,3,4,5],[2,6]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,4,5],[3,6]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,3,5],[4,6]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,2,3,4],[5,6]] => [4,2] => [[1,2,3,4],[5,6]] => 00010
[[1,4,5,6],[2],[3]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,3,5,6],[2],[4]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,5,6],[3],[4]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,3,4,6],[2],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,4,6],[3],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,3,6],[4],[5]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,3,4,5],[2],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,4,5],[3],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,3,5],[4],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,2,3,4],[5],[6]] => [4,1,1] => [[1,2,3,4],[5],[6]] => 00011
[[1,3,5],[2,4,6]] => [3,3] => [[1,2,3],[4,5,6]] => 00100
[[1,2,5],[3,4,6]] => [3,3] => [[1,2,3],[4,5,6]] => 00100
[[1,3,4],[2,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 00100
[[1,2,4],[3,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 00100
[[1,2,3],[4,5,6]] => [3,3] => [[1,2,3],[4,5,6]] => 00100
[[1,4,6],[2,5],[3]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,6],[2,5],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,6],[3,5],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,6],[2,4],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,6],[3,4],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,4,5],[2,6],[3]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,5],[2,6],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,5],[3,6],[4]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,4],[2,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,4],[3,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,3],[4,6],[5]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,5],[2,4],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,5],[3,4],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,3,4],[2,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,4],[3,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,2,3],[4,5],[6]] => [3,2,1] => [[1,2,3],[4,5],[6]] => 00101
[[1,5,6],[2],[3],[4]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,4,6],[2],[3],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,3,6],[2],[4],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,2,6],[3],[4],[5]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,4,5],[2],[3],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,3,5],[2],[4],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,2,5],[3],[4],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,3,4],[2],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,2,4],[3],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,2,3],[4],[5],[6]] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 00111
[[1,4],[2,5],[3,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010
[[1,3],[2,5],[4,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010
>>> Load all 1752 entries. <<<
[[1,2],[3,5],[4,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010
[[1,3],[2,4],[5,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010
[[1,2],[3,4],[5,6]] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010
[[1,5],[2,6],[3],[4]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,4],[2,6],[3],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,3],[2,6],[4],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,2],[3,6],[4],[5]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,4],[2,5],[3],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,3],[2,5],[4],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,2],[3,5],[4],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,3],[2,4],[5],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,2],[3,4],[5],[6]] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 01011
[[1,6],[2],[3],[4],[5]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[[1,5],[2],[3],[4],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[[1,4],[2],[3],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[[1,3],[2],[4],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 01111
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111
[[1,2,3,4,5,6,7]] => [7] => [[1,2,3,4,5,6,7]] => 000000
[[1,3,4,5,6,7],[2]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,4,5,6,7],[3]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,3,5,6,7],[4]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,3,4,6,7],[5]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,3,4,5,7],[6]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,2,3,4,5,6],[7]] => [6,1] => [[1,2,3,4,5,6],[7]] => 000001
[[1,3,5,6,7],[2,4]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,5,6,7],[3,4]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,3,4,6,7],[2,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,4,6,7],[3,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,6,7],[4,5]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,3,4,5,7],[2,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,4,5,7],[3,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,5,7],[4,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,4,7],[5,6]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,3,4,5,6],[2,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,4,5,6],[3,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,5,6],[4,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,4,6],[5,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,2,3,4,5],[6,7]] => [5,2] => [[1,2,3,4,5],[6,7]] => 000010
[[1,4,5,6,7],[2],[3]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,5,6,7],[2],[4]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,5,6,7],[3],[4]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,4,6,7],[2],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,4,6,7],[3],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,6,7],[4],[5]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,4,5,7],[2],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,4,5,7],[3],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,5,7],[4],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,4,7],[5],[6]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,4,5,6],[2],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,4,5,6],[3],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,5,6],[4],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,4,6],[5],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,2,3,4,5],[6],[7]] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 000011
[[1,3,5,7],[2,4,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,5,7],[3,4,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,3,4,7],[2,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,4,7],[3,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,3,7],[4,5,6]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,3,5,6],[2,4,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,5,6],[3,4,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,3,4,6],[2,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,4,6],[3,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,3,6],[4,5,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,3,4,5],[2,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,4,5],[3,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,3,5],[4,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,2,3,4],[5,6,7]] => [4,3] => [[1,2,3,4],[5,6,7]] => 000100
[[1,4,6,7],[2,5],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,6,7],[2,5],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,6,7],[3,5],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,6,7],[2,4],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,6,7],[3,4],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,4,5,7],[2,6],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,5,7],[2,6],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,5,7],[3,6],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,7],[2,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,7],[3,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,7],[4,6],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,5,7],[2,4],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,5,7],[3,4],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,7],[2,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,7],[3,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,7],[4,5],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,4,5,6],[2,7],[3]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,5,6],[2,7],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,5,6],[3,7],[4]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,6],[2,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,6],[3,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,6],[4,7],[5]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,5],[2,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,5],[3,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,5],[4,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,4],[5,7],[6]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,5,6],[2,4],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,5,6],[3,4],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,6],[2,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,6],[3,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,6],[4,5],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,3,4,5],[2,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,4,5],[3,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,5],[4,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,2,3,4],[5,6],[7]] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 000101
[[1,5,6,7],[2],[3],[4]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,4,6,7],[2],[3],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,6,7],[2],[4],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,6,7],[3],[4],[5]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,4,5,7],[2],[3],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,5,7],[2],[4],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,5,7],[3],[4],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,4,7],[2],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,4,7],[3],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,3,7],[4],[5],[6]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,4,5,6],[2],[3],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,5,6],[2],[4],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,5,6],[3],[4],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,4,6],[2],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,4,6],[3],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,3,6],[4],[5],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,3,4,5],[2],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,4,5],[3],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,3,5],[4],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 000111
[[1,4,6],[2,5,7],[3]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,6],[2,5,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,6],[3,5,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,6],[2,4,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,6],[3,4,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,4,5],[2,6,7],[3]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,5],[2,6,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,5],[3,6,7],[4]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,4],[2,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,4],[3,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,3],[4,6,7],[5]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,5],[2,4,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,5],[3,4,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,4],[2,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,4],[3,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,3],[4,5,7],[6]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,5],[2,4,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,5],[3,4,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,3,4],[2,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,4],[3,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,2,3],[4,5,6],[7]] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 001001
[[1,4,7],[2,5],[3,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,7],[2,5],[4,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,7],[3,5],[4,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,7],[2,4],[5,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,7],[3,4],[5,6]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,4,6],[2,5],[3,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,6],[2,5],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,6],[3,5],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,6],[2,4],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,6],[3,4],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,4,5],[2,6],[3,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,5],[2,6],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,5],[3,6],[4,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,4],[2,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,4],[3,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,3],[4,6],[5,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,5],[2,4],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,5],[3,4],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,3,4],[2,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,4],[3,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,2,3],[4,5],[6,7]] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 001010
[[1,5,7],[2,6],[3],[4]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,7],[2,6],[3],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,7],[2,6],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,7],[3,6],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,7],[2,5],[3],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,7],[2,5],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,7],[3,5],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,7],[2,4],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,7],[3,4],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,5,6],[2,7],[3],[4]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,6],[2,7],[3],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,6],[2,7],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,6],[3,7],[4],[5]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,5],[2,7],[3],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,5],[2,7],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,5],[3,7],[4],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,4],[2,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,4],[3,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,3],[4,7],[5],[6]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,6],[2,5],[3],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,6],[2,5],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,6],[3,5],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,6],[2,4],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,6],[3,4],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,4,5],[2,6],[3],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,5],[2,6],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,5],[3,6],[4],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,4],[2,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,4],[3,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,3],[4,6],[5],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,5],[2,4],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,5],[3,4],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,3,4],[2,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,4],[3,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 001011
[[1,6,7],[2],[3],[4],[5]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,5,7],[2],[3],[4],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,4,7],[2],[3],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,3,7],[2],[4],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,2,7],[3],[4],[5],[6]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,5,6],[2],[3],[4],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,4,6],[2],[3],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,3,6],[2],[4],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,2,6],[3],[4],[5],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,4,5],[2],[3],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,3,5],[2],[4],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,2,5],[3],[4],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,3,4],[2],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,2,4],[3],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 001111
[[1,5],[2,6],[3,7],[4]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,4],[2,6],[3,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,3],[2,6],[4,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,6],[4,7],[5]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,4],[2,5],[3,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,5],[4,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,3],[2,4],[5,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,4],[5,7],[6]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,4],[2,5],[3,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,3],[2,5],[4,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,5],[4,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,3],[2,4],[5,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 010101
[[1,6],[2,7],[3],[4],[5]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,5],[2,7],[3],[4],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,4],[2,7],[3],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,3],[2,7],[4],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,2],[3,7],[4],[5],[6]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,5],[2,6],[3],[4],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,4],[2,6],[3],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,3],[2,6],[4],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,2],[3,6],[4],[5],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,4],[2,5],[3],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,3],[2,5],[4],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,2],[3,5],[4],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,3],[2,4],[5],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 010111
[[1,7],[2],[3],[4],[5],[6]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,6],[2],[3],[4],[5],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,5],[2],[3],[4],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,4],[2],[3],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,3],[2],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 011111
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111
[[1,2,3,4,5,6,7,8]] => [8] => [[1,2,3,4,5,6,7,8]] => 0000000
[[1,3,4,5,6,7,8],[2]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,4,5,6,7,8],[3]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,3,5,6,7,8],[4]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,3,4,6,7,8],[5]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,3,4,5,7,8],[6]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,3,4,5,6,8],[7]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,2,3,4,5,6,7],[8]] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 0000001
[[1,3,5,6,7,8],[2,4]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,5,6,7,8],[3,4]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,3,4,6,7,8],[2,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,4,6,7,8],[3,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,6,7,8],[4,5]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,3,4,5,7,8],[2,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,4,5,7,8],[3,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,5,7,8],[4,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,7,8],[5,6]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,3,4,5,6,8],[2,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,4,5,6,8],[3,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,5,6,8],[4,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,6,8],[5,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,5,8],[6,7]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,3,4,5,6,7],[2,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,4,5,6,7],[3,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,5,6,7],[4,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,6,7],[5,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,5,7],[6,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,2,3,4,5,6],[7,8]] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 0000010
[[1,4,5,6,7,8],[2],[3]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,5,6,7,8],[2],[4]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,5,6,7,8],[3],[4]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,4,6,7,8],[2],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,4,6,7,8],[3],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,6,7,8],[4],[5]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,4,5,7,8],[2],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,4,5,7,8],[3],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,5,7,8],[4],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,7,8],[5],[6]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,4,5,6,8],[2],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,4,5,6,8],[3],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,5,6,8],[4],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,6,8],[5],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,5,8],[6],[7]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,4,5,6,7],[2],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,4,5,6,7],[3],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,5,6,7],[4],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,6,7],[5],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,5,7],[6],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,2,3,4,5,6],[7],[8]] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 0000011
[[1,3,5,7,8],[2,4,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,5,7,8],[3,4,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,7,8],[2,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,7,8],[3,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,7,8],[4,5,6]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,5,6,8],[2,4,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,5,6,8],[3,4,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,6,8],[2,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,6,8],[3,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,6,8],[4,5,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,5,8],[2,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,5,8],[3,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,5,8],[4,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,4,8],[5,6,7]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,5,6,7],[2,4,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,5,6,7],[3,4,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,6,7],[2,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,6,7],[3,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,6,7],[4,5,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,5,7],[2,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,5,7],[3,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,5,7],[4,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,4,7],[5,6,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,3,4,5,6],[2,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,4,5,6],[3,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,5,6],[4,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,4,6],[5,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,2,3,4,5],[6,7,8]] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 0000100
[[1,4,6,7,8],[2,5],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,6,7,8],[2,5],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,6,7,8],[3,5],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,6,7,8],[2,4],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,6,7,8],[3,4],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,4,5,7,8],[2,6],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,7,8],[2,6],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,7,8],[3,6],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,7,8],[2,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,7,8],[3,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,7,8],[4,6],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,7,8],[2,4],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,7,8],[3,4],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,7,8],[2,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,7,8],[3,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,7,8],[4,5],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,4,5,6,8],[2,7],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,6,8],[2,7],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,6,8],[3,7],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,6,8],[2,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,6,8],[3,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,8],[2,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,8],[3,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,8],[4,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,8],[5,7],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,6,8],[2,4],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,6,8],[3,4],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,6,8],[2,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,6,8],[3,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,6,8],[4,5],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,8],[2,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,8],[3,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,8],[4,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,4,5,6,7],[2,8],[3]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,6,7],[2,8],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,6,7],[3,8],[4]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,6,7],[2,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,6,7],[3,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,6,7],[4,8],[5]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,7],[2,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,7],[3,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,7],[4,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,7],[5,8],[6]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,6],[2,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,6],[3,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,6],[4,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,6],[5,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,5],[6,8],[7]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,5,6,7],[2,4],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,5,6,7],[3,4],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,6,7],[2,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,6,7],[3,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,6,7],[4,5],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,7],[2,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,7],[3,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,7],[4,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,7],[5,6],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,3,4,5,6],[2,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,4,5,6],[3,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,5,6],[4,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,6],[5,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,2,3,4,5],[6,7],[8]] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 0000101
[[1,5,6,7,8],[2],[3],[4]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,4,6,7,8],[2],[3],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,6,7,8],[2],[4],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,6,7,8],[3],[4],[5]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,4,5,7,8],[2],[3],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,5,7,8],[2],[4],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,5,7,8],[3],[4],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,7,8],[2],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,7,8],[3],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,7,8],[4],[5],[6]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,4,5,6,8],[2],[3],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,5,6,8],[2],[4],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,5,6,8],[3],[4],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,6,8],[2],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,6,8],[3],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,6,8],[4],[5],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,5,8],[2],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,5,8],[3],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,5,8],[4],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,4,8],[5],[6],[7]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,4,5,6,7],[2],[3],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,5,6,7],[2],[4],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,5,6,7],[3],[4],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,6,7],[2],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,6,7],[3],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,6,7],[4],[5],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,5,7],[2],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,5,7],[3],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,5,7],[4],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,4,7],[5],[6],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,4,5,6],[2],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,4,5,6],[3],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,5,6],[4],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,4,6],[5],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 0000111
[[1,3,5,7],[2,4,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,5,7],[3,4,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,3,4,7],[2,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,4,7],[3,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,3,7],[4,5,6,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,3,5,6],[2,4,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,5,6],[3,4,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,3,4,6],[2,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,4,6],[3,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,3,6],[4,5,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,3,4,5],[2,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,4,5],[3,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,3,5],[4,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,2,3,4],[5,6,7,8]] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000
[[1,4,6,8],[2,5,7],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,6,8],[2,5,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,6,8],[2,4,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,6,8],[3,4,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,4,5,8],[2,6,7],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,8],[2,6,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,8],[3,6,7],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,8],[2,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,8],[3,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,8],[4,6,7],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,8],[2,4,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,8],[3,4,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,8],[2,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,8],[3,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,8],[4,5,7],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,8],[2,4,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,8],[3,4,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,8],[2,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,8],[3,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,4,6,7],[2,5,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,6,7],[2,5,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,6,7],[3,5,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,6,7],[2,4,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,6,7],[3,4,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,4,5,7],[2,6,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,7],[2,6,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,7],[3,6,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,7],[2,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,7],[3,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,7],[4,6,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,7],[2,4,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,7],[3,4,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,7],[2,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,7],[3,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,7],[4,5,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,4,5,6],[2,7,8],[3]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,6],[2,7,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,6],[2,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,6],[3,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,6],[4,7,8],[5]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,5],[2,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,5],[3,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,5],[4,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,4],[5,7,8],[6]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,6],[2,4,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,6],[3,4,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,6],[2,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,6],[3,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,5],[2,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,5],[3,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,4],[5,6,8],[7]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,7],[2,4,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,7],[3,4,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,7],[2,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,7],[3,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,7],[4,5,6],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,5,6],[2,4,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,5,6],[3,4,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,6],[2,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,6],[3,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,6],[4,5,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,3,4,5],[2,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,4,5],[3,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,5],[4,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,2,3,4],[5,6,7],[8]] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 0001001
[[1,4,7,8],[2,5],[3,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,7,8],[2,5],[4,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,7,8],[2,4],[5,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,7,8],[3,4],[5,6]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,6,8],[2,5],[3,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,6,8],[2,5],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,6,8],[3,5],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,6,8],[2,4],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,6,8],[3,4],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,5,8],[2,6],[3,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,8],[2,6],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,8],[3,6],[4,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,8],[2,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,8],[3,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,8],[4,6],[5,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,8],[2,4],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,8],[3,4],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,8],[2,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,8],[3,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,6,7],[2,5],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,6,7],[2,5],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,6,7],[3,5],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,6,7],[2,4],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,6,7],[3,4],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,5,7],[2,6],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,7],[2,6],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,7],[2,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,7],[3,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,7],[4,6],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,7],[2,4],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,7],[3,4],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,7],[2,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,7],[3,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,4,5,6],[2,7],[3,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,6],[2,7],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,6],[3,7],[4,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,6],[2,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,6],[3,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,6],[4,7],[5,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,5],[2,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,5],[3,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,4],[5,7],[6,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,5,6],[2,4],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,5,6],[3,4],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,6],[2,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,6],[3,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,6],[4,5],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,3,4,5],[2,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,4,5],[3,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,5],[4,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,2,3,4],[5,6],[7,8]] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 0001010
[[1,5,7,8],[2,6],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,7,8],[2,6],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,7,8],[2,6],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,7,8],[3,6],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,7,8],[2,5],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,7,8],[2,5],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,7,8],[3,5],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,7,8],[2,4],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,7,8],[3,4],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,5,6,8],[2,7],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,6,8],[2,7],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,8],[2,7],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,8],[3,7],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,8],[2,7],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,8],[2,7],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,8],[3,7],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,8],[2,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,8],[3,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,8],[4,7],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,6,8],[2,5],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,8],[2,5],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,8],[3,5],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,8],[2,4],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,8],[3,4],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,8],[2,6],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,8],[2,6],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,8],[3,6],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,8],[2,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,8],[3,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,8],[4,6],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,8],[2,4],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,8],[3,4],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,8],[2,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,8],[3,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,8],[4,5],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,5,6,7],[2,8],[3],[4]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,6,7],[2,8],[3],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,7],[2,8],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,7],[3,8],[4],[5]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,7],[2,8],[3],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,7],[2,8],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,7],[3,8],[4],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,7],[2,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,7],[3,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,7],[4,8],[5],[6]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,6],[2,8],[3],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,6],[2,8],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,6],[3,8],[4],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,6],[2,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,6],[3,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,6],[4,8],[5],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,5],[2,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,5],[3,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,5],[4,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,4],[5,8],[6],[7]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,6,7],[2,5],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,7],[2,5],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,7],[3,5],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,6,7],[2,4],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,6,7],[3,4],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,7],[2,6],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,7],[2,6],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,7],[3,6],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,7],[2,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,7],[3,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,7],[4,6],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,7],[2,4],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,7],[3,4],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,7],[2,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,7],[3,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,7],[4,5],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,4,5,6],[2,7],[3],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,6],[2,7],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,6],[3,7],[4],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,6],[2,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,6],[3,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,6],[4,7],[5],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,5],[2,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,5],[3,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,5],[4,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,4],[5,7],[6],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,5,6],[2,4],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,5,6],[3,4],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,6],[2,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,6],[3,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,6],[4,5],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,3,4,5],[2,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,4,5],[3,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,5],[4,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 0001011
[[1,6,7,8],[2],[3],[4],[5]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,5,7,8],[2],[3],[4],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,7,8],[2],[3],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,7,8],[2],[4],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,7,8],[3],[4],[5],[6]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,5,6,8],[2],[3],[4],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,6,8],[2],[3],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,6,8],[2],[4],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,6,8],[3],[4],[5],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,5,8],[2],[3],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,5,8],[2],[4],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,5,8],[3],[4],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,4,8],[2],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,4,8],[3],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,3,8],[4],[5],[6],[7]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,5,6,7],[2],[3],[4],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,6,7],[2],[3],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,6,7],[2],[4],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,6,7],[3],[4],[5],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,5,7],[2],[3],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,5,7],[2],[4],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,5,7],[3],[4],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,4,7],[2],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,4,7],[3],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,3,7],[4],[5],[6],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,5,6],[2],[3],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,5,6],[2],[4],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,5,6],[3],[4],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,4,6],[2],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,4,6],[3],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,3,6],[4],[5],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,3,4,5],[2],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,4,5],[3],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,3,5],[4],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 0001111
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,7],[2,5,8],[4,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,7],[3,5,8],[4,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,7],[2,4,8],[5,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,7],[3,4,8],[5,6]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,4,6],[2,5,8],[3,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,6],[2,5,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,6],[3,5,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,6],[2,4,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,6],[3,4,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,4,5],[2,6,8],[3,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,5],[2,6,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,5],[3,6,8],[4,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,4],[3,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,3],[4,6,8],[5,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,5],[2,4,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,3],[4,5,8],[6,7]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,4,6],[2,5,7],[3,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,6],[2,5,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,6],[3,5,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,6],[2,4,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,6],[3,4,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,5],[2,6,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,5],[3,6,7],[4,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,4],[3,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,3],[4,6,7],[5,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,5],[2,4,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,3],[4,5,7],[6,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,5],[2,4,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,5],[3,4,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,3,4],[2,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,4],[3,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,2,3],[4,5,6],[7,8]] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 0010010
[[1,5,7],[2,6,8],[3],[4]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,7],[2,6,8],[3],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,7],[2,6,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,7],[3,6,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,7],[2,5,8],[3],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,7],[2,5,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,7],[3,5,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,7],[2,4,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,7],[3,4,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,5,6],[2,7,8],[3],[4]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,6],[2,7,8],[3],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,6],[2,7,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,6],[3,7,8],[4],[5]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,5],[2,7,8],[3],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,7,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,7,8],[4],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,7,8],[5],[6]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,6],[2,5,8],[3],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,6],[2,5,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,6],[3,5,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,6],[2,4,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,6],[3,4,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,5],[2,6,8],[3],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,6,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,6,8],[4],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,6,8],[5],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,4,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,4,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,5,8],[6],[7]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,6],[2,5,7],[3],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,6],[2,5,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,6],[3,5,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,6],[2,4,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,6],[3,4,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,4,5],[2,6,7],[3],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,6,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,6,7],[4],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,6,7],[5],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,4,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,4,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,5,7],[6],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,5],[2,4,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,5],[3,4,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,3,4],[2,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,4],[3,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 0010011
[[1,5,8],[2,6],[3,7],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,8],[2,6],[4,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,6],[4,7],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,8],[2,5],[3,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,8],[2,5],[4,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,5],[4,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,8],[2,4],[5,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,4],[5,7],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,8],[2,5],[3,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,8],[2,5],[4,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,5],[4,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,8],[2,4],[5,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,5,7],[2,6],[3,8],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,7],[2,6],[3,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,7],[2,6],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,7],[3,6],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,7],[2,5],[3,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,7],[2,5],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,7],[3,5],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,7],[2,4],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,7],[3,4],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,5,6],[2,7],[3,8],[4]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,6],[2,7],[3,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,6],[2,7],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,6],[3,7],[4,8],[5]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,5],[2,7],[3,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,5],[2,7],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,5],[3,7],[4,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,4],[2,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,4],[3,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,3],[4,7],[5,8],[6]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,6],[2,5],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,6],[3,5],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,6],[2,4],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,5],[2,6],[3,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,5],[2,6],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,5],[3,6],[4,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,4],[2,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,3],[4,6],[5,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,5],[2,4],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,5],[3,4],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,4],[2,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,4],[3,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,3],[4,5],[6,8],[7]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,7],[2,5],[3,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,7],[2,5],[4,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,7],[3,5],[4,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,7],[2,4],[5,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,7],[3,4],[5,6],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,6],[2,5],[3,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,6],[2,5],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,6],[3,5],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,6],[2,4],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,6],[3,4],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,4,5],[2,6],[3,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,5],[2,6],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,5],[3,6],[4,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,4],[2,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,4],[3,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,3],[4,6],[5,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,5],[2,4],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,5],[3,4],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,3,4],[2,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,4],[3,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 0010101
[[1,6,8],[2,7],[3],[4],[5]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,8],[2,7],[3],[4],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,8],[2,7],[3],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,8],[2,7],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,8],[3,7],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,8],[2,6],[3],[4],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,8],[2,6],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,8],[3,6],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,8],[2,5],[3],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,8],[2,5],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,8],[3,5],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,8],[2,4],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,8],[3,4],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,6,7],[2,8],[3],[4],[5]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,7],[2,8],[3],[4],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,7],[2,8],[3],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,7],[2,8],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,7],[3,8],[4],[5],[6]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,6],[2,8],[3],[4],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,6],[2,8],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,6],[3,8],[4],[5],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,5],[2,8],[3],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,5],[2,8],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,5],[3,8],[4],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,4],[2,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,4],[3,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,3],[4,8],[5],[6],[7]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,7],[2,6],[3],[4],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,7],[2,6],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,7],[3,6],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,7],[2,5],[3],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,7],[2,5],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,7],[3,5],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,7],[2,4],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,7],[3,4],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,5,6],[2,7],[3],[4],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,6],[2,7],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,6],[3,7],[4],[5],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,5],[2,7],[3],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,5],[2,7],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,5],[3,7],[4],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,4],[2,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,4],[3,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,3],[4,7],[5],[6],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,6],[2,5],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,6],[3,5],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,6],[2,4],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,4,5],[2,6],[3],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,5],[2,6],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,5],[3,6],[4],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,4],[2,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,3],[4,6],[5],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,5],[2,4],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,5],[3,4],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,3,4],[2,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,4],[3,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 0010111
[[1,7,8],[2],[3],[4],[5],[6]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,6,8],[2],[3],[4],[5],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,5,8],[2],[3],[4],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,4,8],[2],[3],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,3,8],[2],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,8],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,6,7],[2],[3],[4],[5],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,5,7],[2],[3],[4],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,4,7],[2],[3],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,3,7],[2],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,7],[3],[4],[5],[6],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,5,6],[2],[3],[4],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,4,6],[2],[3],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,3,6],[2],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,6],[3],[4],[5],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,4,5],[2],[3],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,3,5],[2],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,5],[3],[4],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,3,4],[2],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,4],[3],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 0011111
[[1,5],[2,6],[3,7],[4,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,4],[2,6],[3,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,3],[2,6],[4,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,2],[3,6],[4,7],[5,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,4],[2,5],[3,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,2],[3,5],[4,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,3],[2,4],[5,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,2],[3,4],[5,7],[6,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,4],[2,5],[3,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,3],[2,5],[4,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,2],[3,5],[4,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,3],[2,4],[5,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010
[[1,6],[2,7],[3,8],[4],[5]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,5],[2,7],[3,8],[4],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,7],[3,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,7],[4,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,7],[4,8],[5],[6]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,5],[2,6],[3,8],[4],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,6],[3,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,6],[4,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,6],[4,8],[5],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,5],[3,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,5],[4,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,4],[5,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,5],[2,6],[3,7],[4],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,6],[3,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,6],[4,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,6],[4,7],[5],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,5],[3,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,5],[4,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,4],[5,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,4],[2,5],[3,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,5],[4,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,3],[2,4],[5,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 0101011
[[1,7],[2,8],[3],[4],[5],[6]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,6],[2,8],[3],[4],[5],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,5],[2,8],[3],[4],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,4],[2,8],[3],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,3],[2,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,2],[3,8],[4],[5],[6],[7]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,6],[2,7],[3],[4],[5],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,5],[2,7],[3],[4],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,4],[2,7],[3],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,3],[2,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,2],[3,7],[4],[5],[6],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,5],[2,6],[3],[4],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,4],[2,6],[3],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,3],[2,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,2],[3,6],[4],[5],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,4],[2,5],[3],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,2],[3,5],[4],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,3],[2,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 0101111
[[1,8],[2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,7],[2],[3],[4],[5],[6],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,6],[2],[3],[4],[5],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,5],[2],[3],[4],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,4],[2],[3],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 0111111
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111
[[1,3,5,7,9],[2,4,6,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,7,8],[2,4,6,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,6,9],[2,4,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,6,8],[2,4,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,6,7],[2,4,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,7,9],[2,5,6,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,7,8],[2,5,6,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,6,9],[2,5,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,6,8],[2,5,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,6,7],[2,5,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,5,9],[2,6,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,5,8],[2,6,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,5,7],[2,6,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,4,5,6],[2,7,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,5,7,9],[3,4,6,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,5,7,8],[3,4,6,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,5,6,9],[3,4,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,5,6,8],[3,4,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,5,6,7],[3,4,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,7,9],[3,5,6,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,7,8],[3,5,6,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,6,9],[3,5,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,6,8],[3,5,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,6,7],[3,5,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,5,9],[3,6,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,5,8],[3,6,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,5,7],[3,6,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,4,5,6],[3,7,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,7,9],[4,5,6,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,7,8],[4,5,6,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,6,9],[4,5,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,6,8],[4,5,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,6,7],[4,5,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,5,9],[4,6,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,5,8],[4,6,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,5,7],[4,6,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,5,6],[4,7,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,4,9],[5,6,7,8,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,4,8],[5,6,7,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,4,7],[5,6,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,4,6],[5,7,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,7,9,10],[3,4,6,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,7,8,11],[3,4,6,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,7,8,10],[3,4,6,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,7,8,9],[3,4,6,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,9,11],[3,4,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,9,10],[3,4,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,8,11],[3,4,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,8,10],[3,4,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,8,9],[3,4,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,7,11],[3,4,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,7,10],[3,4,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,7,9],[3,4,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,5,6,7,8],[3,4,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,7,9,11],[3,5,6,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,7,9,10],[3,5,6,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,7,8,11],[3,5,6,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,7,8,10],[3,5,6,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,7,8,9],[3,5,6,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,9,11],[3,5,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,9,10],[3,5,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,8,11],[3,5,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,7,11],[3,5,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,6,7,8],[3,5,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,9,11],[3,6,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,9,10],[3,6,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,8,11],[3,6,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,8,9],[3,6,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,7,11],[3,6,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,7,8],[3,6,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,6,11],[3,7,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,6,10],[3,7,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,6,9],[3,7,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,6,8],[3,7,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,4,5,6,7],[3,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,7,9,11],[4,5,6,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,7,9,10],[4,5,6,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,7,8,11],[4,5,6,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,7,8,10],[4,5,6,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,7,8,9],[4,5,6,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,9,11],[4,5,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,9,10],[4,5,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,8,11],[4,5,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,8,9],[4,5,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,7,11],[4,5,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,7,10],[4,5,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,7,9],[4,5,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,6,7,8],[4,5,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,9,11],[4,6,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,9,10],[4,6,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,8,11],[4,6,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,8,9],[4,6,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,7,11],[4,6,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,7,8],[4,6,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,6,11],[4,7,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,6,10],[4,7,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,6,9],[4,7,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,6,8],[4,7,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,5,6,7],[4,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,9,11],[5,6,7,8,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,9,10],[5,6,7,8,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,8,11],[5,6,7,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,8,10],[5,6,7,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,8,9],[5,6,7,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,7,11],[5,6,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,7,10],[5,6,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,7,9],[5,6,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,7,8],[5,6,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,6,11],[5,7,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,6,10],[5,7,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,6,9],[5,7,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,6,8],[5,7,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,6,7],[5,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,11],[6,7,8,9,10,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,10],[6,7,8,9,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,9],[6,7,8,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,8],[6,7,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,7],[6,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000
[[1,2,3,4,5,6,7,8,9]] => [9] => [[1,2,3,4,5,6,7,8,9]] => 00000000
[[1,2,3,4,5,6,7,8],[9]] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[[1,2,3,4,5,6,7],[8,9]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[[1,2,3,4,5,6],[7,8,9]] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[[1,2,3,4,5],[6,7,8,9]] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[[1,2,3,4,5],[6,7,8],[9]] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,2,3,4,5],[6,7],[8],[9]] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[[1,2,3,4],[5,6,7,8],[9]] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[[1,2,3,4],[5,6,7],[8],[9]] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[[1,2,3,4],[5,6],[7,8],[9]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,2,3,4],[5,6],[7],[8],[9]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[[1,2,3],[4,5,6],[7,8,9]] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100
[[1,2,3],[4,5,6],[7,8],[9]] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 00100101
[[1,2,3],[4,5,6],[7],[8],[9]] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 00100111
[[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 00101010
[[1,2,3],[4,5],[6,7],[8],[9]] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[[1,2,3],[4,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[[1,2],[3,4],[5,6],[7],[8],[9]] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 01010111
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111
[[1,2,3,4,5,6,7,8,9,10]] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000
[[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,6,7,8],[9,10]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[[1,2,3,4,5,6,7],[8,9,10]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,5,6,7],[8,9],[10]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,2,3,4,5,6,7],[8],[9],[10]] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[[1,2,3,4,5,6],[7,8,9,10]] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[[1,2,3,4,5,6],[7,8,9],[10]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,3,4,5,6],[7,8],[9,10]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,2,3,4,5,6],[7,8],[9],[10]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[[1,2,3,4,5],[6,7,8,9],[10]] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,3,4,5],[6,7,8],[9,10]] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,2,3,4,5],[6,7,8],[9],[10]] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[[1,2,3,4,5],[6,7],[8,9],[10]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,2,3,4,5],[6,7],[8],[9],[10]] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[[1,2,3,4],[5,6,7,8],[9,10]] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 000100010
[[1,2,3,4],[5,6,7,8],[9],[10]] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011
[[1,2,3,4],[5,6,7],[8,9,10]] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[[1,2,3,4],[5,6,7],[8,9],[10]] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,2,3,4],[5,6,7],[8],[9],[10]] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[[1,2,3,4],[5,6],[7,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,2,3,4],[5,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[[1,2,3],[4,5,6],[7,8,9],[10]] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001
[[1,2,3],[4,5,6],[7,8],[9,10]] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 001001011
[[1,2,3],[4,5,6],[7],[8],[9],[10]] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[[1,2,3],[4,5],[6,7],[8],[9],[10]] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111
[[1,2,3],[4,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010
[[1,2],[3,4],[5,6],[7,8],[9],[10]] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 010101011
[[1,2],[3,4],[5,6],[7],[8],[9],[10]] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 010101111
[[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111
[[1,2,3,4,5,6,7,8,9,10,11,12]] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 00000000000
[[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,3,4,5,6,7,8,9],[2]] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[[1,2,5,6,7,8,9],[3,4]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,4,5,6,7,8,9],[2],[3]] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[[1,2,3,7,8,9],[4,5,6]] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,3,6,7,8,9],[2,5],[4]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,5,6,7,8,9],[2],[3],[4]] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[[1,2,3,4,9],[5,6,7,8]] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[[1,3,4,8,9],[2,6,7],[5]] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,7,8,9],[3,4],[5,6]] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,4,7,8,9],[2,6],[3],[5]] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[[1,3,4,5],[2,7,8,9],[6]] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 00010001
[[1,2,5,9],[3,4,8],[6,7]] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[[1,4,5,9],[2,7,8],[3],[6]] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[[1,3,8,9],[2,5],[4,7],[6]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,5,8,9],[2,7],[3],[4],[6]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,7,8,9],[2],[3],[4],[5],[6]] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[[1,3,6],[2,5,9],[4,8],[7]] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 00100101
[[1,5,6],[2,8,9],[3],[4],[7]] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 00100111
[[1,2,9],[3,4],[5,6],[7,8]] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 00101010
[[1,4,9],[2,6],[3,8],[5],[7]] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[[1,6,9],[2,8],[3],[4],[5],[7]] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 01010101
[[1,5],[2,7],[3,9],[4],[6],[8]] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 01010111
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 01011111
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 01111111
[[1,3,4,5,6,7,8,9,10],[2]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,5,6,7,8,9,10],[3,4]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,4,5,6,7,8,9,10],[2],[3]] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[[1,2,3,7,8,9,10],[4,5,6]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,3,6,7,8,9,10],[2,5],[4]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,5,6,7,8,9,10],[2],[3],[4]] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[[1,2,3,4,9,10],[5,6,7,8]] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[[1,3,4,8,9,10],[2,6,7],[5]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,7,8,9,10],[3,4],[5,6]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,4,7,8,9,10],[2,6],[3],[5]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[[1,3,4,5,10],[2,7,8,9],[6]] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,5,9,10],[3,4,8],[6,7]] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,4,5,9,10],[2,7,8],[3],[6]] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[[1,3,8,9,10],[2,5],[4,7],[6]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,7,8,9,10],[2],[3],[4],[5],[6]] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[[1,2,5,6],[3,4,9,10],[7,8]] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 000100010
[[1,4,5,6],[2,8,9,10],[3],[7]] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 000100011
[[1,2,3,10],[4,5,6],[7,8,9]] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[[1,3,6,10],[2,5,9],[4,8],[7]] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[[1,2,9,10],[3,4],[5,6],[7,8]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,6,9,10],[2,8],[3],[4],[5],[7]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[[1,3,4],[2,6,7],[5,9,10],[8]] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 001001001
[[1,2,7],[3,4,10],[5,6],[8,9]] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 001001010
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 001001011
[[1,6,7],[2,9,10],[3],[4],[5],[8]] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 001001111
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[[1,5,10],[2,7],[3,9],[4],[6],[8]] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 010101011
[[1,6],[2,8],[3,10],[4],[5],[7],[9]] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 010101111
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 010111111
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 011111111
[[1,2,4],[3,5],[6],[7],[8],[9]] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[[1,2,5],[3,6],[4,7],[8],[9]] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[[1,2,3,5],[4,6],[7],[8],[9]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,2,6],[3,7],[4,8],[5,9]] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 00101010
[[1,2,3,6],[4,7],[5,8],[9]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,2,4,6],[3,5,7],[8],[9]] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[[1,2,3,4,6],[5,7],[8],[9]] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,2,4,7],[3,5,8],[6,9]] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[[1,2,3,4,7],[5,8],[6,9]] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,2,3,5,7],[4,6,8],[9]] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,3,4,5,7],[6,8],[9]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,4,6,8],[3,5,7,9]] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 00001000
[[1,2,3,4,6,8],[5,7,9]] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,2,3,4,5,6,8],[7,9]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,2,4],[3,5],[6],[7],[8],[9],[10]] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[[1,2,5],[3,6],[4,7],[8],[9],[10]] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111
[[1,2,3,5],[4,6],[7],[8],[9],[10]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,2,6],[3,7],[4,8],[5,9],[10]] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[[1,2,3,6],[4,7],[5,8],[9],[10]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,2,4,6],[3,5,7],[8],[9],[10]] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[[1,2,3,4,6],[5,7],[8],[9],[10]] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,2,3,7],[4,8],[5,9],[6,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,7],[3,5,8],[6,9],[10]] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,2,3,4,7],[5,8],[6,9],[10]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,2,3,5,7],[4,6,8],[9],[10]] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[[1,2,3,4,5,7],[6,8],[9],[10]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,5,8],[3,6,9],[4,7,10]] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 000100100
[[1,2,3,5,8],[4,6,9],[7,10]] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,2,3,4,5,8],[6,9],[7,10]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,2,4,6,8],[3,5,7,9],[10]] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,3,4,6,8],[5,7,9],[10]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,3,4,5,6,8],[7,9],[10]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,2,3,5,7,9],[4,6,8,10]] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[[1,2,3,4,5,7,9],[6,8,10]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,5,6,7,9],[8,10]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,6,7,9],[8]] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 00111111
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,6,10],[7,8,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 001111111
[[1,2,4,5,6,7,8,9],[3]] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 00000001
[[1,2,5,7,9],[3,6,8],[4]] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,4,5,6,7,8,9,10],[3]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,5,7,9,10],[3,6,8],[4]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,4,6,8,10],[3,5,7,9]] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 000001000
[[1,2,4,6,8,9,10],[3,5,7]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,6,7,8,10],[3,5,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,6,7,9,10],[3,5,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,6,7,8,9,10],[3,5]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,4,5,6,8,10],[3,7,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,5,6,9,10],[3,7,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,5,7,8,10],[3,6,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,5,7,9,10],[3,6,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,4,5,7,8,9,10],[3,6]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,4,5,6,7,8,10],[3,9]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,4,5,6,7,9,10],[3,8]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,4,5,6,8,9,10],[3,7]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,6,8,10],[5,7,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,6,9,10],[5,7,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,7,8,10],[5,6,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,7,9,10],[5,6,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,4,7,8,9,10],[5,6]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,5,6,8,10],[4,7,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,5,6,9,10],[4,7,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,5,7,8,10],[4,6,9]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,5,7,9,10],[4,6,8]] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 000000100
[[1,2,3,5,7,8,9,10],[4,6]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,5,6,7,8,10],[4,9]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,5,6,7,9,10],[4,8]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,5,6,8,9,10],[4,7]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,5,6,7,8,9,10],[4]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,6,8,10],[7,9]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,6,9,10],[7,8]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,7,8,10],[6,9]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,7,9,10],[6,8]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,5,8,9,10],[6,7]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,6,7,8,10],[5,9]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,6,7,9,10],[5,8]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,6,8,9,10],[5,7]] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 000000010
[[1,2,3,4,6,7,8,9,10],[5]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,6,7,9,10],[8]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,6,8,9,10],[7]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,3,4,5,7,8,9,10],[6]] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 000000001
[[1,2,5,6,7,8,9],[3],[4]] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 00000011
[[1,2,6,7,8,9],[3],[4],[5]] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[[1,2,7,8,9],[3],[4],[5],[6]] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 00001111
[[1,2,8,9],[3],[4],[5],[6],[7]] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[[1,2,5,6,7,8,9,10],[3],[4]] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[[1,2,6,7,8,9,10],[3],[4],[5]] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 000000111
[[1,2,7,8,9,10],[3],[4],[5],[6]] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 000011111
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[[1,2,3,4,7,8,9],[5,6]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,2,4,5,8,9],[3,7],[6]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,4,5,6,7],[3,9],[8]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,5,6,9],[3,8],[4],[7]] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,2,3,4,7,8],[5,6],[9]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,5,6,7,8],[3],[4],[9]] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 00000111
[[1,2,4,5],[3,7],[6,9],[8]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,2,6,7],[3,9],[4],[5],[8]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,2,5,6],[3,8],[4],[7],[9]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,2,7,8],[3],[4],[5],[6],[9]] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 00011111
[[1,2,4,5,8,9,10],[3,7],[6]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,2,4,5,6,7],[3,9,10],[8]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,3,4,9,10],[5,6],[7,8]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,2,5,6,9,10],[3,8],[4],[7]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,4,5,6,7,8,9],[3],[10]] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 000000011
[[1,2,3,4,7,8],[5,6],[9,10]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,2,5,6,7,8],[3,10],[4],[9]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,4,5,10],[3,7],[6,9],[8]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,2,6,7,10],[3,9],[4],[5],[8]] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,2,4,5,8,9],[3,7],[6],[10]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,6,7,8,9],[3],[4],[5],[10]] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 000001111
[[1,2,5,6],[3,8],[4,10],[7],[9]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,2,7,8],[3,10],[4],[5],[6],[9]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,2,4,5],[3,7],[6,9],[8],[10]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,2,6,7],[3,9],[4],[5],[8],[10]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,2,8,9],[3],[4],[5],[6],[7],[10]] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 000111111
[[1,2,3,5,7,9],[4,6,8]] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,2,3,4,5,7,9],[6,8]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,2,4,5],[3,8],[6,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,8],[3,9],[4],[5],[6],[7]] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 00101111
[[1,2,7],[3,8],[4,9],[5],[6]] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 00101011
[[1,2,7,9],[3,8],[4],[5],[6]] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 00010111
[[1,2,6,9],[3,7],[4,8],[5]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,2,6,8],[3,7,9],[4],[5]] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 00010011
[[1,2,6,8,9],[3,7],[4],[5]] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 00001011
[[1,2,5,8],[3,6,9],[4,7]] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 00010010
[[1,2,5,8,9],[3,6],[4,7]] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 00001010
[[1,2,5,7,8,9],[3,6],[4]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,4,6,8,9],[3,5,7]] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 00000100
[[1,2,4,6,7,8,9],[3,5]] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 00000010
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 001011111
[[1,2,8],[3,9],[4,10],[5],[6],[7]] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 001010111
[[1,2,8,10],[3,9],[4],[5],[6],[7]] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 000101111
[[1,2,7],[3,8],[4,9],[5,10],[6]] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 001010101
[[1,2,7,10],[3,8],[4,9],[5],[6]] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 000101011
[[1,2,7,9],[3,8,10],[4],[5],[6]] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 000100111
[[1,2,7,9,10],[3,8],[4],[5],[6]] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 000010111
[[1,2,6,10],[3,7],[4,8],[5,9]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,6,9],[3,7,10],[4,8],[5]] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,2,6,9,10],[3,7],[4,8],[5]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,2,6,8,10],[3,7,9],[4],[5]] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 000010011
[[1,2,6,8,9,10],[3,7],[4],[5]] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 000001011
[[1,2,5,8,10],[3,6,9],[4,7]] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,2,5,8,9,10],[3,6],[4,7]] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 000001010
[[1,2,5,7,9],[3,6,8,10],[4]] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,5,7,8,9,10],[3,6],[4]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
[[1,2,3,4],[5,6],[7,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,4],[5,7],[6,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,4],[5,7],[6,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,4],[5,8],[6,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,5],[4,6],[7,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,5],[4,6],[7,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,5],[4,7],[6,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,5],[4,7],[6,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,5],[4,8],[6,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,6],[4,7],[5,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,6],[4,7],[5,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,6],[4,8],[5,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,6],[3,5],[7,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,6],[3,5],[7,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,7],[3,5],[6,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,7],[3,5],[6,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,8],[3,5],[6,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,5],[3,6],[7,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,5],[3,6],[7,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,5],[3,7],[6,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,5],[3,7],[6,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,6],[3,7],[5,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,6],[3,7],[5,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,6],[3,8],[5,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,4,7],[3,8],[5,9],[6,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,8],[3,6],[4,7],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,9],[3,6],[4,7],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,7],[3,6],[4,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,7],[3,6],[4,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,8],[3,6],[4,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,6],[3,7],[4,8],[9,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,6],[3,7],[4,9],[8,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,6],[3,8],[4,9],[7,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,5,7],[3,8],[4,9],[6,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,6,9],[3,7],[4,8],[5,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,6,8],[3,7],[4,9],[5,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,6,7],[3,8],[4,9],[5,10]] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 000101010
[[1,2,3,4],[5,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,4],[5,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,5],[4,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,7],[5,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,7],[5,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,7],[5,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,7],[5,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,7],[5,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,8],[5,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,8],[5,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,8],[5,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,6],[4,9],[5,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,7],[4,8],[5,9],[6,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,7],[4,8],[5,9],[6,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,7],[4,8],[5,10],[6,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,7],[4,9],[5,10],[6,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,8],[4,9],[5,10],[6,11],[7,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,5],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,5],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,5],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,5],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,5],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,5],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,5],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,5],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,5],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,5],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,8],[3,5],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,8],[3,5],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,8],[3,5],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,9],[3,5],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,6],[7,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,6],[7,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,6],[7,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,6],[7,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,6],[7,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,7],[6,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,7],[6,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,7],[6,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,7],[6,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,7],[6,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,8],[6,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,8],[6,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,8],[6,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,5],[3,9],[6,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,7],[5,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,7],[5,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,7],[5,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,7],[5,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,7],[5,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,8],[5,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,8],[5,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,8],[5,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,6],[3,9],[5,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,8],[5,9],[6,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,8],[5,9],[6,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,8],[5,10],[6,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,7],[3,9],[5,10],[6,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,4,8],[3,9],[5,10],[6,11],[7,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,6],[4,7],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,6],[4,7],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,9],[3,6],[4,7],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,9],[3,6],[4,7],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,10],[3,6],[4,7],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,6],[4,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,6],[4,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,6],[4,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,6],[4,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,6],[4,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,6],[4,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,6],[4,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,6],[4,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,9],[3,6],[4,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,7],[4,8],[9,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,7],[4,8],[9,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,7],[4,9],[8,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,7],[4,9],[8,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,7],[4,10],[8,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,8],[4,9],[7,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,8],[4,9],[7,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,8],[4,10],[7,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,6],[3,9],[4,10],[7,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,8],[4,9],[6,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,8],[4,9],[6,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,8],[4,10],[6,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,7],[3,9],[4,10],[6,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,5,8],[3,9],[4,10],[6,11],[7,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,10],[3,7],[4,8],[5,9],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,11],[3,7],[4,8],[5,9],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,9],[3,7],[4,8],[5,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,9],[3,7],[4,8],[5,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,10],[3,7],[4,8],[5,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,8],[3,7],[4,9],[5,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,8],[3,7],[4,9],[5,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,8],[3,7],[4,10],[5,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,9],[3,7],[4,10],[5,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,7],[3,8],[4,9],[5,10],[11,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,7],[3,8],[4,9],[5,11],[10,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,7],[3,8],[4,10],[5,11],[9,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,7],[3,9],[4,10],[5,11],[8,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,6,8],[3,9],[4,10],[5,11],[7,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,7,12],[3,8],[4,9],[5,10],[6,11]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,7,11],[3,8],[4,9],[5,10],[6,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,7,10],[3,8],[4,9],[5,11],[6,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,7,9],[3,8],[4,10],[5,11],[6,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,7,8],[3,9],[4,10],[5,11],[6,12]] => [4,2,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10],[11,12]] => 00010101010
[[1,2,3,7],[4,8],[5,9],[6]] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 00010101
[[1,2,3,5,8],[4,6,9],[7]] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 00001001
[[1,2,3,4,5,8],[6,9],[7]] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 00000101
[[1,2,4,8],[3,5,9],[6,10],[7]] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 000100101
[[1,2,3,4,8],[5,9],[6,10],[7]] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 000010101
[[1,2,3,6,9],[4,7,10],[5,8]] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 000010010
[[1,2,4,6,9],[3,5,7,10],[8]] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 000010001
[[1,2,3,4,6,9],[5,7,10],[8]] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 000001001
[[1,2,3,4,5,6,9],[7,10],[8]] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 000000101
Map
shape
Description
Sends a tableau to its shape.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
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