Identifier
-
Mp00155:
Standard tableaux
—promotion⟶
Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000297: Binary words ⟶ ℤ
Values
[[1]] => [[1]] => [1] => 1 => 1
[[1,2]] => [[1,2]] => [2] => 10 => 1
[[1],[2]] => [[1],[2]] => [1,1] => 11 => 2
[[1,2,3]] => [[1,2,3]] => [3] => 100 => 1
[[1,3],[2]] => [[1,2],[3]] => [2,1] => 101 => 1
[[1,2],[3]] => [[1,3],[2]] => [1,2] => 110 => 2
[[1],[2],[3]] => [[1],[2],[3]] => [1,1,1] => 111 => 3
[[1,2,3,4]] => [[1,2,3,4]] => [4] => 1000 => 1
[[1,3,4],[2]] => [[1,2,4],[3]] => [2,2] => 1010 => 1
[[1,2,4],[3]] => [[1,2,3],[4]] => [3,1] => 1001 => 1
[[1,2,3],[4]] => [[1,3,4],[2]] => [1,3] => 1100 => 2
[[1,3],[2,4]] => [[1,2],[3,4]] => [2,2] => 1010 => 1
[[1,2],[3,4]] => [[1,3],[2,4]] => [1,2,1] => 1101 => 2
[[1,4],[2],[3]] => [[1,2],[3],[4]] => [2,1,1] => 1011 => 1
[[1,3],[2],[4]] => [[1,4],[2],[3]] => [1,1,2] => 1110 => 3
[[1,2],[3],[4]] => [[1,3],[2],[4]] => [1,2,1] => 1101 => 2
[[1],[2],[3],[4]] => [[1],[2],[3],[4]] => [1,1,1,1] => 1111 => 4
[[1,2,3,4,5]] => [[1,2,3,4,5]] => [5] => 10000 => 1
[[1,3,4,5],[2]] => [[1,2,4,5],[3]] => [2,3] => 10100 => 1
[[1,2,4,5],[3]] => [[1,2,3,5],[4]] => [3,2] => 10010 => 1
[[1,2,3,5],[4]] => [[1,2,3,4],[5]] => [4,1] => 10001 => 1
[[1,2,3,4],[5]] => [[1,3,4,5],[2]] => [1,4] => 11000 => 2
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => [2,2,1] => 10101 => 1
[[1,2,5],[3,4]] => [[1,2,3],[4,5]] => [3,2] => 10010 => 1
[[1,3,4],[2,5]] => [[1,2,5],[3,4]] => [2,3] => 10100 => 1
[[1,2,4],[3,5]] => [[1,3,5],[2,4]] => [1,2,2] => 11010 => 2
[[1,2,3],[4,5]] => [[1,3,4],[2,5]] => [1,3,1] => 11001 => 2
[[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => [2,1,2] => 10110 => 1
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => [2,2,1] => 10101 => 1
[[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => [3,1,1] => 10011 => 1
[[1,3,4],[2],[5]] => [[1,4,5],[2],[3]] => [1,1,3] => 11100 => 3
[[1,2,4],[3],[5]] => [[1,3,5],[2],[4]] => [1,2,2] => 11010 => 2
[[1,2,3],[4],[5]] => [[1,3,4],[2],[5]] => [1,3,1] => 11001 => 2
[[1,4],[2,5],[3]] => [[1,2],[3,5],[4]] => [2,1,2] => 10110 => 1
[[1,3],[2,5],[4]] => [[1,2],[3,4],[5]] => [2,2,1] => 10101 => 1
[[1,2],[3,5],[4]] => [[1,3],[2,4],[5]] => [1,2,1,1] => 11011 => 2
[[1,3],[2,4],[5]] => [[1,4],[2,5],[3]] => [1,1,2,1] => 11101 => 3
[[1,2],[3,4],[5]] => [[1,3],[2,5],[4]] => [1,2,2] => 11010 => 2
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 10111 => 1
[[1,4],[2],[3],[5]] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 11110 => 4
[[1,3],[2],[4],[5]] => [[1,4],[2],[3],[5]] => [1,1,2,1] => 11101 => 3
[[1,2],[3],[4],[5]] => [[1,3],[2],[4],[5]] => [1,2,1,1] => 11011 => 2
[[1],[2],[3],[4],[5]] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 11111 => 5
[[1,2,3,4,5,6]] => [[1,2,3,4,5,6]] => [6] => 100000 => 1
[[1,3,4,5,6],[2]] => [[1,2,4,5,6],[3]] => [2,4] => 101000 => 1
[[1,2,4,5,6],[3]] => [[1,2,3,5,6],[4]] => [3,3] => 100100 => 1
[[1,2,3,5,6],[4]] => [[1,2,3,4,6],[5]] => [4,2] => 100010 => 1
[[1,2,3,4,6],[5]] => [[1,2,3,4,5],[6]] => [5,1] => 100001 => 1
[[1,2,3,4,5],[6]] => [[1,3,4,5,6],[2]] => [1,5] => 110000 => 2
[[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => [2,2,2] => 101010 => 1
[[1,2,5,6],[3,4]] => [[1,2,3,6],[4,5]] => [3,3] => 100100 => 1
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => [2,3,1] => 101001 => 1
[[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => [3,2,1] => 100101 => 1
[[1,2,3,6],[4,5]] => [[1,2,3,4],[5,6]] => [4,2] => 100010 => 1
[[1,3,4,5],[2,6]] => [[1,2,5,6],[3,4]] => [2,4] => 101000 => 1
[[1,2,4,5],[3,6]] => [[1,3,5,6],[2,4]] => [1,2,3] => 110100 => 2
[[1,2,3,5],[4,6]] => [[1,3,4,6],[2,5]] => [1,3,2] => 110010 => 2
[[1,2,3,4],[5,6]] => [[1,3,4,5],[2,6]] => [1,4,1] => 110001 => 2
[[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => [2,1,3] => 101100 => 1
[[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => [2,2,2] => 101010 => 1
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => [3,1,2] => 100110 => 1
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => [2,3,1] => 101001 => 1
[[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => [3,2,1] => 100101 => 1
[[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => [4,1,1] => 100011 => 1
[[1,3,4,5],[2],[6]] => [[1,4,5,6],[2],[3]] => [1,1,4] => 111000 => 3
[[1,2,4,5],[3],[6]] => [[1,3,5,6],[2],[4]] => [1,2,3] => 110100 => 2
[[1,2,3,5],[4],[6]] => [[1,3,4,6],[2],[5]] => [1,3,2] => 110010 => 2
[[1,2,3,4],[5],[6]] => [[1,3,4,5],[2],[6]] => [1,4,1] => 110001 => 2
[[1,3,5],[2,4,6]] => [[1,2,4],[3,5,6]] => [2,2,2] => 101010 => 1
[[1,2,5],[3,4,6]] => [[1,2,3],[4,5,6]] => [3,3] => 100100 => 1
[[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]] => [2,3,1] => 101001 => 1
[[1,2,4],[3,5,6]] => [[1,3,5],[2,4,6]] => [1,2,2,1] => 110101 => 2
[[1,2,3],[4,5,6]] => [[1,3,4],[2,5,6]] => [1,3,2] => 110010 => 2
[[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => [2,1,2,1] => 101101 => 1
[[1,3,6],[2,5],[4]] => [[1,2,4],[3,6],[5]] => [2,2,2] => 101010 => 1
[[1,2,6],[3,5],[4]] => [[1,2,3],[4,6],[5]] => [3,1,2] => 100110 => 1
[[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => [2,2,1,1] => 101011 => 1
[[1,2,6],[3,4],[5]] => [[1,2,3],[4,5],[6]] => [3,2,1] => 100101 => 1
[[1,4,5],[2,6],[3]] => [[1,2,6],[3,5],[4]] => [2,1,3] => 101100 => 1
[[1,3,5],[2,6],[4]] => [[1,2,6],[3,4],[5]] => [2,2,2] => 101010 => 1
[[1,2,5],[3,6],[4]] => [[1,3,6],[2,4],[5]] => [1,2,1,2] => 110110 => 2
[[1,3,4],[2,6],[5]] => [[1,2,5],[3,4],[6]] => [2,3,1] => 101001 => 1
[[1,2,4],[3,6],[5]] => [[1,3,5],[2,4],[6]] => [1,2,2,1] => 110101 => 2
[[1,2,3],[4,6],[5]] => [[1,3,4],[2,5],[6]] => [1,3,1,1] => 110011 => 2
[[1,3,5],[2,4],[6]] => [[1,4,6],[2,5],[3]] => [1,1,2,2] => 111010 => 3
[[1,2,5],[3,4],[6]] => [[1,3,6],[2,5],[4]] => [1,2,3] => 110100 => 2
[[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]] => [1,1,3,1] => 111001 => 3
[[1,2,4],[3,5],[6]] => [[1,3,5],[2,6],[4]] => [1,2,2,1] => 110101 => 2
[[1,2,3],[4,5],[6]] => [[1,3,4],[2,6],[5]] => [1,3,2] => 110010 => 2
[[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => [2,1,1,2] => 101110 => 1
[[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => [2,1,2,1] => 101101 => 1
[[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => [2,2,1,1] => 101011 => 1
[[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 100111 => 1
[[1,4,5],[2],[3],[6]] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 111100 => 4
[[1,3,5],[2],[4],[6]] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 111010 => 3
[[1,2,5],[3],[4],[6]] => [[1,3,6],[2],[4],[5]] => [1,2,1,2] => 110110 => 2
[[1,3,4],[2],[5],[6]] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 111001 => 3
[[1,2,4],[3],[5],[6]] => [[1,3,5],[2],[4],[6]] => [1,2,2,1] => 110101 => 2
[[1,2,3],[4],[5],[6]] => [[1,3,4],[2],[5],[6]] => [1,3,1,1] => 110011 => 2
[[1,4],[2,5],[3,6]] => [[1,2],[3,5],[4,6]] => [2,1,2,1] => 101101 => 1
[[1,3],[2,5],[4,6]] => [[1,2],[3,4],[5,6]] => [2,2,2] => 101010 => 1
>>> Load all 1360 entries. <<<[[1,2],[3,5],[4,6]] => [[1,3],[2,4],[5,6]] => [1,2,1,2] => 110110 => 2
[[1,3],[2,4],[5,6]] => [[1,4],[2,5],[3,6]] => [1,1,2,2] => 111010 => 3
[[1,2],[3,4],[5,6]] => [[1,3],[2,5],[4,6]] => [1,2,2,1] => 110101 => 2
[[1,5],[2,6],[3],[4]] => [[1,2],[3,6],[4],[5]] => [2,1,1,2] => 101110 => 1
[[1,4],[2,6],[3],[5]] => [[1,2],[3,5],[4],[6]] => [2,1,2,1] => 101101 => 1
[[1,3],[2,6],[4],[5]] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 101011 => 1
[[1,2],[3,6],[4],[5]] => [[1,3],[2,4],[5],[6]] => [1,2,1,1,1] => 110111 => 2
[[1,4],[2,5],[3],[6]] => [[1,5],[2,6],[3],[4]] => [1,1,1,2,1] => 111101 => 4
[[1,3],[2,5],[4],[6]] => [[1,4],[2,6],[3],[5]] => [1,1,2,2] => 111010 => 3
[[1,2],[3,5],[4],[6]] => [[1,3],[2,6],[4],[5]] => [1,2,1,2] => 110110 => 2
[[1,3],[2,4],[5],[6]] => [[1,4],[2,5],[3],[6]] => [1,1,2,1,1] => 111011 => 3
[[1,2],[3,4],[5],[6]] => [[1,3],[2,5],[4],[6]] => [1,2,2,1] => 110101 => 2
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 101111 => 1
[[1,5],[2],[3],[4],[6]] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 111110 => 5
[[1,4],[2],[3],[5],[6]] => [[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 111101 => 4
[[1,3],[2],[4],[5],[6]] => [[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => 111011 => 3
[[1,2],[3],[4],[5],[6]] => [[1,3],[2],[4],[5],[6]] => [1,2,1,1,1] => 110111 => 2
[[1],[2],[3],[4],[5],[6]] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 111111 => 6
[[1,2,3,4,5,6,7]] => [[1,2,3,4,5,6,7]] => [7] => 1000000 => 1
[[1,3,4,5,6,7],[2]] => [[1,2,4,5,6,7],[3]] => [2,5] => 1010000 => 1
[[1,2,4,5,6,7],[3]] => [[1,2,3,5,6,7],[4]] => [3,4] => 1001000 => 1
[[1,2,3,5,6,7],[4]] => [[1,2,3,4,6,7],[5]] => [4,3] => 1000100 => 1
[[1,2,3,4,6,7],[5]] => [[1,2,3,4,5,7],[6]] => [5,2] => 1000010 => 1
[[1,2,3,4,5,7],[6]] => [[1,2,3,4,5,6],[7]] => [6,1] => 1000001 => 1
[[1,2,3,4,5,6],[7]] => [[1,3,4,5,6,7],[2]] => [1,6] => 1100000 => 2
[[1,3,5,6,7],[2,4]] => [[1,2,4,6,7],[3,5]] => [2,2,3] => 1010100 => 1
[[1,2,5,6,7],[3,4]] => [[1,2,3,6,7],[4,5]] => [3,4] => 1001000 => 1
[[1,3,4,6,7],[2,5]] => [[1,2,4,5,7],[3,6]] => [2,3,2] => 1010010 => 1
[[1,2,4,6,7],[3,5]] => [[1,2,3,5,7],[4,6]] => [3,2,2] => 1001010 => 1
[[1,2,3,6,7],[4,5]] => [[1,2,3,4,7],[5,6]] => [4,3] => 1000100 => 1
[[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => [2,4,1] => 1010001 => 1
[[1,2,4,5,7],[3,6]] => [[1,2,3,5,6],[4,7]] => [3,3,1] => 1001001 => 1
[[1,2,3,5,7],[4,6]] => [[1,2,3,4,6],[5,7]] => [4,2,1] => 1000101 => 1
[[1,2,3,4,7],[5,6]] => [[1,2,3,4,5],[6,7]] => [5,2] => 1000010 => 1
[[1,3,4,5,6],[2,7]] => [[1,2,5,6,7],[3,4]] => [2,5] => 1010000 => 1
[[1,2,4,5,6],[3,7]] => [[1,3,5,6,7],[2,4]] => [1,2,4] => 1101000 => 2
[[1,2,3,5,6],[4,7]] => [[1,3,4,6,7],[2,5]] => [1,3,3] => 1100100 => 2
[[1,2,3,4,6],[5,7]] => [[1,3,4,5,7],[2,6]] => [1,4,2] => 1100010 => 2
[[1,2,3,4,5],[6,7]] => [[1,3,4,5,6],[2,7]] => [1,5,1] => 1100001 => 2
[[1,4,5,6,7],[2],[3]] => [[1,2,5,6,7],[3],[4]] => [2,1,4] => 1011000 => 1
[[1,3,5,6,7],[2],[4]] => [[1,2,4,6,7],[3],[5]] => [2,2,3] => 1010100 => 1
[[1,2,5,6,7],[3],[4]] => [[1,2,3,6,7],[4],[5]] => [3,1,3] => 1001100 => 1
[[1,3,4,6,7],[2],[5]] => [[1,2,4,5,7],[3],[6]] => [2,3,2] => 1010010 => 1
[[1,2,4,6,7],[3],[5]] => [[1,2,3,5,7],[4],[6]] => [3,2,2] => 1001010 => 1
[[1,2,3,6,7],[4],[5]] => [[1,2,3,4,7],[5],[6]] => [4,1,2] => 1000110 => 1
[[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => [2,4,1] => 1010001 => 1
[[1,2,4,5,7],[3],[6]] => [[1,2,3,5,6],[4],[7]] => [3,3,1] => 1001001 => 1
[[1,2,3,5,7],[4],[6]] => [[1,2,3,4,6],[5],[7]] => [4,2,1] => 1000101 => 1
[[1,2,3,4,7],[5],[6]] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 1000011 => 1
[[1,3,4,5,6],[2],[7]] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 1110000 => 3
[[1,2,4,5,6],[3],[7]] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 1101000 => 2
[[1,2,3,5,6],[4],[7]] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 1100100 => 2
[[1,2,3,4,6],[5],[7]] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 1100010 => 2
[[1,2,3,4,5],[6],[7]] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 1100001 => 2
[[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,4,6]] => [[1,2,3,6],[4,5,7]] => [3,3,1] => 1001001 => 1
[[1,3,4,7],[2,5,6]] => [[1,2,4,5],[3,6,7]] => [2,3,2] => 1010010 => 1
[[1,2,4,7],[3,5,6]] => [[1,2,3,5],[4,6,7]] => [3,2,2] => 1001010 => 1
[[1,2,3,7],[4,5,6]] => [[1,2,3,4],[5,6,7]] => [4,3] => 1000100 => 1
[[1,3,5,6],[2,4,7]] => [[1,2,4,7],[3,5,6]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3,4,7]] => [[1,2,3,7],[4,5,6]] => [3,4] => 1001000 => 1
[[1,3,4,6],[2,5,7]] => [[1,2,5,7],[3,4,6]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3,5,7]] => [[1,3,5,7],[2,4,6]] => [1,2,2,2] => 1101010 => 2
[[1,2,3,6],[4,5,7]] => [[1,3,4,7],[2,5,6]] => [1,3,3] => 1100100 => 2
[[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]] => [2,4,1] => 1010001 => 1
[[1,2,4,5],[3,6,7]] => [[1,3,5,6],[2,4,7]] => [1,2,3,1] => 1101001 => 2
[[1,2,3,5],[4,6,7]] => [[1,3,4,6],[2,5,7]] => [1,3,2,1] => 1100101 => 2
[[1,2,3,4],[5,6,7]] => [[1,3,4,5],[2,6,7]] => [1,4,2] => 1100010 => 2
[[1,4,6,7],[2,5],[3]] => [[1,2,5,7],[3,6],[4]] => [2,1,2,2] => 1011010 => 1
[[1,3,6,7],[2,5],[4]] => [[1,2,4,7],[3,6],[5]] => [2,2,3] => 1010100 => 1
[[1,2,6,7],[3,5],[4]] => [[1,2,3,7],[4,6],[5]] => [3,1,3] => 1001100 => 1
[[1,3,6,7],[2,4],[5]] => [[1,2,4,7],[3,5],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2,6,7],[3,4],[5]] => [[1,2,3,7],[4,5],[6]] => [3,2,2] => 1001010 => 1
[[1,4,5,7],[2,6],[3]] => [[1,2,5,6],[3,7],[4]] => [2,1,3,1] => 1011001 => 1
[[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,7],[5]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,6],[4]] => [[1,2,3,6],[4,7],[5]] => [3,1,2,1] => 1001101 => 1
[[1,3,4,7],[2,6],[5]] => [[1,2,4,5],[3,7],[6]] => [2,3,2] => 1010010 => 1
[[1,2,4,7],[3,6],[5]] => [[1,2,3,5],[4,7],[6]] => [3,2,2] => 1001010 => 1
[[1,2,3,7],[4,6],[5]] => [[1,2,3,4],[5,7],[6]] => [4,1,2] => 1000110 => 1
[[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,5],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,4],[6]] => [[1,2,3,6],[4,5],[7]] => [3,3,1] => 1001001 => 1
[[1,3,4,7],[2,5],[6]] => [[1,2,4,5],[3,6],[7]] => [2,3,1,1] => 1010011 => 1
[[1,2,4,7],[3,5],[6]] => [[1,2,3,5],[4,6],[7]] => [3,2,1,1] => 1001011 => 1
[[1,2,3,7],[4,5],[6]] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 1000101 => 1
[[1,4,5,6],[2,7],[3]] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 1011000 => 1
[[1,3,5,6],[2,7],[4]] => [[1,2,6,7],[3,4],[5]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3,7],[4]] => [[1,3,6,7],[2,4],[5]] => [1,2,1,3] => 1101100 => 2
[[1,3,4,6],[2,7],[5]] => [[1,2,5,7],[3,4],[6]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3,7],[5]] => [[1,3,5,7],[2,4],[6]] => [1,2,2,2] => 1101010 => 2
[[1,2,3,6],[4,7],[5]] => [[1,3,4,7],[2,5],[6]] => [1,3,1,2] => 1100110 => 2
[[1,3,4,5],[2,7],[6]] => [[1,2,5,6],[3,4],[7]] => [2,4,1] => 1010001 => 1
[[1,2,4,5],[3,7],[6]] => [[1,3,5,6],[2,4],[7]] => [1,2,3,1] => 1101001 => 2
[[1,2,3,5],[4,7],[6]] => [[1,3,4,6],[2,5],[7]] => [1,3,2,1] => 1100101 => 2
[[1,2,3,4],[5,7],[6]] => [[1,3,4,5],[2,6],[7]] => [1,4,1,1] => 1100011 => 2
[[1,3,5,6],[2,4],[7]] => [[1,4,6,7],[2,5],[3]] => [1,1,2,3] => 1110100 => 3
[[1,2,5,6],[3,4],[7]] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 1101000 => 2
[[1,3,4,6],[2,5],[7]] => [[1,4,5,7],[2,6],[3]] => [1,1,3,2] => 1110010 => 3
[[1,2,4,6],[3,5],[7]] => [[1,3,5,7],[2,6],[4]] => [1,2,2,2] => 1101010 => 2
[[1,2,3,6],[4,5],[7]] => [[1,3,4,7],[2,6],[5]] => [1,3,3] => 1100100 => 2
[[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]] => [1,1,4,1] => 1110001 => 3
[[1,2,4,5],[3,6],[7]] => [[1,3,5,6],[2,7],[4]] => [1,2,3,1] => 1101001 => 2
[[1,2,3,5],[4,6],[7]] => [[1,3,4,6],[2,7],[5]] => [1,3,2,1] => 1100101 => 2
[[1,2,3,4],[5,6],[7]] => [[1,3,4,5],[2,7],[6]] => [1,4,2] => 1100010 => 2
[[1,5,6,7],[2],[3],[4]] => [[1,2,6,7],[3],[4],[5]] => [2,1,1,3] => 1011100 => 1
[[1,4,6,7],[2],[3],[5]] => [[1,2,5,7],[3],[4],[6]] => [2,1,2,2] => 1011010 => 1
[[1,3,6,7],[2],[4],[5]] => [[1,2,4,7],[3],[5],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2,6,7],[3],[4],[5]] => [[1,2,3,7],[4],[5],[6]] => [3,1,1,2] => 1001110 => 1
[[1,4,5,7],[2],[3],[6]] => [[1,2,5,6],[3],[4],[7]] => [2,1,3,1] => 1011001 => 1
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3],[4],[6]] => [[1,2,3,6],[4],[5],[7]] => [3,1,2,1] => 1001101 => 1
[[1,3,4,7],[2],[5],[6]] => [[1,2,4,5],[3],[6],[7]] => [2,3,1,1] => 1010011 => 1
[[1,2,4,7],[3],[5],[6]] => [[1,2,3,5],[4],[6],[7]] => [3,2,1,1] => 1001011 => 1
[[1,2,3,7],[4],[5],[6]] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 1000111 => 1
[[1,4,5,6],[2],[3],[7]] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 1111000 => 4
[[1,3,5,6],[2],[4],[7]] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 1110100 => 3
[[1,2,5,6],[3],[4],[7]] => [[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 1101100 => 2
[[1,3,4,6],[2],[5],[7]] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 1110010 => 3
[[1,2,4,6],[3],[5],[7]] => [[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 1101010 => 2
[[1,2,3,6],[4],[5],[7]] => [[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 1100110 => 2
[[1,3,4,5],[2],[6],[7]] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 1110001 => 3
[[1,2,4,5],[3],[6],[7]] => [[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 1101001 => 2
[[1,2,3,5],[4],[6],[7]] => [[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 1100101 => 2
[[1,2,3,4],[5],[6],[7]] => [[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 1100011 => 2
[[1,4,6],[2,5,7],[3]] => [[1,2,5],[3,6,7],[4]] => [2,1,2,2] => 1011010 => 1
[[1,3,6],[2,5,7],[4]] => [[1,2,4],[3,6,7],[5]] => [2,2,3] => 1010100 => 1
[[1,2,6],[3,5,7],[4]] => [[1,2,3],[4,6,7],[5]] => [3,1,3] => 1001100 => 1
[[1,3,6],[2,4,7],[5]] => [[1,2,4],[3,5,7],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2,6],[3,4,7],[5]] => [[1,2,3],[4,5,7],[6]] => [3,2,2] => 1001010 => 1
[[1,4,5],[2,6,7],[3]] => [[1,2,6],[3,5,7],[4]] => [2,1,3,1] => 1011001 => 1
[[1,3,5],[2,6,7],[4]] => [[1,2,6],[3,4,7],[5]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,6,7],[4]] => [[1,3,6],[2,4,7],[5]] => [1,2,1,2,1] => 1101101 => 2
[[1,3,4],[2,6,7],[5]] => [[1,2,5],[3,4,7],[6]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,6,7],[5]] => [[1,3,5],[2,4,7],[6]] => [1,2,2,2] => 1101010 => 2
[[1,2,3],[4,6,7],[5]] => [[1,3,4],[2,5,7],[6]] => [1,3,1,2] => 1100110 => 2
[[1,3,5],[2,4,7],[6]] => [[1,2,4],[3,5,6],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,4,7],[6]] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 1001001 => 1
[[1,3,4],[2,5,7],[6]] => [[1,2,5],[3,4,6],[7]] => [2,3,1,1] => 1010011 => 1
[[1,2,4],[3,5,7],[6]] => [[1,3,5],[2,4,6],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,2,3],[4,5,7],[6]] => [[1,3,4],[2,5,6],[7]] => [1,3,2,1] => 1100101 => 2
[[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]] => [1,1,2,2,1] => 1110101 => 3
[[1,2,5],[3,4,6],[7]] => [[1,3,6],[2,5,7],[4]] => [1,2,3,1] => 1101001 => 2
[[1,3,4],[2,5,6],[7]] => [[1,4,5],[2,6,7],[3]] => [1,1,3,2] => 1110010 => 3
[[1,2,4],[3,5,6],[7]] => [[1,3,5],[2,6,7],[4]] => [1,2,2,2] => 1101010 => 2
[[1,2,3],[4,5,6],[7]] => [[1,3,4],[2,6,7],[5]] => [1,3,3] => 1100100 => 2
[[1,4,7],[2,5],[3,6]] => [[1,2,5],[3,6],[4,7]] => [2,1,2,2] => 1011010 => 1
[[1,3,7],[2,5],[4,6]] => [[1,2,4],[3,6],[5,7]] => [2,2,2,1] => 1010101 => 1
[[1,2,7],[3,5],[4,6]] => [[1,2,3],[4,6],[5,7]] => [3,1,2,1] => 1001101 => 1
[[1,3,7],[2,4],[5,6]] => [[1,2,4],[3,5],[6,7]] => [2,2,1,2] => 1010110 => 1
[[1,2,7],[3,4],[5,6]] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 1001010 => 1
[[1,4,6],[2,5],[3,7]] => [[1,2,7],[3,5],[4,6]] => [2,1,2,2] => 1011010 => 1
[[1,3,6],[2,5],[4,7]] => [[1,2,7],[3,4],[5,6]] => [2,2,3] => 1010100 => 1
[[1,2,6],[3,5],[4,7]] => [[1,3,7],[2,4],[5,6]] => [1,2,1,3] => 1101100 => 2
[[1,3,6],[2,4],[5,7]] => [[1,4,7],[2,5],[3,6]] => [1,1,2,3] => 1110100 => 3
[[1,2,6],[3,4],[5,7]] => [[1,3,7],[2,5],[4,6]] => [1,2,2,2] => 1101010 => 2
[[1,4,5],[2,6],[3,7]] => [[1,2,6],[3,5],[4,7]] => [2,1,3,1] => 1011001 => 1
[[1,3,5],[2,6],[4,7]] => [[1,2,6],[3,4],[5,7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,6],[4,7]] => [[1,3,6],[2,4],[5,7]] => [1,2,1,2,1] => 1101101 => 2
[[1,3,4],[2,6],[5,7]] => [[1,2,5],[3,4],[6,7]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,6],[5,7]] => [[1,3,5],[2,4],[6,7]] => [1,2,2,2] => 1101010 => 2
[[1,2,3],[4,6],[5,7]] => [[1,3,4],[2,5],[6,7]] => [1,3,1,2] => 1100110 => 2
[[1,3,5],[2,4],[6,7]] => [[1,4,6],[2,5],[3,7]] => [1,1,2,2,1] => 1110101 => 3
[[1,2,5],[3,4],[6,7]] => [[1,3,6],[2,5],[4,7]] => [1,2,3,1] => 1101001 => 2
[[1,3,4],[2,5],[6,7]] => [[1,4,5],[2,6],[3,7]] => [1,1,3,2] => 1110010 => 3
[[1,2,4],[3,5],[6,7]] => [[1,3,5],[2,6],[4,7]] => [1,2,2,2] => 1101010 => 2
[[1,2,3],[4,5],[6,7]] => [[1,3,4],[2,6],[5,7]] => [1,3,2,1] => 1100101 => 2
[[1,5,7],[2,6],[3],[4]] => [[1,2,6],[3,7],[4],[5]] => [2,1,1,2,1] => 1011101 => 1
[[1,4,7],[2,6],[3],[5]] => [[1,2,5],[3,7],[4],[6]] => [2,1,2,2] => 1011010 => 1
[[1,3,7],[2,6],[4],[5]] => [[1,2,4],[3,7],[5],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2,7],[3,6],[4],[5]] => [[1,2,3],[4,7],[5],[6]] => [3,1,1,2] => 1001110 => 1
[[1,4,7],[2,5],[3],[6]] => [[1,2,5],[3,6],[4],[7]] => [2,1,2,1,1] => 1011011 => 1
[[1,3,7],[2,5],[4],[6]] => [[1,2,4],[3,6],[5],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2,7],[3,5],[4],[6]] => [[1,2,3],[4,6],[5],[7]] => [3,1,2,1] => 1001101 => 1
[[1,3,7],[2,4],[5],[6]] => [[1,2,4],[3,5],[6],[7]] => [2,2,1,1,1] => 1010111 => 1
[[1,2,7],[3,4],[5],[6]] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 1001011 => 1
[[1,5,6],[2,7],[3],[4]] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 1011100 => 1
[[1,4,6],[2,7],[3],[5]] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 1011010 => 1
[[1,3,6],[2,7],[4],[5]] => [[1,2,7],[3,4],[5],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2,6],[3,7],[4],[5]] => [[1,3,7],[2,4],[5],[6]] => [1,2,1,1,2] => 1101110 => 2
[[1,4,5],[2,7],[3],[6]] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 1011001 => 1
[[1,3,5],[2,7],[4],[6]] => [[1,2,6],[3,4],[5],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,7],[4],[6]] => [[1,3,6],[2,4],[5],[7]] => [1,2,1,2,1] => 1101101 => 2
[[1,3,4],[2,7],[5],[6]] => [[1,2,5],[3,4],[6],[7]] => [2,3,1,1] => 1010011 => 1
[[1,2,4],[3,7],[5],[6]] => [[1,3,5],[2,4],[6],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,2,3],[4,7],[5],[6]] => [[1,3,4],[2,5],[6],[7]] => [1,3,1,1,1] => 1100111 => 2
[[1,4,6],[2,5],[3],[7]] => [[1,5,7],[2,6],[3],[4]] => [1,1,1,2,2] => 1111010 => 4
[[1,3,6],[2,5],[4],[7]] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 1110100 => 3
[[1,2,6],[3,5],[4],[7]] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 1101100 => 2
[[1,3,6],[2,4],[5],[7]] => [[1,4,7],[2,5],[3],[6]] => [1,1,2,1,2] => 1110110 => 3
[[1,2,6],[3,4],[5],[7]] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 1101010 => 2
[[1,4,5],[2,6],[3],[7]] => [[1,5,6],[2,7],[3],[4]] => [1,1,1,3,1] => 1111001 => 4
[[1,3,5],[2,6],[4],[7]] => [[1,4,6],[2,7],[3],[5]] => [1,1,2,2,1] => 1110101 => 3
[[1,2,5],[3,6],[4],[7]] => [[1,3,6],[2,7],[4],[5]] => [1,2,1,2,1] => 1101101 => 2
[[1,3,4],[2,6],[5],[7]] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 1110010 => 3
[[1,2,4],[3,6],[5],[7]] => [[1,3,5],[2,7],[4],[6]] => [1,2,2,2] => 1101010 => 2
[[1,2,3],[4,6],[5],[7]] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 1100110 => 2
[[1,3,5],[2,4],[6],[7]] => [[1,4,6],[2,5],[3],[7]] => [1,1,2,2,1] => 1110101 => 3
[[1,2,5],[3,4],[6],[7]] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 1101001 => 2
[[1,3,4],[2,5],[6],[7]] => [[1,4,5],[2,6],[3],[7]] => [1,1,3,1,1] => 1110011 => 3
[[1,2,4],[3,5],[6],[7]] => [[1,3,5],[2,6],[4],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,2,3],[4,5],[6],[7]] => [[1,3,4],[2,6],[5],[7]] => [1,3,2,1] => 1100101 => 2
[[1,6,7],[2],[3],[4],[5]] => [[1,2,7],[3],[4],[5],[6]] => [2,1,1,1,2] => 1011110 => 1
[[1,5,7],[2],[3],[4],[6]] => [[1,2,6],[3],[4],[5],[7]] => [2,1,1,2,1] => 1011101 => 1
[[1,4,7],[2],[3],[5],[6]] => [[1,2,5],[3],[4],[6],[7]] => [2,1,2,1,1] => 1011011 => 1
[[1,3,7],[2],[4],[5],[6]] => [[1,2,4],[3],[5],[6],[7]] => [2,2,1,1,1] => 1010111 => 1
[[1,2,7],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 1001111 => 1
[[1,5,6],[2],[3],[4],[7]] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 1111100 => 5
[[1,4,6],[2],[3],[5],[7]] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 1111010 => 4
[[1,3,6],[2],[4],[5],[7]] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 1110110 => 3
[[1,2,6],[3],[4],[5],[7]] => [[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => 1101110 => 2
[[1,4,5],[2],[3],[6],[7]] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 1111001 => 4
[[1,3,5],[2],[4],[6],[7]] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 1110101 => 3
[[1,2,5],[3],[4],[6],[7]] => [[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => 1101101 => 2
[[1,3,4],[2],[5],[6],[7]] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 1110011 => 3
[[1,2,4],[3],[5],[6],[7]] => [[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,2,3],[4],[5],[6],[7]] => [[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1] => 1100111 => 2
[[1,5],[2,6],[3,7],[4]] => [[1,2],[3,6],[4,7],[5]] => [2,1,1,2,1] => 1011101 => 1
[[1,4],[2,6],[3,7],[5]] => [[1,2],[3,5],[4,7],[6]] => [2,1,2,2] => 1011010 => 1
[[1,3],[2,6],[4,7],[5]] => [[1,2],[3,4],[5,7],[6]] => [2,2,1,2] => 1010110 => 1
[[1,2],[3,6],[4,7],[5]] => [[1,3],[2,4],[5,7],[6]] => [1,2,1,1,2] => 1101110 => 2
[[1,4],[2,5],[3,7],[6]] => [[1,2],[3,5],[4,6],[7]] => [2,1,2,1,1] => 1011011 => 1
[[1,3],[2,5],[4,7],[6]] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 1010101 => 1
[[1,2],[3,5],[4,7],[6]] => [[1,3],[2,4],[5,6],[7]] => [1,2,1,2,1] => 1101101 => 2
[[1,3],[2,4],[5,7],[6]] => [[1,4],[2,5],[3,6],[7]] => [1,1,2,2,1] => 1110101 => 3
[[1,2],[3,4],[5,7],[6]] => [[1,3],[2,5],[4,6],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,4],[2,5],[3,6],[7]] => [[1,5],[2,6],[3,7],[4]] => [1,1,1,2,2] => 1111010 => 4
[[1,3],[2,5],[4,6],[7]] => [[1,4],[2,6],[3,7],[5]] => [1,1,2,2,1] => 1110101 => 3
[[1,2],[3,5],[4,6],[7]] => [[1,3],[2,6],[4,7],[5]] => [1,2,1,2,1] => 1101101 => 2
[[1,3],[2,4],[5,6],[7]] => [[1,4],[2,5],[3,7],[6]] => [1,1,2,1,2] => 1110110 => 3
[[1,2],[3,4],[5,6],[7]] => [[1,3],[2,5],[4,7],[6]] => [1,2,2,2] => 1101010 => 2
[[1,6],[2,7],[3],[4],[5]] => [[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 1011110 => 1
[[1,5],[2,7],[3],[4],[6]] => [[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => 1011101 => 1
[[1,4],[2,7],[3],[5],[6]] => [[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1] => 1011011 => 1
[[1,3],[2,7],[4],[5],[6]] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 1010111 => 1
[[1,2],[3,7],[4],[5],[6]] => [[1,3],[2,4],[5],[6],[7]] => [1,2,1,1,1,1] => 1101111 => 2
[[1,5],[2,6],[3],[4],[7]] => [[1,6],[2,7],[3],[4],[5]] => [1,1,1,1,2,1] => 1111101 => 5
[[1,4],[2,6],[3],[5],[7]] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 1111010 => 4
[[1,3],[2,6],[4],[5],[7]] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 1110110 => 3
[[1,2],[3,6],[4],[5],[7]] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 1101110 => 2
[[1,4],[2,5],[3],[6],[7]] => [[1,5],[2,6],[3],[4],[7]] => [1,1,1,2,1,1] => 1111011 => 4
[[1,3],[2,5],[4],[6],[7]] => [[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => 1110101 => 3
[[1,2],[3,5],[4],[6],[7]] => [[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 1101101 => 2
[[1,3],[2,4],[5],[6],[7]] => [[1,4],[2,5],[3],[6],[7]] => [1,1,2,1,1,1] => 1110111 => 3
[[1,2],[3,4],[5],[6],[7]] => [[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1] => 1101011 => 2
[[1,7],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 1011111 => 1
[[1,6],[2],[3],[4],[5],[7]] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 1111110 => 6
[[1,5],[2],[3],[4],[6],[7]] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 1111101 => 5
[[1,4],[2],[3],[5],[6],[7]] => [[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 1111011 => 4
[[1,3],[2],[4],[5],[6],[7]] => [[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => 1110111 => 3
[[1,2],[3],[4],[5],[6],[7]] => [[1,3],[2],[4],[5],[6],[7]] => [1,2,1,1,1,1] => 1101111 => 2
[[1],[2],[3],[4],[5],[6],[7]] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 1111111 => 7
[[1,2,3,4,5,6,7,8]] => [[1,2,3,4,5,6,7,8]] => [8] => 10000000 => 1
[[1,3,4,5,6,7,8],[2]] => [[1,2,4,5,6,7,8],[3]] => [2,6] => 10100000 => 1
[[1,2,4,5,6,7,8],[3]] => [[1,2,3,5,6,7,8],[4]] => [3,5] => 10010000 => 1
[[1,2,3,5,6,7,8],[4]] => [[1,2,3,4,6,7,8],[5]] => [4,4] => 10001000 => 1
[[1,2,3,4,6,7,8],[5]] => [[1,2,3,4,5,7,8],[6]] => [5,3] => 10000100 => 1
[[1,2,3,4,5,7,8],[6]] => [[1,2,3,4,5,6,8],[7]] => [6,2] => 10000010 => 1
[[1,2,3,4,5,6,8],[7]] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 10000001 => 1
[[1,2,3,4,5,6,7],[8]] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 11000000 => 2
[[1,3,5,6,7,8],[2,4]] => [[1,2,4,6,7,8],[3,5]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7,8],[3,4]] => [[1,2,3,6,7,8],[4,5]] => [3,5] => 10010000 => 1
[[1,3,4,6,7,8],[2,5]] => [[1,2,4,5,7,8],[3,6]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7,8],[3,5]] => [[1,2,3,5,7,8],[4,6]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7,8],[4,5]] => [[1,2,3,4,7,8],[5,6]] => [4,4] => 10001000 => 1
[[1,3,4,5,7,8],[2,6]] => [[1,2,4,5,6,8],[3,7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7,8],[3,6]] => [[1,2,3,5,6,8],[4,7]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7,8],[4,6]] => [[1,2,3,4,6,8],[5,7]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7,8],[5,6]] => [[1,2,3,4,5,8],[6,7]] => [5,3] => 10000100 => 1
[[1,3,4,5,6,8],[2,7]] => [[1,2,4,5,6,7],[3,8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6,8],[3,7]] => [[1,2,3,5,6,7],[4,8]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6,8],[4,7]] => [[1,2,3,4,6,7],[5,8]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6,8],[5,7]] => [[1,2,3,4,5,7],[6,8]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5,8],[6,7]] => [[1,2,3,4,5,6],[7,8]] => [6,2] => 10000010 => 1
[[1,3,4,5,6,7],[2,8]] => [[1,2,5,6,7,8],[3,4]] => [2,6] => 10100000 => 1
[[1,2,4,5,6,7],[3,8]] => [[1,3,5,6,7,8],[2,4]] => [1,2,5] => 11010000 => 2
[[1,2,3,5,6,7],[4,8]] => [[1,3,4,6,7,8],[2,5]] => [1,3,4] => 11001000 => 2
[[1,2,3,4,6,7],[5,8]] => [[1,3,4,5,7,8],[2,6]] => [1,4,3] => 11000100 => 2
[[1,2,3,4,5,7],[6,8]] => [[1,3,4,5,6,8],[2,7]] => [1,5,2] => 11000010 => 2
[[1,2,3,4,5,6],[7,8]] => [[1,3,4,5,6,7],[2,8]] => [1,6,1] => 11000001 => 2
[[1,4,5,6,7,8],[2],[3]] => [[1,2,5,6,7,8],[3],[4]] => [2,1,5] => 10110000 => 1
[[1,3,5,6,7,8],[2],[4]] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7,8],[3],[4]] => [[1,2,3,6,7,8],[4],[5]] => [3,1,4] => 10011000 => 1
[[1,3,4,6,7,8],[2],[5]] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7,8],[3],[5]] => [[1,2,3,5,7,8],[4],[6]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7,8],[4],[5]] => [[1,2,3,4,7,8],[5],[6]] => [4,1,3] => 10001100 => 1
[[1,3,4,5,7,8],[2],[6]] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7,8],[3],[6]] => [[1,2,3,5,6,8],[4],[7]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7,8],[4],[6]] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7,8],[5],[6]] => [[1,2,3,4,5,8],[6],[7]] => [5,1,2] => 10000110 => 1
[[1,3,4,5,6,8],[2],[7]] => [[1,2,4,5,6,7],[3],[8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6,8],[3],[7]] => [[1,2,3,5,6,7],[4],[8]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6,8],[4],[7]] => [[1,2,3,4,6,7],[5],[8]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6,8],[5],[7]] => [[1,2,3,4,5,7],[6],[8]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5,8],[6],[7]] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 10000011 => 1
[[1,3,4,5,6,7],[2],[8]] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 11100000 => 3
[[1,2,4,5,6,7],[3],[8]] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 11010000 => 2
[[1,2,3,5,6,7],[4],[8]] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 11001000 => 2
[[1,2,3,4,6,7],[5],[8]] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 11000100 => 2
[[1,2,3,4,5,7],[6],[8]] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 11000010 => 2
[[1,2,3,4,5,6],[7],[8]] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 11000001 => 2
[[1,3,5,7,8],[2,4,6]] => [[1,2,4,6,8],[3,5,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,4,6]] => [[1,2,3,6,8],[4,5,7]] => [3,3,2] => 10010010 => 1
[[1,3,4,7,8],[2,5,6]] => [[1,2,4,5,8],[3,6,7]] => [2,3,3] => 10100100 => 1
[[1,2,4,7,8],[3,5,6]] => [[1,2,3,5,8],[4,6,7]] => [3,2,3] => 10010100 => 1
[[1,2,3,7,8],[4,5,6]] => [[1,2,3,4,8],[5,6,7]] => [4,4] => 10001000 => 1
[[1,3,5,6,8],[2,4,7]] => [[1,2,4,6,7],[3,5,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,4,7]] => [[1,2,3,6,7],[4,5,8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6,8],[2,5,7]] => [[1,2,4,5,7],[3,6,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,5,7]] => [[1,2,3,5,7],[4,6,8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,5,7]] => [[1,2,3,4,7],[5,6,8]] => [4,3,1] => 10001001 => 1
[[1,3,4,5,8],[2,6,7]] => [[1,2,4,5,6],[3,7,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,8],[3,6,7]] => [[1,2,3,5,6],[4,7,8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,8],[4,6,7]] => [[1,2,3,4,6],[5,7,8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,8],[5,6,7]] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 10000100 => 1
[[1,3,5,6,7],[2,4,8]] => [[1,2,4,7,8],[3,5,6]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3,4,8]] => [[1,2,3,7,8],[4,5,6]] => [3,5] => 10010000 => 1
[[1,3,4,6,7],[2,5,8]] => [[1,2,5,7,8],[3,4,6]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3,5,8]] => [[1,3,5,7,8],[2,4,6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,6,7],[4,5,8]] => [[1,3,4,7,8],[2,5,6]] => [1,3,4] => 11001000 => 2
[[1,3,4,5,7],[2,6,8]] => [[1,2,5,6,8],[3,4,7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3,6,8]] => [[1,3,5,6,8],[2,4,7]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5,7],[4,6,8]] => [[1,3,4,6,8],[2,5,7]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4,7],[5,6,8]] => [[1,3,4,5,8],[2,6,7]] => [1,4,3] => 11000100 => 2
[[1,3,4,5,6],[2,7,8]] => [[1,2,5,6,7],[3,4,8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6],[3,7,8]] => [[1,3,5,6,7],[2,4,8]] => [1,2,4,1] => 11010001 => 2
[[1,2,3,5,6],[4,7,8]] => [[1,3,4,6,7],[2,5,8]] => [1,3,3,1] => 11001001 => 2
[[1,2,3,4,6],[5,7,8]] => [[1,3,4,5,7],[2,6,8]] => [1,4,2,1] => 11000101 => 2
[[1,2,3,4,5],[6,7,8]] => [[1,3,4,5,6],[2,7,8]] => [1,5,2] => 11000010 => 2
[[1,4,6,7,8],[2,5],[3]] => [[1,2,5,7,8],[3,6],[4]] => [2,1,2,3] => 10110100 => 1
[[1,3,6,7,8],[2,5],[4]] => [[1,2,4,7,8],[3,6],[5]] => [2,2,4] => 10101000 => 1
[[1,2,6,7,8],[3,5],[4]] => [[1,2,3,7,8],[4,6],[5]] => [3,1,4] => 10011000 => 1
[[1,3,6,7,8],[2,4],[5]] => [[1,2,4,7,8],[3,5],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,6,7,8],[3,4],[5]] => [[1,2,3,7,8],[4,5],[6]] => [3,2,3] => 10010100 => 1
[[1,4,5,7,8],[2,6],[3]] => [[1,2,5,6,8],[3,7],[4]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,7,8],[2,6],[4]] => [[1,2,4,6,8],[3,7],[5]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,6],[4]] => [[1,2,3,6,8],[4,7],[5]] => [3,1,2,2] => 10011010 => 1
[[1,3,4,7,8],[2,6],[5]] => [[1,2,4,5,8],[3,7],[6]] => [2,3,3] => 10100100 => 1
[[1,2,4,7,8],[3,6],[5]] => [[1,2,3,5,8],[4,7],[6]] => [3,2,3] => 10010100 => 1
[[1,2,3,7,8],[4,6],[5]] => [[1,2,3,4,8],[5,7],[6]] => [4,1,3] => 10001100 => 1
[[1,3,5,7,8],[2,4],[6]] => [[1,2,4,6,8],[3,5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,4],[6]] => [[1,2,3,6,8],[4,5],[7]] => [3,3,2] => 10010010 => 1
[[1,3,4,7,8],[2,5],[6]] => [[1,2,4,5,8],[3,6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,7,8],[3,5],[6]] => [[1,2,3,5,8],[4,6],[7]] => [3,2,1,2] => 10010110 => 1
[[1,2,3,7,8],[4,5],[6]] => [[1,2,3,4,8],[5,6],[7]] => [4,2,2] => 10001010 => 1
[[1,4,5,6,8],[2,7],[3]] => [[1,2,5,6,7],[3,8],[4]] => [2,1,4,1] => 10110001 => 1
[[1,3,5,6,8],[2,7],[4]] => [[1,2,4,6,7],[3,8],[5]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,7],[4]] => [[1,2,3,6,7],[4,8],[5]] => [3,1,3,1] => 10011001 => 1
[[1,3,4,6,8],[2,7],[5]] => [[1,2,4,5,7],[3,8],[6]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,7],[5]] => [[1,2,3,5,7],[4,8],[6]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,7],[5]] => [[1,2,3,4,7],[5,8],[6]] => [4,1,2,1] => 10001101 => 1
[[1,3,4,5,8],[2,7],[6]] => [[1,2,4,5,6],[3,8],[7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,8],[3,7],[6]] => [[1,2,3,5,6],[4,8],[7]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,8],[4,7],[6]] => [[1,2,3,4,6],[5,8],[7]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,8],[5,7],[6]] => [[1,2,3,4,5],[6,8],[7]] => [5,1,2] => 10000110 => 1
[[1,3,5,6,8],[2,4],[7]] => [[1,2,4,6,7],[3,5],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,4],[7]] => [[1,2,3,6,7],[4,5],[8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6,8],[2,5],[7]] => [[1,2,4,5,7],[3,6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,5],[7]] => [[1,2,3,5,7],[4,6],[8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,5],[7]] => [[1,2,3,4,7],[5,6],[8]] => [4,3,1] => 10001001 => 1
[[1,3,4,5,8],[2,6],[7]] => [[1,2,4,5,6],[3,7],[8]] => [2,4,1,1] => 10100011 => 1
[[1,2,4,5,8],[3,6],[7]] => [[1,2,3,5,6],[4,7],[8]] => [3,3,1,1] => 10010011 => 1
[[1,2,3,5,8],[4,6],[7]] => [[1,2,3,4,6],[5,7],[8]] => [4,2,1,1] => 10001011 => 1
[[1,2,3,4,8],[5,6],[7]] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 10000101 => 1
[[1,4,5,6,7],[2,8],[3]] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 10110000 => 1
[[1,3,5,6,7],[2,8],[4]] => [[1,2,6,7,8],[3,4],[5]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3,8],[4]] => [[1,3,6,7,8],[2,4],[5]] => [1,2,1,4] => 11011000 => 2
[[1,3,4,6,7],[2,8],[5]] => [[1,2,5,7,8],[3,4],[6]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3,8],[5]] => [[1,3,5,7,8],[2,4],[6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,6,7],[4,8],[5]] => [[1,3,4,7,8],[2,5],[6]] => [1,3,1,3] => 11001100 => 2
[[1,3,4,5,7],[2,8],[6]] => [[1,2,5,6,8],[3,4],[7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3,8],[6]] => [[1,3,5,6,8],[2,4],[7]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5,7],[4,8],[6]] => [[1,3,4,6,8],[2,5],[7]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4,7],[5,8],[6]] => [[1,3,4,5,8],[2,6],[7]] => [1,4,1,2] => 11000110 => 2
[[1,3,4,5,6],[2,8],[7]] => [[1,2,5,6,7],[3,4],[8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6],[3,8],[7]] => [[1,3,5,6,7],[2,4],[8]] => [1,2,4,1] => 11010001 => 2
[[1,2,3,5,6],[4,8],[7]] => [[1,3,4,6,7],[2,5],[8]] => [1,3,3,1] => 11001001 => 2
[[1,2,3,4,6],[5,8],[7]] => [[1,3,4,5,7],[2,6],[8]] => [1,4,2,1] => 11000101 => 2
[[1,2,3,4,5],[6,8],[7]] => [[1,3,4,5,6],[2,7],[8]] => [1,5,1,1] => 11000011 => 2
[[1,3,5,6,7],[2,4],[8]] => [[1,4,6,7,8],[2,5],[3]] => [1,1,2,4] => 11101000 => 3
[[1,2,5,6,7],[3,4],[8]] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 11010000 => 2
[[1,3,4,6,7],[2,5],[8]] => [[1,4,5,7,8],[2,6],[3]] => [1,1,3,3] => 11100100 => 3
[[1,2,4,6,7],[3,5],[8]] => [[1,3,5,7,8],[2,6],[4]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,6,7],[4,5],[8]] => [[1,3,4,7,8],[2,6],[5]] => [1,3,4] => 11001000 => 2
[[1,3,4,5,7],[2,6],[8]] => [[1,4,5,6,8],[2,7],[3]] => [1,1,4,2] => 11100010 => 3
[[1,2,4,5,7],[3,6],[8]] => [[1,3,5,6,8],[2,7],[4]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5,7],[4,6],[8]] => [[1,3,4,6,8],[2,7],[5]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4,7],[5,6],[8]] => [[1,3,4,5,8],[2,7],[6]] => [1,4,3] => 11000100 => 2
[[1,3,4,5,6],[2,7],[8]] => [[1,4,5,6,7],[2,8],[3]] => [1,1,5,1] => 11100001 => 3
[[1,2,4,5,6],[3,7],[8]] => [[1,3,5,6,7],[2,8],[4]] => [1,2,4,1] => 11010001 => 2
[[1,2,3,5,6],[4,7],[8]] => [[1,3,4,6,7],[2,8],[5]] => [1,3,3,1] => 11001001 => 2
[[1,2,3,4,6],[5,7],[8]] => [[1,3,4,5,7],[2,8],[6]] => [1,4,2,1] => 11000101 => 2
[[1,2,3,4,5],[6,7],[8]] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 11000010 => 2
[[1,5,6,7,8],[2],[3],[4]] => [[1,2,6,7,8],[3],[4],[5]] => [2,1,1,4] => 10111000 => 1
[[1,4,6,7,8],[2],[3],[5]] => [[1,2,5,7,8],[3],[4],[6]] => [2,1,2,3] => 10110100 => 1
[[1,3,6,7,8],[2],[4],[5]] => [[1,2,4,7,8],[3],[5],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,6,7,8],[3],[4],[5]] => [[1,2,3,7,8],[4],[5],[6]] => [3,1,1,3] => 10011100 => 1
[[1,4,5,7,8],[2],[3],[6]] => [[1,2,5,6,8],[3],[4],[7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,7,8],[2],[4],[6]] => [[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3],[4],[6]] => [[1,2,3,6,8],[4],[5],[7]] => [3,1,2,2] => 10011010 => 1
[[1,3,4,7,8],[2],[5],[6]] => [[1,2,4,5,8],[3],[6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,7,8],[3],[5],[6]] => [[1,2,3,5,8],[4],[6],[7]] => [3,2,1,2] => 10010110 => 1
[[1,2,3,7,8],[4],[5],[6]] => [[1,2,3,4,8],[5],[6],[7]] => [4,1,1,2] => 10001110 => 1
[[1,4,5,6,8],[2],[3],[7]] => [[1,2,5,6,7],[3],[4],[8]] => [2,1,4,1] => 10110001 => 1
[[1,3,5,6,8],[2],[4],[7]] => [[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3],[4],[7]] => [[1,2,3,6,7],[4],[5],[8]] => [3,1,3,1] => 10011001 => 1
[[1,3,4,6,8],[2],[5],[7]] => [[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3],[5],[7]] => [[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4],[5],[7]] => [[1,2,3,4,7],[5],[6],[8]] => [4,1,2,1] => 10001101 => 1
[[1,3,4,5,8],[2],[6],[7]] => [[1,2,4,5,6],[3],[7],[8]] => [2,4,1,1] => 10100011 => 1
[[1,2,4,5,8],[3],[6],[7]] => [[1,2,3,5,6],[4],[7],[8]] => [3,3,1,1] => 10010011 => 1
[[1,2,3,5,8],[4],[6],[7]] => [[1,2,3,4,6],[5],[7],[8]] => [4,2,1,1] => 10001011 => 1
[[1,2,3,4,8],[5],[6],[7]] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 10000111 => 1
[[1,4,5,6,7],[2],[3],[8]] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 11110000 => 4
[[1,3,5,6,7],[2],[4],[8]] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 11101000 => 3
[[1,2,5,6,7],[3],[4],[8]] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 11011000 => 2
[[1,3,4,6,7],[2],[5],[8]] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 11100100 => 3
[[1,2,4,6,7],[3],[5],[8]] => [[1,3,5,7,8],[2],[4],[6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,6,7],[4],[5],[8]] => [[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3] => 11001100 => 2
[[1,3,4,5,7],[2],[6],[8]] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 11100010 => 3
[[1,2,4,5,7],[3],[6],[8]] => [[1,3,5,6,8],[2],[4],[7]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5,7],[4],[6],[8]] => [[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4,7],[5],[6],[8]] => [[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2] => 11000110 => 2
[[1,3,4,5,6],[2],[7],[8]] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 11100001 => 3
[[1,2,4,5,6],[3],[7],[8]] => [[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => 11010001 => 2
[[1,2,3,5,6],[4],[7],[8]] => [[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => 11001001 => 2
[[1,2,3,4,6],[5],[7],[8]] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 11000101 => 2
[[1,2,3,4,5],[6],[7],[8]] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 11000011 => 2
[[1,3,5,7],[2,4,6,8]] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4,6,8]] => [[1,2,3,6],[4,5,7,8]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5,6,8]] => [[1,2,4,5],[3,6,7,8]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,5,6,8]] => [[1,2,3,5],[4,6,7,8]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,5,6,8]] => [[1,2,3,4],[5,6,7,8]] => [4,4] => 10001000 => 1
[[1,3,5,6],[2,4,7,8]] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,4,7,8]] => [[1,2,3,7],[4,5,6,8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6],[2,5,7,8]] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,5,7,8]] => [[1,3,5,7],[2,4,6,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,5,7,8]] => [[1,3,4,7],[2,5,6,8]] => [1,3,3,1] => 11001001 => 2
[[1,3,4,5],[2,6,7,8]] => [[1,2,5,6],[3,4,7,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,6,7,8]] => [[1,3,5,6],[2,4,7,8]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,6,7,8]] => [[1,3,4,6],[2,5,7,8]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,6,7,8]] => [[1,3,4,5],[2,6,7,8]] => [1,4,3] => 11000100 => 2
[[1,4,6,8],[2,5,7],[3]] => [[1,2,5,7],[3,6,8],[4]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6,8],[2,5,7],[4]] => [[1,2,4,7],[3,6,8],[5]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5,7],[4]] => [[1,2,3,7],[4,6,8],[5]] => [3,1,3,1] => 10011001 => 1
[[1,3,6,8],[2,4,7],[5]] => [[1,2,4,7],[3,5,8],[6]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6,8],[3,4,7],[5]] => [[1,2,3,7],[4,5,8],[6]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6,7],[3]] => [[1,2,5,6],[3,7,8],[4]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,8],[2,6,7],[4]] => [[1,2,4,6],[3,7,8],[5]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,6,7],[4]] => [[1,2,3,6],[4,7,8],[5]] => [3,1,2,2] => 10011010 => 1
[[1,3,4,8],[2,6,7],[5]] => [[1,2,4,5],[3,7,8],[6]] => [2,3,3] => 10100100 => 1
[[1,2,4,8],[3,6,7],[5]] => [[1,2,3,5],[4,7,8],[6]] => [3,2,3] => 10010100 => 1
[[1,2,3,8],[4,6,7],[5]] => [[1,2,3,4],[5,7,8],[6]] => [4,1,3] => 10001100 => 1
[[1,3,5,8],[2,4,7],[6]] => [[1,2,4,6],[3,5,8],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,4,7],[6]] => [[1,2,3,6],[4,5,8],[7]] => [3,3,2] => 10010010 => 1
[[1,3,4,8],[2,5,7],[6]] => [[1,2,4,5],[3,6,8],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,8],[3,5,7],[6]] => [[1,2,3,5],[4,6,8],[7]] => [3,2,1,2] => 10010110 => 1
[[1,2,3,8],[4,5,7],[6]] => [[1,2,3,4],[5,6,8],[7]] => [4,2,2] => 10001010 => 1
[[1,3,5,8],[2,4,6],[7]] => [[1,2,4,6],[3,5,7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5,8],[3,4,6],[7]] => [[1,2,3,6],[4,5,7],[8]] => [3,3,1,1] => 10010011 => 1
[[1,3,4,8],[2,5,6],[7]] => [[1,2,4,5],[3,6,7],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,5,6],[7]] => [[1,2,3,5],[4,6,7],[8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,5,6],[7]] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 10001001 => 1
[[1,4,6,7],[2,5,8],[3]] => [[1,2,5,8],[3,6,7],[4]] => [2,1,2,3] => 10110100 => 1
[[1,3,6,7],[2,5,8],[4]] => [[1,2,4,8],[3,6,7],[5]] => [2,2,4] => 10101000 => 1
[[1,2,6,7],[3,5,8],[4]] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 10011000 => 1
[[1,3,6,7],[2,4,8],[5]] => [[1,2,4,8],[3,5,7],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,6,7],[3,4,8],[5]] => [[1,2,3,8],[4,5,7],[6]] => [3,2,3] => 10010100 => 1
[[1,4,5,7],[2,6,8],[3]] => [[1,2,6,8],[3,5,7],[4]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,7],[2,6,8],[4]] => [[1,2,6,8],[3,4,7],[5]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,6,8],[4]] => [[1,3,6,8],[2,4,7],[5]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4,7],[2,6,8],[5]] => [[1,2,5,8],[3,4,7],[6]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,6,8],[5]] => [[1,3,5,8],[2,4,7],[6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,7],[4,6,8],[5]] => [[1,3,4,8],[2,5,7],[6]] => [1,3,1,3] => 11001100 => 2
[[1,3,5,7],[2,4,8],[6]] => [[1,2,4,8],[3,5,6],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4,8],[6]] => [[1,2,3,8],[4,5,6],[7]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5,8],[6]] => [[1,2,5,8],[3,4,6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,7],[3,5,8],[6]] => [[1,3,5,8],[2,4,6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3,7],[4,5,8],[6]] => [[1,3,4,8],[2,5,6],[7]] => [1,3,2,2] => 11001010 => 2
[[1,4,5,6],[2,7,8],[3]] => [[1,2,6,7],[3,5,8],[4]] => [2,1,4,1] => 10110001 => 1
[[1,3,5,6],[2,7,8],[4]] => [[1,2,6,7],[3,4,8],[5]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,7,8],[4]] => [[1,3,6,7],[2,4,8],[5]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,4,6],[2,7,8],[5]] => [[1,2,5,7],[3,4,8],[6]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,7,8],[5]] => [[1,3,5,7],[2,4,8],[6]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,7,8],[5]] => [[1,3,4,7],[2,5,8],[6]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,4,5],[2,7,8],[6]] => [[1,2,5,6],[3,4,8],[7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,7,8],[6]] => [[1,3,5,6],[2,4,8],[7]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,7,8],[6]] => [[1,3,4,6],[2,5,8],[7]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,7,8],[6]] => [[1,3,4,5],[2,6,8],[7]] => [1,4,1,2] => 11000110 => 2
[[1,3,5,6],[2,4,8],[7]] => [[1,2,4,7],[3,5,6],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,4,8],[7]] => [[1,2,3,7],[4,5,6],[8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6],[2,5,8],[7]] => [[1,2,5,7],[3,4,6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,5,8],[7]] => [[1,3,5,7],[2,4,6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,5,8],[7]] => [[1,3,4,7],[2,5,6],[8]] => [1,3,3,1] => 11001001 => 2
[[1,3,4,5],[2,6,8],[7]] => [[1,2,5,6],[3,4,7],[8]] => [2,4,1,1] => 10100011 => 1
[[1,2,4,5],[3,6,8],[7]] => [[1,3,5,6],[2,4,7],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,2,3,5],[4,6,8],[7]] => [[1,3,4,6],[2,5,7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,2,3,4],[5,6,8],[7]] => [[1,3,4,5],[2,6,7],[8]] => [1,4,2,1] => 11000101 => 2
[[1,3,5,7],[2,4,6],[8]] => [[1,4,6,8],[2,5,7],[3]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5,7],[3,4,6],[8]] => [[1,3,6,8],[2,5,7],[4]] => [1,2,3,2] => 11010010 => 2
[[1,3,4,7],[2,5,6],[8]] => [[1,4,5,8],[2,6,7],[3]] => [1,1,3,3] => 11100100 => 3
[[1,2,4,7],[3,5,6],[8]] => [[1,3,5,8],[2,6,7],[4]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,7],[4,5,6],[8]] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 11001000 => 2
[[1,3,5,6],[2,4,7],[8]] => [[1,4,6,7],[2,5,8],[3]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,5,6],[3,4,7],[8]] => [[1,3,6,7],[2,5,8],[4]] => [1,2,4,1] => 11010001 => 2
[[1,3,4,6],[2,5,7],[8]] => [[1,4,5,7],[2,6,8],[3]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4,6],[3,5,7],[8]] => [[1,3,5,7],[2,6,8],[4]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,5,7],[8]] => [[1,3,4,7],[2,6,8],[5]] => [1,3,3,1] => 11001001 => 2
[[1,3,4,5],[2,6,7],[8]] => [[1,4,5,6],[2,7,8],[3]] => [1,1,4,2] => 11100010 => 3
[[1,2,4,5],[3,6,7],[8]] => [[1,3,5,6],[2,7,8],[4]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,6,7],[8]] => [[1,3,4,6],[2,7,8],[5]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,6,7],[8]] => [[1,3,4,5],[2,7,8],[6]] => [1,4,3] => 11000100 => 2
[[1,4,7,8],[2,5],[3,6]] => [[1,2,5,8],[3,6],[4,7]] => [2,1,2,3] => 10110100 => 1
[[1,3,7,8],[2,5],[4,6]] => [[1,2,4,8],[3,6],[5,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,7,8],[3,5],[4,6]] => [[1,2,3,8],[4,6],[5,7]] => [3,1,2,2] => 10011010 => 1
[[1,3,7,8],[2,4],[5,6]] => [[1,2,4,8],[3,5],[6,7]] => [2,2,1,3] => 10101100 => 1
[[1,2,7,8],[3,4],[5,6]] => [[1,2,3,8],[4,5],[6,7]] => [3,2,3] => 10010100 => 1
[[1,4,6,8],[2,5],[3,7]] => [[1,2,5,7],[3,6],[4,8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6,8],[2,5],[4,7]] => [[1,2,4,7],[3,6],[5,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5],[4,7]] => [[1,2,3,7],[4,6],[5,8]] => [3,1,3,1] => 10011001 => 1
[[1,3,6,8],[2,4],[5,7]] => [[1,2,4,7],[3,5],[6,8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6,8],[3,4],[5,7]] => [[1,2,3,7],[4,5],[6,8]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6],[3,7]] => [[1,2,5,6],[3,7],[4,8]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,8],[2,6],[4,7]] => [[1,2,4,6],[3,7],[5,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,6],[4,7]] => [[1,2,3,6],[4,7],[5,8]] => [3,1,2,2] => 10011010 => 1
[[1,3,4,8],[2,6],[5,7]] => [[1,2,4,5],[3,7],[6,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,6],[5,7]] => [[1,2,3,5],[4,7],[6,8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,6],[5,7]] => [[1,2,3,4],[5,7],[6,8]] => [4,1,2,1] => 10001101 => 1
[[1,3,5,8],[2,4],[6,7]] => [[1,2,4,6],[3,5],[7,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,4],[6,7]] => [[1,2,3,6],[4,5],[7,8]] => [3,3,2] => 10010010 => 1
[[1,3,4,8],[2,5],[6,7]] => [[1,2,4,5],[3,6],[7,8]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,8],[3,5],[6,7]] => [[1,2,3,5],[4,6],[7,8]] => [3,2,1,2] => 10010110 => 1
[[1,2,3,8],[4,5],[6,7]] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 10001010 => 1
[[1,4,6,7],[2,5],[3,8]] => [[1,2,7,8],[3,5],[4,6]] => [2,1,2,3] => 10110100 => 1
[[1,3,6,7],[2,5],[4,8]] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 10101000 => 1
[[1,2,6,7],[3,5],[4,8]] => [[1,3,7,8],[2,4],[5,6]] => [1,2,1,4] => 11011000 => 2
[[1,3,6,7],[2,4],[5,8]] => [[1,4,7,8],[2,5],[3,6]] => [1,1,2,4] => 11101000 => 3
[[1,2,6,7],[3,4],[5,8]] => [[1,3,7,8],[2,5],[4,6]] => [1,2,2,3] => 11010100 => 2
[[1,4,5,7],[2,6],[3,8]] => [[1,2,6,8],[3,5],[4,7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,7],[2,6],[4,8]] => [[1,2,6,8],[3,4],[5,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,6],[4,8]] => [[1,3,6,8],[2,4],[5,7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4,7],[2,6],[5,8]] => [[1,2,5,8],[3,4],[6,7]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,6],[5,8]] => [[1,3,5,8],[2,4],[6,7]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,7],[4,6],[5,8]] => [[1,3,4,8],[2,5],[6,7]] => [1,3,1,3] => 11001100 => 2
[[1,3,5,7],[2,4],[6,8]] => [[1,4,6,8],[2,5],[3,7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5,7],[3,4],[6,8]] => [[1,3,6,8],[2,5],[4,7]] => [1,2,3,2] => 11010010 => 2
[[1,3,4,7],[2,5],[6,8]] => [[1,4,5,8],[2,6],[3,7]] => [1,1,3,3] => 11100100 => 3
[[1,2,4,7],[3,5],[6,8]] => [[1,3,5,8],[2,6],[4,7]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,7],[4,5],[6,8]] => [[1,3,4,8],[2,6],[5,7]] => [1,3,2,2] => 11001010 => 2
[[1,4,5,6],[2,7],[3,8]] => [[1,2,6,7],[3,5],[4,8]] => [2,1,4,1] => 10110001 => 1
[[1,3,5,6],[2,7],[4,8]] => [[1,2,6,7],[3,4],[5,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,7],[4,8]] => [[1,3,6,7],[2,4],[5,8]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,4,6],[2,7],[5,8]] => [[1,2,5,7],[3,4],[6,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,7],[5,8]] => [[1,3,5,7],[2,4],[6,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,7],[5,8]] => [[1,3,4,7],[2,5],[6,8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,4,5],[2,7],[6,8]] => [[1,2,5,6],[3,4],[7,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,7],[6,8]] => [[1,3,5,6],[2,4],[7,8]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,7],[6,8]] => [[1,3,4,6],[2,5],[7,8]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,7],[6,8]] => [[1,3,4,5],[2,6],[7,8]] => [1,4,1,2] => 11000110 => 2
[[1,3,5,6],[2,4],[7,8]] => [[1,4,6,7],[2,5],[3,8]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,5,6],[3,4],[7,8]] => [[1,3,6,7],[2,5],[4,8]] => [1,2,4,1] => 11010001 => 2
[[1,3,4,6],[2,5],[7,8]] => [[1,4,5,7],[2,6],[3,8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4,6],[3,5],[7,8]] => [[1,3,5,7],[2,6],[4,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,5],[7,8]] => [[1,3,4,7],[2,6],[5,8]] => [1,3,3,1] => 11001001 => 2
[[1,3,4,5],[2,6],[7,8]] => [[1,4,5,6],[2,7],[3,8]] => [1,1,4,2] => 11100010 => 3
[[1,2,4,5],[3,6],[7,8]] => [[1,3,5,6],[2,7],[4,8]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,6],[7,8]] => [[1,3,4,6],[2,7],[5,8]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,6],[7,8]] => [[1,3,4,5],[2,7],[6,8]] => [1,4,2,1] => 11000101 => 2
[[1,5,7,8],[2,6],[3],[4]] => [[1,2,6,8],[3,7],[4],[5]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,7,8],[2,6],[3],[5]] => [[1,2,5,8],[3,7],[4],[6]] => [2,1,2,3] => 10110100 => 1
[[1,3,7,8],[2,6],[4],[5]] => [[1,2,4,8],[3,7],[5],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,7,8],[3,6],[4],[5]] => [[1,2,3,8],[4,7],[5],[6]] => [3,1,1,3] => 10011100 => 1
[[1,4,7,8],[2,5],[3],[6]] => [[1,2,5,8],[3,6],[4],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,7,8],[2,5],[4],[6]] => [[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,7,8],[3,5],[4],[6]] => [[1,2,3,8],[4,6],[5],[7]] => [3,1,2,2] => 10011010 => 1
[[1,3,7,8],[2,4],[5],[6]] => [[1,2,4,8],[3,5],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,7,8],[3,4],[5],[6]] => [[1,2,3,8],[4,5],[6],[7]] => [3,2,1,2] => 10010110 => 1
[[1,5,6,8],[2,7],[3],[4]] => [[1,2,6,7],[3,8],[4],[5]] => [2,1,1,3,1] => 10111001 => 1
[[1,4,6,8],[2,7],[3],[5]] => [[1,2,5,7],[3,8],[4],[6]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6,8],[2,7],[4],[5]] => [[1,2,4,7],[3,8],[5],[6]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6,8],[3,7],[4],[5]] => [[1,2,3,7],[4,8],[5],[6]] => [3,1,1,2,1] => 10011101 => 1
[[1,4,5,8],[2,7],[3],[6]] => [[1,2,5,6],[3,8],[4],[7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,8],[2,7],[4],[6]] => [[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,7],[4],[6]] => [[1,2,3,6],[4,8],[5],[7]] => [3,1,2,2] => 10011010 => 1
[[1,3,4,8],[2,7],[5],[6]] => [[1,2,4,5],[3,8],[6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,8],[3,7],[5],[6]] => [[1,2,3,5],[4,8],[6],[7]] => [3,2,1,2] => 10010110 => 1
[[1,2,3,8],[4,7],[5],[6]] => [[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2] => 10001110 => 1
[[1,4,6,8],[2,5],[3],[7]] => [[1,2,5,7],[3,6],[4],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6,8],[2,5],[4],[7]] => [[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5],[4],[7]] => [[1,2,3,7],[4,6],[5],[8]] => [3,1,3,1] => 10011001 => 1
[[1,3,6,8],[2,4],[5],[7]] => [[1,2,4,7],[3,5],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6,8],[3,4],[5],[7]] => [[1,2,3,7],[4,5],[6],[8]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6],[3],[7]] => [[1,2,5,6],[3,7],[4],[8]] => [2,1,3,1,1] => 10110011 => 1
[[1,3,5,8],[2,6],[4],[7]] => [[1,2,4,6],[3,7],[5],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5,8],[3,6],[4],[7]] => [[1,2,3,6],[4,7],[5],[8]] => [3,1,2,1,1] => 10011011 => 1
[[1,3,4,8],[2,6],[5],[7]] => [[1,2,4,5],[3,7],[6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,6],[5],[7]] => [[1,2,3,5],[4,7],[6],[8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,6],[5],[7]] => [[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1] => 10001101 => 1
[[1,3,5,8],[2,4],[6],[7]] => [[1,2,4,6],[3,5],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5,8],[3,4],[6],[7]] => [[1,2,3,6],[4,5],[7],[8]] => [3,3,1,1] => 10010011 => 1
[[1,3,4,8],[2,5],[6],[7]] => [[1,2,4,5],[3,6],[7],[8]] => [2,3,1,1,1] => 10100111 => 1
[[1,2,4,8],[3,5],[6],[7]] => [[1,2,3,5],[4,6],[7],[8]] => [3,2,1,1,1] => 10010111 => 1
[[1,2,3,8],[4,5],[6],[7]] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 10001011 => 1
[[1,5,6,7],[2,8],[3],[4]] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 10111000 => 1
[[1,4,6,7],[2,8],[3],[5]] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10110100 => 1
[[1,3,6,7],[2,8],[4],[5]] => [[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,6,7],[3,8],[4],[5]] => [[1,3,7,8],[2,4],[5],[6]] => [1,2,1,1,3] => 11011100 => 2
[[1,4,5,7],[2,8],[3],[6]] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5,7],[2,8],[4],[6]] => [[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,8],[4],[6]] => [[1,3,6,8],[2,4],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4,7],[2,8],[5],[6]] => [[1,2,5,8],[3,4],[6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4,7],[3,8],[5],[6]] => [[1,3,5,8],[2,4],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3,7],[4,8],[5],[6]] => [[1,3,4,8],[2,5],[6],[7]] => [1,3,1,1,2] => 11001110 => 2
[[1,4,5,6],[2,8],[3],[7]] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 10110001 => 1
[[1,3,5,6],[2,8],[4],[7]] => [[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,8],[4],[7]] => [[1,3,6,7],[2,4],[5],[8]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,4,6],[2,8],[5],[7]] => [[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,8],[5],[7]] => [[1,3,5,7],[2,4],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,8],[5],[7]] => [[1,3,4,7],[2,5],[6],[8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,4,5],[2,8],[6],[7]] => [[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1] => 10100011 => 1
[[1,2,4,5],[3,8],[6],[7]] => [[1,3,5,6],[2,4],[7],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,2,3,5],[4,8],[6],[7]] => [[1,3,4,6],[2,5],[7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,2,3,4],[5,8],[6],[7]] => [[1,3,4,5],[2,6],[7],[8]] => [1,4,1,1,1] => 11000111 => 2
[[1,4,6,7],[2,5],[3],[8]] => [[1,5,7,8],[2,6],[3],[4]] => [1,1,1,2,3] => 11110100 => 4
[[1,3,6,7],[2,5],[4],[8]] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 11101000 => 3
[[1,2,6,7],[3,5],[4],[8]] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 11011000 => 2
[[1,3,6,7],[2,4],[5],[8]] => [[1,4,7,8],[2,5],[3],[6]] => [1,1,2,1,3] => 11101100 => 3
[[1,2,6,7],[3,4],[5],[8]] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 11010100 => 2
[[1,4,5,7],[2,6],[3],[8]] => [[1,5,6,8],[2,7],[3],[4]] => [1,1,1,3,2] => 11110010 => 4
[[1,3,5,7],[2,6],[4],[8]] => [[1,4,6,8],[2,7],[3],[5]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5,7],[3,6],[4],[8]] => [[1,3,6,8],[2,7],[4],[5]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4,7],[2,6],[5],[8]] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 11100100 => 3
[[1,2,4,7],[3,6],[5],[8]] => [[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3,7],[4,6],[5],[8]] => [[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => 11001100 => 2
[[1,3,5,7],[2,4],[6],[8]] => [[1,4,6,8],[2,5],[3],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5,7],[3,4],[6],[8]] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 11010010 => 2
[[1,3,4,7],[2,5],[6],[8]] => [[1,4,5,8],[2,6],[3],[7]] => [1,1,3,1,2] => 11100110 => 3
[[1,2,4,7],[3,5],[6],[8]] => [[1,3,5,8],[2,6],[4],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3,7],[4,5],[6],[8]] => [[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2] => 11001010 => 2
[[1,4,5,6],[2,7],[3],[8]] => [[1,5,6,7],[2,8],[3],[4]] => [1,1,1,4,1] => 11110001 => 4
[[1,3,5,6],[2,7],[4],[8]] => [[1,4,6,7],[2,8],[3],[5]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,5,6],[3,7],[4],[8]] => [[1,3,6,7],[2,8],[4],[5]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,4,6],[2,7],[5],[8]] => [[1,4,5,7],[2,8],[3],[6]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4,6],[3,7],[5],[8]] => [[1,3,5,7],[2,8],[4],[6]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,7],[5],[8]] => [[1,3,4,7],[2,8],[5],[6]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,4,5],[2,7],[6],[8]] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 11100010 => 3
[[1,2,4,5],[3,7],[6],[8]] => [[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2] => 11010010 => 2
[[1,2,3,5],[4,7],[6],[8]] => [[1,3,4,6],[2,8],[5],[7]] => [1,3,2,2] => 11001010 => 2
[[1,2,3,4],[5,7],[6],[8]] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 11000110 => 2
[[1,3,5,6],[2,4],[7],[8]] => [[1,4,6,7],[2,5],[3],[8]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,5,6],[3,4],[7],[8]] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11010001 => 2
[[1,3,4,6],[2,5],[7],[8]] => [[1,4,5,7],[2,6],[3],[8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4,6],[3,5],[7],[8]] => [[1,3,5,7],[2,6],[4],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4,5],[7],[8]] => [[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1] => 11001001 => 2
[[1,3,4,5],[2,6],[7],[8]] => [[1,4,5,6],[2,7],[3],[8]] => [1,1,4,1,1] => 11100011 => 3
[[1,2,4,5],[3,6],[7],[8]] => [[1,3,5,6],[2,7],[4],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,2,3,5],[4,6],[7],[8]] => [[1,3,4,6],[2,7],[5],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,2,3,4],[5,6],[7],[8]] => [[1,3,4,5],[2,7],[6],[8]] => [1,4,2,1] => 11000101 => 2
[[1,6,7,8],[2],[3],[4],[5]] => [[1,2,7,8],[3],[4],[5],[6]] => [2,1,1,1,3] => 10111100 => 1
[[1,5,7,8],[2],[3],[4],[6]] => [[1,2,6,8],[3],[4],[5],[7]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,7,8],[2],[3],[5],[6]] => [[1,2,5,8],[3],[4],[6],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,7,8],[2],[4],[5],[6]] => [[1,2,4,8],[3],[5],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,7,8],[3],[4],[5],[6]] => [[1,2,3,8],[4],[5],[6],[7]] => [3,1,1,1,2] => 10011110 => 1
[[1,5,6,8],[2],[3],[4],[7]] => [[1,2,6,7],[3],[4],[5],[8]] => [2,1,1,3,1] => 10111001 => 1
[[1,4,6,8],[2],[3],[5],[7]] => [[1,2,5,7],[3],[4],[6],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6,8],[2],[4],[5],[7]] => [[1,2,4,7],[3],[5],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6,8],[3],[4],[5],[7]] => [[1,2,3,7],[4],[5],[6],[8]] => [3,1,1,2,1] => 10011101 => 1
[[1,4,5,8],[2],[3],[6],[7]] => [[1,2,5,6],[3],[4],[7],[8]] => [2,1,3,1,1] => 10110011 => 1
[[1,3,5,8],[2],[4],[6],[7]] => [[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5,8],[3],[4],[6],[7]] => [[1,2,3,6],[4],[5],[7],[8]] => [3,1,2,1,1] => 10011011 => 1
[[1,3,4,8],[2],[5],[6],[7]] => [[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1] => 10100111 => 1
[[1,2,4,8],[3],[5],[6],[7]] => [[1,2,3,5],[4],[6],[7],[8]] => [3,2,1,1,1] => 10010111 => 1
[[1,2,3,8],[4],[5],[6],[7]] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 10001111 => 1
[[1,5,6,7],[2],[3],[4],[8]] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 11111000 => 5
[[1,4,6,7],[2],[3],[5],[8]] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11110100 => 4
[[1,3,6,7],[2],[4],[5],[8]] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 11101100 => 3
[[1,2,6,7],[3],[4],[5],[8]] => [[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => 11011100 => 2
[[1,4,5,7],[2],[3],[6],[8]] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 11110010 => 4
[[1,3,5,7],[2],[4],[6],[8]] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5,7],[3],[4],[6],[8]] => [[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4,7],[2],[5],[6],[8]] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 11100110 => 3
[[1,2,4,7],[3],[5],[6],[8]] => [[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3,7],[4],[5],[6],[8]] => [[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => 11001110 => 2
[[1,4,5,6],[2],[3],[7],[8]] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 11110001 => 4
[[1,3,5,6],[2],[4],[7],[8]] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,5,6],[3],[4],[7],[8]] => [[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,4,6],[2],[5],[7],[8]] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4,6],[3],[5],[7],[8]] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3,6],[4],[5],[7],[8]] => [[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,4,5],[2],[6],[7],[8]] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 11100011 => 3
[[1,2,4,5],[3],[6],[7],[8]] => [[1,3,5,6],[2],[4],[7],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,2,3,5],[4],[6],[7],[8]] => [[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,2,3,4],[5],[6],[7],[8]] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 11000111 => 2
[[1,4,7],[2,5,8],[3,6]] => [[1,2,5],[3,6,8],[4,7]] => [2,1,2,3] => 10110100 => 1
[[1,3,7],[2,5,8],[4,6]] => [[1,2,4],[3,6,8],[5,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5,8],[4,6]] => [[1,2,3],[4,6,8],[5,7]] => [3,1,2,2] => 10011010 => 1
[[1,3,7],[2,4,8],[5,6]] => [[1,2,4],[3,5,8],[6,7]] => [2,2,1,3] => 10101100 => 1
[[1,2,7],[3,4,8],[5,6]] => [[1,2,3],[4,5,8],[6,7]] => [3,2,3] => 10010100 => 1
[[1,4,6],[2,5,8],[3,7]] => [[1,2,5],[3,6,7],[4,8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,5,8],[4,7]] => [[1,2,4],[3,6,7],[5,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5,8],[4,7]] => [[1,2,3],[4,6,7],[5,8]] => [3,1,3,1] => 10011001 => 1
[[1,3,6],[2,4,8],[5,7]] => [[1,2,4],[3,5,7],[6,8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6],[3,4,8],[5,7]] => [[1,2,3],[4,5,7],[6,8]] => [3,2,2,1] => 10010101 => 1
[[1,4,5],[2,6,8],[3,7]] => [[1,2,6],[3,5,7],[4,8]] => [2,1,3,2] => 10110010 => 1
[[1,3,5],[2,6,8],[4,7]] => [[1,2,6],[3,4,7],[5,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,6,8],[4,7]] => [[1,3,6],[2,4,7],[5,8]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,6,8],[5,7]] => [[1,2,5],[3,4,7],[6,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6,8],[5,7]] => [[1,3,5],[2,4,7],[6,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,6,8],[5,7]] => [[1,3,4],[2,5,7],[6,8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,5],[2,4,8],[6,7]] => [[1,2,4],[3,5,6],[7,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,4,8],[6,7]] => [[1,2,3],[4,5,6],[7,8]] => [3,3,2] => 10010010 => 1
[[1,3,4],[2,5,8],[6,7]] => [[1,2,5],[3,4,6],[7,8]] => [2,3,1,2] => 10100110 => 1
[[1,2,4],[3,5,8],[6,7]] => [[1,3,5],[2,4,6],[7,8]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,5,8],[6,7]] => [[1,3,4],[2,5,6],[7,8]] => [1,3,2,2] => 11001010 => 2
[[1,4,6],[2,5,7],[3,8]] => [[1,2,7],[3,5,8],[4,6]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,5,7],[4,8]] => [[1,2,7],[3,4,8],[5,6]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5,7],[4,8]] => [[1,3,7],[2,4,8],[5,6]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,6],[2,4,7],[5,8]] => [[1,4,7],[2,5,8],[3,6]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,6],[3,4,7],[5,8]] => [[1,3,7],[2,5,8],[4,6]] => [1,2,2,2,1] => 11010101 => 2
[[1,4,5],[2,6,7],[3,8]] => [[1,2,6],[3,5,8],[4,7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5],[2,6,7],[4,8]] => [[1,2,6],[3,4,8],[5,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,6,7],[4,8]] => [[1,3,6],[2,4,8],[5,7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,6,7],[5,8]] => [[1,2,5],[3,4,8],[6,7]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,6,7],[5,8]] => [[1,3,5],[2,4,8],[6,7]] => [1,2,2,3] => 11010100 => 2
[[1,2,3],[4,6,7],[5,8]] => [[1,3,4],[2,5,8],[6,7]] => [1,3,1,3] => 11001100 => 2
[[1,3,5],[2,4,7],[6,8]] => [[1,4,6],[2,5,8],[3,7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,4,7],[6,8]] => [[1,3,6],[2,5,8],[4,7]] => [1,2,3,2] => 11010010 => 2
[[1,3,4],[2,5,7],[6,8]] => [[1,4,5],[2,6,8],[3,7]] => [1,1,3,3] => 11100100 => 3
[[1,2,4],[3,5,7],[6,8]] => [[1,3,5],[2,6,8],[4,7]] => [1,2,2,3] => 11010100 => 2
[[1,2,3],[4,5,7],[6,8]] => [[1,3,4],[2,6,8],[5,7]] => [1,3,2,2] => 11001010 => 2
[[1,3,5],[2,4,6],[7,8]] => [[1,4,6],[2,5,7],[3,8]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,4,6],[7,8]] => [[1,3,6],[2,5,7],[4,8]] => [1,2,3,2] => 11010010 => 2
[[1,3,4],[2,5,6],[7,8]] => [[1,4,5],[2,6,7],[3,8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4],[3,5,6],[7,8]] => [[1,3,5],[2,6,7],[4,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,5,6],[7,8]] => [[1,3,4],[2,6,7],[5,8]] => [1,3,3,1] => 11001001 => 2
[[1,5,7],[2,6,8],[3],[4]] => [[1,2,6],[3,7,8],[4],[5]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,7],[2,6,8],[3],[5]] => [[1,2,5],[3,7,8],[4],[6]] => [2,1,2,3] => 10110100 => 1
[[1,3,7],[2,6,8],[4],[5]] => [[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,7],[3,6,8],[4],[5]] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 10011100 => 1
[[1,4,7],[2,5,8],[3],[6]] => [[1,2,5],[3,6,8],[4],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,7],[2,5,8],[4],[6]] => [[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5,8],[4],[6]] => [[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2] => 10011010 => 1
[[1,3,7],[2,4,8],[5],[6]] => [[1,2,4],[3,5,8],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,7],[3,4,8],[5],[6]] => [[1,2,3],[4,5,8],[6],[7]] => [3,2,1,2] => 10010110 => 1
[[1,5,6],[2,7,8],[3],[4]] => [[1,2,7],[3,6,8],[4],[5]] => [2,1,1,3,1] => 10111001 => 1
[[1,4,6],[2,7,8],[3],[5]] => [[1,2,7],[3,5,8],[4],[6]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,7,8],[4],[5]] => [[1,2,7],[3,4,8],[5],[6]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6],[3,7,8],[4],[5]] => [[1,3,7],[2,4,8],[5],[6]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4,5],[2,7,8],[3],[6]] => [[1,2,6],[3,5,8],[4],[7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5],[2,7,8],[4],[6]] => [[1,2,6],[3,4,8],[5],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,7,8],[4],[6]] => [[1,3,6],[2,4,8],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,7,8],[5],[6]] => [[1,2,5],[3,4,8],[6],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4],[3,7,8],[5],[6]] => [[1,3,5],[2,4,8],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,7,8],[5],[6]] => [[1,3,4],[2,5,8],[6],[7]] => [1,3,1,1,2] => 11001110 => 2
[[1,4,6],[2,5,8],[3],[7]] => [[1,2,5],[3,6,7],[4],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,5,8],[4],[7]] => [[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5,8],[4],[7]] => [[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1] => 10011001 => 1
[[1,3,6],[2,4,8],[5],[7]] => [[1,2,4],[3,5,7],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6],[3,4,8],[5],[7]] => [[1,2,3],[4,5,7],[6],[8]] => [3,2,2,1] => 10010101 => 1
[[1,4,5],[2,6,8],[3],[7]] => [[1,2,6],[3,5,7],[4],[8]] => [2,1,3,1,1] => 10110011 => 1
[[1,3,5],[2,6,8],[4],[7]] => [[1,2,6],[3,4,7],[5],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5],[3,6,8],[4],[7]] => [[1,3,6],[2,4,7],[5],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3,4],[2,6,8],[5],[7]] => [[1,2,5],[3,4,7],[6],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6,8],[5],[7]] => [[1,3,5],[2,4,7],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,6,8],[5],[7]] => [[1,3,4],[2,5,7],[6],[8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,5],[2,4,8],[6],[7]] => [[1,2,4],[3,5,6],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5],[3,4,8],[6],[7]] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 10010011 => 1
[[1,3,4],[2,5,8],[6],[7]] => [[1,2,5],[3,4,6],[7],[8]] => [2,3,1,1,1] => 10100111 => 1
[[1,2,4],[3,5,8],[6],[7]] => [[1,3,5],[2,4,6],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,2,3],[4,5,8],[6],[7]] => [[1,3,4],[2,5,6],[7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,4,6],[2,5,7],[3],[8]] => [[1,5,7],[2,6,8],[3],[4]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3,6],[2,5,7],[4],[8]] => [[1,4,7],[2,6,8],[3],[5]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,6],[3,5,7],[4],[8]] => [[1,3,7],[2,6,8],[4],[5]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,6],[2,4,7],[5],[8]] => [[1,4,7],[2,5,8],[3],[6]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2,6],[3,4,7],[5],[8]] => [[1,3,7],[2,5,8],[4],[6]] => [1,2,2,2,1] => 11010101 => 2
[[1,4,5],[2,6,7],[3],[8]] => [[1,5,6],[2,7,8],[3],[4]] => [1,1,1,3,2] => 11110010 => 4
[[1,3,5],[2,6,7],[4],[8]] => [[1,4,6],[2,7,8],[3],[5]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,6,7],[4],[8]] => [[1,3,6],[2,7,8],[4],[5]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,6,7],[5],[8]] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 11100100 => 3
[[1,2,4],[3,6,7],[5],[8]] => [[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3] => 11010100 => 2
[[1,2,3],[4,6,7],[5],[8]] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 11001100 => 2
[[1,3,5],[2,4,7],[6],[8]] => [[1,4,6],[2,5,8],[3],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,4,7],[6],[8]] => [[1,3,6],[2,5,8],[4],[7]] => [1,2,3,2] => 11010010 => 2
[[1,3,4],[2,5,7],[6],[8]] => [[1,4,5],[2,6,8],[3],[7]] => [1,1,3,1,2] => 11100110 => 3
[[1,2,4],[3,5,7],[6],[8]] => [[1,3,5],[2,6,8],[4],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,5,7],[6],[8]] => [[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => 11001010 => 2
[[1,3,5],[2,4,6],[7],[8]] => [[1,4,6],[2,5,7],[3],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2,5],[3,4,6],[7],[8]] => [[1,3,6],[2,5,7],[4],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,3,4],[2,5,6],[7],[8]] => [[1,4,5],[2,6,7],[3],[8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4],[3,5,6],[7],[8]] => [[1,3,5],[2,6,7],[4],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,5,6],[7],[8]] => [[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1] => 11001001 => 2
[[1,5,8],[2,6],[3,7],[4]] => [[1,2,6],[3,7],[4,8],[5]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,8],[2,6],[3,7],[5]] => [[1,2,5],[3,7],[4,8],[6]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,8],[2,6],[4,7],[5]] => [[1,2,4],[3,7],[5,8],[6]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,8],[3,6],[4,7],[5]] => [[1,2,3],[4,7],[5,8],[6]] => [3,1,1,2,1] => 10011101 => 1
[[1,4,8],[2,5],[3,7],[6]] => [[1,2,5],[3,6],[4,8],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,8],[2,5],[4,7],[6]] => [[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,8],[3,5],[4,7],[6]] => [[1,2,3],[4,6],[5,8],[7]] => [3,1,2,2] => 10011010 => 1
[[1,3,8],[2,4],[5,7],[6]] => [[1,2,4],[3,5],[6,8],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,8],[3,4],[5,7],[6]] => [[1,2,3],[4,5],[6,8],[7]] => [3,2,1,2] => 10010110 => 1
[[1,4,8],[2,5],[3,6],[7]] => [[1,2,5],[3,6],[4,7],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,8],[2,5],[4,6],[7]] => [[1,2,4],[3,6],[5,7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,8],[3,5],[4,6],[7]] => [[1,2,3],[4,6],[5,7],[8]] => [3,1,2,1,1] => 10011011 => 1
[[1,3,8],[2,4],[5,6],[7]] => [[1,2,4],[3,5],[6,7],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,8],[3,4],[5,6],[7]] => [[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1] => 10010101 => 1
[[1,5,7],[2,6],[3,8],[4]] => [[1,2,8],[3,6],[4,7],[5]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,7],[2,6],[3,8],[5]] => [[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3] => 10110100 => 1
[[1,3,7],[2,6],[4,8],[5]] => [[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => 10101100 => 1
[[1,2,7],[3,6],[4,8],[5]] => [[1,3,8],[2,4],[5,7],[6]] => [1,2,1,1,3] => 11011100 => 2
[[1,4,7],[2,5],[3,8],[6]] => [[1,2,8],[3,5],[4,6],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,7],[2,5],[4,8],[6]] => [[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5],[4,8],[6]] => [[1,3,8],[2,4],[5,6],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,7],[2,4],[5,8],[6]] => [[1,4,8],[2,5],[3,6],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,7],[3,4],[5,8],[6]] => [[1,3,8],[2,5],[4,6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,5,6],[2,7],[3,8],[4]] => [[1,2,7],[3,6],[4,8],[5]] => [2,1,1,3,1] => 10111001 => 1
[[1,4,6],[2,7],[3,8],[5]] => [[1,2,7],[3,5],[4,8],[6]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,7],[4,8],[5]] => [[1,2,7],[3,4],[5,8],[6]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6],[3,7],[4,8],[5]] => [[1,3,7],[2,4],[5,8],[6]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4,5],[2,7],[3,8],[6]] => [[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2] => 10110010 => 1
[[1,3,5],[2,7],[4,8],[6]] => [[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,7],[4,8],[6]] => [[1,3,6],[2,4],[5,8],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,7],[5,8],[6]] => [[1,2,5],[3,4],[6,8],[7]] => [2,3,1,2] => 10100110 => 1
[[1,2,4],[3,7],[5,8],[6]] => [[1,3,5],[2,4],[6,8],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,7],[5,8],[6]] => [[1,3,4],[2,5],[6,8],[7]] => [1,3,1,1,2] => 11001110 => 2
[[1,4,6],[2,5],[3,8],[7]] => [[1,2,7],[3,5],[4,6],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,5],[4,8],[7]] => [[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5],[4,8],[7]] => [[1,3,7],[2,4],[5,6],[8]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,6],[2,4],[5,8],[7]] => [[1,4,7],[2,5],[3,6],[8]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,6],[3,4],[5,8],[7]] => [[1,3,7],[2,5],[4,6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,4,5],[2,6],[3,8],[7]] => [[1,2,6],[3,5],[4,7],[8]] => [2,1,3,1,1] => 10110011 => 1
[[1,3,5],[2,6],[4,8],[7]] => [[1,2,6],[3,4],[5,7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5],[3,6],[4,8],[7]] => [[1,3,6],[2,4],[5,7],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3,4],[2,6],[5,8],[7]] => [[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6],[5,8],[7]] => [[1,3,5],[2,4],[6,7],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,6],[5,8],[7]] => [[1,3,4],[2,5],[6,7],[8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,5],[2,4],[6,8],[7]] => [[1,4,6],[2,5],[3,7],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2,5],[3,4],[6,8],[7]] => [[1,3,6],[2,5],[4,7],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,3,4],[2,5],[6,8],[7]] => [[1,4,5],[2,6],[3,7],[8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4],[3,5],[6,8],[7]] => [[1,3,5],[2,6],[4,7],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,5],[6,8],[7]] => [[1,3,4],[2,6],[5,7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,4,7],[2,5],[3,6],[8]] => [[1,5,8],[2,6],[3,7],[4]] => [1,1,1,2,3] => 11110100 => 4
[[1,3,7],[2,5],[4,6],[8]] => [[1,4,8],[2,6],[3,7],[5]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,7],[3,5],[4,6],[8]] => [[1,3,8],[2,6],[4,7],[5]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,7],[2,4],[5,6],[8]] => [[1,4,8],[2,5],[3,7],[6]] => [1,1,2,1,3] => 11101100 => 3
[[1,2,7],[3,4],[5,6],[8]] => [[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => 11010100 => 2
[[1,4,6],[2,5],[3,7],[8]] => [[1,5,7],[2,6],[3,8],[4]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3,6],[2,5],[4,7],[8]] => [[1,4,7],[2,6],[3,8],[5]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,6],[3,5],[4,7],[8]] => [[1,3,7],[2,6],[4,8],[5]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,6],[2,4],[5,7],[8]] => [[1,4,7],[2,5],[3,8],[6]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2,6],[3,4],[5,7],[8]] => [[1,3,7],[2,5],[4,8],[6]] => [1,2,2,2,1] => 11010101 => 2
[[1,4,5],[2,6],[3,7],[8]] => [[1,5,6],[2,7],[3,8],[4]] => [1,1,1,3,2] => 11110010 => 4
[[1,3,5],[2,6],[4,7],[8]] => [[1,4,6],[2,7],[3,8],[5]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,6],[4,7],[8]] => [[1,3,6],[2,7],[4,8],[5]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,6],[5,7],[8]] => [[1,4,5],[2,7],[3,8],[6]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4],[3,6],[5,7],[8]] => [[1,3,5],[2,7],[4,8],[6]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,6],[5,7],[8]] => [[1,3,4],[2,7],[5,8],[6]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,5],[2,4],[6,7],[8]] => [[1,4,6],[2,5],[3,8],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,4],[6,7],[8]] => [[1,3,6],[2,5],[4,8],[7]] => [1,2,3,2] => 11010010 => 2
[[1,3,4],[2,5],[6,7],[8]] => [[1,4,5],[2,6],[3,8],[7]] => [1,1,3,1,2] => 11100110 => 3
[[1,2,4],[3,5],[6,7],[8]] => [[1,3,5],[2,6],[4,8],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,5],[6,7],[8]] => [[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => 11001010 => 2
[[1,6,8],[2,7],[3],[4],[5]] => [[1,2,7],[3,8],[4],[5],[6]] => [2,1,1,1,2,1] => 10111101 => 1
[[1,5,8],[2,7],[3],[4],[6]] => [[1,2,6],[3,8],[4],[5],[7]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,8],[2,7],[3],[5],[6]] => [[1,2,5],[3,8],[4],[6],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,8],[2,7],[4],[5],[6]] => [[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,8],[3,7],[4],[5],[6]] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 10011110 => 1
[[1,5,8],[2,6],[3],[4],[7]] => [[1,2,6],[3,7],[4],[5],[8]] => [2,1,1,2,1,1] => 10111011 => 1
[[1,4,8],[2,6],[3],[5],[7]] => [[1,2,5],[3,7],[4],[6],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,8],[2,6],[4],[5],[7]] => [[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,8],[3,6],[4],[5],[7]] => [[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1] => 10011101 => 1
[[1,4,8],[2,5],[3],[6],[7]] => [[1,2,5],[3,6],[4],[7],[8]] => [2,1,2,1,1,1] => 10110111 => 1
[[1,3,8],[2,5],[4],[6],[7]] => [[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,8],[3,5],[4],[6],[7]] => [[1,2,3],[4,6],[5],[7],[8]] => [3,1,2,1,1] => 10011011 => 1
[[1,3,8],[2,4],[5],[6],[7]] => [[1,2,4],[3,5],[6],[7],[8]] => [2,2,1,1,1,1] => 10101111 => 1
[[1,2,8],[3,4],[5],[6],[7]] => [[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1] => 10010111 => 1
[[1,6,7],[2,8],[3],[4],[5]] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 10111100 => 1
[[1,5,7],[2,8],[3],[4],[6]] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 10111010 => 1
[[1,4,7],[2,8],[3],[5],[6]] => [[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3,7],[2,8],[4],[5],[6]] => [[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2,7],[3,8],[4],[5],[6]] => [[1,3,8],[2,4],[5],[6],[7]] => [1,2,1,1,1,2] => 11011110 => 2
[[1,5,6],[2,8],[3],[4],[7]] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 10111001 => 1
[[1,4,6],[2,8],[3],[5],[7]] => [[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3,6],[2,8],[4],[5],[7]] => [[1,2,7],[3,4],[5],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2,6],[3,8],[4],[5],[7]] => [[1,3,7],[2,4],[5],[6],[8]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4,5],[2,8],[3],[6],[7]] => [[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1] => 10110011 => 1
[[1,3,5],[2,8],[4],[6],[7]] => [[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2,5],[3,8],[4],[6],[7]] => [[1,3,6],[2,4],[5],[7],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3,4],[2,8],[5],[6],[7]] => [[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1] => 10100111 => 1
[[1,2,4],[3,8],[5],[6],[7]] => [[1,3,5],[2,4],[6],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,2,3],[4,8],[5],[6],[7]] => [[1,3,4],[2,5],[6],[7],[8]] => [1,3,1,1,1,1] => 11001111 => 2
[[1,5,7],[2,6],[3],[4],[8]] => [[1,6,8],[2,7],[3],[4],[5]] => [1,1,1,1,2,2] => 11111010 => 5
[[1,4,7],[2,6],[3],[5],[8]] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11110100 => 4
[[1,3,7],[2,6],[4],[5],[8]] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 11101100 => 3
[[1,2,7],[3,6],[4],[5],[8]] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 11011100 => 2
[[1,4,7],[2,5],[3],[6],[8]] => [[1,5,8],[2,6],[3],[4],[7]] => [1,1,1,2,1,2] => 11110110 => 4
[[1,3,7],[2,5],[4],[6],[8]] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,7],[3,5],[4],[6],[8]] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,7],[2,4],[5],[6],[8]] => [[1,4,8],[2,5],[3],[6],[7]] => [1,1,2,1,1,2] => 11101110 => 3
[[1,2,7],[3,4],[5],[6],[8]] => [[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,5,6],[2,7],[3],[4],[8]] => [[1,6,7],[2,8],[3],[4],[5]] => [1,1,1,1,3,1] => 11111001 => 5
[[1,4,6],[2,7],[3],[5],[8]] => [[1,5,7],[2,8],[3],[4],[6]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3,6],[2,7],[4],[5],[8]] => [[1,4,7],[2,8],[3],[5],[6]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2,6],[3,7],[4],[5],[8]] => [[1,3,7],[2,8],[4],[5],[6]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4,5],[2,7],[3],[6],[8]] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 11110010 => 4
[[1,3,5],[2,7],[4],[6],[8]] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2,5],[3,7],[4],[6],[8]] => [[1,3,6],[2,8],[4],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3,4],[2,7],[5],[6],[8]] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 11100110 => 3
[[1,2,4],[3,7],[5],[6],[8]] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,2,3],[4,7],[5],[6],[8]] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 11001110 => 2
[[1,4,6],[2,5],[3],[7],[8]] => [[1,5,7],[2,6],[3],[4],[8]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3,6],[2,5],[4],[7],[8]] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 11101001 => 3
[[1,2,6],[3,5],[4],[7],[8]] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 11011001 => 2
[[1,3,6],[2,4],[5],[7],[8]] => [[1,4,7],[2,5],[3],[6],[8]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2,6],[3,4],[5],[7],[8]] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,4,5],[2,6],[3],[7],[8]] => [[1,5,6],[2,7],[3],[4],[8]] => [1,1,1,3,1,1] => 11110011 => 4
[[1,3,5],[2,6],[4],[7],[8]] => [[1,4,6],[2,7],[3],[5],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2,5],[3,6],[4],[7],[8]] => [[1,3,6],[2,7],[4],[5],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3,4],[2,6],[5],[7],[8]] => [[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1] => 11100101 => 3
[[1,2,4],[3,6],[5],[7],[8]] => [[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,2,3],[4,6],[5],[7],[8]] => [[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => 11001101 => 2
[[1,3,5],[2,4],[6],[7],[8]] => [[1,4,6],[2,5],[3],[7],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2,5],[3,4],[6],[7],[8]] => [[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1] => 11010011 => 2
[[1,3,4],[2,5],[6],[7],[8]] => [[1,4,5],[2,6],[3],[7],[8]] => [1,1,3,1,1,1] => 11100111 => 3
[[1,2,4],[3,5],[6],[7],[8]] => [[1,3,5],[2,6],[4],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,2,3],[4,5],[6],[7],[8]] => [[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1] => 11001011 => 2
[[1,7,8],[2],[3],[4],[5],[6]] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 10111110 => 1
[[1,6,8],[2],[3],[4],[5],[7]] => [[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 10111101 => 1
[[1,5,8],[2],[3],[4],[6],[7]] => [[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 10111011 => 1
[[1,4,8],[2],[3],[5],[6],[7]] => [[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 10110111 => 1
[[1,3,8],[2],[4],[5],[6],[7]] => [[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 10101111 => 1
[[1,2,8],[3],[4],[5],[6],[7]] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 10011111 => 1
[[1,6,7],[2],[3],[4],[5],[8]] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 11111100 => 6
[[1,5,7],[2],[3],[4],[6],[8]] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 11111010 => 5
[[1,4,7],[2],[3],[5],[6],[8]] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 11110110 => 4
[[1,3,7],[2],[4],[5],[6],[8]] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 11101110 => 3
[[1,2,7],[3],[4],[5],[6],[8]] => [[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 11011110 => 2
[[1,5,6],[2],[3],[4],[7],[8]] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 11111001 => 5
[[1,4,6],[2],[3],[5],[7],[8]] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3,6],[2],[4],[5],[7],[8]] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2,6],[3],[4],[5],[7],[8]] => [[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4,5],[2],[3],[6],[7],[8]] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 11110011 => 4
[[1,3,5],[2],[4],[6],[7],[8]] => [[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2,5],[3],[4],[6],[7],[8]] => [[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3,4],[2],[5],[6],[7],[8]] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 11100111 => 3
[[1,2,4],[3],[5],[6],[7],[8]] => [[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,2,3],[4],[5],[6],[7],[8]] => [[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => 11001111 => 2
[[1,5],[2,6],[3,7],[4,8]] => [[1,2],[3,6],[4,7],[5,8]] => [2,1,1,2,2] => 10111010 => 1
[[1,4],[2,6],[3,7],[5,8]] => [[1,2],[3,5],[4,7],[6,8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3],[2,6],[4,7],[5,8]] => [[1,2],[3,4],[5,7],[6,8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2],[3,6],[4,7],[5,8]] => [[1,3],[2,4],[5,7],[6,8]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4],[2,5],[3,7],[6,8]] => [[1,2],[3,5],[4,6],[7,8]] => [2,1,2,1,2] => 10110110 => 1
[[1,3],[2,5],[4,7],[6,8]] => [[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 10101010 => 1
[[1,2],[3,5],[4,7],[6,8]] => [[1,3],[2,4],[5,6],[7,8]] => [1,2,1,2,2] => 11011010 => 2
[[1,3],[2,4],[5,7],[6,8]] => [[1,4],[2,5],[3,6],[7,8]] => [1,1,2,2,2] => 11101010 => 3
[[1,2],[3,4],[5,7],[6,8]] => [[1,3],[2,5],[4,6],[7,8]] => [1,2,2,1,2] => 11010110 => 2
[[1,4],[2,5],[3,6],[7,8]] => [[1,5],[2,6],[3,7],[4,8]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3],[2,5],[4,6],[7,8]] => [[1,4],[2,6],[3,7],[5,8]] => [1,1,2,2,2] => 11101010 => 3
[[1,2],[3,5],[4,6],[7,8]] => [[1,3],[2,6],[4,7],[5,8]] => [1,2,1,2,2] => 11011010 => 2
[[1,3],[2,4],[5,6],[7,8]] => [[1,4],[2,5],[3,7],[6,8]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2],[3,4],[5,6],[7,8]] => [[1,3],[2,5],[4,7],[6,8]] => [1,2,2,2,1] => 11010101 => 2
[[1,6],[2,7],[3,8],[4],[5]] => [[1,2],[3,7],[4,8],[5],[6]] => [2,1,1,1,2,1] => 10111101 => 1
[[1,5],[2,7],[3,8],[4],[6]] => [[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2] => 10111010 => 1
[[1,4],[2,7],[3,8],[5],[6]] => [[1,2],[3,5],[4,8],[6],[7]] => [2,1,2,1,2] => 10110110 => 1
[[1,3],[2,7],[4,8],[5],[6]] => [[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => 10101110 => 1
[[1,2],[3,7],[4,8],[5],[6]] => [[1,3],[2,4],[5,8],[6],[7]] => [1,2,1,1,1,2] => 11011110 => 2
[[1,5],[2,6],[3,8],[4],[7]] => [[1,2],[3,6],[4,7],[5],[8]] => [2,1,1,2,1,1] => 10111011 => 1
[[1,4],[2,6],[3,8],[5],[7]] => [[1,2],[3,5],[4,7],[6],[8]] => [2,1,2,2,1] => 10110101 => 1
[[1,3],[2,6],[4,8],[5],[7]] => [[1,2],[3,4],[5,7],[6],[8]] => [2,2,1,2,1] => 10101101 => 1
[[1,2],[3,6],[4,8],[5],[7]] => [[1,3],[2,4],[5,7],[6],[8]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4],[2,5],[3,8],[6],[7]] => [[1,2],[3,5],[4,6],[7],[8]] => [2,1,2,1,1,1] => 10110111 => 1
[[1,3],[2,5],[4,8],[6],[7]] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 10101011 => 1
[[1,2],[3,5],[4,8],[6],[7]] => [[1,3],[2,4],[5,6],[7],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3],[2,4],[5,8],[6],[7]] => [[1,4],[2,5],[3,6],[7],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2],[3,4],[5,8],[6],[7]] => [[1,3],[2,5],[4,6],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,5],[2,6],[3,7],[4],[8]] => [[1,6],[2,7],[3,8],[4],[5]] => [1,1,1,1,2,2] => 11111010 => 5
[[1,4],[2,6],[3,7],[5],[8]] => [[1,5],[2,7],[3,8],[4],[6]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3],[2,6],[4,7],[5],[8]] => [[1,4],[2,7],[3,8],[5],[6]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2],[3,6],[4,7],[5],[8]] => [[1,3],[2,7],[4,8],[5],[6]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4],[2,5],[3,7],[6],[8]] => [[1,5],[2,6],[3,8],[4],[7]] => [1,1,1,2,1,2] => 11110110 => 4
[[1,3],[2,5],[4,7],[6],[8]] => [[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => 11101010 => 3
[[1,2],[3,5],[4,7],[6],[8]] => [[1,3],[2,6],[4,8],[5],[7]] => [1,2,1,2,2] => 11011010 => 2
[[1,3],[2,4],[5,7],[6],[8]] => [[1,4],[2,5],[3,8],[6],[7]] => [1,1,2,1,1,2] => 11101110 => 3
[[1,2],[3,4],[5,7],[6],[8]] => [[1,3],[2,5],[4,8],[6],[7]] => [1,2,2,1,2] => 11010110 => 2
[[1,4],[2,5],[3,6],[7],[8]] => [[1,5],[2,6],[3,7],[4],[8]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3],[2,5],[4,6],[7],[8]] => [[1,4],[2,6],[3,7],[5],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2],[3,5],[4,6],[7],[8]] => [[1,3],[2,6],[4,7],[5],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3],[2,4],[5,6],[7],[8]] => [[1,4],[2,5],[3,7],[6],[8]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2],[3,4],[5,6],[7],[8]] => [[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1] => 11010101 => 2
[[1,7],[2,8],[3],[4],[5],[6]] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 10111110 => 1
[[1,6],[2,8],[3],[4],[5],[7]] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 10111101 => 1
[[1,5],[2,8],[3],[4],[6],[7]] => [[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 10111011 => 1
[[1,4],[2,8],[3],[5],[6],[7]] => [[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 10110111 => 1
[[1,3],[2,8],[4],[5],[6],[7]] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 10101111 => 1
[[1,2],[3,8],[4],[5],[6],[7]] => [[1,3],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 11011111 => 2
[[1,6],[2,7],[3],[4],[5],[8]] => [[1,7],[2,8],[3],[4],[5],[6]] => [1,1,1,1,1,2,1] => 11111101 => 6
[[1,5],[2,7],[3],[4],[6],[8]] => [[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 11111010 => 5
[[1,4],[2,7],[3],[5],[6],[8]] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 11110110 => 4
[[1,3],[2,7],[4],[5],[6],[8]] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 11101110 => 3
[[1,2],[3,7],[4],[5],[6],[8]] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 11011110 => 2
[[1,5],[2,6],[3],[4],[7],[8]] => [[1,6],[2,7],[3],[4],[5],[8]] => [1,1,1,1,2,1,1] => 11111011 => 5
[[1,4],[2,6],[3],[5],[7],[8]] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 11110101 => 4
[[1,3],[2,6],[4],[5],[7],[8]] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 11101101 => 3
[[1,2],[3,6],[4],[5],[7],[8]] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 11011101 => 2
[[1,4],[2,5],[3],[6],[7],[8]] => [[1,5],[2,6],[3],[4],[7],[8]] => [1,1,1,2,1,1,1] => 11110111 => 4
[[1,3],[2,5],[4],[6],[7],[8]] => [[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 11101011 => 3
[[1,2],[3,5],[4],[6],[7],[8]] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 11011011 => 2
[[1,3],[2,4],[5],[6],[7],[8]] => [[1,4],[2,5],[3],[6],[7],[8]] => [1,1,2,1,1,1,1] => 11101111 => 3
[[1,2],[3,4],[5],[6],[7],[8]] => [[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 11010111 => 2
[[1,8],[2],[3],[4],[5],[6],[7]] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 10111111 => 1
[[1,7],[2],[3],[4],[5],[6],[8]] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 11111110 => 7
[[1,6],[2],[3],[4],[5],[7],[8]] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 11111101 => 6
[[1,5],[2],[3],[4],[6],[7],[8]] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 11111011 => 5
[[1,4],[2],[3],[5],[6],[7],[8]] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 11110111 => 4
[[1,3],[2],[4],[5],[6],[7],[8]] => [[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => 11101111 => 3
[[1,2],[3],[4],[5],[6],[7],[8]] => [[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 11011111 => 2
[[1],[2],[3],[4],[5],[6],[7],[8]] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 11111111 => 8
[[1,3,5,7,9],[2,4,6,8,10]] => [[1,2,4,6,8],[3,5,7,9,10]] => [2,2,2,2,2] => 1010101010 => 1
[[1,3,5,7,8],[2,4,6,9,10]] => [[1,2,4,6,9],[3,5,7,8,10]] => [2,2,2,3,1] => 1010101001 => 1
[[1,3,5,6,8],[2,4,7,9,10]] => [[1,2,4,7,9],[3,5,6,8,10]] => [2,2,3,2,1] => 1010100101 => 1
[[1,3,4,6,8],[2,5,7,9,10]] => [[1,2,5,7,9],[3,4,6,8,10]] => [2,3,2,2,1] => 1010010101 => 1
[[1,2,4,6,7],[3,5,8,9,10]] => [[1,3,5,7,8],[2,4,6,9,10]] => [1,2,2,3,2] => 1101010010 => 2
[[1,2,4,5,8],[3,6,7,9,10]] => [[1,3,5,6,9],[2,4,7,8,10]] => [1,2,3,3,1] => 1101001001 => 2
[[1,2,4,5,7],[3,6,8,9,10]] => [[1,3,5,6,8],[2,4,7,9,10]] => [1,2,3,2,2] => 1101001010 => 2
[[1,2,3,6,8],[4,5,7,9,10]] => [[1,3,4,7,9],[2,5,6,8,10]] => [1,3,3,2,1] => 1100100101 => 2
[[1,2,3,5,8],[4,6,7,9,10]] => [[1,3,4,6,9],[2,5,7,8,10]] => [1,3,2,3,1] => 1100101001 => 2
[[1,2,3,5,7],[4,6,8,9,10]] => [[1,3,4,6,8],[2,5,7,9,10]] => [1,3,2,2,2] => 1100101010 => 2
[[1,2,3,4,7],[5,6,8,9,10]] => [[1,3,4,5,8],[2,6,7,9,10]] => [1,4,3,2] => 1100010010 => 2
[[1,2,3,4,5],[6,7,8,9,10]] => [[1,3,4,5,6],[2,7,8,9,10]] => [1,5,4] => 1100001000 => 2
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [2,2,2,2,2,2] => 101010101010 => 1
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [2,2,2,2,3,1] => 101010101001 => 1
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [2,2,2,3,2,1] => 101010100101 => 1
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [2,2,3,2,2,1] => 101010010101 => 1
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => [2,3,2,2,2,1] => 101001010101 => 1
[[1,2,4,6,8,9],[3,5,7,10,11,12]] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [1,2,2,2,3,2] => 110101010010 => 2
[[1,2,4,6,7,10],[3,5,8,9,11,12]] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [1,2,2,3,3,1] => 110101001001 => 2
[[1,2,4,6,7,9],[3,5,8,10,11,12]] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [1,2,2,3,2,2] => 110101001010 => 2
[[1,2,4,5,8,10],[3,6,7,9,11,12]] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [1,2,3,3,2,1] => 110100100101 => 2
[[1,2,4,5,7,10],[3,6,8,9,11,12]] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [1,2,3,2,3,1] => 110100101001 => 2
[[1,2,4,5,7,9],[3,6,8,10,11,12]] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [1,2,3,2,2,2] => 110100101010 => 2
[[1,2,3,6,8,10],[4,5,7,9,11,12]] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [1,3,3,2,2,1] => 110010010101 => 2
[[1,2,3,5,8,10],[4,6,7,9,11,12]] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [1,3,2,3,2,1] => 110010100101 => 2
[[1,2,3,5,7,10],[4,6,8,9,11,12]] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [1,3,2,2,3,1] => 110010101001 => 2
[[1,2,3,5,7,9],[4,6,8,10,11,12]] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [1,3,2,2,2,2] => 110010101010 => 2
[[1,2,3,4,5,6,7,8,9]] => [[1,2,3,4,5,6,7,8,9]] => [9] => 100000000 => 1
[[1,2,3,4,5,6,7,8],[9]] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 110000000 => 2
[[1,2,3,4,5,6,7],[8,9]] => [[1,3,4,5,6,7,8],[2,9]] => [1,7,1] => 110000001 => 2
[[1,2,3,4,5,6,7],[8],[9]] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 110000001 => 2
[[1,2,3,4,5,6],[7,8,9]] => [[1,3,4,5,6,7],[2,8,9]] => [1,6,2] => 110000010 => 2
[[1,2,3,4,5,6],[7,8],[9]] => [[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => 110000010 => 2
[[1,2,3,4,5,6],[7],[8],[9]] => [[1,3,4,5,6,7],[2],[8],[9]] => [1,6,1,1] => 110000011 => 2
[[1,2,3,4,5],[6,7,8,9]] => [[1,3,4,5,6],[2,7,8,9]] => [1,5,3] => 110000100 => 2
[[1,2,3,4,5],[6,7,8],[9]] => [[1,3,4,5,6],[2,8,9],[7]] => [1,5,3] => 110000100 => 2
[[1,2,3,4,5],[6,7],[8,9]] => [[1,3,4,5,6],[2,8],[7,9]] => [1,5,2,1] => 110000101 => 2
[[1,2,3,4,5],[6,7],[8],[9]] => [[1,3,4,5,6],[2,8],[7],[9]] => [1,5,2,1] => 110000101 => 2
[[1,2,3,4,5],[6],[7],[8],[9]] => [[1,3,4,5,6],[2],[7],[8],[9]] => [1,5,1,1,1] => 110000111 => 2
[[1,2,3,4],[5,6,7,8],[9]] => [[1,3,4,5],[2,7,8,9],[6]] => [1,4,4] => 110001000 => 2
[[1,2,3,4],[5,6,7],[8,9]] => [[1,3,4,5],[2,7,8],[6,9]] => [1,4,3,1] => 110001001 => 2
[[1,2,3,4],[5,6,7],[8],[9]] => [[1,3,4,5],[2,7,8],[6],[9]] => [1,4,3,1] => 110001001 => 2
[[1,2,3,4],[5,6],[7,8],[9]] => [[1,3,4,5],[2,7],[6,9],[8]] => [1,4,2,2] => 110001010 => 2
[[1,2,3,4],[5,6],[7],[8],[9]] => [[1,3,4,5],[2,7],[6],[8],[9]] => [1,4,2,1,1] => 110001011 => 2
[[1,2,3,4],[5],[6],[7],[8],[9]] => [[1,3,4,5],[2],[6],[7],[8],[9]] => [1,4,1,1,1,1] => 110001111 => 2
[[1,2,3],[4,5,6],[7,8,9]] => [[1,3,4],[2,6,7],[5,8,9]] => [1,3,3,2] => 110010010 => 2
[[1,2,3],[4,5,6],[7,8],[9]] => [[1,3,4],[2,6,7],[5,9],[8]] => [1,3,3,2] => 110010010 => 2
[[1,2,3],[4,5,6],[7],[8],[9]] => [[1,3,4],[2,6,7],[5],[8],[9]] => [1,3,3,1,1] => 110010011 => 2
[[1,2,3],[4,5],[6,7],[8,9]] => [[1,3,4],[2,6],[5,8],[7,9]] => [1,3,2,2,1] => 110010101 => 2
[[1,2,3],[4,5],[6,7],[8],[9]] => [[1,3,4],[2,6],[5,8],[7],[9]] => [1,3,2,2,1] => 110010101 => 2
[[1,2,3],[4,5],[6],[7],[8],[9]] => [[1,3,4],[2,6],[5],[7],[8],[9]] => [1,3,2,1,1,1] => 110010111 => 2
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [[1,3,4],[2],[5],[6],[7],[8],[9]] => [1,3,1,1,1,1,1] => 110011111 => 2
[[1,2],[3,4],[5,6],[7,8],[9]] => [[1,3],[2,5],[4,7],[6,9],[8]] => [1,2,2,2,2] => 110101010 => 2
[[1,2],[3,4],[5,6],[7],[8],[9]] => [[1,3],[2,5],[4,7],[6],[8],[9]] => [1,2,2,2,1,1] => 110101011 => 2
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [[1,3],[2,5],[4],[6],[7],[8],[9]] => [1,2,2,1,1,1,1] => 110101111 => 2
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [[1,3],[2],[4],[5],[6],[7],[8],[9]] => [1,2,1,1,1,1,1,1] => 110111111 => 2
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,1] => 111111111 => 9
[[1,2,3,4,5,6,7,8,9,10]] => [[1,2,3,4,5,6,7,8,9,10]] => [10] => 1000000000 => 1
[[1,2,3,4,5],[6,7,8,9],[10]] => [[1,3,4,5,6],[2,8,9,10],[7]] => [1,5,4] => 1100001000 => 2
[[1,2,3,4],[5,6,7],[8,9,10]] => [[1,3,4,5],[2,7,8],[6,9,10]] => [1,4,3,2] => 1100010010 => 2
[[1,2,3,4],[5,6,7],[8,9],[10]] => [[1,3,4,5],[2,7,8],[6,10],[9]] => [1,4,3,2] => 1100010010 => 2
[[1,2,3,4],[5,6],[7,8],[9,10]] => [[1,3,4,5],[2,7],[6,9],[8,10]] => [1,4,2,2,1] => 1100010101 => 2
[[1,2,3,4],[5,6],[7,8],[9],[10]] => [[1,3,4,5],[2,7],[6,9],[8],[10]] => [1,4,2,2,1] => 1100010101 => 2
[[1,2,3],[4,5,6],[7,8],[9,10]] => [[1,3,4],[2,6,7],[5,9],[8,10]] => [1,3,3,2,1] => 1100100101 => 2
[[1,2,3],[4,5,6],[7,8],[9],[10]] => [[1,3,4],[2,6,7],[5,9],[8],[10]] => [1,3,3,2,1] => 1100100101 => 2
[[1,2,3],[4,5],[6,7],[8,9],[10]] => [[1,3,4],[2,6],[5,8],[7,10],[9]] => [1,3,2,2,2] => 1100101010 => 2
[[1,3,4,5,6,7,8,9],[2]] => [[1,2,4,5,6,7,8,9],[3]] => [2,7] => 101000000 => 1
[[1,2,5,6,7,8,9],[3,4]] => [[1,2,3,6,7,8,9],[4,5]] => [3,6] => 100100000 => 1
[[1,4,5,6,7,8,9],[2],[3]] => [[1,2,5,6,7,8,9],[3],[4]] => [2,1,6] => 101100000 => 1
[[1,2,3,7,8,9],[4,5,6]] => [[1,2,3,4,8,9],[5,6,7]] => [4,5] => 100010000 => 1
[[1,3,6,7,8,9],[2,5],[4]] => [[1,2,4,7,8,9],[3,6],[5]] => [2,2,5] => 101010000 => 1
[[1,5,6,7,8,9],[2],[3],[4]] => [[1,2,6,7,8,9],[3],[4],[5]] => [2,1,1,5] => 101110000 => 1
[[1,2,3,4,9],[5,6,7,8]] => [[1,2,3,4,5],[6,7,8,9]] => [5,4] => 100001000 => 1
[[1,3,4,8,9],[2,6,7],[5]] => [[1,2,4,5,9],[3,7,8],[6]] => [2,3,4] => 101001000 => 1
[[1,2,7,8,9],[3,4],[5,6]] => [[1,2,3,8,9],[4,5],[6,7]] => [3,2,4] => 100101000 => 1
[[1,4,7,8,9],[2,6],[3],[5]] => [[1,2,5,8,9],[3,7],[4],[6]] => [2,1,2,4] => 101101000 => 1
[[1,6,7,8,9],[2],[3],[4],[5]] => [[1,2,7,8,9],[3],[4],[5],[6]] => [2,1,1,1,4] => 101111000 => 1
[[1,3,4,5],[2,7,8,9],[6]] => [[1,2,5,6],[3,4,8,9],[7]] => [2,4,3] => 101000100 => 1
[[1,2,5,9],[3,4,8],[6,7]] => [[1,2,3,6],[4,5,9],[7,8]] => [3,3,3] => 100100100 => 1
[[1,4,5,9],[2,7,8],[3],[6]] => [[1,2,5,6],[3,8,9],[4],[7]] => [2,1,3,3] => 101100100 => 1
[[1,3,8,9],[2,5],[4,7],[6]] => [[1,2,4,9],[3,6],[5,8],[7]] => [2,2,2,3] => 101010100 => 1
[[1,5,8,9],[2,7],[3],[4],[6]] => [[1,2,6,9],[3,8],[4],[5],[7]] => [2,1,1,2,3] => 101110100 => 1
[[1,7,8,9],[2],[3],[4],[5],[6]] => [[1,2,8,9],[3],[4],[5],[6],[7]] => [2,1,1,1,1,3] => 101111100 => 1
[[1,3,6],[2,5,9],[4,8],[7]] => [[1,2,4],[3,6,7],[5,9],[8]] => [2,2,3,2] => 101010010 => 1
[[1,5,6],[2,8,9],[3],[4],[7]] => [[1,2,7],[3,6,9],[4],[5],[8]] => [2,1,1,3,2] => 101110010 => 1
[[1,2,9],[3,4],[5,6],[7,8]] => [[1,2,3],[4,5],[6,7],[8,9]] => [3,2,2,2] => 100101010 => 1
[[1,4,9],[2,6],[3,8],[5],[7]] => [[1,2,5],[3,7],[4,9],[6],[8]] => [2,1,2,2,2] => 101101010 => 1
[[1,6,9],[2,8],[3],[4],[5],[7]] => [[1,2,7],[3,9],[4],[5],[6],[8]] => [2,1,1,1,2,2] => 101111010 => 1
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [[1,2,9],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,2] => 101111110 => 1
[[1,3],[2,5],[4,7],[6,9],[8]] => [[1,2],[3,4],[5,6],[7,8],[9]] => [2,2,2,2,1] => 101010101 => 1
[[1,5],[2,7],[3,9],[4],[6],[8]] => [[1,2],[3,6],[4,8],[5],[7],[9]] => [2,1,1,2,2,1] => 101110101 => 1
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [[1,2],[3,8],[4],[5],[6],[7],[9]] => [2,1,1,1,1,2,1] => 101111101 => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,1] => 101111111 => 1
[[1,6,7,8,9,10],[2],[3],[4],[5]] => [[1,2,7,8,9,10],[3],[4],[5],[6]] => [2,1,1,1,5] => 1011110000 => 1
[[1,5,8,9,10],[2,7],[3],[4],[6]] => [[1,2,6,9,10],[3,8],[4],[5],[7]] => [2,1,1,2,4] => 1011101000 => 1
[[1,5,6,10],[2,8,9],[3],[4],[7]] => [[1,2,6,7],[3,9,10],[4],[5],[8]] => [2,1,1,3,3] => 1011100100 => 1
[[1,4,9,10],[2,6],[3,8],[5],[7]] => [[1,2,5,10],[3,7],[4,9],[6],[8]] => [2,1,2,2,3] => 1011010100 => 1
[[1,4,7],[2,6,10],[3,9],[5],[8]] => [[1,2,5],[3,7,8],[4,10],[6],[9]] => [2,1,2,3,2] => 1011010010 => 1
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [[1,2,4],[3,6],[5,8],[7,10],[9]] => [2,2,2,2,2] => 1010101010 => 1
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 1011111110 => 1
[[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => [2,1,1,1,1,1,2,1] => 1011111101 => 1
[[1,2,3,7],[4,5,6,11],[8,9,10]] => [[1,2,3,4],[5,6,7,8],[9,10,11]] => [4,4,3] => 10001000100 => 1
[[1,2,5],[3,4,8],[6,7,11],[9,10]] => [[1,2,3],[4,5,6],[7,8,9],[10,11]] => [3,3,3,2] => 10010010010 => 1
[[1,8],[2,9],[3],[4],[5],[6],[7]] => [[1,2],[3,9],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,2] => 101111110 => 1
[[1,7],[2,8],[3,9],[4],[5],[6]] => [[1,2],[3,8],[4,9],[5],[6],[7]] => [2,1,1,1,1,2,1] => 101111101 => 1
[[1,7,9],[2,8],[3],[4],[5],[6]] => [[1,2,8],[3,9],[4],[5],[6],[7]] => [2,1,1,1,1,2,1] => 101111101 => 1
[[1,6],[2,7],[3,8],[4,9],[5]] => [[1,2],[3,7],[4,8],[5,9],[6]] => [2,1,1,1,2,2] => 101111010 => 1
[[1,6,9],[2,7],[3,8],[4],[5]] => [[1,2,7],[3,8],[4,9],[5],[6]] => [2,1,1,1,2,2] => 101111010 => 1
[[1,6,8],[2,7,9],[3],[4],[5]] => [[1,2,7],[3,8,9],[4],[5],[6]] => [2,1,1,1,2,2] => 101111010 => 1
[[1,6,8,9],[2,7],[3],[4],[5]] => [[1,2,7,9],[3,8],[4],[5],[6]] => [2,1,1,1,2,2] => 101111010 => 1
[[1,5,9],[2,6],[3,7],[4,8]] => [[1,2,6],[3,7],[4,8],[5,9]] => [2,1,1,2,2,1] => 101110101 => 1
[[1,5,8],[2,6,9],[3,7],[4]] => [[1,2,6],[3,7,9],[4,8],[5]] => [2,1,1,2,3] => 101110100 => 1
[[1,5,8,9],[2,6],[3,7],[4]] => [[1,2,6,9],[3,7],[4,8],[5]] => [2,1,1,2,3] => 101110100 => 1
[[1,5,7,9],[2,6,8],[3],[4]] => [[1,2,6,8],[3,7,9],[4],[5]] => [2,1,1,2,2,1] => 101110101 => 1
[[1,5,7,8,9],[2,6],[3],[4]] => [[1,2,6,8,9],[3,7],[4],[5]] => [2,1,1,2,3] => 101110100 => 1
[[1,4,7],[2,5,8],[3,6,9]] => [[1,2,5],[3,6,8],[4,7,9]] => [2,1,2,3,1] => 101101001 => 1
[[1,4,7,9],[2,5,8],[3,6]] => [[1,2,5,8],[3,6,9],[4,7]] => [2,1,2,3,1] => 101101001 => 1
[[1,4,7,8,9],[2,5],[3,6]] => [[1,2,5,8,9],[3,6],[4,7]] => [2,1,2,4] => 101101000 => 1
[[1,4,6,8],[2,5,7,9],[3]] => [[1,2,5,7],[3,6,8,9],[4]] => [2,1,2,2,2] => 101101010 => 1
[[1,4,6,8,9],[2,5,7],[3]] => [[1,2,5,7,9],[3,6,8],[4]] => [2,1,2,2,2] => 101101010 => 1
[[1,4,6,7,8,9],[2,5],[3]] => [[1,2,5,7,8,9],[3,6],[4]] => [2,1,2,4] => 101101000 => 1
[[1,3,5,7,9],[2,4,6,8]] => [[1,2,4,6,8],[3,5,7,9]] => [2,2,2,2,1] => 101010101 => 1
[[1,3,5,7,8,9],[2,4,6]] => [[1,2,4,6,8,9],[3,5,7]] => [2,2,2,3] => 101010100 => 1
[[1,3,5,6,7,8,9],[2,4]] => [[1,2,4,6,7,8,9],[3,5]] => [2,2,5] => 101010000 => 1
[[1,9],[2,10],[3],[4],[5],[6],[7],[8]] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 1011111110 => 1
[[1,8],[2,9],[3,10],[4],[5],[6],[7]] => [[1,2],[3,9],[4,10],[5],[6],[7],[8]] => [2,1,1,1,1,1,2,1] => 1011111101 => 1
[[1,8,10],[2,9],[3],[4],[5],[6],[7]] => [[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,2,1] => 1011111101 => 1
[[1,5,8,9,10],[2,6],[3,7],[4]] => [[1,2,6,9,10],[3,7],[4,8],[5]] => [2,1,1,2,4] => 1011101000 => 1
[[1,5,7,8,9,10],[2,6],[3],[4]] => [[1,2,6,8,9,10],[3,7],[4],[5]] => [2,1,1,2,4] => 1011101000 => 1
[[1,4,7,10],[2,5,8],[3,6,9]] => [[1,2,5,8],[3,6,9],[4,7,10]] => [2,1,2,3,2] => 1011010010 => 1
[[1,4,7,9],[2,5,8,10],[3,6]] => [[1,2,5,8],[3,6,9,10],[4,7]] => [2,1,2,3,2] => 1011010010 => 1
[[1,4,7,9,10],[2,5,8],[3,6]] => [[1,2,5,8,10],[3,6,9],[4,7]] => [2,1,2,3,2] => 1011010010 => 1
[[1,4,6,8,9,10],[2,5,7],[3]] => [[1,2,5,7,9,10],[3,6,8],[4]] => [2,1,2,2,3] => 1011010100 => 1
[[1,3,5,7,9,10],[2,4,6,8]] => [[1,2,4,6,8,10],[3,5,7,9]] => [2,2,2,2,2] => 1010101010 => 1
[[1,3],[2,4],[5],[6],[7],[8],[9]] => [[1,4],[2,5],[3],[6],[7],[8],[9]] => [1,1,2,1,1,1,1,1] => 111011111 => 3
[[1,4],[2,5],[3,6],[7],[8],[9]] => [[1,5],[2,6],[3,7],[4],[8],[9]] => [1,1,1,2,2,1,1] => 111101011 => 4
[[1,2,4],[3,5],[6],[7],[8],[9]] => [[1,3,5],[2,6],[4],[7],[8],[9]] => [1,2,2,1,1,1,1] => 110101111 => 2
[[1,5],[2,6],[3,7],[4,8],[9]] => [[1,6],[2,7],[3,8],[4,9],[5]] => [1,1,1,1,2,2,1] => 111110101 => 5
[[1,2,5],[3,6],[4,7],[8],[9]] => [[1,3,6],[2,7],[4,8],[5],[9]] => [1,2,1,2,2,1] => 110110101 => 2
[[1,3,5],[2,4,6],[7],[8],[9]] => [[1,4,6],[2,5,7],[3],[8],[9]] => [1,1,2,2,1,1,1] => 111010111 => 3
[[1,2,3,5],[4,6],[7],[8],[9]] => [[1,3,4,6],[2,7],[5],[8],[9]] => [1,3,2,1,1,1] => 110010111 => 2
[[1,2,6],[3,7],[4,8],[5,9]] => [[1,3,7],[2,4],[5,8],[6,9]] => [1,2,1,1,2,2] => 110111010 => 2
[[1,3,6],[2,4,7],[5,8],[9]] => [[1,4,7],[2,5,8],[3,9],[6]] => [1,1,2,1,2,2] => 111011010 => 3
[[1,2,3,6],[4,7],[5,8],[9]] => [[1,3,4,7],[2,8],[5,9],[6]] => [1,3,1,2,2] => 110011010 => 2
[[1,2,4,6],[3,5,7],[8],[9]] => [[1,3,5,7],[2,6,8],[4],[9]] => [1,2,2,2,1,1] => 110101011 => 2
[[1,2,3,4,6],[5,7],[8],[9]] => [[1,3,4,5,7],[2,8],[6],[9]] => [1,4,2,1,1] => 110001011 => 2
[[1,2,4,7],[3,5,8],[6,9]] => [[1,3,5,8],[2,6,9],[4,7]] => [1,2,2,3,1] => 110101001 => 2
[[1,2,3,4,7],[5,8],[6,9]] => [[1,3,4,5,8],[2,6],[7,9]] => [1,4,1,2,1] => 110001101 => 2
[[1,3,5,7],[2,4,6,8],[9]] => [[1,4,6,8],[2,5,7,9],[3]] => [1,1,2,2,2,1] => 111010101 => 3
[[1,2,3,5,7],[4,6,8],[9]] => [[1,3,4,6,8],[2,7,9],[5]] => [1,3,2,2,1] => 110010101 => 2
[[1,2,3,4,5,7],[6,8],[9]] => [[1,3,4,5,6,8],[2,9],[7]] => [1,5,2,1] => 110000101 => 2
[[1,2,4,6,8],[3,5,7,9]] => [[1,3,5,7,9],[2,4,6,8]] => [1,2,2,2,2] => 110101010 => 2
[[1,2,3,4,6,8],[5,7,9]] => [[1,3,4,5,7,9],[2,6,8]] => [1,4,2,2] => 110001010 => 2
[[1,2,3,4,5,6,8],[7,9]] => [[1,3,4,5,6,7,9],[2,8]] => [1,6,2] => 110000010 => 2
[[1,2,3,5,8],[4,6,9],[7,10]] => [[1,3,4,6,9],[2,7,10],[5,8]] => [1,3,2,3,1] => 1100101001 => 2
[[1,2,3,4,6,8],[5,7,9],[10]] => [[1,3,4,5,7,9],[2,8,10],[6]] => [1,4,2,2,1] => 1100010101 => 2
[[1,2,3,5,7,9],[4,6,8,10]] => [[1,3,4,6,8,10],[2,5,7,9]] => [1,3,2,2,2] => 1100101010 => 2
[[1,3],[2,5],[4,7],[6,9],[8,10]] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => [2,2,2,2,2] => 1010101010 => 1
[[1,3],[2,5],[4,7],[6,9],[8,11],[10,12]] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 101010101010 => 1
[[1,2,3,4,5,6,7,9],[8]] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 100000001 => 1
[[1,2,3,4,5,6,9],[7],[8]] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 100000011 => 1
[[1,2,3,4,5,9],[6],[7],[8]] => [[1,2,3,4,5,6],[7],[8],[9]] => [6,1,1,1] => 100000111 => 1
[[1,2,3,4,9],[5,6],[7,8]] => [[1,2,3,4,5],[6,7],[8,9]] => [5,2,2] => 100001010 => 1
[[1,2,3,4,9],[5],[6],[7],[8]] => [[1,2,3,4,5],[6],[7],[8],[9]] => [5,1,1,1,1] => 100001111 => 1
[[1,2,3,9],[4,5,6],[7,8]] => [[1,2,3,4],[5,6,7],[8,9]] => [4,3,2] => 100010010 => 1
[[1,2,3,9],[4],[5],[6],[7],[8]] => [[1,2,3,4],[5],[6],[7],[8],[9]] => [4,1,1,1,1,1] => 100011111 => 1
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,1] => 100111111 => 1
[[1,2,3,4,5,6,10],[7,8,9]] => [[1,2,3,4,5,6,7],[8,9,10]] => [7,3] => 1000000100 => 1
[[1,5,7],[2,8],[3],[4],[6],[9]] => [[1,6,8],[2,9],[3],[4],[5],[7]] => [1,1,1,1,2,2,1] => 111110101 => 5
[[1,4],[2,6],[3,8],[5],[7],[9]] => [[1,5],[2,7],[3,9],[4],[6],[8]] => [1,1,1,2,2,2] => 111101010 => 4
[[1,6],[2,8],[3],[4],[5],[7],[9]] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,2] => 111111010 => 6
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,2] => 111111110 => 8
[[1,3,5,7,8,10],[2,4,6,9]] => [[1,2,4,6,8,9],[3,5,7,10]] => [2,2,2,3,1] => 1010101001 => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [1,1,1,1,1,1,1,1,2] => 1111111110 => 9
[[1,3,4,5,6,7,8],[2,9]] => [[1,2,5,6,7,8,9],[3,4]] => [2,7] => 101000000 => 1
[[1,3,4,5,6,7,8],[2],[9]] => [[1,4,5,6,7,8,9],[2],[3]] => [1,1,7] => 111000000 => 3
[[1,3,4,5,6,7],[2,8,9]] => [[1,2,5,6,7,8],[3,4,9]] => [2,6,1] => 101000001 => 1
[[1,3,4,5,6,7],[2,9],[8]] => [[1,2,5,6,7,8],[3,4],[9]] => [2,6,1] => 101000001 => 1
[[1,3,4,5,6,7],[2],[8],[9]] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 111000001 => 3
[[1,3,4,5],[2,7,8],[6],[9]] => [[1,4,5,6],[2,8,9],[3],[7]] => [1,1,4,3] => 111000100 => 3
[[1,3,4],[2,6,7],[5,8,9]] => [[1,2,5],[3,4,8],[6,7,9]] => [2,3,3,1] => 101001001 => 1
[[1,3,4],[2,6,7],[5,9],[8]] => [[1,2,5],[3,4,8],[6,7],[9]] => [2,3,3,1] => 101001001 => 1
[[1,3,4],[2,6,7],[5],[8],[9]] => [[1,4,5],[2,7,8],[3],[6],[9]] => [1,1,3,3,1] => 111001001 => 3
[[1,3],[2,5],[4,7],[6],[8],[9]] => [[1,4],[2,6],[3,8],[5],[7],[9]] => [1,1,2,2,2,1] => 111010101 => 3
[[1,3,4],[2,6,7],[5,9],[8],[10]] => [[1,4,5],[2,7,8],[3,10],[6],[9]] => [1,1,3,3,2] => 1110010010 => 3
[[1,2,4,6,8,10],[3,5,7,9]] => [[1,2,3,5,7,9],[4,6,8,10]] => [3,2,2,2,1] => 1001010101 => 1
[[1,2,3,4,5,6,9,10],[7,8]] => [[1,2,3,4,5,6,7,10],[8,9]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,7,9,10],[6,8]] => [[1,2,3,4,5,6,8,10],[7,9]] => [6,2,2] => 1000001010 => 1
[[1,2,3,4,5,6,7,9,10],[8]] => [[1,2,3,4,5,6,7,8,10],[9]] => [8,2] => 1000000010 => 1
[[1,2,3,4,5,6,8,9,10],[7]] => [[1,2,3,4,5,6,7,9,10],[8]] => [7,3] => 1000000100 => 1
[[1,2,3,6,7,8,9],[4,5]] => [[1,2,3,4,7,8,9],[5,6]] => [4,5] => 100010000 => 1
[[1,2,3,4,8,9],[5,6,7]] => [[1,2,3,4,5,9],[6,7,8]] => [5,4] => 100001000 => 1
[[1,2,3,8,9],[4,5],[6,7]] => [[1,2,3,4,9],[5,6],[7,8]] => [4,2,3] => 100010100 => 1
[[1,2,5,6],[3,4,8,9],[7]] => [[1,2,3,7],[4,5,6,9],[8]] => [3,4,2] => 100100010 => 1
[[1,2,4,9],[3,6],[5,8],[7]] => [[1,2,3,5],[4,7],[6,9],[8]] => [3,2,2,2] => 100101010 => 1
[[1,2,8,9],[3],[4],[5],[6],[7]] => [[1,2,3,9],[4],[5],[6],[7],[8]] => [3,1,1,1,1,2] => 100111110 => 1
[[1,2,7],[3,6,9],[4],[5],[8]] => [[1,2,3],[4,7,8],[5],[6],[9]] => [3,1,1,3,1] => 100111001 => 1
[[1,2],[3,8],[4],[5],[6],[7],[9]] => [[1,3],[2,9],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,2] => 110111110 => 2
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [[1,2,3,10],[4],[5],[6],[7],[8],[9]] => [3,1,1,1,1,1,2] => 1001111110 => 1
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => [[1,3],[2,10],[4],[5],[6],[7],[8],[9]] => [1,2,1,1,1,1,1,2] => 1101111110 => 2
[[1,2,3,4,7,8,9],[5,6]] => [[1,2,3,4,5,8,9],[6,7]] => [5,4] => 100001000 => 1
[[1,2,4,5,6,7],[3,9],[8]] => [[1,3,5,6,7,8],[2,4],[9]] => [1,2,5,1] => 110100001 => 2
[[1,2,3,4,7,8],[5,6],[9]] => [[1,3,4,5,8,9],[2,7],[6]] => [1,4,4] => 110001000 => 2
[[1,8],[2],[3],[4],[5],[6],[7],[9],[10]] => [[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [1,1,1,1,1,1,1,2,1] => 1111111101 => 8
[[1,2,3,4,6,9],[5,8],[7]] => [[1,2,3,4,5,7],[6,9],[8]] => [5,2,2] => 100001010 => 1
[[1,2,3,5,7,9],[4,6,8]] => [[1,2,3,4,6,8],[5,7,9]] => [4,2,2,1] => 100010101 => 1
[[1,2,3,4,5,7,9],[6,8]] => [[1,2,3,4,5,6,8],[7,9]] => [6,2,1] => 100000101 => 1
[[1,2,3,4],[5,6,7,9],[8],[10]] => [[1,3,4,5],[2,7,8,10],[6],[9]] => [1,4,3,2] => 1100010010 => 2
[[1,2,3,4,5,7,10],[6,9],[8]] => [[1,2,3,4,5,6,8],[7,10],[9]] => [6,2,2] => 1000001010 => 1
[[1,2,8],[3,9],[4],[5],[6],[7]] => [[1,3,9],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,2] => 110111110 => 2
[[1,2,6,9],[3,7],[4,8],[5]] => [[1,2,3,7],[4,8],[5,9],[6]] => [3,1,1,2,2] => 100111010 => 1
[[1,2,5,8],[3,6,9],[4,7]] => [[1,3,6,9],[2,4,7],[5,8]] => [1,2,1,2,3] => 110110100 => 2
[[1,2,5,8,9],[3,6],[4,7]] => [[1,2,3,6,9],[4,7],[5,8]] => [3,1,2,3] => 100110100 => 1
[[1,2,4,6,8,9],[3,5,7]] => [[1,2,3,5,7,9],[4,6,8]] => [3,2,2,2] => 100101010 => 1
[[1,2,9],[3,10],[4],[5],[6],[7],[8]] => [[1,3,10],[2,4],[5],[6],[7],[8],[9]] => [1,2,1,1,1,1,1,2] => 1101111110 => 2
[[1,2,5,8,10],[3,6,9],[4,7]] => [[1,2,3,6,9],[4,7,10],[5,8]] => [3,1,2,3,1] => 1001101001 => 1
[[1,3,8],[2,9],[4],[5],[6],[7]] => [[1,2,9],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,2] => 101011110 => 1
[[1,5,7],[2,6,8],[3],[4],[9]] => [[1,6,8],[2,7,9],[3],[4],[5]] => [1,1,1,1,2,2,1] => 111110101 => 5
[[1,4,7],[2,6,9],[3,8,10],[5]] => [[1,2,5],[3,7,8],[4,9,10],[6]] => [2,1,2,3,2] => 1011010010 => 1
[[1,4,7],[2,5,8],[3,6],[9]] => [[1,5,8],[2,6,9],[3,7],[4]] => [1,1,1,2,3,1] => 111101001 => 4
[[1,3,6,9],[2,4,7],[5,8,10]] => [[1,4,7,10],[2,5,8],[3,6,9]] => [1,1,2,3,3] => 1110100100 => 3
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [[1,3],[2,4],[5],[6],[7],[8],[9]] => [1,2,1,1,1,1,1,1] => 110111111 => 2
[[1,2],[3,8],[4,9],[5],[6],[7]] => [[1,3],[2,4],[5,9],[6],[7],[8]] => [1,2,1,1,1,1,2] => 110111110 => 2
[[1,2,5],[3,6,8],[4,7,9]] => [[1,3,6],[2,4,7],[5,8,9]] => [1,2,1,2,3] => 110110100 => 2
[[1,2],[3,9],[4,10],[5],[6],[7],[8]] => [[1,3],[2,4],[5,10],[6],[7],[8],[9]] => [1,2,1,1,1,1,1,2] => 1101111110 => 2
[[1,2,3,5,7],[4,6,8,9]] => [[1,3,4,6,8],[2,5,7,9]] => [1,3,2,2,1] => 110010101 => 2
[[1,3,6,10],[2,4,7],[5,8,9]] => [[1,2,4,7],[3,5,8],[6,9,10]] => [2,2,1,2,3] => 1010110100 => 1
[[1,2,4,6,9],[3,5,7],[8]] => [[1,2,3,5,7],[4,6,8],[9]] => [3,2,2,1,1] => 100101011 => 1
[[1,4],[2,5],[3],[6],[7],[8],[9]] => [[1,5],[2,6],[3],[4],[7],[8],[9]] => [1,1,1,2,1,1,1,1] => 111101111 => 4
[[1,5],[2,6],[3,7],[4],[8],[9]] => [[1,6],[2,7],[3,8],[4],[5],[9]] => [1,1,1,1,2,2,1] => 111110101 => 5
[[1,4,6],[2,5,7],[3],[8],[9]] => [[1,5,7],[2,6,8],[3],[4],[9]] => [1,1,1,2,2,1,1] => 111101011 => 4
[[1,3,7],[2,4],[5,8],[6,9]] => [[1,4,8],[2,5],[3,6],[7,9]] => [1,1,2,2,2,1] => 111010101 => 3
[[1,3,5,7],[2,6,8],[4],[9]] => [[1,4,6,8],[2,7,9],[3],[5]] => [1,1,2,2,2,1] => 111010101 => 3
[[1,3,4,5,8],[2,6],[7,9]] => [[1,4,5,6,9],[2,7],[3,8]] => [1,1,4,3] => 111000100 => 3
[[1,3,4,5,6,8],[2,9],[7]] => [[1,2,5,6,7,9],[3,4],[8]] => [2,5,2] => 101000010 => 1
[[1,3,4,5,6,7,9],[2,8]] => [[1,2,4,5,6,7,8],[3,9]] => [2,6,1] => 101000001 => 1
[[1,3,4,6,8,10],[2,5,7,9]] => [[1,2,4,5,7,9],[3,6,8,10]] => [2,3,2,2,1] => 1010010101 => 1
[[1,2,3,4,5,8,9],[6,7]] => [[1,2,3,4,5,6,9],[7,8]] => [6,3] => 100000100 => 1
[[1,2,3,5],[4,6,8],[7,9,10]] => [[1,3,4,6],[2,7,9],[5,8,10]] => [1,3,2,3,1] => 1100101001 => 2
[[1,2,3,4,7,9],[5,8],[6]] => [[1,2,3,4,5,8],[6,9],[7]] => [5,1,2,1] => 100001101 => 1
[[1,2,3,6,8],[4,7],[5],[9]] => [[1,3,4,7,9],[2,8],[5],[6]] => [1,3,1,2,2] => 110011010 => 2
[[1,3,6,9],[2,5],[4],[7],[8]] => [[1,2,4,7],[3,6],[5],[8],[9]] => [2,2,3,1,1] => 101010011 => 1
[[1,3,8],[2,5],[4,7],[6,10],[9]] => [[1,2,9],[3,4],[5,6],[7,8],[10]] => [2,2,2,3,1] => 1010101001 => 1
[[1,2,4,7],[3,5,8],[6,9,10]] => [[1,3,5,8],[2,6,9],[4,7,10]] => [1,2,2,3,2] => 1101010010 => 2
[[1,2,5],[3,4,8],[6,7,9],[10]] => [[1,3,6],[2,5,9],[4,8,10],[7]] => [1,2,3,3,1] => 1101001001 => 2
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,1,1 5,3,1,1 13,8,3,1,1 38,24,9,3,1,1 116,74,28,9,3,1,1 382,246,93,29,9,3,1,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2} + q^{3}$
$F_{4} = 5\ q + 3\ q^{2} + q^{3} + q^{4}$
$F_{5} = 13\ q + 8\ q^{2} + 3\ q^{3} + q^{4} + q^{5}$
$F_{6} = 38\ q + 24\ q^{2} + 9\ q^{3} + 3\ q^{4} + q^{5} + q^{6}$
$F_{7} = 116\ q + 74\ q^{2} + 28\ q^{3} + 9\ q^{4} + 3\ q^{5} + q^{6} + q^{7}$
$F_{8} = 382\ q + 246\ q^{2} + 93\ q^{3} + 29\ q^{4} + 9\ q^{5} + 3\ q^{6} + q^{7} + q^{8}$
Description
The number of leading ones in a binary word.
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Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.
Map
promotion
Description
The promotion of a standard Young tableau.
This map replaces the largest entry of the tableau with a zero, uses the jeu de taquin to move it to the origin, and finally increases all entries by one.
This map replaces the largest entry of the tableau with a zero, uses the jeu de taquin to move it to the origin, and finally increases all entries by one.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
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