Identifier
-
Mp00295:
Standard tableaux
—valley composition⟶
Integer compositions
Mp00094: Integer compositions —to binary word⟶ Binary words
St000392: Binary words ⟶ ℤ
Values
[[1]] => [1] => 1 => 1
[[1,2]] => [2] => 10 => 1
[[1],[2]] => [2] => 10 => 1
[[1,2,3]] => [3] => 100 => 1
[[1,3],[2]] => [2,1] => 101 => 1
[[1,2],[3]] => [3] => 100 => 1
[[1],[2],[3]] => [3] => 100 => 1
[[1,2,3,4]] => [4] => 1000 => 1
[[1,3,4],[2]] => [2,2] => 1010 => 1
[[1,2,4],[3]] => [3,1] => 1001 => 1
[[1,2,3],[4]] => [4] => 1000 => 1
[[1,3],[2,4]] => [2,2] => 1010 => 1
[[1,2],[3,4]] => [3,1] => 1001 => 1
[[1,4],[2],[3]] => [3,1] => 1001 => 1
[[1,3],[2],[4]] => [2,2] => 1010 => 1
[[1,2],[3],[4]] => [4] => 1000 => 1
[[1],[2],[3],[4]] => [4] => 1000 => 1
[[1,2,3,4,5]] => [5] => 10000 => 1
[[1,3,4,5],[2]] => [2,3] => 10100 => 1
[[1,2,4,5],[3]] => [3,2] => 10010 => 1
[[1,2,3,5],[4]] => [4,1] => 10001 => 1
[[1,2,3,4],[5]] => [5] => 10000 => 1
[[1,3,5],[2,4]] => [2,2,1] => 10101 => 1
[[1,2,5],[3,4]] => [3,2] => 10010 => 1
[[1,3,4],[2,5]] => [2,3] => 10100 => 1
[[1,2,4],[3,5]] => [3,2] => 10010 => 1
[[1,2,3],[4,5]] => [4,1] => 10001 => 1
[[1,4,5],[2],[3]] => [3,2] => 10010 => 1
[[1,3,5],[2],[4]] => [2,2,1] => 10101 => 1
[[1,2,5],[3],[4]] => [4,1] => 10001 => 1
[[1,3,4],[2],[5]] => [2,3] => 10100 => 1
[[1,2,4],[3],[5]] => [3,2] => 10010 => 1
[[1,2,3],[4],[5]] => [5] => 10000 => 1
[[1,4],[2,5],[3]] => [3,2] => 10010 => 1
[[1,3],[2,5],[4]] => [2,2,1] => 10101 => 1
[[1,2],[3,5],[4]] => [4,1] => 10001 => 1
[[1,3],[2,4],[5]] => [2,3] => 10100 => 1
[[1,2],[3,4],[5]] => [3,2] => 10010 => 1
[[1,5],[2],[3],[4]] => [4,1] => 10001 => 1
[[1,4],[2],[3],[5]] => [3,2] => 10010 => 1
[[1,3],[2],[4],[5]] => [2,3] => 10100 => 1
[[1,2],[3],[4],[5]] => [5] => 10000 => 1
[[1],[2],[3],[4],[5]] => [5] => 10000 => 1
[[1,2,3,4,5,6]] => [6] => 100000 => 1
[[1,3,4,5,6],[2]] => [2,4] => 101000 => 1
[[1,2,4,5,6],[3]] => [3,3] => 100100 => 1
[[1,2,3,5,6],[4]] => [4,2] => 100010 => 1
[[1,2,3,4,6],[5]] => [5,1] => 100001 => 1
[[1,2,3,4,5],[6]] => [6] => 100000 => 1
[[1,3,5,6],[2,4]] => [2,2,2] => 101010 => 1
[[1,2,5,6],[3,4]] => [3,3] => 100100 => 1
[[1,3,4,6],[2,5]] => [2,3,1] => 101001 => 1
[[1,2,4,6],[3,5]] => [3,2,1] => 100101 => 1
[[1,2,3,6],[4,5]] => [4,2] => 100010 => 1
[[1,3,4,5],[2,6]] => [2,4] => 101000 => 1
[[1,2,4,5],[3,6]] => [3,3] => 100100 => 1
[[1,2,3,5],[4,6]] => [4,2] => 100010 => 1
[[1,2,3,4],[5,6]] => [5,1] => 100001 => 1
[[1,4,5,6],[2],[3]] => [3,3] => 100100 => 1
[[1,3,5,6],[2],[4]] => [2,2,2] => 101010 => 1
[[1,2,5,6],[3],[4]] => [4,2] => 100010 => 1
[[1,3,4,6],[2],[5]] => [2,3,1] => 101001 => 1
[[1,2,4,6],[3],[5]] => [3,2,1] => 100101 => 1
[[1,2,3,6],[4],[5]] => [5,1] => 100001 => 1
[[1,3,4,5],[2],[6]] => [2,4] => 101000 => 1
[[1,2,4,5],[3],[6]] => [3,3] => 100100 => 1
[[1,2,3,5],[4],[6]] => [4,2] => 100010 => 1
[[1,2,3,4],[5],[6]] => [6] => 100000 => 1
[[1,3,5],[2,4,6]] => [2,2,2] => 101010 => 1
[[1,2,5],[3,4,6]] => [3,3] => 100100 => 1
[[1,3,4],[2,5,6]] => [2,3,1] => 101001 => 1
[[1,2,4],[3,5,6]] => [3,2,1] => 100101 => 1
[[1,2,3],[4,5,6]] => [4,2] => 100010 => 1
[[1,4,6],[2,5],[3]] => [3,2,1] => 100101 => 1
[[1,3,6],[2,5],[4]] => [2,2,2] => 101010 => 1
[[1,2,6],[3,5],[4]] => [4,2] => 100010 => 1
[[1,3,6],[2,4],[5]] => [2,3,1] => 101001 => 1
[[1,2,6],[3,4],[5]] => [3,2,1] => 100101 => 1
[[1,4,5],[2,6],[3]] => [3,3] => 100100 => 1
[[1,3,5],[2,6],[4]] => [2,2,2] => 101010 => 1
[[1,2,5],[3,6],[4]] => [4,2] => 100010 => 1
[[1,3,4],[2,6],[5]] => [2,3,1] => 101001 => 1
[[1,2,4],[3,6],[5]] => [3,2,1] => 100101 => 1
[[1,2,3],[4,6],[5]] => [5,1] => 100001 => 1
[[1,3,5],[2,4],[6]] => [2,2,2] => 101010 => 1
[[1,2,5],[3,4],[6]] => [3,3] => 100100 => 1
[[1,3,4],[2,5],[6]] => [2,4] => 101000 => 1
[[1,2,4],[3,5],[6]] => [3,3] => 100100 => 1
[[1,2,3],[4,5],[6]] => [4,2] => 100010 => 1
[[1,5,6],[2],[3],[4]] => [4,2] => 100010 => 1
[[1,4,6],[2],[3],[5]] => [3,2,1] => 100101 => 1
[[1,3,6],[2],[4],[5]] => [2,3,1] => 101001 => 1
[[1,2,6],[3],[4],[5]] => [5,1] => 100001 => 1
[[1,4,5],[2],[3],[6]] => [3,3] => 100100 => 1
[[1,3,5],[2],[4],[6]] => [2,2,2] => 101010 => 1
[[1,2,5],[3],[4],[6]] => [4,2] => 100010 => 1
[[1,3,4],[2],[5],[6]] => [2,4] => 101000 => 1
[[1,2,4],[3],[5],[6]] => [3,3] => 100100 => 1
[[1,2,3],[4],[5],[6]] => [6] => 100000 => 1
[[1,4],[2,5],[3,6]] => [3,3] => 100100 => 1
[[1,3],[2,5],[4,6]] => [2,2,2] => 101010 => 1
>>> Load all 1367 entries. <<<[[1,2],[3,5],[4,6]] => [4,2] => 100010 => 1
[[1,3],[2,4],[5,6]] => [2,3,1] => 101001 => 1
[[1,2],[3,4],[5,6]] => [3,2,1] => 100101 => 1
[[1,5],[2,6],[3],[4]] => [4,2] => 100010 => 1
[[1,4],[2,6],[3],[5]] => [3,2,1] => 100101 => 1
[[1,3],[2,6],[4],[5]] => [2,3,1] => 101001 => 1
[[1,2],[3,6],[4],[5]] => [5,1] => 100001 => 1
[[1,4],[2,5],[3],[6]] => [3,3] => 100100 => 1
[[1,3],[2,5],[4],[6]] => [2,2,2] => 101010 => 1
[[1,2],[3,5],[4],[6]] => [4,2] => 100010 => 1
[[1,3],[2,4],[5],[6]] => [2,4] => 101000 => 1
[[1,2],[3,4],[5],[6]] => [3,3] => 100100 => 1
[[1,6],[2],[3],[4],[5]] => [5,1] => 100001 => 1
[[1,5],[2],[3],[4],[6]] => [4,2] => 100010 => 1
[[1,4],[2],[3],[5],[6]] => [3,3] => 100100 => 1
[[1,3],[2],[4],[5],[6]] => [2,4] => 101000 => 1
[[1,2],[3],[4],[5],[6]] => [6] => 100000 => 1
[[1],[2],[3],[4],[5],[6]] => [6] => 100000 => 1
[[1,2,3,4,5,6,7]] => [7] => 1000000 => 1
[[1,3,4,5,6,7],[2]] => [2,5] => 1010000 => 1
[[1,2,4,5,6,7],[3]] => [3,4] => 1001000 => 1
[[1,2,3,5,6,7],[4]] => [4,3] => 1000100 => 1
[[1,2,3,4,6,7],[5]] => [5,2] => 1000010 => 1
[[1,2,3,4,5,7],[6]] => [6,1] => 1000001 => 1
[[1,2,3,4,5,6],[7]] => [7] => 1000000 => 1
[[1,3,5,6,7],[2,4]] => [2,2,3] => 1010100 => 1
[[1,2,5,6,7],[3,4]] => [3,4] => 1001000 => 1
[[1,3,4,6,7],[2,5]] => [2,3,2] => 1010010 => 1
[[1,2,4,6,7],[3,5]] => [3,2,2] => 1001010 => 1
[[1,2,3,6,7],[4,5]] => [4,3] => 1000100 => 1
[[1,3,4,5,7],[2,6]] => [2,4,1] => 1010001 => 1
[[1,2,4,5,7],[3,6]] => [3,3,1] => 1001001 => 1
[[1,2,3,5,7],[4,6]] => [4,2,1] => 1000101 => 1
[[1,2,3,4,7],[5,6]] => [5,2] => 1000010 => 1
[[1,3,4,5,6],[2,7]] => [2,5] => 1010000 => 1
[[1,2,4,5,6],[3,7]] => [3,4] => 1001000 => 1
[[1,2,3,5,6],[4,7]] => [4,3] => 1000100 => 1
[[1,2,3,4,6],[5,7]] => [5,2] => 1000010 => 1
[[1,2,3,4,5],[6,7]] => [6,1] => 1000001 => 1
[[1,4,5,6,7],[2],[3]] => [3,4] => 1001000 => 1
[[1,3,5,6,7],[2],[4]] => [2,2,3] => 1010100 => 1
[[1,2,5,6,7],[3],[4]] => [4,3] => 1000100 => 1
[[1,3,4,6,7],[2],[5]] => [2,3,2] => 1010010 => 1
[[1,2,4,6,7],[3],[5]] => [3,2,2] => 1001010 => 1
[[1,2,3,6,7],[4],[5]] => [5,2] => 1000010 => 1
[[1,3,4,5,7],[2],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4,5,7],[3],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3,5,7],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,2,3,4,7],[5],[6]] => [6,1] => 1000001 => 1
[[1,3,4,5,6],[2],[7]] => [2,5] => 1010000 => 1
[[1,2,4,5,6],[3],[7]] => [3,4] => 1001000 => 1
[[1,2,3,5,6],[4],[7]] => [4,3] => 1000100 => 1
[[1,2,3,4,6],[5],[7]] => [5,2] => 1000010 => 1
[[1,2,3,4,5],[6],[7]] => [7] => 1000000 => 1
[[1,3,5,7],[2,4,6]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,4,6]] => [3,3,1] => 1001001 => 1
[[1,3,4,7],[2,5,6]] => [2,3,2] => 1010010 => 1
[[1,2,4,7],[3,5,6]] => [3,2,2] => 1001010 => 1
[[1,2,3,7],[4,5,6]] => [4,3] => 1000100 => 1
[[1,3,5,6],[2,4,7]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3,4,7]] => [3,4] => 1001000 => 1
[[1,3,4,6],[2,5,7]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3,5,7]] => [3,2,2] => 1001010 => 1
[[1,2,3,6],[4,5,7]] => [4,3] => 1000100 => 1
[[1,3,4,5],[2,6,7]] => [2,4,1] => 1010001 => 1
[[1,2,4,5],[3,6,7]] => [3,3,1] => 1001001 => 1
[[1,2,3,5],[4,6,7]] => [4,2,1] => 1000101 => 1
[[1,2,3,4],[5,6,7]] => [5,2] => 1000010 => 1
[[1,4,6,7],[2,5],[3]] => [3,2,2] => 1001010 => 1
[[1,3,6,7],[2,5],[4]] => [2,2,3] => 1010100 => 1
[[1,2,6,7],[3,5],[4]] => [4,3] => 1000100 => 1
[[1,3,6,7],[2,4],[5]] => [2,3,2] => 1010010 => 1
[[1,2,6,7],[3,4],[5]] => [3,2,2] => 1001010 => 1
[[1,4,5,7],[2,6],[3]] => [3,3,1] => 1001001 => 1
[[1,3,5,7],[2,6],[4]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,6],[4]] => [4,2,1] => 1000101 => 1
[[1,3,4,7],[2,6],[5]] => [2,3,2] => 1010010 => 1
[[1,2,4,7],[3,6],[5]] => [3,2,2] => 1001010 => 1
[[1,2,3,7],[4,6],[5]] => [5,2] => 1000010 => 1
[[1,3,5,7],[2,4],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3,4],[6]] => [3,3,1] => 1001001 => 1
[[1,3,4,7],[2,5],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4,7],[3,5],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3,7],[4,5],[6]] => [4,2,1] => 1000101 => 1
[[1,4,5,6],[2,7],[3]] => [3,4] => 1001000 => 1
[[1,3,5,6],[2,7],[4]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3,7],[4]] => [4,3] => 1000100 => 1
[[1,3,4,6],[2,7],[5]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3,7],[5]] => [3,2,2] => 1001010 => 1
[[1,2,3,6],[4,7],[5]] => [5,2] => 1000010 => 1
[[1,3,4,5],[2,7],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4,5],[3,7],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3,5],[4,7],[6]] => [4,2,1] => 1000101 => 1
[[1,2,3,4],[5,7],[6]] => [6,1] => 1000001 => 1
[[1,3,5,6],[2,4],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3,4],[7]] => [3,4] => 1001000 => 1
[[1,3,4,6],[2,5],[7]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3,5],[7]] => [3,2,2] => 1001010 => 1
[[1,2,3,6],[4,5],[7]] => [4,3] => 1000100 => 1
[[1,3,4,5],[2,6],[7]] => [2,5] => 1010000 => 1
[[1,2,4,5],[3,6],[7]] => [3,4] => 1001000 => 1
[[1,2,3,5],[4,6],[7]] => [4,3] => 1000100 => 1
[[1,2,3,4],[5,6],[7]] => [5,2] => 1000010 => 1
[[1,5,6,7],[2],[3],[4]] => [4,3] => 1000100 => 1
[[1,4,6,7],[2],[3],[5]] => [3,2,2] => 1001010 => 1
[[1,3,6,7],[2],[4],[5]] => [2,3,2] => 1010010 => 1
[[1,2,6,7],[3],[4],[5]] => [5,2] => 1000010 => 1
[[1,4,5,7],[2],[3],[6]] => [3,3,1] => 1001001 => 1
[[1,3,5,7],[2],[4],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2,5,7],[3],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,3,4,7],[2],[5],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4,7],[3],[5],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3,7],[4],[5],[6]] => [6,1] => 1000001 => 1
[[1,4,5,6],[2],[3],[7]] => [3,4] => 1001000 => 1
[[1,3,5,6],[2],[4],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5,6],[3],[4],[7]] => [4,3] => 1000100 => 1
[[1,3,4,6],[2],[5],[7]] => [2,3,2] => 1010010 => 1
[[1,2,4,6],[3],[5],[7]] => [3,2,2] => 1001010 => 1
[[1,2,3,6],[4],[5],[7]] => [5,2] => 1000010 => 1
[[1,3,4,5],[2],[6],[7]] => [2,5] => 1010000 => 1
[[1,2,4,5],[3],[6],[7]] => [3,4] => 1001000 => 1
[[1,2,3,5],[4],[6],[7]] => [4,3] => 1000100 => 1
[[1,2,3,4],[5],[6],[7]] => [7] => 1000000 => 1
[[1,4,6],[2,5,7],[3]] => [3,2,2] => 1001010 => 1
[[1,3,6],[2,5,7],[4]] => [2,2,3] => 1010100 => 1
[[1,2,6],[3,5,7],[4]] => [4,3] => 1000100 => 1
[[1,3,6],[2,4,7],[5]] => [2,3,2] => 1010010 => 1
[[1,2,6],[3,4,7],[5]] => [3,2,2] => 1001010 => 1
[[1,4,5],[2,6,7],[3]] => [3,3,1] => 1001001 => 1
[[1,3,5],[2,6,7],[4]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,6,7],[4]] => [4,2,1] => 1000101 => 1
[[1,3,4],[2,6,7],[5]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,6,7],[5]] => [3,2,2] => 1001010 => 1
[[1,2,3],[4,6,7],[5]] => [5,2] => 1000010 => 1
[[1,3,5],[2,4,7],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,4,7],[6]] => [3,3,1] => 1001001 => 1
[[1,3,4],[2,5,7],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4],[3,5,7],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3],[4,5,7],[6]] => [4,2,1] => 1000101 => 1
[[1,3,5],[2,4,6],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5],[3,4,6],[7]] => [3,4] => 1001000 => 1
[[1,3,4],[2,5,6],[7]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,5,6],[7]] => [3,2,2] => 1001010 => 1
[[1,2,3],[4,5,6],[7]] => [4,3] => 1000100 => 1
[[1,4,7],[2,5],[3,6]] => [3,3,1] => 1001001 => 1
[[1,3,7],[2,5],[4,6]] => [2,2,2,1] => 1010101 => 1
[[1,2,7],[3,5],[4,6]] => [4,2,1] => 1000101 => 1
[[1,3,7],[2,4],[5,6]] => [2,3,2] => 1010010 => 1
[[1,2,7],[3,4],[5,6]] => [3,2,2] => 1001010 => 1
[[1,4,6],[2,5],[3,7]] => [3,2,2] => 1001010 => 1
[[1,3,6],[2,5],[4,7]] => [2,2,3] => 1010100 => 1
[[1,2,6],[3,5],[4,7]] => [4,3] => 1000100 => 1
[[1,3,6],[2,4],[5,7]] => [2,3,2] => 1010010 => 1
[[1,2,6],[3,4],[5,7]] => [3,2,2] => 1001010 => 1
[[1,4,5],[2,6],[3,7]] => [3,4] => 1001000 => 1
[[1,3,5],[2,6],[4,7]] => [2,2,3] => 1010100 => 1
[[1,2,5],[3,6],[4,7]] => [4,3] => 1000100 => 1
[[1,3,4],[2,6],[5,7]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,6],[5,7]] => [3,2,2] => 1001010 => 1
[[1,2,3],[4,6],[5,7]] => [5,2] => 1000010 => 1
[[1,3,5],[2,4],[6,7]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,4],[6,7]] => [3,3,1] => 1001001 => 1
[[1,3,4],[2,5],[6,7]] => [2,4,1] => 1010001 => 1
[[1,2,4],[3,5],[6,7]] => [3,3,1] => 1001001 => 1
[[1,2,3],[4,5],[6,7]] => [4,2,1] => 1000101 => 1
[[1,5,7],[2,6],[3],[4]] => [4,2,1] => 1000101 => 1
[[1,4,7],[2,6],[3],[5]] => [3,2,2] => 1001010 => 1
[[1,3,7],[2,6],[4],[5]] => [2,3,2] => 1010010 => 1
[[1,2,7],[3,6],[4],[5]] => [5,2] => 1000010 => 1
[[1,4,7],[2,5],[3],[6]] => [3,3,1] => 1001001 => 1
[[1,3,7],[2,5],[4],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2,7],[3,5],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,3,7],[2,4],[5],[6]] => [2,4,1] => 1010001 => 1
[[1,2,7],[3,4],[5],[6]] => [3,3,1] => 1001001 => 1
[[1,5,6],[2,7],[3],[4]] => [4,3] => 1000100 => 1
[[1,4,6],[2,7],[3],[5]] => [3,2,2] => 1001010 => 1
[[1,3,6],[2,7],[4],[5]] => [2,3,2] => 1010010 => 1
[[1,2,6],[3,7],[4],[5]] => [5,2] => 1000010 => 1
[[1,4,5],[2,7],[3],[6]] => [3,3,1] => 1001001 => 1
[[1,3,5],[2,7],[4],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2,5],[3,7],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,3,4],[2,7],[5],[6]] => [2,4,1] => 1010001 => 1
[[1,2,4],[3,7],[5],[6]] => [3,3,1] => 1001001 => 1
[[1,2,3],[4,7],[5],[6]] => [6,1] => 1000001 => 1
[[1,4,6],[2,5],[3],[7]] => [3,2,2] => 1001010 => 1
[[1,3,6],[2,5],[4],[7]] => [2,2,3] => 1010100 => 1
[[1,2,6],[3,5],[4],[7]] => [4,3] => 1000100 => 1
[[1,3,6],[2,4],[5],[7]] => [2,3,2] => 1010010 => 1
[[1,2,6],[3,4],[5],[7]] => [3,2,2] => 1001010 => 1
[[1,4,5],[2,6],[3],[7]] => [3,4] => 1001000 => 1
[[1,3,5],[2,6],[4],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5],[3,6],[4],[7]] => [4,3] => 1000100 => 1
[[1,3,4],[2,6],[5],[7]] => [2,3,2] => 1010010 => 1
[[1,2,4],[3,6],[5],[7]] => [3,2,2] => 1001010 => 1
[[1,2,3],[4,6],[5],[7]] => [5,2] => 1000010 => 1
[[1,3,5],[2,4],[6],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5],[3,4],[6],[7]] => [3,4] => 1001000 => 1
[[1,3,4],[2,5],[6],[7]] => [2,5] => 1010000 => 1
[[1,2,4],[3,5],[6],[7]] => [3,4] => 1001000 => 1
[[1,2,3],[4,5],[6],[7]] => [4,3] => 1000100 => 1
[[1,6,7],[2],[3],[4],[5]] => [5,2] => 1000010 => 1
[[1,5,7],[2],[3],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,4,7],[2],[3],[5],[6]] => [3,3,1] => 1001001 => 1
[[1,3,7],[2],[4],[5],[6]] => [2,4,1] => 1010001 => 1
[[1,2,7],[3],[4],[5],[6]] => [6,1] => 1000001 => 1
[[1,5,6],[2],[3],[4],[7]] => [4,3] => 1000100 => 1
[[1,4,6],[2],[3],[5],[7]] => [3,2,2] => 1001010 => 1
[[1,3,6],[2],[4],[5],[7]] => [2,3,2] => 1010010 => 1
[[1,2,6],[3],[4],[5],[7]] => [5,2] => 1000010 => 1
[[1,4,5],[2],[3],[6],[7]] => [3,4] => 1001000 => 1
[[1,3,5],[2],[4],[6],[7]] => [2,2,3] => 1010100 => 1
[[1,2,5],[3],[4],[6],[7]] => [4,3] => 1000100 => 1
[[1,3,4],[2],[5],[6],[7]] => [2,5] => 1010000 => 1
[[1,2,4],[3],[5],[6],[7]] => [3,4] => 1001000 => 1
[[1,2,3],[4],[5],[6],[7]] => [7] => 1000000 => 1
[[1,5],[2,6],[3,7],[4]] => [4,3] => 1000100 => 1
[[1,4],[2,6],[3,7],[5]] => [3,2,2] => 1001010 => 1
[[1,3],[2,6],[4,7],[5]] => [2,3,2] => 1010010 => 1
[[1,2],[3,6],[4,7],[5]] => [5,2] => 1000010 => 1
[[1,4],[2,5],[3,7],[6]] => [3,3,1] => 1001001 => 1
[[1,3],[2,5],[4,7],[6]] => [2,2,2,1] => 1010101 => 1
[[1,2],[3,5],[4,7],[6]] => [4,2,1] => 1000101 => 1
[[1,3],[2,4],[5,7],[6]] => [2,4,1] => 1010001 => 1
[[1,2],[3,4],[5,7],[6]] => [3,3,1] => 1001001 => 1
[[1,4],[2,5],[3,6],[7]] => [3,4] => 1001000 => 1
[[1,3],[2,5],[4,6],[7]] => [2,2,3] => 1010100 => 1
[[1,2],[3,5],[4,6],[7]] => [4,3] => 1000100 => 1
[[1,3],[2,4],[5,6],[7]] => [2,3,2] => 1010010 => 1
[[1,2],[3,4],[5,6],[7]] => [3,2,2] => 1001010 => 1
[[1,6],[2,7],[3],[4],[5]] => [5,2] => 1000010 => 1
[[1,5],[2,7],[3],[4],[6]] => [4,2,1] => 1000101 => 1
[[1,4],[2,7],[3],[5],[6]] => [3,3,1] => 1001001 => 1
[[1,3],[2,7],[4],[5],[6]] => [2,4,1] => 1010001 => 1
[[1,2],[3,7],[4],[5],[6]] => [6,1] => 1000001 => 1
[[1,5],[2,6],[3],[4],[7]] => [4,3] => 1000100 => 1
[[1,4],[2,6],[3],[5],[7]] => [3,2,2] => 1001010 => 1
[[1,3],[2,6],[4],[5],[7]] => [2,3,2] => 1010010 => 1
[[1,2],[3,6],[4],[5],[7]] => [5,2] => 1000010 => 1
[[1,4],[2,5],[3],[6],[7]] => [3,4] => 1001000 => 1
[[1,3],[2,5],[4],[6],[7]] => [2,2,3] => 1010100 => 1
[[1,2],[3,5],[4],[6],[7]] => [4,3] => 1000100 => 1
[[1,3],[2,4],[5],[6],[7]] => [2,5] => 1010000 => 1
[[1,2],[3,4],[5],[6],[7]] => [3,4] => 1001000 => 1
[[1,7],[2],[3],[4],[5],[6]] => [6,1] => 1000001 => 1
[[1,6],[2],[3],[4],[5],[7]] => [5,2] => 1000010 => 1
[[1,5],[2],[3],[4],[6],[7]] => [4,3] => 1000100 => 1
[[1,4],[2],[3],[5],[6],[7]] => [3,4] => 1001000 => 1
[[1,3],[2],[4],[5],[6],[7]] => [2,5] => 1010000 => 1
[[1,2],[3],[4],[5],[6],[7]] => [7] => 1000000 => 1
[[1],[2],[3],[4],[5],[6],[7]] => [7] => 1000000 => 1
[[1,2,3,4,5,6,7,8]] => [8] => 10000000 => 1
[[1,3,4,5,6,7,8],[2]] => [2,6] => 10100000 => 1
[[1,2,4,5,6,7,8],[3]] => [3,5] => 10010000 => 1
[[1,2,3,5,6,7,8],[4]] => [4,4] => 10001000 => 1
[[1,2,3,4,6,7,8],[5]] => [5,3] => 10000100 => 1
[[1,2,3,4,5,7,8],[6]] => [6,2] => 10000010 => 1
[[1,2,3,4,5,6,8],[7]] => [7,1] => 10000001 => 1
[[1,2,3,4,5,6,7],[8]] => [8] => 10000000 => 1
[[1,3,5,6,7,8],[2,4]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7,8],[3,4]] => [3,5] => 10010000 => 1
[[1,3,4,6,7,8],[2,5]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7,8],[3,5]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7,8],[4,5]] => [4,4] => 10001000 => 1
[[1,3,4,5,7,8],[2,6]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7,8],[3,6]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7,8],[4,6]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7,8],[5,6]] => [5,3] => 10000100 => 1
[[1,3,4,5,6,8],[2,7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6,8],[3,7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6,8],[4,7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6,8],[5,7]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5,8],[6,7]] => [6,2] => 10000010 => 1
[[1,3,4,5,6,7],[2,8]] => [2,6] => 10100000 => 1
[[1,2,4,5,6,7],[3,8]] => [3,5] => 10010000 => 1
[[1,2,3,5,6,7],[4,8]] => [4,4] => 10001000 => 1
[[1,2,3,4,6,7],[5,8]] => [5,3] => 10000100 => 1
[[1,2,3,4,5,7],[6,8]] => [6,2] => 10000010 => 1
[[1,2,3,4,5,6],[7,8]] => [7,1] => 10000001 => 1
[[1,4,5,6,7,8],[2],[3]] => [3,5] => 10010000 => 1
[[1,3,5,6,7,8],[2],[4]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7,8],[3],[4]] => [4,4] => 10001000 => 1
[[1,3,4,6,7,8],[2],[5]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7,8],[3],[5]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7,8],[4],[5]] => [5,3] => 10000100 => 1
[[1,3,4,5,7,8],[2],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7,8],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7,8],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7,8],[5],[6]] => [6,2] => 10000010 => 1
[[1,3,4,5,6,8],[2],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6,8],[3],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6,8],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6,8],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5,8],[6],[7]] => [7,1] => 10000001 => 1
[[1,3,4,5,6,7],[2],[8]] => [2,6] => 10100000 => 1
[[1,2,4,5,6,7],[3],[8]] => [3,5] => 10010000 => 1
[[1,2,3,5,6,7],[4],[8]] => [4,4] => 10001000 => 1
[[1,2,3,4,6,7],[5],[8]] => [5,3] => 10000100 => 1
[[1,2,3,4,5,7],[6],[8]] => [6,2] => 10000010 => 1
[[1,2,3,4,5,6],[7],[8]] => [8] => 10000000 => 1
[[1,3,5,7,8],[2,4,6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,4,6]] => [3,3,2] => 10010010 => 1
[[1,3,4,7,8],[2,5,6]] => [2,3,3] => 10100100 => 1
[[1,2,4,7,8],[3,5,6]] => [3,2,3] => 10010100 => 1
[[1,2,3,7,8],[4,5,6]] => [4,4] => 10001000 => 1
[[1,3,5,6,8],[2,4,7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,4,7]] => [3,4,1] => 10010001 => 1
[[1,3,4,6,8],[2,5,7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,5,7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,5,7]] => [4,3,1] => 10001001 => 1
[[1,3,4,5,8],[2,6,7]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,8],[3,6,7]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,8],[4,6,7]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,8],[5,6,7]] => [5,3] => 10000100 => 1
[[1,3,5,6,7],[2,4,8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3,4,8]] => [3,5] => 10010000 => 1
[[1,3,4,6,7],[2,5,8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3,5,8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7],[4,5,8]] => [4,4] => 10001000 => 1
[[1,3,4,5,7],[2,6,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3,6,8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7],[4,6,8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7],[5,6,8]] => [5,3] => 10000100 => 1
[[1,3,4,5,6],[2,7,8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6],[3,7,8]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6],[4,7,8]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6],[5,7,8]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5],[6,7,8]] => [6,2] => 10000010 => 1
[[1,4,6,7,8],[2,5],[3]] => [3,2,3] => 10010100 => 1
[[1,3,6,7,8],[2,5],[4]] => [2,2,4] => 10101000 => 1
[[1,2,6,7,8],[3,5],[4]] => [4,4] => 10001000 => 1
[[1,3,6,7,8],[2,4],[5]] => [2,3,3] => 10100100 => 1
[[1,2,6,7,8],[3,4],[5]] => [3,2,3] => 10010100 => 1
[[1,4,5,7,8],[2,6],[3]] => [3,3,2] => 10010010 => 1
[[1,3,5,7,8],[2,6],[4]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,6],[4]] => [4,2,2] => 10001010 => 1
[[1,3,4,7,8],[2,6],[5]] => [2,3,3] => 10100100 => 1
[[1,2,4,7,8],[3,6],[5]] => [3,2,3] => 10010100 => 1
[[1,2,3,7,8],[4,6],[5]] => [5,3] => 10000100 => 1
[[1,3,5,7,8],[2,4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3,4],[6]] => [3,3,2] => 10010010 => 1
[[1,3,4,7,8],[2,5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,7,8],[3,5],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,7,8],[4,5],[6]] => [4,2,2] => 10001010 => 1
[[1,4,5,6,8],[2,7],[3]] => [3,4,1] => 10010001 => 1
[[1,3,5,6,8],[2,7],[4]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,7],[4]] => [4,3,1] => 10001001 => 1
[[1,3,4,6,8],[2,7],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,7],[5]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,7],[5]] => [5,2,1] => 10000101 => 1
[[1,3,4,5,8],[2,7],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,8],[3,7],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,8],[4,7],[6]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,8],[5,7],[6]] => [6,2] => 10000010 => 1
[[1,3,5,6,8],[2,4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3,4],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4,6,8],[2,5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3,5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4,5],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,5,8],[2,6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,8],[3,6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,8],[4,6],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,8],[5,6],[7]] => [5,2,1] => 10000101 => 1
[[1,4,5,6,7],[2,8],[3]] => [3,5] => 10010000 => 1
[[1,3,5,6,7],[2,8],[4]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3,8],[4]] => [4,4] => 10001000 => 1
[[1,3,4,6,7],[2,8],[5]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3,8],[5]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7],[4,8],[5]] => [5,3] => 10000100 => 1
[[1,3,4,5,7],[2,8],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3,8],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7],[4,8],[6]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7],[5,8],[6]] => [6,2] => 10000010 => 1
[[1,3,4,5,6],[2,8],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,6],[3,8],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,6],[4,8],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,6],[5,8],[7]] => [5,2,1] => 10000101 => 1
[[1,2,3,4,5],[6,8],[7]] => [7,1] => 10000001 => 1
[[1,3,5,6,7],[2,4],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3,4],[8]] => [3,5] => 10010000 => 1
[[1,3,4,6,7],[2,5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3,5],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7],[4,5],[8]] => [4,4] => 10001000 => 1
[[1,3,4,5,7],[2,6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3,6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7],[4,6],[8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7],[5,6],[8]] => [5,3] => 10000100 => 1
[[1,3,4,5,6],[2,7],[8]] => [2,6] => 10100000 => 1
[[1,2,4,5,6],[3,7],[8]] => [3,5] => 10010000 => 1
[[1,2,3,5,6],[4,7],[8]] => [4,4] => 10001000 => 1
[[1,2,3,4,6],[5,7],[8]] => [5,3] => 10000100 => 1
[[1,2,3,4,5],[6,7],[8]] => [6,2] => 10000010 => 1
[[1,5,6,7,8],[2],[3],[4]] => [4,4] => 10001000 => 1
[[1,4,6,7,8],[2],[3],[5]] => [3,2,3] => 10010100 => 1
[[1,3,6,7,8],[2],[4],[5]] => [2,3,3] => 10100100 => 1
[[1,2,6,7,8],[3],[4],[5]] => [5,3] => 10000100 => 1
[[1,4,5,7,8],[2],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,5,7,8],[2],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7,8],[3],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,4,7,8],[2],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,7,8],[3],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,7,8],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,4,5,6,8],[2],[3],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5,6,8],[2],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6,8],[3],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,6,8],[2],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6,8],[3],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6,8],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,3,4,5,8],[2],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5,8],[3],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5,8],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4,8],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,4,5,6,7],[2],[3],[8]] => [3,5] => 10010000 => 1
[[1,3,5,6,7],[2],[4],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6,7],[3],[4],[8]] => [4,4] => 10001000 => 1
[[1,3,4,6,7],[2],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6,7],[3],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6,7],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,3,4,5,7],[2],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5,7],[3],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5,7],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4,7],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,3,4,5,6],[2],[7],[8]] => [2,6] => 10100000 => 1
[[1,2,4,5,6],[3],[7],[8]] => [3,5] => 10010000 => 1
[[1,2,3,5,6],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,2,3,4,6],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,2,3,4,5],[6],[7],[8]] => [8] => 10000000 => 1
[[1,3,5,7],[2,4,6,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4,6,8]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5,6,8]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,5,6,8]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,5,6,8]] => [4,4] => 10001000 => 1
[[1,3,5,6],[2,4,7,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,4,7,8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6],[2,5,7,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,5,7,8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6],[4,5,7,8]] => [4,3,1] => 10001001 => 1
[[1,3,4,5],[2,6,7,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,6,7,8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5],[4,6,7,8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4],[5,6,7,8]] => [5,3] => 10000100 => 1
[[1,4,6,8],[2,5,7],[3]] => [3,2,2,1] => 10010101 => 1
[[1,3,6,8],[2,5,7],[4]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5,7],[4]] => [4,3,1] => 10001001 => 1
[[1,3,6,8],[2,4,7],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,6,8],[3,4,7],[5]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6,7],[3]] => [3,3,2] => 10010010 => 1
[[1,3,5,8],[2,6,7],[4]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,6,7],[4]] => [4,2,2] => 10001010 => 1
[[1,3,4,8],[2,6,7],[5]] => [2,3,3] => 10100100 => 1
[[1,2,4,8],[3,6,7],[5]] => [3,2,3] => 10010100 => 1
[[1,2,3,8],[4,6,7],[5]] => [5,3] => 10000100 => 1
[[1,3,5,8],[2,4,7],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,4,7],[6]] => [3,3,2] => 10010010 => 1
[[1,3,4,8],[2,5,7],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,8],[3,5,7],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,8],[4,5,7],[6]] => [4,2,2] => 10001010 => 1
[[1,3,5,8],[2,4,6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,8],[3,4,6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4,8],[2,5,6],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,5,6],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,5,6],[7]] => [4,3,1] => 10001001 => 1
[[1,4,6,7],[2,5,8],[3]] => [3,2,3] => 10010100 => 1
[[1,3,6,7],[2,5,8],[4]] => [2,2,4] => 10101000 => 1
[[1,2,6,7],[3,5,8],[4]] => [4,4] => 10001000 => 1
[[1,3,6,7],[2,4,8],[5]] => [2,3,3] => 10100100 => 1
[[1,2,6,7],[3,4,8],[5]] => [3,2,3] => 10010100 => 1
[[1,4,5,7],[2,6,8],[3]] => [3,3,2] => 10010010 => 1
[[1,3,5,7],[2,6,8],[4]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,6,8],[4]] => [4,2,2] => 10001010 => 1
[[1,3,4,7],[2,6,8],[5]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,6,8],[5]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,6,8],[5]] => [5,3] => 10000100 => 1
[[1,3,5,7],[2,4,8],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4,8],[6]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5,8],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,7],[3,5,8],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,7],[4,5,8],[6]] => [4,2,2] => 10001010 => 1
[[1,4,5,6],[2,7,8],[3]] => [3,4,1] => 10010001 => 1
[[1,3,5,6],[2,7,8],[4]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,7,8],[4]] => [4,3,1] => 10001001 => 1
[[1,3,4,6],[2,7,8],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,7,8],[5]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6],[4,7,8],[5]] => [5,2,1] => 10000101 => 1
[[1,3,4,5],[2,7,8],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,7,8],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,5],[4,7,8],[6]] => [4,2,2] => 10001010 => 1
[[1,2,3,4],[5,7,8],[6]] => [6,2] => 10000010 => 1
[[1,3,5,6],[2,4,8],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,4,8],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4,6],[2,5,8],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,5,8],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6],[4,5,8],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,5],[2,6,8],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5],[3,6,8],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5],[4,6,8],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4],[5,6,8],[7]] => [5,2,1] => 10000101 => 1
[[1,3,5,7],[2,4,6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4,6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5,6],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,5,6],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,5,6],[8]] => [4,4] => 10001000 => 1
[[1,3,5,6],[2,4,7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6],[3,4,7],[8]] => [3,5] => 10010000 => 1
[[1,3,4,6],[2,5,7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6],[3,5,7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6],[4,5,7],[8]] => [4,4] => 10001000 => 1
[[1,3,4,5],[2,6,7],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,6,7],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5],[4,6,7],[8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4],[5,6,7],[8]] => [5,3] => 10000100 => 1
[[1,4,7,8],[2,5],[3,6]] => [3,3,2] => 10010010 => 1
[[1,3,7,8],[2,5],[4,6]] => [2,2,2,2] => 10101010 => 1
[[1,2,7,8],[3,5],[4,6]] => [4,2,2] => 10001010 => 1
[[1,3,7,8],[2,4],[5,6]] => [2,3,3] => 10100100 => 1
[[1,2,7,8],[3,4],[5,6]] => [3,2,3] => 10010100 => 1
[[1,4,6,8],[2,5],[3,7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6,8],[2,5],[4,7]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5],[4,7]] => [4,3,1] => 10001001 => 1
[[1,3,6,8],[2,4],[5,7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6,8],[3,4],[5,7]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6],[3,7]] => [3,4,1] => 10010001 => 1
[[1,3,5,8],[2,6],[4,7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,8],[3,6],[4,7]] => [4,3,1] => 10001001 => 1
[[1,3,4,8],[2,6],[5,7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,6],[5,7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,6],[5,7]] => [5,2,1] => 10000101 => 1
[[1,3,5,8],[2,4],[6,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,4],[6,7]] => [3,3,2] => 10010010 => 1
[[1,3,4,8],[2,5],[6,7]] => [2,4,2] => 10100010 => 1
[[1,2,4,8],[3,5],[6,7]] => [3,3,2] => 10010010 => 1
[[1,2,3,8],[4,5],[6,7]] => [4,2,2] => 10001010 => 1
[[1,4,6,7],[2,5],[3,8]] => [3,2,3] => 10010100 => 1
[[1,3,6,7],[2,5],[4,8]] => [2,2,4] => 10101000 => 1
[[1,2,6,7],[3,5],[4,8]] => [4,4] => 10001000 => 1
[[1,3,6,7],[2,4],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2,6,7],[3,4],[5,8]] => [3,2,3] => 10010100 => 1
[[1,4,5,7],[2,6],[3,8]] => [3,3,2] => 10010010 => 1
[[1,3,5,7],[2,6],[4,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,6],[4,8]] => [4,2,2] => 10001010 => 1
[[1,3,4,7],[2,6],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,6],[5,8]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,6],[5,8]] => [5,3] => 10000100 => 1
[[1,3,5,7],[2,4],[6,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4],[6,8]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5],[6,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,7],[3,5],[6,8]] => [3,3,2] => 10010010 => 1
[[1,2,3,7],[4,5],[6,8]] => [4,2,2] => 10001010 => 1
[[1,4,5,6],[2,7],[3,8]] => [3,5] => 10010000 => 1
[[1,3,5,6],[2,7],[4,8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6],[3,7],[4,8]] => [4,4] => 10001000 => 1
[[1,3,4,6],[2,7],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6],[3,7],[5,8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6],[4,7],[5,8]] => [5,3] => 10000100 => 1
[[1,3,4,5],[2,7],[6,8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,7],[6,8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5],[4,7],[6,8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4],[5,7],[6,8]] => [6,2] => 10000010 => 1
[[1,3,5,6],[2,4],[7,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,4],[7,8]] => [3,4,1] => 10010001 => 1
[[1,3,4,6],[2,5],[7,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,5],[7,8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6],[4,5],[7,8]] => [4,3,1] => 10001001 => 1
[[1,3,4,5],[2,6],[7,8]] => [2,5,1] => 10100001 => 1
[[1,2,4,5],[3,6],[7,8]] => [3,4,1] => 10010001 => 1
[[1,2,3,5],[4,6],[7,8]] => [4,3,1] => 10001001 => 1
[[1,2,3,4],[5,6],[7,8]] => [5,2,1] => 10000101 => 1
[[1,5,7,8],[2,6],[3],[4]] => [4,2,2] => 10001010 => 1
[[1,4,7,8],[2,6],[3],[5]] => [3,2,3] => 10010100 => 1
[[1,3,7,8],[2,6],[4],[5]] => [2,3,3] => 10100100 => 1
[[1,2,7,8],[3,6],[4],[5]] => [5,3] => 10000100 => 1
[[1,4,7,8],[2,5],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,7,8],[2,5],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,7,8],[3,5],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,7,8],[2,4],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,7,8],[3,4],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,5,6,8],[2,7],[3],[4]] => [4,3,1] => 10001001 => 1
[[1,4,6,8],[2,7],[3],[5]] => [3,2,2,1] => 10010101 => 1
[[1,3,6,8],[2,7],[4],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,6,8],[3,7],[4],[5]] => [5,2,1] => 10000101 => 1
[[1,4,5,8],[2,7],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,5,8],[2,7],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,8],[3,7],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,4,8],[2,7],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,8],[3,7],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,8],[4,7],[5],[6]] => [6,2] => 10000010 => 1
[[1,4,6,8],[2,5],[3],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6,8],[2,5],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,6,8],[3,5],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,6,8],[2,4],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6,8],[3,4],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,4,5,8],[2,6],[3],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5,8],[2,6],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,8],[3,6],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,8],[2,6],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,8],[3,6],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,8],[4,6],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,3,5,8],[2,4],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,8],[3,4],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4,8],[2,5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,8],[3,5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,8],[4,5],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,5,6,7],[2,8],[3],[4]] => [4,4] => 10001000 => 1
[[1,4,6,7],[2,8],[3],[5]] => [3,2,3] => 10010100 => 1
[[1,3,6,7],[2,8],[4],[5]] => [2,3,3] => 10100100 => 1
[[1,2,6,7],[3,8],[4],[5]] => [5,3] => 10000100 => 1
[[1,4,5,7],[2,8],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,5,7],[2,8],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,8],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,4,7],[2,8],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4,7],[3,8],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3,7],[4,8],[5],[6]] => [6,2] => 10000010 => 1
[[1,4,5,6],[2,8],[3],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5,6],[2,8],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,6],[3,8],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,6],[2,8],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4,6],[3,8],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3,6],[4,8],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,3,4,5],[2,8],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,5],[3,8],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,5],[4,8],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,2,3,4],[5,8],[6],[7]] => [7,1] => 10000001 => 1
[[1,4,6,7],[2,5],[3],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6,7],[2,5],[4],[8]] => [2,2,4] => 10101000 => 1
[[1,2,6,7],[3,5],[4],[8]] => [4,4] => 10001000 => 1
[[1,3,6,7],[2,4],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6,7],[3,4],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,4,5,7],[2,6],[3],[8]] => [3,3,2] => 10010010 => 1
[[1,3,5,7],[2,6],[4],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,6],[4],[8]] => [4,2,2] => 10001010 => 1
[[1,3,4,7],[2,6],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,7],[3,6],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,7],[4,6],[5],[8]] => [5,3] => 10000100 => 1
[[1,3,5,7],[2,4],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3,4],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,4,7],[2,5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,7],[3,5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,7],[4,5],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,4,5,6],[2,7],[3],[8]] => [3,5] => 10010000 => 1
[[1,3,5,6],[2,7],[4],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6],[3,7],[4],[8]] => [4,4] => 10001000 => 1
[[1,3,4,6],[2,7],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6],[3,7],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6],[4,7],[5],[8]] => [5,3] => 10000100 => 1
[[1,3,4,5],[2,7],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,5],[3,7],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,5],[4,7],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,2,3,4],[5,7],[6],[8]] => [6,2] => 10000010 => 1
[[1,3,5,6],[2,4],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6],[3,4],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,4,6],[2,5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6],[3,5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6],[4,5],[7],[8]] => [4,4] => 10001000 => 1
[[1,3,4,5],[2,6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2,4,5],[3,6],[7],[8]] => [3,5] => 10010000 => 1
[[1,2,3,5],[4,6],[7],[8]] => [4,4] => 10001000 => 1
[[1,2,3,4],[5,6],[7],[8]] => [5,3] => 10000100 => 1
[[1,6,7,8],[2],[3],[4],[5]] => [5,3] => 10000100 => 1
[[1,5,7,8],[2],[3],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,4,7,8],[2],[3],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,3,7,8],[2],[4],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,7,8],[3],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,5,6,8],[2],[3],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,4,6,8],[2],[3],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6,8],[2],[4],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6,8],[3],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,4,5,8],[2],[3],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5,8],[2],[4],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5,8],[3],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4,8],[2],[5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4,8],[3],[5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3,8],[4],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,5,6,7],[2],[3],[4],[8]] => [4,4] => 10001000 => 1
[[1,4,6,7],[2],[3],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6,7],[2],[4],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6,7],[3],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,4,5,7],[2],[3],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,5,7],[2],[4],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5,7],[3],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,3,4,7],[2],[5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4,7],[3],[5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3,7],[4],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,4,5,6],[2],[3],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,5,6],[2],[4],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5,6],[3],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,3,4,6],[2],[5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4,6],[3],[5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3,6],[4],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,3,4,5],[2],[6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2,4,5],[3],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,2,3,5],[4],[6],[7],[8]] => [4,4] => 10001000 => 1
[[1,2,3,4],[5],[6],[7],[8]] => [8] => 10000000 => 1
[[1,4,7],[2,5,8],[3,6]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,5,8],[4,6]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5,8],[4,6]] => [4,2,2] => 10001010 => 1
[[1,3,7],[2,4,8],[5,6]] => [2,3,3] => 10100100 => 1
[[1,2,7],[3,4,8],[5,6]] => [3,2,3] => 10010100 => 1
[[1,4,6],[2,5,8],[3,7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6],[2,5,8],[4,7]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5,8],[4,7]] => [4,3,1] => 10001001 => 1
[[1,3,6],[2,4,8],[5,7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6],[3,4,8],[5,7]] => [3,2,2,1] => 10010101 => 1
[[1,4,5],[2,6,8],[3,7]] => [3,4,1] => 10010001 => 1
[[1,3,5],[2,6,8],[4,7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,6,8],[4,7]] => [4,3,1] => 10001001 => 1
[[1,3,4],[2,6,8],[5,7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6,8],[5,7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3],[4,6,8],[5,7]] => [5,2,1] => 10000101 => 1
[[1,3,5],[2,4,8],[6,7]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,4,8],[6,7]] => [3,3,2] => 10010010 => 1
[[1,3,4],[2,5,8],[6,7]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,5,8],[6,7]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,5,8],[6,7]] => [4,2,2] => 10001010 => 1
[[1,4,6],[2,5,7],[3,8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,5,7],[4,8]] => [2,2,4] => 10101000 => 1
[[1,2,6],[3,5,7],[4,8]] => [4,4] => 10001000 => 1
[[1,3,6],[2,4,7],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,4,7],[5,8]] => [3,2,3] => 10010100 => 1
[[1,4,5],[2,6,7],[3,8]] => [3,3,2] => 10010010 => 1
[[1,3,5],[2,6,7],[4,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,6,7],[4,8]] => [4,2,2] => 10001010 => 1
[[1,3,4],[2,6,7],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,6,7],[5,8]] => [3,2,3] => 10010100 => 1
[[1,2,3],[4,6,7],[5,8]] => [5,3] => 10000100 => 1
[[1,3,5],[2,4,7],[6,8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,4,7],[6,8]] => [3,3,2] => 10010010 => 1
[[1,3,4],[2,5,7],[6,8]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,5,7],[6,8]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,5,7],[6,8]] => [4,2,2] => 10001010 => 1
[[1,3,5],[2,4,6],[7,8]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,4,6],[7,8]] => [3,4,1] => 10010001 => 1
[[1,3,4],[2,5,6],[7,8]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,5,6],[7,8]] => [3,2,2,1] => 10010101 => 1
[[1,2,3],[4,5,6],[7,8]] => [4,3,1] => 10001001 => 1
[[1,5,7],[2,6,8],[3],[4]] => [4,2,2] => 10001010 => 1
[[1,4,7],[2,6,8],[3],[5]] => [3,2,3] => 10010100 => 1
[[1,3,7],[2,6,8],[4],[5]] => [2,3,3] => 10100100 => 1
[[1,2,7],[3,6,8],[4],[5]] => [5,3] => 10000100 => 1
[[1,4,7],[2,5,8],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,5,8],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5,8],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,7],[2,4,8],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,7],[3,4,8],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,5,6],[2,7,8],[3],[4]] => [4,3,1] => 10001001 => 1
[[1,4,6],[2,7,8],[3],[5]] => [3,2,2,1] => 10010101 => 1
[[1,3,6],[2,7,8],[4],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,6],[3,7,8],[4],[5]] => [5,2,1] => 10000101 => 1
[[1,4,5],[2,7,8],[3],[6]] => [3,3,2] => 10010010 => 1
[[1,3,5],[2,7,8],[4],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,7,8],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,3,4],[2,7,8],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,7,8],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,7,8],[5],[6]] => [6,2] => 10000010 => 1
[[1,4,6],[2,5,8],[3],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6],[2,5,8],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5,8],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,6],[2,4,8],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6],[3,4,8],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,4,5],[2,6,8],[3],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5],[2,6,8],[4],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,6,8],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4],[2,6,8],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6,8],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3],[4,6,8],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,3,5],[2,4,8],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,4,8],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4],[2,5,8],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4],[3,5,8],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3],[4,5,8],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,4,6],[2,5,7],[3],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,5,7],[4],[8]] => [2,2,4] => 10101000 => 1
[[1,2,6],[3,5,7],[4],[8]] => [4,4] => 10001000 => 1
[[1,3,6],[2,4,7],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,4,7],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,4,5],[2,6,7],[3],[8]] => [3,3,2] => 10010010 => 1
[[1,3,5],[2,6,7],[4],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,6,7],[4],[8]] => [4,2,2] => 10001010 => 1
[[1,3,4],[2,6,7],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,6,7],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3],[4,6,7],[5],[8]] => [5,3] => 10000100 => 1
[[1,3,5],[2,4,7],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,4,7],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,4],[2,5,7],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,5,7],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,5,7],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,3,5],[2,4,6],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5],[3,4,6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,4],[2,5,6],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,5,6],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3],[4,5,6],[7],[8]] => [4,4] => 10001000 => 1
[[1,5,8],[2,6],[3,7],[4]] => [4,3,1] => 10001001 => 1
[[1,4,8],[2,6],[3,7],[5]] => [3,2,2,1] => 10010101 => 1
[[1,3,8],[2,6],[4,7],[5]] => [2,3,2,1] => 10100101 => 1
[[1,2,8],[3,6],[4,7],[5]] => [5,2,1] => 10000101 => 1
[[1,4,8],[2,5],[3,7],[6]] => [3,3,2] => 10010010 => 1
[[1,3,8],[2,5],[4,7],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,8],[3,5],[4,7],[6]] => [4,2,2] => 10001010 => 1
[[1,3,8],[2,4],[5,7],[6]] => [2,4,2] => 10100010 => 1
[[1,2,8],[3,4],[5,7],[6]] => [3,3,2] => 10010010 => 1
[[1,4,8],[2,5],[3,6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,8],[2,5],[4,6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,8],[3,5],[4,6],[7]] => [4,3,1] => 10001001 => 1
[[1,3,8],[2,4],[5,6],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,8],[3,4],[5,6],[7]] => [3,2,2,1] => 10010101 => 1
[[1,5,7],[2,6],[3,8],[4]] => [4,2,2] => 10001010 => 1
[[1,4,7],[2,6],[3,8],[5]] => [3,2,3] => 10010100 => 1
[[1,3,7],[2,6],[4,8],[5]] => [2,3,3] => 10100100 => 1
[[1,2,7],[3,6],[4,8],[5]] => [5,3] => 10000100 => 1
[[1,4,7],[2,5],[3,8],[6]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,5],[4,8],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5],[4,8],[6]] => [4,2,2] => 10001010 => 1
[[1,3,7],[2,4],[5,8],[6]] => [2,4,2] => 10100010 => 1
[[1,2,7],[3,4],[5,8],[6]] => [3,3,2] => 10010010 => 1
[[1,5,6],[2,7],[3,8],[4]] => [4,4] => 10001000 => 1
[[1,4,6],[2,7],[3,8],[5]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,7],[4,8],[5]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,7],[4,8],[5]] => [5,3] => 10000100 => 1
[[1,4,5],[2,7],[3,8],[6]] => [3,3,2] => 10010010 => 1
[[1,3,5],[2,7],[4,8],[6]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,7],[4,8],[6]] => [4,2,2] => 10001010 => 1
[[1,3,4],[2,7],[5,8],[6]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,7],[5,8],[6]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,7],[5,8],[6]] => [6,2] => 10000010 => 1
[[1,4,6],[2,5],[3,8],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6],[2,5],[4,8],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,6],[3,5],[4,8],[7]] => [4,3,1] => 10001001 => 1
[[1,3,6],[2,4],[5,8],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6],[3,4],[5,8],[7]] => [3,2,2,1] => 10010101 => 1
[[1,4,5],[2,6],[3,8],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5],[2,6],[4,8],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,6],[4,8],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4],[2,6],[5,8],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,4],[3,6],[5,8],[7]] => [3,2,2,1] => 10010101 => 1
[[1,2,3],[4,6],[5,8],[7]] => [5,2,1] => 10000101 => 1
[[1,3,5],[2,4],[6,8],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,4],[6,8],[7]] => [3,4,1] => 10010001 => 1
[[1,3,4],[2,5],[6,8],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4],[3,5],[6,8],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3],[4,5],[6,8],[7]] => [4,3,1] => 10001001 => 1
[[1,4,7],[2,5],[3,6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,5],[4,6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5],[4,6],[8]] => [4,2,2] => 10001010 => 1
[[1,3,7],[2,4],[5,6],[8]] => [2,3,3] => 10100100 => 1
[[1,2,7],[3,4],[5,6],[8]] => [3,2,3] => 10010100 => 1
[[1,4,6],[2,5],[3,7],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,5],[4,7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,6],[3,5],[4,7],[8]] => [4,4] => 10001000 => 1
[[1,3,6],[2,4],[5,7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,4],[5,7],[8]] => [3,2,3] => 10010100 => 1
[[1,4,5],[2,6],[3,7],[8]] => [3,5] => 10010000 => 1
[[1,3,5],[2,6],[4,7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5],[3,6],[4,7],[8]] => [4,4] => 10001000 => 1
[[1,3,4],[2,6],[5,7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,6],[5,7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3],[4,6],[5,7],[8]] => [5,3] => 10000100 => 1
[[1,3,5],[2,4],[6,7],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,4],[6,7],[8]] => [3,3,2] => 10010010 => 1
[[1,3,4],[2,5],[6,7],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,5],[6,7],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,5],[6,7],[8]] => [4,2,2] => 10001010 => 1
[[1,6,8],[2,7],[3],[4],[5]] => [5,2,1] => 10000101 => 1
[[1,5,8],[2,7],[3],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,4,8],[2,7],[3],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,3,8],[2,7],[4],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,8],[3,7],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,5,8],[2,6],[3],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,4,8],[2,6],[3],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,8],[2,6],[4],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,8],[3,6],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,4,8],[2,5],[3],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,8],[2,5],[4],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,8],[3,5],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,3,8],[2,4],[5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,8],[3,4],[5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,6,7],[2,8],[3],[4],[5]] => [5,3] => 10000100 => 1
[[1,5,7],[2,8],[3],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,4,7],[2,8],[3],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,8],[4],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2,7],[3,8],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,5,6],[2,8],[3],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,4,6],[2,8],[3],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3,6],[2,8],[4],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2,6],[3,8],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,4,5],[2,8],[3],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,5],[2,8],[4],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2,5],[3,8],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,3,4],[2,8],[5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,4],[3,8],[5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,2,3],[4,8],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,5,7],[2,6],[3],[4],[8]] => [4,2,2] => 10001010 => 1
[[1,4,7],[2,6],[3],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,3,7],[2,6],[4],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,7],[3,6],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,4,7],[2,5],[3],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2,5],[4],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,7],[3,5],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,3,7],[2,4],[5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,7],[3,4],[5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,5,6],[2,7],[3],[4],[8]] => [4,4] => 10001000 => 1
[[1,4,6],[2,7],[3],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,7],[4],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,7],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,4,5],[2,7],[3],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,5],[2,7],[4],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2,5],[3,7],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,3,4],[2,7],[5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,4],[3,7],[5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,2,3],[4,7],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,4,6],[2,5],[3],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2,5],[4],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,6],[3,5],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,3,6],[2,4],[5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3,4],[5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,4,5],[2,6],[3],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,5],[2,6],[4],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5],[3,6],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,3,4],[2,6],[5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,4],[3,6],[5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,2,3],[4,6],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,3,5],[2,4],[6],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5],[3,4],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,4],[2,5],[6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2,4],[3,5],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,2,3],[4,5],[6],[7],[8]] => [4,4] => 10001000 => 1
[[1,7,8],[2],[3],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,6,8],[2],[3],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,5,8],[2],[3],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,4,8],[2],[3],[5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3,8],[2],[4],[5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2,8],[3],[4],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,6,7],[2],[3],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,5,7],[2],[3],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,4,7],[2],[3],[5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3,7],[2],[4],[5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2,7],[3],[4],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,5,6],[2],[3],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,4,6],[2],[3],[5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,3,6],[2],[4],[5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2,6],[3],[4],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,4,5],[2],[3],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3,5],[2],[4],[6],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2,5],[3],[4],[6],[7],[8]] => [4,4] => 10001000 => 1
[[1,3,4],[2],[5],[6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2,4],[3],[5],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,2,3],[4],[5],[6],[7],[8]] => [8] => 10000000 => 1
[[1,5],[2,6],[3,7],[4,8]] => [4,4] => 10001000 => 1
[[1,4],[2,6],[3,7],[5,8]] => [3,2,3] => 10010100 => 1
[[1,3],[2,6],[4,7],[5,8]] => [2,3,3] => 10100100 => 1
[[1,2],[3,6],[4,7],[5,8]] => [5,3] => 10000100 => 1
[[1,4],[2,5],[3,7],[6,8]] => [3,3,2] => 10010010 => 1
[[1,3],[2,5],[4,7],[6,8]] => [2,2,2,2] => 10101010 => 1
[[1,2],[3,5],[4,7],[6,8]] => [4,2,2] => 10001010 => 1
[[1,3],[2,4],[5,7],[6,8]] => [2,4,2] => 10100010 => 1
[[1,2],[3,4],[5,7],[6,8]] => [3,3,2] => 10010010 => 1
[[1,4],[2,5],[3,6],[7,8]] => [3,4,1] => 10010001 => 1
[[1,3],[2,5],[4,6],[7,8]] => [2,2,3,1] => 10101001 => 1
[[1,2],[3,5],[4,6],[7,8]] => [4,3,1] => 10001001 => 1
[[1,3],[2,4],[5,6],[7,8]] => [2,3,2,1] => 10100101 => 1
[[1,2],[3,4],[5,6],[7,8]] => [3,2,2,1] => 10010101 => 1
[[1,6],[2,7],[3,8],[4],[5]] => [5,3] => 10000100 => 1
[[1,5],[2,7],[3,8],[4],[6]] => [4,2,2] => 10001010 => 1
[[1,4],[2,7],[3,8],[5],[6]] => [3,3,2] => 10010010 => 1
[[1,3],[2,7],[4,8],[5],[6]] => [2,4,2] => 10100010 => 1
[[1,2],[3,7],[4,8],[5],[6]] => [6,2] => 10000010 => 1
[[1,5],[2,6],[3,8],[4],[7]] => [4,3,1] => 10001001 => 1
[[1,4],[2,6],[3,8],[5],[7]] => [3,2,2,1] => 10010101 => 1
[[1,3],[2,6],[4,8],[5],[7]] => [2,3,2,1] => 10100101 => 1
[[1,2],[3,6],[4,8],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,4],[2,5],[3,8],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3],[2,5],[4,8],[6],[7]] => [2,2,3,1] => 10101001 => 1
[[1,2],[3,5],[4,8],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,3],[2,4],[5,8],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2],[3,4],[5,8],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,5],[2,6],[3,7],[4],[8]] => [4,4] => 10001000 => 1
[[1,4],[2,6],[3,7],[5],[8]] => [3,2,3] => 10010100 => 1
[[1,3],[2,6],[4,7],[5],[8]] => [2,3,3] => 10100100 => 1
[[1,2],[3,6],[4,7],[5],[8]] => [5,3] => 10000100 => 1
[[1,4],[2,5],[3,7],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3],[2,5],[4,7],[6],[8]] => [2,2,2,2] => 10101010 => 1
[[1,2],[3,5],[4,7],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,3],[2,4],[5,7],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2],[3,4],[5,7],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,4],[2,5],[3,6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3],[2,5],[4,6],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2],[3,5],[4,6],[7],[8]] => [4,4] => 10001000 => 1
[[1,3],[2,4],[5,6],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2],[3,4],[5,6],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,7],[2,8],[3],[4],[5],[6]] => [6,2] => 10000010 => 1
[[1,6],[2,8],[3],[4],[5],[7]] => [5,2,1] => 10000101 => 1
[[1,5],[2,8],[3],[4],[6],[7]] => [4,3,1] => 10001001 => 1
[[1,4],[2,8],[3],[5],[6],[7]] => [3,4,1] => 10010001 => 1
[[1,3],[2,8],[4],[5],[6],[7]] => [2,5,1] => 10100001 => 1
[[1,2],[3,8],[4],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,6],[2,7],[3],[4],[5],[8]] => [5,3] => 10000100 => 1
[[1,5],[2,7],[3],[4],[6],[8]] => [4,2,2] => 10001010 => 1
[[1,4],[2,7],[3],[5],[6],[8]] => [3,3,2] => 10010010 => 1
[[1,3],[2,7],[4],[5],[6],[8]] => [2,4,2] => 10100010 => 1
[[1,2],[3,7],[4],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,5],[2,6],[3],[4],[7],[8]] => [4,4] => 10001000 => 1
[[1,4],[2,6],[3],[5],[7],[8]] => [3,2,3] => 10010100 => 1
[[1,3],[2,6],[4],[5],[7],[8]] => [2,3,3] => 10100100 => 1
[[1,2],[3,6],[4],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,4],[2,5],[3],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3],[2,5],[4],[6],[7],[8]] => [2,2,4] => 10101000 => 1
[[1,2],[3,5],[4],[6],[7],[8]] => [4,4] => 10001000 => 1
[[1,3],[2,4],[5],[6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2],[3,4],[5],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,1] => 10000001 => 1
[[1,7],[2],[3],[4],[5],[6],[8]] => [6,2] => 10000010 => 1
[[1,6],[2],[3],[4],[5],[7],[8]] => [5,3] => 10000100 => 1
[[1,5],[2],[3],[4],[6],[7],[8]] => [4,4] => 10001000 => 1
[[1,4],[2],[3],[5],[6],[7],[8]] => [3,5] => 10010000 => 1
[[1,3],[2],[4],[5],[6],[7],[8]] => [2,6] => 10100000 => 1
[[1,2],[3],[4],[5],[6],[7],[8]] => [8] => 10000000 => 1
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8] => 10000000 => 1
[[1,3,5,7,9],[2,4,6,8,10]] => [2,2,2,2,2] => 1010101010 => 1
[[1,3,5,7,8],[2,4,6,9,10]] => [2,2,2,3,1] => 1010101001 => 1
[[1,3,5,6,8],[2,4,7,9,10]] => [2,2,3,2,1] => 1010100101 => 1
[[1,3,4,6,8],[2,5,7,9,10]] => [2,3,2,2,1] => 1010010101 => 1
[[1,2,4,6,8],[3,5,7,9,10]] => [3,2,2,2,1] => 1001010101 => 1
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [2,2,2,2,2,2] => 101010101010 => 1
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [2,2,2,2,3,1] => 101010101001 => 1
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [2,2,2,3,2,1] => 101010100101 => 1
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [2,2,3,2,2,1] => 101010010101 => 1
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [2,3,2,2,2,1] => 101001010101 => 1
[[1,2,4,6,8,10],[3,5,7,9,11,12]] => [3,2,2,2,2,1] => 100101010101 => 1
[[1,2,3,4,5,6,7,8,9]] => [9] => 100000000 => 1
[[1,2,3,4,5,6,7,8],[9]] => [9] => 100000000 => 1
[[1,2,3,4,5,6,7],[8,9]] => [8,1] => 100000001 => 1
[[1,2,3,4,5,6,7],[8],[9]] => [9] => 100000000 => 1
[[1,2,3,4,5,6],[7,8,9]] => [7,2] => 100000010 => 1
[[1,2,3,4,5,6],[7,8],[9]] => [7,2] => 100000010 => 1
[[1,2,3,4,5,6],[7],[8],[9]] => [9] => 100000000 => 1
[[1,2,3,4,5],[6,7,8,9]] => [6,3] => 100000100 => 1
[[1,2,3,4,5],[6,7,8],[9]] => [6,3] => 100000100 => 1
[[1,2,3,4,5],[6,7],[8,9]] => [6,2,1] => 100000101 => 1
[[1,2,3,4,5],[6,7],[8],[9]] => [6,3] => 100000100 => 1
[[1,2,3,4,5],[6],[7],[8],[9]] => [9] => 100000000 => 1
[[1,2,3,4],[5,6,7,8],[9]] => [5,4] => 100001000 => 1
[[1,2,3,4],[5,6,7],[8,9]] => [5,3,1] => 100001001 => 1
[[1,2,3,4],[5,6,7],[8],[9]] => [5,4] => 100001000 => 1
[[1,2,3,4],[5,6],[7,8],[9]] => [5,2,2] => 100001010 => 1
[[1,2,3,4],[5,6],[7],[8],[9]] => [5,4] => 100001000 => 1
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9] => 100000000 => 1
[[1,2,3],[4,5,6],[7,8,9]] => [4,3,2] => 100010010 => 1
[[1,2,3],[4,5,6],[7,8],[9]] => [4,3,2] => 100010010 => 1
[[1,2,3],[4,5,6],[7],[8],[9]] => [4,5] => 100010000 => 1
[[1,2,3],[4,5],[6,7],[8,9]] => [4,2,2,1] => 100010101 => 1
[[1,2,3],[4,5],[6,7],[8],[9]] => [4,2,3] => 100010100 => 1
[[1,2,3],[4,5],[6],[7],[8],[9]] => [4,5] => 100010000 => 1
[[1,2,3],[4],[5],[6],[7],[8],[9]] => [9] => 100000000 => 1
[[1,2],[3,4],[5,6],[7,8],[9]] => [3,2,2,2] => 100101010 => 1
[[1,2],[3,4],[5,6],[7],[8],[9]] => [3,2,4] => 100101000 => 1
[[1,2],[3,4],[5],[6],[7],[8],[9]] => [3,6] => 100100000 => 1
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9] => 100000000 => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9] => 100000000 => 1
[[1,2,3,4,5,6,7,8,9,10]] => [10] => 1000000000 => 1
[[1,2,3,4,5,6,7,8,9],[10]] => [10] => 1000000000 => 1
[[1,2,3,4,5,6,7,8],[9],[10]] => [10] => 1000000000 => 1
[[1,2,3,4,5,6,7],[8,9,10]] => [8,2] => 1000000010 => 1
[[1,2,3,4,5,6,7],[8,9],[10]] => [8,2] => 1000000010 => 1
[[1,2,3,4,5,6,7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,2,3,4,5,6],[7,8,9,10]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,6],[7,8,9],[10]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,6],[7,8],[9],[10]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,2,3,4,5],[6,7],[8,9],[10]] => [6,2,2] => 1000001010 => 1
[[1,2,3,4,5],[6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [3,2,2,2,1] => 1001010101 => 1
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10] => 1000000000 => 1
[[1,3,4,5,6,7,8,9],[2]] => [2,7] => 101000000 => 1
[[1,2,5,6,7,8,9],[3,4]] => [3,6] => 100100000 => 1
[[1,4,5,6,7,8,9],[2],[3]] => [3,6] => 100100000 => 1
[[1,2,3,7,8,9],[4,5,6]] => [4,5] => 100010000 => 1
[[1,3,6,7,8,9],[2,5],[4]] => [2,2,5] => 101010000 => 1
[[1,5,6,7,8,9],[2],[3],[4]] => [4,5] => 100010000 => 1
[[1,2,3,4,9],[5,6,7,8]] => [5,4] => 100001000 => 1
[[1,3,4,8,9],[2,6,7],[5]] => [2,3,4] => 101001000 => 1
[[1,2,7,8,9],[3,4],[5,6]] => [3,2,4] => 100101000 => 1
[[1,4,7,8,9],[2,6],[3],[5]] => [3,2,4] => 100101000 => 1
[[1,6,7,8,9],[2],[3],[4],[5]] => [5,4] => 100001000 => 1
[[1,3,4,5],[2,7,8,9],[6]] => [2,4,3] => 101000100 => 1
[[1,2,5,9],[3,4,8],[6,7]] => [3,3,3] => 100100100 => 1
[[1,4,5,9],[2,7,8],[3],[6]] => [3,3,3] => 100100100 => 1
[[1,3,8,9],[2,5],[4,7],[6]] => [2,2,2,3] => 101010100 => 1
[[1,5,8,9],[2,7],[3],[4],[6]] => [4,2,3] => 100010100 => 1
[[1,7,8,9],[2],[3],[4],[5],[6]] => [6,3] => 100000100 => 1
[[1,3,6],[2,5,9],[4,8],[7]] => [2,2,3,2] => 101010010 => 1
[[1,5,6],[2,8,9],[3],[4],[7]] => [4,3,2] => 100010010 => 1
[[1,2,9],[3,4],[5,6],[7,8]] => [3,2,2,2] => 100101010 => 1
[[1,4,9],[2,6],[3,8],[5],[7]] => [3,2,2,2] => 100101010 => 1
[[1,6,9],[2,8],[3],[4],[5],[7]] => [5,2,2] => 100001010 => 1
[[1,8,9],[2],[3],[4],[5],[6],[7]] => [7,2] => 100000010 => 1
[[1,3],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,1] => 101010101 => 1
[[1,5],[2,7],[3,9],[4],[6],[8]] => [4,2,2,1] => 100010101 => 1
[[1,7],[2,9],[3],[4],[5],[6],[8]] => [6,2,1] => 100000101 => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,1] => 100000001 => 1
[[1,8,9,10],[2],[3],[4],[5],[6],[7]] => [7,3] => 1000000100 => 1
[[1,3,10],[2,5],[4,7],[6,9],[8]] => [2,2,2,2,2] => 1010101010 => 1
[[1,7,10],[2,9],[3],[4],[5],[6],[8]] => [6,2,2] => 1000001010 => 1
[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => [8,2] => 1000000010 => 1
[[1,4],[2,6],[3,8],[5,10],[7],[9]] => [3,2,2,2,1] => 1001010101 => 1
[[1,2,5,6,11],[3,4,9,10],[7,8]] => [3,4,4] => 10010001000 => 1
[[1,4,5,6,11],[2,8,9,10],[3],[7]] => [3,4,4] => 10010001000 => 1
[[1,2,3,7],[4,5,6,11],[8,9,10]] => [4,4,3] => 10001000100 => 1
[[1,5,6,7],[2,9,10,11],[3],[4],[8]] => [4,4,3] => 10001000100 => 1
[[1,3,4,11],[2,6,7],[5,9,10],[8]] => [2,3,3,3] => 10100100100 => 1
[[1,2,5],[3,4,8],[6,7,11],[9,10]] => [3,3,3,2] => 10010010010 => 1
[[1,4,5],[2,7,8],[3,10,11],[6],[9]] => [3,3,3,2] => 10010010010 => 1
[[1,4,7],[2,5,8],[3,6,9]] => [3,3,3] => 100100100 => 1
[[1,3],[2,5],[4,7],[6,9],[8,10]] => [2,2,2,2,2] => 1010101010 => 1
[[1,2,3,4,5,6,7,9],[8]] => [8,1] => 100000001 => 1
[[1,2,3,4,5,6,9],[7,8]] => [7,2] => 100000010 => 1
[[1,2,3,4,5,6,9],[7],[8]] => [8,1] => 100000001 => 1
[[1,2,3,4,5,9],[6,7,8]] => [6,3] => 100000100 => 1
[[1,2,3,4,5,9],[6,7],[8]] => [6,2,1] => 100000101 => 1
[[1,2,3,4,5,9],[6],[7],[8]] => [8,1] => 100000001 => 1
[[1,2,3,4,9],[5,6,7],[8]] => [5,3,1] => 100001001 => 1
[[1,2,3,4,9],[5,6],[7,8]] => [5,2,2] => 100001010 => 1
[[1,2,3,4,9],[5,6],[7],[8]] => [5,3,1] => 100001001 => 1
[[1,2,3,4,9],[5],[6],[7],[8]] => [8,1] => 100000001 => 1
[[1,2,3,7],[4,5,6,9],[8]] => [4,4,1] => 100010001 => 1
[[1,2,3,9],[4,5,6],[7,8]] => [4,3,2] => 100010010 => 1
[[1,2,3,9],[4,5,6],[7],[8]] => [4,4,1] => 100010001 => 1
[[1,2,3,9],[4,5],[6,7],[8]] => [4,2,2,1] => 100010101 => 1
[[1,2,3,9],[4,5],[6],[7],[8]] => [4,4,1] => 100010001 => 1
[[1,2,3,9],[4],[5],[6],[7],[8]] => [8,1] => 100000001 => 1
[[1,2,5],[3,4,8],[6,7,9]] => [3,3,3] => 100100100 => 1
[[1,2,5],[3,4,9],[6,7],[8]] => [3,3,2,1] => 100100101 => 1
[[1,2,5],[3,4,9],[6],[7],[8]] => [3,5,1] => 100100001 => 1
[[1,2,9],[3,4],[5,6],[7],[8]] => [3,2,3,1] => 100101001 => 1
[[1,2,9],[3,4],[5],[6],[7],[8]] => [3,5,1] => 100100001 => 1
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,1] => 100000001 => 1
[[1,3],[2,5],[4,9],[6],[7],[8]] => [2,2,4,1] => 101010001 => 1
[[1,3],[2,9],[4],[5],[6],[7],[8]] => [2,6,1] => 101000001 => 1
[[1,2,3,4,5,6,7,10],[8,9]] => [8,2] => 1000000010 => 1
[[1,2,3,4,5,6,10],[7,8,9]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,10],[6,7],[8,9]] => [6,2,2] => 1000001010 => 1
[[1,2,10],[3,4],[5,6],[7,8],[9]] => [3,2,2,2,1] => 1001010101 => 1
[[1,3],[2,5],[4,7],[6,10],[8],[9]] => [2,2,2,3,1] => 1010101001 => 1
[[1,2,4,5,6,7,8,9],[3]] => [3,6] => 100100000 => 1
[[1,3,4,6,7,8,9],[2,5]] => [2,3,4] => 101001000 => 1
[[1,3,5,6,7,8,9],[2],[4]] => [2,2,5] => 101010000 => 1
[[1,3,5,6,8,9],[2,4,7]] => [2,2,3,2] => 101010010 => 1
[[1,2,4,7,8,9],[3,5],[6]] => [3,3,3] => 100100100 => 1
[[1,4,6,7,8,9],[2],[3],[5]] => [3,2,4] => 100101000 => 1
[[1,3,5,7,8],[2,4,6,9]] => [2,2,2,3] => 101010100 => 1
[[1,2,5,7,9],[3,6,8],[4]] => [4,2,2,1] => 100010101 => 1
[[1,4,6,8,9],[2,5],[3,7]] => [3,2,2,2] => 100101010 => 1
[[1,3,5,8,9],[2,6],[4],[7]] => [2,2,3,2] => 101010010 => 1
[[1,5,7,8,9],[2],[3],[4],[6]] => [4,2,3] => 100010100 => 1
[[1,2,5,6],[3,7,8,9],[4]] => [4,3,2] => 100010010 => 1
[[1,3,4,7],[2,6,8],[5,9]] => [2,3,4] => 101001000 => 1
[[1,3,6,8],[2,7,9],[4],[5]] => [2,3,2,2] => 101001010 => 1
[[1,2,6,9],[3,4],[5,7],[8]] => [3,2,3,1] => 100101001 => 1
[[1,4,6,9],[2,7],[3],[5],[8]] => [3,2,3,1] => 100101001 => 1
[[1,6,8,9],[2],[3],[4],[5],[7]] => [5,2,2] => 100001010 => 1
[[1,2,4],[3,5,7],[6,8],[9]] => [3,3,3] => 100100100 => 1
[[1,4,7],[2,8,9],[3],[5],[6]] => [3,3,2,1] => 100100101 => 1
[[1,5,8],[2,6],[3,7],[4,9]] => [4,3,2] => 100010010 => 1
[[1,3,7],[2,5],[4,8],[6],[9]] => [2,2,2,3] => 101010100 => 1
[[1,5,7],[2,8],[3],[4],[6],[9]] => [4,2,3] => 100010100 => 1
[[1,7,9],[2],[3],[4],[5],[6],[8]] => [6,2,1] => 100000101 => 1
[[1,4],[2,6],[3,8],[5],[7],[9]] => [3,2,2,2] => 100101010 => 1
[[1,6],[2,8],[3],[4],[5],[7],[9]] => [5,2,2] => 100001010 => 1
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [7,2] => 100000010 => 1
[[1,3,5,7,8,10],[2,4,6,9]] => [2,2,2,3,1] => 1010101001 => 1
[[1,3,6,8,10],[2,7,9],[4],[5]] => [2,3,2,2,1] => 1010010101 => 1
[[1,3,4,8],[2,6,9,10],[5,7]] => [2,3,2,2,1] => 1010010101 => 1
[[1,3,7,10],[2,5],[4,8],[6],[9]] => [2,2,2,3,1] => 1010101001 => 1
[[1,7,9,10],[2],[3],[4],[5],[6],[8]] => [6,2,2] => 1000001010 => 1
[[1,3],[2,5],[4,7],[6,9],[8],[10]] => [2,2,2,2,2] => 1010101010 => 1
[[1,7],[2,9],[3],[4],[5],[6],[8],[10]] => [6,2,2] => 1000001010 => 1
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [8,2] => 1000000010 => 1
[[1,3,4,5,6,7,8],[2,9]] => [2,7] => 101000000 => 1
[[1,3,4,5,6,7,8],[2],[9]] => [2,7] => 101000000 => 1
[[1,3,4,5,6,7],[2,8,9]] => [2,6,1] => 101000001 => 1
[[1,3,4,5,6,7],[2,9],[8]] => [2,6,1] => 101000001 => 1
[[1,3,4,5,6,7],[2],[8],[9]] => [2,7] => 101000000 => 1
[[1,3,4,5,6],[2,7,8,9]] => [2,5,2] => 101000010 => 1
[[1,3,4,5,6],[2,8,9],[7]] => [2,5,2] => 101000010 => 1
[[1,3,4,5,6],[2,8],[7,9]] => [2,5,2] => 101000010 => 1
[[1,3,4,5,6],[2,8],[7],[9]] => [2,5,2] => 101000010 => 1
[[1,3,4,5,6],[2],[7],[8],[9]] => [2,7] => 101000000 => 1
[[1,3,4,5],[2,7,8],[6,9]] => [2,4,3] => 101000100 => 1
[[1,3,4,5],[2,7,8],[6],[9]] => [2,4,3] => 101000100 => 1
[[1,3,4,5],[2,7],[6,9],[8]] => [2,4,2,1] => 101000101 => 1
[[1,3,4,5],[2,7],[6],[8],[9]] => [2,4,3] => 101000100 => 1
[[1,3,4,5],[2],[6],[7],[8],[9]] => [2,7] => 101000000 => 1
[[1,3,4],[2,6,7],[5,8,9]] => [2,3,3,1] => 101001001 => 1
[[1,3,4],[2,6,7],[5,9],[8]] => [2,3,3,1] => 101001001 => 1
[[1,3,4],[2,6,7],[5],[8],[9]] => [2,3,4] => 101001000 => 1
[[1,3,4],[2,6],[5,8],[7,9]] => [2,3,2,2] => 101001010 => 1
[[1,3,4],[2,6],[5,8],[7],[9]] => [2,3,2,2] => 101001010 => 1
[[1,3,4],[2,6],[5],[7],[8],[9]] => [2,3,4] => 101001000 => 1
[[1,3,4],[2],[5],[6],[7],[8],[9]] => [2,7] => 101000000 => 1
[[1,3],[2,5],[4,7],[6],[8],[9]] => [2,2,2,3] => 101010100 => 1
[[1,3],[2,5],[4],[6],[7],[8],[9]] => [2,2,5] => 101010000 => 1
[[1,3],[2],[4],[5],[6],[7],[8],[9]] => [2,7] => 101000000 => 1
[[1,3,4],[2,6],[5,8],[7,10],[9]] => [2,3,2,2,1] => 1010010101 => 1
[[1,2,4,6,8,10],[3,5,7,9]] => [3,2,2,2,1] => 1001010101 => 1
[[1,2,3,4,5,6,9,10],[7,8]] => [7,3] => 1000000100 => 1
[[1,2,3,4,5,7,9,10],[6,8]] => [6,2,2] => 1000001010 => 1
[[1,2,3,4,5,6,7,9,10],[8]] => [8,2] => 1000000010 => 1
[[1,2,3,4,5,6,8,9,10],[7]] => [7,3] => 1000000100 => 1
[[1,2,4,6,8,10,12],[3,5,7,9,11]] => [3,2,2,2,2,1] => 100101010101 => 1
[[1,2,5,6,7,8],[3,4,9]] => [3,6] => 100100000 => 1
[[1,2,5,6,7,8],[3,4],[9]] => [3,6] => 100100000 => 1
[[1,4,5,6,7,8],[2],[3],[9]] => [3,6] => 100100000 => 1
[[1,2,3,7,8],[4,5,6,9]] => [4,5] => 100010000 => 1
[[1,2,3,7,8],[4,5,6],[9]] => [4,5] => 100010000 => 1
[[1,3,6,7,8],[2,5],[4,9]] => [2,2,5] => 101010000 => 1
[[1,3,6,7,8],[2,5],[4],[9]] => [2,2,5] => 101010000 => 1
[[1,5,6,7,8],[2],[3],[4],[9]] => [4,5] => 100010000 => 1
[[1,3,4,8],[2,6,7],[5,9]] => [2,3,4] => 101001000 => 1
[[1,3,4,8],[2,6,7],[5],[9]] => [2,3,4] => 101001000 => 1
[[1,2,7,8],[3,4],[5,6],[9]] => [3,2,4] => 100101000 => 1
[[1,4,7,8],[2,6],[3],[5],[9]] => [3,2,4] => 100101000 => 1
[[1,6,7,8],[2],[3],[4],[5],[9]] => [5,4] => 100001000 => 1
[[1,2,5],[3,4,8],[6,7],[9]] => [3,3,3] => 100100100 => 1
[[1,4,5],[2,7,8],[3],[6],[9]] => [3,3,3] => 100100100 => 1
[[1,3,8],[2,5],[4,7],[6,9]] => [2,2,2,3] => 101010100 => 1
[[1,3,8],[2,5],[4,7],[6],[9]] => [2,2,2,3] => 101010100 => 1
[[1,5,8],[2,7],[3],[4],[6],[9]] => [4,2,3] => 100010100 => 1
[[1,7,8],[2],[3],[4],[5],[6],[9]] => [6,3] => 100000100 => 1
[[1,8,9],[2],[3],[4],[5],[6],[7],[10]] => [7,3] => 1000000100 => 1
[[1,2,3,6,7,8,9],[4,5]] => [4,5] => 100010000 => 1
[[1,2,5,6,7,8,9],[3],[4]] => [4,5] => 100010000 => 1
[[1,2,3,4,8,9],[5,6,7]] => [5,4] => 100001000 => 1
[[1,2,4,7,8,9],[3,6],[5]] => [3,2,4] => 100101000 => 1
[[1,2,6,7,8,9],[3],[4],[5]] => [5,4] => 100001000 => 1
[[1,2,4,5,9],[3,7,8],[6]] => [3,3,3] => 100100100 => 1
[[1,2,3,8,9],[4,5],[6,7]] => [4,2,3] => 100010100 => 1
[[1,2,5,8,9],[3,7],[4],[6]] => [4,2,3] => 100010100 => 1
[[1,2,7,8,9],[3],[4],[5],[6]] => [6,3] => 100000100 => 1
[[1,2,5,6],[3,4,8,9],[7]] => [3,4,2] => 100100010 => 1
[[1,2,3,6],[4,5,9],[7,8]] => [4,3,2] => 100010010 => 1
[[1,2,5,6],[3,8,9],[4],[7]] => [4,3,2] => 100010010 => 1
[[1,2,4,9],[3,6],[5,8],[7]] => [3,2,2,2] => 100101010 => 1
[[1,2,6,9],[3,8],[4],[5],[7]] => [5,2,2] => 100001010 => 1
[[1,2,8,9],[3],[4],[5],[6],[7]] => [7,2] => 100000010 => 1
[[1,2,4],[3,6,7],[5,9],[8]] => [3,2,3,1] => 100101001 => 1
[[1,2,7],[3,6,9],[4],[5],[8]] => [5,3,1] => 100001001 => 1
[[1,2,5],[3,7],[4,9],[6],[8]] => [4,2,2,1] => 100010101 => 1
[[1,2,7],[3,9],[4],[5],[6],[8]] => [6,2,1] => 100000101 => 1
[[1,2],[3,6],[4,8],[5],[7],[9]] => [5,2,2] => 100001010 => 1
[[1,2],[3,8],[4],[5],[6],[7],[9]] => [7,2] => 100000010 => 1
[[1,2,8,9,10],[3],[4],[5],[6],[7]] => [7,3] => 1000000100 => 1
[[1,2,7,10],[3,9],[4],[5],[6],[8]] => [6,2,2] => 1000001010 => 1
[[1,2,9,10],[3],[4],[5],[6],[7],[8]] => [8,2] => 1000000010 => 1
[[1,2,4],[3,6],[5,8],[7,10],[9]] => [3,2,2,2,1] => 1001010101 => 1
[[1,2],[3,7],[4,9],[5],[6],[8],[10]] => [6,2,2] => 1000001010 => 1
[[1,2],[3,9],[4],[5],[6],[7],[8],[10]] => [8,2] => 1000000010 => 1
[[1,2,3,4,7,8,9],[5,6]] => [5,4] => 100001000 => 1
[[1,2,4,5,8,9],[3,7],[6]] => [3,3,3] => 100100100 => 1
[[1,2,4,5,6,7],[3,9],[8]] => [3,5,1] => 100100001 => 1
[[1,2,5,6,9],[3,8],[4],[7]] => [4,3,2] => 100010010 => 1
[[1,2,3,4,7,8],[5,6],[9]] => [5,4] => 100001000 => 1
[[1,2,5,6,7,8],[3],[4],[9]] => [4,5] => 100010000 => 1
[[1,2,4,5],[3,7],[6,9],[8]] => [3,3,2,1] => 100100101 => 1
[[1,2,6,7],[3,9],[4],[5],[8]] => [5,3,1] => 100001001 => 1
[[1,2,5,6],[3,8],[4],[7],[9]] => [4,3,2] => 100010010 => 1
[[1,2,7,8],[3],[4],[5],[6],[9]] => [6,3] => 100000100 => 1
[[1,2,8,9],[3],[4],[5],[6],[7],[10]] => [7,3] => 1000000100 => 1
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Generating function
$F_{1} = q$
$F_{2} = 2\ q$
$F_{3} = 4\ q$
$F_{4} = 10\ q$
$F_{5} = 26\ q$
$F_{6} = 76\ q$
$F_{7} = 232\ q$
$F_{8} = 764\ q$
Description
The length of the longest run of ones in a binary word.
Map
valley composition
Description
The composition corresponding to the valley set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a valley if $i-1$ is a descent and $i$ is an ascent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the valley set of $T$.
Map
to binary word
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 $0$.
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