Identifier
-
Mp00189:
Skew partitions
—rotate⟶
Skew partitions
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000291: Binary words ⟶ ℤ
Values
[[1],[]] => [[1],[]] => [1] => 10 => 1
[[2],[]] => [[2],[]] => [2] => 100 => 1
[[1,1],[]] => [[1,1],[]] => [1,1] => 110 => 1
[[2,1],[1]] => [[2,1],[1]] => [2,1] => 1010 => 2
[[3],[]] => [[3],[]] => [3] => 1000 => 1
[[2,1],[]] => [[2,2],[1]] => [2,2] => 1100 => 1
[[3,1],[1]] => [[3,2],[2]] => [3,2] => 10100 => 2
[[2,2],[1]] => [[2,1],[]] => [2,1] => 1010 => 2
[[3,2],[2]] => [[3,1],[1]] => [3,1] => 10010 => 2
[[1,1,1],[]] => [[1,1,1],[]] => [1,1,1] => 1110 => 1
[[2,2,1],[1,1]] => [[2,1,1],[1]] => [2,1,1] => 10110 => 2
[[2,1,1],[1]] => [[2,2,1],[1,1]] => [2,2,1] => 11010 => 2
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => [3,2,1] => 101010 => 3
[[4],[]] => [[4],[]] => [4] => 10000 => 1
[[3,1],[]] => [[3,3],[2]] => [3,3] => 11000 => 1
[[4,1],[1]] => [[4,3],[3]] => [4,3] => 101000 => 2
[[2,2],[]] => [[2,2],[]] => [2,2] => 1100 => 1
[[3,2],[1]] => [[3,2],[1]] => [3,2] => 10100 => 2
[[4,2],[2]] => [[4,2],[2]] => [4,2] => 100100 => 2
[[2,1,1],[]] => [[2,2,2],[1,1]] => [2,2,2] => 11100 => 1
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => [3,2,2] => 101100 => 2
[[3,1,1],[1]] => [[3,3,2],[2,2]] => [3,3,2] => 110100 => 2
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => [4,3,2] => 1010100 => 3
[[3,3],[2]] => [[3,1],[]] => [3,1] => 10010 => 2
[[4,3],[3]] => [[4,1],[1]] => [4,1] => 100010 => 2
[[2,2,1],[1]] => [[2,2,1],[1]] => [2,2,1] => 11010 => 2
[[3,3,1],[2,1]] => [[3,2,1],[2]] => [3,2,1] => 101010 => 3
[[3,2,1],[2]] => [[3,3,1],[2,1]] => [3,3,1] => 110010 => 2
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => [4,3,1] => 1010010 => 3
[[2,2,2],[1,1]] => [[2,1,1],[]] => [2,1,1] => 10110 => 2
[[3,3,2],[2,2]] => [[3,1,1],[1]] => [3,1,1] => 100110 => 2
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => [3,2,1] => 101010 => 3
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => [4,2,1] => 1001010 => 3
[[1,1,1,1],[]] => [[1,1,1,1],[]] => [1,1,1,1] => 11110 => 1
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => [2,1,1,1] => 101110 => 2
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => [2,2,1,1] => 110110 => 2
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => [3,2,1,1] => 1010110 => 3
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => [2,2,2,1] => 111010 => 2
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => [3,2,2,1] => 1011010 => 3
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => [3,3,2,1] => 1101010 => 3
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => [4,3,2,1] => 10101010 => 4
[[5],[]] => [[5],[]] => [5] => 100000 => 1
[[4,1],[]] => [[4,4],[3]] => [4,4] => 110000 => 1
[[5,1],[1]] => [[5,4],[4]] => [5,4] => 1010000 => 2
[[3,2],[]] => [[3,3],[1]] => [3,3] => 11000 => 1
[[4,2],[1]] => [[4,3],[2]] => [4,3] => 101000 => 2
[[5,2],[2]] => [[5,3],[3]] => [5,3] => 1001000 => 2
[[3,1,1],[]] => [[3,3,3],[2,2]] => [3,3,3] => 111000 => 1
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => [4,3,3] => 1011000 => 2
[[4,1,1],[1]] => [[4,4,3],[3,3]] => [4,4,3] => 1101000 => 2
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => [5,4,3] => 10101000 => 3
[[3,3],[1]] => [[3,2],[]] => [3,2] => 10100 => 2
[[4,3],[2]] => [[4,2],[1]] => [4,2] => 100100 => 2
[[5,3],[3]] => [[5,2],[2]] => [5,2] => 1000100 => 2
[[2,2,1],[]] => [[2,2,2],[1]] => [2,2,2] => 11100 => 1
[[3,3,1],[1,1]] => [[3,2,2],[2]] => [3,2,2] => 101100 => 2
[[3,2,1],[1]] => [[3,3,2],[2,1]] => [3,3,2] => 110100 => 2
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => [4,3,2] => 1010100 => 3
[[4,2,1],[2]] => [[4,4,2],[3,2]] => [4,4,2] => 1100100 => 2
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => [5,4,2] => 10100100 => 3
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => [3,2,2] => 101100 => 2
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => [4,2,2] => 1001100 => 2
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => [4,3,2] => 1010100 => 3
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => [5,3,2] => 10010100 => 3
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [2,2,2,2] => 111100 => 1
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => [3,2,2,2] => 1011100 => 2
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => [3,3,2,2] => 1101100 => 2
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => [4,3,2,2] => 10101100 => 3
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => [3,3,3,2] => 1110100 => 2
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => [4,3,3,2] => 10110100 => 3
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => [4,4,3,2] => 11010100 => 3
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => [5,4,3,2] => 101010100 => 4
[[4,4],[3]] => [[4,1],[]] => [4,1] => 100010 => 2
[[5,4],[4]] => [[5,1],[1]] => [5,1] => 1000010 => 2
[[3,3,1],[2]] => [[3,3,1],[2]] => [3,3,1] => 110010 => 2
[[4,4,1],[3,1]] => [[4,3,1],[3]] => [4,3,1] => 1010010 => 3
[[4,3,1],[3]] => [[4,4,1],[3,1]] => [4,4,1] => 1100010 => 2
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => [5,4,1] => 10100010 => 3
[[2,2,2],[1]] => [[2,2,1],[]] => [2,2,1] => 11010 => 2
[[3,3,2],[2,1]] => [[3,2,1],[1]] => [3,2,1] => 101010 => 3
[[4,4,2],[3,2]] => [[4,2,1],[2]] => [4,2,1] => 1001010 => 3
[[3,2,2],[2]] => [[3,3,1],[1,1]] => [3,3,1] => 110010 => 2
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => [4,3,1] => 1010010 => 3
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => [5,3,1] => 10010010 => 3
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => [2,2,2,1] => 111010 => 2
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => [3,2,2,1] => 1011010 => 3
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => [3,3,2,1] => 1101010 => 3
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => [4,3,2,1] => 10101010 => 4
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => [3,3,3,1] => 1110010 => 2
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => [4,3,3,1] => 10110010 => 3
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => [4,4,3,1] => 11010010 => 3
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => [5,4,3,1] => 101010010 => 4
[[3,3,3],[2,2]] => [[3,1,1],[]] => [3,1,1] => 100110 => 2
[[4,4,3],[3,3]] => [[4,1,1],[1]] => [4,1,1] => 1000110 => 2
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => [4,2,1] => 1001010 => 3
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => [5,2,1] => 10001010 => 3
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => [2,2,1,1] => 110110 => 2
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => [3,2,1,1] => 1010110 => 3
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => [3,3,1,1] => 1100110 => 2
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => [4,3,1,1] => 10100110 => 3
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => [3,3,2,1] => 1101010 => 3
>>> Load all 1054 entries. <<<[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => [4,3,2,1] => 10101010 => 4
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => [4,4,2,1] => 11001010 => 3
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => [5,4,2,1] => 101001010 => 4
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => [2,1,1,1] => 101110 => 2
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => [3,1,1,1] => 1001110 => 2
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => [3,2,1,1] => 1010110 => 3
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => [4,2,1,1] => 10010110 => 3
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => [3,2,2,1] => 1011010 => 3
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => [4,2,2,1] => 10011010 => 3
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => [4,3,2,1] => 10101010 => 4
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => [5,3,2,1] => 100101010 => 4
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => [1,1,1,1,1] => 111110 => 1
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => [2,1,1,1,1] => 1011110 => 2
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => [2,2,1,1,1] => 1101110 => 2
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => [3,2,1,1,1] => 10101110 => 3
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => [2,2,2,1,1] => 1110110 => 2
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => [3,2,2,1,1] => 10110110 => 3
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => [3,3,2,1,1] => 11010110 => 3
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => [4,3,2,1,1] => 101010110 => 4
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,1] => 1111010 => 2
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => [3,2,2,2,1] => 10111010 => 3
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => [3,3,2,2,1] => 11011010 => 3
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => [4,3,2,2,1] => 101011010 => 4
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => [3,3,3,2,1] => 11101010 => 3
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => [4,3,3,2,1] => 101101010 => 4
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => [5,4,3,2,1] => 1010101010 => 5
[[6],[]] => [[6],[]] => [6] => 1000000 => 1
[[5,1],[]] => [[5,5],[4]] => [5,5] => 1100000 => 1
[[6,1],[1]] => [[6,5],[5]] => [6,5] => 10100000 => 2
[[4,2],[]] => [[4,4],[2]] => [4,4] => 110000 => 1
[[5,2],[1]] => [[5,4],[3]] => [5,4] => 1010000 => 2
[[6,2],[2]] => [[6,4],[4]] => [6,4] => 10010000 => 2
[[4,1,1],[]] => [[4,4,4],[3,3]] => [4,4,4] => 1110000 => 1
[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => [5,4,4] => 10110000 => 2
[[5,1,1],[1]] => [[5,5,4],[4,4]] => [5,5,4] => 11010000 => 2
[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => [6,5,4] => 101010000 => 3
[[3,3],[]] => [[3,3],[]] => [3,3] => 11000 => 1
[[4,3],[1]] => [[4,3],[1]] => [4,3] => 101000 => 2
[[5,3],[2]] => [[5,3],[2]] => [5,3] => 1001000 => 2
[[6,3],[3]] => [[6,3],[3]] => [6,3] => 10001000 => 2
[[3,2,1],[]] => [[3,3,3],[2,1]] => [3,3,3] => 111000 => 1
[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => [4,3,3] => 1011000 => 2
[[4,2,1],[1]] => [[4,4,3],[3,2]] => [4,4,3] => 1101000 => 2
[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => [5,4,3] => 10101000 => 3
[[5,2,1],[2]] => [[5,5,3],[4,3]] => [5,5,3] => 11001000 => 2
[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => [6,5,3] => 101001000 => 3
[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => [4,3,3] => 1011000 => 2
[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => [5,3,3] => 10011000 => 2
[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => [5,4,3] => 10101000 => 3
[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => [6,4,3] => 100101000 => 3
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [3,3,3,3] => 1111000 => 1
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => [4,3,3,3] => 10111000 => 2
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => [4,4,3,3] => 11011000 => 2
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => [5,4,3,3] => 101011000 => 3
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => [4,4,4,3] => 11101000 => 2
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => [5,4,4,3] => 101101000 => 3
[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] => [5,5,4,3] => 110101000 => 3
[[4,4],[2]] => [[4,2],[]] => [4,2] => 100100 => 2
[[5,4],[3]] => [[5,2],[1]] => [5,2] => 1000100 => 2
[[6,4],[4]] => [[6,2],[2]] => [6,2] => 10000100 => 2
[[3,3,1],[1]] => [[3,3,2],[2]] => [3,3,2] => 110100 => 2
[[4,4,1],[2,1]] => [[4,3,2],[3]] => [4,3,2] => 1010100 => 3
[[4,3,1],[2]] => [[4,4,2],[3,1]] => [4,4,2] => 1100100 => 2
[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => [5,4,2] => 10100100 => 3
[[5,3,1],[3]] => [[5,5,2],[4,2]] => [5,5,2] => 11000100 => 2
[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => [6,5,2] => 101000100 => 3
[[2,2,2],[]] => [[2,2,2],[]] => [2,2,2] => 11100 => 1
[[3,3,2],[1,1]] => [[3,2,2],[1]] => [3,2,2] => 101100 => 2
[[4,4,2],[2,2]] => [[4,2,2],[2]] => [4,2,2] => 1001100 => 2
[[3,2,2],[1]] => [[3,3,2],[1,1]] => [3,3,2] => 110100 => 2
[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => [4,3,2] => 1010100 => 3
[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => [5,3,2] => 10010100 => 3
[[4,2,2],[2]] => [[4,4,2],[2,2]] => [4,4,2] => 1100100 => 2
[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => [5,4,2] => 10100100 => 3
[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => [6,4,2] => 100100100 => 3
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [2,2,2,2] => 111100 => 1
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => [3,2,2,2] => 1011100 => 2
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => [3,3,2,2] => 1101100 => 2
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => [4,3,2,2] => 10101100 => 3
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => [3,3,3,2] => 1110100 => 2
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => [4,3,3,2] => 10110100 => 3
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => [4,4,3,2] => 11010100 => 3
[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] => [5,4,3,2] => 101010100 => 4
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => [4,4,4,2] => 11100100 => 2
[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] => [5,4,4,2] => 101100100 => 3
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => [5,5,4,2] => 110100100 => 3
[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => [4,2,2] => 1001100 => 2
[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => [5,2,2] => 10001100 => 2
[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => [5,3,2] => 10010100 => 3
[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => [6,3,2] => 100010100 => 3
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => [3,3,2,2] => 1101100 => 2
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => [4,3,2,2] => 10101100 => 3
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => [4,4,2,2] => 11001100 => 2
[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] => [5,4,2,2] => 101001100 => 3
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => [4,4,3,2] => 11010100 => 3
[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] => [5,4,3,2] => 101010100 => 4
[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] => [5,5,3,2] => 110010100 => 3
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => [3,2,2,2] => 1011100 => 2
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => [4,2,2,2] => 10011100 => 2
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => [4,3,2,2] => 10101100 => 3
[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] => [5,3,2,2] => 100101100 => 3
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => [4,3,3,2] => 10110100 => 3
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => [5,3,3,2] => 100110100 => 3
[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] => [5,4,3,2] => 101010100 => 4
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2] => 1111100 => 1
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => [3,2,2,2,2] => 10111100 => 2
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => [3,3,2,2,2] => 11011100 => 2
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => [4,3,2,2,2] => 101011100 => 3
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => [3,3,3,2,2] => 11101100 => 2
[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] => [4,3,3,2,2] => 101101100 => 3
[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] => [4,4,3,2,2] => 110101100 => 3
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => [5,4,3,2,2] => 1010101100 => 4
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => [3,3,3,3,2] => 11110100 => 2
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => [4,3,3,3,2] => 101110100 => 3
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => [4,4,3,3,2] => 110110100 => 3
[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]] => [5,4,3,3,2] => 1010110100 => 4
[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] => [4,4,4,3,2] => 111010100 => 3
[[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]] => [5,4,4,3,2] => 1011010100 => 4
[[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]] => [5,5,4,3,2] => 1101010100 => 4
[[5,5],[4]] => [[5,1],[]] => [5,1] => 1000010 => 2
[[6,5],[5]] => [[6,1],[1]] => [6,1] => 10000010 => 2
[[4,4,1],[3]] => [[4,4,1],[3]] => [4,4,1] => 1100010 => 2
[[5,5,1],[4,1]] => [[5,4,1],[4]] => [5,4,1] => 10100010 => 3
[[5,4,1],[4]] => [[5,5,1],[4,1]] => [5,5,1] => 11000010 => 2
[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => [6,5,1] => 101000010 => 3
[[3,3,2],[2]] => [[3,3,1],[1]] => [3,3,1] => 110010 => 2
[[4,4,2],[3,1]] => [[4,3,1],[2]] => [4,3,1] => 1010010 => 3
[[5,5,2],[4,2]] => [[5,3,1],[3]] => [5,3,1] => 10010010 => 3
[[4,3,2],[3]] => [[4,4,1],[2,1]] => [4,4,1] => 1100010 => 2
[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => [5,4,1] => 10100010 => 3
[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => [6,4,1] => 100100010 => 3
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => [3,3,3,1] => 1110010 => 2
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => [4,3,3,1] => 10110010 => 3
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => [4,4,3,1] => 11010010 => 3
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => [5,4,3,1] => 101010010 => 4
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => [4,4,4,1] => 11100010 => 2
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => [5,4,4,1] => 101100010 => 3
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => [5,5,4,1] => 110100010 => 3
[[3,3,3],[2,1]] => [[3,2,1],[]] => [3,2,1] => 101010 => 3
[[4,4,3],[3,2]] => [[4,2,1],[1]] => [4,2,1] => 1001010 => 3
[[5,5,3],[4,3]] => [[5,2,1],[2]] => [5,2,1] => 10001010 => 3
[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => [4,3,1] => 1010010 => 3
[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => [5,3,1] => 10010010 => 3
[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => [6,3,1] => 100010010 => 3
[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => [2,2,2,1] => 111010 => 2
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => [3,2,2,1] => 1011010 => 3
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => [3,3,2,1] => 1101010 => 3
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => [4,3,2,1] => 10101010 => 4
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => [4,4,2,1] => 11001010 => 3
[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] => [5,4,2,1] => 101001010 => 4
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => [3,3,3,1] => 1110010 => 2
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => [4,3,3,1] => 10110010 => 3
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => [4,4,3,1] => 11010010 => 3
[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] => [5,4,3,1] => 101010010 => 4
[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] => [5,5,3,1] => 110010010 => 3
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => [3,2,2,1] => 1011010 => 3
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => [4,2,2,1] => 10011010 => 3
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => [4,3,2,1] => 10101010 => 4
[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] => [5,3,2,1] => 100101010 => 4
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => [4,3,3,1] => 10110010 => 3
[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] => [5,3,3,1] => 100110010 => 3
[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] => [5,4,3,1] => 101010010 => 4
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => [2,2,2,2,1] => 1111010 => 2
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => [3,2,2,2,1] => 10111010 => 3
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => [3,3,2,2,1] => 11011010 => 3
[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] => [4,3,2,2,1] => 101011010 => 4
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => [3,3,3,2,1] => 11101010 => 3
[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] => [4,3,3,2,1] => 101101010 => 4
[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] => [4,4,3,2,1] => 110101010 => 4
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => [5,4,3,2,1] => 1010101010 => 5
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => [3,3,3,3,1] => 11110010 => 2
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => [4,3,3,3,1] => 101110010 => 3
[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] => [4,4,3,3,1] => 110110010 => 3
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => [5,4,3,3,1] => 1010110010 => 4
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => [4,4,4,3,1] => 111010010 => 3
[[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]] => [5,4,4,3,1] => 1011010010 => 4
[[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]] => [5,5,4,3,1] => 1101010010 => 4
[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => [6,5,4,3,1] => 10101010010 => 5
[[4,4,4],[3,3]] => [[4,1,1],[]] => [4,1,1] => 1000110 => 2
[[5,5,4],[4,4]] => [[5,1,1],[1]] => [5,1,1] => 10000110 => 2
[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => [5,2,1] => 10001010 => 3
[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => [6,2,1] => 100001010 => 3
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => [3,3,1,1] => 1100110 => 2
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => [4,3,1,1] => 10100110 => 3
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => [4,4,1,1] => 11000110 => 2
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => [5,4,1,1] => 101000110 => 3
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => [4,4,2,1] => 11001010 => 3
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => [5,4,2,1] => 101001010 => 4
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => [5,5,2,1] => 110001010 => 3
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => [2,2,1,1] => 110110 => 2
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => [3,2,1,1] => 1010110 => 3
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => [4,2,1,1] => 10010110 => 3
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => [3,3,1,1] => 1100110 => 2
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => [4,3,1,1] => 10100110 => 3
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => [5,3,1,1] => 100100110 => 3
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => [3,3,2,1] => 1101010 => 3
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => [4,3,2,1] => 10101010 => 4
[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] => [5,3,2,1] => 100101010 => 4
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => [4,4,2,1] => 11001010 => 3
[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] => [5,4,2,1] => 101001010 => 4
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => [2,2,2,1,1] => 1110110 => 2
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => [3,2,2,1,1] => 10110110 => 3
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => [3,3,2,1,1] => 11010110 => 3
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => [4,3,2,1,1] => 101010110 => 4
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => [3,3,3,1,1] => 11100110 => 2
[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] => [4,3,3,1,1] => 101100110 => 3
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => [4,4,3,1,1] => 110100110 => 3
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] => [5,4,3,1,1] => 1010100110 => 4
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => [3,3,3,2,1] => 11101010 => 3
[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] => [4,3,3,2,1] => 101101010 => 4
[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => [5,4,3,2,1] => 1010101010 => 5
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => [4,4,4,2,1] => 111001010 => 3
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] => [5,4,4,2,1] => 1011001010 => 4
[[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]] => [5,5,4,2,1] => 1101001010 => 4
[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => [6,5,4,2,1] => 10101001010 => 5
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => [3,1,1,1] => 1001110 => 2
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => [4,1,1,1] => 10001110 => 2
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => [4,2,1,1] => 10010110 => 3
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => [5,2,1,1] => 100010110 => 3
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => [4,2,2,1] => 10011010 => 3
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => [5,2,2,1] => 100011010 => 3
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => [5,3,2,1] => 100101010 => 4
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => [2,2,1,1,1] => 1101110 => 2
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => [3,2,1,1,1] => 10101110 => 3
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => [3,3,1,1,1] => 11001110 => 2
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => [4,3,1,1,1] => 101001110 => 3
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => [3,3,2,1,1] => 11010110 => 3
[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] => [4,3,2,1,1] => 101010110 => 4
[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] => [4,4,2,1,1] => 110010110 => 3
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] => [5,4,2,1,1] => 1010010110 => 4
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => [3,3,2,2,1] => 11011010 => 3
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => [4,3,2,2,1] => 101011010 => 4
[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] => [4,4,2,2,1] => 110011010 => 3
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] => [5,4,2,2,1] => 1010011010 => 4
[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] => [5,4,3,2,1] => 1010101010 => 5
[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] => [5,5,3,2,1] => 1100101010 => 4
[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] => [6,5,3,2,1] => 10100101010 => 5
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => [2,1,1,1,1] => 1011110 => 2
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => [3,1,1,1,1] => 10011110 => 2
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => [3,2,1,1,1] => 10101110 => 3
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => [4,2,1,1,1] => 100101110 => 3
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => [3,2,2,1,1] => 10110110 => 3
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => [4,2,2,1,1] => 100110110 => 3
[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] => [4,3,2,1,1] => 101010110 => 4
[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] => [5,3,2,1,1] => 1001010110 => 4
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => [3,2,2,2,1] => 10111010 => 3
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => [4,2,2,2,1] => 100111010 => 3
[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] => [4,3,2,2,1] => 101011010 => 4
[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] => [5,3,2,2,1] => 1001011010 => 4
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => [4,3,3,2,1] => 101101010 => 4
[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] => [5,3,3,2,1] => 1001101010 => 4
[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] => [5,4,3,2,1] => 1010101010 => 5
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => [6,4,3,2,1] => 10010101010 => 5
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => 1111110 => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => 10111110 => 2
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => [2,2,1,1,1,1] => 11011110 => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => [3,2,1,1,1,1] => 101011110 => 3
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => [2,2,2,1,1,1] => 11101110 => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => [3,2,2,1,1,1] => 101101110 => 3
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => [3,3,2,1,1,1] => 110101110 => 3
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => [2,2,2,2,1,1] => 11110110 => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => [3,2,2,2,1,1] => 101110110 => 3
[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] => [3,3,2,2,1,1] => 110110110 => 3
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => [3,3,3,2,1,1] => 111010110 => 3
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => [2,2,2,2,2,1] => 11111010 => 2
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => [3,2,2,2,2,1] => 101111010 => 3
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => [3,3,2,2,2,1] => 110111010 => 3
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => [3,3,3,2,2,1] => 111011010 => 3
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => [3,3,3,3,2,1] => 111101010 => 3
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => [6,5,4,3,2,1] => 101010101010 => 6
[[7],[]] => [[7],[]] => [7] => 10000000 => 1
[[6,1],[]] => [[6,6],[5]] => [6,6] => 11000000 => 1
[[7,1],[1]] => [[7,6],[6]] => [7,6] => 101000000 => 2
[[5,2],[]] => [[5,5],[3]] => [5,5] => 1100000 => 1
[[6,2],[1]] => [[6,5],[4]] => [6,5] => 10100000 => 2
[[7,2],[2]] => [[7,5],[5]] => [7,5] => 100100000 => 2
[[5,1,1],[]] => [[5,5,5],[4,4]] => [5,5,5] => 11100000 => 1
[[6,2,1],[1,1]] => [[6,5,5],[5,4]] => [6,5,5] => 101100000 => 2
[[6,1,1],[1]] => [[6,6,5],[5,5]] => [6,6,5] => 110100000 => 2
[[4,3],[]] => [[4,4],[1]] => [4,4] => 110000 => 1
[[5,3],[1]] => [[5,4],[2]] => [5,4] => 1010000 => 2
[[6,3],[2]] => [[6,4],[3]] => [6,4] => 10010000 => 2
[[7,3],[3]] => [[7,4],[4]] => [7,4] => 100010000 => 2
[[4,2,1],[]] => [[4,4,4],[3,2]] => [4,4,4] => 1110000 => 1
[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => [5,4,4] => 10110000 => 2
[[5,2,1],[1]] => [[5,5,4],[4,3]] => [5,5,4] => 11010000 => 2
[[6,3,1],[2,1]] => [[6,5,4],[5,3]] => [6,5,4] => 101010000 => 3
[[6,2,1],[2]] => [[6,6,4],[5,4]] => [6,6,4] => 110010000 => 2
[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => [5,4,4] => 10110000 => 2
[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => [6,4,4] => 100110000 => 2
[[6,2,2],[2,1]] => [[6,5,4],[4,4]] => [6,5,4] => 101010000 => 3
[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => [4,4,4,4] => 11110000 => 1
[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] => [5,4,4,4] => 101110000 => 2
[[4,4],[1]] => [[4,3],[]] => [4,3] => 101000 => 2
[[5,4],[2]] => [[5,3],[1]] => [5,3] => 1001000 => 2
[[6,4],[3]] => [[6,3],[2]] => [6,3] => 10001000 => 2
[[7,4],[4]] => [[7,3],[3]] => [7,3] => 100001000 => 2
[[3,3,1],[]] => [[3,3,3],[2]] => [3,3,3] => 111000 => 1
[[4,4,1],[1,1]] => [[4,3,3],[3]] => [4,3,3] => 1011000 => 2
[[4,3,1],[1]] => [[4,4,3],[3,1]] => [4,4,3] => 1101000 => 2
[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => [5,4,3] => 10101000 => 3
[[5,3,1],[2]] => [[5,5,3],[4,2]] => [5,5,3] => 11001000 => 2
[[6,4,1],[3,1]] => [[6,5,3],[5,2]] => [6,5,3] => 101001000 => 3
[[6,3,1],[3]] => [[6,6,3],[5,3]] => [6,6,3] => 110001000 => 2
[[3,2,2],[]] => [[3,3,3],[1,1]] => [3,3,3] => 111000 => 1
[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => [4,3,3] => 1011000 => 2
[[5,4,2],[2,2]] => [[5,3,3],[3,1]] => [5,3,3] => 10011000 => 2
[[4,2,2],[1]] => [[4,4,3],[2,2]] => [4,4,3] => 1101000 => 2
[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => [5,4,3] => 10101000 => 3
[[6,4,2],[3,2]] => [[6,4,3],[4,2]] => [6,4,3] => 100101000 => 3
[[5,2,2],[2]] => [[5,5,3],[3,3]] => [5,5,3] => 11001000 => 2
[[6,3,2],[3,1]] => [[6,5,3],[4,3]] => [6,5,3] => 101001000 => 3
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [3,3,3,3] => 1111000 => 1
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => [4,3,3,3] => 10111000 => 2
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] => [4,4,3,3] => 11011000 => 2
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => [5,4,3,3] => 101011000 => 3
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => [4,4,4,3] => 11101000 => 2
[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] => [5,4,4,3] => 101101000 => 3
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] => [5,5,4,3] => 110101000 => 3
[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => [5,3,3] => 10011000 => 2
[[6,4,3],[3,3]] => [[6,3,3],[3,2]] => [6,3,3] => 100011000 => 2
[[6,3,3],[3,2]] => [[6,4,3],[3,3]] => [6,4,3] => 100101000 => 3
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => [4,4,3,3] => 11011000 => 2
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] => [5,4,3,3] => 101011000 => 3
[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] => [5,5,3,3] => 110011000 => 2
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] => [5,5,4,3] => 110101000 => 3
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => [4,3,3,3] => 10111000 => 2
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] => [5,3,3,3] => 100111000 => 2
[[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]] => [5,4,3,3] => 101011000 => 3
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] => [5,4,4,3] => 101101000 => 3
[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => [3,3,3,3,3] => 11111000 => 1
[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] => [4,3,3,3,3] => 101111000 => 2
[[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]] => [4,4,3,3,3] => 110111000 => 2
[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]] => [5,4,3,3,3] => 1010111000 => 3
[[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]] => [5,4,4,4,3] => 1011101000 => 3
[[5,5],[3]] => [[5,2],[]] => [5,2] => 1000100 => 2
[[6,5],[4]] => [[6,2],[1]] => [6,2] => 10000100 => 2
[[7,5],[5]] => [[7,2],[2]] => [7,2] => 100000100 => 2
[[4,4,1],[2]] => [[4,4,2],[3]] => [4,4,2] => 1100100 => 2
[[5,5,1],[3,1]] => [[5,4,2],[4]] => [5,4,2] => 10100100 => 3
[[5,4,1],[3]] => [[5,5,2],[4,1]] => [5,5,2] => 11000100 => 2
[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => [6,5,2] => 101000100 => 3
[[6,4,1],[4]] => [[6,6,2],[5,2]] => [6,6,2] => 110000100 => 2
[[3,3,2],[1]] => [[3,3,2],[1]] => [3,3,2] => 110100 => 2
[[4,4,2],[2,1]] => [[4,3,2],[2]] => [4,3,2] => 1010100 => 3
[[5,5,2],[3,2]] => [[5,3,2],[3]] => [5,3,2] => 10010100 => 3
[[4,3,2],[2]] => [[4,4,2],[2,1]] => [4,4,2] => 1100100 => 2
[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => [5,4,2] => 10100100 => 3
[[6,5,2],[4,2]] => [[6,4,2],[4,1]] => [6,4,2] => 100100100 => 3
[[5,3,2],[3]] => [[5,5,2],[3,2]] => [5,5,2] => 11000100 => 2
[[6,4,2],[4,1]] => [[6,5,2],[4,2]] => [6,5,2] => 101000100 => 3
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => [3,3,3,2] => 1110100 => 2
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] => [4,3,3,2] => 10110100 => 3
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] => [4,4,3,2] => 11010100 => 3
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => [5,4,3,2] => 101010100 => 4
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => [4,4,4,2] => 11100100 => 2
[[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]] => [5,4,4,2] => 101100100 => 3
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] => [5,5,4,2] => 110100100 => 3
[[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]] => [5,5,5,2] => 111000100 => 2
[[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]] => [7,6,5,2] => 10101000100 => 4
[[3,3,3],[1,1]] => [[3,2,2],[]] => [3,2,2] => 101100 => 2
[[4,4,3],[2,2]] => [[4,2,2],[1]] => [4,2,2] => 1001100 => 2
[[5,5,3],[3,3]] => [[5,2,2],[2]] => [5,2,2] => 10001100 => 2
[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => [4,3,2] => 1010100 => 3
[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => [5,3,2] => 10010100 => 3
[[6,5,3],[4,3]] => [[6,3,2],[3,1]] => [6,3,2] => 100010100 => 3
[[5,3,3],[3,1]] => [[5,4,2],[2,2]] => [5,4,2] => 10100100 => 3
[[6,4,3],[4,2]] => [[6,4,2],[3,2]] => [6,4,2] => 100100100 => 3
[[2,2,2,1],[]] => [[2,2,2,2],[1]] => [2,2,2,2] => 111100 => 1
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] => [3,2,2,2] => 1011100 => 2
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => [3,3,2,2] => 1101100 => 2
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] => [4,3,2,2] => 10101100 => 3
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => [4,4,2,2] => 11001100 => 2
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] => [5,4,2,2] => 101001100 => 3
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => [3,3,3,2] => 1110100 => 2
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] => [4,3,3,2] => 10110100 => 3
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => [4,4,3,2] => 11010100 => 3
[[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]] => [5,4,3,2] => 101010100 => 4
[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] => [5,5,3,2] => 110010100 => 3
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] => [4,4,4,2] => 11100100 => 2
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] => [5,4,4,2] => 101100100 => 3
[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] => [5,5,4,2] => 110100100 => 3
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => [3,2,2,2] => 1011100 => 2
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] => [4,2,2,2] => 10011100 => 2
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] => [4,3,2,2] => 10101100 => 3
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] => [5,3,2,2] => 100101100 => 3
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => [4,3,3,2] => 10110100 => 3
[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] => [5,3,3,2] => 100110100 => 3
[[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]] => [5,4,3,2] => 101010100 => 4
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] => [5,4,4,2] => 101100100 => 3
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [2,2,2,2,2] => 1111100 => 1
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => [3,2,2,2,2] => 10111100 => 2
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] => [3,3,2,2,2] => 11011100 => 2
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => [4,3,2,2,2] => 101011100 => 3
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] => [3,3,3,2,2] => 11101100 => 2
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] => [4,3,3,2,2] => 101101100 => 3
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] => [4,4,3,2,2] => 110101100 => 3
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => [5,4,3,2,2] => 1010101100 => 4
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => [3,3,3,3,2] => 11110100 => 2
[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] => [4,3,3,3,2] => 101110100 => 3
[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] => [4,4,3,3,2] => 110110100 => 3
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => [5,4,3,3,2] => 1010110100 => 4
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] => [4,4,4,3,2] => 111010100 => 3
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] => [5,4,4,3,2] => 1011010100 => 4
[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] => [5,5,4,3,2] => 1101010100 => 4
[[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]] => [4,4,4,4,2] => 111100100 => 2
[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => [5,2,2] => 10001100 => 2
[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => [6,2,2] => 100001100 => 2
[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => [6,3,2] => 100010100 => 3
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => [4,4,2,2] => 11001100 => 2
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] => [5,4,2,2] => 101001100 => 3
[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] => [5,5,2,2] => 110001100 => 2
[[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]] => [5,5,3,2] => 110010100 => 3
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => [3,3,2,2] => 1101100 => 2
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => [4,3,2,2] => 10101100 => 3
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] => [5,3,2,2] => 100101100 => 3
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => [4,4,2,2] => 11001100 => 2
[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] => [5,4,2,2] => 101001100 => 3
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] => [4,4,3,2] => 11010100 => 3
[[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]] => [5,4,3,2] => 101010100 => 4
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] => [5,5,3,2] => 110010100 => 3
[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] => [7,5,3,2] => 10010010100 => 4
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => [3,3,3,2,2] => 11101100 => 2
[[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]] => [4,3,3,2,2] => 101101100 => 3
[[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]] => [4,4,3,2,2] => 110101100 => 3
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]] => [5,4,3,2,2] => 1010101100 => 4
[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] => [4,4,4,2,2] => 111001100 => 2
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => [5,4,4,2,2] => 1011001100 => 3
[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] => [5,5,4,2,2] => 1101001100 => 3
[[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]] => [4,4,4,3,2] => 111010100 => 3
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] => [5,4,4,3,2] => 1011010100 => 4
[[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]] => [5,5,4,3,2] => 1101010100 => 4
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => [4,2,2,2] => 10011100 => 2
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] => [5,2,2,2] => 100011100 => 2
[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] => [5,3,2,2] => 100101100 => 3
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] => [5,3,3,2] => 100110100 => 3
[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] => [7,4,3,2] => 10001010100 => 4
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => [3,3,2,2,2] => 11011100 => 2
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] => [4,3,2,2,2] => 101011100 => 3
[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] => [4,4,2,2,2] => 110011100 => 2
[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] => [4,4,3,2,2] => 110101100 => 3
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => [5,4,3,2,2] => 1010101100 => 4
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => [5,5,3,2,2] => 1100101100 => 3
[[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]] => [4,4,3,3,2] => 110110100 => 3
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]] => [5,4,3,3,2] => 1010110100 => 4
[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] => [5,5,3,3,2] => 1100110100 => 3
[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] => [5,5,4,3,2] => 1101010100 => 4
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => [3,2,2,2,2] => 10111100 => 2
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => [4,2,2,2,2] => 100111100 => 2
[[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]] => [4,3,2,2,2] => 101011100 => 3
[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] => [4,3,3,2,2] => 101101100 => 3
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => [5,3,3,2,2] => 1001101100 => 3
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => [5,4,3,2,2] => 1010101100 => 4
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => [4,3,3,3,2] => 101110100 => 3
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] => [5,3,3,3,2] => 1001110100 => 3
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] => [5,4,3,3,2] => 1010110100 => 4
[[5,3,2,2,2],[3,2,1,1]] => [[5,4,4,3,2],[3,3,3,2]] => [5,4,4,3,2] => 1011010100 => 4
[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [2,2,2,2,2,2] => 11111100 => 1
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => [3,2,2,2,2,2] => 101111100 => 2
[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => [3,3,2,2,2,2] => 110111100 => 2
[[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]] => [3,3,3,2,2,2] => 111011100 => 2
[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => [3,3,3,3,2,2] => 111101100 => 2
[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] => [6,5,4,3,2,2] => 101010101100 => 5
[[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]] => [3,3,3,3,3,2] => 111110100 => 2
[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] => [6,5,4,3,3,2] => 101010110100 => 5
[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] => [6,5,4,4,3,2] => 101011010100 => 5
[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] => [6,5,5,4,3,2] => 101101010100 => 5
[[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]] => [6,6,5,4,3,2] => 110101010100 => 5
[[6,6],[5]] => [[6,1],[]] => [6,1] => 10000010 => 2
[[7,6],[6]] => [[7,1],[1]] => [7,1] => 100000010 => 2
[[5,5,1],[4]] => [[5,5,1],[4]] => [5,5,1] => 11000010 => 2
[[6,6,1],[5,1]] => [[6,5,1],[5]] => [6,5,1] => 101000010 => 3
[[6,5,1],[5]] => [[6,6,1],[5,1]] => [6,6,1] => 110000010 => 2
[[4,4,2],[3]] => [[4,4,1],[2]] => [4,4,1] => 1100010 => 2
[[5,5,2],[4,1]] => [[5,4,1],[3]] => [5,4,1] => 10100010 => 3
[[6,6,2],[5,2]] => [[6,4,1],[4]] => [6,4,1] => 100100010 => 3
[[5,4,2],[4]] => [[5,5,1],[3,1]] => [5,5,1] => 11000010 => 2
[[6,5,2],[5,1]] => [[6,5,1],[4,1]] => [6,5,1] => 101000010 => 3
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => [4,4,4,1] => 11100010 => 2
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] => [5,4,4,1] => 101100010 => 3
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => [5,5,4,1] => 110100010 => 3
[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] => [5,5,5,1] => 111000010 => 2
[[3,3,3],[2]] => [[3,3,1],[]] => [3,3,1] => 110010 => 2
[[4,4,3],[3,1]] => [[4,3,1],[1]] => [4,3,1] => 1010010 => 3
[[5,5,3],[4,2]] => [[5,3,1],[2]] => [5,3,1] => 10010010 => 3
[[6,6,3],[5,3]] => [[6,3,1],[3]] => [6,3,1] => 100010010 => 3
[[4,3,3],[3]] => [[4,4,1],[1,1]] => [4,4,1] => 1100010 => 2
[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => [5,4,1] => 10100010 => 3
[[6,5,3],[5,2]] => [[6,4,1],[3,1]] => [6,4,1] => 100100010 => 3
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => [3,3,3,1] => 1110010 => 2
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] => [4,3,3,1] => 10110010 => 3
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => [4,4,3,1] => 11010010 => 3
[[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]] => [5,4,3,1] => 101010010 => 4
[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] => [5,5,3,1] => 110010010 => 3
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => [4,4,4,1] => 11100010 => 2
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => [5,4,4,1] => 101100010 => 3
[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] => [5,5,4,1] => 110100010 => 3
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => [4,3,3,1] => 10110010 => 3
[[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]] => [5,3,3,1] => 100110010 => 3
[[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]] => [5,4,3,1] => 101010010 => 4
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] => [5,4,4,1] => 101100010 => 3
[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] => [7,5,4,1] => 10010100010 => 4
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => [3,3,3,3,1] => 11110010 => 2
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] => [4,3,3,3,1] => 101110010 => 3
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] => [4,4,3,3,1] => 110110010 => 3
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]] => [5,4,3,3,1] => 1010110010 => 4
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] => [4,4,4,3,1] => 111010010 => 3
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]] => [5,4,4,3,1] => 1011010010 => 4
[[5,5,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3]] => [5,5,4,3,1] => 1101010010 => 4
[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => [6,5,4,3,1] => 10101010010 => 5
[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] => [4,4,4,4,1] => 111100010 => 2
[[4,4,4],[3,2]] => [[4,2,1],[]] => [4,2,1] => 1001010 => 3
[[5,5,4],[4,3]] => [[5,2,1],[1]] => [5,2,1] => 10001010 => 3
[[6,6,4],[5,4]] => [[6,2,1],[2]] => [6,2,1] => 100001010 => 3
[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => [5,3,1] => 10010010 => 3
[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => [6,3,1] => 100010010 => 3
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => [3,3,2,1] => 1101010 => 3
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => [4,3,2,1] => 10101010 => 4
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => [4,4,2,1] => 11001010 => 3
[[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]] => [5,4,2,1] => 101001010 => 4
[[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]] => [5,5,2,1] => 110001010 => 3
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] => [4,4,3,1] => 11010010 => 3
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => [5,4,3,1] => 101010010 => 4
[[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]] => [5,5,3,1] => 110010010 => 3
[[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]] => [6,6,3,1] => 1100010010 => 3
[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] => [7,6,3,1] => 10100010010 => 4
[[2,2,2,2],[1]] => [[2,2,2,1],[]] => [2,2,2,1] => 111010 => 2
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => [3,2,2,1] => 1011010 => 3
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] => [4,2,2,1] => 10011010 => 3
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => [3,3,2,1] => 1101010 => 3
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => [4,3,2,1] => 10101010 => 4
[[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]] => [5,3,2,1] => 100101010 => 4
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] => [4,4,2,1] => 11001010 => 3
[[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]] => [5,4,2,1] => 101001010 => 4
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] => [3,3,3,1] => 1110010 => 2
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] => [4,3,3,1] => 10110010 => 3
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] => [5,3,3,1] => 100110010 => 3
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] => [4,4,3,1] => 11010010 => 3
[[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]] => [5,4,3,1] => 101010010 => 4
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] => [5,5,3,1] => 110010010 => 3
[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] => [7,5,3,1] => 10010010010 => 4
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => [2,2,2,2,1] => 1111010 => 2
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => [3,2,2,2,1] => 10111010 => 3
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] => [3,3,2,2,1] => 11011010 => 3
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => [4,3,2,2,1] => 101011010 => 4
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => [3,3,3,2,1] => 11101010 => 3
[[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]] => [4,3,3,2,1] => 101101010 => 4
[[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => [5,4,3,2,1] => 1010101010 => 5
[[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]] => [4,4,4,2,1] => 111001010 => 3
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => [5,4,4,2,1] => 1011001010 => 4
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] => [5,5,4,2,1] => 1101001010 => 4
[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] => [6,5,4,2,1] => 10101001010 => 5
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => [3,3,3,3,1] => 11110010 => 2
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => [4,3,3,3,1] => 101110010 => 3
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] => [4,4,3,3,1] => 110110010 => 3
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => [5,4,3,3,1] => 1010110010 => 4
[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] => [4,4,4,3,1] => 111010010 => 3
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => [5,4,4,3,1] => 1011010010 => 4
[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] => [5,5,4,3,1] => 1101010010 => 4
[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => [6,5,4,3,1] => 10101010010 => 5
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => [4,2,2,1] => 10011010 => 3
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] => [5,2,2,1] => 100011010 => 3
[[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]] => [5,3,2,1] => 100101010 => 4
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] => [5,3,3,1] => 100110010 => 3
[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] => [7,4,3,1] => 10001010010 => 4
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => [3,3,2,2,1] => 11011010 => 3
[[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]] => [4,3,2,2,1] => 101011010 => 4
[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] => [4,4,2,2,1] => 110011010 => 3
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => [5,4,2,2,1] => 1010011010 => 4
[[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]] => [4,4,3,2,1] => 110101010 => 4
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => [5,4,3,2,1] => 1010101010 => 5
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => [5,5,3,2,1] => 1100101010 => 4
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => [6,5,3,2,1] => 10100101010 => 5
[[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]] => [4,4,3,3,1] => 110110010 => 3
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]] => [5,4,3,3,1] => 1010110010 => 4
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => [5,5,3,3,1] => 1100110010 => 3
[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] => [5,5,4,3,1] => 1101010010 => 4
[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] => [6,5,4,3,1] => 10101010010 => 5
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => [3,2,2,2,1] => 10111010 => 3
[[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]] => [4,2,2,2,1] => 100111010 => 3
[[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]] => [4,3,2,2,1] => 101011010 => 4
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => [5,3,2,2,1] => 1001011010 => 4
[[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]] => [4,3,3,2,1] => 101101010 => 4
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] => [5,3,3,2,1] => 1001101010 => 4
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => [5,4,3,2,1] => 1010101010 => 5
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => [6,4,3,2,1] => 10010101010 => 5
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] => [4,3,3,3,1] => 101110010 => 3
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => [5,4,3,3,1] => 1010110010 => 4
[[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]] => [5,4,4,3,1] => 1011010010 => 4
[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] => [6,5,4,3,1] => 10101010010 => 5
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,2,1] => 11111010 => 2
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => [3,2,2,2,2,1] => 101111010 => 3
[[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]] => [3,3,2,2,2,1] => 110111010 => 3
[[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]] => [3,3,3,2,2,1] => 111011010 => 3
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] => [3,3,3,3,2,1] => 111101010 => 3
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => [6,5,4,3,2,1] => 101010101010 => 6
[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => [3,3,3,3,3,1] => 111110010 => 2
[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] => [6,5,5,4,3,1] => 101101010010 => 5
[[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]] => [6,6,5,4,3,1] => 110101010010 => 5
[[5,5,5],[4,4]] => [[5,1,1],[]] => [5,1,1] => 10000110 => 2
[[6,6,5],[5,5]] => [[6,1,1],[1]] => [6,1,1] => 100000110 => 2
[[6,5,5],[5,4]] => [[6,2,1],[1,1]] => [6,2,1] => 100001010 => 3
[[7,6,5],[6,5]] => [[7,2,1],[2,1]] => [7,2,1] => 1000001010 => 3
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => [4,4,1,1] => 11000110 => 2
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => [5,4,1,1] => 101000110 => 3
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => [5,5,1,1] => 110000110 => 2
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] => [5,5,2,1] => 110001010 => 3
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => [3,3,1,1] => 1100110 => 2
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => [4,3,1,1] => 10100110 => 3
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] => [5,3,1,1] => 100100110 => 3
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] => [4,4,1,1] => 11000110 => 2
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] => [5,4,1,1] => 101000110 => 3
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] => [4,4,2,1] => 11001010 => 3
[[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]] => [5,4,2,1] => 101001010 => 4
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => [5,5,2,1] => 110001010 => 3
[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] => [7,5,2,1] => 10010001010 => 4
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => [3,3,3,1,1] => 11100110 => 2
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] => [4,3,3,1,1] => 101100110 => 3
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] => [4,4,3,1,1] => 110100110 => 3
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => [5,4,3,1,1] => 1010100110 => 4
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] => [4,4,4,1,1] => 111000110 => 2
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] => [4,4,4,2,1] => 111001010 => 3
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]] => [5,4,4,2,1] => 1011001010 => 4
[[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]] => [5,5,4,2,1] => 1101001010 => 4
[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => [6,5,4,2,1] => 10101001010 => 5
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => [3,2,1,1] => 1010110 => 3
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => [4,2,1,1] => 10010110 => 3
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] => [5,2,1,1] => 100010110 => 3
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] => [4,3,1,1] => 10100110 => 3
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] => [5,3,1,1] => 100100110 => 3
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => [4,3,2,1] => 10101010 => 4
[[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]] => [5,3,2,1] => 100101010 => 4
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => [5,4,2,1] => 101001010 => 4
[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] => [7,4,2,1] => 10001001010 => 4
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => [2,2,2,1,1] => 1110110 => 2
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => [3,2,2,1,1] => 10110110 => 3
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => [3,3,2,1,1] => 11010110 => 3
[[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]] => [4,3,2,1,1] => 101010110 => 4
[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] => [4,4,2,1,1] => 110010110 => 3
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]] => [5,4,2,1,1] => 1010010110 => 4
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] => [3,3,3,1,1] => 11100110 => 2
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] => [4,3,3,1,1] => 101100110 => 3
[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] => [4,4,3,1,1] => 110100110 => 3
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => [5,4,3,1,1] => 1010100110 => 4
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => [5,5,3,1,1] => 1100100110 => 3
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => [3,3,3,2,1] => 11101010 => 3
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => [4,3,3,2,1] => 101101010 => 4
[[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => [5,4,3,2,1] => 1010101010 => 5
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => [5,5,3,2,1] => 1100101010 => 4
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => [6,5,3,2,1] => 10100101010 => 5
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => [4,4,4,2,1] => 111001010 => 3
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => [5,4,4,2,1] => 1011001010 => 4
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => [5,5,4,2,1] => 1101001010 => 4
[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] => [6,5,4,2,1] => 10101001010 => 5
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => [3,2,2,1,1] => 10110110 => 3
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] => [4,2,2,1,1] => 100110110 => 3
[[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]] => [4,3,2,1,1] => 101010110 => 4
[[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]] => [5,3,2,1,1] => 1001010110 => 4
[[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]] => [4,3,3,1,1] => 101100110 => 3
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => [5,3,3,1,1] => 1001100110 => 3
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] => [5,4,3,1,1] => 1010100110 => 4
[[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]] => [4,3,3,2,1] => 101101010 => 4
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => [5,3,3,2,1] => 1001101010 => 4
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => [5,4,3,2,1] => 1010101010 => 5
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => [6,4,3,2,1] => 10010101010 => 5
[[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]] => [5,4,4,2,1] => 1011001010 => 4
[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] => [6,5,4,2,1] => 10101001010 => 5
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => [2,2,2,2,1,1] => 11110110 => 2
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] => [3,2,2,2,1,1] => 101110110 => 3
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] => [3,3,2,2,1,1] => 110110110 => 3
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] => [3,3,3,2,1,1] => 111010110 => 3
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => [3,3,3,3,1,1] => 111100110 => 2
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => [3,3,3,3,2,1] => 111101010 => 3
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => [6,5,4,3,2,1] => 101010101010 => 6
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => [4,1,1,1] => 10001110 => 2
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] => [5,1,1,1] => 100001110 => 2
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => [5,2,1,1] => 100010110 => 3
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => [6,2,1,1] => 1000010110 => 3
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => [5,2,2,1] => 100011010 => 3
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => [3,3,1,1,1] => 11001110 => 2
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => [4,3,1,1,1] => 101001110 => 3
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] => [4,4,1,1,1] => 110001110 => 2
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => [5,4,1,1,1] => 1010001110 => 3
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] => [4,4,2,1,1] => 110010110 => 3
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]] => [5,4,2,1,1] => 1010010110 => 4
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] => [4,4,2,2,1] => 110011010 => 3
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => [5,4,2,2,1] => 1010011010 => 4
[[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]] => [5,5,3,2,1] => 1100101010 => 4
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => [6,5,3,2,1] => 10100101010 => 5
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => [2,2,1,1,1] => 1101110 => 2
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => [3,2,1,1,1] => 10101110 => 3
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => [4,2,1,1,1] => 100101110 => 3
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] => [3,3,1,1,1] => 11001110 => 2
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] => [4,3,1,1,1] => 101001110 => 3
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] => [5,3,1,1,1] => 1001001110 => 3
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] => [3,3,2,1,1] => 11010110 => 3
[[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]] => [4,3,2,1,1] => 101010110 => 4
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] => [5,3,2,1,1] => 1001010110 => 4
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] => [4,4,2,1,1] => 110010110 => 3
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => [5,4,2,1,1] => 1010010110 => 4
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => [3,3,2,2,1] => 11011010 => 3
[[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]] => [4,3,2,2,1] => 101011010 => 4
[[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]] => [5,3,2,2,1] => 1001011010 => 4
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] => [4,4,2,2,1] => 110011010 => 3
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => [5,4,2,2,1] => 1010011010 => 4
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => [4,4,3,2,1] => 110101010 => 4
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => [5,4,3,2,1] => 1010101010 => 5
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => [6,4,3,2,1] => 10010101010 => 5
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => [5,5,3,2,1] => 1100101010 => 4
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => [6,5,3,2,1] => 10100101010 => 5
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => [2,2,2,1,1,1] => 11101110 => 2
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => [3,2,2,1,1,1] => 101101110 => 3
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => [3,3,2,1,1,1] => 110101110 => 3
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] => [3,3,3,1,1,1] => 111001110 => 2
[[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]] => [4,4,3,1,1,1] => 1101001110 => 3
[[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]] => [3,3,3,2,1,1] => 111010110 => 3
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => [3,3,3,2,2,1] => 111011010 => 3
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => [6,5,4,3,2,1] => 101010101010 => 6
[[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]] => [6,6,5,3,2,1] => 110100101010 => 5
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => [3,1,1,1,1] => 10011110 => 2
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] => [4,1,1,1,1] => 100011110 => 2
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] => [4,2,1,1,1] => 100101110 => 3
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => [5,2,1,1,1] => 1000101110 => 3
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] => [4,2,2,1,1] => 100110110 => 3
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] => [5,2,2,1,1] => 1000110110 => 3
[[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]] => [5,3,2,1,1] => 1001010110 => 4
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => [4,2,2,2,1] => 100111010 => 3
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => [5,2,2,2,1] => 1000111010 => 3
[[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]] => [5,3,2,2,1] => 1001011010 => 4
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => [5,3,3,2,1] => 1001101010 => 4
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => [6,4,3,2,1] => 10010101010 => 5
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => [2,2,1,1,1,1] => 11011110 => 2
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] => [3,2,1,1,1,1] => 101011110 => 3
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => [3,3,1,1,1,1] => 110011110 => 2
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] => [3,3,2,1,1,1] => 110101110 => 3
[[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]] => [3,3,2,2,1,1] => 110110110 => 3
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => [3,3,2,2,2,1] => 110111010 => 3
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => [6,5,4,3,2,1] => 101010101010 => 6
[[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]] => [6,6,4,3,2,1] => 110010101010 => 5
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => 10111110 => 2
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]] => [3,1,1,1,1,1] => 100111110 => 2
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] => [3,2,1,1,1,1] => 101011110 => 3
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => [4,2,1,1,1,1] => 1001011110 => 3
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] => [3,2,2,1,1,1] => 101101110 => 3
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => [3,2,2,2,1,1] => 101110110 => 3
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => [3,2,2,2,2,1] => 101111010 => 3
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => [6,5,4,3,2,1] => 101010101010 => 6
[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => 11111110 => 1
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]] => [2,1,1,1,1,1,1] => 101111110 => 2
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]] => [2,2,1,1,1,1,1] => 110111110 => 2
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] => [3,2,1,1,1,1,1] => 1010111110 => 3
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]] => [2,2,2,1,1,1,1] => 111011110 => 2
[[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]] => [2,2,2,2,1,1,1] => 111101110 => 2
[[2,2,1,1,1,1,1],[1,1]] => [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [2,2,2,2,2,1,1] => 111110110 => 2
[[2,1,1,1,1,1,1],[1]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [2,2,2,2,2,2,1] => 111111010 => 2
[[8],[]] => [[8],[]] => [8] => 100000000 => 1
[[7,1],[]] => [[7,7],[6]] => [7,7] => 110000000 => 1
[[6,2],[]] => [[6,6],[4]] => [6,6] => 11000000 => 1
[[6,1,1],[]] => [[6,6,6],[5,5]] => [6,6,6] => 111000000 => 1
[[5,3],[]] => [[5,5],[2]] => [5,5] => 1100000 => 1
[[5,2,1],[]] => [[5,5,5],[4,3]] => [5,5,5] => 11100000 => 1
[[5,1,1,1],[]] => [[5,5,5,5],[4,4,4]] => [5,5,5,5] => 111100000 => 1
[[4,4],[]] => [[4,4],[]] => [4,4] => 110000 => 1
[[4,3,1],[]] => [[4,4,4],[3,1]] => [4,4,4] => 1110000 => 1
[[4,2,2],[]] => [[4,4,4],[2,2]] => [4,4,4] => 1110000 => 1
[[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [4,4,4,4] => 11110000 => 1
[[4,1,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,3]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,2],[]] => [[3,3,3],[1]] => [3,3,3] => 111000 => 1
[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [3,3,3,3] => 1111000 => 1
[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [3,3,3,3] => 1111000 => 1
[[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,1,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [3,3,3,3,3,3] => 111111000 => 1
[[2,2,2,2],[]] => [[2,2,2,2],[]] => [2,2,2,2] => 111100 => 1
[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [2,2,2,2,2] => 1111100 => 1
[[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2,2] => 11111100 => 1
[[2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [2,2,2,2,2,2,2] => 111111100 => 1
[[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => 111111110 => 1
[[9],[]] => [[9],[]] => [9] => 1000000000 => 1
[[7,2],[]] => [[7,7],[5]] => [7,7] => 110000000 => 1
[[6,3],[]] => [[6,6],[3]] => [6,6] => 11000000 => 1
[[6,2,1],[]] => [[6,6,6],[5,4]] => [6,6,6] => 111000000 => 1
[[5,4],[]] => [[5,5],[1]] => [5,5] => 1100000 => 1
[[5,3,1],[]] => [[5,5,5],[4,2]] => [5,5,5] => 11100000 => 1
[[5,2,2],[]] => [[5,5,5],[3,3]] => [5,5,5] => 11100000 => 1
[[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]] => [5,5,5,5] => 111100000 => 1
[[5,1,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,4]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,1],[]] => [[4,4,4],[3]] => [4,4,4] => 1110000 => 1
[[4,3,2],[]] => [[4,4,4],[2,1]] => [4,4,4] => 1110000 => 1
[[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [4,4,4,4] => 11110000 => 1
[[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [4,4,4,4] => 11110000 => 1
[[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3],[]] => [[3,3,3],[]] => [3,3,3] => 111000 => 1
[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [3,3,3,3] => 1111000 => 1
[[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [3,3,3,3,3] => 11111000 => 1
[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [3,3,3,3] => 1111000 => 1
[[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [3,3,3,3,3,3] => 111111000 => 1
[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [2,2,2,2,2] => 1111100 => 1
[[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]] => [2,2,2,2,2,2] => 11111100 => 1
[[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [2,2,2,2,2,2,2] => 111111100 => 1
[[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => 1111111110 => 1
[[10],[]] => [[10],[]] => [10] => 10000000000 => 1
[[7,3],[]] => [[7,7],[4]] => [7,7] => 110000000 => 1
[[6,4],[]] => [[6,6],[2]] => [6,6] => 11000000 => 1
[[6,3,1],[]] => [[6,6,6],[5,3]] => [6,6,6] => 111000000 => 1
[[6,2,2],[]] => [[6,6,6],[4,4]] => [6,6,6] => 111000000 => 1
[[5,5],[]] => [[5,5],[]] => [5,5] => 1100000 => 1
[[5,4,1],[]] => [[5,5,5],[4,1]] => [5,5,5] => 11100000 => 1
[[5,3,2],[]] => [[5,5,5],[3,2]] => [5,5,5] => 11100000 => 1
[[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [5,5,5,5] => 111100000 => 1
[[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [5,5,5,5] => 111100000 => 1
[[5,2,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,3]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,2],[]] => [[4,4,4],[2]] => [4,4,4] => 1110000 => 1
[[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [4,4,4,4] => 11110000 => 1
[[4,3,3],[]] => [[4,4,4],[1,1]] => [4,4,4] => 1110000 => 1
[[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [4,4,4,4] => 11110000 => 1
[[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [4,4,4,4,4] => 111110000 => 1
[[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [4,4,4,4] => 11110000 => 1
[[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3,1],[]] => [[3,3,3,3],[2]] => [3,3,3,3] => 1111000 => 1
[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [3,3,3,3] => 1111000 => 1
[[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,3,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2]] => [3,3,3,3,3,3] => 111111000 => 1
[[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [3,3,3,3,3,3] => 111111000 => 1
[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => [2,2,2,2,2] => 1111100 => 1
[[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]] => [2,2,2,2,2,2] => 11111100 => 1
[[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2,2,2] => 111111100 => 1
[[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1] => 11111111110 => 1
[[6,5],[]] => [[6,6],[1]] => [6,6] => 11000000 => 1
[[5,5,1],[]] => [[5,5,5],[4]] => [5,5,5] => 11100000 => 1
[[5,4,2],[]] => [[5,5,5],[3,1]] => [5,5,5] => 11100000 => 1
[[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]] => [5,5,5,5] => 111100000 => 1
[[5,3,3],[]] => [[5,5,5],[2,2]] => [5,5,5] => 11100000 => 1
[[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [5,5,5,5] => 111100000 => 1
[[5,3,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,2]] => [5,5,5,5,5] => 1111100000 => 1
[[5,2,2,2],[]] => [[5,5,5,5],[3,3,3]] => [5,5,5,5] => 111100000 => 1
[[5,2,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,3]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,3],[]] => [[4,4,4],[1]] => [4,4,4] => 1110000 => 1
[[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [4,4,4,4] => 11110000 => 1
[[4,4,1,1,1],[]] => [[4,4,4,4,4],[3,3,3]] => [4,4,4,4,4] => 111110000 => 1
[[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [4,4,4,4] => 11110000 => 1
[[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [4,4,4,4] => 11110000 => 1
[[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [4,4,4,4,4] => 111110000 => 1
[[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3,2],[]] => [[3,3,3,3],[1]] => [3,3,3,3] => 1111000 => 1
[[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]] => [3,3,3,3,3] => 11111000 => 1
[[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [3,3,3,3,3] => 11111000 => 1
[[6,6],[]] => [[6,6],[]] => [6,6] => 11000000 => 1
[[6,4,2],[]] => [[6,6,6],[4,2]] => [6,6,6] => 111000000 => 1
[[5,5,2],[]] => [[5,5,5],[3]] => [5,5,5] => 11100000 => 1
[[5,4,3],[]] => [[5,5,5],[2,1]] => [5,5,5] => 11100000 => 1
[[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [5,5,5,5] => 111100000 => 1
[[5,4,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,1]] => [5,5,5,5,5] => 1111100000 => 1
[[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [5,5,5,5] => 111100000 => 1
[[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [5,5,5,5] => 111100000 => 1
[[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]] => [5,5,5,5,5] => 1111100000 => 1
[[5,2,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,3]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,4],[]] => [[4,4,4],[]] => [4,4,4] => 1110000 => 1
[[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [4,4,4,4] => 11110000 => 1
[[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [4,4,4,4] => 11110000 => 1
[[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [4,4,4,4,4] => 111110000 => 1
[[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [4,4,4,4] => 11110000 => 1
[[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [4,4,4,4,4] => 111110000 => 1
[[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3,3],[]] => [[3,3,3,3],[]] => [3,3,3,3] => 1111000 => 1
[[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [3,3,3,3,3] => 11111000 => 1
[[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [3,3,3,3,3,3] => 111111000 => 1
[[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => [2,2,2,2,2,2] => 11111100 => 1
[[5,5,3],[]] => [[5,5,5],[2]] => [5,5,5] => 11100000 => 1
[[5,4,4],[]] => [[5,5,5],[1,1]] => [5,5,5] => 11100000 => 1
[[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [5,5,5,5] => 111100000 => 1
[[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [5,5,5,5] => 111100000 => 1
[[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]] => [5,5,5,5,5] => 1111100000 => 1
[[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [5,5,5,5] => 111100000 => 1
[[5,3,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,2]] => [5,5,5,5,5] => 1111100000 => 1
[[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,4,1],[]] => [[4,4,4,4],[3]] => [4,4,4,4] => 11110000 => 1
[[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [4,4,4,4] => 11110000 => 1
[[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [4,4,4,4,4] => 111110000 => 1
[[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [4,4,4,4,4] => 111110000 => 1
[[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [4,4,4,4] => 11110000 => 1
[[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [3,3,3,3,3] => 11111000 => 1
[[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [3,3,3,3,3] => 11111000 => 1
[[5,5,4],[]] => [[5,5,5],[1]] => [5,5,5] => 11100000 => 1
[[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [5,5,5,5] => 111100000 => 1
[[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]] => [5,5,5,5,5] => 1111100000 => 1
[[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]] => [5,5,5,5,5] => 1111100000 => 1
[[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,4,2],[]] => [[4,4,4,4],[2]] => [4,4,4,4] => 11110000 => 1
[[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [4,4,4,4] => 11110000 => 1
[[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [4,4,4,4,4] => 111110000 => 1
[[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [3,3,3,3,3] => 11111000 => 1
[[5,5,5],[]] => [[5,5,5],[]] => [5,5,5] => 11100000 => 1
[[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [5,5,5,5,5] => 1111100000 => 1
[[4,4,4,3],[]] => [[4,4,4,4],[1]] => [4,4,4,4] => 11110000 => 1
[[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => [3,3,3,3,3] => 11111000 => 1
[[4,4,4,4],[]] => [[4,4,4,4],[]] => [4,4,4,4] => 11110000 => 1
[[3,3,3],[1]] => [[3,3,2],[]] => [3,3,2] => 110100 => 2
[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => [3,3,2,2] => 1101100 => 2
[[4,4,1],[1]] => [[4,4,3],[3]] => [4,4,3] => 1101000 => 2
[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => [3,3,3,2] => 1110100 => 2
[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => [2,2,2,2,1] => 1111010 => 2
[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => [3,3,3,1] => 1110010 => 2
[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => [3,3,3,2] => 1110100 => 2
[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => [3,2,2,2] => 1011100 => 2
[[4,4,2],[1,1]] => [[4,3,3],[2]] => [4,3,3] => 1011000 => 2
[[4,4,4],[2,2]] => [[4,2,2],[]] => [4,2,2] => 1001100 => 2
[[5,5],[2]] => [[5,3],[]] => [5,3] => 1001000 => 2
[[4,4,3],[2,1]] => [[4,3,2],[1]] => [4,3,2] => 1010100 => 3
[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => [3,2,2,1] => 1011010 => 3
[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => [4,3,3] => 1011000 => 2
[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => [3,2,2,2] => 1011100 => 2
[[4,4,3],[1,1]] => [[4,3,3],[1]] => [4,3,3] => 1011000 => 2
[[4,4,4],[3,1]] => [[4,3,1],[]] => [4,3,1] => 1010010 => 3
[[5,4],[1]] => [[5,4],[1]] => [5,4] => 1010000 => 2
[[4,4,4],[2,1]] => [[4,3,2],[]] => [4,3,2] => 1010100 => 3
[[5,5],[1]] => [[5,4],[]] => [5,4] => 1010000 => 2
[[4,4,4],[1,1]] => [[4,3,3],[]] => [4,3,3] => 1011000 => 2
[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => [3,3,2,2] => 1101100 => 2
[[4,4,2],[2]] => [[4,4,2],[2]] => [4,4,2] => 1100100 => 2
[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => [3,3,2,1] => 1101010 => 3
[[4,3,2],[1]] => [[4,4,3],[2,1]] => [4,4,3] => 1101000 => 2
[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => [3,3,2,2] => 1101100 => 2
[[4,4,2],[1]] => [[4,4,3],[2]] => [4,4,3] => 1101000 => 2
[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => [2,2,2,1,1] => 1110110 => 2
[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => [3,3,3,2] => 1110100 => 2
[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => [3,3,3,1] => 1110010 => 2
[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => [3,3,3,2] => 1110100 => 2
[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => [2,2,2,2,1] => 1111010 => 2
[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => [3,3,3,1] => 1110010 => 2
[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => [3,3,3,2] => 1110100 => 2
[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => [3,3,1,1] => 1100110 => 2
[[4,3,3],[2]] => [[4,4,2],[1,1]] => [4,4,2] => 1100100 => 2
[[4,4,3],[3]] => [[4,4,1],[1]] => [4,4,1] => 1100010 => 2
[[4,4,3],[2]] => [[4,4,2],[1]] => [4,4,2] => 1100100 => 2
[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => [3,3,2,1] => 1101010 => 3
[[4,3,3],[1]] => [[4,4,3],[1,1]] => [4,4,3] => 1101000 => 2
[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => [3,3,2,2] => 1101100 => 2
[[4,4,3],[1]] => [[4,4,3],[1]] => [4,4,3] => 1101000 => 2
[[4,4,4],[3]] => [[4,4,1],[]] => [4,4,1] => 1100010 => 2
[[4,4,4],[2]] => [[4,4,2],[]] => [4,4,2] => 1100100 => 2
[[4,4,4],[1]] => [[4,4,3],[]] => [4,4,3] => 1101000 => 2
[[3,3,3,3],[2]] => [[3,3,3,1],[]] => [3,3,3,1] => 1110010 => 2
[[3,3,3,3],[1]] => [[3,3,3,2],[]] => [3,3,3,2] => 1110100 => 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:
2,1 3,5,1 5,14,8,1 7,34,34,11,1
$F_{1} = q$
$F_{2} = 2\ q + q^{2}$
$F_{3} = 3\ q + 5\ q^{2} + q^{3}$
$F_{4} = 5\ q + 14\ q^{2} + 8\ q^{3} + q^{4}$
$F_{5} = 7\ q + 34\ q^{2} + 34\ q^{3} + 11\ q^{4} + q^{5}$
Description
The number of descents of a binary word.
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rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
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outer shape
Description
The outer shape of the skew partition.
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to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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