Identifier
-
Mp00036:
Gelfand-Tsetlin patterns
—to semistandard tableau⟶
Semistandard tableaux
Mp00225: Semistandard tableaux —weight⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St000293: Binary words ⟶ ℤ
Values
[[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0],[1]] => [[1]] => [1] => 10 => 1
[[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[3,0],[0]] => [[2,2,2]] => [3] => 1000 => 3
[[3,0],[1]] => [[1,2,2]] => [2,1] => 1010 => 3
[[3,0],[2]] => [[1,1,2]] => [2,1] => 1010 => 3
[[3,0],[3]] => [[1,1,1]] => [3] => 1000 => 3
[[2,1],[1]] => [[1,2],[2]] => [2,1] => 1010 => 3
[[2,1],[2]] => [[1,1],[2]] => [2,1] => 1010 => 3
[[2,0,0],[0,0],[0]] => [[3,3]] => [2] => 100 => 2
[[2,0,0],[1,0],[0]] => [[2,3]] => [1,1] => 110 => 2
[[2,0,0],[1,0],[1]] => [[1,3]] => [1,1] => 110 => 2
[[2,0,0],[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0,0],[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0,0],[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => 110 => 2
[[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => 110 => 2
[[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => 10 => 1
[[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[4,0],[0]] => [[2,2,2,2]] => [4] => 10000 => 4
[[4,0],[1]] => [[1,2,2,2]] => [3,1] => 10010 => 4
[[4,0],[2]] => [[1,1,2,2]] => [2,2] => 1100 => 4
[[4,0],[3]] => [[1,1,1,2]] => [3,1] => 10010 => 4
[[4,0],[4]] => [[1,1,1,1]] => [4] => 10000 => 4
[[3,1],[1]] => [[1,2,2],[2]] => [3,1] => 10010 => 4
[[3,1],[2]] => [[1,1,2],[2]] => [2,2] => 1100 => 4
[[3,1],[3]] => [[1,1,1],[2]] => [3,1] => 10010 => 4
[[2,2],[2]] => [[1,1],[2,2]] => [2,2] => 1100 => 4
[[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => 1000 => 3
[[3,0,0],[1,0],[0]] => [[2,3,3]] => [2,1] => 1010 => 3
[[3,0,0],[1,0],[1]] => [[1,3,3]] => [2,1] => 1010 => 3
[[3,0,0],[2,0],[0]] => [[2,2,3]] => [2,1] => 1010 => 3
[[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,1,1] => 1110 => 3
[[3,0,0],[2,0],[2]] => [[1,1,3]] => [2,1] => 1010 => 3
[[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => 1000 => 3
[[3,0,0],[3,0],[1]] => [[1,2,2]] => [2,1] => 1010 => 3
[[3,0,0],[3,0],[2]] => [[1,1,2]] => [2,1] => 1010 => 3
[[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => 1000 => 3
[[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => 1010 => 3
[[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => 1010 => 3
[[2,1,0],[1,1],[1]] => [[1,3],[2]] => [1,1,1] => 1110 => 3
[[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => 1010 => 3
[[2,1,0],[2,0],[1]] => [[1,2],[3]] => [1,1,1] => 1110 => 3
[[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => 1010 => 3
[[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => 1010 => 3
[[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => 1010 => 3
[[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => 1110 => 3
[[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => 100 => 2
[[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,1] => 110 => 2
[[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,1] => 110 => 2
[[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,1] => 110 => 2
[[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => 100 => 2
[[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,1] => 110 => 2
[[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,1] => 110 => 2
[[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => 110 => 2
[[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => 110 => 2
[[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => 110 => 2
[[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => 110 => 2
[[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => 110 => 2
[[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => 10 => 1
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => 10 => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[5,0],[0]] => [[2,2,2,2,2]] => [5] => 100000 => 5
[[5,0],[1]] => [[1,2,2,2,2]] => [4,1] => 100010 => 5
[[5,0],[2]] => [[1,1,2,2,2]] => [3,2] => 10100 => 5
[[5,0],[3]] => [[1,1,1,2,2]] => [3,2] => 10100 => 5
[[5,0],[4]] => [[1,1,1,1,2]] => [4,1] => 100010 => 5
[[5,0],[5]] => [[1,1,1,1,1]] => [5] => 100000 => 5
[[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => 100010 => 5
[[4,1],[2]] => [[1,1,2,2],[2]] => [3,2] => 10100 => 5
[[4,1],[3]] => [[1,1,1,2],[2]] => [3,2] => 10100 => 5
[[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => 100010 => 5
[[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => 10100 => 5
[[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => 10100 => 5
[[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => 10000 => 4
[[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [2,2] => 1100 => 4
[[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [2,1,1] => 10110 => 4
[[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [2,2] => 1100 => 4
[[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [3,1] => 10010 => 4
[[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [3,1] => 10010 => 4
[[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => 10000 => 4
[[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [3,1] => 10010 => 4
>>> Load all 1550 entries. <<<[[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [2,2] => 1100 => 4
[[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [3,1] => 10010 => 4
[[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => 10000 => 4
[[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [2,2] => 1100 => 4
[[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [2,1,1] => 10110 => 4
[[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [2,2] => 1100 => 4
[[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => 10010 => 4
[[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => 10010 => 4
[[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => 10010 => 4
[[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [2,2] => 1100 => 4
[[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => 10010 => 4
[[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => 1100 => 4
[[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,1,1] => 10110 => 4
[[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => 1100 => 4
[[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => 1100 => 4
[[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => 10110 => 4
[[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => 1000 => 3
[[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => 1000 => 3
[[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,1,1] => 1110 => 3
[[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => 1000 => 3
[[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [2,1] => 1010 => 3
[[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => 1000 => 3
[[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => 1010 => 3
[[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => 1010 => 3
[[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => 1110 => 3
[[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => 100 => 2
[[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,1] => 110 => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,1] => 110 => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,1] => 110 => 2
[[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => 100 => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => 100 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => 10 => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => 10 => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => 10 => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[6,0],[0]] => [[2,2,2,2,2,2]] => [6] => 1000000 => 6
[[6,0],[1]] => [[1,2,2,2,2,2]] => [5,1] => 1000010 => 6
[[6,0],[2]] => [[1,1,2,2,2,2]] => [4,2] => 100100 => 6
[[6,0],[3]] => [[1,1,1,2,2,2]] => [3,3] => 11000 => 6
[[6,0],[4]] => [[1,1,1,1,2,2]] => [4,2] => 100100 => 6
[[6,0],[5]] => [[1,1,1,1,1,2]] => [5,1] => 1000010 => 6
[[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1] => 1000010 => 6
[[5,1],[2]] => [[1,1,2,2,2],[2]] => [4,2] => 100100 => 6
[[5,1],[3]] => [[1,1,1,2,2],[2]] => [3,3] => 11000 => 6
[[5,1],[4]] => [[1,1,1,1,2],[2]] => [4,2] => 100100 => 6
[[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1] => 1000010 => 6
[[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2] => 100100 => 6
[[4,2],[3]] => [[1,1,1,2],[2,2]] => [3,3] => 11000 => 6
[[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2] => 100100 => 6
[[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => 11000 => 6
[[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5] => 100000 => 5
[[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [4,1] => 100010 => 5
[[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [4,1] => 100010 => 5
[[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [3,2] => 10100 => 5
[[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [3,1,1] => 100110 => 5
[[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [3,2] => 10100 => 5
[[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [3,2] => 10100 => 5
[[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [2,2,1] => 11010 => 5
[[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [2,2,1] => 11010 => 5
[[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [3,2] => 10100 => 5
[[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [4,1] => 100010 => 5
[[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [3,1,1] => 100110 => 5
[[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [2,2,1] => 11010 => 5
[[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [3,1,1] => 100110 => 5
[[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [4,1] => 100010 => 5
[[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5] => 100000 => 5
[[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [4,1] => 100010 => 5
[[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [3,2] => 10100 => 5
[[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [3,2] => 10100 => 5
[[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [4,1] => 100010 => 5
[[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5] => 100000 => 5
[[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1] => 100010 => 5
[[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1] => 100010 => 5
[[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,2] => 10100 => 5
[[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,1] => 100110 => 5
[[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,2] => 10100 => 5
[[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [3,2] => 10100 => 5
[[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [2,2,1] => 11010 => 5
[[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [2,2,1] => 11010 => 5
[[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [3,2] => 10100 => 5
[[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1] => 100010 => 5
[[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [3,1,1] => 100110 => 5
[[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [2,2,1] => 11010 => 5
[[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [3,1,1] => 100110 => 5
[[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1] => 100010 => 5
[[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => 100010 => 5
[[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,2] => 10100 => 5
[[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [3,2] => 10100 => 5
[[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => 100010 => 5
[[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2] => 10100 => 5
[[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,1,1] => 100110 => 5
[[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2] => 10100 => 5
[[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [2,2,1] => 11010 => 5
[[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2] => 10100 => 5
[[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2] => 10100 => 5
[[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,1,1] => 100110 => 5
[[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,1,1] => 100110 => 5
[[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => 10100 => 5
[[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => 10100 => 5
[[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => 100110 => 5
[[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => 100110 => 5
[[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => 100110 => 5
[[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1] => 11010 => 5
[[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1] => 11010 => 5
[[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1] => 11010 => 5
[[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4] => 10000 => 4
[[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => 10000 => 4
[[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [2,2] => 1100 => 4
[[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [2,2] => 1100 => 4
[[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => 10000 => 4
[[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [2,2] => 1100 => 4
[[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [3,1] => 10010 => 4
[[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => 10000 => 4
[[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [2,2] => 1100 => 4
[[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [2,2] => 1100 => 4
[[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => 10010 => 4
[[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [2,2] => 1100 => 4
[[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => 10010 => 4
[[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => 1100 => 4
[[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => 1100 => 4
[[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => 1100 => 4
[[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => 10110 => 4
[[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => 11110 => 4
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3] => 1000 => 3
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => 1000 => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => 1000 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => 1000 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [2,1] => 1010 => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => 1000 => 3
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => 1010 => 3
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => 1010 => 3
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => 1110 => 3
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2] => 100 => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => 100 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => 100 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => 100 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => 10 => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => 10 => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => 10 => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[7,0],[0]] => [[2,2,2,2,2,2,2]] => [7] => 10000000 => 7
[[7,0],[1]] => [[1,2,2,2,2,2,2]] => [6,1] => 10000010 => 7
[[7,0],[2]] => [[1,1,2,2,2,2,2]] => [5,2] => 1000100 => 7
[[7,0],[3]] => [[1,1,1,2,2,2,2]] => [4,3] => 101000 => 7
[[7,0],[4]] => [[1,1,1,1,2,2,2]] => [4,3] => 101000 => 7
[[7,0],[5]] => [[1,1,1,1,1,2,2]] => [5,2] => 1000100 => 7
[[7,0],[6]] => [[1,1,1,1,1,1,2]] => [6,1] => 10000010 => 7
[[6,1],[1]] => [[1,2,2,2,2,2],[2]] => [6,1] => 10000010 => 7
[[6,1],[2]] => [[1,1,2,2,2,2],[2]] => [5,2] => 1000100 => 7
[[6,1],[3]] => [[1,1,1,2,2,2],[2]] => [4,3] => 101000 => 7
[[6,1],[4]] => [[1,1,1,1,2,2],[2]] => [4,3] => 101000 => 7
[[6,1],[5]] => [[1,1,1,1,1,2],[2]] => [5,2] => 1000100 => 7
[[6,1],[6]] => [[1,1,1,1,1,1],[2]] => [6,1] => 10000010 => 7
[[5,2],[2]] => [[1,1,2,2,2],[2,2]] => [5,2] => 1000100 => 7
[[5,2],[3]] => [[1,1,1,2,2],[2,2]] => [4,3] => 101000 => 7
[[5,2],[4]] => [[1,1,1,1,2],[2,2]] => [4,3] => 101000 => 7
[[5,2],[5]] => [[1,1,1,1,1],[2,2]] => [5,2] => 1000100 => 7
[[4,3],[3]] => [[1,1,1,2],[2,2,2]] => [4,3] => 101000 => 7
[[4,3],[4]] => [[1,1,1,1],[2,2,2]] => [4,3] => 101000 => 7
[[6,0,0],[0,0],[0]] => [[3,3,3,3,3,3]] => [6] => 1000000 => 6
[[6,0,0],[1,0],[0]] => [[2,3,3,3,3,3]] => [5,1] => 1000010 => 6
[[6,0,0],[1,0],[1]] => [[1,3,3,3,3,3]] => [5,1] => 1000010 => 6
[[6,0,0],[2,0],[0]] => [[2,2,3,3,3,3]] => [4,2] => 100100 => 6
[[6,0,0],[2,0],[1]] => [[1,2,3,3,3,3]] => [4,1,1] => 1000110 => 6
[[6,0,0],[2,0],[2]] => [[1,1,3,3,3,3]] => [4,2] => 100100 => 6
[[6,0,0],[3,0],[0]] => [[2,2,2,3,3,3]] => [3,3] => 11000 => 6
[[6,0,0],[3,0],[1]] => [[1,2,2,3,3,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[3,0],[2]] => [[1,1,2,3,3,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[3,0],[3]] => [[1,1,1,3,3,3]] => [3,3] => 11000 => 6
[[6,0,0],[4,0],[0]] => [[2,2,2,2,3,3]] => [4,2] => 100100 => 6
[[6,0,0],[4,0],[1]] => [[1,2,2,2,3,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[4,0],[2]] => [[1,1,2,2,3,3]] => [2,2,2] => 11100 => 6
[[6,0,0],[4,0],[3]] => [[1,1,1,2,3,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[4,0],[4]] => [[1,1,1,1,3,3]] => [4,2] => 100100 => 6
[[6,0,0],[5,0],[0]] => [[2,2,2,2,2,3]] => [5,1] => 1000010 => 6
[[6,0,0],[5,0],[1]] => [[1,2,2,2,2,3]] => [4,1,1] => 1000110 => 6
[[6,0,0],[5,0],[2]] => [[1,1,2,2,2,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[5,0],[3]] => [[1,1,1,2,2,3]] => [3,2,1] => 101010 => 6
[[6,0,0],[5,0],[4]] => [[1,1,1,1,2,3]] => [4,1,1] => 1000110 => 6
[[6,0,0],[5,0],[5]] => [[1,1,1,1,1,3]] => [5,1] => 1000010 => 6
[[6,0,0],[6,0],[0]] => [[2,2,2,2,2,2]] => [6] => 1000000 => 6
[[6,0,0],[6,0],[1]] => [[1,2,2,2,2,2]] => [5,1] => 1000010 => 6
[[6,0,0],[6,0],[2]] => [[1,1,2,2,2,2]] => [4,2] => 100100 => 6
[[6,0,0],[6,0],[3]] => [[1,1,1,2,2,2]] => [3,3] => 11000 => 6
[[6,0,0],[6,0],[4]] => [[1,1,1,1,2,2]] => [4,2] => 100100 => 6
[[6,0,0],[6,0],[5]] => [[1,1,1,1,1,2]] => [5,1] => 1000010 => 6
[[5,1,0],[1,0],[0]] => [[2,3,3,3,3],[3]] => [5,1] => 1000010 => 6
[[5,1,0],[1,0],[1]] => [[1,3,3,3,3],[3]] => [5,1] => 1000010 => 6
[[5,1,0],[1,1],[1]] => [[1,3,3,3,3],[2]] => [4,1,1] => 1000110 => 6
[[5,1,0],[2,0],[0]] => [[2,2,3,3,3],[3]] => [4,2] => 100100 => 6
[[5,1,0],[2,0],[1]] => [[1,2,3,3,3],[3]] => [4,1,1] => 1000110 => 6
[[5,1,0],[2,0],[2]] => [[1,1,3,3,3],[3]] => [4,2] => 100100 => 6
[[5,1,0],[2,1],[1]] => [[1,2,3,3,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[2,1],[2]] => [[1,1,3,3,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[3,0],[0]] => [[2,2,2,3,3],[3]] => [3,3] => 11000 => 6
[[5,1,0],[3,0],[1]] => [[1,2,2,3,3],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[3,0],[2]] => [[1,1,2,3,3],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[3,0],[3]] => [[1,1,1,3,3],[3]] => [3,3] => 11000 => 6
[[5,1,0],[3,1],[1]] => [[1,2,2,3,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[3,1],[2]] => [[1,1,2,3,3],[2]] => [2,2,2] => 11100 => 6
[[5,1,0],[3,1],[3]] => [[1,1,1,3,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[4,0],[0]] => [[2,2,2,2,3],[3]] => [4,2] => 100100 => 6
[[5,1,0],[4,0],[1]] => [[1,2,2,2,3],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[4,0],[2]] => [[1,1,2,2,3],[3]] => [2,2,2] => 11100 => 6
[[5,1,0],[4,0],[3]] => [[1,1,1,2,3],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[4,0],[4]] => [[1,1,1,1,3],[3]] => [4,2] => 100100 => 6
[[5,1,0],[4,1],[1]] => [[1,2,2,2,3],[2]] => [4,1,1] => 1000110 => 6
[[5,1,0],[4,1],[2]] => [[1,1,2,2,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[4,1],[3]] => [[1,1,1,2,3],[2]] => [3,2,1] => 101010 => 6
[[5,1,0],[4,1],[4]] => [[1,1,1,1,3],[2]] => [4,1,1] => 1000110 => 6
[[5,1,0],[5,0],[0]] => [[2,2,2,2,2],[3]] => [5,1] => 1000010 => 6
[[5,1,0],[5,0],[1]] => [[1,2,2,2,2],[3]] => [4,1,1] => 1000110 => 6
[[5,1,0],[5,0],[2]] => [[1,1,2,2,2],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[5,0],[3]] => [[1,1,1,2,2],[3]] => [3,2,1] => 101010 => 6
[[5,1,0],[5,0],[4]] => [[1,1,1,1,2],[3]] => [4,1,1] => 1000110 => 6
[[5,1,0],[5,0],[5]] => [[1,1,1,1,1],[3]] => [5,1] => 1000010 => 6
[[5,1,0],[5,1],[1]] => [[1,2,2,2,2],[2]] => [5,1] => 1000010 => 6
[[5,1,0],[5,1],[2]] => [[1,1,2,2,2],[2]] => [4,2] => 100100 => 6
[[5,1,0],[5,1],[3]] => [[1,1,1,2,2],[2]] => [3,3] => 11000 => 6
[[5,1,0],[5,1],[4]] => [[1,1,1,1,2],[2]] => [4,2] => 100100 => 6
[[5,1,0],[5,1],[5]] => [[1,1,1,1,1],[2]] => [5,1] => 1000010 => 6
[[4,2,0],[2,0],[0]] => [[2,2,3,3],[3,3]] => [4,2] => 100100 => 6
[[4,2,0],[2,0],[1]] => [[1,2,3,3],[3,3]] => [4,1,1] => 1000110 => 6
[[4,2,0],[2,0],[2]] => [[1,1,3,3],[3,3]] => [4,2] => 100100 => 6
[[4,2,0],[2,1],[1]] => [[1,2,3,3],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[2,1],[2]] => [[1,1,3,3],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[2,2],[2]] => [[1,1,3,3],[2,2]] => [2,2,2] => 11100 => 6
[[4,2,0],[3,0],[0]] => [[2,2,2,3],[3,3]] => [3,3] => 11000 => 6
[[4,2,0],[3,0],[1]] => [[1,2,2,3],[3,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[3,0],[2]] => [[1,1,2,3],[3,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[3,0],[3]] => [[1,1,1,3],[3,3]] => [3,3] => 11000 => 6
[[4,2,0],[3,1],[1]] => [[1,2,2,3],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[3,1],[2]] => [[1,1,2,3],[2,3]] => [2,2,2] => 11100 => 6
[[4,2,0],[3,1],[3]] => [[1,1,1,3],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[3,2],[2]] => [[1,1,2,3],[2,2]] => [3,2,1] => 101010 => 6
[[4,2,0],[3,2],[3]] => [[1,1,1,3],[2,2]] => [3,2,1] => 101010 => 6
[[4,2,0],[4,0],[0]] => [[2,2,2,2],[3,3]] => [4,2] => 100100 => 6
[[4,2,0],[4,0],[1]] => [[1,2,2,2],[3,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[4,0],[2]] => [[1,1,2,2],[3,3]] => [2,2,2] => 11100 => 6
[[4,2,0],[4,0],[3]] => [[1,1,1,2],[3,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[4,0],[4]] => [[1,1,1,1],[3,3]] => [4,2] => 100100 => 6
[[4,2,0],[4,1],[1]] => [[1,2,2,2],[2,3]] => [4,1,1] => 1000110 => 6
[[4,2,0],[4,1],[2]] => [[1,1,2,2],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[4,1],[3]] => [[1,1,1,2],[2,3]] => [3,2,1] => 101010 => 6
[[4,2,0],[4,1],[4]] => [[1,1,1,1],[2,3]] => [4,1,1] => 1000110 => 6
[[4,2,0],[4,2],[2]] => [[1,1,2,2],[2,2]] => [4,2] => 100100 => 6
[[4,2,0],[4,2],[3]] => [[1,1,1,2],[2,2]] => [3,3] => 11000 => 6
[[4,2,0],[4,2],[4]] => [[1,1,1,1],[2,2]] => [4,2] => 100100 => 6
[[4,1,1],[1,1],[1]] => [[1,3,3,3],[2],[3]] => [4,1,1] => 1000110 => 6
[[4,1,1],[2,1],[1]] => [[1,2,3,3],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[2,1],[2]] => [[1,1,3,3],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[3,1],[1]] => [[1,2,2,3],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[3,1],[2]] => [[1,1,2,3],[2],[3]] => [2,2,2] => 11100 => 6
[[4,1,1],[3,1],[3]] => [[1,1,1,3],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[4,1],[1]] => [[1,2,2,2],[2],[3]] => [4,1,1] => 1000110 => 6
[[4,1,1],[4,1],[2]] => [[1,1,2,2],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[4,1],[3]] => [[1,1,1,2],[2],[3]] => [3,2,1] => 101010 => 6
[[4,1,1],[4,1],[4]] => [[1,1,1,1],[2],[3]] => [4,1,1] => 1000110 => 6
[[3,3,0],[3,0],[0]] => [[2,2,2],[3,3,3]] => [3,3] => 11000 => 6
[[3,3,0],[3,0],[1]] => [[1,2,2],[3,3,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,0],[2]] => [[1,1,2],[3,3,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,0],[3]] => [[1,1,1],[3,3,3]] => [3,3] => 11000 => 6
[[3,3,0],[3,1],[1]] => [[1,2,2],[2,3,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,1],[2]] => [[1,1,2],[2,3,3]] => [2,2,2] => 11100 => 6
[[3,3,0],[3,1],[3]] => [[1,1,1],[2,3,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,2],[2]] => [[1,1,2],[2,2,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,2],[3]] => [[1,1,1],[2,2,3]] => [3,2,1] => 101010 => 6
[[3,3,0],[3,3],[3]] => [[1,1,1],[2,2,2]] => [3,3] => 11000 => 6
[[3,2,1],[2,1],[1]] => [[1,2,3],[2,3],[3]] => [3,2,1] => 101010 => 6
[[3,2,1],[2,1],[2]] => [[1,1,3],[2,3],[3]] => [3,2,1] => 101010 => 6
[[3,2,1],[2,2],[2]] => [[1,1,3],[2,2],[3]] => [2,2,2] => 11100 => 6
[[3,2,1],[3,1],[1]] => [[1,2,2],[2,3],[3]] => [3,2,1] => 101010 => 6
[[3,2,1],[3,1],[2]] => [[1,1,2],[2,3],[3]] => [2,2,2] => 11100 => 6
[[3,2,1],[3,1],[3]] => [[1,1,1],[2,3],[3]] => [3,2,1] => 101010 => 6
[[3,2,1],[3,2],[2]] => [[1,1,2],[2,2],[3]] => [3,2,1] => 101010 => 6
[[3,2,1],[3,2],[3]] => [[1,1,1],[2,2],[3]] => [3,2,1] => 101010 => 6
[[2,2,2],[2,2],[2]] => [[1,1],[2,2],[3,3]] => [2,2,2] => 11100 => 6
[[5,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4,4]] => [5] => 100000 => 5
[[5,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,4]] => [2,1,1,1] => 101110 => 5
[[5,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4,4]] => [3,2] => 10100 => 5
[[5,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3,4]] => [2,1,1,1] => 101110 => 5
[[5,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3,4]] => [2,1,1,1] => 101110 => 5
[[5,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3,4]] => [2,1,1,1] => 101110 => 5
[[5,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2,4]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2,4]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1,4]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[0,0],[0]] => [[3,3,3,3,3]] => [5] => 100000 => 5
[[5,0,0,0],[5,0,0],[1,0],[0]] => [[2,3,3,3,3]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[1,0],[1]] => [[1,3,3,3,3]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[2,0],[0]] => [[2,2,3,3,3]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[2,0],[1]] => [[1,2,3,3,3]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[5,0,0],[2,0],[2]] => [[1,1,3,3,3]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[3,0],[0]] => [[2,2,2,3,3]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[3,0],[1]] => [[1,2,2,3,3]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[5,0,0],[3,0],[2]] => [[1,1,2,3,3]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[5,0,0],[3,0],[3]] => [[1,1,1,3,3]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[4,0],[0]] => [[2,2,2,2,3]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[4,0],[1]] => [[1,2,2,2,3]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[5,0,0],[4,0],[2]] => [[1,1,2,2,3]] => [2,2,1] => 11010 => 5
[[5,0,0,0],[5,0,0],[4,0],[3]] => [[1,1,1,2,3]] => [3,1,1] => 100110 => 5
[[5,0,0,0],[5,0,0],[4,0],[4]] => [[1,1,1,1,3]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[5,0],[0]] => [[2,2,2,2,2]] => [5] => 100000 => 5
[[5,0,0,0],[5,0,0],[5,0],[1]] => [[1,2,2,2,2]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[5,0],[2]] => [[1,1,2,2,2]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[5,0],[3]] => [[1,1,1,2,2]] => [3,2] => 10100 => 5
[[5,0,0,0],[5,0,0],[5,0],[4]] => [[1,1,1,1,2]] => [4,1] => 100010 => 5
[[5,0,0,0],[5,0,0],[5,0],[5]] => [[1,1,1,1,1]] => [5] => 100000 => 5
[[4,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4,4],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,4],[2]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,4],[3]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4,4],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4,4],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[4]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4],[4]] => [3,2] => 10100 => 5
[[4,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3,4],[2]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3,4],[3]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3,4],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3,4],[2]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3,4],[2]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2,4],[3]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2,4],[3]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1,4],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2,4],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2,4],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1,4],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3],[4]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3],[4]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3],[4]] => [2,1,1,1] => 101110 => 5
[[4,1,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2],[4]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2],[4]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1],[4]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[1,0],[0]] => [[2,3,3,3],[3]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[1,0],[1]] => [[1,3,3,3],[3]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[1,1],[1]] => [[1,3,3,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[2,0],[0]] => [[2,2,3,3],[3]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[2,0],[1]] => [[1,2,3,3],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[2,0],[2]] => [[1,1,3,3],[3]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[2,1],[1]] => [[1,2,3,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[2,1],[2]] => [[1,1,3,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[3,0],[0]] => [[2,2,2,3],[3]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[3,0],[1]] => [[1,2,2,3],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[3,0],[2]] => [[1,1,2,3],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[3,0],[3]] => [[1,1,1,3],[3]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[3,1],[1]] => [[1,2,2,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[3,1],[2]] => [[1,1,2,3],[2]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[3,1],[3]] => [[1,1,1,3],[2]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[4,0],[0]] => [[2,2,2,2],[3]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[4,0],[1]] => [[1,2,2,2],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[4,0],[2]] => [[1,1,2,2],[3]] => [2,2,1] => 11010 => 5
[[4,1,0,0],[4,1,0],[4,0],[3]] => [[1,1,1,2],[3]] => [3,1,1] => 100110 => 5
[[4,1,0,0],[4,1,0],[4,0],[4]] => [[1,1,1,1],[3]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[4,1],[1]] => [[1,2,2,2],[2]] => [4,1] => 100010 => 5
[[4,1,0,0],[4,1,0],[4,1],[2]] => [[1,1,2,2],[2]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[4,1],[3]] => [[1,1,1,2],[2]] => [3,2] => 10100 => 5
[[4,1,0,0],[4,1,0],[4,1],[4]] => [[1,1,1,1],[2]] => [4,1] => 100010 => 5
[[3,2,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,2,0],[2,0],[0]] => [[2,2,4],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,2,0],[2,0],[1]] => [[1,2,4],[3,3]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[2,2,0],[2,0],[2]] => [[1,1,4],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[2,2,0],[2,1],[1]] => [[1,2,4],[2,3]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[2,2,0],[2,1],[2]] => [[1,1,4],[2,3]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[2,2,0],[2,2],[2]] => [[1,1,4],[2,2]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4,4]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3,4]] => [2,1,1,1] => 101110 => 5
[[3,2,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2,4]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2,4]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,2,0],[2,0],[0]] => [[2,2,3],[3,3]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,2,0],[2,0],[1]] => [[1,2,3],[3,3]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,2,0],[2,0],[2]] => [[1,1,3],[3,3]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,2,0],[2,1],[1]] => [[1,2,3],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[2,1],[2]] => [[1,1,3],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[2,2],[2]] => [[1,1,3],[2,2]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[3,0],[0]] => [[2,2,2],[3,3]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,2,0],[3,0],[1]] => [[1,2,2],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[3,0],[2]] => [[1,1,2],[3,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[3,0],[3]] => [[1,1,1],[3,3]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,2,0],[3,1],[1]] => [[1,2,2],[2,3]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,2,0],[3,1],[2]] => [[1,1,2],[2,3]] => [2,2,1] => 11010 => 5
[[3,2,0,0],[3,2,0],[3,1],[3]] => [[1,1,1],[2,3]] => [3,1,1] => 100110 => 5
[[3,2,0,0],[3,2,0],[3,2],[2]] => [[1,1,2],[2,2]] => [3,2] => 10100 => 5
[[3,2,0,0],[3,2,0],[3,2],[3]] => [[1,1,1],[2,2]] => [3,2] => 10100 => 5
[[3,1,1,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,4],[2],[3]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[2,1,1],[1,1],[1]] => [[1,3,4],[2],[3]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[2,1,1],[2,1],[1]] => [[1,2,4],[2],[3]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[2,1,1],[2,1],[2]] => [[1,1,4],[2],[3]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[3,1,1,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2],[4]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2],[4]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,1],[1,1],[1]] => [[1,3,3],[2],[3]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,1],[2,1],[1]] => [[1,2,3],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,1],[2,1],[2]] => [[1,1,3],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,1],[3,1],[1]] => [[1,2,2],[2],[3]] => [3,1,1] => 100110 => 5
[[3,1,1,0],[3,1,1],[3,1],[2]] => [[1,1,2],[2],[3]] => [2,2,1] => 11010 => 5
[[3,1,1,0],[3,1,1],[3,1],[3]] => [[1,1,1],[2],[3]] => [3,1,1] => 100110 => 5
[[2,2,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[4]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[4]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2,4],[3]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2,4],[3]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2,4],[3]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3],[4]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3],[4]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3],[4]] => [2,1,1,1] => 101110 => 5
[[2,2,1,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2],[4]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,2,1],[2,1],[1]] => [[1,2],[2,3],[3]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,2,1],[2,1],[2]] => [[1,1],[2,3],[3]] => [2,2,1] => 11010 => 5
[[2,2,1,0],[2,2,1],[2,2],[2]] => [[1,1],[2,2],[3]] => [2,2,1] => 11010 => 5
[[2,1,1,1],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[2,1,1,1],[2,1,1],[1,1],[1]] => [[1,3],[2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[2,1,1,1],[2,1,1],[2,1],[1]] => [[1,2],[2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[2,1,1,1],[2,1,1],[2,1],[2]] => [[1,1],[2],[3],[4]] => [2,1,1,1] => 101110 => 5
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5,5]] => [4] => 10000 => 4
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5,5]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5,5]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5,5]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5,5]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,5]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,5]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,5]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,5]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,5]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4,4]] => [4] => 10000 => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4,4]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4]] => [1,1,1,1] => 11110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2,4]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1,4]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => [[3,3,3,3]] => [4] => 10000 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => [[2,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => [[1,3,3,3]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => [[2,2,3,3]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => [[1,2,3,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => [[1,1,3,3]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => [[2,2,2,3]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => [[1,2,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => [[1,1,2,3]] => [2,1,1] => 10110 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => [[1,1,1,3]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => [[2,2,2,2]] => [4] => 10000 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => [[1,2,2,2]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => [[1,1,2,2]] => [2,2] => 1100 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => [[1,1,1,2]] => [3,1] => 10010 => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => [[1,1,1,1]] => [4] => 10000 => 4
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5,5],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5],[5]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[5]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[5]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[5]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,5],[3]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,5],[3]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,5],[2]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,5],[4]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,5],[4]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,5],[4]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,5],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,5],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,5],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,5],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[5]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[5]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[5]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[5]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[5]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[5]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => [[3,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => [[2,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => [[1,4,4],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => [[2,4,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => [[1,4,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => [[1,4,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => [[3,3,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => [[2,3,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => [[1,3,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => [[2,2,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => [[1,2,4],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => [[1,1,4],[4]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => [[2,3,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => [[1,3,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => [[2,2,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => [[1,1,4],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => [[1,2,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => [[1,1,4],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => [[3,3,3],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => [[2,3,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => [[1,3,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => [[2,2,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4]] => [1,1,1,1] => 11110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => [[1,1,3],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => [[2,2,2],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => [[1,2,2],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => [[1,1,2],[4]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => [[1,1,1],[4]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => [[2,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => [[1,3,3],[3]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => [[1,3,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => [[2,2,3],[3]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => [[1,2,3],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => [[1,1,3],[3]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => [[1,2,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => [[1,1,3],[2]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => [[2,2,2],[3]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => [[1,2,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => [[1,1,2],[3]] => [2,1,1] => 10110 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => [[1,1,1],[3]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => [[1,2,2],[2]] => [3,1] => 10010 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => [[1,1,2],[2]] => [2,2] => 1100 => 4
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => [[1,1,1],[2]] => [3,1] => 10010 => 4
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5,5]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5,5]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5,5]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5,5]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,5]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4,4]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4]] => [1,1,1,1] => 11110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2,4]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => [[2,2],[3,3]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => [[1,2],[3,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => [[1,1],[3,3]] => [2,2] => 1100 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => [[1,2],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => [[1,1],[2,3]] => [2,1,1] => 10110 => 4
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => [[1,1],[2,2]] => [2,2] => 1100 => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2,5],[3],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1,5],[3],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1,5],[2],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1,5],[2],[3]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[5]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[5]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => [[2,4],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => [[1,4],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => [[1,4],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => [[2,3],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => [[1,3],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => [[2,2],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4]] => [1,1,1,1] => 11110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => [[1,1],[3],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => [[1,2],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => [[1,1],[2],[4]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => [[1,3],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => [[1,2],[2],[3]] => [2,1,1] => 10110 => 4
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => [[1,1],[2],[3]] => [2,1,1] => 10110 => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4],[5]] => [1,1,1,1] => 11110 => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4],[5]] => [1,1,1,1] => 11110 => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4],[5]] => [1,1,1,1] => 11110 => 4
[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3],[5]] => [1,1,1,1] => 11110 => 4
[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4]] => [1,1,1,1] => 11110 => 4
[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6,6]] => [3] => 1000 => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,6]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,6]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5,5]] => [3] => 1000 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,5]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,5]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => [[4,4,4]] => [3] => 1000 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => [[3,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => [[2,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => [[1,4,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => [[3,3,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => [[2,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => [[1,3,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => [[2,2,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => [[1,2,4]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => [[1,1,4]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => [[3,3,3]] => [3] => 1000 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => [[2,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => [[1,3,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => [[2,2,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3]] => [1,1,1] => 1110 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => [[1,1,3]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => [[2,2,2]] => [3] => 1000 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => [[1,2,2]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => [[1,1,2]] => [2,1] => 1010 => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => [[1,1,1]] => [3] => 1000 => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,6],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,6],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,6],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,6],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,6],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,6],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[6]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[6]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1,5],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2,5],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1,5],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1,5],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2],[5]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1],[5]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => [[3,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => [[2,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => [[1,4],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => [[2,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => [[1,4],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => [[1,4],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => [[3,3],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => [[2,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => [[1,3],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => [[2,2],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => [[1,2],[4]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => [[1,1],[4]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => [[2,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => [[1,3],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => [[2,2],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3]] => [1,1,1] => 1110 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => [[1,1],[3]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => [[1,2],[2]] => [2,1] => 1010 => 3
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => [[1,1],[2]] => [2,1] => 1010 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[6]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2],[5]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => [[2],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => [[1],[3],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => [[1],[2],[4]] => [1,1,1] => 1110 => 3
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => [[1],[2],[3]] => [1,1,1] => 1110 => 3
[[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[7,7]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,7]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6,6]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,6]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5,5]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1,5]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => [[4,4]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => [[3,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => [[2,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => [[1,4]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => [[3,3]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => [[2,3]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => [[1,3]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => [[2,2]] => [2] => 100 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => [[1,2]] => [1,1] => 110 => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => [[1,1]] => [2] => 100 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[7]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[6]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1],[5]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => [[3],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => [[2],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => [[1],[4]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => [[2],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => [[1],[3]] => [1,1] => 110 => 2
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => [[1],[2]] => [1,1] => 110 => 2
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[6]] => [1] => 10 => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => [[5]] => [1] => 10 => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => [[4]] => [1] => 10 => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => [[3]] => [1] => 10 => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => [[2]] => [1] => 10 => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => [[1]] => [1] => 10 => 1
[[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5]] => [1,1,1,1,1] => 111110 => 5
[[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5]] => [1,1,1,1,1] => 111110 => 5
[[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4]] => [1,1,1,1,1] => 111110 => 5
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3]] => [1,1,1,1,1] => 111110 => 5
[[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2]] => [1,1,1,1,1] => 111110 => 5
[[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5]] => [1,1,1,1,1] => 111110 => 5
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5]] => [1,1,1,1,1] => 111110 => 5
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4]] => [1,1,1,1,1] => 111110 => 5
[[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5]] => [1,1,1,1,1] => 111110 => 5
[[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4]] => [1,1,1,1,1] => 111110 => 5
[[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3]] => [1,1,1,1,1] => 111110 => 5
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5]] => [1,1,1,1,1] => 111110 => 5
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4]] => [1,1,1,1,1] => 111110 => 5
[[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5]] => [1,1,1,1,1] => 111110 => 5
[[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4]] => [1,1,1,1,1] => 111110 => 5
[[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3]] => [1,1,1,1,1] => 111110 => 5
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5]] => [1,1,1,1,1] => 111110 => 5
[[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5]] => [1,1,1,1,1] => 111110 => 5
[[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5]] => [1,1,1,1,1] => 111110 => 5
[[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4]] => [1,1,1,1,1] => 111110 => 5
[[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 111110 => 5
[[1]] => [[1]] => [1] => 10 => 1
[[6,0,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5,6],[2]] => [1,1,1,1,1,1] => 1111110 => 6
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5,6],[3]] => [1,1,1,1,1,1] => 1111110 => 6
[[5,1,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5,6],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[5,1,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,6],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[5,1,0,0,0,0],[5,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4,5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2,4]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3,4]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2,5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3,5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4,5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,2,0,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5,6],[2],[3]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5,6],[2],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5,6],[3],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,6],[2],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,6],[3],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,6],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4,5],[2],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4,5],[3],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[4,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,5],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[4,1,1,0,0,0],[4,1,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => [[1,2,3,4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,3,0,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,3,0,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2,5],[3]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,5],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,5],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2,4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3,4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2,6],[3]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,6],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,6],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,6],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,6],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,6],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2,4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3,4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2,5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3,5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,2,1,0,0,0],[3,2,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4,5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5,6],[2],[3],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,6],[2],[3],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,6],[2],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,6],[3],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4,5],[2],[3],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3,5],[2],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2,5],[3],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => [[1,3,4],[2],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => [[1,2,4],[3],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[3,1,1,1,0,0],[3,1,1,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => [[1,2,3],[4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,2,0,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,2,0,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5,6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2,6],[3],[4]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,6],[3],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,6],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,6],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2,5],[3],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2,5],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,2,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3,5],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => [[1,3],[2,4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,2,1,1,0,0],[2,2,1,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => [[1,2],[3,4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,1,1,1,1,0],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,1,1,1,1,0],[2,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1,5],[2],[3],[4],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[1,1,1],[1,1],[1]] => [[1,4],[2],[3],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[1,1],[1]] => [[1,3],[2],[4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2,1,1,1,1,0],[2,1,1,1,0],[2,1,1,0],[2,1,0],[2,0],[1]] => [[1,2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[1,1,1,1,1,1],[1,1,1,1,1],[1,1,1,1],[1,1,1],[1,1],[1]] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 1111110 => 6
[[2]] => [[1,1]] => [2] => 100 => 2
[[3]] => [[1,1,1]] => [3] => 1000 => 3
[[4]] => [[1,1,1,1]] => [4] => 10000 => 4
[[5]] => [[1,1,1,1,1]] => [5] => 100000 => 5
[[4,3,2,1],[4,3,2],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,2],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,2],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,2],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,3],[4]] => [3,3,3,1] => 1110010 => 10
[[4,3,2,1],[4,3,2],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,2],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,2],[3,2],[2]] => [[1,1,2,3],[2,2,3],[3,3],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,3],[4]] => [[1,1,1,1],[2,2,2],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,3],[3]] => [[1,1,1,2],[2,2,2],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,2],[4]] => [[1,1,1,1],[2,2,3],[3,4],[4]] => [4,2,2,2] => 10011100 => 10
[[4,3,2,1],[4,3,1],[4,2],[3]] => [[1,1,1,2],[2,2,3],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,3,1],[3,2],[3]] => [[1,1,1,3],[2,2,3],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,3,1],[4,2],[2]] => [[1,1,2,2],[2,2,3],[3,4],[4]] => [4,2,2,2] => 10011100 => 10
[[4,3,2,1],[4,2,1],[4,2],[4]] => [[1,1,1,1],[2,2,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[4,2],[3]] => [[1,1,1,2],[2,2,4],[3,4],[4]] => [3,3,3,1] => 1110010 => 10
[[4,3,2,1],[3,2,1],[3,2],[3]] => [[1,1,1,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[4,2],[2]] => [[1,1,2,2],[2,2,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[3,2],[2]] => [[1,1,2,3],[2,2,4],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[3,2,1],[3,2],[2]] => [[1,1,2,4],[2,2,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,1],[4]] => [[1,1,1,1],[2,3,3],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,1],[3]] => [[1,1,1,2],[2,3,3],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,3,1],[3,1],[3]] => [[1,1,1,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,1],[2]] => [[1,1,2,2],[2,3,3],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,3,1],[3,1],[2]] => [[1,1,2,3],[2,3,3],[3,4],[4]] => [4,2,2,2] => 10011100 => 10
[[4,3,2,1],[4,2,1],[4,1],[4]] => [[1,1,1,1],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[4,1],[3]] => [[1,1,1,2],[2,3,4],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,2,1],[3,1],[3]] => [[1,1,1,3],[2,3,4],[3,4],[4]] => [3,3,3,1] => 1110010 => 10
[[4,3,2,1],[3,2,1],[3,1],[3]] => [[1,1,1,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[4,1],[2]] => [[1,1,2,2],[2,3,4],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[4,2,1],[3,1],[2]] => [[1,1,2,3],[2,3,4],[3,4],[4]] => [3,3,2,2] => 1101100 => 10
[[4,3,2,1],[3,2,1],[3,1],[2]] => [[1,1,2,4],[2,3,4],[3,4],[4]] => [4,2,2,2] => 10011100 => 10
[[4,3,2,1],[4,2,1],[2,1],[2]] => [[1,1,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[3,2,1],[2,1],[2]] => [[1,1,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[4,1],[1]] => [[1,2,2,2],[2,3,3],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,3,1],[3,1],[1]] => [[1,2,2,3],[2,3,3],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[4,1],[1]] => [[1,2,2,2],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[3,1],[1]] => [[1,2,2,3],[2,3,4],[3,4],[4]] => [3,3,3,1] => 1110010 => 10
[[4,3,2,1],[3,2,1],[3,1],[1]] => [[1,2,2,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[4,2,1],[2,1],[1]] => [[1,2,3,3],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
[[4,3,2,1],[3,2,1],[2,1],[1]] => [[1,2,3,4],[2,3,4],[3,4],[4]] => [4,3,2,1] => 10101010 => 10
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Generating function
F(2,1)=2 q
F(2,2)=4 q2
F(3,1)=3 q
F(2,3)=6 q3
F(3,2)=9 q2
F(4,1)=4 q
F(2,4)=9 q4
F(3,3)=19 q3
F(4,2)=16 q2
F(5,1)=5 q
F(2,5)=12 q5
F(3,4)=39 q4
F(4,3)=44 q3
F(5,2)=25 q2
F(6,1)=6 q
F(3,5)=69 q5
F(4,4)=116 q4
F(5,3)=85 q3
F(6,2)=36 q2
F(4,5)=260 q5
F(5,4)=275 q4
F(6,3)=146 q3
F(7,2)=49 q2
Description
The number of inversions of a binary word.
Map
to semistandard tableau
Description
Return the Gelfand-Tsetlin pattern as a semistandard Young tableau.
Let G be a Gelfand-Tsetlin pattern and let λ(k) be its (n−k+1)-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
λ(0)⊆λ(1)⊆⋯⊆λ(n),
where λ(0) is the empty partition.
Each skew shape λ(k)/λ(k−1) is moreover a horizontal strip.
We now define a semistandard tableau T(G) by inserting k into the cells of the skew shape λ(k)/λ(k−1), for k=1,…,n.
Let G be a Gelfand-Tsetlin pattern and let λ(k) be its (n−k+1)-st row. The defining inequalities of a Gelfand-Tsetlin pattern imply, regarding each row as a partition,
λ(0)⊆λ(1)⊆⋯⊆λ(n),
where λ(0) is the empty partition.
Each skew shape λ(k)/λ(k−1) is moreover a horizontal strip.
We now define a semistandard tableau T(G) by inserting k into the cells of the skew shape λ(k)/λ(k−1), for k=1,…,n.
Map
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.
Map
weight
Description
The weight of a semistandard tableau as an integer partition.
The weight (or content) of a semistandard tableaux T with maximal entry m is the weak composition (α1,…,αm) such that αi is the number of letters i occurring in T.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.
The weight (or content) of a semistandard tableaux T with maximal entry m is the weak composition (α1,…,αm) such that αi is the number of letters i occurring in T.
This map returns the integer partition obtained by sorting the weight into decreasing order and omitting zeros.
Since semistandard tableaux are bigraded by the size of the partition and the maximal occurring entry, this map is not graded.
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