Identifier
-
Mp00186:
Skew partitions
—dominating partition⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000913: Integer partitions ⟶ ℤ
Values
[[1],[]] => [1] => [1] => 1
[[2],[]] => [2] => [1,1] => 1
[[1,1],[]] => [1,1] => [2] => 1
[[2,1],[1]] => [2] => [1,1] => 1
[[3],[]] => [3] => [1,1,1] => 1
[[2,1],[]] => [2,1] => [2,1] => 1
[[3,1],[1]] => [3] => [1,1,1] => 1
[[2,2],[1]] => [2,1] => [2,1] => 1
[[3,2],[2]] => [3] => [1,1,1] => 1
[[1,1,1],[]] => [1,1,1] => [3] => 1
[[2,2,1],[1,1]] => [2,1] => [2,1] => 1
[[2,1,1],[1]] => [2,1] => [2,1] => 1
[[3,2,1],[2,1]] => [3] => [1,1,1] => 1
[[4],[]] => [4] => [1,1,1,1] => 1
[[3,1],[]] => [3,1] => [2,1,1] => 1
[[4,1],[1]] => [4] => [1,1,1,1] => 1
[[2,2],[]] => [2,2] => [2,2] => 1
[[3,2],[1]] => [3,1] => [2,1,1] => 1
[[4,2],[2]] => [4] => [1,1,1,1] => 1
[[2,1,1],[]] => [2,1,1] => [3,1] => 1
[[3,2,1],[1,1]] => [3,1] => [2,1,1] => 1
[[3,1,1],[1]] => [3,1] => [2,1,1] => 1
[[4,2,1],[2,1]] => [4] => [1,1,1,1] => 1
[[3,3],[2]] => [3,1] => [2,1,1] => 1
[[4,3],[3]] => [4] => [1,1,1,1] => 1
[[2,2,1],[1]] => [2,2] => [2,2] => 1
[[3,3,1],[2,1]] => [3,1] => [2,1,1] => 1
[[3,2,1],[2]] => [3,1] => [2,1,1] => 1
[[4,3,1],[3,1]] => [4] => [1,1,1,1] => 1
[[2,2,2],[1,1]] => [2,1,1] => [3,1] => 1
[[3,3,2],[2,2]] => [3,1] => [2,1,1] => 1
[[3,2,2],[2,1]] => [3,1] => [2,1,1] => 1
[[4,3,2],[3,2]] => [4] => [1,1,1,1] => 1
[[1,1,1,1],[]] => [1,1,1,1] => [4] => 2
[[2,2,2,1],[1,1,1]] => [2,1,1] => [3,1] => 1
[[2,2,1,1],[1,1]] => [2,2] => [2,2] => 1
[[3,3,2,1],[2,2,1]] => [3,1] => [2,1,1] => 1
[[2,1,1,1],[1]] => [2,1,1] => [3,1] => 1
[[3,2,2,1],[2,1,1]] => [3,1] => [2,1,1] => 1
[[3,2,1,1],[2,1]] => [3,1] => [2,1,1] => 1
[[4,3,2,1],[3,2,1]] => [4] => [1,1,1,1] => 1
[[5],[]] => [5] => [1,1,1,1,1] => 1
[[4,1],[]] => [4,1] => [2,1,1,1] => 1
[[5,1],[1]] => [5] => [1,1,1,1,1] => 1
[[3,2],[]] => [3,2] => [2,2,1] => 1
[[4,2],[1]] => [4,1] => [2,1,1,1] => 1
[[5,2],[2]] => [5] => [1,1,1,1,1] => 1
[[3,1,1],[]] => [3,1,1] => [3,1,1] => 1
[[4,2,1],[1,1]] => [4,1] => [2,1,1,1] => 1
[[4,1,1],[1]] => [4,1] => [2,1,1,1] => 1
[[5,2,1],[2,1]] => [5] => [1,1,1,1,1] => 1
[[3,3],[1]] => [3,2] => [2,2,1] => 1
[[4,3],[2]] => [4,1] => [2,1,1,1] => 1
[[5,3],[3]] => [5] => [1,1,1,1,1] => 1
[[2,2,1],[]] => [2,2,1] => [3,2] => 2
[[3,3,1],[1,1]] => [3,2] => [2,2,1] => 1
[[3,2,1],[1]] => [3,2] => [2,2,1] => 1
[[4,3,1],[2,1]] => [4,1] => [2,1,1,1] => 1
[[4,2,1],[2]] => [4,1] => [2,1,1,1] => 1
[[5,3,1],[3,1]] => [5] => [1,1,1,1,1] => 1
[[3,2,2],[1,1]] => [3,1,1] => [3,1,1] => 1
[[4,3,2],[2,2]] => [4,1] => [2,1,1,1] => 1
[[4,2,2],[2,1]] => [4,1] => [2,1,1,1] => 1
[[5,3,2],[3,2]] => [5] => [1,1,1,1,1] => 1
[[2,1,1,1],[]] => [2,1,1,1] => [4,1] => 2
[[3,2,2,1],[1,1,1]] => [3,1,1] => [3,1,1] => 1
[[3,2,1,1],[1,1]] => [3,2] => [2,2,1] => 1
[[4,3,2,1],[2,2,1]] => [4,1] => [2,1,1,1] => 1
[[3,1,1,1],[1]] => [3,1,1] => [3,1,1] => 1
[[4,2,2,1],[2,1,1]] => [4,1] => [2,1,1,1] => 1
[[4,2,1,1],[2,1]] => [4,1] => [2,1,1,1] => 1
[[5,3,2,1],[3,2,1]] => [5] => [1,1,1,1,1] => 1
[[4,4],[3]] => [4,1] => [2,1,1,1] => 1
[[5,4],[4]] => [5] => [1,1,1,1,1] => 1
[[3,3,1],[2]] => [3,2] => [2,2,1] => 1
[[4,4,1],[3,1]] => [4,1] => [2,1,1,1] => 1
[[4,3,1],[3]] => [4,1] => [2,1,1,1] => 1
[[5,4,1],[4,1]] => [5] => [1,1,1,1,1] => 1
[[2,2,2],[1]] => [2,2,1] => [3,2] => 2
[[3,3,2],[2,1]] => [3,2] => [2,2,1] => 1
[[4,4,2],[3,2]] => [4,1] => [2,1,1,1] => 1
[[3,2,2],[2]] => [3,2] => [2,2,1] => 1
[[4,3,2],[3,1]] => [4,1] => [2,1,1,1] => 1
[[5,4,2],[4,2]] => [5] => [1,1,1,1,1] => 1
[[2,2,1,1],[1]] => [2,2,1] => [3,2] => 2
[[3,3,2,1],[2,1,1]] => [3,2] => [2,2,1] => 1
[[3,3,1,1],[2,1]] => [3,2] => [2,2,1] => 1
[[4,4,2,1],[3,2,1]] => [4,1] => [2,1,1,1] => 1
[[3,2,1,1],[2]] => [3,1,1] => [3,1,1] => 1
[[4,3,2,1],[3,1,1]] => [4,1] => [2,1,1,1] => 1
[[4,3,1,1],[3,1]] => [4,1] => [2,1,1,1] => 1
[[5,4,2,1],[4,2,1]] => [5] => [1,1,1,1,1] => 1
[[3,3,3],[2,2]] => [3,1,1] => [3,1,1] => 1
[[4,4,3],[3,3]] => [4,1] => [2,1,1,1] => 1
[[4,3,3],[3,2]] => [4,1] => [2,1,1,1] => 1
[[5,4,3],[4,3]] => [5] => [1,1,1,1,1] => 1
[[2,2,2,1],[1,1]] => [2,2,1] => [3,2] => 2
[[3,3,3,1],[2,2,1]] => [3,1,1] => [3,1,1] => 1
[[3,3,2,1],[2,2]] => [3,2] => [2,2,1] => 1
[[4,4,3,1],[3,3,1]] => [4,1] => [2,1,1,1] => 1
[[3,2,2,1],[2,1]] => [3,2] => [2,2,1] => 1
>>> Load all 1516 entries. <<<[[4,3,3,1],[3,2,1]] => [4,1] => [2,1,1,1] => 1
[[4,3,2,1],[3,2]] => [4,1] => [2,1,1,1] => 1
[[5,4,3,1],[4,3,1]] => [5] => [1,1,1,1,1] => 1
[[2,2,2,2],[1,1,1]] => [2,1,1,1] => [4,1] => 2
[[3,3,3,2],[2,2,2]] => [3,1,1] => [3,1,1] => 1
[[3,3,2,2],[2,2,1]] => [3,2] => [2,2,1] => 1
[[4,4,3,2],[3,3,2]] => [4,1] => [2,1,1,1] => 1
[[3,2,2,2],[2,1,1]] => [3,1,1] => [3,1,1] => 1
[[4,3,3,2],[3,2,2]] => [4,1] => [2,1,1,1] => 1
[[4,3,2,2],[3,2,1]] => [4,1] => [2,1,1,1] => 1
[[5,4,3,2],[4,3,2]] => [5] => [1,1,1,1,1] => 1
[[1,1,1,1,1],[]] => [1,1,1,1,1] => [5] => 4
[[2,2,2,2,1],[1,1,1,1]] => [2,1,1,1] => [4,1] => 2
[[2,2,2,1,1],[1,1,1]] => [2,2,1] => [3,2] => 2
[[3,3,3,2,1],[2,2,2,1]] => [3,1,1] => [3,1,1] => 1
[[2,2,1,1,1],[1,1]] => [2,2,1] => [3,2] => 2
[[3,3,2,2,1],[2,2,1,1]] => [3,2] => [2,2,1] => 1
[[3,3,2,1,1],[2,2,1]] => [3,2] => [2,2,1] => 1
[[4,4,3,2,1],[3,3,2,1]] => [4,1] => [2,1,1,1] => 1
[[2,1,1,1,1],[1]] => [2,1,1,1] => [4,1] => 2
[[3,2,2,2,1],[2,1,1,1]] => [3,1,1] => [3,1,1] => 1
[[3,2,2,1,1],[2,1,1]] => [3,2] => [2,2,1] => 1
[[4,3,3,2,1],[3,2,2,1]] => [4,1] => [2,1,1,1] => 1
[[3,2,1,1,1],[2,1]] => [3,1,1] => [3,1,1] => 1
[[4,3,2,2,1],[3,2,1,1]] => [4,1] => [2,1,1,1] => 1
[[4,3,2,1,1],[3,2,1]] => [4,1] => [2,1,1,1] => 1
[[5,4,3,2,1],[4,3,2,1]] => [5] => [1,1,1,1,1] => 1
[[6],[]] => [6] => [1,1,1,1,1,1] => 1
[[5,1],[]] => [5,1] => [2,1,1,1,1] => 1
[[6,1],[1]] => [6] => [1,1,1,1,1,1] => 1
[[4,2],[]] => [4,2] => [2,2,1,1] => 1
[[5,2],[1]] => [5,1] => [2,1,1,1,1] => 1
[[6,2],[2]] => [6] => [1,1,1,1,1,1] => 1
[[4,1,1],[]] => [4,1,1] => [3,1,1,1] => 1
[[5,2,1],[1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,1,1],[1]] => [5,1] => [2,1,1,1,1] => 1
[[6,2,1],[2,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,3],[]] => [3,3] => [2,2,2] => 1
[[4,3],[1]] => [4,2] => [2,2,1,1] => 1
[[5,3],[2]] => [5,1] => [2,1,1,1,1] => 1
[[6,3],[3]] => [6] => [1,1,1,1,1,1] => 1
[[3,2,1],[]] => [3,2,1] => [3,2,1] => 2
[[4,3,1],[1,1]] => [4,2] => [2,2,1,1] => 1
[[4,2,1],[1]] => [4,2] => [2,2,1,1] => 1
[[5,3,1],[2,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,2,1],[2]] => [5,1] => [2,1,1,1,1] => 1
[[6,3,1],[3,1]] => [6] => [1,1,1,1,1,1] => 1
[[4,2,2],[1,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,3,2],[2,2]] => [5,1] => [2,1,1,1,1] => 1
[[5,2,2],[2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,3,2],[3,2]] => [6] => [1,1,1,1,1,1] => 1
[[3,1,1,1],[]] => [3,1,1,1] => [4,1,1] => 2
[[4,2,2,1],[1,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,2,1,1],[1,1]] => [4,2] => [2,2,1,1] => 1
[[5,3,2,1],[2,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,1,1,1],[1]] => [4,1,1] => [3,1,1,1] => 1
[[5,2,2,1],[2,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,2,1,1],[2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,3,2,1],[3,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[4,4],[2]] => [4,2] => [2,2,1,1] => 1
[[5,4],[3]] => [5,1] => [2,1,1,1,1] => 1
[[6,4],[4]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,1],[1]] => [3,3] => [2,2,2] => 1
[[4,4,1],[2,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,1],[2]] => [4,2] => [2,2,1,1] => 1
[[5,4,1],[3,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,1],[3]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,1],[4,1]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2],[]] => [2,2,2] => [3,3] => 2
[[3,3,2],[1,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,2],[2,2]] => [4,2] => [2,2,1,1] => 1
[[3,2,2],[1]] => [3,2,1] => [3,2,1] => 2
[[4,3,2],[2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,2],[3,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,2,2],[2]] => [4,2] => [2,2,1,1] => 1
[[5,3,2],[3,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,2],[4,2]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,1,1],[]] => [2,2,1,1] => [4,2] => 5
[[3,3,2,1],[1,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,1,1],[1,1]] => [3,3] => [2,2,2] => 1
[[4,4,2,1],[2,2,1]] => [4,2] => [2,2,1,1] => 1
[[3,2,1,1],[1]] => [3,2,1] => [3,2,1] => 2
[[4,3,2,1],[2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,1,1],[2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,2,1],[3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,2,1,1],[2]] => [4,1,1] => [3,1,1,1] => 1
[[5,3,2,1],[3,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,1,1],[3,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,2,1],[4,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[4,3,3],[2,2]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,3],[3,3]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,3],[3,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,3],[4,3]] => [6] => [1,1,1,1,1,1] => 1
[[3,2,2,1],[1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,1],[2,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,2,1],[2,2]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,1],[3,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,2,2,1],[2,1]] => [4,2] => [2,2,1,1] => 1
[[5,3,3,1],[3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,2,1],[3,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,3,1],[4,3,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,2,2,2],[1,1,1]] => [3,1,1,1] => [4,1,1] => 2
[[4,3,3,2],[2,2,2]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,2,2],[2,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,2],[3,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,2,2,2],[2,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,3,3,2],[3,2,2]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,2,2],[3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,3,2],[4,3,2]] => [6] => [1,1,1,1,1,1] => 1
[[2,1,1,1,1],[]] => [2,1,1,1,1] => [5,1] => 4
[[3,2,2,2,1],[1,1,1,1]] => [3,1,1,1] => [4,1,1] => 2
[[3,2,2,1,1],[1,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,2,1],[2,2,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[3,2,1,1,1],[1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,2,2,1],[2,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,2,1,1],[2,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,2,1],[3,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,1,1,1,1],[1]] => [3,1,1,1] => [4,1,1] => 2
[[4,2,2,2,1],[2,1,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,2,2,1,1],[2,1,1]] => [4,2] => [2,2,1,1] => 1
[[5,3,3,2,1],[3,2,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,2,1,1,1],[2,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,3,2,2,1],[3,2,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,3,2,1,1],[3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,4,3,2,1],[4,3,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[5,5],[4]] => [5,1] => [2,1,1,1,1] => 1
[[6,5],[5]] => [6] => [1,1,1,1,1,1] => 1
[[4,4,1],[3]] => [4,2] => [2,2,1,1] => 1
[[5,5,1],[4,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,1],[4]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,1],[5,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,2],[2]] => [3,3] => [2,2,2] => 1
[[4,4,2],[3,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,2],[4,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2],[3]] => [4,2] => [2,2,1,1] => 1
[[5,4,2],[4,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,2],[5,2]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,1,1],[2]] => [3,2,1] => [3,2,1] => 2
[[4,4,2,1],[3,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,1,1],[3,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,2,1],[4,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,1,1],[3]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,2,1],[4,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,1,1],[4,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,2,1],[5,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,3],[2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,3],[3,2]] => [4,2] => [2,2,1,1] => 1
[[5,5,3],[4,3]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,3],[3,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3],[4,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,3],[5,3]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2,1],[1]] => [2,2,2] => [3,3] => 2
[[3,3,3,1],[2,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,2,1],[2,1]] => [3,3] => [2,2,2] => 1
[[4,4,3,1],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,2,1],[3,2]] => [4,2] => [2,2,1,1] => 1
[[5,5,3,1],[4,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,2,1],[2]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,1],[3,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,2,1],[3,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,1],[4,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,2,1],[4,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,3,1],[5,3,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,2,2],[2,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,3,2],[3,2,2]] => [4,2] => [2,2,1,1] => 1
[[4,4,2,2],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,3,2],[4,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,2],[3,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,3,2],[4,2,2]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,2,2],[4,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,3,2],[5,3,2]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,1,1,1],[1]] => [2,2,1,1] => [4,2] => 5
[[3,3,2,2,1],[2,1,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,2,1,1],[2,1,1]] => [3,3] => [2,2,2] => 1
[[4,4,3,2,1],[3,2,2,1]] => [4,2] => [2,2,1,1] => 1
[[3,3,1,1,1],[2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,2,2,1],[3,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,2,1,1],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,3,2,1],[4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,1,1,1],[2]] => [3,1,1,1] => [4,1,1] => 2
[[4,3,2,2,1],[3,1,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,2,1,1],[3,1,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,2,1],[4,2,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,1,1,1],[3,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,2,2,1],[4,2,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,2,1,1],[4,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,3,2,1],[5,3,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[4,4,4],[3,3]] => [4,1,1] => [3,1,1,1] => 1
[[5,5,4],[4,4]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,4],[4,3]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4],[5,4]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,3,1],[2,2]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,1],[3,3,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,4,3,1],[3,3]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,1],[4,4,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,3,1],[3,2]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,1],[4,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,1],[4,3]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,1],[5,4,1]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2,2],[1,1]] => [2,2,1,1] => [4,2] => 5
[[3,3,3,2],[2,2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,2],[3,3,2]] => [4,1,1] => [3,1,1,1] => 1
[[3,3,2,2],[2,2]] => [3,3] => [2,2,2] => 1
[[4,4,3,2],[3,3,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,2],[4,4,2]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,2,2],[2,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,2],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,2],[4,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,2],[3,2]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,2],[4,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,2],[5,4,2]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2,1,1],[1,1]] => [2,2,2] => [3,3] => 2
[[3,3,3,2,1],[2,2,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,3,1,1],[2,2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,2,1],[3,3,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[3,3,2,1,1],[2,2]] => [3,2,1] => [3,2,1] => 2
[[4,4,3,2,1],[3,3,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,3,1,1],[3,3,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,2,1],[4,4,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,2,1,1],[2,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,2,1],[3,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,3,1,1],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,2,1],[4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,1,1],[3,2]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,3,2,1],[4,3,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,1,1],[4,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,2,1],[5,4,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[3,3,3,3],[2,2,2]] => [3,1,1,1] => [4,1,1] => 2
[[4,4,4,3],[3,3,3]] => [4,1,1] => [3,1,1,1] => 1
[[4,4,3,3],[3,3,2]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,3],[4,4,3]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,3,3],[3,2,2]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,4,3],[4,3,3]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,3],[4,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,3],[5,4,3]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2,2,1],[1,1,1]] => [2,2,1,1] => [4,2] => 5
[[3,3,3,3,1],[2,2,2,1]] => [3,1,1,1] => [4,1,1] => 2
[[3,3,3,2,1],[2,2,2]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,3,1],[3,3,3,1]] => [4,1,1] => [3,1,1,1] => 1
[[3,3,2,2,1],[2,2,1]] => [3,3] => [2,2,2] => 1
[[4,4,3,3,1],[3,3,2,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,3,2,1],[3,3,2]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,3,1],[4,4,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,2,2,1],[2,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,3,1],[3,2,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,3,2,1],[3,2,2]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,3,1],[4,3,3,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,2,1],[3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,3,1],[4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,2,1],[4,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,3,1],[5,4,3,1]] => [6] => [1,1,1,1,1,1] => 1
[[2,2,2,2,2],[1,1,1,1]] => [2,1,1,1,1] => [5,1] => 4
[[3,3,3,3,2],[2,2,2,2]] => [3,1,1,1] => [4,1,1] => 2
[[3,3,3,2,2],[2,2,2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,3,2],[3,3,3,2]] => [4,1,1] => [3,1,1,1] => 1
[[3,3,2,2,2],[2,2,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,3,3,2],[3,3,2,2]] => [4,2] => [2,2,1,1] => 1
[[4,4,3,2,2],[3,3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,3,2],[4,4,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,2,2,2],[2,1,1,1]] => [3,1,1,1] => [4,1,1] => 2
[[4,3,3,3,2],[3,2,2,2]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,3,2,2],[3,2,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,3,2],[4,3,3,2]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,2,2],[3,2,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,3,3,2],[4,3,2,2]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,2,2],[4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,3,2],[5,4,3,2]] => [6] => [1,1,1,1,1,1] => 1
[[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => [6] => 11
[[2,2,2,2,2,1],[1,1,1,1,1]] => [2,1,1,1,1] => [5,1] => 4
[[2,2,2,2,1,1],[1,1,1,1]] => [2,2,1,1] => [4,2] => 5
[[3,3,3,3,2,1],[2,2,2,2,1]] => [3,1,1,1] => [4,1,1] => 2
[[2,2,2,1,1,1],[1,1,1]] => [2,2,2] => [3,3] => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,3,2,1,1],[2,2,2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,4,3,2,1],[3,3,3,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[2,2,1,1,1,1],[1,1]] => [2,2,1,1] => [4,2] => 5
[[3,3,2,2,2,1],[2,2,1,1,1]] => [3,2,1] => [3,2,1] => 2
[[3,3,2,2,1,1],[2,2,1,1]] => [3,3] => [2,2,2] => 1
[[4,4,3,3,2,1],[3,3,2,2,1]] => [4,2] => [2,2,1,1] => 1
[[3,3,2,1,1,1],[2,2,1]] => [3,2,1] => [3,2,1] => 2
[[4,4,3,2,2,1],[3,3,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,4,3,2,1,1],[3,3,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,5,4,3,2,1],[4,4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[2,1,1,1,1,1],[1]] => [2,1,1,1,1] => [5,1] => 4
[[3,2,2,2,2,1],[2,1,1,1,1]] => [3,1,1,1] => [4,1,1] => 2
[[3,2,2,2,1,1],[2,1,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,3,2,1],[3,2,2,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[3,2,2,1,1,1],[2,1,1]] => [3,2,1] => [3,2,1] => 2
[[4,3,3,2,2,1],[3,2,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[4,3,3,2,1,1],[3,2,2,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,4,3,2,1],[4,3,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[3,2,1,1,1,1],[2,1]] => [3,1,1,1] => [4,1,1] => 2
[[4,3,2,2,2,1],[3,2,1,1,1]] => [4,1,1] => [3,1,1,1] => 1
[[4,3,2,2,1,1],[3,2,1,1]] => [4,2] => [2,2,1,1] => 1
[[5,4,3,3,2,1],[4,3,2,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[4,3,2,1,1,1],[3,2,1]] => [4,1,1] => [3,1,1,1] => 1
[[5,4,3,2,2,1],[4,3,2,1,1]] => [5,1] => [2,1,1,1,1] => 1
[[5,4,3,2,1,1],[4,3,2,1]] => [5,1] => [2,1,1,1,1] => 1
[[6,5,4,3,2,1],[5,4,3,2,1]] => [6] => [1,1,1,1,1,1] => 1
[[7],[]] => [7] => [1,1,1,1,1,1,1] => 1
[[6,1],[]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,1],[1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,2],[]] => [5,2] => [2,2,1,1,1] => 1
[[6,2],[1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,2],[2]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,1,1],[]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,2,1],[1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,1,1],[1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,2,1],[2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,3],[]] => [4,3] => [2,2,2,1] => 1
[[5,3],[1]] => [5,2] => [2,2,1,1,1] => 1
[[6,3],[2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,3],[3]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,2,1],[]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,1],[1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,2,1],[1]] => [5,2] => [2,2,1,1,1] => 1
[[6,3,1],[2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,2,1],[2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,3,1],[3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,2,2],[1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,3,2],[2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,2,2],[2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,3,2],[3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,1,1,1],[]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,2,2,1],[1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,2,1,1],[1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,3,2,1],[2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,1,1,1],[1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,2,2,1],[2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,2,1,1],[2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,3,2,1],[3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4],[1]] => [4,3] => [2,2,2,1] => 1
[[5,4],[2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4],[3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4],[4]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,1],[]] => [3,3,1] => [3,2,2] => 3
[[4,4,1],[1,1]] => [4,3] => [2,2,2,1] => 1
[[4,3,1],[1]] => [4,3] => [2,2,2,1] => 1
[[5,4,1],[2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,1],[2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,1],[3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,1],[3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,1],[4,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,2],[]] => [3,2,2] => [3,3,1] => 2
[[4,3,2],[1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,2],[2,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,2,2],[1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,2],[2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,2],[3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,2,2],[2]] => [5,2] => [2,2,1,1,1] => 1
[[6,3,2],[3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,2],[4,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,1,1],[]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,2,1],[1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,1,1],[1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,2,1],[2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,2,1,1],[1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,2,1],[2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,1,1],[2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,2,1],[3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,2,1,1],[2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,3,2,1],[3,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,1,1],[3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,2,1],[4,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,3,3],[2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,3],[3,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,3],[3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,3],[4,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,2,2,1],[1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,1],[2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,2,1],[2,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,1],[3,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,2,2,1],[2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,3,3,1],[3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,2,1],[3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,3,1],[4,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,2,2,2],[1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,3,3,2],[2,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,2,2],[2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,2],[3,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,2,2,2],[2,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,3,3,2],[3,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,2,2],[3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,3,2],[4,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,1,1,1,1],[]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,2,2,2,1],[1,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,2,2,1,1],[1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,2,1],[2,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,2,1,1,1],[1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,2,2,1],[2,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,2,1,1],[2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,2,1],[3,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,1,1,1,1],[1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,2,2,2,1],[2,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,2,2,1,1],[2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,3,3,2,1],[3,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,2,1,1,1],[2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,3,2,2,1],[3,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,3,2,1,1],[3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,4,3,2,1],[4,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,5],[3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5],[4]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5],[5]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,1],[2]] => [4,3] => [2,2,2,1] => 1
[[5,5,1],[3,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,1],[3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,1],[4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,1],[4]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,1],[5,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,2],[1]] => [3,3,1] => [3,2,2] => 3
[[4,4,2],[2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,2],[3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,2],[2]] => [4,3] => [2,2,2,1] => 1
[[5,4,2],[3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,2],[4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2],[3]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,2],[4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,2],[5,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,1,1],[1]] => [3,3,1] => [3,2,2] => 3
[[4,4,2,1],[2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,1,1],[2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,2,1],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,1,1],[2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,2,1],[3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,1,1],[3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,2,1],[4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,1,1],[3]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,2,1],[4,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,1,1],[4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,2,1],[5,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3],[1,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,3],[2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,3],[3,3]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,3],[2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3],[3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3],[4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,3],[3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3],[4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,3],[5,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,1],[]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,1],[1,1,1]] => [3,2,2] => [3,3,1] => 2
[[3,3,2,1],[1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,1],[2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,2,1],[2,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,1],[3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[3,2,2,1],[1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,1],[2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,2,1],[2,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,3,1],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,2,1],[3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,1],[4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,2,1],[2]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,1],[3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,2,1],[3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,1],[4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,2,1],[4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,3,1],[5,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,2,2],[1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,3,2],[2,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,2,2],[2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,2],[3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,2,2],[2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2],[3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,2,2],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,2],[4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,2],[3,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,3,2],[4,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,2,2],[4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,3,2],[5,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,1,1,1],[]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,2,2,1],[1,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,2,1,1],[1,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,2,1],[2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,1,1,1],[1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,2,2,1],[2,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,2,1,1],[2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,2,1],[3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[3,2,1,1,1],[1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,2,2,1],[2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,2,1,1],[2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,3,2,1],[3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,1,1,1],[2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,2,2,1],[3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,2,1,1],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,2,1],[4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,1,1,1],[2]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,3,2,2,1],[3,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,2,1,1],[3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,2,1],[4,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,1,1,1],[3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,2,2,1],[4,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,2,1,1],[4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,3,2,1],[5,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,4,4],[3,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4],[4,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,4],[4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4],[5,4]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,3,3,1],[2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,1],[3,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,1],[3,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,1],[4,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,3,1],[3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,1],[4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,1],[4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,1],[5,4,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,2,2],[1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,2],[2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,2],[3,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,2],[2,2]] => [4,3] => [2,2,2,1] => 1
[[5,4,3,2],[3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,2],[4,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,2,2],[2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,2],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,2],[4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,2],[3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,2],[4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,2],[5,4,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,2,1,1],[1,1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,2,1],[2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,1,1],[2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,2,1],[3,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,1,1],[2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2,1],[3,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,1,1],[3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,2,1],[4,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,2,1,1],[2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,2,1],[3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,3,1,1],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,2,1],[4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,1,1],[3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,3,2,1],[4,3,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,1,1],[4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,2,1],[5,4,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,3,3,3],[2,2,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,4,3],[3,3,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,3],[3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3],[4,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,3,3],[3,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,4,3],[4,3,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,3],[4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,3],[5,4,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,2,2,1],[1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,3,1],[2,2,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,3,2,1],[2,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,1],[3,3,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,2,1],[2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,3,3,1],[3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,2,1],[3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,1],[4,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,2,2,1],[2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,3,1],[3,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,3,2,1],[3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,3,1],[4,3,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,2,1],[3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,3,1],[4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,2,1],[4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,3,1],[5,4,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,2,2,2,2],[1,1,1,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,3,3,3,2],[2,2,2,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,3,2,2],[2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,2],[3,3,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,2,2],[2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,2],[3,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,2,2],[3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2],[4,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,2,2,2],[2,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,3,3,3,2],[3,2,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,3,2,2],[3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,3,2],[4,3,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,2,2],[3,2,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,3,3,2],[4,3,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,2,2],[4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,3,2],[5,4,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => [6,1] => 11
[[3,2,2,2,2,1],[1,1,1,1,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[3,2,2,2,1,1],[1,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,3,2,1],[2,2,2,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,2,2,1,1,1],[1,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,2,2,1],[2,2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,2,1,1],[2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,2,1],[3,3,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,2,1,1,1,1],[1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,2,2,2,1],[2,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,2,2,1,1],[2,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,3,3,2,1],[3,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,2,1,1,1],[2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2,2,1],[3,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,2,1,1],[3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2,1],[4,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,1,1,1,1,1],[1]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,2,2,2,2,1],[2,1,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,2,2,2,1,1],[2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,3,2,1],[3,2,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,2,2,1,1,1],[2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,3,3,2,2,1],[3,2,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,3,3,2,1,1],[3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,4,3,2,1],[4,3,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,2,1,1,1,1],[2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,3,2,2,2,1],[3,2,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,3,2,2,1,1],[3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,4,3,3,2,1],[4,3,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,3,2,1,1,1],[3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,4,3,2,2,1],[4,3,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,4,3,2,1,1],[4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,5,4,3,2,1],[5,4,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[6,6],[5]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6],[6]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,5,1],[4]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,1],[5,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,1],[5]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,1],[6,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,2],[3]] => [4,3] => [2,2,2,1] => 1
[[5,5,2],[4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,2],[5,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2],[4]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,2],[5,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,2],[6,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,1,1],[3]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,2,1],[4,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,1,1],[4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,2,1],[5,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,1,1],[4]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,2,1],[5,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,1,1],[5,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,2,1],[6,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3],[2]] => [3,3,1] => [3,2,2] => 3
[[4,4,3],[3,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3],[4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,3],[5,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3],[3]] => [4,3] => [2,2,2,1] => 1
[[5,4,3],[4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3],[5,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,3],[6,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,2,1],[2]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,1],[3,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,2,1],[3,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,1],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,2,1],[4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,3,1],[5,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,1],[3]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,1],[4,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,2,1],[4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,1],[5,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,2,1],[5,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,3,1],[6,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,2,2],[3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,3,2],[4,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,2,2],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,3,2],[5,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,2],[4,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,3,2],[5,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,2,2],[5,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,3,2],[6,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,1,1,1],[2]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,2,2,1],[3,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,2,1,1],[3,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,2,1],[4,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,1,1,1],[3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,2,2,1],[4,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,2,1,1],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,3,2,1],[5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,1,1,1],[3]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,2,2,1],[4,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,2,1,1],[4,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,2,1],[5,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,1,1,1],[4,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,2,2,1],[5,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,2,1,1],[5,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,3,2,1],[6,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,4],[3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4],[4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4],[5,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,4],[4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4],[5,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4],[6,4]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,1],[2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,1],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,1],[3,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,1],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,1],[4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,1],[5,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,1],[3,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,1],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,1],[4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,1],[5,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,1],[5,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,1],[6,4,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2],[1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,2],[2,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,2],[3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,2,2],[2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,2],[3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,2],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,2,2],[3,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,2],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,2],[5,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2],[2]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,2],[3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,2],[4,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,2,2],[3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,2],[5,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,2],[4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,2],[5,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,2],[6,4,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,1,1],[1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,2,1],[2,1,1,1]] => [3,2,2] => [3,3,1] => 2
[[3,3,3,1,1],[2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,2,1],[3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,2,1,1],[2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,2,1],[3,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,3,1,1],[3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,2,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,2,1,1],[3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,3,2,1],[4,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,1,1],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,2,1],[5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,1,1],[2]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,2,1],[3,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,1,1],[3,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,2,1],[4,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,2,1,1],[3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2,1],[4,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,1,1],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,2,1],[5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,1,1],[4,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,3,2,1],[5,3,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,1,1],[5,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,2,1],[6,4,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,3,3],[3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,3],[4,3,3]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,3],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,3],[5,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,3],[4,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,3],[5,3,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,3],[5,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,3],[6,4,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,2,2,1],[2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,1],[3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,2,1],[3,2,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,1],[4,3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,2,2,1],[3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,3,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,2,1],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,3,1],[5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,1],[3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,1],[4,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,2,1],[4,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,1],[5,3,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,2,1],[4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,3,1],[5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,2,1],[5,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,3,1],[6,4,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,2,2,2],[2,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,3,3,2],[3,2,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,2,2],[3,2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,2],[4,3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,2,2,2],[3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,3,3,2],[4,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,2,2],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,3,2],[5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,2],[3,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,3,3,2],[4,2,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,2,2],[4,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2],[5,3,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,2,2],[4,2,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,3,3,2],[5,3,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,2,2],[5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,3,2],[6,4,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,1,1,1,1],[1]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,2,2,2,1],[2,1,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,2,2,1,1],[2,1,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,2,1],[3,2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,2,1,1,1],[2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,2,2,1],[3,2,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,3,2,1,1],[3,2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,2,1],[4,3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[3,3,1,1,1,1],[2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,2,2,2,1],[3,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,2,2,1,1],[3,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,3,3,2,1],[4,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,2,1,1,1],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,3,2,2,1],[4,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,3,2,1,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,4,3,2,1],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,1,1,1,1],[2]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,3,2,2,2,1],[3,1,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,2,2,1,1],[3,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,2,1],[4,2,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,1,1,1],[3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,2,2,1],[4,2,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,2,1,1],[4,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2,1],[5,3,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,1,1,1,1],[3,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,2,2,2,1],[4,2,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,2,2,1,1],[4,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,3,3,2,1],[5,3,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,2,1,1,1],[4,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,3,2,2,1],[5,3,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,3,2,1,1],[5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,4,3,2,1],[6,4,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[5,5,5],[4,4]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,6,5],[5,5]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,5],[5,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5],[6,5]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,4,1],[3,3]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,1],[4,4,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,5,4,1],[4,4]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,1],[5,5,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,4,1],[4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,1],[5,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,1],[5,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,1],[6,5,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,2],[2,2]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,2],[3,3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,2],[4,4,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,2],[3,3]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,2],[4,4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,2],[5,5,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,2],[3,2]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,2],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,2],[5,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2],[4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,2],[5,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,2],[6,5,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,1,1],[2,2]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,2,1],[3,3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,1,1],[3,3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,2,1],[4,4,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,1,1],[3,3]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,2,1],[4,4,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,1,1],[4,4,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,2,1],[5,5,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,1,1],[3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,2,1],[4,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,1,1],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,2,1],[5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,1,1],[4,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,2,1],[5,4,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,1,1],[5,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,2,1],[6,5,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,3],[2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,3],[3,3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,3],[4,4,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,3],[3,3,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3],[4,4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,3],[5,5,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,3],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,3],[5,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,3],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3],[5,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,3],[6,5,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,1],[1,1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,3,1],[2,2,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,3,2,1],[2,2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,3,1],[3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,2,1],[3,3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,3,1],[4,4,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,2,1],[2,2]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,1],[3,3,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,3,2,1],[3,3,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,1],[4,4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,2,1],[4,4,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,3,1],[5,5,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2,1],[2,1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,3,1],[3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,2,1],[3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,3,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,2,1],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,3,1],[5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,1],[3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,1],[4,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,2,1],[4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,1],[5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,2,1],[5,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,3,1],[6,5,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,2,2],[2,2,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,3,2],[3,3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,2,2],[3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,3,2],[4,4,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,2,2],[3,3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,3,2],[4,4,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,2,2],[4,4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,3,2],[5,5,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,2,2],[3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,2],[4,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,2,2],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,3,2],[5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,2],[4,3,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,3,2],[5,4,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,2,2],[5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,3,2],[6,5,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,1,1,1],[1,1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,2,2,1],[2,2,1,1,1]] => [3,2,2] => [3,3,1] => 2
[[3,3,3,2,1,1],[2,2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,3,2,1],[3,3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,3,1,1,1],[2,2,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,2,2,1],[3,3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,2,1,1],[3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,3,2,1],[4,4,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,1,1,1],[2,2]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,3,2,2,1],[3,3,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,2,1,1],[3,3,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,2,1],[4,4,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,1,1,1],[3,3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,2,2,1],[4,4,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,2,1,1],[4,4,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,3,2,1],[5,5,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,1,1,1],[2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,2,2,1],[3,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,2,1,1],[3,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,3,2,1],[4,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,3,1,1,1],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,2,2,1],[4,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,2,1,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,3,2,1],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,1,1,1],[3,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,3,2,2,1],[4,3,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,2,1,1],[4,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2,1],[5,4,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,1,1,1],[4,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,2,2,1],[5,4,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,2,1,1],[5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,3,2,1],[6,5,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[4,4,4,4],[3,3,3]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,5,5,4],[4,4,4]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,5,4,4],[4,4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4],[5,5,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,4,4],[4,3,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,5,4],[5,4,4]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,4],[5,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4],[6,5,4]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,1],[2,2,2]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,1],[3,3,3,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,4,4,3,1],[3,3,3]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,1],[4,4,4,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,3,1],[3,3,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,1],[4,4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,1],[4,4,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,1],[5,5,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,3,1],[3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,1],[4,3,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,4,3,1],[4,3,3]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,1],[5,4,4,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,3,1],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,1],[5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,1],[5,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,1],[6,5,4,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,2],[1,1,1]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,3,3,2],[2,2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,2],[3,3,3,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,3,3,2,2],[2,2,2]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,3,2],[3,3,3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,2],[4,4,4,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,2,2],[2,2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,2],[3,3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,2],[4,4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,2,2],[3,3,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,2],[4,4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,2],[5,5,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2,2],[2,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,3,2],[3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,2],[4,3,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,3,2,2],[3,2,2]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,3,2],[4,3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,2],[5,4,4,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,2],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,2],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,2],[5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,2],[4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,2],[5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,2],[6,5,4,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,1,1],[1,1,1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,3,2,1],[2,2,2,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,3,3,1,1],[2,2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,2,1],[3,3,3,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,3,3,2,1,1],[2,2,2]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,3,2,1],[3,3,3,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,3,1,1],[3,3,3,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,2,1],[4,4,4,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,2,1,1],[2,2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,2,1],[3,3,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,3,3,1,1],[3,3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,2,1],[4,4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,2,1,1],[3,3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,3,2,1],[4,4,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,1,1],[4,4,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,2,1],[5,5,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2,1,1],[2,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,3,2,1],[3,2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,3,1,1],[3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,2,1],[4,3,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,3,2,1,1],[3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,2,1],[4,3,3,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,3,1,1],[4,3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,2,1],[5,4,4,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,1,1],[3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,2,1],[4,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,3,1,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,2,1],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,1,1],[4,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,3,2,1],[5,4,3,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,1,1],[5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,2,1],[6,5,4,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[3,3,3,3,3],[2,2,2,2]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,4,4,4,3],[3,3,3,3]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,4,4,3,3],[3,3,3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,3],[4,4,4,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,4,3,3,3],[3,3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,4,3],[4,4,3,3]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,3],[4,4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,3],[5,5,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,3,3,3],[3,2,2,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,4,4,3],[4,3,3,3]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,4,3,3],[4,3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,3],[5,4,4,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,3,3],[4,3,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,4,3],[5,4,3,3]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,3],[5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,3],[6,5,4,3]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,2,1],[1,1,1,1]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,3,3,3,1],[2,2,2,2,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[3,3,3,3,2,1],[2,2,2,2]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,3,1],[3,3,3,3,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,3,3,2,2,1],[2,2,2,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,3,3,1],[3,3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,3,2,1],[3,3,3,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,3,1],[4,4,4,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,2,2,1],[2,2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,3,1],[3,3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,3,2,1],[3,3,2,2]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,3,1],[4,4,3,3,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,2,2,1],[3,3,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,3,1],[4,4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,2,1],[4,4,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,3,1],[5,5,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2,2,1],[2,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,3,3,1],[3,2,2,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,3,3,2,1],[3,2,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,3,1],[4,3,3,3,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,3,2,2,1],[3,2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,3,3,1],[4,3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,3,2,1],[4,3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,3,1],[5,4,4,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,2,1],[3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,3,1],[4,3,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,3,2,1],[4,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,3,1],[5,4,3,3,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,2,1],[4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,3,1],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,2,1],[5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,3,1],[6,5,4,3,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[2,2,2,2,2,2],[1,1,1,1,1]] => [2,1,1,1,1,1] => [6,1] => 11
[[3,3,3,3,3,2],[2,2,2,2,2]] => [3,1,1,1,1] => [5,1,1] => 4
[[3,3,3,3,2,2],[2,2,2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,3,2],[3,3,3,3,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,3,3,2,2,2],[2,2,2,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,3,3,2],[3,3,3,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,3,2,2],[3,3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,3,2],[4,4,4,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,3,2,2,2,2],[2,2,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,3,3,3,2],[3,3,2,2,2]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,3,2,2],[3,3,2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,3,2],[4,4,3,3,2]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,2,2,2],[3,3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,3,3,2],[4,4,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,2,2],[4,4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,3,2],[5,5,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,2,2,2,2],[2,1,1,1,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,3,3,3,3,2],[3,2,2,2,2]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,3,3,2,2],[3,2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,3,2],[4,3,3,3,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,3,2,2,2],[3,2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,3,2],[4,3,3,2,2]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,3,2,2],[4,3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,3,2],[5,4,4,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,2,2,2],[3,2,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,3,3,3,2],[4,3,2,2,2]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,3,2,2],[4,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,3,2],[5,4,3,3,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,2,2],[4,3,2,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,3,3,2],[5,4,3,2,2]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,2,2],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,3,2],[6,5,4,3,2]] => [7] => [1,1,1,1,1,1,1] => 1
[[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => [7] => 33
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [2,1,1,1,1,1] => [6,1] => 11
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[2,2,2,2,1,1,1],[1,1,1,1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[2,2,2,1,1,1,1],[1,1,1]] => [2,2,2,1] => [4,3] => 10
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [3,2,2] => [3,3,1] => 2
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,3,2,1,1,1],[2,2,2,1]] => [3,2,2] => [3,3,1] => 2
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[2,2,1,1,1,1,1],[1,1]] => [2,2,1,1,1] => [5,2] => 12
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[3,3,2,2,1,1,1],[2,2,1,1]] => [3,3,1] => [3,2,2] => 3
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[3,3,2,1,1,1,1],[2,2,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,4,3,2,1,1,1],[3,3,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[2,1,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => [6,1] => 11
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[3,2,2,2,1,1,1],[2,1,1,1]] => [3,2,2] => [3,3,1] => 2
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[3,2,2,1,1,1,1],[2,1,1]] => [3,2,1,1] => [4,2,1] => 5
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [4,3] => [2,2,2,1] => 1
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[4,3,3,2,1,1,1],[3,2,2,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[3,2,1,1,1,1,1],[2,1]] => [3,1,1,1,1] => [5,1,1] => 4
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[4,3,2,2,1,1,1],[3,2,1,1]] => [4,2,1] => [3,2,1,1] => 2
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[4,3,2,1,1,1,1],[3,2,1]] => [4,1,1,1] => [4,1,1,1] => 2
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [5,2] => [2,2,1,1,1] => 1
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[5,4,3,2,1,1,1],[4,3,2,1]] => [5,1,1] => [3,1,1,1,1] => 1
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [6,1] => [2,1,1,1,1,1] => 1
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [7] => [1,1,1,1,1,1,1] => 1
[[8],[]] => [8] => [1,1,1,1,1,1,1,1] => 1
[[7,1],[]] => [7,1] => [2,1,1,1,1,1,1] => 1
[[6,2],[]] => [6,2] => [2,2,1,1,1,1] => 1
[[6,1,1],[]] => [6,1,1] => [3,1,1,1,1,1] => 1
[[5,3],[]] => [5,3] => [2,2,2,1,1] => 1
[[5,2,1],[]] => [5,2,1] => [3,2,1,1,1] => 2
[[5,1,1,1],[]] => [5,1,1,1] => [4,1,1,1,1] => 2
[[4,4],[]] => [4,4] => [2,2,2,2] => 1
[[4,3,1],[]] => [4,3,1] => [3,2,2,1] => 3
[[4,2,2],[]] => [4,2,2] => [3,3,1,1] => 2
[[4,2,1,1],[]] => [4,2,1,1] => [4,2,1,1] => 5
[[4,1,1,1,1],[]] => [4,1,1,1,1] => [5,1,1,1] => 4
[[3,3,2],[]] => [3,3,2] => [3,3,2] => 5
[[3,3,1,1],[]] => [3,3,1,1] => [4,2,2] => 9
[[3,2,2,1],[]] => [3,2,2,1] => [4,3,1] => 10
[[3,2,1,1,1],[]] => [3,2,1,1,1] => [5,2,1] => 12
[[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => [6,1,1] => 11
[[2,2,2,2],[]] => [2,2,2,2] => [4,4] => 19
[[2,2,2,1,1],[]] => [2,2,2,1,1] => [5,3] => 27
[[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => [6,2] => 37
[[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1] => [7,1] => 33
[[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => [8] => 116
[[9],[]] => [9] => [1,1,1,1,1,1,1,1,1] => 1
[[8,1],[]] => [8,1] => [2,1,1,1,1,1,1,1] => 1
[[7,2],[]] => [7,2] => [2,2,1,1,1,1,1] => 1
[[7,1,1],[]] => [7,1,1] => [3,1,1,1,1,1,1] => 1
[[6,3],[]] => [6,3] => [2,2,2,1,1,1] => 1
[[6,2,1],[]] => [6,2,1] => [3,2,1,1,1,1] => 2
[[6,1,1,1],[]] => [6,1,1,1] => [4,1,1,1,1,1] => 2
[[5,4],[]] => [5,4] => [2,2,2,2,1] => 1
[[5,3,1],[]] => [5,3,1] => [3,2,2,1,1] => 3
[[5,2,2],[]] => [5,2,2] => [3,3,1,1,1] => 2
[[5,2,1,1],[]] => [5,2,1,1] => [4,2,1,1,1] => 5
[[5,1,1,1,1],[]] => [5,1,1,1,1] => [5,1,1,1,1] => 4
[[4,4,1],[]] => [4,4,1] => [3,2,2,2] => 4
[[4,3,2],[]] => [4,3,2] => [3,3,2,1] => 5
[[4,3,1,1],[]] => [4,3,1,1] => [4,2,2,1] => 9
[[4,2,2,1],[]] => [4,2,2,1] => [4,3,1,1] => 10
[[4,2,1,1,1],[]] => [4,2,1,1,1] => [5,2,1,1] => 12
[[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => [6,1,1,1] => 11
[[3,3,3],[]] => [3,3,3] => [3,3,3] => 5
[[3,3,2,1],[]] => [3,3,2,1] => [4,3,2] => 28
[[3,3,1,1,1],[]] => [3,3,1,1,1] => [5,2,2] => 25
[[3,2,2,2],[]] => [3,2,2,2] => [4,4,1] => 19
[[3,2,2,1,1],[]] => [3,2,2,1,1] => [5,3,1] => 27
[[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => [6,2,1] => 37
[[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1] => [7,1,1] => 33
[[2,2,2,2,1],[]] => [2,2,2,2,1] => [5,4] => 99
[[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => [6,3] => 97
[[2,2,1,1,1,1,1],[]] => [2,2,1,1,1,1,1] => [7,2] => 123
[[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1] => [8,1] => 116
[[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => [9] => 435
[[10],[]] => [10] => [1,1,1,1,1,1,1,1,1,1] => 1
[[9,1],[]] => [9,1] => [2,1,1,1,1,1,1,1,1] => 1
[[8,2],[]] => [8,2] => [2,2,1,1,1,1,1,1] => 1
[[8,1,1],[]] => [8,1,1] => [3,1,1,1,1,1,1,1] => 1
[[7,3],[]] => [7,3] => [2,2,2,1,1,1,1] => 1
[[7,2,1],[]] => [7,2,1] => [3,2,1,1,1,1,1] => 2
[[7,1,1,1],[]] => [7,1,1,1] => [4,1,1,1,1,1,1] => 2
[[6,4],[]] => [6,4] => [2,2,2,2,1,1] => 1
[[6,3,1],[]] => [6,3,1] => [3,2,2,1,1,1] => 3
[[6,2,2],[]] => [6,2,2] => [3,3,1,1,1,1] => 2
[[6,2,1,1],[]] => [6,2,1,1] => [4,2,1,1,1,1] => 5
[[6,1,1,1,1],[]] => [6,1,1,1,1] => [5,1,1,1,1,1] => 4
[[5,5],[]] => [5,5] => [2,2,2,2,2] => 1
[[5,4,1],[]] => [5,4,1] => [3,2,2,2,1] => 4
[[5,3,2],[]] => [5,3,2] => [3,3,2,1,1] => 5
[[5,3,1,1],[]] => [5,3,1,1] => [4,2,2,1,1] => 9
[[5,2,2,1],[]] => [5,2,2,1] => [4,3,1,1,1] => 10
[[5,2,1,1,1],[]] => [5,2,1,1,1] => [5,2,1,1,1] => 12
[[5,1,1,1,1,1],[]] => [5,1,1,1,1,1] => [6,1,1,1,1] => 11
[[4,4,2],[]] => [4,4,2] => [3,3,2,2] => 9
[[4,4,1,1],[]] => [4,4,1,1] => [4,2,2,2] => 14
[[4,3,3],[]] => [4,3,3] => [3,3,3,1] => 5
[[4,3,2,1],[]] => [4,3,2,1] => [4,3,2,1] => 28
[[4,3,1,1,1],[]] => [4,3,1,1,1] => [5,2,2,1] => 25
[[4,2,2,2],[]] => [4,2,2,2] => [4,4,1,1] => 19
[[4,2,2,1,1],[]] => [4,2,2,1,1] => [5,3,1,1] => 27
[[4,2,1,1,1,1],[]] => [4,2,1,1,1,1] => [6,2,1,1] => 37
[[4,1,1,1,1,1,1],[]] => [4,1,1,1,1,1,1] => [7,1,1,1] => 33
[[3,3,3,1],[]] => [3,3,3,1] => [4,3,3] => 42
[[3,3,2,2],[]] => [3,3,2,2] => [4,4,2] => 61
[[3,3,2,1,1],[]] => [3,3,2,1,1] => [5,3,2] => 89
[[3,3,1,1,1,1],[]] => [3,3,1,1,1,1] => [6,2,2] => 85
[[3,2,2,2,1],[]] => [3,2,2,2,1] => [5,4,1] => 99
[[3,2,2,1,1,1],[]] => [3,2,2,1,1,1] => [6,3,1] => 97
[[3,2,1,1,1,1,1],[]] => [3,2,1,1,1,1,1] => [7,2,1] => 123
[[3,1,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1,1] => [8,1,1] => 116
[[2,2,2,2,2],[]] => [2,2,2,2,2] => [5,5] => 188
[[2,2,2,2,1,1],[]] => [2,2,2,2,1,1] => [6,4] => 384
[[2,2,2,1,1,1,1],[]] => [2,2,2,1,1,1,1] => [7,3] => 351
[[2,2,1,1,1,1,1,1],[]] => [2,2,1,1,1,1,1,1] => [8,2] => 474
[[2,1,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1,1] => [9,1] => 435
[[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1] => [10] => 1832
[[6,5],[]] => [6,5] => [2,2,2,2,2,1] => 1
[[5,5,1],[]] => [5,5,1] => [3,2,2,2,2] => 5
[[5,4,2],[]] => [5,4,2] => [3,3,2,2,1] => 9
[[5,3,3],[]] => [5,3,3] => [3,3,3,1,1] => 5
[[4,4,3],[]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,2,1],[]] => [4,4,2,1] => [4,3,2,2] => 56
[[4,3,3,1],[]] => [4,3,3,1] => [4,3,3,1] => 42
[[4,3,2,2],[]] => [4,3,2,2] => [4,4,2,1] => 61
[[3,3,3,2],[]] => [3,3,3,2] => [4,4,3] => 159
[[3,2,2,2,2],[]] => [3,2,2,2,2] => [5,5,1] => 188
[[6,6],[]] => [6,6] => [2,2,2,2,2,2] => 1
[[5,5,2],[]] => [5,5,2] => [3,3,2,2,2] => 14
[[5,4,3],[]] => [5,4,3] => [3,3,3,2,1] => 14
[[4,4,4],[]] => [4,4,4] => [3,3,3,3] => 14
[[4,4,3,1],[]] => [4,4,3,1] => [4,3,3,2] => 126
[[4,4,2,2],[]] => [4,4,2,2] => [4,4,2,2] => 137
[[4,3,3,2],[]] => [4,3,3,2] => [4,4,3,1] => 159
[[3,3,3,3],[]] => [3,3,3,3] => [4,4,4] => 296
[[3,3,3,2,1],[]] => [3,3,3,2,1] => [5,4,3] => 982
[[3,3,2,2,2],[]] => [3,3,2,2,2] => [5,5,2] => 740
[[2,2,2,2,2,2],[]] => [2,2,2,2,2,2] => [6,6] => 3533
[[4,4,3,2],[]] => [4,4,3,2] => [4,4,3,2] => 518
[[3,3,3],[1]] => [3,3,2] => [3,3,2] => 5
[[3,3,3,1],[1,1]] => [3,3,2] => [3,3,2] => 5
[[4,4,1],[1]] => [4,4] => [2,2,2,2] => 1
[[3,3,2,1],[1]] => [3,3,2] => [3,3,2] => 5
[[2,2,2,2,1],[1]] => [2,2,2,2] => [4,4] => 19
[[3,3,3,1],[2]] => [3,3,2] => [3,3,2] => 5
[[3,3,3,1],[1]] => [3,3,3] => [3,3,3] => 5
[[3,3,3,2],[1,1,1]] => [3,2,2,1] => [4,3,1] => 10
[[4,4,2],[1,1]] => [4,3,1] => [3,2,2,1] => 3
[[4,4,4],[2,2]] => [4,2,2] => [3,3,1,1] => 2
[[5,5],[2]] => [5,3] => [2,2,2,1,1] => 1
[[4,4,3],[2,1]] => [4,3,1] => [3,2,2,1] => 3
[[3,3,3,3],[2,1,1]] => [3,2,2,1] => [4,3,1] => 10
[[4,3,3],[1,1]] => [4,2,2] => [3,3,1,1] => 2
[[3,3,3,3],[1,1,1]] => [3,2,2,2] => [4,4,1] => 19
[[4,4,3],[1,1]] => [4,3,2] => [3,3,2,1] => 5
[[4,4,4],[3,1]] => [4,3,1] => [3,2,2,1] => 3
[[5,4],[1]] => [5,3] => [2,2,2,1,1] => 1
[[4,4,4],[2,1]] => [4,3,2] => [3,3,2,1] => 5
[[5,5],[1]] => [5,4] => [2,2,2,2,1] => 1
[[4,4,4],[1,1]] => [4,3,3] => [3,3,3,1] => 5
[[3,3,2,2],[1,1]] => [3,3,1,1] => [4,2,2] => 9
[[4,4,2],[2]] => [4,4] => [2,2,2,2] => 1
[[3,3,3,2],[2,1]] => [3,3,2] => [3,3,2] => 5
[[4,3,2],[1]] => [4,3,1] => [3,2,2,1] => 3
[[3,3,3,2],[1,1]] => [3,3,2,1] => [4,3,2] => 28
[[4,4,2],[1]] => [4,4,1] => [3,2,2,2] => 4
[[2,2,2,2,2],[1,1]] => [2,2,2,1,1] => [5,3] => 27
[[3,2,2,2],[1]] => [3,2,2,1] => [4,3,1] => 10
[[3,3,2,2],[2]] => [3,3,2] => [3,3,2] => 5
[[3,3,2,2],[1]] => [3,3,2,1] => [4,3,2] => 28
[[2,2,2,2,2],[1]] => [2,2,2,2,1] => [5,4] => 99
[[3,3,3,2],[2]] => [3,3,3] => [3,3,3] => 5
[[3,3,3,2],[1]] => [3,3,3,1] => [4,3,3] => 42
[[3,3,3,3],[2,2]] => [3,3,1,1] => [4,2,2] => 9
[[4,3,3],[2]] => [4,3,1] => [3,2,2,1] => 3
[[4,4,3],[3]] => [4,4] => [2,2,2,2] => 1
[[4,4,3],[2]] => [4,4,1] => [3,2,2,2] => 4
[[3,3,3,3],[2,1]] => [3,3,2,1] => [4,3,2] => 28
[[4,3,3],[1]] => [4,3,2] => [3,3,2,1] => 5
[[3,3,3,3],[1,1]] => [3,3,2,2] => [4,4,2] => 61
[[4,4,3],[1]] => [4,4,2] => [3,3,2,2] => 9
[[4,4,4],[3]] => [4,4,1] => [3,2,2,2] => 4
[[4,4,4],[2]] => [4,4,2] => [3,3,2,2] => 9
[[4,4,4],[1]] => [4,4,3] => [3,3,3,2] => 14
[[3,3,3,3],[2]] => [3,3,3,1] => [4,3,3] => 42
[[3,3,3,3],[1]] => [3,3,3,2] => [4,4,3] => 159
[[4,4,4,1],[1,1]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,3,1],[1]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,4,1],[2]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,4,1],[1]] => [4,4,4] => [3,3,3,3] => 14
[[3,3,3,3,1],[1]] => [3,3,3,3] => [4,4,4] => 296
[[4,4,4,2],[1,1,1]] => [4,3,3,1] => [4,3,3,1] => 42
[[6,6],[4]] => [6,2] => [2,2,1,1,1,1] => 1
[[6,5],[3]] => [6,2] => [2,2,1,1,1,1] => 1
[[5,5,5],[3,3]] => [5,2,2] => [3,3,1,1,1] => 2
[[6,6],[3]] => [6,3] => [2,2,2,1,1,1] => 1
[[6,4],[2]] => [6,2] => [2,2,1,1,1,1] => 1
[[5,5,4],[3,2]] => [5,3,1] => [3,2,2,1,1] => 3
[[5,4,4],[2,2]] => [5,2,2] => [3,3,1,1,1] => 2
[[4,4,4,4],[2,2,2]] => [4,2,2,2] => [4,4,1,1] => 19
[[5,5,4],[2,2]] => [5,3,2] => [3,3,2,1,1] => 5
[[6,5],[2]] => [6,3] => [2,2,2,1,1,1] => 1
[[5,5,5],[3,2]] => [5,3,2] => [3,3,2,1,1] => 5
[[6,6],[2]] => [6,4] => [2,2,2,2,1,1] => 1
[[5,5,5],[2,2]] => [5,3,3] => [3,3,3,1,1] => 5
[[6,3],[1]] => [6,2] => [2,2,1,1,1,1] => 1
[[5,5,3],[3,1]] => [5,4] => [2,2,2,2,1] => 1
[[5,4,3],[2,1]] => [5,3,1] => [3,2,2,1,1] => 3
[[4,4,4,3],[2,2,1]] => [4,3,2,1] => [4,3,2,1] => 28
[[5,5,3],[2,1]] => [5,4,1] => [3,2,2,2,1] => 4
[[5,3,3],[1,1]] => [5,2,2] => [3,3,1,1,1] => 2
[[4,4,3,3],[2,1,1]] => [4,3,2,1] => [4,3,2,1] => 28
[[4,3,3,3],[1,1,1]] => [4,2,2,2] => [4,4,1,1] => 19
[[3,3,3,3,3],[1,1,1,1]] => [3,2,2,2,2] => [5,5,1] => 188
[[4,4,3,3],[1,1,1]] => [4,3,2,2] => [4,4,2,1] => 61
[[5,4,3],[1,1]] => [5,3,2] => [3,3,2,1,1] => 5
[[4,4,4,3],[2,1,1]] => [4,3,3,1] => [4,3,3,1] => 42
[[5,5,3],[1,1]] => [5,4,2] => [3,3,2,2,1] => 9
[[4,4,4,3],[1,1,1]] => [4,3,3,2] => [4,4,3,1] => 159
[[6,4],[1]] => [6,3] => [2,2,2,1,1,1] => 1
[[5,5,4],[3,1]] => [5,4,1] => [3,2,2,2,1] => 4
[[5,4,4],[2,1]] => [5,3,2] => [3,3,2,1,1] => 5
[[4,4,4,4],[2,2,1]] => [4,3,2,2] => [4,4,2,1] => 61
[[5,5,4],[2,1]] => [5,4,2] => [3,3,2,2,1] => 9
[[6,5],[1]] => [6,4] => [2,2,2,2,1,1] => 1
[[5,5,5],[3,1]] => [5,4,2] => [3,3,2,2,1] => 9
[[6,6],[1]] => [6,5] => [2,2,2,2,2,1] => 1
[[5,5,5],[2,1]] => [5,4,3] => [3,3,3,2,1] => 14
[[4,4,4,4],[3,1,1]] => [4,3,3,1] => [4,3,3,1] => 42
[[5,4,4],[1,1]] => [5,3,3] => [3,3,3,1,1] => 5
[[4,4,4,4],[2,1,1]] => [4,3,3,2] => [4,4,3,1] => 159
[[5,5,4],[1,1]] => [5,4,3] => [3,3,3,2,1] => 14
[[5,5,2],[3]] => [5,4] => [2,2,2,2,1] => 1
[[5,4,2],[2]] => [5,4] => [2,2,2,2,1] => 1
[[4,4,4,2],[2,2]] => [4,4,2] => [3,3,2,2] => 9
[[5,5,2],[2]] => [5,5] => [2,2,2,2,2] => 1
[[5,3,2],[1]] => [5,3,1] => [3,2,2,1,1] => 3
[[4,4,3,2],[2,1]] => [4,4,2] => [3,3,2,2] => 9
[[4,3,3,2],[1,1]] => [4,3,2,1] => [4,3,2,1] => 28
[[3,3,3,3,2],[1,1,1]] => [3,3,2,2,1] => [5,4,2] => 349
[[4,4,3,2],[1,1]] => [4,4,2,1] => [4,3,2,2] => 56
[[5,4,2],[1]] => [5,4,1] => [3,2,2,2,1] => 4
[[4,4,4,2],[2,1]] => [4,4,3] => [3,3,3,2] => 14
[[5,5,2],[1]] => [5,5,1] => [3,2,2,2,2] => 5
[[4,4,4,2],[1,1]] => [4,4,3,1] => [4,3,3,2] => 126
[[4,4,2,2],[2]] => [4,4,2] => [3,3,2,2] => 9
[[4,3,2,2],[1]] => [4,3,2,1] => [4,3,2,1] => 28
[[3,3,3,2,2],[1,1]] => [3,3,3,1,1] => [5,3,3] => 145
[[4,4,2,2],[1]] => [4,4,2,1] => [4,3,2,2] => 56
[[3,3,2,2,2],[1]] => [3,3,2,2,1] => [5,4,2] => 349
[[3,3,3,2,2],[1]] => [3,3,3,2,1] => [5,4,3] => 982
[[4,4,3,2],[2]] => [4,4,3] => [3,3,3,2] => 14
[[4,3,3,2],[1]] => [4,3,3,1] => [4,3,3,1] => 42
[[3,3,3,3,2],[1,1]] => [3,3,3,2,1] => [5,4,3] => 982
[[4,4,3,2],[1]] => [4,4,3,1] => [4,3,3,2] => 126
[[4,4,4,2],[3]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,4,2],[2]] => [4,4,4] => [3,3,3,3] => 14
[[3,3,3,3,2],[2]] => [3,3,3,3] => [4,4,4] => 296
[[5,5,3],[3]] => [5,5] => [2,2,2,2,2] => 1
[[5,4,3],[2]] => [5,4,1] => [3,2,2,2,1] => 4
[[4,4,4,3],[2,2]] => [4,4,2,1] => [4,3,2,2] => 56
[[5,5,3],[2]] => [5,5,1] => [3,2,2,2,2] => 5
[[5,3,3],[1]] => [5,3,2] => [3,3,2,1,1] => 5
[[4,4,3,3],[2,1]] => [4,4,2,1] => [4,3,2,2] => 56
[[4,3,3,3],[1,1]] => [4,3,2,2] => [4,4,2,1] => 61
[[3,3,3,3,3],[1,1,1]] => [3,3,2,2,2] => [5,5,2] => 740
[[4,4,3,3],[1,1]] => [4,4,2,2] => [4,4,2,2] => 137
[[4,4,4,3],[3,1]] => [4,4,3] => [3,3,3,2] => 14
[[5,4,3],[1]] => [5,4,2] => [3,3,2,2,1] => 9
[[4,4,4,3],[2,1]] => [4,4,3,1] => [4,3,3,2] => 126
[[5,5,3],[1]] => [5,5,2] => [3,3,2,2,2] => 14
[[4,4,4,3],[1,1]] => [4,4,3,2] => [4,4,3,2] => 518
[[5,5,4],[3]] => [5,5,1] => [3,2,2,2,2] => 5
[[4,4,4,4],[3,2]] => [4,4,2,1] => [4,3,2,2] => 56
[[5,4,4],[2]] => [5,4,2] => [3,3,2,2,1] => 9
[[4,4,4,4],[2,2]] => [4,4,2,2] => [4,4,2,2] => 137
[[5,5,4],[2]] => [5,5,2] => [3,3,2,2,2] => 14
[[5,5,5],[4]] => [5,5,1] => [3,2,2,2,2] => 5
[[5,5,5],[3]] => [5,5,2] => [3,3,2,2,2] => 14
[[4,4,4,4],[3,1]] => [4,4,3,1] => [4,3,3,2] => 126
[[5,4,4],[1]] => [5,4,3] => [3,3,3,2,1] => 14
[[4,4,4,4],[2,1]] => [4,4,3,2] => [4,4,3,2] => 518
[[4,3,3,3],[2]] => [4,3,3,1] => [4,3,3,1] => 42
[[4,4,3,3],[3]] => [4,4,3] => [3,3,3,2] => 14
[[4,4,3,3],[2]] => [4,4,3,1] => [4,3,3,2] => 126
[[3,3,3,3,3],[2,1]] => [3,3,3,2,1] => [5,4,3] => 982
[[4,3,3,3],[1]] => [4,3,3,2] => [4,4,3,1] => 159
[[4,4,3,3],[1]] => [4,4,3,2] => [4,4,3,2] => 518
[[4,4,4,3],[3]] => [4,4,4] => [3,3,3,3] => 14
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
27,1 76,10,0,1 213,48,0,4,6,0,0,0,0,0,1 588,172,27,12,32,0,0,0,0,8,4,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
$F_{1} = q$
$F_{2} = 3\ q$
$F_{3} = 9\ q$
$F_{4} = 27\ q + q^{2}$
$F_{5} = 76\ q + 10\ q^{2} + q^{4}$
$F_{6} = 213\ q + 48\ q^{2} + 4\ q^{4} + 6\ q^{5} + q^{11}$
$F_{7} = 588\ q + 172\ q^{2} + 27\ q^{3} + 12\ q^{4} + 32\ q^{5} + 8\ q^{10} + 4\ q^{11} + 6\ q^{12} + q^{33}$
Description
The number of ways to refine the partition into singletons.
For example there is only one way to refine $[2,2]$: $[2,2] > [2,1,1] > [1,1,1,1]$. However, there are two ways to refine $[3,2]$: $[3,2] > [2,2,1] > [2,1,1,1] > [1,1,1,1,1$ and $[3,2] > [3,1,1] > [2,1,1,1] > [1,1,1,1,1]$.
In other words, this is the number of saturated chains in the refinement order from the bottom element to the given partition.
The sequence of values on the partitions with only one part is A002846.
For example there is only one way to refine $[2,2]$: $[2,2] > [2,1,1] > [1,1,1,1]$. However, there are two ways to refine $[3,2]$: $[3,2] > [2,2,1] > [2,1,1,1] > [1,1,1,1,1$ and $[3,2] > [3,1,1] > [2,1,1,1] > [1,1,1,1,1]$.
In other words, this is the number of saturated chains in the refinement order from the bottom element to the given partition.
The sequence of values on the partitions with only one part is A002846.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
dominating partition
Description
The dominating partition in the Schur expansion.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$ s_{331/2} = s_{311} + s_{32}, $$
and the partition $32$ dominates $311$.
Consider the expansion of the skew Schur function $s_{\lambda/\mu}=\sum_\nu c^\lambda_{\mu, \nu} s_\nu$ as a linear combination of straight Schur functions.
It is shown in [1] that the partitions $\nu$ with $c^\lambda_{\mu, \nu} > 0$ form a sublattice of the dominance order and that its top element is the conjugate of the partition formed by sorting the column lengths of $\lambda / \mu$ into decreasing order.
This map returns the largest partition $\nu$ in dominance order for which $c^\lambda_{\mu, \nu}$ is positive.
For example,
$$ s_{331/2} = s_{311} + s_{32}, $$
and the partition $32$ dominates $311$.
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