Identifier
Mp00181:
Skew partitions
—row lengths⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00315: Integer compositions —inverse Foata bijection⟶ Integer compositions
Images
[[1],[]] => [1] => [1] => [1]
[[2],[]] => [2] => [1] => [1]
[[1,1],[]] => [1,1] => [2] => [2]
[[2,1],[1]] => [1,1] => [2] => [2]
[[3],[]] => [3] => [1] => [1]
[[2,1],[]] => [2,1] => [1,1] => [1,1]
[[3,1],[1]] => [2,1] => [1,1] => [1,1]
[[2,2],[1]] => [1,2] => [1,1] => [1,1]
[[3,2],[2]] => [1,2] => [1,1] => [1,1]
[[1,1,1],[]] => [1,1,1] => [3] => [3]
[[2,2,1],[1,1]] => [1,1,1] => [3] => [3]
[[2,1,1],[1]] => [1,1,1] => [3] => [3]
[[3,2,1],[2,1]] => [1,1,1] => [3] => [3]
[[4],[]] => [4] => [1] => [1]
[[3,1],[]] => [3,1] => [1,1] => [1,1]
[[4,1],[1]] => [3,1] => [1,1] => [1,1]
[[2,2],[]] => [2,2] => [2] => [2]
[[3,2],[1]] => [2,2] => [2] => [2]
[[4,2],[2]] => [2,2] => [2] => [2]
[[2,1,1],[]] => [2,1,1] => [1,2] => [1,2]
[[3,2,1],[1,1]] => [2,1,1] => [1,2] => [1,2]
[[3,1,1],[1]] => [2,1,1] => [1,2] => [1,2]
[[4,2,1],[2,1]] => [2,1,1] => [1,2] => [1,2]
[[3,3],[2]] => [1,3] => [1,1] => [1,1]
[[4,3],[3]] => [1,3] => [1,1] => [1,1]
[[2,2,1],[1]] => [1,2,1] => [1,1,1] => [1,1,1]
[[3,3,1],[2,1]] => [1,2,1] => [1,1,1] => [1,1,1]
[[3,2,1],[2]] => [1,2,1] => [1,1,1] => [1,1,1]
[[4,3,1],[3,1]] => [1,2,1] => [1,1,1] => [1,1,1]
[[2,2,2],[1,1]] => [1,1,2] => [2,1] => [2,1]
[[3,3,2],[2,2]] => [1,1,2] => [2,1] => [2,1]
[[3,2,2],[2,1]] => [1,1,2] => [2,1] => [2,1]
[[4,3,2],[3,2]] => [1,1,2] => [2,1] => [2,1]
[[1,1,1,1],[]] => [1,1,1,1] => [4] => [4]
[[2,2,2,1],[1,1,1]] => [1,1,1,1] => [4] => [4]
[[2,2,1,1],[1,1]] => [1,1,1,1] => [4] => [4]
[[3,3,2,1],[2,2,1]] => [1,1,1,1] => [4] => [4]
[[2,1,1,1],[1]] => [1,1,1,1] => [4] => [4]
[[3,2,2,1],[2,1,1]] => [1,1,1,1] => [4] => [4]
[[3,2,1,1],[2,1]] => [1,1,1,1] => [4] => [4]
[[4,3,2,1],[3,2,1]] => [1,1,1,1] => [4] => [4]
[[5],[]] => [5] => [1] => [1]
[[4,1],[]] => [4,1] => [1,1] => [1,1]
[[5,1],[1]] => [4,1] => [1,1] => [1,1]
[[3,2],[]] => [3,2] => [1,1] => [1,1]
[[4,2],[1]] => [3,2] => [1,1] => [1,1]
[[5,2],[2]] => [3,2] => [1,1] => [1,1]
[[3,1,1],[]] => [3,1,1] => [1,2] => [1,2]
[[4,2,1],[1,1]] => [3,1,1] => [1,2] => [1,2]
[[4,1,1],[1]] => [3,1,1] => [1,2] => [1,2]
[[5,2,1],[2,1]] => [3,1,1] => [1,2] => [1,2]
[[3,3],[1]] => [2,3] => [1,1] => [1,1]
[[4,3],[2]] => [2,3] => [1,1] => [1,1]
[[5,3],[3]] => [2,3] => [1,1] => [1,1]
[[2,2,1],[]] => [2,2,1] => [2,1] => [2,1]
[[3,3,1],[1,1]] => [2,2,1] => [2,1] => [2,1]
[[3,2,1],[1]] => [2,2,1] => [2,1] => [2,1]
[[4,3,1],[2,1]] => [2,2,1] => [2,1] => [2,1]
[[4,2,1],[2]] => [2,2,1] => [2,1] => [2,1]
[[5,3,1],[3,1]] => [2,2,1] => [2,1] => [2,1]
[[3,2,2],[1,1]] => [2,1,2] => [1,1,1] => [1,1,1]
[[4,3,2],[2,2]] => [2,1,2] => [1,1,1] => [1,1,1]
[[4,2,2],[2,1]] => [2,1,2] => [1,1,1] => [1,1,1]
[[5,3,2],[3,2]] => [2,1,2] => [1,1,1] => [1,1,1]
[[2,1,1,1],[]] => [2,1,1,1] => [1,3] => [1,3]
[[3,2,2,1],[1,1,1]] => [2,1,1,1] => [1,3] => [1,3]
[[3,2,1,1],[1,1]] => [2,1,1,1] => [1,3] => [1,3]
[[4,3,2,1],[2,2,1]] => [2,1,1,1] => [1,3] => [1,3]
[[3,1,1,1],[1]] => [2,1,1,1] => [1,3] => [1,3]
[[4,2,2,1],[2,1,1]] => [2,1,1,1] => [1,3] => [1,3]
[[4,2,1,1],[2,1]] => [2,1,1,1] => [1,3] => [1,3]
[[5,3,2,1],[3,2,1]] => [2,1,1,1] => [1,3] => [1,3]
[[4,4],[3]] => [1,4] => [1,1] => [1,1]
[[5,4],[4]] => [1,4] => [1,1] => [1,1]
[[3,3,1],[2]] => [1,3,1] => [1,1,1] => [1,1,1]
[[4,4,1],[3,1]] => [1,3,1] => [1,1,1] => [1,1,1]
[[4,3,1],[3]] => [1,3,1] => [1,1,1] => [1,1,1]
[[5,4,1],[4,1]] => [1,3,1] => [1,1,1] => [1,1,1]
[[2,2,2],[1]] => [1,2,2] => [1,2] => [1,2]
[[3,3,2],[2,1]] => [1,2,2] => [1,2] => [1,2]
[[4,4,2],[3,2]] => [1,2,2] => [1,2] => [1,2]
[[3,2,2],[2]] => [1,2,2] => [1,2] => [1,2]
[[4,3,2],[3,1]] => [1,2,2] => [1,2] => [1,2]
[[5,4,2],[4,2]] => [1,2,2] => [1,2] => [1,2]
[[2,2,1,1],[1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[3,3,2,1],[2,1,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[3,3,1,1],[2,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[4,4,2,1],[3,2,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[3,2,1,1],[2]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[4,3,2,1],[3,1,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[4,3,1,1],[3,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[5,4,2,1],[4,2,1]] => [1,2,1,1] => [1,1,2] => [1,1,2]
[[3,3,3],[2,2]] => [1,1,3] => [2,1] => [2,1]
[[4,4,3],[3,3]] => [1,1,3] => [2,1] => [2,1]
[[4,3,3],[3,2]] => [1,1,3] => [2,1] => [2,1]
[[5,4,3],[4,3]] => [1,1,3] => [2,1] => [2,1]
[[2,2,2,1],[1,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[3,3,3,1],[2,2,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[3,3,2,1],[2,2]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[4,4,3,1],[3,3,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[3,2,2,1],[2,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
>>> Load all 1478 entries. <<<
[[4,3,3,1],[3,2,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[4,3,2,1],[3,2]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[5,4,3,1],[4,3,1]] => [1,1,2,1] => [2,1,1] => [1,2,1]
[[2,2,2,2],[1,1,1]] => [1,1,1,2] => [3,1] => [3,1]
[[3,3,3,2],[2,2,2]] => [1,1,1,2] => [3,1] => [3,1]
[[3,3,2,2],[2,2,1]] => [1,1,1,2] => [3,1] => [3,1]
[[4,4,3,2],[3,3,2]] => [1,1,1,2] => [3,1] => [3,1]
[[3,2,2,2],[2,1,1]] => [1,1,1,2] => [3,1] => [3,1]
[[4,3,3,2],[3,2,2]] => [1,1,1,2] => [3,1] => [3,1]
[[4,3,2,2],[3,2,1]] => [1,1,1,2] => [3,1] => [3,1]
[[5,4,3,2],[4,3,2]] => [1,1,1,2] => [3,1] => [3,1]
[[1,1,1,1,1],[]] => [1,1,1,1,1] => [5] => [5]
[[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,1] => [5] => [5]
[[2,2,2,1,1],[1,1,1]] => [1,1,1,1,1] => [5] => [5]
[[3,3,3,2,1],[2,2,2,1]] => [1,1,1,1,1] => [5] => [5]
[[2,2,1,1,1],[1,1]] => [1,1,1,1,1] => [5] => [5]
[[3,3,2,2,1],[2,2,1,1]] => [1,1,1,1,1] => [5] => [5]
[[3,3,2,1,1],[2,2,1]] => [1,1,1,1,1] => [5] => [5]
[[4,4,3,2,1],[3,3,2,1]] => [1,1,1,1,1] => [5] => [5]
[[2,1,1,1,1],[1]] => [1,1,1,1,1] => [5] => [5]
[[3,2,2,2,1],[2,1,1,1]] => [1,1,1,1,1] => [5] => [5]
[[3,2,2,1,1],[2,1,1]] => [1,1,1,1,1] => [5] => [5]
[[4,3,3,2,1],[3,2,2,1]] => [1,1,1,1,1] => [5] => [5]
[[3,2,1,1,1],[2,1]] => [1,1,1,1,1] => [5] => [5]
[[4,3,2,2,1],[3,2,1,1]] => [1,1,1,1,1] => [5] => [5]
[[4,3,2,1,1],[3,2,1]] => [1,1,1,1,1] => [5] => [5]
[[5,4,3,2,1],[4,3,2,1]] => [1,1,1,1,1] => [5] => [5]
[[6],[]] => [6] => [1] => [1]
[[5,1],[]] => [5,1] => [1,1] => [1,1]
[[6,1],[1]] => [5,1] => [1,1] => [1,1]
[[4,2],[]] => [4,2] => [1,1] => [1,1]
[[5,2],[1]] => [4,2] => [1,1] => [1,1]
[[6,2],[2]] => [4,2] => [1,1] => [1,1]
[[4,1,1],[]] => [4,1,1] => [1,2] => [1,2]
[[5,2,1],[1,1]] => [4,1,1] => [1,2] => [1,2]
[[5,1,1],[1]] => [4,1,1] => [1,2] => [1,2]
[[6,2,1],[2,1]] => [4,1,1] => [1,2] => [1,2]
[[3,3],[]] => [3,3] => [2] => [2]
[[4,3],[1]] => [3,3] => [2] => [2]
[[5,3],[2]] => [3,3] => [2] => [2]
[[6,3],[3]] => [3,3] => [2] => [2]
[[3,2,1],[]] => [3,2,1] => [1,1,1] => [1,1,1]
[[4,3,1],[1,1]] => [3,2,1] => [1,1,1] => [1,1,1]
[[4,2,1],[1]] => [3,2,1] => [1,1,1] => [1,1,1]
[[5,3,1],[2,1]] => [3,2,1] => [1,1,1] => [1,1,1]
[[5,2,1],[2]] => [3,2,1] => [1,1,1] => [1,1,1]
[[6,3,1],[3,1]] => [3,2,1] => [1,1,1] => [1,1,1]
[[4,2,2],[1,1]] => [3,1,2] => [1,1,1] => [1,1,1]
[[5,3,2],[2,2]] => [3,1,2] => [1,1,1] => [1,1,1]
[[5,2,2],[2,1]] => [3,1,2] => [1,1,1] => [1,1,1]
[[6,3,2],[3,2]] => [3,1,2] => [1,1,1] => [1,1,1]
[[3,1,1,1],[]] => [3,1,1,1] => [1,3] => [1,3]
[[4,2,2,1],[1,1,1]] => [3,1,1,1] => [1,3] => [1,3]
[[4,2,1,1],[1,1]] => [3,1,1,1] => [1,3] => [1,3]
[[5,3,2,1],[2,2,1]] => [3,1,1,1] => [1,3] => [1,3]
[[4,1,1,1],[1]] => [3,1,1,1] => [1,3] => [1,3]
[[5,2,2,1],[2,1,1]] => [3,1,1,1] => [1,3] => [1,3]
[[5,2,1,1],[2,1]] => [3,1,1,1] => [1,3] => [1,3]
[[6,3,2,1],[3,2,1]] => [3,1,1,1] => [1,3] => [1,3]
[[4,4],[2]] => [2,4] => [1,1] => [1,1]
[[5,4],[3]] => [2,4] => [1,1] => [1,1]
[[6,4],[4]] => [2,4] => [1,1] => [1,1]
[[3,3,1],[1]] => [2,3,1] => [1,1,1] => [1,1,1]
[[4,4,1],[2,1]] => [2,3,1] => [1,1,1] => [1,1,1]
[[4,3,1],[2]] => [2,3,1] => [1,1,1] => [1,1,1]
[[5,4,1],[3,1]] => [2,3,1] => [1,1,1] => [1,1,1]
[[5,3,1],[3]] => [2,3,1] => [1,1,1] => [1,1,1]
[[6,4,1],[4,1]] => [2,3,1] => [1,1,1] => [1,1,1]
[[2,2,2],[]] => [2,2,2] => [3] => [3]
[[3,3,2],[1,1]] => [2,2,2] => [3] => [3]
[[4,4,2],[2,2]] => [2,2,2] => [3] => [3]
[[3,2,2],[1]] => [2,2,2] => [3] => [3]
[[4,3,2],[2,1]] => [2,2,2] => [3] => [3]
[[5,4,2],[3,2]] => [2,2,2] => [3] => [3]
[[4,2,2],[2]] => [2,2,2] => [3] => [3]
[[5,3,2],[3,1]] => [2,2,2] => [3] => [3]
[[6,4,2],[4,2]] => [2,2,2] => [3] => [3]
[[2,2,1,1],[]] => [2,2,1,1] => [2,2] => [2,2]
[[3,3,2,1],[1,1,1]] => [2,2,1,1] => [2,2] => [2,2]
[[3,3,1,1],[1,1]] => [2,2,1,1] => [2,2] => [2,2]
[[4,4,2,1],[2,2,1]] => [2,2,1,1] => [2,2] => [2,2]
[[3,2,1,1],[1]] => [2,2,1,1] => [2,2] => [2,2]
[[4,3,2,1],[2,1,1]] => [2,2,1,1] => [2,2] => [2,2]
[[4,3,1,1],[2,1]] => [2,2,1,1] => [2,2] => [2,2]
[[5,4,2,1],[3,2,1]] => [2,2,1,1] => [2,2] => [2,2]
[[4,2,1,1],[2]] => [2,2,1,1] => [2,2] => [2,2]
[[5,3,2,1],[3,1,1]] => [2,2,1,1] => [2,2] => [2,2]
[[5,3,1,1],[3,1]] => [2,2,1,1] => [2,2] => [2,2]
[[6,4,2,1],[4,2,1]] => [2,2,1,1] => [2,2] => [2,2]
[[4,3,3],[2,2]] => [2,1,3] => [1,1,1] => [1,1,1]
[[5,4,3],[3,3]] => [2,1,3] => [1,1,1] => [1,1,1]
[[5,3,3],[3,2]] => [2,1,3] => [1,1,1] => [1,1,1]
[[6,4,3],[4,3]] => [2,1,3] => [1,1,1] => [1,1,1]
[[3,2,2,1],[1,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,3,3,1],[2,2,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,3,2,1],[2,2]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,1],[3,3,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,2,2,1],[2,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,3,3,1],[3,2,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,3,2,1],[3,2]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,4,3,1],[4,3,1]] => [2,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[3,2,2,2],[1,1,1]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[4,3,3,2],[2,2,2]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[4,3,2,2],[2,2,1]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[5,4,3,2],[3,3,2]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[4,2,2,2],[2,1,1]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[5,3,3,2],[3,2,2]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[5,3,2,2],[3,2,1]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[6,4,3,2],[4,3,2]] => [2,1,1,2] => [1,2,1] => [2,1,1]
[[2,1,1,1,1],[]] => [2,1,1,1,1] => [1,4] => [1,4]
[[3,2,2,2,1],[1,1,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[3,2,2,1,1],[1,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,3,3,2,1],[2,2,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[3,2,1,1,1],[1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,3,2,2,1],[2,2,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,3,2,1,1],[2,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[5,4,3,2,1],[3,3,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[3,1,1,1,1],[1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,2,2,1,1],[2,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[5,3,3,2,1],[3,2,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[4,2,1,1,1],[2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[5,3,2,2,1],[3,2,1,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[5,3,2,1,1],[3,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[6,4,3,2,1],[4,3,2,1]] => [2,1,1,1,1] => [1,4] => [1,4]
[[5,5],[4]] => [1,5] => [1,1] => [1,1]
[[6,5],[5]] => [1,5] => [1,1] => [1,1]
[[4,4,1],[3]] => [1,4,1] => [1,1,1] => [1,1,1]
[[5,5,1],[4,1]] => [1,4,1] => [1,1,1] => [1,1,1]
[[5,4,1],[4]] => [1,4,1] => [1,1,1] => [1,1,1]
[[6,5,1],[5,1]] => [1,4,1] => [1,1,1] => [1,1,1]
[[3,3,2],[2]] => [1,3,2] => [1,1,1] => [1,1,1]
[[4,4,2],[3,1]] => [1,3,2] => [1,1,1] => [1,1,1]
[[5,5,2],[4,2]] => [1,3,2] => [1,1,1] => [1,1,1]
[[4,3,2],[3]] => [1,3,2] => [1,1,1] => [1,1,1]
[[5,4,2],[4,1]] => [1,3,2] => [1,1,1] => [1,1,1]
[[6,5,2],[5,2]] => [1,3,2] => [1,1,1] => [1,1,1]
[[3,3,1,1],[2]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[4,4,2,1],[3,1,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[4,4,1,1],[3,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[5,5,2,1],[4,2,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[4,3,1,1],[3]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[5,4,2,1],[4,1,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[5,4,1,1],[4,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[6,5,2,1],[5,2,1]] => [1,3,1,1] => [1,1,2] => [1,1,2]
[[3,3,3],[2,1]] => [1,2,3] => [1,1,1] => [1,1,1]
[[4,4,3],[3,2]] => [1,2,3] => [1,1,1] => [1,1,1]
[[5,5,3],[4,3]] => [1,2,3] => [1,1,1] => [1,1,1]
[[4,3,3],[3,1]] => [1,2,3] => [1,1,1] => [1,1,1]
[[5,4,3],[4,2]] => [1,2,3] => [1,1,1] => [1,1,1]
[[6,5,3],[5,3]] => [1,2,3] => [1,1,1] => [1,1,1]
[[2,2,2,1],[1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[3,3,3,1],[2,1,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[3,3,2,1],[2,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[4,4,3,1],[3,2,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[4,4,2,1],[3,2]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[5,5,3,1],[4,3,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[3,2,2,1],[2]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[4,3,3,1],[3,1,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[4,3,2,1],[3,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[5,4,3,1],[4,2,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[5,4,2,1],[4,2]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[6,5,3,1],[5,3,1]] => [1,2,2,1] => [1,2,1] => [2,1,1]
[[3,3,2,2],[2,1,1]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[4,4,3,2],[3,2,2]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[4,4,2,2],[3,2,1]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,5,3,2],[4,3,2]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[4,3,2,2],[3,1,1]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,2],[4,2,2]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,4,2,2],[4,2,1]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[6,5,3,2],[5,3,2]] => [1,2,1,2] => [1,1,1,1] => [1,1,1,1]
[[2,2,1,1,1],[1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[3,3,2,2,1],[2,1,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[3,3,2,1,1],[2,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,3,2,1],[3,2,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[3,3,1,1,1],[2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,2,2,1],[3,2,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,2,1,1],[3,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[5,5,3,2,1],[4,3,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[3,2,1,1,1],[2]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,3,2,2,1],[3,1,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,3,2,1,1],[3,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,3,2,1],[4,2,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,3,1,1,1],[3,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,2,2,1],[4,2,1,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,2,1,1],[4,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[6,5,3,2,1],[5,3,2,1]] => [1,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,4],[3,3]] => [1,1,4] => [2,1] => [2,1]
[[5,5,4],[4,4]] => [1,1,4] => [2,1] => [2,1]
[[5,4,4],[4,3]] => [1,1,4] => [2,1] => [2,1]
[[6,5,4],[5,4]] => [1,1,4] => [2,1] => [2,1]
[[3,3,3,1],[2,2]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[4,4,4,1],[3,3,1]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[4,4,3,1],[3,3]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[5,5,4,1],[4,4,1]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[4,3,3,1],[3,2]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[5,4,4,1],[4,3,1]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[5,4,3,1],[4,3]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[6,5,4,1],[5,4,1]] => [1,1,3,1] => [2,1,1] => [1,2,1]
[[2,2,2,2],[1,1]] => [1,1,2,2] => [2,2] => [2,2]
[[3,3,3,2],[2,2,1]] => [1,1,2,2] => [2,2] => [2,2]
[[4,4,4,2],[3,3,2]] => [1,1,2,2] => [2,2] => [2,2]
[[3,3,2,2],[2,2]] => [1,1,2,2] => [2,2] => [2,2]
[[4,4,3,2],[3,3,1]] => [1,1,2,2] => [2,2] => [2,2]
[[5,5,4,2],[4,4,2]] => [1,1,2,2] => [2,2] => [2,2]
[[3,2,2,2],[2,1]] => [1,1,2,2] => [2,2] => [2,2]
[[4,3,3,2],[3,2,1]] => [1,1,2,2] => [2,2] => [2,2]
[[5,4,4,2],[4,3,2]] => [1,1,2,2] => [2,2] => [2,2]
[[4,3,2,2],[3,2]] => [1,1,2,2] => [2,2] => [2,2]
[[5,4,3,2],[4,3,1]] => [1,1,2,2] => [2,2] => [2,2]
[[6,5,4,2],[5,4,2]] => [1,1,2,2] => [2,2] => [2,2]
[[2,2,2,1,1],[1,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[3,3,3,2,1],[2,2,1,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[3,3,3,1,1],[2,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,4,4,2,1],[3,3,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[3,3,2,1,1],[2,2]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,4,3,2,1],[3,3,1,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,4,3,1,1],[3,3,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[5,5,4,2,1],[4,4,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[3,2,2,1,1],[2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,3,3,2,1],[3,2,1,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,3,3,1,1],[3,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[5,4,4,2,1],[4,3,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[4,3,2,1,1],[3,2]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[5,4,3,2,1],[4,3,1,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[5,4,3,1,1],[4,3,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[6,5,4,2,1],[5,4,2,1]] => [1,1,2,1,1] => [2,1,2] => [2,1,2]
[[3,3,3,3],[2,2,2]] => [1,1,1,3] => [3,1] => [3,1]
[[4,4,4,3],[3,3,3]] => [1,1,1,3] => [3,1] => [3,1]
[[4,4,3,3],[3,3,2]] => [1,1,1,3] => [3,1] => [3,1]
[[5,5,4,3],[4,4,3]] => [1,1,1,3] => [3,1] => [3,1]
[[4,3,3,3],[3,2,2]] => [1,1,1,3] => [3,1] => [3,1]
[[5,4,4,3],[4,3,3]] => [1,1,1,3] => [3,1] => [3,1]
[[5,4,3,3],[4,3,2]] => [1,1,1,3] => [3,1] => [3,1]
[[6,5,4,3],[5,4,3]] => [1,1,1,3] => [3,1] => [3,1]
[[2,2,2,2,1],[1,1,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[3,3,3,3,1],[2,2,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[3,3,3,2,1],[2,2,2]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,4,4,3,1],[3,3,3,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[3,3,2,2,1],[2,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,4,3,3,1],[3,3,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,4,3,2,1],[3,3,2]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[5,5,4,3,1],[4,4,3,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[3,2,2,2,1],[2,1,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,3,3,3,1],[3,2,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,3,3,2,1],[3,2,2]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[5,4,4,3,1],[4,3,3,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[4,3,2,2,1],[3,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[5,4,3,3,1],[4,3,2,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[5,4,3,2,1],[4,3,2]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[6,5,4,3,1],[5,4,3,1]] => [1,1,1,2,1] => [3,1,1] => [1,3,1]
[[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[3,3,3,3,2],[2,2,2,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[3,3,3,2,2],[2,2,2,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,4,4,3,2],[3,3,3,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[3,3,2,2,2],[2,2,1,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,4,3,3,2],[3,3,2,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,4,3,2,2],[3,3,2,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[5,5,4,3,2],[4,4,3,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[3,2,2,2,2],[2,1,1,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,3,3,3,2],[3,2,2,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,3,3,2,2],[3,2,2,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[5,4,4,3,2],[4,3,3,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[4,3,2,2,2],[3,2,1,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[5,4,3,3,2],[4,3,2,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[5,4,3,2,2],[4,3,2,1]] => [1,1,1,1,2] => [4,1] => [4,1]
[[6,5,4,3,2],[5,4,3,2]] => [1,1,1,1,2] => [4,1] => [4,1]
[[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => [6] => [6]
[[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[2,2,2,1,1,1],[1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,3,2,1,1],[2,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[2,2,1,1,1,1],[1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,2,2,1,1],[2,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,3,2,1,1,1],[2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,4,3,2,1,1],[3,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[2,1,1,1,1,1],[1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,2,2,2,1,1],[2,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,2,2,1,1,1],[2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,3,2,1,1],[3,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[3,2,1,1,1,1],[2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,2,2,1,1],[3,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[4,3,2,1,1,1],[3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [1,1,1,1,1,1] => [6] => [6]
[[5,4,3,2,1,1],[4,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [1,1,1,1,1,1] => [6] => [6]
[[7],[]] => [7] => [1] => [1]
[[6,1],[]] => [6,1] => [1,1] => [1,1]
[[7,1],[1]] => [6,1] => [1,1] => [1,1]
[[5,2],[]] => [5,2] => [1,1] => [1,1]
[[6,2],[1]] => [5,2] => [1,1] => [1,1]
[[7,2],[2]] => [5,2] => [1,1] => [1,1]
[[5,1,1],[]] => [5,1,1] => [1,2] => [1,2]
[[6,2,1],[1,1]] => [5,1,1] => [1,2] => [1,2]
[[6,1,1],[1]] => [5,1,1] => [1,2] => [1,2]
[[7,2,1],[2,1]] => [5,1,1] => [1,2] => [1,2]
[[4,3],[]] => [4,3] => [1,1] => [1,1]
[[5,3],[1]] => [4,3] => [1,1] => [1,1]
[[6,3],[2]] => [4,3] => [1,1] => [1,1]
[[7,3],[3]] => [4,3] => [1,1] => [1,1]
[[4,2,1],[]] => [4,2,1] => [1,1,1] => [1,1,1]
[[5,3,1],[1,1]] => [4,2,1] => [1,1,1] => [1,1,1]
[[5,2,1],[1]] => [4,2,1] => [1,1,1] => [1,1,1]
[[6,3,1],[2,1]] => [4,2,1] => [1,1,1] => [1,1,1]
[[6,2,1],[2]] => [4,2,1] => [1,1,1] => [1,1,1]
[[7,3,1],[3,1]] => [4,2,1] => [1,1,1] => [1,1,1]
[[5,2,2],[1,1]] => [4,1,2] => [1,1,1] => [1,1,1]
[[6,3,2],[2,2]] => [4,1,2] => [1,1,1] => [1,1,1]
[[6,2,2],[2,1]] => [4,1,2] => [1,1,1] => [1,1,1]
[[7,3,2],[3,2]] => [4,1,2] => [1,1,1] => [1,1,1]
[[4,1,1,1],[]] => [4,1,1,1] => [1,3] => [1,3]
[[5,2,2,1],[1,1,1]] => [4,1,1,1] => [1,3] => [1,3]
[[5,2,1,1],[1,1]] => [4,1,1,1] => [1,3] => [1,3]
[[6,3,2,1],[2,2,1]] => [4,1,1,1] => [1,3] => [1,3]
[[5,1,1,1],[1]] => [4,1,1,1] => [1,3] => [1,3]
[[6,2,2,1],[2,1,1]] => [4,1,1,1] => [1,3] => [1,3]
[[6,2,1,1],[2,1]] => [4,1,1,1] => [1,3] => [1,3]
[[7,3,2,1],[3,2,1]] => [4,1,1,1] => [1,3] => [1,3]
[[4,4],[1]] => [3,4] => [1,1] => [1,1]
[[5,4],[2]] => [3,4] => [1,1] => [1,1]
[[6,4],[3]] => [3,4] => [1,1] => [1,1]
[[7,4],[4]] => [3,4] => [1,1] => [1,1]
[[3,3,1],[]] => [3,3,1] => [2,1] => [2,1]
[[4,4,1],[1,1]] => [3,3,1] => [2,1] => [2,1]
[[4,3,1],[1]] => [3,3,1] => [2,1] => [2,1]
[[5,4,1],[2,1]] => [3,3,1] => [2,1] => [2,1]
[[5,3,1],[2]] => [3,3,1] => [2,1] => [2,1]
[[6,4,1],[3,1]] => [3,3,1] => [2,1] => [2,1]
[[6,3,1],[3]] => [3,3,1] => [2,1] => [2,1]
[[7,4,1],[4,1]] => [3,3,1] => [2,1] => [2,1]
[[3,2,2],[]] => [3,2,2] => [1,2] => [1,2]
[[4,3,2],[1,1]] => [3,2,2] => [1,2] => [1,2]
[[5,4,2],[2,2]] => [3,2,2] => [1,2] => [1,2]
[[4,2,2],[1]] => [3,2,2] => [1,2] => [1,2]
[[5,3,2],[2,1]] => [3,2,2] => [1,2] => [1,2]
[[6,4,2],[3,2]] => [3,2,2] => [1,2] => [1,2]
[[5,2,2],[2]] => [3,2,2] => [1,2] => [1,2]
[[6,3,2],[3,1]] => [3,2,2] => [1,2] => [1,2]
[[7,4,2],[4,2]] => [3,2,2] => [1,2] => [1,2]
[[3,2,1,1],[]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[4,3,2,1],[1,1,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[4,3,1,1],[1,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[5,4,2,1],[2,2,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[4,2,1,1],[1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[5,3,2,1],[2,1,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[5,3,1,1],[2,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[6,4,2,1],[3,2,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[5,2,1,1],[2]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[6,3,2,1],[3,1,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[6,3,1,1],[3,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[7,4,2,1],[4,2,1]] => [3,2,1,1] => [1,1,2] => [1,1,2]
[[5,3,3],[2,2]] => [3,1,3] => [1,1,1] => [1,1,1]
[[6,4,3],[3,3]] => [3,1,3] => [1,1,1] => [1,1,1]
[[6,3,3],[3,2]] => [3,1,3] => [1,1,1] => [1,1,1]
[[7,4,3],[4,3]] => [3,1,3] => [1,1,1] => [1,1,1]
[[4,2,2,1],[1,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,3,3,1],[2,2,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,3,2,1],[2,2]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,4,3,1],[3,3,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,2,2,1],[2,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,3,3,1],[3,2,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,3,2,1],[3,2]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[7,4,3,1],[4,3,1]] => [3,1,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,2,2,2],[1,1,1]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[5,3,3,2],[2,2,2]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[5,3,2,2],[2,2,1]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[6,4,3,2],[3,3,2]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[5,2,2,2],[2,1,1]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[6,3,3,2],[3,2,2]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[6,3,2,2],[3,2,1]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[7,4,3,2],[4,3,2]] => [3,1,1,2] => [1,2,1] => [2,1,1]
[[3,1,1,1,1],[]] => [3,1,1,1,1] => [1,4] => [1,4]
[[4,2,2,2,1],[1,1,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[4,2,2,1,1],[1,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,3,3,2,1],[2,2,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[4,2,1,1,1],[1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,3,2,2,1],[2,2,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,3,2,1,1],[2,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[6,4,3,2,1],[3,3,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[4,1,1,1,1],[1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,2,2,2,1],[2,1,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,2,2,1,1],[2,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[6,3,3,2,1],[3,2,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,2,1,1,1],[2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[6,3,2,2,1],[3,2,1,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[6,3,2,1,1],[3,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[7,4,3,2,1],[4,3,2,1]] => [3,1,1,1,1] => [1,4] => [1,4]
[[5,5],[3]] => [2,5] => [1,1] => [1,1]
[[6,5],[4]] => [2,5] => [1,1] => [1,1]
[[7,5],[5]] => [2,5] => [1,1] => [1,1]
[[4,4,1],[2]] => [2,4,1] => [1,1,1] => [1,1,1]
[[5,5,1],[3,1]] => [2,4,1] => [1,1,1] => [1,1,1]
[[5,4,1],[3]] => [2,4,1] => [1,1,1] => [1,1,1]
[[6,5,1],[4,1]] => [2,4,1] => [1,1,1] => [1,1,1]
[[6,4,1],[4]] => [2,4,1] => [1,1,1] => [1,1,1]
[[7,5,1],[5,1]] => [2,4,1] => [1,1,1] => [1,1,1]
[[3,3,2],[1]] => [2,3,2] => [1,1,1] => [1,1,1]
[[4,4,2],[2,1]] => [2,3,2] => [1,1,1] => [1,1,1]
[[5,5,2],[3,2]] => [2,3,2] => [1,1,1] => [1,1,1]
[[4,3,2],[2]] => [2,3,2] => [1,1,1] => [1,1,1]
[[5,4,2],[3,1]] => [2,3,2] => [1,1,1] => [1,1,1]
[[6,5,2],[4,2]] => [2,3,2] => [1,1,1] => [1,1,1]
[[5,3,2],[3]] => [2,3,2] => [1,1,1] => [1,1,1]
[[6,4,2],[4,1]] => [2,3,2] => [1,1,1] => [1,1,1]
[[7,5,2],[5,2]] => [2,3,2] => [1,1,1] => [1,1,1]
[[3,3,1,1],[1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[4,4,2,1],[2,1,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[4,4,1,1],[2,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[5,5,2,1],[3,2,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[4,3,1,1],[2]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[5,4,2,1],[3,1,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[5,4,1,1],[3,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[6,5,2,1],[4,2,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[5,3,1,1],[3]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[6,4,2,1],[4,1,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[6,4,1,1],[4,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[7,5,2,1],[5,2,1]] => [2,3,1,1] => [1,1,2] => [1,1,2]
[[3,3,3],[1,1]] => [2,2,3] => [2,1] => [2,1]
[[4,4,3],[2,2]] => [2,2,3] => [2,1] => [2,1]
[[5,5,3],[3,3]] => [2,2,3] => [2,1] => [2,1]
[[4,3,3],[2,1]] => [2,2,3] => [2,1] => [2,1]
[[5,4,3],[3,2]] => [2,2,3] => [2,1] => [2,1]
[[6,5,3],[4,3]] => [2,2,3] => [2,1] => [2,1]
[[5,3,3],[3,1]] => [2,2,3] => [2,1] => [2,1]
[[6,4,3],[4,2]] => [2,2,3] => [2,1] => [2,1]
[[7,5,3],[5,3]] => [2,2,3] => [2,1] => [2,1]
[[2,2,2,1],[]] => [2,2,2,1] => [3,1] => [3,1]
[[3,3,3,1],[1,1,1]] => [2,2,2,1] => [3,1] => [3,1]
[[3,3,2,1],[1,1]] => [2,2,2,1] => [3,1] => [3,1]
[[4,4,3,1],[2,2,1]] => [2,2,2,1] => [3,1] => [3,1]
[[4,4,2,1],[2,2]] => [2,2,2,1] => [3,1] => [3,1]
[[5,5,3,1],[3,3,1]] => [2,2,2,1] => [3,1] => [3,1]
[[3,2,2,1],[1]] => [2,2,2,1] => [3,1] => [3,1]
[[4,3,3,1],[2,1,1]] => [2,2,2,1] => [3,1] => [3,1]
[[4,3,2,1],[2,1]] => [2,2,2,1] => [3,1] => [3,1]
[[5,4,3,1],[3,2,1]] => [2,2,2,1] => [3,1] => [3,1]
[[5,4,2,1],[3,2]] => [2,2,2,1] => [3,1] => [3,1]
[[6,5,3,1],[4,3,1]] => [2,2,2,1] => [3,1] => [3,1]
[[4,2,2,1],[2]] => [2,2,2,1] => [3,1] => [3,1]
[[5,3,3,1],[3,1,1]] => [2,2,2,1] => [3,1] => [3,1]
[[5,3,2,1],[3,1]] => [2,2,2,1] => [3,1] => [3,1]
[[6,4,3,1],[4,2,1]] => [2,2,2,1] => [3,1] => [3,1]
[[6,4,2,1],[4,2]] => [2,2,2,1] => [3,1] => [3,1]
[[7,5,3,1],[5,3,1]] => [2,2,2,1] => [3,1] => [3,1]
[[3,3,2,2],[1,1,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[4,4,3,2],[2,2,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[4,4,2,2],[2,2,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[5,5,3,2],[3,3,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[4,3,2,2],[2,1,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[5,4,3,2],[3,2,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[5,4,2,2],[3,2,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[6,5,3,2],[4,3,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[5,3,2,2],[3,1,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[6,4,3,2],[4,2,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[6,4,2,2],[4,2,1]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[7,5,3,2],[5,3,2]] => [2,2,1,2] => [2,1,1] => [1,2,1]
[[2,2,1,1,1],[]] => [2,2,1,1,1] => [2,3] => [2,3]
[[3,3,2,2,1],[1,1,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[3,3,2,1,1],[1,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,4,3,2,1],[2,2,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[3,3,1,1,1],[1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,4,2,1,1],[2,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,5,3,2,1],[3,3,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[3,2,1,1,1],[1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,3,2,2,1],[2,1,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,3,2,1,1],[2,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,4,3,2,1],[3,2,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,3,1,1,1],[2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,4,2,2,1],[3,2,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,4,2,1,1],[3,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[6,5,3,2,1],[4,3,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[4,2,1,1,1],[2]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,3,2,2,1],[3,1,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,3,2,1,1],[3,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[6,4,3,2,1],[4,2,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,3,1,1,1],[3,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[6,4,2,2,1],[4,2,1,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[6,4,2,1,1],[4,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[7,5,3,2,1],[5,3,2,1]] => [2,2,1,1,1] => [2,3] => [2,3]
[[5,4,4],[3,3]] => [2,1,4] => [1,1,1] => [1,1,1]
[[6,5,4],[4,4]] => [2,1,4] => [1,1,1] => [1,1,1]
[[6,4,4],[4,3]] => [2,1,4] => [1,1,1] => [1,1,1]
[[7,5,4],[5,4]] => [2,1,4] => [1,1,1] => [1,1,1]
[[4,3,3,1],[2,2]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,4,1],[3,3,1]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,1],[3,3]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,5,4,1],[4,4,1]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,3,3,1],[3,2]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,4,4,1],[4,3,1]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,4,3,1],[4,3]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[7,5,4,1],[5,4,1]] => [2,1,3,1] => [1,1,1,1] => [1,1,1,1]
[[3,2,2,2],[1,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[4,3,3,2],[2,2,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[5,4,4,2],[3,3,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[4,3,2,2],[2,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[5,4,3,2],[3,3,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[6,5,4,2],[4,4,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[4,2,2,2],[2,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[5,3,3,2],[3,2,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[6,4,4,2],[4,3,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[5,3,2,2],[3,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[6,4,3,2],[4,3,1]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[7,5,4,2],[5,4,2]] => [2,1,2,2] => [1,1,2] => [1,1,2]
[[3,2,2,1,1],[1,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[4,3,3,2,1],[2,2,1,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[4,3,3,1,1],[2,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,4,4,2,1],[3,3,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[4,3,2,1,1],[2,2]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,4,3,2,1],[3,3,1,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,4,3,1,1],[3,3,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[6,5,4,2,1],[4,4,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[4,2,2,1,1],[2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,3,3,2,1],[3,2,1,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,3,3,1,1],[3,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[6,4,4,2,1],[4,3,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[5,3,2,1,1],[3,2]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[6,4,3,2,1],[4,3,1,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[6,4,3,1,1],[4,3,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[7,5,4,2,1],[5,4,2,1]] => [2,1,2,1,1] => [1,1,1,2] => [1,1,1,2]
[[4,3,3,3],[2,2,2]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[5,4,4,3],[3,3,3]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[5,4,3,3],[3,3,2]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[6,5,4,3],[4,4,3]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[5,3,3,3],[3,2,2]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[6,4,4,3],[4,3,3]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[6,4,3,3],[4,3,2]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[7,5,4,3],[5,4,3]] => [2,1,1,3] => [1,2,1] => [2,1,1]
[[3,2,2,2,1],[1,1,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[4,3,3,3,1],[2,2,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[4,3,3,2,1],[2,2,2]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,4,4,3,1],[3,3,3,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[4,3,2,2,1],[2,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,4,3,3,1],[3,3,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,4,3,2,1],[3,3,2]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[6,5,4,3,1],[4,4,3,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[4,2,2,2,1],[2,1,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,3,3,3,1],[3,2,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,3,3,2,1],[3,2,2]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[6,4,4,3,1],[4,3,3,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[5,3,2,2,1],[3,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[6,4,3,3,1],[4,3,2,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[6,4,3,2,1],[4,3,2]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[7,5,4,3,1],[5,4,3,1]] => [2,1,1,2,1] => [1,2,1,1] => [1,2,1,1]
[[3,2,2,2,2],[1,1,1,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[4,3,3,3,2],[2,2,2,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[4,3,3,2,2],[2,2,2,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,4,4,3,2],[3,3,3,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[4,3,2,2,2],[2,2,1,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,4,3,3,2],[3,3,2,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,4,3,2,2],[3,3,2,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[6,5,4,3,2],[4,4,3,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,3,3,3,2],[3,2,2,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,3,3,2,2],[3,2,2,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[6,4,4,3,2],[4,3,3,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[5,3,2,2,2],[3,2,1,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[6,4,3,3,2],[4,3,2,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[6,4,3,2,2],[4,3,2,1]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[7,5,4,3,2],[5,4,3,2]] => [2,1,1,1,2] => [1,3,1] => [3,1,1]
[[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[3,2,2,2,2,1],[1,1,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[3,2,2,2,1,1],[1,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[3,2,2,1,1,1],[1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,3,2,1,1],[2,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[3,2,1,1,1,1],[1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,2,2,1,1],[2,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,3,2,1,1,1],[2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,4,3,2,1,1],[3,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[3,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,2,2,1,1,1],[2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,3,2,1,1],[3,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[4,2,1,1,1,1],[2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,2,2,1,1],[3,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[5,3,2,1,1,1],[3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,4,3,2,1,1],[4,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [2,1,1,1,1,1] => [1,5] => [1,5]
[[6,6],[5]] => [1,6] => [1,1] => [1,1]
[[7,6],[6]] => [1,6] => [1,1] => [1,1]
[[5,5,1],[4]] => [1,5,1] => [1,1,1] => [1,1,1]
[[6,6,1],[5,1]] => [1,5,1] => [1,1,1] => [1,1,1]
[[6,5,1],[5]] => [1,5,1] => [1,1,1] => [1,1,1]
[[7,6,1],[6,1]] => [1,5,1] => [1,1,1] => [1,1,1]
[[4,4,2],[3]] => [1,4,2] => [1,1,1] => [1,1,1]
[[5,5,2],[4,1]] => [1,4,2] => [1,1,1] => [1,1,1]
[[6,6,2],[5,2]] => [1,4,2] => [1,1,1] => [1,1,1]
[[5,4,2],[4]] => [1,4,2] => [1,1,1] => [1,1,1]
[[6,5,2],[5,1]] => [1,4,2] => [1,1,1] => [1,1,1]
[[7,6,2],[6,2]] => [1,4,2] => [1,1,1] => [1,1,1]
[[4,4,1,1],[3]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[5,5,2,1],[4,1,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[5,5,1,1],[4,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[6,6,2,1],[5,2,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[5,4,1,1],[4]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[6,5,2,1],[5,1,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[6,5,1,1],[5,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[7,6,2,1],[6,2,1]] => [1,4,1,1] => [1,1,2] => [1,1,2]
[[3,3,3],[2]] => [1,3,3] => [1,2] => [1,2]
[[4,4,3],[3,1]] => [1,3,3] => [1,2] => [1,2]
[[5,5,3],[4,2]] => [1,3,3] => [1,2] => [1,2]
[[6,6,3],[5,3]] => [1,3,3] => [1,2] => [1,2]
[[4,3,3],[3]] => [1,3,3] => [1,2] => [1,2]
[[5,4,3],[4,1]] => [1,3,3] => [1,2] => [1,2]
[[6,5,3],[5,2]] => [1,3,3] => [1,2] => [1,2]
[[7,6,3],[6,3]] => [1,3,3] => [1,2] => [1,2]
[[3,3,2,1],[2]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,4,3,1],[3,1,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,4,2,1],[3,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,5,3,1],[4,2,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,5,2,1],[4,2]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,6,3,1],[5,3,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,3,2,1],[3]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,1],[4,1,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,2,1],[4,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,5,3,1],[5,2,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[6,5,2,1],[5,2]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[7,6,3,1],[6,3,1]] => [1,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,4,2,2],[3,1,1]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,5,3,2],[4,2,2]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,5,2,2],[4,2,1]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[6,6,3,2],[5,3,2]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[5,4,2,2],[4,1,1]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[6,5,3,2],[5,2,2]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[6,5,2,2],[5,2,1]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[7,6,3,2],[6,3,2]] => [1,3,1,2] => [1,1,1,1] => [1,1,1,1]
[[3,3,1,1,1],[2]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,2,2,1],[3,1,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,2,1,1],[3,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,5,3,2,1],[4,2,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,1,1,1],[3,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,5,2,2,1],[4,2,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,5,2,1,1],[4,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[6,6,3,2,1],[5,3,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,3,1,1,1],[3]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,2,2,1],[4,1,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,2,1,1],[4,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[6,5,3,2,1],[5,2,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[5,4,1,1,1],[4,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[6,5,2,2,1],[5,2,1,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[6,5,2,1,1],[5,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[7,6,3,2,1],[6,3,2,1]] => [1,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,4,4],[3,2]] => [1,2,4] => [1,1,1] => [1,1,1]
[[5,5,4],[4,3]] => [1,2,4] => [1,1,1] => [1,1,1]
[[6,6,4],[5,4]] => [1,2,4] => [1,1,1] => [1,1,1]
[[5,4,4],[4,2]] => [1,2,4] => [1,1,1] => [1,1,1]
[[6,5,4],[5,3]] => [1,2,4] => [1,1,1] => [1,1,1]
[[7,6,4],[6,4]] => [1,2,4] => [1,1,1] => [1,1,1]
[[3,3,3,1],[2,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[4,4,4,1],[3,2,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[4,4,3,1],[3,2]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,5,4,1],[4,3,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,5,3,1],[4,3]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,6,4,1],[5,4,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[4,3,3,1],[3,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,4,1],[4,2,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,1],[4,2]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,5,4,1],[5,3,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[6,5,3,1],[5,3]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[7,6,4,1],[6,4,1]] => [1,2,3,1] => [1,1,1,1] => [1,1,1,1]
[[2,2,2,2],[1]] => [1,2,2,2] => [1,3] => [1,3]
[[3,3,3,2],[2,1,1]] => [1,2,2,2] => [1,3] => [1,3]
[[4,4,4,2],[3,2,2]] => [1,2,2,2] => [1,3] => [1,3]
[[3,3,2,2],[2,1]] => [1,2,2,2] => [1,3] => [1,3]
[[4,4,3,2],[3,2,1]] => [1,2,2,2] => [1,3] => [1,3]
[[5,5,4,2],[4,3,2]] => [1,2,2,2] => [1,3] => [1,3]
[[4,4,2,2],[3,2]] => [1,2,2,2] => [1,3] => [1,3]
[[5,5,3,2],[4,3,1]] => [1,2,2,2] => [1,3] => [1,3]
[[6,6,4,2],[5,4,2]] => [1,2,2,2] => [1,3] => [1,3]
[[3,2,2,2],[2]] => [1,2,2,2] => [1,3] => [1,3]
[[4,3,3,2],[3,1,1]] => [1,2,2,2] => [1,3] => [1,3]
[[5,4,4,2],[4,2,2]] => [1,2,2,2] => [1,3] => [1,3]
[[4,3,2,2],[3,1]] => [1,2,2,2] => [1,3] => [1,3]
[[5,4,3,2],[4,2,1]] => [1,2,2,2] => [1,3] => [1,3]
[[6,5,4,2],[5,3,2]] => [1,2,2,2] => [1,3] => [1,3]
[[5,4,2,2],[4,2]] => [1,2,2,2] => [1,3] => [1,3]
[[6,5,3,2],[5,3,1]] => [1,2,2,2] => [1,3] => [1,3]
[[7,6,4,2],[6,4,2]] => [1,2,2,2] => [1,3] => [1,3]
[[2,2,2,1,1],[1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[3,3,3,2,1],[2,1,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[3,3,3,1,1],[2,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,4,4,2,1],[3,2,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[3,3,2,1,1],[2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,4,3,2,1],[3,2,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,4,3,1,1],[3,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,5,4,2,1],[4,3,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,4,2,1,1],[3,2]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,5,3,2,1],[4,3,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,5,3,1,1],[4,3,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[6,6,4,2,1],[5,4,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[3,2,2,1,1],[2]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,3,3,2,1],[3,1,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,3,3,1,1],[3,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,4,4,2,1],[4,2,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,3,2,1,1],[3,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,4,3,2,1],[4,2,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,4,3,1,1],[4,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[6,5,4,2,1],[5,3,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[5,4,2,1,1],[4,2]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[6,5,3,2,1],[5,3,1,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[6,5,3,1,1],[5,3,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[7,6,4,2,1],[6,4,2,1]] => [1,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,4,3,3],[3,2,2]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[5,5,4,3],[4,3,3]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[5,5,3,3],[4,3,2]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[6,6,4,3],[5,4,3]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[5,4,3,3],[4,2,2]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[6,5,4,3],[5,3,3]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[6,5,3,3],[5,3,2]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[7,6,4,3],[6,4,3]] => [1,2,1,3] => [1,1,1,1] => [1,1,1,1]
[[3,3,2,2,1],[2,1,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[4,4,3,3,1],[3,2,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[4,4,3,2,1],[3,2,2]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,5,4,3,1],[4,3,3,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[4,4,2,2,1],[3,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,5,3,3,1],[4,3,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,5,3,2,1],[4,3,2]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[6,6,4,3,1],[5,4,3,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[4,3,2,2,1],[3,1,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,4,3,3,1],[4,2,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,4,3,2,1],[4,2,2]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[6,5,4,3,1],[5,3,3,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[5,4,2,2,1],[4,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[6,5,3,3,1],[5,3,2,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[6,5,3,2,1],[5,3,2]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[7,6,4,3,1],[6,4,3,1]] => [1,2,1,2,1] => [1,1,1,1,1] => [1,1,1,1,1]
[[3,3,2,2,2],[2,1,1,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[4,4,3,3,2],[3,2,2,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[4,4,3,2,2],[3,2,2,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,5,4,3,2],[4,3,3,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[4,4,2,2,2],[3,2,1,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,5,3,3,2],[4,3,2,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,5,3,2,2],[4,3,2,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[6,6,4,3,2],[5,4,3,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[4,3,2,2,2],[3,1,1,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,4,3,3,2],[4,2,2,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,4,3,2,2],[4,2,2,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[6,5,4,3,2],[5,3,3,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[5,4,2,2,2],[4,2,1,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[6,5,3,3,2],[5,3,2,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[6,5,3,2,2],[5,3,2,1]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[7,6,4,3,2],[6,4,3,2]] => [1,2,1,1,2] => [1,1,2,1] => [2,1,1,1]
[[2,2,1,1,1,1],[1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,3,2,2,1,1],[2,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,3,2,1,1,1],[2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,3,2,1,1],[3,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,3,1,1,1,1],[2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,2,2,1,1],[3,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,4,2,1,1,1],[3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,5,3,2,1,1],[4,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,2,1,1,1,1],[2]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,3,2,2,1,1],[3,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,3,2,1,1,1],[3,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,3,2,1,1],[4,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,3,1,1,1,1],[3,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,2,2,1,1],[4,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,4,2,1,1,1],[4,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[6,5,3,2,1,1],[5,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [1,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[5,5,5],[4,4]] => [1,1,5] => [2,1] => [2,1]
[[6,6,5],[5,5]] => [1,1,5] => [2,1] => [2,1]
[[6,5,5],[5,4]] => [1,1,5] => [2,1] => [2,1]
[[7,6,5],[6,5]] => [1,1,5] => [2,1] => [2,1]
[[4,4,4,1],[3,3]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[5,5,5,1],[4,4,1]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[5,5,4,1],[4,4]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[6,6,5,1],[5,5,1]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[5,4,4,1],[4,3]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[6,5,5,1],[5,4,1]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[6,5,4,1],[5,4]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[7,6,5,1],[6,5,1]] => [1,1,4,1] => [2,1,1] => [1,2,1]
[[3,3,3,2],[2,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[4,4,4,2],[3,3,1]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[5,5,5,2],[4,4,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[4,4,3,2],[3,3]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[5,5,4,2],[4,4,1]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[6,6,5,2],[5,5,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[4,3,3,2],[3,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[5,4,4,2],[4,3,1]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[6,5,5,2],[5,4,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[5,4,3,2],[4,3]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[6,5,4,2],[5,4,1]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[7,6,5,2],[6,5,2]] => [1,1,3,2] => [2,1,1] => [1,2,1]
[[3,3,3,1,1],[2,2]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[4,4,4,2,1],[3,3,1,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[4,4,4,1,1],[3,3,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,5,5,2,1],[4,4,2,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[4,4,3,1,1],[3,3]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,5,4,2,1],[4,4,1,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,5,4,1,1],[4,4,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[6,6,5,2,1],[5,5,2,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[4,3,3,1,1],[3,2]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,4,4,2,1],[4,3,1,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,4,4,1,1],[4,3,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[6,5,5,2,1],[5,4,2,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[5,4,3,1,1],[4,3]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[6,5,4,2,1],[5,4,1,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[6,5,4,1,1],[5,4,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[7,6,5,2,1],[6,5,2,1]] => [1,1,3,1,1] => [2,1,2] => [2,1,2]
[[3,3,3,3],[2,2,1]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[4,4,4,3],[3,3,2]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[5,5,5,3],[4,4,3]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[4,4,3,3],[3,3,1]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[5,5,4,3],[4,4,2]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[6,6,5,3],[5,5,3]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[4,3,3,3],[3,2,1]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[5,4,4,3],[4,3,2]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[6,5,5,3],[5,4,3]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[5,4,3,3],[4,3,1]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[6,5,4,3],[5,4,2]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[7,6,5,3],[6,5,3]] => [1,1,2,3] => [2,1,1] => [1,2,1]
[[2,2,2,2,1],[1,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[3,3,3,3,1],[2,2,1,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[3,3,3,2,1],[2,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,4,4,3,1],[3,3,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,4,4,2,1],[3,3,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,5,5,3,1],[4,4,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[3,3,2,2,1],[2,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,4,3,3,1],[3,3,1,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,4,3,2,1],[3,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,5,4,3,1],[4,4,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,5,4,2,1],[4,4,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[6,6,5,3,1],[5,5,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[3,2,2,2,1],[2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,3,3,3,1],[3,2,1,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,3,3,2,1],[3,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,4,4,3,1],[4,3,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,4,4,2,1],[4,3,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[6,5,5,3,1],[5,4,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[4,3,2,2,1],[3,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,4,3,3,1],[4,3,1,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[5,4,3,2,1],[4,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[6,5,4,3,1],[5,4,2,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[6,5,4,2,1],[5,4,2]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[7,6,5,3,1],[6,5,3,1]] => [1,1,2,2,1] => [2,2,1] => [2,2,1]
[[3,3,3,2,2],[2,2,1,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[4,4,4,3,2],[3,3,2,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[4,4,4,2,2],[3,3,2,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,5,5,3,2],[4,4,3,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[4,4,3,2,2],[3,3,1,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,5,4,3,2],[4,4,2,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,5,4,2,2],[4,4,2,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[6,6,5,3,2],[5,5,3,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[4,3,3,2,2],[3,2,1,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,4,4,3,2],[4,3,2,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,4,4,2,2],[4,3,2,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[6,5,5,3,2],[5,4,3,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[5,4,3,2,2],[4,3,1,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[6,5,4,3,2],[5,4,2,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[6,5,4,2,2],[5,4,2,1]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[7,6,5,3,2],[6,5,3,2]] => [1,1,2,1,2] => [2,1,1,1] => [1,1,2,1]
[[2,2,2,1,1,1],[1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[3,3,3,2,1,1],[2,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[3,3,3,1,1,1],[2,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,4,2,1,1],[3,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[3,3,2,1,1,1],[2,2]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,3,2,1,1],[3,3,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,3,1,1,1],[3,3,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,5,4,2,1,1],[4,4,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[3,2,2,1,1,1],[2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,3,3,2,1,1],[3,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,3,3,1,1,1],[3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,4,2,1,1],[4,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,3,2,1,1,1],[3,2]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,3,2,1,1],[4,3,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[5,4,3,1,1,1],[4,3,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[6,5,4,2,1,1],[5,4,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [1,1,2,1,1,1] => [2,1,3] => [2,1,3]
[[4,4,4,4],[3,3,3]] => [1,1,1,4] => [3,1] => [3,1]
[[5,5,5,4],[4,4,4]] => [1,1,1,4] => [3,1] => [3,1]
[[5,5,4,4],[4,4,3]] => [1,1,1,4] => [3,1] => [3,1]
[[6,6,5,4],[5,5,4]] => [1,1,1,4] => [3,1] => [3,1]
[[5,4,4,4],[4,3,3]] => [1,1,1,4] => [3,1] => [3,1]
[[6,5,5,4],[5,4,4]] => [1,1,1,4] => [3,1] => [3,1]
[[6,5,4,4],[5,4,3]] => [1,1,1,4] => [3,1] => [3,1]
[[7,6,5,4],[6,5,4]] => [1,1,1,4] => [3,1] => [3,1]
[[3,3,3,3,1],[2,2,2]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[4,4,4,4,1],[3,3,3,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[4,4,4,3,1],[3,3,3]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,5,5,4,1],[4,4,4,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[4,4,3,3,1],[3,3,2]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,5,4,4,1],[4,4,3,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,5,4,3,1],[4,4,3]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[6,6,5,4,1],[5,5,4,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[4,3,3,3,1],[3,2,2]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,4,4,4,1],[4,3,3,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,4,4,3,1],[4,3,3]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[6,5,5,4,1],[5,4,4,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[5,4,3,3,1],[4,3,2]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[6,5,4,4,1],[5,4,3,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[6,5,4,3,1],[5,4,3]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[7,6,5,4,1],[6,5,4,1]] => [1,1,1,3,1] => [3,1,1] => [1,3,1]
[[2,2,2,2,2],[1,1,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[3,3,3,3,2],[2,2,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,4,4,4,2],[3,3,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[3,3,3,2,2],[2,2,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,4,4,3,2],[3,3,3,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,5,5,4,2],[4,4,4,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[3,3,2,2,2],[2,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,4,3,3,2],[3,3,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,5,4,4,2],[4,4,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,4,3,2,2],[3,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,5,4,3,2],[4,4,3,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[6,6,5,4,2],[5,5,4,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[3,2,2,2,2],[2,1,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,3,3,3,2],[3,2,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,4,4,4,2],[4,3,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,3,3,2,2],[3,2,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,4,4,3,2],[4,3,3,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[6,5,5,4,2],[5,4,4,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[4,3,2,2,2],[3,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,4,3,3,2],[4,3,2,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[6,5,4,4,2],[5,4,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[5,4,3,2,2],[4,3,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[6,5,4,3,2],[5,4,3,1]] => [1,1,1,2,2] => [3,2] => [3,2]
[[7,6,5,4,2],[6,5,4,2]] => [1,1,1,2,2] => [3,2] => [3,2]
[[2,2,2,2,1,1],[1,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,3,3,3,1,1],[2,2,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,3,3,2,1,1],[2,2,2]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,4,3,1,1],[3,3,3,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,3,2,2,1,1],[2,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,3,3,1,1],[3,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,4,3,2,1,1],[3,3,2]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,5,4,3,1,1],[4,4,3,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,2,2,2,1,1],[2,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,3,3,3,1,1],[3,2,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,3,3,2,1,1],[3,2,2]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,4,3,1,1],[4,3,3,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[4,3,2,2,1,1],[3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,3,3,1,1],[4,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[6,5,4,4,2,1],[5,4,3,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[5,4,3,2,1,1],[4,3,2]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[6,5,4,3,1,1],[5,4,3,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [1,1,1,2,1,1] => [3,1,2] => [1,3,2]
[[3,3,3,3,3],[2,2,2,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[4,4,4,4,3],[3,3,3,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[4,4,4,3,3],[3,3,3,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,5,5,4,3],[4,4,4,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[4,4,3,3,3],[3,3,2,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,5,4,4,3],[4,4,3,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,5,4,3,3],[4,4,3,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[6,6,5,4,3],[5,5,4,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[4,3,3,3,3],[3,2,2,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,4,4,4,3],[4,3,3,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,4,4,3,3],[4,3,3,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[6,5,5,4,3],[5,4,4,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[5,4,3,3,3],[4,3,2,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[6,5,4,4,3],[5,4,3,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[6,5,4,3,3],[5,4,3,2]] => [1,1,1,1,3] => [4,1] => [4,1]
[[7,6,5,4,3],[6,5,4,3]] => [1,1,1,1,3] => [4,1] => [4,1]
[[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[3,3,3,3,2,1],[2,2,2,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[3,3,3,2,2,1],[2,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,4,3,2,1],[3,3,3,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[3,3,2,2,2,1],[2,2,1,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,3,3,2,1],[3,3,2,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,4,3,2,2,1],[3,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,5,4,3,2,1],[4,4,3,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[3,2,2,2,2,1],[2,1,1,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,3,3,3,2,1],[3,2,2,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,3,3,2,2,1],[3,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,4,3,2,1],[4,3,3,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[4,3,2,2,2,1],[3,2,1,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,3,3,2,1],[4,3,2,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[5,4,3,2,2,1],[4,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[6,5,4,3,2,1],[5,4,3,2]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [1,1,1,1,2,1] => [4,1,1] => [1,4,1]
[[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[3,3,3,3,3,2],[2,2,2,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [1,1,1,1,1,2] => [5,1] => [5,1]
[[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,2,1,1,1,1,1],[1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,2,2,1,1,1],[2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,3,2,1,1,1,1],[2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,4,3,2,1,1,1],[3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[2,1,1,1,1,1,1],[1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,2,2,2,1,1,1],[2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,2,2,1,1,1,1],[2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,3,2,1,1,1],[3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[3,2,1,1,1,1,1],[2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,2,2,1,1,1],[3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[4,3,2,1,1,1,1],[3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[5,4,3,2,1,1,1],[4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [1,1,1,1,1,1,1] => [7] => [7]
[[8],[]] => [8] => [1] => [1]
[[7,1],[]] => [7,1] => [1,1] => [1,1]
[[6,2],[]] => [6,2] => [1,1] => [1,1]
[[6,1,1],[]] => [6,1,1] => [1,2] => [1,2]
[[5,3],[]] => [5,3] => [1,1] => [1,1]
[[5,2,1],[]] => [5,2,1] => [1,1,1] => [1,1,1]
[[5,1,1,1],[]] => [5,1,1,1] => [1,3] => [1,3]
[[4,4],[]] => [4,4] => [2] => [2]
[[4,3,1],[]] => [4,3,1] => [1,1,1] => [1,1,1]
[[4,2,2],[]] => [4,2,2] => [1,2] => [1,2]
[[4,2,1,1],[]] => [4,2,1,1] => [1,1,2] => [1,1,2]
[[4,1,1,1,1],[]] => [4,1,1,1,1] => [1,4] => [1,4]
[[3,3,2],[]] => [3,3,2] => [2,1] => [2,1]
[[3,3,1,1],[]] => [3,3,1,1] => [2,2] => [2,2]
[[3,2,2,1],[]] => [3,2,2,1] => [1,2,1] => [2,1,1]
[[3,2,1,1,1],[]] => [3,2,1,1,1] => [1,1,3] => [1,1,3]
[[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => [1,5] => [1,5]
[[2,2,2,2],[]] => [2,2,2,2] => [4] => [4]
[[2,2,2,1,1],[]] => [2,2,2,1,1] => [3,2] => [3,2]
[[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => [2,4] => [2,4]
[[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1] => [1,6] => [1,6]
[[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => [8] => [8]
[[9],[]] => [9] => [1] => [1]
[[8,1],[]] => [8,1] => [1,1] => [1,1]
[[7,2],[]] => [7,2] => [1,1] => [1,1]
[[7,1,1],[]] => [7,1,1] => [1,2] => [1,2]
[[6,3],[]] => [6,3] => [1,1] => [1,1]
[[6,2,1],[]] => [6,2,1] => [1,1,1] => [1,1,1]
[[6,1,1,1],[]] => [6,1,1,1] => [1,3] => [1,3]
[[5,4],[]] => [5,4] => [1,1] => [1,1]
[[5,3,1],[]] => [5,3,1] => [1,1,1] => [1,1,1]
[[5,2,2],[]] => [5,2,2] => [1,2] => [1,2]
[[5,2,1,1],[]] => [5,2,1,1] => [1,1,2] => [1,1,2]
[[5,1,1,1,1],[]] => [5,1,1,1,1] => [1,4] => [1,4]
[[4,4,1],[]] => [4,4,1] => [2,1] => [2,1]
[[4,3,2],[]] => [4,3,2] => [1,1,1] => [1,1,1]
[[4,3,1,1],[]] => [4,3,1,1] => [1,1,2] => [1,1,2]
[[4,2,2,1],[]] => [4,2,2,1] => [1,2,1] => [2,1,1]
[[4,2,1,1,1],[]] => [4,2,1,1,1] => [1,1,3] => [1,1,3]
[[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => [1,5] => [1,5]
[[3,3,3],[]] => [3,3,3] => [3] => [3]
[[3,3,2,1],[]] => [3,3,2,1] => [2,1,1] => [1,2,1]
[[3,3,1,1,1],[]] => [3,3,1,1,1] => [2,3] => [2,3]
[[3,2,2,2],[]] => [3,2,2,2] => [1,3] => [1,3]
[[3,2,2,1,1],[]] => [3,2,2,1,1] => [1,2,2] => [1,2,2]
[[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1] => [1,6] => [1,6]
[[2,2,2,2,1],[]] => [2,2,2,2,1] => [4,1] => [4,1]
[[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => [3,3] => [3,3]
[[2,2,1,1,1,1,1],[]] => [2,2,1,1,1,1,1] => [2,5] => [2,5]
[[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1] => [1,7] => [1,7]
[[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => [9] => [9]
[[10],[]] => [10] => [1] => [1]
[[9,1],[]] => [9,1] => [1,1] => [1,1]
[[8,2],[]] => [8,2] => [1,1] => [1,1]
[[8,1,1],[]] => [8,1,1] => [1,2] => [1,2]
[[7,3],[]] => [7,3] => [1,1] => [1,1]
[[7,2,1],[]] => [7,2,1] => [1,1,1] => [1,1,1]
[[7,1,1,1],[]] => [7,1,1,1] => [1,3] => [1,3]
[[6,4],[]] => [6,4] => [1,1] => [1,1]
[[6,3,1],[]] => [6,3,1] => [1,1,1] => [1,1,1]
[[6,2,2],[]] => [6,2,2] => [1,2] => [1,2]
[[6,2,1,1],[]] => [6,2,1,1] => [1,1,2] => [1,1,2]
[[6,1,1,1,1],[]] => [6,1,1,1,1] => [1,4] => [1,4]
[[5,5],[]] => [5,5] => [2] => [2]
[[5,4,1],[]] => [5,4,1] => [1,1,1] => [1,1,1]
[[5,3,2],[]] => [5,3,2] => [1,1,1] => [1,1,1]
[[5,3,1,1],[]] => [5,3,1,1] => [1,1,2] => [1,1,2]
[[5,2,2,1],[]] => [5,2,2,1] => [1,2,1] => [2,1,1]
[[5,2,1,1,1],[]] => [5,2,1,1,1] => [1,1,3] => [1,1,3]
[[5,1,1,1,1,1],[]] => [5,1,1,1,1,1] => [1,5] => [1,5]
[[4,4,2],[]] => [4,4,2] => [2,1] => [2,1]
[[4,4,1,1],[]] => [4,4,1,1] => [2,2] => [2,2]
[[4,3,3],[]] => [4,3,3] => [1,2] => [1,2]
[[4,3,2,1],[]] => [4,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[4,3,1,1,1],[]] => [4,3,1,1,1] => [1,1,3] => [1,1,3]
[[4,2,2,2],[]] => [4,2,2,2] => [1,3] => [1,3]
[[4,2,2,1,1],[]] => [4,2,2,1,1] => [1,2,2] => [1,2,2]
[[4,2,1,1,1,1],[]] => [4,2,1,1,1,1] => [1,1,4] => [1,1,4]
[[4,1,1,1,1,1,1],[]] => [4,1,1,1,1,1,1] => [1,6] => [1,6]
[[3,3,3,1],[]] => [3,3,3,1] => [3,1] => [3,1]
[[3,3,2,2],[]] => [3,3,2,2] => [2,2] => [2,2]
[[3,3,2,1,1],[]] => [3,3,2,1,1] => [2,1,2] => [2,1,2]
[[3,3,1,1,1,1],[]] => [3,3,1,1,1,1] => [2,4] => [2,4]
[[3,2,2,2,1],[]] => [3,2,2,2,1] => [1,3,1] => [3,1,1]
[[3,2,2,1,1,1],[]] => [3,2,2,1,1,1] => [1,2,3] => [1,2,3]
[[3,2,1,1,1,1,1],[]] => [3,2,1,1,1,1,1] => [1,1,5] => [1,1,5]
[[3,1,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1,1] => [1,7] => [1,7]
[[2,2,2,2,2],[]] => [2,2,2,2,2] => [5] => [5]
[[2,2,2,2,1,1],[]] => [2,2,2,2,1,1] => [4,2] => [4,2]
[[2,2,2,1,1,1,1],[]] => [2,2,2,1,1,1,1] => [3,4] => [3,4]
[[2,2,1,1,1,1,1,1],[]] => [2,2,1,1,1,1,1,1] => [2,6] => [2,6]
[[2,1,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1,1] => [1,8] => [1,8]
[[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1] => [10] => [10]
[[4,4,3],[]] => [4,4,3] => [2,1] => [2,1]
[[3,3,3,2],[]] => [3,3,3,2] => [3,1] => [3,1]
[[6,6],[]] => [6,6] => [2] => [2]
[[5,5,2],[]] => [5,5,2] => [2,1] => [2,1]
[[5,4,3],[]] => [5,4,3] => [1,1,1] => [1,1,1]
[[4,4,4],[]] => [4,4,4] => [3] => [3]
[[4,4,3,1],[]] => [4,4,3,1] => [2,1,1] => [1,2,1]
[[4,4,2,2],[]] => [4,4,2,2] => [2,2] => [2,2]
[[4,3,3,2],[]] => [4,3,3,2] => [1,2,1] => [2,1,1]
[[3,3,3,3],[]] => [3,3,3,3] => [4] => [4]
[[3,3,3,2,1],[]] => [3,3,3,2,1] => [3,1,1] => [1,3,1]
[[3,3,2,2,2],[]] => [3,3,2,2,2] => [2,3] => [2,3]
[[2,2,2,2,2,2],[]] => [2,2,2,2,2,2] => [6] => [6]
[[3,3,3],[1]] => [2,3,3] => [1,2] => [1,2]
[[3,3,3,1],[1,1]] => [2,2,3,1] => [2,1,1] => [1,2,1]
[[4,4,1],[1]] => [3,4,1] => [1,1,1] => [1,1,1]
[[3,3,2,1],[1]] => [2,3,2,1] => [1,1,1,1] => [1,1,1,1]
[[2,2,2,2,1],[1]] => [1,2,2,2,1] => [1,3,1] => [3,1,1]
[[3,3,3,1],[2]] => [1,3,3,1] => [1,2,1] => [2,1,1]
[[3,3,3,1],[1]] => [2,3,3,1] => [1,2,1] => [2,1,1]
[[3,3,3,2],[1,1,1]] => [2,2,2,2] => [4] => [4]
[[4,4,2],[1,1]] => [3,3,2] => [2,1] => [2,1]
[[4,4,4],[2,2]] => [2,2,4] => [2,1] => [2,1]
[[5,5],[2]] => [3,5] => [1,1] => [1,1]
[[4,4,3],[2,1]] => [2,3,3] => [1,2] => [1,2]
[[3,3,3,3],[2,1,1]] => [1,2,2,3] => [1,2,1] => [2,1,1]
[[4,3,3],[1,1]] => [3,2,3] => [1,1,1] => [1,1,1]
[[3,3,3,3],[1,1,1]] => [2,2,2,3] => [3,1] => [3,1]
[[4,4,3],[1,1]] => [3,3,3] => [3] => [3]
[[4,4,4],[3,1]] => [1,3,4] => [1,1,1] => [1,1,1]
[[5,4],[1]] => [4,4] => [2] => [2]
[[4,4,4],[2,1]] => [2,3,4] => [1,1,1] => [1,1,1]
[[5,5],[1]] => [4,5] => [1,1] => [1,1]
[[4,4,4],[1,1]] => [3,3,4] => [2,1] => [2,1]
[[3,3,2,2],[1,1]] => [2,2,2,2] => [4] => [4]
[[4,4,2],[2]] => [2,4,2] => [1,1,1] => [1,1,1]
[[3,3,3,2],[2,1]] => [1,2,3,2] => [1,1,1,1] => [1,1,1,1]
[[4,3,2],[1]] => [3,3,2] => [2,1] => [2,1]
[[3,3,3,2],[1,1]] => [2,2,3,2] => [2,1,1] => [1,2,1]
[[4,4,2],[1]] => [3,4,2] => [1,1,1] => [1,1,1]
[[2,2,2,2,2],[1,1]] => [1,1,2,2,2] => [2,3] => [2,3]
[[3,2,2,2],[1]] => [2,2,2,2] => [4] => [4]
[[3,3,2,2],[2]] => [1,3,2,2] => [1,1,2] => [1,1,2]
[[3,3,2,2],[1]] => [2,3,2,2] => [1,1,2] => [1,1,2]
[[2,2,2,2,2],[1]] => [1,2,2,2,2] => [1,4] => [1,4]
[[3,3,3,2],[2]] => [1,3,3,2] => [1,2,1] => [2,1,1]
[[3,3,3,2],[1]] => [2,3,3,2] => [1,2,1] => [2,1,1]
[[3,3,3,3],[2,2]] => [1,1,3,3] => [2,2] => [2,2]
[[4,3,3],[2]] => [2,3,3] => [1,2] => [1,2]
[[4,4,3],[3]] => [1,4,3] => [1,1,1] => [1,1,1]
[[4,4,3],[2]] => [2,4,3] => [1,1,1] => [1,1,1]
[[3,3,3,3],[2,1]] => [1,2,3,3] => [1,1,2] => [1,1,2]
[[4,3,3],[1]] => [3,3,3] => [3] => [3]
[[3,3,3,3],[1,1]] => [2,2,3,3] => [2,2] => [2,2]
[[4,4,3],[1]] => [3,4,3] => [1,1,1] => [1,1,1]
[[4,4,4],[3]] => [1,4,4] => [1,2] => [1,2]
[[4,4,4],[2]] => [2,4,4] => [1,2] => [1,2]
[[4,4,4],[1]] => [3,4,4] => [1,2] => [1,2]
[[3,3,3,3],[2]] => [1,3,3,3] => [1,3] => [1,3]
[[3,3,3,3],[1]] => [2,3,3,3] => [1,3] => [1,3]
[[4,4,4,1],[1]] => [3,4,4,1] => [1,2,1] => [2,1,1]
[[3,3,3,3,1],[1]] => [2,3,3,3,1] => [1,3,1] => [3,1,1]
[[4,4,4,2],[1,1,1]] => [3,3,3,2] => [3,1] => [3,1]
[[6,6],[4]] => [2,6] => [1,1] => [1,1]
[[6,5],[3]] => [3,5] => [1,1] => [1,1]
[[5,5,5],[3,3]] => [2,2,5] => [2,1] => [2,1]
[[6,6],[3]] => [3,6] => [1,1] => [1,1]
[[6,4],[2]] => [4,4] => [2] => [2]
[[5,5,4],[3,2]] => [2,3,4] => [1,1,1] => [1,1,1]
[[5,4,4],[2,2]] => [3,2,4] => [1,1,1] => [1,1,1]
[[4,4,4,4],[2,2,2]] => [2,2,2,4] => [3,1] => [3,1]
[[5,5,4],[2,2]] => [3,3,4] => [2,1] => [2,1]
[[6,5],[2]] => [4,5] => [1,1] => [1,1]
[[5,5,5],[3,2]] => [2,3,5] => [1,1,1] => [1,1,1]
[[6,6],[2]] => [4,6] => [1,1] => [1,1]
[[6,3],[1]] => [5,3] => [1,1] => [1,1]
[[5,5,3],[3,1]] => [2,4,3] => [1,1,1] => [1,1,1]
[[5,4,3],[2,1]] => [3,3,3] => [3] => [3]
[[4,4,4,3],[2,2,1]] => [2,2,3,3] => [2,2] => [2,2]
[[5,5,3],[2,1]] => [3,4,3] => [1,1,1] => [1,1,1]
[[5,3,3],[1,1]] => [4,2,3] => [1,1,1] => [1,1,1]
[[4,4,3,3],[2,1,1]] => [2,3,2,3] => [1,1,1,1] => [1,1,1,1]
[[4,3,3,3],[1,1,1]] => [3,2,2,3] => [1,2,1] => [2,1,1]
[[5,4,3],[1,1]] => [4,3,3] => [1,2] => [1,2]
[[4,4,4,3],[2,1,1]] => [2,3,3,3] => [1,3] => [1,3]
[[5,5,3],[1,1]] => [4,4,3] => [2,1] => [2,1]
[[4,4,4,3],[1,1,1]] => [3,3,3,3] => [4] => [4]
[[6,4],[1]] => [5,4] => [1,1] => [1,1]
[[5,5,4],[3,1]] => [2,4,4] => [1,2] => [1,2]
[[5,4,4],[2,1]] => [3,3,4] => [2,1] => [2,1]
[[5,5,4],[2,1]] => [3,4,4] => [1,2] => [1,2]
[[6,5],[1]] => [5,5] => [2] => [2]
[[5,5,5],[2,1]] => [3,4,5] => [1,1,1] => [1,1,1]
[[4,4,4,4],[2,1,1]] => [2,3,3,4] => [1,2,1] => [2,1,1]
[[5,5,4],[1,1]] => [4,4,4] => [3] => [3]
[[5,5,2],[3]] => [2,5,2] => [1,1,1] => [1,1,1]
[[5,4,2],[2]] => [3,4,2] => [1,1,1] => [1,1,1]
[[4,4,4,2],[2,2]] => [2,2,4,2] => [2,1,1] => [1,2,1]
[[5,5,2],[2]] => [3,5,2] => [1,1,1] => [1,1,1]
[[5,3,2],[1]] => [4,3,2] => [1,1,1] => [1,1,1]
[[4,4,3,2],[2,1]] => [2,3,3,2] => [1,2,1] => [2,1,1]
[[4,3,3,2],[1,1]] => [3,2,3,2] => [1,1,1,1] => [1,1,1,1]
[[4,4,3,2],[1,1]] => [3,3,3,2] => [3,1] => [3,1]
[[5,4,2],[1]] => [4,4,2] => [2,1] => [2,1]
[[4,4,4,2],[1,1]] => [3,3,4,2] => [2,1,1] => [1,2,1]
[[4,4,2,2],[2]] => [2,4,2,2] => [1,1,2] => [1,1,2]
[[4,3,2,2],[1]] => [3,3,2,2] => [2,2] => [2,2]
[[3,3,3,2,2],[1]] => [2,3,3,2,2] => [1,2,2] => [1,2,2]
[[4,3,3,2],[1]] => [3,3,3,2] => [3,1] => [3,1]
[[3,3,3,3,2],[1,1]] => [2,2,3,3,2] => [2,2,1] => [2,2,1]
[[4,4,3,2],[1]] => [3,4,3,2] => [1,1,1,1] => [1,1,1,1]
[[4,4,4,2],[2]] => [2,4,4,2] => [1,2,1] => [2,1,1]
[[3,3,3,3,2],[2]] => [1,3,3,3,2] => [1,3,1] => [3,1,1]
[[5,5,3],[3]] => [2,5,3] => [1,1,1] => [1,1,1]
[[5,4,3],[2]] => [3,4,3] => [1,1,1] => [1,1,1]
[[5,3,3],[1]] => [4,3,3] => [1,2] => [1,2]
[[4,4,3,3],[2,1]] => [2,3,3,3] => [1,3] => [1,3]
[[3,3,3,3,3],[1,1,1]] => [2,2,2,3,3] => [3,2] => [3,2]
[[4,4,3,3],[1,1]] => [3,3,3,3] => [4] => [4]
[[5,4,3],[1]] => [4,4,3] => [2,1] => [2,1]
[[4,4,4,3],[2,1]] => [2,3,4,3] => [1,1,1,1] => [1,1,1,1]
[[5,5,3],[1]] => [4,5,3] => [1,1,1] => [1,1,1]
[[5,4,4],[2]] => [3,4,4] => [1,2] => [1,2]
[[4,4,4,4],[2,2]] => [2,2,4,4] => [2,2] => [2,2]
[[5,5,4],[2]] => [3,5,4] => [1,1,1] => [1,1,1]
[[5,5,5],[4]] => [1,5,5] => [1,2] => [1,2]
[[5,5,5],[3]] => [2,5,5] => [1,2] => [1,2]
[[4,4,4,4],[3,1]] => [1,3,4,4] => [1,1,2] => [1,1,2]
[[5,4,4],[1]] => [4,4,4] => [3] => [3]
[[4,3,3,3],[2]] => [2,3,3,3] => [1,3] => [1,3]
[[4,4,3,3],[2]] => [2,4,3,3] => [1,1,2] => [1,1,2]
[[3,3,3,3,3],[2,1]] => [1,2,3,3,3] => [1,1,3] => [1,1,3]
[[4,3,3,3],[1]] => [3,3,3,3] => [4] => [4]
[[4,4,4,3],[3]] => [1,4,4,3] => [1,2,1] => [2,1,1]
Map
row lengths
Description
The sequence of row lengths from top to bottom.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00314Foata bijection.
See Mp00314Foata bijection.
searching the database
Sorry, this map was not found in the database.