Identifier
Mp00189:
Skew partitions
—rotate⟶
Skew partitions
Mp00181: Skew partitions —row lengths⟶ Integer compositions
Mp00181: Skew partitions —row lengths⟶ Integer compositions
Images
[[1],[]] => [[1],[]] => [1]
[[2],[]] => [[2],[]] => [2]
[[1,1],[]] => [[1,1],[]] => [1,1]
[[2,1],[1]] => [[2,1],[1]] => [1,1]
[[3],[]] => [[3],[]] => [3]
[[2,1],[]] => [[2,2],[1]] => [1,2]
[[3,1],[1]] => [[3,2],[2]] => [1,2]
[[2,2],[1]] => [[2,1],[]] => [2,1]
[[3,2],[2]] => [[3,1],[1]] => [2,1]
[[1,1,1],[]] => [[1,1,1],[]] => [1,1,1]
[[2,2,1],[1,1]] => [[2,1,1],[1]] => [1,1,1]
[[2,1,1],[1]] => [[2,2,1],[1,1]] => [1,1,1]
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => [1,1,1]
[[4],[]] => [[4],[]] => [4]
[[3,1],[]] => [[3,3],[2]] => [1,3]
[[4,1],[1]] => [[4,3],[3]] => [1,3]
[[2,2],[]] => [[2,2],[]] => [2,2]
[[3,2],[1]] => [[3,2],[1]] => [2,2]
[[4,2],[2]] => [[4,2],[2]] => [2,2]
[[2,1,1],[]] => [[2,2,2],[1,1]] => [1,1,2]
[[3,2,1],[1,1]] => [[3,2,2],[2,1]] => [1,1,2]
[[3,1,1],[1]] => [[3,3,2],[2,2]] => [1,1,2]
[[4,2,1],[2,1]] => [[4,3,2],[3,2]] => [1,1,2]
[[3,3],[2]] => [[3,1],[]] => [3,1]
[[4,3],[3]] => [[4,1],[1]] => [3,1]
[[2,2,1],[1]] => [[2,2,1],[1]] => [1,2,1]
[[3,3,1],[2,1]] => [[3,2,1],[2]] => [1,2,1]
[[3,2,1],[2]] => [[3,3,1],[2,1]] => [1,2,1]
[[4,3,1],[3,1]] => [[4,3,1],[3,1]] => [1,2,1]
[[2,2,2],[1,1]] => [[2,1,1],[]] => [2,1,1]
[[3,3,2],[2,2]] => [[3,1,1],[1]] => [2,1,1]
[[3,2,2],[2,1]] => [[3,2,1],[1,1]] => [2,1,1]
[[4,3,2],[3,2]] => [[4,2,1],[2,1]] => [2,1,1]
[[1,1,1,1],[]] => [[1,1,1,1],[]] => [1,1,1,1]
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]] => [1,1,1,1]
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]] => [1,1,1,1]
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]] => [1,1,1,1]
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]] => [1,1,1,1]
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]] => [1,1,1,1]
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]] => [1,1,1,1]
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => [1,1,1,1]
[[5],[]] => [[5],[]] => [5]
[[4,1],[]] => [[4,4],[3]] => [1,4]
[[5,1],[1]] => [[5,4],[4]] => [1,4]
[[3,2],[]] => [[3,3],[1]] => [2,3]
[[4,2],[1]] => [[4,3],[2]] => [2,3]
[[5,2],[2]] => [[5,3],[3]] => [2,3]
[[3,1,1],[]] => [[3,3,3],[2,2]] => [1,1,3]
[[4,2,1],[1,1]] => [[4,3,3],[3,2]] => [1,1,3]
[[4,1,1],[1]] => [[4,4,3],[3,3]] => [1,1,3]
[[5,2,1],[2,1]] => [[5,4,3],[4,3]] => [1,1,3]
[[3,3],[1]] => [[3,2],[]] => [3,2]
[[4,3],[2]] => [[4,2],[1]] => [3,2]
[[5,3],[3]] => [[5,2],[2]] => [3,2]
[[2,2,1],[]] => [[2,2,2],[1]] => [1,2,2]
[[3,3,1],[1,1]] => [[3,2,2],[2]] => [1,2,2]
[[3,2,1],[1]] => [[3,3,2],[2,1]] => [1,2,2]
[[4,3,1],[2,1]] => [[4,3,2],[3,1]] => [1,2,2]
[[4,2,1],[2]] => [[4,4,2],[3,2]] => [1,2,2]
[[5,3,1],[3,1]] => [[5,4,2],[4,2]] => [1,2,2]
[[3,2,2],[1,1]] => [[3,2,2],[1,1]] => [2,1,2]
[[4,3,2],[2,2]] => [[4,2,2],[2,1]] => [2,1,2]
[[4,2,2],[2,1]] => [[4,3,2],[2,2]] => [2,1,2]
[[5,3,2],[3,2]] => [[5,3,2],[3,2]] => [2,1,2]
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [1,1,1,2]
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]] => [1,1,1,2]
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]] => [1,1,1,2]
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]] => [1,1,1,2]
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]] => [1,1,1,2]
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]] => [1,1,1,2]
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]] => [1,1,1,2]
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]] => [1,1,1,2]
[[4,4],[3]] => [[4,1],[]] => [4,1]
[[5,4],[4]] => [[5,1],[1]] => [4,1]
[[3,3,1],[2]] => [[3,3,1],[2]] => [1,3,1]
[[4,4,1],[3,1]] => [[4,3,1],[3]] => [1,3,1]
[[4,3,1],[3]] => [[4,4,1],[3,1]] => [1,3,1]
[[5,4,1],[4,1]] => [[5,4,1],[4,1]] => [1,3,1]
[[2,2,2],[1]] => [[2,2,1],[]] => [2,2,1]
[[3,3,2],[2,1]] => [[3,2,1],[1]] => [2,2,1]
[[4,4,2],[3,2]] => [[4,2,1],[2]] => [2,2,1]
[[3,2,2],[2]] => [[3,3,1],[1,1]] => [2,2,1]
[[4,3,2],[3,1]] => [[4,3,1],[2,1]] => [2,2,1]
[[5,4,2],[4,2]] => [[5,3,1],[3,1]] => [2,2,1]
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]] => [1,1,2,1]
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]] => [1,1,2,1]
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]] => [1,1,2,1]
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]] => [1,1,2,1]
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]] => [1,1,2,1]
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]] => [1,1,2,1]
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]] => [1,1,2,1]
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]] => [1,1,2,1]
[[3,3,3],[2,2]] => [[3,1,1],[]] => [3,1,1]
[[4,4,3],[3,3]] => [[4,1,1],[1]] => [3,1,1]
[[4,3,3],[3,2]] => [[4,2,1],[1,1]] => [3,1,1]
[[5,4,3],[4,3]] => [[5,2,1],[2,1]] => [3,1,1]
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]] => [1,2,1,1]
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]] => [1,2,1,1]
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]] => [1,2,1,1]
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]] => [1,2,1,1]
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]] => [1,2,1,1]
>>> Load all 1367 entries. <<<
[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]] => [1,2,1,1]
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]] => [1,2,1,1]
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]] => [1,2,1,1]
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]] => [2,1,1,1]
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]] => [2,1,1,1]
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]] => [2,1,1,1]
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]] => [2,1,1,1]
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]] => [2,1,1,1]
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]] => [2,1,1,1]
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]] => [2,1,1,1]
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]] => [2,1,1,1]
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => [1,1,1,1,1]
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]] => [1,1,1,1,1]
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]] => [1,1,1,1,1]
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]] => [1,1,1,1,1]
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]] => [1,1,1,1,1]
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]] => [1,1,1,1,1]
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]] => [1,1,1,1,1]
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]] => [1,1,1,1,1]
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,1]
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]] => [1,1,1,1,1]
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]] => [1,1,1,1,1]
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => [1,1,1,1,1]
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]] => [1,1,1,1,1]
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]] => [1,1,1,1,1]
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]] => [1,1,1,1,1]
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => [1,1,1,1,1]
[[6],[]] => [[6],[]] => [6]
[[5,1],[]] => [[5,5],[4]] => [1,5]
[[6,1],[1]] => [[6,5],[5]] => [1,5]
[[4,2],[]] => [[4,4],[2]] => [2,4]
[[5,2],[1]] => [[5,4],[3]] => [2,4]
[[6,2],[2]] => [[6,4],[4]] => [2,4]
[[4,1,1],[]] => [[4,4,4],[3,3]] => [1,1,4]
[[5,2,1],[1,1]] => [[5,4,4],[4,3]] => [1,1,4]
[[5,1,1],[1]] => [[5,5,4],[4,4]] => [1,1,4]
[[6,2,1],[2,1]] => [[6,5,4],[5,4]] => [1,1,4]
[[3,3],[]] => [[3,3],[]] => [3,3]
[[4,3],[1]] => [[4,3],[1]] => [3,3]
[[5,3],[2]] => [[5,3],[2]] => [3,3]
[[6,3],[3]] => [[6,3],[3]] => [3,3]
[[3,2,1],[]] => [[3,3,3],[2,1]] => [1,2,3]
[[4,3,1],[1,1]] => [[4,3,3],[3,1]] => [1,2,3]
[[4,2,1],[1]] => [[4,4,3],[3,2]] => [1,2,3]
[[5,3,1],[2,1]] => [[5,4,3],[4,2]] => [1,2,3]
[[5,2,1],[2]] => [[5,5,3],[4,3]] => [1,2,3]
[[6,3,1],[3,1]] => [[6,5,3],[5,3]] => [1,2,3]
[[4,2,2],[1,1]] => [[4,3,3],[2,2]] => [2,1,3]
[[5,3,2],[2,2]] => [[5,3,3],[3,2]] => [2,1,3]
[[5,2,2],[2,1]] => [[5,4,3],[3,3]] => [2,1,3]
[[6,3,2],[3,2]] => [[6,4,3],[4,3]] => [2,1,3]
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [1,1,1,3]
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]] => [1,1,1,3]
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]] => [1,1,1,3]
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]] => [1,1,1,3]
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]] => [1,1,1,3]
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]] => [1,1,1,3]
[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]] => [1,1,1,3]
[[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]] => [1,1,1,3]
[[4,4],[2]] => [[4,2],[]] => [4,2]
[[5,4],[3]] => [[5,2],[1]] => [4,2]
[[6,4],[4]] => [[6,2],[2]] => [4,2]
[[3,3,1],[1]] => [[3,3,2],[2]] => [1,3,2]
[[4,4,1],[2,1]] => [[4,3,2],[3]] => [1,3,2]
[[4,3,1],[2]] => [[4,4,2],[3,1]] => [1,3,2]
[[5,4,1],[3,1]] => [[5,4,2],[4,1]] => [1,3,2]
[[5,3,1],[3]] => [[5,5,2],[4,2]] => [1,3,2]
[[6,4,1],[4,1]] => [[6,5,2],[5,2]] => [1,3,2]
[[2,2,2],[]] => [[2,2,2],[]] => [2,2,2]
[[3,3,2],[1,1]] => [[3,2,2],[1]] => [2,2,2]
[[4,4,2],[2,2]] => [[4,2,2],[2]] => [2,2,2]
[[3,2,2],[1]] => [[3,3,2],[1,1]] => [2,2,2]
[[4,3,2],[2,1]] => [[4,3,2],[2,1]] => [2,2,2]
[[5,4,2],[3,2]] => [[5,3,2],[3,1]] => [2,2,2]
[[4,2,2],[2]] => [[4,4,2],[2,2]] => [2,2,2]
[[5,3,2],[3,1]] => [[5,4,2],[3,2]] => [2,2,2]
[[6,4,2],[4,2]] => [[6,4,2],[4,2]] => [2,2,2]
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [1,1,2,2]
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]] => [1,1,2,2]
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]] => [1,1,2,2]
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => [1,1,2,2]
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]] => [1,1,2,2]
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]] => [1,1,2,2]
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]] => [1,1,2,2]
[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]] => [1,1,2,2]
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]] => [1,1,2,2]
[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]] => [1,1,2,2]
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]] => [1,1,2,2]
[[6,4,2,1],[4,2,1]] => [[6,5,4,2],[5,4,2]] => [1,1,2,2]
[[4,3,3],[2,2]] => [[4,2,2],[1,1]] => [3,1,2]
[[5,4,3],[3,3]] => [[5,2,2],[2,1]] => [3,1,2]
[[5,3,3],[3,2]] => [[5,3,2],[2,2]] => [3,1,2]
[[6,4,3],[4,3]] => [[6,3,2],[3,2]] => [3,1,2]
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]] => [1,2,1,2]
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]] => [1,2,1,2]
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]] => [1,2,1,2]
[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]] => [1,2,1,2]
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]] => [1,2,1,2]
[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]] => [1,2,1,2]
[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]] => [1,2,1,2]
[[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]] => [1,2,1,2]
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]] => [2,1,1,2]
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]] => [2,1,1,2]
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]] => [2,1,1,2]
[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]] => [2,1,1,2]
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]] => [2,1,1,2]
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]] => [2,1,1,2]
[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]] => [2,1,1,2]
[[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]] => [2,1,1,2]
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1,2]
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]] => [1,1,1,1,2]
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]] => [1,1,1,1,2]
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => [1,1,1,1,2]
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]] => [1,1,1,1,2]
[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]] => [1,1,1,1,2]
[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]] => [1,1,1,1,2]
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => [1,1,1,1,2]
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]] => [1,1,1,1,2]
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]] => [1,1,1,1,2]
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]] => [1,1,1,1,2]
[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]] => [1,1,1,1,2]
[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]] => [1,1,1,1,2]
[[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]] => [1,1,1,1,2]
[[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]] => [1,1,1,1,2]
[[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] => [1,1,1,1,2]
[[5,5],[4]] => [[5,1],[]] => [5,1]
[[6,5],[5]] => [[6,1],[1]] => [5,1]
[[4,4,1],[3]] => [[4,4,1],[3]] => [1,4,1]
[[5,5,1],[4,1]] => [[5,4,1],[4]] => [1,4,1]
[[5,4,1],[4]] => [[5,5,1],[4,1]] => [1,4,1]
[[6,5,1],[5,1]] => [[6,5,1],[5,1]] => [1,4,1]
[[3,3,2],[2]] => [[3,3,1],[1]] => [2,3,1]
[[4,4,2],[3,1]] => [[4,3,1],[2]] => [2,3,1]
[[5,5,2],[4,2]] => [[5,3,1],[3]] => [2,3,1]
[[4,3,2],[3]] => [[4,4,1],[2,1]] => [2,3,1]
[[5,4,2],[4,1]] => [[5,4,1],[3,1]] => [2,3,1]
[[6,5,2],[5,2]] => [[6,4,1],[4,1]] => [2,3,1]
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]] => [1,1,3,1]
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]] => [1,1,3,1]
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]] => [1,1,3,1]
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]] => [1,1,3,1]
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]] => [1,1,3,1]
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]] => [1,1,3,1]
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]] => [1,1,3,1]
[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]] => [1,1,3,1]
[[3,3,3],[2,1]] => [[3,2,1],[]] => [3,2,1]
[[4,4,3],[3,2]] => [[4,2,1],[1]] => [3,2,1]
[[5,5,3],[4,3]] => [[5,2,1],[2]] => [3,2,1]
[[4,3,3],[3,1]] => [[4,3,1],[1,1]] => [3,2,1]
[[5,4,3],[4,2]] => [[5,3,1],[2,1]] => [3,2,1]
[[6,5,3],[5,3]] => [[6,3,1],[3,1]] => [3,2,1]
[[2,2,2,1],[1]] => [[2,2,2,1],[1]] => [1,2,2,1]
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]] => [1,2,2,1]
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]] => [1,2,2,1]
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]] => [1,2,2,1]
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]] => [1,2,2,1]
[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]] => [1,2,2,1]
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]] => [1,2,2,1]
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => [1,2,2,1]
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]] => [1,2,2,1]
[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]] => [1,2,2,1]
[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]] => [1,2,2,1]
[[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]] => [1,2,2,1]
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]] => [2,1,2,1]
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]] => [2,1,2,1]
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]] => [2,1,2,1]
[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]] => [2,1,2,1]
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]] => [2,1,2,1]
[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]] => [2,1,2,1]
[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]] => [2,1,2,1]
[[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]] => [2,1,2,1]
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]] => [1,1,1,2,1]
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]] => [1,1,1,2,1]
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]] => [1,1,1,2,1]
[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]] => [1,1,1,2,1]
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]] => [1,1,1,2,1]
[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]] => [1,1,1,2,1]
[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]] => [1,1,1,2,1]
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => [1,1,1,2,1]
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]] => [1,1,1,2,1]
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]] => [1,1,1,2,1]
[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]] => [1,1,1,2,1]
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => [1,1,1,2,1]
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]] => [1,1,1,2,1]
[[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]] => [1,1,1,2,1]
[[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]] => [1,1,1,2,1]
[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => [1,1,1,2,1]
[[4,4,4],[3,3]] => [[4,1,1],[]] => [4,1,1]
[[5,5,4],[4,4]] => [[5,1,1],[1]] => [4,1,1]
[[5,4,4],[4,3]] => [[5,2,1],[1,1]] => [4,1,1]
[[6,5,4],[5,4]] => [[6,2,1],[2,1]] => [4,1,1]
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]] => [1,3,1,1]
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]] => [1,3,1,1]
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]] => [1,3,1,1]
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]] => [1,3,1,1]
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]] => [1,3,1,1]
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]] => [1,3,1,1]
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]] => [1,3,1,1]
[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]] => [1,3,1,1]
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]] => [2,2,1,1]
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]] => [2,2,1,1]
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]] => [2,2,1,1]
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]] => [2,2,1,1]
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]] => [2,2,1,1]
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]] => [2,2,1,1]
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]] => [2,2,1,1]
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]] => [2,2,1,1]
[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]] => [2,2,1,1]
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => [2,2,1,1]
[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]] => [2,2,1,1]
[[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]] => [2,2,1,1]
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]] => [1,1,2,1,1]
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]] => [1,1,2,1,1]
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]] => [1,1,2,1,1]
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]] => [1,1,2,1,1]
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]] => [1,1,2,1,1]
[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]] => [1,1,2,1,1]
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]] => [1,1,2,1,1]
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]] => [1,1,2,1,1]
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]] => [1,1,2,1,1]
[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]] => [1,1,2,1,1]
[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]] => [1,1,2,1,1]
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => [1,1,2,1,1]
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]] => [1,1,2,1,1]
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]] => [1,1,2,1,1]
[[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]] => [1,1,2,1,1]
[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => [1,1,2,1,1]
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]] => [3,1,1,1]
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]] => [3,1,1,1]
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]] => [3,1,1,1]
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]] => [3,1,1,1]
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]] => [3,1,1,1]
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]] => [3,1,1,1]
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]] => [3,1,1,1]
[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]] => [3,1,1,1]
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]] => [1,2,1,1,1]
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]] => [1,2,1,1,1]
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]] => [1,2,1,1,1]
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]] => [1,2,1,1,1]
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]] => [1,2,1,1,1]
[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]] => [1,2,1,1,1]
[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]] => [1,2,1,1,1]
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]] => [1,2,1,1,1]
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]] => [1,2,1,1,1]
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]] => [1,2,1,1,1]
[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]] => [1,2,1,1,1]
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]] => [1,2,1,1,1]
[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]] => [1,2,1,1,1]
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]] => [1,2,1,1,1]
[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]] => [1,2,1,1,1]
[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]] => [1,2,1,1,1]
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]] => [2,1,1,1,1]
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]] => [2,1,1,1,1]
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]] => [2,1,1,1,1]
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]] => [2,1,1,1,1]
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]] => [2,1,1,1,1]
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]] => [2,1,1,1,1]
[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]] => [2,1,1,1,1]
[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]] => [2,1,1,1,1]
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]] => [2,1,1,1,1]
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1,1]
[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]] => [2,1,1,1,1]
[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]] => [2,1,1,1,1]
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]] => [2,1,1,1,1]
[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]] => [2,1,1,1,1]
[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]] => [2,1,1,1,1]
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]] => [2,1,1,1,1]
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => [1,1,1,1,1,1]
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]] => [1,1,1,1,1,1]
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]] => [1,1,1,1,1,1]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]] => [1,1,1,1,1,1]
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]] => [1,1,1,1,1,1]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]] => [1,1,1,1,1,1]
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]] => [1,1,1,1,1,1]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => [1,1,1,1,1,1]
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1,1,1]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => [1,1,1,1,1,1]
[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]] => [1,1,1,1,1,1]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] => [1,1,1,1,1,1]
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]] => [1,1,1,1,1,1]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]] => [1,1,1,1,1,1]
[[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]] => [1,1,1,1,1,1]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => [1,1,1,1,1,1]
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1,1]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => [1,1,1,1,1,1]
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => [1,1,1,1,1,1]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] => [1,1,1,1,1,1]
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => [1,1,1,1,1,1]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] => [1,1,1,1,1,1]
[[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]] => [1,1,1,1,1,1]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] => [1,1,1,1,1,1]
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => [1,1,1,1,1,1]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] => [1,1,1,1,1,1]
[[4,3,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2,1]] => [1,1,1,1,1,1]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] => [1,1,1,1,1,1]
[[4,3,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2,1]] => [1,1,1,1,1,1]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] => [1,1,1,1,1,1]
[[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]] => [1,1,1,1,1,1]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => [1,1,1,1,1,1]
[[7],[]] => [[7],[]] => [7]
[[6,1],[]] => [[6,6],[5]] => [1,6]
[[7,1],[1]] => [[7,6],[6]] => [1,6]
[[5,2],[]] => [[5,5],[3]] => [2,5]
[[6,2],[1]] => [[6,5],[4]] => [2,5]
[[7,2],[2]] => [[7,5],[5]] => [2,5]
[[5,1,1],[]] => [[5,5,5],[4,4]] => [1,1,5]
[[6,2,1],[1,1]] => [[6,5,5],[5,4]] => [1,1,5]
[[6,1,1],[1]] => [[6,6,5],[5,5]] => [1,1,5]
[[7,2,1],[2,1]] => [[7,6,5],[6,5]] => [1,1,5]
[[4,3],[]] => [[4,4],[1]] => [3,4]
[[5,3],[1]] => [[5,4],[2]] => [3,4]
[[6,3],[2]] => [[6,4],[3]] => [3,4]
[[7,3],[3]] => [[7,4],[4]] => [3,4]
[[4,2,1],[]] => [[4,4,4],[3,2]] => [1,2,4]
[[5,3,1],[1,1]] => [[5,4,4],[4,2]] => [1,2,4]
[[5,2,1],[1]] => [[5,5,4],[4,3]] => [1,2,4]
[[6,3,1],[2,1]] => [[6,5,4],[5,3]] => [1,2,4]
[[6,2,1],[2]] => [[6,6,4],[5,4]] => [1,2,4]
[[7,3,1],[3,1]] => [[7,6,4],[6,4]] => [1,2,4]
[[5,2,2],[1,1]] => [[5,4,4],[3,3]] => [2,1,4]
[[6,3,2],[2,2]] => [[6,4,4],[4,3]] => [2,1,4]
[[6,2,2],[2,1]] => [[6,5,4],[4,4]] => [2,1,4]
[[7,3,2],[3,2]] => [[7,5,4],[5,4]] => [2,1,4]
[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => [1,1,1,4]
[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]] => [1,1,1,4]
[[5,2,1,1],[1,1]] => [[5,5,4,4],[4,4,3]] => [1,1,1,4]
[[6,3,2,1],[2,2,1]] => [[6,5,4,4],[5,4,3]] => [1,1,1,4]
[[5,1,1,1],[1]] => [[5,5,5,4],[4,4,4]] => [1,1,1,4]
[[6,2,2,1],[2,1,1]] => [[6,5,5,4],[5,4,4]] => [1,1,1,4]
[[6,2,1,1],[2,1]] => [[6,6,5,4],[5,5,4]] => [1,1,1,4]
[[7,3,2,1],[3,2,1]] => [[7,6,5,4],[6,5,4]] => [1,1,1,4]
[[4,4],[1]] => [[4,3],[]] => [4,3]
[[5,4],[2]] => [[5,3],[1]] => [4,3]
[[6,4],[3]] => [[6,3],[2]] => [4,3]
[[7,4],[4]] => [[7,3],[3]] => [4,3]
[[3,3,1],[]] => [[3,3,3],[2]] => [1,3,3]
[[4,4,1],[1,1]] => [[4,3,3],[3]] => [1,3,3]
[[4,3,1],[1]] => [[4,4,3],[3,1]] => [1,3,3]
[[5,4,1],[2,1]] => [[5,4,3],[4,1]] => [1,3,3]
[[5,3,1],[2]] => [[5,5,3],[4,2]] => [1,3,3]
[[6,4,1],[3,1]] => [[6,5,3],[5,2]] => [1,3,3]
[[6,3,1],[3]] => [[6,6,3],[5,3]] => [1,3,3]
[[7,4,1],[4,1]] => [[7,6,3],[6,3]] => [1,3,3]
[[3,2,2],[]] => [[3,3,3],[1,1]] => [2,2,3]
[[4,3,2],[1,1]] => [[4,3,3],[2,1]] => [2,2,3]
[[5,4,2],[2,2]] => [[5,3,3],[3,1]] => [2,2,3]
[[4,2,2],[1]] => [[4,4,3],[2,2]] => [2,2,3]
[[5,3,2],[2,1]] => [[5,4,3],[3,2]] => [2,2,3]
[[6,4,2],[3,2]] => [[6,4,3],[4,2]] => [2,2,3]
[[5,2,2],[2]] => [[5,5,3],[3,3]] => [2,2,3]
[[6,3,2],[3,1]] => [[6,5,3],[4,3]] => [2,2,3]
[[7,4,2],[4,2]] => [[7,5,3],[5,3]] => [2,2,3]
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [1,1,2,3]
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]] => [1,1,2,3]
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]] => [1,1,2,3]
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]] => [1,1,2,3]
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]] => [1,1,2,3]
[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]] => [1,1,2,3]
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]] => [1,1,2,3]
[[6,4,2,1],[3,2,1]] => [[6,5,4,3],[5,4,2]] => [1,1,2,3]
[[5,2,1,1],[2]] => [[5,5,5,3],[4,4,3]] => [1,1,2,3]
[[6,3,2,1],[3,1,1]] => [[6,5,5,3],[5,4,3]] => [1,1,2,3]
[[6,3,1,1],[3,1]] => [[6,6,5,3],[5,5,3]] => [1,1,2,3]
[[7,4,2,1],[4,2,1]] => [[7,6,5,3],[6,5,3]] => [1,1,2,3]
[[5,3,3],[2,2]] => [[5,3,3],[2,2]] => [3,1,3]
[[6,4,3],[3,3]] => [[6,3,3],[3,2]] => [3,1,3]
[[6,3,3],[3,2]] => [[6,4,3],[3,3]] => [3,1,3]
[[7,4,3],[4,3]] => [[7,4,3],[4,3]] => [3,1,3]
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]] => [1,2,1,3]
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]] => [1,2,1,3]
[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]] => [1,2,1,3]
[[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]] => [1,2,1,3]
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]] => [1,2,1,3]
[[6,3,3,1],[3,2,1]] => [[6,5,4,3],[5,3,3]] => [1,2,1,3]
[[6,3,2,1],[3,2]] => [[6,6,4,3],[5,4,3]] => [1,2,1,3]
[[7,4,3,1],[4,3,1]] => [[7,6,4,3],[6,4,3]] => [1,2,1,3]
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]] => [2,1,1,3]
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]] => [2,1,1,3]
[[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]] => [2,1,1,3]
[[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]] => [2,1,1,3]
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]] => [2,1,1,3]
[[6,3,3,2],[3,2,2]] => [[6,4,4,3],[4,3,3]] => [2,1,1,3]
[[6,3,2,2],[3,2,1]] => [[6,5,4,3],[4,4,3]] => [2,1,1,3]
[[7,4,3,2],[4,3,2]] => [[7,5,4,3],[5,4,3]] => [2,1,1,3]
[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => [1,1,1,1,3]
[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]] => [1,1,1,1,3]
[[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]] => [1,1,1,1,3]
[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]] => [1,1,1,1,3]
[[4,2,1,1,1],[1,1]] => [[4,4,4,3,3],[3,3,3,2]] => [1,1,1,1,3]
[[5,3,2,2,1],[2,2,1,1]] => [[5,4,4,3,3],[4,3,3,2]] => [1,1,1,1,3]
[[5,3,2,1,1],[2,2,1]] => [[5,5,4,3,3],[4,4,3,2]] => [1,1,1,1,3]
[[6,4,3,2,1],[3,3,2,1]] => [[6,5,4,3,3],[5,4,3,2]] => [1,1,1,1,3]
[[4,1,1,1,1],[1]] => [[4,4,4,4,3],[3,3,3,3]] => [1,1,1,1,3]
[[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]] => [1,1,1,1,3]
[[5,2,2,1,1],[2,1,1]] => [[5,5,4,4,3],[4,4,3,3]] => [1,1,1,1,3]
[[6,3,3,2,1],[3,2,2,1]] => [[6,5,4,4,3],[5,4,3,3]] => [1,1,1,1,3]
[[5,2,1,1,1],[2,1]] => [[5,5,5,4,3],[4,4,4,3]] => [1,1,1,1,3]
[[6,3,2,2,1],[3,2,1,1]] => [[6,5,5,4,3],[5,4,4,3]] => [1,1,1,1,3]
[[6,3,2,1,1],[3,2,1]] => [[6,6,5,4,3],[5,5,4,3]] => [1,1,1,1,3]
[[7,4,3,2,1],[4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]] => [1,1,1,1,3]
[[5,5],[3]] => [[5,2],[]] => [5,2]
[[6,5],[4]] => [[6,2],[1]] => [5,2]
[[7,5],[5]] => [[7,2],[2]] => [5,2]
[[4,4,1],[2]] => [[4,4,2],[3]] => [1,4,2]
[[5,5,1],[3,1]] => [[5,4,2],[4]] => [1,4,2]
[[5,4,1],[3]] => [[5,5,2],[4,1]] => [1,4,2]
[[6,5,1],[4,1]] => [[6,5,2],[5,1]] => [1,4,2]
[[6,4,1],[4]] => [[6,6,2],[5,2]] => [1,4,2]
[[7,5,1],[5,1]] => [[7,6,2],[6,2]] => [1,4,2]
[[3,3,2],[1]] => [[3,3,2],[1]] => [2,3,2]
[[4,4,2],[2,1]] => [[4,3,2],[2]] => [2,3,2]
[[5,5,2],[3,2]] => [[5,3,2],[3]] => [2,3,2]
[[4,3,2],[2]] => [[4,4,2],[2,1]] => [2,3,2]
[[5,4,2],[3,1]] => [[5,4,2],[3,1]] => [2,3,2]
[[6,5,2],[4,2]] => [[6,4,2],[4,1]] => [2,3,2]
[[5,3,2],[3]] => [[5,5,2],[3,2]] => [2,3,2]
[[6,4,2],[4,1]] => [[6,5,2],[4,2]] => [2,3,2]
[[7,5,2],[5,2]] => [[7,5,2],[5,2]] => [2,3,2]
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]] => [1,1,3,2]
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]] => [1,1,3,2]
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]] => [1,1,3,2]
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]] => [1,1,3,2]
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]] => [1,1,3,2]
[[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]] => [1,1,3,2]
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]] => [1,1,3,2]
[[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]] => [1,1,3,2]
[[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]] => [1,1,3,2]
[[6,4,2,1],[4,1,1]] => [[6,5,5,2],[5,4,2]] => [1,1,3,2]
[[6,4,1,1],[4,1]] => [[6,6,5,2],[5,5,2]] => [1,1,3,2]
[[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]] => [1,1,3,2]
[[3,3,3],[1,1]] => [[3,2,2],[]] => [3,2,2]
[[4,4,3],[2,2]] => [[4,2,2],[1]] => [3,2,2]
[[5,5,3],[3,3]] => [[5,2,2],[2]] => [3,2,2]
[[4,3,3],[2,1]] => [[4,3,2],[1,1]] => [3,2,2]
[[5,4,3],[3,2]] => [[5,3,2],[2,1]] => [3,2,2]
[[6,5,3],[4,3]] => [[6,3,2],[3,1]] => [3,2,2]
[[5,3,3],[3,1]] => [[5,4,2],[2,2]] => [3,2,2]
[[6,4,3],[4,2]] => [[6,4,2],[3,2]] => [3,2,2]
[[7,5,3],[5,3]] => [[7,4,2],[4,2]] => [3,2,2]
[[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1,2,2,2]
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]] => [1,2,2,2]
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]] => [1,2,2,2]
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]] => [1,2,2,2]
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]] => [1,2,2,2]
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]] => [1,2,2,2]
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]] => [1,2,2,2]
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]] => [1,2,2,2]
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]] => [1,2,2,2]
[[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]] => [1,2,2,2]
[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]] => [1,2,2,2]
[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]] => [1,2,2,2]
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]] => [1,2,2,2]
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]] => [1,2,2,2]
[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]] => [1,2,2,2]
[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]] => [1,2,2,2]
[[6,4,2,1],[4,2]] => [[6,6,4,2],[5,4,2]] => [1,2,2,2]
[[7,5,3,1],[5,3,1]] => [[7,6,4,2],[6,4,2]] => [1,2,2,2]
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]] => [2,1,2,2]
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]] => [2,1,2,2]
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]] => [2,1,2,2]
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]] => [2,1,2,2]
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]] => [2,1,2,2]
[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]] => [2,1,2,2]
[[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]] => [2,1,2,2]
[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]] => [2,1,2,2]
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]] => [2,1,2,2]
[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]] => [2,1,2,2]
[[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]] => [2,1,2,2]
[[7,5,3,2],[5,3,2]] => [[7,5,4,2],[5,4,2]] => [2,1,2,2]
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1,2,2]
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]] => [1,1,1,2,2]
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]] => [1,1,1,2,2]
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]] => [1,1,1,2,2]
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]] => [1,1,1,2,2]
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]] => [1,1,1,2,2]
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]] => [1,1,1,2,2]
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => [1,1,1,2,2]
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]] => [1,1,1,2,2]
[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]] => [1,1,1,2,2]
[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]] => [1,1,1,2,2]
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => [1,1,1,2,2]
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]] => [1,1,1,2,2]
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]] => [1,1,1,2,2]
[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]] => [1,1,1,2,2]
[[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] => [1,1,1,2,2]
[[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]] => [1,1,1,2,2]
[[5,3,2,2,1],[3,1,1,1]] => [[5,4,4,4,2],[4,3,3,2]] => [1,1,1,2,2]
[[5,3,2,1,1],[3,1,1]] => [[5,5,4,4,2],[4,4,3,2]] => [1,1,1,2,2]
[[6,4,3,2,1],[4,2,2,1]] => [[6,5,4,4,2],[5,4,3,2]] => [1,1,1,2,2]
[[5,3,1,1,1],[3,1]] => [[5,5,5,4,2],[4,4,4,2]] => [1,1,1,2,2]
[[6,4,2,2,1],[4,2,1,1]] => [[6,5,5,4,2],[5,4,4,2]] => [1,1,1,2,2]
[[6,4,2,1,1],[4,2,1]] => [[6,6,5,4,2],[5,5,4,2]] => [1,1,1,2,2]
[[7,5,3,2,1],[5,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]] => [1,1,1,2,2]
[[5,4,4],[3,3]] => [[5,2,2],[1,1]] => [4,1,2]
[[6,5,4],[4,4]] => [[6,2,2],[2,1]] => [4,1,2]
[[6,4,4],[4,3]] => [[6,3,2],[2,2]] => [4,1,2]
[[7,5,4],[5,4]] => [[7,3,2],[3,2]] => [4,1,2]
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]] => [1,3,1,2]
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]] => [1,3,1,2]
[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]] => [1,3,1,2]
[[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]] => [1,3,1,2]
[[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]] => [1,3,1,2]
[[6,4,4,1],[4,3,1]] => [[6,5,3,2],[5,2,2]] => [1,3,1,2]
[[6,4,3,1],[4,3]] => [[6,6,3,2],[5,3,2]] => [1,3,1,2]
[[7,5,4,1],[5,4,1]] => [[7,6,3,2],[6,3,2]] => [1,3,1,2]
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]] => [2,2,1,2]
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]] => [2,2,1,2]
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]] => [2,2,1,2]
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]] => [2,2,1,2]
[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]] => [2,2,1,2]
[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]] => [2,2,1,2]
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]] => [2,2,1,2]
[[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]] => [2,2,1,2]
[[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]] => [2,2,1,2]
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]] => [2,2,1,2]
[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]] => [2,2,1,2]
[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]] => [2,2,1,2]
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]] => [1,1,2,1,2]
[[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]] => [1,1,2,1,2]
[[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]] => [1,1,2,1,2]
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]] => [1,1,2,1,2]
[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]] => [1,1,2,1,2]
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]] => [1,1,2,1,2]
[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]] => [1,1,2,1,2]
[[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]] => [1,1,2,1,2]
[[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]] => [1,1,2,1,2]
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]] => [1,1,2,1,2]
[[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]] => [1,1,2,1,2]
[[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]] => [1,1,2,1,2]
[[5,3,2,1,1],[3,2]] => [[5,5,5,3,2],[4,4,3,2]] => [1,1,2,1,2]
[[6,4,3,2,1],[4,3,1,1]] => [[6,5,5,3,2],[5,4,3,2]] => [1,1,2,1,2]
[[6,4,3,1,1],[4,3,1]] => [[6,6,5,3,2],[5,5,3,2]] => [1,1,2,1,2]
[[7,5,4,2,1],[5,4,2,1]] => [[7,6,5,3,2],[6,5,3,2]] => [1,1,2,1,2]
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]] => [3,1,1,2]
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]] => [3,1,1,2]
[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]] => [3,1,1,2]
[[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]] => [3,1,1,2]
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]] => [3,1,1,2]
[[6,4,4,3],[4,3,3]] => [[6,3,3,2],[3,2,2]] => [3,1,1,2]
[[6,4,3,3],[4,3,2]] => [[6,4,3,2],[3,3,2]] => [3,1,1,2]
[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]] => [3,1,1,2]
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]] => [1,2,1,1,2]
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]] => [1,2,1,1,2]
[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]] => [1,2,1,1,2]
[[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]] => [1,2,1,1,2]
[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]] => [1,2,1,1,2]
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]] => [1,2,1,1,2]
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]] => [1,2,1,1,2]
[[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]] => [1,2,1,1,2]
[[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]] => [1,2,1,1,2]
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]] => [1,2,1,1,2]
[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]] => [1,2,1,1,2]
[[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]] => [1,2,1,1,2]
[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]] => [1,2,1,1,2]
[[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]] => [1,2,1,1,2]
[[6,4,3,2,1],[4,3,2]] => [[6,6,4,3,2],[5,4,3,2]] => [1,2,1,1,2]
[[7,5,4,3,1],[5,4,3,1]] => [[7,6,4,3,2],[6,4,3,2]] => [1,2,1,1,2]
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]] => [2,1,1,1,2]
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1,2]
[[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]] => [2,1,1,1,2]
[[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]] => [2,1,1,1,2]
[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]] => [2,1,1,1,2]
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]] => [2,1,1,1,2]
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]] => [2,1,1,1,2]
[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]] => [2,1,1,1,2]
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]] => [2,1,1,1,2]
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]] => [2,1,1,1,2]
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]] => [2,1,1,1,2]
[[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]] => [2,1,1,1,2]
[[5,3,2,2,2],[3,2,1,1]] => [[5,4,4,3,2],[3,3,3,2]] => [2,1,1,1,2]
[[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]] => [2,1,1,1,2]
[[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]] => [2,1,1,1,2]
[[7,5,4,3,2],[5,4,3,2]] => [[7,5,4,3,2],[5,4,3,2]] => [2,1,1,1,2]
[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1,2]
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => [1,1,1,1,1,2]
[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => [1,1,1,1,1,2]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]] => [1,1,1,1,1,2]
[[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]] => [1,1,1,1,1,2]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]] => [1,1,1,1,1,2]
[[4,3,3,2,1,1],[2,2,2,1]] => [[4,4,3,2,2,2],[3,3,2,1,1]] => [1,1,1,1,1,2]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [[5,4,3,2,2,2],[4,3,2,1,1]] => [1,1,1,1,1,2]
[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => [1,1,1,1,1,2]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]] => [1,1,1,1,1,2]
[[4,3,2,2,1,1],[2,2,1,1]] => [[4,4,3,3,2,2],[3,3,2,2,1]] => [1,1,1,1,1,2]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]] => [1,1,1,1,1,2]
[[4,3,2,1,1,1],[2,2,1]] => [[4,4,4,3,2,2],[3,3,3,2,1]] => [1,1,1,1,1,2]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]] => [1,1,1,1,1,2]
[[5,4,3,2,1,1],[3,3,2,1]] => [[5,5,4,3,2,2],[4,4,3,2,1]] => [1,1,1,1,1,2]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] => [1,1,1,1,1,2]
[[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]] => [1,1,1,1,1,2]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]] => [1,1,1,1,1,2]
[[4,2,2,2,1,1],[2,1,1,1]] => [[4,4,3,3,3,2],[3,3,2,2,2]] => [1,1,1,1,1,2]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]] => [1,1,1,1,1,2]
[[4,2,2,1,1,1],[2,1,1]] => [[4,4,4,3,3,2],[3,3,3,2,2]] => [1,1,1,1,1,2]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]] => [1,1,1,1,1,2]
[[5,3,3,2,1,1],[3,2,2,1]] => [[5,5,4,3,3,2],[4,4,3,2,2]] => [1,1,1,1,1,2]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] => [1,1,1,1,1,2]
[[4,2,1,1,1,1],[2,1]] => [[4,4,4,4,3,2],[3,3,3,3,2]] => [1,1,1,1,1,2]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]] => [1,1,1,1,1,2]
[[5,3,2,2,1,1],[3,2,1,1]] => [[5,5,4,4,3,2],[4,4,3,3,2]] => [1,1,1,1,1,2]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] => [1,1,1,1,1,2]
[[5,3,2,1,1,1],[3,2,1]] => [[5,5,5,4,3,2],[4,4,4,3,2]] => [1,1,1,1,1,2]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] => [1,1,1,1,1,2]
[[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]] => [1,1,1,1,1,2]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]] => [1,1,1,1,1,2]
[[6,6],[5]] => [[6,1],[]] => [6,1]
[[7,6],[6]] => [[7,1],[1]] => [6,1]
[[5,5,1],[4]] => [[5,5,1],[4]] => [1,5,1]
[[6,6,1],[5,1]] => [[6,5,1],[5]] => [1,5,1]
[[6,5,1],[5]] => [[6,6,1],[5,1]] => [1,5,1]
[[7,6,1],[6,1]] => [[7,6,1],[6,1]] => [1,5,1]
[[4,4,2],[3]] => [[4,4,1],[2]] => [2,4,1]
[[5,5,2],[4,1]] => [[5,4,1],[3]] => [2,4,1]
[[6,6,2],[5,2]] => [[6,4,1],[4]] => [2,4,1]
[[5,4,2],[4]] => [[5,5,1],[3,1]] => [2,4,1]
[[6,5,2],[5,1]] => [[6,5,1],[4,1]] => [2,4,1]
[[7,6,2],[6,2]] => [[7,5,1],[5,1]] => [2,4,1]
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]] => [1,1,4,1]
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]] => [1,1,4,1]
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]] => [1,1,4,1]
[[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]] => [1,1,4,1]
[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]] => [1,1,4,1]
[[6,5,2,1],[5,1,1]] => [[6,5,5,1],[5,4,1]] => [1,1,4,1]
[[6,5,1,1],[5,1]] => [[6,6,5,1],[5,5,1]] => [1,1,4,1]
[[7,6,2,1],[6,2,1]] => [[7,6,5,1],[6,5,1]] => [1,1,4,1]
[[3,3,3],[2]] => [[3,3,1],[]] => [3,3,1]
[[4,4,3],[3,1]] => [[4,3,1],[1]] => [3,3,1]
[[5,5,3],[4,2]] => [[5,3,1],[2]] => [3,3,1]
[[6,6,3],[5,3]] => [[6,3,1],[3]] => [3,3,1]
[[4,3,3],[3]] => [[4,4,1],[1,1]] => [3,3,1]
[[5,4,3],[4,1]] => [[5,4,1],[2,1]] => [3,3,1]
[[6,5,3],[5,2]] => [[6,4,1],[3,1]] => [3,3,1]
[[7,6,3],[6,3]] => [[7,4,1],[4,1]] => [3,3,1]
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]] => [1,2,3,1]
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]] => [1,2,3,1]
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]] => [1,2,3,1]
[[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]] => [1,2,3,1]
[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]] => [1,2,3,1]
[[6,6,3,1],[5,3,1]] => [[6,5,3,1],[5,3]] => [1,2,3,1]
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]] => [1,2,3,1]
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]] => [1,2,3,1]
[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]] => [1,2,3,1]
[[6,5,3,1],[5,2,1]] => [[6,5,4,1],[5,3,1]] => [1,2,3,1]
[[6,5,2,1],[5,2]] => [[6,6,4,1],[5,4,1]] => [1,2,3,1]
[[7,6,3,1],[6,3,1]] => [[7,6,4,1],[6,4,1]] => [1,2,3,1]
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]] => [2,1,3,1]
[[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]] => [2,1,3,1]
[[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]] => [2,1,3,1]
[[6,6,3,2],[5,3,2]] => [[6,4,3,1],[4,3]] => [2,1,3,1]
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]] => [2,1,3,1]
[[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]] => [2,1,3,1]
[[6,5,2,2],[5,2,1]] => [[6,5,4,1],[4,4,1]] => [2,1,3,1]
[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]] => [2,1,3,1]
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]] => [1,1,1,3,1]
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]] => [1,1,1,3,1]
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]] => [1,1,1,3,1]
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]] => [1,1,1,3,1]
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]] => [1,1,1,3,1]
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]] => [1,1,1,3,1]
[[5,5,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3]] => [1,1,1,3,1]
[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => [1,1,1,3,1]
[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]] => [1,1,1,3,1]
[[5,4,2,2,1],[4,1,1,1]] => [[5,4,4,4,1],[4,3,3,1]] => [1,1,1,3,1]
[[5,4,2,1,1],[4,1,1]] => [[5,5,4,4,1],[4,4,3,1]] => [1,1,1,3,1]
[[6,5,3,2,1],[5,2,2,1]] => [[6,5,4,4,1],[5,4,3,1]] => [1,1,1,3,1]
[[5,4,1,1,1],[4,1]] => [[5,5,5,4,1],[4,4,4,1]] => [1,1,1,3,1]
[[6,5,2,2,1],[5,2,1,1]] => [[6,5,5,4,1],[5,4,4,1]] => [1,1,1,3,1]
[[6,5,2,1,1],[5,2,1]] => [[6,6,5,4,1],[5,5,4,1]] => [1,1,1,3,1]
[[7,6,3,2,1],[6,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]] => [1,1,1,3,1]
[[4,4,4],[3,2]] => [[4,2,1],[]] => [4,2,1]
[[5,5,4],[4,3]] => [[5,2,1],[1]] => [4,2,1]
[[6,6,4],[5,4]] => [[6,2,1],[2]] => [4,2,1]
[[5,4,4],[4,2]] => [[5,3,1],[1,1]] => [4,2,1]
[[6,5,4],[5,3]] => [[6,3,1],[2,1]] => [4,2,1]
[[7,6,4],[6,4]] => [[7,3,1],[3,1]] => [4,2,1]
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]] => [1,3,2,1]
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]] => [1,3,2,1]
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]] => [1,3,2,1]
[[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]] => [1,3,2,1]
[[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]] => [1,3,2,1]
[[6,6,4,1],[5,4,1]] => [[6,5,2,1],[5,2]] => [1,3,2,1]
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]] => [1,3,2,1]
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]] => [1,3,2,1]
[[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]] => [1,3,2,1]
[[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]] => [1,3,2,1]
[[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]] => [1,3,2,1]
[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]] => [1,3,2,1]
[[2,2,2,2],[1]] => [[2,2,2,1],[]] => [2,2,2,1]
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]] => [2,2,2,1]
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]] => [2,2,2,1]
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]] => [2,2,2,1]
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]] => [2,2,2,1]
[[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]] => [2,2,2,1]
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]] => [2,2,2,1]
[[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]] => [2,2,2,1]
[[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]] => [2,2,2,1]
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]] => [2,2,2,1]
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]] => [2,2,2,1]
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]] => [2,2,2,1]
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]] => [2,2,2,1]
[[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]] => [2,2,2,1]
[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]] => [2,2,2,1]
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]] => [2,2,2,1]
[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]] => [2,2,2,1]
[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]] => [2,2,2,1]
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]] => [1,1,2,2,1]
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]] => [1,1,2,2,1]
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]] => [1,1,2,2,1]
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]] => [1,1,2,2,1]
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]] => [1,1,2,2,1]
[[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]] => [1,1,2,2,1]
[[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]] => [1,1,2,2,1]
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]] => [1,1,2,2,1]
[[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]] => [1,1,2,2,1]
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]] => [1,1,2,2,1]
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]] => [1,1,2,2,1]
[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]] => [1,1,2,2,1]
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]] => [1,1,2,2,1]
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]] => [1,1,2,2,1]
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]] => [1,1,2,2,1]
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => [1,1,2,2,1]
[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]] => [1,1,2,2,1]
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]] => [1,1,2,2,1]
[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]] => [1,1,2,2,1]
[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => [1,1,2,2,1]
[[5,4,2,1,1],[4,2]] => [[5,5,5,3,1],[4,4,3,1]] => [1,1,2,2,1]
[[6,5,3,2,1],[5,3,1,1]] => [[6,5,5,3,1],[5,4,3,1]] => [1,1,2,2,1]
[[6,5,3,1,1],[5,3,1]] => [[6,6,5,3,1],[5,5,3,1]] => [1,1,2,2,1]
[[7,6,4,2,1],[6,4,2,1]] => [[7,6,5,3,1],[6,5,3,1]] => [1,1,2,2,1]
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]] => [3,1,2,1]
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]] => [3,1,2,1]
[[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]] => [3,1,2,1]
[[6,6,4,3],[5,4,3]] => [[6,3,2,1],[3,2]] => [3,1,2,1]
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]] => [3,1,2,1]
[[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]] => [3,1,2,1]
[[6,5,3,3],[5,3,2]] => [[6,4,3,1],[3,3,1]] => [3,1,2,1]
[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]] => [3,1,2,1]
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]] => [1,2,1,2,1]
[[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]] => [1,2,1,2,1]
[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]] => [1,2,1,2,1]
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]] => [1,2,1,2,1]
[[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]] => [1,2,1,2,1]
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]] => [1,2,1,2,1]
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]] => [1,2,1,2,1]
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]] => [1,2,1,2,1]
[[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]] => [1,2,1,2,1]
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]] => [1,2,1,2,1]
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]] => [1,2,1,2,1]
[[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]] => [1,2,1,2,1]
[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]] => [1,2,1,2,1]
[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]] => [1,2,1,2,1]
[[6,5,3,2,1],[5,3,2]] => [[6,6,4,3,1],[5,4,3,1]] => [1,2,1,2,1]
[[7,6,4,3,1],[6,4,3,1]] => [[7,6,4,3,1],[6,4,3,1]] => [1,2,1,2,1]
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]] => [2,1,1,2,1]
[[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]] => [2,1,1,2,1]
[[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]] => [2,1,1,2,1]
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]] => [2,1,1,2,1]
[[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]] => [2,1,1,2,1]
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]] => [2,1,1,2,1]
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]] => [2,1,1,2,1]
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]] => [2,1,1,2,1]
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]] => [2,1,1,2,1]
[[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]] => [2,1,1,2,1]
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]] => [2,1,1,2,1]
[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]] => [2,1,1,2,1]
[[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]] => [2,1,1,2,1]
[[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]] => [2,1,1,2,1]
[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]] => [2,1,1,2,1]
[[7,6,4,3,2],[6,4,3,2]] => [[7,5,4,3,1],[5,4,3,1]] => [2,1,1,2,1]
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1,2,1]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => [1,1,1,1,2,1]
[[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]] => [1,1,1,1,2,1]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]] => [1,1,1,1,2,1]
[[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]] => [1,1,1,1,2,1]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => [1,1,1,1,2,1]
[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]] => [1,1,1,1,2,1]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => [1,1,1,1,2,1]
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]] => [1,1,1,1,2,1]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2]] => [1,1,1,1,2,1]
[[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]] => [1,1,1,1,2,1]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] => [1,1,1,1,2,1]
[[4,4,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2]] => [1,1,1,1,2,1]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]] => [1,1,1,1,2,1]
[[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]] => [1,1,1,1,2,1]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => [1,1,1,1,2,1]
[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => [1,1,1,1,2,1]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]] => [1,1,1,1,2,1]
[[4,3,2,2,1,1],[3,1,1,1]] => [[4,4,3,3,3,1],[3,3,2,2,1]] => [1,1,1,1,2,1]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [[5,4,3,3,3,1],[4,3,2,2,1]] => [1,1,1,1,2,1]
[[4,3,2,1,1,1],[3,1,1]] => [[4,4,4,3,3,1],[3,3,3,2,1]] => [1,1,1,1,2,1]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]] => [1,1,1,1,2,1]
[[5,4,3,2,1,1],[4,2,2,1]] => [[5,5,4,3,3,1],[4,4,3,2,1]] => [1,1,1,1,2,1]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]] => [1,1,1,1,2,1]
[[4,3,1,1,1,1],[3,1]] => [[4,4,4,4,3,1],[3,3,3,3,1]] => [1,1,1,1,2,1]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]] => [1,1,1,1,2,1]
[[5,4,2,2,1,1],[4,2,1,1]] => [[5,5,4,4,3,1],[4,4,3,3,1]] => [1,1,1,1,2,1]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]] => [1,1,1,1,2,1]
[[5,4,2,1,1,1],[4,2,1]] => [[5,5,5,4,3,1],[4,4,4,3,1]] => [1,1,1,1,2,1]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] => [1,1,1,1,2,1]
[[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]] => [1,1,1,1,2,1]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]] => [1,1,1,1,2,1]
[[5,5,5],[4,4]] => [[5,1,1],[]] => [5,1,1]
[[6,6,5],[5,5]] => [[6,1,1],[1]] => [5,1,1]
[[6,5,5],[5,4]] => [[6,2,1],[1,1]] => [5,1,1]
[[7,6,5],[6,5]] => [[7,2,1],[2,1]] => [5,1,1]
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]] => [1,4,1,1]
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]] => [1,4,1,1]
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]] => [1,4,1,1]
[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]] => [1,4,1,1]
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]] => [1,4,1,1]
[[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]] => [1,4,1,1]
[[6,5,4,1],[5,4]] => [[6,6,2,1],[5,2,1]] => [1,4,1,1]
[[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]] => [1,4,1,1]
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]] => [2,3,1,1]
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]] => [2,3,1,1]
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]] => [2,3,1,1]
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]] => [2,3,1,1]
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]] => [2,3,1,1]
[[6,6,5,2],[5,5,2]] => [[6,4,1,1],[4,1]] => [2,3,1,1]
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]] => [2,3,1,1]
[[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]] => [2,3,1,1]
[[6,5,5,2],[5,4,2]] => [[6,4,2,1],[4,1,1]] => [2,3,1,1]
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]] => [2,3,1,1]
[[6,5,4,2],[5,4,1]] => [[6,5,2,1],[4,2,1]] => [2,3,1,1]
[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]] => [2,3,1,1]
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]] => [1,1,3,1,1]
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]] => [1,1,3,1,1]
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]] => [1,1,3,1,1]
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]] => [1,1,3,1,1]
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]] => [1,1,3,1,1]
[[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]] => [1,1,3,1,1]
[[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]] => [1,1,3,1,1]
[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]] => [1,1,3,1,1]
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]] => [1,1,3,1,1]
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]] => [1,1,3,1,1]
[[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]] => [1,1,3,1,1]
[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => [1,1,3,1,1]
[[5,4,3,1,1],[4,3]] => [[5,5,5,2,1],[4,4,2,1]] => [1,1,3,1,1]
[[6,5,4,2,1],[5,4,1,1]] => [[6,5,5,2,1],[5,4,2,1]] => [1,1,3,1,1]
[[6,5,4,1,1],[5,4,1]] => [[6,6,5,2,1],[5,5,2,1]] => [1,1,3,1,1]
[[7,6,5,2,1],[6,5,2,1]] => [[7,6,5,2,1],[6,5,2,1]] => [1,1,3,1,1]
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]] => [3,2,1,1]
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]] => [3,2,1,1]
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]] => [3,2,1,1]
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]] => [3,2,1,1]
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]] => [3,2,1,1]
[[6,6,5,3],[5,5,3]] => [[6,3,1,1],[3,1]] => [3,2,1,1]
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]] => [3,2,1,1]
[[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]] => [3,2,1,1]
[[6,5,5,3],[5,4,3]] => [[6,3,2,1],[3,1,1]] => [3,2,1,1]
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]] => [3,2,1,1]
[[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]] => [3,2,1,1]
[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]] => [3,2,1,1]
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]] => [1,2,2,1,1]
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]] => [1,2,2,1,1]
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]] => [1,2,2,1,1]
[[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]] => [1,2,2,1,1]
[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]] => [1,2,2,1,1]
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]] => [1,2,2,1,1]
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]] => [1,2,2,1,1]
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]] => [1,2,2,1,1]
[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]] => [1,2,2,1,1]
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]] => [1,2,2,1,1]
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]] => [1,2,2,1,1]
[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]] => [1,2,2,1,1]
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]] => [1,2,2,1,1]
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => [1,2,2,1,1]
[[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]] => [1,2,2,1,1]
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]] => [1,2,2,1,1]
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]] => [1,2,2,1,1]
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]] => [1,2,2,1,1]
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]] => [1,2,2,1,1]
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => [1,2,2,1,1]
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]] => [1,2,2,1,1]
[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]] => [1,2,2,1,1]
[[6,5,4,2,1],[5,4,2]] => [[6,6,4,2,1],[5,4,2,1]] => [1,2,2,1,1]
[[7,6,5,3,1],[6,5,3,1]] => [[7,6,4,2,1],[6,4,2,1]] => [1,2,2,1,1]
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]] => [2,1,2,1,1]
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]] => [2,1,2,1,1]
[[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]] => [2,1,2,1,1]
[[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]] => [2,1,2,1,1]
[[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]] => [2,1,2,1,1]
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]] => [2,1,2,1,1]
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]] => [2,1,2,1,1]
[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]] => [2,1,2,1,1]
[[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]] => [2,1,2,1,1]
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]] => [2,1,2,1,1]
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]] => [2,1,2,1,1]
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]] => [2,1,2,1,1]
[[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]] => [2,1,2,1,1]
[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]] => [2,1,2,1,1]
[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]] => [2,1,2,1,1]
[[7,6,5,3,2],[6,5,3,2]] => [[7,5,4,2,1],[5,4,2,1]] => [2,1,2,1,1]
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1,2,1,1]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]] => [1,1,1,2,1,1]
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]] => [1,1,1,2,1,1]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]] => [1,1,1,2,1,1]
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]] => [1,1,1,2,1,1]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2]] => [1,1,1,2,1,1]
[[4,4,4,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2]] => [1,1,1,2,1,1]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => [1,1,1,2,1,1]
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]] => [1,1,1,2,1,1]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]] => [1,1,1,2,1,1]
[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]] => [1,1,1,2,1,1]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => [1,1,1,2,1,1]
[[4,4,3,1,1,1],[3,3,1]] => [[4,4,4,3,1,1],[3,3,3,1]] => [1,1,1,2,1,1]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]] => [1,1,1,2,1,1]
[[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]] => [1,1,1,2,1,1]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] => [1,1,1,2,1,1]
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => [1,1,1,2,1,1]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]] => [1,1,1,2,1,1]
[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => [1,1,1,2,1,1]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] => [1,1,1,2,1,1]
[[4,3,3,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,1,1]] => [1,1,1,2,1,1]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] => [1,1,1,2,1,1]
[[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]] => [1,1,1,2,1,1]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => [1,1,1,2,1,1]
[[4,3,2,1,1,1],[3,2]] => [[4,4,4,4,2,1],[3,3,3,2,1]] => [1,1,1,2,1,1]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [[5,4,4,4,2,1],[4,3,3,2,1]] => [1,1,1,2,1,1]
[[5,4,3,2,1,1],[4,3,1,1]] => [[5,5,4,4,2,1],[4,4,3,2,1]] => [1,1,1,2,1,1]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]] => [1,1,1,2,1,1]
[[5,4,3,1,1,1],[4,3,1]] => [[5,5,5,4,2,1],[4,4,4,2,1]] => [1,1,1,2,1,1]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]] => [1,1,1,2,1,1]
[[6,5,4,2,1,1],[5,4,2,1]] => [[6,6,5,4,2,1],[5,5,4,2,1]] => [1,1,1,2,1,1]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]] => [1,1,1,2,1,1]
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]] => [4,1,1,1]
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]] => [4,1,1,1]
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]] => [4,1,1,1]
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]] => [4,1,1,1]
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]] => [4,1,1,1]
[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]] => [4,1,1,1]
[[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]] => [4,1,1,1]
[[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]] => [4,1,1,1]
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]] => [1,3,1,1,1]
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]] => [1,3,1,1,1]
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]] => [1,3,1,1,1]
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]] => [1,3,1,1,1]
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]] => [1,3,1,1,1]
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]] => [1,3,1,1,1]
[[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]] => [1,3,1,1,1]
[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]] => [1,3,1,1,1]
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]] => [1,3,1,1,1]
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]] => [1,3,1,1,1]
[[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]] => [1,3,1,1,1]
[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]] => [1,3,1,1,1]
[[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]] => [1,3,1,1,1]
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]] => [1,3,1,1,1]
[[6,5,4,3,1],[5,4,3]] => [[6,6,3,2,1],[5,3,2,1]] => [1,3,1,1,1]
[[7,6,5,4,1],[6,5,4,1]] => [[7,6,3,2,1],[6,3,2,1]] => [1,3,1,1,1]
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]] => [2,2,1,1,1]
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]] => [2,2,1,1,1]
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]] => [2,2,1,1,1]
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]] => [2,2,1,1,1]
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]] => [2,2,1,1,1]
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]] => [2,2,1,1,1]
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]] => [2,2,1,1,1]
[[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]] => [2,2,1,1,1]
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]] => [2,2,1,1,1]
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]] => [2,2,1,1,1]
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]] => [2,2,1,1,1]
[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]] => [2,2,1,1,1]
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]] => [2,2,1,1,1]
[[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]] => [2,2,1,1,1]
[[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]] => [2,2,1,1,1]
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1,1]
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]] => [2,2,1,1,1]
[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]] => [2,2,1,1,1]
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]] => [2,2,1,1,1]
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]] => [2,2,1,1,1]
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]] => [2,2,1,1,1]
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => [2,2,1,1,1]
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]] => [2,2,1,1,1]
[[7,6,5,4,2],[6,5,4,2]] => [[7,5,3,2,1],[5,3,2,1]] => [2,2,1,1,1]
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]] => [1,1,2,1,1,1]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]] => [1,1,2,1,1,1]
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]] => [1,1,2,1,1,1]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]] => [1,1,2,1,1,1]
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]] => [1,1,2,1,1,1]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]] => [1,1,2,1,1,1]
[[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]] => [1,1,2,1,1,1]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => [1,1,2,1,1,1]
[[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]] => [1,1,2,1,1,1]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => [1,1,2,1,1,1]
[[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]] => [1,1,2,1,1,1]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => [1,1,2,1,1,1]
[[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] => [1,1,2,1,1,1]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => [1,1,2,1,1,1]
[[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]] => [1,1,2,1,1,1]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] => [1,1,2,1,1,1]
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => [1,1,2,1,1,1]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] => [1,1,2,1,1,1]
[[4,3,3,3,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,1,1,1]] => [1,1,2,1,1,1]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => [1,1,2,1,1,1]
[[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] => [1,1,2,1,1,1]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] => [1,1,2,1,1,1]
[[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]] => [1,1,2,1,1,1]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] => [1,1,2,1,1,1]
[[4,3,2,2,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,2,2,1]] => [1,1,2,1,1,1]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] => [1,1,2,1,1,1]
[[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]] => [1,1,2,1,1,1]
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => [1,1,2,1,1,1]
[[5,4,3,2,1,1],[4,3,2]] => [[5,5,5,3,2,1],[4,4,3,2,1]] => [1,1,2,1,1,1]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]] => [1,1,2,1,1,1]
[[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]] => [1,1,2,1,1,1]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]] => [1,1,2,1,1,1]
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]] => [3,1,1,1,1]
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]] => [3,1,1,1,1]
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]] => [3,1,1,1,1]
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]] => [3,1,1,1,1]
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]] => [3,1,1,1,1]
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]] => [3,1,1,1,1]
[[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]] => [3,1,1,1,1]
[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]] => [3,1,1,1,1]
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]] => [3,1,1,1,1]
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]] => [3,1,1,1,1]
[[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]] => [3,1,1,1,1]
[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]] => [3,1,1,1,1]
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]] => [3,1,1,1,1]
[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]] => [3,1,1,1,1]
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => [3,1,1,1,1]
[[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]] => [3,1,1,1,1]
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]] => [1,2,1,1,1,1]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]] => [1,2,1,1,1,1]
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]] => [1,2,1,1,1,1]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]] => [1,2,1,1,1,1]
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]] => [1,2,1,1,1,1]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,1,1]] => [1,2,1,1,1,1]
[[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]] => [1,2,1,1,1,1]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]] => [1,2,1,1,1,1]
[[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]] => [1,2,1,1,1,1]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,1,1,1]] => [1,2,1,1,1,1]
[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]] => [1,2,1,1,1,1]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => [1,2,1,1,1,1]
[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => [1,2,1,1,1,1]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => [1,2,1,1,1,1]
[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]] => [1,2,1,1,1,1]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]] => [1,2,1,1,1,1]
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => [1,2,1,1,1,1]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] => [1,2,1,1,1,1]
[[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]] => [1,2,1,1,1,1]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => [1,2,1,1,1,1]
[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => [1,2,1,1,1,1]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => [1,2,1,1,1,1]
[[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]] => [1,2,1,1,1,1]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] => [1,2,1,1,1,1]
[[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] => [1,2,1,1,1,1]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] => [1,2,1,1,1,1]
[[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]] => [1,2,1,1,1,1]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] => [1,2,1,1,1,1]
[[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] => [1,2,1,1,1,1]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => [1,2,1,1,1,1]
[[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]] => [1,2,1,1,1,1]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]] => [1,2,1,1,1,1]
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]] => [2,1,1,1,1,1]
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]] => [2,1,1,1,1,1]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]] => [2,1,1,1,1,1]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]] => [2,1,1,1,1,1]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]] => [2,1,1,1,1,1]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[4,2,2,1,1,1],[2,1,1]] => [2,1,1,1,1,1]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[4,3,2,1,1,1],[2,2,1]] => [2,1,1,1,1,1]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]] => [2,1,1,1,1,1]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]] => [2,1,1,1,1,1]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1,1,1]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]] => [2,1,1,1,1,1]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]] => [2,1,1,1,1,1]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[4,3,3,2,1,1],[2,2,2,1]] => [2,1,1,1,1,1]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]] => [2,1,1,1,1,1]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]] => [2,1,1,1,1,1]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]] => [2,1,1,1,1,1]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => [2,1,1,1,1,1]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1,1]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[4,3,2,2,2,1],[2,2,1,1,1]] => [2,1,1,1,1,1]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => [2,1,1,1,1,1]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[4,3,3,2,2,1],[2,2,2,1,1]] => [2,1,1,1,1,1]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => [2,1,1,1,1,1]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => [2,1,1,1,1,1]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]] => [2,1,1,1,1,1]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]] => [2,1,1,1,1,1]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => [2,1,1,1,1,1]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]] => [2,1,1,1,1,1]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]] => [2,1,1,1,1,1]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]] => [2,1,1,1,1,1]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]] => [2,1,1,1,1,1]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => [2,1,1,1,1,1]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [[7,5,4,3,2,1],[5,4,3,2,1]] => [2,1,1,1,1,1]
[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1]
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]] => [1,1,1,1,1,1,1]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]] => [1,1,1,1,1,1,1]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]] => [1,1,1,1,1,1,1]
[[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[3,3,2,2,1,1,1],[2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] => [1,1,1,1,1,1,1]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [[3,3,3,2,1,1,1],[2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [[4,4,3,2,1,1,1],[3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [[5,4,3,2,1,1,1],[4,3,2,1]] => [1,1,1,1,1,1,1]
[[2,2,1,1,1,1,1],[1,1]] => [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [[3,2,2,2,2,1,1],[2,1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [[3,3,2,2,2,1,1],[2,2,1,1,1]] => [1,1,1,1,1,1,1]
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [[4,3,2,2,2,1,1],[3,2,1,1,1]] => [1,1,1,1,1,1,1]
[[3,3,2,2,1,1,1],[2,2,1,1]] => [[3,3,3,2,2,1,1],[2,2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [[4,3,3,2,2,1,1],[3,2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [[4,4,3,2,2,1,1],[3,3,2,1,1]] => [1,1,1,1,1,1,1]
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [[5,4,3,2,2,1,1],[4,3,2,1,1]] => [1,1,1,1,1,1,1]
[[3,3,2,1,1,1,1],[2,2,1]] => [[3,3,3,3,2,1,1],[2,2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [[4,3,3,3,2,1,1],[3,2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [[4,4,3,3,2,1,1],[3,3,2,2,1]] => [1,1,1,1,1,1,1]
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [[5,4,3,3,2,1,1],[4,3,2,2,1]] => [1,1,1,1,1,1,1]
[[4,4,3,2,1,1,1],[3,3,2,1]] => [[4,4,4,3,2,1,1],[3,3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [[5,4,4,3,2,1,1],[4,3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [[5,5,4,3,2,1,1],[4,4,3,2,1]] => [1,1,1,1,1,1,1]
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [[6,5,4,3,2,1,1],[5,4,3,2,1]] => [1,1,1,1,1,1,1]
[[2,1,1,1,1,1,1],[1]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [1,1,1,1,1,1,1]
[[3,2,2,2,1,1,1],[2,1,1,1]] => [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [1,1,1,1,1,1,1]
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [1,1,1,1,1,1,1]
[[3,2,2,1,1,1,1],[2,1,1]] => [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [1,1,1,1,1,1,1]
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [1,1,1,1,1,1,1]
[[4,3,3,2,1,1,1],[3,2,2,1]] => [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [1,1,1,1,1,1,1]
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [1,1,1,1,1,1,1]
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [1,1,1,1,1,1,1]
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [1,1,1,1,1,1,1]
[[3,2,1,1,1,1,1],[2,1]] => [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [1,1,1,1,1,1,1]
[[4,3,2,2,1,1,1],[3,2,1,1]] => [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [1,1,1,1,1,1,1]
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [1,1,1,1,1,1,1]
[[4,3,2,1,1,1,1],[3,2,1]] => [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [1,1,1,1,1,1,1]
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [1,1,1,1,1,1,1]
[[5,4,3,2,1,1,1],[4,3,2,1]] => [[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [1,1,1,1,1,1,1]
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [1,1,1,1,1,1,1]
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [1,1,1,1,1,1,1]
[[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [[7,6,5,4,3,2,1],[6,5,4,3,2,1]] => [1,1,1,1,1,1,1]
[[8],[]] => [[8],[]] => [8]
[[6,2],[]] => [[6,6],[4]] => [2,6]
[[5,3],[]] => [[5,5],[2]] => [3,5]
[[4,4],[]] => [[4,4],[]] => [4,4]
[[4,3,1],[]] => [[4,4,4],[3,1]] => [1,3,4]
[[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2,4]
[[3,3,2],[]] => [[3,3,3],[1]] => [2,3,3]
[[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [1,1,3,3]
[[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [1,2,2,3]
[[2,2,2,2],[]] => [[2,2,2,2],[]] => [2,2,2,2]
[[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1,2,2,2]
[[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1]
[[9],[]] => [[9],[]] => [9]
[[6,3],[]] => [[6,6],[3]] => [3,6]
[[5,4],[]] => [[5,5],[1]] => [4,5]
[[5,2,2],[]] => [[5,5,5],[3,3]] => [2,2,5]
[[4,4,1],[]] => [[4,4,4],[3]] => [1,4,4]
[[4,3,2],[]] => [[4,4,4],[2,1]] => [2,3,4]
[[3,3,3],[]] => [[3,3,3],[]] => [3,3,3]
[[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [1,2,3,3]
[[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [2,2,2,3]
[[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1,2,2,2,2]
[[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1]
[[10],[]] => [[10],[]] => [10]
[[6,4],[]] => [[6,6],[2]] => [4,6]
[[5,5],[]] => [[5,5],[]] => [5,5]
[[5,3,2],[]] => [[5,5,5],[3,2]] => [2,3,5]
[[4,4,2],[]] => [[4,4,4],[2]] => [2,4,4]
[[4,3,3],[]] => [[4,4,4],[1,1]] => [3,3,4]
[[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2,4]
[[3,3,3,1],[]] => [[3,3,3,3],[2]] => [1,3,3,3]
[[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [2,2,3,3]
[[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => [2,2,2,2,2]
[[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1]
[[6,5],[]] => [[6,6],[1]] => [5,6]
[[5,5,1],[]] => [[5,5,5],[4]] => [1,5,5]
[[5,4,2],[]] => [[5,5,5],[3,1]] => [2,4,5]
[[5,3,3],[]] => [[5,5,5],[2,2]] => [3,3,5]
[[4,4,3],[]] => [[4,4,4],[1]] => [3,4,4]
[[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [1,2,4,4]
[[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [1,3,3,4]
[[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,3,4]
[[3,3,3,2],[]] => [[3,3,3,3],[1]] => [2,3,3,3]
[[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [2,2,2,2,3]
[[6,6],[]] => [[6,6],[]] => [6,6]
[[5,5,2],[]] => [[5,5,5],[3]] => [2,5,5]
[[5,4,3],[]] => [[5,5,5],[2,1]] => [3,4,5]
[[4,4,4],[]] => [[4,4,4],[]] => [4,4,4]
[[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [1,3,4,4]
[[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2,4,4]
[[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,3,3,4]
[[3,3,3,3],[]] => [[3,3,3,3],[]] => [3,3,3,3]
[[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [1,2,3,3,3]
[[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [2,2,2,3,3]
[[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => [2,2,2,2,2,2]
[[5,5,3],[]] => [[5,5,5],[2]] => [3,5,5]
[[5,4,4],[]] => [[5,5,5],[1,1]] => [4,4,5]
[[4,4,4,1],[]] => [[4,4,4,4],[3]] => [1,4,4,4]
[[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,3,4,4]
[[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [3,3,3,4]
[[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [1,3,3,3,3]
[[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [2,2,3,3,3]
[[5,5,4],[]] => [[5,5,5],[1]] => [4,5,5]
[[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2,4,4,4]
[[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [3,3,4,4]
[[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [2,3,3,3,3]
[[5,5,5],[]] => [[5,5,5],[]] => [5,5,5]
[[4,4,4,3],[]] => [[4,4,4,4],[1]] => [3,4,4,4]
[[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => [3,3,3,3,3]
[[4,4,4,4],[]] => [[4,4,4,4],[]] => [4,4,4,4]
[[3,3,3],[1]] => [[3,3,2],[]] => [3,3,2]
[[3,3,3,1],[1,1]] => [[3,3,2,2],[2]] => [1,3,2,2]
[[4,4,1],[1]] => [[4,4,3],[3]] => [1,4,3]
[[3,3,2,1],[1]] => [[3,3,3,2],[2,1]] => [1,2,3,2]
[[2,2,2,2,1],[1]] => [[2,2,2,2,1],[1]] => [1,2,2,2,1]
[[3,3,3,1],[2]] => [[3,3,3,1],[2]] => [1,3,3,1]
[[3,3,3,1],[1]] => [[3,3,3,2],[2]] => [1,3,3,2]
[[3,3,3,2],[1,1,1]] => [[3,2,2,2],[1]] => [2,2,2,2]
[[4,4,2],[1,1]] => [[4,3,3],[2]] => [2,3,3]
[[4,4,4],[2,2]] => [[4,2,2],[]] => [4,2,2]
[[5,5],[2]] => [[5,3],[]] => [5,3]
[[4,4,3],[2,1]] => [[4,3,2],[1]] => [3,3,2]
[[3,3,3,3],[2,1,1]] => [[3,2,2,1],[]] => [3,2,2,1]
[[4,3,3],[1,1]] => [[4,3,3],[1,1]] => [3,2,3]
[[3,3,3,3],[1,1,1]] => [[3,2,2,2],[]] => [3,2,2,2]
[[4,4,3],[1,1]] => [[4,3,3],[1]] => [3,3,3]
[[4,4,4],[3,1]] => [[4,3,1],[]] => [4,3,1]
[[5,4],[1]] => [[5,4],[1]] => [4,4]
[[4,4,4],[2,1]] => [[4,3,2],[]] => [4,3,2]
[[5,5],[1]] => [[5,4],[]] => [5,4]
[[4,4,4],[1,1]] => [[4,3,3],[]] => [4,3,3]
[[3,3,2,2],[1,1]] => [[3,3,2,2],[1,1]] => [2,2,2,2]
[[4,4,2],[2]] => [[4,4,2],[2]] => [2,4,2]
[[3,3,3,2],[2,1]] => [[3,3,2,1],[1]] => [2,3,2,1]
[[4,3,2],[1]] => [[4,4,3],[2,1]] => [2,3,3]
[[3,3,3,2],[1,1]] => [[3,3,2,2],[1]] => [2,3,2,2]
[[4,4,2],[1]] => [[4,4,3],[2]] => [2,4,3]
[[2,2,2,2,2],[1,1]] => [[2,2,2,1,1],[]] => [2,2,2,1,1]
[[3,2,2,2],[1]] => [[3,3,3,2],[1,1,1]] => [2,2,2,2]
[[3,3,2,2],[2]] => [[3,3,3,1],[1,1]] => [2,2,3,1]
[[3,3,2,2],[1]] => [[3,3,3,2],[1,1]] => [2,2,3,2]
[[2,2,2,2,2],[1]] => [[2,2,2,2,1],[]] => [2,2,2,2,1]
[[3,3,3,2],[2]] => [[3,3,3,1],[1]] => [2,3,3,1]
[[3,3,3,2],[1]] => [[3,3,3,2],[1]] => [2,3,3,2]
[[3,3,3,3],[2,2]] => [[3,3,1,1],[]] => [3,3,1,1]
[[4,3,3],[2]] => [[4,4,2],[1,1]] => [3,3,2]
[[4,4,3],[3]] => [[4,4,1],[1]] => [3,4,1]
[[4,4,3],[2]] => [[4,4,2],[1]] => [3,4,2]
[[3,3,3,3],[2,1]] => [[3,3,2,1],[]] => [3,3,2,1]
[[4,3,3],[1]] => [[4,4,3],[1,1]] => [3,3,3]
[[3,3,3,3],[1,1]] => [[3,3,2,2],[]] => [3,3,2,2]
[[4,4,3],[1]] => [[4,4,3],[1]] => [3,4,3]
[[4,4,4],[3]] => [[4,4,1],[]] => [4,4,1]
[[4,4,4],[2]] => [[4,4,2],[]] => [4,4,2]
[[4,4,4],[1]] => [[4,4,3],[]] => [4,4,3]
[[3,3,3,3],[2]] => [[3,3,3,1],[]] => [3,3,3,1]
[[3,3,3,3],[1]] => [[3,3,3,2],[]] => [3,3,3,2]
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition λ/μ, its rotation (λ/μ)♮ is the skew partition with cells {(a−i,b−j)|(i,j)∈λ/μ}, where b and a are the first part and the number of parts of λ respectively.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition λ/μ, its rotation (λ/μ)♮ is the skew partition with cells {(a−i,b−j)|(i,j)∈λ/μ}, where b and a are the first part and the number of parts of λ respectively.
Map
row lengths
Description
The sequence of row lengths from top to bottom.
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