Identifier
Mp00187:
Skew partitions
—conjugate⟶
Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Images
[[1],[]] => [[1],[]] => []
[[2],[]] => [[1,1],[]] => []
[[1,1],[]] => [[2],[]] => []
[[2,1],[1]] => [[2,1],[1]] => [1]
[[3],[]] => [[1,1,1],[]] => []
[[2,1],[]] => [[2,1],[]] => []
[[3,1],[1]] => [[2,1,1],[1]] => [1]
[[2,2],[1]] => [[2,2],[1]] => [1]
[[3,2],[2]] => [[2,2,1],[1,1]] => [1,1]
[[1,1,1],[]] => [[3],[]] => []
[[2,2,1],[1,1]] => [[3,2],[2]] => [2]
[[2,1,1],[1]] => [[3,1],[1]] => [1]
[[3,2,1],[2,1]] => [[3,2,1],[2,1]] => [2,1]
[[4],[]] => [[1,1,1,1],[]] => []
[[3,1],[]] => [[2,1,1],[]] => []
[[4,1],[1]] => [[2,1,1,1],[1]] => [1]
[[2,2],[]] => [[2,2],[]] => []
[[3,2],[1]] => [[2,2,1],[1]] => [1]
[[4,2],[2]] => [[2,2,1,1],[1,1]] => [1,1]
[[2,1,1],[]] => [[3,1],[]] => []
[[3,2,1],[1,1]] => [[3,2,1],[2]] => [2]
[[3,1,1],[1]] => [[3,1,1],[1]] => [1]
[[4,2,1],[2,1]] => [[3,2,1,1],[2,1]] => [2,1]
[[3,3],[2]] => [[2,2,2],[1,1]] => [1,1]
[[4,3],[3]] => [[2,2,2,1],[1,1,1]] => [1,1,1]
[[2,2,1],[1]] => [[3,2],[1]] => [1]
[[3,3,1],[2,1]] => [[3,2,2],[2,1]] => [2,1]
[[3,2,1],[2]] => [[3,2,1],[1,1]] => [1,1]
[[4,3,1],[3,1]] => [[3,2,2,1],[2,1,1]] => [2,1,1]
[[2,2,2],[1,1]] => [[3,3],[2]] => [2]
[[3,3,2],[2,2]] => [[3,3,2],[2,2]] => [2,2]
[[3,2,2],[2,1]] => [[3,3,1],[2,1]] => [2,1]
[[4,3,2],[3,2]] => [[3,3,2,1],[2,2,1]] => [2,2,1]
[[1,1,1,1],[]] => [[4],[]] => []
[[2,2,2,1],[1,1,1]] => [[4,3],[3]] => [3]
[[2,2,1,1],[1,1]] => [[4,2],[2]] => [2]
[[3,3,2,1],[2,2,1]] => [[4,3,2],[3,2]] => [3,2]
[[2,1,1,1],[1]] => [[4,1],[1]] => [1]
[[3,2,2,1],[2,1,1]] => [[4,3,1],[3,1]] => [3,1]
[[3,2,1,1],[2,1]] => [[4,2,1],[2,1]] => [2,1]
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]] => [3,2,1]
[[5],[]] => [[1,1,1,1,1],[]] => []
[[4,1],[]] => [[2,1,1,1],[]] => []
[[5,1],[1]] => [[2,1,1,1,1],[1]] => [1]
[[3,2],[]] => [[2,2,1],[]] => []
[[4,2],[1]] => [[2,2,1,1],[1]] => [1]
[[5,2],[2]] => [[2,2,1,1,1],[1,1]] => [1,1]
[[3,1,1],[]] => [[3,1,1],[]] => []
[[4,2,1],[1,1]] => [[3,2,1,1],[2]] => [2]
[[4,1,1],[1]] => [[3,1,1,1],[1]] => [1]
[[5,2,1],[2,1]] => [[3,2,1,1,1],[2,1]] => [2,1]
[[3,3],[1]] => [[2,2,2],[1]] => [1]
[[4,3],[2]] => [[2,2,2,1],[1,1]] => [1,1]
[[5,3],[3]] => [[2,2,2,1,1],[1,1,1]] => [1,1,1]
[[2,2,1],[]] => [[3,2],[]] => []
[[3,3,1],[1,1]] => [[3,2,2],[2]] => [2]
[[3,2,1],[1]] => [[3,2,1],[1]] => [1]
[[4,3,1],[2,1]] => [[3,2,2,1],[2,1]] => [2,1]
[[4,2,1],[2]] => [[3,2,1,1],[1,1]] => [1,1]
[[5,3,1],[3,1]] => [[3,2,2,1,1],[2,1,1]] => [2,1,1]
[[3,2,2],[1,1]] => [[3,3,1],[2]] => [2]
[[4,3,2],[2,2]] => [[3,3,2,1],[2,2]] => [2,2]
[[4,2,2],[2,1]] => [[3,3,1,1],[2,1]] => [2,1]
[[5,3,2],[3,2]] => [[3,3,2,1,1],[2,2,1]] => [2,2,1]
[[2,1,1,1],[]] => [[4,1],[]] => []
[[3,2,2,1],[1,1,1]] => [[4,3,1],[3]] => [3]
[[3,2,1,1],[1,1]] => [[4,2,1],[2]] => [2]
[[4,3,2,1],[2,2,1]] => [[4,3,2,1],[3,2]] => [3,2]
[[3,1,1,1],[1]] => [[4,1,1],[1]] => [1]
[[4,2,2,1],[2,1,1]] => [[4,3,1,1],[3,1]] => [3,1]
[[4,2,1,1],[2,1]] => [[4,2,1,1],[2,1]] => [2,1]
[[5,3,2,1],[3,2,1]] => [[4,3,2,1,1],[3,2,1]] => [3,2,1]
[[4,4],[3]] => [[2,2,2,2],[1,1,1]] => [1,1,1]
[[5,4],[4]] => [[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1]
[[3,3,1],[2]] => [[3,2,2],[1,1]] => [1,1]
[[4,4,1],[3,1]] => [[3,2,2,2],[2,1,1]] => [2,1,1]
[[4,3,1],[3]] => [[3,2,2,1],[1,1,1]] => [1,1,1]
[[5,4,1],[4,1]] => [[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[2,2,2],[1]] => [[3,3],[1]] => [1]
[[3,3,2],[2,1]] => [[3,3,2],[2,1]] => [2,1]
[[4,4,2],[3,2]] => [[3,3,2,2],[2,2,1]] => [2,2,1]
[[3,2,2],[2]] => [[3,3,1],[1,1]] => [1,1]
[[4,3,2],[3,1]] => [[3,3,2,1],[2,1,1]] => [2,1,1]
[[5,4,2],[4,2]] => [[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1]
[[2,2,1,1],[1]] => [[4,2],[1]] => [1]
[[3,3,2,1],[2,1,1]] => [[4,3,2],[3,1]] => [3,1]
[[3,3,1,1],[2,1]] => [[4,2,2],[2,1]] => [2,1]
[[4,4,2,1],[3,2,1]] => [[4,3,2,2],[3,2,1]] => [3,2,1]
[[3,2,1,1],[2]] => [[4,2,1],[1,1]] => [1,1]
[[4,3,2,1],[3,1,1]] => [[4,3,2,1],[3,1,1]] => [3,1,1]
[[4,3,1,1],[3,1]] => [[4,2,2,1],[2,1,1]] => [2,1,1]
[[5,4,2,1],[4,2,1]] => [[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[3,3,3],[2,2]] => [[3,3,3],[2,2]] => [2,2]
[[4,4,3],[3,3]] => [[3,3,3,2],[2,2,2]] => [2,2,2]
[[4,3,3],[3,2]] => [[3,3,3,1],[2,2,1]] => [2,2,1]
[[5,4,3],[4,3]] => [[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1]
[[2,2,2,1],[1,1]] => [[4,3],[2]] => [2]
[[3,3,3,1],[2,2,1]] => [[4,3,3],[3,2]] => [3,2]
[[3,3,2,1],[2,2]] => [[4,3,2],[2,2]] => [2,2]
[[4,4,3,1],[3,3,1]] => [[4,3,3,2],[3,2,2]] => [3,2,2]
[[3,2,2,1],[2,1]] => [[4,3,1],[2,1]] => [2,1]
>>> Load all 1612 entries. <<<
[[4,3,3,1],[3,2,1]] => [[4,3,3,1],[3,2,1]] => [3,2,1]
[[4,3,2,1],[3,2]] => [[4,3,2,1],[2,2,1]] => [2,2,1]
[[5,4,3,1],[4,3,1]] => [[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1]
[[2,2,2,2],[1,1,1]] => [[4,4],[3]] => [3]
[[3,3,3,2],[2,2,2]] => [[4,4,3],[3,3]] => [3,3]
[[3,3,2,2],[2,2,1]] => [[4,4,2],[3,2]] => [3,2]
[[4,4,3,2],[3,3,2]] => [[4,4,3,2],[3,3,2]] => [3,3,2]
[[3,2,2,2],[2,1,1]] => [[4,4,1],[3,1]] => [3,1]
[[4,3,3,2],[3,2,2]] => [[4,4,3,1],[3,3,1]] => [3,3,1]
[[4,3,2,2],[3,2,1]] => [[4,4,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,2],[4,3,2]] => [[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1]
[[1,1,1,1,1],[]] => [[5],[]] => []
[[2,2,2,2,1],[1,1,1,1]] => [[5,4],[4]] => [4]
[[2,2,2,1,1],[1,1,1]] => [[5,3],[3]] => [3]
[[3,3,3,2,1],[2,2,2,1]] => [[5,4,3],[4,3]] => [4,3]
[[2,2,1,1,1],[1,1]] => [[5,2],[2]] => [2]
[[3,3,2,2,1],[2,2,1,1]] => [[5,4,2],[4,2]] => [4,2]
[[3,3,2,1,1],[2,2,1]] => [[5,3,2],[3,2]] => [3,2]
[[4,4,3,2,1],[3,3,2,1]] => [[5,4,3,2],[4,3,2]] => [4,3,2]
[[2,1,1,1,1],[1]] => [[5,1],[1]] => [1]
[[3,2,2,2,1],[2,1,1,1]] => [[5,4,1],[4,1]] => [4,1]
[[3,2,2,1,1],[2,1,1]] => [[5,3,1],[3,1]] => [3,1]
[[4,3,3,2,1],[3,2,2,1]] => [[5,4,3,1],[4,3,1]] => [4,3,1]
[[3,2,1,1,1],[2,1]] => [[5,2,1],[2,1]] => [2,1]
[[4,3,2,2,1],[3,2,1,1]] => [[5,4,2,1],[4,2,1]] => [4,2,1]
[[4,3,2,1,1],[3,2,1]] => [[5,3,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1]
[[6],[]] => [[1,1,1,1,1,1],[]] => []
[[5,1],[]] => [[2,1,1,1,1],[]] => []
[[6,1],[1]] => [[2,1,1,1,1,1],[1]] => [1]
[[4,2],[]] => [[2,2,1,1],[]] => []
[[5,2],[1]] => [[2,2,1,1,1],[1]] => [1]
[[6,2],[2]] => [[2,2,1,1,1,1],[1,1]] => [1,1]
[[4,1,1],[]] => [[3,1,1,1],[]] => []
[[5,2,1],[1,1]] => [[3,2,1,1,1],[2]] => [2]
[[5,1,1],[1]] => [[3,1,1,1,1],[1]] => [1]
[[6,2,1],[2,1]] => [[3,2,1,1,1,1],[2,1]] => [2,1]
[[3,3],[]] => [[2,2,2],[]] => []
[[4,3],[1]] => [[2,2,2,1],[1]] => [1]
[[5,3],[2]] => [[2,2,2,1,1],[1,1]] => [1,1]
[[6,3],[3]] => [[2,2,2,1,1,1],[1,1,1]] => [1,1,1]
[[3,2,1],[]] => [[3,2,1],[]] => []
[[4,3,1],[1,1]] => [[3,2,2,1],[2]] => [2]
[[4,2,1],[1]] => [[3,2,1,1],[1]] => [1]
[[5,3,1],[2,1]] => [[3,2,2,1,1],[2,1]] => [2,1]
[[5,2,1],[2]] => [[3,2,1,1,1],[1,1]] => [1,1]
[[6,3,1],[3,1]] => [[3,2,2,1,1,1],[2,1,1]] => [2,1,1]
[[4,2,2],[1,1]] => [[3,3,1,1],[2]] => [2]
[[5,3,2],[2,2]] => [[3,3,2,1,1],[2,2]] => [2,2]
[[5,2,2],[2,1]] => [[3,3,1,1,1],[2,1]] => [2,1]
[[6,3,2],[3,2]] => [[3,3,2,1,1,1],[2,2,1]] => [2,2,1]
[[3,1,1,1],[]] => [[4,1,1],[]] => []
[[4,2,2,1],[1,1,1]] => [[4,3,1,1],[3]] => [3]
[[4,2,1,1],[1,1]] => [[4,2,1,1],[2]] => [2]
[[5,3,2,1],[2,2,1]] => [[4,3,2,1,1],[3,2]] => [3,2]
[[4,1,1,1],[1]] => [[4,1,1,1],[1]] => [1]
[[5,2,2,1],[2,1,1]] => [[4,3,1,1,1],[3,1]] => [3,1]
[[5,2,1,1],[2,1]] => [[4,2,1,1,1],[2,1]] => [2,1]
[[6,3,2,1],[3,2,1]] => [[4,3,2,1,1,1],[3,2,1]] => [3,2,1]
[[4,4],[2]] => [[2,2,2,2],[1,1]] => [1,1]
[[5,4],[3]] => [[2,2,2,2,1],[1,1,1]] => [1,1,1]
[[6,4],[4]] => [[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1]
[[3,3,1],[1]] => [[3,2,2],[1]] => [1]
[[4,4,1],[2,1]] => [[3,2,2,2],[2,1]] => [2,1]
[[4,3,1],[2]] => [[3,2,2,1],[1,1]] => [1,1]
[[5,4,1],[3,1]] => [[3,2,2,2,1],[2,1,1]] => [2,1,1]
[[5,3,1],[3]] => [[3,2,2,1,1],[1,1,1]] => [1,1,1]
[[6,4,1],[4,1]] => [[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1]
[[2,2,2],[]] => [[3,3],[]] => []
[[3,3,2],[1,1]] => [[3,3,2],[2]] => [2]
[[4,4,2],[2,2]] => [[3,3,2,2],[2,2]] => [2,2]
[[3,2,2],[1]] => [[3,3,1],[1]] => [1]
[[4,3,2],[2,1]] => [[3,3,2,1],[2,1]] => [2,1]
[[5,4,2],[3,2]] => [[3,3,2,2,1],[2,2,1]] => [2,2,1]
[[4,2,2],[2]] => [[3,3,1,1],[1,1]] => [1,1]
[[5,3,2],[3,1]] => [[3,3,2,1,1],[2,1,1]] => [2,1,1]
[[6,4,2],[4,2]] => [[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1]
[[2,2,1,1],[]] => [[4,2],[]] => []
[[3,3,2,1],[1,1,1]] => [[4,3,2],[3]] => [3]
[[3,3,1,1],[1,1]] => [[4,2,2],[2]] => [2]
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]] => [3,2]
[[3,2,1,1],[1]] => [[4,2,1],[1]] => [1]
[[4,3,2,1],[2,1,1]] => [[4,3,2,1],[3,1]] => [3,1]
[[4,3,1,1],[2,1]] => [[4,2,2,1],[2,1]] => [2,1]
[[5,4,2,1],[3,2,1]] => [[4,3,2,2,1],[3,2,1]] => [3,2,1]
[[4,2,1,1],[2]] => [[4,2,1,1],[1,1]] => [1,1]
[[5,3,2,1],[3,1,1]] => [[4,3,2,1,1],[3,1,1]] => [3,1,1]
[[5,3,1,1],[3,1]] => [[4,2,2,1,1],[2,1,1]] => [2,1,1]
[[6,4,2,1],[4,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1]
[[4,3,3],[2,2]] => [[3,3,3,1],[2,2]] => [2,2]
[[5,4,3],[3,3]] => [[3,3,3,2,1],[2,2,2]] => [2,2,2]
[[5,3,3],[3,2]] => [[3,3,3,1,1],[2,2,1]] => [2,2,1]
[[6,4,3],[4,3]] => [[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1]
[[3,2,2,1],[1,1]] => [[4,3,1],[2]] => [2]
[[4,3,3,1],[2,2,1]] => [[4,3,3,1],[3,2]] => [3,2]
[[4,3,2,1],[2,2]] => [[4,3,2,1],[2,2]] => [2,2]
[[5,4,3,1],[3,3,1]] => [[4,3,3,2,1],[3,2,2]] => [3,2,2]
[[4,2,2,1],[2,1]] => [[4,3,1,1],[2,1]] => [2,1]
[[5,3,3,1],[3,2,1]] => [[4,3,3,1,1],[3,2,1]] => [3,2,1]
[[5,3,2,1],[3,2]] => [[4,3,2,1,1],[2,2,1]] => [2,2,1]
[[6,4,3,1],[4,3,1]] => [[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1]
[[3,2,2,2],[1,1,1]] => [[4,4,1],[3]] => [3]
[[4,3,3,2],[2,2,2]] => [[4,4,3,1],[3,3]] => [3,3]
[[4,3,2,2],[2,2,1]] => [[4,4,2,1],[3,2]] => [3,2]
[[5,4,3,2],[3,3,2]] => [[4,4,3,2,1],[3,3,2]] => [3,3,2]
[[4,2,2,2],[2,1,1]] => [[4,4,1,1],[3,1]] => [3,1]
[[5,3,3,2],[3,2,2]] => [[4,4,3,1,1],[3,3,1]] => [3,3,1]
[[5,3,2,2],[3,2,1]] => [[4,4,2,1,1],[3,2,1]] => [3,2,1]
[[6,4,3,2],[4,3,2]] => [[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1]
[[2,1,1,1,1],[]] => [[5,1],[]] => []
[[3,2,2,2,1],[1,1,1,1]] => [[5,4,1],[4]] => [4]
[[3,2,2,1,1],[1,1,1]] => [[5,3,1],[3]] => [3]
[[4,3,3,2,1],[2,2,2,1]] => [[5,4,3,1],[4,3]] => [4,3]
[[3,2,1,1,1],[1,1]] => [[5,2,1],[2]] => [2]
[[4,3,2,2,1],[2,2,1,1]] => [[5,4,2,1],[4,2]] => [4,2]
[[4,3,2,1,1],[2,2,1]] => [[5,3,2,1],[3,2]] => [3,2]
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,1],[4,3,2]] => [4,3,2]
[[3,1,1,1,1],[1]] => [[5,1,1],[1]] => [1]
[[4,2,2,2,1],[2,1,1,1]] => [[5,4,1,1],[4,1]] => [4,1]
[[4,2,2,1,1],[2,1,1]] => [[5,3,1,1],[3,1]] => [3,1]
[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,1,1],[4,3,1]] => [4,3,1]
[[4,2,1,1,1],[2,1]] => [[5,2,1,1],[2,1]] => [2,1]
[[5,3,2,2,1],[3,2,1,1]] => [[5,4,2,1,1],[4,2,1]] => [4,2,1]
[[5,3,2,1,1],[3,2,1]] => [[5,3,2,1,1],[3,2,1]] => [3,2,1]
[[6,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1]
[[5,5],[4]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[6,5],[5]] => [[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1]
[[4,4,1],[3]] => [[3,2,2,2],[1,1,1]] => [1,1,1]
[[5,5,1],[4,1]] => [[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1]
[[5,4,1],[4]] => [[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1]
[[6,5,1],[5,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1]
[[3,3,2],[2]] => [[3,3,2],[1,1]] => [1,1]
[[4,4,2],[3,1]] => [[3,3,2,2],[2,1,1]] => [2,1,1]
[[5,5,2],[4,2]] => [[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1]
[[4,3,2],[3]] => [[3,3,2,1],[1,1,1]] => [1,1,1]
[[5,4,2],[4,1]] => [[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,5,2],[5,2]] => [[3,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1]
[[3,3,1,1],[2]] => [[4,2,2],[1,1]] => [1,1]
[[4,4,2,1],[3,1,1]] => [[4,3,2,2],[3,1,1]] => [3,1,1]
[[4,4,1,1],[3,1]] => [[4,2,2,2],[2,1,1]] => [2,1,1]
[[5,5,2,1],[4,2,1]] => [[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1]
[[4,3,1,1],[3]] => [[4,2,2,1],[1,1,1]] => [1,1,1]
[[5,4,2,1],[4,1,1]] => [[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1]
[[5,4,1,1],[4,1]] => [[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,5,2,1],[5,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1]
[[3,3,3],[2,1]] => [[3,3,3],[2,1]] => [2,1]
[[4,4,3],[3,2]] => [[3,3,3,2],[2,2,1]] => [2,2,1]
[[5,5,3],[4,3]] => [[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1]
[[4,3,3],[3,1]] => [[3,3,3,1],[2,1,1]] => [2,1,1]
[[5,4,3],[4,2]] => [[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,3],[5,3]] => [[3,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1]
[[2,2,2,1],[1]] => [[4,3],[1]] => [1]
[[3,3,3,1],[2,1,1]] => [[4,3,3],[3,1]] => [3,1]
[[3,3,2,1],[2,1]] => [[4,3,2],[2,1]] => [2,1]
[[4,4,3,1],[3,2,1]] => [[4,3,3,2],[3,2,1]] => [3,2,1]
[[4,4,2,1],[3,2]] => [[4,3,2,2],[2,2,1]] => [2,2,1]
[[5,5,3,1],[4,3,1]] => [[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1]
[[3,2,2,1],[2]] => [[4,3,1],[1,1]] => [1,1]
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]] => [3,1,1]
[[4,3,2,1],[3,1]] => [[4,3,2,1],[2,1,1]] => [2,1,1]
[[5,4,3,1],[4,2,1]] => [[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1]
[[5,4,2,1],[4,2]] => [[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,3,1],[5,3,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1]
[[3,3,2,2],[2,1,1]] => [[4,4,2],[3,1]] => [3,1]
[[4,4,3,2],[3,2,2]] => [[4,4,3,2],[3,3,1]] => [3,3,1]
[[4,4,2,2],[3,2,1]] => [[4,4,2,2],[3,2,1]] => [3,2,1]
[[5,5,3,2],[4,3,2]] => [[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1]
[[4,3,2,2],[3,1,1]] => [[4,4,2,1],[3,1,1]] => [3,1,1]
[[5,4,3,2],[4,2,2]] => [[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1]
[[5,4,2,2],[4,2,1]] => [[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,3,2],[5,3,2]] => [[4,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1]
[[2,2,1,1,1],[1]] => [[5,2],[1]] => [1]
[[3,3,2,2,1],[2,1,1,1]] => [[5,4,2],[4,1]] => [4,1]
[[3,3,2,1,1],[2,1,1]] => [[5,3,2],[3,1]] => [3,1]
[[4,4,3,2,1],[3,2,2,1]] => [[5,4,3,2],[4,3,1]] => [4,3,1]
[[3,3,1,1,1],[2,1]] => [[5,2,2],[2,1]] => [2,1]
[[4,4,2,2,1],[3,2,1,1]] => [[5,4,2,2],[4,2,1]] => [4,2,1]
[[4,4,2,1,1],[3,2,1]] => [[5,3,2,2],[3,2,1]] => [3,2,1]
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1]
[[3,2,1,1,1],[2]] => [[5,2,1],[1,1]] => [1,1]
[[4,3,2,2,1],[3,1,1,1]] => [[5,4,2,1],[4,1,1]] => [4,1,1]
[[4,3,2,1,1],[3,1,1]] => [[5,3,2,1],[3,1,1]] => [3,1,1]
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1]
[[4,3,1,1,1],[3,1]] => [[5,2,2,1],[2,1,1]] => [2,1,1]
[[5,4,2,2,1],[4,2,1,1]] => [[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1]
[[5,4,2,1,1],[4,2,1]] => [[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,3,2,1],[5,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[4,4,4],[3,3]] => [[3,3,3,3],[2,2,2]] => [2,2,2]
[[5,5,4],[4,4]] => [[3,3,3,3,2],[2,2,2,2]] => [2,2,2,2]
[[5,4,4],[4,3]] => [[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1]
[[6,5,4],[5,4]] => [[3,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1]
[[3,3,3,1],[2,2]] => [[4,3,3],[2,2]] => [2,2]
[[4,4,4,1],[3,3,1]] => [[4,3,3,3],[3,2,2]] => [3,2,2]
[[4,4,3,1],[3,3]] => [[4,3,3,2],[2,2,2]] => [2,2,2]
[[5,5,4,1],[4,4,1]] => [[4,3,3,3,2],[3,2,2,2]] => [3,2,2,2]
[[4,3,3,1],[3,2]] => [[4,3,3,1],[2,2,1]] => [2,2,1]
[[5,4,4,1],[4,3,1]] => [[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1]
[[5,4,3,1],[4,3]] => [[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1]
[[6,5,4,1],[5,4,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1]
[[2,2,2,2],[1,1]] => [[4,4],[2]] => [2]
[[3,3,3,2],[2,2,1]] => [[4,4,3],[3,2]] => [3,2]
[[4,4,4,2],[3,3,2]] => [[4,4,3,3],[3,3,2]] => [3,3,2]
[[3,3,2,2],[2,2]] => [[4,4,2],[2,2]] => [2,2]
[[4,4,3,2],[3,3,1]] => [[4,4,3,2],[3,2,2]] => [3,2,2]
[[5,5,4,2],[4,4,2]] => [[4,4,3,3,2],[3,3,2,2]] => [3,3,2,2]
[[3,2,2,2],[2,1]] => [[4,4,1],[2,1]] => [2,1]
[[4,3,3,2],[3,2,1]] => [[4,4,3,1],[3,2,1]] => [3,2,1]
[[5,4,4,2],[4,3,2]] => [[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1]
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]] => [2,2,1]
[[5,4,3,2],[4,3,1]] => [[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,4,2],[5,4,2]] => [[4,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1]
[[2,2,2,1,1],[1,1]] => [[5,3],[2]] => [2]
[[3,3,3,2,1],[2,2,1,1]] => [[5,4,3],[4,2]] => [4,2]
[[3,3,3,1,1],[2,2,1]] => [[5,3,3],[3,2]] => [3,2]
[[4,4,4,2,1],[3,3,2,1]] => [[5,4,3,3],[4,3,2]] => [4,3,2]
[[3,3,2,1,1],[2,2]] => [[5,3,2],[2,2]] => [2,2]
[[4,4,3,2,1],[3,3,1,1]] => [[5,4,3,2],[4,2,2]] => [4,2,2]
[[4,4,3,1,1],[3,3,1]] => [[5,3,3,2],[3,2,2]] => [3,2,2]
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,3,2],[4,3,2,2]] => [4,3,2,2]
[[3,2,2,1,1],[2,1]] => [[5,3,1],[2,1]] => [2,1]
[[4,3,3,2,1],[3,2,1,1]] => [[5,4,3,1],[4,2,1]] => [4,2,1]
[[4,3,3,1,1],[3,2,1]] => [[5,3,3,1],[3,2,1]] => [3,2,1]
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1]
[[4,3,2,1,1],[3,2]] => [[5,3,2,1],[2,2,1]] => [2,2,1]
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1]
[[5,4,3,1,1],[4,3,1]] => [[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,4,2,1],[5,4,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[3,3,3,3],[2,2,2]] => [[4,4,4],[3,3]] => [3,3]
[[4,4,4,3],[3,3,3]] => [[4,4,4,3],[3,3,3]] => [3,3,3]
[[4,4,3,3],[3,3,2]] => [[4,4,4,2],[3,3,2]] => [3,3,2]
[[5,5,4,3],[4,4,3]] => [[4,4,4,3,2],[3,3,3,2]] => [3,3,3,2]
[[4,3,3,3],[3,2,2]] => [[4,4,4,1],[3,3,1]] => [3,3,1]
[[5,4,4,3],[4,3,3]] => [[4,4,4,3,1],[3,3,3,1]] => [3,3,3,1]
[[5,4,3,3],[4,3,2]] => [[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,4,3],[5,4,3]] => [[4,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1]
[[2,2,2,2,1],[1,1,1]] => [[5,4],[3]] => [3]
[[3,3,3,3,1],[2,2,2,1]] => [[5,4,4],[4,3]] => [4,3]
[[3,3,3,2,1],[2,2,2]] => [[5,4,3],[3,3]] => [3,3]
[[4,4,4,3,1],[3,3,3,1]] => [[5,4,4,3],[4,3,3]] => [4,3,3]
[[3,3,2,2,1],[2,2,1]] => [[5,4,2],[3,2]] => [3,2]
[[4,4,3,3,1],[3,3,2,1]] => [[5,4,4,2],[4,3,2]] => [4,3,2]
[[4,4,3,2,1],[3,3,2]] => [[5,4,3,2],[3,3,2]] => [3,3,2]
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,4,3,2],[4,3,3,2]] => [4,3,3,2]
[[3,2,2,2,1],[2,1,1]] => [[5,4,1],[3,1]] => [3,1]
[[4,3,3,3,1],[3,2,2,1]] => [[5,4,4,1],[4,3,1]] => [4,3,1]
[[4,3,3,2,1],[3,2,2]] => [[5,4,3,1],[3,3,1]] => [3,3,1]
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,4,3,1],[4,3,3,1]] => [4,3,3,1]
[[4,3,2,2,1],[3,2,1]] => [[5,4,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1]
[[5,4,3,2,1],[4,3,2]] => [[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,4,3,1],[5,4,3,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[2,2,2,2,2],[1,1,1,1]] => [[5,5],[4]] => [4]
[[3,3,3,3,2],[2,2,2,2]] => [[5,5,4],[4,4]] => [4,4]
[[3,3,3,2,2],[2,2,2,1]] => [[5,5,3],[4,3]] => [4,3]
[[4,4,4,3,2],[3,3,3,2]] => [[5,5,4,3],[4,4,3]] => [4,4,3]
[[3,3,2,2,2],[2,2,1,1]] => [[5,5,2],[4,2]] => [4,2]
[[4,4,3,3,2],[3,3,2,2]] => [[5,5,4,2],[4,4,2]] => [4,4,2]
[[4,4,3,2,2],[3,3,2,1]] => [[5,5,3,2],[4,3,2]] => [4,3,2]
[[5,5,4,3,2],[4,4,3,2]] => [[5,5,4,3,2],[4,4,3,2]] => [4,4,3,2]
[[3,2,2,2,2],[2,1,1,1]] => [[5,5,1],[4,1]] => [4,1]
[[4,3,3,3,2],[3,2,2,2]] => [[5,5,4,1],[4,4,1]] => [4,4,1]
[[4,3,3,2,2],[3,2,2,1]] => [[5,5,3,1],[4,3,1]] => [4,3,1]
[[5,4,4,3,2],[4,3,3,2]] => [[5,5,4,3,1],[4,4,3,1]] => [4,4,3,1]
[[4,3,2,2,2],[3,2,1,1]] => [[5,5,2,1],[4,2,1]] => [4,2,1]
[[5,4,3,3,2],[4,3,2,2]] => [[5,5,4,2,1],[4,4,2,1]] => [4,4,2,1]
[[5,4,3,2,2],[4,3,2,1]] => [[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,3,2],[5,4,3,2]] => [[5,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[1,1,1,1,1,1],[]] => [[6],[]] => []
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[6,5],[5]] => [5]
[[2,2,2,2,1,1],[1,1,1,1]] => [[6,4],[4]] => [4]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[6,5,4],[5,4]] => [5,4]
[[2,2,2,1,1,1],[1,1,1]] => [[6,3],[3]] => [3]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[6,5,3],[5,3]] => [5,3]
[[3,3,3,2,1,1],[2,2,2,1]] => [[6,4,3],[4,3]] => [4,3]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[6,5,4,3],[5,4,3]] => [5,4,3]
[[2,2,1,1,1,1],[1,1]] => [[6,2],[2]] => [2]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[6,5,2],[5,2]] => [5,2]
[[3,3,2,2,1,1],[2,2,1,1]] => [[6,4,2],[4,2]] => [4,2]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[6,5,4,2],[5,4,2]] => [5,4,2]
[[3,3,2,1,1,1],[2,2,1]] => [[6,3,2],[3,2]] => [3,2]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[6,5,3,2],[5,3,2]] => [5,3,2]
[[4,4,3,2,1,1],[3,3,2,1]] => [[6,4,3,2],[4,3,2]] => [4,3,2]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]] => [5,4,3,2]
[[2,1,1,1,1,1],[1]] => [[6,1],[1]] => [1]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[6,5,1],[5,1]] => [5,1]
[[3,2,2,2,1,1],[2,1,1,1]] => [[6,4,1],[4,1]] => [4,1]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[6,5,4,1],[5,4,1]] => [5,4,1]
[[3,2,2,1,1,1],[2,1,1]] => [[6,3,1],[3,1]] => [3,1]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[6,5,3,1],[5,3,1]] => [5,3,1]
[[4,3,3,2,1,1],[3,2,2,1]] => [[6,4,3,1],[4,3,1]] => [4,3,1]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]] => [5,4,3,1]
[[3,2,1,1,1,1],[2,1]] => [[6,2,1],[2,1]] => [2,1]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[6,5,2,1],[5,2,1]] => [5,2,1]
[[4,3,2,2,1,1],[3,2,1,1]] => [[6,4,2,1],[4,2,1]] => [4,2,1]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,2,1],[5,4,2,1]] => [5,4,2,1]
[[4,3,2,1,1,1],[3,2,1]] => [[6,3,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,3,2,1],[5,3,2,1]] => [5,3,2,1]
[[5,4,3,2,1,1],[4,3,2,1]] => [[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[7],[]] => [[1,1,1,1,1,1,1],[]] => []
[[6,1],[]] => [[2,1,1,1,1,1],[]] => []
[[7,1],[1]] => [[2,1,1,1,1,1,1],[1]] => [1]
[[5,2],[]] => [[2,2,1,1,1],[]] => []
[[6,2],[1]] => [[2,2,1,1,1,1],[1]] => [1]
[[7,2],[2]] => [[2,2,1,1,1,1,1],[1,1]] => [1,1]
[[5,1,1],[]] => [[3,1,1,1,1],[]] => []
[[6,2,1],[1,1]] => [[3,2,1,1,1,1],[2]] => [2]
[[6,1,1],[1]] => [[3,1,1,1,1,1],[1]] => [1]
[[7,2,1],[2,1]] => [[3,2,1,1,1,1,1],[2,1]] => [2,1]
[[4,3],[]] => [[2,2,2,1],[]] => []
[[5,3],[1]] => [[2,2,2,1,1],[1]] => [1]
[[6,3],[2]] => [[2,2,2,1,1,1],[1,1]] => [1,1]
[[7,3],[3]] => [[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1]
[[4,2,1],[]] => [[3,2,1,1],[]] => []
[[5,3,1],[1,1]] => [[3,2,2,1,1],[2]] => [2]
[[5,2,1],[1]] => [[3,2,1,1,1],[1]] => [1]
[[6,3,1],[2,1]] => [[3,2,2,1,1,1],[2,1]] => [2,1]
[[6,2,1],[2]] => [[3,2,1,1,1,1],[1,1]] => [1,1]
[[7,3,1],[3,1]] => [[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1]
[[5,2,2],[1,1]] => [[3,3,1,1,1],[2]] => [2]
[[6,3,2],[2,2]] => [[3,3,2,1,1,1],[2,2]] => [2,2]
[[6,2,2],[2,1]] => [[3,3,1,1,1,1],[2,1]] => [2,1]
[[7,3,2],[3,2]] => [[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1]
[[4,1,1,1],[]] => [[4,1,1,1],[]] => []
[[5,2,2,1],[1,1,1]] => [[4,3,1,1,1],[3]] => [3]
[[5,2,1,1],[1,1]] => [[4,2,1,1,1],[2]] => [2]
[[6,3,2,1],[2,2,1]] => [[4,3,2,1,1,1],[3,2]] => [3,2]
[[5,1,1,1],[1]] => [[4,1,1,1,1],[1]] => [1]
[[6,2,2,1],[2,1,1]] => [[4,3,1,1,1,1],[3,1]] => [3,1]
[[6,2,1,1],[2,1]] => [[4,2,1,1,1,1],[2,1]] => [2,1]
[[7,3,2,1],[3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1]
[[4,4],[1]] => [[2,2,2,2],[1]] => [1]
[[5,4],[2]] => [[2,2,2,2,1],[1,1]] => [1,1]
[[6,4],[3]] => [[2,2,2,2,1,1],[1,1,1]] => [1,1,1]
[[7,4],[4]] => [[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1]
[[3,3,1],[]] => [[3,2,2],[]] => []
[[4,4,1],[1,1]] => [[3,2,2,2],[2]] => [2]
[[4,3,1],[1]] => [[3,2,2,1],[1]] => [1]
[[5,4,1],[2,1]] => [[3,2,2,2,1],[2,1]] => [2,1]
[[5,3,1],[2]] => [[3,2,2,1,1],[1,1]] => [1,1]
[[6,4,1],[3,1]] => [[3,2,2,2,1,1],[2,1,1]] => [2,1,1]
[[6,3,1],[3]] => [[3,2,2,1,1,1],[1,1,1]] => [1,1,1]
[[7,4,1],[4,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1]
[[3,2,2],[]] => [[3,3,1],[]] => []
[[4,3,2],[1,1]] => [[3,3,2,1],[2]] => [2]
[[5,4,2],[2,2]] => [[3,3,2,2,1],[2,2]] => [2,2]
[[4,2,2],[1]] => [[3,3,1,1],[1]] => [1]
[[5,3,2],[2,1]] => [[3,3,2,1,1],[2,1]] => [2,1]
[[6,4,2],[3,2]] => [[3,3,2,2,1,1],[2,2,1]] => [2,2,1]
[[5,2,2],[2]] => [[3,3,1,1,1],[1,1]] => [1,1]
[[6,3,2],[3,1]] => [[3,3,2,1,1,1],[2,1,1]] => [2,1,1]
[[7,4,2],[4,2]] => [[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1]
[[3,2,1,1],[]] => [[4,2,1],[]] => []
[[4,3,2,1],[1,1,1]] => [[4,3,2,1],[3]] => [3]
[[4,3,1,1],[1,1]] => [[4,2,2,1],[2]] => [2]
[[5,4,2,1],[2,2,1]] => [[4,3,2,2,1],[3,2]] => [3,2]
[[4,2,1,1],[1]] => [[4,2,1,1],[1]] => [1]
[[5,3,2,1],[2,1,1]] => [[4,3,2,1,1],[3,1]] => [3,1]
[[5,3,1,1],[2,1]] => [[4,2,2,1,1],[2,1]] => [2,1]
[[6,4,2,1],[3,2,1]] => [[4,3,2,2,1,1],[3,2,1]] => [3,2,1]
[[5,2,1,1],[2]] => [[4,2,1,1,1],[1,1]] => [1,1]
[[6,3,2,1],[3,1,1]] => [[4,3,2,1,1,1],[3,1,1]] => [3,1,1]
[[6,3,1,1],[3,1]] => [[4,2,2,1,1,1],[2,1,1]] => [2,1,1]
[[7,4,2,1],[4,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1]
[[5,3,3],[2,2]] => [[3,3,3,1,1],[2,2]] => [2,2]
[[6,4,3],[3,3]] => [[3,3,3,2,1,1],[2,2,2]] => [2,2,2]
[[6,3,3],[3,2]] => [[3,3,3,1,1,1],[2,2,1]] => [2,2,1]
[[7,4,3],[4,3]] => [[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1]
[[4,2,2,1],[1,1]] => [[4,3,1,1],[2]] => [2]
[[5,3,3,1],[2,2,1]] => [[4,3,3,1,1],[3,2]] => [3,2]
[[5,3,2,1],[2,2]] => [[4,3,2,1,1],[2,2]] => [2,2]
[[6,4,3,1],[3,3,1]] => [[4,3,3,2,1,1],[3,2,2]] => [3,2,2]
[[5,2,2,1],[2,1]] => [[4,3,1,1,1],[2,1]] => [2,1]
[[6,3,3,1],[3,2,1]] => [[4,3,3,1,1,1],[3,2,1]] => [3,2,1]
[[6,3,2,1],[3,2]] => [[4,3,2,1,1,1],[2,2,1]] => [2,2,1]
[[7,4,3,1],[4,3,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1]
[[4,2,2,2],[1,1,1]] => [[4,4,1,1],[3]] => [3]
[[5,3,3,2],[2,2,2]] => [[4,4,3,1,1],[3,3]] => [3,3]
[[5,3,2,2],[2,2,1]] => [[4,4,2,1,1],[3,2]] => [3,2]
[[6,4,3,2],[3,3,2]] => [[4,4,3,2,1,1],[3,3,2]] => [3,3,2]
[[5,2,2,2],[2,1,1]] => [[4,4,1,1,1],[3,1]] => [3,1]
[[6,3,3,2],[3,2,2]] => [[4,4,3,1,1,1],[3,3,1]] => [3,3,1]
[[6,3,2,2],[3,2,1]] => [[4,4,2,1,1,1],[3,2,1]] => [3,2,1]
[[7,4,3,2],[4,3,2]] => [[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1]
[[3,1,1,1,1],[]] => [[5,1,1],[]] => []
[[4,2,2,2,1],[1,1,1,1]] => [[5,4,1,1],[4]] => [4]
[[4,2,2,1,1],[1,1,1]] => [[5,3,1,1],[3]] => [3]
[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,1,1],[4,3]] => [4,3]
[[4,2,1,1,1],[1,1]] => [[5,2,1,1],[2]] => [2]
[[5,3,2,2,1],[2,2,1,1]] => [[5,4,2,1,1],[4,2]] => [4,2]
[[5,3,2,1,1],[2,2,1]] => [[5,3,2,1,1],[3,2]] => [3,2]
[[6,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]] => [4,3,2]
[[4,1,1,1,1],[1]] => [[5,1,1,1],[1]] => [1]
[[5,2,2,2,1],[2,1,1,1]] => [[5,4,1,1,1],[4,1]] => [4,1]
[[5,2,2,1,1],[2,1,1]] => [[5,3,1,1,1],[3,1]] => [3,1]
[[6,3,3,2,1],[3,2,2,1]] => [[5,4,3,1,1,1],[4,3,1]] => [4,3,1]
[[5,2,1,1,1],[2,1]] => [[5,2,1,1,1],[2,1]] => [2,1]
[[6,3,2,2,1],[3,2,1,1]] => [[5,4,2,1,1,1],[4,2,1]] => [4,2,1]
[[6,3,2,1,1],[3,2,1]] => [[5,3,2,1,1,1],[3,2,1]] => [3,2,1]
[[7,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1,1,1],[4,3,2,1]] => [4,3,2,1]
[[5,5],[3]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1]
[[6,5],[4]] => [[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1]
[[7,5],[5]] => [[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1]
[[4,4,1],[2]] => [[3,2,2,2],[1,1]] => [1,1]
[[5,5,1],[3,1]] => [[3,2,2,2,2],[2,1,1]] => [2,1,1]
[[5,4,1],[3]] => [[3,2,2,2,1],[1,1,1]] => [1,1,1]
[[6,5,1],[4,1]] => [[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,4,1],[4]] => [[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1]
[[7,5,1],[5,1]] => [[3,2,2,2,2,1,1],[2,1,1,1,1]] => [2,1,1,1,1]
[[3,3,2],[1]] => [[3,3,2],[1]] => [1]
[[4,4,2],[2,1]] => [[3,3,2,2],[2,1]] => [2,1]
[[5,5,2],[3,2]] => [[3,3,2,2,2],[2,2,1]] => [2,2,1]
[[4,3,2],[2]] => [[3,3,2,1],[1,1]] => [1,1]
[[5,4,2],[3,1]] => [[3,3,2,2,1],[2,1,1]] => [2,1,1]
[[6,5,2],[4,2]] => [[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1]
[[5,3,2],[3]] => [[3,3,2,1,1],[1,1,1]] => [1,1,1]
[[6,4,2],[4,1]] => [[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1]
[[7,5,2],[5,2]] => [[3,3,2,2,2,1,1],[2,2,1,1,1]] => [2,2,1,1,1]
[[3,3,1,1],[1]] => [[4,2,2],[1]] => [1]
[[4,4,2,1],[2,1,1]] => [[4,3,2,2],[3,1]] => [3,1]
[[4,4,1,1],[2,1]] => [[4,2,2,2],[2,1]] => [2,1]
[[5,5,2,1],[3,2,1]] => [[4,3,2,2,2],[3,2,1]] => [3,2,1]
[[4,3,1,1],[2]] => [[4,2,2,1],[1,1]] => [1,1]
[[5,4,2,1],[3,1,1]] => [[4,3,2,2,1],[3,1,1]] => [3,1,1]
[[5,4,1,1],[3,1]] => [[4,2,2,2,1],[2,1,1]] => [2,1,1]
[[6,5,2,1],[4,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[5,3,1,1],[3]] => [[4,2,2,1,1],[1,1,1]] => [1,1,1]
[[6,4,2,1],[4,1,1]] => [[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1]
[[6,4,1,1],[4,1]] => [[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1]
[[7,5,2,1],[5,2,1]] => [[4,3,2,2,2,1,1],[3,2,1,1,1]] => [3,2,1,1,1]
[[3,3,3],[1,1]] => [[3,3,3],[2]] => [2]
[[4,4,3],[2,2]] => [[3,3,3,2],[2,2]] => [2,2]
[[5,5,3],[3,3]] => [[3,3,3,2,2],[2,2,2]] => [2,2,2]
[[4,3,3],[2,1]] => [[3,3,3,1],[2,1]] => [2,1]
[[5,4,3],[3,2]] => [[3,3,3,2,1],[2,2,1]] => [2,2,1]
[[6,5,3],[4,3]] => [[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1]
[[5,3,3],[3,1]] => [[3,3,3,1,1],[2,1,1]] => [2,1,1]
[[6,4,3],[4,2]] => [[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1]
[[7,5,3],[5,3]] => [[3,3,3,2,2,1,1],[2,2,2,1,1]] => [2,2,2,1,1]
[[2,2,2,1],[]] => [[4,3],[]] => []
[[3,3,3,1],[1,1,1]] => [[4,3,3],[3]] => [3]
[[3,3,2,1],[1,1]] => [[4,3,2],[2]] => [2]
[[4,4,3,1],[2,2,1]] => [[4,3,3,2],[3,2]] => [3,2]
[[4,4,2,1],[2,2]] => [[4,3,2,2],[2,2]] => [2,2]
[[5,5,3,1],[3,3,1]] => [[4,3,3,2,2],[3,2,2]] => [3,2,2]
[[3,2,2,1],[1]] => [[4,3,1],[1]] => [1]
[[4,3,3,1],[2,1,1]] => [[4,3,3,1],[3,1]] => [3,1]
[[4,3,2,1],[2,1]] => [[4,3,2,1],[2,1]] => [2,1]
[[5,4,3,1],[3,2,1]] => [[4,3,3,2,1],[3,2,1]] => [3,2,1]
[[5,4,2,1],[3,2]] => [[4,3,2,2,1],[2,2,1]] => [2,2,1]
[[6,5,3,1],[4,3,1]] => [[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1]
[[4,2,2,1],[2]] => [[4,3,1,1],[1,1]] => [1,1]
[[5,3,3,1],[3,1,1]] => [[4,3,3,1,1],[3,1,1]] => [3,1,1]
[[5,3,2,1],[3,1]] => [[4,3,2,1,1],[2,1,1]] => [2,1,1]
[[6,4,3,1],[4,2,1]] => [[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1]
[[6,4,2,1],[4,2]] => [[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1]
[[7,5,3,1],[5,3,1]] => [[4,3,3,2,2,1,1],[3,2,2,1,1]] => [3,2,2,1,1]
[[3,3,2,2],[1,1,1]] => [[4,4,2],[3]] => [3]
[[4,4,3,2],[2,2,2]] => [[4,4,3,2],[3,3]] => [3,3]
[[4,4,2,2],[2,2,1]] => [[4,4,2,2],[3,2]] => [3,2]
[[5,5,3,2],[3,3,2]] => [[4,4,3,2,2],[3,3,2]] => [3,3,2]
[[4,3,2,2],[2,1,1]] => [[4,4,2,1],[3,1]] => [3,1]
[[5,4,3,2],[3,2,2]] => [[4,4,3,2,1],[3,3,1]] => [3,3,1]
[[5,4,2,2],[3,2,1]] => [[4,4,2,2,1],[3,2,1]] => [3,2,1]
[[6,5,3,2],[4,3,2]] => [[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1]
[[5,3,2,2],[3,1,1]] => [[4,4,2,1,1],[3,1,1]] => [3,1,1]
[[6,4,3,2],[4,2,2]] => [[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1]
[[6,4,2,2],[4,2,1]] => [[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1]
[[7,5,3,2],[5,3,2]] => [[4,4,3,2,2,1,1],[3,3,2,1,1]] => [3,3,2,1,1]
[[2,2,1,1,1],[]] => [[5,2],[]] => []
[[3,3,2,2,1],[1,1,1,1]] => [[5,4,2],[4]] => [4]
[[3,3,2,1,1],[1,1,1]] => [[5,3,2],[3]] => [3]
[[4,4,3,2,1],[2,2,2,1]] => [[5,4,3,2],[4,3]] => [4,3]
[[3,3,1,1,1],[1,1]] => [[5,2,2],[2]] => [2]
[[4,4,2,2,1],[2,2,1,1]] => [[5,4,2,2],[4,2]] => [4,2]
[[4,4,2,1,1],[2,2,1]] => [[5,3,2,2],[3,2]] => [3,2]
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]] => [4,3,2]
[[3,2,1,1,1],[1]] => [[5,2,1],[1]] => [1]
[[4,3,2,2,1],[2,1,1,1]] => [[5,4,2,1],[4,1]] => [4,1]
[[4,3,2,1,1],[2,1,1]] => [[5,3,2,1],[3,1]] => [3,1]
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,2,1],[4,3,1]] => [4,3,1]
[[4,3,1,1,1],[2,1]] => [[5,2,2,1],[2,1]] => [2,1]
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,2,2,1],[4,2,1]] => [4,2,1]
[[5,4,2,1,1],[3,2,1]] => [[5,3,2,2,1],[3,2,1]] => [3,2,1]
[[6,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1]
[[4,2,1,1,1],[2]] => [[5,2,1,1],[1,1]] => [1,1]
[[5,3,2,2,1],[3,1,1,1]] => [[5,4,2,1,1],[4,1,1]] => [4,1,1]
[[5,3,2,1,1],[3,1,1]] => [[5,3,2,1,1],[3,1,1]] => [3,1,1]
[[6,4,3,2,1],[4,2,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1]
[[5,3,1,1,1],[3,1]] => [[5,2,2,1,1],[2,1,1]] => [2,1,1]
[[6,4,2,2,1],[4,2,1,1]] => [[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1]
[[6,4,2,1,1],[4,2,1]] => [[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1]
[[7,5,3,2,1],[5,3,2,1]] => [[5,4,3,2,2,1,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[5,4,4],[3,3]] => [[3,3,3,3,1],[2,2,2]] => [2,2,2]
[[6,5,4],[4,4]] => [[3,3,3,3,2,1],[2,2,2,2]] => [2,2,2,2]
[[6,4,4],[4,3]] => [[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1]
[[7,5,4],[5,4]] => [[3,3,3,3,2,1,1],[2,2,2,2,1]] => [2,2,2,2,1]
[[4,3,3,1],[2,2]] => [[4,3,3,1],[2,2]] => [2,2]
[[5,4,4,1],[3,3,1]] => [[4,3,3,3,1],[3,2,2]] => [3,2,2]
[[5,4,3,1],[3,3]] => [[4,3,3,2,1],[2,2,2]] => [2,2,2]
[[6,5,4,1],[4,4,1]] => [[4,3,3,3,2,1],[3,2,2,2]] => [3,2,2,2]
[[5,3,3,1],[3,2]] => [[4,3,3,1,1],[2,2,1]] => [2,2,1]
[[6,4,4,1],[4,3,1]] => [[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1]
[[6,4,3,1],[4,3]] => [[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1]
[[7,5,4,1],[5,4,1]] => [[4,3,3,3,2,1,1],[3,2,2,2,1]] => [3,2,2,2,1]
[[3,2,2,2],[1,1]] => [[4,4,1],[2]] => [2]
[[4,3,3,2],[2,2,1]] => [[4,4,3,1],[3,2]] => [3,2]
[[5,4,4,2],[3,3,2]] => [[4,4,3,3,1],[3,3,2]] => [3,3,2]
[[4,3,2,2],[2,2]] => [[4,4,2,1],[2,2]] => [2,2]
[[5,4,3,2],[3,3,1]] => [[4,4,3,2,1],[3,2,2]] => [3,2,2]
[[6,5,4,2],[4,4,2]] => [[4,4,3,3,2,1],[3,3,2,2]] => [3,3,2,2]
[[4,2,2,2],[2,1]] => [[4,4,1,1],[2,1]] => [2,1]
[[5,3,3,2],[3,2,1]] => [[4,4,3,1,1],[3,2,1]] => [3,2,1]
[[6,4,4,2],[4,3,2]] => [[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1]
[[5,3,2,2],[3,2]] => [[4,4,2,1,1],[2,2,1]] => [2,2,1]
[[6,4,3,2],[4,3,1]] => [[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1]
[[7,5,4,2],[5,4,2]] => [[4,4,3,3,2,1,1],[3,3,2,2,1]] => [3,3,2,2,1]
[[3,2,2,1,1],[1,1]] => [[5,3,1],[2]] => [2]
[[4,3,3,2,1],[2,2,1,1]] => [[5,4,3,1],[4,2]] => [4,2]
[[4,3,3,1,1],[2,2,1]] => [[5,3,3,1],[3,2]] => [3,2]
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,3,1],[4,3,2]] => [4,3,2]
[[4,3,2,1,1],[2,2]] => [[5,3,2,1],[2,2]] => [2,2]
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,3,2,1],[4,2,2]] => [4,2,2]
[[5,4,3,1,1],[3,3,1]] => [[5,3,3,2,1],[3,2,2]] => [3,2,2]
[[6,5,4,2,1],[4,4,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]] => [4,3,2,2]
[[4,2,2,1,1],[2,1]] => [[5,3,1,1],[2,1]] => [2,1]
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,3,1,1],[4,2,1]] => [4,2,1]
[[5,3,3,1,1],[3,2,1]] => [[5,3,3,1,1],[3,2,1]] => [3,2,1]
[[6,4,4,2,1],[4,3,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1]
[[5,3,2,1,1],[3,2]] => [[5,3,2,1,1],[2,2,1]] => [2,2,1]
[[6,4,3,2,1],[4,3,1,1]] => [[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1]
[[6,4,3,1,1],[4,3,1]] => [[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1]
[[7,5,4,2,1],[5,4,2,1]] => [[5,4,3,3,2,1,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[4,3,3,3],[2,2,2]] => [[4,4,4,1],[3,3]] => [3,3]
[[5,4,4,3],[3,3,3]] => [[4,4,4,3,1],[3,3,3]] => [3,3,3]
[[5,4,3,3],[3,3,2]] => [[4,4,4,2,1],[3,3,2]] => [3,3,2]
[[6,5,4,3],[4,4,3]] => [[4,4,4,3,2,1],[3,3,3,2]] => [3,3,3,2]
[[5,3,3,3],[3,2,2]] => [[4,4,4,1,1],[3,3,1]] => [3,3,1]
[[6,4,4,3],[4,3,3]] => [[4,4,4,3,1,1],[3,3,3,1]] => [3,3,3,1]
[[6,4,3,3],[4,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1]
[[7,5,4,3],[5,4,3]] => [[4,4,4,3,2,1,1],[3,3,3,2,1]] => [3,3,3,2,1]
[[3,2,2,2,1],[1,1,1]] => [[5,4,1],[3]] => [3]
[[4,3,3,3,1],[2,2,2,1]] => [[5,4,4,1],[4,3]] => [4,3]
[[4,3,3,2,1],[2,2,2]] => [[5,4,3,1],[3,3]] => [3,3]
[[5,4,4,3,1],[3,3,3,1]] => [[5,4,4,3,1],[4,3,3]] => [4,3,3]
[[4,3,2,2,1],[2,2,1]] => [[5,4,2,1],[3,2]] => [3,2]
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,4,2,1],[4,3,2]] => [4,3,2]
[[5,4,3,2,1],[3,3,2]] => [[5,4,3,2,1],[3,3,2]] => [3,3,2]
[[6,5,4,3,1],[4,4,3,1]] => [[5,4,4,3,2,1],[4,3,3,2]] => [4,3,3,2]
[[4,2,2,2,1],[2,1,1]] => [[5,4,1,1],[3,1]] => [3,1]
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,4,1,1],[4,3,1]] => [4,3,1]
[[5,3,3,2,1],[3,2,2]] => [[5,4,3,1,1],[3,3,1]] => [3,3,1]
[[6,4,4,3,1],[4,3,3,1]] => [[5,4,4,3,1,1],[4,3,3,1]] => [4,3,3,1]
[[5,3,2,2,1],[3,2,1]] => [[5,4,2,1,1],[3,2,1]] => [3,2,1]
[[6,4,3,3,1],[4,3,2,1]] => [[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1]
[[6,4,3,2,1],[4,3,2]] => [[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1]
[[7,5,4,3,1],[5,4,3,1]] => [[5,4,4,3,2,1,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[3,2,2,2,2],[1,1,1,1]] => [[5,5,1],[4]] => [4]
[[4,3,3,3,2],[2,2,2,2]] => [[5,5,4,1],[4,4]] => [4,4]
[[4,3,3,2,2],[2,2,2,1]] => [[5,5,3,1],[4,3]] => [4,3]
[[5,4,4,3,2],[3,3,3,2]] => [[5,5,4,3,1],[4,4,3]] => [4,4,3]
[[4,3,2,2,2],[2,2,1,1]] => [[5,5,2,1],[4,2]] => [4,2]
[[5,4,3,3,2],[3,3,2,2]] => [[5,5,4,2,1],[4,4,2]] => [4,4,2]
[[5,4,3,2,2],[3,3,2,1]] => [[5,5,3,2,1],[4,3,2]] => [4,3,2]
[[6,5,4,3,2],[4,4,3,2]] => [[5,5,4,3,2,1],[4,4,3,2]] => [4,4,3,2]
[[4,2,2,2,2],[2,1,1,1]] => [[5,5,1,1],[4,1]] => [4,1]
[[5,3,3,3,2],[3,2,2,2]] => [[5,5,4,1,1],[4,4,1]] => [4,4,1]
[[5,3,3,2,2],[3,2,2,1]] => [[5,5,3,1,1],[4,3,1]] => [4,3,1]
[[6,4,4,3,2],[4,3,3,2]] => [[5,5,4,3,1,1],[4,4,3,1]] => [4,4,3,1]
[[5,3,2,2,2],[3,2,1,1]] => [[5,5,2,1,1],[4,2,1]] => [4,2,1]
[[6,4,3,3,2],[4,3,2,2]] => [[5,5,4,2,1,1],[4,4,2,1]] => [4,4,2,1]
[[6,4,3,2,2],[4,3,2,1]] => [[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1]
[[7,5,4,3,2],[5,4,3,2]] => [[5,5,4,3,2,1,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[2,1,1,1,1,1],[]] => [[6,1],[]] => []
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[6,5,1],[5]] => [5]
[[3,2,2,2,1,1],[1,1,1,1]] => [[6,4,1],[4]] => [4]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [[6,5,4,1],[5,4]] => [5,4]
[[3,2,2,1,1,1],[1,1,1]] => [[6,3,1],[3]] => [3]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [[6,5,3,1],[5,3]] => [5,3]
[[4,3,3,2,1,1],[2,2,2,1]] => [[6,4,3,1],[4,3]] => [4,3]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [[6,5,4,3,1],[5,4,3]] => [5,4,3]
[[3,2,1,1,1,1],[1,1]] => [[6,2,1],[2]] => [2]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [[6,5,2,1],[5,2]] => [5,2]
[[4,3,2,2,1,1],[2,2,1,1]] => [[6,4,2,1],[4,2]] => [4,2]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [[6,5,4,2,1],[5,4,2]] => [5,4,2]
[[4,3,2,1,1,1],[2,2,1]] => [[6,3,2,1],[3,2]] => [3,2]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [[6,5,3,2,1],[5,3,2]] => [5,3,2]
[[5,4,3,2,1,1],[3,3,2,1]] => [[6,4,3,2,1],[4,3,2]] => [4,3,2]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]] => [5,4,3,2]
[[3,1,1,1,1,1],[1]] => [[6,1,1],[1]] => [1]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [[6,5,1,1],[5,1]] => [5,1]
[[4,2,2,2,1,1],[2,1,1,1]] => [[6,4,1,1],[4,1]] => [4,1]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [[6,5,4,1,1],[5,4,1]] => [5,4,1]
[[4,2,2,1,1,1],[2,1,1]] => [[6,3,1,1],[3,1]] => [3,1]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [[6,5,3,1,1],[5,3,1]] => [5,3,1]
[[5,3,3,2,1,1],[3,2,2,1]] => [[6,4,3,1,1],[4,3,1]] => [4,3,1]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]] => [5,4,3,1]
[[4,2,1,1,1,1],[2,1]] => [[6,2,1,1],[2,1]] => [2,1]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [[6,5,2,1,1],[5,2,1]] => [5,2,1]
[[5,3,2,2,1,1],[3,2,1,1]] => [[6,4,2,1,1],[4,2,1]] => [4,2,1]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]] => [5,4,2,1]
[[5,3,2,1,1,1],[3,2,1]] => [[6,3,2,1,1],[3,2,1]] => [3,2,1]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,3,2,1,1],[5,3,2,1]] => [5,3,2,1]
[[6,4,3,2,1,1],[4,3,2,1]] => [[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[6,6],[5]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[7,6],[6]] => [[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[5,5,1],[4]] => [[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[6,6,1],[5,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1]
[[6,5,1],[5]] => [[3,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1]
[[7,6,1],[6,1]] => [[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [2,1,1,1,1,1]
[[4,4,2],[3]] => [[3,3,2,2],[1,1,1]] => [1,1,1]
[[5,5,2],[4,1]] => [[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1]
[[6,6,2],[5,2]] => [[3,3,2,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1]
[[5,4,2],[4]] => [[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1]
[[6,5,2],[5,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1]
[[7,6,2],[6,2]] => [[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [2,2,1,1,1,1]
[[4,4,1,1],[3]] => [[4,2,2,2],[1,1,1]] => [1,1,1]
[[5,5,2,1],[4,1,1]] => [[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1]
[[5,5,1,1],[4,1]] => [[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1]
[[6,6,2,1],[5,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]] => [3,2,1,1,1]
[[5,4,1,1],[4]] => [[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1]
[[6,5,2,1],[5,1,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]] => [3,1,1,1,1]
[[6,5,1,1],[5,1]] => [[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1]
[[7,6,2,1],[6,2,1]] => [[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [3,2,1,1,1,1]
[[3,3,3],[2]] => [[3,3,3],[1,1]] => [1,1]
[[4,4,3],[3,1]] => [[3,3,3,2],[2,1,1]] => [2,1,1]
[[5,5,3],[4,2]] => [[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1]
[[6,6,3],[5,3]] => [[3,3,3,2,2,2],[2,2,2,1,1]] => [2,2,2,1,1]
[[4,3,3],[3]] => [[3,3,3,1],[1,1,1]] => [1,1,1]
[[5,4,3],[4,1]] => [[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,5,3],[5,2]] => [[3,3,3,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1]
[[7,6,3],[6,3]] => [[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [2,2,2,1,1,1]
[[3,3,2,1],[2]] => [[4,3,2],[1,1]] => [1,1]
[[4,4,3,1],[3,1,1]] => [[4,3,3,2],[3,1,1]] => [3,1,1]
[[4,4,2,1],[3,1]] => [[4,3,2,2],[2,1,1]] => [2,1,1]
[[5,5,3,1],[4,2,1]] => [[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1]
[[5,5,2,1],[4,2]] => [[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1]
[[6,6,3,1],[5,3,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]] => [3,2,2,1,1]
[[4,3,2,1],[3]] => [[4,3,2,1],[1,1,1]] => [1,1,1]
[[5,4,3,1],[4,1,1]] => [[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1]
[[5,4,2,1],[4,1]] => [[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,5,3,1],[5,2,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1]
[[6,5,2,1],[5,2]] => [[4,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1]
[[7,6,3,1],[6,3,1]] => [[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [3,2,2,1,1,1]
[[4,4,2,2],[3,1,1]] => [[4,4,2,2],[3,1,1]] => [3,1,1]
[[5,5,3,2],[4,2,2]] => [[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1]
[[5,5,2,2],[4,2,1]] => [[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1]
[[6,6,3,2],[5,3,2]] => [[4,4,3,2,2,2],[3,3,2,1,1]] => [3,3,2,1,1]
[[5,4,2,2],[4,1,1]] => [[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1]
[[6,5,3,2],[5,2,2]] => [[4,4,3,2,2,1],[3,3,1,1,1]] => [3,3,1,1,1]
[[6,5,2,2],[5,2,1]] => [[4,4,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1]
[[7,6,3,2],[6,3,2]] => [[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [3,3,2,1,1,1]
[[3,3,1,1,1],[2]] => [[5,2,2],[1,1]] => [1,1]
[[4,4,2,2,1],[3,1,1,1]] => [[5,4,2,2],[4,1,1]] => [4,1,1]
[[4,4,2,1,1],[3,1,1]] => [[5,3,2,2],[3,1,1]] => [3,1,1]
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1]
[[4,4,1,1,1],[3,1]] => [[5,2,2,2],[2,1,1]] => [2,1,1]
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1]
[[5,5,2,1,1],[4,2,1]] => [[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1]
[[6,6,3,2,1],[5,3,2,1]] => [[5,4,3,2,2,2],[4,3,2,1,1]] => [4,3,2,1,1]
[[4,3,1,1,1],[3]] => [[5,2,2,1],[1,1,1]] => [1,1,1]
[[5,4,2,2,1],[4,1,1,1]] => [[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1]
[[5,4,2,1,1],[4,1,1]] => [[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1]
[[6,5,3,2,1],[5,2,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]] => [4,3,1,1,1]
[[5,4,1,1,1],[4,1]] => [[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1]
[[6,5,2,2,1],[5,2,1,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]] => [4,2,1,1,1]
[[6,5,2,1,1],[5,2,1]] => [[5,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1]
[[7,6,3,2,1],[6,3,2,1]] => [[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [4,3,2,1,1,1]
[[4,4,4],[3,2]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[5,5,4],[4,3]] => [[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1]
[[6,6,4],[5,4]] => [[3,3,3,3,2,2],[2,2,2,2,1]] => [2,2,2,2,1]
[[5,4,4],[4,2]] => [[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,4],[5,3]] => [[3,3,3,3,2,1],[2,2,2,1,1]] => [2,2,2,1,1]
[[7,6,4],[6,4]] => [[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [2,2,2,2,1,1]
[[3,3,3,1],[2,1]] => [[4,3,3],[2,1]] => [2,1]
[[4,4,4,1],[3,2,1]] => [[4,3,3,3],[3,2,1]] => [3,2,1]
[[4,4,3,1],[3,2]] => [[4,3,3,2],[2,2,1]] => [2,2,1]
[[5,5,4,1],[4,3,1]] => [[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1]
[[5,5,3,1],[4,3]] => [[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1]
[[6,6,4,1],[5,4,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]] => [3,2,2,2,1]
[[4,3,3,1],[3,1]] => [[4,3,3,1],[2,1,1]] => [2,1,1]
[[5,4,4,1],[4,2,1]] => [[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1]
[[5,4,3,1],[4,2]] => [[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,4,1],[5,3,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]] => [3,2,2,1,1]
[[6,5,3,1],[5,3]] => [[4,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1]
[[7,6,4,1],[6,4,1]] => [[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [3,2,2,2,1,1]
[[2,2,2,2],[1]] => [[4,4],[1]] => [1]
[[3,3,3,2],[2,1,1]] => [[4,4,3],[3,1]] => [3,1]
[[4,4,4,2],[3,2,2]] => [[4,4,3,3],[3,3,1]] => [3,3,1]
[[3,3,2,2],[2,1]] => [[4,4,2],[2,1]] => [2,1]
[[4,4,3,2],[3,2,1]] => [[4,4,3,2],[3,2,1]] => [3,2,1]
[[5,5,4,2],[4,3,2]] => [[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1]
[[4,4,2,2],[3,2]] => [[4,4,2,2],[2,2,1]] => [2,2,1]
[[5,5,3,2],[4,3,1]] => [[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1]
[[6,6,4,2],[5,4,2]] => [[4,4,3,3,2,2],[3,3,2,2,1]] => [3,3,2,2,1]
[[3,2,2,2],[2]] => [[4,4,1],[1,1]] => [1,1]
[[4,3,3,2],[3,1,1]] => [[4,4,3,1],[3,1,1]] => [3,1,1]
[[5,4,4,2],[4,2,2]] => [[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1]
[[4,3,2,2],[3,1]] => [[4,4,2,1],[2,1,1]] => [2,1,1]
[[5,4,3,2],[4,2,1]] => [[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,4,2],[5,3,2]] => [[4,4,3,3,2,1],[3,3,2,1,1]] => [3,3,2,1,1]
[[5,4,2,2],[4,2]] => [[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,3,2],[5,3,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1]
[[7,6,4,2],[6,4,2]] => [[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [3,3,2,2,1,1]
[[2,2,2,1,1],[1]] => [[5,3],[1]] => [1]
[[3,3,3,2,1],[2,1,1,1]] => [[5,4,3],[4,1]] => [4,1]
[[3,3,3,1,1],[2,1,1]] => [[5,3,3],[3,1]] => [3,1]
[[4,4,4,2,1],[3,2,2,1]] => [[5,4,3,3],[4,3,1]] => [4,3,1]
[[3,3,2,1,1],[2,1]] => [[5,3,2],[2,1]] => [2,1]
[[4,4,3,2,1],[3,2,1,1]] => [[5,4,3,2],[4,2,1]] => [4,2,1]
[[4,4,3,1,1],[3,2,1]] => [[5,3,3,2],[3,2,1]] => [3,2,1]
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1]
[[4,4,2,1,1],[3,2]] => [[5,3,2,2],[2,2,1]] => [2,2,1]
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1]
[[5,5,3,1,1],[4,3,1]] => [[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1]
[[6,6,4,2,1],[5,4,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]] => [4,3,2,2,1]
[[3,2,2,1,1],[2]] => [[5,3,1],[1,1]] => [1,1]
[[4,3,3,2,1],[3,1,1,1]] => [[5,4,3,1],[4,1,1]] => [4,1,1]
[[4,3,3,1,1],[3,1,1]] => [[5,3,3,1],[3,1,1]] => [3,1,1]
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1]
[[4,3,2,1,1],[3,1]] => [[5,3,2,1],[2,1,1]] => [2,1,1]
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1]
[[5,4,3,1,1],[4,2,1]] => [[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,4,2,1],[5,3,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[5,4,2,1,1],[4,2]] => [[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1]
[[6,5,3,2,1],[5,3,1,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]] => [4,2,2,1,1]
[[6,5,3,1,1],[5,3,1]] => [[5,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1]
[[7,6,4,2,1],[6,4,2,1]] => [[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [4,3,2,2,1,1]
[[4,4,3,3],[3,2,2]] => [[4,4,4,2],[3,3,1]] => [3,3,1]
[[5,5,4,3],[4,3,3]] => [[4,4,4,3,2],[3,3,3,1]] => [3,3,3,1]
[[5,5,3,3],[4,3,2]] => [[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1]
[[6,6,4,3],[5,4,3]] => [[4,4,4,3,2,2],[3,3,3,2,1]] => [3,3,3,2,1]
[[5,4,3,3],[4,2,2]] => [[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1]
[[6,5,4,3],[5,3,3]] => [[4,4,4,3,2,1],[3,3,3,1,1]] => [3,3,3,1,1]
[[6,5,3,3],[5,3,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1]
[[7,6,4,3],[6,4,3]] => [[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [3,3,3,2,1,1]
[[3,3,2,2,1],[2,1,1]] => [[5,4,2],[3,1]] => [3,1]
[[4,4,3,3,1],[3,2,2,1]] => [[5,4,4,2],[4,3,1]] => [4,3,1]
[[4,4,3,2,1],[3,2,2]] => [[5,4,3,2],[3,3,1]] => [3,3,1]
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,4,3,2],[4,3,3,1]] => [4,3,3,1]
[[4,4,2,2,1],[3,2,1]] => [[5,4,2,2],[3,2,1]] => [3,2,1]
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1]
[[5,5,3,2,1],[4,3,2]] => [[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1]
[[6,6,4,3,1],[5,4,3,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]] => [4,3,3,2,1]
[[4,3,2,2,1],[3,1,1]] => [[5,4,2,1],[3,1,1]] => [3,1,1]
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1]
[[5,4,3,2,1],[4,2,2]] => [[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1]
[[6,5,4,3,1],[5,3,3,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]] => [4,3,3,1,1]
[[5,4,2,2,1],[4,2,1]] => [[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,3,3,1],[5,3,2,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[6,5,3,2,1],[5,3,2]] => [[5,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1]
[[7,6,4,3,1],[6,4,3,1]] => [[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [4,3,3,2,1,1]
[[3,3,2,2,2],[2,1,1,1]] => [[5,5,2],[4,1]] => [4,1]
[[4,4,3,3,2],[3,2,2,2]] => [[5,5,4,2],[4,4,1]] => [4,4,1]
[[4,4,3,2,2],[3,2,2,1]] => [[5,5,3,2],[4,3,1]] => [4,3,1]
[[5,5,4,3,2],[4,3,3,2]] => [[5,5,4,3,2],[4,4,3,1]] => [4,4,3,1]
[[4,4,2,2,2],[3,2,1,1]] => [[5,5,2,2],[4,2,1]] => [4,2,1]
[[5,5,3,3,2],[4,3,2,2]] => [[5,5,4,2,2],[4,4,2,1]] => [4,4,2,1]
[[5,5,3,2,2],[4,3,2,1]] => [[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1]
[[6,6,4,3,2],[5,4,3,2]] => [[5,5,4,3,2,2],[4,4,3,2,1]] => [4,4,3,2,1]
[[4,3,2,2,2],[3,1,1,1]] => [[5,5,2,1],[4,1,1]] => [4,1,1]
[[5,4,3,3,2],[4,2,2,2]] => [[5,5,4,2,1],[4,4,1,1]] => [4,4,1,1]
[[5,4,3,2,2],[4,2,2,1]] => [[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1]
[[6,5,4,3,2],[5,3,3,2]] => [[5,5,4,3,2,1],[4,4,3,1,1]] => [4,4,3,1,1]
[[5,4,2,2,2],[4,2,1,1]] => [[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1]
[[6,5,3,3,2],[5,3,2,2]] => [[5,5,4,2,2,1],[4,4,2,1,1]] => [4,4,2,1,1]
[[6,5,3,2,2],[5,3,2,1]] => [[5,5,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[7,6,4,3,2],[6,4,3,2]] => [[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [4,4,3,2,1,1]
[[2,2,1,1,1,1],[1]] => [[6,2],[1]] => [1]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[6,5,2],[5,1]] => [5,1]
[[3,3,2,2,1,1],[2,1,1,1]] => [[6,4,2],[4,1]] => [4,1]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[6,5,4,2],[5,4,1]] => [5,4,1]
[[3,3,2,1,1,1],[2,1,1]] => [[6,3,2],[3,1]] => [3,1]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[6,5,3,2],[5,3,1]] => [5,3,1]
[[4,4,3,2,1,1],[3,2,2,1]] => [[6,4,3,2],[4,3,1]] => [4,3,1]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]] => [5,4,3,1]
[[3,3,1,1,1,1],[2,1]] => [[6,2,2],[2,1]] => [2,1]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[6,5,2,2],[5,2,1]] => [5,2,1]
[[4,4,2,2,1,1],[3,2,1,1]] => [[6,4,2,2],[4,2,1]] => [4,2,1]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,2,2],[5,4,2,1]] => [5,4,2,1]
[[4,4,2,1,1,1],[3,2,1]] => [[6,3,2,2],[3,2,1]] => [3,2,1]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [[6,5,3,2,2],[5,3,2,1]] => [5,3,2,1]
[[5,5,3,2,1,1],[4,3,2,1]] => [[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]] => [5,4,3,2,1]
[[3,2,1,1,1,1],[2]] => [[6,2,1],[1,1]] => [1,1]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [[6,5,2,1],[5,1,1]] => [5,1,1]
[[4,3,2,2,1,1],[3,1,1,1]] => [[6,4,2,1],[4,1,1]] => [4,1,1]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [[6,5,4,2,1],[5,4,1,1]] => [5,4,1,1]
[[4,3,2,1,1,1],[3,1,1]] => [[6,3,2,1],[3,1,1]] => [3,1,1]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [[6,5,3,2,1],[5,3,1,1]] => [5,3,1,1]
[[5,4,3,2,1,1],[4,2,2,1]] => [[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]] => [5,4,3,1,1]
[[4,3,1,1,1,1],[3,1]] => [[6,2,2,1],[2,1,1]] => [2,1,1]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [[6,5,2,2,1],[5,2,1,1]] => [5,2,1,1]
[[5,4,2,2,1,1],[4,2,1,1]] => [[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]] => [5,4,2,1,1]
[[5,4,2,1,1,1],[4,2,1]] => [[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]] => [5,3,2,1,1]
[[6,5,3,2,1,1],[5,3,2,1]] => [[6,4,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [5,4,3,2,1,1]
[[5,5,5],[4,4]] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[6,6,5],[5,5]] => [[3,3,3,3,3,2],[2,2,2,2,2]] => [2,2,2,2,2]
[[6,5,5],[5,4]] => [[3,3,3,3,3,1],[2,2,2,2,1]] => [2,2,2,2,1]
[[7,6,5],[6,5]] => [[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [2,2,2,2,2,1]
[[4,4,4,1],[3,3]] => [[4,3,3,3],[2,2,2]] => [2,2,2]
[[5,5,5,1],[4,4,1]] => [[4,3,3,3,3],[3,2,2,2]] => [3,2,2,2]
[[5,5,4,1],[4,4]] => [[4,3,3,3,2],[2,2,2,2]] => [2,2,2,2]
[[6,6,5,1],[5,5,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]] => [3,2,2,2,2]
[[5,4,4,1],[4,3]] => [[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1]
[[6,5,5,1],[5,4,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]] => [3,2,2,2,1]
[[6,5,4,1],[5,4]] => [[4,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1]
[[7,6,5,1],[6,5,1]] => [[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [3,2,2,2,2,1]
[[3,3,3,2],[2,2]] => [[4,4,3],[2,2]] => [2,2]
[[4,4,4,2],[3,3,1]] => [[4,4,3,3],[3,2,2]] => [3,2,2]
[[5,5,5,2],[4,4,2]] => [[4,4,3,3,3],[3,3,2,2]] => [3,3,2,2]
[[4,4,3,2],[3,3]] => [[4,4,3,2],[2,2,2]] => [2,2,2]
[[5,5,4,2],[4,4,1]] => [[4,4,3,3,2],[3,2,2,2]] => [3,2,2,2]
[[6,6,5,2],[5,5,2]] => [[4,4,3,3,3,2],[3,3,2,2,2]] => [3,3,2,2,2]
[[4,3,3,2],[3,2]] => [[4,4,3,1],[2,2,1]] => [2,2,1]
[[5,4,4,2],[4,3,1]] => [[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,5,2],[5,4,2]] => [[4,4,3,3,3,1],[3,3,2,2,1]] => [3,3,2,2,1]
[[5,4,3,2],[4,3]] => [[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1]
[[6,5,4,2],[5,4,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1]
[[7,6,5,2],[6,5,2]] => [[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [3,3,2,2,2,1]
[[3,3,3,1,1],[2,2]] => [[5,3,3],[2,2]] => [2,2]
[[4,4,4,2,1],[3,3,1,1]] => [[5,4,3,3],[4,2,2]] => [4,2,2]
[[4,4,4,1,1],[3,3,1]] => [[5,3,3,3],[3,2,2]] => [3,2,2]
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,3,3],[4,3,2,2]] => [4,3,2,2]
[[4,4,3,1,1],[3,3]] => [[5,3,3,2],[2,2,2]] => [2,2,2]
[[5,5,4,2,1],[4,4,1,1]] => [[5,4,3,3,2],[4,2,2,2]] => [4,2,2,2]
[[5,5,4,1,1],[4,4,1]] => [[5,3,3,3,2],[3,2,2,2]] => [3,2,2,2]
[[6,6,5,2,1],[5,5,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]] => [4,3,2,2,2]
[[4,3,3,1,1],[3,2]] => [[5,3,3,1],[2,2,1]] => [2,2,1]
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1]
[[5,4,4,1,1],[4,3,1]] => [[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,5,2,1],[5,4,2,1]] => [[5,4,3,3,3,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[5,4,3,1,1],[4,3]] => [[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1]
[[6,5,4,2,1],[5,4,1,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]] => [4,2,2,2,1]
[[6,5,4,1,1],[5,4,1]] => [[5,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1]
[[7,6,5,2,1],[6,5,2,1]] => [[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [4,3,2,2,2,1]
[[3,3,3,3],[2,2,1]] => [[4,4,4],[3,2]] => [3,2]
[[4,4,4,3],[3,3,2]] => [[4,4,4,3],[3,3,2]] => [3,3,2]
[[5,5,5,3],[4,4,3]] => [[4,4,4,3,3],[3,3,3,2]] => [3,3,3,2]
[[4,4,3,3],[3,3,1]] => [[4,4,4,2],[3,2,2]] => [3,2,2]
[[5,5,4,3],[4,4,2]] => [[4,4,4,3,2],[3,3,2,2]] => [3,3,2,2]
[[6,6,5,3],[5,5,3]] => [[4,4,4,3,3,2],[3,3,3,2,2]] => [3,3,3,2,2]
[[4,3,3,3],[3,2,1]] => [[4,4,4,1],[3,2,1]] => [3,2,1]
[[5,4,4,3],[4,3,2]] => [[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,5,3],[5,4,3]] => [[4,4,4,3,3,1],[3,3,3,2,1]] => [3,3,3,2,1]
[[5,4,3,3],[4,3,1]] => [[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,4,3],[5,4,2]] => [[4,4,4,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1]
[[7,6,5,3],[6,5,3]] => [[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [3,3,3,2,2,1]
[[2,2,2,2,1],[1,1]] => [[5,4],[2]] => [2]
[[3,3,3,3,1],[2,2,1,1]] => [[5,4,4],[4,2]] => [4,2]
[[3,3,3,2,1],[2,2,1]] => [[5,4,3],[3,2]] => [3,2]
[[4,4,4,3,1],[3,3,2,1]] => [[5,4,4,3],[4,3,2]] => [4,3,2]
[[4,4,4,2,1],[3,3,2]] => [[5,4,3,3],[3,3,2]] => [3,3,2]
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,4,3,3],[4,3,3,2]] => [4,3,3,2]
[[3,3,2,2,1],[2,2]] => [[5,4,2],[2,2]] => [2,2]
[[4,4,3,3,1],[3,3,1,1]] => [[5,4,4,2],[4,2,2]] => [4,2,2]
[[4,4,3,2,1],[3,3,1]] => [[5,4,3,2],[3,2,2]] => [3,2,2]
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,4,3,2],[4,3,2,2]] => [4,3,2,2]
[[5,5,4,2,1],[4,4,2]] => [[5,4,3,3,2],[3,3,2,2]] => [3,3,2,2]
[[6,6,5,3,1],[5,5,3,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]] => [4,3,3,2,2]
[[3,2,2,2,1],[2,1]] => [[5,4,1],[2,1]] => [2,1]
[[4,3,3,3,1],[3,2,1,1]] => [[5,4,4,1],[4,2,1]] => [4,2,1]
[[4,3,3,2,1],[3,2,1]] => [[5,4,3,1],[3,2,1]] => [3,2,1]
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1]
[[5,4,4,2,1],[4,3,2]] => [[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,5,3,1],[5,4,3,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[4,3,2,2,1],[3,2]] => [[5,4,2,1],[2,2,1]] => [2,2,1]
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1]
[[5,4,3,2,1],[4,3,1]] => [[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,4,3,1],[5,4,2,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[6,5,4,2,1],[5,4,2]] => [[5,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1]
[[7,6,5,3,1],[6,5,3,1]] => [[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [4,3,3,2,2,1]
[[3,3,3,2,2],[2,2,1,1]] => [[5,5,3],[4,2]] => [4,2]
[[4,4,4,3,2],[3,3,2,2]] => [[5,5,4,3],[4,4,2]] => [4,4,2]
[[4,4,4,2,2],[3,3,2,1]] => [[5,5,3,3],[4,3,2]] => [4,3,2]
[[5,5,5,3,2],[4,4,3,2]] => [[5,5,4,3,3],[4,4,3,2]] => [4,4,3,2]
[[4,4,3,2,2],[3,3,1,1]] => [[5,5,3,2],[4,2,2]] => [4,2,2]
[[5,5,4,3,2],[4,4,2,2]] => [[5,5,4,3,2],[4,4,2,2]] => [4,4,2,2]
[[5,5,4,2,2],[4,4,2,1]] => [[5,5,3,3,2],[4,3,2,2]] => [4,3,2,2]
[[6,6,5,3,2],[5,5,3,2]] => [[5,5,4,3,3,2],[4,4,3,2,2]] => [4,4,3,2,2]
[[4,3,3,2,2],[3,2,1,1]] => [[5,5,3,1],[4,2,1]] => [4,2,1]
[[5,4,4,3,2],[4,3,2,2]] => [[5,5,4,3,1],[4,4,2,1]] => [4,4,2,1]
[[5,4,4,2,2],[4,3,2,1]] => [[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,5,3,2],[5,4,3,2]] => [[5,5,4,3,3,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[5,4,3,2,2],[4,3,1,1]] => [[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1]
[[6,5,4,3,2],[5,4,2,2]] => [[5,5,4,3,2,1],[4,4,2,2,1]] => [4,4,2,2,1]
[[6,5,4,2,2],[5,4,2,1]] => [[5,5,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[7,6,5,3,2],[6,5,3,2]] => [[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [4,4,3,2,2,1]
[[2,2,2,1,1,1],[1,1]] => [[6,3],[2]] => [2]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[6,5,3],[5,2]] => [5,2]
[[3,3,3,2,1,1],[2,2,1,1]] => [[6,4,3],[4,2]] => [4,2]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[6,5,4,3],[5,4,2]] => [5,4,2]
[[3,3,3,1,1,1],[2,2,1]] => [[6,3,3],[3,2]] => [3,2]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[6,5,3,3],[5,3,2]] => [5,3,2]
[[4,4,4,2,1,1],[3,3,2,1]] => [[6,4,3,3],[4,3,2]] => [4,3,2]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,3],[5,4,3,2]] => [5,4,3,2]
[[3,3,2,1,1,1],[2,2]] => [[6,3,2],[2,2]] => [2,2]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[6,5,3,2],[5,2,2]] => [5,2,2]
[[4,4,3,2,1,1],[3,3,1,1]] => [[6,4,3,2],[4,2,2]] => [4,2,2]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[6,5,4,3,2],[5,4,2,2]] => [5,4,2,2]
[[4,4,3,1,1,1],[3,3,1]] => [[6,3,3,2],[3,2,2]] => [3,2,2]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [[6,5,3,3,2],[5,3,2,2]] => [5,3,2,2]
[[5,5,4,2,1,1],[4,4,2,1]] => [[6,4,3,3,2],[4,3,2,2]] => [4,3,2,2]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]] => [5,4,3,2,2]
[[3,2,2,1,1,1],[2,1]] => [[6,3,1],[2,1]] => [2,1]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[6,5,3,1],[5,2,1]] => [5,2,1]
[[4,3,3,2,1,1],[3,2,1,1]] => [[6,4,3,1],[4,2,1]] => [4,2,1]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [[6,5,4,3,1],[5,4,2,1]] => [5,4,2,1]
[[4,3,3,1,1,1],[3,2,1]] => [[6,3,3,1],[3,2,1]] => [3,2,1]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [[6,5,3,3,1],[5,3,2,1]] => [5,3,2,1]
[[5,4,4,2,1,1],[4,3,2,1]] => [[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[4,3,2,1,1,1],[3,2]] => [[6,3,2,1],[2,2,1]] => [2,2,1]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [[6,5,3,2,1],[5,2,2,1]] => [5,2,2,1]
[[5,4,3,2,1,1],[4,3,1,1]] => [[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]] => [5,4,2,2,1]
[[5,4,3,1,1,1],[4,3,1]] => [[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]] => [5,3,2,2,1]
[[6,5,4,2,1,1],[5,4,2,1]] => [[6,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [5,4,3,2,2,1]
[[4,4,4,4],[3,3,3]] => [[4,4,4,4],[3,3,3]] => [3,3,3]
[[5,5,5,4],[4,4,4]] => [[4,4,4,4,3],[3,3,3,3]] => [3,3,3,3]
[[5,5,4,4],[4,4,3]] => [[4,4,4,4,2],[3,3,3,2]] => [3,3,3,2]
[[6,6,5,4],[5,5,4]] => [[4,4,4,4,3,2],[3,3,3,3,2]] => [3,3,3,3,2]
[[5,4,4,4],[4,3,3]] => [[4,4,4,4,1],[3,3,3,1]] => [3,3,3,1]
[[6,5,5,4],[5,4,4]] => [[4,4,4,4,3,1],[3,3,3,3,1]] => [3,3,3,3,1]
[[6,5,4,4],[5,4,3]] => [[4,4,4,4,2,1],[3,3,3,2,1]] => [3,3,3,2,1]
[[7,6,5,4],[6,5,4]] => [[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [3,3,3,3,2,1]
[[3,3,3,3,1],[2,2,2]] => [[5,4,4],[3,3]] => [3,3]
[[4,4,4,4,1],[3,3,3,1]] => [[5,4,4,4],[4,3,3]] => [4,3,3]
[[4,4,4,3,1],[3,3,3]] => [[5,4,4,3],[3,3,3]] => [3,3,3]
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,4,4,3],[4,3,3,3]] => [4,3,3,3]
[[4,4,3,3,1],[3,3,2]] => [[5,4,4,2],[3,3,2]] => [3,3,2]
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,4,4,2],[4,3,3,2]] => [4,3,3,2]
[[5,5,4,3,1],[4,4,3]] => [[5,4,4,3,2],[3,3,3,2]] => [3,3,3,2]
[[6,6,5,4,1],[5,5,4,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]] => [4,3,3,3,2]
[[4,3,3,3,1],[3,2,2]] => [[5,4,4,1],[3,3,1]] => [3,3,1]
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,4,4,1],[4,3,3,1]] => [4,3,3,1]
[[5,4,4,3,1],[4,3,3]] => [[5,4,4,3,1],[3,3,3,1]] => [3,3,3,1]
[[6,5,5,4,1],[5,4,4,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]] => [4,3,3,3,1]
[[5,4,3,3,1],[4,3,2]] => [[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,4,4,1],[5,4,3,1]] => [[5,4,4,4,2,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[6,5,4,3,1],[5,4,3]] => [[5,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1]
[[7,6,5,4,1],[6,5,4,1]] => [[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [4,3,3,3,2,1]
[[2,2,2,2,2],[1,1,1]] => [[5,5],[3]] => [3]
[[3,3,3,3,2],[2,2,2,1]] => [[5,5,4],[4,3]] => [4,3]
[[4,4,4,4,2],[3,3,3,2]] => [[5,5,4,4],[4,4,3]] => [4,4,3]
[[3,3,3,2,2],[2,2,2]] => [[5,5,3],[3,3]] => [3,3]
[[4,4,4,3,2],[3,3,3,1]] => [[5,5,4,3],[4,3,3]] => [4,3,3]
[[5,5,5,4,2],[4,4,4,2]] => [[5,5,4,4,3],[4,4,3,3]] => [4,4,3,3]
[[3,3,2,2,2],[2,2,1]] => [[5,5,2],[3,2]] => [3,2]
[[4,4,3,3,2],[3,3,2,1]] => [[5,5,4,2],[4,3,2]] => [4,3,2]
[[5,5,4,4,2],[4,4,3,2]] => [[5,5,4,4,2],[4,4,3,2]] => [4,4,3,2]
[[4,4,3,2,2],[3,3,2]] => [[5,5,3,2],[3,3,2]] => [3,3,2]
[[5,5,4,3,2],[4,4,3,1]] => [[5,5,4,3,2],[4,3,3,2]] => [4,3,3,2]
[[6,6,5,4,2],[5,5,4,2]] => [[5,5,4,4,3,2],[4,4,3,3,2]] => [4,4,3,3,2]
[[3,2,2,2,2],[2,1,1]] => [[5,5,1],[3,1]] => [3,1]
[[4,3,3,3,2],[3,2,2,1]] => [[5,5,4,1],[4,3,1]] => [4,3,1]
[[5,4,4,4,2],[4,3,3,2]] => [[5,5,4,4,1],[4,4,3,1]] => [4,4,3,1]
[[4,3,3,2,2],[3,2,2]] => [[5,5,3,1],[3,3,1]] => [3,3,1]
[[5,4,4,3,2],[4,3,3,1]] => [[5,5,4,3,1],[4,3,3,1]] => [4,3,3,1]
[[6,5,5,4,2],[5,4,4,2]] => [[5,5,4,4,3,1],[4,4,3,3,1]] => [4,4,3,3,1]
[[4,3,2,2,2],[3,2,1]] => [[5,5,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,3,2],[4,3,2,1]] => [[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,4,2],[5,4,3,2]] => [[5,5,4,4,2,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,4,3,2],[5,4,3,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[7,6,5,4,2],[6,5,4,2]] => [[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [4,4,3,3,2,1]
[[2,2,2,2,1,1],[1,1,1]] => [[6,4],[3]] => [3]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[6,5,4],[5,3]] => [5,3]
[[3,3,3,3,1,1],[2,2,2,1]] => [[6,4,4],[4,3]] => [4,3]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[6,5,4,4],[5,4,3]] => [5,4,3]
[[3,3,3,2,1,1],[2,2,2]] => [[6,4,3],[3,3]] => [3,3]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[6,5,4,3],[5,3,3]] => [5,3,3]
[[4,4,4,3,1,1],[3,3,3,1]] => [[6,4,4,3],[4,3,3]] => [4,3,3]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[6,5,4,4,3],[5,4,3,3]] => [5,4,3,3]
[[3,3,2,2,1,1],[2,2,1]] => [[6,4,2],[3,2]] => [3,2]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[6,5,4,2],[5,3,2]] => [5,3,2]
[[4,4,3,3,1,1],[3,3,2,1]] => [[6,4,4,2],[4,3,2]] => [4,3,2]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[6,5,4,4,2],[5,4,3,2]] => [5,4,3,2]
[[4,4,3,2,1,1],[3,3,2]] => [[6,4,3,2],[3,3,2]] => [3,3,2]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[6,5,4,3,2],[5,3,3,2]] => [5,3,3,2]
[[5,5,4,3,1,1],[4,4,3,1]] => [[6,4,4,3,2],[4,3,3,2]] => [4,3,3,2]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]] => [5,4,3,3,2]
[[3,2,2,2,1,1],[2,1,1]] => [[6,4,1],[3,1]] => [3,1]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[6,5,4,1],[5,3,1]] => [5,3,1]
[[4,3,3,3,1,1],[3,2,2,1]] => [[6,4,4,1],[4,3,1]] => [4,3,1]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[6,5,4,4,1],[5,4,3,1]] => [5,4,3,1]
[[4,3,3,2,1,1],[3,2,2]] => [[6,4,3,1],[3,3,1]] => [3,3,1]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [[6,5,4,3,1],[5,3,3,1]] => [5,3,3,1]
[[5,4,4,3,1,1],[4,3,3,1]] => [[6,4,4,3,1],[4,3,3,1]] => [4,3,3,1]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]] => [5,4,3,3,1]
[[4,3,2,2,1,1],[3,2,1]] => [[6,4,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [[6,5,4,2,1],[5,3,2,1]] => [5,3,2,1]
[[5,4,3,3,1,1],[4,3,2,1]] => [[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[5,4,3,2,1,1],[4,3,2]] => [[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]] => [5,3,3,2,1]
[[6,5,4,3,1,1],[5,4,3,1]] => [[6,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [5,4,3,3,2,1]
[[3,3,3,3,3],[2,2,2,2]] => [[5,5,5],[4,4]] => [4,4]
[[4,4,4,4,3],[3,3,3,3]] => [[5,5,5,4],[4,4,4]] => [4,4,4]
[[4,4,4,3,3],[3,3,3,2]] => [[5,5,5,3],[4,4,3]] => [4,4,3]
[[5,5,5,4,3],[4,4,4,3]] => [[5,5,5,4,3],[4,4,4,3]] => [4,4,4,3]
[[4,4,3,3,3],[3,3,2,2]] => [[5,5,5,2],[4,4,2]] => [4,4,2]
[[5,5,4,4,3],[4,4,3,3]] => [[5,5,5,4,2],[4,4,4,2]] => [4,4,4,2]
[[5,5,4,3,3],[4,4,3,2]] => [[5,5,5,3,2],[4,4,3,2]] => [4,4,3,2]
[[6,6,5,4,3],[5,5,4,3]] => [[5,5,5,4,3,2],[4,4,4,3,2]] => [4,4,4,3,2]
[[4,3,3,3,3],[3,2,2,2]] => [[5,5,5,1],[4,4,1]] => [4,4,1]
[[5,4,4,4,3],[4,3,3,3]] => [[5,5,5,4,1],[4,4,4,1]] => [4,4,4,1]
[[5,4,4,3,3],[4,3,3,2]] => [[5,5,5,3,1],[4,4,3,1]] => [4,4,3,1]
[[6,5,5,4,3],[5,4,4,3]] => [[5,5,5,4,3,1],[4,4,4,3,1]] => [4,4,4,3,1]
[[5,4,3,3,3],[4,3,2,2]] => [[5,5,5,2,1],[4,4,2,1]] => [4,4,2,1]
[[6,5,4,4,3],[5,4,3,3]] => [[5,5,5,4,2,1],[4,4,4,2,1]] => [4,4,4,2,1]
[[6,5,4,3,3],[5,4,3,2]] => [[5,5,5,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[7,6,5,4,3],[6,5,4,3]] => [[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [4,4,4,3,2,1]
[[2,2,2,2,2,1],[1,1,1,1]] => [[6,5],[4]] => [4]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[6,5,5],[5,4]] => [5,4]
[[3,3,3,3,2,1],[2,2,2,2]] => [[6,5,4],[4,4]] => [4,4]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[6,5,5,4],[5,4,4]] => [5,4,4]
[[3,3,3,2,2,1],[2,2,2,1]] => [[6,5,3],[4,3]] => [4,3]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[6,5,5,3],[5,4,3]] => [5,4,3]
[[4,4,4,3,2,1],[3,3,3,2]] => [[6,5,4,3],[4,4,3]] => [4,4,3]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[6,5,5,4,3],[5,4,4,3]] => [5,4,4,3]
[[3,3,2,2,2,1],[2,2,1,1]] => [[6,5,2],[4,2]] => [4,2]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[6,5,5,2],[5,4,2]] => [5,4,2]
[[4,4,3,3,2,1],[3,3,2,2]] => [[6,5,4,2],[4,4,2]] => [4,4,2]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[6,5,5,4,2],[5,4,4,2]] => [5,4,4,2]
[[4,4,3,2,2,1],[3,3,2,1]] => [[6,5,3,2],[4,3,2]] => [4,3,2]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[6,5,5,3,2],[5,4,3,2]] => [5,4,3,2]
[[5,5,4,3,2,1],[4,4,3,2]] => [[6,5,4,3,2],[4,4,3,2]] => [4,4,3,2]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]] => [5,4,4,3,2]
[[3,2,2,2,2,1],[2,1,1,1]] => [[6,5,1],[4,1]] => [4,1]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[6,5,5,1],[5,4,1]] => [5,4,1]
[[4,3,3,3,2,1],[3,2,2,2]] => [[6,5,4,1],[4,4,1]] => [4,4,1]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[6,5,5,4,1],[5,4,4,1]] => [5,4,4,1]
[[4,3,3,2,2,1],[3,2,2,1]] => [[6,5,3,1],[4,3,1]] => [4,3,1]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[6,5,5,3,1],[5,4,3,1]] => [5,4,3,1]
[[5,4,4,3,2,1],[4,3,3,2]] => [[6,5,4,3,1],[4,4,3,1]] => [4,4,3,1]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]] => [5,4,4,3,1]
[[4,3,2,2,2,1],[3,2,1,1]] => [[6,5,2,1],[4,2,1]] => [4,2,1]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [[6,5,5,2,1],[5,4,2,1]] => [5,4,2,1]
[[5,4,3,3,2,1],[4,3,2,2]] => [[6,5,4,2,1],[4,4,2,1]] => [4,4,2,1]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]] => [5,4,4,2,1]
[[5,4,3,2,2,1],[4,3,2,1]] => [[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[6,5,4,3,2,1],[5,4,3,2]] => [[6,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [5,4,4,3,2,1]
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[6,6],[5]] => [5]
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[6,6,5],[5,5]] => [5,5]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[6,6,4],[5,4]] => [5,4]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[6,6,5,4],[5,5,4]] => [5,5,4]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[6,6,3],[5,3]] => [5,3]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[6,6,5,3],[5,5,3]] => [5,5,3]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[6,6,4,3],[5,4,3]] => [5,4,3]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[6,6,5,4,3],[5,5,4,3]] => [5,5,4,3]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[6,6,2],[5,2]] => [5,2]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[6,6,5,2],[5,5,2]] => [5,5,2]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[6,6,4,2],[5,4,2]] => [5,4,2]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[6,6,5,4,2],[5,5,4,2]] => [5,5,4,2]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[6,6,3,2],[5,3,2]] => [5,3,2]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[6,6,5,3,2],[5,5,3,2]] => [5,5,3,2]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[6,6,4,3,2],[5,4,3,2]] => [5,4,3,2]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,6,5,4,3,2],[5,5,4,3,2]] => [5,5,4,3,2]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[6,6,1],[5,1]] => [5,1]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[6,6,5,1],[5,5,1]] => [5,5,1]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[6,6,4,1],[5,4,1]] => [5,4,1]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[6,6,5,4,1],[5,5,4,1]] => [5,5,4,1]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[6,6,3,1],[5,3,1]] => [5,3,1]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[6,6,5,3,1],[5,5,3,1]] => [5,5,3,1]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[6,6,4,3,1],[5,4,3,1]] => [5,4,3,1]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,6,5,4,3,1],[5,5,4,3,1]] => [5,5,4,3,1]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[6,6,2,1],[5,2,1]] => [5,2,1]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[6,6,5,2,1],[5,5,2,1]] => [5,5,2,1]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [[6,6,4,2,1],[5,4,2,1]] => [5,4,2,1]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,6,5,4,2,1],[5,5,4,2,1]] => [5,5,4,2,1]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [[6,6,3,2,1],[5,3,2,1]] => [5,3,2,1]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,6,5,3,2,1],[5,5,3,2,1]] => [5,5,3,2,1]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,6,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [5,5,4,3,2,1]
[[1,1,1,1,1,1,1],[]] => [[7],[]] => []
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[7,6],[6]] => [6]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[7,5],[5]] => [5]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[7,6,5],[6,5]] => [6,5]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[7,4],[4]] => [4]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[7,6,4],[6,4]] => [6,4]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[7,5,4],[5,4]] => [5,4]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[7,6,5,4],[6,5,4]] => [6,5,4]
[[2,2,2,1,1,1,1],[1,1,1]] => [[7,3],[3]] => [3]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[7,6,3],[6,3]] => [6,3]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[7,5,3],[5,3]] => [5,3]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[7,6,5,3],[6,5,3]] => [6,5,3]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [[7,4,3],[4,3]] => [4,3]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[7,6,4,3],[6,4,3]] => [6,4,3]
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [[7,5,4,3],[5,4,3]] => [5,4,3]
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]] => [6,5,4,3]
[[2,2,1,1,1,1,1],[1,1]] => [[7,2],[2]] => [2]
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [[7,6,2],[6,2]] => [6,2]
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [[7,5,2],[5,2]] => [5,2]
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [[7,6,5,2],[6,5,2]] => [6,5,2]
[[3,3,2,2,1,1,1],[2,2,1,1]] => [[7,4,2],[4,2]] => [4,2]
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [[7,6,4,2],[6,4,2]] => [6,4,2]
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [[7,5,4,2],[5,4,2]] => [5,4,2]
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]] => [6,5,4,2]
[[3,3,2,1,1,1,1],[2,2,1]] => [[7,3,2],[3,2]] => [3,2]
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [[7,6,3,2],[6,3,2]] => [6,3,2]
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [[7,5,3,2],[5,3,2]] => [5,3,2]
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [[7,6,5,3,2],[6,5,3,2]] => [6,5,3,2]
[[4,4,3,2,1,1,1],[3,3,2,1]] => [[7,4,3,2],[4,3,2]] => [4,3,2]
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [[7,6,4,3,2],[6,4,3,2]] => [6,4,3,2]
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [[7,5,4,3,2],[5,4,3,2]] => [5,4,3,2]
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]] => [6,5,4,3,2]
[[2,1,1,1,1,1,1],[1]] => [[7,1],[1]] => [1]
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [[7,6,1],[6,1]] => [6,1]
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [[7,5,1],[5,1]] => [5,1]
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [[7,6,5,1],[6,5,1]] => [6,5,1]
[[3,2,2,2,1,1,1],[2,1,1,1]] => [[7,4,1],[4,1]] => [4,1]
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [[7,6,4,1],[6,4,1]] => [6,4,1]
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [[7,5,4,1],[5,4,1]] => [5,4,1]
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]] => [6,5,4,1]
[[3,2,2,1,1,1,1],[2,1,1]] => [[7,3,1],[3,1]] => [3,1]
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [[7,6,3,1],[6,3,1]] => [6,3,1]
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [[7,5,3,1],[5,3,1]] => [5,3,1]
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [[7,6,5,3,1],[6,5,3,1]] => [6,5,3,1]
[[4,3,3,2,1,1,1],[3,2,2,1]] => [[7,4,3,1],[4,3,1]] => [4,3,1]
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [[7,6,4,3,1],[6,4,3,1]] => [6,4,3,1]
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [[7,5,4,3,1],[5,4,3,1]] => [5,4,3,1]
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]] => [6,5,4,3,1]
[[3,2,1,1,1,1,1],[2,1]] => [[7,2,1],[2,1]] => [2,1]
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [[7,6,2,1],[6,2,1]] => [6,2,1]
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [[7,5,2,1],[5,2,1]] => [5,2,1]
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [[7,6,5,2,1],[6,5,2,1]] => [6,5,2,1]
[[4,3,2,2,1,1,1],[3,2,1,1]] => [[7,4,2,1],[4,2,1]] => [4,2,1]
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [[7,6,4,2,1],[6,4,2,1]] => [6,4,2,1]
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [[7,5,4,2,1],[5,4,2,1]] => [5,4,2,1]
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]] => [6,5,4,2,1]
[[4,3,2,1,1,1,1],[3,2,1]] => [[7,3,2,1],[3,2,1]] => [3,2,1]
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [[7,6,3,2,1],[6,3,2,1]] => [6,3,2,1]
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [[7,5,3,2,1],[5,3,2,1]] => [5,3,2,1]
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]] => [6,5,3,2,1]
[[5,4,3,2,1,1,1],[4,3,2,1]] => [[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1]
[[6,5,4,3,2,2,1],[5,4,3,2,1,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]] => [6,4,3,2,1]
[[6,5,4,3,2,1,1],[5,4,3,2,1]] => [[7,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1]
[[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]] => [6,5,4,3,2,1]
[[8],[]] => [[1,1,1,1,1,1,1,1],[]] => []
[[7,1],[]] => [[2,1,1,1,1,1,1],[]] => []
[[6,2],[]] => [[2,2,1,1,1,1],[]] => []
[[6,1,1],[]] => [[3,1,1,1,1,1],[]] => []
[[5,3],[]] => [[2,2,2,1,1],[]] => []
[[5,2,1],[]] => [[3,2,1,1,1],[]] => []
[[5,1,1,1],[]] => [[4,1,1,1,1],[]] => []
[[4,4],[]] => [[2,2,2,2],[]] => []
[[4,3,1],[]] => [[3,2,2,1],[]] => []
[[4,2,2],[]] => [[3,3,1,1],[]] => []
[[4,2,1,1],[]] => [[4,2,1,1],[]] => []
[[4,1,1,1,1],[]] => [[5,1,1,1],[]] => []
[[3,3,2],[]] => [[3,3,2],[]] => []
[[3,3,1,1],[]] => [[4,2,2],[]] => []
[[3,2,2,1],[]] => [[4,3,1],[]] => []
[[3,2,1,1,1],[]] => [[5,2,1],[]] => []
[[3,1,1,1,1,1],[]] => [[6,1,1],[]] => []
[[2,2,2,2],[]] => [[4,4],[]] => []
[[2,2,2,1,1],[]] => [[5,3],[]] => []
[[2,2,1,1,1,1],[]] => [[6,2],[]] => []
[[2,1,1,1,1,1,1],[]] => [[7,1],[]] => []
[[1,1,1,1,1,1,1,1],[]] => [[8],[]] => []
[[9],[]] => [[1,1,1,1,1,1,1,1,1],[]] => []
[[8,1],[]] => [[2,1,1,1,1,1,1,1],[]] => []
[[7,2],[]] => [[2,2,1,1,1,1,1],[]] => []
[[7,1,1],[]] => [[3,1,1,1,1,1,1],[]] => []
[[6,3],[]] => [[2,2,2,1,1,1],[]] => []
[[6,2,1],[]] => [[3,2,1,1,1,1],[]] => []
[[6,1,1,1],[]] => [[4,1,1,1,1,1],[]] => []
[[5,4],[]] => [[2,2,2,2,1],[]] => []
[[5,3,1],[]] => [[3,2,2,1,1],[]] => []
[[5,2,2],[]] => [[3,3,1,1,1],[]] => []
[[5,2,1,1],[]] => [[4,2,1,1,1],[]] => []
[[5,1,1,1,1],[]] => [[5,1,1,1,1],[]] => []
[[4,4,1],[]] => [[3,2,2,2],[]] => []
[[4,3,2],[]] => [[3,3,2,1],[]] => []
[[4,3,1,1],[]] => [[4,2,2,1],[]] => []
[[4,2,2,1],[]] => [[4,3,1,1],[]] => []
[[4,2,1,1,1],[]] => [[5,2,1,1],[]] => []
[[4,1,1,1,1,1],[]] => [[6,1,1,1],[]] => []
[[3,3,3],[]] => [[3,3,3],[]] => []
[[3,3,2,1],[]] => [[4,3,2],[]] => []
[[3,3,1,1,1],[]] => [[5,2,2],[]] => []
[[3,2,2,2],[]] => [[4,4,1],[]] => []
[[3,2,2,1,1],[]] => [[5,3,1],[]] => []
[[3,2,1,1,1,1],[]] => [[6,2,1],[]] => []
[[3,1,1,1,1,1,1],[]] => [[7,1,1],[]] => []
[[2,2,2,2,1],[]] => [[5,4],[]] => []
[[2,2,2,1,1,1],[]] => [[6,3],[]] => []
[[2,2,1,1,1,1,1],[]] => [[7,2],[]] => []
[[2,1,1,1,1,1,1,1],[]] => [[8,1],[]] => []
[[1,1,1,1,1,1,1,1,1],[]] => [[9],[]] => []
[[10],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => []
[[9,1],[]] => [[2,1,1,1,1,1,1,1,1],[]] => []
[[8,2],[]] => [[2,2,1,1,1,1,1,1],[]] => []
[[8,1,1],[]] => [[3,1,1,1,1,1,1,1],[]] => []
[[7,3],[]] => [[2,2,2,1,1,1,1],[]] => []
[[7,2,1],[]] => [[3,2,1,1,1,1,1],[]] => []
[[7,1,1,1],[]] => [[4,1,1,1,1,1,1],[]] => []
[[6,4],[]] => [[2,2,2,2,1,1],[]] => []
[[6,3,1],[]] => [[3,2,2,1,1,1],[]] => []
[[6,2,2],[]] => [[3,3,1,1,1,1],[]] => []
[[6,2,1,1],[]] => [[4,2,1,1,1,1],[]] => []
[[6,1,1,1,1],[]] => [[5,1,1,1,1,1],[]] => []
[[5,5],[]] => [[2,2,2,2,2],[]] => []
[[5,4,1],[]] => [[3,2,2,2,1],[]] => []
[[5,3,2],[]] => [[3,3,2,1,1],[]] => []
[[5,3,1,1],[]] => [[4,2,2,1,1],[]] => []
[[5,2,2,1],[]] => [[4,3,1,1,1],[]] => []
[[5,2,1,1,1],[]] => [[5,2,1,1,1],[]] => []
[[5,1,1,1,1,1],[]] => [[6,1,1,1,1],[]] => []
[[4,4,2],[]] => [[3,3,2,2],[]] => []
[[4,4,1,1],[]] => [[4,2,2,2],[]] => []
[[4,3,3],[]] => [[3,3,3,1],[]] => []
[[4,3,2,1],[]] => [[4,3,2,1],[]] => []
[[4,3,1,1,1],[]] => [[5,2,2,1],[]] => []
[[4,2,2,2],[]] => [[4,4,1,1],[]] => []
[[4,2,2,1,1],[]] => [[5,3,1,1],[]] => []
[[4,2,1,1,1,1],[]] => [[6,2,1,1],[]] => []
[[4,1,1,1,1,1,1],[]] => [[7,1,1,1],[]] => []
[[3,3,3,1],[]] => [[4,3,3],[]] => []
[[3,3,2,2],[]] => [[4,4,2],[]] => []
[[3,3,2,1,1],[]] => [[5,3,2],[]] => []
[[3,3,1,1,1,1],[]] => [[6,2,2],[]] => []
[[3,2,2,2,1],[]] => [[5,4,1],[]] => []
[[3,2,2,1,1,1],[]] => [[6,3,1],[]] => []
[[3,2,1,1,1,1,1],[]] => [[7,2,1],[]] => []
[[3,1,1,1,1,1,1,1],[]] => [[8,1,1],[]] => []
[[2,2,2,2,2],[]] => [[5,5],[]] => []
[[2,2,2,2,1,1],[]] => [[6,4],[]] => []
[[2,2,2,1,1,1,1],[]] => [[7,3],[]] => []
[[2,2,1,1,1,1,1,1],[]] => [[8,2],[]] => []
[[2,1,1,1,1,1,1,1,1],[]] => [[9,1],[]] => []
[[1,1,1,1,1,1,1,1,1,1],[]] => [[10],[]] => []
[[5,5,1],[]] => [[3,2,2,2,2],[]] => []
[[4,4,3],[]] => [[3,3,3,2],[]] => []
[[4,4,2,1],[]] => [[4,3,2,2],[]] => []
[[4,3,3,1],[]] => [[4,3,3,1],[]] => []
[[4,3,2,2],[]] => [[4,4,2,1],[]] => []
[[3,3,3,2],[]] => [[4,4,3],[]] => []
[[3,3,3,1,1],[]] => [[5,3,3],[]] => []
[[3,3,2,2,1],[]] => [[5,4,2],[]] => []
[[3,2,2,2,2],[]] => [[5,5,1],[]] => []
[[2,2,2,2,2,1],[]] => [[6,5],[]] => []
[[6,6],[]] => [[2,2,2,2,2,2],[]] => []
[[5,5,2],[]] => [[3,3,2,2,2],[]] => []
[[5,4,3],[]] => [[3,3,3,2,1],[]] => []
[[4,4,4],[]] => [[3,3,3,3],[]] => []
[[4,4,3,1],[]] => [[4,3,3,2],[]] => []
[[4,4,2,2],[]] => [[4,4,2,2],[]] => []
[[4,3,3,2],[]] => [[4,4,3,1],[]] => []
[[3,3,3,3],[]] => [[4,4,4],[]] => []
[[3,3,3,2,1],[]] => [[5,4,3],[]] => []
[[3,3,2,2,2],[]] => [[5,5,2],[]] => []
[[2,2,2,2,2,2],[]] => [[6,6],[]] => []
[[5,5,3],[]] => [[3,3,3,2,2],[]] => []
[[5,4,4],[]] => [[3,3,3,3,1],[]] => []
[[4,4,4,1],[]] => [[4,3,3,3],[]] => []
[[4,4,3,2],[]] => [[4,4,3,2],[]] => []
[[4,3,3,3],[]] => [[4,4,4,1],[]] => []
[[3,3,3,3,1],[]] => [[5,4,4],[]] => []
[[3,3,3,2,2],[]] => [[5,5,3],[]] => []
[[5,5,4],[]] => [[3,3,3,3,2],[]] => []
[[4,4,4,2],[]] => [[4,4,3,3],[]] => []
[[4,4,3,3],[]] => [[4,4,4,2],[]] => []
[[3,3,3,3,2],[]] => [[5,5,4],[]] => []
[[5,5,5],[]] => [[3,3,3,3,3],[]] => []
[[4,4,4,3],[]] => [[4,4,4,3],[]] => []
[[3,3,3,3,3],[]] => [[5,5,5],[]] => []
[[6,5,5],[]] => [[3,3,3,3,3,1],[]] => []
[[5,4,4,3],[]] => [[4,4,4,3,1],[]] => []
[[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[4,3,3,3,3],[]] => [[5,5,5,1],[]] => []
[[5,4,4,4],[]] => [[4,4,4,4,1],[]] => []
[[3,2,2,2,1,1],[1,1,1]] => [[6,4,1],[3]] => [3]
[[4,2,2,1,1],[1,1]] => [[5,3,1,1],[2]] => [2]
[[4,3,3,3,1],[2,2,2]] => [[5,4,4,1],[3,3]] => [3,3]
[[5,3,3,1],[2,2]] => [[4,3,3,1,1],[2,2]] => [2,2]
[[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [[7,7],[6]] => [6]
[[3,3,3,2,2,2],[2,2,1,1,1]] => [[6,6,3],[5,2]] => [5,2]
[[7,2],[1]] => [[2,2,1,1,1,1,1],[1]] => [1]
[[3,3,3,3,3,3],[2,2,2,2,2]] => [[6,6,6],[5,5]] => [5,5]
[[4,4,4,4,4],[3,3,3,3]] => [[5,5,5,5],[4,4,4]] => [4,4,4]
[[5,5,5,5],[4,4,4]] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3]
[[6,6,6],[5,5]] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2]
[[7,6],[5]] => [[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1]
[[7,7],[6]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [[8,8],[7]] => [7]
[[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [[7,7,7],[6,6]] => [6,6]
[[5,5,5,5,5],[4,4,4,4]] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4]
[[7,7,7],[6,6]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2]
[[8,8],[7]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1]
[[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [[9,9],[8]] => [8]
[[9,9],[8]] => [[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]
[[3,3,3],[1]] => [[3,3,3],[1]] => [1]
[[3,3,3,1],[1,1]] => [[4,3,3],[2]] => [2]
[[4,4,1],[1]] => [[3,2,2,2],[1]] => [1]
[[3,3,2,1],[1]] => [[4,3,2],[1]] => [1]
[[2,2,2,2,1],[1]] => [[5,4],[1]] => [1]
[[3,3,3,1],[2]] => [[4,3,3],[1,1]] => [1,1]
[[3,3,3,1],[1]] => [[4,3,3],[1]] => [1]
[[3,3,3,2],[1,1,1]] => [[4,4,3],[3]] => [3]
[[4,4,2],[1,1]] => [[3,3,2,2],[2]] => [2]
[[4,4,4],[2,2]] => [[3,3,3,3],[2,2]] => [2,2]
[[5,5],[2]] => [[2,2,2,2,2],[1,1]] => [1,1]
[[4,4,3],[2,1]] => [[3,3,3,2],[2,1]] => [2,1]
[[3,3,3,3],[2,1,1]] => [[4,4,4],[3,1]] => [3,1]
[[4,3,3],[1,1]] => [[3,3,3,1],[2]] => [2]
[[3,3,3,3],[1,1,1]] => [[4,4,4],[3]] => [3]
[[4,4,3],[1,1]] => [[3,3,3,2],[2]] => [2]
[[4,4,4],[3,1]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[5,4],[1]] => [[2,2,2,2,1],[1]] => [1]
[[4,4,4],[2,1]] => [[3,3,3,3],[2,1]] => [2,1]
[[5,5],[1]] => [[2,2,2,2,2],[1]] => [1]
[[4,4,4],[1,1]] => [[3,3,3,3],[2]] => [2]
[[3,3,2,2],[1,1]] => [[4,4,2],[2]] => [2]
[[4,4,2],[2]] => [[3,3,2,2],[1,1]] => [1,1]
[[3,3,3,2],[2,1]] => [[4,4,3],[2,1]] => [2,1]
[[4,3,2],[1]] => [[3,3,2,1],[1]] => [1]
[[3,3,3,2],[1,1]] => [[4,4,3],[2]] => [2]
[[4,4,2],[1]] => [[3,3,2,2],[1]] => [1]
[[2,2,2,2,2],[1,1]] => [[5,5],[2]] => [2]
[[3,2,2,2],[1]] => [[4,4,1],[1]] => [1]
[[3,3,2,2],[2]] => [[4,4,2],[1,1]] => [1,1]
[[3,3,2,2],[1]] => [[4,4,2],[1]] => [1]
[[2,2,2,2,2],[1]] => [[5,5],[1]] => [1]
[[3,3,3,2],[2]] => [[4,4,3],[1,1]] => [1,1]
[[3,3,3,2],[1]] => [[4,4,3],[1]] => [1]
[[3,3,3,3],[2,2]] => [[4,4,4],[2,2]] => [2,2]
[[4,3,3],[2]] => [[3,3,3,1],[1,1]] => [1,1]
[[4,4,3],[3]] => [[3,3,3,2],[1,1,1]] => [1,1,1]
[[4,4,3],[2]] => [[3,3,3,2],[1,1]] => [1,1]
[[3,3,3,3],[2,1]] => [[4,4,4],[2,1]] => [2,1]
[[4,3,3],[1]] => [[3,3,3,1],[1]] => [1]
[[3,3,3,3],[1,1]] => [[4,4,4],[2]] => [2]
[[4,4,3],[1]] => [[3,3,3,2],[1]] => [1]
[[4,4,4],[3]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,4,4],[2]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,4],[1]] => [[3,3,3,3],[1]] => [1]
[[3,3,3,3],[2]] => [[4,4,4],[1,1]] => [1,1]
[[3,3,3,3],[1]] => [[4,4,4],[1]] => [1]
[[2,2,2,1,1,1],[1]] => [[6,3],[1]] => [1]
[[2,2,2,2,1,1],[1,1]] => [[6,4],[2]] => [2]
[[3,3,2,1,1],[1]] => [[5,3,2],[1]] => [1]
[[2,2,2,2,1,1],[1]] => [[6,4],[1]] => [1]
[[3,3,3,1,1],[2]] => [[5,3,3],[1,1]] => [1,1]
[[3,3,3,1,1],[1]] => [[5,3,3],[1]] => [1]
[[4,4,4,1],[1,1]] => [[4,3,3,3],[2]] => [2]
[[2,2,2,2,2,1],[1,1,1]] => [[6,5],[3]] => [3]
[[3,3,2,2,1],[1,1]] => [[5,4,2],[2]] => [2]
[[3,3,3,2,1],[2,1]] => [[5,4,3],[2,1]] => [2,1]
[[3,3,3,2,1],[1,1]] => [[5,4,3],[2]] => [2]
[[4,4,2,1],[1]] => [[4,3,2,2],[1]] => [1]
[[2,2,2,2,2,1],[1,1]] => [[6,5],[2]] => [2]
[[3,3,2,2,1],[1]] => [[5,4,2],[1]] => [1]
[[2,2,2,2,2,1],[1]] => [[6,5],[1]] => [1]
[[3,3,3,2,1],[2]] => [[5,4,3],[1,1]] => [1,1]
[[3,3,3,2,1],[1]] => [[5,4,3],[1]] => [1]
[[3,3,3,3,1],[2,2]] => [[5,4,4],[2,2]] => [2,2]
[[4,4,3,1],[2]] => [[4,3,3,2],[1,1]] => [1,1]
[[3,3,3,3,1],[2,1]] => [[5,4,4],[2,1]] => [2,1]
[[3,3,3,3,1],[1,1]] => [[5,4,4],[2]] => [2]
[[4,4,3,1],[1]] => [[4,3,3,2],[1]] => [1]
[[4,4,4,1],[3]] => [[4,3,3,3],[1,1,1]] => [1,1,1]
[[4,4,4,1],[2]] => [[4,3,3,3],[1,1]] => [1,1]
[[4,4,4,1],[1]] => [[4,3,3,3],[1]] => [1]
[[3,3,3,3,1],[2]] => [[5,4,4],[1,1]] => [1,1]
[[3,3,3,3,1],[1]] => [[5,4,4],[1]] => [1]
[[4,4,4,2],[1,1,1]] => [[4,4,3,3],[3]] => [3]
[[6,6],[4]] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[5,5,5],[4,3]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[5,5,5],[3,3]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2]
[[6,6],[3]] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1]
[[4,4,4,4],[3,3,2]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[4,4,4,4],[3,2,2]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[4,4,4,4],[2,2,2]] => [[4,4,4,4],[3,3]] => [3,3]
[[5,5,5],[4,2]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[5,5,5],[3,2]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[6,6],[2]] => [[2,2,2,2,2,2],[1,1]] => [1,1]
[[5,5,5],[2,2]] => [[3,3,3,3,3],[2,2]] => [2,2]
[[3,3,3,3,3],[2,2,2,1]] => [[5,5,5],[4,3]] => [4,3]
[[3,3,3,3,3],[2,2,1,1]] => [[5,5,5],[4,2]] => [4,2]
[[3,3,3,3,3],[2,1,1,1]] => [[5,5,5],[4,1]] => [4,1]
[[3,3,3,3,3],[1,1,1,1]] => [[5,5,5],[4]] => [4]
[[4,4,3,3],[1,1,1]] => [[4,4,4,2],[3]] => [3]
[[4,4,4,3],[2,1,1]] => [[4,4,4,3],[3,1]] => [3,1]
[[4,4,4,3],[1,1,1]] => [[4,4,4,3],[3]] => [3]
[[4,4,4,4],[3,3,1]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[4,4,4,4],[3,2,1]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[4,4,4,4],[2,2,1]] => [[4,4,4,4],[3,2]] => [3,2]
[[5,5,5],[4,1]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[5,5,5],[3,1]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[5,5,5],[2,1]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[4,4,4,4],[3,1,1]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,4,4,4],[2,1,1]] => [[4,4,4,4],[3,1]] => [3,1]
[[5,5,4],[1,1]] => [[3,3,3,3,2],[2]] => [2]
[[4,4,4,4],[1,1,1]] => [[4,4,4,4],[3]] => [3]
[[5,5,5],[1,1]] => [[3,3,3,3,3],[2]] => [2]
[[2,2,2,2,2,2],[1,1,1,1]] => [[6,6],[4]] => [4]
[[3,3,2,2,2],[1,1,1]] => [[5,5,2],[3]] => [3]
[[3,3,3,2,2],[2,1,1]] => [[5,5,3],[3,1]] => [3,1]
[[3,3,3,2,2],[1,1,1]] => [[5,5,3],[3]] => [3]
[[4,4,2,2],[1,1]] => [[4,4,2,2],[2]] => [2]
[[3,3,3,3,2],[2,2,1]] => [[5,5,4],[3,2]] => [3,2]
[[4,4,3,2],[2,1]] => [[4,4,3,2],[2,1]] => [2,1]
[[3,3,3,3,2],[2,1,1]] => [[5,5,4],[3,1]] => [3,1]
[[3,3,3,3,2],[1,1,1]] => [[5,5,4],[3]] => [3]
[[4,4,3,2],[1,1]] => [[4,4,3,2],[2]] => [2]
[[4,4,4,2],[3,1]] => [[4,4,3,3],[2,1,1]] => [2,1,1]
[[4,4,4,2],[2,1]] => [[4,4,3,3],[2,1]] => [2,1]
[[5,5,2],[1]] => [[3,3,2,2,2],[1]] => [1]
[[4,4,4,2],[1,1]] => [[4,4,3,3],[2]] => [2]
[[2,2,2,2,2,2],[1,1,1]] => [[6,6],[3]] => [3]
[[3,3,2,2,2],[1,1]] => [[5,5,2],[2]] => [2]
[[3,3,3,2,2],[2,1]] => [[5,5,3],[2,1]] => [2,1]
[[3,3,3,2,2],[1,1]] => [[5,5,3],[2]] => [2]
[[4,4,2,2],[1]] => [[4,4,2,2],[1]] => [1]
[[2,2,2,2,2,2],[1,1]] => [[6,6],[2]] => [2]
[[3,3,2,2,2],[1]] => [[5,5,2],[1]] => [1]
[[2,2,2,2,2,2],[1]] => [[6,6],[1]] => [1]
[[3,3,3,2,2],[2]] => [[5,5,3],[1,1]] => [1,1]
[[3,3,3,2,2],[1]] => [[5,5,3],[1]] => [1]
[[3,3,3,3,2],[2,2]] => [[5,5,4],[2,2]] => [2,2]
[[4,4,3,2],[2]] => [[4,4,3,2],[1,1]] => [1,1]
[[3,3,3,3,2],[2,1]] => [[5,5,4],[2,1]] => [2,1]
[[4,3,3,2],[1]] => [[4,4,3,1],[1]] => [1]
[[3,3,3,3,2],[1,1]] => [[5,5,4],[2]] => [2]
[[4,4,3,2],[1]] => [[4,4,3,2],[1]] => [1]
[[4,4,4,2],[3]] => [[4,4,3,3],[1,1,1]] => [1,1,1]
[[4,4,4,2],[2]] => [[4,4,3,3],[1,1]] => [1,1]
[[4,4,4,2],[1]] => [[4,4,3,3],[1]] => [1]
[[3,3,3,3,2],[2]] => [[5,5,4],[1,1]] => [1,1]
[[3,3,3,3,2],[1]] => [[5,5,4],[1]] => [1]
[[3,3,3,3,3],[2,2,2]] => [[5,5,5],[3,3]] => [3,3]
[[4,4,3,3],[2,2]] => [[4,4,4,2],[2,2]] => [2,2]
[[4,4,4,3],[3,2]] => [[4,4,4,3],[2,2,1]] => [2,2,1]
[[4,4,4,3],[2,2]] => [[4,4,4,3],[2,2]] => [2,2]
[[5,5,3],[2]] => [[3,3,3,2,2],[1,1]] => [1,1]
[[3,3,3,3,3],[2,2,1]] => [[5,5,5],[3,2]] => [3,2]
[[4,4,3,3],[2,1]] => [[4,4,4,2],[2,1]] => [2,1]
[[3,3,3,3,3],[2,1,1]] => [[5,5,5],[3,1]] => [3,1]
[[4,3,3,3],[1,1]] => [[4,4,4,1],[2]] => [2]
[[3,3,3,3,3],[1,1,1]] => [[5,5,5],[3]] => [3]
[[4,4,3,3],[1,1]] => [[4,4,4,2],[2]] => [2]
[[4,4,4,3],[3,1]] => [[4,4,4,3],[2,1,1]] => [2,1,1]
[[4,4,4,3],[2,1]] => [[4,4,4,3],[2,1]] => [2,1]
[[5,5,3],[1]] => [[3,3,3,2,2],[1]] => [1]
[[4,4,4,3],[1,1]] => [[4,4,4,3],[2]] => [2]
[[4,4,4,4],[3,3]] => [[4,4,4,4],[2,2,2]] => [2,2,2]
[[5,5,4],[3]] => [[3,3,3,3,2],[1,1,1]] => [1,1,1]
[[4,4,4,4],[3,2]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[4,4,4,4],[2,2]] => [[4,4,4,4],[2,2]] => [2,2]
[[5,5,4],[2]] => [[3,3,3,3,2],[1,1]] => [1,1]
[[5,5,5],[4]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1]
[[5,5,5],[3]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[5,5,5],[2]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[4,4,4,4],[3,1]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[5,4,4],[1]] => [[3,3,3,3,1],[1]] => [1]
[[4,4,4,4],[2,1]] => [[4,4,4,4],[2,1]] => [2,1]
[[5,5,4],[1]] => [[3,3,3,3,2],[1]] => [1]
[[4,4,4,4],[1,1]] => [[4,4,4,4],[2]] => [2]
[[5,5,5],[1]] => [[3,3,3,3,3],[1]] => [1]
[[3,3,3,3,3],[2,2]] => [[5,5,5],[2,2]] => [2,2]
[[4,3,3,3],[2]] => [[4,4,4,1],[1,1]] => [1,1]
[[4,4,3,3],[3]] => [[4,4,4,2],[1,1,1]] => [1,1,1]
[[4,4,3,3],[2]] => [[4,4,4,2],[1,1]] => [1,1]
[[3,3,3,3,3],[2,1]] => [[5,5,5],[2,1]] => [2,1]
[[4,3,3,3],[1]] => [[4,4,4,1],[1]] => [1]
[[3,3,3,3,3],[1,1]] => [[5,5,5],[2]] => [2]
[[4,4,3,3],[1]] => [[4,4,4,2],[1]] => [1]
[[4,4,4,3],[3]] => [[4,4,4,3],[1,1,1]] => [1,1,1]
[[4,4,4,3],[2]] => [[4,4,4,3],[1,1]] => [1,1]
[[4,4,4,3],[1]] => [[4,4,4,3],[1]] => [1]
[[3,3,3,3,3],[2]] => [[5,5,5],[1,1]] => [1,1]
[[3,3,3,3,3],[1]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[3]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[4,4,4,4],[2]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,4,4,4],[1]] => [[4,4,4,4],[1]] => [1]
[[7,7],[5]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[6,6,6],[4,4]] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[7,7],[4]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[5,5,5,5],[3,3,3]] => [[4,4,4,4,4],[3,3,3]] => [3,3,3]
[[4,4,4,4,4],[3,3,3,2]] => [[5,5,5,5],[4,4,3]] => [4,4,3]
[[5,5,5,5],[4,2,2]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[3,3,3,3,3,3],[2,2,2,2,1]] => [[6,6,6],[5,4]] => [5,4]
[[4,4,4,4,4],[1,1,1,1]] => [[5,5,5,5],[4]] => [4]
[[5,5,5,5],[2,1,1]] => [[4,4,4,4,4],[3,1]] => [3,1]
[[6,6,6],[1,1]] => [[3,3,3,3,3,3],[2]] => [2]
[[5,5,5,5],[1,1,1]] => [[4,4,4,4,4],[3]] => [3]
[[2,2,2,2,2,2,2],[1,1,1,1,1]] => [[7,7],[5]] => [5]
[[2,2,2,2,2,2,2],[1,1,1,1]] => [[7,7],[4]] => [4]
[[3,3,3,3,3,3],[2,2,2,2]] => [[6,6,6],[4,4]] => [4,4]
[[5,4,4,4],[1]] => [[4,4,4,4,1],[1]] => [1]
[[8,8],[6]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [[7,7,7],[6,5]] => [6,5]
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [[8,8],[6]] => [6]
[[5,5,5,5,5],[1,1,1,1]] => [[5,5,5,5,5],[4]] => [4]
[[5,4,4,4,4],[]] => [[5,5,5,5,1],[]] => []
[[6,6,6,6,6],[1,1,1,1]] => [[5,5,5,5,5,5],[4]] => [4]
[[6,6,6,6],[1,1,1]] => [[4,4,4,4,4,4],[3]] => [3]
[[6,5,5,5],[]] => [[4,4,4,4,4,1],[]] => []
[[6,5,5,5,5],[]] => [[5,5,5,5,5,1],[]] => []
Map
conjugate
Description
The conjugate of the skew partition.
The conjugate of a skew partition λ is the skew partition λ∗ whose Ferrers diagram is obtained from the Ferrers diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate of a skew partition λ is the skew partition λ∗ whose Ferrers diagram is obtained from the Ferrers diagram of λ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
Map
inner shape
Description
The inner shape of a skew partition.
searching the database
Sorry, this map was not found in the database.