Identifier
Mp00183:
Skew partitions
—inner shape⟶
Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
Images
[[1],[]] => [] => []
[[2],[]] => [] => []
[[1,1],[]] => [] => []
[[2,1],[1]] => [1] => [1]
[[3],[]] => [] => []
[[2,1],[]] => [] => []
[[3,1],[1]] => [1] => [1]
[[2,2],[1]] => [1] => [1]
[[3,2],[2]] => [2] => [1,1]
[[1,1,1],[]] => [] => []
[[2,2,1],[1,1]] => [1,1] => [2]
[[2,1,1],[1]] => [1] => [1]
[[3,2,1],[2,1]] => [2,1] => [2,1]
[[4],[]] => [] => []
[[3,1],[]] => [] => []
[[4,1],[1]] => [1] => [1]
[[2,2],[]] => [] => []
[[3,2],[1]] => [1] => [1]
[[4,2],[2]] => [2] => [1,1]
[[2,1,1],[]] => [] => []
[[3,2,1],[1,1]] => [1,1] => [2]
[[3,1,1],[1]] => [1] => [1]
[[4,2,1],[2,1]] => [2,1] => [2,1]
[[3,3],[2]] => [2] => [1,1]
[[4,3],[3]] => [3] => [1,1,1]
[[2,2,1],[1]] => [1] => [1]
[[3,3,1],[2,1]] => [2,1] => [2,1]
[[3,2,1],[2]] => [2] => [1,1]
[[4,3,1],[3,1]] => [3,1] => [2,1,1]
[[2,2,2],[1,1]] => [1,1] => [2]
[[3,3,2],[2,2]] => [2,2] => [2,2]
[[3,2,2],[2,1]] => [2,1] => [2,1]
[[4,3,2],[3,2]] => [3,2] => [2,2,1]
[[1,1,1,1],[]] => [] => []
[[2,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[2,2,1,1],[1,1]] => [1,1] => [2]
[[3,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[2,1,1,1],[1]] => [1] => [1]
[[3,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[3,2,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5],[]] => [] => []
[[4,1],[]] => [] => []
[[5,1],[1]] => [1] => [1]
[[3,2],[]] => [] => []
[[4,2],[1]] => [1] => [1]
[[5,2],[2]] => [2] => [1,1]
[[3,1,1],[]] => [] => []
[[4,2,1],[1,1]] => [1,1] => [2]
[[4,1,1],[1]] => [1] => [1]
[[5,2,1],[2,1]] => [2,1] => [2,1]
[[3,3],[1]] => [1] => [1]
[[4,3],[2]] => [2] => [1,1]
[[5,3],[3]] => [3] => [1,1,1]
[[2,2,1],[]] => [] => []
[[3,3,1],[1,1]] => [1,1] => [2]
[[3,2,1],[1]] => [1] => [1]
[[4,3,1],[2,1]] => [2,1] => [2,1]
[[4,2,1],[2]] => [2] => [1,1]
[[5,3,1],[3,1]] => [3,1] => [2,1,1]
[[3,2,2],[1,1]] => [1,1] => [2]
[[4,3,2],[2,2]] => [2,2] => [2,2]
[[4,2,2],[2,1]] => [2,1] => [2,1]
[[5,3,2],[3,2]] => [3,2] => [2,2,1]
[[2,1,1,1],[]] => [] => []
[[3,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[3,2,1,1],[1,1]] => [1,1] => [2]
[[4,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[3,1,1,1],[1]] => [1] => [1]
[[4,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,2,1,1],[2,1]] => [2,1] => [2,1]
[[5,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4],[3]] => [3] => [1,1,1]
[[5,4],[4]] => [4] => [1,1,1,1]
[[3,3,1],[2]] => [2] => [1,1]
[[4,4,1],[3,1]] => [3,1] => [2,1,1]
[[4,3,1],[3]] => [3] => [1,1,1]
[[5,4,1],[4,1]] => [4,1] => [2,1,1,1]
[[2,2,2],[1]] => [1] => [1]
[[3,3,2],[2,1]] => [2,1] => [2,1]
[[4,4,2],[3,2]] => [3,2] => [2,2,1]
[[3,2,2],[2]] => [2] => [1,1]
[[4,3,2],[3,1]] => [3,1] => [2,1,1]
[[5,4,2],[4,2]] => [4,2] => [2,2,1,1]
[[2,2,1,1],[1]] => [1] => [1]
[[3,3,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[3,3,1,1],[2,1]] => [2,1] => [2,1]
[[4,4,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[3,2,1,1],[2]] => [2] => [1,1]
[[4,3,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[4,3,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[3,3,3],[2,2]] => [2,2] => [2,2]
[[4,4,3],[3,3]] => [3,3] => [2,2,2]
[[4,3,3],[3,2]] => [3,2] => [2,2,1]
[[5,4,3],[4,3]] => [4,3] => [2,2,2,1]
[[2,2,2,1],[1,1]] => [1,1] => [2]
[[3,3,3,1],[2,2,1]] => [2,2,1] => [3,2]
[[3,3,2,1],[2,2]] => [2,2] => [2,2]
[[4,4,3,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[3,2,2,1],[2,1]] => [2,1] => [2,1]
>>> Load all 1751 entries. <<<
[[4,3,3,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,3,2,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,3,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[2,2,2,2],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,2],[2,2,2]] => [2,2,2] => [3,3]
[[3,3,2,2],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[3,2,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[4,3,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[1,1,1,1,1],[]] => [] => []
[[2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[2,2,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[2,2,1,1,1],[1,1]] => [1,1] => [2]
[[3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[3,3,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[2,1,1,1,1],[1]] => [1] => [1]
[[3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[3,2,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[3,2,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[4,3,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6],[]] => [] => []
[[5,1],[]] => [] => []
[[6,1],[1]] => [1] => [1]
[[4,2],[]] => [] => []
[[5,2],[1]] => [1] => [1]
[[6,2],[2]] => [2] => [1,1]
[[4,1,1],[]] => [] => []
[[5,2,1],[1,1]] => [1,1] => [2]
[[5,1,1],[1]] => [1] => [1]
[[6,2,1],[2,1]] => [2,1] => [2,1]
[[3,3],[]] => [] => []
[[4,3],[1]] => [1] => [1]
[[5,3],[2]] => [2] => [1,1]
[[6,3],[3]] => [3] => [1,1,1]
[[3,2,1],[]] => [] => []
[[4,3,1],[1,1]] => [1,1] => [2]
[[4,2,1],[1]] => [1] => [1]
[[5,3,1],[2,1]] => [2,1] => [2,1]
[[5,2,1],[2]] => [2] => [1,1]
[[6,3,1],[3,1]] => [3,1] => [2,1,1]
[[4,2,2],[1,1]] => [1,1] => [2]
[[5,3,2],[2,2]] => [2,2] => [2,2]
[[5,2,2],[2,1]] => [2,1] => [2,1]
[[6,3,2],[3,2]] => [3,2] => [2,2,1]
[[3,1,1,1],[]] => [] => []
[[4,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[4,2,1,1],[1,1]] => [1,1] => [2]
[[5,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,1,1,1],[1]] => [1] => [1]
[[5,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,2,1,1],[2,1]] => [2,1] => [2,1]
[[6,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4],[2]] => [2] => [1,1]
[[5,4],[3]] => [3] => [1,1,1]
[[6,4],[4]] => [4] => [1,1,1,1]
[[3,3,1],[1]] => [1] => [1]
[[4,4,1],[2,1]] => [2,1] => [2,1]
[[4,3,1],[2]] => [2] => [1,1]
[[5,4,1],[3,1]] => [3,1] => [2,1,1]
[[5,3,1],[3]] => [3] => [1,1,1]
[[6,4,1],[4,1]] => [4,1] => [2,1,1,1]
[[2,2,2],[]] => [] => []
[[3,3,2],[1,1]] => [1,1] => [2]
[[4,4,2],[2,2]] => [2,2] => [2,2]
[[3,2,2],[1]] => [1] => [1]
[[4,3,2],[2,1]] => [2,1] => [2,1]
[[5,4,2],[3,2]] => [3,2] => [2,2,1]
[[4,2,2],[2]] => [2] => [1,1]
[[5,3,2],[3,1]] => [3,1] => [2,1,1]
[[6,4,2],[4,2]] => [4,2] => [2,2,1,1]
[[2,2,1,1],[]] => [] => []
[[3,3,2,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,1,1],[1,1]] => [1,1] => [2]
[[4,4,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[3,2,1,1],[1]] => [1] => [1]
[[4,3,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,1,1],[2,1]] => [2,1] => [2,1]
[[5,4,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,2,1,1],[2]] => [2] => [1,1]
[[5,3,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,3,1,1],[3,1]] => [3,1] => [2,1,1]
[[6,4,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[4,3,3],[2,2]] => [2,2] => [2,2]
[[5,4,3],[3,3]] => [3,3] => [2,2,2]
[[5,3,3],[3,2]] => [3,2] => [2,2,1]
[[6,4,3],[4,3]] => [4,3] => [2,2,2,1]
[[3,2,2,1],[1,1]] => [1,1] => [2]
[[4,3,3,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,3,2,1],[2,2]] => [2,2] => [2,2]
[[5,4,3,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[4,2,2,1],[2,1]] => [2,1] => [2,1]
[[5,3,3,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,3,2,1],[3,2]] => [3,2] => [2,2,1]
[[6,4,3,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[3,2,2,2],[1,1,1]] => [1,1,1] => [3]
[[4,3,3,2],[2,2,2]] => [2,2,2] => [3,3]
[[4,3,2,2],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,3,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[4,2,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[5,3,3,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,3,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,3,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[2,1,1,1,1],[]] => [] => []
[[3,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,2,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[4,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[3,2,1,1,1],[1,1]] => [1,1] => [2]
[[4,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,3,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[3,1,1,1,1],[1]] => [1] => [1]
[[4,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,2,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[4,2,1,1,1],[2,1]] => [2,1] => [2,1]
[[5,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,3,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,5],[4]] => [4] => [1,1,1,1]
[[6,5],[5]] => [5] => [1,1,1,1,1]
[[4,4,1],[3]] => [3] => [1,1,1]
[[5,5,1],[4,1]] => [4,1] => [2,1,1,1]
[[5,4,1],[4]] => [4] => [1,1,1,1]
[[6,5,1],[5,1]] => [5,1] => [2,1,1,1,1]
[[3,3,2],[2]] => [2] => [1,1]
[[4,4,2],[3,1]] => [3,1] => [2,1,1]
[[5,5,2],[4,2]] => [4,2] => [2,2,1,1]
[[4,3,2],[3]] => [3] => [1,1,1]
[[5,4,2],[4,1]] => [4,1] => [2,1,1,1]
[[6,5,2],[5,2]] => [5,2] => [2,2,1,1,1]
[[3,3,1,1],[2]] => [2] => [1,1]
[[4,4,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[4,4,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,5,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[4,3,1,1],[3]] => [3] => [1,1,1]
[[5,4,2,1],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[5,4,1,1],[4,1]] => [4,1] => [2,1,1,1]
[[6,5,2,1],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[3,3,3],[2,1]] => [2,1] => [2,1]
[[4,4,3],[3,2]] => [3,2] => [2,2,1]
[[5,5,3],[4,3]] => [4,3] => [2,2,2,1]
[[4,3,3],[3,1]] => [3,1] => [2,1,1]
[[5,4,3],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,3],[5,3]] => [5,3] => [2,2,2,1,1]
[[2,2,2,1],[1]] => [1] => [1]
[[3,3,3,1],[2,1,1]] => [2,1,1] => [3,1]
[[3,3,2,1],[2,1]] => [2,1] => [2,1]
[[4,4,3,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4,2,1],[3,2]] => [3,2] => [2,2,1]
[[5,5,3,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[3,2,2,1],[2]] => [2] => [1,1]
[[4,3,3,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[4,3,2,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,3,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,4,2,1],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,3,1],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[3,3,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,3,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[4,4,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,3,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[4,3,2,2],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,3,2],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[5,4,2,2],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,3,2],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[2,2,1,1,1],[1]] => [1] => [1]
[[3,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[3,3,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[3,3,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[4,4,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[3,2,1,1,1],[2]] => [2] => [1,1]
[[4,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[4,3,2,1,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[4,3,1,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[5,4,2,1,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,3,2,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[4,4,4],[3,3]] => [3,3] => [2,2,2]
[[5,5,4],[4,4]] => [4,4] => [2,2,2,2]
[[5,4,4],[4,3]] => [4,3] => [2,2,2,1]
[[6,5,4],[5,4]] => [5,4] => [2,2,2,2,1]
[[3,3,3,1],[2,2]] => [2,2] => [2,2]
[[4,4,4,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[4,4,3,1],[3,3]] => [3,3] => [2,2,2]
[[5,5,4,1],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[4,3,3,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,4,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[5,4,3,1],[4,3]] => [4,3] => [2,2,2,1]
[[6,5,4,1],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[2,2,2,2],[1,1]] => [1,1] => [2]
[[3,3,3,2],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[3,3,2,2],[2,2]] => [2,2] => [2,2]
[[4,4,3,2],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,2],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[3,2,2,2],[2,1]] => [2,1] => [2,1]
[[4,3,3,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[4,3,2,2],[3,2]] => [3,2] => [2,2,1]
[[5,4,3,2],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,4,2],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[2,2,2,1,1],[1,1]] => [1,1] => [2]
[[3,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[3,3,3,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[3,3,2,1,1],[2,2]] => [2,2] => [2,2]
[[4,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[4,4,3,1,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,2,1],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[3,2,2,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[4,3,3,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[4,3,2,1,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[5,4,3,1,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,4,2,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[3,3,3,3],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,3],[3,3,3]] => [3,3,3] => [3,3,3]
[[4,4,3,3],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,3],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[4,3,3,3],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4,3],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[5,4,3,3],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,4,3],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[2,2,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[3,3,3,2,1],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[3,3,2,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[4,4,3,2,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,3,1],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[3,2,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[4,3,3,2,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4,3,1],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[4,3,2,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,4,3,2,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,4,3,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => [4,4]
[[3,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,3,2],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[3,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[4,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,3,2],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[3,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[4,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,3,2],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[4,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,3,3,2],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[5,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,4,3,2],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[1,1,1,1,1,1],[]] => [] => []
[[2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[3,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[2,2,1,1,1,1],[1,1]] => [1,1] => [2]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[3,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[3,3,2,1,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[4,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[2,1,1,1,1,1],[1]] => [1] => [1]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[3,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[3,2,2,1,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[4,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[3,2,1,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[4,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[4,3,2,1,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[5,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[7],[]] => [] => []
[[6,1],[]] => [] => []
[[7,1],[1]] => [1] => [1]
[[5,2],[]] => [] => []
[[6,2],[1]] => [1] => [1]
[[7,2],[2]] => [2] => [1,1]
[[5,1,1],[]] => [] => []
[[6,2,1],[1,1]] => [1,1] => [2]
[[6,1,1],[1]] => [1] => [1]
[[7,2,1],[2,1]] => [2,1] => [2,1]
[[4,3],[]] => [] => []
[[5,3],[1]] => [1] => [1]
[[6,3],[2]] => [2] => [1,1]
[[7,3],[3]] => [3] => [1,1,1]
[[4,2,1],[]] => [] => []
[[5,3,1],[1,1]] => [1,1] => [2]
[[5,2,1],[1]] => [1] => [1]
[[6,3,1],[2,1]] => [2,1] => [2,1]
[[6,2,1],[2]] => [2] => [1,1]
[[7,3,1],[3,1]] => [3,1] => [2,1,1]
[[5,2,2],[1,1]] => [1,1] => [2]
[[6,3,2],[2,2]] => [2,2] => [2,2]
[[6,2,2],[2,1]] => [2,1] => [2,1]
[[7,3,2],[3,2]] => [3,2] => [2,2,1]
[[4,1,1,1],[]] => [] => []
[[5,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[5,2,1,1],[1,1]] => [1,1] => [2]
[[6,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,1,1,1],[1]] => [1] => [1]
[[6,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[6,2,1,1],[2,1]] => [2,1] => [2,1]
[[7,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4],[1]] => [1] => [1]
[[5,4],[2]] => [2] => [1,1]
[[6,4],[3]] => [3] => [1,1,1]
[[7,4],[4]] => [4] => [1,1,1,1]
[[3,3,1],[]] => [] => []
[[4,4,1],[1,1]] => [1,1] => [2]
[[4,3,1],[1]] => [1] => [1]
[[5,4,1],[2,1]] => [2,1] => [2,1]
[[5,3,1],[2]] => [2] => [1,1]
[[6,4,1],[3,1]] => [3,1] => [2,1,1]
[[6,3,1],[3]] => [3] => [1,1,1]
[[7,4,1],[4,1]] => [4,1] => [2,1,1,1]
[[3,2,2],[]] => [] => []
[[4,3,2],[1,1]] => [1,1] => [2]
[[5,4,2],[2,2]] => [2,2] => [2,2]
[[4,2,2],[1]] => [1] => [1]
[[5,3,2],[2,1]] => [2,1] => [2,1]
[[6,4,2],[3,2]] => [3,2] => [2,2,1]
[[5,2,2],[2]] => [2] => [1,1]
[[6,3,2],[3,1]] => [3,1] => [2,1,1]
[[7,4,2],[4,2]] => [4,2] => [2,2,1,1]
[[3,2,1,1],[]] => [] => []
[[4,3,2,1],[1,1,1]] => [1,1,1] => [3]
[[4,3,1,1],[1,1]] => [1,1] => [2]
[[5,4,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,2,1,1],[1]] => [1] => [1]
[[5,3,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,3,1,1],[2,1]] => [2,1] => [2,1]
[[6,4,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,2,1,1],[2]] => [2] => [1,1]
[[6,3,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[6,3,1,1],[3,1]] => [3,1] => [2,1,1]
[[7,4,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,3,3],[2,2]] => [2,2] => [2,2]
[[6,4,3],[3,3]] => [3,3] => [2,2,2]
[[6,3,3],[3,2]] => [3,2] => [2,2,1]
[[7,4,3],[4,3]] => [4,3] => [2,2,2,1]
[[4,2,2,1],[1,1]] => [1,1] => [2]
[[5,3,3,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,3,2,1],[2,2]] => [2,2] => [2,2]
[[6,4,3,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,2,2,1],[2,1]] => [2,1] => [2,1]
[[6,3,3,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,3,2,1],[3,2]] => [3,2] => [2,2,1]
[[7,4,3,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[4,2,2,2],[1,1,1]] => [1,1,1] => [3]
[[5,3,3,2],[2,2,2]] => [2,2,2] => [3,3]
[[5,3,2,2],[2,2,1]] => [2,2,1] => [3,2]
[[6,4,3,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,2,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[6,3,3,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[6,3,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[7,4,3,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[3,1,1,1,1],[]] => [] => []
[[4,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[4,2,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[5,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,2,1,1,1],[1,1]] => [1,1] => [2]
[[5,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[5,3,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[6,4,3,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[4,1,1,1,1],[1]] => [1] => [1]
[[5,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[5,2,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[6,3,3,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,2,1,1,1],[2,1]] => [2,1] => [2,1]
[[6,3,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[6,3,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[7,4,3,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,5],[3]] => [3] => [1,1,1]
[[6,5],[4]] => [4] => [1,1,1,1]
[[7,5],[5]] => [5] => [1,1,1,1,1]
[[4,4,1],[2]] => [2] => [1,1]
[[5,5,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,1],[3]] => [3] => [1,1,1]
[[6,5,1],[4,1]] => [4,1] => [2,1,1,1]
[[6,4,1],[4]] => [4] => [1,1,1,1]
[[7,5,1],[5,1]] => [5,1] => [2,1,1,1,1]
[[3,3,2],[1]] => [1] => [1]
[[4,4,2],[2,1]] => [2,1] => [2,1]
[[5,5,2],[3,2]] => [3,2] => [2,2,1]
[[4,3,2],[2]] => [2] => [1,1]
[[5,4,2],[3,1]] => [3,1] => [2,1,1]
[[6,5,2],[4,2]] => [4,2] => [2,2,1,1]
[[5,3,2],[3]] => [3] => [1,1,1]
[[6,4,2],[4,1]] => [4,1] => [2,1,1,1]
[[7,5,2],[5,2]] => [5,2] => [2,2,1,1,1]
[[3,3,1,1],[1]] => [1] => [1]
[[4,4,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,1,1],[2,1]] => [2,1] => [2,1]
[[5,5,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,3,1,1],[2]] => [2] => [1,1]
[[5,4,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,1,1],[3,1]] => [3,1] => [2,1,1]
[[6,5,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,3,1,1],[3]] => [3] => [1,1,1]
[[6,4,2,1],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[6,4,1,1],[4,1]] => [4,1] => [2,1,1,1]
[[7,5,2,1],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[3,3,3],[1,1]] => [1,1] => [2]
[[4,4,3],[2,2]] => [2,2] => [2,2]
[[5,5,3],[3,3]] => [3,3] => [2,2,2]
[[4,3,3],[2,1]] => [2,1] => [2,1]
[[5,4,3],[3,2]] => [3,2] => [2,2,1]
[[6,5,3],[4,3]] => [4,3] => [2,2,2,1]
[[5,3,3],[3,1]] => [3,1] => [2,1,1]
[[6,4,3],[4,2]] => [4,2] => [2,2,1,1]
[[7,5,3],[5,3]] => [5,3] => [2,2,2,1,1]
[[2,2,2,1],[]] => [] => []
[[3,3,3,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,2,1],[1,1]] => [1,1] => [2]
[[4,4,3,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,2,1],[2,2]] => [2,2] => [2,2]
[[5,5,3,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[3,2,2,1],[1]] => [1] => [1]
[[4,3,3,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,2,1],[2,1]] => [2,1] => [2,1]
[[5,4,3,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,2,1],[3,2]] => [3,2] => [2,2,1]
[[6,5,3,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[4,2,2,1],[2]] => [2] => [1,1]
[[5,3,3,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,3,2,1],[3,1]] => [3,1] => [2,1,1]
[[6,4,3,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,4,2,1],[4,2]] => [4,2] => [2,2,1,1]
[[7,5,3,1],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[3,3,2,2],[1,1,1]] => [1,1,1] => [3]
[[4,4,3,2],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,2,2],[2,2,1]] => [2,2,1] => [3,2]
[[5,5,3,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[4,3,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[5,4,3,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,5,3,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[5,3,2,2],[3,1,1]] => [3,1,1] => [3,1,1]
[[6,4,3,2],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[6,4,2,2],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[7,5,3,2],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[2,2,1,1,1],[]] => [] => []
[[3,3,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[4,4,3,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[3,3,1,1,1],[1,1]] => [1,1] => [2]
[[4,4,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,5,3,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[3,2,1,1,1],[1]] => [1] => [1]
[[4,3,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,4,3,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[4,3,1,1,1],[2,1]] => [2,1] => [2,1]
[[5,4,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,5,3,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[4,2,1,1,1],[2]] => [2] => [1,1]
[[5,3,2,2,1],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[5,3,2,1,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[6,4,3,2,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[5,3,1,1,1],[3,1]] => [3,1] => [2,1,1]
[[6,4,2,2,1],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[6,4,2,1,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[7,5,3,2,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[5,4,4],[3,3]] => [3,3] => [2,2,2]
[[6,5,4],[4,4]] => [4,4] => [2,2,2,2]
[[6,4,4],[4,3]] => [4,3] => [2,2,2,1]
[[7,5,4],[5,4]] => [5,4] => [2,2,2,2,1]
[[4,3,3,1],[2,2]] => [2,2] => [2,2]
[[5,4,4,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,4,3,1],[3,3]] => [3,3] => [2,2,2]
[[6,5,4,1],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[5,3,3,1],[3,2]] => [3,2] => [2,2,1]
[[6,4,4,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,4,3,1],[4,3]] => [4,3] => [2,2,2,1]
[[7,5,4,1],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[3,2,2,2],[1,1]] => [1,1] => [2]
[[4,3,3,2],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,4,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[4,3,2,2],[2,2]] => [2,2] => [2,2]
[[5,4,3,2],[3,3,1]] => [3,3,1] => [3,2,2]
[[6,5,4,2],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[4,2,2,2],[2,1]] => [2,1] => [2,1]
[[5,3,3,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,4,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[5,3,2,2],[3,2]] => [3,2] => [2,2,1]
[[6,4,3,2],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[7,5,4,2],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[3,2,2,1,1],[1,1]] => [1,1] => [2]
[[4,3,3,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,3,3,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,4,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[4,3,2,1,1],[2,2]] => [2,2] => [2,2]
[[5,4,3,2,1],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[5,4,3,1,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[6,5,4,2,1],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[4,2,2,1,1],[2,1]] => [2,1] => [2,1]
[[5,3,3,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,3,3,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,4,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,3,2,1,1],[3,2]] => [3,2] => [2,2,1]
[[6,4,3,2,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[6,4,3,1,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[7,5,4,2,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[4,3,3,3],[2,2,2]] => [2,2,2] => [3,3]
[[5,4,4,3],[3,3,3]] => [3,3,3] => [3,3,3]
[[5,4,3,3],[3,3,2]] => [3,3,2] => [3,3,2]
[[6,5,4,3],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[5,3,3,3],[3,2,2]] => [3,2,2] => [3,3,1]
[[6,4,4,3],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[6,4,3,3],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[7,5,4,3],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[3,2,2,2,1],[1,1,1]] => [1,1,1] => [3]
[[4,3,3,3,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,3,3,2,1],[2,2,2]] => [2,2,2] => [3,3]
[[5,4,4,3,1],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[4,3,2,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,3,3,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,4,3,2,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[6,5,4,3,1],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[4,2,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,3,3,3,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,3,3,2,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[6,4,4,3,1],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[5,3,2,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,3,3,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,4,3,2,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[7,5,4,3,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[3,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [4]
[[4,3,3,3,2],[2,2,2,2]] => [2,2,2,2] => [4,4]
[[4,3,3,2,2],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[5,4,4,3,2],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[4,3,2,2,2],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[5,4,3,3,2],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[5,4,3,2,2],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[6,5,4,3,2],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[4,2,2,2,2],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[5,3,3,3,2],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[5,3,3,2,2],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[6,4,4,3,2],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[5,3,2,2,2],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[6,4,3,3,2],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[6,4,3,2,2],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[7,5,4,3,2],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[2,1,1,1,1,1],[]] => [] => []
[[3,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[3,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[3,2,2,1,1,1],[1,1,1]] => [1,1,1] => [3]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[4,3,3,2,1,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[3,2,1,1,1,1],[1,1]] => [1,1] => [2]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[4,3,2,2,1,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[4,3,2,1,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[5,4,3,2,1,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[3,1,1,1,1,1],[1]] => [1] => [1]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[4,2,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[4,2,2,1,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[5,3,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[4,2,1,1,1,1],[2,1]] => [2,1] => [2,1]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[5,3,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[5,3,2,1,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[6,4,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[6,6],[5]] => [5] => [1,1,1,1,1]
[[7,6],[6]] => [6] => [1,1,1,1,1,1]
[[5,5,1],[4]] => [4] => [1,1,1,1]
[[6,6,1],[5,1]] => [5,1] => [2,1,1,1,1]
[[6,5,1],[5]] => [5] => [1,1,1,1,1]
[[7,6,1],[6,1]] => [6,1] => [2,1,1,1,1,1]
[[4,4,2],[3]] => [3] => [1,1,1]
[[5,5,2],[4,1]] => [4,1] => [2,1,1,1]
[[6,6,2],[5,2]] => [5,2] => [2,2,1,1,1]
[[5,4,2],[4]] => [4] => [1,1,1,1]
[[6,5,2],[5,1]] => [5,1] => [2,1,1,1,1]
[[7,6,2],[6,2]] => [6,2] => [2,2,1,1,1,1]
[[4,4,1,1],[3]] => [3] => [1,1,1]
[[5,5,2,1],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[5,5,1,1],[4,1]] => [4,1] => [2,1,1,1]
[[6,6,2,1],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[5,4,1,1],[4]] => [4] => [1,1,1,1]
[[6,5,2,1],[5,1,1]] => [5,1,1] => [3,1,1,1,1]
[[6,5,1,1],[5,1]] => [5,1] => [2,1,1,1,1]
[[7,6,2,1],[6,2,1]] => [6,2,1] => [3,2,1,1,1,1]
[[3,3,3],[2]] => [2] => [1,1]
[[4,4,3],[3,1]] => [3,1] => [2,1,1]
[[5,5,3],[4,2]] => [4,2] => [2,2,1,1]
[[6,6,3],[5,3]] => [5,3] => [2,2,2,1,1]
[[4,3,3],[3]] => [3] => [1,1,1]
[[5,4,3],[4,1]] => [4,1] => [2,1,1,1]
[[6,5,3],[5,2]] => [5,2] => [2,2,1,1,1]
[[7,6,3],[6,3]] => [6,3] => [2,2,2,1,1,1]
[[3,3,2,1],[2]] => [2] => [1,1]
[[4,4,3,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[4,4,2,1],[3,1]] => [3,1] => [2,1,1]
[[5,5,3,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,5,2,1],[4,2]] => [4,2] => [2,2,1,1]
[[6,6,3,1],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[4,3,2,1],[3]] => [3] => [1,1,1]
[[5,4,3,1],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[5,4,2,1],[4,1]] => [4,1] => [2,1,1,1]
[[6,5,3,1],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[6,5,2,1],[5,2]] => [5,2] => [2,2,1,1,1]
[[7,6,3,1],[6,3,1]] => [6,3,1] => [3,2,2,1,1,1]
[[4,4,2,2],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,5,3,2],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[5,5,2,2],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,6,3,2],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[5,4,2,2],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[6,5,3,2],[5,2,2]] => [5,2,2] => [3,3,1,1,1]
[[6,5,2,2],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[7,6,3,2],[6,3,2]] => [6,3,2] => [3,3,2,1,1,1]
[[3,3,1,1,1],[2]] => [2] => [1,1]
[[4,4,2,2,1],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[4,4,2,1,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,5,3,2,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[4,4,1,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,5,2,2,1],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[5,5,2,1,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,6,3,2,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[4,3,1,1,1],[3]] => [3] => [1,1,1]
[[5,4,2,2,1],[4,1,1,1]] => [4,1,1,1] => [4,1,1,1]
[[5,4,2,1,1],[4,1,1]] => [4,1,1] => [3,1,1,1]
[[6,5,3,2,1],[5,2,2,1]] => [5,2,2,1] => [4,3,1,1,1]
[[5,4,1,1,1],[4,1]] => [4,1] => [2,1,1,1]
[[6,5,2,2,1],[5,2,1,1]] => [5,2,1,1] => [4,2,1,1,1]
[[6,5,2,1,1],[5,2,1]] => [5,2,1] => [3,2,1,1,1]
[[7,6,3,2,1],[6,3,2,1]] => [6,3,2,1] => [4,3,2,1,1,1]
[[4,4,4],[3,2]] => [3,2] => [2,2,1]
[[5,5,4],[4,3]] => [4,3] => [2,2,2,1]
[[6,6,4],[5,4]] => [5,4] => [2,2,2,2,1]
[[5,4,4],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,4],[5,3]] => [5,3] => [2,2,2,1,1]
[[7,6,4],[6,4]] => [6,4] => [2,2,2,2,1,1]
[[3,3,3,1],[2,1]] => [2,1] => [2,1]
[[4,4,4,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4,3,1],[3,2]] => [3,2] => [2,2,1]
[[5,5,4,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[5,5,3,1],[4,3]] => [4,3] => [2,2,2,1]
[[6,6,4,1],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[4,3,3,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,4,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,4,3,1],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,4,1],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[6,5,3,1],[5,3]] => [5,3] => [2,2,2,1,1]
[[7,6,4,1],[6,4,1]] => [6,4,1] => [3,2,2,2,1,1]
[[2,2,2,2],[1]] => [1] => [1]
[[3,3,3,2],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,4,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[3,3,2,2],[2,1]] => [2,1] => [2,1]
[[4,4,3,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,4,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[4,4,2,2],[3,2]] => [3,2] => [2,2,1]
[[5,5,3,2],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,6,4,2],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[3,2,2,2],[2]] => [2] => [1,1]
[[4,3,3,2],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,4,2],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[4,3,2,2],[3,1]] => [3,1] => [2,1,1]
[[5,4,3,2],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,4,2],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[5,4,2,2],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,3,2],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[7,6,4,2],[6,4,2]] => [6,4,2] => [3,3,2,2,1,1]
[[2,2,2,1,1],[1]] => [1] => [1]
[[3,3,3,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[3,3,3,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,4,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[3,3,2,1,1],[2,1]] => [2,1] => [2,1]
[[4,4,3,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[4,4,3,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,4,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[4,4,2,1,1],[3,2]] => [3,2] => [2,2,1]
[[5,5,3,2,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[5,5,3,1,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,6,4,2,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[3,2,2,1,1],[2]] => [2] => [1,1]
[[4,3,3,2,1],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[4,3,3,1,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,4,2,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[4,3,2,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,3,2,1],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[5,4,3,1,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,4,2,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[5,4,2,1,1],[4,2]] => [4,2] => [2,2,1,1]
[[6,5,3,2,1],[5,3,1,1]] => [5,3,1,1] => [4,2,2,1,1]
[[6,5,3,1,1],[5,3,1]] => [5,3,1] => [3,2,2,1,1]
[[7,6,4,2,1],[6,4,2,1]] => [6,4,2,1] => [4,3,2,2,1,1]
[[4,4,3,3],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,5,4,3],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[5,5,3,3],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,6,4,3],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[5,4,3,3],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[6,5,4,3],[5,3,3]] => [5,3,3] => [3,3,3,1,1]
[[6,5,3,3],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[7,6,4,3],[6,4,3]] => [6,4,3] => [3,3,3,2,1,1]
[[3,3,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,3,3,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[4,4,3,2,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,5,4,3,1],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[4,4,2,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,3,3,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,5,3,2,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,6,4,3,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[4,3,2,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,3,3,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[5,4,3,2,1],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[6,5,4,3,1],[5,3,3,1]] => [5,3,3,1] => [4,3,3,1,1]
[[5,4,2,2,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,3,3,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[6,5,3,2,1],[5,3,2]] => [5,3,2] => [3,3,2,1,1]
[[7,6,4,3,1],[6,4,3,1]] => [6,4,3,1] => [4,3,3,2,1,1]
[[3,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,4,3,3,2],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[4,4,3,2,2],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,5,4,3,2],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[4,4,2,2,2],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,5,3,3,2],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[5,5,3,2,2],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,6,4,3,2],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[4,3,2,2,2],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[5,4,3,3,2],[4,2,2,2]] => [4,2,2,2] => [4,4,1,1]
[[5,4,3,2,2],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[6,5,4,3,2],[5,3,3,2]] => [5,3,3,2] => [4,4,3,1,1]
[[5,4,2,2,2],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[6,5,3,3,2],[5,3,2,2]] => [5,3,2,2] => [4,4,2,1,1]
[[6,5,3,2,2],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[7,6,4,3,2],[6,4,3,2]] => [6,4,3,2] => [4,4,3,2,1,1]
[[2,2,1,1,1,1],[1]] => [1] => [1]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[3,3,2,2,1,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[3,3,2,1,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[4,4,3,2,1,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[3,3,1,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[4,4,2,2,1,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[4,4,2,1,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[5,5,3,2,1,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[3,2,1,1,1,1],[2]] => [2] => [1,1]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [3,1,1,1,1] => [5,1,1]
[[4,3,2,2,1,1],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [4,2,2,2,1] => [5,4,1,1]
[[4,3,2,1,1,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [4,2,2,1,1] => [5,3,1,1]
[[5,4,3,2,1,1],[4,2,2,1]] => [4,2,2,1] => [4,3,1,1]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [5,3,3,2,1] => [5,4,3,1,1]
[[4,3,1,1,1,1],[3,1]] => [3,1] => [2,1,1]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [4,2,1,1,1] => [5,2,1,1]
[[5,4,2,2,1,1],[4,2,1,1]] => [4,2,1,1] => [4,2,1,1]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [5,3,2,2,1] => [5,4,2,1,1]
[[5,4,2,1,1,1],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [5,3,2,1,1] => [5,3,2,1,1]
[[6,5,3,2,1,1],[5,3,2,1]] => [5,3,2,1] => [4,3,2,1,1]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [6,4,3,2,1] => [5,4,3,2,1,1]
[[5,5,5],[4,4]] => [4,4] => [2,2,2,2]
[[6,6,5],[5,5]] => [5,5] => [2,2,2,2,2]
[[6,5,5],[5,4]] => [5,4] => [2,2,2,2,1]
[[7,6,5],[6,5]] => [6,5] => [2,2,2,2,2,1]
[[4,4,4,1],[3,3]] => [3,3] => [2,2,2]
[[5,5,5,1],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[5,5,4,1],[4,4]] => [4,4] => [2,2,2,2]
[[6,6,5,1],[5,5,1]] => [5,5,1] => [3,2,2,2,2]
[[5,4,4,1],[4,3]] => [4,3] => [2,2,2,1]
[[6,5,5,1],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[6,5,4,1],[5,4]] => [5,4] => [2,2,2,2,1]
[[7,6,5,1],[6,5,1]] => [6,5,1] => [3,2,2,2,2,1]
[[3,3,3,2],[2,2]] => [2,2] => [2,2]
[[4,4,4,2],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,5,2],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[4,4,3,2],[3,3]] => [3,3] => [2,2,2]
[[5,5,4,2],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[6,6,5,2],[5,5,2]] => [5,5,2] => [3,3,2,2,2]
[[4,3,3,2],[3,2]] => [3,2] => [2,2,1]
[[5,4,4,2],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,5,2],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[5,4,3,2],[4,3]] => [4,3] => [2,2,2,1]
[[6,5,4,2],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[7,6,5,2],[6,5,2]] => [6,5,2] => [3,3,2,2,2,1]
[[3,3,3,1,1],[2,2]] => [2,2] => [2,2]
[[4,4,4,2,1],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[4,4,4,1,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,5,2,1],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[4,4,3,1,1],[3,3]] => [3,3] => [2,2,2]
[[5,5,4,2,1],[4,4,1,1]] => [4,4,1,1] => [4,2,2,2]
[[5,5,4,1,1],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[6,6,5,2,1],[5,5,2,1]] => [5,5,2,1] => [4,3,2,2,2]
[[4,3,3,1,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,4,2,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[5,4,4,1,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,5,2,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[5,4,3,1,1],[4,3]] => [4,3] => [2,2,2,1]
[[6,5,4,2,1],[5,4,1,1]] => [5,4,1,1] => [4,2,2,2,1]
[[6,5,4,1,1],[5,4,1]] => [5,4,1] => [3,2,2,2,1]
[[7,6,5,2,1],[6,5,2,1]] => [6,5,2,1] => [4,3,2,2,2,1]
[[3,3,3,3],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,3],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,5,3],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[4,4,3,3],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,3],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[6,6,5,3],[5,5,3]] => [5,5,3] => [3,3,3,2,2]
[[4,3,3,3],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4,3],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,5,3],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[5,4,3,3],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,4,3],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[7,6,5,3],[6,5,3]] => [6,5,3] => [3,3,3,2,2,1]
[[2,2,2,2,1],[1,1]] => [1,1] => [2]
[[3,3,3,3,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[3,3,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,3,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[4,4,4,2,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,5,3,1],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[3,3,2,2,1],[2,2]] => [2,2] => [2,2]
[[4,4,3,3,1],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[4,4,3,2,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,3,1],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[5,5,4,2,1],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[6,6,5,3,1],[5,5,3,1]] => [5,5,3,1] => [4,3,3,2,2]
[[3,2,2,2,1],[2,1]] => [2,1] => [2,1]
[[4,3,3,3,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[4,3,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4,3,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,4,4,2,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,5,3,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[4,3,2,2,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,3,3,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[5,4,3,2,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,4,3,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[6,5,4,2,1],[5,4,2]] => [5,4,2] => [3,3,2,2,1]
[[7,6,5,3,1],[6,5,3,1]] => [6,5,3,1] => [4,3,3,2,2,1]
[[3,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,4,3,2],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[4,4,4,2,2],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,5,3,2],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[4,4,3,2,2],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[5,5,4,3,2],[4,4,2,2]] => [4,4,2,2] => [4,4,2,2]
[[5,5,4,2,2],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[6,6,5,3,2],[5,5,3,2]] => [5,5,3,2] => [4,4,3,2,2]
[[4,3,3,2,2],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,4,3,2],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[5,4,4,2,2],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,5,3,2],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[5,4,3,2,2],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[6,5,4,3,2],[5,4,2,2]] => [5,4,2,2] => [4,4,2,2,1]
[[6,5,4,2,2],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[7,6,5,3,2],[6,5,3,2]] => [6,5,3,2] => [4,4,3,2,2,1]
[[2,2,2,1,1,1],[1,1]] => [1,1] => [2]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[3,3,3,2,1,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[3,3,3,1,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[4,4,4,2,1,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[3,3,2,1,1,1],[2,2]] => [2,2] => [2,2]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [3,3,1,1,1] => [5,2,2]
[[4,4,3,2,1,1],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [4,4,2,2,1] => [5,4,2,2]
[[4,4,3,1,1,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [4,4,2,1,1] => [5,3,2,2]
[[5,5,4,2,1,1],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [5,5,3,2,1] => [5,4,3,2,2]
[[3,2,2,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[4,3,3,2,1,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[4,3,3,1,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[5,4,4,2,1,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[4,3,2,1,1,1],[3,2]] => [3,2] => [2,2,1]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [4,3,1,1,1] => [5,2,2,1]
[[5,4,3,2,1,1],[4,3,1,1]] => [4,3,1,1] => [4,2,2,1]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [5,4,2,2,1] => [5,4,2,2,1]
[[5,4,3,1,1,1],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [5,4,2,1,1] => [5,3,2,2,1]
[[6,5,4,2,1,1],[5,4,2,1]] => [5,4,2,1] => [4,3,2,2,1]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [6,5,3,2,1] => [5,4,3,2,2,1]
[[4,4,4,4],[3,3,3]] => [3,3,3] => [3,3,3]
[[5,5,5,4],[4,4,4]] => [4,4,4] => [3,3,3,3]
[[5,5,4,4],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[6,6,5,4],[5,5,4]] => [5,5,4] => [3,3,3,3,2]
[[5,4,4,4],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[6,5,5,4],[5,4,4]] => [5,4,4] => [3,3,3,3,1]
[[6,5,4,4],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[7,6,5,4],[6,5,4]] => [6,5,4] => [3,3,3,3,2,1]
[[3,3,3,3,1],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,4,1],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[4,4,4,3,1],[3,3,3]] => [3,3,3] => [3,3,3]
[[5,5,5,4,1],[4,4,4,1]] => [4,4,4,1] => [4,3,3,3]
[[4,4,3,3,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,4,1],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[5,5,4,3,1],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[6,6,5,4,1],[5,5,4,1]] => [5,5,4,1] => [4,3,3,3,2]
[[4,3,3,3,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4,4,1],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[5,4,4,3,1],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[6,5,5,4,1],[5,4,4,1]] => [5,4,4,1] => [4,3,3,3,1]
[[5,4,3,3,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,4,4,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[6,5,4,3,1],[5,4,3]] => [5,4,3] => [3,3,3,2,1]
[[7,6,5,4,1],[6,5,4,1]] => [6,5,4,1] => [4,3,3,3,2,1]
[[2,2,2,2,2],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,4,2],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[3,3,3,2,2],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,3,2],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[5,5,5,4,2],[4,4,4,2]] => [4,4,4,2] => [4,4,3,3]
[[3,3,2,2,2],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,3,2],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,4,2],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[4,4,3,2,2],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,3,2],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[6,6,5,4,2],[5,5,4,2]] => [5,5,4,2] => [4,4,3,3,2]
[[3,2,2,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,3,2],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,4,2],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[4,3,3,2,2],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4,3,2],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[6,5,5,4,2],[5,4,4,2]] => [5,4,4,2] => [4,4,3,3,1]
[[4,3,2,2,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,3,2],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,4,4,2],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[5,4,3,2,2],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,4,3,2],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[7,6,5,4,2],[6,5,4,2]] => [6,5,4,2] => [4,4,3,3,2,1]
[[2,2,2,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[3,3,3,3,1,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[3,3,3,2,1,1],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [3,3,3,1,1] => [5,3,3]
[[4,4,4,3,1,1],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [4,4,4,2,1] => [5,4,3,3]
[[3,3,2,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[4,4,3,3,1,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[4,4,3,2,1,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [4,4,3,1,1] => [5,3,3,2]
[[5,5,4,3,1,1],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [5,5,4,2,1] => [5,4,3,3,2]
[[3,2,2,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[4,3,3,3,1,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[4,3,3,2,1,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [4,3,3,1,1] => [5,3,3,1]
[[5,4,4,3,1,1],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [5,4,4,2,1] => [5,4,3,3,1]
[[4,3,2,2,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[5,4,3,3,1,1],[4,3,2,1]] => [4,3,2,1] => [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]
[[5,4,3,2,1,1],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [5,4,3,1,1] => [5,3,3,2,1]
[[6,5,4,3,1,1],[5,4,3,1]] => [5,4,3,1] => [4,3,3,2,1]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [6,5,4,2,1] => [5,4,3,3,2,1]
[[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [4,4]
[[4,4,4,4,3],[3,3,3,3]] => [3,3,3,3] => [4,4,4]
[[4,4,4,3,3],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[5,5,5,4,3],[4,4,4,3]] => [4,4,4,3] => [4,4,4,3]
[[4,4,3,3,3],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[5,5,4,4,3],[4,4,3,3]] => [4,4,3,3] => [4,4,4,2]
[[5,5,4,3,3],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[6,6,5,4,3],[5,5,4,3]] => [5,5,4,3] => [4,4,4,3,2]
[[4,3,3,3,3],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[5,4,4,4,3],[4,3,3,3]] => [4,3,3,3] => [4,4,4,1]
[[5,4,4,3,3],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[6,5,5,4,3],[5,4,4,3]] => [5,4,4,3] => [4,4,4,3,1]
[[5,4,3,3,3],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[6,5,4,4,3],[5,4,3,3]] => [5,4,3,3] => [4,4,4,2,1]
[[6,5,4,3,3],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[7,6,5,4,3],[6,5,4,3]] => [6,5,4,3] => [4,4,4,3,2,1]
[[2,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[3,3,3,3,2,1],[2,2,2,2]] => [2,2,2,2] => [4,4]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [3,3,3,3,1] => [5,4,4]
[[3,3,3,2,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[4,4,4,3,2,1],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [4,4,4,3,1] => [5,4,4,3]
[[3,3,2,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[4,4,3,3,2,1],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [4,4,3,3,1] => [5,4,4,2]
[[4,4,3,2,2,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[5,5,4,3,2,1],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [5,5,4,3,1] => [5,4,4,3,2]
[[3,2,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[4,3,3,3,2,1],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [4,3,3,3,1] => [5,4,4,1]
[[4,3,3,2,2,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[5,4,4,3,2,1],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [5,4,4,3,1] => [5,4,4,3,1]
[[4,3,2,2,2,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[5,4,3,3,2,1],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [5,4,3,3,1] => [5,4,4,2,1]
[[5,4,3,2,2,1],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[6,5,4,3,2,1],[5,4,3,2]] => [5,4,3,2] => [4,4,3,2,1]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [6,5,4,3,1] => [5,4,4,3,2,1]
[[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[3,3,3,3,3,2],[2,2,2,2,2]] => [2,2,2,2,2] => [5,5]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [3,3,3,3,2] => [5,5,4]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [3,3,3,2,2] => [5,5,3]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [4,4,4,3,2] => [5,5,4,3]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [3,3,2,2,2] => [5,5,2]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [4,4,3,3,2] => [5,5,4,2]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [4,4,3,2,2] => [5,5,3,2]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [5,5,4,3,2] => [5,5,4,3,2]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [3,2,2,2,2] => [5,5,1]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [4,3,3,3,2] => [5,5,4,1]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [4,3,3,2,2] => [5,5,3,1]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [5,4,4,3,2] => [5,5,4,3,1]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [4,3,2,2,2] => [5,5,2,1]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [5,4,3,3,2] => [5,5,4,2,1]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [5,4,3,2,2] => [5,5,3,2,1]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [5,4,3,2,1] => [5,4,3,2,1]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [6,5,4,3,2] => [5,5,4,3,2,1]
[[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] => [6]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => [6,5]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [2,2,2,2,1,1] => [6,4]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [3,3,3,3,2,1] => [6,5,4]
[[2,2,2,1,1,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [2,2,2,1,1,1] => [6,3]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [3,3,3,2,2,1] => [6,5,3]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [3,3,3,2,1,1] => [6,4,3]
[[4,4,4,3,2,1,1],[3,3,3,2,1]] => [3,3,3,2,1] => [5,4,3]
[[5,5,5,4,3,2,1],[4,4,4,3,2,1]] => [4,4,4,3,2,1] => [6,5,4,3]
[[2,2,1,1,1,1,1],[1,1]] => [1,1] => [2]
[[3,3,2,2,2,2,1],[2,2,1,1,1,1]] => [2,2,1,1,1,1] => [6,2]
[[3,3,2,2,2,1,1],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[4,4,3,3,3,2,1],[3,3,2,2,2,1]] => [3,3,2,2,2,1] => [6,5,2]
[[3,3,2,2,1,1,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,3,3,2,2,1],[3,3,2,2,1,1]] => [3,3,2,2,1,1] => [6,4,2]
[[4,4,3,3,2,1,1],[3,3,2,2,1]] => [3,3,2,2,1] => [5,4,2]
[[5,5,4,4,3,2,1],[4,4,3,3,2,1]] => [4,4,3,3,2,1] => [6,5,4,2]
[[3,3,2,1,1,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,2,2,2,1],[3,3,2,1,1,1]] => [3,3,2,1,1,1] => [6,3,2]
[[4,4,3,2,2,1,1],[3,3,2,1,1]] => [3,3,2,1,1] => [5,3,2]
[[5,5,4,3,3,2,1],[4,4,3,2,2,1]] => [4,4,3,2,2,1] => [6,5,3,2]
[[4,4,3,2,1,1,1],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,5,4,3,2,2,1],[4,4,3,2,1,1]] => [4,4,3,2,1,1] => [6,4,3,2]
[[5,5,4,3,2,1,1],[4,4,3,2,1]] => [4,4,3,2,1] => [5,4,3,2]
[[6,6,5,4,3,2,1],[5,5,4,3,2,1]] => [5,5,4,3,2,1] => [6,5,4,3,2]
[[2,1,1,1,1,1,1],[1]] => [1] => [1]
[[3,2,2,2,2,2,1],[2,1,1,1,1,1]] => [2,1,1,1,1,1] => [6,1]
[[3,2,2,2,2,1,1],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[4,3,3,3,3,2,1],[3,2,2,2,2,1]] => [3,2,2,2,2,1] => [6,5,1]
[[3,2,2,2,1,1,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,3,3,2,2,1],[3,2,2,2,1,1]] => [3,2,2,2,1,1] => [6,4,1]
[[4,3,3,3,2,1,1],[3,2,2,2,1]] => [3,2,2,2,1] => [5,4,1]
[[5,4,4,4,3,2,1],[4,3,3,3,2,1]] => [4,3,3,3,2,1] => [6,5,4,1]
[[3,2,2,1,1,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,2,2,2,1],[3,2,2,1,1,1]] => [3,2,2,1,1,1] => [6,3,1]
[[4,3,3,2,2,1,1],[3,2,2,1,1]] => [3,2,2,1,1] => [5,3,1]
[[5,4,4,3,3,2,1],[4,3,3,2,2,1]] => [4,3,3,2,2,1] => [6,5,3,1]
[[4,3,3,2,1,1,1],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,4,4,3,2,2,1],[4,3,3,2,1,1]] => [4,3,3,2,1,1] => [6,4,3,1]
[[5,4,4,3,2,1,1],[4,3,3,2,1]] => [4,3,3,2,1] => [5,4,3,1]
[[6,5,5,4,3,2,1],[5,4,4,3,2,1]] => [5,4,4,3,2,1] => [6,5,4,3,1]
[[3,2,1,1,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,2,2,2,2,1],[3,2,1,1,1,1]] => [3,2,1,1,1,1] => [6,2,1]
[[4,3,2,2,2,1,1],[3,2,1,1,1]] => [3,2,1,1,1] => [5,2,1]
[[5,4,3,3,3,2,1],[4,3,2,2,2,1]] => [4,3,2,2,2,1] => [6,5,2,1]
[[4,3,2,2,1,1,1],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,4,3,3,2,2,1],[4,3,2,2,1,1]] => [4,3,2,2,1,1] => [6,4,2,1]
[[5,4,3,3,2,1,1],[4,3,2,2,1]] => [4,3,2,2,1] => [5,4,2,1]
[[6,5,4,4,3,2,1],[5,4,3,3,2,1]] => [5,4,3,3,2,1] => [6,5,4,2,1]
[[4,3,2,1,1,1,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,3,2,2,2,1],[4,3,2,1,1,1]] => [4,3,2,1,1,1] => [6,3,2,1]
[[5,4,3,2,2,1,1],[4,3,2,1,1]] => [4,3,2,1,1] => [5,3,2,1]
[[6,5,4,3,3,2,1],[5,4,3,2,2,1]] => [5,4,3,2,2,1] => [6,5,3,2,1]
[[5,4,3,2,1,1,1],[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]] => [5,4,3,2,1,1] => [6,4,3,2,1]
[[6,5,4,3,2,1,1],[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]] => [6,5,4,3,2,1] => [6,5,4,3,2,1]
[[8],[]] => [] => []
[[7,1],[]] => [] => []
[[6,2],[]] => [] => []
[[6,1,1],[]] => [] => []
[[5,3],[]] => [] => []
[[5,2,1],[]] => [] => []
[[5,1,1,1],[]] => [] => []
[[4,4],[]] => [] => []
[[4,3,1],[]] => [] => []
[[4,2,2],[]] => [] => []
[[4,2,1,1],[]] => [] => []
[[4,1,1,1,1],[]] => [] => []
[[3,3,2],[]] => [] => []
[[3,3,1,1],[]] => [] => []
[[3,2,2,1],[]] => [] => []
[[3,2,1,1,1],[]] => [] => []
[[3,1,1,1,1,1],[]] => [] => []
[[2,2,2,2],[]] => [] => []
[[2,2,2,1,1],[]] => [] => []
[[2,2,1,1,1,1],[]] => [] => []
[[2,1,1,1,1,1,1],[]] => [] => []
[[1,1,1,1,1,1,1,1],[]] => [] => []
[[9],[]] => [] => []
[[8,1],[]] => [] => []
[[7,2],[]] => [] => []
[[7,1,1],[]] => [] => []
[[6,3],[]] => [] => []
[[6,2,1],[]] => [] => []
[[6,1,1,1],[]] => [] => []
[[5,4],[]] => [] => []
[[5,3,1],[]] => [] => []
[[5,2,2],[]] => [] => []
[[5,2,1,1],[]] => [] => []
[[5,1,1,1,1],[]] => [] => []
[[4,4,1],[]] => [] => []
[[4,3,2],[]] => [] => []
[[4,3,1,1],[]] => [] => []
[[4,2,2,1],[]] => [] => []
[[4,2,1,1,1],[]] => [] => []
[[4,1,1,1,1,1],[]] => [] => []
[[3,3,3],[]] => [] => []
[[3,3,2,1],[]] => [] => []
[[3,3,1,1,1],[]] => [] => []
[[3,2,2,2],[]] => [] => []
[[3,2,2,1,1],[]] => [] => []
[[3,2,1,1,1,1],[]] => [] => []
[[3,1,1,1,1,1,1],[]] => [] => []
[[2,2,2,2,1],[]] => [] => []
[[2,2,2,1,1,1],[]] => [] => []
[[2,2,1,1,1,1,1],[]] => [] => []
[[2,1,1,1,1,1,1,1],[]] => [] => []
[[1,1,1,1,1,1,1,1,1],[]] => [] => []
[[10],[]] => [] => []
[[9,1],[]] => [] => []
[[8,2],[]] => [] => []
[[8,1,1],[]] => [] => []
[[7,3],[]] => [] => []
[[7,2,1],[]] => [] => []
[[7,1,1,1],[]] => [] => []
[[6,4],[]] => [] => []
[[6,3,1],[]] => [] => []
[[6,2,2],[]] => [] => []
[[6,2,1,1],[]] => [] => []
[[6,1,1,1,1],[]] => [] => []
[[5,5],[]] => [] => []
[[5,4,1],[]] => [] => []
[[5,3,2],[]] => [] => []
[[5,3,1,1],[]] => [] => []
[[5,2,2,1],[]] => [] => []
[[5,2,1,1,1],[]] => [] => []
[[5,1,1,1,1,1],[]] => [] => []
[[4,4,2],[]] => [] => []
[[4,4,1,1],[]] => [] => []
[[4,3,3],[]] => [] => []
[[4,3,2,1],[]] => [] => []
[[4,3,1,1,1],[]] => [] => []
[[4,2,2,2],[]] => [] => []
[[4,2,2,1,1],[]] => [] => []
[[4,2,1,1,1,1],[]] => [] => []
[[4,1,1,1,1,1,1],[]] => [] => []
[[3,3,3,1],[]] => [] => []
[[3,3,2,2],[]] => [] => []
[[3,3,2,1,1],[]] => [] => []
[[3,3,1,1,1,1],[]] => [] => []
[[3,2,2,2,1],[]] => [] => []
[[3,2,2,1,1,1],[]] => [] => []
[[3,2,1,1,1,1,1],[]] => [] => []
[[3,1,1,1,1,1,1,1],[]] => [] => []
[[2,2,2,2,2],[]] => [] => []
[[2,2,2,2,1,1],[]] => [] => []
[[2,2,2,1,1,1,1],[]] => [] => []
[[2,2,1,1,1,1,1,1],[]] => [] => []
[[2,1,1,1,1,1,1,1,1],[]] => [] => []
[[1,1,1,1,1,1,1,1,1,1],[]] => [] => []
[[6,5],[]] => [] => []
[[5,5,1],[]] => [] => []
[[5,4,2],[]] => [] => []
[[5,3,3],[]] => [] => []
[[4,4,3],[]] => [] => []
[[4,4,2,1],[]] => [] => []
[[4,3,3,1],[]] => [] => []
[[4,3,2,2],[]] => [] => []
[[3,3,3,2],[]] => [] => []
[[3,2,2,2,2],[]] => [] => []
[[6,6],[]] => [] => []
[[5,5,2],[]] => [] => []
[[5,4,3],[]] => [] => []
[[4,4,4],[]] => [] => []
[[4,4,3,1],[]] => [] => []
[[4,4,2,2],[]] => [] => []
[[4,3,3,2],[]] => [] => []
[[3,3,3,3],[]] => [] => []
[[3,3,3,2,1],[]] => [] => []
[[3,3,2,2,2],[]] => [] => []
[[2,2,2,2,2,2],[]] => [] => []
[[5,5,3],[]] => [] => []
[[5,4,4],[]] => [] => []
[[4,4,4,1],[]] => [] => []
[[4,4,3,2],[]] => [] => []
[[4,3,3,3],[]] => [] => []
[[3,3,3,3,1],[]] => [] => []
[[3,3,3,2,2],[]] => [] => []
[[5,5,4],[]] => [] => []
[[4,4,4,2],[]] => [] => []
[[4,4,3,3],[]] => [] => []
[[3,3,3,3,2],[]] => [] => []
[[5,5,5],[]] => [] => []
[[5,5,4,1],[]] => [] => []
[[4,4,4,3],[]] => [] => []
[[3,3,3,3,3],[]] => [] => []
[[5,5,5,1],[]] => [] => []
[[4,4,4,4],[]] => [] => []
[[4,4,4,3,1],[]] => [] => []
[[3,3,3,3,3,1],[]] => [] => []
[[4,4,4,4,1],[]] => [] => []
[[2,2,1,1,1,1,1],[1]] => [1] => [1]
[[2,2,2,1,1,1,1],[1,1]] => [1,1] => [2]
[[3,2,1,1,1,1],[1]] => [1] => [1]
[[2,2,2,2,1,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,2,2,1,1,1],[1,1]] => [1,1] => [2]
[[3,3,2,1,1,1],[2,1]] => [2,1] => [2,1]
[[4,3,1,1,1],[2]] => [2] => [1,1]
[[2,2,2,2,2,1,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,2,2,2,1,1],[1,1,1]] => [1,1,1] => [3]
[[3,3,2,2,1,1],[2,1,1]] => [2,1,1] => [3,1]
[[3,3,3,2,1,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,3,2,1,1],[2,1]] => [2,1] => [2,1]
[[4,4,2,1,1],[3,1]] => [3,1] => [2,1,1]
[[4,3,3,1,1],[2,2]] => [2,2] => [2,2]
[[4,4,3,1,1],[3,2]] => [3,2] => [2,2,1]
[[5,3,1,1],[2]] => [2] => [1,1]
[[2,2,2,2,2,2,1],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[3,2,2,2,2,1],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,2,2,2,1],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[3,3,3,2,2,1],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,3,2,2,1],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,2,2,1],[3,1,1]] => [3,1,1] => [3,1,1]
[[3,3,3,3,2,1],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,3,3,2,1],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,3,2,1],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,3,2,1],[2,1]] => [2,1] => [2,1]
[[4,4,4,2,1],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,4,2,1],[3,1]] => [3,1] => [2,1,1]
[[4,3,3,3,1],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,3,3,1],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,3,3,1],[2,2]] => [2,2] => [2,2]
[[4,4,4,3,1],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,4,3,1],[3,2]] => [3,2] => [2,2,1]
[[5,5,3,1],[4,2]] => [4,2] => [2,2,1,1]
[[4,4,4,4,1],[3,3,3]] => [3,3,3] => [3,3,3]
[[5,4,4,1],[3,3]] => [3,3] => [2,2,2]
[[5,5,4,1],[4,3]] => [4,3] => [2,2,2,1]
[[6,4,1],[3]] => [3] => [1,1,1]
[[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [6]
[[3,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[3,3,2,2,2,2],[2,1,1,1,1]] => [2,1,1,1,1] => [5,1]
[[3,3,3,2,2,2],[2,2,1,1,1]] => [2,2,1,1,1] => [5,2]
[[4,3,2,2,2],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,4,2,2,2],[3,1,1,1]] => [3,1,1,1] => [4,1,1]
[[3,3,3,3,2,2],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[4,3,3,2,2],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,3,2,2],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[5,3,2,2],[2,1,1]] => [2,1,1] => [3,1]
[[4,4,4,2,2],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[5,4,2,2],[3,1,1]] => [3,1,1] => [3,1,1]
[[3,3,3,3,3,2],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[4,3,3,3,2],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[4,4,3,3,2],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,3,3,2],[2,2,1]] => [2,2,1] => [3,2]
[[4,4,4,3,2],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[5,4,3,2],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,3,2],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[4,4,4,4,2],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[5,4,4,2],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,4,2],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[6,4,2],[3,1]] => [3,1] => [2,1,1]
[[5,5,5,2],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[6,5,2],[4,1]] => [4,1] => [2,1,1,1]
[[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2] => [5,5]
[[4,4,3,3,3],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[5,3,3,3],[2,2,2]] => [2,2,2] => [3,3]
[[4,4,4,3,3],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[5,4,3,3],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,5,3,3],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[4,4,4,4,3],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[5,4,4,3],[3,3,2]] => [3,3,2] => [3,3,2]
[[5,5,4,3],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[6,4,3],[3,2]] => [3,2] => [2,2,1]
[[5,5,5,3],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[6,5,3],[4,2]] => [4,2] => [2,2,1,1]
[[6,6,3],[5,2]] => [5,2] => [2,2,1,1,1]
[[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3] => [4,4,4]
[[5,4,4,4],[3,3,3]] => [3,3,3] => [3,3,3]
[[5,5,4,4],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[6,4,4],[3,3]] => [3,3] => [2,2,2]
[[5,5,5,4],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[6,5,4],[4,3]] => [4,3] => [2,2,2,1]
[[6,6,4],[5,3]] => [5,3] => [2,2,2,1,1]
[[7,4],[3]] => [3] => [1,1,1]
[[5,5,5,5],[4,4,4]] => [4,4,4] => [3,3,3,3]
[[6,6,6],[5,5]] => [5,5] => [2,2,2,2,2]
[[7,7],[6]] => [6] => [1,1,1,1,1,1]
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1] => [7]
[[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2] => [6,6]
[[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3] => [5,5,5]
[[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4] => [4,4,4,4]
[[6,6,6,6],[5,5,5]] => [5,5,5] => [3,3,3,3,3]
[[7,7,7],[6,6]] => [6,6] => [2,2,2,2,2,2]
[[8,8],[7]] => [7] => [1,1,1,1,1,1,1]
[[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] => [8]
[[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2] => [7,7]
[[4,4,4,4,4,4,4],[3,3,3,3,3,3]] => [3,3,3,3,3,3] => [6,6,6]
[[5,5,5,5,5,5],[4,4,4,4,4]] => [4,4,4,4,4] => [5,5,5,5]
[[6,6,6,6,6],[5,5,5,5]] => [5,5,5,5] => [4,4,4,4,4]
[[7,7,7,7],[6,6,6]] => [6,6,6] => [3,3,3,3,3,3]
[[8,8,8],[7,7]] => [7,7] => [2,2,2,2,2,2,2]
[[9,9],[8]] => [8] => [1,1,1,1,1,1,1,1]
[[3,3,3],[1]] => [1] => [1]
[[3,3,3,1],[1,1]] => [1,1] => [2]
[[4,4,1],[1]] => [1] => [1]
[[3,3,2,1],[1]] => [1] => [1]
[[2,2,2,2,1],[1]] => [1] => [1]
[[3,3,3,1],[2]] => [2] => [1,1]
[[3,3,3,1],[1]] => [1] => [1]
[[3,3,3,2],[1,1,1]] => [1,1,1] => [3]
[[4,4,2],[1,1]] => [1,1] => [2]
[[4,4,4],[2,2]] => [2,2] => [2,2]
[[5,5],[2]] => [2] => [1,1]
[[4,4,3],[2,1]] => [2,1] => [2,1]
[[3,3,3,3],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3],[1,1]] => [1,1] => [2]
[[3,3,3,3],[1,1,1]] => [1,1,1] => [3]
[[4,4,3],[1,1]] => [1,1] => [2]
[[4,4,4],[3,1]] => [3,1] => [2,1,1]
[[5,4],[1]] => [1] => [1]
[[4,4,4],[2,1]] => [2,1] => [2,1]
[[5,5],[1]] => [1] => [1]
[[4,4,4],[1,1]] => [1,1] => [2]
[[3,3,2,2],[1,1]] => [1,1] => [2]
[[4,4,2],[2]] => [2] => [1,1]
[[3,3,3,2],[2,1]] => [2,1] => [2,1]
[[4,3,2],[1]] => [1] => [1]
[[3,3,3,2],[1,1]] => [1,1] => [2]
[[4,4,2],[1]] => [1] => [1]
[[2,2,2,2,2],[1,1]] => [1,1] => [2]
[[3,2,2,2],[1]] => [1] => [1]
[[3,3,2,2],[2]] => [2] => [1,1]
[[3,3,2,2],[1]] => [1] => [1]
[[2,2,2,2,2],[1]] => [1] => [1]
[[3,3,3,2],[2]] => [2] => [1,1]
[[3,3,3,2],[1]] => [1] => [1]
[[3,3,3,3],[2,2]] => [2,2] => [2,2]
[[4,3,3],[2]] => [2] => [1,1]
[[4,4,3],[3]] => [3] => [1,1,1]
[[4,4,3],[2]] => [2] => [1,1]
[[3,3,3,3],[2,1]] => [2,1] => [2,1]
[[4,3,3],[1]] => [1] => [1]
[[3,3,3,3],[1,1]] => [1,1] => [2]
[[4,4,3],[1]] => [1] => [1]
[[4,4,4],[3]] => [3] => [1,1,1]
[[4,4,4],[2]] => [2] => [1,1]
[[4,4,4],[1]] => [1] => [1]
[[3,3,3,3],[2]] => [2] => [1,1]
[[3,3,3,3],[1]] => [1] => [1]
[[4,4,4,1],[1,1]] => [1,1] => [2]
[[4,4,3,1],[1]] => [1] => [1]
[[4,4,4,1],[2]] => [2] => [1,1]
[[4,4,4,1],[1]] => [1] => [1]
[[3,3,3,3,1],[1]] => [1] => [1]
[[4,4,4,2],[1,1,1]] => [1,1,1] => [3]
[[6,6],[4]] => [4] => [1,1,1,1]
[[5,5,5],[4,3]] => [4,3] => [2,2,2,1]
[[6,5],[3]] => [3] => [1,1,1]
[[5,5,5],[3,3]] => [3,3] => [2,2,2]
[[6,6],[3]] => [3] => [1,1,1]
[[4,4,4,4],[3,3,2]] => [3,3,2] => [3,3,2]
[[6,4],[2]] => [2] => [1,1]
[[5,5,4],[3,2]] => [3,2] => [2,2,1]
[[4,4,4,4],[3,2,2]] => [3,2,2] => [3,3,1]
[[5,4,4],[2,2]] => [2,2] => [2,2]
[[4,4,4,4],[2,2,2]] => [2,2,2] => [3,3]
[[5,5,4],[2,2]] => [2,2] => [2,2]
[[5,5,5],[4,2]] => [4,2] => [2,2,1,1]
[[6,5],[2]] => [2] => [1,1]
[[5,5,5],[3,2]] => [3,2] => [2,2,1]
[[6,6],[2]] => [2] => [1,1]
[[5,5,5],[2,2]] => [2,2] => [2,2]
[[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1] => [4,3]
[[6,3],[1]] => [1] => [1]
[[5,5,3],[3,1]] => [3,1] => [2,1,1]
[[5,4,3],[2,1]] => [2,1] => [2,1]
[[4,4,4,3],[2,2,1]] => [2,2,1] => [3,2]
[[5,5,3],[2,1]] => [2,1] => [2,1]
[[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[5,3,3],[1,1]] => [1,1] => [2]
[[4,4,3,3],[2,1,1]] => [2,1,1] => [3,1]
[[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1] => [4,1]
[[4,3,3,3],[1,1,1]] => [1,1,1] => [3]
[[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1] => [4]
[[4,4,3,3],[1,1,1]] => [1,1,1] => [3]
[[5,4,3],[1,1]] => [1,1] => [2]
[[4,4,4,3],[2,1,1]] => [2,1,1] => [3,1]
[[5,5,3],[1,1]] => [1,1] => [2]
[[4,4,4,3],[1,1,1]] => [1,1,1] => [3]
[[4,4,4,4],[3,3,1]] => [3,3,1] => [3,2,2]
[[6,4],[1]] => [1] => [1]
[[5,5,4],[3,1]] => [3,1] => [2,1,1]
[[4,4,4,4],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,4,4],[2,1]] => [2,1] => [2,1]
[[4,4,4,4],[2,2,1]] => [2,2,1] => [3,2]
[[5,5,4],[2,1]] => [2,1] => [2,1]
[[5,5,5],[4,1]] => [4,1] => [2,1,1,1]
[[6,5],[1]] => [1] => [1]
[[5,5,5],[3,1]] => [3,1] => [2,1,1]
[[6,6],[1]] => [1] => [1]
[[5,5,5],[2,1]] => [2,1] => [2,1]
[[4,4,4,4],[3,1,1]] => [3,1,1] => [3,1,1]
[[5,4,4],[1,1]] => [1,1] => [2]
[[4,4,4,4],[2,1,1]] => [2,1,1] => [3,1]
[[5,5,4],[1,1]] => [1,1] => [2]
[[4,4,4,4],[1,1,1]] => [1,1,1] => [3]
[[5,5,5],[1,1]] => [1,1] => [2]
[[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [4]
[[5,5,2],[3]] => [3] => [1,1,1]
[[5,4,2],[2]] => [2] => [1,1]
[[4,4,4,2],[2,2]] => [2,2] => [2,2]
[[5,5,2],[2]] => [2] => [1,1]
[[5,3,2],[1]] => [1] => [1]
[[4,4,3,2],[2,1]] => [2,1] => [2,1]
[[4,3,3,2],[1,1]] => [1,1] => [2]
[[3,3,3,3,2],[1,1,1]] => [1,1,1] => [3]
[[4,4,3,2],[1,1]] => [1,1] => [2]
[[5,4,2],[1]] => [1] => [1]
[[4,4,4,2],[2,1]] => [2,1] => [2,1]
[[5,5,2],[1]] => [1] => [1]
[[4,4,4,2],[1,1]] => [1,1] => [2]
[[2,2,2,2,2,2],[1,1,1]] => [1,1,1] => [3]
[[4,4,2,2],[2]] => [2] => [1,1]
[[4,3,2,2],[1]] => [1] => [1]
[[3,3,3,2,2],[1,1]] => [1,1] => [2]
[[4,4,2,2],[1]] => [1] => [1]
[[2,2,2,2,2,2],[1,1]] => [1,1] => [2]
[[3,3,2,2,2],[1]] => [1] => [1]
[[3,3,3,2,2],[1]] => [1] => [1]
[[4,4,3,2],[2]] => [2] => [1,1]
[[4,3,3,2],[1]] => [1] => [1]
[[3,3,3,3,2],[1,1]] => [1,1] => [2]
[[4,4,3,2],[1]] => [1] => [1]
[[4,4,4,2],[3]] => [3] => [1,1,1]
[[4,4,4,2],[2]] => [2] => [1,1]
[[4,4,4,2],[1]] => [1] => [1]
[[3,3,3,3,2],[2]] => [2] => [1,1]
[[3,3,3,3,2],[1]] => [1] => [1]
[[3,3,3,3,3],[2,2,2]] => [2,2,2] => [3,3]
[[5,5,3],[3]] => [3] => [1,1,1]
[[5,4,3],[2]] => [2] => [1,1]
[[4,4,4,3],[2,2]] => [2,2] => [2,2]
[[5,5,3],[2]] => [2] => [1,1]
[[3,3,3,3,3],[2,2,1]] => [2,2,1] => [3,2]
[[5,3,3],[1]] => [1] => [1]
[[4,4,3,3],[2,1]] => [2,1] => [2,1]
[[3,3,3,3,3],[2,1,1]] => [2,1,1] => [3,1]
[[4,3,3,3],[1,1]] => [1,1] => [2]
[[3,3,3,3,3],[1,1,1]] => [1,1,1] => [3]
[[4,4,3,3],[1,1]] => [1,1] => [2]
[[4,4,4,3],[3,1]] => [3,1] => [2,1,1]
[[5,4,3],[1]] => [1] => [1]
[[4,4,4,3],[2,1]] => [2,1] => [2,1]
[[5,5,3],[1]] => [1] => [1]
[[4,4,4,3],[1,1]] => [1,1] => [2]
[[4,4,4,4],[3,3]] => [3,3] => [2,2,2]
[[5,5,4],[3]] => [3] => [1,1,1]
[[4,4,4,4],[3,2]] => [3,2] => [2,2,1]
[[5,4,4],[2]] => [2] => [1,1]
[[4,4,4,4],[2,2]] => [2,2] => [2,2]
[[5,5,4],[2]] => [2] => [1,1]
[[5,5,5],[4]] => [4] => [1,1,1,1]
[[5,5,5],[3]] => [3] => [1,1,1]
[[5,5,5],[2]] => [2] => [1,1]
[[4,4,4,4],[3,1]] => [3,1] => [2,1,1]
[[5,4,4],[1]] => [1] => [1]
[[4,4,4,4],[2,1]] => [2,1] => [2,1]
[[5,5,4],[1]] => [1] => [1]
[[4,4,4,4],[1,1]] => [1,1] => [2]
[[5,5,5],[1]] => [1] => [1]
[[3,3,3,3,3],[2,2]] => [2,2] => [2,2]
[[4,3,3,3],[2]] => [2] => [1,1]
[[4,4,3,3],[3]] => [3] => [1,1,1]
[[4,4,3,3],[2]] => [2] => [1,1]
[[3,3,3,3,3],[2,1]] => [2,1] => [2,1]
[[4,3,3,3],[1]] => [1] => [1]
[[3,3,3,3,3],[1,1]] => [1,1] => [2]
[[4,4,3,3],[1]] => [1] => [1]
[[4,4,4,3],[3]] => [3] => [1,1,1]
[[4,4,4,3],[2]] => [2] => [1,1]
[[4,4,4,3],[1]] => [1] => [1]
[[3,3,3,3,3],[2]] => [2] => [1,1]
[[3,3,3,3,3],[1]] => [1] => [1]
[[4,4,4,4],[3]] => [3] => [1,1,1]
[[4,4,4,4],[2]] => [2] => [1,1]
[[4,4,4,4],[1]] => [1] => [1]
[[5,5,5,1],[1]] => [1] => [1]
[[4,4,4,4,1],[1]] => [1] => [1]
[[7,7],[5]] => [5] => [1,1,1,1,1]
[[6,6,6],[5,4]] => [5,4] => [2,2,2,2,1]
[[6,6,6],[4,4]] => [4,4] => [2,2,2,2]
[[7,7],[4]] => [4] => [1,1,1,1]
[[5,5,5,5],[4,4,3]] => [4,4,3] => [3,3,3,2]
[[5,5,5,5],[4,3,3]] => [4,3,3] => [3,3,3,1]
[[5,5,5,5],[3,3,3]] => [3,3,3] => [3,3,3]
[[6,6,6],[5,3]] => [5,3] => [2,2,2,1,1]
[[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2] => [4,4,3]
[[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2] => [4,4,2]
[[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2] => [4,4,1]
[[5,5,5,5],[4,4,2]] => [4,4,2] => [3,3,2,2]
[[5,5,5,5],[4,3,2]] => [4,3,2] => [3,3,2,1]
[[5,5,5,5],[3,3,2]] => [3,3,2] => [3,3,2]
[[6,6,6],[4,2]] => [4,2] => [2,2,1,1]
[[5,5,5,5],[4,2,2]] => [4,2,2] => [3,3,1,1]
[[5,5,5,5],[3,2,2]] => [3,2,2] => [3,3,1]
[[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1] => [5,4]
[[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1] => [5,3]
[[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1] => [4,3,3]
[[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1] => [4,3,2]
[[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1] => [4,3,1]
[[5,5,5,5],[4,4,1]] => [4,4,1] => [3,2,2,2]
[[5,5,5,5],[4,3,1]] => [4,3,1] => [3,2,2,1]
[[5,5,5,5],[3,3,1]] => [3,3,1] => [3,2,2]
[[5,5,5,5],[4,2,1]] => [4,2,1] => [3,2,1,1]
[[5,5,5,5],[3,2,1]] => [3,2,1] => [3,2,1]
[[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1] => [4,2,2]
[[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1] => [4,2,1]
[[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1] => [5]
[[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1] => [4]
[[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2] => [4,4]
[[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1] => [4,2]
[[4,4,4,4,4],[3,3,3]] => [3,3,3] => [3,3,3]
[[4,4,4,4,4],[3,3,2]] => [3,3,2] => [3,3,2]
[[4,4,4,4,4],[3,2,2]] => [3,2,2] => [3,3,1]
[[4,4,4,4,4],[3,3,1]] => [3,3,1] => [3,2,2]
[[4,4,4,4,4],[3,2,1]] => [3,2,1] => [3,2,1]
[[5,5,5,5],[4,1]] => [4,1] => [2,1,1,1]
[[3,3,3,3,3,3],[2]] => [2] => [1,1]
[[4,4,4,4,3],[3]] => [3] => [1,1,1]
[[5,5,5,4],[4]] => [4] => [1,1,1,1]
[[4,4,4,4,4],[3,1]] => [3,1] => [2,1,1]
[[5,5,5,5],[4]] => [4] => [1,1,1,1]
[[4,4,4,4,4],[3]] => [3] => [1,1,1]
[[8,8],[6]] => [6] => [1,1,1,1,1,1]
[[7,7,7],[6,5]] => [6,5] => [2,2,2,2,2,1]
[[6,6,6,6],[5,5,4]] => [5,5,4] => [3,3,3,3,2]
[[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3] => [4,4,4,3]
[[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2] => [5,5,4]
[[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1] => [6,5]
[[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1] => [6]
[[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1] => [4,3,2,1]
[[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2] => [4,4,2,1]
[[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1] => [4,3,3,1]
[[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2] => [4,4,3,1]
[[5,5,5,5,5],[4,3,3,3]] => [4,3,3,3] => [4,4,4,1]
[[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1] => [4,3,2,2]
[[5,5,5,5,5],[4,4,2,2]] => [4,4,2,2] => [4,4,2,2]
[[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1] => [4,3,3,2]
[[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2] => [4,4,3,2]
[[5,5,5,5,5],[4,4,3,3]] => [4,4,3,3] => [4,4,4,2]
[[5,5,5,5,5],[4,4,4,1]] => [4,4,4,1] => [4,3,3,3]
[[5,5,5,5,5],[4,4,4,2]] => [4,4,4,2] => [4,4,3,3]
[[5,5,5,5,5],[4]] => [4] => [1,1,1,1]
[[5,5,5,5,1],[]] => [] => []
[[5,5,5,5,5,5],[4]] => [4] => [1,1,1,1]
[[4,4,4,4,4,4],[3]] => [3] => [1,1,1]
[[4,4,4,4,4,1],[]] => [] => []
[[5,5,5,5,5,1],[]] => [] => []
[[6,6,6,6,6,6],[5]] => [5] => [1,1,1,1,1]
[[6,6,6,6,6],[5]] => [5] => [1,1,1,1,1]
[[5,5,5,5,4],[4]] => [4] => [1,1,1,1]
[[5,5,5,5,5],[4,1]] => [4,1] => [2,1,1,1]
[[5,5,5,4,1],[]] => [] => []
[[5,5,5,5,1],[1]] => [1] => [1]
[[6,6,6,6,1],[]] => [] => []
[[6,6,6,6,6,1],[]] => [] => []
Map
inner shape
Description
The inner shape of a skew partition.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.
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