Identifier
Mp00182: Skew partitions —outer shape⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00189: Skew partitions —rotate⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Images
[[1],[]] => [1] => [[1],[]] => [[1],[]] => []
[[2],[]] => [2] => [[2],[]] => [[2],[]] => []
[[1,1],[]] => [1,1] => [[1,1],[]] => [[1,1],[]] => []
[[2,1],[1]] => [2,1] => [[2,1],[]] => [[2,2],[1]] => [1]
[[3],[]] => [3] => [[3],[]] => [[3],[]] => []
[[2,1],[]] => [2,1] => [[2,1],[]] => [[2,2],[1]] => [1]
[[3,1],[1]] => [3,1] => [[3,1],[]] => [[3,3],[2]] => [2]
[[2,2],[1]] => [2,2] => [[2,2],[]] => [[2,2],[]] => []
[[3,2],[2]] => [3,2] => [[3,2],[]] => [[3,3],[1]] => [1]
[[1,1,1],[]] => [1,1,1] => [[1,1,1],[]] => [[1,1,1],[]] => []
[[2,2,1],[1,1]] => [2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]] => [1]
[[2,1,1],[1]] => [2,1,1] => [[2,1,1],[]] => [[2,2,2],[1,1]] => [1,1]
[[3,2,1],[2,1]] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1]
[[4],[]] => [4] => [[4],[]] => [[4],[]] => []
[[3,1],[]] => [3,1] => [[3,1],[]] => [[3,3],[2]] => [2]
[[4,1],[1]] => [4,1] => [[4,1],[]] => [[4,4],[3]] => [3]
[[2,2],[]] => [2,2] => [[2,2],[]] => [[2,2],[]] => []
[[3,2],[1]] => [3,2] => [[3,2],[]] => [[3,3],[1]] => [1]
[[4,2],[2]] => [4,2] => [[4,2],[]] => [[4,4],[2]] => [2]
[[2,1,1],[]] => [2,1,1] => [[2,1,1],[]] => [[2,2,2],[1,1]] => [1,1]
[[3,2,1],[1,1]] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1]
[[3,1,1],[1]] => [3,1,1] => [[3,1,1],[]] => [[3,3,3],[2,2]] => [2,2]
[[4,2,1],[2,1]] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2]
[[3,3],[2]] => [3,3] => [[3,3],[]] => [[3,3],[]] => []
[[4,3],[3]] => [4,3] => [[4,3],[]] => [[4,4],[1]] => [1]
[[2,2,1],[1]] => [2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]] => [1]
[[3,3,1],[2,1]] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]] => [2]
[[3,2,1],[2]] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1]
[[4,3,1],[3,1]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[2,2,2],[1,1]] => [2,2,2] => [[2,2,2],[]] => [[2,2,2],[]] => []
[[3,3,2],[2,2]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[3,2,2],[2,1]] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1]
[[4,3,2],[3,2]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[1,1,1,1],[]] => [1,1,1,1] => [[1,1,1,1],[]] => [[1,1,1,1],[]] => []
[[2,2,2,1],[1,1,1]] => [2,2,2,1] => [[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1]
[[2,2,1,1],[1,1]] => [2,2,1,1] => [[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [1,1]
[[3,3,2,1],[2,2,1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[2,1,1,1],[1]] => [2,1,1,1] => [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [1,1,1]
[[3,2,2,1],[2,1,1]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[3,2,1,1],[2,1]] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[4,3,2,1],[3,2,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5],[]] => [5] => [[5],[]] => [[5],[]] => []
[[4,1],[]] => [4,1] => [[4,1],[]] => [[4,4],[3]] => [3]
[[5,1],[1]] => [5,1] => [[5,1],[]] => [[5,5],[4]] => [4]
[[3,2],[]] => [3,2] => [[3,2],[]] => [[3,3],[1]] => [1]
[[4,2],[1]] => [4,2] => [[4,2],[]] => [[4,4],[2]] => [2]
[[5,2],[2]] => [5,2] => [[5,2],[]] => [[5,5],[3]] => [3]
[[3,1,1],[]] => [3,1,1] => [[3,1,1],[]] => [[3,3,3],[2,2]] => [2,2]
[[4,2,1],[1,1]] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2]
[[4,1,1],[1]] => [4,1,1] => [[4,1,1],[]] => [[4,4,4],[3,3]] => [3,3]
[[5,2,1],[2,1]] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3]
[[3,3],[1]] => [3,3] => [[3,3],[]] => [[3,3],[]] => []
[[4,3],[2]] => [4,3] => [[4,3],[]] => [[4,4],[1]] => [1]
[[5,3],[3]] => [5,3] => [[5,3],[]] => [[5,5],[2]] => [2]
[[2,2,1],[]] => [2,2,1] => [[2,2,1],[]] => [[2,2,2],[1]] => [1]
[[3,3,1],[1,1]] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]] => [2]
[[3,2,1],[1]] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1]
[[4,3,1],[2,1]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[4,2,1],[2]] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2]
[[5,3,1],[3,1]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[3,2,2],[1,1]] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1]
[[4,3,2],[2,2]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[4,2,2],[2,1]] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2]
[[5,3,2],[3,2]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[2,1,1,1],[]] => [2,1,1,1] => [[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]] => [1,1,1]
[[3,2,2,1],[1,1,1]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[3,2,1,1],[1,1]] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[4,3,2,1],[2,2,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[3,1,1,1],[1]] => [3,1,1,1] => [[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [2,2,2]
[[4,2,2,1],[2,1,1]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[4,2,1,1],[2,1]] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[5,3,2,1],[3,2,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[4,4],[3]] => [4,4] => [[4,4],[]] => [[4,4],[]] => []
[[5,4],[4]] => [5,4] => [[5,4],[]] => [[5,5],[1]] => [1]
[[3,3,1],[2]] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]] => [2]
[[4,4,1],[3,1]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[4,3,1],[3]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[5,4,1],[4,1]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[2,2,2],[1]] => [2,2,2] => [[2,2,2],[]] => [[2,2,2],[]] => []
[[3,3,2],[2,1]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[4,4,2],[3,2]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[3,2,2],[2]] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1]
[[4,3,2],[3,1]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[5,4,2],[4,2]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[2,2,1,1],[1]] => [2,2,1,1] => [[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [1,1]
[[3,3,2,1],[2,1,1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[3,3,1,1],[2,1]] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2]
[[4,4,2,1],[3,2,1]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[3,2,1,1],[2]] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[4,3,2,1],[3,1,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[4,3,1,1],[3,1]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[5,4,2,1],[4,2,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[3,3,3],[2,2]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[4,4,3],[3,3]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[4,3,3],[3,2]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[5,4,3],[4,3]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[2,2,2,1],[1,1]] => [2,2,2,1] => [[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1]
[[3,3,3,1],[2,2,1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,2,1],[2,2]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[4,4,3,1],[3,3,1]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[3,2,2,1],[2,1]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
>>> Load all 946 entries. <<<
[[4,3,3,1],[3,2,1]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,3,2,1],[3,2]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5,4,3,1],[4,3,1]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[2,2,2,2],[1,1,1]] => [2,2,2,2] => [[2,2,2,2],[]] => [[2,2,2,2],[]] => []
[[3,3,3,2],[2,2,2]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[3,3,2,2],[2,2,1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[3,3,2]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[3,2,2,2],[2,1,1]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,3,3,2],[3,2,2]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[4,3,2,2],[3,2,1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[4,3,2]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[1,1,1,1,1],[]] => [1,1,1,1,1] => [[1,1,1,1,1],[]] => [[1,1,1,1,1],[]] => []
[[2,2,2,2,1],[1,1,1,1]] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1]
[[2,2,2,1,1],[1,1,1]] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1]
[[3,3,3,2,1],[2,2,2,1]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[2,2,1,1,1],[1,1]] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1]
[[3,3,2,2,1],[2,2,1,1]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[3,3,2,1,1],[2,2,1]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[4,4,3,2,1],[3,3,2,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[2,1,1,1,1],[1]] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[3,2,2,2,1],[2,1,1,1]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[3,2,2,1,1],[2,1,1]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,3,2,1],[3,2,2,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[3,2,1,1,1],[2,1]] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[4,3,2,2,1],[3,2,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[4,3,2,1,1],[3,2,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[4,3,2,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[6],[]] => [6] => [[6],[]] => [[6],[]] => []
[[5,1],[]] => [5,1] => [[5,1],[]] => [[5,5],[4]] => [4]
[[6,1],[1]] => [6,1] => [[6,1],[]] => [[6,6],[5]] => [5]
[[4,2],[]] => [4,2] => [[4,2],[]] => [[4,4],[2]] => [2]
[[5,2],[1]] => [5,2] => [[5,2],[]] => [[5,5],[3]] => [3]
[[6,2],[2]] => [6,2] => [[6,2],[]] => [[6,6],[4]] => [4]
[[4,1,1],[]] => [4,1,1] => [[4,1,1],[]] => [[4,4,4],[3,3]] => [3,3]
[[5,2,1],[1,1]] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3]
[[5,1,1],[1]] => [5,1,1] => [[5,1,1],[]] => [[5,5,5],[4,4]] => [4,4]
[[6,2,1],[2,1]] => [6,2,1] => [[6,2,1],[]] => [[6,6,6],[5,4]] => [5,4]
[[3,3],[]] => [3,3] => [[3,3],[]] => [[3,3],[]] => []
[[4,3],[1]] => [4,3] => [[4,3],[]] => [[4,4],[1]] => [1]
[[5,3],[2]] => [5,3] => [[5,3],[]] => [[5,5],[2]] => [2]
[[6,3],[3]] => [6,3] => [[6,3],[]] => [[6,6],[3]] => [3]
[[3,2,1],[]] => [3,2,1] => [[3,2,1],[]] => [[3,3,3],[2,1]] => [2,1]
[[4,3,1],[1,1]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[4,2,1],[1]] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2]
[[5,3,1],[2,1]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[5,2,1],[2]] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3]
[[6,3,1],[3,1]] => [6,3,1] => [[6,3,1],[]] => [[6,6,6],[5,3]] => [5,3]
[[4,2,2],[1,1]] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2]
[[5,3,2],[2,2]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[5,2,2],[2,1]] => [5,2,2] => [[5,2,2],[]] => [[5,5,5],[3,3]] => [3,3]
[[3,1,1,1],[]] => [3,1,1,1] => [[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]] => [2,2,2]
[[4,2,2,1],[1,1,1]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[4,2,1,1],[1,1]] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[5,3,2,1],[2,2,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[4,1,1,1],[1]] => [4,1,1,1] => [[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => [3,3,3]
[[5,2,2,1],[2,1,1]] => [5,2,2,1] => [[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [4,3,3]
[[5,2,1,1],[2,1]] => [5,2,1,1] => [[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]] => [4,4,3]
[[4,4],[2]] => [4,4] => [[4,4],[]] => [[4,4],[]] => []
[[5,4],[3]] => [5,4] => [[5,4],[]] => [[5,5],[1]] => [1]
[[6,4],[4]] => [6,4] => [[6,4],[]] => [[6,6],[2]] => [2]
[[3,3,1],[1]] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]] => [2]
[[4,4,1],[2,1]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[4,3,1],[2]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[5,4,1],[3,1]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[5,3,1],[3]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[2,2,2],[]] => [2,2,2] => [[2,2,2],[]] => [[2,2,2],[]] => []
[[3,3,2],[1,1]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[4,4,2],[2,2]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[3,2,2],[1]] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1]
[[4,3,2],[2,1]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[5,4,2],[3,2]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[4,2,2],[2]] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2]
[[5,3,2],[3,1]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[6,4,2],[4,2]] => [6,4,2] => [[6,4,2],[]] => [[6,6,6],[4,2]] => [4,2]
[[2,2,1,1],[]] => [2,2,1,1] => [[2,2,1,1],[]] => [[2,2,2,2],[1,1]] => [1,1]
[[3,3,2,1],[1,1,1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[3,3,1,1],[1,1]] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2]
[[4,4,2,1],[2,2,1]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[3,2,1,1],[1]] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[4,3,2,1],[2,1,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[4,3,1,1],[2,1]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[5,4,2,1],[3,2,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[4,2,1,1],[2]] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[5,3,2,1],[3,1,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[5,3,1,1],[3,1]] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2]
[[4,3,3],[2,2]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[5,4,3],[3,3]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[5,3,3],[3,2]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[3,2,2,1],[1,1]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[4,3,3,1],[2,2,1]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,3,2,1],[2,2]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5,4,3,1],[3,3,1]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[4,2,2,1],[2,1]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[5,3,3,1],[3,2,1]] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2]
[[5,3,2,1],[3,2]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[3,2,2,2],[1,1,1]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,3,3,2],[2,2,2]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[4,3,2,2],[2,2,1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[3,3,2]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[4,2,2,2],[2,1,1]] => [4,2,2,2] => [[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2]
[[5,3,3,2],[3,2,2]] => [5,3,3,2] => [[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [3,2,2]
[[5,3,2,2],[3,2,1]] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2]
[[2,1,1,1,1],[]] => [2,1,1,1,1] => [[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[3,2,2,2,1],[1,1,1,1]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[3,2,2,1,1],[1,1,1]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,3,2,1],[2,2,2,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[3,2,1,1,1],[1,1]] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[4,3,2,2,1],[2,2,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[4,3,2,1,1],[2,2,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[3,3,2,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[3,1,1,1,1],[1]] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[4,2,2,2,1],[2,1,1,1]] => [4,2,2,2,1] => [[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2]
[[4,2,2,1,1],[2,1,1]] => [4,2,2,1,1] => [[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2]
[[5,3,3,2,1],[3,2,2,1]] => [5,3,3,2,1] => [[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2]
[[4,2,1,1,1],[2,1]] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2]
[[5,3,2,2,1],[3,2,1,1]] => [5,3,2,2,1] => [[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2]
[[5,3,2,1,1],[3,2,1]] => [5,3,2,1,1] => [[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2]
[[5,5],[4]] => [5,5] => [[5,5],[]] => [[5,5],[]] => []
[[6,5],[5]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[4,4,1],[3]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[5,5,1],[4,1]] => [5,5,1] => [[5,5,1],[]] => [[5,5,5],[4]] => [4]
[[5,4,1],[4]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[3,3,2],[2]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[4,4,2],[3,1]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[5,5,2],[4,2]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[4,3,2],[3]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[5,4,2],[4,1]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[3,3,1,1],[2]] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2]
[[4,4,2,1],[3,1,1]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[4,4,1,1],[3,1]] => [4,4,1,1] => [[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [3,3]
[[4,3,1,1],[3]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[5,4,2,1],[4,1,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[5,4,1,1],[4,1]] => [5,4,1,1] => [[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]] => [4,4,1]
[[3,3,3],[2,1]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[4,4,3],[3,2]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[5,5,3],[4,3]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[4,3,3],[3,1]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[5,4,3],[4,2]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[2,2,2,1],[1]] => [2,2,2,1] => [[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1]
[[3,3,3,1],[2,1,1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,2,1],[2,1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[4,4,3,1],[3,2,1]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,4,2,1],[3,2]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[3,2,2,1],[2]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[4,3,3,1],[3,1,1]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,3,2,1],[3,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5,4,3,1],[4,2,1]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[5,4,2,1],[4,2]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[3,3,2,2],[2,1,1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[3,2,2]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,4,2,2],[3,2,1]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[4,3,2,2],[3,1,1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[4,2,2]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[5,4,2,2],[4,2,1]] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1]
[[2,2,1,1,1],[1]] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1]
[[3,3,2,2,1],[2,1,1,1]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[3,3,2,1,1],[2,1,1]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[4,4,3,2,1],[3,2,2,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[3,3,1,1,1],[2,1]] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2]
[[4,4,2,2,1],[3,2,1,1]] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2]
[[4,4,2,1,1],[3,2,1]] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2]
[[3,2,1,1,1],[2]] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[4,3,2,2,1],[3,1,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[4,3,2,1,1],[3,1,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[4,2,2,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[4,3,1,1,1],[3,1]] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1]
[[5,4,2,2,1],[4,2,1,1]] => [5,4,2,2,1] => [[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1]
[[5,4,2,1,1],[4,2,1]] => [5,4,2,1,1] => [[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1]
[[4,4,4],[3,3]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[5,5,4],[4,4]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[5,4,4],[4,3]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[3,3,3,1],[2,2]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[4,4,4,1],[3,3,1]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[4,4,3,1],[3,3]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,3,3,1],[3,2]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[5,4,3,1],[4,3]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[2,2,2,2],[1,1]] => [2,2,2,2] => [[2,2,2,2],[]] => [[2,2,2,2],[]] => []
[[3,3,3,2],[2,2,1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,4,4,2],[3,3,2]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[3,3,2,2],[2,2]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[3,3,1]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[3,2,2,2],[2,1]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,3,3,2],[3,2,1]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[4,3,2,2],[3,2]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[4,3,1]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[2,2,2,1,1],[1,1]] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1]
[[3,3,3,2,1],[2,2,1,1]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[3,3,3,1,1],[2,2,1]] => [3,3,3,1,1] => [[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]] => [2,2]
[[3,3,2,1,1],[2,2]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[4,4,3,2,1],[3,3,1,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[4,4,3,1,1],[3,3,1]] => [4,4,3,1,1] => [[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [3,3,1]
[[3,2,2,1,1],[2,1]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,3,2,1],[3,2,1,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,3,1,1],[3,2,1]] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[4,3,2,1,1],[3,2]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[4,3,1,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[5,4,3,1,1],[4,3,1]] => [5,4,3,1,1] => [[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1]
[[3,3,3,3],[2,2,2]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,4,4,3],[3,3,3]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,3,3],[3,3,2]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,3,3,3],[3,2,2]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[2,2,2,2,1],[1,1,1]] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1]
[[3,3,3,3,1],[2,2,2,1]] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2]
[[3,3,3,2,1],[2,2,2]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[3,3,2,2,1],[2,2,1]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[4,4,3,2,1],[3,3,2]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[3,2,2,2,1],[2,1,1]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[4,3,3,2,1],[3,2,2]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,2,2,1],[3,2,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[5,4,3,2,1],[4,3,2]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => []
[[3,3,3,3,2],[2,2,2,2]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[3,3,3,2,2],[2,2,2,1]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[3,3,2,2,2],[2,2,1,1]] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[3,2,2,2,2],[2,1,1,1]] => [3,2,2,2,2] => [[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1]
[[1,1,1,1,1,1],[]] => [1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]] => []
[[2,2,2,2,1,1],[1,1,1,1]] => [2,2,2,2,1,1] => [[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]] => [1,1]
[[2,2,2,1,1,1],[1,1,1]] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1]
[[2,2,1,1,1,1],[1,1]] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[3,3,2,2,1,1],[2,2,1,1]] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[2,1,1,1,1,1],[1]] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[3,2,2,1,1,1],[2,1,1]] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1]
[[3,2,1,1,1,1],[2,1]] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1]
[[7],[]] => [7] => [[7],[]] => [[7],[]] => []
[[6,1],[]] => [6,1] => [[6,1],[]] => [[6,6],[5]] => [5]
[[7,1],[1]] => [7,1] => [[7,1],[]] => [[7,7],[6]] => [6]
[[5,2],[]] => [5,2] => [[5,2],[]] => [[5,5],[3]] => [3]
[[6,2],[1]] => [6,2] => [[6,2],[]] => [[6,6],[4]] => [4]
[[7,2],[2]] => [7,2] => [[7,2],[]] => [[7,7],[5]] => [5]
[[5,1,1],[]] => [5,1,1] => [[5,1,1],[]] => [[5,5,5],[4,4]] => [4,4]
[[6,2,1],[1,1]] => [6,2,1] => [[6,2,1],[]] => [[6,6,6],[5,4]] => [5,4]
[[6,1,1],[1]] => [6,1,1] => [[6,1,1],[]] => [[6,6,6],[5,5]] => [5,5]
[[7,2,1],[2,1]] => [7,2,1] => [[7,2,1],[]] => [[7,7,7],[6,5]] => [6,5]
[[4,3],[]] => [4,3] => [[4,3],[]] => [[4,4],[1]] => [1]
[[5,3],[1]] => [5,3] => [[5,3],[]] => [[5,5],[2]] => [2]
[[6,3],[2]] => [6,3] => [[6,3],[]] => [[6,6],[3]] => [3]
[[7,3],[3]] => [7,3] => [[7,3],[]] => [[7,7],[4]] => [4]
[[4,2,1],[]] => [4,2,1] => [[4,2,1],[]] => [[4,4,4],[3,2]] => [3,2]
[[5,3,1],[1,1]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[5,2,1],[1]] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3]
[[6,3,1],[2,1]] => [6,3,1] => [[6,3,1],[]] => [[6,6,6],[5,3]] => [5,3]
[[6,2,1],[2]] => [6,2,1] => [[6,2,1],[]] => [[6,6,6],[5,4]] => [5,4]
[[5,2,2],[1,1]] => [5,2,2] => [[5,2,2],[]] => [[5,5,5],[3,3]] => [3,3]
[[6,2,2],[2,1]] => [6,2,2] => [[6,2,2],[]] => [[6,6,6],[4,4]] => [4,4]
[[4,1,1,1],[]] => [4,1,1,1] => [[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]] => [3,3,3]
[[5,2,2,1],[1,1,1]] => [5,2,2,1] => [[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [4,3,3]
[[5,2,1,1],[1,1]] => [5,2,1,1] => [[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]] => [4,4,3]
[[5,1,1,1],[1]] => [5,1,1,1] => [[5,1,1,1],[]] => [[5,5,5,5],[4,4,4]] => [4,4,4]
[[6,2,1,1],[2,1]] => [6,2,1,1] => [[6,2,1,1],[]] => [[6,6,6,6],[5,5,4]] => [5,5,4]
[[4,4],[1]] => [4,4] => [[4,4],[]] => [[4,4],[]] => []
[[5,4],[2]] => [5,4] => [[5,4],[]] => [[5,5],[1]] => [1]
[[6,4],[3]] => [6,4] => [[6,4],[]] => [[6,6],[2]] => [2]
[[3,3,1],[]] => [3,3,1] => [[3,3,1],[]] => [[3,3,3],[2]] => [2]
[[4,4,1],[1,1]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[4,3,1],[1]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[5,4,1],[2,1]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[5,3,1],[2]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[6,3,1],[3]] => [6,3,1] => [[6,3,1],[]] => [[6,6,6],[5,3]] => [5,3]
[[3,2,2],[]] => [3,2,2] => [[3,2,2],[]] => [[3,3,3],[1,1]] => [1,1]
[[4,3,2],[1,1]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[5,4,2],[2,2]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[4,2,2],[1]] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2]
[[5,3,2],[2,1]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[6,4,2],[3,2]] => [6,4,2] => [[6,4,2],[]] => [[6,6,6],[4,2]] => [4,2]
[[5,2,2],[2]] => [5,2,2] => [[5,2,2],[]] => [[5,5,5],[3,3]] => [3,3]
[[3,2,1,1],[]] => [3,2,1,1] => [[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]] => [2,2,1]
[[4,3,2,1],[1,1,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[4,3,1,1],[1,1]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[5,4,2,1],[2,2,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[4,2,1,1],[1]] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[5,3,2,1],[2,1,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[5,3,1,1],[2,1]] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2]
[[5,2,1,1],[2]] => [5,2,1,1] => [[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]] => [4,4,3]
[[5,3,3],[2,2]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[4,2,2,1],[1,1]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[5,3,3,1],[2,2,1]] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2]
[[5,3,2,1],[2,2]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[5,2,2,1],[2,1]] => [5,2,2,1] => [[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [4,3,3]
[[4,2,2,2],[1,1,1]] => [4,2,2,2] => [[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2]
[[5,3,3,2],[2,2,2]] => [5,3,3,2] => [[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [3,2,2]
[[5,3,2,2],[2,2,1]] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2]
[[5,2,2,2],[2,1,1]] => [5,2,2,2] => [[5,2,2,2],[]] => [[5,5,5,5],[3,3,3]] => [3,3,3]
[[3,1,1,1,1],[]] => [3,1,1,1,1] => [[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[4,2,2,2,1],[1,1,1,1]] => [4,2,2,2,1] => [[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2]
[[4,2,2,1,1],[1,1,1]] => [4,2,2,1,1] => [[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2]
[[5,3,3,2,1],[2,2,2,1]] => [5,3,3,2,1] => [[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2]
[[4,2,1,1,1],[1,1]] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2]
[[5,3,2,2,1],[2,2,1,1]] => [5,3,2,2,1] => [[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2]
[[5,3,2,1,1],[2,2,1]] => [5,3,2,1,1] => [[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2]
[[4,1,1,1,1],[1]] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3]
[[5,2,2,2,1],[2,1,1,1]] => [5,2,2,2,1] => [[5,2,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,3]] => [4,3,3,3]
[[5,2,2,1,1],[2,1,1]] => [5,2,2,1,1] => [[5,2,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,3]] => [4,4,3,3]
[[5,2,1,1,1],[2,1]] => [5,2,1,1,1] => [[5,2,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3]
[[5,5],[3]] => [5,5] => [[5,5],[]] => [[5,5],[]] => []
[[6,5],[4]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[4,4,1],[2]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[5,5,1],[3,1]] => [5,5,1] => [[5,5,1],[]] => [[5,5,5],[4]] => [4]
[[5,4,1],[3]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[3,3,2],[1]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[4,4,2],[2,1]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[5,5,2],[3,2]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[4,3,2],[2]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[5,4,2],[3,1]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[5,3,2],[3]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[6,4,2],[4,1]] => [6,4,2] => [[6,4,2],[]] => [[6,6,6],[4,2]] => [4,2]
[[3,3,1,1],[1]] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2]
[[4,4,2,1],[2,1,1]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[4,4,1,1],[2,1]] => [4,4,1,1] => [[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [3,3]
[[4,3,1,1],[2]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[5,4,2,1],[3,1,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[5,4,1,1],[3,1]] => [5,4,1,1] => [[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]] => [4,4,1]
[[5,3,1,1],[3]] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2]
[[3,3,3],[1,1]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[4,4,3],[2,2]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[5,5,3],[3,3]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[4,3,3],[2,1]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[5,4,3],[3,2]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[5,3,3],[3,1]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[2,2,2,1],[]] => [2,2,2,1] => [[2,2,2,1],[]] => [[2,2,2,2],[1]] => [1]
[[3,3,3,1],[1,1,1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,2,1],[1,1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[4,4,3,1],[2,2,1]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,4,2,1],[2,2]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[3,2,2,1],[1]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[4,3,3,1],[2,1,1]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,3,2,1],[2,1]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5,4,3,1],[3,2,1]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[5,4,2,1],[3,2]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[4,2,2,1],[2]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[5,3,3,1],[3,1,1]] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2]
[[5,3,2,1],[3,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[3,3,2,2],[1,1,1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[2,2,2]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,4,2,2],[2,2,1]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[4,3,2,2],[2,1,1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[3,2,2]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[5,4,2,2],[3,2,1]] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1]
[[5,3,2,2],[3,1,1]] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2]
[[2,2,1,1,1],[]] => [2,2,1,1,1] => [[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]] => [1,1,1]
[[3,3,2,2,1],[1,1,1,1]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[3,3,2,1,1],[1,1,1]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[4,4,3,2,1],[2,2,2,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[3,3,1,1,1],[1,1]] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2]
[[4,4,2,2,1],[2,2,1,1]] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2]
[[4,4,2,1,1],[2,2,1]] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2]
[[3,2,1,1,1],[1]] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[4,3,2,2,1],[2,1,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[4,3,2,1,1],[2,1,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[3,2,2,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[4,3,1,1,1],[2,1]] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1]
[[5,4,2,2,1],[3,2,1,1]] => [5,4,2,2,1] => [[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1]
[[5,4,2,1,1],[3,2,1]] => [5,4,2,1,1] => [[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1]
[[4,2,1,1,1],[2]] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2]
[[5,3,2,2,1],[3,1,1,1]] => [5,3,2,2,1] => [[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2]
[[5,3,2,1,1],[3,1,1]] => [5,3,2,1,1] => [[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2]
[[5,3,1,1,1],[3,1]] => [5,3,1,1,1] => [[5,3,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,2]] => [4,4,4,2]
[[5,4,4],[3,3]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,3,3,1],[2,2]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[5,4,3,1],[3,3]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[5,3,3,1],[3,2]] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2]
[[3,2,2,2],[1,1]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,3,3,2],[2,2,1]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[4,3,2,2],[2,2]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[3,3,1]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[4,2,2,2],[2,1]] => [4,2,2,2] => [[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2]
[[5,3,3,2],[3,2,1]] => [5,3,3,2] => [[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [3,2,2]
[[5,3,2,2],[3,2]] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2]
[[3,2,2,1,1],[1,1]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,3,2,1],[2,2,1,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,3,1,1],[2,2,1]] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[4,3,2,1,1],[2,2]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[3,3,1,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[5,4,3,1,1],[3,3,1]] => [5,4,3,1,1] => [[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1]
[[4,2,2,1,1],[2,1]] => [4,2,2,1,1] => [[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2]
[[5,3,3,2,1],[3,2,1,1]] => [5,3,3,2,1] => [[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2]
[[5,3,3,1,1],[3,2,1]] => [5,3,3,1,1] => [[5,3,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,2]] => [4,4,2,2]
[[5,3,2,1,1],[3,2]] => [5,3,2,1,1] => [[5,3,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,2]] => [4,4,3,2]
[[4,3,3,3],[2,2,2]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[3,2,2,2,1],[1,1,1]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[4,3,3,2,1],[2,2,2]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,2,2,1],[2,2,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[5,4,3,2,1],[3,3,2]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[4,2,2,2,1],[2,1,1]] => [4,2,2,2,1] => [[4,2,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,2]] => [3,2,2,2]
[[5,3,3,2,1],[3,2,2]] => [5,3,3,2,1] => [[5,3,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,2]] => [4,3,2,2]
[[5,3,2,2,1],[3,2,1]] => [5,3,2,2,1] => [[5,3,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,2]] => [4,3,3,2]
[[3,2,2,2,2],[1,1,1,1]] => [3,2,2,2,2] => [[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1]
[[2,1,1,1,1,1],[]] => [2,1,1,1,1,1] => [[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[3,2,2,1,1,1],[1,1,1]] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1]
[[3,2,1,1,1,1],[1,1]] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1]
[[3,1,1,1,1,1],[1]] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2]
[[4,2,1,1,1,1],[2,1]] => [4,2,1,1,1,1] => [[4,2,1,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2]
[[6,6],[5]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[5,5,1],[4]] => [5,5,1] => [[5,5,1],[]] => [[5,5,5],[4]] => [4]
[[4,4,2],[3]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[5,5,2],[4,1]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[5,4,2],[4]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[4,4,1,1],[3]] => [4,4,1,1] => [[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [3,3]
[[5,4,1,1],[4]] => [5,4,1,1] => [[5,4,1,1],[]] => [[5,5,5,5],[4,4,1]] => [4,4,1]
[[3,3,3],[2]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[4,4,3],[3,1]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[5,5,3],[4,2]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[4,3,3],[3]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[5,4,3],[4,1]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[3,3,2,1],[2]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[4,4,3,1],[3,1,1]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,4,2,1],[3,1]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[4,3,2,1],[3]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[5,4,3,1],[4,1,1]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[5,4,2,1],[4,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[4,4,2,2],[3,1,1]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[5,4,2,2],[4,1,1]] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1]
[[3,3,1,1,1],[2]] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2]
[[4,4,2,2,1],[3,1,1,1]] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2]
[[4,4,2,1,1],[3,1,1]] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2]
[[4,4,1,1,1],[3,1]] => [4,4,1,1,1] => [[4,4,1,1,1],[]] => [[4,4,4,4,4],[3,3,3]] => [3,3,3]
[[4,3,1,1,1],[3]] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1]
[[5,4,2,2,1],[4,1,1,1]] => [5,4,2,2,1] => [[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1]
[[5,4,2,1,1],[4,1,1]] => [5,4,2,1,1] => [[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1]
[[5,4,1,1,1],[4,1]] => [5,4,1,1,1] => [[5,4,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,1]] => [4,4,4,1]
[[4,4,4],[3,2]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[5,5,4],[4,3]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[5,4,4],[4,2]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[3,3,3,1],[2,1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[4,4,4,1],[3,2,1]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[4,4,3,1],[3,2]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,3,3,1],[3,1]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[5,4,3,1],[4,2]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[2,2,2,2],[1]] => [2,2,2,2] => [[2,2,2,2],[]] => [[2,2,2,2],[]] => []
[[3,3,3,2],[2,1,1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,4,4,2],[3,2,2]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[3,3,2,2],[2,1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[3,2,1]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,4,2,2],[3,2]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[3,2,2,2],[2]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[4,3,3,2],[3,1,1]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[4,3,2,2],[3,1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[5,4,3,2],[4,2,1]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[5,4,2,2],[4,2]] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1]
[[2,2,2,1,1],[1]] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1]
[[3,3,3,2,1],[2,1,1,1]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[3,3,3,1,1],[2,1,1]] => [3,3,3,1,1] => [[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]] => [2,2]
[[3,3,2,1,1],[2,1]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[4,4,3,2,1],[3,2,1,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[4,4,3,1,1],[3,2,1]] => [4,4,3,1,1] => [[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [3,3,1]
[[4,4,2,1,1],[3,2]] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2]
[[3,2,2,1,1],[2]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,3,2,1],[3,1,1,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,3,1,1],[3,1,1]] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[4,3,2,1,1],[3,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[5,4,3,2,1],[4,2,1,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[5,4,3,1,1],[4,2,1]] => [5,4,3,1,1] => [[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1]
[[5,4,2,1,1],[4,2]] => [5,4,2,1,1] => [[5,4,2,1,1],[]] => [[5,5,5,5,5],[4,4,3,1]] => [4,4,3,1]
[[4,4,3,3],[3,2,2]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[3,3,2,2,1],[2,1,1]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[4,4,3,2,1],[3,2,2]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[4,4,2,2,1],[3,2,1]] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2]
[[4,3,2,2,1],[3,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[5,4,3,2,1],[4,2,2]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[5,4,2,2,1],[4,2,1]] => [5,4,2,2,1] => [[5,4,2,2,1],[]] => [[5,5,5,5,5],[4,3,3,1]] => [4,3,3,1]
[[3,3,2,2,2],[2,1,1,1]] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[2,2,1,1,1,1],[1]] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[3,3,2,2,1,1],[2,1,1,1]] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[3,3,1,1,1,1],[2,1]] => [3,3,1,1,1,1] => [[3,3,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[3,2,1,1,1,1],[2]] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1]
[[5,5,5],[4,4]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[4,4,4,1],[3,3]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[3,3,3,2],[2,2]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,4,4,2],[3,3,1]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[4,4,3,2],[3,3]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,3,3,2],[3,2]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[5,4,3,2],[4,3]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[3,3,3,1,1],[2,2]] => [3,3,3,1,1] => [[3,3,3,1,1],[]] => [[3,3,3,3,3],[2,2]] => [2,2]
[[4,4,3,1,1],[3,3]] => [4,4,3,1,1] => [[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [3,3,1]
[[4,3,3,1,1],[3,2]] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[5,4,3,1,1],[4,3]] => [5,4,3,1,1] => [[5,4,3,1,1],[]] => [[5,5,5,5,5],[4,4,2,1]] => [4,4,2,1]
[[3,3,3,3],[2,2,1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,4,4,3],[3,3,2]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,3,3],[3,3,1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,3,3,3],[3,2,1]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[2,2,2,2,1],[1,1]] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1]
[[3,3,3,3,1],[2,2,1,1]] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2]
[[3,3,3,2,1],[2,2,1]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[3,3,2,2,1],[2,2]] => [3,3,2,2,1] => [[3,3,2,2,1],[]] => [[3,3,3,3,3],[2,1,1]] => [2,1,1]
[[4,4,3,2,1],[3,3,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[3,2,2,2,1],[2,1]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[4,3,3,2,1],[3,2,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,3,2,2,1],[3,2]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[5,4,3,2,1],[4,3,1]] => [5,4,3,2,1] => [[5,4,3,2,1],[]] => [[5,5,5,5,5],[4,3,2,1]] => [4,3,2,1]
[[3,3,3,2,2],[2,2,1,1]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[2,2,2,1,1,1],[1,1]] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1]
[[3,2,2,1,1,1],[2,1]] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1]
[[4,4,4,4],[3,3,3]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[3,3,3,3,1],[2,2,2]] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2]
[[2,2,2,2,2],[1,1,1]] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => []
[[3,3,3,3,2],[2,2,2,1]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[3,3,3,2,2],[2,2,2]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[3,3,2,2,2],[2,2,1]] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[3,2,2,2,2],[2,1,1]] => [3,2,2,2,2] => [[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1]
[[2,2,2,2,1,1],[1,1,1]] => [2,2,2,2,1,1] => [[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]] => [1,1]
[[3,3,2,2,1,1],[2,2,1]] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[3,3,3,3,3],[2,2,2,2]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[2,2,2,2,2,2],[1,1,1,1,1]] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => []
[[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]] => []
[[2,2,2,1,1,1,1],[1,1,1]] => [2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[2,2,1,1,1,1,1],[1,1]] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[2,1,1,1,1,1,1],[1]] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[3,2,1,1,1,1,1],[2,1]] => [3,2,1,1,1,1,1] => [[3,2,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1]
[[8],[]] => [8] => [[8],[]] => [[8],[]] => []
[[7,1],[]] => [7,1] => [[7,1],[]] => [[7,7],[6]] => [6]
[[6,2],[]] => [6,2] => [[6,2],[]] => [[6,6],[4]] => [4]
[[6,1,1],[]] => [6,1,1] => [[6,1,1],[]] => [[6,6,6],[5,5]] => [5,5]
[[5,3],[]] => [5,3] => [[5,3],[]] => [[5,5],[2]] => [2]
[[5,2,1],[]] => [5,2,1] => [[5,2,1],[]] => [[5,5,5],[4,3]] => [4,3]
[[5,1,1,1],[]] => [5,1,1,1] => [[5,1,1,1],[]] => [[5,5,5,5],[4,4,4]] => [4,4,4]
[[4,4],[]] => [4,4] => [[4,4],[]] => [[4,4],[]] => []
[[4,3,1],[]] => [4,3,1] => [[4,3,1],[]] => [[4,4,4],[3,1]] => [3,1]
[[4,2,2],[]] => [4,2,2] => [[4,2,2],[]] => [[4,4,4],[2,2]] => [2,2]
[[4,2,1,1],[]] => [4,2,1,1] => [[4,2,1,1],[]] => [[4,4,4,4],[3,3,2]] => [3,3,2]
[[4,1,1,1,1],[]] => [4,1,1,1,1] => [[4,1,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,3]] => [3,3,3,3]
[[3,3,2],[]] => [3,3,2] => [[3,3,2],[]] => [[3,3,3],[1]] => [1]
[[3,3,1,1],[]] => [3,3,1,1] => [[3,3,1,1],[]] => [[3,3,3,3],[2,2]] => [2,2]
[[3,2,2,1],[]] => [3,2,2,1] => [[3,2,2,1],[]] => [[3,3,3,3],[2,1,1]] => [2,1,1]
[[3,2,1,1,1],[]] => [3,2,1,1,1] => [[3,2,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,1]] => [2,2,2,1]
[[3,1,1,1,1,1],[]] => [3,1,1,1,1,1] => [[3,1,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,2]] => [2,2,2,2,2]
[[2,2,2,2],[]] => [2,2,2,2] => [[2,2,2,2],[]] => [[2,2,2,2],[]] => []
[[2,2,2,1,1],[]] => [2,2,2,1,1] => [[2,2,2,1,1],[]] => [[2,2,2,2,2],[1,1]] => [1,1]
[[2,2,1,1,1,1],[]] => [2,2,1,1,1,1] => [[2,2,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[2,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1] => [[2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1],[]] => []
[[9],[]] => [9] => [[9],[]] => [[9],[]] => []
[[8,1],[]] => [8,1] => [[8,1],[]] => [[8,8],[7]] => [7]
[[7,2],[]] => [7,2] => [[7,2],[]] => [[7,7],[5]] => [5]
[[7,1,1],[]] => [7,1,1] => [[7,1,1],[]] => [[7,7,7],[6,6]] => [6,6]
[[6,3],[]] => [6,3] => [[6,3],[]] => [[6,6],[3]] => [3]
[[6,2,1],[]] => [6,2,1] => [[6,2,1],[]] => [[6,6,6],[5,4]] => [5,4]
[[6,1,1,1],[]] => [6,1,1,1] => [[6,1,1,1],[]] => [[6,6,6,6],[5,5,5]] => [5,5,5]
[[5,4],[]] => [5,4] => [[5,4],[]] => [[5,5],[1]] => [1]
[[5,3,1],[]] => [5,3,1] => [[5,3,1],[]] => [[5,5,5],[4,2]] => [4,2]
[[5,2,2],[]] => [5,2,2] => [[5,2,2],[]] => [[5,5,5],[3,3]] => [3,3]
[[5,2,1,1],[]] => [5,2,1,1] => [[5,2,1,1],[]] => [[5,5,5,5],[4,4,3]] => [4,4,3]
[[5,1,1,1,1],[]] => [5,1,1,1,1] => [[5,1,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,4]] => [4,4,4,4]
[[4,4,1],[]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[4,3,2],[]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[4,3,1,1],[]] => [4,3,1,1] => [[4,3,1,1],[]] => [[4,4,4,4],[3,3,1]] => [3,3,1]
[[4,2,2,1],[]] => [4,2,2,1] => [[4,2,2,1],[]] => [[4,4,4,4],[3,2,2]] => [3,2,2]
[[4,2,1,1,1],[]] => [4,2,1,1,1] => [[4,2,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,2]] => [3,3,3,2]
[[4,1,1,1,1,1],[]] => [4,1,1,1,1,1] => [[4,1,1,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3,3,3]] => [3,3,3,3,3]
[[3,3,3],[]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[3,3,2,1],[]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[3,3,1,1,1],[]] => [3,3,1,1,1] => [[3,3,1,1,1],[]] => [[3,3,3,3,3],[2,2,2]] => [2,2,2]
[[3,2,2,2],[]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[3,2,2,1,1],[]] => [3,2,2,1,1] => [[3,2,2,1,1],[]] => [[3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[3,2,1,1,1,1],[]] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1]
[[3,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1] => [[3,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,2]] => [2,2,2,2,2,2]
[[2,2,2,2,1],[]] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1]
[[2,2,2,1,1,1],[]] => [2,2,2,1,1,1] => [[2,2,2,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1]] => [1,1,1]
[[2,2,1,1,1,1,1],[]] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[2,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1],[]] => []
[[10],[]] => [10] => [[10],[]] => [[10],[]] => []
[[9,1],[]] => [9,1] => [[9,1],[]] => [[9,9],[8]] => [8]
[[8,2],[]] => [8,2] => [[8,2],[]] => [[8,8],[6]] => [6]
[[8,1,1],[]] => [8,1,1] => [[8,1,1],[]] => [[8,8,8],[7,7]] => [7,7]
[[7,3],[]] => [7,3] => [[7,3],[]] => [[7,7],[4]] => [4]
[[7,2,1],[]] => [7,2,1] => [[7,2,1],[]] => [[7,7,7],[6,5]] => [6,5]
[[7,1,1,1],[]] => [7,1,1,1] => [[7,1,1,1],[]] => [[7,7,7,7],[6,6,6]] => [6,6,6]
[[6,4],[]] => [6,4] => [[6,4],[]] => [[6,6],[2]] => [2]
[[6,3,1],[]] => [6,3,1] => [[6,3,1],[]] => [[6,6,6],[5,3]] => [5,3]
[[6,2,2],[]] => [6,2,2] => [[6,2,2],[]] => [[6,6,6],[4,4]] => [4,4]
[[6,2,1,1],[]] => [6,2,1,1] => [[6,2,1,1],[]] => [[6,6,6,6],[5,5,4]] => [5,5,4]
[[6,1,1,1,1],[]] => [6,1,1,1,1] => [[6,1,1,1,1],[]] => [[6,6,6,6,6],[5,5,5,5]] => [5,5,5,5]
[[5,5],[]] => [5,5] => [[5,5],[]] => [[5,5],[]] => []
[[5,4,1],[]] => [5,4,1] => [[5,4,1],[]] => [[5,5,5],[4,1]] => [4,1]
[[5,3,2],[]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[5,3,1,1],[]] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2]
[[5,2,2,1],[]] => [5,2,2,1] => [[5,2,2,1],[]] => [[5,5,5,5],[4,3,3]] => [4,3,3]
[[5,2,1,1,1],[]] => [5,2,1,1,1] => [[5,2,1,1,1],[]] => [[5,5,5,5,5],[4,4,4,3]] => [4,4,4,3]
[[5,1,1,1,1,1],[]] => [5,1,1,1,1,1] => [[5,1,1,1,1,1],[]] => [[5,5,5,5,5,5],[4,4,4,4,4]] => [4,4,4,4,4]
[[4,4,2],[]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[4,4,1,1],[]] => [4,4,1,1] => [[4,4,1,1],[]] => [[4,4,4,4],[3,3]] => [3,3]
[[4,3,3],[]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[4,3,2,1],[]] => [4,3,2,1] => [[4,3,2,1],[]] => [[4,4,4,4],[3,2,1]] => [3,2,1]
[[4,3,1,1,1],[]] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1]
[[4,2,2,2],[]] => [4,2,2,2] => [[4,2,2,2],[]] => [[4,4,4,4],[2,2,2]] => [2,2,2]
[[4,2,2,1,1],[]] => [4,2,2,1,1] => [[4,2,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,2]] => [3,3,2,2]
[[4,2,1,1,1,1],[]] => [4,2,1,1,1,1] => [[4,2,1,1,1,1],[]] => [[4,4,4,4,4,4],[3,3,3,3,2]] => [3,3,3,3,2]
[[4,1,1,1,1,1,1],[]] => [4,1,1,1,1,1,1] => [[4,1,1,1,1,1,1],[]] => [[4,4,4,4,4,4,4],[3,3,3,3,3,3]] => [3,3,3,3,3,3]
[[3,3,3,1],[]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,2,2],[]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[3,3,2,1,1],[]] => [3,3,2,1,1] => [[3,3,2,1,1],[]] => [[3,3,3,3,3],[2,2,1]] => [2,2,1]
[[3,3,1,1,1,1],[]] => [3,3,1,1,1,1] => [[3,3,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2]] => [2,2,2,2]
[[3,2,2,2,1],[]] => [3,2,2,2,1] => [[3,2,2,2,1],[]] => [[3,3,3,3,3],[2,1,1,1]] => [2,1,1,1]
[[3,2,2,1,1,1],[]] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1]
[[3,2,1,1,1,1,1],[]] => [3,2,1,1,1,1,1] => [[3,2,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3],[2,2,2,2,2,1]] => [2,2,2,2,2,1]
[[3,1,1,1,1,1,1,1],[]] => [3,1,1,1,1,1,1,1] => [[3,1,1,1,1,1,1,1],[]] => [[3,3,3,3,3,3,3,3],[2,2,2,2,2,2,2]] => [2,2,2,2,2,2,2]
[[2,2,2,2,2],[]] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => []
[[2,2,2,2,1,1],[]] => [2,2,2,2,1,1] => [[2,2,2,2,1,1],[]] => [[2,2,2,2,2,2],[1,1]] => [1,1]
[[2,2,2,1,1,1,1],[]] => [2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[2,2,1,1,1,1,1,1],[]] => [2,2,1,1,1,1,1,1] => [[2,2,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2],[1,1,1,1,1,1]] => [1,1,1,1,1,1]
[[2,1,1,1,1,1,1,1,1],[]] => [2,1,1,1,1,1,1,1,1] => [[2,1,1,1,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2,2,2],[1,1,1,1,1,1,1,1]] => [1,1,1,1,1,1,1,1]
[[1,1,1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1,1,1,1],[]] => []
[[6,5],[]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[5,5,1],[]] => [5,5,1] => [[5,5,1],[]] => [[5,5,5],[4]] => [4]
[[5,4,2],[]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[5,3,3],[]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[4,4,3],[]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[4,4,2,1],[]] => [4,4,2,1] => [[4,4,2,1],[]] => [[4,4,4,4],[3,2]] => [3,2]
[[4,3,3,1],[]] => [4,3,3,1] => [[4,3,3,1],[]] => [[4,4,4,4],[3,1,1]] => [3,1,1]
[[4,3,2,2],[]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[3,3,3,2],[]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[3,2,2,2,2],[]] => [3,2,2,2,2] => [[3,2,2,2,2],[]] => [[3,3,3,3,3],[1,1,1,1]] => [1,1,1,1]
[[6,6],[]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[5,5,2],[]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[5,4,3],[]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[4,4,4],[]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[4,4,3,1],[]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,4,2,2],[]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[4,3,3,2],[]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[3,3,3,3],[]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[3,3,3,2,1],[]] => [3,3,3,2,1] => [[3,3,3,2,1],[]] => [[3,3,3,3,3],[2,1]] => [2,1]
[[3,3,2,2,2],[]] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[2,2,2,2,2,2],[]] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => []
[[5,5,3],[]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[5,4,4],[]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,1],[]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[4,4,3,2],[]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,3,3,3],[]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[3,3,3,3,1],[]] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2]
[[3,3,3,2,2],[]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[5,5,4],[]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,2],[]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[4,4,3,3],[]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[3,3,3,3,2],[]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[5,5,5],[]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[4,4,4,3],[]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[3,3,3,3,3],[]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,4,4,4],[]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[2,2,1,1,1,1,1],[1]] => [2,2,1,1,1,1,1] => [[2,2,1,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1,1]] => [1,1,1,1,1]
[[2,2,2,1,1,1,1],[1,1]] => [2,2,2,1,1,1,1] => [[2,2,2,1,1,1,1],[]] => [[2,2,2,2,2,2,2],[1,1,1,1]] => [1,1,1,1]
[[3,2,1,1,1,1],[1]] => [3,2,1,1,1,1] => [[3,2,1,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,2,1]] => [2,2,2,2,1]
[[3,2,2,1,1,1],[1,1]] => [3,2,2,1,1,1] => [[3,2,2,1,1,1],[]] => [[3,3,3,3,3,3],[2,2,2,1,1]] => [2,2,2,1,1]
[[4,3,1,1,1],[2]] => [4,3,1,1,1] => [[4,3,1,1,1],[]] => [[4,4,4,4,4],[3,3,3,1]] => [3,3,3,1]
[[3,3,2,2,1,1],[2,1,1]] => [3,3,2,2,1,1] => [[3,3,2,2,1,1],[]] => [[3,3,3,3,3,3],[2,2,1,1]] => [2,2,1,1]
[[4,3,2,1,1],[2,1]] => [4,3,2,1,1] => [[4,3,2,1,1],[]] => [[4,4,4,4,4],[3,3,2,1]] => [3,3,2,1]
[[4,4,2,1,1],[3,1]] => [4,4,2,1,1] => [[4,4,2,1,1],[]] => [[4,4,4,4,4],[3,3,2]] => [3,3,2]
[[4,3,3,1,1],[2,2]] => [4,3,3,1,1] => [[4,3,3,1,1],[]] => [[4,4,4,4,4],[3,3,1,1]] => [3,3,1,1]
[[4,4,3,1,1],[3,2]] => [4,4,3,1,1] => [[4,4,3,1,1],[]] => [[4,4,4,4,4],[3,3,1]] => [3,3,1]
[[5,3,1,1],[2]] => [5,3,1,1] => [[5,3,1,1],[]] => [[5,5,5,5],[4,4,2]] => [4,4,2]
[[4,3,2,2,1],[2,1,1]] => [4,3,2,2,1] => [[4,3,2,2,1],[]] => [[4,4,4,4,4],[3,2,2,1]] => [3,2,2,1]
[[4,4,2,2,1],[3,1,1]] => [4,4,2,2,1] => [[4,4,2,2,1],[]] => [[4,4,4,4,4],[3,2,2]] => [3,2,2]
[[4,3,3,2,1],[2,2,1]] => [4,3,3,2,1] => [[4,3,3,2,1],[]] => [[4,4,4,4,4],[3,2,1,1]] => [3,2,1,1]
[[4,4,3,2,1],[3,2,1]] => [4,4,3,2,1] => [[4,4,3,2,1],[]] => [[4,4,4,4,4],[3,2,1]] => [3,2,1]
[[5,3,2,1],[2,1]] => [5,3,2,1] => [[5,3,2,1],[]] => [[5,5,5,5],[4,3,2]] => [4,3,2]
[[5,4,2,1],[3,1]] => [5,4,2,1] => [[5,4,2,1],[]] => [[5,5,5,5],[4,3,1]] => [4,3,1]
[[5,3,3,1],[2,2]] => [5,3,3,1] => [[5,3,3,1],[]] => [[5,5,5,5],[4,2,2]] => [4,2,2]
[[5,4,3,1],[3,2]] => [5,4,3,1] => [[5,4,3,1],[]] => [[5,5,5,5],[4,2,1]] => [4,2,1]
[[5,3,2,2],[2,1,1]] => [5,3,2,2] => [[5,3,2,2],[]] => [[5,5,5,5],[3,3,2]] => [3,3,2]
[[5,4,2,2],[3,1,1]] => [5,4,2,2] => [[5,4,2,2],[]] => [[5,5,5,5],[3,3,1]] => [3,3,1]
[[5,3,3,2],[2,2,1]] => [5,3,3,2] => [[5,3,3,2],[]] => [[5,5,5,5],[3,2,2]] => [3,2,2]
[[5,4,3,2],[3,2,1]] => [5,4,3,2] => [[5,4,3,2],[]] => [[5,5,5,5],[3,2,1]] => [3,2,1]
[[6,4,2],[3,1]] => [6,4,2] => [[6,4,2],[]] => [[6,6,6],[4,2]] => [4,2]
[[3,3,3],[1]] => [3,3,3] => [[3,3,3],[]] => [[3,3,3],[]] => []
[[3,3,3,1],[1,1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[4,4,1],[1]] => [4,4,1] => [[4,4,1],[]] => [[4,4,4],[3]] => [3]
[[3,3,2,1],[1]] => [3,3,2,1] => [[3,3,2,1],[]] => [[3,3,3,3],[2,1]] => [2,1]
[[2,2,2,2,1],[1]] => [2,2,2,2,1] => [[2,2,2,2,1],[]] => [[2,2,2,2,2],[1]] => [1]
[[3,3,3,1],[2]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,3,1],[1]] => [3,3,3,1] => [[3,3,3,1],[]] => [[3,3,3,3],[2]] => [2]
[[3,3,3,2],[1,1,1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,4,2],[1,1]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[4,4,4],[2,2]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[5,5],[2]] => [5,5] => [[5,5],[]] => [[5,5],[]] => []
[[4,4,3],[2,1]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[3,3,3,3],[2,1,1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,3,3],[1,1]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[3,3,3,3],[1,1,1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,4,3],[1,1]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[4,4,4],[3,1]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[5,4],[1]] => [5,4] => [[5,4],[]] => [[5,5],[1]] => [1]
[[4,4,4],[2,1]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[5,5],[1]] => [5,5] => [[5,5],[]] => [[5,5],[]] => []
[[4,4,4],[1,1]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[3,3,2,2],[1,1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[4,4,2],[2]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[3,3,3,2],[2,1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,3,2],[1]] => [4,3,2] => [[4,3,2],[]] => [[4,4,4],[2,1]] => [2,1]
[[3,3,3,2],[1,1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[4,4,2],[1]] => [4,4,2] => [[4,4,2],[]] => [[4,4,4],[2]] => [2]
[[2,2,2,2,2],[1,1]] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => []
[[3,2,2,2],[1]] => [3,2,2,2] => [[3,2,2,2],[]] => [[3,3,3,3],[1,1,1]] => [1,1,1]
[[3,3,2,2],[2]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[3,3,2,2],[1]] => [3,3,2,2] => [[3,3,2,2],[]] => [[3,3,3,3],[1,1]] => [1,1]
[[2,2,2,2,2],[1]] => [2,2,2,2,2] => [[2,2,2,2,2],[]] => [[2,2,2,2,2],[]] => []
[[3,3,3,2],[2]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[3,3,3,2],[1]] => [3,3,3,2] => [[3,3,3,2],[]] => [[3,3,3,3],[1]] => [1]
[[3,3,3,3],[2,2]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,3,3],[2]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[4,4,3],[3]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[4,4,3],[2]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[3,3,3,3],[2,1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,3,3],[1]] => [4,3,3] => [[4,3,3],[]] => [[4,4,4],[1,1]] => [1,1]
[[3,3,3,3],[1,1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,4,3],[1]] => [4,4,3] => [[4,4,3],[]] => [[4,4,4],[1]] => [1]
[[4,4,4],[3]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[4,4,4],[2]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[4,4,4],[1]] => [4,4,4] => [[4,4,4],[]] => [[4,4,4],[]] => []
[[3,3,3,3],[2]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[3,3,3,3],[1]] => [3,3,3,3] => [[3,3,3,3],[]] => [[3,3,3,3],[]] => []
[[4,4,4,1],[1,1]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[4,4,3,1],[1]] => [4,4,3,1] => [[4,4,3,1],[]] => [[4,4,4,4],[3,1]] => [3,1]
[[4,4,4,1],[2]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[4,4,4,1],[1]] => [4,4,4,1] => [[4,4,4,1],[]] => [[4,4,4,4],[3]] => [3]
[[3,3,3,3,1],[1]] => [3,3,3,3,1] => [[3,3,3,3,1],[]] => [[3,3,3,3,3],[2]] => [2]
[[4,4,4,2],[1,1,1]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[6,6],[4]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[5,5,5],[4,3]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,5],[3]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[5,5,5],[3,3]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,6],[3]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[4,4,4,4],[3,3,2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[6,4],[2]] => [6,4] => [[6,4],[]] => [[6,6],[2]] => [2]
[[5,5,4],[3,2]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[3,2,2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,4,4],[2,2]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,4],[2,2,2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[2,2]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[5,5,5],[4,2]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,5],[2]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[5,5,5],[3,2]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,6],[2]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[5,5,5],[2,2]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[3,3,3,3,3],[2,2,2,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[6,3],[1]] => [6,3] => [[6,3],[]] => [[6,6],[3]] => [3]
[[5,5,3],[3,1]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[5,4,3],[2,1]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[4,4,4,3],[2,2,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[5,5,3],[2,1]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[3,3,3,3,3],[2,2,1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[5,3,3],[1,1]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[4,4,3,3],[2,1,1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[3,3,3,3,3],[2,1,1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,3,3,3],[1,1,1]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[3,3,3,3,3],[1,1,1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,4,3,3],[1,1,1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[5,4,3],[1,1]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[4,4,4,3],[2,1,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[5,5,3],[1,1]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[4,4,4,3],[1,1,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,4,4],[3,3,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[6,4],[1]] => [6,4] => [[6,4],[]] => [[6,6],[2]] => [2]
[[5,5,4],[3,1]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[3,2,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,4,4],[2,1]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,4],[2,2,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[2,1]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[5,5,5],[4,1]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,5],[1]] => [6,5] => [[6,5],[]] => [[6,6],[1]] => [1]
[[5,5,5],[3,1]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[6,6],[1]] => [6,6] => [[6,6],[]] => [[6,6],[]] => []
[[5,5,5],[2,1]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[4,4,4,4],[3,1,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,4,4],[1,1]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,4],[2,1,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[1,1]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[1,1,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,5],[1,1]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[2,2,2,2,2,2],[1,1,1,1]] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => []
[[5,5,2],[3]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[5,4,2],[2]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[4,4,4,2],[2,2]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[5,5,2],[2]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[5,3,2],[1]] => [5,3,2] => [[5,3,2],[]] => [[5,5,5],[3,2]] => [3,2]
[[4,4,3,2],[2,1]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,3,3,2],[1,1]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[3,3,3,3,2],[1,1,1]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[4,4,3,2],[1,1]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[5,4,2],[1]] => [5,4,2] => [[5,4,2],[]] => [[5,5,5],[3,1]] => [3,1]
[[4,4,4,2],[2,1]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[5,5,2],[1]] => [5,5,2] => [[5,5,2],[]] => [[5,5,5],[3]] => [3]
[[4,4,4,2],[1,1]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[2,2,2,2,2,2],[1,1,1]] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => []
[[4,4,2,2],[2]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[4,3,2,2],[1]] => [4,3,2,2] => [[4,3,2,2],[]] => [[4,4,4,4],[2,2,1]] => [2,2,1]
[[3,3,3,2,2],[1,1]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[4,4,2,2],[1]] => [4,4,2,2] => [[4,4,2,2],[]] => [[4,4,4,4],[2,2]] => [2,2]
[[2,2,2,2,2,2],[1,1]] => [2,2,2,2,2,2] => [[2,2,2,2,2,2],[]] => [[2,2,2,2,2,2],[]] => []
[[3,3,2,2,2],[1]] => [3,3,2,2,2] => [[3,3,2,2,2],[]] => [[3,3,3,3,3],[1,1,1]] => [1,1,1]
[[3,3,3,2,2],[1]] => [3,3,3,2,2] => [[3,3,3,2,2],[]] => [[3,3,3,3,3],[1,1]] => [1,1]
[[4,4,3,2],[2]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,3,3,2],[1]] => [4,3,3,2] => [[4,3,3,2],[]] => [[4,4,4,4],[2,1,1]] => [2,1,1]
[[3,3,3,3,2],[1,1]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[4,4,3,2],[1]] => [4,4,3,2] => [[4,4,3,2],[]] => [[4,4,4,4],[2,1]] => [2,1]
[[4,4,4,2],[3]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[4,4,4,2],[2]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[4,4,4,2],[1]] => [4,4,4,2] => [[4,4,4,2],[]] => [[4,4,4,4],[2]] => [2]
[[3,3,3,3,2],[2]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[3,3,3,3,2],[1]] => [3,3,3,3,2] => [[3,3,3,3,2],[]] => [[3,3,3,3,3],[1]] => [1]
[[3,3,3,3,3],[2,2,2]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[5,5,3],[3]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[5,4,3],[2]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[4,4,4,3],[2,2]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[5,5,3],[2]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[3,3,3,3,3],[2,2,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[5,3,3],[1]] => [5,3,3] => [[5,3,3],[]] => [[5,5,5],[2,2]] => [2,2]
[[4,4,3,3],[2,1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[3,3,3,3,3],[2,1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,3,3,3],[1,1]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[3,3,3,3,3],[1,1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,4,3,3],[1,1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,4,4,3],[3,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[5,4,3],[1]] => [5,4,3] => [[5,4,3],[]] => [[5,5,5],[2,1]] => [2,1]
[[4,4,4,3],[2,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[5,5,3],[1]] => [5,5,3] => [[5,5,3],[]] => [[5,5,5],[2]] => [2]
[[4,4,4,3],[1,1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,4,4],[3,3]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[3]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[3,2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,4,4],[2]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,4],[2,2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[2]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[5,5,5],[4]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[5,5,5],[3]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[5,5,5],[2]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[4,4,4,4],[3,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,4,4],[1]] => [5,4,4] => [[5,4,4],[]] => [[5,5,5],[1,1]] => [1,1]
[[4,4,4,4],[2,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,4],[1]] => [5,5,4] => [[5,5,4],[]] => [[5,5,5],[1]] => [1]
[[4,4,4,4],[1,1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[5,5,5],[1]] => [5,5,5] => [[5,5,5],[]] => [[5,5,5],[]] => []
[[3,3,3,3,3],[2,2]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,3,3,3],[2]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[4,4,3,3],[3]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,4,3,3],[2]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[3,3,3,3,3],[2,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,3,3,3],[1]] => [4,3,3,3] => [[4,3,3,3],[]] => [[4,4,4,4],[1,1,1]] => [1,1,1]
[[3,3,3,3,3],[1,1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,4,3,3],[1]] => [4,4,3,3] => [[4,4,3,3],[]] => [[4,4,4,4],[1,1]] => [1,1]
[[4,4,4,3],[3]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,4,3],[2]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[4,4,4,3],[1]] => [4,4,4,3] => [[4,4,4,3],[]] => [[4,4,4,4],[1]] => [1]
[[3,3,3,3,3],[2]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[3,3,3,3,3],[1]] => [3,3,3,3,3] => [[3,3,3,3,3],[]] => [[3,3,3,3,3],[]] => []
[[4,4,4,4],[3]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[4,4,4,4],[2]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
[[4,4,4,4],[1]] => [4,4,4,4] => [[4,4,4,4],[]] => [[4,4,4,4],[]] => []
Map
outer shape
Description
The outer shape of the skew partition.
Map
to skew partition
Description
The partition regarded as a skew partition.
Map
rotate
Description
The rotation of a skew partition.
This is the skew partition obtained by rotating the diagram by 180 degrees. Equivalently, given a skew partition $\lambda/\mu$, its rotation $(\lambda/\mu)^\natural$ is the skew partition with cells $\{(a-i, b-j)| (i, j) \in \lambda/\mu\}$, where $b$ and $a$ are the first part and the number of parts of $\lambda$ respectively.
Map
inner shape
Description
The inner shape of a skew partition.