edit this map or download as text // json
Identifier
Mp00177: Plane partitions —transpose⟶ Plane partitions
Images
[[1]] => [[1]]
[[1],[1]] => [[1,1]]
[[2]] => [[2]]
[[1,1]] => [[1],[1]]
[[1],[1],[1]] => [[1,1,1]]
[[2],[1]] => [[2,1]]
[[1,1],[1]] => [[1,1],[1]]
[[3]] => [[3]]
[[2,1]] => [[2],[1]]
[[1,1,1]] => [[1],[1],[1]]
[[1],[1],[1],[1]] => [[1,1,1,1]]
[[2],[1],[1]] => [[2,1,1]]
[[2],[2]] => [[2,2]]
[[1,1],[1],[1]] => [[1,1,1],[1]]
[[1,1],[1,1]] => [[1,1],[1,1]]
[[3],[1]] => [[3,1]]
[[2,1],[1]] => [[2,1],[1]]
[[1,1,1],[1]] => [[1,1],[1],[1]]
[[4]] => [[4]]
[[3,1]] => [[3],[1]]
[[2,2]] => [[2],[2]]
[[2,1,1]] => [[2],[1],[1]]
[[1,1,1,1]] => [[1],[1],[1],[1]]
[[1],[1],[1],[1],[1]] => [[1,1,1,1,1]]
[[2],[1],[1],[1]] => [[2,1,1,1]]
[[2],[2],[1]] => [[2,2,1]]
[[1,1],[1],[1],[1]] => [[1,1,1,1],[1]]
[[1,1],[1,1],[1]] => [[1,1,1],[1,1]]
[[3],[1],[1]] => [[3,1,1]]
[[3],[2]] => [[3,2]]
[[2,1],[1],[1]] => [[2,1,1],[1]]
[[2,1],[2]] => [[2,2],[1]]
[[2,1],[1,1]] => [[2,1],[1,1]]
[[1,1,1],[1],[1]] => [[1,1,1],[1],[1]]
[[1,1,1],[1,1]] => [[1,1],[1,1],[1]]
[[4],[1]] => [[4,1]]
[[3,1],[1]] => [[3,1],[1]]
[[2,2],[1]] => [[2,1],[2]]
[[2,1,1],[1]] => [[2,1],[1],[1]]
[[1,1,1,1],[1]] => [[1,1],[1],[1],[1]]
[[5]] => [[5]]
[[4,1]] => [[4],[1]]
[[3,2]] => [[3],[2]]
[[3,1,1]] => [[3],[1],[1]]
[[2,2,1]] => [[2],[2],[1]]
[[2,1,1,1]] => [[2],[1],[1],[1]]
[[1,1,1,1,1]] => [[1],[1],[1],[1],[1]]
[[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1]]
[[2],[1],[1],[1],[1]] => [[2,1,1,1,1]]
[[2],[2],[1],[1]] => [[2,2,1,1]]
[[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]]
[[3],[1],[1],[1]] => [[3,1,1,1]]
[[3],[2],[1]] => [[3,2,1]]
[[3],[3]] => [[3,3]]
[[2,1],[1],[1],[1]] => [[2,1,1,1],[1]]
[[2,1],[2],[1]] => [[2,2,1],[1]]
[[2,1],[1,1],[1]] => [[2,1,1],[1,1]]
[[2,1],[2,1]] => [[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]]
[[4],[1],[1]] => [[4,1,1]]
[[4],[2]] => [[4,2]]
[[3,1],[1],[1]] => [[3,1,1],[1]]
[[3,1],[2]] => [[3,2],[1]]
[[3,1],[1,1]] => [[3,1],[1,1]]
[[2,2],[1],[1]] => [[2,1,1],[2]]
[[2,2],[2]] => [[2,2],[2]]
[[2,2],[1,1]] => [[2,1],[2,1]]
[[2,1,1],[1],[1]] => [[2,1,1],[1],[1]]
[[2,1,1],[2]] => [[2,2],[1],[1]]
[[2,1,1],[1,1]] => [[2,1],[1,1],[1]]
[[1,1,1,1],[1],[1]] => [[1,1,1],[1],[1],[1]]
[[1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1]]
[[5],[1]] => [[5,1]]
[[4,1],[1]] => [[4,1],[1]]
[[3,2],[1]] => [[3,1],[2]]
[[3,1,1],[1]] => [[3,1],[1],[1]]
[[2,2,1],[1]] => [[2,1],[2],[1]]
[[2,1,1,1],[1]] => [[2,1],[1],[1],[1]]
[[1,1,1,1,1],[1]] => [[1,1],[1],[1],[1],[1]]
[[6]] => [[6]]
[[5,1]] => [[5],[1]]
[[4,2]] => [[4],[2]]
[[4,1,1]] => [[4],[1],[1]]
[[3,3]] => [[3],[3]]
[[3,2,1]] => [[3],[2],[1]]
[[3,1,1,1]] => [[3],[1],[1],[1]]
[[2,2,2]] => [[2],[2],[2]]
[[2,2,1,1]] => [[2],[2],[1],[1]]
[[2,1,1,1,1]] => [[2],[1],[1],[1],[1]]
[[1,1,1,1,1,1]] => [[1],[1],[1],[1],[1],[1]]
[[1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1]]
[[2],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1]]
[[2],[2],[1],[1],[1]] => [[2,2,1,1,1]]
[[2],[2],[2],[1]] => [[2,2,2,1]]
[[1,1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1],[1]]
[[1,1],[1,1],[1],[1],[1]] => [[1,1,1,1,1],[1,1]]
>>> Load all 1123 entries. <<<
[[1,1],[1,1],[1,1],[1]] => [[1,1,1,1],[1,1,1]]
[[3],[1],[1],[1],[1]] => [[3,1,1,1,1]]
[[3],[2],[1],[1]] => [[3,2,1,1]]
[[3],[2],[2]] => [[3,2,2]]
[[3],[3],[1]] => [[3,3,1]]
[[2,1],[1],[1],[1],[1]] => [[2,1,1,1,1],[1]]
[[2,1],[2],[1],[1]] => [[2,2,1,1],[1]]
[[2,1],[2],[2]] => [[2,2,2],[1]]
[[2,1],[1,1],[1],[1]] => [[2,1,1,1],[1,1]]
[[2,1],[1,1],[1,1]] => [[2,1,1],[1,1,1]]
[[2,1],[2,1],[1]] => [[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],[1,1],[1,1]]
[[4],[1],[1],[1]] => [[4,1,1,1]]
[[4],[2],[1]] => [[4,2,1]]
[[4],[3]] => [[4,3]]
[[3,1],[1],[1],[1]] => [[3,1,1,1],[1]]
[[3,1],[2],[1]] => [[3,2,1],[1]]
[[3,1],[1,1],[1]] => [[3,1,1],[1,1]]
[[3,1],[3]] => [[3,3],[1]]
[[3,1],[2,1]] => [[3,2],[1,1]]
[[2,2],[1],[1],[1]] => [[2,1,1,1],[2]]
[[2,2],[2],[1]] => [[2,2,1],[2]]
[[2,2],[1,1],[1]] => [[2,1,1],[2,1]]
[[2,2],[2,1]] => [[2,2],[2,1]]
[[2,1,1],[1],[1],[1]] => [[2,1,1,1],[1],[1]]
[[2,1,1],[2],[1]] => [[2,2,1],[1],[1]]
[[2,1,1],[1,1],[1]] => [[2,1,1],[1,1],[1]]
[[2,1,1],[2,1]] => [[2,2],[1,1],[1]]
[[2,1,1],[1,1,1]] => [[2,1],[1,1],[1,1]]
[[1,1,1,1],[1],[1],[1]] => [[1,1,1,1],[1],[1],[1]]
[[1,1,1,1],[1,1],[1]] => [[1,1,1],[1,1],[1],[1]]
[[1,1,1,1],[1,1,1]] => [[1,1],[1,1],[1,1],[1]]
[[5],[1],[1]] => [[5,1,1]]
[[5],[2]] => [[5,2]]
[[4,1],[1],[1]] => [[4,1,1],[1]]
[[4,1],[2]] => [[4,2],[1]]
[[4,1],[1,1]] => [[4,1],[1,1]]
[[3,2],[1],[1]] => [[3,1,1],[2]]
[[3,2],[2]] => [[3,2],[2]]
[[3,2],[1,1]] => [[3,1],[2,1]]
[[3,1,1],[1],[1]] => [[3,1,1],[1],[1]]
[[3,1,1],[2]] => [[3,2],[1],[1]]
[[3,1,1],[1,1]] => [[3,1],[1,1],[1]]
[[2,2,1],[1],[1]] => [[2,1,1],[2],[1]]
[[2,2,1],[2]] => [[2,2],[2],[1]]
[[2,2,1],[1,1]] => [[2,1],[2,1],[1]]
[[2,1,1,1],[1],[1]] => [[2,1,1],[1],[1],[1]]
[[2,1,1,1],[2]] => [[2,2],[1],[1],[1]]
[[2,1,1,1],[1,1]] => [[2,1],[1,1],[1],[1]]
[[1,1,1,1,1],[1],[1]] => [[1,1,1],[1],[1],[1],[1]]
[[1,1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1],[1]]
[[6],[1]] => [[6,1]]
[[5,1],[1]] => [[5,1],[1]]
[[4,2],[1]] => [[4,1],[2]]
[[4,1,1],[1]] => [[4,1],[1],[1]]
[[3,3],[1]] => [[3,1],[3]]
[[3,2,1],[1]] => [[3,1],[2],[1]]
[[3,1,1,1],[1]] => [[3,1],[1],[1],[1]]
[[2,2,2],[1]] => [[2,1],[2],[2]]
[[2,2,1,1],[1]] => [[2,1],[2],[1],[1]]
[[2,1,1,1,1],[1]] => [[2,1],[1],[1],[1],[1]]
[[1,1,1,1,1,1],[1]] => [[1,1],[1],[1],[1],[1],[1]]
[[7]] => [[7]]
[[6,1]] => [[6],[1]]
[[5,2]] => [[5],[2]]
[[5,1,1]] => [[5],[1],[1]]
[[4,3]] => [[4],[3]]
[[4,2,1]] => [[4],[2],[1]]
[[4,1,1,1]] => [[4],[1],[1],[1]]
[[3,3,1]] => [[3],[3],[1]]
[[3,2,2]] => [[3],[2],[2]]
[[3,2,1,1]] => [[3],[2],[1],[1]]
[[3,1,1,1,1]] => [[3],[1],[1],[1],[1]]
[[2,2,2,1]] => [[2],[2],[2],[1]]
[[2,2,1,1,1]] => [[2],[2],[1],[1],[1]]
[[2,1,1,1,1,1]] => [[2],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1]] => [[1],[1],[1],[1],[1],[1],[1]]
[[1],[1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1,1]]
[[2],[1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1,1]]
[[2],[2],[1],[1],[1],[1]] => [[2,2,1,1,1,1]]
[[2],[2],[2],[1],[1]] => [[2,2,2,1,1]]
[[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],[1,1],[1,1],[1,1]] => [[1,1,1,1],[1,1,1,1]]
[[3],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1]]
[[3],[2],[1],[1],[1]] => [[3,2,1,1,1]]
[[3],[2],[2],[1]] => [[3,2,2,1]]
[[3],[3],[1],[1]] => [[3,3,1,1]]
[[3],[3],[2]] => [[3,3,2]]
[[2,1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[1]]
[[2,1],[2],[1],[1],[1]] => [[2,2,1,1,1],[1]]
[[2,1],[2],[2],[1]] => [[2,2,2,1],[1]]
[[2,1],[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]]
[[2,1],[2,1],[1],[1]] => [[2,2,1,1],[1,1]]
[[2,1],[2,1],[2]] => [[2,2,2],[1,1]]
[[2,1],[2,1],[1,1]] => [[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],[1,1,1],[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]]
[[4],[1],[1],[1],[1]] => [[4,1,1,1,1]]
[[4],[2],[1],[1]] => [[4,2,1,1]]
[[4],[2],[2]] => [[4,2,2]]
[[4],[3],[1]] => [[4,3,1]]
[[4],[4]] => [[4,4]]
[[3,1],[1],[1],[1],[1]] => [[3,1,1,1,1],[1]]
[[3,1],[2],[1],[1]] => [[3,2,1,1],[1]]
[[3,1],[2],[2]] => [[3,2,2],[1]]
[[3,1],[1,1],[1],[1]] => [[3,1,1,1],[1,1]]
[[3,1],[1,1],[1,1]] => [[3,1,1],[1,1,1]]
[[3,1],[3],[1]] => [[3,3,1],[1]]
[[3,1],[2,1],[1]] => [[3,2,1],[1,1]]
[[3,1],[3,1]] => [[3,3],[1,1]]
[[2,2],[1],[1],[1],[1]] => [[2,1,1,1,1],[2]]
[[2,2],[2],[1],[1]] => [[2,2,1,1],[2]]
[[2,2],[2],[2]] => [[2,2,2],[2]]
[[2,2],[1,1],[1],[1]] => [[2,1,1,1],[2,1]]
[[2,2],[1,1],[1,1]] => [[2,1,1],[2,1,1]]
[[2,2],[2,1],[1]] => [[2,2,1],[2,1]]
[[2,2],[2,2]] => [[2,2],[2,2]]
[[2,1,1],[1],[1],[1],[1]] => [[2,1,1,1,1],[1],[1]]
[[2,1,1],[2],[1],[1]] => [[2,2,1,1],[1],[1]]
[[2,1,1],[2],[2]] => [[2,2,2],[1],[1]]
[[2,1,1],[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]]
[[2,1,1],[2,1],[1]] => [[2,2,1],[1,1],[1]]
[[2,1,1],[1,1,1],[1]] => [[2,1,1],[1,1],[1,1]]
[[2,1,1],[2,1,1]] => [[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],[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]]
[[5],[1],[1],[1]] => [[5,1,1,1]]
[[5],[2],[1]] => [[5,2,1]]
[[5],[3]] => [[5,3]]
[[4,1],[1],[1],[1]] => [[4,1,1,1],[1]]
[[4,1],[2],[1]] => [[4,2,1],[1]]
[[4,1],[1,1],[1]] => [[4,1,1],[1,1]]
[[4,1],[3]] => [[4,3],[1]]
[[4,1],[2,1]] => [[4,2],[1,1]]
[[3,2],[1],[1],[1]] => [[3,1,1,1],[2]]
[[3,2],[2],[1]] => [[3,2,1],[2]]
[[3,2],[1,1],[1]] => [[3,1,1],[2,1]]
[[3,2],[3]] => [[3,3],[2]]
[[3,2],[2,1]] => [[3,2],[2,1]]
[[3,1,1],[1],[1],[1]] => [[3,1,1,1],[1],[1]]
[[3,1,1],[2],[1]] => [[3,2,1],[1],[1]]
[[3,1,1],[1,1],[1]] => [[3,1,1],[1,1],[1]]
[[3,1,1],[3]] => [[3,3],[1],[1]]
[[3,1,1],[2,1]] => [[3,2],[1,1],[1]]
[[3,1,1],[1,1,1]] => [[3,1],[1,1],[1,1]]
[[2,2,1],[1],[1],[1]] => [[2,1,1,1],[2],[1]]
[[2,2,1],[2],[1]] => [[2,2,1],[2],[1]]
[[2,2,1],[1,1],[1]] => [[2,1,1],[2,1],[1]]
[[2,2,1],[2,1]] => [[2,2],[2,1],[1]]
[[2,2,1],[1,1,1]] => [[2,1],[2,1],[1,1]]
[[2,1,1,1],[1],[1],[1]] => [[2,1,1,1],[1],[1],[1]]
[[2,1,1,1],[2],[1]] => [[2,2,1],[1],[1],[1]]
[[2,1,1,1],[1,1],[1]] => [[2,1,1],[1,1],[1],[1]]
[[2,1,1,1],[2,1]] => [[2,2],[1,1],[1],[1]]
[[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],[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],[1],[1]] => [[6,1,1]]
[[6],[2]] => [[6,2]]
[[5,1],[1],[1]] => [[5,1,1],[1]]
[[5,1],[2]] => [[5,2],[1]]
[[5,1],[1,1]] => [[5,1],[1,1]]
[[4,2],[1],[1]] => [[4,1,1],[2]]
[[4,2],[2]] => [[4,2],[2]]
[[4,2],[1,1]] => [[4,1],[2,1]]
[[4,1,1],[1],[1]] => [[4,1,1],[1],[1]]
[[4,1,1],[2]] => [[4,2],[1],[1]]
[[4,1,1],[1,1]] => [[4,1],[1,1],[1]]
[[3,3],[1],[1]] => [[3,1,1],[3]]
[[3,3],[2]] => [[3,2],[3]]
[[3,3],[1,1]] => [[3,1],[3,1]]
[[3,2,1],[1],[1]] => [[3,1,1],[2],[1]]
[[3,2,1],[2]] => [[3,2],[2],[1]]
[[3,2,1],[1,1]] => [[3,1],[2,1],[1]]
[[3,1,1,1],[1],[1]] => [[3,1,1],[1],[1],[1]]
[[3,1,1,1],[2]] => [[3,2],[1],[1],[1]]
[[3,1,1,1],[1,1]] => [[3,1],[1,1],[1],[1]]
[[2,2,2],[1],[1]] => [[2,1,1],[2],[2]]
[[2,2,2],[2]] => [[2,2],[2],[2]]
[[2,2,2],[1,1]] => [[2,1],[2,1],[2]]
[[2,2,1,1],[1],[1]] => [[2,1,1],[2],[1],[1]]
[[2,2,1,1],[2]] => [[2,2],[2],[1],[1]]
[[2,2,1,1],[1,1]] => [[2,1],[2,1],[1],[1]]
[[2,1,1,1,1],[1],[1]] => [[2,1,1],[1],[1],[1],[1]]
[[2,1,1,1,1],[2]] => [[2,2],[1],[1],[1],[1]]
[[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],[1],[1],[1],[1]]
[[1,1,1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1],[1],[1]]
[[7],[1]] => [[7,1]]
[[6,1],[1]] => [[6,1],[1]]
[[5,2],[1]] => [[5,1],[2]]
[[5,1,1],[1]] => [[5,1],[1],[1]]
[[4,3],[1]] => [[4,1],[3]]
[[4,2,1],[1]] => [[4,1],[2],[1]]
[[4,1,1,1],[1]] => [[4,1],[1],[1],[1]]
[[3,3,1],[1]] => [[3,1],[3],[1]]
[[3,2,2],[1]] => [[3,1],[2],[2]]
[[3,2,1,1],[1]] => [[3,1],[2],[1],[1]]
[[3,1,1,1,1],[1]] => [[3,1],[1],[1],[1],[1]]
[[2,2,2,1],[1]] => [[2,1],[2],[2],[1]]
[[2,2,1,1,1],[1]] => [[2,1],[2],[1],[1],[1]]
[[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],[1],[1],[1],[1]]
[[8]] => [[8]]
[[7,1]] => [[7],[1]]
[[6,2]] => [[6],[2]]
[[6,1,1]] => [[6],[1],[1]]
[[5,3]] => [[5],[3]]
[[5,2,1]] => [[5],[2],[1]]
[[5,1,1,1]] => [[5],[1],[1],[1]]
[[4,4]] => [[4],[4]]
[[4,3,1]] => [[4],[3],[1]]
[[4,2,2]] => [[4],[2],[2]]
[[4,2,1,1]] => [[4],[2],[1],[1]]
[[4,1,1,1,1]] => [[4],[1],[1],[1],[1]]
[[3,3,2]] => [[3],[3],[2]]
[[3,3,1,1]] => [[3],[3],[1],[1]]
[[3,2,2,1]] => [[3],[2],[2],[1]]
[[3,2,1,1,1]] => [[3],[2],[1],[1],[1]]
[[3,1,1,1,1,1]] => [[3],[1],[1],[1],[1],[1]]
[[2,2,2,2]] => [[2],[2],[2],[2]]
[[2,2,2,1,1]] => [[2],[2],[2],[1],[1]]
[[2,2,1,1,1,1]] => [[2],[2],[1],[1],[1],[1]]
[[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],[1],[1],[1],[1]]
[[1],[1],[1],[1],[1],[1],[1],[1],[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],[2],[1],[1],[1],[1],[1]] => [[2,2,1,1,1,1,1]]
[[2],[2],[2],[1],[1],[1]] => [[2,2,2,1,1,1]]
[[2],[2],[2],[2],[1]] => [[2,2,2,2,1]]
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1,1],[1]]
[[1,1],[1,1],[1],[1],[1],[1],[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]]
[[3],[1],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1,1]]
[[3],[2],[1],[1],[1],[1]] => [[3,2,1,1,1,1]]
[[3],[2],[2],[1],[1]] => [[3,2,2,1,1]]
[[3],[2],[2],[2]] => [[3,2,2,2]]
[[3],[3],[1],[1],[1]] => [[3,3,1,1,1]]
[[3],[3],[2],[1]] => [[3,3,2,1]]
[[3],[3],[3]] => [[3,3,3]]
[[2,1],[1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1,1],[1]]
[[2,1],[2],[1],[1],[1],[1]] => [[2,2,1,1,1,1],[1]]
[[2,1],[2],[2],[1],[1]] => [[2,2,2,1,1],[1]]
[[2,1],[2],[2],[2]] => [[2,2,2,2],[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]] => [[2,1,1,1,1],[1,1,1]]
[[2,1],[1,1],[1,1],[1,1]] => [[2,1,1,1],[1,1,1,1]]
[[2,1],[2,1],[1],[1],[1]] => [[2,2,1,1,1],[1,1]]
[[2,1],[2,1],[2],[1]] => [[2,2,2,1],[1,1]]
[[2,1],[2,1],[1,1],[1]] => [[2,2,1,1],[1,1,1]]
[[2,1],[2,1],[2,1]] => [[2,2,2],[1,1,1]]
[[1,1,1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1],[1],[1]]
[[1,1,1],[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],[1,1,1],[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]]
[[4],[1],[1],[1],[1],[1]] => [[4,1,1,1,1,1]]
[[4],[2],[1],[1],[1]] => [[4,2,1,1,1]]
[[4],[2],[2],[1]] => [[4,2,2,1]]
[[4],[3],[1],[1]] => [[4,3,1,1]]
[[4],[3],[2]] => [[4,3,2]]
[[4],[4],[1]] => [[4,4,1]]
[[3,1],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1],[1]]
[[3,1],[2],[1],[1],[1]] => [[3,2,1,1,1],[1]]
[[3,1],[2],[2],[1]] => [[3,2,2,1],[1]]
[[3,1],[1,1],[1],[1],[1]] => [[3,1,1,1,1],[1,1]]
[[3,1],[1,1],[1,1],[1]] => [[3,1,1,1],[1,1,1]]
[[3,1],[3],[1],[1]] => [[3,3,1,1],[1]]
[[3,1],[3],[2]] => [[3,3,2],[1]]
[[3,1],[2,1],[1],[1]] => [[3,2,1,1],[1,1]]
[[3,1],[2,1],[2]] => [[3,2,2],[1,1]]
[[3,1],[2,1],[1,1]] => [[3,2,1],[1,1,1]]
[[3,1],[3,1],[1]] => [[3,3,1],[1,1]]
[[2,2],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[2]]
[[2,2],[2],[1],[1],[1]] => [[2,2,1,1,1],[2]]
[[2,2],[2],[2],[1]] => [[2,2,2,1],[2]]
[[2,2],[1,1],[1],[1],[1]] => [[2,1,1,1,1],[2,1]]
[[2,2],[1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1]]
[[2,2],[2,1],[1],[1]] => [[2,2,1,1],[2,1]]
[[2,2],[2,1],[2]] => [[2,2,2],[2,1]]
[[2,2],[2,1],[1,1]] => [[2,2,1],[2,1,1]]
[[2,2],[2,2],[1]] => [[2,2,1],[2,2]]
[[2,1,1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[1],[1]]
[[2,1,1],[2],[1],[1],[1]] => [[2,2,1,1,1],[1],[1]]
[[2,1,1],[2],[2],[1]] => [[2,2,2,1],[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]] => [[2,1,1,1],[1,1,1],[1]]
[[2,1,1],[2,1],[1],[1]] => [[2,2,1,1],[1,1],[1]]
[[2,1,1],[2,1],[2]] => [[2,2,2],[1,1],[1]]
[[2,1,1],[2,1],[1,1]] => [[2,2,1],[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]] => [[2,1,1],[1,1,1],[1,1]]
[[2,1,1],[2,1,1],[1]] => [[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],[1,1,1],[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],[1,1]]
[[5],[1],[1],[1],[1]] => [[5,1,1,1,1]]
[[5],[2],[1],[1]] => [[5,2,1,1]]
[[5],[2],[2]] => [[5,2,2]]
[[5],[3],[1]] => [[5,3,1]]
[[5],[4]] => [[5,4]]
[[4,1],[1],[1],[1],[1]] => [[4,1,1,1,1],[1]]
[[4,1],[2],[1],[1]] => [[4,2,1,1],[1]]
[[4,1],[2],[2]] => [[4,2,2],[1]]
[[4,1],[1,1],[1],[1]] => [[4,1,1,1],[1,1]]
[[4,1],[1,1],[1,1]] => [[4,1,1],[1,1,1]]
[[4,1],[3],[1]] => [[4,3,1],[1]]
[[4,1],[2,1],[1]] => [[4,2,1],[1,1]]
[[4,1],[4]] => [[4,4],[1]]
[[4,1],[3,1]] => [[4,3],[1,1]]
[[3,2],[1],[1],[1],[1]] => [[3,1,1,1,1],[2]]
[[3,2],[2],[1],[1]] => [[3,2,1,1],[2]]
[[3,2],[2],[2]] => [[3,2,2],[2]]
[[3,2],[1,1],[1],[1]] => [[3,1,1,1],[2,1]]
[[3,2],[1,1],[1,1]] => [[3,1,1],[2,1,1]]
[[3,2],[3],[1]] => [[3,3,1],[2]]
[[3,2],[2,1],[1]] => [[3,2,1],[2,1]]
[[3,2],[3,1]] => [[3,3],[2,1]]
[[3,2],[2,2]] => [[3,2],[2,2]]
[[3,1,1],[1],[1],[1],[1]] => [[3,1,1,1,1],[1],[1]]
[[3,1,1],[2],[1],[1]] => [[3,2,1,1],[1],[1]]
[[3,1,1],[2],[2]] => [[3,2,2],[1],[1]]
[[3,1,1],[1,1],[1],[1]] => [[3,1,1,1],[1,1],[1]]
[[3,1,1],[1,1],[1,1]] => [[3,1,1],[1,1,1],[1]]
[[3,1,1],[3],[1]] => [[3,3,1],[1],[1]]
[[3,1,1],[2,1],[1]] => [[3,2,1],[1,1],[1]]
[[3,1,1],[1,1,1],[1]] => [[3,1,1],[1,1],[1,1]]
[[3,1,1],[3,1]] => [[3,3],[1,1],[1]]
[[3,1,1],[2,1,1]] => [[3,2],[1,1],[1,1]]
[[2,2,1],[1],[1],[1],[1]] => [[2,1,1,1,1],[2],[1]]
[[2,2,1],[2],[1],[1]] => [[2,2,1,1],[2],[1]]
[[2,2,1],[2],[2]] => [[2,2,2],[2],[1]]
[[2,2,1],[1,1],[1],[1]] => [[2,1,1,1],[2,1],[1]]
[[2,2,1],[1,1],[1,1]] => [[2,1,1],[2,1,1],[1]]
[[2,2,1],[2,1],[1]] => [[2,2,1],[2,1],[1]]
[[2,2,1],[1,1,1],[1]] => [[2,1,1],[2,1],[1,1]]
[[2,2,1],[2,2]] => [[2,2],[2,2],[1]]
[[2,2,1],[2,1,1]] => [[2,2],[2,1],[1,1]]
[[2,1,1,1],[1],[1],[1],[1]] => [[2,1,1,1,1],[1],[1],[1]]
[[2,1,1,1],[2],[1],[1]] => [[2,2,1,1],[1],[1],[1]]
[[2,1,1,1],[2],[2]] => [[2,2,2],[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]] => [[2,1,1],[1,1,1],[1],[1]]
[[2,1,1,1],[2,1],[1]] => [[2,2,1],[1,1],[1],[1]]
[[2,1,1,1],[1,1,1],[1]] => [[2,1,1],[1,1],[1,1],[1]]
[[2,1,1,1],[2,1,1]] => [[2,2],[1,1],[1,1],[1]]
[[2,1,1,1],[1,1,1,1]] => [[2,1],[1,1],[1,1],[1,1]]
[[1,1,1,1,1],[1],[1],[1],[1]] => [[1,1,1,1,1],[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],[1,1],[1,1],[1],[1]]
[[1,1,1,1,1],[1,1,1,1]] => [[1,1],[1,1],[1,1],[1,1],[1]]
[[6],[1],[1],[1]] => [[6,1,1,1]]
[[6],[2],[1]] => [[6,2,1]]
[[6],[3]] => [[6,3]]
[[5,1],[1],[1],[1]] => [[5,1,1,1],[1]]
[[5,1],[2],[1]] => [[5,2,1],[1]]
[[5,1],[1,1],[1]] => [[5,1,1],[1,1]]
[[5,1],[3]] => [[5,3],[1]]
[[5,1],[2,1]] => [[5,2],[1,1]]
[[4,2],[1],[1],[1]] => [[4,1,1,1],[2]]
[[4,2],[2],[1]] => [[4,2,1],[2]]
[[4,2],[1,1],[1]] => [[4,1,1],[2,1]]
[[4,2],[3]] => [[4,3],[2]]
[[4,2],[2,1]] => [[4,2],[2,1]]
[[4,1,1],[1],[1],[1]] => [[4,1,1,1],[1],[1]]
[[4,1,1],[2],[1]] => [[4,2,1],[1],[1]]
[[4,1,1],[1,1],[1]] => [[4,1,1],[1,1],[1]]
[[4,1,1],[3]] => [[4,3],[1],[1]]
[[4,1,1],[2,1]] => [[4,2],[1,1],[1]]
[[4,1,1],[1,1,1]] => [[4,1],[1,1],[1,1]]
[[3,3],[1],[1],[1]] => [[3,1,1,1],[3]]
[[3,3],[2],[1]] => [[3,2,1],[3]]
[[3,3],[1,1],[1]] => [[3,1,1],[3,1]]
[[3,3],[3]] => [[3,3],[3]]
[[3,3],[2,1]] => [[3,2],[3,1]]
[[3,2,1],[1],[1],[1]] => [[3,1,1,1],[2],[1]]
[[3,2,1],[2],[1]] => [[3,2,1],[2],[1]]
[[3,2,1],[1,1],[1]] => [[3,1,1],[2,1],[1]]
[[3,2,1],[3]] => [[3,3],[2],[1]]
[[3,2,1],[2,1]] => [[3,2],[2,1],[1]]
[[3,2,1],[1,1,1]] => [[3,1],[2,1],[1,1]]
[[3,1,1,1],[1],[1],[1]] => [[3,1,1,1],[1],[1],[1]]
[[3,1,1,1],[2],[1]] => [[3,2,1],[1],[1],[1]]
[[3,1,1,1],[1,1],[1]] => [[3,1,1],[1,1],[1],[1]]
[[3,1,1,1],[3]] => [[3,3],[1],[1],[1]]
[[3,1,1,1],[2,1]] => [[3,2],[1,1],[1],[1]]
[[3,1,1,1],[1,1,1]] => [[3,1],[1,1],[1,1],[1]]
[[2,2,2],[1],[1],[1]] => [[2,1,1,1],[2],[2]]
[[2,2,2],[2],[1]] => [[2,2,1],[2],[2]]
[[2,2,2],[1,1],[1]] => [[2,1,1],[2,1],[2]]
[[2,2,2],[2,1]] => [[2,2],[2,1],[2]]
[[2,2,2],[1,1,1]] => [[2,1],[2,1],[2,1]]
[[2,2,1,1],[1],[1],[1]] => [[2,1,1,1],[2],[1],[1]]
[[2,2,1,1],[2],[1]] => [[2,2,1],[2],[1],[1]]
[[2,2,1,1],[1,1],[1]] => [[2,1,1],[2,1],[1],[1]]
[[2,2,1,1],[2,1]] => [[2,2],[2,1],[1],[1]]
[[2,2,1,1],[1,1,1]] => [[2,1],[2,1],[1,1],[1]]
[[2,1,1,1,1],[1],[1],[1]] => [[2,1,1,1],[1],[1],[1],[1]]
[[2,1,1,1,1],[2],[1]] => [[2,2,1],[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],[2,1]] => [[2,2],[1,1],[1],[1],[1]]
[[2,1,1,1,1],[1,1,1]] => [[2,1],[1,1],[1,1],[1],[1]]
[[1,1,1,1,1,1],[1],[1],[1]] => [[1,1,1,1],[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]]
[[7],[1],[1]] => [[7,1,1]]
[[7],[2]] => [[7,2]]
[[6,1],[1],[1]] => [[6,1,1],[1]]
[[6,1],[2]] => [[6,2],[1]]
[[6,1],[1,1]] => [[6,1],[1,1]]
[[5,2],[1],[1]] => [[5,1,1],[2]]
[[5,2],[2]] => [[5,2],[2]]
[[5,2],[1,1]] => [[5,1],[2,1]]
[[5,1,1],[1],[1]] => [[5,1,1],[1],[1]]
[[5,1,1],[2]] => [[5,2],[1],[1]]
[[5,1,1],[1,1]] => [[5,1],[1,1],[1]]
[[4,3],[1],[1]] => [[4,1,1],[3]]
[[4,3],[2]] => [[4,2],[3]]
[[4,3],[1,1]] => [[4,1],[3,1]]
[[4,2,1],[1],[1]] => [[4,1,1],[2],[1]]
[[4,2,1],[2]] => [[4,2],[2],[1]]
[[4,2,1],[1,1]] => [[4,1],[2,1],[1]]
[[4,1,1,1],[1],[1]] => [[4,1,1],[1],[1],[1]]
[[4,1,1,1],[2]] => [[4,2],[1],[1],[1]]
[[4,1,1,1],[1,1]] => [[4,1],[1,1],[1],[1]]
[[3,3,1],[1],[1]] => [[3,1,1],[3],[1]]
[[3,3,1],[2]] => [[3,2],[3],[1]]
[[3,3,1],[1,1]] => [[3,1],[3,1],[1]]
[[3,2,2],[1],[1]] => [[3,1,1],[2],[2]]
[[3,2,2],[2]] => [[3,2],[2],[2]]
[[3,2,2],[1,1]] => [[3,1],[2,1],[2]]
[[3,2,1,1],[1],[1]] => [[3,1,1],[2],[1],[1]]
[[3,2,1,1],[2]] => [[3,2],[2],[1],[1]]
[[3,2,1,1],[1,1]] => [[3,1],[2,1],[1],[1]]
[[3,1,1,1,1],[1],[1]] => [[3,1,1],[1],[1],[1],[1]]
[[3,1,1,1,1],[2]] => [[3,2],[1],[1],[1],[1]]
[[3,1,1,1,1],[1,1]] => [[3,1],[1,1],[1],[1],[1]]
[[2,2,2,1],[1],[1]] => [[2,1,1],[2],[2],[1]]
[[2,2,2,1],[2]] => [[2,2],[2],[2],[1]]
[[2,2,2,1],[1,1]] => [[2,1],[2,1],[2],[1]]
[[2,2,1,1,1],[1],[1]] => [[2,1,1],[2],[1],[1],[1]]
[[2,2,1,1,1],[2]] => [[2,2],[2],[1],[1],[1]]
[[2,2,1,1,1],[1,1]] => [[2,1],[2,1],[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],[2]] => [[2,2],[1],[1],[1],[1],[1]]
[[2,1,1,1,1,1],[1,1]] => [[2,1],[1,1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1],[1],[1]] => [[1,1,1],[1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1],[1,1]] => [[1,1],[1,1],[1],[1],[1],[1],[1]]
[[8],[1]] => [[8,1]]
[[7,1],[1]] => [[7,1],[1]]
[[6,2],[1]] => [[6,1],[2]]
[[6,1,1],[1]] => [[6,1],[1],[1]]
[[5,3],[1]] => [[5,1],[3]]
[[5,2,1],[1]] => [[5,1],[2],[1]]
[[5,1,1,1],[1]] => [[5,1],[1],[1],[1]]
[[4,4],[1]] => [[4,1],[4]]
[[4,3,1],[1]] => [[4,1],[3],[1]]
[[4,2,2],[1]] => [[4,1],[2],[2]]
[[4,2,1,1],[1]] => [[4,1],[2],[1],[1]]
[[4,1,1,1,1],[1]] => [[4,1],[1],[1],[1],[1]]
[[3,3,2],[1]] => [[3,1],[3],[2]]
[[3,3,1,1],[1]] => [[3,1],[3],[1],[1]]
[[3,2,2,1],[1]] => [[3,1],[2],[2],[1]]
[[3,2,1,1,1],[1]] => [[3,1],[2],[1],[1],[1]]
[[3,1,1,1,1,1],[1]] => [[3,1],[1],[1],[1],[1],[1]]
[[2,2,2,2],[1]] => [[2,1],[2],[2],[2]]
[[2,2,2,1,1],[1]] => [[2,1],[2],[2],[1],[1]]
[[2,2,1,1,1,1],[1]] => [[2,1],[2],[1],[1],[1],[1]]
[[2,1,1,1,1,1,1],[1]] => [[2,1],[1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1,1],[1]] => [[1,1],[1],[1],[1],[1],[1],[1],[1]]
[[9]] => [[9]]
[[8,1]] => [[8],[1]]
[[7,2]] => [[7],[2]]
[[7,1,1]] => [[7],[1],[1]]
[[6,3]] => [[6],[3]]
[[6,2,1]] => [[6],[2],[1]]
[[6,1,1,1]] => [[6],[1],[1],[1]]
[[5,4]] => [[5],[4]]
[[5,3,1]] => [[5],[3],[1]]
[[5,2,2]] => [[5],[2],[2]]
[[5,2,1,1]] => [[5],[2],[1],[1]]
[[5,1,1,1,1]] => [[5],[1],[1],[1],[1]]
[[4,4,1]] => [[4],[4],[1]]
[[4,3,2]] => [[4],[3],[2]]
[[4,3,1,1]] => [[4],[3],[1],[1]]
[[4,2,2,1]] => [[4],[2],[2],[1]]
[[4,2,1,1,1]] => [[4],[2],[1],[1],[1]]
[[4,1,1,1,1,1]] => [[4],[1],[1],[1],[1],[1]]
[[3,3,3]] => [[3],[3],[3]]
[[3,3,2,1]] => [[3],[3],[2],[1]]
[[3,3,1,1,1]] => [[3],[3],[1],[1],[1]]
[[3,2,2,2]] => [[3],[2],[2],[2]]
[[3,2,2,1,1]] => [[3],[2],[2],[1],[1]]
[[3,2,1,1,1,1]] => [[3],[2],[1],[1],[1],[1]]
[[3,1,1,1,1,1,1]] => [[3],[1],[1],[1],[1],[1],[1]]
[[2,2,2,2,1]] => [[2],[2],[2],[2],[1]]
[[2,2,2,1,1,1]] => [[2],[2],[2],[1],[1],[1]]
[[2,2,1,1,1,1,1]] => [[2],[2],[1],[1],[1],[1],[1]]
[[2,1,1,1,1,1,1,1]] => [[2],[1],[1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1,1,1]] => [[1],[1],[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],[1],[1],[1],[1],[1],[1],[1],[1]] => [[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],[2],[1],[1],[1],[1]] => [[2,2,2,1,1,1,1]]
[[2],[2],[2],[2],[1],[1]] => [[2,2,2,2,1,1]]
[[2],[2],[2],[2],[2]] => [[2,2,2,2,2]]
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1,1,1],[1]]
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => [[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],[1,1],[1,1]] => [[1,1,1,1,1],[1,1,1,1,1]]
[[3],[1],[1],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1,1,1]]
[[3],[2],[1],[1],[1],[1],[1]] => [[3,2,1,1,1,1,1]]
[[3],[2],[2],[1],[1],[1]] => [[3,2,2,1,1,1]]
[[3],[2],[2],[2],[1]] => [[3,2,2,2,1]]
[[3],[3],[1],[1],[1],[1]] => [[3,3,1,1,1,1]]
[[3],[3],[2],[1],[1]] => [[3,3,2,1,1]]
[[3],[3],[2],[2]] => [[3,3,2,2]]
[[3],[3],[3],[1]] => [[3,3,3,1]]
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1,1,1],[1]]
[[2,1],[2],[1],[1],[1],[1],[1]] => [[2,2,1,1,1,1,1],[1]]
[[2,1],[2],[2],[1],[1],[1]] => [[2,2,2,1,1,1],[1]]
[[2,1],[2],[2],[2],[1]] => [[2,2,2,2,1],[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]] => [[2,1,1,1,1,1],[1,1,1]]
[[2,1],[1,1],[1,1],[1,1],[1]] => [[2,1,1,1,1],[1,1,1,1]]
[[2,1],[2,1],[1],[1],[1],[1]] => [[2,2,1,1,1,1],[1,1]]
[[2,1],[2,1],[2],[1],[1]] => [[2,2,2,1,1],[1,1]]
[[2,1],[2,1],[2],[2]] => [[2,2,2,2],[1,1]]
[[2,1],[2,1],[1,1],[1],[1]] => [[2,2,1,1,1],[1,1,1]]
[[2,1],[2,1],[1,1],[1,1]] => [[2,2,1,1],[1,1,1,1]]
[[2,1],[2,1],[2,1],[1]] => [[2,2,2,1],[1,1,1]]
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => [[1,1,1,1,1,1,1,1],[1],[1]]
[[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],[1,1,1,1],[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]] => [[1,1,1,1],[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]]
[[4],[1],[1],[1],[1],[1],[1]] => [[4,1,1,1,1,1,1]]
[[4],[2],[1],[1],[1],[1]] => [[4,2,1,1,1,1]]
[[4],[2],[2],[1],[1]] => [[4,2,2,1,1]]
[[4],[2],[2],[2]] => [[4,2,2,2]]
[[4],[3],[1],[1],[1]] => [[4,3,1,1,1]]
[[4],[3],[2],[1]] => [[4,3,2,1]]
[[4],[3],[3]] => [[4,3,3]]
[[4],[4],[1],[1]] => [[4,4,1,1]]
[[4],[4],[2]] => [[4,4,2]]
[[3,1],[1],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1,1],[1]]
[[3,1],[2],[1],[1],[1],[1]] => [[3,2,1,1,1,1],[1]]
[[3,1],[2],[2],[1],[1]] => [[3,2,2,1,1],[1]]
[[3,1],[2],[2],[2]] => [[3,2,2,2],[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]] => [[3,1,1,1,1],[1,1,1]]
[[3,1],[1,1],[1,1],[1,1]] => [[3,1,1,1],[1,1,1,1]]
[[3,1],[3],[1],[1],[1]] => [[3,3,1,1,1],[1]]
[[3,1],[3],[2],[1]] => [[3,3,2,1],[1]]
[[3,1],[3],[3]] => [[3,3,3],[1]]
[[3,1],[2,1],[1],[1],[1]] => [[3,2,1,1,1],[1,1]]
[[3,1],[2,1],[2],[1]] => [[3,2,2,1],[1,1]]
[[3,1],[2,1],[1,1],[1]] => [[3,2,1,1],[1,1,1]]
[[3,1],[2,1],[2,1]] => [[3,2,2],[1,1,1]]
[[3,1],[3,1],[1],[1]] => [[3,3,1,1],[1,1]]
[[3,1],[3,1],[2]] => [[3,3,2],[1,1]]
[[3,1],[3,1],[1,1]] => [[3,3,1],[1,1,1]]
[[2,2],[1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1,1],[2]]
[[2,2],[2],[1],[1],[1],[1]] => [[2,2,1,1,1,1],[2]]
[[2,2],[2],[2],[1],[1]] => [[2,2,2,1,1],[2]]
[[2,2],[2],[2],[2]] => [[2,2,2,2],[2]]
[[2,2],[1,1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[2,1]]
[[2,2],[1,1],[1,1],[1],[1]] => [[2,1,1,1,1],[2,1,1]]
[[2,2],[1,1],[1,1],[1,1]] => [[2,1,1,1],[2,1,1,1]]
[[2,2],[2,1],[1],[1],[1]] => [[2,2,1,1,1],[2,1]]
[[2,2],[2,1],[2],[1]] => [[2,2,2,1],[2,1]]
[[2,2],[2,1],[1,1],[1]] => [[2,2,1,1],[2,1,1]]
[[2,2],[2,1],[2,1]] => [[2,2,2],[2,1,1]]
[[2,2],[2,2],[1],[1]] => [[2,2,1,1],[2,2]]
[[2,2],[2,2],[2]] => [[2,2,2],[2,2]]
[[2,2],[2,2],[1,1]] => [[2,2,1],[2,2,1]]
[[2,1,1],[1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1,1],[1],[1]]
[[2,1,1],[2],[1],[1],[1],[1]] => [[2,2,1,1,1,1],[1],[1]]
[[2,1,1],[2],[2],[1],[1]] => [[2,2,2,1,1],[1],[1]]
[[2,1,1],[2],[2],[2]] => [[2,2,2,2],[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]] => [[2,1,1,1,1],[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],[2,1],[1],[1],[1]] => [[2,2,1,1,1],[1,1],[1]]
[[2,1,1],[2,1],[2],[1]] => [[2,2,2,1],[1,1],[1]]
[[2,1,1],[2,1],[1,1],[1]] => [[2,2,1,1],[1,1,1],[1]]
[[2,1,1],[2,1],[2,1]] => [[2,2,2],[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]] => [[2,1,1,1],[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],[2,1,1],[1],[1]] => [[2,2,1,1],[1,1],[1,1]]
[[2,1,1],[2,1,1],[2]] => [[2,2,2],[1,1],[1,1]]
[[2,1,1],[2,1,1],[1,1]] => [[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]] => [[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],[1,1,1],[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]]
[[1,1,1,1],[1,1,1,1],[1,1]] => [[1,1,1],[1,1,1],[1,1],[1,1]]
[[5],[1],[1],[1],[1],[1]] => [[5,1,1,1,1,1]]
[[5],[2],[1],[1],[1]] => [[5,2,1,1,1]]
[[5],[2],[2],[1]] => [[5,2,2,1]]
[[5],[3],[1],[1]] => [[5,3,1,1]]
[[5],[3],[2]] => [[5,3,2]]
[[5],[4],[1]] => [[5,4,1]]
[[5],[5]] => [[5,5]]
[[4,1],[1],[1],[1],[1],[1]] => [[4,1,1,1,1,1],[1]]
[[4,1],[2],[1],[1],[1]] => [[4,2,1,1,1],[1]]
[[4,1],[2],[2],[1]] => [[4,2,2,1],[1]]
[[4,1],[1,1],[1],[1],[1]] => [[4,1,1,1,1],[1,1]]
[[4,1],[1,1],[1,1],[1]] => [[4,1,1,1],[1,1,1]]
[[4,1],[3],[1],[1]] => [[4,3,1,1],[1]]
[[4,1],[3],[2]] => [[4,3,2],[1]]
[[4,1],[2,1],[1],[1]] => [[4,2,1,1],[1,1]]
[[4,1],[2,1],[2]] => [[4,2,2],[1,1]]
[[4,1],[2,1],[1,1]] => [[4,2,1],[1,1,1]]
[[4,1],[4],[1]] => [[4,4,1],[1]]
[[4,1],[3,1],[1]] => [[4,3,1],[1,1]]
[[4,1],[4,1]] => [[4,4],[1,1]]
[[3,2],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1],[2]]
[[3,2],[2],[1],[1],[1]] => [[3,2,1,1,1],[2]]
[[3,2],[2],[2],[1]] => [[3,2,2,1],[2]]
[[3,2],[1,1],[1],[1],[1]] => [[3,1,1,1,1],[2,1]]
[[3,2],[1,1],[1,1],[1]] => [[3,1,1,1],[2,1,1]]
[[3,2],[3],[1],[1]] => [[3,3,1,1],[2]]
[[3,2],[3],[2]] => [[3,3,2],[2]]
[[3,2],[2,1],[1],[1]] => [[3,2,1,1],[2,1]]
[[3,2],[2,1],[2]] => [[3,2,2],[2,1]]
[[3,2],[2,1],[1,1]] => [[3,2,1],[2,1,1]]
[[3,2],[3,1],[1]] => [[3,3,1],[2,1]]
[[3,2],[2,2],[1]] => [[3,2,1],[2,2]]
[[3,2],[3,2]] => [[3,3],[2,2]]
[[3,1,1],[1],[1],[1],[1],[1]] => [[3,1,1,1,1,1],[1],[1]]
[[3,1,1],[2],[1],[1],[1]] => [[3,2,1,1,1],[1],[1]]
[[3,1,1],[2],[2],[1]] => [[3,2,2,1],[1],[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]] => [[3,1,1,1],[1,1,1],[1]]
[[3,1,1],[3],[1],[1]] => [[3,3,1,1],[1],[1]]
[[3,1,1],[3],[2]] => [[3,3,2],[1],[1]]
[[3,1,1],[2,1],[1],[1]] => [[3,2,1,1],[1,1],[1]]
[[3,1,1],[2,1],[2]] => [[3,2,2],[1,1],[1]]
[[3,1,1],[2,1],[1,1]] => [[3,2,1],[1,1,1],[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]] => [[3,1,1],[1,1,1],[1,1]]
[[3,1,1],[3,1],[1]] => [[3,3,1],[1,1],[1]]
[[3,1,1],[2,1,1],[1]] => [[3,2,1],[1,1],[1,1]]
[[3,1,1],[3,1,1]] => [[3,3],[1,1],[1,1]]
[[2,2,1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[2],[1]]
[[2,2,1],[2],[1],[1],[1]] => [[2,2,1,1,1],[2],[1]]
[[2,2,1],[2],[2],[1]] => [[2,2,2,1],[2],[1]]
[[2,2,1],[1,1],[1],[1],[1]] => [[2,1,1,1,1],[2,1],[1]]
[[2,2,1],[1,1],[1,1],[1]] => [[2,1,1,1],[2,1,1],[1]]
[[2,2,1],[2,1],[1],[1]] => [[2,2,1,1],[2,1],[1]]
[[2,2,1],[2,1],[2]] => [[2,2,2],[2,1],[1]]
[[2,2,1],[2,1],[1,1]] => [[2,2,1],[2,1,1],[1]]
[[2,2,1],[1,1,1],[1],[1]] => [[2,1,1,1],[2,1],[1,1]]
[[2,2,1],[1,1,1],[1,1]] => [[2,1,1],[2,1,1],[1,1]]
[[2,2,1],[2,2],[1]] => [[2,2,1],[2,2],[1]]
[[2,2,1],[2,1,1],[1]] => [[2,2,1],[2,1],[1,1]]
[[2,2,1],[2,2,1]] => [[2,2],[2,2],[1,1]]
[[2,1,1,1],[1],[1],[1],[1],[1]] => [[2,1,1,1,1,1],[1],[1],[1]]
[[2,1,1,1],[2],[1],[1],[1]] => [[2,2,1,1,1],[1],[1],[1]]
[[2,1,1,1],[2],[2],[1]] => [[2,2,2,1],[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]] => [[2,1,1,1],[1,1,1],[1],[1]]
[[2,1,1,1],[2,1],[1],[1]] => [[2,2,1,1],[1,1],[1],[1]]
[[2,1,1,1],[2,1],[2]] => [[2,2,2],[1,1],[1],[1]]
[[2,1,1,1],[2,1],[1,1]] => [[2,2,1],[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]] => [[2,1,1],[1,1,1],[1,1],[1]]
[[2,1,1,1],[2,1,1],[1]] => [[2,2,1],[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],[2,1,1,1]] => [[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]] => [[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],[1,1,1,1],[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],[1],[1],[1],[1]] => [[6,1,1,1,1]]
[[6],[2],[1],[1]] => [[6,2,1,1]]
[[6],[2],[2]] => [[6,2,2]]
[[6],[3],[1]] => [[6,3,1]]
[[6],[4]] => [[6,4]]
[[5,1],[1],[1],[1],[1]] => [[5,1,1,1,1],[1]]
[[5,1],[2],[1],[1]] => [[5,2,1,1],[1]]
[[5,1],[2],[2]] => [[5,2,2],[1]]
[[5,1],[1,1],[1],[1]] => [[5,1,1,1],[1,1]]
[[5,1],[1,1],[1,1]] => [[5,1,1],[1,1,1]]
[[5,1],[3],[1]] => [[5,3,1],[1]]
[[5,1],[2,1],[1]] => [[5,2,1],[1,1]]
[[5,1],[4]] => [[5,4],[1]]
[[5,1],[3,1]] => [[5,3],[1,1]]
[[4,2],[1],[1],[1],[1]] => [[4,1,1,1,1],[2]]
[[4,2],[2],[1],[1]] => [[4,2,1,1],[2]]
[[4,2],[2],[2]] => [[4,2,2],[2]]
[[4,2],[1,1],[1],[1]] => [[4,1,1,1],[2,1]]
[[4,2],[1,1],[1,1]] => [[4,1,1],[2,1,1]]
[[4,2],[3],[1]] => [[4,3,1],[2]]
[[4,2],[2,1],[1]] => [[4,2,1],[2,1]]
[[4,2],[4]] => [[4,4],[2]]
[[4,2],[3,1]] => [[4,3],[2,1]]
[[4,2],[2,2]] => [[4,2],[2,2]]
[[4,1,1],[1],[1],[1],[1]] => [[4,1,1,1,1],[1],[1]]
[[4,1,1],[2],[1],[1]] => [[4,2,1,1],[1],[1]]
[[4,1,1],[2],[2]] => [[4,2,2],[1],[1]]
[[4,1,1],[1,1],[1],[1]] => [[4,1,1,1],[1,1],[1]]
[[4,1,1],[1,1],[1,1]] => [[4,1,1],[1,1,1],[1]]
[[4,1,1],[3],[1]] => [[4,3,1],[1],[1]]
[[4,1,1],[2,1],[1]] => [[4,2,1],[1,1],[1]]
[[4,1,1],[1,1,1],[1]] => [[4,1,1],[1,1],[1,1]]
[[4,1,1],[4]] => [[4,4],[1],[1]]
[[4,1,1],[3,1]] => [[4,3],[1,1],[1]]
[[4,1,1],[2,1,1]] => [[4,2],[1,1],[1,1]]
[[3,3],[1],[1],[1],[1]] => [[3,1,1,1,1],[3]]
[[3,3],[2],[1],[1]] => [[3,2,1,1],[3]]
[[3,3],[2],[2]] => [[3,2,2],[3]]
[[3,3],[1,1],[1],[1]] => [[3,1,1,1],[3,1]]
[[3,3],[1,1],[1,1]] => [[3,1,1],[3,1,1]]
[[3,3],[3],[1]] => [[3,3,1],[3]]
[[3,3],[2,1],[1]] => [[3,2,1],[3,1]]
[[3,3],[3,1]] => [[3,3],[3,1]]
[[3,3],[2,2]] => [[3,2],[3,2]]
[[3,2,1],[1],[1],[1],[1]] => [[3,1,1,1,1],[2],[1]]
[[3,2,1],[2],[1],[1]] => [[3,2,1,1],[2],[1]]
[[3,2,1],[2],[2]] => [[3,2,2],[2],[1]]
[[3,2,1],[1,1],[1],[1]] => [[3,1,1,1],[2,1],[1]]
[[3,2,1],[1,1],[1,1]] => [[3,1,1],[2,1,1],[1]]
[[3,2,1],[3],[1]] => [[3,3,1],[2],[1]]
[[3,2,1],[2,1],[1]] => [[3,2,1],[2,1],[1]]
[[3,2,1],[1,1,1],[1]] => [[3,1,1],[2,1],[1,1]]
[[3,2,1],[3,1]] => [[3,3],[2,1],[1]]
[[3,2,1],[2,2]] => [[3,2],[2,2],[1]]
[[3,2,1],[2,1,1]] => [[3,2],[2,1],[1,1]]
[[3,1,1,1],[1],[1],[1],[1]] => [[3,1,1,1,1],[1],[1],[1]]
[[3,1,1,1],[2],[1],[1]] => [[3,2,1,1],[1],[1],[1]]
[[3,1,1,1],[2],[2]] => [[3,2,2],[1],[1],[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]] => [[3,1,1],[1,1,1],[1],[1]]
[[3,1,1,1],[3],[1]] => [[3,3,1],[1],[1],[1]]
[[3,1,1,1],[2,1],[1]] => [[3,2,1],[1,1],[1],[1]]
[[3,1,1,1],[1,1,1],[1]] => [[3,1,1],[1,1],[1,1],[1]]
[[3,1,1,1],[3,1]] => [[3,3],[1,1],[1],[1]]
[[3,1,1,1],[2,1,1]] => [[3,2],[1,1],[1,1],[1]]
[[3,1,1,1],[1,1,1,1]] => [[3,1],[1,1],[1,1],[1,1]]
[[2,2,2],[1],[1],[1],[1]] => [[2,1,1,1,1],[2],[2]]
[[2,2,2],[2],[1],[1]] => [[2,2,1,1],[2],[2]]
[[2,2,2],[2],[2]] => [[2,2,2],[2],[2]]
[[2,2,2],[1,1],[1],[1]] => [[2,1,1,1],[2,1],[2]]
[[2,2,2],[1,1],[1,1]] => [[2,1,1],[2,1,1],[2]]
[[2,2,2],[2,1],[1]] => [[2,2,1],[2,1],[2]]
[[2,2,2],[1,1,1],[1]] => [[2,1,1],[2,1],[2,1]]
[[2,2,2],[2,2]] => [[2,2],[2,2],[2]]
[[2,2,2],[2,1,1]] => [[2,2],[2,1],[2,1]]
[[2,2,1,1],[1],[1],[1],[1]] => [[2,1,1,1,1],[2],[1],[1]]
[[2,2,1,1],[2],[1],[1]] => [[2,2,1,1],[2],[1],[1]]
[[2,2,1,1],[2],[2]] => [[2,2,2],[2],[1],[1]]
[[2,2,1,1],[1,1],[1],[1]] => [[2,1,1,1],[2,1],[1],[1]]
[[2,2,1,1],[1,1],[1,1]] => [[2,1,1],[2,1,1],[1],[1]]
[[2,2,1,1],[2,1],[1]] => [[2,2,1],[2,1],[1],[1]]
[[2,2,1,1],[1,1,1],[1]] => [[2,1,1],[2,1],[1,1],[1]]
[[2,2,1,1],[2,2]] => [[2,2],[2,2],[1],[1]]
[[2,2,1,1],[2,1,1]] => [[2,2],[2,1],[1,1],[1]]
[[2,2,1,1],[1,1,1,1]] => [[2,1],[2,1],[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],[2],[1],[1]] => [[2,2,1,1],[1],[1],[1],[1]]
[[2,1,1,1,1],[2],[2]] => [[2,2,2],[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]] => [[2,1,1],[1,1,1],[1],[1],[1]]
[[2,1,1,1,1],[2,1],[1]] => [[2,2,1],[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],[2,1,1]] => [[2,2],[1,1],[1,1],[1],[1]]
[[2,1,1,1,1],[1,1,1,1]] => [[2,1],[1,1],[1,1],[1,1],[1]]
[[1,1,1,1,1,1],[1],[1],[1],[1]] => [[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],[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]]
[[7],[1],[1],[1]] => [[7,1,1,1]]
[[7],[2],[1]] => [[7,2,1]]
[[7],[3]] => [[7,3]]
[[6,1],[1],[1],[1]] => [[6,1,1,1],[1]]
[[6,1],[2],[1]] => [[6,2,1],[1]]
[[6,1],[1,1],[1]] => [[6,1,1],[1,1]]
[[6,1],[3]] => [[6,3],[1]]
[[6,1],[2,1]] => [[6,2],[1,1]]
[[5,2],[1],[1],[1]] => [[5,1,1,1],[2]]
[[5,2],[2],[1]] => [[5,2,1],[2]]
[[5,2],[1,1],[1]] => [[5,1,1],[2,1]]
[[5,2],[3]] => [[5,3],[2]]
[[5,2],[2,1]] => [[5,2],[2,1]]
[[5,1,1],[1],[1],[1]] => [[5,1,1,1],[1],[1]]
[[5,1,1],[2],[1]] => [[5,2,1],[1],[1]]
[[5,1,1],[1,1],[1]] => [[5,1,1],[1,1],[1]]
[[5,1,1],[3]] => [[5,3],[1],[1]]
[[5,1,1],[2,1]] => [[5,2],[1,1],[1]]
[[5,1,1],[1,1,1]] => [[5,1],[1,1],[1,1]]
[[4,3],[1],[1],[1]] => [[4,1,1,1],[3]]
[[4,3],[2],[1]] => [[4,2,1],[3]]
[[4,3],[1,1],[1]] => [[4,1,1],[3,1]]
[[4,3],[3]] => [[4,3],[3]]
[[4,3],[2,1]] => [[4,2],[3,1]]
[[4,2,1],[1],[1],[1]] => [[4,1,1,1],[2],[1]]
[[4,2,1],[2],[1]] => [[4,2,1],[2],[1]]
[[4,2,1],[1,1],[1]] => [[4,1,1],[2,1],[1]]
[[4,2,1],[3]] => [[4,3],[2],[1]]
[[4,2,1],[2,1]] => [[4,2],[2,1],[1]]
[[4,2,1],[1,1,1]] => [[4,1],[2,1],[1,1]]
[[4,1,1,1],[1],[1],[1]] => [[4,1,1,1],[1],[1],[1]]
[[4,1,1,1],[2],[1]] => [[4,2,1],[1],[1],[1]]
[[4,1,1,1],[1,1],[1]] => [[4,1,1],[1,1],[1],[1]]
[[4,1,1,1],[3]] => [[4,3],[1],[1],[1]]
[[4,1,1,1],[2,1]] => [[4,2],[1,1],[1],[1]]
[[4,1,1,1],[1,1,1]] => [[4,1],[1,1],[1,1],[1]]
[[3,3,1],[1],[1],[1]] => [[3,1,1,1],[3],[1]]
[[3,3,1],[2],[1]] => [[3,2,1],[3],[1]]
[[3,3,1],[1,1],[1]] => [[3,1,1],[3,1],[1]]
[[3,3,1],[3]] => [[3,3],[3],[1]]
[[3,3,1],[2,1]] => [[3,2],[3,1],[1]]
[[3,3,1],[1,1,1]] => [[3,1],[3,1],[1,1]]
[[3,2,2],[1],[1],[1]] => [[3,1,1,1],[2],[2]]
[[3,2,2],[2],[1]] => [[3,2,1],[2],[2]]
[[3,2,2],[1,1],[1]] => [[3,1,1],[2,1],[2]]
[[3,2,2],[3]] => [[3,3],[2],[2]]
[[3,2,2],[2,1]] => [[3,2],[2,1],[2]]
[[3,2,2],[1,1,1]] => [[3,1],[2,1],[2,1]]
[[3,2,1,1],[1],[1],[1]] => [[3,1,1,1],[2],[1],[1]]
[[3,2,1,1],[2],[1]] => [[3,2,1],[2],[1],[1]]
[[3,2,1,1],[1,1],[1]] => [[3,1,1],[2,1],[1],[1]]
[[3,2,1,1],[3]] => [[3,3],[2],[1],[1]]
[[3,2,1,1],[2,1]] => [[3,2],[2,1],[1],[1]]
[[3,2,1,1],[1,1,1]] => [[3,1],[2,1],[1,1],[1]]
[[3,1,1,1,1],[1],[1],[1]] => [[3,1,1,1],[1],[1],[1],[1]]
[[3,1,1,1,1],[2],[1]] => [[3,2,1],[1],[1],[1],[1]]
[[3,1,1,1,1],[1,1],[1]] => [[3,1,1],[1,1],[1],[1],[1]]
[[3,1,1,1,1],[3]] => [[3,3],[1],[1],[1],[1]]
[[3,1,1,1,1],[2,1]] => [[3,2],[1,1],[1],[1],[1]]
[[3,1,1,1,1],[1,1,1]] => [[3,1],[1,1],[1,1],[1],[1]]
[[2,2,2,1],[1],[1],[1]] => [[2,1,1,1],[2],[2],[1]]
[[2,2,2,1],[2],[1]] => [[2,2,1],[2],[2],[1]]
[[2,2,2,1],[1,1],[1]] => [[2,1,1],[2,1],[2],[1]]
[[2,2,2,1],[2,1]] => [[2,2],[2,1],[2],[1]]
[[2,2,2,1],[1,1,1]] => [[2,1],[2,1],[2,1],[1]]
[[2,2,1,1,1],[1],[1],[1]] => [[2,1,1,1],[2],[1],[1],[1]]
[[2,2,1,1,1],[2],[1]] => [[2,2,1],[2],[1],[1],[1]]
[[2,2,1,1,1],[1,1],[1]] => [[2,1,1],[2,1],[1],[1],[1]]
[[2,2,1,1,1],[2,1]] => [[2,2],[2,1],[1],[1],[1]]
[[2,2,1,1,1],[1,1,1]] => [[2,1],[2,1],[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],[2],[1]] => [[2,2,1],[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],[2,1]] => [[2,2],[1,1],[1],[1],[1],[1]]
[[2,1,1,1,1,1],[1,1,1]] => [[2,1],[1,1],[1,1],[1],[1],[1]]
[[1,1,1,1,1,1,1],[1],[1],[1]] => [[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]]
[[8],[1],[1]] => [[8,1,1]]
[[8],[2]] => [[8,2]]
[[7,1],[1],[1]] => [[7,1,1],[1]]
[[7,1],[2]] => [[7,2],[1]]
[[7,1],[1,1]] => [[7,1],[1,1]]
[[6,2],[1],[1]] => [[6,1,1],[2]]
[[6,2],[2]] => [[6,2],[2]]
[[6,2],[1,1]] => [[6,1],[2,1]]
[[6,1,1],[1],[1]] => [[6,1,1],[1],[1]]
[[6,1,1],[2]] => [[6,2],[1],[1]]
[[6,1,1],[1,1]] => [[6,1],[1,1],[1]]
[[5,3],[1],[1]] => [[5,1,1],[3]]
[[5,3],[2]] => [[5,2],[3]]
[[5,3],[1,1]] => [[5,1],[3,1]]
[[5,2,1],[1],[1]] => [[5,1,1],[2],[1]]
[[5,2,1],[2]] => [[5,2],[2],[1]]
[[5,2,1],[1,1]] => [[5,1],[2,1],[1]]
[[5,1,1,1],[1],[1]] => [[5,1,1],[1],[1],[1]]
[[5,1,1,1],[2]] => [[5,2],[1],[1],[1]]
[[5,1,1,1],[1,1]] => [[5,1],[1,1],[1],[1]]
[[4,4],[1],[1]] => [[4,1,1],[4]]
[[4,4],[2]] => [[4,2],[4]]
[[4,4],[1,1]] => [[4,1],[4,1]]
[[4,3,1],[1],[1]] => [[4,1,1],[3],[1]]
[[4,3,1],[2]] => [[4,2],[3],[1]]
[[4,3,1],[1,1]] => [[4,1],[3,1],[1]]
[[4,2,2],[1],[1]] => [[4,1,1],[2],[2]]
[[4,2,2],[2]] => [[4,2],[2],[2]]
[[4,2,2],[1,1]] => [[4,1],[2,1],[2]]
[[4,2,1,1],[1],[1]] => [[4,1,1],[2],[1],[1]]
[[4,2,1,1],[2]] => [[4,2],[2],[1],[1]]
[[4,2,1,1],[1,1]] => [[4,1],[2,1],[1],[1]]
[[4,1,1,1,1],[1],[1]] => [[4,1,1],[1],[1],[1],[1]]
[[4,1,1,1,1],[2]] => [[4,2],[1],[1],[1],[1]]
[[4,1,1,1,1],[1,1]] => [[4,1],[1,1],[1],[1],[1]]
[[3,3,2],[1],[1]] => [[3,1,1],[3],[2]]
[[3,3,2],[2]] => [[3,2],[3],[2]]
[[3,3,2],[1,1]] => [[3,1],[3,1],[2]]
[[3,3,1,1],[1],[1]] => [[3,1,1],[3],[1],[1]]
[[3,3,1,1],[2]] => [[3,2],[3],[1],[1]]
[[3,3,1,1],[1,1]] => [[3,1],[3,1],[1],[1]]
[[3,2,2,1],[1],[1]] => [[3,1,1],[2],[2],[1]]
[[3,2,2,1],[2]] => [[3,2],[2],[2],[1]]
[[3,2,2,1],[1,1]] => [[3,1],[2,1],[2],[1]]
[[3,2,1,1,1],[1],[1]] => [[3,1,1],[2],[1],[1],[1]]
[[3,2,1,1,1],[2]] => [[3,2],[2],[1],[1],[1]]
[[3,2,1,1,1],[1,1]] => [[3,1],[2,1],[1],[1],[1]]
[[3,1,1,1,1,1],[1],[1]] => [[3,1,1],[1],[1],[1],[1],[1]]
[[3,1,1,1,1,1],[2]] => [[3,2],[1],[1],[1],[1],[1]]
[[3,1,1,1,1,1],[1,1]] => [[3,1],[1,1],[1],[1],[1],[1]]
[[2,2,2,2],[1],[1]] => [[2,1,1],[2],[2],[2]]
[[2,2,2,2],[2]] => [[2,2],[2],[2],[2]]
[[2,2,2,2],[1,1]] => [[2,1],[2,1],[2],[2]]
[[2,2,2,1,1],[1],[1]] => [[2,1,1],[2],[2],[1],[1]]
[[2,2,2,1,1],[2]] => [[2,2],[2],[2],[1],[1]]
[[2,2,2,1,1],[1,1]] => [[2,1],[2,1],[2],[1],[1]]
[[2,2,1,1,1,1],[1],[1]] => [[2,1,1],[2],[1],[1],[1],[1]]
[[2,2,1,1,1,1],[2]] => [[2,2],[2],[1],[1],[1],[1]]
[[2,2,1,1,1,1],[1,1]] => [[2,1],[2,1],[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],[2]] => [[2,2],[1],[1],[1],[1],[1],[1]]
[[2,1,1,1,1,1,1],[1,1]] => [[2,1],[1,1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1,1],[1],[1]] => [[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],[1]] => [[9,1]]
[[8,1],[1]] => [[8,1],[1]]
[[7,2],[1]] => [[7,1],[2]]
[[7,1,1],[1]] => [[7,1],[1],[1]]
[[6,3],[1]] => [[6,1],[3]]
[[6,2,1],[1]] => [[6,1],[2],[1]]
[[6,1,1,1],[1]] => [[6,1],[1],[1],[1]]
[[5,4],[1]] => [[5,1],[4]]
[[5,3,1],[1]] => [[5,1],[3],[1]]
[[5,2,2],[1]] => [[5,1],[2],[2]]
[[5,2,1,1],[1]] => [[5,1],[2],[1],[1]]
[[5,1,1,1,1],[1]] => [[5,1],[1],[1],[1],[1]]
[[4,4,1],[1]] => [[4,1],[4],[1]]
[[4,3,2],[1]] => [[4,1],[3],[2]]
[[4,3,1,1],[1]] => [[4,1],[3],[1],[1]]
[[4,2,2,1],[1]] => [[4,1],[2],[2],[1]]
[[4,2,1,1,1],[1]] => [[4,1],[2],[1],[1],[1]]
[[4,1,1,1,1,1],[1]] => [[4,1],[1],[1],[1],[1],[1]]
[[3,3,3],[1]] => [[3,1],[3],[3]]
[[3,3,2,1],[1]] => [[3,1],[3],[2],[1]]
[[3,3,1,1,1],[1]] => [[3,1],[3],[1],[1],[1]]
[[3,2,2,2],[1]] => [[3,1],[2],[2],[2]]
[[3,2,2,1,1],[1]] => [[3,1],[2],[2],[1],[1]]
[[3,2,1,1,1,1],[1]] => [[3,1],[2],[1],[1],[1],[1]]
[[3,1,1,1,1,1,1],[1]] => [[3,1],[1],[1],[1],[1],[1],[1]]
[[2,2,2,2,1],[1]] => [[2,1],[2],[2],[2],[1]]
[[2,2,2,1,1,1],[1]] => [[2,1],[2],[2],[1],[1],[1]]
[[2,2,1,1,1,1,1],[1]] => [[2,1],[2],[1],[1],[1],[1],[1]]
[[2,1,1,1,1,1,1,1],[1]] => [[2,1],[1],[1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1,1,1],[1]] => [[1,1],[1],[1],[1],[1],[1],[1],[1],[1]]
[[10]] => [[10]]
[[9,1]] => [[9],[1]]
[[8,2]] => [[8],[2]]
[[8,1,1]] => [[8],[1],[1]]
[[7,3]] => [[7],[3]]
[[7,2,1]] => [[7],[2],[1]]
[[7,1,1,1]] => [[7],[1],[1],[1]]
[[6,4]] => [[6],[4]]
[[6,3,1]] => [[6],[3],[1]]
[[6,2,2]] => [[6],[2],[2]]
[[6,2,1,1]] => [[6],[2],[1],[1]]
[[6,1,1,1,1]] => [[6],[1],[1],[1],[1]]
[[5,5]] => [[5],[5]]
[[5,4,1]] => [[5],[4],[1]]
[[5,3,2]] => [[5],[3],[2]]
[[5,3,1,1]] => [[5],[3],[1],[1]]
[[5,2,2,1]] => [[5],[2],[2],[1]]
[[5,2,1,1,1]] => [[5],[2],[1],[1],[1]]
[[5,1,1,1,1,1]] => [[5],[1],[1],[1],[1],[1]]
[[4,4,2]] => [[4],[4],[2]]
[[4,4,1,1]] => [[4],[4],[1],[1]]
[[4,3,3]] => [[4],[3],[3]]
[[4,3,2,1]] => [[4],[3],[2],[1]]
[[4,3,1,1,1]] => [[4],[3],[1],[1],[1]]
[[4,2,2,2]] => [[4],[2],[2],[2]]
[[4,2,2,1,1]] => [[4],[2],[2],[1],[1]]
[[4,2,1,1,1,1]] => [[4],[2],[1],[1],[1],[1]]
[[4,1,1,1,1,1,1]] => [[4],[1],[1],[1],[1],[1],[1]]
[[3,3,3,1]] => [[3],[3],[3],[1]]
[[3,3,2,2]] => [[3],[3],[2],[2]]
[[3,3,2,1,1]] => [[3],[3],[2],[1],[1]]
[[3,3,1,1,1,1]] => [[3],[3],[1],[1],[1],[1]]
[[3,2,2,2,1]] => [[3],[2],[2],[2],[1]]
[[3,2,2,1,1,1]] => [[3],[2],[2],[1],[1],[1]]
[[3,2,1,1,1,1,1]] => [[3],[2],[1],[1],[1],[1],[1]]
[[3,1,1,1,1,1,1,1]] => [[3],[1],[1],[1],[1],[1],[1],[1]]
[[2,2,2,2,2]] => [[2],[2],[2],[2],[2]]
[[2,2,2,2,1,1]] => [[2],[2],[2],[2],[1],[1]]
[[2,2,2,1,1,1,1]] => [[2],[2],[2],[1],[1],[1],[1]]
[[2,2,1,1,1,1,1,1]] => [[2],[2],[1],[1],[1],[1],[1],[1]]
[[2,1,1,1,1,1,1,1,1]] => [[2],[1],[1],[1],[1],[1],[1],[1],[1]]
[[1,1,1,1,1,1,1,1,1,1]] => [[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The transpose of a plane partition.
This is the mirror symmetry along the vertical axis.
Properties
graded, involutive
Sage code
def mapping(pp):
    return PlanePartition([Partition(la) for la in pp.transpose()])
Weight
11
Created
Sep 13, 2020 at 11:45 by Martin Rubey
Updated
Sep 13, 2020 at 11:45 by Martin Rubey