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------------------------------------------------------------------------
Map identifier: Mp00189
------------------------------------------------------------------------
Map name: rotate
------------------------------------------------------------------------
Domain: Skew partitions
------------------------------------------------------------------------
Codomain: Skew partitions
------------------------------------------------------------------------
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.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(a):
if a:
la = a.outer()
n = len(la)
width = la[0]
nu = [width - p for p in reversed(la)]
ka = [x + y for x, y in zip(nu, reversed(a.row_lengths()))]
return SkewPartition([ka, nu])
return a
------------------------------------------------------------------------
Map images:
[[1],[]] => [[1],[]]
[[2],[]] => [[2],[]]
[[1,1],[]] => [[1,1],[]]
[[2,1],[1]] => [[2,1],[1]]
[[3],[]] => [[3],[]]
[[2,1],[]] => [[2,2],[1]]
[[3,1],[1]] => [[3,2],[2]]
[[2,2],[1]] => [[2,1],[]]
[[3,2],[2]] => [[3,1],[1]]
[[1,1,1],[]] => [[1,1,1],[]]
[[2,2,1],[1,1]] => [[2,1,1],[1]]
[[2,1,1],[1]] => [[2,2,1],[1,1]]
[[3,2,1],[2,1]] => [[3,2,1],[2,1]]
[[4],[]] => [[4],[]]
[[3,1],[]] => [[3,3],[2]]
[[4,1],[1]] => [[4,3],[3]]
[[2,2],[]] => [[2,2],[]]
[[3,2],[1]] => [[3,2],[1]]
[[4,2],[2]] => [[4,2],[2]]
[[2,1,1],[]] => [[2,2,2],[1,1]]
[[3,2,1],[1,1]] => [[3,2,2],[2,1]]
[[3,1,1],[1]] => [[3,3,2],[2,2]]
[[4,2,1],[2,1]] => [[4,3,2],[3,2]]
[[3,3],[2]] => [[3,1],[]]
[[4,3],[3]] => [[4,1],[1]]
[[2,2,1],[1]] => [[2,2,1],[1]]
[[3,3,1],[2,1]] => [[3,2,1],[2]]
[[3,2,1],[2]] => [[3,3,1],[2,1]]
[[4,3,1],[3,1]] => [[4,3,1],[3,1]]
[[2,2,2],[1,1]] => [[2,1,1],[]]
[[3,3,2],[2,2]] => [[3,1,1],[1]]
[[3,2,2],[2,1]] => [[3,2,1],[1,1]]
[[4,3,2],[3,2]] => [[4,2,1],[2,1]]
[[1,1,1,1],[]] => [[1,1,1,1],[]]
[[2,2,2,1],[1,1,1]] => [[2,1,1,1],[1]]
[[2,2,1,1],[1,1]] => [[2,2,1,1],[1,1]]
[[3,3,2,1],[2,2,1]] => [[3,2,1,1],[2,1]]
[[2,1,1,1],[1]] => [[2,2,2,1],[1,1,1]]
[[3,2,2,1],[2,1,1]] => [[3,2,2,1],[2,1,1]]
[[3,2,1,1],[2,1]] => [[3,3,2,1],[2,2,1]]
[[4,3,2,1],[3,2,1]] => [[4,3,2,1],[3,2,1]]
[[5],[]] => [[5],[]]
[[4,1],[]] => [[4,4],[3]]
[[5,1],[1]] => [[5,4],[4]]
[[3,2],[]] => [[3,3],[1]]
[[4,2],[1]] => [[4,3],[2]]
[[5,2],[2]] => [[5,3],[3]]
[[3,1,1],[]] => [[3,3,3],[2,2]]
[[4,2,1],[1,1]] => [[4,3,3],[3,2]]
[[4,1,1],[1]] => [[4,4,3],[3,3]]
[[5,2,1],[2,1]] => [[5,4,3],[4,3]]
[[3,3],[1]] => [[3,2],[]]
[[4,3],[2]] => [[4,2],[1]]
[[5,3],[3]] => [[5,2],[2]]
[[2,2,1],[]] => [[2,2,2],[1]]
[[3,3,1],[1,1]] => [[3,2,2],[2]]
[[3,2,1],[1]] => [[3,3,2],[2,1]]
[[4,3,1],[2,1]] => [[4,3,2],[3,1]]
[[4,2,1],[2]] => [[4,4,2],[3,2]]
[[5,3,1],[3,1]] => [[5,4,2],[4,2]]
[[3,2,2],[1,1]] => [[3,2,2],[1,1]]
[[4,3,2],[2,2]] => [[4,2,2],[2,1]]
[[4,2,2],[2,1]] => [[4,3,2],[2,2]]
[[5,3,2],[3,2]] => [[5,3,2],[3,2]]
[[2,1,1,1],[]] => [[2,2,2,2],[1,1,1]]
[[3,2,2,1],[1,1,1]] => [[3,2,2,2],[2,1,1]]
[[3,2,1,1],[1,1]] => [[3,3,2,2],[2,2,1]]
[[4,3,2,1],[2,2,1]] => [[4,3,2,2],[3,2,1]]
[[3,1,1,1],[1]] => [[3,3,3,2],[2,2,2]]
[[4,2,2,1],[2,1,1]] => [[4,3,3,2],[3,2,2]]
[[4,2,1,1],[2,1]] => [[4,4,3,2],[3,3,2]]
[[5,3,2,1],[3,2,1]] => [[5,4,3,2],[4,3,2]]
[[4,4],[3]] => [[4,1],[]]
[[5,4],[4]] => [[5,1],[1]]
[[3,3,1],[2]] => [[3,3,1],[2]]
[[4,4,1],[3,1]] => [[4,3,1],[3]]
[[4,3,1],[3]] => [[4,4,1],[3,1]]
[[5,4,1],[4,1]] => [[5,4,1],[4,1]]
[[2,2,2],[1]] => [[2,2,1],[]]
[[3,3,2],[2,1]] => [[3,2,1],[1]]
[[4,4,2],[3,2]] => [[4,2,1],[2]]
[[3,2,2],[2]] => [[3,3,1],[1,1]]
[[4,3,2],[3,1]] => [[4,3,1],[2,1]]
[[5,4,2],[4,2]] => [[5,3,1],[3,1]]
[[2,2,1,1],[1]] => [[2,2,2,1],[1,1]]
[[3,3,2,1],[2,1,1]] => [[3,2,2,1],[2,1]]
[[3,3,1,1],[2,1]] => [[3,3,2,1],[2,2]]
[[4,4,2,1],[3,2,1]] => [[4,3,2,1],[3,2]]
[[3,2,1,1],[2]] => [[3,3,3,1],[2,2,1]]
[[4,3,2,1],[3,1,1]] => [[4,3,3,1],[3,2,1]]
[[4,3,1,1],[3,1]] => [[4,4,3,1],[3,3,1]]
[[5,4,2,1],[4,2,1]] => [[5,4,3,1],[4,3,1]]
[[3,3,3],[2,2]] => [[3,1,1],[]]
[[4,4,3],[3,3]] => [[4,1,1],[1]]
[[4,3,3],[3,2]] => [[4,2,1],[1,1]]
[[5,4,3],[4,3]] => [[5,2,1],[2,1]]
[[2,2,2,1],[1,1]] => [[2,2,1,1],[1]]
[[3,3,3,1],[2,2,1]] => [[3,2,1,1],[2]]
[[3,3,2,1],[2,2]] => [[3,3,1,1],[2,1]]
[[4,4,3,1],[3,3,1]] => [[4,3,1,1],[3,1]]
[[3,2,2,1],[2,1]] => [[3,3,2,1],[2,1,1]]
[[4,3,3,1],[3,2,1]] => [[4,3,2,1],[3,1,1]]
[[4,3,2,1],[3,2]] => [[4,4,2,1],[3,2,1]]
[[5,4,3,1],[4,3,1]] => [[5,4,2,1],[4,2,1]]
[[2,2,2,2],[1,1,1]] => [[2,1,1,1],[]]
[[3,3,3,2],[2,2,2]] => [[3,1,1,1],[1]]
[[3,3,2,2],[2,2,1]] => [[3,2,1,1],[1,1]]
[[4,4,3,2],[3,3,2]] => [[4,2,1,1],[2,1]]
[[3,2,2,2],[2,1,1]] => [[3,2,2,1],[1,1,1]]
[[4,3,3,2],[3,2,2]] => [[4,2,2,1],[2,1,1]]
[[4,3,2,2],[3,2,1]] => [[4,3,2,1],[2,2,1]]
[[5,4,3,2],[4,3,2]] => [[5,3,2,1],[3,2,1]]
[[1,1,1,1,1],[]] => [[1,1,1,1,1],[]]
[[2,2,2,2,1],[1,1,1,1]] => [[2,1,1,1,1],[1]]
[[2,2,2,1,1],[1,1,1]] => [[2,2,1,1,1],[1,1]]
[[3,3,3,2,1],[2,2,2,1]] => [[3,2,1,1,1],[2,1]]
[[2,2,1,1,1],[1,1]] => [[2,2,2,1,1],[1,1,1]]
[[3,3,2,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1,1]]
[[3,3,2,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2,1]]
[[4,4,3,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2,1]]
[[2,1,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1,1]]
[[3,2,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1,1]]
[[3,2,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1,1]]
[[4,3,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1,1]]
[[3,2,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2,1]]
[[4,3,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2,1]]
[[4,3,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2,1]]
[[5,4,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2,1]]
[[6],[]] => [[6],[]]
[[5,1],[]] => [[5,5],[4]]
[[6,1],[1]] => [[6,5],[5]]
[[4,2],[]] => [[4,4],[2]]
[[5,2],[1]] => [[5,4],[3]]
[[6,2],[2]] => [[6,4],[4]]
[[4,1,1],[]] => [[4,4,4],[3,3]]
[[5,2,1],[1,1]] => [[5,4,4],[4,3]]
[[5,1,1],[1]] => [[5,5,4],[4,4]]
[[6,2,1],[2,1]] => [[6,5,4],[5,4]]
[[3,3],[]] => [[3,3],[]]
[[4,3],[1]] => [[4,3],[1]]
[[5,3],[2]] => [[5,3],[2]]
[[6,3],[3]] => [[6,3],[3]]
[[3,2,1],[]] => [[3,3,3],[2,1]]
[[4,3,1],[1,1]] => [[4,3,3],[3,1]]
[[4,2,1],[1]] => [[4,4,3],[3,2]]
[[5,3,1],[2,1]] => [[5,4,3],[4,2]]
[[5,2,1],[2]] => [[5,5,3],[4,3]]
[[6,3,1],[3,1]] => [[6,5,3],[5,3]]
[[4,2,2],[1,1]] => [[4,3,3],[2,2]]
[[5,3,2],[2,2]] => [[5,3,3],[3,2]]
[[5,2,2],[2,1]] => [[5,4,3],[3,3]]
[[6,3,2],[3,2]] => [[6,4,3],[4,3]]
[[3,1,1,1],[]] => [[3,3,3,3],[2,2,2]]
[[4,2,2,1],[1,1,1]] => [[4,3,3,3],[3,2,2]]
[[4,2,1,1],[1,1]] => [[4,4,3,3],[3,3,2]]
[[5,3,2,1],[2,2,1]] => [[5,4,3,3],[4,3,2]]
[[4,1,1,1],[1]] => [[4,4,4,3],[3,3,3]]
[[5,2,2,1],[2,1,1]] => [[5,4,4,3],[4,3,3]]
[[5,2,1,1],[2,1]] => [[5,5,4,3],[4,4,3]]
[[6,3,2,1],[3,2,1]] => [[6,5,4,3],[5,4,3]]
[[4,4],[2]] => [[4,2],[]]
[[5,4],[3]] => [[5,2],[1]]
[[6,4],[4]] => [[6,2],[2]]
[[3,3,1],[1]] => [[3,3,2],[2]]
[[4,4,1],[2,1]] => [[4,3,2],[3]]
[[4,3,1],[2]] => [[4,4,2],[3,1]]
[[5,4,1],[3,1]] => [[5,4,2],[4,1]]
[[5,3,1],[3]] => [[5,5,2],[4,2]]
[[6,4,1],[4,1]] => [[6,5,2],[5,2]]
[[2,2,2],[]] => [[2,2,2],[]]
[[3,3,2],[1,1]] => [[3,2,2],[1]]
[[4,4,2],[2,2]] => [[4,2,2],[2]]
[[3,2,2],[1]] => [[3,3,2],[1,1]]
[[4,3,2],[2,1]] => [[4,3,2],[2,1]]
[[5,4,2],[3,2]] => [[5,3,2],[3,1]]
[[4,2,2],[2]] => [[4,4,2],[2,2]]
[[5,3,2],[3,1]] => [[5,4,2],[3,2]]
[[6,4,2],[4,2]] => [[6,4,2],[4,2]]
[[2,2,1,1],[]] => [[2,2,2,2],[1,1]]
[[3,3,2,1],[1,1,1]] => [[3,2,2,2],[2,1]]
[[3,3,1,1],[1,1]] => [[3,3,2,2],[2,2]]
[[4,4,2,1],[2,2,1]] => [[4,3,2,2],[3,2]]
[[3,2,1,1],[1]] => [[3,3,3,2],[2,2,1]]
[[4,3,2,1],[2,1,1]] => [[4,3,3,2],[3,2,1]]
[[4,3,1,1],[2,1]] => [[4,4,3,2],[3,3,1]]
[[5,4,2,1],[3,2,1]] => [[5,4,3,2],[4,3,1]]
[[4,2,1,1],[2]] => [[4,4,4,2],[3,3,2]]
[[5,3,2,1],[3,1,1]] => [[5,4,4,2],[4,3,2]]
[[5,3,1,1],[3,1]] => [[5,5,4,2],[4,4,2]]
[[6,4,2,1],[4,2,1]] => [[6,5,4,2],[5,4,2]]
[[4,3,3],[2,2]] => [[4,2,2],[1,1]]
[[5,4,3],[3,3]] => [[5,2,2],[2,1]]
[[5,3,3],[3,2]] => [[5,3,2],[2,2]]
[[6,4,3],[4,3]] => [[6,3,2],[3,2]]
[[3,2,2,1],[1,1]] => [[3,3,2,2],[2,1,1]]
[[4,3,3,1],[2,2,1]] => [[4,3,2,2],[3,1,1]]
[[4,3,2,1],[2,2]] => [[4,4,2,2],[3,2,1]]
[[5,4,3,1],[3,3,1]] => [[5,4,2,2],[4,2,1]]
[[4,2,2,1],[2,1]] => [[4,4,3,2],[3,2,2]]
[[5,3,3,1],[3,2,1]] => [[5,4,3,2],[4,2,2]]
[[5,3,2,1],[3,2]] => [[5,5,3,2],[4,3,2]]
[[6,4,3,1],[4,3,1]] => [[6,5,3,2],[5,3,2]]
[[3,2,2,2],[1,1,1]] => [[3,2,2,2],[1,1,1]]
[[4,3,3,2],[2,2,2]] => [[4,2,2,2],[2,1,1]]
[[4,3,2,2],[2,2,1]] => [[4,3,2,2],[2,2,1]]
[[5,4,3,2],[3,3,2]] => [[5,3,2,2],[3,2,1]]
[[4,2,2,2],[2,1,1]] => [[4,3,3,2],[2,2,2]]
[[5,3,3,2],[3,2,2]] => [[5,3,3,2],[3,2,2]]
[[5,3,2,2],[3,2,1]] => [[5,4,3,2],[3,3,2]]
[[6,4,3,2],[4,3,2]] => [[6,4,3,2],[4,3,2]]
[[2,1,1,1,1],[]] => [[2,2,2,2,2],[1,1,1,1]]
[[3,2,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1,1]]
[[3,2,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1,1]]
[[4,3,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1,1]]
[[3,2,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2,1]]
[[4,3,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2,1]]
[[4,3,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2,1]]
[[5,4,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2,1]]
[[3,1,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,2]]
[[4,2,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,2]]
[[4,2,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,2]]
[[5,3,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,2]]
[[4,2,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,2]]
[[5,3,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,2]]
[[5,3,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,2]]
[[6,4,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,2]]
[[5,5],[4]] => [[5,1],[]]
[[6,5],[5]] => [[6,1],[1]]
[[4,4,1],[3]] => [[4,4,1],[3]]
[[5,5,1],[4,1]] => [[5,4,1],[4]]
[[5,4,1],[4]] => [[5,5,1],[4,1]]
[[6,5,1],[5,1]] => [[6,5,1],[5,1]]
[[3,3,2],[2]] => [[3,3,1],[1]]
[[4,4,2],[3,1]] => [[4,3,1],[2]]
[[5,5,2],[4,2]] => [[5,3,1],[3]]
[[4,3,2],[3]] => [[4,4,1],[2,1]]
[[5,4,2],[4,1]] => [[5,4,1],[3,1]]
[[6,5,2],[5,2]] => [[6,4,1],[4,1]]
[[3,3,1,1],[2]] => [[3,3,3,1],[2,2]]
[[4,4,2,1],[3,1,1]] => [[4,3,3,1],[3,2]]
[[4,4,1,1],[3,1]] => [[4,4,3,1],[3,3]]
[[5,5,2,1],[4,2,1]] => [[5,4,3,1],[4,3]]
[[4,3,1,1],[3]] => [[4,4,4,1],[3,3,1]]
[[5,4,2,1],[4,1,1]] => [[5,4,4,1],[4,3,1]]
[[5,4,1,1],[4,1]] => [[5,5,4,1],[4,4,1]]
[[6,5,2,1],[5,2,1]] => [[6,5,4,1],[5,4,1]]
[[3,3,3],[2,1]] => [[3,2,1],[]]
[[4,4,3],[3,2]] => [[4,2,1],[1]]
[[5,5,3],[4,3]] => [[5,2,1],[2]]
[[4,3,3],[3,1]] => [[4,3,1],[1,1]]
[[5,4,3],[4,2]] => [[5,3,1],[2,1]]
[[6,5,3],[5,3]] => [[6,3,1],[3,1]]
[[2,2,2,1],[1]] => [[2,2,2,1],[1]]
[[3,3,3,1],[2,1,1]] => [[3,2,2,1],[2]]
[[3,3,2,1],[2,1]] => [[3,3,2,1],[2,1]]
[[4,4,3,1],[3,2,1]] => [[4,3,2,1],[3,1]]
[[4,4,2,1],[3,2]] => [[4,4,2,1],[3,2]]
[[5,5,3,1],[4,3,1]] => [[5,4,2,1],[4,2]]
[[3,2,2,1],[2]] => [[3,3,3,1],[2,1,1]]
[[4,3,3,1],[3,1,1]] => [[4,3,3,1],[3,1,1]]
[[4,3,2,1],[3,1]] => [[4,4,3,1],[3,2,1]]
[[5,4,3,1],[4,2,1]] => [[5,4,3,1],[4,2,1]]
[[5,4,2,1],[4,2]] => [[5,5,3,1],[4,3,1]]
[[6,5,3,1],[5,3,1]] => [[6,5,3,1],[5,3,1]]
[[3,3,2,2],[2,1,1]] => [[3,2,2,1],[1,1]]
[[4,4,3,2],[3,2,2]] => [[4,2,2,1],[2,1]]
[[4,4,2,2],[3,2,1]] => [[4,3,2,1],[2,2]]
[[5,5,3,2],[4,3,2]] => [[5,3,2,1],[3,2]]
[[4,3,2,2],[3,1,1]] => [[4,3,3,1],[2,2,1]]
[[5,4,3,2],[4,2,2]] => [[5,3,3,1],[3,2,1]]
[[5,4,2,2],[4,2,1]] => [[5,4,3,1],[3,3,1]]
[[6,5,3,2],[5,3,2]] => [[6,4,3,1],[4,3,1]]
[[2,2,1,1,1],[1]] => [[2,2,2,2,1],[1,1,1]]
[[3,3,2,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1,1]]
[[3,3,2,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2,1]]
[[4,4,3,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2,1]]
[[3,3,1,1,1],[2,1]] => [[3,3,3,2,1],[2,2,2]]
[[4,4,2,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,2]]
[[4,4,2,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,2]]
[[5,5,3,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,2]]
[[3,2,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2,1]]
[[4,3,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2,1]]
[[4,3,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2,1]]
[[5,4,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2,1]]
[[4,3,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3,1]]
[[5,4,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3,1]]
[[5,4,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3,1]]
[[6,5,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3,1]]
[[4,4,4],[3,3]] => [[4,1,1],[]]
[[5,5,4],[4,4]] => [[5,1,1],[1]]
[[5,4,4],[4,3]] => [[5,2,1],[1,1]]
[[6,5,4],[5,4]] => [[6,2,1],[2,1]]
[[3,3,3,1],[2,2]] => [[3,3,1,1],[2]]
[[4,4,4,1],[3,3,1]] => [[4,3,1,1],[3]]
[[4,4,3,1],[3,3]] => [[4,4,1,1],[3,1]]
[[5,5,4,1],[4,4,1]] => [[5,4,1,1],[4,1]]
[[4,3,3,1],[3,2]] => [[4,4,2,1],[3,1,1]]
[[5,4,4,1],[4,3,1]] => [[5,4,2,1],[4,1,1]]
[[5,4,3,1],[4,3]] => [[5,5,2,1],[4,2,1]]
[[6,5,4,1],[5,4,1]] => [[6,5,2,1],[5,2,1]]
[[2,2,2,2],[1,1]] => [[2,2,1,1],[]]
[[3,3,3,2],[2,2,1]] => [[3,2,1,1],[1]]
[[4,4,4,2],[3,3,2]] => [[4,2,1,1],[2]]
[[3,3,2,2],[2,2]] => [[3,3,1,1],[1,1]]
[[4,4,3,2],[3,3,1]] => [[4,3,1,1],[2,1]]
[[5,5,4,2],[4,4,2]] => [[5,3,1,1],[3,1]]
[[3,2,2,2],[2,1]] => [[3,3,2,1],[1,1,1]]
[[4,3,3,2],[3,2,1]] => [[4,3,2,1],[2,1,1]]
[[5,4,4,2],[4,3,2]] => [[5,3,2,1],[3,1,1]]
[[4,3,2,2],[3,2]] => [[4,4,2,1],[2,2,1]]
[[5,4,3,2],[4,3,1]] => [[5,4,2,1],[3,2,1]]
[[6,5,4,2],[5,4,2]] => [[6,4,2,1],[4,2,1]]
[[2,2,2,1,1],[1,1]] => [[2,2,2,1,1],[1,1]]
[[3,3,3,2,1],[2,2,1,1]] => [[3,2,2,1,1],[2,1]]
[[3,3,3,1,1],[2,2,1]] => [[3,3,2,1,1],[2,2]]
[[4,4,4,2,1],[3,3,2,1]] => [[4,3,2,1,1],[3,2]]
[[3,3,2,1,1],[2,2]] => [[3,3,3,1,1],[2,2,1]]
[[4,4,3,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2,1]]
[[4,4,3,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3,1]]
[[5,5,4,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3,1]]
[[3,2,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1,1]]
[[4,3,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1,1]]
[[4,3,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1,1]]
[[5,4,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1,1]]
[[4,3,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2,1]]
[[5,4,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2,1]]
[[5,4,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2,1]]
[[6,5,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2,1]]
[[3,3,3,3],[2,2,2]] => [[3,1,1,1],[]]
[[4,4,4,3],[3,3,3]] => [[4,1,1,1],[1]]
[[4,4,3,3],[3,3,2]] => [[4,2,1,1],[1,1]]
[[5,5,4,3],[4,4,3]] => [[5,2,1,1],[2,1]]
[[4,3,3,3],[3,2,2]] => [[4,2,2,1],[1,1,1]]
[[5,4,4,3],[4,3,3]] => [[5,2,2,1],[2,1,1]]
[[5,4,3,3],[4,3,2]] => [[5,3,2,1],[2,2,1]]
[[6,5,4,3],[5,4,3]] => [[6,3,2,1],[3,2,1]]
[[2,2,2,2,1],[1,1,1]] => [[2,2,1,1,1],[1]]
[[3,3,3,3,1],[2,2,2,1]] => [[3,2,1,1,1],[2]]
[[3,3,3,2,1],[2,2,2]] => [[3,3,1,1,1],[2,1]]
[[4,4,4,3,1],[3,3,3,1]] => [[4,3,1,1,1],[3,1]]
[[3,3,2,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1,1]]
[[4,4,3,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1,1]]
[[4,4,3,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2,1]]
[[5,5,4,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2,1]]
[[3,2,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1,1]]
[[4,3,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1,1]]
[[4,3,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1,1]]
[[5,4,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1,1]]
[[4,3,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2,1]]
[[5,4,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2,1]]
[[5,4,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2,1]]
[[6,5,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2,1]]
[[2,2,2,2,2],[1,1,1,1]] => [[2,1,1,1,1],[]]
[[3,3,3,3,2],[2,2,2,2]] => [[3,1,1,1,1],[1]]
[[3,3,3,2,2],[2,2,2,1]] => [[3,2,1,1,1],[1,1]]
[[4,4,4,3,2],[3,3,3,2]] => [[4,2,1,1,1],[2,1]]
[[3,3,2,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1,1]]
[[4,4,3,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1,1]]
[[4,4,3,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2,1]]
[[5,5,4,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2,1]]
[[3,2,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1,1]]
[[4,3,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1,1]]
[[4,3,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1,1]]
[[5,4,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1,1]]
[[4,3,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2,1]]
[[5,4,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2,1]]
[[5,4,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2,1]]
[[6,5,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2,1]]
[[1,1,1,1,1,1],[]] => [[1,1,1,1,1,1],[]]
[[2,2,2,2,2,1],[1,1,1,1,1]] => [[2,1,1,1,1,1],[1]]
[[2,2,2,2,1,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1,1]]
[[3,3,3,3,2,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2,1]]
[[2,2,2,1,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1,1]]
[[3,3,3,2,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1,1]]
[[3,3,3,2,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2,1]]
[[4,4,4,3,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2,1]]
[[2,2,1,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1,1]]
[[3,3,2,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1,1]]
[[3,3,2,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1,1]]
[[4,4,3,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1,1]]
[[3,3,2,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2,1]]
[[4,4,3,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2,1]]
[[4,4,3,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2,1]]
[[5,5,4,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2,1]]
[[2,1,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1,1]]
[[3,2,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1,1]]
[[3,2,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1,1]]
[[4,3,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1,1]]
[[3,2,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1,1]]
[[4,3,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1,1]]
[[4,3,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1,1]]
[[5,4,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1,1]]
[[3,2,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2,1]]
[[4,3,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2,1]]
[[4,3,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2,1]]
[[5,4,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2,1]]
[[4,3,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2,1]]
[[5,4,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2,1]]
[[5,4,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2,1]]
[[6,5,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2,1]]
[[7],[]] => [[7],[]]
[[6,1],[]] => [[6,6],[5]]
[[7,1],[1]] => [[7,6],[6]]
[[5,2],[]] => [[5,5],[3]]
[[6,2],[1]] => [[6,5],[4]]
[[7,2],[2]] => [[7,5],[5]]
[[5,1,1],[]] => [[5,5,5],[4,4]]
[[6,2,1],[1,1]] => [[6,5,5],[5,4]]
[[6,1,1],[1]] => [[6,6,5],[5,5]]
[[7,2,1],[2,1]] => [[7,6,5],[6,5]]
[[4,3],[]] => [[4,4],[1]]
[[5,3],[1]] => [[5,4],[2]]
[[6,3],[2]] => [[6,4],[3]]
[[7,3],[3]] => [[7,4],[4]]
[[4,2,1],[]] => [[4,4,4],[3,2]]
[[5,3,1],[1,1]] => [[5,4,4],[4,2]]
[[5,2,1],[1]] => [[5,5,4],[4,3]]
[[6,3,1],[2,1]] => [[6,5,4],[5,3]]
[[6,2,1],[2]] => [[6,6,4],[5,4]]
[[7,3,1],[3,1]] => [[7,6,4],[6,4]]
[[5,2,2],[1,1]] => [[5,4,4],[3,3]]
[[6,3,2],[2,2]] => [[6,4,4],[4,3]]
[[6,2,2],[2,1]] => [[6,5,4],[4,4]]
[[7,3,2],[3,2]] => [[7,5,4],[5,4]]
[[4,1,1,1],[]] => [[4,4,4,4],[3,3,3]]
[[5,2,2,1],[1,1,1]] => [[5,4,4,4],[4,3,3]]
[[5,2,1,1],[1,1]] => [[5,5,4,4],[4,4,3]]
[[6,3,2,1],[2,2,1]] => [[6,5,4,4],[5,4,3]]
[[5,1,1,1],[1]] => [[5,5,5,4],[4,4,4]]
[[6,2,2,1],[2,1,1]] => [[6,5,5,4],[5,4,4]]
[[6,2,1,1],[2,1]] => [[6,6,5,4],[5,5,4]]
[[7,3,2,1],[3,2,1]] => [[7,6,5,4],[6,5,4]]
[[4,4],[1]] => [[4,3],[]]
[[5,4],[2]] => [[5,3],[1]]
[[6,4],[3]] => [[6,3],[2]]
[[7,4],[4]] => [[7,3],[3]]
[[3,3,1],[]] => [[3,3,3],[2]]
[[4,4,1],[1,1]] => [[4,3,3],[3]]
[[4,3,1],[1]] => [[4,4,3],[3,1]]
[[5,4,1],[2,1]] => [[5,4,3],[4,1]]
[[5,3,1],[2]] => [[5,5,3],[4,2]]
[[6,4,1],[3,1]] => [[6,5,3],[5,2]]
[[6,3,1],[3]] => [[6,6,3],[5,3]]
[[7,4,1],[4,1]] => [[7,6,3],[6,3]]
[[3,2,2],[]] => [[3,3,3],[1,1]]
[[4,3,2],[1,1]] => [[4,3,3],[2,1]]
[[5,4,2],[2,2]] => [[5,3,3],[3,1]]
[[4,2,2],[1]] => [[4,4,3],[2,2]]
[[5,3,2],[2,1]] => [[5,4,3],[3,2]]
[[6,4,2],[3,2]] => [[6,4,3],[4,2]]
[[5,2,2],[2]] => [[5,5,3],[3,3]]
[[6,3,2],[3,1]] => [[6,5,3],[4,3]]
[[7,4,2],[4,2]] => [[7,5,3],[5,3]]
[[3,2,1,1],[]] => [[3,3,3,3],[2,2,1]]
[[4,3,2,1],[1,1,1]] => [[4,3,3,3],[3,2,1]]
[[4,3,1,1],[1,1]] => [[4,4,3,3],[3,3,1]]
[[5,4,2,1],[2,2,1]] => [[5,4,3,3],[4,3,1]]
[[4,2,1,1],[1]] => [[4,4,4,3],[3,3,2]]
[[5,3,2,1],[2,1,1]] => [[5,4,4,3],[4,3,2]]
[[5,3,1,1],[2,1]] => [[5,5,4,3],[4,4,2]]
[[6,4,2,1],[3,2,1]] => [[6,5,4,3],[5,4,2]]
[[5,2,1,1],[2]] => [[5,5,5,3],[4,4,3]]
[[6,3,2,1],[3,1,1]] => [[6,5,5,3],[5,4,3]]
[[6,3,1,1],[3,1]] => [[6,6,5,3],[5,5,3]]
[[7,4,2,1],[4,2,1]] => [[7,6,5,3],[6,5,3]]
[[5,3,3],[2,2]] => [[5,3,3],[2,2]]
[[6,4,3],[3,3]] => [[6,3,3],[3,2]]
[[6,3,3],[3,2]] => [[6,4,3],[3,3]]
[[7,4,3],[4,3]] => [[7,4,3],[4,3]]
[[4,2,2,1],[1,1]] => [[4,4,3,3],[3,2,2]]
[[5,3,3,1],[2,2,1]] => [[5,4,3,3],[4,2,2]]
[[5,3,2,1],[2,2]] => [[5,5,3,3],[4,3,2]]
[[6,4,3,1],[3,3,1]] => [[6,5,3,3],[5,3,2]]
[[5,2,2,1],[2,1]] => [[5,5,4,3],[4,3,3]]
[[6,3,3,1],[3,2,1]] => [[6,5,4,3],[5,3,3]]
[[6,3,2,1],[3,2]] => [[6,6,4,3],[5,4,3]]
[[7,4,3,1],[4,3,1]] => [[7,6,4,3],[6,4,3]]
[[4,2,2,2],[1,1,1]] => [[4,3,3,3],[2,2,2]]
[[5,3,3,2],[2,2,2]] => [[5,3,3,3],[3,2,2]]
[[5,3,2,2],[2,2,1]] => [[5,4,3,3],[3,3,2]]
[[6,4,3,2],[3,3,2]] => [[6,4,3,3],[4,3,2]]
[[5,2,2,2],[2,1,1]] => [[5,4,4,3],[3,3,3]]
[[6,3,3,2],[3,2,2]] => [[6,4,4,3],[4,3,3]]
[[6,3,2,2],[3,2,1]] => [[6,5,4,3],[4,4,3]]
[[7,4,3,2],[4,3,2]] => [[7,5,4,3],[5,4,3]]
[[3,1,1,1,1],[]] => [[3,3,3,3,3],[2,2,2,2]]
[[4,2,2,2,1],[1,1,1,1]] => [[4,3,3,3,3],[3,2,2,2]]
[[4,2,2,1,1],[1,1,1]] => [[4,4,3,3,3],[3,3,2,2]]
[[5,3,3,2,1],[2,2,2,1]] => [[5,4,3,3,3],[4,3,2,2]]
[[4,2,1,1,1],[1,1]] => [[4,4,4,3,3],[3,3,3,2]]
[[5,3,2,2,1],[2,2,1,1]] => [[5,4,4,3,3],[4,3,3,2]]
[[5,3,2,1,1],[2,2,1]] => [[5,5,4,3,3],[4,4,3,2]]
[[6,4,3,2,1],[3,3,2,1]] => [[6,5,4,3,3],[5,4,3,2]]
[[4,1,1,1,1],[1]] => [[4,4,4,4,3],[3,3,3,3]]
[[5,2,2,2,1],[2,1,1,1]] => [[5,4,4,4,3],[4,3,3,3]]
[[5,2,2,1,1],[2,1,1]] => [[5,5,4,4,3],[4,4,3,3]]
[[6,3,3,2,1],[3,2,2,1]] => [[6,5,4,4,3],[5,4,3,3]]
[[5,2,1,1,1],[2,1]] => [[5,5,5,4,3],[4,4,4,3]]
[[6,3,2,2,1],[3,2,1,1]] => [[6,5,5,4,3],[5,4,4,3]]
[[6,3,2,1,1],[3,2,1]] => [[6,6,5,4,3],[5,5,4,3]]
[[7,4,3,2,1],[4,3,2,1]] => [[7,6,5,4,3],[6,5,4,3]]
[[5,5],[3]] => [[5,2],[]]
[[6,5],[4]] => [[6,2],[1]]
[[7,5],[5]] => [[7,2],[2]]
[[4,4,1],[2]] => [[4,4,2],[3]]
[[5,5,1],[3,1]] => [[5,4,2],[4]]
[[5,4,1],[3]] => [[5,5,2],[4,1]]
[[6,5,1],[4,1]] => [[6,5,2],[5,1]]
[[6,4,1],[4]] => [[6,6,2],[5,2]]
[[7,5,1],[5,1]] => [[7,6,2],[6,2]]
[[3,3,2],[1]] => [[3,3,2],[1]]
[[4,4,2],[2,1]] => [[4,3,2],[2]]
[[5,5,2],[3,2]] => [[5,3,2],[3]]
[[4,3,2],[2]] => [[4,4,2],[2,1]]
[[5,4,2],[3,1]] => [[5,4,2],[3,1]]
[[6,5,2],[4,2]] => [[6,4,2],[4,1]]
[[5,3,2],[3]] => [[5,5,2],[3,2]]
[[6,4,2],[4,1]] => [[6,5,2],[4,2]]
[[7,5,2],[5,2]] => [[7,5,2],[5,2]]
[[3,3,1,1],[1]] => [[3,3,3,2],[2,2]]
[[4,4,2,1],[2,1,1]] => [[4,3,3,2],[3,2]]
[[4,4,1,1],[2,1]] => [[4,4,3,2],[3,3]]
[[5,5,2,1],[3,2,1]] => [[5,4,3,2],[4,3]]
[[4,3,1,1],[2]] => [[4,4,4,2],[3,3,1]]
[[5,4,2,1],[3,1,1]] => [[5,4,4,2],[4,3,1]]
[[5,4,1,1],[3,1]] => [[5,5,4,2],[4,4,1]]
[[6,5,2,1],[4,2,1]] => [[6,5,4,2],[5,4,1]]
[[5,3,1,1],[3]] => [[5,5,5,2],[4,4,2]]
[[6,4,2,1],[4,1,1]] => [[6,5,5,2],[5,4,2]]
[[6,4,1,1],[4,1]] => [[6,6,5,2],[5,5,2]]
[[7,5,2,1],[5,2,1]] => [[7,6,5,2],[6,5,2]]
[[3,3,3],[1,1]] => [[3,2,2],[]]
[[4,4,3],[2,2]] => [[4,2,2],[1]]
[[5,5,3],[3,3]] => [[5,2,2],[2]]
[[4,3,3],[2,1]] => [[4,3,2],[1,1]]
[[5,4,3],[3,2]] => [[5,3,2],[2,1]]
[[6,5,3],[4,3]] => [[6,3,2],[3,1]]
[[5,3,3],[3,1]] => [[5,4,2],[2,2]]
[[6,4,3],[4,2]] => [[6,4,2],[3,2]]
[[7,5,3],[5,3]] => [[7,4,2],[4,2]]
[[2,2,2,1],[]] => [[2,2,2,2],[1]]
[[3,3,3,1],[1,1,1]] => [[3,2,2,2],[2]]
[[3,3,2,1],[1,1]] => [[3,3,2,2],[2,1]]
[[4,4,3,1],[2,2,1]] => [[4,3,2,2],[3,1]]
[[4,4,2,1],[2,2]] => [[4,4,2,2],[3,2]]
[[5,5,3,1],[3,3,1]] => [[5,4,2,2],[4,2]]
[[3,2,2,1],[1]] => [[3,3,3,2],[2,1,1]]
[[4,3,3,1],[2,1,1]] => [[4,3,3,2],[3,1,1]]
[[4,3,2,1],[2,1]] => [[4,4,3,2],[3,2,1]]
[[5,4,3,1],[3,2,1]] => [[5,4,3,2],[4,2,1]]
[[5,4,2,1],[3,2]] => [[5,5,3,2],[4,3,1]]
[[6,5,3,1],[4,3,1]] => [[6,5,3,2],[5,3,1]]
[[4,2,2,1],[2]] => [[4,4,4,2],[3,2,2]]
[[5,3,3,1],[3,1,1]] => [[5,4,4,2],[4,2,2]]
[[5,3,2,1],[3,1]] => [[5,5,4,2],[4,3,2]]
[[6,4,3,1],[4,2,1]] => [[6,5,4,2],[5,3,2]]
[[6,4,2,1],[4,2]] => [[6,6,4,2],[5,4,2]]
[[7,5,3,1],[5,3,1]] => [[7,6,4,2],[6,4,2]]
[[3,3,2,2],[1,1,1]] => [[3,2,2,2],[1,1]]
[[4,4,3,2],[2,2,2]] => [[4,2,2,2],[2,1]]
[[4,4,2,2],[2,2,1]] => [[4,3,2,2],[2,2]]
[[5,5,3,2],[3,3,2]] => [[5,3,2,2],[3,2]]
[[4,3,2,2],[2,1,1]] => [[4,3,3,2],[2,2,1]]
[[5,4,3,2],[3,2,2]] => [[5,3,3,2],[3,2,1]]
[[5,4,2,2],[3,2,1]] => [[5,4,3,2],[3,3,1]]
[[6,5,3,2],[4,3,2]] => [[6,4,3,2],[4,3,1]]
[[5,3,2,2],[3,1,1]] => [[5,4,4,2],[3,3,2]]
[[6,4,3,2],[4,2,2]] => [[6,4,4,2],[4,3,2]]
[[6,4,2,2],[4,2,1]] => [[6,5,4,2],[4,4,2]]
[[7,5,3,2],[5,3,2]] => [[7,5,4,2],[5,4,2]]
[[2,2,1,1,1],[]] => [[2,2,2,2,2],[1,1,1]]
[[3,3,2,2,1],[1,1,1,1]] => [[3,2,2,2,2],[2,1,1]]
[[3,3,2,1,1],[1,1,1]] => [[3,3,2,2,2],[2,2,1]]
[[4,4,3,2,1],[2,2,2,1]] => [[4,3,2,2,2],[3,2,1]]
[[3,3,1,1,1],[1,1]] => [[3,3,3,2,2],[2,2,2]]
[[4,4,2,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,2]]
[[4,4,2,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,2]]
[[5,5,3,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,2]]
[[3,2,1,1,1],[1]] => [[3,3,3,3,2],[2,2,2,1]]
[[4,3,2,2,1],[2,1,1,1]] => [[4,3,3,3,2],[3,2,2,1]]
[[4,3,2,1,1],[2,1,1]] => [[4,4,3,3,2],[3,3,2,1]]
[[5,4,3,2,1],[3,2,2,1]] => [[5,4,3,3,2],[4,3,2,1]]
[[4,3,1,1,1],[2,1]] => [[4,4,4,3,2],[3,3,3,1]]
[[5,4,2,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,3,1]]
[[5,4,2,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,3,1]]
[[6,5,3,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,3,1]]
[[4,2,1,1,1],[2]] => [[4,4,4,4,2],[3,3,3,2]]
[[5,3,2,2,1],[3,1,1,1]] => [[5,4,4,4,2],[4,3,3,2]]
[[5,3,2,1,1],[3,1,1]] => [[5,5,4,4,2],[4,4,3,2]]
[[6,4,3,2,1],[4,2,2,1]] => [[6,5,4,4,2],[5,4,3,2]]
[[5,3,1,1,1],[3,1]] => [[5,5,5,4,2],[4,4,4,2]]
[[6,4,2,2,1],[4,2,1,1]] => [[6,5,5,4,2],[5,4,4,2]]
[[6,4,2,1,1],[4,2,1]] => [[6,6,5,4,2],[5,5,4,2]]
[[7,5,3,2,1],[5,3,2,1]] => [[7,6,5,4,2],[6,5,4,2]]
[[5,4,4],[3,3]] => [[5,2,2],[1,1]]
[[6,5,4],[4,4]] => [[6,2,2],[2,1]]
[[6,4,4],[4,3]] => [[6,3,2],[2,2]]
[[7,5,4],[5,4]] => [[7,3,2],[3,2]]
[[4,3,3,1],[2,2]] => [[4,4,2,2],[3,1,1]]
[[5,4,4,1],[3,3,1]] => [[5,4,2,2],[4,1,1]]
[[5,4,3,1],[3,3]] => [[5,5,2,2],[4,2,1]]
[[6,5,4,1],[4,4,1]] => [[6,5,2,2],[5,2,1]]
[[5,3,3,1],[3,2]] => [[5,5,3,2],[4,2,2]]
[[6,4,4,1],[4,3,1]] => [[6,5,3,2],[5,2,2]]
[[6,4,3,1],[4,3]] => [[6,6,3,2],[5,3,2]]
[[7,5,4,1],[5,4,1]] => [[7,6,3,2],[6,3,2]]
[[3,2,2,2],[1,1]] => [[3,3,2,2],[1,1,1]]
[[4,3,3,2],[2,2,1]] => [[4,3,2,2],[2,1,1]]
[[5,4,4,2],[3,3,2]] => [[5,3,2,2],[3,1,1]]
[[4,3,2,2],[2,2]] => [[4,4,2,2],[2,2,1]]
[[5,4,3,2],[3,3,1]] => [[5,4,2,2],[3,2,1]]
[[6,5,4,2],[4,4,2]] => [[6,4,2,2],[4,2,1]]
[[4,2,2,2],[2,1]] => [[4,4,3,2],[2,2,2]]
[[5,3,3,2],[3,2,1]] => [[5,4,3,2],[3,2,2]]
[[6,4,4,2],[4,3,2]] => [[6,4,3,2],[4,2,2]]
[[5,3,2,2],[3,2]] => [[5,5,3,2],[3,3,2]]
[[6,4,3,2],[4,3,1]] => [[6,5,3,2],[4,3,2]]
[[7,5,4,2],[5,4,2]] => [[7,5,3,2],[5,3,2]]
[[3,2,2,1,1],[1,1]] => [[3,3,3,2,2],[2,2,1,1]]
[[4,3,3,2,1],[2,2,1,1]] => [[4,3,3,2,2],[3,2,1,1]]
[[4,3,3,1,1],[2,2,1]] => [[4,4,3,2,2],[3,3,1,1]]
[[5,4,4,2,1],[3,3,2,1]] => [[5,4,3,2,2],[4,3,1,1]]
[[4,3,2,1,1],[2,2]] => [[4,4,4,2,2],[3,3,2,1]]
[[5,4,3,2,1],[3,3,1,1]] => [[5,4,4,2,2],[4,3,2,1]]
[[5,4,3,1,1],[3,3,1]] => [[5,5,4,2,2],[4,4,2,1]]
[[6,5,4,2,1],[4,4,2,1]] => [[6,5,4,2,2],[5,4,2,1]]
[[4,2,2,1,1],[2,1]] => [[4,4,4,3,2],[3,3,2,2]]
[[5,3,3,2,1],[3,2,1,1]] => [[5,4,4,3,2],[4,3,2,2]]
[[5,3,3,1,1],[3,2,1]] => [[5,5,4,3,2],[4,4,2,2]]
[[6,4,4,2,1],[4,3,2,1]] => [[6,5,4,3,2],[5,4,2,2]]
[[5,3,2,1,1],[3,2]] => [[5,5,5,3,2],[4,4,3,2]]
[[6,4,3,2,1],[4,3,1,1]] => [[6,5,5,3,2],[5,4,3,2]]
[[6,4,3,1,1],[4,3,1]] => [[6,6,5,3,2],[5,5,3,2]]
[[7,5,4,2,1],[5,4,2,1]] => [[7,6,5,3,2],[6,5,3,2]]
[[4,3,3,3],[2,2,2]] => [[4,2,2,2],[1,1,1]]
[[5,4,4,3],[3,3,3]] => [[5,2,2,2],[2,1,1]]
[[5,4,3,3],[3,3,2]] => [[5,3,2,2],[2,2,1]]
[[6,5,4,3],[4,4,3]] => [[6,3,2,2],[3,2,1]]
[[5,3,3,3],[3,2,2]] => [[5,3,3,2],[2,2,2]]
[[6,4,4,3],[4,3,3]] => [[6,3,3,2],[3,2,2]]
[[6,4,3,3],[4,3,2]] => [[6,4,3,2],[3,3,2]]
[[7,5,4,3],[5,4,3]] => [[7,4,3,2],[4,3,2]]
[[3,2,2,2,1],[1,1,1]] => [[3,3,2,2,2],[2,1,1,1]]
[[4,3,3,3,1],[2,2,2,1]] => [[4,3,2,2,2],[3,1,1,1]]
[[4,3,3,2,1],[2,2,2]] => [[4,4,2,2,2],[3,2,1,1]]
[[5,4,4,3,1],[3,3,3,1]] => [[5,4,2,2,2],[4,2,1,1]]
[[4,3,2,2,1],[2,2,1]] => [[4,4,3,2,2],[3,2,2,1]]
[[5,4,3,3,1],[3,3,2,1]] => [[5,4,3,2,2],[4,2,2,1]]
[[5,4,3,2,1],[3,3,2]] => [[5,5,3,2,2],[4,3,2,1]]
[[6,5,4,3,1],[4,4,3,1]] => [[6,5,3,2,2],[5,3,2,1]]
[[4,2,2,2,1],[2,1,1]] => [[4,4,3,3,2],[3,2,2,2]]
[[5,3,3,3,1],[3,2,2,1]] => [[5,4,3,3,2],[4,2,2,2]]
[[5,3,3,2,1],[3,2,2]] => [[5,5,3,3,2],[4,3,2,2]]
[[6,4,4,3,1],[4,3,3,1]] => [[6,5,3,3,2],[5,3,2,2]]
[[5,3,2,2,1],[3,2,1]] => [[5,5,4,3,2],[4,3,3,2]]
[[6,4,3,3,1],[4,3,2,1]] => [[6,5,4,3,2],[5,3,3,2]]
[[6,4,3,2,1],[4,3,2]] => [[6,6,4,3,2],[5,4,3,2]]
[[7,5,4,3,1],[5,4,3,1]] => [[7,6,4,3,2],[6,4,3,2]]
[[3,2,2,2,2],[1,1,1,1]] => [[3,2,2,2,2],[1,1,1,1]]
[[4,3,3,3,2],[2,2,2,2]] => [[4,2,2,2,2],[2,1,1,1]]
[[4,3,3,2,2],[2,2,2,1]] => [[4,3,2,2,2],[2,2,1,1]]
[[5,4,4,3,2],[3,3,3,2]] => [[5,3,2,2,2],[3,2,1,1]]
[[4,3,2,2,2],[2,2,1,1]] => [[4,3,3,2,2],[2,2,2,1]]
[[5,4,3,3,2],[3,3,2,2]] => [[5,3,3,2,2],[3,2,2,1]]
[[5,4,3,2,2],[3,3,2,1]] => [[5,4,3,2,2],[3,3,2,1]]
[[6,5,4,3,2],[4,4,3,2]] => [[6,4,3,2,2],[4,3,2,1]]
[[4,2,2,2,2],[2,1,1,1]] => [[4,3,3,3,2],[2,2,2,2]]
[[5,3,3,3,2],[3,2,2,2]] => [[5,3,3,3,2],[3,2,2,2]]
[[5,3,3,2,2],[3,2,2,1]] => [[5,4,3,3,2],[3,3,2,2]]
[[6,4,4,3,2],[4,3,3,2]] => [[6,4,3,3,2],[4,3,2,2]]
[[5,3,2,2,2],[3,2,1,1]] => [[5,4,4,3,2],[3,3,3,2]]
[[6,4,3,3,2],[4,3,2,2]] => [[6,4,4,3,2],[4,3,3,2]]
[[6,4,3,2,2],[4,3,2,1]] => [[6,5,4,3,2],[4,4,3,2]]
[[7,5,4,3,2],[5,4,3,2]] => [[7,5,4,3,2],[5,4,3,2]]
[[2,1,1,1,1,1],[]] => [[2,2,2,2,2,2],[1,1,1,1,1]]
[[3,2,2,2,2,1],[1,1,1,1,1]] => [[3,2,2,2,2,2],[2,1,1,1,1]]
[[3,2,2,2,1,1],[1,1,1,1]] => [[3,3,2,2,2,2],[2,2,1,1,1]]
[[4,3,3,3,2,1],[2,2,2,2,1]] => [[4,3,2,2,2,2],[3,2,1,1,1]]
[[3,2,2,1,1,1],[1,1,1]] => [[3,3,3,2,2,2],[2,2,2,1,1]]
[[4,3,3,2,2,1],[2,2,2,1,1]] => [[4,3,3,2,2,2],[3,2,2,1,1]]
[[4,3,3,2,1,1],[2,2,2,1]] => [[4,4,3,2,2,2],[3,3,2,1,1]]
[[5,4,4,3,2,1],[3,3,3,2,1]] => [[5,4,3,2,2,2],[4,3,2,1,1]]
[[3,2,1,1,1,1],[1,1]] => [[3,3,3,3,2,2],[2,2,2,2,1]]
[[4,3,2,2,2,1],[2,2,1,1,1]] => [[4,3,3,3,2,2],[3,2,2,2,1]]
[[4,3,2,2,1,1],[2,2,1,1]] => [[4,4,3,3,2,2],[3,3,2,2,1]]
[[5,4,3,3,2,1],[3,3,2,2,1]] => [[5,4,3,3,2,2],[4,3,2,2,1]]
[[4,3,2,1,1,1],[2,2,1]] => [[4,4,4,3,2,2],[3,3,3,2,1]]
[[5,4,3,2,2,1],[3,3,2,1,1]] => [[5,4,4,3,2,2],[4,3,3,2,1]]
[[5,4,3,2,1,1],[3,3,2,1]] => [[5,5,4,3,2,2],[4,4,3,2,1]]
[[6,5,4,3,2,1],[4,4,3,2,1]] => [[6,5,4,3,2,2],[5,4,3,2,1]]
[[3,1,1,1,1,1],[1]] => [[3,3,3,3,3,2],[2,2,2,2,2]]
[[4,2,2,2,2,1],[2,1,1,1,1]] => [[4,3,3,3,3,2],[3,2,2,2,2]]
[[4,2,2,2,1,1],[2,1,1,1]] => [[4,4,3,3,3,2],[3,3,2,2,2]]
[[5,3,3,3,2,1],[3,2,2,2,1]] => [[5,4,3,3,3,2],[4,3,2,2,2]]
[[4,2,2,1,1,1],[2,1,1]] => [[4,4,4,3,3,2],[3,3,3,2,2]]
[[5,3,3,2,2,1],[3,2,2,1,1]] => [[5,4,4,3,3,2],[4,3,3,2,2]]
[[5,3,3,2,1,1],[3,2,2,1]] => [[5,5,4,3,3,2],[4,4,3,2,2]]
[[6,4,4,3,2,1],[4,3,3,2,1]] => [[6,5,4,3,3,2],[5,4,3,2,2]]
[[4,2,1,1,1,1],[2,1]] => [[4,4,4,4,3,2],[3,3,3,3,2]]
[[5,3,2,2,2,1],[3,2,1,1,1]] => [[5,4,4,4,3,2],[4,3,3,3,2]]
[[5,3,2,2,1,1],[3,2,1,1]] => [[5,5,4,4,3,2],[4,4,3,3,2]]
[[6,4,3,3,2,1],[4,3,2,2,1]] => [[6,5,4,4,3,2],[5,4,3,3,2]]
[[5,3,2,1,1,1],[3,2,1]] => [[5,5,5,4,3,2],[4,4,4,3,2]]
[[6,4,3,2,2,1],[4,3,2,1,1]] => [[6,5,5,4,3,2],[5,4,4,3,2]]
[[6,4,3,2,1,1],[4,3,2,1]] => [[6,6,5,4,3,2],[5,5,4,3,2]]
[[7,5,4,3,2,1],[5,4,3,2,1]] => [[7,6,5,4,3,2],[6,5,4,3,2]]
[[6,6],[5]] => [[6,1],[]]
[[7,6],[6]] => [[7,1],[1]]
[[5,5,1],[4]] => [[5,5,1],[4]]
[[6,6,1],[5,1]] => [[6,5,1],[5]]
[[6,5,1],[5]] => [[6,6,1],[5,1]]
[[7,6,1],[6,1]] => [[7,6,1],[6,1]]
[[4,4,2],[3]] => [[4,4,1],[2]]
[[5,5,2],[4,1]] => [[5,4,1],[3]]
[[6,6,2],[5,2]] => [[6,4,1],[4]]
[[5,4,2],[4]] => [[5,5,1],[3,1]]
[[6,5,2],[5,1]] => [[6,5,1],[4,1]]
[[7,6,2],[6,2]] => [[7,5,1],[5,1]]
[[4,4,1,1],[3]] => [[4,4,4,1],[3,3]]
[[5,5,2,1],[4,1,1]] => [[5,4,4,1],[4,3]]
[[5,5,1,1],[4,1]] => [[5,5,4,1],[4,4]]
[[6,6,2,1],[5,2,1]] => [[6,5,4,1],[5,4]]
[[5,4,1,1],[4]] => [[5,5,5,1],[4,4,1]]
[[6,5,2,1],[5,1,1]] => [[6,5,5,1],[5,4,1]]
[[6,5,1,1],[5,1]] => [[6,6,5,1],[5,5,1]]
[[7,6,2,1],[6,2,1]] => [[7,6,5,1],[6,5,1]]
[[3,3,3],[2]] => [[3,3,1],[]]
[[4,4,3],[3,1]] => [[4,3,1],[1]]
[[5,5,3],[4,2]] => [[5,3,1],[2]]
[[6,6,3],[5,3]] => [[6,3,1],[3]]
[[4,3,3],[3]] => [[4,4,1],[1,1]]
[[5,4,3],[4,1]] => [[5,4,1],[2,1]]
[[6,5,3],[5,2]] => [[6,4,1],[3,1]]
[[7,6,3],[6,3]] => [[7,4,1],[4,1]]
[[3,3,2,1],[2]] => [[3,3,3,1],[2,1]]
[[4,4,3,1],[3,1,1]] => [[4,3,3,1],[3,1]]
[[4,4,2,1],[3,1]] => [[4,4,3,1],[3,2]]
[[5,5,3,1],[4,2,1]] => [[5,4,3,1],[4,2]]
[[5,5,2,1],[4,2]] => [[5,5,3,1],[4,3]]
[[6,6,3,1],[5,3,1]] => [[6,5,3,1],[5,3]]
[[4,3,2,1],[3]] => [[4,4,4,1],[3,2,1]]
[[5,4,3,1],[4,1,1]] => [[5,4,4,1],[4,2,1]]
[[5,4,2,1],[4,1]] => [[5,5,4,1],[4,3,1]]
[[6,5,3,1],[5,2,1]] => [[6,5,4,1],[5,3,1]]
[[6,5,2,1],[5,2]] => [[6,6,4,1],[5,4,1]]
[[7,6,3,1],[6,3,1]] => [[7,6,4,1],[6,4,1]]
[[4,4,2,2],[3,1,1]] => [[4,3,3,1],[2,2]]
[[5,5,3,2],[4,2,2]] => [[5,3,3,1],[3,2]]
[[5,5,2,2],[4,2,1]] => [[5,4,3,1],[3,3]]
[[6,6,3,2],[5,3,2]] => [[6,4,3,1],[4,3]]
[[5,4,2,2],[4,1,1]] => [[5,4,4,1],[3,3,1]]
[[6,5,3,2],[5,2,2]] => [[6,4,4,1],[4,3,1]]
[[6,5,2,2],[5,2,1]] => [[6,5,4,1],[4,4,1]]
[[7,6,3,2],[6,3,2]] => [[7,5,4,1],[5,4,1]]
[[3,3,1,1,1],[2]] => [[3,3,3,3,1],[2,2,2]]
[[4,4,2,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,2]]
[[4,4,2,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,2]]
[[5,5,3,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,2]]
[[4,4,1,1,1],[3,1]] => [[4,4,4,3,1],[3,3,3]]
[[5,5,2,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,3]]
[[5,5,2,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,3]]
[[6,6,3,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,3]]
[[4,3,1,1,1],[3]] => [[4,4,4,4,1],[3,3,3,1]]
[[5,4,2,2,1],[4,1,1,1]] => [[5,4,4,4,1],[4,3,3,1]]
[[5,4,2,1,1],[4,1,1]] => [[5,5,4,4,1],[4,4,3,1]]
[[6,5,3,2,1],[5,2,2,1]] => [[6,5,4,4,1],[5,4,3,1]]
[[5,4,1,1,1],[4,1]] => [[5,5,5,4,1],[4,4,4,1]]
[[6,5,2,2,1],[5,2,1,1]] => [[6,5,5,4,1],[5,4,4,1]]
[[6,5,2,1,1],[5,2,1]] => [[6,6,5,4,1],[5,5,4,1]]
[[7,6,3,2,1],[6,3,2,1]] => [[7,6,5,4,1],[6,5,4,1]]
[[4,4,4],[3,2]] => [[4,2,1],[]]
[[5,5,4],[4,3]] => [[5,2,1],[1]]
[[6,6,4],[5,4]] => [[6,2,1],[2]]
[[5,4,4],[4,2]] => [[5,3,1],[1,1]]
[[6,5,4],[5,3]] => [[6,3,1],[2,1]]
[[7,6,4],[6,4]] => [[7,3,1],[3,1]]
[[3,3,3,1],[2,1]] => [[3,3,2,1],[2]]
[[4,4,4,1],[3,2,1]] => [[4,3,2,1],[3]]
[[4,4,3,1],[3,2]] => [[4,4,2,1],[3,1]]
[[5,5,4,1],[4,3,1]] => [[5,4,2,1],[4,1]]
[[5,5,3,1],[4,3]] => [[5,5,2,1],[4,2]]
[[6,6,4,1],[5,4,1]] => [[6,5,2,1],[5,2]]
[[4,3,3,1],[3,1]] => [[4,4,3,1],[3,1,1]]
[[5,4,4,1],[4,2,1]] => [[5,4,3,1],[4,1,1]]
[[5,4,3,1],[4,2]] => [[5,5,3,1],[4,2,1]]
[[6,5,4,1],[5,3,1]] => [[6,5,3,1],[5,2,1]]
[[6,5,3,1],[5,3]] => [[6,6,3,1],[5,3,1]]
[[7,6,4,1],[6,4,1]] => [[7,6,3,1],[6,3,1]]
[[2,2,2,2],[1]] => [[2,2,2,1],[]]
[[3,3,3,2],[2,1,1]] => [[3,2,2,1],[1]]
[[4,4,4,2],[3,2,2]] => [[4,2,2,1],[2]]
[[3,3,2,2],[2,1]] => [[3,3,2,1],[1,1]]
[[4,4,3,2],[3,2,1]] => [[4,3,2,1],[2,1]]
[[5,5,4,2],[4,3,2]] => [[5,3,2,1],[3,1]]
[[4,4,2,2],[3,2]] => [[4,4,2,1],[2,2]]
[[5,5,3,2],[4,3,1]] => [[5,4,2,1],[3,2]]
[[6,6,4,2],[5,4,2]] => [[6,4,2,1],[4,2]]
[[3,2,2,2],[2]] => [[3,3,3,1],[1,1,1]]
[[4,3,3,2],[3,1,1]] => [[4,3,3,1],[2,1,1]]
[[5,4,4,2],[4,2,2]] => [[5,3,3,1],[3,1,1]]
[[4,3,2,2],[3,1]] => [[4,4,3,1],[2,2,1]]
[[5,4,3,2],[4,2,1]] => [[5,4,3,1],[3,2,1]]
[[6,5,4,2],[5,3,2]] => [[6,4,3,1],[4,2,1]]
[[5,4,2,2],[4,2]] => [[5,5,3,1],[3,3,1]]
[[6,5,3,2],[5,3,1]] => [[6,5,3,1],[4,3,1]]
[[7,6,4,2],[6,4,2]] => [[7,5,3,1],[5,3,1]]
[[2,2,2,1,1],[1]] => [[2,2,2,2,1],[1,1]]
[[3,3,3,2,1],[2,1,1,1]] => [[3,2,2,2,1],[2,1]]
[[3,3,3,1,1],[2,1,1]] => [[3,3,2,2,1],[2,2]]
[[4,4,4,2,1],[3,2,2,1]] => [[4,3,2,2,1],[3,2]]
[[3,3,2,1,1],[2,1]] => [[3,3,3,2,1],[2,2,1]]
[[4,4,3,2,1],[3,2,1,1]] => [[4,3,3,2,1],[3,2,1]]
[[4,4,3,1,1],[3,2,1]] => [[4,4,3,2,1],[3,3,1]]
[[5,5,4,2,1],[4,3,2,1]] => [[5,4,3,2,1],[4,3,1]]
[[4,4,2,1,1],[3,2]] => [[4,4,4,2,1],[3,3,2]]
[[5,5,3,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,2]]
[[5,5,3,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,2]]
[[6,6,4,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,2]]
[[3,2,2,1,1],[2]] => [[3,3,3,3,1],[2,2,1,1]]
[[4,3,3,2,1],[3,1,1,1]] => [[4,3,3,3,1],[3,2,1,1]]
[[4,3,3,1,1],[3,1,1]] => [[4,4,3,3,1],[3,3,1,1]]
[[5,4,4,2,1],[4,2,2,1]] => [[5,4,3,3,1],[4,3,1,1]]
[[4,3,2,1,1],[3,1]] => [[4,4,4,3,1],[3,3,2,1]]
[[5,4,3,2,1],[4,2,1,1]] => [[5,4,4,3,1],[4,3,2,1]]
[[5,4,3,1,1],[4,2,1]] => [[5,5,4,3,1],[4,4,2,1]]
[[6,5,4,2,1],[5,3,2,1]] => [[6,5,4,3,1],[5,4,2,1]]
[[5,4,2,1,1],[4,2]] => [[5,5,5,3,1],[4,4,3,1]]
[[6,5,3,2,1],[5,3,1,1]] => [[6,5,5,3,1],[5,4,3,1]]
[[6,5,3,1,1],[5,3,1]] => [[6,6,5,3,1],[5,5,3,1]]
[[7,6,4,2,1],[6,4,2,1]] => [[7,6,5,3,1],[6,5,3,1]]
[[4,4,3,3],[3,2,2]] => [[4,2,2,1],[1,1]]
[[5,5,4,3],[4,3,3]] => [[5,2,2,1],[2,1]]
[[5,5,3,3],[4,3,2]] => [[5,3,2,1],[2,2]]
[[6,6,4,3],[5,4,3]] => [[6,3,2,1],[3,2]]
[[5,4,3,3],[4,2,2]] => [[5,3,3,1],[2,2,1]]
[[6,5,4,3],[5,3,3]] => [[6,3,3,1],[3,2,1]]
[[6,5,3,3],[5,3,2]] => [[6,4,3,1],[3,3,1]]
[[7,6,4,3],[6,4,3]] => [[7,4,3,1],[4,3,1]]
[[3,3,2,2,1],[2,1,1]] => [[3,3,2,2,1],[2,1,1]]
[[4,4,3,3,1],[3,2,2,1]] => [[4,3,2,2,1],[3,1,1]]
[[4,4,3,2,1],[3,2,2]] => [[4,4,2,2,1],[3,2,1]]
[[5,5,4,3,1],[4,3,3,1]] => [[5,4,2,2,1],[4,2,1]]
[[4,4,2,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,2]]
[[5,5,3,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,2]]
[[5,5,3,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,2]]
[[6,6,4,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,2]]
[[4,3,2,2,1],[3,1,1]] => [[4,4,3,3,1],[3,2,2,1]]
[[5,4,3,3,1],[4,2,2,1]] => [[5,4,3,3,1],[4,2,2,1]]
[[5,4,3,2,1],[4,2,2]] => [[5,5,3,3,1],[4,3,2,1]]
[[6,5,4,3,1],[5,3,3,1]] => [[6,5,3,3,1],[5,3,2,1]]
[[5,4,2,2,1],[4,2,1]] => [[5,5,4,3,1],[4,3,3,1]]
[[6,5,3,3,1],[5,3,2,1]] => [[6,5,4,3,1],[5,3,3,1]]
[[6,5,3,2,1],[5,3,2]] => [[6,6,4,3,1],[5,4,3,1]]
[[7,6,4,3,1],[6,4,3,1]] => [[7,6,4,3,1],[6,4,3,1]]
[[3,3,2,2,2],[2,1,1,1]] => [[3,2,2,2,1],[1,1,1]]
[[4,4,3,3,2],[3,2,2,2]] => [[4,2,2,2,1],[2,1,1]]
[[4,4,3,2,2],[3,2,2,1]] => [[4,3,2,2,1],[2,2,1]]
[[5,5,4,3,2],[4,3,3,2]] => [[5,3,2,2,1],[3,2,1]]
[[4,4,2,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,2]]
[[5,5,3,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,2]]
[[5,5,3,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,2]]
[[6,6,4,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,2]]
[[4,3,2,2,2],[3,1,1,1]] => [[4,3,3,3,1],[2,2,2,1]]
[[5,4,3,3,2],[4,2,2,2]] => [[5,3,3,3,1],[3,2,2,1]]
[[5,4,3,2,2],[4,2,2,1]] => [[5,4,3,3,1],[3,3,2,1]]
[[6,5,4,3,2],[5,3,3,2]] => [[6,4,3,3,1],[4,3,2,1]]
[[5,4,2,2,2],[4,2,1,1]] => [[5,4,4,3,1],[3,3,3,1]]
[[6,5,3,3,2],[5,3,2,2]] => [[6,4,4,3,1],[4,3,3,1]]
[[6,5,3,2,2],[5,3,2,1]] => [[6,5,4,3,1],[4,4,3,1]]
[[7,6,4,3,2],[6,4,3,2]] => [[7,5,4,3,1],[5,4,3,1]]
[[2,2,1,1,1,1],[1]] => [[2,2,2,2,2,1],[1,1,1,1]]
[[3,3,2,2,2,1],[2,1,1,1,1]] => [[3,2,2,2,2,1],[2,1,1,1]]
[[3,3,2,2,1,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,2,1,1]]
[[4,4,3,3,2,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,2,1,1]]
[[3,3,2,1,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,2,1]]
[[4,4,3,2,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,2,1]]
[[4,4,3,2,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,2,1]]
[[5,5,4,3,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,2,1]]
[[3,3,1,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,2]]
[[4,4,2,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,2]]
[[4,4,2,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,2]]
[[5,5,3,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,2]]
[[4,4,2,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,2]]
[[5,5,3,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,2]]
[[5,5,3,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,2]]
[[6,6,4,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,2]]
[[3,2,1,1,1,1],[2]] => [[3,3,3,3,3,1],[2,2,2,2,1]]
[[4,3,2,2,2,1],[3,1,1,1,1]] => [[4,3,3,3,3,1],[3,2,2,2,1]]
[[4,3,2,2,1,1],[3,1,1,1]] => [[4,4,3,3,3,1],[3,3,2,2,1]]
[[5,4,3,3,2,1],[4,2,2,2,1]] => [[5,4,3,3,3,1],[4,3,2,2,1]]
[[4,3,2,1,1,1],[3,1,1]] => [[4,4,4,3,3,1],[3,3,3,2,1]]
[[5,4,3,2,2,1],[4,2,2,1,1]] => [[5,4,4,3,3,1],[4,3,3,2,1]]
[[5,4,3,2,1,1],[4,2,2,1]] => [[5,5,4,3,3,1],[4,4,3,2,1]]
[[6,5,4,3,2,1],[5,3,3,2,1]] => [[6,5,4,3,3,1],[5,4,3,2,1]]
[[4,3,1,1,1,1],[3,1]] => [[4,4,4,4,3,1],[3,3,3,3,1]]
[[5,4,2,2,2,1],[4,2,1,1,1]] => [[5,4,4,4,3,1],[4,3,3,3,1]]
[[5,4,2,2,1,1],[4,2,1,1]] => [[5,5,4,4,3,1],[4,4,3,3,1]]
[[6,5,3,3,2,1],[5,3,2,2,1]] => [[6,5,4,4,3,1],[5,4,3,3,1]]
[[5,4,2,1,1,1],[4,2,1]] => [[5,5,5,4,3,1],[4,4,4,3,1]]
[[6,5,3,2,2,1],[5,3,2,1,1]] => [[6,5,5,4,3,1],[5,4,4,3,1]]
[[6,5,3,2,1,1],[5,3,2,1]] => [[6,6,5,4,3,1],[5,5,4,3,1]]
[[7,6,4,3,2,1],[6,4,3,2,1]] => [[7,6,5,4,3,1],[6,5,4,3,1]]
[[5,5,5],[4,4]] => [[5,1,1],[]]
[[6,6,5],[5,5]] => [[6,1,1],[1]]
[[6,5,5],[5,4]] => [[6,2,1],[1,1]]
[[7,6,5],[6,5]] => [[7,2,1],[2,1]]
[[4,4,4,1],[3,3]] => [[4,4,1,1],[3]]
[[5,5,5,1],[4,4,1]] => [[5,4,1,1],[4]]
[[5,5,4,1],[4,4]] => [[5,5,1,1],[4,1]]
[[6,6,5,1],[5,5,1]] => [[6,5,1,1],[5,1]]
[[5,4,4,1],[4,3]] => [[5,5,2,1],[4,1,1]]
[[6,5,5,1],[5,4,1]] => [[6,5,2,1],[5,1,1]]
[[6,5,4,1],[5,4]] => [[6,6,2,1],[5,2,1]]
[[7,6,5,1],[6,5,1]] => [[7,6,2,1],[6,2,1]]
[[3,3,3,2],[2,2]] => [[3,3,1,1],[1]]
[[4,4,4,2],[3,3,1]] => [[4,3,1,1],[2]]
[[5,5,5,2],[4,4,2]] => [[5,3,1,1],[3]]
[[4,4,3,2],[3,3]] => [[4,4,1,1],[2,1]]
[[5,5,4,2],[4,4,1]] => [[5,4,1,1],[3,1]]
[[6,6,5,2],[5,5,2]] => [[6,4,1,1],[4,1]]
[[4,3,3,2],[3,2]] => [[4,4,2,1],[2,1,1]]
[[5,4,4,2],[4,3,1]] => [[5,4,2,1],[3,1,1]]
[[6,5,5,2],[5,4,2]] => [[6,4,2,1],[4,1,1]]
[[5,4,3,2],[4,3]] => [[5,5,2,1],[3,2,1]]
[[6,5,4,2],[5,4,1]] => [[6,5,2,1],[4,2,1]]
[[7,6,5,2],[6,5,2]] => [[7,5,2,1],[5,2,1]]
[[3,3,3,1,1],[2,2]] => [[3,3,3,1,1],[2,2]]
[[4,4,4,2,1],[3,3,1,1]] => [[4,3,3,1,1],[3,2]]
[[4,4,4,1,1],[3,3,1]] => [[4,4,3,1,1],[3,3]]
[[5,5,5,2,1],[4,4,2,1]] => [[5,4,3,1,1],[4,3]]
[[4,4,3,1,1],[3,3]] => [[4,4,4,1,1],[3,3,1]]
[[5,5,4,2,1],[4,4,1,1]] => [[5,4,4,1,1],[4,3,1]]
[[5,5,4,1,1],[4,4,1]] => [[5,5,4,1,1],[4,4,1]]
[[6,6,5,2,1],[5,5,2,1]] => [[6,5,4,1,1],[5,4,1]]
[[4,3,3,1,1],[3,2]] => [[4,4,4,2,1],[3,3,1,1]]
[[5,4,4,2,1],[4,3,1,1]] => [[5,4,4,2,1],[4,3,1,1]]
[[5,4,4,1,1],[4,3,1]] => [[5,5,4,2,1],[4,4,1,1]]
[[6,5,5,2,1],[5,4,2,1]] => [[6,5,4,2,1],[5,4,1,1]]
[[5,4,3,1,1],[4,3]] => [[5,5,5,2,1],[4,4,2,1]]
[[6,5,4,2,1],[5,4,1,1]] => [[6,5,5,2,1],[5,4,2,1]]
[[6,5,4,1,1],[5,4,1]] => [[6,6,5,2,1],[5,5,2,1]]
[[7,6,5,2,1],[6,5,2,1]] => [[7,6,5,2,1],[6,5,2,1]]
[[3,3,3,3],[2,2,1]] => [[3,2,1,1],[]]
[[4,4,4,3],[3,3,2]] => [[4,2,1,1],[1]]
[[5,5,5,3],[4,4,3]] => [[5,2,1,1],[2]]
[[4,4,3,3],[3,3,1]] => [[4,3,1,1],[1,1]]
[[5,5,4,3],[4,4,2]] => [[5,3,1,1],[2,1]]
[[6,6,5,3],[5,5,3]] => [[6,3,1,1],[3,1]]
[[4,3,3,3],[3,2,1]] => [[4,3,2,1],[1,1,1]]
[[5,4,4,3],[4,3,2]] => [[5,3,2,1],[2,1,1]]
[[6,5,5,3],[5,4,3]] => [[6,3,2,1],[3,1,1]]
[[5,4,3,3],[4,3,1]] => [[5,4,2,1],[2,2,1]]
[[6,5,4,3],[5,4,2]] => [[6,4,2,1],[3,2,1]]
[[7,6,5,3],[6,5,3]] => [[7,4,2,1],[4,2,1]]
[[2,2,2,2,1],[1,1]] => [[2,2,2,1,1],[1]]
[[3,3,3,3,1],[2,2,1,1]] => [[3,2,2,1,1],[2]]
[[3,3,3,2,1],[2,2,1]] => [[3,3,2,1,1],[2,1]]
[[4,4,4,3,1],[3,3,2,1]] => [[4,3,2,1,1],[3,1]]
[[4,4,4,2,1],[3,3,2]] => [[4,4,2,1,1],[3,2]]
[[5,5,5,3,1],[4,4,3,1]] => [[5,4,2,1,1],[4,2]]
[[3,3,2,2,1],[2,2]] => [[3,3,3,1,1],[2,1,1]]
[[4,4,3,3,1],[3,3,1,1]] => [[4,3,3,1,1],[3,1,1]]
[[4,4,3,2,1],[3,3,1]] => [[4,4,3,1,1],[3,2,1]]
[[5,5,4,3,1],[4,4,2,1]] => [[5,4,3,1,1],[4,2,1]]
[[5,5,4,2,1],[4,4,2]] => [[5,5,3,1,1],[4,3,1]]
[[6,6,5,3,1],[5,5,3,1]] => [[6,5,3,1,1],[5,3,1]]
[[3,2,2,2,1],[2,1]] => [[3,3,3,2,1],[2,1,1,1]]
[[4,3,3,3,1],[3,2,1,1]] => [[4,3,3,2,1],[3,1,1,1]]
[[4,3,3,2,1],[3,2,1]] => [[4,4,3,2,1],[3,2,1,1]]
[[5,4,4,3,1],[4,3,2,1]] => [[5,4,3,2,1],[4,2,1,1]]
[[5,4,4,2,1],[4,3,2]] => [[5,5,3,2,1],[4,3,1,1]]
[[6,5,5,3,1],[5,4,3,1]] => [[6,5,3,2,1],[5,3,1,1]]
[[4,3,2,2,1],[3,2]] => [[4,4,4,2,1],[3,2,2,1]]
[[5,4,3,3,1],[4,3,1,1]] => [[5,4,4,2,1],[4,2,2,1]]
[[5,4,3,2,1],[4,3,1]] => [[5,5,4,2,1],[4,3,2,1]]
[[6,5,4,3,1],[5,4,2,1]] => [[6,5,4,2,1],[5,3,2,1]]
[[6,5,4,2,1],[5,4,2]] => [[6,6,4,2,1],[5,4,2,1]]
[[7,6,5,3,1],[6,5,3,1]] => [[7,6,4,2,1],[6,4,2,1]]
[[3,3,3,2,2],[2,2,1,1]] => [[3,2,2,1,1],[1,1]]
[[4,4,4,3,2],[3,3,2,2]] => [[4,2,2,1,1],[2,1]]
[[4,4,4,2,2],[3,3,2,1]] => [[4,3,2,1,1],[2,2]]
[[5,5,5,3,2],[4,4,3,2]] => [[5,3,2,1,1],[3,2]]
[[4,4,3,2,2],[3,3,1,1]] => [[4,3,3,1,1],[2,2,1]]
[[5,5,4,3,2],[4,4,2,2]] => [[5,3,3,1,1],[3,2,1]]
[[5,5,4,2,2],[4,4,2,1]] => [[5,4,3,1,1],[3,3,1]]
[[6,6,5,3,2],[5,5,3,2]] => [[6,4,3,1,1],[4,3,1]]
[[4,3,3,2,2],[3,2,1,1]] => [[4,3,3,2,1],[2,2,1,1]]
[[5,4,4,3,2],[4,3,2,2]] => [[5,3,3,2,1],[3,2,1,1]]
[[5,4,4,2,2],[4,3,2,1]] => [[5,4,3,2,1],[3,3,1,1]]
[[6,5,5,3,2],[5,4,3,2]] => [[6,4,3,2,1],[4,3,1,1]]
[[5,4,3,2,2],[4,3,1,1]] => [[5,4,4,2,1],[3,3,2,1]]
[[6,5,4,3,2],[5,4,2,2]] => [[6,4,4,2,1],[4,3,2,1]]
[[6,5,4,2,2],[5,4,2,1]] => [[6,5,4,2,1],[4,4,2,1]]
[[7,6,5,3,2],[6,5,3,2]] => [[7,5,4,2,1],[5,4,2,1]]
[[2,2,2,1,1,1],[1,1]] => [[2,2,2,2,1,1],[1,1,1]]
[[3,3,3,2,2,1],[2,2,1,1,1]] => [[3,2,2,2,1,1],[2,1,1]]
[[3,3,3,2,1,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,2,1]]
[[4,4,4,3,2,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,2,1]]
[[3,3,3,1,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,2]]
[[4,4,4,2,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,2]]
[[4,4,4,2,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,2]]
[[5,5,5,3,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,2]]
[[3,3,2,1,1,1],[2,2]] => [[3,3,3,3,1,1],[2,2,2,1]]
[[4,4,3,2,2,1],[3,3,1,1,1]] => [[4,3,3,3,1,1],[3,2,2,1]]
[[4,4,3,2,1,1],[3,3,1,1]] => [[4,4,3,3,1,1],[3,3,2,1]]
[[5,5,4,3,2,1],[4,4,2,2,1]] => [[5,4,3,3,1,1],[4,3,2,1]]
[[4,4,3,1,1,1],[3,3,1]] => [[4,4,4,3,1,1],[3,3,3,1]]
[[5,5,4,2,2,1],[4,4,2,1,1]] => [[5,4,4,3,1,1],[4,3,3,1]]
[[5,5,4,2,1,1],[4,4,2,1]] => [[5,5,4,3,1,1],[4,4,3,1]]
[[6,6,5,3,2,1],[5,5,3,2,1]] => [[6,5,4,3,1,1],[5,4,3,1]]
[[3,2,2,1,1,1],[2,1]] => [[3,3,3,3,2,1],[2,2,2,1,1]]
[[4,3,3,2,2,1],[3,2,1,1,1]] => [[4,3,3,3,2,1],[3,2,2,1,1]]
[[4,3,3,2,1,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,3,2,1,1]]
[[5,4,4,3,2,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,3,2,1,1]]
[[4,3,3,1,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,3,1,1]]
[[5,4,4,2,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,3,1,1]]
[[5,4,4,2,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,3,1,1]]
[[6,5,5,3,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,3,1,1]]
[[4,3,2,1,1,1],[3,2]] => [[4,4,4,4,2,1],[3,3,3,2,1]]
[[5,4,3,2,2,1],[4,3,1,1,1]] => [[5,4,4,4,2,1],[4,3,3,2,1]]
[[5,4,3,2,1,1],[4,3,1,1]] => [[5,5,4,4,2,1],[4,4,3,2,1]]
[[6,5,4,3,2,1],[5,4,2,2,1]] => [[6,5,4,4,2,1],[5,4,3,2,1]]
[[5,4,3,1,1,1],[4,3,1]] => [[5,5,5,4,2,1],[4,4,4,2,1]]
[[6,5,4,2,2,1],[5,4,2,1,1]] => [[6,5,5,4,2,1],[5,4,4,2,1]]
[[6,5,4,2,1,1],[5,4,2,1]] => [[6,6,5,4,2,1],[5,5,4,2,1]]
[[7,6,5,3,2,1],[6,5,3,2,1]] => [[7,6,5,4,2,1],[6,5,4,2,1]]
[[4,4,4,4],[3,3,3]] => [[4,1,1,1],[]]
[[5,5,5,4],[4,4,4]] => [[5,1,1,1],[1]]
[[5,5,4,4],[4,4,3]] => [[5,2,1,1],[1,1]]
[[6,6,5,4],[5,5,4]] => [[6,2,1,1],[2,1]]
[[5,4,4,4],[4,3,3]] => [[5,2,2,1],[1,1,1]]
[[6,5,5,4],[5,4,4]] => [[6,2,2,1],[2,1,1]]
[[6,5,4,4],[5,4,3]] => [[6,3,2,1],[2,2,1]]
[[7,6,5,4],[6,5,4]] => [[7,3,2,1],[3,2,1]]
[[3,3,3,3,1],[2,2,2]] => [[3,3,1,1,1],[2]]
[[4,4,4,4,1],[3,3,3,1]] => [[4,3,1,1,1],[3]]
[[4,4,4,3,1],[3,3,3]] => [[4,4,1,1,1],[3,1]]
[[5,5,5,4,1],[4,4,4,1]] => [[5,4,1,1,1],[4,1]]
[[4,4,3,3,1],[3,3,2]] => [[4,4,2,1,1],[3,1,1]]
[[5,5,4,4,1],[4,4,3,1]] => [[5,4,2,1,1],[4,1,1]]
[[5,5,4,3,1],[4,4,3]] => [[5,5,2,1,1],[4,2,1]]
[[6,6,5,4,1],[5,5,4,1]] => [[6,5,2,1,1],[5,2,1]]
[[4,3,3,3,1],[3,2,2]] => [[4,4,2,2,1],[3,1,1,1]]
[[5,4,4,4,1],[4,3,3,1]] => [[5,4,2,2,1],[4,1,1,1]]
[[5,4,4,3,1],[4,3,3]] => [[5,5,2,2,1],[4,2,1,1]]
[[6,5,5,4,1],[5,4,4,1]] => [[6,5,2,2,1],[5,2,1,1]]
[[5,4,3,3,1],[4,3,2]] => [[5,5,3,2,1],[4,2,2,1]]
[[6,5,4,4,1],[5,4,3,1]] => [[6,5,3,2,1],[5,2,2,1]]
[[6,5,4,3,1],[5,4,3]] => [[6,6,3,2,1],[5,3,2,1]]
[[7,6,5,4,1],[6,5,4,1]] => [[7,6,3,2,1],[6,3,2,1]]
[[2,2,2,2,2],[1,1,1]] => [[2,2,1,1,1],[]]
[[3,3,3,3,2],[2,2,2,1]] => [[3,2,1,1,1],[1]]
[[4,4,4,4,2],[3,3,3,2]] => [[4,2,1,1,1],[2]]
[[3,3,3,2,2],[2,2,2]] => [[3,3,1,1,1],[1,1]]
[[4,4,4,3,2],[3,3,3,1]] => [[4,3,1,1,1],[2,1]]
[[5,5,5,4,2],[4,4,4,2]] => [[5,3,1,1,1],[3,1]]
[[3,3,2,2,2],[2,2,1]] => [[3,3,2,1,1],[1,1,1]]
[[4,4,3,3,2],[3,3,2,1]] => [[4,3,2,1,1],[2,1,1]]
[[5,5,4,4,2],[4,4,3,2]] => [[5,3,2,1,1],[3,1,1]]
[[4,4,3,2,2],[3,3,2]] => [[4,4,2,1,1],[2,2,1]]
[[5,5,4,3,2],[4,4,3,1]] => [[5,4,2,1,1],[3,2,1]]
[[6,6,5,4,2],[5,5,4,2]] => [[6,4,2,1,1],[4,2,1]]
[[3,2,2,2,2],[2,1,1]] => [[3,3,2,2,1],[1,1,1,1]]
[[4,3,3,3,2],[3,2,2,1]] => [[4,3,2,2,1],[2,1,1,1]]
[[5,4,4,4,2],[4,3,3,2]] => [[5,3,2,2,1],[3,1,1,1]]
[[4,3,3,2,2],[3,2,2]] => [[4,4,2,2,1],[2,2,1,1]]
[[5,4,4,3,2],[4,3,3,1]] => [[5,4,2,2,1],[3,2,1,1]]
[[6,5,5,4,2],[5,4,4,2]] => [[6,4,2,2,1],[4,2,1,1]]
[[4,3,2,2,2],[3,2,1]] => [[4,4,3,2,1],[2,2,2,1]]
[[5,4,3,3,2],[4,3,2,1]] => [[5,4,3,2,1],[3,2,2,1]]
[[6,5,4,4,2],[5,4,3,2]] => [[6,4,3,2,1],[4,2,2,1]]
[[5,4,3,2,2],[4,3,2]] => [[5,5,3,2,1],[3,3,2,1]]
[[6,5,4,3,2],[5,4,3,1]] => [[6,5,3,2,1],[4,3,2,1]]
[[7,6,5,4,2],[6,5,4,2]] => [[7,5,3,2,1],[5,3,2,1]]
[[2,2,2,2,1,1],[1,1,1]] => [[2,2,2,1,1,1],[1,1]]
[[3,3,3,3,2,1],[2,2,2,1,1]] => [[3,2,2,1,1,1],[2,1]]
[[3,3,3,3,1,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,2]]
[[4,4,4,4,2,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,2]]
[[3,3,3,2,1,1],[2,2,2]] => [[3,3,3,1,1,1],[2,2,1]]
[[4,4,4,3,2,1],[3,3,3,1,1]] => [[4,3,3,1,1,1],[3,2,1]]
[[4,4,4,3,1,1],[3,3,3,1]] => [[4,4,3,1,1,1],[3,3,1]]
[[5,5,5,4,2,1],[4,4,4,2,1]] => [[5,4,3,1,1,1],[4,3,1]]
[[3,3,2,2,1,1],[2,2,1]] => [[3,3,3,2,1,1],[2,2,1,1]]
[[4,4,3,3,2,1],[3,3,2,1,1]] => [[4,3,3,2,1,1],[3,2,1,1]]
[[4,4,3,3,1,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,3,1,1]]
[[5,5,4,4,2,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,3,1,1]]
[[4,4,3,2,1,1],[3,3,2]] => [[4,4,4,2,1,1],[3,3,2,1]]
[[5,5,4,3,2,1],[4,4,3,1,1]] => [[5,4,4,2,1,1],[4,3,2,1]]
[[5,5,4,3,1,1],[4,4,3,1]] => [[5,5,4,2,1,1],[4,4,2,1]]
[[6,6,5,4,2,1],[5,5,4,2,1]] => [[6,5,4,2,1,1],[5,4,2,1]]
[[3,2,2,2,1,1],[2,1,1]] => [[3,3,3,2,2,1],[2,2,1,1,1]]
[[4,3,3,3,2,1],[3,2,2,1,1]] => [[4,3,3,2,2,1],[3,2,1,1,1]]
[[4,3,3,3,1,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,3,1,1,1]]
[[5,4,4,4,2,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,3,1,1,1]]
[[4,3,3,2,1,1],[3,2,2]] => [[4,4,4,2,2,1],[3,3,2,1,1]]
[[5,4,4,3,2,1],[4,3,3,1,1]] => [[5,4,4,2,2,1],[4,3,2,1,1]]
[[5,4,4,3,1,1],[4,3,3,1]] => [[5,5,4,2,2,1],[4,4,2,1,1]]
[[6,5,5,4,2,1],[5,4,4,2,1]] => [[6,5,4,2,2,1],[5,4,2,1,1]]
[[4,3,2,2,1,1],[3,2,1]] => [[4,4,4,3,2,1],[3,3,2,2,1]]
[[5,4,3,3,2,1],[4,3,2,1,1]] => [[5,4,4,3,2,1],[4,3,2,2,1]]
[[5,4,3,3,1,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,4,2,2,1]]
[[6,5,4,4,2,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,4,2,2,1]]
[[5,4,3,2,1,1],[4,3,2]] => [[5,5,5,3,2,1],[4,4,3,2,1]]
[[6,5,4,3,2,1],[5,4,3,1,1]] => [[6,5,5,3,2,1],[5,4,3,2,1]]
[[6,5,4,3,1,1],[5,4,3,1]] => [[6,6,5,3,2,1],[5,5,3,2,1]]
[[7,6,5,4,2,1],[6,5,4,2,1]] => [[7,6,5,3,2,1],[6,5,3,2,1]]
[[3,3,3,3,3],[2,2,2,2]] => [[3,1,1,1,1],[]]
[[4,4,4,4,3],[3,3,3,3]] => [[4,1,1,1,1],[1]]
[[4,4,4,3,3],[3,3,3,2]] => [[4,2,1,1,1],[1,1]]
[[5,5,5,4,3],[4,4,4,3]] => [[5,2,1,1,1],[2,1]]
[[4,4,3,3,3],[3,3,2,2]] => [[4,2,2,1,1],[1,1,1]]
[[5,5,4,4,3],[4,4,3,3]] => [[5,2,2,1,1],[2,1,1]]
[[5,5,4,3,3],[4,4,3,2]] => [[5,3,2,1,1],[2,2,1]]
[[6,6,5,4,3],[5,5,4,3]] => [[6,3,2,1,1],[3,2,1]]
[[4,3,3,3,3],[3,2,2,2]] => [[4,2,2,2,1],[1,1,1,1]]
[[5,4,4,4,3],[4,3,3,3]] => [[5,2,2,2,1],[2,1,1,1]]
[[5,4,4,3,3],[4,3,3,2]] => [[5,3,2,2,1],[2,2,1,1]]
[[6,5,5,4,3],[5,4,4,3]] => [[6,3,2,2,1],[3,2,1,1]]
[[5,4,3,3,3],[4,3,2,2]] => [[5,3,3,2,1],[2,2,2,1]]
[[6,5,4,4,3],[5,4,3,3]] => [[6,3,3,2,1],[3,2,2,1]]
[[6,5,4,3,3],[5,4,3,2]] => [[6,4,3,2,1],[3,3,2,1]]
[[7,6,5,4,3],[6,5,4,3]] => [[7,4,3,2,1],[4,3,2,1]]
[[2,2,2,2,2,1],[1,1,1,1]] => [[2,2,1,1,1,1],[1]]
[[3,3,3,3,3,1],[2,2,2,2,1]] => [[3,2,1,1,1,1],[2]]
[[3,3,3,3,2,1],[2,2,2,2]] => [[3,3,1,1,1,1],[2,1]]
[[4,4,4,4,3,1],[3,3,3,3,1]] => [[4,3,1,1,1,1],[3,1]]
[[3,3,3,2,2,1],[2,2,2,1]] => [[3,3,2,1,1,1],[2,1,1]]
[[4,4,4,3,3,1],[3,3,3,2,1]] => [[4,3,2,1,1,1],[3,1,1]]
[[4,4,4,3,2,1],[3,3,3,2]] => [[4,4,2,1,1,1],[3,2,1]]
[[5,5,5,4,3,1],[4,4,4,3,1]] => [[5,4,2,1,1,1],[4,2,1]]
[[3,3,2,2,2,1],[2,2,1,1]] => [[3,3,2,2,1,1],[2,1,1,1]]
[[4,4,3,3,3,1],[3,3,2,2,1]] => [[4,3,2,2,1,1],[3,1,1,1]]
[[4,4,3,3,2,1],[3,3,2,2]] => [[4,4,2,2,1,1],[3,2,1,1]]
[[5,5,4,4,3,1],[4,4,3,3,1]] => [[5,4,2,2,1,1],[4,2,1,1]]
[[4,4,3,2,2,1],[3,3,2,1]] => [[4,4,3,2,1,1],[3,2,2,1]]
[[5,5,4,3,3,1],[4,4,3,2,1]] => [[5,4,3,2,1,1],[4,2,2,1]]
[[5,5,4,3,2,1],[4,4,3,2]] => [[5,5,3,2,1,1],[4,3,2,1]]
[[6,6,5,4,3,1],[5,5,4,3,1]] => [[6,5,3,2,1,1],[5,3,2,1]]
[[3,2,2,2,2,1],[2,1,1,1]] => [[3,3,2,2,2,1],[2,1,1,1,1]]
[[4,3,3,3,3,1],[3,2,2,2,1]] => [[4,3,2,2,2,1],[3,1,1,1,1]]
[[4,3,3,3,2,1],[3,2,2,2]] => [[4,4,2,2,2,1],[3,2,1,1,1]]
[[5,4,4,4,3,1],[4,3,3,3,1]] => [[5,4,2,2,2,1],[4,2,1,1,1]]
[[4,3,3,2,2,1],[3,2,2,1]] => [[4,4,3,2,2,1],[3,2,2,1,1]]
[[5,4,4,3,3,1],[4,3,3,2,1]] => [[5,4,3,2,2,1],[4,2,2,1,1]]
[[5,4,4,3,2,1],[4,3,3,2]] => [[5,5,3,2,2,1],[4,3,2,1,1]]
[[6,5,5,4,3,1],[5,4,4,3,1]] => [[6,5,3,2,2,1],[5,3,2,1,1]]
[[4,3,2,2,2,1],[3,2,1,1]] => [[4,4,3,3,2,1],[3,2,2,2,1]]
[[5,4,3,3,3,1],[4,3,2,2,1]] => [[5,4,3,3,2,1],[4,2,2,2,1]]
[[5,4,3,3,2,1],[4,3,2,2]] => [[5,5,3,3,2,1],[4,3,2,2,1]]
[[6,5,4,4,3,1],[5,4,3,3,1]] => [[6,5,3,3,2,1],[5,3,2,2,1]]
[[5,4,3,2,2,1],[4,3,2,1]] => [[5,5,4,3,2,1],[4,3,3,2,1]]
[[6,5,4,3,3,1],[5,4,3,2,1]] => [[6,5,4,3,2,1],[5,3,3,2,1]]
[[6,5,4,3,2,1],[5,4,3,2]] => [[6,6,4,3,2,1],[5,4,3,2,1]]
[[7,6,5,4,3,1],[6,5,4,3,1]] => [[7,6,4,3,2,1],[6,4,3,2,1]]
[[2,2,2,2,2,2],[1,1,1,1,1]] => [[2,1,1,1,1,1],[]]
[[3,3,3,3,3,2],[2,2,2,2,2]] => [[3,1,1,1,1,1],[1]]
[[3,3,3,3,2,2],[2,2,2,2,1]] => [[3,2,1,1,1,1],[1,1]]
[[4,4,4,4,3,2],[3,3,3,3,2]] => [[4,2,1,1,1,1],[2,1]]
[[3,3,3,2,2,2],[2,2,2,1,1]] => [[3,2,2,1,1,1],[1,1,1]]
[[4,4,4,3,3,2],[3,3,3,2,2]] => [[4,2,2,1,1,1],[2,1,1]]
[[4,4,4,3,2,2],[3,3,3,2,1]] => [[4,3,2,1,1,1],[2,2,1]]
[[5,5,5,4,3,2],[4,4,4,3,2]] => [[5,3,2,1,1,1],[3,2,1]]
[[3,3,2,2,2,2],[2,2,1,1,1]] => [[3,2,2,2,1,1],[1,1,1,1]]
[[4,4,3,3,3,2],[3,3,2,2,2]] => [[4,2,2,2,1,1],[2,1,1,1]]
[[4,4,3,3,2,2],[3,3,2,2,1]] => [[4,3,2,2,1,1],[2,2,1,1]]
[[5,5,4,4,3,2],[4,4,3,3,2]] => [[5,3,2,2,1,1],[3,2,1,1]]
[[4,4,3,2,2,2],[3,3,2,1,1]] => [[4,3,3,2,1,1],[2,2,2,1]]
[[5,5,4,3,3,2],[4,4,3,2,2]] => [[5,3,3,2,1,1],[3,2,2,1]]
[[5,5,4,3,2,2],[4,4,3,2,1]] => [[5,4,3,2,1,1],[3,3,2,1]]
[[6,6,5,4,3,2],[5,5,4,3,2]] => [[6,4,3,2,1,1],[4,3,2,1]]
[[3,2,2,2,2,2],[2,1,1,1,1]] => [[3,2,2,2,2,1],[1,1,1,1,1]]
[[4,3,3,3,3,2],[3,2,2,2,2]] => [[4,2,2,2,2,1],[2,1,1,1,1]]
[[4,3,3,3,2,2],[3,2,2,2,1]] => [[4,3,2,2,2,1],[2,2,1,1,1]]
[[5,4,4,4,3,2],[4,3,3,3,2]] => [[5,3,2,2,2,1],[3,2,1,1,1]]
[[4,3,3,2,2,2],[3,2,2,1,1]] => [[4,3,3,2,2,1],[2,2,2,1,1]]
[[5,4,4,3,3,2],[4,3,3,2,2]] => [[5,3,3,2,2,1],[3,2,2,1,1]]
[[5,4,4,3,2,2],[4,3,3,2,1]] => [[5,4,3,2,2,1],[3,3,2,1,1]]
[[6,5,5,4,3,2],[5,4,4,3,2]] => [[6,4,3,2,2,1],[4,3,2,1,1]]
[[4,3,2,2,2,2],[3,2,1,1,1]] => [[4,3,3,3,2,1],[2,2,2,2,1]]
[[5,4,3,3,3,2],[4,3,2,2,2]] => [[5,3,3,3,2,1],[3,2,2,2,1]]
[[5,4,3,3,2,2],[4,3,2,2,1]] => [[5,4,3,3,2,1],[3,3,2,2,1]]
[[6,5,4,4,3,2],[5,4,3,3,2]] => [[6,4,3,3,2,1],[4,3,2,2,1]]
[[5,4,3,2,2,2],[4,3,2,1,1]] => [[5,4,4,3,2,1],[3,3,3,2,1]]
[[6,5,4,3,3,2],[5,4,3,2,2]] => [[6,4,4,3,2,1],[4,3,3,2,1]]
[[6,5,4,3,2,2],[5,4,3,2,1]] => [[6,5,4,3,2,1],[4,4,3,2,1]]
[[7,6,5,4,3,2],[6,5,4,3,2]] => [[7,5,4,3,2,1],[5,4,3,2,1]]
[[1,1,1,1,1,1,1],[]] => [[1,1,1,1,1,1,1],[]]
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => [[2,1,1,1,1,1,1],[1]]
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => [[2,2,1,1,1,1,1],[1,1]]
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => [[3,2,1,1,1,1,1],[2,1]]
[[2,2,2,2,1,1,1],[1,1,1,1]] => [[2,2,2,1,1,1,1],[1,1,1]]
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => [[3,2,2,1,1,1,1],[2,1,1]]
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => [[3,3,2,1,1,1,1],[2,2,1]]
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => [[4,3,2,1,1,1,1],[3,2,1]]
[[2,2,2,1,1,1,1],[1,1,1]] => [[2,2,2,2,1,1,1],[1,1,1,1]]
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => [[3,2,2,2,1,1,1],[2,1,1,1]]
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => [[3,3,2,2,1,1,1],[2,2,1,1]]
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => [[4,3,2,2,1,1,1],[3,2,1,1]]
[[3,3,3,2,1,1,1],[2,2,2,1]] => [[3,3,3,2,1,1,1],[2,2,2,1]]
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => [[4,3,3,2,1,1,1],[3,2,2,1]]
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Created: Sep 26, 2020 at 18:34 by Martin Rubey
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Last Updated: Sep 26, 2020 at 18:34 by Martin Rubey